LMFDB - Embedded newform 1638.2.m.i.1621.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.1
Root			$1.33821 + 2.31784i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.i.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.651388 - 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.651388 - 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +(-0.651388 - 1.12824i) q^{10} +(1.05939 + 1.83493i) q^{11} +(0.0315412 - 3.60541i) q^{13} +(-2.36323 + 1.18960i) q^{14} +1.00000 q^{16} +0.486762 q^{17} +(3.13815 - 5.43544i) q^{19} +(-0.651388 - 1.12824i) q^{20} +(1.05939 + 1.83493i) q^{22} +4.78954 q^{23} +(1.65139 - 2.86029i) q^{25} +(0.0315412 - 3.60541i) q^{26} +(-2.36323 + 1.18960i) q^{28} +(-1.74338 + 3.01962i) q^{29} +(2.24338 - 3.88565i) q^{31} +1.00000 q^{32} +0.486762 q^{34} +(2.88153 + 1.89139i) q^{35} -1.15751 q^{37} +(3.13815 - 5.43544i) q^{38} +(-0.651388 - 1.12824i) q^{40} +(6.31845 - 10.9439i) q^{41} +(-4.01356 - 6.95169i) q^{43} +(1.05939 + 1.83493i) q^{44} +4.78954 q^{46} +(3.98570 + 6.90344i) q^{47} +(4.16969 - 5.62260i) q^{49} +(1.65139 - 2.86029i) q^{50} +(0.0315412 - 3.60541i) q^{52} +(-4.29060 + 7.43153i) q^{53} +(1.38015 - 2.39050i) q^{55} +(-2.36323 + 1.18960i) q^{56} +(-1.74338 + 3.01962i) q^{58} +9.15014 q^{59} +(5.09231 - 8.82015i) q^{61} +(2.24338 - 3.88565i) q^{62} +1.00000 q^{64} +(-4.08831 + 2.31294i) q^{65} +(1.67924 + 2.90853i) q^{67} +0.486762 q^{68} +(2.88153 + 1.89139i) q^{70} +(-1.46740 - 2.54161i) q^{71} +(-8.09337 + 14.0181i) q^{73} -1.15751 q^{74} +(3.13815 - 5.43544i) q^{76} +(-4.68642 - 3.07609i) q^{77} +(-7.16738 - 12.4143i) q^{79} +(-0.651388 - 1.12824i) q^{80} +(6.31845 - 10.9439i) q^{82} -3.48676 q^{83} +(-0.317071 - 0.549183i) q^{85} +(-4.01356 - 6.95169i) q^{86} +(1.05939 + 1.83493i) q^{88} -9.39720 q^{89} +(4.21447 + 8.55793i) q^{91} +4.78954 q^{92} +(3.98570 + 6.90344i) q^{94} -8.17661 q^{95} +(0.698602 + 1.21001i) q^{97} +(4.16969 - 5.62260i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8} + 2 q^{10} + 2 q^{11} + 7 q^{13} + 3 q^{14} + 8 q^{16} - 12 q^{17} + 2 q^{19} + 2 q^{20} + 2 q^{22} + 8 q^{23} + 6 q^{25} + 7 q^{26} + 3 q^{28} - 6 q^{29} + 10 q^{31} + 8 q^{32} - 12 q^{34} - 8 q^{35} + 24 q^{37} + 2 q^{38} + 2 q^{40} + 6 q^{41} - 4 q^{43} + 2 q^{44} + 8 q^{46} + 17 q^{47} + 17 q^{49} + 6 q^{50} + 7 q^{52} - 3 q^{53} + 25 q^{55} + 3 q^{56} - 6 q^{58} - 4 q^{61} + 10 q^{62} + 8 q^{64} - 12 q^{65} - 7 q^{67} - 12 q^{68} - 8 q^{70} - 6 q^{71} - 19 q^{73} + 24 q^{74} + 2 q^{76} + 10 q^{77} + 24 q^{79} + 2 q^{80} + 6 q^{82} - 12 q^{83} - 3 q^{85} - 4 q^{86} + 2 q^{88} - 14 q^{89} + 40 q^{91} + 8 q^{92} + 17 q^{94} - 24 q^{95} - 25 q^{97} + 17 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8 + 2 * q^10 + 2 * q^11 + 7 * q^13 + 3 * q^14 + 8 * q^16 - 12 * q^17 + 2 * q^19 + 2 * q^20 + 2 * q^22 + 8 * q^23 + 6 * q^25 + 7 * q^26 + 3 * q^28 - 6 * q^29 + 10 * q^31 + 8 * q^32 - 12 * q^34 - 8 * q^35 + 24 * q^37 + 2 * q^38 + 2 * q^40 + 6 * q^41 - 4 * q^43 + 2 * q^44 + 8 * q^46 + 17 * q^47 + 17 * q^49 + 6 * q^50 + 7 * q^52 - 3 * q^53 + 25 * q^55 + 3 * q^56 - 6 * q^58 - 4 * q^61 + 10 * q^62 + 8 * q^64 - 12 * q^65 - 7 * q^67 - 12 * q^68 - 8 * q^70 - 6 * q^71 - 19 * q^73 + 24 * q^74 + 2 * q^76 + 10 * q^77 + 24 * q^79 + 2 * q^80 + 6 * q^82 - 12 * q^83 - 3 * q^85 - 4 * q^86 + 2 * q^88 - 14 * q^89 + 40 * q^91 + 8 * q^92 + 17 * q^94 - 24 * q^95 - 25 * q^97 + 17 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.651388	−	1.12824i	−0.291309	−	0.504563i	0.682810	−	0.730596i	$-0.260758\pi$
$5$	−0.651388	−	1.12824i	−0.291309	−	0.504563i	−0.974120	+	0.226033i	$0.927424\pi$
$6$		0			0
$7$	−2.36323	+	1.18960i	−0.893216	+	0.449628i
$7$	−2.36323	+	1.18960i	−0.893216	+	0.449628i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.651388	−	1.12824i	−0.205987	−	0.356780i
$11$	1.05939	+	1.83493i	0.319419	+	0.553251i	0.980367	−	0.197181i	$-0.0631788\pi$
$11$	1.05939	+	1.83493i	0.319419	+	0.553251i	−0.660948	+	0.750432i	$0.729845\pi$
$12$		0			0
$13$	0.0315412	−	3.60541i	0.00874794	−	0.999962i
$13$	0.0315412	−	3.60541i	0.00874794	−	0.999962i
$14$	−2.36323	+	1.18960i	−0.631599	+	0.317935i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.486762			0.118057			0.0590286	−	0.998256i	$-0.481200\pi$
$17$	0.486762			0.118057			0.0590286	+	0.998256i	$0.481200\pi$
$18$		0			0
$19$	3.13815	−	5.43544i	0.719941	−	1.24697i	−0.241082	−	0.970505i	$-0.577502\pi$
$19$	3.13815	−	5.43544i	0.719941	−	1.24697i	0.961023	−	0.276470i	$-0.0891645\pi$
$20$	−0.651388	−	1.12824i	−0.145655	−	0.252281i
$21$		0			0
$22$	1.05939	+	1.83493i	0.225864	+	0.391207i
$23$	4.78954			0.998688			0.499344	−	0.866404i	$-0.333574\pi$
$23$	4.78954			0.998688			0.499344	+	0.866404i	$0.333574\pi$
$24$		0			0
$25$	1.65139	−	2.86029i	0.330278	−	0.572058i
$26$	0.0315412	−	3.60541i	0.00618573	−	0.707080i
$27$		0			0
$28$	−2.36323	+	1.18960i	−0.446608	+	0.224814i
$29$	−1.74338	+	3.01962i	−0.323738	+	0.560730i	−0.981256	−	0.192708i	$-0.938273\pi$
$29$	−1.74338	+	3.01962i	−0.323738	+	0.560730i	0.657518	+	0.753439i	$0.271606\pi$
$30$		0			0
$31$	2.24338	−	3.88565i	0.402923	−	0.697883i	−0.591154	−	0.806559i	$-0.701328\pi$
$31$	2.24338	−	3.88565i	0.402923	−	0.697883i	0.994077	+	0.108675i	$0.0346609\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	0.486762			0.0834790
$35$	2.88153	+	1.89139i	0.487068	+	0.319703i
$36$		0			0
$37$	−1.15751			−0.190294			−0.0951468	−	0.995463i	$-0.530332\pi$
$37$	−1.15751			−0.190294			−0.0951468	+	0.995463i	$0.530332\pi$
$38$	3.13815	−	5.43544i	0.509075	−	0.881744i
$39$		0			0
$40$	−0.651388	−	1.12824i	−0.102993	−	0.178390i
$41$	6.31845	−	10.9439i	0.986776	−	1.70915i	0.353014	−	0.935618i	$-0.385157\pi$
$41$	6.31845	−	10.9439i	0.986776	−	1.70915i	0.633762	−	0.773528i	$-0.281510\pi$
$42$		0			0
$43$	−4.01356	−	6.95169i	−0.612062	−	1.06012i	−0.990892	−	0.134656i	$-0.957007\pi$
$43$	−4.01356	−	6.95169i	−0.612062	−	1.06012i	0.378831	−	0.925466i	$-0.376326\pi$
$44$	1.05939	+	1.83493i	0.159710	+	0.276625i
$45$		0			0
$46$	4.78954			0.706179
$47$	3.98570	+	6.90344i	0.581375	+	1.00697i	0.995317	+	0.0966674i	$0.0308183\pi$
$47$	3.98570	+	6.90344i	0.581375	+	1.00697i	−0.413942	+	0.910303i	$0.635848\pi$
$48$		0			0
$49$	4.16969	−	5.62260i	0.595670	−	0.803229i
$50$	1.65139	−	2.86029i	0.233542	−	0.404506i
$51$		0			0
$52$	0.0315412	−	3.60541i	0.00437397	−	0.499981i
$53$	−4.29060	+	7.43153i	−0.589359	+	1.02080i	0.404958	+	0.914335i	$0.367286\pi$
$53$	−4.29060	+	7.43153i	−0.589359	+	1.02080i	−0.994317	+	0.106464i	$0.966047\pi$
$54$		0			0
$55$	1.38015	−	2.39050i	0.186100	−	0.322334i
$56$	−2.36323	+	1.18960i	−0.315800	+	0.158967i
$57$		0			0
$58$	−1.74338	+	3.01962i	−0.228917	+	0.396496i
$59$	9.15014			1.19125			0.595623	−	0.803264i	$-0.296905\pi$
$59$	9.15014			1.19125			0.595623	+	0.803264i	$0.296905\pi$
$60$		0			0
$61$	5.09231	−	8.82015i	0.652004	−	1.12930i	−0.330632	−	0.943760i	$-0.607262\pi$
$61$	5.09231	−	8.82015i	0.652004	−	1.12930i	0.982636	−	0.185544i	$-0.0594048\pi$
$62$	2.24338	−	3.88565i	0.284910	−	0.493478i
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.08831	+	2.31294i	−0.507092	+	0.286884i
$66$		0			0
$67$	1.67924	+	2.90853i	0.205152	+	0.355334i	0.950181	−	0.311698i	$-0.100898\pi$
$67$	1.67924	+	2.90853i	0.205152	+	0.355334i	−0.745029	+	0.667032i	$0.767564\pi$
$68$	0.486762			0.0590286
$69$		0			0
$70$	2.88153	+	1.89139i	0.344409	+	0.226064i
$71$	−1.46740	−	2.54161i	−0.174148	−	0.301634i	0.765718	−	0.643177i	$-0.222384\pi$
$71$	−1.46740	−	2.54161i	−0.174148	−	0.301634i	−0.939866	+	0.341543i	$0.889051\pi$
$72$		0			0
$73$	−8.09337	+	14.0181i	−0.947257	+	1.64070i	−0.196090	+	0.980586i	$0.562825\pi$
$73$	−8.09337	+	14.0181i	−0.947257	+	1.64070i	−0.751167	+	0.660112i	$0.770509\pi$
$74$	−1.15751			−0.134558
$75$		0			0
$76$	3.13815	−	5.43544i	0.359971	−	0.623487i
$77$	−4.68642	−	3.07609i	−0.534067	−	0.350553i
$78$		0			0
$79$	−7.16738	−	12.4143i	−0.806393	−	1.39671i	−0.915346	−	0.402667i	$-0.868083\pi$
$79$	−7.16738	−	12.4143i	−0.806393	−	1.39671i	0.108953	−	0.994047i	$-0.465250\pi$
$80$	−0.651388	−	1.12824i	−0.0728274	−	0.126141i
$81$		0			0
$82$	6.31845	−	10.9439i	0.697756	−	1.20855i
$83$	−3.48676			−0.382722			−0.191361	−	0.981520i	$-0.561290\pi$
$83$	−3.48676			−0.382722			−0.191361	+	0.981520i	$0.561290\pi$
$84$		0			0
$85$	−0.317071	−	0.549183i	−0.0343912	−	0.0595673i
$86$	−4.01356	−	6.95169i	−0.432793	−	0.749620i
$87$		0			0
$88$	1.05939	+	1.83493i	0.112932	+	0.195604i
$89$	−9.39720			−0.996102			−0.498051	−	0.867148i	$-0.665951\pi$
$89$	−9.39720			−0.996102			−0.498051	+	0.867148i	$0.665951\pi$
$90$		0			0
$91$	4.21447	+	8.55793i	0.441797	+	0.897115i
$92$	4.78954			0.499344
$93$		0			0
$94$	3.98570	+	6.90344i	0.411094	+	0.712036i
$95$	−8.17661			−0.838903
$96$		0			0
$97$	0.698602	+	1.21001i	0.0709323	+	0.122858i	0.899310	−	0.437311i	$-0.144069\pi$
$97$	0.698602	+	1.21001i	0.0709323	+	0.122858i	−0.828378	+	0.560170i	$0.810736\pi$
$98$	4.16969	−	5.62260i	0.421202	−	0.567969i
$99$		0			0
$100$	1.65139	−	2.86029i	0.165139	−	0.286029i
$101$	−3.01725	−	5.22602i	−0.300227	−	0.520009i	0.675960	−	0.736938i	$-0.263729\pi$
$101$	−3.01725	−	5.22602i	−0.300227	−	0.520009i	−0.976187	+	0.216930i	$0.930396\pi$
$102$		0			0
$103$	5.64770	+	9.78210i	0.556484	+	0.963859i	0.997786	+	0.0665006i	$0.0211834\pi$
$103$	5.64770	+	9.78210i	0.556484	+	0.963859i	−0.441302	+	0.897359i	$0.645483\pi$
$104$	0.0315412	−	3.60541i	0.00309287	−	0.353540i
$105$		0			0
$106$	−4.29060	+	7.43153i	−0.416739	+	0.721814i
$107$	14.0292			1.35626			0.678128	−	0.734943i	$-0.262791\pi$
$107$	14.0292			1.35626			0.678128	+	0.734943i	$0.262791\pi$
$108$		0			0
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$	1.38015	−	2.39050i	0.131592	−	0.227925i
$111$		0			0
$112$	−2.36323	+	1.18960i	−0.223304	+	0.112407i
$113$	−3.56552	−	6.17566i	−0.335416	−	0.580957i	0.648149	−	0.761514i	$-0.275543\pi$
$113$	−3.56552	−	6.17566i	−0.335416	−	0.580957i	−0.983565	+	0.180557i	$0.942210\pi$
$114$		0			0
$115$	−3.11985	−	5.40373i	−0.290927	−	0.503901i
$116$	−1.74338	+	3.01962i	−0.161869	+	0.280365i
$117$		0			0
$118$	9.15014			0.842338
$119$	−1.15033	+	0.579054i	−0.105451	+	0.0530818i
$120$		0			0
$121$	3.25537	−	5.63846i	0.295942	−	0.512587i
$122$	5.09231	−	8.82015i	0.461036	−	0.798538i
$123$		0			0
$124$	2.24338	−	3.88565i	0.201462	−	0.348942i
$125$	−10.8167			−0.967471
$126$		0			0
$127$	2.59305	−	4.49130i	0.230096	−	0.398538i	−0.727740	−	0.685853i	$-0.759429\pi$
$127$	2.59305	−	4.49130i	0.230096	−	0.398538i	0.957836	+	0.287315i	$0.0927626\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−4.08831	+	2.31294i	−0.358568	+	0.202858i
$131$	−4.03186	−	6.98339i	−0.352265	−	0.610142i	0.634381	−	0.773021i	$-0.281255\pi$
$131$	−4.03186	−	6.98339i	−0.352265	−	0.610142i	−0.986646	+	0.162879i	$0.947922\pi$
$132$		0			0
$133$	−0.950155	+	16.5783i	−0.0823889	+	1.43752i
$134$	1.67924	+	2.90853i	0.145064	+	0.251259i
$135$		0			0
$136$	0.486762			0.0417395
$137$	6.79165			0.580250			0.290125	−	0.956989i	$-0.406303\pi$
$137$	6.79165			0.580250			0.290125	+	0.956989i	$0.406303\pi$
$138$		0			0
$139$	6.45522	+	11.1808i	0.547525	+	0.948341i	0.998443	+	0.0557755i	$0.0177631\pi$
$139$	6.45522	+	11.1808i	0.547525	+	0.948341i	−0.450919	+	0.892565i	$0.648904\pi$
$140$	2.88153	+	1.89139i	0.243534	+	0.159851i
$141$		0			0
$142$	−1.46740	−	2.54161i	−0.123142	−	0.213287i
$143$	6.64908	−	3.76168i	0.556024	−	0.314567i
$144$		0			0
$145$	4.54247			0.377232
$146$	−8.09337	+	14.0181i	−0.669812	+	1.16015i
$147$		0			0
$148$	−1.15751			−0.0951468
$149$	−11.6820	+	20.2338i	−0.957026	+	1.65762i	−0.227365	+	0.973810i	$0.573011\pi$
$149$	−11.6820	+	20.2338i	−0.957026	+	1.65762i	−0.729661	+	0.683809i	$0.760322\pi$
$150$		0			0
$151$	−2.93692	+	5.08689i	−0.239003	+	0.413965i	−0.960428	−	0.278527i	$-0.910154\pi$
$151$	−2.93692	+	5.08689i	−0.239003	+	0.413965i	0.721425	+	0.692492i	$0.243487\pi$
$152$	3.13815	−	5.43544i	0.254538	−	0.440872i
$153$		0			0
$154$	−4.68642	−	3.07609i	−0.377643	−	0.247878i
$155$	−5.84524			−0.469501
$156$		0			0
$157$	−3.12248	+	5.40829i	−0.249201	+	0.431628i	−0.963304	−	0.268412i	$-0.913501\pi$
$157$	−3.12248	+	5.40829i	−0.249201	+	0.431628i	0.714104	+	0.700040i	$0.246835\pi$
$158$	−7.16738	−	12.4143i	−0.570206	−	0.987626i
$159$		0			0
$160$	−0.651388	−	1.12824i	−0.0514967	−	0.0891950i
$161$	−11.3188	+	5.69765i	−0.892044	+	0.449037i
$162$		0			0
$163$	1.30383	−	2.25831i	0.102124	−	0.176884i	−0.810435	−	0.585828i	$-0.800769\pi$
$163$	1.30383	−	2.25831i	0.102124	−	0.176884i	0.912560	+	0.408944i	$0.134103\pi$
$164$	6.31845	−	10.9439i	0.493388	−	0.854573i
$165$		0			0
$166$	−3.48676			−0.270625
$167$	3.45416	−	5.98279i	0.267291	−	0.462962i	−0.700870	−	0.713289i	$-0.747205\pi$
$167$	3.45416	−	5.98279i	0.267291	−	0.462962i	0.968161	+	0.250327i	$0.0805381\pi$
$168$		0			0
$169$	−12.9980	−	0.227438i	−0.999847	−	0.0174952i
$170$	−0.317071	−	0.549183i	−0.0243182	−	0.0421204i
$171$		0			0
$172$	−4.01356	−	6.95169i	−0.306031	−	0.530061i
$173$	−3.86355	+	6.69186i	−0.293740	+	0.508773i	−0.974691	−	0.223556i	$-0.928233\pi$
$173$	−3.86355	+	6.69186i	−0.293740	+	0.508773i	0.680951	+	0.732329i	$0.261567\pi$
$174$		0			0
$175$	−0.500000	+	8.72401i	−0.0377964	+	0.659473i
$176$	1.05939	+	1.83493i	0.0798549	+	0.138313i
$177$		0			0
$178$	−9.39720			−0.704350
$179$	9.57539	+	16.5851i	0.715698	+	1.23963i	0.962690	+	0.270608i	$0.0872247\pi$
$179$	9.57539	+	16.5851i	0.715698	+	1.23963i	−0.246992	+	0.969018i	$0.579442\pi$
$180$		0			0
$181$	13.0972			0.973506			0.486753	−	0.873540i	$-0.338181\pi$
$181$	13.0972			0.973506			0.486753	+	0.873540i	$0.338181\pi$
$182$	4.21447	+	8.55793i	0.312397	+	0.634356i
$183$		0			0
$184$	4.78954			0.353089
$185$	0.753989	+	1.30595i	0.0554344	+	0.0960151i
$186$		0			0
$187$	0.515673	+	0.893172i	0.0377098	+	0.0653152i
$188$	3.98570	+	6.90344i	0.290687	+	0.503485i
$189$		0			0
$190$	−8.17661			−0.593194
$191$	−5.74444	+	9.94966i	−0.415653	+	0.719932i	−0.995497	−	0.0947956i	$-0.969780\pi$
$191$	−5.74444	+	9.94966i	−0.415653	+	0.719932i	0.579844	+	0.814728i	$0.303114\pi$
$192$		0			0
$193$	0.138150	+	0.239283i	0.00994426	+	0.0172240i	0.870955	−	0.491363i	$-0.163501\pi$
$193$	0.138150	+	0.239283i	0.00994426	+	0.0172240i	−0.861010	+	0.508587i	$0.830168\pi$
$194$	0.698602	+	1.21001i	0.0501567	+	0.0868740i
$195$		0			0
$196$	4.16969	−	5.62260i	0.297835	−	0.401615i
$197$	6.63552	−	11.4931i	0.472761	−	0.818846i	−0.526753	−	0.850019i	$-0.676591\pi$
$197$	6.63552	−	11.4931i	0.472761	−	0.818846i	0.999514	+	0.0311721i	$0.00992398\pi$
$198$		0			0
$199$	19.0219			1.34842			0.674212	−	0.738538i	$-0.264483\pi$
$199$	19.0219			1.34842			0.674212	+	0.738538i	$0.264483\pi$
$200$	1.65139	−	2.86029i	0.116771	−	0.202253i
$201$		0			0
$202$	−3.01725	−	5.22602i	−0.212293	−	0.367702i
$203$	0.527853	−	9.20999i	0.0370480	−	0.646415i
$204$		0			0
$205$	−16.4630			−1.14983
$206$	5.64770	+	9.78210i	0.393494	+	0.681551i
$207$		0			0
$208$	0.0315412	−	3.60541i	0.00218699	−	0.249990i
$209$	13.2982			0.919853
$210$		0			0
$211$	−1.98750	+	3.44245i	−0.136825	+	0.236988i	−0.926293	−	0.376804i	$-0.877023\pi$
$211$	−1.98750	+	3.44245i	−0.136825	+	0.236988i	0.789468	+	0.613792i	$0.210357\pi$
$212$	−4.29060	+	7.43153i	−0.294679	+	0.510400i
$213$		0			0
$214$	14.0292			0.959019
$215$	−5.22877	+	9.05649i	−0.356599	+	0.617647i
$216$		0			0
$217$	−0.679241	+	11.8514i	−0.0461099	+	0.804526i
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$		0			0
$220$	1.38015	−	2.39050i	0.0930499	−	0.161167i
$221$	0.0153530	−	1.75498i	0.00103276	−	0.118053i
$222$		0			0
$223$	9.58013	−	16.5933i	0.641533	−	1.11117i	−0.343557	−	0.939132i	$-0.611632\pi$
$223$	9.58013	−	16.5933i	0.641533	−	1.11117i	0.985091	−	0.172036i	$-0.0550347\pi$
$224$	−2.36323	+	1.18960i	−0.157900	+	0.0794837i
$225$		0			0
$226$	−3.56552	−	6.17566i	−0.237175	−	0.410799i
$227$	1.18251			0.0784861			0.0392430	−	0.999230i	$-0.487505\pi$
$227$	1.18251			0.0784861			0.0392430	+	0.999230i	$0.487505\pi$
$228$		0			0
$229$	7.51599	+	13.0181i	0.496671	+	0.860259i	0.999993	−	0.00383994i	$-0.00122229\pi$
$229$	7.51599	+	13.0181i	0.496671	+	0.860259i	−0.503322	+	0.864099i	$0.667889\pi$
$230$	−3.11985	−	5.40373i	−0.205717	−	0.356312i
$231$		0			0
$232$	−1.74338	+	3.01962i	−0.114459	+	0.198248i
$233$	2.59706	+	4.49824i	0.170139	+	0.294689i	0.938468	−	0.345365i	$-0.112245\pi$
$233$	2.59706	+	4.49824i	0.170139	+	0.294689i	−0.768329	+	0.640055i	$0.778912\pi$
$234$		0			0
$235$	5.19248	−	8.99364i	0.338720	−	0.586680i
$236$	9.15014			0.595623
$237$		0			0
$238$	−1.15033	+	0.579054i	−0.0745648	+	0.0375345i
$239$	−25.3978			−1.64285			−0.821425	−	0.570317i	$-0.806821\pi$
$239$	−25.3978			−1.64285			−0.821425	+	0.570317i	$0.806821\pi$
$240$		0			0
$241$	−11.8575			−0.763808			−0.381904	−	0.924202i	$-0.624732\pi$
$241$	−11.8575			−0.763808			−0.381904	+	0.924202i	$0.624732\pi$
$242$	3.25537	−	5.63846i	0.209263	−	0.362454i
$243$		0			0
$244$	5.09231	−	8.82015i	0.326002	−	0.564652i
$245$	−9.05971	−	1.04190i	−0.578804	−	0.0665648i
$246$		0			0
$247$	−19.4980	−	11.4858i	−1.24063	−	0.730822i
$248$	2.24338	−	3.88565i	0.142455	−	0.246739i
$249$		0			0
$250$	−10.8167			−0.684105
$251$	−10.7397	−	18.6017i	−0.677883	−	1.17413i	−0.975617	−	0.219480i	$-0.929564\pi$
$251$	−10.7397	−	18.6017i	−0.677883	−	1.17413i	0.297734	−	0.954649i	$-0.403769\pi$
$252$		0			0
$253$	5.07401	+	8.78844i	0.319000	+	0.552525i
$254$	2.59305	−	4.49130i	0.162702	−	0.281809i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.84589			0.427035			0.213517	−	0.976939i	$-0.431508\pi$
$257$	6.84589			0.427035			0.213517	+	0.976939i	$0.431508\pi$
$258$		0			0
$259$	2.73546	−	1.37698i	0.169973	−	0.0855613i
$260$	−4.08831	+	2.31294i	−0.253546	+	0.143442i
$261$		0			0
$262$	−4.03186	−	6.98339i	−0.249089	−	0.431435i
$263$	7.69998	+	13.3368i	0.474801	+	0.822380i	0.999584	−	0.0288567i	$-0.00918666\pi$
$263$	7.69998	+	13.3368i	0.474801	+	0.822380i	−0.524782	+	0.851236i	$0.675853\pi$
$264$		0			0
$265$	11.1794			0.686743
$266$	−0.950155	+	16.5783i	−0.0582578	+	1.01648i
$267$		0			0
$268$	1.67924	+	2.90853i	0.102576	+	0.177667i
$269$	11.7313			0.715272			0.357636	−	0.933861i	$-0.383583\pi$
$269$	11.7313			0.715272			0.357636	+	0.933861i	$0.383583\pi$
$270$		0			0
$271$	−26.0856			−1.58459			−0.792293	−	0.610141i	$-0.791113\pi$
$271$	−26.0856			−1.58459			−0.792293	+	0.610141i	$0.791113\pi$
$272$	0.486762			0.0295143
$273$		0			0
$274$	6.79165			0.410299
$275$	6.99788			0.421988
$276$		0			0
$277$	23.4307			1.40781			0.703906	−	0.710293i	$-0.251438\pi$
$277$	23.4307			1.40781			0.703906	+	0.710293i	$0.251438\pi$
$278$	6.45522	+	11.1808i	0.387158	+	0.670578i
$279$		0			0
$280$	2.88153	+	1.89139i	0.172204	+	0.113032i
$281$	−6.15751			−0.367326			−0.183663	−	0.982989i	$-0.558796\pi$
$281$	−6.15751			−0.367326			−0.183663	+	0.982989i	$0.558796\pi$
$282$		0			0
$283$	−10.9661	−	18.9939i	−0.651870	−	1.12907i	−0.982669	−	0.185370i	$-0.940651\pi$
$283$	−10.9661	−	18.9939i	−0.651870	−	1.12907i	0.330799	−	0.943701i	$-0.392682\pi$
$284$	−1.46740	−	2.54161i	−0.0870742	−	0.150817i
$285$		0			0
$286$	6.64908	−	3.76168i	0.393168	−	0.222433i
$287$	−1.91307	+	33.3793i	−0.112925	+	1.97032i
$288$		0			0
$289$	−16.7631			−0.986062
$290$	4.54247			0.266743
$291$		0			0
$292$	−8.09337	+	14.0181i	−0.473629	+	0.820349i
$293$	8.74075	+	15.1394i	0.510640	+	0.884455i	0.999924	+	0.0123300i	$0.00392488\pi$
$293$	8.74075	+	15.1394i	0.510640	+	0.884455i	−0.489284	+	0.872125i	$0.662742\pi$
$294$		0			0
$295$	−5.96029	−	10.3235i	−0.347021	−	0.601059i
$296$	−1.15751			−0.0672790
$297$		0			0
$298$	−11.6820	+	20.2338i	−0.676720	+	1.17211i
$299$	0.151068	−	17.2683i	0.00873646	−	0.998649i
$300$		0			0
$301$	17.7547	+	11.6539i	1.02336	+	0.671718i
$302$	−2.93692	+	5.08689i	−0.169001	+	0.292718i
$303$		0			0
$304$	3.13815	−	5.43544i	0.179985	−	0.311744i
$305$	−13.2683			−0.759740
$306$		0			0
$307$	−12.0673			−0.688718			−0.344359	−	0.938838i	$-0.611904\pi$
$307$	−12.0673			−0.688718			−0.344359	+	0.938838i	$0.611904\pi$
$308$	−4.68642	−	3.07609i	−0.267034	−	0.175276i
$309$		0			0
$310$	−5.84524			−0.331988
$311$	−0.755881	+	1.30923i	−0.0428621	+	0.0742393i	−0.886661	−	0.462421i	$-0.846981\pi$
$311$	−0.755881	+	1.30923i	−0.0428621	+	0.0742393i	0.843798	+	0.536660i	$0.180314\pi$
$312$		0			0
$313$	−0.862908	−	1.49460i	−0.0487744	−	0.0844798i	0.840607	−	0.541645i	$-0.182198\pi$
$313$	−0.862908	−	1.49460i	−0.0487744	−	0.0844798i	−0.889382	+	0.457165i	$0.848865\pi$
$314$	−3.12248	+	5.40829i	−0.176212	+	0.305207i
$315$		0			0
$316$	−7.16738	−	12.4143i	−0.403197	−	0.698357i
$317$	10.6520	+	18.4499i	0.598278	+	1.03625i	0.993075	+	0.117479i	$0.0374813\pi$
$317$	10.6520	+	18.4499i	0.598278	+	1.03625i	−0.394798	+	0.918768i	$0.629185\pi$
$318$		0			0
$319$	−7.38771			−0.413633
$320$	−0.651388	−	1.12824i	−0.0364137	−	0.0630704i
$321$		0			0
$322$	−11.3188	+	5.69765i	−0.630770	+	0.317517i
$323$	1.52753	−	2.64576i	0.0849942	−	0.147214i
$324$		0			0
$325$	−10.2604	−	6.04415i	−0.569146	−	0.335269i
$326$	1.30383	−	2.25831i	0.0722126	−	0.125076i
$327$		0			0
$328$	6.31845	−	10.9439i	0.348878	−	0.604274i
$329$	−17.6315	−	11.5730i	−0.972055	−	0.638040i
$330$		0			0
$331$	−8.21691	+	14.2321i	−0.451642	+	0.782267i	−0.998488	−	0.0549662i	$-0.982495\pi$
$331$	−8.21691	+	14.2321i	−0.451642	+	0.782267i	0.546846	+	0.837233i	$0.315828\pi$
$332$	−3.48676			−0.191361
$333$		0			0
$334$	3.45416	−	5.98279i	0.189003	−	0.327364i
$335$	2.18767	−	3.78916i	0.119525	−	0.207024i
$336$		0			0
$337$	−12.9178			−0.703678			−0.351839	−	0.936060i	$-0.614444\pi$
$337$	−12.9178			−0.703678			−0.351839	+	0.936060i	$0.614444\pi$
$338$	−12.9980	−	0.227438i	−0.706999	−	0.0123710i
$339$		0			0
$340$	−0.317071	−	0.549183i	−0.0171956	−	0.0297836i
$341$	9.50650			0.514806
$342$		0			0
$343$	−3.16527	+	18.2478i	−0.170908	+	0.985287i
$344$	−4.01356	−	6.95169i	−0.216397	−	0.374810i
$345$		0			0
$346$	−3.86355	+	6.69186i	−0.207706	+	0.359757i
$347$	16.0387			0.861004			0.430502	−	0.902590i	$-0.358337\pi$
$347$	16.0387			0.861004			0.430502	+	0.902590i	$0.358337\pi$
$348$		0			0
$349$	−3.81951	+	6.61558i	−0.204453	+	0.354124i	−0.949958	−	0.312376i	$-0.898875\pi$
$349$	−3.81951	+	6.61558i	−0.204453	+	0.354124i	0.745505	+	0.666500i	$0.232208\pi$
$350$	−0.500000	+	8.72401i	−0.0267261	+	0.466318i
$351$		0			0
$352$	1.05939	+	1.83493i	0.0564659	+	0.0978018i
$353$	−16.1956	−	28.0515i	−0.862002	−	1.49303i	−0.869993	−	0.493064i	$-0.835877\pi$
$353$	−16.1956	−	28.0515i	−0.862002	−	1.49303i	0.00799069	−	0.999968i	$-0.497456\pi$
$354$		0			0
$355$	−1.91169	+	3.31115i	−0.101462	+	0.175738i
$356$	−9.39720			−0.498051
$357$		0			0
$358$	9.57539	+	16.5851i	0.506075	+	0.876548i
$359$	−1.57507	−	2.72810i	−0.0831289	−	0.143983i	0.821463	−	0.570261i	$-0.193158\pi$
$359$	−1.57507	−	2.72810i	−0.0831289	−	0.143983i	−0.904592	+	0.426278i	$0.859825\pi$
$360$		0			0
$361$	−10.1960	−	17.6599i	−0.536630	−	0.929471i
$362$	13.0972			0.688373
$363$		0			0
$364$	4.21447	+	8.55793i	0.220898	+	0.448558i
$365$	21.0877			1.10378
$366$		0			0
$367$	2.23463	+	3.87049i	0.116647	+	0.202038i	0.918437	−	0.395568i	$-0.129452\pi$
$367$	2.23463	+	3.87049i	0.116647	+	0.202038i	−0.801790	+	0.597606i	$0.796119\pi$
$368$	4.78954			0.249672
$369$		0			0
$370$	0.753989	+	1.30595i	0.0391980	+	0.0678929i
$371$	1.29909	−	22.6665i	0.0674453	−	1.17679i
$372$		0			0
$373$	−2.47615	+	4.28883i	−0.128210	+	0.222067i	−0.922983	−	0.384840i	$-0.874257\pi$
$373$	−2.47615	+	4.28883i	−0.128210	+	0.222067i	0.794773	+	0.606907i	$0.207590\pi$
$374$	0.515673	+	0.893172i	0.0266648	+	0.0461848i
$375$		0			0
$376$	3.98570	+	6.90344i	0.205547	+	0.356018i
$377$	10.8320	+	6.38085i	0.557877	+	0.328631i
$378$		0			0
$379$	6.55920	−	11.3609i	0.336923	−	0.583569i	−0.646929	−	0.762550i	$-0.723947\pi$
$379$	6.55920	−	11.3609i	0.336923	−	0.583569i	0.983852	+	0.178982i	$0.0572803\pi$
$380$	−8.17661			−0.419451
$381$		0			0
$382$	−5.74444	+	9.94966i	−0.293911	+	0.509069i
$383$	−6.09000	+	10.5482i	−0.311185	+	0.538988i	−0.978619	−	0.205681i	$-0.934059\pi$
$383$	−6.09000	+	10.5482i	−0.311185	+	0.538988i	0.667434	+	0.744669i	$0.267392\pi$
$384$		0			0
$385$	−0.417877	+	7.29112i	−0.0212970	+	0.371590i
$386$	0.138150	+	0.239283i	0.00703165	+	0.0121792i
$387$		0			0
$388$	0.698602	+	1.21001i	0.0354662	+	0.0614292i
$389$	−3.34598	+	5.79541i	−0.169648	+	0.293839i	−0.938296	−	0.345833i	$-0.887596\pi$
$389$	−3.34598	+	5.79541i	−0.169648	+	0.293839i	0.768648	+	0.639672i	$0.220930\pi$
$390$		0			0
$391$	2.33137			0.117902
$392$	4.16969	−	5.62260i	0.210601	−	0.283984i
$393$		0			0
$394$	6.63552	−	11.4931i	0.334293	−	0.579012i
$395$	−9.33749	+	16.1730i	−0.469820	+	0.813752i
$396$		0			0
$397$	−12.2912	+	21.2890i	−0.616879	+	1.06847i	0.373172	+	0.927762i	$0.378270\pi$
$397$	−12.2912	+	21.2890i	−0.616879	+	1.06847i	−0.990052	+	0.140704i	$0.955063\pi$
$398$	19.0219			0.953479
$399$		0			0
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	−34.6545			−1.73056			−0.865282	−	0.501285i	$-0.832861\pi$
$401$	−34.6545			−1.73056			−0.865282	+	0.501285i	$0.832861\pi$
$402$		0			0
$403$	−13.9386	−	8.21087i	−0.694332	−	0.409013i
$404$	−3.01725	−	5.22602i	−0.150114	−	0.260004i
$405$		0			0
$406$	0.527853	−	9.20999i	0.0261969	−	0.457084i
$407$	−1.22626	−	2.12395i	−0.0607835	−	0.105280i
$408$		0			0
$409$	−23.9090			−1.18222			−0.591111	−	0.806590i	$-0.701311\pi$
$409$	−23.9090			−1.18222			−0.591111	+	0.806590i	$0.701311\pi$
$410$	−16.4630			−0.813052
$411$		0			0
$412$	5.64770	+	9.78210i	0.278242	+	0.481930i
$413$	−21.6239	+	10.8850i	−1.06404	+	0.535617i
$414$		0			0
$415$	2.27123	+	3.93389i	0.111491	+	0.193107i
$416$	0.0315412	−	3.60541i	0.00154643	−	0.176770i
$417$		0			0
$418$	13.2982			0.650434
$419$	6.09738	−	10.5610i	0.297876	−	0.515937i	−0.677773	−	0.735271i	$-0.737055\pi$
$419$	6.09738	−	10.5610i	0.297876	−	0.515937i	0.975650	+	0.219334i	$0.0703883\pi$
$420$		0			0
$421$	14.0504			0.684777			0.342388	−	0.939558i	$-0.388764\pi$
$421$	14.0504			0.684777			0.342388	+	0.939558i	$0.388764\pi$
$422$	−1.98750	+	3.44245i	−0.0967500	+	0.167576i
$423$		0			0
$424$	−4.29060	+	7.43153i	−0.208370	+	0.360907i
$425$	0.803833	−	1.39228i	0.0389916	−	0.0675355i
$426$		0			0
$427$	−1.54183	+	26.9018i	−0.0746143	+	1.30187i
$428$	14.0292			0.678128
$429$		0			0
$430$	−5.22877	+	9.05649i	−0.252153	+	0.436743i
$431$	8.65171	+	14.9852i	0.416738	+	0.721812i	0.995609	−	0.0936075i	$-0.0298399\pi$
$431$	8.65171	+	14.9852i	0.416738	+	0.721812i	−0.578871	+	0.815419i	$0.696507\pi$
$432$		0			0
$433$	10.1803	+	17.6328i	0.489234	+	0.847378i	0.999923	−	0.0123873i	$-0.00394309\pi$
$433$	10.1803	+	17.6328i	0.489234	+	0.847378i	−0.510689	+	0.859765i	$0.670610\pi$
$434$	−0.679241	+	11.8514i	−0.0326046	+	0.568886i
$435$		0			0
$436$	−5.50000	+	9.52628i	−0.263402	+	0.456226i
$437$	15.0303	−	26.0332i	0.718996	−	1.24534i
$438$		0			0
$439$	4.04398			0.193009			0.0965044	−	0.995333i	$-0.469234\pi$
$439$	4.04398			0.193009			0.0965044	+	0.995333i	$0.469234\pi$
$440$	1.38015	−	2.39050i	0.0657962	−	0.113962i
$441$		0			0
$442$	0.0153530	−	1.75498i	0.000730270	−	0.0834758i
$443$	−10.1092	−	17.5097i	−0.480304	−	0.831912i	0.519440	−	0.854507i	$-0.326140\pi$
$443$	−10.1092	−	17.5097i	−0.480304	−	0.831912i	−0.999745	+	0.0225951i	$0.992807\pi$
$444$		0			0
$445$	6.12122	+	10.6023i	0.290174	+	0.502596i
$446$	9.58013	−	16.5933i	0.453632	−	0.785714i
$447$		0			0
$448$	−2.36323	+	1.18960i	−0.111652	+	0.0562034i
$449$	19.8059	+	34.3047i	0.934696	+	1.61894i	0.775175	+	0.631746i	$0.217662\pi$
$449$	19.8059	+	34.3047i	0.934696	+	1.61894i	0.159521	+	0.987195i	$0.449005\pi$
$450$		0			0
$451$	26.7749			1.26078
$452$	−3.56552	−	6.17566i	−0.167708	−	0.290479i
$453$		0			0
$454$	1.18251			0.0554980
$455$	6.91012	−	10.3295i	0.323952	−	0.484252i
$456$		0			0
$457$	−6.64742			−0.310953			−0.155477	−	0.987840i	$-0.549691\pi$
$457$	−6.64742			−0.310953			−0.155477	+	0.987840i	$0.549691\pi$
$458$	7.51599	+	13.0181i	0.351199	+	0.608295i
$459$		0			0
$460$	−3.11985	−	5.40373i	−0.145464	−	0.251950i
$461$	10.2371	+	17.7311i	0.476788	+	0.825820i	0.999646	−	0.0265991i	$-0.00846777\pi$
$461$	10.2371	+	17.7311i	0.476788	+	0.825820i	−0.522859	+	0.852419i	$0.675134\pi$
$462$		0			0
$463$	17.2668			0.802457			0.401228	−	0.915978i	$-0.368583\pi$
$463$	17.2668			0.802457			0.401228	+	0.915978i	$0.368583\pi$
$464$	−1.74338	+	3.01962i	−0.0809344	+	0.140183i
$465$		0			0
$466$	2.59706	+	4.49824i	0.120306	+	0.208377i
$467$	−4.37922	−	7.58503i	−0.202646	−	0.350994i	0.746734	−	0.665123i	$-0.231621\pi$
$467$	−4.37922	−	7.58503i	−0.202646	−	0.350994i	−0.949380	+	0.314129i	$0.898287\pi$
$468$		0			0
$469$	−7.42843	−	4.87589i	−0.343013	−	0.225148i
$470$	5.19248	−	8.99364i	0.239511	−	0.414846i
$471$		0			0
$472$	9.15014			0.421169
$473$	8.50388	−	14.7292i	0.391009	−	0.677247i
$474$		0			0
$475$	−10.3646	−	17.9520i	−0.475561	−	0.823695i
$476$	−1.15033	+	0.579054i	−0.0527253	+	0.0265409i
$477$		0			0
$478$	−25.3978			−1.16167
$479$	−13.5126	−	23.4046i	−0.617408	−	1.06938i	−0.989957	−	0.141369i	$-0.954850\pi$
$479$	−13.5126	−	23.4046i	−0.617408	−	1.06938i	0.372549	−	0.928012i	$-0.378484\pi$
$480$		0			0
$481$	−0.0365092	+	4.17331i	−0.00166468	+	0.190286i
$482$	−11.8575			−0.540094
$483$		0			0
$484$	3.25537	−	5.63846i	0.147971	−	0.256294i
$485$	0.910122	−	1.57638i	0.0413265	−	0.0715796i
$486$		0			0
$487$	21.9435			0.994353			0.497177	−	0.867649i	$-0.334370\pi$
$487$	21.9435			0.994353			0.497177	+	0.867649i	$0.334370\pi$
$488$	5.09231	−	8.82015i	0.230518	−	0.399269i
$489$		0			0
$490$	−9.05971	−	1.04190i	−0.409276	−	0.0470684i
$491$	7.09020	−	12.2806i	0.319976	−	0.554215i	−0.660507	−	0.750820i	$-0.729658\pi$
$491$	7.09020	−	12.2806i	0.319976	−	0.554215i	0.980483	+	0.196605i	$0.0629918\pi$
$492$		0			0
$493$	−0.848612	+	1.46984i	−0.0382196	+	0.0661982i
$494$	−19.4980	−	11.4858i	−0.877257	−	0.516769i
$495$		0			0
$496$	2.24338	−	3.88565i	0.100731	−	0.174471i
$497$	6.49131	+	4.26079i	0.291175	+	0.191122i
$498$		0			0
$499$	14.7488	+	25.5456i	0.660245	+	1.14358i	0.980551	+	0.196264i	$0.0628811\pi$
$499$	14.7488	+	25.5456i	0.660245	+	1.14358i	−0.320306	+	0.947314i	$0.603786\pi$
$500$	−10.8167			−0.483735
$501$		0			0
$502$	−10.7397	−	18.6017i	−0.479336	−	0.830234i
$503$	7.49400	+	12.9800i	0.334141	+	0.578749i	0.983319	−	0.181887i	$-0.0582205\pi$
$503$	7.49400	+	12.9800i	0.334141	+	0.578749i	−0.649178	+	0.760636i	$0.724887\pi$
$504$		0			0
$505$	−3.93079	+	6.80834i	−0.174918	+	0.302967i
$506$	5.07401	+	8.78844i	0.225567	+	0.390694i
$507$		0			0
$508$	2.59305	−	4.49130i	0.115048	−	0.199269i
$509$	−41.9674			−1.86017			−0.930087	−	0.367340i	$-0.880269\pi$
$509$	−41.9674			−1.86017			−0.930087	+	0.367340i	$0.880269\pi$
$510$		0			0
$511$	2.45048	−	42.7559i	0.108403	−	1.89141i
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.84589			0.301959
$515$	7.35769	−	12.7439i	0.324218	−	0.561563i
$516$		0			0
$517$	−8.44487	+	14.6269i	−0.371405	+	0.643292i
$518$	2.73546	−	1.37698i	0.120189	−	0.0605010i
$519$		0			0
$520$	−4.08831	+	2.31294i	−0.179284	+	0.101429i
$521$	8.68748	−	15.0472i	0.380605	−	0.659228i	−0.610544	−	0.791983i	$-0.709049\pi$
$521$	8.68748	−	15.0472i	0.380605	−	0.659228i	0.991149	+	0.132755i	$0.0423823\pi$
$522$		0			0
$523$	33.0034			1.44314			0.721569	−	0.692343i	$-0.243421\pi$
$523$	33.0034			1.44314			0.721569	+	0.692343i	$0.243421\pi$
$524$	−4.03186	−	6.98339i	−0.176133	−	0.305071i
$525$		0			0
$526$	7.69998	+	13.3368i	0.335735	+	0.581510i
$527$	1.09199	−	1.89139i	0.0475680	−	0.0823902i
$528$		0			0
$529$	−0.0603265			−0.00262289
$530$	11.1794			0.485601
$531$		0			0
$532$	−0.950155	+	16.5783i	−0.0411945	+	0.718761i
$533$	−39.2579	−	23.1258i	−1.70045	−	1.00169i
$534$		0			0
$535$	−9.13847	−	15.8283i	−0.395091	−	0.684317i
$536$	1.67924	+	2.90853i	0.0725322	+	0.125629i
$537$		0			0
$538$	11.7313			0.505773
$539$	14.7344	+	1.69452i	0.634656	+	0.0729879i
$540$		0			0
$541$	−8.93967	−	15.4840i	−0.384347	−	0.665708i	0.607332	−	0.794448i	$-0.292240\pi$
$541$	−8.93967	−	15.4840i	−0.384347	−	0.665708i	−0.991678	+	0.128741i	$0.958907\pi$
$542$	−26.0856			−1.12047
$543$		0			0
$544$	0.486762			0.0208698
$545$	14.3305			0.613853
$546$		0			0
$547$	11.4550			0.489782			0.244891	−	0.969551i	$-0.421248\pi$
$547$	11.4550			0.489782			0.244891	+	0.969551i	$0.421248\pi$
$548$	6.79165			0.290125
$549$		0			0
$550$	6.99788			0.298391
$551$	10.9420	+	18.9521i	0.466144	+	0.807385i
$552$		0			0
$553$	31.7062	+	20.8114i	1.34828	+	0.884991i
$554$	23.4307			0.995474
$555$		0			0
$556$	6.45522	+	11.1808i	0.273762	+	0.474170i
$557$	20.3122	+	35.1817i	0.860654	+	1.49070i	0.871298	+	0.490754i	$0.163278\pi$
$557$	20.3122	+	35.1817i	0.860654	+	1.49070i	−0.0106442	+	0.999943i	$0.503388\pi$
$558$		0			0
$559$	−25.1903	+	14.2513i	−1.06544	+	0.602765i
$560$	2.88153	+	1.89139i	0.121767	+	0.0799257i
$561$		0			0
$562$	−6.15751			−0.259739
$563$	−33.1855			−1.39860			−0.699301	−	0.714827i	$-0.746505\pi$
$563$	−33.1855			−1.39860			−0.699301	+	0.714827i	$0.746505\pi$
$564$		0			0
$565$	−4.64507	+	8.04550i	−0.195420	+	0.338477i
$566$	−10.9661	−	18.9939i	−0.460942	−	0.798374i
$567$		0			0
$568$	−1.46740	−	2.54161i	−0.0615708	−	0.106644i
$569$	−0.0679534			−0.00284876			−0.00142438	−	0.999999i	$-0.500453\pi$
$569$	−0.0679534			−0.00284876			−0.00142438	+	0.999999i	$0.500453\pi$
$570$		0			0
$571$	−10.2822	+	17.8092i	−0.430295	+	0.745293i	−0.996899	−	0.0786977i	$-0.974924\pi$
$571$	−10.2822	+	17.8092i	−0.430295	+	0.745293i	0.566603	+	0.823991i	$0.308257\pi$
$572$	6.64908	−	3.76168i	0.278012	−	0.157284i
$573$		0			0
$574$	−1.91307	+	33.3793i	−0.0798501	+	1.39323i
$575$	7.90938	−	13.6995i	0.329844	−	0.571307i
$576$		0			0
$577$	22.7814	−	39.4586i	0.948403	−	1.64268i	0.199613	−	0.979875i	$-0.436031\pi$
$577$	22.7814	−	39.4586i	0.948403	−	1.64268i	0.748790	−	0.662808i	$-0.230635\pi$
$578$	−16.7631			−0.697251
$579$		0			0
$580$	4.54247			0.188616
$581$	8.24001	−	4.14786i	0.341853	−	0.172082i
$582$		0			0
$583$	−18.1817			−0.753010
$584$	−8.09337	+	14.0181i	−0.334906	+	0.580074i
$585$		0			0
$586$	8.74075	+	15.1394i	0.361077	+	0.625404i
$587$	−2.71527	+	4.70298i	−0.112071	+	0.194113i	−0.916605	−	0.399794i	$-0.869082\pi$
$587$	−2.71527	+	4.70298i	−0.112071	+	0.194113i	0.804534	+	0.593906i	$0.202415\pi$
$588$		0			0
$589$	−14.0801	−	24.3875i	−0.580162	−	1.00487i
$590$	−5.96029	−	10.3235i	−0.245381	−	0.425013i
$591$		0			0
$592$	−1.15751			−0.0475734
$593$	2.77524	+	4.80686i	0.113966	+	0.197394i	0.917366	−	0.398045i	$-0.130311\pi$
$593$	2.77524	+	4.80686i	0.113966	+	0.197394i	−0.803400	+	0.595439i	$0.796978\pi$
$594$		0			0
$595$	1.40262	+	0.920656i	0.0575018	+	0.0377432i
$596$	−11.6820	+	20.2338i	−0.478513	+	0.828809i
$597$		0			0
$598$	0.151068	−	17.2683i	0.00617761	−	0.706152i
$599$	7.94019	−	13.7528i	0.324427	−	0.561925i	−0.656969	−	0.753918i	$-0.728162\pi$
$599$	7.94019	−	13.7528i	0.324427	−	0.561925i	0.981396	+	0.191993i	$0.0614951\pi$
$600$		0			0
$601$	19.1239	−	33.1235i	0.780078	−	1.35114i	−0.151817	−	0.988409i	$-0.548513\pi$
$601$	19.1239	−	33.1235i	0.780078	−	1.35114i	0.931896	−	0.362727i	$-0.118154\pi$
$602$	17.7547	+	11.6539i	0.723627	+	0.474977i
$603$		0			0
$604$	−2.93692	+	5.08689i	−0.119501	+	0.206983i
$605$	−8.48202			−0.344843
$606$		0			0
$607$	9.66094	−	16.7332i	0.392125	−	0.679181i	−0.600604	−	0.799546i	$-0.705073\pi$
$607$	9.66094	−	16.7332i	0.392125	−	0.679181i	0.992730	+	0.120365i	$0.0384066\pi$
$608$	3.13815	−	5.43544i	0.127269	−	0.220436i
$609$		0			0
$610$	−13.2683			−0.537217
$611$	25.0155	−	14.1524i	1.01202	−	0.572544i
$612$		0			0
$613$	15.2625	+	26.4355i	0.616448	+	1.06772i	0.990129	+	0.140162i	$0.0447625\pi$
$613$	15.2625	+	26.4355i	0.616448	+	1.06772i	−0.373680	+	0.927558i	$0.621904\pi$
$614$	−12.0673			−0.486997
$615$		0			0
$616$	−4.68642	−	3.07609i	−0.188821	−	0.123939i
$617$	12.5446	+	21.7279i	0.505026	+	0.874731i	0.999983	+	0.00581322i	$0.00185042\pi$
$617$	12.5446	+	21.7279i	0.505026	+	0.874731i	−0.494957	+	0.868917i	$0.664816\pi$
$618$		0			0
$619$	9.35717	−	16.2071i	0.376096	−	0.651418i	−0.614394	−	0.788999i	$-0.710599\pi$
$619$	9.35717	−	16.2071i	0.376096	−	0.651418i	0.990490	+	0.137581i	$0.0439328\pi$
$620$	−5.84524			−0.234751
$621$		0			0
$622$	−0.755881	+	1.30923i	−0.0303081	+	0.0524951i
$623$	22.2077	−	11.1789i	0.889734	−	0.447875i
$624$		0			0
$625$	−1.21110	−	2.09769i	−0.0484441	−	0.0839076i
$626$	−0.862908	−	1.49460i	−0.0344887	−	0.0597362i
$627$		0			0
$628$	−3.12248	+	5.40829i	−0.124600	+	0.215814i
$629$	−0.563433			−0.0224655
$630$		0			0
$631$	−14.4362	−	25.0042i	−0.574695	−	0.995401i	−0.996075	−	0.0885169i	$-0.971787\pi$
$631$	−14.4362	−	25.0042i	−0.574695	−	0.995401i	0.421379	−	0.906884i	$-0.361546\pi$
$632$	−7.16738	−	12.4143i	−0.285103	−	0.493813i
$633$		0			0
$634$	10.6520	+	18.4499i	0.423046	+	0.732737i
$635$	−6.75633			−0.268117
$636$		0			0
$637$	−20.1403	−	15.2108i	−0.797988	−	0.602674i
$638$	−7.38771			−0.292482
$639$		0			0
$640$	−0.651388	−	1.12824i	−0.0257484	−	0.0445975i
$641$	−2.19822			−0.0868243			−0.0434121	−	0.999057i	$-0.513823\pi$
$641$	−2.19822			−0.0868243			−0.0434121	+	0.999057i	$0.513823\pi$
$642$		0			0
$643$	8.74713	+	15.1505i	0.344953	+	0.597476i	0.985345	−	0.170572i	$-0.0545615\pi$
$643$	8.74713	+	15.1505i	0.344953	+	0.597476i	−0.640392	+	0.768048i	$0.721228\pi$
$644$	−11.3188	+	5.69765i	−0.446022	+	0.224519i
$645$		0			0
$646$	1.52753	−	2.64576i	0.0601000	−	0.104096i
$647$	16.0868	+	27.8631i	0.632436	+	1.09541i	0.987052	+	0.160400i	$0.0512783\pi$
$647$	16.0868	+	27.8631i	0.632436	+	1.09541i	−0.354616	+	0.935012i	$0.615388\pi$
$648$		0			0
$649$	9.69360	+	16.7898i	0.380507	+	0.659058i
$650$	−10.2604	−	6.04415i	−0.402447	−	0.237071i
$651$		0			0
$652$	1.30383	−	2.25831i	0.0510621	−	0.0884421i
$653$	−47.5661			−1.86141			−0.930703	−	0.365775i	$-0.880804\pi$
$653$	−47.5661			−1.86141			−0.930703	+	0.365775i	$0.880804\pi$
$654$		0			0
$655$	−5.25261	+	9.09779i	−0.205236	+	0.355480i
$656$	6.31845	−	10.9439i	0.246694	−	0.427287i
$657$		0			0
$658$	−17.6315	−	11.5730i	−0.687347	−	0.451163i
$659$	3.69892	+	6.40672i	0.144090	+	0.249570i	0.929033	−	0.369997i	$-0.120641\pi$
$659$	3.69892	+	6.40672i	0.144090	+	0.249570i	−0.784943	+	0.619568i	$0.787308\pi$
$660$		0			0
$661$	−6.11485	−	10.5912i	−0.237840	−	0.411951i	0.722254	−	0.691628i	$-0.243106\pi$
$661$	−6.11485	−	10.5912i	−0.237840	−	0.411951i	−0.960094	+	0.279677i	$0.909773\pi$
$662$	−8.21691	+	14.2321i	−0.319359	+	0.553146i
$663$		0			0
$664$	−3.48676			−0.135313
$665$	19.3232	−	9.72692i	0.749321	−	0.377194i
$666$		0			0
$667$	−8.34999	+	14.4626i	−0.323313	+	0.559994i
$668$	3.45416	−	5.98279i	0.133646	−	0.231481i
$669$		0			0
$670$	2.18767	−	3.78916i	0.0845172	−	0.146388i
$671$	21.5791			0.833051
$672$		0			0
$673$	24.4511	−	42.3506i	0.942521	−	1.63249i	0.181882	−	0.983320i	$-0.441781\pi$
$673$	24.4511	−	42.3506i	0.942521	−	1.63249i	0.760640	−	0.649174i	$-0.224885\pi$
$674$	−12.9178			−0.497576
$675$		0			0
$676$	−12.9980	−	0.227438i	−0.499923	−	0.00874761i
$677$	9.74027	+	16.8707i	0.374349	+	0.648392i	0.990229	−	0.139448i	$-0.0445328\pi$
$677$	9.74027	+	16.8707i	0.374349	+	0.648392i	−0.615880	+	0.787840i	$0.711199\pi$
$678$		0			0
$679$	−3.09039	−	2.02848i	−0.118598	−	0.0778460i
$680$	−0.317071	−	0.549183i	−0.0121591	−	0.0210602i
$681$		0			0
$682$	9.50650			0.364023
$683$	18.1603			0.694883			0.347442	−	0.937702i	$-0.387050\pi$
$683$	18.1603			0.694883			0.347442	+	0.937702i	$0.387050\pi$
$684$		0			0
$685$	−4.42400	−	7.66259i	−0.169032	−	0.292773i
$686$	−3.16527	+	18.2478i	−0.120850	+	0.696703i
$687$		0			0
$688$	−4.01356	−	6.95169i	−0.153015	−	0.265031i
$689$	26.6584	+	15.7038i	1.01560	+	0.598266i
$690$		0			0
$691$	37.0049			1.40773			0.703866	−	0.710333i	$-0.251456\pi$
$691$	37.0049			1.40773			0.703866	+	0.710333i	$0.251456\pi$
$692$	−3.86355	+	6.69186i	−0.146870	+	0.254386i
$693$		0			0
$694$	16.0387			0.608822
$695$	8.40970	−	14.5660i	0.318998	−	0.552521i
$696$		0			0
$697$	3.07558	−	5.32707i	0.116496	−	0.201777i
$698$	−3.81951	+	6.61558i	−0.144570	+	0.250403i
$699$		0			0
$700$	−0.500000	+	8.72401i	−0.0188982	+	0.329736i
$701$	−36.3972			−1.37470			−0.687352	−	0.726325i	$-0.741227\pi$
$701$	−36.3972			−1.37470			−0.687352	+	0.726325i	$0.741227\pi$
$702$		0			0
$703$	−3.63244	+	6.29158i	−0.137000	+	0.237291i
$704$	1.05939	+	1.83493i	0.0399274	+	0.0691563i
$705$		0			0
$706$	−16.1956	−	28.0515i	−0.609528	−	1.05573i
$707$	13.3473	+	8.76096i	0.501978	+	0.329490i
$708$		0			0
$709$	0.165683	−	0.286972i	0.00622236	−	0.0107774i	−0.862897	−	0.505379i	$-0.831353\pi$
$709$	0.165683	−	0.286972i	0.00622236	−	0.0107774i	0.869120	+	0.494602i	$0.164686\pi$
$710$	−1.91169	+	3.31115i	−0.0717446	+	0.124265i
$711$		0			0
$712$	−9.39720			−0.352175
$713$	10.7448	−	18.6105i	0.402394	−	0.696968i
$714$		0			0
$715$	−8.57519	−	5.05142i	−0.320694	−	0.188912i
$716$	9.57539	+	16.5851i	0.357849	+	0.619813i
$717$		0			0
$718$	−1.57507	−	2.72810i	−0.0587810	−	0.101812i
$719$	23.7931	−	41.2108i	0.887333	−	1.53691i	0.0443159	−	0.999018i	$-0.485889\pi$
$719$	23.7931	−	41.2108i	0.887333	−	1.53691i	0.843017	−	0.537887i	$-0.180777\pi$
$720$		0			0
$721$	−24.9836	−	16.3988i	−0.930439	−	0.610724i
$722$	−10.1960	−	17.6599i	−0.379455	−	0.657235i
$723$		0			0
$724$	13.0972			0.486753
$725$	5.75800	+	9.97314i	0.213847	+	0.370393i
$726$		0			0
$727$	−32.9021			−1.22027			−0.610136	−	0.792297i	$-0.708885\pi$
$727$	−32.9021			−1.22027			−0.610136	+	0.792297i	$0.708885\pi$
$728$	4.21447	+	8.55793i	0.156199	+	0.317178i
$729$		0			0
$730$	21.0877			0.780491
$731$	−1.95365	−	3.38382i	−0.0722583	−	0.125155i
$732$		0			0
$733$	−10.5040	−	18.1935i	−0.387974	−	0.671991i	0.604203	−	0.796831i	$-0.293492\pi$
$733$	−10.5040	−	18.1935i	−0.387974	−	0.671991i	−0.992177	+	0.124839i	$0.960158\pi$
$734$	2.23463	+	3.87049i	0.0824816	+	0.142862i
$735$		0			0
$736$	4.78954			0.176545
$737$	−3.55796	+	6.16256i	−0.131059	+	0.227001i
$738$		0			0
$739$	−3.26085	−	5.64796i	−0.119952	−	0.207763i	0.799796	−	0.600272i	$-0.204941\pi$
$739$	−3.26085	−	5.64796i	−0.119952	−	0.207763i	−0.919749	+	0.392508i	$0.871607\pi$
$740$	0.753989	+	1.30595i	0.0277172	+	0.0480076i
$741$		0			0
$742$	1.29909	−	22.6665i	0.0476910	−	0.832113i
$743$	8.64802	−	14.9788i	0.317265	−	0.549519i	−0.662651	−	0.748928i	$-0.730569\pi$
$743$	8.64802	−	14.9788i	0.317265	−	0.549519i	0.979916	+	0.199409i	$0.0639022\pi$
$744$		0			0
$745$	30.4380			1.11516
$746$	−2.47615	+	4.28883i	−0.0906585	+	0.157025i
$747$		0			0
$748$	0.515673	+	0.893172i	0.0188549	+	0.0326576i
$749$	−33.1543	+	16.6892i	−1.21143	+	0.609810i
$750$		0			0
$751$	−9.62426			−0.351194			−0.175597	−	0.984462i	$-0.556186\pi$
$751$	−9.62426			−0.351194			−0.175597	+	0.984462i	$0.556186\pi$
$752$	3.98570	+	6.90344i	0.145344	+	0.251743i
$753$		0			0
$754$	10.8320	+	6.38085i	0.394478	+	0.232377i
$755$	7.65229			0.278495
$756$		0			0
$757$	−19.5740	+	33.9032i	−0.711429	+	1.23223i	0.252891	+	0.967495i	$0.418619\pi$
$757$	−19.5740	+	33.9032i	−0.711429	+	1.23223i	−0.964321	+	0.264737i	$0.914715\pi$
$758$	6.55920	−	11.3609i	0.238241	−	0.412645i
$759$		0			0
$760$	−8.17661			−0.296597
$761$	−5.18879	+	8.98725i	−0.188094	+	0.325788i	−0.944615	−	0.328182i	$-0.893564\pi$
$761$	−5.18879	+	8.98725i	−0.188094	+	0.325788i	0.756521	+	0.653969i	$0.226897\pi$
$762$		0			0
$763$	1.66527	−	29.0556i	0.0602867	−	1.05188i
$764$	−5.74444	+	9.94966i	−0.207827	+	0.359966i
$765$		0			0
$766$	−6.09000	+	10.5482i	−0.220041	+	0.381122i
$767$	0.288606	−	32.9900i	0.0104210	−	1.19120i
$768$		0			0
$769$	17.5102	−	30.3285i	0.631434	−	1.09368i	−0.355825	−	0.934553i	$-0.615800\pi$
$769$	17.5102	−	30.3285i	0.631434	−	1.09368i	0.987259	−	0.159123i	$-0.0508665\pi$
$770$	−0.417877	+	7.29112i	−0.0150592	+	0.262754i
$771$		0			0
$772$	0.138150	+	0.239283i	0.00497213	+	0.00861198i
$773$	−20.1234			−0.723789			−0.361894	−	0.932219i	$-0.617870\pi$
$773$	−20.1234			−0.723789			−0.361894	+	0.932219i	$0.617870\pi$
$774$		0			0
$775$	−7.40938	−	12.8334i	−0.266153	−	0.460990i
$776$	0.698602	+	1.21001i	0.0250784	+	0.0434370i
$777$		0			0
$778$	−3.34598	+	5.79541i	−0.119959	+	0.207776i
$779$	−39.6565	−	68.6870i	−1.42084	−	2.46097i
$780$		0			0
$781$	3.10911	−	5.38514i	0.111253	−	0.192696i
$782$	2.33137			0.0833695
$783$		0			0
$784$	4.16969	−	5.62260i	0.148918	−	0.200807i
$785$	8.13577			0.290378
$786$		0			0
$787$	1.90307			0.0678370			0.0339185	−	0.999425i	$-0.489201\pi$
$787$	1.90307			0.0678370			0.0339185	+	0.999425i	$0.489201\pi$
$788$	6.63552	−	11.4931i	0.236381	−	0.409423i
$789$		0			0
$790$	−9.33749	+	16.1730i	−0.332213	+	0.575410i
$791$	15.7727	+	10.3529i	0.560813	+	0.368108i
$792$		0			0
$793$	−31.6397	−	18.6381i	−1.12356	−	0.661858i
$794$	−12.2912	+	21.2890i	−0.436200	+	0.755520i
$795$		0			0
$796$	19.0219			0.674212
$797$	−10.9112	−	18.8987i	−0.386494	−	0.669427i	0.605481	−	0.795859i	$-0.292981\pi$
$797$	−10.9112	−	18.8987i	−0.386494	−	0.669427i	−0.991975	+	0.126433i	$0.959647\pi$
$798$		0			0
$799$	1.94009	+	3.36034i	0.0686355	+	0.118880i
$800$	1.65139	−	2.86029i	0.0583854	−	0.101126i
$801$		0			0
$802$	−34.6545			−1.22369
$803$	−34.2963			−1.21029
$804$		0			0
$805$	13.8012	+	9.05887i	0.486428	+	0.319283i
$806$	−13.9386	−	8.21087i	−0.490967	−	0.289216i
$807$		0			0
$808$	−3.01725	−	5.22602i	−0.106146	−	0.183851i
$809$	22.9519	+	39.7538i	0.806944	+	1.39767i	0.914971	+	0.403520i	$0.132214\pi$
$809$	22.9519	+	39.7538i	0.806944	+	1.39767i	−0.108026	+	0.994148i	$0.534453\pi$
$810$		0			0
$811$	3.66652			0.128749			0.0643744	−	0.997926i	$-0.479495\pi$
$811$	3.66652			0.128749			0.0643744	+	0.997926i	$0.479495\pi$
$812$	0.527853	−	9.20999i	0.0185240	−	0.323207i
$813$		0			0
$814$	−1.22626	−	2.12395i	−0.0429804	−	0.0744443i
$815$	−3.39720			−0.118999
$816$		0			0
$817$	−50.3806			−1.76259
$818$	−23.9090			−0.835957
$819$		0			0
$820$	−16.4630			−0.574914
$821$	20.3484			0.710162			0.355081	−	0.934835i	$-0.384453\pi$
$821$	20.3484			0.710162			0.355081	+	0.934835i	$0.384453\pi$
$822$		0			0
$823$	27.7345			0.966763			0.483381	−	0.875410i	$-0.339408\pi$
$823$	27.7345			0.966763			0.483381	+	0.875410i	$0.339408\pi$
$824$	5.64770	+	9.78210i	0.196747	+	0.340776i
$825$		0			0
$826$	−21.6239	+	10.8850i	−0.752390	+	0.378738i
$827$	−36.6640			−1.27493			−0.637466	−	0.770478i	$-0.720017\pi$
$827$	−36.6640			−1.27493			−0.637466	+	0.770478i	$0.720017\pi$
$828$		0			0
$829$	−7.23120	−	12.5248i	−0.251150	−	0.435005i	0.712693	−	0.701476i	$-0.247475\pi$
$829$	−7.23120	−	12.5248i	−0.251150	−	0.435005i	−0.963843	+	0.266472i	$0.914142\pi$
$830$	2.27123	+	3.93389i	0.0788357	+	0.136547i
$831$		0			0
$832$	0.0315412	−	3.60541i	0.00109349	−	0.124995i
$833$	2.02965	−	2.73687i	0.0703232	−	0.0948270i
$834$		0			0
$835$	−9.00000			−0.311458
$836$	13.2982			0.459926
$837$		0			0
$838$	6.09738	−	10.5610i	0.210630	−	0.364823i
$839$	2.51779	+	4.36094i	0.0869237	+	0.150556i	0.906209	−	0.422829i	$-0.138963\pi$
$839$	2.51779	+	4.36094i	0.0869237	+	0.150556i	−0.819286	+	0.573386i	$0.805630\pi$
$840$		0			0
$841$	8.42124	+	14.5860i	0.290388	+	0.502966i
$842$	14.0504			0.484210
$843$		0			0
$844$	−1.98750	+	3.44245i	−0.0684126	+	0.118494i
$845$	8.21014	+	14.8130i	0.282437	+	0.509582i
$846$		0			0
$847$	−0.985646	+	17.1976i	−0.0338672	+	0.590915i
$848$	−4.29060	+	7.43153i	−0.147340	+	0.255200i
$849$		0			0
$850$	0.803833	−	1.39228i	0.0275713	−	0.0477548i
$851$	−5.54394			−0.190044
$852$		0			0
$853$	21.9833			0.752693			0.376346	−	0.926479i	$-0.377180\pi$
$853$	21.9833			0.752693			0.376346	+	0.926479i	$0.377180\pi$
$854$	−1.54183	+	26.9018i	−0.0527603	+	0.920562i
$855$		0			0
$856$	14.0292			0.479509
$857$	−21.6450	+	37.4902i	−0.739378	+	1.28064i	0.213397	+	0.976965i	$0.431547\pi$
$857$	−21.6450	+	37.4902i	−0.739378	+	1.28064i	−0.952776	+	0.303675i	$0.901786\pi$
$858$		0			0
$859$	22.6834	+	39.2888i	0.773947	+	1.34052i	0.935385	+	0.353632i	$0.115054\pi$
$859$	22.6834	+	39.2888i	0.773947	+	1.34052i	−0.161438	+	0.986883i	$0.551613\pi$
$860$	−5.22877	+	9.05649i	−0.178299	+	0.308824i
$861$		0			0
$862$	8.65171	+	14.9852i	0.294678	+	0.510398i
$863$	6.76755	+	11.7217i	0.230370	+	0.399012i	0.957917	−	0.287045i	$-0.0926730\pi$
$863$	6.76755	+	11.7217i	0.230370	+	0.399012i	−0.727547	+	0.686058i	$0.759340\pi$
$864$		0			0
$865$	10.0667			0.342277
$866$	10.1803	+	17.6328i	0.345941	+	0.599187i
$867$		0			0
$868$	−0.679241	+	11.8514i	−0.0230549	+	0.402263i
$869$	15.1862	−	26.3032i	0.515155	−	0.892275i
$870$		0			0
$871$	10.5394	−	5.96262i	0.357115	−	0.202036i
$872$	−5.50000	+	9.52628i	−0.186254	+	0.322601i
$873$		0			0
$874$	15.0303	−	26.0332i	0.508407	−	0.880587i
$875$	25.5622	−	12.8675i	0.864161	−	0.435002i
$876$		0			0
$877$	−9.71091	+	16.8198i	−0.327914	+	0.567964i	−0.982098	−	0.188372i	$-0.939679\pi$
$877$	−9.71091	+	16.8198i	−0.327914	+	0.567964i	0.654184	+	0.756336i	$0.273012\pi$
$878$	4.04398			0.136478
$879$		0			0
$880$	1.38015	−	2.39050i	0.0465250	−	0.0805836i
$881$	2.77059	−	4.79881i	0.0933437	−	0.161676i	−0.815572	−	0.578655i	$-0.803578\pi$
$881$	2.77059	−	4.79881i	0.0933437	−	0.161676i	0.908916	+	0.416979i	$0.136911\pi$
$882$		0			0
$883$	51.6940			1.73964			0.869821	−	0.493367i	$-0.164234\pi$
$883$	51.6940			1.73964			0.869821	+	0.493367i	$0.164234\pi$
$884$	0.0153530	−	1.75498i	0.000516379	−	0.0590263i
$885$		0			0
$886$	−10.1092	−	17.5097i	−0.339627	−	0.588250i
$887$	3.54837			0.119143			0.0595713	−	0.998224i	$-0.481027\pi$
$887$	3.54837			0.119143			0.0595713	+	0.998224i	$0.481027\pi$
$888$		0			0
$889$	−0.785113	+	13.6987i	−0.0263318	+	0.459438i
$890$	6.12122	+	10.6023i	0.205184	+	0.355389i
$891$		0			0
$892$	9.58013	−	16.5933i	0.320767	−	0.555584i
$893$	50.0310			1.67422
$894$		0			0
$895$	12.4746	−	21.6066i	0.416979	−	0.722229i
$896$	−2.36323	+	1.18960i	−0.0789499	+	0.0397418i
$897$		0			0
$898$	19.8059	+	34.3047i	0.660930	+	1.14476i
$899$	7.82214	+	13.5483i	0.260883	+	0.451862i
$900$		0			0
$901$	−2.08850	+	3.61739i	−0.0695780	+	0.120513i
$902$	26.7749			0.891507
$903$		0			0
$904$	−3.56552	−	6.17566i	−0.118587	−	0.205399i
$905$	−8.53135	−	14.7767i	−0.283592	−	0.491195i
$906$		0			0
$907$	21.8453	+	37.8372i	0.725362	+	1.25636i	0.958825	+	0.283998i	$0.0916608\pi$
$907$	21.8453	+	37.8372i	0.725362	+	1.25636i	−0.233463	+	0.972366i	$0.575006\pi$
$908$	1.18251			0.0392430
$909$		0			0
$910$	6.91012	−	10.3295i	0.229068	−	0.342418i
$911$	5.97013			0.197799			0.0988996	−	0.995097i	$-0.468468\pi$
$911$	5.97013			0.197799			0.0988996	+	0.995097i	$0.468468\pi$
$912$		0			0
$913$	−3.69386	−	6.39795i	−0.122249	−	0.211741i
$914$	−6.64742			−0.219877
$915$		0			0
$916$	7.51599	+	13.0181i	0.248335	+	0.430130i
$917$	17.8357	+	11.7070i	0.588986	+	0.386600i
$918$		0			0
$919$	28.8290	−	49.9332i	0.950980	−	1.64715i	0.207668	−	0.978199i	$-0.433413\pi$
$919$	28.8290	−	49.9332i	0.950980	−	1.64715i	0.743311	−	0.668946i	$-0.233254\pi$
$920$	−3.11985	−	5.40373i	−0.102858	−	0.178156i
$921$		0			0
$922$	10.2371	+	17.7311i	0.337140	+	0.583943i
$923$	−9.20985	+	5.21042i	−0.303146	+	0.171503i
$924$		0			0
$925$	−1.91150	+	3.31081i	−0.0628497	+	0.108859i
$926$	17.2668			0.567423
$927$		0			0
$928$	−1.74338	+	3.01962i	−0.0572293	+	0.0991240i
$929$	2.05959	−	3.56731i	0.0675729	−	0.117040i	−0.830259	−	0.557377i	$-0.811808\pi$
$929$	2.05959	−	3.56731i	0.0675729	−	0.117040i	0.897832	+	0.440337i	$0.145141\pi$
$930$		0			0
$931$	−17.4762	−	40.3087i	−0.572759	−	1.32106i
$932$	2.59706	+	4.49824i	0.0850695	+	0.147345i
$933$		0			0
$934$	−4.37922	−	7.58503i	−0.143292	−	0.248190i
$935$	0.671807	−	1.16360i	0.0219704	−	0.0380539i
$936$		0			0
$937$	22.6483			0.739888			0.369944	−	0.929054i	$-0.379377\pi$
$937$	22.6483			0.739888			0.369944	+	0.929054i	$0.379377\pi$
$938$	−7.42843	−	4.87589i	−0.242547	−	0.159204i
$939$		0			0
$940$	5.19248	−	8.99364i	0.169360	−	0.293340i
$941$	−10.0011	+	17.3223i	−0.326025	+	0.564692i	−0.981719	−	0.190334i	$-0.939043\pi$
$941$	−10.0011	+	17.3223i	−0.326025	+	0.564692i	0.655694	+	0.755027i	$0.272376\pi$
$942$		0			0
$943$	30.2625	−	52.4161i	0.985481	−	1.70690i
$944$	9.15014			0.297812
$945$		0			0
$946$	8.50388	−	14.7292i	0.276485	−	0.478886i
$947$	−7.53183			−0.244752			−0.122376	−	0.992484i	$-0.539051\pi$
$947$	−7.53183			−0.244752			−0.122376	+	0.992484i	$0.539051\pi$
$948$		0			0
$949$	50.2859	+	29.6221i	1.63235	+	0.961574i
$950$	−10.3646	−	17.9520i	−0.336272	−	0.582441i
$951$		0			0
$952$	−1.15033	+	0.579054i	−0.0372824	+	0.0187672i
$953$	2.65075	+	4.59123i	0.0858661	+	0.148724i	0.905760	−	0.423791i	$-0.139301\pi$
$953$	2.65075	+	4.59123i	0.0858661	+	0.148724i	−0.819894	+	0.572516i	$0.805968\pi$
$954$		0			0
$955$	14.9674			0.484335
$956$	−25.3978			−0.821425
$957$		0			0
$958$	−13.5126	−	23.4046i	−0.436573	−	0.756167i
$959$	−16.0502	+	8.07937i	−0.518289	+	0.260896i
$960$		0			0
$961$	5.43448	+	9.41280i	0.175306	+	0.303639i
$962$	−0.0365092	+	4.17331i	−0.00117711	+	0.134553i
$963$		0			0
$964$	−11.8575			−0.381904
$965$	0.179979	−	0.311732i	0.00579372	−	0.0100350i
$966$		0			0
$967$	−7.46926			−0.240195			−0.120098	−	0.992762i	$-0.538321\pi$
$967$	−7.46926			−0.240195			−0.120098	+	0.992762i	$0.538321\pi$
$968$	3.25537	−	5.63846i	0.104631	−	0.181227i
$969$		0			0
$970$	0.910122	−	1.57638i	0.0292223	−	0.0506144i
$971$	−1.64395	+	2.84741i	−0.0527570	+	0.0913778i	−0.891198	−	0.453615i	$-0.850134\pi$
$971$	−1.64395	+	2.84741i	−0.0527570	+	0.0913778i	0.838441	+	0.544993i	$0.183468\pi$
$972$		0			0
$973$	−28.5558	−	18.7436i	−0.915458	−	0.600891i
$974$	21.9435			0.703114
$975$		0			0
$976$	5.09231	−	8.82015i	0.163001	−	0.282326i
$977$	−0.416499	−	0.721397i	−0.0133250	−	0.0230795i	0.859286	−	0.511495i	$-0.170908\pi$
$977$	−0.416499	−	0.721397i	−0.0133250	−	0.0230795i	−0.872611	+	0.488416i	$0.837575\pi$
$978$		0			0
$979$	−9.95535	−	17.2432i	−0.318174	−	0.551094i
$980$	−9.05971	−	1.04190i	−0.289402	−	0.0332824i
$981$		0			0
$982$	7.09020	−	12.2806i	0.226257	−	0.391889i
$983$	−20.9860	+	36.3487i	−0.669348	+	1.15934i	0.308739	+	0.951147i	$0.400093\pi$
$983$	−20.9860	+	36.3487i	−0.669348	+	1.15934i	−0.978087	+	0.208198i	$0.933240\pi$
$984$		0			0
$985$	−17.2892			−0.550879
$986$	−0.848612	+	1.46984i	−0.0270253	+	0.0468092i
$987$		0			0
$988$	−19.4980	−	11.4858i	−0.620314	−	0.365411i
$989$	−19.2231	−	33.2954i	−0.611259	−	1.05873i
$990$		0			0
$991$	25.9607	+	44.9653i	0.824670	+	1.42837i	0.902171	+	0.431378i	$0.141972\pi$
$991$	25.9607	+	44.9653i	0.824670	+	1.42837i	−0.0775015	+	0.996992i	$0.524694\pi$
$992$	2.24338	−	3.88565i	0.0712274	−	0.123370i
$993$		0			0
$994$	6.49131	+	4.26079i	0.205892	+	0.135144i
$995$	−12.3906	−	21.4612i	−0.392809	−	0.680364i
$996$		0			0
$997$	−48.5174			−1.53656			−0.768281	−	0.640113i	$-0.778888\pi$
$997$	−48.5174			−1.53656			−0.768281	+	0.640113i	$0.778888\pi$
$998$	14.7488	+	25.5456i	0.466864	+	0.808632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.i.1621.1		8
3.2	odd	2		546.2.j.b.529.3	yes	8
7.2	even	3		1638.2.p.g.919.2		8
13.3	even	3		1638.2.p.g.991.2		8
21.2	odd	6		546.2.k.d.373.4	yes	8
39.29	odd	6		546.2.k.d.445.4	yes	8
91.16	even	3	inner	1638.2.m.i.289.1		8
273.107	odd	6		546.2.j.b.289.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.b.289.3	✓	8	273.107	odd	6
546.2.j.b.529.3	yes	8	3.2	odd	2
546.2.k.d.373.4	yes	8	21.2	odd	6
546.2.k.d.445.4	yes	8	39.29	odd	6
1638.2.m.i.289.1		8	91.16	even	3	inner
1638.2.m.i.1621.1		8	1.1	even	1	trivial
1638.2.p.g.919.2		8	7.2	even	3
1638.2.p.g.991.2		8	13.3	even	3

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.651388 - 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.651388 - 1.12824i) q^{5} +(-2.36323 + 1.18960i) q^{7} +1.00000 q^{8} +(-0.651388 - 1.12824i) q^{10} +(1.05939 + 1.83493i) q^{11} +(0.0315412 - 3.60541i) q^{13} +(-2.36323 + 1.18960i) q^{14} +1.00000 q^{16} +0.486762 q^{17} +(3.13815 - 5.43544i) q^{19} +(-0.651388 - 1.12824i) q^{20} +(1.05939 + 1.83493i) q^{22} +4.78954 q^{23} +(1.65139 - 2.86029i) q^{25} +(0.0315412 - 3.60541i) q^{26} +(-2.36323 + 1.18960i) q^{28} +(-1.74338 + 3.01962i) q^{29} +(2.24338 - 3.88565i) q^{31} +1.00000 q^{32} +0.486762 q^{34} +(2.88153 + 1.89139i) q^{35} -1.15751 q^{37} +(3.13815 - 5.43544i) q^{38} +(-0.651388 - 1.12824i) q^{40} +(6.31845 - 10.9439i) q^{41} +(-4.01356 - 6.95169i) q^{43} +(1.05939 + 1.83493i) q^{44} +4.78954 q^{46} +(3.98570 + 6.90344i) q^{47} +(4.16969 - 5.62260i) q^{49} +(1.65139 - 2.86029i) q^{50} +(0.0315412 - 3.60541i) q^{52} +(-4.29060 + 7.43153i) q^{53} +(1.38015 - 2.39050i) q^{55} +(-2.36323 + 1.18960i) q^{56} +(-1.74338 + 3.01962i) q^{58} +9.15014 q^{59} +(5.09231 - 8.82015i) q^{61} +(2.24338 - 3.88565i) q^{62} +1.00000 q^{64} +(-4.08831 + 2.31294i) q^{65} +(1.67924 + 2.90853i) q^{67} +0.486762 q^{68} +(2.88153 + 1.89139i) q^{70} +(-1.46740 - 2.54161i) q^{71} +(-8.09337 + 14.0181i) q^{73} -1.15751 q^{74} +(3.13815 - 5.43544i) q^{76} +(-4.68642 - 3.07609i) q^{77} +(-7.16738 - 12.4143i) q^{79} +(-0.651388 - 1.12824i) q^{80} +(6.31845 - 10.9439i) q^{82} -3.48676 q^{83} +(-0.317071 - 0.549183i) q^{85} +(-4.01356 - 6.95169i) q^{86} +(1.05939 + 1.83493i) q^{88} -9.39720 q^{89} +(4.21447 + 8.55793i) q^{91} +4.78954 q^{92} +(3.98570 + 6.90344i) q^{94} -8.17661 q^{95} +(0.698602 + 1.21001i) q^{97} +(4.16969 - 5.62260i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 3 q^{7} + 8 q^{8} + 2 q^{10} + 2 q^{11} + 7 q^{13} + 3 q^{14} + 8 q^{16} - 12 q^{17} + 2 q^{19} + 2 q^{20} + 2 q^{22} + 8 q^{23} + 6 q^{25} + 7 q^{26} + 3 q^{28} - 6 q^{29} + 10 q^{31} + 8 q^{32} - 12 q^{34} - 8 q^{35} + 24 q^{37} + 2 q^{38} + 2 q^{40} + 6 q^{41} - 4 q^{43} + 2 q^{44} + 8 q^{46} + 17 q^{47} + 17 q^{49} + 6 q^{50} + 7 q^{52} - 3 q^{53} + 25 q^{55} + 3 q^{56} - 6 q^{58} - 4 q^{61} + 10 q^{62} + 8 q^{64} - 12 q^{65} - 7 q^{67} - 12 q^{68} - 8 q^{70} - 6 q^{71} - 19 q^{73} + 24 q^{74} + 2 q^{76} + 10 q^{77} + 24 q^{79} + 2 q^{80} + 6 q^{82} - 12 q^{83} - 3 q^{85} - 4 q^{86} + 2 q^{88} - 14 q^{89} + 40 q^{91} + 8 q^{92} + 17 q^{94} - 24 q^{95} - 25 q^{97} + 17 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 3 * q^7 + 8 * q^8 + 2 * q^10 + 2 * q^11 + 7 * q^13 + 3 * q^14 + 8 * q^16 - 12 * q^17 + 2 * q^19 + 2 * q^20 + 2 * q^22 + 8 * q^23 + 6 * q^25 + 7 * q^26 + 3 * q^28 - 6 * q^29 + 10 * q^31 + 8 * q^32 - 12 * q^34 - 8 * q^35 + 24 * q^37 + 2 * q^38 + 2 * q^40 + 6 * q^41 - 4 * q^43 + 2 * q^44 + 8 * q^46 + 17 * q^47 + 17 * q^49 + 6 * q^50 + 7 * q^52 - 3 * q^53 + 25 * q^55 + 3 * q^56 - 6 * q^58 - 4 * q^61 + 10 * q^62 + 8 * q^64 - 12 * q^65 - 7 * q^67 - 12 * q^68 - 8 * q^70 - 6 * q^71 - 19 * q^73 + 24 * q^74 + 2 * q^76 + 10 * q^77 + 24 * q^79 + 2 * q^80 + 6 * q^82 - 12 * q^83 - 3 * q^85 - 4 * q^86 + 2 * q^88 - 14 * q^89 + 40 * q^91 + 8 * q^92 + 17 * q^94 - 24 * q^95 - 25 * q^97 + 17 * q^98

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