LMFDB - Embedded newform 585.2.bt.a.376.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, 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:	$4.67124851824$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.a.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 - 0.500000i) q^{5} +3.46410 q^{6} +(1.73205 + 1.00000i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 - 0.500000i) q^{5} +3.46410 q^{6} +(1.73205 + 1.00000i) q^{7} +(1.50000 - 2.59808i) q^{9} +2.00000 q^{10} +(-5.19615 - 3.00000i) q^{11} +(3.00000 + 1.73205i) q^{12} +(-0.232051 + 3.59808i) q^{13} +(2.00000 + 3.46410i) q^{14} +(0.866025 - 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} -1.00000 q^{17} +(5.19615 - 3.00000i) q^{18} +8.00000i q^{19} +(1.73205 + 1.00000i) q^{20} +3.46410 q^{21} +(-6.00000 - 10.3923i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-4.00000 + 6.00000i) q^{26} -5.19615i q^{27} +4.00000i q^{28} +(-1.00000 + 1.73205i) q^{29} +(3.00000 - 1.73205i) q^{30} +(-6.92820 + 4.00000i) q^{31} +(6.92820 - 4.00000i) q^{32} -10.3923 q^{33} +(-1.73205 - 1.00000i) q^{34} +2.00000 q^{35} +6.00000 q^{36} -2.00000i q^{37} +(-8.00000 + 13.8564i) q^{38} +(2.76795 + 5.59808i) q^{39} +(-1.73205 + 1.00000i) q^{41} +(6.00000 + 3.46410i) q^{42} +(-2.50000 + 4.33013i) q^{43} -12.0000i q^{44} -3.00000i q^{45} -2.00000i q^{46} +(8.66025 + 5.00000i) q^{47} -6.92820i q^{48} +(-1.50000 - 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} +(-1.50000 + 0.866025i) q^{51} +(-6.46410 + 3.19615i) q^{52} +9.00000 q^{53} +(5.19615 - 9.00000i) q^{54} -6.00000 q^{55} +(6.92820 + 12.0000i) q^{57} +(-3.46410 + 2.00000i) q^{58} +(-5.19615 + 3.00000i) q^{59} +3.46410 q^{60} +(2.50000 - 4.33013i) q^{61} -16.0000 q^{62} +(5.19615 - 3.00000i) q^{63} +8.00000 q^{64} +(1.59808 + 3.23205i) q^{65} +(-18.0000 - 10.3923i) q^{66} +(-1.00000 - 1.73205i) q^{68} +(-1.50000 - 0.866025i) q^{69} +(3.46410 + 2.00000i) q^{70} -10.0000i q^{71} +4.00000i q^{73} +(2.00000 - 3.46410i) q^{74} -1.73205i q^{75} +(-13.8564 + 8.00000i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(-0.803848 + 12.4641i) q^{78} +(-0.500000 + 0.866025i) q^{79} -4.00000i q^{80} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{82} +(3.46410 + 6.00000i) q^{84} +(-0.866025 + 0.500000i) q^{85} +(-8.66025 + 5.00000i) q^{86} +3.46410i q^{87} +(3.00000 - 5.19615i) q^{90} +(-4.00000 + 6.00000i) q^{91} +(1.00000 - 1.73205i) q^{92} +(-6.92820 + 12.0000i) q^{93} +(10.0000 + 17.3205i) q^{94} +(4.00000 + 6.92820i) q^{95} +(6.92820 - 12.0000i) q^{96} +(-8.66025 - 5.00000i) q^{97} -6.00000i q^{98} +(-15.5885 + 9.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 4 q^{4} + 6 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 4 * q^4 + 6 * q^9	$ 4 q + 6 q^{3} + 4 q^{4} + 6 q^{9} + 8 q^{10} + 12 q^{12} + 6 q^{13} + 8 q^{14} + 8 q^{16} - 4 q^{17} - 24 q^{22} - 2 q^{23} + 2 q^{25} - 16 q^{26} - 4 q^{29} + 12 q^{30} + 8 q^{35} + 24 q^{36} - 32 q^{38} + 18 q^{39} + 24 q^{42} - 10 q^{43} - 6 q^{49} - 6 q^{51} - 12 q^{52} + 36 q^{53} - 24 q^{55} + 10 q^{61} - 64 q^{62} + 32 q^{64} - 4 q^{65} - 72 q^{66} - 4 q^{68} - 6 q^{69} + 8 q^{74} - 24 q^{77} - 24 q^{78} - 2 q^{79} - 18 q^{81} - 16 q^{82} + 12 q^{90} - 16 q^{91} + 4 q^{92} + 40 q^{94} + 16 q^{95}+O(q^{100}) $ 4 * q + 6 * q^3 + 4 * q^4 + 6 * q^9 + 8 * q^10 + 12 * q^12 + 6 * q^13 + 8 * q^14 + 8 * q^16 - 4 * q^17 - 24 * q^22 - 2 * q^23 + 2 * q^25 - 16 * q^26 - 4 * q^29 + 12 * q^30 + 8 * q^35 + 24 * q^36 - 32 * q^38 + 18 * q^39 + 24 * q^42 - 10 * q^43 - 6 * q^49 - 6 * q^51 - 12 * q^52 + 36 * q^53 - 24 * q^55 + 10 * q^61 - 64 * q^62 + 32 * q^64 - 4 * q^65 - 72 * q^66 - 4 * q^68 - 6 * q^69 + 8 * q^74 - 24 * q^77 - 24 * q^78 - 2 * q^79 - 18 * q^81 - 16 * q^82 + 12 * q^90 - 16 * q^91 + 4 * q^92 + 40 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	1.73205	+	1.00000i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	1.73205	+	1.00000i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	3.46410			1.41421
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	2.00000			0.632456
$11$	−5.19615	−	3.00000i	−1.56670	−	0.904534i	−0.996550	−	0.0829925i	$-0.973552\pi$
$11$	−5.19615	−	3.00000i	−1.56670	−	0.904534i	−0.570149	−	0.821541i	$-0.693114\pi$
$12$	3.00000	+	1.73205i	0.866025	+	0.500000i
$13$	−0.232051	+	3.59808i	−0.0643593	+	0.997927i
$13$	−0.232051	+	3.59808i	−0.0643593	+	0.997927i
$14$	2.00000	+	3.46410i	0.534522	+	0.925820i
$15$	0.866025	−	1.50000i	0.223607	−	0.387298i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$	5.19615	−	3.00000i	1.22474	−	0.707107i
$19$			8.00000i			1.83533i	0.397360	+	0.917663i	$0.369927\pi$
$19$			8.00000i			1.83533i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	1.73205	+	1.00000i	0.387298	+	0.223607i
$21$	3.46410			0.755929
$22$	−6.00000	−	10.3923i	−1.27920	−	2.21565i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−4.00000	+	6.00000i	−0.784465	+	1.17670i
$27$		−	5.19615i		−	1.00000i
$28$			4.00000i			0.755929i
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$	3.00000	−	1.73205i	0.547723	−	0.316228i
$31$	−6.92820	+	4.00000i	−1.24434	+	0.718421i	−0.969975	−	0.243204i	$-0.921802\pi$
$31$	−6.92820	+	4.00000i	−1.24434	+	0.718421i	−0.274367	+	0.961625i	$0.588468\pi$
$32$	6.92820	−	4.00000i	1.22474	−	0.707107i
$33$	−10.3923			−1.80907
$34$	−1.73205	−	1.00000i	−0.297044	−	0.171499i
$35$	2.00000			0.338062
$36$	6.00000			1.00000
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	−8.00000	+	13.8564i	−1.29777	+	2.24781i
$39$	2.76795	+	5.59808i	0.443227	+	0.896410i
$40$		0			0
$41$	−1.73205	+	1.00000i	−0.270501	+	0.156174i	−0.629115	−	0.777312i	$-0.716583\pi$
$41$	−1.73205	+	1.00000i	−0.270501	+	0.156174i	0.358614	+	0.933486i	$0.383249\pi$
$42$	6.00000	+	3.46410i	0.925820	+	0.534522i
$43$	−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	$0.291172\pi$
$44$		−	12.0000i		−	1.80907i
$45$		−	3.00000i		−	0.447214i
$46$		−	2.00000i		−	0.294884i
$47$	8.66025	+	5.00000i	1.26323	+	0.729325i	0.973698	−	0.227844i	$-0.0731676\pi$
$47$	8.66025	+	5.00000i	1.26323	+	0.729325i	0.289530	+	0.957169i	$0.406501\pi$
$48$		−	6.92820i		−	1.00000i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	1.73205	−	1.00000i	0.244949	−	0.141421i
$51$	−1.50000	+	0.866025i	−0.210042	+	0.121268i
$52$	−6.46410	+	3.19615i	−0.896410	+	0.443227i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$	5.19615	−	9.00000i	0.707107	−	1.22474i
$55$	−6.00000			−0.809040
$56$		0			0
$57$	6.92820	+	12.0000i	0.917663	+	1.58944i
$58$	−3.46410	+	2.00000i	−0.454859	+	0.262613i
$59$	−5.19615	+	3.00000i	−0.676481	+	0.390567i	−0.798528	−	0.601958i	$-0.794388\pi$
$59$	−5.19615	+	3.00000i	−0.676481	+	0.390567i	0.122047	+	0.992524i	$0.461054\pi$
$60$	3.46410			0.447214
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	−16.0000			−2.03200
$63$	5.19615	−	3.00000i	0.654654	−	0.377964i
$64$	8.00000			1.00000
$65$	1.59808	+	3.23205i	0.198217	+	0.400887i
$66$	−18.0000	−	10.3923i	−2.21565	−	1.27920i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	−1.50000	−	0.866025i	−0.180579	−	0.104257i
$70$	3.46410	+	2.00000i	0.414039	+	0.239046i
$71$		−	10.0000i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$71$		−	10.0000i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$72$		0			0
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		−	1.73205i		−	0.200000i
$76$	−13.8564	+	8.00000i	−1.58944	+	0.917663i
$77$	−6.00000	−	10.3923i	−0.683763	−	1.18431i
$78$	−0.803848	+	12.4641i	−0.0910178	+	1.41128i
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$		−	4.00000i		−	0.447214i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−4.00000			−0.441726
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$	3.46410	+	6.00000i	0.377964	+	0.654654i
$85$	−0.866025	+	0.500000i	−0.0939336	+	0.0542326i
$86$	−8.66025	+	5.00000i	−0.933859	+	0.539164i
$87$			3.46410i			0.371391i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	3.00000	−	5.19615i	0.316228	−	0.547723i
$91$	−4.00000	+	6.00000i	−0.419314	+	0.628971i
$92$	1.00000	−	1.73205i	0.104257	−	0.180579i
$93$	−6.92820	+	12.0000i	−0.718421	+	1.24434i
$94$	10.0000	+	17.3205i	1.03142	+	1.78647i
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$	6.92820	−	12.0000i	0.707107	−	1.22474i
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.00888289	−	0.999961i	$-0.502828\pi$
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.870433	+	0.492287i	$0.836161\pi$
$98$		−	6.00000i		−	0.606092i
$99$	−15.5885	+	9.00000i	−1.56670	+	0.904534i
$100$	2.00000			0.200000
$101$	−3.50000	+	6.06218i	−0.348263	+	0.603209i	−0.985941	−	0.167094i	$-0.946562\pi$
$101$	−3.50000	+	6.06218i	−0.348263	+	0.603209i	0.637678	+	0.770303i	$0.279895\pi$
$102$	−3.46410			−0.342997
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$		0			0
$105$	3.00000	−	1.73205i	0.292770	−	0.169031i
$106$	15.5885	+	9.00000i	1.51408	+	0.874157i
$107$	17.0000			1.64345			0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000			1.64345			0.821726	+	0.569883i	$0.193011\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$		−	20.0000i		−	1.91565i	−0.287348	−	0.957826i	$-0.592774\pi$
$109$		−	20.0000i		−	1.91565i	0.287348	−	0.957826i	$-0.407226\pi$
$110$	−10.3923	−	6.00000i	−0.990867	−	0.572078i
$111$	−1.73205	−	3.00000i	−0.164399	−	0.284747i
$112$	6.92820	−	4.00000i	0.654654	−	0.377964i
$113$	−9.50000	−	16.4545i	−0.893685	−	1.54791i	−0.835424	−	0.549606i	$-0.814778\pi$
$113$	−9.50000	−	16.4545i	−0.893685	−	1.54791i	−0.0582609	−	0.998301i	$-0.518556\pi$
$114$			27.7128i			2.59554i
$115$	−0.866025	−	0.500000i	−0.0807573	−	0.0466252i
$116$	−4.00000			−0.371391
$117$	9.00000	+	6.00000i	0.832050	+	0.554700i
$118$	−12.0000			−1.10469
$119$	−1.73205	−	1.00000i	−0.158777	−	0.0916698i
$120$		0			0
$121$	12.5000	+	21.6506i	1.13636	+	1.96824i
$122$	8.66025	−	5.00000i	0.784063	−	0.452679i
$123$	−1.73205	+	3.00000i	−0.156174	+	0.270501i
$124$	−13.8564	−	8.00000i	−1.24434	−	0.718421i
$125$		−	1.00000i		−	0.0894427i
$126$	12.0000			1.06904
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$			8.66025i			0.762493i
$130$	−0.464102	+	7.19615i	−0.0407044	+	0.631144i
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$	−10.3923	−	18.0000i	−0.904534	−	1.56670i
$133$	−8.00000	+	13.8564i	−0.693688	+	1.20150i
$134$		0			0
$135$	−2.59808	−	4.50000i	−0.223607	−	0.387298i
$136$		0			0
$137$	5.19615	+	3.00000i	0.443937	+	0.256307i	0.705266	−	0.708942i	$-0.250827\pi$
$137$	5.19615	+	3.00000i	0.443937	+	0.256307i	−0.261329	+	0.965250i	$0.584161\pi$
$138$	−1.73205	−	3.00000i	−0.147442	−	0.255377i
$139$	5.50000	+	9.52628i	0.466504	+	0.808008i	0.999268	−	0.0382553i	$-0.0121800\pi$
$139$	5.50000	+	9.52628i	0.466504	+	0.808008i	−0.532764	+	0.846264i	$0.678847\pi$
$140$	2.00000	+	3.46410i	0.169031	+	0.292770i
$141$	17.3205			1.45865
$142$	10.0000	−	17.3205i	0.839181	−	1.45350i
$143$	12.0000	−	18.0000i	1.00349	−	1.50524i
$144$	−6.00000	−	10.3923i	−0.500000	−	0.866025i
$145$			2.00000i			0.166091i
$146$	−4.00000	+	6.92820i	−0.331042	+	0.573382i
$147$	−4.50000	−	2.59808i	−0.371154	−	0.214286i
$148$	3.46410	−	2.00000i	0.284747	−	0.164399i
$149$	−1.73205	+	1.00000i	−0.141895	+	0.0819232i	−0.569267	−	0.822153i	$-0.692773\pi$
$149$	−1.73205	+	1.00000i	−0.141895	+	0.0819232i	0.427372	+	0.904076i	$0.359440\pi$
$150$	1.73205	−	3.00000i	0.141421	−	0.244949i
$151$	3.46410	+	2.00000i	0.281905	+	0.162758i	0.634285	−	0.773099i	$-0.281294\pi$
$151$	3.46410	+	2.00000i	0.281905	+	0.162758i	−0.352381	+	0.935857i	$0.614628\pi$
$152$		0			0
$153$	−1.50000	+	2.59808i	−0.121268	+	0.210042i
$154$		−	24.0000i		−	1.93398i
$155$	−4.00000	+	6.92820i	−0.321288	+	0.556487i
$156$	−6.92820	+	10.3923i	−0.554700	+	0.832050i
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	−1.73205	+	1.00000i	−0.137795	+	0.0795557i
$159$	13.5000	−	7.79423i	1.07062	−	0.618123i
$160$	4.00000	−	6.92820i	0.316228	−	0.547723i
$161$		−	2.00000i		−	0.157622i
$162$		−	18.0000i		−	1.41421i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$	−3.46410	−	2.00000i	−0.270501	−	0.156174i
$165$	−9.00000	+	5.19615i	−0.700649	+	0.404520i
$166$		0			0
$167$	−1.73205	+	1.00000i	−0.134030	+	0.0773823i	−0.565516	−	0.824737i	$-0.691323\pi$
$167$	−1.73205	+	1.00000i	−0.134030	+	0.0773823i	0.431486	+	0.902120i	$0.357990\pi$
$168$		0			0
$169$	−12.8923	−	1.66987i	−0.991716	−	0.128452i
$170$	−2.00000			−0.153393
$171$	20.7846	+	12.0000i	1.58944	+	0.917663i
$172$	−10.0000			−0.762493
$173$	−6.50000	+	11.2583i	−0.494186	+	0.855955i	−0.999978	−	0.00670064i	$-0.997867\pi$
$173$	−6.50000	+	11.2583i	−0.494186	+	0.855955i	0.505792	+	0.862656i	$0.331200\pi$
$174$	−3.46410	+	6.00000i	−0.262613	+	0.454859i
$175$	1.73205	−	1.00000i	0.130931	−	0.0755929i
$176$	−20.7846	+	12.0000i	−1.56670	+	0.904534i
$177$	−5.19615	+	9.00000i	−0.390567	+	0.676481i
$178$		0			0
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$	5.19615	−	3.00000i	0.387298	−	0.223607i
$181$	21.0000			1.56092			0.780459	−	0.625207i	$-0.214986\pi$
$181$	21.0000			1.56092			0.780459	+	0.625207i	$0.214986\pi$
$182$	−12.9282	+	6.39230i	−0.958302	+	0.473829i
$183$		−	8.66025i		−	0.640184i
$184$		0			0
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	−24.0000	+	13.8564i	−1.75977	+	1.01600i
$187$	5.19615	+	3.00000i	0.379980	+	0.219382i
$188$			20.0000i			1.45865i
$189$	5.19615	−	9.00000i	0.377964	−	0.654654i
$190$			16.0000i			1.16076i
$191$	−9.50000	+	16.4545i	−0.687396	+	1.19060i	0.285282	+	0.958444i	$0.407913\pi$
$191$	−9.50000	+	16.4545i	−0.687396	+	1.19060i	−0.972677	+	0.232161i	$0.925420\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	−0.370116	−	0.928986i	$-0.620682\pi$
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	0.619467	+	0.785022i	$0.287349\pi$
$194$	−10.0000	−	17.3205i	−0.717958	−	1.24354i
$195$	5.19615	+	3.46410i	0.372104	+	0.248069i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$		−	20.0000i		−	1.42494i	−0.701702	−	0.712470i	$-0.747576\pi$
$197$		−	20.0000i		−	1.42494i	0.701702	−	0.712470i	$-0.252424\pi$
$198$	−36.0000			−2.55841
$199$	3.00000			0.212664			0.106332	−	0.994331i	$-0.466089\pi$
$199$	3.00000			0.212664			0.106332	+	0.994331i	$0.466089\pi$
$200$		0			0
$201$		0			0
$202$	−12.1244	+	7.00000i	−0.853067	+	0.492518i
$203$	−3.46410	+	2.00000i	−0.243132	+	0.140372i
$204$	−3.00000	−	1.73205i	−0.210042	−	0.121268i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$		−	32.0000i		−	2.22955i
$207$	−3.00000			−0.208514
$208$	12.0000	+	8.00000i	0.832050	+	0.554700i
$209$	24.0000	−	41.5692i	1.66011	−	2.87540i
$210$	6.92820			0.478091
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	0.999820	+	0.0189499i	$0.00603229\pi$
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	−0.483499	+	0.875345i	$0.660634\pi$
$212$	9.00000	+	15.5885i	0.618123	+	1.07062i
$213$	−8.66025	−	15.0000i	−0.593391	−	1.02778i
$214$	29.4449	+	17.0000i	2.01281	+	1.16210i
$215$			5.00000i			0.340997i
$216$		0			0
$217$	−16.0000			−1.08615
$218$	20.0000	−	34.6410i	1.35457	−	2.34619i
$219$	3.46410	+	6.00000i	0.234082	+	0.405442i
$220$	−6.00000	−	10.3923i	−0.404520	−	0.700649i
$221$	0.232051	−	3.59808i	0.0156094	−	0.242033i
$222$		−	6.92820i		−	0.464991i
$223$	−12.1244	−	7.00000i	−0.811907	−	0.468755i	0.0357107	−	0.999362i	$-0.488630\pi$
$223$	−12.1244	−	7.00000i	−0.811907	−	0.468755i	−0.847618	+	0.530607i	$0.821964\pi$
$224$	16.0000			1.06904
$225$	−1.50000	−	2.59808i	−0.100000	−	0.173205i
$226$		−	38.0000i		−	2.52772i
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	−13.8564	+	24.0000i	−0.917663	+	1.58944i
$229$	22.5167	−	13.0000i	1.48794	−	0.859064i	0.488037	−	0.872823i	$-0.337713\pi$
$229$	22.5167	−	13.0000i	1.48794	−	0.859064i	0.999905	+	0.0137585i	$0.00437961\pi$
$230$	−1.00000	−	1.73205i	−0.0659380	−	0.114208i
$231$	−18.0000	−	10.3923i	−1.18431	−	0.683763i
$232$		0			0
$233$	−19.0000			−1.24473			−0.622366	−	0.782727i	$-0.713828\pi$
$233$	−19.0000			−1.24473			−0.622366	+	0.782727i	$0.713828\pi$
$234$	9.58846	+	19.3923i	0.626817	+	1.26771i
$235$	10.0000			0.652328
$236$	−10.3923	−	6.00000i	−0.676481	−	0.390567i
$237$			1.73205i			0.112509i
$238$	−2.00000	−	3.46410i	−0.129641	−	0.224544i
$239$	17.3205	−	10.0000i	1.12037	−	0.646846i	0.178875	−	0.983872i	$-0.442754\pi$
$239$	17.3205	−	10.0000i	1.12037	−	0.646846i	0.941495	+	0.337026i	$0.109421\pi$
$240$	−3.46410	−	6.00000i	−0.223607	−	0.387298i
$241$	25.9808	+	15.0000i	1.67357	+	0.966235i	0.965615	+	0.259975i	$0.0837143\pi$
$241$	25.9808	+	15.0000i	1.67357	+	0.966235i	0.707953	+	0.706260i	$0.249619\pi$
$242$			50.0000i			3.21412i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	10.0000			0.640184
$245$	−2.59808	−	1.50000i	−0.165985	−	0.0958315i
$246$	−6.00000	+	3.46410i	−0.382546	+	0.220863i
$247$	−28.7846	−	1.85641i	−1.83152	−	0.118120i
$248$		0			0
$249$		0			0
$250$	1.00000	−	1.73205i	0.0632456	−	0.109545i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$	10.3923	+	6.00000i	0.654654	+	0.377964i
$253$			6.00000i			0.377217i
$254$		0			0
$255$	−0.866025	+	1.50000i	−0.0542326	+	0.0939336i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	−8.66025	+	15.0000i	−0.539164	+	0.933859i
$259$	2.00000	−	3.46410i	0.124274	−	0.215249i
$260$	−4.00000	+	6.00000i	−0.248069	+	0.372104i
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		−	30.0000i		−	1.85341i
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$		0			0
$265$	7.79423	−	4.50000i	0.478796	−	0.276433i
$266$	−27.7128	+	16.0000i	−1.69918	+	0.981023i
$267$		0			0
$268$		0			0
$269$	−14.0000			−0.853595			−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000			−0.853595			−0.426798	+	0.904347i	$0.640358\pi$
$270$		−	10.3923i		−	0.632456i
$271$			28.0000i			1.70088i	0.526073	+	0.850439i	$0.323664\pi$
$271$			28.0000i			1.70088i	−0.526073	+	0.850439i	$0.676336\pi$
$272$	−2.00000	+	3.46410i	−0.121268	+	0.210042i
$273$	−0.803848	+	12.4641i	−0.0486511	+	0.754362i
$274$	6.00000	+	10.3923i	0.362473	+	0.627822i
$275$	−5.19615	+	3.00000i	−0.313340	+	0.180907i
$276$		−	3.46410i		−	0.208514i
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	−0.976231	−	0.216731i	$-0.930460\pi$
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	0.675810	+	0.737075i	$0.263794\pi$
$278$			22.0000i			1.31947i
$279$			24.0000i			1.43684i
$280$		0			0
$281$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$281$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$282$	30.0000	+	17.3205i	1.78647	+	1.03142i
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.797283	+	0.603606i	$0.206270\pi$
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.124096	+	0.992270i	$0.460397\pi$
$284$	17.3205	−	10.0000i	1.02778	−	0.593391i
$285$	12.0000	+	6.92820i	0.710819	+	0.410391i
$286$	38.7846	−	19.1769i	2.29338	−	1.13395i
$287$	−4.00000			−0.236113
$288$		−	24.0000i		−	1.41421i
$289$	−16.0000			−0.941176
$290$	−2.00000	+	3.46410i	−0.117444	+	0.203419i
$291$	−17.3205			−1.01535
$292$	−6.92820	+	4.00000i	−0.405442	+	0.234082i
$293$	5.19615	−	3.00000i	0.303562	−	0.175262i	−0.340480	−	0.940252i	$-0.610589\pi$
$293$	5.19615	−	3.00000i	0.303562	−	0.175262i	0.644042	+	0.764990i	$0.277256\pi$
$294$	−5.19615	−	9.00000i	−0.303046	−	0.524891i
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$		0			0
$297$	−15.5885	+	27.0000i	−0.904534	+	1.56670i
$298$	−4.00000			−0.231714
$299$	3.23205	−	1.59808i	0.186914	−	0.0924191i
$300$	3.00000	−	1.73205i	0.173205	−	0.100000i
$301$	−8.66025	+	5.00000i	−0.499169	+	0.288195i
$302$	4.00000	+	6.92820i	0.230174	+	0.398673i
$303$			12.1244i			0.696526i
$304$	27.7128	+	16.0000i	1.58944	+	0.917663i
$305$		−	5.00000i		−	0.286299i
$306$	−5.19615	+	3.00000i	−0.297044	+	0.171499i
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$	12.0000	−	20.7846i	0.683763	−	1.18431i
$309$	−24.0000	−	13.8564i	−1.36531	−	0.788263i
$310$	−13.8564	+	8.00000i	−0.786991	+	0.454369i
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	0.956864	−	0.290537i	$-0.0938340\pi$
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	−0.730044	+	0.683400i	$0.760501\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$			26.0000i			1.46726i
$315$	3.00000	−	5.19615i	0.169031	−	0.292770i
$316$	−2.00000			−0.112509
$317$	22.5167	+	13.0000i	1.26466	+	0.730153i	0.973973	−	0.226665i	$-0.0727822\pi$
$317$	22.5167	+	13.0000i	1.26466	+	0.730153i	0.290689	+	0.956818i	$0.406116\pi$
$318$	31.1769			1.74831
$319$	10.3923	−	6.00000i	0.581857	−	0.335936i
$320$	6.92820	−	4.00000i	0.387298	−	0.223607i
$321$	25.5000	−	14.7224i	1.42327	−	0.821726i
$322$	2.00000	−	3.46410i	0.111456	−	0.193047i
$323$		−	8.00000i		−	0.445132i
$324$	9.00000	−	15.5885i	0.500000	−	0.866025i
$325$	3.00000	+	2.00000i	0.166410	+	0.110940i
$326$		0			0
$327$	−17.3205	−	30.0000i	−0.957826	−	1.65900i
$328$		0			0
$329$	10.0000	+	17.3205i	0.551318	+	0.954911i
$330$	−20.7846			−1.14416
$331$	6.92820	+	4.00000i	0.380808	+	0.219860i	0.678170	−	0.734905i	$-0.262773\pi$
$331$	6.92820	+	4.00000i	0.380808	+	0.219860i	−0.297361	+	0.954765i	$0.596107\pi$
$332$		0			0
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$	−4.00000			−0.218870
$335$		0			0
$336$	6.92820	−	12.0000i	0.377964	−	0.654654i
$337$	−1.50000	−	2.59808i	−0.0817102	−	0.141526i	0.822274	−	0.569091i	$-0.192705\pi$
$337$	−1.50000	−	2.59808i	−0.0817102	−	0.141526i	−0.903985	+	0.427565i	$0.859372\pi$
$338$	−20.6603	−	15.7846i	−1.12377	−	0.858570i
$339$	−28.5000	−	16.4545i	−1.54791	−	0.893685i
$340$	−1.73205	−	1.00000i	−0.0939336	−	0.0542326i
$341$	48.0000			2.59935
$342$	24.0000	+	41.5692i	1.29777	+	2.24781i
$343$		−	20.0000i		−	1.07990i
$344$		0			0
$345$	−1.73205			−0.0932505
$346$	−22.5167	+	13.0000i	−1.21050	+	0.698884i
$347$	2.50000	+	4.33013i	0.134207	+	0.232453i	0.925294	−	0.379250i	$-0.123818\pi$
$347$	2.50000	+	4.33013i	0.134207	+	0.232453i	−0.791087	+	0.611703i	$0.790485\pi$
$348$	−6.00000	+	3.46410i	−0.321634	+	0.185695i
$349$	1.73205	+	1.00000i	0.0927146	+	0.0535288i	0.545640	−	0.838019i	$-0.316286\pi$
$349$	1.73205	+	1.00000i	0.0927146	+	0.0535288i	−0.452926	+	0.891548i	$0.649620\pi$
$350$	4.00000			0.213809
$351$	18.6962	+	1.20577i	0.997927	+	0.0643593i
$352$	−48.0000			−2.55841
$353$	5.19615	+	3.00000i	0.276563	+	0.159674i	0.631867	−	0.775077i	$-0.282289\pi$
$353$	5.19615	+	3.00000i	0.276563	+	0.159674i	−0.355303	+	0.934751i	$0.615622\pi$
$354$	−18.0000	+	10.3923i	−0.956689	+	0.552345i
$355$	−5.00000	−	8.66025i	−0.265372	−	0.459639i
$356$		0			0
$357$	−3.46410			−0.183340
$358$	25.9808	+	15.0000i	1.37313	+	0.792775i
$359$			10.0000i			0.527780i	0.964553	+	0.263890i	$0.0850056\pi$
$359$			10.0000i			0.527780i	−0.964553	+	0.263890i	$0.914994\pi$
$360$		0			0
$361$	−45.0000			−2.36842
$362$	36.3731	+	21.0000i	1.91173	+	1.10374i
$363$	37.5000	+	21.6506i	1.96824	+	1.13636i
$364$	−14.3923	−	0.928203i	−0.754362	−	0.0486511i
$365$	2.00000	+	3.46410i	0.104685	+	0.181319i
$366$	8.66025	−	15.0000i	0.452679	−	0.784063i
$367$	−10.5000	+	18.1865i	−0.548096	+	0.949329i	0.450310	+	0.892873i	$0.351314\pi$
$367$	−10.5000	+	18.1865i	−0.548096	+	0.949329i	−0.998405	+	0.0564568i	$0.982020\pi$
$368$	−4.00000			−0.208514
$369$			6.00000i			0.312348i
$370$		−	4.00000i		−	0.207950i
$371$	15.5885	+	9.00000i	0.809312	+	0.467257i
$372$	−27.7128			−1.43684
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	0.508065	−	0.861319i	$-0.330361\pi$
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	−0.999956	+	0.00933789i	$0.997028\pi$
$374$	6.00000	+	10.3923i	0.310253	+	0.537373i
$375$	−0.866025	−	1.50000i	−0.0447214	−	0.0774597i
$376$		0			0
$377$	−6.00000	−	4.00000i	−0.309016	−	0.206010i
$378$	18.0000	−	10.3923i	0.925820	−	0.534522i
$379$		−	18.0000i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$	−8.00000	+	13.8564i	−0.410391	+	0.710819i
$381$		0			0
$382$	−32.9090	+	19.0000i	−1.68377	+	0.972125i
$383$	−22.5167	+	13.0000i	−1.15055	+	0.664269i	−0.949021	−	0.315214i	$-0.897924\pi$
$383$	−22.5167	+	13.0000i	−1.15055	+	0.664269i	−0.201527	+	0.979483i	$0.564590\pi$
$384$		0			0
$385$	−10.3923	−	6.00000i	−0.529641	−	0.305788i
$386$	8.00000			0.407189
$387$	7.50000	+	12.9904i	0.381246	+	0.660338i
$388$		−	20.0000i		−	1.01535i
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	−0.412039	−	0.911166i	$-0.635183\pi$
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	0.995113	−	0.0987463i	$-0.0314832\pi$
$390$	5.53590	+	11.1962i	0.280321	+	0.566939i
$391$	0.500000	+	0.866025i	0.0252861	+	0.0437968i
$392$		0			0
$393$	−22.5000	−	12.9904i	−1.13497	−	0.655278i
$394$	20.0000	−	34.6410i	1.00759	−	1.74519i
$395$			1.00000i			0.0503155i
$396$	−31.1769	−	18.0000i	−1.56670	−	0.904534i
$397$		−	28.0000i		−	1.40528i	−0.711546	−	0.702640i	$-0.752005\pi$
$397$		−	28.0000i		−	1.40528i	0.711546	−	0.702640i	$-0.247995\pi$
$398$	5.19615	+	3.00000i	0.260460	+	0.150376i
$399$			27.7128i			1.38738i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	27.7128	−	16.0000i	1.38391	−	0.799002i	0.391292	−	0.920267i	$-0.372028\pi$
$401$	27.7128	−	16.0000i	1.38391	−	0.799002i	0.992620	+	0.121265i	$0.0386950\pi$
$402$		0			0
$403$	−12.7846	−	25.8564i	−0.636847	−	1.28800i
$404$	−14.0000			−0.696526
$405$	−7.79423	−	4.50000i	−0.387298	−	0.223607i
$406$	−8.00000			−0.397033
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$	−3.46410	+	2.00000i	−0.171080	+	0.0987730i
$411$	10.3923			0.512615
$412$	16.0000	−	27.7128i	0.788263	−	1.36531i
$413$	−12.0000			−0.590481
$414$	−5.19615	−	3.00000i	−0.255377	−	0.147442i
$415$		0			0
$416$	12.7846	+	25.8564i	0.626817	+	1.26771i
$417$	16.5000	+	9.52628i	0.808008	+	0.466504i
$418$	83.1384	−	48.0000i	4.06643	−	2.34776i
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	0.622601	−	0.782540i	$-0.286076\pi$
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	−0.989000	+	0.147918i	$0.952743\pi$
$420$	6.00000	+	3.46410i	0.292770	+	0.169031i
$421$	−6.92820	−	4.00000i	−0.337660	−	0.194948i	0.321577	−	0.946883i	$-0.395787\pi$
$421$	−6.92820	−	4.00000i	−0.337660	−	0.194948i	−0.659237	+	0.751935i	$0.729121\pi$
$422$			30.0000i			1.46038i
$423$	25.9808	−	15.0000i	1.26323	−	0.729325i
$424$		0			0
$425$	−0.500000	+	0.866025i	−0.0242536	+	0.0420084i
$426$		−	34.6410i		−	1.67836i
$427$	8.66025	−	5.00000i	0.419099	−	0.241967i
$428$	17.0000	+	29.4449i	0.821726	+	1.42327i
$429$	2.41154	−	37.3923i	0.116430	−	1.80532i
$430$	−5.00000	+	8.66025i	−0.241121	+	0.417635i
$431$		−	24.0000i		−	1.15604i	−0.816023	−	0.578020i	$-0.803826\pi$
$431$		−	24.0000i		−	1.15604i	0.816023	−	0.578020i	$-0.196174\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$	5.00000			0.240285			0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000			0.240285			0.120142	+	0.992757i	$0.461665\pi$
$434$	−27.7128	−	16.0000i	−1.33026	−	0.768025i
$435$	1.73205	+	3.00000i	0.0830455	+	0.143839i
$436$	34.6410	−	20.0000i	1.65900	−	0.957826i
$437$	6.92820	−	4.00000i	0.331421	−	0.191346i
$438$			13.8564i			0.662085i
$439$	−12.5000	+	21.6506i	−0.596592	+	1.03333i	0.396728	+	0.917936i	$0.370146\pi$
$439$	−12.5000	+	21.6506i	−0.596592	+	1.03333i	−0.993320	+	0.115392i	$0.963188\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$	4.00000	−	6.00000i	0.190261	−	0.285391i
$443$	−10.5000	+	18.1865i	−0.498870	+	0.864068i	−0.999999	−	0.00130426i	$-0.999585\pi$
$443$	−10.5000	+	18.1865i	−0.498870	+	0.864068i	0.501129	+	0.865373i	$0.332918\pi$
$444$	3.46410	−	6.00000i	0.164399	−	0.284747i
$445$		0			0
$446$	−14.0000	−	24.2487i	−0.662919	−	1.14821i
$447$	−1.73205	+	3.00000i	−0.0819232	+	0.141895i
$448$	13.8564	+	8.00000i	0.654654	+	0.377964i
$449$			36.0000i			1.69895i	0.527633	+	0.849473i	$0.323080\pi$
$449$			36.0000i			1.69895i	−0.527633	+	0.849473i	$0.676920\pi$
$450$		−	6.00000i		−	0.282843i
$451$	12.0000			0.565058
$452$	19.0000	−	32.9090i	0.893685	−	1.54791i
$453$	6.92820			0.325515
$454$		0			0
$455$	−0.464102	+	7.19615i	−0.0217574	+	0.337361i
$456$		0			0
$457$	−6.92820	−	4.00000i	−0.324088	−	0.187112i	0.329125	−	0.944286i	$-0.393246\pi$
$457$	−6.92820	−	4.00000i	−0.324088	−	0.187112i	−0.653213	+	0.757174i	$0.726579\pi$
$458$	52.0000			2.42980
$459$			5.19615i			0.242536i
$460$		−	2.00000i		−	0.0932505i
$461$	−1.73205	−	1.00000i	−0.0806696	−	0.0465746i	0.459123	−	0.888373i	$-0.348164\pi$
$461$	−1.73205	−	1.00000i	−0.0806696	−	0.0465746i	−0.539792	+	0.841798i	$0.681497\pi$
$462$	−20.7846	−	36.0000i	−0.966988	−	1.67487i
$463$	−19.0526	+	11.0000i	−0.885448	+	0.511213i	−0.872451	−	0.488702i	$-0.837470\pi$
$463$	−19.0526	+	11.0000i	−0.885448	+	0.511213i	−0.0129968	+	0.999916i	$0.504137\pi$
$464$	4.00000	+	6.92820i	0.185695	+	0.321634i
$465$			13.8564i			0.642575i
$466$	−32.9090	−	19.0000i	−1.52448	−	0.880158i
$467$	−21.0000			−0.971764			−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000			−0.971764			−0.485882	+	0.874024i	$0.661502\pi$
$468$	−1.39230	+	21.5885i	−0.0643593	+	0.997927i
$469$		0			0
$470$	17.3205	+	10.0000i	0.798935	+	0.461266i
$471$	19.5000	+	11.2583i	0.898513	+	0.518756i
$472$		0			0
$473$	25.9808	−	15.0000i	1.19460	−	0.689701i
$474$	−1.73205	+	3.00000i	−0.0795557	+	0.137795i
$475$	6.92820	+	4.00000i	0.317888	+	0.183533i
$476$		−	4.00000i		−	0.183340i
$477$	13.5000	−	23.3827i	0.618123	−	1.07062i
$478$	40.0000			1.82956
$479$	−15.5885	−	9.00000i	−0.712255	−	0.411220i	0.0996406	−	0.995023i	$-0.468231\pi$
$479$	−15.5885	−	9.00000i	−0.712255	−	0.411220i	−0.811895	+	0.583803i	$0.801564\pi$
$480$		−	13.8564i		−	0.632456i
$481$	7.19615	+	0.464102i	0.328116	+	0.0211612i
$482$	30.0000	+	51.9615i	1.36646	+	2.36678i
$483$	−1.73205	−	3.00000i	−0.0788110	−	0.136505i
$484$	−25.0000	+	43.3013i	−1.13636	+	1.96824i
$485$	−10.0000			−0.454077
$486$	−15.5885	−	27.0000i	−0.707107	−	1.22474i
$487$			24.0000i			1.08754i	0.839233	+	0.543772i	$0.183004\pi$
$487$			24.0000i			1.08754i	−0.839233	+	0.543772i	$0.816996\pi$
$488$		0			0
$489$		0			0
$490$	−3.00000	−	5.19615i	−0.135526	−	0.234738i
$491$	8.00000	+	13.8564i	0.361035	+	0.625331i	0.988131	−	0.153611i	$-0.0490902\pi$
$491$	8.00000	+	13.8564i	0.361035	+	0.625331i	−0.627096	+	0.778942i	$0.715757\pi$
$492$	−6.92820			−0.312348
$493$	1.00000	−	1.73205i	0.0450377	−	0.0780076i
$494$	−48.0000	−	32.0000i	−2.15962	−	1.43975i
$495$	−9.00000	+	15.5885i	−0.404520	+	0.700649i
$496$			32.0000i			1.43684i
$497$	10.0000	−	17.3205i	0.448561	−	0.776931i
$498$		0			0
$499$	−24.2487	+	14.0000i	−1.08552	+	0.626726i	−0.932381	−	0.361478i	$-0.882272\pi$
$499$	−24.2487	+	14.0000i	−1.08552	+	0.626726i	−0.153141	+	0.988204i	$0.548939\pi$
$500$	1.73205	−	1.00000i	0.0774597	−	0.0447214i
$501$	−1.73205	+	3.00000i	−0.0773823	+	0.134030i
$502$	5.19615	+	3.00000i	0.231916	+	0.133897i
$503$	−25.0000			−1.11469			−0.557347	−	0.830279i	$-0.688181\pi$
$503$	−25.0000			−1.11469			−0.557347	+	0.830279i	$0.688181\pi$
$504$		0			0
$505$			7.00000i			0.311496i
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$	−20.7846	+	8.66025i	−0.923077	+	0.384615i
$508$		0			0
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	−0.380402	−	0.924821i	$-0.624214\pi$
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	0.610718	+	0.791849i	$0.290881\pi$
$510$	−3.00000	+	1.73205i	−0.132842	+	0.0766965i
$511$	−4.00000	+	6.92820i	−0.176950	+	0.306486i
$512$		−	32.0000i		−	1.41421i
$513$	41.5692			1.83533
$514$			6.00000i			0.264649i
$515$	−13.8564	−	8.00000i	−0.610586	−	0.352522i
$516$	−15.0000	+	8.66025i	−0.660338	+	0.381246i
$517$	−30.0000	−	51.9615i	−1.31940	−	2.28527i
$518$	6.92820	−	4.00000i	0.304408	−	0.175750i
$519$			22.5167i			0.988372i
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$			12.0000i			0.525226i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	15.0000	−	25.9808i	0.655278	−	1.13497i
$525$	1.73205	−	3.00000i	0.0755929	−	0.130931i
$526$	−15.5885	+	9.00000i	−0.679689	+	0.392419i
$527$	6.92820	−	4.00000i	0.301797	−	0.174243i
$528$	−20.7846	+	36.0000i	−0.904534	+	1.56670i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	18.0000			0.781870
$531$			18.0000i			0.781133i
$532$	−32.0000			−1.38738
$533$	−3.19615	−	6.46410i	−0.138441	−	0.279991i
$534$		0			0
$535$	14.7224	−	8.50000i	0.636506	−	0.367487i
$536$		0			0
$537$	22.5000	−	12.9904i	0.970947	−	0.560576i
$538$	−24.2487	−	14.0000i	−1.04544	−	0.603583i
$539$			18.0000i			0.775315i
$540$	5.19615	−	9.00000i	0.223607	−	0.387298i
$541$		−	32.0000i		−	1.37579i	−0.725811	−	0.687894i	$-0.758536\pi$
$541$		−	32.0000i		−	1.37579i	0.725811	−	0.687894i	$-0.241464\pi$
$542$	−28.0000	+	48.4974i	−1.20270	+	2.08314i
$543$	31.5000	−	18.1865i	1.35179	−	0.780459i
$544$	−6.92820	+	4.00000i	−0.297044	+	0.171499i
$545$	−10.0000	−	17.3205i	−0.428353	−	0.741929i
$546$	−13.8564	+	20.7846i	−0.592999	+	0.889499i
$547$	2.00000	−	3.46410i	0.0855138	−	0.148114i	−0.820096	−	0.572226i	$-0.806080\pi$
$547$	2.00000	−	3.46410i	0.0855138	−	0.148114i	0.905610	+	0.424111i	$0.139413\pi$
$548$			12.0000i			0.512615i
$549$	−7.50000	−	12.9904i	−0.320092	−	0.554416i
$550$	−12.0000			−0.511682
$551$	−13.8564	−	8.00000i	−0.590303	−	0.340811i
$552$		0			0
$553$	−1.73205	+	1.00000i	−0.0736543	+	0.0425243i
$554$	−17.3205	+	10.0000i	−0.735878	+	0.424859i
$555$	−3.00000	−	1.73205i	−0.127343	−	0.0735215i
$556$	−11.0000	+	19.0526i	−0.466504	+	0.808008i
$557$			12.0000i			0.508456i	0.967144	+	0.254228i	$0.0818214\pi$
$557$			12.0000i			0.508456i	−0.967144	+	0.254228i	$0.918179\pi$
$558$	−24.0000	+	41.5692i	−1.01600	+	1.75977i
$559$	−15.0000	−	10.0000i	−0.634432	−	0.422955i
$560$	4.00000	−	6.92820i	0.169031	−	0.292770i
$561$	10.3923			0.438763
$562$		0			0
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	−0.904320	−	0.426855i	$-0.859622\pi$
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	0.0824933	−	0.996592i	$-0.473712\pi$
$564$	17.3205	+	30.0000i	0.729325	+	1.26323i
$565$	−16.4545	−	9.50000i	−0.692245	−	0.399668i
$566$			62.0000i			2.60605i
$567$		−	18.0000i		−	0.755929i
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$	13.8564	+	24.0000i	0.580381	+	1.00525i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	43.1769	+	2.78461i	1.80532	+	0.116430i
$573$			32.9090i			1.37479i
$574$	−6.92820	−	4.00000i	−0.289178	−	0.166957i
$575$	−1.00000			−0.0417029
$576$	12.0000	−	20.7846i	0.500000	−	0.866025i
$577$			28.0000i			1.16566i	0.812596	+	0.582828i	$0.198054\pi$
$577$			28.0000i			1.16566i	−0.812596	+	0.582828i	$0.801946\pi$
$578$	−27.7128	−	16.0000i	−1.15270	−	0.665512i
$579$	3.46410	−	6.00000i	0.143963	−	0.249351i
$580$	−3.46410	+	2.00000i	−0.143839	+	0.0830455i
$581$		0			0
$582$	−30.0000	−	17.3205i	−1.24354	−	0.717958i
$583$	−46.7654	−	27.0000i	−1.93682	−	1.11823i
$584$		0			0
$585$	10.7942	+	0.696152i	0.446286	+	0.0287824i
$586$	12.0000			0.495715
$587$	−24.2487	−	14.0000i	−1.00085	−	0.577842i	−0.0923513	−	0.995726i	$-0.529438\pi$
$587$	−24.2487	−	14.0000i	−1.00085	−	0.577842i	−0.908500	+	0.417885i	$0.862772\pi$
$588$		−	10.3923i		−	0.428571i
$589$	−32.0000	−	55.4256i	−1.31854	−	2.28377i
$590$	−10.3923	+	6.00000i	−0.427844	+	0.247016i
$591$	−17.3205	−	30.0000i	−0.712470	−	1.23404i
$592$	−6.92820	−	4.00000i	−0.284747	−	0.164399i
$593$		−	16.0000i		−	0.657041i	−0.944497	−	0.328521i	$-0.893450\pi$
$593$		−	16.0000i		−	0.657041i	0.944497	−	0.328521i	$-0.106550\pi$
$594$	−54.0000	+	31.1769i	−2.21565	+	1.27920i
$595$	−2.00000			−0.0819920
$596$	−3.46410	−	2.00000i	−0.141895	−	0.0819232i
$597$	4.50000	−	2.59808i	0.184173	−	0.106332i
$598$	7.19615	+	0.464102i	0.294273	+	0.0189785i
$599$	−3.50000	−	6.06218i	−0.143006	−	0.247694i	0.785621	−	0.618708i	$-0.212344\pi$
$599$	−3.50000	−	6.06218i	−0.143006	−	0.247694i	−0.928627	+	0.371014i	$0.879010\pi$
$600$		0			0
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	−0.912499	−	0.409079i	$-0.865850\pi$
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	0.810522	+	0.585708i	$0.199184\pi$
$602$	−20.0000			−0.815139
$603$		0			0
$604$			8.00000i			0.325515i
$605$	21.6506	+	12.5000i	0.880223	+	0.508197i
$606$	−12.1244	+	21.0000i	−0.492518	+	0.853067i
$607$	5.50000	+	9.52628i	0.223238	+	0.386660i	0.955789	−	0.294052i	$-0.0950039\pi$
$607$	5.50000	+	9.52628i	0.223238	+	0.386660i	−0.732551	+	0.680712i	$0.761671\pi$
$608$	32.0000	+	55.4256i	1.29777	+	2.24781i
$609$	−3.46410	+	6.00000i	−0.140372	+	0.243132i
$610$	5.00000	−	8.66025i	0.202444	−	0.350643i
$611$	−20.0000	+	30.0000i	−0.809113	+	1.21367i
$612$	−6.00000			−0.242536
$613$			28.0000i			1.13091i	0.824779	+	0.565455i	$0.191299\pi$
$613$			28.0000i			1.13091i	−0.824779	+	0.565455i	$0.808701\pi$
$614$	4.00000	−	6.92820i	0.161427	−	0.279600i
$615$			3.46410i			0.139686i
$616$		0			0
$617$	1.73205	−	1.00000i	0.0697297	−	0.0402585i	−0.464730	−	0.885453i	$-0.653849\pi$
$617$	1.73205	−	1.00000i	0.0697297	−	0.0402585i	0.534460	+	0.845194i	$0.320515\pi$
$618$	−27.7128	−	48.0000i	−1.11477	−	1.93084i
$619$	8.66025	+	5.00000i	0.348085	+	0.200967i	0.663842	−	0.747873i	$-0.268925\pi$
$619$	8.66025	+	5.00000i	0.348085	+	0.200967i	−0.315757	+	0.948840i	$0.602258\pi$
$620$	−16.0000			−0.642575
$621$	−4.50000	+	2.59808i	−0.180579	+	0.104257i
$622$			16.0000i			0.641542i
$623$		0			0
$624$	24.9282	+	1.60770i	0.997927	+	0.0643593i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	17.3205	−	10.0000i	0.692267	−	0.399680i
$627$		−	83.1384i		−	3.32023i
$628$	−13.0000	+	22.5167i	−0.518756	+	0.898513i
$629$			2.00000i			0.0797452i
$630$	10.3923	−	6.00000i	0.414039	−	0.239046i
$631$			2.00000i			0.0796187i	0.999207	+	0.0398094i	$0.0126751\pi$
$631$			2.00000i			0.0796187i	−0.999207	+	0.0398094i	$0.987325\pi$
$632$		0			0
$633$	22.5000	+	12.9904i	0.894295	+	0.516321i
$634$	26.0000	+	45.0333i	1.03259	+	1.78850i
$635$		0			0
$636$	27.0000	+	15.5885i	1.07062	+	0.618123i
$637$	9.69615	−	4.79423i	0.384176	−	0.189954i
$638$	24.0000			0.950169
$639$	−25.9808	−	15.0000i	−1.02778	−	0.593391i
$640$		0			0
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	−0.800678	−	0.599095i	$-0.795527\pi$
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	0.919171	+	0.393860i	$0.128860\pi$
$642$	58.8897			2.32419
$643$	−27.7128	+	16.0000i	−1.09289	+	0.630978i	−0.934344	−	0.356374i	$-0.884013\pi$
$643$	−27.7128	+	16.0000i	−1.09289	+	0.630978i	−0.158543	+	0.987352i	$0.550680\pi$
$644$	3.46410	−	2.00000i	0.136505	−	0.0788110i
$645$	4.33013	+	7.50000i	0.170499	+	0.295312i
$646$	8.00000	−	13.8564i	0.314756	−	0.545173i
$647$	−17.0000			−0.668339			−0.334169	−	0.942513i	$-0.608456\pi$
$647$	−17.0000			−0.668339			−0.334169	+	0.942513i	$0.608456\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$	3.19615	+	6.46410i	0.125363	+	0.253543i
$651$	−24.0000	+	13.8564i	−0.940634	+	0.543075i
$652$		0			0
$653$	−17.0000	−	29.4449i	−0.665261	−	1.15227i	−0.979214	−	0.202828i	$-0.934987\pi$
$653$	−17.0000	−	29.4449i	−0.665261	−	1.15227i	0.313953	−	0.949439i	$-0.398347\pi$
$654$		−	69.2820i		−	2.70914i
$655$	−12.9904	−	7.50000i	−0.507576	−	0.293049i
$656$			8.00000i			0.312348i
$657$	10.3923	+	6.00000i	0.405442	+	0.234082i
$658$			40.0000i			1.55936i
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$	−18.0000	−	10.3923i	−0.700649	−	0.404520i
$661$	1.73205	−	1.00000i	0.0673690	−	0.0388955i	−0.465937	−	0.884818i	$-0.654283\pi$
$661$	1.73205	−	1.00000i	0.0673690	−	0.0388955i	0.533306	+	0.845922i	$0.320949\pi$
$662$	8.00000	+	13.8564i	0.310929	+	0.538545i
$663$	−2.76795	−	5.59808i	−0.107498	−	0.217411i
$664$		0			0
$665$			16.0000i			0.620453i
$666$	−6.00000	−	10.3923i	−0.232495	−	0.402694i
$667$	2.00000			0.0774403
$668$	−3.46410	−	2.00000i	−0.134030	−	0.0773823i
$669$	−24.2487			−0.937509
$670$		0			0
$671$	−25.9808	+	15.0000i	−1.00298	+	0.579069i
$672$	24.0000	−	13.8564i	0.925820	−	0.534522i
$673$	−15.5000	+	26.8468i	−0.597481	+	1.03487i	0.395711	+	0.918375i	$0.370498\pi$
$673$	−15.5000	+	26.8468i	−0.597481	+	1.03487i	−0.993192	+	0.116492i	$0.962835\pi$
$674$		−	6.00000i		−	0.231111i
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	−10.0000	−	24.0000i	−0.384615	−	0.923077i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$	−32.9090	−	57.0000i	−1.26386	−	2.18907i
$679$	−10.0000	−	17.3205i	−0.383765	−	0.664700i
$680$		0			0
$681$		0			0
$682$	83.1384	+	48.0000i	3.18354	+	1.83801i
$683$		−	34.0000i		−	1.30097i	−0.759517	−	0.650487i	$-0.774565\pi$
$683$		−	34.0000i		−	1.30097i	0.759517	−	0.650487i	$-0.225435\pi$
$684$			48.0000i			1.83533i
$685$	6.00000			0.229248
$686$	20.0000	−	34.6410i	0.763604	−	1.32260i
$687$	22.5167	−	39.0000i	0.859064	−	1.48794i
$688$	10.0000	+	17.3205i	0.381246	+	0.660338i
$689$	−2.08846	+	32.3827i	−0.0795639	+	1.23368i
$690$	−3.00000	−	1.73205i	−0.114208	−	0.0659380i
$691$	8.66025	+	5.00000i	0.329452	+	0.190209i	0.655598	−	0.755110i	$-0.272417\pi$
$691$	8.66025	+	5.00000i	0.329452	+	0.190209i	−0.326146	+	0.945319i	$0.605750\pi$
$692$	−26.0000			−0.988372
$693$	−36.0000			−1.36753
$694$			10.0000i			0.379595i
$695$	9.52628	+	5.50000i	0.361352	+	0.208627i
$696$		0			0
$697$	1.73205	−	1.00000i	0.0656061	−	0.0378777i
$698$	2.00000	+	3.46410i	0.0757011	+	0.131118i
$699$	−28.5000	+	16.4545i	−1.07797	+	0.622366i
$700$	3.46410	+	2.00000i	0.130931	+	0.0755929i
$701$	−39.0000			−1.47301			−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000			−1.47301			−0.736505	+	0.676432i	$0.763525\pi$
$702$	31.1769	+	20.7846i	1.17670	+	0.784465i
$703$	16.0000			0.603451
$704$	−41.5692	−	24.0000i	−1.56670	−	0.904534i
$705$	15.0000	−	8.66025i	0.564933	−	0.326164i
$706$	6.00000	+	10.3923i	0.225813	+	0.391120i
$707$	−12.1244	+	7.00000i	−0.455983	+	0.263262i
$708$	−20.7846			−0.781133
$709$	6.92820	+	4.00000i	0.260194	+	0.150223i	0.624423	−	0.781086i	$-0.285334\pi$
$709$	6.92820	+	4.00000i	0.260194	+	0.150223i	−0.364229	+	0.931309i	$0.618667\pi$
$710$		−	20.0000i		−	0.750587i
$711$	1.50000	+	2.59808i	0.0562544	+	0.0974355i
$712$		0			0
$713$	6.92820	+	4.00000i	0.259463	+	0.149801i
$714$	−6.00000	−	3.46410i	−0.224544	−	0.129641i
$715$	1.39230	−	21.5885i	0.0520692	−	0.807363i
$716$	15.0000	+	25.9808i	0.560576	+	0.970947i
$717$	17.3205	−	30.0000i	0.646846	−	1.12037i
$718$	−10.0000	+	17.3205i	−0.373197	+	0.646396i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$	−10.3923	−	6.00000i	−0.387298	−	0.223607i
$721$		−	32.0000i		−	1.19174i
$722$	−77.9423	−	45.0000i	−2.90071	−	1.67473i
$723$	51.9615			1.93247
$724$	21.0000	+	36.3731i	0.780459	+	1.35179i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	43.3013	+	75.0000i	1.60706	+	2.78351i
$727$	18.5000	−	32.0429i	0.686127	−	1.18841i	−0.286954	−	0.957944i	$-0.592643\pi$
$727$	18.5000	−	32.0429i	0.686127	−	1.18841i	0.973081	−	0.230463i	$-0.0740239\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$			8.00000i			0.296093i
$731$	2.50000	−	4.33013i	0.0924658	−	0.160156i
$732$	15.0000	−	8.66025i	0.554416	−	0.320092i
$733$	20.7846	−	12.0000i	0.767697	−	0.443230i	−0.0643554	−	0.997927i	$-0.520499\pi$
$733$	20.7846	−	12.0000i	0.767697	−	0.443230i	0.832052	+	0.554697i	$0.187166\pi$
$734$	−36.3731	+	21.0000i	−1.34255	+	0.775124i
$735$	−5.19615			−0.191663
$736$	−6.92820	−	4.00000i	−0.255377	−	0.147442i
$737$		0			0
$738$	−6.00000	+	10.3923i	−0.220863	+	0.382546i
$739$			12.0000i			0.441427i	0.975339	+	0.220714i	$0.0708386\pi$
$739$			12.0000i			0.441427i	−0.975339	+	0.220714i	$0.929161\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$	−44.7846	+	22.1436i	−1.64520	+	0.813465i
$742$	18.0000	+	31.1769i	0.660801	+	1.14454i
$743$	−38.1051	+	22.0000i	−1.39794	+	0.807102i	−0.994177	−	0.107761i	$-0.965632\pi$
$743$	−38.1051	+	22.0000i	−1.39794	+	0.807102i	−0.403764	+	0.914863i	$0.632298\pi$
$744$		0			0
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$		−	38.0000i		−	1.39128i
$747$		0			0
$748$			12.0000i			0.438763i
$749$	29.4449	+	17.0000i	1.07589	+	0.621166i
$750$		−	3.46410i		−	0.126491i
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	34.6410	−	20.0000i	1.26323	−	0.729325i
$753$	4.50000	−	2.59808i	0.163989	−	0.0946792i
$754$	−6.39230	−	12.9282i	−0.232794	−	0.470817i
$755$	4.00000			0.145575
$756$	20.7846			0.755929
$757$	29.0000			1.05402			0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000			1.05402			0.527011	+	0.849858i	$0.323312\pi$
$758$	18.0000	−	31.1769i	0.653789	−	1.13240i
$759$	5.19615	+	9.00000i	0.188608	+	0.326679i
$760$		0			0
$761$	39.8372	−	23.0000i	1.44410	−	0.833749i	0.445977	−	0.895045i	$-0.352856\pi$
$761$	39.8372	−	23.0000i	1.44410	−	0.833749i	0.998120	+	0.0612953i	$0.0195231\pi$
$762$		0			0
$763$	20.0000	−	34.6410i	0.724049	−	1.25409i
$764$	−38.0000			−1.37479
$765$			3.00000i			0.108465i
$766$	−52.0000			−1.87884
$767$	−9.58846	−	19.3923i	−0.346219	−	0.700216i
$768$	−24.0000	−	13.8564i	−0.866025	−	0.500000i
$769$	34.6410	−	20.0000i	1.24919	−	0.721218i	0.278240	−	0.960512i	$-0.410249\pi$
$769$	34.6410	−	20.0000i	1.24919	−	0.721218i	0.970947	+	0.239293i	$0.0769157\pi$
$770$	−12.0000	−	20.7846i	−0.432450	−	0.749025i
$771$	4.50000	+	2.59808i	0.162064	+	0.0935674i
$772$	6.92820	+	4.00000i	0.249351	+	0.143963i
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$			30.0000i			1.07833i
$775$			8.00000i			0.287368i
$776$		0			0
$777$		−	6.92820i		−	0.248548i
$778$	39.8372	−	23.0000i	1.42823	−	0.824590i
$779$	−8.00000	−	13.8564i	−0.286630	−	0.496457i
$780$	−0.803848	+	12.4641i	−0.0287824	+	0.446286i
$781$	−30.0000	+	51.9615i	−1.07348	+	1.85933i
$782$			2.00000i			0.0715199i
$783$	9.00000	+	5.19615i	0.321634	+	0.185695i
$784$	−12.0000			−0.428571
$785$	11.2583	+	6.50000i	0.401827	+	0.231995i
$786$	−25.9808	−	45.0000i	−0.926703	−	1.60510i
$787$	−1.73205	+	1.00000i	−0.0617409	+	0.0356462i	−0.530553	−	0.847652i	$-0.678016\pi$
$787$	−1.73205	+	1.00000i	−0.0617409	+	0.0356462i	0.468812	+	0.883298i	$0.344682\pi$
$788$	34.6410	−	20.0000i	1.23404	−	0.712470i
$789$			15.5885i			0.554964i
$790$	−1.00000	+	1.73205i	−0.0355784	+	0.0616236i
$791$		−	38.0000i		−	1.35112i
$792$		0			0
$793$	15.0000	+	10.0000i	0.532666	+	0.355110i
$794$	28.0000	−	48.4974i	0.993683	−	1.72111i
$795$	7.79423	−	13.5000i	0.276433	−	0.478796i
$796$	3.00000	+	5.19615i	0.106332	+	0.184173i
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	−0.992492	−	0.122312i	$-0.960969\pi$
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	0.390321	−	0.920679i	$-0.372364\pi$
$798$	−27.7128	+	48.0000i	−0.981023	+	1.69918i
$799$	−8.66025	−	5.00000i	−0.306378	−	0.176887i
$800$		−	8.00000i		−	0.282843i
$801$		0			0
$802$	64.0000			2.25992
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$		0			0
$805$	−1.00000	−	1.73205i	−0.0352454	−	0.0610468i
$806$	3.71281	−	57.5692i	0.130778	−	2.02779i
$807$	−21.0000	+	12.1244i	−0.739235	+	0.426798i
$808$		0			0
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$		−	32.0000i		−	1.12367i	−0.827249	−	0.561836i	$-0.810095\pi$
$811$		−	32.0000i		−	1.12367i	0.827249	−	0.561836i	$-0.189905\pi$
$812$	−6.92820	−	4.00000i	−0.243132	−	0.140372i
$813$	24.2487	+	42.0000i	0.850439	+	1.47300i
$814$	−20.7846	+	12.0000i	−0.728500	+	0.420600i
$815$		0			0
$816$			6.92820i			0.242536i
$817$	−34.6410	−	20.0000i	−1.21194	−	0.699711i
$818$		0			0
$819$	9.58846	+	19.3923i	0.335048	+	0.677622i
$820$	−4.00000			−0.139686
$821$	15.5885	+	9.00000i	0.544041	+	0.314102i	0.746715	−	0.665144i	$-0.231630\pi$
$821$	15.5885	+	9.00000i	0.544041	+	0.314102i	−0.202674	+	0.979246i	$0.564963\pi$
$822$	18.0000	+	10.3923i	0.627822	+	0.362473i
$823$	16.5000	+	28.5788i	0.575154	+	0.996196i	0.996025	+	0.0890752i	$0.0283911\pi$
$823$	16.5000	+	28.5788i	0.575154	+	0.996196i	−0.420871	+	0.907120i	$0.638276\pi$
$824$		0			0
$825$	−5.19615	+	9.00000i	−0.180907	+	0.313340i
$826$	−20.7846	−	12.0000i	−0.723189	−	0.417533i
$827$		−	4.00000i		−	0.139094i	−0.997579	−	0.0695468i	$-0.977845\pi$
$827$		−	4.00000i		−	0.139094i	0.997579	−	0.0695468i	$-0.0221553\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$		0			0
$831$			17.3205i			0.600842i
$832$	−1.85641	+	28.7846i	−0.0643593	+	0.997927i
$833$	1.50000	+	2.59808i	0.0519719	+	0.0900180i
$834$	19.0526	+	33.0000i	0.659736	+	1.14270i
$835$	−1.00000	+	1.73205i	−0.0346064	+	0.0599401i
$836$	96.0000			3.32023
$837$	20.7846	+	36.0000i	0.718421	+	1.24434i
$838$		−	30.0000i		−	1.03633i
$839$	−31.1769	−	18.0000i	−1.07635	−	0.621429i	−0.146438	−	0.989220i	$-0.546781\pi$
$839$	−31.1769	−	18.0000i	−1.07635	−	0.621429i	−0.929909	+	0.367791i	$0.880114\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−8.00000	−	13.8564i	−0.275698	−	0.477523i
$843$		0			0
$844$	−15.0000	+	25.9808i	−0.516321	+	0.894295i
$845$	−12.0000	+	5.00000i	−0.412813	+	0.172005i
$846$	60.0000			2.06284
$847$			50.0000i			1.71802i
$848$	18.0000	−	31.1769i	0.618123	−	1.07062i
$849$	46.5000	+	26.8468i	1.59588	+	0.921379i
$850$	−1.73205	+	1.00000i	−0.0594089	+	0.0342997i
$851$	−1.73205	+	1.00000i	−0.0593739	+	0.0342796i
$852$	17.3205	−	30.0000i	0.593391	−	1.02778i
$853$	−15.5885	−	9.00000i	−0.533739	−	0.308154i	0.208799	−	0.977959i	$-0.433045\pi$
$853$	−15.5885	−	9.00000i	−0.533739	−	0.308154i	−0.742538	+	0.669804i	$0.766378\pi$
$854$	20.0000			0.684386
$855$	24.0000			0.820783
$856$		0			0
$857$	5.00000	−	8.66025i	0.170797	−	0.295829i	−0.767902	−	0.640567i	$-0.778699\pi$
$857$	5.00000	−	8.66025i	0.170797	−	0.295829i	0.938699	+	0.344739i	$0.112033\pi$
$858$	41.5692	−	62.3538i	1.41915	−	2.12872i
$859$	24.5000	+	42.4352i	0.835929	+	1.44787i	0.893272	+	0.449517i	$0.148404\pi$
$859$	24.5000	+	42.4352i	0.835929	+	1.44787i	−0.0573424	+	0.998355i	$0.518263\pi$
$860$	−8.66025	+	5.00000i	−0.295312	+	0.170499i
$861$	−6.00000	+	3.46410i	−0.204479	+	0.118056i
$862$	24.0000	−	41.5692i	0.817443	−	1.41585i
$863$			18.0000i			0.612727i	0.951915	+	0.306364i	$0.0991123\pi$
$863$			18.0000i			0.612727i	−0.951915	+	0.306364i	$0.900888\pi$
$864$	−20.7846	−	36.0000i	−0.707107	−	1.22474i
$865$			13.0000i			0.442013i
$866$	8.66025	+	5.00000i	0.294287	+	0.169907i
$867$	−24.0000	+	13.8564i	−0.815083	+	0.470588i
$868$	−16.0000	−	27.7128i	−0.543075	−	0.940634i
$869$	5.19615	−	3.00000i	0.176267	−	0.101768i
$870$			6.92820i			0.234888i
$871$		0			0
$872$		0			0
$873$	−25.9808	+	15.0000i	−0.879316	+	0.507673i
$874$	16.0000			0.541208
$875$	1.00000	−	1.73205i	0.0338062	−	0.0585540i
$876$	−6.92820	+	12.0000i	−0.234082	+	0.405442i
$877$	27.7128	−	16.0000i	0.935795	−	0.540282i	0.0471555	−	0.998888i	$-0.484984\pi$
$877$	27.7128	−	16.0000i	0.935795	−	0.540282i	0.888640	+	0.458606i	$0.151651\pi$
$878$	−43.3013	+	25.0000i	−1.46135	+	0.843709i
$879$	5.19615	−	9.00000i	0.175262	−	0.303562i
$880$	−12.0000	+	20.7846i	−0.404520	+	0.700649i
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$	−15.5885	−	9.00000i	−0.524891	−	0.303046i
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$	6.46410	−	3.19615i	0.217411	−	0.107498i
$885$			10.3923i			0.349334i
$886$	−36.3731	+	21.0000i	−1.22198	+	0.705509i
$887$	12.5000	+	21.6506i	0.419709	+	0.726957i	0.995910	−	0.0903508i	$-0.0287988\pi$
$887$	12.5000	+	21.6506i	0.419709	+	0.726957i	−0.576201	+	0.817308i	$0.695465\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$			54.0000i			1.80907i
$892$		−	28.0000i		−	0.937509i
$893$	−40.0000	+	69.2820i	−1.33855	+	2.31843i
$894$	−6.00000	+	3.46410i	−0.200670	+	0.115857i
$895$	12.9904	−	7.50000i	0.434221	−	0.250697i
$896$		0			0
$897$	3.46410	−	5.19615i	0.115663	−	0.173494i
$898$	−36.0000	+	62.3538i	−1.20134	+	2.08077i
$899$		−	16.0000i		−	0.533630i
$900$	3.00000	−	5.19615i	0.100000	−	0.173205i
$901$	−9.00000			−0.299833
$902$	20.7846	+	12.0000i	0.692052	+	0.399556i
$903$	−8.66025	+	15.0000i	−0.288195	+	0.499169i
$904$		0			0
$905$	18.1865	−	10.5000i	0.604541	−	0.349032i
$906$	12.0000	+	6.92820i	0.398673	+	0.230174i
$907$	11.5000	−	19.9186i	0.381851	−	0.661386i	−0.609476	−	0.792805i	$-0.708620\pi$
$907$	11.5000	−	19.9186i	0.381851	−	0.661386i	0.991327	+	0.131419i	$0.0419533\pi$
$908$		0			0
$909$	10.5000	+	18.1865i	0.348263	+	0.603209i
$910$	−8.00000	+	12.0000i	−0.265197	+	0.397796i
$911$	−11.5000	+	19.9186i	−0.381012	+	0.659932i	−0.991207	−	0.132319i	$-0.957758\pi$
$911$	−11.5000	+	19.9186i	−0.381012	+	0.659932i	0.610195	+	0.792251i	$0.291091\pi$
$912$	55.4256			1.83533
$913$		0			0
$914$	−8.00000	−	13.8564i	−0.264616	−	0.458329i
$915$	−4.33013	−	7.50000i	−0.143150	−	0.247942i
$916$	45.0333	+	26.0000i	1.48794	+	0.859064i
$917$		−	30.0000i		−	0.990687i
$918$	−5.19615	+	9.00000i	−0.171499	+	0.297044i
$919$	−5.00000			−0.164935			−0.0824674	−	0.996594i	$-0.526280\pi$
$919$	−5.00000			−0.164935			−0.0824674	+	0.996594i	$0.526280\pi$
$920$		0			0
$921$	−3.46410	−	6.00000i	−0.114146	−	0.197707i
$922$	−2.00000	−	3.46410i	−0.0658665	−	0.114084i
$923$	35.9808	+	2.32051i	1.18432	+	0.0763805i
$924$		−	41.5692i		−	1.36753i
$925$	−1.73205	−	1.00000i	−0.0569495	−	0.0328798i
$926$	−44.0000			−1.44593
$927$	−48.0000			−1.57653
$928$			16.0000i			0.525226i
$929$	−3.46410	−	2.00000i	−0.113653	−	0.0656179i	0.442096	−	0.896968i	$-0.354235\pi$
$929$	−3.46410	−	2.00000i	−0.113653	−	0.0656179i	−0.555749	+	0.831350i	$0.687569\pi$
$930$	−13.8564	+	24.0000i	−0.454369	+	0.786991i
$931$	20.7846	−	12.0000i	0.681188	−	0.393284i
$932$	−19.0000	−	32.9090i	−0.622366	−	1.07797i
$933$	12.0000	+	6.92820i	0.392862	+	0.226819i
$934$	−36.3731	−	21.0000i	−1.19016	−	0.687141i
$935$	6.00000			0.196221
$936$		0			0
$937$	17.0000			0.555366			0.277683	−	0.960673i	$-0.410434\pi$
$937$	17.0000			0.555366			0.277683	+	0.960673i	$0.410434\pi$
$938$		0			0
$939$		−	17.3205i		−	0.565233i
$940$	10.0000	+	17.3205i	0.326164	+	0.564933i
$941$	−24.2487	+	14.0000i	−0.790485	+	0.456387i	−0.840133	−	0.542380i	$-0.817523\pi$
$941$	−24.2487	+	14.0000i	−0.790485	+	0.456387i	0.0496480	+	0.998767i	$0.484190\pi$
$942$	22.5167	+	39.0000i	0.733632	+	1.27069i
$943$	1.73205	+	1.00000i	0.0564033	+	0.0325645i
$944$			24.0000i			0.781133i
$945$		−	10.3923i		−	0.338062i
$946$	60.0000			1.95077
$947$	−25.9808	−	15.0000i	−0.844261	−	0.487435i	0.0144491	−	0.999896i	$-0.495401\pi$
$947$	−25.9808	−	15.0000i	−0.844261	−	0.487435i	−0.858710	+	0.512461i	$0.828734\pi$
$948$	−3.00000	+	1.73205i	−0.0974355	+	0.0562544i
$949$	−14.3923	−	0.928203i	−0.467194	−	0.0301308i
$950$	8.00000	+	13.8564i	0.259554	+	0.449561i
$951$	45.0333			1.46031
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	46.7654	−	27.0000i	1.51408	−	0.874157i
$955$			19.0000i			0.614826i
$956$	34.6410	+	20.0000i	1.12037	+	0.646846i
$957$	10.3923	−	18.0000i	0.335936	−	0.581857i
$958$	−18.0000	−	31.1769i	−0.581554	−	1.00728i
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$	6.92820	−	12.0000i	0.223607	−	0.387298i
$961$	16.5000	−	28.5788i	0.532258	−	0.921898i
$962$	12.0000	+	8.00000i	0.386896	+	0.257930i
$963$	25.5000	−	44.1673i	0.821726	−	1.42327i
$964$			60.0000i			1.93247i
$965$	2.00000	−	3.46410i	0.0643823	−	0.111513i
$966$		−	6.92820i		−	0.222911i
$967$	−17.3205	+	10.0000i	−0.556990	+	0.321578i	−0.751936	−	0.659236i	$-0.770880\pi$
$967$	−17.3205	+	10.0000i	−0.556990	+	0.321578i	0.194946	+	0.980814i	$0.437547\pi$
$968$		0			0
$969$	−6.92820	−	12.0000i	−0.222566	−	0.385496i
$970$	−17.3205	−	10.0000i	−0.556128	−	0.321081i
$971$	60.0000			1.92549			0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000			1.92549			0.962746	+	0.270408i	$0.0871586\pi$
$972$		−	31.1769i		−	1.00000i
$973$			22.0000i			0.705288i
$974$	−24.0000	+	41.5692i	−0.769010	+	1.33196i
$975$	6.23205	+	0.401924i	0.199585	+	0.0128719i
$976$	−10.0000	−	17.3205i	−0.320092	−	0.554416i
$977$	−17.3205	+	10.0000i	−0.554132	+	0.319928i	−0.750787	−	0.660544i	$-0.770326\pi$
$977$	−17.3205	+	10.0000i	−0.554132	+	0.319928i	0.196655	+	0.980473i	$0.436992\pi$
$978$		0			0
$979$		0			0
$980$		−	6.00000i		−	0.191663i
$981$	−51.9615	−	30.0000i	−1.65900	−	0.957826i
$982$			32.0000i			1.02116i
$983$	−17.3205	−	10.0000i	−0.552438	−	0.318950i	0.197666	−	0.980269i	$-0.436664\pi$
$983$	−17.3205	−	10.0000i	−0.552438	−	0.318950i	−0.750105	+	0.661319i	$0.769997\pi$
$984$		0			0
$985$	−10.0000	−	17.3205i	−0.318626	−	0.551877i
$986$	3.46410	−	2.00000i	0.110319	−	0.0636930i
$987$	30.0000	+	17.3205i	0.954911	+	0.551318i
$988$	−25.5692	−	51.7128i	−0.813465	−	1.64520i
$989$	5.00000			0.158991
$990$	−31.1769	+	18.0000i	−0.990867	+	0.572078i
$991$	25.0000			0.794151			0.397076	−	0.917786i	$-0.370025\pi$
$991$	25.0000			0.794151			0.397076	+	0.917786i	$0.370025\pi$
$992$	−32.0000	+	55.4256i	−1.01600	+	1.75977i
$993$	13.8564			0.439720
$994$	34.6410	−	20.0000i	1.09875	−	0.634361i
$995$	2.59808	−	1.50000i	0.0823646	−	0.0475532i
$996$		0			0
$997$	−28.5000	+	49.3634i	−0.902604	+	1.56336i	−0.0785026	+	0.996914i	$0.525014\pi$
$997$	−28.5000	+	49.3634i	−0.902604	+	1.56336i	−0.824101	+	0.566442i	$0.808319\pi$
$998$	−56.0000			−1.77265
$999$	−10.3923			−0.328798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.a.376.2	yes	4
9.4	even	3	inner	585.2.bt.a.571.1	yes	4
13.12	even	2	inner	585.2.bt.a.376.1	✓	4
117.103	even	6	inner	585.2.bt.a.571.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.a.376.1	✓	4	13.12	even	2	inner
585.2.bt.a.376.2	yes	4	1.1	even	1	trivial
585.2.bt.a.571.1	yes	4	9.4	even	3	inner
585.2.bt.a.571.2	yes	4	117.103	even	6	inner

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 - 0.500000i) q^{5} +3.46410 q^{6} +(1.73205 + 1.00000i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 - 0.500000i) q^{5} +3.46410 q^{6} +(1.73205 + 1.00000i) q^{7} +(1.50000 - 2.59808i) q^{9} +2.00000 q^{10} +(-5.19615 - 3.00000i) q^{11} +(3.00000 + 1.73205i) q^{12} +(-0.232051 + 3.59808i) q^{13} +(2.00000 + 3.46410i) q^{14} +(0.866025 - 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} -1.00000 q^{17} +(5.19615 - 3.00000i) q^{18} +8.00000i q^{19} +(1.73205 + 1.00000i) q^{20} +3.46410 q^{21} +(-6.00000 - 10.3923i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-4.00000 + 6.00000i) q^{26} -5.19615i q^{27} +4.00000i q^{28} +(-1.00000 + 1.73205i) q^{29} +(3.00000 - 1.73205i) q^{30} +(-6.92820 + 4.00000i) q^{31} +(6.92820 - 4.00000i) q^{32} -10.3923 q^{33} +(-1.73205 - 1.00000i) q^{34} +2.00000 q^{35} +6.00000 q^{36} -2.00000i q^{37} +(-8.00000 + 13.8564i) q^{38} +(2.76795 + 5.59808i) q^{39} +(-1.73205 + 1.00000i) q^{41} +(6.00000 + 3.46410i) q^{42} +(-2.50000 + 4.33013i) q^{43} -12.0000i q^{44} -3.00000i q^{45} -2.00000i q^{46} +(8.66025 + 5.00000i) q^{47} -6.92820i q^{48} +(-1.50000 - 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} +(-1.50000 + 0.866025i) q^{51} +(-6.46410 + 3.19615i) q^{52} +9.00000 q^{53} +(5.19615 - 9.00000i) q^{54} -6.00000 q^{55} +(6.92820 + 12.0000i) q^{57} +(-3.46410 + 2.00000i) q^{58} +(-5.19615 + 3.00000i) q^{59} +3.46410 q^{60} +(2.50000 - 4.33013i) q^{61} -16.0000 q^{62} +(5.19615 - 3.00000i) q^{63} +8.00000 q^{64} +(1.59808 + 3.23205i) q^{65} +(-18.0000 - 10.3923i) q^{66} +(-1.00000 - 1.73205i) q^{68} +(-1.50000 - 0.866025i) q^{69} +(3.46410 + 2.00000i) q^{70} -10.0000i q^{71} +4.00000i q^{73} +(2.00000 - 3.46410i) q^{74} -1.73205i q^{75} +(-13.8564 + 8.00000i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(-0.803848 + 12.4641i) q^{78} +(-0.500000 + 0.866025i) q^{79} -4.00000i q^{80} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{82} +(3.46410 + 6.00000i) q^{84} +(-0.866025 + 0.500000i) q^{85} +(-8.66025 + 5.00000i) q^{86} +3.46410i q^{87} +(3.00000 - 5.19615i) q^{90} +(-4.00000 + 6.00000i) q^{91} +(1.00000 - 1.73205i) q^{92} +(-6.92820 + 12.0000i) q^{93} +(10.0000 + 17.3205i) q^{94} +(4.00000 + 6.92820i) q^{95} +(6.92820 - 12.0000i) q^{96} +(-8.66025 - 5.00000i) q^{97} -6.00000i q^{98} +(-15.5885 + 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 4 q^{4} + 6 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 4 * q^4 + 6 * q^9	\( 4 q + 6 q^{3} + 4 q^{4} + 6 q^{9} + 8 q^{10} + 12 q^{12} + 6 q^{13} + 8 q^{14} + 8 q^{16} - 4 q^{17} - 24 q^{22} - 2 q^{23} + 2 q^{25} - 16 q^{26} - 4 q^{29} + 12 q^{30} + 8 q^{35} + 24 q^{36} - 32 q^{38} + 18 q^{39} + 24 q^{42} - 10 q^{43} - 6 q^{49} - 6 q^{51} - 12 q^{52} + 36 q^{53} - 24 q^{55} + 10 q^{61} - 64 q^{62} + 32 q^{64} - 4 q^{65} - 72 q^{66} - 4 q^{68} - 6 q^{69} + 8 q^{74} - 24 q^{77} - 24 q^{78} - 2 q^{79} - 18 q^{81} - 16 q^{82} + 12 q^{90} - 16 q^{91} + 4 q^{92} + 40 q^{94} + 16 q^{95}+O(q^{100}) \) 4 * q + 6 * q^3 + 4 * q^4 + 6 * q^9 + 8 * q^10 + 12 * q^12 + 6 * q^13 + 8 * q^14 + 8 * q^16 - 4 * q^17 - 24 * q^22 - 2 * q^23 + 2 * q^25 - 16 * q^26 - 4 * q^29 + 12 * q^30 + 8 * q^35 + 24 * q^36 - 32 * q^38 + 18 * q^39 + 24 * q^42 - 10 * q^43 - 6 * q^49 - 6 * q^51 - 12 * q^52 + 36 * q^53 - 24 * q^55 + 10 * q^61 - 64 * q^62 + 32 * q^64 - 4 * q^65 - 72 * q^66 - 4 * q^68 - 6 * q^69 + 8 * q^74 - 24 * q^77 - 24 * q^78 - 2 * q^79 - 18 * q^81 - 16 * q^82 + 12 * q^90 - 16 * q^91 + 4 * q^92 + 40 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

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