LMFDB - Embedded newform 1170.2.bp.b.919.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(289,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2,-8,0,0,0,0,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			919.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.919
Dual form			1170.2.bp.b.289.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(4.33013 - 2.50000i) q^{7} +1.00000i q^{8} +(-2.23205 - 0.133975i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-2.59808 - 2.50000i) q^{13} +5.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-1.86603 - 1.23205i) q^{20} +(2.59808 - 1.50000i) q^{22} +(3.00000 - 4.00000i) q^{25} +(-1.00000 - 3.46410i) q^{26} +(4.33013 + 2.50000i) q^{28} +(-1.00000 + 1.73205i) q^{29} +4.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +4.00000 q^{34} +(-6.16025 + 9.33013i) q^{35} +(7.79423 + 4.50000i) q^{37} -1.00000i q^{38} +(-1.00000 - 2.00000i) q^{40} +(5.00000 - 8.66025i) q^{41} +(-10.3923 + 6.00000i) q^{43} +3.00000 q^{44} +7.00000i q^{47} +(9.00000 - 15.5885i) q^{49} +(4.59808 - 1.96410i) q^{50} +(0.866025 - 3.50000i) q^{52} -3.00000i q^{53} +(-0.401924 + 6.69615i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-1.73205 + 1.00000i) q^{58} +(3.46410 + 2.00000i) q^{62} -1.00000 q^{64} +(7.69615 + 2.40192i) q^{65} +(-5.19615 - 3.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-10.0000 + 5.00000i) q^{70} +(6.00000 + 10.3923i) q^{71} +16.0000i q^{73} +(4.50000 + 7.79423i) q^{74} +(0.500000 - 0.866025i) q^{76} -15.0000i q^{77} +14.0000 q^{79} +(0.133975 - 2.23205i) q^{80} +(8.66025 - 5.00000i) q^{82} -10.0000i q^{83} +(-4.92820 + 7.46410i) q^{85} -12.0000 q^{86} +(2.59808 + 1.50000i) q^{88} +(0.500000 - 0.866025i) q^{89} +(-17.5000 - 4.33013i) q^{91} +(-3.50000 + 6.06218i) q^{94} +(1.86603 + 1.23205i) q^{95} +(-8.66025 + 5.00000i) q^{97} +(15.5885 - 9.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 8 q^{5} - 2 q^{10} + 6 q^{11} + 20 q^{14} - 2 q^{16} - 2 q^{19} - 4 q^{20} + 12 q^{25} - 4 q^{26} - 4 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} - 4 q^{40} + 20 q^{41} + 12 q^{44} + 36 q^{49}+ \cdots + 4 q^{95}+O(q^{100}) $ 4 * q + 2 * q^4 - 8 * q^5 - 2 * q^10 + 6 * q^11 + 20 * q^14 - 2 * q^16 - 2 * q^19 - 4 * q^20 + 12 * q^25 - 4 * q^26 - 4 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 - 4 * q^40 + 20 * q^41 + 12 * q^44 + 36 * q^49 + 8 * q^50 - 12 * q^55 + 10 * q^56 - 4 * q^64 + 10 * q^65 - 40 * q^70 + 24 * q^71 + 18 * q^74 + 2 * q^76 + 56 * q^79 + 4 * q^80 + 8 * q^85 - 48 * q^86 + 2 * q^89 - 70 * q^91 - 14 * q^94 + 4 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$		0			0
$7$	4.33013	−	2.50000i	1.63663	−	0.944911i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	4.33013	−	2.50000i	1.63663	−	0.944911i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.23205	−	0.133975i	−0.705836	−	0.0423665i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$	5.00000			1.33631
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	−0.0171533	−	0.999853i	$-0.505460\pi$
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	0.857321	+	0.514782i	$0.172127\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.86603	−	1.23205i	−0.417256	−	0.275495i
$21$		0			0
$22$	2.59808	−	1.50000i	0.553912	−	0.319801i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$		0			0
$28$	4.33013	+	2.50000i	0.818317	+	0.472456i
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	4.00000			0.685994
$35$	−6.16025	+	9.33013i	−1.04127	+	1.57708i
$36$		0			0
$37$	7.79423	+	4.50000i	1.28136	+	0.739795i	0.977098	−	0.212792i	$-0.0682556\pi$
$37$	7.79423	+	4.50000i	1.28136	+	0.739795i	0.304266	+	0.952587i	$0.401589\pi$
$38$		−	1.00000i		−	0.162221i
$39$		0			0
$40$	−1.00000	−	2.00000i	−0.158114	−	0.316228i
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	−0.150567	−	0.988600i	$-0.548110\pi$
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	0.931436	−	0.363905i	$-0.118557\pi$
$42$		0			0
$43$	−10.3923	+	6.00000i	−1.58481	+	0.914991i	−0.590669	+	0.806914i	$0.701136\pi$
$43$	−10.3923	+	6.00000i	−1.58481	+	0.914991i	−0.994142	+	0.108078i	$0.965531\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$		0			0
$47$			7.00000i			1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$			7.00000i			1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$		0			0
$49$	9.00000	−	15.5885i	1.28571	−	2.22692i
$50$	4.59808	−	1.96410i	0.650266	−	0.277766i
$51$		0			0
$52$	0.866025	−	3.50000i	0.120096	−	0.485363i
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$		0			0
$55$	−0.401924	+	6.69615i	−0.0541954	+	0.902909i
$56$	2.50000	+	4.33013i	0.334077	+	0.578638i
$57$		0			0
$58$	−1.73205	+	1.00000i	−0.227429	+	0.131306i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	3.46410	+	2.00000i	0.439941	+	0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.69615	+	2.40192i	0.954590	+	0.297922i
$66$		0			0
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	0.147802	−	0.989017i	$-0.452780\pi$
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	−0.782613	+	0.622509i	$0.786114\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$		0			0
$70$	−10.0000	+	5.00000i	−1.19523	+	0.597614i
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$		0			0
$73$			16.0000i			1.87266i	0.351123	+	0.936329i	$0.385800\pi$
$73$			16.0000i			1.87266i	−0.351123	+	0.936329i	$0.614200\pi$
$74$	4.50000	+	7.79423i	0.523114	+	0.906061i
$75$		0			0
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$		−	15.0000i		−	1.70941i
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	0.133975	−	2.23205i	0.0149788	−	0.249551i
$81$		0			0
$82$	8.66025	−	5.00000i	0.956365	−	0.552158i
$83$		−	10.0000i		−	1.09764i	−0.835940	−	0.548821i	$-0.815077\pi$
$83$		−	10.0000i		−	1.09764i	0.835940	−	0.548821i	$-0.184923\pi$
$84$		0			0
$85$	−4.92820	+	7.46410i	−0.534539	+	0.809595i
$86$	−12.0000			−1.29399
$87$		0			0
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	−0.838308	−	0.545197i	$-0.816455\pi$
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	0.891308	+	0.453398i	$0.149788\pi$
$90$		0			0
$91$	−17.5000	−	4.33013i	−1.83450	−	0.453921i
$92$		0			0
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$	1.86603	+	1.23205i	0.191450	+	0.126406i
$96$		0			0
$97$	−8.66025	+	5.00000i	−0.879316	+	0.507673i	−0.870433	−	0.492287i	$-0.836161\pi$
$97$	−8.66025	+	5.00000i	−0.879316	+	0.507673i	−0.00888289	+	0.999961i	$0.502828\pi$
$98$	15.5885	−	9.00000i	1.57467	−	0.909137i
$99$		0			0
$100$	4.96410	+	0.598076i	0.496410	+	0.0598076i
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$		−	7.00000i		−	0.689730i	−0.938652	−	0.344865i	$-0.887925\pi$
$103$		−	7.00000i		−	0.689730i	0.938652	−	0.344865i	$-0.112075\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.909624	−	0.415432i	$-0.136370\pi$
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.0950377	+	0.995474i	$0.469703\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−3.69615	+	5.59808i	−0.352414	+	0.533756i
$111$		0			0
$112$			5.00000i			0.472456i
$113$	−3.46410	+	2.00000i	−0.325875	+	0.188144i	−0.654008	−	0.756487i	$-0.726914\pi$
$113$	−3.46410	+	2.00000i	−0.325875	+	0.188144i	0.328133	+	0.944632i	$0.393581\pi$
$114$		0			0
$115$		0			0
$116$	−2.00000			−0.185695
$117$		0			0
$118$		0			0
$119$	10.0000	−	17.3205i	0.916698	−	1.58777i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$	−14.7224	−	8.50000i	−1.30640	−	0.754253i	−0.324910	−	0.945745i	$-0.605334\pi$
$127$	−14.7224	−	8.50000i	−1.30640	−	0.754253i	−0.981494	+	0.191492i	$0.938667\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	5.46410	+	5.92820i	0.479233	+	0.519938i
$131$	−7.00000			−0.611593			−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000			−0.611593			−0.305796	+	0.952097i	$0.598923\pi$
$132$		0			0
$133$	−4.33013	−	2.50000i	−0.375470	−	0.216777i
$134$	−3.00000	−	5.19615i	−0.259161	−	0.448879i
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	−8.66025	+	5.00000i	−0.739895	+	0.427179i	−0.822031	−	0.569442i	$-0.807159\pi$
$137$	−8.66025	+	5.00000i	−0.739895	+	0.427179i	0.0821359	+	0.996621i	$0.473826\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	−11.1603	−	0.669873i	−0.943214	−	0.0566146i
$141$		0			0
$142$			12.0000i			1.00702i
$143$	−10.3923	+	3.00000i	−0.869048	+	0.250873i
$144$		0			0
$145$	0.267949	−	4.46410i	0.0222520	−	0.370723i
$146$	−8.00000	+	13.8564i	−0.662085	+	1.14676i
$147$		0			0
$148$			9.00000i			0.739795i
$149$	−8.00000	−	13.8564i	−0.655386	−	1.13516i	−0.981797	−	0.189933i	$-0.939173\pi$
$149$	−8.00000	−	13.8564i	−0.655386	−	1.13516i	0.326411	−	0.945228i	$-0.394160\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	0.866025	−	0.500000i	0.0702439	−	0.0405554i
$153$		0			0
$154$	7.50000	−	12.9904i	0.604367	−	1.04679i
$155$	−8.00000	+	4.00000i	−0.642575	+	0.321288i
$156$		0			0
$157$		−	3.00000i		−	0.239426i	−0.992809	−	0.119713i	$-0.961803\pi$
$157$		−	3.00000i		−	0.239426i	0.992809	−	0.119713i	$-0.0381975\pi$
$158$	12.1244	+	7.00000i	0.964562	+	0.556890i
$159$		0			0
$160$	1.23205	−	1.86603i	0.0974022	−	0.147522i
$161$		0			0
$162$		0			0
$163$	−6.92820	+	4.00000i	−0.542659	+	0.313304i	−0.746156	−	0.665771i	$-0.768103\pi$
$163$	−6.92820	+	4.00000i	−0.542659	+	0.313304i	0.203497	+	0.979076i	$0.434769\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$	5.00000	−	8.66025i	0.388075	−	0.672166i
$167$	−16.4545	−	9.50000i	−1.27329	−	0.735132i	−0.297681	−	0.954665i	$-0.596213\pi$
$167$	−16.4545	−	9.50000i	−1.27329	−	0.735132i	−0.975605	+	0.219533i	$0.929547\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	−8.00000	+	4.00000i	−0.613572	+	0.306786i
$171$		0			0
$172$	−10.3923	−	6.00000i	−0.792406	−	0.457496i
$173$	−6.06218	+	3.50000i	−0.460899	+	0.266100i	−0.712422	−	0.701751i	$-0.752402\pi$
$173$	−6.06218	+	3.50000i	−0.460899	+	0.266100i	0.251523	+	0.967851i	$0.419068\pi$
$174$		0			0
$175$	2.99038	−	24.8205i	0.226052	−	1.87625i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	0.866025	−	0.500000i	0.0649113	−	0.0374766i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	−12.9904	−	12.5000i	−0.962911	−	0.926562i
$183$		0			0
$184$		0			0
$185$	−20.0885	−	1.20577i	−1.47693	−	0.0886501i
$186$		0			0
$187$		−	12.0000i		−	0.877527i
$188$	−6.06218	+	3.50000i	−0.442130	+	0.255264i
$189$		0			0
$190$	1.00000	+	2.00000i	0.0725476	+	0.145095i
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	0.619467	−	0.785022i	$-0.287349\pi$
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	−0.370116	+	0.928986i	$0.620682\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	18.0000			1.28571
$197$	12.9904	+	7.50000i	0.925526	+	0.534353i	0.885394	−	0.464841i	$-0.153889\pi$
$197$	12.9904	+	7.50000i	0.925526	+	0.534353i	0.0401324	+	0.999194i	$0.487222\pi$
$198$		0			0
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$		0			0
$202$	8.66025	−	5.00000i	0.609333	−	0.351799i
$203$			10.0000i			0.701862i
$204$		0			0
$205$	−1.33975	+	22.3205i	−0.0935719	+	1.55893i
$206$	3.50000	−	6.06218i	0.243857	−	0.422372i
$207$		0			0
$208$	3.46410	−	1.00000i	0.240192	−	0.0693375i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	2.59808	−	1.50000i	0.178437	−	0.103020i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	14.7846	−	22.3923i	1.00830	−	1.52714i
$216$		0			0
$217$	17.3205	−	10.0000i	1.17579	−	0.678844i
$218$	−8.66025	−	5.00000i	−0.586546	−	0.338643i
$219$		0			0
$220$	−6.00000	+	3.00000i	−0.404520	+	0.202260i
$221$	−14.0000	−	3.46410i	−0.941742	−	0.233021i
$222$		0			0
$223$	−0.866025	−	0.500000i	−0.0579934	−	0.0334825i	0.470723	−	0.882281i	$-0.343993\pi$
$223$	−0.866025	−	0.500000i	−0.0579934	−	0.0334825i	−0.528716	+	0.848799i	$0.677326\pi$
$224$	−2.50000	+	4.33013i	−0.167038	+	0.289319i
$225$		0			0
$226$	−4.00000			−0.266076
$227$	−1.73205	+	1.00000i	−0.114960	+	0.0663723i	−0.556378	−	0.830930i	$-0.687809\pi$
$227$	−1.73205	+	1.00000i	−0.114960	+	0.0663723i	0.441417	+	0.897302i	$0.354476\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$		0			0
$232$	−1.73205	−	1.00000i	−0.113715	−	0.0656532i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$	−7.00000	−	14.0000i	−0.456630	−	0.913259i
$236$		0			0
$237$		0			0
$238$	17.3205	−	10.0000i	1.12272	−	0.648204i
$239$	14.0000			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$240$		0			0
$241$	−1.50000	−	2.59808i	−0.0966235	−	0.167357i	0.813662	−	0.581339i	$-0.197471\pi$
$241$	−1.50000	−	2.59808i	−0.0966235	−	0.167357i	−0.910285	+	0.413982i	$0.864138\pi$
$242$			2.00000i			0.128565i
$243$		0			0
$244$		0			0
$245$	−2.41154	+	40.1769i	−0.154068	+	2.56681i
$246$		0			0
$247$	−0.866025	+	3.50000i	−0.0551039	+	0.222700i
$248$			4.00000i			0.254000i
$249$		0			0
$250$	−7.23205	+	8.52628i	−0.457395	+	0.539249i
$251$	6.50000	+	11.2583i	0.410276	+	0.710620i	0.994920	−	0.100671i	$-0.0320989\pi$
$251$	6.50000	+	11.2583i	0.410276	+	0.710620i	−0.584643	+	0.811290i	$0.698766\pi$
$252$		0			0
$253$		0			0
$254$	−8.50000	−	14.7224i	−0.533337	−	0.923768i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.66025	+	5.00000i	0.540212	+	0.311891i	0.745165	−	0.666880i	$-0.232371\pi$
$257$	8.66025	+	5.00000i	0.540212	+	0.311891i	−0.204953	+	0.978772i	$0.565704\pi$
$258$		0			0
$259$	45.0000			2.79616
$260$	1.76795	+	7.86603i	0.109644	+	0.487830i
$261$		0			0
$262$	−6.06218	−	3.50000i	−0.374523	−	0.216231i
$263$	6.06218	+	3.50000i	0.373810	+	0.215819i	0.675122	−	0.737706i	$-0.264091\pi$
$263$	6.06218	+	3.50000i	0.373810	+	0.215819i	−0.301312	+	0.953526i	$0.597424\pi$
$264$		0			0
$265$	3.00000	+	6.00000i	0.184289	+	0.368577i
$266$	−2.50000	−	4.33013i	−0.153285	−	0.265497i
$267$		0			0
$268$		−	6.00000i		−	0.366508i
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	0.961817	−	0.273692i	$-0.0882449\pi$
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	−0.717933	+	0.696112i	$0.754912\pi$
$270$		0			0
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$			4.00000i			0.242536i
$273$		0			0
$274$	−10.0000			−0.604122
$275$	−5.89230	−	13.7942i	−0.355319	−	0.831823i
$276$		0			0
$277$	−14.7224	+	8.50000i	−0.884585	+	0.510716i	−0.872167	−	0.489207i	$-0.837286\pi$
$277$	−14.7224	+	8.50000i	−0.884585	+	0.510716i	−0.0124177	+	0.999923i	$0.503953\pi$
$278$		−	5.00000i		−	0.299880i
$279$		0			0
$280$	−9.33013	−	6.16025i	−0.557582	−	0.368146i
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$	5.19615	+	3.00000i	0.308879	+	0.178331i	0.646425	−	0.762978i	$-0.276263\pi$
$283$	5.19615	+	3.00000i	0.308879	+	0.178331i	−0.337546	+	0.941309i	$0.609597\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$	−10.5000	−	2.59808i	−0.620878	−	0.153627i
$287$		−	50.0000i		−	2.95141i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	2.46410	−	3.73205i	0.144697	−	0.219154i
$291$		0			0
$292$	−13.8564	+	8.00000i	−0.810885	+	0.468165i
$293$	2.59808	−	1.50000i	0.151781	−	0.0876309i	−0.422186	−	0.906509i	$-0.638737\pi$
$293$	2.59808	−	1.50000i	0.151781	−	0.0876309i	0.573967	+	0.818878i	$0.305404\pi$
$294$		0			0
$295$		0			0
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$		0			0
$298$		−	16.0000i		−	0.926855i
$299$		0			0
$300$		0			0
$301$	−30.0000	+	51.9615i	−1.72917	+	2.99501i
$302$	−6.92820	−	4.00000i	−0.398673	−	0.230174i
$303$		0			0
$304$	1.00000			0.0573539
$305$		0			0
$306$		0			0
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$	12.9904	−	7.50000i	0.740196	−	0.427352i
$309$		0			0
$310$	−8.92820	−	0.535898i	−0.507088	−	0.0304370i
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$		0			0
$313$			14.0000i			0.791327i	0.918396	+	0.395663i	$0.129485\pi$
$313$			14.0000i			0.791327i	−0.918396	+	0.395663i	$0.870515\pi$
$314$	1.50000	−	2.59808i	0.0846499	−	0.146618i
$315$		0			0
$316$	7.00000	+	12.1244i	0.393781	+	0.682048i
$317$			7.00000i			0.393159i	0.980488	+	0.196580i	$0.0629834\pi$
$317$			7.00000i			0.393159i	−0.980488	+	0.196580i	$0.937017\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	2.00000	−	1.00000i	0.111803	−	0.0559017i
$321$		0			0
$322$		0			0
$323$	−3.46410	−	2.00000i	−0.192748	−	0.111283i
$324$		0			0
$325$	−17.7942	+	2.89230i	−0.987046	+	0.160436i
$326$	−8.00000			−0.443079
$327$		0			0
$328$	8.66025	+	5.00000i	0.478183	+	0.276079i
$329$	17.5000	+	30.3109i	0.964806	+	1.67109i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	8.66025	−	5.00000i	0.475293	−	0.274411i
$333$		0			0
$334$	−9.50000	−	16.4545i	−0.519817	−	0.900349i
$335$	13.3923	+	0.803848i	0.731700	+	0.0439189i
$336$		0			0
$337$			10.0000i			0.544735i	0.962193	+	0.272367i	$0.0878066\pi$
$337$			10.0000i			0.544735i	−0.962193	+	0.272367i	$0.912193\pi$
$338$	−6.06218	+	11.5000i	−0.329739	+	0.625518i
$339$		0			0
$340$	−8.92820	−	0.535898i	−0.484200	−	0.0290632i
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$		−	55.0000i		−	2.96972i
$344$	−6.00000	−	10.3923i	−0.323498	−	0.560316i
$345$		0			0
$346$	−7.00000			−0.376322
$347$	−19.0526	+	11.0000i	−1.02279	+	0.590511i	−0.914912	−	0.403653i	$-0.867740\pi$
$347$	−19.0526	+	11.0000i	−1.02279	+	0.590511i	−0.107883	+	0.994164i	$0.534407\pi$
$348$		0			0
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$	15.0000	−	20.0000i	0.801784	−	1.06904i
$351$		0			0
$352$			3.00000i			0.159901i
$353$	−29.4449	−	17.0000i	−1.56719	−	0.904819i	−0.996495	−	0.0836583i	$-0.973340\pi$
$353$	−29.4449	−	17.0000i	−1.56719	−	0.904819i	−0.570697	−	0.821160i	$-0.693327\pi$
$354$		0			0
$355$	−22.3923	−	14.7846i	−1.18846	−	0.784686i
$356$	1.00000			0.0529999
$357$		0			0
$358$	−10.3923	+	6.00000i	−0.549250	+	0.317110i
$359$	−20.0000			−1.05556			−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−5.19615	−	3.00000i	−0.273104	−	0.157676i
$363$		0			0
$364$	−5.00000	−	17.3205i	−0.262071	−	0.907841i
$365$	−16.0000	−	32.0000i	−0.837478	−	1.67496i
$366$		0			0
$367$	20.7846	+	12.0000i	1.08495	+	0.626395i	0.932227	−	0.361874i	$-0.117863\pi$
$367$	20.7846	+	12.0000i	1.08495	+	0.626395i	0.152721	+	0.988269i	$0.451196\pi$
$368$		0			0
$369$		0			0
$370$	−16.7942	−	11.0885i	−0.873090	−	0.576461i
$371$	−7.50000	−	12.9904i	−0.389381	−	0.674427i
$372$		0			0
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	−0.628454	−	0.777847i	$-0.716312\pi$
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	0.359408	+	0.933181i	$0.382979\pi$
$374$	6.00000	−	10.3923i	0.310253	−	0.537373i
$375$		0			0
$376$	−7.00000			−0.360997
$377$	6.92820	−	2.00000i	0.356821	−	0.103005i
$378$		0			0
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	−0.511922	−	0.859032i	$-0.671066\pi$
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	0.999904	+	0.0138218i	$0.00439975\pi$
$380$	−0.133975	+	2.23205i	−0.00687275	+	0.114502i
$381$		0			0
$382$			12.0000i			0.613973i
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	−0.810331	−	0.585973i	$-0.800713\pi$
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	0.102302	+	0.994753i	$0.467379\pi$
$384$		0			0
$385$	15.0000	+	30.0000i	0.764471	+	1.52894i
$386$	2.00000	+	3.46410i	0.101797	+	0.176318i
$387$		0			0
$388$	−8.66025	−	5.00000i	−0.439658	−	0.253837i
$389$	24.0000			1.21685			0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000			1.21685			0.608424	+	0.793612i	$0.291802\pi$
$390$		0			0
$391$		0			0
$392$	15.5885	+	9.00000i	0.787336	+	0.454569i
$393$		0			0
$394$	7.50000	+	12.9904i	0.377845	+	0.654446i
$395$	−28.0000	+	14.0000i	−1.40883	+	0.704416i
$396$		0			0
$397$	19.9186	−	11.5000i	0.999685	−	0.577168i	0.0915300	−	0.995802i	$-0.470824\pi$
$397$	19.9186	−	11.5000i	0.999685	−	0.577168i	0.908155	+	0.418634i	$0.137491\pi$
$398$		−	14.0000i		−	0.701757i
$399$		0			0
$400$	1.96410	+	4.59808i	0.0982051	+	0.229904i
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	0.475253	+	0.879849i	$0.342356\pi$
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	−0.999598	+	0.0283431i	$0.990977\pi$
$402$		0			0
$403$	−10.3923	−	10.0000i	−0.517678	−	0.498135i
$404$	10.0000			0.497519
$405$		0			0
$406$	−5.00000	+	8.66025i	−0.248146	+	0.429801i
$407$	23.3827	−	13.5000i	1.15904	−	0.669170i
$408$		0			0
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$410$	−12.3205	+	18.6603i	−0.608467	+	0.921564i
$411$		0			0
$412$	6.06218	−	3.50000i	0.298662	−	0.172433i
$413$		0			0
$414$		0			0
$415$	10.0000	+	20.0000i	0.490881	+	0.981761i
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$		0			0
$418$	−2.59808	−	1.50000i	−0.127076	−	0.0733674i
$419$	14.0000	−	24.2487i	0.683945	−	1.18463i	−0.289822	−	0.957080i	$-0.593596\pi$
$419$	14.0000	−	24.2487i	0.683945	−	1.18463i	0.973767	−	0.227547i	$-0.0730704\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	−11.2583	+	6.50000i	−0.548047	+	0.316415i
$423$		0			0
$424$	3.00000			0.145693
$425$	2.39230	−	19.8564i	0.116044	−	0.963177i
$426$		0			0
$427$		0			0
$428$			12.0000i			0.580042i
$429$		0			0
$430$	24.0000	−	12.0000i	1.15738	−	0.578691i
$431$	−20.0000	+	34.6410i	−0.963366	+	1.66860i	−0.249424	+	0.968394i	$0.580241\pi$
$431$	−20.0000	+	34.6410i	−0.963366	+	1.66860i	−0.713942	+	0.700205i	$0.753092\pi$
$432$		0			0
$433$	6.92820	−	4.00000i	0.332948	−	0.192228i	−0.324201	−	0.945988i	$-0.605095\pi$
$433$	6.92820	−	4.00000i	0.332948	−	0.192228i	0.657149	+	0.753760i	$0.271762\pi$
$434$	20.0000			0.960031
$435$		0			0
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$		0			0
$438$		0			0
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$	−6.69615	−	0.401924i	−0.319227	−	0.0191610i
$441$		0			0
$442$	−10.3923	−	10.0000i	−0.494312	−	0.475651i
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$		0			0
$445$	−0.133975	+	2.23205i	−0.00635100	+	0.105809i
$446$	−0.500000	−	0.866025i	−0.0236757	−	0.0410075i
$447$		0			0
$448$	−4.33013	+	2.50000i	−0.204579	+	0.118114i
$449$	6.50000	+	11.2583i	0.306754	+	0.531313i	0.977650	−	0.210238i	$-0.0674238\pi$
$449$	6.50000	+	11.2583i	0.306754	+	0.531313i	−0.670896	+	0.741551i	$0.734090\pi$
$450$		0			0
$451$	−15.0000	−	25.9808i	−0.706322	−	1.22339i
$452$	−3.46410	−	2.00000i	−0.162938	−	0.0940721i
$453$		0			0
$454$	−2.00000			−0.0938647
$455$	39.3301	−	8.83975i	1.84382	−	0.414414i
$456$		0			0
$457$	24.2487	+	14.0000i	1.13431	+	0.654892i	0.945015	−	0.327028i	$-0.106047\pi$
$457$	24.2487	+	14.0000i	1.13431	+	0.654892i	0.189292	+	0.981921i	$0.439381\pi$
$458$	19.0526	+	11.0000i	0.890268	+	0.513996i
$459$		0			0
$460$		0			0
$461$	−11.0000	−	19.0526i	−0.512321	−	0.887366i	−0.999898	−	0.0142861i	$-0.995452\pi$
$461$	−11.0000	−	19.0526i	−0.512321	−	0.887366i	0.487577	−	0.873080i	$-0.337881\pi$
$462$		0			0
$463$			8.00000i			0.371792i	0.982569	+	0.185896i	$0.0595187\pi$
$463$			8.00000i			0.371792i	−0.982569	+	0.185896i	$0.940481\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$		0			0
$466$		0			0
$467$			34.0000i			1.57333i	0.617379	+	0.786666i	$0.288195\pi$
$467$			34.0000i			1.57333i	−0.617379	+	0.786666i	$0.711805\pi$
$468$		0			0
$469$	−30.0000			−1.38527
$470$	0.937822	−	15.6244i	0.0432585	−	0.720698i
$471$		0			0
$472$		0			0
$473$			36.0000i			1.65528i
$474$		0			0
$475$	−4.96410	−	0.598076i	−0.227769	−	0.0274416i
$476$	20.0000			0.916698
$477$		0			0
$478$	12.1244	+	7.00000i	0.554555	+	0.320173i
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	−0.957351	−	0.288929i	$-0.906701\pi$
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	0.728895	+	0.684626i	$0.240034\pi$
$480$		0			0
$481$	−9.00000	−	31.1769i	−0.410365	−	1.42154i
$482$		−	3.00000i		−	0.136646i
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$	12.3205	−	18.6603i	0.559445	−	0.847318i
$486$		0			0
$487$	−0.866025	+	0.500000i	−0.0392434	+	0.0226572i	−0.519493	−	0.854475i	$-0.673879\pi$
$487$	−0.866025	+	0.500000i	−0.0392434	+	0.0226572i	0.480250	+	0.877132i	$0.340546\pi$
$488$		0			0
$489$		0			0
$490$	−22.1769	+	33.5885i	−1.00185	+	1.51737i
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$		0			0
$493$			8.00000i			0.360302i
$494$	−2.50000	+	2.59808i	−0.112480	+	0.116893i
$495$		0			0
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	51.9615	+	30.0000i	2.33079	+	1.34568i
$498$		0			0
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$	−10.5263	+	3.76795i	−0.470750	+	0.168508i
$501$		0			0
$502$			13.0000i			0.580218i
$503$	−9.52628	+	5.50000i	−0.424756	+	0.245233i	−0.697110	−	0.716964i	$-0.745531\pi$
$503$	−9.52628	+	5.50000i	−0.424756	+	0.245233i	0.272354	+	0.962197i	$0.412198\pi$
$504$		0			0
$505$	−1.33975	+	22.3205i	−0.0596179	+	0.993250i
$506$		0			0
$507$		0			0
$508$		−	17.0000i		−	0.754253i
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	−0.843012	−	0.537895i	$-0.819220\pi$
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	0.887336	+	0.461123i	$0.152553\pi$
$510$		0			0
$511$	40.0000	+	69.2820i	1.76950	+	3.06486i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	5.00000	+	8.66025i	0.220541	+	0.381987i
$515$	7.00000	+	14.0000i	0.308457	+	0.616914i
$516$		0			0
$517$	18.1865	+	10.5000i	0.799843	+	0.461789i
$518$	38.9711	+	22.5000i	1.71229	+	0.988593i
$519$		0			0
$520$	−2.40192	+	7.69615i	−0.105331	+	0.337499i
$521$	45.0000			1.97149			0.985743	−	0.168259i	$-0.0538144\pi$
$521$	45.0000			1.97149			0.985743	+	0.168259i	$0.0538144\pi$
$522$		0			0
$523$	13.8564	+	8.00000i	0.605898	+	0.349816i	0.771358	−	0.636401i	$-0.219578\pi$
$523$	13.8564	+	8.00000i	0.605898	+	0.349816i	−0.165460	+	0.986216i	$0.552911\pi$
$524$	−3.50000	−	6.06218i	−0.152898	−	0.264827i
$525$		0			0
$526$	3.50000	+	6.06218i	0.152607	+	0.264324i
$527$	13.8564	−	8.00000i	0.603595	−	0.348485i
$528$		0			0
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$	−0.401924	+	6.69615i	−0.0174585	+	0.290862i
$531$		0			0
$532$		−	5.00000i		−	0.216777i
$533$	−34.6410	+	10.0000i	−1.50047	+	0.433148i
$534$		0			0
$535$	−26.7846	−	1.60770i	−1.15800	−	0.0695067i
$536$	3.00000	−	5.19615i	0.129580	−	0.224440i
$537$		0			0
$538$			8.00000i			0.344904i
$539$	−27.0000	−	46.7654i	−1.16297	−	2.01433i
$540$		0			0
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$	1.73205	−	1.00000i	0.0743980	−	0.0429537i
$543$		0			0
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	20.0000	−	10.0000i	0.856706	−	0.428353i
$546$		0			0
$547$			6.00000i			0.256541i	0.991739	+	0.128271i	$0.0409426\pi$
$547$			6.00000i			0.256541i	−0.991739	+	0.128271i	$0.959057\pi$
$548$	−8.66025	−	5.00000i	−0.369948	−	0.213589i
$549$		0			0
$550$	1.79423	−	14.8923i	0.0765062	−	0.635010i
$551$	2.00000			0.0852029
$552$		0			0
$553$	60.6218	−	35.0000i	2.57790	−	1.48835i
$554$	−17.0000			−0.722261
$555$		0			0
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.997204	−	0.0747252i	$-0.0238080\pi$
$557$	33.7750	+	19.5000i	1.43109	+	0.826242i	0.433888	+	0.900967i	$0.357141\pi$
$558$		0			0
$559$	42.0000	+	10.3923i	1.77641	+	0.439548i
$560$	−5.00000	−	10.0000i	−0.211289	−	0.422577i
$561$		0			0
$562$	−25.9808	−	15.0000i	−1.09593	−	0.632737i
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	−0.791123	−	0.611656i	$-0.790503\pi$
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	0.134148	+	0.990961i	$0.457170\pi$
$564$		0			0
$565$	4.92820	−	7.46410i	0.207331	−	0.314017i
$566$	3.00000	+	5.19615i	0.126099	+	0.218411i
$567$		0			0
$568$	−10.3923	+	6.00000i	−0.436051	+	0.251754i
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	0.0900490	+	0.995937i	$0.471298\pi$
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	−0.907532	+	0.419984i	$0.862036\pi$
$570$		0			0
$571$	15.0000			0.627730			0.313865	−	0.949468i	$-0.398376\pi$
$571$	15.0000			0.627730			0.313865	+	0.949468i	$0.398376\pi$
$572$	−7.79423	−	7.50000i	−0.325893	−	0.313591i
$573$		0			0
$574$	25.0000	−	43.3013i	1.04348	−	1.80736i
$575$		0			0
$576$		0			0
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$		0			0
$580$	4.00000	−	2.00000i	0.166091	−	0.0830455i
$581$	−25.0000	−	43.3013i	−1.03717	−	1.79644i
$582$		0			0
$583$	−7.79423	−	4.50000i	−0.322804	−	0.186371i
$584$	−16.0000			−0.662085
$585$		0			0
$586$	3.00000			0.123929
$587$	−29.4449	−	17.0000i	−1.21532	−	0.701665i	−0.251406	−	0.967882i	$-0.580893\pi$
$587$	−29.4449	−	17.0000i	−1.21532	−	0.701665i	−0.963913	+	0.266217i	$0.914226\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$		0			0
$591$		0			0
$592$	−7.79423	+	4.50000i	−0.320341	+	0.184949i
$593$			20.0000i			0.821302i	0.911793	+	0.410651i	$0.134698\pi$
$593$			20.0000i			0.821302i	−0.911793	+	0.410651i	$0.865302\pi$
$594$		0			0
$595$	−2.67949	+	44.6410i	−0.109848	+	1.83010i
$596$	8.00000	−	13.8564i	0.327693	−	0.567581i
$597$		0			0
$598$		0			0
$599$	10.0000			0.408589			0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000			0.408589			0.204294	+	0.978909i	$0.434510\pi$
$600$		0			0
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$	−51.9615	+	30.0000i	−2.11779	+	1.22271i
$603$		0			0
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	−3.73205	−	2.46410i	−0.151729	−	0.100180i
$606$		0			0
$607$	−2.59808	+	1.50000i	−0.105453	+	0.0608831i	−0.551799	−	0.833977i	$-0.686058\pi$
$607$	−2.59808	+	1.50000i	−0.105453	+	0.0608831i	0.446346	+	0.894860i	$0.352725\pi$
$608$	0.866025	+	0.500000i	0.0351220	+	0.0202777i
$609$		0			0
$610$		0			0
$611$	17.5000	−	18.1865i	0.707974	−	0.735748i
$612$		0			0
$613$	−25.1147	−	14.5000i	−1.01437	−	0.585649i	−0.101905	−	0.994794i	$-0.532494\pi$
$613$	−25.1147	−	14.5000i	−1.01437	−	0.585649i	−0.912470	+	0.409145i	$0.865827\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		0			0
$616$	15.0000			0.604367
$617$	−41.5692	+	24.0000i	−1.67351	+	0.966204i	−0.707867	+	0.706346i	$0.750342\pi$
$617$	−41.5692	+	24.0000i	−1.67351	+	0.966204i	−0.965647	+	0.259858i	$0.916324\pi$
$618$		0			0
$619$	−5.00000			−0.200967			−0.100483	−	0.994939i	$-0.532039\pi$
$619$	−5.00000			−0.200967			−0.100483	+	0.994939i	$0.532039\pi$
$620$	−7.46410	−	4.92820i	−0.299766	−	0.197921i
$621$		0			0
$622$	17.3205	+	10.0000i	0.694489	+	0.400963i
$623$		−	5.00000i		−	0.200321i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−7.00000	+	12.1244i	−0.279776	+	0.484587i
$627$		0			0
$628$	2.59808	−	1.50000i	0.103675	−	0.0598565i
$629$	36.0000			1.43541
$630$		0			0
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	−0.997718	−	0.0675178i	$-0.978492\pi$
$631$	−14.0000	−	24.2487i	−0.557331	−	0.965326i	0.440387	−	0.897808i	$-0.354841\pi$
$632$			14.0000i			0.556890i
$633$		0			0
$634$	−3.50000	+	6.06218i	−0.139003	+	0.240760i
$635$	37.9449	+	2.27757i	1.50580	+	0.0903825i
$636$		0			0
$637$	−62.3538	+	18.0000i	−2.47055	+	0.713186i
$638$			6.00000i			0.237542i
$639$		0			0
$640$	2.23205	+	0.133975i	0.0882296	+	0.00529581i
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	0.995400	−	0.0958109i	$-0.0305444\pi$
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	−0.580674	+	0.814136i	$0.697211\pi$
$642$		0			0
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	−0.747686	−	0.664052i	$-0.768835\pi$
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	0.201243	+	0.979541i	$0.435502\pi$
$644$		0			0
$645$		0			0
$646$	−2.00000	−	3.46410i	−0.0786889	−	0.136293i
$647$	−28.5788	−	16.5000i	−1.12355	−	0.648682i	−0.181245	−	0.983438i	$-0.558013\pi$
$647$	−28.5788	−	16.5000i	−1.12355	−	0.648682i	−0.942305	+	0.334756i	$0.891346\pi$
$648$		0			0
$649$		0			0
$650$	−16.8564	−	6.39230i	−0.661163	−	0.250727i
$651$		0			0
$652$	−6.92820	−	4.00000i	−0.271329	−	0.156652i
$653$	11.2583	+	6.50000i	0.440573	+	0.254365i	0.703840	−	0.710358i	$-0.251467\pi$
$653$	11.2583	+	6.50000i	0.440573	+	0.254365i	−0.263268	+	0.964723i	$0.584800\pi$
$654$		0			0
$655$	14.0000	−	7.00000i	0.547025	−	0.273513i
$656$	5.00000	+	8.66025i	0.195217	+	0.338126i
$657$		0			0
$658$			35.0000i			1.36444i
$659$	10.0000	+	17.3205i	0.389545	+	0.674711i	0.992388	−	0.123148i	$-0.0392990\pi$
$659$	10.0000	+	17.3205i	0.389545	+	0.674711i	−0.602844	+	0.797859i	$0.705966\pi$
$660$		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	$0.228968\pi$
$662$			4.00000i			0.155464i
$663$		0			0
$664$	10.0000			0.388075
$665$	11.1603	+	0.669873i	0.432776	+	0.0259766i
$666$		0			0
$667$		0			0
$668$		−	19.0000i		−	0.735132i
$669$		0			0
$670$	11.1962	+	7.39230i	0.432545	+	0.285590i
$671$		0			0
$672$		0			0
$673$	6.92820	+	4.00000i	0.267063	+	0.154189i	0.627552	−	0.778575i	$-0.284057\pi$
$673$	6.92820	+	4.00000i	0.267063	+	0.154189i	−0.360489	+	0.932763i	$0.617390\pi$
$674$	−5.00000	+	8.66025i	−0.192593	+	0.333581i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$		0			0
$679$	−25.0000	+	43.3013i	−0.959412	+	1.66175i
$680$	−7.46410	−	4.92820i	−0.286235	−	0.188988i
$681$		0			0
$682$	10.3923	−	6.00000i	0.397942	−	0.229752i
$683$	13.8564	−	8.00000i	0.530201	−	0.306111i	−0.210898	−	0.977508i	$-0.567639\pi$
$683$	13.8564	−	8.00000i	0.530201	−	0.306111i	0.741098	+	0.671397i	$0.234305\pi$
$684$		0			0
$685$	12.3205	−	18.6603i	0.470742	−	0.712972i
$686$	27.5000	−	47.6314i	1.04995	−	1.81858i
$687$		0			0
$688$		−	12.0000i		−	0.457496i
$689$	−7.50000	+	7.79423i	−0.285727	+	0.296936i
$690$		0			0
$691$	−4.50000	+	7.79423i	−0.171188	+	0.296506i	−0.938835	−	0.344366i	$-0.888094\pi$
$691$	−4.50000	+	7.79423i	−0.171188	+	0.296506i	0.767647	+	0.640872i	$0.221427\pi$
$692$	−6.06218	−	3.50000i	−0.230449	−	0.133050i
$693$		0			0
$694$	−22.0000			−0.835109
$695$	9.33013	+	6.16025i	0.353912	+	0.233672i
$696$		0			0
$697$		−	40.0000i		−	1.51511i
$698$	−8.66025	+	5.00000i	−0.327795	+	0.189253i
$699$		0			0
$700$	22.9904	−	9.82051i	0.868955	−	0.371180i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$		−	9.00000i		−	0.339441i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	−17.0000	−	29.4449i	−0.639803	−	1.10817i
$707$		−	50.0000i		−	1.88044i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	−12.0000	−	24.0000i	−0.450352	−	0.900704i
$711$		0			0
$712$	0.866025	+	0.500000i	0.0324557	+	0.0187383i
$713$		0			0
$714$		0			0
$715$	17.7846	−	16.3923i	0.665107	−	0.613037i
$716$	−12.0000			−0.448461
$717$		0			0
$718$	−17.3205	−	10.0000i	−0.646396	−	0.373197i
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	−0.993305	−	0.115524i	$-0.963145\pi$
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	0.396605	−	0.917989i	$-0.370188\pi$
$720$		0			0
$721$	−17.5000	−	30.3109i	−0.651734	−	1.12884i
$722$	15.5885	−	9.00000i	0.580142	−	0.334945i
$723$		0			0
$724$	−3.00000	−	5.19615i	−0.111494	−	0.193113i
$725$	3.92820	+	9.19615i	0.145890	+	0.341537i
$726$		0			0
$727$		−	37.0000i		−	1.37225i	−0.727482	−	0.686127i	$-0.759309\pi$
$727$		−	37.0000i		−	1.37225i	0.727482	−	0.686127i	$-0.240691\pi$
$728$	4.33013	−	17.5000i	0.160485	−	0.648593i
$729$		0			0
$730$	2.14359	−	35.7128i	0.0793380	−	1.32179i
$731$	−24.0000	+	41.5692i	−0.887672	+	1.53749i
$732$		0			0
$733$			45.0000i			1.66211i	0.556188	+	0.831056i	$0.312263\pi$
$733$			45.0000i			1.66211i	−0.556188	+	0.831056i	$0.687737\pi$
$734$	12.0000	+	20.7846i	0.442928	+	0.767174i
$735$		0			0
$736$		0			0
$737$	−15.5885	+	9.00000i	−0.574208	+	0.331519i
$738$		0			0
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	0.465848	+	0.884865i	$0.345749\pi$
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	−0.999239	+	0.0389959i	$0.987584\pi$
$740$	−9.00000	−	18.0000i	−0.330847	−	0.661693i
$741$		0			0
$742$		−	15.0000i		−	0.550667i
$743$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$743$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$	29.8564	+	19.7128i	1.09385	+	0.722222i
$746$	−6.00000			−0.219676
$747$		0			0
$748$	10.3923	−	6.00000i	0.379980	−	0.219382i
$749$	60.0000			2.19235
$750$		0			0
$751$	15.0000	−	25.9808i	0.547358	−	0.948051i	−0.451097	−	0.892475i	$-0.648967\pi$
$751$	15.0000	−	25.9808i	0.547358	−	0.948051i	0.998454	−	0.0555764i	$-0.0176996\pi$
$752$	−6.06218	−	3.50000i	−0.221065	−	0.127632i
$753$		0			0
$754$	7.00000	+	1.73205i	0.254925	+	0.0630776i
$755$	16.0000	−	8.00000i	0.582300	−	0.291150i
$756$		0			0
$757$	21.6506	+	12.5000i	0.786906	+	0.454320i	0.838872	−	0.544329i	$-0.183216\pi$
$757$	21.6506	+	12.5000i	0.786906	+	0.454320i	−0.0519664	+	0.998649i	$0.516549\pi$
$758$	16.4545	−	9.50000i	0.597654	−	0.345056i
$759$		0			0
$760$	−1.23205	+	1.86603i	−0.0446912	+	0.0676879i
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$	−43.3013	+	25.0000i	−1.56761	+	0.905061i
$764$	−6.00000	+	10.3923i	−0.217072	+	0.375980i
$765$		0			0
$766$	−16.0000			−0.578103
$767$		0			0
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$	−2.00962	+	33.4808i	−0.0724216	+	1.20656i
$771$		0			0
$772$			4.00000i			0.143963i
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	−0.135910	−	0.990721i	$-0.543396\pi$
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	0.790034	+	0.613062i	$0.210063\pi$
$774$		0			0
$775$	12.0000	−	16.0000i	0.431053	−	0.574737i
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$		0			0
$778$	20.7846	+	12.0000i	0.745164	+	0.430221i
$779$	−10.0000			−0.358287
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$		0			0
$784$	9.00000	+	15.5885i	0.321429	+	0.556731i
$785$	3.00000	+	6.00000i	0.107075	+	0.214149i
$786$		0			0
$787$	−36.3731	+	21.0000i	−1.29656	+	0.748569i	−0.979808	−	0.199939i	$-0.935925\pi$
$787$	−36.3731	+	21.0000i	−1.29656	+	0.748569i	−0.316752	+	0.948509i	$0.602592\pi$
$788$			15.0000i			0.534353i
$789$		0			0
$790$	−31.2487	−	1.87564i	−1.11178	−	0.0667324i
$791$	−10.0000	+	17.3205i	−0.355559	+	0.615846i
$792$		0			0
$793$		0			0
$794$	23.0000			0.816239
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	−0.197826	−	0.980237i	$-0.563388\pi$
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	0.749997	+	0.661441i	$0.230055\pi$
$798$		0			0
$799$	14.0000	+	24.2487i	0.495284	+	0.857858i
$800$	−0.598076	+	4.96410i	−0.0211452	+	0.175507i
$801$		0			0
$802$	−18.1865	+	10.5000i	−0.642189	+	0.370768i
$803$	41.5692	+	24.0000i	1.46695	+	0.846942i
$804$		0			0
$805$		0			0
$806$	−4.00000	−	13.8564i	−0.140894	−	0.488071i
$807$		0			0
$808$	8.66025	+	5.00000i	0.304667	+	0.175899i
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	−0.940435	−	0.339975i	$-0.889582\pi$
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	0.764644	+	0.644453i	$0.222915\pi$
$810$		0			0
$811$	13.0000			0.456492			0.228246	−	0.973604i	$-0.426701\pi$
$811$	13.0000			0.456492			0.228246	+	0.973604i	$0.426701\pi$
$812$	−8.66025	+	5.00000i	−0.303915	+	0.175466i
$813$		0			0
$814$	27.0000			0.946350
$815$	9.85641	−	14.9282i	0.345255	−	0.522912i
$816$		0			0
$817$	10.3923	+	6.00000i	0.363581	+	0.209913i
$818$		−	19.0000i		−	0.664319i
$819$		0			0
$820$	−20.0000	+	10.0000i	−0.698430	+	0.349215i
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	−0.939989	−	0.341206i	$-0.889165\pi$
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	0.765487	+	0.643451i	$0.222498\pi$
$822$		0			0
$823$	35.5070	−	20.5000i	1.23770	−	0.714585i	0.269075	−	0.963119i	$-0.413282\pi$
$823$	35.5070	−	20.5000i	1.23770	−	0.714585i	0.968623	+	0.248534i	$0.0799489\pi$
$824$	7.00000			0.243857
$825$		0			0
$826$		0			0
$827$			2.00000i			0.0695468i	0.999395	+	0.0347734i	$0.0110710\pi$
$827$			2.00000i			0.0695468i	−0.999395	+	0.0347734i	$0.988929\pi$
$828$		0			0
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$	−1.33975	+	22.3205i	−0.0465033	+	0.774756i
$831$		0			0
$832$	2.59808	+	2.50000i	0.0900721	+	0.0866719i
$833$		−	72.0000i		−	2.49465i
$834$		0			0
$835$	42.4090	+	2.54552i	1.46762	+	0.0880913i
$836$	−1.50000	−	2.59808i	−0.0518786	−	0.0898563i
$837$		0			0
$838$	24.2487	−	14.0000i	0.837658	−	0.483622i
$839$	−23.0000	−	39.8372i	−0.794048	−	1.37533i	−0.923442	−	0.383738i	$-0.874636\pi$
$839$	−23.0000	−	39.8372i	−0.794048	−	1.37533i	0.129394	−	0.991593i	$-0.458697\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	13.8564	+	8.00000i	0.477523	+	0.275698i
$843$		0			0
$844$	−13.0000			−0.447478
$845$	−13.9904	−	25.4808i	−0.481284	−	0.876565i
$846$		0			0
$847$	8.66025	+	5.00000i	0.297570	+	0.171802i
$848$	2.59808	+	1.50000i	0.0892183	+	0.0515102i
$849$		0			0
$850$	12.0000	−	16.0000i	0.411597	−	0.548795i
$851$		0			0
$852$		0			0
$853$		−	10.0000i		−	0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	−55.0000			−1.87658			−0.938288	−	0.345855i	$-0.887589\pi$
$859$	−55.0000			−1.87658			−0.938288	+	0.345855i	$0.887589\pi$
$860$	26.7846	+	1.60770i	0.913348	+	0.0548219i
$861$		0			0
$862$	−34.6410	+	20.0000i	−1.17988	+	0.681203i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$		0			0
$865$	8.62436	−	13.0622i	0.293237	−	0.444127i
$866$	8.00000			0.271851
$867$		0			0
$868$	17.3205	+	10.0000i	0.587896	+	0.339422i
$869$	21.0000	−	36.3731i	0.712376	−	1.23387i
$870$		0			0
$871$	6.00000	+	20.7846i	0.203302	+	0.704260i
$872$		−	10.0000i		−	0.338643i
$873$		0			0
$874$		0			0
$875$	18.8397	+	52.6314i	0.636900	+	1.77927i
$876$		0			0
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	−0.739543	−	0.673109i	$-0.764958\pi$
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	0.213158	+	0.977018i	$0.431625\pi$
$878$	13.8564	−	8.00000i	0.467631	−	0.269987i
$879$		0			0
$880$	−5.59808	−	3.69615i	−0.188711	−	0.124597i
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	−0.711582	−	0.702603i	$-0.752021\pi$
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	0.964263	+	0.264946i	$0.0853542\pi$
$882$		0			0
$883$			50.0000i			1.68263i	0.540542	+	0.841317i	$0.318219\pi$
$883$			50.0000i			1.68263i	−0.540542	+	0.841317i	$0.681781\pi$
$884$	−4.00000	−	13.8564i	−0.134535	−	0.466041i
$885$		0			0
$886$	12.0000	−	20.7846i	0.403148	−	0.698273i
$887$	28.5788	+	16.5000i	0.959583	+	0.554016i	0.896045	−	0.443964i	$-0.146428\pi$
$887$	28.5788	+	16.5000i	0.959583	+	0.554016i	0.0635387	+	0.997979i	$0.479761\pi$
$888$		0			0
$889$	−85.0000			−2.85081
$890$	−1.23205	+	1.86603i	−0.0412984	+	0.0625493i
$891$		0			0
$892$		−	1.00000i		−	0.0334825i
$893$	6.06218	−	3.50000i	0.202863	−	0.117123i
$894$		0			0
$895$	1.60770	−	26.7846i	0.0537393	−	0.895311i
$896$	−5.00000			−0.167038
$897$		0			0
$898$			13.0000i			0.433816i
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$		−	30.0000i		−	0.998891i
$903$		0			0
$904$	−2.00000	−	3.46410i	−0.0665190	−	0.115214i
$905$	12.0000	−	6.00000i	0.398893	−	0.199447i
$906$		0			0
$907$	−13.8564	−	8.00000i	−0.460094	−	0.265636i	0.251990	−	0.967730i	$-0.418915\pi$
$907$	−13.8564	−	8.00000i	−0.460094	−	0.265636i	−0.712084	+	0.702094i	$0.752248\pi$
$908$	−1.73205	−	1.00000i	−0.0574801	−	0.0331862i
$909$		0			0
$910$	38.4808	+	12.0096i	1.27562	+	0.398115i
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	−25.9808	−	15.0000i	−0.859838	−	0.496428i
$914$	14.0000	+	24.2487i	0.463079	+	0.802076i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$	−30.3109	+	17.5000i	−1.00095	+	0.577901i
$918$		0			0
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$		0			0
$922$		−	22.0000i		−	0.724531i
$923$	10.3923	−	42.0000i	0.342067	−	1.38245i
$924$		0			0
$925$	41.3827	−	17.6769i	1.36065	−	0.581213i
$926$	−4.00000	+	6.92820i	−0.131448	+	0.227675i
$927$		0			0
$928$		−	2.00000i		−	0.0656532i
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	−0.997684	−	0.0680235i	$-0.978331\pi$
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	0.439932	−	0.898031i	$-0.355003\pi$
$930$		0			0
$931$	−18.0000			−0.589926
$932$		0			0
$933$		0			0
$934$	−17.0000	+	29.4449i	−0.556257	+	0.963465i
$935$	12.0000	+	24.0000i	0.392442	+	0.784884i
$936$		0			0
$937$			36.0000i			1.17607i	0.808836	+	0.588034i	$0.200098\pi$
$937$			36.0000i			1.17607i	−0.808836	+	0.588034i	$0.799902\pi$
$938$	−25.9808	−	15.0000i	−0.848302	−	0.489767i
$939$		0			0
$940$	8.62436	−	13.0622i	0.281295	−	0.426041i
$941$	−52.0000			−1.69515			−0.847576	−	0.530674i	$-0.821939\pi$
$941$	−52.0000			−1.69515			−0.847576	+	0.530674i	$0.821939\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−18.0000	+	31.1769i	−0.585230	+	1.01365i
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	0.659256	−	0.751918i	$-0.270871\pi$
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	−0.321552	+	0.946892i	$0.604204\pi$
$948$		0			0
$949$	40.0000	−	41.5692i	1.29845	−	1.34939i
$950$	−4.00000	−	3.00000i	−0.129777	−	0.0973329i
$951$		0			0
$952$	17.3205	+	10.0000i	0.561361	+	0.324102i
$953$	25.9808	−	15.0000i	0.841599	−	0.485898i	−0.0162081	−	0.999869i	$-0.505159\pi$
$953$	25.9808	−	15.0000i	0.841599	−	0.485898i	0.857808	+	0.513971i	$0.171826\pi$
$954$		0			0
$955$	−22.3923	−	14.7846i	−0.724598	−	0.478419i
$956$	7.00000	+	12.1244i	0.226396	+	0.392130i
$957$		0			0
$958$	−8.66025	+	5.00000i	−0.279800	+	0.161543i
$959$	−25.0000	+	43.3013i	−0.807292	+	1.39827i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	7.79423	−	31.5000i	0.251296	−	1.01560i
$963$		0			0
$964$	1.50000	−	2.59808i	0.0483117	−	0.0836784i
$965$	−8.92820	−	0.535898i	−0.287409	−	0.0172512i
$966$		0			0
$967$		−	37.0000i		−	1.18984i	−0.803785	−	0.594920i	$-0.797184\pi$
$967$		−	37.0000i		−	1.18984i	0.803785	−	0.594920i	$-0.202816\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$		0			0
$970$	20.0000	−	10.0000i	0.642161	−	0.321081i
$971$	−25.5000	−	44.1673i	−0.818334	−	1.41740i	−0.906909	−	0.421326i	$-0.861565\pi$
$971$	−25.5000	−	44.1673i	−0.818334	−	1.41740i	0.0885751	−	0.996070i	$-0.471769\pi$
$972$		0			0
$973$	−21.6506	−	12.5000i	−0.694087	−	0.400732i
$974$	−1.00000			−0.0320421
$975$		0			0
$976$		0			0
$977$	−32.9090	−	19.0000i	−1.05285	−	0.607864i	−0.129405	−	0.991592i	$-0.541307\pi$
$977$	−32.9090	−	19.0000i	−1.05285	−	0.607864i	−0.923446	+	0.383728i	$0.874640\pi$
$978$		0			0
$979$	−1.50000	−	2.59808i	−0.0479402	−	0.0830349i
$980$	−36.0000	+	18.0000i	−1.14998	+	0.574989i
$981$		0			0
$982$	12.9904	−	7.50000i	0.414540	−	0.239335i
$983$			23.0000i			0.733586i	0.930303	+	0.366793i	$0.119544\pi$
$983$			23.0000i			0.733586i	−0.930303	+	0.366793i	$0.880456\pi$
$984$		0			0
$985$	−33.4808	−	2.00962i	−1.06679	−	0.0640318i
$986$	−4.00000	+	6.92820i	−0.127386	+	0.220639i
$987$		0			0
$988$	−3.46410	+	1.00000i	−0.110208	+	0.0318142i
$989$		0			0
$990$		0			0
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	−0.491698	−	0.870766i	$-0.663623\pi$
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	0.999954	−	0.00956046i	$-0.00304324\pi$
$992$	−3.46410	+	2.00000i	−0.109985	+	0.0635001i
$993$		0			0
$994$	30.0000	+	51.9615i	0.951542	+	1.64812i
$995$	26.1244	+	17.2487i	0.828198	+	0.546821i
$996$		0			0
$997$	45.8993	−	26.5000i	1.45365	−	0.839263i	0.454961	−	0.890511i	$-0.349653\pi$
$997$	45.8993	−	26.5000i	1.45365	−	0.839263i	0.998686	+	0.0512480i	$0.0163199\pi$
$998$	20.7846	+	12.0000i	0.657925	+	0.379853i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bp.b.919.2		4
3.2	odd	2		390.2.y.e.139.1	✓	4
5.4	even	2	inner	1170.2.bp.b.919.1		4
13.3	even	3	inner	1170.2.bp.b.289.1		4
15.2	even	4		1950.2.i.x.451.1		2
15.8	even	4		1950.2.i.a.451.1		2
15.14	odd	2		390.2.y.e.139.2	yes	4
39.29	odd	6		390.2.y.e.289.2	yes	4
65.29	even	6	inner	1170.2.bp.b.289.2		4
195.29	odd	6		390.2.y.e.289.1	yes	4
195.68	even	12		1950.2.i.a.601.1		2
195.107	even	12		1950.2.i.x.601.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.e.139.1	✓	4	3.2	odd	2
390.2.y.e.139.2	yes	4	15.14	odd	2
390.2.y.e.289.1	yes	4	195.29	odd	6
390.2.y.e.289.2	yes	4	39.29	odd	6
1170.2.bp.b.289.1		4	13.3	even	3	inner
1170.2.bp.b.289.2		4	65.29	even	6	inner
1170.2.bp.b.919.1		4	5.4	even	2	inner
1170.2.bp.b.919.2		4	1.1	even	1	trivial
1950.2.i.a.451.1		2	15.8	even	4
1950.2.i.a.601.1		2	195.68	even	12
1950.2.i.x.451.1		2	15.2	even	4
1950.2.i.x.601.1		2	195.107	even	12

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(4.33013 - 2.50000i) q^{7} +1.00000i q^{8} +(-2.23205 - 0.133975i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-2.59808 - 2.50000i) q^{13} +5.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-1.86603 - 1.23205i) q^{20} +(2.59808 - 1.50000i) q^{22} +(3.00000 - 4.00000i) q^{25} +(-1.00000 - 3.46410i) q^{26} +(4.33013 + 2.50000i) q^{28} +(-1.00000 + 1.73205i) q^{29} +4.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +4.00000 q^{34} +(-6.16025 + 9.33013i) q^{35} +(7.79423 + 4.50000i) q^{37} -1.00000i q^{38} +(-1.00000 - 2.00000i) q^{40} +(5.00000 - 8.66025i) q^{41} +(-10.3923 + 6.00000i) q^{43} +3.00000 q^{44} +7.00000i q^{47} +(9.00000 - 15.5885i) q^{49} +(4.59808 - 1.96410i) q^{50} +(0.866025 - 3.50000i) q^{52} -3.00000i q^{53} +(-0.401924 + 6.69615i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-1.73205 + 1.00000i) q^{58} +(3.46410 + 2.00000i) q^{62} -1.00000 q^{64} +(7.69615 + 2.40192i) q^{65} +(-5.19615 - 3.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-10.0000 + 5.00000i) q^{70} +(6.00000 + 10.3923i) q^{71} +16.0000i q^{73} +(4.50000 + 7.79423i) q^{74} +(0.500000 - 0.866025i) q^{76} -15.0000i q^{77} +14.0000 q^{79} +(0.133975 - 2.23205i) q^{80} +(8.66025 - 5.00000i) q^{82} -10.0000i q^{83} +(-4.92820 + 7.46410i) q^{85} -12.0000 q^{86} +(2.59808 + 1.50000i) q^{88} +(0.500000 - 0.866025i) q^{89} +(-17.5000 - 4.33013i) q^{91} +(-3.50000 + 6.06218i) q^{94} +(1.86603 + 1.23205i) q^{95} +(-8.66025 + 5.00000i) q^{97} +(15.5885 - 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 8 q^{5} - 2 q^{10} + 6 q^{11} + 20 q^{14} - 2 q^{16} - 2 q^{19} - 4 q^{20} + 12 q^{25} - 4 q^{26} - 4 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} - 4 q^{40} + 20 q^{41} + 12 q^{44} + 36 q^{49}+ \cdots + 4 q^{95}+O(q^{100}) \) 4 * q + 2 * q^4 - 8 * q^5 - 2 * q^10 + 6 * q^11 + 20 * q^14 - 2 * q^16 - 2 * q^19 - 4 * q^20 + 12 * q^25 - 4 * q^26 - 4 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 - 4 * q^40 + 20 * q^41 + 12 * q^44 + 36 * q^49 + 8 * q^50 - 12 * q^55 + 10 * q^56 - 4 * q^64 + 10 * q^65 - 40 * q^70 + 24 * q^71 + 18 * q^74 + 2 * q^76 + 56 * q^79 + 4 * q^80 + 8 * q^85 - 48 * q^86 + 2 * q^89 - 70 * q^91 - 14 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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