LMFDB - Embedded newform 950.2.e.o.201.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

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("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 10x^{8} - 12x^{7} + 85x^{6} - 70x^{5} + 186x^{4} - 110x^{3} + 285x^{2} - 150x + 100 $ x^10 + 10x^8 - 12x^7 + 85x^6 - 70x^5 + 186x^4 - 110x^3 + 285x^2 - 150x + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.5
Root			$-1.58826 + 2.75095i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.o.501.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.58826 - 2.75095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58826 - 2.75095i) q^{6} +4.17652 q^{7} -1.00000 q^{8} +(-3.54514 - 6.14037i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.58826 - 2.75095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58826 - 2.75095i) q^{6} +4.17652 q^{7} -1.00000 q^{8} +(-3.54514 - 6.14037i) q^{9} -3.90260 q^{11} -3.17652 q^{12} +(0.239434 + 0.414711i) q^{13} +(2.08826 - 3.61697i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.245018 + 0.424383i) q^{17} -7.09029 q^{18} +(2.74077 + 3.38942i) q^{19} +(6.63340 - 11.4894i) q^{21} +(-1.95130 + 3.37975i) q^{22} +(-2.84883 - 4.93431i) q^{23} +(-1.58826 + 2.75095i) q^{24} +0.478867 q^{26} -12.9929 q^{27} +(-2.08826 - 3.61697i) q^{28} +(-1.21745 - 2.10868i) q^{29} +2.42373 q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.19834 + 10.7358i) q^{33} +(0.245018 + 0.424383i) q^{34} +(-3.54514 + 6.14037i) q^{36} +8.47175 q^{37} +(4.30571 - 0.678866i) q^{38} +1.52113 q^{39} +(0.254982 - 0.441643i) q^{41} +(-6.63340 - 11.4894i) q^{42} +(-2.91377 + 5.04679i) q^{43} +(1.95130 + 3.37975i) q^{44} -5.69765 q^{46} +(-0.485788 - 0.841410i) q^{47} +(1.58826 + 2.75095i) q^{48} +10.4433 q^{49} +(0.778304 + 1.34806i) q^{51} +(0.239434 - 0.414711i) q^{52} +(2.77899 + 4.81336i) q^{53} +(-6.49644 + 11.2522i) q^{54} -4.17652 q^{56} +(13.6772 - 2.15643i) q^{57} -2.43490 q^{58} +(3.82769 - 6.62976i) q^{59} +(4.65673 + 8.06569i) q^{61} +(1.21187 - 2.09901i) q^{62} +(-14.8064 - 25.6454i) q^{63} +1.00000 q^{64} +(6.19834 + 10.7358i) q^{66} +(0.809957 + 1.40289i) q^{67} +0.490035 q^{68} -18.0987 q^{69} +(0.937088 - 1.62308i) q^{71} +(3.54514 + 6.14037i) q^{72} +(-2.35307 + 4.07564i) q^{73} +(4.23588 - 7.33675i) q^{74} +(1.56494 - 4.06829i) q^{76} -16.2993 q^{77} +(0.760566 - 1.31734i) q^{78} +(-3.19984 + 5.54229i) q^{79} +(-10.0007 + 17.3216i) q^{81} +(-0.254982 - 0.441643i) q^{82} +7.96179 q^{83} -13.2668 q^{84} +(2.91377 + 5.04679i) q^{86} -7.73451 q^{87} +3.90260 q^{88} +(2.76126 + 4.78264i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-2.84883 + 4.93431i) q^{92} +(3.84952 - 6.66756i) q^{93} -0.971577 q^{94} +3.17652 q^{96} +(-7.24499 + 12.5487i) q^{97} +(5.22167 - 9.04419i) q^{98} +(13.8353 + 23.9634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9	$ 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{13} + 5 q^{14} - 5 q^{16} - 4 q^{17} - 10 q^{18} + 11 q^{19} + 20 q^{21} - 3 q^{22} - 13 q^{23} + 4 q^{26} - 36 q^{27} - 5 q^{28} + 2 q^{29} - 8 q^{31} + 5 q^{32} - 2 q^{33} + 4 q^{34} - 5 q^{36} - 10 q^{37} + 13 q^{38} + 16 q^{39} + q^{41} - 20 q^{42} + 3 q^{44} - 26 q^{46} + 10 q^{47} - 20 q^{49} + 4 q^{51} + 2 q^{52} - 5 q^{53} - 18 q^{54} - 10 q^{56} + 10 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{61} - 4 q^{62} - 23 q^{63} + 10 q^{64} + 2 q^{66} - 4 q^{67} + 8 q^{68} - 24 q^{69} - 22 q^{71} + 5 q^{72} - 26 q^{73} - 5 q^{74} + 2 q^{76} - 10 q^{77} + 8 q^{78} + 2 q^{79} - 5 q^{81} - q^{82} - 12 q^{83} - 40 q^{84} + 20 q^{87} + 6 q^{88} - q^{89} + 10 q^{91} - 13 q^{92} - 6 q^{93} + 20 q^{94} - 8 q^{97} - 10 q^{98} + 13 q^{99}+O(q^{100}) $ 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^13 + 5 * q^14 - 5 * q^16 - 4 * q^17 - 10 * q^18 + 11 * q^19 + 20 * q^21 - 3 * q^22 - 13 * q^23 + 4 * q^26 - 36 * q^27 - 5 * q^28 + 2 * q^29 - 8 * q^31 + 5 * q^32 - 2 * q^33 + 4 * q^34 - 5 * q^36 - 10 * q^37 + 13 * q^38 + 16 * q^39 + q^41 - 20 * q^42 + 3 * q^44 - 26 * q^46 + 10 * q^47 - 20 * q^49 + 4 * q^51 + 2 * q^52 - 5 * q^53 - 18 * q^54 - 10 * q^56 + 10 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^61 - 4 * q^62 - 23 * q^63 + 10 * q^64 + 2 * q^66 - 4 * q^67 + 8 * q^68 - 24 * q^69 - 22 * q^71 + 5 * q^72 - 26 * q^73 - 5 * q^74 + 2 * q^76 - 10 * q^77 + 8 * q^78 + 2 * q^79 - 5 * q^81 - q^82 - 12 * q^83 - 40 * q^84 + 20 * q^87 + 6 * q^88 - q^89 + 10 * q^91 - 13 * q^92 - 6 * q^93 + 20 * q^94 - 8 * q^97 - 10 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.58826	−	2.75095i	0.916983	−	1.58826i	0.113011	−	0.993594i	$-0.463951\pi$
$3$	1.58826	−	2.75095i	0.916983	−	1.58826i	0.803972	−	0.594667i	$-0.202716\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.58826	−	2.75095i	−0.648405	−	1.12307i
$7$	4.17652			1.57858			0.789288	−	0.614023i	$-0.210450\pi$
$7$	4.17652			1.57858			0.789288	+	0.614023i	$0.210450\pi$
$8$	−1.00000			−0.353553
$9$	−3.54514	−	6.14037i	−1.18171	−	2.04679i
$10$		0			0
$11$	−3.90260			−1.17668			−0.588339	−	0.808614i	$-0.700218\pi$
$11$	−3.90260			−1.17668			−0.588339	+	0.808614i	$0.700218\pi$
$12$	−3.17652			−0.916983
$13$	0.239434	+	0.414711i	0.0664070	+	0.115020i	0.897317	−	0.441386i	$-0.145513\pi$
$13$	0.239434	+	0.414711i	0.0664070	+	0.115020i	−0.830910	+	0.556406i	$0.812180\pi$
$14$	2.08826	−	3.61697i	0.558111	−	0.966677i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.245018	+	0.424383i	−0.0594255	+	0.102928i	−0.894208	−	0.447652i	$-0.852260\pi$
$17$	−0.245018	+	0.424383i	−0.0594255	+	0.102928i	0.834782	+	0.550580i	$0.185594\pi$
$18$	−7.09029			−1.67120
$19$	2.74077	+	3.38942i	0.628776	+	0.777587i
$19$	2.74077	+	3.38942i	0.628776	+	0.777587i
$20$		0			0
$21$	6.63340	−	11.4894i	1.44753	−	2.50719i
$22$	−1.95130	+	3.37975i	−0.416018	+	0.720565i
$23$	−2.84883	−	4.93431i	−0.594021	−	1.02888i	−0.993684	−	0.112213i	$-0.964206\pi$
$23$	−2.84883	−	4.93431i	−0.594021	−	1.02888i	0.399663	−	0.916662i	$-0.369127\pi$
$24$	−1.58826	+	2.75095i	−0.324202	+	0.561535i
$25$		0			0
$26$	0.478867			0.0939136
$27$	−12.9929			−2.50048
$28$	−2.08826	−	3.61697i	−0.394644	−	0.683544i
$29$	−1.21745	−	2.10868i	−0.226075	−	0.391573i	0.730567	−	0.682841i	$-0.239256\pi$
$29$	−1.21745	−	2.10868i	−0.226075	−	0.391573i	−0.956641	+	0.291269i	$0.905923\pi$
$30$		0			0
$31$	2.42373			0.435315			0.217657	−	0.976025i	$-0.430158\pi$
$31$	2.42373			0.435315			0.217657	+	0.976025i	$0.430158\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−6.19834	+	10.7358i	−1.07899	+	1.86887i
$34$	0.245018	+	0.424383i	0.0420202	+	0.0727811i
$35$		0			0
$36$	−3.54514	+	6.14037i	−0.590857	+	1.02339i
$37$	8.47175			1.39275			0.696374	−	0.717679i	$-0.254796\pi$
$37$	8.47175			1.39275			0.696374	+	0.717679i	$0.254796\pi$
$38$	4.30571	−	0.678866i	0.698478	−	0.110127i
$39$	1.52113			0.243576
$40$		0			0
$41$	0.254982	−	0.441643i	0.0398216	−	0.0689730i	−0.845428	−	0.534090i	$-0.820654\pi$
$41$	0.254982	−	0.441643i	0.0398216	−	0.0689730i	0.885249	+	0.465117i	$0.153988\pi$
$42$	−6.63340	−	11.4894i	−1.02356	−	1.77285i
$43$	−2.91377	+	5.04679i	−0.444345	+	0.769629i	−0.998006	−	0.0631136i	$-0.979897\pi$
$43$	−2.91377	+	5.04679i	−0.444345	+	0.769629i	0.553661	+	0.832742i	$0.313230\pi$
$44$	1.95130	+	3.37975i	0.294169	+	0.509516i
$45$		0			0
$46$	−5.69765			−0.840073
$47$	−0.485788	−	0.841410i	−0.0708595	−	0.122732i	0.828419	−	0.560109i	$-0.189241\pi$
$47$	−0.485788	−	0.841410i	−0.0708595	−	0.122732i	−0.899278	+	0.437377i	$0.855908\pi$
$48$	1.58826	+	2.75095i	0.229246	+	0.397065i
$49$	10.4433			1.49190
$50$		0			0
$51$	0.778304	+	1.34806i	0.108984	+	0.188766i
$52$	0.239434	−	0.414711i	0.0332035	−	0.0575101i
$53$	2.77899	+	4.81336i	0.381724	+	0.661166i	0.991309	−	0.131555i	$-0.0419971\pi$
$53$	2.77899	+	4.81336i	0.381724	+	0.661166i	−0.609585	+	0.792721i	$0.708664\pi$
$54$	−6.49644	+	11.2522i	−0.884054	+	1.53123i
$55$		0			0
$56$	−4.17652			−0.558111
$57$	13.6772	−	2.15643i	1.81159	−	0.285627i
$58$	−2.43490			−0.319718
$59$	3.82769	−	6.62976i	0.498323	−	0.863121i	−0.501675	−	0.865056i	$-0.667283\pi$
$59$	3.82769	−	6.62976i	0.498323	−	0.863121i	0.999998	+	0.00193493i	$0.000615909\pi$
$60$		0			0
$61$	4.65673	+	8.06569i	0.596233	+	1.03271i	0.993372	+	0.114947i	$0.0366697\pi$
$61$	4.65673	+	8.06569i	0.596233	+	1.03271i	−0.397139	+	0.917758i	$0.629997\pi$
$62$	1.21187	−	2.09901i	0.153907	−	0.266575i
$63$	−14.8064	−	25.6454i	−1.86543	−	3.23101i
$64$	1.00000			0.125000
$65$		0			0
$66$	6.19834	+	10.7358i	0.762963	+	1.32149i
$67$	0.809957	+	1.40289i	0.0989520	+	0.171390i	0.911251	−	0.411851i	$-0.135118\pi$
$67$	0.809957	+	1.40289i	0.0989520	+	0.171390i	−0.812299	+	0.583241i	$0.801784\pi$
$68$	0.490035			0.0594255
$69$	−18.0987			−2.17883
$70$		0			0
$71$	0.937088	−	1.62308i	0.111212	−	0.192625i	−0.805047	−	0.593211i	$-0.797860\pi$
$71$	0.937088	−	1.62308i	0.111212	−	0.192625i	0.916259	+	0.400586i	$0.131193\pi$
$72$	3.54514	+	6.14037i	0.417799	+	0.723649i
$73$	−2.35307	+	4.07564i	−0.275406	+	0.477018i	−0.970238	−	0.242155i	$-0.922146\pi$
$73$	−2.35307	+	4.07564i	−0.275406	+	0.477018i	0.694831	+	0.719173i	$0.255479\pi$
$74$	4.23588	−	7.33675i	0.492411	−	0.852880i
$75$		0			0
$76$	1.56494	−	4.06829i	0.179511	−	0.466665i
$77$	−16.2993			−1.85748
$78$	0.760566	−	1.31734i	0.0861172	−	0.149159i
$79$	−3.19984	+	5.54229i	−0.360010	+	0.623556i	−0.987962	−	0.154696i	$-0.950560\pi$
$79$	−3.19984	+	5.54229i	−0.360010	+	0.623556i	0.627952	+	0.778252i	$0.283894\pi$
$80$		0			0
$81$	−10.0007	+	17.3216i	−1.11118	+	1.92463i
$82$	−0.254982	−	0.441643i	−0.0281581	−	0.0487713i
$83$	7.96179			0.873920			0.436960	−	0.899481i	$-0.356055\pi$
$83$	7.96179			0.873920			0.436960	+	0.899481i	$0.356055\pi$
$84$	−13.2668			−1.44753
$85$		0			0
$86$	2.91377	+	5.04679i	0.314200	+	0.544210i
$87$	−7.73451			−0.829226
$88$	3.90260			0.416018
$89$	2.76126	+	4.78264i	0.292693	+	0.506958i	0.974445	−	0.224624i	$-0.0721154\pi$
$89$	2.76126	+	4.78264i	0.292693	+	0.506958i	−0.681753	+	0.731583i	$0.738782\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−2.84883	+	4.93431i	−0.297011	+	0.514438i
$93$	3.84952	−	6.66756i	0.399176	−	0.691394i
$94$	−0.971577			−0.100210
$95$		0			0
$96$	3.17652			0.324202
$97$	−7.24499	+	12.5487i	−0.735617	+	1.27413i	0.218835	+	0.975762i	$0.429774\pi$
$97$	−7.24499	+	12.5487i	−0.735617	+	1.27413i	−0.954452	+	0.298364i	$0.903559\pi$
$98$	5.22167	−	9.04419i	0.527468	−	0.913601i
$99$	13.8353	+	23.9634i	1.39050	+	2.40841i
$100$		0			0
$101$	0.280362	+	0.485601i	0.0278971	+	0.0483191i	0.879637	−	0.475646i	$-0.157786\pi$
$101$	0.280362	+	0.485601i	0.0278971	+	0.0483191i	−0.851740	+	0.523965i	$0.824452\pi$
$102$	1.55661			0.154127
$103$	−12.9533			−1.27633			−0.638163	−	0.769901i	$-0.720305\pi$
$103$	−12.9533			−1.27633			−0.638163	+	0.769901i	$0.720305\pi$
$104$	−0.239434	−	0.414711i	−0.0234784	−	0.0406658i
$105$		0			0
$106$	5.55799			0.539839
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$	6.49644	+	11.2522i	0.625121	+	1.08274i
$109$	4.83191	−	8.36911i	0.462813	−	0.801616i	−0.536287	−	0.844036i	$-0.680173\pi$
$109$	4.83191	−	8.36911i	0.462813	−	0.801616i	0.999100	+	0.0424201i	$0.0135068\pi$
$110$		0			0
$111$	13.4554	−	23.3054i	1.27713	−	2.21205i
$112$	−2.08826	+	3.61697i	−0.197322	+	0.341772i
$113$	5.17920			0.487218			0.243609	−	0.969874i	$-0.421669\pi$
$113$	5.17920			0.487218			0.243609	+	0.969874i	$0.421669\pi$
$114$	4.97106	−	12.9230i	0.465583	−	1.21035i
$115$		0			0
$116$	−1.21745	+	2.10868i	−0.113037	+	0.195786i
$117$	1.69765	−	2.94042i	0.156948	−	0.271842i
$118$	−3.82769	−	6.62976i	−0.352368	−	0.610319i
$119$	−1.02332	+	1.77244i	−0.0938077	+	0.162480i
$120$		0			0
$121$	4.23028			0.384571
$122$	9.31345			0.843200
$123$	−0.809957	−	1.40289i	−0.0730314	−	0.126494i
$124$	−1.21187	−	2.09901i	−0.108829	−	0.188497i
$125$		0			0
$126$	−29.6127			−2.63811
$127$	−2.35526	−	4.07943i	−0.208996	−	0.361991i	0.742403	−	0.669954i	$-0.233686\pi$
$127$	−2.35526	−	4.07943i	−0.208996	−	0.361991i	−0.951398	+	0.307963i	$0.900353\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	9.25564	+	16.0312i	0.814914	+	1.41147i
$130$		0			0
$131$	−6.65454	+	11.5260i	−0.581410	+	1.00703i	0.413903	+	0.910321i	$0.364165\pi$
$131$	−6.65454	+	11.5260i	−0.581410	+	1.00703i	−0.995313	+	0.0967100i	$0.969168\pi$
$132$	12.3967			1.07899
$133$	11.4469	+	14.1560i	0.992571	+	1.22748i
$134$	1.61991			0.139939
$135$		0			0
$136$	0.245018	−	0.424383i	0.0210101	−	0.0363905i
$137$	−0.194290	−	0.336520i	−0.0165993	−	0.0287508i	0.857606	−	0.514307i	$-0.171951\pi$
$137$	−0.194290	−	0.336520i	−0.0165993	−	0.0287508i	−0.874206	+	0.485556i	$0.838617\pi$
$138$	−9.04936	+	15.6740i	−0.770333	+	1.33426i
$139$	−8.82058	−	15.2777i	−0.748152	−	1.29584i	−0.948708	−	0.316155i	$-0.897608\pi$
$139$	−8.82058	−	15.2777i	−0.748152	−	1.29584i	0.200556	−	0.979682i	$-0.435725\pi$
$140$		0			0
$141$	−3.08623			−0.259908
$142$	−0.937088	−	1.62308i	−0.0786386	−	0.136206i
$143$	−0.934414	−	1.61845i	−0.0781396	−	0.135342i
$144$	7.09029			0.590857
$145$		0			0
$146$	2.35307	+	4.07564i	0.194742	+	0.337303i
$147$	16.5867	−	28.7291i	1.36805	−	2.36953i
$148$	−4.23588	−	7.33675i	−0.348187	−	0.603077i
$149$	7.64556	−	13.2425i	0.626349	−	1.08487i	−0.361930	−	0.932205i	$-0.617882\pi$
$149$	7.64556	−	13.2425i	0.626349	−	1.08487i	0.988278	−	0.152662i	$-0.0487846\pi$
$150$		0			0
$151$	16.6266			1.35306			0.676528	−	0.736416i	$-0.263484\pi$
$151$	16.6266			1.35306			0.676528	+	0.736416i	$0.263484\pi$
$152$	−2.74077	−	3.38942i	−0.222306	−	0.274918i
$153$	3.47449			0.280896
$154$	−8.14964	+	14.1156i	−0.656717	+	1.13747i
$155$		0			0
$156$	−0.760566	−	1.31734i	−0.0608940	−	0.105472i
$157$	−6.08401	+	10.5378i	−0.485557	+	0.841010i	−0.999862	−	0.0165976i	$-0.994717\pi$
$157$	−6.08401	+	10.5378i	−0.485557	+	0.841010i	0.514305	+	0.857607i	$0.328050\pi$
$158$	3.19984	+	5.54229i	0.254566	+	0.440921i
$159$	17.6551			1.40014
$160$		0			0
$161$	−11.8982	−	20.6083i	−0.937708	−	1.62416i
$162$	10.0007	+	17.3216i	0.785726	+	1.36092i
$163$	14.4674			1.13317			0.566586	−	0.824002i	$-0.308264\pi$
$163$	14.4674			1.13317			0.566586	+	0.824002i	$0.308264\pi$
$164$	−0.509965			−0.0398216
$165$		0			0
$166$	3.98089	−	6.89511i	0.308977	−	0.535164i
$167$	1.64911	+	2.85635i	0.127612	+	0.221031i	0.922751	−	0.385397i	$-0.125935\pi$
$167$	1.64911	+	2.85635i	0.127612	+	0.221031i	−0.795139	+	0.606428i	$0.792602\pi$
$168$	−6.63340	+	11.4894i	−0.511778	+	0.886426i
$169$	6.38534	−	11.0597i	0.491180	−	0.850749i
$170$		0			0
$171$	11.0959	−	28.8453i	0.848523	−	2.20586i
$172$	5.82753			0.444345
$173$	−4.96668	+	8.60255i	−0.377610	+	0.654040i	−0.990714	−	0.135963i	$-0.956587\pi$
$173$	−4.96668	+	8.60255i	−0.377610	+	0.654040i	0.613104	+	0.790002i	$0.289921\pi$
$174$	−3.86725	+	6.69828i	−0.293176	+	0.507795i
$175$		0			0
$176$	1.95130	−	3.37975i	0.147085	−	0.254758i
$177$	−12.1588	−	21.0596i	−0.913908	−	1.58293i
$178$	5.52251			0.413930
$179$	−10.7923			−0.806656			−0.403328	−	0.915056i	$-0.632147\pi$
$179$	−10.7923			−0.806656			−0.403328	+	0.915056i	$0.632147\pi$
$180$		0			0
$181$	−5.95907	−	10.3214i	−0.442934	−	0.767185i	0.554971	−	0.831869i	$-0.312729\pi$
$181$	−5.95907	−	10.3214i	−0.442934	−	0.767185i	−0.997906	+	0.0646847i	$0.979396\pi$
$182$	2.00000			0.148250
$183$	29.5844			2.18694
$184$	2.84883	+	4.93431i	0.210018	+	0.363762i
$185$		0			0
$186$	−3.84952	−	6.66756i	−0.282260	−	0.488889i
$187$	0.956205	−	1.65620i	0.0699247	−	0.121113i
$188$	−0.485788	+	0.841410i	−0.0354297	+	0.0613661i
$189$	−54.2651			−3.94720
$190$		0			0
$191$	−4.86980			−0.352366			−0.176183	−	0.984357i	$-0.556375\pi$
$191$	−4.86980			−0.352366			−0.176183	+	0.984357i	$0.556375\pi$
$192$	1.58826	−	2.75095i	0.114623	−	0.198533i
$193$	−10.8919	+	18.8653i	−0.784017	+	1.35796i	0.145568	+	0.989348i	$0.453499\pi$
$193$	−10.8919	+	18.8653i	−0.784017	+	1.35796i	−0.929585	+	0.368609i	$0.879834\pi$
$194$	7.24499	+	12.5487i	0.520160	+	0.900943i
$195$		0			0
$196$	−5.22167	−	9.04419i	−0.372976	−	0.646014i
$197$	−13.7359			−0.978642			−0.489321	−	0.872104i	$-0.662755\pi$
$197$	−13.7359			−0.978642			−0.489321	+	0.872104i	$0.662755\pi$
$198$	27.6705			1.96646
$199$	−10.4433	−	18.0884i	−0.740308	−	1.28225i	−0.952355	−	0.304992i	$-0.901346\pi$
$199$	−10.4433	−	18.0884i	−0.740308	−	1.28225i	0.212047	−	0.977259i	$-0.431987\pi$
$200$		0			0
$201$	5.14569			0.362949
$202$	0.560724			0.0394524
$203$	−5.08470	−	8.80697i	−0.356876	−	0.618128i
$204$	0.778304	−	1.34806i	0.0544921	−	0.0943832i
$205$		0			0
$206$	−6.47665	+	11.2179i	−0.451249	+	0.781587i
$207$	−20.1990	+	34.9857i	−1.40393	+	2.43167i
$208$	−0.478867			−0.0332035
$209$	−10.6961	−	13.2276i	−0.739867	−	0.914969i
$210$		0			0
$211$	8.30571	−	14.3859i	0.571789	−	0.990367i	−0.424594	−	0.905384i	$-0.639583\pi$
$211$	8.30571	−	14.3859i	0.571789	−	0.990367i	0.996382	−	0.0849830i	$-0.0270836\pi$
$212$	2.77899	−	4.81336i	0.190862	−	0.330583i
$213$	−2.97668	−	5.15576i	−0.203959	−	0.353267i
$214$	5.00000	−	8.66025i	0.341793	−	0.592003i
$215$		0			0
$216$	12.9929			0.884054
$217$	10.1228			0.687178
$218$	−4.83191	−	8.36911i	−0.327258	−	0.566828i
$219$	7.47459	+	12.9464i	0.505086	+	0.874835i
$220$		0			0
$221$	−0.234662			−0.0157851
$222$	−13.4554	−	23.3054i	−0.903064	−	1.56415i
$223$	5.08826	−	8.81313i	0.340735	−	0.590171i	−0.643834	−	0.765165i	$-0.722657\pi$
$223$	5.08826	−	8.81313i	0.340735	−	0.590171i	0.984569	+	0.174994i	$0.0559907\pi$
$224$	2.08826	+	3.61697i	0.139528	+	0.241669i
$225$		0			0
$226$	2.58960	−	4.48531i	0.172257	−	0.298359i
$227$	8.50963			0.564804			0.282402	−	0.959296i	$-0.408869\pi$
$227$	8.50963			0.564804			0.282402	+	0.959296i	$0.408869\pi$
$228$	−8.70612	−	10.7666i	−0.576577	−	0.713033i
$229$	−6.80760			−0.449859			−0.224930	−	0.974375i	$-0.572215\pi$
$229$	−6.80760			−0.449859			−0.224930	+	0.974375i	$0.572215\pi$
$230$		0			0
$231$	−25.8875	+	44.8385i	−1.70327	+	2.95016i
$232$	1.21745	+	2.10868i	0.0799295	+	0.138442i
$233$	12.5225	−	21.6896i	0.820375	−	1.42093i	−0.0850282	−	0.996379i	$-0.527098\pi$
$233$	12.5225	−	21.6896i	0.820375	−	1.42093i	0.905403	−	0.424553i	$-0.139569\pi$
$234$	−1.69765	−	2.94042i	−0.110979	−	0.192221i
$235$		0			0
$236$	−7.65539			−0.498323
$237$	10.1644	+	17.6052i	0.660247	+	1.14358i
$238$	1.02332	+	1.77244i	0.0663321	+	0.114890i
$239$	21.4122			1.38504			0.692519	−	0.721400i	$-0.256501\pi$
$239$	21.4122			1.38504			0.692519	+	0.721400i	$0.256501\pi$
$240$		0			0
$241$	−5.64540	−	9.77811i	−0.363652	−	0.629864i	0.624907	−	0.780699i	$-0.285137\pi$
$241$	−5.64540	−	9.77811i	−0.363652	−	0.629864i	−0.988559	+	0.150836i	$0.951804\pi$
$242$	2.11514	−	3.66353i	0.135966	−	0.235500i
$243$	12.2780	+	21.2661i	0.787633	+	1.36422i
$244$	4.65673	−	8.06569i	0.298116	−	0.516353i
$245$		0			0
$246$	−1.61991			−0.103282
$247$	−0.749399	+	1.94817i	−0.0476831	+	0.123959i
$248$	−2.42373			−0.153907
$249$	12.6454	−	21.9025i	0.801369	−	1.38801i
$250$		0			0
$251$	8.08892	+	14.0104i	0.510568	+	0.884330i	0.999925	+	0.0122463i	$0.00389820\pi$
$251$	8.08892	+	14.0104i	0.510568	+	0.884330i	−0.489357	+	0.872084i	$0.662768\pi$
$252$	−14.8064	+	25.6454i	−0.932714	+	1.61551i
$253$	11.1178	+	19.2566i	0.698972	+	1.21065i
$254$	−4.71052			−0.295565
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.92085	−	8.52316i	−0.306954	−	0.531660i	0.670740	−	0.741692i	$-0.265976\pi$
$257$	−4.92085	−	8.52316i	−0.306954	−	0.531660i	−0.977694	+	0.210032i	$0.932643\pi$
$258$	18.5113			1.15246
$259$	35.3825			2.19856
$260$		0			0
$261$	−8.63207	+	14.9512i	−0.534312	+	0.925455i
$262$	6.65454	+	11.5260i	0.411119	+	0.712078i
$263$	−14.1329	+	24.4789i	−0.871471	+	1.50943i	−0.0109968	+	0.999940i	$0.503500\pi$
$263$	−14.1329	+	24.4789i	−0.871471	+	1.50943i	−0.860475	+	0.509493i	$0.829833\pi$
$264$	6.19834	−	10.7358i	0.381482	−	0.660746i
$265$		0			0
$266$	17.9829	−	2.83530i	1.10260	−	0.173843i
$267$	17.5424			1.07358
$268$	0.809957	−	1.40289i	0.0494760	−	0.0856950i
$269$	−16.1099	+	27.9031i	−0.982237	+	1.70128i	−0.328614	+	0.944464i	$0.606582\pi$
$269$	−16.1099	+	27.9031i	−0.982237	+	1.70128i	−0.653623	+	0.756820i	$0.726752\pi$
$270$		0			0
$271$	5.35390	−	9.27322i	0.325226	−	0.563308i	−0.656332	−	0.754472i	$-0.727893\pi$
$271$	5.35390	−	9.27322i	0.325226	−	0.563308i	0.981558	+	0.191164i	$0.0612262\pi$
$272$	−0.245018	−	0.424383i	−0.0148564	−	0.0257320i
$273$	6.35304			0.384504
$274$	−0.388580			−0.0234750
$275$		0			0
$276$	9.04936	+	15.6740i	0.544707	+	0.943461i
$277$	−0.293522			−0.0176360			−0.00881801	−	0.999961i	$-0.502807\pi$
$277$	−0.293522			−0.0176360			−0.00881801	+	0.999961i	$0.502807\pi$
$278$	−17.6412			−1.05805
$279$	−8.59248	−	14.8826i	−0.514418	−	0.890998i
$280$		0			0
$281$	8.30301	+	14.3812i	0.495316	+	0.857912i	0.999985	−	0.00540048i	$-0.00171903\pi$
$281$	8.30301	+	14.3812i	0.495316	+	0.857912i	−0.504670	+	0.863313i	$0.668386\pi$
$282$	−1.54312	+	2.67276i	−0.0918913	+	0.159160i
$283$	5.07118	−	8.78355i	0.301451	−	0.522128i	−0.675014	−	0.737805i	$-0.735863\pi$
$283$	5.07118	−	8.78355i	0.301451	−	0.522128i	0.976465	+	0.215677i	$0.0691959\pi$
$284$	−1.87418			−0.111212
$285$		0			0
$286$	−1.86883			−0.110506
$287$	1.06494	−	1.84453i	0.0628614	−	0.108879i
$288$	3.54514	−	6.14037i	0.208900	−	0.361825i
$289$	8.37993	+	14.5145i	0.492937	+	0.853792i
$290$		0			0
$291$	23.0139	+	39.8612i	1.34910	+	2.33670i
$292$	4.70615			0.275406
$293$	5.09200			0.297478			0.148739	−	0.988877i	$-0.452479\pi$
$293$	5.09200			0.297478			0.148739	+	0.988877i	$0.452479\pi$
$294$	−16.5867	−	28.7291i	−0.967358	−	1.67551i
$295$		0			0
$296$	−8.47175			−0.492411
$297$	50.7060			2.94226
$298$	−7.64556	−	13.2425i	−0.442895	−	0.767117i
$299$	1.36421	−	2.36288i	0.0788943	−	0.136649i
$300$		0			0
$301$	−12.1694	+	21.0780i	−0.701433	+	1.21492i
$302$	8.31332	−	14.3991i	0.478378	−	0.828575i
$303$	1.78115			0.102324
$304$	−4.30571	+	0.678866i	−0.246949	+	0.0389357i
$305$		0			0
$306$	1.73725	−	3.00900i	0.0993117	−	0.172013i
$307$	−9.46802	+	16.3991i	−0.540368	+	0.935946i	0.458514	+	0.888687i	$0.348382\pi$
$307$	−9.46802	+	16.3991i	−0.540368	+	0.935946i	−0.998883	+	0.0472585i	$0.984952\pi$
$308$	8.14964	+	14.1156i	0.464369	+	0.804311i
$309$	−20.5732	+	35.6338i	−1.17037	+	2.02714i
$310$		0			0
$311$	−8.61109			−0.488290			−0.244145	−	0.969739i	$-0.578507\pi$
$311$	−8.61109			−0.488290			−0.244145	+	0.969739i	$0.578507\pi$
$312$	−1.52113			−0.0861172
$313$	0.410884	+	0.711672i	0.0232245	+	0.0402261i	0.877404	−	0.479752i	$-0.159273\pi$
$313$	0.410884	+	0.711672i	0.0232245	+	0.0402261i	−0.854180	+	0.519978i	$0.825940\pi$
$314$	6.08401	+	10.5378i	0.343341	+	0.594684i
$315$		0			0
$316$	6.39968			0.360010
$317$	3.46887	+	6.00826i	0.194831	+	0.337458i	0.946845	−	0.321690i	$-0.104251\pi$
$317$	3.46887	+	6.00826i	0.194831	+	0.337458i	−0.752014	+	0.659147i	$0.770917\pi$
$318$	8.82753	−	15.2897i	0.495023	−	0.857406i
$319$	4.75122	+	8.22935i	0.266017	+	0.460755i
$320$		0			0
$321$	15.8826	−	27.5095i	0.886481	−	1.53543i
$322$	−23.7964			−1.32612
$323$	−2.10995	+	0.332668i	−0.117401	+	0.0185102i
$324$	20.0013			1.11118
$325$		0			0
$326$	7.23369	−	12.5291i	0.400637	−	0.693924i
$327$	−15.3487	−	26.5847i	−0.848783	−	1.47014i
$328$	−0.254982	+	0.441643i	−0.0140790	+	0.0243856i
$329$	−2.02891	−	3.51417i	−0.111857	−	0.193742i
$330$		0			0
$331$	−35.4051			−1.94604			−0.973021	−	0.230718i	$-0.925893\pi$
$331$	−35.4051			−1.94604			−0.973021	+	0.230718i	$0.925893\pi$
$332$	−3.98089	−	6.89511i	−0.218480	−	0.378418i
$333$	−30.0336	−	52.0197i	−1.64583	−	2.85066i
$334$	3.29823			0.180471
$335$		0			0
$336$	6.63340	+	11.4894i	0.361882	+	0.626798i
$337$	−1.27608	+	2.21024i	−0.0695127	+	0.120400i	−0.898687	−	0.438591i	$-0.855478\pi$
$337$	−1.27608	+	2.21024i	−0.0695127	+	0.120400i	0.829174	+	0.558990i	$0.188811\pi$
$338$	−6.38534	−	11.0597i	−0.347317	−	0.601570i
$339$	8.22591	−	14.2477i	0.446770	−	0.773829i
$340$		0			0
$341$	−9.45885			−0.512225
$342$	−19.4329	−	24.0320i	−1.05081	−	1.29950i
$343$	14.3811			0.776509
$344$	2.91377	−	5.04679i	0.157100	−	0.272105i
$345$		0			0
$346$	4.96668	+	8.60255i	0.267011	+	0.462476i
$347$	14.1149	−	24.4477i	0.757728	−	1.31242i	−0.186278	−	0.982497i	$-0.559643\pi$
$347$	14.1149	−	24.4477i	0.757728	−	1.31242i	0.944006	−	0.329927i	$-0.107024\pi$
$348$	3.86725	+	6.69828i	0.207307	+	0.359066i
$349$	18.2442			0.976590			0.488295	−	0.872679i	$-0.337619\pi$
$349$	18.2442			0.976590			0.488295	+	0.872679i	$0.337619\pi$
$350$		0			0
$351$	−3.11094	−	5.38830i	−0.166049	−	0.287606i
$352$	−1.95130	−	3.37975i	−0.104005	−	0.180141i
$353$	−35.7778			−1.90426			−0.952129	−	0.305696i	$-0.901111\pi$
$353$	−35.7778			−1.90426			−0.952129	+	0.305696i	$0.901111\pi$
$354$	−24.3175			−1.29246
$355$		0			0
$356$	2.76126	−	4.78264i	0.146346	−	0.253479i
$357$	3.25060	+	5.63021i	0.172040	+	0.297982i
$358$	−5.39616	+	9.34642i	−0.285196	+	0.493974i
$359$	−15.9454	+	27.6182i	−0.841565	+	1.45763i	0.0470054	+	0.998895i	$0.485032\pi$
$359$	−15.9454	+	27.6182i	−0.841565	+	1.45763i	−0.888571	+	0.458739i	$0.848301\pi$
$360$		0			0
$361$	−3.97635	+	18.5793i	−0.209282	+	0.977855i
$362$	−11.9181			−0.626404
$363$	6.71878	−	11.6373i	0.352645	−	0.610798i
$364$	1.00000	−	1.73205i	0.0524142	−	0.0907841i
$365$		0			0
$366$	14.7922	−	25.6208i	0.773200	−	1.33922i
$367$	16.4554	+	28.5015i	0.858962	+	1.48777i	0.872920	+	0.487864i	$0.162224\pi$
$367$	16.4554	+	28.5015i	0.858962	+	1.48777i	−0.0139572	+	0.999903i	$0.504443\pi$
$368$	5.69765			0.297011
$369$	−3.61580			−0.188231
$370$		0			0
$371$	11.6065	+	20.1031i	0.602581	+	1.04370i
$372$	−7.69903			−0.399176
$373$	−14.9290			−0.772994			−0.386497	−	0.922291i	$-0.626315\pi$
$373$	−14.9290			−0.772994			−0.386497	+	0.922291i	$0.626315\pi$
$374$	−0.956205	−	1.65620i	−0.0494442	−	0.0856399i
$375$		0			0
$376$	0.485788	+	0.841410i	0.0250526	+	0.0433924i
$377$	0.582997	−	1.00978i	0.0300259	−	0.0520063i
$378$	−27.1325	+	46.9949i	−1.39555	+	2.41716i
$379$	−26.5535			−1.36396			−0.681982	−	0.731369i	$-0.738882\pi$
$379$	−26.5535			−1.36396			−0.681982	+	0.731369i	$0.738882\pi$
$380$		0			0
$381$	−14.9631			−0.766582
$382$	−2.43490	+	4.21737i	−0.124580	+	0.215779i
$383$	−18.5490	+	32.1279i	−0.947811	+	1.64166i	−0.197789	+	0.980245i	$0.563376\pi$
$383$	−18.5490	+	32.1279i	−0.947811	+	1.64166i	−0.750022	+	0.661413i	$0.769957\pi$
$384$	−1.58826	−	2.75095i	−0.0810506	−	0.140384i
$385$		0			0
$386$	10.8919	+	18.8653i	0.554384	+	0.960221i
$387$	41.3189			2.10036
$388$	14.4900			0.735617
$389$	3.91887	+	6.78768i	0.198695	+	0.344149i	0.948105	−	0.317956i	$-0.102997\pi$
$389$	3.91887	+	6.78768i	0.198695	+	0.344149i	−0.749411	+	0.662105i	$0.769663\pi$
$390$		0			0
$391$	2.79205			0.141200
$392$	−10.4433			−0.527468
$393$	21.1383	+	36.6126i	1.06629	+	1.84686i
$394$	−6.86794	+	11.8956i	−0.346002	+	0.599293i
$395$		0			0
$396$	13.8353	−	23.9634i	0.695249	−	1.20421i
$397$	−11.5460	+	19.9983i	−0.579477	+	1.00368i	0.416062	+	0.909336i	$0.363410\pi$
$397$	−11.5460	+	19.9983i	−0.579477	+	1.00368i	−0.995539	+	0.0943476i	$0.969923\pi$
$398$	−20.8867			−1.04695
$399$	57.1230	−	9.00639i	2.85973	−	0.450884i
$400$		0			0
$401$	−1.94555	+	3.36979i	−0.0971561	+	0.168279i	−0.910506	−	0.413495i	$-0.864308\pi$
$401$	−1.94555	+	3.36979i	−0.0971561	+	0.168279i	0.813350	+	0.581774i	$0.197641\pi$
$402$	2.57285	−	4.45630i	0.128322	−	0.222260i
$403$	0.580323	+	1.00515i	0.0289079	+	0.0500700i
$404$	0.280362	−	0.485601i	0.0139485	−	0.0241596i
$405$		0			0
$406$	−10.1694			−0.504699
$407$	−33.0619			−1.63882
$408$	−0.778304	−	1.34806i	−0.0385318	−	0.0667390i
$409$	−11.6831	−	20.2357i	−0.577692	−	1.00059i	−0.995743	−	0.0921681i	$-0.970620\pi$
$409$	−11.6831	−	20.2357i	−0.577692	−	1.00059i	0.418052	−	0.908423i	$-0.362713\pi$
$410$		0			0
$411$	−1.23433			−0.0608851
$412$	6.47665	+	11.2179i	0.319082	+	0.552665i
$413$	15.9864	−	27.6893i	0.786642	−	1.36250i
$414$	20.1990	+	34.9857i	0.992727	+	1.71945i
$415$		0			0
$416$	−0.239434	+	0.414711i	−0.0117392	+	0.0203329i
$417$	−56.0375			−2.74417
$418$	−16.8035	+	2.64934i	−0.821884	+	0.129584i
$419$	−3.10343			−0.151612			−0.0758062	−	0.997123i	$-0.524153\pi$
$419$	−3.10343			−0.151612			−0.0758062	+	0.997123i	$0.524153\pi$
$420$		0			0
$421$	12.3730	−	21.4307i	0.603024	−	1.04447i	−0.389337	−	0.921096i	$-0.627296\pi$
$421$	12.3730	−	21.4307i	0.603024	−	1.04447i	0.992360	−	0.123372i	$-0.0393710\pi$
$422$	−8.30571	−	14.3859i	−0.404316	−	0.700295i
$423$	−3.44438	+	5.96584i	−0.167471	+	0.290069i
$424$	−2.77899	−	4.81336i	−0.134960	−	0.233757i
$425$		0			0
$426$	−5.95336			−0.288441
$427$	19.4489	+	33.6865i	0.941199	+	1.63020i
$428$	−5.00000	−	8.66025i	−0.241684	−	0.418609i
$429$	−5.93637			−0.286611
$430$		0			0
$431$	−18.1220	−	31.3883i	−0.872908	−	1.51192i	−0.858975	−	0.512018i	$-0.828898\pi$
$431$	−18.1220	−	31.3883i	−0.872908	−	1.51192i	−0.0139333	−	0.999903i	$-0.504435\pi$
$432$	6.49644	−	11.2522i	0.312560	−	0.541370i
$433$	−3.41037	−	5.90694i	−0.163892	−	0.283869i	0.772369	−	0.635174i	$-0.219072\pi$
$433$	−3.41037	−	5.90694i	−0.163892	−	0.283869i	−0.936261	+	0.351305i	$0.885738\pi$
$434$	5.06138	−	8.76657i	0.242954	−	0.420809i
$435$		0			0
$436$	−9.66382			−0.462813
$437$	8.91648	−	23.1797i	0.426533	−	1.10884i
$438$	14.9492			0.714299
$439$	−17.4391	+	30.2054i	−0.832322	+	1.44162i	0.0638702	+	0.997958i	$0.479656\pi$
$439$	−17.4391	+	30.2054i	−0.832322	+	1.44162i	−0.896192	+	0.443666i	$0.853678\pi$
$440$		0			0
$441$	−37.0231	−	64.1259i	−1.76301	−	3.05361i
$442$	−0.117331	+	0.203223i	−0.00558086	+	0.00966634i
$443$	11.6008	+	20.0932i	0.551171	+	0.954656i	0.998190	+	0.0601320i	$0.0191522\pi$
$443$	11.6008	+	20.0932i	0.551171	+	0.954656i	−0.447019	+	0.894524i	$0.647515\pi$
$444$	−26.9107			−1.27713
$445$		0			0
$446$	−5.08826	−	8.81313i	−0.240936	−	0.417314i
$447$	−24.2863	−	42.0651i	−1.14870	−	1.98961i
$448$	4.17652			0.197322
$449$	−38.9584			−1.83856			−0.919280	−	0.393603i	$-0.871228\pi$
$449$	−38.9584			−1.83856			−0.919280	+	0.393603i	$0.871228\pi$
$450$		0			0
$451$	−0.995094	+	1.72355i	−0.0468572	+	0.0811590i
$452$	−2.58960	−	4.48531i	−0.121804	−	0.210971i
$453$	26.4074	−	45.7390i	1.24073	−	2.14901i
$454$	4.25482	−	7.36956i	0.199688	−	0.345871i
$455$		0			0
$456$	−13.6772	+	2.15643i	−0.640493	+	0.100984i
$457$	−10.0845			−0.471732			−0.235866	−	0.971786i	$-0.575793\pi$
$457$	−10.0845			−0.471732			−0.235866	+	0.971786i	$0.575793\pi$
$458$	−3.40380	+	5.89556i	−0.159049	+	0.275481i
$459$	3.18349	−	5.51396i	0.148592	−	0.257370i
$460$		0			0
$461$	1.74501	−	3.02245i	0.0812734	−	0.140770i	−0.822524	−	0.568731i	$-0.807435\pi$
$461$	1.74501	−	3.02245i	0.0812734	−	0.140770i	0.903797	+	0.427961i	$0.140768\pi$
$462$	25.8875	+	44.8385i	1.20440	+	2.08608i
$463$	−6.70988			−0.311835			−0.155917	−	0.987770i	$-0.549833\pi$
$463$	−6.70988			−0.311835			−0.155917	+	0.987770i	$0.549833\pi$
$464$	2.43490			0.113037
$465$		0			0
$466$	−12.5225	−	21.6896i	−0.580093	−	1.00475i
$467$	32.1400			1.48726			0.743630	−	0.668592i	$-0.233103\pi$
$467$	32.1400			1.48726			0.743630	+	0.668592i	$0.233103\pi$
$468$	−3.39531			−0.156948
$469$	3.38280	+	5.85919i	0.156203	+	0.270552i
$470$		0			0
$471$	19.3260	+	33.4736i	0.890495	+	1.54238i
$472$	−3.82769	+	6.62976i	−0.176184	+	0.305159i
$473$	11.3713	−	19.6956i	0.522851	−	0.905605i
$474$	20.3287			0.933730
$475$		0			0
$476$	2.04664			0.0938077
$477$	19.7039	−	34.1281i	0.902178	−	1.56262i
$478$	10.7061	−	18.5435i	0.489685	−	0.848159i
$479$	−5.69498	−	9.86399i	−0.260210	−	0.450697i	0.706087	−	0.708125i	$-0.250459\pi$
$479$	−5.69498	−	9.86399i	−0.260210	−	0.450697i	−0.966298	+	0.257427i	$0.917125\pi$
$480$		0			0
$481$	2.02842	+	3.51333i	0.0924882	+	0.160194i
$482$	−11.2908			−0.514282
$483$	−75.5897			−3.43945
$484$	−2.11514	−	3.66353i	−0.0961427	−	0.166524i
$485$		0			0
$486$	24.5560			1.11388
$487$	−28.3103			−1.28286			−0.641432	−	0.767180i	$-0.721659\pi$
$487$	−28.3103			−1.28286			−0.641432	+	0.767180i	$0.721659\pi$
$488$	−4.65673	−	8.06569i	−0.210800	−	0.365116i
$489$	22.9780	−	39.7990i	1.03910	−	1.79977i
$490$		0			0
$491$	7.91187	−	13.7038i	0.357058	−	0.618442i	−0.630410	−	0.776262i	$-0.717113\pi$
$491$	7.91187	−	13.7038i	0.357058	−	0.618442i	0.987468	+	0.157820i	$0.0504466\pi$
$492$	−0.809957	+	1.40289i	−0.0365157	+	0.0632470i
$493$	1.19319			0.0537384
$494$	1.31247	+	1.62308i	0.0590506	+	0.0730260i
$495$		0			0
$496$	−1.21187	+	2.09901i	−0.0544144	+	0.0942485i
$497$	3.91377	−	6.77884i	0.175556	−	0.304073i
$498$	−12.6454	−	21.9025i	−0.566654	−	0.981473i
$499$	−0.827004	+	1.43241i	−0.0370218	+	0.0641236i	−0.883943	−	0.467595i	$-0.845120\pi$
$499$	−0.827004	+	1.43241i	−0.0370218	+	0.0641236i	0.846921	+	0.531719i	$0.178454\pi$
$500$		0			0
$501$	10.4769			0.468073
$502$	16.1778			0.722052
$503$	8.21135	+	14.2225i	0.366126	+	0.634149i	0.988956	−	0.148208i	$-0.0473506\pi$
$503$	8.21135	+	14.2225i	0.366126	+	0.634149i	−0.622830	+	0.782357i	$0.714017\pi$
$504$	14.8064	+	25.6454i	0.659528	+	1.14234i
$505$		0			0
$506$	22.2357			0.988496
$507$	−20.2832	−	35.1315i	−0.900808	−	1.56024i
$508$	−2.35526	+	4.07943i	−0.104498	+	0.180996i
$509$	3.12210	+	5.40764i	0.138385	+	0.239689i	0.926885	−	0.375345i	$-0.122476\pi$
$509$	3.12210	+	5.40764i	0.138385	+	0.239689i	−0.788501	+	0.615034i	$0.789142\pi$
$510$		0			0
$511$	−9.82766	+	17.0220i	−0.434750	+	0.753009i
$512$	−1.00000			−0.0441942
$513$	−35.6105	−	44.0384i	−1.57224	−	1.94434i
$514$	−9.84170			−0.434099
$515$		0			0
$516$	9.25564	−	16.0312i	0.407457	−	0.705736i
$517$	1.89584	+	3.28369i	0.0833788	+	0.144416i
$518$	17.6912	−	30.6421i	0.777308	−	1.34634i
$519$	15.7768	+	27.3262i	0.692524	+	1.19949i
$520$		0			0
$521$	−7.60025			−0.332973			−0.166487	−	0.986044i	$-0.553242\pi$
$521$	−7.60025			−0.332973			−0.166487	+	0.986044i	$0.553242\pi$
$522$	8.63207	+	14.9512i	0.377815	+	0.654395i
$523$	13.3321	+	23.0919i	0.582971	+	1.00974i	0.995125	+	0.0986218i	$0.0314434\pi$
$523$	13.3321	+	23.0919i	0.582971	+	1.00974i	−0.412153	+	0.911114i	$0.635223\pi$
$524$	13.3091			0.581410
$525$		0			0
$526$	14.1329	+	24.4789i	0.616223	+	1.06733i
$527$	−0.593857	+	1.02859i	−0.0258688	+	0.0448061i
$528$	−6.19834	−	10.7358i	−0.269748	−	0.467218i
$529$	−4.73163	+	8.19542i	−0.205723	+	0.356323i
$530$		0			0
$531$	−54.2789			−2.35550
$532$	6.53600	−	16.9913i	0.283372	−	0.736666i
$533$	0.244206			0.0105777
$534$	8.77119	−	15.1921i	0.379567	−	0.657428i
$535$		0			0
$536$	−0.809957	−	1.40289i	−0.0349848	−	0.0605955i
$537$	−17.1410	+	29.6891i	−0.739689	+	1.28118i
$538$	16.1099	+	27.9031i	0.694547	+	1.20299i
$539$	−40.7561			−1.75549
$540$		0			0
$541$	7.84818	+	13.5934i	0.337420	+	0.584428i	0.983947	−	0.178463i	$-0.0571125\pi$
$541$	7.84818	+	13.5934i	0.337420	+	0.584428i	−0.646527	+	0.762891i	$0.723779\pi$
$542$	−5.35390	−	9.27322i	−0.229970	−	0.398319i
$543$	−37.8582			−1.62465
$544$	−0.490035			−0.0210101
$545$		0			0
$546$	3.17652	−	5.50190i	0.135943	−	0.235459i
$547$	−8.69054	−	15.0525i	−0.371581	−	0.643597i	0.618228	−	0.785999i	$-0.287851\pi$
$547$	−8.69054	−	15.0525i	−0.371581	−	0.643597i	−0.989809	+	0.142402i	$0.954517\pi$
$548$	−0.194290	+	0.336520i	−0.00829965	+	0.0143754i
$549$	33.0175	−	57.1880i	1.40915	−	2.44073i
$550$		0			0
$551$	3.81047	−	9.90587i	0.162331	−	0.422004i
$552$	18.0987			0.770333
$553$	−13.3642	+	23.1475i	−0.568304	+	0.984331i
$554$	−0.146761	+	0.254197i	−0.00623527	+	0.0107998i
$555$		0			0
$556$	−8.82058	+	15.2777i	−0.374076	+	0.647919i
$557$	−1.07696	−	1.86535i	−0.0456324	−	0.0790376i	0.842307	−	0.538998i	$-0.181197\pi$
$557$	−1.07696	−	1.86535i	−0.0456324	−	0.0790376i	−0.887939	+	0.459960i	$0.847864\pi$
$558$	−17.1850			−0.727497
$559$	−2.79062			−0.118030
$560$		0			0
$561$	−3.03741	−	5.26094i	−0.128239	−	0.222117i
$562$	16.6060			0.700482
$563$	12.2897			0.517951			0.258975	−	0.965884i	$-0.416615\pi$
$563$	12.2897			0.517951			0.258975	+	0.965884i	$0.416615\pi$
$564$	1.54312	+	2.67276i	0.0649769	+	0.112543i
$565$		0			0
$566$	−5.07118	−	8.78355i	−0.213158	−	0.369200i
$567$	−41.7680	+	72.3442i	−1.75409	+	3.03817i
$568$	−0.937088	+	1.62308i	−0.0393193	+	0.0681031i
$569$	−14.8699			−0.623377			−0.311688	−	0.950184i	$-0.600894\pi$
$569$	−14.8699			−0.623377			−0.311688	+	0.950184i	$0.600894\pi$
$570$		0			0
$571$	44.1772			1.84876			0.924379	−	0.381475i	$-0.124584\pi$
$571$	44.1772			1.84876			0.924379	+	0.381475i	$0.124584\pi$
$572$	−0.934414	+	1.61845i	−0.0390698	+	0.0676709i
$573$	−7.73451	+	13.3966i	−0.323114	+	0.559649i
$574$	−1.06494	−	1.84453i	−0.0444497	−	0.0769892i
$575$		0			0
$576$	−3.54514	−	6.14037i	−0.147714	−	0.255849i
$577$	28.4224			1.18324			0.591621	−	0.806216i	$-0.298488\pi$
$577$	28.4224			1.18324			0.591621	+	0.806216i	$0.298488\pi$
$578$	16.7599			0.697119
$579$	34.5984	+	59.9262i	1.43786	+	2.49045i
$580$		0			0
$581$	33.2526			1.37955
$582$	46.0277			1.90791
$583$	−10.8453	−	18.7846i	−0.449166	−	0.777979i
$584$	2.35307	−	4.07564i	0.0973709	−	0.168651i
$585$		0			0
$586$	2.54600	−	4.40980i	0.105174	−	0.182167i
$587$	9.18228	−	15.9042i	0.378993	−	0.656435i	−0.611923	−	0.790917i	$-0.709604\pi$
$587$	9.18228	−	15.9042i	0.378993	−	0.656435i	0.990916	+	0.134482i	$0.0429370\pi$
$588$	−33.1735			−1.36805
$589$	6.64289	+	8.21505i	0.273716	+	0.338495i
$590$		0			0
$591$	−21.8162	+	37.7867i	−0.897397	+	1.55434i
$592$	−4.23588	+	7.33675i	−0.174093	+	0.301539i
$593$	−1.90092	−	3.29249i	−0.0780614	−	0.135206i	0.824352	−	0.566077i	$-0.191540\pi$
$593$	−1.90092	−	3.29249i	−0.0780614	−	0.135206i	−0.902413	+	0.430871i	$0.858206\pi$
$594$	25.3530	−	43.9127i	1.04025	−	1.80176i
$595$		0			0
$596$	−15.2911			−0.626349
$597$	−66.3469			−2.71540
$598$	−1.36421	−	2.36288i	−0.0557867	−	0.0966254i
$599$	−17.1530	−	29.7099i	−0.700853	−	1.21391i	−0.968167	−	0.250303i	$-0.919470\pi$
$599$	−17.1530	−	29.7099i	−0.700853	−	1.21391i	0.267315	−	0.963609i	$-0.413864\pi$
$600$		0			0
$601$	−18.1820			−0.741660			−0.370830	−	0.928701i	$-0.620927\pi$
$601$	−18.1820			−0.741660			−0.370830	+	0.928701i	$0.620927\pi$
$602$	12.1694	+	21.0780i	0.495988	+	0.859076i
$603$	5.74283	−	9.94687i	0.233866	−	0.405068i
$604$	−8.31332	−	14.3991i	−0.338264	−	0.585891i
$605$		0			0
$606$	0.890576	−	1.54252i	0.0361772	−	0.0626607i
$607$	2.01961			0.0819733			0.0409867	−	0.999160i	$-0.486950\pi$
$607$	2.01961			0.0819733			0.0409867	+	0.999160i	$0.486950\pi$
$608$	−1.56494	+	4.06829i	−0.0634667	+	0.164991i
$609$	−32.3033			−1.30900
$610$		0			0
$611$	0.232628	−	0.402924i	0.00941113	−	0.0163006i
$612$	−1.73725	−	3.00900i	−0.0702240	−	0.121631i
$613$	3.11850	−	5.40141i	0.125955	−	0.218161i	−0.796151	−	0.605098i	$-0.793134\pi$
$613$	3.11850	−	5.40141i	0.125955	−	0.218161i	0.922106	+	0.386938i	$0.126467\pi$
$614$	9.46802	+	16.3991i	0.382098	+	0.661813i
$615$		0			0
$616$	16.2993			0.656717
$617$	3.84830	+	6.66545i	0.154927	+	0.268341i	0.933032	−	0.359793i	$-0.117153\pi$
$617$	3.84830	+	6.66545i	0.154927	+	0.268341i	−0.778106	+	0.628133i	$0.783819\pi$
$618$	20.5732	+	35.6338i	0.827576	+	1.43340i
$619$	41.1392			1.65352			0.826762	−	0.562551i	$-0.190180\pi$
$619$	41.1392			1.65352			0.826762	+	0.562551i	$0.190180\pi$
$620$		0			0
$621$	37.0145	+	64.1110i	1.48534	+	2.57268i
$622$	−4.30554	+	7.45742i	−0.172637	+	0.299015i
$623$	11.5324	+	19.9748i	0.462038	+	0.800273i
$624$	−0.760566	+	1.31734i	−0.0304470	+	0.0527358i
$625$		0			0
$626$	0.821768			0.0328444
$627$	−53.3765	+	8.41570i	−2.13165	+	0.336091i
$628$	12.1680			0.485557
$629$	−2.07573	+	3.59527i	−0.0827647	+	0.143353i
$630$		0			0
$631$	7.59739	+	13.1591i	0.302447	+	0.523854i	0.976690	−	0.214656i	$-0.0688631\pi$
$631$	7.59739	+	13.1591i	0.302447	+	0.523854i	−0.674243	+	0.738510i	$0.735530\pi$
$632$	3.19984	−	5.54229i	0.127283	−	0.220460i
$633$	−26.3833	−	45.6972i	−1.04864	−	1.81630i
$634$	6.93774			0.275533
$635$		0			0
$636$	−8.82753	−	15.2897i	−0.350034	−	0.606277i
$637$	2.50049	+	4.33097i	0.0990728	+	0.171599i
$638$	9.50243			0.376205
$639$	−13.2884			−0.525683
$640$		0			0
$641$	−18.0506	+	31.2645i	−0.712955	+	1.23487i	0.250788	+	0.968042i	$0.419310\pi$
$641$	−18.0506	+	31.2645i	−0.712955	+	1.23487i	−0.963743	+	0.266832i	$0.914023\pi$
$642$	−15.8826	−	27.5095i	−0.626836	−	1.08571i
$643$	2.05734	−	3.56342i	0.0811336	−	0.140528i	−0.822604	−	0.568615i	$-0.807479\pi$
$643$	2.05734	−	3.56342i	0.0811336	−	0.140528i	0.903737	+	0.428088i	$0.140813\pi$
$644$	−11.8982	+	20.6083i	−0.468854	+	0.812079i
$645$		0			0
$646$	−0.766875	+	1.99360i	−0.0301723	+	0.0784373i
$647$	−10.0471			−0.394991			−0.197495	−	0.980304i	$-0.563281\pi$
$647$	−10.0471			−0.394991			−0.197495	+	0.980304i	$0.563281\pi$
$648$	10.0007	−	17.3216i	0.392863	−	0.680459i
$649$	−14.9380	+	25.8733i	−0.586366	+	1.01562i
$650$		0			0
$651$	16.0776	−	27.8472i	0.630130	−	1.09142i
$652$	−7.23369	−	12.5291i	−0.283293	−	0.490678i
$653$	−41.5606			−1.62639			−0.813196	−	0.581989i	$-0.802275\pi$
$653$	−41.5606			−1.62639			−0.813196	+	0.581989i	$0.802275\pi$
$654$	−30.6973			−1.20036
$655$		0			0
$656$	0.254982	+	0.441643i	0.00995539	+	0.0172432i
$657$	33.3679			1.30181
$658$	−4.05781			−0.158190
$659$	−6.16587	−	10.6796i	−0.240188	−	0.416018i	0.720580	−	0.693372i	$-0.243876\pi$
$659$	−6.16587	−	10.6796i	−0.240188	−	0.416018i	−0.960768	+	0.277354i	$0.910542\pi$
$660$		0			0
$661$	9.49203	+	16.4407i	0.369197	+	0.639469i	0.989440	−	0.144941i	$-0.0462993\pi$
$661$	9.49203	+	16.4407i	0.369197	+	0.639469i	−0.620243	+	0.784410i	$0.712966\pi$
$662$	−17.7026	+	30.6617i	−0.688030	+	1.19170i
$663$	−0.372704	+	0.645543i	−0.0144746	+	0.0250708i
$664$	−7.96179			−0.308977
$665$		0			0
$666$	−60.0672			−2.32756
$667$	−6.93661	+	12.0146i	−0.268586	+	0.465205i
$668$	1.64911	−	2.85635i	0.0638062	−	0.110516i
$669$	−16.1630	−	27.9951i	−0.624896	−	1.08235i
$670$		0			0
$671$	−18.1733	−	31.4771i	−0.701574	−	1.21516i
$672$	13.2668			0.511778
$673$	−7.23063			−0.278720			−0.139360	−	0.990242i	$-0.544505\pi$
$673$	−7.23063			−0.278720			−0.139360	+	0.990242i	$0.544505\pi$
$674$	1.27608	+	2.21024i	0.0491529	+	0.0851353i
$675$		0			0
$676$	−12.7707			−0.491180
$677$	13.0555			0.501762			0.250881	−	0.968018i	$-0.419280\pi$
$677$	13.0555			0.501762			0.250881	+	0.968018i	$0.419280\pi$
$678$	−8.22591	−	14.2477i	−0.315914	−	0.547180i
$679$	−30.2588	+	52.4098i	−1.16123	+	2.01131i
$680$		0			0
$681$	13.5155	−	23.4096i	0.517916	−	0.897056i
$682$	−4.72943	+	8.19161i	−0.181099	+	0.313673i
$683$	4.98007			0.190557			0.0952785	−	0.995451i	$-0.469626\pi$
$683$	4.98007			0.190557			0.0952785	+	0.995451i	$0.469626\pi$
$684$	−30.5287	+	4.81336i	−1.16729	+	0.184043i
$685$		0			0
$686$	7.19057	−	12.4544i	0.274537	−	0.475513i
$687$	−10.8122	+	18.7274i	−0.412513	+	0.714493i
$688$	−2.91377	−	5.04679i	−0.111086	−	0.192407i
$689$	−1.33077	+	2.30496i	−0.0506983	+	0.0878120i
$690$		0			0
$691$	20.2330			0.769699			0.384849	−	0.922979i	$-0.374253\pi$
$691$	20.2330			0.769699			0.384849	+	0.922979i	$0.374253\pi$
$692$	9.93337			0.377610
$693$	57.7833	+	100.084i	2.19501	+	3.80186i
$694$	−14.1149	−	24.4477i	−0.535795	−	0.928024i
$695$		0			0
$696$	7.73451			0.293176
$697$	0.124950	+	0.216420i	0.00473283	+	0.00819751i
$698$	9.12210	−	15.7999i	0.345277	−	0.598037i
$699$	−39.7779	−	68.8974i	−1.50454	−	2.60594i
$700$		0			0
$701$	−5.51907	+	9.55931i	−0.208452	+	0.361050i	−0.951227	−	0.308491i	$-0.900176\pi$
$701$	−5.51907	+	9.55931i	−0.208452	+	0.361050i	0.742775	+	0.669541i	$0.233509\pi$
$702$	−6.22187			−0.234829
$703$	23.2191	+	28.7143i	0.875726	+	1.08298i
$704$	−3.90260			−0.147085
$705$		0			0
$706$	−17.8889	+	30.9845i	−0.673257	+	1.16612i
$707$	1.17094	+	2.02812i	0.0440376	+	0.0762754i
$708$	−12.1588	+	21.0596i	−0.456954	+	0.791467i
$709$	17.6384	+	30.5507i	0.662426	+	1.14735i	0.979976	+	0.199114i	$0.0638063\pi$
$709$	17.6384	+	30.5507i	0.662426	+	1.14735i	−0.317551	+	0.948241i	$0.602860\pi$
$710$		0			0
$711$	45.3756			1.70172
$712$	−2.76126	−	4.78264i	−0.103482	−	0.179237i
$713$	−6.90479	−	11.9594i	−0.258586	−	0.447885i
$714$	6.50120			0.243301
$715$		0			0
$716$	5.39616	+	9.34642i	0.201664	+	0.349292i
$717$	34.0081	−	58.9038i	1.27006	−	2.19980i
$718$	15.9454	+	27.6182i	0.595077	+	1.03070i
$719$	17.9276	−	31.0515i	0.668587	−	1.15803i	−0.309712	−	0.950830i	$-0.600233\pi$
$719$	17.9276	−	31.0515i	0.668587	−	1.15803i	0.978299	−	0.207196i	$-0.0664339\pi$
$720$		0			0
$721$	−54.0997			−2.01478
$722$	14.1019	+	12.7332i	0.524819	+	0.473882i
$723$	−35.8654			−1.33385
$724$	−5.95907	+	10.3214i	−0.221467	+	0.383592i
$725$		0			0
$726$	−6.71878	−	11.6373i	−0.249357	−	0.431900i
$727$	17.7426	−	30.7311i	0.658037	−	1.13975i	−0.323086	−	0.946370i	$-0.604720\pi$
$727$	17.7426	−	30.7311i	0.658037	−	1.13975i	0.981123	−	0.193384i	$-0.0619464\pi$
$728$	−1.00000	−	1.73205i	−0.0370625	−	0.0641941i
$729$	17.9986			0.666613
$730$		0			0
$731$	−1.42785	−	2.47311i	−0.0528109	−	0.0914711i
$732$	−14.7922	−	25.6208i	−0.546735	−	0.946973i
$733$	8.13294			0.300397			0.150198	−	0.988656i	$-0.452009\pi$
$733$	8.13294			0.300397			0.150198	+	0.988656i	$0.452009\pi$
$734$	32.9107			1.21476
$735$		0			0
$736$	2.84883	−	4.93431i	0.105009	−	0.181881i
$737$	−3.16094	−	5.47490i	−0.116435	−	0.201671i
$738$	−1.80790	+	3.13137i	−0.0665497	+	0.115267i
$739$	−3.35916	+	5.81823i	−0.123569	+	0.214027i	−0.921172	−	0.389155i	$-0.872767\pi$
$739$	−3.35916	+	5.81823i	−0.123569	+	0.214027i	0.797604	+	0.603182i	$0.206101\pi$
$740$		0			0
$741$	4.16908	+	5.15576i	0.153155	+	0.189402i
$742$	23.2131			0.852178
$743$	17.5641	−	30.4219i	0.644363	−	1.11607i	−0.340085	−	0.940395i	$-0.610456\pi$
$743$	17.5641	−	30.4219i	0.644363	−	1.11607i	0.984448	−	0.175675i	$-0.0562108\pi$
$744$	−3.84952	+	6.66756i	−0.141130	+	0.244445i
$745$		0			0
$746$	−7.46449	+	12.9289i	−0.273295	+	0.473360i
$747$	−28.2257	−	48.8883i	−1.03272	−	1.78873i
$748$	−1.91241			−0.0699247
$749$	41.7652			1.52607
$750$		0			0
$751$	−11.2029	−	19.4040i	−0.408800	−	0.708062i	0.585956	−	0.810343i	$-0.300719\pi$
$751$	−11.2029	−	19.4040i	−0.408800	−	0.708062i	−0.994756	+	0.102281i	$0.967386\pi$
$752$	0.971577			0.0354297
$753$	51.3893			1.87273
$754$	−0.582997	−	1.00978i	−0.0212315	−	0.0367740i
$755$		0			0
$756$	27.1325	+	46.9949i	0.986801	+	1.70919i
$757$	−2.64407	+	4.57967i	−0.0961005	+	0.166451i	−0.910067	−	0.414460i	$-0.863970\pi$
$757$	−2.64407	+	4.57967i	−0.0961005	+	0.166451i	0.813967	+	0.580911i	$0.197304\pi$
$758$	−13.2768	+	22.9960i	−0.482234	+	0.835254i
$759$	70.6320			2.56378
$760$		0			0
$761$	−25.9435			−0.940451			−0.470226	−	0.882546i	$-0.655827\pi$
$761$	−25.9435			−0.940451			−0.470226	+	0.882546i	$0.655827\pi$
$762$	−7.48154	+	12.9584i	−0.271028	+	0.469434i
$763$	20.1806	−	34.9538i	0.730586	−	1.26541i
$764$	2.43490	+	4.21737i	0.0880916	+	0.152579i
$765$		0			0
$766$	18.5490	+	32.1279i	0.670204	+	1.16083i
$767$	3.66592			0.132369
$768$	−3.17652			−0.114623
$769$	−16.4046	−	28.4137i	−0.591566	−	1.02462i	−0.994022	−	0.109183i	$-0.965176\pi$
$769$	−16.4046	−	28.4137i	−0.591566	−	1.02462i	0.402455	−	0.915440i	$-0.368157\pi$
$770$		0			0
$771$	−31.2624			−1.12589
$772$	21.7838			0.784017
$773$	0.437731	+	0.758172i	0.0157441	+	0.0272695i	0.873790	−	0.486303i	$-0.161655\pi$
$773$	0.437731	+	0.758172i	0.0157441	+	0.0272695i	−0.858046	+	0.513573i	$0.828322\pi$
$774$	20.6594	−	35.7832i	0.742588	−	1.28620i
$775$		0			0
$776$	7.24499	−	12.5487i	0.260080	−	0.450472i
$777$	56.1966	−	97.3353i	2.01604	−	3.49189i
$778$	7.83774			0.280997
$779$	2.19576	−	0.346198i	0.0786713	−	0.0124038i
$780$		0			0
$781$	−3.65708	+	6.33424i	−0.130861	+	0.226657i
$782$	1.39603	−	2.41799i	0.0499218	−	0.0864670i
$783$	15.8182	+	27.3979i	0.565296	+	0.979121i
$784$	−5.22167	+	9.04419i	−0.186488	+	0.323007i
$785$		0			0
$786$	42.2766			1.50795
$787$	37.3477			1.33130			0.665651	−	0.746264i	$-0.268154\pi$
$787$	37.3477			1.33130			0.665651	+	0.746264i	$0.268154\pi$
$788$	6.86794	+	11.8956i	0.244660	+	0.423764i
$789$	44.8934	+	77.7577i	1.59825	+	2.76825i
$790$		0			0
$791$	21.6310			0.769111
$792$	−13.8353	−	23.9634i	−0.491615	−	0.851502i
$793$	−2.22995	+	3.86239i	−0.0791880	+	0.137158i
$794$	11.5460	+	19.9983i	0.409752	+	0.709712i
$795$		0			0
$796$	−10.4433	+	18.0884i	−0.370154	+	0.641126i
$797$	33.5863			1.18969			0.594844	−	0.803841i	$-0.297214\pi$
$797$	33.5863			1.18969			0.594844	+	0.803841i	$0.297214\pi$
$798$	20.7618	−	53.9732i	0.734958	−	1.91063i
$799$	0.476107			0.0168434
$800$		0			0
$801$	19.5781	−	33.9103i	0.691758	−	1.19816i
$802$	1.94555	+	3.36979i	0.0686998	+	0.118991i
$803$	9.18310	−	15.9056i	0.324065	−	0.561296i
$804$	−2.57285	−	4.45630i	−0.0907373	−	0.157162i
$805$		0			0
$806$	1.16065			0.0408820
$807$	51.1734	+	88.6349i	1.80139	+	3.12010i
$808$	−0.280362	−	0.485601i	−0.00986310	−	0.0170834i
$809$	−52.7700			−1.85529			−0.927647	−	0.373459i	$-0.878172\pi$
$809$	−52.7700			−1.85529			−0.927647	+	0.373459i	$0.878172\pi$
$810$		0			0
$811$	−15.9288	−	27.5895i	−0.559336	−	0.968798i	−0.997552	−	0.0699286i	$-0.977723\pi$
$811$	−15.9288	−	27.5895i	−0.559336	−	0.968798i	0.438216	−	0.898870i	$-0.355610\pi$
$812$	−5.08470	+	8.80697i	−0.178438	+	0.309064i
$813$	−17.0068	−	29.4566i	−0.596454	−	1.03309i
$814$	−16.5309	+	28.6324i	−0.579409	+	1.00357i
$815$		0			0
$816$	−1.55661			−0.0544921
$817$	−25.0917	+	3.95612i	−0.877846	+	0.138407i
$818$	−23.3662			−0.816979
$819$	7.09029	−	12.2807i	0.247755	−	0.429124i
$820$		0			0
$821$	4.08891	+	7.08220i	0.142704	+	0.247170i	0.928514	−	0.371298i	$-0.121087\pi$
$821$	4.08891	+	7.08220i	0.142704	+	0.247170i	−0.785810	+	0.618468i	$0.787754\pi$
$822$	−0.617166	+	1.06896i	−0.0215261	+	0.0372843i
$823$	−17.7080	−	30.6711i	−0.617261	−	1.06913i	−0.989983	−	0.141185i	$-0.954909\pi$
$823$	−17.7080	−	30.6711i	−0.617261	−	1.06913i	0.372722	−	0.927943i	$-0.378425\pi$
$824$	12.9533			0.451249
$825$		0			0
$826$	−15.9864	−	27.6893i	−0.556240	−	0.963435i
$827$	14.3322	+	24.8241i	0.498380	+	0.863220i	0.999998	−	0.00186921i	$-0.000594989\pi$
$827$	14.3322	+	24.8241i	0.498380	+	0.863220i	−0.501618	+	0.865089i	$0.667262\pi$
$828$	40.3980			1.40393
$829$	−27.3040			−0.948307			−0.474153	−	0.880442i	$-0.657246\pi$
$829$	−27.3040			−0.948307			−0.474153	+	0.880442i	$0.657246\pi$
$830$		0			0
$831$	−0.466189	+	0.807463i	−0.0161719	+	0.0280106i
$832$	0.239434	+	0.414711i	0.00830087	+	0.0143775i
$833$	−2.55880	+	4.43197i	−0.0886571	+	0.153559i
$834$	−28.0188	+	48.5299i	−0.970210	+	1.68045i
$835$		0			0
$836$	−6.10733	+	15.8769i	−0.211226	+	0.549114i
$837$	−31.4913			−1.08850
$838$	−1.55171	+	2.68765i	−0.0536031	+	0.0928432i
$839$	11.9964	−	20.7784i	0.414162	−	0.717350i	−0.581178	−	0.813776i	$-0.697408\pi$
$839$	11.9964	−	20.7784i	0.414162	−	0.717350i	0.995340	+	0.0964268i	$0.0307414\pi$
$840$		0			0
$841$	11.5356	−	19.9803i	0.397780	−	0.688976i
$842$	−12.3730	−	21.4307i	−0.426402	−	0.738550i
$843$	52.7493			1.81678
$844$	−16.6114			−0.571789
$845$		0			0
$846$	3.44438	+	5.96584i	0.118420	+	0.205110i
$847$	17.6678			0.607074
$848$	−5.55799			−0.190862
$849$	−16.1087	−	27.9011i	−0.552850	−	0.957564i
$850$		0			0
$851$	−24.1346	−	41.8023i	−0.827322	−	1.43296i
$852$	−2.97668	+	5.15576i	−0.101979	+	0.176633i
$853$	−6.80016	+	11.7782i	−0.232833	+	0.403279i	−0.958641	−	0.284619i	$-0.908133\pi$
$853$	−6.80016	+	11.7782i	−0.232833	+	0.403279i	0.725808	+	0.687898i	$0.241466\pi$
$854$	38.8978			1.33106
$855$		0			0
$856$	−10.0000			−0.341793
$857$	−27.6443	+	47.8814i	−0.944313	+	1.63560i	−0.187192	+	0.982323i	$0.559939\pi$
$857$	−27.6443	+	47.8814i	−0.944313	+	1.63560i	−0.757121	+	0.653275i	$0.773395\pi$
$858$	−2.96819	+	5.14105i	−0.101332	+	0.175512i
$859$	5.60651	+	9.71077i	0.191292	+	0.331327i	0.945679	−	0.325103i	$-0.105399\pi$
$859$	5.60651	+	9.71077i	0.191292	+	0.331327i	−0.754387	+	0.656430i	$0.772066\pi$
$860$		0			0
$861$	−3.38280	−	5.85919i	−0.115286	−	0.199681i
$862$	−36.2441			−1.23448
$863$	10.3639			0.352791			0.176396	−	0.984319i	$-0.443556\pi$
$863$	10.3639			0.352791			0.176396	+	0.984319i	$0.443556\pi$
$864$	−6.49644	−	11.2522i	−0.221013	−	0.382807i
$865$		0			0
$866$	−6.82074			−0.231778
$867$	53.2381			1.80806
$868$	−5.06138	−	8.76657i	−0.171795	−	0.297557i
$869$	12.4877	−	21.6293i	0.423616	−	0.733725i
$870$		0			0
$871$	−0.387862	+	0.671797i	−0.0131422	+	0.0227630i
$872$	−4.83191	+	8.36911i	−0.163629	+	0.283414i
$873$	102.738			3.47716
$874$	−15.6160	−	19.3117i	−0.528218	−	0.653230i
$875$		0			0
$876$	7.47459	−	12.9464i	0.252543	−	0.437417i
$877$	−16.1304	+	27.9386i	−0.544684	+	0.943421i	0.453943	+	0.891031i	$0.350017\pi$
$877$	−16.1304	+	27.9386i	−0.544684	+	0.943421i	−0.998627	+	0.0523896i	$0.983316\pi$
$878$	17.4391	+	30.2054i	0.588541	+	1.01938i
$879$	8.08742	−	14.0078i	0.272782	−	0.472472i
$880$		0			0
$881$	32.8935			1.10821			0.554104	−	0.832447i	$-0.313061\pi$
$881$	32.8935			1.10821			0.554104	+	0.832447i	$0.313061\pi$
$882$	−74.0462			−2.49327
$883$	8.03433	+	13.9159i	0.270377	+	0.468306i	0.968958	−	0.247224i	$-0.0795184\pi$
$883$	8.03433	+	13.9159i	0.270377	+	0.468306i	−0.698582	+	0.715530i	$0.746185\pi$
$884$	0.117331	+	0.203223i	0.00394627	+	0.00683513i
$885$		0			0
$886$	23.2016			0.779474
$887$	−5.56000	−	9.63020i	−0.186686	−	0.323350i	0.757457	−	0.652885i	$-0.226442\pi$
$887$	−5.56000	−	9.63020i	−0.186686	−	0.323350i	−0.944144	+	0.329535i	$0.893108\pi$
$888$	−13.4554	+	23.3054i	−0.451532	+	0.782077i
$889$	−9.83680	−	17.0378i	−0.329916	−	0.571431i
$890$		0			0
$891$	39.0286	−	67.5994i	1.30751	−	2.26467i
$892$	−10.1765			−0.340735
$893$	1.52046	−	3.95265i	0.0508802	−	0.132270i
$894$	−48.5726			−1.62451
$895$		0			0
$896$	2.08826	−	3.61697i	0.0697639	−	0.120835i
$897$	−4.33344	−	7.50574i	−0.144689	−	0.250610i
$898$	−19.4792	+	33.7390i	−0.650029	+	1.12588i
$899$	−2.95077	−	5.11088i	−0.0984137	−	0.170458i
$900$		0			0
$901$	−2.72361			−0.0907366
$902$	0.995094	+	1.72355i	0.0331330	+	0.0573881i
$903$	38.6564	+	66.9548i	1.28640	+	2.22812i
$904$	−5.17920			−0.172257
$905$		0			0
$906$	−26.4074	−	45.7390i	−0.877329	−	1.51958i
$907$	−5.03280	+	8.71706i	−0.167111	+	0.289445i	−0.937403	−	0.348246i	$-0.886777\pi$
$907$	−5.03280	+	8.71706i	−0.167111	+	0.289445i	0.770292	+	0.637692i	$0.220111\pi$
$908$	−4.25482	−	7.36956i	−0.141201	−	0.244567i
$909$	1.98785	−	3.44305i	0.0659327	−	0.114199i
$910$		0			0
$911$	−4.04379			−0.133977			−0.0669884	−	0.997754i	$-0.521339\pi$
$911$	−4.04379			−0.133977			−0.0669884	+	0.997754i	$0.521339\pi$
$912$	−4.97106	+	12.9230i	−0.164608	+	0.427923i
$913$	−31.0717			−1.02832
$914$	−5.04223	+	8.73341i	−0.166782	+	0.288875i
$915$		0			0
$916$	3.40380	+	5.89556i	0.112465	+	0.194795i
$917$	−27.7928	+	48.1386i	−0.917800	+	1.58968i
$918$	−3.18349	−	5.51396i	−0.105071	−	0.181988i
$919$	50.1596			1.65461			0.827305	−	0.561752i	$-0.189873\pi$
$919$	50.1596			1.65461			0.827305	+	0.561752i	$0.189873\pi$
$920$		0			0
$921$	30.0754	+	52.0921i	0.991017	+	1.71649i
$922$	−1.74501	−	3.02245i	−0.0574690	−	0.0995392i
$923$	0.897481			0.0295410
$924$	51.7750			1.70327
$925$		0			0
$926$	−3.35494	+	5.81093i	−0.110250	+	0.190959i
$927$	45.9213	+	79.5380i	1.50825	+	2.61237i
$928$	1.21745	−	2.10868i	0.0399647	−	0.0692210i
$929$	−20.1114	+	34.8339i	−0.659832	+	1.14286i	0.320827	+	0.947138i	$0.396039\pi$
$929$	−20.1114	+	34.8339i	−0.659832	+	1.14286i	−0.980659	+	0.195725i	$0.937294\pi$
$930$		0			0
$931$	28.6228	+	35.3968i	0.938074	+	1.16008i
$932$	−25.0450			−0.820375
$933$	−13.6767	+	23.6887i	−0.447754	+	0.775532i
$934$	16.0700	−	27.8340i	0.525826	−	0.910757i
$935$		0			0
$936$	−1.69765	+	2.94042i	−0.0554896	+	0.0961107i
$937$	7.53227	+	13.0463i	0.246069	+	0.426203i	0.962431	−	0.271525i	$-0.0875278\pi$
$937$	7.53227	+	13.0463i	0.246069	+	0.426203i	−0.716363	+	0.697728i	$0.754195\pi$
$938$	6.76561			0.220905
$939$	2.61036			0.0851860
$940$		0			0
$941$	5.39804	+	9.34969i	0.175971	+	0.304791i	0.940497	−	0.339802i	$-0.110360\pi$
$941$	5.39804	+	9.34969i	0.175971	+	0.304791i	−0.764526	+	0.644593i	$0.777027\pi$
$942$	38.6520			1.25935
$943$	−2.90560			−0.0946195
$944$	3.82769	+	6.62976i	0.124581	+	0.215780i
$945$		0			0
$946$	−11.3713	−	19.6956i	−0.369712	−	0.640359i
$947$	5.24715	−	9.08833i	0.170509	−	0.295331i	−0.768089	−	0.640343i	$-0.778792\pi$
$947$	5.24715	−	9.08833i	0.170509	−	0.295331i	0.938598	+	0.345013i	$0.112125\pi$
$948$	10.1644	−	17.6052i	0.330123	−	0.571790i
$949$	−2.25362			−0.0731556
$950$		0			0
$951$	22.0379			0.714627
$952$	1.02332	−	1.77244i	0.0331660	−	0.0574452i
$953$	3.91647	−	6.78353i	0.126867	−	0.219740i	−0.795594	−	0.605830i	$-0.792841\pi$
$953$	3.91647	−	6.78353i	0.126867	−	0.219740i	0.922461	+	0.386090i	$0.126175\pi$
$954$	−19.7039	−	34.1281i	−0.637936	−	1.10494i
$955$		0			0
$956$	−10.7061	−	18.5435i	−0.346260	−	0.599739i
$957$	30.1847			0.975732
$958$	−11.3900			−0.367993
$959$	−0.811455	−	1.40548i	−0.0262033	−	0.0453854i
$960$		0			0
$961$	−25.1255			−0.810501
$962$	4.05685			0.130798
$963$	−35.4514	−	61.4037i	−1.14241	−	1.97871i
$964$	−5.64540	+	9.77811i	−0.181826	+	0.314932i
$965$		0			0
$966$	−37.7948	+	65.4626i	−1.21603	+	2.10622i
$967$	1.05241	−	1.82282i	0.0338431	−	0.0586180i	−0.848608	−	0.529023i	$-0.822559\pi$
$967$	1.05241	−	1.82282i	0.0338431	−	0.0586180i	0.882451	+	0.470405i	$0.155892\pi$
$968$	−4.23028			−0.135966
$969$	−2.43600	+	6.33273i	−0.0782555	+	0.203436i
$970$		0			0
$971$	4.88113	−	8.45436i	0.156643	−	0.271313i	−0.777013	−	0.629484i	$-0.783266\pi$
$971$	4.88113	−	8.45436i	0.156643	−	0.271313i	0.933656	+	0.358171i	$0.116600\pi$
$972$	12.2780	−	21.2661i	0.393816	−	0.682110i
$973$	−36.8393	−	63.8076i	−1.18102	−	2.04558i
$974$	−14.1552	+	24.5175i	−0.453561	+	0.785590i
$975$		0			0
$976$	−9.31345			−0.298116
$977$	−40.9784			−1.31102			−0.655508	−	0.755189i	$-0.727545\pi$
$977$	−40.9784			−1.31102			−0.655508	+	0.755189i	$0.727545\pi$
$978$	−22.9780	−	39.7990i	−0.734754	−	1.27263i
$979$	−10.7761	−	18.6647i	−0.344405	−	0.596527i
$980$		0			0
$981$	−68.5193			−2.18765
$982$	−7.91187	−	13.7038i	−0.252478	−	0.437305i
$983$	−10.0238	+	17.3617i	−0.319709	+	0.553752i	−0.980427	−	0.196882i	$-0.936918\pi$
$983$	−10.0238	+	17.3617i	−0.319709	+	0.553752i	0.660718	+	0.750634i	$0.270252\pi$
$984$	0.809957	+	1.40289i	0.0258205	+	0.0447224i
$985$		0			0
$986$	0.596593	−	1.03333i	0.0189994	−	0.0329079i
$987$	−12.8897			−0.410284
$988$	2.06186	−	0.325087i	0.0655966	−	0.0103424i
$989$	33.2033			1.05580
$990$		0			0
$991$	17.0676	−	29.5620i	0.542171	−	0.939068i	−0.456608	−	0.889668i	$-0.650936\pi$
$991$	17.0676	−	29.5620i	0.542171	−	0.939068i	0.998779	−	0.0493996i	$-0.0157308\pi$
$992$	1.21187	+	2.09901i	0.0384768	+	0.0666437i
$993$	−56.2326	+	97.3976i	−1.78449	+	3.09082i
$994$	−3.91377	−	6.77884i	−0.124137	−	0.215012i
$995$		0			0
$996$	−25.2908			−0.801369
$997$	−15.7564	−	27.2908i	−0.499009	−	0.864309i	0.500991	−	0.865453i	$-0.332969\pi$
$997$	−15.7564	−	27.2908i	−0.499009	−	0.864309i	−0.999999	+	0.00114415i	$0.999636\pi$
$998$	0.827004	+	1.43241i	0.0261784	+	0.0453422i
$999$	−110.073			−3.48254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.o.201.5		10
5.2	odd	4		190.2.i.a.49.6	yes	20
5.3	odd	4		190.2.i.a.49.5	✓	20
5.4	even	2		950.2.e.n.201.1		10
15.2	even	4		1710.2.t.d.1189.4		20
15.8	even	4		1710.2.t.d.1189.8		20
19.7	even	3	inner	950.2.e.o.501.5		10
95.7	odd	12		190.2.i.a.159.5	yes	20
95.64	even	6		950.2.e.n.501.1		10
95.83	odd	12		190.2.i.a.159.6	yes	20
285.83	even	12		1710.2.t.d.919.4		20
285.197	even	12		1710.2.t.d.919.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.5	✓	20	5.3	odd	4
190.2.i.a.49.6	yes	20	5.2	odd	4
190.2.i.a.159.5	yes	20	95.7	odd	12
190.2.i.a.159.6	yes	20	95.83	odd	12
950.2.e.n.201.1		10	5.4	even	2
950.2.e.n.501.1		10	95.64	even	6
950.2.e.o.201.5		10	1.1	even	1	trivial
950.2.e.o.501.5		10	19.7	even	3	inner
1710.2.t.d.919.4		20	285.83	even	12
1710.2.t.d.919.8		20	285.197	even	12
1710.2.t.d.1189.4		20	15.2	even	4
1710.2.t.d.1189.8		20	15.8	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.58826 - 2.75095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58826 - 2.75095i) q^{6} +4.17652 q^{7} -1.00000 q^{8} +(-3.54514 - 6.14037i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.58826 - 2.75095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58826 - 2.75095i) q^{6} +4.17652 q^{7} -1.00000 q^{8} +(-3.54514 - 6.14037i) q^{9} -3.90260 q^{11} -3.17652 q^{12} +(0.239434 + 0.414711i) q^{13} +(2.08826 - 3.61697i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.245018 + 0.424383i) q^{17} -7.09029 q^{18} +(2.74077 + 3.38942i) q^{19} +(6.63340 - 11.4894i) q^{21} +(-1.95130 + 3.37975i) q^{22} +(-2.84883 - 4.93431i) q^{23} +(-1.58826 + 2.75095i) q^{24} +0.478867 q^{26} -12.9929 q^{27} +(-2.08826 - 3.61697i) q^{28} +(-1.21745 - 2.10868i) q^{29} +2.42373 q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.19834 + 10.7358i) q^{33} +(0.245018 + 0.424383i) q^{34} +(-3.54514 + 6.14037i) q^{36} +8.47175 q^{37} +(4.30571 - 0.678866i) q^{38} +1.52113 q^{39} +(0.254982 - 0.441643i) q^{41} +(-6.63340 - 11.4894i) q^{42} +(-2.91377 + 5.04679i) q^{43} +(1.95130 + 3.37975i) q^{44} -5.69765 q^{46} +(-0.485788 - 0.841410i) q^{47} +(1.58826 + 2.75095i) q^{48} +10.4433 q^{49} +(0.778304 + 1.34806i) q^{51} +(0.239434 - 0.414711i) q^{52} +(2.77899 + 4.81336i) q^{53} +(-6.49644 + 11.2522i) q^{54} -4.17652 q^{56} +(13.6772 - 2.15643i) q^{57} -2.43490 q^{58} +(3.82769 - 6.62976i) q^{59} +(4.65673 + 8.06569i) q^{61} +(1.21187 - 2.09901i) q^{62} +(-14.8064 - 25.6454i) q^{63} +1.00000 q^{64} +(6.19834 + 10.7358i) q^{66} +(0.809957 + 1.40289i) q^{67} +0.490035 q^{68} -18.0987 q^{69} +(0.937088 - 1.62308i) q^{71} +(3.54514 + 6.14037i) q^{72} +(-2.35307 + 4.07564i) q^{73} +(4.23588 - 7.33675i) q^{74} +(1.56494 - 4.06829i) q^{76} -16.2993 q^{77} +(0.760566 - 1.31734i) q^{78} +(-3.19984 + 5.54229i) q^{79} +(-10.0007 + 17.3216i) q^{81} +(-0.254982 - 0.441643i) q^{82} +7.96179 q^{83} -13.2668 q^{84} +(2.91377 + 5.04679i) q^{86} -7.73451 q^{87} +3.90260 q^{88} +(2.76126 + 4.78264i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-2.84883 + 4.93431i) q^{92} +(3.84952 - 6.66756i) q^{93} -0.971577 q^{94} +3.17652 q^{96} +(-7.24499 + 12.5487i) q^{97} +(5.22167 - 9.04419i) q^{98} +(13.8353 + 23.9634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9	\( 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{13} + 5 q^{14} - 5 q^{16} - 4 q^{17} - 10 q^{18} + 11 q^{19} + 20 q^{21} - 3 q^{22} - 13 q^{23} + 4 q^{26} - 36 q^{27} - 5 q^{28} + 2 q^{29} - 8 q^{31} + 5 q^{32} - 2 q^{33} + 4 q^{34} - 5 q^{36} - 10 q^{37} + 13 q^{38} + 16 q^{39} + q^{41} - 20 q^{42} + 3 q^{44} - 26 q^{46} + 10 q^{47} - 20 q^{49} + 4 q^{51} + 2 q^{52} - 5 q^{53} - 18 q^{54} - 10 q^{56} + 10 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{61} - 4 q^{62} - 23 q^{63} + 10 q^{64} + 2 q^{66} - 4 q^{67} + 8 q^{68} - 24 q^{69} - 22 q^{71} + 5 q^{72} - 26 q^{73} - 5 q^{74} + 2 q^{76} - 10 q^{77} + 8 q^{78} + 2 q^{79} - 5 q^{81} - q^{82} - 12 q^{83} - 40 q^{84} + 20 q^{87} + 6 q^{88} - q^{89} + 10 q^{91} - 13 q^{92} - 6 q^{93} + 20 q^{94} - 8 q^{97} - 10 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^13 + 5 * q^14 - 5 * q^16 - 4 * q^17 - 10 * q^18 + 11 * q^19 + 20 * q^21 - 3 * q^22 - 13 * q^23 + 4 * q^26 - 36 * q^27 - 5 * q^28 + 2 * q^29 - 8 * q^31 + 5 * q^32 - 2 * q^33 + 4 * q^34 - 5 * q^36 - 10 * q^37 + 13 * q^38 + 16 * q^39 + q^41 - 20 * q^42 + 3 * q^44 - 26 * q^46 + 10 * q^47 - 20 * q^49 + 4 * q^51 + 2 * q^52 - 5 * q^53 - 18 * q^54 - 10 * q^56 + 10 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^61 - 4 * q^62 - 23 * q^63 + 10 * q^64 + 2 * q^66 - 4 * q^67 + 8 * q^68 - 24 * q^69 - 22 * q^71 + 5 * q^72 - 26 * q^73 - 5 * q^74 + 2 * q^76 - 10 * q^77 + 8 * q^78 + 2 * q^79 - 5 * q^81 - q^82 - 12 * q^83 - 40 * q^84 + 20 * q^87 + 6 * q^88 - q^89 + 10 * q^91 - 13 * q^92 - 6 * q^93 + 20 * q^94 - 8 * q^97 - 10 * q^98 + 13 * q^99

Introduction

L-functions

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