LMFDB - Embedded newform 2646.2.f.e.1765.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (of order $3$, 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:	$21.1284163748$
Analytic rank:	$1$
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 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1765.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.1765
Dual form			2646.2.f.e.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{8} -3.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} +5.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{26} +(-1.50000 - 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} -7.00000 q^{37} +(2.50000 + 4.33013i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-4.50000 + 7.79423i) q^{41} +(-5.50000 - 9.52628i) q^{43} +3.00000 q^{44} -3.00000 q^{46} +(2.00000 - 3.46410i) q^{50} +(-2.50000 - 4.33013i) q^{52} +3.00000 q^{53} +9.00000 q^{55} +(1.50000 - 2.59808i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-7.50000 - 12.9904i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +11.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(-4.00000 - 6.92820i) q^{79} +3.00000 q^{80} -9.00000 q^{82} +(1.50000 + 2.59808i) q^{83} +(4.50000 - 7.79423i) q^{85} +(5.50000 - 9.52628i) q^{86} +(1.50000 + 2.59808i) q^{88} -15.0000 q^{89} +(-1.50000 - 2.59808i) q^{92} +(-7.50000 + 12.9904i) q^{95} +(0.500000 + 0.866025i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 3 q^{5} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 3 * q^5 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 3 q^{5} - 2 q^{8} - 6 q^{10} - 3 q^{11} - 5 q^{13} - q^{16} - 6 q^{17} + 10 q^{19} - 3 q^{20} + 3 q^{22} - 3 q^{23} - 4 q^{25} - 10 q^{26} - 3 q^{29} + 4 q^{31} + q^{32} - 3 q^{34} - 14 q^{37} + 5 q^{38} + 3 q^{40} - 9 q^{41} - 11 q^{43} + 6 q^{44} - 6 q^{46} + 4 q^{50} - 5 q^{52} + 6 q^{53} + 18 q^{55} + 3 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{62} + 2 q^{64} - 15 q^{65} + 4 q^{67} + 3 q^{68} + 22 q^{73} - 7 q^{74} - 5 q^{76} - 8 q^{79} + 6 q^{80} - 18 q^{82} + 3 q^{83} + 9 q^{85} + 11 q^{86} + 3 q^{88} - 30 q^{89} - 3 q^{92} - 15 q^{95} + q^{97}+O(q^{100}) $ 2 * q + q^2 - q^4 - 3 * q^5 - 2 * q^8 - 6 * q^10 - 3 * q^11 - 5 * q^13 - q^16 - 6 * q^17 + 10 * q^19 - 3 * q^20 + 3 * q^22 - 3 * q^23 - 4 * q^25 - 10 * q^26 - 3 * q^29 + 4 * q^31 + q^32 - 3 * q^34 - 14 * q^37 + 5 * q^38 + 3 * q^40 - 9 * q^41 - 11 * q^43 + 6 * q^44 - 6 * q^46 + 4 * q^50 - 5 * q^52 + 6 * q^53 + 18 * q^55 + 3 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 15 * q^65 + 4 * q^67 + 3 * q^68 + 22 * q^73 - 7 * q^74 - 5 * q^76 - 8 * q^79 + 6 * q^80 - 18 * q^82 + 3 * q^83 + 9 * q^85 + 11 * q^86 + 3 * q^88 - 30 * q^89 - 3 * q^92 - 15 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		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
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−3.00000			−0.948683
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	5.00000			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−5.00000			−0.980581
$27$		0			0
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$		0			0
$36$		0			0
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$	2.50000	+	4.33013i	0.405554	+	0.702439i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−3.00000			−0.442326
$47$		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
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$		0			0
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.50000	−	12.9904i	−0.930261	−	1.61126i
$66$		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
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$		0			0
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$		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	$0.981922\pi$
$80$	3.00000			0.335410
$81$		0			0
$82$	−9.00000			−0.993884
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	0.936530	−	0.350588i	$-0.114018\pi$
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	−0.771883	+	0.635764i	$0.780685\pi$
$84$		0			0
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$	5.50000	−	9.52628i	0.593080	−	1.02725i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$		0			0
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$		0			0
$94$		0			0
$95$	−7.50000	+	12.9904i	−0.769484	+	1.33278i
$96$		0			0
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$		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
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$	2.50000	−	4.33013i	0.245145	−	0.424604i
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	15.0000			1.45010			0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000			1.45010			0.725052	+	0.688694i	$0.241816\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	4.50000	+	7.79423i	0.429058	+	0.743151i
$111$		0			0
$112$		0			0
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	3.00000			0.278543
$117$		0			0
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	1.00000	−	1.73205i	0.0905357	−	0.156813i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	7.50000	−	12.9904i	0.657794	−	1.13933i
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$	3.00000			0.257248
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	15.0000			1.25436
$144$		0			0
$145$	9.00000			0.747409
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	−5.00000			−0.405554
$153$		0			0
$154$		0			0
$155$	6.00000	+	10.3923i	0.481932	+	0.834730i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$	1.50000	+	2.59808i	0.118585	+	0.205396i
$161$		0			0
$162$		0			0
$163$	17.0000			1.33154			0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000			1.33154			0.665771	+	0.746156i	$0.268103\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	−0.802135	−	0.597143i	$-0.796303\pi$
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	9.00000			0.690268
$171$		0			0
$172$	11.0000			0.838742
$173$	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
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$		0			0
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		0			0
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	10.5000	−	18.1865i	0.771975	−	1.33710i
$186$		0			0
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$	−15.0000			−1.08821
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	−0.500000	+	0.866025i	−0.0358979	+	0.0621770i
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−7.00000			−0.496217			−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000			−0.496217			−0.248108	+	0.968732i	$0.579809\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		0			0
$202$	1.50000	−	2.59808i	0.105540	−	0.182800i
$203$		0			0
$204$		0			0
$205$	−13.5000	−	23.3827i	−0.942881	−	1.63312i
$206$	−5.00000			−0.348367
$207$		0			0
$208$	5.00000			0.346688
$209$	−7.50000	−	12.9904i	−0.518786	−	0.898563i
$210$		0			0
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	−0.939156	−	0.343490i	$-0.888391\pi$
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	0.767049	+	0.641588i	$0.221724\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		0			0
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	33.0000			2.25058
$216$		0			0
$217$		0			0
$218$	−3.50000	−	6.06218i	−0.237050	−	0.410582i
$219$		0			0
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$	7.50000	−	12.9904i	0.504505	−	0.873828i
$222$		0			0
$223$	−8.50000	−	14.7224i	−0.569202	−	0.985887i	−0.996645	−	0.0818447i	$-0.973919\pi$
$223$	−8.50000	−	14.7224i	−0.569202	−	0.985887i	0.427443	−	0.904042i	$-0.359414\pi$
$224$		0			0
$225$		0			0
$226$	15.0000			0.997785
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$		0			0
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	0.435653	+	0.900115i	$0.356518\pi$
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	−0.997349	+	0.0727709i	$0.976816\pi$
$230$	4.50000	−	7.79423i	0.296721	−	0.513936i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−27.0000			−1.76883			−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000			−1.76883			−0.884414	+	0.466702i	$0.845442\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$		0			0
$238$		0			0
$239$	13.5000	−	23.3827i	0.873242	−	1.51250i	0.0146191	−	0.999893i	$-0.495346\pi$
$239$	13.5000	−	23.3827i	0.873242	−	1.51250i	0.858623	−	0.512607i	$-0.171320\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$	2.00000			0.128565
$243$		0			0
$244$	2.00000			0.128037
$245$		0			0
$246$		0			0
$247$	−12.5000	+	21.6506i	−0.795356	+	1.37760i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	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
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$		0			0
$260$	15.0000			0.930261
$261$		0			0
$262$	3.00000			0.185341
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	−4.50000	+	7.79423i	−0.276433	+	0.478796i
$266$		0			0
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−21.0000			−1.28039			−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000			−1.28039			−0.640196	+	0.768211i	$0.721147\pi$
$270$		0			0
$271$	−13.0000			−0.789694			−0.394847	−	0.918747i	$-0.629202\pi$
$271$	−13.0000			−0.789694			−0.394847	+	0.918747i	$0.629202\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$	−5.00000			−0.299880
$279$		0			0
$280$		0			0
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	0.907293	−	0.420500i	$-0.138145\pi$
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	−0.817810	+	0.575488i	$0.804812\pi$
$282$		0			0
$283$	−4.00000	+	6.92820i	−0.237775	+	0.411839i	−0.960076	−	0.279741i	$-0.909752\pi$
$283$	−4.00000	+	6.92820i	−0.237775	+	0.411839i	0.722300	+	0.691580i	$0.243085\pi$
$284$		0			0
$285$		0			0
$286$	7.50000	+	12.9904i	0.443484	+	0.768137i
$287$		0			0
$288$		0			0
$289$	−8.00000			−0.470588
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$		0			0
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	−13.5000	+	23.3827i	−0.788678	+	1.36603i	0.138098	+	0.990419i	$0.455901\pi$
$293$	−13.5000	+	23.3827i	−0.788678	+	1.36603i	−0.926777	+	0.375613i	$0.877432\pi$
$294$		0			0
$295$	18.0000	+	31.1769i	1.04800	+	1.81519i
$296$	7.00000			0.406867
$297$		0			0
$298$	−3.00000			−0.173785
$299$	−7.50000	−	12.9904i	−0.433736	−	0.751253i
$300$		0			0
$301$		0			0
$302$	5.50000	−	9.52628i	0.316489	−	0.548176i
$303$		0			0
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	6.00000			0.343559
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$		0			0
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$		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
$323$	−15.0000			−0.834622
$324$		0			0
$325$	20.0000			1.10940
$326$	8.50000	+	14.7224i	0.470771	+	0.815400i
$327$		0			0
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−3.00000			−0.164646
$333$		0			0
$334$	3.00000			0.164153
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	−0.293783	−	0.955872i	$-0.594914\pi$
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	0.974701	−	0.223513i	$-0.0717525\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	−12.0000			−0.649836
$342$		0			0
$343$		0			0
$344$	5.50000	+	9.52628i	0.296540	+	0.513623i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	−2.50000	−	4.33013i	−0.133822	−	0.231786i	0.791325	−	0.611396i	$-0.209392\pi$
$349$	−2.50000	−	4.33013i	−0.133822	−	0.231786i	−0.925147	+	0.379610i	$0.876058\pi$
$350$		0			0
$351$		0			0
$352$	−3.00000			−0.159901
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	−	12.9904i	0.397499	−	0.688489i
$357$		0			0
$358$	−1.50000	−	2.59808i	−0.0792775	−	0.137313i
$359$	−15.0000			−0.791670			−0.395835	−	0.918322i	$-0.629545\pi$
$359$	−15.0000			−0.791670			−0.395835	+	0.918322i	$0.629545\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$		0			0
$364$		0			0
$365$	−16.5000	+	28.5788i	−0.863649	+	1.49588i
$366$		0			0
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	0.878780	−	0.477227i	$-0.158358\pi$
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	−0.852680	+	0.522433i	$0.825025\pi$
$368$	3.00000			0.156386
$369$		0			0
$370$	21.0000			1.09174
$371$		0			0
$372$		0			0
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	−0.997697	−	0.0678218i	$-0.978395\pi$
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	0.557584	+	0.830120i	$0.311728\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	15.0000			0.772539
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−7.50000	−	12.9904i	−0.384742	−	0.666392i
$381$		0			0
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$		0			0
$386$	−14.0000			−0.712581
$387$		0			0
$388$	−1.00000			−0.0507673
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$		0			0
$391$	4.50000	−	7.79423i	0.227575	−	0.394171i
$392$		0			0
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	24.0000			1.20757
$396$		0			0
$397$	29.0000			1.45547			0.727734	−	0.685859i	$-0.240573\pi$
$397$	29.0000			1.45547			0.727734	+	0.685859i	$0.240573\pi$
$398$	−3.50000	−	6.06218i	−0.175439	−	0.303870i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	3.00000			0.149256
$405$		0			0
$406$		0			0
$407$	10.5000	+	18.1865i	0.520466	+	0.901473i
$408$		0			0
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$	13.5000	−	23.3827i	0.666717	−	1.15479i
$411$		0			0
$412$	−2.50000	−	4.33013i	−0.123166	−	0.213330i
$413$		0			0
$414$		0			0
$415$	−9.00000			−0.441793
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$		0			0
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	−0.900337	−	0.435194i	$-0.856680\pi$
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	0.827057	+	0.562118i	$0.190013\pi$
$420$		0			0
$421$	15.5000	+	26.8468i	0.755424	+	1.30843i	0.945163	+	0.326598i	$0.105902\pi$
$421$	15.5000	+	26.8468i	0.755424	+	1.30843i	−0.189740	+	0.981834i	$0.560764\pi$
$422$	−5.00000			−0.243396
$423$		0			0
$424$	−3.00000			−0.145693
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$		0			0
$428$	−7.50000	+	12.9904i	−0.362526	+	0.627914i
$429$		0			0
$430$	16.5000	+	28.5788i	0.795701	+	1.37819i
$431$	3.00000			0.144505			0.0722525	−	0.997386i	$-0.476981\pi$
$431$	3.00000			0.144505			0.0722525	+	0.997386i	$0.476981\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−7.50000	+	12.9904i	−0.358774	+	0.621414i
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	15.0000			0.713477
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$	22.5000	−	38.9711i	1.06660	−	1.84741i
$446$	8.50000	−	14.7224i	0.402487	−	0.697127i
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	27.0000			1.27138
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$		0			0
$454$	−4.50000	+	7.79423i	−0.211195	+	0.365801i
$455$		0			0
$456$		0			0
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	0.922695	+	0.385530i	$0.125981\pi$
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	−0.127469	+	0.991843i	$0.540685\pi$
$458$	−17.0000			−0.794358
$459$		0			0
$460$	9.00000			0.419627
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$		0			0
$463$	−17.5000	+	30.3109i	−0.813294	+	1.40867i	0.0972525	+	0.995260i	$0.468995\pi$
$463$	−17.5000	+	30.3109i	−0.813294	+	1.40867i	−0.910546	+	0.413407i	$0.864339\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	−13.5000	−	23.3827i	−0.625375	−	1.08318i
$467$	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
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−16.5000	+	28.5788i	−0.758671	+	1.31406i
$474$		0			0
$475$	−10.0000	−	17.3205i	−0.458831	−	0.794719i
$476$		0			0
$477$		0			0
$478$	27.0000			1.23495
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	0.744717	−	0.667381i	$-0.232585\pi$
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	−0.950327	+	0.311253i	$0.899251\pi$
$480$		0			0
$481$	17.5000	−	30.3109i	0.797931	−	1.38206i
$482$	11.5000	−	19.9186i	0.523811	−	0.907267i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−3.00000			−0.136223
$486$		0			0
$487$	−31.0000			−1.40474			−0.702372	−	0.711810i	$-0.747876\pi$
$487$	−31.0000			−1.40474			−0.702372	+	0.711810i	$0.747876\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$		0			0
$490$		0			0
$491$	−19.5000	+	33.7750i	−0.880023	+	1.52424i	−0.0287085	+	0.999588i	$0.509139\pi$
$491$	−19.5000	+	33.7750i	−0.880023	+	1.52424i	−0.851314	+	0.524656i	$0.824194\pi$
$492$		0			0
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$	−25.0000			−1.12480
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	0.716258	+	0.697835i	$0.245853\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	4.50000	+	7.79423i	0.200049	+	0.346496i
$507$		0			0
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	0.394684	+	0.918817i	$0.370854\pi$
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	−0.993061	+	0.117602i	$0.962479\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	15.0000			0.661622
$515$	−7.50000	−	12.9904i	−0.330489	−	0.572425i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	7.50000	+	12.9904i	0.328897	+	0.569666i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	−7.00000			−0.306089			−0.153044	−	0.988219i	$-0.548908\pi$
$523$	−7.00000			−0.306089			−0.153044	+	0.988219i	$0.548908\pi$
$524$	1.50000	+	2.59808i	0.0655278	+	0.113497i
$525$		0			0
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−9.00000			−0.390935
$531$		0			0
$532$		0			0
$533$	−22.5000	−	38.9711i	−0.974583	−	1.68803i
$534$		0			0
$535$	−22.5000	+	38.9711i	−0.972760	+	1.68487i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$		0			0
$538$	−10.5000	−	18.1865i	−0.452687	−	0.784077i
$539$		0			0
$540$		0			0
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$	−6.50000	−	11.2583i	−0.279199	−	0.483587i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	10.5000	−	18.1865i	0.449771	−	0.779026i
$546$		0			0
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	0.724157	−	0.689635i	$-0.242229\pi$
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	−0.959320	+	0.282321i	$0.908896\pi$
$548$	−3.00000			−0.128154
$549$		0			0
$550$	−12.0000			−0.511682
$551$	−7.50000	−	12.9904i	−0.319511	−	0.553409i
$552$		0			0
$553$		0			0
$554$	−3.50000	+	6.06218i	−0.148701	+	0.257557i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	3.00000			0.127114			0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000			0.127114			0.0635570	+	0.997978i	$0.479756\pi$
$558$		0			0
$559$	55.0000			2.32625
$560$		0			0
$561$		0			0
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	22.5000	+	38.9711i	0.946582	+	1.63953i
$566$	−8.00000			−0.336265
$567$		0			0
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	−7.50000	+	12.9904i	−0.313591	+	0.543155i
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	−4.50000	+	7.79423i	−0.186852	+	0.323638i
$581$		0			0
$582$		0			0
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	−11.0000			−0.455183
$585$		0			0
$586$	−27.0000			−1.11536
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	−0.974668	−	0.223659i	$-0.928200\pi$
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	0.293640	−	0.955916i	$-0.405133\pi$
$588$		0			0
$589$	10.0000	−	17.3205i	0.412043	−	0.713679i
$590$	−18.0000	+	31.1769i	−0.741048	+	1.28353i
$591$		0			0
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	21.0000			0.862367			0.431183	−	0.902264i	$-0.358096\pi$
$593$	21.0000			0.862367			0.431183	+	0.902264i	$0.358096\pi$
$594$		0			0
$595$		0			0
$596$	−1.50000	−	2.59808i	−0.0614424	−	0.106421i
$597$		0			0
$598$	7.50000	−	12.9904i	0.306698	−	0.531216i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	0.876043	−	0.482233i	$-0.160174\pi$
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	−0.855648	+	0.517559i	$0.826841\pi$
$602$		0			0
$603$		0			0
$604$	11.0000			0.447584
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$		0			0
$612$		0			0
$613$	−31.0000			−1.25208			−0.626039	−	0.779792i	$-0.715325\pi$
$613$	−31.0000			−1.25208			−0.626039	+	0.779792i	$0.715325\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	−0.834251	−	0.551385i	$-0.814100\pi$
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	0.894639	+	0.446790i	$0.147433\pi$
$618$		0			0
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$	−12.0000			−0.481932
$621$		0			0
$622$	−24.0000			−0.962312
$623$		0			0
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	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	$0.449096\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$		0			0
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$	24.0000	−	41.5692i	0.952411	−	1.64962i
$636$		0			0
$637$		0			0
$638$	−9.00000			−0.356313
$639$		0			0
$640$	−3.00000			−0.118585
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.0472793	−	0.998882i	$-0.515055\pi$
$642$		0			0
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	0.424555	+	0.905402i	$0.360431\pi$
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	−0.996379	+	0.0850262i	$0.972903\pi$
$644$		0			0
$645$		0			0
$646$	−7.50000	−	12.9904i	−0.295084	−	0.511100i
$647$	3.00000			0.117942			0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000			0.117942			0.0589711	+	0.998260i	$0.481218\pi$
$648$		0			0
$649$	−36.0000			−1.41312
$650$	10.0000	+	17.3205i	0.392232	+	0.679366i
$651$		0			0
$652$	−8.50000	+	14.7224i	−0.332886	+	0.576575i
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	0.940541	+	0.339680i	$0.110319\pi$
$654$		0			0
$655$	4.50000	+	7.79423i	0.175830	+	0.304546i
$656$	9.00000			0.351391
$657$		0			0
$658$		0			0
$659$	19.5000	+	33.7750i	0.759612	+	1.31569i	0.943049	+	0.332655i	$0.107945\pi$
$659$	19.5000	+	33.7750i	0.759612	+	1.31569i	−0.183436	+	0.983032i	$0.558722\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	10.0000	−	17.3205i	0.388661	−	0.673181i
$663$		0			0
$664$	−1.50000	−	2.59808i	−0.0582113	−	0.100825i
$665$		0			0
$666$		0			0
$667$	9.00000			0.348481
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	−3.00000	+	5.19615i	−0.115814	+	0.200595i
$672$		0			0
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	0.740334	−	0.672239i	$-0.234667\pi$
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	−0.952343	+	0.305028i	$0.901334\pi$
$674$	25.0000			0.962964
$675$		0			0
$676$	12.0000			0.461538
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$		0			0
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	33.0000			1.26271			0.631355	−	0.775494i	$-0.282499\pi$
$683$	33.0000			1.26271			0.631355	+	0.775494i	$0.282499\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$		0			0
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$		0			0
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−7.50000	−	12.9904i	−0.284491	−	0.492753i
$696$		0			0
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$	2.50000	−	4.33013i	0.0946264	−	0.163898i
$699$		0			0
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	−35.0000			−1.32005
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	4.50000	−	7.79423i	0.169360	−	0.293340i
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$	15.0000			0.562149
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$	−22.5000	+	38.9711i	−0.841452	+	1.45744i
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$		0			0
$718$	−7.50000	−	12.9904i	−0.279898	−	0.484797i
$719$	−39.0000			−1.45445			−0.727227	−	0.686397i	$-0.759191\pi$
$719$	−39.0000			−1.45445			−0.727227	+	0.686397i	$0.759191\pi$
$720$		0			0
$721$		0			0
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	−2.50000	−	4.33013i	−0.0927199	−	0.160596i	0.815935	−	0.578144i	$-0.196223\pi$
$727$	−2.50000	−	4.33013i	−0.0927199	−	0.160596i	−0.908655	+	0.417548i	$0.862889\pi$
$728$		0			0
$729$		0			0
$730$	−33.0000			−1.22138
$731$	16.5000	+	28.5788i	0.610275	+	1.05703i
$732$		0			0
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	0.187096	+	0.982342i	$0.440092\pi$
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	−0.944281	+	0.329141i	$0.893241\pi$
$734$	−0.500000	+	0.866025i	−0.0184553	+	0.0319656i
$735$		0			0
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$	−12.0000			−0.442026
$738$		0			0
$739$	47.0000			1.72892			0.864461	−	0.502699i	$-0.167660\pi$
$739$	47.0000			1.72892			0.864461	+	0.502699i	$0.167660\pi$
$740$	10.5000	+	18.1865i	0.385988	+	0.668550i
$741$		0			0
$742$		0			0
$743$	1.50000	−	2.59808i	0.0550297	−	0.0953142i	−0.837198	−	0.546899i	$-0.815808\pi$
$743$	1.50000	−	2.59808i	0.0550297	−	0.0953142i	0.892228	+	0.451585i	$0.149141\pi$
$744$		0			0
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$	−17.0000			−0.622414
$747$		0			0
$748$	−9.00000			−0.329073
$749$		0			0
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$		0			0
$753$		0			0
$754$	7.50000	+	12.9904i	0.273134	+	0.473082i
$755$	33.0000			1.20099
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$		0			0
$760$	7.50000	−	12.9904i	0.272054	−	0.471211i
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$		0			0
$763$		0			0
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−15.0000			−0.541972
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$		0			0
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	−0.856869	−	0.515534i	$-0.827594\pi$
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	0.874900	+	0.484304i	$0.160927\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	−21.0000			−0.755318			−0.377659	−	0.925945i	$-0.623271\pi$
$773$	−21.0000			−0.755318			−0.377659	+	0.925945i	$0.623271\pi$
$774$		0			0
$775$	−16.0000			−0.574737
$776$	−0.500000	−	0.866025i	−0.0179490	−	0.0310885i
$777$		0			0
$778$	−4.50000	+	7.79423i	−0.161333	+	0.279437i
$779$	−22.5000	+	38.9711i	−0.806146	+	1.39629i
$780$		0			0
$781$		0			0
$782$	9.00000			0.321839
$783$		0			0
$784$		0			0
$785$	−21.0000	−	36.3731i	−0.749522	−	1.29821i
$786$		0			0
$787$	−22.0000	+	38.1051i	−0.784215	+	1.35830i	0.145251	+	0.989395i	$0.453601\pi$
$787$	−22.0000	+	38.1051i	−0.784215	+	1.35830i	−0.929467	+	0.368906i	$0.879732\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		0			0
$790$	12.0000	+	20.7846i	0.426941	+	0.739483i
$791$		0			0
$792$		0			0
$793$	10.0000			0.355110
$794$	14.5000	+	25.1147i	0.514586	+	0.891289i
$795$		0			0
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$	−13.5000	+	23.3827i	−0.478195	+	0.828257i	−0.999687	−	0.0249984i	$-0.992042\pi$
$797$	−13.5000	+	23.3827i	−0.478195	+	0.828257i	0.521493	+	0.853256i	$0.325375\pi$
$798$		0			0
$799$		0			0
$800$	−4.00000			−0.141421
$801$		0			0
$802$	27.0000			0.953403
$803$	−16.5000	−	28.5788i	−0.582272	−	1.00853i
$804$		0			0
$805$		0			0
$806$	−10.0000	+	17.3205i	−0.352235	+	0.610089i
$807$		0			0
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	−39.0000			−1.37117			−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000			−1.37117			−0.685583	+	0.727994i	$0.740453\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$		0			0
$813$		0			0
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	−25.5000	+	44.1673i	−0.893226	+	1.54711i
$816$		0			0
$817$	−27.5000	−	47.6314i	−0.962103	−	1.66641i
$818$	22.0000			0.769212
$819$		0			0
$820$	27.0000			0.942881
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.761056	−	0.648686i	$-0.775319\pi$
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.181250	−	0.983437i	$-0.558014\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	2.50000	−	4.33013i	0.0870916	−	0.150847i
$825$		0			0
$826$		0			0
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$		0			0
$829$	41.0000			1.42399			0.711994	−	0.702185i	$-0.247792\pi$
$829$	41.0000			1.42399			0.711994	+	0.702185i	$0.247792\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$		0			0
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$		0			0
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	15.0000			0.518786
$837$		0			0
$838$	−3.00000			−0.103633
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	−0.976987	−	0.213298i	$-0.931580\pi$
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	0.303773	−	0.952745i	$-0.401754\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−15.5000	+	26.8468i	−0.534165	+	0.925201i
$843$		0			0
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	36.0000			1.23844
$846$		0			0
$847$		0			0
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$		0			0
$850$	−6.00000	+	10.3923i	−0.205798	+	0.356453i
$851$	10.5000	−	18.1865i	0.359935	−	0.623426i
$852$		0			0
$853$	−8.50000	−	14.7224i	−0.291034	−	0.504086i	0.683020	−	0.730400i	$-0.260666\pi$
$853$	−8.50000	−	14.7224i	−0.291034	−	0.504086i	−0.974055	+	0.226313i	$0.927333\pi$
$854$		0			0
$855$		0			0
$856$	−15.0000			−0.512689
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	−0.944469	−	0.328601i	$-0.893423\pi$
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	0.756811	+	0.653633i	$0.226756\pi$
$860$	−16.5000	+	28.5788i	−0.562645	+	0.974530i
$861$		0			0
$862$	1.50000	+	2.59808i	0.0510902	+	0.0884908i
$863$	−15.0000			−0.510606			−0.255303	−	0.966861i	$-0.582175\pi$
$863$	−15.0000			−0.510606			−0.255303	+	0.966861i	$0.582175\pi$
$864$		0			0
$865$	−18.0000			−0.612018
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$		0			0
$868$		0			0
$869$	−12.0000	+	20.7846i	−0.407072	+	0.705070i
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	7.00000			0.237050
$873$		0			0
$874$	−15.0000			−0.507383
$875$		0			0
$876$		0			0
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	−0.232556	−	0.972583i	$-0.574709\pi$
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	0.958560	−	0.284892i	$-0.0919577\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$		0			0
$880$	−4.50000	−	7.79423i	−0.151695	−	0.262743i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	7.50000	+	12.9904i	0.252252	+	0.436914i
$885$		0			0
$886$		0			0
$887$	−19.5000	+	33.7750i	−0.654746	+	1.13405i	0.327212	+	0.944951i	$0.393891\pi$
$887$	−19.5000	+	33.7750i	−0.654746	+	1.13405i	−0.981957	+	0.189102i	$0.939442\pi$
$888$		0			0
$889$		0			0
$890$	45.0000			1.50840
$891$		0			0
$892$	17.0000			0.569202
$893$		0			0
$894$		0			0
$895$	4.50000	−	7.79423i	0.150418	−	0.260532i
$896$		0			0
$897$		0			0
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$	−12.0000			−0.400222
$900$		0			0
$901$	−9.00000			−0.299833
$902$	13.5000	+	23.3827i	0.449501	+	0.778558i
$903$		0			0
$904$	−7.50000	+	12.9904i	−0.249446	+	0.432054i
$905$	15.0000	−	25.9808i	0.498617	−	0.863630i
$906$		0			0
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$	−9.00000			−0.298675
$909$		0			0
$910$		0			0
$911$	4.50000	+	7.79423i	0.149092	+	0.258234i	0.930892	−	0.365295i	$-0.119032\pi$
$911$	4.50000	+	7.79423i	0.149092	+	0.258234i	−0.781800	+	0.623529i	$0.785698\pi$
$912$		0			0
$913$	4.50000	−	7.79423i	0.148928	−	0.257951i
$914$	−17.0000	+	29.4449i	−0.562310	+	0.973950i
$915$		0			0
$916$	−8.50000	−	14.7224i	−0.280848	−	0.486443i
$917$		0			0
$918$		0			0
$919$	−1.00000			−0.0329870			−0.0164935	−	0.999864i	$-0.505250\pi$
$919$	−1.00000			−0.0329870			−0.0164935	+	0.999864i	$0.505250\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$		0			0
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$		0			0
$924$		0			0
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$	−35.0000			−1.15017
$927$		0			0
$928$	−3.00000			−0.0984798
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$		0			0
$932$	13.5000	−	23.3827i	0.442207	−	0.765925i
$933$		0			0
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$	−27.0000			−0.882994
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.0290288	−	0.999579i	$-0.490759\pi$
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.851146	−	0.524929i	$-0.175908\pi$
$942$		0			0
$943$	−13.5000	−	23.3827i	−0.439620	−	0.761445i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−33.0000			−1.07292
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	−27.5000	+	47.6314i	−0.892688	+	1.54618i
$950$	10.0000	−	17.3205i	0.324443	−	0.561951i
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	−36.0000			−1.16493
$956$	13.5000	+	23.3827i	0.436621	+	0.756250i
$957$		0			0
$958$	4.50000	−	7.79423i	0.145388	−	0.251820i
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	35.0000			1.12845
$963$		0			0
$964$	23.0000			0.740780
$965$	−21.0000	−	36.3731i	−0.676014	−	1.17089i
$966$		0			0
$967$	24.5000	−	42.4352i	0.787867	−	1.36463i	−0.139404	−	0.990236i	$-0.544519\pi$
$967$	24.5000	−	42.4352i	0.787867	−	1.36463i	0.927271	−	0.374390i	$-0.122148\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		0			0
$970$	−1.50000	−	2.59808i	−0.0481621	−	0.0834192i
$971$	27.0000			0.866471			0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000			0.866471			0.433236	+	0.901281i	$0.357372\pi$
$972$		0			0
$973$		0			0
$974$	−15.5000	−	26.8468i	−0.496652	−	0.860227i
$975$		0			0
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$		0			0
$979$	22.5000	+	38.9711i	0.719103	+	1.24552i
$980$		0			0
$981$		0			0
$982$	−39.0000			−1.24454
$983$	−10.5000	−	18.1865i	−0.334898	−	0.580060i	0.648567	−	0.761157i	$-0.275369\pi$
$983$	−10.5000	−	18.1865i	−0.334898	−	0.580060i	−0.983465	+	0.181097i	$0.942035\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−4.50000	+	7.79423i	−0.143309	+	0.248219i
$987$		0			0
$988$	−12.5000	−	21.6506i	−0.397678	−	0.688798i
$989$	33.0000			1.04934
$990$		0			0
$991$	29.0000			0.921215			0.460608	−	0.887604i	$-0.347632\pi$
$991$	29.0000			0.921215			0.460608	+	0.887604i	$0.347632\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$		0			0
$995$	10.5000	−	18.1865i	0.332872	−	0.576552i
$996$		0			0
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$	−11.0000			−0.348199
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.e.1765.1		2
3.2	odd	2		882.2.f.e.589.1		2
7.2	even	3		378.2.h.b.361.1		2
7.3	odd	6		2646.2.e.e.1549.1		2
7.4	even	3		378.2.e.a.37.1		2
7.5	odd	6		2646.2.h.f.361.1		2
7.6	odd	2		2646.2.f.i.1765.1		2
9.2	odd	6		882.2.f.e.295.1		2
9.4	even	3		7938.2.a.o.1.1		1
9.5	odd	6		7938.2.a.r.1.1		1
9.7	even	3	inner	2646.2.f.e.883.1		2
21.2	odd	6		126.2.h.a.67.1	yes	2
21.5	even	6		882.2.h.e.67.1		2
21.11	odd	6		126.2.e.b.121.1	yes	2
21.17	even	6		882.2.e.h.373.1		2
21.20	even	2		882.2.f.a.589.1		2
28.11	odd	6		3024.2.q.a.2305.1		2
28.23	odd	6		3024.2.t.f.1873.1		2
63.2	odd	6		126.2.e.b.25.1	✓	2
63.4	even	3		1134.2.g.f.163.1		2
63.11	odd	6		126.2.h.a.79.1	yes	2
63.13	odd	6		7938.2.a.c.1.1		1
63.16	even	3		378.2.e.a.235.1		2
63.20	even	6		882.2.f.a.295.1		2
63.23	odd	6		1134.2.g.d.487.1		2
63.25	even	3		378.2.h.b.289.1		2
63.32	odd	6		1134.2.g.d.163.1		2
63.34	odd	6		2646.2.f.i.883.1		2
63.38	even	6		882.2.h.e.79.1		2
63.41	even	6		7938.2.a.bd.1.1		1
63.47	even	6		882.2.e.h.655.1		2
63.52	odd	6		2646.2.h.f.667.1		2
63.58	even	3		1134.2.g.f.487.1		2
63.61	odd	6		2646.2.e.e.2125.1		2
84.11	even	6		1008.2.q.e.625.1		2
84.23	even	6		1008.2.t.c.193.1		2
252.11	even	6		1008.2.t.c.961.1		2
252.79	odd	6		3024.2.q.a.2881.1		2
252.151	odd	6		3024.2.t.f.289.1		2
252.191	even	6		1008.2.q.e.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	63.2	odd	6
126.2.e.b.121.1	yes	2	21.11	odd	6
126.2.h.a.67.1	yes	2	21.2	odd	6
126.2.h.a.79.1	yes	2	63.11	odd	6
378.2.e.a.37.1		2	7.4	even	3
378.2.e.a.235.1		2	63.16	even	3
378.2.h.b.289.1		2	63.25	even	3
378.2.h.b.361.1		2	7.2	even	3
882.2.e.h.373.1		2	21.17	even	6
882.2.e.h.655.1		2	63.47	even	6
882.2.f.a.295.1		2	63.20	even	6
882.2.f.a.589.1		2	21.20	even	2
882.2.f.e.295.1		2	9.2	odd	6
882.2.f.e.589.1		2	3.2	odd	2
882.2.h.e.67.1		2	21.5	even	6
882.2.h.e.79.1		2	63.38	even	6
1008.2.q.e.529.1		2	252.191	even	6
1008.2.q.e.625.1		2	84.11	even	6
1008.2.t.c.193.1		2	84.23	even	6
1008.2.t.c.961.1		2	252.11	even	6
1134.2.g.d.163.1		2	63.32	odd	6
1134.2.g.d.487.1		2	63.23	odd	6
1134.2.g.f.163.1		2	63.4	even	3
1134.2.g.f.487.1		2	63.58	even	3
2646.2.e.e.1549.1		2	7.3	odd	6
2646.2.e.e.2125.1		2	63.61	odd	6
2646.2.f.e.883.1		2	9.7	even	3	inner
2646.2.f.e.1765.1		2	1.1	even	1	trivial
2646.2.f.i.883.1		2	63.34	odd	6
2646.2.f.i.1765.1		2	7.6	odd	2
2646.2.h.f.361.1		2	7.5	odd	6
2646.2.h.f.667.1		2	63.52	odd	6
3024.2.q.a.2305.1		2	28.11	odd	6
3024.2.q.a.2881.1		2	252.79	odd	6
3024.2.t.f.289.1		2	252.151	odd	6
3024.2.t.f.1873.1		2	28.23	odd	6
7938.2.a.c.1.1		1	63.13	odd	6
7938.2.a.o.1.1		1	9.4	even	3
7938.2.a.r.1.1		1	9.5	odd	6
7938.2.a.bd.1.1		1	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{8} -3.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} +5.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{26} +(-1.50000 - 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} -7.00000 q^{37} +(2.50000 + 4.33013i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-4.50000 + 7.79423i) q^{41} +(-5.50000 - 9.52628i) q^{43} +3.00000 q^{44} -3.00000 q^{46} +(2.00000 - 3.46410i) q^{50} +(-2.50000 - 4.33013i) q^{52} +3.00000 q^{53} +9.00000 q^{55} +(1.50000 - 2.59808i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-7.50000 - 12.9904i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +11.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(-4.00000 - 6.92820i) q^{79} +3.00000 q^{80} -9.00000 q^{82} +(1.50000 + 2.59808i) q^{83} +(4.50000 - 7.79423i) q^{85} +(5.50000 - 9.52628i) q^{86} +(1.50000 + 2.59808i) q^{88} -15.0000 q^{89} +(-1.50000 - 2.59808i) q^{92} +(-7.50000 + 12.9904i) q^{95} +(0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 3 q^{5} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 3 * q^5 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 3 q^{5} - 2 q^{8} - 6 q^{10} - 3 q^{11} - 5 q^{13} - q^{16} - 6 q^{17} + 10 q^{19} - 3 q^{20} + 3 q^{22} - 3 q^{23} - 4 q^{25} - 10 q^{26} - 3 q^{29} + 4 q^{31} + q^{32} - 3 q^{34} - 14 q^{37} + 5 q^{38} + 3 q^{40} - 9 q^{41} - 11 q^{43} + 6 q^{44} - 6 q^{46} + 4 q^{50} - 5 q^{52} + 6 q^{53} + 18 q^{55} + 3 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{62} + 2 q^{64} - 15 q^{65} + 4 q^{67} + 3 q^{68} + 22 q^{73} - 7 q^{74} - 5 q^{76} - 8 q^{79} + 6 q^{80} - 18 q^{82} + 3 q^{83} + 9 q^{85} + 11 q^{86} + 3 q^{88} - 30 q^{89} - 3 q^{92} - 15 q^{95} + q^{97}+O(q^{100}) \) 2 * q + q^2 - q^4 - 3 * q^5 - 2 * q^8 - 6 * q^10 - 3 * q^11 - 5 * q^13 - q^16 - 6 * q^17 + 10 * q^19 - 3 * q^20 + 3 * q^22 - 3 * q^23 - 4 * q^25 - 10 * q^26 - 3 * q^29 + 4 * q^31 + q^32 - 3 * q^34 - 14 * q^37 + 5 * q^38 + 3 * q^40 - 9 * q^41 - 11 * q^43 + 6 * q^44 - 6 * q^46 + 4 * q^50 - 5 * q^52 + 6 * q^53 + 18 * q^55 + 3 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 15 * q^65 + 4 * q^67 + 3 * q^68 + 22 * q^73 - 7 * q^74 - 5 * q^76 - 8 * q^79 + 6 * q^80 - 18 * q^82 + 3 * q^83 + 9 * q^85 + 11 * q^86 + 3 * q^88 - 30 * q^89 - 3 * q^92 - 15 * q^95 + q^97

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