LMFDB - Embedded newform 336.2.q.b.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("336.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$336 = 2^{4} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	336.q (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:	$2.68297350792$
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:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.2.q.b.289.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.50000 - 4.33013i) q^{11} +1.00000 q^{15} +(2.00000 - 3.46410i) q^{17} +(4.00000 + 6.92820i) q^{19} +(2.50000 + 0.866025i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +1.00000 q^{27} -5.00000 q^{29} +(1.50000 - 2.59808i) q^{31} +(2.50000 + 4.33013i) q^{33} +(-2.00000 + 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} -2.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{51} +(4.50000 - 7.79423i) q^{53} -5.00000 q^{55} -8.00000 q^{57} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-2.00000 + 1.73205i) q^{63} +(-1.00000 + 1.73205i) q^{67} +4.00000 q^{69} -2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{75} +(-12.5000 - 4.33013i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.00000 q^{83} -4.00000 q^{85} +(2.50000 - 4.33013i) q^{87} +(3.00000 + 5.19615i) q^{89} +(1.50000 + 2.59808i) q^{93} +(4.00000 - 6.92820i) q^{95} +7.00000 q^{97} -5.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - q^{3} - q^{5} - q^{7} - q^{9} + 5 q^{11} + 2 q^{15} + 4 q^{17} + 8 q^{19} + 5 q^{21} - 4 q^{23} + 4 q^{25} + 2 q^{27} - 10 q^{29} + 3 q^{31} + 5 q^{33} - 4 q^{35} + 4 q^{37} - 4 q^{43} - q^{45}+ \cdots - 10 q^{99}+O(q^{100})$ 2 * q - q^3 - q^5 - q^7 - q^9 + 5 * q^11 + 2 * q^15 + 4 * q^17 + 8 * q^19 + 5 * q^21 - 4 * q^23 + 4 * q^25 + 2 * q^27 - 10 * q^29 + 3 * q^31 + 5 * q^33 - 4 * q^35 + 4 * q^37 - 4 * q^43 - q^45 - 6 * q^47 - 13 * q^49 + 4 * q^51 + 9 * q^53 - 10 * q^55 - 16 * q^57 - 11 * q^59 + 6 * q^61 - 4 * q^63 - 2 * q^67 + 8 * q^69 - 4 * q^71 - 10 * q^73 + 4 * q^75 - 25 * q^77 + 3 * q^79 - q^81 + 14 * q^83 - 8 * q^85 + 5 * q^87 + 6 * q^89 + 3 * q^93 + 8 * q^95 + 14 * q^97 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$ .

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$		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			0
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.802955	+	0.596040i	$0.203260\pi$
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	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			0
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	−0.699301	−	0.714827i	$-0.746505\pi$
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	0.968709	+	0.248199i	$0.0798387\pi$
$32$		0			0
$33$	2.50000	+	4.33013i	0.435194	+	0.753778i
$34$		0			0
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		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	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$	2.00000	+	3.46410i	0.280056	+	0.485071i
$52$		0			0
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$		0			0
$57$	−8.00000			−1.05963
$58$		0			0
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		0			0
$63$	−2.00000	+	1.73205i	−0.251976	+	0.218218i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$		0			0
$77$	−12.5000	−	4.33013i	−1.42451	−	0.493464i
$78$		0			0
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$		0			0
$81$	−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
$86$		0			0
$87$	2.50000	−	4.33013i	0.268028	−	0.464238i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$		0			0
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$		0			0
$99$	−5.00000			−0.502519
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$		0			0
$105$	−0.500000	−	2.59808i	−0.0487950	−	0.253546i
$106$		0			0
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$	−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	$0.228811\pi$
$114$		0			0
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$		0			0
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$		0			0
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$		0			0
$133$	16.0000	−	13.8564i	1.38738	−	1.20150i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$		0			0
$139$	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
$142$		0			0
$143$		0			0
$144$		0			0
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$		0			0
$147$	1.00000	−	6.92820i	0.0824786	−	0.571429i
$148$		0			0
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	0.935857	−	0.352381i	$-0.114628\pi$
$152$		0			0
$153$	−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	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$		0			0
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$		0			0
$161$	−8.00000	+	6.92820i	−0.630488	+	0.546019i
$162$		0			0
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$		0			0
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$		0			0
$167$	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
$170$		0			0
$171$	4.00000	−	6.92820i	0.305888	−	0.529813i
$172$		0			0
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	−0.892956	−	0.450145i	$-0.851372\pi$
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	0.0566411	−	0.998395i	$-0.481961\pi$
$174$		0			0
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$		0			0
$177$	−5.50000	−	9.52628i	−0.413405	−	0.716039i
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	−6.00000			−0.443533
$184$		0			0
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	−10.0000	−	17.3205i	−0.731272	−	1.26660i
$188$		0			0
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$		0			0
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.863743	+	0.503932i	$0.168114\pi$
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.00454614	+	0.999990i	$0.498553\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$		0			0
$195$		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	$0.477302\pi$
$198$		0			0
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$		0			0
$203$	2.50000	+	12.9904i	0.175466	+	0.911746i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−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	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$		0			0
$213$	1.00000	−	1.73205i	0.0685189	−	0.118678i
$214$		0			0
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$		0			0
$217$	−7.50000	−	2.59808i	−0.509133	−	0.176369i
$218$		0			0
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	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
$226$		0			0
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$		0			0
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$		0			0
$231$	10.0000	−	8.66025i	0.657952	−	0.569803i
$232$		0			0
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	0.924072	−	0.382219i	$-0.124840\pi$
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	−0.793047	+	0.609160i	$0.791507\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$	−3.00000			−0.194871
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−3.50000	+	6.06218i	−0.221803	+	0.384175i
$250$		0			0
$251$	−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
$254$		0			0
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$		0			0
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	8.00000	−	6.92820i	0.497096	−	0.430498i
$260$		0			0
$261$	2.50000	+	4.33013i	0.154746	+	0.268028i
$262$		0			0
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$		0			0
$267$	−6.00000			−0.367194
$268$		0			0
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.189404	+	0.981899i	$0.560656\pi$
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.755648	+	0.654978i	$0.772678\pi$
$270$		0			0
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	0.998722	−	0.0505395i	$-0.0160941\pi$
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	−0.543130	+	0.839649i	$0.682761\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.0000	−	17.3205i	−0.603023	−	1.04447i
$276$		0			0
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$		0			0
$279$	−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	$0.481000\pi$
$282$		0			0
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$		0			0
$285$	4.00000	+	6.92820i	0.236940	+	0.410391i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	−3.50000	+	6.06218i	−0.205174	+	0.355371i
$292$		0			0
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$		0			0
$295$	11.0000			0.640445
$296$		0			0
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.00000	+	5.19615i	0.0576390	+	0.299501i
$302$		0			0
$303$	−5.00000	−	8.66025i	−0.287242	−	0.497519i
$304$		0			0
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$		0			0
$307$	−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
$310$		0			0
$311$	−16.0000	+	27.7128i	−0.907277	+	1.57145i	−0.0894452	+	0.995992i	$0.528509\pi$
$311$	−16.0000	+	27.7128i	−0.907277	+	1.57145i	−0.817832	+	0.575458i	$0.804824\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$		0			0
$315$	2.50000	+	0.866025i	0.140859	+	0.0487950i
$316$		0			0
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	0.820822	−	0.571184i	$-0.193516\pi$
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	−0.905071	+	0.425261i	$0.860182\pi$
$318$		0			0
$319$	−12.5000	+	21.6506i	−0.699866	+	1.21220i
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$	32.0000			1.78053
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$		0			0
$329$	−12.0000	+	10.3923i	−0.661581	+	0.572946i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$		0			0
$333$	2.00000	−	3.46410i	0.109599	−	0.189832i
$334$		0			0
$335$	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	$0.421169\pi$
$338$		0			0
$339$	−8.00000	+	13.8564i	−0.434500	+	0.752577i
$340$		0			0
$341$	−7.50000	−	12.9904i	−0.406148	−	0.703469i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	−2.00000	−	3.46410i	−0.107676	−	0.186501i
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	1.00000	+	1.73205i	0.0530745	+	0.0919277i
$356$		0			0
$357$	8.00000	−	6.92820i	0.423405	−	0.366679i
$358$		0			0
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$	14.0000			0.734809
$364$		0			0
$365$	10.0000			0.523424
$366$		0			0
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	−0.554264	−	0.832341i	$-0.687000\pi$
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	0.997960	+	0.0638362i	$0.0203335\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−22.5000	−	7.79423i	−1.16814	−	0.404656i
$372$		0			0
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$		0			0
$375$	4.50000	−	7.79423i	0.232379	−	0.402492i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	4.50000	−	7.79423i	0.230542	−	0.399310i
$382$		0			0
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.863367	−	0.504576i	$-0.831649\pi$
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.00529229	−	0.999986i	$-0.501685\pi$
$384$		0			0
$385$	2.50000	+	12.9904i	0.127412	+	0.662051i
$386$		0			0
$387$	1.00000	+	1.73205i	0.0508329	+	0.0880451i
$388$		0			0
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	−0.839561	−	0.543266i	$-0.817187\pi$
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	0.890263	+	0.455448i	$0.150521\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$	−1.00000			−0.0504433
$394$		0			0
$395$	1.50000	−	2.59808i	0.0754732	−	0.130723i
$396$		0			0
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.823058	−	0.567957i	$-0.807734\pi$
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.0803356	−	0.996768i	$-0.525599\pi$
$398$		0			0
$399$	4.00000	+	20.7846i	0.200250	+	1.04053i
$400$		0			0
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	−0.992932	−	0.118686i	$-0.962132\pi$
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	0.393680	−	0.919247i	$-0.371202\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	20.0000			0.991363
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$	1.00000	+	1.73205i	0.0493264	+	0.0854358i
$412$		0			0
$413$	27.5000	+	9.52628i	1.35319	+	0.468758i
$414$		0			0
$415$	−3.50000	−	6.06218i	−0.171808	−	0.297581i
$416$		0			0
$417$	−7.00000	+	12.1244i	−0.342791	+	0.593732i
$418$		0			0
$419$		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	$0.239028\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	−8.00000	−	13.8564i	−0.388057	−	0.672134i
$426$		0			0
$427$	12.0000	−	10.3923i	0.580721	−	0.502919i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	−5.00000			−0.239732
$436$		0			0
$437$	16.0000	−	27.7128i	0.765384	−	1.32568i
$438$		0			0
$439$	7.50000	+	12.9904i	0.357955	+	0.619997i	0.987619	−	0.156871i	$-0.0501406\pi$
$439$	7.50000	+	12.9904i	0.357955	+	0.619997i	−0.629664	+	0.776868i	$0.716807\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	0.994187	−	0.107671i	$-0.0343394\pi$
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	−0.590339	+	0.807155i	$0.701006\pi$
$444$		0			0
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$		0			0
$447$	−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	$0.376769\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	9.50000	+	16.4545i	0.446349	+	0.773099i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	0.233890	−	0.972263i	$-0.424854\pi$
$458$		0			0
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	1.50000	−	2.59808i	0.0695608	−	0.120483i
$466$		0			0
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	0.536352	−	0.843995i	$-0.319802\pi$
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	−0.999097	+	0.0424970i	$0.986469\pi$
$468$		0			0
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$		0			0
$471$	2.00000	+	3.46410i	0.0921551	+	0.159617i
$472$		0			0
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$		0			0
$475$	32.0000			1.46826
$476$		0			0
$477$	−9.00000			−0.412082
$478$		0			0
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.00422900	−	0.999991i	$-0.498654\pi$
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.863903	−	0.503658i	$-0.168013\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−2.00000	−	10.3923i	−0.0910032	−	0.472866i
$484$		0			0
$485$	−3.50000	−	6.06218i	−0.158927	−	0.275269i
$486$		0			0
$487$	2.50000	−	4.33013i	0.113286	−	0.196217i	−0.803807	−	0.594890i	$-0.797196\pi$
$487$	2.50000	−	4.33013i	0.113286	−	0.196217i	0.917093	+	0.398673i	$0.130529\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	−9.00000			−0.406164			−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000			−0.406164			−0.203082	+	0.979162i	$0.565096\pi$
$492$		0			0
$493$	−10.0000	+	17.3205i	−0.450377	+	0.780076i
$494$		0			0
$495$	2.50000	+	4.33013i	0.112367	+	0.194625i
$496$		0			0
$497$	1.00000	+	5.19615i	0.0448561	+	0.233079i
$498$		0			0
$499$	5.00000	+	8.66025i	0.223831	+	0.387686i	0.955968	−	0.293471i	$-0.0948104\pi$
$499$	5.00000	+	8.66025i	0.223831	+	0.387686i	−0.732137	+	0.681157i	$0.761477\pi$
$500$		0			0
$501$	−7.00000	+	12.1244i	−0.312737	+	0.541676i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$		0			0
$507$	6.50000	−	11.2583i	0.288675	−	0.500000i
$508$		0			0
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$		0			0
$511$	25.0000	+	8.66025i	1.10593	+	0.383107i
$512$		0			0
$513$	4.00000	+	6.92820i	0.176604	+	0.305888i
$514$		0			0
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$		0			0
$517$	−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	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$		0			0
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	0.940129	−	0.340818i	$-0.110704\pi$
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	−0.765222	+	0.643767i	$0.777371\pi$
$524$		0			0
$525$	8.00000	−	6.92820i	0.349149	−	0.302372i
$526$		0			0
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	11.0000			0.477359
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.50000	−	2.59808i	0.0648507	−	0.112325i
$536$		0			0
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$		0			0
$539$	−5.00000	+	34.6410i	−0.215365	+	1.49209i
$540$		0			0
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	0.992036	−	0.125952i	$-0.0401986\pi$
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	−0.605096	+	0.796152i	$0.706865\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$		0			0
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$		0			0
$551$	−20.0000	−	34.6410i	−0.852029	−	1.47576i
$552$		0			0
$553$	6.00000	−	5.19615i	0.255146	−	0.220963i
$554$		0			0
$555$	2.00000	+	3.46410i	0.0848953	+	0.147043i
$556$		0			0
$557$	11.5000	−	19.9186i	0.487271	−	0.843978i	−0.512622	−	0.858614i	$-0.671326\pi$
$557$	11.5000	−	19.9186i	0.487271	−	0.843978i	0.999893	+	0.0146368i	$0.00465919\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	20.0000			0.844401
$562$		0			0
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	0.987666	+	0.156578i	$0.0500463\pi$
$564$		0			0
$565$	−8.00000	−	13.8564i	−0.336563	−	0.582943i
$566$		0			0
$567$	2.50000	+	0.866025i	0.104990	+	0.0363696i
$568$		0			0
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	−0.999994	−	0.00354413i	$-0.998872\pi$
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	0.496928	−	0.867792i	$-0.334461\pi$
$570$		0			0
$571$	−15.0000	+	25.9808i	−0.627730	+	1.08726i	0.360276	+	0.932846i	$0.382683\pi$
$571$	−15.0000	+	25.9808i	−0.627730	+	1.08726i	−0.988006	+	0.154415i	$0.950651\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	−16.0000			−0.667246
$576$		0			0
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$		0			0
$579$	−2.50000	−	4.33013i	−0.103896	−	0.179954i
$580$		0			0
$581$	−3.50000	−	18.1865i	−0.145204	−	0.754505i
$582$		0			0
$583$	−22.5000	−	38.9711i	−0.931855	−	1.61402i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−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
$590$		0			0
$591$	−1.00000	+	1.73205i	−0.0411345	+	0.0712470i
$592$		0			0
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	−0.952869	−	0.303383i	$-0.901884\pi$
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	0.213697	−	0.976900i	$-0.431449\pi$
$594$		0			0
$595$	2.00000	+	10.3923i	0.0819920	+	0.426043i
$596$		0			0
$597$	−2.00000	−	3.46410i	−0.0818546	−	0.141776i
$598$		0			0
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	0.377869	+	0.925859i	$0.376657\pi$
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	−0.990752	+	0.135686i	$0.956676\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$		0			0
$605$	−7.00000	+	12.1244i	−0.284590	+	0.492925i
$606$		0			0
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	−0.998415	−	0.0562808i	$-0.982076\pi$
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	0.450467	−	0.892793i	$-0.351258\pi$
$608$		0			0
$609$	−12.5000	−	4.33013i	−0.506526	−	0.175466i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$		0			0
$615$		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	$0.487182\pi$
$618$		0			0
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$		0			0
$623$	12.0000	−	10.3923i	0.480770	−	0.416359i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	−20.0000	+	34.6410i	−0.798723	+	1.38343i
$628$		0			0
$629$	16.0000			0.637962
$630$		0			0
$631$	19.0000			0.756378			0.378189	−	0.925728i	$-0.376547\pi$
$631$	19.0000			0.756378			0.378189	+	0.925728i	$0.376547\pi$
$632$		0			0
$633$	1.00000	−	1.73205i	0.0397464	−	0.0688428i
$634$		0			0
$635$	4.50000	+	7.79423i	0.178577	+	0.309305i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$		0			0
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	0.486409	+	0.873731i	$0.338307\pi$
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	−0.999878	+	0.0156233i	$0.995027\pi$
$642$		0			0
$643$	−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
$646$		0			0
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	−0.986916	−	0.161233i	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$		0			0
$649$	27.5000	+	47.6314i	1.07947	+	1.86970i
$650$		0			0
$651$	6.00000	−	5.19615i	0.235159	−	0.203653i
$652$		0			0
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$	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	$-0.215682\pi$
$659$	40.0000			1.55818			0.779089	+	0.626913i	$0.215682\pi$
$660$		0			0
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−20.0000	−	6.92820i	−0.775567	−	0.268664i
$666$		0			0
$667$	10.0000	+	17.3205i	0.387202	+	0.670653i
$668$		0			0
$669$	−3.50000	+	6.06218i	−0.135318	+	0.234377i
$670$		0			0
$671$	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	$0.619341\pi$
$674$		0			0
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$		0			0
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$		0			0
$679$	−3.50000	−	18.1865i	−0.134318	−	0.697935i
$680$		0			0
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$		0			0
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$		0			0
$687$	−20.0000			−0.763048
$688$		0			0
$689$		0			0
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$		0			0
$693$	2.50000	+	12.9904i	0.0949671	+	0.493464i
$694$		0			0
$695$	−7.00000	−	12.1244i	−0.265525	−	0.459903i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−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
$704$		0			0
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$		0			0
$707$	25.0000	+	8.66025i	0.940222	+	0.325702i
$708$		0			0
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$		0			0
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$		0			0
$713$	−12.0000			−0.449404
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$		0			0
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	16.0000	−	13.8564i	0.595871	−	0.516040i
$722$		0			0
$723$	12.5000	+	21.6506i	0.464880	+	0.805196i
$724$		0			0
$725$	−10.0000	+	17.3205i	−0.371391	+	0.643268i
$726$		0			0
$727$	−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
$730$		0			0
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$		0			0
$735$	−6.50000	+	2.59808i	−0.239756	+	0.0958315i
$736$		0			0
$737$	5.00000	+	8.66025i	0.184177	+	0.319005i
$738$		0			0
$739$	−15.0000	+	25.9808i	−0.551784	+	0.955718i	0.446362	+	0.894852i	$0.352719\pi$
$739$	−15.0000	+	25.9808i	−0.551784	+	0.955718i	−0.998146	+	0.0608653i	$0.980614\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.0000			−1.10059			−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000			−1.10059			−0.550297	+	0.834969i	$0.685485\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$	−3.50000	−	6.06218i	−0.128058	−	0.221803i
$748$		0			0
$749$	6.00000	−	5.19615i	0.219235	−	0.189863i
$750$		0			0
$751$	22.5000	+	38.9711i	0.821037	+	1.42208i	0.904911	+	0.425601i	$0.139937\pi$
$751$	22.5000	+	38.9711i	0.821037	+	1.42208i	−0.0838743	+	0.996476i	$0.526729\pi$
$752$		0			0
$753$	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	$0.938398\pi$
$758$		0			0
$759$	10.0000	−	17.3205i	0.362977	−	0.628695i
$760$		0			0
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	0.784373	−	0.620289i	$-0.212985\pi$
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	−0.929373	+	0.369142i	$0.879652\pi$
$762$		0			0
$763$	−5.00000	−	1.73205i	−0.181012	−	0.0627044i
$764$		0			0
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−35.0000			−1.26213			−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000			−1.26213			−0.631066	+	0.775729i	$0.717382\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$		0			0
$773$	−5.00000	+	8.66025i	−0.179838	+	0.311488i	−0.941825	−	0.336104i	$-0.890891\pi$
$773$	−5.00000	+	8.66025i	−0.179838	+	0.311488i	0.761987	+	0.647592i	$0.224224\pi$
$774$		0			0
$775$	−6.00000	−	10.3923i	−0.215526	−	0.373303i
$776$		0			0
$777$	2.00000	+	10.3923i	0.0717496	+	0.372822i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$		0			0
$783$	−5.00000			−0.178685
$784$		0			0
$785$	−4.00000			−0.142766
$786$		0			0
$787$	−9.00000	+	15.5885i	−0.320815	+	0.555668i	−0.980656	−	0.195737i	$-0.937290\pi$
$787$	−9.00000	+	15.5885i	−0.320815	+	0.555668i	0.659841	+	0.751405i	$0.270624\pi$
$788$		0			0
$789$	−15.0000	−	25.9808i	−0.534014	−	0.924940i
$790$		0			0
$791$	−8.00000	−	41.5692i	−0.284447	−	1.47803i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	4.50000	−	7.79423i	0.159599	−	0.276433i
$796$		0			0
$797$	21.0000			0.743858			0.371929	−	0.928261i	$-0.378696\pi$
$797$	21.0000			0.743858			0.371929	+	0.928261i	$0.378696\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$		0			0
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$		0			0
$803$	25.0000	+	43.3013i	0.882231	+	1.52807i
$804$		0			0
$805$	10.0000	+	3.46410i	0.352454	+	0.122094i
$806$		0			0
$807$	−15.5000	−	26.8468i	−0.545626	−	0.945052i
$808$		0			0
$809$	−20.0000	+	34.6410i	−0.703163	+	1.21791i	0.264188	+	0.964471i	$0.414896\pi$
$809$	−20.0000	+	34.6410i	−0.703163	+	1.21791i	−0.967351	+	0.253442i	$0.918437\pi$
$810$		0			0
$811$	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
$814$		0			0
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$		0			0
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	0.997397	−	0.0721058i	$-0.0229719\pi$
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	−0.561144	+	0.827718i	$0.689639\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$		0			0
$825$	20.0000			0.696311
$826$		0			0
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$		0			0
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	−0.442145	−	0.896943i	$-0.645783\pi$
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	0.997848	−	0.0655624i	$-0.0208842\pi$
$830$		0			0
$831$	8.00000	+	13.8564i	0.277517	+	0.480673i
$832$		0			0
$833$	−4.00000	+	27.7128i	−0.138592	+	0.960192i
$834$		0			0
$835$	−7.00000	−	12.1244i	−0.242245	−	0.419581i
$836$		0			0
$837$	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
$842$		0			0
$843$	−1.00000	+	1.73205i	−0.0344418	+	0.0596550i
$844$		0			0
$845$	6.50000	+	11.2583i	0.223607	+	0.387298i
$846$		0			0
$847$	−28.0000	+	24.2487i	−0.962091	+	0.833196i
$848$		0			0
$849$	5.00000	+	8.66025i	0.171600	+	0.297219i
$850$		0			0
$851$	8.00000	−	13.8564i	0.274236	−	0.474991i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	−8.00000			−0.273594
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	−0.995475	−	0.0950262i	$-0.969707\pi$
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	0.415442	−	0.909620i	$-0.363627\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.00000	+	8.66025i	0.170202	+	0.294798i	0.938490	−	0.345305i	$-0.112225\pi$
$863$	5.00000	+	8.66025i	0.170202	+	0.294798i	−0.768288	+	0.640104i	$0.778891\pi$
$864$		0			0
$865$	−11.0000	+	19.0526i	−0.374011	+	0.647806i
$866$		0			0
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	15.0000			0.508840
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−3.50000	−	6.06218i	−0.118457	−	0.205174i
$874$		0			0
$875$	4.50000	+	23.3827i	0.152128	+	0.790479i
$876$		0			0
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$		0			0
$879$	10.5000	−	18.1865i	0.354156	−	0.613417i
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	40.0000			1.34611			0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000			1.34611			0.673054	+	0.739594i	$0.264982\pi$
$884$		0			0
$885$	−5.50000	+	9.52628i	−0.184880	+	0.320222i
$886$		0			0
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	4.50000	+	23.3827i	0.150925	+	0.784230i
$890$		0			0
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$		0			0
$893$	24.0000	−	41.5692i	0.803129	−	1.39106i
$894$		0			0
$895$	−12.0000			−0.401116
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.50000	+	12.9904i	−0.250139	+	0.433253i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$	−5.00000	−	1.73205i	−0.166390	−	0.0576390i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$		0			0
$909$	10.0000			0.331679
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	17.5000	−	30.3109i	0.579165	−	1.00314i
$914$		0			0
$915$	3.00000	+	5.19615i	0.0991769	+	0.171780i
$916$		0			0
$917$	2.00000	−	1.73205i	0.0660458	−	0.0571974i
$918$		0			0
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	−0.999475	−	0.0323936i	$-0.989687\pi$
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	0.471684	−	0.881768i	$-0.343646\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	16.0000			0.526077
$926$		0			0
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$		0			0
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	−44.0000	−	34.6410i	−1.44204	−	1.13531i
$932$		0			0
$933$	−16.0000	−	27.7128i	−0.523816	−	0.907277i
$934$		0			0
$935$	−10.0000	+	17.3205i	−0.327035	+	0.566441i
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$		0			0
$939$	1.00000			0.0326338
$940$		0			0
$941$	5.50000	−	9.52628i	0.179295	−	0.310548i	−0.762344	−	0.647172i	$-0.775952\pi$
$941$	5.50000	−	9.52628i	0.179295	−	0.310548i	0.941639	+	0.336624i	$0.109285\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−2.00000	+	1.73205i	−0.0650600	+	0.0563436i
$946$		0			0
$947$	−16.0000	−	27.7128i	−0.519930	−	0.900545i	−0.999732	−	0.0231683i	$-0.992625\pi$
$947$	−16.0000	−	27.7128i	−0.519930	−	0.900545i	0.479801	−	0.877377i	$-0.340709\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	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	$0.489687\pi$
$954$		0			0
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$		0			0
$957$	−12.5000	−	21.6506i	−0.404068	−	0.699866i
$958$		0			0
$959$	−5.00000	−	1.73205i	−0.161458	−	0.0559308i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$		0			0
$963$	1.50000	−	2.59808i	0.0483368	−	0.0837218i
$964$		0			0
$965$	5.00000			0.160956
$966$		0			0
$967$	61.0000			1.96163			0.980814	−	0.194946i	$-0.0624533\pi$
$967$	61.0000			1.96163			0.980814	+	0.194946i	$0.0624533\pi$
$968$		0			0
$969$	−16.0000	+	27.7128i	−0.513994	+	0.890264i
$970$		0			0
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	−7.00000	−	36.3731i	−0.224410	−	1.16607i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	30.0000			0.958804
$980$		0			0
$981$	−2.00000			−0.0638551
$982$		0			0
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.226778	+	0.973946i	$0.572819\pi$
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.730073	+	0.683369i	$0.760514\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$		0			0
$987$	−3.00000	−	15.5885i	−0.0954911	−	0.496186i
$988$		0			0
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$		0			0
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	−0.202988	−	0.979181i	$-0.565065\pi$
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	0.949490	−	0.313798i	$-0.101602\pi$
$992$		0			0
$993$	4.00000			0.126936
$994$		0			0
$995$	4.00000			0.126809
$996$		0			0
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	0.390822	+	0.920466i	$0.372191\pi$
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	−0.992558	+	0.121771i	$0.961143\pi$
$998$		0			0
$999$	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	336.2.q.b.193.1		2
3.2	odd	2		1008.2.s.k.865.1		2
4.3	odd	2		42.2.e.a.25.1	✓	2
7.2	even	3	inner	336.2.q.b.289.1		2
7.3	odd	6		2352.2.a.f.1.1		1
7.4	even	3		2352.2.a.t.1.1		1
7.5	odd	6		2352.2.q.u.961.1		2
7.6	odd	2		2352.2.q.u.1537.1		2
8.3	odd	2		1344.2.q.g.193.1		2
8.5	even	2		1344.2.q.s.193.1		2
12.11	even	2		126.2.g.c.109.1		2
20.3	even	4		1050.2.o.a.949.1		4
20.7	even	4		1050.2.o.a.949.2		4
20.19	odd	2		1050.2.i.l.151.1		2
21.2	odd	6		1008.2.s.k.289.1		2
21.11	odd	6		7056.2.a.w.1.1		1
21.17	even	6		7056.2.a.bl.1.1		1
28.3	even	6		294.2.a.f.1.1		1
28.11	odd	6		294.2.a.e.1.1		1
28.19	even	6		294.2.e.b.79.1		2
28.23	odd	6		42.2.e.a.37.1	yes	2
28.27	even	2		294.2.e.b.67.1		2
36.7	odd	6		1134.2.h.e.109.1		2
36.11	even	6		1134.2.h.l.109.1		2
36.23	even	6		1134.2.e.e.865.1		2
36.31	odd	6		1134.2.e.l.865.1		2
56.3	even	6		9408.2.a.z.1.1		1
56.11	odd	6		9408.2.a.ce.1.1		1
56.37	even	6		1344.2.q.s.961.1		2
56.45	odd	6		9408.2.a.cr.1.1		1
56.51	odd	6		1344.2.q.g.961.1		2
56.53	even	6		9408.2.a.q.1.1		1
84.11	even	6		882.2.a.c.1.1		1
84.23	even	6		126.2.g.c.37.1		2
84.47	odd	6		882.2.g.i.667.1		2
84.59	odd	6		882.2.a.d.1.1		1
84.83	odd	2		882.2.g.i.361.1		2
140.23	even	12		1050.2.o.a.499.2		4
140.39	odd	6		7350.2.a.bl.1.1		1
140.59	even	6		7350.2.a.q.1.1		1
140.79	odd	6		1050.2.i.l.751.1		2
140.107	even	12		1050.2.o.a.499.1		4
252.23	even	6		1134.2.h.l.541.1		2
252.79	odd	6		1134.2.e.l.919.1		2
252.191	even	6		1134.2.e.e.919.1		2
252.247	odd	6		1134.2.h.e.541.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	4.3	odd	2
42.2.e.a.37.1	yes	2	28.23	odd	6
126.2.g.c.37.1		2	84.23	even	6
126.2.g.c.109.1		2	12.11	even	2
294.2.a.e.1.1		1	28.11	odd	6
294.2.a.f.1.1		1	28.3	even	6
294.2.e.b.67.1		2	28.27	even	2
294.2.e.b.79.1		2	28.19	even	6
336.2.q.b.193.1		2	1.1	even	1	trivial
336.2.q.b.289.1		2	7.2	even	3	inner
882.2.a.c.1.1		1	84.11	even	6
882.2.a.d.1.1		1	84.59	odd	6
882.2.g.i.361.1		2	84.83	odd	2
882.2.g.i.667.1		2	84.47	odd	6
1008.2.s.k.289.1		2	21.2	odd	6
1008.2.s.k.865.1		2	3.2	odd	2
1050.2.i.l.151.1		2	20.19	odd	2
1050.2.i.l.751.1		2	140.79	odd	6
1050.2.o.a.499.1		4	140.107	even	12
1050.2.o.a.499.2		4	140.23	even	12
1050.2.o.a.949.1		4	20.3	even	4
1050.2.o.a.949.2		4	20.7	even	4
1134.2.e.e.865.1		2	36.23	even	6
1134.2.e.e.919.1		2	252.191	even	6
1134.2.e.l.865.1		2	36.31	odd	6
1134.2.e.l.919.1		2	252.79	odd	6
1134.2.h.e.109.1		2	36.7	odd	6
1134.2.h.e.541.1		2	252.247	odd	6
1134.2.h.l.109.1		2	36.11	even	6
1134.2.h.l.541.1		2	252.23	even	6
1344.2.q.g.193.1		2	8.3	odd	2
1344.2.q.g.961.1		2	56.51	odd	6
1344.2.q.s.193.1		2	8.5	even	2
1344.2.q.s.961.1		2	56.37	even	6
2352.2.a.f.1.1		1	7.3	odd	6
2352.2.a.t.1.1		1	7.4	even	3
2352.2.q.u.961.1		2	7.5	odd	6
2352.2.q.u.1537.1		2	7.6	odd	2
7056.2.a.w.1.1		1	21.11	odd	6
7056.2.a.bl.1.1		1	21.17	even	6
7350.2.a.q.1.1		1	140.59	even	6
7350.2.a.bl.1.1		1	140.39	odd	6
9408.2.a.q.1.1		1	56.53	even	6
9408.2.a.z.1.1		1	56.3	even	6
9408.2.a.ce.1.1		1	56.11	odd	6
9408.2.a.cr.1.1		1	56.45	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

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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	336.2.q.b.193.1

Level	$336$
Weight	$2$
Character	336.193
Analytic conductor	$2.683$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$