LMFDB - Embedded newform 504.2.p.b.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(307,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

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

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

chi := DirichletCharacter("504.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.p (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	504.307
Dual form			504.2.p.b.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -3.46410 q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -3.46410 q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(3.46410 + 3.46410i) q^{10} +2.00000 q^{11} +3.46410 q^{13} +(3.73205 - 0.267949i) q^{14} -4.00000 q^{16} -3.46410i q^{17} -6.92820i q^{19} -6.92820i q^{20} +(-2.00000 - 2.00000i) q^{22} +2.00000i q^{23} +7.00000 q^{25} +(-3.46410 - 3.46410i) q^{26} +(-4.00000 - 3.46410i) q^{28} -8.00000i q^{29} +3.46410 q^{31} +(4.00000 + 4.00000i) q^{32} +(-3.46410 + 3.46410i) q^{34} +(6.00000 - 6.92820i) q^{35} -4.00000i q^{37} +(-6.92820 + 6.92820i) q^{38} +(-6.92820 + 6.92820i) q^{40} +10.3923i q^{41} +6.00000 q^{43} +4.00000i q^{44} +(2.00000 - 2.00000i) q^{46} +6.92820 q^{47} +(-1.00000 - 6.92820i) q^{49} +(-7.00000 - 7.00000i) q^{50} +6.92820i q^{52} -4.00000i q^{53} -6.92820 q^{55} +(0.535898 + 7.46410i) q^{56} +(-8.00000 + 8.00000i) q^{58} -6.92820i q^{59} -10.3923 q^{61} +(-3.46410 - 3.46410i) q^{62} -8.00000i q^{64} -12.0000 q^{65} +10.0000 q^{67} +6.92820 q^{68} +(-12.9282 + 0.928203i) q^{70} -2.00000i q^{71} +(-4.00000 + 4.00000i) q^{74} +13.8564 q^{76} +(-3.46410 + 4.00000i) q^{77} -12.0000i q^{79} +13.8564 q^{80} +(10.3923 - 10.3923i) q^{82} +6.92820i q^{83} +12.0000i q^{85} +(-6.00000 - 6.00000i) q^{86} +(4.00000 - 4.00000i) q^{88} +10.3923i q^{89} +(-6.00000 + 6.92820i) q^{91} -4.00000 q^{92} +(-6.92820 - 6.92820i) q^{94} +24.0000i q^{95} -13.8564i q^{97} +(-5.92820 + 7.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 8 * q^8	$ 4 q - 4 q^{2} + 8 q^{8} + 8 q^{11} + 8 q^{14} - 16 q^{16} - 8 q^{22} + 28 q^{25} - 16 q^{28} + 16 q^{32} + 24 q^{35} + 24 q^{43} + 8 q^{46} - 4 q^{49} - 28 q^{50} + 16 q^{56} - 32 q^{58} - 48 q^{65} + 40 q^{67} - 24 q^{70} - 16 q^{74} - 24 q^{86} + 16 q^{88} - 24 q^{91} - 16 q^{92} + 4 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 8 * q^8 + 8 * q^11 + 8 * q^14 - 16 * q^16 - 8 * q^22 + 28 * q^25 - 16 * q^28 + 16 * q^32 + 24 * q^35 + 24 * q^43 + 8 * q^46 - 4 * q^49 - 28 * q^50 + 16 * q^56 - 32 * q^58 - 48 * q^65 + 40 * q^67 - 24 * q^70 - 16 * q^74 - 24 * q^86 + 16 * q^88 - 24 * q^91 - 16 * q^92 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$	−3.46410			−1.54919			−0.774597	−	0.632456i	$-0.782047\pi$
$5$	−3.46410			−1.54919			−0.774597	+	0.632456i	$0.782047\pi$
$6$		0			0
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	3.46410	+	3.46410i	1.09545	+	1.09545i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	3.46410			0.960769			0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410			0.960769			0.480384	+	0.877058i	$0.340497\pi$
$14$	3.73205	−	0.267949i	0.997433	−	0.0716124i
$15$		0			0
$16$	−4.00000			−1.00000
$17$		−	3.46410i		−	0.840168i	−0.907485	−	0.420084i	$-0.862001\pi$
$17$		−	3.46410i		−	0.840168i	0.907485	−	0.420084i	$-0.137999\pi$
$18$		0			0
$19$		−	6.92820i		−	1.58944i	−0.606977	−	0.794719i	$-0.707618\pi$
$19$		−	6.92820i		−	1.58944i	0.606977	−	0.794719i	$-0.292382\pi$
$20$		−	6.92820i		−	1.54919i
$21$		0			0
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$			2.00000i			0.417029i	0.978019	+	0.208514i	$0.0668628\pi$
$23$			2.00000i			0.417029i	−0.978019	+	0.208514i	$0.933137\pi$
$24$		0			0
$25$	7.00000			1.40000
$26$	−3.46410	−	3.46410i	−0.679366	−	0.679366i
$27$		0			0
$28$	−4.00000	−	3.46410i	−0.755929	−	0.654654i
$29$		−	8.00000i		−	1.48556i	−0.669534	−	0.742781i	$-0.733506\pi$
$29$		−	8.00000i		−	1.48556i	0.669534	−	0.742781i	$-0.266494\pi$
$30$		0			0
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		0			0
$34$	−3.46410	+	3.46410i	−0.594089	+	0.594089i
$35$	6.00000	−	6.92820i	1.01419	−	1.17108i
$36$		0			0
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	−6.92820	+	6.92820i	−1.12390	+	1.12390i
$39$		0			0
$40$	−6.92820	+	6.92820i	−1.09545	+	1.09545i
$41$			10.3923i			1.62301i	0.584349	+	0.811503i	$0.301350\pi$
$41$			10.3923i			1.62301i	−0.584349	+	0.811503i	$0.698650\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$			4.00000i			0.603023i
$45$		0			0
$46$	2.00000	−	2.00000i	0.294884	−	0.294884i
$47$	6.92820			1.01058			0.505291	−	0.862949i	$-0.331385\pi$
$47$	6.92820			1.01058			0.505291	+	0.862949i	$0.331385\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	−7.00000	−	7.00000i	−0.989949	−	0.989949i
$51$		0			0
$52$			6.92820i			0.960769i
$53$		−	4.00000i		−	0.549442i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$		−	4.00000i		−	0.549442i	0.961524	−	0.274721i	$-0.0885855\pi$
$54$		0			0
$55$	−6.92820			−0.934199
$56$	0.535898	+	7.46410i	0.0716124	+	0.997433i
$57$		0			0
$58$	−8.00000	+	8.00000i	−1.05045	+	1.05045i
$59$		−	6.92820i		−	0.901975i	−0.892530	−	0.450988i	$-0.851072\pi$
$59$		−	6.92820i		−	0.901975i	0.892530	−	0.450988i	$-0.148928\pi$
$60$		0			0
$61$	−10.3923			−1.33060			−0.665299	−	0.746577i	$-0.731696\pi$
$61$	−10.3923			−1.33060			−0.665299	+	0.746577i	$0.731696\pi$
$62$	−3.46410	−	3.46410i	−0.439941	−	0.439941i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−12.0000			−1.48842
$66$		0			0
$67$	10.0000			1.22169			0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000			1.22169			0.610847	+	0.791748i	$0.290829\pi$
$68$	6.92820			0.840168
$69$		0			0
$70$	−12.9282	+	0.928203i	−1.54522	+	0.110942i
$71$		−	2.00000i		−	0.237356i	−0.992933	−	0.118678i	$-0.962134\pi$
$71$		−	2.00000i		−	0.237356i	0.992933	−	0.118678i	$-0.0378657\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−4.00000	+	4.00000i	−0.464991	+	0.464991i
$75$		0			0
$76$	13.8564			1.58944
$77$	−3.46410	+	4.00000i	−0.394771	+	0.455842i
$78$		0			0
$79$		−	12.0000i		−	1.35011i	−0.737769	−	0.675053i	$-0.764121\pi$
$79$		−	12.0000i		−	1.35011i	0.737769	−	0.675053i	$-0.235879\pi$
$80$	13.8564			1.54919
$81$		0			0
$82$	10.3923	−	10.3923i	1.14764	−	1.14764i
$83$			6.92820i			0.760469i	0.924890	+	0.380235i	$0.124157\pi$
$83$			6.92820i			0.760469i	−0.924890	+	0.380235i	$0.875843\pi$
$84$		0			0
$85$			12.0000i			1.30158i
$86$	−6.00000	−	6.00000i	−0.646997	−	0.646997i
$87$		0			0
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$			10.3923i			1.10158i	0.834643	+	0.550791i	$0.185674\pi$
$89$			10.3923i			1.10158i	−0.834643	+	0.550791i	$0.814326\pi$
$90$		0			0
$91$	−6.00000	+	6.92820i	−0.628971	+	0.726273i
$92$	−4.00000			−0.417029
$93$		0			0
$94$	−6.92820	−	6.92820i	−0.714590	−	0.714590i
$95$			24.0000i			2.46235i
$96$		0			0
$97$		−	13.8564i		−	1.40690i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$		−	13.8564i		−	1.40690i	0.710742	−	0.703452i	$-0.248359\pi$
$98$	−5.92820	+	7.92820i	−0.598839	+	0.800869i
$99$		0			0
$100$			14.0000i			1.40000i
$101$	−3.46410			−0.344691			−0.172345	−	0.985037i	$-0.555135\pi$
$101$	−3.46410			−0.344691			−0.172345	+	0.985037i	$0.555135\pi$
$102$		0			0
$103$	17.3205			1.70664			0.853320	−	0.521387i	$-0.174585\pi$
$103$	17.3205			1.70664			0.853320	+	0.521387i	$0.174585\pi$
$104$	6.92820	−	6.92820i	0.679366	−	0.679366i
$105$		0			0
$106$	−4.00000	+	4.00000i	−0.388514	+	0.388514i
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$		0			0
$109$		−	8.00000i		−	0.766261i	−0.923694	−	0.383131i	$-0.874846\pi$
$109$		−	8.00000i		−	0.766261i	0.923694	−	0.383131i	$-0.125154\pi$
$110$	6.92820	+	6.92820i	0.660578	+	0.660578i
$111$		0			0
$112$	6.92820	−	8.00000i	0.654654	−	0.755929i
$113$	−20.0000			−1.88144			−0.940721	−	0.339182i	$-0.889850\pi$
$113$	−20.0000			−1.88144			−0.940721	+	0.339182i	$0.889850\pi$
$114$		0			0
$115$		−	6.92820i		−	0.646058i
$116$	16.0000			1.48556
$117$		0			0
$118$	−6.92820	+	6.92820i	−0.637793	+	0.637793i
$119$	6.92820	+	6.00000i	0.635107	+	0.550019i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	10.3923	+	10.3923i	0.940875	+	0.940875i
$123$		0			0
$124$			6.92820i			0.622171i
$125$	−6.92820			−0.619677
$126$		0			0
$127$			12.0000i			1.06483i	0.846484	+	0.532414i	$0.178715\pi$
$127$			12.0000i			1.06483i	−0.846484	+	0.532414i	$0.821285\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$		0			0
$130$	12.0000	+	12.0000i	1.05247	+	1.05247i
$131$		−	6.92820i		−	0.605320i	−0.953099	−	0.302660i	$-0.902125\pi$
$131$		−	6.92820i		−	0.605320i	0.953099	−	0.302660i	$-0.0978746\pi$
$132$		0			0
$133$	13.8564	+	12.0000i	1.20150	+	1.04053i
$134$	−10.0000	−	10.0000i	−0.863868	−	0.863868i
$135$		0			0
$136$	−6.92820	−	6.92820i	−0.594089	−	0.594089i
$137$	16.0000			1.36697			0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000			1.36697			0.683486	+	0.729964i	$0.260463\pi$
$138$		0			0
$139$			13.8564i			1.17529i	0.809121	+	0.587643i	$0.199944\pi$
$139$			13.8564i			1.17529i	−0.809121	+	0.587643i	$0.800056\pi$
$140$	13.8564	+	12.0000i	1.17108	+	1.01419i
$141$		0			0
$142$	−2.00000	+	2.00000i	−0.167836	+	0.167836i
$143$	6.92820			0.579365
$144$		0			0
$145$			27.7128i			2.30142i
$146$		0			0
$147$		0			0
$148$	8.00000			0.657596
$149$		−	4.00000i		−	0.327693i	−0.986486	−	0.163846i	$-0.947610\pi$
$149$		−	4.00000i		−	0.327693i	0.986486	−	0.163846i	$-0.0523901\pi$
$150$		0			0
$151$		−	4.00000i		−	0.325515i	−0.986666	−	0.162758i	$-0.947961\pi$
$151$		−	4.00000i		−	0.325515i	0.986666	−	0.162758i	$-0.0520389\pi$
$152$	−13.8564	−	13.8564i	−1.12390	−	1.12390i
$153$		0			0
$154$	7.46410	−	0.535898i	0.601474	−	0.0431839i
$155$	−12.0000			−0.963863
$156$		0			0
$157$	−10.3923			−0.829396			−0.414698	−	0.909959i	$-0.636113\pi$
$157$	−10.3923			−0.829396			−0.414698	+	0.909959i	$0.636113\pi$
$158$	−12.0000	+	12.0000i	−0.954669	+	0.954669i
$159$		0			0
$160$	−13.8564	−	13.8564i	−1.09545	−	1.09545i
$161$	−4.00000	−	3.46410i	−0.315244	−	0.273009i
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	−20.7846			−1.62301
$165$		0			0
$166$	6.92820	−	6.92820i	0.537733	−	0.537733i
$167$	13.8564			1.07224			0.536120	−	0.844141i	$-0.319889\pi$
$167$	13.8564			1.07224			0.536120	+	0.844141i	$0.319889\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	12.0000	−	12.0000i	0.920358	−	0.920358i
$171$		0			0
$172$			12.0000i			0.914991i
$173$	3.46410			0.263371			0.131685	−	0.991292i	$-0.457961\pi$
$173$	3.46410			0.263371			0.131685	+	0.991292i	$0.457961\pi$
$174$		0			0
$175$	−12.1244	+	14.0000i	−0.916515	+	1.05830i
$176$	−8.00000			−0.603023
$177$		0			0
$178$	10.3923	−	10.3923i	0.778936	−	0.778936i
$179$	−2.00000			−0.149487			−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000			−0.149487			−0.0747435	+	0.997203i	$0.523814\pi$
$180$		0			0
$181$	10.3923			0.772454			0.386227	−	0.922404i	$-0.373778\pi$
$181$	10.3923			0.772454			0.386227	+	0.922404i	$0.373778\pi$
$182$	12.9282	−	0.928203i	0.958302	−	0.0688030i
$183$		0			0
$184$	4.00000	+	4.00000i	0.294884	+	0.294884i
$185$			13.8564i			1.01874i
$186$		0			0
$187$		−	6.92820i		−	0.506640i
$188$			13.8564i			1.01058i
$189$		0			0
$190$	24.0000	−	24.0000i	1.74114	−	1.74114i
$191$		−	22.0000i		−	1.59186i	−0.605386	−	0.795932i	$-0.706981\pi$
$191$		−	22.0000i		−	1.59186i	0.605386	−	0.795932i	$-0.293019\pi$
$192$		0			0
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$	−13.8564	+	13.8564i	−0.994832	+	0.994832i
$195$		0			0
$196$	13.8564	−	2.00000i	0.989743	−	0.142857i
$197$		−	16.0000i		−	1.13995i	−0.821661	−	0.569976i	$-0.806952\pi$
$197$		−	16.0000i		−	1.13995i	0.821661	−	0.569976i	$-0.193048\pi$
$198$		0			0
$199$	−10.3923			−0.736691			−0.368345	−	0.929689i	$-0.620076\pi$
$199$	−10.3923			−0.736691			−0.368345	+	0.929689i	$0.620076\pi$
$200$	14.0000	−	14.0000i	0.989949	−	0.989949i
$201$		0			0
$202$	3.46410	+	3.46410i	0.243733	+	0.243733i
$203$	16.0000	+	13.8564i	1.12298	+	0.972529i
$204$		0			0
$205$		−	36.0000i		−	2.51435i
$206$	−17.3205	−	17.3205i	−1.20678	−	1.20678i
$207$		0			0
$208$	−13.8564			−0.960769
$209$		−	13.8564i		−	0.958468i
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	8.00000			0.549442
$213$		0			0
$214$	−10.0000	−	10.0000i	−0.683586	−	0.683586i
$215$	−20.7846			−1.41750
$216$		0			0
$217$	−6.00000	+	6.92820i	−0.407307	+	0.470317i
$218$	−8.00000	+	8.00000i	−0.541828	+	0.541828i
$219$		0			0
$220$		−	13.8564i		−	0.934199i
$221$		−	12.0000i		−	0.807207i
$222$		0			0
$223$	−3.46410			−0.231973			−0.115987	−	0.993251i	$-0.537003\pi$
$223$	−3.46410			−0.231973			−0.115987	+	0.993251i	$0.537003\pi$
$224$	−14.9282	+	1.07180i	−0.997433	+	0.0716124i
$225$		0			0
$226$	20.0000	+	20.0000i	1.33038	+	1.33038i
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$	−3.46410			−0.228914			−0.114457	−	0.993428i	$-0.536513\pi$
$229$	−3.46410			−0.228914			−0.114457	+	0.993428i	$0.536513\pi$
$230$	−6.92820	+	6.92820i	−0.456832	+	0.456832i
$231$		0			0
$232$	−16.0000	−	16.0000i	−1.05045	−	1.05045i
$233$	−4.00000			−0.262049			−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000			−0.262049			−0.131024	+	0.991379i	$0.541827\pi$
$234$		0			0
$235$	−24.0000			−1.56559
$236$	13.8564			0.901975
$237$		0			0
$238$	−0.928203	−	12.9282i	−0.0601665	−	0.838011i
$239$		−	2.00000i		−	0.129369i	−0.997906	−	0.0646846i	$-0.979396\pi$
$239$		−	2.00000i		−	0.129369i	0.997906	−	0.0646846i	$-0.0206041\pi$
$240$		0			0
$241$			13.8564i			0.892570i	0.894891	+	0.446285i	$0.147253\pi$
$241$			13.8564i			0.892570i	−0.894891	+	0.446285i	$0.852747\pi$
$242$	7.00000	+	7.00000i	0.449977	+	0.449977i
$243$		0			0
$244$		−	20.7846i		−	1.33060i
$245$	3.46410	+	24.0000i	0.221313	+	1.53330i
$246$		0			0
$247$		−	24.0000i		−	1.52708i
$248$	6.92820	−	6.92820i	0.439941	−	0.439941i
$249$		0			0
$250$	6.92820	+	6.92820i	0.438178	+	0.438178i
$251$		−	27.7128i		−	1.74922i	−0.484830	−	0.874609i	$-0.661118\pi$
$251$		−	27.7128i		−	1.74922i	0.484830	−	0.874609i	$-0.338882\pi$
$252$		0			0
$253$			4.00000i			0.251478i
$254$	12.0000	−	12.0000i	0.752947	−	0.752947i
$255$		0			0
$256$	16.0000			1.00000
$257$		−	17.3205i		−	1.08042i	−0.841529	−	0.540212i	$-0.818344\pi$
$257$		−	17.3205i		−	1.08042i	0.841529	−	0.540212i	$-0.181656\pi$
$258$		0			0
$259$	8.00000	+	6.92820i	0.497096	+	0.430498i
$260$		−	24.0000i		−	1.48842i
$261$		0			0
$262$	−6.92820	+	6.92820i	−0.428026	+	0.428026i
$263$			10.0000i			0.616626i	0.951285	+	0.308313i	$0.0997645\pi$
$263$			10.0000i			0.616626i	−0.951285	+	0.308313i	$0.900236\pi$
$264$		0			0
$265$			13.8564i			0.851192i
$266$	−1.85641	−	25.8564i	−0.113824	−	1.58536i
$267$		0			0
$268$			20.0000i			1.22169i
$269$	−3.46410			−0.211210			−0.105605	−	0.994408i	$-0.533678\pi$
$269$	−3.46410			−0.211210			−0.105605	+	0.994408i	$0.533678\pi$
$270$		0			0
$271$	−3.46410			−0.210429			−0.105215	−	0.994450i	$-0.533553\pi$
$271$	−3.46410			−0.210429			−0.105215	+	0.994450i	$0.533553\pi$
$272$			13.8564i			0.840168i
$273$		0			0
$274$	−16.0000	−	16.0000i	−0.966595	−	0.966595i
$275$	14.0000			0.844232
$276$		0			0
$277$			12.0000i			0.721010i	0.932757	+	0.360505i	$0.117396\pi$
$277$			12.0000i			0.721010i	−0.932757	+	0.360505i	$0.882604\pi$
$278$	13.8564	−	13.8564i	0.831052	−	0.831052i
$279$		0			0
$280$	−1.85641	−	25.8564i	−0.110942	−	1.54522i
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$		0			0
$283$			6.92820i			0.411839i	0.978569	+	0.205919i	$0.0660185\pi$
$283$			6.92820i			0.411839i	−0.978569	+	0.205919i	$0.933982\pi$
$284$	4.00000			0.237356
$285$		0			0
$286$	−6.92820	−	6.92820i	−0.409673	−	0.409673i
$287$	−20.7846	−	18.0000i	−1.22688	−	1.06251i
$288$		0			0
$289$	5.00000			0.294118
$290$	27.7128	−	27.7128i	1.62735	−	1.62735i
$291$		0			0
$292$		0			0
$293$	3.46410			0.202375			0.101187	−	0.994867i	$-0.467736\pi$
$293$	3.46410			0.202375			0.101187	+	0.994867i	$0.467736\pi$
$294$		0			0
$295$			24.0000i			1.39733i
$296$	−8.00000	−	8.00000i	−0.464991	−	0.464991i
$297$		0			0
$298$	−4.00000	+	4.00000i	−0.231714	+	0.231714i
$299$			6.92820i			0.400668i
$300$		0			0
$301$	−10.3923	+	12.0000i	−0.599002	+	0.691669i
$302$	−4.00000	+	4.00000i	−0.230174	+	0.230174i
$303$		0			0
$304$			27.7128i			1.58944i
$305$	36.0000			2.06135
$306$		0			0
$307$			6.92820i			0.395413i	0.980261	+	0.197707i	$0.0633494\pi$
$307$			6.92820i			0.395413i	−0.980261	+	0.197707i	$0.936651\pi$
$308$	−8.00000	−	6.92820i	−0.455842	−	0.394771i
$309$		0			0
$310$	12.0000	+	12.0000i	0.681554	+	0.681554i
$311$	−6.92820			−0.392862			−0.196431	−	0.980518i	$-0.562935\pi$
$311$	−6.92820			−0.392862			−0.196431	+	0.980518i	$0.562935\pi$
$312$		0			0
$313$		−	27.7128i		−	1.56642i	−0.621757	−	0.783210i	$-0.713581\pi$
$313$		−	27.7128i		−	1.56642i	0.621757	−	0.783210i	$-0.286419\pi$
$314$	10.3923	+	10.3923i	0.586472	+	0.586472i
$315$		0			0
$316$	24.0000			1.35011
$317$			28.0000i			1.57264i	0.617822	+	0.786318i	$0.288015\pi$
$317$			28.0000i			1.57264i	−0.617822	+	0.786318i	$0.711985\pi$
$318$		0			0
$319$		−	16.0000i		−	0.895828i
$320$			27.7128i			1.54919i
$321$		0			0
$322$	0.535898	+	7.46410i	0.0298644	+	0.415958i
$323$	−24.0000			−1.33540
$324$		0			0
$325$	24.2487			1.34508
$326$	10.0000	+	10.0000i	0.553849	+	0.553849i
$327$		0			0
$328$	20.7846	+	20.7846i	1.14764	+	1.14764i
$329$	−12.0000	+	13.8564i	−0.661581	+	0.763928i
$330$		0			0
$331$	18.0000			0.989369			0.494685	−	0.869072i	$-0.335284\pi$
$331$	18.0000			0.989369			0.494685	+	0.869072i	$0.335284\pi$
$332$	−13.8564			−0.760469
$333$		0			0
$334$	−13.8564	−	13.8564i	−0.758189	−	0.758189i
$335$	−34.6410			−1.89264
$336$		0			0
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	1.00000	+	1.00000i	0.0543928	+	0.0543928i
$339$		0			0
$340$	−24.0000			−1.30158
$341$	6.92820			0.375183
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	12.0000	−	12.0000i	0.646997	−	0.646997i
$345$		0			0
$346$	−3.46410	−	3.46410i	−0.186231	−	0.186231i
$347$	−34.0000			−1.82522			−0.912608	−	0.408836i	$-0.865935\pi$
$347$	−34.0000			−1.82522			−0.912608	+	0.408836i	$0.865935\pi$
$348$		0			0
$349$	−17.3205			−0.927146			−0.463573	−	0.886059i	$-0.653433\pi$
$349$	−17.3205			−0.927146			−0.463573	+	0.886059i	$0.653433\pi$
$350$	26.1244	−	1.87564i	1.39641	−	0.100257i
$351$		0			0
$352$	8.00000	+	8.00000i	0.426401	+	0.426401i
$353$			3.46410i			0.184376i	0.995742	+	0.0921878i	$0.0293860\pi$
$353$			3.46410i			0.184376i	−0.995742	+	0.0921878i	$0.970614\pi$
$354$		0			0
$355$			6.92820i			0.367711i
$356$	−20.7846			−1.10158
$357$		0			0
$358$	2.00000	+	2.00000i	0.105703	+	0.105703i
$359$		−	14.0000i		−	0.738892i	−0.929252	−	0.369446i	$-0.879548\pi$
$359$		−	14.0000i		−	0.738892i	0.929252	−	0.369446i	$-0.120452\pi$
$360$		0			0
$361$	−29.0000			−1.52632
$362$	−10.3923	−	10.3923i	−0.546207	−	0.546207i
$363$		0			0
$364$	−13.8564	−	12.0000i	−0.726273	−	0.628971i
$365$		0			0
$366$		0			0
$367$	31.1769			1.62742			0.813711	−	0.581270i	$-0.197444\pi$
$367$	31.1769			1.62742			0.813711	+	0.581270i	$0.197444\pi$
$368$		−	8.00000i		−	0.417029i
$369$		0			0
$370$	13.8564	−	13.8564i	0.720360	−	0.720360i
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	−6.92820	+	6.92820i	−0.358249	+	0.358249i
$375$		0			0
$376$	13.8564	−	13.8564i	0.714590	−	0.714590i
$377$		−	27.7128i		−	1.42728i
$378$		0			0
$379$	6.00000			0.308199			0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000			0.308199			0.154100	+	0.988055i	$0.450752\pi$
$380$	−48.0000			−2.46235
$381$		0			0
$382$	−22.0000	+	22.0000i	−1.12562	+	1.12562i
$383$	34.6410			1.77007			0.885037	−	0.465521i	$-0.154133\pi$
$383$	34.6410			1.77007			0.885037	+	0.465521i	$0.154133\pi$
$384$		0			0
$385$	12.0000	−	13.8564i	0.611577	−	0.706188i
$386$	6.00000	+	6.00000i	0.305392	+	0.305392i
$387$		0			0
$388$	27.7128			1.40690
$389$		−	16.0000i		−	0.811232i	−0.914044	−	0.405616i	$-0.867057\pi$
$389$		−	16.0000i		−	0.811232i	0.914044	−	0.405616i	$-0.132943\pi$
$390$		0			0
$391$	6.92820			0.350374
$392$	−15.8564	−	11.8564i	−0.800869	−	0.598839i
$393$		0			0
$394$	−16.0000	+	16.0000i	−0.806068	+	0.806068i
$395$			41.5692i			2.09157i
$396$		0			0
$397$	−3.46410			−0.173858			−0.0869291	−	0.996214i	$-0.527705\pi$
$397$	−3.46410			−0.173858			−0.0869291	+	0.996214i	$0.527705\pi$
$398$	10.3923	+	10.3923i	0.520919	+	0.520919i
$399$		0			0
$400$	−28.0000			−1.40000
$401$	−16.0000			−0.799002			−0.399501	−	0.916733i	$-0.630817\pi$
$401$	−16.0000			−0.799002			−0.399501	+	0.916733i	$0.630817\pi$
$402$		0			0
$403$	12.0000			0.597763
$404$		−	6.92820i		−	0.344691i
$405$		0			0
$406$	−2.14359	−	29.8564i	−0.106385	−	1.48175i
$407$		−	8.00000i		−	0.396545i
$408$		0			0
$409$		−	13.8564i		−	0.685155i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$		−	13.8564i		−	0.685155i	0.939490	−	0.342578i	$-0.111300\pi$
$410$	−36.0000	+	36.0000i	−1.77791	+	1.77791i
$411$		0			0
$412$			34.6410i			1.70664i
$413$	13.8564	+	12.0000i	0.681829	+	0.590481i
$414$		0			0
$415$		−	24.0000i		−	1.17811i
$416$	13.8564	+	13.8564i	0.679366	+	0.679366i
$417$		0			0
$418$	−13.8564	+	13.8564i	−0.677739	+	0.677739i
$419$			6.92820i			0.338465i	0.985576	+	0.169232i	$0.0541289\pi$
$419$			6.92820i			0.338465i	−0.985576	+	0.169232i	$0.945871\pi$
$420$		0			0
$421$			36.0000i			1.75453i	0.480004	+	0.877266i	$0.340635\pi$
$421$			36.0000i			1.75453i	−0.480004	+	0.877266i	$0.659365\pi$
$422$	18.0000	+	18.0000i	0.876226	+	0.876226i
$423$		0			0
$424$	−8.00000	−	8.00000i	−0.388514	−	0.388514i
$425$		−	24.2487i		−	1.17624i
$426$		0			0
$427$	18.0000	−	20.7846i	0.871081	−	1.00584i
$428$			20.0000i			0.966736i
$429$		0			0
$430$	20.7846	+	20.7846i	1.00232	+	1.00232i
$431$			10.0000i			0.481683i	0.970564	+	0.240842i	$0.0774234\pi$
$431$			10.0000i			0.481683i	−0.970564	+	0.240842i	$0.922577\pi$
$432$		0			0
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$	12.9282	−	0.928203i	0.620574	−	0.0445552i
$435$		0			0
$436$	16.0000			0.766261
$437$	13.8564			0.662842
$438$		0			0
$439$	−24.2487			−1.15733			−0.578664	−	0.815566i	$-0.696426\pi$
$439$	−24.2487			−1.15733			−0.578664	+	0.815566i	$0.696426\pi$
$440$	−13.8564	+	13.8564i	−0.660578	+	0.660578i
$441$		0			0
$442$	−12.0000	+	12.0000i	−0.570782	+	0.570782i
$443$	−14.0000			−0.665160			−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000			−0.665160			−0.332580	+	0.943075i	$0.607919\pi$
$444$		0			0
$445$		−	36.0000i		−	1.70656i
$446$	3.46410	+	3.46410i	0.164030	+	0.164030i
$447$		0			0
$448$	16.0000	+	13.8564i	0.755929	+	0.654654i
$449$	20.0000			0.943858			0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000			0.943858			0.471929	+	0.881636i	$0.343558\pi$
$450$		0			0
$451$			20.7846i			0.978709i
$452$		−	40.0000i		−	1.88144i
$453$		0			0
$454$		0			0
$455$	20.7846	−	24.0000i	0.974398	−	1.12514i
$456$		0			0
$457$	30.0000			1.40334			0.701670	−	0.712502i	$-0.252438\pi$
$457$	30.0000			1.40334			0.701670	+	0.712502i	$0.252438\pi$
$458$	3.46410	+	3.46410i	0.161867	+	0.161867i
$459$		0			0
$460$	13.8564			0.646058
$461$	31.1769			1.45205			0.726027	−	0.687666i	$-0.241365\pi$
$461$	31.1769			1.45205			0.726027	+	0.687666i	$0.241365\pi$
$462$		0			0
$463$			12.0000i			0.557687i	0.960337	+	0.278844i	$0.0899511\pi$
$463$			12.0000i			0.557687i	−0.960337	+	0.278844i	$0.910049\pi$
$464$			32.0000i			1.48556i
$465$		0			0
$466$	4.00000	+	4.00000i	0.185296	+	0.185296i
$467$			27.7128i			1.28240i	0.767375	+	0.641198i	$0.221562\pi$
$467$			27.7128i			1.28240i	−0.767375	+	0.641198i	$0.778438\pi$
$468$		0			0
$469$	−17.3205	+	20.0000i	−0.799787	+	0.923514i
$470$	24.0000	+	24.0000i	1.10704	+	1.10704i
$471$		0			0
$472$	−13.8564	−	13.8564i	−0.637793	−	0.637793i
$473$	12.0000			0.551761
$474$		0			0
$475$		−	48.4974i		−	2.22521i
$476$	−12.0000	+	13.8564i	−0.550019	+	0.635107i
$477$		0			0
$478$	−2.00000	+	2.00000i	−0.0914779	+	0.0914779i
$479$	−6.92820			−0.316558			−0.158279	−	0.987394i	$-0.550594\pi$
$479$	−6.92820			−0.316558			−0.158279	+	0.987394i	$0.550594\pi$
$480$		0			0
$481$		−	13.8564i		−	0.631798i
$482$	13.8564	−	13.8564i	0.631142	−	0.631142i
$483$		0			0
$484$		−	14.0000i		−	0.636364i
$485$			48.0000i			2.17957i
$486$		0			0
$487$			4.00000i			0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$			4.00000i			0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$	−20.7846	+	20.7846i	−0.940875	+	0.940875i
$489$		0			0
$490$	20.5359	−	27.4641i	0.927717	−	1.24070i
$491$	14.0000			0.631811			0.315906	−	0.948791i	$-0.397692\pi$
$491$	14.0000			0.631811			0.315906	+	0.948791i	$0.397692\pi$
$492$		0			0
$493$	−27.7128			−1.24812
$494$	−24.0000	+	24.0000i	−1.07981	+	1.07981i
$495$		0			0
$496$	−13.8564			−0.622171
$497$	4.00000	+	3.46410i	0.179425	+	0.155386i
$498$		0			0
$499$	6.00000			0.268597			0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000			0.268597			0.134298	+	0.990941i	$0.457122\pi$
$500$		−	13.8564i		−	0.619677i
$501$		0			0
$502$	−27.7128	+	27.7128i	−1.23688	+	1.23688i
$503$	20.7846			0.926740			0.463370	−	0.886165i	$-0.346640\pi$
$503$	20.7846			0.926740			0.463370	+	0.886165i	$0.346640\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	4.00000	−	4.00000i	0.177822	−	0.177822i
$507$		0			0
$508$	−24.0000			−1.06483
$509$	−10.3923			−0.460631			−0.230315	−	0.973116i	$-0.573976\pi$
$509$	−10.3923			−0.460631			−0.230315	+	0.973116i	$0.573976\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	−17.3205	+	17.3205i	−0.763975	+	0.763975i
$515$	−60.0000			−2.64392
$516$		0			0
$517$	13.8564			0.609404
$518$	−1.07180	−	14.9282i	−0.0470920	−	0.655908i
$519$		0			0
$520$	−24.0000	+	24.0000i	−1.05247	+	1.05247i
$521$		−	31.1769i		−	1.36589i	−0.730472	−	0.682943i	$-0.760700\pi$
$521$		−	31.1769i		−	1.36589i	0.730472	−	0.682943i	$-0.239300\pi$
$522$		0			0
$523$			13.8564i			0.605898i	0.953007	+	0.302949i	$0.0979712\pi$
$523$			13.8564i			0.605898i	−0.953007	+	0.302949i	$0.902029\pi$
$524$	13.8564			0.605320
$525$		0			0
$526$	10.0000	−	10.0000i	0.436021	−	0.436021i
$527$		−	12.0000i		−	0.522728i
$528$		0			0
$529$	19.0000			0.826087
$530$	13.8564	−	13.8564i	0.601884	−	0.601884i
$531$		0			0
$532$	−24.0000	+	27.7128i	−1.04053	+	1.20150i
$533$			36.0000i			1.55933i
$534$		0			0
$535$	−34.6410			−1.49766
$536$	20.0000	−	20.0000i	0.863868	−	0.863868i
$537$		0			0
$538$	3.46410	+	3.46410i	0.149348	+	0.149348i
$539$	−2.00000	−	13.8564i	−0.0861461	−	0.596838i
$540$		0			0
$541$		−	36.0000i		−	1.54776i	−0.633332	−	0.773880i	$-0.718313\pi$
$541$		−	36.0000i		−	1.54776i	0.633332	−	0.773880i	$-0.281687\pi$
$542$	3.46410	+	3.46410i	0.148796	+	0.148796i
$543$		0			0
$544$	13.8564	−	13.8564i	0.594089	−	0.594089i
$545$			27.7128i			1.18709i
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$			32.0000i			1.36697i
$549$		0			0
$550$	−14.0000	−	14.0000i	−0.596962	−	0.596962i
$551$	−55.4256			−2.36121
$552$		0			0
$553$	24.0000	+	20.7846i	1.02058	+	0.883852i
$554$	12.0000	−	12.0000i	0.509831	−	0.509831i
$555$		0			0
$556$	−27.7128			−1.17529
$557$		−	20.0000i		−	0.847427i	−0.905796	−	0.423714i	$-0.860726\pi$
$557$		−	20.0000i		−	0.847427i	0.905796	−	0.423714i	$-0.139274\pi$
$558$		0			0
$559$	20.7846			0.879095
$560$	−24.0000	+	27.7128i	−1.01419	+	1.17108i
$561$		0			0
$562$	−20.0000	−	20.0000i	−0.843649	−	0.843649i
$563$		−	20.7846i		−	0.875967i	−0.898983	−	0.437983i	$-0.855693\pi$
$563$		−	20.7846i		−	0.875967i	0.898983	−	0.437983i	$-0.144307\pi$
$564$		0			0
$565$	69.2820			2.91472
$566$	6.92820	−	6.92820i	0.291214	−	0.291214i
$567$		0			0
$568$	−4.00000	−	4.00000i	−0.167836	−	0.167836i
$569$	−20.0000			−0.838444			−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000			−0.838444			−0.419222	+	0.907884i	$0.637697\pi$
$570$		0			0
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$			13.8564i			0.579365i
$573$		0			0
$574$	2.78461	+	38.7846i	0.116227	+	1.61884i
$575$			14.0000i			0.583840i
$576$		0			0
$577$		−	27.7128i		−	1.15370i	−0.816850	−	0.576850i	$-0.804282\pi$
$577$		−	27.7128i		−	1.15370i	0.816850	−	0.576850i	$-0.195718\pi$
$578$	−5.00000	−	5.00000i	−0.207973	−	0.207973i
$579$		0			0
$580$	−55.4256			−2.30142
$581$	−13.8564	−	12.0000i	−0.574861	−	0.497844i
$582$		0			0
$583$		−	8.00000i		−	0.331326i
$584$		0			0
$585$		0			0
$586$	−3.46410	−	3.46410i	−0.143101	−	0.143101i
$587$			41.5692i			1.71575i	0.513862	+	0.857873i	$0.328214\pi$
$587$			41.5692i			1.71575i	−0.513862	+	0.857873i	$0.671786\pi$
$588$		0			0
$589$		−	24.0000i		−	0.988903i
$590$	24.0000	−	24.0000i	0.988064	−	0.988064i
$591$		0			0
$592$			16.0000i			0.657596i
$593$			45.0333i			1.84930i	0.380822	+	0.924648i	$0.375641\pi$
$593$			45.0333i			1.84930i	−0.380822	+	0.924648i	$0.624359\pi$
$594$		0			0
$595$	−24.0000	−	20.7846i	−0.983904	−	0.852086i
$596$	8.00000			0.327693
$597$		0			0
$598$	6.92820	−	6.92820i	0.283315	−	0.283315i
$599$			38.0000i			1.55264i	0.630340	+	0.776319i	$0.282915\pi$
$599$			38.0000i			1.55264i	−0.630340	+	0.776319i	$0.717085\pi$
$600$		0			0
$601$			13.8564i			0.565215i	0.959236	+	0.282607i	$0.0911993\pi$
$601$			13.8564i			0.565215i	−0.959236	+	0.282607i	$0.908801\pi$
$602$	22.3923	−	1.60770i	0.912642	−	0.0655248i
$603$		0			0
$604$	8.00000			0.325515
$605$	24.2487			0.985850
$606$		0			0
$607$	−31.1769			−1.26543			−0.632716	−	0.774384i	$-0.718060\pi$
$607$	−31.1769			−1.26543			−0.632716	+	0.774384i	$0.718060\pi$
$608$	27.7128	−	27.7128i	1.12390	−	1.12390i
$609$		0			0
$610$	−36.0000	−	36.0000i	−1.45760	−	1.45760i
$611$	24.0000			0.970936
$612$		0			0
$613$			24.0000i			0.969351i	0.874694	+	0.484675i	$0.161062\pi$
$613$			24.0000i			0.969351i	−0.874694	+	0.484675i	$0.838938\pi$
$614$	6.92820	−	6.92820i	0.279600	−	0.279600i
$615$		0			0
$616$	1.07180	+	14.9282i	0.0431839	+	0.601474i
$617$	16.0000			0.644136			0.322068	−	0.946717i	$-0.395622\pi$
$617$	16.0000			0.644136			0.322068	+	0.946717i	$0.395622\pi$
$618$		0			0
$619$		−	41.5692i		−	1.67081i	−0.549636	−	0.835404i	$-0.685234\pi$
$619$		−	41.5692i		−	1.67081i	0.549636	−	0.835404i	$-0.314766\pi$
$620$		−	24.0000i		−	0.963863i
$621$		0			0
$622$	6.92820	+	6.92820i	0.277796	+	0.277796i
$623$	−20.7846	−	18.0000i	−0.832718	−	0.721155i
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−27.7128	+	27.7128i	−1.10763	+	1.10763i
$627$		0			0
$628$		−	20.7846i		−	0.829396i
$629$	−13.8564			−0.552491
$630$		0			0
$631$		−	12.0000i		−	0.477712i	−0.971055	−	0.238856i	$-0.923228\pi$
$631$		−	12.0000i		−	0.477712i	0.971055	−	0.238856i	$-0.0767725\pi$
$632$	−24.0000	−	24.0000i	−0.954669	−	0.954669i
$633$		0			0
$634$	28.0000	−	28.0000i	1.11202	−	1.11202i
$635$		−	41.5692i		−	1.64962i
$636$		0			0
$637$	−3.46410	−	24.0000i	−0.137253	−	0.950915i
$638$	−16.0000	+	16.0000i	−0.633446	+	0.633446i
$639$		0			0
$640$	27.7128	−	27.7128i	1.09545	−	1.09545i
$641$	40.0000			1.57991			0.789953	−	0.613168i	$-0.210105\pi$
$641$	40.0000			1.57991			0.789953	+	0.613168i	$0.210105\pi$
$642$		0			0
$643$		−	20.7846i		−	0.819665i	−0.912161	−	0.409832i	$-0.865587\pi$
$643$		−	20.7846i		−	0.819665i	0.912161	−	0.409832i	$-0.134413\pi$
$644$	6.92820	−	8.00000i	0.273009	−	0.315244i
$645$		0			0
$646$	24.0000	+	24.0000i	0.944267	+	0.944267i
$647$	−27.7128			−1.08950			−0.544752	−	0.838597i	$-0.683376\pi$
$647$	−27.7128			−1.08950			−0.544752	+	0.838597i	$0.683376\pi$
$648$		0			0
$649$		−	13.8564i		−	0.543912i
$650$	−24.2487	−	24.2487i	−0.951113	−	0.951113i
$651$		0			0
$652$		−	20.0000i		−	0.783260i
$653$			4.00000i			0.156532i	0.996933	+	0.0782660i	$0.0249384\pi$
$653$			4.00000i			0.156532i	−0.996933	+	0.0782660i	$0.975062\pi$
$654$		0			0
$655$			24.0000i			0.937758i
$656$		−	41.5692i		−	1.62301i
$657$		0			0
$658$	25.8564	−	1.85641i	1.00799	−	0.0723703i
$659$	22.0000			0.856998			0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000			0.856998			0.428499	+	0.903542i	$0.359042\pi$
$660$		0			0
$661$	24.2487			0.943166			0.471583	−	0.881822i	$-0.343683\pi$
$661$	24.2487			0.943166			0.471583	+	0.881822i	$0.343683\pi$
$662$	−18.0000	−	18.0000i	−0.699590	−	0.699590i
$663$		0			0
$664$	13.8564	+	13.8564i	0.537733	+	0.537733i
$665$	−48.0000	−	41.5692i	−1.86136	−	1.61199i
$666$		0			0
$667$	16.0000			0.619522
$668$			27.7128i			1.07224i
$669$		0			0
$670$	34.6410	+	34.6410i	1.33830	+	1.33830i
$671$	−20.7846			−0.802381
$672$		0			0
$673$	6.00000			0.231283			0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000			0.231283			0.115642	+	0.993291i	$0.463108\pi$
$674$	6.00000	+	6.00000i	0.231111	+	0.231111i
$675$		0			0
$676$		−	2.00000i		−	0.0769231i
$677$	17.3205			0.665681			0.332841	−	0.942983i	$-0.391993\pi$
$677$	17.3205			0.665681			0.332841	+	0.942983i	$0.391993\pi$
$678$		0			0
$679$	27.7128	+	24.0000i	1.06352	+	0.921035i
$680$	24.0000	+	24.0000i	0.920358	+	0.920358i
$681$		0			0
$682$	−6.92820	−	6.92820i	−0.265295	−	0.265295i
$683$	−22.0000			−0.841807			−0.420903	−	0.907106i	$-0.638287\pi$
$683$	−22.0000			−0.841807			−0.420903	+	0.907106i	$0.638287\pi$
$684$		0			0
$685$	−55.4256			−2.11770
$686$	−5.58846	−	25.5885i	−0.213368	−	0.976972i
$687$		0			0
$688$	−24.0000			−0.914991
$689$		−	13.8564i		−	0.527887i
$690$		0			0
$691$			41.5692i			1.58137i	0.612225	+	0.790684i	$0.290275\pi$
$691$			41.5692i			1.58137i	−0.612225	+	0.790684i	$0.709725\pi$
$692$			6.92820i			0.263371i
$693$		0			0
$694$	34.0000	+	34.0000i	1.29062	+	1.29062i
$695$		−	48.0000i		−	1.82074i
$696$		0			0
$697$	36.0000			1.36360
$698$	17.3205	+	17.3205i	0.655591	+	0.655591i
$699$		0			0
$700$	−28.0000	−	24.2487i	−1.05830	−	0.916515i
$701$		−	4.00000i		−	0.151078i	−0.997143	−	0.0755390i	$-0.975932\pi$
$701$		−	4.00000i		−	0.151078i	0.997143	−	0.0755390i	$-0.0240677\pi$
$702$		0			0
$703$	−27.7128			−1.04521
$704$		−	16.0000i		−	0.603023i
$705$		0			0
$706$	3.46410	−	3.46410i	0.130373	−	0.130373i
$707$	6.00000	−	6.92820i	0.225653	−	0.260562i
$708$		0			0
$709$			16.0000i			0.600893i	0.953799	+	0.300446i	$0.0971356\pi$
$709$			16.0000i			0.600893i	−0.953799	+	0.300446i	$0.902864\pi$
$710$	6.92820	−	6.92820i	0.260011	−	0.260011i
$711$		0			0
$712$	20.7846	+	20.7846i	0.778936	+	0.778936i
$713$			6.92820i			0.259463i
$714$		0			0
$715$	−24.0000			−0.897549
$716$		−	4.00000i		−	0.149487i
$717$		0			0
$718$	−14.0000	+	14.0000i	−0.522475	+	0.522475i
$719$	48.4974			1.80865			0.904324	−	0.426846i	$-0.140375\pi$
$719$	48.4974			1.80865			0.904324	+	0.426846i	$0.140375\pi$
$720$		0			0
$721$	−30.0000	+	34.6410i	−1.11726	+	1.29010i
$722$	29.0000	+	29.0000i	1.07927	+	1.07927i
$723$		0			0
$724$			20.7846i			0.772454i
$725$		−	56.0000i		−	2.07979i
$726$		0			0
$727$	10.3923			0.385429			0.192715	−	0.981255i	$-0.438271\pi$
$727$	10.3923			0.385429			0.192715	+	0.981255i	$0.438271\pi$
$728$	1.85641	+	25.8564i	0.0688030	+	0.958302i
$729$		0			0
$730$		0			0
$731$		−	20.7846i		−	0.768747i
$732$		0			0
$733$	−10.3923			−0.383849			−0.191924	−	0.981410i	$-0.561473\pi$
$733$	−10.3923			−0.383849			−0.191924	+	0.981410i	$0.561473\pi$
$734$	−31.1769	−	31.1769i	−1.15076	−	1.15076i
$735$		0			0
$736$	−8.00000	+	8.00000i	−0.294884	+	0.294884i
$737$	20.0000			0.736709
$738$		0			0
$739$	10.0000			0.367856			0.183928	−	0.982940i	$-0.441119\pi$
$739$	10.0000			0.367856			0.183928	+	0.982940i	$0.441119\pi$
$740$	−27.7128			−1.01874
$741$		0			0
$742$	−1.07180	−	14.9282i	−0.0393469	−	0.548032i
$743$			46.0000i			1.68758i	0.536676	+	0.843788i	$0.319680\pi$
$743$			46.0000i			1.68758i	−0.536676	+	0.843788i	$0.680320\pi$
$744$		0			0
$745$			13.8564i			0.507659i
$746$		0			0
$747$		0			0
$748$	13.8564			0.506640
$749$	−17.3205	+	20.0000i	−0.632878	+	0.730784i
$750$		0			0
$751$			28.0000i			1.02173i	0.859660	+	0.510867i	$0.170676\pi$
$751$			28.0000i			1.02173i	−0.859660	+	0.510867i	$0.829324\pi$
$752$	−27.7128			−1.01058
$753$		0			0
$754$	−27.7128	+	27.7128i	−1.00924	+	1.00924i
$755$			13.8564i			0.504286i
$756$		0			0
$757$			32.0000i			1.16306i	0.813525	+	0.581530i	$0.197546\pi$
$757$			32.0000i			1.16306i	−0.813525	+	0.581530i	$0.802454\pi$
$758$	−6.00000	−	6.00000i	−0.217930	−	0.217930i
$759$		0			0
$760$	48.0000	+	48.0000i	1.74114	+	1.74114i
$761$			3.46410i			0.125574i	0.998027	+	0.0627868i	$0.0199988\pi$
$761$			3.46410i			0.125574i	−0.998027	+	0.0627868i	$0.980001\pi$
$762$		0			0
$763$	16.0000	+	13.8564i	0.579239	+	0.501636i
$764$	44.0000			1.59186
$765$		0			0
$766$	−34.6410	−	34.6410i	−1.25163	−	1.25163i
$767$		−	24.0000i		−	0.866590i
$768$		0			0
$769$			13.8564i			0.499675i	0.968288	+	0.249837i	$0.0803772\pi$
$769$			13.8564i			0.499675i	−0.968288	+	0.249837i	$0.919623\pi$
$770$	−25.8564	+	1.85641i	−0.931800	+	0.0669002i
$771$		0			0
$772$		−	12.0000i		−	0.431889i
$773$	−10.3923			−0.373785			−0.186893	−	0.982380i	$-0.559842\pi$
$773$	−10.3923			−0.373785			−0.186893	+	0.982380i	$0.559842\pi$
$774$		0			0
$775$	24.2487			0.871039
$776$	−27.7128	−	27.7128i	−0.994832	−	0.994832i
$777$		0			0
$778$	−16.0000	+	16.0000i	−0.573628	+	0.573628i
$779$	72.0000			2.57967
$780$		0			0
$781$		−	4.00000i		−	0.143131i
$782$	−6.92820	−	6.92820i	−0.247752	−	0.247752i
$783$		0			0
$784$	4.00000	+	27.7128i	0.142857	+	0.989743i
$785$	36.0000			1.28490
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$	32.0000			1.13995
$789$		0			0
$790$	41.5692	−	41.5692i	1.47897	−	1.47897i
$791$	34.6410	−	40.0000i	1.23169	−	1.42224i
$792$		0			0
$793$	−36.0000			−1.27840
$794$	3.46410	+	3.46410i	0.122936	+	0.122936i
$795$		0			0
$796$		−	20.7846i		−	0.736691i
$797$	−45.0333			−1.59516			−0.797581	−	0.603212i	$-0.793887\pi$
$797$	−45.0333			−1.59516			−0.797581	+	0.603212i	$0.793887\pi$
$798$		0			0
$799$		−	24.0000i		−	0.849059i
$800$	28.0000	+	28.0000i	0.989949	+	0.989949i
$801$		0			0
$802$	16.0000	+	16.0000i	0.564980	+	0.564980i
$803$		0			0
$804$		0			0
$805$	13.8564	+	12.0000i	0.488374	+	0.422944i
$806$	−12.0000	−	12.0000i	−0.422682	−	0.422682i
$807$		0			0
$808$	−6.92820	+	6.92820i	−0.243733	+	0.243733i
$809$	−28.0000			−0.984428			−0.492214	−	0.870474i	$-0.663812\pi$
$809$	−28.0000			−0.984428			−0.492214	+	0.870474i	$0.663812\pi$
$810$		0			0
$811$			41.5692i			1.45969i	0.683611	+	0.729846i	$0.260408\pi$
$811$			41.5692i			1.45969i	−0.683611	+	0.729846i	$0.739592\pi$
$812$	−27.7128	+	32.0000i	−0.972529	+	1.12298i
$813$		0			0
$814$	−8.00000	+	8.00000i	−0.280400	+	0.280400i
$815$	34.6410			1.21342
$816$		0			0
$817$		−	41.5692i		−	1.45432i
$818$	−13.8564	+	13.8564i	−0.484478	+	0.484478i
$819$		0			0
$820$	72.0000			2.51435
$821$		−	20.0000i		−	0.698005i	−0.937122	−	0.349002i	$-0.886521\pi$
$821$		−	20.0000i		−	0.698005i	0.937122	−	0.349002i	$-0.113479\pi$
$822$		0			0
$823$		−	36.0000i		−	1.25488i	−0.778664	−	0.627441i	$-0.784103\pi$
$823$		−	36.0000i		−	1.25488i	0.778664	−	0.627441i	$-0.215897\pi$
$824$	34.6410	−	34.6410i	1.20678	−	1.20678i
$825$		0			0
$826$	−1.85641	−	25.8564i	−0.0645926	−	0.899659i
$827$	−22.0000			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$828$		0			0
$829$	10.3923			0.360940			0.180470	−	0.983581i	$-0.442238\pi$
$829$	10.3923			0.360940			0.180470	+	0.983581i	$0.442238\pi$
$830$	−24.0000	+	24.0000i	−0.833052	+	0.833052i
$831$		0			0
$832$		−	27.7128i		−	0.960769i
$833$	−24.0000	+	3.46410i	−0.831551	+	0.120024i
$834$		0			0
$835$	−48.0000			−1.66111
$836$	27.7128			0.958468
$837$		0			0
$838$	6.92820	−	6.92820i	0.239331	−	0.239331i
$839$	41.5692			1.43513			0.717564	−	0.696492i	$-0.245257\pi$
$839$	41.5692			1.43513			0.717564	+	0.696492i	$0.245257\pi$
$840$		0			0
$841$	−35.0000			−1.20690
$842$	36.0000	−	36.0000i	1.24064	−	1.24064i
$843$		0			0
$844$		−	36.0000i		−	1.23917i
$845$	3.46410			0.119169
$846$		0			0
$847$	12.1244	−	14.0000i	0.416598	−	0.481046i
$848$			16.0000i			0.549442i
$849$		0			0
$850$	−24.2487	+	24.2487i	−0.831724	+	0.831724i
$851$	8.00000			0.274236
$852$		0			0
$853$	3.46410			0.118609			0.0593043	−	0.998240i	$-0.481112\pi$
$853$	3.46410			0.118609			0.0593043	+	0.998240i	$0.481112\pi$
$854$	−38.7846	+	2.78461i	−1.32718	+	0.0952874i
$855$		0			0
$856$	20.0000	−	20.0000i	0.683586	−	0.683586i
$857$		−	10.3923i		−	0.354994i	−0.984121	−	0.177497i	$-0.943200\pi$
$857$		−	10.3923i		−	0.354994i	0.984121	−	0.177497i	$-0.0568001\pi$
$858$		0			0
$859$			6.92820i			0.236387i	0.992991	+	0.118194i	$0.0377103\pi$
$859$			6.92820i			0.236387i	−0.992991	+	0.118194i	$0.962290\pi$
$860$		−	41.5692i		−	1.41750i
$861$		0			0
$862$	10.0000	−	10.0000i	0.340601	−	0.340601i
$863$			34.0000i			1.15737i	0.815550	+	0.578687i	$0.196435\pi$
$863$			34.0000i			1.15737i	−0.815550	+	0.578687i	$0.803565\pi$
$864$		0			0
$865$	−12.0000			−0.408012
$866$		0			0
$867$		0			0
$868$	−13.8564	−	12.0000i	−0.470317	−	0.407307i
$869$		−	24.0000i		−	0.814144i
$870$		0			0
$871$	34.6410			1.17377
$872$	−16.0000	−	16.0000i	−0.541828	−	0.541828i
$873$		0			0
$874$	−13.8564	−	13.8564i	−0.468700	−	0.468700i
$875$	12.0000	−	13.8564i	0.405674	−	0.468432i
$876$		0			0
$877$			24.0000i			0.810422i	0.914223	+	0.405211i	$0.132802\pi$
$877$			24.0000i			0.810422i	−0.914223	+	0.405211i	$0.867198\pi$
$878$	24.2487	+	24.2487i	0.818354	+	0.818354i
$879$		0			0
$880$	27.7128			0.934199
$881$			24.2487i			0.816960i	0.912767	+	0.408480i	$0.133941\pi$
$881$			24.2487i			0.816960i	−0.912767	+	0.408480i	$0.866059\pi$
$882$		0			0
$883$	42.0000			1.41341			0.706706	−	0.707507i	$-0.250180\pi$
$883$	42.0000			1.41341			0.706706	+	0.707507i	$0.250180\pi$
$884$	24.0000			0.807207
$885$		0			0
$886$	14.0000	+	14.0000i	0.470339	+	0.470339i
$887$	−41.5692			−1.39576			−0.697879	−	0.716216i	$-0.745873\pi$
$887$	−41.5692			−1.39576			−0.697879	+	0.716216i	$0.745873\pi$
$888$		0			0
$889$	−24.0000	−	20.7846i	−0.804934	−	0.697093i
$890$	−36.0000	+	36.0000i	−1.20672	+	1.20672i
$891$		0			0
$892$		−	6.92820i		−	0.231973i
$893$		−	48.0000i		−	1.60626i
$894$		0			0
$895$	6.92820			0.231584
$896$	−2.14359	−	29.8564i	−0.0716124	−	0.997433i
$897$		0			0
$898$	−20.0000	−	20.0000i	−0.667409	−	0.667409i
$899$		−	27.7128i		−	0.924274i
$900$		0			0
$901$	−13.8564			−0.461624
$902$	20.7846	−	20.7846i	0.692052	−	0.692052i
$903$		0			0
$904$	−40.0000	+	40.0000i	−1.33038	+	1.33038i
$905$	−36.0000			−1.19668
$906$		0			0
$907$	6.00000			0.199227			0.0996134	−	0.995026i	$-0.468239\pi$
$907$	6.00000			0.199227			0.0996134	+	0.995026i	$0.468239\pi$
$908$		0			0
$909$		0			0
$910$	−44.7846	+	3.21539i	−1.48460	+	0.106589i
$911$			38.0000i			1.25900i	0.777002	+	0.629498i	$0.216739\pi$
$911$			38.0000i			1.25900i	−0.777002	+	0.629498i	$0.783261\pi$
$912$		0			0
$913$			13.8564i			0.458580i
$914$	−30.0000	−	30.0000i	−0.992312	−	0.992312i
$915$		0			0
$916$		−	6.92820i		−	0.228914i
$917$	13.8564	+	12.0000i	0.457579	+	0.396275i
$918$		0			0
$919$		−	4.00000i		−	0.131948i	−0.997821	−	0.0659739i	$-0.978985\pi$
$919$		−	4.00000i		−	0.131948i	0.997821	−	0.0659739i	$-0.0210154\pi$
$920$	−13.8564	−	13.8564i	−0.456832	−	0.456832i
$921$		0			0
$922$	−31.1769	−	31.1769i	−1.02676	−	1.02676i
$923$		−	6.92820i		−	0.228045i
$924$		0			0
$925$		−	28.0000i		−	0.920634i
$926$	12.0000	−	12.0000i	0.394344	−	0.394344i
$927$		0			0
$928$	32.0000	−	32.0000i	1.05045	−	1.05045i
$929$		−	10.3923i		−	0.340960i	−0.985361	−	0.170480i	$-0.945468\pi$
$929$		−	10.3923i		−	0.340960i	0.985361	−	0.170480i	$-0.0545319\pi$
$930$		0			0
$931$	−48.0000	+	6.92820i	−1.57314	+	0.227063i
$932$		−	8.00000i		−	0.262049i
$933$		0			0
$934$	27.7128	−	27.7128i	0.906791	−	0.906791i
$935$			24.0000i			0.784884i
$936$		0			0
$937$		−	13.8564i		−	0.452669i	−0.974050	−	0.226335i	$-0.927326\pi$
$937$		−	13.8564i		−	0.452669i	0.974050	−	0.226335i	$-0.0726743\pi$
$938$	37.3205	−	2.67949i	1.21856	−	0.0874885i
$939$		0			0
$940$		−	48.0000i		−	1.56559i
$941$	−58.8897			−1.91975			−0.959875	−	0.280428i	$-0.909524\pi$
$941$	−58.8897			−1.91975			−0.959875	+	0.280428i	$0.909524\pi$
$942$		0			0
$943$	−20.7846			−0.676840
$944$			27.7128i			0.901975i
$945$		0			0
$946$	−12.0000	−	12.0000i	−0.390154	−	0.390154i
$947$	−10.0000			−0.324956			−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000			−0.324956			−0.162478	+	0.986712i	$0.551949\pi$
$948$		0			0
$949$		0			0
$950$	−48.4974	+	48.4974i	−1.57346	+	1.57346i
$951$		0			0
$952$	25.8564	−	1.85641i	0.838011	−	0.0601665i
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$		0			0
$955$			76.2102i			2.46611i
$956$	4.00000			0.129369
$957$		0			0
$958$	6.92820	+	6.92820i	0.223840	+	0.223840i
$959$	−27.7128	+	32.0000i	−0.894893	+	1.03333i
$960$		0			0
$961$	−19.0000			−0.612903
$962$	−13.8564	+	13.8564i	−0.446748	+	0.446748i
$963$		0			0
$964$	−27.7128			−0.892570
$965$	20.7846			0.669080
$966$		0			0
$967$			12.0000i			0.385894i	0.981209	+	0.192947i	$0.0618045\pi$
$967$			12.0000i			0.385894i	−0.981209	+	0.192947i	$0.938195\pi$
$968$	−14.0000	+	14.0000i	−0.449977	+	0.449977i
$969$		0			0
$970$	48.0000	−	48.0000i	1.54119	−	1.54119i
$971$			41.5692i			1.33402i	0.745049	+	0.667010i	$0.232426\pi$
$971$			41.5692i			1.33402i	−0.745049	+	0.667010i	$0.767574\pi$
$972$		0			0
$973$	−27.7128	−	24.0000i	−0.888432	−	0.769405i
$974$	4.00000	−	4.00000i	0.128168	−	0.128168i
$975$		0			0
$976$	41.5692			1.33060
$977$	−4.00000			−0.127971			−0.0639857	−	0.997951i	$-0.520381\pi$
$977$	−4.00000			−0.127971			−0.0639857	+	0.997951i	$0.520381\pi$
$978$		0			0
$979$			20.7846i			0.664279i
$980$	−48.0000	+	6.92820i	−1.53330	+	0.221313i
$981$		0			0
$982$	−14.0000	−	14.0000i	−0.446758	−	0.446758i
$983$	13.8564			0.441951			0.220975	−	0.975279i	$-0.429076\pi$
$983$	13.8564			0.441951			0.220975	+	0.975279i	$0.429076\pi$
$984$		0			0
$985$			55.4256i			1.76601i
$986$	27.7128	+	27.7128i	0.882556	+	0.882556i
$987$		0			0
$988$	48.0000			1.52708
$989$			12.0000i			0.381578i
$990$		0			0
$991$			4.00000i			0.127064i	0.997980	+	0.0635321i	$0.0202365\pi$
$991$			4.00000i			0.127064i	−0.997980	+	0.0635321i	$0.979763\pi$
$992$	13.8564	+	13.8564i	0.439941	+	0.439941i
$993$		0			0
$994$	−0.535898	−	7.46410i	−0.0169977	−	0.236747i
$995$	36.0000			1.14128
$996$		0			0
$997$	−24.2487			−0.767964			−0.383982	−	0.923340i	$-0.625448\pi$
$997$	−24.2487			−0.767964			−0.383982	+	0.923340i	$0.625448\pi$
$998$	−6.00000	−	6.00000i	−0.189927	−	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.p.b.307.1	✓	4
3.2	odd	2		504.2.p.e.307.4	yes	4
4.3	odd	2		2016.2.p.b.559.1		4
7.6	odd	2	inner	504.2.p.b.307.2	yes	4
8.3	odd	2	inner	504.2.p.b.307.4	yes	4
8.5	even	2		2016.2.p.b.559.4		4
12.11	even	2		2016.2.p.f.559.3		4
21.20	even	2		504.2.p.e.307.3	yes	4
24.5	odd	2		2016.2.p.f.559.2		4
24.11	even	2		504.2.p.e.307.1	yes	4
28.27	even	2		2016.2.p.b.559.3		4
56.13	odd	2		2016.2.p.b.559.2		4
56.27	even	2	inner	504.2.p.b.307.3	yes	4
84.83	odd	2		2016.2.p.f.559.1		4
168.83	odd	2		504.2.p.e.307.2	yes	4
168.125	even	2		2016.2.p.f.559.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.p.b.307.1	✓	4	1.1	even	1	trivial
504.2.p.b.307.2	yes	4	7.6	odd	2	inner
504.2.p.b.307.3	yes	4	56.27	even	2	inner
504.2.p.b.307.4	yes	4	8.3	odd	2	inner
504.2.p.e.307.1	yes	4	24.11	even	2
504.2.p.e.307.2	yes	4	168.83	odd	2
504.2.p.e.307.3	yes	4	21.20	even	2
504.2.p.e.307.4	yes	4	3.2	odd	2
2016.2.p.b.559.1		4	4.3	odd	2
2016.2.p.b.559.2		4	56.13	odd	2
2016.2.p.b.559.3		4	28.27	even	2
2016.2.p.b.559.4		4	8.5	even	2
2016.2.p.f.559.1		4	84.83	odd	2
2016.2.p.f.559.2		4	24.5	odd	2
2016.2.p.f.559.3		4	12.11	even	2
2016.2.p.f.559.4		4	168.125	even	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -3.46410 q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -3.46410 q^{5} +(-1.73205 + 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(3.46410 + 3.46410i) q^{10} +2.00000 q^{11} +3.46410 q^{13} +(3.73205 - 0.267949i) q^{14} -4.00000 q^{16} -3.46410i q^{17} -6.92820i q^{19} -6.92820i q^{20} +(-2.00000 - 2.00000i) q^{22} +2.00000i q^{23} +7.00000 q^{25} +(-3.46410 - 3.46410i) q^{26} +(-4.00000 - 3.46410i) q^{28} -8.00000i q^{29} +3.46410 q^{31} +(4.00000 + 4.00000i) q^{32} +(-3.46410 + 3.46410i) q^{34} +(6.00000 - 6.92820i) q^{35} -4.00000i q^{37} +(-6.92820 + 6.92820i) q^{38} +(-6.92820 + 6.92820i) q^{40} +10.3923i q^{41} +6.00000 q^{43} +4.00000i q^{44} +(2.00000 - 2.00000i) q^{46} +6.92820 q^{47} +(-1.00000 - 6.92820i) q^{49} +(-7.00000 - 7.00000i) q^{50} +6.92820i q^{52} -4.00000i q^{53} -6.92820 q^{55} +(0.535898 + 7.46410i) q^{56} +(-8.00000 + 8.00000i) q^{58} -6.92820i q^{59} -10.3923 q^{61} +(-3.46410 - 3.46410i) q^{62} -8.00000i q^{64} -12.0000 q^{65} +10.0000 q^{67} +6.92820 q^{68} +(-12.9282 + 0.928203i) q^{70} -2.00000i q^{71} +(-4.00000 + 4.00000i) q^{74} +13.8564 q^{76} +(-3.46410 + 4.00000i) q^{77} -12.0000i q^{79} +13.8564 q^{80} +(10.3923 - 10.3923i) q^{82} +6.92820i q^{83} +12.0000i q^{85} +(-6.00000 - 6.00000i) q^{86} +(4.00000 - 4.00000i) q^{88} +10.3923i q^{89} +(-6.00000 + 6.92820i) q^{91} -4.00000 q^{92} +(-6.92820 - 6.92820i) q^{94} +24.0000i q^{95} -13.8564i q^{97} +(-5.92820 + 7.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 8 * q^8	\( 4 q - 4 q^{2} + 8 q^{8} + 8 q^{11} + 8 q^{14} - 16 q^{16} - 8 q^{22} + 28 q^{25} - 16 q^{28} + 16 q^{32} + 24 q^{35} + 24 q^{43} + 8 q^{46} - 4 q^{49} - 28 q^{50} + 16 q^{56} - 32 q^{58} - 48 q^{65} + 40 q^{67} - 24 q^{70} - 16 q^{74} - 24 q^{86} + 16 q^{88} - 24 q^{91} - 16 q^{92} + 4 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 8 * q^8 + 8 * q^11 + 8 * q^14 - 16 * q^16 - 8 * q^22 + 28 * q^25 - 16 * q^28 + 16 * q^32 + 24 * q^35 + 24 * q^43 + 8 * q^46 - 4 * q^49 - 28 * q^50 + 16 * q^56 - 32 * q^58 - 48 * q^65 + 40 * q^67 - 24 * q^70 - 16 * q^74 - 24 * q^86 + 16 * q^88 - 24 * q^91 - 16 * q^92 + 4 * q^98

Introduction

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