LMFDB - Embedded newform 1323.2.o.a.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.a.440.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{8} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{8} -5.19615i q^{10} +(1.50000 - 0.866025i) q^{11} +(-1.50000 - 0.866025i) q^{13} +(2.50000 + 4.33013i) q^{16} +3.00000 q^{17} -5.19615i q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +3.00000 q^{26} +(4.50000 - 2.59808i) q^{29} +(3.00000 + 1.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(-4.50000 + 2.59808i) q^{34} +7.00000 q^{37} +(4.50000 + 7.79423i) q^{38} +(4.50000 + 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} -1.73205i q^{44} -9.00000 q^{46} +(6.00000 + 3.46410i) q^{50} +(-1.50000 + 0.866025i) q^{52} -8.66025i q^{53} +5.19615i q^{55} +(-4.50000 + 7.79423i) q^{58} +(-12.0000 + 6.92820i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(4.50000 - 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +3.46410i q^{71} +5.19615i q^{73} +(-10.5000 + 6.06218i) q^{74} +(-4.50000 - 2.59808i) q^{76} +(-4.00000 - 6.92820i) q^{79} -15.0000 q^{80} -5.19615i q^{82} +(7.50000 + 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(1.50000 + 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{89} +(4.50000 - 2.59808i) q^{92} +(13.5000 + 7.79423i) q^{95} +(-1.50000 + 0.866025i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + q^{4} - 3 q^{5}+O(q^{10}) $ 2 * q - 3 * q^2 + q^4 - 3 * q^5	$ 2 q - 3 q^{2} + q^{4} - 3 q^{5} + 3 q^{11} - 3 q^{13} + 5 q^{16} + 6 q^{17} + 3 q^{20} - 3 q^{22} + 9 q^{23} - 4 q^{25} + 6 q^{26} + 9 q^{29} + 6 q^{31} - 9 q^{32} - 9 q^{34} + 14 q^{37} + 9 q^{38} + 9 q^{40} - 3 q^{41} - q^{43} - 18 q^{46} + 12 q^{50} - 3 q^{52} - 9 q^{58} - 24 q^{61} - 12 q^{62} - 2 q^{64} + 9 q^{65} + 4 q^{67} + 3 q^{68} - 21 q^{74} - 9 q^{76} - 8 q^{79} - 30 q^{80} + 15 q^{83} - 9 q^{85} + 3 q^{86} - 3 q^{88} + 6 q^{89} + 9 q^{92} + 27 q^{95} - 3 q^{97}+O(q^{100}) $ 2 * q - 3 * q^2 + q^4 - 3 * q^5 + 3 * q^11 - 3 * q^13 + 5 * q^16 + 6 * q^17 + 3 * q^20 - 3 * q^22 + 9 * q^23 - 4 * q^25 + 6 * q^26 + 9 * q^29 + 6 * q^31 - 9 * q^32 - 9 * q^34 + 14 * q^37 + 9 * q^38 + 9 * q^40 - 3 * q^41 - q^43 - 18 * q^46 + 12 * q^50 - 3 * q^52 - 9 * q^58 - 24 * q^61 - 12 * q^62 - 2 * q^64 + 9 * q^65 + 4 * q^67 + 3 * q^68 - 21 * q^74 - 9 * q^76 - 8 * q^79 - 30 * q^80 + 15 * q^83 - 9 * q^85 + 3 * q^86 - 3 * q^88 + 6 * q^89 + 9 * q^92 + 27 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$		−	5.19615i		−	1.64317i
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		0			0
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$		−	5.19615i		−	1.19208i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$		−	5.19615i		−	1.19208i	0.802955	−	0.596040i	$-0.203260\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.889432	−	0.457068i	$-0.151100\pi$
$23$	4.50000	+	2.59808i	0.938315	+	0.541736i	0.0488832	+	0.998805i	$0.484434\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	3.00000			0.588348
$27$		0			0
$28$		0			0
$29$	4.50000	−	2.59808i	0.835629	−	0.482451i	−0.0201471	−	0.999797i	$-0.506413\pi$
$29$	4.50000	−	2.59808i	0.835629	−	0.482451i	0.855776	+	0.517346i	$0.173080\pi$
$30$		0			0
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	0.744599	−	0.667512i	$-0.232641\pi$
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	−0.205783	+	0.978598i	$0.565974\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$		0			0
$34$	−4.50000	+	2.59808i	−0.771744	+	0.445566i
$35$		0			0
$36$		0			0
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$	4.50000	+	7.79423i	0.729996	+	1.26439i
$39$		0			0
$40$	4.50000	+	2.59808i	0.711512	+	0.410792i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		−	1.73205i		−	0.261116i
$45$		0			0
$46$	−9.00000			−1.32698
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$	6.00000	+	3.46410i	0.848528	+	0.489898i
$51$		0			0
$52$	−1.50000	+	0.866025i	−0.208013	+	0.120096i
$53$		−	8.66025i		−	1.18958i	−0.803882	−	0.594789i	$-0.797236\pi$
$53$		−	8.66025i		−	1.18958i	0.803882	−	0.594789i	$-0.202764\pi$
$54$		0			0
$55$			5.19615i			0.700649i
$56$		0			0
$57$		0			0
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−12.0000	+	6.92820i	−1.53644	+	0.887066i	−0.537400	+	0.843328i	$0.680593\pi$
$61$	−12.0000	+	6.92820i	−1.53644	+	0.887066i	−0.999043	+	0.0437377i	$0.986073\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.50000	−	2.59808i	0.558156	−	0.322252i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$		0			0
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$			5.19615i			0.608164i	0.952646	+	0.304082i	$0.0983496\pi$
$73$			5.19615i			0.608164i	−0.952646	+	0.304082i	$0.901650\pi$
$74$	−10.5000	+	6.06218i	−1.22060	+	0.704714i
$75$		0			0
$76$	−4.50000	−	2.59808i	−0.516185	−	0.298020i
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−15.0000			−1.67705
$81$		0			0
$82$		−	5.19615i		−	0.573819i
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	0.903263	+	0.429087i	$0.141165\pi$
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	−0.0800311	+	0.996792i	$0.525502\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	1.50000	+	0.866025i	0.161749	+	0.0933859i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$		0			0
$92$	4.50000	−	2.59808i	0.469157	−	0.270868i
$93$		0			0
$94$		0			0
$95$	13.5000	+	7.79423i	1.38507	+	0.799671i
$96$		0			0
$97$	−1.50000	+	0.866025i	−0.152302	+	0.0879316i	−0.574214	−	0.818705i	$-0.694692\pi$
$97$	−1.50000	+	0.866025i	−0.152302	+	0.0879316i	0.421912	+	0.906637i	$0.361359\pi$
$98$		0			0
$99$		0			0
$100$	−4.00000			−0.400000
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	10.5000	+	6.06218i	1.03460	+	0.597324i	0.918298	−	0.395890i	$-0.129564\pi$
$103$	10.5000	+	6.06218i	1.03460	+	0.597324i	0.116298	+	0.993214i	$0.462897\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	7.50000	+	12.9904i	0.728464	+	1.26174i
$107$			8.66025i			0.837218i	0.908166	+	0.418609i	$0.137482\pi$
$107$			8.66025i			0.837218i	−0.908166	+	0.418609i	$0.862518\pi$
$108$		0			0
$109$	19.0000			1.81987			0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000			1.81987			0.909935	+	0.414751i	$0.136131\pi$
$110$	−4.50000	−	7.79423i	−0.429058	−	0.743151i
$111$		0			0
$112$		0			0
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	0.427784	−	0.903881i	$-0.359294\pi$
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	−0.568892	+	0.822412i	$0.692628\pi$
$114$		0			0
$115$	−13.5000	+	7.79423i	−1.25888	+	0.726816i
$116$		−	5.19615i		−	0.482451i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	12.0000	−	20.7846i	1.08643	−	1.88175i
$123$		0			0
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$		0			0
$130$	−4.50000	+	7.79423i	−0.394676	+	0.683599i
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		0			0
$133$		0			0
$134$			6.92820i			0.598506i
$135$		0			0
$136$		−	5.19615i		−	0.445566i
$137$	−10.5000	+	6.06218i	−0.897076	+	0.517927i	−0.876250	−	0.481856i	$-0.839963\pi$
$137$	−10.5000	+	6.06218i	−0.897076	+	0.517927i	−0.0208253	+	0.999783i	$0.506629\pi$
$138$		0			0
$139$	−7.50000	−	4.33013i	−0.636142	−	0.367277i	0.146985	−	0.989139i	$-0.453043\pi$
$139$	−7.50000	−	4.33013i	−0.636142	−	0.367277i	−0.783127	+	0.621862i	$0.786376\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−3.00000			−0.250873
$144$		0			0
$145$			15.5885i			1.29455i
$146$	−4.50000	−	7.79423i	−0.372423	−	0.645055i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	1.50000	+	0.866025i	0.122885	+	0.0709476i	0.560182	−	0.828369i	$-0.310731\pi$
$149$	1.50000	+	0.866025i	0.122885	+	0.0709476i	−0.437298	+	0.899317i	$0.644064\pi$
$150$		0			0
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$	−9.00000			−0.729996
$153$		0			0
$154$		0			0
$155$	−9.00000	+	5.19615i	−0.722897	+	0.417365i
$156$		0			0
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$	12.0000	+	6.92820i	0.954669	+	0.551178i
$159$		0			0
$160$	13.5000	−	7.79423i	1.06727	−	0.616188i
$161$		0			0
$162$		0			0
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	−22.5000	−	12.9904i	−1.74634	−	1.00825i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$		−	15.5885i		−	1.19558i
$171$		0			0
$172$	−1.00000			−0.0762493
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$	7.50000	+	4.33013i	0.565334	+	0.326396i
$177$		0			0
$178$	−4.50000	+	2.59808i	−0.337289	+	0.194734i
$179$			15.5885i			1.16514i	0.812782	+	0.582568i	$0.197952\pi$
$179$			15.5885i			1.16514i	−0.812782	+	0.582568i	$0.802048\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−10.5000	+	18.1865i	−0.771975	+	1.33710i
$186$		0			0
$187$	4.50000	−	2.59808i	0.329073	−	0.189990i
$188$		0			0
$189$		0			0
$190$	−27.0000			−1.95879
$191$	−15.0000	+	8.66025i	−1.08536	+	0.626634i	−0.932338	−	0.361588i	$-0.882235\pi$
$191$	−15.0000	+	8.66025i	−1.08536	+	0.626634i	−0.153024	+	0.988222i	$0.548901\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$	1.50000	−	2.59808i	0.107694	−	0.186531i
$195$		0			0
$196$		0			0
$197$		−	13.8564i		−	0.987228i	−0.869681	−	0.493614i	$-0.835676\pi$
$197$		−	13.8564i		−	0.987228i	0.869681	−	0.493614i	$-0.164324\pi$
$198$		0			0
$199$			8.66025i			0.613909i	0.951724	+	0.306955i	$0.0993100\pi$
$199$			8.66025i			0.613909i	−0.951724	+	0.306955i	$0.900690\pi$
$200$	−6.00000	+	3.46410i	−0.424264	+	0.244949i
$201$		0			0
$202$	4.50000	+	2.59808i	0.316619	+	0.182800i
$203$		0			0
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−21.0000			−1.46314
$207$		0			0
$208$		−	8.66025i		−	0.600481i
$209$	−4.50000	−	7.79423i	−0.311272	−	0.539138i
$210$		0			0
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	−7.50000	−	4.33013i	−0.515102	−	0.297394i
$213$		0			0
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$	3.00000			0.204598
$216$		0			0
$217$		0			0
$218$	−28.5000	+	16.4545i	−1.93026	+	1.11444i
$219$		0			0
$220$	4.50000	+	2.59808i	0.303390	+	0.175162i
$221$	−4.50000	−	2.59808i	−0.302703	−	0.174766i
$222$		0			0
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	−0.643046	−	0.765828i	$-0.722329\pi$
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	0.341703	+	0.939808i	$0.388996\pi$
$224$		0			0
$225$		0			0
$226$	3.00000			0.199557
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	0.969533	+	0.244962i	$0.0787754\pi$
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	−0.272623	+	0.962121i	$0.587891\pi$
$228$		0			0
$229$	7.50000	+	4.33013i	0.495614	+	0.286143i	0.726900	−	0.686743i	$-0.240960\pi$
$229$	7.50000	+	4.33013i	0.495614	+	0.286143i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	13.5000	−	23.3827i	0.890164	−	1.54181i
$231$		0			0
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$		−	5.19615i		−	0.340411i	−0.985409	−	0.170206i	$-0.945557\pi$
$233$		−	5.19615i		−	0.340411i	0.985409	−	0.170206i	$-0.0544432\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.50000	−	0.866025i	−0.0970269	−	0.0560185i	0.450701	−	0.892675i	$-0.351174\pi$
$239$	−1.50000	−	0.866025i	−0.0970269	−	0.0560185i	−0.547728	+	0.836656i	$0.684507\pi$
$240$		0			0
$241$	19.5000	−	11.2583i	1.25611	−	0.725213i	0.283790	−	0.958886i	$-0.408408\pi$
$241$	19.5000	−	11.2583i	1.25611	−	0.725213i	0.972315	+	0.233674i	$0.0750747\pi$
$242$		−	13.8564i		−	0.890724i
$243$		0			0
$244$			13.8564i			0.887066i
$245$		0			0
$246$		0			0
$247$	−4.50000	+	7.79423i	−0.286328	+	0.495935i
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$		0			0
$250$	4.50000	−	2.59808i	0.284605	−	0.164317i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	−30.0000	+	17.3205i	−1.88237	+	1.08679i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$		0			0
$260$		−	5.19615i		−	0.322252i
$261$		0			0
$262$		−	15.5885i		−	0.963058i
$263$	19.5000	−	11.2583i	1.20242	−	0.694218i	0.241329	−	0.970443i	$-0.422417\pi$
$263$	19.5000	−	11.2583i	1.20242	−	0.694218i	0.961093	+	0.276225i	$0.0890835\pi$
$264$		0			0
$265$	22.5000	+	12.9904i	1.38216	+	0.797993i
$266$		0			0
$267$		0			0
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$		0			0
$271$		−	12.1244i		−	0.736502i	−0.929726	−	0.368251i	$-0.879957\pi$
$271$		−	12.1244i		−	0.736502i	0.929726	−	0.368251i	$-0.120043\pi$
$272$	7.50000	+	12.9904i	0.454754	+	0.787658i
$273$		0			0
$274$	10.5000	−	18.1865i	0.634328	−	1.09869i
$275$	−6.00000	−	3.46410i	−0.361814	−	0.208893i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	15.0000			0.899640
$279$		0			0
$280$		0			0
$281$	16.5000	−	9.52628i	0.984307	−	0.568290i	0.0807396	−	0.996735i	$-0.474272\pi$
$281$	16.5000	−	9.52628i	0.984307	−	0.568290i	0.903568	+	0.428445i	$0.140938\pi$
$282$		0			0
$283$	−3.00000	−	1.73205i	−0.178331	−	0.102960i	0.408177	−	0.912903i	$-0.366165\pi$
$283$	−3.00000	−	1.73205i	−0.178331	−	0.102960i	−0.586509	+	0.809943i	$0.699498\pi$
$284$	3.00000	+	1.73205i	0.178017	+	0.102778i
$285$		0			0
$286$	4.50000	−	2.59808i	0.266091	−	0.153627i
$287$		0			0
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−13.5000	−	23.3827i	−0.792747	−	1.37308i
$291$		0			0
$292$	4.50000	+	2.59808i	0.263343	+	0.152041i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$		0			0
$295$		0			0
$296$		−	12.1244i		−	0.704714i
$297$		0			0
$298$	−3.00000			−0.173785
$299$	−4.50000	−	7.79423i	−0.260242	−	0.450752i
$300$		0			0
$301$		0			0
$302$	−25.5000	−	14.7224i	−1.46736	−	0.847181i
$303$		0			0
$304$	22.5000	−	12.9904i	1.29046	−	0.745049i
$305$		−	41.5692i		−	2.38025i
$306$		0			0
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$		0			0
$309$		0			0
$310$	9.00000	−	15.5885i	0.511166	−	0.885365i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	18.0000	−	10.3923i	1.01742	−	0.587408i	0.104065	−	0.994571i	$-0.466815\pi$
$313$	18.0000	−	10.3923i	1.01742	−	0.587408i	0.913356	+	0.407163i	$0.133482\pi$
$314$		0			0
$315$		0			0
$316$	−8.00000			−0.450035
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$		0			0
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$		0			0
$322$		0			0
$323$		−	15.5885i		−	0.867365i
$324$		0			0
$325$			6.92820i			0.384308i
$326$	−16.5000	+	9.52628i	−0.913850	+	0.527612i
$327$		0			0
$328$	4.50000	+	2.59808i	0.248471	+	0.143455i
$329$		0			0
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	15.0000			0.823232
$333$		0			0
$334$			15.5885i			0.852962i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	0.482295	+	0.876009i	$0.339803\pi$
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	−0.999793	+	0.0203242i	$0.993530\pi$
$338$	15.0000	+	8.66025i	0.815892	+	0.471056i
$339$		0			0
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	6.00000			0.324918
$342$		0			0
$343$		0			0
$344$	−1.50000	+	0.866025i	−0.0808746	+	0.0466930i
$345$		0			0
$346$	−9.00000	−	5.19615i	−0.483843	−	0.279347i
$347$	−3.00000	−	1.73205i	−0.161048	−	0.0929814i	0.417310	−	0.908764i	$-0.362973\pi$
$347$	−3.00000	−	1.73205i	−0.161048	−	0.0929814i	−0.578358	+	0.815783i	$0.696306\pi$
$348$		0			0
$349$	10.5000	−	6.06218i	0.562052	−	0.324501i	−0.191917	−	0.981411i	$-0.561470\pi$
$349$	10.5000	−	6.06218i	0.562052	−	0.324501i	0.753969	+	0.656910i	$0.228137\pi$
$350$		0			0
$351$		0			0
$352$	−9.00000			−0.479702
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$		0			0
$355$	−9.00000	−	5.19615i	−0.477670	−	0.275783i
$356$	1.50000	−	2.59808i	0.0794998	−	0.137698i
$357$		0			0
$358$	−13.5000	−	23.3827i	−0.713497	−	1.23581i
$359$			22.5167i			1.18838i	0.804323	+	0.594192i	$0.202528\pi$
$359$			22.5167i			1.18838i	−0.804323	+	0.594192i	$0.797472\pi$
$360$		0			0
$361$	−8.00000			−0.421053
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.5000	−	7.79423i	−0.706622	−	0.407969i
$366$		0			0
$367$	−4.50000	+	2.59808i	−0.234898	+	0.135618i	−0.612830	−	0.790215i	$-0.709969\pi$
$367$	−4.50000	+	2.59808i	−0.234898	+	0.135618i	0.377932	+	0.925834i	$0.376635\pi$
$368$			25.9808i			1.35434i
$369$		0			0
$370$		−	36.3731i		−	1.89095i
$371$		0			0
$372$		0			0
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.230291	−	0.973122i	$-0.426032\pi$
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.727603	−	0.685999i	$-0.240634\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	13.5000	−	7.79423i	0.692535	−	0.399835i
$381$		0			0
$382$	15.0000	−	25.9808i	0.767467	−	1.32929i
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	−0.957790	−	0.287469i	$-0.907186\pi$
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	0.727851	+	0.685736i	$0.240519\pi$
$384$		0			0
$385$		0			0
$386$			3.46410i			0.176318i
$387$		0			0
$388$			1.73205i			0.0879316i
$389$	31.5000	−	18.1865i	1.59711	−	0.922094i	0.605074	−	0.796170i	$-0.293144\pi$
$389$	31.5000	−	18.1865i	1.59711	−	0.922094i	0.992040	−	0.125924i	$-0.0401896\pi$
$390$		0			0
$391$	13.5000	+	7.79423i	0.682724	+	0.394171i
$392$		0			0
$393$		0			0
$394$	12.0000	+	20.7846i	0.604551	+	1.04711i
$395$	24.0000			1.20757
$396$		0			0
$397$			8.66025i			0.434646i	0.976100	+	0.217323i	$0.0697324\pi$
$397$			8.66025i			0.434646i	−0.976100	+	0.217323i	$0.930268\pi$
$398$	−7.50000	−	12.9904i	−0.375941	−	0.651149i
$399$		0			0
$400$	10.0000	−	17.3205i	0.500000	−	0.866025i
$401$	−28.5000	−	16.4545i	−1.42322	−	0.821698i	−0.426649	−	0.904417i	$-0.640306\pi$
$401$	−28.5000	−	16.4545i	−1.42322	−	0.821698i	−0.996573	+	0.0827195i	$0.973639\pi$
$402$		0			0
$403$	−3.00000	−	5.19615i	−0.149441	−	0.258839i
$404$	−3.00000			−0.149256
$405$		0			0
$406$		0			0
$407$	10.5000	−	6.06218i	0.520466	−	0.300491i
$408$		0			0
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	0.640951	−	0.767582i	$-0.278540\pi$
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	−0.344270	+	0.938871i	$0.611874\pi$
$410$	13.5000	+	7.79423i	0.666717	+	0.384930i
$411$		0			0
$412$	10.5000	−	6.06218i	0.517298	−	0.298662i
$413$		0			0
$414$		0			0
$415$	−45.0000			−2.20896
$416$	4.50000	+	7.79423i	0.220631	+	0.382143i
$417$		0			0
$418$	13.5000	+	7.79423i	0.660307	+	0.381228i
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	−0.109483	−	0.993989i	$-0.534920\pi$
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	0.915561	−	0.402179i	$-0.131747\pi$
$420$		0			0
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	0.700306	−	0.713843i	$-0.253047\pi$
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	−0.968359	+	0.249561i	$0.919714\pi$
$422$			8.66025i			0.421575i
$423$		0			0
$424$	−15.0000			−0.728464
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$		0			0
$428$	7.50000	+	4.33013i	0.362526	+	0.209305i
$429$		0			0
$430$	−4.50000	+	2.59808i	−0.217009	+	0.125290i
$431$			15.5885i			0.750870i	0.926849	+	0.375435i	$0.122507\pi$
$431$			15.5885i			0.750870i	−0.926849	+	0.375435i	$0.877493\pi$
$432$		0			0
$433$			13.8564i			0.665896i	0.942945	+	0.332948i	$0.108043\pi$
$433$			13.8564i			0.665896i	−0.942945	+	0.332948i	$0.891957\pi$
$434$		0			0
$435$		0			0
$436$	9.50000	−	16.4545i	0.454967	−	0.788027i
$437$	13.5000	−	23.3827i	0.645793	−	1.11855i
$438$		0			0
$439$	−27.0000	+	15.5885i	−1.28864	+	0.743996i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−27.0000	+	15.5885i	−1.28864	+	0.743996i	−0.310228	+	0.950662i	$0.600405\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$	9.00000			0.428086
$443$	27.0000	−	15.5885i	1.28281	−	0.740630i	0.305448	−	0.952209i	$-0.401194\pi$
$443$	27.0000	−	15.5885i	1.28281	−	0.740630i	0.977361	+	0.211579i	$0.0678605\pi$
$444$		0			0
$445$	−4.50000	+	7.79423i	−0.213320	+	0.369482i
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$		0			0
$448$		0			0
$449$			34.6410i			1.63481i	0.576063	+	0.817405i	$0.304588\pi$
$449$			34.6410i			1.63481i	−0.576063	+	0.817405i	$0.695412\pi$
$450$		0			0
$451$			5.19615i			0.244677i
$452$	−1.50000	+	0.866025i	−0.0705541	+	0.0407344i
$453$		0			0
$454$	−31.5000	−	18.1865i	−1.47837	−	0.853536i
$455$		0			0
$456$		0			0
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	0.991551	+	0.129718i	$0.0414071\pi$
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	−0.383437	+	0.923567i	$0.625260\pi$
$458$	−15.0000			−0.700904
$459$		0			0
$460$			15.5885i			0.726816i
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$	22.5000	+	12.9904i	1.04454	+	0.603063i
$465$		0			0
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.50000	−	0.866025i	−0.0689701	−	0.0398199i
$474$		0			0
$475$	−18.0000	+	10.3923i	−0.825897	+	0.476832i
$476$		0			0
$477$		0			0
$478$	3.00000			0.137217
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	−0.990060	−	0.140643i	$-0.955083\pi$
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	0.373230	−	0.927739i	$-0.378250\pi$
$480$		0			0
$481$	−10.5000	−	6.06218i	−0.478759	−	0.276412i
$482$	−19.5000	+	33.7750i	−0.888201	+	1.53841i
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$		−	5.19615i		−	0.235945i
$486$		0			0
$487$	−23.0000			−1.04223			−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000			−1.04223			−0.521115	+	0.853487i	$0.674484\pi$
$488$	12.0000	+	20.7846i	0.543214	+	0.940875i
$489$		0			0
$490$		0			0
$491$	22.5000	+	12.9904i	1.01541	+	0.586248i	0.912771	−	0.408471i	$-0.133938\pi$
$491$	22.5000	+	12.9904i	1.01541	+	0.586248i	0.102639	+	0.994719i	$0.467271\pi$
$492$		0			0
$493$	13.5000	−	7.79423i	0.608009	−	0.351034i
$494$		−	15.5885i		−	0.701358i
$495$		0			0
$496$			17.3205i			0.777714i
$497$		0			0
$498$		0			0
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	0.437955	+	0.898997i	$0.355703\pi$
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	−0.997532	+	0.0702185i	$0.977630\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$	18.0000	−	10.3923i	0.803379	−	0.463831i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	−13.5000	+	7.79423i	−0.600148	+	0.346496i
$507$		0			0
$508$	10.0000	−	17.3205i	0.443678	−	0.768473i
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	−0.224957	−	0.974369i	$-0.572224\pi$
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	0.956306	−	0.292366i	$-0.0944425\pi$
$510$		0			0
$511$		0			0
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$		−	5.19615i		−	0.229192i
$515$	−31.5000	+	18.1865i	−1.38806	+	0.801394i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	−45.0000			−1.97149			−0.985743	−	0.168259i	$-0.946186\pi$
$521$	−45.0000			−1.97149			−0.985743	+	0.168259i	$0.946186\pi$
$522$		0			0
$523$		−	19.0526i		−	0.833110i	−0.909110	−	0.416555i	$-0.863237\pi$
$523$		−	19.0526i		−	0.833110i	0.909110	−	0.416555i	$-0.136763\pi$
$524$	4.50000	+	7.79423i	0.196583	+	0.340492i
$525$		0			0
$526$	−19.5000	+	33.7750i	−0.850240	+	1.47266i
$527$	9.00000	+	5.19615i	0.392046	+	0.226348i
$528$		0			0
$529$	2.00000	+	3.46410i	0.0869565	+	0.150613i
$530$	−45.0000			−1.95468
$531$		0			0
$532$		0			0
$533$	4.50000	−	2.59808i	0.194917	−	0.112535i
$534$		0			0
$535$	−22.5000	−	12.9904i	−0.972760	−	0.561623i
$536$	−6.00000	−	3.46410i	−0.259161	−	0.149626i
$537$		0			0
$538$	−22.5000	+	12.9904i	−0.970044	+	0.560055i
$539$		0			0
$540$		0			0
$541$	−13.0000			−0.558914			−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000			−0.558914			−0.279457	+	0.960158i	$0.590154\pi$
$542$	10.5000	+	18.1865i	0.451014	+	0.781179i
$543$		0			0
$544$	−13.5000	−	7.79423i	−0.578808	−	0.334175i
$545$	−28.5000	+	49.3634i	−1.22081	+	2.11450i
$546$		0			0
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	0.994459	−	0.105123i	$-0.0335235\pi$
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	−0.588269	+	0.808666i	$0.700190\pi$
$548$			12.1244i			0.517927i
$549$		0			0
$550$	12.0000			0.511682
$551$	−13.5000	−	23.3827i	−0.575119	−	0.996136i
$552$		0			0
$553$		0			0
$554$	−1.50000	−	0.866025i	−0.0637289	−	0.0367939i
$555$		0			0
$556$	−7.50000	+	4.33013i	−0.318071	+	0.183638i
$557$			12.1244i			0.513725i	0.966448	+	0.256863i	$0.0826888\pi$
$557$			12.1244i			0.513725i	−0.966448	+	0.256863i	$0.917311\pi$
$558$		0			0
$559$			1.73205i			0.0732579i
$560$		0			0
$561$		0			0
$562$	−16.5000	+	28.5788i	−0.696010	+	1.20553i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$		0			0
$565$	4.50000	−	2.59808i	0.189316	−	0.109302i
$566$	6.00000			0.252199
$567$		0			0
$568$	6.00000			0.251754
$569$	6.00000	−	3.46410i	0.251533	−	0.145223i	−0.368933	−	0.929456i	$-0.620277\pi$
$569$	6.00000	−	3.46410i	0.251533	−	0.145223i	0.620466	+	0.784233i	$0.286943\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$		0			0
$574$		0			0
$575$		−	20.7846i		−	0.866778i
$576$		0			0
$577$			39.8372i			1.65844i	0.558920	+	0.829222i	$0.311216\pi$
$577$			39.8372i			1.65844i	−0.558920	+	0.829222i	$0.688784\pi$
$578$	12.0000	−	6.92820i	0.499134	−	0.288175i
$579$		0			0
$580$	13.5000	+	7.79423i	0.560557	+	0.323638i
$581$		0			0
$582$		0			0
$583$	−7.50000	−	12.9904i	−0.310618	−	0.538007i
$584$	9.00000			0.372423
$585$		0			0
$586$			15.5885i			0.643953i
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	0.563781	−	0.825925i	$-0.309346\pi$
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	−0.997162	+	0.0752860i	$0.976013\pi$
$588$		0			0
$589$	9.00000	−	15.5885i	0.370839	−	0.642311i
$590$		0			0
$591$		0			0
$592$	17.5000	+	30.3109i	0.719246	+	1.24577i
$593$	39.0000			1.60154			0.800769	−	0.598973i	$-0.204424\pi$
$593$	39.0000			1.60154			0.800769	+	0.598973i	$0.204424\pi$
$594$		0			0
$595$		0			0
$596$	1.50000	−	0.866025i	0.0614424	−	0.0354738i
$597$		0			0
$598$	13.5000	+	7.79423i	0.552056	+	0.318730i
$599$	−21.0000	−	12.1244i	−0.858037	−	0.495388i	0.00531761	−	0.999986i	$-0.498307\pi$
$599$	−21.0000	−	12.1244i	−0.858037	−	0.495388i	−0.863354	+	0.504598i	$0.831641\pi$
$600$		0			0
$601$	−25.5000	+	14.7224i	−1.04017	+	0.600541i	−0.919881	−	0.392199i	$-0.871715\pi$
$601$	−25.5000	+	14.7224i	−1.04017	+	0.600541i	−0.120286	+	0.992739i	$0.538381\pi$
$602$		0			0
$603$		0			0
$604$	17.0000			0.691720
$605$	−12.0000	−	20.7846i	−0.487869	−	0.845015i
$606$		0			0
$607$	−13.5000	−	7.79423i	−0.547948	−	0.316358i	0.200346	−	0.979725i	$-0.435793\pi$
$607$	−13.5000	−	7.79423i	−0.547948	−	0.316358i	−0.748294	+	0.663367i	$0.769127\pi$
$608$	−13.5000	+	23.3827i	−0.547497	+	0.948293i
$609$		0			0
$610$	36.0000	+	62.3538i	1.45760	+	2.52463i
$611$		0			0
$612$		0			0
$613$	47.0000			1.89831			0.949156	−	0.314806i	$-0.101939\pi$
$613$	47.0000			1.89831			0.949156	+	0.314806i	$0.101939\pi$
$614$	21.0000	+	36.3731i	0.847491	+	1.46790i
$615$		0			0
$616$		0			0
$617$	4.50000	+	2.59808i	0.181163	+	0.104595i	0.587839	−	0.808978i	$-0.299979\pi$
$617$	4.50000	+	2.59808i	0.181163	+	0.104595i	−0.406676	+	0.913573i	$0.633312\pi$
$618$		0			0
$619$	−16.5000	+	9.52628i	−0.663191	+	0.382893i	−0.793492	−	0.608581i	$-0.791739\pi$
$619$	−16.5000	+	9.52628i	−0.663191	+	0.382893i	0.130301	+	0.991475i	$0.458406\pi$
$620$			10.3923i			0.417365i
$621$		0			0
$622$			41.5692i			1.66677i
$623$		0			0
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−18.0000	+	31.1769i	−0.719425	+	1.24608i
$627$		0			0
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−12.0000	+	6.92820i	−0.477334	+	0.275589i
$633$		0			0
$634$		0			0
$635$	−30.0000	+	51.9615i	−1.19051	+	2.06203i
$636$		0			0
$637$		0			0
$638$			15.5885i			0.617153i
$639$		0			0
$640$			36.3731i			1.43777i
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	−0.692818	−	0.721113i	$-0.743631\pi$
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	0.278093	+	0.960554i	$0.410298\pi$
$642$		0			0
$643$	10.5000	+	6.06218i	0.414080	+	0.239069i	0.692541	−	0.721378i	$-0.256491\pi$
$643$	10.5000	+	6.06218i	0.414080	+	0.239069i	−0.278462	+	0.960447i	$0.589824\pi$
$644$		0			0
$645$		0			0
$646$	13.5000	+	23.3827i	0.531150	+	0.919979i
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$		0			0
$649$		0			0
$650$	−6.00000	−	10.3923i	−0.235339	−	0.407620i
$651$		0			0
$652$	5.50000	−	9.52628i	0.215397	−	0.373078i
$653$	−34.5000	−	19.9186i	−1.35009	−	0.779474i	−0.361828	−	0.932245i	$-0.617847\pi$
$653$	−34.5000	−	19.9186i	−1.35009	−	0.779474i	−0.988262	+	0.152771i	$0.951180\pi$
$654$		0			0
$655$	−13.5000	−	23.3827i	−0.527489	−	0.913637i
$656$	−15.0000			−0.585652
$657$		0			0
$658$		0			0
$659$	−10.5000	+	6.06218i	−0.409022	+	0.236149i	−0.690369	−	0.723457i	$-0.742552\pi$
$659$	−10.5000	+	6.06218i	−0.409022	+	0.236149i	0.281347	+	0.959606i	$0.409219\pi$
$660$		0			0
$661$	−36.0000	−	20.7846i	−1.40024	−	0.808428i	−0.405821	−	0.913953i	$-0.633014\pi$
$661$	−36.0000	−	20.7846i	−1.40024	−	0.808428i	−0.994417	+	0.105525i	$0.966348\pi$
$662$	−12.0000	−	6.92820i	−0.466393	−	0.269272i
$663$		0			0
$664$	22.5000	−	12.9904i	0.873169	−	0.504125i
$665$		0			0
$666$		0			0
$667$	27.0000			1.04544
$668$	−4.50000	−	7.79423i	−0.174110	−	0.301568i
$669$		0			0
$670$	−18.0000	−	10.3923i	−0.695401	−	0.401490i
$671$	−12.0000	+	20.7846i	−0.463255	+	0.802381i
$672$		0			0
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$		−	32.9090i		−	1.26761i
$675$		0			0
$676$	−10.0000			−0.384615
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$		0			0
$679$		0			0
$680$	13.5000	+	7.79423i	0.517701	+	0.298895i
$681$		0			0
$682$	−9.00000	+	5.19615i	−0.344628	+	0.198971i
$683$			8.66025i			0.331375i	0.986178	+	0.165688i	$0.0529844\pi$
$683$			8.66025i			0.331375i	−0.986178	+	0.165688i	$0.947016\pi$
$684$		0			0
$685$		−	36.3731i		−	1.38974i
$686$		0			0
$687$		0			0
$688$	2.50000	−	4.33013i	0.0953116	−	0.165085i
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$		0			0
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	−0.441851	−	0.897089i	$-0.645678\pi$
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	0.555976	+	0.831198i	$0.312345\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	6.00000			0.227757
$695$	22.5000	−	12.9904i	0.853474	−	0.492753i
$696$		0			0
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$	−10.5000	+	18.1865i	−0.397431	+	0.688370i
$699$		0			0
$700$		0			0
$701$			34.6410i			1.30837i	0.756333	+	0.654187i	$0.226989\pi$
$701$			34.6410i			1.30837i	−0.756333	+	0.654187i	$0.773011\pi$
$702$		0			0
$703$		−	36.3731i		−	1.37184i
$704$	−1.50000	+	0.866025i	−0.0565334	+	0.0326396i
$705$		0			0
$706$	−31.5000	−	18.1865i	−1.18552	−	0.684459i
$707$		0			0
$708$		0			0
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$	18.0000			0.675528
$711$		0			0
$712$		−	5.19615i		−	0.194734i
$713$	9.00000	+	15.5885i	0.337053	+	0.583792i
$714$		0			0
$715$	4.50000	−	7.79423i	0.168290	−	0.291488i
$716$	13.5000	+	7.79423i	0.504519	+	0.291284i
$717$		0			0
$718$	−19.5000	−	33.7750i	−0.727734	−	1.26047i
$719$	−9.00000			−0.335643			−0.167822	−	0.985817i	$-0.553673\pi$
$719$	−9.00000			−0.335643			−0.167822	+	0.985817i	$0.553673\pi$
$720$		0			0
$721$		0			0
$722$	12.0000	−	6.92820i	0.446594	−	0.257841i
$723$		0			0
$724$		0			0
$725$	−18.0000	−	10.3923i	−0.668503	−	0.385961i
$726$		0			0
$727$	−10.5000	+	6.06218i	−0.389423	+	0.224834i	−0.681910	−	0.731436i	$-0.738851\pi$
$727$	−10.5000	+	6.06218i	−0.389423	+	0.224834i	0.292487	+	0.956270i	$0.405517\pi$
$728$		0			0
$729$		0			0
$730$	27.0000			0.999315
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	37.5000	+	21.6506i	1.38509	+	0.799684i	0.992757	−	0.120137i	$-0.0383334\pi$
$733$	37.5000	+	21.6506i	1.38509	+	0.799684i	0.392337	+	0.919822i	$0.371667\pi$
$734$	4.50000	−	7.79423i	0.166098	−	0.287690i
$735$		0			0
$736$	−13.5000	−	23.3827i	−0.497617	−	0.861897i
$737$		−	6.92820i		−	0.255204i
$738$		0			0
$739$	−7.00000			−0.257499			−0.128750	−	0.991677i	$-0.541096\pi$
$739$	−7.00000			−0.257499			−0.128750	+	0.991677i	$0.541096\pi$
$740$	10.5000	+	18.1865i	0.385988	+	0.668550i
$741$		0			0
$742$		0			0
$743$	10.5000	+	6.06218i	0.385208	+	0.222400i	0.680082	−	0.733136i	$-0.261944\pi$
$743$	10.5000	+	6.06218i	0.385208	+	0.222400i	−0.294874	+	0.955536i	$0.595278\pi$
$744$		0			0
$745$	−4.50000	+	2.59808i	−0.164867	+	0.0951861i
$746$			64.0859i			2.34635i
$747$		0			0
$748$		−	5.19615i		−	0.189990i
$749$		0			0
$750$		0			0
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	0.301373	+	0.953506i	$0.402555\pi$
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	−0.976447	+	0.215757i	$0.930778\pi$
$752$		0			0
$753$		0			0
$754$	13.5000	−	7.79423i	0.491641	−	0.283849i
$755$	−51.0000			−1.85608
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	30.0000	−	17.3205i	1.08965	−	0.629109i
$759$		0			0
$760$	13.5000	−	23.3827i	0.489696	−	0.848179i
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	−0.0932544	−	0.995642i	$-0.529727\pi$
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	0.908879	−	0.417061i	$-0.136940\pi$
$762$		0			0
$763$		0			0
$764$			17.3205i			0.626634i
$765$		0			0
$766$		−	15.5885i		−	0.563234i
$767$		0			0
$768$		0			0
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	51.0000			1.83434			0.917171	−	0.398493i	$-0.130467\pi$
$773$	51.0000			1.83434			0.917171	+	0.398493i	$0.130467\pi$
$774$		0			0
$775$		−	13.8564i		−	0.497737i
$776$	1.50000	+	2.59808i	0.0538469	+	0.0932655i
$777$		0			0
$778$	−31.5000	+	54.5596i	−1.12933	+	1.95606i
$779$	13.5000	+	7.79423i	0.483688	+	0.279257i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−27.0000			−0.965518
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	33.0000	+	19.0526i	1.17632	+	0.679150i	0.955161	−	0.296087i	$-0.0956817\pi$
$787$	33.0000	+	19.0526i	1.17632	+	0.679150i	0.221162	+	0.975237i	$0.429015\pi$
$788$	−12.0000	−	6.92820i	−0.427482	−	0.246807i
$789$		0			0
$790$	−36.0000	+	20.7846i	−1.28082	+	0.739483i
$791$		0			0
$792$		0			0
$793$	24.0000			0.852265
$794$	−7.50000	−	12.9904i	−0.266165	−	0.461011i
$795$		0			0
$796$	7.50000	+	4.33013i	0.265830	+	0.153477i
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	−0.124576	−	0.992210i	$-0.539757\pi$
$797$	22.5000	−	38.9711i	0.796991	−	1.38043i	0.921567	−	0.388219i	$-0.126909\pi$
$798$		0			0
$799$		0			0
$800$			20.7846i			0.734847i
$801$		0			0
$802$	57.0000			2.01274
$803$	4.50000	+	7.79423i	0.158802	+	0.275052i
$804$		0			0
$805$		0			0
$806$	9.00000	+	5.19615i	0.317011	+	0.183027i
$807$		0			0
$808$	−4.50000	+	2.59808i	−0.158309	+	0.0914000i
$809$		−	1.73205i		−	0.0608957i	−0.999536	−	0.0304478i	$-0.990307\pi$
$809$		−	1.73205i		−	0.0608957i	0.999536	−	0.0304478i	$-0.00969334\pi$
$810$		0			0
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$		0			0
$813$		0			0
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	−16.5000	+	28.5788i	−0.577970	+	1.00107i
$816$		0			0
$817$	−4.50000	+	2.59808i	−0.157435	+	0.0908952i
$818$	−12.0000			−0.419570
$819$		0			0
$820$	−9.00000			−0.314294
$821$	6.00000	−	3.46410i	0.209401	−	0.120898i	−0.391632	−	0.920122i	$-0.628089\pi$
$821$	6.00000	−	3.46410i	0.209401	−	0.120898i	0.601033	+	0.799224i	$0.294756\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	10.5000	−	18.1865i	0.365785	−	0.633558i
$825$		0			0
$826$		0			0
$827$		−	24.2487i		−	0.843210i	−0.906780	−	0.421605i	$-0.861467\pi$
$827$		−	24.2487i		−	0.843210i	0.906780	−	0.421605i	$-0.138533\pi$
$828$		0			0
$829$		−	36.3731i		−	1.26329i	−0.775258	−	0.631644i	$-0.782380\pi$
$829$		−	36.3731i		−	1.26329i	0.775258	−	0.631644i	$-0.217620\pi$
$830$	67.5000	−	38.9711i	2.34296	−	1.35271i
$831$		0			0
$832$	1.50000	+	0.866025i	0.0520031	+	0.0300240i
$833$		0			0
$834$		0			0
$835$	13.5000	+	23.3827i	0.467187	+	0.809191i
$836$	−9.00000			−0.311272
$837$		0			0
$838$			57.1577i			1.97448i
$839$	19.5000	+	33.7750i	0.673215	+	1.16604i	0.976987	+	0.213298i	$0.0684204\pi$
$839$	19.5000	+	33.7750i	0.673215	+	1.16604i	−0.303773	+	0.952745i	$0.598246\pi$
$840$		0			0
$841$	−1.00000	+	1.73205i	−0.0344828	+	0.0597259i
$842$	16.5000	+	9.52628i	0.568628	+	0.328297i
$843$		0			0
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	30.0000			1.03203
$846$		0			0
$847$		0			0
$848$	37.5000	−	21.6506i	1.28776	−	0.743486i
$849$		0			0
$850$	18.0000	+	10.3923i	0.617395	+	0.356453i
$851$	31.5000	+	18.1865i	1.07981	+	0.623426i
$852$		0			0
$853$	22.5000	−	12.9904i	0.770385	−	0.444782i	−0.0626267	−	0.998037i	$-0.519948\pi$
$853$	22.5000	−	12.9904i	0.770385	−	0.444782i	0.833012	+	0.553255i	$0.186614\pi$
$854$		0			0
$855$		0			0
$856$	15.0000			0.512689
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	0.537867	−	0.843029i	$-0.319230\pi$
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	−0.999019	+	0.0442921i	$0.985897\pi$
$858$		0			0
$859$	−43.5000	−	25.1147i	−1.48420	−	0.856904i	−0.484362	−	0.874868i	$-0.660948\pi$
$859$	−43.5000	−	25.1147i	−1.48420	−	0.856904i	−0.999839	+	0.0179638i	$0.994282\pi$
$860$	1.50000	−	2.59808i	0.0511496	−	0.0885937i
$861$		0			0
$862$	−13.5000	−	23.3827i	−0.459812	−	0.796417i
$863$			43.3013i			1.47399i	0.675897	+	0.736996i	$0.263756\pi$
$863$			43.3013i			1.47399i	−0.675897	+	0.736996i	$0.736244\pi$
$864$		0			0
$865$	−18.0000			−0.612018
$866$	−12.0000	−	20.7846i	−0.407777	−	0.706290i
$867$		0			0
$868$		0			0
$869$	−12.0000	−	6.92820i	−0.407072	−	0.235023i
$870$		0			0
$871$	−6.00000	+	3.46410i	−0.203302	+	0.117377i
$872$		−	32.9090i		−	1.11444i
$873$		0			0
$874$			46.7654i			1.58186i
$875$		0			0
$876$		0			0
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$	27.0000	−	46.7654i	0.911206	−	1.57825i
$879$		0			0
$880$	−22.5000	+	12.9904i	−0.758475	+	0.437906i
$881$	54.0000			1.81931			0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000			1.81931			0.909653	+	0.415369i	$0.136347\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−4.50000	+	2.59808i	−0.151351	+	0.0873828i
$885$		0			0
$886$	−27.0000	+	46.7654i	−0.907083	+	1.57111i
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	−0.712203	−	0.701974i	$-0.752302\pi$
$887$	7.50000	−	12.9904i	0.251825	−	0.436174i	0.964028	+	0.265799i	$0.0856358\pi$
$888$		0			0
$889$		0			0
$890$		−	15.5885i		−	0.522526i
$891$		0			0
$892$			5.19615i			0.173980i
$893$		0			0
$894$		0			0
$895$	−40.5000	−	23.3827i	−1.35377	−	0.781597i
$896$		0			0
$897$		0			0
$898$	−30.0000	−	51.9615i	−1.00111	−	1.73398i
$899$	18.0000			0.600334
$900$		0			0
$901$		−	25.9808i		−	0.865545i
$902$	−4.50000	−	7.79423i	−0.149834	−	0.259519i
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$		0			0
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	0.664089	−	0.747653i	$-0.268820\pi$
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	−0.979531	+	0.201291i	$0.935486\pi$
$908$	21.0000			0.696909
$909$		0			0
$910$		0			0
$911$	−4.50000	+	2.59808i	−0.149092	+	0.0860781i	−0.572690	−	0.819772i	$-0.694100\pi$
$911$	−4.50000	+	2.59808i	−0.149092	+	0.0860781i	0.423598	+	0.905850i	$0.360767\pi$
$912$		0			0
$913$	22.5000	+	12.9904i	0.744641	+	0.429919i
$914$	−39.0000	−	22.5167i	−1.29001	−	0.744785i
$915$		0			0
$916$	7.50000	−	4.33013i	0.247807	−	0.143071i
$917$		0			0
$918$		0			0
$919$	−29.0000			−0.956622			−0.478311	−	0.878191i	$-0.658751\pi$
$919$	−29.0000			−0.956622			−0.478311	+	0.878191i	$0.658751\pi$
$920$	13.5000	+	23.3827i	0.445082	+	0.770904i
$921$		0			0
$922$	22.5000	+	12.9904i	0.740998	+	0.427815i
$923$	3.00000	−	5.19615i	0.0987462	−	0.171033i
$924$		0			0
$925$	−14.0000	−	24.2487i	−0.460317	−	0.797293i
$926$			1.73205i			0.0569187i
$927$		0			0
$928$	−27.0000			−0.886318
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$		0			0
$932$	−4.50000	−	2.59808i	−0.147402	−	0.0851028i
$933$		0			0
$934$	−4.50000	+	2.59808i	−0.147244	+	0.0850117i
$935$			15.5885i			0.509797i
$936$		0			0
$937$			13.8564i			0.452669i	0.974050	+	0.226335i	$0.0726743\pi$
$937$			13.8564i			0.452669i	−0.974050	+	0.226335i	$0.927326\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$		0			0
$943$	−13.5000	+	7.79423i	−0.439620	+	0.253815i
$944$		0			0
$945$		0			0
$946$	3.00000			0.0975384
$947$	−45.0000	+	25.9808i	−1.46230	+	0.844261i	−0.999118	−	0.0419998i	$-0.986627\pi$
$947$	−45.0000	+	25.9808i	−1.46230	+	0.844261i	−0.463186	+	0.886261i	$0.653294\pi$
$948$		0			0
$949$	4.50000	−	7.79423i	0.146076	−	0.253011i
$950$	18.0000	−	31.1769i	0.583997	−	1.01151i
$951$		0			0
$952$		0			0
$953$			20.7846i			0.673280i	0.941634	+	0.336640i	$0.109290\pi$
$953$			20.7846i			0.673280i	−0.941634	+	0.336640i	$0.890710\pi$
$954$		0			0
$955$		−	51.9615i		−	1.68144i
$956$	−1.50000	+	0.866025i	−0.0485135	+	0.0280093i
$957$		0			0
$958$	40.5000	+	23.3827i	1.30850	+	0.755460i
$959$		0			0
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	21.0000			0.677067
$963$		0			0
$964$		−	22.5167i		−	0.725213i
$965$	3.00000	+	5.19615i	0.0965734	+	0.167270i
$966$		0			0
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	−0.591991	−	0.805945i	$-0.701658\pi$
$967$	12.5000	−	21.6506i	0.401973	−	0.696237i	0.993964	+	0.109707i	$0.0349913\pi$
$968$	12.0000	+	6.92820i	0.385695	+	0.222681i
$969$		0			0
$970$	4.50000	+	7.79423i	0.144486	+	0.250258i
$971$	−57.0000			−1.82922			−0.914609	−	0.404341i	$-0.867501\pi$
$971$	−57.0000			−1.82922			−0.914609	+	0.404341i	$0.867501\pi$
$972$		0			0
$973$		0			0
$974$	34.5000	−	19.9186i	1.10545	−	0.638233i
$975$		0			0
$976$	−60.0000	−	34.6410i	−1.92055	−	1.10883i
$977$	−36.0000	−	20.7846i	−1.15174	−	0.664959i	−0.202431	−	0.979297i	$-0.564884\pi$
$977$	−36.0000	−	20.7846i	−1.15174	−	0.664959i	−0.949311	+	0.314338i	$0.898217\pi$
$978$		0			0
$979$	4.50000	−	2.59808i	0.143821	−	0.0830349i
$980$		0			0
$981$		0			0
$982$	−45.0000			−1.43601
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	−0.989122	−	0.147100i	$-0.953006\pi$
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	0.367168	−	0.930155i	$-0.380327\pi$
$984$		0			0
$985$	36.0000	+	20.7846i	1.14706	+	0.662253i
$986$	−13.5000	+	23.3827i	−0.429928	+	0.744656i
$987$		0			0
$988$	4.50000	+	7.79423i	0.143164	+	0.247967i
$989$		−	5.19615i		−	0.165228i
$990$		0			0
$991$	−47.0000			−1.49300			−0.746502	−	0.665383i	$-0.768268\pi$
$991$	−47.0000			−1.49300			−0.746502	+	0.665383i	$0.768268\pi$
$992$	−9.00000	−	15.5885i	−0.285750	−	0.494934i
$993$		0			0
$994$		0			0
$995$	−22.5000	−	12.9904i	−0.713298	−	0.411823i
$996$		0			0
$997$	7.50000	−	4.33013i	0.237527	−	0.137136i	−0.376512	−	0.926412i	$-0.622877\pi$
$997$	7.50000	−	4.33013i	0.237527	−	0.137136i	0.614040	+	0.789275i	$0.289543\pi$
$998$		−	43.3013i		−	1.37068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.a.881.1		2
3.2	odd	2		441.2.o.b.293.1		2
7.2	even	3		189.2.s.a.17.1		2
7.3	odd	6		189.2.i.a.152.1		2
7.4	even	3		1323.2.i.a.1097.1		2
7.5	odd	6		1323.2.s.a.962.1		2
7.6	odd	2		1323.2.o.b.881.1		2
9.2	odd	6		1323.2.o.b.440.1		2
9.7	even	3		441.2.o.a.146.1		2
21.2	odd	6		63.2.s.a.59.1	yes	2
21.5	even	6		441.2.s.a.374.1		2
21.11	odd	6		441.2.i.a.68.1		2
21.17	even	6		63.2.i.a.5.1	✓	2
21.20	even	2		441.2.o.a.293.1		2
28.3	even	6		3024.2.ca.a.2609.1		2
28.23	odd	6		3024.2.df.a.17.1		2
63.2	odd	6		189.2.i.a.143.1		2
63.11	odd	6		1323.2.s.a.656.1		2
63.16	even	3		63.2.i.a.38.1	yes	2
63.20	even	6	inner	1323.2.o.a.440.1		2
63.23	odd	6		567.2.p.b.80.1		2
63.25	even	3		441.2.s.a.362.1		2
63.31	odd	6		567.2.p.b.404.1		2
63.34	odd	6		441.2.o.b.146.1		2
63.38	even	6		189.2.s.a.89.1		2
63.47	even	6		1323.2.i.a.521.1		2
63.52	odd	6		63.2.s.a.47.1	yes	2
63.58	even	3		567.2.p.a.80.1		2
63.59	even	6		567.2.p.a.404.1		2
63.61	odd	6		441.2.i.a.227.1		2
84.23	even	6		1008.2.df.a.689.1		2
84.59	odd	6		1008.2.ca.a.257.1		2
252.79	odd	6		1008.2.ca.a.353.1		2
252.115	even	6		1008.2.df.a.929.1		2
252.191	even	6		3024.2.ca.a.2033.1		2
252.227	odd	6		3024.2.df.a.1601.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.a.5.1	✓	2	21.17	even	6
63.2.i.a.38.1	yes	2	63.16	even	3
63.2.s.a.47.1	yes	2	63.52	odd	6
63.2.s.a.59.1	yes	2	21.2	odd	6
189.2.i.a.143.1		2	63.2	odd	6
189.2.i.a.152.1		2	7.3	odd	6
189.2.s.a.17.1		2	7.2	even	3
189.2.s.a.89.1		2	63.38	even	6
441.2.i.a.68.1		2	21.11	odd	6
441.2.i.a.227.1		2	63.61	odd	6
441.2.o.a.146.1		2	9.7	even	3
441.2.o.a.293.1		2	21.20	even	2
441.2.o.b.146.1		2	63.34	odd	6
441.2.o.b.293.1		2	3.2	odd	2
441.2.s.a.362.1		2	63.25	even	3
441.2.s.a.374.1		2	21.5	even	6
567.2.p.a.80.1		2	63.58	even	3
567.2.p.a.404.1		2	63.59	even	6
567.2.p.b.80.1		2	63.23	odd	6
567.2.p.b.404.1		2	63.31	odd	6
1008.2.ca.a.257.1		2	84.59	odd	6
1008.2.ca.a.353.1		2	252.79	odd	6
1008.2.df.a.689.1		2	84.23	even	6
1008.2.df.a.929.1		2	252.115	even	6
1323.2.i.a.521.1		2	63.47	even	6
1323.2.i.a.1097.1		2	7.4	even	3
1323.2.o.a.440.1		2	63.20	even	6	inner
1323.2.o.a.881.1		2	1.1	even	1	trivial
1323.2.o.b.440.1		2	9.2	odd	6
1323.2.o.b.881.1		2	7.6	odd	2
1323.2.s.a.656.1		2	63.11	odd	6
1323.2.s.a.962.1		2	7.5	odd	6
3024.2.ca.a.2033.1		2	252.191	even	6
3024.2.ca.a.2609.1		2	28.3	even	6
3024.2.df.a.17.1		2	28.23	odd	6
3024.2.df.a.1601.1		2	252.227	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{8} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{8} -5.19615i q^{10} +(1.50000 - 0.866025i) q^{11} +(-1.50000 - 0.866025i) q^{13} +(2.50000 + 4.33013i) q^{16} +3.00000 q^{17} -5.19615i q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +3.00000 q^{26} +(4.50000 - 2.59808i) q^{29} +(3.00000 + 1.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(-4.50000 + 2.59808i) q^{34} +7.00000 q^{37} +(4.50000 + 7.79423i) q^{38} +(4.50000 + 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} -1.73205i q^{44} -9.00000 q^{46} +(6.00000 + 3.46410i) q^{50} +(-1.50000 + 0.866025i) q^{52} -8.66025i q^{53} +5.19615i q^{55} +(-4.50000 + 7.79423i) q^{58} +(-12.0000 + 6.92820i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(4.50000 - 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +3.46410i q^{71} +5.19615i q^{73} +(-10.5000 + 6.06218i) q^{74} +(-4.50000 - 2.59808i) q^{76} +(-4.00000 - 6.92820i) q^{79} -15.0000 q^{80} -5.19615i q^{82} +(7.50000 + 12.9904i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(1.50000 + 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{89} +(4.50000 - 2.59808i) q^{92} +(13.5000 + 7.79423i) q^{95} +(-1.50000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + q^{4} - 3 q^{5}+O(q^{10}) \) 2 * q - 3 * q^2 + q^4 - 3 * q^5	\( 2 q - 3 q^{2} + q^{4} - 3 q^{5} + 3 q^{11} - 3 q^{13} + 5 q^{16} + 6 q^{17} + 3 q^{20} - 3 q^{22} + 9 q^{23} - 4 q^{25} + 6 q^{26} + 9 q^{29} + 6 q^{31} - 9 q^{32} - 9 q^{34} + 14 q^{37} + 9 q^{38} + 9 q^{40} - 3 q^{41} - q^{43} - 18 q^{46} + 12 q^{50} - 3 q^{52} - 9 q^{58} - 24 q^{61} - 12 q^{62} - 2 q^{64} + 9 q^{65} + 4 q^{67} + 3 q^{68} - 21 q^{74} - 9 q^{76} - 8 q^{79} - 30 q^{80} + 15 q^{83} - 9 q^{85} + 3 q^{86} - 3 q^{88} + 6 q^{89} + 9 q^{92} + 27 q^{95} - 3 q^{97}+O(q^{100}) \) 2 * q - 3 * q^2 + q^4 - 3 * q^5 + 3 * q^11 - 3 * q^13 + 5 * q^16 + 6 * q^17 + 3 * q^20 - 3 * q^22 + 9 * q^23 - 4 * q^25 + 6 * q^26 + 9 * q^29 + 6 * q^31 - 9 * q^32 - 9 * q^34 + 14 * q^37 + 9 * q^38 + 9 * q^40 - 3 * q^41 - q^43 - 18 * q^46 + 12 * q^50 - 3 * q^52 - 9 * q^58 - 24 * q^61 - 12 * q^62 - 2 * q^64 + 9 * q^65 + 4 * q^67 + 3 * q^68 - 21 * q^74 - 9 * q^76 - 8 * q^79 - 30 * q^80 + 15 * q^83 - 9 * q^85 + 3 * q^86 - 3 * q^88 + 6 * q^89 + 9 * q^92 + 27 * q^95 - 3 * q^97

Introduction

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