LMFDB - Embedded newform 1338.2.e.b.1075.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1338,2,Mod(931,1338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1338, 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("1338.931");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1338 = 2 \cdot 3 \cdot 223$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^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			1075.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1338.1075
Dual form			1338.2.e.b.931.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{6} +3.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} -5.00000 q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(1.50000 + 2.59808i) q^{21} +(2.00000 - 3.46410i) q^{22} +(4.00000 + 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} -4.00000 q^{26} -1.00000 q^{27} +3.00000 q^{28} +(-2.50000 - 4.33013i) q^{31} -1.00000 q^{32} -4.00000 q^{33} +5.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.00000 + 5.19615i) q^{37} +(1.00000 + 1.73205i) q^{38} +(2.00000 + 3.46410i) q^{39} +7.00000 q^{41} +(-1.50000 - 2.59808i) q^{42} +(-3.00000 - 5.19615i) q^{43} +(-2.00000 + 3.46410i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(-4.50000 + 7.79423i) q^{47} +(0.500000 + 0.866025i) q^{48} +2.00000 q^{49} +(-2.50000 - 4.33013i) q^{50} +(-2.50000 - 4.33013i) q^{51} +4.00000 q^{52} +(6.00000 - 10.3923i) q^{53} +1.00000 q^{54} -3.00000 q^{56} +(1.00000 - 1.73205i) q^{57} +8.00000 q^{59} +(7.00000 + 12.1244i) q^{61} +(2.50000 + 4.33013i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +4.00000 q^{66} -5.00000 q^{68} +(-4.00000 + 6.92820i) q^{69} +(-0.500000 - 0.866025i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(3.00000 - 5.19615i) q^{74} +(-2.50000 + 4.33013i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(-2.00000 - 3.46410i) q^{78} +(-0.500000 - 0.866025i) q^{81} -7.00000 q^{82} +(-4.00000 + 6.92820i) q^{83} +(1.50000 + 2.59808i) q^{84} +(3.00000 + 5.19615i) q^{86} +(2.00000 - 3.46410i) q^{88} +(-6.50000 - 11.2583i) q^{89} +12.0000 q^{91} +(4.00000 + 6.92820i) q^{92} +(2.50000 - 4.33013i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{96} +(-2.50000 + 4.33013i) q^{97} -2.00000 q^{98} +(-2.00000 - 3.46410i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 6 q^{7} - 2 q^{8} - q^{9} - 4 q^{11} + q^{12} + 8 q^{13} - 6 q^{14} + 2 q^{16} - 10 q^{17} + q^{18} - 2 q^{19} + 3 q^{21} + 4 q^{22} + 8 q^{23} - q^{24} + 5 q^{25}+ \cdots - 4 q^{99}+O(q^{100})$ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 6 * q^7 - 2 * q^8 - q^9 - 4 * q^11 + q^12 + 8 * q^13 - 6 * q^14 + 2 * q^16 - 10 * q^17 + q^18 - 2 * q^19 + 3 * q^21 + 4 * q^22 + 8 * q^23 - q^24 + 5 * q^25 - 8 * q^26 - 2 * q^27 + 6 * q^28 - 5 * q^31 - 2 * q^32 - 8 * q^33 + 10 * q^34 - q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 + 14 * q^41 - 3 * q^42 - 6 * q^43 - 4 * q^44 - 8 * q^46 - 9 * q^47 + q^48 + 4 * q^49 - 5 * q^50 - 5 * q^51 + 8 * q^52 + 12 * q^53 + 2 * q^54 - 6 * q^56 + 2 * q^57 + 16 * q^59 + 14 * q^61 + 5 * q^62 - 3 * q^63 + 2 * q^64 + 8 * q^66 - 10 * q^68 - 8 * q^69 - q^71 + q^72 + 2 * q^73 + 6 * q^74 - 5 * q^75 - 2 * q^76 - 12 * q^77 - 4 * q^78 - q^81 - 14 * q^82 - 8 * q^83 + 3 * q^84 + 6 * q^86 + 4 * q^88 - 13 * q^89 + 24 * q^91 + 8 * q^92 + 5 * q^93 + 9 * q^94 - q^96 - 5 * q^97 - 4 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$ .

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	−3.00000			−0.801784
$15$		0			0
$16$	1.00000			0.250000
$17$	−5.00000			−1.21268			−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000			−1.21268			−0.606339	+	0.795206i	$0.707363\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$	1.50000	+	2.59808i	0.327327	+	0.566947i
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	−4.00000			−0.784465
$27$	−1.00000			−0.192450
$28$	3.00000			0.566947
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−1.00000			−0.176777
$33$	−4.00000			−0.696311
$34$	5.00000			0.857493
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$	−1.50000	−	2.59808i	−0.231455	−	0.400892i
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$		0			0
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	0.325150	+	0.945662i	$0.394585\pi$
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	−0.981543	+	0.191243i	$0.938748\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	2.00000			0.285714
$50$	−2.50000	−	4.33013i	−0.353553	−	0.612372i
$51$	−2.50000	−	4.33013i	−0.350070	−	0.606339i
$52$	4.00000			0.554700
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−3.00000			−0.400892
$57$	1.00000	−	1.73205i	0.132453	−	0.229416i
$58$		0			0
$59$	8.00000			1.04151			0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000			1.04151			0.520756	+	0.853706i	$0.325650\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	2.50000	+	4.33013i	0.317500	+	0.549927i
$63$	−1.50000	+	2.59808i	−0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.00000			0.492366
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$	−5.00000			−0.606339
$69$	−4.00000	+	6.92820i	−0.481543	+	0.834058i
$70$		0			0
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	0.834830	−	0.550508i	$-0.185566\pi$
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$	−2.50000	+	4.33013i	−0.288675	+	0.500000i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−6.00000	+	10.3923i	−0.683763	+	1.18431i
$78$	−2.00000	−	3.46410i	−0.226455	−	0.392232i
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.00000			−0.773021
$83$	−4.00000	+	6.92820i	−0.439057	+	0.760469i	−0.997617	−	0.0689950i	$-0.978021\pi$
$83$	−4.00000	+	6.92820i	−0.439057	+	0.760469i	0.558560	+	0.829464i	$0.311354\pi$
$84$	1.50000	+	2.59808i	0.163663	+	0.283473i
$85$		0			0
$86$	3.00000	+	5.19615i	0.323498	+	0.560316i
$87$		0			0
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	−6.50000	−	11.2583i	−0.688999	−	1.19338i	−0.972162	−	0.234309i	$-0.924717\pi$
$89$	−6.50000	−	11.2583i	−0.688999	−	1.19338i	0.283164	−	0.959072i	$-0.408616\pi$
$90$		0			0
$91$	12.0000			1.25794
$92$	4.00000	+	6.92820i	0.417029	+	0.722315i
$93$	2.50000	−	4.33013i	0.259238	−	0.449013i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$		0			0
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$	−2.00000			−0.202031
$99$	−2.00000	−	3.46410i	−0.201008	−	0.348155i
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	8.00000	+	13.8564i	0.796030	+	1.37876i	0.922183	+	0.386753i	$0.126403\pi$
$101$	8.00000	+	13.8564i	0.796030	+	1.37876i	−0.126153	+	0.992011i	$0.540263\pi$
$102$	2.50000	+	4.33013i	0.247537	+	0.428746i
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−1.00000			−0.0962250
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	3.00000			0.283473
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	0.927914	−	0.372794i	$-0.121600\pi$
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	−0.786806	+	0.617200i	$0.788267\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$		0			0
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	−8.00000			−0.736460
$119$	−15.0000			−1.37505
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−7.00000	−	12.1244i	−0.633750	−	1.09769i
$123$	3.50000	+	6.06218i	0.315584	+	0.546608i
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$		0			0
$126$	1.50000	−	2.59808i	0.133631	−	0.231455i
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	0.999905	−	0.0137486i	$-0.00437646\pi$
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	−0.511859	+	0.859069i	$0.671043\pi$
$128$	−1.00000			−0.0883883
$129$	3.00000	−	5.19615i	0.264135	−	0.457496i
$130$		0			0
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$	−4.00000			−0.348155
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$		0			0
$135$		0			0
$136$	5.00000			0.428746
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	7.00000	+	12.1244i	0.593732	+	1.02837i	0.993724	+	0.111856i	$0.0356795\pi$
$139$	7.00000	+	12.1244i	0.593732	+	1.02837i	−0.399992	+	0.916519i	$0.630987\pi$
$140$		0			0
$141$	−9.00000			−0.757937
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$	−8.00000	+	13.8564i	−0.668994	+	1.15873i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	1.00000	+	1.73205i	0.0824786	+	0.142857i
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	0.326411	+	0.945228i	$0.394160\pi$
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	−0.981797	+	0.189933i	$0.939173\pi$
$150$	2.50000	−	4.33013i	0.204124	−	0.353553i
$151$	−1.50000	+	2.59808i	−0.122068	+	0.211428i	−0.920583	−	0.390547i	$-0.872286\pi$
$151$	−1.50000	+	2.59808i	−0.122068	+	0.211428i	0.798515	+	0.601975i	$0.205619\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	2.50000	−	4.33013i	0.202113	−	0.350070i
$154$	6.00000	−	10.3923i	0.483494	−	0.837436i
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$	12.0000			0.951662
$160$		0			0
$161$	12.0000	+	20.7846i	0.945732	+	1.63806i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−2.00000			−0.156652			−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000			−0.156652			−0.0783260	+	0.996928i	$0.524958\pi$
$164$	7.00000			0.546608
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$	20.0000			1.54765			0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000			1.54765			0.773823	+	0.633402i	$0.218342\pi$
$168$	−1.50000	−	2.59808i	−0.115728	−	0.200446i
$169$	3.00000			0.230769
$170$		0			0
$171$	2.00000			0.152944
$172$	−3.00000	−	5.19615i	−0.228748	−	0.396203i
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	0.825505	−	0.564396i	$-0.190891\pi$
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	−0.901533	+	0.432710i	$0.857557\pi$
$174$		0			0
$175$	7.50000	+	12.9904i	0.566947	+	0.981981i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$	4.00000	+	6.92820i	0.300658	+	0.520756i
$178$	6.50000	+	11.2583i	0.487196	+	0.843848i
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	−0.395175	−	0.918606i	$-0.629316\pi$
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	0.993124	−	0.117071i	$-0.0373504\pi$
$180$		0			0
$181$	3.00000	+	5.19615i	0.222988	+	0.386227i	0.955714	−	0.294297i	$-0.0950855\pi$
$181$	3.00000	+	5.19615i	0.222988	+	0.386227i	−0.732726	+	0.680524i	$0.761752\pi$
$182$	−12.0000			−0.889499
$183$	−7.00000	+	12.1244i	−0.517455	+	0.896258i
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$		0			0
$186$	−2.50000	+	4.33013i	−0.183309	+	0.317500i
$187$	10.0000	−	17.3205i	0.731272	−	1.26660i
$188$	−4.50000	+	7.79423i	−0.328196	+	0.568453i
$189$	−3.00000			−0.218218
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	2.50000	−	4.33013i	0.179490	−	0.310885i
$195$		0			0
$196$	2.00000			0.142857
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$	−2.50000	−	4.33013i	−0.176777	−	0.306186i
$201$		0			0
$202$	−8.00000	−	13.8564i	−0.562878	−	0.974933i
$203$		0			0
$204$	−2.50000	−	4.33013i	−0.175035	−	0.303170i
$205$		0			0
$206$	8.00000			0.557386
$207$	−8.00000			−0.556038
$208$	4.00000			0.277350
$209$	8.00000			0.553372
$210$		0			0
$211$	−3.00000	−	5.19615i	−0.206529	−	0.357718i	0.744090	−	0.668079i	$-0.232883\pi$
$211$	−3.00000	−	5.19615i	−0.206529	−	0.357718i	−0.950619	+	0.310361i	$0.899550\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	0.500000	−	0.866025i	0.0342594	−	0.0593391i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−7.50000	−	12.9904i	−0.509133	−	0.881845i
$218$	−2.00000	+	3.46410i	−0.135457	+	0.234619i
$219$	2.00000			0.135147
$220$		0			0
$221$	−20.0000			−1.34535
$222$	6.00000			0.402694
$223$	14.0000	−	5.19615i	0.937509	−	0.347960i
$223$	14.0000	−	5.19615i	0.937509	−	0.347960i
$224$	−3.00000			−0.200446
$225$	−5.00000			−0.333333
$226$	−1.50000	−	2.59808i	−0.0997785	−	0.172821i
$227$	−2.00000			−0.132745			−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000			−0.132745			−0.0663723	+	0.997795i	$0.521143\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$		0			0
$231$	−12.0000			−0.789542
$232$		0			0
$233$	13.0000	−	22.5167i	0.851658	−	1.47512i	−0.0280525	−	0.999606i	$-0.508931\pi$
$233$	13.0000	−	22.5167i	0.851658	−	1.47512i	0.879711	−	0.475509i	$-0.157736\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	8.00000			0.520756
$237$		0			0
$238$	15.0000			0.972306
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$		0			0
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	−0.211360	−	0.977408i	$-0.567789\pi$
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	0.952141	−	0.305661i	$-0.0988773\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$		0			0
$246$	−3.50000	−	6.06218i	−0.223152	−	0.386510i
$247$	−4.00000	−	6.92820i	−0.254514	−	0.440831i
$248$	2.50000	+	4.33013i	0.158750	+	0.274963i
$249$	−8.00000			−0.506979
$250$		0			0
$251$	−14.0000			−0.883672			−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000			−0.883672			−0.441836	+	0.897096i	$0.645673\pi$
$252$	−1.50000	+	2.59808i	−0.0944911	+	0.163663i
$253$	−32.0000			−2.01182
$254$	−5.50000	−	9.52628i	−0.345101	−	0.597732i
$255$		0			0
$256$	1.00000			0.0625000
$257$	21.0000			1.30994			0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000			1.30994			0.654972	+	0.755653i	$0.272680\pi$
$258$	−3.00000	+	5.19615i	−0.186772	+	0.323498i
$259$	−9.00000	+	15.5885i	−0.559233	+	0.968620i
$260$		0			0
$261$		0			0
$262$	7.00000	+	12.1244i	0.432461	+	0.749045i
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$	4.00000			0.246183
$265$		0			0
$266$	3.00000	+	5.19615i	0.183942	+	0.318597i
$267$	6.50000	−	11.2583i	0.397794	−	0.688999i
$268$		0			0
$269$	−10.0000	−	17.3205i	−0.609711	−	1.05605i	−0.991288	−	0.131713i	$-0.957952\pi$
$269$	−10.0000	−	17.3205i	−0.609711	−	1.05605i	0.381577	−	0.924337i	$-0.375381\pi$
$270$		0			0
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	0.943197	+	0.332233i	$0.107802\pi$
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	−0.183876	+	0.982949i	$0.558865\pi$
$272$	−5.00000			−0.303170
$273$	6.00000	+	10.3923i	0.363137	+	0.628971i
$274$	5.00000	+	8.66025i	0.302061	+	0.523185i
$275$	−20.0000			−1.20605
$276$	−4.00000	+	6.92820i	−0.240772	+	0.417029i
$277$	−8.00000			−0.480673			−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000			−0.480673			−0.240337	+	0.970690i	$0.577258\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$	5.00000			0.299342
$280$		0			0
$281$	3.50000	−	6.06218i	0.208792	−	0.361639i	−0.742542	−	0.669800i	$-0.766380\pi$
$281$	3.50000	−	6.06218i	0.208792	−	0.361639i	0.951334	+	0.308160i	$0.0997133\pi$
$282$	9.00000			0.535942
$283$	−6.00000			−0.356663			−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000			−0.356663			−0.178331	+	0.983970i	$0.557070\pi$
$284$	−0.500000	−	0.866025i	−0.0296695	−	0.0513892i
$285$		0			0
$286$	8.00000	−	13.8564i	0.473050	−	0.819346i
$287$	21.0000			1.23959
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	8.00000			0.470588
$290$		0			0
$291$	−5.00000			−0.293105
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	−0.267052	−	0.963682i	$-0.586049\pi$
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	0.968099	−	0.250568i	$-0.0806172\pi$
$294$	−1.00000	−	1.73205i	−0.0583212	−	0.101015i
$295$		0			0
$296$	3.00000	−	5.19615i	0.174371	−	0.302020i
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$	8.00000	−	13.8564i	0.463428	−	0.802680i
$299$	16.0000	+	27.7128i	0.925304	+	1.60267i
$300$	−2.50000	+	4.33013i	−0.144338	+	0.250000i
$301$	−9.00000	−	15.5885i	−0.518751	−	0.898504i
$302$	1.50000	−	2.59808i	0.0863153	−	0.149502i
$303$	−8.00000	+	13.8564i	−0.459588	+	0.796030i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$		0			0
$306$	−2.50000	+	4.33013i	−0.142915	+	0.247537i
$307$	4.00000	+	6.92820i	0.228292	+	0.395413i	0.957302	−	0.289090i	$-0.0933526\pi$
$307$	4.00000	+	6.92820i	0.228292	+	0.395413i	−0.729010	+	0.684503i	$0.760019\pi$
$308$	−6.00000	+	10.3923i	−0.341882	+	0.592157i
$309$	−4.00000	−	6.92820i	−0.227552	−	0.394132i
$310$		0			0
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	−0.709771	−	0.704433i	$-0.751201\pi$
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	0.964942	+	0.262463i	$0.0845347\pi$
$312$	−2.00000	−	3.46410i	−0.113228	−	0.196116i
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	0.621757	−	0.783210i	$-0.286419\pi$
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	−0.989158	+	0.146852i	$0.953086\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$		0			0
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$	−12.0000			−0.672927
$319$		0			0
$320$		0			0
$321$	−12.0000			−0.669775
$322$	−12.0000	−	20.7846i	−0.668734	−	1.15828i
$323$	5.00000	+	8.66025i	0.278207	+	0.481869i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	10.0000	+	17.3205i	0.554700	+	0.960769i
$326$	2.00000			0.110770
$327$	4.00000			0.221201
$328$	−7.00000			−0.386510
$329$	−13.5000	+	23.3827i	−0.744279	+	1.28913i
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$	−4.00000	+	6.92820i	−0.219529	+	0.380235i
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$	−20.0000			−1.09435
$335$		0			0
$336$	1.50000	+	2.59808i	0.0818317	+	0.141737i
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	−0.293783	−	0.955872i	$-0.594914\pi$
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	0.974701	−	0.223513i	$-0.0717525\pi$
$338$	−3.00000			−0.163178
$339$	−1.50000	+	2.59808i	−0.0814688	+	0.141108i
$340$		0			0
$341$	20.0000			1.08306
$342$	−2.00000			−0.108148
$343$	−15.0000			−0.809924
$344$	3.00000	+	5.19615i	0.161749	+	0.280158i
$345$		0			0
$346$	1.00000	+	1.73205i	0.0537603	+	0.0931156i
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	0.807337	−	0.590091i	$-0.200908\pi$
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	−0.914702	+	0.404128i	$0.867575\pi$
$348$		0			0
$349$	12.0000	−	20.7846i	0.642345	−	1.11257i	−0.342563	−	0.939495i	$-0.611295\pi$
$349$	12.0000	−	20.7846i	0.642345	−	1.11257i	0.984908	−	0.173080i	$-0.0553718\pi$
$350$	−7.50000	−	12.9904i	−0.400892	−	0.694365i
$351$	−4.00000			−0.213504
$352$	2.00000	−	3.46410i	0.106600	−	0.184637i
$353$	11.5000	−	19.9186i	0.612083	−	1.06016i	−0.378806	−	0.925476i	$-0.623665\pi$
$353$	11.5000	−	19.9186i	0.612083	−	1.06016i	0.990889	−	0.134683i	$-0.0430016\pi$
$354$	−4.00000	−	6.92820i	−0.212598	−	0.368230i
$355$		0			0
$356$	−6.50000	−	11.2583i	−0.344499	−	0.596690i
$357$	−7.50000	−	12.9904i	−0.396942	−	0.687524i
$358$	−8.00000	+	13.8564i	−0.422813	+	0.732334i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−3.00000	−	5.19615i	−0.157676	−	0.273104i
$363$	2.50000	−	4.33013i	0.131216	−	0.227273i
$364$	12.0000			0.628971
$365$		0			0
$366$	7.00000	−	12.1244i	0.365896	−	0.633750i
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	−0.852680	−	0.522433i	$-0.825025\pi$
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	0.878780	+	0.477227i	$0.158358\pi$
$368$	4.00000	+	6.92820i	0.208514	+	0.361158i
$369$	−3.50000	+	6.06218i	−0.182203	+	0.315584i
$370$		0			0
$371$	18.0000	−	31.1769i	0.934513	−	1.61862i
$372$	2.50000	−	4.33013i	0.129619	−	0.224507i
$373$	19.0000	−	32.9090i	0.983783	−	1.70396i	0.336557	−	0.941663i	$-0.390737\pi$
$373$	19.0000	−	32.9090i	0.983783	−	1.70396i	0.647225	−	0.762299i	$-0.275929\pi$
$374$	−10.0000	+	17.3205i	−0.517088	+	0.895622i
$375$		0			0
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$		0			0
$378$	3.00000			0.154303
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	0.999874	+	0.0158521i	$0.00504609\pi$
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	−0.486209	+	0.873843i	$0.661621\pi$
$380$		0			0
$381$	−5.50000	+	9.52628i	−0.281774	+	0.488046i
$382$	−3.00000			−0.153493
$383$	−0.500000	+	0.866025i	−0.0255488	+	0.0442518i	−0.878517	−	0.477711i	$-0.841467\pi$
$383$	−0.500000	+	0.866025i	−0.0255488	+	0.0442518i	0.852968	+	0.521963i	$0.174800\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−5.00000			−0.254493
$387$	6.00000			0.304997
$388$	−2.50000	+	4.33013i	−0.126918	+	0.219829i
$389$	−11.0000	+	19.0526i	−0.557722	+	0.966003i	0.439964	+	0.898015i	$0.354991\pi$
$389$	−11.0000	+	19.0526i	−0.557722	+	0.966003i	−0.997686	+	0.0679877i	$0.978342\pi$
$390$		0			0
$391$	−20.0000	−	34.6410i	−1.01144	−	1.75187i
$392$	−2.00000			−0.101015
$393$	7.00000	−	12.1244i	0.353103	−	0.611593i
$394$	18.0000			0.906827
$395$		0			0
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$	8.00000	+	13.8564i	0.401004	+	0.694559i
$399$	3.00000	−	5.19615i	0.150188	−	0.260133i
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	−17.0000	−	29.4449i	−0.848939	−	1.47041i	−0.882156	−	0.470958i	$-0.843908\pi$
$401$	−17.0000	−	29.4449i	−0.848939	−	1.47041i	0.0332161	−	0.999448i	$-0.489425\pi$
$402$		0			0
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$	8.00000	+	13.8564i	0.398015	+	0.689382i
$405$		0			0
$406$		0			0
$407$	−12.0000	−	20.7846i	−0.594818	−	1.03025i
$408$	2.50000	+	4.33013i	0.123768	+	0.214373i
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	−0.210017	−	0.977698i	$-0.567352\pi$
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	0.951720	−	0.306968i	$-0.0993146\pi$
$410$		0			0
$411$	5.00000	−	8.66025i	0.246632	−	0.427179i
$412$	−8.00000			−0.394132
$413$	24.0000			1.18096
$414$	8.00000			0.393179
$415$		0			0
$416$	−4.00000			−0.196116
$417$	−7.00000	+	12.1244i	−0.342791	+	0.593732i
$418$	−8.00000			−0.391293
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−14.0000	−	24.2487i	−0.682318	−	1.18181i	−0.974272	−	0.225377i	$-0.927639\pi$
$421$	−14.0000	−	24.2487i	−0.682318	−	1.18181i	0.291953	−	0.956433i	$-0.405695\pi$
$422$	3.00000	+	5.19615i	0.146038	+	0.252945i
$423$	−4.50000	−	7.79423i	−0.218797	−	0.378968i
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$	−12.5000	−	21.6506i	−0.606339	−	1.05021i
$426$	−0.500000	+	0.866025i	−0.0242251	+	0.0419591i
$427$	21.0000	+	36.3731i	1.01626	+	1.76022i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$	−16.0000			−0.772487
$430$		0			0
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	−1.00000			−0.0481125
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	7.50000	+	12.9904i	0.360012	+	0.623558i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	8.00000	−	13.8564i	0.382692	−	0.662842i
$438$	−2.00000			−0.0955637
$439$	−21.0000			−1.00228			−0.501138	−	0.865368i	$-0.667085\pi$
$439$	−21.0000			−1.00228			−0.501138	+	0.865368i	$0.667085\pi$
$440$		0			0
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$	20.0000			0.951303
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$	−6.00000			−0.284747
$445$		0			0
$446$	−14.0000	+	5.19615i	−0.662919	+	0.246045i
$447$	−16.0000			−0.756774
$448$	3.00000			0.141737
$449$	−13.5000	−	23.3827i	−0.637104	−	1.10350i	−0.986065	−	0.166360i	$-0.946799\pi$
$449$	−13.5000	−	23.3827i	−0.637104	−	1.10350i	0.348961	−	0.937137i	$-0.386535\pi$
$450$	5.00000			0.235702
$451$	−14.0000	+	24.2487i	−0.659234	+	1.14183i
$452$	1.50000	+	2.59808i	0.0705541	+	0.122203i
$453$	−3.00000			−0.140952
$454$	2.00000			0.0938647
$455$		0			0
$456$	−1.00000	+	1.73205i	−0.0468293	+	0.0811107i
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	5.00000			0.233380
$460$		0			0
$461$	−40.0000			−1.86299			−0.931493	−	0.363760i	$-0.881493\pi$
$461$	−40.0000			−1.86299			−0.931493	+	0.363760i	$0.881493\pi$
$462$	12.0000			0.558291
$463$	25.0000			1.16185			0.580924	−	0.813958i	$-0.302691\pi$
$463$	25.0000			1.16185			0.580924	+	0.813958i	$0.302691\pi$
$464$		0			0
$465$		0			0
$466$	−13.0000	+	22.5167i	−0.602213	+	1.04306i
$467$	15.0000	+	25.9808i	0.694117	+	1.20225i	0.970477	+	0.241192i	$0.0775384\pi$
$467$	15.0000	+	25.9808i	0.694117	+	1.20225i	−0.276360	+	0.961054i	$0.589128\pi$
$468$	−2.00000	+	3.46410i	−0.0924500	+	0.160128i
$469$		0			0
$470$		0			0
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$	−8.00000			−0.368230
$473$	24.0000			1.10352
$474$		0			0
$475$	5.00000	−	8.66025i	0.229416	−	0.397360i
$476$	−15.0000			−0.687524
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$	15.0000			0.686084
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$	−12.0000	+	20.7846i	−0.547153	+	0.947697i
$482$	−11.5000	+	19.9186i	−0.523811	+	0.907267i
$483$	−12.0000	+	20.7846i	−0.546019	+	0.945732i
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$		0			0
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−1.00000			−0.0453143			−0.0226572	−	0.999743i	$-0.507213\pi$
$487$	−1.00000			−0.0453143			−0.0226572	+	0.999743i	$0.507213\pi$
$488$	−7.00000	−	12.1244i	−0.316875	−	0.548844i
$489$	−1.00000	−	1.73205i	−0.0452216	−	0.0783260i
$490$		0			0
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	0.911230	+	0.411897i	$0.135134\pi$
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	−0.0989017	+	0.995097i	$0.531533\pi$
$492$	3.50000	+	6.06218i	0.157792	+	0.273304i
$493$		0			0
$494$	4.00000	+	6.92820i	0.179969	+	0.311715i
$495$		0			0
$496$	−2.50000	−	4.33013i	−0.112253	−	0.194428i
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$	8.00000			0.358489
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$		0			0
$501$	10.0000	+	17.3205i	0.446767	+	0.773823i
$502$	14.0000			0.624851
$503$	13.5000	−	23.3827i	0.601935	−	1.04258i	−0.390593	−	0.920564i	$-0.627730\pi$
$503$	13.5000	−	23.3827i	0.601935	−	1.04258i	0.992528	−	0.122019i	$-0.0389368\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	32.0000			1.42257
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$	5.50000	+	9.52628i	0.244023	+	0.422660i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	3.00000	−	5.19615i	0.132712	−	0.229864i
$512$	−1.00000			−0.0441942
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$	−21.0000			−0.926270
$515$		0			0
$516$	3.00000	−	5.19615i	0.132068	−	0.228748i
$517$	−18.0000	−	31.1769i	−0.791639	−	1.37116i
$518$	9.00000	−	15.5885i	0.395437	−	0.684917i
$519$	1.00000	−	1.73205i	0.0438951	−	0.0760286i
$520$		0			0
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	−0.897011	−	0.442007i	$-0.854267\pi$
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	0.831295	+	0.555831i	$0.187600\pi$
$522$		0			0
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	0.428269	+	0.903651i	$0.359124\pi$
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	−0.996719	+	0.0809336i	$0.974210\pi$
$524$	−7.00000	−	12.1244i	−0.305796	−	0.529655i
$525$	−7.50000	+	12.9904i	−0.327327	+	0.566947i
$526$	−12.0000	+	20.7846i	−0.523225	+	0.906252i
$527$	12.5000	+	21.6506i	0.544509	+	0.943116i
$528$	−4.00000			−0.174078
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$	−4.00000	+	6.92820i	−0.173585	+	0.300658i
$532$	−3.00000	−	5.19615i	−0.130066	−	0.225282i
$533$	28.0000			1.21281
$534$	−6.50000	+	11.2583i	−0.281283	+	0.487196i
$535$		0			0
$536$		0			0
$537$	16.0000			0.690451
$538$	10.0000	+	17.3205i	0.431131	+	0.746740i
$539$	−4.00000	+	6.92820i	−0.172292	+	0.298419i
$540$		0			0
$541$	−40.0000			−1.71973			−0.859867	−	0.510518i	$-0.829454\pi$
$541$	−40.0000			−1.71973			−0.859867	+	0.510518i	$0.829454\pi$
$542$	−12.5000	−	21.6506i	−0.536921	−	0.929974i
$543$	−3.00000	+	5.19615i	−0.128742	+	0.222988i
$544$	5.00000			0.214373
$545$		0			0
$546$	−6.00000	−	10.3923i	−0.256776	−	0.444750i
$547$	7.00000	+	12.1244i	0.299298	+	0.518400i	0.975976	−	0.217880i	$-0.0699141\pi$
$547$	7.00000	+	12.1244i	0.299298	+	0.518400i	−0.676677	+	0.736280i	$0.736581\pi$
$548$	−5.00000	−	8.66025i	−0.213589	−	0.369948i
$549$	−14.0000			−0.597505
$550$	20.0000			0.852803
$551$		0			0
$552$	4.00000	−	6.92820i	0.170251	−	0.294884i
$553$		0			0
$554$	8.00000			0.339887
$555$		0			0
$556$	7.00000	+	12.1244i	0.296866	+	0.514187i
$557$	38.0000			1.61011			0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000			1.61011			0.805056	+	0.593199i	$0.202135\pi$
$558$	−5.00000			−0.211667
$559$	−12.0000	−	20.7846i	−0.507546	−	0.879095i
$560$		0			0
$561$	20.0000			0.844401
$562$	−3.50000	+	6.06218i	−0.147639	+	0.255718i
$563$	−11.0000	+	19.0526i	−0.463595	+	0.802970i	−0.999137	−	0.0415389i	$-0.986774\pi$
$563$	−11.0000	+	19.0526i	−0.463595	+	0.802970i	0.535542	+	0.844508i	$0.320107\pi$
$564$	−9.00000			−0.378968
$565$		0			0
$566$	6.00000			0.252199
$567$	−1.50000	−	2.59808i	−0.0629941	−	0.109109i
$568$	0.500000	+	0.866025i	0.0209795	+	0.0363376i
$569$	−7.00000	−	12.1244i	−0.293455	−	0.508279i	0.681169	−	0.732126i	$-0.261472\pi$
$569$	−7.00000	−	12.1244i	−0.293455	−	0.508279i	−0.974624	+	0.223847i	$0.928139\pi$
$570$		0			0
$571$	8.00000			0.334790			0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000			0.334790			0.167395	+	0.985890i	$0.446465\pi$
$572$	−8.00000	+	13.8564i	−0.334497	+	0.579365i
$573$	1.50000	+	2.59808i	0.0626634	+	0.108536i
$574$	−21.0000			−0.876523
$575$	−20.0000	+	34.6410i	−0.834058	+	1.44463i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	0.999719	+	0.0236970i	$0.00754370\pi$
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	−0.479337	+	0.877631i	$0.659123\pi$
$578$	−8.00000			−0.332756
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$		0			0
$581$	−12.0000	+	20.7846i	−0.497844	+	0.862291i
$582$	5.00000			0.207257
$583$	24.0000	+	41.5692i	0.993978	+	1.72162i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$	16.0000			0.660391			0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000			0.660391			0.330195	+	0.943913i	$0.392885\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$		0			0
$591$	−9.00000	−	15.5885i	−0.370211	−	0.641223i
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	19.0000	+	32.9090i	0.780236	+	1.35141i	0.931804	+	0.362962i	$0.118235\pi$
$593$	19.0000	+	32.9090i	0.780236	+	1.35141i	−0.151567	+	0.988447i	$0.548432\pi$
$594$	−2.00000	+	3.46410i	−0.0820610	+	0.142134i
$595$		0			0
$596$	−8.00000	+	13.8564i	−0.327693	+	0.567581i
$597$	8.00000	−	13.8564i	0.327418	−	0.567105i
$598$	−16.0000	−	27.7128i	−0.654289	−	1.13326i
$599$	21.5000	−	37.2391i	0.878466	−	1.52155i	0.0254422	−	0.999676i	$-0.491901\pi$
$599$	21.5000	−	37.2391i	0.878466	−	1.52155i	0.853024	−	0.521872i	$-0.174766\pi$
$600$	2.50000	−	4.33013i	0.102062	−	0.176777i
$601$	−1.00000			−0.0407909			−0.0203954	−	0.999792i	$-0.506493\pi$
$601$	−1.00000			−0.0407909			−0.0203954	+	0.999792i	$0.506493\pi$
$602$	9.00000	+	15.5885i	0.366813	+	0.635338i
$603$		0			0
$604$	−1.50000	+	2.59808i	−0.0610341	+	0.105714i
$605$		0			0
$606$	8.00000	−	13.8564i	0.324978	−	0.562878i
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	0.999889	−	0.0148722i	$-0.00473415\pi$
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	−0.512824	+	0.858494i	$0.671401\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$		0			0
$610$		0			0
$611$	−18.0000	+	31.1769i	−0.728202	+	1.26128i
$612$	2.50000	−	4.33013i	0.101057	−	0.175035i
$613$	46.0000			1.85792			0.928961	−	0.370177i	$-0.120703\pi$
$613$	46.0000			1.85792			0.928961	+	0.370177i	$0.120703\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$		0			0
$616$	6.00000	−	10.3923i	0.241747	−	0.418718i
$617$	25.0000			1.00646			0.503231	−	0.864152i	$-0.332144\pi$
$617$	25.0000			1.00646			0.503231	+	0.864152i	$0.332144\pi$
$618$	4.00000	+	6.92820i	0.160904	+	0.278693i
$619$	15.0000	+	25.9808i	0.602901	+	1.04425i	0.992379	+	0.123219i	$0.0393219\pi$
$619$	15.0000	+	25.9808i	0.602901	+	1.04425i	−0.389479	+	0.921036i	$0.627345\pi$
$620$		0			0
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	−4.50000	+	7.79423i	−0.180434	+	0.312520i
$623$	−19.5000	−	33.7750i	−0.781251	−	1.35317i
$624$	2.00000	+	3.46410i	0.0800641	+	0.138675i
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	6.50000	+	11.2583i	0.259792	+	0.449973i
$627$	4.00000	+	6.92820i	0.159745	+	0.276686i
$628$	14.0000			0.558661
$629$	15.0000	−	25.9808i	0.598089	−	1.03592i
$630$		0			0
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	0.995795	+	0.0916122i	$0.0292020\pi$
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	−0.418559	+	0.908190i	$0.637465\pi$
$632$		0			0
$633$	3.00000	−	5.19615i	0.119239	−	0.206529i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	12.0000			0.475831
$637$	8.00000			0.316972
$638$		0			0
$639$	1.00000			0.0395594
$640$		0			0
$641$	−5.00000			−0.197488			−0.0987441	−	0.995113i	$-0.531483\pi$
$641$	−5.00000			−0.197488			−0.0987441	+	0.995113i	$0.531483\pi$
$642$	12.0000			0.473602
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	12.0000	+	20.7846i	0.472866	+	0.819028i
$645$		0			0
$646$	−5.00000	−	8.66025i	−0.196722	−	0.340733i
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	−0.933878	−	0.357591i	$-0.883598\pi$
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	0.776622	+	0.629967i	$0.216932\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−16.0000	+	27.7128i	−0.628055	+	1.08782i
$650$	−10.0000	−	17.3205i	−0.392232	−	0.679366i
$651$	7.50000	−	12.9904i	0.293948	−	0.509133i
$652$	−2.00000			−0.0783260
$653$	4.00000			0.156532			0.0782660	−	0.996933i	$-0.475062\pi$
$653$	4.00000			0.156532			0.0782660	+	0.996933i	$0.475062\pi$
$654$	−4.00000			−0.156412
$655$		0			0
$656$	7.00000			0.273304
$657$	1.00000	+	1.73205i	0.0390137	+	0.0675737i
$658$	13.5000	−	23.3827i	0.526285	−	0.911552i
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	−0.918523	−	0.395367i	$-0.870617\pi$
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	0.801660	+	0.597781i	$0.203951\pi$
$660$		0			0
$661$	−24.0000			−0.933492			−0.466746	−	0.884391i	$-0.654574\pi$
$661$	−24.0000			−0.933492			−0.466746	+	0.884391i	$0.654574\pi$
$662$	28.0000			1.08825
$663$	−10.0000	−	17.3205i	−0.388368	−	0.672673i
$664$	4.00000	−	6.92820i	0.155230	−	0.268866i
$665$		0			0
$666$	3.00000	+	5.19615i	0.116248	+	0.201347i
$667$		0			0
$668$	20.0000			0.773823
$669$	11.5000	+	9.52628i	0.444616	+	0.368307i
$670$		0			0
$671$	−56.0000			−2.16186
$672$	−1.50000	−	2.59808i	−0.0578638	−	0.100223i
$673$	5.00000			0.192736			0.0963679	−	0.995346i	$-0.469277\pi$
$673$	5.00000			0.192736			0.0963679	+	0.995346i	$0.469277\pi$
$674$	−12.5000	+	21.6506i	−0.481482	+	0.833951i
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	3.00000			0.115385
$677$	−22.0000			−0.845529			−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000			−0.845529			−0.422764	+	0.906240i	$0.638940\pi$
$678$	1.50000	−	2.59808i	0.0576072	−	0.0997785i
$679$	−7.50000	+	12.9904i	−0.287824	+	0.498525i
$680$		0			0
$681$	−1.00000	−	1.73205i	−0.0383201	−	0.0663723i
$682$	−20.0000			−0.765840
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$	2.00000			0.0764719
$685$		0			0
$686$	15.0000			0.572703
$687$	−5.00000	+	8.66025i	−0.190762	+	0.330409i
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$		0			0
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	−0.945319	−	0.326146i	$-0.894250\pi$
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	0.755110	+	0.655598i	$0.227583\pi$
$692$	−1.00000	−	1.73205i	−0.0380143	−	0.0658427i
$693$	−6.00000	−	10.3923i	−0.227921	−	0.394771i
$694$	2.00000	+	3.46410i	0.0759190	+	0.131495i
$695$		0			0
$696$		0			0
$697$	−35.0000			−1.32572
$698$	−12.0000	+	20.7846i	−0.454207	+	0.786709i
$699$	26.0000			0.983410
$700$	7.50000	+	12.9904i	0.283473	+	0.490990i
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$	4.00000			0.150970
$703$	12.0000			0.452589
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	−11.5000	+	19.9186i	−0.432808	+	0.749646i
$707$	24.0000	+	41.5692i	0.902613	+	1.56337i
$708$	4.00000	+	6.92820i	0.150329	+	0.260378i
$709$	−14.0000	+	24.2487i	−0.525781	+	0.910679i	0.473768	+	0.880650i	$0.342894\pi$
$709$	−14.0000	+	24.2487i	−0.525781	+	0.910679i	−0.999549	+	0.0300298i	$0.990440\pi$
$710$		0			0
$711$		0			0
$712$	6.50000	+	11.2583i	0.243598	+	0.421924i
$713$	20.0000	−	34.6410i	0.749006	−	1.29732i
$714$	7.50000	+	12.9904i	0.280680	+	0.486153i
$715$		0			0
$716$	8.00000	−	13.8564i	0.298974	−	0.517838i
$717$	−7.50000	−	12.9904i	−0.280093	−	0.485135i
$718$		0			0
$719$	−5.50000	−	9.52628i	−0.205115	−	0.355270i	0.745054	−	0.667004i	$-0.232424\pi$
$719$	−5.50000	−	9.52628i	−0.205115	−	0.355270i	−0.950169	+	0.311734i	$0.899090\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$	23.0000			0.855379
$724$	3.00000	+	5.19615i	0.111494	+	0.193113i
$725$		0			0
$726$	−2.50000	+	4.33013i	−0.0927837	+	0.160706i
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	−0.678676	−	0.734438i	$-0.737446\pi$
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	0.975380	+	0.220532i	$0.0707793\pi$
$728$	−12.0000			−0.444750
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.0000	+	25.9808i	0.554795	+	0.960933i
$732$	−7.00000	+	12.1244i	−0.258727	+	0.448129i
$733$	−50.0000			−1.84679			−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000			−1.84679			−0.923396	+	0.383849i	$0.874598\pi$
$734$	−0.500000	+	0.866025i	−0.0184553	+	0.0319656i
$735$		0			0
$736$	−4.00000	−	6.92820i	−0.147442	−	0.255377i
$737$		0			0
$738$	3.50000	−	6.06218i	0.128837	−	0.223152i
$739$	26.0000	−	45.0333i	0.956425	−	1.65658i	0.225354	−	0.974277i	$-0.427646\pi$
$739$	26.0000	−	45.0333i	0.956425	−	1.65658i	0.731072	−	0.682300i	$-0.239020\pi$
$740$		0			0
$741$	4.00000	−	6.92820i	0.146944	−	0.254514i
$742$	−18.0000	+	31.1769i	−0.660801	+	1.14454i
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	−0.734725	−	0.678365i	$-0.762689\pi$
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	0.954844	+	0.297108i	$0.0960222\pi$
$744$	−2.50000	+	4.33013i	−0.0916544	+	0.158750i
$745$		0			0
$746$	−19.0000	+	32.9090i	−0.695639	+	1.20488i
$747$	−4.00000	−	6.92820i	−0.146352	−	0.253490i
$748$	10.0000	−	17.3205i	0.365636	−	0.633300i
$749$	−18.0000	+	31.1769i	−0.657706	+	1.13918i
$750$		0			0
$751$	5.00000			0.182453			0.0912263	−	0.995830i	$-0.470921\pi$
$751$	5.00000			0.182453			0.0912263	+	0.995830i	$0.470921\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−7.00000	−	12.1244i	−0.255094	−	0.441836i
$754$		0			0
$755$		0			0
$756$	−3.00000			−0.109109
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	−0.593899	−	0.804539i	$-0.702412\pi$
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	0.993701	+	0.112062i	$0.0357456\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$	−16.0000	−	27.7128i	−0.580763	−	1.00591i
$760$		0			0
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	0.991152	−	0.132734i	$-0.0423756\pi$
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	−0.610527	+	0.791995i	$0.709042\pi$
$762$	5.50000	−	9.52628i	0.199244	−	0.345101i
$763$	6.00000	−	10.3923i	0.217215	−	0.376227i
$764$	3.00000			0.108536
$765$		0			0
$766$	0.500000	−	0.866025i	0.0180657	−	0.0312908i
$767$	32.0000			1.15545
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−26.5000	−	45.8993i	−0.955614	−	1.65517i	−0.732956	−	0.680276i	$-0.761860\pi$
$769$	−26.5000	−	45.8993i	−0.955614	−	1.65517i	−0.222659	−	0.974896i	$-0.571474\pi$
$770$		0			0
$771$	10.5000	+	18.1865i	0.378148	+	0.654972i
$772$	5.00000			0.179954
$773$	40.0000			1.43870			0.719350	−	0.694648i	$-0.244440\pi$
$773$	40.0000			1.43870			0.719350	+	0.694648i	$0.244440\pi$
$774$	−6.00000			−0.215666
$775$	12.5000	−	21.6506i	0.449013	−	0.777714i
$776$	2.50000	−	4.33013i	0.0897448	−	0.155443i
$777$	−18.0000			−0.645746
$778$	11.0000	−	19.0526i	0.394369	−	0.683067i
$779$	−7.00000	−	12.1244i	−0.250801	−	0.434400i
$780$		0			0
$781$	4.00000			0.143131
$782$	20.0000	+	34.6410i	0.715199	+	1.23876i
$783$		0			0
$784$	2.00000			0.0714286
$785$		0			0
$786$	−7.00000	+	12.1244i	−0.249682	+	0.432461i
$787$	−48.0000			−1.71102			−0.855508	−	0.517790i	$-0.826755\pi$
$787$	−48.0000			−1.71102			−0.855508	+	0.517790i	$0.826755\pi$
$788$	−18.0000			−0.641223
$789$	24.0000			0.854423
$790$		0			0
$791$	4.50000	+	7.79423i	0.160002	+	0.277131i
$792$	2.00000	+	3.46410i	0.0710669	+	0.123091i
$793$	28.0000	+	48.4974i	0.994309	+	1.72219i
$794$	−8.00000			−0.283909
$795$		0			0
$796$	−8.00000	−	13.8564i	−0.283552	−	0.491127i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$	−3.00000	+	5.19615i	−0.106199	+	0.183942i
$799$	22.5000	−	38.9711i	0.795993	−	1.37870i
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	13.0000			0.459332
$802$	17.0000	+	29.4449i	0.600291	+	1.03973i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$		0			0
$805$		0			0
$806$	10.0000	+	17.3205i	0.352235	+	0.610089i
$807$	10.0000	−	17.3205i	0.352017	−	0.609711i
$808$	−8.00000	−	13.8564i	−0.281439	−	0.487467i
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$		0			0
$811$	1.00000	+	1.73205i	0.0351147	+	0.0608205i	0.883049	−	0.469281i	$-0.155487\pi$
$811$	1.00000	+	1.73205i	0.0351147	+	0.0608205i	−0.847934	+	0.530102i	$0.822154\pi$
$812$		0			0
$813$	−12.5000	+	21.6506i	−0.438394	+	0.759321i
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$		0			0
$816$	−2.50000	−	4.33013i	−0.0875175	−	0.151585i
$817$	−6.00000	+	10.3923i	−0.209913	+	0.363581i
$818$	−15.0000	+	25.9808i	−0.524463	+	0.908396i
$819$	−6.00000	+	10.3923i	−0.209657	+	0.363137i
$820$		0			0
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	0.577016	−	0.816733i	$-0.304217\pi$
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	−0.995819	+	0.0913446i	$0.970884\pi$
$822$	−5.00000	+	8.66025i	−0.174395	+	0.302061i
$823$	20.5000	−	35.5070i	0.714585	−	1.23770i	−0.248534	−	0.968623i	$-0.579949\pi$
$823$	20.5000	−	35.5070i	0.714585	−	1.23770i	0.963119	−	0.269075i	$-0.0867178\pi$
$824$	8.00000			0.278693
$825$	−10.0000	−	17.3205i	−0.348155	−	0.603023i
$826$	−24.0000			−0.835067
$827$	−15.0000	+	25.9808i	−0.521601	+	0.903440i	0.478083	+	0.878315i	$0.341332\pi$
$827$	−15.0000	+	25.9808i	−0.521601	+	0.903440i	−0.999684	+	0.0251251i	$0.992002\pi$
$828$	−8.00000			−0.278019
$829$	−18.0000	+	31.1769i	−0.625166	+	1.08282i	0.363343	+	0.931655i	$0.381635\pi$
$829$	−18.0000	+	31.1769i	−0.625166	+	1.08282i	−0.988509	+	0.151164i	$0.951698\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	4.00000			0.138675
$833$	−10.0000			−0.346479
$834$	7.00000	−	12.1244i	0.242390	−	0.419832i
$835$		0			0
$836$	8.00000			0.276686
$837$	2.50000	+	4.33013i	0.0864126	+	0.149671i
$838$		0			0
$839$	6.50000	−	11.2583i	0.224405	−	0.388681i	−0.731736	−	0.681588i	$-0.761290\pi$
$839$	6.50000	−	11.2583i	0.224405	−	0.388681i	0.956141	+	0.292908i	$0.0946228\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	14.0000	+	24.2487i	0.482472	+	0.835666i
$843$	7.00000			0.241093
$844$	−3.00000	−	5.19615i	−0.103264	−	0.178859i
$845$		0			0
$846$	4.50000	+	7.79423i	0.154713	+	0.267971i
$847$	−7.50000	−	12.9904i	−0.257703	−	0.446355i
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$	−3.00000	−	5.19615i	−0.102960	−	0.178331i
$850$	12.5000	+	21.6506i	0.428746	+	0.742611i
$851$	−48.0000			−1.64542
$852$	0.500000	−	0.866025i	0.0171297	−	0.0296695i
$853$	−17.0000	−	29.4449i	−0.582069	−	1.00817i	−0.995234	−	0.0975167i	$-0.968910\pi$
$853$	−17.0000	−	29.4449i	−0.582069	−	1.00817i	0.413165	−	0.910656i	$-0.364423\pi$
$854$	−21.0000	−	36.3731i	−0.718605	−	1.24466i
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	2.50000	−	4.33013i	0.0853984	−	0.147914i	−0.820163	−	0.572131i	$-0.806117\pi$
$857$	2.50000	−	4.33013i	0.0853984	−	0.147914i	0.905561	+	0.424216i	$0.139450\pi$
$858$	16.0000			0.546231
$859$	36.0000			1.22830			0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000			1.22830			0.614152	+	0.789188i	$0.289498\pi$
$860$		0			0
$861$	10.5000	+	18.1865i	0.357839	+	0.619795i
$862$	−12.0000			−0.408722
$863$	−4.50000	+	7.79423i	−0.153182	+	0.265319i	−0.932395	−	0.361440i	$-0.882285\pi$
$863$	−4.50000	+	7.79423i	−0.153182	+	0.265319i	0.779214	+	0.626758i	$0.215619\pi$
$864$	1.00000			0.0340207
$865$		0			0
$866$	7.00000			0.237870
$867$	4.00000	+	6.92820i	0.135847	+	0.235294i
$868$	−7.50000	−	12.9904i	−0.254567	−	0.440922i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−2.00000	+	3.46410i	−0.0677285	+	0.117309i
$873$	−2.50000	−	4.33013i	−0.0846122	−	0.146553i
$874$	−8.00000	+	13.8564i	−0.270604	+	0.468700i
$875$		0			0
$876$	2.00000			0.0675737
$877$	−8.00000			−0.270141			−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000			−0.270141			−0.135070	+	0.990836i	$0.543126\pi$
$878$	21.0000			0.708716
$879$	24.0000			0.809500
$880$		0			0
$881$	−28.5000	+	49.3634i	−0.960189	+	1.66310i	−0.238171	+	0.971223i	$0.576548\pi$
$881$	−28.5000	+	49.3634i	−0.960189	+	1.66310i	−0.722019	+	0.691873i	$0.756786\pi$
$882$	1.00000	−	1.73205i	0.0336718	−	0.0583212i
$883$	15.0000	−	25.9808i	0.504790	−	0.874322i	−0.495194	−	0.868782i	$-0.664903\pi$
$883$	15.0000	−	25.9808i	0.504790	−	0.874322i	0.999985	−	0.00554010i	$-0.00176348\pi$
$884$	−20.0000			−0.672673
$885$		0			0
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	−0.545302	−	0.838240i	$-0.683585\pi$
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	0.998588	+	0.0531258i	$0.0169184\pi$
$888$	6.00000			0.201347
$889$	16.5000	+	28.5788i	0.553392	+	0.958503i
$890$		0			0
$891$	4.00000			0.134005
$892$	14.0000	−	5.19615i	0.468755	−	0.173980i
$893$	18.0000			0.602347
$894$	16.0000			0.535120
$895$		0			0
$896$	−3.00000			−0.100223
$897$	−16.0000	+	27.7128i	−0.534224	+	0.925304i
$898$	13.5000	+	23.3827i	0.450501	+	0.780290i
$899$		0			0
$900$	−5.00000			−0.166667
$901$	−30.0000	+	51.9615i	−0.999445	+	1.73109i
$902$	14.0000	−	24.2487i	0.466149	−	0.807394i
$903$	9.00000	−	15.5885i	0.299501	−	0.518751i
$904$	−1.50000	−	2.59808i	−0.0498893	−	0.0864107i
$905$		0			0
$906$	3.00000			0.0996683
$907$	−28.0000			−0.929725			−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000			−0.929725			−0.464862	+	0.885383i	$0.653896\pi$
$908$	−2.00000			−0.0663723
$909$	−16.0000			−0.530687
$910$		0			0
$911$	−20.0000	−	34.6410i	−0.662630	−	1.14771i	−0.979922	−	0.199380i	$-0.936107\pi$
$911$	−20.0000	−	34.6410i	−0.662630	−	1.14771i	0.317293	−	0.948328i	$-0.397226\pi$
$912$	1.00000	−	1.73205i	0.0331133	−	0.0573539i
$913$	−16.0000	−	27.7128i	−0.529523	−	0.917160i
$914$	9.00000	−	15.5885i	0.297694	−	0.515620i
$915$		0			0
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$	−21.0000	−	36.3731i	−0.693481	−	1.20114i
$918$	−5.00000			−0.165025
$919$	−9.00000			−0.296883			−0.148441	−	0.988921i	$-0.547426\pi$
$919$	−9.00000			−0.296883			−0.148441	+	0.988921i	$0.547426\pi$
$920$		0			0
$921$	−4.00000	+	6.92820i	−0.131804	+	0.228292i
$922$	40.0000			1.31733
$923$	−2.00000	−	3.46410i	−0.0658308	−	0.114022i
$924$	−12.0000			−0.394771
$925$	−30.0000			−0.986394
$926$	−25.0000			−0.821551
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$		0			0
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	−0.457480	−	0.889220i	$-0.651248\pi$
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	0.998827	−	0.0484211i	$-0.0154190\pi$
$930$		0			0
$931$	−2.00000	−	3.46410i	−0.0655474	−	0.113531i
$932$	13.0000	−	22.5167i	0.425829	−	0.737558i
$933$	9.00000			0.294647
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	10.5000	+	18.1865i	0.343020	+	0.594128i	0.984992	−	0.172600i	$-0.0552168\pi$
$937$	10.5000	+	18.1865i	0.343020	+	0.594128i	−0.641972	+	0.766728i	$0.721883\pi$
$938$		0			0
$939$	6.50000	−	11.2583i	0.212119	−	0.367402i
$940$		0			0
$941$	20.0000			0.651981			0.325991	−	0.945373i	$-0.394302\pi$
$941$	20.0000			0.651981			0.325991	+	0.945373i	$0.394302\pi$
$942$	−7.00000	−	12.1244i	−0.228072	−	0.395033i
$943$	28.0000	+	48.4974i	0.911805	+	1.57929i
$944$	8.00000			0.260378
$945$		0			0
$946$	−24.0000			−0.780307
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	0.602494	−	0.798123i	$-0.294174\pi$
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	−0.992442	+	0.122714i	$0.960840\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−5.00000	+	8.66025i	−0.162221	+	0.280976i
$951$	12.0000			0.389127
$952$	15.0000			0.486153
$953$	4.50000	+	7.79423i	0.145769	+	0.252480i	0.929660	−	0.368419i	$-0.120101\pi$
$953$	4.50000	+	7.79423i	0.145769	+	0.252480i	−0.783890	+	0.620899i	$0.786768\pi$
$954$	−6.00000	−	10.3923i	−0.194257	−	0.336463i
$955$		0			0
$956$	−15.0000			−0.485135
$957$		0			0
$958$		0			0
$959$	−15.0000	−	25.9808i	−0.484375	−	0.838963i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	12.0000	−	20.7846i	0.386896	−	0.670123i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	11.5000	−	19.9186i	0.370390	−	0.641534i
$965$		0			0
$966$	12.0000	−	20.7846i	0.386094	−	0.668734i
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	−0.951408	−	0.307933i	$-0.900363\pi$
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	0.742382	+	0.669977i	$0.233696\pi$
$968$	2.50000	+	4.33013i	0.0803530	+	0.139176i
$969$	−5.00000	+	8.66025i	−0.160623	+	0.278207i
$970$		0			0
$971$	−26.0000	+	45.0333i	−0.834380	+	1.44519i	0.0601548	+	0.998189i	$0.480841\pi$
$971$	−26.0000	+	45.0333i	−0.834380	+	1.44519i	−0.894534	+	0.446999i	$0.852493\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	21.0000	+	36.3731i	0.673229	+	1.16607i
$974$	1.00000			0.0320421
$975$	−10.0000	+	17.3205i	−0.320256	+	0.554700i
$976$	7.00000	+	12.1244i	0.224065	+	0.388091i
$977$	13.0000	−	22.5167i	0.415907	−	0.720372i	−0.579616	−	0.814890i	$-0.696798\pi$
$977$	13.0000	−	22.5167i	0.415907	−	0.720372i	0.995523	+	0.0945177i	$0.0301309\pi$
$978$	1.00000	+	1.73205i	0.0319765	+	0.0553849i
$979$	52.0000			1.66193
$980$		0			0
$981$	2.00000	+	3.46410i	0.0638551	+	0.110600i
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	9.00000			0.287055			0.143528	−	0.989646i	$-0.454155\pi$
$983$	9.00000			0.287055			0.143528	+	0.989646i	$0.454155\pi$
$984$	−3.50000	−	6.06218i	−0.111576	−	0.193255i
$985$		0			0
$986$		0			0
$987$	−27.0000			−0.859419
$988$	−4.00000	−	6.92820i	−0.127257	−	0.220416i
$989$	24.0000	−	41.5692i	0.763156	−	1.32182i
$990$		0			0
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	2.50000	+	4.33013i	0.0793751	+	0.137482i
$993$	−14.0000	−	24.2487i	−0.444277	−	0.769510i
$994$	1.50000	+	2.59808i	0.0475771	+	0.0824060i
$995$		0			0
$996$	−8.00000			−0.253490
$997$	−26.0000			−0.823428			−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000			−0.823428			−0.411714	+	0.911313i	$0.635070\pi$
$998$	5.00000	−	8.66025i	0.158272	−	0.274136i
$999$	3.00000	−	5.19615i	0.0949158	−	0.164399i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.b.1075.1	yes	2
223.39	even	3	inner	1338.2.e.b.931.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.b.931.1	✓	2	223.39	even	3	inner
1338.2.e.b.1075.1	yes	2	1.1	even	1	trivial

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 $\F_{q}$

Introduction

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Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1338.2.e.b.1075.1

Level	$1338$
Weight	$2$
Character	1338.1075
Analytic conductor	$10.684$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$