LMFDB - Embedded newform 686.2.c.a.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(361,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("686.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	686.667
Dual form			686.2.c.a.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.777479 - 1.34663i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.722521 + 1.25144i) q^{5} +1.55496 q^{6} +1.00000 q^{8} +(0.291053 - 0.504118i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.777479 - 1.34663i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.722521 + 1.25144i) q^{5} +1.55496 q^{6} +1.00000 q^{8} +(0.291053 - 0.504118i) q^{9} +(-0.722521 - 1.25144i) q^{10} +(0.153989 + 0.266717i) q^{11} +(-0.777479 + 1.34663i) q^{12} -0.603875 q^{13} +2.24698 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.77144 - 4.80027i) q^{17} +(0.291053 + 0.504118i) q^{18} +(-1.94504 + 3.36891i) q^{19} +1.44504 q^{20} -0.307979 q^{22} +(1.45593 - 2.52174i) q^{23} +(-0.777479 - 1.34663i) q^{24} +(1.45593 + 2.52174i) q^{25} +(0.301938 - 0.522971i) q^{26} -5.57002 q^{27} -0.594187 q^{29} +(-1.12349 + 1.94594i) q^{30} +(-4.03534 - 6.98942i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.239447 - 0.414734i) q^{33} +5.54288 q^{34} -0.582105 q^{36} +(3.52446 - 6.10454i) q^{37} +(-1.94504 - 3.36891i) q^{38} +(0.469501 + 0.813199i) q^{39} +(-0.722521 + 1.25144i) q^{40} -8.87800 q^{41} -10.9487 q^{43} +(0.153989 - 0.266717i) q^{44} +(0.420583 + 0.728471i) q^{45} +(1.45593 + 2.52174i) q^{46} +(3.68329 - 6.37965i) q^{47} +1.55496 q^{48} -2.91185 q^{50} +(-4.30947 + 7.46422i) q^{51} +(0.301938 + 0.522971i) q^{52} +(-5.47434 - 9.48184i) q^{53} +(2.78501 - 4.82378i) q^{54} -0.445042 q^{55} +6.04892 q^{57} +(0.297093 - 0.514581i) q^{58} +(-5.82036 - 10.0812i) q^{59} +(-1.12349 - 1.94594i) q^{60} +(-0.763906 + 1.32312i) q^{61} +8.07069 q^{62} +1.00000 q^{64} +(0.436313 - 0.755716i) q^{65} +(0.239447 + 0.414734i) q^{66} +(-0.826396 - 1.43136i) q^{67} +(-2.77144 + 4.80027i) q^{68} -4.52781 q^{69} -9.44265 q^{71} +(0.291053 - 0.504118i) q^{72} +(6.58426 + 11.4043i) q^{73} +(3.52446 + 6.10454i) q^{74} +(2.26391 - 3.92120i) q^{75} +3.89008 q^{76} -0.939001 q^{78} +(-5.01842 + 8.69215i) q^{79} +(-0.722521 - 1.25144i) q^{80} +(3.45742 + 5.98843i) q^{81} +(4.43900 - 7.68858i) q^{82} -2.44504 q^{83} +8.00969 q^{85} +(5.47434 - 9.48184i) q^{86} +(0.461968 + 0.800152i) q^{87} +(0.153989 + 0.266717i) q^{88} +(4.67845 - 8.10331i) q^{89} -0.841166 q^{90} -2.91185 q^{92} +(-6.27479 + 10.8683i) q^{93} +(3.68329 + 6.37965i) q^{94} +(-2.81067 - 4.86822i) q^{95} +(-0.777479 + 1.34663i) q^{96} +13.1347 q^{97} +0.179276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 5 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 5 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 + 6 * q^8 - 4 * q^9	$ 6 q - 3 q^{2} - 5 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} + 6 q^{8} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 5 q^{12} + 14 q^{13} + 4 q^{15} - 3 q^{16} + 2 q^{17} - 4 q^{18} - 11 q^{19} + 8 q^{20} - 12 q^{22} + 5 q^{23} - 5 q^{24} + 5 q^{25} - 7 q^{26} + 16 q^{27} - 30 q^{29} - 2 q^{30} - 12 q^{31} - 3 q^{32} + 17 q^{33} - 4 q^{34} + 8 q^{36} + 12 q^{37} - 11 q^{38} - 7 q^{39} - 4 q^{40} - 14 q^{41} - 2 q^{43} + 6 q^{44} + 11 q^{45} + 5 q^{46} - 4 q^{47} + 10 q^{48} - 10 q^{50} + 8 q^{51} - 7 q^{52} - q^{53} - 8 q^{54} - 2 q^{55} + 18 q^{57} + 15 q^{58} + 2 q^{59} - 2 q^{60} - 11 q^{61} + 24 q^{62} + 6 q^{64} - 14 q^{65} + 17 q^{66} + 13 q^{67} + 2 q^{68} - 40 q^{69} + 26 q^{71} - 4 q^{72} + 9 q^{73} + 12 q^{74} + 20 q^{75} + 22 q^{76} + 14 q^{78} - 2 q^{79} - 4 q^{80} - 27 q^{81} + 7 q^{82} - 14 q^{83} + 4 q^{85} + q^{86} + 18 q^{87} + 6 q^{88} + 24 q^{89} - 22 q^{90} - 10 q^{92} - 41 q^{93} - 4 q^{94} - 24 q^{95} - 5 q^{96} - 14 q^{97} - 72 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 5 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 + 6 * q^8 - 4 * q^9 - 4 * q^10 + 6 * q^11 - 5 * q^12 + 14 * q^13 + 4 * q^15 - 3 * q^16 + 2 * q^17 - 4 * q^18 - 11 * q^19 + 8 * q^20 - 12 * q^22 + 5 * q^23 - 5 * q^24 + 5 * q^25 - 7 * q^26 + 16 * q^27 - 30 * q^29 - 2 * q^30 - 12 * q^31 - 3 * q^32 + 17 * q^33 - 4 * q^34 + 8 * q^36 + 12 * q^37 - 11 * q^38 - 7 * q^39 - 4 * q^40 - 14 * q^41 - 2 * q^43 + 6 * q^44 + 11 * q^45 + 5 * q^46 - 4 * q^47 + 10 * q^48 - 10 * q^50 + 8 * q^51 - 7 * q^52 - q^53 - 8 * q^54 - 2 * q^55 + 18 * q^57 + 15 * q^58 + 2 * q^59 - 2 * q^60 - 11 * q^61 + 24 * q^62 + 6 * q^64 - 14 * q^65 + 17 * q^66 + 13 * q^67 + 2 * q^68 - 40 * q^69 + 26 * q^71 - 4 * q^72 + 9 * q^73 + 12 * q^74 + 20 * q^75 + 22 * q^76 + 14 * q^78 - 2 * q^79 - 4 * q^80 - 27 * q^81 + 7 * q^82 - 14 * q^83 + 4 * q^85 + q^86 + 18 * q^87 + 6 * q^88 + 24 * q^89 - 22 * q^90 - 10 * q^92 - 41 * q^93 - 4 * q^94 - 24 * q^95 - 5 * q^96 - 14 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

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

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
$3$	−0.777479	−	1.34663i	−0.448878	−	0.777479i	0.549436	−	0.835536i	$-0.314843\pi$
$3$	−0.777479	−	1.34663i	−0.448878	−	0.777479i	−0.998313	+	0.0580571i	$0.981509\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.722521	+	1.25144i	−0.323121	+	0.559662i	−0.981130	−	0.193348i	$-0.938065\pi$
$5$	−0.722521	+	1.25144i	−0.323121	+	0.559662i	0.658009	+	0.753010i	$0.271399\pi$
$6$	1.55496			0.634809
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	0.291053	−	0.504118i	0.0970175	−	0.168039i
$10$	−0.722521	−	1.25144i	−0.228481	−	0.395741i
$11$	0.153989	+	0.266717i	0.0464295	+	0.0804183i	0.888306	−	0.459252i	$-0.151882\pi$
$11$	0.153989	+	0.266717i	0.0464295	+	0.0804183i	−0.841877	+	0.539670i	$0.818549\pi$
$12$	−0.777479	+	1.34663i	−0.224439	+	0.388740i
$13$	−0.603875			−0.167485			−0.0837425	−	0.996487i	$-0.526687\pi$
$13$	−0.603875			−0.167485			−0.0837425	+	0.996487i	$0.526687\pi$
$14$		0			0
$15$	2.24698			0.580168
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.77144	−	4.80027i	−0.672173	−	1.16424i	−0.977287	−	0.211921i	$-0.932028\pi$
$17$	−2.77144	−	4.80027i	−0.672173	−	1.16424i	0.305114	−	0.952316i	$-0.401305\pi$
$18$	0.291053	+	0.504118i	0.0686018	+	0.118822i
$19$	−1.94504	+	3.36891i	−0.446223	+	0.772881i	−0.998137	−	0.0610202i	$-0.980565\pi$
$19$	−1.94504	+	3.36891i	−0.446223	+	0.772881i	0.551913	+	0.833901i	$0.313898\pi$
$20$	1.44504			0.323121
$21$		0			0
$22$	−0.307979			−0.0656612
$23$	1.45593	−	2.52174i	0.303582	−	0.525819i	−0.673363	−	0.739312i	$-0.735151\pi$
$23$	1.45593	−	2.52174i	0.303582	−	0.525819i	0.976945	+	0.213493i	$0.0684841\pi$
$24$	−0.777479	−	1.34663i	−0.158702	−	0.274880i
$25$	1.45593	+	2.52174i	0.291185	+	0.504348i
$26$	0.301938	−	0.522971i	0.0592149	−	0.102563i
$27$	−5.57002			−1.07195
$28$		0			0
$29$	−0.594187			−0.110338			−0.0551689	−	0.998477i	$-0.517570\pi$
$29$	−0.594187			−0.110338			−0.0551689	+	0.998477i	$0.517570\pi$
$30$	−1.12349	+	1.94594i	−0.205120	+	0.355279i
$31$	−4.03534	−	6.98942i	−0.724769	−	1.25534i	−0.959069	−	0.283173i	$-0.908613\pi$
$31$	−4.03534	−	6.98942i	−0.724769	−	1.25534i	0.234300	−	0.972164i	$-0.424720\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.239447	−	0.414734i	0.0416823	−	0.0721959i
$34$	5.54288			0.950595
$35$		0			0
$36$	−0.582105			−0.0970175
$37$	3.52446	−	6.10454i	0.579417	−	1.00358i	−0.416129	−	0.909306i	$-0.636613\pi$
$37$	3.52446	−	6.10454i	0.579417	−	1.00358i	0.995546	−	0.0942747i	$-0.0300532\pi$
$38$	−1.94504	−	3.36891i	−0.315527	−	0.546510i
$39$	0.469501	+	0.813199i	0.0751803	+	0.130216i
$40$	−0.722521	+	1.25144i	−0.114241	+	0.197871i
$41$	−8.87800			−1.38651			−0.693255	−	0.720692i	$-0.743824\pi$
$41$	−8.87800			−1.38651			−0.693255	+	0.720692i	$0.743824\pi$
$42$		0			0
$43$	−10.9487			−1.66966			−0.834830	−	0.550508i	$-0.814434\pi$
$43$	−10.9487			−1.66966			−0.834830	+	0.550508i	$0.814434\pi$
$44$	0.153989	−	0.266717i	0.0232148	−	0.0402091i
$45$	0.420583	+	0.728471i	0.0626968	+	0.108594i
$46$	1.45593	+	2.52174i	0.214665	+	0.371810i
$47$	3.68329	−	6.37965i	0.537263	−	0.930567i	−0.461787	−	0.886991i	$-0.652791\pi$
$47$	3.68329	−	6.37965i	0.537263	−	0.930567i	0.999050	−	0.0435765i	$-0.0138752\pi$
$48$	1.55496			0.224439
$49$		0			0
$50$	−2.91185			−0.411798
$51$	−4.30947	+	7.46422i	−0.603447	+	1.04520i
$52$	0.301938	+	0.522971i	0.0418712	+	0.0725231i
$53$	−5.47434	−	9.48184i	−0.751959	−	1.30243i	−0.946872	−	0.321611i	$-0.895776\pi$
$53$	−5.47434	−	9.48184i	−0.751959	−	1.30243i	0.194913	−	0.980821i	$-0.437558\pi$
$54$	2.78501	−	4.82378i	0.378992	−	0.656434i
$55$	−0.445042			−0.0600094
$56$		0			0
$57$	6.04892			0.801199
$58$	0.297093	−	0.514581i	0.0390103	−	0.0675678i
$59$	−5.82036	−	10.0812i	−0.757746	−	1.31245i	−0.943998	−	0.329952i	$-0.892967\pi$
$59$	−5.82036	−	10.0812i	−0.757746	−	1.31245i	0.186252	−	0.982502i	$-0.440366\pi$
$60$	−1.12349	−	1.94594i	−0.145042	−	0.251220i
$61$	−0.763906	+	1.32312i	−0.0978081	+	0.169409i	−0.910777	−	0.412898i	$-0.864516\pi$
$61$	−0.763906	+	1.32312i	−0.0978081	+	0.169409i	0.812969	+	0.582307i	$0.197850\pi$
$62$	8.07069			1.02498
$63$		0			0
$64$	1.00000			0.125000
$65$	0.436313	−	0.755716i	0.0541179	−	0.0937350i
$66$	0.239447	+	0.414734i	0.0294739	+	0.0510502i
$67$	−0.826396	−	1.43136i	−0.100960	−	0.174869i	0.811120	−	0.584879i	$-0.198858\pi$
$67$	−0.826396	−	1.43136i	−0.100960	−	0.174869i	−0.912081	+	0.410011i	$0.865525\pi$
$68$	−2.77144	+	4.80027i	−0.336086	+	0.582118i
$69$	−4.52781			−0.545084
$70$		0			0
$71$	−9.44265			−1.12064			−0.560318	−	0.828277i	$-0.689321\pi$
$71$	−9.44265			−1.12064			−0.560318	+	0.828277i	$0.689321\pi$
$72$	0.291053	−	0.504118i	0.0343009	−	0.0594109i
$73$	6.58426	+	11.4043i	0.770629	+	1.33477i	0.937218	+	0.348743i	$0.113391\pi$
$73$	6.58426	+	11.4043i	0.770629	+	1.33477i	−0.166589	+	0.986026i	$0.553275\pi$
$74$	3.52446	+	6.10454i	0.409710	+	0.709639i
$75$	2.26391	−	3.92120i	0.261413	−	0.452781i
$76$	3.89008			0.446223
$77$		0			0
$78$	−0.939001			−0.106321
$79$	−5.01842	+	8.69215i	−0.564616	+	0.977944i	0.432469	+	0.901649i	$0.357642\pi$
$79$	−5.01842	+	8.69215i	−0.564616	+	0.977944i	−0.997085	+	0.0762951i	$0.975691\pi$
$80$	−0.722521	−	1.25144i	−0.0807803	−	0.139916i
$81$	3.45742	+	5.98843i	0.384158	+	0.665381i
$82$	4.43900	−	7.68858i	0.490206	−	0.849061i
$83$	−2.44504			−0.268378			−0.134189	−	0.990956i	$-0.542843\pi$
$83$	−2.44504			−0.268378			−0.134189	+	0.990956i	$0.542843\pi$
$84$		0			0
$85$	8.00969			0.868773
$86$	5.47434	−	9.48184i	0.590314	−	1.02245i
$87$	0.461968	+	0.800152i	0.0495281	+	0.0857853i
$88$	0.153989	+	0.266717i	0.0164153	+	0.0284322i
$89$	4.67845	−	8.10331i	0.495914	−	0.858949i	−0.504074	−	0.863660i	$-0.668166\pi$
$89$	4.67845	−	8.10331i	0.495914	−	0.858949i	0.999989	+	0.00471113i	$0.00149961\pi$
$90$	−0.841166			−0.0886667
$91$		0			0
$92$	−2.91185			−0.303582
$93$	−6.27479	+	10.8683i	−0.650665	+	1.12699i
$94$	3.68329	+	6.37965i	0.379903	+	0.658011i
$95$	−2.81067	−	4.86822i	−0.288368	−	0.499469i
$96$	−0.777479	+	1.34663i	−0.0793511	+	0.137440i
$97$	13.1347			1.33362			0.666812	−	0.745226i	$-0.267658\pi$
$97$	13.1347			1.33362			0.666812	+	0.745226i	$0.267658\pi$
$98$		0			0
$99$	0.179276			0.0180179
$100$	1.45593	−	2.52174i	0.145593	−	0.252174i
$101$	4.37316	+	7.57453i	0.435145	+	0.753694i	0.997308	−	0.0733331i	$-0.0233636\pi$
$101$	4.37316	+	7.57453i	0.435145	+	0.753694i	−0.562162	+	0.827027i	$0.690030\pi$
$102$	−4.30947	−	7.46422i	−0.426701	−	0.739068i
$103$	−2.38135	+	4.12463i	−0.234642	+	0.406412i	−0.959169	−	0.282835i	$-0.908725\pi$
$103$	−2.38135	+	4.12463i	−0.234642	+	0.406412i	0.724527	+	0.689247i	$0.242058\pi$
$104$	−0.603875			−0.0592149
$105$		0			0
$106$	10.9487			1.06343
$107$	3.85958	−	6.68500i	0.373120	−	0.646263i	−0.616924	−	0.787023i	$-0.711621\pi$
$107$	3.85958	−	6.68500i	0.373120	−	0.646263i	0.990044	+	0.140760i	$0.0449546\pi$
$108$	2.78501	+	4.82378i	0.267988	+	0.464169i
$109$	4.29105	+	7.43232i	0.411008	+	0.711887i	0.995000	−	0.0998722i	$-0.0318434\pi$
$109$	4.29105	+	7.43232i	0.411008	+	0.711887i	−0.583992	+	0.811759i	$0.698510\pi$
$110$	0.222521	−	0.385418i	0.0212165	−	0.0367481i
$111$	−10.9608			−1.04035
$112$		0			0
$113$	18.5646			1.74642			0.873208	−	0.487349i	$-0.162036\pi$
$113$	18.5646			1.74642			0.873208	+	0.487349i	$0.162036\pi$
$114$	−3.02446	+	5.23852i	−0.283267	+	0.490632i
$115$	2.10388	+	3.64402i	0.196187	+	0.339807i
$116$	0.297093	+	0.514581i	0.0275844	+	0.0477776i
$117$	−0.175760	+	0.304424i	−0.0162490	+	0.0281440i
$118$	11.6407			1.07161
$119$		0			0
$120$	2.24698			0.205120
$121$	5.45257	−	9.44414i	0.495689	−	0.858558i
$122$	−0.763906	−	1.32312i	−0.0691608	−	0.119790i
$123$	6.90246	+	11.9554i	0.622374	+	1.07798i
$124$	−4.03534	+	6.98942i	−0.362385	+	0.627668i
$125$	−11.4330			−1.02260
$126$		0			0
$127$	1.59850			0.141844			0.0709219	−	0.997482i	$-0.477406\pi$
$127$	1.59850			0.141844			0.0709219	+	0.997482i	$0.477406\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	8.51238	+	14.7439i	0.749473	+	1.29813i
$130$	0.436313	+	0.755716i	0.0382672	+	0.0662807i
$131$	−0.890084	+	1.54167i	−0.0777670	+	0.134696i	−0.902286	−	0.431138i	$-0.858112\pi$
$131$	−0.890084	+	1.54167i	−0.0777670	+	0.134696i	0.824519	+	0.565834i	$0.191446\pi$
$132$	−0.478894			−0.0416823
$133$		0			0
$134$	1.65279			0.142780
$135$	4.02446	−	6.97057i	0.346370	−	0.599931i
$136$	−2.77144	−	4.80027i	−0.237649	−	0.411620i
$137$	−0.181136	−	0.313737i	−0.0154755	−	0.0268044i	0.858184	−	0.513342i	$-0.171593\pi$
$137$	−0.181136	−	0.313737i	−0.0154755	−	0.0268044i	−0.873659	+	0.486538i	$0.838260\pi$
$138$	2.26391	−	3.92120i	0.192716	−	0.333795i
$139$	9.59419			0.813768			0.406884	−	0.913480i	$-0.366615\pi$
$139$	9.59419			0.813768			0.406884	+	0.913480i	$0.366615\pi$
$140$		0			0
$141$	−11.4547			−0.964662
$142$	4.72132	−	8.17757i	0.396205	−	0.686247i
$143$	−0.0929903	−	0.161064i	−0.00777624	−	0.0134688i
$144$	0.291053	+	0.504118i	0.0242544	+	0.0420098i
$145$	0.429312	−	0.743591i	0.0356525	−	0.0617519i
$146$	−13.1685			−1.08983
$147$		0			0
$148$	−7.04892			−0.579417
$149$	−3.40097	+	5.89065i	−0.278618	+	0.482581i	−0.971042	−	0.238911i	$-0.923210\pi$
$149$	−3.40097	+	5.89065i	−0.278618	+	0.482581i	0.692423	+	0.721491i	$0.256543\pi$
$150$	2.26391	+	3.92120i	0.184847	+	0.320165i
$151$	−11.7066	−	20.2763i	−0.952666	−	1.65007i	−0.739621	−	0.673023i	$-0.764995\pi$
$151$	−11.7066	−	20.2763i	−0.952666	−	1.65007i	−0.213045	−	0.977042i	$-0.568338\pi$
$152$	−1.94504	+	3.36891i	−0.157764	+	0.273255i
$153$	−3.22654			−0.260850
$154$		0			0
$155$	11.6625			0.936753
$156$	0.469501	−	0.813199i	0.0375901	−	0.0651080i
$157$	9.63318	+	16.6852i	0.768811	+	1.33162i	0.938208	+	0.346072i	$0.112485\pi$
$157$	9.63318	+	16.6852i	0.768811	+	1.33162i	−0.169396	+	0.985548i	$0.554182\pi$
$158$	−5.01842	−	8.69215i	−0.399244	−	0.691511i
$159$	−8.51238	+	14.7439i	−0.675075	+	1.16926i
$160$	1.44504			0.114241
$161$		0			0
$162$	−6.91484			−0.543281
$163$	−0.00872920	+	0.0151194i	−0.000683724	+	0.00118424i	−0.866367	−	0.499408i	$-0.833551\pi$
$163$	−0.00872920	+	0.0151194i	−0.000683724	+	0.00118424i	0.865683	+	0.500592i	$0.166884\pi$
$164$	4.43900	+	7.68858i	0.346628	+	0.600377i
$165$	0.346011	+	0.599308i	0.0269369	+	0.0466561i
$166$	1.22252	−	2.11747i	0.0948860	−	0.164347i
$167$	−1.87800			−0.145324			−0.0726621	−	0.997357i	$-0.523149\pi$
$167$	−1.87800			−0.145324			−0.0726621	+	0.997357i	$0.523149\pi$
$168$		0			0
$169$	−12.6353			−0.971949
$170$	−4.00484	+	6.93659i	−0.307158	+	0.532012i
$171$	1.13222	+	1.96106i	0.0865830	+	0.149966i
$172$	5.47434	+	9.48184i	0.417415	+	0.722984i
$173$	−6.03415	+	10.4514i	−0.458768	+	0.794609i	−0.998896	−	0.0469736i	$-0.985042\pi$
$173$	−6.03415	+	10.4514i	−0.458768	+	0.794609i	0.540128	+	0.841583i	$0.318376\pi$
$174$	−0.923936			−0.0700434
$175$		0			0
$176$	−0.307979			−0.0232148
$177$	−9.05041	+	15.6758i	−0.680270	+	1.17826i
$178$	4.67845	+	8.10331i	0.350664	+	0.607369i
$179$	12.2153	+	21.1575i	0.913013	+	1.58139i	0.809784	+	0.586728i	$0.199584\pi$
$179$	12.2153	+	21.1575i	0.913013	+	1.58139i	0.103229	+	0.994658i	$0.467083\pi$
$180$	0.420583	−	0.728471i	0.0313484	−	0.0542971i
$181$	7.85623			0.583949			0.291975	−	0.956426i	$-0.405688\pi$
$181$	7.85623			0.583949			0.291975	+	0.956426i	$0.405688\pi$
$182$		0			0
$183$	2.37568			0.175615
$184$	1.45593	−	2.52174i	0.107332	−	0.185905i
$185$	5.09299	+	8.82132i	0.374444	+	0.648556i
$186$	−6.27479	−	10.8683i	−0.460090	−	0.796899i
$187$	0.853543	−	1.47838i	0.0624173	−	0.108110i
$188$	−7.36658			−0.537263
$189$		0			0
$190$	5.62133			0.407814
$191$	−2.87531	+	4.98019i	−0.208050	+	0.360354i	−0.951100	−	0.308882i	$-0.900045\pi$
$191$	−2.87531	+	4.98019i	−0.208050	+	0.360354i	0.743050	+	0.669236i	$0.233378\pi$
$192$	−0.777479	−	1.34663i	−0.0561097	−	0.0971849i
$193$	−10.6996	−	18.5322i	−0.770171	−	1.33397i	−0.937469	−	0.348069i	$-0.886838\pi$
$193$	−10.6996	−	18.5322i	−0.770171	−	1.33397i	0.167298	−	0.985906i	$-0.446496\pi$
$194$	−6.56734	+	11.3750i	−0.471507	+	0.816674i
$195$	−1.35690			−0.0971693
$196$		0			0
$197$	−13.9312			−0.992559			−0.496280	−	0.868163i	$-0.665301\pi$
$197$	−13.9312			−0.992559			−0.496280	+	0.868163i	$0.665301\pi$
$198$	−0.0896380	+	0.155257i	−0.00637029	+	0.0110337i
$199$	−2.52566	−	4.37456i	−0.179039	−	0.310105i	0.762513	−	0.646973i	$-0.223965\pi$
$199$	−2.52566	−	4.37456i	−0.179039	−	0.310105i	−0.941552	+	0.336869i	$0.890632\pi$
$200$	1.45593	+	2.52174i	0.102950	+	0.178314i
$201$	−1.28501	+	2.22571i	−0.0906377	+	0.156989i
$202$	−8.74632			−0.615389
$203$		0			0
$204$	8.61894			0.603447
$205$	6.41454	−	11.1103i	0.448011	−	0.775978i
$206$	−2.38135	−	4.12463i	−0.165917	−	0.287376i
$207$	−0.847503	−	1.46792i	−0.0589055	−	0.102027i
$208$	0.301938	−	0.522971i	0.0209356	−	0.0362615i
$209$	−1.19806			−0.0828717
$210$		0			0
$211$	−1.61596			−0.111247			−0.0556235	−	0.998452i	$-0.517715\pi$
$211$	−1.61596			−0.111247			−0.0556235	+	0.998452i	$0.517715\pi$
$212$	−5.47434	+	9.48184i	−0.375980	+	0.651216i
$213$	7.34146	+	12.7158i	0.503029	+	0.871271i
$214$	3.85958	+	6.68500i	0.263836	+	0.456977i
$215$	7.91066	−	13.7017i	0.539502	−	0.934446i
$216$	−5.57002			−0.378992
$217$		0			0
$218$	−8.58211			−0.581254
$219$	10.2383	−	17.7332i	0.691837	−	1.19830i
$220$	0.222521	+	0.385418i	0.0150024	+	0.0259848i
$221$	1.67360	+	2.89877i	0.112579	+	0.194992i
$222$	5.48039	−	9.49231i	0.367819	−	0.637082i
$223$	27.8418			1.86442			0.932211	−	0.361915i	$-0.117877\pi$
$223$	27.8418			1.86442			0.932211	+	0.361915i	$0.117877\pi$
$224$		0			0
$225$	1.69501			0.113000
$226$	−9.28232	+	16.0775i	−0.617451	+	1.06946i
$227$	−9.14460	−	15.8389i	−0.606948	−	1.05127i	−0.991740	−	0.128262i	$-0.959060\pi$
$227$	−9.14460	−	15.8389i	−0.606948	−	1.05127i	0.384792	−	0.923003i	$-0.374273\pi$
$228$	−3.02446	−	5.23852i	−0.200300	−	0.346929i
$229$	−10.2687	+	17.7860i	−0.678578	+	1.17533i	0.296831	+	0.954930i	$0.404070\pi$
$229$	−10.2687	+	17.7860i	−0.678578	+	1.17533i	−0.975409	+	0.220402i	$0.929263\pi$
$230$	−4.20775			−0.277451
$231$		0			0
$232$	−0.594187			−0.0390103
$233$	3.22252	−	5.58157i	0.211114	−	0.365661i	−0.740949	−	0.671561i	$-0.765624\pi$
$233$	3.22252	−	5.58157i	0.211114	−	0.365661i	0.952064	+	0.305900i	$0.0989574\pi$
$234$	−0.175760	−	0.304424i	−0.0114898	−	0.0199008i
$235$	5.32251	+	9.21886i	0.347202	+	0.601372i
$236$	−5.82036	+	10.0812i	−0.378873	+	0.656227i
$237$	15.6069			1.01377
$238$		0			0
$239$	−14.4155			−0.932461			−0.466231	−	0.884663i	$-0.654388\pi$
$239$	−14.4155			−0.932461			−0.466231	+	0.884663i	$0.654388\pi$
$240$	−1.12349	+	1.94594i	−0.0725210	+	0.125610i
$241$	0.169719	+	0.293961i	0.0109325	+	0.0189357i	0.871440	−	0.490502i	$-0.163187\pi$
$241$	0.169719	+	0.293961i	0.0109325	+	0.0189357i	−0.860507	+	0.509438i	$0.829853\pi$
$242$	5.45257	+	9.44414i	0.350505	+	0.607092i
$243$	−2.97889	+	5.15960i	−0.191096	+	0.330988i
$244$	1.52781			0.0978081
$245$		0			0
$246$	−13.8049			−0.880170
$247$	1.17456	−	2.03440i	0.0747357	−	0.129446i
$248$	−4.03534	−	6.98942i	−0.256245	−	0.443829i
$249$	1.90097	+	3.29257i	0.120469	+	0.208658i
$250$	5.71648	−	9.90123i	0.361542	−	0.626209i
$251$	−3.78554			−0.238941			−0.119471	−	0.992838i	$-0.538120\pi$
$251$	−3.78554			−0.238941			−0.119471	+	0.992838i	$0.538120\pi$
$252$		0			0
$253$	0.896789			0.0563806
$254$	−0.799249	+	1.38434i	−0.0501494	+	0.0868612i
$255$	−6.22737	−	10.7861i	−0.389973	−	0.675453i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.7262	−	27.2385i	0.980971	−	1.69909i	0.322345	−	0.946622i	$-0.395529\pi$
$257$	15.7262	−	27.2385i	0.980971	−	1.69909i	0.658626	−	0.752470i	$-0.271138\pi$
$258$	−17.0248			−1.05991
$259$		0			0
$260$	−0.872625			−0.0541179
$261$	−0.172940	+	0.299540i	−0.0107047	+	0.0185411i
$262$	−0.890084	−	1.54167i	−0.0549896	−	0.0952447i
$263$	−7.41670	−	12.8461i	−0.457333	−	0.792124i	0.541486	−	0.840710i	$-0.317862\pi$
$263$	−7.41670	−	12.8461i	−0.457333	−	0.792124i	−0.998819	+	0.0485855i	$0.984529\pi$
$264$	0.239447	−	0.414734i	0.0147369	−	0.0255251i
$265$	15.8213			0.971896
$266$		0			0
$267$	−14.5496			−0.890420
$268$	−0.826396	+	1.43136i	−0.0504802	+	0.0874343i
$269$	−6.24847	−	10.8227i	−0.380976	−	0.659870i	0.610226	−	0.792227i	$-0.291079\pi$
$269$	−6.24847	−	10.8227i	−0.380976	−	0.659870i	−0.991202	+	0.132358i	$0.957745\pi$
$270$	4.02446	+	6.97057i	0.244921	+	0.424215i
$271$	2.17725	−	3.77111i	0.132259	−	0.229079i	−0.792288	−	0.610147i	$-0.791110\pi$
$271$	2.17725	−	3.77111i	0.132259	−	0.229079i	0.924547	+	0.381068i	$0.124444\pi$
$272$	5.54288			0.336086
$273$		0			0
$274$	0.362273			0.0218857
$275$	−0.448394	+	0.776642i	−0.0270392	+	0.0468333i
$276$	2.26391	+	3.92120i	0.136271	+	0.236028i
$277$	6.62014	+	11.4664i	0.397766	+	0.688950i	0.993450	−	0.114269i	$-0.0364524\pi$
$277$	6.62014	+	11.4664i	0.397766	+	0.688950i	−0.595684	+	0.803219i	$0.703119\pi$
$278$	−4.79709	+	8.30881i	−0.287711	+	0.498329i
$279$	−4.69799			−0.281261
$280$		0			0
$281$	12.2513			0.730851			0.365425	−	0.930841i	$-0.380924\pi$
$281$	12.2513			0.730851			0.365425	+	0.930841i	$0.380924\pi$
$282$	5.72737	−	9.92009i	0.341060	−	0.590733i
$283$	−2.92058	−	5.05860i	−0.173611	−	0.300702i	0.766069	−	0.642758i	$-0.222210\pi$
$283$	−2.92058	−	5.05860i	−0.173611	−	0.300702i	−0.939680	+	0.342056i	$0.888877\pi$
$284$	4.72132	+	8.17757i	0.280159	+	0.485250i
$285$	−4.37047	+	7.56988i	−0.258884	+	0.448401i
$286$	0.185981			0.0109973
$287$		0			0
$288$	−0.582105			−0.0343009
$289$	−6.86174	+	11.8849i	−0.403632	+	0.699111i
$290$	0.429312	+	0.743591i	0.0252101	+	0.0436652i
$291$	−10.2119	−	17.6876i	−0.598634	−	1.03686i
$292$	6.58426	−	11.4043i	0.385315	−	0.667385i
$293$	−4.10752			−0.239964			−0.119982	−	0.992776i	$-0.538284\pi$
$293$	−4.10752			−0.239964			−0.119982	+	0.992776i	$0.538284\pi$
$294$		0			0
$295$	16.8213			0.979375
$296$	3.52446	−	6.10454i	0.204855	−	0.354819i
$297$	−0.857724	−	1.48562i	−0.0497702	−	0.0862045i
$298$	−3.40097	−	5.89065i	−0.197013	−	0.341236i
$299$	−0.879199	+	1.52282i	−0.0508454	+	0.0880668i
$300$	−4.52781			−0.261413
$301$		0			0
$302$	23.4131			1.34727
$303$	6.80008	−	11.7781i	0.390654	−	0.676633i
$304$	−1.94504	−	3.36891i	−0.111556	−	0.193220i
$305$	−1.10388	−	1.91197i	−0.0632077	−	0.109479i
$306$	1.61327	−	2.79426i	0.0922244	−	0.159737i
$307$	29.4010			1.67801			0.839003	−	0.544127i	$-0.183139\pi$
$307$	29.4010			1.67801			0.839003	+	0.544127i	$0.183139\pi$
$308$		0			0
$309$	7.40581			0.421302
$310$	−5.83124	+	10.1000i	−0.331192	+	0.573642i
$311$	−11.5233	−	19.9589i	−0.653424	−	1.13176i	−0.982286	−	0.187386i	$-0.939998\pi$
$311$	−11.5233	−	19.9589i	−0.653424	−	1.13176i	0.328862	−	0.944378i	$-0.393335\pi$
$312$	0.469501	+	0.813199i	0.0265802	+	0.0460383i
$313$	7.94653	−	13.7638i	0.449165	−	0.777976i	−0.549167	−	0.835712i	$-0.685055\pi$
$313$	7.94653	−	13.7638i	0.449165	−	0.777976i	0.998332	+	0.0577365i	$0.0183883\pi$
$314$	−19.2664			−1.08726
$315$		0			0
$316$	10.0368			0.564616
$317$	10.4499	−	18.0997i	0.586924	−	1.01658i	−0.407708	−	0.913112i	$-0.633672\pi$
$317$	10.4499	−	18.0997i	0.586924	−	1.01658i	0.994633	−	0.103470i	$-0.0329946\pi$
$318$	−8.51238	−	14.7439i	−0.477350	−	0.826795i
$319$	−0.0914984	−	0.158480i	−0.00512293	−	0.00887317i
$320$	−0.722521	+	1.25144i	−0.0403901	+	0.0699578i
$321$	−12.0030			−0.669941
$322$		0			0
$323$	21.5623			1.19976
$324$	3.45742	−	5.98843i	0.192079	−	0.332690i
$325$	−0.879199	−	1.52282i	−0.0487692	−	0.0844707i
$326$	−0.00872920	−	0.0151194i	−0.000483466	−	0.000837387i
$327$	6.67241	−	11.5569i	0.368985	−	0.639101i
$328$	−8.87800			−0.490206
$329$		0			0
$330$	−0.692021			−0.0380945
$331$	−6.15615	+	10.6628i	−0.338372	+	0.586078i	−0.984127	−	0.177467i	$-0.943210\pi$
$331$	−6.15615	+	10.6628i	−0.338372	+	0.586078i	0.645754	+	0.763545i	$0.276543\pi$
$332$	1.22252	+	2.11747i	0.0670946	+	0.116211i
$333$	−2.05161	−	3.55349i	−0.112427	−	0.194730i
$334$	0.939001	−	1.62640i	0.0513799	−	0.0889925i
$335$	2.38835			0.130490
$336$		0			0
$337$	−2.92692			−0.159439			−0.0797197	−	0.996817i	$-0.525403\pi$
$337$	−2.92692			−0.159439			−0.0797197	+	0.996817i	$0.525403\pi$
$338$	6.31767	−	10.9425i	0.343636	−	0.595195i
$339$	−14.4336	−	24.9998i	−0.783927	−	1.35780i
$340$	−4.00484	−	6.93659i	−0.217193	−	0.376190i
$341$	1.24280	−	2.15259i	0.0673014	−	0.116569i
$342$	−2.26444			−0.122447
$343$		0			0
$344$	−10.9487			−0.590314
$345$	3.27144	−	5.66630i	0.176128	−	0.305063i
$346$	−6.03415	−	10.4514i	−0.324398	−	0.561873i
$347$	0.131023	+	0.226938i	0.00703366	+	0.0121827i	0.869521	−	0.493896i	$-0.164428\pi$
$347$	0.131023	+	0.226938i	0.00703366	+	0.0121827i	−0.862487	+	0.506079i	$0.831094\pi$
$348$	0.461968	−	0.800152i	0.0247641	−	0.0428926i
$349$	30.6310			1.63964			0.819821	−	0.572621i	$-0.194073\pi$
$349$	30.6310			1.63964			0.819821	+	0.572621i	$0.194073\pi$
$350$		0			0
$351$	3.36360			0.179536
$352$	0.153989	−	0.266717i	0.00820766	−	0.0142161i
$353$	9.27144	+	16.0586i	0.493469	+	0.854713i	0.999972	−	0.00752515i	$-0.00239535\pi$
$353$	9.27144	+	16.0586i	0.493469	+	0.854713i	−0.506503	+	0.862238i	$0.669062\pi$
$354$	−9.05041	−	15.6758i	−0.481024	−	0.833158i
$355$	6.82251	−	11.8169i	0.362101	−	0.627178i
$356$	−9.35690			−0.495914
$357$		0			0
$358$	−24.4306			−1.29120
$359$	−4.59030	+	7.95064i	−0.242267	+	0.419619i	−0.961360	−	0.275296i	$-0.911224\pi$
$359$	−4.59030	+	7.95064i	−0.242267	+	0.419619i	0.719093	+	0.694914i	$0.244558\pi$
$360$	0.420583	+	0.728471i	0.0221667	+	0.0383938i
$361$	1.93362	+	3.34914i	0.101770	+	0.176270i
$362$	−3.92812	+	6.80370i	−0.206457	+	0.357594i
$363$	−16.9571			−0.890014
$364$		0			0
$365$	−19.0291			−0.996027
$366$	−1.18784	+	2.05740i	−0.0620894	+	0.107542i
$367$	−12.0821	−	20.9268i	−0.630681	−	1.09237i	−0.987413	−	0.158164i	$-0.949442\pi$
$367$	−12.0821	−	20.9268i	−0.630681	−	1.09237i	0.356732	−	0.934207i	$-0.383891\pi$
$368$	1.45593	+	2.52174i	0.0758954	+	0.131455i
$369$	−2.58397	+	4.47556i	−0.134516	+	0.232988i
$370$	−10.1860			−0.529544
$371$		0			0
$372$	12.5496			0.650665
$373$	−12.9574	+	22.4429i	−0.670910	+	1.16205i	0.306737	+	0.951794i	$0.400763\pi$
$373$	−12.9574	+	22.4429i	−0.670910	+	1.16205i	−0.977647	+	0.210255i	$0.932570\pi$
$374$	0.853543	+	1.47838i	0.0441357	+	0.0764452i
$375$	8.88889	+	15.3960i	0.459020	+	0.795046i
$376$	3.68329	−	6.37965i	0.189951	−	0.329005i
$377$	0.358815			0.0184799
$378$		0			0
$379$	32.0844			1.64807			0.824033	−	0.566542i	$-0.191719\pi$
$379$	32.0844			1.64807			0.824033	+	0.566542i	$0.191719\pi$
$380$	−2.81067	+	4.86822i	−0.144184	+	0.249734i
$381$	−1.24280	−	2.15259i	−0.0636705	−	0.110281i
$382$	−2.87531	−	4.98019i	−0.147114	−	0.254809i
$383$	−6.31402	+	10.9362i	−0.322631	+	0.558814i	−0.981030	−	0.193855i	$-0.937901\pi$
$383$	−6.31402	+	10.9362i	−0.322631	+	0.558814i	0.658399	+	0.752669i	$0.271234\pi$
$384$	1.55496			0.0793511
$385$		0			0
$386$	21.3991			1.08919
$387$	−3.18664	+	5.51943i	−0.161986	+	0.280568i
$388$	−6.56734	−	11.3750i	−0.333406	−	0.577476i
$389$	−0.170915	−	0.296034i	−0.00866574	−	0.0150095i	0.861660	−	0.507486i	$-0.169425\pi$
$389$	−0.170915	−	0.296034i	−0.00866574	−	0.0150095i	−0.870326	+	0.492476i	$0.836092\pi$
$390$	0.678448	−	1.17511i	0.0343545	−	0.0595038i
$391$	−16.1400			−0.816237
$392$		0			0
$393$	2.76809			0.139631
$394$	6.96562	−	12.0648i	0.350923	−	0.607816i
$395$	−7.25182	−	12.5605i	−0.364879	−	0.631989i
$396$	−0.0896380	−	0.155257i	−0.00450448	−	0.00780198i
$397$	4.39493	−	7.61224i	0.220575	−	0.382047i	−0.734408	−	0.678709i	$-0.762540\pi$
$397$	4.39493	−	7.61224i	0.220575	−	0.382047i	0.954983	+	0.296661i	$0.0958733\pi$
$398$	5.05131			0.253199
$399$		0			0
$400$	−2.91185			−0.145593
$401$	−4.74967	+	8.22667i	−0.237187	+	0.410820i	−0.959906	−	0.280322i	$-0.909559\pi$
$401$	−4.74967	+	8.22667i	−0.237187	+	0.410820i	0.722719	+	0.691142i	$0.242892\pi$
$402$	−1.28501	−	2.22571i	−0.0640906	−	0.111008i
$403$	2.43685	+	4.22074i	0.121388	+	0.210250i
$404$	4.37316	−	7.57453i	0.217573	−	0.376847i
$405$	−9.99223			−0.496518
$406$		0			0
$407$	2.17092			0.107608
$408$	−4.30947	+	7.46422i	−0.213351	+	0.369534i
$409$	−8.77628	−	15.2010i	−0.433959	−	0.751639i	0.563251	−	0.826286i	$-0.309550\pi$
$409$	−8.77628	−	15.2010i	−0.433959	−	0.751639i	−0.997210	+	0.0746465i	$0.976217\pi$
$410$	6.41454	+	11.1103i	0.316792	+	0.548699i
$411$	−0.281659	+	0.487848i	−0.0138932	+	0.0240638i
$412$	4.76271			0.234642
$413$		0			0
$414$	1.69501			0.0833050
$415$	1.76659	−	3.05983i	0.0867187	−	0.150201i
$416$	0.301938	+	0.522971i	0.0148037	+	0.0256408i
$417$	−7.45928	−	12.9199i	−0.365282	−	0.632688i
$418$	0.599031	−	1.03755i	0.0292996	−	0.0507483i
$419$	19.0965			0.932925			0.466463	−	0.884541i	$-0.345528\pi$
$419$	19.0965			0.932925			0.466463	+	0.884541i	$0.345528\pi$
$420$		0			0
$421$	−19.9095			−0.970328			−0.485164	−	0.874423i	$-0.661240\pi$
$421$	−19.9095			−0.970328			−0.485164	+	0.874423i	$0.661240\pi$
$422$	0.807979	−	1.39946i	0.0393318	−	0.0681246i
$423$	−2.14406	−	3.71363i	−0.104248	−	0.180563i
$424$	−5.47434	−	9.48184i	−0.265858	−	0.460479i
$425$	8.07002	−	13.9777i	0.391454	−	0.678018i
$426$	−14.6829			−0.711390
$427$		0			0
$428$	−7.71917			−0.373120
$429$	−0.144596	+	0.250448i	−0.00698116	+	0.0120917i
$430$	7.91066	+	13.7017i	0.381486	+	0.660753i
$431$	3.10537	+	5.37865i	0.149580	+	0.259081i	0.931072	−	0.364834i	$-0.118874\pi$
$431$	3.10537	+	5.37865i	0.149580	+	0.259081i	−0.781492	+	0.623915i	$0.785541\pi$
$432$	2.78501	−	4.82378i	0.133994	−	0.232084i
$433$	8.81163			0.423460			0.211730	−	0.977328i	$-0.432090\pi$
$433$	8.81163			0.423460			0.211730	+	0.977328i	$0.432090\pi$
$434$		0			0
$435$	−1.33513			−0.0640144
$436$	4.29105	−	7.43232i	0.205504	−	0.355944i
$437$	5.66368	+	9.80978i	0.270930	+	0.469265i
$438$	10.2383	+	17.7332i	0.489203	+	0.847324i
$439$	−18.0836	+	31.3217i	−0.863083	+	1.49490i	0.00585511	+	0.999983i	$0.498136\pi$
$439$	−18.0836	+	31.3217i	−0.863083	+	1.49490i	−0.868938	+	0.494921i	$0.835197\pi$
$440$	−0.445042			−0.0212165
$441$		0			0
$442$	−3.34721			−0.159210
$443$	−10.1441	+	17.5700i	−0.481959	+	0.834777i	−0.999786	−	0.0207081i	$-0.993408\pi$
$443$	−10.1441	+	17.5700i	−0.481959	+	0.834777i	0.517827	+	0.855486i	$0.326741\pi$
$444$	5.48039	+	9.49231i	0.260088	+	0.450485i
$445$	6.76055	+	11.7096i	0.320481	+	0.555089i
$446$	−13.9209	+	24.1117i	−0.659173	+	1.14172i
$447$	10.5767			0.500262
$448$		0			0
$449$	−31.3448			−1.47925			−0.739627	−	0.673017i	$-0.764998\pi$
$449$	−31.3448			−1.47925			−0.739627	+	0.673017i	$0.764998\pi$
$450$	−0.847503	+	1.46792i	−0.0399517	+	0.0691983i
$451$	−1.36712	−	2.36792i	−0.0643750	−	0.111501i
$452$	−9.28232	−	16.0775i	−0.436604	−	0.756220i
$453$	−18.2032	+	31.5289i	−0.855261	+	1.48136i
$454$	18.2892			0.858354
$455$		0			0
$456$	6.04892			0.283267
$457$	−4.39158	+	7.60643i	−0.205429	+	0.355814i	−0.950269	−	0.311429i	$-0.899192\pi$
$457$	−4.39158	+	7.60643i	−0.205429	+	0.355814i	0.744840	+	0.667243i	$0.232526\pi$
$458$	−10.2687	−	17.7860i	−0.479827	−	0.831085i
$459$	15.4370	+	26.7376i	0.720536	+	1.24801i
$460$	2.10388	−	3.64402i	0.0980937	−	0.169903i
$461$	−16.0968			−0.749701			−0.374851	−	0.927085i	$-0.622306\pi$
$461$	−16.0968			−0.749701			−0.374851	+	0.927085i	$0.622306\pi$
$462$		0			0
$463$	−1.68963			−0.0785237			−0.0392618	−	0.999229i	$-0.512501\pi$
$463$	−1.68963			−0.0785237			−0.0392618	+	0.999229i	$0.512501\pi$
$464$	0.297093	−	0.514581i	0.0137922	−	0.0238888i
$465$	−9.06734	−	15.7051i	−0.420488	−	0.728306i
$466$	3.22252	+	5.58157i	0.149280	+	0.258561i
$467$	16.7811	−	29.0658i	0.776538	−	1.34500i	−0.157388	−	0.987537i	$-0.550307\pi$
$467$	16.7811	−	29.0658i	0.776538	−	1.34500i	0.933926	−	0.357466i	$-0.116359\pi$
$468$	0.351519			0.0162490
$469$		0			0
$470$	−10.6450			−0.491018
$471$	14.9792	−	25.9447i	0.690205	−	1.19547i
$472$	−5.82036	−	10.0812i	−0.267904	−	0.464023i
$473$	−1.68598	−	2.92020i	−0.0775215	−	0.134271i
$474$	−7.80343	+	13.5159i	−0.358423	+	0.620808i
$475$	−11.3274			−0.519735
$476$		0			0
$477$	−6.37329			−0.291813
$478$	7.20775	−	12.4842i	0.329675	−	0.571014i
$479$	3.97166	+	6.87911i	0.181470	+	0.314315i	0.942381	−	0.334541i	$-0.108581\pi$
$479$	3.97166	+	6.87911i	0.181470	+	0.314315i	−0.760912	+	0.648856i	$0.775248\pi$
$480$	−1.12349	−	1.94594i	−0.0512801	−	0.0888197i
$481$	−2.12833	+	3.68638i	−0.0970437	+	0.168085i
$482$	−0.339437			−0.0154610
$483$		0			0
$484$	−10.9051			−0.495689
$485$	−9.49007	+	16.4373i	−0.430922	+	0.746379i
$486$	−2.97889	−	5.15960i	−0.135125	−	0.234044i
$487$	−17.9499	−	31.0901i	−0.813387	−	1.40883i	−0.910480	−	0.413552i	$-0.864288\pi$
$487$	−17.9499	−	31.0901i	−0.813387	−	1.40883i	0.0970934	−	0.995275i	$-0.469045\pi$
$488$	−0.763906	+	1.32312i	−0.0345804	+	0.0598950i
$489$	0.0271471			0.00122763
$490$		0			0
$491$	−6.17092			−0.278490			−0.139245	−	0.990258i	$-0.544467\pi$
$491$	−6.17092			−0.278490			−0.139245	+	0.990258i	$0.544467\pi$
$492$	6.90246	−	11.9554i	0.311187	−	0.538992i
$493$	1.64675	+	2.85226i	0.0741660	+	0.128459i
$494$	1.17456	+	2.03440i	0.0528461	+	0.0915321i
$495$	−0.129531	+	0.224354i	−0.00582197	+	0.0100839i
$496$	8.07069			0.362385
$497$		0			0
$498$	−3.80194			−0.170369
$499$	−2.59837	+	4.50050i	−0.116319	+	0.201470i	−0.918306	−	0.395871i	$-0.870443\pi$
$499$	−2.59837	+	4.50050i	−0.116319	+	0.201470i	0.801987	+	0.597341i	$0.203776\pi$
$500$	5.71648	+	9.90123i	0.255649	+	0.442797i
$501$	1.46011	+	2.52898i	0.0652328	+	0.112986i
$502$	1.89277	−	3.27838i	0.0844786	−	0.146321i
$503$	11.4058			0.508560			0.254280	−	0.967131i	$-0.418162\pi$
$503$	11.4058			0.508560			0.254280	+	0.967131i	$0.418162\pi$
$504$		0			0
$505$	−12.6388			−0.562419
$506$	−0.448394	+	0.776642i	−0.0199336	+	0.0345259i
$507$	9.82371	+	17.0152i	0.436286	+	0.755670i
$508$	−0.799249	−	1.38434i	−0.0354610	−	0.0614202i
$509$	−21.0661	+	36.4876i	−0.933740	+	1.61729i	−0.156875	+	0.987618i	$0.550142\pi$
$509$	−21.0661	+	36.4876i	−0.933740	+	1.61729i	−0.776865	+	0.629667i	$0.783191\pi$
$510$	12.4547			0.551505
$511$		0			0
$512$	1.00000			0.0441942
$513$	10.8339	−	18.7649i	0.478330	−	0.828491i
$514$	15.7262	+	27.2385i	0.693652	+	1.20144i
$515$	−3.44116	−	5.96026i	−0.151635	−	0.262640i
$516$	8.51238	−	14.7439i	0.374737	−	0.649063i
$517$	2.26875			0.0997795
$518$		0			0
$519$	18.7657			0.823722
$520$	0.436313	−	0.755716i	0.0191336	−	0.0331403i
$521$	10.7361	+	18.5955i	0.470357	+	0.814682i	0.999425	−	0.0338972i	$-0.0107919\pi$
$521$	10.7361	+	18.5955i	0.470357	+	0.814682i	−0.529068	+	0.848579i	$0.677459\pi$
$522$	−0.172940	−	0.299540i	−0.00756936	−	0.0131105i
$523$	−6.02393	+	10.4337i	−0.263408	+	0.456236i	−0.967145	−	0.254224i	$-0.918180\pi$
$523$	−6.02393	+	10.4337i	−0.263408	+	0.456236i	0.703737	+	0.710460i	$0.251513\pi$
$524$	1.78017			0.0777670
$525$		0			0
$526$	14.8334			0.646767
$527$	−22.3674	+	38.7415i	−0.974340	+	1.68761i
$528$	0.239447	+	0.414734i	0.0104206	+	0.0180490i
$529$	7.26055	+	12.5756i	0.315676	+	0.546767i
$530$	−7.91066	+	13.7017i	−0.343617	+	0.595162i
$531$	−6.77612			−0.294059
$532$		0			0
$533$	5.36121			0.232220
$534$	7.27479	−	12.6003i	0.314811	−	0.545269i
$535$	5.57726	+	9.66010i	0.241126	+	0.417643i
$536$	−0.826396	−	1.43136i	−0.0356949	−	0.0618254i
$537$	18.9943	−	32.8990i	0.819663	−	1.41970i
$538$	12.4969			0.538781
$539$		0			0
$540$	−8.04892			−0.346370
$541$	12.7687	−	22.1161i	0.548971	−	0.950846i	−0.449374	−	0.893344i	$-0.648353\pi$
$541$	12.7687	−	22.1161i	0.548971	−	0.950846i	0.998345	−	0.0575027i	$-0.0183138\pi$
$542$	2.17725	+	3.77111i	0.0935210	+	0.161983i
$543$	−6.10806	−	10.5795i	−0.262122	−	0.454008i
$544$	−2.77144	+	4.80027i	−0.118824	+	0.205810i
$545$	−12.4015			−0.531222
$546$		0			0
$547$	−24.1497			−1.03257			−0.516284	−	0.856417i	$-0.672685\pi$
$547$	−24.1497			−1.03257			−0.516284	+	0.856417i	$0.672685\pi$
$548$	−0.181136	+	0.313737i	−0.00773776	+	0.0134022i
$549$	0.444673	+	0.770197i	0.0189782	+	0.0328712i
$550$	−0.448394	−	0.776642i	−0.0191196	−	0.0331161i
$551$	1.15572	−	2.00176i	0.0492353	−	0.0852780i
$552$	−4.52781			−0.192716
$553$		0			0
$554$	−13.2403			−0.562525
$555$	7.91939	−	13.7168i	0.336159	−	0.582245i
$556$	−4.79709	−	8.30881i	−0.203442	−	0.352372i
$557$	−4.18382	−	7.24660i	−0.177274	−	0.307048i	0.763672	−	0.645605i	$-0.223395\pi$
$557$	−4.18382	−	7.24660i	−0.177274	−	0.307048i	−0.940946	+	0.338557i	$0.890061\pi$
$558$	2.34899	−	4.06858i	0.0994409	−	0.172237i
$559$	6.61165			0.279643
$560$		0			0
$561$	−2.65445			−0.112071
$562$	−6.12565	+	10.6099i	−0.258395	+	0.447553i
$563$	18.4284	+	31.9189i	0.776665	+	1.34522i	0.933854	+	0.357655i	$0.116423\pi$
$563$	18.4284	+	31.9189i	0.776665	+	1.34522i	−0.157189	+	0.987569i	$0.550243\pi$
$564$	5.72737	+	9.92009i	0.241166	+	0.417711i
$565$	−13.4133	+	23.2326i	−0.564304	+	0.977403i
$566$	5.84117			0.245523
$567$		0			0
$568$	−9.44265			−0.396205
$569$	19.9068	−	34.4795i	0.834535	−	1.44546i	−0.0598729	−	0.998206i	$-0.519070\pi$
$569$	19.9068	−	34.4795i	0.834535	−	1.44546i	0.894408	−	0.447252i	$-0.147597\pi$
$570$	−4.37047	−	7.56988i	−0.183059	−	0.317067i
$571$	6.05310	+	10.4843i	0.253314	+	0.438753i	0.964436	−	0.264315i	$-0.0851460\pi$
$571$	6.05310	+	10.4843i	0.253314	+	0.438753i	−0.711122	+	0.703069i	$0.751813\pi$
$572$	−0.0929903	+	0.161064i	−0.00388812	+	0.00673442i
$573$	8.94198			0.373557
$574$		0			0
$575$	8.47889			0.353594
$576$	0.291053	−	0.504118i	0.0121272	−	0.0210049i
$577$	4.08964	+	7.08346i	0.170254	+	0.294888i	0.938509	−	0.345256i	$-0.112208\pi$
$577$	4.08964	+	7.08346i	0.170254	+	0.294888i	−0.768255	+	0.640144i	$0.778875\pi$
$578$	−6.86174	−	11.8849i	−0.285411	−	0.494346i
$579$	−16.6374	+	28.8168i	−0.691425	+	1.19758i
$580$	−0.858625			−0.0356525
$581$		0			0
$582$	20.4239			0.846596
$583$	1.68598	−	2.92020i	0.0698262	−	0.120943i
$584$	6.58426	+	11.4043i	0.272459	+	0.471912i
$585$	−0.253980	−	0.439906i	−0.0105008	−	0.0181879i
$586$	2.05376	−	3.55722i	0.0848401	−	0.146947i
$587$	−11.5386			−0.476248			−0.238124	−	0.971235i	$-0.576532\pi$
$587$	−11.5386			−0.476248			−0.238124	+	0.971235i	$0.576532\pi$
$588$		0			0
$589$	31.3957			1.29364
$590$	−8.41066	+	14.5677i	−0.346261	+	0.599742i
$591$	10.8312	+	18.7603i	0.445538	+	0.771694i
$592$	3.52446	+	6.10454i	0.144854	+	0.250895i
$593$	19.3339	−	33.4873i	0.793949	−	1.37516i	−0.129555	−	0.991572i	$-0.541355\pi$
$593$	19.3339	−	33.4873i	0.793949	−	1.37516i	0.923504	−	0.383588i	$-0.125312\pi$
$594$	1.71545			0.0703857
$595$		0			0
$596$	6.80194			0.278618
$597$	−3.92729	+	6.80226i	−0.160733	+	0.278398i
$598$	−0.879199	−	1.52282i	−0.0359531	−	0.0622726i
$599$	−12.7947	−	22.1611i	−0.522777	−	0.905477i	−0.999649	−	0.0265038i	$-0.991563\pi$
$599$	−12.7947	−	22.1611i	−0.522777	−	0.905477i	0.476871	−	0.878973i	$-0.341771\pi$
$600$	2.26391	−	3.92120i	0.0924236	−	0.160082i
$601$	0.881723			0.0359662			0.0179831	−	0.999838i	$-0.494275\pi$
$601$	0.881723			0.0359662			0.0179831	+	0.999838i	$0.494275\pi$
$602$		0			0
$603$	−0.962099			−0.0391797
$604$	−11.7066	+	20.2763i	−0.476333	+	0.825033i
$605$	7.87920	+	13.6472i	0.320335	+	0.554836i
$606$	6.80008	+	11.7781i	0.276234	+	0.478452i
$607$	3.81402	−	6.60608i	0.154806	−	0.268132i	−0.778182	−	0.628039i	$-0.783858\pi$
$607$	3.81402	−	6.60608i	0.154806	−	0.268132i	0.932988	+	0.359906i	$0.117191\pi$
$608$	3.89008			0.157764
$609$		0			0
$610$	2.20775			0.0893892
$611$	−2.22425	+	3.85251i	−0.0899835	+	0.155856i
$612$	1.61327	+	2.79426i	0.0652125	+	0.112951i
$613$	−15.0788	−	26.1172i	−0.609025	−	1.05486i	−0.991401	−	0.130856i	$-0.958228\pi$
$613$	−15.0788	−	26.1172i	−0.609025	−	1.05486i	0.382376	−	0.924007i	$-0.375106\pi$
$614$	−14.7005	+	25.4620i	−0.593264	+	1.02756i
$615$	−19.9487			−0.804409
$616$		0			0
$617$	−1.54958			−0.0623838			−0.0311919	−	0.999513i	$-0.509930\pi$
$617$	−1.54958			−0.0623838			−0.0311919	+	0.999513i	$0.509930\pi$
$618$	−3.70291	+	6.41362i	−0.148953	+	0.257994i
$619$	−3.43147	−	5.94348i	−0.137922	−	0.238889i	0.788788	−	0.614666i	$-0.210709\pi$
$619$	−3.43147	−	5.94348i	−0.137922	−	0.238889i	−0.926710	+	0.375777i	$0.877376\pi$
$620$	−5.83124	−	10.1000i	−0.234188	−	0.405626i
$621$	−8.10955	+	14.0461i	−0.325425	+	0.563653i
$622$	23.0465			0.924081
$623$		0			0
$624$	−0.939001			−0.0375901
$625$	0.980918	−	1.69900i	0.0392367	−	0.0679600i
$626$	7.94653	+	13.7638i	0.317607	+	0.550112i
$627$	0.931468	+	1.61335i	0.0371993	+	0.0644310i
$628$	9.63318	−	16.6852i	0.384406	−	0.665810i
$629$	−39.0713			−1.55787
$630$		0			0
$631$	−9.08708			−0.361751			−0.180875	−	0.983506i	$-0.557893\pi$
$631$	−9.08708			−0.361751			−0.180875	+	0.983506i	$0.557893\pi$
$632$	−5.01842	+	8.69215i	−0.199622	+	0.345755i
$633$	1.25637	+	2.17610i	0.0499363	+	0.0864923i
$634$	10.4499	+	18.0997i	0.415018	+	0.718832i
$635$	−1.15495	+	2.00043i	−0.0458327	+	0.0793846i
$636$	17.0248			0.675075
$637$		0			0
$638$	0.182997			0.00724491
$639$	−2.74831	+	4.76021i	−0.108721	+	0.188311i
$640$	−0.722521	−	1.25144i	−0.0285601	−	0.0494676i
$641$	12.0477	+	20.8673i	0.475856	+	0.824207i	0.999617	−	0.0276578i	$-0.00880487\pi$
$641$	12.0477	+	20.8673i	0.475856	+	0.824207i	−0.523761	+	0.851865i	$0.675472\pi$
$642$	6.00149	−	10.3949i	0.236860	−	0.410254i
$643$	−44.6915			−1.76246			−0.881231	−	0.472685i	$-0.843285\pi$
$643$	−44.6915			−1.76246			−0.881231	+	0.472685i	$0.843285\pi$
$644$		0			0
$645$	−24.6015			−0.968682
$646$	−10.7811	+	18.6735i	−0.424178	+	0.734697i
$647$	6.07792	+	10.5273i	0.238948	+	0.413870i	0.960413	−	0.278581i	$-0.0898642\pi$
$647$	6.07792	+	10.5273i	0.238948	+	0.413870i	−0.721465	+	0.692451i	$0.756531\pi$
$648$	3.45742	+	5.98843i	0.135820	+	0.235248i
$649$	1.79254	−	3.10478i	0.0703635	−	0.121873i
$650$	1.75840			0.0689700
$651$		0			0
$652$	0.0174584			0.000683724
$653$	13.6434	−	23.6311i	0.533907	−	0.924755i	−0.465308	−	0.885149i	$-0.654056\pi$
$653$	13.6434	−	23.6311i	0.533907	−	0.924755i	0.999215	−	0.0396060i	$-0.0126103\pi$
$654$	6.67241	+	11.5569i	0.260912	+	0.451912i
$655$	−1.28621	−	2.22778i	−0.0502563	−	0.0870465i
$656$	4.43900	−	7.68858i	0.173314	−	0.300188i
$657$	7.66547			0.299058
$658$		0			0
$659$	−0.126310			−0.00492033			−0.00246016	−	0.999997i	$-0.500783\pi$
$659$	−0.126310			−0.00492033			−0.00246016	+	0.999997i	$0.500783\pi$
$660$	0.346011	−	0.599308i	0.0134684	−	0.0233280i
$661$	7.78017	+	13.4756i	0.302613	+	0.524142i	0.976727	−	0.214486i	$-0.0688076\pi$
$661$	7.78017	+	13.4756i	0.302613	+	0.524142i	−0.674114	+	0.738628i	$0.735474\pi$
$662$	−6.15615	−	10.6628i	−0.239265	−	0.414420i
$663$	2.60238	−	4.50746i	0.101068	−	0.175055i
$664$	−2.44504			−0.0948860
$665$		0			0
$666$	4.10321			0.158996
$667$	−0.865093	+	1.49838i	−0.0334965	+	0.0580177i
$668$	0.939001	+	1.62640i	0.0363310	+	0.0629272i
$669$	−21.6464	−	37.4926i	−0.836898	−	1.44955i
$670$	−1.19418	+	2.06838i	−0.0461351	+	0.0799083i
$671$	−0.470533			−0.0181647
$672$		0			0
$673$	20.5295			0.791353			0.395676	−	0.918390i	$-0.370510\pi$
$673$	20.5295			0.791353			0.395676	+	0.918390i	$0.370510\pi$
$674$	1.46346	−	2.53479i	0.0563704	−	0.0976363i
$675$	−8.10955	−	14.0461i	−0.312137	−	0.540637i
$676$	6.31767	+	10.9425i	0.242987	+	0.420866i
$677$	19.4499	−	33.6882i	0.747520	−	1.29474i	−0.201488	−	0.979491i	$-0.564578\pi$
$677$	19.4499	−	33.6882i	0.747520	−	1.29474i	0.949008	−	0.315251i	$-0.102089\pi$
$678$	28.8672			1.10864
$679$		0			0
$680$	8.00969			0.307158
$681$	−14.2195	+	24.6288i	−0.544891	+	0.943779i
$682$	1.24280	+	2.15259i	0.0475892	+	0.0824270i
$683$	16.0172	+	27.7426i	0.612882	+	1.06154i	0.990752	+	0.135684i	$0.0433232\pi$
$683$	16.0172	+	27.7426i	0.612882	+	1.06154i	−0.377870	+	0.925859i	$0.623343\pi$
$684$	1.13222	−	1.96106i	0.0432915	−	0.0749830i
$685$	0.523499			0.0200019
$686$		0			0
$687$	31.9350			1.21839
$688$	5.47434	−	9.48184i	0.208707	−	0.361492i
$689$	3.30582	+	5.72585i	0.125942	+	0.218138i
$690$	3.27144	+	5.66630i	0.124542	+	0.215712i
$691$	−1.93482	+	3.35121i	−0.0736040	+	0.127486i	−0.900478	−	0.434901i	$-0.856783\pi$
$691$	−1.93482	+	3.35121i	−0.0736040	+	0.127486i	0.826874	+	0.562387i	$0.190117\pi$
$692$	12.0683			0.458768
$693$		0			0
$694$	−0.262045			−0.00994710
$695$	−6.93200	+	12.0066i	−0.262946	+	0.455435i
$696$	0.461968	+	0.800152i	0.0175108	+	0.0303297i
$697$	24.6048	+	42.6168i	0.931975	+	1.61423i
$698$	−15.3155	+	26.5272i	−0.579701	+	1.00407i
$699$	−10.0218			−0.379058
$700$		0			0
$701$	38.5411			1.45568			0.727838	−	0.685749i	$-0.240525\pi$
$701$	38.5411			1.45568			0.727838	+	0.685749i	$0.240525\pi$
$702$	−1.68180	+	2.91296i	−0.0634755	+	0.109943i
$703$	13.7104	+	23.7472i	0.517099	+	0.895642i
$704$	0.153989	+	0.266717i	0.00580369	+	0.0100523i
$705$	8.27628	−	14.3349i	0.311703	−	0.539885i
$706$	−18.5429			−0.697870
$707$		0			0
$708$	18.1008			0.680270
$709$	1.28017	−	2.21732i	0.0480777	−	0.0832730i	−0.840985	−	0.541058i	$-0.818024\pi$
$709$	1.28017	−	2.21732i	0.0480777	−	0.0832730i	0.889063	+	0.457785i	$0.151357\pi$
$710$	6.82251	+	11.8169i	0.256044	+	0.443482i
$711$	2.92125	+	5.05975i	0.109555	+	0.189755i
$712$	4.67845	−	8.10331i	0.175332	−	0.303684i
$713$	−23.5007			−0.880107
$714$		0			0
$715$	0.268750			0.0100507
$716$	12.2153	−	21.1575i	0.456507	−	0.790693i
$717$	11.2078	+	19.4124i	0.418561	+	0.724969i
$718$	−4.59030	−	7.95064i	−0.171309	−	0.296715i
$719$	19.3376	−	33.4937i	0.721170	−	1.24910i	−0.239361	−	0.970931i	$-0.576938\pi$
$719$	19.3376	−	33.4937i	0.721170	−	1.24910i	0.960531	−	0.278172i	$-0.0897286\pi$
$720$	−0.841166			−0.0313484
$721$		0			0
$722$	−3.86725			−0.143924
$723$	0.263906	−	0.457098i	0.00981475	−	0.0169996i
$724$	−3.92812	−	6.80370i	−0.145987	−	0.252857i
$725$	−0.865093	−	1.49838i	−0.0321287	−	0.0556486i
$726$	8.47853	−	14.6852i	0.314668	−	0.545020i
$727$	−19.0597			−0.706884			−0.353442	−	0.935456i	$-0.614989\pi$
$727$	−19.0597			−0.706884			−0.353442	+	0.935456i	$0.614989\pi$
$728$		0			0
$729$	30.0086			1.11143
$730$	9.51453	−	16.4797i	0.352149	−	0.609939i
$731$	30.3436	+	52.5567i	1.12230	+	1.94388i
$732$	−1.18784	−	2.05740i	−0.0439039	−	0.0760437i
$733$	−15.1313	+	26.2082i	−0.558888	+	0.968022i	0.438702	+	0.898633i	$0.355438\pi$
$733$	−15.1313	+	26.2082i	−0.558888	+	0.968022i	−0.997590	+	0.0693896i	$0.977895\pi$
$734$	24.1642			0.891917
$735$		0			0
$736$	−2.91185			−0.107332
$737$	0.254512	−	0.440828i	0.00937508	−	0.0162381i
$738$	−2.58397	−	4.47556i	−0.0951171	−	0.164748i
$739$	3.44869	+	5.97331i	0.126862	+	0.219732i	0.922459	−	0.386094i	$-0.126176\pi$
$739$	3.44869	+	5.97331i	0.126862	+	0.219732i	−0.795597	+	0.605826i	$0.792843\pi$
$740$	5.09299	−	8.82132i	0.187222	−	0.324278i
$741$	−3.65279			−0.134189
$742$		0			0
$743$	0.440730			0.0161688			0.00808441	−	0.999967i	$-0.497427\pi$
$743$	0.440730			0.0161688			0.00808441	+	0.999967i	$0.497427\pi$
$744$	−6.27479	+	10.8683i	−0.230045	+	0.398450i
$745$	−4.91454	−	8.51224i	−0.180055	−	0.311864i
$746$	−12.9574	−	22.4429i	−0.474405	−	0.821693i
$747$	−0.711636	+	1.23259i	−0.0260374	+	0.0450981i
$748$	−1.70709			−0.0624173
$749$		0			0
$750$	−17.7778			−0.649153
$751$	9.03319	−	15.6459i	0.329626	−	0.570928i	−0.652812	−	0.757520i	$-0.726411\pi$
$751$	9.03319	−	15.6459i	0.329626	−	0.570928i	0.982438	+	0.186592i	$0.0597441\pi$
$752$	3.68329	+	6.37965i	0.134316	+	0.232642i
$753$	2.94318	+	5.09774i	0.107255	+	0.185772i
$754$	−0.179407	+	0.310743i	−0.00653363	+	0.0113166i
$755$	33.8329			1.23131
$756$		0			0
$757$	36.8491			1.33930			0.669651	−	0.742676i	$-0.266444\pi$
$757$	36.8491			1.33930			0.669651	+	0.742676i	$0.266444\pi$
$758$	−16.0422	+	27.7859i	−0.582679	+	1.00923i
$759$	−0.697234	−	1.20765i	−0.0253080	−	0.0438347i
$760$	−2.81067	−	4.86822i	−0.101954	−	0.176589i
$761$	−1.64675	+	2.85226i	−0.0596947	+	0.103394i	−0.894328	−	0.447411i	$-0.852346\pi$
$761$	−1.64675	+	2.85226i	−0.0596947	+	0.103394i	0.834634	+	0.550805i	$0.185679\pi$
$762$	2.48560			0.0900437
$763$		0			0
$764$	5.75063			0.208050
$765$	2.33124	−	4.03783i	0.0842862	−	0.145988i
$766$	−6.31402	−	10.9362i	−0.228135	−	0.395141i
$767$	3.51477	+	6.08776i	0.126911	+	0.219816i
$768$	−0.777479	+	1.34663i	−0.0280549	+	0.0485924i
$769$	−19.1752			−0.691476			−0.345738	−	0.938331i	$-0.612371\pi$
$769$	−19.1752			−0.691476			−0.345738	+	0.938331i	$0.612371\pi$
$770$		0			0
$771$	−48.9071			−1.76135
$772$	−10.6996	+	18.5322i	−0.385085	+	0.666987i
$773$	−17.9148	−	31.0294i	−0.644352	−	1.11605i	−0.984451	−	0.175661i	$-0.943794\pi$
$773$	−17.9148	−	31.0294i	−0.644352	−	1.11605i	0.340099	−	0.940390i	$-0.389539\pi$
$774$	−3.18664	−	5.51943i	−0.114542	−	0.198392i
$775$	11.7503	−	20.3522i	0.422084	−	0.731072i
$776$	13.1347			0.471507
$777$		0			0
$778$	0.341830			0.0122552
$779$	17.2681	−	29.9092i	0.618693	−	1.07161i
$780$	0.678448	+	1.17511i	0.0242923	+	0.0420756i
$781$	−1.45407	−	2.51852i	−0.0520306	−	0.0901196i
$782$	8.07002	−	13.9777i	0.288583	−	0.499841i
$783$	3.30963			0.118277
$784$		0			0
$785$	−27.8407			−0.993677
$786$	−1.38404	+	2.39723i	−0.0493672	+	0.0855065i
$787$	1.31604	+	2.27945i	0.0469119	+	0.0812538i	0.888528	−	0.458823i	$-0.151729\pi$
$787$	1.31604	+	2.27945i	0.0469119	+	0.0812538i	−0.841616	+	0.540076i	$0.818395\pi$
$788$	6.96562	+	12.0648i	0.248140	+	0.429791i
$789$	−11.5327	+	19.9751i	−0.410573	+	0.711134i
$790$	14.5036			0.516017
$791$		0			0
$792$	0.179276			0.00637029
$793$	0.461304	−	0.799002i	0.0163814	−	0.0283734i
$794$	4.39493	+	7.61224i	0.155970	+	0.270148i
$795$	−12.3007	−	21.3055i	−0.436262	−	0.755629i
$796$	−2.52566	+	4.37456i	−0.0895195	+	0.155052i
$797$	−20.2674			−0.717909			−0.358954	−	0.933355i	$-0.616867\pi$
$797$	−20.2674			−0.717909			−0.358954	+	0.933355i	$0.616867\pi$
$798$		0			0
$799$	−40.8321			−1.44453
$800$	1.45593	−	2.52174i	0.0514748	−	0.0891570i
$801$	−2.72335	−	4.71698i	−0.0962248	−	0.166666i
$802$	−4.74967	−	8.22667i	−0.167717	−	0.290494i
$803$	−2.02781	+	3.51227i	−0.0715599	+	0.123945i
$804$	2.57002			0.0906377
$805$		0			0
$806$	−4.87369			−0.171668
$807$	−9.71611	+	16.8288i	−0.342023	+	0.592402i
$808$	4.37316	+	7.57453i	0.153847	+	0.266471i
$809$	−20.3572	−	35.2597i	−0.715721	−	1.23966i	−0.962681	−	0.270639i	$-0.912765\pi$
$809$	−20.3572	−	35.2597i	−0.715721	−	1.23966i	0.246960	−	0.969026i	$-0.420568\pi$
$810$	4.99612	−	8.65353i	0.175546	−	0.304054i
$811$	−3.19806			−0.112299			−0.0561496	−	0.998422i	$-0.517882\pi$
$811$	−3.19806			−0.112299			−0.0561496	+	0.998422i	$0.517882\pi$
$812$		0			0
$813$	−6.77107			−0.237472
$814$	−1.08546	+	1.88007i	−0.0380453	+	0.0658963i
$815$	−0.0126141	−	0.0218482i	−0.000441851	−	0.000765309i
$816$	−4.30947	−	7.46422i	−0.150862	−	0.261300i
$817$	21.2957	−	36.8852i	0.745041	−	1.29045i
$818$	17.5526			0.613711
$819$		0			0
$820$	−12.8291			−0.448011
$821$	−5.88082	+	10.1859i	−0.205242	+	0.355490i	−0.950210	−	0.311611i	$-0.899132\pi$
$821$	−5.88082	+	10.1859i	−0.205242	+	0.355490i	0.744968	+	0.667100i	$0.232465\pi$
$822$	−0.281659	−	0.487848i	−0.00982400	−	0.0170157i
$823$	11.8847	+	20.5849i	0.414275	+	0.717545i	0.995352	−	0.0963034i	$-0.0307019\pi$
$823$	11.8847	+	20.5849i	0.414275	+	0.717545i	−0.581077	+	0.813848i	$0.697369\pi$
$824$	−2.38135	+	4.12463i	−0.0829584	+	0.143688i
$825$	1.39447			0.0485492
$826$		0			0
$827$	−14.2631			−0.495977			−0.247988	−	0.968763i	$-0.579770\pi$
$827$	−14.2631			−0.495977			−0.247988	+	0.968763i	$0.579770\pi$
$828$	−0.847503	+	1.46792i	−0.0294528	+	0.0510137i
$829$	−17.8530	−	30.9223i	−0.620061	−	1.07398i	−0.989474	−	0.144711i	$-0.953775\pi$
$829$	−17.8530	−	30.9223i	−0.620061	−	1.07398i	0.369413	−	0.929265i	$-0.379559\pi$
$830$	1.76659	+	3.05983i	0.0613194	+	0.106208i
$831$	10.2940	−	17.8298i	0.357096	−	0.618509i
$832$	−0.603875			−0.0209356
$833$		0			0
$834$	14.9186			0.516587
$835$	1.35690	−	2.35021i	0.0469573	−	0.0813325i
$836$	0.599031	+	1.03755i	0.0207179	+	0.0358845i
$837$	22.4770	+	38.9312i	0.776917	+	1.34566i
$838$	−9.54825	+	16.5381i	−0.329839	+	0.571298i
$839$	4.55496			0.157255			0.0786273	−	0.996904i	$-0.474946\pi$
$839$	4.55496			0.157255			0.0786273	+	0.996904i	$0.474946\pi$
$840$		0			0
$841$	−28.6469			−0.987826
$842$	9.95473	−	17.2421i	0.343063	−	0.594202i
$843$	−9.52512	−	16.4980i	−0.328063	−	0.568221i
$844$	0.807979	+	1.39946i	0.0278118	+	0.0481714i
$845$	9.12929	−	15.8124i	0.314057	−	0.543963i
$846$	4.28813			0.147429
$847$		0			0
$848$	10.9487			0.375980
$849$	−4.54138	+	7.86591i	−0.155860	+	0.269957i
$850$	8.07002	+	13.9777i	0.276800	+	0.479431i
$851$	−10.2627	−	17.7755i	−0.351801	−	0.609337i
$852$	7.34146	−	12.7158i	0.251514	−	0.435636i
$853$	38.7560			1.32698			0.663490	−	0.748185i	$-0.269074\pi$
$853$	38.7560			1.32698			0.663490	+	0.748185i	$0.269074\pi$
$854$		0			0
$855$	−3.27221			−0.111907
$856$	3.85958	−	6.68500i	0.131918	−	0.228488i
$857$	−2.53952	−	4.39858i	−0.0867485	−	0.150253i	0.819386	−	0.573242i	$-0.194314\pi$
$857$	−2.53952	−	4.39858i	−0.0867485	−	0.150253i	−0.906135	+	0.422989i	$0.860981\pi$
$858$	−0.144596	−	0.250448i	−0.00493643	−	0.00855015i
$859$	−9.46980	+	16.4022i	−0.323105	+	0.559635i	−0.981127	−	0.193364i	$-0.938060\pi$
$859$	−9.46980	+	16.4022i	−0.323105	+	0.559635i	0.658022	+	0.752999i	$0.271393\pi$
$860$	−15.8213			−0.539502
$861$		0			0
$862$	−6.21073			−0.211538
$863$	23.8460	−	41.3025i	0.811728	−	1.40595i	−0.0999263	−	0.994995i	$-0.531861\pi$
$863$	23.8460	−	41.3025i	0.811728	−	1.40595i	0.911654	−	0.410959i	$-0.134806\pi$
$864$	2.78501	+	4.82378i	0.0947480	+	0.164108i
$865$	−8.71960	−	15.1028i	−0.296475	−	0.513510i
$866$	−4.40581	+	7.63109i	−0.149716	+	0.259315i
$867$	21.3394			0.724725
$868$		0			0
$869$	−3.09113			−0.104859
$870$	0.667563	−	1.15625i	0.0226325	−	0.0392006i
$871$	0.499041	+	0.864364i	0.0169093	+	0.0292878i
$872$	4.29105	+	7.43232i	0.145313	+	0.251690i
$873$	3.82288	−	6.62142i	0.129385	−	0.224101i
$874$	−11.3274			−0.383154
$875$		0			0
$876$	−20.4765			−0.691837
$877$	12.6876	−	21.9756i	0.428430	−	0.742062i	−0.568304	−	0.822819i	$-0.692400\pi$
$877$	12.6876	−	21.9756i	0.428430	−	0.742062i	0.996734	+	0.0807563i	$0.0257335\pi$
$878$	−18.0836	−	31.3217i	−0.610292	−	1.05706i
$879$	3.19351	+	5.53133i	0.107715	+	0.186567i
$880$	0.222521	−	0.385418i	0.00750118	−	0.0129924i
$881$	−4.35258			−0.146642			−0.0733211	−	0.997308i	$-0.523360\pi$
$881$	−4.35258			−0.146642			−0.0733211	+	0.997308i	$0.523360\pi$
$882$		0			0
$883$	39.6088			1.33294			0.666471	−	0.745531i	$-0.267804\pi$
$883$	39.6088			1.33294			0.666471	+	0.745531i	$0.267804\pi$
$884$	1.67360	−	2.89877i	0.0562894	−	0.0974961i
$885$	−13.0782	−	22.6521i	−0.439620	−	0.761443i
$886$	−10.1441	−	17.5700i	−0.340796	−	0.590277i
$887$	−9.43094	+	16.3349i	−0.316660	+	0.548471i	−0.979789	−	0.200034i	$-0.935895\pi$
$887$	−9.43094	+	16.3349i	−0.316660	+	0.548471i	0.663129	+	0.748505i	$0.269228\pi$
$888$	−10.9608			−0.367819
$889$		0			0
$890$	−13.5211			−0.453229
$891$	−1.06481	+	1.84431i	−0.0356725	+	0.0617866i
$892$	−13.9209	−	24.1117i	−0.466105	−	0.807318i
$893$	14.3283	+	24.8174i	0.479479	+	0.830482i
$894$	−5.28836	+	9.15972i	−0.176869	+	0.306347i
$895$	−35.3032			−1.18006
$896$		0			0
$897$	2.73423			0.0912934
$898$	15.6724	−	27.1454i	0.522995	−	0.905854i
$899$	2.39775	+	4.15302i	0.0799694	+	0.138511i
$900$	−0.847503	−	1.46792i	−0.0282501	−	0.0489306i
$901$	−30.3436	+	52.5567i	−1.01089	+	1.75092i
$902$	2.73423			0.0910400
$903$		0			0
$904$	18.5646			0.617451
$905$	−5.67629	+	9.83163i	−0.188686	+	0.326814i
$906$	−18.2032	−	31.5289i	−0.604761	−	1.04748i
$907$	−13.7751	−	23.8591i	−0.457394	−	0.792230i	0.541428	−	0.840747i	$-0.317884\pi$
$907$	−13.7751	−	23.8591i	−0.457394	−	0.792230i	−0.998822	+	0.0485170i	$0.984550\pi$
$908$	−9.14460	+	15.8389i	−0.303474	+	0.525633i
$909$	5.09128			0.168867
$910$		0			0
$911$	−20.8576			−0.691042			−0.345521	−	0.938411i	$-0.612298\pi$
$911$	−20.8576			−0.691042			−0.345521	+	0.938411i	$0.612298\pi$
$912$	−3.02446	+	5.23852i	−0.100150	+	0.173465i
$913$	−0.376510	−	0.652135i	−0.0124607	−	0.0215825i
$914$	−4.39158	−	7.60643i	−0.145260	−	0.251598i
$915$	−1.71648	+	2.97303i	−0.0567451	+	0.0982854i
$916$	20.5375			0.678578
$917$		0			0
$918$	−30.8740			−1.01899
$919$	−19.0618	+	33.0161i	−0.628792	+	1.08910i	0.359003	+	0.933336i	$0.383117\pi$
$919$	−19.0618	+	33.0161i	−0.628792	+	1.08910i	−0.987795	+	0.155763i	$0.950217\pi$
$920$	2.10388	+	3.64402i	0.0693627	+	0.120140i
$921$	−22.8587	−	39.5924i	−0.753219	−	1.30461i
$922$	8.04838	−	13.9402i	0.265059	−	0.459096i
$923$	5.70218			0.187690
$924$		0			0
$925$	20.5254			0.674872
$926$	0.844814	−	1.46326i	0.0277623	−	0.0480857i
$927$	1.38620	+	2.40097i	0.0455287	+	0.0788581i
$928$	0.297093	+	0.514581i	0.00975257	+	0.0168919i
$929$	−0.143637	+	0.248786i	−0.00471256	+	0.00816240i	−0.868372	−	0.495913i	$-0.834833\pi$
$929$	−0.143637	+	0.248786i	−0.00471256	+	0.00816240i	0.863660	+	0.504076i	$0.168167\pi$
$930$	18.1347			0.594659
$931$		0			0
$932$	−6.44504			−0.211114
$933$	−17.9182	+	31.0352i	−0.586615	+	1.01605i
$934$	16.7811	+	29.0658i	0.549095	+	0.951061i
$935$	1.23341	+	2.13632i	0.0403367	+	0.0698652i
$936$	−0.175760	+	0.304424i	−0.00574488	+	0.00995042i
$937$	−29.3773			−0.959716			−0.479858	−	0.877346i	$-0.659312\pi$
$937$	−29.3773			−0.959716			−0.479858	+	0.877346i	$0.659312\pi$
$938$		0			0
$939$	−24.7131			−0.806480
$940$	5.32251	−	9.21886i	0.173601	−	0.300686i
$941$	−12.6196	−	21.8578i	−0.411387	−	0.712544i	0.583654	−	0.812002i	$-0.301622\pi$
$941$	−12.6196	−	21.8578i	−0.411387	−	0.712544i	−0.995042	+	0.0994584i	$0.968289\pi$
$942$	14.9792	+	25.9447i	0.488048	+	0.845325i
$943$	−12.9257	+	22.3880i	−0.420919	+	0.729054i
$944$	11.6407			0.378873
$945$		0			0
$946$	3.37196			0.109632
$947$	16.6887	−	28.9056i	0.542309	−	0.939307i	−0.456462	−	0.889743i	$-0.650884\pi$
$947$	16.6887	−	28.9056i	0.542309	−	0.939307i	0.998771	−	0.0495637i	$-0.0157831\pi$
$948$	−7.80343	−	13.5159i	−0.253444	−	0.438977i
$949$	−3.97607	−	6.88676i	−0.129069	−	0.223554i
$950$	5.66368	−	9.80978i	0.183754	−	0.318271i
$951$	−32.4983			−1.05383
$952$		0			0
$953$	29.0683			0.941614			0.470807	−	0.882236i	$-0.343963\pi$
$953$	29.0683			0.941614			0.470807	+	0.882236i	$0.343963\pi$
$954$	3.18664	−	5.51943i	0.103171	−	0.178698i
$955$	−4.15495	−	7.19658i	−0.134451	−	0.232876i
$956$	7.20775	+	12.4842i	0.233115	+	0.403768i
$957$	−0.142276	+	0.246430i	−0.00459914	+	0.00796594i
$958$	−7.94331			−0.256637
$959$		0			0
$960$	2.24698			0.0725210
$961$	−17.0680	+	29.5626i	−0.550581	+	0.953634i
$962$	−2.12833	−	3.68638i	−0.0686202	−	0.118854i
$963$	−2.24668	−	3.89137i	−0.0723984	−	0.125398i
$964$	0.169719	−	0.293961i	0.00546627	−	0.00946786i
$965$	30.9226			0.995434
$966$		0			0
$967$	−45.7036			−1.46973			−0.734865	−	0.678214i	$-0.762754\pi$
$967$	−45.7036			−1.46973			−0.734865	+	0.678214i	$0.762754\pi$
$968$	5.45257	−	9.44414i	0.175252	−	0.303546i
$969$	−16.7642	−	29.0364i	−0.538544	−	0.932785i
$970$	−9.49007	−	16.4373i	−0.304708	−	0.527770i
$971$	15.4943	−	26.8368i	0.497234	−	0.861235i	−0.502761	−	0.864426i	$-0.667682\pi$
$971$	15.4943	−	26.8368i	0.497234	−	0.861235i	0.999995	+	0.00319062i	$0.00101561\pi$
$972$	5.95779			0.191096
$973$		0			0
$974$	35.8998			1.15030
$975$	−1.36712	+	2.36792i	−0.0437828	+	0.0758340i
$976$	−0.763906	−	1.32312i	−0.0244520	−	0.0423521i
$977$	29.3240	+	50.7907i	0.938158	+	1.62494i	0.768903	+	0.639365i	$0.220803\pi$
$977$	29.3240	+	50.7907i	0.938158	+	1.62494i	0.169255	+	0.985572i	$0.445864\pi$
$978$	−0.0135735	+	0.0235101i	−0.000434034	+	0.000751769i
$979$	2.88172			0.0921003
$980$		0			0
$981$	4.99569			0.159500
$982$	3.08546	−	5.34417i	0.0984609	−	0.170539i
$983$	−0.666071	−	1.15367i	−0.0212444	−	0.0367963i	0.855208	−	0.518285i	$-0.173429\pi$
$983$	−0.666071	−	1.15367i	−0.0212444	−	0.0367963i	−0.876452	+	0.481489i	$0.840096\pi$
$984$	6.90246	+	11.9554i	0.220042	+	0.381125i
$985$	10.0656	−	17.4341i	0.320717	−	0.555498i
$986$	−3.29350			−0.104887
$987$		0			0
$988$	−2.34913			−0.0747357
$989$	−15.9405	+	27.6097i	−0.506878	+	0.877939i
$990$	−0.129531	−	0.224354i	−0.00411675	−	0.00713042i
$991$	28.2563	+	48.9413i	0.897591	+	1.55467i	0.830565	+	0.556922i	$0.188018\pi$
$991$	28.2563	+	48.9413i	0.897591	+	1.55467i	0.0670261	+	0.997751i	$0.478649\pi$
$992$	−4.03534	+	6.98942i	−0.128122	+	0.221914i
$993$	19.1451			0.607551
$994$		0			0
$995$	7.29935			0.231405
$996$	1.90097	−	3.29257i	0.0602345	−	0.104329i
$997$	−27.6516	−	47.8940i	−0.875735	−	1.51682i	−0.855978	−	0.517012i	$-0.827044\pi$
$997$	−27.6516	−	47.8940i	−0.875735	−	1.51682i	−0.0197570	−	0.999805i	$-0.506289\pi$
$998$	−2.59837	−	4.50050i	−0.0822499	−	0.142461i
$999$	−19.6313	+	34.0024i	−0.621107	+	1.07579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.c.a.667.2		6
7.2	even	3		686.2.a.d.1.2	yes	3
7.3	odd	6		686.2.c.b.361.2		6
7.4	even	3	inner	686.2.c.a.361.2		6
7.5	odd	6		686.2.a.c.1.2	✓	3
7.6	odd	2		686.2.c.b.667.2		6
21.2	odd	6		6174.2.a.c.1.2		3
21.5	even	6		6174.2.a.e.1.2		3
28.19	even	6		5488.2.a.f.1.2		3
28.23	odd	6		5488.2.a.a.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
686.2.a.c.1.2	✓	3	7.5	odd	6
686.2.a.d.1.2	yes	3	7.2	even	3
686.2.c.a.361.2		6	7.4	even	3	inner
686.2.c.a.667.2		6	1.1	even	1	trivial
686.2.c.b.361.2		6	7.3	odd	6
686.2.c.b.667.2		6	7.6	odd	2
5488.2.a.a.1.2		3	28.23	odd	6
5488.2.a.f.1.2		3	28.19	even	6
6174.2.a.c.1.2		3	21.2	odd	6
6174.2.a.e.1.2		3	21.5	even	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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.777479 - 1.34663i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.722521 + 1.25144i) q^{5} +1.55496 q^{6} +1.00000 q^{8} +(0.291053 - 0.504118i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.777479 - 1.34663i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.722521 + 1.25144i) q^{5} +1.55496 q^{6} +1.00000 q^{8} +(0.291053 - 0.504118i) q^{9} +(-0.722521 - 1.25144i) q^{10} +(0.153989 + 0.266717i) q^{11} +(-0.777479 + 1.34663i) q^{12} -0.603875 q^{13} +2.24698 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.77144 - 4.80027i) q^{17} +(0.291053 + 0.504118i) q^{18} +(-1.94504 + 3.36891i) q^{19} +1.44504 q^{20} -0.307979 q^{22} +(1.45593 - 2.52174i) q^{23} +(-0.777479 - 1.34663i) q^{24} +(1.45593 + 2.52174i) q^{25} +(0.301938 - 0.522971i) q^{26} -5.57002 q^{27} -0.594187 q^{29} +(-1.12349 + 1.94594i) q^{30} +(-4.03534 - 6.98942i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.239447 - 0.414734i) q^{33} +5.54288 q^{34} -0.582105 q^{36} +(3.52446 - 6.10454i) q^{37} +(-1.94504 - 3.36891i) q^{38} +(0.469501 + 0.813199i) q^{39} +(-0.722521 + 1.25144i) q^{40} -8.87800 q^{41} -10.9487 q^{43} +(0.153989 - 0.266717i) q^{44} +(0.420583 + 0.728471i) q^{45} +(1.45593 + 2.52174i) q^{46} +(3.68329 - 6.37965i) q^{47} +1.55496 q^{48} -2.91185 q^{50} +(-4.30947 + 7.46422i) q^{51} +(0.301938 + 0.522971i) q^{52} +(-5.47434 - 9.48184i) q^{53} +(2.78501 - 4.82378i) q^{54} -0.445042 q^{55} +6.04892 q^{57} +(0.297093 - 0.514581i) q^{58} +(-5.82036 - 10.0812i) q^{59} +(-1.12349 - 1.94594i) q^{60} +(-0.763906 + 1.32312i) q^{61} +8.07069 q^{62} +1.00000 q^{64} +(0.436313 - 0.755716i) q^{65} +(0.239447 + 0.414734i) q^{66} +(-0.826396 - 1.43136i) q^{67} +(-2.77144 + 4.80027i) q^{68} -4.52781 q^{69} -9.44265 q^{71} +(0.291053 - 0.504118i) q^{72} +(6.58426 + 11.4043i) q^{73} +(3.52446 + 6.10454i) q^{74} +(2.26391 - 3.92120i) q^{75} +3.89008 q^{76} -0.939001 q^{78} +(-5.01842 + 8.69215i) q^{79} +(-0.722521 - 1.25144i) q^{80} +(3.45742 + 5.98843i) q^{81} +(4.43900 - 7.68858i) q^{82} -2.44504 q^{83} +8.00969 q^{85} +(5.47434 - 9.48184i) q^{86} +(0.461968 + 0.800152i) q^{87} +(0.153989 + 0.266717i) q^{88} +(4.67845 - 8.10331i) q^{89} -0.841166 q^{90} -2.91185 q^{92} +(-6.27479 + 10.8683i) q^{93} +(3.68329 + 6.37965i) q^{94} +(-2.81067 - 4.86822i) q^{95} +(-0.777479 + 1.34663i) q^{96} +13.1347 q^{97} +0.179276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 5 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 5 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} - 5 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} + 6 q^{8} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 5 q^{12} + 14 q^{13} + 4 q^{15} - 3 q^{16} + 2 q^{17} - 4 q^{18} - 11 q^{19} + 8 q^{20} - 12 q^{22} + 5 q^{23} - 5 q^{24} + 5 q^{25} - 7 q^{26} + 16 q^{27} - 30 q^{29} - 2 q^{30} - 12 q^{31} - 3 q^{32} + 17 q^{33} - 4 q^{34} + 8 q^{36} + 12 q^{37} - 11 q^{38} - 7 q^{39} - 4 q^{40} - 14 q^{41} - 2 q^{43} + 6 q^{44} + 11 q^{45} + 5 q^{46} - 4 q^{47} + 10 q^{48} - 10 q^{50} + 8 q^{51} - 7 q^{52} - q^{53} - 8 q^{54} - 2 q^{55} + 18 q^{57} + 15 q^{58} + 2 q^{59} - 2 q^{60} - 11 q^{61} + 24 q^{62} + 6 q^{64} - 14 q^{65} + 17 q^{66} + 13 q^{67} + 2 q^{68} - 40 q^{69} + 26 q^{71} - 4 q^{72} + 9 q^{73} + 12 q^{74} + 20 q^{75} + 22 q^{76} + 14 q^{78} - 2 q^{79} - 4 q^{80} - 27 q^{81} + 7 q^{82} - 14 q^{83} + 4 q^{85} + q^{86} + 18 q^{87} + 6 q^{88} + 24 q^{89} - 22 q^{90} - 10 q^{92} - 41 q^{93} - 4 q^{94} - 24 q^{95} - 5 q^{96} - 14 q^{97} - 72 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 5 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 + 6 * q^8 - 4 * q^9 - 4 * q^10 + 6 * q^11 - 5 * q^12 + 14 * q^13 + 4 * q^15 - 3 * q^16 + 2 * q^17 - 4 * q^18 - 11 * q^19 + 8 * q^20 - 12 * q^22 + 5 * q^23 - 5 * q^24 + 5 * q^25 - 7 * q^26 + 16 * q^27 - 30 * q^29 - 2 * q^30 - 12 * q^31 - 3 * q^32 + 17 * q^33 - 4 * q^34 + 8 * q^36 + 12 * q^37 - 11 * q^38 - 7 * q^39 - 4 * q^40 - 14 * q^41 - 2 * q^43 + 6 * q^44 + 11 * q^45 + 5 * q^46 - 4 * q^47 + 10 * q^48 - 10 * q^50 + 8 * q^51 - 7 * q^52 - q^53 - 8 * q^54 - 2 * q^55 + 18 * q^57 + 15 * q^58 + 2 * q^59 - 2 * q^60 - 11 * q^61 + 24 * q^62 + 6 * q^64 - 14 * q^65 + 17 * q^66 + 13 * q^67 + 2 * q^68 - 40 * q^69 + 26 * q^71 - 4 * q^72 + 9 * q^73 + 12 * q^74 + 20 * q^75 + 22 * q^76 + 14 * q^78 - 2 * q^79 - 4 * q^80 - 27 * q^81 + 7 * q^82 - 14 * q^83 + 4 * q^85 + q^86 + 18 * q^87 + 6 * q^88 + 24 * q^89 - 22 * q^90 - 10 * q^92 - 41 * q^93 - 4 * q^94 - 24 * q^95 - 5 * q^96 - 14 * q^97 - 72 * q^99

Introduction

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