LMFDB - Embedded newform 1134.2.m.a.755.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(377,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1134.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.m (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:	$9.05503558921$
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 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			755.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.755
Dual form			1134.2.m.a.377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.73205 + 3.00000i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.73205 + 3.00000i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +3.46410i q^{10} +(-5.19615 - 3.00000i) q^{11} +(-1.50000 + 0.866025i) q^{13} +(-2.59808 - 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.73205 q^{17} +6.92820i q^{19} +(-1.73205 + 3.00000i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-2.59808 + 1.50000i) q^{23} +(-3.50000 + 6.06218i) q^{25} -1.73205 q^{26} +(-2.00000 - 1.73205i) q^{28} +(-2.59808 - 1.50000i) q^{29} +(4.50000 - 2.59808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.50000 + 0.866025i) q^{34} +(-6.92820 - 6.00000i) q^{35} -2.00000 q^{37} +(-3.46410 + 6.00000i) q^{38} +(-3.00000 + 1.73205i) q^{40} +(3.46410 + 6.00000i) q^{41} +(5.50000 - 9.52628i) q^{43} -6.00000i q^{44} -3.00000 q^{46} +(-3.46410 + 6.00000i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-6.06218 + 3.50000i) q^{50} +(-1.50000 - 0.866025i) q^{52} +3.00000i q^{53} -20.7846i q^{55} +(-0.866025 - 2.50000i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-4.33013 - 7.50000i) q^{59} +(12.0000 + 6.92820i) q^{61} +5.19615 q^{62} -1.00000 q^{64} +(-5.19615 - 3.00000i) q^{65} +(3.50000 + 6.06218i) q^{67} +(0.866025 + 1.50000i) q^{68} +(-3.00000 - 8.66025i) q^{70} +3.00000i q^{71} +6.92820i q^{73} +(-1.73205 - 1.00000i) q^{74} +(-6.00000 + 3.46410i) q^{76} +(15.5885 + 3.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} -3.46410 q^{80} +6.92820i q^{82} +(-1.73205 + 3.00000i) q^{83} +(3.00000 + 5.19615i) q^{85} +(9.52628 - 5.50000i) q^{86} +(3.00000 - 5.19615i) q^{88} -5.19615 q^{89} +(3.00000 - 3.46410i) q^{91} +(-2.59808 - 1.50000i) q^{92} +(-6.00000 + 3.46410i) q^{94} +(-20.7846 + 12.0000i) q^{95} +(6.00000 + 3.46410i) q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 10 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 - 10 * q^7	$ 4 q + 2 q^{4} - 10 q^{7} - 6 q^{13} - 2 q^{16} - 12 q^{22} - 14 q^{25} - 8 q^{28} + 18 q^{31} + 6 q^{34} - 8 q^{37} - 12 q^{40} + 22 q^{43} - 12 q^{46} + 22 q^{49} - 6 q^{52} - 6 q^{58} + 48 q^{61} - 4 q^{64} + 14 q^{67} - 12 q^{70} - 24 q^{76} - 16 q^{79} + 12 q^{85} + 12 q^{88} + 12 q^{91} - 24 q^{94} + 24 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 10 * q^7 - 6 * q^13 - 2 * q^16 - 12 * q^22 - 14 * q^25 - 8 * q^28 + 18 * q^31 + 6 * q^34 - 8 * q^37 - 12 * q^40 + 22 * q^43 - 12 * q^46 + 22 * q^49 - 6 * q^52 - 6 * q^58 + 48 * q^61 - 4 * q^64 + 14 * q^67 - 12 * q^70 - 24 * q^76 - 16 * q^79 + 12 * q^85 + 12 * q^88 + 12 * q^91 - 24 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.73205	+	3.00000i	0.774597	+	1.34164i	0.935021	+	0.354593i	$0.115380\pi$
$5$	1.73205	+	3.00000i	0.774597	+	1.34164i	−0.160424	+	0.987048i	$0.551286\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$			1.00000i			0.353553i
$9$		0			0
$10$			3.46410i			1.09545i
$11$	−5.19615	−	3.00000i	−1.56670	−	0.904534i	−0.996550	−	0.0829925i	$-0.973552\pi$
$11$	−5.19615	−	3.00000i	−1.56670	−	0.904534i	−0.570149	−	0.821541i	$-0.693114\pi$
$12$		0			0
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	0.277350	+	0.960769i	$0.410544\pi$
$14$	−2.59808	−	0.500000i	−0.694365	−	0.133631i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.73205			0.420084			0.210042	−	0.977692i	$-0.432640\pi$
$17$	1.73205			0.420084			0.210042	+	0.977692i	$0.432640\pi$
$18$		0			0
$19$			6.92820i			1.58944i	0.606977	+	0.794719i	$0.292382\pi$
$19$			6.92820i			1.58944i	−0.606977	+	0.794719i	$0.707618\pi$
$20$	−1.73205	+	3.00000i	−0.387298	+	0.670820i
$21$		0			0
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	−0.745782	−	0.666190i	$-0.767924\pi$
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	0.204046	+	0.978961i	$0.434591\pi$
$24$		0			0
$25$	−3.50000	+	6.06218i	−0.700000	+	1.21244i
$26$	−1.73205			−0.339683
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−2.59808	−	1.50000i	−0.482451	−	0.278543i	0.238987	−	0.971023i	$-0.423185\pi$
$29$	−2.59808	−	1.50000i	−0.482451	−	0.278543i	−0.721437	+	0.692480i	$0.756518\pi$
$30$		0			0
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	−0.0381148	−	0.999273i	$-0.512135\pi$
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	0.846339	+	0.532645i	$0.178802\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	1.50000	+	0.866025i	0.257248	+	0.148522i
$35$	−6.92820	−	6.00000i	−1.17108	−	1.01419i
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	−3.46410	+	6.00000i	−0.561951	+	0.973329i
$39$		0			0
$40$	−3.00000	+	1.73205i	−0.474342	+	0.273861i
$41$	3.46410	+	6.00000i	0.541002	+	0.937043i	0.998847	+	0.0480106i	$0.0152881\pi$
$41$	3.46410	+	6.00000i	0.541002	+	0.937043i	−0.457845	+	0.889032i	$0.651379\pi$
$42$		0			0
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	−0.0522047	−	0.998636i	$-0.516625\pi$
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	0.890947	−	0.454108i	$-0.150042\pi$
$44$		−	6.00000i		−	0.904534i
$45$		0			0
$46$	−3.00000			−0.442326
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	0.494690	+	0.869069i	$0.335282\pi$
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	−0.999981	+	0.00612051i	$0.998052\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−6.06218	+	3.50000i	−0.857321	+	0.494975i
$51$		0			0
$52$	−1.50000	−	0.866025i	−0.208013	−	0.120096i
$53$			3.00000i			0.412082i	0.978543	+	0.206041i	$0.0660580\pi$
$53$			3.00000i			0.412082i	−0.978543	+	0.206041i	$0.933942\pi$
$54$		0			0
$55$		−	20.7846i		−	2.80260i
$56$	−0.866025	−	2.50000i	−0.115728	−	0.334077i
$57$		0			0
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	−0.997166	−	0.0752304i	$-0.976031\pi$
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	0.433432	−	0.901186i	$-0.357303\pi$
$60$		0			0
$61$	12.0000	+	6.92820i	1.53644	+	0.887066i	0.999043	+	0.0437377i	$0.0139266\pi$
$61$	12.0000	+	6.92820i	1.53644	+	0.887066i	0.537400	+	0.843328i	$0.319407\pi$
$62$	5.19615			0.659912
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.19615	−	3.00000i	−0.644503	−	0.372104i
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	0.866025	+	1.50000i	0.105021	+	0.181902i
$69$		0			0
$70$	−3.00000	−	8.66025i	−0.358569	−	1.03510i
$71$			3.00000i			0.356034i	0.984027	+	0.178017i	$0.0569683\pi$
$71$			3.00000i			0.356034i	−0.984027	+	0.178017i	$0.943032\pi$
$72$		0			0
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	−1.73205	−	1.00000i	−0.201347	−	0.116248i
$75$		0			0
$76$	−6.00000	+	3.46410i	−0.688247	+	0.397360i
$77$	15.5885	+	3.00000i	1.77647	+	0.341882i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−3.46410			−0.387298
$81$		0			0
$82$			6.92820i			0.765092i
$83$	−1.73205	+	3.00000i	−0.190117	+	0.329293i	−0.945289	−	0.326234i	$-0.894220\pi$
$83$	−1.73205	+	3.00000i	−0.190117	+	0.329293i	0.755172	+	0.655527i	$0.227553\pi$
$84$		0			0
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$	9.52628	−	5.50000i	1.02725	−	0.593080i
$87$		0			0
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	−5.19615			−0.550791			−0.275396	−	0.961331i	$-0.588809\pi$
$89$	−5.19615			−0.550791			−0.275396	+	0.961331i	$0.588809\pi$
$90$		0			0
$91$	3.00000	−	3.46410i	0.314485	−	0.363137i
$92$	−2.59808	−	1.50000i	−0.270868	−	0.156386i
$93$		0			0
$94$	−6.00000	+	3.46410i	−0.618853	+	0.357295i
$95$	−20.7846	+	12.0000i	−2.13246	+	1.23117i
$96$		0			0
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	0.772655	−	0.634826i	$-0.218928\pi$
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	−0.163448	+	0.986552i	$0.552261\pi$
$98$	6.92820	−	1.00000i	0.699854	−	0.101015i
$99$		0			0
$100$	−7.00000			−0.700000
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	−0.821705	−	0.569914i	$-0.806977\pi$
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	0.0827075	+	0.996574i	$0.473643\pi$
$104$	−0.866025	−	1.50000i	−0.0849208	−	0.147087i
$105$		0			0
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	10.3923	−	18.0000i	0.990867	−	1.71623i
$111$		0			0
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	−0.724082	−	0.689714i	$-0.757736\pi$
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	0.235269	+	0.971930i	$0.424403\pi$
$114$		0			0
$115$	−9.00000	−	5.19615i	−0.839254	−	0.484544i
$116$		−	3.00000i		−	0.278543i
$117$		0			0
$118$		−	8.66025i		−	0.797241i
$119$	−4.33013	+	1.50000i	−0.396942	+	0.137505i
$120$		0			0
$121$	12.5000	+	21.6506i	1.13636	+	1.96824i
$122$	6.92820	+	12.0000i	0.627250	+	1.08643i
$123$		0			0
$124$	4.50000	+	2.59808i	0.404112	+	0.233314i
$125$	−6.92820			−0.619677
$126$		0			0
$127$	14.0000			1.24230			0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000			1.24230			0.621150	+	0.783692i	$0.286666\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$		0			0
$133$	−6.00000	−	17.3205i	−0.520266	−	1.50188i
$134$			7.00000i			0.604708i
$135$		0			0
$136$			1.73205i			0.148522i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	−3.00000	+	1.73205i	−0.254457	+	0.146911i	−0.621803	−	0.783174i	$-0.713600\pi$
$139$	−3.00000	+	1.73205i	−0.254457	+	0.146911i	0.367347	+	0.930084i	$0.380266\pi$
$140$	1.73205	−	9.00000i	0.146385	−	0.760639i
$141$		0			0
$142$	−1.50000	+	2.59808i	−0.125877	+	0.218026i
$143$	10.3923			0.869048
$144$		0			0
$145$		−	10.3923i		−	0.863034i
$146$	−3.46410	+	6.00000i	−0.286691	+	0.496564i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	12.9904	−	7.50000i	1.06421	−	0.614424i	0.137619	−	0.990485i	$-0.456055\pi$
$149$	12.9904	−	7.50000i	1.06421	−	0.614424i	0.926595	+	0.376061i	$0.122722\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	−6.92820			−0.561951
$153$		0			0
$154$	12.0000	+	10.3923i	0.966988	+	0.837436i
$155$	15.5885	+	9.00000i	1.25210	+	0.722897i
$156$		0			0
$157$	13.5000	−	7.79423i	1.07742	−	0.622047i	0.147219	−	0.989104i	$-0.452968\pi$
$157$	13.5000	−	7.79423i	1.07742	−	0.622047i	0.930199	+	0.367057i	$0.119635\pi$
$158$	−6.92820	+	4.00000i	−0.551178	+	0.318223i
$159$		0			0
$160$	−3.00000	−	1.73205i	−0.237171	−	0.136931i
$161$	5.19615	−	6.00000i	0.409514	−	0.472866i
$162$		0			0
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$		0			0
$166$	−3.00000	+	1.73205i	−0.232845	+	0.134433i
$167$	−8.66025	−	15.0000i	−0.670151	−	1.16073i	−0.977861	−	0.209255i	$-0.932896\pi$
$167$	−8.66025	−	15.0000i	−0.670151	−	1.16073i	0.307711	−	0.951480i	$-0.400437\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$			6.00000i			0.460179i
$171$		0			0
$172$	11.0000			0.838742
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	0.135785	+	0.990738i	$0.456644\pi$
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	−0.925897	+	0.377776i	$0.876689\pi$
$174$		0			0
$175$	3.50000	−	18.1865i	0.264575	−	1.37477i
$176$	5.19615	−	3.00000i	0.391675	−	0.226134i
$177$		0			0
$178$	−4.50000	−	2.59808i	−0.337289	−	0.194734i
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$		0			0
$181$		−	1.73205i		−	0.128742i	−0.997926	−	0.0643712i	$-0.979496\pi$
$181$		−	1.73205i		−	0.128742i	0.997926	−	0.0643712i	$-0.0205042\pi$
$182$	4.33013	−	1.50000i	0.320970	−	0.111187i
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	−3.46410	−	6.00000i	−0.254686	−	0.441129i
$186$		0			0
$187$	−9.00000	−	5.19615i	−0.658145	−	0.379980i
$188$	−6.92820			−0.505291
$189$		0			0
$190$	−24.0000			−1.74114
$191$	20.7846	+	12.0000i	1.50392	+	0.868290i	0.999990	+	0.00454614i	$0.00144709\pi$
$191$	20.7846	+	12.0000i	1.50392	+	0.868290i	0.503932	+	0.863743i	$0.331886\pi$
$192$		0			0
$193$	−6.50000	−	11.2583i	−0.467880	−	0.810392i	0.531446	−	0.847092i	$-0.321649\pi$
$193$	−6.50000	−	11.2583i	−0.467880	−	0.810392i	−0.999326	+	0.0366998i	$0.988315\pi$
$194$	3.46410	+	6.00000i	0.248708	+	0.430775i
$195$		0			0
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		0			0
$199$			8.66025i			0.613909i	0.951724	+	0.306955i	$0.0993100\pi$
$199$			8.66025i			0.613909i	−0.951724	+	0.306955i	$0.900690\pi$
$200$	−6.06218	−	3.50000i	−0.428661	−	0.247487i
$201$		0			0
$202$		0			0
$203$	7.79423	+	1.50000i	0.547048	+	0.105279i
$204$		0			0
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	−8.66025			−0.603388
$207$		0			0
$208$		−	1.73205i		−	0.120096i
$209$	20.7846	−	36.0000i	1.43770	−	2.49017i
$210$		0			0
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	0.720035	−	0.693938i	$-0.244126\pi$
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	−0.960985	+	0.276600i	$0.910792\pi$
$212$	−2.59808	+	1.50000i	−0.178437	+	0.103020i
$213$		0			0
$214$		0			0
$215$	38.1051			2.59875
$216$		0			0
$217$	−9.00000	+	10.3923i	−0.610960	+	0.705476i
$218$	3.46410	+	2.00000i	0.234619	+	0.135457i
$219$		0			0
$220$	18.0000	−	10.3923i	1.21356	−	0.700649i
$221$	−2.59808	+	1.50000i	−0.174766	+	0.100901i
$222$		0			0
$223$	9.00000	+	5.19615i	0.602685	+	0.347960i	0.770097	−	0.637927i	$-0.220208\pi$
$223$	9.00000	+	5.19615i	0.602685	+	0.347960i	−0.167412	+	0.985887i	$0.553541\pi$
$224$	1.73205	−	2.00000i	0.115728	−	0.133631i
$225$		0			0
$226$	−6.00000			−0.399114
$227$	12.9904	−	22.5000i	0.862202	−	1.49338i	−0.00759708	−	0.999971i	$-0.502418\pi$
$227$	12.9904	−	22.5000i	0.862202	−	1.49338i	0.869799	−	0.493406i	$-0.164248\pi$
$228$		0			0
$229$	18.0000	−	10.3923i	1.18947	−	0.686743i	0.231287	−	0.972886i	$-0.425707\pi$
$229$	18.0000	−	10.3923i	1.18947	−	0.686743i	0.958187	+	0.286143i	$0.0923732\pi$
$230$	−5.19615	−	9.00000i	−0.342624	−	0.593442i
$231$		0			0
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$		−	24.0000i		−	1.57229i	−0.618041	−	0.786146i	$-0.712073\pi$
$233$		−	24.0000i		−	1.57229i	0.618041	−	0.786146i	$-0.287927\pi$
$234$		0			0
$235$	−24.0000			−1.56559
$236$	4.33013	−	7.50000i	0.281867	−	0.488208i
$237$		0			0
$238$	−4.50000	−	0.866025i	−0.291692	−	0.0561361i
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$		0			0
$241$	12.0000	+	6.92820i	0.772988	+	0.446285i	0.833939	−	0.551856i	$-0.186080\pi$
$241$	12.0000	+	6.92820i	0.772988	+	0.446285i	−0.0609515	+	0.998141i	$0.519414\pi$
$242$			25.0000i			1.60706i
$243$		0			0
$244$			13.8564i			0.887066i
$245$	22.5167	+	9.00000i	1.43854	+	0.574989i
$246$		0			0
$247$	−6.00000	−	10.3923i	−0.381771	−	0.661247i
$248$	2.59808	+	4.50000i	0.164978	+	0.285750i
$249$		0			0
$250$	−6.00000	−	3.46410i	−0.379473	−	0.219089i
$251$	−3.46410			−0.218652			−0.109326	−	0.994006i	$-0.534869\pi$
$251$	−3.46410			−0.218652			−0.109326	+	0.994006i	$0.534869\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	12.1244	+	7.00000i	0.760750	+	0.439219i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.3923	−	18.0000i	−0.648254	−	1.12281i	−0.983540	−	0.180693i	$-0.942166\pi$
$257$	−10.3923	−	18.0000i	−0.648254	−	1.12281i	0.335285	−	0.942117i	$-0.391167\pi$
$258$		0			0
$259$	5.00000	−	1.73205i	0.310685	−	0.107624i
$260$		−	6.00000i		−	0.372104i
$261$		0			0
$262$		−	5.19615i		−	0.321019i
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	0.240059	−	0.970758i	$-0.422833\pi$
$263$	−7.79423	−	4.50000i	−0.480613	−	0.277482i	−0.720672	+	0.693276i	$0.756167\pi$
$264$		0			0
$265$	−9.00000	+	5.19615i	−0.552866	+	0.319197i
$266$	3.46410	−	18.0000i	0.212398	−	1.10365i
$267$		0			0
$268$	−3.50000	+	6.06218i	−0.213797	+	0.370306i
$269$	3.46410			0.211210			0.105605	−	0.994408i	$-0.466322\pi$
$269$	3.46410			0.211210			0.105605	+	0.994408i	$0.466322\pi$
$270$		0			0
$271$		−	12.1244i		−	0.736502i	−0.929726	−	0.368251i	$-0.879957\pi$
$271$		−	12.1244i		−	0.736502i	0.929726	−	0.368251i	$-0.120043\pi$
$272$	−0.866025	+	1.50000i	−0.0525105	+	0.0909509i
$273$		0			0
$274$		0			0
$275$	36.3731	−	21.0000i	2.19338	−	1.26635i
$276$		0			0
$277$	−10.0000	+	17.3205i	−0.600842	+	1.04069i	0.391852	+	0.920028i	$0.371834\pi$
$277$	−10.0000	+	17.3205i	−0.600842	+	1.04069i	−0.992694	+	0.120660i	$0.961499\pi$
$278$	−3.46410			−0.207763
$279$		0			0
$280$	6.00000	−	6.92820i	0.358569	−	0.414039i
$281$	−25.9808	−	15.0000i	−1.54988	−	0.894825i	−0.998150	−	0.0608039i	$-0.980634\pi$
$281$	−25.9808	−	15.0000i	−1.54988	−	0.894825i	−0.551733	−	0.834021i	$-0.686033\pi$
$282$		0			0
$283$	−18.0000	+	10.3923i	−1.06999	+	0.617758i	−0.928178	−	0.372135i	$-0.878626\pi$
$283$	−18.0000	+	10.3923i	−1.06999	+	0.617758i	−0.141810	+	0.989894i	$0.545292\pi$
$284$	−2.59808	+	1.50000i	−0.154167	+	0.0890086i
$285$		0			0
$286$	9.00000	+	5.19615i	0.532181	+	0.307255i
$287$	−13.8564	−	12.0000i	−0.817918	−	0.708338i
$288$		0			0
$289$	−14.0000			−0.823529
$290$	5.19615	−	9.00000i	0.305129	−	0.528498i
$291$		0			0
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	8.66025	+	15.0000i	0.505937	+	0.876309i	0.999976	+	0.00686959i	$0.00218668\pi$
$293$	8.66025	+	15.0000i	0.505937	+	0.876309i	−0.494039	+	0.869440i	$0.664480\pi$
$294$		0			0
$295$	15.0000	−	25.9808i	0.873334	−	1.51266i
$296$		−	2.00000i		−	0.116248i
$297$		0			0
$298$	15.0000			0.868927
$299$	2.59808	−	4.50000i	0.150251	−	0.260242i
$300$		0			0
$301$	−5.50000	+	28.5788i	−0.317015	+	1.64726i
$302$	6.92820	−	4.00000i	0.398673	−	0.230174i
$303$		0			0
$304$	−6.00000	−	3.46410i	−0.344124	−	0.198680i
$305$			48.0000i			2.74847i
$306$		0			0
$307$			31.1769i			1.77936i	0.456584	+	0.889680i	$0.349073\pi$
$307$			31.1769i			1.77936i	−0.456584	+	0.889680i	$0.650927\pi$
$308$	5.19615	+	15.0000i	0.296078	+	0.854704i
$309$		0			0
$310$	9.00000	+	15.5885i	0.511166	+	0.885365i
$311$	6.92820	+	12.0000i	0.392862	+	0.680458i	0.992826	−	0.119570i	$-0.0381515\pi$
$311$	6.92820	+	12.0000i	0.392862	+	0.680458i	−0.599963	+	0.800027i	$0.704818\pi$
$312$		0			0
$313$	−12.0000	−	6.92820i	−0.678280	−	0.391605i	0.120927	−	0.992661i	$-0.461413\pi$
$313$	−12.0000	−	6.92820i	−0.678280	−	0.391605i	−0.799207	+	0.601056i	$0.794747\pi$
$314$	15.5885			0.879708
$315$		0			0
$316$	−8.00000			−0.450035
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$	−1.73205	−	3.00000i	−0.0968246	−	0.167705i
$321$		0			0
$322$	7.50000	−	2.59808i	0.417959	−	0.144785i
$323$			12.0000i			0.667698i
$324$		0			0
$325$		−	12.1244i		−	0.672538i
$326$	9.52628	+	5.50000i	0.527612	+	0.304617i
$327$		0			0
$328$	−6.00000	+	3.46410i	−0.331295	+	0.191273i
$329$	3.46410	−	18.0000i	0.190982	−	0.992372i
$330$		0			0
$331$	8.50000	−	14.7224i	0.467202	−	0.809218i	−0.532096	−	0.846684i	$-0.678595\pi$
$331$	8.50000	−	14.7224i	0.467202	−	0.809218i	0.999298	+	0.0374662i	$0.0119287\pi$
$332$	−3.46410			−0.190117
$333$		0			0
$334$		−	17.3205i		−	0.947736i
$335$	−12.1244	+	21.0000i	−0.662424	+	1.14735i
$336$		0			0
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$	−8.66025	+	5.00000i	−0.471056	+	0.271964i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−31.1769			−1.68832
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	9.52628	+	5.50000i	0.513623	+	0.296540i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	−0.856186	−	0.516667i	$-0.827172\pi$
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	0.0193540	+	0.999813i	$0.493839\pi$
$348$		0			0
$349$	16.5000	+	9.52628i	0.883225	+	0.509930i	0.871720	−	0.490004i	$-0.163005\pi$
$349$	16.5000	+	9.52628i	0.883225	+	0.509930i	0.0115044	+	0.999934i	$0.496338\pi$
$350$	12.1244	−	14.0000i	0.648074	−	0.748331i
$351$		0			0
$352$	6.00000			0.319801
$353$	4.33013	−	7.50000i	0.230469	−	0.399185i	−0.727477	−	0.686132i	$-0.759307\pi$
$353$	4.33013	−	7.50000i	0.230469	−	0.399185i	0.957946	+	0.286947i	$0.0926405\pi$
$354$		0			0
$355$	−9.00000	+	5.19615i	−0.477670	+	0.275783i
$356$	−2.59808	−	4.50000i	−0.137698	−	0.238500i
$357$		0			0
$358$	−3.00000	+	5.19615i	−0.158555	+	0.274625i
$359$		−	27.0000i		−	1.42501i	−0.701669	−	0.712503i	$-0.747562\pi$
$359$		−	27.0000i		−	1.42501i	0.701669	−	0.712503i	$-0.252438\pi$
$360$		0			0
$361$	−29.0000			−1.52632
$362$	0.866025	−	1.50000i	0.0455173	−	0.0788382i
$363$		0			0
$364$	4.50000	+	0.866025i	0.235864	+	0.0453921i
$365$	−20.7846	+	12.0000i	−1.08792	+	0.628109i
$366$		0			0
$367$	−16.5000	−	9.52628i	−0.861293	−	0.497268i	0.00315207	−	0.999995i	$-0.498997\pi$
$367$	−16.5000	−	9.52628i	−0.861293	−	0.497268i	−0.864445	+	0.502727i	$0.832330\pi$
$368$		−	3.00000i		−	0.156386i
$369$		0			0
$370$		−	6.92820i		−	0.360180i
$371$	−2.59808	−	7.50000i	−0.134885	−	0.389381i
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	−5.19615	−	9.00000i	−0.268687	−	0.465379i
$375$		0			0
$376$	−6.00000	−	3.46410i	−0.309426	−	0.178647i
$377$	5.19615			0.267615
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	−20.7846	−	12.0000i	−1.06623	−	0.615587i
$381$		0			0
$382$	12.0000	+	20.7846i	0.613973	+	1.06343i
$383$	−1.73205	−	3.00000i	−0.0885037	−	0.153293i	0.818375	−	0.574684i	$-0.194875\pi$
$383$	−1.73205	−	3.00000i	−0.0885037	−	0.153293i	−0.906879	+	0.421392i	$0.861542\pi$
$384$		0			0
$385$	18.0000	+	51.9615i	0.917365	+	2.64820i
$386$		−	13.0000i		−	0.661683i
$387$		0			0
$388$			6.92820i			0.351726i
$389$	5.19615	+	3.00000i	0.263455	+	0.152106i	0.625910	−	0.779895i	$-0.284728\pi$
$389$	5.19615	+	3.00000i	0.263455	+	0.152106i	−0.362454	+	0.932002i	$0.618061\pi$
$390$		0			0
$391$	−4.50000	+	2.59808i	−0.227575	+	0.131390i
$392$	4.33013	+	5.50000i	0.218704	+	0.277792i
$393$		0			0
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−27.7128			−1.39438
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−4.33013	+	7.50000i	−0.217050	+	0.375941i
$399$		0			0
$400$	−3.50000	−	6.06218i	−0.175000	−	0.303109i
$401$	15.5885	−	9.00000i	0.778450	−	0.449439i	−0.0574304	−	0.998350i	$-0.518291\pi$
$401$	15.5885	−	9.00000i	0.778450	−	0.449439i	0.835881	+	0.548911i	$0.184957\pi$
$402$		0			0
$403$	−4.50000	+	7.79423i	−0.224161	+	0.388258i
$404$		0			0
$405$		0			0
$406$	6.00000	+	5.19615i	0.297775	+	0.257881i
$407$	10.3923	+	6.00000i	0.515127	+	0.297409i
$408$		0			0
$409$	−3.00000	+	1.73205i	−0.148340	+	0.0856444i	−0.572333	−	0.820021i	$-0.693962\pi$
$409$	−3.00000	+	1.73205i	−0.148340	+	0.0856444i	0.423993	+	0.905666i	$0.360628\pi$
$410$	−20.7846	+	12.0000i	−1.02648	+	0.592638i
$411$		0			0
$412$	−7.50000	−	4.33013i	−0.369498	−	0.213330i
$413$	17.3205	+	15.0000i	0.852286	+	0.738102i
$414$		0			0
$415$	−12.0000			−0.589057
$416$	0.866025	−	1.50000i	0.0424604	−	0.0735436i
$417$		0			0
$418$	36.0000	−	20.7846i	1.76082	−	1.01661i
$419$	14.7224	+	25.5000i	0.719238	+	1.24576i	0.961302	+	0.275496i	$0.0888422\pi$
$419$	14.7224	+	25.5000i	0.719238	+	1.24576i	−0.242064	+	0.970260i	$0.577824\pi$
$420$		0			0
$421$	20.0000	−	34.6410i	0.974740	−	1.68830i	0.293951	−	0.955820i	$-0.405030\pi$
$421$	20.0000	−	34.6410i	0.974740	−	1.68830i	0.680789	−	0.732479i	$-0.261637\pi$
$422$		−	7.00000i		−	0.340755i
$423$		0			0
$424$	−3.00000			−0.145693
$425$	−6.06218	+	10.5000i	−0.294059	+	0.509325i
$426$		0			0
$427$	−36.0000	−	6.92820i	−1.74216	−	0.335279i
$428$		0			0
$429$		0			0
$430$	33.0000	+	19.0526i	1.59140	+	0.918796i
$431$			12.0000i			0.578020i	0.957326	+	0.289010i	$0.0933260\pi$
$431$			12.0000i			0.578020i	−0.957326	+	0.289010i	$0.906674\pi$
$432$		0			0
$433$			20.7846i			0.998845i	0.866359	+	0.499422i	$0.166454\pi$
$433$			20.7846i			0.998845i	−0.866359	+	0.499422i	$0.833546\pi$
$434$	−12.9904	+	4.50000i	−0.623558	+	0.216007i
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	−10.3923	−	18.0000i	−0.497131	−	0.861057i
$438$		0			0
$439$	−4.50000	−	2.59808i	−0.214773	−	0.123999i	0.388755	−	0.921341i	$-0.372905\pi$
$439$	−4.50000	−	2.59808i	−0.214773	−	0.123999i	−0.603528	+	0.797342i	$0.706239\pi$
$440$	20.7846			0.990867
$441$		0			0
$442$	−3.00000			−0.142695
$443$	−15.5885	−	9.00000i	−0.740630	−	0.427603i	0.0816684	−	0.996660i	$-0.473975\pi$
$443$	−15.5885	−	9.00000i	−0.740630	−	0.427603i	−0.822298	+	0.569057i	$0.807309\pi$
$444$		0			0
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	5.19615	+	9.00000i	0.246045	+	0.426162i
$447$		0			0
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$		−	6.00000i		−	0.283158i	−0.989927	−	0.141579i	$-0.954782\pi$
$449$		−	6.00000i		−	0.283158i	0.989927	−	0.141579i	$-0.0452178\pi$
$450$		0			0
$451$		−	41.5692i		−	1.95742i
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$		0			0
$454$	22.5000	−	12.9904i	1.05598	−	0.609669i
$455$	15.5885	+	3.00000i	0.730798	+	0.140642i
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$	20.7846			0.971201
$459$		0			0
$460$		−	10.3923i		−	0.484544i
$461$	3.46410	−	6.00000i	0.161339	−	0.279448i	−0.774010	−	0.633173i	$-0.781752\pi$
$461$	3.46410	−	6.00000i	0.161339	−	0.279448i	0.935349	+	0.353726i	$0.115085\pi$
$462$		0			0
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	0.908750	−	0.417340i	$-0.137038\pi$
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	−0.815802	+	0.578331i	$0.803704\pi$
$464$	2.59808	−	1.50000i	0.120613	−	0.0696358i
$465$		0			0
$466$	12.0000	−	20.7846i	0.555889	−	0.962828i
$467$	31.1769			1.44270			0.721348	−	0.692573i	$-0.243523\pi$
$467$	31.1769			1.44270			0.721348	+	0.692573i	$0.243523\pi$
$468$		0			0
$469$	−14.0000	−	12.1244i	−0.646460	−	0.559851i
$470$	−20.7846	−	12.0000i	−0.958723	−	0.553519i
$471$		0			0
$472$	7.50000	−	4.33013i	0.345215	−	0.199310i
$473$	−57.1577	+	33.0000i	−2.62811	+	1.51734i
$474$		0			0
$475$	−42.0000	−	24.2487i	−1.92709	−	1.11261i
$476$	−3.46410	−	3.00000i	−0.158777	−	0.137505i
$477$		0			0
$478$		0			0
$479$	−12.1244	+	21.0000i	−0.553976	+	0.959514i	0.444006	+	0.896024i	$0.353557\pi$
$479$	−12.1244	+	21.0000i	−0.553976	+	0.959514i	−0.997982	+	0.0634909i	$0.979777\pi$
$480$		0			0
$481$	3.00000	−	1.73205i	0.136788	−	0.0789747i
$482$	6.92820	+	12.0000i	0.315571	+	0.546585i
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$			24.0000i			1.08978i
$486$		0			0
$487$	28.0000			1.26880			0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000			1.26880			0.634401	+	0.773004i	$0.281247\pi$
$488$	−6.92820	+	12.0000i	−0.313625	+	0.543214i
$489$		0			0
$490$	15.0000	+	19.0526i	0.677631	+	0.860707i
$491$	15.5885	−	9.00000i	0.703497	−	0.406164i	−0.105151	−	0.994456i	$-0.533533\pi$
$491$	15.5885	−	9.00000i	0.703497	−	0.406164i	0.808649	+	0.588292i	$0.200199\pi$
$492$		0			0
$493$	−4.50000	−	2.59808i	−0.202670	−	0.117011i
$494$		−	12.0000i		−	0.539906i
$495$		0			0
$496$			5.19615i			0.233314i
$497$	−2.59808	−	7.50000i	−0.116540	−	0.336421i
$498$		0			0
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	−0.988204	−	0.153141i	$-0.951061\pi$
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$500$	−3.46410	−	6.00000i	−0.154919	−	0.268328i
$501$		0			0
$502$	−3.00000	−	1.73205i	−0.133897	−	0.0773052i
$503$	−17.3205			−0.772283			−0.386142	−	0.922440i	$-0.626192\pi$
$503$	−17.3205			−0.772283			−0.386142	+	0.922440i	$0.626192\pi$
$504$		0			0
$505$		0			0
$506$	15.5885	+	9.00000i	0.692991	+	0.400099i
$507$		0			0
$508$	7.00000	+	12.1244i	0.310575	+	0.537931i
$509$	−1.73205	−	3.00000i	−0.0767718	−	0.132973i	0.825084	−	0.565011i	$-0.191128\pi$
$509$	−1.73205	−	3.00000i	−0.0767718	−	0.132973i	−0.901855	+	0.432038i	$0.857795\pi$
$510$		0			0
$511$	−6.00000	−	17.3205i	−0.265424	−	0.766214i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	20.7846i		−	0.916770i
$515$	−25.9808	−	15.0000i	−1.14485	−	0.660979i
$516$		0			0
$517$	36.0000	−	20.7846i	1.58328	−	0.914106i
$518$	5.19615	+	1.00000i	0.228306	+	0.0439375i
$519$		0			0
$520$	3.00000	−	5.19615i	0.131559	−	0.227866i
$521$	−1.73205			−0.0758825			−0.0379413	−	0.999280i	$-0.512080\pi$
$521$	−1.73205			−0.0758825			−0.0379413	+	0.999280i	$0.512080\pi$
$522$		0			0
$523$		−	17.3205i		−	0.757373i	−0.925525	−	0.378686i	$-0.876376\pi$
$523$		−	17.3205i		−	0.757373i	0.925525	−	0.378686i	$-0.123624\pi$
$524$	2.59808	−	4.50000i	0.113497	−	0.196583i
$525$		0			0
$526$	−4.50000	−	7.79423i	−0.196209	−	0.339845i
$527$	7.79423	−	4.50000i	0.339522	−	0.196023i
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$	−10.3923			−0.451413
$531$		0			0
$532$	12.0000	−	13.8564i	0.520266	−	0.600751i
$533$	−10.3923	−	6.00000i	−0.450141	−	0.259889i
$534$		0			0
$535$		0			0
$536$	−6.06218	+	3.50000i	−0.261846	+	0.151177i
$537$		0			0
$538$	3.00000	+	1.73205i	0.129339	+	0.0746740i
$539$	−41.5692	+	6.00000i	−1.79051	+	0.258438i
$540$		0			0
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	6.06218	−	10.5000i	0.260393	−	0.451014i
$543$		0			0
$544$	−1.50000	+	0.866025i	−0.0643120	+	0.0371305i
$545$	6.92820	+	12.0000i	0.296772	+	0.514024i
$546$		0			0
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	−0.938779	−	0.344519i	$-0.888042\pi$
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	0.767752	+	0.640747i	$0.221375\pi$
$548$		0			0
$549$		0			0
$550$	42.0000			1.79089
$551$	10.3923	−	18.0000i	0.442727	−	0.766826i
$552$		0			0
$553$	4.00000	−	20.7846i	0.170097	−	0.883852i
$554$	−17.3205	+	10.0000i	−0.735878	+	0.424859i
$555$		0			0
$556$	−3.00000	−	1.73205i	−0.127228	−	0.0734553i
$557$		−	39.0000i		−	1.65248i	−0.563316	−	0.826242i	$-0.690475\pi$
$557$		−	39.0000i		−	1.65248i	0.563316	−	0.826242i	$-0.309525\pi$
$558$		0			0
$559$			19.0526i			0.805837i
$560$	8.66025	−	3.00000i	0.365963	−	0.126773i
$561$		0			0
$562$	−15.0000	−	25.9808i	−0.632737	−	1.09593i
$563$	18.1865	+	31.5000i	0.766471	+	1.32757i	0.939465	+	0.342644i	$0.111322\pi$
$563$	18.1865	+	31.5000i	0.766471	+	1.32757i	−0.172994	+	0.984923i	$0.555344\pi$
$564$		0			0
$565$	−18.0000	−	10.3923i	−0.757266	−	0.437208i
$566$	−20.7846			−0.873642
$567$		0			0
$568$	−3.00000			−0.125877
$569$	−15.5885	−	9.00000i	−0.653502	−	0.377300i	0.136295	−	0.990668i	$-0.456481\pi$
$569$	−15.5885	−	9.00000i	−0.653502	−	0.377300i	−0.789797	+	0.613369i	$0.789814\pi$
$570$		0			0
$571$	−20.5000	−	35.5070i	−0.857898	−	1.48592i	−0.873930	−	0.486052i	$-0.838437\pi$
$571$	−20.5000	−	35.5070i	−0.857898	−	1.48592i	0.0160316	−	0.999871i	$-0.494897\pi$
$572$	5.19615	+	9.00000i	0.217262	+	0.376309i
$573$		0			0
$574$	−6.00000	−	17.3205i	−0.250435	−	0.722944i
$575$		−	21.0000i		−	0.875761i
$576$		0			0
$577$			38.1051i			1.58634i	0.609002	+	0.793168i	$0.291570\pi$
$577$			38.1051i			1.58634i	−0.609002	+	0.793168i	$0.708430\pi$
$578$	−12.1244	−	7.00000i	−0.504307	−	0.291162i
$579$		0			0
$580$	9.00000	−	5.19615i	0.373705	−	0.215758i
$581$	1.73205	−	9.00000i	0.0718576	−	0.373383i
$582$		0			0
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$	−6.92820			−0.286691
$585$		0			0
$586$			17.3205i			0.715504i
$587$	−12.9904	+	22.5000i	−0.536170	+	0.928674i	0.462935	+	0.886392i	$0.346796\pi$
$587$	−12.9904	+	22.5000i	−0.536170	+	0.928674i	−0.999106	+	0.0422823i	$0.986537\pi$
$588$		0			0
$589$	18.0000	+	31.1769i	0.741677	+	1.28462i
$590$	25.9808	−	15.0000i	1.06961	−	0.617540i
$591$		0			0
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−6.92820			−0.284507			−0.142254	−	0.989830i	$-0.545435\pi$
$593$	−6.92820			−0.284507			−0.142254	+	0.989830i	$0.545435\pi$
$594$		0			0
$595$	−12.0000	−	10.3923i	−0.491952	−	0.426043i
$596$	12.9904	+	7.50000i	0.532107	+	0.307212i
$597$		0			0
$598$	4.50000	−	2.59808i	0.184019	−	0.106243i
$599$	−7.79423	+	4.50000i	−0.318464	+	0.183865i	−0.650708	−	0.759328i	$-0.725528\pi$
$599$	−7.79423	+	4.50000i	−0.318464	+	0.183865i	0.332244	+	0.943193i	$0.392194\pi$
$600$		0			0
$601$	−27.0000	−	15.5885i	−1.10135	−	0.635866i	−0.164777	−	0.986331i	$-0.552690\pi$
$601$	−27.0000	−	15.5885i	−1.10135	−	0.635866i	−0.936576	+	0.350464i	$0.886024\pi$
$602$	−19.0526	+	22.0000i	−0.776524	+	0.896653i
$603$		0			0
$604$	8.00000			0.325515
$605$	−43.3013	+	75.0000i	−1.76045	+	3.04918i
$606$		0			0
$607$	−1.50000	+	0.866025i	−0.0608831	+	0.0351509i	−0.530133	−	0.847915i	$-0.677858\pi$
$607$	−1.50000	+	0.866025i	−0.0608831	+	0.0351509i	0.469249	+	0.883066i	$0.344525\pi$
$608$	−3.46410	−	6.00000i	−0.140488	−	0.243332i
$609$		0			0
$610$	−24.0000	+	41.5692i	−0.971732	+	1.68309i
$611$		−	12.0000i		−	0.485468i
$612$		0			0
$613$	−28.0000			−1.13091			−0.565455	−	0.824779i	$-0.691299\pi$
$613$	−28.0000			−1.13091			−0.565455	+	0.824779i	$0.691299\pi$
$614$	−15.5885	+	27.0000i	−0.629099	+	1.08963i
$615$		0			0
$616$	−3.00000	+	15.5885i	−0.120873	+	0.628077i
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	−0.779809	−	0.626017i	$-0.784684\pi$
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	0.152242	+	0.988343i	$0.451351\pi$
$618$		0			0
$619$	33.0000	+	19.0526i	1.32638	+	0.765787i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	33.0000	+	19.0526i	1.32638	+	0.765787i	0.341644	+	0.939829i	$0.389016\pi$
$620$			18.0000i			0.722897i
$621$		0			0
$622$			13.8564i			0.555591i
$623$	12.9904	−	4.50000i	0.520449	−	0.180289i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−6.92820	−	12.0000i	−0.276907	−	0.479616i
$627$		0			0
$628$	13.5000	+	7.79423i	0.538709	+	0.311024i
$629$	−3.46410			−0.138123
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−6.92820	−	4.00000i	−0.275589	−	0.159111i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	24.2487	+	42.0000i	0.962281	+	1.66672i
$636$		0			0
$637$	−4.50000	+	11.2583i	−0.178296	+	0.446071i
$638$			18.0000i			0.712627i
$639$		0			0
$640$		−	3.46410i		−	0.136931i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$	9.00000	−	5.19615i	0.354925	−	0.204916i	−0.311927	−	0.950106i	$-0.600974\pi$
$643$	9.00000	−	5.19615i	0.354925	−	0.204916i	0.666852	+	0.745190i	$0.267641\pi$
$644$	7.79423	+	1.50000i	0.307136	+	0.0591083i
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	10.3923			0.408564			0.204282	−	0.978912i	$-0.434514\pi$
$647$	10.3923			0.408564			0.204282	+	0.978912i	$0.434514\pi$
$648$		0			0
$649$			51.9615i			2.03967i
$650$	6.06218	−	10.5000i	0.237778	−	0.411844i
$651$		0			0
$652$	5.50000	+	9.52628i	0.215397	+	0.373078i
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.882048	−	0.471160i	$-0.843835\pi$
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.0329874	+	0.999456i	$0.510502\pi$
$654$		0			0
$655$	9.00000	−	15.5885i	0.351659	−	0.609091i
$656$	−6.92820			−0.270501
$657$		0			0
$658$	12.0000	−	13.8564i	0.467809	−	0.540179i
$659$	−41.5692	−	24.0000i	−1.61931	−	0.934907i	−0.987099	−	0.160108i	$-0.948816\pi$
$659$	−41.5692	−	24.0000i	−1.61931	−	0.934907i	−0.632207	−	0.774799i	$-0.717851\pi$
$660$		0			0
$661$	−42.0000	+	24.2487i	−1.63361	+	0.943166i	−0.650644	+	0.759383i	$0.725501\pi$
$661$	−42.0000	+	24.2487i	−1.63361	+	0.943166i	−0.982967	+	0.183782i	$0.941166\pi$
$662$	14.7224	−	8.50000i	0.572204	−	0.330362i
$663$		0			0
$664$	−3.00000	−	1.73205i	−0.116423	−	0.0672166i
$665$	41.5692	−	48.0000i	1.61199	−	1.86136i
$666$		0			0
$667$	9.00000			0.348481
$668$	8.66025	−	15.0000i	0.335075	−	0.580367i
$669$		0			0
$670$	−21.0000	+	12.1244i	−0.811301	+	0.468405i
$671$	−41.5692	−	72.0000i	−1.60476	−	2.77953i
$672$		0			0
$673$	−15.5000	+	26.8468i	−0.597481	+	1.03487i	0.395711	+	0.918375i	$0.370498\pi$
$673$	−15.5000	+	26.8468i	−0.597481	+	1.03487i	−0.993192	+	0.116492i	$0.962835\pi$
$674$		−	13.0000i		−	0.500741i
$675$		0			0
$676$	−10.0000			−0.384615
$677$	5.19615	−	9.00000i	0.199704	−	0.345898i	−0.748728	−	0.662877i	$-0.769335\pi$
$677$	5.19615	−	9.00000i	0.199704	−	0.345898i	0.948433	+	0.316979i	$0.102668\pi$
$678$		0			0
$679$	−18.0000	−	3.46410i	−0.690777	−	0.132940i
$680$	−5.19615	+	3.00000i	−0.199263	+	0.115045i
$681$		0			0
$682$	−27.0000	−	15.5885i	−1.03388	−	0.596913i
$683$			42.0000i			1.60709i	0.595247	+	0.803543i	$0.297054\pi$
$683$			42.0000i			1.60709i	−0.595247	+	0.803543i	$0.702946\pi$
$684$		0			0
$685$		0			0
$686$	−16.4545	+	8.50000i	−0.628235	+	0.324532i
$687$		0			0
$688$	5.50000	+	9.52628i	0.209686	+	0.363186i
$689$	−2.59808	−	4.50000i	−0.0989788	−	0.171436i
$690$		0			0
$691$	9.00000	+	5.19615i	0.342376	+	0.197671i	0.661322	−	0.750102i	$-0.269996\pi$
$691$	9.00000	+	5.19615i	0.342376	+	0.197671i	−0.318946	+	0.947773i	$0.603329\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	−18.0000			−0.683271
$695$	−10.3923	−	6.00000i	−0.394203	−	0.227593i
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$	9.52628	+	16.5000i	0.360575	+	0.624534i
$699$		0			0
$700$	17.5000	−	6.06218i	0.661438	−	0.229129i
$701$		−	30.0000i		−	1.13308i	−0.824033	−	0.566542i	$-0.808281\pi$
$701$		−	30.0000i		−	1.13308i	0.824033	−	0.566542i	$-0.191719\pi$
$702$		0			0
$703$		−	13.8564i		−	0.522604i
$704$	5.19615	+	3.00000i	0.195837	+	0.113067i
$705$		0			0
$706$	7.50000	−	4.33013i	0.282266	−	0.162966i
$707$		0			0
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$	−10.3923			−0.390016
$711$		0			0
$712$		−	5.19615i		−	0.194734i
$713$	−7.79423	+	13.5000i	−0.291896	+	0.505579i
$714$		0			0
$715$	18.0000	+	31.1769i	0.673162	+	1.16595i
$716$	−5.19615	+	3.00000i	−0.194189	+	0.112115i
$717$		0			0
$718$	13.5000	−	23.3827i	0.503816	−	0.872634i
$719$	−6.92820			−0.258378			−0.129189	−	0.991620i	$-0.541237\pi$
$719$	−6.92820			−0.258378			−0.129189	+	0.991620i	$0.541237\pi$
$720$		0			0
$721$	15.0000	−	17.3205i	0.558629	−	0.645049i
$722$	−25.1147	−	14.5000i	−0.934674	−	0.539634i
$723$		0			0
$724$	1.50000	−	0.866025i	0.0557471	−	0.0321856i
$725$	18.1865	−	10.5000i	0.675431	−	0.389960i
$726$		0			0
$727$	−22.5000	−	12.9904i	−0.834479	−	0.481787i	0.0209049	−	0.999781i	$-0.493345\pi$
$727$	−22.5000	−	12.9904i	−0.834479	−	0.481787i	−0.855384	+	0.517995i	$0.826679\pi$
$728$	3.46410	+	3.00000i	0.128388	+	0.111187i
$729$		0			0
$730$	−24.0000			−0.888280
$731$	9.52628	−	16.5000i	0.352342	−	0.610275i
$732$		0			0
$733$	−31.5000	+	18.1865i	−1.16348	+	0.671735i	−0.952135	−	0.305677i	$-0.901117\pi$
$733$	−31.5000	+	18.1865i	−1.16348	+	0.671735i	−0.211344	+	0.977412i	$0.567784\pi$
$734$	−9.52628	−	16.5000i	−0.351621	−	0.609026i
$735$		0			0
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$		−	42.0000i		−	1.54709i
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	3.46410	−	6.00000i	0.127343	−	0.220564i
$741$		0			0
$742$	1.50000	−	7.79423i	0.0550667	−	0.286135i
$743$	−7.79423	+	4.50000i	−0.285943	+	0.165089i	−0.636111	−	0.771598i	$-0.719458\pi$
$743$	−7.79423	+	4.50000i	−0.285943	+	0.165089i	0.350168	+	0.936687i	$0.386124\pi$
$744$		0			0
$745$	45.0000	+	25.9808i	1.64867	+	0.951861i
$746$			4.00000i			0.146450i
$747$		0			0
$748$		−	10.3923i		−	0.379980i
$749$		0			0
$750$		0			0
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	0.883694	−	0.468065i	$-0.155049\pi$
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	−0.847203	+	0.531269i	$0.821715\pi$
$752$	−3.46410	−	6.00000i	−0.126323	−	0.218797i
$753$		0			0
$754$	4.50000	+	2.59808i	0.163880	+	0.0946164i
$755$	27.7128			1.00857
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	13.8564	+	8.00000i	0.503287	+	0.290573i
$759$		0			0
$760$	−12.0000	−	20.7846i	−0.435286	−	0.753937i
$761$	−9.52628	−	16.5000i	−0.345327	−	0.598125i	0.640086	−	0.768303i	$-0.278899\pi$
$761$	−9.52628	−	16.5000i	−0.345327	−	0.598125i	−0.985413	+	0.170179i	$0.945565\pi$
$762$		0			0
$763$	−10.0000	+	3.46410i	−0.362024	+	0.125409i
$764$			24.0000i			0.868290i
$765$		0			0
$766$		−	3.46410i		−	0.125163i
$767$	12.9904	+	7.50000i	0.469055	+	0.270809i
$768$		0			0
$769$	−3.00000	+	1.73205i	−0.108183	+	0.0624593i	−0.553115	−	0.833105i	$-0.686561\pi$
$769$	−3.00000	+	1.73205i	−0.108183	+	0.0624593i	0.444932	+	0.895564i	$0.353228\pi$
$770$	−10.3923	+	54.0000i	−0.374513	+	1.94602i
$771$		0			0
$772$	6.50000	−	11.2583i	0.233940	−	0.405196i
$773$	38.1051			1.37055			0.685273	−	0.728286i	$-0.259683\pi$
$773$	38.1051			1.37055			0.685273	+	0.728286i	$0.259683\pi$
$774$		0			0
$775$			36.3731i			1.30656i
$776$	−3.46410	+	6.00000i	−0.124354	+	0.215387i
$777$		0			0
$778$	3.00000	+	5.19615i	0.107555	+	0.186291i
$779$	−41.5692	+	24.0000i	−1.48937	+	0.859889i
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$	−5.19615			−0.185814
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	46.7654	+	27.0000i	1.66913	+	0.963671i
$786$		0			0
$787$	3.00000	−	1.73205i	0.106938	−	0.0617409i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	3.00000	−	1.73205i	0.106938	−	0.0617409i	0.552515	+	0.833503i	$0.313668\pi$
$788$	−5.19615	+	3.00000i	−0.185105	+	0.106871i
$789$		0			0
$790$	−24.0000	−	13.8564i	−0.853882	−	0.492989i
$791$	10.3923	−	12.0000i	0.369508	−	0.426671i
$792$		0			0
$793$	−24.0000			−0.852265
$794$		0			0
$795$		0			0
$796$	−7.50000	+	4.33013i	−0.265830	+	0.153477i
$797$	15.5885	+	27.0000i	0.552171	+	0.956389i	0.998118	+	0.0613293i	$0.0195340\pi$
$797$	15.5885	+	27.0000i	0.552171	+	0.956389i	−0.445946	+	0.895060i	$0.647133\pi$
$798$		0			0
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$		−	7.00000i		−	0.247487i
$801$		0			0
$802$	18.0000			0.635602
$803$	20.7846	−	36.0000i	0.733473	−	1.27041i
$804$		0			0
$805$	27.0000	+	5.19615i	0.951625	+	0.183140i
$806$	−7.79423	+	4.50000i	−0.274540	+	0.158506i
$807$		0			0
$808$		0			0
$809$			24.0000i			0.843795i	0.906644	+	0.421898i	$0.138636\pi$
$809$			24.0000i			0.843795i	−0.906644	+	0.421898i	$0.861364\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$	2.59808	+	7.50000i	0.0911746	+	0.263198i
$813$		0			0
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$	19.0526	+	33.0000i	0.667382	+	1.15594i
$816$		0			0
$817$	66.0000	+	38.1051i	2.30905	+	1.33313i
$818$	−3.46410			−0.121119
$819$		0			0
$820$	−24.0000			−0.838116
$821$	28.5788	+	16.5000i	0.997408	+	0.575854i	0.907480	−	0.420094i	$-0.138003\pi$
$821$	28.5788	+	16.5000i	0.997408	+	0.575854i	0.0899279	+	0.995948i	$0.471336\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	−4.33013	−	7.50000i	−0.150847	−	0.261275i
$825$		0			0
$826$	7.50000	+	21.6506i	0.260958	+	0.753322i
$827$			48.0000i			1.66912i	0.550914	+	0.834562i	$0.314279\pi$
$827$			48.0000i			1.66912i	−0.550914	+	0.834562i	$0.685721\pi$
$828$		0			0
$829$		−	27.7128i		−	0.962506i	−0.876582	−	0.481253i	$-0.840182\pi$
$829$		−	27.7128i		−	0.962506i	0.876582	−	0.481253i	$-0.159818\pi$
$830$	−10.3923	−	6.00000i	−0.360722	−	0.208263i
$831$		0			0
$832$	1.50000	−	0.866025i	0.0520031	−	0.0300240i
$833$	9.52628	−	7.50000i	0.330066	−	0.259860i
$834$		0			0
$835$	30.0000	−	51.9615i	1.03819	−	1.79820i
$836$	41.5692			1.43770
$837$		0			0
$838$			29.4449i			1.01716i
$839$	−8.66025	+	15.0000i	−0.298985	+	0.517858i	−0.975904	−	0.218200i	$-0.929981\pi$
$839$	−8.66025	+	15.0000i	−0.298985	+	0.517858i	0.676919	+	0.736058i	$0.263315\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	34.6410	−	20.0000i	1.19381	−	0.689246i
$843$		0			0
$844$	3.50000	−	6.06218i	0.120475	−	0.208669i
$845$	−34.6410			−1.19169
$846$		0			0
$847$	−50.0000	−	43.3013i	−1.71802	−	1.48785i
$848$	−2.59808	−	1.50000i	−0.0892183	−	0.0515102i
$849$		0			0
$850$	−10.5000	+	6.06218i	−0.360147	+	0.207931i
$851$	5.19615	−	3.00000i	0.178122	−	0.102839i
$852$		0			0
$853$	10.5000	+	6.06218i	0.359513	+	0.207565i	0.668867	−	0.743382i	$-0.266779\pi$
$853$	10.5000	+	6.06218i	0.359513	+	0.207565i	−0.309354	+	0.950947i	$0.600113\pi$
$854$	−27.7128	−	24.0000i	−0.948313	−	0.821263i
$855$		0			0
$856$		0			0
$857$	−11.2583	+	19.5000i	−0.384577	+	0.666107i	−0.991710	−	0.128493i	$-0.958986\pi$
$857$	−11.2583	+	19.5000i	−0.384577	+	0.666107i	0.607133	+	0.794600i	$0.292319\pi$
$858$		0			0
$859$	39.0000	−	22.5167i	1.33066	−	0.768259i	0.345262	−	0.938506i	$-0.387790\pi$
$859$	39.0000	−	22.5167i	1.33066	−	0.768259i	0.985401	+	0.170248i	$0.0544569\pi$
$860$	19.0526	+	33.0000i	0.649687	+	1.12529i
$861$		0			0
$862$	−6.00000	+	10.3923i	−0.204361	+	0.353963i
$863$			45.0000i			1.53182i	0.642949	+	0.765909i	$0.277711\pi$
$863$			45.0000i			1.53182i	−0.642949	+	0.765909i	$0.722289\pi$
$864$		0			0
$865$	−72.0000			−2.44807
$866$	−10.3923	+	18.0000i	−0.353145	+	0.611665i
$867$		0			0
$868$	−13.5000	−	2.59808i	−0.458220	−	0.0881845i
$869$	41.5692	−	24.0000i	1.41014	−	0.814144i
$870$		0			0
$871$	−10.5000	−	6.06218i	−0.355779	−	0.205409i
$872$			4.00000i			0.135457i
$873$		0			0
$874$		−	20.7846i		−	0.703050i
$875$	17.3205	−	6.00000i	0.585540	−	0.202837i
$876$		0			0
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	−0.998888	−	0.0471555i	$-0.984984\pi$
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	0.458606	−	0.888640i	$-0.348349\pi$
$878$	−2.59808	−	4.50000i	−0.0876808	−	0.151868i
$879$		0			0
$880$	18.0000	+	10.3923i	0.606780	+	0.350325i
$881$	5.19615			0.175063			0.0875314	−	0.996162i	$-0.472102\pi$
$881$	5.19615			0.175063			0.0875314	+	0.996162i	$0.472102\pi$
$882$		0			0
$883$	25.0000			0.841317			0.420658	−	0.907219i	$-0.361799\pi$
$883$	25.0000			0.841317			0.420658	+	0.907219i	$0.361799\pi$
$884$	−2.59808	−	1.50000i	−0.0873828	−	0.0504505i
$885$		0			0
$886$	−9.00000	−	15.5885i	−0.302361	−	0.523704i
$887$	−24.2487	−	42.0000i	−0.814192	−	1.41022i	−0.909907	−	0.414813i	$-0.863847\pi$
$887$	−24.2487	−	42.0000i	−0.814192	−	1.41022i	0.0957146	−	0.995409i	$-0.469486\pi$
$888$		0			0
$889$	−35.0000	+	12.1244i	−1.17386	+	0.406638i
$890$		−	18.0000i		−	0.603361i
$891$		0			0
$892$			10.3923i			0.347960i
$893$	−41.5692	−	24.0000i	−1.39106	−	0.803129i
$894$		0			0
$895$	−18.0000	+	10.3923i	−0.601674	+	0.347376i
$896$	2.59808	+	0.500000i	0.0867956	+	0.0167038i
$897$		0			0
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	−15.5885			−0.519904
$900$		0			0
$901$			5.19615i			0.173109i
$902$	20.7846	−	36.0000i	0.692052	−	1.19867i
$903$		0			0
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	5.19615	−	3.00000i	0.172726	−	0.0997234i
$906$		0			0
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	25.9808			0.862202
$909$		0			0
$910$	12.0000	+	10.3923i	0.397796	+	0.344502i
$911$	20.7846	+	12.0000i	0.688625	+	0.397578i	0.803097	−	0.595849i	$-0.203184\pi$
$911$	20.7846	+	12.0000i	0.688625	+	0.397578i	−0.114472	+	0.993426i	$0.536518\pi$
$912$		0			0
$913$	18.0000	−	10.3923i	0.595713	−	0.343935i
$914$	14.7224	−	8.50000i	0.486975	−	0.281155i
$915$		0			0
$916$	18.0000	+	10.3923i	0.594737	+	0.343371i
$917$	10.3923	+	9.00000i	0.343184	+	0.297206i
$918$		0			0
$919$	−32.0000			−1.05558			−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000			−1.05558			−0.527791	+	0.849374i	$0.676980\pi$
$920$	5.19615	−	9.00000i	0.171312	−	0.296721i
$921$		0			0
$922$	6.00000	−	3.46410i	0.197599	−	0.114084i
$923$	−2.59808	−	4.50000i	−0.0855167	−	0.148119i
$924$		0			0
$925$	7.00000	−	12.1244i	0.230159	−	0.398646i
$926$			4.00000i			0.131448i
$927$		0			0
$928$	3.00000			0.0984798
$929$	−3.46410	+	6.00000i	−0.113653	+	0.196854i	−0.917241	−	0.398333i	$-0.869589\pi$
$929$	−3.46410	+	6.00000i	−0.113653	+	0.196854i	0.803587	+	0.595187i	$0.202922\pi$
$930$		0			0
$931$	30.0000	+	38.1051i	0.983210	+	1.24884i
$932$	20.7846	−	12.0000i	0.680823	−	0.393073i
$933$		0			0
$934$	27.0000	+	15.5885i	0.883467	+	0.510070i
$935$		−	36.0000i		−	1.17733i
$936$		0			0
$937$		−	24.2487i		−	0.792171i	−0.918214	−	0.396085i	$-0.870368\pi$
$937$		−	24.2487i		−	0.792171i	0.918214	−	0.396085i	$-0.129632\pi$
$938$	−6.06218	−	17.5000i	−0.197937	−	0.571395i
$939$		0			0
$940$	−12.0000	−	20.7846i	−0.391397	−	0.677919i
$941$	−12.1244	−	21.0000i	−0.395243	−	0.684580i	0.597889	−	0.801579i	$-0.296006\pi$
$941$	−12.1244	−	21.0000i	−0.395243	−	0.684580i	−0.993132	+	0.116998i	$0.962673\pi$
$942$		0			0
$943$	−18.0000	−	10.3923i	−0.586161	−	0.338420i
$944$	8.66025			0.281867
$945$		0			0
$946$	−66.0000			−2.14585
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	0.659256	−	0.751918i	$-0.270871\pi$
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	−0.321552	+	0.946892i	$0.604204\pi$
$948$		0			0
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$	−24.2487	−	42.0000i	−0.786732	−	1.36266i
$951$		0			0
$952$	−1.50000	−	4.33013i	−0.0486153	−	0.140340i
$953$			18.0000i			0.583077i	0.956559	+	0.291539i	$0.0941672\pi$
$953$			18.0000i			0.583077i	−0.956559	+	0.291539i	$0.905833\pi$
$954$		0			0
$955$			83.1384i			2.69030i
$956$		0			0
$957$		0			0
$958$	−21.0000	+	12.1244i	−0.678479	+	0.391720i
$959$		0			0
$960$		0			0
$961$	−2.00000	+	3.46410i	−0.0645161	+	0.111745i
$962$	3.46410			0.111687
$963$		0			0
$964$			13.8564i			0.446285i
$965$	22.5167	−	39.0000i	0.724837	−	1.25545i
$966$		0			0
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	0.849499	−	0.527591i	$-0.176905\pi$
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	−0.881656	+	0.471892i	$0.843571\pi$
$968$	−21.6506	+	12.5000i	−0.695878	+	0.401765i
$969$		0			0
$970$	−12.0000	+	20.7846i	−0.385297	+	0.667354i
$971$	−22.5167			−0.722594			−0.361297	−	0.932451i	$-0.617666\pi$
$971$	−22.5167			−0.722594			−0.361297	+	0.932451i	$0.617666\pi$
$972$		0			0
$973$	6.00000	−	6.92820i	0.192351	−	0.222108i
$974$	24.2487	+	14.0000i	0.776979	+	0.448589i
$975$		0			0
$976$	−12.0000	+	6.92820i	−0.384111	+	0.221766i
$977$	20.7846	−	12.0000i	0.664959	−	0.383914i	−0.129205	−	0.991618i	$-0.541243\pi$
$977$	20.7846	−	12.0000i	0.664959	−	0.383914i	0.794164	+	0.607704i	$0.207909\pi$
$978$		0			0
$979$	27.0000	+	15.5885i	0.862924	+	0.498209i
$980$	3.46410	+	24.0000i	0.110657	+	0.766652i
$981$		0			0
$982$	18.0000			0.574403
$983$	19.0526	−	33.0000i	0.607682	−	1.05254i	−0.383939	−	0.923358i	$-0.625433\pi$
$983$	19.0526	−	33.0000i	0.607682	−	1.05254i	0.991621	−	0.129178i	$-0.0412339\pi$
$984$		0			0
$985$	−18.0000	+	10.3923i	−0.573528	+	0.331126i
$986$	−2.59808	−	4.50000i	−0.0827396	−	0.143309i
$987$		0			0
$988$	6.00000	−	10.3923i	0.190885	−	0.330623i
$989$			33.0000i			1.04934i
$990$		0			0
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	−2.59808	+	4.50000i	−0.0824890	+	0.142875i
$993$		0			0
$994$	1.50000	−	7.79423i	0.0475771	−	0.247218i
$995$	−25.9808	+	15.0000i	−0.823646	+	0.475532i
$996$		0			0
$997$	−40.5000	−	23.3827i	−1.28265	−	0.740537i	−0.305316	−	0.952251i	$-0.598762\pi$
$997$	−40.5000	−	23.3827i	−1.28265	−	0.740537i	−0.977332	+	0.211714i	$0.932095\pi$
$998$		−	28.0000i		−	0.886325i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.m.a.755.2		4
3.2	odd	2	inner	1134.2.m.a.755.1		4
7.6	odd	2		1134.2.m.d.755.2		4
9.2	odd	6		378.2.d.c.377.4	yes	4
9.4	even	3		1134.2.m.d.377.1		4
9.5	odd	6		1134.2.m.d.377.2		4
9.7	even	3		378.2.d.c.377.1	✓	4
21.20	even	2		1134.2.m.d.755.1		4
36.7	odd	6		3024.2.k.f.1889.1		4
36.11	even	6		3024.2.k.f.1889.3		4
63.13	odd	6	inner	1134.2.m.a.377.1		4
63.20	even	6		378.2.d.c.377.3	yes	4
63.34	odd	6		378.2.d.c.377.2	yes	4
63.41	even	6	inner	1134.2.m.a.377.2		4
252.83	odd	6		3024.2.k.f.1889.2		4
252.223	even	6		3024.2.k.f.1889.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.d.c.377.1	✓	4	9.7	even	3
378.2.d.c.377.2	yes	4	63.34	odd	6
378.2.d.c.377.3	yes	4	63.20	even	6
378.2.d.c.377.4	yes	4	9.2	odd	6
1134.2.m.a.377.1		4	63.13	odd	6	inner
1134.2.m.a.377.2		4	63.41	even	6	inner
1134.2.m.a.755.1		4	3.2	odd	2	inner
1134.2.m.a.755.2		4	1.1	even	1	trivial
1134.2.m.d.377.1		4	9.4	even	3
1134.2.m.d.377.2		4	9.5	odd	6
1134.2.m.d.755.1		4	21.20	even	2
1134.2.m.d.755.2		4	7.6	odd	2
3024.2.k.f.1889.1		4	36.7	odd	6
3024.2.k.f.1889.2		4	252.83	odd	6
3024.2.k.f.1889.3		4	36.11	even	6
3024.2.k.f.1889.4		4	252.223	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.73205 + 3.00000i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.73205 + 3.00000i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +3.46410i q^{10} +(-5.19615 - 3.00000i) q^{11} +(-1.50000 + 0.866025i) q^{13} +(-2.59808 - 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.73205 q^{17} +6.92820i q^{19} +(-1.73205 + 3.00000i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-2.59808 + 1.50000i) q^{23} +(-3.50000 + 6.06218i) q^{25} -1.73205 q^{26} +(-2.00000 - 1.73205i) q^{28} +(-2.59808 - 1.50000i) q^{29} +(4.50000 - 2.59808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.50000 + 0.866025i) q^{34} +(-6.92820 - 6.00000i) q^{35} -2.00000 q^{37} +(-3.46410 + 6.00000i) q^{38} +(-3.00000 + 1.73205i) q^{40} +(3.46410 + 6.00000i) q^{41} +(5.50000 - 9.52628i) q^{43} -6.00000i q^{44} -3.00000 q^{46} +(-3.46410 + 6.00000i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-6.06218 + 3.50000i) q^{50} +(-1.50000 - 0.866025i) q^{52} +3.00000i q^{53} -20.7846i q^{55} +(-0.866025 - 2.50000i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-4.33013 - 7.50000i) q^{59} +(12.0000 + 6.92820i) q^{61} +5.19615 q^{62} -1.00000 q^{64} +(-5.19615 - 3.00000i) q^{65} +(3.50000 + 6.06218i) q^{67} +(0.866025 + 1.50000i) q^{68} +(-3.00000 - 8.66025i) q^{70} +3.00000i q^{71} +6.92820i q^{73} +(-1.73205 - 1.00000i) q^{74} +(-6.00000 + 3.46410i) q^{76} +(15.5885 + 3.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} -3.46410 q^{80} +6.92820i q^{82} +(-1.73205 + 3.00000i) q^{83} +(3.00000 + 5.19615i) q^{85} +(9.52628 - 5.50000i) q^{86} +(3.00000 - 5.19615i) q^{88} -5.19615 q^{89} +(3.00000 - 3.46410i) q^{91} +(-2.59808 - 1.50000i) q^{92} +(-6.00000 + 3.46410i) q^{94} +(-20.7846 + 12.0000i) q^{95} +(6.00000 + 3.46410i) q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 10 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 - 10 * q^7	\( 4 q + 2 q^{4} - 10 q^{7} - 6 q^{13} - 2 q^{16} - 12 q^{22} - 14 q^{25} - 8 q^{28} + 18 q^{31} + 6 q^{34} - 8 q^{37} - 12 q^{40} + 22 q^{43} - 12 q^{46} + 22 q^{49} - 6 q^{52} - 6 q^{58} + 48 q^{61} - 4 q^{64} + 14 q^{67} - 12 q^{70} - 24 q^{76} - 16 q^{79} + 12 q^{85} + 12 q^{88} + 12 q^{91} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 10 * q^7 - 6 * q^13 - 2 * q^16 - 12 * q^22 - 14 * q^25 - 8 * q^28 + 18 * q^31 + 6 * q^34 - 8 * q^37 - 12 * q^40 + 22 * q^43 - 12 * q^46 + 22 * q^49 - 6 * q^52 - 6 * q^58 + 48 * q^61 - 4 * q^64 + 14 * q^67 - 12 * q^70 - 24 * q^76 - 16 * q^79 + 12 * q^85 + 12 * q^88 + 12 * q^91 - 24 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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