LMFDB - Embedded newform 882.4.g.a.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 126)
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.a.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-11.0000 - 19.0526i) q^{5} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-11.0000 - 19.0526i) q^{5} +8.00000 q^{8} +(-22.0000 + 38.1051i) q^{10} +(13.0000 - 22.5167i) q^{11} +54.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-37.0000 + 64.0859i) q^{17} +(58.0000 + 100.459i) q^{19} +88.0000 q^{20} -52.0000 q^{22} +(-29.0000 - 50.2295i) q^{23} +(-179.500 + 310.903i) q^{25} +(-54.0000 - 93.5307i) q^{26} -208.000 q^{29} +(-126.000 + 218.238i) q^{31} +(-16.0000 + 27.7128i) q^{32} +148.000 q^{34} +(-25.0000 - 43.3013i) q^{37} +(116.000 - 200.918i) q^{38} +(-88.0000 - 152.420i) q^{40} +126.000 q^{41} +164.000 q^{43} +(52.0000 + 90.0666i) q^{44} +(-58.0000 + 100.459i) q^{46} +(222.000 + 384.515i) q^{47} +718.000 q^{50} +(-108.000 + 187.061i) q^{52} +(6.00000 - 10.3923i) q^{53} -572.000 q^{55} +(208.000 + 360.267i) q^{58} +(-62.0000 + 107.387i) q^{59} +(-81.0000 - 140.296i) q^{61} +504.000 q^{62} +64.0000 q^{64} +(-594.000 - 1028.84i) q^{65} +(430.000 - 744.782i) q^{67} +(-148.000 - 256.344i) q^{68} +238.000 q^{71} +(-73.0000 + 126.440i) q^{73} +(-50.0000 + 86.6025i) q^{74} -464.000 q^{76} +(492.000 + 852.169i) q^{79} +(-176.000 + 304.841i) q^{80} +(-126.000 - 218.238i) q^{82} +656.000 q^{83} +1628.00 q^{85} +(-164.000 - 284.056i) q^{86} +(104.000 - 180.133i) q^{88} +(477.000 + 826.188i) q^{89} +232.000 q^{92} +(444.000 - 769.031i) q^{94} +(1276.00 - 2210.10i) q^{95} -526.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} - 22 q^{5} + 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 - 22 * q^5 + 16 * q^8	$ 2 q - 2 q^{2} - 4 q^{4} - 22 q^{5} + 16 q^{8} - 44 q^{10} + 26 q^{11} + 108 q^{13} - 16 q^{16} - 74 q^{17} + 116 q^{19} + 176 q^{20} - 104 q^{22} - 58 q^{23} - 359 q^{25} - 108 q^{26} - 416 q^{29} - 252 q^{31} - 32 q^{32} + 296 q^{34} - 50 q^{37} + 232 q^{38} - 176 q^{40} + 252 q^{41} + 328 q^{43} + 104 q^{44} - 116 q^{46} + 444 q^{47} + 1436 q^{50} - 216 q^{52} + 12 q^{53} - 1144 q^{55} + 416 q^{58} - 124 q^{59} - 162 q^{61} + 1008 q^{62} + 128 q^{64} - 1188 q^{65} + 860 q^{67} - 296 q^{68} + 476 q^{71} - 146 q^{73} - 100 q^{74} - 928 q^{76} + 984 q^{79} - 352 q^{80} - 252 q^{82} + 1312 q^{83} + 3256 q^{85} - 328 q^{86} + 208 q^{88} + 954 q^{89} + 464 q^{92} + 888 q^{94} + 2552 q^{95} - 1052 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 - 22 * q^5 + 16 * q^8 - 44 * q^10 + 26 * q^11 + 108 * q^13 - 16 * q^16 - 74 * q^17 + 116 * q^19 + 176 * q^20 - 104 * q^22 - 58 * q^23 - 359 * q^25 - 108 * q^26 - 416 * q^29 - 252 * q^31 - 32 * q^32 + 296 * q^34 - 50 * q^37 + 232 * q^38 - 176 * q^40 + 252 * q^41 + 328 * q^43 + 104 * q^44 - 116 * q^46 + 444 * q^47 + 1436 * q^50 - 216 * q^52 + 12 * q^53 - 1144 * q^55 + 416 * q^58 - 124 * q^59 - 162 * q^61 + 1008 * q^62 + 128 * q^64 - 1188 * q^65 + 860 * q^67 - 296 * q^68 + 476 * q^71 - 146 * q^73 - 100 * q^74 - 928 * q^76 + 984 * q^79 - 352 * q^80 - 252 * q^82 + 1312 * q^83 + 3256 * q^85 - 328 * q^86 + 208 * q^88 + 954 * q^89 + 464 * q^92 + 888 * q^94 + 2552 * q^95 - 1052 * 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
$5$	−11.0000	−	19.0526i	−0.983870	−	1.70411i	−0.646854	−	0.762614i	$-0.723916\pi$
$5$	−11.0000	−	19.0526i	−0.983870	−	1.70411i	−0.337016	−	0.941499i	$-0.609418\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$		0			0
$10$	−22.0000	+	38.1051i	−0.695701	+	1.20499i
$11$	13.0000	−	22.5167i	0.356332	−	0.617184i	−0.631013	−	0.775772i	$-0.717361\pi$
$11$	13.0000	−	22.5167i	0.356332	−	0.617184i	0.987345	+	0.158588i	$0.0506940\pi$
$12$		0			0
$13$	54.0000			1.15207			0.576035	−	0.817425i	$-0.304599\pi$
$13$	54.0000			1.15207			0.576035	+	0.817425i	$0.304599\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−37.0000	+	64.0859i	−0.527872	+	0.914301i	0.471600	+	0.881812i	$0.343676\pi$
$17$	−37.0000	+	64.0859i	−0.527872	+	0.914301i	−0.999472	+	0.0324882i	$0.989657\pi$
$18$		0			0
$19$	58.0000	+	100.459i	0.700322	+	1.21299i	0.968353	+	0.249583i	$0.0802934\pi$
$19$	58.0000	+	100.459i	0.700322	+	1.21299i	−0.268032	+	0.963410i	$0.586373\pi$
$20$	88.0000			0.983870
$21$		0			0
$22$	−52.0000			−0.503929
$23$	−29.0000	−	50.2295i	−0.262909	−	0.455373i	0.704104	−	0.710097i	$-0.251349\pi$
$23$	−29.0000	−	50.2295i	−0.262909	−	0.455373i	−0.967014	+	0.254724i	$0.918015\pi$
$24$		0			0
$25$	−179.500	+	310.903i	−1.43600	+	2.48722i
$26$	−54.0000	−	93.5307i	−0.407318	−	0.705496i
$27$		0			0
$28$		0			0
$29$	−208.000			−1.33188			−0.665942	−	0.746004i	$-0.731970\pi$
$29$	−208.000			−1.33188			−0.665942	+	0.746004i	$0.731970\pi$
$30$		0			0
$31$	−126.000	+	218.238i	−0.730009	+	1.26441i	0.226870	+	0.973925i	$0.427151\pi$
$31$	−126.000	+	218.238i	−0.730009	+	1.26441i	−0.956879	+	0.290487i	$0.906183\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	148.000			0.746523
$35$		0			0
$36$		0			0
$37$	−25.0000	−	43.3013i	−0.111080	−	0.192397i	0.805126	−	0.593104i	$-0.202098\pi$
$37$	−25.0000	−	43.3013i	−0.111080	−	0.192397i	−0.916206	+	0.400707i	$0.868764\pi$
$38$	116.000	−	200.918i	0.495202	−	0.857715i
$39$		0			0
$40$	−88.0000	−	152.420i	−0.347851	−	0.602495i
$41$	126.000			0.479949			0.239974	−	0.970779i	$-0.422861\pi$
$41$	126.000			0.479949			0.239974	+	0.970779i	$0.422861\pi$
$42$		0			0
$43$	164.000			0.581622			0.290811	−	0.956780i	$-0.406075\pi$
$43$	164.000			0.581622			0.290811	+	0.956780i	$0.406075\pi$
$44$	52.0000	+	90.0666i	0.178166	+	0.308592i
$45$		0			0
$46$	−58.0000	+	100.459i	−0.185905	+	0.321997i
$47$	222.000	+	384.515i	0.688979	+	1.19335i	0.972168	+	0.234283i	$0.0752743\pi$
$47$	222.000	+	384.515i	0.688979	+	1.19335i	−0.283189	+	0.959064i	$0.591392\pi$
$48$		0			0
$49$		0			0
$50$	718.000			2.03081
$51$		0			0
$52$	−108.000	+	187.061i	−0.288017	+	0.498861i
$53$	6.00000	−	10.3923i	0.0155503	−	0.0269338i	−0.858146	−	0.513406i	$-0.828383\pi$
$53$	6.00000	−	10.3923i	0.0155503	−	0.0269338i	0.873696	+	0.486473i	$0.161717\pi$
$54$		0			0
$55$	−572.000			−1.40234
$56$		0			0
$57$		0			0
$58$	208.000	+	360.267i	0.470892	+	0.815609i
$59$	−62.0000	+	107.387i	−0.136809	+	0.236960i	−0.926287	−	0.376819i	$-0.877018\pi$
$59$	−62.0000	+	107.387i	−0.136809	+	0.236960i	0.789478	+	0.613779i	$0.210351\pi$
$60$		0			0
$61$	−81.0000	−	140.296i	−0.170016	−	0.294477i	0.768409	−	0.639959i	$-0.221049\pi$
$61$	−81.0000	−	140.296i	−0.170016	−	0.294477i	−0.938425	+	0.345482i	$0.887715\pi$
$62$	504.000			1.03239
$63$		0			0
$64$	64.0000			0.125000
$65$	−594.000	−	1028.84i	−1.13349	−	1.96326i
$66$		0			0
$67$	430.000	−	744.782i	0.784073	−	1.35805i	−0.145479	−	0.989361i	$-0.546472\pi$
$67$	430.000	−	744.782i	0.784073	−	1.35805i	0.929552	−	0.368692i	$-0.120194\pi$
$68$	−148.000	−	256.344i	−0.263936	−	0.457150i
$69$		0			0
$70$		0			0
$71$	238.000			0.397823			0.198911	−	0.980017i	$-0.436259\pi$
$71$	238.000			0.397823			0.198911	+	0.980017i	$0.436259\pi$
$72$		0			0
$73$	−73.0000	+	126.440i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−73.0000	+	126.440i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−50.0000	+	86.6025i	−0.0785457	+	0.136045i
$75$		0			0
$76$	−464.000			−0.700322
$77$		0			0
$78$		0			0
$79$	492.000	+	852.169i	0.700688	+	1.21363i	0.968225	+	0.250079i	$0.0804567\pi$
$79$	492.000	+	852.169i	0.700688	+	1.21363i	−0.267538	+	0.963547i	$0.586210\pi$
$80$	−176.000	+	304.841i	−0.245967	+	0.426028i
$81$		0			0
$82$	−126.000	−	218.238i	−0.169687	−	0.293907i
$83$	656.000			0.867534			0.433767	−	0.901025i	$-0.357184\pi$
$83$	656.000			0.867534			0.433767	+	0.901025i	$0.357184\pi$
$84$		0			0
$85$	1628.00			2.07743
$86$	−164.000	−	284.056i	−0.205635	−	0.356170i
$87$		0			0
$88$	104.000	−	180.133i	0.125982	−	0.218208i
$89$	477.000	+	826.188i	0.568111	+	0.983998i	0.996753	+	0.0805229i	$0.0256590\pi$
$89$	477.000	+	826.188i	0.568111	+	0.983998i	−0.428642	+	0.903475i	$0.641008\pi$
$90$		0			0
$91$		0			0
$92$	232.000			0.262909
$93$		0			0
$94$	444.000	−	769.031i	0.487182	−	0.843824i
$95$	1276.00	−	2210.10i	1.37805	−	2.38685i
$96$		0			0
$97$	−526.000			−0.550590			−0.275295	−	0.961360i	$-0.588775\pi$
$97$	−526.000			−0.550590			−0.275295	+	0.961360i	$0.588775\pi$
$98$		0			0
$99$		0			0
$100$	−718.000	−	1243.61i	−0.718000	−	1.24361i
$101$	−653.000	+	1131.03i	−0.643326	+	1.11427i	0.341359	+	0.939933i	$0.389113\pi$
$101$	−653.000	+	1131.03i	−0.643326	+	1.11427i	−0.984685	+	0.174341i	$0.944221\pi$
$102$		0			0
$103$	−254.000	−	439.941i	−0.242984	−	0.420861i	0.718579	−	0.695446i	$-0.244793\pi$
$103$	−254.000	−	439.941i	−0.242984	−	0.420861i	−0.961563	+	0.274585i	$0.911460\pi$
$104$	432.000			0.407318
$105$		0			0
$106$	−24.0000			−0.0219914
$107$	249.000	+	431.281i	0.224970	+	0.389659i	0.956310	−	0.292354i	$-0.0944384\pi$
$107$	249.000	+	431.281i	0.224970	+	0.389659i	−0.731341	+	0.682012i	$0.761105\pi$
$108$		0			0
$109$	307.000	−	531.740i	0.269773	−	0.467261i	−0.699030	−	0.715092i	$-0.746385\pi$
$109$	307.000	−	531.740i	0.269773	−	0.467261i	0.968803	+	0.247832i	$0.0797180\pi$
$110$	572.000	+	990.733i	0.495801	+	0.858752i
$111$		0			0
$112$		0			0
$113$	1232.00			1.02564			0.512818	−	0.858498i	$-0.328602\pi$
$113$	1232.00			1.02564			0.512818	+	0.858498i	$0.328602\pi$
$114$		0			0
$115$	−638.000	+	1105.05i	−0.517337	+	0.896055i
$116$	416.000	−	720.533i	0.332971	−	0.576723i
$117$		0			0
$118$	248.000			0.193477
$119$		0			0
$120$		0			0
$121$	327.500	+	567.247i	0.246056	+	0.426181i
$122$	−162.000	+	280.592i	−0.120220	+	0.208226i
$123$		0			0
$124$	−504.000	−	872.954i	−0.365004	−	0.632206i
$125$	5148.00			3.68361
$126$		0			0
$127$	−2808.00			−1.96197			−0.980983	−	0.194093i	$-0.937824\pi$
$127$	−2808.00			−1.96197			−0.980983	+	0.194093i	$0.937824\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1188.00	+	2057.68i	−0.801496	+	1.38823i
$131$	−260.000	−	450.333i	−0.173407	−	0.300350i	0.766202	−	0.642600i	$-0.222144\pi$
$131$	−260.000	−	450.333i	−0.173407	−	0.300350i	−0.939609	+	0.342250i	$0.888811\pi$
$132$		0			0
$133$		0			0
$134$	−1720.00			−1.10885
$135$		0			0
$136$	−296.000	+	512.687i	−0.186631	+	0.323254i
$137$	−1258.00	+	2178.92i	−0.784512	+	1.35882i	0.144778	+	0.989464i	$0.453753\pi$
$137$	−1258.00	+	2178.92i	−0.784512	+	1.35882i	−0.929290	+	0.369351i	$0.879580\pi$
$138$		0			0
$139$	2672.00			1.63048			0.815238	−	0.579126i	$-0.196606\pi$
$139$	2672.00			1.63048			0.815238	+	0.579126i	$0.196606\pi$
$140$		0			0
$141$		0			0
$142$	−238.000	−	412.228i	−0.140652	−	0.243616i
$143$	702.000	−	1215.90i	0.410519	−	0.711039i
$144$		0			0
$145$	2288.00	+	3962.93i	1.31040	+	2.26968i
$146$	292.000			0.165521
$147$		0			0
$148$	200.000			0.111080
$149$	−582.000	−	1008.05i	−0.319995	−	0.554248i	0.660491	−	0.750834i	$-0.270348\pi$
$149$	−582.000	−	1008.05i	−0.319995	−	0.554248i	−0.980487	+	0.196586i	$0.937015\pi$
$150$		0			0
$151$	−836.000	+	1447.99i	−0.450548	+	0.780372i	−0.998420	−	0.0561903i	$-0.982105\pi$
$151$	−836.000	+	1447.99i	−0.450548	+	0.780372i	0.547872	+	0.836562i	$0.315438\pi$
$152$	464.000	+	803.672i	0.247601	+	0.428858i
$153$		0			0
$154$		0			0
$155$	5544.00			2.87293
$156$		0			0
$157$	223.000	−	386.247i	0.113359	−	0.196343i	−0.803764	−	0.594949i	$-0.797172\pi$
$157$	223.000	−	386.247i	0.113359	−	0.196343i	0.917123	+	0.398605i	$0.130506\pi$
$158$	984.000	−	1704.34i	0.495461	−	0.858164i
$159$		0			0
$160$	704.000			0.347851
$161$		0			0
$162$		0			0
$163$	−214.000	−	370.659i	−0.102833	−	0.178112i	0.810018	−	0.586405i	$-0.199457\pi$
$163$	−214.000	−	370.659i	−0.102833	−	0.178112i	−0.912851	+	0.408293i	$0.866124\pi$
$164$	−252.000	+	436.477i	−0.119987	+	0.207824i
$165$		0			0
$166$	−656.000	−	1136.23i	−0.306720	−	0.531254i
$167$	4.00000			0.00185347			0.000926734	−	1.00000i	$-0.499705\pi$
$167$	4.00000			0.00185347			0.000926734		1.00000i	$0.499705\pi$
$168$		0			0
$169$	719.000			0.327264
$170$	−1628.00	−	2819.78i	−0.734482	−	1.27216i
$171$		0			0
$172$	−328.000	+	568.113i	−0.145406	+	0.251850i
$173$	295.000	+	510.955i	0.129644	+	0.224550i	0.923539	−	0.383505i	$-0.125283\pi$
$173$	295.000	+	510.955i	0.129644	+	0.224550i	−0.793895	+	0.608055i	$0.791950\pi$
$174$		0			0
$175$		0			0
$176$	−416.000			−0.178166
$177$		0			0
$178$	954.000	−	1652.38i	0.401715	−	0.695791i
$179$	1767.00	−	3060.53i	0.737831	−	1.27796i	−0.215639	−	0.976473i	$-0.569183\pi$
$179$	1767.00	−	3060.53i	0.737831	−	1.27796i	0.953470	−	0.301488i	$-0.0974833\pi$
$180$		0			0
$181$	−1098.00			−0.450904			−0.225452	−	0.974254i	$-0.572386\pi$
$181$	−1098.00			−0.450904			−0.225452	+	0.974254i	$0.572386\pi$
$182$		0			0
$183$		0			0
$184$	−232.000	−	401.836i	−0.0929525	−	0.160999i
$185$	−550.000	+	952.628i	−0.218577	+	0.378587i
$186$		0			0
$187$	962.000	+	1666.23i	0.376195	+	0.651588i
$188$	−1776.00			−0.688979
$189$		0			0
$190$	−5104.00			−1.94886
$191$	−2427.00	−	4203.69i	−0.919432	−	1.59250i	−0.800279	−	0.599627i	$-0.795315\pi$
$191$	−2427.00	−	4203.69i	−0.919432	−	1.59250i	−0.119153	−	0.992876i	$-0.538018\pi$
$192$		0			0
$193$	749.000	−	1297.31i	0.279348	−	0.483845i	−0.691875	−	0.722018i	$-0.743215\pi$
$193$	749.000	−	1297.31i	0.279348	−	0.483845i	0.971223	+	0.238172i	$0.0765483\pi$
$194$	526.000	+	911.059i	0.194663	+	0.337166i
$195$		0			0
$196$		0			0
$197$	−620.000			−0.224229			−0.112115	−	0.993695i	$-0.535762\pi$
$197$	−620.000			−0.224229			−0.112115	+	0.993695i	$0.535762\pi$
$198$		0			0
$199$	16.0000	−	27.7128i	0.00569955	−	0.00987191i	−0.863162	−	0.504928i	$-0.831519\pi$
$199$	16.0000	−	27.7128i	0.00569955	−	0.00987191i	0.868861	+	0.495056i	$0.164852\pi$
$200$	−1436.00	+	2487.22i	−0.507703	+	0.879367i
$201$		0			0
$202$	2612.00			0.909800
$203$		0			0
$204$		0			0
$205$	−1386.00	−	2400.62i	−0.472207	−	0.817887i
$206$	−508.000	+	879.882i	−0.171816	+	0.297594i
$207$		0			0
$208$	−432.000	−	748.246i	−0.144009	−	0.249430i
$209$	3016.00			0.998187
$210$		0			0
$211$	4268.00			1.39252			0.696259	−	0.717791i	$-0.254847\pi$
$211$	4268.00			1.39252			0.696259	+	0.717791i	$0.254847\pi$
$212$	24.0000	+	41.5692i	0.00777513	+	0.0134669i
$213$		0			0
$214$	498.000	−	862.561i	0.159077	−	0.275530i
$215$	−1804.00	−	3124.62i	−0.572241	−	0.991150i
$216$		0			0
$217$		0			0
$218$	−1228.00			−0.381517
$219$		0			0
$220$	1144.00	−	1981.47i	0.350584	−	0.607229i
$221$	−1998.00	+	3460.64i	−0.608145	+	1.05334i
$222$		0			0
$223$	−3464.00			−1.04021			−0.520104	−	0.854103i	$-0.674107\pi$
$223$	−3464.00			−1.04021			−0.520104	+	0.854103i	$0.674107\pi$
$224$		0			0
$225$		0			0
$226$	−1232.00	−	2133.89i	−0.362617	−	0.628071i
$227$	1626.00	−	2816.31i	0.475425	−	0.823460i	−0.524179	−	0.851608i	$-0.675628\pi$
$227$	1626.00	−	2816.31i	0.475425	−	0.823460i	0.999604	+	0.0281483i	$0.00896107\pi$
$228$		0			0
$229$	209.000	+	361.999i	0.0603105	+	0.104461i	0.894604	−	0.446859i	$-0.147458\pi$
$229$	209.000	+	361.999i	0.0603105	+	0.104461i	−0.834294	+	0.551320i	$0.814124\pi$
$230$	2552.00			0.731626
$231$		0			0
$232$	−1664.00			−0.470892
$233$	1042.00	+	1804.80i	0.292977	+	0.507451i	0.974512	−	0.224334i	$-0.0720207\pi$
$233$	1042.00	+	1804.80i	0.292977	+	0.507451i	−0.681535	+	0.731785i	$0.738687\pi$
$234$		0			0
$235$	4884.00	−	8459.34i	1.35573	−	2.34820i
$236$	−248.000	−	429.549i	−0.0684043	−	0.118480i
$237$		0			0
$238$		0			0
$239$	−1662.00			−0.449815			−0.224908	−	0.974380i	$-0.572208\pi$
$239$	−1662.00			−0.449815			−0.224908	+	0.974380i	$0.572208\pi$
$240$		0			0
$241$	3091.00	−	5353.77i	0.826178	−	1.43098i	−0.0748383	−	0.997196i	$-0.523844\pi$
$241$	3091.00	−	5353.77i	0.826178	−	1.43098i	0.901016	−	0.433786i	$-0.142823\pi$
$242$	655.000	−	1134.49i	0.173988	−	0.301355i
$243$		0			0
$244$	648.000			0.170016
$245$		0			0
$246$		0			0
$247$	3132.00	+	5424.78i	0.806819	+	1.39745i
$248$	−1008.00	+	1745.91i	−0.258097	+	0.447037i
$249$		0			0
$250$	−5148.00	−	8916.60i	−1.30235	−	2.25574i
$251$	−996.000			−0.250466			−0.125233	−	0.992127i	$-0.539968\pi$
$251$	−996.000			−0.250466			−0.125233	+	0.992127i	$0.539968\pi$
$252$		0			0
$253$	−1508.00			−0.374732
$254$	2808.00	+	4863.60i	0.693660	+	1.20145i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2997.00	+	5190.96i	0.727423	+	1.25993i	0.957969	+	0.286872i	$0.0926155\pi$
$257$	2997.00	+	5190.96i	0.727423	+	1.25993i	−0.230546	+	0.973061i	$0.574051\pi$
$258$		0			0
$259$		0			0
$260$	4752.00			1.13349
$261$		0			0
$262$	−520.000	+	900.666i	−0.122617	+	0.212379i
$263$	3207.00	−	5554.69i	0.751909	−	1.30234i	−0.194987	−	0.980806i	$-0.562467\pi$
$263$	3207.00	−	5554.69i	0.751909	−	1.30234i	0.946896	−	0.321539i	$-0.104200\pi$
$264$		0			0
$265$	−264.000			−0.0611977
$266$		0			0
$267$		0			0
$268$	1720.00	+	2979.13i	0.392036	+	0.679027i
$269$	−1343.00	+	2326.14i	−0.304402	+	0.527240i	−0.977128	−	0.212652i	$-0.931790\pi$
$269$	−1343.00	+	2326.14i	−0.304402	+	0.527240i	0.672726	+	0.739892i	$0.265123\pi$
$270$		0			0
$271$	2550.00	+	4416.73i	0.571592	+	0.990027i	0.996403	+	0.0847444i	$0.0270074\pi$
$271$	2550.00	+	4416.73i	0.571592	+	0.990027i	−0.424811	+	0.905282i	$0.639659\pi$
$272$	1184.00			0.263936
$273$		0			0
$274$	5032.00			1.10947
$275$	4667.00	+	8083.48i	1.02338	+	1.77255i
$276$		0			0
$277$	2213.00	−	3833.03i	0.480023	−	0.831424i	−0.519715	−	0.854340i	$-0.673962\pi$
$277$	2213.00	−	3833.03i	0.480023	−	0.831424i	0.999737	+	0.0229162i	$0.00729509\pi$
$278$	−2672.00	−	4628.04i	−0.576460	−	0.998458i
$279$		0			0
$280$		0			0
$281$	−7508.00			−1.59391			−0.796957	−	0.604036i	$-0.793558\pi$
$281$	−7508.00			−1.59391			−0.796957	+	0.604036i	$0.793558\pi$
$282$		0			0
$283$	1706.00	−	2954.88i	0.358343	−	0.620669i	−0.629341	−	0.777129i	$-0.716675\pi$
$283$	1706.00	−	2954.88i	0.358343	−	0.620669i	0.987684	+	0.156460i	$0.0500084\pi$
$284$	−476.000	+	824.456i	−0.0994556	+	0.172262i
$285$		0			0
$286$	−2808.00			−0.580561
$287$		0			0
$288$		0			0
$289$	−281.500	−	487.572i	−0.0572970	−	0.0992413i
$290$	4576.00	−	7925.86i	0.926593	−	1.60491i
$291$		0			0
$292$	−292.000	−	505.759i	−0.0585206	−	0.101361i
$293$	−4734.00			−0.943902			−0.471951	−	0.881625i	$-0.656450\pi$
$293$	−4734.00			−0.943902			−0.471951	+	0.881625i	$0.656450\pi$
$294$		0			0
$295$	2728.00			0.538408
$296$	−200.000	−	346.410i	−0.0392729	−	0.0680226i
$297$		0			0
$298$	−1164.00	+	2016.11i	−0.226271	+	0.391913i
$299$	−1566.00	−	2712.39i	−0.302890	−	0.524621i
$300$		0			0
$301$		0			0
$302$	3344.00			0.637171
$303$		0			0
$304$	928.000	−	1607.34i	0.175080	−	0.303248i
$305$	−1782.00	+	3086.51i	−0.334548	+	0.579453i
$306$		0			0
$307$	−5836.00			−1.08494			−0.542472	−	0.840074i	$-0.682512\pi$
$307$	−5836.00			−1.08494			−0.542472	+	0.840074i	$0.682512\pi$
$308$		0			0
$309$		0			0
$310$	−5544.00	−	9602.49i	−1.01574	−	1.75931i
$311$	−2810.00	+	4867.06i	−0.512349	+	0.887414i	0.487549	+	0.873096i	$0.337891\pi$
$311$	−2810.00	+	4867.06i	−0.512349	+	0.887414i	−0.999897	+	0.0143184i	$0.995442\pi$
$312$		0			0
$313$	3041.00	+	5267.17i	0.549161	+	0.951175i	0.998332	+	0.0577294i	$0.0183861\pi$
$313$	3041.00	+	5267.17i	0.549161	+	0.951175i	−0.449171	+	0.893446i	$0.648281\pi$
$314$	−892.000			−0.160314
$315$		0			0
$316$	−3936.00			−0.700688
$317$	−3654.00	−	6328.91i	−0.647410	−	1.12135i	−0.983739	−	0.179603i	$-0.942519\pi$
$317$	−3654.00	−	6328.91i	−0.647410	−	1.12135i	0.336329	−	0.941745i	$-0.390815\pi$
$318$		0			0
$319$	−2704.00	+	4683.47i	−0.474592	+	0.822018i
$320$	−704.000	−	1219.36i	−0.122984	−	0.213014i
$321$		0			0
$322$		0			0
$323$	−8584.00			−1.47872
$324$		0			0
$325$	−9693.00	+	16788.8i	−1.65437	+	2.86546i
$326$	−428.000	+	741.318i	−0.0727139	+	0.125944i
$327$		0			0
$328$	1008.00			0.169687
$329$		0			0
$330$		0			0
$331$	4010.00	+	6945.52i	0.665890	+	1.15336i	0.979043	+	0.203652i	$0.0652813\pi$
$331$	4010.00	+	6945.52i	0.665890	+	1.15336i	−0.313153	+	0.949703i	$0.601385\pi$
$332$	−1312.00	+	2272.45i	−0.216884	+	0.375653i
$333$		0			0
$334$	−4.00000	−	6.92820i	−0.000655300	−	0.00113501i
$335$	−18920.0			−3.08570
$336$		0			0
$337$	4590.00			0.741938			0.370969	−	0.928645i	$-0.379026\pi$
$337$	4590.00			0.741938			0.370969	+	0.928645i	$0.379026\pi$
$338$	−719.000	−	1245.34i	−0.115705	−	0.200408i
$339$		0			0
$340$	−3256.00	+	5639.56i	−0.519357	+	0.899553i
$341$	3276.00	+	5674.20i	0.520250	+	0.901100i
$342$		0			0
$343$		0			0
$344$	1312.00			0.205635
$345$		0			0
$346$	590.000	−	1021.91i	0.0916722	−	0.158781i
$347$	−3273.00	+	5669.00i	−0.506351	+	0.877026i	0.493622	+	0.869677i	$0.335673\pi$
$347$	−3273.00	+	5669.00i	−0.506351	+	0.877026i	−0.999973	+	0.00734926i	$0.997661\pi$
$348$		0			0
$349$	7994.00			1.22610			0.613050	−	0.790044i	$-0.289942\pi$
$349$	7994.00			1.22610			0.613050	+	0.790044i	$0.289942\pi$
$350$		0			0
$351$		0			0
$352$	416.000	+	720.533i	0.0629911	+	0.109104i
$353$	−2325.00	+	4027.02i	−0.350559	+	0.607186i	−0.986347	−	0.164678i	$-0.947342\pi$
$353$	−2325.00	+	4027.02i	−0.350559	+	0.607186i	0.635789	+	0.771863i	$0.280675\pi$
$354$		0			0
$355$	−2618.00	−	4534.51i	−0.391406	−	0.677935i
$356$	−3816.00			−0.568111
$357$		0			0
$358$	−7068.00			−1.04345
$359$	173.000	+	299.645i	0.0254334	+	0.0440519i	0.878462	−	0.477812i	$-0.158570\pi$
$359$	173.000	+	299.645i	0.0254334	+	0.0440519i	−0.853029	+	0.521864i	$0.825237\pi$
$360$		0			0
$361$	−3298.50	+	5713.17i	−0.480901	+	0.832945i
$362$	1098.00	+	1901.79i	0.159419	+	0.276121i
$363$		0			0
$364$		0			0
$365$	3212.00			0.460613
$366$		0			0
$367$	−3392.00	+	5875.12i	−0.482455	+	0.835636i	−0.999797	−	0.0201422i	$-0.993588\pi$
$367$	−3392.00	+	5875.12i	−0.482455	+	0.835636i	0.517342	+	0.855779i	$0.326921\pi$
$368$	−464.000	+	803.672i	−0.0657274	+	0.113843i
$369$		0			0
$370$	2200.00			0.309115
$371$		0			0
$372$		0			0
$373$	3049.00	+	5281.02i	0.423247	+	0.733086i	0.996255	−	0.0864642i	$-0.0275568\pi$
$373$	3049.00	+	5281.02i	0.423247	+	0.733086i	−0.573008	+	0.819550i	$0.694223\pi$
$374$	1924.00	−	3332.47i	0.266010	−	0.460743i
$375$		0			0
$376$	1776.00	+	3076.12i	0.243591	+	0.421912i
$377$	−11232.0			−1.53442
$378$		0			0
$379$	−2660.00			−0.360515			−0.180257	−	0.983619i	$-0.557693\pi$
$379$	−2660.00			−0.360515			−0.180257	+	0.983619i	$0.557693\pi$
$380$	5104.00	+	8840.39i	0.689025	+	1.19343i
$381$		0			0
$382$	−4854.00	+	8407.37i	−0.650137	+	1.12607i
$383$	380.000	+	658.179i	0.0506974	+	0.0878104i	0.890260	−	0.455452i	$-0.150522\pi$
$383$	380.000	+	658.179i	0.0506974	+	0.0878104i	−0.839563	+	0.543262i	$0.817189\pi$
$384$		0			0
$385$		0			0
$386$	−2996.00			−0.395058
$387$		0			0
$388$	1052.00	−	1822.12i	0.137647	−	0.238412i
$389$	−52.0000	+	90.0666i	−0.00677765	+	0.0117392i	−0.869394	−	0.494119i	$-0.835491\pi$
$389$	−52.0000	+	90.0666i	−0.00677765	+	0.0117392i	0.862617	+	0.505858i	$0.168824\pi$
$390$		0			0
$391$	4292.00			0.555130
$392$		0			0
$393$		0			0
$394$	620.000	+	1073.87i	0.0792770	+	0.137312i
$395$	10824.0	−	18747.7i	1.37877	−	2.38810i
$396$		0			0
$397$	2199.00	+	3808.78i	0.277997	+	0.481504i	0.970887	−	0.239539i	$-0.0769963\pi$
$397$	2199.00	+	3808.78i	0.277997	+	0.481504i	−0.692890	+	0.721043i	$0.743663\pi$
$398$	−64.0000			−0.00806038
$399$		0			0
$400$	5744.00			0.718000
$401$	6618.00	+	11462.7i	0.824157	+	1.42748i	0.902561	+	0.430561i	$0.141684\pi$
$401$	6618.00	+	11462.7i	0.824157	+	1.42748i	−0.0784040	+	0.996922i	$0.524982\pi$
$402$		0			0
$403$	−6804.00	+	11784.9i	−0.841021	+	1.45669i
$404$	−2612.00	−	4524.12i	−0.321663	−	0.557137i
$405$		0			0
$406$		0			0
$407$	−1300.00			−0.158326
$408$		0			0
$409$	−4745.00	+	8218.58i	−0.573656	+	0.993601i	0.422531	+	0.906349i	$0.361142\pi$
$409$	−4745.00	+	8218.58i	−0.573656	+	0.993601i	−0.996186	+	0.0872520i	$0.972191\pi$
$410$	−2772.00	+	4801.24i	−0.333901	+	0.578333i
$411$		0			0
$412$	2032.00			0.242984
$413$		0			0
$414$		0			0
$415$	−7216.00	−	12498.5i	−0.853541	−	1.47838i
$416$	−864.000	+	1496.49i	−0.101830	+	0.176374i
$417$		0			0
$418$	−3016.00	−	5223.87i	−0.352912	−	0.611262i
$419$	4236.00			0.493895			0.246948	−	0.969029i	$-0.420572\pi$
$419$	4236.00			0.493895			0.246948	+	0.969029i	$0.420572\pi$
$420$		0			0
$421$	918.000			0.106272			0.0531361	−	0.998587i	$-0.483078\pi$
$421$	918.000			0.106272			0.0531361	+	0.998587i	$0.483078\pi$
$422$	−4268.00	−	7392.39i	−0.492329	−	0.852739i
$423$		0			0
$424$	48.0000	−	83.1384i	0.00549784	−	0.00952255i
$425$	−13283.0	−	23006.8i	−1.51605	−	2.62587i
$426$		0			0
$427$		0			0
$428$	−1992.00			−0.224970
$429$		0			0
$430$	−3608.00	+	6249.24i	−0.404635	+	0.700849i
$431$	−5907.00	+	10231.2i	−0.660163	+	1.14344i	0.320410	+	0.947279i	$0.396179\pi$
$431$	−5907.00	+	10231.2i	−0.660163	+	1.14344i	−0.980573	+	0.196157i	$0.937154\pi$
$432$		0			0
$433$	8374.00			0.929397			0.464698	−	0.885469i	$-0.346163\pi$
$433$	8374.00			0.929397			0.464698	+	0.885469i	$0.346163\pi$
$434$		0			0
$435$		0			0
$436$	1228.00	+	2126.96i	0.134887	+	0.233630i
$437$	3364.00	−	5826.62i	0.368242	−	0.637815i
$438$		0			0
$439$	1920.00	+	3325.54i	0.208739	+	0.361547i	0.951318	−	0.308212i	$-0.0997306\pi$
$439$	1920.00	+	3325.54i	0.208739	+	0.361547i	−0.742578	+	0.669759i	$0.766397\pi$
$440$	−4576.00			−0.495801
$441$		0			0
$442$	7992.00			0.860047
$443$	5083.00	+	8804.01i	0.545148	+	0.944224i	0.998598	+	0.0529423i	$0.0168599\pi$
$443$	5083.00	+	8804.01i	0.545148	+	0.944224i	−0.453449	+	0.891282i	$0.649807\pi$
$444$		0			0
$445$	10494.0	−	18176.1i	1.11790	−	1.93625i
$446$	3464.00	+	5999.82i	0.367769	+	0.636995i
$447$		0			0
$448$		0			0
$449$	−8200.00			−0.861875			−0.430938	−	0.902382i	$-0.641817\pi$
$449$	−8200.00			−0.861875			−0.430938	+	0.902382i	$0.641817\pi$
$450$		0			0
$451$	1638.00	−	2837.10i	0.171021	−	0.296217i
$452$	−2464.00	+	4267.77i	−0.256409	+	0.444113i
$453$		0			0
$454$	−6504.00			−0.672352
$455$		0			0
$456$		0			0
$457$	3037.00	+	5260.24i	0.310864	+	0.538432i	0.978550	−	0.206011i	$-0.0660483\pi$
$457$	3037.00	+	5260.24i	0.310864	+	0.538432i	−0.667686	+	0.744443i	$0.732715\pi$
$458$	418.000	−	723.997i	0.0426460	−	0.0738650i
$459$		0			0
$460$	−2552.00	−	4420.19i	−0.258669	−	0.448027i
$461$	−2006.00			−0.202665			−0.101333	−	0.994853i	$-0.532311\pi$
$461$	−2006.00			−0.202665			−0.101333	+	0.994853i	$0.532311\pi$
$462$		0			0
$463$	−3728.00			−0.374201			−0.187100	−	0.982341i	$-0.559909\pi$
$463$	−3728.00			−0.374201			−0.187100	+	0.982341i	$0.559909\pi$
$464$	1664.00	+	2882.13i	0.166485	+	0.288361i
$465$		0			0
$466$	2084.00	−	3609.59i	0.207166	−	0.358822i
$467$	3190.00	+	5525.24i	0.316093	+	0.547490i	0.979669	−	0.200619i	$-0.0642954\pi$
$467$	3190.00	+	5525.24i	0.316093	+	0.547490i	−0.663576	+	0.748109i	$0.730962\pi$
$468$		0			0
$469$		0			0
$470$	−19536.0			−1.91729
$471$		0			0
$472$	−496.000	+	859.097i	−0.0483692	+	0.0837779i
$473$	2132.00	−	3692.73i	0.207250	−	0.358968i
$474$		0			0
$475$	−41644.0			−4.02265
$476$		0			0
$477$		0			0
$478$	1662.00	+	2878.67i	0.159034	+	0.275454i
$479$	−8590.00	+	14878.3i	−0.819389	+	1.41922i	0.0867448	+	0.996231i	$0.472354\pi$
$479$	−8590.00	+	14878.3i	−0.819389	+	1.41922i	−0.906133	+	0.422992i	$0.860980\pi$
$480$		0			0
$481$	−1350.00	−	2338.27i	−0.127972	−	0.221655i
$482$	−12364.0			−1.16839
$483$		0			0
$484$	−2620.00			−0.246056
$485$	5786.00	+	10021.6i	0.541709	+	0.938267i
$486$		0			0
$487$	1364.00	−	2362.52i	0.126917	−	0.219827i	−0.795563	−	0.605870i	$-0.792825\pi$
$487$	1364.00	−	2362.52i	0.126917	−	0.219827i	0.922481	+	0.386043i	$0.126158\pi$
$488$	−648.000	−	1122.37i	−0.0601098	−	0.104113i
$489$		0			0
$490$		0			0
$491$	−2574.00			−0.236585			−0.118292	−	0.992979i	$-0.537742\pi$
$491$	−2574.00			−0.236585			−0.118292	+	0.992979i	$0.537742\pi$
$492$		0			0
$493$	7696.00	−	13329.9i	0.703064	−	1.21774i
$494$	6264.00	−	10849.6i	0.570507	−	0.988148i
$495$		0			0
$496$	4032.00			0.365004
$497$		0			0
$498$		0			0
$499$	3742.00	+	6481.33i	0.335701	+	0.581452i	0.983619	−	0.180258i	$-0.0576934\pi$
$499$	3742.00	+	6481.33i	0.335701	+	0.581452i	−0.647918	+	0.761710i	$0.724360\pi$
$500$	−10296.0	+	17833.2i	−0.920902	+	1.59505i
$501$		0			0
$502$	996.000	+	1725.12i	0.0885531	+	0.153378i
$503$	7920.00			0.702058			0.351029	−	0.936365i	$-0.385832\pi$
$503$	7920.00			0.702058			0.351029	+	0.936365i	$0.385832\pi$
$504$		0			0
$505$	28732.0			2.53180
$506$	1508.00	+	2611.93i	0.132488	+	0.229475i
$507$		0			0
$508$	5616.00	−	9727.20i	0.490492	−	0.849556i
$509$	−3627.00	−	6282.15i	−0.315843	−	0.547056i	0.663774	−	0.747934i	$-0.268954\pi$
$509$	−3627.00	−	6282.15i	−0.315843	−	0.547056i	−0.979616	+	0.200878i	$0.935621\pi$
$510$		0			0
$511$		0			0
$512$	512.000			0.0441942
$513$		0			0
$514$	5994.00	−	10381.9i	0.514366	−	0.890908i
$515$	−5588.00	+	9678.70i	−0.478130	+	0.828145i
$516$		0			0
$517$	11544.0			0.982020
$518$		0			0
$519$		0			0
$520$	−4752.00	−	8230.71i	−0.400748	−	0.694116i
$521$	8931.00	−	15468.9i	0.751006	−	1.30078i	−0.196329	−	0.980538i	$-0.562902\pi$
$521$	8931.00	−	15468.9i	0.751006	−	1.30078i	0.947335	−	0.320243i	$-0.103765\pi$
$522$		0			0
$523$	−296.000	−	512.687i	−0.0247479	−	0.0428647i	0.853386	−	0.521279i	$-0.174545\pi$
$523$	−296.000	−	512.687i	−0.0247479	−	0.0428647i	−0.878134	+	0.478415i	$0.841212\pi$
$524$	2080.00			0.173407
$525$		0			0
$526$	−12828.0			−1.06336
$527$	−9324.00	−	16149.6i	−0.770702	−	1.33489i
$528$		0			0
$529$	4401.50	−	7623.62i	0.361757	−	0.626582i
$530$	264.000	+	457.261i	0.0216367	+	0.0374758i
$531$		0			0
$532$		0			0
$533$	6804.00			0.552934
$534$		0			0
$535$	5478.00	−	9488.17i	0.442681	−	0.766747i
$536$	3440.00	−	5958.25i	0.277212	−	0.480144i
$537$		0			0
$538$	5372.00			0.430490
$539$		0			0
$540$		0			0
$541$	3201.00	+	5544.29i	0.254384	+	0.440606i	0.964728	−	0.263249i	$-0.0847940\pi$
$541$	3201.00	+	5544.29i	0.254384	+	0.440606i	−0.710344	+	0.703855i	$0.751461\pi$
$542$	5100.00	−	8833.46i	0.404177	−	0.700055i
$543$		0			0
$544$	−1184.00	−	2050.75i	−0.0933154	−	0.161627i
$545$	−13508.0			−1.06169
$546$		0			0
$547$	−8988.00			−0.702558			−0.351279	−	0.936271i	$-0.614253\pi$
$547$	−8988.00			−0.702558			−0.351279	+	0.936271i	$0.614253\pi$
$548$	−5032.00	−	8715.68i	−0.392256	−	0.679408i
$549$		0			0
$550$	9334.00	−	16167.0i	0.723642	−	1.25338i
$551$	−12064.0	−	20895.5i	−0.932747	−	1.61557i
$552$		0			0
$553$		0			0
$554$	−8852.00			−0.678855
$555$		0			0
$556$	−5344.00	+	9256.08i	−0.407619	+	0.706017i
$557$	1622.00	−	2809.39i	0.123387	−	0.213712i	−0.797715	−	0.603035i	$-0.793958\pi$
$557$	1622.00	−	2809.39i	0.123387	−	0.213712i	0.921101	+	0.389323i	$0.127291\pi$
$558$		0			0
$559$	8856.00			0.670070
$560$		0			0
$561$		0			0
$562$	7508.00	+	13004.2i	0.563534	+	0.976069i
$563$	−4906.00	+	8497.44i	−0.367253	+	0.636100i	−0.989135	−	0.147010i	$-0.953035\pi$
$563$	−4906.00	+	8497.44i	−0.367253	+	0.636100i	0.621882	+	0.783111i	$0.286368\pi$
$564$		0			0
$565$	−13552.0	−	23472.8i	−1.00909	−	1.74780i
$566$	−6824.00			−0.506774
$567$		0			0
$568$	1904.00			0.140652
$569$	−6078.00	−	10527.4i	−0.447808	−	0.775627i	0.550435	−	0.834878i	$-0.314462\pi$
$569$	−6078.00	−	10527.4i	−0.447808	−	0.775627i	−0.998243	+	0.0592513i	$0.981129\pi$
$570$		0			0
$571$	−3438.00	+	5954.79i	−0.251972	+	0.436428i	−0.964069	−	0.265653i	$-0.914412\pi$
$571$	−3438.00	+	5954.79i	−0.251972	+	0.436428i	0.712097	+	0.702081i	$0.247746\pi$
$572$	2808.00	+	4863.60i	0.205259	+	0.355520i
$573$		0			0
$574$		0			0
$575$	20822.0			1.51015
$576$		0			0
$577$	10001.0	−	17322.2i	0.721572	−	1.24980i	−0.238797	−	0.971069i	$-0.576753\pi$
$577$	10001.0	−	17322.2i	0.721572	−	1.24980i	0.960369	−	0.278730i	$-0.0899135\pi$
$578$	−563.000	+	975.145i	−0.0405151	+	0.0701742i
$579$		0			0
$580$	−18304.0			−1.31040
$581$		0			0
$582$		0			0
$583$	−156.000	−	270.200i	−0.0110821	−	0.0191947i
$584$	−584.000	+	1011.52i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	4734.00	+	8199.53i	0.333720	+	0.578019i
$587$	18404.0			1.29406			0.647031	−	0.762464i	$-0.276010\pi$
$587$	18404.0			1.29406			0.647031	+	0.762464i	$0.276010\pi$
$588$		0			0
$589$	−29232.0			−2.04496
$590$	−2728.00	−	4725.03i	−0.190356	−	0.329706i
$591$		0			0
$592$	−400.000	+	692.820i	−0.0277701	+	0.0480992i
$593$	4923.00	+	8526.89i	0.340916	+	0.590484i	0.984603	−	0.174805i	$-0.0559294\pi$
$593$	4923.00	+	8526.89i	0.340916	+	0.590484i	−0.643687	+	0.765289i	$0.722596\pi$
$594$		0			0
$595$		0			0
$596$	4656.00			0.319995
$597$		0			0
$598$	−3132.00	+	5424.78i	−0.214176	+	0.370963i
$599$	4617.00	−	7996.88i	0.314934	−	0.545482i	−0.664489	−	0.747298i	$-0.731351\pi$
$599$	4617.00	−	7996.88i	0.314934	−	0.545482i	0.979423	+	0.201816i	$0.0646843\pi$
$600$		0			0
$601$	1510.00			0.102486			0.0512431	−	0.998686i	$-0.483682\pi$
$601$	1510.00			0.102486			0.0512431	+	0.998686i	$0.483682\pi$
$602$		0			0
$603$		0			0
$604$	−3344.00	−	5791.98i	−0.225274	−	0.390186i
$605$	7205.00	−	12479.4i	0.484173	−	0.838613i
$606$		0			0
$607$	8772.00	+	15193.5i	0.586564	+	1.01596i	0.994678	+	0.103028i	$0.0328532\pi$
$607$	8772.00	+	15193.5i	0.586564	+	1.01596i	−0.408114	+	0.912931i	$0.633813\pi$
$608$	−3712.00			−0.247601
$609$		0			0
$610$	7128.00			0.473122
$611$	11988.0	+	20763.8i	0.793752	+	1.37482i
$612$		0			0
$613$	−4623.00	+	8007.27i	−0.304602	+	0.527587i	−0.977173	−	0.212446i	$-0.931857\pi$
$613$	−4623.00	+	8007.27i	−0.304602	+	0.527587i	0.672570	+	0.740033i	$0.265190\pi$
$614$	5836.00	+	10108.2i	0.383586	+	0.664390i
$615$		0			0
$616$		0			0
$617$	29212.0			1.90605			0.953023	−	0.302897i	$-0.0979537\pi$
$617$	29212.0			1.90605			0.953023	+	0.302897i	$0.0979537\pi$
$618$		0			0
$619$	3548.00	−	6145.32i	0.230382	−	0.399032i	−0.727539	−	0.686066i	$-0.759336\pi$
$619$	3548.00	−	6145.32i	0.230382	−	0.399032i	0.957920	+	0.287034i	$0.0926693\pi$
$620$	−11088.0	+	19205.0i	−0.718234	+	1.24402i
$621$		0			0
$622$	11240.0			0.724571
$623$		0			0
$624$		0			0
$625$	−34190.5	−	59219.7i	−2.18819	−	3.79006i
$626$	6082.00	−	10534.3i	0.388316	−	0.672582i
$627$		0			0
$628$	892.000	+	1544.99i	0.0566794	+	0.0981716i
$629$	3700.00			0.234545
$630$		0			0
$631$	488.000			0.0307876			0.0153938	−	0.999882i	$-0.495100\pi$
$631$	488.000			0.0307876			0.0153938	+	0.999882i	$0.495100\pi$
$632$	3936.00	+	6817.35i	0.247730	+	0.429082i
$633$		0			0
$634$	−7308.00	+	12657.8i	−0.457788	+	0.792913i
$635$	30888.0	+	53499.6i	1.93032	+	3.34341i
$636$		0			0
$637$		0			0
$638$	10816.0			0.671175
$639$		0			0
$640$	−1408.00	+	2438.73i	−0.0869626	+	0.150624i
$641$	4378.00	−	7582.92i	0.269767	−	0.467250i	−0.699035	−	0.715088i	$-0.746387\pi$
$641$	4378.00	−	7582.92i	0.269767	−	0.467250i	0.968802	+	0.247838i	$0.0797200\pi$
$642$		0			0
$643$	3364.00			0.206319			0.103160	−	0.994665i	$-0.467105\pi$
$643$	3364.00			0.206319			0.103160	+	0.994665i	$0.467105\pi$
$644$		0			0
$645$		0			0
$646$	8584.00	+	14867.9i	0.522806	+	0.905527i
$647$	−10902.0	+	18882.8i	−0.662445	+	1.14739i	0.317526	+	0.948249i	$0.397148\pi$
$647$	−10902.0	+	18882.8i	−0.662445	+	1.14739i	−0.979971	+	0.199139i	$0.936186\pi$
$648$		0			0
$649$	1612.00	+	2792.07i	0.0974985	+	0.168872i
$650$	38772.0			2.33964
$651$		0			0
$652$	1712.00			0.102833
$653$	6744.00	+	11681.0i	0.404155	+	0.700017i	0.994223	−	0.107337i	$-0.0342324\pi$
$653$	6744.00	+	11681.0i	0.404155	+	0.700017i	−0.590068	+	0.807354i	$0.700899\pi$
$654$		0			0
$655$	−5720.00	+	9907.33i	−0.341220	+	0.591010i
$656$	−1008.00	−	1745.91i	−0.0599936	−	0.103912i
$657$		0			0
$658$		0			0
$659$	−28946.0			−1.71104			−0.855521	−	0.517769i	$-0.826763\pi$
$659$	−28946.0			−1.71104			−0.855521	+	0.517769i	$0.826763\pi$
$660$		0			0
$661$	−10321.0	+	17876.5i	−0.607323	+	1.05191i	0.384357	+	0.923185i	$0.374423\pi$
$661$	−10321.0	+	17876.5i	−0.607323	+	1.05191i	−0.991680	+	0.128729i	$0.958910\pi$
$662$	8020.00	−	13891.0i	0.470855	−	0.815545i
$663$		0			0
$664$	5248.00			0.306720
$665$		0			0
$666$		0			0
$667$	6032.00	+	10447.7i	0.350165	+	0.606503i
$668$	−8.00000	+	13.8564i	−0.000463367	+	0.000802576i
$669$		0			0
$670$	18920.0	+	32770.4i	1.09096	+	1.88960i
$671$	−4212.00			−0.242329
$672$		0			0
$673$	−17602.0			−1.00818			−0.504092	−	0.863650i	$-0.668173\pi$
$673$	−17602.0			−1.00818			−0.504092	+	0.863650i	$0.668173\pi$
$674$	−4590.00	−	7950.11i	−0.262315	−	0.454343i
$675$		0			0
$676$	−1438.00	+	2490.69i	−0.0818161	+	0.141710i
$677$	−2133.00	−	3694.46i	−0.121090	−	0.209734i	0.799108	−	0.601188i	$-0.205306\pi$
$677$	−2133.00	−	3694.46i	−0.121090	−	0.209734i	−0.920198	+	0.391454i	$0.871972\pi$
$678$		0			0
$679$		0			0
$680$	13024.0			0.734482
$681$		0			0
$682$	6552.00	−	11348.4i	0.367873	−	0.637174i
$683$	−13437.0	+	23273.6i	−0.752786	+	1.30386i	0.193682	+	0.981064i	$0.437957\pi$
$683$	−13437.0	+	23273.6i	−0.752786	+	1.30386i	−0.946468	+	0.322798i	$0.895376\pi$
$684$		0			0
$685$	55352.0			3.08743
$686$		0			0
$687$		0			0
$688$	−1312.00	−	2272.45i	−0.0727028	−	0.125925i
$689$	324.000	−	561.184i	0.0179150	−	0.0310296i
$690$		0			0
$691$	−8564.00	−	14833.3i	−0.471476	−	0.816620i	0.527992	−	0.849250i	$-0.322945\pi$
$691$	−8564.00	−	14833.3i	−0.471476	−	0.816620i	−0.999468	+	0.0326293i	$0.989612\pi$
$692$	−2360.00			−0.129644
$693$		0			0
$694$	13092.0			0.716089
$695$	−29392.0	−	50908.4i	−1.60418	−	2.77851i
$696$		0			0
$697$	−4662.00	+	8074.82i	−0.253351	+	0.438817i
$698$	−7994.00	−	13846.0i	−0.433492	−	0.750830i
$699$		0			0
$700$		0			0
$701$	−11968.0			−0.644829			−0.322414	−	0.946599i	$-0.604494\pi$
$701$	−11968.0			−0.644829			−0.322414	+	0.946599i	$0.604494\pi$
$702$		0			0
$703$	2900.00	−	5022.95i	0.155584	−	0.269479i
$704$	832.000	−	1441.07i	0.0445414	−	0.0771481i
$705$		0			0
$706$	9300.00			0.495765
$707$		0			0
$708$		0			0
$709$	2639.00	+	4570.88i	0.139788	+	0.242120i	0.927416	−	0.374031i	$-0.122025\pi$
$709$	2639.00	+	4570.88i	0.139788	+	0.242120i	−0.787628	+	0.616151i	$0.788691\pi$
$710$	−5236.00	+	9069.02i	−0.276766	+	0.479372i
$711$		0			0
$712$	3816.00	+	6609.51i	0.200858	+	0.347896i
$713$	14616.0			0.767705
$714$		0			0
$715$	−30888.0			−1.61559
$716$	7068.00	+	12242.1i	0.368916	+	0.638981i
$717$		0			0
$718$	346.000	−	599.290i	0.0179841	−	0.0311494i
$719$	−3360.00	−	5819.69i	−0.174279	−	0.301861i	0.765632	−	0.643278i	$-0.222426\pi$
$719$	−3360.00	−	5819.69i	−0.174279	−	0.301861i	−0.939912	+	0.341418i	$0.889093\pi$
$720$		0			0
$721$		0			0
$722$	13194.0			0.680097
$723$		0			0
$724$	2196.00	−	3803.58i	0.112726	−	0.195247i
$725$	37336.0	−	64667.8i	1.91259	−	3.31269i
$726$		0			0
$727$	−16804.0			−0.857257			−0.428629	−	0.903481i	$-0.641003\pi$
$727$	−16804.0			−0.857257			−0.428629	+	0.903481i	$0.641003\pi$
$728$		0			0
$729$		0			0
$730$	−3212.00	−	5563.35i	−0.162851	−	0.282067i
$731$	−6068.00	+	10510.1i	−0.307022	+	0.531778i
$732$		0			0
$733$	13761.0	+	23834.8i	0.693416	+	1.20103i	0.970712	+	0.240248i	$0.0772286\pi$
$733$	13761.0	+	23834.8i	0.693416	+	1.20103i	−0.277295	+	0.960785i	$0.589438\pi$
$734$	13568.0			0.682294
$735$		0			0
$736$	1856.00			0.0929525
$737$	−11180.0	−	19364.3i	−0.558780	−	0.967835i
$738$		0			0
$739$	−10566.0	+	18300.8i	−0.525949	+	0.910971i	0.473594	+	0.880743i	$0.342957\pi$
$739$	−10566.0	+	18300.8i	−0.525949	+	0.910971i	−0.999543	+	0.0302276i	$0.990377\pi$
$740$	−2200.00	−	3810.51i	−0.109289	−	0.189294i
$741$		0			0
$742$		0			0
$743$	30.0000			0.00148128			0.000740641	−	1.00000i	$-0.499764\pi$
$743$	30.0000			0.00148128			0.000740641		1.00000i	$0.499764\pi$
$744$		0			0
$745$	−12804.0	+	22177.2i	−0.629667	+	1.09062i
$746$	6098.00	−	10562.0i	0.299281	−	0.518370i
$747$		0			0
$748$	−7696.00			−0.376195
$749$		0			0
$750$		0			0
$751$	7740.00	+	13406.1i	0.376081	+	0.651391i	0.990488	−	0.137598i	$-0.0439382\pi$
$751$	7740.00	+	13406.1i	0.376081	+	0.651391i	−0.614407	+	0.788989i	$0.710605\pi$
$752$	3552.00	−	6152.24i	0.172245	−	0.298337i
$753$		0			0
$754$	11232.0	+	19454.4i	0.542500	+	0.939638i
$755$	36784.0			1.77312
$756$		0			0
$757$	28770.0			1.38133			0.690663	−	0.723177i	$-0.257319\pi$
$757$	28770.0			1.38133			0.690663	+	0.723177i	$0.257319\pi$
$758$	2660.00	+	4607.26i	0.127461	+	0.220769i
$759$		0			0
$760$	10208.0	−	17680.8i	0.487215	−	0.843880i
$761$	6209.00	+	10754.3i	0.295764	+	0.512278i	0.975162	−	0.221492i	$-0.0710926\pi$
$761$	6209.00	+	10754.3i	0.295764	+	0.512278i	−0.679399	+	0.733769i	$0.737759\pi$
$762$		0			0
$763$		0			0
$764$	19416.0			0.919432
$765$		0			0
$766$	760.000	−	1316.36i	0.0358485	−	0.0620913i
$767$	−3348.00	+	5798.91i	−0.157613	+	0.272994i
$768$		0			0
$769$	−12346.0			−0.578944			−0.289472	−	0.957186i	$-0.593480\pi$
$769$	−12346.0			−0.578944			−0.289472	+	0.957186i	$0.593480\pi$
$770$		0			0
$771$		0			0
$772$	2996.00	+	5189.22i	0.139674	+	0.241923i
$773$	−19049.0	+	32993.8i	−0.886345	+	1.53520i	−0.0421813	+	0.999110i	$0.513431\pi$
$773$	−19049.0	+	32993.8i	−0.886345	+	1.53520i	−0.844164	+	0.536085i	$0.819903\pi$
$774$		0			0
$775$	−45234.0	−	78347.6i	−2.09658	−	3.63139i
$776$	−4208.00			−0.194663
$777$		0			0
$778$	208.000			0.00958504
$779$	7308.00	+	12657.8i	0.336118	+	0.582174i
$780$		0			0
$781$	3094.00	−	5358.97i	0.141757	−	0.245530i
$782$	−4292.00	−	7433.96i	−0.196268	−	0.339946i
$783$		0			0
$784$		0			0
$785$	−9812.00			−0.446121
$786$		0			0
$787$	6912.00	−	11971.9i	0.313070	−	0.542253i	−0.665955	−	0.745992i	$-0.731976\pi$
$787$	6912.00	−	11971.9i	0.313070	−	0.542253i	0.979025	+	0.203738i	$0.0653092\pi$
$788$	1240.00	−	2147.74i	0.0560573	−	0.0970941i
$789$		0			0
$790$	−43296.0			−1.94988
$791$		0			0
$792$		0			0
$793$	−4374.00	−	7575.99i	−0.195870	−	0.339258i
$794$	4398.00	−	7617.56i	0.196573	−	0.340475i
$795$		0			0
$796$	64.0000	+	110.851i	0.00284977	+	0.00493595i
$797$	22170.0			0.985322			0.492661	−	0.870221i	$-0.336024\pi$
$797$	22170.0			0.985322			0.492661	+	0.870221i	$0.336024\pi$
$798$		0			0
$799$	−32856.0			−1.45477
$800$	−5744.00	−	9948.90i	−0.253851	−	0.439683i
$801$		0			0
$802$	13236.0	−	22925.4i	0.582767	−	1.00938i
$803$	1898.00	+	3287.43i	0.0834109	+	0.144472i
$804$		0			0
$805$		0			0
$806$	27216.0			1.18938
$807$		0			0
$808$	−5224.00	+	9048.23i	−0.227450	+	0.393955i
$809$	8144.00	−	14105.8i	0.353928	−	0.613021i	−0.633006	−	0.774147i	$-0.718179\pi$
$809$	8144.00	−	14105.8i	0.353928	−	0.613021i	0.986934	+	0.161126i	$0.0515124\pi$
$810$		0			0
$811$	8720.00			0.377559			0.188780	−	0.982019i	$-0.439547\pi$
$811$	8720.00			0.377559			0.188780	+	0.982019i	$0.439547\pi$
$812$		0			0
$813$		0			0
$814$	1300.00	+	2251.67i	0.0559766	+	0.0969544i
$815$	−4708.00	+	8154.50i	−0.202349	+	0.350478i
$816$		0			0
$817$	9512.00	+	16475.3i	0.407323	+	0.705504i
$818$	18980.0			0.811272
$819$		0			0
$820$	11088.0			0.472207
$821$	−15686.0	−	27168.9i	−0.666803	−	1.15494i	−0.978793	−	0.204851i	$-0.934329\pi$
$821$	−15686.0	−	27168.9i	−0.666803	−	1.15494i	0.311990	−	0.950085i	$-0.399004\pi$
$822$		0			0
$823$	8824.00	−	15283.6i	0.373737	−	0.647331i	−0.616400	−	0.787433i	$-0.711410\pi$
$823$	8824.00	−	15283.6i	0.373737	−	0.647331i	0.990137	+	0.140102i	$0.0447430\pi$
$824$	−2032.00	−	3519.53i	−0.0859079	−	0.148797i
$825$		0			0
$826$		0			0
$827$	2382.00			0.100158			0.0500788	−	0.998745i	$-0.484053\pi$
$827$	2382.00			0.100158			0.0500788	+	0.998745i	$0.484053\pi$
$828$		0			0
$829$	13325.0	−	23079.6i	0.558259	−	0.966932i	−0.439383	−	0.898300i	$-0.644803\pi$
$829$	13325.0	−	23079.6i	0.558259	−	0.966932i	0.997642	−	0.0686326i	$-0.0218636\pi$
$830$	−14432.0	+	24997.0i	−0.603545	+	1.04537i
$831$		0			0
$832$	3456.00			0.144009
$833$		0			0
$834$		0			0
$835$	−44.0000	−	76.2102i	−0.00182357	−	0.00315852i
$836$	−6032.00	+	10447.7i	−0.249547	+	0.432228i
$837$		0			0
$838$	−4236.00	−	7336.97i	−0.174618	−	0.302448i
$839$	24092.0			0.991357			0.495678	−	0.868506i	$-0.334920\pi$
$839$	24092.0			0.991357			0.495678	+	0.868506i	$0.334920\pi$
$840$		0			0
$841$	18875.0			0.773914
$842$	−918.000	−	1590.02i	−0.0375729	−	0.0650781i
$843$		0			0
$844$	−8536.00	+	14784.8i	−0.348129	+	0.602978i
$845$	−7909.00	−	13698.8i	−0.321986	−	0.557695i
$846$		0			0
$847$		0			0
$848$	−192.000			−0.00777513
$849$		0			0
$850$	−26566.0	+	46013.7i	−1.07201	+	1.85677i
$851$	−1450.00	+	2511.47i	−0.0584082	+	0.101166i
$852$		0			0
$853$	8194.00			0.328906			0.164453	−	0.986385i	$-0.447414\pi$
$853$	8194.00			0.328906			0.164453	+	0.986385i	$0.447414\pi$
$854$		0			0
$855$		0			0
$856$	1992.00	+	3450.25i	0.0795387	+	0.137765i
$857$	8481.00	−	14689.5i	0.338046	−	0.585513i	−0.646019	−	0.763321i	$-0.723567\pi$
$857$	8481.00	−	14689.5i	0.338046	−	0.585513i	0.984065	+	0.177808i	$0.0569007\pi$
$858$		0			0
$859$	−24278.0	−	42050.7i	−0.964324	−	1.67026i	−0.711419	−	0.702768i	$-0.751947\pi$
$859$	−24278.0	−	42050.7i	−0.964324	−	1.67026i	−0.252905	−	0.967491i	$-0.581386\pi$
$860$	14432.0			0.572241
$861$		0			0
$862$	23628.0			0.933611
$863$	−17137.0	−	29682.2i	−0.675956	−	1.17079i	−0.976188	−	0.216924i	$-0.930397\pi$
$863$	−17137.0	−	29682.2i	−0.675956	−	1.17079i	0.300232	−	0.953866i	$-0.402936\pi$
$864$		0			0
$865$	6490.00	−	11241.0i	0.255106	−	0.441856i
$866$	−8374.00	−	14504.2i	−0.328591	−	0.569137i
$867$		0			0
$868$		0			0
$869$	25584.0			0.998709
$870$		0			0
$871$	23220.0	−	40218.2i	0.903306	−	1.56457i
$872$	2456.00	−	4253.92i	0.0953792	−	0.165202i
$873$		0			0
$874$	−13456.0			−0.520773
$875$		0			0
$876$		0			0
$877$	−3563.00	−	6171.30i	−0.137188	−	0.237617i	0.789243	−	0.614081i	$-0.210473\pi$
$877$	−3563.00	−	6171.30i	−0.137188	−	0.237617i	−0.926431	+	0.376464i	$0.877140\pi$
$878$	3840.00	−	6651.08i	0.147601	−	0.255653i
$879$		0			0
$880$	4576.00	+	7925.86i	0.175292	+	0.303615i
$881$	−9222.00			−0.352664			−0.176332	−	0.984331i	$-0.556423\pi$
$881$	−9222.00			−0.352664			−0.176332	+	0.984331i	$0.556423\pi$
$882$		0			0
$883$	37652.0			1.43498			0.717492	−	0.696567i	$-0.245290\pi$
$883$	37652.0			1.43498			0.717492	+	0.696567i	$0.245290\pi$
$884$	−7992.00	−	13842.6i	−0.304072	−	0.526669i
$885$		0			0
$886$	10166.0	−	17608.0i	0.385478	−	0.667667i
$887$	10998.0	+	19049.1i	0.416321	+	0.721089i	0.995566	−	0.0940643i	$-0.0299859\pi$
$887$	10998.0	+	19049.1i	0.416321	+	0.721089i	−0.579245	+	0.815153i	$0.696653\pi$
$888$		0			0
$889$		0			0
$890$	−41976.0			−1.58094
$891$		0			0
$892$	6928.00	−	11999.6i	0.260052	−	0.450424i
$893$	−25752.0	+	44603.8i	−0.965014	+	1.67145i
$894$		0			0
$895$	−77748.0			−2.90372
$896$		0			0
$897$		0			0
$898$	8200.00	+	14202.8i	0.304719	+	0.527789i
$899$	26208.0	−	45393.6i	0.972287	−	1.68405i
$900$		0			0
$901$	444.000	+	769.031i	0.0164171	+	0.0284352i
$902$	−6552.00			−0.241860
$903$		0			0
$904$	9856.00			0.362617
$905$	12078.0	+	20919.7i	0.443631	+	0.768392i
$906$		0			0
$907$	−7422.00	+	12855.3i	−0.271713	+	0.470620i	−0.969301	−	0.245879i	$-0.920923\pi$
$907$	−7422.00	+	12855.3i	−0.271713	+	0.470620i	0.697588	+	0.716499i	$0.254257\pi$
$908$	6504.00	+	11265.3i	0.237712	+	0.411730i
$909$		0			0
$910$		0			0
$911$	19446.0			0.707217			0.353609	−	0.935394i	$-0.384955\pi$
$911$	19446.0			0.707217			0.353609	+	0.935394i	$0.384955\pi$
$912$		0			0
$913$	8528.00	−	14770.9i	0.309130	−	0.535429i
$914$	6074.00	−	10520.5i	0.219814	−	0.380729i
$915$		0			0
$916$	−1672.00			−0.0603105
$917$		0			0
$918$		0			0
$919$	19600.0	+	33948.2i	0.703530	+	1.21855i	0.967219	+	0.253942i	$0.0817274\pi$
$919$	19600.0	+	33948.2i	0.703530	+	1.21855i	−0.263689	+	0.964608i	$0.584939\pi$
$920$	−5104.00	+	8840.39i	−0.182906	+	0.316803i
$921$		0			0
$922$	2006.00	+	3474.49i	0.0716530	+	0.124107i
$923$	12852.0			0.458319
$924$		0			0
$925$	17950.0			0.638046
$926$	3728.00	+	6457.09i	0.132300	+	0.229150i
$927$		0			0
$928$	3328.00	−	5764.27i	0.117723	−	0.203902i
$929$	7977.00	+	13816.6i	0.281719	+	0.487951i	0.971808	−	0.235773i	$-0.0757621\pi$
$929$	7977.00	+	13816.6i	0.281719	+	0.487951i	−0.690089	+	0.723724i	$0.742429\pi$
$930$		0			0
$931$		0			0
$932$	−8336.00			−0.292977
$933$		0			0
$934$	6380.00	−	11050.5i	0.223512	−	0.387134i
$935$	21164.0	−	36657.1i	0.740253	−	1.28216i
$936$		0			0
$937$	−2546.00			−0.0887665			−0.0443832	−	0.999015i	$-0.514132\pi$
$937$	−2546.00			−0.0887665			−0.0443832	+	0.999015i	$0.514132\pi$
$938$		0			0
$939$		0			0
$940$	19536.0	+	33837.3i	0.677866	+	1.17410i
$941$	−215.000	+	372.391i	−0.00744825	+	0.0129007i	−0.869726	−	0.493536i	$-0.835704\pi$
$941$	−215.000	+	372.391i	−0.00744825	+	0.0129007i	0.862277	+	0.506437i	$0.169038\pi$
$942$		0			0
$943$	−3654.00	−	6328.91i	−0.126183	−	0.218555i
$944$	1984.00			0.0684043
$945$		0			0
$946$	−8528.00			−0.293096
$947$	19133.0	+	33139.3i	0.656535	+	1.13715i	0.981507	+	0.191429i	$0.0613121\pi$
$947$	19133.0	+	33139.3i	0.656535	+	1.13715i	−0.324971	+	0.945724i	$0.605355\pi$
$948$		0			0
$949$	−3942.00	+	6827.74i	−0.134840	+	0.233549i
$950$	41644.0	+	72129.5i	1.42222	+	2.46336i
$951$		0			0
$952$		0			0
$953$	28216.0			0.959083			0.479541	−	0.877519i	$-0.340803\pi$
$953$	28216.0			0.959083			0.479541	+	0.877519i	$0.340803\pi$
$954$		0			0
$955$	−53394.0	+	92481.1i	−1.80920	+	3.13363i
$956$	3324.00	−	5757.34i	0.112454	−	0.194776i
$957$		0			0
$958$	34360.0			1.15879
$959$		0			0
$960$		0			0
$961$	−16856.5	−	29196.3i	−0.565825	−	0.980038i
$962$	−2700.00	+	4676.54i	−0.0904901	+	0.156733i
$963$		0			0
$964$	12364.0	+	21415.1i	0.413089	+	0.715491i
$965$	−32956.0			−1.09937
$966$		0			0
$967$	−27712.0			−0.921570			−0.460785	−	0.887512i	$-0.652432\pi$
$967$	−27712.0			−0.921570			−0.460785	+	0.887512i	$0.652432\pi$
$968$	2620.00	+	4537.97i	0.0869938	+	0.150678i
$969$		0			0
$970$	11572.0	−	20043.3i	0.383046	−	0.663455i
$971$	−16488.0	−	28558.1i	−0.544928	−	0.943843i	−0.998611	−	0.0526801i	$-0.983224\pi$
$971$	−16488.0	−	28558.1i	−0.544928	−	0.943843i	0.453683	−	0.891163i	$-0.350110\pi$
$972$		0			0
$973$		0			0
$974$	−5456.00			−0.179488
$975$		0			0
$976$	−1296.00	+	2244.74i	−0.0425040	+	0.0736192i
$977$	−4470.00	+	7742.27i	−0.146375	+	0.253528i	−0.929885	−	0.367851i	$-0.880094\pi$
$977$	−4470.00	+	7742.27i	−0.146375	+	0.253528i	0.783510	+	0.621379i	$0.213427\pi$
$978$		0			0
$979$	24804.0			0.809744
$980$		0			0
$981$		0			0
$982$	2574.00	+	4458.30i	0.0836453	+	0.144878i
$983$	1644.00	−	2847.49i	0.0533423	−	0.0923915i	−0.838121	−	0.545484i	$-0.816346\pi$
$983$	1644.00	−	2847.49i	0.0533423	−	0.0923915i	0.891464	+	0.453092i	$0.149679\pi$
$984$		0			0
$985$	6820.00	+	11812.6i	0.220612	+	0.382112i
$986$	−30784.0			−0.994282
$987$		0			0
$988$	−25056.0			−0.806819
$989$	−4756.00	−	8237.63i	−0.152914	−	0.264855i
$990$		0			0
$991$	−16972.0	+	29396.4i	−0.544030	+	0.942287i	0.454638	+	0.890676i	$0.349769\pi$
$991$	−16972.0	+	29396.4i	−0.544030	+	0.942287i	−0.998667	+	0.0516105i	$0.983565\pi$
$992$	−4032.00	−	6983.63i	−0.129049	−	0.223519i
$993$		0			0
$994$		0			0
$995$	−704.000			−0.0224305
$996$		0			0
$997$	−27281.0	+	47252.1i	−0.866598	+	1.50099i	−0.00114579	+	0.999999i	$0.500365\pi$
$997$	−27281.0	+	47252.1i	−0.866598	+	1.50099i	−0.865452	+	0.500992i	$0.832969\pi$
$998$	7484.00	−	12962.7i	0.237377	−	0.411148i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.a.361.1		2
3.2	odd	2		882.4.g.x.361.1		2
7.2	even	3	inner	882.4.g.a.667.1		2
7.3	odd	6		126.4.a.f.1.1	yes	1
7.4	even	3		882.4.a.s.1.1		1
7.5	odd	6		882.4.g.m.667.1		2
7.6	odd	2		882.4.g.m.361.1		2
21.2	odd	6		882.4.g.x.667.1		2
21.5	even	6		882.4.g.n.667.1		2
21.11	odd	6		882.4.a.a.1.1		1
21.17	even	6		126.4.a.e.1.1	✓	1
21.20	even	2		882.4.g.n.361.1		2
28.3	even	6		1008.4.a.a.1.1		1
84.59	odd	6		1008.4.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.a.e.1.1	✓	1	21.17	even	6
126.4.a.f.1.1	yes	1	7.3	odd	6
882.4.a.a.1.1		1	21.11	odd	6
882.4.a.s.1.1		1	7.4	even	3
882.4.g.a.361.1		2	1.1	even	1	trivial
882.4.g.a.667.1		2	7.2	even	3	inner
882.4.g.m.361.1		2	7.6	odd	2
882.4.g.m.667.1		2	7.5	odd	6
882.4.g.n.361.1		2	21.20	even	2
882.4.g.n.667.1		2	21.5	even	6
882.4.g.x.361.1		2	3.2	odd	2
882.4.g.x.667.1		2	21.2	odd	6
1008.4.a.a.1.1		1	28.3	even	6
1008.4.a.w.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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-11.0000 - 19.0526i) q^{5} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-11.0000 - 19.0526i) q^{5} +8.00000 q^{8} +(-22.0000 + 38.1051i) q^{10} +(13.0000 - 22.5167i) q^{11} +54.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-37.0000 + 64.0859i) q^{17} +(58.0000 + 100.459i) q^{19} +88.0000 q^{20} -52.0000 q^{22} +(-29.0000 - 50.2295i) q^{23} +(-179.500 + 310.903i) q^{25} +(-54.0000 - 93.5307i) q^{26} -208.000 q^{29} +(-126.000 + 218.238i) q^{31} +(-16.0000 + 27.7128i) q^{32} +148.000 q^{34} +(-25.0000 - 43.3013i) q^{37} +(116.000 - 200.918i) q^{38} +(-88.0000 - 152.420i) q^{40} +126.000 q^{41} +164.000 q^{43} +(52.0000 + 90.0666i) q^{44} +(-58.0000 + 100.459i) q^{46} +(222.000 + 384.515i) q^{47} +718.000 q^{50} +(-108.000 + 187.061i) q^{52} +(6.00000 - 10.3923i) q^{53} -572.000 q^{55} +(208.000 + 360.267i) q^{58} +(-62.0000 + 107.387i) q^{59} +(-81.0000 - 140.296i) q^{61} +504.000 q^{62} +64.0000 q^{64} +(-594.000 - 1028.84i) q^{65} +(430.000 - 744.782i) q^{67} +(-148.000 - 256.344i) q^{68} +238.000 q^{71} +(-73.0000 + 126.440i) q^{73} +(-50.0000 + 86.6025i) q^{74} -464.000 q^{76} +(492.000 + 852.169i) q^{79} +(-176.000 + 304.841i) q^{80} +(-126.000 - 218.238i) q^{82} +656.000 q^{83} +1628.00 q^{85} +(-164.000 - 284.056i) q^{86} +(104.000 - 180.133i) q^{88} +(477.000 + 826.188i) q^{89} +232.000 q^{92} +(444.000 - 769.031i) q^{94} +(1276.00 - 2210.10i) q^{95} -526.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} - 22 q^{5} + 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 - 22 * q^5 + 16 * q^8	\( 2 q - 2 q^{2} - 4 q^{4} - 22 q^{5} + 16 q^{8} - 44 q^{10} + 26 q^{11} + 108 q^{13} - 16 q^{16} - 74 q^{17} + 116 q^{19} + 176 q^{20} - 104 q^{22} - 58 q^{23} - 359 q^{25} - 108 q^{26} - 416 q^{29} - 252 q^{31} - 32 q^{32} + 296 q^{34} - 50 q^{37} + 232 q^{38} - 176 q^{40} + 252 q^{41} + 328 q^{43} + 104 q^{44} - 116 q^{46} + 444 q^{47} + 1436 q^{50} - 216 q^{52} + 12 q^{53} - 1144 q^{55} + 416 q^{58} - 124 q^{59} - 162 q^{61} + 1008 q^{62} + 128 q^{64} - 1188 q^{65} + 860 q^{67} - 296 q^{68} + 476 q^{71} - 146 q^{73} - 100 q^{74} - 928 q^{76} + 984 q^{79} - 352 q^{80} - 252 q^{82} + 1312 q^{83} + 3256 q^{85} - 328 q^{86} + 208 q^{88} + 954 q^{89} + 464 q^{92} + 888 q^{94} + 2552 q^{95} - 1052 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 - 22 * q^5 + 16 * q^8 - 44 * q^10 + 26 * q^11 + 108 * q^13 - 16 * q^16 - 74 * q^17 + 116 * q^19 + 176 * q^20 - 104 * q^22 - 58 * q^23 - 359 * q^25 - 108 * q^26 - 416 * q^29 - 252 * q^31 - 32 * q^32 + 296 * q^34 - 50 * q^37 + 232 * q^38 - 176 * q^40 + 252 * q^41 + 328 * q^43 + 104 * q^44 - 116 * q^46 + 444 * q^47 + 1436 * q^50 - 216 * q^52 + 12 * q^53 - 1144 * q^55 + 416 * q^58 - 124 * q^59 - 162 * q^61 + 1008 * q^62 + 128 * q^64 - 1188 * q^65 + 860 * q^67 - 296 * q^68 + 476 * q^71 - 146 * q^73 - 100 * q^74 - 928 * q^76 + 984 * q^79 - 352 * q^80 - 252 * q^82 + 1312 * q^83 + 3256 * q^85 - 328 * q^86 + 208 * q^88 + 954 * q^89 + 464 * q^92 + 888 * q^94 + 2552 * q^95 - 1052 * q^97

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