LMFDB - Embedded newform 882.4.g.i.361.1

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 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.i.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} +8.00000 q^{8} +(6.00000 - 10.3923i) q^{10} +(6.00000 - 10.3923i) q^{11} +38.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-63.0000 + 109.119i) q^{17} +(-10.0000 - 17.3205i) q^{19} -24.0000 q^{20} -24.0000 q^{22} +(84.0000 + 145.492i) q^{23} +(44.5000 - 77.0763i) q^{25} +(-38.0000 - 65.8179i) q^{26} -30.0000 q^{29} +(44.0000 - 76.2102i) q^{31} +(-16.0000 + 27.7128i) q^{32} +252.000 q^{34} +(-127.000 - 219.970i) q^{37} +(-20.0000 + 34.6410i) q^{38} +(24.0000 + 41.5692i) q^{40} -42.0000 q^{41} -52.0000 q^{43} +(24.0000 + 41.5692i) q^{44} +(168.000 - 290.985i) q^{46} +(-48.0000 - 83.1384i) q^{47} -178.000 q^{50} +(-76.0000 + 131.636i) q^{52} +(99.0000 - 171.473i) q^{53} +72.0000 q^{55} +(30.0000 + 51.9615i) q^{58} +(-330.000 + 571.577i) q^{59} +(269.000 + 465.922i) q^{61} -176.000 q^{62} +64.0000 q^{64} +(114.000 + 197.454i) q^{65} +(-442.000 + 765.566i) q^{67} +(-252.000 - 436.477i) q^{68} -792.000 q^{71} +(-109.000 + 188.794i) q^{73} +(-254.000 + 439.941i) q^{74} +80.0000 q^{76} +(260.000 + 450.333i) q^{79} +(48.0000 - 83.1384i) q^{80} +(42.0000 + 72.7461i) q^{82} +492.000 q^{83} -756.000 q^{85} +(52.0000 + 90.0666i) q^{86} +(48.0000 - 83.1384i) q^{88} +(405.000 + 701.481i) q^{89} -672.000 q^{92} +(-96.0000 + 166.277i) q^{94} +(60.0000 - 103.923i) q^{95} +1154.00 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} + 6 q^{5} + 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^5 + 16 * q^8	$ 2 q - 2 q^{2} - 4 q^{4} + 6 q^{5} + 16 q^{8} + 12 q^{10} + 12 q^{11} + 76 q^{13} - 16 q^{16} - 126 q^{17} - 20 q^{19} - 48 q^{20} - 48 q^{22} + 168 q^{23} + 89 q^{25} - 76 q^{26} - 60 q^{29} + 88 q^{31} - 32 q^{32} + 504 q^{34} - 254 q^{37} - 40 q^{38} + 48 q^{40} - 84 q^{41} - 104 q^{43} + 48 q^{44} + 336 q^{46} - 96 q^{47} - 356 q^{50} - 152 q^{52} + 198 q^{53} + 144 q^{55} + 60 q^{58} - 660 q^{59} + 538 q^{61} - 352 q^{62} + 128 q^{64} + 228 q^{65} - 884 q^{67} - 504 q^{68} - 1584 q^{71} - 218 q^{73} - 508 q^{74} + 160 q^{76} + 520 q^{79} + 96 q^{80} + 84 q^{82} + 984 q^{83} - 1512 q^{85} + 104 q^{86} + 96 q^{88} + 810 q^{89} - 1344 q^{92} - 192 q^{94} + 120 q^{95} + 2308 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^5 + 16 * q^8 + 12 * q^10 + 12 * q^11 + 76 * q^13 - 16 * q^16 - 126 * q^17 - 20 * q^19 - 48 * q^20 - 48 * q^22 + 168 * q^23 + 89 * q^25 - 76 * q^26 - 60 * q^29 + 88 * q^31 - 32 * q^32 + 504 * q^34 - 254 * q^37 - 40 * q^38 + 48 * q^40 - 84 * q^41 - 104 * q^43 + 48 * q^44 + 336 * q^46 - 96 * q^47 - 356 * q^50 - 152 * q^52 + 198 * q^53 + 144 * q^55 + 60 * q^58 - 660 * q^59 + 538 * q^61 - 352 * q^62 + 128 * q^64 + 228 * q^65 - 884 * q^67 - 504 * q^68 - 1584 * q^71 - 218 * q^73 - 508 * q^74 + 160 * q^76 + 520 * q^79 + 96 * q^80 + 84 * q^82 + 984 * q^83 - 1512 * q^85 + 104 * q^86 + 96 * q^88 + 810 * q^89 - 1344 * q^92 - 192 * q^94 + 120 * q^95 + 2308 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−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
$5$	3.00000	+	5.19615i	0.268328	+	0.464758i	0.968430	−	0.249285i	$-0.0801955\pi$
$5$	3.00000	+	5.19615i	0.268328	+	0.464758i	−0.700102	+	0.714043i	$0.746862\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$		0			0
$10$	6.00000	−	10.3923i	0.189737	−	0.328634i
$11$	6.00000	−	10.3923i	0.164461	−	0.284854i	−0.772003	−	0.635619i	$-0.780745\pi$
$11$	6.00000	−	10.3923i	0.164461	−	0.284854i	0.936464	+	0.350765i	$0.114078\pi$
$12$		0			0
$13$	38.0000			0.810716			0.405358	−	0.914158i	$-0.367147\pi$
$13$	38.0000			0.810716			0.405358	+	0.914158i	$0.367147\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.0697893	+	0.997562i	$0.522233\pi$
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.829019	+	0.559220i	$0.811101\pi$
$18$		0			0
$19$	−10.0000	−	17.3205i	−0.120745	−	0.209137i	0.799317	−	0.600910i	$-0.205195\pi$
$19$	−10.0000	−	17.3205i	−0.120745	−	0.209137i	−0.920062	+	0.391773i	$0.871862\pi$
$20$	−24.0000			−0.268328
$21$		0			0
$22$	−24.0000			−0.232583
$23$	84.0000	+	145.492i	0.761531	+	1.31901i	0.942061	+	0.335441i	$0.108885\pi$
$23$	84.0000	+	145.492i	0.761531	+	1.31901i	−0.180530	+	0.983569i	$0.557781\pi$
$24$		0			0
$25$	44.5000	−	77.0763i	0.356000	−	0.616610i
$26$	−38.0000	−	65.8179i	−0.286631	−	0.496460i
$27$		0			0
$28$		0			0
$29$	−30.0000			−0.192099			−0.0960493	−	0.995377i	$-0.530621\pi$
$29$	−30.0000			−0.192099			−0.0960493	+	0.995377i	$0.530621\pi$
$30$		0			0
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	−0.709951	−	0.704251i	$-0.751283\pi$
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	0.964875	+	0.262710i	$0.0846163\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	252.000			1.27111
$35$		0			0
$36$		0			0
$37$	−127.000	−	219.970i	−0.564288	−	0.977376i	−0.997115	−	0.0758992i	$-0.975817\pi$
$37$	−127.000	−	219.970i	−0.564288	−	0.977376i	0.432827	−	0.901477i	$-0.357516\pi$
$38$	−20.0000	+	34.6410i	−0.0853797	+	0.147882i
$39$		0			0
$40$	24.0000	+	41.5692i	0.0948683	+	0.164317i
$41$	−42.0000			−0.159983			−0.0799914	−	0.996796i	$-0.525489\pi$
$41$	−42.0000			−0.159983			−0.0799914	+	0.996796i	$0.525489\pi$
$42$		0			0
$43$	−52.0000			−0.184417			−0.0922084	−	0.995740i	$-0.529393\pi$
$43$	−52.0000			−0.184417			−0.0922084	+	0.995740i	$0.529393\pi$
$44$	24.0000	+	41.5692i	0.0822304	+	0.142427i
$45$		0			0
$46$	168.000	−	290.985i	0.538484	−	0.932681i
$47$	−48.0000	−	83.1384i	−0.148969	−	0.258021i	0.781878	−	0.623431i	$-0.214262\pi$
$47$	−48.0000	−	83.1384i	−0.148969	−	0.258021i	−0.930846	+	0.365410i	$0.880929\pi$
$48$		0			0
$49$		0			0
$50$	−178.000			−0.503460
$51$		0			0
$52$	−76.0000	+	131.636i	−0.202679	+	0.351050i
$53$	99.0000	−	171.473i	0.256579	−	0.444408i	−0.708744	−	0.705466i	$-0.750738\pi$
$53$	99.0000	−	171.473i	0.256579	−	0.444408i	0.965323	+	0.261058i	$0.0840712\pi$
$54$		0			0
$55$	72.0000			0.176518
$56$		0			0
$57$		0			0
$58$	30.0000	+	51.9615i	0.0679171	+	0.117636i
$59$	−330.000	+	571.577i	−0.728175	+	1.26124i	0.229478	+	0.973314i	$0.426298\pi$
$59$	−330.000	+	571.577i	−0.728175	+	1.26124i	−0.957654	+	0.287923i	$0.907035\pi$
$60$		0			0
$61$	269.000	+	465.922i	0.564622	+	0.977953i	0.997085	+	0.0763018i	$0.0243112\pi$
$61$	269.000	+	465.922i	0.564622	+	0.977953i	−0.432463	+	0.901652i	$0.642355\pi$
$62$	−176.000			−0.360516
$63$		0			0
$64$	64.0000			0.125000
$65$	114.000	+	197.454i	0.217538	+	0.376787i
$66$		0			0
$67$	−442.000	+	765.566i	−0.805954	+	1.39595i	0.109692	+	0.993966i	$0.465014\pi$
$67$	−442.000	+	765.566i	−0.805954	+	1.39595i	−0.915645	+	0.401987i	$0.868320\pi$
$68$	−252.000	−	436.477i	−0.449404	−	0.778391i
$69$		0			0
$70$		0			0
$71$	−792.000			−1.32385			−0.661923	−	0.749572i	$-0.730260\pi$
$71$	−792.000			−1.32385			−0.661923	+	0.749572i	$0.730260\pi$
$72$		0			0
$73$	−109.000	+	188.794i	−0.174760	+	0.302693i	−0.940078	−	0.340959i	$-0.889248\pi$
$73$	−109.000	+	188.794i	−0.174760	+	0.302693i	0.765318	+	0.643652i	$0.222582\pi$
$74$	−254.000	+	439.941i	−0.399012	+	0.691109i
$75$		0			0
$76$	80.0000			0.120745
$77$		0			0
$78$		0			0
$79$	260.000	+	450.333i	0.370282	+	0.641347i	0.989609	−	0.143786i	$-0.0459277\pi$
$79$	260.000	+	450.333i	0.370282	+	0.641347i	−0.619327	+	0.785133i	$0.712594\pi$
$80$	48.0000	−	83.1384i	0.0670820	−	0.116190i
$81$		0			0
$82$	42.0000	+	72.7461i	0.0565625	+	0.0979691i
$83$	492.000			0.650651			0.325325	−	0.945602i	$-0.394526\pi$
$83$	492.000			0.650651			0.325325	+	0.945602i	$0.394526\pi$
$84$		0			0
$85$	−756.000			−0.964703
$86$	52.0000	+	90.0666i	0.0652012	+	0.112932i
$87$		0			0
$88$	48.0000	−	83.1384i	0.0581456	−	0.100711i
$89$	405.000	+	701.481i	0.482359	+	0.835470i	0.999795	−	0.0202521i	$-0.00644690\pi$
$89$	405.000	+	701.481i	0.482359	+	0.835470i	−0.517436	+	0.855722i	$0.673114\pi$
$90$		0			0
$91$		0			0
$92$	−672.000			−0.761531
$93$		0			0
$94$	−96.0000	+	166.277i	−0.105337	+	0.182448i
$95$	60.0000	−	103.923i	0.0647986	−	0.112235i
$96$		0			0
$97$	1154.00			1.20795			0.603974	−	0.797004i	$-0.293583\pi$
$97$	1154.00			1.20795			0.603974	+	0.797004i	$0.293583\pi$
$98$		0			0
$99$		0			0
$100$	178.000	+	308.305i	0.178000	+	0.308305i
$101$	−309.000	+	535.204i	−0.304422	+	0.527275i	−0.977133	−	0.212631i	$-0.931797\pi$
$101$	−309.000	+	535.204i	−0.304422	+	0.527275i	0.672710	+	0.739906i	$0.265130\pi$
$102$		0			0
$103$	−64.0000	−	110.851i	−0.0612243	−	0.106044i	0.833789	−	0.552084i	$-0.186167\pi$
$103$	−64.0000	−	110.851i	−0.0612243	−	0.106044i	−0.895013	+	0.446040i	$0.852834\pi$
$104$	304.000			0.286631
$105$		0			0
$106$	−396.000			−0.362858
$107$	−738.000	−	1278.25i	−0.666777	−	1.15489i	−0.978800	−	0.204817i	$-0.934340\pi$
$107$	−738.000	−	1278.25i	−0.666777	−	1.15489i	0.312023	−	0.950075i	$-0.398993\pi$
$108$		0			0
$109$	−595.000	+	1030.57i	−0.522850	+	0.905603i	0.476796	+	0.879014i	$0.341798\pi$
$109$	−595.000	+	1030.57i	−0.522850	+	0.905603i	−0.999646	+	0.0265892i	$0.991535\pi$
$110$	−72.0000	−	124.708i	−0.0624085	−	0.108095i
$111$		0			0
$112$		0			0
$113$	462.000			0.384613			0.192307	−	0.981335i	$-0.438403\pi$
$113$	462.000			0.384613			0.192307	+	0.981335i	$0.438403\pi$
$114$		0			0
$115$	−504.000	+	872.954i	−0.408680	+	0.707855i
$116$	60.0000	−	103.923i	0.0480247	−	0.0831811i
$117$		0			0
$118$	1320.00			1.02980
$119$		0			0
$120$		0			0
$121$	593.500	+	1027.97i	0.445905	+	0.772331i
$122$	538.000	−	931.843i	0.399248	−	0.691517i
$123$		0			0
$124$	176.000	+	304.841i	0.127462	+	0.220770i
$125$	1284.00			0.918756
$126$		0			0
$127$	−2536.00			−1.77192			−0.885959	−	0.463763i	$-0.846499\pi$
$127$	−2536.00			−1.77192			−0.885959	+	0.463763i	$0.846499\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	228.000	−	394.908i	0.153822	−	0.266428i
$131$	1146.00	+	1984.93i	0.764324	+	1.32385i	0.940603	+	0.339508i	$0.110261\pi$
$131$	1146.00	+	1984.93i	0.764324	+	1.32385i	−0.176279	+	0.984340i	$0.556406\pi$
$132$		0			0
$133$		0			0
$134$	1768.00			1.13979
$135$		0			0
$136$	−504.000	+	872.954i	−0.317777	+	0.550406i
$137$	−363.000	+	628.734i	−0.226374	+	0.392091i	−0.956731	−	0.290975i	$-0.906020\pi$
$137$	−363.000	+	628.734i	−0.226374	+	0.392091i	0.730357	+	0.683066i	$0.239354\pi$
$138$		0			0
$139$	380.000			0.231879			0.115939	−	0.993256i	$-0.463012\pi$
$139$	380.000			0.231879			0.115939	+	0.993256i	$0.463012\pi$
$140$		0			0
$141$		0			0
$142$	792.000	+	1371.78i	0.468050	+	0.810687i
$143$	228.000	−	394.908i	0.133331	−	0.230936i
$144$		0			0
$145$	−90.0000	−	155.885i	−0.0515455	−	0.0892794i
$146$	436.000			0.247148
$147$		0			0
$148$	1016.00			0.564288
$149$	795.000	+	1376.98i	0.437107	+	0.757091i	0.997465	−	0.0711590i	$-0.0226698\pi$
$149$	795.000	+	1376.98i	0.437107	+	0.757091i	−0.560358	+	0.828251i	$0.689336\pi$
$150$		0			0
$151$	−1216.00	+	2106.17i	−0.655342	+	1.13509i	0.326466	+	0.945209i	$0.394142\pi$
$151$	−1216.00	+	2106.17i	−0.655342	+	1.13509i	−0.981808	+	0.189877i	$0.939191\pi$
$152$	−80.0000	−	138.564i	−0.0426898	−	0.0739410i
$153$		0			0
$154$		0			0
$155$	528.000			0.273613
$156$		0			0
$157$	−307.000	+	531.740i	−0.156059	+	0.270302i	−0.933444	−	0.358723i	$-0.883212\pi$
$157$	−307.000	+	531.740i	−0.156059	+	0.270302i	0.777385	+	0.629025i	$0.216546\pi$
$158$	520.000	−	900.666i	0.261829	−	0.453501i
$159$		0			0
$160$	−192.000			−0.0948683
$161$		0			0
$162$		0			0
$163$	926.000	+	1603.88i	0.444969	+	0.770709i	0.998050	−	0.0624187i	$-0.0198814\pi$
$163$	926.000	+	1603.88i	0.444969	+	0.770709i	−0.553081	+	0.833127i	$0.686548\pi$
$164$	84.0000	−	145.492i	0.0399957	−	0.0692746i
$165$		0			0
$166$	−492.000	−	852.169i	−0.230040	−	0.398441i
$167$	2136.00			0.989752			0.494876	−	0.868964i	$-0.335213\pi$
$167$	2136.00			0.989752			0.494876	+	0.868964i	$0.335213\pi$
$168$		0			0
$169$	−753.000			−0.342740
$170$	756.000	+	1309.43i	0.341074	+	0.590757i
$171$		0			0
$172$	104.000	−	180.133i	0.0461042	−	0.0798548i
$173$	879.000	+	1522.47i	0.386296	+	0.669084i	0.991948	−	0.126646i	$-0.0404211\pi$
$173$	879.000	+	1522.47i	0.386296	+	0.669084i	−0.605652	+	0.795729i	$0.707088\pi$
$174$		0			0
$175$		0			0
$176$	−192.000			−0.0822304
$177$		0			0
$178$	810.000	−	1402.96i	0.341079	−	0.590766i
$179$	−270.000	+	467.654i	−0.112742	+	0.195274i	−0.916875	−	0.399175i	$-0.869297\pi$
$179$	−270.000	+	467.654i	−0.112742	+	0.195274i	0.804133	+	0.594449i	$0.202630\pi$
$180$		0			0
$181$	1982.00			0.813928			0.406964	−	0.913444i	$-0.366588\pi$
$181$	1982.00			0.813928			0.406964	+	0.913444i	$0.366588\pi$
$182$		0			0
$183$		0			0
$184$	672.000	+	1163.94i	0.269242	+	0.466341i
$185$	762.000	−	1319.82i	0.302829	−	0.524515i
$186$		0			0
$187$	756.000	+	1309.43i	0.295637	+	0.512059i
$188$	384.000			0.148969
$189$		0			0
$190$	−240.000			−0.0916391
$191$	−1344.00	−	2327.88i	−0.509154	−	0.881881i	−0.999944	−	0.0106027i	$-0.996625\pi$
$191$	−1344.00	−	2327.88i	−0.509154	−	0.881881i	0.490790	−	0.871278i	$-0.336708\pi$
$192$		0			0
$193$	1151.00	−	1993.59i	0.429279	−	0.743533i	−0.567531	−	0.823352i	$-0.692101\pi$
$193$	1151.00	−	1993.59i	0.429279	−	0.743533i	0.996809	+	0.0798198i	$0.0254345\pi$
$194$	−1154.00	−	1998.79i	−0.427074	−	0.739714i
$195$		0			0
$196$		0			0
$197$	−4374.00			−1.58190			−0.790951	−	0.611880i	$-0.790414\pi$
$197$	−4374.00			−1.58190			−0.790951	+	0.611880i	$0.790414\pi$
$198$		0			0
$199$	800.000	−	1385.64i	0.284977	−	0.493595i	−0.687626	−	0.726065i	$-0.741347\pi$
$199$	800.000	−	1385.64i	0.284977	−	0.493595i	0.972604	+	0.232469i	$0.0746806\pi$
$200$	356.000	−	616.610i	0.125865	−	0.218005i
$201$		0			0
$202$	1236.00			0.430518
$203$		0			0
$204$		0			0
$205$	−126.000	−	218.238i	−0.0429279	−	0.0743533i
$206$	−128.000	+	221.703i	−0.0432921	+	0.0749842i
$207$		0			0
$208$	−304.000	−	526.543i	−0.101339	−	0.175525i
$209$	−240.000			−0.0794313
$210$		0			0
$211$	3332.00			1.08713			0.543565	−	0.839367i	$-0.317074\pi$
$211$	3332.00			1.08713			0.543565	+	0.839367i	$0.317074\pi$
$212$	396.000	+	685.892i	0.128290	+	0.222204i
$213$		0			0
$214$	−1476.00	+	2556.51i	−0.471483	+	0.816632i
$215$	−156.000	−	270.200i	−0.0494842	−	0.0857092i
$216$		0			0
$217$		0			0
$218$	2380.00			0.739422
$219$		0			0
$220$	−144.000	+	249.415i	−0.0441294	+	0.0764344i
$221$	−2394.00	+	4146.53i	−0.728678	+	1.26211i
$222$		0			0
$223$	2648.00			0.795171			0.397586	−	0.917565i	$-0.369848\pi$
$223$	2648.00			0.795171			0.397586	+	0.917565i	$0.369848\pi$
$224$		0			0
$225$		0			0
$226$	−462.000	−	800.207i	−0.135981	−	0.235527i
$227$	1122.00	−	1943.36i	0.328061	−	0.568218i	−0.654066	−	0.756437i	$-0.726938\pi$
$227$	1122.00	−	1943.36i	0.328061	−	0.568218i	0.982127	+	0.188220i	$0.0602716\pi$
$228$		0			0
$229$	2825.00	+	4893.04i	0.815202	+	1.41197i	0.909183	+	0.416397i	$0.136707\pi$
$229$	2825.00	+	4893.04i	0.815202	+	1.41197i	−0.0939808	+	0.995574i	$0.529959\pi$
$230$	2016.00			0.577961
$231$		0			0
$232$	−240.000			−0.0679171
$233$	2349.00	+	4068.59i	0.660464	+	1.14396i	0.980494	+	0.196550i	$0.0629737\pi$
$233$	2349.00	+	4068.59i	0.660464	+	1.14396i	−0.320030	+	0.947407i	$0.603693\pi$
$234$		0			0
$235$	288.000	−	498.831i	0.0799449	−	0.138469i
$236$	−1320.00	−	2286.31i	−0.364088	−	0.630618i
$237$		0			0
$238$		0			0
$239$	1200.00			0.324776			0.162388	−	0.986727i	$-0.448080\pi$
$239$	1200.00			0.324776			0.162388	+	0.986727i	$0.448080\pi$
$240$		0			0
$241$	359.000	−	621.806i	0.0959553	−	0.166199i	−0.814052	−	0.580793i	$-0.802743\pi$
$241$	359.000	−	621.806i	0.0959553	−	0.166199i	0.910007	+	0.414593i	$0.136076\pi$
$242$	1187.00	−	2055.94i	0.315303	−	0.546120i
$243$		0			0
$244$	−2152.00			−0.564622
$245$		0			0
$246$		0			0
$247$	−380.000	−	658.179i	−0.0978900	−	0.169550i
$248$	352.000	−	609.682i	0.0901291	−	0.156108i
$249$		0			0
$250$	−1284.00	−	2223.95i	−0.324829	−	0.562621i
$251$	−6012.00			−1.51185			−0.755924	−	0.654659i	$-0.772812\pi$
$251$	−6012.00			−1.51185			−0.755924	+	0.654659i	$0.772812\pi$
$252$		0			0
$253$	2016.00			0.500968
$254$	2536.00	+	4392.48i	0.626468	+	1.08507i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1023.00	−	1771.89i	−0.248300	−	0.430067i	0.714755	−	0.699375i	$-0.246538\pi$
$257$	−1023.00	−	1771.89i	−0.248300	−	0.430067i	−0.963054	+	0.269308i	$0.913205\pi$
$258$		0			0
$259$		0			0
$260$	−912.000			−0.217538
$261$		0			0
$262$	2292.00	−	3969.86i	0.540459	−	0.936102i
$263$	−3036.00	+	5258.51i	−0.711817	+	1.23290i	0.252358	+	0.967634i	$0.418794\pi$
$263$	−3036.00	+	5258.51i	−0.711817	+	1.23290i	−0.964175	+	0.265269i	$0.914539\pi$
$264$		0			0
$265$	1188.00			0.275390
$266$		0			0
$267$		0			0
$268$	−1768.00	−	3062.27i	−0.402977	−	0.697976i
$269$	−3465.00	+	6001.56i	−0.785371	+	1.36030i	0.143406	+	0.989664i	$0.454194\pi$
$269$	−3465.00	+	6001.56i	−0.785371	+	1.36030i	−0.928777	+	0.370638i	$0.879139\pi$
$270$		0			0
$271$	−676.000	−	1170.87i	−0.151528	−	0.262454i	0.780261	−	0.625454i	$-0.215086\pi$
$271$	−676.000	−	1170.87i	−0.151528	−	0.262454i	−0.931789	+	0.362999i	$0.881753\pi$
$272$	2016.00			0.449404
$273$		0			0
$274$	1452.00			0.320141
$275$	−534.000	−	924.915i	−0.117096	−	0.202816i
$276$		0			0
$277$	593.000	−	1027.11i	0.128628	−	0.222790i	−0.794517	−	0.607241i	$-0.792276\pi$
$277$	593.000	−	1027.11i	0.128628	−	0.222790i	0.923145	+	0.384451i	$0.125609\pi$
$278$	−380.000	−	658.179i	−0.0819816	−	0.141996i
$279$		0			0
$280$		0			0
$281$	−2442.00			−0.518425			−0.259213	−	0.965820i	$-0.583463\pi$
$281$	−2442.00			−0.518425			−0.259213	+	0.965820i	$0.583463\pi$
$282$		0			0
$283$	−1414.00	+	2449.12i	−0.297009	+	0.514435i	−0.975450	−	0.220220i	$-0.929323\pi$
$283$	−1414.00	+	2449.12i	−0.297009	+	0.514435i	0.678441	+	0.734655i	$0.262656\pi$
$284$	1584.00	−	2743.57i	0.330962	−	0.573242i
$285$		0			0
$286$	−912.000			−0.188558
$287$		0			0
$288$		0			0
$289$	−5481.50	−	9494.24i	−1.11571	−	1.93247i
$290$	−180.000	+	311.769i	−0.0364482	+	0.0631301i
$291$		0			0
$292$	−436.000	−	755.174i	−0.0873800	−	0.151347i
$293$	−4758.00			−0.948687			−0.474344	−	0.880340i	$-0.657315\pi$
$293$	−4758.00			−0.948687			−0.474344	+	0.880340i	$0.657315\pi$
$294$		0			0
$295$	−3960.00			−0.781560
$296$	−1016.00	−	1759.76i	−0.199506	−	0.345555i
$297$		0			0
$298$	1590.00	−	2753.96i	0.309081	−	0.535345i
$299$	3192.00	+	5528.71i	0.617385	+	1.06934i
$300$		0			0
$301$		0			0
$302$	4864.00			0.926794
$303$		0			0
$304$	−160.000	+	277.128i	−0.0301863	+	0.0522842i
$305$	−1614.00	+	2795.53i	−0.303008	+	0.524825i
$306$		0			0
$307$	−8476.00			−1.57574			−0.787868	−	0.615844i	$-0.788815\pi$
$307$	−8476.00			−1.57574			−0.787868	+	0.615844i	$0.788815\pi$
$308$		0			0
$309$		0			0
$310$	−528.000	−	914.523i	−0.0967367	−	0.167553i
$311$	2316.00	−	4011.43i	0.422278	−	0.731406i	−0.573884	−	0.818936i	$-0.694564\pi$
$311$	2316.00	−	4011.43i	0.422278	−	0.731406i	0.996162	+	0.0875302i	$0.0278974\pi$
$312$		0			0
$313$	2411.00	+	4175.97i	0.435392	+	0.754122i	0.997328	−	0.0730597i	$-0.0232764\pi$
$313$	2411.00	+	4175.97i	0.435392	+	0.754122i	−0.561935	+	0.827181i	$0.689943\pi$
$314$	1228.00			0.220701
$315$		0			0
$316$	−2080.00			−0.370282
$317$	−1713.00	−	2967.00i	−0.303507	−	0.525689i	0.673421	−	0.739259i	$-0.264824\pi$
$317$	−1713.00	−	2967.00i	−0.303507	−	0.525689i	−0.976928	+	0.213570i	$0.931491\pi$
$318$		0			0
$319$	−180.000	+	311.769i	−0.0315927	+	0.0547201i
$320$	192.000	+	332.554i	0.0335410	+	0.0580948i
$321$		0			0
$322$		0			0
$323$	2520.00			0.434107
$324$		0			0
$325$	1691.00	−	2928.90i	0.288615	−	0.499895i
$326$	1852.00	−	3207.76i	0.314640	−	0.544973i
$327$		0			0
$328$	−336.000			−0.0565625
$329$		0			0
$330$		0			0
$331$	1394.00	+	2414.48i	0.231484	+	0.400942i	0.958245	−	0.285948i	$-0.0923086\pi$
$331$	1394.00	+	2414.48i	0.231484	+	0.400942i	−0.726761	+	0.686890i	$0.758975\pi$
$332$	−984.000	+	1704.34i	−0.162663	+	0.281740i
$333$		0			0
$334$	−2136.00	−	3699.66i	−0.349930	−	0.606097i
$335$	−5304.00			−0.865040
$336$		0			0
$337$	434.000			0.0701528			0.0350764	−	0.999385i	$-0.488833\pi$
$337$	434.000			0.0701528			0.0350764	+	0.999385i	$0.488833\pi$
$338$	753.000	+	1304.23i	0.121177	+	0.209885i
$339$		0			0
$340$	1512.00	−	2618.86i	0.241176	−	0.417728i
$341$	−528.000	−	914.523i	−0.0838499	−	0.145232i
$342$		0			0
$343$		0			0
$344$	−416.000			−0.0652012
$345$		0			0
$346$	1758.00	−	3044.95i	0.273152	−	0.473114i
$347$	3342.00	−	5788.51i	0.517026	−	0.895515i	−0.482779	−	0.875742i	$-0.660372\pi$
$347$	3342.00	−	5788.51i	0.517026	−	0.895515i	0.999805	−	0.0197726i	$-0.00629422\pi$
$348$		0			0
$349$	2630.00			0.403383			0.201692	−	0.979449i	$-0.435356\pi$
$349$	2630.00			0.403383			0.201692	+	0.979449i	$0.435356\pi$
$350$		0			0
$351$		0			0
$352$	192.000	+	332.554i	0.0290728	+	0.0503556i
$353$	−3711.00	+	6427.64i	−0.559537	+	0.969147i	0.437998	+	0.898976i	$0.355688\pi$
$353$	−3711.00	+	6427.64i	−0.559537	+	0.969147i	−0.997535	+	0.0701707i	$0.977646\pi$
$354$		0			0
$355$	−2376.00	−	4115.35i	−0.355225	−	0.615268i
$356$	−3240.00			−0.482359
$357$		0			0
$358$	1080.00			0.159441
$359$	−5220.00	−	9041.31i	−0.767412	−	1.32920i	−0.938962	−	0.344022i	$-0.888211\pi$
$359$	−5220.00	−	9041.31i	−0.767412	−	1.32920i	0.171549	−	0.985176i	$-0.445123\pi$
$360$		0			0
$361$	3229.50	−	5593.66i	0.470841	−	0.815521i
$362$	−1982.00	−	3432.92i	−0.287767	−	0.498427i
$363$		0			0
$364$		0			0
$365$	−1308.00			−0.187572
$366$		0			0
$367$	−5212.00	+	9027.45i	−0.741319	+	1.28400i	0.210575	+	0.977578i	$0.432466\pi$
$367$	−5212.00	+	9027.45i	−0.741319	+	1.28400i	−0.951895	+	0.306425i	$0.900867\pi$
$368$	1344.00	−	2327.88i	0.190383	−	0.329753i
$369$		0			0
$370$	−3048.00			−0.428265
$371$		0			0
$372$		0			0
$373$	−1639.00	−	2838.83i	−0.227518	−	0.394073i	0.729554	−	0.683923i	$-0.239728\pi$
$373$	−1639.00	−	2838.83i	−0.227518	−	0.394073i	−0.957072	+	0.289851i	$0.906394\pi$
$374$	1512.00	−	2618.86i	0.209047	−	0.362080i
$375$		0			0
$376$	−384.000	−	665.108i	−0.0526683	−	0.0912242i
$377$	−1140.00			−0.155737
$378$		0			0
$379$	6140.00			0.832165			0.416083	−	0.909327i	$-0.363403\pi$
$379$	6140.00			0.832165			0.416083	+	0.909327i	$0.363403\pi$
$380$	240.000	+	415.692i	0.0323993	+	0.0561173i
$381$		0			0
$382$	−2688.00	+	4655.75i	−0.360026	+	0.623584i
$383$	−1536.00	−	2660.43i	−0.204924	−	0.354939i	0.745184	−	0.666858i	$-0.232361\pi$
$383$	−1536.00	−	2660.43i	−0.204924	−	0.354939i	−0.950109	+	0.311919i	$0.899028\pi$
$384$		0			0
$385$		0			0
$386$	−4604.00			−0.607092
$387$		0			0
$388$	−2308.00	+	3997.57i	−0.301987	+	0.523057i
$389$	3075.00	−	5326.06i	0.400794	−	0.694195i	−0.593028	−	0.805182i	$-0.702068\pi$
$389$	3075.00	−	5326.06i	0.400794	−	0.694195i	0.993822	+	0.110987i	$0.0354011\pi$
$390$		0			0
$391$	−21168.0			−2.73788
$392$		0			0
$393$		0			0
$394$	4374.00	+	7575.99i	0.559287	+	0.968713i
$395$	−1560.00	+	2702.00i	−0.198714	+	0.344183i
$396$		0			0
$397$	53.0000	+	91.7987i	0.00670024	+	0.0116051i	0.869356	−	0.494186i	$-0.164534\pi$
$397$	53.0000	+	91.7987i	0.00670024	+	0.0116051i	−0.862656	+	0.505791i	$0.831201\pi$
$398$	−3200.00			−0.403019
$399$		0			0
$400$	−1424.00			−0.178000
$401$	−879.000	−	1522.47i	−0.109464	−	0.189598i	0.806089	−	0.591794i	$-0.201580\pi$
$401$	−879.000	−	1522.47i	−0.109464	−	0.189598i	−0.915553	+	0.402197i	$0.868247\pi$
$402$		0			0
$403$	1672.00	−	2895.99i	0.206671	−	0.357964i
$404$	−1236.00	−	2140.81i	−0.152211	−	0.263637i
$405$		0			0
$406$		0			0
$407$	−3048.00			−0.371213
$408$		0			0
$409$	1835.00	−	3178.31i	0.221846	−	0.384248i	−0.733523	−	0.679665i	$-0.762125\pi$
$409$	1835.00	−	3178.31i	0.221846	−	0.384248i	0.955368	+	0.295417i	$0.0954585\pi$
$410$	−252.000	+	436.477i	−0.0303546	+	0.0525757i
$411$		0			0
$412$	512.000			0.0612243
$413$		0			0
$414$		0			0
$415$	1476.00	+	2556.51i	0.174588	+	0.302395i
$416$	−608.000	+	1053.09i	−0.0716578	+	0.124115i
$417$		0			0
$418$	240.000	+	415.692i	0.0280832	+	0.0486416i
$419$	9660.00			1.12631			0.563153	−	0.826353i	$-0.309588\pi$
$419$	9660.00			1.12631			0.563153	+	0.826353i	$0.309588\pi$
$420$		0			0
$421$	8462.00			0.979602			0.489801	−	0.871834i	$-0.337069\pi$
$421$	8462.00			0.979602			0.489801	+	0.871834i	$0.337069\pi$
$422$	−3332.00	−	5771.19i	−0.384358	−	0.665728i
$423$		0			0
$424$	792.000	−	1371.78i	0.0907144	−	0.157122i
$425$	5607.00	+	9711.61i	0.639952	+	1.10843i
$426$		0			0
$427$		0			0
$428$	5904.00			0.666777
$429$		0			0
$430$	−312.000	+	540.400i	−0.0349906	+	0.0606056i
$431$	4896.00	−	8480.12i	0.547174	−	0.947733i	−0.451293	−	0.892376i	$-0.649037\pi$
$431$	4896.00	−	8480.12i	0.547174	−	0.947733i	0.998467	−	0.0553572i	$-0.0176298\pi$
$432$		0			0
$433$	−7342.00			−0.814859			−0.407430	−	0.913237i	$-0.633575\pi$
$433$	−7342.00			−0.814859			−0.407430	+	0.913237i	$0.633575\pi$
$434$		0			0
$435$		0			0
$436$	−2380.00	−	4122.28i	−0.261425	−	0.452801i
$437$	1680.00	−	2909.85i	0.183902	−	0.318528i
$438$		0			0
$439$	−5320.00	−	9214.51i	−0.578382	−	1.00179i	−0.995665	−	0.0930106i	$-0.970351\pi$
$439$	−5320.00	−	9214.51i	−0.578382	−	1.00179i	0.417283	−	0.908777i	$-0.362982\pi$
$440$	576.000			0.0624085
$441$		0			0
$442$	9576.00			1.03051
$443$	−8706.00	−	15079.2i	−0.933712	−	1.61724i	−0.776914	−	0.629606i	$-0.783216\pi$
$443$	−8706.00	−	15079.2i	−0.933712	−	1.61724i	−0.156798	−	0.987631i	$-0.550117\pi$
$444$		0			0
$445$	−2430.00	+	4208.88i	−0.258861	+	0.448360i
$446$	−2648.00	−	4586.47i	−0.281136	−	0.486941i
$447$		0			0
$448$		0			0
$449$	1710.00			0.179732			0.0898662	−	0.995954i	$-0.471356\pi$
$449$	1710.00			0.179732			0.0898662	+	0.995954i	$0.471356\pi$
$450$		0			0
$451$	−252.000	+	436.477i	−0.0263109	+	0.0455718i
$452$	−924.000	+	1600.41i	−0.0961533	+	0.166542i
$453$		0			0
$454$	−4488.00			−0.463948
$455$		0			0
$456$		0			0
$457$	323.000	+	559.452i	0.0330619	+	0.0572649i	0.882083	−	0.471094i	$-0.156141\pi$
$457$	323.000	+	559.452i	0.0330619	+	0.0572649i	−0.849021	+	0.528359i	$0.822807\pi$
$458$	5650.00	−	9786.09i	0.576435	−	0.998414i
$459$		0			0
$460$	−2016.00	−	3491.81i	−0.204340	−	0.353928i
$461$	6018.00			0.607996			0.303998	−	0.952673i	$-0.401678\pi$
$461$	6018.00			0.607996			0.303998	+	0.952673i	$0.401678\pi$
$462$		0			0
$463$	−6712.00			−0.673722			−0.336861	−	0.941554i	$-0.609365\pi$
$463$	−6712.00			−0.673722			−0.336861	+	0.941554i	$0.609365\pi$
$464$	240.000	+	415.692i	0.0240123	+	0.0415906i
$465$		0			0
$466$	4698.00	−	8137.17i	0.467019	−	0.808900i
$467$	2682.00	+	4645.36i	0.265756	+	0.460303i	0.967761	−	0.251868i	$-0.0810450\pi$
$467$	2682.00	+	4645.36i	0.265756	+	0.460303i	−0.702005	+	0.712172i	$0.747712\pi$
$468$		0			0
$469$		0			0
$470$	−1152.00			−0.113059
$471$		0			0
$472$	−2640.00	+	4572.61i	−0.257449	+	0.445914i
$473$	−312.000	+	540.400i	−0.0303293	+	0.0525319i
$474$		0			0
$475$	−1780.00			−0.171941
$476$		0			0
$477$		0			0
$478$	−1200.00	−	2078.46i	−0.114826	−	0.198884i
$479$	4920.00	−	8521.69i	0.469312	−	0.812873i	−0.530072	−	0.847952i	$-0.677835\pi$
$479$	4920.00	−	8521.69i	0.469312	−	0.812873i	0.999385	+	0.0350799i	$0.0111686\pi$
$480$		0			0
$481$	−4826.00	−	8358.88i	−0.457477	−	0.792374i
$482$	−1436.00			−0.135701
$483$		0			0
$484$	−4748.00			−0.445905
$485$	3462.00	+	5996.36i	0.324126	+	0.561403i
$486$		0			0
$487$	−712.000	+	1233.22i	−0.0662501	+	0.114749i	−0.897248	−	0.441527i	$-0.854437\pi$
$487$	−712.000	+	1233.22i	−0.0662501	+	0.114749i	0.830998	+	0.556276i	$0.187770\pi$
$488$	2152.00	+	3727.37i	0.199624	+	0.345759i
$489$		0			0
$490$		0			0
$491$	4548.00			0.418021			0.209011	−	0.977913i	$-0.432976\pi$
$491$	4548.00			0.418021			0.209011	+	0.977913i	$0.432976\pi$
$492$		0			0
$493$	1890.00	−	3273.58i	0.172660	−	0.299056i
$494$	−760.000	+	1316.36i	−0.0692187	+	0.119890i
$495$		0			0
$496$	−1408.00			−0.127462
$497$		0			0
$498$		0			0
$499$	−3250.00	−	5629.17i	−0.291563	−	0.505002i	0.682616	−	0.730777i	$-0.260842\pi$
$499$	−3250.00	−	5629.17i	−0.291563	−	0.505002i	−0.974180	+	0.225775i	$0.927509\pi$
$500$	−2568.00	+	4447.91i	−0.229689	+	0.397833i
$501$		0			0
$502$	6012.00	+	10413.1i	0.534519	+	0.925815i
$503$	−12168.0			−1.07862			−0.539308	−	0.842108i	$-0.681314\pi$
$503$	−12168.0			−1.07862			−0.539308	+	0.842108i	$0.681314\pi$
$504$		0			0
$505$	−3708.00			−0.326740
$506$	−2016.00	−	3491.81i	−0.177119	−	0.306779i
$507$		0			0
$508$	5072.00	−	8784.96i	0.442980	−	0.767263i
$509$	−10545.0	−	18264.5i	−0.918269	−	1.59049i	−0.802043	−	0.597266i	$-0.796254\pi$
$509$	−10545.0	−	18264.5i	−0.918269	−	1.59049i	−0.116226	−	0.993223i	$-0.537080\pi$
$510$		0			0
$511$		0			0
$512$	512.000			0.0441942
$513$		0			0
$514$	−2046.00	+	3543.78i	−0.175574	+	0.304104i
$515$	384.000	−	665.108i	0.0328564	−	0.0569090i
$516$		0			0
$517$	−1152.00			−0.0979979
$518$		0			0
$519$		0			0
$520$	912.000	+	1579.63i	0.0769112	+	0.133214i
$521$	−2619.00	+	4536.24i	−0.220231	+	0.381452i	−0.954878	−	0.296998i	$-0.904015\pi$
$521$	−2619.00	+	4536.24i	−0.220231	+	0.381452i	0.734647	+	0.678450i	$0.237348\pi$
$522$		0			0
$523$	−4294.00	−	7437.43i	−0.359012	−	0.621828i	0.628784	−	0.777580i	$-0.283553\pi$
$523$	−4294.00	−	7437.43i	−0.359012	−	0.621828i	−0.987796	+	0.155752i	$0.950220\pi$
$524$	−9168.00			−0.764324
$525$		0			0
$526$	12144.0			1.00666
$527$	5544.00	+	9602.49i	0.458255	+	0.793721i
$528$		0			0
$529$	−8028.50	+	13905.8i	−0.659859	+	1.14291i
$530$	−1188.00	−	2057.68i	−0.0973649	−	0.168641i
$531$		0			0
$532$		0			0
$533$	−1596.00			−0.129701
$534$		0			0
$535$	4428.00	−	7669.52i	0.357830	−	0.619780i
$536$	−3536.00	+	6124.53i	−0.284948	+	0.493544i
$537$		0			0
$538$	13860.0			1.11068
$539$		0			0
$540$		0			0
$541$	−1531.00	−	2651.77i	−0.121669	−	0.210737i	0.798757	−	0.601654i	$-0.205491\pi$
$541$	−1531.00	−	2651.77i	−0.121669	−	0.210737i	−0.920426	+	0.390917i	$0.872158\pi$
$542$	−1352.00	+	2341.73i	−0.107146	+	0.185583i
$543$		0			0
$544$	−2016.00	−	3491.81i	−0.158888	−	0.275203i
$545$	−7140.00			−0.561182
$546$		0			0
$547$	−8476.00			−0.662537			−0.331268	−	0.943537i	$-0.607477\pi$
$547$	−8476.00			−0.662537			−0.331268	+	0.943537i	$0.607477\pi$
$548$	−1452.00	−	2514.94i	−0.113187	−	0.196045i
$549$		0			0
$550$	−1068.00	+	1849.83i	−0.0827994	+	0.143413i
$551$	300.000	+	519.615i	0.0231950	+	0.0401749i
$552$		0			0
$553$		0			0
$554$	−2372.00			−0.181907
$555$		0			0
$556$	−760.000	+	1316.36i	−0.0579697	+	0.100407i
$557$	−6273.00	+	10865.2i	−0.477191	+	0.826520i	−0.999658	−	0.0261400i	$-0.991678\pi$
$557$	−6273.00	+	10865.2i	−0.477191	+	0.826520i	0.522467	+	0.852659i	$0.325012\pi$
$558$		0			0
$559$	−1976.00			−0.149510
$560$		0			0
$561$		0			0
$562$	2442.00	+	4229.67i	0.183291	+	0.317469i
$563$	−6.00000	+	10.3923i	−0.000449147	+	0.000777946i	−0.866250	−	0.499611i	$-0.833476\pi$
$563$	−6.00000	+	10.3923i	−0.000449147	+	0.000777946i	0.865801	+	0.500389i	$0.166810\pi$
$564$		0			0
$565$	1386.00	+	2400.62i	0.103203	+	0.178752i
$566$	5656.00			0.420034
$567$		0			0
$568$	−6336.00			−0.468050
$569$	9645.00	+	16705.6i	0.710614	+	1.23082i	0.964627	+	0.263619i	$0.0849161\pi$
$569$	9645.00	+	16705.6i	0.710614	+	1.23082i	−0.254013	+	0.967201i	$0.581751\pi$
$570$		0			0
$571$	6074.00	−	10520.5i	0.445165	−	0.771048i	−0.552899	−	0.833248i	$-0.686478\pi$
$571$	6074.00	−	10520.5i	0.445165	−	0.771048i	0.998064	+	0.0622005i	$0.0198118\pi$
$572$	912.000	+	1579.63i	0.0666654	+	0.115468i
$573$		0			0
$574$		0			0
$575$	14952.0			1.08442
$576$		0			0
$577$	5183.00	−	8977.22i	0.373953	−	0.647706i	−0.616216	−	0.787577i	$-0.711335\pi$
$577$	5183.00	−	8977.22i	0.373953	−	0.647706i	0.990170	+	0.139871i	$0.0446687\pi$
$578$	−10963.0	+	18988.5i	−0.788929	+	1.36646i
$579$		0			0
$580$	720.000			0.0515455
$581$		0			0
$582$		0			0
$583$	−1188.00	−	2057.68i	−0.0843944	−	0.146175i
$584$	−872.000	+	1510.35i	−0.0617870	+	0.107018i
$585$		0			0
$586$	4758.00	+	8241.10i	0.335412	+	0.580950i
$587$	−7644.00			−0.537482			−0.268741	−	0.963213i	$-0.586607\pi$
$587$	−7644.00			−0.537482			−0.268741	+	0.963213i	$0.586607\pi$
$588$		0			0
$589$	−1760.00			−0.123123
$590$	3960.00	+	6858.92i	0.276323	+	0.478606i
$591$		0			0
$592$	−2032.00	+	3519.53i	−0.141072	+	0.244344i
$593$	4329.00	+	7498.05i	0.299782	+	0.519238i	0.976086	−	0.217385i	$-0.0697527\pi$
$593$	4329.00	+	7498.05i	0.299782	+	0.519238i	−0.676304	+	0.736623i	$0.736419\pi$
$594$		0			0
$595$		0			0
$596$	−6360.00			−0.437107
$597$		0			0
$598$	6384.00	−	11057.4i	0.436557	−	0.756139i
$599$	12900.0	−	22343.5i	0.879933	−	1.52409i	0.0285192	−	0.999593i	$-0.490921\pi$
$599$	12900.0	−	22343.5i	0.879933	−	1.52409i	0.851414	−	0.524495i	$-0.175746\pi$
$600$		0			0
$601$	16202.0			1.09966			0.549828	−	0.835278i	$-0.314693\pi$
$601$	16202.0			1.09966			0.549828	+	0.835278i	$0.314693\pi$
$602$		0			0
$603$		0			0
$604$	−4864.00	−	8424.70i	−0.327671	−	0.567543i
$605$	−3561.00	+	6167.83i	−0.239298	+	0.414476i
$606$		0			0
$607$	12068.0	+	20902.4i	0.806960	+	1.39770i	0.914960	+	0.403546i	$0.132222\pi$
$607$	12068.0	+	20902.4i	0.806960	+	1.39770i	−0.107999	+	0.994151i	$0.534444\pi$
$608$	640.000			0.0426898
$609$		0			0
$610$	6456.00			0.428518
$611$	−1824.00	−	3159.26i	−0.120771	−	0.209182i
$612$		0			0
$613$	2321.00	−	4020.09i	0.152927	−	0.264877i	−0.779375	−	0.626557i	$-0.784463\pi$
$613$	2321.00	−	4020.09i	0.152927	−	0.264877i	0.932302	+	0.361680i	$0.117797\pi$
$614$	8476.00	+	14680.9i	0.557107	+	0.964937i
$615$		0			0
$616$		0			0
$617$	6726.00			0.438863			0.219432	−	0.975628i	$-0.429580\pi$
$617$	6726.00			0.438863			0.219432	+	0.975628i	$0.429580\pi$
$618$		0			0
$619$	10610.0	−	18377.1i	0.688937	−	1.19327i	−0.283245	−	0.959047i	$-0.591411\pi$
$619$	10610.0	−	18377.1i	0.688937	−	1.19327i	0.972182	−	0.234226i	$-0.0752556\pi$
$620$	−1056.00	+	1829.05i	−0.0684032	+	0.118478i
$621$		0			0
$622$	−9264.00			−0.597191
$623$		0			0
$624$		0			0
$625$	−1710.50	−	2962.67i	−0.109472	−	0.189611i
$626$	4822.00	−	8351.95i	0.307869	−	0.533244i
$627$		0			0
$628$	−1228.00	−	2126.96i	−0.0780295	−	0.135151i
$629$	32004.0			2.02875
$630$		0			0
$631$	29792.0			1.87956			0.939779	−	0.341783i	$-0.111031\pi$
$631$	29792.0			1.87956			0.939779	+	0.341783i	$0.111031\pi$
$632$	2080.00	+	3602.67i	0.130914	+	0.226751i
$633$		0			0
$634$	−3426.00	+	5934.01i	−0.214612	+	0.371718i
$635$	−7608.00	−	13177.4i	−0.475456	−	0.823513i
$636$		0			0
$637$		0			0
$638$	720.000			0.0446788
$639$		0			0
$640$	384.000	−	665.108i	0.0237171	−	0.0410792i
$641$	−5079.00	+	8797.09i	−0.312962	+	0.542066i	−0.979002	−	0.203850i	$-0.934654\pi$
$641$	−5079.00	+	8797.09i	−0.312962	+	0.542066i	0.666040	+	0.745916i	$0.267988\pi$
$642$		0			0
$643$	29828.0			1.82940			0.914698	−	0.404138i	$-0.132429\pi$
$643$	29828.0			1.82940			0.914698	+	0.404138i	$0.132429\pi$
$644$		0			0
$645$		0			0
$646$	−2520.00	−	4364.77i	−0.153480	−	0.265835i
$647$	972.000	−	1683.55i	0.0590622	−	0.102299i	−0.834982	−	0.550277i	$-0.814522\pi$
$647$	972.000	−	1683.55i	0.0590622	−	0.102299i	0.894045	+	0.447978i	$0.147856\pi$
$648$		0			0
$649$	3960.00	+	6858.92i	0.239512	+	0.414848i
$650$	−6764.00			−0.408163
$651$		0			0
$652$	−7408.00			−0.444969
$653$	13359.0	+	23138.5i	0.800579	+	1.38664i	0.919236	+	0.393708i	$0.128808\pi$
$653$	13359.0	+	23138.5i	0.800579	+	1.38664i	−0.118657	+	0.992935i	$0.537859\pi$
$654$		0			0
$655$	−6876.00	+	11909.6i	−0.410179	+	0.710452i
$656$	336.000	+	581.969i	0.0199979	+	0.0346373i
$657$		0			0
$658$		0			0
$659$	−4260.00			−0.251815			−0.125907	−	0.992042i	$-0.540184\pi$
$659$	−4260.00			−0.251815			−0.125907	+	0.992042i	$0.540184\pi$
$660$		0			0
$661$	−11431.0	+	19799.1i	−0.672639	+	1.16504i	0.304514	+	0.952508i	$0.401506\pi$
$661$	−11431.0	+	19799.1i	−0.672639	+	1.16504i	−0.977153	+	0.212537i	$0.931827\pi$
$662$	2788.00	−	4828.96i	0.163684	−	0.283509i
$663$		0			0
$664$	3936.00			0.230040
$665$		0			0
$666$		0			0
$667$	−2520.00	−	4364.77i	−0.146289	−	0.253380i
$668$	−4272.00	+	7399.32i	−0.247438	+	0.428575i
$669$		0			0
$670$	5304.00	+	9186.80i	0.305838	+	0.529727i
$671$	6456.00			0.371432
$672$		0			0
$673$	−32542.0			−1.86390			−0.931948	−	0.362592i	$-0.881892\pi$
$673$	−32542.0			−1.86390			−0.931948	+	0.362592i	$0.881892\pi$
$674$	−434.000	−	751.710i	−0.0248028	−	0.0429596i
$675$		0			0
$676$	1506.00	−	2608.47i	0.0856850	−	0.148411i
$677$	7107.00	+	12309.7i	0.403463	+	0.698818i	0.994141	−	0.108089i	$-0.0344732\pi$
$677$	7107.00	+	12309.7i	0.403463	+	0.698818i	−0.590679	+	0.806907i	$0.701140\pi$
$678$		0			0
$679$		0			0
$680$	−6048.00			−0.341074
$681$		0			0
$682$	−1056.00	+	1829.05i	−0.0592908	+	0.102695i
$683$	−3546.00	+	6141.85i	−0.198659	+	0.344087i	−0.948094	−	0.317991i	$-0.896992\pi$
$683$	−3546.00	+	6141.85i	−0.198659	+	0.344087i	0.749435	+	0.662078i	$0.230325\pi$
$684$		0			0
$685$	−4356.00			−0.242970
$686$		0			0
$687$		0			0
$688$	416.000	+	720.533i	0.0230521	+	0.0399274i
$689$	3762.00	−	6515.98i	0.208013	−	0.360289i
$690$		0			0
$691$	6614.00	+	11455.8i	0.364122	+	0.630678i	0.988635	−	0.150337i	$-0.0480357\pi$
$691$	6614.00	+	11455.8i	0.364122	+	0.630678i	−0.624513	+	0.781015i	$0.714702\pi$
$692$	−7032.00			−0.386296
$693$		0			0
$694$	−13368.0			−0.731185
$695$	1140.00	+	1974.54i	0.0622197	+	0.107768i
$696$		0			0
$697$	2646.00	−	4583.01i	0.143794	−	0.249058i
$698$	−2630.00	−	4555.29i	−0.142617	−	0.247021i
$699$		0			0
$700$		0			0
$701$	−28062.0			−1.51196			−0.755982	−	0.654592i	$-0.772840\pi$
$701$	−28062.0			−1.51196			−0.755982	+	0.654592i	$0.772840\pi$
$702$		0			0
$703$	−2540.00	+	4399.41i	−0.136270	+	0.236027i
$704$	384.000	−	665.108i	0.0205576	−	0.0356068i
$705$		0			0
$706$	14844.0			0.791305
$707$		0			0
$708$		0			0
$709$	13625.0	+	23599.2i	0.721717	+	1.25005i	0.960311	+	0.278932i	$0.0899803\pi$
$709$	13625.0	+	23599.2i	0.721717	+	1.25005i	−0.238594	+	0.971120i	$0.576686\pi$
$710$	−4752.00	+	8230.71i	−0.251182	+	0.435060i
$711$		0			0
$712$	3240.00	+	5611.84i	0.170540	+	0.295383i
$713$	14784.0			0.776529
$714$		0			0
$715$	2736.00			0.143106
$716$	−1080.00	−	1870.61i	−0.0563708	−	0.0976371i
$717$		0			0
$718$	−10440.0	+	18082.6i	−0.542643	+	0.939884i
$719$	−7200.00	−	12470.8i	−0.373456	−	0.646844i	0.616639	−	0.787246i	$-0.288494\pi$
$719$	−7200.00	−	12470.8i	−0.373456	−	0.646844i	−0.990095	+	0.140402i	$0.955161\pi$
$720$		0			0
$721$		0			0
$722$	−12918.0			−0.665870
$723$		0			0
$724$	−3964.00	+	6865.85i	−0.203482	+	0.352441i
$725$	−1335.00	+	2312.29i	−0.0683871	+	0.118450i
$726$		0			0
$727$	17984.0			0.917455			0.458727	−	0.888577i	$-0.348305\pi$
$727$	17984.0			0.917455			0.458727	+	0.888577i	$0.348305\pi$
$728$		0			0
$729$		0			0
$730$	1308.00	+	2265.52i	0.0663168	+	0.114864i
$731$	3276.00	−	5674.20i	0.165755	−	0.287097i
$732$		0			0
$733$	−8299.00	−	14374.3i	−0.418186	−	0.724320i	0.577571	−	0.816341i	$-0.304001\pi$
$733$	−8299.00	−	14374.3i	−0.418186	−	0.724320i	−0.995757	+	0.0920207i	$0.970667\pi$
$734$	20848.0			1.04838
$735$		0			0
$736$	−5376.00			−0.269242
$737$	5304.00	+	9186.80i	0.265095	+	0.459159i
$738$		0			0
$739$	−730.000	+	1264.40i	−0.0363376	+	0.0629386i	−0.883622	−	0.468201i	$-0.844902\pi$
$739$	−730.000	+	1264.40i	−0.0363376	+	0.0629386i	0.847285	+	0.531139i	$0.178236\pi$
$740$	3048.00	+	5279.29i	0.151414	+	0.262258i
$741$		0			0
$742$		0			0
$743$	30072.0			1.48484			0.742419	−	0.669936i	$-0.233678\pi$
$743$	30072.0			1.48484			0.742419	+	0.669936i	$0.233678\pi$
$744$		0			0
$745$	−4770.00	+	8261.88i	−0.234576	+	0.406298i
$746$	−3278.00	+	5677.66i	−0.160880	+	0.278651i
$747$		0			0
$748$	−6048.00			−0.295637
$749$		0			0
$750$		0			0
$751$	9044.00	+	15664.7i	0.439441	+	0.761134i	0.997646	−	0.0685686i	$-0.0218432\pi$
$751$	9044.00	+	15664.7i	0.439441	+	0.761134i	−0.558205	+	0.829703i	$0.688510\pi$
$752$	−768.000	+	1330.22i	−0.0372421	+	0.0645053i
$753$		0			0
$754$	1140.00	+	1974.54i	0.0550615	+	0.0953693i
$755$	−14592.0			−0.703387
$756$		0			0
$757$	24734.0			1.18755			0.593773	−	0.804633i	$-0.297638\pi$
$757$	24734.0			1.18755			0.593773	+	0.804633i	$0.297638\pi$
$758$	−6140.00	−	10634.8i	−0.294215	−	0.509595i
$759$		0			0
$760$	480.000	−	831.384i	0.0229098	−	0.0396809i
$761$	−11139.0	−	19293.3i	−0.530602	−	0.919030i	−0.999362	−	0.0357047i	$-0.988632\pi$
$761$	−11139.0	−	19293.3i	−0.530602	−	0.919030i	0.468760	−	0.883326i	$-0.344701\pi$
$762$		0			0
$763$		0			0
$764$	10752.0			0.509154
$765$		0			0
$766$	−3072.00	+	5320.86i	−0.144903	+	0.250980i
$767$	−12540.0	+	21719.9i	−0.590343	+	1.02250i
$768$		0			0
$769$	16130.0			0.756388			0.378194	−	0.925726i	$-0.376545\pi$
$769$	16130.0			0.756388			0.378194	+	0.925726i	$0.376545\pi$
$770$		0			0
$771$		0			0
$772$	4604.00	+	7974.36i	0.214639	+	0.371766i
$773$	14859.0	−	25736.5i	0.691386	−	1.19752i	−0.279998	−	0.960000i	$-0.590334\pi$
$773$	14859.0	−	25736.5i	0.691386	−	1.19752i	0.971384	−	0.237515i	$-0.0763327\pi$
$774$		0			0
$775$	−3916.00	−	6782.71i	−0.181506	−	0.314377i
$776$	9232.00			0.427074
$777$		0			0
$778$	−12300.0			−0.566808
$779$	420.000	+	727.461i	0.0193172	+	0.0334583i
$780$		0			0
$781$	−4752.00	+	8230.71i	−0.217721	+	0.377103i
$782$	21168.0	+	36664.1i	0.967987	+	1.67660i
$783$		0			0
$784$		0			0
$785$	−3684.00			−0.167500
$786$		0			0
$787$	−4762.00	+	8248.03i	−0.215689	+	0.373584i	−0.953485	−	0.301439i	$-0.902533\pi$
$787$	−4762.00	+	8248.03i	−0.215689	+	0.373584i	0.737797	+	0.675023i	$0.235866\pi$
$788$	8748.00	−	15152.0i	0.395475	−	0.684983i
$789$		0			0
$790$	6240.00			0.281024
$791$		0			0
$792$		0			0
$793$	10222.0	+	17705.0i	0.457748	+	0.792842i
$794$	106.000	−	183.597i	0.00473778	−	0.00820608i
$795$		0			0
$796$	3200.00	+	5542.56i	0.142489	+	0.246798i
$797$	33906.0			1.50692			0.753458	−	0.657496i	$-0.228384\pi$
$797$	33906.0			1.50692			0.753458	+	0.657496i	$0.228384\pi$
$798$		0			0
$799$	12096.0			0.535577
$800$	1424.00	+	2466.44i	0.0629325	+	0.109002i
$801$		0			0
$802$	−1758.00	+	3044.95i	−0.0774029	+	0.134066i
$803$	1308.00	+	2265.52i	0.0574823	+	0.0995623i
$804$		0			0
$805$		0			0
$806$	−6688.00			−0.292276
$807$		0			0
$808$	−2472.00	+	4281.63i	−0.107630	+	0.186420i
$809$	−315.000	+	545.596i	−0.0136895	+	0.0237109i	−0.872789	−	0.488098i	$-0.837691\pi$
$809$	−315.000	+	545.596i	−0.0136895	+	0.0237109i	0.859099	+	0.511809i	$0.171024\pi$
$810$		0			0
$811$	−20788.0			−0.900081			−0.450040	−	0.893008i	$-0.648590\pi$
$811$	−20788.0			−0.900081			−0.450040	+	0.893008i	$0.648590\pi$
$812$		0			0
$813$		0			0
$814$	3048.00	+	5279.29i	0.131244	+	0.227321i
$815$	−5556.00	+	9623.27i	−0.238795	+	0.413606i
$816$		0			0
$817$	520.000	+	900.666i	0.0222674	+	0.0385683i
$818$	−7340.00			−0.313737
$819$		0			0
$820$	1008.00			0.0429279
$821$	−21549.0	−	37324.0i	−0.916036	−	1.58662i	−0.805378	−	0.592762i	$-0.798038\pi$
$821$	−21549.0	−	37324.0i	−0.916036	−	1.58662i	−0.110658	−	0.993859i	$-0.535296\pi$
$822$		0			0
$823$	7136.00	−	12359.9i	0.302242	−	0.523499i	−0.674401	−	0.738365i	$-0.735598\pi$
$823$	7136.00	−	12359.9i	0.302242	−	0.523499i	0.976644	+	0.214866i	$0.0689315\pi$
$824$	−512.000	−	886.810i	−0.0216461	−	0.0374921i
$825$		0			0
$826$		0			0
$827$	−13644.0			−0.573698			−0.286849	−	0.957976i	$-0.592608\pi$
$827$	−13644.0			−0.573698			−0.286849	+	0.957976i	$0.592608\pi$
$828$		0			0
$829$	1205.00	−	2087.12i	0.0504842	−	0.0874412i	−0.839679	−	0.543083i	$-0.817257\pi$
$829$	1205.00	−	2087.12i	0.0504842	−	0.0874412i	0.890163	+	0.455642i	$0.150590\pi$
$830$	2952.00	−	5113.01i	0.123452	−	0.213826i
$831$		0			0
$832$	2432.00			0.101339
$833$		0			0
$834$		0			0
$835$	6408.00	+	11099.0i	0.265578	+	0.459995i
$836$	480.000	−	831.384i	0.0198578	−	0.0343948i
$837$		0			0
$838$	−9660.00	−	16731.6i	−0.398209	−	0.689718i
$839$	−23160.0			−0.953006			−0.476503	−	0.879173i	$-0.658096\pi$
$839$	−23160.0			−0.953006			−0.476503	+	0.879173i	$0.658096\pi$
$840$		0			0
$841$	−23489.0			−0.963098
$842$	−8462.00	−	14656.6i	−0.346342	−	0.599882i
$843$		0			0
$844$	−6664.00	+	11542.4i	−0.271782	+	0.470741i
$845$	−2259.00	−	3912.70i	−0.0919668	−	0.159291i
$846$		0			0
$847$		0			0
$848$	−3168.00			−0.128290
$849$		0			0
$850$	11214.0	−	19423.2i	0.452514	−	0.783777i
$851$	21336.0	−	36955.0i	0.859446	−	1.48860i
$852$		0			0
$853$	32078.0			1.28761			0.643804	−	0.765190i	$-0.277355\pi$
$853$	32078.0			1.28761			0.643804	+	0.765190i	$0.277355\pi$
$854$		0			0
$855$		0			0
$856$	−5904.00	−	10226.0i	−0.235741	−	0.408316i
$857$	−7203.00	+	12476.0i	−0.287106	+	0.497282i	−0.973118	−	0.230308i	$-0.926027\pi$
$857$	−7203.00	+	12476.0i	−0.287106	+	0.497282i	0.686012	+	0.727590i	$0.259360\pi$
$858$		0			0
$859$	−15310.0	−	26517.7i	−0.608115	−	1.05329i	−0.991551	−	0.129718i	$-0.958593\pi$
$859$	−15310.0	−	26517.7i	−0.608115	−	1.05329i	0.383436	−	0.923567i	$-0.374741\pi$
$860$	1248.00			0.0494842
$861$		0			0
$862$	−19584.0			−0.773821
$863$	8784.00	+	15214.3i	0.346478	+	0.600118i	0.985621	−	0.168970i	$-0.0540441\pi$
$863$	8784.00	+	15214.3i	0.346478	+	0.600118i	−0.639143	+	0.769088i	$0.720711\pi$
$864$		0			0
$865$	−5274.00	+	9134.84i	−0.207308	+	0.359068i
$866$	7342.00	+	12716.7i	0.288096	+	0.498997i
$867$		0			0
$868$		0			0
$869$	6240.00			0.243587
$870$		0			0
$871$	−16796.0	+	29091.5i	−0.653399	+	1.13172i
$872$	−4760.00	+	8244.56i	−0.184855	+	0.320179i
$873$		0			0
$874$	−6720.00			−0.260077
$875$		0			0
$876$		0			0
$877$	10853.0	+	18797.9i	0.417879	+	0.723787i	0.995726	−	0.0923577i	$-0.0294403\pi$
$877$	10853.0	+	18797.9i	0.417879	+	0.723787i	−0.577847	+	0.816145i	$0.696107\pi$
$878$	−10640.0	+	18429.0i	−0.408978	+	0.708371i
$879$		0			0
$880$	−576.000	−	997.661i	−0.0220647	−	0.0382172i
$881$	14958.0			0.572018			0.286009	−	0.958227i	$-0.407671\pi$
$881$	14958.0			0.572018			0.286009	+	0.958227i	$0.407671\pi$
$882$		0			0
$883$	−32812.0			−1.25052			−0.625261	−	0.780415i	$-0.715008\pi$
$883$	−32812.0			−1.25052			−0.625261	+	0.780415i	$0.715008\pi$
$884$	−9576.00	−	16586.1i	−0.364339	−	0.631054i
$885$		0			0
$886$	−17412.0	+	30158.5i	−0.660234	+	1.14356i
$887$	−19428.0	−	33650.3i	−0.735432	−	1.27381i	−0.954533	−	0.298104i	$-0.903646\pi$
$887$	−19428.0	−	33650.3i	−0.735432	−	1.27381i	0.219101	−	0.975702i	$-0.429688\pi$
$888$		0			0
$889$		0			0
$890$	9720.00			0.366084
$891$		0			0
$892$	−5296.00	+	9172.94i	−0.198793	+	0.344319i
$893$	−960.000	+	1662.77i	−0.0359744	+	0.0623096i
$894$		0			0
$895$	−3240.00			−0.121007
$896$		0			0
$897$		0			0
$898$	−1710.00	−	2961.81i	−0.0635450	−	0.110063i
$899$	−1320.00	+	2286.31i	−0.0489705	+	0.0848194i
$900$		0			0
$901$	12474.0	+	21605.6i	0.461231	+	0.798876i
$902$	1008.00			0.0372092
$903$		0			0
$904$	3696.00			0.135981
$905$	5946.00	+	10298.8i	0.218400	+	0.378279i
$906$		0			0
$907$	14138.0	−	24487.7i	0.517579	−	0.896474i	−0.482212	−	0.876055i	$-0.660167\pi$
$907$	14138.0	−	24487.7i	0.517579	−	0.896474i	0.999792	−	0.0204194i	$-0.00650015\pi$
$908$	4488.00	+	7773.44i	0.164030	+	0.284109i
$909$		0			0
$910$		0			0
$911$	−8112.00			−0.295019			−0.147510	−	0.989061i	$-0.547126\pi$
$911$	−8112.00			−0.295019			−0.147510	+	0.989061i	$0.547126\pi$
$912$		0			0
$913$	2952.00	−	5113.01i	0.107007	−	0.185341i
$914$	646.000	−	1118.90i	0.0233783	−	0.0404924i
$915$		0			0
$916$	−22600.0			−0.815202
$917$		0			0
$918$		0			0
$919$	13040.0	+	22585.9i	0.468063	+	0.810709i	0.999334	−	0.0364931i	$-0.0116187\pi$
$919$	13040.0	+	22585.9i	0.468063	+	0.810709i	−0.531271	+	0.847202i	$0.678285\pi$
$920$	−4032.00	+	6983.63i	−0.144490	+	0.250265i
$921$		0			0
$922$	−6018.00	−	10423.5i	−0.214959	−	0.372320i
$923$	−30096.0			−1.07326
$924$		0			0
$925$	−22606.0			−0.803547
$926$	6712.00	+	11625.5i	0.238197	+	0.412569i
$927$		0			0
$928$	480.000	−	831.384i	0.0169793	−	0.0294090i
$929$	24585.0	+	42582.5i	0.868254	+	1.50386i	0.863780	+	0.503870i	$0.168091\pi$
$929$	24585.0	+	42582.5i	0.868254	+	1.50386i	0.00447392	+	0.999990i	$0.498576\pi$
$930$		0			0
$931$		0			0
$932$	−18792.0			−0.660464
$933$		0			0
$934$	5364.00	−	9290.72i	0.187918	−	0.325484i
$935$	−4536.00	+	7856.58i	−0.158656	+	0.274800i
$936$		0			0
$937$	48314.0			1.68447			0.842236	−	0.539110i	$-0.181239\pi$
$937$	48314.0			1.68447			0.842236	+	0.539110i	$0.181239\pi$
$938$		0			0
$939$		0			0
$940$	1152.00	+	1995.32i	0.0399724	+	0.0692343i
$941$	17391.0	−	30122.1i	0.602477	−	1.04352i	−0.389968	−	0.920828i	$-0.627514\pi$
$941$	17391.0	−	30122.1i	0.602477	−	1.04352i	0.992445	−	0.122692i	$-0.0391526\pi$
$942$		0			0
$943$	−3528.00	−	6110.68i	−0.121832	−	0.211019i
$944$	10560.0			0.364088
$945$		0			0
$946$	1248.00			0.0428922
$947$	−12558.0	−	21751.1i	−0.430919	−	0.746373i	0.566034	−	0.824382i	$-0.308477\pi$
$947$	−12558.0	−	21751.1i	−0.430919	−	0.746373i	−0.996953	+	0.0780087i	$0.975144\pi$
$948$		0			0
$949$	−4142.00	+	7174.15i	−0.141681	+	0.245398i
$950$	1780.00	+	3083.05i	0.0607903	+	0.105292i
$951$		0			0
$952$		0			0
$953$	15462.0			0.525565			0.262782	−	0.964855i	$-0.415360\pi$
$953$	15462.0			0.525565			0.262782	+	0.964855i	$0.415360\pi$
$954$		0			0
$955$	8064.00	−	13967.3i	0.273241	−	0.473267i
$956$	−2400.00	+	4156.92i	−0.0811941	+	0.140632i
$957$		0			0
$958$	−19680.0			−0.663708
$959$		0			0
$960$		0			0
$961$	11023.5	+	19093.3i	0.370028	+	0.640907i
$962$	−9652.00	+	16717.8i	−0.323485	+	0.560293i
$963$		0			0
$964$	1436.00	+	2487.22i	0.0479776	+	0.0830997i
$965$	13812.0			0.460750
$966$		0			0
$967$	−736.000			−0.0244759			−0.0122379	−	0.999925i	$-0.503896\pi$
$967$	−736.000			−0.0244759			−0.0122379	+	0.999925i	$0.503896\pi$
$968$	4748.00	+	8223.78i	0.157651	+	0.273060i
$969$		0			0
$970$	6924.00	−	11992.7i	0.229192	−	0.396972i
$971$	−14634.0	−	25346.8i	−0.483653	−	0.837712i	0.516170	−	0.856486i	$-0.327357\pi$
$971$	−14634.0	−	25346.8i	−0.483653	−	0.837712i	−0.999824	+	0.0187737i	$0.994024\pi$
$972$		0			0
$973$		0			0
$974$	2848.00			0.0936918
$975$		0			0
$976$	4304.00	−	7454.75i	0.141155	−	0.244488i
$977$	8337.00	−	14440.1i	0.273003	−	0.472856i	−0.696626	−	0.717434i	$-0.745316\pi$
$977$	8337.00	−	14440.1i	0.273003	−	0.472856i	0.969629	+	0.244579i	$0.0786497\pi$
$978$		0			0
$979$	9720.00			0.317316
$980$		0			0
$981$		0			0
$982$	−4548.00	−	7877.37i	−0.147793	−	0.255985i
$983$	−15636.0	+	27082.3i	−0.507336	+	0.878731i	0.492628	+	0.870240i	$0.336036\pi$
$983$	−15636.0	+	27082.3i	−0.507336	+	0.878731i	−0.999964	+	0.00849130i	$0.997297\pi$
$984$		0			0
$985$	−13122.0	−	22728.0i	−0.424469	−	0.735201i
$986$	−7560.00			−0.244178
$987$		0			0
$988$	3040.00			0.0978900
$989$	−4368.00	−	7565.60i	−0.140439	−	0.243248i
$990$		0			0
$991$	7964.00	−	13794.1i	0.255282	−	0.442162i	−0.709690	−	0.704514i	$-0.751165\pi$
$991$	7964.00	−	13794.1i	0.255282	−	0.442162i	0.964972	+	0.262352i	$0.0844982\pi$
$992$	1408.00	+	2438.73i	0.0450646	+	0.0780541i
$993$		0			0
$994$		0			0
$995$	9600.00			0.305870
$996$		0			0
$997$	−21007.0	+	36385.2i	−0.667300	+	1.15580i	0.311356	+	0.950293i	$0.399217\pi$
$997$	−21007.0	+	36385.2i	−0.667300	+	1.15580i	−0.978656	+	0.205505i	$0.934116\pi$
$998$	−6500.00	+	11258.3i	−0.206166	+	0.357090i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.i.361.1		2
3.2	odd	2		294.4.e.h.67.1		2
7.2	even	3	inner	882.4.g.i.667.1		2
7.3	odd	6		882.4.a.n.1.1		1
7.4	even	3		18.4.a.a.1.1		1
7.5	odd	6		882.4.g.f.667.1		2
7.6	odd	2		882.4.g.f.361.1		2
21.2	odd	6		294.4.e.h.79.1		2
21.5	even	6		294.4.e.g.79.1		2
21.11	odd	6		6.4.a.a.1.1	✓	1
21.17	even	6		294.4.a.e.1.1		1
21.20	even	2		294.4.e.g.67.1		2
28.11	odd	6		144.4.a.c.1.1		1
35.4	even	6		450.4.a.h.1.1		1
35.18	odd	12		450.4.c.e.199.1		2
35.32	odd	12		450.4.c.e.199.2		2
56.11	odd	6		576.4.a.r.1.1		1
56.53	even	6		576.4.a.q.1.1		1
63.4	even	3		162.4.c.c.55.1		2
63.11	odd	6		162.4.c.f.109.1		2
63.25	even	3		162.4.c.c.109.1		2
63.32	odd	6		162.4.c.f.55.1		2
77.32	odd	6		2178.4.a.e.1.1		1
84.11	even	6		48.4.a.c.1.1		1
84.59	odd	6		2352.4.a.e.1.1		1
105.32	even	12		150.4.c.d.49.1		2
105.53	even	12		150.4.c.d.49.2		2
105.74	odd	6		150.4.a.i.1.1		1
168.11	even	6		192.4.a.c.1.1		1
168.53	odd	6		192.4.a.i.1.1		1
231.32	even	6		726.4.a.f.1.1		1
273.116	odd	6		1014.4.a.g.1.1		1
273.200	even	12		1014.4.b.d.337.2		2
273.242	even	12		1014.4.b.d.337.1		2
336.11	even	12		768.4.d.c.385.1		2
336.53	odd	12		768.4.d.n.385.2		2
336.179	even	12		768.4.d.c.385.2		2
336.221	odd	12		768.4.d.n.385.1		2
357.305	odd	6		1734.4.a.d.1.1		1
399.284	even	6		2166.4.a.i.1.1		1
420.179	even	6		1200.4.a.b.1.1		1
420.263	odd	12		1200.4.f.j.49.2		2
420.347	odd	12		1200.4.f.j.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.4.a.a.1.1	✓	1	21.11	odd	6
18.4.a.a.1.1		1	7.4	even	3
48.4.a.c.1.1		1	84.11	even	6
144.4.a.c.1.1		1	28.11	odd	6
150.4.a.i.1.1		1	105.74	odd	6
150.4.c.d.49.1		2	105.32	even	12
150.4.c.d.49.2		2	105.53	even	12
162.4.c.c.55.1		2	63.4	even	3
162.4.c.c.109.1		2	63.25	even	3
162.4.c.f.55.1		2	63.32	odd	6
162.4.c.f.109.1		2	63.11	odd	6
192.4.a.c.1.1		1	168.11	even	6
192.4.a.i.1.1		1	168.53	odd	6
294.4.a.e.1.1		1	21.17	even	6
294.4.e.g.67.1		2	21.20	even	2
294.4.e.g.79.1		2	21.5	even	6
294.4.e.h.67.1		2	3.2	odd	2
294.4.e.h.79.1		2	21.2	odd	6
450.4.a.h.1.1		1	35.4	even	6
450.4.c.e.199.1		2	35.18	odd	12
450.4.c.e.199.2		2	35.32	odd	12
576.4.a.q.1.1		1	56.53	even	6
576.4.a.r.1.1		1	56.11	odd	6
726.4.a.f.1.1		1	231.32	even	6
768.4.d.c.385.1		2	336.11	even	12
768.4.d.c.385.2		2	336.179	even	12
768.4.d.n.385.1		2	336.221	odd	12
768.4.d.n.385.2		2	336.53	odd	12
882.4.a.n.1.1		1	7.3	odd	6
882.4.g.f.361.1		2	7.6	odd	2
882.4.g.f.667.1		2	7.5	odd	6
882.4.g.i.361.1		2	1.1	even	1	trivial
882.4.g.i.667.1		2	7.2	even	3	inner
1014.4.a.g.1.1		1	273.116	odd	6
1014.4.b.d.337.1		2	273.242	even	12
1014.4.b.d.337.2		2	273.200	even	12
1200.4.a.b.1.1		1	420.179	even	6
1200.4.f.j.49.1		2	420.347	odd	12
1200.4.f.j.49.2		2	420.263	odd	12
1734.4.a.d.1.1		1	357.305	odd	6
2166.4.a.i.1.1		1	399.284	even	6
2178.4.a.e.1.1		1	77.32	odd	6
2352.4.a.e.1.1		1	84.59	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} +8.00000 q^{8} +(6.00000 - 10.3923i) q^{10} +(6.00000 - 10.3923i) q^{11} +38.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-63.0000 + 109.119i) q^{17} +(-10.0000 - 17.3205i) q^{19} -24.0000 q^{20} -24.0000 q^{22} +(84.0000 + 145.492i) q^{23} +(44.5000 - 77.0763i) q^{25} +(-38.0000 - 65.8179i) q^{26} -30.0000 q^{29} +(44.0000 - 76.2102i) q^{31} +(-16.0000 + 27.7128i) q^{32} +252.000 q^{34} +(-127.000 - 219.970i) q^{37} +(-20.0000 + 34.6410i) q^{38} +(24.0000 + 41.5692i) q^{40} -42.0000 q^{41} -52.0000 q^{43} +(24.0000 + 41.5692i) q^{44} +(168.000 - 290.985i) q^{46} +(-48.0000 - 83.1384i) q^{47} -178.000 q^{50} +(-76.0000 + 131.636i) q^{52} +(99.0000 - 171.473i) q^{53} +72.0000 q^{55} +(30.0000 + 51.9615i) q^{58} +(-330.000 + 571.577i) q^{59} +(269.000 + 465.922i) q^{61} -176.000 q^{62} +64.0000 q^{64} +(114.000 + 197.454i) q^{65} +(-442.000 + 765.566i) q^{67} +(-252.000 - 436.477i) q^{68} -792.000 q^{71} +(-109.000 + 188.794i) q^{73} +(-254.000 + 439.941i) q^{74} +80.0000 q^{76} +(260.000 + 450.333i) q^{79} +(48.0000 - 83.1384i) q^{80} +(42.0000 + 72.7461i) q^{82} +492.000 q^{83} -756.000 q^{85} +(52.0000 + 90.0666i) q^{86} +(48.0000 - 83.1384i) q^{88} +(405.000 + 701.481i) q^{89} -672.000 q^{92} +(-96.0000 + 166.277i) q^{94} +(60.0000 - 103.923i) q^{95} +1154.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} + 6 q^{5} + 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^5 + 16 * q^8	\( 2 q - 2 q^{2} - 4 q^{4} + 6 q^{5} + 16 q^{8} + 12 q^{10} + 12 q^{11} + 76 q^{13} - 16 q^{16} - 126 q^{17} - 20 q^{19} - 48 q^{20} - 48 q^{22} + 168 q^{23} + 89 q^{25} - 76 q^{26} - 60 q^{29} + 88 q^{31} - 32 q^{32} + 504 q^{34} - 254 q^{37} - 40 q^{38} + 48 q^{40} - 84 q^{41} - 104 q^{43} + 48 q^{44} + 336 q^{46} - 96 q^{47} - 356 q^{50} - 152 q^{52} + 198 q^{53} + 144 q^{55} + 60 q^{58} - 660 q^{59} + 538 q^{61} - 352 q^{62} + 128 q^{64} + 228 q^{65} - 884 q^{67} - 504 q^{68} - 1584 q^{71} - 218 q^{73} - 508 q^{74} + 160 q^{76} + 520 q^{79} + 96 q^{80} + 84 q^{82} + 984 q^{83} - 1512 q^{85} + 104 q^{86} + 96 q^{88} + 810 q^{89} - 1344 q^{92} - 192 q^{94} + 120 q^{95} + 2308 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^5 + 16 * q^8 + 12 * q^10 + 12 * q^11 + 76 * q^13 - 16 * q^16 - 126 * q^17 - 20 * q^19 - 48 * q^20 - 48 * q^22 + 168 * q^23 + 89 * q^25 - 76 * q^26 - 60 * q^29 + 88 * q^31 - 32 * q^32 + 504 * q^34 - 254 * q^37 - 40 * q^38 + 48 * q^40 - 84 * q^41 - 104 * q^43 + 48 * q^44 + 336 * q^46 - 96 * q^47 - 356 * q^50 - 152 * q^52 + 198 * q^53 + 144 * q^55 + 60 * q^58 - 660 * q^59 + 538 * q^61 - 352 * q^62 + 128 * q^64 + 228 * q^65 - 884 * q^67 - 504 * q^68 - 1584 * q^71 - 218 * q^73 - 508 * q^74 + 160 * q^76 + 520 * q^79 + 96 * q^80 + 84 * q^82 + 984 * q^83 - 1512 * q^85 + 104 * q^86 + 96 * q^88 + 810 * q^89 - 1344 * q^92 - 192 * q^94 + 120 * q^95 + 2308 * q^97

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