LMFDB - Embedded newform 1134.2.l.b.215.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(215,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1134.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.l (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.215
Dual form			1134.2.l.b.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 0.866025i) q^{10} +(-0.866025 + 2.50000i) q^{14} +1.00000 q^{16} +(-1.73205 - 3.00000i) q^{17} +(6.00000 + 3.46410i) q^{19} +(-0.866025 - 1.50000i) q^{20} +(5.19615 - 3.00000i) q^{23} +(1.00000 - 1.73205i) q^{25} +(2.50000 + 0.866025i) q^{28} +(7.79423 - 4.50000i) q^{29} +3.46410i q^{31} -1.00000i q^{32} +(-3.00000 + 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(3.46410 - 6.00000i) q^{38} +(-1.50000 + 0.866025i) q^{40} +(1.73205 - 3.00000i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{46} +3.46410 q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.73205 - 1.00000i) q^{50} +(-2.59808 + 1.50000i) q^{53} +(0.866025 - 2.50000i) q^{56} +(-4.50000 - 7.79423i) q^{58} +12.1244 q^{59} -3.46410i q^{61} +3.46410 q^{62} -1.00000 q^{64} +14.0000 q^{67} +(1.73205 + 3.00000i) q^{68} +(-4.50000 + 0.866025i) q^{70} -6.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} +(3.46410 + 2.00000i) q^{74} +(-6.00000 - 3.46410i) q^{76} +11.0000 q^{79} +(0.866025 + 1.50000i) q^{80} +(-3.00000 - 1.73205i) q^{82} +(-8.66025 - 15.0000i) q^{83} +(3.00000 - 5.19615i) q^{85} +(6.92820 - 4.00000i) q^{86} +(-5.19615 + 9.00000i) q^{89} +(-5.19615 + 3.00000i) q^{92} -3.46410i q^{94} +12.0000i q^{95} +(-6.00000 + 3.46410i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 10 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 - 10 * q^7	$ 4 q - 4 q^{4} - 10 q^{7} + 6 q^{10} + 4 q^{16} + 24 q^{19} + 4 q^{25} + 10 q^{28} - 12 q^{34} - 8 q^{37} - 6 q^{40} + 16 q^{43} - 12 q^{46} + 22 q^{49} - 18 q^{58} - 4 q^{64} + 56 q^{67} - 18 q^{70} - 42 q^{73} - 24 q^{76} + 44 q^{79} - 12 q^{82} + 12 q^{85} - 24 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 - 10 * q^7 + 6 * q^10 + 4 * q^16 + 24 * q^19 + 4 * q^25 + 10 * q^28 - 12 * q^34 - 8 * q^37 - 6 * q^40 + 16 * q^43 - 12 * q^46 + 22 * q^49 - 18 * q^58 - 4 * q^64 + 56 * q^67 - 18 * q^70 - 42 * q^73 - 24 * q^76 + 44 * q^79 - 12 * q^82 + 12 * q^85 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.50000	−	0.866025i	0.474342	−	0.273861i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$	−0.866025	+	2.50000i	−0.231455	+	0.668153i
$15$		0			0
$16$	1.00000			0.250000
$17$	−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
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$		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	$-0.351770\pi$
$29$	7.79423	−	4.50000i	1.44735	−	0.835629i	0.998323	+	0.0578882i	$0.0184367\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$		−	1.00000i		−	0.176777i
$33$		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	$0.273310\pi$
$38$	3.46410	−	6.00000i	0.561951	−	0.973329i
$39$		0			0
$40$	−1.50000	+	0.866025i	−0.237171	+	0.136931i
$41$	1.73205	−	3.00000i	0.270501	−	0.468521i	−0.698489	−	0.715621i	$-0.746144\pi$
$41$	1.73205	−	3.00000i	0.270501	−	0.468521i	0.968990	+	0.247099i	$0.0794774\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−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
$56$	0.866025	−	2.50000i	0.115728	−	0.334077i
$57$		0			0
$58$	−4.50000	−	7.79423i	−0.590879	−	1.02343i
$59$	12.1244			1.57846			0.789228	−	0.614100i	$-0.210481\pi$
$59$	12.1244			1.57846			0.789228	+	0.614100i	$0.210481\pi$
$60$		0			0
$61$		−	3.46410i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$61$		−	3.46410i		−	0.443533i	0.975100	−	0.221766i	$-0.0711822\pi$
$62$	3.46410			0.439941
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	14.0000			1.71037			0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000			1.71037			0.855186	+	0.518321i	$0.173443\pi$
$68$	1.73205	+	3.00000i	0.210042	+	0.363803i
$69$		0			0
$70$	−4.50000	+	0.866025i	−0.537853	+	0.103510i
$71$		−	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	$0.584423\pi$
$74$	3.46410	+	2.00000i	0.402694	+	0.232495i
$75$		0			0
$76$	−6.00000	−	3.46410i	−0.688247	−	0.397360i
$77$		0			0
$78$		0			0
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$	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	−0.744160	−	0.668002i	$-0.767150\pi$
$83$	−8.66025	−	15.0000i	−0.950586	−	1.64646i	−0.206427	−	0.978462i	$-0.566184\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	6.92820	−	4.00000i	0.747087	−	0.431331i
$87$		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
$94$		−	3.46410i		−	0.357295i
$95$			12.0000i			1.23117i
$96$		0			0
$97$	−6.00000	+	3.46410i	−0.609208	+	0.351726i	−0.772655	−	0.634826i	$-0.781072\pi$
$97$	−6.00000	+	3.46410i	−0.609208	+	0.351726i	0.163448	+	0.986552i	$0.447739\pi$
$98$	4.33013	−	5.50000i	0.437409	−	0.555584i
$99$		0			0
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	2.59808	−	4.50000i	0.258518	−	0.447767i	−0.707327	−	0.706887i	$-0.750099\pi$
$101$	2.59808	−	4.50000i	0.258518	−	0.447767i	0.965845	+	0.259120i	$0.0834325\pi$
$102$		0			0
$103$	−9.00000	+	5.19615i	−0.886796	+	0.511992i	−0.872893	−	0.487911i	$-0.837759\pi$
$103$	−9.00000	+	5.19615i	−0.886796	+	0.511992i	−0.0139031	+	0.999903i	$0.504426\pi$
$104$		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
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	−15.5885	−	9.00000i	−1.46644	−	0.846649i	−0.467143	−	0.884182i	$-0.654717\pi$
$113$	−15.5885	−	9.00000i	−1.46644	−	0.846649i	−0.999295	+	0.0375328i	$0.988050\pi$
$114$		0			0
$115$	9.00000	+	5.19615i	0.839254	+	0.484544i
$116$	−7.79423	+	4.50000i	−0.723676	+	0.417815i
$117$		0			0
$118$		−	12.1244i		−	1.11614i
$119$	1.73205	+	9.00000i	0.158777	+	0.825029i
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	−3.46410			−0.313625
$123$		0			0
$124$		−	3.46410i		−	0.311086i
$125$	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	$0.600522\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$		0			0
$131$	5.19615	+	9.00000i	0.453990	+	0.786334i	0.998630	−	0.0523366i	$-0.0166669\pi$
$131$	5.19615	+	9.00000i	0.453990	+	0.786334i	−0.544640	+	0.838670i	$0.683334\pi$
$132$		0			0
$133$	−12.0000	−	13.8564i	−1.04053	−	1.20150i
$134$		−	14.0000i		−	1.20942i
$135$		0			0
$136$	3.00000	−	1.73205i	0.257248	−	0.148522i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	9.00000	+	5.19615i	0.763370	+	0.440732i	0.830504	−	0.557012i	$-0.188052\pi$
$139$	9.00000	+	5.19615i	0.763370	+	0.440732i	−0.0671344	+	0.997744i	$0.521386\pi$
$140$	0.866025	+	4.50000i	0.0731925	+	0.380319i
$141$		0			0
$142$	−6.00000			−0.503509
$143$		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
$149$	−12.9904	+	7.50000i	−1.06421	+	0.614424i	−0.926595	−	0.376061i	$-0.877278\pi$
$149$	−12.9904	+	7.50000i	−1.06421	+	0.614424i	−0.137619	+	0.990485i	$0.543945\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	−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
$157$			10.3923i			0.829396i	0.909959	+	0.414698i	$0.136113\pi$
$157$			10.3923i			0.829396i	−0.909959	+	0.414698i	$0.863887\pi$
$158$		−	11.0000i		−	0.875113i
$159$		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	$0.191624\pi$
$164$	−1.73205	+	3.00000i	−0.135250	+	0.234261i
$165$		0			0
$166$	−15.0000	+	8.66025i	−1.16423	+	0.672166i
$167$	8.66025	−	15.0000i	0.670151	−	1.16073i	−0.307711	−	0.951480i	$-0.599563\pi$
$167$	8.66025	−	15.0000i	0.670151	−	1.16073i	0.977861	−	0.209255i	$-0.0671038\pi$
$168$		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
$173$	5.19615			0.395056			0.197528	−	0.980297i	$-0.436709\pi$
$173$	5.19615			0.395056			0.197528	+	0.980297i	$0.436709\pi$
$174$		0			0
$175$	−4.00000	+	3.46410i	−0.302372	+	0.261861i
$176$		0			0
$177$		0			0
$178$	9.00000	+	5.19615i	0.674579	+	0.389468i
$179$	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
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−6.92820			−0.509372
$186$		0			0
$187$		0			0
$188$	−3.46410			−0.252646
$189$		0			0
$190$	12.0000			0.870572
$191$			6.00000i			0.434145i	0.976156	+	0.217072i	$0.0696508\pi$
$191$			6.00000i			0.434145i	−0.976156	+	0.217072i	$0.930349\pi$
$192$		0			0
$193$	10.0000			0.719816			0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000			0.719816			0.359908	+	0.932988i	$0.382808\pi$
$194$	3.46410	+	6.00000i	0.248708	+	0.430775i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$			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	$0.234023\pi$
$200$	1.73205	+	1.00000i	0.122474	+	0.0707107i
$201$		0			0
$202$	−4.50000	−	2.59808i	−0.316619	−	0.182800i
$203$	−23.3827	+	4.50000i	−1.64114	+	0.315838i
$204$		0			0
$205$	6.00000			0.419058
$206$	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	0.447478	+	0.894295i	$0.352322\pi$
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	2.59808	−	1.50000i	0.178437	−	0.103020i
$213$		0			0
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$	−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	$-0.841458\pi$
$223$	−13.5000	+	7.79423i	−0.904027	+	0.521940i	−0.0255224	+	0.999674i	$0.508125\pi$
$224$	−0.866025	+	2.50000i	−0.0578638	+	0.167038i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	−12.9904	+	22.5000i	−0.862202	+	1.49338i	0.00759708	+	0.999971i	$0.497582\pi$
$227$	−12.9904	+	22.5000i	−0.862202	+	1.49338i	−0.869799	+	0.493406i	$0.835752\pi$
$228$		0			0
$229$	3.00000	−	1.73205i	0.198246	−	0.114457i	−0.397591	−	0.917563i	$-0.630154\pi$
$229$	3.00000	−	1.73205i	0.198246	−	0.114457i	0.595837	+	0.803105i	$0.296820\pi$
$230$	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
$236$	−12.1244			−0.789228
$237$		0			0
$238$	9.00000	−	1.73205i	0.583383	−	0.112272i
$239$	−20.7846	−	12.0000i	−1.34444	−	0.776215i	−0.356988	−	0.934109i	$-0.616196\pi$
$239$	−20.7846	−	12.0000i	−1.34444	−	0.776215i	−0.987456	+	0.157893i	$0.949530\pi$
$240$		0			0
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−9.52628	+	5.50000i	−0.612372	+	0.353553i
$243$		0			0
$244$			3.46410i			0.221766i
$245$	−1.73205	+	12.0000i	−0.110657	+	0.766652i
$246$		0			0
$247$		0			0
$248$	−3.46410			−0.219971
$249$		0			0
$250$		−	12.1244i		−	0.766812i
$251$	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
$254$			7.00000i			0.439219i
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.3923	+	18.0000i	0.648254	+	1.12281i	0.983540	+	0.180693i	$0.0578339\pi$
$257$	10.3923	+	18.0000i	0.648254	+	1.12281i	−0.335285	+	0.942117i	$0.608833\pi$
$258$		0			0
$259$	8.00000	−	6.92820i	0.497096	−	0.430498i
$260$		0			0
$261$		0			0
$262$	9.00000	−	5.19615i	0.556022	−	0.321019i
$263$	−15.5885	−	9.00000i	−0.961225	−	0.554964i	−0.0646755	−	0.997906i	$-0.520601\pi$
$263$	−15.5885	−	9.00000i	−0.961225	−	0.554964i	−0.896550	+	0.442943i	$0.853935\pi$
$264$		0			0
$265$	−4.50000	−	2.59808i	−0.276433	−	0.159599i
$266$	−13.8564	+	12.0000i	−0.849591	+	0.735767i
$267$		0			0
$268$	−14.0000			−0.855186
$269$	−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
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	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	$-0.847070\pi$
$281$	−15.5885	+	9.00000i	−0.929929	+	0.536895i	−0.0431402	+	0.999069i	$0.513736\pi$
$282$		0			0
$283$			6.92820i			0.411839i	0.978569	+	0.205919i	$0.0660185\pi$
$283$			6.92820i			0.411839i	−0.978569	+	0.205919i	$0.933982\pi$
$284$			6.00000i			0.356034i
$285$		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
$290$	7.79423	−	13.5000i	0.457693	−	0.792747i
$291$		0			0
$292$	10.5000	−	6.06218i	0.614466	−	0.354762i
$293$	14.7224	−	25.5000i	0.860094	−	1.48973i	−0.0117441	−	0.999931i	$-0.503738\pi$
$293$	14.7224	−	25.5000i	0.860094	−	1.48973i	0.871838	−	0.489795i	$-0.162928\pi$
$294$		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
$301$	−4.00000	−	20.7846i	−0.230556	−	1.19800i
$302$	−6.92820	−	4.00000i	−0.398673	−	0.230174i
$303$		0			0
$304$	6.00000	+	3.46410i	0.344124	+	0.198680i
$305$	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
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$	13.8564			0.785725			0.392862	−	0.919597i	$-0.371485\pi$
$311$	13.8564			0.785725			0.392862	+	0.919597i	$0.371485\pi$
$312$		0			0
$313$			22.5167i			1.27272i	0.771393	+	0.636358i	$0.219560\pi$
$313$			22.5167i			1.27272i	−0.771393	+	0.636358i	$0.780440\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	−11.0000			−0.618798
$317$		−	6.00000i		−	0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$		−	6.00000i		−	0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$		0			0
$319$		0			0
$320$	−0.866025	−	1.50000i	−0.0484123	−	0.0838525i
$321$		0			0
$322$	3.00000	+	15.5885i	0.167183	+	0.868711i
$323$		−	24.0000i		−	1.33540i
$324$		0			0
$325$		0			0
$326$	1.73205	+	1.00000i	0.0959294	+	0.0553849i
$327$		0			0
$328$	3.00000	+	1.73205i	0.165647	+	0.0956365i
$329$	−8.66025	−	3.00000i	−0.477455	−	0.165395i
$330$		0			0
$331$	10.0000			0.549650			0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000			0.549650			0.274825	+	0.961494i	$0.411380\pi$
$332$	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	−0.361815	−	0.932250i	$-0.617843\pi$
$337$	11.5000	−	19.9186i	0.626445	−	1.08503i	0.988260	−	0.152784i	$-0.0488240\pi$
$338$	−11.2583	+	6.50000i	−0.612372	+	0.353553i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$		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
$346$		−	5.19615i		−	0.279347i
$347$			33.0000i			1.77153i	0.464131	+	0.885766i	$0.346367\pi$
$347$			33.0000i			1.77153i	−0.464131	+	0.885766i	$0.653633\pi$
$348$		0			0
$349$	−3.00000	+	1.73205i	−0.160586	+	0.0927146i	−0.578140	−	0.815938i	$-0.696221\pi$
$349$	−3.00000	+	1.73205i	−0.160586	+	0.0927146i	0.417553	+	0.908652i	$0.362888\pi$
$350$	3.46410	+	4.00000i	0.185164	+	0.213809i
$351$		0			0
$352$		0			0
$353$	−1.73205	+	3.00000i	−0.0921878	+	0.159674i	−0.908431	−	0.418034i	$-0.862719\pi$
$353$	−1.73205	+	3.00000i	−0.0921878	+	0.159674i	0.816244	+	0.577708i	$0.196053\pi$
$354$		0			0
$355$	9.00000	−	5.19615i	0.477670	−	0.275783i
$356$	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
$362$	17.3205			0.910346
$363$		0			0
$364$		0			0
$365$	−18.1865	−	10.5000i	−0.951927	−	0.549595i
$366$		0			0
$367$	7.50000	+	4.33013i	0.391497	+	0.226031i	0.682808	−	0.730597i	$-0.260758\pi$
$367$	7.50000	+	4.33013i	0.391497	+	0.226031i	−0.291312	+	0.956628i	$0.594092\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$		0			0
$370$			6.92820i			0.360180i
$371$	7.79423	−	1.50000i	0.404656	−	0.0778761i
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$		0			0
$376$			3.46410i			0.178647i
$377$		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	$0.617075\pi$
$380$		−	12.0000i		−	0.615587i
$381$		0			0
$382$	6.00000			0.306987
$383$	−8.66025	−	15.0000i	−0.442518	−	0.766464i	0.555357	−	0.831612i	$-0.312581\pi$
$383$	−8.66025	−	15.0000i	−0.442518	−	0.766464i	−0.997876	+	0.0651476i	$0.979248\pi$
$384$		0			0
$385$		0			0
$386$		−	10.0000i		−	0.508987i
$387$		0			0
$388$	6.00000	−	3.46410i	0.304604	−	0.175863i
$389$	18.1865	+	10.5000i	0.922094	+	0.532371i	0.884302	−	0.466915i	$-0.154634\pi$
$389$	18.1865	+	10.5000i	0.922094	+	0.532371i	0.0377914	+	0.999286i	$0.487968\pi$
$390$		0			0
$391$	−18.0000	−	10.3923i	−0.910299	−	0.525561i
$392$	−4.33013	+	5.50000i	−0.218704	+	0.277792i
$393$		0			0
$394$	3.00000			0.151138
$395$	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
$401$	5.19615	−	3.00000i	0.259483	−	0.149813i	−0.364615	−	0.931158i	$-0.618800\pi$
$401$	5.19615	−	3.00000i	0.259483	−	0.149813i	0.624099	+	0.781345i	$0.285466\pi$
$402$		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
$409$		−	15.5885i		−	0.770800i	−0.922750	−	0.385400i	$-0.874064\pi$
$409$		−	15.5885i		−	0.770800i	0.922750	−	0.385400i	$-0.125936\pi$
$410$		−	6.00000i		−	0.296319i
$411$		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	−0.905228	−	0.424927i	$-0.860300\pi$
$419$	−1.73205	+	3.00000i	−0.0846162	+	0.146560i	0.820611	+	0.571487i	$0.193633\pi$
$420$		0			0
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	−0.932061	−	0.362301i	$-0.881991\pi$
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	0.152269	−	0.988339i	$-0.451342\pi$
$422$	13.8564	+	8.00000i	0.674519	+	0.389434i
$423$		0			0
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	−6.92820			−0.336067
$426$		0			0
$427$	−3.00000	+	8.66025i	−0.145180	+	0.419099i
$428$	−2.59808	−	1.50000i	−0.125583	−	0.0725052i
$429$		0			0
$430$	12.0000	+	6.92820i	0.578691	+	0.334108i
$431$	−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	$0.986749\pi$
$434$	−8.66025	−	3.00000i	−0.415705	−	0.144005i
$435$		0			0
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	41.5692			1.98853
$438$		0			0
$439$			31.1769i			1.48799i	0.668184	+	0.743996i	$0.267072\pi$
$439$			31.1769i			1.48799i	−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	9.00000i		−	0.427603i	−0.976877	−	0.213801i	$-0.931415\pi$
$443$		−	9.00000i		−	0.427603i	0.976877	−	0.213801i	$-0.0685846\pi$
$444$		0			0
$445$	−18.0000			−0.853282
$446$	7.79423	+	13.5000i	0.369067	+	0.639244i
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$		−	6.00000i		−	0.283158i	−0.989927	−	0.141579i	$-0.954782\pi$
$449$		−	6.00000i		−	0.283158i	0.989927	−	0.141579i	$-0.0452178\pi$
$450$		0			0
$451$		0			0
$452$	15.5885	+	9.00000i	0.733219	+	0.423324i
$453$		0			0
$454$	22.5000	+	12.9904i	1.05598	+	0.609669i
$455$		0			0
$456$		0			0
$457$	−41.0000			−1.91790			−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−41.0000			−1.91790			−0.958950	+	0.283577i	$0.908479\pi$
$458$	−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	−0.999598	−	0.0283522i	$-0.990974\pi$
$461$	−11.2583	−	19.5000i	−0.524353	−	0.908206i	0.475245	−	0.879853i	$-0.342359\pi$
$462$		0			0
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	0.464739	+	0.885448i	$0.346148\pi$
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	7.79423	−	4.50000i	0.361838	−	0.208907i
$465$		0			0
$466$	15.0000	−	25.9808i	0.694862	−	1.20354i
$467$	−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
$472$			12.1244i			0.558069i
$473$		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
$479$	6.92820	−	12.0000i	0.316558	−	0.548294i	−0.663210	−	0.748434i	$-0.730806\pi$
$479$	6.92820	−	12.0000i	0.316558	−	0.548294i	0.979767	+	0.200140i	$0.0641396\pi$
$480$		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	$0.840546\pi$
$488$	3.46410			0.156813
$489$		0			0
$490$	12.0000	+	1.73205i	0.542105	+	0.0782461i
$491$	2.59808	+	1.50000i	0.117250	+	0.0676941i	0.557478	−	0.830192i	$-0.311769\pi$
$491$	2.59808	+	1.50000i	0.117250	+	0.0676941i	−0.440228	+	0.897886i	$0.645102\pi$
$492$		0			0
$493$	−27.0000	−	15.5885i	−1.21602	−	0.702069i
$494$		0			0
$495$		0			0
$496$			3.46410i			0.155543i
$497$	−5.19615	+	15.0000i	−0.233079	+	0.672842i
$498$		0			0
$499$	7.00000	+	12.1244i	0.313363	+	0.542761i	0.979088	−	0.203436i	$-0.0652110\pi$
$499$	7.00000	+	12.1244i	0.313363	+	0.542761i	−0.665725	+	0.746197i	$0.731878\pi$
$500$	−12.1244			−0.542218
$501$		0			0
$502$		−	8.66025i		−	0.386526i
$503$	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
$508$	7.00000			0.310575
$509$	17.3205	+	30.0000i	0.767718	+	1.32973i	0.938798	+	0.344469i	$0.111941\pi$
$509$	17.3205	+	30.0000i	0.767718	+	1.32973i	−0.171080	+	0.985257i	$0.554726\pi$
$510$		0			0
$511$	31.5000	−	6.06218i	1.39348	−	0.268175i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	18.0000	−	10.3923i	0.793946	−	0.458385i
$515$	−15.5885	−	9.00000i	−0.686909	−	0.396587i
$516$		0			0
$517$		0			0
$518$	−6.92820	−	8.00000i	−0.304408	−	0.351500i
$519$		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
$527$	10.3923	−	6.00000i	0.452696	−	0.261364i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$	−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
$535$			5.19615i			0.224649i
$536$			14.0000i			0.604708i
$537$		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	$-0.0942267\pi$
$542$	6.06218	−	10.5000i	0.260393	−	0.451014i
$543$		0			0
$544$	−3.00000	+	1.73205i	−0.128624	+	0.0742611i
$545$	13.8564	−	24.0000i	0.593543	−	1.02805i
$546$		0			0
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	62.3538			2.65636
$552$		0			0
$553$	−27.5000	−	9.52628i	−1.16942	−	0.405099i
$554$	6.92820	+	4.00000i	0.294351	+	0.169944i
$555$		0			0
$556$	−9.00000	−	5.19615i	−0.381685	−	0.220366i
$557$	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
$560$	−0.866025	−	4.50000i	−0.0365963	−	0.190160i
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−5.19615			−0.218992			−0.109496	−	0.993987i	$-0.534924\pi$
$563$	−5.19615			−0.218992			−0.109496	+	0.993987i	$0.534924\pi$
$564$		0			0
$565$		−	31.1769i		−	1.31162i
$566$	6.92820			0.291214
$567$		0			0
$568$	6.00000			0.251754
$569$		−	42.0000i		−	1.76073i	−0.474295	−	0.880366i	$-0.657297\pi$
$569$		−	42.0000i		−	1.76073i	0.474295	−	0.880366i	$-0.342703\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		0			0
$573$		0			0
$574$	6.00000	+	6.92820i	0.250435	+	0.289178i
$575$		−	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	$0.438522\pi$
$578$	−4.33013	−	2.50000i	−0.180110	−	0.103986i
$579$		0			0
$580$	−13.5000	−	7.79423i	−0.560557	−	0.323638i
$581$	8.66025	+	45.0000i	0.359288	+	1.86691i
$582$		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	−0.947514	−	0.319716i	$-0.896413\pi$
$587$	−18.1865	−	31.5000i	−0.750639	−	1.30014i	0.196875	−	0.980429i	$-0.436921\pi$
$588$		0			0
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$	18.1865	−	10.5000i	0.748728	−	0.432278i
$591$		0			0
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	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
$599$		−	24.0000i		−	0.980613i	−0.871550	−	0.490307i	$-0.836885\pi$
$599$		−	24.0000i		−	0.980613i	0.871550	−	0.490307i	$-0.163115\pi$
$600$		0			0
$601$	−1.50000	+	0.866025i	−0.0611863	+	0.0353259i	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−1.50000	+	0.866025i	−0.0611863	+	0.0353259i	0.469095	+	0.883148i	$0.344580\pi$
$602$	−20.7846	+	4.00000i	−0.847117	+	0.163028i
$603$		0			0
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	9.52628	−	16.5000i	0.387298	−	0.670820i
$606$		0			0
$607$	28.5000	−	16.4545i	1.15678	−	0.667867i	0.206249	−	0.978499i	$-0.433874\pi$
$607$	28.5000	−	16.4545i	1.15678	−	0.667867i	0.950530	+	0.310633i	$0.100541\pi$
$608$	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	$0.884985\pi$
$614$	−6.92820			−0.279600
$615$		0			0
$616$		0			0
$617$	−5.19615	−	3.00000i	−0.209189	−	0.120775i	0.391745	−	0.920074i	$-0.371871\pi$
$617$	−5.19615	−	3.00000i	−0.209189	−	0.120775i	−0.600935	+	0.799298i	$0.705205\pi$
$618$		0			0
$619$	−18.0000	−	10.3923i	−0.723481	−	0.417702i	0.0925515	−	0.995708i	$-0.470498\pi$
$619$	−18.0000	−	10.3923i	−0.723481	−	0.417702i	−0.816033	+	0.578006i	$0.803831\pi$
$620$	5.19615	−	3.00000i	0.208683	−	0.120483i
$621$		0			0
$622$		−	13.8564i		−	0.555591i
$623$	20.7846	−	18.0000i	0.832718	−	0.721155i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	22.5167			0.899947
$627$		0			0
$628$		−	10.3923i		−	0.414698i
$629$	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	$0.369672\pi$
$632$			11.0000i			0.437557i
$633$		0			0
$634$	−6.00000			−0.238290
$635$	−6.06218	−	10.5000i	−0.240570	−	0.416680i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−1.50000	+	0.866025i	−0.0592927	+	0.0342327i
$641$	10.3923	+	6.00000i	0.410471	+	0.236986i	0.690992	−	0.722862i	$-0.257174\pi$
$641$	10.3923	+	6.00000i	0.410471	+	0.236986i	−0.280521	+	0.959848i	$0.590507\pi$
$642$		0			0
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.0544858	−	0.998515i	$-0.517352\pi$
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.891982	+	0.452071i	$0.850685\pi$
$644$	15.5885	−	3.00000i	0.614271	−	0.118217i
$645$		0			0
$646$	−24.0000			−0.944267
$647$	−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
$653$	12.9904	−	7.50000i	0.508353	−	0.293498i	−0.223803	−	0.974634i	$-0.571847\pi$
$653$	12.9904	−	7.50000i	0.508353	−	0.293498i	0.732156	+	0.681137i	$0.238514\pi$
$654$		0			0
$655$	−9.00000	+	15.5885i	−0.351659	+	0.609091i
$656$	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	$-0.490401\pi$
$659$	23.3827	−	13.5000i	0.910860	−	0.525885i	0.880708	+	0.473660i	$0.157067\pi$
$660$		0			0
$661$		−	13.8564i		−	0.538952i	−0.963007	−	0.269476i	$-0.913150\pi$
$661$		−	13.8564i		−	0.538952i	0.963007	−	0.269476i	$-0.0868504\pi$
$662$		−	10.0000i		−	0.388661i
$663$		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
$668$	−8.66025	+	15.0000i	−0.335075	+	0.580367i
$669$		0			0
$670$	21.0000	−	12.1244i	0.811301	−	0.468405i
$671$		0			0
$672$		0			0
$673$	2.50000	+	4.33013i	0.0963679	+	0.166914i	0.910179	−	0.414216i	$-0.135944\pi$
$673$	2.50000	+	4.33013i	0.0963679	+	0.166914i	−0.813811	+	0.581130i	$0.802611\pi$
$674$	−19.9186	−	11.5000i	−0.767235	−	0.442963i
$675$		0			0
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	−25.9808			−0.998522			−0.499261	−	0.866452i	$-0.666395\pi$
$677$	−25.9808			−0.998522			−0.499261	+	0.866452i	$0.666395\pi$
$678$		0			0
$679$	18.0000	−	3.46410i	0.690777	−	0.132940i
$680$	5.19615	+	3.00000i	0.199263	+	0.115045i
$681$		0			0
$682$		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
$686$	−15.5885	+	10.0000i	−0.595170	+	0.381802i
$687$		0			0
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$		0			0
$690$		0			0
$691$			27.7128i			1.05425i	0.849789	+	0.527123i	$0.176729\pi$
$691$			27.7128i			1.05425i	−0.849789	+	0.527123i	$0.823271\pi$
$692$	−5.19615			−0.197528
$693$		0			0
$694$	33.0000			1.25266
$695$			18.0000i			0.682779i
$696$		0			0
$697$	−12.0000			−0.454532
$698$	1.73205	+	3.00000i	0.0655591	+	0.113552i
$699$		0			0
$700$	4.00000	−	3.46410i	0.151186	−	0.130931i
$701$			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
$707$	−10.3923	+	9.00000i	−0.390843	+	0.338480i
$708$		0			0
$709$	28.0000			1.05156			0.525781	−	0.850620i	$-0.323773\pi$
$709$	28.0000			1.05156			0.525781	+	0.850620i	$0.323773\pi$
$710$	−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
$716$	−12.9904	+	7.50000i	−0.485473	+	0.280288i
$717$		0			0
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	−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
$724$		−	17.3205i		−	0.643712i
$725$		−	18.0000i		−	0.668503i
$726$		0			0
$727$	10.5000	−	6.06218i	0.389423	−	0.224834i	−0.292487	−	0.956270i	$-0.594483\pi$
$727$	10.5000	−	6.06218i	0.389423	−	0.224834i	0.681910	+	0.731436i	$0.261149\pi$
$728$		0			0
$729$		0			0
$730$	−10.5000	+	18.1865i	−0.388622	+	0.673114i
$731$	13.8564	−	24.0000i	0.512498	−	0.887672i
$732$		0			0
$733$	6.00000	−	3.46410i	0.221615	−	0.127950i	−0.385083	−	0.922882i	$-0.625827\pi$
$733$	6.00000	−	3.46410i	0.221615	−	0.127950i	0.606698	+	0.794933i	$0.292494\pi$
$734$	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	$0.774452\pi$
$740$	6.92820			0.254686
$741$		0			0
$742$	−1.50000	−	7.79423i	−0.0550667	−	0.286135i
$743$	−31.1769	−	18.0000i	−1.14377	−	0.660356i	−0.196409	−	0.980522i	$-0.562928\pi$
$743$	−31.1769	−	18.0000i	−1.14377	−	0.660356i	−0.947361	+	0.320166i	$0.896261\pi$
$744$		0			0
$745$	−22.5000	−	12.9904i	−0.824336	−	0.475931i
$746$	−12.1244	+	7.00000i	−0.443904	+	0.256288i
$747$		0			0
$748$		0			0
$749$	−5.19615	−	6.00000i	−0.189863	−	0.219235i
$750$		0			0
$751$	−3.50000	−	6.06218i	−0.127717	−	0.221212i	0.795075	−	0.606511i	$-0.207432\pi$
$751$	−3.50000	−	6.06218i	−0.127717	−	0.221212i	−0.922792	+	0.385299i	$0.874098\pi$
$752$	3.46410			0.126323
$753$		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	$0.742639\pi$
$758$			14.0000i			0.508503i
$759$		0			0
$760$	−12.0000			−0.435286
$761$	17.3205	+	30.0000i	0.627868	+	1.08750i	0.987979	+	0.154590i	$0.0494055\pi$
$761$	17.3205	+	30.0000i	0.627868	+	1.08750i	−0.360111	+	0.932910i	$0.617261\pi$
$762$		0			0
$763$	8.00000	+	41.5692i	0.289619	+	1.50491i
$764$		−	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	0.999854	+	0.0170631i	$0.00543163\pi$
$769$	42.0000	+	24.2487i	1.51456	+	0.874431i	0.514704	+	0.857368i	$0.327902\pi$
$770$		0			0
$771$		0			0
$772$	−10.0000			−0.359908
$773$	−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
$779$	20.7846	−	12.0000i	0.744686	−	0.429945i
$780$		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
$787$			3.46410i			0.123482i	0.998092	+	0.0617409i	$0.0196653\pi$
$787$			3.46410i			0.123482i	−0.998092	+	0.0617409i	$0.980335\pi$
$788$		−	3.00000i		−	0.106871i
$789$		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
$794$	−13.8564	+	24.0000i	−0.491745	+	0.851728i
$795$		0			0
$796$	−7.50000	+	4.33013i	−0.265830	+	0.153477i
$797$	−20.7846	+	36.0000i	−0.736229	+	1.27519i	0.217954	+	0.975959i	$0.430062\pi$
$797$	−20.7846	+	36.0000i	−0.736229	+	1.27519i	−0.954182	+	0.299226i	$0.903271\pi$
$798$		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
$805$	−18.0000	−	20.7846i	−0.634417	−	0.732561i
$806$		0			0
$807$		0			0
$808$	4.50000	+	2.59808i	0.158309	+	0.0914000i
$809$	−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			$\pi$
$812$	23.3827	−	4.50000i	0.820571	−	0.157919i
$813$		0			0
$814$		0			0
$815$	−3.46410			−0.121342
$816$		0			0
$817$			55.4256i			1.93910i
$818$	−15.5885			−0.545038
$819$		0			0
$820$	−6.00000			−0.209529
$821$			9.00000i			0.314102i	0.987590	+	0.157051i	$0.0501987\pi$
$821$			9.00000i			0.314102i	−0.987590	+	0.157051i	$0.949801\pi$
$822$		0			0
$823$	5.00000			0.174289			0.0871445	−	0.996196i	$-0.472226\pi$
$823$	5.00000			0.174289			0.0871445	+	0.996196i	$0.472226\pi$
$824$	−5.19615	−	9.00000i	−0.181017	−	0.313530i
$825$		0			0
$826$	−10.5000	+	30.3109i	−0.365342	+	1.05465i
$827$		−	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	$0.538790\pi$
$830$	−25.9808	−	15.0000i	−0.901805	−	0.520658i
$831$		0			0
$832$		0			0
$833$	3.46410	−	24.0000i	0.120024	−	0.831551i
$834$		0			0
$835$	30.0000			1.03819
$836$		0			0
$837$		0			0
$838$	3.00000	+	1.73205i	0.103633	+	0.0598327i
$839$	3.46410	+	6.00000i	0.119594	+	0.207143i	0.919607	−	0.392840i	$-0.128507\pi$
$839$	3.46410	+	6.00000i	0.119594	+	0.207143i	−0.800013	+	0.599983i	$0.795174\pi$
$840$		0			0
$841$	26.0000	−	45.0333i	0.896552	−	1.55287i
$842$	−27.7128	+	16.0000i	−0.955047	+	0.551396i
$843$		0			0
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	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
$850$			6.92820i			0.237635i
$851$			24.0000i			0.822709i
$852$		0			0
$853$	6.00000	−	3.46410i	0.205436	−	0.118609i	−0.393753	−	0.919216i	$-0.628823\pi$
$853$	6.00000	−	3.46410i	0.205436	−	0.118609i	0.599189	+	0.800608i	$0.295490\pi$
$854$	8.66025	+	3.00000i	0.296348	+	0.102658i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	3.46410	−	6.00000i	0.118331	−	0.204956i	−0.800775	−	0.598965i	$-0.795579\pi$
$857$	3.46410	−	6.00000i	0.118331	−	0.204956i	0.919107	+	0.394009i	$0.128912\pi$
$858$		0			0
$859$	21.0000	−	12.1244i	0.716511	−	0.413678i	−0.0969563	−	0.995289i	$-0.530911\pi$
$859$	21.0000	−	12.1244i	0.716511	−	0.413678i	0.813467	+	0.581611i	$0.197577\pi$
$860$	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
$866$	1.73205			0.0588575
$867$		0			0
$868$	−3.00000	+	8.66025i	−0.101827	+	0.293948i
$869$		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
$875$	−30.3109	−	10.5000i	−1.02470	−	0.354965i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	31.1769			1.05217
$879$		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
$886$	−9.00000			−0.302361
$887$	8.66025	+	15.0000i	0.290783	+	0.503651i	0.973995	−	0.226569i	$-0.0727509\pi$
$887$	8.66025	+	15.0000i	0.290783	+	0.503651i	−0.683212	+	0.730220i	$0.739418\pi$
$888$		0			0
$889$	17.5000	+	6.06218i	0.586931	+	0.203319i
$890$			18.0000i			0.603361i
$891$		0			0
$892$	13.5000	−	7.79423i	0.452013	−	0.260970i
$893$	20.7846	+	12.0000i	0.695530	+	0.401565i
$894$		0			0
$895$	22.5000	+	12.9904i	0.752092	+	0.434221i
$896$	0.866025	−	2.50000i	0.0289319	−	0.0835191i
$897$		0			0
$898$	−6.00000			−0.200223
$899$	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
$905$	−25.9808	+	15.0000i	−0.863630	+	0.498617i
$906$		0			0
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	−0.967730	−	0.251990i	$-0.918915\pi$
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	0.702094	+	0.712084i	$0.252248\pi$
$908$	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	$-0.832222\pi$
$911$	−25.9808	+	15.0000i	−0.860781	+	0.496972i	0.00349271	+	0.999994i	$0.498888\pi$
$912$		0			0
$913$		0			0
$914$			41.0000i			1.35616i
$915$		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	$0.203499\pi$
$920$	−5.19615	+	9.00000i	−0.171312	+	0.296721i
$921$		0			0
$922$	−19.5000	+	11.2583i	−0.642198	+	0.370773i
$923$		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
$929$	−38.1051			−1.25019			−0.625094	−	0.780549i	$-0.714939\pi$
$929$	−38.1051			−1.25019			−0.625094	+	0.780549i	$0.714939\pi$
$930$		0			0
$931$	18.0000	+	45.0333i	0.589926	+	1.47591i
$932$	−25.9808	−	15.0000i	−0.851028	−	0.491341i
$933$		0			0
$934$	4.50000	+	2.59808i	0.147244	+	0.0850117i
$935$		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	$0.616623\pi$
$938$	−12.1244	+	35.0000i	−0.395874	+	1.14279i
$939$		0			0
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−55.4256			−1.80682			−0.903412	−	0.428774i	$-0.858946\pi$
$941$	−55.4256			−1.80682			−0.903412	+	0.428774i	$0.858946\pi$
$942$		0			0
$943$		−	20.7846i		−	0.676840i
$944$	12.1244			0.394614
$945$		0			0
$946$		0			0
$947$			27.0000i			0.877382i	0.898638	+	0.438691i	$0.144558\pi$
$947$			27.0000i			0.877382i	−0.898638	+	0.438691i	$0.855442\pi$
$948$		0			0
$949$		0			0
$950$	−6.92820	−	12.0000i	−0.224781	−	0.389331i
$951$		0			0
$952$	−9.00000	+	1.73205i	−0.291692	+	0.0561361i
$953$		−	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
$956$	20.7846	+	12.0000i	0.672222	+	0.388108i
$957$		0			0
$958$	−12.0000	−	6.92820i	−0.387702	−	0.223840i
$959$		0			0
$960$		0			0
$961$	19.0000			0.612903
$962$		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	−0.989536	−	0.144283i	$-0.953912\pi$
$967$	−11.5000	+	19.9186i	−0.369815	+	0.640538i	0.619721	+	0.784822i	$0.287246\pi$
$968$	9.52628	−	5.50000i	0.306186	−	0.176777i
$969$		0			0
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	−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
$976$		−	3.46410i		−	0.110883i
$977$		−	12.0000i		−	0.383914i	−0.981403	−	0.191957i	$-0.938517\pi$
$977$		−	12.0000i		−	0.383914i	0.981403	−	0.191957i	$-0.0614834\pi$
$978$		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
$983$	−13.8564	+	24.0000i	−0.441951	+	0.765481i	−0.997834	−	0.0657791i	$-0.979047\pi$
$983$	−13.8564	+	24.0000i	−0.441951	+	0.765481i	0.555883	+	0.831260i	$0.312380\pi$
$984$		0			0
$985$	−4.50000	+	2.59808i	−0.143382	+	0.0827816i
$986$	−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	$0.808028\pi$
$992$	3.46410			0.109985
$993$		0			0
$994$	15.0000	+	5.19615i	0.475771	+	0.164812i
$995$	12.9904	+	7.50000i	0.411823	+	0.237766i
$996$		0			0
$997$	−42.0000	−	24.2487i	−1.33015	−	0.767964i	−0.344830	−	0.938665i	$-0.612064\pi$
$997$	−42.0000	−	24.2487i	−1.33015	−	0.767964i	−0.985323	+	0.170701i	$0.945397\pi$
$998$	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.l.b.215.1		4
3.2	odd	2	inner	1134.2.l.b.215.2		4
7.3	odd	6		1134.2.t.c.1025.2		4
9.2	odd	6		1134.2.t.c.593.2		4
9.4	even	3		378.2.k.c.215.2	yes	4
9.5	odd	6		378.2.k.c.215.1	✓	4
9.7	even	3		1134.2.t.c.593.1		4
21.17	even	6		1134.2.t.c.1025.1		4
63.5	even	6		2646.2.d.a.2645.3		4
63.23	odd	6		2646.2.d.a.2645.4		4
63.31	odd	6		378.2.k.c.269.1	yes	4
63.38	even	6	inner	1134.2.l.b.269.2		4
63.40	odd	6		2646.2.d.a.2645.2		4
63.52	odd	6	inner	1134.2.l.b.269.1		4
63.58	even	3		2646.2.d.a.2645.1		4
63.59	even	6		378.2.k.c.269.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.c.215.1	✓	4	9.5	odd	6
378.2.k.c.215.2	yes	4	9.4	even	3
378.2.k.c.269.1	yes	4	63.31	odd	6
378.2.k.c.269.2	yes	4	63.59	even	6
1134.2.l.b.215.1		4	1.1	even	1	trivial
1134.2.l.b.215.2		4	3.2	odd	2	inner
1134.2.l.b.269.1		4	63.52	odd	6	inner
1134.2.l.b.269.2		4	63.38	even	6	inner
1134.2.t.c.593.1		4	9.7	even	3
1134.2.t.c.593.2		4	9.2	odd	6
1134.2.t.c.1025.1		4	21.17	even	6
1134.2.t.c.1025.2		4	7.3	odd	6
2646.2.d.a.2645.1		4	63.58	even	3
2646.2.d.a.2645.2		4	63.40	odd	6
2646.2.d.a.2645.3		4	63.5	even	6
2646.2.d.a.2645.4		4	63.23	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(1.50000 - 0.866025i) q^{10} +(-0.866025 + 2.50000i) q^{14} +1.00000 q^{16} +(-1.73205 - 3.00000i) q^{17} +(6.00000 + 3.46410i) q^{19} +(-0.866025 - 1.50000i) q^{20} +(5.19615 - 3.00000i) q^{23} +(1.00000 - 1.73205i) q^{25} +(2.50000 + 0.866025i) q^{28} +(7.79423 - 4.50000i) q^{29} +3.46410i q^{31} -1.00000i q^{32} +(-3.00000 + 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(3.46410 - 6.00000i) q^{38} +(-1.50000 + 0.866025i) q^{40} +(1.73205 - 3.00000i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{46} +3.46410 q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.73205 - 1.00000i) q^{50} +(-2.59808 + 1.50000i) q^{53} +(0.866025 - 2.50000i) q^{56} +(-4.50000 - 7.79423i) q^{58} +12.1244 q^{59} -3.46410i q^{61} +3.46410 q^{62} -1.00000 q^{64} +14.0000 q^{67} +(1.73205 + 3.00000i) q^{68} +(-4.50000 + 0.866025i) q^{70} -6.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} +(3.46410 + 2.00000i) q^{74} +(-6.00000 - 3.46410i) q^{76} +11.0000 q^{79} +(0.866025 + 1.50000i) q^{80} +(-3.00000 - 1.73205i) q^{82} +(-8.66025 - 15.0000i) q^{83} +(3.00000 - 5.19615i) q^{85} +(6.92820 - 4.00000i) q^{86} +(-5.19615 + 9.00000i) q^{89} +(-5.19615 + 3.00000i) q^{92} -3.46410i q^{94} +12.0000i q^{95} +(-6.00000 + 3.46410i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 10 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 - 10 * q^7	\( 4 q - 4 q^{4} - 10 q^{7} + 6 q^{10} + 4 q^{16} + 24 q^{19} + 4 q^{25} + 10 q^{28} - 12 q^{34} - 8 q^{37} - 6 q^{40} + 16 q^{43} - 12 q^{46} + 22 q^{49} - 18 q^{58} - 4 q^{64} + 56 q^{67} - 18 q^{70} - 42 q^{73} - 24 q^{76} + 44 q^{79} - 12 q^{82} + 12 q^{85} - 24 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 - 10 * q^7 + 6 * q^10 + 4 * q^16 + 24 * q^19 + 4 * q^25 + 10 * q^28 - 12 * q^34 - 8 * q^37 - 6 * q^40 + 16 * q^43 - 12 * q^46 + 22 * q^49 - 18 * q^58 - 4 * q^64 + 56 * q^67 - 18 * q^70 - 42 * q^73 - 24 * q^76 + 44 * q^79 - 12 * q^82 + 12 * q^85 - 24 * q^97

Introduction

L-functions

Modular forms

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Database

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