LMFDB - Embedded newform 1323.2.h.e.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1323.226
Dual form			1323.2.h.e.802.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69963 q^{2} +0.888736 q^{4} +(1.79418 + 3.10761i) q^{5} +1.88874 q^{8} +O(q^{10})$	\(q-1.69963 q^{2} +0.888736 q^{4} +(1.79418 + 3.10761i) q^{5} +1.88874 q^{8} +(-3.04944 - 5.28179i) q^{10} +(-1.40545 + 2.43430i) q^{11} +(0.500000 - 0.866025i) q^{13} -4.98762 q^{16} +(2.05563 + 3.56046i) q^{17} +(-0.444368 + 0.769668i) q^{19} +(1.59455 + 2.76185i) q^{20} +(2.38874 - 4.13741i) q^{22} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} +(-0.849814 + 1.47192i) q^{26} +(-0.849814 - 1.47192i) q^{29} +6.98762 q^{31} +4.69963 q^{32} +(-3.49381 - 6.05146i) q^{34} +(-2.38255 + 4.12669i) q^{37} +(0.755260 - 1.30815i) q^{38} +(3.38874 + 5.86946i) q^{40} +(2.70582 - 4.68661i) q^{41} +(-2.60507 - 4.51212i) q^{43} +(-1.24907 + 2.16345i) q^{44} +(-4.99381 - 8.64953i) q^{46} -2.66621 q^{47} +(6.69344 - 11.5934i) q^{50} +(0.444368 - 0.769668i) q^{52} +(-0.0618219 - 0.107079i) q^{53} -10.0865 q^{55} +(1.44437 + 2.50172i) q^{58} -8.87636 q^{59} -3.87636 q^{61} -11.8764 q^{62} +1.98762 q^{64} +3.58836 q^{65} +12.3090 q^{67} +(1.82691 + 3.16431i) q^{68} +2.87636 q^{71} +(-5.32072 - 9.21576i) q^{73} +(4.04944 - 7.01384i) q^{74} +(-0.394926 + 0.684031i) q^{76} -7.08650 q^{79} +(-8.94870 - 15.4996i) q^{80} +(-4.59888 + 7.96550i) q^{82} +(2.05563 + 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} +(4.42766 + 7.66893i) q^{86} +(-2.65452 + 4.59776i) q^{88} +(-4.80470 + 8.32199i) q^{89} +(2.61126 + 4.52284i) q^{92} +4.53156 q^{94} -3.18911 q^{95} +(3.66071 + 6.34053i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8	$ 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} + 6 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} + q^{26} + q^{29} + 6 q^{31} + 16 q^{32} - 3 q^{34} + 3 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 18 q^{47} + 10 q^{50} + 3 q^{52} - 18 q^{53} + 12 q^{55} + 9 q^{58} - 18 q^{59} + 12 q^{61} - 36 q^{62} - 24 q^{64} + 10 q^{65} - 6 q^{68} - 18 q^{71} + 3 q^{73} + 6 q^{74} - 21 q^{76} + 30 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 2 q^{89} + 15 q^{92} - 48 q^{94} - 32 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8 - 2 * q^11 + 3 * q^13 + 6 * q^16 + 12 * q^17 - 3 * q^19 + 16 * q^20 + 15 * q^22 - 6 * q^25 + q^26 + q^29 + 6 * q^31 + 16 * q^32 - 3 * q^34 + 3 * q^37 - 8 * q^38 + 21 * q^40 + 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 - 18 * q^47 + 10 * q^50 + 3 * q^52 - 18 * q^53 + 12 * q^55 + 9 * q^58 - 18 * q^59 + 12 * q^61 - 36 * q^62 - 24 * q^64 + 10 * q^65 - 6 * q^68 - 18 * q^71 + 3 * q^73 + 6 * q^74 - 21 * q^76 + 30 * q^79 - 11 * q^80 + 9 * q^82 + 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 2 * q^89 + 15 * q^92 - 48 * q^94 - 32 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.69963			−1.20182			−0.600909	−	0.799317i	$-0.705195\pi$
$2$	−1.69963			−1.20182			−0.600909	+	0.799317i	$0.705195\pi$
$3$		0			0
$3$		0			0
$4$	0.888736			0.444368
$5$	1.79418	+	3.10761i	0.802383	+	1.38977i	0.918044	+	0.396479i	$0.129768\pi$
$5$	1.79418	+	3.10761i	0.802383	+	1.38977i	−0.115661	+	0.993289i	$0.536899\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.88874			0.667769
$9$		0			0
$10$	−3.04944	−	5.28179i	−0.964318	−	1.67025i
$11$	−1.40545	+	2.43430i	−0.423758	+	0.733970i	−0.996304	−	0.0859026i	$-0.972623\pi$
$11$	−1.40545	+	2.43430i	−0.423758	+	0.733970i	0.572546	+	0.819873i	$0.305956\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$		0			0
$16$	−4.98762			−1.24691
$17$	2.05563	+	3.56046i	0.498564	+	0.863538i	0.999999	−	0.00165734i	$-0.000527549\pi$
$17$	2.05563	+	3.56046i	0.498564	+	0.863538i	−0.501435	+	0.865196i	$0.667194\pi$
$18$		0			0
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	−0.912486	−	0.409108i	$-0.865840\pi$
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	0.810541	+	0.585682i	$0.199173\pi$
$20$	1.59455	+	2.76185i	0.356553	+	0.617568i
$21$		0			0
$22$	2.38874	−	4.13741i	0.509280	−	0.882099i
$23$	2.93818	+	5.08907i	0.612652	+	1.06115i	0.990792	+	0.135396i	$0.0432308\pi$
$23$	2.93818	+	5.08907i	0.612652	+	1.06115i	−0.378139	+	0.925749i	$0.623436\pi$
$24$		0			0
$25$	−3.93818	+	6.82112i	−0.787636	+	1.36422i
$26$	−0.849814	+	1.47192i	−0.166662	+	0.288667i
$27$		0			0
$28$		0			0
$29$	−0.849814	−	1.47192i	−0.157807	−	0.273329i	0.776271	−	0.630399i	$-0.217109\pi$
$29$	−0.849814	−	1.47192i	−0.157807	−	0.273329i	−0.934077	+	0.357071i	$0.883776\pi$
$30$		0			0
$31$	6.98762			1.25501			0.627507	−	0.778611i	$-0.284075\pi$
$31$	6.98762			1.25501			0.627507	+	0.778611i	$0.284075\pi$
$32$	4.69963			0.830785
$33$		0			0
$34$	−3.49381	−	6.05146i	−0.599183	−	1.03782i
$35$		0			0
$36$		0			0
$37$	−2.38255	+	4.12669i	−0.391688	+	0.678424i	−0.992672	−	0.120837i	$-0.961442\pi$
$37$	−2.38255	+	4.12669i	−0.391688	+	0.678424i	0.600984	+	0.799261i	$0.294775\pi$
$38$	0.755260	−	1.30815i	0.122519	−	0.212210i
$39$		0			0
$40$	3.38874	+	5.86946i	0.535806	+	0.928044i
$41$	2.70582	−	4.68661i	0.422578	−	0.731926i	−0.573613	−	0.819126i	$-0.694459\pi$
$41$	2.70582	−	4.68661i	0.422578	−	0.731926i	0.996191	+	0.0872002i	$0.0277920\pi$
$42$		0			0
$43$	−2.60507	−	4.51212i	−0.397270	−	0.688092i	0.596118	−	0.802897i	$-0.296709\pi$
$43$	−2.60507	−	4.51212i	−0.397270	−	0.688092i	−0.993388	+	0.114805i	$0.963376\pi$
$44$	−1.24907	+	2.16345i	−0.188304	+	0.326153i
$45$		0			0
$46$	−4.99381	−	8.64953i	−0.736297	−	1.27530i
$47$	−2.66621			−0.388906			−0.194453	−	0.980912i	$-0.562293\pi$
$47$	−2.66621			−0.388906			−0.194453	+	0.980912i	$0.562293\pi$
$48$		0			0
$49$		0			0
$50$	6.69344	−	11.5934i	0.946595	−	1.63955i
$51$		0			0
$52$	0.444368	−	0.769668i	0.0616227	−	0.106734i
$53$	−0.0618219	−	0.107079i	−0.00849190	−	0.0147084i	0.861748	−	0.507336i	$-0.169370\pi$
$53$	−0.0618219	−	0.107079i	−0.00849190	−	0.0147084i	−0.870240	+	0.492628i	$0.836036\pi$
$54$		0			0
$55$	−10.0865			−1.36006
$56$		0			0
$57$		0			0
$58$	1.44437	+	2.50172i	0.189655	+	0.328492i
$59$	−8.87636			−1.15560			−0.577802	−	0.816177i	$-0.696089\pi$
$59$	−8.87636			−1.15560			−0.577802	+	0.816177i	$0.696089\pi$
$60$		0			0
$61$	−3.87636			−0.496317			−0.248158	−	0.968720i	$-0.579825\pi$
$61$	−3.87636			−0.496317			−0.248158	+	0.968720i	$0.579825\pi$
$62$	−11.8764			−1.50830
$63$		0			0
$64$	1.98762			0.248453
$65$	3.58836			0.445082
$66$		0			0
$67$	12.3090			1.50379			0.751894	−	0.659284i	$-0.229141\pi$
$67$	12.3090			1.50379			0.751894	+	0.659284i	$0.229141\pi$
$68$	1.82691	+	3.16431i	0.221546	+	0.383729i
$69$		0			0
$70$		0			0
$71$	2.87636			0.341361			0.170680	−	0.985326i	$-0.445403\pi$
$71$	2.87636			0.341361			0.170680	+	0.985326i	$0.445403\pi$
$72$		0			0
$73$	−5.32072	−	9.21576i	−0.622744	−	1.07862i	−0.988973	−	0.148099i	$-0.952685\pi$
$73$	−5.32072	−	9.21576i	−0.622744	−	1.07862i	0.366229	−	0.930525i	$-0.380649\pi$
$74$	4.04944	−	7.01384i	0.470738	−	0.815342i
$75$		0			0
$76$	−0.394926	+	0.684031i	−0.0453011	+	0.0784638i
$77$		0			0
$78$		0			0
$79$	−7.08650			−0.797294			−0.398647	−	0.917104i	$-0.630520\pi$
$79$	−7.08650			−0.797294			−0.398647	+	0.917104i	$0.630520\pi$
$80$	−8.94870	−	15.4996i	−1.00049	−	1.73291i
$81$		0			0
$82$	−4.59888	+	7.96550i	−0.507862	+	0.879642i
$83$	2.05563	+	3.56046i	0.225635	+	0.390811i	0.956510	−	0.291700i	$-0.0942210\pi$
$83$	2.05563	+	3.56046i	0.225635	+	0.390811i	−0.730875	+	0.682512i	$0.760888\pi$
$84$		0			0
$85$	−7.37636	+	12.7762i	−0.800078	+	1.38578i
$86$	4.42766	+	7.66893i	0.477447	+	0.826962i
$87$		0			0
$88$	−2.65452	+	4.59776i	−0.282972	+	0.490123i
$89$	−4.80470	+	8.32199i	−0.509297	+	0.882129i	0.490645	+	0.871360i	$0.336761\pi$
$89$	−4.80470	+	8.32199i	−0.509297	+	0.882129i	−0.999942	+	0.0107692i	$0.996572\pi$
$90$		0			0
$91$		0			0
$92$	2.61126	+	4.52284i	0.272243	+	0.471539i
$93$		0			0
$94$	4.53156			0.467395
$95$	−3.18911			−0.327196
$96$		0			0
$97$	3.66071	+	6.34053i	0.371688	+	0.643783i	0.989825	−	0.142287i	$-0.0454456\pi$
$97$	3.66071	+	6.34053i	0.371688	+	0.643783i	−0.618137	+	0.786070i	$0.712112\pi$
$98$		0			0
$99$		0			0
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	−1.73236	+	3.00054i	−0.172376	+	0.298564i	−0.939250	−	0.343233i	$-0.888478\pi$
$101$	−1.73236	+	3.00054i	−0.172376	+	0.298564i	0.766874	+	0.641798i	$0.221811\pi$
$102$		0			0
$103$	−7.93818	−	13.7493i	−0.782172	−	1.35476i	−0.930674	−	0.365849i	$-0.880779\pi$
$103$	−7.93818	−	13.7493i	−0.782172	−	1.35476i	0.148502	−	0.988912i	$-0.452555\pi$
$104$	0.944368	−	1.63569i	0.0926029	−	0.160393i
$105$		0			0
$106$	0.105074	+	0.181994i	0.0102057	+	0.0176768i
$107$	−2.67673	+	4.63623i	−0.258769	+	0.448201i	−0.965912	−	0.258869i	$-0.916650\pi$
$107$	−2.67673	+	4.63623i	−0.258769	+	0.448201i	0.707143	+	0.707070i	$0.249984\pi$
$108$		0			0
$109$	9.43199	+	16.3367i	0.903421	+	1.56477i	0.823023	+	0.568008i	$0.192286\pi$
$109$	9.43199	+	16.3367i	0.903421	+	1.56477i	0.0803973	+	0.996763i	$0.474381\pi$
$110$	17.1433			1.63455
$111$		0			0
$112$		0			0
$113$	−9.27561	+	16.0658i	−0.872576	+	1.51135i	−0.0132538	+	0.999912i	$0.504219\pi$
$113$	−9.27561	+	16.0658i	−0.872576	+	1.51135i	−0.859322	+	0.511434i	$0.829114\pi$
$114$		0			0
$115$	−10.5433	+	18.2614i	−0.983163	+	1.70289i
$116$	−0.755260	−	1.30815i	−0.0701242	−	0.121459i
$117$		0			0
$118$	15.0865			1.38883
$119$		0			0
$120$		0			0
$121$	1.54944	+	2.68371i	0.140858	+	0.243974i
$122$	6.58836			0.596482
$123$		0			0
$124$	6.21015			0.557688
$125$	−10.3214			−0.923175
$126$		0			0
$127$	9.98762			0.886258			0.443129	−	0.896458i	$-0.353868\pi$
$127$	9.98762			0.886258			0.443129	+	0.896458i	$0.353868\pi$
$128$	−12.7775			−1.12938
$129$		0			0
$130$	−6.09888			−0.534908
$131$	−8.02654	−	13.9024i	−0.701282	−	1.21466i	−0.968017	−	0.250886i	$-0.919278\pi$
$131$	−8.02654	−	13.9024i	−0.701282	−	1.21466i	0.266734	−	0.963770i	$-0.414055\pi$
$132$		0			0
$133$		0			0
$134$	−20.9208			−1.80728
$135$		0			0
$136$	3.88255	+	6.72477i	0.332926	+	0.576644i
$137$	−6.49381	+	11.2476i	−0.554804	+	0.960948i	0.443115	+	0.896465i	$0.353873\pi$
$137$	−6.49381	+	11.2476i	−0.554804	+	0.960948i	−0.997919	+	0.0644834i	$0.979460\pi$
$138$		0			0
$139$	0.555632	−	0.962383i	0.0471281	−	0.0816283i	−0.841499	−	0.540259i	$-0.818326\pi$
$139$	0.555632	−	0.962383i	0.0471281	−	0.0816283i	0.888627	+	0.458630i	$0.151660\pi$
$140$		0			0
$141$		0			0
$142$	−4.88874			−0.410254
$143$	1.40545	+	2.43430i	0.117529	+	0.203567i
$144$		0			0
$145$	3.04944	−	5.28179i	0.253242	−	0.438629i
$146$	9.04325	+	15.6634i	0.748425	+	1.29631i
$147$		0			0
$148$	−2.11745	+	3.66754i	−0.174054	+	0.301470i
$149$	4.21634	+	7.30291i	0.345416	+	0.598278i	0.985429	−	0.170086i	$-0.0544045\pi$
$149$	4.21634	+	7.30291i	0.345416	+	0.598278i	−0.640013	+	0.768364i	$0.721071\pi$
$150$		0			0
$151$	7.42580	−	12.8619i	0.604303	−	1.04668i	−0.387858	−	0.921719i	$-0.626785\pi$
$151$	7.42580	−	12.8619i	0.604303	−	1.04668i	0.992161	−	0.124964i	$-0.0398816\pi$
$152$	−0.839294	+	1.45370i	−0.0680757	+	0.117911i
$153$		0			0
$154$		0			0
$155$	12.5371	+	21.7148i	1.00700	+	1.74418i
$156$		0			0
$157$	−2.88874			−0.230546			−0.115273	−	0.993334i	$-0.536774\pi$
$157$	−2.88874			−0.230546			−0.115273	+	0.993334i	$0.536774\pi$
$158$	12.0444			0.958203
$159$		0			0
$160$	8.43199	+	14.6046i	0.666607	+	1.15460i
$161$		0			0
$162$		0			0
$163$	5.15452	−	8.92788i	0.403733	−	0.699286i	−0.590440	−	0.807081i	$-0.701046\pi$
$163$	5.15452	−	8.92788i	0.403733	−	0.699286i	0.994173	+	0.107796i	$0.0343792\pi$
$164$	2.40476	−	4.16516i	0.187780	−	0.325245i
$165$		0			0
$166$	−3.49381	−	6.05146i	−0.271172	−	0.469684i
$167$	−6.07598	+	10.5239i	−0.470174	+	0.814365i	−0.999418	−	0.0341045i	$-0.989142\pi$
$167$	−6.07598	+	10.5239i	−0.470174	+	0.814365i	0.529244	+	0.848469i	$0.322475\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	12.5371	−	21.7148i	0.961549	−	1.66545i
$171$		0			0
$172$	−2.31522	−	4.01008i	−0.176534	−	0.305766i
$173$	−6.60940			−0.502504			−0.251252	−	0.967922i	$-0.580842\pi$
$173$	−6.60940			−0.502504			−0.251252	+	0.967922i	$0.580842\pi$
$174$		0			0
$175$		0			0
$176$	7.00983	−	12.1414i	0.528386	−	0.915191i
$177$		0			0
$178$	8.16621	−	14.1443i	0.612083	−	1.06016i
$179$	−1.92147	−	3.32808i	−0.143617	−	0.248752i	0.785239	−	0.619193i	$-0.212540\pi$
$179$	−1.92147	−	3.32808i	−0.143617	−	0.248752i	−0.928856	+	0.370440i	$0.879207\pi$
$180$		0			0
$181$	−18.5426			−1.37826			−0.689129	−	0.724639i	$-0.742007\pi$
$181$	−18.5426			−1.37826			−0.689129	+	0.724639i	$0.742007\pi$
$182$		0			0
$183$		0			0
$184$	5.54944	+	9.61192i	0.409110	+	0.708600i
$185$	−17.0989			−1.25713
$186$		0			0
$187$	−11.5563			−0.845082
$188$	−2.36955			−0.172818
$189$		0			0
$190$	5.42030			0.393230
$191$	−4.63416			−0.335316			−0.167658	−	0.985845i	$-0.553620\pi$
$191$	−4.63416			−0.335316			−0.167658	+	0.985845i	$0.553620\pi$
$192$		0			0
$193$	−25.2967			−1.82089			−0.910446	−	0.413627i	$-0.864262\pi$
$193$	−25.2967			−1.82089			−0.910446	+	0.413627i	$0.864262\pi$
$194$	−6.22184	−	10.7765i	−0.446702	−	0.773711i
$195$		0			0
$196$		0			0
$197$	−10.7207			−0.763816			−0.381908	−	0.924200i	$-0.624733\pi$
$197$	−10.7207			−0.763816			−0.381908	+	0.924200i	$0.624733\pi$
$198$		0			0
$199$	−4.38323	−	7.59199i	−0.310719	−	0.538182i	0.667799	−	0.744342i	$-0.267237\pi$
$199$	−4.38323	−	7.59199i	−0.310719	−	0.538182i	−0.978518	+	0.206160i	$0.933903\pi$
$200$	−7.43818	+	12.8833i	−0.525959	+	0.910987i
$201$		0			0
$202$	2.94437	−	5.09979i	0.207165	−	0.358820i
$203$		0			0
$204$		0			0
$205$	19.4189			1.35628
$206$	13.4920	+	23.3687i	0.940029	+	1.62818i
$207$		0			0
$208$	−2.49381	+	4.31941i	−0.172915	+	0.299497i
$209$	−1.24907	−	2.16345i	−0.0864000	−	0.149649i
$210$		0			0
$211$	−5.26509	+	9.11941i	−0.362464	+	0.627806i	−0.988366	−	0.152096i	$-0.951398\pi$
$211$	−5.26509	+	9.11941i	−0.362464	+	0.627806i	0.625902	+	0.779902i	$0.284731\pi$
$212$	−0.0549434	−	0.0951647i	−0.00377353	−	0.00653594i
$213$		0			0
$214$	4.54944	−	7.87987i	0.310993	−	0.538656i
$215$	9.34795	−	16.1911i	0.637525	−	1.10423i
$216$		0			0
$217$		0			0
$218$	−16.0309	−	27.7663i	−1.08575	−	1.88057i
$219$		0			0
$220$	−8.96424			−0.604369
$221$	4.11126			0.276554
$222$		0			0
$223$	−2.83379	−	4.90827i	−0.189765	−	0.328682i	0.755407	−	0.655256i	$-0.227439\pi$
$223$	−2.83379	−	4.90827i	−0.189765	−	0.328682i	−0.945172	+	0.326574i	$0.894106\pi$
$224$		0			0
$225$		0			0
$226$	15.7651	−	27.3059i	1.04868	−	1.81636i
$227$	5.54944	−	9.61192i	0.368329	−	0.637965i	−0.620975	−	0.783830i	$-0.713263\pi$
$227$	5.54944	−	9.61192i	0.368329	−	0.637965i	0.989304	+	0.145865i	$0.0465965\pi$
$228$		0			0
$229$	9.82141	+	17.0112i	0.649017	+	1.12413i	0.983358	+	0.181679i	$0.0581530\pi$
$229$	9.82141	+	17.0112i	0.649017	+	1.12413i	−0.334341	+	0.942452i	$0.608514\pi$
$230$	17.9196	−	31.0377i	1.18158	−	2.04656i
$231$		0			0
$232$	−1.60507	−	2.78007i	−0.105378	−	0.182521i
$233$	4.48143	−	7.76207i	0.293588	−	0.508510i	−0.681067	−	0.732221i	$-0.738484\pi$
$233$	4.48143	−	7.76207i	0.293588	−	0.508510i	0.974656	+	0.223711i	$0.0718172\pi$
$234$		0			0
$235$	−4.78366	−	8.28554i	−0.312052	−	0.540489i
$236$	−7.88874			−0.513513
$237$		0			0
$238$		0			0
$239$	5.61126	−	9.71899i	0.362963	−	0.628670i	−0.625484	−	0.780237i	$-0.715099\pi$
$239$	5.61126	−	9.71899i	0.362963	−	0.628670i	0.988447	+	0.151567i	$0.0484320\pi$
$240$		0			0
$241$	−3.49312	+	6.05026i	−0.225012	+	0.389732i	−0.956323	−	0.292312i	$-0.905575\pi$
$241$	−3.49312	+	6.05026i	−0.225012	+	0.389732i	0.731311	+	0.682044i	$0.238909\pi$
$242$	−2.63348	−	4.56131i	−0.169286	−	0.293212i
$243$		0			0
$244$	−3.44506			−0.220547
$245$		0			0
$246$		0			0
$247$	0.444368	+	0.769668i	0.0282745	+	0.0489728i
$248$	13.1978			0.838059
$249$		0			0
$250$	17.5426			1.10949
$251$	4.62041			0.291638			0.145819	−	0.989311i	$-0.453418\pi$
$251$	4.62041			0.291638			0.145819	+	0.989311i	$0.453418\pi$
$252$		0			0
$253$	−16.5178			−1.03847
$254$	−16.9752			−1.06512
$255$		0			0
$256$	17.7417			1.10886
$257$	0.712008	+	1.23323i	0.0444138	+	0.0769270i	0.887378	−	0.461043i	$-0.152525\pi$
$257$	0.712008	+	1.23323i	0.0444138	+	0.0769270i	−0.842964	+	0.537970i	$0.819191\pi$
$258$		0			0
$259$		0			0
$260$	3.18911			0.197780
$261$		0			0
$262$	13.6421	+	23.6289i	0.842814	+	1.45980i
$263$	8.13162	−	14.0844i	0.501417	−	0.868480i	−0.498582	−	0.866843i	$-0.666146\pi$
$263$	8.13162	−	14.0844i	0.501417	−	0.868480i	0.999999	−	0.00163692i	$-0.000521048\pi$
$264$		0			0
$265$	0.221840	−	0.384237i	0.0136275	−	0.0236035i
$266$		0			0
$267$		0			0
$268$	10.9395			0.668235
$269$	9.32691	+	16.1547i	0.568672	+	0.984969i	0.996698	+	0.0812022i	$0.0258759\pi$
$269$	9.32691	+	16.1547i	0.568672	+	0.984969i	−0.428026	+	0.903767i	$0.640791\pi$
$270$		0			0
$271$	1.98143	−	3.43194i	0.120363	−	0.208475i	−0.799548	−	0.600603i	$-0.794927\pi$
$271$	1.98143	−	3.43194i	0.120363	−	0.208475i	0.919911	+	0.392127i	$0.128261\pi$
$272$	−10.2527	−	17.7582i	−0.621662	−	1.07675i
$273$		0			0
$274$	11.0371	−	19.1168i	0.666773	−	1.15489i
$275$	−11.0698	−	19.1734i	−0.667534	−	1.15620i
$276$		0			0
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	−0.828838	−	0.559488i	$-0.810998\pi$
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	0.898950	+	0.438051i	$0.144331\pi$
$278$	−0.944368	+	1.63569i	−0.0566394	+	0.0981024i
$279$		0			0
$280$		0			0
$281$	13.9975	+	24.2443i	0.835018	+	1.44629i	0.894016	+	0.448035i	$0.147876\pi$
$281$	13.9975	+	24.2443i	0.835018	+	1.44629i	−0.0589978	+	0.998258i	$0.518790\pi$
$282$		0			0
$283$	−10.3200			−0.613462			−0.306731	−	0.951796i	$-0.599235\pi$
$283$	−10.3200			−0.613462			−0.306731	+	0.951796i	$0.599235\pi$
$284$	2.55632			0.151690
$285$		0			0
$286$	−2.38874	−	4.13741i	−0.141249	−	0.244650i
$287$		0			0
$288$		0			0
$289$	0.0487535	−	0.0844436i	0.00286785	−	0.00496727i
$290$	−5.18292	+	8.97708i	−0.304351	+	0.527152i
$291$		0			0
$292$	−4.72872	−	8.19038i	−0.276727	−	0.479306i
$293$	15.3480	−	26.5834i	0.896637	−	1.55302i	0.0648718	−	0.997894i	$-0.479336\pi$
$293$	15.3480	−	26.5834i	0.896637	−	1.55302i	0.831765	−	0.555127i	$-0.187330\pi$
$294$		0			0
$295$	−15.9258	−	27.5843i	−0.927236	−	1.60602i
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$		0			0
$298$	−7.16621	−	12.4122i	−0.415127	−	0.719021i
$299$	5.87636			0.339838
$300$		0			0
$301$		0			0
$302$	−12.6211	+	21.8604i	−0.726262	+	1.25792i
$303$		0			0
$304$	2.21634	−	3.83881i	0.127116	−	0.220171i
$305$	−6.95489	−	12.0462i	−0.398236	−	0.689765i
$306$		0			0
$307$	11.4437			0.653125			0.326563	−	0.945176i	$-0.394110\pi$
$307$	11.4437			0.653125			0.326563	+	0.945176i	$0.394110\pi$
$308$		0			0
$309$		0			0
$310$	−21.3083	−	36.9071i	−1.21023	−	2.09618i
$311$	11.9629			0.678352			0.339176	−	0.940723i	$-0.389852\pi$
$311$	11.9629			0.678352			0.339176	+	0.940723i	$0.389852\pi$
$312$		0			0
$313$	13.5439			0.765549			0.382774	−	0.923842i	$-0.374969\pi$
$313$	13.5439			0.765549			0.382774	+	0.923842i	$0.374969\pi$
$314$	4.90978			0.277075
$315$		0			0
$316$	−6.29803			−0.354292
$317$	29.9629			1.68288			0.841441	−	0.540349i	$-0.181708\pi$
$317$	29.9629			1.68288			0.841441	+	0.540349i	$0.181708\pi$
$318$		0			0
$319$	4.77747			0.267487
$320$	3.56615	+	6.17676i	0.199354	+	0.345291i
$321$		0			0
$322$		0			0
$323$	−3.65383			−0.203304
$324$		0			0
$325$	3.93818	+	6.82112i	0.218451	+	0.378368i
$326$	−8.76076	+	15.1741i	−0.485214	+	0.840415i
$327$		0			0
$328$	5.11058	−	8.85178i	0.282184	−	0.488758i
$329$		0			0
$330$		0			0
$331$	2.08650			0.114685			0.0573423	−	0.998355i	$-0.481737\pi$
$331$	2.08650			0.114685			0.0573423	+	0.998355i	$0.481737\pi$
$332$	1.82691	+	3.16431i	0.100265	+	0.173664i
$333$		0			0
$334$	10.3269	−	17.8867i	0.565064	−	0.978719i
$335$	22.0846	+	38.2517i	1.20661	+	2.08992i
$336$		0			0
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	−0.556325	−	0.830965i	$-0.687789\pi$
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	0.997799	+	0.0663093i	$0.0211224\pi$
$338$	−10.1978	−	17.6631i	−0.554686	−	0.960743i
$339$		0			0
$340$	−6.55563	+	11.3547i	−0.355529	+	0.615794i
$341$	−9.82072	+	17.0100i	−0.531822	+	0.921143i
$342$		0			0
$343$		0			0
$344$	−4.92030	−	8.52220i	−0.265285	−	0.459486i
$345$		0			0
$346$	11.2335			0.603918
$347$	−11.2670			−0.604842			−0.302421	−	0.953175i	$-0.597795\pi$
$347$	−11.2670			−0.604842			−0.302421	+	0.953175i	$0.597795\pi$
$348$		0			0
$349$	−0.0988844	−	0.171273i	−0.00529316	−	0.00916803i	0.863367	−	0.504577i	$-0.168352\pi$
$349$	−0.0988844	−	0.171273i	−0.00529316	−	0.00916803i	−0.868660	+	0.495409i	$0.835018\pi$
$350$		0			0
$351$		0			0
$352$	−6.60507	+	11.4403i	−0.352052	+	0.609771i
$353$	6.25093	−	10.8269i	0.332703	−	0.576259i	−0.650338	−	0.759645i	$-0.725373\pi$
$353$	6.25093	−	10.8269i	0.332703	−	0.576259i	0.983041	+	0.183386i	$0.0587059\pi$
$354$		0			0
$355$	5.16071	+	8.93861i	0.273902	+	0.474412i
$356$	−4.27011	+	7.39605i	−0.226315	+	0.391990i
$357$		0			0
$358$	3.26578	+	5.65650i	0.172602	+	0.298955i
$359$	10.0098	−	17.3375i	0.528299	−	0.915040i	−0.471157	−	0.882049i	$-0.656163\pi$
$359$	10.0098	−	17.3375i	0.528299	−	0.915040i	0.999456	−	0.0329908i	$-0.0105032\pi$
$360$		0			0
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	31.5155			1.65642
$363$		0			0
$364$		0			0
$365$	19.0927	−	33.0695i	0.999357	−	1.73094i
$366$		0			0
$367$	15.0364	−	26.0438i	0.784892	−	1.35947i	−0.144171	−	0.989553i	$-0.546052\pi$
$367$	15.0364	−	26.0438i	0.784892	−	1.35947i	0.929063	−	0.369921i	$-0.120615\pi$
$368$	−14.6545	−	25.3824i	−0.763919	−	1.32315i
$369$		0			0
$370$	29.0617			1.51085
$371$		0			0
$372$		0			0
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	0.760863	−	0.648913i	$-0.224776\pi$
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	−0.942406	+	0.334470i	$0.891443\pi$
$374$	19.6414			1.01564
$375$		0			0
$376$	−5.03576			−0.259700
$377$	−1.69963			−0.0875353
$378$		0			0
$379$	−19.0741			−0.979772			−0.489886	−	0.871787i	$-0.662962\pi$
$379$	−19.0741			−0.979772			−0.489886	+	0.871787i	$0.662962\pi$
$380$	−2.83427			−0.145395
$381$		0			0
$382$	7.87636			0.402989
$383$	−1.60507	−	2.78007i	−0.0820155	−	0.142055i	0.822100	−	0.569343i	$-0.192802\pi$
$383$	−1.60507	−	2.78007i	−0.0820155	−	0.142055i	−0.904116	+	0.427288i	$0.859469\pi$
$384$		0			0
$385$		0			0
$386$	42.9949			2.18838
$387$		0			0
$388$	3.25340	+	5.63506i	0.165166	+	0.286077i
$389$	2.56801	−	4.44793i	0.130203	−	0.225519i	−0.793552	−	0.608503i	$-0.791770\pi$
$389$	2.56801	−	4.44793i	0.130203	−	0.225519i	0.923755	+	0.382984i	$0.125104\pi$
$390$		0			0
$391$	−12.0796	+	20.9225i	−0.610893	+	1.05810i
$392$		0			0
$393$		0			0
$394$	18.2212			0.917968
$395$	−12.7145	−	22.0221i	−0.639735	−	1.10805i
$396$		0			0
$397$	11.4691	−	19.8650i	0.575615	−	0.996995i	−0.420359	−	0.907358i	$-0.638096\pi$
$397$	11.4691	−	19.8650i	0.575615	−	0.996995i	0.995975	−	0.0896370i	$-0.0285707\pi$
$398$	7.44987	+	12.9036i	0.373428	+	0.646797i
$399$		0			0
$400$	19.6421	−	34.0212i	0.982107	−	1.70106i
$401$	−9.10507	−	15.7705i	−0.454686	−	0.787539i	0.543984	−	0.839095i	$-0.316915\pi$
$401$	−9.10507	−	15.7705i	−0.454686	−	0.787539i	−0.998670	+	0.0515566i	$0.983582\pi$
$402$		0			0
$403$	3.49381	−	6.05146i	0.174039	−	0.301445i
$404$	−1.53961	+	2.66668i	−0.0765985	+	0.132672i
$405$		0			0
$406$		0			0
$407$	−6.69708	−	11.5997i	−0.331962	−	0.574975i
$408$		0			0
$409$	15.3324			0.758139			0.379070	−	0.925368i	$-0.376244\pi$
$409$	15.3324			0.758139			0.379070	+	0.925368i	$0.376244\pi$
$410$	−33.0049			−1.63000
$411$		0			0
$412$	−7.05494	−	12.2195i	−0.347572	−	0.602013i
$413$		0			0
$414$		0			0
$415$	−7.37636	+	12.7762i	−0.362091	+	0.627160i
$416$	2.34981	−	4.07000i	0.115209	−	0.199548i
$417$		0			0
$418$	2.12296	+	3.67707i	0.103837	+	0.179851i
$419$	−5.28435	+	9.15276i	−0.258157	+	0.447142i	−0.965748	−	0.259481i	$-0.916449\pi$
$419$	−5.28435	+	9.15276i	−0.258157	+	0.447142i	0.707591	+	0.706622i	$0.249782\pi$
$420$		0			0
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.849731	+	0.527217i	$0.176765\pi$
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.0317181	+	0.999497i	$0.489902\pi$
$422$	8.94870	−	15.4996i	0.435616	−	0.754509i
$423$		0			0
$424$	−0.116765	−	0.202243i	−0.00567062	−	0.00982181i
$425$	−32.3818			−1.57075
$426$		0			0
$427$		0			0
$428$	−2.37890	+	4.12038i	−0.114989	+	0.199166i
$429$		0			0
$430$	−15.8880	+	27.5189i	−0.766190	+	1.32708i
$431$	17.5494	+	30.3965i	0.845327	+	1.46415i	0.885337	+	0.464950i	$0.153928\pi$
$431$	17.5494	+	30.3965i	0.845327	+	1.46415i	−0.0400101	+	0.999199i	$0.512739\pi$
$432$		0			0
$433$	41.1730			1.97865			0.989324	−	0.145731i	$-0.0465533\pi$
$433$	41.1730			1.97865			0.989324	+	0.145731i	$0.0465533\pi$
$434$		0			0
$435$		0			0
$436$	8.38255	+	14.5190i	0.401451	+	0.695334i
$437$	−5.22253			−0.249827
$438$		0			0
$439$	4.67859			0.223297			0.111648	−	0.993748i	$-0.464387\pi$
$439$	4.67859			0.223297			0.111648	+	0.993748i	$0.464387\pi$
$440$	−19.0507			−0.908209
$441$		0			0
$442$	−6.98762			−0.332367
$443$	−30.1730			−1.43356			−0.716781	−	0.697298i	$-0.754385\pi$
$443$	−30.1730			−1.43356			−0.716781	+	0.697298i	$0.754385\pi$
$444$		0			0
$445$	−34.4820			−1.63461
$446$	4.81639	+	8.34224i	0.228063	+	0.395016i
$447$		0			0
$448$		0			0
$449$	−0.333792			−0.0157526			−0.00787632	−	0.999969i	$-0.502507\pi$
$449$	−0.333792			−0.0157526			−0.00787632	+	0.999969i	$0.502507\pi$
$450$		0			0
$451$	7.60576	+	13.1736i	0.358141	+	0.620319i
$452$	−8.24357	+	14.2783i	−0.387745	+	0.671594i
$453$		0			0
$454$	−9.43199	+	16.3367i	−0.442665	+	0.766719i
$455$		0			0
$456$		0			0
$457$	−19.3090			−0.903238			−0.451619	−	0.892211i	$-0.649153\pi$
$457$	−19.3090			−0.903238			−0.451619	+	0.892211i	$0.649153\pi$
$458$	−16.6927	−	28.9127i	−0.780001	−	1.35100i
$459$		0			0
$460$	−9.37017	+	16.2296i	−0.436886	+	0.756709i
$461$	−19.5538	−	33.8681i	−0.910710	−	1.57740i	−0.813064	−	0.582175i	$-0.802202\pi$
$461$	−19.5538	−	33.8681i	−0.910710	−	1.57740i	−0.0976463	−	0.995221i	$-0.531131\pi$
$462$		0			0
$463$	−10.9382	+	18.9455i	−0.508340	+	0.880471i	0.491613	+	0.870814i	$0.336407\pi$
$463$	−10.9382	+	18.9455i	−0.508340	+	0.880471i	−0.999953	+	0.00965741i	$0.996926\pi$
$464$	4.23855	+	7.34138i	0.196770	+	0.340815i
$465$		0			0
$466$	−7.61677	+	13.1926i	−0.352840	+	0.611137i
$467$	6.16002	−	10.6695i	0.285052	−	0.493724i	−0.687570	−	0.726118i	$-0.741323\pi$
$467$	6.16002	−	10.6695i	0.285052	−	0.493724i	0.972622	+	0.232394i	$0.0746559\pi$
$468$		0			0
$469$		0			0
$470$	8.13045	+	14.0823i	0.375029	+	0.649570i
$471$		0			0
$472$	−16.7651			−0.771676
$473$	14.6452			0.673385
$474$		0			0
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$	−9.53706	+	16.5187i	−0.436215	+	0.755547i
$479$	−6.74474	+	11.6822i	−0.308175	+	0.533775i	−0.977963	−	0.208777i	$-0.933052\pi$
$479$	−6.74474	+	11.6822i	−0.308175	+	0.533775i	0.669788	+	0.742552i	$0.266385\pi$
$480$		0			0
$481$	2.38255	+	4.12669i	0.108635	+	0.188161i
$482$	5.93701	−	10.2832i	0.270423	−	0.468387i
$483$		0			0
$484$	1.37704	+	2.38511i	0.0625929	+	0.108414i
$485$	−13.1359	+	22.7521i	−0.596473	+	1.03312i
$486$		0			0
$487$	−3.77197	−	6.53324i	−0.170924	−	0.296050i	0.767819	−	0.640667i	$-0.221342\pi$
$487$	−3.77197	−	6.53324i	−0.170924	−	0.296050i	−0.938743	+	0.344617i	$0.888009\pi$
$488$	−7.32141			−0.331425
$489$		0			0
$490$		0			0
$491$	−8.06979	+	13.9773i	−0.364185	+	0.630786i	−0.988645	−	0.150270i	$-0.951986\pi$
$491$	−8.06979	+	13.9773i	−0.364185	+	0.630786i	0.624460	+	0.781057i	$0.285319\pi$
$492$		0			0
$493$	3.49381	−	6.05146i	0.157353	−	0.272544i
$494$	−0.755260	−	1.30815i	−0.0339808	−	0.0588564i
$495$		0			0
$496$	−34.8516			−1.56488
$497$		0			0
$498$		0			0
$499$	15.4327	+	26.7302i	0.690862	+	1.19661i	0.971556	+	0.236810i	$0.0761019\pi$
$499$	15.4327	+	26.7302i	0.690862	+	1.19661i	−0.280694	+	0.959797i	$0.590565\pi$
$500$	−9.17301			−0.410229
$501$		0			0
$502$	−7.85297			−0.350495
$503$	24.6304			1.09822			0.549109	−	0.835751i	$-0.314967\pi$
$503$	24.6304			1.09822			0.549109	+	0.835751i	$0.314967\pi$
$504$		0			0
$505$	−12.4327			−0.553247
$506$	28.0741			1.24805
$507$		0			0
$508$	8.87636			0.393825
$509$	−6.79487	−	11.7691i	−0.301177	−	0.521654i	0.675226	−	0.737611i	$-0.264046\pi$
$509$	−6.79487	−	11.7691i	−0.301177	−	0.521654i	−0.976403	+	0.215957i	$0.930713\pi$
$510$		0			0
$511$		0			0
$512$	−4.59937			−0.203265
$513$		0			0
$514$	−1.21015	−	2.09604i	−0.0533774	−	0.0924523i
$515$	28.4851	−	49.3376i	1.25520	−	2.17407i
$516$		0			0
$517$	3.74721	−	6.49036i	0.164802	−	0.285446i
$518$		0			0
$519$		0			0
$520$	6.77747			0.297212
$521$	19.5865	+	33.9248i	0.858100	+	1.48627i	0.873739	+	0.486396i	$0.161689\pi$
$521$	19.5865	+	33.9248i	0.858100	+	1.48627i	−0.0156383	+	0.999878i	$0.504978\pi$
$522$		0			0
$523$	9.56182	−	16.5616i	0.418109	−	0.724187i	−0.577640	−	0.816292i	$-0.696026\pi$
$523$	9.56182	−	16.5616i	0.418109	−	0.724187i	0.995749	+	0.0921051i	$0.0293596\pi$
$524$	−7.13348	−	12.3555i	−0.311627	−	0.539754i
$525$		0			0
$526$	−13.8207	+	23.9382i	−0.602612	+	1.04375i
$527$	14.3640	+	24.8791i	0.625705	+	1.08375i
$528$		0			0
$529$	−5.76578	+	9.98663i	−0.250686	+	0.434201i
$530$	−0.377045	+	0.653061i	−0.0163778	+	0.0283671i
$531$		0			0
$532$		0			0
$533$	−2.70582	−	4.68661i	−0.117202	−	0.203000i
$534$		0			0
$535$	−19.2101			−0.830527
$536$	23.2485			1.00418
$537$		0			0
$538$	−15.8523	−	27.4570i	−0.683441	−	1.18375i
$539$		0			0
$540$		0			0
$541$	−1.26509	+	2.19120i	−0.0543906	+	0.0942072i	−0.891939	−	0.452156i	$-0.850655\pi$
$541$	−1.26509	+	2.19120i	−0.0543906	+	0.0942072i	0.837548	+	0.546363i	$0.183988\pi$
$542$	−3.36769	+	5.83302i	−0.144655	+	0.250550i
$543$		0			0
$544$	9.66071	+	16.7328i	0.414199	+	0.717414i
$545$	−33.8454	+	58.6220i	−1.44978	+	2.51109i
$546$		0			0
$547$	−8.92580	−	15.4599i	−0.381640	−	0.661019i	0.609657	−	0.792665i	$-0.291307\pi$
$547$	−8.92580	−	15.4599i	−0.381640	−	0.661019i	−0.991297	+	0.131646i	$0.957974\pi$
$548$	−5.77128	+	9.99615i	−0.246537	+	0.427015i
$549$		0			0
$550$	18.8145	+	32.5877i	0.802254	+	1.38955i
$551$	1.51052			0.0643503
$552$		0			0
$553$		0			0
$554$	−1.98329	+	3.43516i	−0.0842619	+	0.145946i
$555$		0			0
$556$	0.493810	−	0.855304i	0.0209422	−	0.0362730i
$557$	20.6804	+	35.8195i	0.876255	+	1.51772i	0.855419	+	0.517936i	$0.173299\pi$
$557$	20.6804	+	35.8195i	0.876255	+	1.51772i	0.0208360	+	0.999783i	$0.493367\pi$
$558$		0			0
$559$	−5.21015			−0.220366
$560$		0			0
$561$		0			0
$562$	−23.7905	−	41.2063i	−1.00354	−	1.73818i
$563$	−20.7366			−0.873944			−0.436972	−	0.899475i	$-0.643949\pi$
$563$	−20.7366			−0.873944			−0.436972	+	0.899475i	$0.643949\pi$
$564$		0			0
$565$	−66.5685			−2.80056
$566$	17.5402			0.737271
$567$		0			0
$568$	5.43268			0.227950
$569$	0.268329			0.0112489			0.00562446	−	0.999984i	$-0.498210\pi$
$569$	0.268329			0.0112489			0.00562446	+	0.999984i	$0.498210\pi$
$570$		0			0
$571$	35.9367			1.50391			0.751953	−	0.659217i	$-0.229112\pi$
$571$	35.9367			1.50391			0.751953	+	0.659217i	$0.229112\pi$
$572$	1.24907	+	2.16345i	0.0522263	+	0.0904585i
$573$		0			0
$574$		0			0
$575$	−46.2843			−1.93019
$576$		0			0
$577$	2.71565	+	4.70364i	0.113054	+	0.195815i	0.917000	−	0.398887i	$-0.130603\pi$
$577$	2.71565	+	4.70364i	0.113054	+	0.195815i	−0.803946	+	0.594702i	$0.797270\pi$
$578$	−0.0828628	+	0.143523i	−0.00344664	+	0.00596976i
$579$		0			0
$580$	2.71015	−	4.69412i	0.112533	−	0.194913i
$581$		0			0
$582$		0			0
$583$	0.347550			0.0143940
$584$	−10.0494	−	17.4061i	−0.415849	−	0.720271i
$585$		0			0
$586$	−26.0858	+	45.1820i	−1.07760	+	1.86645i
$587$	−17.5822	−	30.4532i	−0.725694	−	1.25694i	−0.958688	−	0.284461i	$-0.908185\pi$
$587$	−17.5822	−	30.4532i	−0.725694	−	1.25694i	0.232994	−	0.972478i	$-0.425148\pi$
$588$		0			0
$589$	−3.10507	+	5.37815i	−0.127942	+	0.221603i
$590$	27.0679	+	46.8830i	1.11437	+	1.93014i
$591$		0			0
$592$	11.8832	−	20.5824i	0.488398	−	0.845930i
$593$	16.7534	−	29.0177i	0.687980	−	1.19162i	−0.284511	−	0.958673i	$-0.591831\pi$
$593$	16.7534	−	29.0177i	0.687980	−	1.19162i	0.972490	−	0.232943i	$-0.0748355\pi$
$594$		0			0
$595$		0			0
$596$	3.74721	+	6.49036i	0.153492	+	0.265856i
$597$		0			0
$598$	−9.98762			−0.408424
$599$	−6.24729			−0.255257			−0.127629	−	0.991822i	$-0.540737\pi$
$599$	−6.24729			−0.255257			−0.127629	+	0.991822i	$0.540737\pi$
$600$		0			0
$601$	11.2040	+	19.4058i	0.457019	+	0.791580i	0.998802	−	0.0489384i	$-0.0155838\pi$
$601$	11.2040	+	19.4058i	0.457019	+	0.791580i	−0.541783	+	0.840519i	$0.682250\pi$
$602$		0			0
$603$		0			0
$604$	6.59957	−	11.4308i	0.268533	−	0.465112i
$605$	−5.55996	+	9.63014i	−0.226045	+	0.391521i
$606$		0			0
$607$	7.47524	+	12.9475i	0.303411	+	0.525523i	0.976906	−	0.213669i	$-0.0685413\pi$
$607$	7.47524	+	12.9475i	0.303411	+	0.525523i	−0.673496	+	0.739191i	$0.735208\pi$
$608$	−2.08836	+	3.61715i	−0.0846943	+	0.146695i
$609$		0			0
$610$	11.8207	+	20.4741i	0.478607	+	0.828972i
$611$	−1.33310	+	2.30900i	−0.0539316	+	0.0934123i
$612$		0			0
$613$	−17.5989	−	30.4822i	−0.710812	−	1.23116i	−0.964553	−	0.263891i	$-0.914994\pi$
$613$	−17.5989	−	30.4822i	−0.710812	−	1.23116i	0.253740	−	0.967272i	$-0.418339\pi$
$614$	−19.4500			−0.784938
$615$		0			0
$616$		0			0
$617$	−1.00619	+	1.74277i	−0.0405077	+	0.0701614i	−0.885568	−	0.464509i	$-0.846231\pi$
$617$	−1.00619	+	1.74277i	−0.0405077	+	0.0701614i	0.845061	+	0.534670i	$0.179564\pi$
$618$		0			0
$619$	19.6909	−	34.1056i	0.791444	−	1.37082i	−0.133629	−	0.991031i	$-0.542663\pi$
$619$	19.6909	−	34.1056i	0.791444	−	1.37082i	0.925073	−	0.379789i	$-0.124004\pi$
$620$	11.1421	+	19.2987i	0.447479	+	0.775056i
$621$		0			0
$622$	−20.3324			−0.815256
$623$		0			0
$624$		0			0
$625$	1.17240	+	2.03065i	0.0468959	+	0.0812261i
$626$	−23.0197			−0.920051
$627$		0			0
$628$	−2.56732			−0.102447
$629$	−19.5906			−0.781126
$630$		0			0
$631$	44.3832			1.76687			0.883433	−	0.468558i	$-0.155226\pi$
$631$	44.3832			1.76687			0.883433	+	0.468558i	$0.155226\pi$
$632$	−13.3845			−0.532408
$633$		0			0
$634$	−50.9257			−2.02252
$635$	17.9196	+	31.0377i	0.711118	+	1.23169i
$636$		0			0
$637$		0			0
$638$	−8.11993			−0.321471
$639$		0			0
$640$	−22.9251	−	39.7075i	−0.906195	−	1.56957i
$641$	−7.49312	+	12.9785i	−0.295961	+	0.512619i	−0.975208	−	0.221291i	$-0.928973\pi$
$641$	−7.49312	+	12.9785i	−0.295961	+	0.512619i	0.679247	+	0.733909i	$0.262306\pi$
$642$		0			0
$643$	−5.32691	+	9.22649i	−0.210073	+	0.363857i	−0.951737	−	0.306914i	$-0.900703\pi$
$643$	−5.32691	+	9.22649i	−0.210073	+	0.363857i	0.741664	+	0.670771i	$0.234037\pi$
$644$		0			0
$645$		0			0
$646$	6.21015			0.244335
$647$	−1.06478	−	1.84424i	−0.0418606	−	0.0725047i	0.844336	−	0.535814i	$-0.179995\pi$
$647$	−1.06478	−	1.84424i	−0.0418606	−	0.0725047i	−0.886197	+	0.463309i	$0.846662\pi$
$648$		0			0
$649$	12.4752	−	21.6078i	0.489696	−	0.848178i
$650$	−6.69344	−	11.5934i	−0.262538	−	0.454730i
$651$		0			0
$652$	4.58100	−	7.93453i	0.179406	−	0.310740i
$653$	5.58582	+	9.67492i	0.218590	+	0.378609i	0.954377	−	0.298604i	$-0.0965210\pi$
$653$	5.58582	+	9.67492i	0.218590	+	0.378609i	−0.735787	+	0.677213i	$0.763188\pi$
$654$		0			0
$655$	28.8022	−	49.8868i	1.12539	−	1.94924i
$656$	−13.4956	+	23.3751i	−0.526914	+	0.912642i
$657$		0			0
$658$		0			0
$659$	−5.65452	−	9.79391i	−0.220269	−	0.381517i	0.734621	−	0.678478i	$-0.237360\pi$
$659$	−5.65452	−	9.79391i	−0.220269	−	0.381517i	−0.954890	+	0.296961i	$0.904027\pi$
$660$		0			0
$661$	−32.3570			−1.25854			−0.629271	−	0.777186i	$-0.716646\pi$
$661$	−32.3570			−1.25854			−0.629271	+	0.777186i	$0.716646\pi$
$662$	−3.54628			−0.137830
$663$		0			0
$664$	3.88255	+	6.72477i	0.150672	+	0.260972i
$665$		0			0
$666$		0			0
$667$	4.99381	−	8.64953i	0.193361	−	0.334911i
$668$	−5.39995	+	9.35298i	−0.208930	+	0.361878i
$669$		0			0
$670$	−37.5357	−	65.0137i	−1.45013	−	2.51170i
$671$	5.44801	−	9.43623i	0.210318	−	0.364282i
$672$		0			0
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	0.999231	−	0.0392063i	$-0.0124830\pi$
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	−0.533569	+	0.845756i	$0.679150\pi$
$674$	−13.7744	+	23.8580i	−0.530572	+	0.918977i
$675$		0			0
$676$	5.33242	+	9.23601i	0.205093	+	0.355231i
$677$	25.0741			0.963677			0.481838	−	0.876260i	$-0.339969\pi$
$677$	25.0741			0.963677			0.481838	+	0.876260i	$0.339969\pi$
$678$		0			0
$679$		0			0
$680$	−13.9320	+	24.1309i	−0.534267	+	0.925378i
$681$		0			0
$682$	16.6916	−	28.9107i	0.639154	−	1.10705i
$683$	−23.8392	−	41.2907i	−0.912182	−	1.57995i	−0.810975	−	0.585081i	$-0.801063\pi$
$683$	−23.8392	−	41.2907i	−0.912182	−	1.57995i	−0.101207	−	0.994865i	$-0.532271\pi$
$684$		0			0
$685$	−46.6043			−1.78066
$686$		0			0
$687$		0			0
$688$	12.9931	+	22.5047i	0.495358	+	0.857985i
$689$	−0.123644			−0.00471046
$690$		0			0
$691$	24.6800			0.938870			0.469435	−	0.882967i	$-0.344458\pi$
$691$	24.6800			0.938870			0.469435	+	0.882967i	$0.344458\pi$
$692$	−5.87402			−0.223297
$693$		0			0
$694$	19.1496			0.726910
$695$	3.98762			0.151259
$696$		0			0
$697$	22.2487			0.842728
$698$	0.168067	+	0.291100i	0.00636142	+	0.0110183i
$699$		0			0
$700$		0			0
$701$	29.6784			1.12094			0.560469	−	0.828175i	$-0.310621\pi$
$701$	29.6784			1.12094			0.560469	+	0.828175i	$0.310621\pi$
$702$		0			0
$703$	−2.11745	−	3.66754i	−0.0798613	−	0.138324i
$704$	−2.79349	+	4.83847i	−0.105284	+	0.182357i
$705$		0			0
$706$	−10.6243	+	18.4018i	−0.399849	+	0.692559i
$707$		0			0
$708$		0			0
$709$	−29.2581			−1.09881			−0.549406	−	0.835555i	$-0.685146\pi$
$709$	−29.2581			−1.09881			−0.549406	+	0.835555i	$0.685146\pi$
$710$	−8.77128	−	15.1923i	−0.329180	−	0.570157i
$711$		0			0
$712$	−9.07481	+	15.7180i	−0.340093	+	0.589058i
$713$	20.5309	+	35.5605i	0.768887	+	1.33175i
$714$		0			0
$715$	−5.04325	+	8.73517i	−0.188607	+	0.326677i
$716$	−1.70768	−	2.95778i	−0.0638189	−	0.110538i
$717$		0			0
$718$	−17.0130	+	29.4674i	−0.634919	+	1.09971i
$719$	−0.537063	+	0.930220i	−0.0200291	+	0.0346913i	−0.875866	−	0.482554i	$-0.839709\pi$
$719$	−0.537063	+	0.930220i	−0.0200291	+	0.0346913i	0.855837	+	0.517245i	$0.173043\pi$
$720$		0			0
$721$		0			0
$722$	−15.4752	−	26.8039i	−0.575929	−	0.997538i
$723$		0			0
$724$	−16.4794			−0.612454
$725$	13.3869			0.497176
$726$		0			0
$727$	12.7163	+	22.0253i	0.471623	+	0.816875i	0.999473	−	0.0324628i	$-0.0103350\pi$
$727$	12.7163	+	22.0253i	0.471623	+	0.816875i	−0.527850	+	0.849338i	$0.677002\pi$
$728$		0			0
$729$		0			0
$730$	−32.4505	+	56.2059i	−1.20105	+	2.08027i
$731$	10.7101	−	18.5505i	0.396129	−	0.686116i
$732$		0			0
$733$	−5.69777	−	9.86883i	−0.210452	−	0.364513i	0.741404	−	0.671059i	$-0.234160\pi$
$733$	−5.69777	−	9.86883i	−0.210452	−	0.364513i	−0.951856	+	0.306545i	$0.900827\pi$
$734$	−25.5562	+	44.2647i	−0.943298	+	1.63384i
$735$		0			0
$736$	13.8083	+	23.9168i	0.508982	+	0.881583i
$737$	−17.2997	+	29.9639i	−0.637242	+	1.10374i
$738$		0			0
$739$	14.9697	+	25.9283i	0.550671	+	0.953790i	0.998226	+	0.0595336i	$0.0189613\pi$
$739$	14.9697	+	25.9283i	0.550671	+	0.953790i	−0.447556	+	0.894256i	$0.647705\pi$
$740$	−15.1964			−0.558630
$741$		0			0
$742$		0			0
$743$	−9.50069	+	16.4557i	−0.348546	+	0.603700i	−0.985991	−	0.166796i	$-0.946658\pi$
$743$	−9.50069	+	16.4557i	−0.348546	+	0.603700i	0.637445	+	0.770496i	$0.279991\pi$
$744$		0			0
$745$	−15.1298	+	26.2055i	−0.554311	+	0.960096i
$746$	5.95922	+	10.3217i	0.218183	+	0.377903i
$747$		0			0
$748$	−10.2705			−0.375527
$749$		0			0
$750$		0			0
$751$	−0.0130684	−	0.0226352i	−0.000476873	−	0.000825969i	0.865787	−	0.500413i	$-0.166818\pi$
$751$	−0.0130684	−	0.0226352i	−0.000476873	−	0.000825969i	−0.866264	+	0.499587i	$0.833485\pi$
$752$	13.2980			0.484929
$753$		0			0
$754$	2.88874			0.105202
$755$	53.2929			1.93953
$756$		0			0
$757$	−13.6910			−0.497607			−0.248803	−	0.968554i	$-0.580037\pi$
$757$	−13.6910			−0.497607			−0.248803	+	0.968554i	$0.580037\pi$
$758$	32.4189			1.17751
$759$		0			0
$760$	−6.02338			−0.218491
$761$	7.32141	+	12.6811i	0.265401	+	0.459688i	0.967669	−	0.252225i	$-0.0811623\pi$
$761$	7.32141	+	12.6811i	0.265401	+	0.459688i	−0.702268	+	0.711913i	$0.747829\pi$
$762$		0			0
$763$		0			0
$764$	−4.11855			−0.149004
$765$		0			0
$766$	2.72803	+	4.72509i	0.0985677	+	0.170724i
$767$	−4.43818	+	7.68715i	−0.160253	+	0.277567i
$768$		0			0
$769$	24.5672	−	42.5517i	0.885918	−	1.53445i	0.0412592	−	0.999148i	$-0.486863\pi$
$769$	24.5672	−	42.5517i	0.885918	−	1.53445i	0.844658	−	0.535306i	$-0.179804\pi$
$770$		0			0
$771$		0			0
$772$	−22.4820			−0.809146
$773$	−6.22067	−	10.7745i	−0.223742	−	0.387532i	0.732199	−	0.681090i	$-0.238494\pi$
$773$	−6.22067	−	10.7745i	−0.223742	−	0.387532i	−0.955941	+	0.293558i	$0.905161\pi$
$774$		0			0
$775$	−27.5185	+	47.6634i	−0.988493	+	1.71212i
$776$	6.91411	+	11.9756i	0.248202	+	0.429898i
$777$		0			0
$778$	−4.36467	+	7.55982i	−0.156481	+	0.271033i
$779$	2.40476	+	4.16516i	0.0861594	+	0.149232i
$780$		0			0
$781$	−4.04256	+	7.00193i	−0.144654	+	0.250549i
$782$	20.5309	−	35.5605i	0.734183	−	1.27164i
$783$		0			0
$784$		0			0
$785$	−5.18292	−	8.97708i	−0.184986	−	0.320406i
$786$		0			0
$787$	32.9133			1.17323			0.586617	−	0.809865i	$-0.300459\pi$
$787$	32.9133			1.17323			0.586617	+	0.809865i	$0.300459\pi$
$788$	−9.52784			−0.339415
$789$		0			0
$790$	21.6099	+	37.4294i	0.768845	+	1.33168i
$791$		0			0
$792$		0			0
$793$	−1.93818	+	3.35702i	−0.0688267	+	0.119211i
$794$	−19.4931	+	33.7631i	−0.691785	+	1.19821i
$795$		0			0
$796$	−3.89554	−	6.74727i	−0.138074	−	0.239151i
$797$	−13.1989	+	22.8612i	−0.467530	+	0.809786i	−0.999312	−	0.0370953i	$-0.988189\pi$
$797$	−13.1989	+	22.8612i	−0.467530	+	0.809786i	0.531781	+	0.846882i	$0.321523\pi$
$798$		0			0
$799$	−5.48074	−	9.49292i	−0.193895	−	0.335835i
$800$	−18.5080	+	32.0567i	−0.654356	+	1.13338i
$801$		0			0
$802$	15.4752	+	26.8039i	0.546450	+	0.946479i
$803$	29.9120			1.05557
$804$		0			0
$805$		0			0
$806$	−5.93818	+	10.2852i	−0.209163	+	0.362282i
$807$		0			0
$808$	−3.27197	+	5.66722i	−0.115108	+	0.199372i
$809$	17.7960	+	30.8235i	0.625673	+	1.08370i	0.988410	+	0.151806i	$0.0485088\pi$
$809$	17.7960	+	30.8235i	0.625673	+	1.08370i	−0.362738	+	0.931891i	$0.618158\pi$
$810$		0			0
$811$	37.8268			1.32828			0.664140	−	0.747608i	$-0.268798\pi$
$811$	37.8268			1.32828			0.664140	+	0.747608i	$0.268798\pi$
$812$		0			0
$813$		0			0
$814$	11.3825	+	19.7151i	0.398958	+	0.691016i
$815$	36.9926			1.29579
$816$		0			0
$817$	4.63045			0.161999
$818$	−26.0594			−0.911146
$819$		0			0
$820$	17.2583			0.602686
$821$	18.3128			0.639119			0.319560	−	0.947566i	$-0.396465\pi$
$821$	18.3128			0.639119			0.319560	+	0.947566i	$0.396465\pi$
$822$		0			0
$823$	−36.0000			−1.25488			−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000			−1.25488			−0.627441	+	0.778664i	$0.715897\pi$
$824$	−14.9931	−	25.9688i	−0.522310	−	0.904668i
$825$		0			0
$826$		0			0
$827$	28.2115			0.981011			0.490505	−	0.871438i	$-0.336812\pi$
$827$	28.2115			0.981011			0.490505	+	0.871438i	$0.336812\pi$
$828$		0			0
$829$	−5.64214	−	9.77247i	−0.195960	−	0.339412i	0.751255	−	0.660012i	$-0.229449\pi$
$829$	−5.64214	−	9.77247i	−0.195960	−	0.339412i	−0.947215	+	0.320600i	$0.896115\pi$
$830$	12.5371	−	21.7148i	0.435168	−	0.753733i
$831$		0			0
$832$	0.993810	−	1.72133i	0.0344542	−	0.0596764i
$833$		0			0
$834$		0			0
$835$	−43.6057			−1.50904
$836$	−1.11009	−	1.92274i	−0.0383934	−	0.0664993i
$837$		0			0
$838$	8.98143	−	15.5563i	0.310258	−	0.537383i
$839$	1.02152	+	1.76933i	0.0352669	+	0.0610840i	0.883120	−	0.469147i	$-0.155439\pi$
$839$	1.02152	+	1.76933i	0.0352669	+	0.0610840i	−0.847853	+	0.530231i	$0.822105\pi$
$840$		0			0
$841$	13.0556	−	22.6130i	0.450194	−	0.779759i
$842$	−30.7392	−	53.2418i	−1.05934	−	1.83483i
$843$		0			0
$844$	−4.67928	+	8.10474i	−0.161067	+	0.278977i
$845$	−21.5302	+	37.2914i	−0.740661	+	1.28286i
$846$		0			0
$847$		0			0
$848$	0.308344	+	0.534068i	0.0105886	+	0.0183400i
$849$		0			0
$850$	55.0370			1.88775
$851$	−28.0014			−0.959875
$852$		0			0
$853$	−24.2960	−	42.0818i	−0.831878	−	1.44085i	−0.896547	−	0.442948i	$-0.853933\pi$
$853$	−24.2960	−	42.0818i	−0.831878	−	1.44085i	0.0646692	−	0.997907i	$-0.479401\pi$
$854$		0			0
$855$		0			0
$856$	−5.05563	+	8.75661i	−0.172798	+	0.299295i
$857$	22.4487	−	38.8823i	0.766833	−	1.32819i	−0.172439	−	0.985020i	$-0.555165\pi$
$857$	22.4487	−	38.8823i	0.766833	−	1.32819i	0.939272	−	0.343173i	$-0.111502\pi$
$858$		0			0
$859$	14.9065	+	25.8189i	0.508605	+	0.880929i	0.999950	+	0.00996438i	$0.00317181\pi$
$859$	14.9065	+	25.8189i	0.508605	+	0.880929i	−0.491346	+	0.870965i	$0.663495\pi$
$860$	8.30786	−	14.3896i	0.283296	−	0.490683i
$861$		0			0
$862$	−29.8275	−	51.6628i	−1.01593	−	1.75964i
$863$	−21.1298	+	36.5978i	−0.719265	+	1.24580i	0.242026	+	0.970270i	$0.422188\pi$
$863$	−21.1298	+	36.5978i	−0.719265	+	1.24580i	−0.961291	+	0.275534i	$0.911145\pi$
$864$		0			0
$865$	−11.8585	−	20.5395i	−0.403200	−	0.698363i
$866$	−69.9788			−2.37798
$867$		0			0
$868$		0			0
$869$	9.95970	−	17.2507i	0.337860	−	0.585190i
$870$		0			0
$871$	6.15452	−	10.6599i	0.208538	−	0.361198i
$872$	17.8145	+	30.8557i	0.603276	+	1.04491i
$873$		0			0
$874$	8.87636			0.300247
$875$		0			0
$876$		0			0
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	0.999838	+	0.0179782i	$0.00572295\pi$
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	−0.484350	+	0.874875i	$0.660944\pi$
$878$	−7.95186			−0.268362
$879$		0			0
$880$	50.3077			1.69587
$881$	−13.4079			−0.451724			−0.225862	−	0.974159i	$-0.572520\pi$
$881$	−13.4079			−0.451724			−0.225862	+	0.974159i	$0.572520\pi$
$882$		0			0
$883$	−14.1250			−0.475345			−0.237672	−	0.971345i	$-0.576384\pi$
$883$	−14.1250			−0.475345			−0.237672	+	0.971345i	$0.576384\pi$
$884$	3.65383			0.122892
$885$		0			0
$886$	51.2829			1.72288
$887$	19.9716	+	34.5918i	0.670581	+	1.16148i	0.977740	+	0.209822i	$0.0672883\pi$
$887$	19.9716	+	34.5918i	0.670581	+	1.16148i	−0.307159	+	0.951658i	$0.599378\pi$
$888$		0			0
$889$		0			0
$890$	58.6067			1.96450
$891$		0			0
$892$	−2.51849	−	4.36216i	−0.0843254	−	0.146056i
$893$	1.18478	−	2.05209i	0.0396471	−	0.0686707i
$894$		0			0
$895$	6.89493	−	11.9424i	0.230472	−	0.399189i
$896$		0			0
$897$		0			0
$898$	0.567323			0.0189318
$899$	−5.93818	−	10.2852i	−0.198049	−	0.343031i
$900$		0			0
$901$	0.254166	−	0.440229i	0.00846751	−	0.0146662i
$902$	−12.9270	−	22.3902i	−0.430421	−	0.745511i
$903$		0			0
$904$	−17.5192	+	30.3441i	−0.582679	+	1.00923i
$905$	−33.2687	−	57.6231i	−1.10589	−	1.91546i
$906$		0			0
$907$	−20.7101	+	35.8710i	−0.687669	+	1.19108i	0.284921	+	0.958551i	$0.408033\pi$
$907$	−20.7101	+	35.8710i	−0.687669	+	1.19108i	−0.972590	+	0.232527i	$0.925301\pi$
$908$	4.93199	−	8.54245i	0.163674	−	0.283491i
$909$		0			0
$910$		0			0
$911$	0.894237	+	1.54886i	0.0296274	+	0.0513162i	0.880459	−	0.474122i	$-0.157235\pi$
$911$	0.894237	+	1.54886i	0.0296274	+	0.0513162i	−0.850832	+	0.525439i	$0.823901\pi$
$912$		0			0
$913$	−11.5563			−0.382458
$914$	32.8182			1.08553
$915$		0			0
$916$	8.72864	+	15.1185i	0.288402	+	0.499528i
$917$		0			0
$918$		0			0
$919$	28.7341	−	49.7690i	0.947852	−	1.64173i	0.197914	−	0.980219i	$-0.436583\pi$
$919$	28.7341	−	49.7690i	0.947852	−	1.64173i	0.749938	−	0.661508i	$-0.230083\pi$
$920$	−19.9134	+	34.4911i	−0.656526	+	1.13714i
$921$		0			0
$922$	33.2341	+	57.5632i	1.09451	+	1.89574i
$923$	1.43818	−	2.49100i	0.0473382	−	0.0819922i
$924$		0			0
$925$	−18.7658	−	32.5033i	−0.617015	−	1.06870i
$926$	18.5908	−	32.2003i	0.610933	−	1.05817i
$927$		0			0
$928$	−3.99381	−	6.91748i	−0.131103	−	0.227077i
$929$	34.7352			1.13963			0.569813	−	0.821774i	$-0.307016\pi$
$929$	34.7352			1.13963			0.569813	+	0.821774i	$0.307016\pi$
$930$		0			0
$931$		0			0
$932$	3.98281	−	6.89843i	0.130461	−	0.225965i
$933$		0			0
$934$	−10.4697	+	18.1341i	−0.342580	+	0.593367i
$935$	−20.7341	−	35.9126i	−0.678079	−	1.17447i
$936$		0			0
$937$	−11.6662			−0.381118			−0.190559	−	0.981676i	$-0.561030\pi$
$937$	−11.6662			−0.381118			−0.190559	+	0.981676i	$0.561030\pi$
$938$		0			0
$939$		0			0
$940$	−4.25141	−	7.36366i	−0.138666	−	0.240176i
$941$	−50.3374			−1.64095			−0.820475	−	0.571682i	$-0.806291\pi$
$941$	−50.3374			−1.64095			−0.820475	+	0.571682i	$0.806291\pi$
$942$		0			0
$943$	31.8007			1.03557
$944$	44.2719			1.44093
$945$		0			0
$946$	−24.8913			−0.809287
$947$	32.3883			1.05248			0.526238	−	0.850337i	$-0.323602\pi$
$947$	32.3883			1.05248			0.526238	+	0.850337i	$0.323602\pi$
$948$		0			0
$949$	−10.6414			−0.345436
$950$	5.94870	+	10.3034i	0.193001	+	0.334288i
$951$		0			0
$952$		0			0
$953$	12.5367			0.406102			0.203051	−	0.979168i	$-0.434914\pi$
$953$	12.5367			0.406102			0.203051	+	0.979168i	$0.434914\pi$
$954$		0			0
$955$	−8.31453	−	14.4012i	−0.269052	−	0.466012i
$956$	4.98693	−	8.63762i	0.161289	−	0.279361i
$957$		0			0
$958$	11.4635	−	19.8555i	0.370370	−	0.641500i
$959$		0			0
$960$		0			0
$961$	17.8268			0.575059
$962$	−4.04944	−	7.01384i	−0.130559	−	0.226135i
$963$		0			0
$964$	−3.10446	+	5.37709i	−0.0999880	+	0.173184i
$965$	−45.3868	−	78.6122i	−1.46105	−	2.53062i
$966$		0			0
$967$	28.9937	−	50.2186i	0.932376	−	1.61492i	0.153127	−	0.988206i	$-0.451065\pi$
$967$	28.9937	−	50.2186i	0.932376	−	1.61492i	0.779248	−	0.626715i	$-0.215601\pi$
$968$	2.92649	+	5.06882i	0.0940609	+	0.162918i
$969$		0			0
$970$	22.3262	−	38.6702i	0.716852	−	1.24162i
$971$	−14.0185	+	24.2807i	−0.449875	+	0.779206i	−0.998377	−	0.0569428i	$-0.981865\pi$
$971$	−14.0185	+	24.2807i	−0.449875	+	0.779206i	0.548503	+	0.836149i	$0.315198\pi$
$972$		0			0
$973$		0			0
$974$	6.41095	+	11.1041i	0.205420	+	0.355798i
$975$		0			0
$976$	19.3338			0.618860
$977$	−9.84059			−0.314829			−0.157414	−	0.987533i	$-0.550316\pi$
$977$	−9.84059			−0.314829			−0.157414	+	0.987533i	$0.550316\pi$
$978$		0			0
$979$	−13.5055	−	23.3922i	−0.431638	−	0.747618i
$980$		0			0
$981$		0			0
$982$	13.7156	−	23.7562i	0.437684	−	0.758091i
$983$	24.3447	−	42.1663i	0.776476	−	1.34490i	−0.157485	−	0.987521i	$-0.550339\pi$
$983$	24.3447	−	42.1663i	0.776476	−	1.34490i	0.933961	−	0.357374i	$-0.116328\pi$
$984$		0			0
$985$	−19.2348	−	33.3157i	−0.612873	−	1.06153i
$986$	−5.93818	+	10.2852i	−0.189110	+	0.327548i
$987$		0			0
$988$	0.394926	+	0.684031i	0.0125643	+	0.0217619i
$989$	15.3083	−	26.5148i	0.486777	−	0.843123i
$990$		0			0
$991$	−1.43199	−	2.48028i	−0.0454886	−	0.0787886i	0.842385	−	0.538877i	$-0.181151\pi$
$991$	−1.43199	−	2.48028i	−0.0454886	−	0.0787886i	−0.887873	+	0.460088i	$0.847818\pi$
$992$	32.8392			1.04265
$993$		0			0
$994$		0			0
$995$	15.7286	−	27.2428i	0.498631	−	0.863655i
$996$		0			0
$997$	−25.4203	+	44.0292i	−0.805069	+	1.39442i	0.111176	+	0.993801i	$0.464538\pi$
$997$	−25.4203	+	44.0292i	−0.805069	+	1.39442i	−0.916245	+	0.400619i	$0.868795\pi$
$998$	−26.2298	−	45.4314i	−0.830290	−	1.43810i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.e.226.1		6
3.2	odd	2		441.2.h.b.373.3		6
7.2	even	3		1323.2.f.c.442.3		6
7.3	odd	6		1323.2.g.c.361.3		6
7.4	even	3		1323.2.g.b.361.3		6
7.5	odd	6		189.2.f.a.64.3		6
7.6	odd	2		1323.2.h.d.226.1		6
9.2	odd	6		441.2.g.d.79.1		6
9.7	even	3		1323.2.g.b.667.3		6
21.2	odd	6		441.2.f.d.148.1		6
21.5	even	6		63.2.f.b.22.1	✓	6
21.11	odd	6		441.2.g.d.67.1		6
21.17	even	6		441.2.g.e.67.1		6
21.20	even	2		441.2.h.c.373.3		6
28.19	even	6		3024.2.r.g.1009.1		6
63.2	odd	6		441.2.f.d.295.1		6
63.5	even	6		567.2.a.d.1.3		3
63.11	odd	6		441.2.h.b.214.3		6
63.16	even	3		1323.2.f.c.883.3		6
63.20	even	6		441.2.g.e.79.1		6
63.23	odd	6		3969.2.a.m.1.3		3
63.25	even	3	inner	1323.2.h.e.802.1		6
63.34	odd	6		1323.2.g.c.667.3		6
63.38	even	6		441.2.h.c.214.3		6
63.40	odd	6		567.2.a.g.1.1		3
63.47	even	6		63.2.f.b.43.1	yes	6
63.52	odd	6		1323.2.h.d.802.1		6
63.58	even	3		3969.2.a.p.1.1		3
63.61	odd	6		189.2.f.a.127.3		6
84.47	odd	6		1008.2.r.k.337.1		6
252.47	odd	6		1008.2.r.k.673.1		6
252.103	even	6		9072.2.a.cd.1.3		3
252.131	odd	6		9072.2.a.bq.1.1		3
252.187	even	6		3024.2.r.g.2017.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.1	✓	6	21.5	even	6
63.2.f.b.43.1	yes	6	63.47	even	6
189.2.f.a.64.3		6	7.5	odd	6
189.2.f.a.127.3		6	63.61	odd	6
441.2.f.d.148.1		6	21.2	odd	6
441.2.f.d.295.1		6	63.2	odd	6
441.2.g.d.67.1		6	21.11	odd	6
441.2.g.d.79.1		6	9.2	odd	6
441.2.g.e.67.1		6	21.17	even	6
441.2.g.e.79.1		6	63.20	even	6
441.2.h.b.214.3		6	63.11	odd	6
441.2.h.b.373.3		6	3.2	odd	2
441.2.h.c.214.3		6	63.38	even	6
441.2.h.c.373.3		6	21.20	even	2
567.2.a.d.1.3		3	63.5	even	6
567.2.a.g.1.1		3	63.40	odd	6
1008.2.r.k.337.1		6	84.47	odd	6
1008.2.r.k.673.1		6	252.47	odd	6
1323.2.f.c.442.3		6	7.2	even	3
1323.2.f.c.883.3		6	63.16	even	3
1323.2.g.b.361.3		6	7.4	even	3
1323.2.g.b.667.3		6	9.7	even	3
1323.2.g.c.361.3		6	7.3	odd	6
1323.2.g.c.667.3		6	63.34	odd	6
1323.2.h.d.226.1		6	7.6	odd	2
1323.2.h.d.802.1		6	63.52	odd	6
1323.2.h.e.226.1		6	1.1	even	1	trivial
1323.2.h.e.802.1		6	63.25	even	3	inner
3024.2.r.g.1009.1		6	28.19	even	6
3024.2.r.g.2017.1		6	252.187	even	6
3969.2.a.m.1.3		3	63.23	odd	6
3969.2.a.p.1.1		3	63.58	even	3
9072.2.a.bq.1.1		3	252.131	odd	6
9072.2.a.cd.1.3		3	252.103	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.69963 q^{2} +0.888736 q^{4} +(1.79418 + 3.10761i) q^{5} +1.88874 q^{8} +O(q^{10})\)	\(q-1.69963 q^{2} +0.888736 q^{4} +(1.79418 + 3.10761i) q^{5} +1.88874 q^{8} +(-3.04944 - 5.28179i) q^{10} +(-1.40545 + 2.43430i) q^{11} +(0.500000 - 0.866025i) q^{13} -4.98762 q^{16} +(2.05563 + 3.56046i) q^{17} +(-0.444368 + 0.769668i) q^{19} +(1.59455 + 2.76185i) q^{20} +(2.38874 - 4.13741i) q^{22} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} +(-0.849814 + 1.47192i) q^{26} +(-0.849814 - 1.47192i) q^{29} +6.98762 q^{31} +4.69963 q^{32} +(-3.49381 - 6.05146i) q^{34} +(-2.38255 + 4.12669i) q^{37} +(0.755260 - 1.30815i) q^{38} +(3.38874 + 5.86946i) q^{40} +(2.70582 - 4.68661i) q^{41} +(-2.60507 - 4.51212i) q^{43} +(-1.24907 + 2.16345i) q^{44} +(-4.99381 - 8.64953i) q^{46} -2.66621 q^{47} +(6.69344 - 11.5934i) q^{50} +(0.444368 - 0.769668i) q^{52} +(-0.0618219 - 0.107079i) q^{53} -10.0865 q^{55} +(1.44437 + 2.50172i) q^{58} -8.87636 q^{59} -3.87636 q^{61} -11.8764 q^{62} +1.98762 q^{64} +3.58836 q^{65} +12.3090 q^{67} +(1.82691 + 3.16431i) q^{68} +2.87636 q^{71} +(-5.32072 - 9.21576i) q^{73} +(4.04944 - 7.01384i) q^{74} +(-0.394926 + 0.684031i) q^{76} -7.08650 q^{79} +(-8.94870 - 15.4996i) q^{80} +(-4.59888 + 7.96550i) q^{82} +(2.05563 + 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} +(4.42766 + 7.66893i) q^{86} +(-2.65452 + 4.59776i) q^{88} +(-4.80470 + 8.32199i) q^{89} +(2.61126 + 4.52284i) q^{92} +4.53156 q^{94} -3.18911 q^{95} +(3.66071 + 6.34053i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8	\( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} + 6 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} + q^{26} + q^{29} + 6 q^{31} + 16 q^{32} - 3 q^{34} + 3 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 18 q^{47} + 10 q^{50} + 3 q^{52} - 18 q^{53} + 12 q^{55} + 9 q^{58} - 18 q^{59} + 12 q^{61} - 36 q^{62} - 24 q^{64} + 10 q^{65} - 6 q^{68} - 18 q^{71} + 3 q^{73} + 6 q^{74} - 21 q^{76} + 30 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 2 q^{89} + 15 q^{92} - 48 q^{94} - 32 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8 - 2 * q^11 + 3 * q^13 + 6 * q^16 + 12 * q^17 - 3 * q^19 + 16 * q^20 + 15 * q^22 - 6 * q^25 + q^26 + q^29 + 6 * q^31 + 16 * q^32 - 3 * q^34 + 3 * q^37 - 8 * q^38 + 21 * q^40 + 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 - 18 * q^47 + 10 * q^50 + 3 * q^52 - 18 * q^53 + 12 * q^55 + 9 * q^58 - 18 * q^59 + 12 * q^61 - 36 * q^62 - 24 * q^64 + 10 * q^65 - 6 * q^68 - 18 * q^71 + 3 * q^73 + 6 * q^74 - 21 * q^76 + 30 * q^79 - 11 * q^80 + 9 * q^82 + 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 2 * q^89 + 15 * q^92 - 48 * q^94 - 32 * q^95 + 3 * q^97

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