LMFDB - Embedded newform 1274.2.g.p.393.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(295,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, 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("1274.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.g (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:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.23207289578928.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 3x^{8} + 13x^{7} + x^{6} - 39x^{5} + 3x^{4} + 117x^{3} - 81x^{2} - 162x + 243 $ x^10 - 2x^9 - 3x^8 + 13x^7 + x^6 - 39x^5 + 3x^4 + 117x^3 - 81x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.1
Root			$-1.73100 - 0.0603688i$ of defining polynomial
Character	$\chi$	$=$	1274.393
Dual form			1274.2.g.p.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.31322 - 2.27456i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.83556 q^{5} +(-1.31322 + 2.27456i) q^{6} +1.00000 q^{8} +(-1.94908 + 3.37591i) q^{9} +(-0.917780 - 1.58964i) q^{10} +(0.0436264 + 0.0755631i) q^{11} +2.62644 q^{12} +(3.59786 + 0.235328i) q^{13} +(-2.41049 - 4.17509i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.40546 + 2.43433i) q^{17} +3.89817 q^{18} +(3.48542 - 6.03693i) q^{19} +(-0.917780 + 1.58964i) q^{20} +(0.0436264 - 0.0755631i) q^{22} +(-0.813218 - 1.40854i) q^{23} +(-1.31322 - 2.27456i) q^{24} -1.63072 q^{25} +(-1.59513 - 3.23350i) q^{26} +2.35899 q^{27} +(-1.05151 - 1.82126i) q^{29} +(-2.41049 + 4.17509i) q^{30} +7.42160 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.114582 - 0.198462i) q^{33} +2.81092 q^{34} +(-1.94908 - 3.37591i) q^{36} +(-4.41108 - 7.64022i) q^{37} -6.97084 q^{38} +(-4.18951 - 8.49260i) q^{39} +1.83556 q^{40} +(-5.21139 - 9.02639i) q^{41} +(2.99057 - 5.17982i) q^{43} -0.0872528 q^{44} +(-3.57766 + 6.19669i) q^{45} +(-0.813218 + 1.40854i) q^{46} +8.00118 q^{47} +(-1.31322 + 2.27456i) q^{48} +(0.815359 + 1.41224i) q^{50} +7.38270 q^{51} +(-2.00273 + 2.99818i) q^{52} +0.894821 q^{53} +(-1.17949 - 2.04294i) q^{54} +(0.0800789 + 0.138701i) q^{55} -18.3085 q^{57} +(-1.05151 + 1.82126i) q^{58} +(3.41945 - 5.92267i) q^{59} +4.82098 q^{60} +(-4.43283 + 7.67789i) q^{61} +(-3.71080 - 6.42729i) q^{62} +1.00000 q^{64} +(6.60409 + 0.431958i) q^{65} -0.229164 q^{66} +(-3.30485 - 5.72416i) q^{67} +(-1.40546 - 2.43433i) q^{68} +(-2.13587 + 3.69943i) q^{69} +(-3.79147 + 6.56701i) q^{71} +(-1.94908 + 3.37591i) q^{72} -10.9094 q^{73} +(-4.41108 + 7.64022i) q^{74} +(2.14149 + 3.70917i) q^{75} +(3.48542 + 6.03693i) q^{76} +(-5.26005 + 7.87452i) q^{78} -9.21793 q^{79} +(-0.917780 - 1.58964i) q^{80} +(2.74939 + 4.76209i) q^{81} +(-5.21139 + 9.02639i) q^{82} +16.8793 q^{83} +(-2.57980 + 4.46835i) q^{85} -5.98114 q^{86} +(-2.76171 + 4.78343i) q^{87} +(0.0436264 + 0.0755631i) q^{88} +(4.95471 + 8.58181i) q^{89} +7.15533 q^{90} +1.62644 q^{92} +(-9.74617 - 16.8809i) q^{93} +(-4.00059 - 6.92923i) q^{94} +(6.39770 - 11.0811i) q^{95} +2.62644 q^{96} +(1.42051 - 2.46040i) q^{97} -0.340126 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 4 q^{5} - q^{6} + 10 q^{8} - 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 6 q^{13} + 3 q^{15} - 5 q^{16} - 3 q^{17} + 8 q^{18} - 5 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23}+ \cdots + 54 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 4 * q^5 - q^6 + 10 * q^8 - 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 6 * q^13 + 3 * q^15 - 5 * q^16 - 3 * q^17 + 8 * q^18 - 5 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 - q^24 + 6 * q^25 + 8 * q^27 + q^29 + 3 * q^30 + 42 * q^31 - 5 * q^32 + 6 * q^34 - 4 * q^36 + 10 * q^37 + 10 * q^38 - 28 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^43 + 8 * q^44 + 3 * q^45 + 4 * q^46 + 26 * q^47 - q^48 - 3 * q^50 + 12 * q^51 + 6 * q^52 + 30 * q^53 - 4 * q^54 + 7 * q^55 - 26 * q^57 + q^58 + q^59 - 6 * q^60 - 15 * q^61 - 21 * q^62 + 10 * q^64 + 44 * q^65 - 3 * q^68 - 18 * q^69 - q^71 - 4 * q^72 + 8 * q^73 + 10 * q^74 - 25 * q^75 - 5 * q^76 + 11 * q^78 + 2 * q^79 - 2 * q^80 + 23 * q^81 - 9 * q^82 + 96 * q^83 + 12 * q^85 - 18 * q^86 - 27 * q^87 - 4 * q^88 - 9 * q^89 - 6 * q^90 - 8 * q^92 - 2 * q^93 - 13 * q^94 + 6 * q^95 + 2 * q^96 - 19 * q^97 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.31322	−	2.27456i	−0.758187	−	1.31322i	−0.943774	−	0.330591i	$-0.892752\pi$
$3$	−1.31322	−	2.27456i	−0.758187	−	1.31322i	0.185587	−	0.982628i	$-0.440581\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.83556			0.820887			0.410444	−	0.911886i	$-0.365374\pi$
$5$	1.83556			0.820887			0.410444	+	0.911886i	$0.365374\pi$
$6$	−1.31322	+	2.27456i	−0.536119	+	0.928586i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.94908	+	3.37591i	−0.649695	+	1.12530i
$10$	−0.917780	−	1.58964i	−0.290228	−	0.502689i
$11$	0.0436264	+	0.0755631i	0.0131539	+	0.0227831i	0.872527	−	0.488565i	$-0.162480\pi$
$11$	0.0436264	+	0.0755631i	0.0131539	+	0.0227831i	−0.859374	+	0.511348i	$0.829146\pi$
$12$	2.62644			0.758187
$13$	3.59786	+	0.235328i	0.997868	+	0.0652682i
$13$	3.59786	+	0.235328i	0.997868	+	0.0652682i
$14$		0			0
$15$	−2.41049	−	4.17509i	−0.622386	−	1.07800i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.40546	+	2.43433i	−0.340874	+	0.590411i	−0.984595	−	0.174849i	$-0.944056\pi$
$17$	−1.40546	+	2.43433i	−0.340874	+	0.590411i	0.643721	+	0.765260i	$0.277390\pi$
$18$	3.89817			0.918807
$19$	3.48542	−	6.03693i	0.799611	−	1.38497i	−0.120259	−	0.992743i	$-0.538373\pi$
$19$	3.48542	−	6.03693i	0.799611	−	1.38497i	0.919870	−	0.392224i	$-0.128294\pi$
$20$	−0.917780	+	1.58964i	−0.205222	+	0.355455i
$21$		0			0
$22$	0.0436264	−	0.0755631i	0.00930118	−	0.0161101i
$23$	−0.813218	−	1.40854i	−0.169568	−	0.293700i	0.768700	−	0.639609i	$-0.220904\pi$
$23$	−0.813218	−	1.40854i	−0.169568	−	0.293700i	−0.938268	+	0.345909i	$0.887570\pi$
$24$	−1.31322	−	2.27456i	−0.268060	−	0.464293i
$25$	−1.63072			−0.326144
$26$	−1.59513	−	3.23350i	−0.312831	−	0.634142i
$27$	2.35899			0.453987
$28$		0			0
$29$	−1.05151	−	1.82126i	−0.195260	−	0.338200i	0.751726	−	0.659476i	$-0.229222\pi$
$29$	−1.05151	−	1.82126i	−0.195260	−	0.338200i	−0.946986	+	0.321276i	$0.895888\pi$
$30$	−2.41049	+	4.17509i	−0.440093	+	0.762264i
$31$	7.42160			1.33296			0.666479	−	0.745524i	$-0.267801\pi$
$31$	7.42160			1.33296			0.666479	+	0.745524i	$0.267801\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.114582	−	0.198462i	0.0199462	−	0.0345478i
$34$	2.81092			0.482068
$35$		0			0
$36$	−1.94908	−	3.37591i	−0.324847	−	0.562652i
$37$	−4.41108	−	7.64022i	−0.725177	−	1.25604i	−0.958901	−	0.283741i	$-0.908424\pi$
$37$	−4.41108	−	7.64022i	−0.725177	−	1.25604i	0.233724	−	0.972303i	$-0.424909\pi$
$38$	−6.97084			−1.13082
$39$	−4.18951	−	8.49260i	−0.670859	−	1.35990i
$40$	1.83556			0.290228
$41$	−5.21139	−	9.02639i	−0.813882	−	1.40969i	−0.910128	−	0.414327i	$-0.864017\pi$
$41$	−5.21139	−	9.02639i	−0.813882	−	1.40969i	0.0962458	−	0.995358i	$-0.469317\pi$
$42$		0			0
$43$	2.99057	−	5.17982i	0.456058	−	0.789915i	−0.542691	−	0.839933i	$-0.682594\pi$
$43$	2.99057	−	5.17982i	0.456058	−	0.789915i	0.998748	+	0.0500176i	$0.0159277\pi$
$44$	−0.0872528			−0.0131539
$45$	−3.57766	+	6.19669i	−0.533326	+	0.923748i
$46$	−0.813218	+	1.40854i	−0.119903	+	0.207677i
$47$	8.00118			1.16709			0.583546	−	0.812080i	$-0.301665\pi$
$47$	8.00118			1.16709			0.583546	+	0.812080i	$0.301665\pi$
$48$	−1.31322	+	2.27456i	−0.189547	+	0.328305i
$49$		0			0
$50$	0.815359	+	1.41224i	0.115309	+	0.199721i
$51$	7.38270			1.03378
$52$	−2.00273	+	2.99818i	−0.277729	+	0.415772i
$53$	0.894821			0.122913			0.0614566	−	0.998110i	$-0.480425\pi$
$53$	0.894821			0.122913			0.0614566	+	0.998110i	$0.480425\pi$
$54$	−1.17949	−	2.04294i	−0.160509	−	0.278009i
$55$	0.0800789	+	0.138701i	0.0107978	+	0.0187024i
$56$		0			0
$57$	−18.3085			−2.42502
$58$	−1.05151	+	1.82126i	−0.138069	+	0.239143i
$59$	3.41945	−	5.92267i	0.445175	−	0.771066i	−0.552889	−	0.833255i	$-0.686475\pi$
$59$	3.41945	−	5.92267i	0.445175	−	0.771066i	0.998064	+	0.0621889i	$0.0198081\pi$
$60$	4.82098			0.622386
$61$	−4.43283	+	7.67789i	−0.567566	+	0.983053i	0.429240	+	0.903191i	$0.358782\pi$
$61$	−4.43283	+	7.67789i	−0.567566	+	0.983053i	−0.996806	+	0.0798628i	$0.974552\pi$
$62$	−3.71080	−	6.42729i	−0.471272	−	0.816267i
$63$		0			0
$64$	1.00000			0.125000
$65$	6.60409	+	0.431958i	0.819137	+	0.0535778i
$66$	−0.229164			−0.0282081
$67$	−3.30485	−	5.72416i	−0.403751	−	0.699318i	0.590424	−	0.807093i	$-0.298961\pi$
$67$	−3.30485	−	5.72416i	−0.403751	−	0.699318i	−0.994175	+	0.107776i	$0.965627\pi$
$68$	−1.40546	−	2.43433i	−0.170437	−	0.295205i
$69$	−2.13587	+	3.69943i	−0.257128	+	0.445359i
$70$		0			0
$71$	−3.79147	+	6.56701i	−0.449964	+	0.779361i	−0.998383	−	0.0568427i	$-0.981897\pi$
$71$	−3.79147	+	6.56701i	−0.449964	+	0.779361i	0.548419	+	0.836204i	$0.315230\pi$
$72$	−1.94908	+	3.37591i	−0.229702	+	0.397855i
$73$	−10.9094			−1.27685			−0.638425	−	0.769684i	$-0.720414\pi$
$73$	−10.9094			−1.27685			−0.638425	+	0.769684i	$0.720414\pi$
$74$	−4.41108	+	7.64022i	−0.512778	+	0.888157i
$75$	2.14149	+	3.70917i	0.247278	+	0.428298i
$76$	3.48542	+	6.03693i	0.399805	+	0.692483i
$77$		0			0
$78$	−5.26005	+	7.87452i	−0.595583	+	0.891614i
$79$	−9.21793			−1.03710			−0.518549	−	0.855048i	$-0.673528\pi$
$79$	−9.21793			−1.03710			−0.518549	+	0.855048i	$0.673528\pi$
$80$	−0.917780	−	1.58964i	−0.102611	−	0.177727i
$81$	2.74939	+	4.76209i	0.305488	+	0.529121i
$82$	−5.21139	+	9.02639i	−0.575502	+	0.996798i
$83$	16.8793			1.85274			0.926372	−	0.376609i	$-0.122910\pi$
$83$	16.8793			1.85274			0.926372	+	0.376609i	$0.122910\pi$
$84$		0			0
$85$	−2.57980	+	4.46835i	−0.279819	+	0.484661i
$86$	−5.98114			−0.644963
$87$	−2.76171	+	4.78343i	−0.296087	+	0.512837i
$88$	0.0436264	+	0.0755631i	0.00465059	+	0.00805506i
$89$	4.95471	+	8.58181i	0.525198	+	0.909670i	0.999569	+	0.0293448i	$0.00934208\pi$
$89$	4.95471	+	8.58181i	0.525198	+	0.909670i	−0.474371	+	0.880325i	$0.657325\pi$
$90$	7.15533			0.754237
$91$		0			0
$92$	1.62644			0.169568
$93$	−9.74617	−	16.8809i	−1.01063	−	1.75046i
$94$	−4.00059	−	6.92923i	−0.412629	−	0.714695i
$95$	6.39770	−	11.0811i	0.656390	−	1.13690i
$96$	2.62644			0.268060
$97$	1.42051	−	2.46040i	0.144231	−	0.249816i	−0.784855	−	0.619680i	$-0.787262\pi$
$97$	1.42051	−	2.46040i	0.144231	−	0.249816i	0.929086	+	0.369864i	$0.120596\pi$
$98$		0			0
$99$	−0.340126			−0.0341840
$100$	0.815359	−	1.41224i	0.0815359	−	0.141224i
$101$	1.88300	+	3.26145i	0.187366	+	0.324527i	0.944371	−	0.328882i	$-0.106672\pi$
$101$	1.88300	+	3.26145i	0.187366	+	0.324527i	−0.757005	+	0.653409i	$0.773338\pi$
$102$	−3.69135	−	6.39360i	−0.365498	−	0.633061i
$103$	−9.45771			−0.931896			−0.465948	−	0.884812i	$-0.654287\pi$
$103$	−9.45771			−0.931896			−0.465948	+	0.884812i	$0.654287\pi$
$104$	3.59786	+	0.235328i	0.352800	+	0.0230758i
$105$		0			0
$106$	−0.447411	−	0.774938i	−0.0434564	−	0.0752686i
$107$	−3.67949	−	6.37307i	−0.355710	−	0.616108i	0.631529	−	0.775352i	$-0.282428\pi$
$107$	−3.67949	−	6.37307i	−0.355710	−	0.616108i	−0.987239	+	0.159244i	$0.949094\pi$
$108$	−1.17949	+	2.04294i	−0.113497	+	0.196582i
$109$	3.92498			0.375945			0.187972	−	0.982174i	$-0.439808\pi$
$109$	3.92498			0.375945			0.187972	+	0.982174i	$0.439808\pi$
$110$	0.0800789	−	0.138701i	0.00763522	−	0.0132246i
$111$	−11.5854	+	20.0665i	−1.09964	+	1.90463i
$112$		0			0
$113$	−7.47705	+	12.9506i	−0.703382	+	1.21829i	0.263891	+	0.964553i	$0.414994\pi$
$113$	−7.47705	+	12.9506i	−0.703382	+	1.21829i	−0.967272	+	0.253740i	$0.918339\pi$
$114$	9.15424	+	15.8556i	0.857373	+	1.48501i
$115$	−1.49271	−	2.58545i	−0.139196	−	0.241095i
$116$	2.10301			0.195260
$117$	−7.80699	+	11.6874i	−0.721756	+	1.08050i
$118$	−6.83891			−0.629573
$119$		0			0
$120$	−2.41049	−	4.17509i	−0.220047	−	0.381132i
$121$	5.49619	−	9.51969i	0.499654	−	0.865426i
$122$	8.86567			0.802660
$123$	−13.6874	+	23.7072i	−1.23415	+	2.13761i
$124$	−3.71080	+	6.42729i	−0.333239	+	0.577188i
$125$	−12.1711			−1.08861
$126$		0			0
$127$	−0.323239	−	0.559866i	−0.0286828	−	0.0496800i	0.851328	−	0.524634i	$-0.175798\pi$
$127$	−0.323239	−	0.559866i	−0.0286828	−	0.0496800i	−0.880010	+	0.474954i	$0.842465\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−15.7091			−1.38311
$130$	−2.92796	−	5.93529i	−0.256799	−	0.520560i
$131$	−2.79634			−0.244317			−0.122159	−	0.992511i	$-0.538982\pi$
$131$	−2.79634			−0.244317			−0.122159	+	0.992511i	$0.538982\pi$
$132$	0.114582	+	0.198462i	0.00997308	+	0.0172739i
$133$		0			0
$134$	−3.30485	+	5.72416i	−0.285495	+	0.494492i
$135$	4.33006			0.372672
$136$	−1.40546	+	2.43433i	−0.120517	+	0.208742i
$137$	5.20854	−	9.02146i	0.444996	−	0.770755i	−0.553056	−	0.833144i	$-0.686539\pi$
$137$	5.20854	−	9.02146i	0.444996	−	0.770755i	0.998052	+	0.0623887i	$0.0198719\pi$
$138$	4.27173			0.363634
$139$	6.12235	−	10.6042i	0.519291	−	0.899438i	−0.480458	−	0.877018i	$-0.659530\pi$
$139$	6.12235	−	10.6042i	0.519291	−	0.899438i	0.999749	−	0.0224200i	$-0.00713711\pi$
$140$		0			0
$141$	−10.5073	−	18.1992i	−0.884874	−	1.53265i
$142$	7.58293			0.636346
$143$	0.139180	+	0.282132i	0.0116388	+	0.0235931i
$144$	3.89817			0.324847
$145$	−1.93010	−	3.34303i	−0.160286	−	0.277624i
$146$	5.45471	+	9.44783i	0.451435	+	0.781908i
$147$		0			0
$148$	8.82216			0.725177
$149$	−11.0012	+	19.0546i	−0.901253	+	1.56102i	−0.0753825	+	0.997155i	$0.524018\pi$
$149$	−11.0012	+	19.0546i	−0.901253	+	1.56102i	−0.825870	+	0.563861i	$0.809316\pi$
$150$	2.14149	−	3.70917i	0.174852	−	0.302852i
$151$	−11.8869			−0.967345			−0.483673	−	0.875249i	$-0.660698\pi$
$151$	−11.8869			−0.967345			−0.483673	+	0.875249i	$0.660698\pi$
$152$	3.48542	−	6.03693i	0.282705	−	0.489660i
$153$	−5.47872	−	9.48941i	−0.442928	−	0.767174i
$154$		0			0
$155$	13.6228			1.09421
$156$	9.44956	+	0.618073i	0.756570	+	0.0494855i
$157$	−1.60038			−0.127724			−0.0638622	−	0.997959i	$-0.520342\pi$
$157$	−1.60038			−0.127724			−0.0638622	+	0.997959i	$0.520342\pi$
$158$	4.60897	+	7.98297i	0.366670	+	0.635091i
$159$	−1.17510	−	2.03533i	−0.0931912	−	0.161412i
$160$	−0.917780	+	1.58964i	−0.0725569	+	0.125672i
$161$		0			0
$162$	2.74939	−	4.76209i	0.216013	−	0.374145i
$163$	2.30469	−	3.99183i	0.180517	−	0.312664i	−0.761540	−	0.648118i	$-0.775556\pi$
$163$	2.30469	−	3.99183i	0.180517	−	0.312664i	0.942057	+	0.335454i	$0.108890\pi$
$164$	10.4228			0.813882
$165$	0.210322	−	0.364289i	0.0163736	−	0.0283598i
$166$	−8.43966	−	14.6179i	−0.655044	−	1.13457i
$167$	−9.67113	−	16.7509i	−0.748374	−	1.29622i	−0.948602	−	0.316473i	$-0.897501\pi$
$167$	−9.67113	−	16.7509i	−0.748374	−	1.29622i	0.200227	−	0.979750i	$-0.435832\pi$
$168$		0			0
$169$	12.8892	+	1.69335i	0.991480	+	0.130258i
$170$	5.15961			0.395724
$171$	13.5868	+	23.5330i	1.03901	+	1.79961i
$172$	2.99057	+	5.17982i	0.228029	+	0.394958i
$173$	7.10168	−	12.3005i	0.539931	−	0.935187i	−0.458977	−	0.888448i	$-0.651784\pi$
$173$	7.10168	−	12.3005i	0.539931	−	0.935187i	0.998907	−	0.0467389i	$-0.0148829\pi$
$174$	5.52343			0.418730
$175$		0			0
$176$	0.0436264	−	0.0755631i	0.00328846	−	0.00569579i
$177$	−17.9620			−1.35010
$178$	4.95471	−	8.58181i	0.371371	−	0.643234i
$179$	5.26777	+	9.12404i	0.393731	+	0.681963i	0.992938	−	0.118631i	$-0.0378507\pi$
$179$	5.26777	+	9.12404i	0.393731	+	0.681963i	−0.599207	+	0.800594i	$0.704517\pi$
$180$	−3.57766	−	6.19669i	−0.266663	−	0.461874i
$181$	18.5808			1.38110			0.690549	−	0.723285i	$-0.257369\pi$
$181$	18.5808			1.38110			0.690549	+	0.723285i	$0.257369\pi$
$182$		0			0
$183$	23.2851			1.72128
$184$	−0.813218	−	1.40854i	−0.0599513	−	0.103839i
$185$	−8.09681	−	14.0241i	−0.595289	−	1.03107i
$186$	−9.74617	+	16.8809i	−0.714624	+	1.23777i
$187$	−0.245260			−0.0179352
$188$	−4.00059	+	6.92923i	−0.291773	+	0.505366i
$189$		0			0
$190$	−12.7954			−0.928276
$191$	−11.4140	+	19.7696i	−0.825886	+	1.43048i	0.0753540	+	0.997157i	$0.475991\pi$
$191$	−11.4140	+	19.7696i	−0.825886	+	1.43048i	−0.901240	+	0.433320i	$0.857342\pi$
$192$	−1.31322	−	2.27456i	−0.0947734	−	0.164152i
$193$	1.46152	+	2.53143i	0.105203	+	0.182216i	0.913821	−	0.406117i	$-0.133118\pi$
$193$	1.46152	+	2.53143i	0.105203	+	0.182216i	−0.808618	+	0.588334i	$0.799784\pi$
$194$	−2.84102			−0.203974
$195$	−7.69010	−	15.5887i	−0.550700	−	1.11633i
$196$		0			0
$197$	2.37415	+	4.11215i	0.169151	+	0.292979i	0.938122	−	0.346306i	$-0.112564\pi$
$197$	2.37415	+	4.11215i	0.169151	+	0.292979i	−0.768970	+	0.639284i	$0.779231\pi$
$198$	0.170063	+	0.294558i	0.0120859	+	0.0209333i
$199$	4.92265	−	8.52628i	0.348958	−	0.604412i	−0.637107	−	0.770775i	$-0.719869\pi$
$199$	4.92265	−	8.52628i	0.348958	−	0.604412i	0.986065	+	0.166363i	$0.0532024\pi$
$200$	−1.63072			−0.115309
$201$	−8.67997	+	15.0341i	−0.612238	+	1.06043i
$202$	1.88300	−	3.26145i	0.132488	−	0.229475i
$203$		0			0
$204$	−3.69135	+	6.39360i	−0.258446	+	0.447642i
$205$	−9.56582	−	16.5685i	−0.668106	−	1.15719i
$206$	4.72886	+	8.19062i	0.329475	+	0.570668i
$207$	6.34013			0.440669
$208$	−1.59513	−	3.23350i	−0.110603	−	0.224203i
$209$	0.608226			0.0420718
$210$		0			0
$211$	2.18356	+	3.78203i	0.150322	+	0.260366i	0.931346	−	0.364136i	$-0.118636\pi$
$211$	2.18356	+	3.78203i	0.150322	+	0.260366i	−0.781024	+	0.624501i	$0.785302\pi$
$212$	−0.447411	+	0.774938i	−0.0307283	+	0.0532230i
$213$	19.9161			1.36463
$214$	−3.67949	+	6.37307i	−0.251525	+	0.435654i
$215$	5.48937	−	9.50787i	0.374372	−	0.648431i
$216$	2.35899			0.160509
$217$		0			0
$218$	−1.96249	−	3.39913i	−0.132917	−	0.230218i
$219$	14.3264	+	24.8141i	0.968091	+	1.67678i
$220$	−0.160158			−0.0107978
$221$	−5.62951	+	8.42763i	−0.378682	+	0.566904i
$222$	23.1709			1.55513
$223$	−14.0542	−	24.3427i	−0.941142	−	1.63011i	−0.763298	−	0.646047i	$-0.776421\pi$
$223$	−14.0542	−	24.3427i	−0.941142	−	1.63011i	−0.177844	−	0.984059i	$-0.556912\pi$
$224$		0			0
$225$	3.17841	−	5.50517i	0.211894	−	0.367011i
$226$	14.9541			0.994732
$227$	13.3454	−	23.1150i	0.885767	−	1.53419i	0.0409354	−	0.999162i	$-0.486966\pi$
$227$	13.3454	−	23.1150i	0.885767	−	1.53419i	0.844832	−	0.535032i	$-0.179700\pi$
$228$	9.15424	−	15.8556i	0.606254	−	1.05006i
$229$	9.40945			0.621794			0.310897	−	0.950444i	$-0.399371\pi$
$229$	9.40945			0.621794			0.310897	+	0.950444i	$0.399371\pi$
$230$	−1.49271	+	2.58545i	−0.0984265	+	0.170480i
$231$		0			0
$232$	−1.05151	−	1.82126i	−0.0690347	−	0.119572i
$233$	23.0215			1.50819			0.754093	−	0.656767i	$-0.228077\pi$
$233$	23.0215			1.50819			0.754093	+	0.656767i	$0.228077\pi$
$234$	14.0251	+	0.917347i	0.916848	+	0.0599689i
$235$	14.6866			0.958051
$236$	3.41945	+	5.92267i	0.222588	+	0.385533i
$237$	12.1052	+	20.9668i	0.786315	+	1.36194i
$238$		0			0
$239$	11.0321			0.713610			0.356805	−	0.934179i	$-0.383866\pi$
$239$	11.0321			0.713610			0.356805	+	0.934179i	$0.383866\pi$
$240$	−2.41049	+	4.17509i	−0.155597	+	0.269501i
$241$	−3.69969	+	6.40806i	−0.238318	+	0.412779i	−0.960232	−	0.279204i	$-0.909929\pi$
$241$	−3.69969	+	6.40806i	−0.238318	+	0.412779i	0.721914	+	0.691983i	$0.243263\pi$
$242$	−10.9924			−0.706617
$243$	10.7596	−	18.6361i	0.690227	−	1.19551i
$244$	−4.43283	−	7.67789i	−0.283783	−	0.491527i
$245$		0			0
$246$	27.3748			1.74535
$247$	13.9607	−	20.8998i	0.888300	−	1.32982i
$248$	7.42160			0.471272
$249$	−22.1662	−	38.3930i	−1.40473	−	2.43306i
$250$	6.08554	+	10.5405i	0.384883	+	0.666638i
$251$	−1.94394	+	3.36700i	−0.122700	+	0.212523i	−0.920832	−	0.389960i	$-0.872489\pi$
$251$	−1.94394	+	3.36700i	−0.122700	+	0.212523i	0.798131	+	0.602483i	$0.205822\pi$
$252$		0			0
$253$	0.0709556	−	0.122899i	0.00446094	−	0.00772657i
$254$	−0.323239	+	0.559866i	−0.0202818	+	0.0351291i
$255$	13.5514			0.848620
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.86569	−	13.6238i	−0.490648	−	0.849828i	0.509294	−	0.860593i	$-0.329907\pi$
$257$	−7.86569	−	13.6238i	−0.490648	−	0.849828i	−0.999942	+	0.0107648i	$0.996573\pi$
$258$	7.85454	+	13.6045i	0.489003	+	0.846977i
$259$		0			0
$260$	−3.67613	+	5.50333i	−0.227984	+	0.341302i
$261$	8.19789			0.507437
$262$	1.39817	+	2.42170i	0.0863792	+	0.149613i
$263$	6.37994	+	11.0504i	0.393404	+	0.681395i	0.992896	−	0.118985i	$-0.0379641\pi$
$263$	6.37994	+	11.0504i	0.393404	+	0.681395i	−0.599492	+	0.800381i	$0.704631\pi$
$264$	0.114582	−	0.198462i	0.00705203	−	0.0122145i
$265$	1.64250			0.100898
$266$		0			0
$267$	13.0132	−	22.5396i	0.796397	−	1.37940i
$268$	6.60969			0.403751
$269$	−6.51291	+	11.2807i	−0.397099	+	0.687796i	−0.993367	−	0.114990i	$-0.963316\pi$
$269$	−6.51291	+	11.2807i	−0.397099	+	0.687796i	0.596267	+	0.802786i	$0.296650\pi$
$270$	−2.16503	−	3.74994i	−0.131760	−	0.228214i
$271$	4.68905	+	8.12167i	0.284839	+	0.493356i	0.972570	−	0.232610i	$-0.0747264\pi$
$271$	4.68905	+	8.12167i	0.284839	+	0.493356i	−0.687731	+	0.725966i	$0.741393\pi$
$272$	2.81092			0.170437
$273$		0			0
$274$	−10.4171			−0.629319
$275$	−0.0711424	−	0.123222i	−0.00429005	−	0.00743058i
$276$	−2.13587	−	3.69943i	−0.128564	−	0.222679i
$277$	8.79375	−	15.2312i	0.528365	−	0.915155i	−0.471088	−	0.882086i	$-0.656139\pi$
$277$	8.79375	−	15.2312i	0.528365	−	0.915155i	0.999453	−	0.0330692i	$-0.0105282\pi$
$278$	−12.2447			−0.734388
$279$	−14.4653	+	25.0547i	−0.866016	+	1.49998i
$280$		0			0
$281$	13.5973			0.811146			0.405573	−	0.914063i	$-0.367072\pi$
$281$	13.5973			0.811146			0.405573	+	0.914063i	$0.367072\pi$
$282$	−10.5073	+	18.1992i	−0.625700	+	1.08374i
$283$	−3.22420	−	5.58448i	−0.191659	−	0.331963i	0.754141	−	0.656712i	$-0.228053\pi$
$283$	−3.22420	−	5.58448i	−0.191659	−	0.331963i	−0.945800	+	0.324749i	$0.894720\pi$
$284$	−3.79147	−	6.56701i	−0.224982	−	0.389681i
$285$	−33.6063			−1.99067
$286$	0.174744	−	0.261599i	0.0103328	−	0.0154687i
$287$		0			0
$288$	−1.94908	−	3.37591i	−0.114851	−	0.198928i
$289$	4.54937	+	7.87975i	0.267610	+	0.463514i
$290$	−1.93010	+	3.34303i	−0.113339	+	0.196310i
$291$	−7.46177			−0.437417
$292$	5.45471	−	9.44783i	0.319213	−	0.552893i
$293$	−0.972625	+	1.68464i	−0.0568214	+	0.0984175i	−0.893037	−	0.449983i	$-0.851430\pi$
$293$	−0.972625	+	1.68464i	−0.0568214	+	0.0984175i	0.836216	+	0.548401i	$0.184763\pi$
$294$		0			0
$295$	6.27661	−	10.8714i	0.365439	−	0.632958i
$296$	−4.41108	−	7.64022i	−0.256389	−	0.444079i
$297$	0.102914	+	0.178252i	0.00597168	+	0.0103432i
$298$	22.0024			1.27456
$299$	−2.59438	−	5.25909i	−0.150037	−	0.304141i
$300$	−4.28298			−0.247278
$301$		0			0
$302$	5.94347	+	10.2944i	0.342008	+	0.592376i
$303$	4.94558	−	8.56600i	0.284116	−	0.492104i
$304$	−6.97084			−0.399805
$305$	−8.13673	+	14.0932i	−0.465908	+	0.806976i
$306$	−5.47872	+	9.48941i	−0.313197	+	0.542474i
$307$	6.07696			0.346830			0.173415	−	0.984849i	$-0.444520\pi$
$307$	6.07696			0.346830			0.173415	+	0.984849i	$0.444520\pi$
$308$		0			0
$309$	12.4200	+	21.5121i	0.706552	+	1.22378i
$310$	−6.81139	−	11.7977i	−0.386861	−	0.670063i
$311$	−12.2417			−0.694164			−0.347082	−	0.937835i	$-0.612827\pi$
$311$	−12.2417			−0.694164			−0.347082	+	0.937835i	$0.612827\pi$
$312$	−4.18951	−	8.49260i	−0.237184	−	0.480799i
$313$	9.38839			0.530663			0.265332	−	0.964157i	$-0.414519\pi$
$313$	9.38839			0.530663			0.265332	+	0.964157i	$0.414519\pi$
$314$	0.800191	+	1.38597i	0.0451574	+	0.0782149i
$315$		0			0
$316$	4.60897	−	7.98297i	0.259275	−	0.449077i
$317$	−2.79657			−0.157071			−0.0785355	−	0.996911i	$-0.525024\pi$
$317$	−2.79657			−0.157071			−0.0785355	+	0.996911i	$0.525024\pi$
$318$	−1.17510	+	2.03533i	−0.0658961	+	0.114135i
$319$	0.0917468	−	0.158910i	0.00513683	−	0.00889726i
$320$	1.83556			0.102611
$321$	−9.66396	+	16.7385i	−0.539389	+	0.934250i
$322$		0			0
$323$	9.79723	+	16.9693i	0.545133	+	0.944197i
$324$	−5.49878			−0.305488
$325$	−5.86710	−	0.383753i	−0.325448	−	0.0212868i
$326$	−4.60937			−0.255289
$327$	−5.15436	−	8.92761i	−0.285037	−	0.493698i
$328$	−5.21139	−	9.02639i	−0.287751	−	0.498399i
$329$		0			0
$330$	−0.420644			−0.0231557
$331$	12.8582	−	22.2711i	0.706752	−	1.22413i	−0.259304	−	0.965796i	$-0.583493\pi$
$331$	12.8582	−	22.2711i	0.706752	−	1.22413i	0.966056	−	0.258334i	$-0.0831735\pi$
$332$	−8.43966	+	14.6179i	−0.463186	+	0.802262i
$333$	34.3903			1.88458
$334$	−9.67113	+	16.7509i	−0.529181	+	0.916568i
$335$	−6.06624	−	10.5070i	−0.331434	−	0.574061i
$336$		0			0
$337$	−34.3496			−1.87114			−0.935570	−	0.353141i	$-0.885114\pi$
$337$	−34.3496			−1.87114			−0.935570	+	0.353141i	$0.885114\pi$
$338$	−4.97813	−	12.0091i	−0.270775	−	0.653208i
$339$	39.2760			2.13318
$340$	−2.57980	−	4.46835i	−0.139909	−	0.242330i
$341$	0.323777	+	0.560799i	0.0175335	+	0.0303690i
$342$	13.5868	−	23.5330i	0.734688	−	1.27252i
$343$		0			0
$344$	2.99057	−	5.17982i	0.161241	−	0.279277i
$345$	−3.92051	+	6.79053i	−0.211073	+	0.365590i
$346$	−14.2034			−0.763577
$347$	6.46296	−	11.1942i	0.346950	−	0.600935i	−0.638756	−	0.769409i	$-0.720551\pi$
$347$	6.46296	−	11.1942i	0.346950	−	0.600935i	0.985706	+	0.168475i	$0.0538841\pi$
$348$	−2.76171	−	4.78343i	−0.148043	−	0.256419i
$349$	4.74593	+	8.22019i	0.254044	+	0.440017i	0.964635	−	0.263588i	$-0.0849060\pi$
$349$	4.74593	+	8.22019i	0.254044	+	0.440017i	−0.710592	+	0.703605i	$0.751573\pi$
$350$		0			0
$351$	8.48731	+	0.555135i	0.453019	+	0.0296309i
$352$	−0.0872528			−0.00465059
$353$	4.58281	+	7.93766i	0.243918	+	0.422479i	0.961827	−	0.273658i	$-0.0882338\pi$
$353$	4.58281	+	7.93766i	0.243918	+	0.422479i	−0.717909	+	0.696137i	$0.754900\pi$
$354$	8.98098	+	15.5555i	0.477334	+	0.826766i
$355$	−6.95947	+	12.0541i	−0.369370	+	0.639768i
$356$	−9.90942			−0.525198
$357$		0			0
$358$	5.26777	−	9.12404i	0.278410	−	0.482220i
$359$	−8.14802			−0.430036			−0.215018	−	0.976610i	$-0.568981\pi$
$359$	−8.14802			−0.430036			−0.215018	+	0.976610i	$0.568981\pi$
$360$	−3.57766	+	6.19669i	−0.188559	+	0.326594i
$361$	−14.7963	−	25.6280i	−0.778755	−	1.34884i
$362$	−9.29039	−	16.0914i	−0.488292	−	0.845747i
$363$	−28.8708			−1.51532
$364$		0			0
$365$	−20.0249			−1.04815
$366$	−11.6426	−	20.1655i	−0.608566	−	1.05407i
$367$	12.7538	+	22.0902i	0.665742	+	1.15310i	0.979084	+	0.203458i	$0.0652181\pi$
$367$	12.7538	+	22.0902i	0.665742	+	1.15310i	−0.313342	+	0.949640i	$0.601449\pi$
$368$	−0.813218	+	1.40854i	−0.0423919	+	0.0734250i
$369$	40.6297			2.11510
$370$	−8.09681	+	14.0241i	−0.420933	+	0.729077i
$371$		0			0
$372$	19.4923			1.01063
$373$	−1.41945	+	2.45855i	−0.0734961	+	0.127299i	−0.900431	−	0.434998i	$-0.856749\pi$
$373$	−1.41945	+	2.45855i	−0.0734961	+	0.127299i	0.826935	+	0.562297i	$0.190082\pi$
$374$	0.122630	+	0.212402i	0.00634105	+	0.0109830i
$375$	15.9833	+	27.6839i	0.825374	+	1.42959i
$376$	8.00118			0.412629
$377$	−3.35458	−	6.80010i	−0.172770	−	0.350223i
$378$		0			0
$379$	0.804301	+	1.39309i	0.0413142	+	0.0715582i	0.885943	−	0.463794i	$-0.153512\pi$
$379$	0.804301	+	1.39309i	0.0413142	+	0.0715582i	−0.844629	+	0.535352i	$0.820179\pi$
$380$	6.39770	+	11.0811i	0.328195	+	0.568451i
$381$	−0.848966	+	1.47045i	−0.0434938	+	0.0753335i
$382$	22.8279			1.16798
$383$	−7.97493	+	13.8130i	−0.407500	+	0.705810i	−0.994609	−	0.103698i	$-0.966933\pi$
$383$	−7.97493	+	13.8130i	−0.407500	+	0.705810i	0.587109	+	0.809508i	$0.300266\pi$
$384$	−1.31322	+	2.27456i	−0.0670149	+	0.116073i
$385$		0			0
$386$	1.46152	−	2.53143i	0.0743895	−	0.128846i
$387$	11.6578	+	20.1918i	0.592597	+	1.02641i
$388$	1.42051	+	2.46040i	0.0721155	+	0.124908i
$389$	4.25349			0.215660			0.107830	−	0.994169i	$-0.465610\pi$
$389$	4.25349			0.215660			0.107830	+	0.994169i	$0.465610\pi$
$390$	−9.65513	+	14.4542i	−0.488907	+	0.731915i
$391$	4.57178			0.231205
$392$		0			0
$393$	3.67220	+	6.36044i	0.185238	+	0.320842i
$394$	2.37415	−	4.11215i	0.119608	−	0.207167i
$395$	−16.9201			−0.851341
$396$	0.170063	−	0.294558i	0.00854599	−	0.0148021i
$397$	0.830554	−	1.43856i	0.0416843	−	0.0721993i	−0.844431	−	0.535665i	$-0.820061\pi$
$397$	0.830554	−	1.43856i	0.0416843	−	0.0721993i	0.886115	+	0.463466i	$0.153394\pi$
$398$	−9.84531			−0.493501
$399$		0			0
$400$	0.815359	+	1.41224i	0.0407680	+	0.0706122i
$401$	1.30242	+	2.25586i	0.0650398	+	0.112652i	0.896712	−	0.442615i	$-0.145949\pi$
$401$	1.30242	+	2.25586i	0.0650398	+	0.112652i	−0.831672	+	0.555267i	$0.812616\pi$
$402$	17.3599			0.865835
$403$	26.7019	+	1.74651i	1.33012	+	0.0869997i
$404$	−3.76600			−0.187366
$405$	5.04667	+	8.74109i	0.250771	+	0.434348i
$406$		0			0
$407$	0.384879	−	0.666630i	0.0190778	−	0.0330436i
$408$	7.38270			0.365498
$409$	3.17978	−	5.50753i	0.157230	−	0.272330i	−0.776639	−	0.629946i	$-0.783077\pi$
$409$	3.17978	−	5.50753i	0.157230	−	0.272330i	0.933869	+	0.357616i	$0.116410\pi$
$410$	−9.56582	+	16.5685i	−0.472422	+	0.818259i
$411$	−27.3598			−1.34956
$412$	4.72886	−	8.19062i	0.232974	−	0.403523i
$413$		0			0
$414$	−3.17006	−	5.49071i	−0.155800	−	0.269854i
$415$	30.9830			1.52090
$416$	−2.00273	+	2.99818i	−0.0981920	+	0.146998i
$417$	−32.1599			−1.57488
$418$	−0.304113	−	0.526739i	−0.0148746	−	0.0257636i
$419$	4.71852	+	8.17271i	0.230515	+	0.399263i	0.957960	−	0.286903i	$-0.0926257\pi$
$419$	4.71852	+	8.17271i	0.230515	+	0.399263i	−0.727445	+	0.686166i	$0.759292\pi$
$420$		0			0
$421$	−30.3009			−1.47677			−0.738387	−	0.674377i	$-0.764412\pi$
$421$	−30.3009			−1.47677			−0.738387	+	0.674377i	$0.764412\pi$
$422$	2.18356	−	3.78203i	0.106294	−	0.184106i
$423$	−15.5950	+	27.0113i	−0.758254	+	1.31333i
$424$	0.894821			0.0434564
$425$	2.29191	−	3.96970i	0.111174	−	0.192559i
$426$	−9.95805	−	17.2478i	−0.482469	−	0.835661i
$427$		0			0
$428$	7.35899			0.355710
$429$	0.458954	−	0.687074i	0.0221585	−	0.0331722i
$430$	−10.9787			−0.529442
$431$	2.39419	+	4.14687i	0.115324	+	0.199747i	0.917909	−	0.396790i	$-0.129876\pi$
$431$	2.39419	+	4.14687i	0.115324	+	0.199747i	−0.802585	+	0.596538i	$0.796543\pi$
$432$	−1.17949	−	2.04294i	−0.0567484	−	0.0982911i
$433$	20.1875	−	34.9658i	0.970151	−	1.68035i	0.275063	−	0.961426i	$-0.411301\pi$
$433$	20.1875	−	34.9658i	0.970151	−	1.68035i	0.695088	−	0.718925i	$-0.255365\pi$
$434$		0			0
$435$	−5.06929	+	8.78027i	−0.243054	+	0.420982i
$436$	−1.96249	+	3.39913i	−0.0939862	+	0.162789i
$437$	−11.3376			−0.542353
$438$	14.3264	−	24.8141i	0.684544	−	1.18567i
$439$	−0.509403	−	0.882313i	−0.0243125	−	0.0421105i	0.853613	−	0.520907i	$-0.174406\pi$
$439$	−0.509403	−	0.882313i	−0.0243125	−	0.0421105i	−0.877926	+	0.478797i	$0.841073\pi$
$440$	0.0800789	+	0.138701i	0.00381761	+	0.00661229i
$441$		0			0
$442$	10.1133	+	0.661487i	0.481040	+	0.0314637i
$443$	−26.9164			−1.27884			−0.639419	−	0.768858i	$-0.720825\pi$
$443$	−26.9164			−1.27884			−0.639419	+	0.768858i	$0.720825\pi$
$444$	−11.5854	−	20.0665i	−0.549820	−	0.952316i
$445$	9.09467	+	15.7524i	0.431128	+	0.746736i
$446$	−14.0542	+	24.3427i	−0.665488	+	1.15266i
$447$	57.7879			2.73327
$448$		0			0
$449$	−4.41776	+	7.65179i	−0.208487	+	0.361110i	−0.951238	−	0.308457i	$-0.900187\pi$
$449$	−4.41776	+	7.65179i	−0.208487	+	0.361110i	0.742751	+	0.669568i	$0.233521\pi$
$450$	−6.35682			−0.299663
$451$	0.454708	−	0.787578i	0.0214114	−	0.0370856i
$452$	−7.47705	−	12.9506i	−0.351691	−	0.609146i
$453$	15.6101	+	27.0376i	0.733429	+	1.27034i
$454$	−26.6909			−1.25266
$455$		0			0
$456$	−18.3085			−0.857373
$457$	17.9361	+	31.0662i	0.839014	+	1.45321i	0.890720	+	0.454552i	$0.150201\pi$
$457$	17.9361	+	31.0662i	0.839014	+	1.45321i	−0.0517063	+	0.998662i	$0.516466\pi$
$458$	−4.70473	−	8.14883i	−0.219837	−	0.380770i
$459$	−3.31546	+	5.74254i	−0.154752	+	0.268039i
$460$	2.98542			0.139196
$461$	−20.6169	+	35.7095i	−0.960224	+	1.66316i	−0.238292	+	0.971193i	$0.576588\pi$
$461$	−20.6169	+	35.7095i	−0.960224	+	1.66316i	−0.721932	+	0.691964i	$0.756746\pi$
$462$		0			0
$463$	21.0313			0.977408			0.488704	−	0.872450i	$-0.337470\pi$
$463$	21.0313			0.977408			0.488704	+	0.872450i	$0.337470\pi$
$464$	−1.05151	+	1.82126i	−0.0488149	+	0.0845499i
$465$	−17.8897	−	30.9859i	−0.829615	−	1.43693i
$466$	−11.5107	−	19.9372i	−0.533224	−	0.923572i
$467$	−20.4320			−0.945479			−0.472740	−	0.881202i	$-0.656735\pi$
$467$	−20.4320			−0.945479			−0.472740	+	0.881202i	$0.656735\pi$
$468$	−6.21809	−	12.6048i	−0.287432	−	0.582655i
$469$		0			0
$470$	−7.34332	−	12.7190i	−0.338722	−	0.586684i
$471$	2.10165	+	3.64017i	0.0968390	+	0.167730i
$472$	3.41945	−	5.92267i	0.157393	−	0.272613i
$473$	0.521871			0.0239957
$474$	12.1052	−	20.9668i	0.556008	−	0.963035i
$475$	−5.68374	+	9.84453i	−0.260788	+	0.451698i
$476$		0			0
$477$	−1.74408	+	3.02084i	−0.0798561	+	0.138315i
$478$	−5.51607	−	9.55412i	−0.252299	−	0.436995i
$479$	19.6000	+	33.9482i	0.895547	+	1.55113i	0.833126	+	0.553084i	$0.186549\pi$
$479$	19.6000	+	33.9482i	0.895547	+	1.55113i	0.0624218	+	0.998050i	$0.480118\pi$
$480$	4.82098			0.220047
$481$	−14.0725	−	28.5265i	−0.641651	−	1.30070i
$482$	7.39939			0.337033
$483$		0			0
$484$	5.49619	+	9.51969i	0.249827	+	0.432713i
$485$	2.60743	−	4.51621i	0.118397	−	0.205070i
$486$	−21.5192			−0.976129
$487$	5.80410	−	10.0530i	0.263009	−	0.455545i	−0.704031	−	0.710169i	$-0.748618\pi$
$487$	5.80410	−	10.0530i	0.263009	−	0.455545i	0.967040	+	0.254624i	$0.0819518\pi$
$488$	−4.43283	+	7.67789i	−0.200665	+	0.347562i
$489$	−12.1062			−0.547462
$490$		0			0
$491$	11.9193	+	20.6448i	0.537910	+	0.931688i	0.999016	+	0.0443428i	$0.0141194\pi$
$491$	11.9193	+	20.6448i	0.537910	+	0.931688i	−0.461106	+	0.887345i	$0.652547\pi$
$492$	−13.6874	−	23.7072i	−0.617075	−	1.06880i
$493$	5.91139			0.266236
$494$	−25.0801	−	1.64043i	−1.12841	−	0.0738066i
$495$	−0.624322			−0.0280612
$496$	−3.71080	−	6.42729i	−0.166620	−	0.288594i
$497$		0			0
$498$	−22.1662	+	38.3930i	−0.993292	+	1.72043i
$499$	8.18261			0.366304			0.183152	−	0.983085i	$-0.441370\pi$
$499$	8.18261			0.366304			0.183152	+	0.983085i	$0.441370\pi$
$500$	6.08554	−	10.5405i	0.272154	−	0.471384i
$501$	−25.4006	+	43.9951i	−1.13482	+	1.96556i
$502$	3.88787			0.173524
$503$	−4.28341	+	7.41908i	−0.190988	+	0.330801i	−0.945578	−	0.325396i	$-0.894502\pi$
$503$	−4.28341	+	7.41908i	−0.190988	+	0.330801i	0.754590	+	0.656196i	$0.227836\pi$
$504$		0			0
$505$	3.45636	+	5.98660i	0.153806	+	0.266400i
$506$	−0.141911			−0.00630872
$507$	−13.0748	−	31.5411i	−0.580670	−	1.40079i
$508$	0.646477			0.0286828
$509$	7.42352	+	12.8579i	0.329042	+	0.569917i	0.982322	−	0.187199i	$-0.0599410\pi$
$509$	7.42352	+	12.8579i	0.329042	+	0.569917i	−0.653280	+	0.757116i	$0.726608\pi$
$510$	−6.77569	−	11.7358i	−0.300033	−	0.519672i
$511$		0			0
$512$	1.00000			0.0441942
$513$	8.22206	−	14.2410i	0.363013	−	0.628757i
$514$	−7.86569	+	13.6238i	−0.346941	+	0.600919i
$515$	−17.3602			−0.764982
$516$	7.85454	−	13.6045i	0.345777	−	0.598903i
$517$	0.349063	+	0.604594i	0.0153518	+	0.0265900i
$518$		0			0
$519$	−37.3042			−1.63747
$520$	6.60409	+	0.431958i	0.289609	+	0.0189426i
$521$	19.1170			0.837533			0.418766	−	0.908094i	$-0.362463\pi$
$521$	19.1170			0.837533			0.418766	+	0.908094i	$0.362463\pi$
$522$	−4.09895	−	7.09958i	−0.179406	−	0.310740i
$523$	4.84605	+	8.39360i	0.211903	+	0.367027i	0.952310	−	0.305132i	$-0.0987006\pi$
$523$	4.84605	+	8.39360i	0.211903	+	0.367027i	−0.740407	+	0.672159i	$0.765367\pi$
$524$	1.39817	−	2.42170i	0.0610793	−	0.105792i
$525$		0			0
$526$	6.37994	−	11.0504i	0.278178	−	0.481819i
$527$	−10.4307	+	18.0666i	−0.454370	+	0.786992i
$528$	−0.229164			−0.00997308
$529$	10.1774	−	17.6277i	0.442494	−	0.766421i
$530$	−0.821249	−	1.42245i	−0.0356728	−	0.0617871i
$531$	13.3296	+	23.0876i	0.578456	+	1.00192i
$532$		0			0
$533$	−16.6257	−	33.7021i	−0.720139	−	1.45980i
$534$	−26.0265			−1.12627
$535$	−6.75393	−	11.6982i	−0.291998	−	0.505755i
$536$	−3.30485	−	5.72416i	−0.142748	−	0.247246i
$537$	13.8355	−	23.9637i	0.597044	−	1.03411i
$538$	13.0258			0.561583
$539$		0			0
$540$	−2.16503	+	3.74994i	−0.0931681	+	0.161372i
$541$	−5.60466			−0.240963			−0.120482	−	0.992716i	$-0.538444\pi$
$541$	−5.60466			−0.240963			−0.120482	+	0.992716i	$0.538444\pi$
$542$	4.68905	−	8.12167i	0.201412	−	0.348855i
$543$	−24.4006	−	42.2631i	−1.04713	−	1.81368i
$544$	−1.40546	−	2.43433i	−0.0602585	−	0.104371i
$545$	7.20454			0.308608
$546$		0			0
$547$	−37.1487			−1.58836			−0.794181	−	0.607681i	$-0.792100\pi$
$547$	−37.1487			−1.58836			−0.794181	+	0.607681i	$0.792100\pi$
$548$	5.20854	+	9.02146i	0.222498	+	0.385378i
$549$	−17.2799	−	29.9297i	−0.737490	−	1.27737i
$550$	−0.0711424	+	0.123222i	−0.00303352	+	0.00525421i
$551$	−14.6598			−0.624527
$552$	−2.13587	+	3.69943i	−0.0909085	+	0.157458i
$553$		0			0
$554$	−17.5875			−0.747221
$555$	−21.2657	+	36.8334i	−0.902681	+	1.56349i
$556$	6.12235	+	10.6042i	0.259645	+	0.449719i
$557$	14.8717	+	25.7586i	0.630136	+	1.09143i	0.987524	+	0.157472i	$0.0503342\pi$
$557$	14.8717	+	25.7586i	0.630136	+	1.09143i	−0.357387	+	0.933956i	$0.616332\pi$
$558$	28.9306			1.22473
$559$	11.9786	−	17.9325i	0.506642	−	0.758465i
$560$		0			0
$561$	0.322080	+	0.557860i	0.0135982	+	0.0235528i
$562$	−6.79864	−	11.7756i	−0.286783	−	0.496723i
$563$	−4.48827	+	7.77391i	−0.189158	+	0.327631i	−0.944970	−	0.327158i	$-0.893909\pi$
$563$	−4.48827	+	7.77391i	−0.189158	+	0.327631i	0.755812	+	0.654789i	$0.227242\pi$
$564$	21.0146			0.884874
$565$	−13.7246	+	23.7717i	−0.577397	+	1.00008i
$566$	−3.22420	+	5.58448i	−0.135523	+	0.234733i
$567$		0			0
$568$	−3.79147	+	6.56701i	−0.159086	+	0.275546i
$569$	6.68319	+	11.5756i	0.280174	+	0.485276i	0.971427	−	0.237337i	$-0.0762745\pi$
$569$	6.68319	+	11.5756i	0.280174	+	0.485276i	−0.691253	+	0.722612i	$0.742941\pi$
$570$	16.8032	+	29.1039i	0.703807	+	1.21903i
$571$	−32.4655			−1.35864			−0.679319	−	0.733843i	$-0.737725\pi$
$571$	−32.4655			−1.35864			−0.679319	+	0.733843i	$0.737725\pi$
$572$	−0.313924	−	0.0205330i	−0.0131258	−	0.000858528i
$573$	59.9562			2.50470
$574$		0			0
$575$	1.32613	+	2.29693i	0.0553035	+	0.0957884i
$576$	−1.94908	+	3.37591i	−0.0812119	+	0.140663i
$577$	13.2037			0.549678			0.274839	−	0.961490i	$-0.411375\pi$
$577$	13.2037			0.549678			0.274839	+	0.961490i	$0.411375\pi$
$578$	4.54937	−	7.87975i	0.189229	−	0.327754i
$579$	3.83859	−	6.64864i	0.159526	−	0.276308i
$580$	3.86020			0.160286
$581$		0			0
$582$	3.73088	+	6.46208i	0.154650	+	0.267862i
$583$	0.0390378	+	0.0676155i	0.00161678	+	0.00280035i
$584$	−10.9094			−0.451435
$585$	−14.3302	+	21.4529i	−0.592481	+	0.886970i
$586$	1.94525			0.0803576
$587$	5.18691	+	8.98398i	0.214086	+	0.370809i	0.952990	−	0.303003i	$-0.0979892\pi$
$587$	5.18691	+	8.98398i	0.214086	+	0.370809i	−0.738903	+	0.673812i	$0.764656\pi$
$588$		0			0
$589$	25.8674	−	44.8036i	1.06585	−	1.84610i
$590$	−12.5532			−0.516808
$591$	6.23556	−	10.8003i	0.256497	−	0.444266i
$592$	−4.41108	+	7.64022i	−0.181294	+	0.314011i
$593$	36.6549			1.50524			0.752619	−	0.658456i	$-0.228790\pi$
$593$	36.6549			1.50524			0.752619	+	0.658456i	$0.228790\pi$
$594$	0.102914	−	0.178252i	0.00422261	−	0.00731378i
$595$		0			0
$596$	−11.0012	−	19.0546i	−0.450626	−	0.780508i
$597$	−25.8581			−1.05830
$598$	−3.25732	+	4.87635i	−0.133202	+	0.199409i
$599$	37.4356			1.52958			0.764789	−	0.644280i	$-0.222843\pi$
$599$	37.4356			1.52958			0.764789	+	0.644280i	$0.222843\pi$
$600$	2.14149	+	3.70917i	0.0874260	+	0.151426i
$601$	−0.994692	−	1.72286i	−0.0405743	−	0.0702768i	0.845025	−	0.534727i	$-0.179585\pi$
$601$	−0.994692	−	1.72286i	−0.0405743	−	0.0702768i	−0.885599	+	0.464450i	$0.846252\pi$
$602$		0			0
$603$	25.7657			1.04926
$604$	5.94347	−	10.2944i	0.241836	−	0.418873i
$605$	10.0886	−	17.4740i	0.410160	−	0.710417i
$606$	−9.89117			−0.401801
$607$	2.69926	−	4.67526i	0.109560	−	0.189763i	−0.806032	−	0.591872i	$-0.798389\pi$
$607$	2.69926	−	4.67526i	0.109560	−	0.189763i	0.915592	+	0.402109i	$0.131723\pi$
$608$	3.48542	+	6.03693i	0.141353	+	0.244830i
$609$		0			0
$610$	16.2735			0.658893
$611$	28.7872	+	1.88290i	1.16460	+	0.0761739i
$612$	10.9574			0.442928
$613$	2.02034	+	3.49934i	0.0816009	+	0.141337i	0.903938	−	0.427664i	$-0.140663\pi$
$613$	2.02034	+	3.49934i	0.0816009	+	0.141337i	−0.822337	+	0.569001i	$0.807330\pi$
$614$	−3.03848	−	5.26280i	−0.122623	−	0.212389i
$615$	−25.1240	+	43.5161i	−1.01310	+	1.75474i
$616$		0			0
$617$	12.1383	−	21.0241i	0.488669	−	0.846400i	−0.511246	−	0.859435i	$-0.670816\pi$
$617$	12.1383	−	21.0241i	0.488669	−	0.846400i	0.999915	+	0.0130346i	$0.00414917\pi$
$618$	12.4200	−	21.5121i	0.499607	−	0.865346i
$619$	14.5515			0.584875			0.292437	−	0.956285i	$-0.405534\pi$
$619$	14.5515			0.584875			0.292437	+	0.956285i	$0.405534\pi$
$620$	−6.81139	+	11.7977i	−0.273552	+	0.473806i
$621$	−1.91837	−	3.32272i	−0.0769816	−	0.133336i
$622$	6.12086	+	10.6016i	0.245424	+	0.425087i
$623$		0			0
$624$	−5.26005	+	7.87452i	−0.210570	+	0.315233i
$625$	−14.1872			−0.567487
$626$	−4.69419	−	8.13058i	−0.187618	−	0.324963i
$627$	−0.798733	−	1.38345i	−0.0318983	−	0.0552495i
$628$	0.800191	−	1.38597i	0.0319311	−	0.0553063i
$629$	24.7984			0.988776
$630$		0			0
$631$	4.19668	−	7.26886i	0.167067	−	0.289369i	−0.770320	−	0.637657i	$-0.779904\pi$
$631$	4.19668	−	7.26886i	0.167067	−	0.289369i	0.937387	+	0.348288i	$0.113237\pi$
$632$	−9.21793			−0.366670
$633$	5.73497	−	9.93327i	0.227945	−	0.394812i
$634$	1.39828	+	2.42190i	0.0555330	+	0.0961859i
$635$	−0.593324	−	1.02767i	−0.0235453	−	0.0407817i
$636$	2.35019			0.0931912
$637$		0			0
$638$	−0.183494			−0.00726458
$639$	−14.7798	−	25.5993i	−0.584679	−	1.01269i
$640$	−0.917780	−	1.58964i	−0.0362784	−	0.0628361i
$641$	−0.194764	+	0.337341i	−0.00769272	+	0.0133242i	−0.869846	−	0.493323i	$-0.835782\pi$
$641$	−0.194764	+	0.337341i	−0.00769272	+	0.0133242i	0.862153	+	0.506647i	$0.169115\pi$
$642$	19.3279			0.762812
$643$	−5.93499	+	10.2797i	−0.234053	+	0.405392i	−0.958997	−	0.283416i	$-0.908532\pi$
$643$	−5.93499	+	10.2797i	−0.234053	+	0.405392i	0.724944	+	0.688808i	$0.241866\pi$
$644$		0			0
$645$	−28.8350			−1.13538
$646$	9.79723	−	16.9693i	0.385467	−	0.667648i
$647$	−9.90422	−	17.1546i	−0.389375	−	0.674418i	0.602990	−	0.797748i	$-0.293976\pi$
$647$	−9.90422	−	17.1546i	−0.389375	−	0.674418i	−0.992366	+	0.123331i	$0.960642\pi$
$648$	2.74939	+	4.76209i	0.108006	+	0.187072i
$649$	0.596714			0.0234231
$650$	2.60121	+	5.27294i	0.102028	+	0.206822i
$651$		0			0
$652$	2.30469	+	3.99183i	0.0902584	+	0.156332i
$653$	2.79653	+	4.84373i	0.109437	+	0.189550i	0.915542	−	0.402222i	$-0.131762\pi$
$653$	2.79653	+	4.84373i	0.109437	+	0.189550i	−0.806106	+	0.591772i	$0.798429\pi$
$654$	−5.15436	+	8.92761i	−0.201551	+	0.349097i
$655$	−5.13285			−0.200557
$656$	−5.21139	+	9.02639i	−0.203471	+	0.352421i
$657$	21.2634	−	36.8293i	0.829563	−	1.43685i
$658$		0			0
$659$	−5.58265	+	9.66943i	−0.217469	+	0.376668i	−0.954034	−	0.299700i	$-0.903113\pi$
$659$	−5.58265	+	9.66943i	−0.217469	+	0.376668i	0.736564	+	0.676367i	$0.236447\pi$
$660$	0.210322	+	0.364289i	0.00818678	+	0.0141799i
$661$	−4.11021	−	7.11910i	−0.159869	−	0.276901i	0.774952	−	0.632019i	$-0.217774\pi$
$661$	−4.11021	−	7.11910i	−0.159869	−	0.276901i	−0.934821	+	0.355119i	$0.884440\pi$
$662$	−25.7164			−0.999498
$663$	26.5619	+	1.73735i	1.03158	+	0.0674732i
$664$	16.8793			0.655044
$665$		0			0
$666$	−17.1951	−	29.7829i	−0.666298	−	1.15406i
$667$	−1.71021	+	2.96217i	−0.0662195	+	0.114696i
$668$	19.3423			0.748374
$669$	−36.9126	+	63.9345i	−1.42712	+	2.47185i
$670$	−6.06624	+	10.5070i	−0.234359	+	0.405922i
$671$	−0.773554			−0.0298627
$672$		0			0
$673$	−1.98340	−	3.43536i	−0.0764546	−	0.132423i	0.825263	−	0.564748i	$-0.191027\pi$
$673$	−1.98340	−	3.43536i	−0.0764546	−	0.132423i	−0.901718	+	0.432325i	$0.857693\pi$
$674$	17.1748	+	29.7476i	0.661548	+	1.14583i
$675$	−3.84684			−0.148065
$676$	−7.91111	+	10.3157i	−0.304273	+	0.396759i
$677$	24.8848			0.956402			0.478201	−	0.878251i	$-0.341289\pi$
$677$	24.8848			0.956402			0.478201	+	0.878251i	$0.341289\pi$
$678$	−19.6380	−	34.0140i	−0.754193	−	1.30630i
$679$		0			0
$680$	−2.57980	+	4.46835i	−0.0989310	+	0.171353i
$681$	−70.1018			−2.68631
$682$	0.323777	−	0.560799i	0.0123981	−	0.0214741i
$683$	−25.3588	+	43.9227i	−0.970327	+	1.68066i	−0.275761	+	0.961226i	$0.588930\pi$
$683$	−25.3588	+	43.9227i	−0.970327	+	1.68066i	−0.694566	+	0.719429i	$0.744403\pi$
$684$	−27.1735			−1.03901
$685$	9.56059	−	16.5594i	0.365291	−	0.632703i
$686$		0			0
$687$	−12.3567	−	21.4024i	−0.471436	−	0.816552i
$688$	−5.98114			−0.228029
$689$	3.21945	+	0.210576i	0.122651	+	0.00802232i
$690$	7.84102			0.298503
$691$	6.05622	+	10.4897i	0.230389	+	0.399046i	0.957923	−	0.287026i	$-0.0926667\pi$
$691$	6.05622	+	10.4897i	0.230389	+	0.399046i	−0.727533	+	0.686072i	$0.759333\pi$
$692$	7.10168	+	12.3005i	0.269965	+	0.467594i
$693$		0			0
$694$	−12.9259			−0.490661
$695$	11.2379	−	19.4647i	0.426279	−	0.738337i
$696$	−2.76171	+	4.78343i	−0.104682	+	0.181315i
$697$	29.2976			1.10972
$698$	4.74593	−	8.22019i	0.179636	−	0.311139i
$699$	−30.2322	−	52.3637i	−1.14349	−	1.98058i
$700$		0			0
$701$	2.45486			0.0927186			0.0463593	−	0.998925i	$-0.485238\pi$
$701$	2.45486			0.0927186			0.0463593	+	0.998925i	$0.485238\pi$
$702$	−3.76289	−	7.62779i	−0.142021	−	0.287892i
$703$	−61.4979			−2.31944
$704$	0.0436264	+	0.0755631i	0.00164423	+	0.00284789i
$705$	−19.2868	−	33.4057i	−0.726382	−	1.25813i
$706$	4.58281	−	7.93766i	0.172476	−	0.298738i
$707$		0			0
$708$	8.98098	−	15.5555i	0.337526	−	0.584612i
$709$	−1.81867	+	3.15003i	−0.0683017	+	0.118302i	−0.898154	−	0.439681i	$-0.855091\pi$
$709$	−1.81867	+	3.15003i	−0.0683017	+	0.118302i	0.829852	+	0.557983i	$0.188425\pi$
$710$	13.9189			0.522368
$711$	17.9665	−	31.1190i	0.673798	−	1.16705i
$712$	4.95471	+	8.58181i	0.185686	+	0.321617i
$713$	−6.03538	−	10.4536i	−0.226027	−	0.391490i
$714$		0			0
$715$	0.255473	+	0.517871i	0.00955414	+	0.0193673i
$716$	−10.5355			−0.393731
$717$	−14.4876	−	25.0933i	−0.541050	−	0.937126i
$718$	4.07401	+	7.05639i	0.152041	+	0.263342i
$719$	20.6024	−	35.6844i	0.768339	−	1.33080i	−0.170124	−	0.985423i	$-0.554417\pi$
$719$	20.6024	−	35.6844i	0.768339	−	1.33080i	0.938463	−	0.345379i	$-0.112250\pi$
$720$	7.15533			0.266663
$721$		0			0
$722$	−14.7963	+	25.6280i	−0.550663	+	0.953776i
$723$	19.4340			0.722759
$724$	−9.29039	+	16.0914i	−0.345275	+	0.598033i
$725$	1.71471	+	2.96996i	0.0636827	+	0.110302i
$726$	14.4354	+	25.0029i	0.535748	+	0.927943i
$727$	−24.1162			−0.894422			−0.447211	−	0.894428i	$-0.647583\pi$
$727$	−24.1162			−0.894422			−0.447211	+	0.894428i	$0.647583\pi$
$728$		0			0
$729$	−40.0224			−1.48231
$730$	10.0124	+	17.3421i	0.370577	+	0.641859i
$731$	8.40624	+	14.5600i	0.310916	+	0.538523i
$732$	−11.6426	+	20.1655i	−0.430321	+	0.745338i
$733$	18.7490			0.692509			0.346254	−	0.938141i	$-0.387453\pi$
$733$	18.7490			0.692509			0.346254	+	0.938141i	$0.387453\pi$
$734$	12.7538	−	22.0902i	0.470751	−	0.815364i
$735$		0			0
$736$	1.62644			0.0599513
$737$	0.288357	−	0.499449i	0.0106218	−	0.0183974i
$738$	−20.3149	−	35.1864i	−0.747801	−	1.29523i
$739$	−0.465734	−	0.806675i	−0.0171323	−	0.0296740i	0.857332	−	0.514764i	$-0.172120\pi$
$739$	−0.465734	−	0.806675i	−0.0171323	−	0.0296740i	−0.874464	+	0.485090i	$0.838787\pi$
$740$	16.1936			0.595289
$741$	−65.8714	−	4.30849i	−2.41985	−	0.158276i
$742$		0			0
$743$	14.8945	+	25.7980i	0.546425	+	0.946437i	0.998516	+	0.0544644i	$0.0173451\pi$
$743$	14.8945	+	25.7980i	0.546425	+	0.946437i	−0.452090	+	0.891972i	$0.649322\pi$
$744$	−9.74617	−	16.8809i	−0.357312	−	0.618883i
$745$	−20.1933	+	34.9759i	−0.739827	+	1.28142i
$746$	2.83889			0.103939
$747$	−32.8992	+	56.9831i	−1.20372	+	2.08490i
$748$	0.122630	−	0.212402i	0.00448380	−	0.00776617i
$749$		0			0
$750$	15.9833	−	27.6839i	0.583627	−	1.01087i
$751$	6.49099	+	11.2427i	0.236860	+	0.410253i	0.959812	−	0.280645i	$-0.0905485\pi$
$751$	6.49099	+	11.2427i	0.236860	+	0.410253i	−0.722952	+	0.690898i	$0.757215\pi$
$752$	−4.00059	−	6.92923i	−0.145887	−	0.252683i
$753$	10.2113			0.372119
$754$	−4.21177	+	6.30520i	−0.153383	+	0.229622i
$755$	−21.8192			−0.794082
$756$		0			0
$757$	13.6228	+	23.5954i	0.495129	+	0.857589i	0.999984	−	0.00561523i	$-0.00178739\pi$
$757$	13.6228	+	23.5954i	0.495129	+	0.857589i	−0.504855	+	0.863204i	$0.668454\pi$
$758$	0.804301	−	1.39309i	0.0292135	−	0.0505993i
$759$	−0.372721			−0.0135289
$760$	6.39770	−	11.0811i	0.232069	−	0.401955i
$761$	−2.89436	+	5.01318i	−0.104921	+	0.181728i	−0.913706	−	0.406376i	$-0.866792\pi$
$761$	−2.89436	+	5.01318i	−0.104921	+	0.181728i	0.808785	+	0.588104i	$0.200126\pi$
$762$	1.69793			0.0615096
$763$		0			0
$764$	−11.4140	−	19.7696i	−0.412943	−	0.715238i
$765$	−10.0565	−	17.4184i	−0.363594	−	0.629763i
$766$	15.9499			0.576292
$767$	13.6965	−	20.5043i	0.494552	−	0.740366i
$768$	2.62644			0.0947734
$769$	13.8054	+	23.9117i	0.497836	+	0.862277i	0.999997	−	0.00249727i	$-0.000794907\pi$
$769$	13.8054	+	23.9117i	0.497836	+	0.862277i	−0.502161	+	0.864774i	$0.667462\pi$
$770$		0			0
$771$	−20.6587	+	35.7820i	−0.744006	+	1.28866i
$772$	−2.92304			−0.105203
$773$	−15.7900	+	27.3490i	−0.567926	+	0.983676i	0.428845	+	0.903378i	$0.358921\pi$
$773$	−15.7900	+	27.3490i	−0.567926	+	0.983676i	−0.996771	+	0.0802984i	$0.974413\pi$
$774$	11.6578	−	20.1918i	0.419029	−	0.725780i
$775$	−12.1025			−0.434736
$776$	1.42051	−	2.46040i	0.0509934	−	0.0883231i
$777$		0			0
$778$	−2.12674	−	3.68363i	−0.0762474	−	0.132064i
$779$	−72.6556			−2.60316
$780$	17.3452	+	1.13451i	0.621059	+	0.0406220i
$781$	−0.661632			−0.0236751
$782$	−2.28589	−	3.95928i	−0.0817432	−	0.141583i
$783$	−2.48049	−	4.29633i	−0.0886454	−	0.153538i
$784$		0			0
$785$	−2.93760			−0.104847
$786$	3.67220	−	6.36044i	0.130983	−	0.226870i
$787$	−10.8572	+	18.8052i	−0.387017	+	0.670333i	−0.992047	−	0.125870i	$-0.959828\pi$
$787$	−10.8572	+	18.8052i	−0.387017	+	0.670333i	0.605030	+	0.796203i	$0.293161\pi$
$788$	−4.74831			−0.169151
$789$	16.7565	−	29.0231i	0.596547	−	1.03325i
$790$	8.46004	+	14.6532i	0.300995	+	0.521338i
$791$		0			0
$792$	−0.340126			−0.0120859
$793$	−17.7555	+	26.5808i	−0.630518	+	0.943913i
$794$	−1.66111			−0.0589505
$795$	−2.15696	−	3.73596i	−0.0764995	−	0.132501i
$796$	4.92265	+	8.52628i	0.174479	+	0.302206i
$797$	−22.9458	+	39.7433i	−0.812783	+	1.40778i	0.0981258	+	0.995174i	$0.468715\pi$
$797$	−22.9458	+	39.7433i	−0.812783	+	1.40778i	−0.910909	+	0.412608i	$0.864618\pi$
$798$		0			0
$799$	−11.2453	+	19.4775i	−0.397831	+	0.689064i
$800$	0.815359	−	1.41224i	0.0288273	−	0.0499304i
$801$	−38.6286			−1.36487
$802$	1.30242	−	2.25586i	0.0459901	−	0.0796572i
$803$	−0.475938	−	0.824350i	−0.0167955	−	0.0290907i
$804$	−8.67997	−	15.0341i	−0.306119	−	0.530213i
$805$		0			0
$806$	−11.8384	−	23.9978i	−0.416991	−	0.845285i
$807$	34.2115			1.20430
$808$	1.88300	+	3.26145i	0.0662438	+	0.114738i
$809$	−17.8761	−	30.9623i	−0.628489	−	1.08858i	−0.987855	−	0.155379i	$-0.950340\pi$
$809$	−17.8761	−	30.9623i	−0.628489	−	1.08858i	0.359366	−	0.933197i	$-0.382993\pi$
$810$	5.04667	−	8.74109i	0.177322	−	0.307131i
$811$	38.5968			1.35532			0.677658	−	0.735377i	$-0.262995\pi$
$811$	38.5968			1.35532			0.677658	+	0.735377i	$0.262995\pi$
$812$		0			0
$813$	12.3155	−	21.3310i	0.431923	−	0.748112i
$814$	−0.769758			−0.0269800
$815$	4.23039	−	7.32725i	0.148184	−	0.256662i
$816$	−3.69135	−	6.39360i	−0.129223	−	0.223821i
$817$	−20.8468	−	36.1077i	−0.729337	−	1.26325i
$818$	−6.35955			−0.222357
$819$		0			0
$820$	19.1316			0.668106
$821$	−11.3932	−	19.7336i	−0.397626	−	0.688708i	0.595807	−	0.803128i	$-0.296832\pi$
$821$	−11.3932	−	19.7336i	−0.397626	−	0.688708i	−0.993433	+	0.114420i	$0.963499\pi$
$822$	13.6799	+	23.6943i	0.477141	+	0.826433i
$823$	17.7822	−	30.7996i	0.619848	−	1.07361i	−0.369666	−	0.929165i	$-0.620528\pi$
$823$	17.7822	−	30.7996i	0.619848	−	1.07361i	0.989513	−	0.144443i	$-0.0461389\pi$
$824$	−9.45771			−0.329475
$825$	−0.186851	+	0.323635i	−0.00650531	+	0.0112675i
$826$		0			0
$827$	−29.9739			−1.04229			−0.521147	−	0.853467i	$-0.674496\pi$
$827$	−29.9739			−1.04229			−0.521147	+	0.853467i	$0.674496\pi$
$828$	−3.17006	+	5.49071i	−0.110167	+	0.190815i
$829$	12.1380	+	21.0237i	0.421571	+	0.730182i	0.996093	−	0.0883068i	$-0.0281456\pi$
$829$	12.1380	+	21.0237i	0.421571	+	0.730182i	−0.574523	+	0.818489i	$0.694812\pi$
$830$	−15.4915	−	26.8321i	−0.537718	−	0.931354i
$831$	−46.1925			−1.60240
$832$	3.59786	+	0.235328i	0.124733	+	0.00815852i
$833$		0			0
$834$	16.0800	+	27.8513i	0.556803	+	0.964412i
$835$	−17.7519	−	30.7473i	−0.614331	−	1.06405i
$836$	−0.304113	+	0.526739i	−0.0105180	+	0.0182176i
$837$	17.5074			0.605146
$838$	4.71852	−	8.17271i	0.162998	−	0.282322i
$839$	−11.0416	+	19.1246i	−0.381197	+	0.660253i	−0.991234	−	0.132120i	$-0.957821\pi$
$839$	−11.0416	+	19.1246i	−0.381197	+	0.660253i	0.610037	+	0.792373i	$0.291155\pi$
$840$		0			0
$841$	12.2887	−	21.2846i	0.423747	−	0.733952i
$842$	15.1504	+	26.2413i	0.522118	+	0.904336i
$843$	−17.8562	−	30.9278i	−0.615000	−	1.06521i
$844$	−4.36711			−0.150322
$845$	23.6590	+	3.10825i	0.813894	+	0.106927i
$846$	31.1900			1.07233
$847$		0			0
$848$	−0.447411	−	0.774938i	−0.0153641	−	0.0266115i
$849$	−8.46816	+	14.6673i	−0.290627	+	0.503380i
$850$	−4.58381			−0.157224
$851$	−7.17435	+	12.4263i	−0.245933	+	0.425969i
$852$	−9.95805	+	17.2478i	−0.341157	+	0.590901i
$853$	42.8773			1.46809			0.734045	−	0.679100i	$-0.237630\pi$
$853$	42.8773			1.46809			0.734045	+	0.679100i	$0.237630\pi$
$854$		0			0
$855$	24.9393	+	43.1962i	0.852907	+	1.47728i
$856$	−3.67949	−	6.37307i	−0.125762	−	0.217827i
$857$	−15.8241			−0.540540			−0.270270	−	0.962785i	$-0.587113\pi$
$857$	−15.8241			−0.540540			−0.270270	+	0.962785i	$0.587113\pi$
$858$	−0.824500	−	0.0539286i	−0.0281480	−	0.00184109i
$859$	−31.4242			−1.07218			−0.536090	−	0.844161i	$-0.680099\pi$
$859$	−31.4242			−1.07218			−0.536090	+	0.844161i	$0.680099\pi$
$860$	5.48937	+	9.50787i	0.187186	+	0.324216i
$861$		0			0
$862$	2.39419	−	4.14687i	0.0815466	−	0.141243i
$863$	50.3444			1.71374			0.856872	−	0.515530i	$-0.172405\pi$
$863$	50.3444			1.71374			0.856872	+	0.515530i	$0.172405\pi$
$864$	−1.17949	+	2.04294i	−0.0401272	+	0.0695023i
$865$	13.0356	−	22.5782i	0.443222	−	0.767684i
$866$	−40.3751			−1.37200
$867$	11.9486	−	20.6957i	0.405797	−	0.702861i
$868$		0			0
$869$	−0.402145	−	0.696536i	−0.0136418	−	0.0236284i
$870$	10.1386			0.343730
$871$	−10.5433	−	21.3725i	−0.357247	−	0.724179i
$872$	3.92498			0.132917
$873$	5.53739	+	9.59105i	0.187412	+	0.324608i
$874$	5.66882	+	9.81868i	0.191751	+	0.332122i
$875$		0			0
$876$	−28.6529			−0.968091
$877$	−1.18759	+	2.05697i	−0.0401021	+	0.0694588i	−0.885380	−	0.464868i	$-0.846102\pi$
$877$	−1.18759	+	2.05697i	−0.0401021	+	0.0694588i	0.845278	+	0.534327i	$0.179435\pi$
$878$	−0.509403	+	0.882313i	−0.0171915	+	0.0297766i
$879$	5.10908			0.172325
$880$	0.0800789	−	0.138701i	0.00269946	−	0.00467560i
$881$	−9.38846	−	16.2613i	−0.316305	−	0.547857i	0.663409	−	0.748257i	$-0.269109\pi$
$881$	−9.38846	−	16.2613i	−0.316305	−	0.547857i	−0.979714	+	0.200400i	$0.935776\pi$
$882$		0			0
$883$	16.9385			0.570026			0.285013	−	0.958524i	$-0.408002\pi$
$883$	16.9385			0.570026			0.285013	+	0.958524i	$0.408002\pi$
$884$	−4.48378	−	9.08911i	−0.150806	−	0.305700i
$885$	−32.9703			−1.10828
$886$	13.4582	+	23.3103i	0.452138	+	0.783125i
$887$	9.68429	+	16.7737i	0.325167	+	0.563205i	0.981546	−	0.191226i	$-0.0612463\pi$
$887$	9.68429	+	16.7737i	0.325167	+	0.563205i	−0.656379	+	0.754431i	$0.727913\pi$
$888$	−11.5854	+	20.0665i	−0.388781	+	0.673389i
$889$		0			0
$890$	9.09467	−	15.7524i	0.304854	−	0.528022i
$891$	−0.239892	+	0.415505i	−0.00803669	+	0.0139199i
$892$	28.1085			0.941142
$893$	27.8875	−	48.3026i	0.933219	−	1.61638i
$894$	−28.8939	−	50.0458i	−0.966357	−	1.67378i
$895$	9.66930	+	16.7477i	0.323209	+	0.559815i
$896$		0			0
$897$	−8.55513	+	12.8074i	−0.285648	+	0.427627i
$898$	8.83552			0.294845
$899$	−7.80385	−	13.5167i	−0.260273	−	0.450806i
$900$	3.17841	+	5.50517i	0.105947	+	0.183506i
$901$	−1.25763	+	2.17829i	−0.0418979	+	0.0725692i
$902$	−0.909416			−0.0302802
$903$		0			0
$904$	−7.47705	+	12.9506i	−0.248683	+	0.430732i
$905$	34.1061			1.13373
$906$	15.6101	−	27.0376i	0.518612	−	0.898263i
$907$	−13.4045	−	23.2173i	−0.445090	−	0.770919i	0.552968	−	0.833202i	$-0.313495\pi$
$907$	−13.4045	−	23.2173i	−0.445090	−	0.770919i	−0.998059	+	0.0622834i	$0.980162\pi$
$908$	13.3454	+	23.1150i	0.442884	+	0.767097i
$909$	−14.6805			−0.486922
$910$		0			0
$911$	0.383210			0.0126963			0.00634816	−	0.999980i	$-0.497979\pi$
$911$	0.383210			0.0126963			0.00634816	+	0.999980i	$0.497979\pi$
$912$	9.15424	+	15.8556i	0.303127	+	0.525032i
$913$	0.736383	+	1.27545i	0.0243707	+	0.0422113i
$914$	17.9361	−	31.0662i	0.593272	−	1.02758i
$915$	42.7412			1.41298
$916$	−4.70473	+	8.14883i	−0.155449	+	0.269245i
$917$		0			0
$918$	6.63091			0.218853
$919$	18.7896	−	32.5445i	0.619812	−	1.07355i	−0.369708	−	0.929148i	$-0.620542\pi$
$919$	18.7896	−	32.5445i	0.619812	−	1.07355i	0.989520	−	0.144398i	$-0.0461244\pi$
$920$	−1.49271	−	2.58545i	−0.0492132	−	0.0852398i
$921$	−7.98037	−	13.8224i	−0.262962	−	0.455464i
$922$	41.2338			1.35796
$923$	−15.1866	+	22.7350i	−0.499872	+	0.748331i
$924$		0			0
$925$	7.19323	+	12.4590i	0.236512	+	0.409651i
$926$	−10.5157	−	18.2136i	−0.345566	−	0.598537i
$927$	18.4339	−	31.9284i	0.605448	−	1.04867i
$928$	2.10301			0.0690347
$929$	−5.68966	+	9.85479i	−0.186672	+	0.323325i	−0.944139	−	0.329549i	$-0.893103\pi$
$929$	−5.68966	+	9.85479i	−0.186672	+	0.323325i	0.757467	+	0.652874i	$0.226437\pi$
$930$	−17.8897	+	30.9859i	−0.586626	+	1.01607i
$931$		0			0
$932$	−11.5107	+	19.9372i	−0.377047	+	0.653064i
$933$	16.0760	+	27.8445i	0.526306	+	0.911589i
$934$	10.2160	+	17.6946i	0.334277	+	0.578986i
$935$	−0.450190			−0.0147228
$936$	−7.80699	+	11.6874i	−0.255179	+	0.382015i
$937$	−3.70274			−0.120963			−0.0604817	−	0.998169i	$-0.519264\pi$
$937$	−3.70274			−0.120963			−0.0604817	+	0.998169i	$0.519264\pi$
$938$		0			0
$939$	−12.3290	−	21.3545i	−0.402342	−	0.696876i
$940$	−7.34332	+	12.7190i	−0.239513	+	0.414848i
$941$	53.2334			1.73536			0.867680	−	0.497123i	$-0.165610\pi$
$941$	53.2334			1.73536			0.867680	+	0.497123i	$0.165610\pi$
$942$	2.10165	−	3.64017i	0.0684755	−	0.118603i
$943$	−8.47599	+	14.6808i	−0.276016	+	0.478074i
$944$	−6.83891			−0.222588
$945$		0			0
$946$	−0.260936	−	0.451954i	−0.00848375	−	0.0146943i
$947$	11.3032	+	19.5778i	0.367306	+	0.636193i	0.989143	−	0.146953i	$-0.0469468\pi$
$947$	11.3032	+	19.5778i	0.367306	+	0.636193i	−0.621837	+	0.783147i	$0.713613\pi$
$948$	−24.2103			−0.786315
$949$	−39.2506	−	2.56729i	−1.27413	−	0.0833377i
$950$	11.3675			0.368810
$951$	3.67251	+	6.36097i	0.119089	+	0.206268i
$952$		0			0
$953$	7.94844	−	13.7671i	0.257475	−	0.445960i	−0.708090	−	0.706123i	$-0.750443\pi$
$953$	7.94844	−	13.7671i	0.257475	−	0.445960i	0.965565	+	0.260162i	$0.0837761\pi$
$954$	3.48817			0.112934
$955$	−20.9510	+	36.2883i	−0.677960	+	1.17426i
$956$	−5.51607	+	9.55412i	−0.178403	+	0.309002i
$957$	−0.481934			−0.0155787
$958$	19.6000	−	33.9482i	0.633248	−	1.09682i
$959$		0			0
$960$	−2.41049	−	4.17509i	−0.0777983	−	0.134751i
$961$	24.0801			0.776777
$962$	−17.6684	+	26.4504i	−0.569653	+	0.852795i
$963$	28.6866			0.924412
$964$	−3.69969	−	6.40806i	−0.119159	−	0.206390i
$965$	2.68271	+	4.64659i	0.0863595	+	0.149579i
$966$		0			0
$967$	−26.3252			−0.846560			−0.423280	−	0.905999i	$-0.639121\pi$
$967$	−26.3252			−0.846560			−0.423280	+	0.905999i	$0.639121\pi$
$968$	5.49619	−	9.51969i	0.176654	−	0.305974i
$969$	25.7318	−	44.5688i	0.826625	−	1.43176i
$970$	−5.21487			−0.167439
$971$	9.36842	−	16.2266i	0.300647	−	0.520735i	−0.675636	−	0.737236i	$-0.736131\pi$
$971$	9.36842	−	16.2266i	0.300647	−	0.520735i	0.976283	+	0.216500i	$0.0694641\pi$
$972$	10.7596	+	18.6361i	0.345114	+	0.597754i
$973$		0			0
$974$	−11.6082			−0.371951
$975$	6.83192	+	13.8490i	0.218796	+	0.443524i
$976$	8.86567			0.283783
$977$	16.3471	+	28.3139i	0.522989	+	0.905843i	0.999642	+	0.0267516i	$0.00851630\pi$
$977$	16.3471	+	28.3139i	0.522989	+	0.905843i	−0.476654	+	0.879091i	$0.658150\pi$
$978$	6.05311	+	10.4843i	0.193557	+	0.335251i
$979$	−0.432312	+	0.748786i	−0.0138168	+	0.0239313i
$980$		0			0
$981$	−7.65012	+	13.2504i	−0.244250	+	0.423053i
$982$	11.9193	−	20.6448i	0.380360	−	0.658803i
$983$	−16.1384			−0.514733			−0.257367	−	0.966314i	$-0.582855\pi$
$983$	−16.1384			−0.514733			−0.257367	+	0.966314i	$0.582855\pi$
$984$	−13.6874	+	23.7072i	−0.436338	+	0.755759i
$985$	4.35790	+	7.54811i	0.138854	+	0.240503i
$986$	−2.95569	−	5.11941i	−0.0941285	−	0.163035i
$987$		0			0
$988$	11.1194	+	22.5403i	0.353756	+	0.717101i
$989$	−9.72795			−0.309331
$990$	0.312161	+	0.540679i	0.00992113	+	0.0171839i
$991$	14.5529	+	25.2064i	0.462289	+	0.800709i	0.999075	−	0.0430102i	$-0.0136948\pi$
$991$	14.5529	+	25.2064i	0.462289	+	0.800709i	−0.536785	+	0.843719i	$0.680361\pi$
$992$	−3.71080	+	6.42729i	−0.117818	+	0.204067i
$993$	−67.5426			−2.14340
$994$		0			0
$995$	9.03583	−	15.6505i	0.286455	−	0.496154i
$996$	44.3324			1.40473
$997$	−13.6617	+	23.6627i	−0.432670	+	0.749406i	−0.997102	−	0.0760733i	$-0.975762\pi$
$997$	−13.6617	+	23.6627i	−0.432670	+	0.749406i	0.564432	+	0.825479i	$0.309095\pi$
$998$	−4.09131	−	7.08635i	−0.129508	−	0.224314i
$999$	−10.4057	−	18.0232i	−0.329221	−	0.570228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.g.p.393.1		10
7.2	even	3		182.2.h.d.81.5	yes	10
7.3	odd	6		1274.2.e.s.471.5		10
7.4	even	3		182.2.e.d.107.1	✓	10
7.5	odd	6		1274.2.h.s.263.1		10
7.6	odd	2		1274.2.g.q.393.5		10
13.9	even	3	inner	1274.2.g.p.295.1		10
21.2	odd	6		1638.2.p.k.991.4		10
21.11	odd	6		1638.2.m.j.289.4		10
91.9	even	3		182.2.e.d.165.1	yes	10
91.48	odd	6		1274.2.g.q.295.5		10
91.61	odd	6		1274.2.e.s.165.5		10
91.74	even	3		182.2.h.d.9.5	yes	10
91.87	odd	6		1274.2.h.s.373.1		10
273.74	odd	6		1638.2.p.k.919.4		10
273.191	odd	6		1638.2.m.j.1621.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.e.d.107.1	✓	10	7.4	even	3
182.2.e.d.165.1	yes	10	91.9	even	3
182.2.h.d.9.5	yes	10	91.74	even	3
182.2.h.d.81.5	yes	10	7.2	even	3
1274.2.e.s.165.5		10	91.61	odd	6
1274.2.e.s.471.5		10	7.3	odd	6
1274.2.g.p.295.1		10	13.9	even	3	inner
1274.2.g.p.393.1		10	1.1	even	1	trivial
1274.2.g.q.295.5		10	91.48	odd	6
1274.2.g.q.393.5		10	7.6	odd	2
1274.2.h.s.263.1		10	7.5	odd	6
1274.2.h.s.373.1		10	91.87	odd	6
1638.2.m.j.289.4		10	21.11	odd	6
1638.2.m.j.1621.4		10	273.191	odd	6
1638.2.p.k.919.4		10	273.74	odd	6
1638.2.p.k.991.4		10	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.31322 - 2.27456i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.83556 q^{5} +(-1.31322 + 2.27456i) q^{6} +1.00000 q^{8} +(-1.94908 + 3.37591i) q^{9} +(-0.917780 - 1.58964i) q^{10} +(0.0436264 + 0.0755631i) q^{11} +2.62644 q^{12} +(3.59786 + 0.235328i) q^{13} +(-2.41049 - 4.17509i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.40546 + 2.43433i) q^{17} +3.89817 q^{18} +(3.48542 - 6.03693i) q^{19} +(-0.917780 + 1.58964i) q^{20} +(0.0436264 - 0.0755631i) q^{22} +(-0.813218 - 1.40854i) q^{23} +(-1.31322 - 2.27456i) q^{24} -1.63072 q^{25} +(-1.59513 - 3.23350i) q^{26} +2.35899 q^{27} +(-1.05151 - 1.82126i) q^{29} +(-2.41049 + 4.17509i) q^{30} +7.42160 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.114582 - 0.198462i) q^{33} +2.81092 q^{34} +(-1.94908 - 3.37591i) q^{36} +(-4.41108 - 7.64022i) q^{37} -6.97084 q^{38} +(-4.18951 - 8.49260i) q^{39} +1.83556 q^{40} +(-5.21139 - 9.02639i) q^{41} +(2.99057 - 5.17982i) q^{43} -0.0872528 q^{44} +(-3.57766 + 6.19669i) q^{45} +(-0.813218 + 1.40854i) q^{46} +8.00118 q^{47} +(-1.31322 + 2.27456i) q^{48} +(0.815359 + 1.41224i) q^{50} +7.38270 q^{51} +(-2.00273 + 2.99818i) q^{52} +0.894821 q^{53} +(-1.17949 - 2.04294i) q^{54} +(0.0800789 + 0.138701i) q^{55} -18.3085 q^{57} +(-1.05151 + 1.82126i) q^{58} +(3.41945 - 5.92267i) q^{59} +4.82098 q^{60} +(-4.43283 + 7.67789i) q^{61} +(-3.71080 - 6.42729i) q^{62} +1.00000 q^{64} +(6.60409 + 0.431958i) q^{65} -0.229164 q^{66} +(-3.30485 - 5.72416i) q^{67} +(-1.40546 - 2.43433i) q^{68} +(-2.13587 + 3.69943i) q^{69} +(-3.79147 + 6.56701i) q^{71} +(-1.94908 + 3.37591i) q^{72} -10.9094 q^{73} +(-4.41108 + 7.64022i) q^{74} +(2.14149 + 3.70917i) q^{75} +(3.48542 + 6.03693i) q^{76} +(-5.26005 + 7.87452i) q^{78} -9.21793 q^{79} +(-0.917780 - 1.58964i) q^{80} +(2.74939 + 4.76209i) q^{81} +(-5.21139 + 9.02639i) q^{82} +16.8793 q^{83} +(-2.57980 + 4.46835i) q^{85} -5.98114 q^{86} +(-2.76171 + 4.78343i) q^{87} +(0.0436264 + 0.0755631i) q^{88} +(4.95471 + 8.58181i) q^{89} +7.15533 q^{90} +1.62644 q^{92} +(-9.74617 - 16.8809i) q^{93} +(-4.00059 - 6.92923i) q^{94} +(6.39770 - 11.0811i) q^{95} +2.62644 q^{96} +(1.42051 - 2.46040i) q^{97} -0.340126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 4 q^{5} - q^{6} + 10 q^{8} - 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 6 q^{13} + 3 q^{15} - 5 q^{16} - 3 q^{17} + 8 q^{18} - 5 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23}+ \cdots + 54 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 4 * q^5 - q^6 + 10 * q^8 - 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 6 * q^13 + 3 * q^15 - 5 * q^16 - 3 * q^17 + 8 * q^18 - 5 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 - q^24 + 6 * q^25 + 8 * q^27 + q^29 + 3 * q^30 + 42 * q^31 - 5 * q^32 + 6 * q^34 - 4 * q^36 + 10 * q^37 + 10 * q^38 - 28 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^43 + 8 * q^44 + 3 * q^45 + 4 * q^46 + 26 * q^47 - q^48 - 3 * q^50 + 12 * q^51 + 6 * q^52 + 30 * q^53 - 4 * q^54 + 7 * q^55 - 26 * q^57 + q^58 + q^59 - 6 * q^60 - 15 * q^61 - 21 * q^62 + 10 * q^64 + 44 * q^65 - 3 * q^68 - 18 * q^69 - q^71 - 4 * q^72 + 8 * q^73 + 10 * q^74 - 25 * q^75 - 5 * q^76 + 11 * q^78 + 2 * q^79 - 2 * q^80 + 23 * q^81 - 9 * q^82 + 96 * q^83 + 12 * q^85 - 18 * q^86 - 27 * q^87 - 4 * q^88 - 9 * q^89 - 6 * q^90 - 8 * q^92 - 2 * q^93 - 13 * q^94 + 6 * q^95 + 2 * q^96 - 19 * q^97 + 54 * q^99

Introduction

L-functions

Modular forms

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