LMFDB - Embedded newform 2646.2.f.i.883.1

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:	$0$
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 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.883
Dual form			2646.2.f.i.1765.1

$q$-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 $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		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	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	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	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		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	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	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	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−3.00000			−0.442326
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		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	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	−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	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−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	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−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	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−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	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$		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	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		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	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$		0			0
$100$	4.00000			0.400000
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	−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	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		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	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$		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	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		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	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	−0.998228	−	0.0595022i	$-0.981049\pi$
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	0.550645	+	0.834740i	$0.314382\pi$
$152$	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	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	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	$-0.203697\pi$
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$168$		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	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		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	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		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	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	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	$-0.420191\pi$
$199$	7.00000			0.496217			0.248108	+	0.968732i	$0.420191\pi$
$200$	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	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	−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	−0.427443	−	0.904042i	$-0.640586\pi$
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	0.996645	−	0.0818447i	$-0.0260811\pi$
$224$		0			0
$225$		0			0
$226$	15.0000			0.997785
$227$	−4.50000	+	7.79423i	−0.298675	+	0.517321i	−0.975833	−	0.218517i	$-0.929878\pi$
$227$	−4.50000	+	7.79423i	−0.298675	+	0.517321i	0.677158	+	0.735838i	$0.263211\pi$
$228$		0			0
$229$	8.50000	+	14.7224i	0.561696	+	0.972886i	0.997349	+	0.0727709i	$0.0231842\pi$
$229$	8.50000	+	14.7224i	0.561696	+	0.972886i	−0.435653	+	0.900115i	$0.643482\pi$
$230$	−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	0.858623	+	0.512607i	$0.171320\pi$
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.0146191	+	0.999893i	$0.495346\pi$
$240$		0			0
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	−0.211360	−	0.977408i	$-0.567789\pi$
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	0.952141	−	0.305661i	$-0.0988773\pi$
$242$	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	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		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	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$		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	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$		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	$-0.278853\pi$
$269$	21.0000			1.28039			0.640196	+	0.768211i	$0.278853\pi$
$270$		0			0
$271$	13.0000			0.789694			0.394847	−	0.918747i	$-0.370798\pi$
$271$	13.0000			0.789694			0.394847	+	0.918747i	$0.370798\pi$
$272$	−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	−0.741512	−	0.670940i	$-0.765891\pi$
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	0.951807	+	0.306699i	$0.0992243\pi$
$278$	5.00000			0.299880
$279$		0			0
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	0.960076	−	0.279741i	$-0.0902485\pi$
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	−0.722300	+	0.691580i	$0.756915\pi$
$284$		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	0.926777	+	0.375613i	$0.122568\pi$
$293$	13.5000	+	23.3827i	0.788678	+	1.36603i	−0.138098	+	0.990419i	$0.544099\pi$
$294$		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	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$		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	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	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	0.974701	+	0.223513i	$0.0717525\pi$
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	−0.293783	+	0.955872i	$0.594914\pi$
$338$	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	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	−0.791325	−	0.611396i	$-0.790608\pi$
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	0.925147	+	0.379610i	$0.123942\pi$
$350$		0			0
$351$		0			0
$352$	−3.00000			−0.159901
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	0.960574	+	0.278024i	$0.0896796\pi$
$354$		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	$-0.841642\pi$
$367$	−0.500000	+	0.866025i	−0.0260998	+	0.0452062i	0.852680	+	0.522433i	$0.174975\pi$
$368$	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	0.557584	−	0.830120i	$-0.311728\pi$
$373$	−8.50000	−	14.7224i	−0.440113	−	0.762299i	−0.997697	+	0.0678218i	$0.978395\pi$
$374$	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	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$		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	−0.729103	−	0.684403i	$-0.760063\pi$
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	0.957263	+	0.289220i	$0.0933960\pi$
$390$		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	$-0.759427\pi$
$397$	−29.0000			−1.45547			−0.727734	+	0.685859i	$0.759427\pi$
$398$	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	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$		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	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$	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	$-0.143320\pi$
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	−0.827057	+	0.562118i	$0.809987\pi$
$420$		0			0
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	−0.189740	−	0.981834i	$-0.560764\pi$
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	0.945163	−	0.326598i	$-0.105902\pi$
$422$	−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	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		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	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$	15.0000			0.713477
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$		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	−0.127469	−	0.991843i	$-0.540685\pi$
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	0.922695	−	0.385530i	$-0.125981\pi$
$458$	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	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		0			0
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	−0.910546	−	0.413407i	$-0.864339\pi$
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	0.0972525	−	0.995260i	$-0.468995\pi$
$464$	−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	$-0.522112\pi$
$467$	−3.00000			−0.138823			−0.0694117	+	0.997588i	$0.522112\pi$
$468$		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	$-0.767415\pi$
$479$	4.50000	−	7.79423i	0.205610	−	0.356127i	0.950327	+	0.311253i	$0.100749\pi$
$480$		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	−0.851314	−	0.524656i	$-0.824194\pi$
$491$	−19.5000	−	33.7750i	−0.880023	−	1.52424i	−0.0287085	−	0.999588i	$-0.509139\pi$
$492$		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	0.716258	−	0.697835i	$-0.245853\pi$
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	−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	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		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	0.993061	+	0.117602i	$0.0375208\pi$
$509$	13.5000	+	23.3827i	0.598377	+	1.03642i	−0.394684	+	0.918817i	$0.629146\pi$
$510$		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	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$	7.00000			0.306089			0.153044	−	0.988219i	$-0.451092\pi$
$523$	7.00000			0.306089			0.153044	+	0.988219i	$0.451092\pi$
$524$	−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	−0.959320	−	0.282321i	$-0.908896\pi$
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	0.724157	+	0.689635i	$0.242229\pi$
$548$	−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	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		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	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	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	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	−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	−0.293640	−	0.955916i	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$		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	$-0.641904\pi$
$593$	−21.0000			−0.862367			−0.431183	+	0.902264i	$0.641904\pi$
$594$		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	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−0.500000	+	0.866025i	−0.0203954	+	0.0353259i	−0.876043	−	0.482233i	$-0.839826\pi$
$601$	−0.500000	+	0.866025i	−0.0203954	+	0.0353259i	0.855648	+	0.517559i	$0.173159\pi$
$602$		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	−0.859237	−	0.511578i	$-0.829061\pi$
$607$	−21.5000	−	37.2391i	−0.872658	−	1.51149i	−0.0134214	−	0.999910i	$-0.504272\pi$
$608$	−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	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	−0.991325	−	0.131434i	$-0.958042\pi$
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	0.609488	+	0.792796i	$0.291375\pi$
$620$	−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	−0.0472793	+	0.998882i	$0.515055\pi$
$641$	−22.5000	+	38.9711i	−0.888697	+	1.53927i	−0.841417	+	0.540386i	$0.818278\pi$
$642$		0			0
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	0.996379	+	0.0850262i	$0.0270974\pi$
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	−0.424555	+	0.905402i	$0.639569\pi$
$644$		0			0
$645$		0			0
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$		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	0.940541	−	0.339680i	$-0.110319\pi$
$653$	4.50000	+	7.79423i	0.176099	+	0.305012i	−0.764442	+	0.644692i	$0.776986\pi$
$654$		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	−0.183436	−	0.983032i	$-0.558722\pi$
$659$	19.5000	−	33.7750i	0.759612	−	1.31569i	0.943049	−	0.332655i	$-0.107945\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	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	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$	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	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$		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	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$	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	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		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	$-0.240809\pi$
$719$	39.0000			1.45445			0.727227	+	0.686397i	$0.240809\pi$
$720$		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	$-0.803777\pi$
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	0.908655	+	0.417548i	$0.137111\pi$
$728$		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	0.944281	+	0.329141i	$0.106759\pi$
$733$	20.5000	+	35.5070i	0.757185	+	1.31148i	−0.187096	+	0.982342i	$0.559908\pi$
$734$	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	0.892228	−	0.451585i	$-0.149141\pi$
$743$	1.50000	+	2.59808i	0.0550297	+	0.0953142i	−0.837198	+	0.546899i	$0.815808\pi$
$744$		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	−0.999424	−	0.0339490i	$-0.989192\pi$
$751$	−14.5000	−	25.1147i	−0.529113	−	0.916450i	0.470311	−	0.882501i	$-0.344142\pi$
$752$		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	$-0.183983\pi$
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	−0.891932	+	0.452170i	$0.850650\pi$
$762$		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	$-0.172406\pi$
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	−0.874900	+	0.484304i	$0.839073\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	21.0000			0.755318			0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000			0.755318			0.377659	+	0.925945i	$0.376729\pi$
$774$		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	0.929467	+	0.368906i	$0.120268\pi$
$787$	22.0000	+	38.1051i	0.784215	+	1.35830i	−0.145251	+	0.989395i	$0.546399\pi$
$788$	−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	$-0.00795805\pi$
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	−0.521493	+	0.853256i	$0.674625\pi$
$798$		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	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		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	−0.181250	+	0.983437i	$0.558014\pi$
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.761056	+	0.648686i	$0.775319\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	−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	$-0.752208\pi$
$829$	−41.0000			−1.42399			−0.711994	+	0.702185i	$0.752208\pi$
$830$	−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	−0.303773	−	0.952745i	$-0.598246\pi$
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	0.976987	−	0.213298i	$-0.0684204\pi$
$840$		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	$-0.739334\pi$
$853$	8.50000	−	14.7224i	0.291034	−	0.504086i	0.974055	+	0.226313i	$0.0726672\pi$
$854$		0			0
$855$		0			0
$856$	−15.0000			−0.512689
$857$	16.5000	−	28.5788i	0.563629	−	0.976235i	−0.433546	−	0.901131i	$-0.642738\pi$
$857$	16.5000	−	28.5788i	0.563629	−	0.976235i	0.997176	−	0.0751033i	$-0.0239287\pi$
$858$		0			0
$859$	5.50000	+	9.52628i	0.187658	+	0.325032i	0.944469	−	0.328601i	$-0.106577\pi$
$859$	5.50000	+	9.52628i	0.187658	+	0.325032i	−0.756811	+	0.653633i	$0.773244\pi$
$860$	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	0.958560	+	0.284892i	$0.0919577\pi$
$877$	21.5000	+	37.2391i	0.726003	+	1.25747i	−0.232556	+	0.972583i	$0.574709\pi$
$878$	−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	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		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	0.981957	+	0.189102i	$0.0605577\pi$
$887$	19.5000	+	33.7750i	0.654746	+	1.13405i	−0.327212	+	0.944951i	$0.606109\pi$
$888$		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	−0.971936	−	0.235247i	$-0.924410\pi$
$907$	−8.50000	+	14.7224i	−0.282238	+	0.488850i	0.689698	+	0.724097i	$0.257743\pi$
$908$	9.00000			0.298675
$909$		0			0
$910$		0			0
$911$	4.50000	−	7.79423i	0.149092	−	0.258234i	−0.781800	−	0.623529i	$-0.785698\pi$
$911$	4.50000	−	7.79423i	0.149092	−	0.258234i	0.930892	+	0.365295i	$0.119032\pi$
$912$		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	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		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	$-0.312578\pi$
$937$	34.0000			1.11073			0.555366	+	0.831606i	$0.312578\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.851146	−	0.524929i	$-0.824092\pi$
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.0290288	−	0.999579i	$-0.509241\pi$
$942$		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	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$		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	0.927271	+	0.374390i	$0.122148\pi$
$967$	24.5000	+	42.4352i	0.787867	+	1.36463i	−0.139404	+	0.990236i	$0.544519\pi$
$968$	−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	$-0.642628\pi$
$971$	−27.0000			−0.866471			−0.433236	+	0.901281i	$0.642628\pi$
$972$		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	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		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	$-0.724631\pi$
$983$	10.5000	−	18.1865i	0.334898	−	0.580060i	0.983465	+	0.181097i	$0.0579648\pi$
$984$		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	−0.334063	−	0.942551i	$-0.608420\pi$
$997$	20.5000	−	35.5070i	0.649242	−	1.12452i	0.983304	−	0.181968i	$-0.0582469\pi$
$998$	−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.i.883.1		2
3.2	odd	2		882.2.f.a.295.1		2
7.2	even	3		2646.2.e.e.2125.1		2
7.3	odd	6		378.2.h.b.289.1		2
7.4	even	3		2646.2.h.f.667.1		2
7.5	odd	6		378.2.e.a.235.1		2
7.6	odd	2		2646.2.f.e.883.1		2
9.2	odd	6		7938.2.a.bd.1.1		1
9.4	even	3	inner	2646.2.f.i.1765.1		2
9.5	odd	6		882.2.f.a.589.1		2
9.7	even	3		7938.2.a.c.1.1		1
21.2	odd	6		882.2.e.h.655.1		2
21.5	even	6		126.2.e.b.25.1	✓	2
21.11	odd	6		882.2.h.e.79.1		2
21.17	even	6		126.2.h.a.79.1	yes	2
21.20	even	2		882.2.f.e.295.1		2
28.3	even	6		3024.2.t.f.289.1		2
28.19	even	6		3024.2.q.a.2881.1		2
63.4	even	3		2646.2.e.e.1549.1		2
63.5	even	6		126.2.h.a.67.1	yes	2
63.13	odd	6		2646.2.f.e.1765.1		2
63.20	even	6		7938.2.a.r.1.1		1
63.23	odd	6		882.2.h.e.67.1		2
63.31	odd	6		378.2.e.a.37.1		2
63.32	odd	6		882.2.e.h.373.1		2
63.34	odd	6		7938.2.a.o.1.1		1
63.38	even	6		1134.2.g.d.163.1		2
63.40	odd	6		378.2.h.b.361.1		2
63.41	even	6		882.2.f.e.589.1		2
63.47	even	6		1134.2.g.d.487.1		2
63.52	odd	6		1134.2.g.f.163.1		2
63.58	even	3		2646.2.h.f.361.1		2
63.59	even	6		126.2.e.b.121.1	yes	2
63.61	odd	6		1134.2.g.f.487.1		2
84.47	odd	6		1008.2.q.e.529.1		2
84.59	odd	6		1008.2.t.c.961.1		2
252.31	even	6		3024.2.q.a.2305.1		2
252.59	odd	6		1008.2.q.e.625.1		2
252.103	even	6		3024.2.t.f.1873.1		2
252.131	odd	6		1008.2.t.c.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	21.5	even	6
126.2.e.b.121.1	yes	2	63.59	even	6
126.2.h.a.67.1	yes	2	63.5	even	6
126.2.h.a.79.1	yes	2	21.17	even	6
378.2.e.a.37.1		2	63.31	odd	6
378.2.e.a.235.1		2	7.5	odd	6
378.2.h.b.289.1		2	7.3	odd	6
378.2.h.b.361.1		2	63.40	odd	6
882.2.e.h.373.1		2	63.32	odd	6
882.2.e.h.655.1		2	21.2	odd	6
882.2.f.a.295.1		2	3.2	odd	2
882.2.f.a.589.1		2	9.5	odd	6
882.2.f.e.295.1		2	21.20	even	2
882.2.f.e.589.1		2	63.41	even	6
882.2.h.e.67.1		2	63.23	odd	6
882.2.h.e.79.1		2	21.11	odd	6
1008.2.q.e.529.1		2	84.47	odd	6
1008.2.q.e.625.1		2	252.59	odd	6
1008.2.t.c.193.1		2	252.131	odd	6
1008.2.t.c.961.1		2	84.59	odd	6
1134.2.g.d.163.1		2	63.38	even	6
1134.2.g.d.487.1		2	63.47	even	6
1134.2.g.f.163.1		2	63.52	odd	6
1134.2.g.f.487.1		2	63.61	odd	6
2646.2.e.e.1549.1		2	63.4	even	3
2646.2.e.e.2125.1		2	7.2	even	3
2646.2.f.e.883.1		2	7.6	odd	2
2646.2.f.e.1765.1		2	63.13	odd	6
2646.2.f.i.883.1		2	1.1	even	1	trivial
2646.2.f.i.1765.1		2	9.4	even	3	inner
2646.2.h.f.361.1		2	63.58	even	3
2646.2.h.f.667.1		2	7.4	even	3
3024.2.q.a.2305.1		2	252.31	even	6
3024.2.q.a.2881.1		2	28.19	even	6
3024.2.t.f.289.1		2	28.3	even	6
3024.2.t.f.1873.1		2	252.103	even	6
7938.2.a.c.1.1		1	9.7	even	3
7938.2.a.o.1.1		1	63.34	odd	6
7938.2.a.r.1.1		1	63.20	even	6
7938.2.a.bd.1.1		1	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more