LMFDB - Embedded newform 1470.2.n.c.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1470.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1470.79
Dual form			1470.2.n.c.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.86603 - 1.23205i) q^{10} +(1.00000 + 1.73205i) q^{11} +(0.866025 + 0.500000i) q^{12} -2.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.92820 - 4.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(-1.00000 - 2.00000i) q^{20} +2.00000i q^{22} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +6.00000 q^{29} +(-2.23205 - 0.133975i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +8.00000 q^{34} +1.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(0.133975 - 2.23205i) q^{40} -6.00000 q^{41} +8.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.23205 + 1.86603i) q^{45} +(-3.46410 - 2.00000i) q^{47} +1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(4.00000 - 6.92820i) q^{51} +(1.73205 - 1.00000i) q^{52} +(-1.73205 + 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 - 4.00000i) q^{55} -2.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-1.86603 - 1.23205i) q^{60} +(5.00000 - 8.66025i) q^{61} +6.00000i q^{62} -1.00000 q^{64} +(-0.267949 + 4.46410i) q^{65} +(1.00000 + 1.73205i) q^{66} +(10.3923 - 6.00000i) q^{67} +(6.92820 + 4.00000i) q^{68} -14.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} +(4.59808 - 1.96410i) q^{75} +2.00000 q^{76} -2.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(1.23205 - 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.19615 - 3.00000i) q^{82} -16.0000i q^{83} +(-16.0000 + 8.00000i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(5.19615 - 3.00000i) q^{87} +(-1.73205 + 1.00000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(5.19615 + 3.00000i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(-2.46410 + 3.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} +10.0000i q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 8 q^{15} - 2 q^{16} + 4 q^{19} - 4 q^{20} + 2 q^{24} + 6 q^{25} + 4 q^{26} + 24 q^{29} - 2 q^{30} + 12 q^{31} + 32 q^{34} + 4 q^{36} - 4 q^{39} + 4 q^{40} - 24 q^{41} - 4 q^{44} + 2 q^{45} + 16 q^{50} + 16 q^{51} + 2 q^{54} - 8 q^{55} + 16 q^{59} - 4 q^{60} + 20 q^{61} - 4 q^{64} - 8 q^{65} + 4 q^{66} - 56 q^{71} + 16 q^{74} + 8 q^{75} + 8 q^{76} + 8 q^{79} - 2 q^{80} - 2 q^{81} - 64 q^{85} - 16 q^{86} - 20 q^{89} - 8 q^{90} - 8 q^{94} + 4 q^{95} - 2 q^{96} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 8 * q^15 - 2 * q^16 + 4 * q^19 - 4 * q^20 + 2 * q^24 + 6 * q^25 + 4 * q^26 + 24 * q^29 - 2 * q^30 + 12 * q^31 + 32 * q^34 + 4 * q^36 - 4 * q^39 + 4 * q^40 - 24 * q^41 - 4 * q^44 + 2 * q^45 + 16 * q^50 + 16 * q^51 + 2 * q^54 - 8 * q^55 + 16 * q^59 - 4 * q^60 + 20 * q^61 - 4 * q^64 - 8 * q^65 + 4 * q^66 - 56 * q^71 + 16 * q^74 + 8 * q^75 + 8 * q^76 + 8 * q^79 - 2 * q^80 - 2 * q^81 - 64 * q^85 - 16 * q^86 - 20 * q^89 - 8 * q^90 - 8 * q^94 + 4 * q^95 - 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.86603	−	1.23205i	−0.590089	−	0.389609i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$	−2.00000	+	1.00000i	−0.516398	+	0.258199i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.92820	−	4.00000i	1.68034	−	0.970143i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	6.92820	−	4.00000i	1.68034	−	0.970143i	0.961436	−	0.275029i	$-0.0886875\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$			2.00000i			0.426401i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−2.23205	−	0.133975i	−0.407515	−	0.0244603i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$	8.00000			1.37199
$35$		0			0
$36$	1.00000			0.166667
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.946180	−	0.323640i	$-0.104907\pi$
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.192809	+	0.981236i	$0.438240\pi$
$38$	1.73205	−	1.00000i	0.280976	−	0.162221i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$	0.133975	−	2.23205i	0.0211832	−	0.352918i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−1.23205	+	1.86603i	−0.183663	+	0.278171i
$46$		0			0
$47$	−3.46410	−	2.00000i	−0.505291	−	0.291730i	0.225605	−	0.974219i	$-0.427564\pi$
$47$	−3.46410	−	2.00000i	−0.505291	−	0.291730i	−0.730896	+	0.682489i	$0.760898\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$	4.00000	−	6.92820i	0.560112	−	0.970143i
$52$	1.73205	−	1.00000i	0.240192	−	0.138675i
$53$	−1.73205	+	1.00000i	−0.237915	+	0.137361i	−0.614218	−	0.789136i	$-0.710529\pi$
$53$	−1.73205	+	1.00000i	−0.237915	+	0.137361i	0.376303	+	0.926497i	$0.377195\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−2.00000	−	4.00000i	−0.269680	−	0.539360i
$56$		0			0
$57$		−	2.00000i		−	0.264906i
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$	−1.86603	−	1.23205i	−0.240903	−	0.159057i
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$			6.00000i			0.762001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.267949	+	4.46410i	−0.0332350	+	0.553704i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	10.3923	−	6.00000i	1.26962	−	0.733017i	0.294706	−	0.955588i	$-0.404778\pi$
$67$	10.3923	−	6.00000i	1.26962	−	0.733017i	0.974916	+	0.222571i	$0.0714450\pi$
$68$	6.92820	+	4.00000i	0.840168	+	0.485071i
$69$		0			0
$70$		0			0
$71$	−14.0000			−1.66149			−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000			−1.66149			−0.830747	+	0.556650i	$0.812086\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.101361	−	0.994850i	$-0.467680\pi$
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.912245	+	0.409644i	$0.134347\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$	4.59808	−	1.96410i	0.530940	−	0.226795i
$76$	2.00000			0.229416
$77$		0			0
$78$		−	2.00000i		−	0.226455i
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	1.23205	−	1.86603i	0.137747	−	0.208628i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.19615	−	3.00000i	−0.573819	−	0.331295i
$83$		−	16.0000i		−	1.75623i	−0.478451	−	0.878114i	$-0.658802\pi$
$83$		−	16.0000i		−	1.75623i	0.478451	−	0.878114i	$-0.341198\pi$
$84$		0			0
$85$	−16.0000	+	8.00000i	−1.73544	+	0.867722i
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	5.19615	−	3.00000i	0.557086	−	0.321634i
$88$	−1.73205	+	1.00000i	−0.184637	+	0.106600i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	−2.00000	+	1.00000i	−0.210819	+	0.105409i
$91$		0			0
$92$		0			0
$93$	5.19615	+	3.00000i	0.538816	+	0.311086i
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$	−2.46410	+	3.73205i	−0.252811	+	0.382900i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$	1.96410	+	4.59808i	0.196410	+	0.459808i
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	6.92820	−	4.00000i	0.685994	−	0.396059i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.0950377	−	0.995474i	$-0.530297\pi$
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.909624	+	0.415432i	$0.863630\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$	0.267949	−	4.46410i	0.0255480	−	0.425635i
$111$	8.00000			0.759326
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−1.73205	−	1.00000i	−0.160128	−	0.0924500i
$118$			8.00000i			0.736460i
$119$		0			0
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	8.66025	−	5.00000i	0.784063	−	0.452679i
$123$	−5.19615	+	3.00000i	−0.468521	+	0.270501i
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$		−	12.0000i		−	1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$127$		−	12.0000i		−	1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$	−2.46410	+	3.73205i	−0.216116	+	0.327323i
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.0155672	+	0.999879i	$0.504955\pi$
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.858137	+	0.513421i	$0.828378\pi$
$132$			2.00000i			0.174078i
$133$		0			0
$134$	12.0000			1.03664
$135$	−0.133975	+	2.23205i	−0.0115307	+	0.192104i
$136$	4.00000	+	6.92820i	0.342997	+	0.594089i
$137$	12.1244	−	7.00000i	1.03585	−	0.598050i	0.117198	−	0.993109i	$-0.462609\pi$
$137$	12.1244	−	7.00000i	1.03585	−	0.598050i	0.918656	+	0.395058i	$0.129276\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	−4.00000			−0.336861
$142$	−12.1244	−	7.00000i	−1.01745	−	0.587427i
$143$	3.46410	−	2.00000i	0.289683	−	0.167248i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−13.3923	−	0.803848i	−1.11217	−	0.0667559i
$146$	10.0000			0.827606
$147$		0			0
$148$			8.00000i			0.657596i
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$	4.96410	+	0.598076i	0.405317	+	0.0488327i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	1.73205	+	1.00000i	0.140488	+	0.0811107i
$153$		−	8.00000i		−	0.646762i
$154$		0			0
$155$	−6.00000	−	12.0000i	−0.481932	−	0.963863i
$156$	1.00000	−	1.73205i	0.0800641	−	0.138675i
$157$	−8.66025	+	5.00000i	−0.691164	+	0.399043i	−0.804048	−	0.594565i	$-0.797324\pi$
$157$	−8.66025	+	5.00000i	−0.691164	+	0.399043i	0.112884	+	0.993608i	$0.463991\pi$
$158$	3.46410	−	2.00000i	0.275589	−	0.159111i
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$	−3.73205	−	2.46410i	−0.290540	−	0.191830i
$166$	8.00000	−	13.8564i	0.620920	−	1.07547i
$167$		−	8.00000i		−	0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$		−	8.00000i		−	0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−17.8564	−	1.07180i	−1.36952	−	0.0822031i
$171$	−1.00000	−	1.73205i	−0.0764719	−	0.132453i
$172$	−6.92820	+	4.00000i	−0.528271	+	0.304997i
$173$	−13.8564	−	8.00000i	−1.05348	−	0.608229i	−0.129861	−	0.991532i	$-0.541453\pi$
$173$	−13.8564	−	8.00000i	−1.05348	−	0.608229i	−0.923622	+	0.383304i	$0.874786\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$	−2.00000			−0.150756
$177$	6.92820	+	4.00000i	0.520756	+	0.300658i
$178$	−8.66025	+	5.00000i	−0.649113	+	0.374766i
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	0.826231	−	0.563331i	$-0.190480\pi$
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	−0.900975	+	0.433872i	$0.857147\pi$
$180$	−2.23205	−	0.133975i	−0.166367	−	0.00998588i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$		−	10.0000i		−	0.739221i
$184$		0			0
$185$	−14.9282	−	9.85641i	−1.09754	−	0.724657i
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$	13.8564	+	8.00000i	1.01328	+	0.585018i
$188$		−	4.00000i		−	0.291730i
$189$		0			0
$190$	−4.00000	+	2.00000i	−0.290191	+	0.145095i
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	0.493469	+	0.869763i	$0.335728\pi$
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	−0.999972	+	0.00752447i	$0.997605\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$	2.00000	+	4.00000i	0.143223	+	0.286446i
$196$		0			0
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$	1.73205	+	1.00000i	0.123091	+	0.0710669i
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.797025	+	0.603947i	$0.206406\pi$
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.124521	+	0.992217i	$0.460261\pi$
$200$	−0.598076	+	4.96410i	−0.0422904	+	0.351015i
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$		−	10.0000i		−	0.703598i
$203$		0			0
$204$	8.00000			0.560112
$205$	13.3923	+	0.803848i	0.935359	+	0.0561432i
$206$		0			0
$207$		0			0
$208$	1.73205	+	1.00000i	0.120096	+	0.0693375i
$209$	4.00000			0.276686
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−1.73205	−	1.00000i	−0.118958	−	0.0686803i
$213$	−12.1244	+	7.00000i	−0.830747	+	0.479632i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	1.07180	−	17.8564i	0.0730959	−	1.21780i
$216$	1.00000			0.0680414
$217$		0			0
$218$		−	6.00000i		−	0.406371i
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$	2.46410	−	3.73205i	0.166130	−	0.251615i
$221$	−8.00000	−	13.8564i	−0.538138	−	0.932083i
$222$	6.92820	+	4.00000i	0.464991	+	0.268462i
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$		0			0
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	−0.711977	−	0.702202i	$-0.752200\pi$
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	0.252136	+	0.967692i	$0.418867\pi$
$228$	1.73205	−	1.00000i	0.114708	−	0.0662266i
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$		0			0
$231$		0			0
$232$			6.00000i			0.393919i
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	0.320043	−	0.947403i	$-0.396303\pi$
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	−0.660454	+	0.750867i	$0.729636\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$	7.46410	+	4.92820i	0.486904	+	0.321481i
$236$	−4.00000	+	6.92820i	−0.260378	+	0.450988i
$237$		−	4.00000i		−	0.259828i
$238$		0			0
$239$	22.0000			1.42306			0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000			1.42306			0.711531	+	0.702655i	$0.248002\pi$
$240$	0.133975	−	2.23205i	0.00864802	−	0.144078i
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	6.06218	−	3.50000i	0.389692	−	0.224989i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	10.0000			0.640184
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−3.46410	−	2.00000i	−0.220416	−	0.127257i
$248$	−5.19615	+	3.00000i	−0.329956	+	0.190500i
$249$	−8.00000	−	13.8564i	−0.506979	−	0.878114i
$250$	−8.52628	−	7.23205i	−0.539249	−	0.457395i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$	−9.85641	+	14.9282i	−0.617232	+	0.934840i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.3205	+	10.0000i	1.08042	+	0.623783i	0.931011	−	0.364992i	$-0.118928\pi$
$257$	17.3205	+	10.0000i	1.08042	+	0.623783i	0.149413	+	0.988775i	$0.452262\pi$
$258$			8.00000i			0.498058i
$259$		0			0
$260$	−4.00000	+	2.00000i	−0.248069	+	0.124035i
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−17.3205	+	10.0000i	−1.07006	+	0.617802i
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.977147	−	0.212565i	$-0.931818\pi$
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.304487	+	0.952517i	$0.598485\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$	4.00000	−	2.00000i	0.245718	−	0.122859i
$266$		0			0
$267$			10.0000i			0.611990i
$268$	10.3923	+	6.00000i	0.634811	+	0.366508i
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$	−1.23205	+	1.86603i	−0.0749802	+	0.113563i
$271$	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	$0.147319\pi$
$272$			8.00000i			0.485071i
$273$		0			0
$274$	14.0000			0.845771
$275$	3.92820	+	9.19615i	0.236880	+	0.554549i
$276$		0			0
$277$	6.92820	−	4.00000i	0.416275	−	0.240337i	−0.277207	−	0.960810i	$-0.589409\pi$
$277$	6.92820	−	4.00000i	0.416275	−	0.240337i	0.693482	+	0.720473i	$0.256075\pi$
$278$	−1.73205	−	1.00000i	−0.103882	−	0.0599760i
$279$	6.00000			0.359211
$280$		0			0
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$	−3.46410	−	2.00000i	−0.206284	−	0.119098i
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	−0.599414	−	0.800439i	$-0.704600\pi$
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	0.393494	+	0.919327i	$0.371266\pi$
$284$	−7.00000	−	12.1244i	−0.415374	−	0.719448i
$285$	−0.267949	+	4.46410i	−0.0158719	+	0.264431i
$286$	4.00000			0.236525
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	23.5000	−	40.7032i	1.38235	−	2.39431i
$290$	−11.1962	−	7.39230i	−0.657461	−	0.434091i
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	8.66025	+	5.00000i	0.506803	+	0.292603i
$293$			16.0000i			0.934730i	0.884064	+	0.467365i	$0.154797\pi$
$293$			16.0000i			0.934730i	−0.884064	+	0.467365i	$0.845203\pi$
$294$		0			0
$295$	−8.00000	−	16.0000i	−0.465778	−	0.931556i
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$	1.73205	−	1.00000i	0.100504	−	0.0580259i
$298$	−15.5885	+	9.00000i	−0.903015	+	0.521356i
$299$		0			0
$300$	4.00000	+	3.00000i	0.230940	+	0.173205i
$301$		0			0
$302$		−	8.00000i		−	0.460348i
$303$	−8.66025	−	5.00000i	−0.497519	−	0.287242i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$	−12.3205	+	18.6603i	−0.705470	+	1.06848i
$306$	4.00000	−	6.92820i	0.228665	−	0.396059i
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$		0			0
$309$		0			0
$310$	0.803848	−	13.3923i	0.0456555	−	0.760632i
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$	1.73205	−	1.00000i	0.0980581	−	0.0566139i
$313$	8.66025	+	5.00000i	0.489506	+	0.282617i	0.724370	−	0.689412i	$-0.242131\pi$
$313$	8.66025	+	5.00000i	0.489506	+	0.282617i	−0.234863	+	0.972028i	$0.575464\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	4.00000			0.225018
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	0.450570	−	0.892741i	$-0.351221\pi$
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	−0.547852	+	0.836576i	$0.684554\pi$
$318$	−1.73205	+	1.00000i	−0.0971286	+	0.0560772i
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$	2.23205	+	0.133975i	0.124775	+	0.00748941i
$321$	−12.0000			−0.669775
$322$		0			0
$323$		−	16.0000i		−	0.890264i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	1.19615	−	9.92820i	0.0663506	−	0.550718i
$326$		0			0
$327$	−5.19615	−	3.00000i	−0.287348	−	0.165900i
$328$		−	6.00000i		−	0.331295i
$329$		0			0
$330$	−2.00000	−	4.00000i	−0.110096	−	0.220193i
$331$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$331$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$332$	13.8564	−	8.00000i	0.760469	−	0.439057i
$333$	6.92820	−	4.00000i	0.379663	−	0.219199i
$334$	4.00000	−	6.92820i	0.218870	−	0.379094i
$335$	−24.0000	+	12.0000i	−1.31126	+	0.655630i
$336$		0			0
$337$		−	32.0000i		−	1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$		−	32.0000i		−	1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$	−14.9282	−	9.85641i	−0.809595	−	0.534539i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$		−	2.00000i		−	0.108148i
$343$		0			0
$344$	−8.00000			−0.431331
$345$		0			0
$346$	−8.00000	−	13.8564i	−0.430083	−	0.744925i
$347$	−3.46410	+	2.00000i	−0.185963	+	0.107366i	−0.590091	−	0.807337i	$-0.700908\pi$
$347$	−3.46410	+	2.00000i	−0.185963	+	0.107366i	0.404128	+	0.914702i	$0.367575\pi$
$348$	5.19615	+	3.00000i	0.278543	+	0.160817i
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$	−1.73205	−	1.00000i	−0.0923186	−	0.0533002i
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$	4.00000	+	6.92820i	0.212598	+	0.368230i
$355$	31.2487	+	1.87564i	1.65851	+	0.0995489i
$356$	−10.0000			−0.529999
$357$		0			0
$358$		−	2.00000i		−	0.105703i
$359$	7.00000	−	12.1244i	0.369446	−	0.639899i	−0.620033	−	0.784576i	$-0.712881\pi$
$359$	7.00000	−	12.1244i	0.369446	−	0.639899i	0.989479	+	0.144677i	$0.0462142\pi$
$360$	−1.86603	−	1.23205i	−0.0983482	−	0.0649348i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−19.0526	−	11.0000i	−1.00138	−	0.578147i
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$	−20.0000	+	10.0000i	−1.04685	+	0.523424i
$366$	5.00000	−	8.66025i	0.261354	−	0.452679i
$367$	−27.7128	+	16.0000i	−1.44660	+	0.835193i	−0.998277	−	0.0586798i	$-0.981311\pi$
$367$	−27.7128	+	16.0000i	−1.44660	+	0.835193i	−0.448320	+	0.893873i	$0.647978\pi$
$368$		0			0
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$	−8.00000	−	16.0000i	−0.415900	−	0.831800i
$371$		0			0
$372$			6.00000i			0.311086i
$373$	−31.1769	−	18.0000i	−1.61428	−	0.932005i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−31.1769	−	18.0000i	−1.61428	−	0.932005i	−0.625917	−	0.779890i	$-0.715275\pi$
$374$	8.00000	+	13.8564i	0.413670	+	0.716498i
$375$	−10.5263	+	3.76795i	−0.543575	+	0.194576i
$376$	2.00000	−	3.46410i	0.103142	−	0.178647i
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	−4.46410	−	0.267949i	−0.229004	−	0.0137455i
$381$	−6.00000	−	10.3923i	−0.307389	−	0.532414i
$382$	−12.1244	+	7.00000i	−0.620336	+	0.358151i
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$		0			0
$387$	6.92820	+	4.00000i	0.352180	+	0.203331i
$388$	−8.66025	+	5.00000i	−0.439658	+	0.253837i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$	−0.267949	+	4.46410i	−0.0135681	+	0.226049i
$391$		0			0
$392$		0			0
$393$			20.0000i			1.00887i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−4.92820	+	7.46410i	−0.247965	+	0.375560i
$396$	1.00000	+	1.73205i	0.0502519	+	0.0870388i
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	0.455905	−	0.890028i	$-0.349316\pi$
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	−0.542834	+	0.839840i	$0.682649\pi$
$398$			26.0000i			1.30326i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	10.3923	−	6.00000i	0.518321	−	0.299253i
$403$	10.3923	−	6.00000i	0.517678	−	0.298881i
$404$	5.00000	−	8.66025i	0.248759	−	0.430864i
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$		0			0
$407$			16.0000i			0.793091i
$408$	6.92820	+	4.00000i	0.342997	+	0.198030i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	11.1962	+	7.39230i	0.552939	+	0.365080i
$411$	7.00000	−	12.1244i	0.345285	−	0.598050i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.14359	+	35.7128i	−0.105225	+	1.75307i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	−1.73205	+	1.00000i	−0.0848189	+	0.0489702i
$418$	3.46410	+	2.00000i	0.169435	+	0.0978232i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	−6.92820	−	4.00000i	−0.337260	−	0.194717i
$423$	−3.46410	+	2.00000i	−0.168430	+	0.0972433i
$424$	−1.00000	−	1.73205i	−0.0485643	−	0.0841158i
$425$	36.7846	−	15.7128i	1.78432	−	0.762183i
$426$	−14.0000			−0.678302
$427$		0			0
$428$		−	12.0000i		−	0.580042i
$429$	2.00000	−	3.46410i	0.0965609	−	0.167248i
$430$	9.85641	−	14.9282i	0.475318	−	0.719902i
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$		−	26.0000i		−	1.24948i	−0.780833	−	0.624740i	$-0.785205\pi$
$433$		−	26.0000i		−	1.24948i	0.780833	−	0.624740i	$-0.214795\pi$
$434$		0			0
$435$	−12.0000	+	6.00000i	−0.575356	+	0.287678i
$436$	3.00000	−	5.19615i	0.143674	−	0.248851i
$437$		0			0
$438$	8.66025	−	5.00000i	0.413803	−	0.238909i
$439$	−3.00000	+	5.19615i	−0.143182	+	0.247999i	−0.928693	−	0.370849i	$-0.879067\pi$
$439$	−3.00000	+	5.19615i	−0.143182	+	0.247999i	0.785511	+	0.618848i	$0.212400\pi$
$440$	4.00000	−	2.00000i	0.190693	−	0.0953463i
$441$		0			0
$442$		−	16.0000i		−	0.761042i
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.481486	−	0.876454i	$-0.659903\pi$
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.999774	+	0.0212481i	$0.993236\pi$
$444$	4.00000	+	6.92820i	0.189832	+	0.328798i
$445$	12.3205	−	18.6603i	0.584048	−	0.884581i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$			18.0000i			0.851371i
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	4.59808	−	1.96410i	0.216755	−	0.0925886i
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	−5.19615	+	3.00000i	−0.244406	+	0.141108i
$453$	−6.92820	−	4.00000i	−0.325515	−	0.187936i
$454$	−8.00000			−0.375459
$455$		0			0
$456$	2.00000			0.0936586
$457$	−24.2487	−	14.0000i	−1.13431	−	0.654892i	−0.189292	−	0.981921i	$-0.560619\pi$
$457$	−24.2487	−	14.0000i	−1.13431	−	0.654892i	−0.945015	+	0.327028i	$0.893953\pi$
$458$	−22.5167	+	13.0000i	−1.05213	+	0.607450i
$459$	−4.00000	−	6.92820i	−0.186704	−	0.323381i
$460$		0			0
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$		−	12.0000i		−	0.557687i	−0.960337	−	0.278844i	$-0.910049\pi$
$463$		−	12.0000i		−	0.557687i	0.960337	−	0.278844i	$-0.0899511\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−11.1962	−	7.39230i	−0.519209	−	0.342810i
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−13.8564	−	8.00000i	−0.641198	−	0.370196i	0.143878	−	0.989595i	$-0.454043\pi$
$467$	−13.8564	−	8.00000i	−0.641198	−	0.370196i	−0.785076	+	0.619400i	$0.787376\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		0			0
$470$	4.00000	+	8.00000i	0.184506	+	0.369012i
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$	−6.92820	+	4.00000i	−0.318896	+	0.184115i
$473$	−13.8564	+	8.00000i	−0.637118	+	0.367840i
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	6.00000	−	8.00000i	0.275299	−	0.367065i
$476$		0			0
$477$			2.00000i			0.0915737i
$478$	19.0526	+	11.0000i	0.871444	+	0.503128i
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	0.760056	−	0.649857i	$-0.225171\pi$
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	−0.942821	+	0.333300i	$0.891838\pi$
$480$	1.23205	−	1.86603i	0.0562352	−	0.0851720i
$481$	8.00000	−	13.8564i	0.364769	−	0.631798i
$482$		−	10.0000i		−	0.455488i
$483$		0			0
$484$	7.00000			0.318182
$485$	1.33975	−	22.3205i	0.0608347	−	1.01352i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−31.1769	+	18.0000i	−1.41276	+	0.815658i	−0.995648	−	0.0931967i	$-0.970291\pi$
$487$	−31.1769	+	18.0000i	−1.41276	+	0.815658i	−0.417113	+	0.908855i	$0.636958\pi$
$488$	8.66025	+	5.00000i	0.392031	+	0.226339i
$489$		0			0
$490$		0			0
$491$	−42.0000			−1.89543			−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000			−1.89543			−0.947717	+	0.319113i	$0.896615\pi$
$492$	−5.19615	−	3.00000i	−0.234261	−	0.135250i
$493$	41.5692	−	24.0000i	1.87218	−	1.08091i
$494$	−2.00000	−	3.46410i	−0.0899843	−	0.155857i
$495$	−4.46410	−	0.267949i	−0.200646	−	0.0120434i
$496$	−6.00000			−0.269408
$497$		0			0
$498$		−	16.0000i		−	0.716977i
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$	−3.76795	−	10.5263i	−0.168508	−	0.470750i
$501$	−4.00000	−	6.92820i	−0.178707	−	0.309529i
$502$		0			0
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$		0			0
$505$	10.0000	+	20.0000i	0.444994	+	0.889988i
$506$		0			0
$507$	7.79423	−	4.50000i	0.346154	−	0.199852i
$508$	10.3923	−	6.00000i	0.461084	−	0.266207i
$509$	−1.00000	+	1.73205i	−0.0443242	+	0.0767718i	−0.887336	−	0.461123i	$-0.847447\pi$
$509$	−1.00000	+	1.73205i	−0.0443242	+	0.0767718i	0.843012	+	0.537895i	$0.180780\pi$
$510$	−16.0000	+	8.00000i	−0.708492	+	0.354246i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−1.73205	−	1.00000i	−0.0764719	−	0.0441511i
$514$	10.0000	+	17.3205i	0.441081	+	0.763975i
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$		−	8.00000i		−	0.351840i
$518$		0			0
$519$	−16.0000			−0.702322
$520$	−4.46410	−	0.267949i	−0.195764	−	0.0117503i
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$	5.19615	−	3.00000i	0.227429	−	0.131306i
$523$	−10.3923	−	6.00000i	−0.454424	−	0.262362i	0.255273	−	0.966869i	$-0.417835\pi$
$523$	−10.3923	−	6.00000i	−0.454424	−	0.262362i	−0.709697	+	0.704507i	$0.751168\pi$
$524$	−20.0000			−0.873704
$525$		0			0
$526$	−24.0000			−1.04645
$527$	41.5692	+	24.0000i	1.81078	+	1.04546i
$528$	−1.73205	+	1.00000i	−0.0753778	+	0.0435194i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$	4.46410	+	0.267949i	0.193908	+	0.0116390i
$531$	8.00000			0.347170
$532$		0			0
$533$			12.0000i			0.519778i
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$	22.3923	+	14.7846i	0.968104	+	0.639194i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	−1.73205	−	1.00000i	−0.0747435	−	0.0431532i
$538$		−	14.0000i		−	0.603583i
$539$		0			0
$540$	−2.00000	+	1.00000i	−0.0860663	+	0.0430331i
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	−0.843728	−	0.536771i	$-0.819644\pi$
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	0.886721	+	0.462304i	$0.152977\pi$
$542$	1.73205	−	1.00000i	0.0743980	−	0.0429537i
$543$	−19.0526	+	11.0000i	−0.817624	+	0.472055i
$544$	−4.00000	+	6.92820i	−0.171499	+	0.297044i
$545$	6.00000	+	12.0000i	0.257012	+	0.514024i
$546$		0			0
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$	12.1244	+	7.00000i	0.517927	+	0.299025i
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$	−1.19615	+	9.92820i	−0.0510041	+	0.423340i
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$	8.00000			0.339887
$555$	−17.8564	−	1.07180i	−0.757962	−	0.0454952i
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−5.19615	+	3.00000i	−0.220168	+	0.127114i	−0.606028	−	0.795443i	$-0.707238\pi$
$557$	−5.19615	+	3.00000i	−0.220168	+	0.127114i	0.385860	+	0.922557i	$0.373905\pi$
$558$	5.19615	+	3.00000i	0.219971	+	0.127000i
$559$	16.0000			0.676728
$560$		0			0
$561$	16.0000			0.675521
$562$	19.0526	+	11.0000i	0.803684	+	0.464007i
$563$	−10.3923	+	6.00000i	−0.437983	+	0.252870i	−0.702742	−	0.711445i	$-0.748041\pi$
$563$	−10.3923	+	6.00000i	−0.437983	+	0.252870i	0.264758	+	0.964315i	$0.414708\pi$
$564$	−2.00000	−	3.46410i	−0.0842152	−	0.145865i
$565$	0.803848	−	13.3923i	0.0338181	−	0.563418i
$566$	−4.00000			−0.168133
$567$		0			0
$568$		−	14.0000i		−	0.587427i
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$	−2.46410	+	3.73205i	−0.103210	+	0.156318i
$571$	22.0000	+	38.1051i	0.920671	+	1.59465i	0.798379	+	0.602155i	$0.205691\pi$
$571$	22.0000	+	38.1051i	0.920671	+	1.59465i	0.122292	+	0.992494i	$0.460975\pi$
$572$	3.46410	+	2.00000i	0.144841	+	0.0836242i
$573$			14.0000i			0.584858i
$574$		0			0
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	15.5885	−	9.00000i	0.648956	−	0.374675i	−0.139100	−	0.990278i	$-0.544421\pi$
$577$	15.5885	−	9.00000i	0.648956	−	0.374675i	0.788056	+	0.615603i	$0.211088\pi$
$578$	40.7032	−	23.5000i	1.69303	−	0.977471i
$579$		0			0
$580$	−6.00000	−	12.0000i	−0.249136	−	0.498273i
$581$		0			0
$582$			10.0000i			0.414513i
$583$	−3.46410	−	2.00000i	−0.143468	−	0.0828315i
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$	3.73205	+	2.46410i	0.154301	+	0.101878i
$586$	−8.00000	+	13.8564i	−0.330477	+	0.572403i
$587$			4.00000i			0.165098i	0.996587	+	0.0825488i	$0.0263060\pi$
$587$			4.00000i			0.165098i	−0.996587	+	0.0825488i	$0.973694\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$	1.07180	−	17.8564i	0.0441252	−	0.735137i
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$	−27.7128	−	16.0000i	−1.13803	−	0.657041i	−0.192087	−	0.981378i	$-0.561526\pi$
$593$	−27.7128	−	16.0000i	−1.13803	−	0.657041i	−0.945942	+	0.324337i	$0.894859\pi$
$594$	2.00000			0.0820610
$595$		0			0
$596$	−18.0000			−0.737309
$597$	22.5167	+	13.0000i	0.921546	+	0.532055i
$598$		0			0
$599$	7.00000	+	12.1244i	0.286012	+	0.495388i	0.972854	−	0.231419i	$-0.0743369\pi$
$599$	7.00000	+	12.1244i	0.286012	+	0.495388i	−0.686842	+	0.726807i	$0.741004\pi$
$600$	1.96410	+	4.59808i	0.0801841	+	0.187716i
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$	−8.62436	+	13.0622i	−0.350630	+	0.531053i
$606$	−5.00000	−	8.66025i	−0.203111	−	0.351799i
$607$	13.8564	+	8.00000i	0.562414	+	0.324710i	0.754114	−	0.656744i	$-0.228067\pi$
$607$	13.8564	+	8.00000i	0.562414	+	0.324710i	−0.191700	+	0.981454i	$0.561400\pi$
$608$			2.00000i			0.0811107i
$609$		0			0
$610$	−20.0000	+	10.0000i	−0.809776	+	0.404888i
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$	6.92820	−	4.00000i	0.280056	−	0.161690i
$613$	27.7128	−	16.0000i	1.11931	−	0.646234i	0.178085	−	0.984015i	$-0.443010\pi$
$613$	27.7128	−	16.0000i	1.11931	−	0.646234i	0.941225	+	0.337781i	$0.109676\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$	12.0000	−	6.00000i	0.483887	−	0.241943i
$616$		0			0
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$		0			0
$619$	9.00000	+	15.5885i	0.361741	+	0.626553i	0.988247	−	0.152863i	$-0.0488493\pi$
$619$	9.00000	+	15.5885i	0.361741	+	0.626553i	−0.626507	+	0.779416i	$0.715516\pi$
$620$	7.39230	−	11.1962i	0.296882	−	0.449648i
$621$		0			0
$622$		−	8.00000i		−	0.320771i
$623$		0			0
$624$	2.00000			0.0800641
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	5.00000	+	8.66025i	0.199840	+	0.346133i
$627$	3.46410	−	2.00000i	0.138343	−	0.0798723i
$628$	−8.66025	−	5.00000i	−0.345582	−	0.199522i
$629$	64.0000			2.55185
$630$		0			0
$631$	12.0000			0.477712			0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000			0.477712			0.238856	+	0.971055i	$0.423228\pi$
$632$	3.46410	+	2.00000i	0.137795	+	0.0795557i
$633$	−6.92820	+	4.00000i	−0.275371	+	0.158986i
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−1.60770	+	26.7846i	−0.0637994	+	1.06291i
$636$	−2.00000			−0.0793052
$637$		0			0
$638$			12.0000i			0.475085i
$639$	−7.00000	+	12.1244i	−0.276916	+	0.479632i
$640$	1.86603	+	1.23205i	0.0737611	+	0.0487011i
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$	−10.3923	−	6.00000i	−0.410152	−	0.236801i
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$		0			0
$645$	−8.00000	−	16.0000i	−0.315000	−	0.629999i
$646$	8.00000	−	13.8564i	0.314756	−	0.545173i
$647$	13.8564	−	8.00000i	0.544752	−	0.314512i	−0.202251	−	0.979334i	$-0.564826\pi$
$647$	13.8564	−	8.00000i	0.544752	−	0.314512i	0.747002	+	0.664821i	$0.231492\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$	6.00000	−	8.00000i	0.235339	−	0.313786i
$651$		0			0
$652$		0			0
$653$	12.1244	+	7.00000i	0.474463	+	0.273931i	0.718106	−	0.695934i	$-0.245009\pi$
$653$	12.1244	+	7.00000i	0.474463	+	0.273931i	−0.243643	+	0.969865i	$0.578343\pi$
$654$	−3.00000	−	5.19615i	−0.117309	−	0.203186i
$655$	24.6410	−	37.3205i	0.962804	−	1.45823i
$656$	3.00000	−	5.19615i	0.117130	−	0.202876i
$657$		−	10.0000i		−	0.390137i
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$	0.267949	−	4.46410i	0.0104299	−	0.173765i
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$		0			0
$663$	−13.8564	−	8.00000i	−0.538138	−	0.310694i
$664$	16.0000			0.620920
$665$		0			0
$666$	8.00000			0.309994
$667$		0			0
$668$	6.92820	−	4.00000i	0.268060	−	0.154765i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$	−26.7846	−	1.60770i	−1.03478	−	0.0621107i
$671$	20.0000			0.772091
$672$		0			0
$673$			12.0000i			0.462566i	0.972887	+	0.231283i	$0.0742923\pi$
$673$			12.0000i			0.462566i	−0.972887	+	0.231283i	$0.925708\pi$
$674$	16.0000	−	27.7128i	0.616297	−	1.06746i
$675$	0.598076	−	4.96410i	0.0230200	−	0.191068i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$			6.00000i			0.230429i
$679$		0			0
$680$	−8.00000	−	16.0000i	−0.306786	−	0.613572i
$681$	−4.00000	+	6.92820i	−0.153280	+	0.265489i
$682$	−10.3923	+	6.00000i	−0.397942	+	0.229752i
$683$	24.2487	−	14.0000i	0.927851	−	0.535695i	0.0417198	−	0.999129i	$-0.486716\pi$
$683$	24.2487	−	14.0000i	0.927851	−	0.535695i	0.886131	+	0.463434i	$0.153383\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$	−28.0000	+	14.0000i	−1.06983	+	0.534913i
$686$		0			0
$687$			26.0000i			0.991962i
$688$	−6.92820	−	4.00000i	−0.264135	−	0.152499i
$689$	2.00000	+	3.46410i	0.0761939	+	0.131972i
$690$		0			0
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	−0.967901	−	0.251330i	$-0.919132\pi$
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	0.701609	+	0.712562i	$0.252465\pi$
$692$		−	16.0000i		−	0.608229i
$693$		0			0
$694$	−4.00000			−0.151838
$695$	4.46410	+	0.267949i	0.169333	+	0.0101639i
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$	−41.5692	+	24.0000i	−1.57455	+	0.909065i
$698$	15.5885	+	9.00000i	0.590032	+	0.340655i
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	−1.73205	−	1.00000i	−0.0653720	−	0.0377426i
$703$	13.8564	−	8.00000i	0.522604	−	0.301726i
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$	8.92820	+	0.535898i	0.336256	+	0.0201831i
$706$		0			0
$707$		0			0
$708$			8.00000i			0.300658i
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	26.1244	+	17.2487i	0.980430	+	0.647333i
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$	−8.66025	−	5.00000i	−0.324557	−	0.187383i
$713$		0			0
$714$		0			0
$715$	−8.00000	+	4.00000i	−0.299183	+	0.149592i
$716$	1.00000	−	1.73205i	0.0373718	−	0.0647298i
$717$	19.0526	−	11.0000i	0.711531	−	0.410803i
$718$	12.1244	−	7.00000i	0.452477	−	0.261238i
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	−0.617079	−	0.786901i	$-0.711684\pi$
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	0.990016	+	0.140955i	$0.0450174\pi$
$720$	−1.00000	−	2.00000i	−0.0372678	−	0.0745356i
$721$		0			0
$722$			15.0000i			0.558242i
$723$	−8.66025	−	5.00000i	−0.322078	−	0.185952i
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	29.7846	+	3.58846i	1.10617	+	0.133272i
$726$	3.50000	−	6.06218i	0.129897	−	0.224989i
$727$			16.0000i			0.593407i	0.954970	+	0.296704i	$0.0958873\pi$
$727$			16.0000i			0.593407i	−0.954970	+	0.296704i	$0.904113\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−22.3205	−	1.33975i	−0.826119	−	0.0495862i
$731$	32.0000	+	55.4256i	1.18356	+	2.04999i
$732$	8.66025	−	5.00000i	0.320092	−	0.184805i
$733$	−25.9808	−	15.0000i	−0.959621	−	0.554038i	−0.0635649	−	0.997978i	$-0.520247\pi$
$733$	−25.9808	−	15.0000i	−0.959621	−	0.554038i	−0.896056	+	0.443940i	$0.853580\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$		0			0
$737$	20.7846	+	12.0000i	0.765611	+	0.442026i
$738$	−5.19615	+	3.00000i	−0.191273	+	0.110432i
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	0.989230	−	0.146369i	$-0.0467586\pi$
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	−0.621374	+	0.783514i	$0.713425\pi$
$740$	1.07180	−	17.8564i	0.0394000	−	0.656415i
$741$	−4.00000			−0.146944
$742$		0			0
$743$			16.0000i			0.586983i	0.955962	+	0.293492i	$0.0948173\pi$
$743$			16.0000i			0.586983i	−0.955962	+	0.293492i	$0.905183\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$	22.1769	−	33.5885i	0.812499	−	1.23059i
$746$	−18.0000	−	31.1769i	−0.659027	−	1.14147i
$747$	−13.8564	−	8.00000i	−0.506979	−	0.292705i
$748$			16.0000i			0.585018i
$749$		0			0
$750$	−11.0000	−	2.00000i	−0.401663	−	0.0730297i
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	3.46410	−	2.00000i	0.126323	−	0.0729325i
$753$		0			0
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$	8.00000	+	16.0000i	0.291150	+	0.582300i
$756$		0			0
$757$			4.00000i			0.145382i	0.997354	+	0.0726912i	$0.0231588\pi$
$757$			4.00000i			0.145382i	−0.997354	+	0.0726912i	$0.976841\pi$
$758$	24.2487	+	14.0000i	0.880753	+	0.508503i
$759$		0			0
$760$	−3.73205	−	2.46410i	−0.135376	−	0.0893824i
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$		−	12.0000i		−	0.434714i
$763$		0			0
$764$	−14.0000			−0.506502
$765$	−1.07180	+	17.8564i	−0.0387509	+	0.645600i
$766$		0			0
$767$	13.8564	−	8.00000i	0.500326	−	0.288863i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−42.0000			−1.51456			−0.757279	−	0.653091i	$-0.773472\pi$
$769$	−42.0000			−1.51456			−0.757279	+	0.653091i	$0.773472\pi$
$770$		0			0
$771$	20.0000			0.720282
$772$		0			0
$773$	27.7128	−	16.0000i	0.996761	−	0.575480i	0.0894724	−	0.995989i	$-0.471482\pi$
$773$	27.7128	−	16.0000i	0.996761	−	0.575480i	0.907288	+	0.420509i	$0.138149\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$	11.7846	+	27.5885i	0.423316	+	0.991007i
$776$	−10.0000			−0.358979
$777$		0			0
$778$			6.00000i			0.215110i
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	−2.46410	+	3.73205i	−0.0882290	+	0.133629i
$781$	−14.0000	−	24.2487i	−0.500959	−	0.867687i
$782$		0			0
$783$		−	6.00000i		−	0.214423i
$784$		0			0
$785$	20.0000	−	10.0000i	0.713831	−	0.356915i
$786$	−10.0000	+	17.3205i	−0.356688	+	0.617802i
$787$	−38.1051	+	22.0000i	−1.35830	+	0.784215i	−0.989395	−	0.145251i	$-0.953601\pi$
$787$	−38.1051	+	22.0000i	−1.35830	+	0.784215i	−0.368906	+	0.929467i	$0.620268\pi$
$788$	−5.19615	+	3.00000i	−0.185105	+	0.106871i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$	−8.00000	+	4.00000i	−0.284627	+	0.142314i
$791$		0			0
$792$			2.00000i			0.0710669i
$793$	−17.3205	−	10.0000i	−0.615069	−	0.355110i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$	2.46410	−	3.73205i	0.0873927	−	0.132362i
$796$	−13.0000	+	22.5167i	−0.460773	+	0.798082i
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$	−4.59808	+	1.96410i	−0.162567	+	0.0694415i
$801$	5.00000	+	8.66025i	0.176666	+	0.305995i
$802$	−15.5885	+	9.00000i	−0.550448	+	0.317801i
$803$	17.3205	+	10.0000i	0.611227	+	0.352892i
$804$	12.0000			0.423207
$805$		0			0
$806$	12.0000			0.422682
$807$	−12.1244	−	7.00000i	−0.426798	−	0.246412i
$808$	8.66025	−	5.00000i	0.304667	−	0.175899i
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$	−0.133975	+	2.23205i	−0.00470739	+	0.0784263i
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$		0			0
$813$		−	2.00000i		−	0.0701431i
$814$	−8.00000	+	13.8564i	−0.280400	+	0.485667i
$815$		0			0
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	13.8564	+	8.00000i	0.484774	+	0.279885i
$818$		−	10.0000i		−	0.349642i
$819$		0			0
$820$	6.00000	+	12.0000i	0.209529	+	0.419058i
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$	12.1244	−	7.00000i	0.422885	−	0.244153i
$823$	−3.46410	+	2.00000i	−0.120751	+	0.0697156i	−0.559159	−	0.829060i	$-0.688876\pi$
$823$	−3.46410	+	2.00000i	−0.120751	+	0.0697156i	0.438408	+	0.898776i	$0.355543\pi$
$824$		0			0
$825$	8.00000	+	6.00000i	0.278524	+	0.208893i
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	0.994174	+	0.107788i	$0.0343769\pi$
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	−0.403739	+	0.914874i	$0.632290\pi$
$830$	−19.7128	+	29.8564i	−0.684242	+	1.03633i
$831$	4.00000	−	6.92820i	0.138758	−	0.240337i
$832$			2.00000i			0.0693375i
$833$		0			0
$834$	−2.00000			−0.0692543
$835$	−1.07180	+	17.8564i	−0.0370911	+	0.617946i
$836$	2.00000	+	3.46410i	0.0691714	+	0.119808i
$837$	5.19615	−	3.00000i	0.179605	−	0.103695i
$838$	10.3923	+	6.00000i	0.358996	+	0.207267i
$839$	44.0000			1.51905			0.759524	−	0.650479i	$-0.225432\pi$
$839$	44.0000			1.51905			0.759524	+	0.650479i	$0.225432\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	8.66025	+	5.00000i	0.298452	+	0.172311i
$843$	19.0526	−	11.0000i	0.656205	−	0.378860i
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−20.0885	−	1.20577i	−0.691064	−	0.0414798i
$846$	−4.00000			−0.137523
$847$		0			0
$848$		−	2.00000i		−	0.0686803i
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$	39.7128	+	4.78461i	1.36214	+	0.164111i
$851$		0			0
$852$	−12.1244	−	7.00000i	−0.415374	−	0.239816i
$853$		−	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
$855$	2.00000	+	4.00000i	0.0683986	+	0.136797i
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	17.3205	−	10.0000i	0.591657	−	0.341593i	−0.174095	−	0.984729i	$-0.555700\pi$
$857$	17.3205	−	10.0000i	0.591657	−	0.341593i	0.765753	+	0.643135i	$0.222367\pi$
$858$	3.46410	−	2.00000i	0.118262	−	0.0682789i
$859$	3.00000	−	5.19615i	0.102359	−	0.177290i	−0.810297	−	0.586019i	$-0.800694\pi$
$859$	3.00000	−	5.19615i	0.102359	−	0.177290i	0.912656	+	0.408729i	$0.134028\pi$
$860$	16.0000	−	8.00000i	0.545595	−	0.272798i
$861$		0			0
$862$			6.00000i			0.204361i
$863$	−41.5692	−	24.0000i	−1.41503	−	0.816970i	−0.419176	−	0.907905i	$-0.637681\pi$
$863$	−41.5692	−	24.0000i	−1.41503	−	0.816970i	−0.995857	+	0.0909355i	$0.971014\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	29.8564	+	19.7128i	1.01515	+	0.670256i
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$		−	47.0000i		−	1.59620i
$868$		0			0
$869$	8.00000			0.271381
$870$	−13.3923	−	0.803848i	−0.454042	−	0.0272530i
$871$	−12.0000	−	20.7846i	−0.406604	−	0.704260i
$872$	5.19615	−	3.00000i	0.175964	−	0.101593i
$873$	8.66025	+	5.00000i	0.293105	+	0.169224i
$874$		0			0
$875$		0			0
$876$	10.0000			0.337869
$877$	−41.5692	−	24.0000i	−1.40369	−	0.810422i	−0.408923	−	0.912569i	$-0.634096\pi$
$877$	−41.5692	−	24.0000i	−1.40369	−	0.810422i	−0.994769	+	0.102146i	$0.967429\pi$
$878$	−5.19615	+	3.00000i	−0.175362	+	0.101245i
$879$	8.00000	+	13.8564i	0.269833	+	0.467365i
$880$	4.46410	+	0.267949i	0.150485	+	0.00903257i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		0			0
$883$			52.0000i			1.74994i	0.484178	+	0.874970i	$0.339119\pi$
$883$			52.0000i			1.74994i	−0.484178	+	0.874970i	$0.660881\pi$
$884$	8.00000	−	13.8564i	0.269069	−	0.466041i
$885$	−14.9282	−	9.85641i	−0.501806	−	0.331319i
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−31.1769	−	18.0000i	−1.04682	−	0.604381i	−0.125061	−	0.992149i	$-0.539913\pi$
$887$	−31.1769	−	18.0000i	−1.04682	−	0.604381i	−0.921757	+	0.387768i	$0.873246\pi$
$888$			8.00000i			0.268462i
$889$		0			0
$890$	20.0000	−	10.0000i	0.670402	−	0.335201i
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$	−13.8564	+	8.00000i	−0.463947	+	0.267860i
$893$	−6.92820	+	4.00000i	−0.231843	+	0.133855i
$894$	−9.00000	+	15.5885i	−0.301005	+	0.521356i
$895$	2.00000	+	4.00000i	0.0668526	+	0.133705i
$896$		0			0
$897$		0			0
$898$	25.9808	+	15.0000i	0.866989	+	0.500556i
$899$	18.0000	+	31.1769i	0.600334	+	1.03981i
$900$	4.96410	+	0.598076i	0.165470	+	0.0199359i
$901$	−8.00000	+	13.8564i	−0.266519	+	0.461624i
$902$		−	12.0000i		−	0.399556i
$903$		0			0
$904$	−6.00000			−0.199557
$905$	49.1051	+	2.94744i	1.63231	+	0.0979763i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	38.1051	−	22.0000i	1.26526	−	0.730498i	0.291172	−	0.956671i	$-0.405955\pi$
$907$	38.1051	−	22.0000i	1.26526	−	0.730498i	0.974087	+	0.226173i	$0.0726213\pi$
$908$	−6.92820	−	4.00000i	−0.229920	−	0.132745i
$909$	−10.0000			−0.331679
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$	1.73205	+	1.00000i	0.0573539	+	0.0331133i
$913$	27.7128	−	16.0000i	0.917160	−	0.529523i
$914$	−14.0000	−	24.2487i	−0.463079	−	0.802076i
$915$	−1.33975	+	22.3205i	−0.0442906	+	0.737893i
$916$	−26.0000			−0.859064
$917$		0			0
$918$		−	8.00000i		−	0.264039i
$919$	−2.00000	+	3.46410i	−0.0659739	+	0.114270i	−0.897126	−	0.441776i	$-0.854349\pi$
$919$	−2.00000	+	3.46410i	−0.0659739	+	0.114270i	0.831152	+	0.556046i	$0.187682\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	−15.5885	−	9.00000i	−0.513378	−	0.296399i
$923$			28.0000i			0.921631i
$924$		0			0
$925$	32.0000	+	24.0000i	1.05215	+	0.789115i
$926$	6.00000	−	10.3923i	0.197172	−	0.341512i
$927$		0			0
$928$	−5.19615	+	3.00000i	−0.170572	+	0.0984798i
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$	−6.00000	−	12.0000i	−0.196748	−	0.393496i
$931$		0			0
$932$		−	6.00000i		−	0.196537i
$933$	−6.92820	−	4.00000i	−0.226819	−	0.130954i
$934$	−8.00000	−	13.8564i	−0.261768	−	0.453395i
$935$	−29.8564	−	19.7128i	−0.976409	−	0.644678i
$936$	1.00000	−	1.73205i	0.0326860	−	0.0566139i
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$		0			0
$939$	10.0000			0.326338
$940$	−0.535898	+	8.92820i	−0.0174791	+	0.291206i
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	0.812975	−	0.582298i	$-0.197846\pi$
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	−0.910773	+	0.412908i	$0.864513\pi$
$942$	−8.66025	+	5.00000i	−0.282166	+	0.162909i
$943$		0			0
$944$	−8.00000			−0.260378
$945$		0			0
$946$	−16.0000			−0.520205
$947$	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	$0.604204\pi$
$948$	3.46410	−	2.00000i	0.112509	−	0.0649570i
$949$	−10.0000	−	17.3205i	−0.324614	−	0.562247i
$950$	9.19615	−	3.92820i	0.298363	−	0.127448i
$951$	−2.00000			−0.0648544
$952$		0			0
$953$		−	18.0000i		−	0.583077i	−0.956559	−	0.291539i	$-0.905833\pi$
$953$		−	18.0000i		−	0.583077i	0.956559	−	0.291539i	$-0.0941672\pi$
$954$	−1.00000	+	1.73205i	−0.0323762	+	0.0560772i
$955$	17.2487	−	26.1244i	0.558155	−	0.845364i
$956$	11.0000	+	19.0526i	0.355765	+	0.616204i
$957$	10.3923	+	6.00000i	0.335936	+	0.193952i
$958$		−	8.00000i		−	0.258468i
$959$		0			0
$960$	2.00000	−	1.00000i	0.0645497	−	0.0322749i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	13.8564	−	8.00000i	0.446748	−	0.257930i
$963$	−10.3923	+	6.00000i	−0.334887	+	0.193347i
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$		0			0
$966$		0			0
$967$			24.0000i			0.771788i	0.922543	+	0.385894i	$0.126107\pi$
$967$			24.0000i			0.771788i	−0.922543	+	0.385894i	$0.873893\pi$
$968$	6.06218	+	3.50000i	0.194846	+	0.112494i
$969$	−8.00000	−	13.8564i	−0.256997	−	0.445132i
$970$	12.3205	−	18.6603i	0.395588	−	0.599145i
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	−36.0000			−1.15351
$975$	−3.92820	−	9.19615i	−0.125803	−	0.294513i
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	−0.229465	−	0.973317i	$-0.573698\pi$
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	0.728184	+	0.685381i	$0.240364\pi$
$978$		0			0
$979$	−20.0000			−0.639203
$980$		0			0
$981$	−6.00000			−0.191565
$982$	−36.3731	−	21.0000i	−1.16071	−	0.670137i
$983$	−10.3923	+	6.00000i	−0.331463	+	0.191370i	−0.656490	−	0.754334i	$-0.727960\pi$
$983$	−10.3923	+	6.00000i	−0.331463	+	0.191370i	0.325027	+	0.945705i	$0.394626\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$	0.803848	−	13.3923i	0.0256127	−	0.426714i
$986$	48.0000			1.52863
$987$		0			0
$988$		−	4.00000i		−	0.127257i
$989$		0			0
$990$	−3.73205	−	2.46410i	−0.118612	−	0.0783143i
$991$	30.0000	+	51.9615i	0.952981	+	1.65061i	0.738921	+	0.673792i	$0.235336\pi$
$991$	30.0000	+	51.9615i	0.952981	+	1.65061i	0.214060	+	0.976820i	$0.431331\pi$
$992$	−5.19615	−	3.00000i	−0.164978	−	0.0952501i
$993$		0			0
$994$		0			0
$995$	−26.0000	−	52.0000i	−0.824255	−	1.64851i
$996$	8.00000	−	13.8564i	0.253490	−	0.439057i
$997$	−32.9090	+	19.0000i	−1.04224	+	0.601736i	−0.920466	−	0.390822i	$-0.872191\pi$
$997$	−32.9090	+	19.0000i	−1.04224	+	0.601736i	−0.121771	+	0.992558i	$0.538857\pi$
$998$	−24.2487	+	14.0000i	−0.767580	+	0.443162i
$999$	4.00000	−	6.92820i	0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.c.79.2		4
5.4	even	2	inner	1470.2.n.c.79.1		4
7.2	even	3		1470.2.g.e.589.1		2
7.3	odd	6		1470.2.n.g.949.1		4
7.4	even	3	inner	1470.2.n.c.949.1		4
7.5	odd	6		210.2.g.a.169.1	✓	2
7.6	odd	2		1470.2.n.g.79.2		4
21.5	even	6		630.2.g.d.379.2		2
28.19	even	6		1680.2.t.d.1009.2		2
35.2	odd	12		7350.2.a.co.1.1		1
35.4	even	6	inner	1470.2.n.c.949.2		4
35.9	even	6		1470.2.g.e.589.2		2
35.12	even	12		1050.2.a.m.1.1		1
35.19	odd	6		210.2.g.a.169.2	yes	2
35.23	odd	12		7350.2.a.g.1.1		1
35.24	odd	6		1470.2.n.g.949.2		4
35.33	even	12		1050.2.a.g.1.1		1
35.34	odd	2		1470.2.n.g.79.1		4
84.47	odd	6		5040.2.t.k.1009.2		2
105.47	odd	12		3150.2.a.q.1.1		1
105.68	odd	12		3150.2.a.be.1.1		1
105.89	even	6		630.2.g.d.379.1		2
140.19	even	6		1680.2.t.d.1009.1		2
140.47	odd	12		8400.2.a.ca.1.1		1
140.103	odd	12		8400.2.a.bd.1.1		1
420.299	odd	6		5040.2.t.k.1009.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.g.a.169.1	✓	2	7.5	odd	6
210.2.g.a.169.2	yes	2	35.19	odd	6
630.2.g.d.379.1		2	105.89	even	6
630.2.g.d.379.2		2	21.5	even	6
1050.2.a.g.1.1		1	35.33	even	12
1050.2.a.m.1.1		1	35.12	even	12
1470.2.g.e.589.1		2	7.2	even	3
1470.2.g.e.589.2		2	35.9	even	6
1470.2.n.c.79.1		4	5.4	even	2	inner
1470.2.n.c.79.2		4	1.1	even	1	trivial
1470.2.n.c.949.1		4	7.4	even	3	inner
1470.2.n.c.949.2		4	35.4	even	6	inner
1470.2.n.g.79.1		4	35.34	odd	2
1470.2.n.g.79.2		4	7.6	odd	2
1470.2.n.g.949.1		4	7.3	odd	6
1470.2.n.g.949.2		4	35.24	odd	6
1680.2.t.d.1009.1		2	140.19	even	6
1680.2.t.d.1009.2		2	28.19	even	6
3150.2.a.q.1.1		1	105.47	odd	12
3150.2.a.be.1.1		1	105.68	odd	12
5040.2.t.k.1009.1		2	420.299	odd	6
5040.2.t.k.1009.2		2	84.47	odd	6
7350.2.a.g.1.1		1	35.23	odd	12
7350.2.a.co.1.1		1	35.2	odd	12
8400.2.a.bd.1.1		1	140.103	odd	12
8400.2.a.ca.1.1		1	140.47	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.86603 - 1.23205i) q^{10} +(1.00000 + 1.73205i) q^{11} +(0.866025 + 0.500000i) q^{12} -2.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.92820 - 4.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(-1.00000 - 2.00000i) q^{20} +2.00000i q^{22} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +6.00000 q^{29} +(-2.23205 - 0.133975i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +8.00000 q^{34} +1.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(0.133975 - 2.23205i) q^{40} -6.00000 q^{41} +8.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.23205 + 1.86603i) q^{45} +(-3.46410 - 2.00000i) q^{47} +1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(4.00000 - 6.92820i) q^{51} +(1.73205 - 1.00000i) q^{52} +(-1.73205 + 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 - 4.00000i) q^{55} -2.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-1.86603 - 1.23205i) q^{60} +(5.00000 - 8.66025i) q^{61} +6.00000i q^{62} -1.00000 q^{64} +(-0.267949 + 4.46410i) q^{65} +(1.00000 + 1.73205i) q^{66} +(10.3923 - 6.00000i) q^{67} +(6.92820 + 4.00000i) q^{68} -14.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} +(4.59808 - 1.96410i) q^{75} +2.00000 q^{76} -2.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(1.23205 - 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.19615 - 3.00000i) q^{82} -16.0000i q^{83} +(-16.0000 + 8.00000i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(5.19615 - 3.00000i) q^{87} +(-1.73205 + 1.00000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(5.19615 + 3.00000i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(-2.46410 + 3.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} +10.0000i q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 8 q^{15} - 2 q^{16} + 4 q^{19} - 4 q^{20} + 2 q^{24} + 6 q^{25} + 4 q^{26} + 24 q^{29} - 2 q^{30} + 12 q^{31} + 32 q^{34} + 4 q^{36} - 4 q^{39} + 4 q^{40} - 24 q^{41} - 4 q^{44} + 2 q^{45} + 16 q^{50} + 16 q^{51} + 2 q^{54} - 8 q^{55} + 16 q^{59} - 4 q^{60} + 20 q^{61} - 4 q^{64} - 8 q^{65} + 4 q^{66} - 56 q^{71} + 16 q^{74} + 8 q^{75} + 8 q^{76} + 8 q^{79} - 2 q^{80} - 2 q^{81} - 64 q^{85} - 16 q^{86} - 20 q^{89} - 8 q^{90} - 8 q^{94} + 4 q^{95} - 2 q^{96} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 8 * q^15 - 2 * q^16 + 4 * q^19 - 4 * q^20 + 2 * q^24 + 6 * q^25 + 4 * q^26 + 24 * q^29 - 2 * q^30 + 12 * q^31 + 32 * q^34 + 4 * q^36 - 4 * q^39 + 4 * q^40 - 24 * q^41 - 4 * q^44 + 2 * q^45 + 16 * q^50 + 16 * q^51 + 2 * q^54 - 8 * q^55 + 16 * q^59 - 4 * q^60 + 20 * q^61 - 4 * q^64 - 8 * q^65 + 4 * q^66 - 56 * q^71 + 16 * q^74 + 8 * q^75 + 8 * q^76 + 8 * q^79 - 2 * q^80 - 2 * q^81 - 64 * q^85 - 16 * q^86 - 20 * q^89 - 8 * q^90 - 8 * q^94 + 4 * q^95 - 2 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

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