LMFDB - Embedded newform 1134.2.t.c.593.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(593,1134)]

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([1, 5]))

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

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

chi := DirichletCharacter("1134.593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.t (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			593.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.593
Dual form			1134.2.t.c.1025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(1.50000 - 0.866025i) q^{10} +(-1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 3.00000i) q^{17} +(6.00000 + 3.46410i) q^{19} +(-0.866025 + 1.50000i) q^{20} +6.00000i q^{23} -2.00000 q^{25} +(2.50000 + 0.866025i) q^{28} +(-7.79423 - 4.50000i) q^{29} +(-3.00000 - 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.00000 + 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-2.00000 + 3.46410i) q^{37} -6.92820 q^{38} -1.73205i q^{40} +(1.73205 + 3.00000i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{46} +(-1.73205 - 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} +(-2.59808 + 1.50000i) q^{53} +(-2.59808 + 0.500000i) q^{56} +9.00000 q^{58} +(-6.06218 + 10.5000i) q^{59} +(-3.00000 + 1.73205i) q^{61} +3.46410 q^{62} -1.00000 q^{64} +(-7.00000 + 12.1244i) q^{67} -3.46410 q^{68} +(3.00000 + 3.46410i) q^{70} -6.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} -4.00000i q^{74} +(6.00000 - 3.46410i) q^{76} +(-5.50000 - 9.52628i) q^{79} +(0.866025 + 1.50000i) q^{80} +(-3.00000 - 1.73205i) q^{82} +(-8.66025 + 15.0000i) q^{83} +(3.00000 + 5.19615i) q^{85} +8.00000i q^{86} +(-5.19615 + 9.00000i) q^{89} +(5.19615 + 3.00000i) q^{92} +(3.00000 + 1.73205i) q^{94} +(-10.3923 - 6.00000i) q^{95} +(6.00000 + 3.46410i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^7	$ 4 q + 2 q^{4} + 2 q^{7} + 6 q^{10} - 2 q^{16} + 24 q^{19} - 8 q^{25} + 10 q^{28} - 12 q^{31} + 12 q^{34} - 8 q^{37} + 16 q^{43} - 12 q^{46} - 26 q^{49} + 36 q^{58} - 12 q^{61} - 4 q^{64} - 28 q^{67} + 12 q^{70} - 42 q^{73} + 24 q^{76} - 22 q^{79} - 12 q^{82} + 12 q^{85} + 12 q^{94} + 24 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^7 + 6 * q^10 - 2 * q^16 + 24 * q^19 - 8 * q^25 + 10 * q^28 - 12 * q^31 + 12 * q^34 - 8 * q^37 + 16 * q^43 - 12 * q^46 - 26 * q^49 + 36 * q^58 - 12 * q^61 - 4 * q^64 - 28 * q^67 + 12 * q^70 - 42 * q^73 + 24 * q^76 - 22 * q^79 - 12 * q^82 + 12 * q^85 + 12 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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			−0.774597			−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205			−0.774597			−0.387298	+	0.921954i	$0.626592\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.50000	−	0.866025i	0.474342	−	0.273861i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−1.73205	−	2.00000i	−0.462910	−	0.534522i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	0.575863	−	0.817546i	$-0.304666\pi$
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	−0.995947	+	0.0899392i	$0.971333\pi$
$18$		0			0
$19$	6.00000	+	3.46410i	1.37649	+	0.794719i	0.991736	−	0.128298i	$-0.0409513\pi$
$19$	6.00000	+	3.46410i	1.37649	+	0.794719i	0.384759	+	0.923017i	$0.374285\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$		0			0
$22$		0			0
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$		0			0
$25$	−2.00000			−0.400000
$26$		0			0
$27$		0			0
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	−7.79423	−	4.50000i	−1.44735	−	0.835629i	−0.449029	−	0.893517i	$-0.648230\pi$
$29$	−7.79423	−	4.50000i	−1.44735	−	0.835629i	−0.998323	+	0.0578882i	$0.981563\pi$
$30$		0			0
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	3.00000	+	1.73205i	0.514496	+	0.297044i
$35$	−0.866025	−	4.50000i	−0.146385	−	0.760639i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	−6.92820			−1.12390
$39$		0			0
$40$		−	1.73205i		−	0.273861i
$41$	1.73205	+	3.00000i	0.270501	+	0.468521i	0.968990	−	0.247099i	$-0.0794774\pi$
$41$	1.73205	+	3.00000i	0.270501	+	0.468521i	−0.698489	+	0.715621i	$0.746144\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	0.711608	−	0.702577i	$-0.247967\pi$
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	−0.964253	+	0.264982i	$0.914634\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	1.73205	−	1.00000i	0.244949	−	0.141421i
$51$		0			0
$52$		0			0
$53$	−2.59808	+	1.50000i	−0.356873	+	0.206041i	−0.667708	−	0.744423i	$-0.732725\pi$
$53$	−2.59808	+	1.50000i	−0.356873	+	0.206041i	0.310835	+	0.950464i	$0.399391\pi$
$54$		0			0
$55$		0			0
$56$	−2.59808	+	0.500000i	−0.347183	+	0.0668153i
$57$		0			0
$58$	9.00000			1.18176
$59$	−6.06218	+	10.5000i	−0.789228	+	1.36698i	0.137212	+	0.990542i	$0.456186\pi$
$59$	−6.06218	+	10.5000i	−0.789228	+	1.36698i	−0.926440	+	0.376442i	$0.877147\pi$
$60$		0			0
$61$	−3.00000	+	1.73205i	−0.384111	+	0.221766i	−0.679605	−	0.733578i	$-0.737849\pi$
$61$	−3.00000	+	1.73205i	−0.384111	+	0.221766i	0.295495	+	0.955344i	$0.404516\pi$
$62$	3.46410			0.439941
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	0.0212861	+	0.999773i	$0.493224\pi$
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	−0.876472	+	0.481452i	$0.840109\pi$
$68$	−3.46410			−0.420084
$69$		0			0
$70$	3.00000	+	3.46410i	0.358569	+	0.414039i
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$		0			0
$73$	−10.5000	+	6.06218i	−1.22893	+	0.709524i	−0.966807	−	0.255510i	$-0.917757\pi$
$73$	−10.5000	+	6.06218i	−1.22893	+	0.709524i	−0.262126	+	0.965034i	$0.584423\pi$
$74$		−	4.00000i		−	0.464991i
$75$		0			0
$76$	6.00000	−	3.46410i	0.688247	−	0.397360i
$77$		0			0
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$	0.866025	+	1.50000i	0.0968246	+	0.167705i
$81$		0			0
$82$	−3.00000	−	1.73205i	−0.331295	−	0.191273i
$83$	−8.66025	+	15.0000i	−0.950586	+	1.64646i	−0.206427	+	0.978462i	$0.566184\pi$
$83$	−8.66025	+	15.0000i	−0.950586	+	1.64646i	−0.744160	+	0.668002i	$0.767150\pi$
$84$		0			0
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$			8.00000i			0.862662i
$87$		0			0
$88$		0			0
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$		0			0
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$		0			0
$94$	3.00000	+	1.73205i	0.309426	+	0.178647i
$95$	−10.3923	−	6.00000i	−1.06623	−	0.615587i
$96$		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	$0.552261\pi$
$98$	4.33013	−	5.50000i	0.437409	−	0.555584i
$99$		0			0
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	−5.19615			−0.517036			−0.258518	−	0.966006i	$-0.583234\pi$
$101$	−5.19615			−0.517036			−0.258518	+	0.966006i	$0.583234\pi$
$102$		0			0
$103$		−	10.3923i		−	1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$		−	10.3923i		−	1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$		0			0
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	2.59808	+	1.50000i	0.251166	+	0.145010i	0.620298	−	0.784366i	$-0.287012\pi$
$107$	2.59808	+	1.50000i	0.251166	+	0.145010i	−0.369132	+	0.929377i	$0.620345\pi$
$108$		0			0
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	−0.939577	−	0.342337i	$-0.888782\pi$
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	0.173316	−	0.984866i	$-0.444552\pi$
$110$		0			0
$111$		0			0
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.467143	−	0.884182i	$-0.345283\pi$
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.999295	+	0.0375328i	$0.0119499\pi$
$114$		0			0
$115$		−	10.3923i		−	0.969087i
$116$	−7.79423	+	4.50000i	−0.723676	+	0.417815i
$117$		0			0
$118$		−	12.1244i		−	1.11614i
$119$	6.92820	−	6.00000i	0.635107	−	0.550019i
$120$		0			0
$121$	11.0000			1.00000
$122$	1.73205	−	3.00000i	0.156813	−	0.271607i
$123$		0			0
$124$	−3.00000	+	1.73205i	−0.269408	+	0.155543i
$125$	12.1244			1.08444
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−10.3923			−0.907980			−0.453990	−	0.891007i	$-0.650000\pi$
$131$	−10.3923			−0.907980			−0.453990	+	0.891007i	$0.650000\pi$
$132$		0			0
$133$	−6.00000	+	17.3205i	−0.520266	+	1.50188i
$134$		−	14.0000i		−	1.20942i
$135$		0			0
$136$	3.00000	−	1.73205i	0.257248	−	0.148522i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$	−9.00000	+	5.19615i	−0.763370	+	0.440732i	−0.830504	−	0.557012i	$-0.811948\pi$
$139$	−9.00000	+	5.19615i	−0.763370	+	0.440732i	0.0671344	+	0.997744i	$0.478614\pi$
$140$	−4.33013	−	1.50000i	−0.365963	−	0.126773i
$141$		0			0
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$		0			0
$144$		0			0
$145$	13.5000	+	7.79423i	1.12111	+	0.647275i
$146$	6.06218	−	10.5000i	0.501709	−	0.868986i
$147$		0			0
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$		−	15.0000i		−	1.22885i	−0.788976	−	0.614424i	$-0.789388\pi$
$149$		−	15.0000i		−	1.22885i	0.788976	−	0.614424i	$-0.210612\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	−3.46410	+	6.00000i	−0.280976	+	0.486664i
$153$		0			0
$154$		0			0
$155$	5.19615	+	3.00000i	0.417365	+	0.240966i
$156$		0			0
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	0.0958404	−	0.995397i	$-0.469446\pi$
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	−0.814119	+	0.580699i	$0.802779\pi$
$158$	9.52628	+	5.50000i	0.757870	+	0.437557i
$159$		0			0
$160$	−1.50000	−	0.866025i	−0.118585	−	0.0684653i
$161$	−15.5885	+	3.00000i	−1.22854	+	0.236433i
$162$		0			0
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	3.46410			0.270501
$165$		0			0
$166$		−	17.3205i		−	1.34433i
$167$	8.66025	+	15.0000i	0.670151	+	1.16073i	0.977861	+	0.209255i	$0.0671038\pi$
$167$	8.66025	+	15.0000i	0.670151	+	1.16073i	−0.307711	+	0.951480i	$0.599563\pi$
$168$		0			0
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$	−5.19615	−	3.00000i	−0.398527	−	0.230089i
$171$		0			0
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−2.59808	−	4.50000i	−0.197528	−	0.342129i	0.750198	−	0.661213i	$-0.229958\pi$
$173$	−2.59808	−	4.50000i	−0.197528	−	0.342129i	−0.947726	+	0.319084i	$0.896625\pi$
$174$		0			0
$175$	−1.00000	−	5.19615i	−0.0755929	−	0.392792i
$176$		0			0
$177$		0			0
$178$		−	10.3923i		−	0.778936i
$179$	12.9904	−	7.50000i	0.970947	−	0.560576i	0.0714220	−	0.997446i	$-0.477246\pi$
$179$	12.9904	−	7.50000i	0.970947	−	0.560576i	0.899525	+	0.436870i	$0.143913\pi$
$180$		0			0
$181$			17.3205i			1.28742i	0.765268	+	0.643712i	$0.222606\pi$
$181$			17.3205i			1.28742i	−0.765268	+	0.643712i	$0.777394\pi$
$182$		0			0
$183$		0			0
$184$	−6.00000			−0.442326
$185$	3.46410	−	6.00000i	0.254686	−	0.441129i
$186$		0			0
$187$		0			0
$188$	−3.46410			−0.252646
$189$		0			0
$190$	12.0000			0.870572
$191$	5.19615	−	3.00000i	0.375980	−	0.217072i	−0.300088	−	0.953912i	$-0.597016\pi$
$191$	5.19615	−	3.00000i	0.375980	−	0.217072i	0.676068	+	0.736839i	$0.263683\pi$
$192$		0			0
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	−6.92820			−0.497416
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			3.00000i			0.213741i	0.994273	+	0.106871i	$0.0340831\pi$
$197$			3.00000i			0.213741i	−0.994273	+	0.106871i	$0.965917\pi$
$198$		0			0
$199$	7.50000	−	4.33013i	0.531661	−	0.306955i	−0.210032	−	0.977695i	$-0.567357\pi$
$199$	7.50000	−	4.33013i	0.531661	−	0.306955i	0.741693	+	0.670740i	$0.234023\pi$
$200$		−	2.00000i		−	0.141421i
$201$		0			0
$202$	4.50000	−	2.59808i	0.316619	−	0.182800i
$203$	7.79423	−	22.5000i	0.547048	−	1.57919i
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	5.19615	+	9.00000i	0.362033	+	0.627060i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−8.00000	−	13.8564i	−0.550743	−	0.953914i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−8.00000	−	13.8564i	−0.550743	−	0.953914i	0.447478	−	0.894295i	$-0.352322\pi$
$212$			3.00000i			0.206041i
$213$		0			0
$214$	−3.00000			−0.205076
$215$	−6.92820	+	12.0000i	−0.472500	+	0.818393i
$216$		0			0
$217$	3.00000	−	8.66025i	0.203653	−	0.587896i
$218$	13.8564	+	8.00000i	0.938474	+	0.541828i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	13.5000	+	7.79423i	0.904027	+	0.521940i	0.878504	−	0.477734i	$-0.158542\pi$
$223$	13.5000	+	7.79423i	0.904027	+	0.521940i	0.0255224	+	0.999674i	$0.491875\pi$
$224$	−0.866025	+	2.50000i	−0.0578638	+	0.167038i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	25.9808			1.72440			0.862202	−	0.506565i	$-0.169085\pi$
$227$	25.9808			1.72440			0.862202	+	0.506565i	$0.169085\pi$
$228$		0			0
$229$			3.46410i			0.228914i	0.993428	+	0.114457i	$0.0365129\pi$
$229$			3.46410i			0.228914i	−0.993428	+	0.114457i	$0.963487\pi$
$230$	5.19615	+	9.00000i	0.342624	+	0.593442i
$231$		0			0
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	25.9808	+	15.0000i	1.70206	+	0.982683i	0.943676	+	0.330870i	$0.107342\pi$
$233$	25.9808	+	15.0000i	1.70206	+	0.982683i	0.758380	+	0.651813i	$0.225991\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	6.06218	+	10.5000i	0.394614	+	0.683492i
$237$		0			0
$238$	−3.00000	+	8.66025i	−0.194461	+	0.561361i
$239$	20.7846	−	12.0000i	1.34444	−	0.776215i	0.356988	−	0.934109i	$-0.383804\pi$
$239$	20.7846	−	12.0000i	1.34444	−	0.776215i	0.987456	+	0.157893i	$0.0504702\pi$
$240$		0			0
$241$			1.73205i			0.111571i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$			1.73205i			0.111571i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−9.52628	+	5.50000i	−0.612372	+	0.353553i
$243$		0			0
$244$			3.46410i			0.221766i
$245$	11.2583	−	4.50000i	0.719268	−	0.287494i
$246$		0			0
$247$		0			0
$248$	1.73205	−	3.00000i	0.109985	−	0.190500i
$249$		0			0
$250$	−10.5000	+	6.06218i	−0.664078	+	0.383406i
$251$	8.66025			0.546630			0.273315	−	0.961925i	$-0.411880\pi$
$251$	8.66025			0.546630			0.273315	+	0.961925i	$0.411880\pi$
$252$		0			0
$253$		0			0
$254$	6.06218	−	3.50000i	0.380375	−	0.219610i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−20.7846			−1.29651			−0.648254	−	0.761424i	$-0.724501\pi$
$257$	−20.7846			−1.29651			−0.648254	+	0.761424i	$0.724501\pi$
$258$		0			0
$259$	−10.0000	−	3.46410i	−0.621370	−	0.215249i
$260$		0			0
$261$		0			0
$262$	9.00000	−	5.19615i	0.556022	−	0.321019i
$263$			18.0000i			1.10993i	0.831875	+	0.554964i	$0.187268\pi$
$263$			18.0000i			1.10993i	−0.831875	+	0.554964i	$0.812732\pi$
$264$		0			0
$265$	4.50000	−	2.59808i	0.276433	−	0.159599i
$266$	−3.46410	−	18.0000i	−0.212398	−	1.10365i
$267$		0			0
$268$	7.00000	+	12.1244i	0.427593	+	0.740613i
$269$	−0.866025	−	1.50000i	−0.0528025	−	0.0914566i	0.838416	−	0.545031i	$-0.183482\pi$
$269$	−0.866025	−	1.50000i	−0.0528025	−	0.0914566i	−0.891219	+	0.453574i	$0.850149\pi$
$270$		0			0
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	0.783778	−	0.621041i	$-0.213290\pi$
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	−0.145948	+	0.989292i	$0.546623\pi$
$272$	−1.73205	+	3.00000i	−0.105021	+	0.181902i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$	5.19615	−	9.00000i	0.311645	−	0.539784i
$279$		0			0
$280$	4.50000	−	0.866025i	0.268926	−	0.0517549i
$281$	15.5885	+	9.00000i	0.929929	+	0.536895i	0.886789	−	0.462174i	$-0.152930\pi$
$281$	15.5885	+	9.00000i	0.929929	+	0.536895i	0.0431402	+	0.999069i	$0.486264\pi$
$282$		0			0
$283$	−6.00000	−	3.46410i	−0.356663	−	0.205919i	0.310953	−	0.950425i	$-0.399352\pi$
$283$	−6.00000	−	3.46410i	−0.356663	−	0.205919i	−0.667616	+	0.744506i	$0.732685\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$		0			0
$287$	−6.92820	+	6.00000i	−0.408959	+	0.354169i
$288$		0			0
$289$	2.50000	−	4.33013i	0.147059	−	0.254713i
$290$	−15.5885			−0.915386
$291$		0			0
$292$			12.1244i			0.709524i
$293$	14.7224	+	25.5000i	0.860094	+	1.48973i	0.871838	+	0.489795i	$0.162928\pi$
$293$	14.7224	+	25.5000i	0.860094	+	1.48973i	−0.0117441	+	0.999931i	$0.503738\pi$
$294$		0			0
$295$	10.5000	−	18.1865i	0.611334	−	1.05886i
$296$	−3.46410	−	2.00000i	−0.201347	−	0.116248i
$297$		0			0
$298$	7.50000	+	12.9904i	0.434463	+	0.752513i
$299$		0			0
$300$		0			0
$301$	20.0000	+	6.92820i	1.15278	+	0.399335i
$302$	6.92820	−	4.00000i	0.398673	−	0.230174i
$303$		0			0
$304$		−	6.92820i		−	0.397360i
$305$	5.19615	−	3.00000i	0.297531	−	0.171780i
$306$		0			0
$307$		−	6.92820i		−	0.395413i	−0.980261	−	0.197707i	$-0.936651\pi$
$307$		−	6.92820i		−	0.395413i	0.980261	−	0.197707i	$-0.0633494\pi$
$308$		0			0
$309$		0			0
$310$	−6.00000			−0.340777
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	−0.992826	−	0.119570i	$-0.961848\pi$
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	0.599963	+	0.800027i	$0.295182\pi$
$312$		0			0
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.165406	−	0.986226i	$-0.447107\pi$
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.936799	+	0.349867i	$0.113773\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	−11.0000			−0.618798
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	−0.638774	−	0.769395i	$-0.720558\pi$
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	0.346929	+	0.937892i	$0.387225\pi$
$318$		0			0
$319$		0			0
$320$	1.73205			0.0968246
$321$		0			0
$322$	12.0000	−	10.3923i	0.668734	−	0.579141i
$323$		−	24.0000i		−	1.33540i
$324$		0			0
$325$		0			0
$326$		−	2.00000i		−	0.110770i
$327$		0			0
$328$	−3.00000	+	1.73205i	−0.165647	+	0.0956365i
$329$	6.92820	−	6.00000i	0.381964	−	0.330791i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	8.66025	+	15.0000i	0.475293	+	0.823232i
$333$		0			0
$334$	−15.0000	−	8.66025i	−0.820763	−	0.473868i
$335$	12.1244	−	21.0000i	0.662424	−	1.14735i
$336$		0			0
$337$	11.5000	+	19.9186i	0.626445	+	1.08503i	0.988260	+	0.152784i	$0.0488240\pi$
$337$	11.5000	+	19.9186i	0.626445	+	1.08503i	−0.361815	+	0.932250i	$0.617843\pi$
$338$		−	13.0000i		−	0.707107i
$339$		0			0
$340$	6.00000			0.325396
$341$		0			0
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	6.92820	+	4.00000i	0.373544	+	0.215666i
$345$		0			0
$346$	4.50000	+	2.59808i	0.241921	+	0.139673i
$347$	−28.5788	−	16.5000i	−1.53419	−	0.885766i	−0.999162	−	0.0409337i	$-0.986967\pi$
$347$	−28.5788	−	16.5000i	−1.53419	−	0.885766i	−0.535031	−	0.844833i	$-0.679700\pi$
$348$		0			0
$349$	3.00000	+	1.73205i	0.160586	+	0.0927146i	0.578140	−	0.815938i	$-0.303779\pi$
$349$	3.00000	+	1.73205i	0.160586	+	0.0927146i	−0.417553	+	0.908652i	$0.637112\pi$
$350$	3.46410	+	4.00000i	0.185164	+	0.213809i
$351$		0			0
$352$		0			0
$353$	3.46410			0.184376			0.0921878	−	0.995742i	$-0.470614\pi$
$353$	3.46410			0.184376			0.0921878	+	0.995742i	$0.470614\pi$
$354$		0			0
$355$			10.3923i			0.551566i
$356$	5.19615	+	9.00000i	0.275396	+	0.476999i
$357$		0			0
$358$	−7.50000	+	12.9904i	−0.396387	+	0.686563i
$359$	−20.7846	−	12.0000i	−1.09697	−	0.633336i	−0.161546	−	0.986865i	$-0.551648\pi$
$359$	−20.7846	−	12.0000i	−1.09697	−	0.633336i	−0.935423	+	0.353529i	$0.884981\pi$
$360$		0			0
$361$	14.5000	+	25.1147i	0.763158	+	1.32183i
$362$	−8.66025	−	15.0000i	−0.455173	−	0.788382i
$363$		0			0
$364$		0			0
$365$	18.1865	−	10.5000i	0.951927	−	0.549595i
$366$		0			0
$367$		−	8.66025i		−	0.452062i	−0.974120	−	0.226031i	$-0.927425\pi$
$367$		−	8.66025i		−	0.452062i	0.974120	−	0.226031i	$-0.0725750\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$		0			0
$370$			6.92820i			0.360180i
$371$	−5.19615	−	6.00000i	−0.269771	−	0.311504i
$372$		0			0
$373$	14.0000			0.724893			0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000			0.724893			0.362446	+	0.932005i	$0.381942\pi$
$374$		0			0
$375$		0			0
$376$	3.00000	−	1.73205i	0.154713	−	0.0893237i
$377$		0			0
$378$		0			0
$379$	−14.0000			−0.719132			−0.359566	−	0.933120i	$-0.617075\pi$
$379$	−14.0000			−0.719132			−0.359566	+	0.933120i	$0.617075\pi$
$380$	−10.3923	+	6.00000i	−0.533114	+	0.307794i
$381$		0			0
$382$	−3.00000	+	5.19615i	−0.153493	+	0.265858i
$383$	17.3205			0.885037			0.442518	−	0.896759i	$-0.354085\pi$
$383$	17.3205			0.885037			0.442518	+	0.896759i	$0.354085\pi$
$384$		0			0
$385$		0			0
$386$		−	10.0000i		−	0.508987i
$387$		0			0
$388$	6.00000	−	3.46410i	0.304604	−	0.175863i
$389$		−	21.0000i		−	1.06474i	−0.846511	−	0.532371i	$-0.821301\pi$
$389$		−	21.0000i		−	1.06474i	0.846511	−	0.532371i	$-0.178699\pi$
$390$		0			0
$391$	18.0000	−	10.3923i	0.910299	−	0.525561i
$392$	−2.59808	−	6.50000i	−0.131223	−	0.328300i
$393$		0			0
$394$	−1.50000	−	2.59808i	−0.0755689	−	0.130889i
$395$	9.52628	+	16.5000i	0.479319	+	0.830205i
$396$		0			0
$397$	−24.0000	−	13.8564i	−1.20453	−	0.695433i	−0.242967	−	0.970034i	$-0.578121\pi$
$397$	−24.0000	−	13.8564i	−1.20453	−	0.695433i	−0.961558	+	0.274601i	$0.911454\pi$
$398$	−4.33013	+	7.50000i	−0.217050	+	0.375941i
$399$		0			0
$400$	1.00000	+	1.73205i	0.0500000	+	0.0866025i
$401$			6.00000i			0.299626i	0.988714	+	0.149813i	$0.0478671\pi$
$401$			6.00000i			0.299626i	−0.988714	+	0.149813i	$0.952133\pi$
$402$		0			0
$403$		0			0
$404$	−2.59808	+	4.50000i	−0.129259	+	0.223883i
$405$		0			0
$406$	4.50000	+	23.3827i	0.223331	+	1.16046i
$407$		0			0
$408$		0			0
$409$	13.5000	+	7.79423i	0.667532	+	0.385400i	0.795141	−	0.606425i	$-0.207397\pi$
$409$	13.5000	+	7.79423i	0.667532	+	0.385400i	−0.127609	+	0.991825i	$0.540730\pi$
$410$	5.19615	+	3.00000i	0.256620	+	0.148159i
$411$		0			0
$412$	−9.00000	−	5.19615i	−0.443398	−	0.255996i
$413$	−30.3109	−	10.5000i	−1.49150	−	0.516671i
$414$		0			0
$415$	15.0000	−	25.9808i	0.736321	−	1.27535i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.73205	−	3.00000i	−0.0846162	−	0.146560i	0.820611	−	0.571487i	$-0.193633\pi$
$419$	−1.73205	−	3.00000i	−0.0846162	−	0.146560i	−0.905228	+	0.424927i	$0.860300\pi$
$420$		0			0
$421$	−16.0000	+	27.7128i	−0.779792	+	1.35064i	0.152269	+	0.988339i	$0.451342\pi$
$421$	−16.0000	+	27.7128i	−0.779792	+	1.35064i	−0.932061	+	0.362301i	$0.881991\pi$
$422$	13.8564	+	8.00000i	0.674519	+	0.389434i
$423$		0			0
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	3.46410	+	6.00000i	0.168034	+	0.291043i
$426$		0			0
$427$	−6.00000	−	6.92820i	−0.290360	−	0.335279i
$428$	2.59808	−	1.50000i	0.125583	−	0.0725052i
$429$		0			0
$430$		−	13.8564i		−	0.668215i
$431$	−31.1769	+	18.0000i	−1.50174	+	0.867029i	−0.501741	+	0.865018i	$0.667307\pi$
$431$	−31.1769	+	18.0000i	−1.50174	+	0.867029i	−0.999998	+	0.00201168i	$0.999360\pi$
$432$		0			0
$433$			1.73205i			0.0832370i	0.999134	+	0.0416185i	$0.0132514\pi$
$433$			1.73205i			0.0832370i	−0.999134	+	0.0416185i	$0.986749\pi$
$434$	1.73205	+	9.00000i	0.0831411	+	0.432014i
$435$		0			0
$436$	−16.0000			−0.766261
$437$	−20.7846	+	36.0000i	−0.994263	+	1.72211i
$438$		0			0
$439$	27.0000	−	15.5885i	1.28864	−	0.743996i	0.310228	−	0.950662i	$-0.399595\pi$
$439$	27.0000	−	15.5885i	1.28864	−	0.743996i	0.978412	+	0.206666i	$0.0662612\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	−0.673596	−	0.739100i	$-0.735251\pi$
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	0.303281	+	0.952901i	$0.401918\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−15.5885			−0.738135
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$		−	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
$451$		0			0
$452$		−	18.0000i		−	0.846649i
$453$		0			0
$454$	−22.5000	+	12.9904i	−1.05598	+	0.609669i
$455$		0			0
$456$		0			0
$457$	20.5000	+	35.5070i	0.958950	+	1.66095i	0.725059	+	0.688686i	$0.241812\pi$
$457$	20.5000	+	35.5070i	0.958950	+	1.66095i	0.233890	+	0.972263i	$0.424854\pi$
$458$	−1.73205	−	3.00000i	−0.0809334	−	0.140181i
$459$		0			0
$460$	−9.00000	−	5.19615i	−0.419627	−	0.242272i
$461$	−11.2583	+	19.5000i	−0.524353	+	0.908206i	0.475245	+	0.879853i	$0.342359\pi$
$461$	−11.2583	+	19.5000i	−0.524353	+	0.908206i	−0.999598	+	0.0283522i	$0.990974\pi$
$462$		0			0
$463$	−11.5000	−	19.9186i	−0.534450	−	0.925695i	−0.999190	−	0.0402476i	$-0.987185\pi$
$463$	−11.5000	−	19.9186i	−0.534450	−	0.925695i	0.464739	−	0.885448i	$-0.346148\pi$
$464$			9.00000i			0.417815i
$465$		0			0
$466$	−30.0000			−1.38972
$467$	−2.59808	+	4.50000i	−0.120225	+	0.208235i	−0.919856	−	0.392256i	$-0.871695\pi$
$467$	−2.59808	+	4.50000i	−0.120225	+	0.208235i	0.799632	+	0.600491i	$0.205028\pi$
$468$		0			0
$469$	−35.0000	−	12.1244i	−1.61615	−	0.559851i
$470$	−5.19615	−	3.00000i	−0.239681	−	0.138380i
$471$		0			0
$472$	−10.5000	−	6.06218i	−0.483302	−	0.279034i
$473$		0			0
$474$		0			0
$475$	−12.0000	−	6.92820i	−0.550598	−	0.317888i
$476$	−1.73205	−	9.00000i	−0.0793884	−	0.412514i
$477$		0			0
$478$	−12.0000	+	20.7846i	−0.548867	+	0.950666i
$479$	−13.8564			−0.633115			−0.316558	−	0.948573i	$-0.602527\pi$
$479$	−13.8564			−0.633115			−0.316558	+	0.948573i	$0.602527\pi$
$480$		0			0
$481$		0			0
$482$	−0.866025	−	1.50000i	−0.0394464	−	0.0683231i
$483$		0			0
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	−10.3923	−	6.00000i	−0.471890	−	0.272446i
$486$		0			0
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	0.854475	−	0.519493i	$-0.173879\pi$
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	−0.877132	+	0.480250i	$0.840546\pi$
$488$	−1.73205	−	3.00000i	−0.0784063	−	0.135804i
$489$		0			0
$490$	−7.50000	+	9.52628i	−0.338815	+	0.430353i
$491$	−2.59808	+	1.50000i	−0.117250	+	0.0676941i	−0.557478	−	0.830192i	$-0.688231\pi$
$491$	−2.59808	+	1.50000i	−0.117250	+	0.0676941i	0.440228	+	0.897886i	$0.354898\pi$
$492$		0			0
$493$			31.1769i			1.40414i
$494$		0			0
$495$		0			0
$496$			3.46410i			0.155543i
$497$	15.5885	−	3.00000i	0.699238	−	0.134568i
$498$		0			0
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$		0			0
$502$	−7.50000	+	4.33013i	−0.334741	+	0.193263i
$503$	27.7128			1.23565			0.617827	−	0.786314i	$-0.288013\pi$
$503$	27.7128			1.23565			0.617827	+	0.786314i	$0.288013\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$		0			0
$508$	−3.50000	+	6.06218i	−0.155287	+	0.268966i
$509$	−34.6410			−1.53544			−0.767718	−	0.640788i	$-0.778608\pi$
$509$	−34.6410			−1.53544			−0.767718	+	0.640788i	$0.778608\pi$
$510$		0			0
$511$	−21.0000	−	24.2487i	−0.928985	−	1.07270i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	18.0000	−	10.3923i	0.793946	−	0.458385i
$515$			18.0000i			0.793175i
$516$		0			0
$517$		0			0
$518$	10.3923	−	2.00000i	0.456612	−	0.0878750i
$519$		0			0
$520$		0			0
$521$	1.73205	+	3.00000i	0.0758825	+	0.131432i	0.901470	−	0.432842i	$-0.142489\pi$
$521$	1.73205	+	3.00000i	0.0758825	+	0.131432i	−0.825587	+	0.564275i	$0.809156\pi$
$522$		0			0
$523$	18.0000	+	10.3923i	0.787085	+	0.454424i	0.838935	−	0.544231i	$-0.183179\pi$
$523$	18.0000	+	10.3923i	0.787085	+	0.454424i	−0.0518503	+	0.998655i	$0.516512\pi$
$524$	−5.19615	+	9.00000i	−0.226995	+	0.393167i
$525$		0			0
$526$	−9.00000	−	15.5885i	−0.392419	−	0.679689i
$527$			12.0000i			0.522728i
$528$		0			0
$529$	−13.0000			−0.565217
$530$	−2.59808	+	4.50000i	−0.112853	+	0.195468i
$531$		0			0
$532$	12.0000	+	13.8564i	0.520266	+	0.600751i
$533$		0			0
$534$		0			0
$535$	−4.50000	−	2.59808i	−0.194552	−	0.112325i
$536$	−12.1244	−	7.00000i	−0.523692	−	0.302354i
$537$		0			0
$538$	1.50000	+	0.866025i	0.0646696	+	0.0373370i
$539$		0			0
$540$		0			0
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	−12.1244			−0.520786
$543$		0			0
$544$		−	3.46410i		−	0.148522i
$545$	13.8564	+	24.0000i	0.593543	+	1.02805i
$546$		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
$550$		0			0
$551$	−31.1769	−	54.0000i	−1.32818	−	2.30048i
$552$		0			0
$553$	22.0000	−	19.0526i	0.935535	−	0.810197i
$554$	−6.92820	+	4.00000i	−0.294351	+	0.169944i
$555$		0			0
$556$			10.3923i			0.440732i
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	−0.131965	−	0.991254i	$-0.542129\pi$
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	0.792469	+	0.609912i	$0.208795\pi$
$558$		0			0
$559$		0			0
$560$	−3.46410	+	3.00000i	−0.146385	+	0.126773i
$561$		0			0
$562$	−18.0000			−0.759284
$563$	2.59808	−	4.50000i	0.109496	−	0.189652i	−0.806070	−	0.591820i	$-0.798410\pi$
$563$	2.59808	−	4.50000i	0.109496	−	0.189652i	0.915566	+	0.402167i	$0.131743\pi$
$564$		0			0
$565$	−27.0000	+	15.5885i	−1.13590	+	0.655811i
$566$	6.92820			0.291214
$567$		0			0
$568$	6.00000			0.251754
$569$	−36.3731	+	21.0000i	−1.52484	+	0.880366i	−0.525271	+	0.850935i	$0.676036\pi$
$569$	−36.3731	+	21.0000i	−1.52484	+	0.880366i	−0.999567	+	0.0294311i	$0.990630\pi$
$570$		0			0
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	−0.0554391	−	0.998462i	$-0.517656\pi$
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	0.892413	−	0.451219i	$-0.149011\pi$
$572$		0			0
$573$		0			0
$574$	3.00000	−	8.66025i	0.125218	−	0.361472i
$575$		−	12.0000i		−	0.500435i
$576$		0			0
$577$	−13.5000	+	7.79423i	−0.562012	+	0.324478i	−0.753953	−	0.656929i	$-0.771855\pi$
$577$	−13.5000	+	7.79423i	−0.562012	+	0.324478i	0.191940	+	0.981407i	$0.438522\pi$
$578$			5.00000i			0.207973i
$579$		0			0
$580$	13.5000	−	7.79423i	0.560557	−	0.323638i
$581$	−43.3013	−	15.0000i	−1.79644	−	0.622305i
$582$		0			0
$583$		0			0
$584$	−6.06218	−	10.5000i	−0.250855	−	0.434493i
$585$		0			0
$586$	−25.5000	−	14.7224i	−1.05340	−	0.608178i
$587$	−18.1865	+	31.5000i	−0.750639	+	1.30014i	0.196875	+	0.980429i	$0.436921\pi$
$587$	−18.1865	+	31.5000i	−0.750639	+	1.30014i	−0.947514	+	0.319716i	$0.896413\pi$
$588$		0			0
$589$	−12.0000	−	20.7846i	−0.494451	−	0.856415i
$590$			21.0000i			0.864556i
$591$		0			0
$592$	4.00000			0.164399
$593$	12.1244	−	21.0000i	0.497888	−	0.862367i	−0.502109	−	0.864804i	$-0.667443\pi$
$593$	12.1244	−	21.0000i	0.497888	−	0.862367i	0.999997	+	0.00243746i	$0.000775869\pi$
$594$		0			0
$595$	−12.0000	+	10.3923i	−0.491952	+	0.426043i
$596$	−12.9904	−	7.50000i	−0.532107	−	0.307212i
$597$		0			0
$598$		0			0
$599$	20.7846	+	12.0000i	0.849236	+	0.490307i	0.860393	−	0.509631i	$-0.170218\pi$
$599$	20.7846	+	12.0000i	0.849236	+	0.490307i	−0.0111569	+	0.999938i	$0.503551\pi$
$600$		0			0
$601$	1.50000	+	0.866025i	0.0611863	+	0.0353259i	0.530281	−	0.847822i	$-0.322086\pi$
$601$	1.50000	+	0.866025i	0.0611863	+	0.0353259i	−0.469095	+	0.883148i	$0.655420\pi$
$602$	−20.7846	+	4.00000i	−0.847117	+	0.163028i
$603$		0			0
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−19.0526			−0.774597
$606$		0			0
$607$			32.9090i			1.33573i	0.744281	+	0.667867i	$0.232792\pi$
$607$			32.9090i			1.33573i	−0.744281	+	0.667867i	$0.767208\pi$
$608$	3.46410	+	6.00000i	0.140488	+	0.243332i
$609$		0			0
$610$	−3.00000	+	5.19615i	−0.121466	+	0.210386i
$611$		0			0
$612$		0			0
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	0.773869	−	0.633345i	$-0.218319\pi$
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	−0.935428	+	0.353518i	$0.884985\pi$
$614$	3.46410	+	6.00000i	0.139800	+	0.242140i
$615$		0			0
$616$		0			0
$617$	5.19615	−	3.00000i	0.209189	−	0.120775i	−0.391745	−	0.920074i	$-0.628129\pi$
$617$	5.19615	−	3.00000i	0.209189	−	0.120775i	0.600935	+	0.799298i	$0.294795\pi$
$618$		0			0
$619$			20.7846i			0.835404i	0.908584	+	0.417702i	$0.137164\pi$
$619$			20.7846i			0.835404i	−0.908584	+	0.417702i	$0.862836\pi$
$620$	5.19615	−	3.00000i	0.208683	−	0.120483i
$621$		0			0
$622$		−	13.8564i		−	0.555591i
$623$	−25.9808	−	9.00000i	−1.04090	−	0.360577i
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−11.2583	+	19.5000i	−0.449973	+	0.779377i
$627$		0			0
$628$	−9.00000	+	5.19615i	−0.359139	+	0.207349i
$629$	13.8564			0.552491
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	9.52628	−	5.50000i	0.378935	−	0.218778i
$633$		0			0
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$	12.1244			0.481140
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−1.50000	+	0.866025i	−0.0592927	+	0.0342327i
$641$		−	12.0000i		−	0.473972i	−0.971513	−	0.236986i	$-0.923841\pi$
$641$		−	12.0000i		−	0.473972i	0.971513	−	0.236986i	$-0.0761595\pi$
$642$		0			0
$643$	24.0000	−	13.8564i	0.946468	−	0.546443i	0.0544858	−	0.998515i	$-0.482648\pi$
$643$	24.0000	−	13.8564i	0.946468	−	0.546443i	0.891982	+	0.452071i	$0.149315\pi$
$644$	−5.19615	+	15.0000i	−0.204757	+	0.591083i
$645$		0			0
$646$	12.0000	+	20.7846i	0.472134	+	0.817760i
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	0.745622	−	0.666369i	$-0.232153\pi$
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	−0.949904	+	0.312543i	$0.898819\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.00000	+	1.73205i	0.0391630	+	0.0678323i
$653$			15.0000i			0.586995i	0.955960	+	0.293498i	$0.0948193\pi$
$653$			15.0000i			0.586995i	−0.955960	+	0.293498i	$0.905181\pi$
$654$		0			0
$655$	18.0000			0.703318
$656$	1.73205	−	3.00000i	0.0676252	−	0.117130i
$657$		0			0
$658$	−3.00000	+	8.66025i	−0.116952	+	0.337612i
$659$	−23.3827	−	13.5000i	−0.910860	−	0.525885i	−0.0301523	−	0.999545i	$-0.509599\pi$
$659$	−23.3827	−	13.5000i	−0.910860	−	0.525885i	−0.880708	+	0.473660i	$0.842933\pi$
$660$		0			0
$661$	12.0000	+	6.92820i	0.466746	+	0.269476i	0.714877	−	0.699251i	$-0.246483\pi$
$661$	12.0000	+	6.92820i	0.466746	+	0.269476i	−0.248131	+	0.968727i	$0.579816\pi$
$662$	8.66025	+	5.00000i	0.336590	+	0.194331i
$663$		0			0
$664$	−15.0000	−	8.66025i	−0.582113	−	0.336083i
$665$	10.3923	−	30.0000i	0.402996	−	1.16335i
$666$		0			0
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	17.3205			0.670151
$669$		0			0
$670$			24.2487i			0.936809i
$671$		0			0
$672$		0			0
$673$	2.50000	−	4.33013i	0.0963679	−	0.166914i	−0.813811	−	0.581130i	$-0.802611\pi$
$673$	2.50000	−	4.33013i	0.0963679	−	0.166914i	0.910179	+	0.414216i	$0.135944\pi$
$674$	−19.9186	−	11.5000i	−0.767235	−	0.442963i
$675$		0			0
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	12.9904	+	22.5000i	0.499261	+	0.864745i	1.00000		0.000853228i	$-0.000271591\pi$
$677$	12.9904	+	22.5000i	0.499261	+	0.864745i	−0.500739	+	0.865598i	$0.666938\pi$
$678$		0			0
$679$	−6.00000	+	17.3205i	−0.230259	+	0.664700i
$680$	−5.19615	+	3.00000i	−0.199263	+	0.115045i
$681$		0			0
$682$		0			0
$683$	7.79423	−	4.50000i	0.298238	−	0.172188i	−0.343413	−	0.939184i	$-0.611583\pi$
$683$	7.79423	−	4.50000i	0.298238	−	0.172188i	0.641651	+	0.766997i	$0.278250\pi$
$684$		0			0
$685$		0			0
$686$	16.4545	+	8.50000i	0.628235	+	0.324532i
$687$		0			0
$688$	−8.00000			−0.304997
$689$		0			0
$690$		0			0
$691$	24.0000	−	13.8564i	0.913003	−	0.527123i	0.0316069	−	0.999500i	$-0.489938\pi$
$691$	24.0000	−	13.8564i	0.913003	−	0.527123i	0.881396	+	0.472378i	$0.156604\pi$
$692$	−5.19615			−0.197528
$693$		0			0
$694$	33.0000			1.25266
$695$	15.5885	−	9.00000i	0.591304	−	0.341389i
$696$		0			0
$697$	6.00000	−	10.3923i	0.227266	−	0.393637i
$698$	−3.46410			−0.131118
$699$		0			0
$700$	−5.00000	−	1.73205i	−0.188982	−	0.0654654i
$701$			27.0000i			1.01978i	0.860241	+	0.509888i	$0.170313\pi$
$701$			27.0000i			1.01978i	−0.860241	+	0.509888i	$0.829687\pi$
$702$		0			0
$703$	−24.0000	+	13.8564i	−0.905177	+	0.522604i
$704$		0			0
$705$		0			0
$706$	−3.00000	+	1.73205i	−0.112906	+	0.0651866i
$707$	−2.59808	−	13.5000i	−0.0977107	−	0.507720i
$708$		0			0
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	−0.999549	−	0.0300298i	$-0.990440\pi$
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	0.473768	−	0.880650i	$-0.342894\pi$
$710$	−5.19615	−	9.00000i	−0.195008	−	0.337764i
$711$		0			0
$712$	−9.00000	−	5.19615i	−0.337289	−	0.194734i
$713$	10.3923	−	18.0000i	0.389195	−	0.674105i
$714$		0			0
$715$		0			0
$716$		−	15.0000i		−	0.560576i
$717$		0			0
$718$	24.0000			0.895672
$719$	−24.2487	+	42.0000i	−0.904324	+	1.56634i	−0.0825027	+	0.996591i	$0.526291\pi$
$719$	−24.2487	+	42.0000i	−0.904324	+	1.56634i	−0.821822	+	0.569745i	$0.807042\pi$
$720$		0			0
$721$	27.0000	−	5.19615i	1.00553	−	0.193515i
$722$	−25.1147	−	14.5000i	−0.934674	−	0.539634i
$723$		0			0
$724$	15.0000	+	8.66025i	0.557471	+	0.321856i
$725$	15.5885	+	9.00000i	0.578941	+	0.334252i
$726$		0			0
$727$	−10.5000	−	6.06218i	−0.389423	−	0.224834i	0.292487	−	0.956270i	$-0.405517\pi$
$727$	−10.5000	−	6.06218i	−0.389423	−	0.224834i	−0.681910	+	0.731436i	$0.738851\pi$
$728$		0			0
$729$		0			0
$730$	−10.5000	+	18.1865i	−0.388622	+	0.673114i
$731$	−27.7128			−1.02500
$732$		0			0
$733$			6.92820i			0.255899i	0.991781	+	0.127950i	$0.0408395\pi$
$733$			6.92820i			0.255899i	−0.991781	+	0.127950i	$0.959160\pi$
$734$	4.33013	+	7.50000i	0.159828	+	0.276830i
$735$		0			0
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$		0			0
$738$		0			0
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	0.943215	−	0.332184i	$-0.107785\pi$
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	−0.759287	+	0.650756i	$0.774452\pi$
$740$	−3.46410	−	6.00000i	−0.127343	−	0.220564i
$741$		0			0
$742$	7.50000	+	2.59808i	0.275334	+	0.0953784i
$743$	31.1769	−	18.0000i	1.14377	−	0.660356i	0.196409	−	0.980522i	$-0.437072\pi$
$743$	31.1769	−	18.0000i	1.14377	−	0.660356i	0.947361	+	0.320166i	$0.103739\pi$
$744$		0			0
$745$			25.9808i			0.951861i
$746$	−12.1244	+	7.00000i	−0.443904	+	0.256288i
$747$		0			0
$748$		0			0
$749$	−2.59808	+	7.50000i	−0.0949316	+	0.274044i
$750$		0			0
$751$	7.00000			0.255434			0.127717	−	0.991811i	$-0.459235\pi$
$751$	7.00000			0.255434			0.127717	+	0.991811i	$0.459235\pi$
$752$	−1.73205	+	3.00000i	−0.0631614	+	0.109399i
$753$		0			0
$754$		0			0
$755$	13.8564			0.504286
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	12.1244	−	7.00000i	0.440376	−	0.254251i
$759$		0			0
$760$	6.00000	−	10.3923i	0.217643	−	0.376969i
$761$	−34.6410			−1.25574			−0.627868	−	0.778320i	$-0.716072\pi$
$761$	−34.6410			−1.25574			−0.627868	+	0.778320i	$0.716072\pi$
$762$		0			0
$763$	32.0000	−	27.7128i	1.15848	−	1.00327i
$764$		−	6.00000i		−	0.217072i
$765$		0			0
$766$	−15.0000	+	8.66025i	−0.541972	+	0.312908i
$767$		0			0
$768$		0			0
$769$	−42.0000	+	24.2487i	−1.51456	+	0.874431i	−0.514704	+	0.857368i	$0.672098\pi$
$769$	−42.0000	+	24.2487i	−1.51456	+	0.874431i	−0.999854	+	0.0170631i	$0.994568\pi$
$770$		0			0
$771$		0			0
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	−6.92820	−	12.0000i	−0.249190	−	0.431610i	0.714111	−	0.700032i	$-0.246831\pi$
$773$	−6.92820	−	12.0000i	−0.249190	−	0.431610i	−0.963301	+	0.268422i	$0.913498\pi$
$774$		0			0
$775$	6.00000	+	3.46410i	0.215526	+	0.124434i
$776$	−3.46410	+	6.00000i	−0.124354	+	0.215387i
$777$		0			0
$778$	10.5000	+	18.1865i	0.376443	+	0.652019i
$779$			24.0000i			0.859889i
$780$		0			0
$781$		0			0
$782$	−10.3923	+	18.0000i	−0.371628	+	0.643679i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	15.5885	+	9.00000i	0.556376	+	0.321224i
$786$		0			0
$787$	−3.00000	−	1.73205i	−0.106938	−	0.0617409i	0.445577	−	0.895244i	$-0.352999\pi$
$787$	−3.00000	−	1.73205i	−0.106938	−	0.0617409i	−0.552515	+	0.833503i	$0.686332\pi$
$788$	2.59808	+	1.50000i	0.0925526	+	0.0534353i
$789$		0			0
$790$	−16.5000	−	9.52628i	−0.587044	−	0.338930i
$791$	31.1769	+	36.0000i	1.10852	+	1.28001i
$792$		0			0
$793$		0			0
$794$	27.7128			0.983491
$795$		0			0
$796$		−	8.66025i		−	0.306955i
$797$	−20.7846	−	36.0000i	−0.736229	−	1.27519i	−0.954182	−	0.299226i	$-0.903271\pi$
$797$	−20.7846	−	36.0000i	−0.736229	−	1.27519i	0.217954	−	0.975959i	$-0.430062\pi$
$798$		0			0
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$	−1.73205	−	1.00000i	−0.0612372	−	0.0353553i
$801$		0			0
$802$	−3.00000	−	5.19615i	−0.105934	−	0.183483i
$803$		0			0
$804$		0			0
$805$	27.0000	−	5.19615i	0.951625	−	0.183140i
$806$		0			0
$807$		0			0
$808$		−	5.19615i		−	0.182800i
$809$	−20.7846	+	12.0000i	−0.730748	+	0.421898i	−0.818696	−	0.574228i	$-0.805302\pi$
$809$	−20.7846	+	12.0000i	−0.730748	+	0.421898i	0.0879478	+	0.996125i	$0.471969\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−15.5885	−	18.0000i	−0.547048	−	0.631676i
$813$		0			0
$814$		0			0
$815$	1.73205	−	3.00000i	0.0606711	−	0.105085i
$816$		0			0
$817$	48.0000	−	27.7128i	1.67931	−	0.969549i
$818$	−15.5885			−0.545038
$819$		0			0
$820$	−6.00000			−0.209529
$821$	7.79423	−	4.50000i	0.272020	−	0.157051i	−0.357785	−	0.933804i	$-0.616468\pi$
$821$	7.79423	−	4.50000i	0.272020	−	0.157051i	0.629805	+	0.776753i	$0.283135\pi$
$822$		0			0
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	0.819159	+	0.573567i	$0.194441\pi$
$824$	10.3923			0.362033
$825$		0			0
$826$	31.5000	−	6.06218i	1.09603	−	0.210930i
$827$		−	3.00000i		−	0.104320i	−0.998639	−	0.0521601i	$-0.983389\pi$
$827$		−	3.00000i		−	0.104320i	0.998639	−	0.0521601i	$-0.0166106\pi$
$828$		0			0
$829$	−30.0000	+	17.3205i	−1.04194	+	0.601566i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−30.0000	+	17.3205i	−1.04194	+	0.601566i	−0.121560	+	0.992584i	$0.538790\pi$
$830$			30.0000i			1.04132i
$831$		0			0
$832$		0			0
$833$	19.0526	+	15.0000i	0.660132	+	0.519719i
$834$		0			0
$835$	−15.0000	−	25.9808i	−0.519096	−	0.899101i
$836$		0			0
$837$		0			0
$838$	3.00000	+	1.73205i	0.103633	+	0.0598327i
$839$	3.46410	−	6.00000i	0.119594	−	0.207143i	−0.800013	−	0.599983i	$-0.795174\pi$
$839$	3.46410	−	6.00000i	0.119594	−	0.207143i	0.919607	+	0.392840i	$0.128507\pi$
$840$		0			0
$841$	26.0000	+	45.0333i	0.896552	+	1.55287i
$842$		−	32.0000i		−	1.10279i
$843$		0			0
$844$	−16.0000			−0.550743
$845$	11.2583	−	19.5000i	0.387298	−	0.670820i
$846$		0			0
$847$	5.50000	+	28.5788i	0.188982	+	0.981981i
$848$	2.59808	+	1.50000i	0.0892183	+	0.0515102i
$849$		0			0
$850$	−6.00000	−	3.46410i	−0.205798	−	0.118818i
$851$	−20.7846	−	12.0000i	−0.712487	−	0.411355i
$852$		0			0
$853$	−6.00000	−	3.46410i	−0.205436	−	0.118609i	0.393753	−	0.919216i	$-0.371177\pi$
$853$	−6.00000	−	3.46410i	−0.205436	−	0.118609i	−0.599189	+	0.800608i	$0.704510\pi$
$854$	8.66025	+	3.00000i	0.296348	+	0.102658i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−6.92820			−0.236663			−0.118331	−	0.992974i	$-0.537755\pi$
$857$	−6.92820			−0.236663			−0.118331	+	0.992974i	$0.537755\pi$
$858$		0			0
$859$			24.2487i			0.827355i	0.910423	+	0.413678i	$0.135756\pi$
$859$			24.2487i			0.827355i	−0.910423	+	0.413678i	$0.864244\pi$
$860$	6.92820	+	12.0000i	0.236250	+	0.409197i
$861$		0			0
$862$	18.0000	−	31.1769i	0.613082	−	1.06189i
$863$	−15.5885	−	9.00000i	−0.530637	−	0.306364i	0.210639	−	0.977564i	$-0.432446\pi$
$863$	−15.5885	−	9.00000i	−0.530637	−	0.306364i	−0.741276	+	0.671200i	$0.765779\pi$
$864$		0			0
$865$	4.50000	+	7.79423i	0.153005	+	0.265012i
$866$	−0.866025	−	1.50000i	−0.0294287	−	0.0509721i
$867$		0			0
$868$	−6.00000	−	6.92820i	−0.203653	−	0.235159i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	13.8564	−	8.00000i	0.469237	−	0.270914i
$873$		0			0
$874$		−	41.5692i		−	1.40610i
$875$	6.06218	+	31.5000i	0.204939	+	1.06489i
$876$		0			0
$877$	−22.0000			−0.742887			−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000			−0.742887			−0.371444	+	0.928456i	$0.621137\pi$
$878$	−15.5885	+	27.0000i	−0.526085	+	0.911206i
$879$		0			0
$880$		0			0
$881$	−31.1769			−1.05038			−0.525188	−	0.850986i	$-0.676005\pi$
$881$	−31.1769			−1.05038			−0.525188	+	0.850986i	$0.676005\pi$
$882$		0			0
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$		0			0
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	−17.3205			−0.581566			−0.290783	−	0.956789i	$-0.593916\pi$
$887$	−17.3205			−0.581566			−0.290783	+	0.956789i	$0.593916\pi$
$888$		0			0
$889$	−3.50000	−	18.1865i	−0.117386	−	0.609957i
$890$			18.0000i			0.603361i
$891$		0			0
$892$	13.5000	−	7.79423i	0.452013	−	0.260970i
$893$		−	24.0000i		−	0.803129i
$894$		0			0
$895$	−22.5000	+	12.9904i	−0.752092	+	0.434221i
$896$	1.73205	+	2.00000i	0.0578638	+	0.0668153i
$897$		0			0
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	15.5885	+	27.0000i	0.519904	+	0.900500i
$900$		0			0
$901$	9.00000	+	5.19615i	0.299833	+	0.173109i
$902$		0			0
$903$		0			0
$904$	9.00000	+	15.5885i	0.299336	+	0.518464i
$905$		−	30.0000i		−	0.997234i
$906$		0			0
$907$	16.0000			0.531271			0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000			0.531271			0.265636	+	0.964073i	$0.414418\pi$
$908$	12.9904	−	22.5000i	0.431101	−	0.746689i
$909$		0			0
$910$		0			0
$911$	25.9808	+	15.0000i	0.860781	+	0.496972i	0.864274	−	0.503022i	$-0.167778\pi$
$911$	25.9808	+	15.0000i	0.860781	+	0.496972i	−0.00349271	+	0.999994i	$0.501112\pi$
$912$		0			0
$913$		0			0
$914$	−35.5070	−	20.5000i	−1.17447	−	0.678080i
$915$		0			0
$916$	3.00000	+	1.73205i	0.0991228	+	0.0572286i
$917$	−5.19615	−	27.0000i	−0.171592	−	0.891619i
$918$		0			0
$919$	−3.50000	+	6.06218i	−0.115454	+	0.199973i	−0.917961	−	0.396670i	$-0.870166\pi$
$919$	−3.50000	+	6.06218i	−0.115454	+	0.199973i	0.802507	+	0.596643i	$0.203499\pi$
$920$	10.3923			0.342624
$921$		0			0
$922$		−	22.5167i		−	0.741547i
$923$		0			0
$924$		0			0
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$	19.9186	+	11.5000i	0.654565	+	0.377913i
$927$		0			0
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	19.0526	+	33.0000i	0.625094	+	1.08269i	0.988523	+	0.151073i	$0.0482728\pi$
$929$	19.0526	+	33.0000i	0.625094	+	1.08269i	−0.363428	+	0.931622i	$0.618394\pi$
$930$		0			0
$931$	−48.0000	−	6.92820i	−1.57314	−	0.227063i
$932$	25.9808	−	15.0000i	0.851028	−	0.491341i
$933$		0			0
$934$		−	5.19615i		−	0.170023i
$935$		0			0
$936$		0			0
$937$			57.1577i			1.86726i	0.358239	+	0.933630i	$0.383377\pi$
$937$			57.1577i			1.86726i	−0.358239	+	0.933630i	$0.616623\pi$
$938$	36.3731	−	7.00000i	1.18762	−	0.228558i
$939$		0			0
$940$	6.00000			0.195698
$941$	27.7128	−	48.0000i	0.903412	−	1.56476i	0.0803769	−	0.996765i	$-0.474388\pi$
$941$	27.7128	−	48.0000i	0.903412	−	1.56476i	0.823035	−	0.567991i	$-0.192279\pi$
$942$		0			0
$943$	−18.0000	+	10.3923i	−0.586161	+	0.338420i
$944$	12.1244			0.394614
$945$		0			0
$946$		0			0
$947$	23.3827	−	13.5000i	0.759835	−	0.438691i	−0.0694014	−	0.997589i	$-0.522109\pi$
$947$	23.3827	−	13.5000i	0.759835	−	0.438691i	0.829237	+	0.558898i	$0.188776\pi$
$948$		0			0
$949$		0			0
$950$	13.8564			0.449561
$951$		0			0
$952$	6.00000	+	6.92820i	0.194461	+	0.224544i
$953$		−	12.0000i		−	0.388718i	−0.980930	−	0.194359i	$-0.937737\pi$
$953$		−	12.0000i		−	0.388718i	0.980930	−	0.194359i	$-0.0622627\pi$
$954$		0			0
$955$	−9.00000	+	5.19615i	−0.291233	+	0.168144i
$956$		−	24.0000i		−	0.776215i
$957$		0			0
$958$	12.0000	−	6.92820i	0.387702	−	0.223840i
$959$		0			0
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$		0			0
$963$		0			0
$964$	1.50000	+	0.866025i	0.0483117	+	0.0278928i
$965$	8.66025	−	15.0000i	0.278783	−	0.482867i
$966$		0			0
$967$	−11.5000	−	19.9186i	−0.369815	−	0.640538i	0.619721	−	0.784822i	$-0.287246\pi$
$967$	−11.5000	−	19.9186i	−0.369815	−	0.640538i	−0.989536	+	0.144283i	$0.953912\pi$
$968$			11.0000i			0.353553i
$969$		0			0
$970$	12.0000			0.385297
$971$	−0.866025	+	1.50000i	−0.0277921	+	0.0481373i	−0.879587	−	0.475738i	$-0.842181\pi$
$971$	−0.866025	+	1.50000i	−0.0277921	+	0.0481373i	0.851795	+	0.523876i	$0.175514\pi$
$972$		0			0
$973$	−18.0000	−	20.7846i	−0.577054	−	0.666324i
$974$	0.866025	+	0.500000i	0.0277492	+	0.0160210i
$975$		0			0
$976$	3.00000	+	1.73205i	0.0960277	+	0.0554416i
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	0.656941	−	0.753942i	$-0.271850\pi$
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	−0.324462	+	0.945899i	$0.605183\pi$
$978$		0			0
$979$		0			0
$980$	1.73205	−	12.0000i	0.0553283	−	0.383326i
$981$		0			0
$982$	1.50000	−	2.59808i	0.0478669	−	0.0829079i
$983$	27.7128			0.883901			0.441951	−	0.897039i	$-0.354287\pi$
$983$	27.7128			0.883901			0.441951	+	0.897039i	$0.354287\pi$
$984$		0			0
$985$		−	5.19615i		−	0.165563i
$986$	−15.5885	−	27.0000i	−0.496438	−	0.859855i
$987$		0			0
$988$		0			0
$989$	41.5692	+	24.0000i	1.32182	+	0.763156i
$990$		0			0
$991$	2.50000	+	4.33013i	0.0794151	+	0.137551i	0.902998	−	0.429645i	$-0.141361\pi$
$991$	2.50000	+	4.33013i	0.0794151	+	0.137551i	−0.823583	+	0.567196i	$0.808028\pi$
$992$	−1.73205	−	3.00000i	−0.0549927	−	0.0952501i
$993$		0			0
$994$	−12.0000	+	10.3923i	−0.380617	+	0.329624i
$995$	−12.9904	+	7.50000i	−0.411823	+	0.237766i
$996$		0			0
$997$			48.4974i			1.53593i	0.640493	+	0.767964i	$0.278730\pi$
$997$			48.4974i			1.53593i	−0.640493	+	0.767964i	$0.721270\pi$
$998$	12.1244	−	7.00000i	0.383790	−	0.221581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.t.c.593.1		4
3.2	odd	2	inner	1134.2.t.c.593.2		4
7.3	odd	6		1134.2.l.b.269.1		4
9.2	odd	6		378.2.k.c.215.1	✓	4
9.4	even	3		1134.2.l.b.215.1		4
9.5	odd	6		1134.2.l.b.215.2		4
9.7	even	3		378.2.k.c.215.2	yes	4
21.17	even	6		1134.2.l.b.269.2		4
63.2	odd	6		2646.2.d.a.2645.4		4
63.16	even	3		2646.2.d.a.2645.1		4
63.31	odd	6	inner	1134.2.t.c.1025.2		4
63.38	even	6		378.2.k.c.269.2	yes	4
63.47	even	6		2646.2.d.a.2645.3		4
63.52	odd	6		378.2.k.c.269.1	yes	4
63.59	even	6	inner	1134.2.t.c.1025.1		4
63.61	odd	6		2646.2.d.a.2645.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.c.215.1	✓	4	9.2	odd	6
378.2.k.c.215.2	yes	4	9.7	even	3
378.2.k.c.269.1	yes	4	63.52	odd	6
378.2.k.c.269.2	yes	4	63.38	even	6
1134.2.l.b.215.1		4	9.4	even	3
1134.2.l.b.215.2		4	9.5	odd	6
1134.2.l.b.269.1		4	7.3	odd	6
1134.2.l.b.269.2		4	21.17	even	6
1134.2.t.c.593.1		4	1.1	even	1	trivial
1134.2.t.c.593.2		4	3.2	odd	2	inner
1134.2.t.c.1025.1		4	63.59	even	6	inner
1134.2.t.c.1025.2		4	63.31	odd	6	inner
2646.2.d.a.2645.1		4	63.16	even	3
2646.2.d.a.2645.2		4	63.61	odd	6
2646.2.d.a.2645.3		4	63.47	even	6
2646.2.d.a.2645.4		4	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(1.50000 - 0.866025i) q^{10} +(-1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 3.00000i) q^{17} +(6.00000 + 3.46410i) q^{19} +(-0.866025 + 1.50000i) q^{20} +6.00000i q^{23} -2.00000 q^{25} +(2.50000 + 0.866025i) q^{28} +(-7.79423 - 4.50000i) q^{29} +(-3.00000 - 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.00000 + 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-2.00000 + 3.46410i) q^{37} -6.92820 q^{38} -1.73205i q^{40} +(1.73205 + 3.00000i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{46} +(-1.73205 - 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} +(-2.59808 + 1.50000i) q^{53} +(-2.59808 + 0.500000i) q^{56} +9.00000 q^{58} +(-6.06218 + 10.5000i) q^{59} +(-3.00000 + 1.73205i) q^{61} +3.46410 q^{62} -1.00000 q^{64} +(-7.00000 + 12.1244i) q^{67} -3.46410 q^{68} +(3.00000 + 3.46410i) q^{70} -6.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} -4.00000i q^{74} +(6.00000 - 3.46410i) q^{76} +(-5.50000 - 9.52628i) q^{79} +(0.866025 + 1.50000i) q^{80} +(-3.00000 - 1.73205i) q^{82} +(-8.66025 + 15.0000i) q^{83} +(3.00000 + 5.19615i) q^{85} +8.00000i q^{86} +(-5.19615 + 9.00000i) q^{89} +(5.19615 + 3.00000i) q^{92} +(3.00000 + 1.73205i) q^{94} +(-10.3923 - 6.00000i) q^{95} +(6.00000 + 3.46410i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^7	\( 4 q + 2 q^{4} + 2 q^{7} + 6 q^{10} - 2 q^{16} + 24 q^{19} - 8 q^{25} + 10 q^{28} - 12 q^{31} + 12 q^{34} - 8 q^{37} + 16 q^{43} - 12 q^{46} - 26 q^{49} + 36 q^{58} - 12 q^{61} - 4 q^{64} - 28 q^{67} + 12 q^{70} - 42 q^{73} + 24 q^{76} - 22 q^{79} - 12 q^{82} + 12 q^{85} + 12 q^{94} + 24 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^7 + 6 * q^10 - 2 * q^16 + 24 * q^19 - 8 * q^25 + 10 * q^28 - 12 * q^31 + 12 * q^34 - 8 * q^37 + 16 * q^43 - 12 * q^46 - 26 * q^49 + 36 * q^58 - 12 * q^61 - 4 * q^64 - 28 * q^67 + 12 * q^70 - 42 * q^73 + 24 * q^76 - 22 * q^79 - 12 * q^82 + 12 * q^85 + 12 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

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Database

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