LMFDB - Embedded newform 882.4.g.k.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (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:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.667
Dual form			882.4.g.k.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} +8.00000 q^{8} +(14.0000 + 24.2487i) q^{10} +(-14.0000 - 24.2487i) q^{11} -18.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-37.0000 - 64.0859i) q^{17} +(40.0000 - 69.2820i) q^{19} -56.0000 q^{20} +56.0000 q^{22} +(-56.0000 + 96.9948i) q^{23} +(-35.5000 - 61.4878i) q^{25} +(18.0000 - 31.1769i) q^{26} -190.000 q^{29} +(36.0000 + 62.3538i) q^{31} +(-16.0000 - 27.7128i) q^{32} +148.000 q^{34} +(173.000 - 299.645i) q^{37} +(80.0000 + 138.564i) q^{38} +(56.0000 - 96.9948i) q^{40} +162.000 q^{41} -412.000 q^{43} +(-56.0000 + 96.9948i) q^{44} +(-112.000 - 193.990i) q^{46} +(-12.0000 + 20.7846i) q^{47} +142.000 q^{50} +(36.0000 + 62.3538i) q^{52} +(159.000 + 275.396i) q^{53} -392.000 q^{55} +(190.000 - 329.090i) q^{58} +(100.000 + 173.205i) q^{59} +(-99.0000 + 171.473i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(-126.000 + 218.238i) q^{65} +(358.000 + 620.074i) q^{67} +(-148.000 + 256.344i) q^{68} -392.000 q^{71} +(269.000 + 465.922i) q^{73} +(346.000 + 599.290i) q^{74} -320.000 q^{76} +(-120.000 + 207.846i) q^{79} +(112.000 + 193.990i) q^{80} +(-162.000 + 280.592i) q^{82} -1072.00 q^{83} -1036.00 q^{85} +(412.000 - 713.605i) q^{86} +(-112.000 - 193.990i) q^{88} +(-405.000 + 701.481i) q^{89} +448.000 q^{92} +(-24.0000 - 41.5692i) q^{94} +(-560.000 - 969.948i) q^{95} -1354.00 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} + 14 q^{5} + 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 + 14 * q^5 + 16 * q^8	$ 2 q - 2 q^{2} - 4 q^{4} + 14 q^{5} + 16 q^{8} + 28 q^{10} - 28 q^{11} - 36 q^{13} - 16 q^{16} - 74 q^{17} + 80 q^{19} - 112 q^{20} + 112 q^{22} - 112 q^{23} - 71 q^{25} + 36 q^{26} - 380 q^{29} + 72 q^{31} - 32 q^{32} + 296 q^{34} + 346 q^{37} + 160 q^{38} + 112 q^{40} + 324 q^{41} - 824 q^{43} - 112 q^{44} - 224 q^{46} - 24 q^{47} + 284 q^{50} + 72 q^{52} + 318 q^{53} - 784 q^{55} + 380 q^{58} + 200 q^{59} - 198 q^{61} - 288 q^{62} + 128 q^{64} - 252 q^{65} + 716 q^{67} - 296 q^{68} - 784 q^{71} + 538 q^{73} + 692 q^{74} - 640 q^{76} - 240 q^{79} + 224 q^{80} - 324 q^{82} - 2144 q^{83} - 2072 q^{85} + 824 q^{86} - 224 q^{88} - 810 q^{89} + 896 q^{92} - 48 q^{94} - 1120 q^{95} - 2708 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 + 14 * q^5 + 16 * q^8 + 28 * q^10 - 28 * q^11 - 36 * q^13 - 16 * q^16 - 74 * q^17 + 80 * q^19 - 112 * q^20 + 112 * q^22 - 112 * q^23 - 71 * q^25 + 36 * q^26 - 380 * q^29 + 72 * q^31 - 32 * q^32 + 296 * q^34 + 346 * q^37 + 160 * q^38 + 112 * q^40 + 324 * q^41 - 824 * q^43 - 112 * q^44 - 224 * q^46 - 24 * q^47 + 284 * q^50 + 72 * q^52 + 318 * q^53 - 784 * q^55 + 380 * q^58 + 200 * q^59 - 198 * q^61 - 288 * q^62 + 128 * q^64 - 252 * q^65 + 716 * q^67 - 296 * q^68 - 784 * q^71 + 538 * q^73 + 692 * q^74 - 640 * q^76 - 240 * q^79 + 224 * q^80 - 324 * q^82 - 2144 * q^83 - 2072 * q^85 + 824 * q^86 - 224 * q^88 - 810 * q^89 + 896 * q^92 - 48 * q^94 - 1120 * q^95 - 2708 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	−0.362228	−	0.932089i	$-0.617984\pi$
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	0.988327	−	0.152346i	$-0.0486828\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$		0			0
$10$	14.0000	+	24.2487i	0.442719	+	0.766812i
$11$	−14.0000	−	24.2487i	−0.383742	−	0.664660i	0.607852	−	0.794050i	$-0.292031\pi$
$11$	−14.0000	−	24.2487i	−0.383742	−	0.664660i	−0.991594	+	0.129390i	$0.958698\pi$
$12$		0			0
$13$	−18.0000			−0.384023			−0.192012	−	0.981393i	$-0.561501\pi$
$13$	−18.0000			−0.384023			−0.192012	+	0.981393i	$0.561501\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−37.0000	−	64.0859i	−0.527872	−	0.914301i	−0.999472	−	0.0324882i	$-0.989657\pi$
$17$	−37.0000	−	64.0859i	−0.527872	−	0.914301i	0.471600	−	0.881812i	$-0.343676\pi$
$18$		0			0
$19$	40.0000	−	69.2820i	0.482980	−	0.836547i	−0.516829	−	0.856089i	$-0.672888\pi$
$19$	40.0000	−	69.2820i	0.482980	−	0.836547i	0.999809	+	0.0195422i	$0.00622087\pi$
$20$	−56.0000			−0.626099
$21$		0			0
$22$	56.0000			0.542693
$23$	−56.0000	+	96.9948i	−0.507687	+	0.879340i	0.492273	+	0.870441i	$0.336166\pi$
$23$	−56.0000	+	96.9948i	−0.507687	+	0.879340i	−0.999960	+	0.00889936i	$0.997167\pi$
$24$		0			0
$25$	−35.5000	−	61.4878i	−0.284000	−	0.491902i
$26$	18.0000	−	31.1769i	0.135773	−	0.235165i
$27$		0			0
$28$		0			0
$29$	−190.000			−1.21662			−0.608312	−	0.793698i	$-0.708153\pi$
$29$	−190.000			−1.21662			−0.608312	+	0.793698i	$0.708153\pi$
$30$		0			0
$31$	36.0000	+	62.3538i	0.208574	+	0.361261i	0.951266	−	0.308373i	$-0.0997845\pi$
$31$	36.0000	+	62.3538i	0.208574	+	0.361261i	−0.742692	+	0.669634i	$0.766451\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$		0			0
$34$	148.000			0.746523
$35$		0			0
$36$		0			0
$37$	173.000	−	299.645i	0.768676	−	1.33139i	−0.169605	−	0.985512i	$-0.554249\pi$
$37$	173.000	−	299.645i	0.768676	−	1.33139i	0.938281	−	0.345874i	$-0.112418\pi$
$38$	80.0000	+	138.564i	0.341519	+	0.591528i
$39$		0			0
$40$	56.0000	−	96.9948i	0.221359	−	0.383406i
$41$	162.000			0.617077			0.308538	−	0.951212i	$-0.400160\pi$
$41$	162.000			0.617077			0.308538	+	0.951212i	$0.400160\pi$
$42$		0			0
$43$	−412.000			−1.46115			−0.730575	−	0.682833i	$-0.760748\pi$
$43$	−412.000			−1.46115			−0.730575	+	0.682833i	$0.760748\pi$
$44$	−56.0000	+	96.9948i	−0.191871	+	0.332330i
$45$		0			0
$46$	−112.000	−	193.990i	−0.358989	−	0.621787i
$47$	−12.0000	+	20.7846i	−0.0372421	+	0.0645053i	−0.884046	−	0.467401i	$-0.845191\pi$
$47$	−12.0000	+	20.7846i	−0.0372421	+	0.0645053i	0.846804	+	0.531906i	$0.178524\pi$
$48$		0			0
$49$		0			0
$50$	142.000			0.401637
$51$		0			0
$52$	36.0000	+	62.3538i	0.0960058	+	0.166287i
$53$	159.000	+	275.396i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	159.000	+	275.396i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	−392.000			−0.961041
$56$		0			0
$57$		0			0
$58$	190.000	−	329.090i	0.430142	−	0.745027i
$59$	100.000	+	173.205i	0.220659	+	0.382193i	0.955008	−	0.296579i	$-0.0958458\pi$
$59$	100.000	+	173.205i	0.220659	+	0.382193i	−0.734349	+	0.678772i	$0.762512\pi$
$60$		0			0
$61$	−99.0000	+	171.473i	−0.207798	+	0.359916i	−0.951020	−	0.309128i	$-0.899963\pi$
$61$	−99.0000	+	171.473i	−0.207798	+	0.359916i	0.743223	+	0.669044i	$0.233296\pi$
$62$	−144.000			−0.294968
$63$		0			0
$64$	64.0000			0.125000
$65$	−126.000	+	218.238i	−0.240437	+	0.416448i
$66$		0			0
$67$	358.000	+	620.074i	0.652786	+	1.13066i	0.982444	+	0.186558i	$0.0597332\pi$
$67$	358.000	+	620.074i	0.652786	+	1.13066i	−0.329658	+	0.944100i	$0.606933\pi$
$68$	−148.000	+	256.344i	−0.263936	+	0.457150i
$69$		0			0
$70$		0			0
$71$	−392.000			−0.655237			−0.327619	−	0.944810i	$-0.606246\pi$
$71$	−392.000			−0.655237			−0.327619	+	0.944810i	$0.606246\pi$
$72$		0			0
$73$	269.000	+	465.922i	0.431289	+	0.747014i	0.996985	−	0.0776001i	$-0.0247257\pi$
$73$	269.000	+	465.922i	0.431289	+	0.747014i	−0.565696	+	0.824614i	$0.691392\pi$
$74$	346.000	+	599.290i	0.543536	+	0.941432i
$75$		0			0
$76$	−320.000			−0.482980
$77$		0			0
$78$		0			0
$79$	−120.000	+	207.846i	−0.170899	+	0.296006i	−0.938735	−	0.344641i	$-0.888001\pi$
$79$	−120.000	+	207.846i	−0.170899	+	0.296006i	0.767835	+	0.640647i	$0.221334\pi$
$80$	112.000	+	193.990i	0.156525	+	0.271109i
$81$		0			0
$82$	−162.000	+	280.592i	−0.218170	+	0.377881i
$83$	−1072.00			−1.41768			−0.708839	−	0.705370i	$-0.750781\pi$
$83$	−1072.00			−1.41768			−0.708839	+	0.705370i	$0.750781\pi$
$84$		0			0
$85$	−1036.00			−1.32200
$86$	412.000	−	713.605i	0.516594	−	0.894767i
$87$		0			0
$88$	−112.000	−	193.990i	−0.135673	−	0.234993i
$89$	−405.000	+	701.481i	−0.482359	+	0.835470i	−0.999795	−	0.0202521i	$-0.993553\pi$
$89$	−405.000	+	701.481i	−0.482359	+	0.835470i	0.517436	+	0.855722i	$0.326886\pi$
$90$		0			0
$91$		0			0
$92$	448.000			0.507687
$93$		0			0
$94$	−24.0000	−	41.5692i	−0.0263342	−	0.0456121i
$95$	−560.000	−	969.948i	−0.604787	−	1.04752i
$96$		0			0
$97$	−1354.00			−1.41730			−0.708649	−	0.705561i	$-0.750695\pi$
$97$	−1354.00			−1.41730			−0.708649	+	0.705561i	$0.750695\pi$
$98$		0			0
$99$		0			0
$100$	−142.000	+	245.951i	−0.142000	+	0.245951i
$101$	679.000	+	1176.06i	0.668941	+	1.15864i	0.978201	+	0.207662i	$0.0665854\pi$
$101$	679.000	+	1176.06i	0.668941	+	1.15864i	−0.309260	+	0.950978i	$0.600081\pi$
$102$		0			0
$103$	−416.000	+	720.533i	−0.397958	+	0.689284i	−0.993474	−	0.114060i	$-0.963614\pi$
$103$	−416.000	+	720.533i	−0.397958	+	0.689284i	0.595516	+	0.803344i	$0.296948\pi$
$104$	−144.000			−0.135773
$105$		0			0
$106$	−636.000			−0.582772
$107$	222.000	−	384.515i	0.200575	−	0.347406i	−0.748139	−	0.663542i	$-0.769052\pi$
$107$	222.000	−	384.515i	0.200575	−	0.347406i	0.948714	+	0.316136i	$0.102386\pi$
$108$		0			0
$109$	−935.000	−	1619.47i	−0.821622	−	1.42309i	−0.904474	−	0.426529i	$-0.859736\pi$
$109$	−935.000	−	1619.47i	−0.821622	−	1.42309i	0.0828525	−	0.996562i	$-0.473597\pi$
$110$	392.000	−	678.964i	0.339779	−	0.588515i
$111$		0			0
$112$		0			0
$113$	−1378.00			−1.14718			−0.573590	−	0.819143i	$-0.694450\pi$
$113$	−1378.00			−1.14718			−0.573590	+	0.819143i	$0.694450\pi$
$114$		0			0
$115$	784.000	+	1357.93i	0.635725	+	1.10111i
$116$	380.000	+	658.179i	0.304156	+	0.526814i
$117$		0			0
$118$	−400.000			−0.312059
$119$		0			0
$120$		0			0
$121$	273.500	−	473.716i	0.205485	−	0.355910i
$122$	−198.000	−	342.946i	−0.146935	−	0.254499i
$123$		0			0
$124$	144.000	−	249.415i	0.104287	−	0.180630i
$125$	756.000			0.540950
$126$		0			0
$127$	1944.00			1.35828			0.679142	−	0.734007i	$-0.262352\pi$
$127$	1944.00			1.35828			0.679142	+	0.734007i	$0.262352\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−252.000	−	436.477i	−0.170014	−	0.294473i
$131$	424.000	−	734.390i	0.282787	−	0.489801i	−0.689283	−	0.724492i	$-0.742074\pi$
$131$	424.000	−	734.390i	0.282787	−	0.489801i	0.972070	+	0.234691i	$0.0754078\pi$
$132$		0			0
$133$		0			0
$134$	−1432.00			−0.923179
$135$		0			0
$136$	−296.000	−	512.687i	−0.186631	−	0.323254i
$137$	−1483.00	−	2568.63i	−0.924827	−	1.60185i	−0.791840	−	0.610729i	$-0.790877\pi$
$137$	−1483.00	−	2568.63i	−0.924827	−	1.60185i	−0.132987	−	0.991118i	$-0.542457\pi$
$138$		0			0
$139$	−2800.00			−1.70858			−0.854291	−	0.519795i	$-0.826008\pi$
$139$	−2800.00			−1.70858			−0.854291	+	0.519795i	$0.826008\pi$
$140$		0			0
$141$		0			0
$142$	392.000	−	678.964i	0.231661	−	0.401249i
$143$	252.000	+	436.477i	0.147366	+	0.255245i
$144$		0			0
$145$	−1330.00	+	2303.63i	−0.761728	+	1.31935i
$146$	−1076.00			−0.609934
$147$		0			0
$148$	−1384.00			−0.768676
$149$	255.000	−	441.673i	0.140204	−	0.242841i	−0.787369	−	0.616482i	$-0.788557\pi$
$149$	255.000	−	441.673i	0.140204	−	0.242841i	0.927573	+	0.373641i	$0.121891\pi$
$150$		0			0
$151$	−296.000	−	512.687i	−0.159524	−	0.276304i	0.775173	−	0.631749i	$-0.217663\pi$
$151$	−296.000	−	512.687i	−0.159524	−	0.276304i	−0.934697	+	0.355445i	$0.884329\pi$
$152$	320.000	−	554.256i	0.170759	−	0.295764i
$153$		0			0
$154$		0			0
$155$	1008.00			0.522352
$156$		0			0
$157$	−1343.00	−	2326.14i	−0.682695	−	1.18246i	−0.974155	−	0.225879i	$-0.927475\pi$
$157$	−1343.00	−	2326.14i	−0.682695	−	1.18246i	0.291461	−	0.956583i	$-0.405859\pi$
$158$	−240.000	−	415.692i	−0.120844	−	0.209308i
$159$		0			0
$160$	−448.000			−0.221359
$161$		0			0
$162$		0			0
$163$	506.000	−	876.418i	0.243147	−	0.421143i	−0.718462	−	0.695566i	$-0.755154\pi$
$163$	506.000	−	876.418i	0.243147	−	0.421143i	0.961609	+	0.274423i	$0.0884869\pi$
$164$	−324.000	−	561.184i	−0.154269	−	0.267202i
$165$		0			0
$166$	1072.00	−	1856.76i	0.501225	−	0.868147i
$167$	544.000			0.252072			0.126036	−	0.992026i	$-0.459775\pi$
$167$	544.000			0.252072			0.126036	+	0.992026i	$0.459775\pi$
$168$		0			0
$169$	−1873.00			−0.852526
$170$	1036.00	−	1794.40i	0.467397	−	0.809556i
$171$		0			0
$172$	824.000	+	1427.21i	0.365287	+	0.632696i
$173$	−929.000	+	1609.08i	−0.408269	+	0.707143i	−0.994696	−	0.102859i	$-0.967201\pi$
$173$	−929.000	+	1609.08i	−0.408269	+	0.707143i	0.586427	+	0.810002i	$0.300534\pi$
$174$		0			0
$175$		0			0
$176$	448.000			0.191871
$177$		0			0
$178$	−810.000	−	1402.96i	−0.341079	−	0.590766i
$179$	−150.000	−	259.808i	−0.0626342	−	0.108486i	0.833008	−	0.553261i	$-0.186617\pi$
$179$	−150.000	−	259.808i	−0.0626342	−	0.108486i	−0.895642	+	0.444775i	$0.853283\pi$
$180$		0			0
$181$	2358.00			0.968336			0.484168	−	0.874975i	$-0.339122\pi$
$181$	2358.00			0.968336			0.484168	+	0.874975i	$0.339122\pi$
$182$		0			0
$183$		0			0
$184$	−448.000	+	775.959i	−0.179495	+	0.310894i
$185$	−2422.00	−	4195.03i	−0.962535	−	1.66716i
$186$		0			0
$187$	−1036.00	+	1794.40i	−0.405133	+	0.701710i
$188$	96.0000			0.0372421
$189$		0			0
$190$	2240.00			0.855298
$191$	696.000	−	1205.51i	0.263669	−	0.456688i	−0.703545	−	0.710651i	$-0.748401\pi$
$191$	696.000	−	1205.51i	0.263669	−	0.456688i	0.967214	+	0.253962i	$0.0817340\pi$
$192$		0			0
$193$	−889.000	−	1539.79i	−0.331563	−	0.574284i	0.651256	−	0.758858i	$-0.274243\pi$
$193$	−889.000	−	1539.79i	−0.331563	−	0.574284i	−0.982818	+	0.184575i	$0.940909\pi$
$194$	1354.00	−	2345.20i	0.501090	−	0.867914i
$195$		0			0
$196$		0			0
$197$	−1214.00			−0.439055			−0.219528	−	0.975606i	$-0.570452\pi$
$197$	−1214.00			−0.439055			−0.219528	+	0.975606i	$0.570452\pi$
$198$		0			0
$199$	520.000	+	900.666i	0.185235	+	0.320837i	0.943656	−	0.330929i	$-0.107362\pi$
$199$	520.000	+	900.666i	0.185235	+	0.320837i	−0.758420	+	0.651766i	$0.774029\pi$
$200$	−284.000	−	491.902i	−0.100409	−	0.173914i
$201$		0			0
$202$	−2716.00			−0.946025
$203$		0			0
$204$		0			0
$205$	1134.00	−	1964.15i	0.386351	−	0.669180i
$206$	−832.000	−	1441.07i	−0.281399	−	0.487397i
$207$		0			0
$208$	144.000	−	249.415i	0.0480029	−	0.0831435i
$209$	−2240.00			−0.741359
$210$		0			0
$211$	−3868.00			−1.26201			−0.631005	−	0.775779i	$-0.717357\pi$
$211$	−3868.00			−1.26201			−0.631005	+	0.775779i	$0.717357\pi$
$212$	636.000	−	1101.58i	0.206041	−	0.356873i
$213$		0			0
$214$	444.000	+	769.031i	0.141828	+	0.245653i
$215$	−2884.00	+	4995.23i	−0.914824	+	1.58452i
$216$		0			0
$217$		0			0
$218$	3740.00			1.16195
$219$		0			0
$220$	784.000	+	1357.93i	0.240260	+	0.416143i
$221$	666.000	+	1153.55i	0.202715	+	0.351113i
$222$		0			0
$223$	−3968.00			−1.19156			−0.595778	−	0.803149i	$-0.703156\pi$
$223$	−3968.00			−1.19156			−0.595778	+	0.803149i	$0.703156\pi$
$224$		0			0
$225$		0			0
$226$	1378.00	−	2386.77i	0.405589	−	0.702501i
$227$	1968.00	+	3408.68i	0.575422	+	0.996660i	0.995996	+	0.0894015i	$0.0284954\pi$
$227$	1968.00	+	3408.68i	0.575422	+	0.996660i	−0.420574	+	0.907258i	$0.638171\pi$
$228$		0			0
$229$	2405.00	−	4165.58i	0.694004	−	1.20205i	−0.276512	−	0.961011i	$-0.589178\pi$
$229$	2405.00	−	4165.58i	0.694004	−	1.20205i	0.970515	−	0.241039i	$-0.0774883\pi$
$230$	−3136.00			−0.899051
$231$		0			0
$232$	−1520.00			−0.430142
$233$	−1091.00	+	1889.67i	−0.306754	+	0.531314i	−0.977650	−	0.210237i	$-0.932576\pi$
$233$	−1091.00	+	1889.67i	−0.306754	+	0.531314i	0.670896	+	0.741551i	$0.265910\pi$
$234$		0			0
$235$	168.000	+	290.985i	0.0466345	+	0.0807734i
$236$	400.000	−	692.820i	0.110330	−	0.191096i
$237$		0			0
$238$		0			0
$239$	3000.00			0.811941			0.405970	−	0.913886i	$-0.366934\pi$
$239$	3000.00			0.811941			0.405970	+	0.913886i	$0.366934\pi$
$240$		0			0
$241$	1021.00	+	1768.42i	0.272898	+	0.472673i	0.969603	−	0.244685i	$-0.0786845\pi$
$241$	1021.00	+	1768.42i	0.272898	+	0.472673i	−0.696705	+	0.717358i	$0.745351\pi$
$242$	547.000	+	947.432i	0.145300	+	0.251666i
$243$		0			0
$244$	792.000			0.207798
$245$		0			0
$246$		0			0
$247$	−720.000	+	1247.08i	−0.185476	+	0.321253i
$248$	288.000	+	498.831i	0.0737420	+	0.127725i
$249$		0			0
$250$	−756.000	+	1309.43i	−0.191255	+	0.331263i
$251$	−528.000			−0.132777			−0.0663886	−	0.997794i	$-0.521148\pi$
$251$	−528.000			−0.132777			−0.0663886	+	0.997794i	$0.521148\pi$
$252$		0			0
$253$	3136.00			0.779283
$254$	−1944.00	+	3367.11i	−0.480226	+	0.831776i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2817.00	+	4879.19i	−0.683734	+	1.18426i	0.290099	+	0.956997i	$0.406312\pi$
$257$	−2817.00	+	4879.19i	−0.683734	+	1.18426i	−0.973833	+	0.227265i	$0.927022\pi$
$258$		0			0
$259$		0			0
$260$	1008.00			0.240437
$261$		0			0
$262$	848.000	+	1468.78i	0.199960	+	0.346342i
$263$	84.0000	+	145.492i	0.0196945	+	0.0341119i	0.875705	−	0.482847i	$-0.160397\pi$
$263$	84.0000	+	145.492i	0.0196945	+	0.0341119i	−0.856010	+	0.516959i	$0.827064\pi$
$264$		0			0
$265$	4452.00			1.03202
$266$		0			0
$267$		0			0
$268$	1432.00	−	2480.30i	0.326393	−	0.565329i
$269$	655.000	+	1134.49i	0.148461	+	0.257142i	0.930659	−	0.365888i	$-0.119235\pi$
$269$	655.000	+	1134.49i	0.148461	+	0.257142i	−0.782198	+	0.623030i	$0.785901\pi$
$270$		0			0
$271$	−1104.00	+	1912.18i	−0.247466	+	0.428623i	−0.962822	−	0.270137i	$-0.912931\pi$
$271$	−1104.00	+	1912.18i	−0.247466	+	0.428623i	0.715356	+	0.698760i	$0.246264\pi$
$272$	1184.00			0.263936
$273$		0			0
$274$	5932.00			1.30790
$275$	−994.000	+	1721.66i	−0.217965	+	0.377527i
$276$		0			0
$277$	−2647.00	−	4584.74i	−0.574162	−	0.994477i	−0.996132	−	0.0878678i	$-0.971995\pi$
$277$	−2647.00	−	4584.74i	−0.574162	−	0.994477i	0.421970	−	0.906610i	$-0.361339\pi$
$278$	2800.00	−	4849.74i	0.604075	−	1.04629i
$279$		0			0
$280$		0			0
$281$	−3242.00			−0.688262			−0.344131	−	0.938922i	$-0.611826\pi$
$281$	−3242.00			−0.688262			−0.344131	+	0.938922i	$0.611826\pi$
$282$		0			0
$283$	−796.000	−	1378.71i	−0.167199	−	0.289597i	0.770235	−	0.637760i	$-0.220139\pi$
$283$	−796.000	−	1378.71i	−0.167199	−	0.289597i	−0.937434	+	0.348163i	$0.886806\pi$
$284$	784.000	+	1357.93i	0.163809	+	0.283726i
$285$		0			0
$286$	−1008.00			−0.208407
$287$		0			0
$288$		0			0
$289$	−281.500	+	487.572i	−0.0572970	+	0.0992413i
$290$	−2660.00	−	4607.26i	−0.538623	−	0.932922i
$291$		0			0
$292$	1076.00	−	1863.69i	0.215644	−	0.373507i
$293$	−5022.00			−1.00133			−0.500663	−	0.865642i	$-0.666910\pi$
$293$	−5022.00			−1.00133			−0.500663	+	0.865642i	$0.666910\pi$
$294$		0			0
$295$	2800.00			0.552618
$296$	1384.00	−	2397.16i	0.271768	−	0.470716i
$297$		0			0
$298$	510.000	+	883.346i	0.0991393	+	0.171714i
$299$	1008.00	−	1745.91i	0.194964	−	0.337687i
$300$		0			0
$301$		0			0
$302$	1184.00			0.225601
$303$		0			0
$304$	640.000	+	1108.51i	0.120745	+	0.209137i
$305$	1386.00	+	2400.62i	0.260204	+	0.450686i
$306$		0			0
$307$	9536.00			1.77280			0.886398	−	0.462924i	$-0.153200\pi$
$307$	9536.00			1.77280			0.886398	+	0.462924i	$0.153200\pi$
$308$		0			0
$309$		0			0
$310$	−1008.00	+	1745.91i	−0.184679	+	0.319874i
$311$	484.000	+	838.313i	0.0882480	+	0.152850i	0.906771	−	0.421624i	$-0.138540\pi$
$311$	484.000	+	838.313i	0.0882480	+	0.152850i	−0.818523	+	0.574474i	$0.805207\pi$
$312$		0			0
$313$	1529.00	−	2648.31i	0.276116	−	0.478246i	−0.694300	−	0.719685i	$-0.744286\pi$
$313$	1529.00	−	2648.31i	0.276116	−	0.478246i	0.970416	+	0.241439i	$0.0776194\pi$
$314$	5372.00			0.965476
$315$		0			0
$316$	960.000			0.170899
$317$	−2493.00	+	4318.00i	−0.441706	+	0.765057i	−0.997816	−	0.0660512i	$-0.978960\pi$
$317$	−2493.00	+	4318.00i	−0.441706	+	0.765057i	0.556110	+	0.831109i	$0.312293\pi$
$318$		0			0
$319$	2660.00	+	4607.26i	0.466870	+	0.808642i
$320$	448.000	−	775.959i	0.0782624	−	0.135554i
$321$		0			0
$322$		0			0
$323$	−5920.00			−1.01981
$324$		0			0
$325$	639.000	+	1106.78i	0.109063	+	0.188902i
$326$	1012.00	+	1752.84i	0.171931	+	0.297793i
$327$		0			0
$328$	1296.00			0.218170
$329$		0			0
$330$		0			0
$331$	−4306.00	+	7458.21i	−0.715043	+	1.23849i	0.247900	+	0.968786i	$0.420259\pi$
$331$	−4306.00	+	7458.21i	−0.715043	+	1.23849i	−0.962943	+	0.269705i	$0.913074\pi$
$332$	2144.00	+	3713.52i	0.354420	+	0.613873i
$333$		0			0
$334$	−544.000	+	942.236i	−0.0891208	+	0.154362i
$335$	10024.0			1.63483
$336$		0			0
$337$	−10206.0			−1.64972			−0.824861	−	0.565336i	$-0.808747\pi$
$337$	−10206.0			−1.64972			−0.824861	+	0.565336i	$0.808747\pi$
$338$	1873.00	−	3244.13i	0.301414	−	0.522064i
$339$		0			0
$340$	2072.00	+	3588.81i	0.330500	+	0.572443i
$341$	1008.00	−	1745.91i	0.160077	−	0.277262i
$342$		0			0
$343$		0			0
$344$	−3296.00			−0.516594
$345$		0			0
$346$	−1858.00	−	3218.15i	−0.288690	−	0.500026i
$347$	1002.00	+	1735.51i	0.155015	+	0.268494i	0.933064	−	0.359709i	$-0.117124\pi$
$347$	1002.00	+	1735.51i	0.155015	+	0.268494i	−0.778050	+	0.628203i	$0.783791\pi$
$348$		0			0
$349$	−1330.00			−0.203992			−0.101996	−	0.994785i	$-0.532523\pi$
$349$	−1330.00			−0.203992			−0.101996	+	0.994785i	$0.532523\pi$
$350$		0			0
$351$		0			0
$352$	−448.000	+	775.959i	−0.0678366	+	0.117496i
$353$	−489.000	−	846.973i	−0.0737304	−	0.127705i	0.826803	−	0.562492i	$-0.190157\pi$
$353$	−489.000	−	846.973i	−0.0737304	−	0.127705i	−0.900533	+	0.434787i	$0.856824\pi$
$354$		0			0
$355$	−2744.00	+	4752.75i	−0.410243	+	0.710562i
$356$	3240.00			0.482359
$357$		0			0
$358$	600.000			0.0885782
$359$	−4840.00	+	8383.13i	−0.711547	+	1.23244i	0.252729	+	0.967537i	$0.418672\pi$
$359$	−4840.00	+	8383.13i	−0.711547	+	1.23244i	−0.964276	+	0.264899i	$0.914661\pi$
$360$		0			0
$361$	229.500	+	397.506i	0.0334597	+	0.0579539i
$362$	−2358.00	+	4084.18i	−0.342358	+	0.592982i
$363$		0			0
$364$		0			0
$365$	7532.00			1.08012
$366$		0			0
$367$	−4328.00	−	7496.32i	−0.615585	−	1.06622i	−0.990282	−	0.139077i	$-0.955586\pi$
$367$	−4328.00	−	7496.32i	−0.615585	−	1.06622i	0.374696	−	0.927148i	$-0.377747\pi$
$368$	−896.000	−	1551.92i	−0.126922	−	0.219835i
$369$		0			0
$370$	9688.00			1.36123
$371$		0			0
$372$		0			0
$373$	−2639.00	+	4570.88i	−0.366333	+	0.634508i	−0.988989	−	0.147988i	$-0.952720\pi$
$373$	−2639.00	+	4570.88i	−0.366333	+	0.634508i	0.622656	+	0.782496i	$0.286054\pi$
$374$	−2072.00	−	3588.81i	−0.286472	−	0.496184i
$375$		0			0
$376$	−96.0000	+	166.277i	−0.0131671	+	0.0228061i
$377$	3420.00			0.467212
$378$		0			0
$379$	6340.00			0.859272			0.429636	−	0.903002i	$-0.358642\pi$
$379$	6340.00			0.859272			0.429636	+	0.903002i	$0.358642\pi$
$380$	−2240.00	+	3879.79i	−0.302394	+	0.523761i
$381$		0			0
$382$	1392.00	+	2411.01i	0.186442	+	0.322927i
$383$	3116.00	−	5397.07i	0.415718	−	0.720045i	−0.579785	−	0.814769i	$-0.696864\pi$
$383$	3116.00	−	5397.07i	0.415718	−	0.720045i	0.995504	+	0.0947240i	$0.0301968\pi$
$384$		0			0
$385$		0			0
$386$	3556.00			0.468901
$387$		0			0
$388$	2708.00	+	4690.39i	0.354324	+	0.613708i
$389$	−7405.00	−	12825.8i	−0.965163	−	1.67171i	−0.709177	−	0.705031i	$-0.750933\pi$
$389$	−7405.00	−	12825.8i	−0.965163	−	1.67171i	−0.255986	−	0.966680i	$-0.582400\pi$
$390$		0			0
$391$	8288.00			1.07197
$392$		0			0
$393$		0			0
$394$	1214.00	−	2102.71i	0.155230	−	0.268865i
$395$	1680.00	+	2909.85i	0.214000	+	0.370659i
$396$		0			0
$397$	2577.00	−	4463.49i	0.325783	−	0.564273i	−0.655887	−	0.754859i	$-0.727705\pi$
$397$	2577.00	−	4463.49i	0.325783	−	0.564273i	0.981671	+	0.190586i	$0.0610387\pi$
$398$	−2080.00			−0.261962
$399$		0			0
$400$	1136.00			0.142000
$401$	1641.00	−	2842.30i	0.204358	−	0.353959i	−0.745570	−	0.666427i	$-0.767823\pi$
$401$	1641.00	−	2842.30i	0.204358	−	0.353959i	0.949928	+	0.312469i	$0.101156\pi$
$402$		0			0
$403$	−648.000	−	1122.37i	−0.0800972	−	0.138732i
$404$	2716.00	−	4704.25i	0.334470	−	0.579320i
$405$		0			0
$406$		0			0
$407$	−9688.00			−1.17989
$408$		0			0
$409$	2905.00	+	5031.61i	0.351205	+	0.608306i	0.986461	−	0.163996i	$-0.0524386\pi$
$409$	2905.00	+	5031.61i	0.351205	+	0.608306i	−0.635256	+	0.772302i	$0.719105\pi$
$410$	2268.00	+	3928.29i	0.273192	+	0.473182i
$411$		0			0
$412$	3328.00			0.397958
$413$		0			0
$414$		0			0
$415$	−7504.00	+	12997.3i	−0.887607	+	1.53738i
$416$	288.000	+	498.831i	0.0339432	+	0.0587913i
$417$		0			0
$418$	2240.00	−	3879.79i	0.262110	−	0.453988i
$419$	13560.0			1.58102			0.790512	−	0.612446i	$-0.209814\pi$
$419$	13560.0			1.58102			0.790512	+	0.612446i	$0.209814\pi$
$420$		0			0
$421$	−738.000			−0.0854345			−0.0427172	−	0.999087i	$-0.513601\pi$
$421$	−738.000			−0.0854345			−0.0427172	+	0.999087i	$0.513601\pi$
$422$	3868.00	−	6699.57i	0.446188	−	0.772820i
$423$		0			0
$424$	1272.00	+	2203.17i	0.145693	+	0.252347i
$425$	−2627.00	+	4550.10i	−0.299831	+	0.519323i
$426$		0			0
$427$		0			0
$428$	−1776.00			−0.200575
$429$		0			0
$430$	−5768.00	−	9990.47i	−0.646878	−	1.12043i
$431$	636.000	+	1101.58i	0.0710790	+	0.123112i	0.899374	−	0.437179i	$-0.144022\pi$
$431$	636.000	+	1101.58i	0.0710790	+	0.123112i	−0.828295	+	0.560292i	$0.810689\pi$
$432$		0			0
$433$	5062.00			0.561811			0.280906	−	0.959735i	$-0.409365\pi$
$433$	5062.00			0.561811			0.280906	+	0.959735i	$0.409365\pi$
$434$		0			0
$435$		0			0
$436$	−3740.00	+	6477.87i	−0.410811	+	0.711545i
$437$	4480.00	+	7759.59i	0.490406	+	0.849408i
$438$		0			0
$439$	2820.00	−	4884.38i	0.306586	−	0.531023i	−0.671027	−	0.741433i	$-0.734147\pi$
$439$	2820.00	−	4884.38i	0.306586	−	0.531023i	0.977613	+	0.210410i	$0.0674800\pi$
$440$	−3136.00			−0.339779
$441$		0			0
$442$	−2664.00			−0.286682
$443$	6694.00	−	11594.3i	0.717927	−	1.24349i	−0.243893	−	0.969802i	$-0.578425\pi$
$443$	6694.00	−	11594.3i	0.717927	−	1.24349i	0.961820	−	0.273683i	$-0.0882421\pi$
$444$		0			0
$445$	5670.00	+	9820.73i	0.604008	+	1.04617i
$446$	3968.00	−	6872.78i	0.421279	−	0.729676i
$447$		0			0
$448$		0			0
$449$	3230.00			0.339495			0.169747	−	0.985488i	$-0.445705\pi$
$449$	3230.00			0.339495			0.169747	+	0.985488i	$0.445705\pi$
$450$		0			0
$451$	−2268.00	−	3928.29i	−0.236798	−	0.410146i
$452$	2756.00	+	4773.53i	0.286795	+	0.496743i
$453$		0			0
$454$	−7872.00			−0.813769
$455$		0			0
$456$		0			0
$457$	5323.00	−	9219.71i	0.544857	−	0.943719i	−0.453759	−	0.891124i	$-0.649917\pi$
$457$	5323.00	−	9219.71i	0.544857	−	0.943719i	0.998616	−	0.0525950i	$-0.0167492\pi$
$458$	4810.00	+	8331.16i	0.490735	+	0.849978i
$459$		0			0
$460$	3136.00	−	5431.71i	0.317863	−	0.550554i
$461$	7282.00			0.735698			0.367849	−	0.929886i	$-0.380094\pi$
$461$	7282.00			0.735698			0.367849	+	0.929886i	$0.380094\pi$
$462$		0			0
$463$	12688.0			1.27357			0.636783	−	0.771043i	$-0.280265\pi$
$463$	12688.0			1.27357			0.636783	+	0.771043i	$0.280265\pi$
$464$	1520.00	−	2632.72i	0.152078	−	0.263407i
$465$		0			0
$466$	−2182.00	−	3779.33i	−0.216908	−	0.375696i
$467$	1408.00	−	2438.73i	0.139517	−	0.241651i	−0.787797	−	0.615935i	$-0.788778\pi$
$467$	1408.00	−	2438.73i	0.139517	−	0.241651i	0.927314	+	0.374285i	$0.122112\pi$
$468$		0			0
$469$		0			0
$470$	−672.000			−0.0659512
$471$		0			0
$472$	800.000	+	1385.64i	0.0780148	+	0.135126i
$473$	5768.00	+	9990.47i	0.560704	+	0.971168i
$474$		0			0
$475$	−5680.00			−0.548666
$476$		0			0
$477$		0			0
$478$	−3000.00	+	5196.15i	−0.287064	+	0.497210i
$479$	1580.00	+	2736.64i	0.150714	+	0.261044i	0.931490	−	0.363766i	$-0.118509\pi$
$479$	1580.00	+	2736.64i	0.150714	+	0.261044i	−0.780776	+	0.624811i	$0.785176\pi$
$480$		0			0
$481$	−3114.00	+	5393.61i	−0.295190	+	0.511283i
$482$	−4084.00			−0.385936
$483$		0			0
$484$	−2188.00			−0.205485
$485$	−9478.00	+	16416.4i	−0.887369	+	1.53697i
$486$		0			0
$487$	7088.00	+	12276.8i	0.659523	+	1.14233i	0.980739	+	0.195322i	$0.0625752\pi$
$487$	7088.00	+	12276.8i	0.659523	+	1.14233i	−0.321216	+	0.947006i	$0.604091\pi$
$488$	−792.000	+	1371.78i	−0.0734675	+	0.127249i
$489$		0			0
$490$		0			0
$491$	11268.0			1.03568			0.517839	−	0.855478i	$-0.326737\pi$
$491$	11268.0			1.03568			0.517839	+	0.855478i	$0.326737\pi$
$492$		0			0
$493$	7030.00	+	12176.3i	0.642222	+	1.11236i
$494$	−1440.00	−	2494.15i	−0.131151	−	0.227160i
$495$		0			0
$496$	−1152.00			−0.104287
$497$		0			0
$498$		0			0
$499$	2230.00	−	3862.47i	0.200057	−	0.346509i	−0.748489	−	0.663147i	$-0.769221\pi$
$499$	2230.00	−	3862.47i	0.200057	−	0.346509i	0.948547	+	0.316638i	$0.102554\pi$
$500$	−1512.00	−	2618.86i	−0.135237	−	0.234238i
$501$		0			0
$502$	528.000	−	914.523i	0.0469438	−	0.0813091i
$503$	−1512.00			−0.134029			−0.0670147	−	0.997752i	$-0.521347\pi$
$503$	−1512.00			−0.134029			−0.0670147	+	0.997752i	$0.521347\pi$
$504$		0			0
$505$	19012.0			1.67529
$506$	−3136.00	+	5431.71i	−0.275518	+	0.477212i
$507$		0			0
$508$	−3888.00	−	6734.21i	−0.339571	−	0.588154i
$509$	5895.00	−	10210.4i	0.513342	−	0.889135i	−0.486538	−	0.873660i	$-0.661740\pi$
$509$	5895.00	−	10210.4i	0.513342	−	0.889135i	0.999880	−	0.0154756i	$-0.00492624\pi$
$510$		0			0
$511$		0			0
$512$	512.000			0.0441942
$513$		0			0
$514$	−5634.00	−	9758.37i	−0.483473	−	0.837400i
$515$	5824.00	+	10087.5i	0.498323	+	0.863120i
$516$		0			0
$517$	672.000			0.0571654
$518$		0			0
$519$		0			0
$520$	−1008.00	+	1745.91i	−0.0850072	+	0.147237i
$521$	−681.000	−	1179.53i	−0.0572652	−	0.0991862i	0.835972	−	0.548773i	$-0.184905\pi$
$521$	−681.000	−	1179.53i	−0.0572652	−	0.0991862i	−0.893237	+	0.449586i	$0.851571\pi$
$522$		0			0
$523$	3484.00	−	6034.47i	0.291290	−	0.504529i	−0.682825	−	0.730582i	$-0.739249\pi$
$523$	3484.00	−	6034.47i	0.291290	−	0.504529i	0.974115	+	0.226053i	$0.0725822\pi$
$524$	−3392.00			−0.282787
$525$		0			0
$526$	−336.000			−0.0278523
$527$	2664.00	−	4614.18i	0.220200	−	0.381398i
$528$		0			0
$529$	−188.500	−	326.492i	−0.0154927	−	0.0268342i
$530$	−4452.00	+	7711.09i	−0.364873	+	0.631978i
$531$		0			0
$532$		0			0
$533$	−2916.00			−0.236972
$534$		0			0
$535$	−3108.00	−	5383.21i	−0.251160	−	0.435022i
$536$	2864.00	+	4960.59i	0.230795	+	0.399748i
$537$		0			0
$538$	−2620.00			−0.209956
$539$		0			0
$540$		0			0
$541$	−3531.00	+	6115.87i	−0.280609	+	0.486029i	−0.971535	−	0.236896i	$-0.923870\pi$
$541$	−3531.00	+	6115.87i	−0.280609	+	0.486029i	0.690926	+	0.722926i	$0.257203\pi$
$542$	−2208.00	−	3824.37i	−0.174985	−	0.303082i
$543$		0			0
$544$	−1184.00	+	2050.75i	−0.0933154	+	0.161627i
$545$	−26180.0			−2.05767
$546$		0			0
$547$	−8196.00			−0.640650			−0.320325	−	0.947308i	$-0.603792\pi$
$547$	−8196.00			−0.640650			−0.320325	+	0.947308i	$0.603792\pi$
$548$	−5932.00	+	10274.5i	−0.462413	+	0.800923i
$549$		0			0
$550$	−1988.00	−	3443.32i	−0.154125	−	0.266952i
$551$	−7600.00	+	13163.6i	−0.587606	+	1.01776i
$552$		0			0
$553$		0			0
$554$	10588.0			0.811987
$555$		0			0
$556$	5600.00	+	9699.48i	0.427146	+	0.739838i
$557$	−3733.00	−	6465.75i	−0.283972	−	0.491854i	0.688388	−	0.725343i	$-0.258319\pi$
$557$	−3733.00	−	6465.75i	−0.283972	−	0.491854i	−0.972359	+	0.233490i	$0.924986\pi$
$558$		0			0
$559$	7416.00			0.561115
$560$		0			0
$561$		0			0
$562$	3242.00	−	5615.31i	0.243337	−	0.421472i
$563$	−12484.0	−	21622.9i	−0.934526	−	1.61865i	−0.775478	−	0.631375i	$-0.782491\pi$
$563$	−12484.0	−	21622.9i	−0.934526	−	1.61865i	−0.159048	−	0.987271i	$-0.550842\pi$
$564$		0			0
$565$	−9646.00	+	16707.4i	−0.718248	+	1.24404i
$566$	3184.00			0.236455
$567$		0			0
$568$	−3136.00			−0.231661
$569$	7125.00	−	12340.9i	0.524948	−	0.909237i	−0.474630	−	0.880186i	$-0.657418\pi$
$569$	7125.00	−	12340.9i	0.524948	−	0.909237i	0.999578	−	0.0290514i	$-0.00924865\pi$
$570$		0			0
$571$	−3186.00	−	5518.31i	−0.233503	−	0.404438i	0.725334	−	0.688397i	$-0.241685\pi$
$571$	−3186.00	−	5518.31i	−0.233503	−	0.404438i	−0.958836	+	0.283959i	$0.908352\pi$
$572$	1008.00	−	1745.91i	0.0736829	−	0.127622i
$573$		0			0
$574$		0			0
$575$	7952.00			0.576733
$576$		0			0
$577$	−4183.00	−	7245.17i	−0.301803	−	0.522739i	0.674741	−	0.738055i	$-0.264255\pi$
$577$	−4183.00	−	7245.17i	−0.301803	−	0.522739i	−0.976545	+	0.215316i	$0.930922\pi$
$578$	−563.000	−	975.145i	−0.0405151	−	0.0701742i
$579$		0			0
$580$	10640.0			0.761728
$581$		0			0
$582$		0			0
$583$	4452.00	−	7711.09i	0.316266	−	0.547789i
$584$	2152.00	+	3727.37i	0.152484	+	0.264109i
$585$		0			0
$586$	5022.00	−	8698.36i	0.354022	−	0.613184i
$587$	20384.0			1.43328			0.716642	−	0.697441i	$-0.245678\pi$
$587$	20384.0			1.43328			0.716642	+	0.697441i	$0.245678\pi$
$588$		0			0
$589$	5760.00			0.402948
$590$	−2800.00	+	4849.74i	−0.195380	+	0.338408i
$591$		0			0
$592$	2768.00	+	4794.32i	0.192169	+	0.332847i
$593$	−4689.00	+	8121.59i	−0.324712	+	0.562417i	−0.981454	−	0.191698i	$-0.938601\pi$
$593$	−4689.00	+	8121.59i	−0.324712	+	0.562417i	0.656742	+	0.754115i	$0.271934\pi$
$594$		0			0
$595$		0			0
$596$	−2040.00			−0.140204
$597$		0			0
$598$	2016.00	+	3491.81i	0.137860	+	0.238781i
$599$	−4500.00	−	7794.23i	−0.306953	−	0.531659i	0.670741	−	0.741692i	$-0.265976\pi$
$599$	−4500.00	−	7794.23i	−0.306953	−	0.531659i	−0.977694	+	0.210033i	$0.932643\pi$
$600$		0			0
$601$	−7562.00			−0.513245			−0.256623	−	0.966512i	$-0.582610\pi$
$601$	−7562.00			−0.513245			−0.256623	+	0.966512i	$0.582610\pi$
$602$		0			0
$603$		0			0
$604$	−1184.00	+	2050.75i	−0.0797620	+	0.138152i
$605$	−3829.00	−	6632.02i	−0.257307	−	0.445670i
$606$		0			0
$607$	−1488.00	+	2577.29i	−0.0994993	+	0.172338i	−0.911478	−	0.411350i	$-0.865057\pi$
$607$	−1488.00	+	2577.29i	−0.0994993	+	0.172338i	0.811978	+	0.583688i	$0.198391\pi$
$608$	−2560.00			−0.170759
$609$		0			0
$610$	−5544.00			−0.367984
$611$	216.000	−	374.123i	0.0143018	−	0.0247715i
$612$		0			0
$613$	−2139.00	−	3704.86i	−0.140935	−	0.244107i	0.786914	−	0.617063i	$-0.211678\pi$
$613$	−2139.00	−	3704.86i	−0.140935	−	0.244107i	−0.927849	+	0.372956i	$0.878344\pi$
$614$	−9536.00	+	16516.8i	−0.626778	+	1.08561i
$615$		0			0
$616$		0			0
$617$	−18794.0			−1.22629			−0.613143	−	0.789972i	$-0.710095\pi$
$617$	−18794.0			−1.22629			−0.613143	+	0.789972i	$0.710095\pi$
$618$		0			0
$619$	9020.00	+	15623.1i	0.585694	+	1.01445i	0.994789	+	0.101959i	$0.0325112\pi$
$619$	9020.00	+	15623.1i	0.585694	+	1.01445i	−0.409095	+	0.912492i	$0.634155\pi$
$620$	−2016.00	−	3491.81i	−0.130588	−	0.226185i
$621$		0			0
$622$	−1936.00			−0.124801
$623$		0			0
$624$		0			0
$625$	9729.50	−	16852.0i	0.622688	−	1.07853i
$626$	3058.00	+	5296.61i	0.195243	+	0.338171i
$627$		0			0
$628$	−5372.00	+	9304.58i	−0.341347	+	0.591231i
$629$	−25604.0			−1.62305
$630$		0			0
$631$	−21688.0			−1.36828			−0.684141	−	0.729350i	$-0.739823\pi$
$631$	−21688.0			−1.36828			−0.684141	+	0.729350i	$0.739823\pi$
$632$	−960.000	+	1662.77i	−0.0604221	+	0.104654i
$633$		0			0
$634$	−4986.00	−	8636.01i	−0.312333	−	0.540977i
$635$	13608.0	−	23569.7i	0.850420	−	1.47297i
$636$		0			0
$637$		0			0
$638$	−10640.0			−0.660253
$639$		0			0
$640$	896.000	+	1551.92i	0.0553399	+	0.0958514i
$641$	−5279.00	−	9143.50i	−0.325285	−	0.563411i	0.656285	−	0.754513i	$-0.272127\pi$
$641$	−5279.00	−	9143.50i	−0.325285	−	0.563411i	−0.981570	+	0.191102i	$0.938794\pi$
$642$		0			0
$643$	26152.0			1.60394			0.801971	−	0.597363i	$-0.203785\pi$
$643$	26152.0			1.60394			0.801971	+	0.597363i	$0.203785\pi$
$644$		0			0
$645$		0			0
$646$	5920.00	−	10253.7i	0.360556	−	0.624502i
$647$	−12792.0	−	22156.4i	−0.777288	−	1.34630i	−0.933499	−	0.358579i	$-0.883261\pi$
$647$	−12792.0	−	22156.4i	−0.777288	−	1.34630i	0.156211	−	0.987724i	$-0.450072\pi$
$648$		0			0
$649$	2800.00	−	4849.74i	0.169352	−	0.293327i
$650$	−2556.00			−0.154238
$651$		0			0
$652$	−4048.00			−0.243147
$653$	7599.00	−	13161.9i	0.455393	−	0.788764i	−0.543317	−	0.839527i	$-0.682832\pi$
$653$	7599.00	−	13161.9i	0.455393	−	0.788764i	0.998711	+	0.0507630i	$0.0161653\pi$
$654$		0			0
$655$	−5936.00	−	10281.5i	−0.354105	−	0.613328i
$656$	−1296.00	+	2244.74i	−0.0771346	+	0.133601i
$657$		0			0
$658$		0			0
$659$	6100.00			0.360580			0.180290	−	0.983613i	$-0.442296\pi$
$659$	6100.00			0.360580			0.180290	+	0.983613i	$0.442296\pi$
$660$		0			0
$661$	−1159.00	−	2007.45i	−0.0681995	−	0.118125i	0.829909	−	0.557898i	$-0.188392\pi$
$661$	−1159.00	−	2007.45i	−0.0681995	−	0.118125i	−0.898109	+	0.439773i	$0.855059\pi$
$662$	−8612.00	−	14916.4i	−0.505612	−	0.875745i
$663$		0			0
$664$	−8576.00			−0.501225
$665$		0			0
$666$		0			0
$667$	10640.0	−	18429.0i	0.617665	−	1.06983i
$668$	−1088.00	−	1884.47i	−0.0630179	−	0.109150i
$669$		0			0
$670$	−10024.0	+	17362.1i	−0.578001	+	1.00113i
$671$	5544.00			0.318962
$672$		0			0
$673$	−10222.0			−0.585482			−0.292741	−	0.956192i	$-0.594567\pi$
$673$	−10222.0			−0.585482			−0.292741	+	0.956192i	$0.594567\pi$
$674$	10206.0	−	17677.3i	0.583265	−	1.01024i
$675$		0			0
$676$	3746.00	+	6488.26i	0.213132	+	0.369155i
$677$	−12717.0	+	22026.5i	−0.721941	+	1.25044i	0.238280	+	0.971197i	$0.423416\pi$
$677$	−12717.0	+	22026.5i	−0.721941	+	1.25044i	−0.960221	+	0.279242i	$0.909917\pi$
$678$		0			0
$679$		0			0
$680$	−8288.00			−0.467397
$681$		0			0
$682$	2016.00	+	3491.81i	0.113192	+	0.196053i
$683$	−4266.00	−	7388.93i	−0.238996	−	0.413952i	0.721431	−	0.692487i	$-0.243485\pi$
$683$	−4266.00	−	7388.93i	−0.238996	−	0.413952i	−0.960426	+	0.278534i	$0.910151\pi$
$684$		0			0
$685$	−41524.0			−2.31613
$686$		0			0
$687$		0			0
$688$	3296.00	−	5708.84i	0.182644	−	0.316348i
$689$	−2862.00	−	4957.13i	−0.158249	−	0.274095i
$690$		0			0
$691$	10336.0	−	17902.5i	0.569030	−	0.985589i	−0.427632	−	0.903953i	$-0.640652\pi$
$691$	10336.0	−	17902.5i	0.569030	−	0.985589i	0.996662	−	0.0816365i	$-0.0260146\pi$
$692$	7432.00			0.408269
$693$		0			0
$694$	−4008.00			−0.219224
$695$	−19600.0	+	33948.2i	−1.06974	+	1.85285i
$696$		0			0
$697$	−5994.00	−	10381.9i	−0.325737	−	0.564194i
$698$	1330.00	−	2303.63i	0.0721221	−	0.124919i
$699$		0			0
$700$		0			0
$701$	21458.0			1.15614			0.578072	−	0.815985i	$-0.303805\pi$
$701$	21458.0			1.15614			0.578072	+	0.815985i	$0.303805\pi$
$702$		0			0
$703$	−13840.0	−	23971.6i	−0.742511	−	1.28607i
$704$	−896.000	−	1551.92i	−0.0479677	−	0.0830825i
$705$		0			0
$706$	1956.00			0.104271
$707$		0			0
$708$		0			0
$709$	4925.00	−	8530.35i	0.260878	−	0.451853i	−0.705598	−	0.708613i	$-0.749321\pi$
$709$	4925.00	−	8530.35i	0.260878	−	0.451853i	0.966475	+	0.256759i	$0.0826547\pi$
$710$	−5488.00	−	9505.49i	−0.290086	−	0.502443i
$711$		0			0
$712$	−3240.00	+	5611.84i	−0.170540	+	0.295383i
$713$	−8064.00			−0.423561
$714$		0			0
$715$	7056.00			0.369062
$716$	−600.000	+	1039.23i	−0.0313171	+	0.0542428i
$717$		0			0
$718$	−9680.00	−	16766.3i	−0.503140	−	0.871464i
$719$	9420.00	−	16315.9i	0.488605	−	0.846288i	−0.511309	−	0.859397i	$-0.670839\pi$
$719$	9420.00	−	16315.9i	0.488605	−	0.846288i	0.999914	+	0.0131086i	$0.00417273\pi$
$720$		0			0
$721$		0			0
$722$	−918.000			−0.0473191
$723$		0			0
$724$	−4716.00	−	8168.35i	−0.242084	−	0.419302i
$725$	6745.00	+	11682.7i	0.345521	+	0.598461i
$726$		0			0
$727$	−37504.0			−1.91327			−0.956634	−	0.291291i	$-0.905915\pi$
$727$	−37504.0			−1.91327			−0.956634	+	0.291291i	$0.905915\pi$
$728$		0			0
$729$		0			0
$730$	−7532.00	+	13045.8i	−0.381879	+	0.661434i
$731$	15244.0	+	26403.4i	0.771299	+	1.33593i
$732$		0			0
$733$	6669.00	−	11551.0i	0.336051	−	0.582057i	−0.647635	−	0.761950i	$-0.724242\pi$
$733$	6669.00	−	11551.0i	0.336051	−	0.582057i	0.983686	+	0.179894i	$0.0575753\pi$
$734$	17312.0			0.870569
$735$		0			0
$736$	3584.00			0.179495
$737$	10024.0	−	17362.1i	0.501002	−	0.867762i
$738$		0			0
$739$	−8550.00	−	14809.0i	−0.425598	−	0.737157i	0.570878	−	0.821035i	$-0.306603\pi$
$739$	−8550.00	−	14809.0i	−0.425598	−	0.737157i	−0.996476	+	0.0838776i	$0.973270\pi$
$740$	−9688.00	+	16780.1i	−0.481268	+	0.833580i
$741$		0			0
$742$		0			0
$743$	19632.0			0.969352			0.484676	−	0.874694i	$-0.338938\pi$
$743$	19632.0			0.969352			0.484676	+	0.874694i	$0.338938\pi$
$744$		0			0
$745$	−3570.00	−	6183.42i	−0.175563	−	0.304085i
$746$	−5278.00	−	9141.76i	−0.259037	−	0.448665i
$747$		0			0
$748$	8288.00			0.405133
$749$		0			0
$750$		0			0
$751$	−16956.0	+	29368.7i	−0.823879	+	1.42700i	0.0788938	+	0.996883i	$0.474861\pi$
$751$	−16956.0	+	29368.7i	−0.823879	+	1.42700i	−0.902773	+	0.430117i	$0.858472\pi$
$752$	−192.000	−	332.554i	−0.00931053	−	0.0161263i
$753$		0			0
$754$	−3420.00	+	5923.61i	−0.165184	+	0.286108i
$755$	−8288.00			−0.399512
$756$		0			0
$757$	−31386.0			−1.50693			−0.753463	−	0.657490i	$-0.771618\pi$
$757$	−31386.0			−1.50693			−0.753463	+	0.657490i	$0.771618\pi$
$758$	−6340.00	+	10981.2i	−0.303798	+	0.526194i
$759$		0			0
$760$	−4480.00	−	7759.59i	−0.213825	−	0.370355i
$761$	17279.0	−	29928.1i	0.823079	−	1.42561i	−0.0802993	−	0.996771i	$-0.525588\pi$
$761$	17279.0	−	29928.1i	0.823079	−	1.42561i	0.903378	−	0.428844i	$-0.141079\pi$
$762$		0			0
$763$		0			0
$764$	−5568.00			−0.263669
$765$		0			0
$766$	6232.00	+	10794.1i	0.293957	+	0.509149i
$767$	−1800.00	−	3117.69i	−0.0847382	−	0.146771i
$768$		0			0
$769$	−39130.0			−1.83493			−0.917467	−	0.397812i	$-0.869769\pi$
$769$	−39130.0			−1.83493			−0.917467	+	0.397812i	$0.869769\pi$
$770$		0			0
$771$		0			0
$772$	−3556.00	+	6159.17i	−0.165781	+	0.287142i
$773$	12991.0	+	22501.1i	0.604468	+	1.04697i	0.992135	+	0.125170i	$0.0399476\pi$
$773$	12991.0	+	22501.1i	0.604468	+	1.04697i	−0.387667	+	0.921799i	$0.626719\pi$
$774$		0			0
$775$	2556.00	−	4427.12i	0.118470	−	0.205196i
$776$	−10832.0			−0.501090
$777$		0			0
$778$	29620.0			1.36495
$779$	6480.00	−	11223.7i	0.298036	−	0.516214i
$780$		0			0
$781$	5488.00	+	9505.49i	0.251442	+	0.435510i
$782$	−8288.00	+	14355.2i	−0.379000	+	0.656448i
$783$		0			0
$784$		0			0
$785$	−37604.0			−1.70974
$786$		0			0
$787$	17712.0	+	30678.1i	0.802242	+	1.38952i	0.918137	+	0.396263i	$0.129693\pi$
$787$	17712.0	+	30678.1i	0.802242	+	1.38952i	−0.115895	+	0.993261i	$0.536974\pi$
$788$	2428.00	+	4205.42i	0.109764	+	0.190117i
$789$		0			0
$790$	−6720.00			−0.302642
$791$		0			0
$792$		0			0
$793$	1782.00	−	3086.51i	0.0797991	−	0.138216i
$794$	5154.00	+	8926.99i	0.230363	+	0.399001i
$795$		0			0
$796$	2080.00	−	3602.67i	0.0926176	−	0.160418i
$797$	−30606.0			−1.36025			−0.680126	−	0.733096i	$-0.738075\pi$
$797$	−30606.0			−1.36025			−0.680126	+	0.733096i	$0.738075\pi$
$798$		0			0
$799$	1776.00			0.0786362
$800$	−1136.00	+	1967.61i	−0.0502046	+	0.0869569i
$801$		0			0
$802$	3282.00	+	5684.59i	0.144503	+	0.250287i
$803$	7532.00	−	13045.8i	0.331007	−	0.573321i
$804$		0			0
$805$		0			0
$806$	2592.00			0.113275
$807$		0			0
$808$	5432.00	+	9408.50i	0.236506	+	0.409641i
$809$	8405.00	+	14557.9i	0.365271	+	0.632668i	0.988820	−	0.149117i	$-0.0476431\pi$
$809$	8405.00	+	14557.9i	0.365271	+	0.632668i	−0.623549	+	0.781784i	$0.714310\pi$
$810$		0			0
$811$	9368.00			0.405616			0.202808	−	0.979218i	$-0.434993\pi$
$811$	9368.00			0.405616			0.202808	+	0.979218i	$0.434993\pi$
$812$		0			0
$813$		0			0
$814$	9688.00	−	16780.1i	0.417155	−	0.722534i
$815$	−7084.00	−	12269.8i	−0.304468	−	0.527355i
$816$		0			0
$817$	−16480.0	+	28544.2i	−0.705707	+	1.22232i
$818$	−11620.0			−0.496679
$819$		0			0
$820$	−9072.00			−0.386351
$821$	17191.0	−	29775.7i	0.730780	−	1.26575i	−0.225771	−	0.974180i	$-0.572490\pi$
$821$	17191.0	−	29775.7i	0.730780	−	1.26575i	0.956550	−	0.291567i	$-0.0941766\pi$
$822$		0			0
$823$	2236.00	+	3872.87i	0.0947048	+	0.164034i	0.909485	−	0.415736i	$-0.136476\pi$
$823$	2236.00	+	3872.87i	0.0947048	+	0.164034i	−0.814781	+	0.579769i	$0.803143\pi$
$824$	−3328.00	+	5764.27i	−0.140699	+	0.243699i
$825$		0			0
$826$		0			0
$827$	1716.00			0.0721538			0.0360769	−	0.999349i	$-0.488514\pi$
$827$	1716.00			0.0721538			0.0360769	+	0.999349i	$0.488514\pi$
$828$		0			0
$829$	−3955.00	−	6850.26i	−0.165697	−	0.286996i	0.771206	−	0.636586i	$-0.219654\pi$
$829$	−3955.00	−	6850.26i	−0.165697	−	0.286996i	−0.936903	+	0.349591i	$0.886321\pi$
$830$	−15008.0	−	25994.6i	−0.627633	−	1.08709i
$831$		0			0
$832$	−1152.00			−0.0480029
$833$		0			0
$834$		0			0
$835$	3808.00	−	6595.65i	0.157822	−	0.273356i
$836$	4480.00	+	7759.59i	0.185340	+	0.321018i
$837$		0			0
$838$	−13560.0	+	23486.6i	−0.558977	+	0.968176i
$839$	−19360.0			−0.796641			−0.398320	−	0.917246i	$-0.630407\pi$
$839$	−19360.0			−0.796641			−0.398320	+	0.917246i	$0.630407\pi$
$840$		0			0
$841$	11711.0			0.480175
$842$	738.000	−	1278.25i	0.0302057	−	0.0523177i
$843$		0			0
$844$	7736.00	+	13399.1i	0.315502	+	0.546466i
$845$	−13111.0	+	22708.9i	−0.533766	+	0.924510i
$846$		0			0
$847$		0			0
$848$	−5088.00			−0.206041
$849$		0			0
$850$	−5254.00	−	9100.19i	−0.212013	−	0.367217i
$851$	19376.0	+	33560.2i	0.780494	+	1.35186i
$852$		0			0
$853$	−698.000			−0.0280177			−0.0140088	−	0.999902i	$-0.504459\pi$
$853$	−698.000			−0.0280177			−0.0140088	+	0.999902i	$0.504459\pi$
$854$		0			0
$855$		0			0
$856$	1776.00	−	3076.12i	0.0709141	−	0.122827i
$857$	11703.0	+	20270.2i	0.466472	+	0.807954i	0.999267	−	0.0382909i	$-0.0121914\pi$
$857$	11703.0	+	20270.2i	0.466472	+	0.807954i	−0.532794	+	0.846245i	$0.678858\pi$
$858$		0			0
$859$	3640.00	−	6304.66i	0.144581	−	0.250422i	−0.784635	−	0.619957i	$-0.787150\pi$
$859$	3640.00	−	6304.66i	0.144581	−	0.250422i	0.929217	+	0.369536i	$0.120483\pi$
$860$	23072.0			0.914824
$861$		0			0
$862$	−2544.00			−0.100521
$863$	4904.00	−	8493.98i	0.193435	−	0.335039i	−0.752952	−	0.658076i	$-0.771371\pi$
$863$	4904.00	−	8493.98i	0.193435	−	0.335039i	0.946386	+	0.323037i	$0.104704\pi$
$864$		0			0
$865$	13006.0	+	22527.1i	0.511234	+	0.885483i
$866$	−5062.00	+	8767.64i	−0.198630	+	0.344038i
$867$		0			0
$868$		0			0
$869$	6720.00			0.262325
$870$		0			0
$871$	−6444.00	−	11161.3i	−0.250685	−	0.434199i
$872$	−7480.00	−	12955.7i	−0.290487	−	0.503138i
$873$		0			0
$874$	−17920.0			−0.693539
$875$		0			0
$876$		0			0
$877$	4033.00	−	6985.36i	0.155285	−	0.268961i	−0.777878	−	0.628415i	$-0.783704\pi$
$877$	4033.00	−	6985.36i	0.155285	−	0.268961i	0.933163	+	0.359454i	$0.117037\pi$
$878$	5640.00	+	9768.77i	0.216789	+	0.375490i
$879$		0			0
$880$	3136.00	−	5431.71i	0.120130	−	0.208072i
$881$	25842.0			0.988240			0.494120	−	0.869394i	$-0.335490\pi$
$881$	25842.0			0.988240			0.494120	+	0.869394i	$0.335490\pi$
$882$		0			0
$883$	−5692.00			−0.216932			−0.108466	−	0.994100i	$-0.534594\pi$
$883$	−5692.00			−0.216932			−0.108466	+	0.994100i	$0.534594\pi$
$884$	2664.00	−	4614.18i	0.101357	−	0.175556i
$885$		0			0
$886$	13388.0	+	23188.7i	0.507651	+	0.879277i
$887$	6768.00	−	11722.5i	0.256198	−	0.443747i	−0.709023	−	0.705186i	$-0.750864\pi$
$887$	6768.00	−	11722.5i	0.256198	−	0.443747i	0.965220	+	0.261439i	$0.0841969\pi$
$888$		0			0
$889$		0			0
$890$	−22680.0			−0.854197
$891$		0			0
$892$	7936.00	+	13745.6i	0.297889	+	0.515959i
$893$	960.000	+	1662.77i	0.0359744	+	0.0623096i
$894$		0			0
$895$	−4200.00			−0.156861
$896$		0			0
$897$		0			0
$898$	−3230.00	+	5594.52i	−0.120030	+	0.207897i
$899$	−6840.00	−	11847.2i	−0.253756	−	0.439519i
$900$		0			0
$901$	11766.0	−	20379.3i	0.435052	−	0.753533i
$902$	9072.00			0.334883
$903$		0			0
$904$	−11024.0			−0.405589
$905$	16506.0	−	28589.2i	0.606274	−	1.05010i
$906$		0			0
$907$	−8502.00	−	14725.9i	−0.311251	−	0.539102i	0.667383	−	0.744715i	$-0.267415\pi$
$907$	−8502.00	−	14725.9i	−0.311251	−	0.539102i	−0.978633	+	0.205613i	$0.934081\pi$
$908$	7872.00	−	13634.7i	0.287711	−	0.498330i
$909$		0			0
$910$		0			0
$911$	14568.0			0.529813			0.264906	−	0.964274i	$-0.414659\pi$
$911$	14568.0			0.529813			0.264906	+	0.964274i	$0.414659\pi$
$912$		0			0
$913$	15008.0	+	25994.6i	0.544022	+	0.942274i
$914$	10646.0	+	18439.4i	0.385272	+	0.667310i
$915$		0			0
$916$	−19240.0			−0.694004
$917$		0			0
$918$		0			0
$919$	700.000	−	1212.44i	0.0251261	−	0.0435197i	−0.853189	−	0.521602i	$-0.825335\pi$
$919$	700.000	−	1212.44i	0.0251261	−	0.0435197i	0.878315	+	0.478082i	$0.158668\pi$
$920$	6272.00	+	10863.4i	0.224763	+	0.389300i
$921$		0			0
$922$	−7282.00	+	12612.8i	−0.260108	+	0.450521i
$923$	7056.00			0.251626
$924$		0			0
$925$	−24566.0			−0.873216
$926$	−12688.0	+	21976.3i	−0.450274	+	0.779897i
$927$		0			0
$928$	3040.00	+	5265.43i	0.107535	+	0.186257i
$929$	6915.00	−	11977.1i	0.244213	−	0.422989i	−0.717697	−	0.696355i	$-0.754804\pi$
$929$	6915.00	−	11977.1i	0.244213	−	0.422989i	0.961910	+	0.273366i	$0.0881371\pi$
$930$		0			0
$931$		0			0
$932$	8728.00			0.306754
$933$		0			0
$934$	2816.00	+	4877.46i	0.0986535	+	0.170873i
$935$	14504.0	+	25121.7i	0.507306	+	0.878681i
$936$		0			0
$937$	24166.0			0.842549			0.421275	−	0.906933i	$-0.361583\pi$
$937$	24166.0			0.842549			0.421275	+	0.906933i	$0.361583\pi$
$938$		0			0
$939$		0			0
$940$	672.000	−	1163.94i	0.0233173	−	0.0403867i
$941$	5419.00	+	9385.98i	0.187730	+	0.325159i	0.944493	−	0.328531i	$-0.106554\pi$
$941$	5419.00	+	9385.98i	0.187730	+	0.325159i	−0.756763	+	0.653690i	$0.773220\pi$
$942$		0			0
$943$	−9072.00	+	15713.2i	−0.313282	+	0.542620i
$944$	−3200.00			−0.110330
$945$		0			0
$946$	−23072.0			−0.792955
$947$	−20458.0	+	35434.3i	−0.702002	+	1.21590i	0.265761	+	0.964039i	$0.414377\pi$
$947$	−20458.0	+	35434.3i	−0.702002	+	1.21590i	−0.967763	+	0.251864i	$0.918957\pi$
$948$		0			0
$949$	−4842.00	−	8386.59i	−0.165625	−	0.286871i
$950$	5680.00	−	9838.05i	0.193983	−	0.335988i
$951$		0			0
$952$		0			0
$953$	−56618.0			−1.92449			−0.962244	−	0.272189i	$-0.912253\pi$
$953$	−56618.0			−1.92449			−0.962244	+	0.272189i	$0.912253\pi$
$954$		0			0
$955$	−9744.00	−	16877.1i	−0.330166	−	0.571864i
$956$	−6000.00	−	10392.3i	−0.202985	−	0.351581i
$957$		0			0
$958$	−6320.00			−0.213142
$959$		0			0
$960$		0			0
$961$	12303.5	−	21310.3i	0.412994	−	0.715326i
$962$	−6228.00	−	10787.2i	−0.208731	−	0.361532i
$963$		0			0
$964$	4084.00	−	7073.70i	0.136449	−	0.236337i
$965$	−24892.0			−0.830365
$966$		0			0
$967$	17504.0			0.582100			0.291050	−	0.956708i	$-0.405995\pi$
$967$	17504.0			0.582100			0.291050	+	0.956708i	$0.405995\pi$
$968$	2188.00	−	3789.73i	0.0726498	−	0.125833i
$969$		0			0
$970$	−18956.0	−	32832.8i	−0.627464	−	1.08680i
$971$	−11556.0	+	20015.6i	−0.381926	+	0.661514i	−0.991337	−	0.131339i	$-0.958072\pi$
$971$	−11556.0	+	20015.6i	−0.381926	+	0.661514i	0.609412	+	0.792854i	$0.291406\pi$
$972$		0			0
$973$		0			0
$974$	−28352.0			−0.932707
$975$		0			0
$976$	−1584.00	−	2743.57i	−0.0519494	−	0.0899790i
$977$	11937.0	+	20675.5i	0.390889	+	0.677039i	0.992567	−	0.121699i	$-0.0388343\pi$
$977$	11937.0	+	20675.5i	0.390889	+	0.677039i	−0.601678	+	0.798739i	$0.705501\pi$
$978$		0			0
$979$	22680.0			0.740404
$980$		0			0
$981$		0			0
$982$	−11268.0	+	19516.7i	−0.366167	+	0.634220i
$983$	7656.00	+	13260.6i	0.248411	+	0.430261i	0.963085	−	0.269197i	$-0.0867582\pi$
$983$	7656.00	+	13260.6i	0.248411	+	0.430261i	−0.714674	+	0.699458i	$0.753425\pi$
$984$		0			0
$985$	−8498.00	+	14719.0i	−0.274892	+	0.476127i
$986$	−28120.0			−0.908239
$987$		0			0
$988$	5760.00			0.185476
$989$	23072.0	−	39961.9i	0.741807	−	1.28485i
$990$		0			0
$991$	8264.00	+	14313.7i	0.264899	+	0.458818i	0.967537	−	0.252729i	$-0.0813281\pi$
$991$	8264.00	+	14313.7i	0.264899	+	0.458818i	−0.702638	+	0.711547i	$0.747995\pi$
$992$	1152.00	−	1995.32i	0.0368710	−	0.0638625i
$993$		0			0
$994$		0			0
$995$	14560.0			0.463903
$996$		0			0
$997$	−14303.0	−	24773.5i	−0.454344	−	0.786946i	0.544307	−	0.838886i	$-0.316793\pi$
$997$	−14303.0	−	24773.5i	−0.454344	−	0.786946i	−0.998650	+	0.0519402i	$0.983459\pi$
$998$	4460.00	+	7724.95i	0.141462	+	0.245019i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.k.667.1		2
3.2	odd	2		98.4.c.f.79.1		2
7.2	even	3		882.4.a.i.1.1		1
7.3	odd	6		882.4.g.b.361.1		2
7.4	even	3	inner	882.4.g.k.361.1		2
7.5	odd	6		126.4.a.h.1.1		1
7.6	odd	2		882.4.g.b.667.1		2
21.2	odd	6		98.4.a.a.1.1		1
21.5	even	6		14.4.a.a.1.1	✓	1
21.11	odd	6		98.4.c.f.67.1		2
21.17	even	6		98.4.c.d.67.1		2
21.20	even	2		98.4.c.d.79.1		2
28.19	even	6		1008.4.a.s.1.1		1
84.23	even	6		784.4.a.s.1.1		1
84.47	odd	6		112.4.a.a.1.1		1
105.44	odd	6		2450.4.a.bo.1.1		1
105.47	odd	12		350.4.c.b.99.1		2
105.68	odd	12		350.4.c.b.99.2		2
105.89	even	6		350.4.a.l.1.1		1
168.5	even	6		448.4.a.b.1.1		1
168.131	odd	6		448.4.a.o.1.1		1
231.131	odd	6		1694.4.a.g.1.1		1
273.194	even	6		2366.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.a.a.1.1	✓	1	21.5	even	6
98.4.a.a.1.1		1	21.2	odd	6
98.4.c.d.67.1		2	21.17	even	6
98.4.c.d.79.1		2	21.20	even	2
98.4.c.f.67.1		2	21.11	odd	6
98.4.c.f.79.1		2	3.2	odd	2
112.4.a.a.1.1		1	84.47	odd	6
126.4.a.h.1.1		1	7.5	odd	6
350.4.a.l.1.1		1	105.89	even	6
350.4.c.b.99.1		2	105.47	odd	12
350.4.c.b.99.2		2	105.68	odd	12
448.4.a.b.1.1		1	168.5	even	6
448.4.a.o.1.1		1	168.131	odd	6
784.4.a.s.1.1		1	84.23	even	6
882.4.a.i.1.1		1	7.2	even	3
882.4.g.b.361.1		2	7.3	odd	6
882.4.g.b.667.1		2	7.6	odd	2
882.4.g.k.361.1		2	7.4	even	3	inner
882.4.g.k.667.1		2	1.1	even	1	trivial
1008.4.a.s.1.1		1	28.19	even	6
1694.4.a.g.1.1		1	231.131	odd	6
2366.4.a.h.1.1		1	273.194	even	6
2450.4.a.bo.1.1		1	105.44	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} +8.00000 q^{8} +(14.0000 + 24.2487i) q^{10} +(-14.0000 - 24.2487i) q^{11} -18.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-37.0000 - 64.0859i) q^{17} +(40.0000 - 69.2820i) q^{19} -56.0000 q^{20} +56.0000 q^{22} +(-56.0000 + 96.9948i) q^{23} +(-35.5000 - 61.4878i) q^{25} +(18.0000 - 31.1769i) q^{26} -190.000 q^{29} +(36.0000 + 62.3538i) q^{31} +(-16.0000 - 27.7128i) q^{32} +148.000 q^{34} +(173.000 - 299.645i) q^{37} +(80.0000 + 138.564i) q^{38} +(56.0000 - 96.9948i) q^{40} +162.000 q^{41} -412.000 q^{43} +(-56.0000 + 96.9948i) q^{44} +(-112.000 - 193.990i) q^{46} +(-12.0000 + 20.7846i) q^{47} +142.000 q^{50} +(36.0000 + 62.3538i) q^{52} +(159.000 + 275.396i) q^{53} -392.000 q^{55} +(190.000 - 329.090i) q^{58} +(100.000 + 173.205i) q^{59} +(-99.0000 + 171.473i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(-126.000 + 218.238i) q^{65} +(358.000 + 620.074i) q^{67} +(-148.000 + 256.344i) q^{68} -392.000 q^{71} +(269.000 + 465.922i) q^{73} +(346.000 + 599.290i) q^{74} -320.000 q^{76} +(-120.000 + 207.846i) q^{79} +(112.000 + 193.990i) q^{80} +(-162.000 + 280.592i) q^{82} -1072.00 q^{83} -1036.00 q^{85} +(412.000 - 713.605i) q^{86} +(-112.000 - 193.990i) q^{88} +(-405.000 + 701.481i) q^{89} +448.000 q^{92} +(-24.0000 - 41.5692i) q^{94} +(-560.000 - 969.948i) q^{95} -1354.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} + 14 q^{5} + 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 + 14 * q^5 + 16 * q^8	\( 2 q - 2 q^{2} - 4 q^{4} + 14 q^{5} + 16 q^{8} + 28 q^{10} - 28 q^{11} - 36 q^{13} - 16 q^{16} - 74 q^{17} + 80 q^{19} - 112 q^{20} + 112 q^{22} - 112 q^{23} - 71 q^{25} + 36 q^{26} - 380 q^{29} + 72 q^{31} - 32 q^{32} + 296 q^{34} + 346 q^{37} + 160 q^{38} + 112 q^{40} + 324 q^{41} - 824 q^{43} - 112 q^{44} - 224 q^{46} - 24 q^{47} + 284 q^{50} + 72 q^{52} + 318 q^{53} - 784 q^{55} + 380 q^{58} + 200 q^{59} - 198 q^{61} - 288 q^{62} + 128 q^{64} - 252 q^{65} + 716 q^{67} - 296 q^{68} - 784 q^{71} + 538 q^{73} + 692 q^{74} - 640 q^{76} - 240 q^{79} + 224 q^{80} - 324 q^{82} - 2144 q^{83} - 2072 q^{85} + 824 q^{86} - 224 q^{88} - 810 q^{89} + 896 q^{92} - 48 q^{94} - 1120 q^{95} - 2708 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 14 * q^5 + 16 * q^8 + 28 * q^10 - 28 * q^11 - 36 * q^13 - 16 * q^16 - 74 * q^17 + 80 * q^19 - 112 * q^20 + 112 * q^22 - 112 * q^23 - 71 * q^25 + 36 * q^26 - 380 * q^29 + 72 * q^31 - 32 * q^32 + 296 * q^34 + 346 * q^37 + 160 * q^38 + 112 * q^40 + 324 * q^41 - 824 * q^43 - 112 * q^44 - 224 * q^46 - 24 * q^47 + 284 * q^50 + 72 * q^52 + 318 * q^53 - 784 * q^55 + 380 * q^58 + 200 * q^59 - 198 * q^61 - 288 * q^62 + 128 * q^64 - 252 * q^65 + 716 * q^67 - 296 * q^68 - 784 * q^71 + 538 * q^73 + 692 * q^74 - 640 * q^76 - 240 * q^79 + 224 * q^80 - 324 * q^82 - 2144 * q^83 - 2072 * q^85 + 824 * q^86 - 224 * q^88 - 810 * q^89 + 896 * q^92 - 48 * q^94 - 1120 * q^95 - 2708 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more