LMFDB - Embedded newform 1008.2.cz.g.607.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.5
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.g.367.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908151 - 1.47488i) q^{3} +(-0.243063 + 0.140332i) q^{5} +(2.20451 + 1.46292i) q^{7} +(-1.35052 + 2.67882i) q^{9} +O(q^{10})$	\(q+(-0.908151 - 1.47488i) q^{3} +(-0.243063 + 0.140332i) q^{5} +(2.20451 + 1.46292i) q^{7} +(-1.35052 + 2.67882i) q^{9} +(-2.44393 - 1.41101i) q^{11} +(4.06955 + 2.34956i) q^{13} +(0.427710 + 0.231045i) q^{15} +(-7.00051 + 4.04175i) q^{17} +(-0.474304 + 0.821518i) q^{19} +(0.155605 - 4.57993i) q^{21} +(-0.339885 + 0.196233i) q^{23} +(-2.46061 + 4.26191i) q^{25} +(5.17741 - 0.440916i) q^{27} +(1.51148 + 2.61795i) q^{29} -2.12709 q^{31} +(0.138400 + 4.88591i) q^{33} +(-0.741129 - 0.0462181i) q^{35} +(-2.43458 + 4.21681i) q^{37} +(-0.230459 - 8.13584i) q^{39} +(0.478990 + 0.276545i) q^{41} +(4.28515 - 2.47404i) q^{43} +(-0.0476630 - 0.840644i) q^{45} -2.78870 q^{47} +(2.71972 + 6.45005i) q^{49} +(12.3186 + 6.65438i) q^{51} +(6.21935 + 10.7722i) q^{53} +0.792039 q^{55} +(1.64238 - 0.0465226i) q^{57} +11.4011 q^{59} -11.1731i q^{61} +(-6.89615 + 3.92977i) q^{63} -1.31887 q^{65} +9.07446i q^{67} +(0.598086 + 0.323080i) q^{69} -1.54594i q^{71} +(-0.542172 + 0.313023i) q^{73} +(8.52040 - 0.241352i) q^{75} +(-3.32348 - 6.68586i) q^{77} +15.4373i q^{79} +(-5.35217 - 7.23563i) q^{81} +(-5.30821 - 9.19409i) q^{83} +(1.13438 - 1.96480i) q^{85} +(2.48851 - 4.60674i) q^{87} +(9.90157 + 5.71667i) q^{89} +(5.53414 + 11.1331i) q^{91} +(1.93172 + 3.13720i) q^{93} -0.266241i q^{95} +(13.6260 - 7.86698i) q^{97} +(7.08043 - 4.64126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.908151	−	1.47488i	−0.524321	−	0.851521i
$3$	−0.908151	−	1.47488i	−0.524321	−	0.851521i
$4$		0			0
$5$	−0.243063	+	0.140332i	−0.108701	+	0.0627585i	−0.553365	−	0.832939i	$-0.686656\pi$
$5$	−0.243063	+	0.140332i	−0.108701	+	0.0627585i	0.444664	+	0.895698i	$0.353323\pi$
$6$		0			0
$7$	2.20451	+	1.46292i	0.833226	+	0.552933i
$7$	2.20451	+	1.46292i	0.833226	+	0.552933i
$8$		0			0
$9$	−1.35052	+	2.67882i	−0.450175	+	0.892940i
$10$		0			0
$11$	−2.44393	−	1.41101i	−0.736874	−	0.425434i	0.0840577	−	0.996461i	$-0.473212\pi$
$11$	−2.44393	−	1.41101i	−0.736874	−	0.425434i	−0.820932	+	0.571027i	$0.806545\pi$
$12$		0			0
$13$	4.06955	+	2.34956i	1.12869	+	0.651650i	0.943605	−	0.331073i	$-0.107411\pi$
$13$	4.06955	+	2.34956i	1.12869	+	0.651650i	0.185085	+	0.982722i	$0.440744\pi$
$14$		0			0
$15$	0.427710	+	0.231045i	0.110434	+	0.0596555i
$16$		0			0
$17$	−7.00051	+	4.04175i	−1.69787	+	0.980268i	−0.750100	+	0.661324i	$0.769995\pi$
$17$	−7.00051	+	4.04175i	−1.69787	+	0.980268i	−0.947774	+	0.318944i	$0.896672\pi$
$18$		0			0
$19$	−0.474304	+	0.821518i	−0.108813	+	0.188469i	−0.915290	−	0.402797i	$-0.868038\pi$
$19$	−0.474304	+	0.821518i	−0.108813	+	0.188469i	0.806477	+	0.591266i	$0.201372\pi$
$20$		0			0
$21$	0.155605	−	4.57993i	0.0339558	−	0.999423i
$22$		0			0
$23$	−0.339885	+	0.196233i	−0.0708710	+	0.0409174i	−0.535017	−	0.844841i	$-0.679695\pi$
$23$	−0.339885	+	0.196233i	−0.0708710	+	0.0409174i	0.464146	+	0.885759i	$0.346361\pi$
$24$		0			0
$25$	−2.46061	+	4.26191i	−0.492123	+	0.852382i
$26$		0			0
$27$	5.17741	−	0.440916i	0.996393	−	0.0848543i
$28$		0			0
$29$	1.51148	+	2.61795i	0.280674	+	0.486142i	0.971551	−	0.236831i	$-0.0761086\pi$
$29$	1.51148	+	2.61795i	0.280674	+	0.486142i	−0.690877	+	0.722973i	$0.742775\pi$
$30$		0			0
$31$	−2.12709			−0.382037			−0.191018	−	0.981586i	$-0.561179\pi$
$31$	−2.12709			−0.382037			−0.191018	+	0.981586i	$0.561179\pi$
$32$		0			0
$33$	0.138400	+	4.88591i	0.0240924	+	0.850528i
$34$		0			0
$35$	−0.741129	−	0.0462181i	−0.125274	−	0.00781229i
$36$		0			0
$37$	−2.43458	+	4.21681i	−0.400242	+	0.693240i	−0.993755	−	0.111585i	$-0.964407\pi$
$37$	−2.43458	+	4.21681i	−0.400242	+	0.693240i	0.593513	+	0.804825i	$0.297741\pi$
$38$		0			0
$39$	−0.230459	−	8.13584i	−0.0369030	−	1.30278i
$40$		0			0
$41$	0.478990	+	0.276545i	0.0748057	+	0.0431891i	0.536936	−	0.843623i	$-0.319582\pi$
$41$	0.478990	+	0.276545i	0.0748057	+	0.0431891i	−0.462131	+	0.886812i	$0.652915\pi$
$42$		0			0
$43$	4.28515	−	2.47404i	0.653480	−	0.377287i	−0.136308	−	0.990666i	$-0.543524\pi$
$43$	4.28515	−	2.47404i	0.653480	−	0.377287i	0.789788	+	0.613380i	$0.210190\pi$
$44$		0			0
$45$	−0.0476630	−	0.840644i	−0.00710519	−	0.125316i
$46$		0			0
$47$	−2.78870			−0.406773			−0.203387	−	0.979098i	$-0.565195\pi$
$47$	−2.78870			−0.406773			−0.203387	+	0.979098i	$0.565195\pi$
$48$		0			0
$49$	2.71972	+	6.45005i	0.388531	+	0.921436i
$50$		0			0
$51$	12.3186	+	6.65438i	1.72495	+	0.931800i
$52$		0			0
$53$	6.21935	+	10.7722i	0.854293	+	1.47968i	0.877300	+	0.479943i	$0.159343\pi$
$53$	6.21935	+	10.7722i	0.854293	+	1.47968i	−0.0230067	+	0.999735i	$0.507324\pi$
$54$		0			0
$55$	0.792039			0.106799
$56$		0			0
$57$	1.64238	−	0.0465226i	0.217538	−	0.00616207i
$58$		0			0
$59$	11.4011			1.48429			0.742146	−	0.670238i	$-0.233808\pi$
$59$	11.4011			1.48429			0.742146	+	0.670238i	$0.233808\pi$
$60$		0			0
$61$		−	11.1731i		−	1.43057i	−0.698833	−	0.715284i	$-0.746297\pi$
$61$		−	11.1731i		−	1.43057i	0.698833	−	0.715284i	$-0.253703\pi$
$62$		0			0
$63$	−6.89615	+	3.92977i	−0.868833	+	0.495105i
$64$		0			0
$65$	−1.31887			−0.163586
$66$		0			0
$67$			9.07446i			1.10862i	0.832310	+	0.554311i	$0.187018\pi$
$67$			9.07446i			1.10862i	−0.832310	+	0.554311i	$0.812982\pi$
$68$		0			0
$69$	0.598086	+	0.323080i	0.0720011	+	0.0388943i
$70$		0			0
$71$		−	1.54594i		−	0.183469i	−0.995784	−	0.0917344i	$-0.970759\pi$
$71$		−	1.54594i		−	0.183469i	0.995784	−	0.0917344i	$-0.0292411\pi$
$72$		0			0
$73$	−0.542172	+	0.313023i	−0.0634564	+	0.0366366i	−0.531393	−	0.847126i	$-0.678331\pi$
$73$	−0.542172	+	0.313023i	−0.0634564	+	0.0366366i	0.467936	+	0.883762i	$0.344998\pi$
$74$		0			0
$75$	8.52040	−	0.241352i	0.983851	−	0.0278689i
$76$		0			0
$77$	−3.32348	−	6.68586i	−0.378746	−	0.761925i
$78$		0			0
$79$			15.4373i			1.73683i	0.495835	+	0.868417i	$0.334862\pi$
$79$			15.4373i			1.73683i	−0.495835	+	0.868417i	$0.665138\pi$
$80$		0			0
$81$	−5.35217	−	7.23563i	−0.594685	−	0.803959i
$82$		0			0
$83$	−5.30821	−	9.19409i	−0.582652	−	1.00918i	−0.995164	−	0.0982303i	$-0.968682\pi$
$83$	−5.30821	−	9.19409i	−0.582652	−	1.00918i	0.412512	−	0.910952i	$-0.364652\pi$
$84$		0			0
$85$	1.13438	−	1.96480i	0.123040	−	0.213112i
$86$		0			0
$87$	2.48851	−	4.60674i	0.266797	−	0.493894i
$88$		0			0
$89$	9.90157	+	5.71667i	1.04956	+	0.605966i	0.922527	−	0.385932i	$-0.126120\pi$
$89$	9.90157	+	5.71667i	1.04956	+	0.605966i	0.127037	+	0.991898i	$0.459453\pi$
$90$		0			0
$91$	5.53414	+	11.1331i	0.580136	+	1.16706i
$92$		0			0
$93$	1.93172	+	3.13720i	0.200310	+	0.325312i
$94$		0			0
$95$		−	0.266241i		−	0.0273157i
$96$		0			0
$97$	13.6260	−	7.86698i	1.38351	−	0.798770i	0.390937	−	0.920417i	$-0.372151\pi$
$97$	13.6260	−	7.86698i	1.38351	−	0.798770i	0.992573	+	0.121647i	$0.0388175\pi$
$98$		0			0
$99$	7.08043	−	4.64126i	0.711610	−	0.466465i
$100$		0			0
$101$	−6.07162	−	3.50545i	−0.604149	−	0.348806i	0.166523	−	0.986038i	$-0.446746\pi$
$101$	−6.07162	−	3.50545i	−0.604149	−	0.348806i	−0.770672	+	0.637232i	$0.780079\pi$
$102$		0			0
$103$	2.81624	+	4.87787i	0.277493	+	0.480631i	0.970761	−	0.240048i	$-0.0771633\pi$
$103$	2.81624	+	4.87787i	0.277493	+	0.480631i	−0.693268	+	0.720680i	$0.743830\pi$
$104$		0			0
$105$	0.604891	+	1.13505i	0.0590313	+	0.110769i
$106$		0			0
$107$	−5.00552	−	2.88994i	−0.483902	−	0.279381i	0.238139	−	0.971231i	$-0.423463\pi$
$107$	−5.00552	−	2.88994i	−0.483902	−	0.279381i	−0.722041	+	0.691850i	$0.756796\pi$
$108$		0			0
$109$	4.12859	+	7.15092i	0.395447	+	0.684934i	0.993158	−	0.116777i	$-0.0372564\pi$
$109$	4.12859	+	7.15092i	0.395447	+	0.684934i	−0.597711	+	0.801712i	$0.703923\pi$
$110$		0			0
$111$	8.43025	−	0.238798i	0.800164	−	0.0226657i
$112$		0			0
$113$	−6.47539	+	11.2157i	−0.609154	+	1.05508i	0.382227	+	0.924069i	$0.375157\pi$
$113$	−6.47539	+	11.2157i	−0.609154	+	1.05508i	−0.991380	+	0.131016i	$0.958176\pi$
$114$		0			0
$115$	0.0550756	−	0.0953938i	0.00513583	−	0.00889552i
$116$		0			0
$117$	−11.7901	+	7.72847i	−1.08999	+	0.714497i
$118$		0			0
$119$	−21.3455	−	1.33114i	−1.95673	−	0.122025i
$120$		0			0
$121$	−1.51812	−	2.62947i	−0.138011	−	0.239043i
$122$		0			0
$123$	−0.0271252	−	0.957596i	−0.00244580	−	0.0863435i
$124$		0			0
$125$		−	2.78454i		−	0.249057i
$126$		0			0
$127$		−	7.77236i		−	0.689685i	−0.938660	−	0.344843i	$-0.887932\pi$
$127$		−	7.77236i		−	0.689685i	0.938660	−	0.344843i	$-0.112068\pi$
$128$		0			0
$129$	−7.54046	−	4.07328i	−0.663901	−	0.358632i
$130$		0			0
$131$	−3.99271	−	6.91558i	−0.348845	−	0.604217i	0.637200	−	0.770699i	$-0.280093\pi$
$131$	−3.99271	−	6.91558i	−0.348845	−	0.604217i	−0.986045	+	0.166482i	$0.946759\pi$
$132$		0			0
$133$	−2.24742	+	1.11717i	−0.194876	+	0.0968713i
$134$		0			0
$135$	−1.19656	+	0.833728i	−0.102984	+	0.0717559i
$136$		0			0
$137$	−4.32470	+	7.49061i	−0.369484	+	0.639966i	−0.989485	−	0.144636i	$-0.953799\pi$
$137$	−4.32470	+	7.49061i	−0.369484	+	0.639966i	0.620001	+	0.784601i	$0.287132\pi$
$138$		0			0
$139$	−7.19469	+	12.4616i	−0.610246	+	1.05698i	0.380953	+	0.924595i	$0.375596\pi$
$139$	−7.19469	+	12.4616i	−0.610246	+	1.05698i	−0.991199	+	0.132383i	$0.957737\pi$
$140$		0			0
$141$	2.53256	+	4.11299i	0.213280	+	0.346376i
$142$		0			0
$143$	−6.63048	−	11.4843i	−0.554468	−	0.960367i
$144$		0			0
$145$	−0.734767	−	0.424218i	−0.0610191	−	0.0352294i
$146$		0			0
$147$	7.04312	−	9.86886i	0.580907	−	0.813970i
$148$		0			0
$149$	0.533820	+	0.924603i	0.0437322	+	0.0757464i	0.887063	−	0.461648i	$-0.152742\pi$
$149$	0.533820	+	0.924603i	0.0437322	+	0.0757464i	−0.843331	+	0.537395i	$0.819408\pi$
$150$		0			0
$151$	−11.2097	−	6.47194i	−0.912235	−	0.526679i	−0.0310854	−	0.999517i	$-0.509896\pi$
$151$	−11.2097	−	6.47194i	−0.912235	−	0.526679i	−0.881150	+	0.472838i	$0.843230\pi$
$152$		0			0
$153$	−1.37276	−	24.2116i	−0.110981	−	1.95739i
$154$		0			0
$155$	0.517016	−	0.298500i	0.0415278	−	0.0239761i
$156$		0			0
$157$		−	8.10255i		−	0.646654i	−0.946287	−	0.323327i	$-0.895199\pi$
$157$		−	8.10255i		−	0.646654i	0.946287	−	0.323327i	$-0.104801\pi$
$158$		0			0
$159$	10.2396	−	18.9556i	0.812053	−	1.50327i
$160$		0			0
$161$	−1.03635	−	0.0646288i	−0.0816761	−	0.00509346i
$162$		0			0
$163$	−15.8164	−	9.13162i	−1.23884	−	0.715244i	−0.269982	−	0.962865i	$-0.587018\pi$
$163$	−15.8164	−	9.13162i	−1.23884	−	0.715244i	−0.968857	+	0.247621i	$0.920351\pi$
$164$		0			0
$165$	−0.719291	−	1.16816i	−0.0559967	−	0.0909411i
$166$		0			0
$167$	−8.41991	+	14.5837i	−0.651553	+	1.12852i	0.331194	+	0.943563i	$0.392549\pi$
$167$	−8.41991	+	14.5837i	−0.651553	+	1.12852i	−0.982746	+	0.184959i	$0.940785\pi$
$168$		0			0
$169$	4.54083	+	7.86496i	0.349295	+	0.604997i
$170$		0			0
$171$	−1.56014	−	2.38006i	−0.119307	−	0.182007i
$172$		0			0
$173$		−	19.8404i		−	1.50844i	−0.656623	−	0.754219i	$-0.728016\pi$
$173$		−	19.8404i		−	1.50844i	0.656623	−	0.754219i	$-0.271984\pi$
$174$		0			0
$175$	−11.6593	+	5.79573i	−0.881359	+	0.438116i
$176$		0			0
$177$	−10.3539	−	16.8152i	−0.778245	−	1.26391i
$178$		0			0
$179$	−21.5488	+	12.4412i	−1.61063	+	0.929899i	−0.621409	+	0.783486i	$0.713439\pi$
$179$	−21.5488	+	12.4412i	−1.61063	+	0.929899i	−0.989224	+	0.146413i	$0.953227\pi$
$180$		0			0
$181$		−	7.30569i		−	0.543027i	−0.962435	−	0.271514i	$-0.912476\pi$
$181$		−	7.30569i		−	0.543027i	0.962435	−	0.271514i	$-0.0875242\pi$
$182$		0			0
$183$	−16.4789	+	10.1469i	−1.21816	+	0.750077i
$184$		0			0
$185$		−	1.36660i		−	0.100474i
$186$		0			0
$187$	22.8117			1.66816
$188$		0			0
$189$	12.0587	+	6.60215i	0.877139	+	0.480236i
$190$		0			0
$191$		−	8.21966i		−	0.594754i	−0.954760	−	0.297377i	$-0.903888\pi$
$191$		−	8.21966i		−	0.594754i	0.954760	−	0.297377i	$-0.0961118\pi$
$192$		0			0
$193$	19.5697			1.40866			0.704331	−	0.709872i	$-0.251247\pi$
$193$	19.5697			1.40866			0.704331	+	0.709872i	$0.251247\pi$
$194$		0			0
$195$	1.19774	+	1.94518i	0.0857717	+	0.139297i
$196$		0			0
$197$	16.3933			1.16797			0.583987	−	0.811763i	$-0.301492\pi$
$197$	16.3933			1.16797			0.583987	+	0.811763i	$0.301492\pi$
$198$		0			0
$199$	−7.86905	−	13.6296i	−0.557822	−	0.966176i	−0.997678	−	0.0681077i	$-0.978304\pi$
$199$	−7.86905	−	13.6296i	−0.557822	−	0.966176i	0.439856	−	0.898068i	$-0.355029\pi$
$200$		0			0
$201$	13.3837	−	8.24098i	0.944015	−	0.581274i
$202$		0			0
$203$	−0.497801	+	7.98248i	−0.0349388	+	0.560260i
$204$		0			0
$205$	−0.155233			−0.0108419
$206$		0			0
$207$	−0.0666493	−	1.17551i	−0.00463245	−	0.0817035i
$208$		0			0
$209$	2.31833	−	1.33849i	0.160363	−	0.0925854i
$210$		0			0
$211$	7.41442	+	4.28072i	0.510430	+	0.294697i	0.733010	−	0.680218i	$-0.238115\pi$
$211$	7.41442	+	4.28072i	0.510430	+	0.294697i	−0.222581	+	0.974914i	$0.571448\pi$
$212$		0			0
$213$	−2.28006	+	1.40394i	−0.156227	+	0.0961965i
$214$		0			0
$215$	−0.694374	+	1.20269i	−0.0473559	+	0.0820229i
$216$		0			0
$217$	−4.68919	−	3.11177i	−0.318323	−	0.211241i
$218$		0			0
$219$	0.954044	+	0.515365i	0.0644683	+	0.0348251i
$220$		0			0
$221$	−37.9853			−2.55517
$222$		0			0
$223$	9.63167	+	16.6825i	0.644984	+	1.11715i	0.984305	+	0.176475i	$0.0564694\pi$
$223$	9.63167	+	16.6825i	0.644984	+	1.11715i	−0.339321	+	0.940671i	$0.610197\pi$
$224$		0			0
$225$	−8.09377	−	12.3474i	−0.539585	−	0.823157i
$226$		0			0
$227$	10.3200	−	17.8747i	0.684960	−	1.18639i	−0.288489	−	0.957483i	$-0.593153\pi$
$227$	10.3200	−	17.8747i	0.684960	−	1.18639i	0.973449	−	0.228902i	$-0.0735137\pi$
$228$		0			0
$229$	−18.3554	+	10.5975i	−1.21296	+	0.700301i	−0.963402	−	0.268060i	$-0.913618\pi$
$229$	−18.3554	+	10.5975i	−1.21296	+	0.700301i	−0.249555	+	0.968361i	$0.580284\pi$
$230$		0			0
$231$	−6.84260	+	10.9735i	−0.450210	+	0.722003i
$232$		0			0
$233$	−7.78510	+	13.4842i	−0.510019	+	0.883378i	0.489914	+	0.871771i	$0.337028\pi$
$233$	−7.78510	+	13.4842i	−0.510019	+	0.883378i	−0.999933	+	0.0116076i	$0.996305\pi$
$234$		0			0
$235$	0.677828	−	0.391344i	0.0442167	−	0.0255285i
$236$		0			0
$237$	22.7681	−	14.0194i	1.47895	−	0.910658i
$238$		0			0
$239$	6.36686	+	3.67591i	0.411838	+	0.237775i	0.691579	−	0.722301i	$-0.256915\pi$
$239$	6.36686	+	3.67591i	0.411838	+	0.237775i	−0.279741	+	0.960075i	$0.590249\pi$
$240$		0			0
$241$	4.98346	+	2.87720i	0.321013	+	0.185337i	0.651844	−	0.758353i	$-0.273996\pi$
$241$	4.98346	+	2.87720i	0.321013	+	0.185337i	−0.330831	+	0.943690i	$0.607329\pi$
$242$		0			0
$243$	−5.81109	+	14.4648i	−0.372781	+	0.927919i
$244$		0			0
$245$	−1.56621	−	1.18610i	−0.100062	−	0.0757773i
$246$		0			0
$247$	−3.86041	+	2.22881i	−0.245632	+	0.141816i
$248$		0			0
$249$	−8.73950	+	16.1786i	−0.553843	+	1.02528i
$250$		0			0
$251$	21.9997			1.38861			0.694305	−	0.719681i	$-0.255712\pi$
$251$	21.9997			1.38861			0.694305	+	0.719681i	$0.255712\pi$
$252$		0			0
$253$	1.10754			0.0696306
$254$		0			0
$255$	−3.92802	+	0.111267i	−0.245982	+	0.00696778i
$256$		0			0
$257$	−1.26062	+	0.727818i	−0.0786351	+	0.0454000i	−0.538802	−	0.842432i	$-0.681123\pi$
$257$	−1.26062	+	0.727818i	−0.0786351	+	0.0454000i	0.460167	+	0.887832i	$0.347790\pi$
$258$		0			0
$259$	−11.5359	+	5.73440i	−0.716807	+	0.356318i
$260$		0			0
$261$	−9.05432	+	0.513364i	−0.560448	+	0.0317764i
$262$		0			0
$263$	−18.3962	−	10.6211i	−1.13436	−	0.654922i	−0.189331	−	0.981913i	$-0.560632\pi$
$263$	−18.3962	−	10.6211i	−1.13436	−	0.654922i	−0.945028	+	0.326991i	$0.893965\pi$
$264$		0			0
$265$	−3.02338	−	1.74555i	−0.185725	−	0.107228i
$266$		0			0
$267$	−0.560726	−	19.7952i	−0.0343159	−	1.21145i
$268$		0			0
$269$	17.4754	−	10.0894i	1.06549	−	0.615162i	0.138546	−	0.990356i	$-0.455757\pi$
$269$	17.4754	−	10.0894i	1.06549	−	0.615162i	0.926946	+	0.375194i	$0.122424\pi$
$270$		0			0
$271$	−8.69232	+	15.0555i	−0.528021	+	0.914559i	0.471445	+	0.881895i	$0.343732\pi$
$271$	−8.69232	+	15.0555i	−0.528021	+	0.914559i	−0.999466	+	0.0326639i	$0.989601\pi$
$272$		0			0
$273$	11.3941	−	18.2727i	0.689600	−	1.10591i
$274$		0			0
$275$	12.0272	−	6.94388i	0.725265	−	0.418732i
$276$		0			0
$277$	−0.566878	+	0.981861i	−0.0340604	+	0.0589943i	−0.882553	−	0.470213i	$-0.844177\pi$
$277$	−0.566878	+	0.981861i	−0.0340604	+	0.0589943i	0.848493	+	0.529207i	$0.177511\pi$
$278$		0			0
$279$	2.87269	−	5.69810i	0.171983	−	0.341136i
$280$		0			0
$281$	−6.37564	−	11.0429i	−0.380339	−	0.658766i	0.610772	−	0.791807i	$-0.290859\pi$
$281$	−6.37564	−	11.0429i	−0.380339	−	0.658766i	−0.991111	+	0.133040i	$0.957526\pi$
$282$		0			0
$283$	6.77001			0.402435			0.201218	−	0.979547i	$-0.435510\pi$
$283$	6.77001			0.402435			0.201218	+	0.979547i	$0.435510\pi$
$284$		0			0
$285$	−0.392672	+	0.241787i	−0.0232599	+	0.0143222i
$286$		0			0
$287$	0.651374	+	1.31037i	0.0384494	+	0.0773488i
$288$		0			0
$289$	24.1715	−	41.8662i	1.42185	−	2.46272i
$290$		0			0
$291$	−23.9773	−	12.9523i	−1.40557	−	0.759276i
$292$		0			0
$293$	−10.5242	−	6.07616i	−0.614831	−	0.354973i	0.160023	−	0.987113i	$-0.448843\pi$
$293$	−10.5242	−	6.07616i	−0.614831	−	0.354973i	−0.774854	+	0.632140i	$0.782177\pi$
$294$		0			0
$295$	−2.77117	+	1.59994i	−0.161344	+	0.0931519i
$296$		0			0
$297$	−13.2754	−	6.22779i	−0.770316	−	0.361373i
$298$		0			0
$299$	−1.84424			−0.106655
$300$		0			0
$301$	13.0660	+	0.814817i	0.753111	+	0.0469653i
$302$		0			0
$303$	0.343836	+	12.1384i	0.0197529	+	0.697332i
$304$		0			0
$305$	1.56795	+	2.71576i	0.0897804	+	0.155504i
$306$		0			0
$307$	17.3006			0.987396			0.493698	−	0.869634i	$-0.335645\pi$
$307$	17.3006			0.987396			0.493698	+	0.869634i	$0.335645\pi$
$308$		0			0
$309$	4.63669	−	8.58346i	0.263772	−	0.488296i
$310$		0			0
$311$	−26.4759			−1.50131			−0.750655	−	0.660694i	$-0.770262\pi$
$311$	−26.4759			−1.50131			−0.750655	+	0.660694i	$0.770262\pi$
$312$		0			0
$313$		−	4.46734i		−	0.252509i	−0.991998	−	0.126255i	$-0.959704\pi$
$313$		−	4.46734i		−	0.252509i	0.991998	−	0.126255i	$-0.0402956\pi$
$314$		0			0
$315$	1.12472	−	1.92293i	0.0633710	−	0.108345i
$316$		0			0
$317$	29.4033			1.65146			0.825728	−	0.564069i	$-0.190765\pi$
$317$	29.4033			1.65146			0.825728	+	0.564069i	$0.190765\pi$
$318$		0			0
$319$		−	8.53081i		−	0.477634i
$320$		0			0
$321$	0.283463	+	10.0070i	0.0158213	+	0.558538i
$322$		0			0
$323$		−	7.66807i		−	0.426663i
$324$		0			0
$325$	−20.0272	+	11.5627i	−1.11091	+	0.641383i
$326$		0			0
$327$	6.79735	−	12.5833i	0.375895	−	0.695857i
$328$		0			0
$329$	−6.14771	−	4.07965i	−0.338934	−	0.224918i
$330$		0			0
$331$			0.981836i			0.0539666i	0.999636	+	0.0269833i	$0.00859009\pi$
$331$			0.981836i			0.0539666i	−0.999636	+	0.0269833i	$0.991410\pi$
$332$		0			0
$333$	−8.00813	−	12.2167i	−0.438843	−	0.669472i
$334$		0			0
$335$	−1.27344	−	2.20566i	−0.0695755	−	0.120508i
$336$		0			0
$337$	5.58390	−	9.67160i	0.304174	−	0.526846i	−0.672903	−	0.739731i	$-0.734953\pi$
$337$	5.58390	−	9.67160i	0.304174	−	0.526846i	0.977077	+	0.212885i	$0.0682861\pi$
$338$		0			0
$339$	22.4224	−	0.635146i	1.21782	−	0.0344964i
$340$		0			0
$341$	5.19847	+	3.00134i	0.281513	+	0.162532i
$342$		0			0
$343$	−3.44029	+	18.1979i	−0.185758	+	0.982596i
$344$		0			0
$345$	−0.190711	+	0.00540215i	−0.0102675	+	0.000290842i
$346$		0			0
$347$			8.78830i			0.471781i	0.971780	+	0.235890i	$0.0758006\pi$
$347$			8.78830i			0.471781i	−0.971780	+	0.235890i	$0.924199\pi$
$348$		0			0
$349$	−18.2265	+	10.5231i	−0.975644	+	0.563288i	−0.900952	−	0.433919i	$-0.857131\pi$
$349$	−18.2265	+	10.5231i	−0.975644	+	0.563288i	−0.0746915	+	0.997207i	$0.523797\pi$
$350$		0			0
$351$	22.1057	+	10.3703i	1.17992	+	0.553525i
$352$		0			0
$353$	−2.28872	−	1.32139i	−0.121816	−	0.0703307i	0.437854	−	0.899046i	$-0.355739\pi$
$353$	−2.28872	−	1.32139i	−0.121816	−	0.0703307i	−0.559670	+	0.828716i	$0.689072\pi$
$354$		0			0
$355$	0.216945	+	0.375759i	0.0115142	+	0.0199432i
$356$		0			0
$357$	17.4216	+	32.6908i	0.922050	+	1.73018i
$358$		0			0
$359$	20.5571	+	11.8687i	1.08496	+	0.626405i	0.932231	−	0.361863i	$-0.117859\pi$
$359$	20.5571	+	11.8687i	1.08496	+	0.626405i	0.152733	+	0.988267i	$0.451192\pi$
$360$		0			0
$361$	9.05007	+	15.6752i	0.476320	+	0.825010i
$362$		0			0
$363$	−2.49946	+	4.62700i	−0.131187	+	0.242854i
$364$		0			0
$365$	0.0878545	−	0.152168i	0.00459852	−	0.00796486i
$366$		0			0
$367$	15.3410	−	26.5714i	0.800793	−	1.38701i	−0.118303	−	0.992978i	$-0.537745\pi$
$367$	15.3410	−	26.5714i	0.800793	−	1.38701i	0.919095	−	0.394036i	$-0.128921\pi$
$368$		0			0
$369$	−1.38770	+	0.909648i	−0.0722409	+	0.0473544i
$370$		0			0
$371$	−2.04833	+	32.8459i	−0.106344	+	1.70527i
$372$		0			0
$373$	−3.29461	−	5.70642i	−0.170588	−	0.295467i	0.768037	−	0.640405i	$-0.221233\pi$
$373$	−3.29461	−	5.70642i	−0.170588	−	0.295467i	−0.938626	+	0.344937i	$0.887900\pi$
$374$		0			0
$375$	−4.10685	+	2.52878i	−0.212077	+	0.130586i
$376$		0			0
$377$			14.2052i			0.731605i
$378$		0			0
$379$			0.316910i			0.0162786i	0.999967	+	0.00813930i	$0.00259085\pi$
$379$			0.316910i			0.0162786i	−0.999967	+	0.00813930i	$0.997409\pi$
$380$		0			0
$381$	−11.4633	+	7.05847i	−0.587281	+	0.361617i
$382$		0			0
$383$	−1.84855	−	3.20179i	−0.0944567	−	0.163604i	0.814925	−	0.579566i	$-0.196778\pi$
$383$	−1.84855	−	3.20179i	−0.0944567	−	0.163604i	−0.909382	+	0.415963i	$0.863445\pi$
$384$		0			0
$385$	1.74606	+	1.15869i	0.0889873	+	0.0590524i
$386$		0			0
$387$	0.840291	+	14.8204i	0.0427144	+	0.753364i
$388$		0			0
$389$	4.29814	−	7.44460i	0.217925	−	0.377456i	−0.736249	−	0.676711i	$-0.763405\pi$
$389$	4.29814	−	7.44460i	0.217925	−	0.377456i	0.954173	+	0.299255i	$0.0967380\pi$
$390$		0			0
$391$	1.58625	−	2.74746i	0.0802200	−	0.138945i
$392$		0			0
$393$	−6.57365	+	12.1691i	−0.331597	+	0.613852i
$394$		0			0
$395$	−2.16635	−	3.75224i	−0.109001	−	0.188795i
$396$		0			0
$397$	−10.9255	−	6.30783i	−0.548334	−	0.316581i	0.200116	−	0.979772i	$-0.435868\pi$
$397$	−10.9255	−	6.30783i	−0.548334	−	0.316581i	−0.748450	+	0.663192i	$0.769201\pi$
$398$		0			0
$399$	3.68870	+	2.30011i	0.184666	+	0.115150i
$400$		0			0
$401$	13.0646	+	22.6285i	0.652414	+	1.13001i	0.982535	+	0.186076i	$0.0595771\pi$
$401$	13.0646	+	22.6285i	0.652414	+	1.13001i	−0.330121	+	0.943939i	$0.607090\pi$
$402$		0			0
$403$	−8.65631	−	4.99772i	−0.431201	−	0.248954i
$404$		0			0
$405$	2.31630	+	1.00763i	0.115098	+	0.0500695i
$406$		0			0
$407$	11.8999	−	6.87041i	0.589856	−	0.340554i
$408$		0			0
$409$			0.288440i			0.0142624i	0.999975	+	0.00713121i	$0.00226995\pi$
$409$			0.288440i			0.0142624i	−0.999975	+	0.00713121i	$0.997730\pi$
$410$		0			0
$411$	14.9752	−	0.424194i	0.738673	−	0.0209239i
$412$		0			0
$413$	25.1337	+	16.6789i	1.23675	+	0.820713i
$414$		0			0
$415$	2.58046	+	1.48983i	0.126670	+	0.0731327i
$416$		0			0
$417$	24.9132	−	0.705700i	1.22000	−	0.0345583i
$418$		0			0
$419$	−9.56824	+	16.5727i	−0.467439	+	0.809629i	−0.999308	−	0.0371983i	$-0.988157\pi$
$419$	−9.56824	+	16.5727i	−0.467439	+	0.809629i	0.531869	+	0.846827i	$0.321490\pi$
$420$		0			0
$421$	−11.5319	−	19.9738i	−0.562030	−	0.973465i	−0.997319	−	0.0731740i	$-0.976687\pi$
$421$	−11.5319	−	19.9738i	−0.562030	−	0.973465i	0.435289	−	0.900291i	$-0.356646\pi$
$422$		0			0
$423$	3.76621	−	7.47042i	0.183119	−	0.363224i
$424$		0			0
$425$		−	39.7807i		−	1.92965i
$426$		0			0
$427$	16.3454	−	24.6312i	0.791008	−	1.19199i
$428$		0			0
$429$	−10.9165	+	20.2086i	−0.527053	+	0.975682i
$430$		0			0
$431$	13.2196	−	7.63235i	0.636766	−	0.367637i	−0.146601	−	0.989196i	$-0.546833\pi$
$431$	13.2196	−	7.63235i	0.636766	−	0.367637i	0.783368	+	0.621558i	$0.213500\pi$
$432$		0			0
$433$			24.5275i			1.17871i	0.807873	+	0.589357i	$0.200619\pi$
$433$			24.5275i			1.17871i	−0.807873	+	0.589357i	$0.799381\pi$
$434$		0			0
$435$	0.0416099	+	1.46895i	0.00199504	+	0.0704305i
$436$		0			0
$437$		−	0.372296i		−	0.0178093i
$438$		0			0
$439$	−18.2801			−0.872460			−0.436230	−	0.899835i	$-0.643687\pi$
$439$	−18.2801			−0.872460			−0.436230	+	0.899835i	$0.643687\pi$
$440$		0			0
$441$	−20.9516	−	1.42532i	−0.997694	−	0.0678724i
$442$		0			0
$443$			5.21155i			0.247608i	0.992307	+	0.123804i	$0.0395094\pi$
$443$			5.21155i			0.247608i	−0.992307	+	0.123804i	$0.960491\pi$
$444$		0			0
$445$	−3.20894			−0.152118
$446$		0			0
$447$	0.878887	−	1.62700i	0.0415699	−	0.0769543i
$448$		0			0
$449$	−9.38031			−0.442684			−0.221342	−	0.975196i	$-0.571044\pi$
$449$	−9.38031			−0.442684			−0.221342	+	0.975196i	$0.571044\pi$
$450$		0			0
$451$	−0.780414	−	1.35172i	−0.0367482	−	0.0636498i
$452$		0			0
$453$	0.634808	+	22.4105i	0.0298259	+	1.05294i
$454$		0			0
$455$	−2.90747	−	1.92941i	−0.136304	−	0.0904522i
$456$		0			0
$457$	29.3621			1.37350			0.686749	−	0.726894i	$-0.259037\pi$
$457$	29.3621			1.37350			0.686749	+	0.726894i	$0.259037\pi$
$458$		0			0
$459$	−34.4625	+	24.0124i	−1.60857	+	1.12080i
$460$		0			0
$461$	−1.10606	+	0.638584i	−0.0515144	+	0.0297418i	−0.525536	−	0.850771i	$-0.676135\pi$
$461$	−1.10606	+	0.638584i	−0.0515144	+	0.0297418i	0.474022	+	0.880513i	$0.342802\pi$
$462$		0			0
$463$	−23.8988	−	13.7980i	−1.11067	−	0.641247i	−0.171669	−	0.985155i	$-0.554916\pi$
$463$	−23.8988	−	13.7980i	−1.11067	−	0.641247i	−0.939004	+	0.343907i	$0.888249\pi$
$464$		0			0
$465$	−0.909779	−	0.491453i	−0.0421900	−	0.0227906i
$466$		0			0
$467$	5.00656	−	8.67162i	0.231676	−	0.401275i	−0.726625	−	0.687034i	$-0.758912\pi$
$467$	5.00656	−	8.67162i	0.231676	−	0.401275i	0.958301	+	0.285759i	$0.0922458\pi$
$468$		0			0
$469$	−13.2752	+	20.0047i	−0.612993	+	0.923733i
$470$		0			0
$471$	−11.9503	+	7.35834i	−0.550639	+	0.339054i
$472$		0			0
$473$	−13.9635			−0.642043
$474$		0			0
$475$	−2.33416	−	4.04288i	−0.107098	−	0.185500i
$476$		0			0
$477$	−37.2562	+	2.11236i	−1.70585	+	0.0967185i
$478$		0			0
$479$	7.39474	−	12.8081i	0.337874	−	0.585216i	−0.646158	−	0.763203i	$-0.723625\pi$
$479$	7.39474	−	12.8081i	0.337874	−	0.585216i	0.984033	+	0.177988i	$0.0569588\pi$
$480$		0			0
$481$	−19.8153	+	11.4404i	−0.903499	+	0.521636i
$482$		0			0
$483$	0.845846	+	1.58719i	0.0384873	+	0.0722195i
$484$		0			0
$485$	−2.20798	+	3.82434i	−0.100259	+	0.173654i
$486$		0			0
$487$	12.8101	−	7.39589i	0.580479	−	0.335140i	−0.180845	−	0.983512i	$-0.557883\pi$
$487$	12.8101	−	7.39589i	0.580479	−	0.335140i	0.761324	+	0.648372i	$0.224550\pi$
$488$		0			0
$489$	0.895686	+	31.6202i	0.0405043	+	1.42991i
$490$		0			0
$491$	12.5410	+	7.24053i	0.565966	+	0.326760i	0.755536	−	0.655107i	$-0.227376\pi$
$491$	12.5410	+	7.24053i	0.565966	+	0.326760i	−0.189571	+	0.981867i	$0.560710\pi$
$492$		0			0
$493$	−21.1622	−	12.2180i	−0.953099	−	0.550272i
$494$		0			0
$495$	−1.06967	+	2.12173i	−0.0480780	+	0.0953647i
$496$		0			0
$497$	2.26158	−	3.40803i	0.101446	−	0.152871i
$498$		0			0
$499$	−7.52679	+	4.34559i	−0.336945	+	0.194536i	−0.658920	−	0.752213i	$-0.728987\pi$
$499$	−7.52679	+	4.34559i	−0.336945	+	0.194536i	0.321975	+	0.946748i	$0.395653\pi$
$500$		0			0
$501$	29.1557	−	0.825877i	1.30258	−	0.0368975i
$502$		0			0
$503$	40.3239			1.79795			0.898977	−	0.437995i	$-0.144311\pi$
$503$	40.3239			1.79795			0.898977	+	0.437995i	$0.144311\pi$
$504$		0			0
$505$	1.96771			0.0875621
$506$		0			0
$507$	7.47608	−	13.8397i	0.332024	−	0.614644i
$508$		0			0
$509$	2.92593	−	1.68929i	0.129690	−	0.0748764i	−0.433752	−	0.901033i	$-0.642810\pi$
$509$	2.92593	−	1.68929i	0.129690	−	0.0748764i	0.563441	+	0.826156i	$0.309477\pi$
$510$		0			0
$511$	−1.65315	−	0.103093i	−0.0731311	−	0.00456058i
$512$		0			0
$513$	−2.09345	+	4.46247i	−0.0924279	+	0.197023i
$514$		0			0
$515$	−1.36905	−	0.790420i	−0.0603274	−	0.0348300i
$516$		0			0
$517$	6.81539	+	3.93487i	0.299741	+	0.173055i
$518$		0			0
$519$	−29.2621	+	18.0181i	−1.28447	+	0.790906i
$520$		0			0
$521$	−34.6315	+	19.9945i	−1.51723	+	0.875976i	−0.517440	+	0.855719i	$0.673115\pi$
$521$	−34.6315	+	19.9945i	−1.51723	+	0.875976i	−0.999795	+	0.0202566i	$0.993552\pi$
$522$		0			0
$523$	6.43351	−	11.1432i	0.281318	−	0.487257i	−0.690392	−	0.723436i	$-0.742562\pi$
$523$	6.43351	−	11.1432i	0.281318	−	0.487257i	0.971710	+	0.236179i	$0.0758951\pi$
$524$		0			0
$525$	19.1364	+	11.9326i	0.835180	+	0.520782i
$526$		0			0
$527$	14.8907	−	8.59716i	0.648650	−	0.374498i
$528$		0			0
$529$	−11.4230	+	19.7852i	−0.496652	+	0.860226i
$530$		0			0
$531$	−15.3974	+	30.5414i	−0.668191	+	1.32538i
$532$		0			0
$533$	1.29952	+	2.25083i	0.0562883	+	0.0974942i
$534$		0			0
$535$	1.62221			0.0701341
$536$		0			0
$537$	37.9188	+	20.4833i	1.63632	+	0.883921i
$538$		0			0
$539$	2.45425	−	19.6010i	0.105712	−	0.844276i
$540$		0			0
$541$	−2.79138	+	4.83481i	−0.120011	+	0.207865i	−0.919772	−	0.392454i	$-0.871626\pi$
$541$	−2.79138	+	4.83481i	−0.120011	+	0.207865i	0.799761	+	0.600319i	$0.204960\pi$
$542$		0			0
$543$	−10.7750	+	6.63467i	−0.462399	+	0.284721i
$544$		0			0
$545$	−2.00701	−	1.15875i	−0.0859709	−	0.0496353i
$546$		0			0
$547$	−9.37486	+	5.41258i	−0.400840	+	0.231425i	−0.686846	−	0.726803i	$-0.741006\pi$
$547$	−9.37486	+	5.41258i	−0.400840	+	0.231425i	0.286006	+	0.958228i	$0.407672\pi$
$548$		0			0
$549$	29.9307	+	15.0895i	1.27741	+	0.644006i
$550$		0			0
$551$	−2.86760			−0.122164
$552$		0			0
$553$	−22.5836	+	34.0317i	−0.960352	+	1.44717i
$554$		0			0
$555$	−2.01557	+	1.24108i	−0.0855561	+	0.0526809i
$556$		0			0
$557$	8.38879	+	14.5298i	0.355445	+	0.615648i	0.987194	−	0.159525i	$-0.0509961\pi$
$557$	8.38879	+	14.5298i	0.355445	+	0.615648i	−0.631749	+	0.775173i	$0.717663\pi$
$558$		0			0
$559$	23.2515			0.983436
$560$		0			0
$561$	−20.7165	−	33.6445i	−0.874651	−	1.42047i
$562$		0			0
$563$	28.6721			1.20838			0.604192	−	0.796839i	$-0.293496\pi$
$563$	28.6721			1.20838			0.604192	+	0.796839i	$0.293496\pi$
$564$		0			0
$565$		−	3.63483i		−	0.152918i
$566$		0			0
$567$	−1.21373	−	23.7808i	−0.0509720	−	0.998700i
$568$		0			0
$569$	33.2571			1.39421			0.697106	−	0.716968i	$-0.254471\pi$
$569$	33.2571			1.39421			0.697106	+	0.716968i	$0.254471\pi$
$570$		0			0
$571$		−	32.5982i		−	1.36419i	−0.731262	−	0.682097i	$-0.761068\pi$
$571$		−	32.5982i		−	1.36419i	0.731262	−	0.682097i	$-0.238932\pi$
$572$		0			0
$573$	−12.1230	+	7.46469i	−0.506445	+	0.311842i
$574$		0			0
$575$		−	1.93141i		−	0.0805455i
$576$		0			0
$577$	11.6155	−	6.70622i	0.483560	−	0.279183i	−0.238339	−	0.971182i	$-0.576603\pi$
$577$	11.6155	−	6.70622i	0.483560	−	0.279183i	0.721899	+	0.691999i	$0.243270\pi$
$578$		0			0
$579$	−17.7723	−	28.8630i	−0.738591	−	1.19950i
$580$		0			0
$581$	1.74825	−	28.0339i	0.0725295	−	1.16304i
$582$		0			0
$583$		−	35.1021i		−	1.45378i
$584$		0			0
$585$	1.78117	−	3.53303i	0.0736424	−	0.146073i
$586$		0			0
$587$	17.2883	+	29.9443i	0.713566	+	1.23593i	0.963510	+	0.267673i	$0.0862546\pi$
$587$	17.2883	+	29.9443i	0.713566	+	1.23593i	−0.249943	+	0.968260i	$0.580412\pi$
$588$		0			0
$589$	1.00889	−	1.74744i	0.0415705	−	0.0720022i
$590$		0			0
$591$	−14.8876	−	24.1781i	−0.612393	−	0.994554i
$592$		0			0
$593$	16.9169	+	9.76697i	0.694693	+	0.401081i	0.805368	−	0.592775i	$-0.201968\pi$
$593$	16.9169	+	9.76697i	0.694693	+	0.401081i	−0.110675	+	0.993857i	$0.535301\pi$
$594$		0			0
$595$	5.37509	−	2.67191i	0.220357	−	0.109538i
$596$		0			0
$597$	−12.9557	+	23.9836i	−0.530241	+	0.981583i
$598$		0			0
$599$			16.8037i			0.686581i	0.939229	+	0.343291i	$0.111542\pi$
$599$			16.8037i			0.686581i	−0.939229	+	0.343291i	$0.888458\pi$
$600$		0			0
$601$	6.18993	−	3.57376i	0.252492	−	0.145777i	−0.368413	−	0.929662i	$-0.620099\pi$
$601$	6.18993	−	3.57376i	0.252492	−	0.145777i	0.620905	+	0.783886i	$0.286765\pi$
$602$		0			0
$603$	−24.3089	−	12.2553i	−0.989933	−	0.499074i
$604$		0			0
$605$	0.737999	+	0.426084i	0.0300039	+	0.0173228i
$606$		0			0
$607$	8.93176	+	15.4703i	0.362529	+	0.627919i	0.988376	−	0.152027i	$-0.0485800\pi$
$607$	8.93176	+	15.4703i	0.362529	+	0.627919i	−0.625847	+	0.779946i	$0.715247\pi$
$608$		0			0
$609$	12.2252	−	6.51510i	0.495392	−	0.264005i
$610$		0			0
$611$	−11.3488	−	6.55220i	−0.459121	−	0.265074i
$612$		0			0
$613$	9.85193	+	17.0640i	0.397916	+	0.689210i	0.993469	−	0.114106i	$-0.0364003\pi$
$613$	9.85193	+	17.0640i	0.397916	+	0.689210i	−0.595553	+	0.803316i	$0.703067\pi$
$614$		0			0
$615$	0.140975	+	0.228949i	0.00568465	+	0.00923213i
$616$		0			0
$617$	−15.2946	+	26.4910i	−0.615738	+	1.06649i	0.374517	+	0.927220i	$0.377809\pi$
$617$	−15.2946	+	26.4910i	−0.615738	+	1.06649i	−0.990255	+	0.139269i	$0.955525\pi$
$618$		0			0
$619$	6.44975	−	11.1713i	0.259237	−	0.449012i	−0.706800	−	0.707413i	$-0.749862\pi$
$619$	6.44975	−	11.1713i	0.259237	−	0.449012i	0.966038	+	0.258401i	$0.0831954\pi$
$620$		0			0
$621$	−1.67320	+	1.16584i	−0.0671434	+	0.0467835i
$622$		0			0
$623$	13.4650	+	27.0877i	0.539466	+	1.08525i
$624$		0			0
$625$	−11.9123	−	20.6327i	−0.476492	−	0.825309i
$626$		0			0
$627$	−4.07951	−	2.20371i	−0.162920	−	0.0880076i
$628$		0			0
$629$		−	39.3598i		−	1.56938i
$630$		0			0
$631$			16.8826i			0.672085i	0.941847	+	0.336042i	$0.109089\pi$
$631$			16.8826i			0.672085i	−0.941847	+	0.336042i	$0.890911\pi$
$632$		0			0
$633$	−0.419879	−	14.8229i	−0.0166887	−	0.589157i
$634$		0			0
$635$	1.09071	+	1.88917i	0.0432836	+	0.0749694i
$636$		0			0
$637$	−4.08674	+	32.6389i	−0.161922	+	1.29320i
$638$		0			0
$639$	4.14128	+	2.08782i	0.163827	+	0.0825930i
$640$		0			0
$641$	−6.14505	+	10.6435i	−0.242715	+	0.420394i	−0.961487	−	0.274852i	$-0.911371\pi$
$641$	−6.14505	+	10.6435i	−0.242715	+	0.420394i	0.718772	+	0.695246i	$0.244705\pi$
$642$		0			0
$643$	20.2664	−	35.1024i	0.799228	−	1.38430i	−0.120891	−	0.992666i	$-0.538575\pi$
$643$	20.2664	−	35.1024i	0.799228	−	1.38430i	0.920119	−	0.391638i	$-0.128091\pi$
$644$		0			0
$645$	2.40442	−	0.0681085i	0.0946739	−	0.00268177i
$646$		0			0
$647$	12.3850	+	21.4515i	0.486905	+	0.843344i	0.999887	−	0.0150552i	$-0.00479241\pi$
$647$	12.3850	+	21.4515i	0.486905	+	0.843344i	−0.512982	+	0.858400i	$0.671459\pi$
$648$		0			0
$649$	−27.8634	−	16.0870i	−1.09374	−	0.631469i
$650$		0			0
$651$	−0.330986	+	9.74193i	−0.0129723	+	0.381816i
$652$		0			0
$653$	9.33573	+	16.1700i	0.365335	+	0.632779i	0.988830	−	0.149048i	$-0.0476210\pi$
$653$	9.33573	+	16.1700i	0.365335	+	0.632779i	−0.623495	+	0.781828i	$0.714288\pi$
$654$		0			0
$655$	1.94096	+	1.12061i	0.0758395	+	0.0437860i
$656$		0			0
$657$	−0.106316	−	1.87513i	−0.00414780	−	0.0731557i
$658$		0			0
$659$	−39.5720	+	22.8469i	−1.54150	+	0.889988i	−0.542761	+	0.839887i	$0.682621\pi$
$659$	−39.5720	+	22.8469i	−1.54150	+	0.889988i	−0.998744	+	0.0501010i	$0.984046\pi$
$660$		0			0
$661$		−	29.3756i		−	1.14258i	−0.820749	−	0.571289i	$-0.806444\pi$
$661$		−	29.3756i		−	1.14258i	0.820749	−	0.571289i	$-0.193556\pi$
$662$		0			0
$663$	34.4964	+	56.0236i	1.33973	+	2.17578i
$664$		0			0
$665$	0.389489	−	0.586930i	0.0151038	−	0.0227602i
$666$		0			0
$667$	−1.02746	−	0.593203i	−0.0397833	−	0.0229689i
$668$		0			0
$669$	15.8577	−	29.3558i	0.613094	−	1.13496i
$670$		0			0
$671$	−15.7653	+	27.3063i	−0.608613	+	1.05415i
$672$		0			0
$673$	13.3294	+	23.0872i	0.513810	+	0.889945i	0.999872	+	0.0160205i	$0.00509972\pi$
$673$	13.3294	+	23.0872i	0.513810	+	0.889945i	−0.486062	+	0.873925i	$0.661567\pi$
$674$		0			0
$675$	−10.8605	+	23.1506i	−0.418020	+	0.891066i
$676$		0			0
$677$		−	47.3055i		−	1.81810i	−0.416687	−	0.909050i	$-0.636809\pi$
$677$		−	47.3055i		−	1.81810i	0.416687	−	0.909050i	$-0.363191\pi$
$678$		0			0
$679$	41.5474	+	2.59097i	1.59444	+	0.0994323i
$680$		0			0
$681$	−35.7351	+	1.01225i	−1.36937	+	0.0387893i
$682$		0			0
$683$	23.6562	−	13.6579i	0.905178	−	0.522605i	0.0263018	−	0.999654i	$-0.491627\pi$
$683$	23.6562	−	13.6579i	0.905178	−	0.522605i	0.878877	+	0.477049i	$0.158294\pi$
$684$		0			0
$685$		−	2.42758i		−	0.0927532i
$686$		0			0
$687$	32.2994	+	17.4478i	1.23230	+	0.665675i
$688$		0			0
$689$			58.4508i			2.22680i
$690$		0			0
$691$	−39.7682			−1.51285			−0.756427	−	0.654078i	$-0.773057\pi$
$691$	−39.7682			−1.51285			−0.756427	+	0.654078i	$0.773057\pi$
$692$		0			0
$693$	22.3987	+	0.126408i	0.850855	+	0.00480184i
$694$		0			0
$695$		−	4.03859i		−	0.153193i
$696$		0			0
$697$	−4.47090			−0.169348
$698$		0			0
$699$	26.9576	−	0.763610i	1.01963	−	0.0288824i
$700$		0			0
$701$	−33.5286			−1.26636			−0.633180	−	0.774005i	$-0.718251\pi$
$701$	−33.5286			−1.26636			−0.633180	+	0.774005i	$0.718251\pi$
$702$		0			0
$703$	−2.30946	−	4.00010i	−0.0871029	−	0.150867i
$704$		0			0
$705$	−1.19276	−	0.644314i	−0.0449218	−	0.0242663i
$706$		0			0
$707$	−8.25674	−	16.6101i	−0.310527	−	0.624688i
$708$		0			0
$709$	−30.3525			−1.13991			−0.569956	−	0.821675i	$-0.693040\pi$
$709$	−30.3525			−1.13991			−0.569956	+	0.821675i	$0.693040\pi$
$710$		0			0
$711$	−41.3538	−	20.8485i	−1.55089	−	0.781879i
$712$		0			0
$713$	0.722967	−	0.417405i	0.0270753	−	0.0156319i
$714$		0			0
$715$	3.22324	+	1.86094i	0.120542	+	0.0695952i
$716$		0			0
$717$	−0.360556	−	12.7286i	−0.0134652	−	0.475359i
$718$		0			0
$719$	17.8512	−	30.9192i	0.665737	−	1.15309i	−0.313348	−	0.949638i	$-0.601451\pi$
$719$	17.8512	−	30.9192i	0.665737	−	1.15309i	0.979085	−	0.203452i	$-0.0652160\pi$
$720$		0			0
$721$	−0.927523	+	14.8733i	−0.0345427	+	0.553909i
$722$		0			0
$723$	−0.282214	−	9.96293i	−0.0104956	−	0.370525i
$724$		0			0
$725$	−14.8766			−0.552505
$726$		0			0
$727$	−4.33546	−	7.50924i	−0.160793	−	0.278502i	0.774360	−	0.632745i	$-0.218072\pi$
$727$	−4.33546	−	7.50924i	−0.160793	−	0.278502i	−0.935153	+	0.354243i	$0.884739\pi$
$728$		0			0
$729$	26.6112	−	4.56560i	0.985600	−	0.169096i
$730$		0			0
$731$	−19.9989	+	34.6390i	−0.739684	+	1.28117i
$732$		0			0
$733$	3.50591	−	2.02414i	0.129494	−	0.0747633i	−0.433854	−	0.900983i	$-0.642847\pi$
$733$	3.50591	−	2.02414i	0.129494	−	0.0747633i	0.563348	+	0.826220i	$0.309513\pi$
$734$		0			0
$735$	−0.326999	+	3.38713i	−0.0120615	+	0.124936i
$736$		0			0
$737$	12.8041	−	22.1774i	0.471646	−	0.816915i
$738$		0			0
$739$	−18.5401	+	10.7042i	−0.682010	+	0.393759i	−0.800612	−	0.599183i	$-0.795492\pi$
$739$	−18.5401	+	10.7042i	−0.682010	+	0.393759i	0.118602	+	0.992942i	$0.462159\pi$
$740$		0			0
$741$	6.79305	+	3.66953i	0.249549	+	0.134804i
$742$		0			0
$743$	43.3251	+	25.0137i	1.58944	+	0.917665i	0.993399	+	0.114714i	$0.0365951\pi$
$743$	43.3251	+	25.0137i	1.58944	+	0.917665i	0.596044	+	0.802952i	$0.296738\pi$
$744$		0			0
$745$	−0.259503	−	0.149824i	−0.00950746	−	0.00548914i
$746$		0			0
$747$	31.7982	−	1.80290i	1.16344	−	0.0659647i
$748$		0			0
$749$	−6.80695	−	13.6936i	−0.248721	−	0.500352i
$750$		0			0
$751$	18.4527	−	10.6537i	0.673349	−	0.388758i	−0.123995	−	0.992283i	$-0.539571\pi$
$751$	18.4527	−	10.6537i	0.673349	−	0.388758i	0.797344	+	0.603525i	$0.206237\pi$
$752$		0			0
$753$	−19.9791	−	32.4469i	−0.728078	−	1.18243i
$754$		0			0
$755$	3.63289			0.132214
$756$		0			0
$757$	13.2589			0.481904			0.240952	−	0.970537i	$-0.422540\pi$
$757$	13.2589			0.481904			0.240952	+	0.970537i	$0.422540\pi$
$758$		0			0
$759$	−1.00582	−	1.63349i	−0.0365088	−	0.0592919i
$760$		0			0
$761$	34.8705	−	20.1325i	1.26406	−	0.729803i	0.290199	−	0.956966i	$-0.406278\pi$
$761$	34.8705	−	20.1325i	1.26406	−	0.729803i	0.973857	+	0.227163i	$0.0729451\pi$
$762$		0			0
$763$	−1.35974	+	21.8041i	−0.0492259	+	0.789361i
$764$		0			0
$765$	3.73134	+	5.69230i	0.134907	+	0.205805i
$766$		0			0
$767$	46.3972	+	26.7874i	1.67531	+	0.967238i
$768$		0			0
$769$	5.51138	+	3.18199i	0.198745	+	0.114746i	0.596070	−	0.802932i	$-0.296728\pi$
$769$	5.51138	+	3.18199i	0.198745	+	0.114746i	−0.397325	+	0.917678i	$0.630061\pi$
$770$		0			0
$771$	2.21827	+	1.19829i	0.0798891	+	0.0431553i
$772$		0			0
$773$	42.9373	−	24.7899i	1.54435	−	0.891629i	0.545790	−	0.837922i	$-0.316230\pi$
$773$	42.9373	−	24.7899i	1.54435	−	0.891629i	0.998557	−	0.0537073i	$-0.0171038\pi$
$774$		0			0
$775$	5.23395	−	9.06546i	0.188009	−	0.325641i
$776$		0			0
$777$	18.9339	+	11.8064i	0.679250	+	0.423551i
$778$		0			0
$779$	−0.454374	+	0.262333i	−0.0162796	+	0.00939905i
$780$		0			0
$781$	−2.18132	+	3.77816i	−0.0780539	+	0.135193i
$782$		0			0
$783$	8.97983	+	12.8878i	0.320913	+	0.460572i
$784$		0			0
$785$	1.13705	+	1.96943i	0.0405831	+	0.0702919i
$786$		0			0
$787$	−28.2267			−1.00617			−0.503086	−	0.864236i	$-0.667802\pi$
$787$	−28.2267			−1.00617			−0.503086	+	0.864236i	$0.667802\pi$
$788$		0			0
$789$	1.04178	+	36.7777i	0.0370883	+	1.30932i
$790$		0			0
$791$	−30.6828	+	15.2521i	−1.09095	+	0.542303i
$792$		0			0
$793$	26.2518	−	45.4695i	0.932230	−	1.61467i
$794$		0			0
$795$	0.171214	+	6.04434i	0.00607234	+	0.214371i
$796$		0			0
$797$	−15.6877	−	9.05731i	−0.555688	−	0.320826i	0.195725	−	0.980659i	$-0.437294\pi$
$797$	−15.6877	−	9.05731i	−0.555688	−	0.320826i	−0.751413	+	0.659832i	$0.770627\pi$
$798$		0			0
$799$	19.5223	−	11.2712i	0.690650	−	0.398747i
$800$		0			0
$801$	−28.6863	+	18.8040i	−1.01358	+	0.664408i
$802$		0			0
$803$	1.76671			0.0623458
$804$		0			0
$805$	0.260968	−	0.129725i	0.00919793	−	0.00457221i
$806$		0			0
$807$	−30.7509	−	16.6113i	−1.08248	−	0.584746i
$808$		0			0
$809$	−1.56171	−	2.70496i	−0.0549067	−	0.0951012i	0.837266	−	0.546796i	$-0.184153\pi$
$809$	−1.56171	−	2.70496i	−0.0549067	−	0.0951012i	−0.892172	+	0.451695i	$0.850819\pi$
$810$		0			0
$811$	−9.66660			−0.339440			−0.169720	−	0.985492i	$-0.554286\pi$
$811$	−9.66660			−0.339440			−0.169720	+	0.985492i	$0.554286\pi$
$812$		0			0
$813$	30.0990	−	0.852596i	1.05562	−	0.0299019i
$814$		0			0
$815$	5.12585			0.179551
$816$		0			0
$817$			4.69378i			0.164214i
$818$		0			0
$819$	−37.2975	−	0.210490i	−1.30328	−	0.00735511i
$820$		0			0
$821$	28.9554			1.01055			0.505275	−	0.862958i	$-0.331391\pi$
$821$	28.9554			1.01055			0.505275	+	0.862958i	$0.331391\pi$
$822$		0			0
$823$		−	39.7963i		−	1.38721i	−0.720355	−	0.693605i	$-0.756021\pi$
$823$		−	39.7963i		−	1.38721i	0.720355	−	0.693605i	$-0.243979\pi$
$824$		0			0
$825$	−21.1638	−	11.4325i	−0.736830	−	0.398028i
$826$		0			0
$827$		−	37.9694i		−	1.32033i	−0.751123	−	0.660163i	$-0.770487\pi$
$827$		−	37.9694i		−	1.32033i	0.751123	−	0.660163i	$-0.229513\pi$
$828$		0			0
$829$	38.3383	−	22.1346i	1.33154	−	0.768766i	0.346006	−	0.938232i	$-0.387538\pi$
$829$	38.3383	−	22.1346i	1.33154	−	0.768766i	0.985536	+	0.169466i	$0.0542042\pi$
$830$		0			0
$831$	1.96293	−	0.0556028i	0.0680934	−	0.00192884i
$832$		0			0
$833$	−45.1089	−	34.1613i	−1.56293	−	1.18362i
$834$		0			0
$835$		−	4.72634i		−	0.163562i
$836$		0			0
$837$	−11.0128	+	0.937868i	−0.380659	+	0.0324174i
$838$		0			0
$839$	−16.3128	−	28.2547i	−0.563182	−	0.975460i	−0.997216	−	0.0745634i	$-0.976244\pi$
$839$	−16.3128	−	28.2547i	−0.563182	−	0.975460i	0.434034	−	0.900896i	$-0.357090\pi$
$840$		0			0
$841$	9.93088	−	17.2008i	0.342444	−	0.593130i
$842$		0			0
$843$	−10.4969	+	19.4319i	−0.361533	+	0.669271i
$844$		0			0
$845$	−2.20741	−	1.27445i	−0.0759374	−	0.0438425i
$846$		0			0
$847$	0.499990	−	8.01758i	0.0171799	−	0.275487i
$848$		0			0
$849$	−6.14819	−	9.98493i	−0.211005	−	0.342682i
$850$		0			0
$851$		−	1.91098i		−	0.0655075i
$852$		0			0
$853$	−9.50254	+	5.48629i	−0.325361	+	0.187847i	−0.653779	−	0.756685i	$-0.726818\pi$
$853$	−9.50254	+	5.48629i	−0.325361	+	0.187847i	0.328419	+	0.944532i	$0.393484\pi$
$854$		0			0
$855$	0.713211	+	0.359565i	0.0243913	+	0.0122968i
$856$		0			0
$857$	−3.04476	−	1.75789i	−0.104007	−	0.0600485i	0.447094	−	0.894487i	$-0.352459\pi$
$857$	−3.04476	−	1.75789i	−0.104007	−	0.0600485i	−0.551101	+	0.834438i	$0.685792\pi$
$858$		0			0
$859$	7.58841	+	13.1435i	0.258913	+	0.448451i	0.965951	−	0.258725i	$-0.0833023\pi$
$859$	7.58841	+	13.1435i	0.258913	+	0.448451i	−0.707038	+	0.707176i	$0.749969\pi$
$860$		0			0
$861$	1.34109	−	2.15071i	0.0457043	−	0.0732960i
$862$		0			0
$863$	29.7041	+	17.1496i	1.01114	+	0.583781i	0.911525	−	0.411245i	$-0.134906\pi$
$863$	29.7041	+	17.1496i	1.01114	+	0.583781i	0.0996133	+	0.995026i	$0.468239\pi$
$864$		0			0
$865$	2.78425	+	4.82246i	0.0946673	+	0.163969i
$866$		0			0
$867$	−83.6988	+	2.37088i	−2.84256	+	0.0805195i
$868$		0			0
$869$	21.7821	−	37.7278i	0.738909	−	1.27983i
$870$		0			0
$871$	−21.3210	+	36.9290i	−0.722433	+	1.25129i
$872$		0			0
$873$	2.67197	+	47.1262i	0.0904325	+	1.59498i
$874$		0			0
$875$	4.07356	−	6.13854i	0.137712	−	0.207520i
$876$		0			0
$877$	−10.6413	−	18.4313i	−0.359332	−	0.622381i	0.628517	−	0.777795i	$-0.283662\pi$
$877$	−10.6413	−	18.4313i	−0.359332	−	0.622381i	−0.987849	+	0.155414i	$0.950329\pi$
$878$		0			0
$879$	0.595987	+	21.0400i	0.0201021	+	0.709661i
$880$		0			0
$881$			20.5029i			0.690761i	0.938463	+	0.345380i	$0.112250\pi$
$881$			20.5029i			0.690761i	−0.938463	+	0.345380i	$0.887750\pi$
$882$		0			0
$883$		−	39.9687i		−	1.34506i	−0.740072	−	0.672528i	$-0.765209\pi$
$883$		−	39.9687i		−	1.34506i	0.740072	−	0.672528i	$-0.234791\pi$
$884$		0			0
$885$	4.87635	+	2.63415i	0.163917	+	0.0885461i
$886$		0			0
$887$	−16.6510	−	28.8404i	−0.559085	−	0.968364i	−0.997573	−	0.0696271i	$-0.977819\pi$
$887$	−16.6510	−	28.8404i	−0.559085	−	0.968364i	0.438488	−	0.898737i	$-0.355514\pi$
$888$		0			0
$889$	11.3704	−	17.1342i	0.381350	−	0.574664i
$890$		0			0
$891$	2.87083	+	25.2353i	0.0961764	+	0.845416i
$892$		0			0
$893$	1.32269	−	2.29097i	0.0442621	−	0.0766643i
$894$		0			0
$895$	3.49181	−	6.04798i	0.116718	−	0.202162i
$896$		0			0
$897$	1.67485	+	2.72003i	0.0559216	+	0.0908191i
$898$		0			0
$899$	−3.21505	−	5.56863i	−0.107228	−	0.185724i
$900$		0			0
$901$	−87.0772	−	50.2741i	−2.90096	−	1.67487i
$902$		0			0
$903$	−10.6641	−	20.0107i	−0.354880	−	0.665914i
$904$		0			0
$905$	1.02522	+	1.77574i	0.0340796	+	0.0590276i
$906$		0			0
$907$	1.48209	+	0.855683i	0.0492119	+	0.0284125i	0.524404	−	0.851470i	$-0.324288\pi$
$907$	1.48209	+	0.855683i	0.0492119	+	0.0284125i	−0.475192	+	0.879882i	$0.657621\pi$
$908$		0			0
$909$	17.5904	−	11.5306i	0.583435	−	0.382446i
$910$		0			0
$911$	−7.22479	+	4.17123i	−0.239368	+	0.138199i	−0.614886	−	0.788616i	$-0.710798\pi$
$911$	−7.22479	+	4.17123i	−0.239368	+	0.138199i	0.375518	+	0.926815i	$0.377465\pi$
$912$		0			0
$913$			29.9597i			0.991520i
$914$		0			0
$915$	2.58149	−	4.77885i	0.0853413	−	0.157984i
$916$		0			0
$917$	1.31499	−	21.0865i	0.0434248	−	0.696337i
$918$		0			0
$919$	−13.4897	−	7.78828i	−0.444984	−	0.256911i	0.260726	−	0.965413i	$-0.416038\pi$
$919$	−13.4897	−	7.78828i	−0.444984	−	0.256911i	−0.705709	+	0.708501i	$0.749372\pi$
$920$		0			0
$921$	−15.7115	−	25.5162i	−0.517712	−	0.840788i
$922$		0			0
$923$	3.63226	−	6.29126i	0.119557	−	0.207079i
$924$		0			0
$925$	−11.9811	−	20.7519i	−0.393937	−	0.682318i
$926$		0			0
$927$	−16.8704	+	0.956520i	−0.554095	+	0.0314162i
$928$		0			0
$929$			2.44492i			0.0802152i	0.999195	+	0.0401076i	$0.0127701\pi$
$929$			2.44492i			0.0802152i	−0.999195	+	0.0401076i	$0.987230\pi$
$930$		0			0
$931$	−6.58881	−	0.824987i	−0.215939	−	0.0270379i
$932$		0			0
$933$	24.0441	+	39.0487i	0.787169	+	1.27840i
$934$		0			0
$935$	−5.54468	+	3.20122i	−0.181330	+	0.104691i
$936$		0			0
$937$			2.32069i			0.0758137i	0.999281	+	0.0379069i	$0.0120690\pi$
$937$			2.32069i			0.0758137i	−0.999281	+	0.0379069i	$0.987931\pi$
$938$		0			0
$939$	−6.58878	+	4.05702i	−0.215017	+	0.132396i
$940$		0			0
$941$		−	15.9023i		−	0.518400i	−0.965824	−	0.259200i	$-0.916541\pi$
$941$		−	15.9023i		−	0.518400i	0.965824	−	0.259200i	$-0.0834588\pi$
$942$		0			0
$943$	−0.217069			−0.00706874
$944$		0			0
$945$	−3.85751	+	0.0874853i	−0.125485	+	0.00284590i
$946$		0			0
$947$		−	36.3372i		−	1.18080i	−0.807111	−	0.590400i	$-0.798970\pi$
$947$		−	36.3372i		−	1.18080i	0.807111	−	0.590400i	$-0.201030\pi$
$948$		0			0
$949$	−2.94186			−0.0954969
$950$		0			0
$951$	−26.7027	−	43.3663i	−0.865893	−	1.40625i
$952$		0			0
$953$	−10.1790			−0.329730			−0.164865	−	0.986316i	$-0.552719\pi$
$953$	−10.1790			−0.329730			−0.164865	+	0.986316i	$0.552719\pi$
$954$		0			0
$955$	1.15348	+	1.99789i	0.0373259	+	0.0646503i
$956$		0			0
$957$	−12.5819	+	7.74726i	−0.406715	+	0.250433i
$958$		0			0
$959$	−20.4920	+	10.1864i	−0.661722	+	0.328936i
$960$		0			0
$961$	−26.4755			−0.854048
$962$		0			0
$963$	14.5017	−	9.50596i	0.467311	−	0.306325i
$964$		0			0
$965$	−4.75668	+	2.74627i	−0.153123	+	0.0884055i
$966$		0			0
$967$	−17.1689	−	9.91247i	−0.552115	−	0.318764i	0.197860	−	0.980230i	$-0.436601\pi$
$967$	−17.1689	−	9.91247i	−0.552115	−	0.318764i	−0.749974	+	0.661467i	$0.769934\pi$
$968$		0			0
$969$	−11.3095	+	6.96376i	−0.363312	+	0.223708i
$970$		0			0
$971$	−12.7738	+	22.1249i	−0.409931	+	0.710021i	−0.994882	−	0.101048i	$-0.967780\pi$
$971$	−12.7738	+	22.1249i	−0.409931	+	0.710021i	0.584951	+	0.811069i	$0.301114\pi$
$972$		0			0
$973$	−34.0911	+	16.9464i	−1.09291	+	0.543276i
$974$		0			0
$975$	35.2413	+	19.0370i	1.12862	+	0.609671i
$976$		0			0
$977$	−22.7971			−0.729343			−0.364671	−	0.931136i	$-0.618819\pi$
$977$	−22.7971			−0.729343			−0.364671	+	0.931136i	$0.618819\pi$
$978$		0			0
$979$	−16.1325	−	27.9424i	−0.515598	−	0.893041i
$980$		0			0
$981$	−24.7318	+	1.40225i	−0.789626	+	0.0447704i
$982$		0			0
$983$	27.9954	−	48.4894i	0.892914	−	1.54657i	0.0565482	−	0.998400i	$-0.481991\pi$
$983$	27.9954	−	48.4894i	0.892914	−	1.54657i	0.836366	−	0.548172i	$-0.184676\pi$
$984$		0			0
$985$	−3.98460	+	2.30051i	−0.126960	+	0.0733003i
$986$		0			0
$987$	−0.433935	+	12.7721i	−0.0138123	+	0.406539i
$988$		0			0
$989$	−0.970974	+	1.68178i	−0.0308752	+	0.0534774i
$990$		0			0
$991$	21.3062	−	12.3011i	0.676814	−	0.390759i	−0.121840	−	0.992550i	$-0.538879\pi$
$991$	21.3062	−	12.3011i	0.676814	−	0.390759i	0.798653	+	0.601791i	$0.205546\pi$
$992$		0			0
$993$	1.44809	−	0.891655i	0.0459537	−	0.0282958i
$994$		0			0
$995$	3.82534	+	2.20856i	0.121272	+	0.0700162i
$996$		0			0
$997$	35.0171	+	20.2171i	1.10900	+	0.640283i	0.938571	−	0.345087i	$-0.112150\pi$
$997$	35.0171	+	20.2171i	1.10900	+	0.640283i	0.170432	+	0.985370i	$0.445484\pi$
$998$		0			0
$999$	−10.7456	+	22.9056i	−0.339974	+	0.724702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.607.5	yes	24
3.2	odd	2		3024.2.cz.h.1279.6		24
4.3	odd	2		1008.2.cz.h.607.8	yes	24
7.3	odd	6		1008.2.bf.g.31.9	✓	24
9.2	odd	6		3024.2.bf.g.2287.6		24
9.7	even	3		1008.2.bf.h.943.4	yes	24
12.11	even	2		3024.2.cz.g.1279.6		24
21.17	even	6		3024.2.bf.h.1711.7		24
28.3	even	6		1008.2.bf.h.31.4	yes	24
36.7	odd	6		1008.2.bf.g.943.9	yes	24
36.11	even	6		3024.2.bf.h.2287.6		24
63.38	even	6		3024.2.cz.g.2719.6		24
63.52	odd	6		1008.2.cz.h.367.8	yes	24
84.59	odd	6		3024.2.bf.g.1711.7		24
252.115	even	6	inner	1008.2.cz.g.367.5	yes	24
252.227	odd	6		3024.2.cz.h.2719.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.9	✓	24	7.3	odd	6
1008.2.bf.g.943.9	yes	24	36.7	odd	6
1008.2.bf.h.31.4	yes	24	28.3	even	6
1008.2.bf.h.943.4	yes	24	9.7	even	3
1008.2.cz.g.367.5	yes	24	252.115	even	6	inner
1008.2.cz.g.607.5	yes	24	1.1	even	1	trivial
1008.2.cz.h.367.8	yes	24	63.52	odd	6
1008.2.cz.h.607.8	yes	24	4.3	odd	2
3024.2.bf.g.1711.7		24	84.59	odd	6
3024.2.bf.g.2287.6		24	9.2	odd	6
3024.2.bf.h.1711.7		24	21.17	even	6
3024.2.bf.h.2287.6		24	36.11	even	6
3024.2.cz.g.1279.6		24	12.11	even	2
3024.2.cz.g.2719.6		24	63.38	even	6
3024.2.cz.h.1279.6		24	3.2	odd	2
3024.2.cz.h.2719.6		24	252.227	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.908151 - 1.47488i) q^{3} +(-0.243063 + 0.140332i) q^{5} +(2.20451 + 1.46292i) q^{7} +(-1.35052 + 2.67882i) q^{9} +O(q^{10})\)	\(q+(-0.908151 - 1.47488i) q^{3} +(-0.243063 + 0.140332i) q^{5} +(2.20451 + 1.46292i) q^{7} +(-1.35052 + 2.67882i) q^{9} +(-2.44393 - 1.41101i) q^{11} +(4.06955 + 2.34956i) q^{13} +(0.427710 + 0.231045i) q^{15} +(-7.00051 + 4.04175i) q^{17} +(-0.474304 + 0.821518i) q^{19} +(0.155605 - 4.57993i) q^{21} +(-0.339885 + 0.196233i) q^{23} +(-2.46061 + 4.26191i) q^{25} +(5.17741 - 0.440916i) q^{27} +(1.51148 + 2.61795i) q^{29} -2.12709 q^{31} +(0.138400 + 4.88591i) q^{33} +(-0.741129 - 0.0462181i) q^{35} +(-2.43458 + 4.21681i) q^{37} +(-0.230459 - 8.13584i) q^{39} +(0.478990 + 0.276545i) q^{41} +(4.28515 - 2.47404i) q^{43} +(-0.0476630 - 0.840644i) q^{45} -2.78870 q^{47} +(2.71972 + 6.45005i) q^{49} +(12.3186 + 6.65438i) q^{51} +(6.21935 + 10.7722i) q^{53} +0.792039 q^{55} +(1.64238 - 0.0465226i) q^{57} +11.4011 q^{59} -11.1731i q^{61} +(-6.89615 + 3.92977i) q^{63} -1.31887 q^{65} +9.07446i q^{67} +(0.598086 + 0.323080i) q^{69} -1.54594i q^{71} +(-0.542172 + 0.313023i) q^{73} +(8.52040 - 0.241352i) q^{75} +(-3.32348 - 6.68586i) q^{77} +15.4373i q^{79} +(-5.35217 - 7.23563i) q^{81} +(-5.30821 - 9.19409i) q^{83} +(1.13438 - 1.96480i) q^{85} +(2.48851 - 4.60674i) q^{87} +(9.90157 + 5.71667i) q^{89} +(5.53414 + 11.1331i) q^{91} +(1.93172 + 3.13720i) q^{93} -0.266241i q^{95} +(13.6260 - 7.86698i) q^{97} +(7.08043 - 4.64126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more