LMFDB - Embedded newform 3510.2.j.e.2341.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3510,2,Mod(1171,3510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3510, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3510.1171"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3510 = 2 \cdot 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3510.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,-1,-1,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$28.0274911095$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2341.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3510.2341
Dual form			3510.2.j.e.1171.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -5.00000 q^{17} +3.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} +2.00000 q^{28} +(4.00000 - 6.92820i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{34} +2.00000 q^{35} -8.00000 q^{37} +(1.50000 - 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{40} +(3.50000 + 6.06218i) q^{41} +(-2.50000 + 4.33013i) q^{43} -1.00000 q^{44} +(-6.00000 + 10.3923i) q^{47} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{52} -2.00000 q^{53} -1.00000 q^{55} +(1.00000 - 1.73205i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(-2.50000 - 4.33013i) q^{59} +(-7.00000 + 12.1244i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(7.50000 + 12.9904i) q^{67} +(2.50000 + 4.33013i) q^{68} +(1.00000 - 1.73205i) q^{70} +2.00000 q^{71} -11.0000 q^{73} +(-4.00000 + 6.92820i) q^{74} +(-1.50000 - 2.59808i) q^{76} +(1.00000 + 1.73205i) q^{77} +(-1.00000 + 1.73205i) q^{79} +1.00000 q^{80} +7.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(2.50000 + 4.33013i) q^{85} +(2.50000 + 4.33013i) q^{86} +(-0.500000 + 0.866025i) q^{88} -10.0000 q^{89} -2.00000 q^{91} +(6.00000 + 10.3923i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(6.50000 - 11.2583i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + q^{11} + q^{13} + 2 q^{14} - q^{16} - 10 q^{17} + 6 q^{19} - q^{20} - q^{22} - q^{25} + 2 q^{26} + 4 q^{28} + 8 q^{29} - 6 q^{31} + q^{32}+ \cdots + 6 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + q^11 + q^13 + 2 * q^14 - q^16 - 10 * q^17 + 6 * q^19 - q^20 - q^22 - q^25 + 2 * q^26 + 4 * q^28 + 8 * q^29 - 6 * q^31 + q^32 - 5 * q^34 + 4 * q^35 - 16 * q^37 + 3 * q^38 + q^40 + 7 * q^41 - 5 * q^43 - 2 * q^44 - 12 * q^47 + 3 * q^49 + q^50 + q^52 - 4 * q^53 - 2 * q^55 + 2 * q^56 - 8 * q^58 - 5 * q^59 - 14 * q^61 - 12 * q^62 + 2 * q^64 + q^65 + 15 * q^67 + 5 * q^68 + 2 * q^70 + 4 * q^71 - 22 * q^73 - 8 * q^74 - 3 * q^76 + 2 * q^77 - 2 * q^79 + 2 * q^80 + 14 * q^82 - 12 * q^83 + 5 * q^85 + 5 * q^86 - q^88 - 20 * q^89 - 4 * q^91 + 12 * q^94 - 3 * q^95 + 13 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3510\mathbb{Z}\right)^\times$.

$n$	$1081$	$2081$	$2107$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	1.00000	+	1.73205i	0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.00000			−1.21268			−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000			−1.21268			−0.606339	+	0.795206i	$0.707363\pi$
$18$		0			0
$19$	3.00000			0.688247			0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000			0.688247			0.344124	+	0.938924i	$0.388176\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000			0.196116
$27$		0			0
$28$	2.00000			0.377964
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	−0.208443	−	0.978035i	$-0.566840\pi$
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	0.951224	−	0.308500i	$-0.0998271\pi$
$30$		0			0
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−2.50000	+	4.33013i	−0.428746	+	0.742611i
$35$	2.00000			0.338062
$36$		0			0
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	1.50000	−	2.59808i	0.243332	−	0.421464i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	0.998504	+	0.0546823i	$0.0174146\pi$
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	−0.451896	+	0.892071i	$0.649252\pi$
$42$		0			0
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	0.609994	+	0.792406i	$0.291172\pi$
$44$	−1.00000			−0.150756
$45$		0			0
$46$		0			0
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.0186297	+	0.999826i	$0.505930\pi$
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.856560	+	0.516047i	$0.827403\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$		0			0
$55$	−1.00000			−0.134840
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$		0			0
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	0.656136	−	0.754643i	$-0.272190\pi$
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	−0.981608	+	0.190909i	$0.938857\pi$
$60$		0			0
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.0640184	+	0.997949i	$0.520392\pi$
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$		0			0
$67$	7.50000	+	12.9904i	0.916271	+	1.58703i	0.805030	+	0.593234i	$0.202149\pi$
$67$	7.50000	+	12.9904i	0.916271	+	1.58703i	0.111241	+	0.993793i	$0.464517\pi$
$68$	2.50000	+	4.33013i	0.303170	+	0.525105i
$69$		0			0
$70$	1.00000	−	1.73205i	0.119523	−	0.207020i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	−1.50000	−	2.59808i	−0.172062	−	0.298020i
$77$	1.00000	+	1.73205i	0.113961	+	0.197386i
$78$		0			0
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	7.00000			0.773021
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$	2.50000	+	4.33013i	0.271163	+	0.469668i
$86$	2.50000	+	4.33013i	0.269582	+	0.466930i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	−2.00000			−0.209657
$92$		0			0
$93$		0			0
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$		0			0
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	−0.320647	−	0.947199i	$-0.603900\pi$
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	0.980622	−	0.195911i	$-0.0627665\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	1.00000			0.100000
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$		0			0
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$		0			0
$106$	−1.00000	+	1.73205i	−0.0971286	+	0.168232i
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$		0			0
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$		0			0
$112$	−1.00000	−	1.73205i	−0.0944911	−	0.163663i
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	0.981003	+	0.193993i	$0.0621440\pi$
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	−0.322498	+	0.946570i	$0.604523\pi$
$114$		0			0
$115$		0			0
$116$	−8.00000			−0.742781
$117$		0			0
$118$	−5.00000			−0.460287
$119$	5.00000	−	8.66025i	0.458349	−	0.793884i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	7.00000	+	12.1244i	0.633750	+	1.09769i
$123$		0			0
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	1.00000			0.0894427
$126$		0			0
$127$	22.0000			1.95218			0.976092	−	0.217357i	$-0.0697436\pi$
$127$	22.0000			1.95218			0.976092	+	0.217357i	$0.0697436\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$		0			0
$133$	−3.00000	+	5.19615i	−0.260133	+	0.450564i
$134$	15.0000			1.29580
$135$		0			0
$136$	5.00000			0.428746
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$		0			0
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	1.00000			0.0836242
$144$		0			0
$145$	−8.00000			−0.664364
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		0			0
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	0.996207	+	0.0870170i	$0.0277334\pi$
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	−0.422744	+	0.906249i	$0.638933\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$	−3.00000			−0.243332
$153$		0			0
$154$	2.00000			0.161165
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.0242497	−	0.999706i	$-0.507720\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	3.50000	−	6.06218i	0.273304	−	0.473377i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	5.00000			0.383482
$171$		0			0
$172$	5.00000			0.381246
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$		0			0
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		0			0
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	−1.00000	+	1.73205i	−0.0741249	+	0.128388i
$183$		0			0
$184$		0			0
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$		0			0
$187$	−2.50000	+	4.33013i	−0.182818	+	0.316650i
$188$	12.0000			0.875190
$189$		0			0
$190$	−3.00000			−0.217643
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	0.999326	−	0.0366998i	$-0.0116845\pi$
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	−0.531446	+	0.847092i	$0.678351\pi$
$194$	−6.50000	−	11.2583i	−0.466673	−	0.808301i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	18.0000			1.27599			0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000			1.27599			0.637993	+	0.770042i	$0.279765\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−1.00000	−	1.73205i	−0.0703598	−	0.121867i
$203$	8.00000	+	13.8564i	0.561490	+	0.972529i
$204$		0			0
$205$	3.50000	−	6.06218i	0.244451	−	0.423401i
$206$		0			0
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	1.50000	−	2.59808i	0.103757	−	0.179713i
$210$		0			0
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	0.972346	+	0.233544i	$0.0750324\pi$
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	−0.283918	+	0.958849i	$0.591634\pi$
$212$	1.00000	+	1.73205i	0.0686803	+	0.118958i
$213$		0			0
$214$	−4.50000	+	7.79423i	−0.307614	+	0.532803i
$215$	5.00000			0.340997
$216$		0			0
$217$	12.0000			0.814613
$218$	3.00000	−	5.19615i	0.203186	−	0.351928i
$219$		0			0
$220$	0.500000	+	0.866025i	0.0337100	+	0.0583874i
$221$	−2.50000	−	4.33013i	−0.168168	−	0.291276i
$222$		0			0
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	−0.530607	−	0.847618i	$-0.678036\pi$
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	0.999362	+	0.0357107i	$0.0113695\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	14.0000			0.931266
$227$	8.50000	−	14.7224i	0.564165	−	0.977162i	−0.432962	−	0.901412i	$-0.642532\pi$
$227$	8.50000	−	14.7224i	0.564165	−	0.977162i	0.997127	−	0.0757500i	$-0.0241351\pi$
$228$		0			0
$229$	4.00000	+	6.92820i	0.264327	+	0.457829i	0.967387	−	0.253302i	$-0.0815167\pi$
$229$	4.00000	+	6.92820i	0.264327	+	0.457829i	−0.703060	+	0.711131i	$0.748183\pi$
$230$		0			0
$231$		0			0
$232$	−4.00000	+	6.92820i	−0.262613	+	0.454859i
$233$	−15.0000			−0.982683			−0.491341	−	0.870967i	$-0.663493\pi$
$233$	−15.0000			−0.982683			−0.491341	+	0.870967i	$0.663493\pi$
$234$		0			0
$235$	12.0000			0.782794
$236$	−2.50000	+	4.33013i	−0.162736	+	0.281867i
$237$		0			0
$238$	−5.00000	−	8.66025i	−0.324102	−	0.561361i
$239$	−1.00000	−	1.73205i	−0.0646846	−	0.112037i	0.831869	−	0.554971i	$-0.187271\pi$
$239$	−1.00000	−	1.73205i	−0.0646846	−	0.112037i	−0.896554	+	0.442934i	$0.853937\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	10.0000			0.642824
$243$		0			0
$244$	14.0000			0.896258
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$		0			0
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−27.0000			−1.70422			−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000			−1.70422			−0.852112	+	0.523359i	$0.824679\pi$
$252$		0			0
$253$		0			0
$254$	11.0000	−	19.0526i	0.690201	−	1.19546i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$		0			0
$259$	8.00000	−	13.8564i	0.497096	−	0.860995i
$260$	−1.00000			−0.0620174
$261$		0			0
$262$	4.00000			0.247121
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	−0.921077	−	0.389380i	$-0.872689\pi$
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	0.797752	+	0.602986i	$0.206023\pi$
$264$		0			0
$265$	1.00000	+	1.73205i	0.0614295	+	0.106399i
$266$	3.00000	+	5.19615i	0.183942	+	0.318597i
$267$		0			0
$268$	7.50000	−	12.9904i	0.458135	−	0.793514i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	2.50000	−	4.33013i	0.151585	−	0.262553i
$273$		0			0
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		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	$0.00705893\pi$
$278$	−7.00000			−0.419832
$279$		0			0
$280$	−2.00000			−0.119523
$281$	−15.0000	+	25.9808i	−0.894825	+	1.54988i	−0.0608039	+	0.998150i	$0.519366\pi$
$281$	−15.0000	+	25.9808i	−0.894825	+	1.54988i	−0.834021	+	0.551733i	$0.813967\pi$
$282$		0			0
$283$	−16.0000	−	27.7128i	−0.951101	−	1.64736i	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−16.0000	−	27.7128i	−0.951101	−	1.64736i	−0.208053	−	0.978117i	$-0.566713\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$	0.500000	−	0.866025i	0.0295656	−	0.0512092i
$287$	−14.0000			−0.826394
$288$		0			0
$289$	8.00000			0.470588
$290$	−4.00000	+	6.92820i	−0.234888	+	0.406838i
$291$		0			0
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	−1.00000	−	1.73205i	−0.0584206	−	0.101187i	0.835336	−	0.549740i	$-0.185273\pi$
$293$	−1.00000	−	1.73205i	−0.0584206	−	0.101187i	−0.893757	+	0.448552i	$0.851940\pi$
$294$		0			0
$295$	−2.50000	+	4.33013i	−0.145556	+	0.252110i
$296$	8.00000			0.464991
$297$		0			0
$298$	14.0000			0.810998
$299$		0			0
$300$		0			0
$301$	−5.00000	−	8.66025i	−0.288195	−	0.499169i
$302$		0			0
$303$		0			0
$304$	−1.50000	+	2.59808i	−0.0860309	+	0.149010i
$305$	14.0000			0.801638
$306$		0			0
$307$	9.00000			0.513657			0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000			0.513657			0.256829	+	0.966457i	$0.417322\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$		0			0
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	−4.50000	+	7.79423i	−0.254355	+	0.440556i	−0.964720	−	0.263278i	$-0.915197\pi$
$313$	−4.50000	+	7.79423i	−0.254355	+	0.440556i	0.710365	+	0.703833i	$0.248530\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	2.00000			0.112509
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$		0			0
$323$	−15.0000			−0.834622
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$		0			0
$328$	−3.50000	−	6.06218i	−0.193255	−	0.334728i
$329$	−12.0000	−	20.7846i	−0.661581	−	1.14589i
$330$		0			0
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	12.0000			0.658586
$333$		0			0
$334$	8.00000			0.437741
$335$	7.50000	−	12.9904i	0.409769	−	0.709740i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	2.50000	−	4.33013i	0.135582	−	0.234834i
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−20.0000			−1.07990
$344$	2.50000	−	4.33013i	0.134791	−	0.233465i
$345$		0			0
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	0.719590	−	0.694399i	$-0.244330\pi$
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	−0.961162	+	0.275983i	$0.910997\pi$
$348$		0			0
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	−0.952998	−	0.302975i	$-0.902020\pi$
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	0.738883	+	0.673833i	$0.235353\pi$
$350$	−2.00000			−0.106904
$351$		0			0
$352$	1.00000			0.0533002
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	−0.974456	−	0.224580i	$-0.927899\pi$
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	0.681720	+	0.731613i	$0.261232\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	5.00000	+	8.66025i	0.264999	+	0.458993i
$357$		0			0
$358$	−10.0000	+	17.3205i	−0.528516	+	0.915417i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	−10.0000			−0.526316
$362$	−7.00000	+	12.1244i	−0.367912	+	0.637242i
$363$		0			0
$364$	1.00000	+	1.73205i	0.0524142	+	0.0907841i
$365$	5.50000	+	9.52628i	0.287883	+	0.498628i
$366$		0			0
$367$	6.00000	−	10.3923i	0.313197	−	0.542474i	−0.665855	−	0.746081i	$-0.731933\pi$
$367$	6.00000	−	10.3923i	0.313197	−	0.542474i	0.979053	+	0.203607i	$0.0652665\pi$
$368$		0			0
$369$		0			0
$370$	8.00000			0.415900
$371$	2.00000	−	3.46410i	0.103835	−	0.179847i
$372$		0			0
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$374$	2.50000	+	4.33013i	0.129272	+	0.223906i
$375$		0			0
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	8.00000			0.412021
$378$		0			0
$379$	15.0000			0.770498			0.385249	−	0.922813i	$-0.374116\pi$
$379$	15.0000			0.770498			0.385249	+	0.922813i	$0.374116\pi$
$380$	−1.50000	+	2.59808i	−0.0769484	+	0.133278i
$381$		0			0
$382$		0			0
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$		0			0
$385$	1.00000	−	1.73205i	0.0509647	−	0.0882735i
$386$	13.0000			0.661683
$387$		0			0
$388$	−13.0000			−0.659975
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$		0			0
$391$		0			0
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$		0			0
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	2.00000			0.100631
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	9.00000	−	15.5885i	0.451129	−	0.781379i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	3.00000	−	5.19615i	0.149441	−	0.258839i
$404$	−2.00000			−0.0995037
$405$		0			0
$406$	16.0000			0.794067
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$		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	$0.988987\pi$
$410$	−3.50000	−	6.06218i	−0.172853	−	0.299390i
$411$		0			0
$412$		0			0
$413$	10.0000			0.492068
$414$		0			0
$415$	12.0000			0.589057
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	−10.0000	−	17.3205i	−0.488532	−	0.846162i	0.511381	−	0.859354i	$-0.329134\pi$
$419$	−10.0000	−	17.3205i	−0.488532	−	0.846162i	−0.999913	+	0.0131919i	$0.995801\pi$
$420$		0			0
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	0.291953	+	0.956433i	$0.405695\pi$
$421$	−14.0000	+	24.2487i	−0.682318	+	1.18181i	−0.974272	+	0.225377i	$0.927639\pi$
$422$	20.0000			0.973585
$423$		0			0
$424$	2.00000			0.0971286
$425$	2.50000	−	4.33013i	0.121268	−	0.210042i
$426$		0			0
$427$	−14.0000	−	24.2487i	−0.677507	−	1.17348i
$428$	4.50000	+	7.79423i	0.217516	+	0.376748i
$429$		0			0
$430$	2.50000	−	4.33013i	0.120561	−	0.208817i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$	6.00000	−	10.3923i	0.288009	−	0.498847i
$435$		0			0
$436$	−3.00000	−	5.19615i	−0.143674	−	0.248851i
$437$		0			0
$438$		0			0
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	1.00000			0.0476731
$441$		0			0
$442$	−5.00000			−0.237826
$443$	0.500000	−	0.866025i	0.0237557	−	0.0411461i	−0.853903	−	0.520432i	$-0.825771\pi$
$443$	0.500000	−	0.866025i	0.0237557	−	0.0411461i	0.877659	+	0.479286i	$0.159104\pi$
$444$		0			0
$445$	5.00000	+	8.66025i	0.237023	+	0.410535i
$446$	−7.00000	−	12.1244i	−0.331460	−	0.574105i
$447$		0			0
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	7.00000			0.329617
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$		0			0
$454$	−8.50000	−	14.7224i	−0.398925	−	0.690958i
$455$	1.00000	+	1.73205i	0.0468807	+	0.0811998i
$456$		0			0
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	0.0880870	+	0.996113i	$0.471925\pi$
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	−0.906702	+	0.421771i	$0.861409\pi$
$458$	8.00000			0.373815
$459$		0			0
$460$		0			0
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$		0			0
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	0.618050	−	0.786139i	$-0.287923\pi$
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	−0.989841	+	0.142177i	$0.954590\pi$
$464$	4.00000	+	6.92820i	0.185695	+	0.321634i
$465$		0			0
$466$	−7.50000	+	12.9904i	−0.347431	+	0.601768i
$467$	−7.00000			−0.323921			−0.161961	−	0.986797i	$-0.551782\pi$
$467$	−7.00000			−0.323921			−0.161961	+	0.986797i	$0.551782\pi$
$468$		0			0
$469$	−30.0000			−1.38527
$470$	6.00000	−	10.3923i	0.276759	−	0.479361i
$471$		0			0
$472$	2.50000	+	4.33013i	0.115072	+	0.199310i
$473$	2.50000	+	4.33013i	0.114950	+	0.199099i
$474$		0			0
$475$	−1.50000	+	2.59808i	−0.0688247	+	0.119208i
$476$	−10.0000			−0.458349
$477$		0			0
$478$	−2.00000			−0.0914779
$479$	4.00000	−	6.92820i	0.182765	−	0.316558i	−0.760056	−	0.649857i	$-0.774829\pi$
$479$	4.00000	−	6.92820i	0.182765	−	0.316558i	0.942821	+	0.333300i	$0.108162\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$	−0.500000	−	0.866025i	−0.0227744	−	0.0394464i
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−13.0000			−0.590300
$486$		0			0
$487$	−34.0000			−1.54069			−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000			−1.54069			−0.770344	+	0.637629i	$0.779915\pi$
$488$	7.00000	−	12.1244i	0.316875	−	0.548844i
$489$		0			0
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	0.897886	−	0.440228i	$-0.145102\pi$
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	−0.830192	+	0.557478i	$0.811769\pi$
$492$		0			0
$493$	−20.0000	+	34.6410i	−0.900755	+	1.56015i
$494$	3.00000			0.134976
$495$		0			0
$496$	6.00000			0.269408
$497$	−2.00000	+	3.46410i	−0.0897123	+	0.155386i
$498$		0			0
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	0.716258	−	0.697835i	$-0.245853\pi$
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−13.5000	+	23.3827i	−0.602534	+	1.04362i
$503$	2.00000			0.0891756			0.0445878	−	0.999005i	$-0.485803\pi$
$503$	2.00000			0.0891756			0.0445878	+	0.999005i	$0.485803\pi$
$504$		0			0
$505$	−2.00000			−0.0889988
$506$		0			0
$507$		0			0
$508$	−11.0000	−	19.0526i	−0.488046	−	0.845321i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$		0			0
$511$	11.0000	−	19.0526i	0.486611	−	0.842836i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	15.0000			0.661622
$515$		0			0
$516$		0			0
$517$	6.00000	+	10.3923i	0.263880	+	0.457053i
$518$	−8.00000	−	13.8564i	−0.351500	−	0.608816i
$519$		0			0
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	23.0000			1.00765			0.503824	−	0.863806i	$-0.331926\pi$
$521$	23.0000			1.00765			0.503824	+	0.863806i	$0.331926\pi$
$522$		0			0
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		0			0
$526$	2.00000	+	3.46410i	0.0872041	+	0.151042i
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	2.00000			0.0868744
$531$		0			0
$532$	6.00000			0.260133
$533$	−3.50000	+	6.06218i	−0.151602	+	0.262582i
$534$		0			0
$535$	4.50000	+	7.79423i	0.194552	+	0.336974i
$536$	−7.50000	−	12.9904i	−0.323951	−	0.561099i
$537$		0			0
$538$		0			0
$539$	3.00000			0.129219
$540$		0			0
$541$	−20.0000			−0.859867			−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000			−0.859867			−0.429934	+	0.902861i	$0.641463\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$		0			0
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	−3.00000	−	5.19615i	−0.128506	−	0.222579i
$546$		0			0
$547$	11.5000	−	19.9186i	0.491704	−	0.851657i	−0.508250	−	0.861210i	$-0.669707\pi$
$547$	11.5000	−	19.9186i	0.491704	−	0.851657i	0.999954	+	0.00955248i	$0.00304070\pi$
$548$	−3.00000			−0.128154
$549$		0			0
$550$	1.00000			0.0426401
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	−8.00000	−	13.8564i	−0.339887	−	0.588702i
$555$		0			0
$556$	−3.50000	+	6.06218i	−0.148433	+	0.257094i
$557$	16.0000			0.677942			0.338971	−	0.940797i	$-0.389921\pi$
$557$	16.0000			0.677942			0.338971	+	0.940797i	$0.389921\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$	−1.00000	+	1.73205i	−0.0422577	+	0.0731925i
$561$		0			0
$562$	15.0000	+	25.9808i	0.632737	+	1.09593i
$563$	7.50000	+	12.9904i	0.316087	+	0.547479i	0.979668	−	0.200625i	$-0.0642974\pi$
$563$	7.50000	+	12.9904i	0.316087	+	0.547479i	−0.663581	+	0.748105i	$0.730964\pi$
$564$		0			0
$565$	7.00000	−	12.1244i	0.294492	−	0.510075i
$566$	−32.0000			−1.34506
$567$		0			0
$568$	−2.00000			−0.0839181
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.184030	−	0.982921i	$-0.441086\pi$
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.759220	−	0.650835i	$-0.225581\pi$
$570$		0			0
$571$	−6.50000	−	11.2583i	−0.272017	−	0.471146i	0.697362	−	0.716720i	$-0.254357\pi$
$571$	−6.50000	−	11.2583i	−0.272017	−	0.471146i	−0.969378	+	0.245573i	$0.921024\pi$
$572$	−0.500000	−	0.866025i	−0.0209061	−	0.0362103i
$573$		0			0
$574$	−7.00000	+	12.1244i	−0.292174	+	0.506061i
$575$		0			0
$576$		0			0
$577$	21.0000			0.874241			0.437121	−	0.899403i	$-0.355998\pi$
$577$	21.0000			0.874241			0.437121	+	0.899403i	$0.355998\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	4.00000	+	6.92820i	0.166091	+	0.287678i
$581$	−12.0000	−	20.7846i	−0.497844	−	0.862291i
$582$		0			0
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$	11.0000			0.455183
$585$		0			0
$586$	−2.00000			−0.0826192
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	0.293640	+	0.955916i	$0.405133\pi$
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	−0.974668	+	0.223659i	$0.928200\pi$
$588$		0			0
$589$	−9.00000	−	15.5885i	−0.370839	−	0.642311i
$590$	2.50000	+	4.33013i	0.102923	+	0.178269i
$591$		0			0
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	−46.0000			−1.88899			−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−46.0000			−1.88899			−0.944497	+	0.328521i	$0.893450\pi$
$594$		0			0
$595$	−10.0000			−0.409960
$596$	7.00000	−	12.1244i	0.286731	−	0.496633i
$597$		0			0
$598$		0			0
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	0.920783	−	0.390075i	$-0.127551\pi$
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	−0.798206	+	0.602384i	$0.794218\pi$
$600$		0			0
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$	−10.0000			−0.407570
$603$		0			0
$604$		0			0
$605$	5.00000	−	8.66025i	0.203279	−	0.352089i
$606$		0			0
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	1.50000	+	2.59808i	0.0608330	+	0.105366i
$609$		0			0
$610$	7.00000	−	12.1244i	0.283422	−	0.490901i
$611$	−12.0000			−0.485468
$612$		0			0
$613$	−4.00000			−0.161558			−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000			−0.161558			−0.0807792	+	0.996732i	$0.525741\pi$
$614$	4.50000	−	7.79423i	0.181605	−	0.314549i
$615$		0			0
$616$	−1.00000	−	1.73205i	−0.0402911	−	0.0697863i
$617$	4.50000	+	7.79423i	0.181163	+	0.313784i	0.942277	−	0.334835i	$-0.108680\pi$
$617$	4.50000	+	7.79423i	0.181163	+	0.313784i	−0.761114	+	0.648618i	$0.775347\pi$
$618$		0			0
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	−0.705319	−	0.708890i	$-0.749196\pi$
$619$	6.50000	−	11.2583i	0.261257	−	0.452510i	0.966576	+	0.256379i	$0.0825296\pi$
$620$	6.00000			0.240966
$621$		0			0
$622$	−24.0000			−0.962312
$623$	10.0000	−	17.3205i	0.400642	−	0.693932i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.50000	+	7.79423i	0.179856	+	0.311520i
$627$		0			0
$628$	−11.0000	+	19.0526i	−0.438948	+	0.760280i
$629$	40.0000			1.59490
$630$		0			0
$631$	−48.0000			−1.91085			−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000			−1.91085			−0.955425	+	0.295234i	$0.904602\pi$
$632$	1.00000	−	1.73205i	0.0397779	−	0.0688973i
$633$		0			0
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	−11.0000	−	19.0526i	−0.436522	−	0.756078i
$636$		0			0
$637$	−1.50000	+	2.59808i	−0.0594322	+	0.102940i
$638$	−8.00000			−0.316723
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.0472793	−	0.998882i	$-0.484945\pi$
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.841417	−	0.540386i	$-0.181722\pi$
$642$		0			0
$643$	0.500000	+	0.866025i	0.0197181	+	0.0341527i	0.875716	−	0.482826i	$-0.160390\pi$
$643$	0.500000	+	0.866025i	0.0197181	+	0.0341527i	−0.855998	+	0.516979i	$0.827056\pi$
$644$		0			0
$645$		0			0
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$		0			0
$649$	−5.00000			−0.196267
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	2.00000	−	3.46410i	0.0781465	−	0.135354i
$656$	−7.00000			−0.273304
$657$		0			0
$658$	−24.0000			−0.935617
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	−0.602844	−	0.797859i	$-0.705966\pi$
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	0.992388	+	0.123148i	$0.0392990\pi$
$660$		0			0
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	0.636200	−	0.771524i	$-0.280505\pi$
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	−0.986260	+	0.165203i	$0.947172\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$		0			0
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$	6.00000			0.232670
$666$		0			0
$667$		0			0
$668$	4.00000	−	6.92820i	0.154765	−	0.268060i
$669$		0			0
$670$	−7.50000	−	12.9904i	−0.289750	−	0.501862i
$671$	7.00000	+	12.1244i	0.270232	+	0.468056i
$672$		0			0
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	−0.572309	−	0.820038i	$-0.693952\pi$
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	0.996328	+	0.0856156i	$0.0272857\pi$
$674$	13.0000			0.500741
$675$		0			0
$676$	1.00000			0.0384615
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$	13.0000	+	22.5167i	0.498894	+	0.864110i
$680$	−2.50000	−	4.33013i	−0.0958706	−	0.166053i
$681$		0			0
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	5.00000			0.191320			0.0956598	−	0.995414i	$-0.469504\pi$
$683$	5.00000			0.191320			0.0956598	+	0.995414i	$0.469504\pi$
$684$		0			0
$685$	−3.00000			−0.114624
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$		0			0
$688$	−2.50000	−	4.33013i	−0.0953116	−	0.165085i
$689$	−1.00000	−	1.73205i	−0.0380970	−	0.0659859i
$690$		0			0
$691$	−2.00000	+	3.46410i	−0.0760836	+	0.131781i	−0.901557	−	0.432660i	$-0.857575\pi$
$691$	−2.00000	+	3.46410i	−0.0760836	+	0.131781i	0.825473	+	0.564441i	$0.190908\pi$
$692$	14.0000			0.532200
$693$		0			0
$694$	−9.00000			−0.341635
$695$	−3.50000	+	6.06218i	−0.132763	+	0.229952i
$696$		0			0
$697$	−17.5000	−	30.3109i	−0.662860	−	1.14811i
$698$	4.00000	+	6.92820i	0.151402	+	0.262236i
$699$		0			0
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	46.0000			1.73740			0.868698	−	0.495342i	$-0.164957\pi$
$701$	46.0000			1.73740			0.868698	+	0.495342i	$0.164957\pi$
$702$		0			0
$703$	−24.0000			−0.905177
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	5.50000	+	9.52628i	0.206995	+	0.358526i
$707$	2.00000	+	3.46410i	0.0752177	+	0.130281i
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	−2.00000			−0.0750587
$711$		0			0
$712$	10.0000			0.374766
$713$		0			0
$714$		0			0
$715$	−0.500000	−	0.866025i	−0.0186989	−	0.0323875i
$716$	10.0000	+	17.3205i	0.373718	+	0.647298i
$717$		0			0
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$		0			0
$721$		0			0
$722$	−5.00000	+	8.66025i	−0.186081	+	0.322301i
$723$		0			0
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$		0			0
$727$	25.0000	−	43.3013i	0.927199	−	1.60596i	0.139212	−	0.990263i	$-0.455543\pi$
$727$	25.0000	−	43.3013i	0.927199	−	1.60596i	0.787986	−	0.615693i	$-0.211124\pi$
$728$	2.00000			0.0741249
$729$		0			0
$730$	11.0000			0.407128
$731$	12.5000	−	21.6506i	0.462329	−	0.800778i
$732$		0			0
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	0.943468	−	0.331463i	$-0.107542\pi$
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	−0.758789	+	0.651336i	$0.774209\pi$
$734$	−6.00000	−	10.3923i	−0.221464	−	0.383587i
$735$		0			0
$736$		0			0
$737$	15.0000			0.552532
$738$		0			0
$739$	27.0000			0.993211			0.496606	−	0.867976i	$-0.334580\pi$
$739$	27.0000			0.993211			0.496606	+	0.867976i	$0.334580\pi$
$740$	4.00000	−	6.92820i	0.147043	−	0.254686i
$741$		0			0
$742$	−2.00000	−	3.46410i	−0.0734223	−	0.127171i
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$		0			0
$745$	7.00000	−	12.1244i	0.256460	−	0.444202i
$746$	14.0000			0.512576
$747$		0			0
$748$	5.00000			0.182818
$749$	9.00000	−	15.5885i	0.328853	−	0.569590i
$750$		0			0
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$	−6.00000	−	10.3923i	−0.218797	−	0.378968i
$753$		0			0
$754$	4.00000	−	6.92820i	0.145671	−	0.252310i
$755$		0			0
$756$		0			0
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$	7.50000	−	12.9904i	0.272412	−	0.471832i
$759$		0			0
$760$	1.50000	+	2.59808i	0.0544107	+	0.0942421i
$761$	−1.00000	−	1.73205i	−0.0362500	−	0.0627868i	0.847331	−	0.531065i	$-0.178208\pi$
$761$	−1.00000	−	1.73205i	−0.0362500	−	0.0627868i	−0.883581	+	0.468278i	$0.844875\pi$
$762$		0			0
$763$	−6.00000	+	10.3923i	−0.217215	+	0.376227i
$764$		0			0
$765$		0			0
$766$	18.0000			0.650366
$767$	2.50000	−	4.33013i	0.0902698	−	0.156352i
$768$		0			0
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	0.999364	−	0.0356685i	$-0.0113561\pi$
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	−0.530572	+	0.847640i	$0.678023\pi$
$770$	−1.00000	−	1.73205i	−0.0360375	−	0.0624188i
$771$		0			0
$772$	6.50000	−	11.2583i	0.233940	−	0.405196i
$773$	40.0000			1.43870			0.719350	−	0.694648i	$-0.244440\pi$
$773$	40.0000			1.43870			0.719350	+	0.694648i	$0.244440\pi$
$774$		0			0
$775$	6.00000			0.215526
$776$	−6.50000	+	11.2583i	−0.233336	+	0.404151i
$777$		0			0
$778$	5.00000	+	8.66025i	0.179259	+	0.310485i
$779$	10.5000	+	18.1865i	0.376202	+	0.651600i
$780$		0			0
$781$	1.00000	−	1.73205i	0.0357828	−	0.0619777i
$782$		0			0
$783$		0			0
$784$	−3.00000			−0.107143
$785$	−11.0000	+	19.0526i	−0.392607	+	0.680015i
$786$		0			0
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		0			0
$790$	1.00000	−	1.73205i	0.0355784	−	0.0616236i
$791$	−28.0000			−0.995565
$792$		0			0
$793$	−14.0000			−0.497155
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$		0			0
$796$	−9.00000	−	15.5885i	−0.318997	−	0.552518i
$797$	19.0000	+	32.9090i	0.673015	+	1.16570i	0.977045	+	0.213033i	$0.0683342\pi$
$797$	19.0000	+	32.9090i	0.673015	+	1.16570i	−0.304030	+	0.952662i	$0.598332\pi$
$798$		0			0
$799$	30.0000	−	51.9615i	1.06132	−	1.83827i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$	3.00000			0.105934
$803$	−5.50000	+	9.52628i	−0.194091	+	0.336175i
$804$		0			0
$805$		0			0
$806$	−3.00000	−	5.19615i	−0.105670	−	0.183027i
$807$		0			0
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	−5.00000			−0.175791			−0.0878953	−	0.996130i	$-0.528014\pi$
$809$	−5.00000			−0.175791			−0.0878953	+	0.996130i	$0.528014\pi$
$810$		0			0
$811$	−47.0000			−1.65039			−0.825197	−	0.564846i	$-0.808936\pi$
$811$	−47.0000			−1.65039			−0.825197	+	0.564846i	$0.808936\pi$
$812$	8.00000	−	13.8564i	0.280745	−	0.486265i
$813$		0			0
$814$	4.00000	+	6.92820i	0.140200	+	0.242833i
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$		0			0
$817$	−7.50000	+	12.9904i	−0.262392	+	0.454476i
$818$	−19.0000			−0.664319
$819$		0			0
$820$	−7.00000			−0.244451
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	−0.787745	−	0.616002i	$-0.788751\pi$
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	0.927346	+	0.374206i	$0.122085\pi$
$822$		0			0
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$		0			0
$825$		0			0
$826$	5.00000	−	8.66025i	0.173972	−	0.301329i
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$		0			0
$829$	−4.00000			−0.138926			−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000			−0.138926			−0.0694629	+	0.997585i	$0.522129\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	−7.50000	−	12.9904i	−0.259860	−	0.450090i
$834$		0			0
$835$	4.00000	−	6.92820i	0.138426	−	0.239760i
$836$	−3.00000			−0.103757
$837$		0			0
$838$	−20.0000			−0.690889
$839$	−8.00000	+	13.8564i	−0.276191	+	0.478376i	−0.970435	−	0.241363i	$-0.922405\pi$
$839$	−8.00000	+	13.8564i	−0.276191	+	0.478376i	0.694244	+	0.719740i	$0.255739\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	14.0000	+	24.2487i	0.482472	+	0.835666i
$843$		0			0
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−20.0000			−0.687208
$848$	1.00000	−	1.73205i	0.0343401	−	0.0594789i
$849$		0			0
$850$	−2.50000	−	4.33013i	−0.0857493	−	0.148522i
$851$		0			0
$852$		0			0
$853$	−8.00000	+	13.8564i	−0.273915	+	0.474434i	−0.969861	−	0.243660i	$-0.921652\pi$
$853$	−8.00000	+	13.8564i	−0.273915	+	0.474434i	0.695946	+	0.718094i	$0.254985\pi$
$854$	−28.0000			−0.958140
$855$		0			0
$856$	9.00000			0.307614
$857$	−13.0000	+	22.5167i	−0.444072	+	0.769154i	−0.997987	−	0.0634184i	$-0.979800\pi$
$857$	−13.0000	+	22.5167i	−0.444072	+	0.769154i	0.553915	+	0.832573i	$0.313133\pi$
$858$		0			0
$859$	−22.5000	−	38.9711i	−0.767690	−	1.32968i	−0.938813	−	0.344428i	$-0.888073\pi$
$859$	−22.5000	−	38.9711i	−0.767690	−	1.32968i	0.171122	−	0.985250i	$-0.445261\pi$
$860$	−2.50000	−	4.33013i	−0.0852493	−	0.147656i
$861$		0			0
$862$	−6.00000	+	10.3923i	−0.204361	+	0.353963i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	14.0000			0.476014
$866$	−5.50000	+	9.52628i	−0.186898	+	0.323716i
$867$		0			0
$868$	−6.00000	−	10.3923i	−0.203653	−	0.352738i
$869$	1.00000	+	1.73205i	0.0339227	+	0.0587558i
$870$		0			0
$871$	−7.50000	+	12.9904i	−0.254128	+	0.440162i
$872$	−6.00000			−0.203186
$873$		0			0
$874$		0			0
$875$	−1.00000	+	1.73205i	−0.0338062	+	0.0585540i
$876$		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	$0.651651\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	35.0000			1.17784			0.588922	−	0.808190i	$-0.299553\pi$
$883$	35.0000			1.17784			0.588922	+	0.808190i	$0.299553\pi$
$884$	−2.50000	+	4.33013i	−0.0840841	+	0.145638i
$885$		0			0
$886$	−0.500000	−	0.866025i	−0.0167978	−	0.0290947i
$887$	2.00000	+	3.46410i	0.0671534	+	0.116313i	0.897647	−	0.440715i	$-0.145275\pi$
$887$	2.00000	+	3.46410i	0.0671534	+	0.116313i	−0.830494	+	0.557028i	$0.811942\pi$
$888$		0			0
$889$	−22.0000	+	38.1051i	−0.737856	+	1.27800i
$890$	10.0000			0.335201
$891$		0			0
$892$	−14.0000			−0.468755
$893$	−18.0000	+	31.1769i	−0.602347	+	1.04330i
$894$		0			0
$895$	10.0000	+	17.3205i	0.334263	+	0.578961i
$896$	1.00000	+	1.73205i	0.0334077	+	0.0578638i
$897$		0			0
$898$	4.50000	−	7.79423i	0.150167	−	0.260097i
$899$	−48.0000			−1.60089
$900$		0			0
$901$	10.0000			0.333148
$902$	3.50000	−	6.06218i	0.116537	−	0.201848i
$903$		0			0
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	7.00000	+	12.1244i	0.232688	+	0.403027i
$906$		0			0
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$	−17.0000			−0.564165
$909$		0			0
$910$	2.00000			0.0662994
$911$	−16.0000	+	27.7128i	−0.530104	+	0.918166i	0.469280	+	0.883050i	$0.344514\pi$
$911$	−16.0000	+	27.7128i	−0.530104	+	0.918166i	−0.999383	+	0.0351168i	$0.988820\pi$
$912$		0			0
$913$	6.00000	+	10.3923i	0.198571	+	0.343935i
$914$	17.5000	+	30.3109i	0.578849	+	1.00260i
$915$		0			0
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$	−8.00000			−0.264183
$918$		0			0
$919$	46.0000			1.51740			0.758700	−	0.651440i	$-0.225835\pi$
$919$	46.0000			1.51740			0.758700	+	0.651440i	$0.225835\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.00000	+	1.73205i	0.0329154	+	0.0570111i
$924$		0			0
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$	−16.0000			−0.525793
$927$		0			0
$928$	8.00000			0.262613
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$		0			0
$931$	4.50000	+	7.79423i	0.147482	+	0.255446i
$932$	7.50000	+	12.9904i	0.245671	+	0.425514i
$933$		0			0
$934$	−3.50000	+	6.06218i	−0.114523	+	0.198361i
$935$	5.00000			0.163517
$936$		0			0
$937$	−54.0000			−1.76410			−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000			−1.76410			−0.882052	+	0.471153i	$0.843838\pi$
$938$	−15.0000	+	25.9808i	−0.489767	+	0.848302i
$939$		0			0
$940$	−6.00000	−	10.3923i	−0.195698	−	0.338960i
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	0.989599	+	0.143856i	$0.0459502\pi$
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	−0.370216	+	0.928946i	$0.620716\pi$
$942$		0			0
$943$		0			0
$944$	5.00000			0.162736
$945$		0			0
$946$	5.00000			0.162564
$947$	21.5000	−	37.2391i	0.698656	−	1.21011i	−0.270276	−	0.962783i	$-0.587115\pi$
$947$	21.5000	−	37.2391i	0.698656	−	1.21011i	0.968933	−	0.247325i	$-0.0795516\pi$
$948$		0			0
$949$	−5.50000	−	9.52628i	−0.178538	−	0.309236i
$950$	1.50000	+	2.59808i	0.0486664	+	0.0842927i
$951$		0			0
$952$	−5.00000	+	8.66025i	−0.162051	+	0.280680i
$953$	−57.0000			−1.84641			−0.923206	−	0.384307i	$-0.874441\pi$
$953$	−57.0000			−1.84641			−0.923206	+	0.384307i	$0.874441\pi$
$954$		0			0
$955$		0			0
$956$	−1.00000	+	1.73205i	−0.0323423	+	0.0560185i
$957$		0			0
$958$	−4.00000	−	6.92820i	−0.129234	−	0.223840i
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−8.00000			−0.257930
$963$		0			0
$964$	−1.00000			−0.0322078
$965$	6.50000	−	11.2583i	0.209242	−	0.362418i
$966$		0			0
$967$	−8.00000	−	13.8564i	−0.257263	−	0.445592i	0.708245	−	0.705967i	$-0.249487\pi$
$967$	−8.00000	−	13.8564i	−0.257263	−	0.445592i	−0.965508	+	0.260375i	$0.916154\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$		0			0
$970$	−6.50000	+	11.2583i	−0.208702	+	0.361483i
$971$	16.0000			0.513464			0.256732	−	0.966483i	$-0.417354\pi$
$971$	16.0000			0.513464			0.256732	+	0.966483i	$0.417354\pi$
$972$		0			0
$973$	14.0000			0.448819
$974$	−17.0000	+	29.4449i	−0.544715	+	0.943474i
$975$		0			0
$976$	−7.00000	−	12.1244i	−0.224065	−	0.388091i
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	0.889022	−	0.457864i	$-0.151385\pi$
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	−0.841033	+	0.540984i	$0.818052\pi$
$978$		0			0
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	−3.00000			−0.0958315
$981$		0			0
$982$	3.00000			0.0957338
$983$	−14.0000	+	24.2487i	−0.446531	+	0.773414i	−0.998157	−	0.0606773i	$-0.980674\pi$
$983$	−14.0000	+	24.2487i	−0.446531	+	0.773414i	0.551627	+	0.834091i	$0.314007\pi$
$984$		0			0
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$	20.0000	+	34.6410i	0.636930	+	1.10319i
$987$		0			0
$988$	1.50000	−	2.59808i	0.0477214	−	0.0826558i
$989$		0			0
$990$		0			0
$991$	−30.0000			−0.952981			−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000			−0.952981			−0.476491	+	0.879180i	$0.658091\pi$
$992$	3.00000	−	5.19615i	0.0952501	−	0.164978i
$993$		0			0
$994$	2.00000	+	3.46410i	0.0634361	+	0.109875i
$995$	−9.00000	−	15.5885i	−0.285319	−	0.494187i
$996$		0			0
$997$	28.0000	−	48.4974i	0.886769	−	1.53593i	0.0430962	−	0.999071i	$-0.486278\pi$
$997$	28.0000	−	48.4974i	0.886769	−	1.53593i	0.843673	−	0.536858i	$-0.180389\pi$
$998$	−11.0000			−0.348199
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3510.2.j.e.2341.1		2
3.2	odd	2		1170.2.j.c.781.1	yes	2
9.4	even	3	inner	3510.2.j.e.1171.1		2
9.5	odd	6		1170.2.j.c.391.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.j.c.391.1	✓	2	9.5	odd	6
1170.2.j.c.781.1	yes	2	3.2	odd	2
3510.2.j.e.1171.1		2	9.4	even	3	inner
3510.2.j.e.2341.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3510 = 2 \cdot 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3510.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -5.00000 q^{17} +3.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} +2.00000 q^{28} +(4.00000 - 6.92820i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{34} +2.00000 q^{35} -8.00000 q^{37} +(1.50000 - 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{40} +(3.50000 + 6.06218i) q^{41} +(-2.50000 + 4.33013i) q^{43} -1.00000 q^{44} +(-6.00000 + 10.3923i) q^{47} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{52} -2.00000 q^{53} -1.00000 q^{55} +(1.00000 - 1.73205i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(-2.50000 - 4.33013i) q^{59} +(-7.00000 + 12.1244i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(7.50000 + 12.9904i) q^{67} +(2.50000 + 4.33013i) q^{68} +(1.00000 - 1.73205i) q^{70} +2.00000 q^{71} -11.0000 q^{73} +(-4.00000 + 6.92820i) q^{74} +(-1.50000 - 2.59808i) q^{76} +(1.00000 + 1.73205i) q^{77} +(-1.00000 + 1.73205i) q^{79} +1.00000 q^{80} +7.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(2.50000 + 4.33013i) q^{85} +(2.50000 + 4.33013i) q^{86} +(-0.500000 + 0.866025i) q^{88} -10.0000 q^{89} -2.00000 q^{91} +(6.00000 + 10.3923i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(6.50000 - 11.2583i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + q^{11} + q^{13} + 2 q^{14} - q^{16} - 10 q^{17} + 6 q^{19} - q^{20} - q^{22} - q^{25} + 2 q^{26} + 4 q^{28} + 8 q^{29} - 6 q^{31} + q^{32}+ \cdots + 6 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + q^11 + q^13 + 2 * q^14 - q^16 - 10 * q^17 + 6 * q^19 - q^20 - q^22 - q^25 + 2 * q^26 + 4 * q^28 + 8 * q^29 - 6 * q^31 + q^32 - 5 * q^34 + 4 * q^35 - 16 * q^37 + 3 * q^38 + q^40 + 7 * q^41 - 5 * q^43 - 2 * q^44 - 12 * q^47 + 3 * q^49 + q^50 + q^52 - 4 * q^53 - 2 * q^55 + 2 * q^56 - 8 * q^58 - 5 * q^59 - 14 * q^61 - 12 * q^62 + 2 * q^64 + q^65 + 15 * q^67 + 5 * q^68 + 2 * q^70 + 4 * q^71 - 22 * q^73 - 8 * q^74 - 3 * q^76 + 2 * q^77 - 2 * q^79 + 2 * q^80 + 14 * q^82 - 12 * q^83 + 5 * q^85 + 5 * q^86 - q^88 - 20 * q^89 - 4 * q^91 + 12 * q^94 - 3 * q^95 + 13 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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