LMFDB - Embedded newform 285.2.i.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.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:	$2.27573645761$
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			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.c.106.1

$q$-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} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} -2.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +1.00000 q^{11} -2.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} -2.00000 q^{18} +(0.500000 - 4.33013i) q^{19} -2.00000 q^{20} +(-1.00000 - 1.73205i) q^{21} +(1.00000 + 1.73205i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{26} -1.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(2.50000 - 4.33013i) q^{29} -2.00000 q^{30} +9.00000 q^{31} +(-4.00000 + 6.92820i) q^{32} +(0.500000 + 0.866025i) q^{33} +(2.00000 - 3.46410i) q^{34} +(-1.00000 - 1.73205i) q^{35} +(-1.00000 - 1.73205i) q^{36} -6.00000 q^{37} +(8.00000 - 3.46410i) q^{38} -2.00000 q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{42} +(5.00000 + 8.66025i) q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} +8.00000 q^{46} +(-2.00000 + 3.46410i) q^{48} -3.00000 q^{49} -2.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{54} +(0.500000 + 0.866025i) q^{55} +(4.00000 - 1.73205i) q^{57} +10.0000 q^{58} +(-3.50000 - 6.06218i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(3.50000 - 6.06218i) q^{61} +(9.00000 + 15.5885i) q^{62} +(1.00000 - 1.73205i) q^{63} -8.00000 q^{64} -2.00000 q^{65} +(-1.00000 + 1.73205i) q^{66} +(-4.00000 + 6.92820i) q^{67} +4.00000 q^{68} +4.00000 q^{69} +(2.00000 - 3.46410i) q^{70} +(-1.50000 - 2.59808i) q^{71} +(1.00000 + 1.73205i) q^{73} +(-6.00000 - 10.3923i) q^{74} -1.00000 q^{75} +(7.00000 + 5.19615i) q^{76} -2.00000 q^{77} +(-2.00000 - 3.46410i) q^{78} +(5.50000 + 9.52628i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} +6.00000 q^{83} +4.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(-10.0000 + 17.3205i) q^{86} +5.00000 q^{87} +(-7.50000 + 12.9904i) q^{89} +(-1.00000 - 1.73205i) q^{90} +(2.00000 - 3.46410i) q^{91} +(4.00000 + 6.92820i) q^{92} +(4.50000 + 7.79423i) q^{93} +(4.00000 - 1.73205i) q^{95} -8.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{9} - 2 q^{10} + 2 q^{11} - 4 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + q^{19} - 4 q^{20} - 2 q^{21} + 2 q^{22}+ \cdots - q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 - 2 * q^4 + q^5 - 2 * q^6 - 4 * q^7 - q^9 - 2 * q^10 + 2 * q^11 - 4 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + q^19 - 4 * q^20 - 2 * q^21 + 2 * q^22 + 4 * q^23 - q^25 - 8 * q^26 - 2 * q^27 + 4 * q^28 + 5 * q^29 - 4 * q^30 + 18 * q^31 - 8 * q^32 + q^33 + 4 * q^34 - 2 * q^35 - 2 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^39 - 6 * q^41 + 4 * q^42 + 10 * q^43 - 2 * q^44 - 2 * q^45 + 16 * q^46 - 4 * q^48 - 6 * q^49 - 4 * q^50 + 2 * q^51 - 4 * q^52 + 2 * q^53 - 2 * q^54 + q^55 + 8 * q^57 + 20 * q^58 - 7 * q^59 - 2 * q^60 + 7 * q^61 + 18 * q^62 + 2 * q^63 - 16 * q^64 - 4 * q^65 - 2 * q^66 - 8 * q^67 + 8 * q^68 + 8 * q^69 + 4 * q^70 - 3 * q^71 + 2 * q^73 - 12 * q^74 - 2 * q^75 + 14 * q^76 - 4 * q^77 - 4 * q^78 + 11 * q^79 - 4 * q^80 - q^81 + 12 * q^82 + 12 * q^83 + 8 * q^84 + 2 * q^85 - 20 * q^86 + 10 * q^87 - 15 * q^89 - 2 * q^90 + 4 * q^91 + 8 * q^92 + 9 * q^93 + 8 * q^95 - 16 * q^96 - 8 * q^97 - 6 * q^98 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	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
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$	−2.00000			−0.577350
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−2.00000			−0.471405
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$20$	−2.00000			−0.447214
$21$	−1.00000	−	1.73205i	−0.218218	−	0.377964i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	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
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.00000			−0.784465
$27$	−1.00000			−0.192450
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$	−2.00000			−0.365148
$31$	9.00000			1.61645			0.808224	−	0.588875i	$-0.200429\pi$
$31$	9.00000			1.61645			0.808224	+	0.588875i	$0.200429\pi$
$32$	−4.00000	+	6.92820i	−0.707107	+	1.22474i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	8.00000	−	3.46410i	1.29777	−	0.561951i
$39$	−2.00000			−0.320256
$40$		0			0
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	2.00000	−	3.46410i	0.308607	−	0.534522i
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−1.00000			−0.149071
$46$	8.00000			1.17954
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−2.00000	+	3.46410i	−0.288675	+	0.500000i
$49$	−3.00000			−0.428571
$50$	−2.00000			−0.282843
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$	−1.00000	−	1.73205i	−0.136083	−	0.235702i
$55$	0.500000	+	0.866025i	0.0674200	+	0.116775i
$56$		0			0
$57$	4.00000	−	1.73205i	0.529813	−	0.229416i
$58$	10.0000			1.31306
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	0.543065	−	0.839691i	$-0.317264\pi$
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	−0.998726	+	0.0504625i	$0.983930\pi$
$60$	−1.00000	−	1.73205i	−0.129099	−	0.223607i
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	9.00000	+	15.5885i	1.14300	+	1.97974i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	−8.00000			−1.00000
$65$	−2.00000			−0.248069
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	4.00000			0.485071
$69$	4.00000			0.481543
$70$	2.00000	−	3.46410i	0.239046	−	0.414039i
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$		0			0
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$	−6.00000	−	10.3923i	−0.697486	−	1.20808i
$75$	−1.00000			−0.115470
$76$	7.00000	+	5.19615i	0.802955	+	0.596040i
$77$	−2.00000			−0.227921
$78$	−2.00000	−	3.46410i	−0.226455	−	0.392232i
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.00000	−	10.3923i	0.662589	−	1.14764i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	4.00000			0.436436
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	−10.0000	+	17.3205i	−1.07833	+	1.86772i
$87$	5.00000			0.536056
$88$		0			0
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$	−1.00000	−	1.73205i	−0.105409	−	0.182574i
$91$	2.00000	−	3.46410i	0.209657	−	0.363137i
$92$	4.00000	+	6.92820i	0.417029	+	0.722315i
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$		0			0
$95$	4.00000	−	1.73205i	0.410391	−	0.177705i
$96$	−8.00000			−0.816497
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	−0.500000	+	0.866025i	−0.0502519	+	0.0870388i
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	−0.637678	−	0.770303i	$-0.720105\pi$
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	0.985941	+	0.167094i	$0.0534383\pi$
$102$	4.00000			0.396059
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$	1.00000	−	1.73205i	0.0975900	−	0.169031i
$106$	4.00000			0.388514
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	1.00000	−	1.73205i	0.0962250	−	0.166667i
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.0957826	−	0.995402i	$-0.530535\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	−3.00000	−	5.19615i	−0.284747	−	0.493197i
$112$	−4.00000	−	6.92820i	−0.377964	−	0.654654i
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$	7.00000	+	5.19615i	0.655610	+	0.486664i
$115$	4.00000			0.373002
$116$	5.00000	+	8.66025i	0.464238	+	0.804084i
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$	7.00000	−	12.1244i	0.644402	−	1.11614i
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	14.0000			1.26750
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$	−9.00000	+	15.5885i	−0.808224	+	1.39988i
$125$	−1.00000			−0.0894427
$126$	4.00000			0.356348
$127$	−2.00000	+	3.46410i	−0.177471	+	0.307389i	−0.941014	−	0.338368i	$-0.890125\pi$
$127$	−2.00000	+	3.46410i	−0.177471	+	0.307389i	0.763542	+	0.645758i	$0.223458\pi$
$128$		0			0
$129$	−5.00000	+	8.66025i	−0.440225	+	0.762493i
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	−8.00000	−	13.8564i	−0.698963	−	1.21064i	−0.968826	−	0.247741i	$-0.920312\pi$
$131$	−8.00000	−	13.8564i	−0.698963	−	1.21064i	0.269863	−	0.962899i	$-0.413022\pi$
$132$	−2.00000			−0.174078
$133$	−1.00000	+	8.66025i	−0.0867110	+	0.750939i
$134$	−16.0000			−1.38219
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$	4.00000	+	6.92820i	0.340503	+	0.589768i
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$	4.00000			0.338062
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$	−4.00000			−0.333333
$145$	5.00000			0.415227
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$	6.00000	−	10.3923i	0.493197	−	0.854242i
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	0.620701	−	0.784047i	$-0.286848\pi$
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	−0.989355	+	0.145519i	$0.953515\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	−3.00000			−0.244137			−0.122068	−	0.992522i	$-0.538953\pi$
$151$	−3.00000			−0.244137			−0.122068	+	0.992522i	$0.538953\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$	−2.00000	−	3.46410i	−0.161165	−	0.279145i
$155$	4.50000	+	7.79423i	0.361449	+	0.626048i
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−6.00000	−	10.3923i	−0.478852	−	0.829396i	0.520854	−	0.853646i	$-0.325614\pi$
$157$	−6.00000	−	10.3923i	−0.478852	−	0.829396i	−0.999706	+	0.0242497i	$0.992280\pi$
$158$	−11.0000	+	19.0526i	−0.875113	+	1.51574i
$159$	2.00000			0.158610
$160$	−8.00000			−0.632456
$161$	−4.00000	+	6.92820i	−0.315244	+	0.546019i
$162$	1.00000	−	1.73205i	0.0785674	−	0.136083i
$163$	−18.0000			−1.40987			−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000			−1.40987			−0.704934	+	0.709273i	$0.749024\pi$
$164$	12.0000			0.937043
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	−0.824737	−	0.565516i	$-0.808677\pi$
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	0.902120	+	0.431486i	$0.142010\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	4.00000			0.306786
$171$	3.50000	+	2.59808i	0.267652	+	0.198680i
$172$	−20.0000			−1.52499
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	5.00000	+	8.66025i	0.379049	+	0.656532i
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	2.00000	+	3.46410i	0.150756	+	0.261116i
$177$	3.50000	−	6.06218i	0.263076	−	0.455661i
$178$	−30.0000			−2.24860
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	−5.00000	+	8.66025i	−0.371647	+	0.643712i	−0.989819	−	0.142331i	$-0.954540\pi$
$181$	−5.00000	+	8.66025i	−0.371647	+	0.643712i	0.618172	+	0.786043i	$0.287874\pi$
$182$	8.00000			0.592999
$183$	7.00000			0.517455
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$	−9.00000	+	15.5885i	−0.659912	+	1.14300i
$187$	−1.00000	−	1.73205i	−0.0731272	−	0.126660i
$188$		0			0
$189$	2.00000			0.145479
$190$	7.00000	+	5.19615i	0.507833	+	0.376969i
$191$	15.0000			1.08536			0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000			1.08536			0.542681	+	0.839939i	$0.317409\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	13.0000	+	22.5167i	0.935760	+	1.62078i	0.773272	+	0.634074i	$0.218619\pi$
$193$	13.0000	+	22.5167i	0.935760	+	1.62078i	0.162488	+	0.986710i	$0.448048\pi$
$194$	8.00000	−	13.8564i	0.574367	−	0.994832i
$195$	−1.00000	−	1.73205i	−0.0716115	−	0.124035i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$	−2.00000			−0.142134
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$		0			0
$201$	−8.00000			−0.564276
$202$	14.0000			0.985037
$203$	−5.00000	+	8.66025i	−0.350931	+	0.607831i
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−8.00000	−	13.8564i	−0.557386	−	0.965422i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	−8.00000			−0.554700
$209$	0.500000	−	4.33013i	0.0345857	−	0.299521i
$210$	4.00000			0.276026
$211$	13.5000	+	23.3827i	0.929378	+	1.60973i	0.784364	+	0.620301i	$0.212990\pi$
$211$	13.5000	+	23.3827i	0.929378	+	1.60973i	0.145014	+	0.989430i	$0.453677\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$	1.50000	−	2.59808i	0.102778	−	0.178017i
$214$		0			0
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$		0			0
$217$	−18.0000			−1.22192
$218$	19.0000	−	32.9090i	1.28684	−	2.22888i
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$	−2.00000			−0.134840
$221$	4.00000			0.269069
$222$	6.00000	−	10.3923i	0.402694	−	0.697486i
$223$	6.00000	+	10.3923i	0.401790	+	0.695920i	0.993942	−	0.109906i	$-0.0350549\pi$
$223$	6.00000	+	10.3923i	0.401790	+	0.695920i	−0.592152	+	0.805826i	$0.701722\pi$
$224$	8.00000	−	13.8564i	0.534522	−	0.925820i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−10.0000	−	17.3205i	−0.665190	−	1.15214i
$227$	18.0000			1.19470			0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000			1.19470			0.597351	+	0.801980i	$0.296220\pi$
$228$	−1.00000	+	8.66025i	−0.0662266	+	0.573539i
$229$	−11.0000			−0.726900			−0.363450	−	0.931614i	$-0.618401\pi$
$229$	−11.0000			−0.726900			−0.363450	+	0.931614i	$0.618401\pi$
$230$	4.00000	+	6.92820i	0.263752	+	0.456832i
$231$	−1.00000	−	1.73205i	−0.0657952	−	0.113961i
$232$		0			0
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	14.0000			0.911322
$237$	−5.50000	+	9.52628i	−0.357263	+	0.618798i
$238$	−4.00000	+	6.92820i	−0.259281	+	0.449089i
$239$	27.0000			1.74648			0.873242	−	0.487286i	$-0.162013\pi$
$239$	27.0000			1.74648			0.873242	+	0.487286i	$0.162013\pi$
$240$	−4.00000			−0.258199
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	−10.0000	−	17.3205i	−0.642824	−	1.11340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	12.0000			0.765092
$247$	7.00000	+	5.19615i	0.445399	+	0.330623i
$248$		0			0
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−1.00000	−	1.73205i	−0.0632456	−	0.109545i
$251$	8.50000	−	14.7224i	0.536515	−	0.929272i	−0.462573	−	0.886581i	$-0.653074\pi$
$251$	8.50000	−	14.7224i	0.536515	−	0.929272i	0.999088	−	0.0426905i	$-0.0135929\pi$
$252$	2.00000	+	3.46410i	0.125988	+	0.218218i
$253$	2.00000	−	3.46410i	0.125739	−	0.217786i
$254$	−8.00000			−0.501965
$255$	2.00000			0.125245
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	0.286909	+	0.957958i	$0.407372\pi$
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	−0.973070	+	0.230508i	$0.925961\pi$
$258$	−20.0000			−1.24515
$259$	12.0000			0.745644
$260$	2.00000	−	3.46410i	0.124035	−	0.214834i
$261$	2.50000	+	4.33013i	0.154746	+	0.268028i
$262$	16.0000	−	27.7128i	0.988483	−	1.71210i
$263$	−10.0000	−	17.3205i	−0.616626	−	1.06803i	−0.990097	−	0.140386i	$-0.955166\pi$
$263$	−10.0000	−	17.3205i	−0.616626	−	1.06803i	0.373470	−	0.927642i	$-0.378168\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	−16.0000	+	6.92820i	−0.981023	+	0.424795i
$267$	−15.0000			−0.917985
$268$	−8.00000	−	13.8564i	−0.488678	−	0.846415i
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	0.850380	−	0.526169i	$-0.176372\pi$
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	−0.880866	+	0.473366i	$0.843039\pi$
$270$	1.00000	−	1.73205i	0.0608581	−	0.105409i
$271$	−13.5000	−	23.3827i	−0.820067	−	1.42040i	−0.905632	−	0.424064i	$-0.860603\pi$
$271$	−13.5000	−	23.3827i	−0.820067	−	1.42040i	0.0855654	−	0.996333i	$-0.472730\pi$
$272$	4.00000	−	6.92820i	0.242536	−	0.420084i
$273$	4.00000			0.242091
$274$	12.0000			0.724947
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−4.00000	+	6.92820i	−0.240772	+	0.417029i
$277$	−8.00000			−0.480673			−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000			−0.480673			−0.240337	+	0.970690i	$0.577258\pi$
$278$	−40.0000			−2.39904
$279$	−4.50000	+	7.79423i	−0.269408	+	0.466628i
$280$		0			0
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	−0.158990	−	0.987280i	$-0.550824\pi$
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	0.934505	−	0.355951i	$-0.115843\pi$
$282$		0			0
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$	6.00000			0.356034
$285$	3.50000	+	2.59808i	0.207322	+	0.153897i
$286$	−4.00000			−0.236525
$287$	6.00000	+	10.3923i	0.354169	+	0.613438i
$288$	−4.00000	−	6.92820i	−0.235702	−	0.408248i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	5.00000	+	8.66025i	0.293610	+	0.508548i
$291$	4.00000	−	6.92820i	0.234484	−	0.406138i
$292$	−4.00000			−0.234082
$293$	−4.00000			−0.233682			−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000			−0.233682			−0.116841	+	0.993151i	$0.537277\pi$
$294$	3.00000	−	5.19615i	0.174964	−	0.303046i
$295$	3.50000	−	6.06218i	0.203778	−	0.352954i
$296$		0			0
$297$	−1.00000			−0.0580259
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$	1.00000	−	1.73205i	0.0577350	−	0.100000i
$301$	−10.0000	−	17.3205i	−0.576390	−	0.998337i
$302$	−3.00000	−	5.19615i	−0.172631	−	0.299005i
$303$	7.00000			0.402139
$304$	16.0000	−	6.92820i	0.917663	−	0.397360i
$305$	7.00000			0.400819
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$	12.0000	+	20.7846i	0.684876	+	1.18624i	0.973476	+	0.228790i	$0.0734771\pi$
$307$	12.0000	+	20.7846i	0.684876	+	1.18624i	−0.288600	+	0.957450i	$0.593190\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$	−4.00000	−	6.92820i	−0.227552	−	0.394132i
$310$	−9.00000	+	15.5885i	−0.511166	+	0.885365i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	10.0000	−	17.3205i	0.565233	−	0.979013i	−0.431795	−	0.901972i	$-0.642119\pi$
$313$	10.0000	−	17.3205i	0.565233	−	0.979013i	0.997028	−	0.0770410i	$-0.0245472\pi$
$314$	12.0000	−	20.7846i	0.677199	−	1.17294i
$315$	2.00000			0.112687
$316$	−22.0000			−1.23760
$317$	−16.0000	+	27.7128i	−0.898650	+	1.55651i	−0.0694277	+	0.997587i	$0.522117\pi$
$317$	−16.0000	+	27.7128i	−0.898650	+	1.55651i	−0.829222	+	0.558920i	$0.811216\pi$
$318$	2.00000	+	3.46410i	0.112154	+	0.194257i
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$		0			0
$322$	−16.0000			−0.891645
$323$	−8.00000	+	3.46410i	−0.445132	+	0.192748i
$324$	2.00000			0.111111
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	−18.0000	−	31.1769i	−0.996928	−	1.72673i
$327$	9.50000	−	16.4545i	0.525351	−	0.909935i
$328$		0			0
$329$		0			0
$330$	−2.00000			−0.110096
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	3.00000	−	5.19615i	0.164399	−	0.284747i
$334$	4.00000			0.218870
$335$	−8.00000			−0.437087
$336$	4.00000	−	6.92820i	0.218218	−	0.377964i
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	0.954164	−	0.299285i	$-0.0967480\pi$
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	−0.736270	+	0.676688i	$0.763415\pi$
$338$	−9.00000	+	15.5885i	−0.489535	+	0.847900i
$339$	−5.00000	−	8.66025i	−0.271563	−	0.470360i
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	9.00000			0.487377
$342$	−1.00000	+	8.66025i	−0.0540738	+	0.468293i
$343$	20.0000			1.07990
$344$		0			0
$345$	2.00000	+	3.46410i	0.107676	+	0.186501i
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	0.994164	+	0.107883i	$0.0344071\pi$
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	−0.403653	+	0.914912i	$0.632260\pi$
$348$	−5.00000	+	8.66025i	−0.268028	+	0.464238i
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$	4.00000			0.213809
$351$	1.00000	−	1.73205i	0.0533761	−	0.0924500i
$352$	−4.00000	+	6.92820i	−0.213201	+	0.369274i
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$	14.0000			0.744092
$355$	1.50000	−	2.59808i	0.0796117	−	0.137892i
$356$	−15.0000	−	25.9808i	−0.794998	−	1.37698i
$357$	−2.00000	+	3.46410i	−0.105851	+	0.183340i
$358$	−3.00000	−	5.19615i	−0.158555	−	0.274625i
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	0.952063	−	0.305903i	$-0.0989582\pi$
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	−0.740951	+	0.671559i	$0.765625\pi$
$360$		0			0
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	−20.0000			−1.05118
$363$	−5.00000	−	8.66025i	−0.262432	−	0.454545i
$364$	4.00000	+	6.92820i	0.209657	+	0.363137i
$365$	−1.00000	+	1.73205i	−0.0523424	+	0.0906597i
$366$	7.00000	+	12.1244i	0.365896	+	0.633750i
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	−0.477677	−	0.878536i	$-0.658521\pi$
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	0.999673	−	0.0255875i	$-0.00814566\pi$
$368$	16.0000			0.834058
$369$	6.00000			0.312348
$370$	6.00000	−	10.3923i	0.311925	−	0.540270i
$371$	−2.00000	+	3.46410i	−0.103835	+	0.179847i
$372$	−18.0000			−0.933257
$373$	−32.0000			−1.65690			−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000			−1.65690			−0.828449	+	0.560065i	$0.810776\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	5.00000	+	8.66025i	0.257513	+	0.446026i
$378$	2.00000	+	3.46410i	0.102869	+	0.178174i
$379$	31.0000			1.59236			0.796182	−	0.605058i	$-0.206850\pi$
$379$	31.0000			1.59236			0.796182	+	0.605058i	$0.206850\pi$
$380$	−1.00000	+	8.66025i	−0.0512989	+	0.444262i
$381$	−4.00000			−0.204926
$382$	15.0000	+	25.9808i	0.767467	+	1.32929i
$383$	−13.0000	−	22.5167i	−0.664269	−	1.15055i	−0.979483	−	0.201527i	$-0.935410\pi$
$383$	−13.0000	−	22.5167i	−0.664269	−	1.15055i	0.315214	−	0.949021i	$-0.397924\pi$
$384$		0			0
$385$	−1.00000	−	1.73205i	−0.0509647	−	0.0882735i
$386$	−26.0000	+	45.0333i	−1.32337	+	2.29214i
$387$	−10.0000			−0.508329
$388$	16.0000			0.812277
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	0.0561516	+	0.998422i	$0.482117\pi$
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	−0.892735	+	0.450582i	$0.851216\pi$
$390$	2.00000	−	3.46410i	0.101274	−	0.175412i
$391$	−8.00000			−0.404577
$392$		0			0
$393$	8.00000	−	13.8564i	0.403547	−	0.698963i
$394$	10.0000	+	17.3205i	0.503793	+	0.872595i
$395$	−5.50000	+	9.52628i	−0.276735	+	0.479319i
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	0.999998	+	0.00217869i	$0.000693499\pi$
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$398$	6.00000			0.300753
$399$	−8.00000	+	3.46410i	−0.400501	+	0.173422i
$400$	−4.00000			−0.200000
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	−8.00000	−	13.8564i	−0.399004	−	0.691095i
$403$	−9.00000	+	15.5885i	−0.448322	+	0.776516i
$404$	7.00000	+	12.1244i	0.348263	+	0.603209i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	−20.0000			−0.992583
$407$	−6.00000			−0.297409
$408$		0			0
$409$	14.5000	−	25.1147i	0.716979	−	1.24184i	−0.245212	−	0.969469i	$-0.578858\pi$
$409$	14.5000	−	25.1147i	0.716979	−	1.24184i	0.962191	−	0.272374i	$-0.0878089\pi$
$410$	12.0000			0.592638
$411$	6.00000			0.295958
$412$	8.00000	−	13.8564i	0.394132	−	0.682656i
$413$	7.00000	+	12.1244i	0.344447	+	0.596601i
$414$	−4.00000	+	6.92820i	−0.196589	+	0.340503i
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$	−8.00000	−	13.8564i	−0.392232	−	0.679366i
$417$	−20.0000			−0.979404
$418$	8.00000	−	3.46410i	0.391293	−	0.169435i
$419$	−5.00000			−0.244266			−0.122133	−	0.992514i	$-0.538973\pi$
$419$	−5.00000			−0.244266			−0.122133	+	0.992514i	$0.538973\pi$
$420$	2.00000	+	3.46410i	0.0975900	+	0.169031i
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	0.938623	−	0.344946i	$-0.112103\pi$
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	−0.768043	+	0.640398i	$0.778769\pi$
$422$	−27.0000	+	46.7654i	−1.31434	+	2.27650i
$423$		0			0
$424$		0			0
$425$	2.00000			0.0970143
$426$	6.00000			0.290701
$427$	−7.00000	+	12.1244i	−0.338754	+	0.586739i
$428$		0			0
$429$	−2.00000			−0.0965609
$430$	−20.0000			−0.964486
$431$	−11.5000	+	19.9186i	−0.553936	+	0.959444i	0.444050	+	0.896002i	$0.353541\pi$
$431$	−11.5000	+	19.9186i	−0.553936	+	0.959444i	−0.997985	+	0.0634424i	$0.979792\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	−3.00000	+	5.19615i	−0.144171	+	0.249711i	−0.929063	−	0.369921i	$-0.879385\pi$
$433$	−3.00000	+	5.19615i	−0.144171	+	0.249711i	0.784892	+	0.619632i	$0.212718\pi$
$434$	−18.0000	−	31.1769i	−0.864028	−	1.49654i
$435$	2.50000	+	4.33013i	0.119866	+	0.207614i
$436$	38.0000			1.81987
$437$	−14.0000	−	10.3923i	−0.669711	−	0.497131i
$438$	−4.00000			−0.191127
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$		0			0
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$	4.00000	+	6.92820i	0.190261	+	0.329541i
$443$	4.00000	−	6.92820i	0.190046	−	0.329169i	−0.755219	−	0.655472i	$-0.772470\pi$
$443$	4.00000	−	6.92820i	0.190046	−	0.329169i	0.945265	+	0.326303i	$0.105803\pi$
$444$	12.0000			0.569495
$445$	−15.0000			−0.711068
$446$	−12.0000	+	20.7846i	−0.568216	+	0.984180i
$447$	4.50000	−	7.79423i	0.212843	−	0.368654i
$448$	16.0000			0.755929
$449$	−39.0000			−1.84052			−0.920262	−	0.391303i	$-0.872024\pi$
$449$	−39.0000			−1.84052			−0.920262	+	0.391303i	$0.872024\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	10.0000	−	17.3205i	0.470360	−	0.814688i
$453$	−1.50000	−	2.59808i	−0.0704761	−	0.122068i
$454$	18.0000	+	31.1769i	0.844782	+	1.46321i
$455$	4.00000			0.187523
$456$		0			0
$457$	−8.00000			−0.374224			−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000			−0.374224			−0.187112	+	0.982339i	$0.559913\pi$
$458$	−11.0000	−	19.0526i	−0.513996	−	0.890268i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	1.50000	+	2.59808i	0.0698620	+	0.121004i	0.898840	−	0.438276i	$-0.144411\pi$
$461$	1.50000	+	2.59808i	0.0698620	+	0.121004i	−0.828978	+	0.559281i	$0.811077\pi$
$462$	2.00000	−	3.46410i	0.0930484	−	0.161165i
$463$	−10.0000			−0.464739			−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000			−0.464739			−0.232370	+	0.972628i	$0.574648\pi$
$464$	20.0000			0.928477
$465$	−4.50000	+	7.79423i	−0.208683	+	0.361449i
$466$	−24.0000	+	41.5692i	−1.11178	+	1.92566i
$467$	−38.0000			−1.75843			−0.879215	−	0.476425i	$-0.841932\pi$
$467$	−38.0000			−1.75843			−0.879215	+	0.476425i	$0.841932\pi$
$468$	4.00000			0.184900
$469$	8.00000	−	13.8564i	0.369406	−	0.639829i
$470$		0			0
$471$	6.00000	−	10.3923i	0.276465	−	0.478852i
$472$		0			0
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$	−22.0000			−1.01049
$475$	3.50000	+	2.59808i	0.160591	+	0.119208i
$476$	−8.00000			−0.366679
$477$	1.00000	+	1.73205i	0.0457869	+	0.0793052i
$478$	27.0000	+	46.7654i	1.23495	+	2.13900i
$479$	−2.50000	+	4.33013i	−0.114228	+	0.197849i	−0.917471	−	0.397803i	$-0.869773\pi$
$479$	−2.50000	+	4.33013i	−0.114228	+	0.197849i	0.803243	+	0.595652i	$0.203106\pi$
$480$	−4.00000	−	6.92820i	−0.182574	−	0.316228i
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	−10.0000			−0.455488
$483$	−8.00000			−0.364013
$484$	10.0000	−	17.3205i	0.454545	−	0.787296i
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$	2.00000			0.0907218
$487$	14.0000			0.634401			0.317200	−	0.948359i	$-0.397257\pi$
$487$	14.0000			0.634401			0.317200	+	0.948359i	$0.397257\pi$
$488$		0			0
$489$	−9.00000	−	15.5885i	−0.406994	−	0.704934i
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	0.950365	+	0.311136i	$0.100710\pi$
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	−0.205731	+	0.978609i	$0.565957\pi$
$492$	6.00000	+	10.3923i	0.270501	+	0.468521i
$493$	−10.0000			−0.450377
$494$	−2.00000	+	17.3205i	−0.0899843	+	0.779287i
$495$	−1.00000			−0.0449467
$496$	18.0000	+	31.1769i	0.808224	+	1.39988i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$	−6.00000	+	10.3923i	−0.268866	+	0.465690i
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	0.550572	−	0.834788i	$-0.314410\pi$
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	−0.998233	+	0.0594153i	$0.981076\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$	2.00000			0.0893534
$502$	34.0000			1.51749
$503$	22.0000	−	38.1051i	0.980932	−	1.69902i	0.322151	−	0.946688i	$-0.395594\pi$
$503$	22.0000	−	38.1051i	0.980932	−	1.69902i	0.658781	−	0.752335i	$-0.271072\pi$
$504$		0			0
$505$	7.00000			0.311496
$506$	8.00000			0.355643
$507$	−4.50000	+	7.79423i	−0.199852	+	0.346154i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	−32.0000			−1.41421
$513$	−0.500000	+	4.33013i	−0.0220755	+	0.191180i
$514$	−44.0000			−1.94076
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$	−10.0000	−	17.3205i	−0.440225	−	0.762493i
$517$		0			0
$518$	12.0000	+	20.7846i	0.527250	+	0.913223i
$519$	3.00000	−	5.19615i	0.131685	−	0.228086i
$520$		0			0
$521$	21.0000			0.920027			0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000			0.920027			0.460013	+	0.887912i	$0.347845\pi$
$522$	−5.00000	+	8.66025i	−0.218844	+	0.379049i
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	−0.518766	−	0.854916i	$-0.673608\pi$
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	0.999762	+	0.0218062i	$0.00694167\pi$
$524$	32.0000			1.39793
$525$	2.00000			0.0872872
$526$	20.0000	−	34.6410i	0.872041	−	1.51042i
$527$	−9.00000	−	15.5885i	−0.392046	−	0.679044i
$528$	−2.00000	+	3.46410i	−0.0870388	+	0.150756i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	2.00000	+	3.46410i	0.0868744	+	0.150471i
$531$	7.00000			0.303774
$532$	−14.0000	−	10.3923i	−0.606977	−	0.450564i
$533$	12.0000			0.519778
$534$	−15.0000	−	25.9808i	−0.649113	−	1.12430i
$535$		0			0
$536$		0			0
$537$	−1.50000	−	2.59808i	−0.0647298	−	0.112115i
$538$	1.00000	−	1.73205i	0.0431131	−	0.0746740i
$539$	−3.00000			−0.129219
$540$	2.00000			0.0860663
$541$	−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	$0.271173\pi$
$542$	27.0000	−	46.7654i	1.15975	−	2.00874i
$543$	−10.0000			−0.429141
$544$	16.0000			0.685994
$545$	9.50000	−	16.4545i	0.406935	−	0.704833i
$546$	4.00000	+	6.92820i	0.171184	+	0.296500i
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	−0.767752	−	0.640747i	$-0.778625\pi$
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	0.938779	+	0.344519i	$0.111958\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$	−2.00000			−0.0852803
$551$	−17.5000	−	12.9904i	−0.745525	−	0.553409i
$552$		0			0
$553$	−11.0000	−	19.0526i	−0.467768	−	0.810197i
$554$	−8.00000	−	13.8564i	−0.339887	−	0.588702i
$555$	3.00000	−	5.19615i	0.127343	−	0.220564i
$556$	−20.0000	−	34.6410i	−0.848189	−	1.46911i
$557$	16.0000	−	27.7128i	0.677942	−	1.17423i	−0.297658	−	0.954673i	$-0.596205\pi$
$557$	16.0000	−	27.7128i	0.677942	−	1.17423i	0.975600	−	0.219557i	$-0.0704612\pi$
$558$	−18.0000			−0.762001
$559$	−20.0000			−0.845910
$560$	4.00000	−	6.92820i	0.169031	−	0.292770i
$561$	1.00000	−	1.73205i	0.0422200	−	0.0731272i
$562$	52.0000			2.19349
$563$	−42.0000			−1.77009			−0.885044	−	0.465506i	$-0.845872\pi$
$563$	−42.0000			−1.77009			−0.885044	+	0.465506i	$0.845872\pi$
$564$		0			0
$565$	−5.00000	−	8.66025i	−0.210352	−	0.364340i
$566$	2.00000	−	3.46410i	0.0840663	−	0.145607i
$567$	1.00000	+	1.73205i	0.0419961	+	0.0727393i
$568$		0			0
$569$	−39.0000			−1.63497			−0.817483	−	0.575953i	$-0.804631\pi$
$569$	−39.0000			−1.63497			−0.817483	+	0.575953i	$0.804631\pi$
$570$	−1.00000	+	8.66025i	−0.0418854	+	0.362738i
$571$	−15.0000			−0.627730			−0.313865	−	0.949468i	$-0.601624\pi$
$571$	−15.0000			−0.627730			−0.313865	+	0.949468i	$0.601624\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$	7.50000	+	12.9904i	0.313317	+	0.542681i
$574$	−12.0000	+	20.7846i	−0.500870	+	0.867533i
$575$	2.00000	+	3.46410i	0.0834058	+	0.144463i
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	12.0000			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$578$	26.0000			1.08146
$579$	−13.0000	+	22.5167i	−0.540262	+	0.935760i
$580$	−5.00000	+	8.66025i	−0.207614	+	0.359597i
$581$	−12.0000			−0.497844
$582$	16.0000			0.663221
$583$	1.00000	−	1.73205i	0.0414158	−	0.0717342i
$584$		0			0
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$	−4.00000	−	6.92820i	−0.165238	−	0.286201i
$587$	−11.0000	−	19.0526i	−0.454019	−	0.786383i	0.544613	−	0.838688i	$-0.316677\pi$
$587$	−11.0000	−	19.0526i	−0.454019	−	0.786383i	−0.998631	+	0.0523045i	$0.983343\pi$
$588$	6.00000			0.247436
$589$	4.50000	−	38.9711i	0.185419	−	1.60578i
$590$	14.0000			0.576371
$591$	5.00000	+	8.66025i	0.205673	+	0.356235i
$592$	−12.0000	−	20.7846i	−0.493197	−	0.854242i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$	−2.00000	+	3.46410i	−0.0819920	+	0.142014i
$596$	18.0000			0.737309
$597$	3.00000			0.122782
$598$	−8.00000	+	13.8564i	−0.327144	+	0.566631i
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	−0.219061	−	0.975711i	$-0.570299\pi$
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	0.954521	−	0.298143i	$-0.0963673\pi$
$600$		0			0
$601$	−15.0000			−0.611863			−0.305931	−	0.952054i	$-0.598968\pi$
$601$	−15.0000			−0.611863			−0.305931	+	0.952054i	$0.598968\pi$
$602$	20.0000	−	34.6410i	0.815139	−	1.41186i
$603$	−4.00000	−	6.92820i	−0.162893	−	0.282138i
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$	7.00000	+	12.1244i	0.284356	+	0.492518i
$607$	−10.0000			−0.405887			−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000			−0.405887			−0.202944	+	0.979190i	$0.565051\pi$
$608$	28.0000	+	20.7846i	1.13555	+	0.842927i
$609$	−10.0000			−0.405220
$610$	7.00000	+	12.1244i	0.283422	+	0.490901i
$611$		0			0
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	0.920229	−	0.391381i	$-0.128002\pi$
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	−0.799060	+	0.601251i	$0.794669\pi$
$614$	−24.0000	+	41.5692i	−0.968561	+	1.67760i
$615$	6.00000			0.241943
$616$		0			0
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	−0.516710	−	0.856161i	$-0.672843\pi$
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	0.999812	+	0.0194037i	$0.00617676\pi$
$618$	8.00000	−	13.8564i	0.321807	−	0.557386i
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$	−18.0000			−0.722897
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	24.0000	+	41.5692i	0.962312	+	1.66677i
$623$	15.0000	−	25.9808i	0.600962	−	1.04090i
$624$	−4.00000	−	6.92820i	−0.160128	−	0.277350i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	40.0000			1.59872
$627$	4.00000	−	1.73205i	0.159745	−	0.0691714i
$628$	24.0000			0.957704
$629$	6.00000	+	10.3923i	0.239236	+	0.414368i
$630$	2.00000	+	3.46410i	0.0796819	+	0.138013i
$631$	1.50000	−	2.59808i	0.0597141	−	0.103428i	−0.834623	−	0.550822i	$-0.814314\pi$
$631$	1.50000	−	2.59808i	0.0597141	−	0.103428i	0.894337	+	0.447394i	$0.147648\pi$
$632$		0			0
$633$	−13.5000	+	23.3827i	−0.536577	+	0.929378i
$634$	−64.0000			−2.54176
$635$	−4.00000			−0.158735
$636$	−2.00000	+	3.46410i	−0.0793052	+	0.137361i
$637$	3.00000	−	5.19615i	0.118864	−	0.205879i
$638$	10.0000			0.395904
$639$	3.00000			0.118678
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$	−22.0000	−	38.1051i	−0.867595	−	1.50272i	−0.864447	−	0.502724i	$-0.832331\pi$
$643$	−22.0000	−	38.1051i	−0.867595	−	1.50272i	−0.00314839	−	0.999995i	$-0.501002\pi$
$644$	−8.00000	−	13.8564i	−0.315244	−	0.546019i
$645$	−10.0000			−0.393750
$646$	−14.0000	−	10.3923i	−0.550823	−	0.408880i
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$		0			0
$649$	−3.50000	−	6.06218i	−0.137387	−	0.237961i
$650$	2.00000	−	3.46410i	0.0784465	−	0.135873i
$651$	−9.00000	−	15.5885i	−0.352738	−	0.610960i
$652$	18.0000	−	31.1769i	0.704934	−	1.22098i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	38.0000			1.48592
$655$	8.00000	−	13.8564i	0.312586	−	0.541415i
$656$	12.0000	−	20.7846i	0.468521	−	0.811503i
$657$	−2.00000			−0.0780274
$658$		0			0
$659$	−20.0000	+	34.6410i	−0.779089	+	1.34942i	0.153378	+	0.988168i	$0.450985\pi$
$659$	−20.0000	+	34.6410i	−0.779089	+	1.34942i	−0.932467	+	0.361255i	$0.882348\pi$
$660$	−1.00000	−	1.73205i	−0.0389249	−	0.0674200i
$661$	−4.50000	+	7.79423i	−0.175030	+	0.303160i	−0.940172	−	0.340701i	$-0.889335\pi$
$661$	−4.50000	+	7.79423i	−0.175030	+	0.303160i	0.765142	+	0.643862i	$0.222669\pi$
$662$	8.00000	+	13.8564i	0.310929	+	0.538545i
$663$	2.00000	+	3.46410i	0.0776736	+	0.134535i
$664$		0			0
$665$	−8.00000	+	3.46410i	−0.310227	+	0.134332i
$666$	12.0000			0.464991
$667$	−10.0000	−	17.3205i	−0.387202	−	0.670653i
$668$	2.00000	+	3.46410i	0.0773823	+	0.134030i
$669$	−6.00000	+	10.3923i	−0.231973	+	0.401790i
$670$	−8.00000	−	13.8564i	−0.309067	−	0.535320i
$671$	3.50000	−	6.06218i	0.135116	−	0.234028i
$672$	16.0000			0.617213
$673$	36.0000			1.38770			0.693849	−	0.720121i	$-0.255914\pi$
$673$	36.0000			1.38770			0.693849	+	0.720121i	$0.255914\pi$
$674$	−8.00000	+	13.8564i	−0.308148	+	0.533729i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−18.0000			−0.692308
$677$	46.0000			1.76792			0.883962	−	0.467559i	$-0.154866\pi$
$677$	46.0000			1.76792			0.883962	+	0.467559i	$0.154866\pi$
$678$	10.0000	−	17.3205i	0.384048	−	0.665190i
$679$	8.00000	+	13.8564i	0.307012	+	0.531760i
$680$		0			0
$681$	9.00000	+	15.5885i	0.344881	+	0.597351i
$682$	9.00000	+	15.5885i	0.344628	+	0.596913i
$683$	−24.0000			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$684$	−8.00000	+	3.46410i	−0.305888	+	0.132453i
$685$	6.00000			0.229248
$686$	20.0000	+	34.6410i	0.763604	+	1.32260i
$687$	−5.50000	−	9.52628i	−0.209838	−	0.363450i
$688$	−20.0000	+	34.6410i	−0.762493	+	1.32068i
$689$	2.00000	+	3.46410i	0.0761939	+	0.131972i
$690$	−4.00000	+	6.92820i	−0.152277	+	0.263752i
$691$	23.0000			0.874961			0.437481	−	0.899228i	$-0.355871\pi$
$691$	23.0000			0.874961			0.437481	+	0.899228i	$0.355871\pi$
$692$	12.0000			0.456172
$693$	1.00000	−	1.73205i	0.0379869	−	0.0657952i
$694$	−22.0000	+	38.1051i	−0.835109	+	1.44645i
$695$	−20.0000			−0.758643
$696$		0			0
$697$	−6.00000	+	10.3923i	−0.227266	+	0.393637i
$698$	6.00000	+	10.3923i	0.227103	+	0.393355i
$699$	−12.0000	+	20.7846i	−0.453882	+	0.786146i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	11.0000	+	19.0526i	0.415464	+	0.719605i	0.995477	−	0.0950021i	$-0.0302858\pi$
$701$	11.0000	+	19.0526i	0.415464	+	0.719605i	−0.580013	+	0.814607i	$0.696952\pi$
$702$	4.00000			0.150970
$703$	−3.00000	+	25.9808i	−0.113147	+	0.979883i
$704$	−8.00000			−0.301511
$705$		0			0
$706$	−14.0000	−	24.2487i	−0.526897	−	0.912612i
$707$	−7.00000	+	12.1244i	−0.263262	+	0.455983i
$708$	7.00000	+	12.1244i	0.263076	+	0.455661i
$709$	13.5000	−	23.3827i	0.507003	−	0.878155i	−0.492964	−	0.870050i	$-0.664087\pi$
$709$	13.5000	−	23.3827i	0.507003	−	0.878155i	0.999967	−	0.00810550i	$-0.00258009\pi$
$710$	6.00000			0.225176
$711$	−11.0000			−0.412532
$712$		0			0
$713$	18.0000	−	31.1769i	0.674105	−	1.16758i
$714$	−8.00000			−0.299392
$715$	−2.00000			−0.0747958
$716$	3.00000	−	5.19615i	0.112115	−	0.194189i
$717$	13.5000	+	23.3827i	0.504167	+	0.873242i
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	0.999992	+	0.00400572i	$0.00127506\pi$
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	−0.496527	+	0.868021i	$0.665392\pi$
$720$	−2.00000	−	3.46410i	−0.0745356	−	0.129099i
$721$	16.0000			0.595871
$722$	−11.0000	−	36.3731i	−0.409378	−	1.35367i
$723$	−5.00000			−0.185952
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$	2.50000	+	4.33013i	0.0928477	+	0.160817i
$726$	10.0000	−	17.3205i	0.371135	−	0.642824i
$727$	1.00000	+	1.73205i	0.0370879	+	0.0642382i	0.883974	−	0.467537i	$-0.154858\pi$
$727$	1.00000	+	1.73205i	0.0370879	+	0.0642382i	−0.846886	+	0.531775i	$0.821525\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−4.00000			−0.148047
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$	−7.00000	+	12.1244i	−0.258727	+	0.448129i
$733$	10.0000			0.369358			0.184679	−	0.982799i	$-0.440875\pi$
$733$	10.0000			0.369358			0.184679	+	0.982799i	$0.440875\pi$
$734$	40.0000			1.47643
$735$	1.50000	−	2.59808i	0.0553283	−	0.0958315i
$736$	16.0000	+	27.7128i	0.589768	+	1.02151i
$737$	−4.00000	+	6.92820i	−0.147342	+	0.255204i
$738$	6.00000	+	10.3923i	0.220863	+	0.382546i
$739$	26.5000	+	45.8993i	0.974818	+	1.68843i	0.680534	+	0.732717i	$0.261748\pi$
$739$	26.5000	+	45.8993i	0.974818	+	1.68843i	0.294285	+	0.955718i	$0.404919\pi$
$740$	12.0000			0.441129
$741$	−1.00000	+	8.66025i	−0.0367359	+	0.318142i
$742$	−8.00000			−0.293689
$743$	−11.0000	−	19.0526i	−0.403551	−	0.698971i	0.590601	−	0.806964i	$-0.298891\pi$
$743$	−11.0000	−	19.0526i	−0.403551	−	0.698971i	−0.994152	+	0.107993i	$0.965557\pi$
$744$		0			0
$745$	4.50000	−	7.79423i	0.164867	−	0.285558i
$746$	−32.0000	−	55.4256i	−1.17160	−	2.02928i
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	4.00000			0.146254
$749$		0			0
$750$	1.00000	−	1.73205i	0.0365148	−	0.0632456i
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	−0.837359	−	0.546653i	$-0.815902\pi$
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	0.892095	+	0.451848i	$0.149235\pi$
$752$		0			0
$753$	17.0000			0.619514
$754$	−10.0000	+	17.3205i	−0.364179	+	0.630776i
$755$	−1.50000	−	2.59808i	−0.0545906	−	0.0945537i
$756$	−2.00000	+	3.46410i	−0.0727393	+	0.125988i
$757$	7.00000	+	12.1244i	0.254419	+	0.440667i	0.964738	−	0.263213i	$-0.0847823\pi$
$757$	7.00000	+	12.1244i	0.254419	+	0.440667i	−0.710318	+	0.703881i	$0.751449\pi$
$758$	31.0000	+	53.6936i	1.12597	+	1.95024i
$759$	4.00000			0.145191
$760$		0			0
$761$	−30.0000			−1.08750			−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000			−1.08750			−0.543750	+	0.839248i	$0.682996\pi$
$762$	−4.00000	−	6.92820i	−0.144905	−	0.250982i
$763$	19.0000	+	32.9090i	0.687846	+	1.19138i
$764$	−15.0000	+	25.9808i	−0.542681	+	0.939951i
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$	26.0000	−	45.0333i	0.939418	−	1.62712i
$767$	14.0000			0.505511
$768$	−16.0000			−0.577350
$769$	21.5000	−	37.2391i	0.775310	−	1.34288i	−0.159310	−	0.987229i	$-0.550927\pi$
$769$	21.5000	−	37.2391i	0.775310	−	1.34288i	0.934620	−	0.355647i	$-0.115740\pi$
$770$	2.00000	−	3.46410i	0.0720750	−	0.124838i
$771$	−22.0000			−0.792311
$772$	−52.0000			−1.87152
$773$	−10.0000	+	17.3205i	−0.359675	+	0.622975i	−0.987906	−	0.155051i	$-0.950446\pi$
$773$	−10.0000	+	17.3205i	−0.359675	+	0.622975i	0.628231	+	0.778027i	$0.283779\pi$
$774$	−10.0000	−	17.3205i	−0.359443	−	0.622573i
$775$	−4.50000	+	7.79423i	−0.161645	+	0.279977i
$776$		0			0
$777$	6.00000	+	10.3923i	0.215249	+	0.372822i
$778$	−66.0000			−2.36621
$779$	−24.0000	+	10.3923i	−0.859889	+	0.372343i
$780$	4.00000			0.143223
$781$	−1.50000	−	2.59808i	−0.0536742	−	0.0929665i
$782$	−8.00000	−	13.8564i	−0.286079	−	0.495504i
$783$	−2.50000	+	4.33013i	−0.0893427	+	0.154746i
$784$	−6.00000	−	10.3923i	−0.214286	−	0.371154i
$785$	6.00000	−	10.3923i	0.214149	−	0.370917i
$786$	32.0000			1.14140
$787$	−8.00000			−0.285169			−0.142585	−	0.989783i	$-0.545541\pi$
$787$	−8.00000			−0.285169			−0.142585	+	0.989783i	$0.545541\pi$
$788$	−10.0000	+	17.3205i	−0.356235	+	0.617018i
$789$	10.0000	−	17.3205i	0.356009	−	0.616626i
$790$	−22.0000			−0.782725
$791$	20.0000			0.711118
$792$		0			0
$793$	7.00000	+	12.1244i	0.248577	+	0.430548i
$794$	−20.0000	+	34.6410i	−0.709773	+	1.22936i
$795$	1.00000	+	1.73205i	0.0354663	+	0.0614295i
$796$	3.00000	+	5.19615i	0.106332	+	0.184173i
$797$	10.0000			0.354218			0.177109	−	0.984191i	$-0.443325\pi$
$797$	10.0000			0.354218			0.177109	+	0.984191i	$0.443325\pi$
$798$	−14.0000	−	10.3923i	−0.495595	−	0.367884i
$799$		0			0
$800$	−4.00000	−	6.92820i	−0.141421	−	0.244949i
$801$	−7.50000	−	12.9904i	−0.264999	−	0.458993i
$802$	−27.0000	+	46.7654i	−0.953403	+	1.65134i
$803$	1.00000	+	1.73205i	0.0352892	+	0.0611227i
$804$	8.00000	−	13.8564i	0.282138	−	0.488678i
$805$	−8.00000			−0.281963
$806$	−36.0000			−1.26805
$807$	0.500000	−	0.866025i	0.0176008	−	0.0304855i
$808$		0			0
$809$	−1.00000			−0.0351581			−0.0175791	−	0.999845i	$-0.505596\pi$
$809$	−1.00000			−0.0351581			−0.0175791	+	0.999845i	$0.505596\pi$
$810$	2.00000			0.0702728
$811$	−24.5000	+	42.4352i	−0.860311	+	1.49010i	0.0113172	+	0.999936i	$0.496398\pi$
$811$	−24.5000	+	42.4352i	−0.860311	+	1.49010i	−0.871629	+	0.490167i	$0.836936\pi$
$812$	−10.0000	−	17.3205i	−0.350931	−	0.607831i
$813$	13.5000	−	23.3827i	0.473466	−	0.820067i
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	−9.00000	−	15.5885i	−0.315256	−	0.546040i
$816$	8.00000			0.280056
$817$	40.0000	−	17.3205i	1.39942	−	0.605968i
$818$	58.0000			2.02792
$819$	2.00000	+	3.46410i	0.0698857	+	0.121046i
$820$	6.00000	+	10.3923i	0.209529	+	0.362915i
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	−0.143591	−	0.989637i	$-0.545865\pi$
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	0.928846	−	0.370465i	$-0.120802\pi$
$822$	6.00000	+	10.3923i	0.209274	+	0.362473i
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	−0.637419	−	0.770517i	$-0.719998\pi$
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	0.985997	+	0.166762i	$0.0533313\pi$
$824$		0			0
$825$	−1.00000			−0.0348155
$826$	−14.0000	+	24.2487i	−0.487122	+	0.843721i
$827$	−6.00000	+	10.3923i	−0.208640	+	0.361376i	−0.951286	−	0.308308i	$-0.900237\pi$
$827$	−6.00000	+	10.3923i	−0.208640	+	0.361376i	0.742646	+	0.669684i	$0.233571\pi$
$828$	−8.00000			−0.278019
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	8.00000	−	13.8564i	0.277350	−	0.480384i
$833$	3.00000	+	5.19615i	0.103944	+	0.180036i
$834$	−20.0000	−	34.6410i	−0.692543	−	1.19952i
$835$	2.00000			0.0692129
$836$	7.00000	+	5.19615i	0.242100	+	0.179713i
$837$	−9.00000			−0.311086
$838$	−5.00000	−	8.66025i	−0.172722	−	0.299164i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	−7.00000	+	12.1244i	−0.241236	+	0.417833i
$843$	26.0000			0.895488
$844$	−54.0000			−1.85876
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	20.0000			0.687208
$848$	8.00000			0.274721
$849$	1.00000	−	1.73205i	0.0343199	−	0.0594438i
$850$	2.00000	+	3.46410i	0.0685994	+	0.118818i
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$	3.00000	+	5.19615i	0.102778	+	0.178017i
$853$	1.00000	+	1.73205i	0.0342393	+	0.0593043i	0.882637	−	0.470055i	$-0.155766\pi$
$853$	1.00000	+	1.73205i	0.0342393	+	0.0593043i	−0.848398	+	0.529359i	$0.822432\pi$
$854$	−28.0000			−0.958140
$855$	−0.500000	+	4.33013i	−0.0170996	+	0.148087i
$856$		0			0
$857$	−5.00000	−	8.66025i	−0.170797	−	0.295829i	0.767902	−	0.640567i	$-0.221301\pi$
$857$	−5.00000	−	8.66025i	−0.170797	−	0.295829i	−0.938699	+	0.344739i	$0.887967\pi$
$858$	−2.00000	−	3.46410i	−0.0682789	−	0.118262i
$859$	−22.5000	+	38.9711i	−0.767690	+	1.32968i	0.171122	+	0.985250i	$0.445261\pi$
$859$	−22.5000	+	38.9711i	−0.767690	+	1.32968i	−0.938813	+	0.344428i	$0.888073\pi$
$860$	−10.0000	−	17.3205i	−0.340997	−	0.590624i
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$	−46.0000			−1.56677
$863$	−38.0000			−1.29354			−0.646768	−	0.762687i	$-0.723880\pi$
$863$	−38.0000			−1.29354			−0.646768	+	0.762687i	$0.723880\pi$
$864$	4.00000	−	6.92820i	0.136083	−	0.235702i
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	−12.0000			−0.407777
$867$	13.0000			0.441503
$868$	18.0000	−	31.1769i	0.610960	−	1.05821i
$869$	5.50000	+	9.52628i	0.186575	+	0.323157i
$870$	−5.00000	+	8.66025i	−0.169516	+	0.293610i
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$		0			0
$873$	8.00000			0.270759
$874$	4.00000	−	34.6410i	0.135302	−	1.17175i
$875$	2.00000			0.0676123
$876$	−2.00000	−	3.46410i	−0.0675737	−	0.117041i
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	0.589135	−	0.808035i	$-0.299469\pi$
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	−0.994346	+	0.106188i	$0.966135\pi$
$878$	−25.0000	+	43.3013i	−0.843709	+	1.46135i
$879$	−2.00000	−	3.46410i	−0.0674583	−	0.116841i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	−1.00000			−0.0336909			−0.0168454	−	0.999858i	$-0.505362\pi$
$881$	−1.00000			−0.0336909			−0.0168454	+	0.999858i	$0.505362\pi$
$882$	6.00000			0.202031
$883$	14.0000	−	24.2487i	0.471138	−	0.816034i	−0.528317	−	0.849047i	$-0.677177\pi$
$883$	14.0000	−	24.2487i	0.471138	−	0.816034i	0.999455	+	0.0330128i	$0.0105102\pi$
$884$	−4.00000	+	6.92820i	−0.134535	+	0.233021i
$885$	7.00000			0.235302
$886$	16.0000			0.537531
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$		0			0
$889$	4.00000	−	6.92820i	0.134156	−	0.232364i
$890$	−15.0000	−	25.9808i	−0.502801	−	0.870877i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−24.0000			−0.803579
$893$		0			0
$894$	18.0000			0.602010
$895$	−1.50000	−	2.59808i	−0.0501395	−	0.0868441i
$896$		0			0
$897$	−4.00000	+	6.92820i	−0.133556	+	0.231326i
$898$	−39.0000	−	67.5500i	−1.30145	−	2.25417i
$899$	22.5000	−	38.9711i	0.750417	−	1.29976i
$900$	2.00000			0.0666667
$901$	−4.00000			−0.133259
$902$	6.00000	−	10.3923i	0.199778	−	0.346026i
$903$	10.0000	−	17.3205i	0.332779	−	0.576390i
$904$		0			0
$905$	−10.0000			−0.332411
$906$	3.00000	−	5.19615i	0.0996683	−	0.172631i
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$	−18.0000	+	31.1769i	−0.597351	+	1.03464i
$909$	3.50000	+	6.06218i	0.116088	+	0.201070i
$910$	4.00000	+	6.92820i	0.132599	+	0.229668i
$911$	−9.00000			−0.298183			−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000			−0.298183			−0.149092	+	0.988823i	$0.547635\pi$
$912$	14.0000	+	10.3923i	0.463586	+	0.344124i
$913$	6.00000			0.198571
$914$	−8.00000	−	13.8564i	−0.264616	−	0.458329i
$915$	3.50000	+	6.06218i	0.115706	+	0.200409i
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$	16.0000	+	27.7128i	0.528367	+	0.915158i
$918$	−2.00000	+	3.46410i	−0.0660098	+	0.114332i
$919$	32.0000			1.05558			0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000			1.05558			0.527791	+	0.849374i	$0.323020\pi$
$920$		0			0
$921$	−12.0000	+	20.7846i	−0.395413	+	0.684876i
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$	6.00000			0.197492
$924$	4.00000			0.131590
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$	−10.0000	−	17.3205i	−0.328620	−	0.569187i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$	20.0000	+	34.6410i	0.656532	+	1.13715i
$929$	5.50000	+	9.52628i	0.180449	+	0.312547i	0.942034	−	0.335519i	$-0.108912\pi$
$929$	5.50000	+	9.52628i	0.180449	+	0.312547i	−0.761584	+	0.648066i	$0.775578\pi$
$930$	−18.0000			−0.590243
$931$	−1.50000	+	12.9904i	−0.0491605	+	0.425743i
$932$	−48.0000			−1.57229
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$	−38.0000	−	65.8179i	−1.24340	−	2.15363i
$935$	1.00000	−	1.73205i	0.0327035	−	0.0566441i
$936$		0			0
$937$	9.00000	−	15.5885i	0.294017	−	0.509253i	−0.680739	−	0.732526i	$-0.738341\pi$
$937$	9.00000	−	15.5885i	0.294017	−	0.509253i	0.974756	+	0.223274i	$0.0716744\pi$
$938$	32.0000			1.04484
$939$	20.0000			0.652675
$940$		0			0
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	−0.984858	−	0.173365i	$-0.944536\pi$
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	0.642567	+	0.766229i	$0.277869\pi$
$942$	24.0000			0.781962
$943$	−24.0000			−0.781548
$944$	14.0000	−	24.2487i	0.455661	−	0.789228i
$945$	1.00000	+	1.73205i	0.0325300	+	0.0563436i
$946$	−10.0000	+	17.3205i	−0.325128	+	0.563138i
$947$	−10.0000	−	17.3205i	−0.324956	−	0.562841i	0.656547	−	0.754285i	$-0.272016\pi$
$947$	−10.0000	−	17.3205i	−0.324956	−	0.562841i	−0.981504	+	0.191444i	$0.938683\pi$
$948$	−11.0000	−	19.0526i	−0.357263	−	0.618798i
$949$	−4.00000			−0.129845
$950$	−1.00000	+	8.66025i	−0.0324443	+	0.280976i
$951$	−32.0000			−1.03767
$952$		0			0
$953$	4.00000	+	6.92820i	0.129573	+	0.224427i	0.923511	−	0.383572i	$-0.125306\pi$
$953$	4.00000	+	6.92820i	0.129573	+	0.224427i	−0.793938	+	0.607998i	$0.791973\pi$
$954$	−2.00000	+	3.46410i	−0.0647524	+	0.112154i
$955$	7.50000	+	12.9904i	0.242694	+	0.420359i
$956$	−27.0000	+	46.7654i	−0.873242	+	1.51250i
$957$	5.00000			0.161627
$958$	−10.0000			−0.323085
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$	4.00000	−	6.92820i	0.129099	−	0.223607i
$961$	50.0000			1.61290
$962$	24.0000			0.773791
$963$		0			0
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	−13.0000	+	22.5167i	−0.418485	+	0.724837i
$966$	−8.00000	−	13.8564i	−0.257396	−	0.445823i
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	0.832075	−	0.554664i	$-0.187153\pi$
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	−0.896390	+	0.443266i	$0.853820\pi$
$968$		0			0
$969$	−7.00000	−	5.19615i	−0.224872	−	0.166924i
$970$	16.0000			0.513729
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	0.991783	−	0.127933i	$-0.0408342\pi$
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	−0.606685	+	0.794943i	$0.707501\pi$
$972$	1.00000	+	1.73205i	0.0320750	+	0.0555556i
$973$	20.0000	−	34.6410i	0.641171	−	1.11054i
$974$	14.0000	+	24.2487i	0.448589	+	0.776979i
$975$	1.00000	−	1.73205i	0.0320256	−	0.0554700i
$976$	28.0000			0.896258
$977$	18.0000			0.575871			0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000			0.575871			0.287936	+	0.957650i	$0.407031\pi$
$978$	18.0000	−	31.1769i	0.575577	−	0.996928i
$979$	−7.50000	+	12.9904i	−0.239701	+	0.415174i
$980$	6.00000			0.191663
$981$	19.0000			0.606623
$982$	−33.0000	+	57.1577i	−1.05307	+	1.82397i
$983$	7.00000	+	12.1244i	0.223265	+	0.386707i	0.955798	−	0.294025i	$-0.0949950\pi$
$983$	7.00000	+	12.1244i	0.223265	+	0.386707i	−0.732532	+	0.680732i	$0.761662\pi$
$984$		0			0
$985$	5.00000	+	8.66025i	0.159313	+	0.275939i
$986$	−10.0000	−	17.3205i	−0.318465	−	0.551597i
$987$		0			0
$988$	−16.0000	+	6.92820i	−0.509028	+	0.220416i
$989$	40.0000			1.27193
$990$	−1.00000	−	1.73205i	−0.0317821	−	0.0550482i
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$	−36.0000	+	62.3538i	−1.14300	+	1.97974i
$993$	4.00000	+	6.92820i	0.126936	+	0.219860i
$994$	−6.00000	+	10.3923i	−0.190308	+	0.329624i
$995$	3.00000			0.0951064
$996$	−12.0000			−0.380235
$997$	−26.0000	+	45.0333i	−0.823428	+	1.42622i	0.0796863	+	0.996820i	$0.474608\pi$
$997$	−26.0000	+	45.0333i	−0.823428	+	1.42622i	−0.903115	+	0.429400i	$0.858725\pi$
$998$	20.0000	−	34.6410i	0.633089	−	1.09654i
$999$	6.00000			0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.c.121.1	yes	2
3.2	odd	2		855.2.k.a.406.1		2
19.7	even	3		5415.2.a.b.1.1		1
19.11	even	3	inner	285.2.i.c.106.1	✓	2
19.12	odd	6		5415.2.a.l.1.1		1
57.11	odd	6		855.2.k.a.676.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.c.106.1	✓	2	19.11	even	3	inner
285.2.i.c.121.1	yes	2	1.1	even	1	trivial
855.2.k.a.406.1		2	3.2	odd	2
855.2.k.a.676.1		2	57.11	odd	6
5415.2.a.b.1.1		1	19.7	even	3
5415.2.a.l.1.1		1	19.12	odd	6

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.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} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} -2.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +1.00000 q^{11} -2.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} -2.00000 q^{18} +(0.500000 - 4.33013i) q^{19} -2.00000 q^{20} +(-1.00000 - 1.73205i) q^{21} +(1.00000 + 1.73205i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{26} -1.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(2.50000 - 4.33013i) q^{29} -2.00000 q^{30} +9.00000 q^{31} +(-4.00000 + 6.92820i) q^{32} +(0.500000 + 0.866025i) q^{33} +(2.00000 - 3.46410i) q^{34} +(-1.00000 - 1.73205i) q^{35} +(-1.00000 - 1.73205i) q^{36} -6.00000 q^{37} +(8.00000 - 3.46410i) q^{38} -2.00000 q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{42} +(5.00000 + 8.66025i) q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} +8.00000 q^{46} +(-2.00000 + 3.46410i) q^{48} -3.00000 q^{49} -2.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{54} +(0.500000 + 0.866025i) q^{55} +(4.00000 - 1.73205i) q^{57} +10.0000 q^{58} +(-3.50000 - 6.06218i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(3.50000 - 6.06218i) q^{61} +(9.00000 + 15.5885i) q^{62} +(1.00000 - 1.73205i) q^{63} -8.00000 q^{64} -2.00000 q^{65} +(-1.00000 + 1.73205i) q^{66} +(-4.00000 + 6.92820i) q^{67} +4.00000 q^{68} +4.00000 q^{69} +(2.00000 - 3.46410i) q^{70} +(-1.50000 - 2.59808i) q^{71} +(1.00000 + 1.73205i) q^{73} +(-6.00000 - 10.3923i) q^{74} -1.00000 q^{75} +(7.00000 + 5.19615i) q^{76} -2.00000 q^{77} +(-2.00000 - 3.46410i) q^{78} +(5.50000 + 9.52628i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} +6.00000 q^{83} +4.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(-10.0000 + 17.3205i) q^{86} +5.00000 q^{87} +(-7.50000 + 12.9904i) q^{89} +(-1.00000 - 1.73205i) q^{90} +(2.00000 - 3.46410i) q^{91} +(4.00000 + 6.92820i) q^{92} +(4.50000 + 7.79423i) q^{93} +(4.00000 - 1.73205i) q^{95} -8.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{9} - 2 q^{10} + 2 q^{11} - 4 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + q^{19} - 4 q^{20} - 2 q^{21} + 2 q^{22}+ \cdots - q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 - 2 * q^4 + q^5 - 2 * q^6 - 4 * q^7 - q^9 - 2 * q^10 + 2 * q^11 - 4 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + q^19 - 4 * q^20 - 2 * q^21 + 2 * q^22 + 4 * q^23 - q^25 - 8 * q^26 - 2 * q^27 + 4 * q^28 + 5 * q^29 - 4 * q^30 + 18 * q^31 - 8 * q^32 + q^33 + 4 * q^34 - 2 * q^35 - 2 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^39 - 6 * q^41 + 4 * q^42 + 10 * q^43 - 2 * q^44 - 2 * q^45 + 16 * q^46 - 4 * q^48 - 6 * q^49 - 4 * q^50 + 2 * q^51 - 4 * q^52 + 2 * q^53 - 2 * q^54 + q^55 + 8 * q^57 + 20 * q^58 - 7 * q^59 - 2 * q^60 + 7 * q^61 + 18 * q^62 + 2 * q^63 - 16 * q^64 - 4 * q^65 - 2 * q^66 - 8 * q^67 + 8 * q^68 + 8 * q^69 + 4 * q^70 - 3 * q^71 + 2 * q^73 - 12 * q^74 - 2 * q^75 + 14 * q^76 - 4 * q^77 - 4 * q^78 + 11 * q^79 - 4 * q^80 - q^81 + 12 * q^82 + 12 * q^83 + 8 * q^84 + 2 * q^85 - 20 * q^86 + 10 * q^87 - 15 * q^89 - 2 * q^90 + 4 * q^91 + 8 * q^92 + 9 * q^93 + 8 * q^95 - 16 * q^96 - 8 * q^97 - 6 * q^98 - q^99

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