LMFDB - Embedded newform 847.2.f.f.372.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.f.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} +(1.61803 + 1.17557i) q^{4} +(0.927051 + 2.85317i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} +(1.61803 + 1.17557i) q^{4} +(0.927051 + 2.85317i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.618034 + 1.90211i) q^{9} -2.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(-2.42705 - 1.76336i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-1.85410 - 5.70634i) q^{17} +(-1.61803 + 1.17557i) q^{19} +(-1.85410 + 5.70634i) q^{20} +1.00000 q^{21} +3.00000 q^{23} +(-3.23607 + 2.35114i) q^{25} +(-1.54508 - 4.75528i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(4.85410 + 3.52671i) q^{29} +(1.54508 - 4.75528i) q^{31} +(0.927051 - 2.85317i) q^{35} +(-3.23607 + 2.35114i) q^{36} +(-8.89919 - 6.46564i) q^{37} +(-1.23607 - 3.80423i) q^{39} +(-4.85410 + 3.52671i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(-3.23607 - 2.35114i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.85410 + 3.52671i) q^{51} +(-6.47214 + 4.70228i) q^{52} +(-1.85410 + 5.70634i) q^{53} +(0.618034 - 1.90211i) q^{57} +(7.28115 + 5.29007i) q^{59} +(-1.85410 - 5.70634i) q^{60} +(-3.09017 - 9.51057i) q^{61} +(1.61803 - 1.17557i) q^{63} +(-2.47214 + 7.60845i) q^{64} -12.0000 q^{65} +5.00000 q^{67} +(3.70820 - 11.4127i) q^{68} +(-2.42705 + 1.76336i) q^{69} +(2.78115 + 8.55951i) q^{71} +(-1.61803 - 1.17557i) q^{73} +(1.23607 - 3.80423i) q^{75} -4.00000 q^{76} +(-3.09017 + 9.51057i) q^{79} +(-9.70820 + 7.05342i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.70820 + 11.4127i) q^{83} +(1.61803 + 1.17557i) q^{84} +(14.5623 - 10.5801i) q^{85} -6.00000 q^{87} -3.00000 q^{89} +(3.23607 - 2.35114i) q^{91} +(4.85410 + 3.52671i) q^{92} +(1.54508 + 4.75528i) q^{93} +(-4.85410 - 3.52671i) q^{95} +(-0.309017 + 0.951057i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9	$ 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9} - 8 q^{12} + 4 q^{13} - 3 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{19} + 6 q^{20} + 4 q^{21} + 12 q^{23} - 4 q^{25} + 5 q^{27} + 2 q^{28} + 6 q^{29} - 5 q^{31} - 3 q^{35} - 4 q^{36} - 11 q^{37} + 4 q^{39} - 6 q^{41} + 32 q^{43} - 24 q^{45} - 4 q^{48} - q^{49} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 2 q^{57} + 9 q^{59} + 6 q^{60} + 10 q^{61} + 2 q^{63} + 8 q^{64} - 48 q^{65} + 20 q^{67} - 12 q^{68} - 3 q^{69} - 9 q^{71} - 2 q^{73} - 4 q^{75} - 16 q^{76} + 10 q^{79} - 12 q^{80} - q^{81} - 12 q^{83} + 2 q^{84} + 18 q^{85} - 24 q^{87} - 12 q^{89} + 4 q^{91} + 6 q^{92} - 5 q^{93} - 6 q^{95} + q^{97}+O(q^{100}) $ 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9 - 8 * q^12 + 4 * q^13 - 3 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^19 + 6 * q^20 + 4 * q^21 + 12 * q^23 - 4 * q^25 + 5 * q^27 + 2 * q^28 + 6 * q^29 - 5 * q^31 - 3 * q^35 - 4 * q^36 - 11 * q^37 + 4 * q^39 - 6 * q^41 + 32 * q^43 - 24 * q^45 - 4 * q^48 - q^49 + 6 * q^51 - 8 * q^52 + 6 * q^53 - 2 * q^57 + 9 * q^59 + 6 * q^60 + 10 * q^61 + 2 * q^63 + 8 * q^64 - 48 * q^65 + 20 * q^67 - 12 * q^68 - 3 * q^69 - 9 * q^71 - 2 * q^73 - 4 * q^75 - 16 * q^76 + 10 * q^79 - 12 * q^80 - q^81 - 12 * q^83 + 2 * q^84 + 18 * q^85 - 24 * q^87 - 12 * q^89 + 4 * q^91 + 6 * q^92 - 5 * q^93 - 6 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$2$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i	−0.796305	−	0.604896i	$-0.793215\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i	0.329218	+	0.944254i	$0.393215\pi$
$4$	1.61803	+	1.17557i	0.809017	+	0.587785i
$5$	0.927051	+	2.85317i	0.414590	+	1.27598i	0.912617	+	0.408815i	$0.134058\pi$
$5$	0.927051	+	2.85317i	0.414590	+	1.27598i	−0.498027	+	0.867161i	$0.665942\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$		0			0
$9$	−0.618034	+	1.90211i	−0.206011	+	0.634038i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	0.619915	+	0.784669i	$0.287167\pi$
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	−0.962739	+	0.270434i	$0.912833\pi$
$14$		0			0
$15$	−2.42705	−	1.76336i	−0.626662	−	0.455296i
$16$	1.23607	+	3.80423i	0.309017	+	0.951057i
$17$	−1.85410	−	5.70634i	−0.449686	−	1.38399i	−0.877262	−	0.480011i	$-0.840633\pi$
$17$	−1.85410	−	5.70634i	−0.449686	−	1.38399i	0.427576	−	0.903979i	$-0.359367\pi$
$18$		0			0
$19$	−1.61803	+	1.17557i	−0.371202	+	0.269694i	−0.757709	−	0.652592i	$-0.773682\pi$
$19$	−1.61803	+	1.17557i	−0.371202	+	0.269694i	0.386507	+	0.922287i	$0.373682\pi$
$20$	−1.85410	+	5.70634i	−0.414590	+	1.27598i
$21$	1.00000			0.218218
$22$		0			0
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$		0			0
$25$	−3.23607	+	2.35114i	−0.647214	+	0.470228i
$26$		0			0
$27$	−1.54508	−	4.75528i	−0.297352	−	0.915155i
$28$	−0.618034	−	1.90211i	−0.116797	−	0.359466i
$29$	4.85410	+	3.52671i	0.901384	+	0.654894i	0.938821	−	0.344405i	$-0.111919\pi$
$29$	4.85410	+	3.52671i	0.901384	+	0.654894i	−0.0374370	+	0.999299i	$0.511919\pi$
$30$		0			0
$31$	1.54508	−	4.75528i	0.277505	−	0.854074i	−0.711040	−	0.703151i	$-0.751776\pi$
$31$	1.54508	−	4.75528i	0.277505	−	0.854074i	0.988546	−	0.150923i	$-0.0482244\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.927051	−	2.85317i	0.156700	−	0.482274i
$36$	−3.23607	+	2.35114i	−0.539345	+	0.391857i
$37$	−8.89919	−	6.46564i	−1.46302	−	1.06294i	−0.982564	−	0.185924i	$-0.940472\pi$
$37$	−8.89919	−	6.46564i	−1.46302	−	1.06294i	−0.480453	−	0.877020i	$-0.659528\pi$
$38$		0			0
$39$	−1.23607	−	3.80423i	−0.197929	−	0.609164i
$40$		0			0
$41$	−4.85410	+	3.52671i	−0.758083	+	0.550780i	−0.898322	−	0.439338i	$-0.855213\pi$
$41$	−4.85410	+	3.52671i	−0.758083	+	0.550780i	0.140238	+	0.990118i	$0.455213\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−6.00000			−0.894427
$46$		0			0
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$	−3.23607	−	2.35114i	−0.467086	−	0.339358i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	4.85410	+	3.52671i	0.679710	+	0.493838i
$52$	−6.47214	+	4.70228i	−0.897524	+	0.652089i
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	0.739212	+	0.673473i	$0.235198\pi$
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	−0.993892	+	0.110353i	$0.964802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.618034	−	1.90211i	0.0818606	−	0.251941i
$58$		0			0
$59$	7.28115	+	5.29007i	0.947925	+	0.688708i	0.950315	−	0.311289i	$-0.100761\pi$
$59$	7.28115	+	5.29007i	0.947925	+	0.688708i	−0.00238991	+	0.999997i	$0.500761\pi$
$60$	−1.85410	−	5.70634i	−0.239364	−	0.736685i
$61$	−3.09017	−	9.51057i	−0.395656	−	1.21770i	−0.928450	−	0.371458i	$-0.878858\pi$
$61$	−3.09017	−	9.51057i	−0.395656	−	1.21770i	0.532794	−	0.846245i	$-0.321142\pi$
$62$		0			0
$63$	1.61803	−	1.17557i	0.203853	−	0.148108i
$64$	−2.47214	+	7.60845i	−0.309017	+	0.951057i
$65$	−12.0000			−1.48842
$66$		0			0
$67$	5.00000			0.610847			0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000			0.610847			0.305424	+	0.952217i	$0.401202\pi$
$68$	3.70820	−	11.4127i	0.449686	−	1.38399i
$69$	−2.42705	+	1.76336i	−0.292183	+	0.212283i
$70$		0			0
$71$	2.78115	+	8.55951i	0.330062	+	1.01583i	0.969104	+	0.246654i	$0.0793313\pi$
$71$	2.78115	+	8.55951i	0.330062	+	1.01583i	−0.639041	+	0.769172i	$0.720669\pi$
$72$		0			0
$73$	−1.61803	−	1.17557i	−0.189377	−	0.137590i	0.489057	−	0.872252i	$-0.337341\pi$
$73$	−1.61803	−	1.17557i	−0.189377	−	0.137590i	−0.678434	+	0.734662i	$0.737341\pi$
$74$		0			0
$75$	1.23607	−	3.80423i	0.142729	−	0.439274i
$76$	−4.00000			−0.458831
$77$		0			0
$78$		0			0
$79$	−3.09017	+	9.51057i	−0.347671	+	1.07002i	0.612467	+	0.790496i	$0.290177\pi$
$79$	−3.09017	+	9.51057i	−0.347671	+	1.07002i	−0.960138	+	0.279526i	$0.909823\pi$
$80$	−9.70820	+	7.05342i	−1.08541	+	0.788597i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	3.70820	+	11.4127i	0.407028	+	1.25270i	0.919190	+	0.393815i	$0.128845\pi$
$83$	3.70820	+	11.4127i	0.407028	+	1.25270i	−0.512161	+	0.858889i	$0.671155\pi$
$84$	1.61803	+	1.17557i	0.176542	+	0.128265i
$85$	14.5623	−	10.5801i	1.57950	−	1.14758i
$86$		0			0
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	3.23607	−	2.35114i	0.339232	−	0.246467i
$92$	4.85410	+	3.52671i	0.506075	+	0.367685i
$93$	1.54508	+	4.75528i	0.160218	+	0.493100i
$94$		0			0
$95$	−4.85410	−	3.52671i	−0.498020	−	0.361833i
$96$		0			0
$97$	−0.309017	+	0.951057i	−0.0313759	+	0.0965652i	−0.965518	−	0.260336i	$-0.916167\pi$
$97$	−0.309017	+	0.951057i	−0.0313759	+	0.0965652i	0.934142	+	0.356901i	$0.116167\pi$
$98$		0			0
$99$		0			0
$100$	−8.00000			−0.800000
$101$	−3.70820	+	11.4127i	−0.368980	+	1.13560i	0.578471	+	0.815703i	$0.303650\pi$
$101$	−3.70820	+	11.4127i	−0.368980	+	1.13560i	−0.947451	+	0.319901i	$0.896350\pi$
$102$		0			0
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	0.735689	−	0.677320i	$-0.236859\pi$
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	−0.416829	+	0.908985i	$0.636859\pi$
$104$		0			0
$105$	0.927051	+	2.85317i	0.0904709	+	0.278441i
$106$		0			0
$107$	−4.85410	+	3.52671i	−0.469264	+	0.340940i	−0.797154	−	0.603776i	$-0.793662\pi$
$107$	−4.85410	+	3.52671i	−0.469264	+	0.340940i	0.327891	+	0.944716i	$0.393662\pi$
$108$	3.09017	−	9.51057i	0.297352	−	0.915155i
$109$	20.0000			1.91565			0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000			1.91565			0.957826	+	0.287348i	$0.0927736\pi$
$110$		0			0
$111$	11.0000			1.04407
$112$	1.23607	−	3.80423i	0.116797	−	0.359466i
$113$	2.42705	−	1.76336i	0.228318	−	0.165883i	−0.467745	−	0.883863i	$-0.654933\pi$
$113$	2.42705	−	1.76336i	0.228318	−	0.165883i	0.696063	+	0.717981i	$0.254933\pi$
$114$		0			0
$115$	2.78115	+	8.55951i	0.259344	+	0.798178i
$116$	3.70820	+	11.4127i	0.344298	+	1.05964i
$117$	−6.47214	−	4.70228i	−0.598349	−	0.434726i
$118$		0			0
$119$	−1.85410	+	5.70634i	−0.169965	+	0.523099i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	1.85410	−	5.70634i	0.167179	−	0.514523i
$124$	8.09017	−	5.87785i	0.726519	−	0.527847i
$125$	2.42705	+	1.76336i	0.217082	+	0.157719i
$126$		0			0
$127$	0.618034	+	1.90211i	0.0548416	+	0.168785i	0.974726	−	0.223405i	$-0.0717174\pi$
$127$	0.618034	+	1.90211i	0.0548416	+	0.168785i	−0.919884	+	0.392191i	$0.871717\pi$
$128$		0			0
$129$	−6.47214	+	4.70228i	−0.569840	+	0.414013i
$130$		0			0
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$	2.00000			0.173422
$134$		0			0
$135$	12.1353	−	8.81678i	1.04444	−	0.758827i
$136$		0			0
$137$	−0.927051	−	2.85317i	−0.0792033	−	0.243763i	0.903613	−	0.428350i	$-0.140905\pi$
$137$	−0.927051	−	2.85317i	−0.0792033	−	0.243763i	−0.982816	+	0.184588i	$0.940905\pi$
$138$		0			0
$139$	−11.3262	−	8.22899i	−0.960679	−	0.697974i	−0.00737063	−	0.999973i	$-0.502346\pi$
$139$	−11.3262	−	8.22899i	−0.960679	−	0.697974i	−0.953308	+	0.301999i	$0.902346\pi$
$140$	4.85410	−	3.52671i	0.410246	−	0.298062i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−8.00000			−0.666667
$145$	−5.56231	+	17.1190i	−0.461924	+	1.42166i
$146$		0			0
$147$	−0.809017	−	0.587785i	−0.0667266	−	0.0484797i
$148$	−6.79837	−	20.9232i	−0.558823	−	1.71988i
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	0.845939	−	0.533280i	$-0.179041\pi$
$149$	−1.85410	−	5.70634i	−0.151894	−	0.467482i	−0.997833	+	0.0657982i	$0.979041\pi$
$150$		0			0
$151$	8.09017	−	5.87785i	0.658369	−	0.478333i	−0.207743	−	0.978183i	$-0.566612\pi$
$151$	8.09017	−	5.87785i	0.658369	−	0.478333i	0.866112	+	0.499851i	$0.166612\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	15.0000			1.20483
$156$	2.47214	−	7.60845i	0.197929	−	0.609164i
$157$	10.5172	−	7.64121i	0.839366	−	0.609835i	−0.0828278	−	0.996564i	$-0.526395\pi$
$157$	10.5172	−	7.64121i	0.839366	−	0.609835i	0.922193	+	0.386729i	$0.126395\pi$
$158$		0			0
$159$	−1.85410	−	5.70634i	−0.147040	−	0.452542i
$160$		0			0
$161$	−2.42705	−	1.76336i	−0.191278	−	0.138972i
$162$		0			0
$163$	6.18034	−	19.0211i	0.484082	−	1.48985i	−0.349225	−	0.937039i	$-0.613555\pi$
$163$	6.18034	−	19.0211i	0.484082	−	1.48985i	0.833307	−	0.552811i	$-0.186445\pi$
$164$	−12.0000			−0.937043
$165$		0			0
$166$		0			0
$167$	1.85410	−	5.70634i	0.143475	−	0.441570i	−0.853337	−	0.521360i	$-0.825425\pi$
$167$	1.85410	−	5.70634i	0.143475	−	0.441570i	0.996812	+	0.0797900i	$0.0254250\pi$
$168$		0			0
$169$	−2.42705	−	1.76336i	−0.186696	−	0.135643i
$170$		0			0
$171$	−1.23607	−	3.80423i	−0.0945245	−	0.290916i
$172$	12.9443	+	9.40456i	0.986991	+	0.717091i
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$	4.00000			0.302372
$176$		0			0
$177$	−9.00000			−0.676481
$178$		0			0
$179$	12.1353	−	8.81678i	0.907032	−	0.658997i	−0.0332308	−	0.999448i	$-0.510580\pi$
$179$	12.1353	−	8.81678i	0.907032	−	0.658997i	0.940262	+	0.340451i	$0.110580\pi$
$180$	−9.70820	−	7.05342i	−0.723607	−	0.525731i
$181$	−2.16312	−	6.65740i	−0.160783	−	0.494840i	0.837918	−	0.545797i	$-0.183773\pi$
$181$	−2.16312	−	6.65740i	−0.160783	−	0.494840i	−0.998701	+	0.0509566i	$0.983773\pi$
$182$		0			0
$183$	8.09017	+	5.87785i	0.598043	+	0.434503i
$184$		0			0
$185$	10.1976	−	31.3849i	0.749740	−	2.30746i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.54508	+	4.75528i	−0.112388	+	0.345896i
$190$		0			0
$191$	21.8435	+	15.8702i	1.58054	+	1.14833i	0.916076	+	0.401005i	$0.131339\pi$
$191$	21.8435	+	15.8702i	1.58054	+	1.14833i	0.664461	+	0.747323i	$0.268661\pi$
$192$	−2.47214	−	7.60845i	−0.178411	−	0.549093i
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	0.977207	+	0.212287i	$0.0680913\pi$
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	−0.665798	+	0.746132i	$0.731909\pi$
$194$		0			0
$195$	9.70820	−	7.05342i	0.695219	−	0.505106i
$196$	−0.618034	+	1.90211i	−0.0441453	+	0.135865i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$		0			0
$201$	−4.04508	+	2.93893i	−0.285318	+	0.207296i
$202$		0			0
$203$	−1.85410	−	5.70634i	−0.130132	−	0.400506i
$204$	3.70820	+	11.4127i	0.259626	+	0.799047i
$205$	−14.5623	−	10.5801i	−1.01708	−	0.738949i
$206$		0			0
$207$	−1.85410	+	5.70634i	−0.128869	+	0.396618i
$208$	−16.0000			−1.10940
$209$		0			0
$210$		0			0
$211$	4.32624	−	13.3148i	0.297831	−	0.916628i	−0.684425	−	0.729083i	$-0.739947\pi$
$211$	4.32624	−	13.3148i	0.297831	−	0.916628i	0.982256	−	0.187545i	$-0.0600531\pi$
$212$	−9.70820	+	7.05342i	−0.666762	+	0.484431i
$213$	−7.28115	−	5.29007i	−0.498896	−	0.362469i
$214$		0			0
$215$	7.41641	+	22.8254i	0.505795	+	1.55668i
$216$		0			0
$217$	−4.04508	+	2.93893i	−0.274598	+	0.199507i
$218$		0			0
$219$	2.00000			0.135147
$220$		0			0
$221$	24.0000			1.61441
$222$		0			0
$223$	15.3713	−	11.1679i	1.02934	−	0.747859i	0.0611635	−	0.998128i	$-0.480519\pi$
$223$	15.3713	−	11.1679i	1.02934	−	0.747859i	0.968176	+	0.250269i	$0.0805189\pi$
$224$		0			0
$225$	−2.47214	−	7.60845i	−0.164809	−	0.507230i
$226$		0			0
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	0.861344	−	0.508022i	$-0.169623\pi$
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	−0.216988	+	0.976174i	$0.569623\pi$
$228$	3.23607	−	2.35114i	0.214314	−	0.155708i
$229$	1.54508	−	4.75528i	0.102102	−	0.314238i	−0.886937	−	0.461890i	$-0.847172\pi$
$229$	1.54508	−	4.75528i	0.102102	−	0.314238i	0.989039	+	0.147652i	$0.0471715\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.85410	−	5.70634i	0.121466	−	0.373835i	−0.871774	−	0.489907i	$-0.837031\pi$
$233$	1.85410	−	5.70634i	0.121466	−	0.373835i	0.993241	+	0.116073i	$0.0370306\pi$
$234$		0			0
$235$		0			0
$236$	5.56231	+	17.1190i	0.362075	+	1.11435i
$237$	−3.09017	−	9.51057i	−0.200728	−	0.617778i
$238$		0			0
$239$	9.70820	−	7.05342i	0.627972	−	0.456248i	−0.227725	−	0.973725i	$-0.573129\pi$
$239$	9.70820	−	7.05342i	0.627972	−	0.456248i	0.855697	+	0.517477i	$0.173129\pi$
$240$	3.70820	−	11.4127i	0.239364	−	0.736685i
$241$	−28.0000			−1.80364			−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000			−1.80364			−0.901819	+	0.432113i	$0.857768\pi$
$242$		0			0
$243$	16.0000			1.02640
$244$	6.18034	−	19.0211i	0.395656	−	1.21770i
$245$	−2.42705	+	1.76336i	−0.155059	+	0.112657i
$246$		0			0
$247$	−2.47214	−	7.60845i	−0.157298	−	0.484114i
$248$		0			0
$249$	−9.70820	−	7.05342i	−0.615232	−	0.446993i
$250$		0			0
$251$	−2.78115	+	8.55951i	−0.175545	+	0.540271i	−0.999658	−	0.0261539i	$-0.991674\pi$
$251$	−2.78115	+	8.55951i	−0.175545	+	0.540271i	0.824113	+	0.566425i	$0.191674\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$		0			0
$255$	−5.56231	+	17.1190i	−0.348325	+	1.07203i
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	0.728797	−	0.684730i	$-0.240080\pi$
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	−0.426006	+	0.904720i	$0.640080\pi$
$258$		0			0
$259$	3.39919	+	10.4616i	0.211215	+	0.650054i
$260$	−19.4164	−	14.1068i	−1.20415	−	0.874869i
$261$	−9.70820	+	7.05342i	−0.600923	+	0.436596i
$262$		0			0
$263$	−30.0000			−1.84988			−0.924940	−	0.380114i	$-0.875885\pi$
$263$	−30.0000			−1.84988			−0.924940	+	0.380114i	$0.875885\pi$
$264$		0			0
$265$	−18.0000			−1.10573
$266$		0			0
$267$	2.42705	−	1.76336i	0.148533	−	0.107916i
$268$	8.09017	+	5.87785i	0.494186	+	0.359047i
$269$	9.27051	+	28.5317i	0.565233	+	1.73961i	0.667258	+	0.744826i	$0.267468\pi$
$269$	9.27051	+	28.5317i	0.565233	+	1.73961i	−0.102025	+	0.994782i	$0.532532\pi$
$270$		0			0
$271$	12.9443	+	9.40456i	0.786309	+	0.571287i	0.906866	−	0.421420i	$-0.138468\pi$
$271$	12.9443	+	9.40456i	0.786309	+	0.571287i	−0.120557	+	0.992706i	$0.538468\pi$
$272$	19.4164	−	14.1068i	1.17729	−	0.855353i
$273$	−1.23607	+	3.80423i	−0.0748102	+	0.230242i
$274$		0			0
$275$		0			0
$276$	−6.00000			−0.361158
$277$	2.47214	−	7.60845i	0.148536	−	0.457148i	−0.848913	−	0.528533i	$-0.822742\pi$
$277$	2.47214	−	7.60845i	0.148536	−	0.457148i	0.997449	+	0.0713858i	$0.0227421\pi$
$278$		0			0
$279$	8.09017	+	5.87785i	0.484346	+	0.351898i
$280$		0			0
$281$	3.70820	+	11.4127i	0.221213	+	0.680823i	0.998654	+	0.0518675i	$0.0165174\pi$
$281$	3.70820	+	11.4127i	0.221213	+	0.680823i	−0.777441	+	0.628956i	$0.783483\pi$
$282$		0			0
$283$	−25.8885	+	18.8091i	−1.53891	+	1.11809i	−0.587902	+	0.808932i	$0.700046\pi$
$283$	−25.8885	+	18.8091i	−1.53891	+	1.11809i	−0.951012	+	0.309155i	$0.899954\pi$
$284$	−5.56231	+	17.1190i	−0.330062	+	1.01583i
$285$	6.00000			0.355409
$286$		0			0
$287$	6.00000			0.354169
$288$		0			0
$289$	−15.3713	+	11.1679i	−0.904195	+	0.656936i
$290$		0			0
$291$	−0.309017	−	0.951057i	−0.0181149	−	0.0557519i
$292$	−1.23607	−	3.80423i	−0.0723354	−	0.222625i
$293$	24.2705	+	17.6336i	1.41790	+	1.03016i	0.992114	+	0.125339i	$0.0400018\pi$
$293$	24.2705	+	17.6336i	1.41790	+	1.03016i	0.425784	+	0.904825i	$0.359998\pi$
$294$		0			0
$295$	−8.34346	+	25.6785i	−0.485775	+	1.49506i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.70820	+	11.4127i	−0.214451	+	0.660012i
$300$	6.47214	−	4.70228i	0.373669	−	0.271486i
$301$	−6.47214	−	4.70228i	−0.373048	−	0.271035i
$302$		0			0
$303$	−3.70820	−	11.4127i	−0.213031	−	0.655641i
$304$	−6.47214	−	4.70228i	−0.371202	−	0.269694i
$305$	24.2705	−	17.6336i	1.38973	−	1.00969i
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$		0			0
$311$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$311$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$312$		0			0
$313$	−5.87132	−	18.0701i	−0.331867	−	1.02138i	−0.968245	−	0.250004i	$-0.919568\pi$
$313$	−5.87132	−	18.0701i	−0.331867	−	1.02138i	0.636378	−	0.771377i	$-0.280432\pi$
$314$		0			0
$315$	4.85410	+	3.52671i	0.273498	+	0.198708i
$316$	−16.1803	+	11.7557i	−0.910215	+	0.661310i
$317$	2.78115	−	8.55951i	0.156205	−	0.480750i	−0.842076	−	0.539359i	$-0.818667\pi$
$317$	2.78115	−	8.55951i	0.156205	−	0.480750i	0.998281	+	0.0586092i	$0.0186666\pi$
$318$		0			0
$319$		0			0
$320$	−24.0000			−1.34164
$321$	1.85410	−	5.70634i	0.103486	−	0.318497i
$322$		0			0
$323$	9.70820	+	7.05342i	0.540179	+	0.392463i
$324$	−0.618034	−	1.90211i	−0.0343352	−	0.105673i
$325$	−4.94427	−	15.2169i	−0.274259	−	0.844082i
$326$		0			0
$327$	−16.1803	+	11.7557i	−0.894775	+	0.650092i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.00000			−0.0549650			−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	−1.00000			−0.0549650			−0.0274825	+	0.999622i	$0.508749\pi$
$332$	−7.41641	+	22.8254i	−0.407028	+	1.25270i
$333$	17.7984	−	12.9313i	0.975345	−	0.708630i
$334$		0			0
$335$	4.63525	+	14.2658i	0.253251	+	0.779427i
$336$	1.23607	+	3.80423i	0.0674330	+	0.207538i
$337$	−11.3262	−	8.22899i	−0.616979	−	0.448262i	0.234886	−	0.972023i	$-0.424528\pi$
$337$	−11.3262	−	8.22899i	−0.616979	−	0.448262i	−0.851865	+	0.523761i	$0.824528\pi$
$338$		0			0
$339$	−0.927051	+	2.85317i	−0.0503505	+	0.154963i
$340$	36.0000			1.95237
$341$		0			0
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$		0			0
$345$	−7.28115	−	5.29007i	−0.392004	−	0.284808i
$346$		0			0
$347$	−5.56231	−	17.1190i	−0.298600	−	0.918997i	−0.981988	−	0.188942i	$-0.939494\pi$
$347$	−5.56231	−	17.1190i	−0.298600	−	0.918997i	0.683388	−	0.730055i	$-0.260506\pi$
$348$	−9.70820	−	7.05342i	−0.520414	−	0.378103i
$349$	8.09017	−	5.87785i	0.433057	−	0.314634i	−0.349813	−	0.936819i	$-0.613755\pi$
$349$	8.09017	−	5.87785i	0.433057	−	0.314634i	0.782870	+	0.622185i	$0.213755\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$		0			0
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$		0			0
$355$	−21.8435	+	15.8702i	−1.15933	+	0.842303i
$356$	−4.85410	−	3.52671i	−0.257267	−	0.186915i
$357$	−1.85410	−	5.70634i	−0.0981295	−	0.302011i
$358$		0			0
$359$	−19.4164	−	14.1068i	−1.02476	−	0.744531i	−0.0575058	−	0.998345i	$-0.518315\pi$
$359$	−19.4164	−	14.1068i	−1.02476	−	0.744531i	−0.967253	+	0.253814i	$0.918315\pi$
$360$		0			0
$361$	−4.63525	+	14.2658i	−0.243961	+	0.750834i
$362$		0			0
$363$		0			0
$364$	8.00000			0.419314
$365$	1.85410	−	5.70634i	0.0970481	−	0.298683i
$366$		0			0
$367$	−13.7533	−	9.99235i	−0.717916	−	0.521596i	0.167802	−	0.985821i	$-0.446333\pi$
$367$	−13.7533	−	9.99235i	−0.717916	−	0.521596i	−0.885718	+	0.464224i	$0.846333\pi$
$368$	3.70820	+	11.4127i	0.193303	+	0.594927i
$369$	−3.70820	−	11.4127i	−0.193041	−	0.594120i
$370$		0			0
$371$	4.85410	−	3.52671i	0.252012	−	0.183098i
$372$	−3.09017	+	9.51057i	−0.160218	+	0.493100i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$		0			0
$377$	−19.4164	+	14.1068i	−0.999996	+	0.726540i
$378$		0			0
$379$	3.39919	+	10.4616i	0.174605	+	0.537377i	0.999615	−	0.0277397i	$-0.00883096\pi$
$379$	3.39919	+	10.4616i	0.174605	+	0.537377i	−0.825011	+	0.565117i	$0.808831\pi$
$380$	−3.70820	−	11.4127i	−0.190227	−	0.585458i
$381$	−1.61803	−	1.17557i	−0.0828944	−	0.0602263i
$382$		0			0
$383$	6.48936	−	19.9722i	0.331591	−	1.02053i	−0.636786	−	0.771040i	$-0.719737\pi$
$383$	6.48936	−	19.9722i	0.331591	−	1.02053i	0.968377	−	0.249491i	$-0.0802633\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.94427	+	15.2169i	−0.251331	+	0.773519i
$388$	−1.61803	+	1.17557i	−0.0821432	+	0.0596806i
$389$	−26.6976	−	19.3969i	−1.35362	−	0.983463i	−0.998822	−	0.0485195i	$-0.984550\pi$
$389$	−26.6976	−	19.3969i	−1.35362	−	0.983463i	−0.354798	−	0.934943i	$-0.615450\pi$
$390$		0			0
$391$	−5.56231	−	17.1190i	−0.281298	−	0.865746i
$392$		0			0
$393$	4.85410	−	3.52671i	0.244857	−	0.177899i
$394$		0			0
$395$	−30.0000			−1.50946
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$		0			0
$399$	−1.61803	+	1.17557i	−0.0810030	+	0.0588521i
$400$	−12.9443	−	9.40456i	−0.647214	−	0.470228i
$401$	−1.85410	−	5.70634i	−0.0925894	−	0.284961i	0.894029	−	0.448010i	$-0.147867\pi$
$401$	−1.85410	−	5.70634i	−0.0925894	−	0.284961i	−0.986618	+	0.163049i	$0.947867\pi$
$402$		0			0
$403$	16.1803	+	11.7557i	0.806000	+	0.585593i
$404$	−19.4164	+	14.1068i	−0.966002	+	0.701842i
$405$	0.927051	−	2.85317i	0.0460655	−	0.141775i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	4.32624	−	13.3148i	0.213919	−	0.658374i	−0.785310	−	0.619103i	$-0.787496\pi$
$409$	4.32624	−	13.3148i	0.213919	−	0.658374i	0.999229	−	0.0392712i	$-0.0125036\pi$
$410$		0			0
$411$	2.42705	+	1.76336i	0.119718	+	0.0869799i
$412$	2.47214	+	7.60845i	0.121793	+	0.374842i
$413$	−2.78115	−	8.55951i	−0.136852	−	0.421186i
$414$		0			0
$415$	−29.1246	+	21.1603i	−1.42967	+	1.03872i
$416$		0			0
$417$	14.0000			0.685583
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$	−1.85410	+	5.70634i	−0.0904709	+	0.278441i
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	−0.372921	−	0.927863i	$-0.621644\pi$
$421$	8.09017	−	5.87785i	0.394291	−	0.286469i	0.767211	+	0.641394i	$0.221644\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	19.4164	+	14.1068i	0.941834	+	0.684283i
$426$		0			0
$427$	−3.09017	+	9.51057i	−0.149544	+	0.460249i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	−0.821162	−	0.570695i	$-0.806674\pi$
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	0.999780	+	0.0209654i	$0.00667397\pi$
$432$	16.1803	−	11.7557i	0.778477	−	0.565597i
$433$	−8.89919	−	6.46564i	−0.427668	−	0.310719i	0.353048	−	0.935605i	$-0.385145\pi$
$433$	−8.89919	−	6.46564i	−0.427668	−	0.310719i	−0.780716	+	0.624886i	$0.785145\pi$
$434$		0			0
$435$	−5.56231	−	17.1190i	−0.266692	−	0.820794i
$436$	32.3607	+	23.5114i	1.54980	+	1.12599i
$437$	−4.85410	+	3.52671i	−0.232203	+	0.168705i
$438$		0			0
$439$	26.0000			1.24091			0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000			1.24091			0.620456	+	0.784241i	$0.286947\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$		0			0
$443$	−7.28115	+	5.29007i	−0.345938	+	0.251339i	−0.747163	−	0.664641i	$-0.768585\pi$
$443$	−7.28115	+	5.29007i	−0.345938	+	0.251339i	0.401225	+	0.915980i	$0.368585\pi$
$444$	17.7984	+	12.9313i	0.844673	+	0.613691i
$445$	−2.78115	−	8.55951i	−0.131839	−	0.405760i
$446$		0			0
$447$	4.85410	+	3.52671i	0.229591	+	0.166808i
$448$	6.47214	−	4.70228i	0.305780	−	0.222162i
$449$	−2.78115	+	8.55951i	−0.131251	+	0.403948i	−0.994988	−	0.0999941i	$-0.968118\pi$
$449$	−2.78115	+	8.55951i	−0.131251	+	0.403948i	0.863737	+	0.503942i	$0.168118\pi$
$450$		0			0
$451$		0			0
$452$	6.00000			0.282216
$453$	−3.09017	+	9.51057i	−0.145189	+	0.446845i
$454$		0			0
$455$	9.70820	+	7.05342i	0.455128	+	0.330670i
$456$		0			0
$457$	2.47214	+	7.60845i	0.115642	+	0.355908i	0.992080	−	0.125605i	$-0.0400872\pi$
$457$	2.47214	+	7.60845i	0.115642	+	0.355908i	−0.876439	+	0.481514i	$0.840087\pi$
$458$		0			0
$459$	−24.2705	+	17.6336i	−1.13285	+	0.823064i
$460$	−5.56231	+	17.1190i	−0.259344	+	0.798178i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	−7.41641	+	22.8254i	−0.344298	+	1.05964i
$465$	−12.1353	+	8.81678i	−0.562759	+	0.408868i
$466$		0			0
$467$	4.63525	+	14.2658i	0.214494	+	0.660145i	0.999189	+	0.0402628i	$0.0128195\pi$
$467$	4.63525	+	14.2658i	0.214494	+	0.660145i	−0.784695	+	0.619882i	$0.787180\pi$
$468$	−4.94427	−	15.2169i	−0.228549	−	0.703402i
$469$	−4.04508	−	2.93893i	−0.186785	−	0.135707i
$470$		0			0
$471$	−4.01722	+	12.3637i	−0.185104	+	0.569691i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	2.47214	−	7.60845i	0.113429	−	0.349100i
$476$	−9.70820	+	7.05342i	−0.444975	+	0.323293i
$477$	−9.70820	−	7.05342i	−0.444508	−	0.322954i
$478$		0			0
$479$	−3.70820	−	11.4127i	−0.169432	−	0.521459i	0.829903	−	0.557907i	$-0.188395\pi$
$479$	−3.70820	−	11.4127i	−0.169432	−	0.521459i	−0.999336	+	0.0364486i	$0.988395\pi$
$480$		0			0
$481$	35.5967	−	25.8626i	1.62307	−	1.17923i
$482$		0			0
$483$	3.00000			0.136505
$484$		0			0
$485$	−3.00000			−0.136223
$486$		0			0
$487$	−8.89919	+	6.46564i	−0.403261	+	0.292986i	−0.770868	−	0.636995i	$-0.780177\pi$
$487$	−8.89919	+	6.46564i	−0.403261	+	0.292986i	0.367607	+	0.929981i	$0.380177\pi$
$488$		0			0
$489$	6.18034	+	19.0211i	0.279485	+	0.860165i
$490$		0			0
$491$	24.2705	+	17.6336i	1.09531	+	0.795791i	0.980289	−	0.197571i	$-0.0633054\pi$
$491$	24.2705	+	17.6336i	1.09531	+	0.795791i	0.115024	+	0.993363i	$0.463305\pi$
$492$	9.70820	−	7.05342i	0.437680	−	0.317993i
$493$	11.1246	−	34.2380i	0.501027	−	1.54200i
$494$		0			0
$495$		0			0
$496$	20.0000			0.898027
$497$	2.78115	−	8.55951i	0.124752	−	0.383946i
$498$		0			0
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	0.657858	−	0.753142i	$-0.271463\pi$
$499$	3.23607	+	2.35114i	0.144866	+	0.105252i	−0.512992	+	0.858394i	$0.671463\pi$
$500$	1.85410	+	5.70634i	0.0829180	+	0.255195i
$501$	1.85410	+	5.70634i	0.0828352	+	0.254940i
$502$		0			0
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$		0			0
$505$	−36.0000			−1.60198
$506$		0			0
$507$	3.00000			0.133235
$508$	−1.23607	+	3.80423i	−0.0548416	+	0.168785i
$509$	−16.9894	+	12.3435i	−0.753040	+	0.547116i	−0.896768	−	0.442502i	$-0.854091\pi$
$509$	−16.9894	+	12.3435i	−0.753040	+	0.547116i	0.143728	+	0.989617i	$0.454091\pi$
$510$		0			0
$511$	0.618034	+	1.90211i	0.0273402	+	0.0841445i
$512$		0			0
$513$	8.09017	+	5.87785i	0.357190	+	0.259514i
$514$		0			0
$515$	−3.70820	+	11.4127i	−0.163403	+	0.502903i
$516$	−16.0000			−0.704361
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.42705	−	1.76336i	−0.106331	−	0.0772540i	0.533349	−	0.845895i	$-0.320933\pi$
$521$	−2.42705	−	1.76336i	−0.106331	−	0.0772540i	−0.639680	+	0.768641i	$0.720933\pi$
$522$		0			0
$523$	−4.94427	−	15.2169i	−0.216198	−	0.665389i	−0.999066	−	0.0432015i	$-0.986244\pi$
$523$	−4.94427	−	15.2169i	−0.216198	−	0.665389i	0.782868	−	0.622187i	$-0.213756\pi$
$524$	−9.70820	−	7.05342i	−0.424105	−	0.308130i
$525$	−3.23607	+	2.35114i	−0.141234	+	0.102612i
$526$		0			0
$527$	−30.0000			−1.30682
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$	−14.5623	+	10.5801i	−0.631950	+	0.459139i
$532$	3.23607	+	2.35114i	0.140301	+	0.101935i
$533$	−7.41641	−	22.8254i	−0.321240	−	0.988676i
$534$		0			0
$535$	−14.5623	−	10.5801i	−0.629583	−	0.457419i
$536$		0			0
$537$	−4.63525	+	14.2658i	−0.200026	+	0.615617i
$538$		0			0
$539$		0			0
$540$	30.0000			1.29099
$541$	−4.94427	+	15.2169i	−0.212571	+	0.654226i	0.786746	+	0.617277i	$0.211764\pi$
$541$	−4.94427	+	15.2169i	−0.212571	+	0.654226i	−0.999317	+	0.0369493i	$0.988236\pi$
$542$		0			0
$543$	5.66312	+	4.11450i	0.243028	+	0.176570i
$544$		0			0
$545$	18.5410	+	57.0634i	0.794210	+	2.44433i
$546$		0			0
$547$	−6.47214	+	4.70228i	−0.276729	+	0.201055i	−0.717489	−	0.696570i	$-0.754709\pi$
$547$	−6.47214	+	4.70228i	−0.276729	+	0.201055i	0.440761	+	0.897625i	$0.354709\pi$
$548$	1.85410	−	5.70634i	0.0792033	−	0.243763i
$549$	20.0000			0.853579
$550$		0			0
$551$	−12.0000			−0.511217
$552$		0			0
$553$	8.09017	−	5.87785i	0.344029	−	0.249952i
$554$		0			0
$555$	10.1976	+	31.3849i	0.432862	+	1.33221i
$556$	−8.65248	−	26.6296i	−0.366947	−	1.12935i
$557$	−24.2705	−	17.6336i	−1.02837	−	0.747158i	−0.0603918	−	0.998175i	$-0.519235\pi$
$557$	−24.2705	−	17.6336i	−1.02837	−	0.747158i	−0.967983	+	0.251017i	$0.919235\pi$
$558$		0			0
$559$	−9.88854	+	30.4338i	−0.418241	+	1.28721i
$560$	12.0000			0.507093
$561$		0			0
$562$		0			0
$563$	11.1246	−	34.2380i	0.468846	−	1.44296i	−0.385233	−	0.922819i	$-0.625879\pi$
$563$	11.1246	−	34.2380i	0.468846	−	1.44296i	0.854080	−	0.520142i	$-0.174121\pi$
$564$		0			0
$565$	7.28115	+	5.29007i	0.306320	+	0.222555i
$566$		0			0
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$		0			0
$569$	14.5623	−	10.5801i	0.610484	−	0.443542i	−0.239101	−	0.970995i	$-0.576853\pi$
$569$	14.5623	−	10.5801i	0.610484	−	0.443542i	0.849585	+	0.527452i	$0.176853\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$	−27.0000			−1.12794
$574$		0			0
$575$	−9.70820	+	7.05342i	−0.404860	+	0.294148i
$576$	−12.9443	−	9.40456i	−0.539345	−	0.391857i
$577$	3.39919	+	10.4616i	0.141510	+	0.435523i	0.996546	−	0.0830461i	$-0.0264649\pi$
$577$	3.39919	+	10.4616i	0.141510	+	0.435523i	−0.855036	+	0.518569i	$0.826465\pi$
$578$		0			0
$579$	−11.3262	−	8.22899i	−0.470702	−	0.341985i
$580$	−29.1246	+	21.1603i	−1.20933	+	0.878632i
$581$	3.70820	−	11.4127i	0.153842	−	0.473478i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	7.41641	−	22.8254i	0.306631	−	0.943712i
$586$		0			0
$587$	−9.70820	−	7.05342i	−0.400700	−	0.291126i	0.369126	−	0.929379i	$-0.379657\pi$
$587$	−9.70820	−	7.05342i	−0.400700	−	0.291126i	−0.769826	+	0.638254i	$0.779657\pi$
$588$	−0.618034	−	1.90211i	−0.0254873	−	0.0784418i
$589$	3.09017	+	9.51057i	0.127328	+	0.391876i
$590$		0			0
$591$	−14.5623	+	10.5801i	−0.599013	+	0.435209i
$592$	13.5967	−	41.8465i	0.558823	−	1.71988i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	−18.0000			−0.737928
$596$	3.70820	−	11.4127i	0.151894	−	0.467482i
$597$	12.9443	−	9.40456i	0.529774	−	0.384903i
$598$		0			0
$599$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$599$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$600$		0			0
$601$	−6.47214	−	4.70228i	−0.264004	−	0.191810i	0.447906	−	0.894080i	$-0.352170\pi$
$601$	−6.47214	−	4.70228i	−0.264004	−	0.191810i	−0.711910	+	0.702270i	$0.752170\pi$
$602$		0			0
$603$	−3.09017	+	9.51057i	−0.125841	+	0.387300i
$604$	20.0000			0.813788
$605$		0			0
$606$		0			0
$607$	4.32624	−	13.3148i	0.175597	−	0.540431i	−0.824064	−	0.566497i	$-0.808298\pi$
$607$	4.32624	−	13.3148i	0.175597	−	0.540431i	0.999660	+	0.0260665i	$0.00829818\pi$
$608$		0			0
$609$	4.85410	+	3.52671i	0.196698	+	0.142910i
$610$		0			0
$611$		0			0
$612$	19.4164	+	14.1068i	0.784862	+	0.570235i
$613$	12.9443	−	9.40456i	0.522814	−	0.379847i	−0.294849	−	0.955544i	$-0.595269\pi$
$613$	12.9443	−	9.40456i	0.522814	−	0.379847i	0.817663	+	0.575697i	$0.195269\pi$
$614$		0			0
$615$	18.0000			0.725830
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	15.3713	−	11.1679i	0.617826	−	0.448877i	−0.234336	−	0.972156i	$-0.575291\pi$
$619$	15.3713	−	11.1679i	0.617826	−	0.448877i	0.852161	+	0.523279i	$0.175291\pi$
$620$	24.2705	+	17.6336i	0.974727	+	0.708181i
$621$	−4.63525	−	14.2658i	−0.186006	−	0.572469i
$622$		0			0
$623$	2.42705	+	1.76336i	0.0972377	+	0.0706474i
$624$	12.9443	−	9.40456i	0.518186	−	0.376484i
$625$	−8.96149	+	27.5806i	−0.358460	+	1.10323i
$626$		0			0
$627$		0			0
$628$	26.0000			1.03751
$629$	−20.3951	+	62.7697i	−0.813207	+	2.50279i
$630$		0			0
$631$	−8.89919	−	6.46564i	−0.354271	−	0.257393i	0.396388	−	0.918083i	$-0.370264\pi$
$631$	−8.89919	−	6.46564i	−0.354271	−	0.257393i	−0.750659	+	0.660690i	$0.770264\pi$
$632$		0			0
$633$	4.32624	+	13.3148i	0.171953	+	0.529215i
$634$		0			0
$635$	−4.85410	+	3.52671i	−0.192629	+	0.139953i
$636$	3.70820	−	11.4127i	0.147040	−	0.452542i
$637$	−4.00000			−0.158486
$638$		0			0
$639$	−18.0000			−0.712069
$640$		0			0
$641$	−12.1353	+	8.81678i	−0.479314	+	0.348242i	−0.801060	−	0.598584i	$-0.795730\pi$
$641$	−12.1353	+	8.81678i	−0.479314	+	0.348242i	0.321746	+	0.946826i	$0.395730\pi$
$642$		0			0
$643$	−15.1418	−	46.6018i	−0.597136	−	1.83779i	−0.543795	−	0.839218i	$-0.683013\pi$
$643$	−15.1418	−	46.6018i	−0.597136	−	1.83779i	−0.0533404	−	0.998576i	$-0.516987\pi$
$644$	−1.85410	−	5.70634i	−0.0730619	−	0.224861i
$645$	−19.4164	−	14.1068i	−0.764520	−	0.555457i
$646$		0			0
$647$	−10.1976	+	31.3849i	−0.400907	+	1.23387i	0.523357	+	0.852114i	$0.324679\pi$
$647$	−10.1976	+	31.3849i	−0.400907	+	1.23387i	−0.924264	+	0.381753i	$0.875321\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	1.54508	−	4.75528i	0.0605567	−	0.186374i
$652$	32.3607	−	23.5114i	1.26734	−	0.920778i
$653$	−31.5517	−	22.9236i	−1.23471	−	0.897071i	−0.237478	−	0.971393i	$-0.576321\pi$
$653$	−31.5517	−	22.9236i	−1.23471	−	0.897071i	−0.997234	+	0.0743222i	$0.976321\pi$
$654$		0			0
$655$	−5.56231	−	17.1190i	−0.217337	−	0.668895i
$656$	−19.4164	−	14.1068i	−0.758083	−	0.550780i
$657$	3.23607	−	2.35114i	0.126251	−	0.0917267i
$658$		0			0
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	−49.0000			−1.90588			−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−49.0000			−1.90588			−0.952940	+	0.303160i	$0.901958\pi$
$662$		0			0
$663$	−19.4164	+	14.1068i	−0.754071	+	0.547865i
$664$		0			0
$665$	1.85410	+	5.70634i	0.0718990	+	0.221282i
$666$		0			0
$667$	14.5623	+	10.5801i	0.563855	+	0.409664i
$668$	9.70820	−	7.05342i	0.375622	−	0.272905i
$669$	−5.87132	+	18.0701i	−0.226998	+	0.698629i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−8.65248	+	26.6296i	−0.333528	+	1.02649i	0.633914	+	0.773404i	$0.281447\pi$
$673$	−8.65248	+	26.6296i	−0.333528	+	1.02649i	−0.967442	+	0.253091i	$0.918553\pi$
$674$		0			0
$675$	16.1803	+	11.7557i	0.622782	+	0.452477i
$676$	−1.85410	−	5.70634i	−0.0713116	−	0.219475i
$677$	−5.56231	−	17.1190i	−0.213777	−	0.657937i	−0.999238	−	0.0390266i	$-0.987574\pi$
$677$	−5.56231	−	17.1190i	−0.213777	−	0.657937i	0.785461	−	0.618911i	$-0.212426\pi$
$678$		0			0
$679$	0.809017	−	0.587785i	0.0310472	−	0.0225571i
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	2.47214	−	7.60845i	0.0945245	−	0.290916i
$685$	7.28115	−	5.29007i	0.278199	−	0.202123i
$686$		0			0
$687$	1.54508	+	4.75528i	0.0589487	+	0.181425i
$688$	9.88854	+	30.4338i	0.376997	+	1.16028i
$689$	−19.4164	−	14.1068i	−0.739706	−	0.537428i
$690$		0			0
$691$	10.8156	−	33.2870i	0.411445	−	1.26630i	−0.503948	−	0.863734i	$-0.668120\pi$
$691$	10.8156	−	33.2870i	0.411445	−	1.26630i	0.915393	−	0.402562i	$-0.131880\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.9787	−	39.9444i	0.492311	−	1.51518i
$696$		0			0
$697$	29.1246	+	21.1603i	1.10317	+	0.801502i
$698$		0			0
$699$	1.85410	+	5.70634i	0.0701286	+	0.215834i
$700$	6.47214	+	4.70228i	0.244624	+	0.177730i
$701$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$701$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$702$		0			0
$703$	22.0000			0.829746
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.70820	−	7.05342i	0.365115	−	0.265271i
$708$	−14.5623	−	10.5801i	−0.547285	−	0.397626i
$709$	−0.309017	−	0.951057i	−0.0116054	−	0.0357177i	0.945086	−	0.326821i	$-0.105978\pi$
$709$	−0.309017	−	0.951057i	−0.0116054	−	0.0357177i	−0.956692	+	0.291104i	$0.905978\pi$
$710$		0			0
$711$	−16.1803	−	11.7557i	−0.606810	−	0.440873i
$712$		0			0
$713$	4.63525	−	14.2658i	0.173592	−	0.534260i
$714$		0			0
$715$		0			0
$716$	30.0000			1.12115
$717$	−3.70820	+	11.4127i	−0.138485	+	0.426214i
$718$		0			0
$719$	31.5517	+	22.9236i	1.17668	+	0.854907i	0.991793	−	0.127853i	$-0.0408086\pi$
$719$	31.5517	+	22.9236i	1.17668	+	0.854907i	0.184885	+	0.982760i	$0.440809\pi$
$720$	−7.41641	−	22.8254i	−0.276393	−	0.850651i
$721$	−1.23607	−	3.80423i	−0.0460336	−	0.141677i
$722$		0			0
$723$	22.6525	−	16.4580i	0.842455	−	0.612079i
$724$	4.32624	−	13.3148i	0.160783	−	0.494840i
$725$	−24.0000			−0.891338
$726$		0			0
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$		0			0
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$		0			0
$731$	−14.8328	−	45.6507i	−0.548612	−	1.68845i
$732$	6.18034	+	19.0211i	0.228432	+	0.703041i
$733$	3.23607	+	2.35114i	0.119527	+	0.0868414i	0.645943	−	0.763386i	$-0.276464\pi$
$733$	3.23607	+	2.35114i	0.119527	+	0.0868414i	−0.526416	+	0.850227i	$0.676464\pi$
$734$		0			0
$735$	0.927051	−	2.85317i	0.0341948	−	0.105241i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−10.5066	+	32.3359i	−0.386491	+	1.18950i	0.548902	+	0.835886i	$0.315046\pi$
$739$	−10.5066	+	32.3359i	−0.386491	+	1.18950i	−0.935393	+	0.353610i	$0.884954\pi$
$740$	53.3951	−	38.7938i	1.96284	−	1.42609i
$741$	6.47214	+	4.70228i	0.237760	+	0.172743i
$742$		0			0
$743$	7.41641	+	22.8254i	0.272082	+	0.837381i	0.989977	+	0.141230i	$0.0451057\pi$
$743$	7.41641	+	22.8254i	0.272082	+	0.837381i	−0.717895	+	0.696151i	$0.754894\pi$
$744$		0			0
$745$	14.5623	−	10.5801i	0.533522	−	0.387626i
$746$		0			0
$747$	−24.0000			−0.878114
$748$		0			0
$749$	6.00000			0.219235
$750$		0			0
$751$	25.0795	−	18.2213i	0.915165	−	0.664906i	−0.0271509	−	0.999631i	$-0.508643\pi$
$751$	25.0795	−	18.2213i	0.915165	−	0.664906i	0.942316	+	0.334725i	$0.108643\pi$
$752$		0			0
$753$	−2.78115	−	8.55951i	−0.101351	−	0.311926i
$754$		0			0
$755$	24.2705	+	17.6336i	0.883294	+	0.641751i
$756$	−8.09017	+	5.87785i	−0.294237	+	0.213775i
$757$	11.7426	−	36.1401i	0.426794	−	1.31354i	−0.474473	−	0.880270i	$-0.657361\pi$
$757$	11.7426	−	36.1401i	0.426794	−	1.31354i	0.901266	−	0.433266i	$-0.142639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.8328	−	45.6507i	0.537689	−	1.65484i	−0.200077	−	0.979780i	$-0.564119\pi$
$761$	14.8328	−	45.6507i	0.537689	−	1.65484i	0.737766	−	0.675057i	$-0.235881\pi$
$762$		0			0
$763$	−16.1803	−	11.7557i	−0.585768	−	0.425585i
$764$	16.6869	+	51.3571i	0.603711	+	1.85803i
$765$	11.1246	+	34.2380i	0.402211	+	1.23788i
$766$		0			0
$767$	−29.1246	+	21.1603i	−1.05163	+	0.764053i
$768$	4.94427	−	15.2169i	0.178411	−	0.549093i
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	−8.65248	+	26.6296i	−0.311409	+	0.958420i
$773$	4.85410	−	3.52671i	0.174590	−	0.126847i	−0.497059	−	0.867717i	$-0.665587\pi$
$773$	4.85410	−	3.52671i	0.174590	−	0.126847i	0.671648	+	0.740870i	$0.265587\pi$
$774$		0			0
$775$	6.18034	+	19.0211i	0.222004	+	0.683259i
$776$		0			0
$777$	−8.89919	−	6.46564i	−0.319257	−	0.231953i
$778$		0			0
$779$	3.70820	−	11.4127i	0.132860	−	0.408902i
$780$	24.0000			0.859338
$781$		0			0
$782$		0			0
$783$	9.27051	−	28.5317i	0.331301	−	1.01964i
$784$	−3.23607	+	2.35114i	−0.115574	+	0.0839693i
$785$	31.5517	+	22.9236i	1.12613	+	0.818179i
$786$		0			0
$787$	15.4508	+	47.5528i	0.550763	+	1.69508i	0.706877	+	0.707336i	$0.250103\pi$
$787$	15.4508	+	47.5528i	0.550763	+	1.69508i	−0.156114	+	0.987739i	$0.549897\pi$
$788$	29.1246	+	21.1603i	1.03752	+	0.753803i
$789$	24.2705	−	17.6336i	0.864053	−	0.627771i
$790$		0			0
$791$	−3.00000			−0.106668
$792$		0			0
$793$	40.0000			1.42044
$794$		0			0
$795$	14.5623	−	10.5801i	0.516472	−	0.375239i
$796$	−25.8885	−	18.8091i	−0.917595	−	0.666672i
$797$	−6.48936	−	19.9722i	−0.229865	−	0.707451i	−0.997761	−	0.0668771i	$-0.978696\pi$
$797$	−6.48936	−	19.9722i	−0.229865	−	0.707451i	0.767896	−	0.640574i	$-0.221304\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	1.85410	−	5.70634i	0.0655115	−	0.201624i
$802$		0			0
$803$		0			0
$804$	−10.0000			−0.352673
$805$	2.78115	−	8.55951i	0.0980228	−	0.301683i
$806$		0			0
$807$	−24.2705	−	17.6336i	−0.854362	−	0.620731i
$808$		0			0
$809$	9.27051	+	28.5317i	0.325934	+	1.00312i	0.971017	+	0.239009i	$0.0768225\pi$
$809$	9.27051	+	28.5317i	0.325934	+	1.00312i	−0.645084	+	0.764112i	$0.723177\pi$
$810$		0			0
$811$	−1.61803	+	1.17557i	−0.0568169	+	0.0412799i	−0.615831	−	0.787878i	$-0.711180\pi$
$811$	−1.61803	+	1.17557i	−0.0568169	+	0.0412799i	0.559014	+	0.829158i	$0.311180\pi$
$812$	3.70820	−	11.4127i	0.130132	−	0.400506i
$813$	−16.0000			−0.561144
$814$		0			0
$815$	60.0000			2.10171
$816$	−7.41641	+	22.8254i	−0.259626	+	0.799047i
$817$	−12.9443	+	9.40456i	−0.452863	+	0.329024i
$818$		0			0
$819$	2.47214	+	7.60845i	0.0863834	+	0.265861i
$820$	−11.1246	−	34.2380i	−0.388488	−	1.19564i
$821$	−14.5623	−	10.5801i	−0.508228	−	0.369249i	0.303923	−	0.952697i	$-0.401703\pi$
$821$	−14.5623	−	10.5801i	−0.508228	−	0.369249i	−0.812151	+	0.583447i	$0.801703\pi$
$822$		0			0
$823$	7.10739	−	21.8743i	0.247748	−	0.762490i	−0.747424	−	0.664347i	$-0.768710\pi$
$823$	7.10739	−	21.8743i	0.247748	−	0.762490i	0.995172	−	0.0981431i	$-0.0312903\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.1246	−	34.2380i	0.386841	−	1.19057i	−0.548296	−	0.836285i	$-0.684723\pi$
$827$	11.1246	−	34.2380i	0.386841	−	1.19057i	0.935136	−	0.354288i	$-0.115277\pi$
$828$	−9.70820	+	7.05342i	−0.337383	+	0.245123i
$829$	20.2254	+	14.6946i	0.702458	+	0.510366i	0.880732	−	0.473615i	$-0.157051\pi$
$829$	20.2254	+	14.6946i	0.702458	+	0.510366i	−0.178274	+	0.983981i	$0.557051\pi$
$830$		0			0
$831$	2.47214	+	7.60845i	0.0857574	+	0.263934i
$832$	−25.8885	−	18.8091i	−0.897524	−	0.652089i
$833$	4.85410	−	3.52671i	0.168185	−	0.122193i
$834$		0			0
$835$	18.0000			0.622916
$836$		0			0
$837$	−25.0000			−0.864126
$838$		0			0
$839$	12.1353	−	8.81678i	0.418956	−	0.304389i	−0.358262	−	0.933621i	$-0.616631\pi$
$839$	12.1353	−	8.81678i	0.418956	−	0.304389i	0.777217	+	0.629232i	$0.216631\pi$
$840$		0			0
$841$	2.16312	+	6.65740i	0.0745903	+	0.229565i
$842$		0			0
$843$	−9.70820	−	7.05342i	−0.334368	−	0.242933i
$844$	22.6525	−	16.4580i	0.779730	−	0.566507i
$845$	2.78115	−	8.55951i	0.0956746	−	0.294456i
$846$		0			0
$847$		0			0
$848$	−24.0000			−0.824163
$849$	9.88854	−	30.4338i	0.339374	−	1.04449i
$850$		0			0
$851$	−26.6976	−	19.3969i	−0.915181	−	0.664918i
$852$	−5.56231	−	17.1190i	−0.190561	−	0.586488i
$853$	−3.09017	−	9.51057i	−0.105805	−	0.325636i	0.884113	−	0.467273i	$-0.154763\pi$
$853$	−3.09017	−	9.51057i	−0.105805	−	0.325636i	−0.989919	+	0.141637i	$0.954763\pi$
$854$		0			0
$855$	9.70820	−	7.05342i	0.332014	−	0.241222i
$856$		0			0
$857$	−12.0000			−0.409912			−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$		0			0
$859$	−13.0000			−0.443554			−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000			−0.443554			−0.221777	+	0.975097i	$0.571186\pi$
$860$	−14.8328	+	45.6507i	−0.505795	+	1.55668i
$861$	−4.85410	+	3.52671i	−0.165427	+	0.120190i
$862$		0			0
$863$	−3.70820	−	11.4127i	−0.126229	−	0.388492i	0.867894	−	0.496749i	$-0.165473\pi$
$863$	−3.70820	−	11.4127i	−0.126229	−	0.388492i	−0.994123	+	0.108257i	$0.965473\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	5.87132	−	18.0701i	0.199401	−	0.613692i
$868$	−10.0000			−0.339422
$869$		0			0
$870$		0			0
$871$	−6.18034	+	19.0211i	−0.209413	+	0.644506i
$872$		0			0
$873$	−1.61803	−	1.17557i	−0.0547622	−	0.0397870i
$874$		0			0
$875$	−0.927051	−	2.85317i	−0.0313400	−	0.0964547i
$876$	3.23607	+	2.35114i	0.109337	+	0.0794377i
$877$	17.7984	−	12.9313i	0.601008	−	0.436658i	−0.245228	−	0.969465i	$-0.578863\pi$
$877$	17.7984	−	12.9313i	0.601008	−	0.436658i	0.846237	+	0.532807i	$0.178863\pi$
$878$		0			0
$879$	−30.0000			−1.01187
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$		0			0
$883$	−16.1803	+	11.7557i	−0.544512	+	0.395611i	−0.825758	−	0.564025i	$-0.809252\pi$
$883$	−16.1803	+	11.7557i	−0.544512	+	0.395611i	0.281246	+	0.959636i	$0.409252\pi$
$884$	38.8328	+	28.2137i	1.30609	+	0.948929i
$885$	−8.34346	−	25.6785i	−0.280462	−	0.863174i
$886$		0			0
$887$	33.9787	+	24.6870i	1.14089	+	0.828908i	0.987244	−	0.159218i	$-0.0508972\pi$
$887$	33.9787	+	24.6870i	1.14089	+	0.828908i	0.153650	+	0.988125i	$0.450897\pi$
$888$		0			0
$889$	0.618034	−	1.90211i	0.0207282	−	0.0637948i
$890$		0			0
$891$		0			0
$892$	38.0000			1.27233
$893$		0			0
$894$		0			0
$895$	36.4058	+	26.4503i	1.21691	+	0.884137i
$896$		0			0
$897$	−3.70820	−	11.4127i	−0.123813	−	0.381058i
$898$		0			0
$899$	24.2705	−	17.6336i	0.809467	−	0.588112i
$900$	4.94427	−	15.2169i	0.164809	−	0.507230i
$901$	36.0000			1.19933
$902$		0			0
$903$	8.00000			0.266223
$904$		0			0
$905$	16.9894	−	12.3435i	0.564745	−	0.410312i
$906$		0			0
$907$	2.47214	+	7.60845i	0.0820859	+	0.252635i	0.983674	−	0.179962i	$-0.0575975\pi$
$907$	2.47214	+	7.60845i	0.0820859	+	0.252635i	−0.901588	+	0.432597i	$0.857597\pi$
$908$	7.41641	+	22.8254i	0.246122	+	0.757486i
$909$	−19.4164	−	14.1068i	−0.644002	−	0.467895i
$910$		0			0
$911$	14.8328	−	45.6507i	0.491433	−	1.51248i	−0.331009	−	0.943627i	$-0.607389\pi$
$911$	14.8328	−	45.6507i	0.491433	−	1.51248i	0.822443	−	0.568848i	$-0.192611\pi$
$912$	8.00000			0.264906
$913$		0			0
$914$		0			0
$915$	−9.27051	+	28.5317i	−0.306474	+	0.943229i
$916$	8.09017	−	5.87785i	0.267307	−	0.194210i
$917$	4.85410	+	3.52671i	0.160297	+	0.116462i
$918$		0			0
$919$	−4.94427	−	15.2169i	−0.163096	−	0.501959i	0.835794	−	0.549042i	$-0.185007\pi$
$919$	−4.94427	−	15.2169i	−0.163096	−	0.501959i	−0.998891	+	0.0470830i	$0.985007\pi$
$920$		0			0
$921$	−16.1803	+	11.7557i	−0.533160	+	0.387364i
$922$		0			0
$923$	−36.0000			−1.18495
$924$		0			0
$925$	44.0000			1.44671
$926$		0			0
$927$	−6.47214	+	4.70228i	−0.212573	+	0.154443i
$928$		0			0
$929$	5.56231	+	17.1190i	0.182493	+	0.561657i	0.999896	−	0.0144098i	$-0.00458693\pi$
$929$	5.56231	+	17.1190i	0.182493	+	0.561657i	−0.817403	+	0.576066i	$0.804587\pi$
$930$		0			0
$931$	−1.61803	−	1.17557i	−0.0530289	−	0.0385278i
$932$	9.70820	−	7.05342i	0.318003	−	0.231043i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	6.18034	−	19.0211i	0.201903	−	0.621393i	−0.797923	−	0.602759i	$-0.794068\pi$
$937$	6.18034	−	19.0211i	0.201903	−	0.621393i	0.999826	−	0.0186345i	$-0.00593188\pi$
$938$		0			0
$939$	15.3713	+	11.1679i	0.501624	+	0.364451i
$940$		0			0
$941$	5.56231	+	17.1190i	0.181326	+	0.558064i	0.999866	−	0.0163859i	$-0.00521602\pi$
$941$	5.56231	+	17.1190i	0.181326	+	0.558064i	−0.818540	+	0.574450i	$0.805216\pi$
$942$		0			0
$943$	−14.5623	+	10.5801i	−0.474214	+	0.344537i
$944$	−11.1246	+	34.2380i	−0.362075	+	1.11435i
$945$	−15.0000			−0.487950
$946$		0			0
$947$	−27.0000			−0.877382			−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000			−0.877382			−0.438691	+	0.898638i	$0.644558\pi$
$948$	6.18034	−	19.0211i	0.200728	−	0.617778i
$949$	6.47214	−	4.70228i	0.210094	−	0.152643i
$950$		0			0
$951$	2.78115	+	8.55951i	0.0901851	+	0.277561i
$952$		0			0
$953$	29.1246	+	21.1603i	0.943439	+	0.685448i	0.949246	−	0.314535i	$-0.101849\pi$
$953$	29.1246	+	21.1603i	0.943439	+	0.685448i	−0.00580723	+	0.999983i	$0.501849\pi$
$954$		0			0
$955$	−25.0304	+	77.0356i	−0.809964	+	2.49281i
$956$	24.0000			0.776215
$957$		0			0
$958$		0			0
$959$	−0.927051	+	2.85317i	−0.0299360	+	0.0921337i
$960$	19.4164	−	14.1068i	0.626662	−	0.455296i
$961$	4.85410	+	3.52671i	0.156584	+	0.113765i
$962$		0			0
$963$	−3.70820	−	11.4127i	−0.119495	−	0.367768i
$964$	−45.3050	−	32.9160i	−1.45917	−	1.06015i
$965$	−33.9787	+	24.6870i	−1.09381	+	0.794702i
$966$		0			0
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$		0			0
$969$	−12.0000			−0.385496
$970$		0			0
$971$	31.5517	−	22.9236i	1.01254	−	0.735654i	0.0478005	−	0.998857i	$-0.484779\pi$
$971$	31.5517	−	22.9236i	1.01254	−	0.735654i	0.964741	+	0.263203i	$0.0847788\pi$
$972$	25.8885	+	18.8091i	0.830375	+	0.603303i
$973$	4.32624	+	13.3148i	0.138693	+	0.426853i
$974$		0			0
$975$	12.9443	+	9.40456i	0.414548	+	0.301187i
$976$	32.3607	−	23.5114i	1.03584	−	0.752582i
$977$	2.78115	−	8.55951i	0.0889770	−	0.273843i	−0.896660	−	0.442719i	$-0.854014\pi$
$977$	2.78115	−	8.55951i	0.0889770	−	0.273843i	0.985637	+	0.168876i	$0.0540138\pi$
$978$		0			0
$979$		0			0
$980$	−6.00000			−0.191663
$981$	−12.3607	+	38.0423i	−0.394646	+	1.21460i
$982$		0			0
$983$	−26.6976	−	19.3969i	−0.851520	−	0.618665i	0.0740448	−	0.997255i	$-0.476409\pi$
$983$	−26.6976	−	19.3969i	−0.851520	−	0.618665i	−0.925565	+	0.378589i	$0.876409\pi$
$984$		0			0
$985$	16.6869	+	51.3571i	0.531689	+	1.63637i
$986$		0			0
$987$		0			0
$988$	4.94427	−	15.2169i	0.157298	−	0.484114i
$989$	24.0000			0.763156
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	0.809017	−	0.587785i	0.0256734	−	0.0186528i
$994$		0			0
$995$	−14.8328	−	45.6507i	−0.470232	−	1.44722i
$996$	−7.41641	−	22.8254i	−0.234998	−	0.723249i
$997$	22.6525	+	16.4580i	0.717411	+	0.521230i	0.885556	−	0.464533i	$-0.153778\pi$
$997$	22.6525	+	16.4580i	0.717411	+	0.521230i	−0.168145	+	0.985762i	$0.553778\pi$
$998$		0			0
$999$	−16.9959	+	52.3081i	−0.537728	+	1.65496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.f.372.1		4
11.2	odd	10		847.2.f.g.729.1		4
11.3	even	5	inner	847.2.f.f.323.1		4
11.4	even	5		77.2.a.b.1.1	✓	1
11.5	even	5	inner	847.2.f.f.148.1		4
11.6	odd	10		847.2.f.g.148.1		4
11.7	odd	10		847.2.a.c.1.1		1
11.8	odd	10		847.2.f.g.323.1		4
11.9	even	5	inner	847.2.f.f.729.1		4
11.10	odd	2		847.2.f.g.372.1		4
33.26	odd	10		693.2.a.b.1.1		1
33.29	even	10		7623.2.a.i.1.1		1
44.15	odd	10		1232.2.a.d.1.1		1
55.4	even	10		1925.2.a.f.1.1		1
55.37	odd	20		1925.2.b.g.1849.1		2
55.48	odd	20		1925.2.b.g.1849.2		2
77.4	even	15		539.2.e.d.177.1		2
77.26	odd	30		539.2.e.e.67.1		2
77.37	even	15		539.2.e.d.67.1		2
77.48	odd	10		539.2.a.b.1.1		1
77.59	odd	30		539.2.e.e.177.1		2
77.62	even	10		5929.2.a.d.1.1		1
88.37	even	10		4928.2.a.i.1.1		1
88.59	odd	10		4928.2.a.x.1.1		1
231.125	even	10		4851.2.a.k.1.1		1
308.279	even	10		8624.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.b.1.1	✓	1	11.4	even	5
539.2.a.b.1.1		1	77.48	odd	10
539.2.e.d.67.1		2	77.37	even	15
539.2.e.d.177.1		2	77.4	even	15
539.2.e.e.67.1		2	77.26	odd	30
539.2.e.e.177.1		2	77.59	odd	30
693.2.a.b.1.1		1	33.26	odd	10
847.2.a.c.1.1		1	11.7	odd	10
847.2.f.f.148.1		4	11.5	even	5	inner
847.2.f.f.323.1		4	11.3	even	5	inner
847.2.f.f.372.1		4	1.1	even	1	trivial
847.2.f.f.729.1		4	11.9	even	5	inner
847.2.f.g.148.1		4	11.6	odd	10
847.2.f.g.323.1		4	11.8	odd	10
847.2.f.g.372.1		4	11.10	odd	2
847.2.f.g.729.1		4	11.2	odd	10
1232.2.a.d.1.1		1	44.15	odd	10
1925.2.a.f.1.1		1	55.4	even	10
1925.2.b.g.1849.1		2	55.37	odd	20
1925.2.b.g.1849.2		2	55.48	odd	20
4851.2.a.k.1.1		1	231.125	even	10
4928.2.a.i.1.1		1	88.37	even	10
4928.2.a.x.1.1		1	88.59	odd	10
5929.2.a.d.1.1		1	77.62	even	10
7623.2.a.i.1.1		1	33.29	even	10
8624.2.a.s.1.1		1	308.279	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(1.61803 + 1.17557i) q^{4} +(0.927051 + 2.85317i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} +(1.61803 + 1.17557i) q^{4} +(0.927051 + 2.85317i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.618034 + 1.90211i) q^{9} -2.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(-2.42705 - 1.76336i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-1.85410 - 5.70634i) q^{17} +(-1.61803 + 1.17557i) q^{19} +(-1.85410 + 5.70634i) q^{20} +1.00000 q^{21} +3.00000 q^{23} +(-3.23607 + 2.35114i) q^{25} +(-1.54508 - 4.75528i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(4.85410 + 3.52671i) q^{29} +(1.54508 - 4.75528i) q^{31} +(0.927051 - 2.85317i) q^{35} +(-3.23607 + 2.35114i) q^{36} +(-8.89919 - 6.46564i) q^{37} +(-1.23607 - 3.80423i) q^{39} +(-4.85410 + 3.52671i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(-3.23607 - 2.35114i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.85410 + 3.52671i) q^{51} +(-6.47214 + 4.70228i) q^{52} +(-1.85410 + 5.70634i) q^{53} +(0.618034 - 1.90211i) q^{57} +(7.28115 + 5.29007i) q^{59} +(-1.85410 - 5.70634i) q^{60} +(-3.09017 - 9.51057i) q^{61} +(1.61803 - 1.17557i) q^{63} +(-2.47214 + 7.60845i) q^{64} -12.0000 q^{65} +5.00000 q^{67} +(3.70820 - 11.4127i) q^{68} +(-2.42705 + 1.76336i) q^{69} +(2.78115 + 8.55951i) q^{71} +(-1.61803 - 1.17557i) q^{73} +(1.23607 - 3.80423i) q^{75} -4.00000 q^{76} +(-3.09017 + 9.51057i) q^{79} +(-9.70820 + 7.05342i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.70820 + 11.4127i) q^{83} +(1.61803 + 1.17557i) q^{84} +(14.5623 - 10.5801i) q^{85} -6.00000 q^{87} -3.00000 q^{89} +(3.23607 - 2.35114i) q^{91} +(4.85410 + 3.52671i) q^{92} +(1.54508 + 4.75528i) q^{93} +(-4.85410 - 3.52671i) q^{95} +(-0.309017 + 0.951057i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9	\( 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9} - 8 q^{12} + 4 q^{13} - 3 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{19} + 6 q^{20} + 4 q^{21} + 12 q^{23} - 4 q^{25} + 5 q^{27} + 2 q^{28} + 6 q^{29} - 5 q^{31} - 3 q^{35} - 4 q^{36} - 11 q^{37} + 4 q^{39} - 6 q^{41} + 32 q^{43} - 24 q^{45} - 4 q^{48} - q^{49} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 2 q^{57} + 9 q^{59} + 6 q^{60} + 10 q^{61} + 2 q^{63} + 8 q^{64} - 48 q^{65} + 20 q^{67} - 12 q^{68} - 3 q^{69} - 9 q^{71} - 2 q^{73} - 4 q^{75} - 16 q^{76} + 10 q^{79} - 12 q^{80} - q^{81} - 12 q^{83} + 2 q^{84} + 18 q^{85} - 24 q^{87} - 12 q^{89} + 4 q^{91} + 6 q^{92} - 5 q^{93} - 6 q^{95} + q^{97}+O(q^{100}) \) 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9 - 8 * q^12 + 4 * q^13 - 3 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^19 + 6 * q^20 + 4 * q^21 + 12 * q^23 - 4 * q^25 + 5 * q^27 + 2 * q^28 + 6 * q^29 - 5 * q^31 - 3 * q^35 - 4 * q^36 - 11 * q^37 + 4 * q^39 - 6 * q^41 + 32 * q^43 - 24 * q^45 - 4 * q^48 - q^49 + 6 * q^51 - 8 * q^52 + 6 * q^53 - 2 * q^57 + 9 * q^59 + 6 * q^60 + 10 * q^61 + 2 * q^63 + 8 * q^64 - 48 * q^65 + 20 * q^67 - 12 * q^68 - 3 * q^69 - 9 * q^71 - 2 * q^73 - 4 * q^75 - 16 * q^76 + 10 * q^79 - 12 * q^80 - q^81 - 12 * q^83 + 2 * q^84 + 18 * q^85 - 24 * q^87 - 12 * q^89 + 4 * q^91 + 6 * q^92 - 5 * q^93 - 6 * q^95 + q^97

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