LMFDB - Embedded newform 1050.2.o.k.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1050.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.499
Dual form			1050.2.o.k.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} +(0.866025 + 0.500000i) q^{12} +1.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 + 2.59808i) q^{21} +4.00000i q^{22} +(1.73205 + 1.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{26} -1.00000i q^{27} +(-2.59808 + 0.500000i) q^{28} -4.00000 q^{29} +(-0.866025 + 0.500000i) q^{32} +(3.46410 + 2.00000i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(2.59808 + 1.50000i) q^{37} +(0.866025 - 0.500000i) q^{38} +(0.500000 + 0.866025i) q^{39} +12.0000 q^{41} +(-0.866025 + 2.50000i) q^{42} +8.00000i q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{46} +(-5.19615 - 3.00000i) q^{47} +1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(1.73205 - 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.50000 - 0.866025i) q^{56} -1.00000i q^{57} +(-3.46410 - 2.00000i) q^{58} +(3.00000 + 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-2.59808 + 1.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +2.00000 q^{69} +16.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-9.52628 + 5.50000i) q^{73} +(1.50000 + 2.59808i) q^{74} +1.00000 q^{76} +(-10.3923 + 2.00000i) q^{77} +1.00000i q^{78} +(6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(10.3923 + 6.00000i) q^{82} -6.00000i q^{83} +(-2.00000 + 1.73205i) q^{84} +(-4.00000 + 6.92820i) q^{86} +(-3.46410 + 2.00000i) q^{87} +(-3.46410 + 2.00000i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(-2.50000 - 0.866025i) q^{91} +2.00000i q^{92} +(-3.00000 - 5.19615i) q^{94} +(-0.500000 + 0.866025i) q^{96} -17.0000i q^{97} +(-2.59808 - 6.50000i) q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} - 8 q^{14} - 2 q^{16} + 2 q^{19} + 2 q^{21} + 2 q^{24} - 2 q^{26} - 16 q^{29} - 8 q^{34} + 4 q^{36} + 2 q^{39} + 48 q^{41} - 8 q^{44} + 4 q^{46} - 22 q^{49} - 4 q^{51} + 2 q^{54} - 10 q^{56} + 12 q^{59} + 26 q^{61} - 4 q^{64} + 8 q^{66} + 8 q^{69} + 64 q^{71} + 6 q^{74} + 4 q^{76} + 26 q^{79} - 2 q^{81} - 8 q^{84} - 16 q^{86} - 4 q^{89} - 10 q^{91} - 12 q^{94} - 2 q^{96} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 - 8 * q^14 - 2 * q^16 + 2 * q^19 + 2 * q^21 + 2 * q^24 - 2 * q^26 - 16 * q^29 - 8 * q^34 + 4 * q^36 + 2 * q^39 + 48 * q^41 - 8 * q^44 + 4 * q^46 - 22 * q^49 - 4 * q^51 + 2 * q^54 - 10 * q^56 + 12 * q^59 + 26 * q^61 - 4 * q^64 + 8 * q^66 + 8 * q^69 + 64 * q^71 + 6 * q^74 + 4 * q^76 + 26 * q^79 - 2 * q^81 - 8 * q^84 - 16 * q^86 - 4 * q^89 - 10 * q^91 - 12 * q^94 - 2 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	0.500000	+	2.59808i	0.109109	+	0.566947i
$22$			4.00000i			0.852803i
$23$	1.73205	+	1.00000i	0.361158	+	0.208514i	0.669588	−	0.742732i	$-0.266471\pi$
$23$	1.73205	+	1.00000i	0.361158	+	0.208514i	−0.308431	+	0.951247i	$0.599804\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$		−	1.00000i		−	0.192450i
$28$	−2.59808	+	0.500000i	−0.490990	+	0.0944911i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.46410	+	2.00000i	0.603023	+	0.348155i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	2.59808	+	1.50000i	0.427121	+	0.246598i	0.698119	−	0.715981i	$-0.254020\pi$
$37$	2.59808	+	1.50000i	0.427121	+	0.246598i	−0.270998	+	0.962580i	$0.587354\pi$
$38$	0.866025	−	0.500000i	0.140488	−	0.0811107i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$	−0.866025	+	2.50000i	−0.133631	+	0.385758i
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$		0			0
$46$	1.00000	+	1.73205i	0.147442	+	0.255377i
$47$	−5.19615	−	3.00000i	−0.757937	−	0.437595i	0.0706177	−	0.997503i	$-0.477503\pi$
$47$	−5.19615	−	3.00000i	−0.757937	−	0.437595i	−0.828554	+	0.559908i	$0.810836\pi$
$48$			1.00000i			0.144338i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	1.73205	−	1.00000i	0.237915	−	0.137361i	−0.376303	−	0.926497i	$-0.622805\pi$
$53$	1.73205	−	1.00000i	0.237915	−	0.137361i	0.614218	+	0.789136i	$0.289471\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$		−	1.00000i		−	0.132453i
$58$	−3.46410	−	2.00000i	−0.454859	−	0.262613i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$	1.73205	+	2.00000i	0.218218	+	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.00000	+	3.46410i	0.246183	+	0.426401i
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	−0.650236	−	0.759733i	$-0.725330\pi$
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	0.332830	+	0.942987i	$0.391996\pi$
$68$	−1.73205	−	1.00000i	−0.210042	−	0.121268i
$69$	2.00000			0.240772
$70$		0			0
$71$	16.0000			1.89885			0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000			1.89885			0.949425	+	0.313993i	$0.101667\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−9.52628	+	5.50000i	−1.11497	+	0.643726i	−0.940111	−	0.340868i	$-0.889279\pi$
$73$	−9.52628	+	5.50000i	−1.11497	+	0.643726i	−0.174855	+	0.984594i	$0.555946\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$		0			0
$76$	1.00000			0.114708
$77$	−10.3923	+	2.00000i	−1.18431	+	0.227921i
$78$			1.00000i			0.113228i
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	0.956325	−	0.292306i	$-0.0944227\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	10.3923	+	6.00000i	1.14764	+	0.662589i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	−2.00000	+	1.73205i	−0.218218	+	0.188982i
$85$		0			0
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	−3.46410	+	2.00000i	−0.371391	+	0.214423i
$88$	−3.46410	+	2.00000i	−0.369274	+	0.213201i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		0			0
$91$	−2.50000	−	0.866025i	−0.262071	−	0.0907841i
$92$			2.00000i			0.208514i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	17.0000i		−	1.72609i	−0.505128	−	0.863044i	$-0.668555\pi$
$97$		−	17.0000i		−	1.72609i	0.505128	−	0.863044i	$-0.331445\pi$
$98$	−2.59808	−	6.50000i	−0.262445	−	0.656599i
$99$	4.00000			0.402015
$100$		0			0
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	−1.73205	+	1.00000i	−0.171499	+	0.0990148i
$103$	−6.06218	−	3.50000i	−0.597324	−	0.344865i	0.170664	−	0.985329i	$-0.445409\pi$
$103$	−6.06218	−	3.50000i	−0.597324	−	0.344865i	−0.767988	+	0.640464i	$0.778742\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	2.00000			0.194257
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−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	$-0.530535\pi$
$110$		0			0
$111$	3.00000			0.284747
$112$	−1.73205	−	2.00000i	−0.163663	−	0.188982i
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$	0.500000	−	0.866025i	0.0468293	−	0.0811107i
$115$		0			0
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$	0.866025	+	0.500000i	0.0800641	+	0.0462250i
$118$			6.00000i			0.552345i
$119$	−1.00000	−	5.19615i	−0.0916698	−	0.476331i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	11.2583	−	6.50000i	1.01928	−	0.588482i
$123$	10.3923	−	6.00000i	0.937043	−	0.541002i
$124$		0			0
$125$		0			0
$126$	0.500000	+	2.59808i	0.0445435	+	0.231455i
$127$			1.00000i			0.0887357i	0.999015	+	0.0443678i	$0.0141274\pi$
$127$			1.00000i			0.0887357i	−0.999015	+	0.0443678i	$0.985873\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$132$			4.00000i			0.348155i
$133$	1.73205	+	2.00000i	0.150188	+	0.173422i
$134$	−3.00000			−0.259161
$135$		0			0
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−8.66025	+	5.00000i	−0.739895	+	0.427179i	−0.822031	−	0.569442i	$-0.807159\pi$
$137$	−8.66025	+	5.00000i	−0.739895	+	0.427179i	0.0821359	+	0.996621i	$0.473826\pi$
$138$	1.73205	+	1.00000i	0.147442	+	0.0851257i
$139$	13.0000			1.10265			0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000			1.10265			0.551323	+	0.834292i	$0.314123\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	13.8564	+	8.00000i	1.16280	+	0.671345i
$143$	−3.46410	+	2.00000i	−0.289683	+	0.167248i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	−11.0000			−0.910366
$147$	−6.92820	−	1.00000i	−0.571429	−	0.0824786i
$148$			3.00000i			0.246598i
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	0.326411	+	0.945228i	$0.394160\pi$
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	−0.981797	+	0.189933i	$0.939173\pi$
$150$		0			0
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	0.866025	+	0.500000i	0.0702439	+	0.0405554i
$153$			2.00000i			0.161690i
$154$	−10.0000	−	3.46410i	−0.805823	−	0.279145i
$155$		0			0
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	18.1865	−	10.5000i	1.45144	−	0.837991i	0.452880	−	0.891572i	$-0.350397\pi$
$157$	18.1865	−	10.5000i	1.45144	−	0.837991i	0.998564	+	0.0535803i	$0.0170633\pi$
$158$	11.2583	−	6.50000i	0.895665	−	0.517112i
$159$	1.00000	−	1.73205i	0.0793052	−	0.137361i
$160$		0			0
$161$	−4.00000	+	3.46410i	−0.315244	+	0.273009i
$162$		−	1.00000i		−	0.0785674i
$163$	−19.9186	−	11.5000i	−1.56014	−	0.900750i	−0.997241	−	0.0742262i	$-0.976351\pi$
$163$	−19.9186	−	11.5000i	−1.56014	−	0.900750i	−0.562902	−	0.826523i	$-0.690315\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$		−	10.0000i		−	0.773823i	−0.922117	−	0.386912i	$-0.873542\pi$
$167$		−	10.0000i		−	0.773823i	0.922117	−	0.386912i	$-0.126458\pi$
$168$	−2.59808	+	0.500000i	−0.200446	+	0.0385758i
$169$	12.0000			0.923077
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−6.92820	+	4.00000i	−0.528271	+	0.304997i
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	0.684349	−	0.729155i	$-0.260087\pi$
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	−0.289292	+	0.957241i	$0.593420\pi$
$174$	−4.00000			−0.303239
$175$		0			0
$176$	−4.00000			−0.301511
$177$	5.19615	+	3.00000i	0.390567	+	0.225494i
$178$	−1.73205	+	1.00000i	−0.129823	+	0.0749532i
$179$	−4.00000	−	6.92820i	−0.298974	−	0.517838i	0.676927	−	0.736050i	$-0.263311\pi$
$179$	−4.00000	−	6.92820i	−0.298974	−	0.517838i	−0.975901	+	0.218212i	$0.929978\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$	−1.73205	−	2.00000i	−0.128388	−	0.148250i
$183$		−	13.0000i		−	0.960988i
$184$	−1.00000	+	1.73205i	−0.0737210	+	0.127688i
$185$		0			0
$186$		0			0
$187$	−6.92820	−	4.00000i	−0.506640	−	0.292509i
$188$		−	6.00000i		−	0.437595i
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$		0			0
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	0.235983	+	0.971757i	$0.424169\pi$
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	−0.959558	+	0.281511i	$0.909164\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−8.66025	+	5.00000i	−0.623379	+	0.359908i	−0.778183	−	0.628037i	$-0.783859\pi$
$193$	−8.66025	+	5.00000i	−0.623379	+	0.359908i	0.154805	+	0.987945i	$0.450525\pi$
$194$	8.50000	−	14.7224i	0.610264	−	1.05701i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	3.46410	+	2.00000i	0.246183	+	0.142134i
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	0.999317	+	0.0369532i	$0.0117652\pi$
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	−0.467656	+	0.883911i	$0.654901\pi$
$200$		0			0
$201$	−1.50000	+	2.59808i	−0.105802	+	0.183254i
$202$		−	12.0000i		−	0.844317i
$203$	3.46410	−	10.0000i	0.243132	−	0.701862i
$204$	−2.00000			−0.140028
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	1.73205	−	1.00000i	0.120386	−	0.0695048i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	4.00000			0.276686
$210$		0			0
$211$	3.00000			0.206529			0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000			0.206529			0.103264	+	0.994654i	$0.467071\pi$
$212$	1.73205	+	1.00000i	0.118958	+	0.0686803i
$213$	13.8564	−	8.00000i	0.949425	−	0.548151i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	1.00000			0.0680414
$217$		0			0
$218$		−	19.0000i		−	1.28684i
$219$	−5.50000	+	9.52628i	−0.371656	+	0.643726i
$220$		0			0
$221$	−1.00000	−	1.73205i	−0.0672673	−	0.116510i
$222$	2.59808	+	1.50000i	0.174371	+	0.100673i
$223$		−	19.0000i		−	1.27233i	−0.771551	−	0.636167i	$-0.780519\pi$
$223$		−	19.0000i		−	1.27233i	0.771551	−	0.636167i	$-0.219481\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	−0.252136	−	0.967692i	$-0.581133\pi$
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	0.711977	+	0.702202i	$0.247800\pi$
$228$	0.866025	−	0.500000i	0.0573539	−	0.0331133i
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−8.00000	+	6.92820i	−0.526361	+	0.455842i
$232$		−	4.00000i		−	0.262613i
$233$	3.46410	+	2.00000i	0.226941	+	0.131024i	0.609160	−	0.793047i	$-0.291507\pi$
$233$	3.46410	+	2.00000i	0.226941	+	0.131024i	−0.382219	+	0.924072i	$0.624840\pi$
$234$	0.500000	+	0.866025i	0.0326860	+	0.0566139i
$235$		0			0
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$		−	13.0000i		−	0.844441i
$238$	1.73205	−	5.00000i	0.112272	−	0.324102i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$	−4.33013	+	2.50000i	−0.278351	+	0.160706i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	13.0000			0.832240
$245$		0			0
$246$	12.0000			0.765092
$247$	0.866025	+	0.500000i	0.0551039	+	0.0318142i
$248$		0			0
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$		0			0
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	−0.866025	+	2.50000i	−0.0545545	+	0.157485i
$253$			8.00000i			0.502956i
$254$	−0.500000	+	0.866025i	−0.0313728	+	0.0543393i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	0.268101	−	0.963391i	$-0.413604\pi$
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	−0.700270	+	0.713878i	$0.746937\pi$
$258$			8.00000i			0.498058i
$259$	−6.00000	+	5.19615i	−0.372822	+	0.322873i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−1.73205	+	1.00000i	−0.107006	+	0.0617802i
$263$	27.7128	−	16.0000i	1.70885	−	0.986602i	0.772851	−	0.634588i	$-0.218830\pi$
$263$	27.7128	−	16.0000i	1.70885	−	0.986602i	0.935995	−	0.352014i	$-0.114503\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$		0			0
$266$	0.500000	+	2.59808i	0.0306570	+	0.159298i
$267$			2.00000i			0.122398i
$268$	−2.59808	−	1.50000i	−0.158703	−	0.0916271i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		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	$-0.0411435\pi$
$272$		−	2.00000i		−	0.121268i
$273$	−2.59808	+	0.500000i	−0.157243	+	0.0302614i
$274$	−10.0000			−0.604122
$275$		0			0
$276$	1.00000	+	1.73205i	0.0601929	+	0.104257i
$277$	−0.866025	+	0.500000i	−0.0520344	+	0.0300421i	−0.525792	−	0.850613i	$-0.676231\pi$
$277$	−0.866025	+	0.500000i	−0.0520344	+	0.0300421i	0.473757	+	0.880656i	$0.342897\pi$
$278$	11.2583	+	6.50000i	0.675230	+	0.389844i
$279$		0			0
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	−5.19615	−	3.00000i	−0.309426	−	0.178647i
$283$	11.2583	−	6.50000i	0.669238	−	0.386385i	−0.126550	−	0.991960i	$-0.540390\pi$
$283$	11.2583	−	6.50000i	0.669238	−	0.386385i	0.795788	+	0.605575i	$0.207057\pi$
$284$	8.00000	+	13.8564i	0.474713	+	0.822226i
$285$		0			0
$286$	−4.00000			−0.236525
$287$	−10.3923	+	30.0000i	−0.613438	+	1.77084i
$288$			1.00000i			0.0589256i
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$	−8.50000	−	14.7224i	−0.498279	−	0.863044i
$292$	−9.52628	−	5.50000i	−0.557483	−	0.321863i
$293$			12.0000i			0.701047i	0.936554	+	0.350524i	$0.113996\pi$
$293$			12.0000i			0.701047i	−0.936554	+	0.350524i	$0.886004\pi$
$294$	−5.50000	−	4.33013i	−0.320767	−	0.252538i
$295$		0			0
$296$	−1.50000	+	2.59808i	−0.0871857	+	0.151010i
$297$	3.46410	−	2.00000i	0.201008	−	0.116052i
$298$	−13.8564	+	8.00000i	−0.802680	+	0.463428i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	−20.0000	−	6.92820i	−1.15278	−	0.399335i
$302$		−	19.0000i		−	1.09333i
$303$	−10.3923	−	6.00000i	−0.597022	−	0.344691i
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$		0			0
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$	−6.92820	−	8.00000i	−0.394771	−	0.455842i
$309$	−7.00000			−0.398216
$310$		0			0
$311$	7.00000	+	12.1244i	0.396934	+	0.687509i	0.993346	−	0.115169i	$-0.0367410\pi$
$311$	7.00000	+	12.1244i	0.396934	+	0.687509i	−0.596412	+	0.802678i	$0.703408\pi$
$312$	−0.866025	+	0.500000i	−0.0490290	+	0.0283069i
$313$	15.5885	+	9.00000i	0.881112	+	0.508710i	0.871025	−	0.491239i	$-0.163456\pi$
$313$	15.5885	+	9.00000i	0.881112	+	0.508710i	0.0100869	+	0.999949i	$0.496789\pi$
$314$	21.0000			1.18510
$315$		0			0
$316$	13.0000			0.731307
$317$	19.0526	+	11.0000i	1.07010	+	0.617822i	0.928208	−	0.372061i	$-0.121349\pi$
$317$	19.0526	+	11.0000i	1.07010	+	0.617822i	0.141890	+	0.989882i	$0.454682\pi$
$318$	1.73205	−	1.00000i	0.0971286	−	0.0560772i
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$		0			0
$321$	6.00000			0.334887
$322$	−5.19615	+	1.00000i	−0.289570	+	0.0557278i
$323$			2.00000i			0.111283i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−11.5000	−	19.9186i	−0.636926	−	1.10319i
$327$	−16.4545	−	9.50000i	−0.909935	−	0.525351i
$328$			12.0000i			0.662589i
$329$	12.0000	−	10.3923i	0.661581	−	0.572946i
$330$		0			0
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	0.418674	+	0.908137i	$0.362495\pi$
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	−0.995806	+	0.0914858i	$0.970838\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$	2.59808	−	1.50000i	0.142374	−	0.0821995i
$334$	5.00000	−	8.66025i	0.273588	−	0.473868i
$335$		0			0
$336$	−2.50000	−	0.866025i	−0.136386	−	0.0472456i
$337$			18.0000i			0.980522i	0.871576	+	0.490261i	$0.163099\pi$
$337$			18.0000i			0.980522i	−0.871576	+	0.490261i	$0.836901\pi$
$338$	10.3923	+	6.00000i	0.565267	+	0.326357i
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$		0			0
$341$		0			0
$342$		−	1.00000i		−	0.0540738i
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	19.0526	−	11.0000i	1.02279	−	0.590511i	0.107883	−	0.994164i	$-0.465593\pi$
$347$	19.0526	−	11.0000i	1.02279	−	0.590511i	0.914912	+	0.403653i	$0.132260\pi$
$348$	−3.46410	−	2.00000i	−0.185695	−	0.107211i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$	−3.46410	−	2.00000i	−0.184637	−	0.106600i
$353$	−17.3205	+	10.0000i	−0.921878	+	0.532246i	−0.884234	−	0.467045i	$-0.845319\pi$
$353$	−17.3205	+	10.0000i	−0.921878	+	0.532246i	−0.0376440	+	0.999291i	$0.511985\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$		0			0
$356$	−2.00000			−0.106000
$357$	−3.46410	−	4.00000i	−0.183340	−	0.211702i
$358$		−	8.00000i		−	0.422813i
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	−0.934268	−	0.356572i	$-0.883946\pi$
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	0.775934	+	0.630814i	$0.217279\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−15.5885	−	9.00000i	−0.819311	−	0.473029i
$363$			5.00000i			0.262432i
$364$	−0.500000	−	2.59808i	−0.0262071	−	0.136176i
$365$		0			0
$366$	6.50000	−	11.2583i	0.339760	−	0.588482i
$367$	6.92820	−	4.00000i	0.361649	−	0.208798i	−0.308155	−	0.951336i	$-0.599711\pi$
$367$	6.92820	−	4.00000i	0.361649	−	0.208798i	0.669804	+	0.742538i	$0.266378\pi$
$368$	−1.73205	+	1.00000i	−0.0902894	+	0.0521286i
$369$	6.00000	−	10.3923i	0.312348	−	0.541002i
$370$		0			0
$371$	1.00000	+	5.19615i	0.0519174	+	0.269771i
$372$		0			0
$373$	−19.9186	−	11.5000i	−1.03135	−	0.595447i	−0.113975	−	0.993484i	$-0.536359\pi$
$373$	−19.9186	−	11.5000i	−1.03135	−	0.595447i	−0.917370	+	0.398036i	$0.869692\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$		−	4.00000i		−	0.206010i
$378$	1.73205	+	2.00000i	0.0890871	+	0.102869i
$379$	5.00000			0.256833			0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000			0.256833			0.128416	+	0.991720i	$0.459011\pi$
$380$		0			0
$381$	0.500000	+	0.866025i	0.0256158	+	0.0443678i
$382$	−17.3205	+	10.0000i	−0.886194	+	0.511645i
$383$	12.1244	+	7.00000i	0.619526	+	0.357683i	0.776684	−	0.629890i	$-0.216900\pi$
$383$	12.1244	+	7.00000i	0.619526	+	0.357683i	−0.157159	+	0.987573i	$0.550233\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−10.0000			−0.508987
$387$	6.92820	+	4.00000i	0.352180	+	0.203331i
$388$	14.7224	−	8.50000i	0.747418	−	0.431522i
$389$	−10.0000	−	17.3205i	−0.507020	−	0.878185i	−0.999967	−	0.00812520i	$-0.997414\pi$
$389$	−10.0000	−	17.3205i	−0.507020	−	0.878185i	0.492947	−	0.870059i	$-0.335920\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	4.33013	−	5.50000i	0.218704	−	0.277792i
$393$			2.00000i			0.100887i
$394$		0			0
$395$		0			0
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−15.5885	−	9.00000i	−0.782362	−	0.451697i	0.0549046	−	0.998492i	$-0.482515\pi$
$397$	−15.5885	−	9.00000i	−0.782362	−	0.451697i	−0.837267	+	0.546795i	$0.815848\pi$
$398$			15.0000i			0.751882i
$399$	2.50000	+	0.866025i	0.125157	+	0.0433555i
$400$		0			0
$401$	−2.00000	+	3.46410i	−0.0998752	+	0.172989i	−0.911633	−	0.411005i	$-0.865178\pi$
$401$	−2.00000	+	3.46410i	−0.0998752	+	0.172989i	0.811758	+	0.583994i	$0.198511\pi$
$402$	−2.59808	+	1.50000i	−0.129580	+	0.0748132i
$403$		0			0
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$		0			0
$406$	8.00000	−	6.92820i	0.397033	−	0.343841i
$407$			12.0000i			0.594818i
$408$	−1.73205	−	1.00000i	−0.0857493	−	0.0495074i
$409$	−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
$412$		−	7.00000i		−	0.344865i
$413$	−15.5885	+	3.00000i	−0.767058	+	0.147620i
$414$	2.00000			0.0982946
$415$		0			0
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	11.2583	−	6.50000i	0.551323	−	0.318306i
$418$	3.46410	+	2.00000i	0.169435	+	0.0978232i
$419$	16.0000			0.781651			0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000			0.781651			0.390826	+	0.920465i	$0.372190\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	2.59808	+	1.50000i	0.126472	+	0.0730189i
$423$	−5.19615	+	3.00000i	−0.252646	+	0.145865i
$424$	1.00000	+	1.73205i	0.0485643	+	0.0841158i
$425$		0			0
$426$	16.0000			0.775203
$427$	22.5167	+	26.0000i	1.08966	+	1.25823i
$428$			6.00000i			0.290021i
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$		0			0
$435$		0			0
$436$	9.50000	−	16.4545i	0.454967	−	0.788027i
$437$	1.73205	−	1.00000i	0.0828552	−	0.0478365i
$438$	−9.52628	+	5.50000i	−0.455183	+	0.262800i
$439$	−11.5000	+	19.9186i	−0.548865	+	0.950662i	0.449488	+	0.893287i	$0.351607\pi$
$439$	−11.5000	+	19.9186i	−0.548865	+	0.950662i	−0.998353	+	0.0573756i	$0.981727\pi$
$440$		0			0
$441$	−6.50000	+	2.59808i	−0.309524	+	0.123718i
$442$		−	2.00000i		−	0.0951303i
$443$	−5.19615	−	3.00000i	−0.246877	−	0.142534i	0.371457	−	0.928450i	$-0.378858\pi$
$443$	−5.19615	−	3.00000i	−0.246877	−	0.142534i	−0.618333	+	0.785916i	$0.712192\pi$
$444$	1.50000	+	2.59808i	0.0711868	+	0.123299i
$445$		0			0
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$			16.0000i			0.756774i
$448$	0.866025	−	2.50000i	0.0409159	−	0.118114i
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$		0			0
$451$	24.0000	+	41.5692i	1.13012	+	1.95742i
$452$	−15.5885	+	9.00000i	−0.733219	+	0.423324i
$453$	−16.4545	−	9.50000i	−0.773099	−	0.446349i
$454$	8.00000			0.375459
$455$		0			0
$456$	1.00000			0.0468293
$457$	32.0429	+	18.5000i	1.49891	+	0.865393i	0.999999	−	0.00126243i	$-0.000401844\pi$
$457$	32.0429	+	18.5000i	1.49891	+	0.865393i	0.498906	+	0.866656i	$0.333735\pi$
$458$	−6.06218	+	3.50000i	−0.283267	+	0.163544i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	26.0000			1.21094			0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000			1.21094			0.605470	+	0.795868i	$0.292985\pi$
$462$	−10.3923	+	2.00000i	−0.483494	+	0.0930484i
$463$		−	3.00000i		−	0.139422i	−0.997567	−	0.0697109i	$-0.977792\pi$
$463$		−	3.00000i		−	0.139422i	0.997567	−	0.0697109i	$-0.0222077\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$		0			0
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	25.9808	+	15.0000i	1.20225	+	0.694117i	0.961054	−	0.276360i	$-0.0891283\pi$
$467$	25.9808	+	15.0000i	1.20225	+	0.694117i	0.241192	+	0.970477i	$0.422462\pi$
$468$			1.00000i			0.0462250i
$469$	−1.50000	−	7.79423i	−0.0692636	−	0.359904i
$470$		0			0
$471$	10.5000	−	18.1865i	0.483814	−	0.837991i
$472$	−5.19615	+	3.00000i	−0.239172	+	0.138086i
$473$	−27.7128	+	16.0000i	−1.27424	+	0.735681i
$474$	6.50000	−	11.2583i	0.298555	−	0.517112i
$475$		0			0
$476$	4.00000	−	3.46410i	0.183340	−	0.158777i
$477$		−	2.00000i		−	0.0915737i
$478$	10.3923	+	6.00000i	0.475333	+	0.274434i
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	−0.933806	−	0.357780i	$-0.883534\pi$
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	0.157056	−	0.987590i	$-0.449800\pi$
$480$		0			0
$481$	−1.50000	+	2.59808i	−0.0683941	+	0.118462i
$482$		−	13.0000i		−	0.592134i
$483$	−1.73205	+	5.00000i	−0.0788110	+	0.227508i
$484$	−5.00000			−0.227273
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−34.6410	+	20.0000i	−1.56973	+	0.906287i	−0.573535	+	0.819181i	$0.694428\pi$
$487$	−34.6410	+	20.0000i	−1.56973	+	0.906287i	−0.996199	+	0.0871056i	$0.972238\pi$
$488$	11.2583	+	6.50000i	0.509641	+	0.294241i
$489$	−23.0000			−1.04010
$490$		0			0
$491$	18.0000			0.812329			0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000			0.812329			0.406164	+	0.913800i	$0.366866\pi$
$492$	10.3923	+	6.00000i	0.468521	+	0.270501i
$493$	6.92820	−	4.00000i	0.312031	−	0.180151i
$494$	0.500000	+	0.866025i	0.0224961	+	0.0389643i
$495$		0			0
$496$		0			0
$497$	−13.8564	+	40.0000i	−0.621545	+	1.79425i
$498$		−	6.00000i		−	0.268866i
$499$	−13.5000	+	23.3827i	−0.604343	+	1.04675i	0.387812	+	0.921739i	$0.373231\pi$
$499$	−13.5000	+	23.3827i	−0.604343	+	1.04675i	−0.992155	+	0.125014i	$0.960102\pi$
$500$		0			0
$501$	−5.00000	−	8.66025i	−0.223384	−	0.386912i
$502$	20.7846	+	12.0000i	0.927663	+	0.535586i
$503$			4.00000i			0.178351i	0.996016	+	0.0891756i	$0.0284232\pi$
$503$			4.00000i			0.178351i	−0.996016	+	0.0891756i	$0.971577\pi$
$504$	−2.00000	+	1.73205i	−0.0890871	+	0.0771517i
$505$		0			0
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	10.3923	−	6.00000i	0.461538	−	0.266469i
$508$	−0.866025	+	0.500000i	−0.0384237	+	0.0221839i
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	0.123187	+	0.992384i	$0.460689\pi$
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	−0.921023	+	0.389509i	$0.872645\pi$
$510$		0			0
$511$	−5.50000	−	28.5788i	−0.243306	−	1.26425i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.866025	−	0.500000i	−0.0382360	−	0.0220755i
$514$	−4.00000	−	6.92820i	−0.176432	−	0.305590i
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$		−	24.0000i		−	1.05552i
$518$	−7.79423	+	1.50000i	−0.342459	+	0.0659062i
$519$	6.00000			0.263371
$520$		0			0
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$	−3.46410	+	2.00000i	−0.151620	+	0.0875376i
$523$	−13.8564	−	8.00000i	−0.605898	−	0.349816i	0.165460	−	0.986216i	$-0.447089\pi$
$523$	−13.8564	−	8.00000i	−0.605898	−	0.349816i	−0.771358	+	0.636401i	$0.780422\pi$
$524$	−2.00000			−0.0873704
$525$		0			0
$526$	32.0000			1.39527
$527$		0			0
$528$	−3.46410	+	2.00000i	−0.150756	+	0.0870388i
$529$	−9.50000	−	16.4545i	−0.413043	−	0.715412i
$530$		0			0
$531$	6.00000			0.260378
$532$	−0.866025	+	2.50000i	−0.0375470	+	0.108389i
$533$			12.0000i			0.519778i
$534$	−1.00000	+	1.73205i	−0.0432742	+	0.0749532i
$535$		0			0
$536$	−1.50000	−	2.59808i	−0.0647901	−	0.112220i
$537$	−6.92820	−	4.00000i	−0.298974	−	0.172613i
$538$		0			0
$539$	4.00000	−	27.7128i	0.172292	−	1.19368i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$	17.3205	−	10.0000i	0.743980	−	0.429537i
$543$	−15.5885	+	9.00000i	−0.668965	+	0.386227i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$		0			0
$546$	−2.50000	−	0.866025i	−0.106990	−	0.0370625i
$547$			12.0000i			0.513083i	0.966533	+	0.256541i	$0.0825830\pi$
$547$			12.0000i			0.513083i	−0.966533	+	0.256541i	$0.917417\pi$
$548$	−8.66025	−	5.00000i	−0.369948	−	0.213589i
$549$	−6.50000	−	11.2583i	−0.277413	−	0.480494i
$550$		0			0
$551$	−2.00000	+	3.46410i	−0.0852029	+	0.147576i
$552$			2.00000i			0.0851257i
$553$	22.5167	+	26.0000i	0.957506	+	1.10563i
$554$	−1.00000			−0.0424859
$555$		0			0
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	−8.00000			−0.337760
$562$	−15.5885	−	9.00000i	−0.657559	−	0.379642i
$563$	−24.2487	+	14.0000i	−1.02196	+	0.590030i	−0.914671	−	0.404198i	$-0.867551\pi$
$563$	−24.2487	+	14.0000i	−1.02196	+	0.590030i	−0.107290	+	0.994228i	$0.534217\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$		0			0
$566$	13.0000			0.546431
$567$	2.59808	−	0.500000i	0.109109	−	0.0209980i
$568$			16.0000i			0.671345i
$569$	−20.0000	+	34.6410i	−0.838444	+	1.45223i	0.0527519	+	0.998608i	$0.483201\pi$
$569$	−20.0000	+	34.6410i	−0.838444	+	1.45223i	−0.891196	+	0.453619i	$0.850133\pi$
$570$		0			0
$571$	17.5000	+	30.3109i	0.732352	+	1.26847i	0.955875	+	0.293773i	$0.0949108\pi$
$571$	17.5000	+	30.3109i	0.732352	+	1.26847i	−0.223523	+	0.974699i	$0.571756\pi$
$572$	−3.46410	−	2.00000i	−0.144841	−	0.0836242i
$573$			20.0000i			0.835512i
$574$	−24.0000	+	20.7846i	−1.00174	+	0.867533i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−19.0526	+	11.0000i	−0.793168	+	0.457936i	−0.841077	−	0.540916i	$-0.818078\pi$
$577$	−19.0526	+	11.0000i	−0.793168	+	0.457936i	0.0479084	+	0.998852i	$0.484744\pi$
$578$	−11.2583	+	6.50000i	−0.468285	+	0.270364i
$579$	−5.00000	+	8.66025i	−0.207793	+	0.359908i
$580$		0			0
$581$	15.0000	+	5.19615i	0.622305	+	0.215573i
$582$		−	17.0000i		−	0.704673i
$583$	6.92820	+	4.00000i	0.286937	+	0.165663i
$584$	−5.50000	−	9.52628i	−0.227592	−	0.394200i
$585$		0			0
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$			42.0000i			1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$			42.0000i			1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$	−2.59808	−	6.50000i	−0.107143	−	0.268055i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−2.59808	+	1.50000i	−0.106780	+	0.0616496i
$593$	−36.3731	−	21.0000i	−1.49366	−	0.862367i	−0.493689	−	0.869638i	$-0.664352\pi$
$593$	−36.3731	−	21.0000i	−1.49366	−	0.862367i	−0.999974	+	0.00727173i	$0.997685\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	−16.0000			−0.655386
$597$	12.9904	+	7.50000i	0.531661	+	0.306955i
$598$	−1.73205	+	1.00000i	−0.0708288	+	0.0408930i
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	0.798206	−	0.602384i	$-0.205782\pi$
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	−0.920783	+	0.390075i	$0.872449\pi$
$600$		0			0
$601$	−29.0000			−1.18293			−0.591467	−	0.806329i	$-0.701451\pi$
$601$	−29.0000			−1.18293			−0.591467	+	0.806329i	$0.701451\pi$
$602$	−13.8564	−	16.0000i	−0.564745	−	0.652111i
$603$			3.00000i			0.122169i
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$		0			0
$606$	−6.00000	−	10.3923i	−0.243733	−	0.422159i
$607$	0.866025	+	0.500000i	0.0351509	+	0.0202944i	0.517472	−	0.855700i	$-0.326873\pi$
$607$	0.866025	+	0.500000i	0.0351509	+	0.0202944i	−0.482322	+	0.875994i	$0.660206\pi$
$608$			1.00000i			0.0405554i
$609$	−2.00000	−	10.3923i	−0.0810441	−	0.421117i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	−1.73205	+	1.00000i	−0.0700140	+	0.0404226i
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	−0.391381	−	0.920229i	$-0.628002\pi$
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	0.601251	+	0.799060i	$0.294669\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$		0			0
$616$	−2.00000	−	10.3923i	−0.0805823	−	0.418718i
$617$		−	44.0000i		−	1.77137i	−0.464283	−	0.885687i	$-0.653688\pi$
$617$		−	44.0000i		−	1.77137i	0.464283	−	0.885687i	$-0.346312\pi$
$618$	−6.06218	−	3.50000i	−0.243857	−	0.140791i
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.846566	+	0.532284i	$0.178666\pi$
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.0376891	+	0.999290i	$0.488000\pi$
$620$		0			0
$621$	1.00000	−	1.73205i	0.0401286	−	0.0695048i
$622$			14.0000i			0.561349i
$623$	−3.46410	−	4.00000i	−0.138786	−	0.160257i
$624$	−1.00000			−0.0400320
$625$		0			0
$626$	9.00000	+	15.5885i	0.359712	+	0.623040i
$627$	3.46410	−	2.00000i	0.138343	−	0.0798723i
$628$	18.1865	+	10.5000i	0.725722	+	0.418996i
$629$	−6.00000			−0.239236
$630$		0			0
$631$	17.0000			0.676759			0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000			0.676759			0.338380	+	0.941010i	$0.390121\pi$
$632$	11.2583	+	6.50000i	0.447832	+	0.258556i
$633$	2.59808	−	1.50000i	0.103264	−	0.0596196i
$634$	11.0000	+	19.0526i	0.436866	+	0.756674i
$635$		0			0
$636$	2.00000			0.0793052
$637$	4.33013	−	5.50000i	0.171566	−	0.217918i
$638$		−	16.0000i		−	0.633446i
$639$	8.00000	−	13.8564i	0.316475	−	0.548151i
$640$		0			0
$641$	−8.00000	−	13.8564i	−0.315981	−	0.547295i	0.663665	−	0.748030i	$-0.269000\pi$
$641$	−8.00000	−	13.8564i	−0.315981	−	0.547295i	−0.979646	+	0.200735i	$0.935667\pi$
$642$	5.19615	+	3.00000i	0.205076	+	0.118401i
$643$			11.0000i			0.433798i	0.976194	+	0.216899i	$0.0695942\pi$
$643$			11.0000i			0.433798i	−0.976194	+	0.216899i	$0.930406\pi$
$644$	−5.00000	−	1.73205i	−0.197028	−	0.0682524i
$645$		0			0
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	−10.3923	+	6.00000i	−0.408564	+	0.235884i	−0.690172	−	0.723645i	$-0.742465\pi$
$647$	−10.3923	+	6.00000i	−0.408564	+	0.235884i	0.281609	+	0.959529i	$0.409132\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−12.0000	+	20.7846i	−0.471041	+	0.815867i
$650$		0			0
$651$		0			0
$652$		−	23.0000i		−	0.900750i
$653$	13.8564	+	8.00000i	0.542243	+	0.313064i	0.745988	−	0.665960i	$-0.231978\pi$
$653$	13.8564	+	8.00000i	0.542243	+	0.313064i	−0.203744	+	0.979024i	$0.565311\pi$
$654$	−9.50000	−	16.4545i	−0.371479	−	0.643421i
$655$		0			0
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$			11.0000i			0.429151i
$658$	15.5885	−	3.00000i	0.607701	−	0.116952i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	0.999874	−	0.0158695i	$-0.00505163\pi$
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	−0.513680	+	0.857982i	$0.671718\pi$
$662$	−18.1865	+	10.5000i	−0.706840	+	0.408094i
$663$	−1.73205	−	1.00000i	−0.0672673	−	0.0388368i
$664$	6.00000			0.232845
$665$		0			0
$666$	3.00000			0.116248
$667$	−6.92820	−	4.00000i	−0.268261	−	0.154881i
$668$	8.66025	−	5.00000i	0.335075	−	0.193456i
$669$	−9.50000	−	16.4545i	−0.367291	−	0.636167i
$670$		0			0
$671$	52.0000			2.00744
$672$	−1.73205	−	2.00000i	−0.0668153	−	0.0771517i
$673$		−	9.00000i		−	0.346925i	−0.984841	−	0.173462i	$-0.944505\pi$
$673$		−	9.00000i		−	0.346925i	0.984841	−	0.173462i	$-0.0554955\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$		0			0
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	0.466347	−	0.884602i	$-0.345570\pi$
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	−0.532915	+	0.846169i	$0.678903\pi$
$678$			18.0000i			0.691286i
$679$	42.5000	+	14.7224i	1.63100	+	0.564995i
$680$		0			0
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$		0			0
$683$	41.5692	−	24.0000i	1.59060	−	0.918334i	0.597398	−	0.801945i	$-0.296201\pi$
$683$	41.5692	−	24.0000i	1.59060	−	0.918334i	0.993204	−	0.116390i	$-0.0371322\pi$
$684$	0.500000	−	0.866025i	0.0191180	−	0.0331133i
$685$		0			0
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$			7.00000i			0.267067i
$688$	−6.92820	−	4.00000i	−0.264135	−	0.152499i
$689$	1.00000	+	1.73205i	0.0380970	+	0.0659859i
$690$		0			0
$691$	19.5000	−	33.7750i	0.741815	−	1.28486i	−0.209853	−	0.977733i	$-0.567299\pi$
$691$	19.5000	−	33.7750i	0.741815	−	1.28486i	0.951668	−	0.307128i	$-0.0993681\pi$
$692$			6.00000i			0.228086i
$693$	−3.46410	+	10.0000i	−0.131590	+	0.379869i
$694$	22.0000			0.835109
$695$		0			0
$696$	−2.00000	−	3.46410i	−0.0758098	−	0.131306i
$697$	−20.7846	+	12.0000i	−0.787273	+	0.454532i
$698$	−1.73205	−	1.00000i	−0.0655591	−	0.0378506i
$699$	4.00000			0.151294
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	0.866025	+	0.500000i	0.0326860	+	0.0188713i
$703$	2.59808	−	1.50000i	0.0979883	−	0.0565736i
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$		0			0
$706$	−20.0000			−0.752710
$707$	31.1769	−	6.00000i	1.17253	−	0.225653i
$708$			6.00000i			0.225494i
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$		0			0
$711$	−6.50000	−	11.2583i	−0.243769	−	0.422220i
$712$	−1.73205	−	1.00000i	−0.0649113	−	0.0374766i
$713$		0			0
$714$	−1.00000	−	5.19615i	−0.0374241	−	0.194461i
$715$		0			0
$716$	4.00000	−	6.92820i	0.149487	−	0.258919i
$717$	10.3923	−	6.00000i	0.388108	−	0.224074i
$718$	−5.19615	+	3.00000i	−0.193919	+	0.111959i
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	−0.781748	−	0.623595i	$-0.785672\pi$
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	0.930923	+	0.365216i	$0.119005\pi$
$720$		0			0
$721$	14.0000	−	12.1244i	0.521387	−	0.451535i
$722$			18.0000i			0.669891i
$723$	−11.2583	−	6.50000i	−0.418702	−	0.241738i
$724$	−9.00000	−	15.5885i	−0.334482	−	0.579340i
$725$		0			0
$726$	−2.50000	+	4.33013i	−0.0927837	+	0.160706i
$727$			1.00000i			0.0370879i	0.999828	+	0.0185440i	$0.00590307\pi$
$727$			1.00000i			0.0370879i	−0.999828	+	0.0185440i	$0.994097\pi$
$728$	0.866025	−	2.50000i	0.0320970	−	0.0926562i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	11.2583	−	6.50000i	0.416120	−	0.240247i
$733$	30.3109	+	17.5000i	1.11956	+	0.646377i	0.941288	−	0.337604i	$-0.109617\pi$
$733$	30.3109	+	17.5000i	1.11956	+	0.646377i	0.178270	+	0.983982i	$0.442950\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	−2.00000			−0.0737210
$737$	−10.3923	−	6.00000i	−0.382805	−	0.221013i
$738$	10.3923	−	6.00000i	0.382546	−	0.220863i
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$		0			0
$741$	1.00000			0.0367359
$742$	−1.73205	+	5.00000i	−0.0635856	+	0.183556i
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$		0			0
$745$		0			0
$746$	−11.5000	−	19.9186i	−0.421045	−	0.729271i
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$		−	8.00000i		−	0.292509i
$749$	−12.0000	+	10.3923i	−0.438470	+	0.379727i
$750$		0			0
$751$	−9.50000	+	16.4545i	−0.346660	+	0.600433i	−0.985654	−	0.168779i	$-0.946018\pi$
$751$	−9.50000	+	16.4545i	−0.346660	+	0.600433i	0.638994	+	0.769212i	$0.279351\pi$
$752$	5.19615	−	3.00000i	0.189484	−	0.109399i
$753$	20.7846	−	12.0000i	0.757433	−	0.437304i
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$		0			0
$756$	0.500000	+	2.59808i	0.0181848	+	0.0944911i
$757$		−	1.00000i		−	0.0363456i	−0.999835	−	0.0181728i	$-0.994215\pi$
$757$		−	1.00000i		−	0.0363456i	0.999835	−	0.0181728i	$-0.00578490\pi$
$758$	4.33013	+	2.50000i	0.157277	+	0.0908041i
$759$	4.00000	+	6.92820i	0.145191	+	0.251478i
$760$		0			0
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	0.373914	+	0.927463i	$0.378015\pi$
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	−0.990164	+	0.139912i	$0.955318\pi$
$762$			1.00000i			0.0362262i
$763$	49.3634	−	9.50000i	1.78708	−	0.343923i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	−5.19615	+	3.00000i	−0.187622	+	0.108324i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$		0			0
$771$	−8.00000			−0.288113
$772$	−8.66025	−	5.00000i	−0.311689	−	0.179954i
$773$	−27.7128	+	16.0000i	−0.996761	+	0.575480i	−0.907288	−	0.420509i	$-0.861851\pi$
$773$	−27.7128	+	16.0000i	−0.996761	+	0.575480i	−0.0894724	+	0.995989i	$0.528518\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$		0			0
$776$	17.0000			0.610264
$777$	−2.59808	+	7.50000i	−0.0932055	+	0.269061i
$778$		−	20.0000i		−	0.717035i
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	32.0000	+	55.4256i	1.14505	+	1.98328i
$782$	−3.46410	−	2.00000i	−0.123876	−	0.0715199i
$783$			4.00000i			0.142948i
$784$	6.50000	−	2.59808i	0.232143	−	0.0927884i
$785$		0			0
$786$	−1.00000	+	1.73205i	−0.0356688	+	0.0617802i
$787$	−19.9186	+	11.5000i	−0.710021	+	0.409931i	−0.811069	−	0.584951i	$-0.801114\pi$
$787$	−19.9186	+	11.5000i	−0.710021	+	0.409931i	0.101048	+	0.994882i	$0.467780\pi$
$788$		0			0
$789$	16.0000	−	27.7128i	0.569615	−	0.986602i
$790$		0			0
$791$	−45.0000	−	15.5885i	−1.60002	−	0.554262i
$792$			4.00000i			0.142134i
$793$	11.2583	+	6.50000i	0.399795	+	0.230822i
$794$	−9.00000	−	15.5885i	−0.319398	−	0.553214i
$795$		0			0
$796$	−7.50000	+	12.9904i	−0.265830	+	0.460432i
$797$		−	42.0000i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$797$		−	42.0000i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$798$	1.73205	+	2.00000i	0.0613139	+	0.0707992i
$799$	12.0000			0.424529
$800$		0			0
$801$	1.00000	+	1.73205i	0.0353333	+	0.0611990i
$802$	−3.46410	+	2.00000i	−0.122322	+	0.0706225i
$803$	−38.1051	−	22.0000i	−1.34470	−	0.776363i
$804$	−3.00000			−0.105802
$805$		0			0
$806$		0			0
$807$		0			0
$808$	10.3923	−	6.00000i	0.365600	−	0.211079i
$809$	7.00000	+	12.1244i	0.246107	+	0.426270i	0.962442	−	0.271487i	$-0.0875152\pi$
$809$	7.00000	+	12.1244i	0.246107	+	0.426270i	−0.716335	+	0.697756i	$0.754182\pi$
$810$		0			0
$811$	−5.00000			−0.175574			−0.0877869	−	0.996139i	$-0.527979\pi$
$811$	−5.00000			−0.175574			−0.0877869	+	0.996139i	$0.527979\pi$
$812$	10.3923	−	2.00000i	0.364698	−	0.0701862i
$813$		−	20.0000i		−	0.701431i
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$		0			0
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	6.92820	+	4.00000i	0.242387	+	0.139942i
$818$		−	11.0000i		−	0.384606i
$819$	−2.00000	+	1.73205i	−0.0698857	+	0.0605228i
$820$		0			0
$821$	22.0000	−	38.1051i	0.767805	−	1.32988i	−0.170945	−	0.985281i	$-0.554682\pi$
$821$	22.0000	−	38.1051i	0.767805	−	1.32988i	0.938751	−	0.344597i	$-0.111985\pi$
$822$	−8.66025	+	5.00000i	−0.302061	+	0.174395i
$823$	7.79423	−	4.50000i	0.271690	−	0.156860i	−0.357966	−	0.933735i	$-0.616529\pi$
$823$	7.79423	−	4.50000i	0.271690	−	0.156860i	0.629655	+	0.776875i	$0.283196\pi$
$824$	3.50000	−	6.06218i	0.121928	−	0.211186i
$825$		0			0
$826$	−15.0000	−	5.19615i	−0.521917	−	0.180797i
$827$		−	40.0000i		−	1.39094i	−0.718557	−	0.695468i	$-0.755197\pi$
$827$		−	40.0000i		−	1.39094i	0.718557	−	0.695468i	$-0.244803\pi$
$828$	1.73205	+	1.00000i	0.0601929	+	0.0347524i
$829$	−1.50000	−	2.59808i	−0.0520972	−	0.0902349i	0.838801	−	0.544438i	$-0.183257\pi$
$829$	−1.50000	−	2.59808i	−0.0520972	−	0.0902349i	−0.890898	+	0.454204i	$0.849924\pi$
$830$		0			0
$831$	−0.500000	+	0.866025i	−0.0173448	+	0.0300421i
$832$		−	1.00000i		−	0.0346688i
$833$	13.8564	+	2.00000i	0.480096	+	0.0692959i
$834$	13.0000			0.450153
$835$		0			0
$836$	2.00000	+	3.46410i	0.0691714	+	0.119808i
$837$		0			0
$838$	13.8564	+	8.00000i	0.478662	+	0.276355i
$839$	−50.0000			−1.72619			−0.863096	−	0.505040i	$-0.831478\pi$
$839$	−50.0000			−1.72619			−0.863096	+	0.505040i	$0.831478\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	0.866025	+	0.500000i	0.0298452	+	0.0172311i
$843$	−15.5885	+	9.00000i	−0.536895	+	0.309976i
$844$	1.50000	+	2.59808i	0.0516321	+	0.0894295i
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−8.66025	−	10.0000i	−0.297570	−	0.343604i
$848$			2.00000i			0.0686803i
$849$	6.50000	−	11.2583i	0.223079	−	0.386385i
$850$		0			0
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$	13.8564	+	8.00000i	0.474713	+	0.274075i
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$	6.50000	+	33.7750i	0.222425	+	1.15576i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−22.5167	+	13.0000i	−0.769154	+	0.444072i	−0.832573	−	0.553915i	$-0.813133\pi$
$857$	−22.5167	+	13.0000i	−0.769154	+	0.444072i	0.0634184	+	0.997987i	$0.479800\pi$
$858$	−3.46410	+	2.00000i	−0.118262	+	0.0682789i
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$		0			0
$861$	6.00000	+	31.1769i	0.204479	+	1.06251i
$862$		−	6.00000i		−	0.204361i
$863$	29.4449	+	17.0000i	1.00231	+	0.578687i	0.908932	−	0.416944i	$-0.136899\pi$
$863$	29.4449	+	17.0000i	1.00231	+	0.578687i	0.0933825	+	0.995630i	$0.470232\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$			13.0000i			0.441503i
$868$		0			0
$869$	52.0000			1.76398
$870$		0			0
$871$	−1.50000	−	2.59808i	−0.0508256	−	0.0880325i
$872$	16.4545	−	9.50000i	0.557219	−	0.321711i
$873$	−14.7224	−	8.50000i	−0.498279	−	0.287681i
$874$	2.00000			0.0676510
$875$		0			0
$876$	−11.0000			−0.371656
$877$	−11.2583	−	6.50000i	−0.380167	−	0.219489i	0.297724	−	0.954652i	$-0.403772\pi$
$877$	−11.2583	−	6.50000i	−0.380167	−	0.219489i	−0.677891	+	0.735163i	$0.737106\pi$
$878$	−19.9186	+	11.5000i	−0.672220	+	0.388106i
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$		0			0
$881$	−40.0000			−1.34763			−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000			−1.34763			−0.673817	+	0.738898i	$0.735346\pi$
$882$	−6.92820	−	1.00000i	−0.233285	−	0.0336718i
$883$		−	1.00000i		−	0.0336527i	−0.999858	−	0.0168263i	$-0.994644\pi$
$883$		−	1.00000i		−	0.0336527i	0.999858	−	0.0168263i	$-0.00535624\pi$
$884$	1.00000	−	1.73205i	0.0336336	−	0.0582552i
$885$		0			0
$886$	−3.00000	−	5.19615i	−0.100787	−	0.174568i
$887$	−39.8372	−	23.0000i	−1.33760	−	0.772264i	−0.351150	−	0.936319i	$-0.614209\pi$
$887$	−39.8372	−	23.0000i	−1.33760	−	0.772264i	−0.986451	+	0.164055i	$0.947543\pi$
$888$			3.00000i			0.100673i
$889$	−2.50000	−	0.866025i	−0.0838473	−	0.0290456i
$890$		0			0
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	16.4545	−	9.50000i	0.550937	−	0.318084i
$893$	−5.19615	+	3.00000i	−0.173883	+	0.100391i
$894$	−8.00000	+	13.8564i	−0.267560	+	0.463428i
$895$		0			0
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$			2.00000i			0.0667781i
$898$	−1.73205	−	1.00000i	−0.0577993	−	0.0333704i
$899$		0			0
$900$		0			0
$901$	−2.00000	+	3.46410i	−0.0666297	+	0.115406i
$902$			48.0000i			1.59823i
$903$	−20.7846	+	4.00000i	−0.691669	+	0.133112i
$904$	−18.0000			−0.598671
$905$		0			0
$906$	−9.50000	−	16.4545i	−0.315616	−	0.546664i
$907$	40.7032	−	23.5000i	1.35153	−	0.780305i	0.363064	−	0.931764i	$-0.381731\pi$
$907$	40.7032	−	23.5000i	1.35153	−	0.780305i	0.988463	+	0.151460i	$0.0483973\pi$
$908$	6.92820	+	4.00000i	0.229920	+	0.132745i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−46.0000			−1.52405			−0.762024	−	0.647549i	$-0.775794\pi$
$911$	−46.0000			−1.52405			−0.762024	+	0.647549i	$0.775794\pi$
$912$	0.866025	+	0.500000i	0.0286770	+	0.0165567i
$913$	20.7846	−	12.0000i	0.687870	−	0.397142i
$914$	18.5000	+	32.0429i	0.611926	+	1.05989i
$915$		0			0
$916$	−7.00000			−0.231287
$917$	−3.46410	−	4.00000i	−0.114395	−	0.132092i
$918$			2.00000i			0.0660098i
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$	22.5167	+	13.0000i	0.741547	+	0.428132i
$923$			16.0000i			0.526646i
$924$	−10.0000	−	3.46410i	−0.328976	−	0.113961i
$925$		0			0
$926$	1.50000	−	2.59808i	0.0492931	−	0.0853781i
$927$	−6.06218	+	3.50000i	−0.199108	+	0.114955i
$928$	3.46410	−	2.00000i	0.113715	−	0.0656532i
$929$	−10.0000	+	17.3205i	−0.328089	+	0.568267i	−0.982133	−	0.188190i	$-0.939738\pi$
$929$	−10.0000	+	17.3205i	−0.328089	+	0.568267i	0.654043	+	0.756457i	$0.273071\pi$
$930$		0			0
$931$	−6.50000	+	2.59808i	−0.213029	+	0.0851485i
$932$			4.00000i			0.131024i
$933$	12.1244	+	7.00000i	0.396934	+	0.229170i
$934$	15.0000	+	25.9808i	0.490815	+	0.850117i
$935$		0			0
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$		−	46.0000i		−	1.50275i	−0.659873	−	0.751377i	$-0.729390\pi$
$937$		−	46.0000i		−	1.50275i	0.659873	−	0.751377i	$-0.270610\pi$
$938$	2.59808	−	7.50000i	0.0848302	−	0.244884i
$939$	18.0000			0.587408
$940$		0			0
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$	18.1865	−	10.5000i	0.592549	−	0.342108i
$943$	20.7846	+	12.0000i	0.676840	+	0.390774i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−32.0000			−1.04041
$947$	−32.9090	−	19.0000i	−1.06940	−	0.617417i	−0.141381	−	0.989955i	$-0.545154\pi$
$947$	−32.9090	−	19.0000i	−1.06940	−	0.617417i	−0.928017	+	0.372538i	$0.878488\pi$
$948$	11.2583	−	6.50000i	0.365654	−	0.211110i
$949$	−5.50000	−	9.52628i	−0.178538	−	0.309236i
$950$		0			0
$951$	22.0000			0.713399
$952$	5.19615	−	1.00000i	0.168408	−	0.0324102i
$953$		−	4.00000i		−	0.129573i	−0.997899	−	0.0647864i	$-0.979363\pi$
$953$		−	4.00000i		−	0.129573i	0.997899	−	0.0647864i	$-0.0206366\pi$
$954$	1.00000	−	1.73205i	0.0323762	−	0.0560772i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	−13.8564	−	8.00000i	−0.447914	−	0.258603i
$958$		−	34.0000i		−	1.09849i
$959$	−5.00000	−	25.9808i	−0.161458	−	0.838963i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−2.59808	+	1.50000i	−0.0837653	+	0.0483619i
$963$	5.19615	−	3.00000i	0.167444	−	0.0966736i
$964$	6.50000	−	11.2583i	0.209351	−	0.362606i
$965$		0			0
$966$	−4.00000	+	3.46410i	−0.128698	+	0.111456i
$967$			11.0000i			0.353736i	0.984235	+	0.176868i	$0.0565966\pi$
$967$			11.0000i			0.353736i	−0.984235	+	0.176868i	$0.943403\pi$
$968$	−4.33013	−	2.50000i	−0.139176	−	0.0803530i
$969$	1.00000	+	1.73205i	0.0321246	+	0.0556415i
$970$		0			0
$971$	−8.00000	+	13.8564i	−0.256732	+	0.444673i	−0.965365	−	0.260905i	$-0.915979\pi$
$971$	−8.00000	+	13.8564i	−0.256732	+	0.444673i	0.708632	+	0.705578i	$0.249313\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−11.2583	+	32.5000i	−0.360925	+	1.04190i
$974$	−40.0000			−1.28168
$975$		0			0
$976$	6.50000	+	11.2583i	0.208060	+	0.360370i
$977$	41.5692	−	24.0000i	1.32992	−	0.767828i	0.344631	−	0.938738i	$-0.388004\pi$
$977$	41.5692	−	24.0000i	1.32992	−	0.767828i	0.985287	+	0.170910i	$0.0546709\pi$
$978$	−19.9186	−	11.5000i	−0.636926	−	0.367729i
$979$	−8.00000			−0.255681
$980$		0			0
$981$	−19.0000			−0.606623
$982$	15.5885	+	9.00000i	0.497448	+	0.287202i
$983$	36.3731	−	21.0000i	1.16012	−	0.669796i	0.208788	−	0.977961i	$-0.433048\pi$
$983$	36.3731	−	21.0000i	1.16012	−	0.669796i	0.951333	+	0.308165i	$0.0997149\pi$
$984$	6.00000	+	10.3923i	0.191273	+	0.331295i
$985$		0			0
$986$	8.00000			0.254772
$987$	5.19615	−	15.0000i	0.165395	−	0.477455i
$988$			1.00000i			0.0318142i
$989$	−8.00000	+	13.8564i	−0.254385	+	0.440608i
$990$		0			0
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$		0			0
$993$			21.0000i			0.666415i
$994$	−32.0000	+	27.7128i	−1.01498	+	0.878997i
$995$		0			0
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$	−26.8468	+	15.5000i	−0.850246	+	0.490890i	−0.860734	−	0.509055i	$-0.829995\pi$
$997$	−26.8468	+	15.5000i	−0.850246	+	0.490890i	0.0104877	+	0.999945i	$0.496662\pi$
$998$	−23.3827	+	13.5000i	−0.740166	+	0.427335i
$999$	1.50000	−	2.59808i	0.0474579	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.o.k.499.2		4
5.2	odd	4		1050.2.i.a.751.1	yes	2
5.3	odd	4		1050.2.i.t.751.1	yes	2
5.4	even	2	inner	1050.2.o.k.499.1		4
7.4	even	3	inner	1050.2.o.k.949.1		4
35.2	odd	12		7350.2.a.cl.1.1		1
35.4	even	6	inner	1050.2.o.k.949.2		4
35.12	even	12		7350.2.a.bp.1.1		1
35.18	odd	12		1050.2.i.t.151.1	yes	2
35.23	odd	12		7350.2.a.c.1.1		1
35.32	odd	12		1050.2.i.a.151.1	✓	2
35.33	even	12		7350.2.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.a.151.1	✓	2	35.32	odd	12
1050.2.i.a.751.1	yes	2	5.2	odd	4
1050.2.i.t.151.1	yes	2	35.18	odd	12
1050.2.i.t.751.1	yes	2	5.3	odd	4
1050.2.o.k.499.1		4	5.4	even	2	inner
1050.2.o.k.499.2		4	1.1	even	1	trivial
1050.2.o.k.949.1		4	7.4	even	3	inner
1050.2.o.k.949.2		4	35.4	even	6	inner
7350.2.a.c.1.1		1	35.23	odd	12
7350.2.a.y.1.1		1	35.33	even	12
7350.2.a.bp.1.1		1	35.12	even	12
7350.2.a.cl.1.1		1	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} +(0.866025 + 0.500000i) q^{12} +1.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 + 2.59808i) q^{21} +4.00000i q^{22} +(1.73205 + 1.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{26} -1.00000i q^{27} +(-2.59808 + 0.500000i) q^{28} -4.00000 q^{29} +(-0.866025 + 0.500000i) q^{32} +(3.46410 + 2.00000i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(2.59808 + 1.50000i) q^{37} +(0.866025 - 0.500000i) q^{38} +(0.500000 + 0.866025i) q^{39} +12.0000 q^{41} +(-0.866025 + 2.50000i) q^{42} +8.00000i q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{46} +(-5.19615 - 3.00000i) q^{47} +1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(1.73205 - 1.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.50000 - 0.866025i) q^{56} -1.00000i q^{57} +(-3.46410 - 2.00000i) q^{58} +(3.00000 + 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-2.59808 + 1.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +2.00000 q^{69} +16.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-9.52628 + 5.50000i) q^{73} +(1.50000 + 2.59808i) q^{74} +1.00000 q^{76} +(-10.3923 + 2.00000i) q^{77} +1.00000i q^{78} +(6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(10.3923 + 6.00000i) q^{82} -6.00000i q^{83} +(-2.00000 + 1.73205i) q^{84} +(-4.00000 + 6.92820i) q^{86} +(-3.46410 + 2.00000i) q^{87} +(-3.46410 + 2.00000i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(-2.50000 - 0.866025i) q^{91} +2.00000i q^{92} +(-3.00000 - 5.19615i) q^{94} +(-0.500000 + 0.866025i) q^{96} -17.0000i q^{97} +(-2.59808 - 6.50000i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} - 8 q^{14} - 2 q^{16} + 2 q^{19} + 2 q^{21} + 2 q^{24} - 2 q^{26} - 16 q^{29} - 8 q^{34} + 4 q^{36} + 2 q^{39} + 48 q^{41} - 8 q^{44} + 4 q^{46} - 22 q^{49} - 4 q^{51} + 2 q^{54} - 10 q^{56} + 12 q^{59} + 26 q^{61} - 4 q^{64} + 8 q^{66} + 8 q^{69} + 64 q^{71} + 6 q^{74} + 4 q^{76} + 26 q^{79} - 2 q^{81} - 8 q^{84} - 16 q^{86} - 4 q^{89} - 10 q^{91} - 12 q^{94} - 2 q^{96} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 - 8 * q^14 - 2 * q^16 + 2 * q^19 + 2 * q^21 + 2 * q^24 - 2 * q^26 - 16 * q^29 - 8 * q^34 + 4 * q^36 + 2 * q^39 + 48 * q^41 - 8 * q^44 + 4 * q^46 - 22 * q^49 - 4 * q^51 + 2 * q^54 - 10 * q^56 + 12 * q^59 + 26 * q^61 - 4 * q^64 + 8 * q^66 + 8 * q^69 + 64 * q^71 + 6 * q^74 + 4 * q^76 + 26 * q^79 - 2 * q^81 - 8 * q^84 - 16 * q^86 - 4 * q^89 - 10 * q^91 - 12 * q^94 - 2 * q^96 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more