LMFDB - Embedded newform 294.2.e.b.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$294 = 2 \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	294.e (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:	$2.34760181943$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.2.e.b.67.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.00000 - 6.92820i) q^{19} -1.00000 q^{20} +5.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +1.00000 q^{27} -5.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(1.50000 + 2.59808i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(4.00000 + 6.92820i) q^{38} +(0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-3.00000 + 5.19615i) q^{47} +1.00000 q^{48} -4.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(4.50000 + 7.79423i) q^{53} +(-0.500000 + 0.866025i) q^{54} -5.00000 q^{55} -8.00000 q^{57} +(2.50000 - 4.33013i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-3.00000 + 5.19615i) q^{61} -3.00000 q^{62} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{66} +(1.00000 + 1.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} -4.00000 q^{69} +2.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{74} +(2.00000 - 3.46410i) q^{75} -8.00000 q^{76} +(-1.50000 + 2.59808i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +7.00000 q^{83} -4.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(2.50000 + 4.33013i) q^{87} +(-2.50000 - 4.33013i) q^{88} +(-3.00000 + 5.19615i) q^{89} -1.00000 q^{90} -4.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{96} -7.00000 q^{97} +5.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 2 q^{8} - q^{9} + q^{10} - 5 q^{11} - q^{12} - 2 q^{15} - q^{16} - 4 q^{17} - q^{18} + 8 q^{19} - 2 q^{20} + 10 q^{22} + 4 q^{23} - q^{24} + 4 q^{25}+ \cdots + 10 q^{99}+O(q^{100})$ 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 + 2 * q^8 - q^9 + q^10 - 5 * q^11 - q^12 - 2 * q^15 - q^16 - 4 * q^17 - q^18 + 8 * q^19 - 2 * q^20 + 10 * q^22 + 4 * q^23 - q^24 + 4 * q^25 + 2 * q^27 - 10 * q^29 + q^30 + 3 * q^31 - q^32 - 5 * q^33 + 8 * q^34 + 2 * q^36 + 4 * q^37 + 8 * q^38 + q^40 + 4 * q^43 - 5 * q^44 + q^45 + 4 * q^46 - 6 * q^47 + 2 * q^48 - 8 * q^50 - 4 * q^51 + 9 * q^53 - q^54 - 10 * q^55 - 16 * q^57 + 5 * q^58 - 11 * q^59 + q^60 - 6 * q^61 - 6 * q^62 + 2 * q^64 - 5 * q^66 + 2 * q^67 - 4 * q^68 - 8 * q^69 + 4 * q^71 - q^72 + 10 * q^73 + 4 * q^74 + 4 * q^75 - 16 * q^76 - 3 * q^79 + q^80 - q^81 + 14 * q^83 - 8 * q^85 - 2 * q^86 + 5 * q^87 - 5 * q^88 - 6 * q^89 - 2 * q^90 - 8 * q^92 + 3 * q^93 - 6 * q^94 - 8 * q^95 - q^96 - 14 * q^97 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$ .

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.802955	−	0.596040i	$-0.203260\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	5.00000			1.06600
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	0.968709	−	0.248199i	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.50000	+	4.33013i	−0.435194	+	0.753778i
$34$	4.00000			0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	4.00000	+	6.92820i	0.648886	+	1.12390i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.50000	+	4.33013i	−0.376889	+	0.652791i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	−4.00000			−0.565685
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−5.00000			−0.674200
$56$		0			0
$57$	−8.00000			−1.05963
$58$	2.50000	−	4.33013i	0.328266	−	0.568574i
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	−0.962557	−	0.271078i	$-0.912620\pi$
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	0.246518	−	0.969138i	$-0.420713\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	−3.00000			−0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.50000	−	4.33013i	−0.307729	−	0.533002i
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	−4.00000			−0.481543
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$	−8.00000			−0.917663
$77$		0			0
$78$		0			0
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	−0.937985	−	0.346675i	$-0.887311\pi$
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	0.769222	+	0.638982i	$0.220644\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	2.50000	+	4.33013i	0.268028	+	0.464238i
$88$	−2.50000	−	4.33013i	−0.266501	−	0.461593i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−4.00000			−0.417029
$93$	1.50000	−	2.59808i	0.155543	−	0.269408i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$		0			0
$99$	5.00000			0.502519
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	−2.00000	−	3.46410i	−0.198030	−	0.342997i
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$		0			0
$105$		0			0
$106$	−9.00000			−0.874157
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	2.50000	−	4.33013i	0.238366	−	0.412861i
$111$	−4.00000			−0.379663
$112$		0			0
$113$	16.0000			1.50515			0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000			1.50515			0.752577	+	0.658505i	$0.228811\pi$
$114$	4.00000	−	6.92820i	0.374634	−	0.648886i
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	2.50000	+	4.33013i	0.232119	+	0.402042i
$117$		0			0
$118$	11.0000			1.01263
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$		0			0
$124$	1.50000	−	2.59808i	0.134704	−	0.233314i
$125$	9.00000			0.804984
$126$		0			0
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.00000	−	1.73205i	−0.0880451	−	0.152499i
$130$		0			0
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	−0.843356	−	0.537355i	$-0.819423\pi$
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	0.887041	+	0.461690i	$0.152757\pi$
$132$	5.00000			0.435194
$133$		0			0
$134$	−2.00000			−0.172774
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	2.00000	−	3.46410i	0.170251	−	0.294884i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.50000	+	4.33013i	−0.207614	+	0.359597i
$146$	−10.0000			−0.827606
$147$		0			0
$148$	−4.00000			−0.328798
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	4.00000	−	6.92820i	0.324443	−	0.561951i
$153$	4.00000			0.323381
$154$		0			0
$155$	3.00000			0.240966
$156$		0			0
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	−1.50000	−	2.59808i	−0.119334	−	0.206692i
$159$	4.50000	−	7.79423i	0.356873	−	0.618123i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$		0			0
$165$	2.50000	+	4.33013i	0.194625	+	0.337100i
$166$	−3.50000	+	6.06218i	−0.271653	+	0.470516i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	2.00000	−	3.46410i	0.153393	−	0.265684i
$171$	4.00000	+	6.92820i	0.305888	+	0.529813i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	−0.0566411	−	0.998395i	$-0.518039\pi$
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	0.892956	−	0.450145i	$-0.148628\pi$
$174$	−5.00000			−0.379049
$175$		0			0
$176$	5.00000			0.376889
$177$	−5.50000	+	9.52628i	−0.413405	+	0.716039i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	6.00000			0.443533
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	1.50000	+	2.59808i	0.109985	+	0.190500i
$187$	−10.0000	+	17.3205i	−0.731272	+	1.26660i
$188$	6.00000			0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−2.50000	+	4.33013i	−0.177667	+	0.307729i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−10.0000			−0.703598
$203$		0			0
$204$	4.00000			0.280056
$205$		0			0
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$		0			0
$209$	−40.0000			−2.76686
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$	−1.00000	−	1.73205i	−0.0685189	−	0.118678i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$	1.00000			0.0680414
$217$		0			0
$218$	−2.00000			−0.135457
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$		0			0
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	7.00000			0.468755			0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000			0.468755			0.234377	+	0.972146i	$0.424695\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$	−8.00000	+	13.8564i	−0.532152	+	0.921714i
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	4.00000	+	6.92820i	0.264906	+	0.458831i
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$	4.00000			0.263752
$231$		0			0
$232$	−5.00000			−0.328266
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	−0.793047	−	0.609160i	$-0.791507\pi$
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	0.924072	+	0.382219i	$0.124840\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	−5.50000	+	9.52628i	−0.358020	+	0.620108i
$237$	3.00000			0.194871
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	−0.916159	−	0.400815i	$-0.868727\pi$
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	0.110963	−	0.993825i	$-0.464606\pi$
$242$	−7.00000	−	12.1244i	−0.449977	−	0.779383i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	6.00000			0.384111
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.50000	+	2.59808i	0.0952501	+	0.164978i
$249$	−3.50000	−	6.06218i	−0.221803	−	0.384175i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$	−4.50000	+	7.79423i	−0.282355	+	0.489053i
$255$	2.00000	+	3.46410i	0.125245	+	0.216930i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	2.00000			0.124515
$259$		0			0
$260$		0			0
$261$	2.50000	−	4.33013i	0.154746	−	0.268028i
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.791658	+	0.610964i	$0.209218\pi$
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.133281	+	0.991078i	$0.457449\pi$
$264$	−2.50000	+	4.33013i	−0.153864	+	0.266501i
$265$	9.00000			0.552866
$266$		0			0
$267$	6.00000			0.367194
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	15.5000	+	26.8468i	0.945052	+	1.63688i	0.755648	+	0.654978i	$0.227322\pi$
$269$	15.5000	+	26.8468i	0.945052	+	1.63688i	0.189404	+	0.981899i	$0.439344\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	−0.543130	−	0.839649i	$-0.682761\pi$
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	0.998722	+	0.0505395i	$0.0160941\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	−7.00000	+	12.1244i	−0.419832	+	0.727171i
$279$	−3.00000			−0.179605
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	0.975499	−	0.220005i	$-0.0706075\pi$
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	−0.678280	+	0.734804i	$0.737274\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$	−4.00000	+	6.92820i	−0.236940	+	0.410391i
$286$		0			0
$287$		0			0
$288$	1.00000			0.0589256
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−2.50000	−	4.33013i	−0.146805	−	0.254274i
$291$	3.50000	+	6.06218i	0.205174	+	0.355371i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$	−11.0000			−0.640445
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−2.50000	−	4.33013i	−0.145065	−	0.251259i
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$		0			0
$300$	−4.00000			−0.230940
$301$		0			0
$302$	19.0000			1.09333
$303$	5.00000	−	8.66025i	0.287242	−	0.497519i
$304$	4.00000	+	6.92820i	0.229416	+	0.397360i
$305$	3.00000	+	5.19615i	0.171780	+	0.297531i
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	−1.50000	+	2.59808i	−0.0851943	+	0.147561i
$311$	−16.0000	−	27.7128i	−0.907277	−	1.57145i	−0.817832	−	0.575458i	$-0.804824\pi$
$311$	−16.0000	−	27.7128i	−0.907277	−	1.57145i	−0.0894452	−	0.995992i	$-0.528509\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	3.00000			0.168763
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	−0.905071	−	0.425261i	$-0.860182\pi$
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	0.820822	+	0.571184i	$0.193516\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$	12.5000	+	21.6506i	0.699866	+	1.21220i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	3.00000			0.167444
$322$		0			0
$323$	−32.0000			−1.78053
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$		0			0
$330$	−5.00000			−0.275241
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−3.50000	−	6.06218i	−0.192087	−	0.332705i
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$	−7.00000	+	12.1244i	−0.383023	+	0.663415i
$335$	2.00000			0.109272
$336$		0			0
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	6.50000	−	11.2583i	0.353553	−	0.612372i
$339$	−8.00000	−	13.8564i	−0.434500	−	0.752577i
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$	−8.00000			−0.432590
$343$		0			0
$344$	2.00000			0.107833
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$	11.0000	+	19.0526i	0.591364	+	1.02427i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	2.50000	−	4.33013i	0.134014	−	0.232119i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$		0			0
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$	−5.50000	−	9.52628i	−0.292322	−	0.506316i
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$	6.00000			0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	−22.5000	−	38.9711i	−1.18421	−	2.05111i
$362$		0			0
$363$	14.0000			0.734809
$364$		0			0
$365$	10.0000			0.523424
$366$	−3.00000	+	5.19615i	−0.156813	+	0.271607i
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$		0			0
$370$	4.00000			0.207950
$371$		0			0
$372$	−3.00000			−0.155543
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	−0.0708063	−	0.997490i	$-0.522557\pi$
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	0.899255	−	0.437425i	$-0.144109\pi$
$374$	−10.0000	−	17.3205i	−0.517088	−	0.895622i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$		0			0
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	−4.00000	+	6.92820i	−0.205196	+	0.355409i
$381$	−4.50000	−	7.79423i	−0.230542	−	0.399310i
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	−17.0000	+	29.4449i	−0.868659	+	1.50456i	−0.00529229	+	0.999986i	$0.501685\pi$
$383$	−17.0000	+	29.4449i	−0.868659	+	1.50456i	−0.863367	+	0.504576i	$0.831649\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	5.00000			0.254493
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	3.50000	+	6.06218i	0.177686	+	0.307760i
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	0.890263	−	0.455448i	$-0.150521\pi$
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	−0.839561	+	0.543266i	$0.817187\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$	−1.00000			−0.0504433
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$	1.50000	+	2.59808i	0.0754732	+	0.130723i
$396$	−2.50000	−	4.33013i	−0.125630	−	0.217597i
$397$	18.0000	−	31.1769i	0.903394	−	1.56472i	0.0803356	−	0.996768i	$-0.474401\pi$
$397$	18.0000	−	31.1769i	0.903394	−	1.56472i	0.823058	−	0.567957i	$-0.192266\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$	1.00000	+	1.73205i	0.0498755	+	0.0863868i
$403$		0			0
$404$	5.00000	−	8.66025i	0.248759	−	0.430864i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−20.0000			−0.991363
$408$	−2.00000	+	3.46410i	−0.0990148	+	0.171499i
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	−0.989835	−	0.142222i	$-0.954575\pi$
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	0.371750	−	0.928333i	$-0.378758\pi$
$410$		0			0
$411$	1.00000	−	1.73205i	0.0493264	−	0.0854358i
$412$	−8.00000			−0.394132
$413$		0			0
$414$	−4.00000			−0.196589
$415$	3.50000	−	6.06218i	0.171808	−	0.297581i
$416$		0			0
$417$	−7.00000	−	12.1244i	−0.342791	−	0.593732i
$418$	20.0000	−	34.6410i	0.978232	−	1.69435i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	−1.00000	+	1.73205i	−0.0486792	+	0.0843149i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	8.00000	−	13.8564i	0.388057	−	0.672134i
$426$	2.00000			0.0969003
$427$		0			0
$428$	3.00000			0.145010
$429$		0			0
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	5.00000			0.239732
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−16.0000	−	27.7128i	−0.765384	−	1.32568i
$438$	5.00000	+	8.66025i	0.238909	+	0.413803i
$439$	7.50000	−	12.9904i	0.357955	−	0.619997i	−0.629664	−	0.776868i	$-0.716807\pi$
$439$	7.50000	−	12.9904i	0.357955	−	0.619997i	0.987619	+	0.156871i	$0.0501406\pi$
$440$	−5.00000			−0.238366
$441$		0			0
$442$		0			0
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	−0.994187	−	0.107671i	$-0.965661\pi$
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	0.590339	+	0.807155i	$0.298994\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−3.50000	+	6.06218i	−0.165730	+	0.287052i
$447$	−18.0000			−0.851371
$448$		0			0
$449$	16.0000			0.755087			0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000			0.755087			0.377543	+	0.925992i	$0.376769\pi$
$450$	2.00000	−	3.46410i	0.0942809	−	0.163299i
$451$		0			0
$452$	−8.00000	−	13.8564i	−0.376288	−	0.651751i
$453$	−9.50000	+	16.4545i	−0.446349	+	0.773099i
$454$	−3.00000			−0.140797
$455$		0			0
$456$	−8.00000			−0.374634
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	0.233890	+	0.972263i	$0.424854\pi$
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	−10.0000	−	17.3205i	−0.467269	−	0.809334i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$	−2.00000	+	3.46410i	−0.0932505	+	0.161515i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$	−1.50000	−	2.59808i	−0.0695608	−	0.120483i
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	−0.999097	−	0.0424970i	$-0.986469\pi$
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	0.536352	+	0.843995i	$0.319802\pi$
$468$		0			0
$469$		0			0
$470$	−6.00000			−0.276759
$471$	−2.00000	+	3.46410i	−0.0921551	+	0.159617i
$472$	−5.50000	−	9.52628i	−0.253158	−	0.438483i
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$	−1.50000	+	2.59808i	−0.0688973	+	0.119334i
$475$	32.0000			1.46826
$476$		0			0
$477$	−9.00000			−0.412082
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	19.0000	+	32.9090i	0.868132	+	1.50365i	0.863903	+	0.503658i	$0.168013\pi$
$479$	19.0000	+	32.9090i	0.868132	+	1.50365i	0.00422900	+	0.999991i	$0.498654\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$		0			0
$482$	25.0000			1.13872
$483$		0			0
$484$	14.0000			0.636364
$485$	−3.50000	+	6.06218i	−0.158927	+	0.275269i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−2.50000	−	4.33013i	−0.113286	−	0.196217i	0.803807	−	0.594890i	$-0.202804\pi$
$487$	−2.50000	−	4.33013i	−0.113286	−	0.196217i	−0.917093	+	0.398673i	$0.869471\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$		0			0
$493$	10.0000	+	17.3205i	0.450377	+	0.780076i
$494$		0			0
$495$	2.50000	−	4.33013i	0.112367	−	0.194625i
$496$	−3.00000			−0.134704
$497$		0			0
$498$	7.00000			0.313678
$499$	−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	$0.238523\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$	−7.00000	−	12.1244i	−0.312737	−	0.541676i
$502$	10.5000	−	18.1865i	0.468638	−	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	10.0000	−	17.3205i	0.444554	−	0.769991i
$507$	6.50000	+	11.2583i	0.288675	+	0.500000i
$508$	−4.50000	−	7.79423i	−0.199655	−	0.345813i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$	−4.00000			−0.177123
$511$		0			0
$512$	1.00000			0.0441942
$513$	4.00000	−	6.92820i	0.176604	−	0.305888i
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	30.0000			1.31940
$518$		0			0
$519$	−22.0000			−0.965693
$520$		0			0
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	2.50000	+	4.33013i	0.109422	+	0.189525i
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	−0.765222	−	0.643767i	$-0.777371\pi$
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	0.940129	+	0.340818i	$0.110704\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$	−30.0000			−1.30806
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	−2.50000	−	4.33013i	−0.108799	−	0.188445i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$	11.0000			0.477359
$532$		0			0
$533$		0			0
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	−31.0000			−1.33650
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$	7.50000	+	12.9904i	0.322153	+	0.557985i
$543$		0			0
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	1.00000	−	1.73205i	0.0427179	−	0.0739895i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	10.0000	+	17.3205i	0.426401	+	0.738549i
$551$	−20.0000	+	34.6410i	−0.852029	+	1.47576i
$552$	−4.00000			−0.170251
$553$		0			0
$554$	−16.0000			−0.679775
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	11.5000	+	19.9186i	0.487271	+	0.843978i	0.999893	−	0.0146368i	$-0.00465919\pi$
$557$	11.5000	+	19.9186i	0.487271	+	0.843978i	−0.512622	+	0.858614i	$0.671326\pi$
$558$	1.50000	−	2.59808i	0.0635001	−	0.109985i
$559$		0			0
$560$		0			0
$561$	20.0000			0.844401
$562$	−1.00000	+	1.73205i	−0.0421825	+	0.0730622i
$563$	8.50000	+	14.7224i	0.358232	+	0.620477i	0.987666	−	0.156578i	$-0.0500463\pi$
$563$	8.50000	+	14.7224i	0.358232	+	0.620477i	−0.629433	+	0.777055i	$0.716713\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	8.00000	−	13.8564i	0.336563	−	0.582943i
$566$	−10.0000			−0.420331
$567$		0			0
$568$	2.00000			0.0839181
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	0.496928	+	0.867792i	$0.334461\pi$
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	−0.999994	+	0.00354413i	$0.998872\pi$
$570$	−4.00000	−	6.92820i	−0.167542	−	0.290191i
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	0.988006	+	0.154415i	$0.0493493\pi$
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	−0.360276	+	0.932846i	$0.617317\pi$
$572$		0			0
$573$	24.0000			1.00261
$574$		0			0
$575$	16.0000			0.667246
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	15.5000	+	26.8468i	0.645273	+	1.11765i	0.984238	+	0.176847i	$0.0565899\pi$
$577$	15.5000	+	26.8468i	0.645273	+	1.11765i	−0.338965	+	0.940799i	$0.610077\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	−2.50000	+	4.33013i	−0.103896	+	0.179954i
$580$	5.00000			0.207614
$581$		0			0
$582$	−7.00000			−0.290159
$583$	22.5000	−	38.9711i	0.931855	−	1.61402i
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$		0			0
$586$	−10.5000	+	18.1865i	−0.433751	+	0.751279i
$587$	−35.0000			−1.44460			−0.722302	−	0.691577i	$-0.756916\pi$
$587$	−35.0000			−1.44460			−0.722302	+	0.691577i	$0.756916\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$	5.50000	−	9.52628i	0.226431	−	0.392191i
$591$	−1.00000	−	1.73205i	−0.0411345	−	0.0712470i
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	−0.213697	−	0.976900i	$-0.568551\pi$
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	0.952869	−	0.303383i	$-0.0981160\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	−18.0000			−0.737309
$597$	−2.00000	+	3.46410i	−0.0818546	+	0.141776i
$598$		0			0
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	−35.0000			−1.42768			−0.713840	−	0.700309i	$-0.753046\pi$
$601$	−35.0000			−1.42768			−0.713840	+	0.700309i	$0.753046\pi$
$602$		0			0
$603$	−2.00000			−0.0814463
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	5.00000	+	8.66025i	0.203111	+	0.351799i
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	0.450467	+	0.892793i	$0.351258\pi$
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	−0.998415	+	0.0562808i	$0.982076\pi$
$608$	−8.00000			−0.324443
$609$		0			0
$610$	−6.00000			−0.242933
$611$		0			0
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	−6.00000	−	10.3923i	−0.242338	−	0.419741i	0.719042	−	0.694967i	$-0.244581\pi$
$613$	−6.00000	−	10.3923i	−0.242338	−	0.419741i	−0.961380	+	0.275225i	$0.911248\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$	4.00000	−	6.92820i	0.160904	−	0.278693i
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$	−1.50000	−	2.59808i	−0.0602414	−	0.104341i
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$	32.0000			1.28308
$623$		0			0
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$	20.0000	+	34.6410i	0.798723	+	1.38343i
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	−1.50000	+	2.59808i	−0.0596668	+	0.103346i
$633$	−1.00000	−	1.73205i	−0.0397464	−	0.0688428i
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	4.50000	−	7.79423i	0.178577	−	0.309305i
$636$	−9.00000			−0.356873
$637$		0			0
$638$	−25.0000			−0.989759
$639$	−1.00000	+	1.73205i	−0.0395594	+	0.0685189i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	−0.999878	−	0.0156233i	$-0.995027\pi$
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	0.486409	−	0.873731i	$-0.338307\pi$
$642$	−1.50000	+	2.59808i	−0.0592003	+	0.102538i
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$		0			0
$645$	−2.00000			−0.0787499
$646$	16.0000	−	27.7128i	0.629512	−	1.09035i
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	0.633090	−	0.774078i	$-0.281786\pi$
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	−0.986916	+	0.161233i	$0.948453\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−27.5000	+	47.6314i	−1.07947	+	1.86970i
$650$		0			0
$651$		0			0
$652$	−4.00000			−0.156652
$653$	19.5000	−	33.7750i	0.763094	−	1.32172i	−0.178154	−	0.984003i	$-0.557013\pi$
$653$	19.5000	−	33.7750i	0.763094	−	1.32172i	0.941248	−	0.337715i	$-0.109654\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$	−0.500000	−	0.866025i	−0.0195366	−	0.0338384i
$656$		0			0
$657$	−10.0000			−0.390137
$658$		0			0
$659$	−40.0000			−1.55818			−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000			−1.55818			−0.779089	+	0.626913i	$0.784318\pi$
$660$	2.50000	−	4.33013i	0.0973124	−	0.168550i
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$		0			0
$664$	7.00000			0.271653
$665$		0			0
$666$	−4.00000			−0.154997
$667$	−10.0000	+	17.3205i	−0.387202	+	0.670653i
$668$	−7.00000	−	12.1244i	−0.270838	−	0.469105i
$669$	−3.50000	−	6.06218i	−0.135318	−	0.234377i
$670$	−1.00000	+	1.73205i	−0.0386334	+	0.0669150i
$671$	30.0000			1.15814
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	−4.50000	+	7.79423i	−0.173334	+	0.300222i
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	0.480913	+	0.876768i	$0.340305\pi$
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	−0.999760	+	0.0219013i	$0.993028\pi$
$678$	16.0000			0.614476
$679$		0			0
$680$	−4.00000			−0.153393
$681$	1.50000	−	2.59808i	0.0574801	−	0.0995585i
$682$	7.50000	+	12.9904i	0.287190	+	0.497427i
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	0.939184	−	0.343413i	$-0.111583\pi$
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	−0.766997	+	0.641651i	$0.778250\pi$
$684$	4.00000	−	6.92820i	0.152944	−	0.264906i
$685$	2.00000			0.0764161
$686$		0			0
$687$	20.0000			0.763048
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$		0			0
$690$	−2.00000	−	3.46410i	−0.0761387	−	0.131876i
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	7.00000	−	12.1244i	0.265525	−	0.459903i
$696$	2.50000	+	4.33013i	0.0947623	+	0.164133i
$697$		0			0
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$	−4.00000			−0.151294
$700$		0			0
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		0			0
$703$	−16.0000	−	27.7128i	−0.603451	−	1.04521i
$704$	−2.50000	−	4.33013i	−0.0942223	−	0.163198i
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$	−24.0000			−0.903252
$707$		0			0
$708$	11.0000			0.413405
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	1.00000	+	1.73205i	0.0375293	+	0.0650027i
$711$	−1.50000	−	2.59808i	−0.0562544	−	0.0974355i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	12.0000			0.449404
$714$		0			0
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	−5.00000	−	8.66025i	−0.186598	−	0.323198i
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	45.0000			1.67473
$723$	−12.5000	+	21.6506i	−0.464880	+	0.805196i
$724$		0			0
$725$	−10.0000	−	17.3205i	−0.371391	−	0.643268i
$726$	−7.00000	+	12.1244i	−0.259794	+	0.449977i
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$	−3.00000	−	5.19615i	−0.110883	−	0.192055i
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	−0.916096	−	0.400959i	$-0.868677\pi$
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	0.805289	+	0.592883i	$0.202010\pi$
$734$	−17.0000			−0.627481
$735$		0			0
$736$	−4.00000			−0.147442
$737$	5.00000	−	8.66025i	0.184177	−	0.319005i
$738$		0			0
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	0.998146	+	0.0608653i	$0.0193860\pi$
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	−0.446362	+	0.894852i	$0.647281\pi$
$740$	−2.00000	+	3.46410i	−0.0735215	+	0.127343i
$741$		0			0
$742$		0			0
$743$	30.0000			1.10059			0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000			1.10059			0.550297	+	0.834969i	$0.314515\pi$
$744$	1.50000	−	2.59808i	0.0549927	−	0.0952501i
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	16.0000	+	27.7128i	0.585802	+	1.01464i
$747$	−3.50000	+	6.06218i	−0.128058	+	0.221803i
$748$	20.0000			0.731272
$749$		0			0
$750$	9.00000			0.328634
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	0.0838743	+	0.996476i	$0.473271\pi$
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	−0.904911	+	0.425601i	$0.860063\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$	10.5000	+	18.1865i	0.382641	+	0.662754i
$754$		0			0
$755$	−19.0000			−0.691481
$756$		0			0
$757$	−54.0000			−1.96266			−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−54.0000			−1.96266			−0.981332	+	0.192323i	$0.938398\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$	10.0000	+	17.3205i	0.362977	+	0.628695i
$760$	−4.00000	−	6.92820i	−0.145095	−	0.251312i
$761$	4.00000	−	6.92820i	0.145000	−	0.251147i	−0.784373	−	0.620289i	$-0.787015\pi$
$761$	4.00000	−	6.92820i	0.145000	−	0.251147i	0.929373	+	0.369142i	$0.120348\pi$
$762$	9.00000			0.326036
$763$		0			0
$764$	24.0000			0.868290
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	−17.0000	−	29.4449i	−0.614235	−	1.06389i
$767$		0			0
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$	6.00000			0.216085
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	0.941825	−	0.336104i	$-0.109109\pi$
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	−0.761987	+	0.647592i	$0.775776\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	−6.00000	+	10.3923i	−0.215526	+	0.373303i
$776$	−7.00000			−0.251285
$777$		0			0
$778$	−2.00000			−0.0717035
$779$		0			0
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$	−5.00000			−0.178685
$784$		0			0
$785$	−4.00000			−0.142766
$786$	0.500000	−	0.866025i	0.0178344	−	0.0308901i
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	0.659841	−	0.751405i	$-0.270624\pi$
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	−0.980656	+	0.195737i	$0.937290\pi$
$788$	−1.00000	−	1.73205i	−0.0356235	−	0.0617018i
$789$	15.0000	−	25.9808i	0.534014	−	0.924940i
$790$	−3.00000			−0.106735
$791$		0			0
$792$	5.00000			0.177667
$793$		0			0
$794$	18.0000	+	31.1769i	0.638796	+	1.10643i
$795$	−4.50000	−	7.79423i	−0.159599	−	0.276433i
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	−21.0000			−0.743858			−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000			−0.743858			−0.371929	+	0.928261i	$0.621304\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$	25.0000	−	43.3013i	0.882231	−	1.52807i
$804$	−2.00000			−0.0705346
$805$		0			0
$806$		0			0
$807$	15.5000	−	26.8468i	0.545626	−	0.945052i
$808$	5.00000	+	8.66025i	0.175899	+	0.304667i
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	−0.967351	−	0.253442i	$-0.918437\pi$
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	0.264188	−	0.964471i	$-0.414896\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	14.0000			0.491606			0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000			0.491606			0.245803	+	0.969320i	$0.420948\pi$
$812$		0			0
$813$	−15.0000			−0.526073
$814$	10.0000	−	17.3205i	0.350500	−	0.607083i
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	25.0000			0.874105
$819$		0			0
$820$		0			0
$821$	12.5000	−	21.6506i	0.436253	−	0.755612i	−0.561144	−	0.827718i	$-0.689639\pi$
$821$	12.5000	−	21.6506i	0.436253	−	0.755612i	0.997397	+	0.0721058i	$0.0229719\pi$
$822$	1.00000	+	1.73205i	0.0348790	+	0.0604122i
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	4.00000	−	6.92820i	0.139347	−	0.241355i
$825$	−20.0000			−0.696311
$826$		0			0
$827$	9.00000			0.312961			0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	−0.997848	−	0.0655624i	$-0.979116\pi$
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	0.442145	−	0.896943i	$-0.354217\pi$
$830$	3.50000	+	6.06218i	0.121487	+	0.210421i
$831$	8.00000	−	13.8564i	0.277517	−	0.480673i
$832$		0			0
$833$		0			0
$834$	14.0000			0.484780
$835$	7.00000	−	12.1244i	0.242245	−	0.419581i
$836$	20.0000	+	34.6410i	0.691714	+	1.19808i
$837$	1.50000	+	2.59808i	0.0518476	+	0.0898027i
$838$		0			0
$839$	28.0000			0.966667			0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000			0.966667			0.483334	+	0.875436i	$0.339426\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−15.0000	+	25.9808i	−0.516934	+	0.895356i
$843$	−1.00000	−	1.73205i	−0.0344418	−	0.0596550i
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$	−6.50000	+	11.2583i	−0.223607	+	0.387298i
$846$	6.00000			0.206284
$847$		0			0
$848$	−9.00000			−0.309061
$849$	5.00000	−	8.66025i	0.171600	−	0.297219i
$850$	8.00000	+	13.8564i	0.274398	+	0.475271i
$851$	−8.00000	−	13.8564i	−0.274236	−	0.474991i
$852$	−1.00000	+	1.73205i	−0.0342594	+	0.0593391i
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	0.415442	+	0.909620i	$0.363627\pi$
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	−0.995475	+	0.0950262i	$0.969707\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	12.0000			0.408722
$863$	−5.00000	+	8.66025i	−0.170202	+	0.294798i	−0.938490	−	0.345305i	$-0.887775\pi$
$863$	−5.00000	+	8.66025i	−0.170202	+	0.294798i	0.768288	+	0.640104i	$0.221109\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−11.0000	−	19.0526i	−0.374011	−	0.647806i
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	15.0000			0.508840
$870$	−2.50000	+	4.33013i	−0.0847579	+	0.146805i
$871$		0			0
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	3.50000	−	6.06218i	0.118457	−	0.205174i
$874$	32.0000			1.08242
$875$		0			0
$876$	−10.0000			−0.337869
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	−0.458606	−	0.888640i	$-0.651651\pi$
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	0.998888	−	0.0471555i	$-0.0150156\pi$
$878$	7.50000	+	12.9904i	0.253113	+	0.438404i
$879$	−10.5000	−	18.1865i	−0.354156	−	0.613417i
$880$	2.50000	−	4.33013i	0.0842750	−	0.145969i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$		0			0
$885$	5.50000	+	9.52628i	0.184880	+	0.320222i
$886$	−8.50000	−	14.7224i	−0.285563	−	0.494610i
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	−0.387768	−	0.921757i	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$	−4.00000			−0.134231
$889$		0			0
$890$	−6.00000			−0.201120
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$	−3.50000	−	6.06218i	−0.117189	−	0.202977i
$893$	24.0000	+	41.5692i	0.803129	+	1.39106i
$894$	9.00000	−	15.5885i	0.301005	−	0.521356i
$895$	−12.0000			−0.401116
$896$		0			0
$897$		0			0
$898$	−8.00000	+	13.8564i	−0.266963	+	0.462394i
$899$	−7.50000	−	12.9904i	−0.250139	−	0.433253i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	16.0000			0.532152
$905$		0			0
$906$	−9.50000	−	16.4545i	−0.315616	−	0.546664i
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$	−10.0000			−0.331679
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	4.00000	−	6.92820i	0.132453	−	0.229416i
$913$	−17.5000	−	30.3109i	−0.579165	−	1.00314i
$914$	−15.5000	−	26.8468i	−0.512694	−	0.888013i
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	20.0000			0.660819
$917$		0			0
$918$	4.00000			0.132020
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	−7.00000	+	12.1244i	−0.230533	+	0.399294i
$923$		0			0
$924$		0			0
$925$	16.0000			0.526077
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$	3.00000			0.0983739
$931$		0			0
$932$	−4.00000			−0.131024
$933$	−16.0000	+	27.7128i	−0.523816	+	0.907277i
$934$	−10.0000	−	17.3205i	−0.327210	−	0.566744i
$935$	10.0000	+	17.3205i	0.327035	+	0.566441i
$936$		0			0
$937$	−35.0000			−1.14340			−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000			−1.14340			−0.571700	+	0.820463i	$0.693716\pi$
$938$		0			0
$939$	−1.00000			−0.0326338
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$	−5.50000	−	9.52628i	−0.179295	−	0.310548i	0.762344	−	0.647172i	$-0.224048\pi$
$941$	−5.50000	−	9.52628i	−0.179295	−	0.310548i	−0.941639	+	0.336624i	$0.890715\pi$
$942$	−2.00000	−	3.46410i	−0.0651635	−	0.112867i
$943$		0			0
$944$	11.0000			0.358020
$945$		0			0
$946$	10.0000			0.325128
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	−0.479801	−	0.877377i	$-0.659291\pi$
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	0.999732	−	0.0231683i	$-0.00737536\pi$
$948$	−1.50000	−	2.59808i	−0.0487177	−	0.0843816i
$949$		0			0
$950$	−16.0000	+	27.7128i	−0.519109	+	0.899122i
$951$	3.00000			0.0972817
$952$		0			0
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$	12.0000	+	20.7846i	0.388311	+	0.672574i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	12.5000	−	21.6506i	0.404068	−	0.699866i
$958$	−38.0000			−1.22772
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$	−1.50000	−	2.59808i	−0.0483368	−	0.0837218i
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$	−5.00000			−0.160956
$966$		0			0
$967$	−61.0000			−1.96163			−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−61.0000			−1.96163			−0.980814	+	0.194946i	$0.937547\pi$
$968$	−7.00000	+	12.1244i	−0.224989	+	0.389692i
$969$	16.0000	+	27.7128i	0.513994	+	0.890264i
$970$	−3.50000	−	6.06218i	−0.112378	−	0.194645i
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	5.00000			0.160210
$975$		0			0
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$	30.0000			0.958804
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.730073	−	0.683369i	$-0.760514\pi$
$983$	−30.0000	−	51.9615i	−0.956851	−	1.65732i	−0.226778	−	0.973946i	$-0.572819\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	0.0318626	−	0.0551877i
$986$	−20.0000			−0.636930
$987$		0			0
$988$		0			0
$989$	4.00000	−	6.92820i	0.127193	−	0.220304i
$990$	2.50000	+	4.33013i	0.0794552	+	0.137620i
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	−0.949490	−	0.313798i	$-0.898398\pi$
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	0.202988	−	0.979181i	$-0.434935\pi$
$992$	1.50000	−	2.59808i	0.0476250	−	0.0824890i
$993$	−4.00000			−0.126936
$994$		0			0
$995$	−4.00000			−0.126809
$996$	−3.50000	+	6.06218i	−0.110902	+	0.192087i
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	0.992558	+	0.121771i	$0.0388574\pi$
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	−0.390822	+	0.920466i	$0.627809\pi$
$998$	−5.00000	−	8.66025i	−0.158272	−	0.274136i
$999$	2.00000	−	3.46410i	0.0632772	−	0.109599i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.e.b.79.1		2
3.2	odd	2		882.2.g.i.667.1		2
4.3	odd	2		2352.2.q.u.961.1		2
7.2	even	3		294.2.a.f.1.1		1
7.3	odd	6		42.2.e.a.25.1	✓	2
7.4	even	3	inner	294.2.e.b.67.1		2
7.5	odd	6		294.2.a.e.1.1		1
7.6	odd	2		42.2.e.a.37.1	yes	2
21.2	odd	6		882.2.a.d.1.1		1
21.5	even	6		882.2.a.c.1.1		1
21.11	odd	6		882.2.g.i.361.1		2
21.17	even	6		126.2.g.c.109.1		2
21.20	even	2		126.2.g.c.37.1		2
28.3	even	6		336.2.q.b.193.1		2
28.11	odd	6		2352.2.q.u.1537.1		2
28.19	even	6		2352.2.a.t.1.1		1
28.23	odd	6		2352.2.a.f.1.1		1
28.27	even	2		336.2.q.b.289.1		2
35.3	even	12		1050.2.o.a.949.1		4
35.9	even	6		7350.2.a.q.1.1		1
35.13	even	4		1050.2.o.a.499.2		4
35.17	even	12		1050.2.o.a.949.2		4
35.19	odd	6		7350.2.a.bl.1.1		1
35.24	odd	6		1050.2.i.l.151.1		2
35.27	even	4		1050.2.o.a.499.1		4
35.34	odd	2		1050.2.i.l.751.1		2
56.3	even	6		1344.2.q.s.193.1		2
56.5	odd	6		9408.2.a.ce.1.1		1
56.13	odd	2		1344.2.q.g.961.1		2
56.19	even	6		9408.2.a.q.1.1		1
56.27	even	2		1344.2.q.s.961.1		2
56.37	even	6		9408.2.a.z.1.1		1
56.45	odd	6		1344.2.q.g.193.1		2
56.51	odd	6		9408.2.a.cr.1.1		1
63.13	odd	6		1134.2.h.e.541.1		2
63.20	even	6		1134.2.e.e.919.1		2
63.31	odd	6		1134.2.e.l.865.1		2
63.34	odd	6		1134.2.e.l.919.1		2
63.38	even	6		1134.2.h.l.109.1		2
63.41	even	6		1134.2.h.l.541.1		2
63.52	odd	6		1134.2.h.e.109.1		2
63.59	even	6		1134.2.e.e.865.1		2
84.23	even	6		7056.2.a.bl.1.1		1
84.47	odd	6		7056.2.a.w.1.1		1
84.59	odd	6		1008.2.s.k.865.1		2
84.83	odd	2		1008.2.s.k.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	7.3	odd	6
42.2.e.a.37.1	yes	2	7.6	odd	2
126.2.g.c.37.1		2	21.20	even	2
126.2.g.c.109.1		2	21.17	even	6
294.2.a.e.1.1		1	7.5	odd	6
294.2.a.f.1.1		1	7.2	even	3
294.2.e.b.67.1		2	7.4	even	3	inner
294.2.e.b.79.1		2	1.1	even	1	trivial
336.2.q.b.193.1		2	28.3	even	6
336.2.q.b.289.1		2	28.27	even	2
882.2.a.c.1.1		1	21.5	even	6
882.2.a.d.1.1		1	21.2	odd	6
882.2.g.i.361.1		2	21.11	odd	6
882.2.g.i.667.1		2	3.2	odd	2
1008.2.s.k.289.1		2	84.83	odd	2
1008.2.s.k.865.1		2	84.59	odd	6
1050.2.i.l.151.1		2	35.24	odd	6
1050.2.i.l.751.1		2	35.34	odd	2
1050.2.o.a.499.1		4	35.27	even	4
1050.2.o.a.499.2		4	35.13	even	4
1050.2.o.a.949.1		4	35.3	even	12
1050.2.o.a.949.2		4	35.17	even	12
1134.2.e.e.865.1		2	63.59	even	6
1134.2.e.e.919.1		2	63.20	even	6
1134.2.e.l.865.1		2	63.31	odd	6
1134.2.e.l.919.1		2	63.34	odd	6
1134.2.h.e.109.1		2	63.52	odd	6
1134.2.h.e.541.1		2	63.13	odd	6
1134.2.h.l.109.1		2	63.38	even	6
1134.2.h.l.541.1		2	63.41	even	6
1344.2.q.g.193.1		2	56.45	odd	6
1344.2.q.g.961.1		2	56.13	odd	2
1344.2.q.s.193.1		2	56.3	even	6
1344.2.q.s.961.1		2	56.27	even	2
2352.2.a.f.1.1		1	28.23	odd	6
2352.2.a.t.1.1		1	28.19	even	6
2352.2.q.u.961.1		2	4.3	odd	2
2352.2.q.u.1537.1		2	28.11	odd	6
7056.2.a.w.1.1		1	84.47	odd	6
7056.2.a.bl.1.1		1	84.23	even	6
7350.2.a.q.1.1		1	35.9	even	6
7350.2.a.bl.1.1		1	35.19	odd	6
9408.2.a.q.1.1		1	56.19	even	6
9408.2.a.z.1.1		1	56.37	even	6
9408.2.a.ce.1.1		1	56.5	odd	6
9408.2.a.cr.1.1		1	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	294.2.e.b.79.1

Level	$294$
Weight	$2$
Character	294.79
Analytic conductor	$2.348$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$