LMFDB - Embedded newform 1050.2.o.b.949.2

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:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.949
Dual form			1050.2.o.b.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-0.500000 + 2.59808i) q^{21} +3.00000i q^{22} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.59808 - 1.50000i) q^{33} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(-3.46410 - 2.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +(0.866025 + 2.50000i) q^{42} -10.0000i q^{43} +(1.50000 + 2.59808i) q^{44} +(5.19615 - 3.00000i) q^{47} +1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(-3.46410 - 2.00000i) q^{52} +(2.59808 + 1.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} +4.00000i q^{57} +(-7.79423 + 4.50000i) q^{58} +(1.50000 - 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} -1.00000i q^{62} +(1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(-8.66025 - 5.00000i) q^{67} -6.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(7.79423 + 1.50000i) q^{77} +4.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -9.00000i q^{83} +(2.00000 + 1.73205i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(7.79423 + 4.50000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-0.866025 + 0.500000i) q^{93} +(3.00000 - 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000i q^{97} +(-2.59808 + 6.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 6 q^{11} - 8 q^{14} - 2 q^{16} - 8 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{26} - 36 q^{29} + 2 q^{31} + 4 q^{36} - 8 q^{39} + 6 q^{44} - 22 q^{49} - 2 q^{54} - 10 q^{56} + 6 q^{59} + 20 q^{61} - 4 q^{64} + 6 q^{66} - 24 q^{71} - 16 q^{74} - 16 q^{76} - 2 q^{79} - 2 q^{81} + 8 q^{84} - 20 q^{86} + 12 q^{89} - 40 q^{91} + 12 q^{94} + 2 q^{96} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 - 6 * q^11 - 8 * q^14 - 2 * q^16 - 8 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^26 - 36 * q^29 + 2 * q^31 + 4 * q^36 - 8 * q^39 + 6 * q^44 - 22 * q^49 - 2 * q^54 - 10 * q^56 + 6 * q^59 + 20 * q^61 - 4 * q^64 + 6 * q^66 - 24 * q^71 - 16 * q^74 - 16 * q^76 - 2 * q^79 - 2 * q^81 + 8 * q^84 - 20 * q^86 + 12 * q^89 - 40 * q^91 + 12 * q^94 + 2 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$			3.00000i			0.639602i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$		−	1.00000i		−	0.192450i
$28$	−2.59808	−	0.500000i	−0.490990	−	0.0944911i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.59808	−	1.50000i	0.452267	−	0.261116i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$	−3.46410	−	2.00000i	−0.561951	−	0.324443i
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.866025	+	2.50000i	0.133631	+	0.385758i
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$		0			0
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$			1.00000i			0.144338i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$	−3.46410	−	2.00000i	−0.480384	−	0.277350i
$53$	2.59808	+	1.50000i	0.356873	+	0.206041i	0.667708	−	0.744423i	$-0.267275\pi$
$53$	2.59808	+	1.50000i	0.356873	+	0.206041i	−0.310835	+	0.950464i	$0.600609\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$			4.00000i			0.529813i
$58$	−7.79423	+	4.50000i	−1.02343	+	0.590879i
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$		−	1.00000i		−	0.127000i
$63$	1.73205	−	2.00000i	0.218218	−	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.50000	−	2.59808i	0.184637	−	0.319801i
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.133135	−	0.991098i	$-0.542504\pi$
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.924883	+	0.380251i	$0.875838\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−1.73205	−	1.00000i	−0.202721	−	0.117041i	0.395203	−	0.918594i	$-0.370674\pi$
$73$	−1.73205	−	1.00000i	−0.202721	−	0.117041i	−0.597924	+	0.801553i	$0.704008\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	−4.00000			−0.458831
$77$	7.79423	+	1.50000i	0.888235	+	0.170941i
$78$			4.00000i			0.452911i
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	9.00000i		−	0.987878i	−0.869496	−	0.493939i	$-0.835557\pi$
$83$		−	9.00000i		−	0.987878i	0.869496	−	0.493939i	$-0.164443\pi$
$84$	2.00000	+	1.73205i	0.218218	+	0.188982i
$85$		0			0
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	7.79423	+	4.50000i	0.835629	+	0.482451i
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$		0			0
$93$	−0.866025	+	0.500000i	−0.0898027	+	0.0518476i
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$			1.00000i			0.101535i	0.998711	+	0.0507673i	$0.0161667\pi$
$97$			1.00000i			0.101535i	−0.998711	+	0.0507673i	$0.983833\pi$
$98$	−2.59808	+	6.50000i	−0.262445	+	0.656599i
$99$	−3.00000			−0.301511
$100$		0			0
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$		0			0
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	−0.118199	−	0.992990i	$-0.537712\pi$
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	0.800855	+	0.598858i	$0.204379\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	3.00000			0.291386
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	−0.369132	−	0.929377i	$-0.620345\pi$
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	0.620298	+	0.784366i	$0.287012\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	−0.307290	−	0.951616i	$-0.599422\pi$
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	0.977769	−	0.209687i	$-0.0672444\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	−1.73205	+	2.00000i	−0.163663	+	0.188982i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$		0			0
$116$	−4.50000	+	7.79423i	−0.417815	+	0.723676i
$117$	3.46410	−	2.00000i	0.320256	−	0.184900i
$118$		−	3.00000i		−	0.276172i
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	8.66025	+	5.00000i	0.784063	+	0.452679i
$123$		0			0
$124$	−0.500000	−	0.866025i	−0.0449013	−	0.0777714i
$125$		0			0
$126$	0.500000	−	2.59808i	0.0445435	−	0.231455i
$127$		−	5.00000i		−	0.443678i	−0.975083	−	0.221839i	$-0.928794\pi$
$127$		−	5.00000i		−	0.443678i	0.975083	−	0.221839i	$-0.0712060\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−5.00000	+	8.66025i	−0.440225	+	0.762493i
$130$		0			0
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$		−	3.00000i		−	0.261116i
$133$	−6.92820	+	8.00000i	−0.600751	+	0.693688i
$134$	−10.0000			−0.863868
$135$		0			0
$136$		0			0
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.985577	−	0.169226i	$-0.0541268\pi$
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.346235	+	0.938148i	$0.387460\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$	10.3923	+	6.00000i	0.869048	+	0.501745i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	6.92820	−	1.00000i	0.571429	−	0.0824786i
$148$			8.00000i			0.657596i
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	−3.46410	+	2.00000i	−0.280976	+	0.162221i
$153$		0			0
$154$	7.50000	−	2.59808i	0.604367	−	0.209359i
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	0.355357	−	0.934731i	$-0.384359\pi$
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	−0.631822	+	0.775113i	$0.717693\pi$
$158$	−0.866025	−	0.500000i	−0.0688973	−	0.0397779i
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$		0			0
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	−13.8564	+	8.00000i	−1.08532	+	0.626608i	−0.932326	−	0.361619i	$-0.882224\pi$
$163$	−13.8564	+	8.00000i	−1.08532	+	0.626608i	−0.152992	+	0.988227i	$0.548891\pi$
$164$		0			0
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$		−	6.00000i		−	0.464294i	−0.972681	−	0.232147i	$-0.925425\pi$
$167$		−	6.00000i		−	0.464294i	0.972681	−	0.232147i	$-0.0745750\pi$
$168$	2.59808	+	0.500000i	0.200446	+	0.0385758i
$169$	−3.00000			−0.230769
$170$		0			0
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$	−8.66025	−	5.00000i	−0.660338	−	0.381246i
$173$	15.5885	−	9.00000i	1.18517	−	0.684257i	0.227964	−	0.973670i	$-0.426793\pi$
$173$	15.5885	−	9.00000i	1.18517	−	0.684257i	0.957205	+	0.289412i	$0.0934598\pi$
$174$	9.00000			0.682288
$175$		0			0
$176$	3.00000			0.226134
$177$	−2.59808	+	1.50000i	−0.195283	+	0.112747i
$178$	5.19615	+	3.00000i	0.389468	+	0.224860i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−6.92820	+	8.00000i	−0.513553	+	0.592999i
$183$		−	10.0000i		−	0.739221i
$184$		0			0
$185$		0			0
$186$	−0.500000	+	0.866025i	−0.0366618	+	0.0635001i
$187$		0			0
$188$		−	6.00000i		−	0.437595i
$189$	−2.50000	+	0.866025i	−0.181848	+	0.0629941i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	16.4545	+	9.50000i	1.18442	+	0.683825i	0.957033	−	0.289980i	$-0.0936485\pi$
$193$	16.4545	+	9.50000i	1.18442	+	0.683825i	0.227387	+	0.973805i	$0.426982\pi$
$194$	0.500000	+	0.866025i	0.0358979	+	0.0621770i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$	−2.59808	+	1.50000i	−0.184637	+	0.106600i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$		0			0
$201$	5.00000	+	8.66025i	0.352673	+	0.610847i
$202$		−	18.0000i		−	1.26648i
$203$	7.79423	+	22.5000i	0.547048	+	1.57919i
$204$		0			0
$205$		0			0
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$		0			0
$208$	−3.46410	+	2.00000i	−0.240192	+	0.138675i
$209$	12.0000			0.830057
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	2.59808	−	1.50000i	0.178437	−	0.103020i
$213$	5.19615	+	3.00000i	0.356034	+	0.205557i
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−2.59808	−	0.500000i	−0.176369	−	0.0339422i
$218$		−	14.0000i		−	0.948200i
$219$	1.00000	+	1.73205i	0.0675737	+	0.117041i
$220$		0			0
$221$		0			0
$222$	6.92820	−	4.00000i	0.464991	−	0.268462i
$223$		−	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
$226$		0			0
$227$	−23.3827	−	13.5000i	−1.55196	−	0.896026i	−0.997982	−	0.0634974i	$-0.979775\pi$
$227$	−23.3827	−	13.5000i	−1.55196	−	0.896026i	−0.553981	−	0.832529i	$-0.686892\pi$
$228$	3.46410	+	2.00000i	0.229416	+	0.132453i
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$	−6.00000	−	5.19615i	−0.394771	−	0.341882i
$232$			9.00000i			0.590879i
$233$	−20.7846	+	12.0000i	−1.36165	+	0.786146i	−0.989843	−	0.142166i	$-0.954593\pi$
$233$	−20.7846	+	12.0000i	−1.36165	+	0.786146i	−0.371802	+	0.928312i	$0.621260\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$			1.00000i			0.0649570i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	1.73205	+	1.00000i	0.111340	+	0.0642824i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	10.0000			0.640184
$245$		0			0
$246$		0			0
$247$	−13.8564	+	8.00000i	−0.881662	+	0.509028i
$248$	−0.866025	−	0.500000i	−0.0549927	−	0.0317500i
$249$	−4.50000	+	7.79423i	−0.285176	+	0.493939i
$250$		0			0
$251$	27.0000			1.70422			0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000			1.70422			0.852112	+	0.523359i	$0.175321\pi$
$252$	−0.866025	−	2.50000i	−0.0545545	−	0.157485i
$253$		0			0
$254$	−2.50000	−	4.33013i	−0.156864	−	0.271696i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	−0.653231	−	0.757159i	$-0.726587\pi$
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	0.329104	+	0.944294i	$0.393253\pi$
$258$			10.0000i			0.622573i
$259$	16.0000	+	13.8564i	0.994192	+	0.860995i
$260$		0			0
$261$	−4.50000	−	7.79423i	−0.278543	−	0.482451i
$262$	7.79423	+	4.50000i	0.481529	+	0.278011i
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	0.651575	−	0.758585i	$-0.274109\pi$
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	−0.331166	+	0.943572i	$0.607442\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$		0			0
$266$	−2.00000	+	10.3923i	−0.122628	+	0.637193i
$267$		−	6.00000i		−	0.367194i
$268$	−8.66025	+	5.00000i	−0.529009	+	0.305424i
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$		0			0
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$		0			0
$273$	10.3923	+	2.00000i	0.628971	+	0.121046i
$274$	18.0000			1.08742
$275$		0			0
$276$		0			0
$277$	6.92820	+	4.00000i	0.416275	+	0.240337i	0.693482	−	0.720473i	$-0.256075\pi$
$277$	6.92820	+	4.00000i	0.416275	+	0.240337i	−0.277207	+	0.960810i	$0.589409\pi$
$278$	−1.73205	+	1.00000i	−0.103882	+	0.0599760i
$279$	1.00000			0.0598684
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	−5.19615	+	3.00000i	−0.309426	+	0.178647i
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	0.0942988	−	0.995544i	$-0.469939\pi$
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	−0.815017	+	0.579437i	$0.803272\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	12.0000			0.709575
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	0.500000	−	0.866025i	0.0293105	−	0.0507673i
$292$	−1.73205	+	1.00000i	−0.101361	+	0.0585206i
$293$			33.0000i			1.92788i	0.266119	+	0.963940i	$0.414259\pi$
$293$			33.0000i			1.92788i	−0.266119	+	0.963940i	$0.585741\pi$
$294$	5.50000	−	4.33013i	0.320767	−	0.252538i
$295$		0			0
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$	2.59808	+	1.50000i	0.150756	+	0.0870388i
$298$	15.5885	+	9.00000i	0.903015	+	0.521356i
$299$		0			0
$300$		0			0
$301$	−25.0000	+	8.66025i	−1.44098	+	0.499169i
$302$		−	1.00000i		−	0.0575435i
$303$	−15.5885	+	9.00000i	−0.895533	+	0.517036i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$		0			0
$306$		0			0
$307$		−	8.00000i		−	0.456584i	−0.973593	−	0.228292i	$-0.926686\pi$
$307$		−	8.00000i		−	0.456584i	0.973593	−	0.228292i	$-0.0733141\pi$
$308$	5.19615	−	6.00000i	0.296078	−	0.341882i
$309$	−8.00000			−0.455104
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$	3.46410	+	2.00000i	0.196116	+	0.113228i
$313$	−26.8468	+	15.5000i	−1.51747	+	0.876112i	−0.517681	+	0.855574i	$0.673205\pi$
$313$	−26.8468	+	15.5000i	−1.51747	+	0.876112i	−0.999789	+	0.0205381i	$0.993462\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	−7.79423	+	4.50000i	−0.437767	+	0.252745i	−0.702650	−	0.711535i	$-0.748000\pi$
$317$	−7.79423	+	4.50000i	−0.437767	+	0.252745i	0.264883	+	0.964281i	$0.414667\pi$
$318$	−2.59808	−	1.50000i	−0.145693	−	0.0841158i
$319$	13.5000	−	23.3827i	0.755855	−	1.30918i
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$		0			0
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$	−12.1244	+	7.00000i	−0.670478	+	0.387101i
$328$		0			0
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−7.79423	−	4.50000i	−0.427764	−	0.246970i
$333$	−6.92820	−	4.00000i	−0.379663	−	0.219199i
$334$	−3.00000	−	5.19615i	−0.164153	−	0.284321i
$335$		0			0
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$			7.00000i			0.381314i	0.981657	+	0.190657i	$0.0610619\pi$
$337$			7.00000i			0.381314i	−0.981657	+	0.190657i	$0.938938\pi$
$338$	−2.59808	+	1.50000i	−0.141317	+	0.0815892i
$339$		0			0
$340$		0			0
$341$	1.50000	+	2.59808i	0.0812296	+	0.140694i
$342$		−	4.00000i		−	0.216295i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$	7.79423	−	4.50000i	0.417815	−	0.241225i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	2.59808	−	1.50000i	0.138478	−	0.0799503i
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.168397	−	0.985719i	$-0.553859\pi$
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.937856	+	0.347024i	$0.887192\pi$
$354$	−1.50000	+	2.59808i	−0.0797241	+	0.138086i
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$		−	12.0000i		−	0.634220i
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	0.924932	+	0.380131i	$0.124121\pi$
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	−0.133263	+	0.991081i	$0.542545\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	6.92820	−	4.00000i	0.364138	−	0.210235i
$363$		−	2.00000i		−	0.104973i
$364$	−2.00000	+	10.3923i	−0.104828	+	0.544705i
$365$		0			0
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	−16.4545	−	9.50000i	−0.858917	−	0.495896i	0.00473247	−	0.999989i	$-0.498494\pi$
$367$	−16.4545	−	9.50000i	−0.858917	−	0.495896i	−0.863649	+	0.504093i	$0.831827\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.50000	−	7.79423i	0.0778761	−	0.404656i
$372$			1.00000i			0.0518476i
$373$	6.92820	−	4.00000i	0.358729	−	0.207112i	−0.309794	−	0.950804i	$-0.600260\pi$
$373$	6.92820	−	4.00000i	0.358729	−	0.207112i	0.668523	+	0.743691i	$0.266927\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$			36.0000i			1.85409i
$378$	−1.73205	+	2.00000i	−0.0890871	+	0.102869i
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	−2.50000	+	4.33013i	−0.128079	+	0.221839i
$382$		0			0
$383$	15.5885	−	9.00000i	0.796533	−	0.459879i	−0.0457244	−	0.998954i	$-0.514560\pi$
$383$	15.5885	−	9.00000i	0.796533	−	0.459879i	0.842257	+	0.539076i	$0.181226\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	19.0000			0.967075
$387$	8.66025	−	5.00000i	0.440225	−	0.254164i
$388$	0.866025	+	0.500000i	0.0439658	+	0.0253837i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$	4.33013	+	5.50000i	0.218704	+	0.277792i
$393$		−	9.00000i		−	0.453990i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	3.46410	−	2.00000i	0.173858	−	0.100377i	−0.410546	−	0.911840i	$-0.634662\pi$
$397$	3.46410	−	2.00000i	0.173858	−	0.100377i	0.584404	+	0.811463i	$0.301328\pi$
$398$		−	20.0000i		−	1.00251i
$399$	10.0000	−	3.46410i	0.500626	−	0.173422i
$400$		0			0
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	−0.992932	−	0.118686i	$-0.962132\pi$
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	0.393680	−	0.919247i	$-0.371202\pi$
$402$	8.66025	+	5.00000i	0.431934	+	0.249377i
$403$	−3.46410	−	2.00000i	−0.172559	−	0.0996271i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$		0			0
$406$	18.0000	+	15.5885i	0.893325	+	0.773642i
$407$		−	24.0000i		−	1.18964i
$408$		0			0
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$		0			0
$411$	−9.00000	−	15.5885i	−0.443937	−	0.768922i
$412$		−	8.00000i		−	0.394132i
$413$	−7.79423	−	1.50000i	−0.383529	−	0.0738102i
$414$		0			0
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	1.73205	+	1.00000i	0.0848189	+	0.0489702i
$418$	10.3923	−	6.00000i	0.508304	−	0.293470i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	12.1244	−	7.00000i	0.590204	−	0.340755i
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$		0			0
$426$	6.00000			0.290701
$427$	17.3205	−	20.0000i	0.838198	−	0.967868i
$428$		−	3.00000i		−	0.145010i
$429$	−6.00000	−	10.3923i	−0.289683	−	0.501745i
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	−2.50000	+	0.866025i	−0.120004	+	0.0415705i
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$	1.73205	+	1.00000i	0.0827606	+	0.0477818i
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	0.893843	+	0.448379i	$0.147999\pi$
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	−0.0586141	+	0.998281i	$0.518668\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−28.5788	+	16.5000i	−1.35782	+	0.783939i	−0.989330	−	0.145692i	$-0.953459\pi$
$443$	−28.5788	+	16.5000i	−1.35782	+	0.783939i	−0.368492	+	0.929631i	$0.620126\pi$
$444$	4.00000	−	6.92820i	0.189832	−	0.328798i
$445$		0			0
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$		−	18.0000i		−	0.851371i
$448$	0.866025	+	2.50000i	0.0409159	+	0.118114i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−0.866025	+	0.500000i	−0.0406894	+	0.0234920i
$454$	−27.0000			−1.26717
$455$		0			0
$456$	4.00000			0.187317
$457$	0.866025	−	0.500000i	0.0405110	−	0.0233890i	−0.479608	−	0.877483i	$-0.659221\pi$
$457$	0.866025	−	0.500000i	0.0405110	−	0.0233890i	0.520119	+	0.854094i	$0.325888\pi$
$458$	−3.46410	−	2.00000i	−0.161867	−	0.0934539i
$459$		0			0
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$	−7.79423	−	1.50000i	−0.362620	−	0.0697863i
$463$			8.00000i			0.371792i	0.982569	+	0.185896i	$0.0595187\pi$
$463$			8.00000i			0.371792i	−0.982569	+	0.185896i	$0.940481\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	−31.1769	+	18.0000i	−1.44270	+	0.832941i	−0.998029	−	0.0627555i	$-0.980011\pi$
$467$	−31.1769	+	18.0000i	−1.44270	+	0.832941i	−0.444667	+	0.895696i	$0.646678\pi$
$468$		−	4.00000i		−	0.184900i
$469$	−5.00000	+	25.9808i	−0.230879	+	1.19968i
$470$		0			0
$471$	2.00000	+	3.46410i	0.0921551	+	0.159617i
$472$	−2.59808	−	1.50000i	−0.119586	−	0.0690431i
$473$	25.9808	+	15.0000i	1.19460	+	0.689701i
$474$	0.500000	+	0.866025i	0.0229658	+	0.0397779i
$475$		0			0
$476$		0			0
$477$			3.00000i			0.137361i
$478$	20.7846	−	12.0000i	0.950666	−	0.548867i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$		−	1.00000i		−	0.0455488i
$483$		0			0
$484$	2.00000			0.0909091
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	35.5070	+	20.5000i	1.60898	+	0.928944i	0.989599	+	0.143851i	$0.0459486\pi$
$487$	35.5070	+	20.5000i	1.60898	+	0.928944i	0.619378	+	0.785093i	$0.287385\pi$
$488$	8.66025	−	5.00000i	0.392031	−	0.226339i
$489$	16.0000			0.723545
$490$		0			0
$491$	−33.0000			−1.48927			−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000			−1.48927			−0.744635	+	0.667472i	$0.767376\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000	+	13.8564i	−0.359937	+	0.623429i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	5.19615	+	15.0000i	0.233079	+	0.672842i
$498$			9.00000i			0.403300i
$499$	1.00000	+	1.73205i	0.0447661	+	0.0775372i	0.887540	−	0.460730i	$-0.152412\pi$
$499$	1.00000	+	1.73205i	0.0447661	+	0.0775372i	−0.842774	+	0.538267i	$0.819079\pi$
$500$		0			0
$501$	−3.00000	+	5.19615i	−0.134030	+	0.232147i
$502$	23.3827	−	13.5000i	1.04362	−	0.602534i
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$	−2.00000	−	1.73205i	−0.0890871	−	0.0771517i
$505$		0			0
$506$		0			0
$507$	2.59808	+	1.50000i	0.115385	+	0.0666173i
$508$	−4.33013	−	2.50000i	−0.192118	−	0.110920i
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	−1.00000	+	5.19615i	−0.0442374	+	0.229864i
$512$			1.00000i			0.0441942i
$513$	−3.46410	+	2.00000i	−0.152944	+	0.0883022i
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$		0			0
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$			18.0000i			0.791639i
$518$	20.7846	+	4.00000i	0.913223	+	0.175750i
$519$	−18.0000			−0.790112
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	−7.79423	−	4.50000i	−0.341144	−	0.196960i
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	−0.573822	−	0.818980i	$-0.694540\pi$
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	0.422347	+	0.906434i	$0.361206\pi$
$524$	9.00000			0.393167
$525$		0			0
$526$	6.00000			0.261612
$527$		0			0
$528$	−2.59808	−	1.50000i	−0.113067	−	0.0652791i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	3.00000			0.130189
$532$	3.46410	+	10.0000i	0.150188	+	0.433555i
$533$		0			0
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$		0			0
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	−10.3923	+	6.00000i	−0.448461	+	0.258919i
$538$		−	21.0000i		−	0.905374i
$539$	−3.00000	−	20.7846i	−0.129219	−	0.895257i
$540$		0			0
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	−0.997587	−	0.0694205i	$-0.977885\pi$
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	0.438674	−	0.898646i	$-0.355448\pi$
$542$	−9.52628	−	5.50000i	−0.409189	−	0.236245i
$543$	−6.92820	−	4.00000i	−0.297318	−	0.171656i
$544$		0			0
$545$		0			0
$546$	10.0000	−	3.46410i	0.427960	−	0.148250i
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	15.5885	−	9.00000i	0.665906	−	0.384461i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$		0			0
$551$	18.0000	+	31.1769i	0.766826	+	1.32818i
$552$		0			0
$553$	−1.73205	+	2.00000i	−0.0736543	+	0.0850487i
$554$	8.00000			0.339887
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	0.554031	−	0.832496i	$-0.313089\pi$
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	−0.443947	+	0.896053i	$0.646422\pi$
$558$	0.866025	−	0.500000i	0.0366618	−	0.0211667i
$559$	−40.0000			−1.69182
$560$		0			0
$561$		0			0
$562$	5.19615	−	3.00000i	0.219186	−	0.126547i
$563$	−33.7750	−	19.5000i	−1.42345	−	0.821827i	−0.426855	−	0.904320i	$-0.640378\pi$
$563$	−33.7750	−	19.5000i	−1.42345	−	0.821827i	−0.996592	+	0.0824933i	$0.973712\pi$
$564$	−3.00000	+	5.19615i	−0.126323	+	0.218797i
$565$		0			0
$566$	−14.0000			−0.588464
$567$	2.59808	+	0.500000i	0.109109	+	0.0209980i
$568$			6.00000i			0.251754i
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	−0.945573	−	0.325409i	$-0.894498\pi$
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	0.190974	−	0.981595i	$-0.438835\pi$
$570$		0			0
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	10.3923	−	6.00000i	0.434524	−	0.250873i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	19.9186	+	11.5000i	0.829222	+	0.478751i	0.853586	−	0.520952i	$-0.174423\pi$
$577$	19.9186	+	11.5000i	0.829222	+	0.478751i	−0.0243645	+	0.999703i	$0.507756\pi$
$578$	−14.7224	−	8.50000i	−0.612372	−	0.353553i
$579$	−9.50000	−	16.4545i	−0.394807	−	0.683825i
$580$		0			0
$581$	−22.5000	+	7.79423i	−0.933457	+	0.323359i
$582$		−	1.00000i		−	0.0414513i
$583$	−7.79423	+	4.50000i	−0.322804	+	0.186371i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	16.5000	+	28.5788i	0.681609	+	1.18058i
$587$		−	21.0000i		−	0.866763i	−0.901211	−	0.433381i	$-0.857320\pi$
$587$		−	21.0000i		−	0.866763i	0.901211	−	0.433381i	$-0.142680\pi$
$588$	2.59808	−	6.50000i	0.107143	−	0.268055i
$589$	−4.00000			−0.164817
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$	20.7846	−	12.0000i	0.853522	−	0.492781i	−0.00831589	−	0.999965i	$-0.502647\pi$
$593$	20.7846	−	12.0000i	0.853522	−	0.492781i	0.861838	+	0.507184i	$0.169314\pi$
$594$	3.00000			0.123091
$595$		0			0
$596$	18.0000			0.737309
$597$	−17.3205	+	10.0000i	−0.708881	+	0.409273i
$598$		0			0
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$		0			0
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$	−17.3205	+	20.0000i	−0.705931	+	0.815139i
$603$		−	10.0000i		−	0.407231i
$604$	−0.500000	−	0.866025i	−0.0203447	−	0.0352381i
$605$		0			0
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	6.06218	−	3.50000i	0.246056	−	0.142061i	−0.371901	−	0.928272i	$-0.621294\pi$
$607$	6.06218	−	3.50000i	0.246056	−	0.142061i	0.617957	+	0.786212i	$0.287961\pi$
$608$			4.00000i			0.162221i
$609$	4.50000	−	23.3827i	0.182349	−	0.947514i
$610$		0			0
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$		0			0
$613$	13.8564	+	8.00000i	0.559655	+	0.323117i	0.753007	−	0.658012i	$-0.228603\pi$
$613$	13.8564	+	8.00000i	0.559655	+	0.323117i	−0.193352	+	0.981129i	$0.561936\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$		0			0
$616$	1.50000	−	7.79423i	0.0604367	−	0.314038i
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	−6.92820	+	4.00000i	−0.278693	+	0.160904i
$619$	−17.0000	+	29.4449i	−0.683288	+	1.18349i	0.290684	+	0.956819i	$0.406117\pi$
$619$	−17.0000	+	29.4449i	−0.683288	+	1.18349i	−0.973972	+	0.226670i	$0.927216\pi$
$620$		0			0
$621$		0			0
$622$			24.0000i			0.962312i
$623$	10.3923	−	12.0000i	0.416359	−	0.480770i
$624$	4.00000			0.160128
$625$		0			0
$626$	−15.5000	+	26.8468i	−0.619505	+	1.07301i
$627$	−10.3923	−	6.00000i	−0.415029	−	0.239617i
$628$	−3.46410	+	2.00000i	−0.138233	+	0.0798087i
$629$		0			0
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	−0.866025	+	0.500000i	−0.0344486	+	0.0198889i
$633$	−12.1244	−	7.00000i	−0.481900	−	0.278225i
$634$	−4.50000	+	7.79423i	−0.178718	+	0.309548i
$635$		0			0
$636$	−3.00000			−0.118958
$637$	17.3205	+	22.0000i	0.686264	+	0.871672i
$638$		−	27.0000i		−	1.06894i
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−2.59808	+	1.50000i	−0.102538	+	0.0592003i
$643$		−	34.0000i		−	1.34083i	−0.741987	−	0.670415i	$-0.766116\pi$
$643$		−	34.0000i		−	1.34083i	0.741987	−	0.670415i	$-0.233884\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.5885	−	9.00000i	−0.612845	−	0.353827i	0.161233	−	0.986916i	$-0.448453\pi$
$647$	−15.5885	−	9.00000i	−0.612845	−	0.353827i	−0.774078	+	0.633090i	$0.781786\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	4.50000	+	7.79423i	0.176640	+	0.305950i
$650$		0			0
$651$	2.00000	+	1.73205i	0.0783862	+	0.0678844i
$652$			16.0000i			0.626608i
$653$	2.59808	−	1.50000i	0.101671	−	0.0586995i	−0.448303	−	0.893882i	$-0.647971\pi$
$653$	2.59808	−	1.50000i	0.101671	−	0.0586995i	0.549973	+	0.835182i	$0.314638\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$		0			0
$656$		0			0
$657$		−	2.00000i		−	0.0780274i
$658$	−15.5885	−	3.00000i	−0.607701	−	0.116952i
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−17.3205	−	10.0000i	−0.673181	−	0.388661i
$663$		0			0
$664$	−9.00000			−0.349268
$665$		0			0
$666$	−8.00000			−0.309994
$667$		0			0
$668$	−5.19615	−	3.00000i	−0.201045	−	0.116073i
$669$	−9.50000	+	16.4545i	−0.367291	+	0.636167i
$670$		0			0
$671$	−30.0000			−1.15814
$672$	1.73205	−	2.00000i	0.0668153	−	0.0771517i
$673$			29.0000i			1.11787i	0.829212	+	0.558934i	$0.188789\pi$
$673$			29.0000i			1.11787i	−0.829212	+	0.558934i	$0.811211\pi$
$674$	3.50000	+	6.06218i	0.134815	+	0.233506i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	28.5788	−	16.5000i	1.09837	−	0.634147i	0.162581	−	0.986695i	$-0.448018\pi$
$677$	28.5788	−	16.5000i	1.09837	−	0.634147i	0.935793	+	0.352549i	$0.114685\pi$
$678$		0			0
$679$	2.50000	−	0.866025i	0.0959412	−	0.0332350i
$680$		0			0
$681$	13.5000	+	23.3827i	0.517321	+	0.896026i
$682$	2.59808	+	1.50000i	0.0994855	+	0.0574380i
$683$	−28.5788	−	16.5000i	−1.09354	−	0.631355i	−0.159022	−	0.987275i	$-0.550834\pi$
$683$	−28.5788	−	16.5000i	−1.09354	−	0.631355i	−0.934516	+	0.355920i	$0.884168\pi$
$684$	−2.00000	−	3.46410i	−0.0764719	−	0.132453i
$685$		0			0
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$			4.00000i			0.152610i
$688$	−8.66025	+	5.00000i	−0.330169	+	0.190623i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		−	18.0000i		−	0.684257i
$693$	2.59808	+	7.50000i	0.0986928	+	0.284901i
$694$	12.0000			0.455514
$695$		0			0
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$		0			0
$698$	−22.5167	+	13.0000i	−0.852268	+	0.492057i
$699$	24.0000			0.907763
$700$		0			0
$701$	−15.0000			−0.566542			−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000			−0.566542			−0.283271	+	0.959040i	$0.591420\pi$
$702$	−3.46410	+	2.00000i	−0.130744	+	0.0754851i
$703$	27.7128	+	16.0000i	1.04521	+	0.603451i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	−24.0000			−0.903252
$707$	−46.7654	−	9.00000i	−1.75879	−	0.338480i
$708$			3.00000i			0.112747i
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$		0			0
$711$	0.500000	−	0.866025i	0.0187515	−	0.0324785i
$712$	5.19615	−	3.00000i	0.194734	−	0.112430i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−20.7846	−	12.0000i	−0.776215	−	0.448148i
$718$	25.9808	+	15.0000i	0.969593	+	0.559795i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$	−16.0000	−	13.8564i	−0.595871	−	0.516040i
$722$		−	3.00000i		−	0.111648i
$723$	−0.866025	+	0.500000i	−0.0322078	+	0.0185952i
$724$	4.00000	−	6.92820i	0.148659	−	0.257485i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$			13.0000i			0.482143i	0.970507	+	0.241072i	$0.0774989\pi$
$727$			13.0000i			0.482143i	−0.970507	+	0.241072i	$0.922501\pi$
$728$	3.46410	+	10.0000i	0.128388	+	0.370625i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		0			0
$732$	−8.66025	−	5.00000i	−0.320092	−	0.184805i
$733$	−8.66025	+	5.00000i	−0.319874	+	0.184679i	−0.651336	−	0.758789i	$-0.725791\pi$
$733$	−8.66025	+	5.00000i	−0.319874	+	0.184679i	0.331463	+	0.943468i	$0.392458\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$		0			0
$737$	25.9808	−	15.0000i	0.957014	−	0.552532i
$738$		0			0
$739$	25.0000	−	43.3013i	0.919640	−	1.59286i	0.119677	−	0.992813i	$-0.461814\pi$
$739$	25.0000	−	43.3013i	0.919640	−	1.59286i	0.799962	−	0.600050i	$-0.204853\pi$
$740$		0			0
$741$	16.0000			0.587775
$742$	−2.59808	−	7.50000i	−0.0953784	−	0.275334i
$743$			42.0000i			1.54083i	0.637542	+	0.770415i	$0.279951\pi$
$743$			42.0000i			1.54083i	−0.637542	+	0.770415i	$0.720049\pi$
$744$	0.500000	+	0.866025i	0.0183309	+	0.0317500i
$745$		0			0
$746$	4.00000	−	6.92820i	0.146450	−	0.253660i
$747$	7.79423	−	4.50000i	0.285176	−	0.164646i
$748$		0			0
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$		0			0
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$	−5.19615	−	3.00000i	−0.189484	−	0.109399i
$753$	−23.3827	−	13.5000i	−0.852112	−	0.491967i
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$		0			0
$756$	−0.500000	+	2.59808i	−0.0181848	+	0.0944911i
$757$		−	38.0000i		−	1.38113i	−0.723269	−	0.690567i	$-0.757361\pi$
$757$		−	38.0000i		−	1.38113i	0.723269	−	0.690567i	$-0.242639\pi$
$758$	−6.92820	+	4.00000i	−0.251644	+	0.145287i
$759$		0			0
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$			5.00000i			0.181131i
$763$	−36.3731	−	7.00000i	−1.31679	−	0.253417i
$764$		0			0
$765$		0			0
$766$	9.00000	−	15.5885i	0.325183	−	0.563234i
$767$	−10.3923	−	6.00000i	−0.375244	−	0.216647i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	19.0000			0.685158			0.342579	−	0.939489i	$-0.388700\pi$
$769$	19.0000			0.685158			0.342579	+	0.939489i	$0.388700\pi$
$770$		0			0
$771$	6.00000			0.216085
$772$	16.4545	−	9.50000i	0.592210	−	0.341912i
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	0.403634	−	0.914920i	$-0.367747\pi$
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	−0.590527	+	0.807018i	$0.701080\pi$
$774$	5.00000	−	8.66025i	0.179721	−	0.311286i
$775$		0			0
$776$	1.00000			0.0358979
$777$	−6.92820	−	20.0000i	−0.248548	−	0.717496i
$778$			6.00000i			0.215110i
$779$		0			0
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$			9.00000i			0.321634i
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$		0			0
$786$	−4.50000	−	7.79423i	−0.160510	−	0.278011i
$787$	43.3013	+	25.0000i	1.54352	+	0.891154i	0.998613	+	0.0526599i	$0.0167699\pi$
$787$	43.3013	+	25.0000i	1.54352	+	0.891154i	0.544911	+	0.838494i	$0.316563\pi$
$788$	−5.19615	−	3.00000i	−0.185105	−	0.106871i
$789$	−3.00000	−	5.19615i	−0.106803	−	0.184988i
$790$		0			0
$791$		0			0
$792$			3.00000i			0.106600i
$793$	34.6410	−	20.0000i	1.23014	−	0.710221i
$794$	2.00000	−	3.46410i	0.0709773	−	0.122936i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$			33.0000i			1.16892i	0.811423	+	0.584460i	$0.198694\pi$
$797$			33.0000i			1.16892i	−0.811423	+	0.584460i	$0.801306\pi$
$798$	6.92820	−	8.00000i	0.245256	−	0.283197i
$799$		0			0
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−20.7846	−	12.0000i	−0.733930	−	0.423735i
$803$	5.19615	−	3.00000i	0.183368	−	0.105868i
$804$	10.0000			0.352673
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−18.1865	+	10.5000i	−0.640196	+	0.369618i
$808$	−15.5885	−	9.00000i	−0.548400	−	0.316619i
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	23.3827	+	4.50000i	0.820571	+	0.157919i
$813$			11.0000i			0.385787i
$814$	−12.0000	−	20.7846i	−0.420600	−	0.728500i
$815$		0			0
$816$		0			0
$817$	−34.6410	+	20.0000i	−1.21194	+	0.699711i
$818$			25.0000i			0.874105i
$819$	−8.00000	−	6.92820i	−0.279543	−	0.242091i
$820$		0			0
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	0.891013	−	0.453978i	$-0.149995\pi$
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	−0.838663	+	0.544651i	$0.816662\pi$
$822$	−15.5885	−	9.00000i	−0.543710	−	0.313911i
$823$	34.6410	+	20.0000i	1.20751	+	0.697156i	0.962215	−	0.272292i	$-0.0877817\pi$
$823$	34.6410	+	20.0000i	1.20751	+	0.697156i	0.245295	+	0.969448i	$0.421115\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$		0			0
$826$	−7.50000	+	2.59808i	−0.260958	+	0.0903986i
$827$		−	15.0000i		−	0.521601i	−0.965393	−	0.260801i	$-0.916014\pi$
$827$		−	15.0000i		−	0.521601i	0.965393	−	0.260801i	$-0.0839865\pi$
$828$		0			0
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	−0.898665	−	0.438636i	$-0.855462\pi$
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	0.829202	+	0.558949i	$0.188795\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$			4.00000i			0.138675i
$833$		0			0
$834$	2.00000			0.0692543
$835$		0			0
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	−0.866025	−	0.500000i	−0.0299342	−	0.0172825i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−19.0526	+	11.0000i	−0.656595	+	0.379085i
$843$	−5.19615	−	3.00000i	−0.178965	−	0.103325i
$844$	7.00000	−	12.1244i	0.240950	−	0.417338i
$845$		0			0
$846$	6.00000			0.206284
$847$	3.46410	−	4.00000i	0.119028	−	0.137442i
$848$		−	3.00000i		−	0.103020i
$849$	7.00000	+	12.1244i	0.240239	+	0.416107i
$850$		0			0
$851$		0			0
$852$	5.19615	−	3.00000i	0.178017	−	0.102778i
$853$		−	10.0000i		−	0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$	5.00000	−	25.9808i	0.171096	−	0.889043i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.272882	−	0.962048i	$-0.587977\pi$
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.969599	+	0.244701i	$0.921310\pi$
$858$	−10.3923	−	6.00000i	−0.354787	−	0.204837i
$859$	25.0000	+	43.3013i	0.852989	+	1.47742i	0.878498	+	0.477746i	$0.158546\pi$
$859$	25.0000	+	43.3013i	0.852989	+	1.47742i	−0.0255092	+	0.999675i	$0.508121\pi$
$860$		0			0
$861$		0			0
$862$			12.0000i			0.408722i
$863$	5.19615	−	3.00000i	0.176879	−	0.102121i	−0.408946	−	0.912558i	$-0.634104\pi$
$863$	5.19615	−	3.00000i	0.176879	−	0.102121i	0.585826	+	0.810437i	$0.300770\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−17.0000	−	29.4449i	−0.577684	−	1.00058i
$867$			17.0000i			0.577350i
$868$	−1.73205	+	2.00000i	−0.0587896	+	0.0678844i
$869$	3.00000			0.101768
$870$		0			0
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$	−12.1244	−	7.00000i	−0.410582	−	0.237050i
$873$	−0.866025	+	0.500000i	−0.0293105	+	0.0169224i
$874$		0			0
$875$		0			0
$876$	2.00000			0.0675737
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.888640	−	0.458606i	$-0.848349\pi$
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.0471555	+	0.998888i	$0.515016\pi$
$878$	30.3109	+	17.5000i	1.02294	+	0.590596i
$879$	16.5000	−	28.5788i	0.556531	−	0.963940i
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$	−6.92820	+	1.00000i	−0.233285	+	0.0336718i
$883$			32.0000i			1.07689i	0.842662	+	0.538443i	$0.180987\pi$
$883$			32.0000i			1.07689i	−0.842662	+	0.538443i	$0.819013\pi$
$884$		0			0
$885$		0			0
$886$	−16.5000	+	28.5788i	−0.554328	+	0.960125i
$887$	20.7846	−	12.0000i	0.697879	−	0.402921i	−0.108678	−	0.994077i	$-0.534662\pi$
$887$	20.7846	−	12.0000i	0.697879	−	0.402921i	0.806557	+	0.591156i	$0.201328\pi$
$888$		−	8.00000i		−	0.268462i
$889$	−12.5000	+	4.33013i	−0.419237	+	0.145228i
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$	−16.4545	−	9.50000i	−0.550937	−	0.318084i
$893$	−20.7846	−	12.0000i	−0.695530	−	0.401565i
$894$	−9.00000	−	15.5885i	−0.301005	−	0.521356i
$895$		0			0
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$		0			0
$898$	−10.3923	+	6.00000i	−0.346796	+	0.200223i
$899$	−4.50000	+	7.79423i	−0.150083	+	0.259952i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	25.9808	+	5.00000i	0.864586	+	0.166390i
$904$		0			0
$905$		0			0
$906$	−0.500000	+	0.866025i	−0.0166114	+	0.0287718i
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	0.610594	−	0.791944i	$-0.290931\pi$
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	−0.380547	+	0.924762i	$0.624264\pi$
$908$	−23.3827	+	13.5000i	−0.775982	+	0.448013i
$909$	18.0000			0.597022
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$	3.46410	−	2.00000i	0.114708	−	0.0662266i
$913$	23.3827	+	13.5000i	0.773854	+	0.446785i
$914$	0.500000	−	0.866025i	0.0165385	−	0.0286456i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	15.5885	−	18.0000i	0.514776	−	0.594412i
$918$		0			0
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	0.924427	−	0.381358i	$-0.124544\pi$
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	−0.792480	+	0.609898i	$0.791210\pi$
$920$		0			0
$921$	−4.00000	+	6.92820i	−0.131804	+	0.228292i
$922$	25.9808	−	15.0000i	0.855631	−	0.493999i
$923$			24.0000i			0.789970i
$924$	−7.50000	+	2.59808i	−0.246732	+	0.0854704i
$925$		0			0
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	6.92820	+	4.00000i	0.227552	+	0.131377i
$928$	7.79423	+	4.50000i	0.255858	+	0.147720i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$	26.0000	+	10.3923i	0.852116	+	0.340594i
$932$			24.0000i			0.786146i
$933$	20.7846	−	12.0000i	0.680458	−	0.392862i
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$		−	35.0000i		−	1.14340i	−0.820463	−	0.571700i	$-0.806284\pi$
$937$		−	35.0000i		−	1.14340i	0.820463	−	0.571700i	$-0.193716\pi$
$938$	8.66025	+	25.0000i	0.282767	+	0.816279i
$939$	31.0000			1.01165
$940$		0			0
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	−0.783309	−	0.621633i	$-0.786469\pi$
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	0.930004	+	0.367549i	$0.119803\pi$
$942$	3.46410	+	2.00000i	0.112867	+	0.0651635i
$943$		0			0
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	30.0000			0.975384
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$	0.866025	+	0.500000i	0.0281272	+	0.0162392i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$	9.00000			0.291845
$952$		0			0
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$	1.50000	+	2.59808i	0.0485643	+	0.0841158i
$955$		0			0
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$	−23.3827	+	13.5000i	−0.755855	+	0.436393i
$958$			18.0000i			0.581554i
$959$	9.00000	−	46.7654i	0.290625	−	1.51013i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	27.7128	+	16.0000i	0.893497	+	0.515861i
$963$	2.59808	+	1.50000i	0.0837218	+	0.0483368i
$964$	−0.500000	−	0.866025i	−0.0161039	−	0.0278928i
$965$		0			0
$966$		0			0
$967$			1.00000i			0.0321578i	0.999871	+	0.0160789i	$0.00511830\pi$
$967$			1.00000i			0.0321578i	−0.999871	+	0.0160789i	$0.994882\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$		0			0
$970$		0			0
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	0.988389	+	0.151948i	$0.0485545\pi$
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	−0.362604	+	0.931943i	$0.618112\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	1.73205	+	5.00000i	0.0555270	+	0.160293i
$974$	41.0000			1.31372
$975$		0			0
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.952183	−	0.305530i	$-0.0988335\pi$
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.211495	+	0.977379i	$0.432167\pi$
$978$	13.8564	−	8.00000i	0.443079	−	0.255812i
$979$	−18.0000			−0.575282
$980$		0			0
$981$	14.0000			0.446986
$982$	−28.5788	+	16.5000i	−0.911987	+	0.526536i
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.0878058	−	0.996138i	$-0.527985\pi$
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.906583	+	0.422027i	$0.861319\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	5.19615	+	15.0000i	0.165395	+	0.477455i
$988$			16.0000i			0.509028i
$989$		0			0
$990$		0			0
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	−0.866025	+	0.500000i	−0.0274963	+	0.0158750i
$993$			20.0000i			0.634681i
$994$	12.0000	+	10.3923i	0.380617	+	0.329624i
$995$		0			0
$996$	4.50000	+	7.79423i	0.142588	+	0.246970i
$997$	12.1244	+	7.00000i	0.383982	+	0.221692i	0.679549	−	0.733630i	$-0.262175\pi$
$997$	12.1244	+	7.00000i	0.383982	+	0.221692i	−0.295567	+	0.955322i	$0.595509\pi$
$998$	1.73205	+	1.00000i	0.0548271	+	0.0316544i
$999$	4.00000	+	6.92820i	0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.o.b.949.2		4
5.2	odd	4		42.2.e.b.25.1	✓	2
5.3	odd	4		1050.2.i.e.151.1		2
5.4	even	2	inner	1050.2.o.b.949.1		4
7.2	even	3	inner	1050.2.o.b.499.1		4
15.2	even	4		126.2.g.b.109.1		2
20.7	even	4		336.2.q.d.193.1		2
35.2	odd	12		42.2.e.b.37.1	yes	2
35.3	even	12		7350.2.a.cw.1.1		1
35.9	even	6	inner	1050.2.o.b.499.2		4
35.12	even	12		294.2.e.f.79.1		2
35.17	even	12		294.2.a.a.1.1		1
35.18	odd	12		7350.2.a.ce.1.1		1
35.23	odd	12		1050.2.i.e.751.1		2
35.27	even	4		294.2.e.f.67.1		2
35.32	odd	12		294.2.a.d.1.1		1
40.27	even	4		1344.2.q.j.193.1		2
40.37	odd	4		1344.2.q.v.193.1		2
45.2	even	12		1134.2.h.a.109.1		2
45.7	odd	12		1134.2.h.p.109.1		2
45.22	odd	12		1134.2.e.a.865.1		2
45.32	even	12		1134.2.e.p.865.1		2
60.47	odd	4		1008.2.s.n.865.1		2
105.2	even	12		126.2.g.b.37.1		2
105.17	odd	12		882.2.a.k.1.1		1
105.32	even	12		882.2.a.g.1.1		1
105.47	odd	12		882.2.g.b.667.1		2
105.62	odd	4		882.2.g.b.361.1		2
140.27	odd	4		2352.2.q.m.1537.1		2
140.47	odd	12		2352.2.q.m.961.1		2
140.67	even	12		2352.2.a.m.1.1		1
140.87	odd	12		2352.2.a.n.1.1		1
140.107	even	12		336.2.q.d.289.1		2
280.37	odd	12		1344.2.q.v.961.1		2
280.67	even	12		9408.2.a.bu.1.1		1
280.107	even	12		1344.2.q.j.961.1		2
280.157	even	12		9408.2.a.db.1.1		1
280.227	odd	12		9408.2.a.bm.1.1		1
280.277	odd	12		9408.2.a.d.1.1		1
315.2	even	12		1134.2.e.p.919.1		2
315.142	odd	12		1134.2.e.a.919.1		2
315.212	even	12		1134.2.h.a.541.1		2
315.247	odd	12		1134.2.h.p.541.1		2
420.107	odd	12		1008.2.s.n.289.1		2
420.227	even	12		7056.2.a.bz.1.1		1
420.347	odd	12		7056.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.b.25.1	✓	2	5.2	odd	4
42.2.e.b.37.1	yes	2	35.2	odd	12
126.2.g.b.37.1		2	105.2	even	12
126.2.g.b.109.1		2	15.2	even	4
294.2.a.a.1.1		1	35.17	even	12
294.2.a.d.1.1		1	35.32	odd	12
294.2.e.f.67.1		2	35.27	even	4
294.2.e.f.79.1		2	35.12	even	12
336.2.q.d.193.1		2	20.7	even	4
336.2.q.d.289.1		2	140.107	even	12
882.2.a.g.1.1		1	105.32	even	12
882.2.a.k.1.1		1	105.17	odd	12
882.2.g.b.361.1		2	105.62	odd	4
882.2.g.b.667.1		2	105.47	odd	12
1008.2.s.n.289.1		2	420.107	odd	12
1008.2.s.n.865.1		2	60.47	odd	4
1050.2.i.e.151.1		2	5.3	odd	4
1050.2.i.e.751.1		2	35.23	odd	12
1050.2.o.b.499.1		4	7.2	even	3	inner
1050.2.o.b.499.2		4	35.9	even	6	inner
1050.2.o.b.949.1		4	5.4	even	2	inner
1050.2.o.b.949.2		4	1.1	even	1	trivial
1134.2.e.a.865.1		2	45.22	odd	12
1134.2.e.a.919.1		2	315.142	odd	12
1134.2.e.p.865.1		2	45.32	even	12
1134.2.e.p.919.1		2	315.2	even	12
1134.2.h.a.109.1		2	45.2	even	12
1134.2.h.a.541.1		2	315.212	even	12
1134.2.h.p.109.1		2	45.7	odd	12
1134.2.h.p.541.1		2	315.247	odd	12
1344.2.q.j.193.1		2	40.27	even	4
1344.2.q.j.961.1		2	280.107	even	12
1344.2.q.v.193.1		2	40.37	odd	4
1344.2.q.v.961.1		2	280.37	odd	12
2352.2.a.m.1.1		1	140.67	even	12
2352.2.a.n.1.1		1	140.87	odd	12
2352.2.q.m.961.1		2	140.47	odd	12
2352.2.q.m.1537.1		2	140.27	odd	4
7056.2.a.g.1.1		1	420.347	odd	12
7056.2.a.bz.1.1		1	420.227	even	12
7350.2.a.ce.1.1		1	35.18	odd	12
7350.2.a.cw.1.1		1	35.3	even	12
9408.2.a.d.1.1		1	280.277	odd	12
9408.2.a.bm.1.1		1	280.227	odd	12
9408.2.a.bu.1.1		1	280.67	even	12
9408.2.a.db.1.1		1	280.157	even	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-0.500000 + 2.59808i) q^{21} +3.00000i q^{22} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.59808 - 1.50000i) q^{33} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(-3.46410 - 2.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +(0.866025 + 2.50000i) q^{42} -10.0000i q^{43} +(1.50000 + 2.59808i) q^{44} +(5.19615 - 3.00000i) q^{47} +1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(-3.46410 - 2.00000i) q^{52} +(2.59808 + 1.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} +4.00000i q^{57} +(-7.79423 + 4.50000i) q^{58} +(1.50000 - 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} -1.00000i q^{62} +(1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(-8.66025 - 5.00000i) q^{67} -6.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(7.79423 + 1.50000i) q^{77} +4.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -9.00000i q^{83} +(2.00000 + 1.73205i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(7.79423 + 4.50000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-0.866025 + 0.500000i) q^{93} +(3.00000 - 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000i q^{97} +(-2.59808 + 6.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} - 6 q^{11} - 8 q^{14} - 2 q^{16} - 8 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{26} - 36 q^{29} + 2 q^{31} + 4 q^{36} - 8 q^{39} + 6 q^{44} - 22 q^{49} - 2 q^{54} - 10 q^{56} + 6 q^{59} + 20 q^{61} - 4 q^{64} + 6 q^{66} - 24 q^{71} - 16 q^{74} - 16 q^{76} - 2 q^{79} - 2 q^{81} + 8 q^{84} - 20 q^{86} + 12 q^{89} - 40 q^{91} + 12 q^{94} + 2 q^{96} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 - 6 * q^11 - 8 * q^14 - 2 * q^16 - 8 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^26 - 36 * q^29 + 2 * q^31 + 4 * q^36 - 8 * q^39 + 6 * q^44 - 22 * q^49 - 2 * q^54 - 10 * q^56 + 6 * q^59 + 20 * q^61 - 4 * q^64 + 6 * q^66 - 24 * q^71 - 16 * q^74 - 16 * q^76 - 2 * q^79 - 2 * q^81 + 8 * q^84 - 20 * q^86 + 12 * q^89 - 40 * q^91 + 12 * q^94 + 2 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

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Database

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