LMFDB - Embedded newform 861.2.i.c.739.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.i (of order $3$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.7873200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 12x^{4} + 36x^{2} + 12 $ x^6 + 12x^4 + 36x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			739.1
Root			$-0.616380i$ of defining polynomial
Character	$\chi$	$=$	861.739
Dual form			861.2.i.c.247.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.27624 - 2.21051i) q^{5} +(-2.58628 + 0.557835i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.27624 - 2.21051i) q^{5} +(-2.58628 + 0.557835i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.08628 + 5.34559i) q^{11} +(-1.00000 - 1.73205i) q^{12} -2.06760 q^{13} -2.55247 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{17} +(0.223763 + 0.387568i) q^{19} -5.10495 q^{20} +(-0.810038 + 2.51870i) q^{21} +(0.276237 + 0.478457i) q^{23} +(-0.757563 + 1.31214i) q^{25} -1.00000 q^{27} +(-1.62008 + 5.03740i) q^{28} -5.10495 q^{29} +(3.86251 - 6.69007i) q^{31} +(3.08628 + 5.34559i) q^{33} +(4.53380 + 5.00505i) q^{35} -2.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-1.03380 + 1.79060i) q^{39} -1.00000 q^{41} -10.6201 q^{43} +(6.17255 + 10.6912i) q^{44} +(-1.27624 + 2.21051i) q^{45} +(4.15388 + 7.19473i) q^{47} -4.00000 q^{48} +(6.37764 - 2.88543i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-2.06760 + 3.58119i) q^{52} +(2.06760 - 3.58119i) q^{53} +15.7553 q^{55} +0.447525 q^{57} +(-4.06760 + 7.04529i) q^{59} +(-2.55247 + 4.42102i) q^{60} +(-3.87764 - 6.71627i) q^{61} +(1.77624 + 1.96086i) q^{63} -8.00000 q^{64} +(2.63875 + 4.57045i) q^{65} +(0.0338006 - 0.0585444i) q^{67} +(-2.00000 - 3.46410i) q^{68} +0.552475 q^{69} +2.13520 q^{71} +(5.31004 - 9.19726i) q^{73} +(0.757563 + 1.31214i) q^{75} +0.895051 q^{76} +(5.00000 - 15.5468i) q^{77} +(-8.39631 - 14.5428i) q^{79} +(-5.10495 + 8.84203i) q^{80} +(-0.500000 + 0.866025i) q^{81} -13.9278 q^{83} +(3.55247 + 3.92172i) q^{84} -5.10495 q^{85} +(-2.55247 + 4.42102i) q^{87} +(-6.15388 - 10.6588i) q^{89} +(5.34739 - 1.15338i) q^{91} +1.10495 q^{92} +(-3.86251 - 6.69007i) q^{93} +(0.571149 - 0.989258i) q^{95} +16.2099 q^{97} +6.17255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9} - 6 q^{12} - 6 q^{13} - 12 q^{16} + 6 q^{17} + 9 q^{19} + 6 q^{21} - 6 q^{23} - 9 q^{25} - 6 q^{27} + 12 q^{28} - 3 q^{31} + 24 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{39} - 6 q^{41} - 42 q^{43} - 24 q^{48} + 21 q^{49} - 6 q^{51} - 6 q^{52} + 6 q^{53} + 60 q^{55} + 18 q^{57} - 18 q^{59} - 6 q^{61} + 3 q^{63} - 48 q^{64} - 18 q^{65} - 3 q^{67} - 12 q^{68} - 12 q^{69} + 21 q^{73} + 9 q^{75} + 36 q^{76} + 30 q^{77} - 21 q^{79} - 3 q^{81} - 12 q^{83} + 6 q^{84} - 12 q^{89} - 3 q^{91} - 24 q^{92} + 3 q^{93} - 24 q^{95} + 36 q^{97}+O(q^{100}) $ 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9 - 6 * q^12 - 6 * q^13 - 12 * q^16 + 6 * q^17 + 9 * q^19 + 6 * q^21 - 6 * q^23 - 9 * q^25 - 6 * q^27 + 12 * q^28 - 3 * q^31 + 24 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^39 - 6 * q^41 - 42 * q^43 - 24 * q^48 + 21 * q^49 - 6 * q^51 - 6 * q^52 + 6 * q^53 + 60 * q^55 + 18 * q^57 - 18 * q^59 - 6 * q^61 + 3 * q^63 - 48 * q^64 - 18 * q^65 - 3 * q^67 - 12 * q^68 - 12 * q^69 + 21 * q^73 + 9 * q^75 + 36 * q^76 + 30 * q^77 - 21 * q^79 - 3 * q^81 - 12 * q^83 + 6 * q^84 - 12 * q^89 - 3 * q^91 - 24 * q^92 + 3 * q^93 - 24 * q^95 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−1.27624	−	2.21051i	−0.570751	−	0.988569i	−0.996489	−	0.0837229i	$-0.973319\pi$
$5$	−1.27624	−	2.21051i	−0.570751	−	0.988569i	0.425738	−	0.904846i	$-0.360014\pi$
$6$		0			0
$7$	−2.58628	+	0.557835i	−0.977520	+	0.210842i
$7$	−2.58628	+	0.557835i	−0.977520	+	0.210842i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.08628	+	5.34559i	−0.930547	+	1.61175i	−0.148159	+	0.988964i	$0.547335\pi$
$11$	−3.08628	+	5.34559i	−0.930547	+	1.61175i	−0.782388	+	0.622791i	$0.785999\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	−2.06760			−0.573449			−0.286725	−	0.958013i	$-0.592567\pi$
$13$	−2.06760			−0.573449			−0.286725	+	0.958013i	$0.592567\pi$
$14$		0			0
$15$	−2.55247			−0.659046
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	0.223763	+	0.387568i	0.0513347	+	0.0889143i	0.890551	−	0.454884i	$-0.150319\pi$
$19$	0.223763	+	0.387568i	0.0513347	+	0.0889143i	−0.839216	+	0.543798i	$0.816986\pi$
$20$	−5.10495			−1.14150
$21$	−0.810038	+	2.51870i	−0.176765	+	0.549625i
$22$		0			0
$23$	0.276237	+	0.478457i	0.0575995	+	0.0997652i	0.893387	−	0.449287i	$-0.148322\pi$
$23$	0.276237	+	0.478457i	0.0575995	+	0.0997652i	−0.835788	+	0.549052i	$0.814989\pi$
$24$		0			0
$25$	−0.757563	+	1.31214i	−0.151513	+	0.262428i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−1.62008	+	5.03740i	−0.306166	+	0.951978i
$29$	−5.10495			−0.947965			−0.473983	−	0.880534i	$-0.657184\pi$
$29$	−5.10495			−0.947965			−0.473983	+	0.880534i	$0.657184\pi$
$30$		0			0
$31$	3.86251	−	6.69007i	0.693728	−	1.20157i	−0.276880	−	0.960905i	$-0.589300\pi$
$31$	3.86251	−	6.69007i	0.693728	−	1.20157i	0.970608	−	0.240667i	$-0.0773662\pi$
$32$		0			0
$33$	3.08628	+	5.34559i	0.537252	+	0.930547i
$34$		0			0
$35$	4.53380	+	5.00505i	0.766352	+	0.846008i
$36$	−2.00000			−0.333333
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−1.03380	+	1.79060i	−0.165541	+	0.286725i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	−10.6201			−1.61955			−0.809773	−	0.586743i	$-0.800410\pi$
$43$	−10.6201			−1.61955			−0.809773	+	0.586743i	$0.800410\pi$
$44$	6.17255	+	10.6912i	0.930547	+	1.61175i
$45$	−1.27624	+	2.21051i	−0.190250	+	0.329523i
$46$		0			0
$47$	4.15388	+	7.19473i	0.605905	+	1.04946i	0.991908	+	0.126961i	$0.0405222\pi$
$47$	4.15388	+	7.19473i	0.605905	+	1.04946i	−0.386003	+	0.922498i	$0.626144\pi$
$48$	−4.00000			−0.577350
$49$	6.37764	−	2.88543i	0.911091	−	0.412205i
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−2.06760	+	3.58119i	−0.286725	+	0.496622i
$53$	2.06760	−	3.58119i	0.284007	−	0.491914i	−0.688361	−	0.725368i	$-0.741669\pi$
$53$	2.06760	−	3.58119i	0.284007	−	0.491914i	0.972368	+	0.233454i	$0.0750028\pi$
$54$		0			0
$55$	15.7553			2.12444
$56$		0			0
$57$	0.447525			0.0592762
$58$		0			0
$59$	−4.06760	+	7.04529i	−0.529557	+	0.917219i	0.469849	+	0.882747i	$0.344308\pi$
$59$	−4.06760	+	7.04529i	−0.529557	+	0.917219i	−0.999406	+	0.0344721i	$0.989025\pi$
$60$	−2.55247	+	4.42102i	−0.329523	+	0.570751i
$61$	−3.87764	−	6.71627i	−0.496481	−	0.859930i	0.503511	−	0.863989i	$-0.332041\pi$
$61$	−3.87764	−	6.71627i	−0.496481	−	0.859930i	−0.999992	+	0.00405884i	$0.998708\pi$
$62$		0			0
$63$	1.77624	+	1.96086i	0.223785	+	0.247045i
$64$	−8.00000			−1.00000
$65$	2.63875	+	4.57045i	0.327297	+	0.566894i
$66$		0			0
$67$	0.0338006	−	0.0585444i	0.00412940	−	0.00715234i	−0.863953	−	0.503572i	$-0.832019\pi$
$67$	0.0338006	−	0.0585444i	0.00412940	−	0.00715234i	0.868083	+	0.496420i	$0.165352\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	0.552475			0.0665101
$70$		0			0
$71$	2.13520			0.253402			0.126701	−	0.991941i	$-0.459561\pi$
$71$	2.13520			0.253402			0.126701	+	0.991941i	$0.459561\pi$
$72$		0			0
$73$	5.31004	−	9.19726i	0.621493	−	1.07646i	−0.367715	−	0.929939i	$-0.619860\pi$
$73$	5.31004	−	9.19726i	0.621493	−	1.07646i	0.989208	−	0.146519i	$-0.0468069\pi$
$74$		0			0
$75$	0.757563	+	1.31214i	0.0874759	+	0.151513i
$76$	0.895051			0.102669
$77$	5.00000	−	15.5468i	0.569803	−	1.77172i
$78$		0			0
$79$	−8.39631	−	14.5428i	−0.944659	−	1.63620i	−0.756432	−	0.654072i	$-0.773059\pi$
$79$	−8.39631	−	14.5428i	−0.944659	−	1.63620i	−0.188227	−	0.982126i	$-0.560274\pi$
$80$	−5.10495	+	8.84203i	−0.570751	+	0.988569i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−13.9278			−1.52878			−0.764389	−	0.644755i	$-0.776959\pi$
$83$	−13.9278			−1.52878			−0.764389	+	0.644755i	$0.776959\pi$
$84$	3.55247	+	3.92172i	0.387607	+	0.427895i
$85$	−5.10495			−0.553709
$86$		0			0
$87$	−2.55247	+	4.42102i	−0.273654	+	0.473983i
$88$		0			0
$89$	−6.15388	−	10.6588i	−0.652310	−	1.12983i	−0.982561	−	0.185940i	$-0.940467\pi$
$89$	−6.15388	−	10.6588i	−0.652310	−	1.12983i	0.330251	−	0.943893i	$-0.392866\pi$
$90$		0			0
$91$	5.34739	−	1.15338i	0.560558	−	0.120907i
$92$	1.10495			0.115199
$93$	−3.86251	−	6.69007i	−0.400524	−	0.693728i
$94$		0			0
$95$	0.571149	−	0.989258i	0.0585986	−	0.101496i
$96$		0			0
$97$	16.2099			1.64587			0.822933	−	0.568139i	$-0.192336\pi$
$97$	16.2099			1.64587			0.822933	+	0.568139i	$0.192336\pi$
$98$		0			0
$99$	6.17255			0.620365
$100$	1.51513	+	2.62428i	0.151513	+	0.262428i
$101$	6.10495	−	10.5741i	0.607465	−	1.05216i	−0.384192	−	0.923253i	$-0.625520\pi$
$101$	6.10495	−	10.5741i	0.607465	−	1.05216i	0.991657	−	0.128907i	$-0.0411469\pi$
$102$		0			0
$103$	4.05247	+	7.01909i	0.399302	+	0.691612i	0.993640	−	0.112604i	$-0.0359191\pi$
$103$	4.05247	+	7.01909i	0.399302	+	0.691612i	−0.594338	+	0.804216i	$0.702586\pi$
$104$		0			0
$105$	6.60140	−	1.42386i	0.644231	−	0.138955i
$106$		0			0
$107$	−1.27624	−	2.21051i	−0.123379	−	0.213698i	0.797719	−	0.603029i	$-0.206040\pi$
$107$	−1.27624	−	2.21051i	−0.123379	−	0.213698i	−0.921098	+	0.389331i	$0.872706\pi$
$108$	−1.00000	+	1.73205i	−0.0962250	+	0.166667i
$109$	−2.29136	+	3.96876i	−0.219473	+	0.380138i	−0.954647	−	0.297740i	$-0.903767\pi$
$109$	−2.29136	+	3.96876i	−0.219473	+	0.380138i	0.735174	+	0.677878i	$0.237100\pi$
$110$		0			0
$111$	1.00000			0.0949158
$112$	7.10495	+	7.84345i	0.671355	+	0.741136i
$113$	−15.0328			−1.41416			−0.707082	−	0.707131i	$-0.749989\pi$
$113$	−15.0328			−1.41416			−0.707082	+	0.707131i	$0.749989\pi$
$114$		0			0
$115$	0.705089	−	1.22125i	0.0657499	−	0.113882i
$116$	−5.10495	+	8.84203i	−0.473983	+	0.820962i
$117$	1.03380	+	1.79060i	0.0955749	+	0.165541i
$118$		0			0
$119$	−1.62008	+	5.03740i	−0.148512	+	0.461777i
$120$		0			0
$121$	−13.5502	−	23.4696i	−1.23184	−	2.13360i
$122$		0			0
$123$	−0.500000	+	0.866025i	−0.0450835	+	0.0780869i
$124$	−7.72503	−	13.3801i	−0.693728	−	1.20157i
$125$	−8.89505			−0.795598
$126$		0			0
$127$	−2.24015			−0.198781			−0.0993907	−	0.995048i	$-0.531689\pi$
$127$	−2.24015			−0.198781			−0.0993907	+	0.995048i	$0.531689\pi$
$128$		0			0
$129$	−5.31004	+	9.19726i	−0.467523	+	0.809773i
$130$		0			0
$131$	8.27624	+	14.3349i	0.723098	+	1.25244i	0.959752	+	0.280849i	$0.0906159\pi$
$131$	8.27624	+	14.3349i	0.723098	+	1.25244i	−0.236654	+	0.971594i	$0.576051\pi$
$132$	12.3451			1.07450
$133$	−0.794911	−	0.877536i	−0.0689276	−	0.0760920i
$134$		0			0
$135$	1.27624	+	2.21051i	0.109841	+	0.190250i
$136$		0			0
$137$	0.0676012	−	0.117089i	0.00577556	−	0.0100036i	−0.863123	−	0.504993i	$-0.831495\pi$
$137$	0.0676012	−	0.117089i	0.00577556	−	0.0100036i	0.868899	+	0.494990i	$0.164828\pi$
$138$		0			0
$139$	−8.37535			−0.710388			−0.355194	−	0.934793i	$-0.615585\pi$
$139$	−8.37535			−0.710388			−0.355194	+	0.934793i	$0.615585\pi$
$140$	13.2028	−	2.84772i	1.11584	−	0.240676i
$141$	8.30775			0.699639
$142$		0			0
$143$	6.38119	−	11.0525i	0.533622	−	0.924260i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	6.51513	+	11.2845i	0.541052	+	0.937129i
$146$		0			0
$147$	0.689962	−	6.96591i	0.0569071	−	0.574539i
$148$	2.00000			0.164399
$149$	1.08628	+	1.88148i	0.0889911	+	0.154137i	0.907085	−	0.420948i	$-0.138302\pi$
$149$	1.08628	+	1.88148i	0.0889911	+	0.154137i	−0.818094	+	0.575085i	$0.804969\pi$
$150$		0			0
$151$	8.05019	−	13.9433i	0.655115	−	1.13469i	−0.326750	−	0.945111i	$-0.605953\pi$
$151$	8.05019	−	13.9433i	0.655115	−	1.13469i	0.981865	−	0.189582i	$-0.0607132\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−19.7179			−1.58378
$156$	2.06760	+	3.58119i	0.165541	+	0.286725i
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$		0			0
$159$	−2.06760	−	3.58119i	−0.163971	−	0.284007i
$160$		0			0
$161$	−0.981326	−	1.08333i	−0.0773393	−	0.0853781i
$162$		0			0
$163$	−3.29491	−	5.70695i	−0.258077	−	0.447003i	0.707649	−	0.706564i	$-0.249756\pi$
$163$	−3.29491	−	5.70695i	−0.258077	−	0.447003i	−0.965727	+	0.259561i	$0.916422\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$	7.87764	−	13.6445i	0.613273	−	1.06222i
$166$		0			0
$167$	−3.86480			−0.299067			−0.149534	−	0.988757i	$-0.547777\pi$
$167$	−3.86480			−0.299067			−0.149534	+	0.988757i	$0.547777\pi$
$168$		0			0
$169$	−8.72503			−0.671156
$170$		0			0
$171$	0.223763	−	0.387568i	0.0171116	−	0.0296381i
$172$	−10.6201	+	18.3945i	−0.809773	+	1.40257i
$173$	2.93240	+	5.07906i	0.222946	+	0.386154i	0.955701	−	0.294338i	$-0.0950993\pi$
$173$	2.93240	+	5.07906i	0.222946	+	0.386154i	−0.732755	+	0.680492i	$0.761766\pi$
$174$		0			0
$175$	1.22731	−	3.81615i	0.0927759	−	0.288474i
$176$	24.6902			1.86109
$177$	4.06760	+	7.04529i	0.305740	+	0.529557i
$178$		0			0
$179$	4.72503	−	8.18398i	0.353165	−	0.611700i	−0.633637	−	0.773630i	$-0.718439\pi$
$179$	4.72503	−	8.18398i	0.353165	−	0.611700i	0.986802	+	0.161931i	$0.0517721\pi$
$180$	2.55247	+	4.42102i	0.190250	+	0.329523i
$181$	7.89758			0.587022			0.293511	−	0.955956i	$-0.405176\pi$
$181$	7.89758			0.587022			0.293511	+	0.955956i	$0.405176\pi$
$182$		0			0
$183$	−7.75528			−0.573287
$184$		0			0
$185$	1.27624	−	2.21051i	0.0938308	−	0.162520i
$186$		0			0
$187$	6.17255	+	10.6912i	0.451382	+	0.781816i
$188$	16.6155			1.21181
$189$	2.58628	−	0.557835i	0.188124	−	0.0405766i
$190$		0			0
$191$	−2.60140	−	4.50576i	−0.188231	−	0.326025i	0.756430	−	0.654075i	$-0.226942\pi$
$191$	−2.60140	−	4.50576i	−0.188231	−	0.326025i	−0.944660	+	0.328050i	$0.893609\pi$
$192$	−4.00000	+	6.92820i	−0.288675	+	0.500000i
$193$	−6.65388	+	11.5249i	−0.478957	+	0.829577i	−0.999709	−	0.0241308i	$-0.992318\pi$
$193$	−6.65388	+	11.5249i	−0.478957	+	0.829577i	0.520752	+	0.853708i	$0.325652\pi$
$194$		0			0
$195$	5.27750			0.377930
$196$	1.37992	−	13.9318i	0.0985660	−	0.995131i
$197$	19.5106			1.39007			0.695035	−	0.718976i	$-0.255389\pi$
$197$	19.5106			1.39007			0.695035	+	0.718976i	$0.255389\pi$
$198$		0			0
$199$	−1.06760	+	1.84914i	−0.0756802	+	0.131082i	−0.901382	−	0.433025i	$-0.857446\pi$
$199$	−1.06760	+	1.84914i	−0.0756802	+	0.131082i	0.825702	+	0.564107i	$0.190779\pi$
$200$		0			0
$201$	−0.0338006	−	0.0585444i	−0.00238411	−	0.00412940i
$202$		0			0
$203$	13.2028	−	2.84772i	0.926655	−	0.199871i
$204$	−4.00000			−0.280056
$205$	1.27624	+	2.21051i	0.0891363	+	0.154389i
$206$		0			0
$207$	0.276237	−	0.478457i	0.0191998	−	0.0332551i
$208$	4.13520	+	7.16238i	0.286725	+	0.496622i
$209$	−2.76237			−0.191077
$210$		0			0
$211$	16.6902			1.14900			0.574500	−	0.818504i	$-0.305196\pi$
$211$	16.6902			1.14900			0.574500	+	0.818504i	$0.305196\pi$
$212$	−4.13520	−	7.16238i	−0.284007	−	0.491914i
$213$	1.06760	−	1.84914i	0.0731508	−	0.126701i
$214$		0			0
$215$	13.5537	+	23.4758i	0.924357	+	1.60103i
$216$		0			0
$217$	−6.25756	+	19.4570i	−0.424791	+	1.32083i
$218$		0			0
$219$	−5.31004	−	9.19726i	−0.358819	−	0.621493i
$220$	15.7553	−	27.2889i	1.06222	−	1.83982i
$221$	−2.06760	+	3.58119i	−0.139082	+	0.240897i
$222$		0			0
$223$	15.9652			1.06911			0.534554	−	0.845135i	$-0.320480\pi$
$223$	15.9652			1.06911			0.534554	+	0.845135i	$0.320480\pi$
$224$		0			0
$225$	1.51513			0.101008
$226$		0			0
$227$	4.06760	−	7.04529i	0.269976	−	0.467612i	−0.698879	−	0.715240i	$-0.746318\pi$
$227$	4.06760	−	7.04529i	0.269976	−	0.467612i	0.968855	+	0.247627i	$0.0796508\pi$
$228$	0.447525	−	0.775137i	0.0296381	−	0.0513347i
$229$	0.0885602	+	0.153391i	0.00585222	+	0.0101363i	0.868937	−	0.494923i	$-0.164804\pi$
$229$	0.0885602	+	0.153391i	0.00585222	+	0.0101363i	−0.863084	+	0.505060i	$0.831471\pi$
$230$		0			0
$231$	−10.9639	−	12.1035i	−0.721373	−	0.796353i
$232$		0			0
$233$	8.08628	+	14.0058i	0.529750	+	0.917553i	0.999398	+	0.0346995i	$0.0110474\pi$
$233$	8.08628	+	14.0058i	0.529750	+	0.917553i	−0.469648	+	0.882854i	$0.655619\pi$
$234$		0			0
$235$	10.6027	−	18.3644i	0.691642	−	1.19796i
$236$	8.13520	+	14.0906i	0.529557	+	0.917219i
$237$	−16.7926			−1.09080
$238$		0			0
$239$	25.4501			1.64623			0.823113	−	0.567877i	$-0.192235\pi$
$239$	25.4501			1.64623			0.823113	+	0.567877i	$0.192235\pi$
$240$	5.10495	+	8.84203i	0.329523	+	0.570751i
$241$	6.81004	−	11.7953i	0.438673	−	0.759804i	−0.558914	−	0.829225i	$-0.688782\pi$
$241$	6.81004	−	11.7953i	0.438673	−	0.759804i	0.997587	+	0.0694213i	$0.0221153\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−15.5106			−0.992962
$245$	−14.5177	−	10.4153i	−0.927499	−	0.665411i
$246$		0			0
$247$	−0.462652	−	0.801337i	−0.0294378	−	0.0509878i
$248$		0			0
$249$	−6.96391	+	12.0619i	−0.441320	+	0.764389i
$250$		0			0
$251$	1.58273			0.0999009			0.0499504	−	0.998752i	$-0.484094\pi$
$251$	1.58273			0.0999009			0.0499504	+	0.998752i	$0.484094\pi$
$252$	5.17255	−	1.11567i	0.325840	−	0.0702807i
$253$	−3.41018			−0.214396
$254$		0			0
$255$	−2.55247	+	4.42102i	−0.159842	+	0.276855i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−4.22148	−	7.31181i	−0.263329	−	0.456098i	0.703796	−	0.710402i	$-0.251487\pi$
$257$	−4.22148	−	7.31181i	−0.263329	−	0.456098i	−0.967124	+	0.254304i	$0.918154\pi$
$258$		0			0
$259$	−1.77624	−	1.96086i	−0.110370	−	0.121842i
$260$	10.5550			0.654593
$261$	2.55247	+	4.42102i	0.157994	+	0.273654i
$262$		0			0
$263$	−3.70635	+	6.41959i	−0.228543	+	0.395849i	−0.957377	−	0.288842i	$-0.906730\pi$
$263$	−3.70635	+	6.41959i	−0.228543	+	0.395849i	0.728833	+	0.684691i	$0.240063\pi$
$264$		0			0
$265$	−10.5550			−0.648388
$266$		0			0
$267$	−12.3078			−0.753222
$268$	−0.0676012	−	0.117089i	−0.00412940	−	0.00715234i
$269$	10.6877	−	18.5116i	0.651639	−	1.12867i	−0.331086	−	0.943601i	$-0.607415\pi$
$269$	10.6877	−	18.5116i	0.651639	−	1.12867i	0.982725	−	0.185072i	$-0.0592517\pi$
$270$		0			0
$271$	−3.20280	−	5.54742i	−0.194556	−	0.336982i	0.752199	−	0.658937i	$-0.228993\pi$
$271$	−3.20280	−	5.54742i	−0.194556	−	0.336982i	−0.946755	+	0.321955i	$0.895660\pi$
$272$	−8.00000			−0.485071
$273$	1.67484	−	5.20766i	0.101366	−	0.315182i
$274$		0			0
$275$	−4.67610	−	8.09924i	−0.281979	−	0.488402i
$276$	0.552475	−	0.956914i	0.0332551	−	0.0575995i
$277$	−6.31004	+	10.9293i	−0.379133	+	0.656678i	−0.990936	−	0.134332i	$-0.957111\pi$
$277$	−6.31004	+	10.9293i	−0.379133	+	0.656678i	0.611803	+	0.791010i	$0.290445\pi$
$278$		0			0
$279$	−7.72503			−0.462485
$280$		0			0
$281$	−20.4430			−1.21952			−0.609762	−	0.792584i	$-0.708735\pi$
$281$	−20.4430			−1.21952			−0.609762	+	0.792584i	$0.708735\pi$
$282$		0			0
$283$	−0.672550	+	1.16489i	−0.0399790	+	0.0692456i	−0.885323	−	0.464977i	$-0.846062\pi$
$283$	−0.672550	+	1.16489i	−0.0399790	+	0.0692456i	0.845344	+	0.534223i	$0.179396\pi$
$284$	2.13520	−	3.69828i	0.126701	−	0.219452i
$285$	−0.571149	−	0.989258i	−0.0338319	−	0.0585986i
$286$		0			0
$287$	2.58628	−	0.557835i	0.152663	−	0.0329280i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	8.10495	−	14.0382i	0.475121	−	0.822933i
$292$	−10.6201	−	18.3945i	−0.621493	−	1.07646i
$293$	−24.3824			−1.42444			−0.712219	−	0.701957i	$-0.752310\pi$
$293$	−24.3824			−1.42444			−0.712219	+	0.701957i	$0.752310\pi$
$294$		0			0
$295$	20.7649			1.20898
$296$		0			0
$297$	3.08628	−	5.34559i	0.179084	−	0.310182i
$298$		0			0
$299$	−0.571149	−	0.989258i	−0.0330304	−	0.0572103i
$300$	3.03025			0.174952
$301$	27.4664	−	5.92426i	1.58314	−	0.341468i
$302$		0			0
$303$	−6.10495	−	10.5741i	−0.350720	−	0.607465i
$304$	0.895051	−	1.55027i	0.0513347	−	0.0889143i
$305$	−9.89758	+	17.1431i	−0.566734	+	0.981611i
$306$		0			0
$307$	−19.2099			−1.09637			−0.548183	−	0.836358i	$-0.684680\pi$
$307$	−19.2099			−1.09637			−0.548183	+	0.836358i	$0.684680\pi$
$308$	−21.9278	−	24.2070i	−1.24945	−	1.37932i
$309$	8.10495			0.461074
$310$		0			0
$311$	15.4990	−	26.8450i	0.878866	−	1.52224i	0.0262802	−	0.999655i	$-0.491634\pi$
$311$	15.4990	−	26.8450i	0.878866	−	1.52224i	0.852586	−	0.522587i	$-0.175033\pi$
$312$		0			0
$313$	8.16900	+	14.1491i	0.461739	+	0.799756i	0.999048	−	0.0436298i	$-0.0138922\pi$
$313$	8.16900	+	14.1491i	0.461739	+	0.799756i	−0.537308	+	0.843386i	$0.680559\pi$
$314$		0			0
$315$	2.06760	−	6.42891i	0.116496	−	0.362228i
$316$	−33.5853			−1.88932
$317$	11.7740	+	20.3931i	0.661291	+	1.14539i	0.980277	+	0.197630i	$0.0633245\pi$
$317$	11.7740	+	20.3931i	0.661291	+	1.14539i	−0.318986	+	0.947760i	$0.603342\pi$
$318$		0			0
$319$	15.7553	−	27.2889i	0.882126	−	1.52789i
$320$	10.2099	+	17.6841i	0.570751	+	0.988569i
$321$	−2.55247			−0.142465
$322$		0			0
$323$	0.895051			0.0498020
$324$	1.00000	+	1.73205i	0.0555556	+	0.0962250i
$325$	1.56634	−	2.71298i	0.0868848	−	0.150489i
$326$		0			0
$327$	2.29136	+	3.96876i	0.126713	+	0.219473i
$328$		0			0
$329$	−14.7565	−	16.2904i	−0.813554	−	0.898117i
$330$		0			0
$331$	12.4639	+	21.5881i	0.685079	+	1.18659i	0.973412	+	0.229061i	$0.0735655\pi$
$331$	12.4639	+	21.5881i	0.685079	+	1.18659i	−0.288333	+	0.957530i	$0.593101\pi$
$332$	−13.9278	+	24.1237i	−0.764389	+	1.32396i
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$		0			0
$335$	−0.172550			−0.00942744
$336$	10.3451	−	2.23134i	0.564372	−	0.121730i
$337$	−27.0000			−1.47078			−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000			−1.47078			−0.735392	+	0.677642i	$0.763002\pi$
$338$		0			0
$339$	−7.51639	+	13.0188i	−0.408234	+	0.707082i
$340$	−5.10495	+	8.84203i	−0.276855	+	0.479526i
$341$	23.8416	+	41.2948i	1.29109	+	2.23624i
$342$		0			0
$343$	−14.8847	+	11.0202i	−0.803700	+	0.595035i
$344$		0			0
$345$	−0.705089	−	1.22125i	−0.0379607	−	0.0657499i
$346$		0			0
$347$	−12.6877	+	21.9757i	−0.681110	+	1.17972i	0.293532	+	0.955949i	$0.405169\pi$
$347$	−12.6877	+	21.9757i	−0.681110	+	1.17972i	−0.974642	+	0.223768i	$0.928164\pi$
$348$	5.10495	+	8.84203i	0.273654	+	0.473983i
$349$	29.9652			1.60400			0.802000	−	0.597325i	$-0.203770\pi$
$349$	29.9652			1.60400			0.802000	+	0.597325i	$0.203770\pi$
$350$		0			0
$351$	2.06760			0.110360
$352$		0			0
$353$	7.55247	−	13.0813i	0.401978	−	0.696246i	−0.591987	−	0.805948i	$-0.701656\pi$
$353$	7.55247	−	13.0813i	0.401978	−	0.696246i	0.993965	+	0.109702i	$0.0349896\pi$
$354$		0			0
$355$	−2.72503	−	4.71988i	−0.144629	−	0.250505i
$356$	−24.6155			−1.30462
$357$	3.55247	+	3.92172i	0.188017	+	0.207560i
$358$		0			0
$359$	−13.2086	−	22.8780i	−0.697125	−	1.20746i	−0.969459	−	0.245253i	$-0.921129\pi$
$359$	−13.2086	−	22.8780i	−0.697125	−	1.20746i	0.272334	−	0.962203i	$-0.412204\pi$
$360$		0			0
$361$	9.39986	−	16.2810i	0.494730	−	0.856897i
$362$		0			0
$363$	−27.1004			−1.42240
$364$	3.34967	−	10.4153i	0.175570	−	0.545911i
$365$	−27.1075			−1.41887
$366$		0			0
$367$	3.79491	−	6.57298i	0.198093	−	0.343107i	−0.749817	−	0.661645i	$-0.769859\pi$
$367$	3.79491	−	6.57298i	0.198093	−	0.343107i	0.947910	+	0.318538i	$0.103192\pi$
$368$	1.10495	−	1.91383i	0.0575995	−	0.0997652i
$369$	0.500000	+	0.866025i	0.0260290	+	0.0450835i
$370$		0			0
$371$	−3.34967	+	10.4153i	−0.173906	+	0.540737i
$372$	−15.4501			−0.801048
$373$	−8.60495	−	14.9042i	−0.445547	−	0.771711i	0.552543	−	0.833485i	$-0.313658\pi$
$373$	−8.60495	−	14.9042i	−0.445547	−	0.771711i	−0.998090	+	0.0617738i	$0.980324\pi$
$374$		0			0
$375$	−4.44753	+	7.70334i	−0.229669	+	0.397799i
$376$		0			0
$377$	10.5550			0.543610
$378$		0			0
$379$	25.3708			1.30321			0.651605	−	0.758559i	$-0.274096\pi$
$379$	25.3708			1.30321			0.651605	+	0.758559i	$0.274096\pi$
$380$	−1.14230	−	1.97852i	−0.0585986	−	0.101496i
$381$	−1.12008	+	1.94003i	−0.0573832	+	0.0993907i
$382$		0			0
$383$	5.41727	+	9.38299i	0.276810	+	0.479448i	0.970590	−	0.240738i	$-0.0773895\pi$
$383$	5.41727	+	9.38299i	0.276810	+	0.479448i	−0.693780	+	0.720187i	$0.744056\pi$
$384$		0			0
$385$	−40.7475	+	8.78885i	−2.07668	+	0.447921i
$386$		0			0
$387$	5.31004	+	9.19726i	0.269924	+	0.467523i
$388$	16.2099	−	28.0764i	0.822933	−	1.42536i
$389$	−7.13646	+	12.3607i	−0.361833	+	0.626713i	−0.988263	−	0.152765i	$-0.951182\pi$
$389$	−7.13646	+	12.3607i	−0.361833	+	0.626713i	0.626429	+	0.779478i	$0.284516\pi$
$390$		0			0
$391$	1.10495			0.0558797
$392$		0			0
$393$	16.5525			0.834962
$394$		0			0
$395$	−21.4314	+	37.1202i	−1.07833	+	1.86772i
$396$	6.17255	−	10.6912i	0.310182	−	0.537252i
$397$	8.93138	+	15.4696i	0.448253	+	0.776397i	0.998272	−	0.0587550i	$-0.0187131\pi$
$397$	8.93138	+	15.4696i	0.448253	+	0.776397i	−0.550020	+	0.835152i	$0.685380\pi$
$398$		0			0
$399$	−1.15742	+	0.249646i	−0.0579437	+	0.0124979i
$400$	6.06051			0.303025
$401$	−7.86023	−	13.6143i	−0.392521	−	0.679866i	0.600260	−	0.799805i	$-0.295064\pi$
$401$	−7.86023	−	13.6143i	−0.392521	−	0.679866i	−0.992781	+	0.119938i	$0.961730\pi$
$402$		0			0
$403$	−7.98614	+	13.8324i	−0.397818	+	0.689041i
$404$	−12.2099	−	21.1482i	−0.607465	−	1.05216i
$405$	2.55247			0.126833
$406$		0			0
$407$	−6.17255			−0.305962
$408$		0			0
$409$	−11.5502	+	20.0055i	−0.571120	+	0.989209i	0.425331	+	0.905038i	$0.360158\pi$
$409$	−11.5502	+	20.0055i	−0.571120	+	0.989209i	−0.996451	+	0.0841713i	$0.973176\pi$
$410$		0			0
$411$	−0.0676012	−	0.117089i	−0.00333452	−	0.00577556i
$412$	16.2099			0.798604
$413$	6.58982	−	20.4901i	0.324264	−	1.00825i
$414$		0			0
$415$	17.7752	+	30.7876i	0.872551	+	1.51130i
$416$		0			0
$417$	−4.18768	+	7.25327i	−0.205071	+	0.355194i
$418$		0			0
$419$	22.3451			1.09163			0.545815	−	0.837906i	$-0.316220\pi$
$419$	22.3451			1.09163			0.545815	+	0.837906i	$0.316220\pi$
$420$	4.13520	−	12.8578i	0.201777	−	0.627398i
$421$	−34.8325			−1.69763			−0.848816	−	0.528688i	$-0.822684\pi$
$421$	−34.8325			−1.69763			−0.848816	+	0.528688i	$0.822684\pi$
$422$		0			0
$423$	4.15388	−	7.19473i	0.201968	−	0.349820i
$424$		0			0
$425$	1.51513	+	2.62428i	0.0734944	+	0.127296i
$426$		0			0
$427$	13.7752	+	15.2070i	0.666629	+	0.735920i
$428$	−5.10495			−0.246757
$429$	−6.38119	−	11.0525i	−0.308087	−	0.533622i
$430$		0			0
$431$	−8.24598	+	14.2825i	−0.397195	+	0.687962i	−0.993379	−	0.114886i	$-0.963350\pi$
$431$	−8.24598	+	14.2825i	−0.397195	+	0.687962i	0.596184	+	0.802848i	$0.296683\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	−19.9349			−0.958011			−0.479006	−	0.877812i	$-0.659003\pi$
$433$	−19.9349			−0.958011			−0.479006	+	0.877812i	$0.659003\pi$
$434$		0			0
$435$	13.0303			0.624753
$436$	4.58273	+	7.93752i	0.219473	+	0.380138i
$437$	−0.123623	+	0.214122i	−0.00591370	+	0.0102428i
$438$		0			0
$439$	12.9452	+	22.4218i	0.617843	+	1.07013i	0.989879	+	0.141917i	$0.0453265\pi$
$439$	12.9452	+	22.4218i	0.617843	+	1.07013i	−0.372036	+	0.928218i	$0.621340\pi$
$440$		0			0
$441$	−5.68768	−	4.08048i	−0.270842	−	0.194309i
$442$		0			0
$443$	−15.7926	−	27.3536i	−0.750330	−	1.29961i	−0.947663	−	0.319274i	$-0.896561\pi$
$443$	−15.7926	−	27.3536i	−0.750330	−	1.29961i	0.197332	−	0.980337i	$-0.436772\pi$
$444$	1.00000	−	1.73205i	0.0474579	−	0.0821995i
$445$	−15.7076	+	27.2064i	−0.744612	+	1.28971i
$446$		0			0
$447$	2.17255			0.102758
$448$	20.6902	−	4.46268i	0.977520	−	0.210842i
$449$	−10.0630			−0.474904			−0.237452	−	0.971399i	$-0.576312\pi$
$449$	−10.0630			−0.474904			−0.237452	+	0.971399i	$0.576312\pi$
$450$		0			0
$451$	3.08628	−	5.34559i	0.145327	−	0.251714i
$452$	−15.0328	+	26.0375i	−0.707082	+	1.22470i
$453$	−8.05019	−	13.9433i	−0.378231	−	0.655115i
$454$		0			0
$455$	−9.37409	−	10.3485i	−0.439464	−	0.485143i
$456$		0			0
$457$	8.56886	+	14.8417i	0.400835	+	0.694266i	0.993827	−	0.110942i	$-0.0353869\pi$
$457$	8.56886	+	14.8417i	0.400835	+	0.694266i	−0.592992	+	0.805208i	$0.702054\pi$
$458$		0			0
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	−1.41018	−	2.44250i	−0.0657499	−	0.113882i
$461$	6.89758			0.321252			0.160626	−	0.987015i	$-0.448649\pi$
$461$	6.89758			0.321252			0.160626	+	0.987015i	$0.448649\pi$
$462$		0			0
$463$	−25.1726			−1.16987			−0.584934	−	0.811081i	$-0.698880\pi$
$463$	−25.1726			−1.16987			−0.584934	+	0.811081i	$0.698880\pi$
$464$	10.2099	+	17.6841i	0.473983	+	0.820962i
$465$	−9.85897	+	17.0762i	−0.457199	+	0.791891i
$466$		0			0
$467$	−4.79136	−	8.29889i	−0.221718	−	0.384027i	0.733612	−	0.679569i	$-0.237833\pi$
$467$	−4.79136	−	8.29889i	−0.221718	−	0.384027i	−0.955330	+	0.295542i	$0.904500\pi$
$468$	4.13520			0.191150
$469$	−0.0547596	+	0.170267i	−0.00252856	+	0.00786220i
$470$		0			0
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$		0			0
$473$	32.7765	−	56.7705i	1.50706	−	2.61031i
$474$		0			0
$475$	−0.678058			−0.0311114
$476$	7.10495	+	7.84345i	0.325655	+	0.359504i
$477$	−4.13520			−0.189338
$478$		0			0
$479$	5.98133	−	10.3600i	0.273294	−	0.473359i	−0.696409	−	0.717645i	$-0.745220\pi$
$479$	5.98133	−	10.3600i	0.273294	−	0.473359i	0.969703	+	0.244286i	$0.0785536\pi$
$480$		0			0
$481$	−1.03380	−	1.79060i	−0.0471373	−	0.0816441i
$482$		0			0
$483$	−1.42885	+	0.308190i	−0.0650150	+	0.0140231i
$484$	−54.2008			−2.46367
$485$	−20.6877	−	35.8321i	−0.939379	−	1.62705i
$486$		0			0
$487$	9.87535	−	17.1046i	0.447495	−	0.775084i	−0.550727	−	0.834685i	$-0.685650\pi$
$487$	9.87535	−	17.1046i	0.447495	−	0.775084i	0.998222	+	0.0596012i	$0.0189829\pi$
$488$		0			0
$489$	−6.58982			−0.298002
$490$		0			0
$491$	4.75985			0.214809			0.107404	−	0.994215i	$-0.465746\pi$
$491$	4.75985			0.214809			0.107404	+	0.994215i	$0.465746\pi$
$492$	1.00000	+	1.73205i	0.0450835	+	0.0780869i
$493$	−5.10495	+	8.84203i	−0.229915	+	0.398225i
$494$		0			0
$495$	−7.87764	−	13.6445i	−0.354074	−	0.613273i
$496$	−30.9001			−1.38746
$497$	−5.52222	+	1.19109i	−0.247705	+	0.0534278i
$498$		0			0
$499$	2.73889	+	4.74390i	0.122610	+	0.212366i	0.920796	−	0.390045i	$-0.127540\pi$
$499$	2.73889	+	4.74390i	0.122610	+	0.212366i	−0.798186	+	0.602410i	$0.794207\pi$
$500$	−8.89505	+	15.4067i	−0.397799	+	0.689008i
$501$	−1.93240	+	3.34701i	−0.0863332	+	0.149534i
$502$		0			0
$503$	3.00709			0.134080			0.0670399	−	0.997750i	$-0.478645\pi$
$503$	3.00709			0.134080			0.0670399	+	0.997750i	$0.478645\pi$
$504$		0			0
$505$	−31.1655			−1.38684
$506$		0			0
$507$	−4.36251	+	7.55609i	−0.193746	+	0.335578i
$508$	−2.24015	+	3.88006i	−0.0993907	+	0.172150i
$509$	−15.8602	−	27.4707i	−0.702992	−	1.21762i	−0.967411	−	0.253210i	$-0.918514\pi$
$509$	−15.8602	−	27.4707i	−0.702992	−	1.21762i	0.264419	−	0.964408i	$-0.414820\pi$
$510$		0			0
$511$	−8.60266	+	26.7488i	−0.380559	+	1.18330i
$512$		0			0
$513$	−0.223763	−	0.387568i	−0.00987936	−	0.0171116i
$514$		0			0
$515$	10.3438	−	17.9161i	0.455804	−	0.789476i
$516$	10.6201	+	18.3945i	0.467523	+	0.809773i
$517$	−51.2800			−2.25529
$518$		0			0
$519$	5.86480			0.257436
$520$		0			0
$521$	12.0560	−	20.8816i	0.528184	−	0.914841i	−0.471276	−	0.881986i	$-0.656206\pi$
$521$	12.0560	−	20.8816i	0.528184	−	0.914841i	0.999460	−	0.0328557i	$-0.0104602\pi$
$522$		0			0
$523$	17.5875	+	30.4625i	0.769049	+	1.33203i	0.938079	+	0.346422i	$0.112603\pi$
$523$	17.5875	+	30.4625i	0.769049	+	1.33203i	−0.169030	+	0.985611i	$0.554063\pi$
$524$	33.1049			1.44620
$525$	−2.69122	−	2.97095i	−0.117455	−	0.129663i
$526$		0			0
$527$	−7.72503	−	13.3801i	−0.336507	−	0.582848i
$528$	12.3451	−	21.3823i	0.537252	−	0.930547i
$529$	11.3474	−	19.6542i	0.493365	−	0.854533i
$530$		0			0
$531$	8.13520			0.353038
$532$	−2.31485	+	0.499291i	−0.100361	+	0.0216470i
$533$	2.06760			0.0895578
$534$		0			0
$535$	−3.25756	+	5.64227i	−0.140837	+	0.243936i
$536$		0			0
$537$	−4.72503	−	8.18398i	−0.203900	−	0.353165i
$538$		0			0
$539$	−4.25883	+	42.9975i	−0.183441	+	1.85203i
$540$	5.10495			0.219682
$541$	−8.31004	−	14.3934i	−0.357276	−	0.618821i	0.630228	−	0.776410i	$-0.282961\pi$
$541$	−8.31004	−	14.3934i	−0.357276	−	0.618821i	−0.987505	+	0.157589i	$0.949628\pi$
$542$		0			0
$543$	3.94879	−	6.83950i	0.169459	−	0.293511i
$544$		0			0
$545$	11.6973			0.501057
$546$		0			0
$547$	18.6760			0.798529			0.399264	−	0.916836i	$-0.369266\pi$
$547$	18.6760			0.798529			0.399264	+	0.916836i	$0.369266\pi$
$548$	−0.135202	−	0.234178i	−0.00577556	−	0.0100036i
$549$	−3.87764	+	6.71627i	−0.165494	+	0.286643i
$550$		0			0
$551$	−1.14230	−	1.97852i	−0.0486635	−	0.0842876i
$552$		0			0
$553$	29.8277	+	32.9280i	1.26840	+	1.40024i
$554$		0			0
$555$	−1.27624	−	2.21051i	−0.0541733	−	0.0938308i
$556$	−8.37535	+	14.5065i	−0.355194	+	0.615214i
$557$	14.8416	−	25.7063i	0.628857	−	1.08921i	−0.358925	−	0.933367i	$-0.616856\pi$
$557$	14.8416	−	25.7063i	0.628857	−	1.08921i	0.987781	−	0.155845i	$-0.0498102\pi$
$558$		0			0
$559$	21.9581			0.928728
$560$	8.27040	−	25.7156i	0.349488	−	1.08668i
$561$	12.3451			0.521211
$562$		0			0
$563$	0.638750	−	1.10635i	0.0269201	−	0.0466270i	−0.852251	−	0.523132i	$-0.824763\pi$
$563$	0.638750	−	1.10635i	0.0269201	−	0.0466270i	0.879172	+	0.476505i	$0.158097\pi$
$564$	8.30775	−	14.3895i	0.349820	−	0.605905i
$565$	19.1854	+	33.2301i	0.807136	+	1.39800i
$566$		0			0
$567$	0.810038	−	2.51870i	0.0340184	−	0.105775i
$568$		0			0
$569$	−5.47904	−	9.48998i	−0.229693	−	0.397841i	0.728024	−	0.685552i	$-0.240439\pi$
$569$	−5.47904	−	9.48998i	−0.229693	−	0.397841i	−0.957717	+	0.287711i	$0.907106\pi$
$570$		0			0
$571$	−16.6867	+	28.9021i	−0.698315	+	1.20952i	0.270736	+	0.962654i	$0.412733\pi$
$571$	−16.6867	+	28.9021i	−0.698315	+	1.20952i	−0.969050	+	0.246863i	$0.920600\pi$
$572$	−12.7624	−	22.1051i	−0.533622	−	0.924260i
$573$	−5.20280			−0.217350
$574$		0			0
$575$	−0.837069			−0.0349082
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	−13.2939	+	23.0257i	−0.553432	+	0.958572i	0.444592	+	0.895733i	$0.353349\pi$
$577$	−13.2939	+	23.0257i	−0.553432	+	0.958572i	−0.998024	+	0.0628388i	$0.979985\pi$
$578$		0			0
$579$	6.65388	+	11.5249i	0.276526	+	0.478957i
$580$	26.0605			1.08210
$581$	36.0212	−	7.76944i	1.49441	−	0.322331i
$582$		0			0
$583$	12.7624	+	22.1051i	0.528563	+	0.915499i
$584$		0			0
$585$	2.63875	−	4.57045i	0.109099	−	0.188965i
$586$		0			0
$587$	−32.2472			−1.33099			−0.665493	−	0.746404i	$-0.731779\pi$
$587$	−32.2472			−1.33099			−0.665493	+	0.746404i	$0.731779\pi$
$588$	−11.3754	−	8.16096i	−0.469112	−	0.336552i
$589$	3.45714			0.142449
$590$		0			0
$591$	9.75528	−	16.8966i	0.401279	−	0.695035i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−14.3940	−	24.9312i	−0.591092	−	1.02380i	−0.994086	−	0.108598i	$-0.965364\pi$
$593$	−14.3940	−	24.9312i	−0.591092	−	1.02380i	0.402994	−	0.915203i	$-0.367970\pi$
$594$		0			0
$595$	13.2028	−	2.84772i	0.541262	−	0.116745i
$596$	4.34510			0.177982
$597$	1.06760	+	1.84914i	0.0436940	+	0.0756802i
$598$		0			0
$599$	−1.03609	+	1.79455i	−0.0423333	+	0.0733234i	−0.886416	−	0.462890i	$-0.846812\pi$
$599$	−1.03609	+	1.79455i	−0.0423333	+	0.0733234i	0.844082	+	0.536213i	$0.180146\pi$
$600$		0			0
$601$	−7.38245			−0.301136			−0.150568	−	0.988600i	$-0.548110\pi$
$601$	−7.38245			−0.301136			−0.150568	+	0.988600i	$0.548110\pi$
$602$		0			0
$603$	−0.0676012			−0.00275294
$604$	−16.1004	−	27.8867i	−0.655115	−	1.13469i
$605$	−34.5865	+	59.9056i	−1.40614	+	2.43551i
$606$		0			0
$607$	7.39758	+	12.8130i	0.300258	+	0.520063i	0.976194	−	0.216898i	$-0.0695938\pi$
$607$	7.39758	+	12.8130i	0.300258	+	0.520063i	−0.675936	+	0.736960i	$0.736260\pi$
$608$		0			0
$609$	4.13520	−	12.8578i	0.167567	−	0.521025i
$610$		0			0
$611$	−8.58856	−	14.8758i	−0.347456	−	0.601811i
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	−16.0328	+	27.7696i	−0.647558	+	1.12160i	0.336147	+	0.941810i	$0.390876\pi$
$613$	−16.0328	+	27.7696i	−0.647558	+	1.12160i	−0.983704	+	0.179793i	$0.942457\pi$
$614$		0			0
$615$	2.55247			0.102926
$616$		0			0
$617$	42.6155			1.71564			0.857818	−	0.513954i	$-0.171820\pi$
$617$	42.6155			1.71564			0.857818	+	0.513954i	$0.171820\pi$
$618$		0			0
$619$	8.61779	−	14.9265i	0.346378	−	0.599945i	−0.639225	−	0.769020i	$-0.720745\pi$
$619$	8.61779	−	14.9265i	0.346378	−	0.599945i	0.985603	+	0.169075i	$0.0540780\pi$
$620$	−19.7179	+	34.1525i	−0.791891	+	1.37160i
$621$	−0.276237	−	0.478457i	−0.0110850	−	0.0191998i
$622$		0			0
$623$	21.8615	+	24.1338i	0.875862	+	0.966901i
$624$	8.27040			0.331081
$625$	15.1400	+	26.2233i	0.605600	+	1.04893i
$626$		0			0
$627$	−1.38119	+	2.39229i	−0.0551593	+	0.0955387i
$628$	−10.0000	−	17.3205i	−0.399043	−	0.691164i
$629$	2.00000			0.0797452
$630$		0			0
$631$	−22.1352			−0.881188			−0.440594	−	0.897706i	$-0.645232\pi$
$631$	−22.1352			−0.881188			−0.440594	+	0.897706i	$0.645232\pi$
$632$		0			0
$633$	8.34510	−	14.4541i	0.331688	−	0.574500i
$634$		0			0
$635$	2.85897	+	4.95187i	0.113455	+	0.196509i
$636$	−8.27040			−0.327943
$637$	−13.1864	+	5.96592i	−0.522465	+	0.236378i
$638$		0			0
$639$	−1.06760	−	1.84914i	−0.0422337	−	0.0731508i
$640$		0			0
$641$	7.39860	−	12.8147i	0.292227	−	0.506152i	−0.682109	−	0.731251i	$-0.738937\pi$
$641$	7.39860	−	12.8147i	0.292227	−	0.506152i	0.974336	+	0.225098i	$0.0722704\pi$
$642$		0			0
$643$	45.2986			1.78640			0.893201	−	0.449657i	$-0.148454\pi$
$643$	45.2986			1.78640			0.893201	+	0.449657i	$0.148454\pi$
$644$	−2.85770	+	0.616380i	−0.112609	+	0.0242888i
$645$	27.1075			1.06736
$646$		0			0
$647$	10.8602	−	18.8105i	0.426960	−	0.739516i	−0.569642	−	0.821893i	$-0.692918\pi$
$647$	10.8602	−	18.8105i	0.426960	−	0.739516i	0.996601	+	0.0823775i	$0.0262513\pi$
$648$		0			0
$649$	−25.1075	−	43.4874i	−0.985555	−	1.70703i
$650$		0			0
$651$	13.7215	+	15.1477i	0.537787	+	0.593686i
$652$	−13.1796			−0.516155
$653$	24.4616	+	42.3688i	0.957258	+	1.65802i	0.729115	+	0.684391i	$0.239932\pi$
$653$	24.4616	+	42.3688i	0.957258	+	1.65802i	0.228142	+	0.973628i	$0.426735\pi$
$654$		0			0
$655$	21.1249	−	36.5894i	0.825418	−	1.42967i
$656$	2.00000	+	3.46410i	0.0780869	+	0.135250i
$657$	−10.6201			−0.414329
$658$		0			0
$659$	−36.4198			−1.41871			−0.709357	−	0.704849i	$-0.751015\pi$
$659$	−36.4198			−1.41871			−0.709357	+	0.704849i	$0.751015\pi$
$660$	−15.7553	−	27.2889i	−0.613273	−	1.06222i
$661$	0.934684	−	1.61892i	0.0363550	−	0.0629687i	−0.847275	−	0.531154i	$-0.821759\pi$
$661$	0.934684	−	1.61892i	0.0363550	−	0.0629687i	0.883630	+	0.468185i	$0.155092\pi$
$662$		0			0
$663$	2.06760	+	3.58119i	0.0802990	+	0.139082i
$664$		0			0
$665$	−0.925304	+	2.87710i	−0.0358818	+	0.111569i
$666$		0			0
$667$	−1.41018	−	2.44250i	−0.0546023	−	0.0945739i
$668$	−3.86480	+	6.69403i	−0.149534	+	0.259000i
$669$	7.98259	−	13.8262i	0.308625	−	0.534554i
$670$		0			0
$671$	47.8698			1.84799
$672$		0			0
$673$	−44.8325			−1.72817			−0.864083	−	0.503349i	$-0.832101\pi$
$673$	−44.8325			−1.72817			−0.864083	+	0.503349i	$0.832101\pi$
$674$		0			0
$675$	0.757563	−	1.31214i	0.0291586	−	0.0505042i
$676$	−8.72503	+	15.1122i	−0.335578	+	0.581238i
$677$	1.06886	+	1.85133i	0.0410798	+	0.0711522i	0.885834	−	0.464002i	$-0.153587\pi$
$677$	1.06886	+	1.85133i	0.0410798	+	0.0711522i	−0.844754	+	0.535154i	$0.820254\pi$
$678$		0			0
$679$	−41.9233	+	9.04246i	−1.60887	+	0.347018i
$680$		0			0
$681$	−4.06760	−	7.04529i	−0.155871	−	0.269976i
$682$		0			0
$683$	−15.2215	+	26.3644i	−0.582434	+	1.00880i	0.412756	+	0.910841i	$0.364566\pi$
$683$	−15.2215	+	26.3644i	−0.582434	+	1.00880i	−0.995190	+	0.0979632i	$0.968767\pi$
$684$	−0.447525	−	0.775137i	−0.0171116	−	0.0296381i
$685$	−0.345101			−0.0131856
$686$		0			0
$687$	0.177120			0.00675756
$688$	21.2402	+	36.7890i	0.809773	+	1.40257i
$689$	−4.27497	+	7.40447i	−0.162864	+	0.282088i
$690$		0			0
$691$	−9.10850	−	15.7764i	−0.346504	−	0.600162i	0.639122	−	0.769105i	$-0.279298\pi$
$691$	−9.10850	−	15.7764i	−0.346504	−	0.600162i	−0.985626	+	0.168943i	$0.945964\pi$
$692$	11.7296			0.445892
$693$	−15.9639	+	3.44327i	−0.606419	+	0.130799i
$694$		0			0
$695$	10.6889	+	18.5138i	0.405455	+	0.702268i
$696$		0			0
$697$	−1.00000	+	1.73205i	−0.0378777	+	0.0656061i
$698$		0			0
$699$	16.1726			0.611702
$700$	−5.38245	−	5.94191i	−0.203437	−	0.224583i
$701$	−23.2427			−0.877864			−0.438932	−	0.898520i	$-0.644643\pi$
$701$	−23.2427			−0.877864			−0.438932	+	0.898520i	$0.644643\pi$
$702$		0			0
$703$	−0.223763	+	0.387568i	−0.00843937	+	0.0146174i
$704$	24.6902	−	42.7647i	0.930547	−	1.61175i
$705$	−10.6027	−	18.3644i	−0.399319	−	0.691642i
$706$		0			0
$707$	−9.89048	+	30.7530i	−0.371970	+	1.15659i
$708$	16.2704			0.611479
$709$	17.3451	+	30.0426i	0.651409	+	1.12827i	0.982781	+	0.184773i	$0.0591551\pi$
$709$	17.3451	+	30.0426i	0.651409	+	1.12827i	−0.331372	+	0.943500i	$0.607512\pi$
$710$		0			0
$711$	−8.39631	+	14.5428i	−0.314886	+	0.545399i
$712$		0			0
$713$	4.26788			0.159833
$714$		0			0
$715$	−32.5756			−1.21826
$716$	−9.45005	−	16.3680i	−0.353165	−	0.611700i
$717$	12.7250	−	22.0404i	0.475225	−	0.823113i
$718$		0			0
$719$	−17.1493	−	29.7035i	−0.639561	−	1.10775i	−0.985529	−	0.169506i	$-0.945783\pi$
$719$	−17.1493	−	29.7035i	−0.639561	−	1.10775i	0.345968	−	0.938246i	$-0.387551\pi$
$720$	10.2099			0.380500
$721$	−14.3963	−	15.8927i	−0.536147	−	0.591875i
$722$		0			0
$723$	−6.81004	−	11.7953i	−0.253268	−	0.438673i
$724$	7.89758	−	13.6790i	0.293511	−	0.508376i
$725$	3.86732	−	6.69840i	0.143629	−	0.248772i
$726$		0			0
$727$	12.6226			0.468146			0.234073	−	0.972219i	$-0.424794\pi$
$727$	12.6226			0.468146			0.234073	+	0.972219i	$0.424794\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−10.6201	+	18.3945i	−0.392798	+	0.680346i
$732$	−7.75528	+	13.4325i	−0.286643	+	0.496481i
$733$	−17.3229	−	30.0041i	−0.639835	−	1.10823i	−0.985469	−	0.169857i	$-0.945669\pi$
$733$	−17.3229	−	30.0041i	−0.639835	−	1.10823i	0.345633	−	0.938370i	$-0.387664\pi$
$734$		0			0
$735$	−16.2788	+	7.36499i	−0.600451	+	0.271662i
$736$		0			0
$737$	0.208636	+	0.361368i	0.00768521	+	0.0133112i
$738$		0			0
$739$	18.4150	−	31.8957i	0.677406	−	1.17330i	−0.298353	−	0.954456i	$-0.596437\pi$
$739$	18.4150	−	31.8957i	0.677406	−	1.17330i	0.975759	−	0.218846i	$-0.0702294\pi$
$740$	−2.55247	−	4.42102i	−0.0938308	−	0.162520i
$741$	−0.925304			−0.0339919
$742$		0			0
$743$	28.3451			1.03988			0.519940	−	0.854203i	$-0.325954\pi$
$743$	28.3451			1.03988			0.519940	+	0.854203i	$0.325954\pi$
$744$		0			0
$745$	2.77269	−	4.80244i	0.101584	−	0.175948i
$746$		0			0
$747$	6.96391	+	12.0619i	0.254796	+	0.441320i
$748$	24.6902			0.902763
$749$	4.53380	+	5.00505i	0.165661	+	0.182881i
$750$		0			0
$751$	1.27852	+	2.21447i	0.0466539	+	0.0808070i	0.888409	−	0.459052i	$-0.151811\pi$
$751$	1.27852	+	2.21447i	0.0466539	+	0.0808070i	−0.841755	+	0.539859i	$0.818478\pi$
$752$	16.6155	−	28.7789i	0.605905	−	1.04946i
$753$	0.791364	−	1.37068i	0.0288389	−	0.0499504i
$754$		0			0
$755$	−41.0958			−1.49563
$756$	1.62008	−	5.03740i	0.0589216	−	0.183208i
$757$	44.9258			1.63286			0.816428	−	0.577448i	$-0.195951\pi$
$757$	44.9258			1.63286			0.816428	+	0.577448i	$0.195951\pi$
$758$		0			0
$759$	−1.70509	+	2.95330i	−0.0618908	+	0.107198i
$760$		0			0
$761$	5.48487	+	9.50008i	0.198827	+	0.344378i	0.948148	−	0.317829i	$-0.102954\pi$
$761$	5.48487	+	9.50008i	0.198827	+	0.344378i	−0.749322	+	0.662206i	$0.769620\pi$
$762$		0			0
$763$	3.71218	−	11.5425i	0.134390	−	0.417867i
$764$	−10.4056			−0.376462
$765$	2.55247	+	4.42102i	0.0922849	+	0.159842i
$766$		0			0
$767$	8.41018	−	14.5669i	0.303674	−	0.525979i
$768$	8.00000	+	13.8564i	0.288675	+	0.500000i
$769$	29.1751			1.05208			0.526040	−	0.850460i	$-0.323676\pi$
$769$	29.1751			1.05208			0.526040	+	0.850460i	$0.323676\pi$
$770$		0			0
$771$	−8.44296			−0.304066
$772$	13.3078	+	23.0497i	0.478957	+	0.829577i
$773$	21.5292	−	37.2897i	0.774353	−	1.34122i	−0.160805	−	0.986986i	$-0.551409\pi$
$773$	21.5292	−	37.2897i	0.774353	−	1.34122i	0.935158	−	0.354232i	$-0.115258\pi$
$774$		0			0
$775$	5.85220	+	10.1363i	0.210217	+	0.364107i
$776$		0			0
$777$	−2.58628	+	0.557835i	−0.0927821	+	0.0200122i
$778$		0			0
$779$	−0.223763	−	0.387568i	−0.00801713	−	0.0138861i
$780$	5.27750	−	9.14090i	0.188965	−	0.327297i
$781$	−6.58982	+	11.4139i	−0.235802	+	0.408422i
$782$		0			0
$783$	5.10495			0.182436
$784$	−22.7507	−	16.3219i	−0.812525	−	0.582926i
$785$	−25.5247			−0.911017
$786$		0			0
$787$	12.4629	−	21.5864i	0.444254	−	0.769471i	−0.553746	−	0.832686i	$-0.686802\pi$
$787$	12.4629	−	21.5864i	0.444254	−	0.769471i	0.998000	+	0.0632151i	$0.0201354\pi$
$788$	19.5106	−	33.7933i	0.695035	−	1.20384i
$789$	3.70635	+	6.41959i	0.131950	+	0.228543i
$790$		0			0
$791$	38.8789	−	8.38582i	1.38237	−	0.298165i
$792$		0			0
$793$	8.01741	+	13.8866i	0.284707	+	0.493126i
$794$		0			0
$795$	−5.27750	+	9.14090i	−0.187174	+	0.324194i
$796$	2.13520	+	3.69828i	0.0756802	+	0.131082i
$797$	−0.137727			−0.00487855			−0.00243928	−	0.999997i	$-0.500776\pi$
$797$	−0.137727			−0.00487855			−0.00243928	+	0.999997i	$0.500776\pi$
$798$		0			0
$799$	16.6155			0.587814
$800$		0			0
$801$	−6.15388	+	10.6588i	−0.217437	+	0.376611i
$802$		0			0
$803$	32.7765	+	56.7705i	1.15666	+	2.00339i
$804$	−0.135202			−0.00476822
$805$	−1.14230	+	3.55181i	−0.0402607	+	0.125185i
$806$		0			0
$807$	−10.6877	−	18.5116i	−0.376224	−	0.651639i
$808$		0			0
$809$	−0.741174	+	1.28375i	−0.0260583	+	0.0451343i	−0.878760	−	0.477263i	$-0.841629\pi$
$809$	−0.741174	+	1.28375i	−0.0260583	+	0.0451343i	0.852702	+	0.522397i	$0.174962\pi$
$810$		0			0
$811$	26.1004			0.916508			0.458254	−	0.888821i	$-0.348475\pi$
$811$	26.1004			0.916508			0.458254	+	0.888821i	$0.348475\pi$
$812$	8.27040	−	25.7156i	0.290234	−	0.902442i
$813$	−6.40561			−0.224654
$814$		0			0
$815$	−8.41018	+	14.5669i	−0.294596	+	0.510255i
$816$	−4.00000	+	6.92820i	−0.140028	+	0.242536i
$817$	−2.37638	−	4.11601i	−0.0831389	−	0.144001i
$818$		0			0
$819$	−3.67255	−	4.05428i	−0.128329	−	0.141668i
$820$	5.10495			0.178273
$821$	3.34510	+	5.79388i	0.116745	+	0.202208i	0.918476	−	0.395477i	$-0.129421\pi$
$821$	3.34510	+	5.79388i	0.116745	+	0.202208i	−0.801731	+	0.597685i	$0.796087\pi$
$822$		0			0
$823$	−5.52222	+	9.56477i	−0.192493	+	0.333407i	−0.946076	−	0.323946i	$-0.894990\pi$
$823$	−5.52222	+	9.56477i	−0.192493	+	0.333407i	0.753583	+	0.657353i	$0.228324\pi$
$824$		0			0
$825$	−9.35220			−0.325602
$826$		0			0
$827$	24.6902			0.858562			0.429281	−	0.903171i	$-0.358767\pi$
$827$	24.6902			0.858562			0.429281	+	0.903171i	$0.358767\pi$
$828$	−0.552475	−	0.956914i	−0.0191998	−	0.0332551i
$829$	11.3300	−	19.6241i	0.393506	−	0.681573i	−0.599403	−	0.800447i	$-0.704595\pi$
$829$	11.3300	−	19.6241i	0.393506	−	0.681573i	0.992909	+	0.118875i	$0.0379286\pi$
$830$		0			0
$831$	6.31004	+	10.9293i	0.218893	+	0.379133i
$832$	16.5408			0.573449
$833$	1.37992	−	13.9318i	0.0478115	−	0.482709i
$834$		0			0
$835$	4.93240	+	8.54317i	0.170693	+	0.295648i
$836$	−2.76237	+	4.78457i	−0.0955387	+	0.165478i
$837$	−3.86251	+	6.69007i	−0.133508	+	0.231243i
$838$		0			0
$839$	−42.1776			−1.45613			−0.728066	−	0.685507i	$-0.759581\pi$
$839$	−42.1776			−1.45613			−0.728066	+	0.685507i	$0.759581\pi$
$840$		0			0
$841$	−2.93949			−0.101362
$842$		0			0
$843$	−10.2215	+	17.7041i	−0.352046	+	0.609762i
$844$	16.6902	−	28.9083i	0.574500	−	0.995064i
$845$	11.1352	+	19.2867i	0.383063	+	0.663484i
$846$		0			0
$847$	48.1367	+	53.1401i	1.65400	+	1.82592i
$848$	−16.5408			−0.568014
$849$	0.672550	+	1.16489i	0.0230819	+	0.0399790i
$850$		0			0
$851$	−0.276237	+	0.478457i	−0.00946929	+	0.0164013i
$852$	−2.13520	−	3.69828i	−0.0731508	−	0.126701i
$853$	−28.9652			−0.991749			−0.495874	−	0.868394i	$-0.665152\pi$
$853$	−28.9652			−0.991749			−0.495874	+	0.868394i	$0.665152\pi$
$854$		0			0
$855$	−1.14230			−0.0390657
$856$		0			0
$857$	−27.3405	+	47.3552i	−0.933935	+	1.61762i	−0.157412	+	0.987533i	$0.550315\pi$
$857$	−27.3405	+	47.3552i	−0.933935	+	1.61762i	−0.776523	+	0.630089i	$0.783018\pi$
$858$		0			0
$859$	−15.2949	−	26.4916i	−0.521856	−	0.903880i	−0.999677	−	0.0254233i	$-0.991907\pi$
$859$	−15.2949	−	26.4916i	−0.521856	−	0.903880i	0.477821	−	0.878457i	$-0.341427\pi$
$860$	54.2149			1.84871
$861$	0.810038	−	2.51870i	0.0276060	−	0.0858370i
$862$		0			0
$863$	−12.3509	−	21.3924i	−0.420431	−	0.728207i	0.575551	−	0.817766i	$-0.304788\pi$
$863$	−12.3509	−	21.3924i	−0.420431	−	0.728207i	−0.995982	+	0.0895587i	$0.971454\pi$
$864$		0			0
$865$	7.48487	−	12.9642i	0.254493	−	0.440795i
$866$		0			0
$867$	13.0000			0.441503
$868$	27.4430	+	30.2954i	0.931475	+	1.02829i
$869$	103.653			3.51620
$870$		0			0
$871$	−0.0698862	+	0.121046i	−0.00236800	+	0.00410150i
$872$		0			0
$873$	−8.10495	−	14.0382i	−0.274311	−	0.475121i
$874$		0			0
$875$	23.0050	−	4.96197i	0.777713	−	0.167745i
$876$	−21.2402			−0.717638
$877$	3.11779	+	5.40017i	0.105280	+	0.182351i	0.913853	−	0.406046i	$-0.133093\pi$
$877$	3.11779	+	5.40017i	0.105280	+	0.182351i	−0.808572	+	0.588397i	$0.799759\pi$
$878$		0			0
$879$	−12.1912	+	21.1158i	−0.411200	+	0.712219i
$880$	−31.5106	−	54.5779i	−1.06222	−	1.83982i
$881$	−42.2755			−1.42430			−0.712148	−	0.702029i	$-0.752278\pi$
$881$	−42.2755			−1.42430			−0.712148	+	0.702029i	$0.752278\pi$
$882$		0			0
$883$	13.9723			0.470204			0.235102	−	0.971971i	$-0.424458\pi$
$883$	13.9723			0.470204			0.235102	+	0.971971i	$0.424458\pi$
$884$	4.13520	+	7.16238i	0.139082	+	0.240897i
$885$	10.3824	−	17.9829i	0.349002	−	0.604490i
$886$		0			0
$887$	15.0328	+	26.0375i	0.504751	+	0.874255i	0.999985	+	0.00549503i	$0.00174913\pi$
$887$	15.0328	+	26.0375i	0.504751	+	0.874255i	−0.495234	+	0.868760i	$0.664918\pi$
$888$		0			0
$889$	5.79365	−	1.24964i	0.194313	−	0.0419114i
$890$		0			0
$891$	−3.08628	−	5.34559i	−0.103394	−	0.179084i
$892$	15.9652	−	27.6525i	0.534554	−	0.925874i
$893$	−1.85897	+	3.21982i	−0.0622079	+	0.107747i
$894$		0			0
$895$	−24.1210			−0.806277
$896$		0			0
$897$	−1.14230			−0.0381402
$898$		0			0
$899$	−19.7179	+	34.1525i	−0.657630	+	1.13905i
$900$	1.51513	−	2.62428i	0.0505042	−	0.0874759i
$901$	−4.13520	−	7.16238i	−0.137764	−	0.238614i
$902$		0			0
$903$	8.60266	−	26.7488i	0.286279	−	0.890143i
$904$		0			0
$905$	−10.0792	−	17.4577i	−0.335043	−	0.580312i
$906$		0			0
$907$	−15.0048	+	25.9891i	−0.498227	+	0.862954i	−0.999998	−	0.00204662i	$-0.999349\pi$
$907$	−15.0048	+	25.9891i	−0.498227	+	0.862954i	0.501771	+	0.865000i	$0.332682\pi$
$908$	−8.13520	−	14.0906i	−0.269976	−	0.467612i
$909$	−12.2099			−0.404977
$910$		0			0
$911$	14.4056			0.477279			0.238640	−	0.971108i	$-0.423299\pi$
$911$	14.4056			0.477279			0.238640	+	0.971108i	$0.423299\pi$
$912$	−0.895051	−	1.55027i	−0.0296381	−	0.0513347i
$913$	42.9851	−	74.4524i	1.42260	−	2.46401i
$914$		0			0
$915$	9.89758	+	17.1431i	0.327204	+	0.566734i
$916$	0.354241			0.0117044
$917$	−29.4011	−	32.4571i	−0.970911	−	1.07183i
$918$		0			0
$919$	−2.18894	−	3.79135i	−0.0722065	−	0.125065i	0.827662	−	0.561227i	$-0.189671\pi$
$919$	−2.18894	−	3.79135i	−0.0722065	−	0.125065i	−0.899868	+	0.436162i	$0.856337\pi$
$920$		0			0
$921$	−9.60495	+	16.6363i	−0.316494	+	0.548183i
$922$		0			0
$923$	−4.41475			−0.145313
$924$	−31.9278	+	6.88654i	−1.05035	+	0.226550i
$925$	−1.51513			−0.0498171
$926$		0			0
$927$	4.05247	−	7.01909i	0.133101	−	0.230537i
$928$		0			0
$929$	−2.79720	−	4.84489i	−0.0917730	−	0.158956i	0.816484	−	0.577368i	$-0.195920\pi$
$929$	−2.79720	−	4.84489i	−0.0917730	−	0.158956i	−0.908257	+	0.418412i	$0.862587\pi$
$930$		0			0
$931$	2.54538	+	1.82612i	0.0834215	+	0.0598486i
$932$	32.3451			1.05950
$933$	−15.4990	−	26.8450i	−0.507414	−	0.878866i
$934$		0			0
$935$	15.7553	−	27.2889i	0.515253	−	0.892444i
$936$		0			0
$937$	−34.0328			−1.11180			−0.555901	−	0.831248i	$-0.687627\pi$
$937$	−34.0328			−1.11180			−0.555901	+	0.831248i	$0.687627\pi$
$938$		0			0
$939$	16.3380			0.533171
$940$	−21.2053	−	36.7287i	−0.691642	−	1.19796i
$941$	1.09785	−	1.90154i	0.0357890	−	0.0619884i	−0.847576	−	0.530674i	$-0.821939\pi$
$941$	1.09785	−	1.90154i	0.0357890	−	0.0619884i	0.883365	+	0.468685i	$0.155272\pi$
$942$		0			0
$943$	−0.276237	−	0.478457i	−0.00899552	−	0.0155807i
$944$	32.5408			1.05911
$945$	−4.53380	−	5.00505i	−0.147485	−	0.162814i
$946$		0			0
$947$	−4.07343	−	7.05539i	−0.132369	−	0.229269i	0.792220	−	0.610235i	$-0.208925\pi$
$947$	−4.07343	−	7.05539i	−0.132369	−	0.229269i	−0.924589	+	0.380966i	$0.875592\pi$
$948$	−16.7926	+	29.0857i	−0.545399	+	0.944659i
$949$	−10.9790	+	19.0163i	−0.356395	+	0.617294i
$950$		0			0
$951$	23.5479			0.763593
$952$		0			0
$953$	−21.5156			−0.696959			−0.348479	−	0.937316i	$-0.613302\pi$
$953$	−21.5156			−0.696959			−0.348479	+	0.937316i	$0.613302\pi$
$954$		0			0
$955$	−6.64001	+	11.5008i	−0.214866	+	0.372158i
$956$	25.4501	−	44.0808i	0.823113	−	1.42567i
$957$	−15.7553	−	27.2889i	−0.509296	−	0.882126i
$958$		0			0
$959$	−0.109519	+	0.340534i	−0.00353656	+	0.0109964i
$960$	20.4198			0.659046
$961$	−14.3380	−	24.8342i	−0.462516	−	0.801102i
$962$		0			0
$963$	−1.27624	+	2.21051i	−0.0411262	+	0.0712326i
$964$	−13.6201	−	23.5907i	−0.438673	−	0.759804i
$965$	33.9677			1.09346
$966$		0			0
$967$	51.8371			1.66697			0.833484	−	0.552544i	$-0.186343\pi$
$967$	51.8371			1.66697			0.833484	+	0.552544i	$0.186343\pi$
$968$		0			0
$969$	0.447525	−	0.775137i	0.0143766	−	0.0249010i
$970$		0			0
$971$	−2.93240	−	5.07906i	−0.0941052	−	0.162995i	0.815130	−	0.579279i	$-0.196666\pi$
$971$	−2.93240	−	5.07906i	−0.0941052	−	0.162995i	−0.909235	+	0.416284i	$0.863332\pi$
$972$	2.00000			0.0641500
$973$	21.6610	−	4.67207i	0.694419	−	0.149780i
$974$		0			0
$975$	−1.56634	−	2.71298i	−0.0501630	−	0.0868848i
$976$	−15.5106	+	26.8651i	−0.496481	+	0.859930i
$977$	−30.6902	+	53.1570i	−0.981867	+	1.70064i	−0.326758	+	0.945108i	$0.605956\pi$
$977$	−30.6902	+	53.1570i	−0.981867	+	1.70064i	−0.655109	+	0.755535i	$0.727377\pi$
$978$		0			0
$979$	75.9702			2.42802
$980$	−32.5575	+	14.7300i	−1.04001	+	0.470532i
$981$	4.58273			0.146315
$982$		0			0
$983$	−2.34841	+	4.06756i	−0.0749026	+	0.129735i	−0.901044	−	0.433728i	$-0.857198\pi$
$983$	−2.34841	+	4.06756i	−0.0749026	+	0.129735i	0.826141	+	0.563463i	$0.190531\pi$
$984$		0			0
$985$	−24.9001	−	43.1282i	−0.793383	−	1.37418i
$986$		0			0
$987$	−21.4861	+	4.63436i	−0.683911	+	0.147513i
$988$	−1.85061			−0.0588757
$989$	−2.93366	−	5.08125i	−0.0932850	−	0.161574i
$990$		0			0
$991$	−3.82643	+	6.62757i	−0.121550	+	0.210532i	−0.920379	−	0.391027i	$-0.872120\pi$
$991$	−3.82643	+	6.62757i	−0.121550	+	0.210532i	0.798829	+	0.601558i	$0.205453\pi$
$992$		0			0
$993$	24.9278			0.791061
$994$		0			0
$995$	5.45005			0.172778
$996$	13.9278	+	24.1237i	0.441320	+	0.764389i
$997$	−16.0164	+	27.7412i	−0.507244	+	0.878573i	0.492721	+	0.870188i	$0.336002\pi$
$997$	−16.0164	+	27.7412i	−0.507244	+	0.878573i	−0.999965	+	0.00838510i	$0.997331\pi$
$998$		0			0
$999$	−0.500000	−	0.866025i	−0.0158193	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.c.739.1	yes	6
7.2	even	3	inner	861.2.i.c.247.1	✓	6
7.3	odd	6		6027.2.a.q.1.1		3
7.4	even	3		6027.2.a.p.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.c.247.1	✓	6	7.2	even	3	inner
861.2.i.c.739.1	yes	6	1.1	even	1	trivial
6027.2.a.p.1.3		3	7.4	even	3
6027.2.a.q.1.1		3	7.3	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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.27624 - 2.21051i) q^{5} +(-2.58628 + 0.557835i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.27624 - 2.21051i) q^{5} +(-2.58628 + 0.557835i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.08628 + 5.34559i) q^{11} +(-1.00000 - 1.73205i) q^{12} -2.06760 q^{13} -2.55247 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{17} +(0.223763 + 0.387568i) q^{19} -5.10495 q^{20} +(-0.810038 + 2.51870i) q^{21} +(0.276237 + 0.478457i) q^{23} +(-0.757563 + 1.31214i) q^{25} -1.00000 q^{27} +(-1.62008 + 5.03740i) q^{28} -5.10495 q^{29} +(3.86251 - 6.69007i) q^{31} +(3.08628 + 5.34559i) q^{33} +(4.53380 + 5.00505i) q^{35} -2.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-1.03380 + 1.79060i) q^{39} -1.00000 q^{41} -10.6201 q^{43} +(6.17255 + 10.6912i) q^{44} +(-1.27624 + 2.21051i) q^{45} +(4.15388 + 7.19473i) q^{47} -4.00000 q^{48} +(6.37764 - 2.88543i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-2.06760 + 3.58119i) q^{52} +(2.06760 - 3.58119i) q^{53} +15.7553 q^{55} +0.447525 q^{57} +(-4.06760 + 7.04529i) q^{59} +(-2.55247 + 4.42102i) q^{60} +(-3.87764 - 6.71627i) q^{61} +(1.77624 + 1.96086i) q^{63} -8.00000 q^{64} +(2.63875 + 4.57045i) q^{65} +(0.0338006 - 0.0585444i) q^{67} +(-2.00000 - 3.46410i) q^{68} +0.552475 q^{69} +2.13520 q^{71} +(5.31004 - 9.19726i) q^{73} +(0.757563 + 1.31214i) q^{75} +0.895051 q^{76} +(5.00000 - 15.5468i) q^{77} +(-8.39631 - 14.5428i) q^{79} +(-5.10495 + 8.84203i) q^{80} +(-0.500000 + 0.866025i) q^{81} -13.9278 q^{83} +(3.55247 + 3.92172i) q^{84} -5.10495 q^{85} +(-2.55247 + 4.42102i) q^{87} +(-6.15388 - 10.6588i) q^{89} +(5.34739 - 1.15338i) q^{91} +1.10495 q^{92} +(-3.86251 - 6.69007i) q^{93} +(0.571149 - 0.989258i) q^{95} +16.2099 q^{97} +6.17255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} + 6 q^{4} + 3 q^{7} - 3 q^{9} - 6 q^{12} - 6 q^{13} - 12 q^{16} + 6 q^{17} + 9 q^{19} + 6 q^{21} - 6 q^{23} - 9 q^{25} - 6 q^{27} + 12 q^{28} - 3 q^{31} + 24 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{39} - 6 q^{41} - 42 q^{43} - 24 q^{48} + 21 q^{49} - 6 q^{51} - 6 q^{52} + 6 q^{53} + 60 q^{55} + 18 q^{57} - 18 q^{59} - 6 q^{61} + 3 q^{63} - 48 q^{64} - 18 q^{65} - 3 q^{67} - 12 q^{68} - 12 q^{69} + 21 q^{73} + 9 q^{75} + 36 q^{76} + 30 q^{77} - 21 q^{79} - 3 q^{81} - 12 q^{83} + 6 q^{84} - 12 q^{89} - 3 q^{91} - 24 q^{92} + 3 q^{93} - 24 q^{95} + 36 q^{97}+O(q^{100}) \) 6 * q + 3 * q^3 + 6 * q^4 + 3 * q^7 - 3 * q^9 - 6 * q^12 - 6 * q^13 - 12 * q^16 + 6 * q^17 + 9 * q^19 + 6 * q^21 - 6 * q^23 - 9 * q^25 - 6 * q^27 + 12 * q^28 - 3 * q^31 + 24 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^39 - 6 * q^41 - 42 * q^43 - 24 * q^48 + 21 * q^49 - 6 * q^51 - 6 * q^52 + 6 * q^53 + 60 * q^55 + 18 * q^57 - 18 * q^59 - 6 * q^61 + 3 * q^63 - 48 * q^64 - 18 * q^65 - 3 * q^67 - 12 * q^68 - 12 * q^69 + 21 * q^73 + 9 * q^75 + 36 * q^76 + 30 * q^77 - 21 * q^79 - 3 * q^81 - 12 * q^83 + 6 * q^84 - 12 * q^89 - 3 * q^91 - 24 * q^92 + 3 * q^93 - 24 * q^95 + 36 * q^97

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