LMFDB - Embedded newform 2646.2.f.a.1765.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(883,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [2,-1,0,-1,-3,0,0,2,0,6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +3.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{17} +7.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-4.50000 + 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +1.00000 q^{26} +(1.50000 + 2.59808i) q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} -1.00000 q^{37} +(-3.50000 - 6.06218i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +3.00000 q^{44} +9.00000 q^{46} +(-2.00000 + 3.46410i) q^{50} +(-0.500000 - 0.866025i) q^{52} -3.00000 q^{53} +9.00000 q^{55} +(1.50000 - 2.59808i) q^{58} +(1.00000 + 1.73205i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} -12.0000 q^{71} -11.0000 q^{73} +(0.500000 + 0.866025i) q^{74} +(-3.50000 + 6.06218i) q^{76} +(8.00000 + 13.8564i) q^{79} +3.00000 q^{80} +3.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(0.500000 - 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{89} +(-4.50000 - 7.79423i) q^{92} +(-10.5000 + 18.1865i) q^{95} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{8} + 6 q^{10} - 3 q^{11} - q^{13} - q^{16} + 6 q^{17} + 14 q^{19} - 3 q^{20} - 3 q^{22} - 9 q^{23} - 4 q^{25} + 2 q^{26} + 3 q^{29} + 8 q^{31} - q^{32} - 3 q^{34}+ \cdots - q^{97}+O(q^{100}) $ 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^8 + 6 * q^10 - 3 * q^11 - q^13 - q^16 + 6 * q^17 + 14 * q^19 - 3 * q^20 - 3 * q^22 - 9 * q^23 - 4 * q^25 + 2 * q^26 + 3 * q^29 + 8 * q^31 - q^32 - 3 * q^34 - 2 * q^37 - 7 * q^38 - 3 * q^40 - 3 * q^41 + q^43 + 6 * q^44 + 18 * q^46 - 4 * q^50 - q^52 - 6 * q^53 + 18 * q^55 + 3 * q^58 + 2 * q^61 - 16 * q^62 + 2 * q^64 - 3 * q^65 + 4 * q^67 - 3 * q^68 - 24 * q^71 - 22 * q^73 + q^74 - 7 * q^76 + 16 * q^79 + 6 * q^80 + 6 * q^82 + 9 * q^83 - 9 * q^85 + q^86 - 3 * q^88 + 6 * q^89 - 9 * q^92 - 21 * q^95 - q^97

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
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		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
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.169701	+	0.985496i	$0.554280\pi$
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.768613	+	0.639713i	$0.779053\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	1.00000			0.196116
$27$		0			0
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	−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
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	9.00000			1.32698
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$		0			0
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$		0			0
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$		0			0
$76$	−3.50000	+	6.06218i	−0.401478	+	0.695379i
$77$		0			0
$78$		0			0
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.827401	+	0.561611i	$0.189818\pi$
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.0726692	+	0.997356i	$0.476848\pi$
$80$	3.00000			0.335410
$81$		0			0
$82$	3.00000			0.331295
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$		0			0
$92$	−4.50000	−	7.79423i	−0.469157	−	0.812605i
$93$		0			0
$94$		0			0
$95$	−10.5000	+	18.1865i	−1.07728	+	1.86590i
$96$		0			0
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$		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
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	0.344865	+	0.938652i	$0.387925\pi$
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$		0			0
$109$	−13.0000			−1.24517			−0.622587	−	0.782551i	$-0.713918\pi$
$109$	−13.0000			−1.24517			−0.622587	+	0.782551i	$0.713918\pi$
$110$	−4.50000	−	7.79423i	−0.429058	−	0.743151i
$111$		0			0
$112$		0			0
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$		0			0
$115$	−13.5000	−	23.3827i	−1.25888	−	2.18045i
$116$	−3.00000			−0.278543
$117$		0			0
$118$		0			0
$119$		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
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.50000	+	2.59808i	−0.131559	+	0.227866i
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$		0			0
$133$		0			0
$134$	−4.00000			−0.345547
$135$		0			0
$136$	3.00000			0.257248
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	3.00000			0.250873
$144$		0			0
$145$	−9.00000			−0.747409
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	3.50000	+	6.06218i	0.284826	+	0.493333i	0.972567	−	0.232623i	$-0.0747309\pi$
$151$	3.50000	+	6.06218i	0.284826	+	0.493333i	−0.687741	+	0.725956i	$0.741398\pi$
$152$	7.00000			0.567775
$153$		0			0
$154$		0			0
$155$	12.0000	+	20.7846i	0.963863	+	1.66946i
$156$		0			0
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.0242497	+	0.999706i	$0.507720\pi$
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.853646	+	0.520854i	$0.825614\pi$
$158$	8.00000	−	13.8564i	0.636446	−	1.10236i
$159$		0			0
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		0			0
$162$		0			0
$163$	−19.0000			−1.48819			−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000			−1.48819			−0.744097	+	0.668071i	$0.767120\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	7.50000	−	12.9904i	0.580367	−	1.00523i	−0.415068	−	0.909790i	$-0.636242\pi$
$167$	7.50000	−	12.9904i	0.580367	−	1.00523i	0.995436	−	0.0954356i	$-0.0304244\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	9.00000			0.690268
$171$		0			0
$172$	−1.00000			−0.0762493
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$		0			0
$178$	−1.50000	−	2.59808i	−0.112430	−	0.194734i
$179$	21.0000			1.56961			0.784807	−	0.619740i	$-0.212762\pi$
$179$	21.0000			1.56961			0.784807	+	0.619740i	$0.212762\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		0			0
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$		0			0
$189$		0			0
$190$	21.0000			1.52350
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		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
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	25.0000			1.77220			0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000			1.77220			0.886102	+	0.463491i	$0.153403\pi$
$200$	−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
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	13.0000			0.905753
$207$		0			0
$208$	1.00000			0.0693375
$209$	−10.5000	−	18.1865i	−0.726300	−	1.25799i
$210$		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
$214$	4.50000	+	7.79423i	0.307614	+	0.532803i
$215$	−3.00000			−0.204598
$216$		0			0
$217$		0			0
$218$	6.50000	+	11.2583i	0.440236	+	0.762510i
$219$		0			0
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$	−1.50000	+	2.59808i	−0.100901	+	0.174766i
$222$		0			0
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	0.848799	−	0.528716i	$-0.177326\pi$
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	−0.882281	+	0.470723i	$0.843993\pi$
$224$		0			0
$225$		0			0
$226$	9.00000			0.598671
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$		0			0
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$	−13.5000	+	23.3827i	−0.890164	+	1.54181i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.50000	+	2.59808i	−0.0970269	+	0.168056i	−0.910453	−	0.413613i	$-0.864267\pi$
$239$	−1.50000	+	2.59808i	−0.0970269	+	0.168056i	0.813426	+	0.581669i	$0.197600\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$	−2.00000			−0.128037
$245$		0			0
$246$		0			0
$247$	−3.50000	+	6.06218i	−0.222700	+	0.385727i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$		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
$253$	27.0000			1.69748
$254$	2.00000	+	3.46410i	0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$		0			0
$259$		0			0
$260$	3.00000			0.186052
$261$		0			0
$262$	15.0000			0.926703
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$		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
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$		0			0
$271$	−5.00000			−0.303728			−0.151864	−	0.988401i	$-0.548528\pi$
$271$	−5.00000			−0.303728			−0.151864	+	0.988401i	$0.548528\pi$
$272$	−1.50000	−	2.59808i	−0.0909509	−	0.157532i
$273$		0			0
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	7.00000			0.419832
$279$		0			0
$280$		0			0
$281$	−10.5000	−	18.1865i	−0.626377	−	1.08492i	−0.988273	−	0.152699i	$-0.951204\pi$
$281$	−10.5000	−	18.1865i	−0.626377	−	1.08492i	0.361895	−	0.932219i	$-0.382130\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$	−1.50000	−	2.59808i	−0.0886969	−	0.153627i
$287$		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
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$		0			0
$295$		0			0
$296$	−1.00000			−0.0581238
$297$		0			0
$298$	9.00000			0.521356
$299$	−4.50000	−	7.79423i	−0.260242	−	0.450752i
$300$		0			0
$301$		0			0
$302$	3.50000	−	6.06218i	0.201402	−	0.348839i
$303$		0			0
$304$	−3.50000	−	6.06218i	−0.200739	−	0.347690i
$305$	−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
$310$	12.0000	−	20.7846i	0.681554	−	1.18049i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$	22.0000			1.24153
$315$		0			0
$316$	−16.0000			−0.900070
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		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
$323$	21.0000			1.16847
$324$		0			0
$325$	4.00000			0.221880
$326$	9.50000	+	16.4545i	0.526156	+	0.911330i
$327$		0			0
$328$	−1.50000	+	2.59808i	−0.0828236	+	0.143455i
$329$		0			0
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	−9.00000			−0.493939
$333$		0			0
$334$	−15.0000			−0.820763
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	−0.632882	−	0.774248i	$-0.718128\pi$
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	0.986960	+	0.160968i	$0.0514616\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	−24.0000			−1.29967
$342$		0			0
$343$		0			0
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	0.990282	+	0.139072i	$0.0444119\pi$
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$	3.00000			0.159901
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	0.823343	−	0.567545i	$-0.192107\pi$
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	−0.903179	+	0.429263i	$0.858773\pi$
$354$		0			0
$355$	18.0000	−	31.1769i	0.955341	−	1.65470i
$356$	−1.50000	+	2.59808i	−0.0794998	+	0.137698i
$357$		0			0
$358$	−10.5000	−	18.1865i	−0.554942	−	0.961188i
$359$	−9.00000			−0.475002			−0.237501	−	0.971387i	$-0.576328\pi$
$359$	−9.00000			−0.475002			−0.237501	+	0.971387i	$0.576328\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$	1.00000	+	1.73205i	0.0525588	+	0.0910346i
$363$		0			0
$364$		0			0
$365$	16.5000	−	28.5788i	0.863649	−	1.49588i
$366$		0			0
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$	9.00000			0.469157
$369$		0			0
$370$	−3.00000			−0.155963
$371$		0			0
$372$		0			0
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−10.5000	−	18.1865i	−0.538639	−	0.932949i
$381$		0			0
$382$		0			0
$383$	−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
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	0.973601	+	0.228257i	$0.0733028\pi$
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	−0.289124	+	0.957292i	$0.593364\pi$
$390$		0			0
$391$	−13.5000	+	23.3827i	−0.682724	+	1.18251i
$392$		0			0
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−48.0000			−2.41514
$396$		0			0
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	−12.5000	−	21.6506i	−0.626568	−	1.08525i
$399$		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
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	3.00000			0.149256
$405$		0			0
$406$		0			0
$407$	1.50000	+	2.59808i	0.0743522	+	0.128782i
$408$		0			0
$409$	−17.0000	+	29.4449i	−0.840596	+	1.45595i	0.0487958	+	0.998809i	$0.484462\pi$
$409$	−17.0000	+	29.4449i	−0.840596	+	1.45595i	−0.889392	+	0.457146i	$0.848872\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$		0			0
$412$	−6.50000	−	11.2583i	−0.320232	−	0.554658i
$413$		0			0
$414$		0			0
$415$	−27.0000			−1.32538
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	−10.5000	+	18.1865i	−0.513572	+	0.889532i
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$		0			0
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	−0.878582	−	0.477592i	$-0.841510\pi$
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	0.0256838	−	0.999670i	$-0.491824\pi$
$422$	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
$428$	4.50000	−	7.79423i	0.217516	−	0.376748i
$429$		0			0
$430$	1.50000	+	2.59808i	0.0723364	+	0.125290i
$431$	−27.0000			−1.30054			−0.650272	−	0.759701i	$-0.725345\pi$
$431$	−27.0000			−1.30054			−0.650272	+	0.759701i	$0.725345\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$		0			0
$436$	6.50000	−	11.2583i	0.311294	−	0.539176i
$437$	−31.5000	+	54.5596i	−1.50685	+	2.60994i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$	3.00000			0.142695
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$		0			0
$445$	−4.50000	+	7.79423i	−0.213320	+	0.369482i
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$		0			0
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	9.00000			0.423793
$452$	−4.50000	−	7.79423i	−0.211662	−	0.366610i
$453$		0			0
$454$	1.50000	−	2.59808i	0.0703985	−	0.121934i
$455$		0			0
$456$		0			0
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	13.0000			0.607450
$459$		0			0
$460$	27.0000			1.25888
$461$	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
$463$	−20.5000	+	35.5070i	−0.952716	+	1.65015i	−0.213205	+	0.977007i	$0.568390\pi$
$463$	−20.5000	+	35.5070i	−0.952716	+	1.65015i	−0.739511	+	0.673145i	$0.764943\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$		0			0
$466$	1.50000	+	2.59808i	0.0694862	+	0.120354i
$467$	−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
$472$		0			0
$473$	1.50000	−	2.59808i	0.0689701	−	0.119460i
$474$		0			0
$475$	−14.0000	−	24.2487i	−0.642364	−	1.11261i
$476$		0			0
$477$		0			0
$478$	3.00000			0.137217
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	0.898257	−	0.439470i	$-0.144834\pi$
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	−0.829721	+	0.558179i	$0.811500\pi$
$480$		0			0
$481$	0.500000	−	0.866025i	0.0227980	−	0.0394874i
$482$	−6.50000	+	11.2583i	−0.296067	+	0.512803i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	3.00000			0.136223
$486$		0			0
$487$	−25.0000			−1.13286			−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−25.0000			−1.13286			−0.566429	+	0.824110i	$0.691675\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$		0			0
$490$		0			0
$491$	10.5000	−	18.1865i	0.473858	−	0.820747i	−0.525694	−	0.850674i	$-0.676194\pi$
$491$	10.5000	−	18.1865i	0.473858	−	0.820747i	0.999552	+	0.0299272i	$0.00952753\pi$
$492$		0			0
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$	7.00000			0.314945
$495$		0			0
$496$	−8.00000			−0.359211
$497$		0			0
$498$		0			0
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	−13.5000	−	23.3827i	−0.600148	−	1.03949i
$507$		0			0
$508$	2.00000	−	3.46410i	0.0887357	−	0.153695i
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	−0.748894	−	0.662690i	$-0.769415\pi$
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	0.948353	+	0.317217i	$0.102748\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−21.0000			−0.926270
$515$	−19.5000	−	33.7750i	−0.859273	−	1.48830i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−1.50000	−	2.59808i	−0.0657794	−	0.113933i
$521$	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	$0.451092\pi$
$524$	−7.50000	−	12.9904i	−0.327639	−	0.567487i
$525$		0			0
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$	−9.00000			−0.390935
$531$		0			0
$532$		0			0
$533$	−1.50000	−	2.59808i	−0.0649722	−	0.112535i
$534$		0			0
$535$	13.5000	−	23.3827i	0.583656	−	1.01092i
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$		0			0
$538$	−7.50000	−	12.9904i	−0.323348	−	0.560055i
$539$		0			0
$540$		0			0
$541$	11.0000			0.472927			0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000			0.472927			0.236463	+	0.971640i	$0.424012\pi$
$542$	2.50000	+	4.33013i	0.107384	+	0.185995i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	19.5000	−	33.7750i	0.835288	−	1.44676i
$546$		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	$0.908896\pi$
$548$	9.00000			0.384461
$549$		0			0
$550$	12.0000			0.511682
$551$	10.5000	+	18.1865i	0.447315	+	0.774772i
$552$		0			0
$553$		0			0
$554$	0.500000	−	0.866025i	0.0212430	−	0.0367939i
$555$		0			0
$556$	−3.50000	−	6.06218i	−0.148433	−	0.257094i
$557$	9.00000			0.381342			0.190671	−	0.981654i	$-0.438934\pi$
$557$	9.00000			0.381342			0.190671	+	0.981654i	$0.438934\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		0			0
$562$	−10.5000	+	18.1865i	−0.442916	+	0.767153i
$563$	−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
$565$	−13.5000	−	23.3827i	−0.567949	−	0.983717i
$566$	4.00000			0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$		0			0
$574$		0			0
$575$	36.0000			1.50130
$576$		0			0
$577$	25.0000			1.04076			0.520382	−	0.853934i	$-0.325790\pi$
$577$	25.0000			1.04076			0.520382	+	0.853934i	$0.325790\pi$
$578$	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
$586$	−9.00000			−0.371787
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$	28.0000	−	48.4974i	1.15372	−	1.99830i
$590$		0			0
$591$		0			0
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	39.0000			1.60154			0.800769	−	0.598973i	$-0.204424\pi$
$593$	39.0000			1.60154			0.800769	+	0.598973i	$0.204424\pi$
$594$		0			0
$595$		0			0
$596$	−4.50000	−	7.79423i	−0.184327	−	0.319264i
$597$		0			0
$598$	−4.50000	+	7.79423i	−0.184019	+	0.318730i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	−0.999934	−	0.0114528i	$-0.996354\pi$
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	0.490049	−	0.871695i	$-0.336979\pi$
$602$		0			0
$603$		0			0
$604$	−7.00000			−0.284826
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	−0.967256	−	0.253804i	$-0.918318\pi$
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	0.703429	+	0.710766i	$0.251651\pi$
$608$	−3.50000	+	6.06218i	−0.141944	+	0.245854i
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$		0			0
$612$		0			0
$613$	23.0000			0.928961			0.464481	−	0.885583i	$-0.346241\pi$
$613$	23.0000			0.928961			0.464481	+	0.885583i	$0.346241\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$	−22.5000	+	38.9711i	−0.905816	+	1.56892i	−0.0859976	+	0.996295i	$0.527408\pi$
$617$	−22.5000	+	38.9711i	−0.905816	+	1.56892i	−0.819818	+	0.572624i	$0.805926\pi$
$618$		0			0
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	−0.643094	+	0.765787i	$0.722350\pi$
$620$	−24.0000			−0.963863
$621$		0			0
$622$	−24.0000			−0.962312
$623$		0			0
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−5.00000	+	8.66025i	−0.199840	+	0.346133i
$627$		0			0
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$	−3.00000			−0.119618
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	8.00000	+	13.8564i	0.318223	+	0.551178i
$633$		0			0
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$		0			0
$637$		0			0
$638$	−9.00000			−0.356313
$639$		0			0
$640$	3.00000			0.118585
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	−0.424555	−	0.905402i	$-0.639569\pi$
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	0.996379	−	0.0850262i	$-0.0270974\pi$
$644$		0			0
$645$		0			0
$646$	−10.5000	−	18.1865i	−0.413117	−	0.715540i
$647$	−21.0000			−0.825595			−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000			−0.825595			−0.412798	+	0.910823i	$0.635448\pi$
$648$		0			0
$649$		0			0
$650$	−2.00000	−	3.46410i	−0.0784465	−	0.135873i
$651$		0			0
$652$	9.50000	−	16.4545i	0.372049	−	0.644407i
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	−0.681137	−	0.732156i	$-0.738514\pi$
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	0.974634	+	0.223803i	$0.0718474\pi$
$654$		0			0
$655$	−22.5000	−	38.9711i	−0.879148	−	1.52273i
$656$	3.00000			0.117130
$657$		0			0
$658$		0			0
$659$	1.50000	+	2.59808i	0.0584317	+	0.101207i	0.893762	−	0.448542i	$-0.148057\pi$
$659$	1.50000	+	2.59808i	0.0584317	+	0.101207i	−0.835330	+	0.549749i	$0.814723\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−4.00000	+	6.92820i	−0.155464	+	0.269272i
$663$		0			0
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$		0			0
$666$		0			0
$667$	−27.0000			−1.04544
$668$	7.50000	+	12.9904i	0.290184	+	0.502613i
$669$		0			0
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	3.00000	−	5.19615i	0.115814	−	0.200595i
$672$		0			0
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$	−13.0000			−0.500741
$675$		0			0
$676$	−12.0000			−0.461538
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	0.995877	+	0.0907112i	$0.0289140\pi$
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	−0.419380	+	0.907811i	$0.637753\pi$
$678$		0			0
$679$		0			0
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$		0			0
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$	9.00000			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$684$		0			0
$685$	27.0000			1.03162
$686$		0			0
$687$		0			0
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	1.50000	−	2.59808i	0.0571454	−	0.0989788i
$690$		0			0
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	0.892458	+	0.451130i	$0.148979\pi$
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	−0.0555386	+	0.998457i	$0.517688\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−10.5000	−	18.1865i	−0.398288	−	0.689855i
$696$		0			0
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$	11.5000	−	19.9186i	0.435281	−	0.753930i
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	−7.00000			−0.264010
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	−1.50000	+	2.59808i	−0.0564532	+	0.0977799i
$707$		0			0
$708$		0			0
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$	−36.0000			−1.35106
$711$		0			0
$712$	3.00000			0.112430
$713$	36.0000	+	62.3538i	1.34821	+	2.33517i
$714$		0			0
$715$	−4.50000	+	7.79423i	−0.168290	+	0.291488i
$716$	−10.5000	+	18.1865i	−0.392403	+	0.679663i
$717$		0			0
$718$	4.50000	+	7.79423i	0.167939	+	0.290878i
$719$	−15.0000			−0.559406			−0.279703	−	0.960087i	$-0.590236\pi$
$719$	−15.0000			−0.559406			−0.279703	+	0.960087i	$0.590236\pi$
$720$		0			0
$721$		0			0
$722$	−15.0000	−	25.9808i	−0.558242	−	0.966904i
$723$		0			0
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	6.00000	−	10.3923i	0.222834	−	0.385961i
$726$		0			0
$727$	−6.50000	−	11.2583i	−0.241072	−	0.417548i	0.719948	−	0.694028i	$-0.244166\pi$
$727$	−6.50000	−	11.2583i	−0.241072	−	0.417548i	−0.961020	+	0.276479i	$0.910832\pi$
$728$		0			0
$729$		0			0
$730$	−33.0000			−1.22138
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	−0.875112	−	0.483921i	$-0.839212\pi$
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	0.856644	+	0.515908i	$0.172546\pi$
$734$	8.50000	−	14.7224i	0.313741	−	0.543415i
$735$		0			0
$736$	−4.50000	−	7.79423i	−0.165872	−	0.287299i
$737$	−12.0000			−0.442026
$738$		0			0
$739$	23.0000			0.846069			0.423034	−	0.906114i	$-0.360965\pi$
$739$	23.0000			0.846069			0.423034	+	0.906114i	$0.360965\pi$
$740$	1.50000	+	2.59808i	0.0551411	+	0.0955072i
$741$		0			0
$742$		0			0
$743$	10.5000	−	18.1865i	0.385208	−	0.667199i	−0.606590	−	0.795015i	$-0.707463\pi$
$743$	10.5000	−	18.1865i	0.385208	−	0.667199i	0.991798	+	0.127815i	$0.0407965\pi$
$744$		0			0
$745$	−13.5000	−	23.3827i	−0.494602	−	0.856675i
$746$	−13.0000			−0.475964
$747$		0			0
$748$	9.00000			0.329073
$749$		0			0
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$		0			0
$753$		0			0
$754$	1.50000	+	2.59808i	0.0546268	+	0.0946164i
$755$	−21.0000			−0.764268
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	14.0000	+	24.2487i	0.508503	+	0.880753i
$759$		0			0
$760$	−10.5000	+	18.1865i	−0.380875	+	0.659695i
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	−0.0932544	−	0.995642i	$-0.529727\pi$
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	0.908879	−	0.417061i	$-0.136940\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	15.0000			0.541972
$767$		0			0
$768$		0			0
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	27.0000			0.971123			0.485561	−	0.874203i	$-0.338615\pi$
$773$	27.0000			0.971123			0.485561	+	0.874203i	$0.338615\pi$
$774$		0			0
$775$	−32.0000			−1.14947
$776$	−0.500000	−	0.866025i	−0.0179490	−	0.0310885i
$777$		0			0
$778$	13.5000	−	23.3827i	0.483998	−	0.838310i
$779$	−10.5000	+	18.1865i	−0.376202	+	0.651600i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	27.0000			0.965518
$783$		0			0
$784$		0			0
$785$	−33.0000	−	57.1577i	−1.17782	−	2.04004i
$786$		0			0
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$	24.0000	+	41.5692i	0.853882	+	1.47897i
$791$		0			0
$792$		0			0
$793$	−2.00000			−0.0710221
$794$	−6.50000	−	11.2583i	−0.230676	−	0.399543i
$795$		0			0
$796$	−12.5000	+	21.6506i	−0.443051	+	0.767386i
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	−0.617933	−	0.786231i	$-0.712030\pi$
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	0.989862	+	0.142031i	$0.0453631\pi$
$798$		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
$806$	4.00000	−	6.92820i	0.140894	−	0.244036i
$807$		0			0
$808$	−1.50000	−	2.59808i	−0.0527698	−	0.0914000i
$809$	33.0000			1.16022			0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000			1.16022			0.580109	+	0.814539i	$0.303010\pi$
$810$		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
$814$	1.50000	−	2.59808i	0.0525750	−	0.0910625i
$815$	28.5000	−	49.3634i	0.998311	−	1.72913i
$816$		0			0
$817$	3.50000	+	6.06218i	0.122449	+	0.212089i
$818$	34.0000			1.18878
$819$		0			0
$820$	9.00000			0.314294
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	−0.955636	−	0.294549i	$-0.904831\pi$
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	0.222731	−	0.974880i	$-0.428503\pi$
$822$		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	$-0.0788849\pi$
$824$	−6.50000	+	11.2583i	−0.226438	+	0.392203i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	−11.0000			−0.382046			−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000			−0.382046			−0.191023	+	0.981586i	$0.561180\pi$
$830$	13.5000	+	23.3827i	0.468592	+	0.811625i
$831$		0			0
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$		0			0
$834$		0			0
$835$	22.5000	+	38.9711i	0.778645	+	1.34865i
$836$	21.0000			0.726300
$837$		0			0
$838$	9.00000			0.310900
$839$	−7.50000	−	12.9904i	−0.258929	−	0.448478i	0.707026	−	0.707187i	$-0.250036\pi$
$839$	−7.50000	−	12.9904i	−0.258929	−	0.448478i	−0.965955	+	0.258709i	$0.916703\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−17.5000	+	30.3109i	−0.603090	+	1.04458i
$843$		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
$851$	4.50000	−	7.79423i	0.154258	−	0.267183i
$852$		0			0
$853$	−0.500000	−	0.866025i	−0.0171197	−	0.0296521i	0.857339	−	0.514753i	$-0.172116\pi$
$853$	−0.500000	−	0.866025i	−0.0171197	−	0.0296521i	−0.874458	+	0.485101i	$0.838783\pi$
$854$		0			0
$855$		0			0
$856$	−9.00000			−0.307614
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$		0			0
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	−0.996559	−	0.0828900i	$-0.973585\pi$
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	0.570064	+	0.821600i	$0.306918\pi$
$860$	1.50000	−	2.59808i	0.0511496	−	0.0885937i
$861$		0			0
$862$	13.5000	+	23.3827i	0.459812	+	0.796417i
$863$	51.0000			1.73606			0.868030	−	0.496512i	$-0.165386\pi$
$863$	51.0000			1.73606			0.868030	+	0.496512i	$0.165386\pi$
$864$		0			0
$865$	−18.0000			−0.612018
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$		0			0
$868$		0			0
$869$	24.0000	−	41.5692i	0.814144	−	1.41014i
$870$		0			0
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$	−13.0000			−0.440236
$873$		0			0
$874$	63.0000			2.13101
$875$		0			0
$876$		0			0
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	0.130224	+	0.991485i	$0.458430\pi$
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	−0.923763	+	0.382965i	$0.874903\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$		0			0
$880$	−4.50000	−	7.79423i	−0.151695	−	0.262743i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−1.50000	−	2.59808i	−0.0504505	−	0.0873828i
$885$		0			0
$886$	18.0000	−	31.1769i	0.604722	−	1.04741i
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	−0.443964	−	0.896045i	$-0.646428\pi$
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	0.997979	−	0.0635387i	$-0.0202386\pi$
$888$		0			0
$889$		0			0
$890$	9.00000			0.301681
$891$		0			0
$892$	1.00000			0.0334825
$893$		0			0
$894$		0			0
$895$	−31.5000	+	54.5596i	−1.05293	+	1.82373i
$896$		0			0
$897$		0			0
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	24.0000			0.800445
$900$		0			0
$901$	−9.00000			−0.299833
$902$	−4.50000	−	7.79423i	−0.149834	−	0.259519i
$903$		0			0
$904$	−4.50000	+	7.79423i	−0.149668	+	0.259232i
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$		0			0
$907$	21.5000	+	37.2391i	0.713896	+	1.23650i	0.963384	+	0.268126i	$0.0864043\pi$
$907$	21.5000	+	37.2391i	0.713896	+	1.23650i	−0.249488	+	0.968378i	$0.580262\pi$
$908$	−3.00000			−0.0995585
$909$		0			0
$910$		0			0
$911$	19.5000	+	33.7750i	0.646064	+	1.11902i	0.984055	+	0.177866i	$0.0569194\pi$
$911$	19.5000	+	33.7750i	0.646064	+	1.11902i	−0.337991	+	0.941149i	$0.609747\pi$
$912$		0			0
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$		0			0
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$		0			0
$918$		0			0
$919$	53.0000			1.74831			0.874154	−	0.485648i	$-0.161416\pi$
$919$	53.0000			1.74831			0.874154	+	0.485648i	$0.161416\pi$
$920$	−13.5000	−	23.3827i	−0.445082	−	0.770904i
$921$		0			0
$922$	4.50000	−	7.79423i	0.148200	−	0.256689i
$923$	6.00000	−	10.3923i	0.197492	−	0.342067i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	41.0000			1.34734
$927$		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
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$		0			0
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$	27.0000			0.882994
$936$		0			0
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	−0.812975	−	0.582298i	$-0.802154\pi$
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	0.910773	+	0.412908i	$0.135487\pi$
$942$		0			0
$943$	−13.5000	−	23.3827i	−0.439620	−	0.761445i
$944$		0			0
$945$		0			0
$946$	−3.00000			−0.0975384
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	5.50000	−	9.52628i	0.178538	−	0.309236i
$950$	−14.0000	+	24.2487i	−0.454220	+	0.786732i
$951$		0			0
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$	−1.50000	−	2.59808i	−0.0485135	−	0.0840278i
$957$		0			0
$958$	1.50000	−	2.59808i	0.0484628	−	0.0839400i
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−1.00000			−0.0322413
$963$		0			0
$964$	13.0000			0.418702
$965$	−21.0000	−	36.3731i	−0.676014	−	1.17089i
$966$		0			0
$967$	−20.5000	+	35.5070i	−0.659236	+	1.14183i	0.321578	+	0.946883i	$0.395787\pi$
$967$	−20.5000	+	35.5070i	−0.659236	+	1.14183i	−0.980814	+	0.194946i	$0.937547\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$	−1.50000	−	2.59808i	−0.0481621	−	0.0834192i
$971$	33.0000			1.05902			0.529510	−	0.848304i	$-0.322376\pi$
$971$	33.0000			1.05902			0.529510	+	0.848304i	$0.322376\pi$
$972$		0			0
$973$		0			0
$974$	12.5000	+	21.6506i	0.400526	+	0.693731i
$975$		0			0
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$		0			0
$979$	−4.50000	−	7.79423i	−0.143821	−	0.249105i
$980$		0			0
$981$		0			0
$982$	−21.0000			−0.670137
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	0.960489	−	0.278319i	$-0.0897773\pi$
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	−0.721276	+	0.692648i	$0.756444\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$	4.50000	−	7.79423i	0.143309	−	0.248219i
$987$		0			0
$988$	−3.50000	−	6.06218i	−0.111350	−	0.192864i
$989$	−9.00000			−0.286183
$990$		0			0
$991$	−25.0000			−0.794151			−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000			−0.794151			−0.397076	+	0.917786i	$0.629975\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$		0			0
$995$	−37.5000	+	64.9519i	−1.18883	+	2.05911i
$996$		0			0
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	0.744548	−	0.667568i	$-0.232665\pi$
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	−0.950405	+	0.311014i	$0.899332\pi$
$998$	−25.0000			−0.791361
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.a.1765.1		2
3.2	odd	2		882.2.f.g.589.1		2
7.2	even	3		2646.2.h.d.361.1		2
7.3	odd	6		378.2.e.b.37.1		2
7.4	even	3		2646.2.e.g.1549.1		2
7.5	odd	6		378.2.h.a.361.1		2
7.6	odd	2		2646.2.f.d.1765.1		2
9.2	odd	6		882.2.f.g.295.1		2
9.4	even	3		7938.2.a.be.1.1		1
9.5	odd	6		7938.2.a.b.1.1		1
9.7	even	3	inner	2646.2.f.a.883.1		2
21.2	odd	6		882.2.h.i.67.1		2
21.5	even	6		126.2.h.b.67.1	yes	2
21.11	odd	6		882.2.e.c.373.1		2
21.17	even	6		126.2.e.a.121.1	yes	2
21.20	even	2		882.2.f.i.589.1		2
28.3	even	6		3024.2.q.f.2305.1		2
28.19	even	6		3024.2.t.a.1873.1		2
63.2	odd	6		882.2.e.c.655.1		2
63.5	even	6		1134.2.g.e.487.1		2
63.11	odd	6		882.2.h.i.79.1		2
63.13	odd	6		7938.2.a.t.1.1		1
63.16	even	3		2646.2.e.g.2125.1		2
63.20	even	6		882.2.f.i.295.1		2
63.25	even	3		2646.2.h.d.667.1		2
63.31	odd	6		1134.2.g.c.163.1		2
63.34	odd	6		2646.2.f.d.883.1		2
63.38	even	6		126.2.h.b.79.1	yes	2
63.40	odd	6		1134.2.g.c.487.1		2
63.41	even	6		7938.2.a.m.1.1		1
63.47	even	6		126.2.e.a.25.1	✓	2
63.52	odd	6		378.2.h.a.289.1		2
63.59	even	6		1134.2.g.e.163.1		2
63.61	odd	6		378.2.e.b.235.1		2
84.47	odd	6		1008.2.t.f.193.1		2
84.59	odd	6		1008.2.q.a.625.1		2
252.47	odd	6		1008.2.q.a.529.1		2
252.115	even	6		3024.2.t.a.289.1		2
252.187	even	6		3024.2.q.f.2881.1		2
252.227	odd	6		1008.2.t.f.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	63.47	even	6
126.2.e.a.121.1	yes	2	21.17	even	6
126.2.h.b.67.1	yes	2	21.5	even	6
126.2.h.b.79.1	yes	2	63.38	even	6
378.2.e.b.37.1		2	7.3	odd	6
378.2.e.b.235.1		2	63.61	odd	6
378.2.h.a.289.1		2	63.52	odd	6
378.2.h.a.361.1		2	7.5	odd	6
882.2.e.c.373.1		2	21.11	odd	6
882.2.e.c.655.1		2	63.2	odd	6
882.2.f.g.295.1		2	9.2	odd	6
882.2.f.g.589.1		2	3.2	odd	2
882.2.f.i.295.1		2	63.20	even	6
882.2.f.i.589.1		2	21.20	even	2
882.2.h.i.67.1		2	21.2	odd	6
882.2.h.i.79.1		2	63.11	odd	6
1008.2.q.a.529.1		2	252.47	odd	6
1008.2.q.a.625.1		2	84.59	odd	6
1008.2.t.f.193.1		2	84.47	odd	6
1008.2.t.f.961.1		2	252.227	odd	6
1134.2.g.c.163.1		2	63.31	odd	6
1134.2.g.c.487.1		2	63.40	odd	6
1134.2.g.e.163.1		2	63.59	even	6
1134.2.g.e.487.1		2	63.5	even	6
2646.2.e.g.1549.1		2	7.4	even	3
2646.2.e.g.2125.1		2	63.16	even	3
2646.2.f.a.883.1		2	9.7	even	3	inner
2646.2.f.a.1765.1		2	1.1	even	1	trivial
2646.2.f.d.883.1		2	63.34	odd	6
2646.2.f.d.1765.1		2	7.6	odd	2
2646.2.h.d.361.1		2	7.2	even	3
2646.2.h.d.667.1		2	63.25	even	3
3024.2.q.f.2305.1		2	28.3	even	6
3024.2.q.f.2881.1		2	252.187	even	6
3024.2.t.a.289.1		2	252.115	even	6
3024.2.t.a.1873.1		2	28.19	even	6
7938.2.a.b.1.1		1	9.5	odd	6
7938.2.a.m.1.1		1	63.41	even	6
7938.2.a.t.1.1		1	63.13	odd	6
7938.2.a.be.1.1		1	9.4	even	3

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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +3.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{17} +7.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-4.50000 + 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +1.00000 q^{26} +(1.50000 + 2.59808i) q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} -1.00000 q^{37} +(-3.50000 - 6.06218i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +3.00000 q^{44} +9.00000 q^{46} +(-2.00000 + 3.46410i) q^{50} +(-0.500000 - 0.866025i) q^{52} -3.00000 q^{53} +9.00000 q^{55} +(1.50000 - 2.59808i) q^{58} +(1.00000 + 1.73205i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} -12.0000 q^{71} -11.0000 q^{73} +(0.500000 + 0.866025i) q^{74} +(-3.50000 + 6.06218i) q^{76} +(8.00000 + 13.8564i) q^{79} +3.00000 q^{80} +3.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(0.500000 - 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{89} +(-4.50000 - 7.79423i) q^{92} +(-10.5000 + 18.1865i) q^{95} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{8} + 6 q^{10} - 3 q^{11} - q^{13} - q^{16} + 6 q^{17} + 14 q^{19} - 3 q^{20} - 3 q^{22} - 9 q^{23} - 4 q^{25} + 2 q^{26} + 3 q^{29} + 8 q^{31} - q^{32} - 3 q^{34}+ \cdots - q^{97}+O(q^{100}) \) 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^8 + 6 * q^10 - 3 * q^11 - q^13 - q^16 + 6 * q^17 + 14 * q^19 - 3 * q^20 - 3 * q^22 - 9 * q^23 - 4 * q^25 + 2 * q^26 + 3 * q^29 + 8 * q^31 - q^32 - 3 * q^34 - 2 * q^37 - 7 * q^38 - 3 * q^40 - 3 * q^41 + q^43 + 6 * q^44 + 18 * q^46 - 4 * q^50 - q^52 - 6 * q^53 + 18 * q^55 + 3 * q^58 + 2 * q^61 - 16 * q^62 + 2 * q^64 - 3 * q^65 + 4 * q^67 - 3 * q^68 - 24 * q^71 - 22 * q^73 + q^74 - 7 * q^76 + 16 * q^79 + 6 * q^80 + 6 * q^82 + 9 * q^83 - 9 * q^85 + q^86 - 3 * q^88 + 6 * q^89 - 9 * q^92 - 21 * q^95 - q^97

Introduction

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