LMFDB - Embedded newform 462.4.g.a.419.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,4,Mod(419,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("462.419");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	462.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.2588824227$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.3
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	462.419
Dual form			462.4.g.a.419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -5.19615 q^{3} -4.00000 q^{4} -19.0526 q^{5} -10.3923i q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -5.19615 q^{3} -4.00000 q^{4} -19.0526 q^{5} -10.3923i q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000i q^{8} +27.0000 q^{9} -38.1051i q^{10} -11.0000i q^{11} +20.7846 q^{12} -57.1577i q^{13} +(-24.2487 + 28.0000i) q^{14} +99.0000 q^{15} +16.0000 q^{16} +55.4256 q^{17} +54.0000i q^{18} +8.66025i q^{19} +76.2102 q^{20} +(-72.7461 - 63.0000i) q^{21} +22.0000 q^{22} +6.00000i q^{23} +41.5692i q^{24} +238.000 q^{25} +114.315 q^{26} -140.296 q^{27} +(-56.0000 - 48.4974i) q^{28} -123.000i q^{29} +198.000i q^{30} +107.387i q^{31} +32.0000i q^{32} +57.1577i q^{33} +110.851i q^{34} +(-266.736 - 231.000i) q^{35} -108.000 q^{36} +91.0000 q^{37} -17.3205 q^{38} +297.000i q^{39} +152.420i q^{40} -103.923 q^{41} +(126.000 - 145.492i) q^{42} -482.000 q^{43} +44.0000i q^{44} -514.419 q^{45} -12.0000 q^{46} +355.070 q^{47} -83.1384 q^{48} +(49.0000 + 339.482i) q^{49} +476.000i q^{50} -288.000 q^{51} +228.631i q^{52} +672.000i q^{53} -280.592i q^{54} +209.578i q^{55} +(96.9948 - 112.000i) q^{56} -45.0000i q^{57} +246.000 q^{58} -739.586 q^{59} -396.000 q^{60} +263.272i q^{61} -214.774 q^{62} +(378.000 + 327.358i) q^{63} -64.0000 q^{64} +1089.00i q^{65} -114.315 q^{66} -169.000 q^{67} -221.703 q^{68} -31.1769i q^{69} +(462.000 - 533.472i) q^{70} -300.000i q^{71} -216.000i q^{72} -465.922i q^{73} +182.000i q^{74} -1236.68 q^{75} -34.6410i q^{76} +(133.368 - 154.000i) q^{77} -594.000 q^{78} +170.000 q^{79} -304.841 q^{80} +729.000 q^{81} -207.846i q^{82} +928.379 q^{83} +(290.985 + 252.000i) q^{84} -1056.00 q^{85} -964.000i q^{86} +639.127i q^{87} -88.0000 q^{88} +699.749 q^{89} -1028.84i q^{90} +(693.000 - 800.207i) q^{91} -24.0000i q^{92} -558.000i q^{93} +710.141i q^{94} -165.000i q^{95} -166.277i q^{96} -1014.98i q^{97} +(-678.964 + 98.0000i) q^{98} -297.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 56 q^{7} + 108 q^{9}+O(q^{10}) $ 4 * q - 16 * q^4 + 56 * q^7 + 108 * q^9	$ 4 q - 16 q^{4} + 56 q^{7} + 108 q^{9} + 396 q^{15} + 64 q^{16} + 88 q^{22} + 952 q^{25} - 224 q^{28} - 432 q^{36} + 364 q^{37} + 504 q^{42} - 1928 q^{43} - 48 q^{46} + 196 q^{49} - 1152 q^{51} + 984 q^{58} - 1584 q^{60} + 1512 q^{63} - 256 q^{64} - 676 q^{67} + 1848 q^{70} - 2376 q^{78} + 680 q^{79} + 2916 q^{81} - 4224 q^{85} - 352 q^{88} + 2772 q^{91}+O(q^{100}) $ 4 * q - 16 * q^4 + 56 * q^7 + 108 * q^9 + 396 * q^15 + 64 * q^16 + 88 * q^22 + 952 * q^25 - 224 * q^28 - 432 * q^36 + 364 * q^37 + 504 * q^42 - 1928 * q^43 - 48 * q^46 + 196 * q^49 - 1152 * q^51 + 984 * q^58 - 1584 * q^60 + 1512 * q^63 - 256 * q^64 - 676 * q^67 + 1848 * q^70 - 2376 * q^78 + 680 * q^79 + 2916 * q^81 - 4224 * q^85 - 352 * q^88 + 2772 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	−5.19615			−1.00000
$3$	−5.19615			−1.00000
$4$	−4.00000			−0.500000
$5$	−19.0526			−1.70411			−0.852056	−	0.523450i	$-0.824645\pi$
$5$	−19.0526			−1.70411			−0.852056	+	0.523450i	$0.824645\pi$
$6$		−	10.3923i		−	0.707107i
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$8$		−	8.00000i		−	0.353553i
$9$	27.0000			1.00000
$10$		−	38.1051i		−	1.20499i
$11$		−	11.0000i		−	0.301511i
$11$		−	11.0000i		−	0.301511i
$12$	20.7846			0.500000
$13$		−	57.1577i		−	1.21944i	−0.792618	−	0.609719i	$-0.791282\pi$
$13$		−	57.1577i		−	1.21944i	0.792618	−	0.609719i	$-0.208718\pi$
$14$	−24.2487	+	28.0000i	−0.462910	+	0.534522i
$15$	99.0000			1.70411
$16$	16.0000			0.250000
$17$	55.4256			0.790746			0.395373	−	0.918521i	$-0.370615\pi$
$17$	55.4256			0.790746			0.395373	+	0.918521i	$0.370615\pi$
$18$			54.0000i			0.707107i
$19$			8.66025i			0.104568i	0.998632	+	0.0522842i	$0.0166502\pi$
$19$			8.66025i			0.104568i	−0.998632	+	0.0522842i	$0.983350\pi$
$20$	76.2102			0.852056
$21$	−72.7461	−	63.0000i	−0.755929	−	0.654654i
$22$	22.0000			0.213201
$23$			6.00000i			0.0543951i	0.999630	+	0.0271975i	$0.00865831\pi$
$23$			6.00000i			0.0543951i	−0.999630	+	0.0271975i	$0.991342\pi$
$24$			41.5692i			0.353553i
$25$	238.000			1.90400
$26$	114.315			0.862273
$27$	−140.296			−1.00000
$28$	−56.0000	−	48.4974i	−0.377964	−	0.327327i
$29$		−	123.000i		−	0.787604i	−0.919195	−	0.393802i	$-0.871159\pi$
$29$		−	123.000i		−	0.787604i	0.919195	−	0.393802i	$-0.128841\pi$
$30$			198.000i			1.20499i
$31$			107.387i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			107.387i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$			32.0000i			0.176777i
$33$			57.1577i			0.301511i
$34$			110.851i			0.559142i
$35$	−266.736	−	231.000i	−1.28819	−	1.11560i
$36$	−108.000			−0.500000
$37$	91.0000			0.404333			0.202166	−	0.979351i	$-0.435202\pi$
$37$	91.0000			0.404333			0.202166	+	0.979351i	$0.435202\pi$
$38$	−17.3205			−0.0739410
$39$			297.000i			1.21944i
$40$			152.420i			0.602495i
$41$	−103.923			−0.395855			−0.197927	−	0.980217i	$-0.563421\pi$
$41$	−103.923			−0.395855			−0.197927	+	0.980217i	$0.563421\pi$
$42$	126.000	−	145.492i	0.462910	−	0.534522i
$43$	−482.000			−1.70940			−0.854701	−	0.519120i	$-0.826260\pi$
$43$	−482.000			−1.70940			−0.854701	+	0.519120i	$0.826260\pi$
$44$			44.0000i			0.150756i
$45$	−514.419			−1.70411
$46$	−12.0000			−0.0384631
$47$	355.070			1.10196			0.550982	−	0.834517i	$-0.314253\pi$
$47$	355.070			1.10196			0.550982	+	0.834517i	$0.314253\pi$
$48$	−83.1384			−0.250000
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$			476.000i			1.34633i
$51$	−288.000			−0.790746
$52$			228.631i			0.609719i
$53$			672.000i			1.74163i	0.491612	+	0.870814i	$0.336408\pi$
$53$			672.000i			1.74163i	−0.491612	+	0.870814i	$0.663592\pi$
$54$		−	280.592i		−	0.707107i
$55$			209.578i			0.513809i
$56$	96.9948	−	112.000i	0.231455	−	0.267261i
$57$		−	45.0000i		−	0.104568i
$58$	246.000			0.556920
$59$	−739.586			−1.63196			−0.815982	−	0.578078i	$-0.803803\pi$
$59$	−739.586			−1.63196			−0.815982	+	0.578078i	$0.803803\pi$
$60$	−396.000			−0.852056
$61$			263.272i			0.552598i	0.961072	+	0.276299i	$0.0891080\pi$
$61$			263.272i			0.552598i	−0.961072	+	0.276299i	$0.910892\pi$
$62$	−214.774			−0.439941
$63$	378.000	+	327.358i	0.755929	+	0.654654i
$64$	−64.0000			−0.125000
$65$			1089.00i			2.07806i
$66$	−114.315			−0.213201
$67$	−169.000			−0.308159			−0.154079	−	0.988058i	$-0.549241\pi$
$67$	−169.000			−0.308159			−0.154079	+	0.988058i	$0.549241\pi$
$68$	−221.703			−0.395373
$69$		−	31.1769i		−	0.0543951i
$70$	462.000	−	533.472i	0.788851	−	0.910887i
$71$		−	300.000i		−	0.501457i	−0.968057	−	0.250729i	$-0.919330\pi$
$71$		−	300.000i		−	0.501457i	0.968057	−	0.250729i	$-0.0806701\pi$
$72$		−	216.000i		−	0.353553i
$73$		−	465.922i		−	0.747014i	−0.927627	−	0.373507i	$-0.878155\pi$
$73$		−	465.922i		−	0.747014i	0.927627	−	0.373507i	$-0.121845\pi$
$74$			182.000i			0.285906i
$75$	−1236.68			−1.90400
$76$		−	34.6410i		−	0.0522842i
$77$	133.368	−	154.000i	0.197386	−	0.227921i
$78$	−594.000			−0.862273
$79$	170.000			0.242108			0.121054	−	0.992646i	$-0.461373\pi$
$79$	170.000			0.242108			0.121054	+	0.992646i	$0.461373\pi$
$80$	−304.841			−0.426028
$81$	729.000			1.00000
$82$		−	207.846i		−	0.279912i
$83$	928.379			1.22775			0.613873	−	0.789405i	$-0.289611\pi$
$83$	928.379			1.22775			0.613873	+	0.789405i	$0.289611\pi$
$84$	290.985	+	252.000i	0.377964	+	0.327327i
$85$	−1056.00			−1.34752
$86$		−	964.000i		−	1.20873i
$87$			639.127i			0.787604i
$88$	−88.0000			−0.106600
$89$	699.749			0.833407			0.416703	−	0.909043i	$-0.363185\pi$
$89$	699.749			0.833407			0.416703	+	0.909043i	$0.363185\pi$
$90$		−	1028.84i		−	1.20499i
$91$	693.000	−	800.207i	0.798309	−	0.921808i
$92$		−	24.0000i		−	0.0271975i
$93$		−	558.000i		−	0.622171i
$94$			710.141i			0.779207i
$95$		−	165.000i		−	0.178196i
$96$		−	166.277i		−	0.176777i
$97$		−	1014.98i		−	1.06243i	−0.847237	−	0.531215i	$-0.821735\pi$
$97$		−	1014.98i		−	1.06243i	0.847237	−	0.531215i	$-0.178265\pi$
$98$	−678.964	+	98.0000i	−0.699854	+	0.101015i
$99$		−	297.000i		−	0.301511i
$100$	−952.000			−0.952000
$101$	−481.510			−0.474377			−0.237188	−	0.971464i	$-0.576226\pi$
$101$	−481.510			−0.474377			−0.237188	+	0.971464i	$0.576226\pi$
$102$		−	576.000i		−	0.559142i
$103$			640.859i			0.613065i	0.951860	+	0.306532i	$0.0991688\pi$
$103$			640.859i			0.613065i	−0.951860	+	0.306532i	$0.900831\pi$
$104$	−457.261			−0.431136
$105$	1386.00	+	1200.31i	1.28819	+	1.11560i
$106$	−1344.00			−1.23152
$107$			2049.00i			1.85126i	0.378436	+	0.925628i	$0.376462\pi$
$107$			2049.00i			1.85126i	−0.378436	+	0.925628i	$0.623538\pi$
$108$	561.184			0.500000
$109$	−398.000			−0.349738			−0.174869	−	0.984592i	$-0.555950\pi$
$109$	−398.000			−0.349738			−0.174869	+	0.984592i	$0.555950\pi$
$110$	−419.156			−0.363318
$111$	−472.850			−0.404333
$112$	224.000	+	193.990i	0.188982	+	0.163663i
$113$			2178.00i			1.81318i	0.422016	+	0.906589i	$0.361323\pi$
$113$			2178.00i			1.81318i	−0.422016	+	0.906589i	$0.638677\pi$
$114$	90.0000			0.0739410
$115$		−	114.315i		−	0.0926953i
$116$			492.000i			0.393802i
$117$		−	1543.26i		−	1.21944i
$118$		−	1479.17i		−	1.15397i
$119$	775.959	+	672.000i	0.597748	+	0.517665i
$120$		−	792.000i		−	0.602495i
$121$	−121.000			−0.0909091
$122$	−526.543			−0.390746
$123$	540.000			0.395855
$124$		−	429.549i		−	0.311086i
$125$	−2152.94			−1.54052
$126$	−654.715	+	756.000i	−0.462910	+	0.534522i
$127$	−304.000			−0.212407			−0.106203	−	0.994344i	$-0.533869\pi$
$127$	−304.000			−0.212407			−0.106203	+	0.994344i	$0.533869\pi$
$128$		−	128.000i		−	0.0883883i
$129$	2504.55			1.70940
$130$	−2178.00			−1.46941
$131$	1406.43			0.938015			0.469007	−	0.883194i	$-0.344612\pi$
$131$	1406.43			0.938015			0.469007	+	0.883194i	$0.344612\pi$
$132$		−	228.631i		−	0.150756i
$133$	−105.000	+	121.244i	−0.0684561	+	0.0790462i
$134$		−	338.000i		−	0.217901i
$135$	2673.00			1.70411
$136$		−	443.405i		−	0.279571i
$137$		−	2700.00i		−	1.68377i	−0.539657	−	0.841885i	$-0.681446\pi$
$137$		−	2700.00i		−	1.68377i	0.539657	−	0.841885i	$-0.318554\pi$
$138$	62.3538			0.0384631
$139$			3044.95i			1.85805i	0.370017	+	0.929025i	$0.379352\pi$
$139$			3044.95i			1.85805i	−0.370017	+	0.929025i	$0.620648\pi$
$140$	1066.94	+	924.000i	0.644094	+	0.557802i
$141$	−1845.00			−1.10196
$142$	600.000			0.354584
$143$	−628.734			−0.367674
$144$	432.000			0.250000
$145$			2343.46i			1.34217i
$146$	931.843			0.528219
$147$	−254.611	−	1764.00i	−0.142857	−	0.989743i
$148$	−364.000			−0.202166
$149$			1719.00i			0.945141i	0.881293	+	0.472570i	$0.156674\pi$
$149$			1719.00i			0.945141i	−0.881293	+	0.472570i	$0.843326\pi$
$150$		−	2473.37i		−	1.34633i
$151$	40.0000			0.0215573			0.0107787	−	0.999942i	$-0.496569\pi$
$151$	40.0000			0.0215573			0.0107787	+	0.999942i	$0.496569\pi$
$152$	69.2820			0.0369705
$153$	1496.49			0.790746
$154$	308.000	+	266.736i	0.161165	+	0.139573i
$155$		−	2046.00i		−	1.06025i
$156$		−	1188.00i		−	0.609719i
$157$			536.936i			0.272944i	0.990644	+	0.136472i	$0.0435763\pi$
$157$			536.936i			0.272944i	−0.990644	+	0.136472i	$0.956424\pi$
$158$			340.000i			0.171196i
$159$		−	3491.81i		−	1.74163i
$160$		−	609.682i		−	0.301247i
$161$	−72.7461	+	84.0000i	−0.0356099	+	0.0411188i
$162$			1458.00i			0.707107i
$163$	−1981.00			−0.951926			−0.475963	−	0.879465i	$-0.657900\pi$
$163$	−1981.00			−0.951926			−0.475963	+	0.879465i	$0.657900\pi$
$164$	415.692			0.197927
$165$		−	1089.00i		−	0.513809i
$166$			1856.76i			0.868147i
$167$	−3758.55			−1.74159			−0.870794	−	0.491647i	$-0.836395\pi$
$167$	−3758.55			−1.74159			−0.870794	+	0.491647i	$0.836395\pi$
$168$	−504.000	+	581.969i	−0.231455	+	0.267261i
$169$	−1070.00			−0.487028
$170$		−	2112.00i		−	0.952841i
$171$			233.827i			0.104568i
$172$	1928.00			0.854701
$173$	2989.52			1.31381			0.656905	−	0.753974i	$-0.271865\pi$
$173$	2989.52			1.31381			0.656905	+	0.753974i	$0.271865\pi$
$174$	−1278.25			−0.556920
$175$	3332.00	+	2885.60i	1.43929	+	1.24646i
$176$		−	176.000i		−	0.0753778i
$177$	3843.00			1.63196
$178$			1399.50i			0.589308i
$179$			1746.00i			0.729062i	0.931191	+	0.364531i	$0.118771\pi$
$179$			1746.00i			0.729062i	−0.931191	+	0.364531i	$0.881229\pi$
$180$	2057.68			0.852056
$181$		−	1420.28i		−	0.583253i	−0.956532	−	0.291626i	$-0.905804\pi$
$181$		−	1420.28i		−	0.583253i	0.956532	−	0.291626i	$-0.0941963\pi$
$182$	1600.41	+	1386.00i	0.651817	+	0.564490i
$183$		−	1368.00i		−	0.552598i
$184$	48.0000			0.0192316
$185$	−1733.78			−0.689028
$186$	1116.00			0.439941
$187$		−	609.682i		−	0.238419i
$188$	−1420.28			−0.550982
$189$	−1964.15	−	1701.00i	−0.755929	−	0.654654i
$190$	330.000			0.126004
$191$		−	504.000i		−	0.190933i	−0.995433	−	0.0954664i	$-0.969566\pi$
$191$		−	504.000i		−	0.190933i	0.995433	−	0.0954664i	$-0.0304342\pi$
$192$	332.554			0.125000
$193$	−1244.00			−0.463964			−0.231982	−	0.972720i	$-0.574521\pi$
$193$	−1244.00			−0.463964			−0.231982	+	0.972720i	$0.574521\pi$
$194$	2029.96			0.751252
$195$		−	5658.61i		−	2.07806i
$196$	−196.000	−	1357.93i	−0.0714286	−	0.494872i
$197$		−	2910.00i		−	1.05243i	−0.850351	−	0.526216i	$-0.823611\pi$
$197$		−	2910.00i		−	1.05243i	0.850351	−	0.526216i	$-0.176389\pi$
$198$	594.000			0.213201
$199$			3654.63i			1.30186i	0.759139	+	0.650929i	$0.225620\pi$
$199$			3654.63i			1.30186i	−0.759139	+	0.650929i	$0.774380\pi$
$200$		−	1904.00i		−	0.673166i
$201$	878.150			0.308159
$202$		−	963.020i		−	0.335435i
$203$	1491.30	−	1722.00i	0.515608	−	0.595373i
$204$	1152.00			0.395373
$205$	1980.00			0.674581
$206$	−1281.72			−0.433502
$207$			162.000i			0.0543951i
$208$		−	914.523i		−	0.304859i
$209$	95.2628			0.0315285
$210$	−2400.62	+	2772.00i	−0.788851	+	0.910887i
$211$	2860.00			0.933130			0.466565	−	0.884487i	$-0.345491\pi$
$211$	2860.00			0.933130			0.466565	+	0.884487i	$0.345491\pi$
$212$		−	2688.00i		−	0.870814i
$213$			1558.85i			0.501457i
$214$	−4098.00			−1.30904
$215$	9183.33			2.91301
$216$			1122.37i			0.353553i
$217$	−1302.00	+	1503.42i	−0.407307	+	0.470317i
$218$		−	796.000i		−	0.247302i
$219$			2421.00i			0.747014i
$220$		−	838.313i		−	0.256905i
$221$		−	3168.00i		−	0.964266i
$222$		−	945.700i		−	0.285906i
$223$			5223.87i			1.56868i	0.620330	+	0.784341i	$0.286998\pi$
$223$			5223.87i			1.56868i	−0.620330	+	0.784341i	$0.713002\pi$
$224$	−387.979	+	448.000i	−0.115728	+	0.133631i
$225$	6426.00			1.90400
$226$	−4356.00			−1.28211
$227$	6394.73			1.86975			0.934875	−	0.354977i	$-0.115511\pi$
$227$	6394.73			1.86975			0.934875	+	0.354977i	$0.115511\pi$
$228$			180.000i			0.0522842i
$229$			5622.24i			1.62239i	0.584774	+	0.811196i	$0.301183\pi$
$229$			5622.24i			1.62239i	−0.584774	+	0.811196i	$0.698817\pi$
$230$	228.631			0.0655455
$231$	−693.000	+	800.207i	−0.197386	+	0.227921i
$232$	−984.000			−0.278460
$233$			1290.00i			0.362707i	0.983418	+	0.181353i	$0.0580478\pi$
$233$			1290.00i			0.362707i	−0.983418	+	0.181353i	$0.941952\pi$
$234$	3086.51			0.862273
$235$	−6765.00			−1.87787
$236$	2958.34			0.815982
$237$	−883.346			−0.242108
$238$	−1344.00	+	1551.92i	−0.366044	+	0.422672i
$239$			6075.00i			1.64418i	0.569357	+	0.822090i	$0.307192\pi$
$239$			6075.00i			1.64418i	−0.569357	+	0.822090i	$0.692808\pi$
$240$	1584.00			0.426028
$241$			3736.03i			0.998585i	0.866433	+	0.499293i	$0.166407\pi$
$241$			3736.03i			0.998585i	−0.866433	+	0.499293i	$0.833593\pi$
$242$		−	242.000i		−	0.0642824i
$243$	−3788.00			−1.00000
$244$		−	1053.09i		−	0.276299i
$245$	−933.575	−	6468.00i	−0.243445	−	1.68663i
$246$			1080.00i			0.279912i
$247$	495.000			0.127515
$248$	859.097			0.219971
$249$	−4824.00			−1.22775
$250$		−	4305.88i		−	1.08931i
$251$	2873.47			0.722597			0.361299	−	0.932450i	$-0.382333\pi$
$251$	2873.47			0.722597			0.361299	+	0.932450i	$0.382333\pi$
$252$	−1512.00	−	1309.43i	−0.377964	−	0.327327i
$253$	66.0000			0.0164007
$254$		−	608.000i		−	0.150194i
$255$	5487.14			1.34752
$256$	256.000			0.0625000
$257$	427.817			0.103838			0.0519192	−	0.998651i	$-0.483466\pi$
$257$	427.817			0.103838			0.0519192	+	0.998651i	$0.483466\pi$
$258$			5009.09i			1.20873i
$259$	1274.00	+	1103.32i	0.305647	+	0.264698i
$260$		−	4356.00i		−	1.03903i
$261$		−	3321.00i		−	0.787604i
$262$			2812.85i			0.663277i
$263$		−	243.000i		−	0.0569735i	−0.999594	−	0.0284867i	$-0.990931\pi$
$263$		−	243.000i		−	0.0569735i	0.999594	−	0.0284867i	$-0.00906884\pi$
$264$	457.261			0.106600
$265$		−	12803.3i		−	2.96793i
$266$	−242.487	−	210.000i	−0.0558941	−	0.0484057i
$267$	−3636.00			−0.833407
$268$	676.000			0.154079
$269$	−623.538			−0.141330			−0.0706651	−	0.997500i	$-0.522512\pi$
$269$	−623.538			−0.141330			−0.0706651	+	0.997500i	$0.522512\pi$
$270$			5346.00i			1.20499i
$271$		−	4640.16i		−	1.04011i	−0.854133	−	0.520055i	$-0.825911\pi$
$271$		−	4640.16i		−	1.04011i	0.854133	−	0.520055i	$-0.174089\pi$
$272$	886.810			0.197687
$273$	−3600.93	+	4158.00i	−0.798309	+	0.921808i
$274$	5400.00			1.19061
$275$		−	2618.00i		−	0.574078i
$276$			124.708i			0.0271975i
$277$	−7486.00			−1.62379			−0.811896	−	0.583803i	$-0.801564\pi$
$277$	−7486.00			−1.62379			−0.811896	+	0.583803i	$0.801564\pi$
$278$	−6089.89			−1.31384
$279$			2899.45i			0.622171i
$280$	−1848.00	+	2133.89i	−0.394425	+	0.455443i
$281$			867.000i			0.184060i	0.995756	+	0.0920300i	$0.0293356\pi$
$281$			867.000i			0.184060i	−0.995756	+	0.0920300i	$0.970664\pi$
$282$		−	3690.00i		−	0.779207i
$283$			6586.99i			1.38359i	0.722094	+	0.691795i	$0.243180\pi$
$283$			6586.99i			1.38359i	−0.722094	+	0.691795i	$0.756820\pi$
$284$			1200.00i			0.250729i
$285$			857.365i			0.178196i
$286$		−	1257.47i		−	0.259985i
$287$	−1454.92	−	1260.00i	−0.299238	−	0.259148i
$288$			864.000i			0.176777i
$289$	−1841.00			−0.374720
$290$	−4686.93			−0.949055
$291$			5274.00i			1.06243i
$292$			1863.69i			0.373507i
$293$	−5410.93			−1.07887			−0.539436	−	0.842026i	$-0.681363\pi$
$293$	−5410.93			−1.07887			−0.539436	+	0.842026i	$0.681363\pi$
$294$	3528.00	−	509.223i	0.699854	−	0.101015i
$295$	14091.0			2.78105
$296$		−	728.000i		−	0.142953i
$297$			1543.26i			0.301511i
$298$	−3438.00			−0.668315
$299$	342.946			0.0663314
$300$	4946.74			0.952000
$301$	−6748.00	−	5843.94i	−1.29219	−	1.11907i
$302$			80.0000i			0.0152433i
$303$	2502.00			0.474377
$304$			138.564i			0.0261421i
$305$		−	5016.00i		−	0.941690i
$306$			2992.98i			0.559142i
$307$			3557.63i			0.661384i	0.943739	+	0.330692i	$0.107282\pi$
$307$			3557.63i			0.661384i	−0.943739	+	0.330692i	$0.892718\pi$
$308$	−533.472	+	616.000i	−0.0986928	+	0.113961i
$309$		−	3330.00i		−	0.613065i
$310$	4092.00			0.749710
$311$	−6335.84			−1.15522			−0.577609	−	0.816314i	$-0.696014\pi$
$311$	−6335.84			−1.15522			−0.577609	+	0.816314i	$0.696014\pi$
$312$	2376.00			0.431136
$313$		−	1829.05i		−	0.330300i	−0.986268	−	0.165150i	$-0.947189\pi$
$313$		−	1829.05i		−	0.330300i	0.986268	−	0.165150i	$-0.0528108\pi$
$314$	−1073.87			−0.193000
$315$	−7201.87	−	6237.00i	−1.28819	−	1.11560i
$316$	−680.000			−0.121054
$317$			72.0000i			0.0127569i	0.999980	+	0.00637843i	$0.00203033\pi$
$317$			72.0000i			0.0127569i	−0.999980	+	0.00637843i	$0.997970\pi$
$318$	6983.63			1.23152
$319$	−1353.00			−0.237472
$320$	1219.36			0.213014
$321$		−	10646.9i		−	1.85126i
$322$	−168.000	−	145.492i	−0.0290754	−	0.0251800i
$323$			480.000i			0.0826870i
$324$	−2916.00			−0.500000
$325$		−	13603.5i		−	2.32181i
$326$		−	3962.00i		−	0.673113i
$327$	2068.07			0.349738
$328$			831.384i			0.139956i
$329$	4970.99	+	4305.00i	0.833007	+	0.721405i
$330$	2178.00			0.363318
$331$	8476.00			1.40750			0.703751	−	0.710447i	$-0.251507\pi$
$331$	8476.00			1.40750			0.703751	+	0.710447i	$0.251507\pi$
$332$	−3713.52			−0.613873
$333$	2457.00			0.404333
$334$		−	7517.10i		−	1.23149i
$335$	3219.88			0.525137
$336$	−1163.94	−	1008.00i	−0.188982	−	0.163663i
$337$	−10538.0			−1.70339			−0.851694	−	0.524040i	$-0.824424\pi$
$337$	−10538.0			−1.70339			−0.851694	+	0.524040i	$0.824424\pi$
$338$		−	2140.00i		−	0.344381i
$339$		−	11317.2i		−	1.81318i
$340$	4224.00			0.673760
$341$	1181.26			0.187592
$342$	−467.654			−0.0739410
$343$	−3430.00	+	5346.84i	−0.539949	+	0.841698i
$344$			3856.00i			0.604365i
$345$			594.000i			0.0926953i
$346$			5979.04i			0.929003i
$347$			7068.00i			1.09346i	0.837309	+	0.546729i	$0.184127\pi$
$347$			7068.00i			1.09346i	−0.837309	+	0.546729i	$0.815873\pi$
$348$		−	2556.51i		−	0.393802i
$349$		−	6029.27i		−	0.924755i	−0.886683	−	0.462377i	$-0.846997\pi$
$349$		−	6029.27i		−	0.924755i	0.886683	−	0.462377i	$-0.153003\pi$
$350$	−5771.19	+	6664.00i	−0.881381	+	1.01773i
$351$			8019.00i			1.21944i
$352$	352.000			0.0533002
$353$	−4827.23			−0.727839			−0.363920	−	0.931430i	$-0.618562\pi$
$353$	−4827.23			−0.727839			−0.363920	+	0.931430i	$0.618562\pi$
$354$			7686.00i			1.15397i
$355$			5715.77i			0.854539i
$356$	−2798.99			−0.416703
$357$	−4032.00	−	3491.81i	−0.597748	−	0.517665i
$358$	−3492.00			−0.515525
$359$		−	3684.00i		−	0.541599i	−0.962636	−	0.270800i	$-0.912712\pi$
$359$		−	3684.00i		−	0.541599i	0.962636	−	0.270800i	$-0.0872881\pi$
$360$			4115.35i			0.602495i
$361$	6784.00			0.989065
$362$	2840.56			0.412422
$363$	628.734			0.0909091
$364$	−2772.00	+	3200.83i	−0.399155	+	0.460904i
$365$			8877.00i			1.27300i
$366$	2736.00			0.390746
$367$		−	9987.00i		−	1.42048i	−0.703958	−	0.710242i	$-0.748586\pi$
$367$		−	9987.00i		−	1.42048i	0.703958	−	0.710242i	$-0.251414\pi$
$368$			96.0000i			0.0135988i
$369$	−2805.92			−0.395855
$370$		−	3467.57i		−	0.487217i
$371$	−8147.57	+	9408.00i	−1.14016	+	1.31655i
$372$			2232.00i			0.311086i
$373$	−3472.00			−0.481966			−0.240983	−	0.970529i	$-0.577470\pi$
$373$	−3472.00			−0.481966			−0.240983	+	0.970529i	$0.577470\pi$
$374$	1219.36			0.168588
$375$	11187.0			1.54052
$376$		−	2840.56i		−	0.389603i
$377$	−7030.39			−0.960434
$378$	3402.00	−	3928.29i	0.462910	−	0.534522i
$379$	11047.0			1.49722			0.748610	−	0.663011i	$-0.230722\pi$
$379$	11047.0			1.49722			0.748610	+	0.663011i	$0.230722\pi$
$380$			660.000i			0.0890981i
$381$	1579.63			0.212407
$382$	1008.00			0.135010
$383$	7769.98			1.03663			0.518313	−	0.855191i	$-0.326560\pi$
$383$	7769.98			1.03663			0.518313	+	0.855191i	$0.326560\pi$
$384$			665.108i			0.0883883i
$385$	−2541.00	+	2934.09i	−0.336367	+	0.388403i
$386$		−	2488.00i		−	0.328072i
$387$	−13014.0			−1.70940
$388$			4059.93i			0.531215i
$389$		−	7464.00i		−	0.972853i	−0.873721	−	0.486427i	$-0.838300\pi$
$389$		−	7464.00i		−	0.972853i	0.873721	−	0.486427i	$-0.161700\pi$
$390$	11317.2			1.46941
$391$			332.554i			0.0430127i
$392$	2715.86	−	392.000i	0.349927	−	0.0505076i
$393$	−7308.00			−0.938015
$394$	5820.00			0.744181
$395$	−3238.94			−0.412578
$396$			1188.00i			0.150756i
$397$		−	2646.57i		−	0.334579i	−0.985908	−	0.167289i	$-0.946499\pi$
$397$		−	2646.57i		−	0.334579i	0.985908	−	0.167289i	$-0.0535014\pi$
$398$	−7309.25			−0.920552
$399$	545.596	−	630.000i	0.0684561	−	0.0790462i
$400$	3808.00			0.476000
$401$			14538.0i			1.81046i	0.424926	+	0.905228i	$0.360300\pi$
$401$			14538.0i			1.81046i	−0.424926	+	0.905228i	$0.639700\pi$
$402$			1756.30i			0.217901i
$403$	6138.00			0.758699
$404$	1926.04			0.237188
$405$	−13889.3			−1.70411
$406$	3444.00	+	2982.59i	0.420992	+	0.364590i
$407$		−	1001.00i		−	0.121911i
$408$			2304.00i			0.279571i
$409$			138.564i			0.0167520i	0.999965	+	0.00837598i	$0.00266619\pi$
$409$			138.564i			0.0167520i	−0.999965	+	0.00837598i	$0.997334\pi$
$410$			3960.00i			0.477001i
$411$			14029.6i			1.68377i
$412$		−	2563.44i		−	0.306532i
$413$	−10354.2	−	8967.00i	−1.23365	−	1.06837i
$414$	−324.000			−0.0384631
$415$	−17688.0			−2.09222
$416$	1829.05			0.215568
$417$		−	15822.0i		−	1.85805i
$418$			190.526i			0.0222940i
$419$	−11783.1			−1.37385			−0.686926	−	0.726727i	$-0.741040\pi$
$419$	−11783.1			−1.37385			−0.686926	+	0.726727i	$0.741040\pi$
$420$	−5544.00	−	4801.24i	−0.644094	−	0.557802i
$421$	−247.000			−0.0285939			−0.0142970	−	0.999898i	$-0.504551\pi$
$421$	−247.000			−0.0285939			−0.0142970	+	0.999898i	$0.504551\pi$
$422$			5720.00i			0.659823i
$423$	9586.90			1.10196
$424$	5376.00			0.615759
$425$	13191.3			1.50558
$426$	−3117.69			−0.354584
$427$	−3192.00	+	3685.80i	−0.361760	+	0.417725i
$428$		−	8196.00i		−	0.925628i
$429$	3267.00			0.367674
$430$			18366.7i			2.05981i
$431$			12333.0i			1.37833i	0.724605	+	0.689164i	$0.242022\pi$
$431$			12333.0i			1.37833i	−0.724605	+	0.689164i	$0.757978\pi$
$432$	−2244.74			−0.250000
$433$			4797.78i			0.532486i	0.963906	+	0.266243i	$0.0857824\pi$
$433$			4797.78i			0.532486i	−0.963906	+	0.266243i	$0.914218\pi$
$434$	−3006.84	−	2604.00i	−0.332564	−	0.288009i
$435$		−	12177.0i		−	1.34217i
$436$	1592.00			0.174869
$437$	−51.9615			−0.00568800
$438$	−4842.00			−0.528219
$439$			7293.67i			0.792956i	0.918044	+	0.396478i	$0.129768\pi$
$439$			7293.67i			0.792956i	−0.918044	+	0.396478i	$0.870232\pi$
$440$	1676.63			0.181659
$441$	1323.00	+	9166.01i	0.142857	+	0.989743i
$442$	6336.00			0.681839
$443$		−	3042.00i		−	0.326252i	−0.986605	−	0.163126i	$-0.947842\pi$
$443$		−	3042.00i		−	0.326252i	0.986605	−	0.163126i	$-0.0521578\pi$
$444$	1891.40			0.202166
$445$	−13332.0			−1.42022
$446$	−10447.7			−1.10923
$447$		−	8932.19i		−	0.945141i
$448$	−896.000	−	775.959i	−0.0944911	−	0.0818317i
$449$			10278.0i			1.08029i	0.841573	+	0.540143i	$0.181630\pi$
$449$			10278.0i			1.08029i	−0.841573	+	0.540143i	$0.818370\pi$
$450$			12852.0i			1.34633i
$451$			1143.15i			0.119355i
$452$		−	8712.00i		−	0.906589i
$453$	−207.846			−0.0215573
$454$			12789.5i			1.32211i
$455$	−13203.4	+	15246.0i	−1.36041	+	1.57086i
$456$	−360.000			−0.0369705
$457$	−14162.0			−1.44961			−0.724804	−	0.688956i	$-0.758069\pi$
$457$	−14162.0			−1.44961			−0.724804	+	0.688956i	$0.758069\pi$
$458$	−11244.5			−1.14720
$459$	−7776.00			−0.790746
$460$			457.261i			0.0463477i
$461$	−1749.37			−0.176738			−0.0883691	−	0.996088i	$-0.528166\pi$
$461$	−1749.37			−0.176738			−0.0883691	+	0.996088i	$0.528166\pi$
$462$	−1600.41	−	1386.00i	−0.161165	−	0.139573i
$463$	−13885.0			−1.39372			−0.696858	−	0.717209i	$-0.745419\pi$
$463$	−13885.0			−1.39372			−0.696858	+	0.717209i	$0.745419\pi$
$464$		−	1968.00i		−	0.196901i
$465$			10631.3i			1.06025i
$466$	−2580.00			−0.256473
$467$	6406.86			0.634848			0.317424	−	0.948284i	$-0.397182\pi$
$467$	6406.86			0.634848			0.317424	+	0.948284i	$0.397182\pi$
$468$			6173.03i			0.609719i
$469$	−2366.00	−	2049.02i	−0.232946	−	0.201737i
$470$		−	13530.0i		−	1.32786i
$471$		−	2790.00i		−	0.272944i
$472$			5916.69i			0.576986i
$473$			5302.00i			0.515404i
$474$		−	1766.69i		−	0.171196i
$475$			2061.14i			0.199098i
$476$	−3103.84	−	2688.00i	−0.298874	−	0.258833i
$477$			18144.0i			1.74163i
$478$	−12150.0			−1.16261
$479$	12879.5			1.22856			0.614281	−	0.789088i	$-0.289446\pi$
$479$	12879.5			1.22856			0.614281	+	0.789088i	$0.289446\pi$
$480$			3168.00i			0.301247i
$481$		−	5201.35i		−	0.493058i
$482$	−7472.07			−0.706107
$483$	378.000	−	436.477i	0.0356099	−	0.0411188i
$484$	484.000			0.0454545
$485$			19338.0i			1.81050i
$486$		−	7575.99i		−	0.707107i
$487$	20056.0			1.86617			0.933084	−	0.359658i	$-0.117107\pi$
$487$	20056.0			1.86617			0.933084	+	0.359658i	$0.117107\pi$
$488$	2106.17			0.195373
$489$	10293.6			0.951926
$490$	12936.0	−	1867.15i	1.19263	−	0.172141i
$491$		−	13743.0i		−	1.26316i	−0.775310	−	0.631581i	$-0.782406\pi$
$491$		−	13743.0i		−	1.26316i	0.775310	−	0.631581i	$-0.217594\pi$
$492$	−2160.00			−0.197927
$493$		−	6817.35i		−	0.622795i
$494$			990.000i			0.0901664i
$495$			5658.61i			0.513809i
$496$			1718.19i			0.155543i
$497$	3637.31	−	4200.00i	0.328281	−	0.379066i
$498$		−	9648.00i		−	0.868147i
$499$	−4061.00			−0.364319			−0.182160	−	0.983269i	$-0.558309\pi$
$499$	−4061.00			−0.364319			−0.182160	+	0.983269i	$0.558309\pi$
$500$	8611.76			0.770259
$501$	19530.0			1.74159
$502$			5746.94i			0.510954i
$503$	−17694.6			−1.56852			−0.784259	−	0.620434i	$-0.786957\pi$
$503$	−17694.6			−1.56852			−0.784259	+	0.620434i	$0.786957\pi$
$504$	2618.86	−	3024.00i	0.231455	−	0.267261i
$505$	9174.00			0.808391
$506$			132.000i			0.0115971i
$507$	5559.88			0.487028
$508$	1216.00			0.106203
$509$	16766.3			1.46002			0.730011	−	0.683436i	$-0.239515\pi$
$509$	16766.3			1.46002			0.730011	+	0.683436i	$0.239515\pi$
$510$			10974.3i			0.952841i
$511$	5649.00	−	6522.90i	0.489035	−	0.564689i
$512$			512.000i			0.0441942i
$513$		−	1215.00i		−	0.104568i
$514$			855.633i			0.0734248i
$515$		−	12210.0i		−	1.04473i
$516$	−10018.2			−0.854701
$517$		−	3905.77i		−	0.332255i
$518$	−2206.63	+	2548.00i	−0.187170	+	0.216125i
$519$	−15534.0			−1.31381
$520$	8712.00			0.734705
$521$	16795.7			1.41235			0.706174	−	0.708039i	$-0.250420\pi$
$521$	16795.7			1.41235			0.706174	+	0.708039i	$0.250420\pi$
$522$	6642.00			0.556920
$523$			12659.6i			1.05844i	0.848485	+	0.529220i	$0.177515\pi$
$523$			12659.6i			1.05844i	−0.848485	+	0.529220i	$0.822485\pi$
$524$	−5625.70			−0.469007
$525$	−17313.6	−	14994.0i	−1.43929	−	1.24646i
$526$	486.000			0.0402863
$527$			5952.00i			0.491979i
$528$			914.523i			0.0753778i
$529$	12131.0			0.997041
$530$	25606.6			2.09864
$531$	−19968.8			−1.63196
$532$	420.000	−	484.974i	0.0342280	−	0.0395231i
$533$			5940.00i			0.482720i
$534$		−	7272.00i		−	0.589308i
$535$		−	39038.7i		−	3.15475i
$536$			1352.00i			0.108951i
$537$		−	9072.48i		−	0.729062i
$538$		−	1247.08i		−	0.0999355i
$539$	3734.30	−	539.000i	0.298419	−	0.0430730i
$540$	−10692.0			−0.852056
$541$	320.000			0.0254305			0.0127152	−	0.999919i	$-0.495953\pi$
$541$	320.000			0.0254305			0.0127152	+	0.999919i	$0.495953\pi$
$542$	9280.33			0.735469
$543$			7380.00i			0.583253i
$544$			1773.62i			0.139786i
$545$	7582.92			0.595994
$546$	−8316.00	−	7201.87i	−0.651817	−	0.564490i
$547$	11126.0			0.869677			0.434839	−	0.900508i	$-0.356805\pi$
$547$	11126.0			0.869677			0.434839	+	0.900508i	$0.356805\pi$
$548$			10800.0i			0.841885i
$549$			7108.34i			0.552598i
$550$	5236.00			0.405934
$551$	1065.21			0.0823585
$552$	−249.415			−0.0192316
$553$	2380.00	+	2061.14i	0.183016	+	0.158497i
$554$		−	14972.0i		−	1.14819i
$555$	9009.00			0.689028
$556$		−	12179.8i		−	0.929025i
$557$		−	18705.0i		−	1.42290i	−0.702736	−	0.711451i	$-0.748038\pi$
$557$		−	18705.0i		−	1.42290i	0.702736	−	0.711451i	$-0.251962\pi$
$558$	−5798.91			−0.439941
$559$			27550.0i			2.08451i
$560$	−4267.77	−	3696.00i	−0.322047	−	0.278901i
$561$			3168.00i			0.238419i
$562$	−1734.00			−0.130150
$563$	−11320.7			−0.847442			−0.423721	−	0.905793i	$-0.639276\pi$
$563$	−11320.7			−0.847442			−0.423721	+	0.905793i	$0.639276\pi$
$564$	7380.00			0.550982
$565$		−	41496.5i		−	3.08986i
$566$	−13174.0			−0.978346
$567$	10206.0	+	8838.66i	0.755929	+	0.654654i
$568$	−2400.00			−0.177292
$569$		−	2190.00i		−	0.161353i	−0.996740	−	0.0806763i	$-0.974292\pi$
$569$		−	2190.00i		−	0.161353i	0.996740	−	0.0806763i	$-0.0257080\pi$
$570$	−1714.73			−0.126004
$571$	20042.0			1.46888			0.734441	−	0.678673i	$-0.237444\pi$
$571$	20042.0			1.46888			0.734441	+	0.678673i	$0.237444\pi$
$572$	2514.94			0.183837
$573$			2618.86i			0.190933i
$574$	2520.00	−	2909.85i	0.183245	−	0.211593i
$575$			1428.00i			0.103568i
$576$	−1728.00			−0.125000
$577$			668.572i			0.0482374i	0.999709	+	0.0241187i	$0.00767797\pi$
$577$			668.572i			0.0482374i	−0.999709	+	0.0241187i	$0.992322\pi$
$578$		−	3682.00i		−	0.264967i
$579$	6464.01			0.463964
$580$		−	9373.86i		−	0.671083i
$581$	12997.3	+	11256.0i	0.928088	+	0.803748i
$582$	−10548.0			−0.751252
$583$	7392.00			0.525121
$584$	−3727.37			−0.264109
$585$			29403.0i			2.07806i
$586$		−	10821.9i		−	0.762878i
$587$	9843.24			0.692120			0.346060	−	0.938212i	$-0.387519\pi$
$587$	9843.24			0.692120			0.346060	+	0.938212i	$0.387519\pi$
$588$	1018.45	+	7056.00i	0.0714286	+	0.494872i
$589$	−930.000			−0.0650594
$590$			28182.0i			1.96650i
$591$			15120.8i			1.05243i
$592$	1456.00			0.101083
$593$	12910.7			0.894063			0.447031	−	0.894518i	$-0.352481\pi$
$593$	12910.7			0.894063			0.447031	+	0.894518i	$0.352481\pi$
$594$	−3086.51			−0.213201
$595$	−14784.0	−	12803.3i	−1.01863	−	0.882160i
$596$		−	6876.00i		−	0.472570i
$597$		−	18990.0i		−	1.30186i
$598$			685.892i			0.0469034i
$599$		−	19290.0i		−	1.31581i	−0.753103	−	0.657903i	$-0.771444\pi$
$599$		−	19290.0i		−	1.31581i	0.753103	−	0.657903i	$-0.228556\pi$
$600$			9893.47i			0.673166i
$601$		−	8468.00i		−	0.574737i	−0.957820	−	0.287368i	$-0.907220\pi$
$601$		−	8468.00i		−	0.574737i	0.957820	−	0.287368i	$-0.0927804\pi$
$602$	11687.9	−	13496.0i	0.791300	−	0.913714i
$603$	−4563.00			−0.308159
$604$	−160.000			−0.0107787
$605$	2305.36			0.154919
$606$			5004.00i			0.335435i
$607$		−	9295.92i		−	0.621597i	−0.950476	−	0.310799i	$-0.899403\pi$
$607$		−	9295.92i		−	0.621597i	0.950476	−	0.310799i	$-0.100597\pi$
$608$	−277.128			−0.0184852
$609$	−7749.00	+	8947.77i	−0.515608	+	0.595373i
$610$	10032.0			0.665875
$611$		−	20295.0i		−	1.34378i
$612$	−5985.97			−0.395373
$613$	1478.00			0.0973831			0.0486916	−	0.998814i	$-0.484495\pi$
$613$	1478.00			0.0973831			0.0486916	+	0.998814i	$0.484495\pi$
$614$	−7115.26			−0.467669
$615$	−10288.4			−0.674581
$616$	−1232.00	−	1066.94i	−0.0805823	−	0.0697863i
$617$			25314.0i			1.65171i	0.563885	+	0.825854i	$0.309306\pi$
$617$			25314.0i			1.65171i	−0.563885	+	0.825854i	$0.690694\pi$
$618$	6660.00			0.433502
$619$			15100.0i			0.980486i	0.871586	+	0.490243i	$0.163092\pi$
$619$			15100.0i			0.980486i	−0.871586	+	0.490243i	$0.836908\pi$
$620$			8184.00i			0.530125i
$621$		−	841.777i		−	0.0543951i
$622$		−	12671.7i		−	0.816862i
$623$	9796.48	+	8484.00i	0.629996	+	0.545593i
$624$			4752.00i			0.304859i
$625$	11269.0			0.721216
$626$	3658.09			0.233557
$627$	−495.000			−0.0315285
$628$		−	2147.74i		−	0.136472i
$629$	5043.73			0.319725
$630$	12474.0	−	14403.7i	0.788851	−	0.910887i
$631$	−1912.00			−0.120627			−0.0603134	−	0.998179i	$-0.519210\pi$
$631$	−1912.00			−0.120627			−0.0603134	+	0.998179i	$0.519210\pi$
$632$		−	1360.00i		−	0.0855979i
$633$	−14861.0			−0.933130
$634$	−144.000			−0.00902046
$635$	5791.98			0.361965
$636$			13967.3i			0.870814i
$637$	19404.0	−	2800.73i	1.20693	−	0.174205i
$638$		−	2706.00i		−	0.167918i
$639$		−	8100.00i		−	0.501457i
$640$			2438.73i			0.150624i
$641$			25050.0i			1.54355i	0.635896	+	0.771775i	$0.280631\pi$
$641$			25050.0i			1.54355i	−0.635896	+	0.771775i	$0.719369\pi$
$642$	21293.8			1.30904
$643$		−	5469.82i		−	0.335472i	−0.985832	−	0.167736i	$-0.946354\pi$
$643$		−	5469.82i		−	0.335472i	0.985832	−	0.167736i	$-0.0536456\pi$
$644$	290.985	−	336.000i	0.0178050	−	0.0205594i
$645$	−47718.0			−2.91301
$646$	−960.000			−0.0584686
$647$	−6382.61			−0.387830			−0.193915	−	0.981018i	$-0.562119\pi$
$647$	−6382.61			−0.387830			−0.193915	+	0.981018i	$0.562119\pi$
$648$		−	5832.00i		−	0.353553i
$649$			8135.44i			0.492056i
$650$	27207.1			1.64177
$651$	6765.39	−	7812.00i	0.407307	−	0.470317i
$652$	7924.00			0.475963
$653$		−	8724.00i		−	0.522812i	−0.965229	−	0.261406i	$-0.915814\pi$
$653$		−	8724.00i		−	0.522812i	0.965229	−	0.261406i	$-0.0841862\pi$
$654$			4136.14i			0.247302i
$655$	−26796.0			−1.59848
$656$	−1662.77			−0.0989637
$657$		−	12579.9i		−	0.747014i
$658$	−8610.00	+	9941.97i	−0.510111	+	0.589025i
$659$		−	28317.0i		−	1.67386i	−0.547310	−	0.836930i	$-0.684348\pi$
$659$		−	28317.0i		−	1.67386i	0.547310	−	0.836930i	$-0.315652\pi$
$660$			4356.00i			0.256905i
$661$		−	31641.1i		−	1.86187i	−0.365184	−	0.930935i	$-0.618994\pi$
$661$		−	31641.1i		−	1.86187i	0.365184	−	0.930935i	$-0.381006\pi$
$662$			16952.0i			0.995254i
$663$			16461.4i			0.964266i
$664$		−	7427.03i		−	0.434074i
$665$	2000.52	−	2310.00i	0.116657	−	0.134704i
$666$			4914.00i			0.285906i
$667$	738.000			0.0428418
$668$	15034.2			0.870794
$669$		−	27144.0i		−	1.56868i
$670$			6439.76i			0.371328i
$671$	2895.99			0.166615
$672$	2016.00	−	2327.88i	0.115728	−	0.133631i
$673$	−12872.0			−0.737265			−0.368632	−	0.929575i	$-0.620174\pi$
$673$	−12872.0			−0.737265			−0.368632	+	0.929575i	$0.620174\pi$
$674$		−	21076.0i		−	1.20448i
$675$	−33390.5			−1.90400
$676$	4280.00			0.243514
$677$	3613.06			0.205112			0.102556	−	0.994727i	$-0.467298\pi$
$677$	3613.06			0.205112			0.102556	+	0.994727i	$0.467298\pi$
$678$	22634.4			1.28211
$679$	12306.0	−	14209.7i	0.695524	−	0.803122i
$680$			8448.00i			0.476421i
$681$	−33228.0			−1.86975
$682$			2362.52i			0.132647i
$683$		−	21282.0i		−	1.19229i	−0.802877	−	0.596144i	$-0.796699\pi$
$683$		−	21282.0i		−	1.19229i	0.802877	−	0.596144i	$-0.203301\pi$
$684$		−	935.307i		−	0.0522842i
$685$			51441.9i			2.86933i
$686$	−10693.7	−	6860.00i	−0.595170	−	0.381802i
$687$		−	29214.0i		−	1.62239i
$688$	−7712.00			−0.427351
$689$	38410.0			2.12381
$690$	−1188.00			−0.0655455
$691$			16277.8i			0.896146i	0.893997	+	0.448073i	$0.147890\pi$
$691$			16277.8i			0.896146i	−0.893997	+	0.448073i	$0.852110\pi$
$692$	−11958.1			−0.656905
$693$	3600.93	−	4158.00i	0.197386	−	0.227921i
$694$	−14136.0			−0.773192
$695$		−	58014.0i		−	3.16633i
$696$	5113.01			0.278460
$697$	−5760.00			−0.313021
$698$	12058.5			0.653900
$699$		−	6703.04i		−	0.362707i
$700$	−13328.0	−	11542.4i	−0.719644	−	0.623230i
$701$			2790.00i			0.150324i	0.997171	+	0.0751618i	$0.0239473\pi$
$701$			2790.00i			0.150324i	−0.997171	+	0.0751618i	$0.976053\pi$
$702$	−16038.0			−0.862273
$703$			788.083i			0.0422804i
$704$			704.000i			0.0376889i
$705$	35152.0			1.87787
$706$		−	9654.45i		−	0.514660i
$707$	−6741.14	−	5838.00i	−0.358595	−	0.310552i
$708$	−15372.0			−0.815982
$709$	−13001.0			−0.688664			−0.344332	−	0.938848i	$-0.611895\pi$
$709$	−13001.0			−0.688664			−0.344332	+	0.938848i	$0.611895\pi$
$710$	−11431.5			−0.604251
$711$	4590.00			0.242108
$712$		−	5597.99i		−	0.294654i
$713$	−644.323			−0.0338430
$714$	6983.63	−	8064.00i	0.366044	−	0.422672i
$715$	11979.0			0.626558
$716$		−	6984.00i		−	0.364531i
$717$		−	31566.6i		−	1.64418i
$718$	7368.00			0.382968
$719$	−10792.4			−0.559790			−0.279895	−	0.960031i	$-0.590300\pi$
$719$	−10792.4			−0.559790			−0.279895	+	0.960031i	$0.590300\pi$
$720$	−8230.71			−0.426028
$721$	−7770.00	+	8972.02i	−0.401345	+	0.463434i
$722$			13568.0i			0.699375i
$723$		−	19413.0i		−	0.998585i
$724$			5681.13i			0.291626i
$725$		−	29274.0i		−	1.49960i
$726$			1257.47i			0.0642824i
$727$			20982.1i			1.07040i	0.844725	+	0.535201i	$0.179764\pi$
$727$			20982.1i			1.07040i	−0.844725	+	0.535201i	$0.820236\pi$
$728$	−6401.66	−	5544.00i	−0.325908	−	0.282245i
$729$	19683.0			1.00000
$730$	−17754.0			−0.900144
$731$	−26715.2			−1.35170
$732$			5472.00i			0.276299i
$733$			29347.9i			1.47884i	0.673246	+	0.739419i	$0.264900\pi$
$733$			29347.9i			1.47884i	−0.673246	+	0.739419i	$0.735100\pi$
$734$	19974.0			1.00443
$735$	4851.00	+	33608.7i	0.243445	+	1.68663i
$736$	−192.000			−0.00961578
$737$			1859.00i			0.0929134i
$738$		−	5611.84i		−	0.279912i
$739$	13202.0			0.657163			0.328581	−	0.944476i	$-0.393429\pi$
$739$	13202.0			0.657163			0.328581	+	0.944476i	$0.393429\pi$
$740$	6935.13			0.344514
$741$	−2572.10			−0.127515
$742$	−18816.0	−	16295.1i	−0.930939	−	0.806217i
$743$			15807.0i			0.780488i	0.920711	+	0.390244i	$0.127609\pi$
$743$			15807.0i			0.780488i	−0.920711	+	0.390244i	$0.872391\pi$
$744$	−4464.00			−0.219971
$745$		−	32751.3i		−	1.61063i
$746$		−	6944.00i		−	0.340801i
$747$	25066.2			1.22775
$748$			2438.73i			0.119210i
$749$	−24842.8	+	28686.0i	−1.21193	+	1.39942i
$750$			22374.0i			1.08931i
$751$	33109.0			1.60874			0.804371	−	0.594128i	$-0.202503\pi$
$751$	33109.0			1.60874			0.804371	+	0.594128i	$0.202503\pi$
$752$	5681.13			0.275491
$753$	−14931.0			−0.722597
$754$		−	14060.8i		−	0.679130i
$755$	−762.102			−0.0367361
$756$	7856.58	+	6804.00i	0.377964	+	0.327327i
$757$	30589.0			1.46866			0.734330	−	0.678792i	$-0.237496\pi$
$757$	30589.0			1.46866			0.734330	+	0.678792i	$0.237496\pi$
$758$			22094.0i			1.05869i
$759$	−342.946			−0.0164007
$760$	−1320.00			−0.0630019
$761$	−16832.1			−0.801790			−0.400895	−	0.916124i	$-0.631301\pi$
$761$	−16832.1			−0.801790			−0.400895	+	0.916124i	$0.631301\pi$
$762$			3159.26i			0.150194i
$763$	−5572.00	−	4825.49i	−0.264377	−	0.228958i
$764$			2016.00i			0.0954664i
$765$	−28512.0			−1.34752
$766$			15540.0i			0.733005i
$767$			42273.0i			1.99008i
$768$	−1330.22			−0.0625000
$769$		−	8603.10i		−	0.403427i	−0.979445	−	0.201714i	$-0.935349\pi$
$769$		−	8603.10i		−	0.403427i	0.979445	−	0.201714i	$-0.0646510\pi$
$770$	−5868.19	−	5082.00i	−0.274643	−	0.237847i
$771$	−2223.00			−0.103838
$772$	4976.00			0.231982
$773$	20325.6			0.945746			0.472873	−	0.881131i	$-0.343217\pi$
$773$	20325.6			0.945746			0.472873	+	0.881131i	$0.343217\pi$
$774$		−	26028.0i		−	1.20873i
$775$			25558.1i			1.18461i
$776$	−8119.85			−0.375626
$777$	−6619.90	−	5733.00i	−0.305647	−	0.264698i
$778$	14928.0			0.687911
$779$		−	900.000i		−	0.0413939i
$780$			22634.4i			1.03903i
$781$	−3300.00			−0.151195
$782$	−665.108			−0.0304146
$783$			17256.4i			0.787604i
$784$	784.000	+	5431.71i	0.0357143	+	0.247436i
$785$		−	10230.0i		−	0.465127i
$786$		−	14616.0i		−	0.663277i
$787$		−	12112.2i		−	0.548608i	−0.961643	−	0.274304i	$-0.911553\pi$
$787$		−	12112.2i		−	0.548608i	0.961643	−	0.274304i	$-0.0884474\pi$
$788$			11640.0i			0.526216i
$789$			1262.67i			0.0569735i
$790$		−	6477.87i		−	0.291737i
$791$	−26406.8	+	30492.0i	−1.18700	+	1.37063i
$792$	−2376.00			−0.106600
$793$	15048.0			0.673859
$794$	5293.15			0.236583
$795$			66528.0i			2.96793i
$796$		−	14618.5i		−	0.650929i
$797$	−16511.6			−0.733842			−0.366921	−	0.930252i	$-0.619588\pi$
$797$	−16511.6			−0.733842			−0.366921	+	0.930252i	$0.619588\pi$
$798$	1260.00	+	1091.19i	0.0558941	+	0.0484057i
$799$	19680.0			0.871375
$800$			7616.00i			0.336583i
$801$	18893.2			0.833407
$802$	−29076.0			−1.28019
$803$	−5125.14			−0.225233
$804$	−3512.60			−0.154079
$805$	1386.00	−	1600.41i	0.0606833	−	0.0700711i
$806$			12276.0i			0.536481i
$807$	3240.00			0.141330
$808$			3852.08i			0.167717i
$809$		−	20379.0i		−	0.885646i	−0.896609	−	0.442823i	$-0.853977\pi$
$809$		−	20379.0i		−	0.885646i	0.896609	−	0.442823i	$-0.146023\pi$
$810$		−	27778.6i		−	1.20499i
$811$			4581.27i			0.198360i	0.995069	+	0.0991802i	$0.0316220\pi$
$811$			4581.27i			0.198360i	−0.995069	+	0.0991802i	$0.968378\pi$
$812$	−5965.18	+	6888.00i	−0.257804	+	0.297686i
$813$			24111.0i			1.04011i
$814$	2002.00			0.0862040
$815$	37743.1			1.62219
$816$	−4608.00			−0.197687
$817$		−	4174.24i		−	0.178749i
$818$	−277.128			−0.0118454
$819$	18711.0	−	21605.6i	0.798309	−	0.921808i
$820$	−7920.00			−0.337291
$821$			34311.0i			1.45854i	0.684226	+	0.729270i	$0.260140\pi$
$821$			34311.0i			1.45854i	−0.684226	+	0.729270i	$0.739860\pi$
$822$	−28059.2			−1.19061
$823$	−12295.0			−0.520749			−0.260375	−	0.965508i	$-0.583846\pi$
$823$	−12295.0			−0.520749			−0.260375	+	0.965508i	$0.583846\pi$
$824$	5126.87			0.216751
$825$			13603.5i			0.574078i
$826$	17934.0	−	20708.4i	0.755452	−	0.872321i
$827$			7815.00i			0.328602i	0.986410	+	0.164301i	$0.0525369\pi$
$827$			7815.00i			0.328602i	−0.986410	+	0.164301i	$0.947463\pi$
$828$		−	648.000i		−	0.0271975i
$829$		−	10385.4i		−	0.435101i	−0.976049	−	0.217551i	$-0.930193\pi$
$829$		−	10385.4i		−	0.435101i	0.976049	−	0.217551i	$-0.0698067\pi$
$830$		−	35376.0i		−	1.47942i
$831$	38898.4			1.62379
$832$			3658.09i			0.152430i
$833$	2715.86	+	18816.0i	0.112964	+	0.782636i
$834$	31644.0			1.31384
$835$	71610.0			2.96786
$836$	−381.051			−0.0157643
$837$		−	15066.0i		−	0.622171i
$838$		−	23566.3i		−	0.971460i
$839$	30364.6			1.24947			0.624733	−	0.780839i	$-0.285208\pi$
$839$	30364.6			1.24947			0.624733	+	0.780839i	$0.285208\pi$
$840$	9602.49	−	11088.0i	0.394425	−	0.455443i
$841$	9260.00			0.379679
$842$		−	494.000i		−	0.0202190i
$843$		−	4505.06i		−	0.184060i
$844$	−11440.0			−0.466565
$845$	20386.2			0.829950
$846$			19173.8i			0.779207i
$847$	−1694.00	−	1467.05i	−0.0687208	−	0.0595140i
$848$			10752.0i			0.435407i
$849$		−	34227.0i		−	1.38359i
$850$			26382.6i			1.06461i
$851$			546.000i			0.0219937i
$852$		−	6235.38i		−	0.250729i
$853$			19343.5i			0.776448i	0.921565	+	0.388224i	$0.126911\pi$
$853$			19343.5i			0.776448i	−0.921565	+	0.388224i	$0.873089\pi$
$854$	−7371.61	−	6384.00i	−0.295376	−	0.255803i
$855$		−	4455.00i		−	0.178196i
$856$	16392.0			0.654518
$857$	−32708.0			−1.30372			−0.651859	−	0.758341i	$-0.726010\pi$
$857$	−32708.0			−1.30372			−0.651859	+	0.758341i	$0.726010\pi$
$858$			6534.00i			0.259985i
$859$			42833.6i			1.70136i	0.525688	+	0.850678i	$0.323808\pi$
$859$			42833.6i			1.70136i	−0.525688	+	0.850678i	$0.676192\pi$
$860$	−36733.3			−1.45651
$861$	7560.00	+	6547.15i	0.299238	+	0.259148i
$862$	−24666.0			−0.974626
$863$			36552.0i			1.44177i	0.693056	+	0.720883i	$0.256264\pi$
$863$			36552.0i			1.44177i	−0.693056	+	0.720883i	$0.743736\pi$
$864$		−	4489.48i		−	0.176777i
$865$	−56958.0			−2.23888
$866$	−9595.56			−0.376525
$867$	9566.12			0.374720
$868$	5208.00	−	6013.68i	0.203653	−	0.235159i
$869$		−	1870.00i		−	0.0729982i
$870$	24354.0			0.949055
$871$			9659.65i			0.375780i
$872$			3184.00i			0.123651i
$873$		−	27404.5i		−	1.06243i
$874$		−	103.923i		−	0.00402202i
$875$	−30141.1	−	26103.0i	−1.16452	−	1.00851i
$876$		−	9684.00i		−	0.373507i
$877$	7820.00			0.301098			0.150549	−	0.988603i	$-0.451896\pi$
$877$	7820.00			0.301098			0.150549	+	0.988603i	$0.451896\pi$
$878$	−14587.3			−0.560705
$879$	28116.0			1.07887
$880$			3353.25i			0.128452i
$881$	−11790.1			−0.450871			−0.225436	−	0.974258i	$-0.572381\pi$
$881$	−11790.1			−0.450871			−0.225436	+	0.974258i	$0.572381\pi$
$882$	−18332.0	+	2646.00i	−0.699854	+	0.101015i
$883$	11581.0			0.441372			0.220686	−	0.975345i	$-0.429170\pi$
$883$	11581.0			0.441372			0.220686	+	0.975345i	$0.429170\pi$
$884$			12672.0i			0.482133i
$885$	−73219.0			−2.78105
$886$	6084.00			0.230695
$887$	−21092.9			−0.798456			−0.399228	−	0.916852i	$-0.630722\pi$
$887$	−21092.9			−0.798456			−0.399228	+	0.916852i	$0.630722\pi$
$888$			3782.80i			0.142953i
$889$	−4256.00	−	3685.80i	−0.160564	−	0.139053i
$890$		−	26664.0i		−	1.00425i
$891$		−	8019.00i		−	0.301511i
$892$		−	20895.5i		−	0.784341i
$893$			3075.00i			0.115231i
$894$	17864.4			0.668315
$895$		−	33265.8i		−	1.24240i
$896$	1551.92	−	1792.00i	0.0578638	−	0.0668153i
$897$	−1782.00			−0.0663314
$898$	−20556.0			−0.763878
$899$	13208.6			0.490025
$900$	−25704.0			−0.952000
$901$			37246.0i			1.37719i
$902$	−2286.31			−0.0843966
$903$	35063.6	+	30366.0i	1.29219	+	1.11907i
$904$	17424.0			0.641055
$905$			27060.0i			0.993928i
$906$		−	415.692i		−	0.0152433i
$907$	−16892.0			−0.618401			−0.309200	−	0.950997i	$-0.600061\pi$
$907$	−16892.0			−0.618401			−0.309200	+	0.950997i	$0.600061\pi$
$908$	−25578.9			−0.934875
$909$	−13000.8			−0.474377
$910$	−30492.0	−	26406.8i	−1.11077	−	0.961954i
$911$		−	19878.0i		−	0.722928i	−0.932386	−	0.361464i	$-0.882277\pi$
$911$		−	19878.0i		−	0.722928i	0.932386	−	0.361464i	$-0.117723\pi$
$912$		−	720.000i		−	0.0261421i
$913$		−	10212.2i		−	0.370179i
$914$		−	28324.0i		−	1.02503i
$915$			26063.9i			0.941690i
$916$		−	22488.9i		−	0.811196i
$917$	19690.0	+	17052.0i	0.709073	+	0.614075i
$918$		−	15552.0i		−	0.559142i
$919$	18100.0			0.649689			0.324844	−	0.945767i	$-0.394688\pi$
$919$	18100.0			0.649689			0.324844	+	0.945767i	$0.394688\pi$
$920$	−914.523			−0.0327727
$921$		−	18486.0i		−	0.661384i
$922$		−	3498.74i		−	0.124973i
$923$	−17147.3			−0.611496
$924$	2772.00	−	3200.83i	0.0986928	−	0.113961i
$925$	21658.0			0.769849
$926$		−	27770.0i		−	0.985506i
$927$			17303.2i			0.613065i
$928$	3936.00			0.139230
$929$	−48253.2			−1.70413			−0.852065	−	0.523436i	$-0.824650\pi$
$929$	−48253.2			−1.70413			−0.852065	+	0.523436i	$0.824650\pi$
$930$	−21262.7			−0.749710
$931$	−2940.00	+	424.352i	−0.103496	+	0.0149383i
$932$		−	5160.00i		−	0.181353i
$933$	32922.0			1.15522
$934$			12813.7i			0.448905i
$935$			11616.0i			0.406293i
$936$	−12346.1			−0.431136
$937$		−	9969.68i		−	0.347594i	−0.984782	−	0.173797i	$-0.944396\pi$
$937$		−	9969.68i		−	0.347594i	0.984782	−	0.173797i	$-0.0556036\pi$
$938$	4098.03	−	4732.00i	0.142650	−	0.164718i
$939$			9504.00i			0.330300i
$940$	27060.0			0.938936
$941$	18300.8			0.633996			0.316998	−	0.948426i	$-0.397325\pi$
$941$	18300.8			0.633996			0.316998	+	0.948426i	$0.397325\pi$
$942$	5580.00			0.193000
$943$		−	623.538i		−	0.0215326i
$944$	−11833.4			−0.407991
$945$	37422.0	+	32408.4i	1.28819	+	1.11560i
$946$	−10604.0			−0.364446
$947$			28470.0i			0.976928i	0.872584	+	0.488464i	$0.162443\pi$
$947$			28470.0i			0.976928i	−0.872584	+	0.488464i	$0.837557\pi$
$948$	3533.38			0.121054
$949$	−26631.0			−0.910937
$950$	−4122.28			−0.140784
$951$		−	374.123i		−	0.0127569i
$952$	5376.00	−	6207.67i	0.183022	−	0.211336i
$953$		−	483.000i		−	0.0164175i	−0.999966	−	0.00820876i	$-0.997387\pi$
$953$		−	483.000i		−	0.0164175i	0.999966	−	0.00820876i	$-0.00261296\pi$
$954$	−36288.0			−1.23152
$955$			9602.49i			0.325371i
$956$		−	24300.0i		−	0.822090i
$957$	7030.39			0.237472
$958$			25759.1i			0.868724i
$959$	32735.8	−	37800.0i	1.10229	−	1.27281i
$960$	−6336.00			−0.213014
$961$	18259.0			0.612903
$962$	10402.7			0.348645
$963$			55323.0i			1.85126i
$964$		−	14944.1i		−	0.499293i
$965$	23701.4			0.790647
$966$	872.954	+	756.000i	0.0290754	+	0.0251800i
$967$	3422.00			0.113799			0.0568997	−	0.998380i	$-0.481878\pi$
$967$	3422.00			0.113799			0.0568997	+	0.998380i	$0.481878\pi$
$968$			968.000i			0.0321412i
$969$		−	2494.15i		−	0.0826870i
$970$	−38676.0			−1.28022
$971$	−7085.82			−0.234186			−0.117093	−	0.993121i	$-0.537358\pi$
$971$	−7085.82			−0.234186			−0.117093	+	0.993121i	$0.537358\pi$
$972$	15152.0			0.500000
$973$	−36918.0	+	42629.2i	−1.21638	+	1.40455i
$974$			40112.0i			1.31958i
$975$			70686.0i			2.32181i
$976$			4212.35i			0.138150i
$977$		−	53562.0i		−	1.75394i	−0.480544	−	0.876970i	$-0.659561\pi$
$977$		−	53562.0i		−	1.75394i	0.480544	−	0.876970i	$-0.340439\pi$
$978$			20587.2i			0.673113i
$979$		−	7697.23i		−	0.251282i
$980$	3734.30	+	25872.0i	0.121722	+	0.843317i
$981$	−10746.0			−0.349738
$982$	27486.0			0.893191
$983$	−1340.61			−0.0434982			−0.0217491	−	0.999763i	$-0.506923\pi$
$983$	−1340.61			−0.0434982			−0.0217491	+	0.999763i	$0.506923\pi$
$984$		−	4320.00i		−	0.139956i
$985$			55442.9i			1.79346i
$986$	13634.7			0.440383
$987$	−25830.0	−	22369.4i	−0.833007	−	0.721405i
$988$	−1980.00			−0.0637573
$989$		−	2892.00i		−	0.0929831i
$990$	−11317.2			−0.363318
$991$	−25931.0			−0.831206			−0.415603	−	0.909546i	$-0.636429\pi$
$991$	−25931.0			−0.831206			−0.415603	+	0.909546i	$0.636429\pi$
$992$	−3436.39			−0.109985
$993$	−44042.6			−1.40750
$994$	8400.00	+	7274.61i	0.268040	+	0.232130i
$995$		−	69630.0i		−	2.21851i
$996$	19296.0			0.613873
$997$		−	24886.1i		−	0.790522i	−0.918569	−	0.395261i	$-0.870654\pi$
$997$		−	24886.1i		−	0.790522i	0.918569	−	0.395261i	$-0.129346\pi$
$998$		−	8122.00i		−	0.257613i
$999$	−12766.9			−0.404333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.4.g.a.419.3	yes	4
3.2	odd	2	inner	462.4.g.a.419.2	yes	4
7.6	odd	2	inner	462.4.g.a.419.4	yes	4
21.20	even	2	inner	462.4.g.a.419.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.4.g.a.419.1	✓	4	21.20	even	2	inner
462.4.g.a.419.2	yes	4	3.2	odd	2	inner
462.4.g.a.419.3	yes	4	1.1	even	1	trivial
462.4.g.a.419.4	yes	4	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	462.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -5.19615 q^{3} -4.00000 q^{4} -19.0526 q^{5} -10.3923i q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -5.19615 q^{3} -4.00000 q^{4} -19.0526 q^{5} -10.3923i q^{6} +(14.0000 + 12.1244i) q^{7} -8.00000i q^{8} +27.0000 q^{9} -38.1051i q^{10} -11.0000i q^{11} +20.7846 q^{12} -57.1577i q^{13} +(-24.2487 + 28.0000i) q^{14} +99.0000 q^{15} +16.0000 q^{16} +55.4256 q^{17} +54.0000i q^{18} +8.66025i q^{19} +76.2102 q^{20} +(-72.7461 - 63.0000i) q^{21} +22.0000 q^{22} +6.00000i q^{23} +41.5692i q^{24} +238.000 q^{25} +114.315 q^{26} -140.296 q^{27} +(-56.0000 - 48.4974i) q^{28} -123.000i q^{29} +198.000i q^{30} +107.387i q^{31} +32.0000i q^{32} +57.1577i q^{33} +110.851i q^{34} +(-266.736 - 231.000i) q^{35} -108.000 q^{36} +91.0000 q^{37} -17.3205 q^{38} +297.000i q^{39} +152.420i q^{40} -103.923 q^{41} +(126.000 - 145.492i) q^{42} -482.000 q^{43} +44.0000i q^{44} -514.419 q^{45} -12.0000 q^{46} +355.070 q^{47} -83.1384 q^{48} +(49.0000 + 339.482i) q^{49} +476.000i q^{50} -288.000 q^{51} +228.631i q^{52} +672.000i q^{53} -280.592i q^{54} +209.578i q^{55} +(96.9948 - 112.000i) q^{56} -45.0000i q^{57} +246.000 q^{58} -739.586 q^{59} -396.000 q^{60} +263.272i q^{61} -214.774 q^{62} +(378.000 + 327.358i) q^{63} -64.0000 q^{64} +1089.00i q^{65} -114.315 q^{66} -169.000 q^{67} -221.703 q^{68} -31.1769i q^{69} +(462.000 - 533.472i) q^{70} -300.000i q^{71} -216.000i q^{72} -465.922i q^{73} +182.000i q^{74} -1236.68 q^{75} -34.6410i q^{76} +(133.368 - 154.000i) q^{77} -594.000 q^{78} +170.000 q^{79} -304.841 q^{80} +729.000 q^{81} -207.846i q^{82} +928.379 q^{83} +(290.985 + 252.000i) q^{84} -1056.00 q^{85} -964.000i q^{86} +639.127i q^{87} -88.0000 q^{88} +699.749 q^{89} -1028.84i q^{90} +(693.000 - 800.207i) q^{91} -24.0000i q^{92} -558.000i q^{93} +710.141i q^{94} -165.000i q^{95} -166.277i q^{96} -1014.98i q^{97} +(-678.964 + 98.0000i) q^{98} -297.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 56 q^{7} + 108 q^{9}+O(q^{10}) \) 4 * q - 16 * q^4 + 56 * q^7 + 108 * q^9	\( 4 q - 16 q^{4} + 56 q^{7} + 108 q^{9} + 396 q^{15} + 64 q^{16} + 88 q^{22} + 952 q^{25} - 224 q^{28} - 432 q^{36} + 364 q^{37} + 504 q^{42} - 1928 q^{43} - 48 q^{46} + 196 q^{49} - 1152 q^{51} + 984 q^{58} - 1584 q^{60} + 1512 q^{63} - 256 q^{64} - 676 q^{67} + 1848 q^{70} - 2376 q^{78} + 680 q^{79} + 2916 q^{81} - 4224 q^{85} - 352 q^{88} + 2772 q^{91}+O(q^{100}) \) 4 * q - 16 * q^4 + 56 * q^7 + 108 * q^9 + 396 * q^15 + 64 * q^16 + 88 * q^22 + 952 * q^25 - 224 * q^28 - 432 * q^36 + 364 * q^37 + 504 * q^42 - 1928 * q^43 - 48 * q^46 + 196 * q^49 - 1152 * q^51 + 984 * q^58 - 1584 * q^60 + 1512 * q^63 - 256 * q^64 - 676 * q^67 + 1848 * q^70 - 2376 * q^78 + 680 * q^79 + 2916 * q^81 - 4224 * q^85 - 352 * q^88 + 2772 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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