LMFDB - Embedded newform 231.2.i.c.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.i (of order $3$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	231.100
Dual form			231.2.i.c.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{12} -5.00000 q^{13} +(1.00000 - 5.19615i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(2.00000 + 1.73205i) q^{21} +2.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-5.00000 + 8.66025i) q^{26} -1.00000 q^{27} +(-4.00000 - 3.46410i) q^{28} -2.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(-0.500000 + 0.866025i) q^{33} -12.0000 q^{34} +2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(7.00000 + 12.1244i) q^{38} +(-2.50000 - 4.33013i) q^{39} +4.00000 q^{41} +(5.00000 - 1.73205i) q^{42} -9.00000 q^{43} +(1.00000 - 1.73205i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(-3.00000 + 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +10.0000 q^{50} +(3.00000 - 5.19615i) q^{51} +(5.00000 + 8.66025i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-1.00000 + 1.73205i) q^{54} -7.00000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +14.0000 q^{62} +(-0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(1.00000 + 1.73205i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(-6.00000 + 10.3923i) q^{68} +4.00000 q^{69} +8.00000 q^{71} +(2.50000 + 4.33013i) q^{73} +(7.00000 + 12.1244i) q^{74} +(-2.50000 + 4.33013i) q^{75} +14.0000 q^{76} +(2.00000 + 1.73205i) q^{77} -10.0000 q^{78} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.00000 - 6.92820i) q^{82} -4.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +(-9.00000 + 15.5885i) q^{86} +(-1.00000 - 1.73205i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-12.5000 + 4.33013i) q^{91} -8.00000 q^{92} +(-3.50000 + 6.06218i) q^{93} +(6.00000 + 10.3923i) q^{94} +(4.00000 - 6.92820i) q^{96} +2.00000 q^{97} +(-2.00000 - 13.8564i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9	$ 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9} + q^{11} + 2 q^{12} - 10 q^{13} + 2 q^{14} + 4 q^{16} - 6 q^{17} + 2 q^{18} - 7 q^{19} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 5 q^{25} - 10 q^{26} - 2 q^{27} - 8 q^{28} - 4 q^{29} + 7 q^{31} - 8 q^{32} - q^{33} - 24 q^{34} + 4 q^{36} - 7 q^{37} + 14 q^{38} - 5 q^{39} + 8 q^{41} + 10 q^{42} - 18 q^{43} + 2 q^{44} - 8 q^{46} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 20 q^{50} + 6 q^{51} + 10 q^{52} + 2 q^{53} - 2 q^{54} - 14 q^{57} - 4 q^{58} - 12 q^{59} + 2 q^{61} + 28 q^{62} - q^{63} - 16 q^{64} + 2 q^{66} - 7 q^{67} - 12 q^{68} + 8 q^{69} + 16 q^{71} + 5 q^{73} + 14 q^{74} - 5 q^{75} + 28 q^{76} + 4 q^{77} - 20 q^{78} + 11 q^{79} - q^{81} + 8 q^{82} - 8 q^{83} + 2 q^{84} - 18 q^{86} - 2 q^{87} - 6 q^{89} - 25 q^{91} - 16 q^{92} - 7 q^{93} + 12 q^{94} + 8 q^{96} + 4 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9 + q^11 + 2 * q^12 - 10 * q^13 + 2 * q^14 + 4 * q^16 - 6 * q^17 + 2 * q^18 - 7 * q^19 + 4 * q^21 + 4 * q^22 + 4 * q^23 + 5 * q^25 - 10 * q^26 - 2 * q^27 - 8 * q^28 - 4 * q^29 + 7 * q^31 - 8 * q^32 - q^33 - 24 * q^34 + 4 * q^36 - 7 * q^37 + 14 * q^38 - 5 * q^39 + 8 * q^41 + 10 * q^42 - 18 * q^43 + 2 * q^44 - 8 * q^46 - 6 * q^47 + 8 * q^48 + 11 * q^49 + 20 * q^50 + 6 * q^51 + 10 * q^52 + 2 * q^53 - 2 * q^54 - 14 * q^57 - 4 * q^58 - 12 * q^59 + 2 * q^61 + 28 * q^62 - q^63 - 16 * q^64 + 2 * q^66 - 7 * q^67 - 12 * q^68 + 8 * q^69 + 16 * q^71 + 5 * q^73 + 14 * q^74 - 5 * q^75 + 28 * q^76 + 4 * q^77 - 20 * q^78 + 11 * q^79 - q^81 + 8 * q^82 - 8 * q^83 + 2 * q^84 - 18 * q^86 - 2 * q^87 - 6 * q^89 - 25 * q^91 - 16 * q^92 - 7 * q^93 + 12 * q^94 + 8 * q^96 + 4 * q^97 - 4 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	2.00000			0.816497
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$	1.00000	−	5.19615i	0.267261	−	1.38873i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	1.00000	+	1.73205i	0.235702	+	0.408248i
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	2.00000	+	1.73205i	0.436436	+	0.377964i
$22$	2.00000			0.426401
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	−5.00000	+	8.66025i	−0.980581	+	1.69842i
$27$	−1.00000			−0.192450
$28$	−4.00000	−	3.46410i	−0.755929	−	0.654654i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−12.0000			−2.05798
$35$		0			0
$36$	2.00000			0.333333
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	7.00000	+	12.1244i	1.13555	+	1.96683i
$39$	−2.50000	−	4.33013i	−0.400320	−	0.693375i
$40$		0			0
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$	5.00000	−	1.73205i	0.771517	−	0.267261i
$43$	−9.00000			−1.37249			−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000			−1.37249			−0.686244	+	0.727372i	$0.740742\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	4.00000			0.577350
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	10.0000			1.41421
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	5.00000	+	8.66025i	0.693375	+	1.20096i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	−1.00000	+	1.73205i	−0.136083	+	0.235702i
$55$		0			0
$56$		0			0
$57$	−7.00000			−0.927173
$58$	−2.00000	+	3.46410i	−0.262613	+	0.454859i
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	14.0000			1.77800
$63$	−0.500000	+	2.59808i	−0.0629941	+	0.327327i
$64$	−8.00000			−1.00000
$65$		0			0
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$	−6.00000	+	10.3923i	−0.727607	+	1.26025i
$69$	4.00000			0.481543
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$	7.00000	+	12.1244i	0.813733	+	1.40943i
$75$	−2.50000	+	4.33013i	−0.288675	+	0.500000i
$76$	14.0000			1.60591
$77$	2.00000	+	1.73205i	0.227921	+	0.197386i
$78$	−10.0000			−1.13228
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.00000	−	6.92820i	0.441726	−	0.765092i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$	1.00000	−	5.19615i	0.109109	−	0.566947i
$85$		0			0
$86$	−9.00000	+	15.5885i	−0.970495	+	1.68095i
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−12.5000	+	4.33013i	−1.31036	+	0.453921i
$92$	−8.00000			−0.834058
$93$	−3.50000	+	6.06218i	−0.362933	+	0.628619i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$		0			0
$96$	4.00000	−	6.92820i	0.408248	−	0.707107i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−2.00000	−	13.8564i	−0.202031	−	1.39971i
$99$	−1.00000			−0.100504
$100$	5.00000	−	8.66025i	0.500000	−	0.866025i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	−6.00000	−	10.3923i	−0.594089	−	1.02899i
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.163335	−	0.986571i	$-0.447775\pi$
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.772728	−	0.634738i	$-0.218892\pi$
$104$		0			0
$105$		0			0
$106$	4.00000			0.388514
$107$	10.0000	−	17.3205i	0.966736	−	1.67444i	0.261861	−	0.965106i	$-0.415664\pi$
$107$	10.0000	−	17.3205i	0.966736	−	1.67444i	0.704875	−	0.709331i	$-0.251003\pi$
$108$	1.00000	+	1.73205i	0.0962250	+	0.166667i
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	0.888977	−	0.457951i	$-0.151417\pi$
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	−0.841086	+	0.540901i	$0.818083\pi$
$110$		0			0
$111$	−7.00000			−0.664411
$112$	2.00000	−	10.3923i	0.188982	−	0.981981i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−7.00000	+	12.1244i	−0.655610	+	1.13555i
$115$		0			0
$116$	2.00000	+	3.46410i	0.185695	+	0.321634i
$117$	2.50000	−	4.33013i	0.231125	−	0.400320i
$118$	−24.0000			−2.20938
$119$	−12.0000	−	10.3923i	−1.10004	−	0.952661i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.00000	−	3.46410i	−0.181071	−	0.313625i
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$	7.00000	−	12.1244i	0.628619	−	1.08880i
$125$		0			0
$126$	4.00000	+	3.46410i	0.356348	+	0.308607i
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$		0			0
$129$	−4.50000	−	7.79423i	−0.396203	−	0.686244i
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$	2.00000			0.174078
$133$	−3.50000	+	18.1865i	−0.303488	+	1.57697i
$134$	−14.0000			−1.20942
$135$		0			0
$136$		0			0
$137$	5.00000	+	8.66025i	0.427179	+	0.739895i	0.996621	−	0.0821359i	$-0.0261741\pi$
$137$	5.00000	+	8.66025i	0.427179	+	0.739895i	−0.569442	+	0.822031i	$0.692841\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	11.0000			0.933008			0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000			0.933008			0.466504	+	0.884519i	$0.345513\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	8.00000	−	13.8564i	0.671345	−	1.16280i
$143$	−2.50000	−	4.33013i	−0.209061	−	0.362103i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$		0			0
$146$	10.0000			0.827606
$147$	6.50000	+	2.59808i	0.536111	+	0.214286i
$148$	14.0000			1.15079
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	5.00000	+	8.66025i	0.408248	+	0.707107i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$	5.00000	−	1.73205i	0.402911	−	0.139573i
$155$		0			0
$156$	−5.00000	+	8.66025i	−0.400320	+	0.693375i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−11.0000	−	19.0526i	−0.875113	−	1.51574i
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$		0			0
$161$	2.00000	−	10.3923i	0.157622	−	0.819028i
$162$	−2.00000			−0.157135
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$	−4.00000	−	6.92820i	−0.312348	−	0.541002i
$165$		0			0
$166$	−4.00000	+	6.92820i	−0.310460	+	0.537733i
$167$	−6.00000			−0.464294			−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000			−0.464294			−0.232147	+	0.972681i	$0.574575\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−3.50000	−	6.06218i	−0.267652	−	0.463586i
$172$	9.00000	+	15.5885i	0.686244	+	1.18861i
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	−0.610939	−	0.791677i	$-0.709208\pi$
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	0.991082	+	0.133250i	$0.0425415\pi$
$174$	−4.00000			−0.303239
$175$	10.0000	+	8.66025i	0.755929	+	0.654654i
$176$	4.00000			0.301511
$177$	6.00000	−	10.3923i	0.450988	−	0.781133i
$178$	6.00000	+	10.3923i	0.449719	+	0.778936i
$179$	8.00000	+	13.8564i	0.597948	+	1.03568i	0.993124	+	0.117071i	$0.0373504\pi$
$179$	8.00000	+	13.8564i	0.597948	+	1.03568i	−0.395175	+	0.918606i	$0.629316\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	−5.00000	+	25.9808i	−0.370625	+	1.92582i
$183$	2.00000			0.147844
$184$		0			0
$185$		0			0
$186$	7.00000	+	12.1244i	0.513265	+	0.889001i
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	12.0000			0.875190
$189$	−2.50000	+	0.866025i	−0.181848	+	0.0629941i
$190$		0			0
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	0.126314	+	0.991990i	$0.459685\pi$
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	−0.922246	+	0.386604i	$0.873648\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	2.00000	−	3.46410i	0.143592	−	0.248708i
$195$		0			0
$196$	−13.0000	−	5.19615i	−0.928571	−	0.371154i
$197$	−4.00000			−0.284988			−0.142494	−	0.989796i	$-0.545512\pi$
$197$	−4.00000			−0.284988			−0.142494	+	0.989796i	$0.545512\pi$
$198$	−1.00000	+	1.73205i	−0.0710669	+	0.123091i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$	4.00000			0.281439
$203$	−5.00000	+	1.73205i	−0.350931	+	0.121566i
$204$	−12.0000			−0.840168
$205$		0			0
$206$	−19.0000	−	32.9090i	−1.32379	−	2.29288i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	−10.0000	+	17.3205i	−0.693375	+	1.20096i
$209$	−7.00000			−0.484200
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	2.00000	−	3.46410i	0.137361	−	0.237915i
$213$	4.00000	+	6.92820i	0.274075	+	0.474713i
$214$	−20.0000	−	34.6410i	−1.36717	−	2.36801i
$215$		0			0
$216$		0			0
$217$	14.0000	+	12.1244i	0.950382	+	0.823055i
$218$	2.00000			0.135457
$219$	−2.50000	+	4.33013i	−0.168934	+	0.292603i
$220$		0			0
$221$	15.0000	+	25.9808i	1.00901	+	1.74766i
$222$	−7.00000	+	12.1244i	−0.469809	+	0.813733i
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$	−16.0000	−	13.8564i	−1.06904	−	0.925820i
$225$	−5.00000			−0.333333
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$	7.00000	+	12.1244i	0.463586	+	0.802955i
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	−0.936728	−	0.350058i	$-0.886162\pi$
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	0.771523	+	0.636201i	$0.219495\pi$
$230$		0			0
$231$	−0.500000	+	2.59808i	−0.0328976	+	0.170941i
$232$		0			0
$233$	10.0000	−	17.3205i	0.655122	−	1.13470i	−0.326741	−	0.945114i	$-0.605951\pi$
$233$	10.0000	−	17.3205i	0.655122	−	1.13470i	0.981863	−	0.189590i	$-0.0607160\pi$
$234$	−5.00000	−	8.66025i	−0.326860	−	0.566139i
$235$		0			0
$236$	−12.0000	+	20.7846i	−0.781133	+	1.35296i
$237$	11.0000			0.714527
$238$	−30.0000	+	10.3923i	−1.94461	+	0.673633i
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.00000			−0.256074
$245$		0			0
$246$	8.00000			0.510061
$247$	17.5000	−	30.3109i	1.11350	−	1.92864i
$248$		0			0
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	5.00000	−	1.73205i	0.314970	−	0.109109i
$253$	4.00000			0.251478
$254$	−13.0000	+	22.5167i	−0.815693	+	1.41282i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	−0.713878	−	0.700270i	$-0.753063\pi$
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	0.963391	+	0.268101i	$0.0863961\pi$
$258$	−18.0000			−1.12063
$259$	−3.50000	+	18.1865i	−0.217479	+	1.13006i
$260$		0			0
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$	−4.00000	−	6.92820i	−0.247121	−	0.428026i
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		0			0
$265$		0			0
$266$	28.0000	+	24.2487i	1.71679	+	1.48678i
$267$	−6.00000			−0.367194
$268$	−7.00000	+	12.1244i	−0.427593	+	0.740613i
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	−24.0000			−1.45521
$273$	−10.0000	−	8.66025i	−0.605228	−	0.524142i
$274$	20.0000			1.20824
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	11.0000	−	19.0526i	0.659736	−	1.14270i
$279$	−7.00000			−0.419079
$280$		0			0
$281$	24.0000			1.43172			0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000			1.43172			0.715860	+	0.698244i	$0.246035\pi$
$282$	−6.00000	+	10.3923i	−0.357295	+	0.618853i
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	−0.973873	−	0.227092i	$-0.927078\pi$
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	0.290269	−	0.956945i	$-0.406255\pi$
$284$	−8.00000	−	13.8564i	−0.474713	−	0.822226i
$285$		0			0
$286$	−10.0000			−0.591312
$287$	10.0000	−	3.46410i	0.590281	−	0.204479i
$288$	8.00000			0.471405
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$	11.0000	−	8.66025i	0.641533	−	0.505076i
$295$		0			0
$296$		0			0
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	−6.00000	−	10.3923i	−0.347571	−	0.602010i
$299$	−10.0000	+	17.3205i	−0.578315	+	1.00167i
$300$	10.0000			0.577350
$301$	−22.5000	+	7.79423i	−1.29688	+	0.449252i
$302$	32.0000			1.84139
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$	14.0000	+	24.2487i	0.802955	+	1.39076i
$305$		0			0
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$	1.00000	−	5.19615i	0.0569803	−	0.296078i
$309$	19.0000			1.08087
$310$		0			0
$311$	8.00000	+	13.8564i	0.453638	+	0.785725i	0.998609	−	0.0527306i	$-0.0167924\pi$
$311$	8.00000	+	13.8564i	0.453638	+	0.785725i	−0.544970	+	0.838455i	$0.683459\pi$
$312$		0			0
$313$	−1.50000	+	2.59808i	−0.0847850	+	0.146852i	−0.905300	−	0.424774i	$-0.860354\pi$
$313$	−1.50000	+	2.59808i	−0.0847850	+	0.146852i	0.820515	+	0.571626i	$0.193687\pi$
$314$	28.0000			1.58013
$315$		0			0
$316$	−22.0000			−1.23760
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$	2.00000	+	3.46410i	0.112154	+	0.194257i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$		0			0
$321$	20.0000			1.11629
$322$	−16.0000	−	13.8564i	−0.891645	−	0.772187i
$323$	42.0000			2.33694
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$	−12.5000	−	21.6506i	−0.693375	−	1.20096i
$326$	−8.00000	−	13.8564i	−0.443079	−	0.767435i
$327$	−0.500000	+	0.866025i	−0.0276501	+	0.0478913i
$328$		0			0
$329$	−3.00000	+	15.5885i	−0.165395	+	0.859419i
$330$		0			0
$331$	16.5000	−	28.5788i	0.906922	−	1.57084i	0.0886058	−	0.996067i	$-0.471759\pi$
$331$	16.5000	−	28.5788i	0.906922	−	1.57084i	0.818316	−	0.574768i	$-0.194908\pi$
$332$	4.00000	+	6.92820i	0.219529	+	0.380235i
$333$	−3.50000	−	6.06218i	−0.191799	−	0.332205i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$		0			0
$336$	10.0000	−	3.46410i	0.545545	−	0.188982i
$337$	−17.0000			−0.926049			−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000			−0.926049			−0.463025	+	0.886345i	$0.653236\pi$
$338$	12.0000	−	20.7846i	0.652714	−	1.13053i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	−3.50000	+	6.06218i	−0.189536	+	0.328285i
$342$	−14.0000			−0.757033
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$	−10.0000	−	17.3205i	−0.537603	−	0.931156i
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	0.837935	−	0.545770i	$-0.183763\pi$
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	−0.891618	+	0.452788i	$0.850429\pi$
$348$	−2.00000	+	3.46410i	−0.107211	+	0.185695i
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$	25.0000	−	8.66025i	1.33631	−	0.462910i
$351$	5.00000			0.266880
$352$	4.00000	−	6.92820i	0.213201	−	0.369274i
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$354$	−12.0000	−	20.7846i	−0.637793	−	1.10469i
$355$		0			0
$356$	12.0000			0.635999
$357$	3.00000	−	15.5885i	0.158777	−	0.825029i
$358$	32.0000			1.69125
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.204595	+	0.978847i	$0.565588\pi$
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.745409	+	0.666608i	$0.767746\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	−1.00000			−0.0524864
$364$	20.0000	+	17.3205i	1.04828	+	0.907841i
$365$		0			0
$366$	2.00000	−	3.46410i	0.104542	−	0.181071i
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$	−8.00000	−	13.8564i	−0.417029	−	0.722315i
$369$	−2.00000	+	3.46410i	−0.104116	+	0.180334i
$370$		0			0
$371$	4.00000	+	3.46410i	0.207670	+	0.179847i
$372$	14.0000			0.725866
$373$	−10.5000	+	18.1865i	−0.543669	+	0.941663i	0.455020	+	0.890481i	$0.349632\pi$
$373$	−10.5000	+	18.1865i	−0.543669	+	0.941663i	−0.998689	+	0.0511818i	$0.983701\pi$
$374$	−6.00000	−	10.3923i	−0.310253	−	0.537373i
$375$		0			0
$376$		0			0
$377$	10.0000			0.515026
$378$	−1.00000	+	5.19615i	−0.0514344	+	0.267261i
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$	−6.50000	−	11.2583i	−0.333005	−	0.576782i
$382$	22.0000	+	38.1051i	1.12562	+	1.94963i
$383$	19.0000	−	32.9090i	0.970855	−	1.68157i	0.277868	−	0.960619i	$-0.410372\pi$
$383$	19.0000	−	32.9090i	0.970855	−	1.68157i	0.692987	−	0.720950i	$-0.256294\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$	4.50000	−	7.79423i	0.228748	−	0.396203i
$388$	−2.00000	−	3.46410i	−0.101535	−	0.175863i
$389$	−11.0000	−	19.0526i	−0.557722	−	0.966003i	−0.997686	−	0.0679877i	$-0.978342\pi$
$389$	−11.0000	−	19.0526i	−0.557722	−	0.966003i	0.439964	−	0.898015i	$-0.354991\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$		0			0
$393$	4.00000			0.201773
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$		0			0
$396$	1.00000	+	1.73205i	0.0502519	+	0.0870388i
$397$	−13.5000	+	23.3827i	−0.677546	+	1.17354i	0.298172	+	0.954512i	$0.403623\pi$
$397$	−13.5000	+	23.3827i	−0.677546	+	1.17354i	−0.975718	+	0.219031i	$0.929710\pi$
$398$	−8.00000			−0.401004
$399$	−17.5000	+	6.06218i	−0.876096	+	0.303488i
$400$	20.0000			1.00000
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.0699455	+	0.997551i	$0.522283\pi$
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.828932	+	0.559350i	$0.811051\pi$
$402$	−7.00000	−	12.1244i	−0.349128	−	0.604708i
$403$	−17.5000	−	30.3109i	−0.871737	−	1.50989i
$404$	2.00000	−	3.46410i	0.0995037	−	0.172345i
$405$		0			0
$406$	−2.00000	+	10.3923i	−0.0992583	+	0.515761i
$407$	−7.00000			−0.346977
$408$		0			0
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$		0			0
$411$	−5.00000	+	8.66025i	−0.246632	+	0.427179i
$412$	−38.0000			−1.87213
$413$	−24.0000	−	20.7846i	−1.18096	−	1.02274i
$414$	8.00000			0.393179
$415$		0			0
$416$	20.0000	+	34.6410i	0.980581	+	1.69842i
$417$	5.50000	+	9.52628i	0.269336	+	0.466504i
$418$	−7.00000	+	12.1244i	−0.342381	+	0.593022i
$419$	−8.00000			−0.390826			−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000			−0.390826			−0.195413	+	0.980721i	$0.562605\pi$
$420$		0			0
$421$	9.00000			0.438633			0.219317	−	0.975654i	$-0.429617\pi$
$421$	9.00000			0.438633			0.219317	+	0.975654i	$0.429617\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	15.0000	−	25.9808i	0.727607	−	1.26025i
$426$	16.0000			0.775203
$427$	1.00000	−	5.19615i	0.0483934	−	0.251459i
$428$	−40.0000			−1.93347
$429$	2.50000	−	4.33013i	0.120701	−	0.209061i
$430$		0			0
$431$	−5.00000	−	8.66025i	−0.240842	−	0.417150i	0.720113	−	0.693857i	$-0.244090\pi$
$431$	−5.00000	−	8.66025i	−0.240842	−	0.417150i	−0.960954	+	0.276707i	$0.910757\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	19.0000			0.913082			0.456541	−	0.889702i	$-0.349088\pi$
$433$	19.0000			0.913082			0.456541	+	0.889702i	$0.349088\pi$
$434$	35.0000	−	12.1244i	1.68005	−	0.581988i
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	14.0000	+	24.2487i	0.669711	+	1.15997i
$438$	5.00000	+	8.66025i	0.238909	+	0.413803i
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	60.0000			2.85391
$443$	−11.0000	+	19.0526i	−0.522626	+	0.905214i	0.477028	+	0.878888i	$0.341714\pi$
$443$	−11.0000	+	19.0526i	−0.522626	+	0.905214i	−0.999653	+	0.0263261i	$0.991619\pi$
$444$	7.00000	+	12.1244i	0.332205	+	0.575396i
$445$		0			0
$446$		0			0
$447$	6.00000			0.283790
$448$	−20.0000	+	6.92820i	−0.944911	+	0.327327i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−5.00000	+	8.66025i	−0.235702	+	0.408248i
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	−8.00000	+	13.8564i	−0.375873	+	0.651031i
$454$	−28.0000			−1.31411
$455$		0			0
$456$		0			0
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	−0.898974	−	0.438001i	$-0.855687\pi$
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	0.828807	+	0.559534i	$0.189020\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$		0			0
$461$	−36.0000			−1.67669			−0.838344	−	0.545142i	$-0.816476\pi$
$461$	−36.0000			−1.67669			−0.838344	+	0.545142i	$0.816476\pi$
$462$	4.00000	+	3.46410i	0.186097	+	0.161165i
$463$	−29.0000			−1.34774			−0.673872	−	0.738848i	$-0.735370\pi$
$463$	−29.0000			−1.34774			−0.673872	+	0.738848i	$0.735370\pi$
$464$	−4.00000	+	6.92820i	−0.185695	+	0.321634i
$465$		0			0
$466$	−20.0000	−	34.6410i	−0.926482	−	1.60471i
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	−0.943610	−	0.331061i	$-0.892594\pi$
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	0.758512	+	0.651660i	$0.225927\pi$
$468$	−10.0000			−0.462250
$469$	−14.0000	−	12.1244i	−0.646460	−	0.559851i
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$		0			0
$473$	−4.50000	−	7.79423i	−0.206910	−	0.358379i
$474$	11.0000	−	19.0526i	0.505247	−	0.875113i
$475$	−35.0000			−1.60591
$476$	−6.00000	+	31.1769i	−0.275010	+	1.42899i
$477$	−2.00000			−0.0915737
$478$	−24.0000	+	41.5692i	−1.09773	+	1.90133i
$479$	19.0000	+	32.9090i	0.868132	+	1.50365i	0.863903	+	0.503658i	$0.168013\pi$
$479$	19.0000	+	32.9090i	0.868132	+	1.50365i	0.00422900	+	0.999991i	$0.498654\pi$
$480$		0			0
$481$	17.5000	−	30.3109i	0.797931	−	1.38206i
$482$	20.0000			0.910975
$483$	10.0000	−	3.46410i	0.455016	−	0.157622i
$484$	2.00000			0.0909091
$485$		0			0
$486$	−1.00000	−	1.73205i	−0.0453609	−	0.0785674i
$487$	14.5000	+	25.1147i	0.657058	+	1.13806i	0.981374	+	0.192109i	$0.0615326\pi$
$487$	14.5000	+	25.1147i	0.657058	+	1.13806i	−0.324316	+	0.945949i	$0.605134\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$	4.00000	−	6.92820i	0.180334	−	0.312348i
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$	−35.0000	−	60.6218i	−1.57472	−	2.72750i
$495$		0			0
$496$	28.0000			1.25724
$497$	20.0000	−	6.92820i	0.897123	−	0.310772i
$498$	−8.00000			−0.358489
$499$	−6.50000	+	11.2583i	−0.290980	+	0.503992i	−0.974042	−	0.226369i	$-0.927315\pi$
$499$	−6.50000	+	11.2583i	−0.290980	+	0.503992i	0.683062	+	0.730361i	$0.260648\pi$
$500$		0			0
$501$	−3.00000	−	5.19615i	−0.134030	−	0.232147i
$502$	−18.0000	+	31.1769i	−0.803379	+	1.39149i
$503$	−44.0000			−1.96186			−0.980932	−	0.194354i	$-0.937739\pi$
$503$	−44.0000			−1.96186			−0.980932	+	0.194354i	$0.937739\pi$
$504$		0			0
$505$		0			0
$506$	4.00000	−	6.92820i	0.177822	−	0.307996i
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	13.0000	+	22.5167i	0.576782	+	0.999015i
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	10.0000	+	8.66025i	0.442374	+	0.383107i
$512$	−32.0000			−1.41421
$513$	3.50000	−	6.06218i	0.154529	−	0.267652i
$514$	−8.00000	−	13.8564i	−0.352865	−	0.611180i
$515$		0			0
$516$	−9.00000	+	15.5885i	−0.396203	+	0.686244i
$517$	−6.00000			−0.263880
$518$	28.0000	+	24.2487i	1.23025	+	1.06543i
$519$	10.0000			0.438951
$520$		0			0
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	0.517866	−	0.855462i	$-0.326727\pi$
$521$	−11.0000	−	19.0526i	−0.481919	−	0.834708i	−0.999785	+	0.0207541i	$0.993393\pi$
$522$	−2.00000	−	3.46410i	−0.0875376	−	0.151620i
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	−0.297884	−	0.954602i	$-0.596281\pi$
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	0.975652	−	0.219326i	$-0.0703858\pi$
$524$	−8.00000			−0.349482
$525$	−2.50000	+	12.9904i	−0.109109	+	0.566947i
$526$	36.0000			1.56967
$527$	21.0000	−	36.3731i	0.914774	−	1.58444i
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	12.0000			0.520756
$532$	35.0000	−	12.1244i	1.51744	−	0.525657i
$533$	−20.0000			−0.866296
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$		0			0
$536$		0			0
$537$	−8.00000	+	13.8564i	−0.345225	+	0.597948i
$538$	28.0000			1.20717
$539$	6.50000	+	2.59808i	0.279975	+	0.111907i
$540$		0			0
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	−0.980993	−	0.194043i	$-0.937840\pi$
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	0.658543	+	0.752543i	$0.271173\pi$
$542$	−20.0000	−	34.6410i	−0.859074	−	1.48796i
$543$	2.50000	+	4.33013i	0.107285	+	0.185824i
$544$	−24.0000	+	41.5692i	−1.02899	+	1.78227i
$545$		0			0
$546$	−25.0000	+	8.66025i	−1.06990	+	0.370625i
$547$	32.0000			1.36822			0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000			1.36822			0.684111	+	0.729378i	$0.260191\pi$
$548$	10.0000	−	17.3205i	0.427179	−	0.739895i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	5.00000	+	8.66025i	0.213201	+	0.369274i
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$		0			0
$553$	5.50000	−	28.5788i	0.233884	−	1.21530i
$554$	2.00000			0.0849719
$555$		0			0
$556$	−11.0000	−	19.0526i	−0.466504	−	0.808008i
$557$	18.0000	+	31.1769i	0.762684	+	1.32101i	0.941462	+	0.337119i	$0.109452\pi$
$557$	18.0000	+	31.1769i	0.762684	+	1.32101i	−0.178778	+	0.983890i	$0.557214\pi$
$558$	−7.00000	+	12.1244i	−0.296334	+	0.513265i
$559$	45.0000			1.90330
$560$		0			0
$561$	6.00000			0.253320
$562$	24.0000	−	41.5692i	1.01238	−	1.75349i
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$		0			0
$566$	−46.0000			−1.93352
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$		0			0
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	−17.5000	−	30.3109i	−0.732352	−	1.26847i	−0.955875	−	0.293773i	$-0.905089\pi$
$571$	−17.5000	−	30.3109i	−0.732352	−	1.26847i	0.223523	−	0.974699i	$-0.428244\pi$
$572$	−5.00000	+	8.66025i	−0.209061	+	0.362103i
$573$	−22.0000			−0.919063
$574$	4.00000	−	20.7846i	0.166957	−	0.867533i
$575$	20.0000			0.834058
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	0.986922	−	0.161198i	$-0.0515357\pi$
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	−0.633062	+	0.774101i	$0.718202\pi$
$578$	19.0000	+	32.9090i	0.790296	+	1.36883i
$579$	−3.50000	+	6.06218i	−0.145455	+	0.251936i
$580$		0			0
$581$	−10.0000	+	3.46410i	−0.414870	+	0.143715i
$582$	4.00000			0.165805
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$		0			0
$585$		0			0
$586$	12.0000	−	20.7846i	0.495715	−	0.858604i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$	−2.00000	−	13.8564i	−0.0824786	−	0.571429i
$589$	−49.0000			−2.01901
$590$		0			0
$591$	−2.00000	−	3.46410i	−0.0822690	−	0.142494i
$592$	14.0000	+	24.2487i	0.575396	+	0.996616i
$593$	13.0000	−	22.5167i	0.533846	−	0.924648i	−0.465372	−	0.885115i	$-0.654080\pi$
$593$	13.0000	−	22.5167i	0.533846	−	0.924648i	0.999218	−	0.0395334i	$-0.0125871\pi$
$594$	−2.00000			−0.0820610
$595$		0			0
$596$	−12.0000			−0.491539
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	20.0000	+	34.6410i	0.817861	+	1.41658i
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	0.745613	−	0.666379i	$-0.232157\pi$
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	−0.949908	+	0.312531i	$0.898823\pi$
$600$		0			0
$601$	−15.0000			−0.611863			−0.305931	−	0.952054i	$-0.598968\pi$
$601$	−15.0000			−0.611863			−0.305931	+	0.952054i	$0.598968\pi$
$602$	−9.00000	+	46.7654i	−0.366813	+	1.90601i
$603$	7.00000			0.285062
$604$	16.0000	−	27.7128i	0.651031	−	1.12762i
$605$		0			0
$606$	2.00000	+	3.46410i	0.0812444	+	0.140720i
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	−0.967256	−	0.253804i	$-0.918318\pi$
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	0.703429	+	0.710766i	$0.251651\pi$
$608$	56.0000			2.27110
$609$	−4.00000	−	3.46410i	−0.162088	−	0.140372i
$610$		0			0
$611$	15.0000	−	25.9808i	0.606835	−	1.05107i
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	0.972924	+	0.231127i	$0.0742412\pi$
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	−0.286300	+	0.958140i	$0.592425\pi$
$614$	−3.00000	+	5.19615i	−0.121070	+	0.209700i
$615$		0			0
$616$		0			0
$617$	−24.0000			−0.966204			−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000			−0.966204			−0.483102	+	0.875564i	$0.660490\pi$
$618$	19.0000	−	32.9090i	0.764292	−	1.32379i
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	0.996138	−	0.0878015i	$-0.0279841\pi$
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	−0.574107	+	0.818780i	$0.694651\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	32.0000			1.28308
$623$	−3.00000	+	15.5885i	−0.120192	+	0.624538i
$624$	−20.0000			−0.800641
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	−3.50000	−	6.06218i	−0.139777	−	0.242100i
$628$	14.0000	−	24.2487i	0.558661	−	0.967629i
$629$	42.0000			1.67465
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$		0			0
$636$	4.00000			0.158610
$637$	−27.5000	+	21.6506i	−1.08959	+	0.857829i
$638$	−4.00000			−0.158362
$639$	−4.00000	+	6.92820i	−0.158238	+	0.274075i
$640$		0			0
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$	20.0000	−	34.6410i	0.789337	−	1.36717i
$643$	21.0000			0.828159			0.414080	−	0.910241i	$-0.364104\pi$
$643$	21.0000			0.828159			0.414080	+	0.910241i	$0.364104\pi$
$644$	−20.0000	+	6.92820i	−0.788110	+	0.273009i
$645$		0			0
$646$	42.0000	−	72.7461i	1.65247	−	2.86216i
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	0.801010	−	0.598651i	$-0.204296\pi$
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	−0.918952	+	0.394369i	$0.870963\pi$
$648$		0			0
$649$	6.00000	−	10.3923i	0.235521	−	0.407934i
$650$	−50.0000			−1.96116
$651$	−3.50000	+	18.1865i	−0.137176	+	0.712786i
$652$	−16.0000			−0.626608
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$		0			0
$656$	8.00000	−	13.8564i	0.312348	−	0.541002i
$657$	−5.00000			−0.195069
$658$	24.0000	+	20.7846i	0.935617	+	0.810268i
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$		0			0
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	0.739014	−	0.673690i	$-0.235292\pi$
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	−0.952940	+	0.303160i	$0.901958\pi$
$662$	−33.0000	−	57.1577i	−1.28258	−	2.22150i
$663$	−15.0000	+	25.9808i	−0.582552	+	1.00901i
$664$		0			0
$665$		0			0
$666$	−14.0000			−0.542489
$667$	−4.00000	+	6.92820i	−0.154881	+	0.268261i
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$		0			0
$670$		0			0
$671$	2.00000			0.0772091
$672$	4.00000	−	20.7846i	0.154303	−	0.801784i
$673$	1.00000			0.0385472			0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000			0.0385472			0.0192736	+	0.999814i	$0.493865\pi$
$674$	−17.0000	+	29.4449i	−0.654816	+	1.13417i
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	−12.0000	−	20.7846i	−0.461538	−	0.799408i
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	−0.957984	−	0.286820i	$-0.907402\pi$
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	0.727386	+	0.686229i	$0.240735\pi$
$678$	−12.0000			−0.460857
$679$	5.00000	−	1.73205i	0.191882	−	0.0664700i
$680$		0			0
$681$	7.00000	−	12.1244i	0.268241	−	0.464606i
$682$	7.00000	+	12.1244i	0.268044	+	0.464266i
$683$	20.0000	+	34.6410i	0.765279	+	1.32550i	0.940099	+	0.340901i	$0.110732\pi$
$683$	20.0000	+	34.6410i	0.765279	+	1.32550i	−0.174820	+	0.984600i	$0.555934\pi$
$684$	−7.00000	+	12.1244i	−0.267652	+	0.463586i
$685$		0			0
$686$	−17.0000	−	32.9090i	−0.649063	−	1.25647i
$687$	−5.00000			−0.190762
$688$	−18.0000	+	31.1769i	−0.686244	+	1.18861i
$689$	−5.00000	−	8.66025i	−0.190485	−	0.329929i
$690$		0			0
$691$	2.50000	−	4.33013i	0.0951045	−	0.164726i	−0.814548	−	0.580097i	$-0.803015\pi$
$691$	2.50000	−	4.33013i	0.0951045	−	0.164726i	0.909652	+	0.415371i	$0.136348\pi$
$692$	−20.0000			−0.760286
$693$	−2.50000	+	0.866025i	−0.0949671	+	0.0328976i
$694$	−4.00000			−0.151838
$695$		0			0
$696$		0			0
$697$	−12.0000	−	20.7846i	−0.454532	−	0.787273i
$698$	6.00000	−	10.3923i	0.227103	−	0.393355i
$699$	20.0000			0.756469
$700$	5.00000	−	25.9808i	0.188982	−	0.981981i
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$	5.00000	−	8.66025i	0.188713	−	0.326860i
$703$	−24.5000	−	42.4352i	−0.924035	−	1.60048i
$704$	−4.00000	−	6.92820i	−0.150756	−	0.261116i
$705$		0			0
$706$	−60.0000			−2.25813
$707$	4.00000	+	3.46410i	0.150435	+	0.130281i
$708$	−24.0000			−0.901975
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	0.433865	+	0.900978i	$0.357149\pi$
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	−0.997202	+	0.0747503i	$0.976184\pi$
$710$		0			0
$711$	5.50000	+	9.52628i	0.206266	+	0.357263i
$712$		0			0
$713$	28.0000			1.04861
$714$	−24.0000	−	20.7846i	−0.898177	−	0.777844i
$715$		0			0
$716$	16.0000	−	27.7128i	0.597948	−	1.03568i
$717$	−12.0000	−	20.7846i	−0.448148	−	0.776215i
$718$	36.0000	+	62.3538i	1.34351	+	2.32702i
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$		0			0
$721$	9.50000	−	49.3634i	0.353798	−	1.83839i
$722$	−60.0000			−2.23297
$723$	−5.00000	+	8.66025i	−0.185952	+	0.322078i
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	−5.00000	−	8.66025i	−0.185695	−	0.321634i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	−5.00000			−0.185440			−0.0927199	−	0.995692i	$-0.529556\pi$
$727$	−5.00000			−0.185440			−0.0927199	+	0.995692i	$0.529556\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	27.0000	+	46.7654i	0.998631	+	1.72968i
$732$	−2.00000	−	3.46410i	−0.0739221	−	0.128037i
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	−0.720655	−	0.693294i	$-0.756159\pi$
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	0.960738	+	0.277458i	$0.0894920\pi$
$734$	34.0000			1.25496
$735$		0			0
$736$	−32.0000			−1.17954
$737$	3.50000	−	6.06218i	0.128924	−	0.223303i
$738$	4.00000	+	6.92820i	0.147242	+	0.255031i
$739$	16.5000	+	28.5788i	0.606962	+	1.05129i	0.991738	+	0.128279i	$0.0409454\pi$
$739$	16.5000	+	28.5788i	0.606962	+	1.05129i	−0.384776	+	0.923010i	$0.625721\pi$
$740$		0			0
$741$	35.0000			1.28576
$742$	10.0000	−	3.46410i	0.367112	−	0.127171i
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$		0			0
$745$		0			0
$746$	21.0000	+	36.3731i	0.768865	+	1.33171i
$747$	2.00000	−	3.46410i	0.0731762	−	0.126745i
$748$	−12.0000			−0.438763
$749$	10.0000	−	51.9615i	0.365392	−	1.89863i
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$	12.0000	+	20.7846i	0.437595	+	0.757937i
$753$	−9.00000	−	15.5885i	−0.327978	−	0.568075i
$754$	10.0000	−	17.3205i	0.364179	−	0.630776i
$755$		0			0
$756$	4.00000	+	3.46410i	0.145479	+	0.125988i
$757$	30.0000			1.09037			0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000			1.09037			0.545184	+	0.838316i	$0.316460\pi$
$758$	−5.00000	+	8.66025i	−0.181608	+	0.314555i
$759$	2.00000	+	3.46410i	0.0725954	+	0.125739i
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$	−26.0000			−0.941881
$763$	2.00000	+	1.73205i	0.0724049	+	0.0627044i
$764$	44.0000			1.59186
$765$		0			0
$766$	−38.0000	−	65.8179i	−1.37300	−	2.37810i
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$	8.00000	−	13.8564i	0.288675	−	0.500000i
$769$	−3.00000			−0.108183			−0.0540914	−	0.998536i	$-0.517226\pi$
$769$	−3.00000			−0.108183			−0.0540914	+	0.998536i	$0.517226\pi$
$770$		0			0
$771$	8.00000			0.288113
$772$	7.00000	−	12.1244i	0.251936	−	0.436365i
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$	−9.00000	−	15.5885i	−0.323498	−	0.560316i
$775$	−17.5000	+	30.3109i	−0.628619	+	1.08880i
$776$		0			0
$777$	−17.5000	+	6.06218i	−0.627809	+	0.217479i
$778$	−44.0000

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{12} -5.00000 q^{13} +(1.00000 - 5.19615i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(2.00000 + 1.73205i) q^{21} +2.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-5.00000 + 8.66025i) q^{26} -1.00000 q^{27} +(-4.00000 - 3.46410i) q^{28} -2.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(-0.500000 + 0.866025i) q^{33} -12.0000 q^{34} +2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(7.00000 + 12.1244i) q^{38} +(-2.50000 - 4.33013i) q^{39} +4.00000 q^{41} +(5.00000 - 1.73205i) q^{42} -9.00000 q^{43} +(1.00000 - 1.73205i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(-3.00000 + 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +10.0000 q^{50} +(3.00000 - 5.19615i) q^{51} +(5.00000 + 8.66025i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-1.00000 + 1.73205i) q^{54} -7.00000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +14.0000 q^{62} +(-0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(1.00000 + 1.73205i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(-6.00000 + 10.3923i) q^{68} +4.00000 q^{69} +8.00000 q^{71} +(2.50000 + 4.33013i) q^{73} +(7.00000 + 12.1244i) q^{74} +(-2.50000 + 4.33013i) q^{75} +14.0000 q^{76} +(2.00000 + 1.73205i) q^{77} -10.0000 q^{78} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.00000 - 6.92820i) q^{82} -4.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +(-9.00000 + 15.5885i) q^{86} +(-1.00000 - 1.73205i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-12.5000 + 4.33013i) q^{91} -8.00000 q^{92} +(-3.50000 + 6.06218i) q^{93} +(6.00000 + 10.3923i) q^{94} +(4.00000 - 6.92820i) q^{96} +2.00000 q^{97} +(-2.00000 - 13.8564i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9	\( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9} + q^{11} + 2 q^{12} - 10 q^{13} + 2 q^{14} + 4 q^{16} - 6 q^{17} + 2 q^{18} - 7 q^{19} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 5 q^{25} - 10 q^{26} - 2 q^{27} - 8 q^{28} - 4 q^{29} + 7 q^{31} - 8 q^{32} - q^{33} - 24 q^{34} + 4 q^{36} - 7 q^{37} + 14 q^{38} - 5 q^{39} + 8 q^{41} + 10 q^{42} - 18 q^{43} + 2 q^{44} - 8 q^{46} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 20 q^{50} + 6 q^{51} + 10 q^{52} + 2 q^{53} - 2 q^{54} - 14 q^{57} - 4 q^{58} - 12 q^{59} + 2 q^{61} + 28 q^{62} - q^{63} - 16 q^{64} + 2 q^{66} - 7 q^{67} - 12 q^{68} + 8 q^{69} + 16 q^{71} + 5 q^{73} + 14 q^{74} - 5 q^{75} + 28 q^{76} + 4 q^{77} - 20 q^{78} + 11 q^{79} - q^{81} + 8 q^{82} - 8 q^{83} + 2 q^{84} - 18 q^{86} - 2 q^{87} - 6 q^{89} - 25 q^{91} - 16 q^{92} - 7 q^{93} + 12 q^{94} + 8 q^{96} + 4 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 5 * q^7 - q^9 + q^11 + 2 * q^12 - 10 * q^13 + 2 * q^14 + 4 * q^16 - 6 * q^17 + 2 * q^18 - 7 * q^19 + 4 * q^21 + 4 * q^22 + 4 * q^23 + 5 * q^25 - 10 * q^26 - 2 * q^27 - 8 * q^28 - 4 * q^29 + 7 * q^31 - 8 * q^32 - q^33 - 24 * q^34 + 4 * q^36 - 7 * q^37 + 14 * q^38 - 5 * q^39 + 8 * q^41 + 10 * q^42 - 18 * q^43 + 2 * q^44 - 8 * q^46 - 6 * q^47 + 8 * q^48 + 11 * q^49 + 20 * q^50 + 6 * q^51 + 10 * q^52 + 2 * q^53 - 2 * q^54 - 14 * q^57 - 4 * q^58 - 12 * q^59 + 2 * q^61 + 28 * q^62 - q^63 - 16 * q^64 + 2 * q^66 - 7 * q^67 - 12 * q^68 + 8 * q^69 + 16 * q^71 + 5 * q^73 + 14 * q^74 - 5 * q^75 + 28 * q^76 + 4 * q^77 - 20 * q^78 + 11 * q^79 - q^81 + 8 * q^82 - 8 * q^83 + 2 * q^84 - 18 * q^86 - 2 * q^87 - 6 * q^89 - 25 * q^91 - 16 * q^92 - 7 * q^93 + 12 * q^94 + 8 * q^96 + 4 * q^97 - 4 * q^98 - 2 * q^99

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