LMFDB - Embedded newform 1110.2.x.a.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.a.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-1.23205 - 2.13397i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-1.23205 - 2.13397i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.866025 - 0.500000i) q^{13} +2.46410i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.73205 - 2.73205i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.59808 - 1.50000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(1.23205 - 2.13397i) q^{21} +(-1.73205 - 1.00000i) q^{22} +1.26795i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{26} -1.00000 q^{27} +(1.23205 - 2.13397i) q^{28} +0.267949i q^{29} +(0.500000 + 0.866025i) q^{30} -1.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.00000 + 1.73205i) q^{33} +(2.73205 + 4.73205i) q^{34} +(2.13397 + 1.23205i) q^{35} -1.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} -3.00000 q^{38} +(0.866025 + 0.500000i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-3.09808 - 5.36603i) q^{41} +(-2.13397 + 1.23205i) q^{42} -8.19615i q^{43} +(1.00000 + 1.73205i) q^{44} -1.00000i q^{45} +(0.633975 - 1.09808i) q^{46} +1.26795 q^{47} -1.00000 q^{48} +(0.464102 - 0.803848i) q^{49} +(-0.866025 + 0.500000i) q^{50} -5.46410i q^{51} +(0.866025 + 0.500000i) q^{52} +(1.36603 - 2.36603i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.73205 + 1.00000i) q^{55} +(-2.13397 + 1.23205i) q^{56} +(2.59808 + 1.50000i) q^{57} +(0.133975 - 0.232051i) q^{58} +(-5.36603 - 3.09808i) q^{59} -1.00000i q^{60} +(11.0263 - 6.36603i) q^{61} +(-0.732051 + 1.26795i) q^{62} +2.46410 q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -2.00000i q^{66} +(-1.73205 - 3.00000i) q^{67} -5.46410i q^{68} +(-1.09808 + 0.633975i) q^{69} +(-1.23205 - 2.13397i) q^{70} +(5.59808 + 9.69615i) q^{71} +(0.866025 + 0.500000i) q^{72} +16.1962 q^{73} +(-0.500000 + 6.06218i) q^{74} +1.00000 q^{75} +(2.59808 + 1.50000i) q^{76} +(-2.46410 - 4.26795i) q^{77} +(-0.500000 - 0.866025i) q^{78} +(8.83013 - 5.09808i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +6.19615i q^{82} +(-1.96410 + 3.40192i) q^{83} +2.46410 q^{84} +5.46410 q^{85} +(-4.09808 + 7.09808i) q^{86} +(-0.232051 + 0.133975i) q^{87} -2.00000i q^{88} +(8.19615 + 4.73205i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-2.13397 - 1.23205i) q^{91} +(-1.09808 + 0.633975i) q^{92} +(1.26795 - 0.732051i) q^{93} +(-1.09808 - 0.633975i) q^{94} +(-1.50000 + 2.59808i) q^{95} +(0.866025 + 0.500000i) q^{96} -9.12436i q^{97} +(-0.803848 + 0.464102i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{16} - 12 q^{17} - 2 q^{21} + 2 q^{25} - 4 q^{26} - 4 q^{27} - 2 q^{28} + 2 q^{30} + 4 q^{33} + 4 q^{34} + 12 q^{35} - 4 q^{36} - 12 q^{38} + 2 q^{40} - 2 q^{41} - 12 q^{42} + 4 q^{44} + 6 q^{46} + 12 q^{47} - 4 q^{48} - 12 q^{49} + 2 q^{53} - 12 q^{56} + 4 q^{58} - 18 q^{59} + 6 q^{61} + 4 q^{62} - 4 q^{63} - 4 q^{64} - 2 q^{65} + 6 q^{69} + 2 q^{70} + 12 q^{71} + 44 q^{73} - 2 q^{74} + 4 q^{75} + 4 q^{77} - 2 q^{78} + 18 q^{79} - 2 q^{81} + 6 q^{83} - 4 q^{84} + 8 q^{85} - 6 q^{86} + 6 q^{87} + 12 q^{89} - 2 q^{90} - 12 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} - 24 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^12 - 2 * q^16 - 12 * q^17 - 2 * q^21 + 2 * q^25 - 4 * q^26 - 4 * q^27 - 2 * q^28 + 2 * q^30 + 4 * q^33 + 4 * q^34 + 12 * q^35 - 4 * q^36 - 12 * q^38 + 2 * q^40 - 2 * q^41 - 12 * q^42 + 4 * q^44 + 6 * q^46 + 12 * q^47 - 4 * q^48 - 12 * q^49 + 2 * q^53 - 12 * q^56 + 4 * q^58 - 18 * q^59 + 6 * q^61 + 4 * q^62 - 4 * q^63 - 4 * q^64 - 2 * q^65 + 6 * q^69 + 2 * q^70 + 12 * q^71 + 44 * q^73 - 2 * q^74 + 4 * q^75 + 4 * q^77 - 2 * q^78 + 18 * q^79 - 2 * q^81 + 6 * q^83 - 4 * q^84 + 8 * q^85 - 6 * q^86 + 6 * q^87 + 12 * q^89 - 2 * q^90 - 12 * q^91 + 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 - 24 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	−1.23205	−	2.13397i	−0.465671	−	0.806567i	0.533560	−	0.845762i	$-0.320854\pi$
$7$	−1.23205	−	2.13397i	−0.465671	−	0.806567i	−0.999232	+	0.0391956i	$0.987520\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.866025	−	0.500000i	0.240192	−	0.138675i	−0.375073	−	0.926995i	$-0.622382\pi$
$13$	0.866025	−	0.500000i	0.240192	−	0.138675i	0.615265	+	0.788320i	$0.289049\pi$
$14$			2.46410i			0.658559i
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.73205	−	2.73205i	−1.14769	−	0.662620i	−0.199367	−	0.979925i	$-0.563889\pi$
$17$	−4.73205	−	2.73205i	−1.14769	−	0.662620i	−0.948323	+	0.317305i	$0.897222\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	2.59808	−	1.50000i	0.596040	−	0.344124i	−0.171442	−	0.985194i	$-0.554843\pi$
$19$	2.59808	−	1.50000i	0.596040	−	0.344124i	0.767482	+	0.641071i	$0.221509\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	1.23205	−	2.13397i	0.268856	−	0.465671i
$22$	−1.73205	−	1.00000i	−0.369274	−	0.213201i
$23$			1.26795i			0.264386i	0.991224	+	0.132193i	$0.0422018\pi$
$23$			1.26795i			0.264386i	−0.991224	+	0.132193i	$0.957798\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000			−0.196116
$27$	−1.00000			−0.192450
$28$	1.23205	−	2.13397i	0.232836	−	0.403283i
$29$			0.267949i			0.0497569i	0.999690	+	0.0248785i	$0.00791988\pi$
$29$			0.267949i			0.0497569i	−0.999690	+	0.0248785i	$0.992080\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	2.73205	+	4.73205i	0.468543	+	0.811540i
$35$	2.13397	+	1.23205i	0.360708	+	0.208255i
$36$	−1.00000			−0.166667
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$38$	−3.00000			−0.486664
$39$	0.866025	+	0.500000i	0.138675	+	0.0800641i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−3.09808	−	5.36603i	−0.483838	−	0.838032i	0.515989	−	0.856595i	$-0.327424\pi$
$41$	−3.09808	−	5.36603i	−0.483838	−	0.838032i	−0.999828	+	0.0185625i	$0.994091\pi$
$42$	−2.13397	+	1.23205i	−0.329279	+	0.190110i
$43$		−	8.19615i		−	1.24990i	−0.780664	−	0.624951i	$-0.785119\pi$
$43$		−	8.19615i		−	1.24990i	0.780664	−	0.624951i	$-0.214881\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		−	1.00000i		−	0.149071i
$46$	0.633975	−	1.09808i	0.0934745	−	0.161903i
$47$	1.26795			0.184949			0.0924747	−	0.995715i	$-0.470522\pi$
$47$	1.26795			0.184949			0.0924747	+	0.995715i	$0.470522\pi$
$48$	−1.00000			−0.144338
$49$	0.464102	−	0.803848i	0.0663002	−	0.114835i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		−	5.46410i		−	0.765127i
$52$	0.866025	+	0.500000i	0.120096	+	0.0693375i
$53$	1.36603	−	2.36603i	0.187638	−	0.324999i	−0.756824	−	0.653618i	$-0.773250\pi$
$53$	1.36603	−	2.36603i	0.187638	−	0.324999i	0.944462	+	0.328620i	$0.106583\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−1.73205	+	1.00000i	−0.233550	+	0.134840i
$56$	−2.13397	+	1.23205i	−0.285164	+	0.164640i
$57$	2.59808	+	1.50000i	0.344124	+	0.198680i
$58$	0.133975	−	0.232051i	0.0175917	−	0.0304698i
$59$	−5.36603	−	3.09808i	−0.698597	−	0.403335i	0.108228	−	0.994126i	$-0.465482\pi$
$59$	−5.36603	−	3.09808i	−0.698597	−	0.403335i	−0.806825	+	0.590791i	$0.798816\pi$
$60$		−	1.00000i		−	0.129099i
$61$	11.0263	−	6.36603i	1.41177	−	0.815086i	0.416215	−	0.909266i	$-0.363356\pi$
$61$	11.0263	−	6.36603i	1.41177	−	0.815086i	0.995555	+	0.0941801i	$0.0300229\pi$
$62$	−0.732051	+	1.26795i	−0.0929705	+	0.161030i
$63$	2.46410			0.310448
$64$	−1.00000			−0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		−	2.00000i		−	0.246183i
$67$	−1.73205	−	3.00000i	−0.211604	−	0.366508i	0.740613	−	0.671932i	$-0.234535\pi$
$67$	−1.73205	−	3.00000i	−0.211604	−	0.366508i	−0.952217	+	0.305424i	$0.901202\pi$
$68$		−	5.46410i		−	0.662620i
$69$	−1.09808	+	0.633975i	−0.132193	+	0.0763216i
$70$	−1.23205	−	2.13397i	−0.147258	−	0.255059i
$71$	5.59808	+	9.69615i	0.664369	+	1.15072i	0.979456	+	0.201659i	$0.0646331\pi$
$71$	5.59808	+	9.69615i	0.664369	+	1.15072i	−0.315086	+	0.949063i	$0.602034\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	16.1962			1.89562			0.947808	−	0.318841i	$-0.103294\pi$
$73$	16.1962			1.89562			0.947808	+	0.318841i	$0.103294\pi$
$74$	−0.500000	+	6.06218i	−0.0581238	+	0.704714i
$75$	1.00000			0.115470
$76$	2.59808	+	1.50000i	0.298020	+	0.172062i
$77$	−2.46410	−	4.26795i	−0.280810	−	0.486378i
$78$	−0.500000	−	0.866025i	−0.0566139	−	0.0980581i
$79$	8.83013	−	5.09808i	0.993467	−	0.573578i	0.0871581	−	0.996194i	$-0.472221\pi$
$79$	8.83013	−	5.09808i	0.993467	−	0.573578i	0.906309	+	0.422616i	$0.138888\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			6.19615i			0.684251i
$83$	−1.96410	+	3.40192i	−0.215588	+	0.373410i	−0.953454	−	0.301537i	$-0.902500\pi$
$83$	−1.96410	+	3.40192i	−0.215588	+	0.373410i	0.737866	+	0.674947i	$0.235834\pi$
$84$	2.46410			0.268856
$85$	5.46410			0.592665
$86$	−4.09808	+	7.09808i	−0.441907	+	0.765405i
$87$	−0.232051	+	0.133975i	−0.0248785	+	0.0143636i
$88$		−	2.00000i		−	0.213201i
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.866946	−	0.498402i	$-0.166080\pi$
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.00184433	+	0.999998i	$0.499413\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−2.13397	−	1.23205i	−0.223701	−	0.129154i
$92$	−1.09808	+	0.633975i	−0.114482	+	0.0660964i
$93$	1.26795	−	0.732051i	0.131480	−	0.0759101i
$94$	−1.09808	−	0.633975i	−0.113258	−	0.0653895i
$95$	−1.50000	+	2.59808i	−0.153897	+	0.266557i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$		−	9.12436i		−	0.926438i	−0.886244	−	0.463219i	$-0.846694\pi$
$97$		−	9.12436i		−	0.926438i	0.886244	−	0.463219i	$-0.153306\pi$
$98$	−0.803848	+	0.464102i	−0.0812009	+	0.0468813i
$99$	−1.00000	+	1.73205i	−0.100504	+	0.174078i
$100$	1.00000			0.100000
$101$	−5.46410			−0.543698			−0.271849	−	0.962340i	$-0.587635\pi$
$101$	−5.46410			−0.543698			−0.271849	+	0.962340i	$0.587635\pi$
$102$	−2.73205	+	4.73205i	−0.270513	+	0.468543i
$103$		−	1.19615i		−	0.117860i	−0.998262	−	0.0589302i	$-0.981231\pi$
$103$		−	1.19615i		−	0.117860i	0.998262	−	0.0589302i	$-0.0187689\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$			2.46410i			0.240472i
$106$	−2.36603	+	1.36603i	−0.229809	+	0.132680i
$107$	−5.19615	−	9.00000i	−0.502331	−	0.870063i	−0.999996	−	0.00269372i	$-0.999143\pi$
$107$	−5.19615	−	9.00000i	−0.502331	−	0.870063i	0.497665	−	0.867369i	$-0.334191\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−1.73205	−	1.00000i	−0.165900	−	0.0957826i	0.414751	−	0.909935i	$-0.363869\pi$
$109$	−1.73205	−	1.00000i	−0.165900	−	0.0957826i	−0.580651	+	0.814152i	$0.697202\pi$
$110$	2.00000			0.190693
$111$	3.46410	−	5.00000i	0.328798	−	0.474579i
$112$	2.46410			0.232836
$113$	−4.79423	−	2.76795i	−0.451003	−	0.260387i	0.257251	−	0.966345i	$-0.417183\pi$
$113$	−4.79423	−	2.76795i	−0.451003	−	0.260387i	−0.708254	+	0.705958i	$0.750517\pi$
$114$	−1.50000	−	2.59808i	−0.140488	−	0.243332i
$115$	−0.633975	−	1.09808i	−0.0591184	−	0.102396i
$116$	−0.232051	+	0.133975i	−0.0215454	+	0.0124392i
$117$			1.00000i			0.0924500i
$118$	3.09808	+	5.36603i	0.285201	+	0.493983i
$119$			13.4641i			1.23425i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−7.00000			−0.636364
$122$	−12.7321			−1.15271
$123$	3.09808	−	5.36603i	0.279344	−	0.483838i
$124$	1.26795	−	0.732051i	0.113865	−	0.0657401i
$125$			1.00000i			0.0894427i
$126$	−2.13397	−	1.23205i	−0.190110	−	0.109760i
$127$	5.23205	−	9.06218i	0.464269	−	0.804138i	−0.534899	−	0.844916i	$-0.679650\pi$
$127$	5.23205	−	9.06218i	0.464269	−	0.804138i	0.999168	+	0.0407779i	$0.0129836\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	7.09808	−	4.09808i	0.624951	−	0.360815i
$130$	0.866025	−	0.500000i	0.0759555	−	0.0438529i
$131$	−11.8301	−	6.83013i	−1.03360	−	0.596751i	−0.115588	−	0.993297i	$-0.536875\pi$
$131$	−11.8301	−	6.83013i	−1.03360	−	0.596751i	−0.918015	+	0.396546i	$0.870209\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	−6.40192	−	3.69615i	−0.555117	−	0.320497i
$134$			3.46410i			0.299253i
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$	−2.73205	+	4.73205i	−0.234271	+	0.405770i
$137$	−1.73205			−0.147979			−0.0739895	−	0.997259i	$-0.523573\pi$
$137$	−1.73205			−0.147979			−0.0739895	+	0.997259i	$0.523573\pi$
$138$	1.26795			0.107935
$139$	−6.92820	+	12.0000i	−0.587643	+	1.01783i	0.406898	+	0.913474i	$0.366611\pi$
$139$	−6.92820	+	12.0000i	−0.587643	+	1.01783i	−0.994540	+	0.104353i	$0.966723\pi$
$140$			2.46410i			0.208255i
$141$	0.633975	+	1.09808i	0.0533903	+	0.0924747i
$142$		−	11.1962i		−	0.939560i
$143$	1.73205	−	1.00000i	0.144841	−	0.0836242i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.133975	−	0.232051i	−0.0111260	−	0.0192708i
$146$	−14.0263	−	8.09808i	−1.16082	−	0.670202i
$147$	0.928203			0.0765569
$148$	3.46410	−	5.00000i	0.284747	−	0.410997i
$149$	2.07180			0.169728			0.0848641	−	0.996393i	$-0.472954\pi$
$149$	2.07180			0.169728			0.0848641	+	0.996393i	$0.472954\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$	−6.26795	−	10.8564i	−0.510078	−	0.883482i	−0.999932	−	0.0116770i	$-0.996283\pi$
$151$	−6.26795	−	10.8564i	−0.510078	−	0.883482i	0.489853	−	0.871805i	$-0.337050\pi$
$152$	−1.50000	−	2.59808i	−0.121666	−	0.210732i
$153$	4.73205	−	2.73205i	0.382564	−	0.220873i
$154$			4.92820i			0.397126i
$155$	0.732051	+	1.26795i	0.0587997	+	0.101844i
$156$			1.00000i			0.0800641i
$157$	−2.13397	+	3.69615i	−0.170310	+	0.294985i	−0.938528	−	0.345203i	$-0.887810\pi$
$157$	−2.13397	+	3.69615i	−0.170310	+	0.294985i	0.768218	+	0.640188i	$0.221143\pi$
$158$	−10.1962			−0.811162
$159$	2.73205			0.216666
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.70577	−	1.56218i	0.213245	−	0.123117i
$162$			1.00000i			0.0785674i
$163$	−19.5622	−	11.2942i	−1.53223	−	0.884632i	−0.999259	−	0.0384977i	$-0.987743\pi$
$163$	−19.5622	−	11.2942i	−1.53223	−	0.884632i	−0.532969	−	0.846135i	$-0.678924\pi$
$164$	3.09808	−	5.36603i	0.241919	−	0.419016i
$165$	−1.73205	−	1.00000i	−0.134840	−	0.0778499i
$166$	3.40192	−	1.96410i	0.264040	−	0.152444i
$167$	1.39230	−	0.803848i	0.107740	−	0.0622036i	−0.445162	−	0.895450i	$-0.646854\pi$
$167$	1.39230	−	0.803848i	0.107740	−	0.0622036i	0.552902	+	0.833247i	$0.313521\pi$
$168$	−2.13397	−	1.23205i	−0.164640	−	0.0950548i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−4.73205	−	2.73205i	−0.362932	−	0.209539i
$171$			3.00000i			0.229416i
$172$	7.09808	−	4.09808i	0.541223	−	0.312475i
$173$	2.53590	−	4.39230i	0.192801	−	0.333941i	−0.753377	−	0.657589i	$-0.771576\pi$
$173$	2.53590	−	4.39230i	0.192801	−	0.333941i	0.946177	+	0.323649i	$0.104910\pi$
$174$	0.267949			0.0203132
$175$	−2.46410			−0.186269
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		−	6.19615i		−	0.465731i
$178$	−4.73205	−	8.19615i	−0.354682	−	0.614328i
$179$		−	2.53590i		−	0.189542i	−0.995499	−	0.0947710i	$-0.969788\pi$
$179$		−	2.53590i		−	0.189542i	0.995499	−	0.0947710i	$-0.0302119\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	13.1962	+	22.8564i	0.980862	+	1.69890i	0.659049	+	0.752100i	$0.270959\pi$
$181$	13.1962	+	22.8564i	0.980862	+	1.69890i	0.321814	+	0.946803i	$0.395708\pi$
$182$	1.23205	+	2.13397i	0.0913257	+	0.158181i
$183$	11.0263	+	6.36603i	0.815086	+	0.470590i
$184$	1.26795			0.0934745
$185$	5.00000	+	3.46410i	0.367607	+	0.254686i
$186$	−1.46410			−0.107353
$187$	−9.46410	−	5.46410i	−0.692084	−	0.399575i
$188$	0.633975	+	1.09808i	0.0462373	+	0.0800854i
$189$	1.23205	+	2.13397i	0.0896185	+	0.155224i
$190$	2.59808	−	1.50000i	0.188484	−	0.108821i
$191$			1.60770i			0.116329i	0.998307	+	0.0581644i	$0.0185247\pi$
$191$			1.60770i			0.116329i	−0.998307	+	0.0581644i	$0.981475\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$			20.7321i			1.49233i	0.665763	+	0.746163i	$0.268106\pi$
$193$			20.7321i			1.49233i	−0.665763	+	0.746163i	$0.731894\pi$
$194$	−4.56218	+	7.90192i	−0.327545	+	0.567325i
$195$	−1.00000			−0.0716115
$196$	0.928203			0.0663002
$197$	−4.83013	+	8.36603i	−0.344132	+	0.596055i	−0.985196	−	0.171433i	$-0.945160\pi$
$197$	−4.83013	+	8.36603i	−0.344132	+	0.596055i	0.641063	+	0.767488i	$0.278494\pi$
$198$	1.73205	−	1.00000i	0.123091	−	0.0710669i
$199$			7.12436i			0.505032i	0.967593	+	0.252516i	$0.0812581\pi$
$199$			7.12436i			0.505032i	−0.967593	+	0.252516i	$0.918742\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	1.73205	−	3.00000i	0.122169	−	0.211604i
$202$	4.73205	+	2.73205i	0.332946	+	0.192226i
$203$	0.571797	−	0.330127i	0.0401323	−	0.0231704i
$204$	4.73205	−	2.73205i	0.331310	−	0.191282i
$205$	5.36603	+	3.09808i	0.374779	+	0.216379i
$206$	−0.598076	+	1.03590i	−0.0416699	+	0.0721745i
$207$	−1.09808	−	0.633975i	−0.0763216	−	0.0440643i
$208$			1.00000i			0.0693375i
$209$	5.19615	−	3.00000i	0.359425	−	0.207514i
$210$	1.23205	−	2.13397i	0.0850196	−	0.147258i
$211$	−0.660254			−0.0454538			−0.0227269	−	0.999742i	$-0.507235\pi$
$211$	−0.660254			−0.0454538			−0.0227269	+	0.999742i	$0.507235\pi$
$212$	2.73205			0.187638
$213$	−5.59808	+	9.69615i	−0.383574	+	0.664369i
$214$			10.3923i			0.710403i
$215$	4.09808	+	7.09808i	0.279486	+	0.484085i
$216$			1.00000i			0.0680414i
$217$	−3.12436	+	1.80385i	−0.212095	+	0.122453i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	8.09808	+	14.0263i	0.547217	+	0.947808i
$220$	−1.73205	−	1.00000i	−0.116775	−	0.0674200i
$221$	−5.46410			−0.367555
$222$	−5.50000	+	2.59808i	−0.369136	+	0.174371i
$223$	−19.4641			−1.30341			−0.651706	−	0.758471i	$-0.725947\pi$
$223$	−19.4641			−1.30341			−0.651706	+	0.758471i	$0.725947\pi$
$224$	−2.13397	−	1.23205i	−0.142582	−	0.0823199i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	2.76795	+	4.79423i	0.184121	+	0.318907i
$227$	−13.6244	+	7.86603i	−0.904280	+	0.522086i	−0.878586	−	0.477583i	$-0.841513\pi$
$227$	−13.6244	+	7.86603i	−0.904280	+	0.522086i	−0.0256938	+	0.999670i	$0.508180\pi$
$228$			3.00000i			0.198680i
$229$	8.73205	+	15.1244i	0.577030	+	0.999446i	0.995818	+	0.0913614i	$0.0291218\pi$
$229$	8.73205	+	15.1244i	0.577030	+	0.999446i	−0.418788	+	0.908084i	$0.637545\pi$
$230$			1.26795i			0.0836061i
$231$	2.46410	−	4.26795i	0.162126	−	0.280810i
$232$	0.267949			0.0175917
$233$	−6.12436			−0.401220			−0.200610	−	0.979671i	$-0.564292\pi$
$233$	−6.12436			−0.401220			−0.200610	+	0.979671i	$0.564292\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	−1.09808	+	0.633975i	−0.0716306	+	0.0413559i
$236$		−	6.19615i		−	0.403335i
$237$	8.83013	+	5.09808i	0.573578	+	0.331156i
$238$	6.73205	−	11.6603i	0.436374	−	0.755822i
$239$	14.1340	+	8.16025i	0.914251	+	0.527843i	0.881796	−	0.471630i	$-0.156334\pi$
$239$	14.1340	+	8.16025i	0.914251	+	0.527843i	0.0324544	+	0.999473i	$0.489668\pi$
$240$	0.866025	−	0.500000i	0.0559017	−	0.0322749i
$241$	3.92820	−	2.26795i	0.253038	−	0.146091i	−0.368117	−	0.929780i	$-0.619997\pi$
$241$	3.92820	−	2.26795i	0.253038	−	0.146091i	0.621154	+	0.783688i	$0.286664\pi$
$242$	6.06218	+	3.50000i	0.389692	+	0.224989i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.0263	+	6.36603i	0.705885	+	0.407543i
$245$			0.928203i			0.0593007i
$246$	−5.36603	+	3.09808i	−0.342125	+	0.197526i
$247$	1.50000	−	2.59808i	0.0954427	−	0.165312i
$248$	−1.46410			−0.0929705
$249$	−3.92820			−0.248940
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$		−	11.8564i		−	0.748370i	−0.927354	−	0.374185i	$-0.877923\pi$
$251$		−	11.8564i		−	0.748370i	0.927354	−	0.374185i	$-0.122077\pi$
$252$	1.23205	+	2.13397i	0.0776119	+	0.134428i
$253$			2.53590i			0.159431i
$254$	−9.06218	+	5.23205i	−0.568612	+	0.328288i
$255$	2.73205	+	4.73205i	0.171088	+	0.296333i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.40192	+	1.96410i	0.212206	+	0.122517i	0.602336	−	0.798242i	$-0.294237\pi$
$257$	3.40192	+	1.96410i	0.212206	+	0.122517i	−0.390130	+	0.920760i	$0.627570\pi$
$258$	−8.19615			−0.510270
$259$	−8.53590	+	12.3205i	−0.530395	+	0.765559i
$260$	−1.00000			−0.0620174
$261$	−0.232051	−	0.133975i	−0.0143636	−	0.00829282i
$262$	6.83013	+	11.8301i	0.421967	+	0.730868i
$263$	−5.63397	−	9.75833i	−0.347406	−	0.601724i	0.638382	−	0.769720i	$-0.279604\pi$
$263$	−5.63397	−	9.75833i	−0.347406	−	0.601724i	−0.985788	+	0.167995i	$0.946271\pi$
$264$	1.73205	−	1.00000i	0.106600	−	0.0615457i
$265$			2.73205i			0.167829i
$266$	3.69615	+	6.40192i	0.226626	+	0.392527i
$267$			9.46410i			0.579194i
$268$	1.73205	−	3.00000i	0.105802	−	0.183254i
$269$	9.53590			0.581414			0.290707	−	0.956812i	$-0.406110\pi$
$269$	9.53590			0.581414			0.290707	+	0.956812i	$0.406110\pi$
$270$	−1.00000			−0.0608581
$271$	6.39230	−	11.0718i	0.388305	−	0.672564i	−0.603917	−	0.797047i	$-0.706394\pi$
$271$	6.39230	−	11.0718i	0.388305	−	0.672564i	0.992222	+	0.124484i	$0.0397274\pi$
$272$	4.73205	−	2.73205i	0.286923	−	0.165655i
$273$		−	2.46410i		−	0.149134i
$274$	1.50000	+	0.866025i	0.0906183	+	0.0523185i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$	−1.09808	−	0.633975i	−0.0660964	−	0.0381608i
$277$	9.86603	−	5.69615i	0.592792	−	0.342249i	−0.173409	−	0.984850i	$-0.555478\pi$
$277$	9.86603	−	5.69615i	0.592792	−	0.342249i	0.766201	+	0.642601i	$0.222145\pi$
$278$	12.0000	−	6.92820i	0.719712	−	0.415526i
$279$	1.26795	+	0.732051i	0.0759101	+	0.0438267i
$280$	1.23205	−	2.13397i	0.0736291	−	0.127529i
$281$	2.83013	+	1.63397i	0.168831	+	0.0974748i	0.582035	−	0.813164i	$-0.302257\pi$
$281$	2.83013	+	1.63397i	0.168831	+	0.0974748i	−0.413203	+	0.910639i	$0.635590\pi$
$282$		−	1.26795i		−	0.0755053i
$283$	−1.73205	+	1.00000i	−0.102960	+	0.0594438i	−0.550596	−	0.834772i	$-0.685599\pi$
$283$	−1.73205	+	1.00000i	−0.102960	+	0.0594438i	0.447636	+	0.894216i	$0.352266\pi$
$284$	−5.59808	+	9.69615i	−0.332185	+	0.575361i
$285$	−3.00000			−0.177705
$286$	−2.00000			−0.118262
$287$	−7.63397	+	13.2224i	−0.450619	+	0.780495i
$288$			1.00000i			0.0589256i
$289$	6.42820	+	11.1340i	0.378130	+	0.654940i
$290$			0.267949i			0.0157345i
$291$	7.90192	−	4.56218i	0.463219	−	0.267440i
$292$	8.09808	+	14.0263i	0.473904	+	0.820826i
$293$	13.2224	+	22.9019i	0.772463	+	1.33794i	0.936210	+	0.351442i	$0.114309\pi$
$293$	13.2224	+	22.9019i	0.772463	+	1.33794i	−0.163747	+	0.986502i	$0.552358\pi$
$294$	−0.803848	−	0.464102i	−0.0468813	−	0.0270670i
$295$	6.19615			0.360754
$296$	−5.50000	+	2.59808i	−0.319681	+	0.151010i
$297$	−2.00000			−0.116052
$298$	−1.79423	−	1.03590i	−0.103937	−	0.0600080i
$299$	0.633975	+	1.09808i	0.0366637	+	0.0635034i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−17.4904	+	10.0981i	−1.00813	+	0.582043i
$302$			12.5359i			0.721360i
$303$	−2.73205	−	4.73205i	−0.156952	−	0.271849i
$304$			3.00000i			0.172062i
$305$	−6.36603	+	11.0263i	−0.364518	+	0.631363i
$306$	−5.46410			−0.312362
$307$	30.0526			1.71519			0.857595	−	0.514325i	$-0.171958\pi$
$307$	30.0526			1.71519			0.857595	+	0.514325i	$0.171958\pi$
$308$	2.46410	−	4.26795i	0.140405	−	0.243189i
$309$	1.03590	−	0.598076i	0.0589302	−	0.0340234i
$310$		−	1.46410i		−	0.0831554i
$311$	−5.53590	−	3.19615i	−0.313912	−	0.181237i	0.334764	−	0.942302i	$-0.391344\pi$
$311$	−5.53590	−	3.19615i	−0.313912	−	0.181237i	−0.648676	+	0.761065i	$0.724677\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	−10.7321	−	6.19615i	−0.606611	−	0.350227i	0.165027	−	0.986289i	$-0.447229\pi$
$313$	−10.7321	−	6.19615i	−0.606611	−	0.350227i	−0.771638	+	0.636062i	$0.780562\pi$
$314$	3.69615	−	2.13397i	0.208586	−	0.120427i
$315$	−2.13397	+	1.23205i	−0.120236	+	0.0694182i
$316$	8.83013	+	5.09808i	0.496733	+	0.286789i
$317$	2.83013	−	4.90192i	0.158956	−	0.275319i	−0.775537	−	0.631303i	$-0.782521\pi$
$317$	2.83013	−	4.90192i	0.158956	−	0.275319i	0.934492	+	0.355983i	$0.115854\pi$
$318$	−2.36603	−	1.36603i	−0.132680	−	0.0766029i
$319$			0.535898i			0.0300045i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	5.19615	−	9.00000i	0.290021	−	0.502331i
$322$	−3.12436			−0.174114
$323$	−16.3923			−0.912092
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		−	1.00000i		−	0.0554700i
$326$	11.2942	+	19.5622i	0.625529	+	1.08345i
$327$		−	2.00000i		−	0.110600i
$328$	−5.36603	+	3.09808i	−0.296289	+	0.171063i
$329$	−1.56218	−	2.70577i	−0.0861257	−	0.149174i
$330$	1.00000	+	1.73205i	0.0550482	+	0.0953463i
$331$	−5.93782	−	3.42820i	−0.326372	−	0.188431i	0.327857	−	0.944727i	$-0.393674\pi$
$331$	−5.93782	−	3.42820i	−0.326372	−	0.188431i	−0.654229	+	0.756296i	$0.727007\pi$
$332$	−3.92820			−0.215588
$333$	6.06218	+	0.500000i	0.332205	+	0.0273998i
$334$	−1.60770			−0.0879692
$335$	3.00000	+	1.73205i	0.163908	+	0.0946320i
$336$	1.23205	+	2.13397i	0.0672139	+	0.116418i
$337$	−1.53590	−	2.66025i	−0.0836657	−	0.144913i	0.821156	−	0.570704i	$-0.193329\pi$
$337$	−1.53590	−	2.66025i	−0.0836657	−	0.144913i	−0.904822	+	0.425790i	$0.859996\pi$
$338$	10.3923	−	6.00000i	0.565267	−	0.326357i
$339$		−	5.53590i		−	0.300669i
$340$	2.73205	+	4.73205i	0.148166	+	0.256631i
$341$		−	2.92820i		−	0.158571i
$342$	1.50000	−	2.59808i	0.0811107	−	0.140488i
$343$	−19.5359			−1.05484
$344$	−8.19615			−0.441907
$345$	0.633975	−	1.09808i	0.0341320	−	0.0591184i
$346$	−4.39230	+	2.53590i	−0.236132	+	0.136331i
$347$			0.660254i			0.0354443i	0.999843	+	0.0177221i	$0.00564143\pi$
$347$			0.660254i			0.0354443i	−0.999843	+	0.0177221i	$0.994359\pi$
$348$	−0.232051	−	0.133975i	−0.0124392	−	0.00718179i
$349$	−8.53590	+	14.7846i	−0.456916	+	0.791402i	−0.998796	−	0.0490539i	$-0.984379\pi$
$349$	−8.53590	+	14.7846i	−0.456916	+	0.791402i	0.541880	+	0.840456i	$0.317713\pi$
$350$	2.13397	+	1.23205i	0.114066	+	0.0658559i
$351$	−0.866025	+	0.500000i	−0.0462250	+	0.0266880i
$352$	1.73205	−	1.00000i	0.0923186	−	0.0533002i
$353$	−19.6699	−	11.3564i	−1.04692	−	0.604441i	−0.125136	−	0.992140i	$-0.539937\pi$
$353$	−19.6699	−	11.3564i	−1.04692	−	0.604441i	−0.921786	+	0.387699i	$0.873270\pi$
$354$	−3.09808	+	5.36603i	−0.164661	+	0.285201i
$355$	−9.69615	−	5.59808i	−0.514618	−	0.297115i
$356$			9.46410i			0.501596i
$357$	−11.6603	+	6.73205i	−0.617126	+	0.356298i
$358$	−1.26795	+	2.19615i	−0.0670132	+	0.116070i
$359$	6.66025			0.351515			0.175757	−	0.984434i	$-0.443763\pi$
$359$	6.66025			0.351515			0.175757	+	0.984434i	$0.443763\pi$
$360$	−1.00000			−0.0527046
$361$	−5.00000	+	8.66025i	−0.263158	+	0.455803i
$362$		−	26.3923i		−	1.38715i
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$		−	2.46410i		−	0.129154i
$365$	−14.0263	+	8.09808i	−0.734169	+	0.423873i
$366$	−6.36603	−	11.0263i	−0.332757	−	0.576353i
$367$	9.69615	+	16.7942i	0.506135	+	0.876652i	0.999975	+	0.00709868i	$0.00225960\pi$
$367$	9.69615	+	16.7942i	0.506135	+	0.876652i	−0.493840	+	0.869553i	$0.664407\pi$
$368$	−1.09808	−	0.633975i	−0.0572412	−	0.0330482i
$369$	6.19615			0.322559
$370$	−2.59808	−	5.50000i	−0.135068	−	0.285931i
$371$	−6.73205			−0.349511
$372$	1.26795	+	0.732051i	0.0657401	+	0.0379551i
$373$	10.3301	+	17.8923i	0.534874	+	0.926428i	0.999169	+	0.0407482i	$0.0129741\pi$
$373$	10.3301	+	17.8923i	0.534874	+	0.926428i	−0.464296	+	0.885680i	$0.653693\pi$
$374$	5.46410	+	9.46410i	0.282542	+	0.489377i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$		−	1.26795i		−	0.0653895i
$377$	0.133975	+	0.232051i	0.00690004	+	0.0119512i
$378$		−	2.46410i		−	0.126740i
$379$	−17.0622	+	29.5526i	−0.876425	+	1.51801i	−0.0211884	+	0.999775i	$0.506745\pi$
$379$	−17.0622	+	29.5526i	−0.876425	+	1.51801i	−0.855237	+	0.518237i	$0.826588\pi$
$380$	−3.00000			−0.153897
$381$	10.4641			0.536092
$382$	0.803848	−	1.39230i	0.0411284	−	0.0712365i
$383$	2.66025	−	1.53590i	0.135933	−	0.0784807i	−0.430491	−	0.902595i	$-0.641660\pi$
$383$	2.66025	−	1.53590i	0.135933	−	0.0784807i	0.566424	+	0.824114i	$0.308326\pi$
$384$			1.00000i			0.0510310i
$385$	4.26795	+	2.46410i	0.217515	+	0.125582i
$386$	10.3660	−	17.9545i	0.527617	−	0.913859i
$387$	7.09808	+	4.09808i	0.360815	+	0.208317i
$388$	7.90192	−	4.56218i	0.401159	−	0.231609i
$389$	25.9641	−	14.9904i	1.31643	−	0.760042i	0.333279	−	0.942828i	$-0.391845\pi$
$389$	25.9641	−	14.9904i	1.31643	−	0.760042i	0.983153	+	0.182786i	$0.0585114\pi$
$390$	0.866025	+	0.500000i	0.0438529	+	0.0253185i
$391$	3.46410	−	6.00000i	0.175187	−	0.303433i
$392$	−0.803848	−	0.464102i	−0.0406004	−	0.0234407i
$393$		−	13.6603i		−	0.689069i
$394$	8.36603	−	4.83013i	0.421474	−	0.243338i
$395$	−5.09808	+	8.83013i	−0.256512	+	0.444292i
$396$	−2.00000			−0.100504
$397$	−1.32051			−0.0662744			−0.0331372	−	0.999451i	$-0.510550\pi$
$397$	−1.32051			−0.0662744			−0.0331372	+	0.999451i	$0.510550\pi$
$398$	3.56218	−	6.16987i	0.178556	−	0.309268i
$399$		−	7.39230i		−	0.370078i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			10.3923i			0.518967i	0.965748	+	0.259483i	$0.0835523\pi$
$401$			10.3923i			0.518967i	−0.965748	+	0.259483i	$0.916448\pi$
$402$	−3.00000	+	1.73205i	−0.149626	+	0.0863868i
$403$	−0.732051	−	1.26795i	−0.0364660	−	0.0631610i
$404$	−2.73205	−	4.73205i	−0.135925	−	0.235428i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−0.660254			−0.0327679
$407$	−5.19615	−	11.0000i	−0.257564	−	0.545250i
$408$	−5.46410			−0.270513
$409$	−4.62436	−	2.66987i	−0.228660	−	0.132017i	0.381294	−	0.924454i	$-0.375479\pi$
$409$	−4.62436	−	2.66987i	−0.228660	−	0.132017i	−0.609954	+	0.792437i	$0.708812\pi$
$410$	−3.09808	−	5.36603i	−0.153003	−	0.265009i
$411$	−0.866025	−	1.50000i	−0.0427179	−	0.0739895i
$412$	1.03590	−	0.598076i	0.0510351	−	0.0294651i
$413$			15.2679i			0.751287i
$414$	0.633975	+	1.09808i	0.0311582	+	0.0539675i
$415$		−	3.92820i		−	0.192828i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	−13.8564			−0.678551
$418$	−6.00000			−0.293470
$419$	4.16987	−	7.22243i	0.203712	−	0.352839i	−0.746010	−	0.665935i	$-0.768033\pi$
$419$	4.16987	−	7.22243i	0.203712	−	0.352839i	0.949721	+	0.313096i	$0.101366\pi$
$420$	−2.13397	+	1.23205i	−0.104127	+	0.0601179i
$421$		−	26.5359i		−	1.29328i	−0.762795	−	0.646640i	$-0.776174\pi$
$421$		−	26.5359i		−	1.29328i	0.762795	−	0.646640i	$-0.223826\pi$
$422$	0.571797	+	0.330127i	0.0278346	+	0.0160703i
$423$	−0.633975	+	1.09808i	−0.0308249	+	0.0533903i
$424$	−2.36603	−	1.36603i	−0.114904	−	0.0663401i
$425$	−4.73205	+	2.73205i	−0.229538	+	0.132524i
$426$	9.69615	−	5.59808i	0.469780	−	0.271228i
$427$	−27.1699	−	15.6865i	−1.31484	−	0.759125i
$428$	5.19615	−	9.00000i	0.251166	−	0.435031i
$429$	1.73205	+	1.00000i	0.0836242	+	0.0482805i
$430$		−	8.19615i		−	0.395254i
$431$	−19.7942	+	11.4282i	−0.953454	+	0.550477i	−0.894152	−	0.447763i	$-0.852221\pi$
$431$	−19.7942	+	11.4282i	−0.953454	+	0.550477i	−0.0593021	+	0.998240i	$0.518888\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	13.5167			0.649569			0.324785	−	0.945788i	$-0.394708\pi$
$433$	13.5167			0.649569			0.324785	+	0.945788i	$0.394708\pi$
$434$	3.60770			0.173175
$435$	0.133975	−	0.232051i	0.00642359	−	0.0111260i
$436$		−	2.00000i		−	0.0957826i
$437$	1.90192	+	3.29423i	0.0909814	+	0.157584i
$438$		−	16.1962i		−	0.773882i
$439$	−17.1506	+	9.90192i	−0.818555	+	0.472593i	−0.849918	−	0.526915i	$-0.823349\pi$
$439$	−17.1506	+	9.90192i	−0.818555	+	0.472593i	0.0313628	+	0.999508i	$0.490015\pi$
$440$	1.00000	+	1.73205i	0.0476731	+	0.0825723i
$441$	0.464102	+	0.803848i	0.0221001	+	0.0382785i
$442$	4.73205	+	2.73205i	0.225081	+	0.129950i
$443$	−12.8564			−0.610826			−0.305413	−	0.952220i	$-0.598795\pi$
$443$	−12.8564			−0.610826			−0.305413	+	0.952220i	$0.598795\pi$
$444$	6.06218	+	0.500000i	0.287698	+	0.0237289i
$445$	−9.46410			−0.448641
$446$	16.8564	+	9.73205i	0.798174	+	0.460826i
$447$	1.03590	+	1.79423i	0.0489963	+	0.0848641i
$448$	1.23205	+	2.13397i	0.0582089	+	0.100821i
$449$	27.7128	−	16.0000i	1.30785	−	0.755087i	0.326112	−	0.945331i	$-0.394261\pi$
$449$	27.7128	−	16.0000i	1.30785	−	0.755087i	0.981737	+	0.190245i	$0.0609281\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−6.19615	−	10.7321i	−0.291765	−	0.505353i
$452$		−	5.53590i		−	0.260387i
$453$	6.26795	−	10.8564i	0.294494	−	0.510078i
$454$	15.7321			0.738342
$455$	2.46410			0.115519
$456$	1.50000	−	2.59808i	0.0702439	−	0.121666i
$457$	21.9282	−	12.6603i	1.02576	−	0.592222i	0.109992	−	0.993933i	$-0.464918\pi$
$457$	21.9282	−	12.6603i	1.02576	−	0.592222i	0.915767	+	0.401711i	$0.131584\pi$
$458$		−	17.4641i		−	0.816044i
$459$	4.73205	+	2.73205i	0.220873	+	0.127521i
$460$	0.633975	−	1.09808i	0.0295592	−	0.0511981i
$461$	33.3564	+	19.2583i	1.55356	+	0.896950i	0.997848	+	0.0655772i	$0.0208888\pi$
$461$	33.3564	+	19.2583i	1.55356	+	0.896950i	0.555715	+	0.831373i	$0.312444\pi$
$462$	−4.26795	+	2.46410i	−0.198563	+	0.114640i
$463$	−1.83975	+	1.06218i	−0.0855002	+	0.0493636i	−0.542141	−	0.840288i	$-0.682386\pi$
$463$	−1.83975	+	1.06218i	−0.0855002	+	0.0493636i	0.456640	+	0.889651i	$0.349053\pi$
$464$	−0.232051	−	0.133975i	−0.0107727	−	0.00621961i
$465$	−0.732051	+	1.26795i	−0.0339480	+	0.0587997i
$466$	5.30385	+	3.06218i	0.245696	+	0.141853i
$467$			0.660254i			0.0305529i	0.999883	+	0.0152765i	$0.00486284\pi$
$467$			0.660254i			0.0305529i	−0.999883	+	0.0152765i	$0.995137\pi$
$468$	−0.866025	+	0.500000i	−0.0400320	+	0.0231125i
$469$	−4.26795	+	7.39230i	−0.197076	+	0.341345i
$470$	1.26795			0.0584861
$471$	−4.26795			−0.196657
$472$	−3.09808	+	5.36603i	−0.142601	+	0.246991i
$473$		−	16.3923i		−	0.753719i
$474$	−5.09808	−	8.83013i	−0.234162	−	0.405581i
$475$		−	3.00000i		−	0.137649i
$476$	−11.6603	+	6.73205i	−0.534447	+	0.308563i
$477$	1.36603	+	2.36603i	0.0625460	+	0.108333i
$478$	−8.16025	−	14.1340i	−0.373241	−	0.646473i
$479$	−25.3923	−	14.6603i	−1.16020	−	0.669844i	−0.208851	−	0.977947i	$-0.566972\pi$
$479$	−25.3923	−	14.6603i	−1.16020	−	0.669844i	−0.951353	+	0.308103i	$0.900306\pi$
$480$	−1.00000			−0.0456435
$481$	−5.00000	−	3.46410i	−0.227980	−	0.157949i
$482$	−4.53590			−0.206605
$483$	2.70577	+	1.56218i	0.123117	+	0.0710816i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	4.56218	+	7.90192i	0.207158	+	0.358808i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$		−	11.0526i		−	0.500839i	−0.968137	−	0.250420i	$-0.919431\pi$
$487$		−	11.0526i		−	0.500839i	0.968137	−	0.250420i	$-0.0805686\pi$
$488$	−6.36603	−	11.0263i	−0.288176	−	0.499136i
$489$		−	22.5885i		−	1.02149i
$490$	0.464102	−	0.803848i	0.0209660	−	0.0363141i
$491$	10.7846			0.486703			0.243351	−	0.969938i	$-0.421753\pi$
$491$	10.7846			0.486703			0.243351	+	0.969938i	$0.421753\pi$
$492$	6.19615			0.279344
$493$	0.732051	−	1.26795i	0.0329699	−	0.0571056i
$494$	−2.59808	+	1.50000i	−0.116893	+	0.0674882i
$495$		−	2.00000i		−	0.0898933i
$496$	1.26795	+	0.732051i	0.0569326	+	0.0328701i
$497$	13.7942	−	23.8923i	0.618756	−	1.07172i
$498$	3.40192	+	1.96410i	0.152444	+	0.0880135i
$499$	−29.1340	+	16.8205i	−1.30422	+	0.752989i	−0.981124	−	0.193378i	$-0.938056\pi$
$499$	−29.1340	+	16.8205i	−1.30422	+	0.752989i	−0.323092	+	0.946368i	$0.604722\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	1.39230	+	0.803848i	0.0622036	+	0.0359133i
$502$	−5.92820	+	10.2679i	−0.264589	+	0.458281i
$503$	35.8301	+	20.6865i	1.59759	+	0.922367i	0.991951	+	0.126625i	$0.0404145\pi$
$503$	35.8301	+	20.6865i	1.59759	+	0.922367i	0.605636	+	0.795742i	$0.292919\pi$
$504$		−	2.46410i		−	0.109760i
$505$	4.73205	−	2.73205i	0.210573	−	0.121575i
$506$	1.26795	−	2.19615i	0.0563672	−	0.0976309i
$507$	−12.0000			−0.532939
$508$	10.4641			0.464269
$509$	6.62436	−	11.4737i	0.293619	−	0.508564i	−0.681043	−	0.732243i	$-0.738474\pi$
$509$	6.62436	−	11.4737i	0.293619	−	0.508564i	0.974663	+	0.223679i	$0.0718068\pi$
$510$		−	5.46410i		−	0.241954i
$511$	−19.9545	−	34.5622i	−0.882734	−	1.52894i
$512$			1.00000i			0.0441942i
$513$	−2.59808	+	1.50000i	−0.114708	+	0.0662266i
$514$	−1.96410	−	3.40192i	−0.0866328	−	0.150052i
$515$	0.598076	+	1.03590i	0.0263544	+	0.0456471i
$516$	7.09808	+	4.09808i	0.312475	+	0.180408i
$517$	2.53590			0.111529
$518$	13.5526	−	6.40192i	0.595465	−	0.281284i
$519$	5.07180			0.222627
$520$	0.866025	+	0.500000i	0.0379777	+	0.0219265i
$521$	−0.0980762	−	0.169873i	−0.00429680	−	0.00744227i	0.863869	−	0.503717i	$-0.168034\pi$
$521$	−0.0980762	−	0.169873i	−0.00429680	−	0.00744227i	−0.868166	+	0.496274i	$0.834701\pi$
$522$	0.133975	+	0.232051i	0.00586391	+	0.0101566i
$523$	−11.0263	+	6.36603i	−0.482146	+	0.278367i	−0.721310	−	0.692612i	$-0.756460\pi$
$523$	−11.0263	+	6.36603i	−0.482146	+	0.278367i	0.239165	+	0.970979i	$0.423126\pi$
$524$		−	13.6603i		−	0.596751i
$525$	−1.23205	−	2.13397i	−0.0537711	−	0.0931343i
$526$			11.2679i			0.491306i
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$	−2.00000			−0.0870388
$529$	21.3923			0.930100
$530$	1.36603	−	2.36603i	0.0593364	−	0.102774i
$531$	5.36603	−	3.09808i	0.232866	−	0.134445i
$532$		−	7.39230i		−	0.320497i
$533$	−5.36603	−	3.09808i	−0.232428	−	0.134193i
$534$	4.73205	−	8.19615i	0.204776	−	0.354682i
$535$	9.00000	+	5.19615i	0.389104	+	0.224649i
$536$	−3.00000	+	1.73205i	−0.129580	+	0.0748132i
$537$	2.19615	−	1.26795i	0.0947710	−	0.0547160i
$538$	−8.25833	−	4.76795i	−0.356042	−	0.205561i
$539$	0.928203	−	1.60770i	0.0399805	−	0.0692483i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$		−	16.3397i		−	0.702501i	−0.936282	−	0.351250i	$-0.885757\pi$
$541$		−	16.3397i		−	0.702501i	0.936282	−	0.351250i	$-0.114243\pi$
$542$	−11.0718	+	6.39230i	−0.475574	+	0.274573i
$543$	−13.1962	+	22.8564i	−0.566301	+	0.980862i
$544$	−5.46410			−0.234271
$545$	2.00000			0.0856706
$546$	−1.23205	+	2.13397i	−0.0527269	+	0.0913257i
$547$		−	22.9282i		−	0.980339i	−0.871627	−	0.490170i	$-0.836935\pi$
$547$		−	22.9282i		−	0.980339i	0.871627	−	0.490170i	$-0.163065\pi$
$548$	−0.866025	−	1.50000i	−0.0369948	−	0.0640768i
$549$			12.7321i			0.543391i
$550$	−1.73205	+	1.00000i	−0.0738549	+	0.0426401i
$551$	0.401924	+	0.696152i	0.0171225	+	0.0296571i
$552$	0.633975	+	1.09808i	0.0269838	+	0.0467372i
$553$	−21.7583	−	12.5622i	−0.925258	−	0.534198i
$554$	−11.3923			−0.484013
$555$	−0.500000	+	6.06218i	−0.0212238	+	0.257325i
$556$	−13.8564			−0.587643
$557$	12.1244	+	7.00000i	0.513725	+	0.296600i	0.734364	−	0.678756i	$-0.237481\pi$
$557$	12.1244	+	7.00000i	0.513725	+	0.296600i	−0.220638	+	0.975356i	$0.570814\pi$
$558$	−0.732051	−	1.26795i	−0.0309902	−	0.0536766i
$559$	−4.09808	−	7.09808i	−0.173330	−	0.300217i
$560$	−2.13397	+	1.23205i	−0.0901769	+	0.0520636i
$561$		−	10.9282i		−	0.461389i
$562$	−1.63397	−	2.83013i	−0.0689251	−	0.119382i
$563$			3.33975i			0.140754i	0.997520	+	0.0703768i	$0.0224202\pi$
$563$			3.33975i			0.140754i	−0.997520	+	0.0703768i	$0.977580\pi$
$564$	−0.633975	+	1.09808i	−0.0266951	+	0.0462373i
$565$	5.53590			0.232897
$566$	2.00000			0.0840663
$567$	−1.23205	+	2.13397i	−0.0517413	+	0.0896185i
$568$	9.69615	−	5.59808i	0.406842	−	0.234890i
$569$		−	43.5167i		−	1.82431i	−0.409842	−	0.912157i	$-0.634416\pi$
$569$		−	43.5167i		−	1.82431i	0.409842	−	0.912157i	$-0.365584\pi$
$570$	2.59808	+	1.50000i	0.108821	+	0.0628281i
$571$	17.5263	−	30.3564i	0.733452	−	1.27038i	−0.221947	−	0.975059i	$-0.571241\pi$
$571$	17.5263	−	30.3564i	0.733452	−	1.27038i	0.955399	−	0.295317i	$-0.0954254\pi$
$572$	1.73205	+	1.00000i	0.0724207	+	0.0418121i
$573$	−1.39230	+	0.803848i	−0.0581644	+	0.0335812i
$574$	13.2224	−	7.63397i	0.551894	−	0.318636i
$575$	1.09808	+	0.633975i	0.0457929	+	0.0264386i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−8.36603	−	4.83013i	−0.348282	−	0.201081i	0.315646	−	0.948877i	$-0.397779\pi$
$577$	−8.36603	−	4.83013i	−0.348282	−	0.201081i	−0.663928	+	0.747796i	$0.731112\pi$
$578$		−	12.8564i		−	0.534756i
$579$	−17.9545	+	10.3660i	−0.746163	+	0.430797i
$580$	0.133975	−	0.232051i	0.00556299	−	0.00963539i
$581$	9.67949			0.401573
$582$	−9.12436			−0.378217
$583$	2.73205	−	4.73205i	0.113150	−	0.195982i
$584$		−	16.1962i		−	0.670202i
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$		−	26.4449i		−	1.09243i
$587$	1.28461	−	0.741670i	0.0530215	−	0.0306120i	−0.473255	−	0.880926i	$-0.656921\pi$
$587$	1.28461	−	0.741670i	0.0530215	−	0.0306120i	0.526276	+	0.850314i	$0.323588\pi$
$588$	0.464102	+	0.803848i	0.0191392	+	0.0331501i
$589$	−2.19615	−	3.80385i	−0.0904909	−	0.156735i
$590$	−5.36603	−	3.09808i	−0.220916	−	0.127546i
$591$	−9.66025			−0.397370
$592$	6.06218	+	0.500000i	0.249154	+	0.0205499i
$593$	−40.7846			−1.67482			−0.837412	−	0.546573i	$-0.815932\pi$
$593$	−40.7846			−1.67482			−0.837412	+	0.546573i	$0.815932\pi$
$594$	1.73205	+	1.00000i	0.0710669	+	0.0410305i
$595$	−6.73205	−	11.6603i	−0.275987	−	0.478024i
$596$	1.03590	+	1.79423i	0.0424321	+	0.0734945i
$597$	−6.16987	+	3.56218i	−0.252516	+	0.145790i
$598$		−	1.26795i		−	0.0518503i
$599$	−5.52628	−	9.57180i	−0.225798	−	0.391093i	0.730761	−	0.682634i	$-0.239165\pi$
$599$	−5.52628	−	9.57180i	−0.225798	−	0.391093i	−0.956558	+	0.291541i	$0.905832\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	3.46410	−	6.00000i	0.141304	−	0.244745i	−0.786684	−	0.617356i	$-0.788204\pi$
$601$	3.46410	−	6.00000i	0.141304	−	0.244745i	0.927988	+	0.372611i	$0.121537\pi$
$602$	20.1962			0.823134
$603$	3.46410			0.141069
$604$	6.26795	−	10.8564i	0.255039	−	0.441741i
$605$	6.06218	−	3.50000i	0.246463	−	0.142295i
$606$			5.46410i			0.221964i
$607$	15.4808	+	8.93782i	0.628345	+	0.362775i	0.780111	−	0.625641i	$-0.215163\pi$
$607$	15.4808	+	8.93782i	0.628345	+	0.362775i	−0.151766	+	0.988416i	$0.548496\pi$
$608$	1.50000	−	2.59808i	0.0608330	−	0.105366i
$609$	0.571797	+	0.330127i	0.0231704	+	0.0133774i
$610$	11.0263	−	6.36603i	0.446441	−	0.257753i
$611$	1.09808	−	0.633975i	0.0444234	−	0.0256479i
$612$	4.73205	+	2.73205i	0.191282	+	0.110437i
$613$	−7.06218	+	12.2321i	−0.285239	+	0.494048i	−0.972667	−	0.232204i	$-0.925406\pi$
$613$	−7.06218	+	12.2321i	−0.285239	+	0.494048i	0.687428	+	0.726252i	$0.258740\pi$
$614$	−26.0263	−	15.0263i	−1.05034	−	0.606411i
$615$			6.19615i			0.249853i
$616$	−4.26795	+	2.46410i	−0.171961	+	0.0992815i
$617$	6.66987	−	11.5526i	0.268519	−	0.465089i	−0.699961	−	0.714181i	$-0.746799\pi$
$617$	6.66987	−	11.5526i	0.268519	−	0.465089i	0.968480	+	0.249093i	$0.0801325\pi$
$618$	−1.19615			−0.0481163
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$	−0.732051	+	1.26795i	−0.0293999	+	0.0509221i
$621$		−	1.26795i		−	0.0508810i
$622$	3.19615	+	5.53590i	0.128154	+	0.221969i
$623$		−	23.3205i		−	0.934316i
$624$	−0.866025	+	0.500000i	−0.0346688	+	0.0200160i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.19615	+	10.7321i	0.247648	+	0.428939i
$627$	5.19615	+	3.00000i	0.207514	+	0.119808i
$628$	−4.26795			−0.170310
$629$	−2.73205	+	33.1244i	−0.108934	+	1.32075i
$630$	2.46410			0.0981722
$631$	−2.83013	−	1.63397i	−0.112666	−	0.0650475i	0.442608	−	0.896715i	$-0.354053\pi$
$631$	−2.83013	−	1.63397i	−0.112666	−	0.0650475i	−0.555274	+	0.831668i	$0.687387\pi$
$632$	−5.09808	−	8.83013i	−0.202791	−	0.351244i
$633$	−0.330127	−	0.571797i	−0.0131214	−	0.0227269i
$634$	−4.90192	+	2.83013i	−0.194680	+	0.112399i
$635$			10.4641i			0.415255i
$636$	1.36603	+	2.36603i	0.0541664	+	0.0938190i
$637$		−	0.928203i		−	0.0367768i
$638$	0.267949	−	0.464102i	0.0106082	−	0.0183740i
$639$	−11.1962			−0.442913
$640$	−1.00000			−0.0395285
$641$	6.09808	−	10.5622i	0.240860	−	0.417181i	−0.720100	−	0.693870i	$-0.755904\pi$
$641$	6.09808	−	10.5622i	0.240860	−	0.417181i	0.960959	+	0.276690i	$0.0892374\pi$
$642$	−9.00000	+	5.19615i	−0.355202	+	0.205076i
$643$			38.5885i			1.52178i	0.648881	+	0.760890i	$0.275237\pi$
$643$			38.5885i			1.52178i	−0.648881	+	0.760890i	$0.724763\pi$
$644$	2.70577	+	1.56218i	0.106622	+	0.0615584i
$645$	−4.09808	+	7.09808i	−0.161362	+	0.279486i
$646$	14.1962	+	8.19615i	0.558540	+	0.322473i
$647$	11.7846	−	6.80385i	0.463301	−	0.267487i	−0.250130	−	0.968212i	$-0.580473\pi$
$647$	11.7846	−	6.80385i	0.463301	−	0.267487i	0.713431	+	0.700725i	$0.247140\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−10.7321	−	6.19615i	−0.421270	−	0.243220i
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$	−3.12436	−	1.80385i	−0.122453	−	0.0706984i
$652$		−	22.5885i		−	0.884632i
$653$	25.8109	−	14.9019i	1.01006	−	0.583157i	0.0988495	−	0.995102i	$-0.468484\pi$
$653$	25.8109	−	14.9019i	1.01006	−	0.583157i	0.911209	+	0.411945i	$0.135150\pi$
$654$	−1.00000	+	1.73205i	−0.0391031	+	0.0677285i
$655$	13.6603			0.533750
$656$	6.19615			0.241919
$657$	−8.09808	+	14.0263i	−0.315936	+	0.547217i
$658$			3.12436i			0.121800i
$659$	9.75833	+	16.9019i	0.380131	+	0.658405i	0.991081	−	0.133264i	$-0.0425457\pi$
$659$	9.75833	+	16.9019i	0.380131	+	0.658405i	−0.610950	+	0.791669i	$0.709212\pi$
$660$		−	2.00000i		−	0.0778499i
$661$	−27.6340	+	15.9545i	−1.07484	+	0.620557i	−0.929499	−	0.368825i	$-0.879760\pi$
$661$	−27.6340	+	15.9545i	−1.07484	+	0.620557i	−0.145338	+	0.989382i	$0.546427\pi$
$662$	3.42820	+	5.93782i	0.133241	+	0.230780i
$663$	−2.73205	−	4.73205i	−0.106104	−	0.183778i
$664$	3.40192	+	1.96410i	0.132020	+	0.0762219i
$665$	7.39230			0.286661
$666$	−5.00000	−	3.46410i	−0.193746	−	0.134231i
$667$	−0.339746			−0.0131550
$668$	1.39230	+	0.803848i	0.0538699	+	0.0311018i
$669$	−9.73205	−	16.8564i	−0.376263	−	0.651706i
$670$	−1.73205	−	3.00000i	−0.0669150	−	0.115900i
$671$	22.0526	−	12.7321i	0.851330	−	0.491515i
$672$		−	2.46410i		−	0.0950548i
$673$	−1.02628	−	1.77757i	−0.0395602	−	0.0685202i	0.845567	−	0.533869i	$-0.179262\pi$
$673$	−1.02628	−	1.77757i	−0.0395602	−	0.0685202i	−0.885128	+	0.465348i	$0.845929\pi$
$674$			3.07180i			0.118321i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−12.0000			−0.461538
$677$	41.5167			1.59561			0.797807	−	0.602912i	$-0.205993\pi$
$677$	41.5167			1.59561			0.797807	+	0.602912i	$0.205993\pi$
$678$	−2.76795	+	4.79423i	−0.106302	+	0.184121i
$679$	−19.4711	+	11.2417i	−0.747234	+	0.431416i
$680$		−	5.46410i		−	0.209539i
$681$	−13.6244	−	7.86603i	−0.522086	−	0.301427i
$682$	−1.46410	+	2.53590i	−0.0560633	+	0.0971046i
$683$	−22.0526	−	12.7321i	−0.843818	−	0.487178i	0.0147424	−	0.999891i	$-0.495307\pi$
$683$	−22.0526	−	12.7321i	−0.843818	−	0.487178i	−0.858560	+	0.512713i	$0.828641\pi$
$684$	−2.59808	+	1.50000i	−0.0993399	+	0.0573539i
$685$	1.50000	−	0.866025i	0.0573121	−	0.0330891i
$686$	16.9186	+	9.76795i	0.645955	+	0.372942i
$687$	−8.73205	+	15.1244i	−0.333149	+	0.577030i
$688$	7.09808	+	4.09808i	0.270612	+	0.156238i
$689$		−	2.73205i		−	0.104083i
$690$	−1.09808	+	0.633975i	−0.0418030	+	0.0241350i
$691$	−3.13397	+	5.42820i	−0.119222	+	0.206499i	−0.919460	−	0.393185i	$-0.871373\pi$
$691$	−3.13397	+	5.42820i	−0.119222	+	0.206499i	0.800238	+	0.599683i	$0.204707\pi$
$692$	5.07180			0.192801
$693$	4.92820			0.187207
$694$	0.330127	−	0.571797i	0.0125315	−	0.0217051i
$695$		−	13.8564i		−	0.525603i
$696$	0.133975	+	0.232051i	0.00507829	+	0.00879586i
$697$			33.8564i			1.28240i
$698$	14.7846	−	8.53590i	0.559606	−	0.323089i
$699$	−3.06218	−	5.30385i	−0.115822	−	0.200610i
$700$	−1.23205	−	2.13397i	−0.0465671	−	0.0806567i
$701$	−7.98076	−	4.60770i	−0.301429	−	0.174030i	0.341656	−	0.939825i	$-0.389012\pi$
$701$	−7.98076	−	4.60770i	−0.301429	−	0.174030i	−0.643085	+	0.765795i	$0.722346\pi$
$702$	1.00000			0.0377426
$703$	−15.0000	−	10.3923i	−0.565736	−	0.391953i
$704$	−2.00000			−0.0753778
$705$	−1.09808	−	0.633975i	−0.0413559	−	0.0238769i
$706$	11.3564	+	19.6699i	0.427404	+	0.740285i
$707$	6.73205	+	11.6603i	0.253185	+	0.438529i
$708$	5.36603	−	3.09808i	0.201668	−	0.116433i
$709$		−	16.1436i		−	0.606285i	−0.952945	−	0.303143i	$-0.901964\pi$
$709$		−	16.1436i		−	0.606285i	0.952945	−	0.303143i	$-0.0980359\pi$
$710$	5.59808	+	9.69615i	0.210092	+	0.363890i
$711$			10.1962i			0.382386i
$712$	4.73205	−	8.19615i	0.177341	−	0.307164i
$713$	1.85641			0.0695230
$714$	13.4641			0.503881
$715$	−1.00000	+	1.73205i	−0.0373979	+	0.0647750i
$716$	2.19615	−	1.26795i	0.0820741	−	0.0473855i
$717$			16.3205i			0.609501i
$718$	−5.76795	−	3.33013i	−0.215258	−	0.124279i
$719$	11.5981	−	20.0885i	0.432535	−	0.749173i	−0.564556	−	0.825395i	$-0.690952\pi$
$719$	11.5981	−	20.0885i	0.432535	−	0.749173i	0.997091	+	0.0762220i	$0.0242858\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	−2.55256	+	1.47372i	−0.0950623	+	0.0548842i
$722$	8.66025	−	5.00000i	0.322301	−	0.186081i
$723$	3.92820	+	2.26795i	0.146091	+	0.0843459i
$724$	−13.1962	+	22.8564i	−0.490431	+	0.849452i
$725$	0.232051	+	0.133975i	0.00861815	+	0.00497569i
$726$			7.00000i			0.259794i
$727$	18.2321	−	10.5263i	0.676189	−	0.390398i	−0.122228	−	0.992502i	$-0.539004\pi$
$727$	18.2321	−	10.5263i	0.676189	−	0.390398i	0.798418	+	0.602104i	$0.205671\pi$
$728$	−1.23205	+	2.13397i	−0.0456628	+	0.0790904i
$729$	1.00000			0.0370370
$730$	16.1962			0.599446
$731$	−22.3923	+	38.7846i	−0.828209	+	1.43450i
$732$			12.7321i			0.470590i
$733$	19.5359	+	33.8372i	0.721575	+	1.24980i	0.960368	+	0.278734i	$0.0899148\pi$
$733$	19.5359	+	33.8372i	0.721575	+	1.24980i	−0.238793	+	0.971070i	$0.576752\pi$
$734$		−	19.3923i		−	0.715783i
$735$	−0.803848	+	0.464102i	−0.0296504	+	0.0171186i
$736$	0.633975	+	1.09808i	0.0233686	+	0.0404756i
$737$	−3.46410	−	6.00000i	−0.127602	−	0.221013i
$738$	−5.36603	−	3.09808i	−0.197526	−	0.114042i
$739$	−7.19615			−0.264715			−0.132357	−	0.991202i	$-0.542255\pi$
$739$	−7.19615			−0.264715			−0.132357	+	0.991202i	$0.542255\pi$
$740$	−0.500000	+	6.06218i	−0.0183804	+	0.222850i
$741$	3.00000			0.110208
$742$	5.83013	+	3.36603i	0.214031	+	0.123571i
$743$	1.07180	+	1.85641i	0.0393204	+	0.0681049i	0.885016	−	0.465561i	$-0.154147\pi$
$743$	1.07180	+	1.85641i	0.0393204	+	0.0681049i	−0.845695	+	0.533666i	$0.820814\pi$
$744$	−0.732051	−	1.26795i	−0.0268383	−	0.0464853i
$745$	−1.79423	+	1.03590i	−0.0657355	+	0.0379524i
$746$		−	20.6603i		−	0.756426i
$747$	−1.96410	−	3.40192i	−0.0718627	−	0.124470i
$748$		−	10.9282i		−	0.399575i
$749$	−12.8038	+	22.1769i	−0.467842	+	0.810327i
$750$	1.00000			0.0365148
$751$	−4.05256			−0.147880			−0.0739400	−	0.997263i	$-0.523557\pi$
$751$	−4.05256			−0.147880			−0.0739400	+	0.997263i	$0.523557\pi$
$752$	−0.633975	+	1.09808i	−0.0231187	+	0.0400427i
$753$	10.2679	−	5.92820i	0.374185	−	0.216036i
$754$		−	0.267949i		−	0.00975813i
$755$	10.8564	+	6.26795i	0.395105	+	0.228114i
$756$	−1.23205	+	2.13397i	−0.0448093	+	0.0776119i
$757$	20.1340	+	11.6244i	0.731782	+	0.422494i	0.819074	−	0.573688i	$-0.194488\pi$
$757$	20.1340	+	11.6244i	0.731782	+	0.422494i	−0.0872919	+	0.996183i	$0.527821\pi$
$758$	29.5526	−	17.0622i	1.07340	−	0.619726i
$759$	−2.19615	+	1.26795i	−0.0797153	+	0.0460236i
$760$	2.59808	+	1.50000i	0.0942421	+	0.0544107i
$761$	16.5622	−	28.6865i	0.600378	−	1.03989i	−0.392385	−	0.919801i	$-0.628350\pi$
$761$	16.5622	−	28.6865i	0.600378	−	1.03989i	0.992764	−	0.120085i	$-0.0383167\pi$
$762$	−9.06218	−	5.23205i	−0.328288	−	0.189537i
$763$			4.92820i			0.178413i
$764$	−1.39230	+	0.803848i	−0.0503718	+	0.0290822i
$765$	−2.73205	+	4.73205i	−0.0987775	+	0.171088i
$766$	−3.07180			−0.110989
$767$	−6.19615			−0.223730
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$		−	2.51666i		−	0.0907531i	−0.998970	−	0.0453765i	$-0.985551\pi$
$769$		−	2.51666i		−	0.0907531i	0.998970	−	0.0453765i	$-0.0144488\pi$
$770$	−2.46410	−	4.26795i	−0.0888001	−	0.153806i
$771$			3.92820i			0.141471i
$772$	−17.9545	+	10.3660i	−0.646196	+	0.373081i
$773$	11.8038	+	20.4449i	0.424555	+	0.735351i	0.996379	−	0.0850258i	$-0.0270973\pi$
$773$	11.8038	+	20.4449i	0.424555	+	0.735351i	−0.571824	+	0.820376i	$0.693764\pi$
$774$	−4.09808	−	7.09808i	−0.147302	−	0.255135i
$775$	−1.26795	−	0.732051i	−0.0455461	−	0.0262960i
$776$	−9.12436			−0.327545
$777$	−14.9378	−	1.23205i	−0.535891	−	0.0441996i
$778$	−29.9808			−1.07486
$779$	−16.0981	−	9.29423i	−0.576773	−	0.333000i
$780$	−0.500000	−	0.866025i	−0.0179029	−	0.0310087i
$781$	11.1962	+	19.3923i	0.400630	+	0.693911i
$782$	−6.00000	+	3.46410i	−0.214560	+	0.123876i
$783$		−	0.267949i		−	0.00957572i
$784$	0.464102	+	0.803848i	0.0165751	+	0.0287088i
$785$		−	4.26795i		−	0.152330i
$786$	−6.83013	+	11.8301i	−0.243623	+	0.421967i
$787$	24.4449			0.871365			0.435683	−	0.900100i	$-0.356507\pi$
$787$	24.4449			0.871365			0.435683	+	0.900100i	$0.356507\pi$
$788$	−9.66025			−0.344132
$789$	5.63397	−	9.75833i	0.200575	−	0.347406i
$790$	8.83013	−	5.09808i	0.314162	−	0.181381i
$791$			13.6410i			0.485019i
$792$	1.73205	+	1.00000i	0.0615457	+	0.0355335i
$793$	6.36603	−	11.0263i	0.226064	−	0.391555i
$794$	1.14359	+	0.660254i	0.0405846	+	0.0234315i
$795$	−2.36603	+	1.36603i	−0.0839143	+	0.0484479i
$796$	−6.16987	+	3.56218i	−0.218685	+	0.126258i
$797$	−30.6340	−	17.6865i	−1.08511	−	0.626489i	−0.152840	−	0.988251i	$-0.548842\pi$
$797$	−30.6340	−	17.6865i	−1.08511	−	0.626489i	−0.932271	+	0.361762i	$0.882175\pi$
$798$	−3.69615	+	6.40192i	−0.130842	+	0.226626i
$799$	−6.00000	−	3.46410i	−0.212265	−	0.122551i
$800$		−	1.00000i		−	0.0353553i
$801$	−8.19615	+	4.73205i	−0.289597	+	0.167199i
$802$	5.19615	−	9.00000i	0.183483	−	0.317801i
$803$	32.3923			1.14310
$804$	3.46410			0.122169
$805$	−1.56218	+	2.70577i	−0.0550595	+	0.0953659i
$806$			1.46410i			0.0515708i
$807$	4.76795	+	8.25833i	0.167840	+	0.290707i
$808$			5.46410i			0.192226i
$809$	41.5692	−	24.0000i	1.46150	−	0.843795i	0.462415	−	0.886664i	$-0.346983\pi$
$809$	41.5692	−	24.0000i	1.46150	−	0.843795i	0.999081	+	0.0428684i	$0.0136496\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	6.73205	+	11.6603i	0.236394	+	0.409447i	0.959677	−	0.281105i	$-0.0907010\pi$
$811$	6.73205	+	11.6603i	0.236394	+	0.409447i	−0.723283	+	0.690552i	$0.757368\pi$
$812$	0.571797	+	0.330127i	0.0200661	+	0.0115852i
$813$	12.7846			0.448376
$814$	−1.00000	+	12.1244i	−0.0350500	+	0.424958i
$815$	22.5885			0.791239
$816$	4.73205	+	2.73205i	0.165655	+	0.0956409i
$817$	−12.2942	−	21.2942i	−0.430121	−	0.744991i
$818$	2.66987	+	4.62436i	0.0933499	+	0.161687i
$819$	2.13397	−	1.23205i	0.0745671	−	0.0430513i
$820$			6.19615i			0.216379i
$821$	−21.2321	−	36.7750i	−0.741004	−	1.28346i	−0.952039	−	0.305978i	$-0.901017\pi$
$821$	−21.2321	−	36.7750i	−0.741004	−	1.28346i	0.211035	−	0.977478i	$-0.432317\pi$
$822$			1.73205i			0.0604122i
$823$	−9.08846	+	15.7417i	−0.316804	+	0.548720i	−0.979819	−	0.199886i	$-0.935943\pi$
$823$	−9.08846	+	15.7417i	−0.316804	+	0.548720i	0.663016	+	0.748606i	$0.269276\pi$
$824$	−1.19615			−0.0416699
$825$	2.00000			0.0696311
$826$	7.63397	−	13.2224i	0.265620	−	0.460067i
$827$	24.4808	−	14.1340i	0.851280	−	0.491486i	−0.00980286	−	0.999952i	$-0.503120\pi$
$827$	24.4808	−	14.1340i	0.851280	−	0.491486i	0.861082	+	0.508465i	$0.169787\pi$
$828$		−	1.26795i		−	0.0440643i
$829$	−35.3205	−	20.3923i	−1.22673	−	0.708254i	−0.260387	−	0.965504i	$-0.583850\pi$
$829$	−35.3205	−	20.3923i	−1.22673	−	0.708254i	−0.966345	+	0.257250i	$0.917184\pi$
$830$	−1.96410	+	3.40192i	−0.0681750	+	0.118082i
$831$	9.86603	+	5.69615i	0.342249	+	0.197597i
$832$	−0.866025	+	0.500000i	−0.0300240	+	0.0173344i
$833$	−4.39230	+	2.53590i	−0.152184	+	0.0878637i
$834$	12.0000	+	6.92820i	0.415526	+	0.239904i
$835$	−0.803848	+	1.39230i	−0.0278183	+	0.0481827i
$836$	5.19615	+	3.00000i	0.179713	+	0.103757i
$837$			1.46410i			0.0506068i
$838$	−7.22243	+	4.16987i	−0.249495	+	0.144046i
$839$	1.26795	−	2.19615i	0.0437745	−	0.0758196i	−0.843308	−	0.537431i	$-0.819395\pi$
$839$	1.26795	−	2.19615i	0.0437745	−	0.0758196i	0.887082	+	0.461611i	$0.152728\pi$
$840$	2.46410			0.0850196
$841$	28.9282			0.997524
$842$	−13.2679	+	22.9808i	−0.457244	+	0.791969i
$843$			3.26795i			0.112554i
$844$	−0.330127	−	0.571797i	−0.0113634	−	0.0196821i
$845$		−	12.0000i		−	0.412813i
$846$	1.09808	−	0.633975i	0.0377526	−	0.0217965i
$847$	8.62436	+	14.9378i	0.296336	+	0.513270i
$848$	1.36603	+	2.36603i	0.0469095	+	0.0812496i
$849$	−1.73205	−	1.00000i	−0.0594438	−	0.0343199i
$850$	5.46410			0.187417
$851$	6.97372	−	3.29423i	0.239056	−	0.112925i
$852$	−11.1962			−0.383574
$853$	48.0000	+	27.7128i	1.64349	+	0.948869i	0.979580	+	0.201055i	$0.0644370\pi$
$853$	48.0000	+	27.7128i	1.64349	+	0.948869i	0.663909	+	0.747814i	$0.268896\pi$
$854$	15.6865	+	27.1699i	0.536782	+	0.929734i
$855$	−1.50000	−	2.59808i	−0.0512989	−	0.0888523i
$856$	−9.00000	+	5.19615i	−0.307614	+	0.177601i
$857$			37.3923i			1.27730i	0.769499	+	0.638648i	$0.220506\pi$
$857$			37.3923i			1.27730i	−0.769499	+	0.638648i	$0.779494\pi$
$858$	−1.00000	−	1.73205i	−0.0341394	−	0.0591312i
$859$		−	14.3205i		−	0.488609i	−0.969699	−	0.244305i	$-0.921440\pi$
$859$		−	14.3205i		−	0.488609i	0.969699	−	0.244305i	$-0.0785597\pi$
$860$	−4.09808	+	7.09808i	−0.139743	+	0.242042i
$861$	−15.2679			−0.520330
$862$	22.8564			0.778492
$863$	−18.5885	+	32.1962i	−0.632758	+	1.09597i	0.354227	+	0.935160i	$0.384744\pi$
$863$	−18.5885	+	32.1962i	−0.632758	+	1.09597i	−0.986985	+	0.160810i	$0.948589\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$			5.07180i			0.172446i
$866$	−11.7058	−	6.75833i	−0.397778	−	0.229657i
$867$	−6.42820	+	11.1340i	−0.218313	+	0.378130i
$868$	−3.12436	−	1.80385i	−0.106048	−	0.0612266i
$869$	17.6603	−	10.1962i	0.599083	−	0.345881i
$870$	−0.232051	+	0.133975i	−0.00786726	+	0.00454216i
$871$	−3.00000	−	1.73205i	−0.101651	−	0.0586883i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$	7.90192	+	4.56218i	0.267440	+	0.154406i
$874$		−	3.80385i		−	0.128667i
$875$	2.13397	−	1.23205i	0.0721415	−	0.0416509i
$876$	−8.09808	+	14.0263i	−0.273609	+	0.473904i
$877$	12.4115			0.419108			0.209554	−	0.977797i	$-0.432799\pi$
$877$	12.4115			0.419108			0.209554	+	0.977797i	$0.432799\pi$
$878$	19.8038			0.668347
$879$	−13.2224	+	22.9019i	−0.445982	+	0.772463i
$880$		−	2.00000i		−	0.0674200i
$881$	10.8564	+	18.8038i	0.365762	+	0.633518i	0.988898	−	0.148595i	$-0.0474752\pi$
$881$	10.8564	+	18.8038i	0.365762	+	0.633518i	−0.623136	+	0.782113i	$0.714142\pi$
$882$		−	0.928203i		−	0.0312542i
$883$	−5.70577	+	3.29423i	−0.192014	+	0.110860i	−0.592925	−	0.805257i	$-0.702027\pi$
$883$	−5.70577	+	3.29423i	−0.192014	+	0.110860i	0.400911	+	0.916117i	$0.368694\pi$
$884$	−2.73205	−	4.73205i	−0.0918888	−	0.159156i
$885$	3.09808	+	5.36603i	0.104141	+	0.180377i
$886$	11.1340	+	6.42820i	0.374053	+	0.215960i
$887$	−40.3923			−1.35624			−0.678120	−	0.734951i	$-0.737205\pi$
$887$	−40.3923			−1.35624			−0.678120	+	0.734951i	$0.737205\pi$
$888$	−5.00000	−	3.46410i	−0.167789	−	0.116248i
$889$	−25.7846			−0.864788
$890$	8.19615	+	4.73205i	0.274736	+	0.158619i
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−9.73205	−	16.8564i	−0.325853	−	0.564394i
$893$	3.29423	−	1.90192i	0.110237	−	0.0636455i
$894$		−	2.07180i		−	0.0692912i
$895$	1.26795	+	2.19615i	0.0423829	+	0.0734093i
$896$		−	2.46410i		−	0.0823199i
$897$	−0.633975	+	1.09808i	−0.0211678	+	0.0366637i
$898$	−32.0000			−1.06785
$899$	0.392305			0.0130841
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−12.9282	+	7.46410i	−0.430701	+	0.248665i
$902$			12.3923i			0.412619i
$903$	−17.4904	−	10.0981i	−0.582043	−	0.336043i
$904$	−2.76795	+	4.79423i	−0.0920606	+	0.159454i
$905$	−22.8564	−	13.1962i	−0.759773	−	0.438655i
$906$	−10.8564	+	6.26795i	−0.360680	+	0.208239i
$907$	43.2679	−	24.9808i	1.43669	−	0.829473i	0.439071	−	0.898453i	$-0.355308\pi$
$907$	43.2679	−	24.9808i	1.43669	−	0.829473i	0.997618	+	0.0689800i	$0.0219745\pi$
$908$	−13.6244	−	7.86603i	−0.452140	−	0.261043i
$909$	2.73205	−	4.73205i	0.0906164	−	0.156952i
$910$	−2.13397	−	1.23205i	−0.0707406	−	0.0408421i
$911$		−	9.00000i		−	0.298183i	−0.988823	−	0.149092i	$-0.952365\pi$
$911$		−	9.00000i		−	0.298183i	0.988823	−	0.149092i	$-0.0476349\pi$
$912$	−2.59808	+	1.50000i	−0.0860309	+	0.0496700i
$913$	−3.92820	+	6.80385i	−0.130005	+	0.225174i
$914$	−25.3205			−0.837528
$915$	−12.7321			−0.420909
$916$	−8.73205	+	15.1244i	−0.288515	+	0.499723i
$917$			33.6603i			1.11156i
$918$	−2.73205	−	4.73205i	−0.0901711	−	0.156181i
$919$			23.6077i			0.778746i	0.921080	+	0.389373i	$0.127308\pi$
$919$			23.6077i			0.778746i	−0.921080	+	0.389373i	$0.872692\pi$
$920$	−1.09808	+	0.633975i	−0.0362025	+	0.0209015i
$921$	15.0263	+	26.0263i	0.495133	+	0.857595i
$922$	−19.2583	−	33.3564i	−0.634239	−	1.09853i
$923$	9.69615	+	5.59808i	0.319153	+	0.184263i
$924$	4.92820			0.162126
$925$	−6.06218	−	0.500000i	−0.199323	−	0.0164399i
$926$	2.12436			0.0698107
$927$	1.03590	+	0.598076i	0.0340234	+	0.0196434i
$928$	0.133975	+	0.232051i	0.00439793	+	0.00761744i
$929$	1.58846	+	2.75129i	0.0521156	+	0.0902669i	0.890906	−	0.454187i	$-0.150070\pi$
$929$	1.58846	+	2.75129i	0.0521156	+	0.0902669i	−0.838791	+	0.544454i	$0.816737\pi$
$930$	1.26795	−	0.732051i	0.0415777	−	0.0240049i
$931$		−	2.78461i		−	0.0912619i
$932$	−3.06218	−	5.30385i	−0.100305	−	0.173733i
$933$		−	6.39230i		−	0.209275i
$934$	0.330127	−	0.571797i	0.0108021	−	0.0187098i
$935$	10.9282			0.357390
$936$	1.00000			0.0326860
$937$	−4.33975	+	7.51666i	−0.141773	+	0.245559i	−0.928164	−	0.372170i	$-0.878614\pi$
$937$	−4.33975	+	7.51666i	−0.141773	+	0.245559i	0.786391	+	0.617729i	$0.211947\pi$
$938$	7.39230	−	4.26795i	0.241367	−	0.139353i
$939$		−	12.3923i		−	0.404408i
$940$	−1.09808	−	0.633975i	−0.0358153	−	0.0206780i
$941$	0.232051	−	0.401924i	0.00756464	−	0.0131023i	−0.862218	−	0.506537i	$-0.830925\pi$
$941$	0.232051	−	0.401924i	0.00756464	−	0.0131023i	0.869783	+	0.493435i	$0.164259\pi$
$942$	3.69615	+	2.13397i	0.120427	+	0.0695286i
$943$	6.80385	−	3.92820i	0.221564	−	0.127920i
$944$	5.36603	−	3.09808i	0.174649	−	0.100834i
$945$	−2.13397	−	1.23205i	−0.0694182	−	0.0400786i
$946$	−8.19615	+	14.1962i	−0.266480	+	0.461557i
$947$	49.0692	+	28.3301i	1.59454	+	0.920605i	0.992515	+	0.122125i	$0.0389708\pi$
$947$	49.0692	+	28.3301i	1.59454	+	0.920605i	0.602021	+	0.798481i	$0.294362\pi$
$948$			10.1962i			0.331156i
$949$	14.0263	−	8.09808i	0.455312	−	0.262875i
$950$	−1.50000	+	2.59808i	−0.0486664	+	0.0842927i
$951$	5.66025			0.183546
$952$	13.4641			0.436374
$953$	−22.2583	+	38.5526i	−0.721018	+	1.24884i	0.239574	+	0.970878i	$0.422992\pi$
$953$	−22.2583	+	38.5526i	−0.721018	+	1.24884i	−0.960592	+	0.277962i	$0.910341\pi$
$954$		−	2.73205i		−	0.0884534i
$955$	−0.803848	−	1.39230i	−0.0260119	−	0.0450539i
$956$			16.3205i			0.527843i
$957$	−0.464102	+	0.267949i	−0.0150023	+	0.00866157i
$958$	14.6603	+	25.3923i	0.473651	+	0.820388i
$959$	2.13397	+	3.69615i	0.0689096	+	0.119355i
$960$	0.866025	+	0.500000i	0.0279508	+	0.0161374i
$961$	28.8564			0.930852
$962$	2.59808	+	5.50000i	0.0837653	+	0.177327i
$963$	10.3923			0.334887
$964$	3.92820	+	2.26795i	0.126519	+	0.0730457i
$965$	−10.3660	−	17.9545i	−0.333694	−	0.577975i
$966$	−1.56218	−	2.70577i	−0.0502622	−	0.0870568i
$967$	2.98334	−	1.72243i	0.0959377	−	0.0553897i	−0.451264	−	0.892391i	$-0.649027\pi$
$967$	2.98334	−	1.72243i	0.0959377	−	0.0553897i	0.547201	+	0.837001i	$0.315693\pi$
$968$			7.00000i			0.224989i
$969$	−8.19615	−	14.1962i	−0.263298	−	0.456046i
$970$		−	9.12436i		−	0.292965i
$971$	−24.1962	+	41.9090i	−0.776491	+	1.34492i	0.157461	+	0.987525i	$0.449669\pi$
$971$	−24.1962	+	41.9090i	−0.776491	+	1.34492i	−0.933952	+	0.357397i	$0.883664\pi$
$972$	1.00000			0.0320750
$973$	34.1436			1.09459
$974$	−5.52628	+	9.57180i	−0.177073	+	0.306700i
$975$	0.866025	−	0.500000i	0.0277350	−	0.0160128i
$976$			12.7321i			0.407543i
$977$	−14.5981	−	8.42820i	−0.467034	−	0.269642i	0.247963	−	0.968769i	$-0.420239\pi$
$977$	−14.5981	−	8.42820i	−0.467034	−	0.269642i	−0.714997	+	0.699127i	$0.753572\pi$
$978$	−11.2942	+	19.5622i	−0.361150	+	0.625529i
$979$	16.3923	+	9.46410i	0.523900	+	0.302474i
$980$	−0.803848	+	0.464102i	−0.0256780	+	0.0148252i
$981$	1.73205	−	1.00000i	0.0553001	−	0.0319275i
$982$	−9.33975	−	5.39230i	−0.298043	−	0.172075i
$983$	−11.9545	+	20.7058i	−0.381289	+	0.660412i	−0.991247	−	0.132022i	$-0.957853\pi$
$983$	−11.9545	+	20.7058i	−0.381289	+	0.660412i	0.609958	+	0.792434i	$0.291186\pi$
$984$	−5.36603	−	3.09808i	−0.171063	−	0.0987631i
$985$		−	9.66025i		−	0.307801i
$986$	−1.26795	+	0.732051i	−0.0403797	+	0.0233132i
$987$	1.56218	−	2.70577i	0.0497247	−	0.0861257i
$988$	3.00000			0.0954427
$989$	10.3923			0.330456
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$		−	13.1244i		−	0.416909i	−0.978032	−	0.208454i	$-0.933157\pi$
$991$		−	13.1244i		−	0.416909i	0.978032	−	0.208454i	$-0.0668433\pi$
$992$	−0.732051	−	1.26795i	−0.0232426	−	0.0402574i
$993$		−	6.85641i		−	0.217581i
$994$	−23.8923	+	13.7942i	−0.757818	+	0.437526i
$995$	−3.56218	−	6.16987i	−0.112929	−	0.195598i
$996$	−1.96410	−	3.40192i	−0.0622349	−	0.107794i
$997$	−39.6506	−	22.8923i	−1.25575	−	0.725007i	−0.283503	−	0.958971i	$-0.591497\pi$
$997$	−39.6506	−	22.8923i	−1.25575	−	0.725007i	−0.972245	+	0.233965i	$0.924830\pi$
$998$	33.6410			1.06489
$999$	2.59808	+	5.50000i	0.0821995	+	0.174012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.a.841.1	yes	4
37.11	even	6	inner	1110.2.x.a.751.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.a.751.1	✓	4	37.11	even	6	inner
1110.2.x.a.841.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-1.23205 - 2.13397i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-1.23205 - 2.13397i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.866025 - 0.500000i) q^{13} +2.46410i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.73205 - 2.73205i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.59808 - 1.50000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(1.23205 - 2.13397i) q^{21} +(-1.73205 - 1.00000i) q^{22} +1.26795i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{26} -1.00000 q^{27} +(1.23205 - 2.13397i) q^{28} +0.267949i q^{29} +(0.500000 + 0.866025i) q^{30} -1.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.00000 + 1.73205i) q^{33} +(2.73205 + 4.73205i) q^{34} +(2.13397 + 1.23205i) q^{35} -1.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} -3.00000 q^{38} +(0.866025 + 0.500000i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-3.09808 - 5.36603i) q^{41} +(-2.13397 + 1.23205i) q^{42} -8.19615i q^{43} +(1.00000 + 1.73205i) q^{44} -1.00000i q^{45} +(0.633975 - 1.09808i) q^{46} +1.26795 q^{47} -1.00000 q^{48} +(0.464102 - 0.803848i) q^{49} +(-0.866025 + 0.500000i) q^{50} -5.46410i q^{51} +(0.866025 + 0.500000i) q^{52} +(1.36603 - 2.36603i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.73205 + 1.00000i) q^{55} +(-2.13397 + 1.23205i) q^{56} +(2.59808 + 1.50000i) q^{57} +(0.133975 - 0.232051i) q^{58} +(-5.36603 - 3.09808i) q^{59} -1.00000i q^{60} +(11.0263 - 6.36603i) q^{61} +(-0.732051 + 1.26795i) q^{62} +2.46410 q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -2.00000i q^{66} +(-1.73205 - 3.00000i) q^{67} -5.46410i q^{68} +(-1.09808 + 0.633975i) q^{69} +(-1.23205 - 2.13397i) q^{70} +(5.59808 + 9.69615i) q^{71} +(0.866025 + 0.500000i) q^{72} +16.1962 q^{73} +(-0.500000 + 6.06218i) q^{74} +1.00000 q^{75} +(2.59808 + 1.50000i) q^{76} +(-2.46410 - 4.26795i) q^{77} +(-0.500000 - 0.866025i) q^{78} +(8.83013 - 5.09808i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +6.19615i q^{82} +(-1.96410 + 3.40192i) q^{83} +2.46410 q^{84} +5.46410 q^{85} +(-4.09808 + 7.09808i) q^{86} +(-0.232051 + 0.133975i) q^{87} -2.00000i q^{88} +(8.19615 + 4.73205i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-2.13397 - 1.23205i) q^{91} +(-1.09808 + 0.633975i) q^{92} +(1.26795 - 0.732051i) q^{93} +(-1.09808 - 0.633975i) q^{94} +(-1.50000 + 2.59808i) q^{95} +(0.866025 + 0.500000i) q^{96} -9.12436i q^{97} +(-0.803848 + 0.464102i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{16} - 12 q^{17} - 2 q^{21} + 2 q^{25} - 4 q^{26} - 4 q^{27} - 2 q^{28} + 2 q^{30} + 4 q^{33} + 4 q^{34} + 12 q^{35} - 4 q^{36} - 12 q^{38} + 2 q^{40} - 2 q^{41} - 12 q^{42} + 4 q^{44} + 6 q^{46} + 12 q^{47} - 4 q^{48} - 12 q^{49} + 2 q^{53} - 12 q^{56} + 4 q^{58} - 18 q^{59} + 6 q^{61} + 4 q^{62} - 4 q^{63} - 4 q^{64} - 2 q^{65} + 6 q^{69} + 2 q^{70} + 12 q^{71} + 44 q^{73} - 2 q^{74} + 4 q^{75} + 4 q^{77} - 2 q^{78} + 18 q^{79} - 2 q^{81} + 6 q^{83} - 4 q^{84} + 8 q^{85} - 6 q^{86} + 6 q^{87} + 12 q^{89} - 2 q^{90} - 12 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} - 24 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^12 - 2 * q^16 - 12 * q^17 - 2 * q^21 + 2 * q^25 - 4 * q^26 - 4 * q^27 - 2 * q^28 + 2 * q^30 + 4 * q^33 + 4 * q^34 + 12 * q^35 - 4 * q^36 - 12 * q^38 + 2 * q^40 - 2 * q^41 - 12 * q^42 + 4 * q^44 + 6 * q^46 + 12 * q^47 - 4 * q^48 - 12 * q^49 + 2 * q^53 - 12 * q^56 + 4 * q^58 - 18 * q^59 + 6 * q^61 + 4 * q^62 - 4 * q^63 - 4 * q^64 - 2 * q^65 + 6 * q^69 + 2 * q^70 + 12 * q^71 + 44 * q^73 - 2 * q^74 + 4 * q^75 + 4 * q^77 - 2 * q^78 + 18 * q^79 - 2 * q^81 + 6 * q^83 - 4 * q^84 + 8 * q^85 - 6 * q^86 + 6 * q^87 + 12 * q^89 - 2 * q^90 - 12 * q^91 + 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 - 24 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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