LMFDB - Embedded newform 441.4.e.l.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (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:	$26.0198423125$
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 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.l.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +(36.0000 - 62.3538i) q^{10} +(-25.0000 + 43.3013i) q^{11} +36.0000 q^{13} +(32.0000 + 55.4256i) q^{16} +(-63.0000 + 109.119i) q^{17} +(-36.0000 - 62.3538i) q^{19} +144.000 q^{20} -200.000 q^{22} +(7.00000 + 12.1244i) q^{23} +(-99.5000 + 172.339i) q^{25} +(72.0000 + 124.708i) q^{26} -158.000 q^{29} +(-18.0000 + 31.1769i) q^{31} +(-128.000 + 221.703i) q^{32} -504.000 q^{34} +(81.0000 + 140.296i) q^{37} +(144.000 - 249.415i) q^{38} -270.000 q^{41} -324.000 q^{43} +(-200.000 - 346.410i) q^{44} +(-28.0000 + 48.4974i) q^{46} +(36.0000 + 62.3538i) q^{47} -796.000 q^{50} +(-144.000 + 249.415i) q^{52} +(-11.0000 + 19.0526i) q^{53} +900.000 q^{55} +(-316.000 - 547.328i) q^{58} +(-234.000 + 405.300i) q^{59} +(396.000 + 685.892i) q^{61} -144.000 q^{62} -512.000 q^{64} +(-324.000 - 561.184i) q^{65} +(-116.000 + 200.918i) q^{67} +(-504.000 - 872.954i) q^{68} +734.000 q^{71} +(90.0000 - 155.885i) q^{73} +(-324.000 + 561.184i) q^{74} +576.000 q^{76} +(-118.000 - 204.382i) q^{79} +(576.000 - 997.661i) q^{80} +(-540.000 - 935.307i) q^{82} +36.0000 q^{83} +2268.00 q^{85} +(-648.000 - 1122.37i) q^{86} +(-117.000 - 202.650i) q^{89} -112.000 q^{92} +(-144.000 + 249.415i) q^{94} +(-648.000 + 1122.37i) q^{95} -468.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 8 q^{4} - 18 q^{5}+O(q^{10}) $ 2 * q + 4 * q^2 - 8 * q^4 - 18 * q^5	$ 2 q + 4 q^{2} - 8 q^{4} - 18 q^{5} + 72 q^{10} - 50 q^{11} + 72 q^{13} + 64 q^{16} - 126 q^{17} - 72 q^{19} + 288 q^{20} - 400 q^{22} + 14 q^{23} - 199 q^{25} + 144 q^{26} - 316 q^{29} - 36 q^{31} - 256 q^{32} - 1008 q^{34} + 162 q^{37} + 288 q^{38} - 540 q^{41} - 648 q^{43} - 400 q^{44} - 56 q^{46} + 72 q^{47} - 1592 q^{50} - 288 q^{52} - 22 q^{53} + 1800 q^{55} - 632 q^{58} - 468 q^{59} + 792 q^{61} - 288 q^{62} - 1024 q^{64} - 648 q^{65} - 232 q^{67} - 1008 q^{68} + 1468 q^{71} + 180 q^{73} - 648 q^{74} + 1152 q^{76} - 236 q^{79} + 1152 q^{80} - 1080 q^{82} + 72 q^{83} + 4536 q^{85} - 1296 q^{86} - 234 q^{89} - 224 q^{92} - 288 q^{94} - 1296 q^{95} - 936 q^{97}+O(q^{100}) $ 2 * q + 4 * q^2 - 8 * q^4 - 18 * q^5 + 72 * q^10 - 50 * q^11 + 72 * q^13 + 64 * q^16 - 126 * q^17 - 72 * q^19 + 288 * q^20 - 400 * q^22 + 14 * q^23 - 199 * q^25 + 144 * q^26 - 316 * q^29 - 36 * q^31 - 256 * q^32 - 1008 * q^34 + 162 * q^37 + 288 * q^38 - 540 * q^41 - 648 * q^43 - 400 * q^44 - 56 * q^46 + 72 * q^47 - 1592 * q^50 - 288 * q^52 - 22 * q^53 + 1800 * q^55 - 632 * q^58 - 468 * q^59 + 792 * q^61 - 288 * q^62 - 1024 * q^64 - 648 * q^65 - 232 * q^67 - 1008 * q^68 + 1468 * q^71 + 180 * q^73 - 648 * q^74 + 1152 * q^76 - 236 * q^79 + 1152 * q^80 - 1080 * q^82 + 72 * q^83 + 4536 * q^85 - 1296 * q^86 - 234 * q^89 - 224 * q^92 - 288 * q^94 - 1296 * q^95 - 936 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$		0			0
$3$		0			0
$4$	−4.00000	+	6.92820i	−0.500000	+	0.866025i
$5$	−9.00000	−	15.5885i	−0.804984	−	1.39427i	−0.916302	−	0.400489i	$-0.868840\pi$
$5$	−9.00000	−	15.5885i	−0.804984	−	1.39427i	0.111317	−	0.993785i	$-0.464493\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$	36.0000	−	62.3538i	1.13842	−	1.97180i
$11$	−25.0000	+	43.3013i	−0.685253	+	1.18689i	0.288104	+	0.957599i	$0.406975\pi$
$11$	−25.0000	+	43.3013i	−0.685253	+	1.18689i	−0.973357	+	0.229294i	$0.926358\pi$
$12$		0			0
$13$	36.0000			0.768046			0.384023	−	0.923323i	$-0.374538\pi$
$13$	36.0000			0.768046			0.384023	+	0.923323i	$0.374538\pi$
$14$		0			0
$15$		0			0
$16$	32.0000	+	55.4256i	0.500000	+	0.866025i
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.0697893	+	0.997562i	$0.522233\pi$
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.829019	+	0.559220i	$0.811101\pi$
$18$		0			0
$19$	−36.0000	−	62.3538i	−0.434682	−	0.752892i	0.562587	−	0.826738i	$-0.309806\pi$
$19$	−36.0000	−	62.3538i	−0.434682	−	0.752892i	−0.997270	+	0.0738459i	$0.976473\pi$
$20$	144.000			1.60997
$21$		0			0
$22$	−200.000			−1.93819
$23$	7.00000	+	12.1244i	0.0634609	+	0.109918i	0.896010	−	0.444033i	$-0.146453\pi$
$23$	7.00000	+	12.1244i	0.0634609	+	0.109918i	−0.832549	+	0.553951i	$0.813120\pi$
$24$		0			0
$25$	−99.5000	+	172.339i	−0.796000	+	1.37871i
$26$	72.0000	+	124.708i	0.543091	+	0.940661i
$27$		0			0
$28$		0			0
$29$	−158.000			−1.01172			−0.505860	−	0.862616i	$-0.668825\pi$
$29$	−158.000			−1.01172			−0.505860	+	0.862616i	$0.668825\pi$
$30$		0			0
$31$	−18.0000	+	31.1769i	−0.104287	+	0.180630i	−0.913447	−	0.406958i	$-0.866589\pi$
$31$	−18.0000	+	31.1769i	−0.104287	+	0.180630i	0.809160	+	0.587589i	$0.199923\pi$
$32$	−128.000	+	221.703i	−0.707107	+	1.22474i
$33$		0			0
$34$	−504.000			−2.54221
$35$		0			0
$36$		0			0
$37$	81.0000	+	140.296i	0.359900	+	0.623366i	0.987944	−	0.154812i	$-0.0494773\pi$
$37$	81.0000	+	140.296i	0.359900	+	0.623366i	−0.628043	+	0.778178i	$0.716144\pi$
$38$	144.000	−	249.415i	0.614734	−	1.06475i
$39$		0			0
$40$		0			0
$41$	−270.000			−1.02846			−0.514231	−	0.857652i	$-0.671922\pi$
$41$	−270.000			−1.02846			−0.514231	+	0.857652i	$0.671922\pi$
$42$		0			0
$43$	−324.000			−1.14906			−0.574529	−	0.818484i	$-0.694815\pi$
$43$	−324.000			−1.14906			−0.574529	+	0.818484i	$0.694815\pi$
$44$	−200.000	−	346.410i	−0.685253	−	1.18689i
$45$		0			0
$46$	−28.0000	+	48.4974i	−0.0897473	+	0.155447i
$47$	36.0000	+	62.3538i	0.111726	+	0.193516i	0.916466	−	0.400112i	$-0.131029\pi$
$47$	36.0000	+	62.3538i	0.111726	+	0.193516i	−0.804740	+	0.593627i	$0.797695\pi$
$48$		0			0
$49$		0			0
$50$	−796.000			−2.25143
$51$		0			0
$52$	−144.000	+	249.415i	−0.384023	+	0.665148i
$53$	−11.0000	+	19.0526i	−0.0285088	+	0.0493787i	−0.879928	−	0.475107i	$-0.842409\pi$
$53$	−11.0000	+	19.0526i	−0.0285088	+	0.0493787i	0.851419	+	0.524486i	$0.175743\pi$
$54$		0			0
$55$	900.000			2.20647
$56$		0			0
$57$		0			0
$58$	−316.000	−	547.328i	−0.715394	−	1.23910i
$59$	−234.000	+	405.300i	−0.516342	+	0.894331i	0.483478	+	0.875357i	$0.339373\pi$
$59$	−234.000	+	405.300i	−0.516342	+	0.894331i	−0.999820	+	0.0189746i	$0.993960\pi$
$60$		0			0
$61$	396.000	+	685.892i	0.831190	+	1.43966i	0.897095	+	0.441838i	$0.145673\pi$
$61$	396.000	+	685.892i	0.831190	+	1.43966i	−0.0659047	+	0.997826i	$0.520993\pi$
$62$	−144.000			−0.294968
$63$		0			0
$64$	−512.000			−1.00000
$65$	−324.000	−	561.184i	−0.618265	−	1.07087i
$66$		0			0
$67$	−116.000	+	200.918i	−0.211517	+	0.366359i	−0.952190	−	0.305508i	$-0.901174\pi$
$67$	−116.000	+	200.918i	−0.211517	+	0.366359i	0.740672	+	0.671866i	$0.234507\pi$
$68$	−504.000	−	872.954i	−0.898808	−	1.55678i
$69$		0			0
$70$		0			0
$71$	734.000			1.22690			0.613449	−	0.789734i	$-0.289782\pi$
$71$	734.000			1.22690			0.613449	+	0.789734i	$0.289782\pi$
$72$		0			0
$73$	90.0000	−	155.885i	0.144297	−	0.249930i	−0.784813	−	0.619732i	$-0.787241\pi$
$73$	90.0000	−	155.885i	0.144297	−	0.249930i	0.929111	+	0.369802i	$0.120575\pi$
$74$	−324.000	+	561.184i	−0.508976	+	0.881573i
$75$		0			0
$76$	576.000			0.869365
$77$		0			0
$78$		0			0
$79$	−118.000	−	204.382i	−0.168051	−	0.291073i	0.769683	−	0.638426i	$-0.220414\pi$
$79$	−118.000	−	204.382i	−0.168051	−	0.291073i	−0.937735	+	0.347353i	$0.887081\pi$
$80$	576.000	−	997.661i	0.804984	−	1.39427i
$81$		0			0
$82$	−540.000	−	935.307i	−0.727232	−	1.25960i
$83$	36.0000			0.0476086			0.0238043	−	0.999717i	$-0.492422\pi$
$83$	36.0000			0.0476086			0.0238043	+	0.999717i	$0.492422\pi$
$84$		0			0
$85$	2268.00			2.89411
$86$	−648.000	−	1122.37i	−0.812507	−	1.40730i
$87$		0			0
$88$		0			0
$89$	−117.000	−	202.650i	−0.139348	−	0.241358i	0.787902	−	0.615801i	$-0.211167\pi$
$89$	−117.000	−	202.650i	−0.139348	−	0.241358i	−0.927250	+	0.374443i	$0.877834\pi$
$90$		0			0
$91$		0			0
$92$	−112.000			−0.126922
$93$		0			0
$94$	−144.000	+	249.415i	−0.158005	+	0.273673i
$95$	−648.000	+	1122.37i	−0.699825	+	1.21213i
$96$		0			0
$97$	−468.000			−0.489878			−0.244939	−	0.969538i	$-0.578768\pi$
$97$	−468.000			−0.489878			−0.244939	+	0.969538i	$0.578768\pi$
$98$		0			0
$99$		0			0
$100$	−796.000	−	1378.71i	−0.796000	−	1.37871i
$101$	333.000	−	576.773i	0.328067	−	0.568228i	−0.654061	−	0.756441i	$-0.726936\pi$
$101$	333.000	−	576.773i	0.328067	−	0.568228i	0.982128	+	0.188213i	$0.0602696\pi$
$102$		0			0
$103$	−126.000	−	218.238i	−0.120535	−	0.208773i	0.799444	−	0.600741i	$-0.205128\pi$
$103$	−126.000	−	218.238i	−0.120535	−	0.208773i	−0.919979	+	0.391968i	$0.871794\pi$
$104$		0			0
$105$		0			0
$106$	−88.0000			−0.0806351
$107$	335.000	+	580.237i	0.302670	+	0.524240i	0.976740	−	0.214428i	$-0.0687887\pi$
$107$	335.000	+	580.237i	0.302670	+	0.524240i	−0.674070	+	0.738668i	$0.735455\pi$
$108$		0			0
$109$	−81.0000	+	140.296i	−0.0711779	+	0.123284i	−0.899418	−	0.437090i	$-0.856009\pi$
$109$	−81.0000	+	140.296i	−0.0711779	+	0.123284i	0.828240	+	0.560374i	$0.189342\pi$
$110$	1800.00	+	3117.69i	1.56021	+	2.70237i
$111$		0			0
$112$		0			0
$113$	1390.00			1.15717			0.578585	−	0.815622i	$-0.303605\pi$
$113$	1390.00			1.15717			0.578585	+	0.815622i	$0.303605\pi$
$114$		0			0
$115$	126.000	−	218.238i	0.102170	−	0.176964i
$116$	632.000	−	1094.66i	0.505860	−	0.876175i
$117$		0			0
$118$	−1872.00			−1.46044
$119$		0			0
$120$		0			0
$121$	−584.500	−	1012.38i	−0.439144	−	0.760619i
$122$	−1584.00	+	2743.57i	−1.17548	+	2.03599i
$123$		0			0
$124$	−144.000	−	249.415i	−0.104287	−	0.180630i
$125$	1332.00			0.953102
$126$		0			0
$127$	916.000			0.640015			0.320007	−	0.947415i	$-0.396315\pi$
$127$	916.000			0.640015			0.320007	+	0.947415i	$0.396315\pi$
$128$		0			0
$129$		0			0
$130$	1296.00	−	2244.74i	0.874359	−	1.51443i
$131$	−1134.00	−	1964.15i	−0.756321	−	1.30999i	−0.944715	−	0.327893i	$-0.893662\pi$
$131$	−1134.00	−	1964.15i	−0.756321	−	1.30999i	0.188394	−	0.982094i	$-0.439672\pi$
$132$		0			0
$133$		0			0
$134$	−928.000			−0.598261
$135$		0			0
$136$		0			0
$137$	403.000	−	698.016i	0.251318	−	0.435296i	−0.712571	−	0.701600i	$-0.752469\pi$
$137$	403.000	−	698.016i	0.251318	−	0.435296i	0.963889	+	0.266304i	$0.0858026\pi$
$138$		0			0
$139$	−2628.00			−1.60363			−0.801813	−	0.597575i	$-0.796131\pi$
$139$	−2628.00			−1.60363			−0.801813	+	0.597575i	$0.796131\pi$
$140$		0			0
$141$		0			0
$142$	1468.00	+	2542.65i	0.867548	+	1.50264i
$143$	−900.000	+	1558.85i	−0.526306	+	0.911589i
$144$		0			0
$145$	1422.00	+	2462.98i	0.814418	+	1.41061i
$146$	720.000			0.408134
$147$		0			0
$148$	−1296.00			−0.719801
$149$	−1195.00	−	2069.80i	−0.657035	−	1.13802i	−0.981379	−	0.192079i	$-0.938477\pi$
$149$	−1195.00	−	2069.80i	−0.657035	−	1.13802i	0.324344	−	0.945939i	$-0.394856\pi$
$150$		0			0
$151$	−1620.00	+	2805.92i	−0.873071	+	1.51220i	−0.0142676	+	0.999898i	$0.504542\pi$
$151$	−1620.00	+	2805.92i	−0.873071	+	1.51220i	−0.858803	+	0.512305i	$0.828792\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	648.000			0.335798
$156$		0			0
$157$	1512.00	−	2618.86i	0.768603	−	1.33126i	−0.169717	−	0.985493i	$-0.554285\pi$
$157$	1512.00	−	2618.86i	0.768603	−	1.33126i	0.938320	−	0.345767i	$-0.112381\pi$
$158$	472.000	−	817.528i	0.237660	−	0.411639i
$159$		0			0
$160$	4608.00			2.27684
$161$		0			0
$162$		0			0
$163$	892.000	+	1544.99i	0.428631	+	0.742410i	0.996752	−	0.0805346i	$-0.0256628\pi$
$163$	892.000	+	1544.99i	0.428631	+	0.742410i	−0.568121	+	0.822945i	$0.692329\pi$
$164$	1080.00	−	1870.61i	0.514231	−	0.890674i
$165$		0			0
$166$	72.0000	+	124.708i	0.0336644	+	0.0583084i
$167$	−3024.00			−1.40122			−0.700611	−	0.713543i	$-0.747089\pi$
$167$	−3024.00			−1.40122			−0.700611	+	0.713543i	$0.747089\pi$
$168$		0			0
$169$	−901.000			−0.410105
$170$	4536.00	+	7856.58i	2.04644	+	3.54454i
$171$		0			0
$172$	1296.00	−	2244.74i	0.574529	−	0.995114i
$173$	−783.000	−	1356.20i	−0.344106	−	0.596010i	0.641085	−	0.767470i	$-0.278485\pi$
$173$	−783.000	−	1356.20i	−0.344106	−	0.596010i	−0.985191	+	0.171461i	$0.945151\pi$
$174$		0			0
$175$		0			0
$176$	−3200.00			−1.37051
$177$		0			0
$178$	468.000	−	810.600i	0.197068	−	0.341332i
$179$	1901.00	−	3292.63i	0.793784	−	1.37487i	−0.129824	−	0.991537i	$-0.541441\pi$
$179$	1901.00	−	3292.63i	0.793784	−	1.37487i	0.923608	−	0.383338i	$-0.125226\pi$
$180$		0			0
$181$	468.000			0.192189			0.0960944	−	0.995372i	$-0.469365\pi$
$181$	468.000			0.192189			0.0960944	+	0.995372i	$0.469365\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1458.00	−	2525.33i	0.579429	−	1.00360i
$186$		0			0
$187$	−3150.00	−	5455.96i	−1.23182	−	2.13358i
$188$	−576.000			−0.223453
$189$		0			0
$190$	−5184.00			−1.97940
$191$	241.000	+	417.424i	0.0912992	+	0.158135i	0.908058	−	0.418844i	$-0.137565\pi$
$191$	241.000	+	417.424i	0.0912992	+	0.158135i	−0.816759	+	0.576979i	$0.804231\pi$
$192$		0			0
$193$	405.000	−	701.481i	0.151049	−	0.261625i	−0.780564	−	0.625076i	$-0.785068\pi$
$193$	405.000	−	701.481i	0.151049	−	0.261625i	0.931614	+	0.363450i	$0.118401\pi$
$194$	−936.000	−	1621.20i	−0.346396	−	0.599976i
$195$		0			0
$196$		0			0
$197$	2462.00			0.890407			0.445204	−	0.895429i	$-0.353131\pi$
$197$	2462.00			0.890407			0.445204	+	0.895429i	$0.353131\pi$
$198$		0			0
$199$	−2268.00	+	3928.29i	−0.807911	+	1.39934i	0.106397	+	0.994324i	$0.466068\pi$
$199$	−2268.00	+	3928.29i	−0.807911	+	1.39934i	−0.914308	+	0.405019i	$0.867265\pi$
$200$		0			0
$201$		0			0
$202$	2664.00			0.927913
$203$		0			0
$204$		0			0
$205$	2430.00	+	4208.88i	0.827895	+	1.43396i
$206$	504.000	−	872.954i	0.170463	−	0.295250i
$207$		0			0
$208$	1152.00	+	1995.32i	0.384023	+	0.665148i
$209$	3600.00			1.19147
$210$		0			0
$211$	2916.00			0.951402			0.475701	−	0.879607i	$-0.342195\pi$
$211$	2916.00			0.951402			0.475701	+	0.879607i	$0.342195\pi$
$212$	−88.0000	−	152.420i	−0.0285088	−	0.0493787i
$213$		0			0
$214$	−1340.00	+	2320.95i	−0.428040	+	0.741387i
$215$	2916.00	+	5050.66i	0.924975	+	1.60210i
$216$		0			0
$217$		0			0
$218$	−648.000			−0.201322
$219$		0			0
$220$	−3600.00	+	6235.38i	−1.10324	+	1.91086i
$221$	−2268.00	+	3928.29i	−0.690327	+	1.19568i
$222$		0			0
$223$	1080.00			0.324315			0.162157	−	0.986765i	$-0.448155\pi$
$223$	1080.00			0.324315			0.162157	+	0.986765i	$0.448155\pi$
$224$		0			0
$225$		0			0
$226$	2780.00	+	4815.10i	0.818243	+	1.41724i
$227$	666.000	−	1153.55i	0.194731	−	0.337284i	−0.752081	−	0.659070i	$-0.770950\pi$
$227$	666.000	−	1153.55i	0.194731	−	0.337284i	0.946812	+	0.321786i	$0.104283\pi$
$228$		0			0
$229$	810.000	+	1402.96i	0.233739	+	0.404848i	0.958906	−	0.283725i	$-0.0915704\pi$
$229$	810.000	+	1402.96i	0.233739	+	0.404848i	−0.725166	+	0.688574i	$0.758237\pi$
$230$	1008.00			0.288981
$231$		0			0
$232$		0			0
$233$	3359.00	+	5817.96i	0.944444	+	1.63582i	0.756861	+	0.653576i	$0.226732\pi$
$233$	3359.00	+	5817.96i	0.944444	+	1.63582i	0.187583	+	0.982249i	$0.439935\pi$
$234$		0			0
$235$	648.000	−	1122.37i	0.179876	−	0.311554i
$236$	−1872.00	−	3242.40i	−0.516342	−	0.894331i
$237$		0			0
$238$		0			0
$239$	3578.00			0.968375			0.484187	−	0.874964i	$-0.339115\pi$
$239$	3578.00			0.968375			0.484187	+	0.874964i	$0.339115\pi$
$240$		0			0
$241$	−378.000	+	654.715i	−0.101034	+	0.174995i	−0.912111	−	0.409944i	$-0.865548\pi$
$241$	−378.000	+	654.715i	−0.101034	+	0.174995i	0.811077	+	0.584939i	$0.198882\pi$
$242$	2338.00	−	4049.53i	0.621043	−	1.07568i
$243$		0			0
$244$	−6336.00			−1.66238
$245$		0			0
$246$		0			0
$247$	−1296.00	−	2244.74i	−0.333856	−	0.578256i
$248$		0			0
$249$		0			0
$250$	2664.00	+	4614.18i	0.673945	+	1.16731i
$251$	−6516.00			−1.63859			−0.819295	−	0.573372i	$-0.805635\pi$
$251$	−6516.00			−1.63859			−0.819295	+	0.573372i	$0.805635\pi$
$252$		0			0
$253$	−700.000			−0.173947
$254$	1832.00	+	3173.12i	0.452559	+	0.783855i
$255$		0			0
$256$	−2048.00	+	3547.24i	−0.500000	+	0.866025i
$257$	3015.00	+	5222.13i	0.731792	+	1.26750i	0.956117	+	0.292986i	$0.0946491\pi$
$257$	3015.00	+	5222.13i	0.731792	+	1.26750i	−0.224325	+	0.974514i	$0.572018\pi$
$258$		0			0
$259$		0			0
$260$	5184.00			1.23653
$261$		0			0
$262$	4536.00	−	7856.58i	1.06960	−	1.85260i
$263$	295.000	−	510.955i	0.0691653	−	0.119798i	−0.829369	−	0.558702i	$-0.811300\pi$
$263$	295.000	−	510.955i	0.0691653	−	0.119798i	0.898534	+	0.438904i	$0.144633\pi$
$264$		0			0
$265$	396.000			0.0917966
$266$		0			0
$267$		0			0
$268$	−928.000	−	1607.34i	−0.211517	−	0.366359i
$269$	495.000	−	857.365i	0.112196	−	0.194329i	−0.804459	−	0.594008i	$-0.797545\pi$
$269$	495.000	−	857.365i	0.112196	−	0.194329i	0.916655	+	0.399679i	$0.130878\pi$
$270$		0			0
$271$	−1710.00	−	2961.81i	−0.383303	−	0.663900i	0.608229	−	0.793761i	$-0.291880\pi$
$271$	−1710.00	−	2961.81i	−0.383303	−	0.663900i	−0.991532	+	0.129861i	$0.958547\pi$
$272$	−8064.00			−1.79762
$273$		0			0
$274$	3224.00			0.710836
$275$	−4975.00	−	8616.95i	−1.09092	−	1.88953i
$276$		0			0
$277$	1367.00	−	2367.71i	0.296516	−	0.513582i	−0.678820	−	0.734305i	$-0.737508\pi$
$277$	1367.00	−	2367.71i	0.296516	−	0.513582i	0.975337	+	0.220723i	$0.0708417\pi$
$278$	−5256.00	−	9103.66i	−1.13394	−	1.96403i
$279$		0			0
$280$		0			0
$281$	−598.000			−0.126953			−0.0634763	−	0.997983i	$-0.520219\pi$
$281$	−598.000			−0.126953			−0.0634763	+	0.997983i	$0.520219\pi$
$282$		0			0
$283$	1800.00	−	3117.69i	0.378088	−	0.654868i	−0.612696	−	0.790319i	$-0.709915\pi$
$283$	1800.00	−	3117.69i	0.378088	−	0.654868i	0.990784	+	0.135451i	$0.0432484\pi$
$284$	−2936.00	+	5085.30i	−0.613449	+	1.06253i
$285$		0			0
$286$	−7200.00			−1.48862
$287$		0			0
$288$		0			0
$289$	−5481.50	−	9494.24i	−1.11571	−	1.93247i
$290$	−5688.00	+	9851.90i	−1.15176	+	1.99491i
$291$		0			0
$292$	720.000	+	1247.08i	0.144297	+	0.249930i
$293$	7902.00			1.57556			0.787781	−	0.615955i	$-0.211230\pi$
$293$	7902.00			1.57556			0.787781	+	0.615955i	$0.211230\pi$
$294$		0			0
$295$	8424.00			1.66259
$296$		0			0
$297$		0			0
$298$	4780.00	−	8279.20i	0.929188	−	1.60940i
$299$	252.000	+	436.477i	0.0487409	+	0.0844218i
$300$		0			0
$301$		0			0
$302$	−12960.0			−2.46942
$303$		0			0
$304$	2304.00	−	3990.65i	0.434682	−	0.752892i
$305$	7128.00	−	12346.1i	1.33819	−	2.31781i
$306$		0			0
$307$	10224.0			1.90070			0.950349	−	0.311185i	$-0.100726\pi$
$307$	10224.0			1.90070			0.950349	+	0.311185i	$0.100726\pi$
$308$		0			0
$309$		0			0
$310$	1296.00	+	2244.74i	0.237445	+	0.411266i
$311$	−1944.00	+	3367.11i	−0.354451	+	0.613926i	−0.987024	−	0.160574i	$-0.948665\pi$
$311$	−1944.00	+	3367.11i	−0.354451	+	0.613926i	0.632573	+	0.774501i	$0.281999\pi$
$312$		0			0
$313$	2556.00	+	4427.12i	0.461577	+	0.799475i	0.999040	−	0.0438124i	$-0.0139504\pi$
$313$	2556.00	+	4427.12i	0.461577	+	0.799475i	−0.537463	+	0.843288i	$0.680617\pi$
$314$	12096.0			2.17394
$315$		0			0
$316$	1888.00			0.336102
$317$	−5051.00	−	8748.59i	−0.894929	−	1.55006i	−0.833893	−	0.551927i	$-0.813893\pi$
$317$	−5051.00	−	8748.59i	−0.894929	−	1.55006i	−0.0610361	−	0.998136i	$-0.519440\pi$
$318$		0			0
$319$	3950.00	−	6841.60i	0.693284	−	1.20080i
$320$	4608.00	+	7981.29i	0.804984	+	1.39427i
$321$		0			0
$322$		0			0
$323$	9072.00			1.56279
$324$		0			0
$325$	−3582.00	+	6204.21i	−0.611365	+	1.05892i
$326$	−3568.00	+	6179.96i	−0.606176	+	1.04993i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2754.00	−	4770.07i	−0.457322	−	0.792105i	0.541497	−	0.840703i	$-0.317858\pi$
$331$	−2754.00	−	4770.07i	−0.457322	−	0.792105i	−0.998818	+	0.0485983i	$0.984525\pi$
$332$	−144.000	+	249.415i	−0.0238043	+	0.0412303i
$333$		0			0
$334$	−6048.00	−	10475.4i	−0.990814	−	1.71614i
$335$	4176.00			0.681072
$336$		0			0
$337$	−9234.00			−1.49261			−0.746303	−	0.665607i	$-0.768173\pi$
$337$	−9234.00			−1.49261			−0.746303	+	0.665607i	$0.768173\pi$
$338$	−1802.00	−	3121.16i	−0.289988	−	0.502274i
$339$		0			0
$340$	−9072.00	+	15713.2i	−1.44705	+	2.50637i
$341$	−900.000	−	1558.85i	−0.142926	−	0.247555i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	3132.00	−	5424.78i	0.486640	−	0.842885i
$347$	−3247.00	+	5623.97i	−0.502329	+	0.870059i	0.497668	+	0.867368i	$0.334190\pi$
$347$	−3247.00	+	5623.97i	−0.502329	+	0.870059i	−0.999996	+	0.00269115i	$0.999143\pi$
$348$		0			0
$349$	−10080.0			−1.54605			−0.773023	−	0.634378i	$-0.781256\pi$
$349$	−10080.0			−1.54605			−0.773023	+	0.634378i	$0.781256\pi$
$350$		0			0
$351$		0			0
$352$	−6400.00	−	11085.1i	−0.969094	−	1.67852i
$353$	369.000	−	639.127i	0.0556371	−	0.0963662i	−0.836865	−	0.547409i	$-0.815614\pi$
$353$	369.000	−	639.127i	0.0556371	−	0.0963662i	0.892503	+	0.451042i	$0.148948\pi$
$354$		0			0
$355$	−6606.00	−	11441.9i	−0.987634	−	1.71063i
$356$	1872.00			0.278696
$357$		0			0
$358$	15208.0			2.24516
$359$	97.0000	+	168.009i	0.0142603	+	0.0246996i	0.873068	−	0.487599i	$-0.162127\pi$
$359$	97.0000	+	168.009i	0.0142603	+	0.0246996i	−0.858807	+	0.512299i	$0.828794\pi$
$360$		0			0
$361$	837.500	−	1450.59i	0.122102	−	0.211487i
$362$	936.000	+	1621.20i	0.135898	+	0.235382i
$363$		0			0
$364$		0			0
$365$	−3240.00			−0.464628
$366$		0			0
$367$	−2376.00	+	4115.35i	−0.337946	+	0.585340i	−0.984046	−	0.177913i	$-0.943065\pi$
$367$	−2376.00	+	4115.35i	−0.337946	+	0.585340i	0.646100	+	0.763253i	$0.276399\pi$
$368$	−448.000	+	775.959i	−0.0634609	+	0.109918i
$369$		0			0
$370$	11664.0			1.63887
$371$		0			0
$372$		0			0
$373$	1153.00	+	1997.05i	0.160054	+	0.277221i	0.934888	−	0.354943i	$-0.115500\pi$
$373$	1153.00	+	1997.05i	0.160054	+	0.277221i	−0.774834	+	0.632165i	$0.782167\pi$
$374$	12600.0	−	21823.8i	1.74206	−	3.01734i
$375$		0			0
$376$		0			0
$377$	−5688.00			−0.777047
$378$		0			0
$379$	−7452.00			−1.00998			−0.504991	−	0.863124i	$-0.668504\pi$
$379$	−7452.00			−1.00998			−0.504991	+	0.863124i	$0.668504\pi$
$380$	−5184.00	−	8978.95i	−0.699825	−	1.21213i
$381$		0			0
$382$	−964.000	+	1669.70i	−0.129117	+	0.223636i
$383$	576.000	+	997.661i	0.0768465	+	0.133102i	0.901888	−	0.431970i	$-0.142182\pi$
$383$	576.000	+	997.661i	0.0768465	+	0.133102i	−0.825041	+	0.565073i	$0.808848\pi$
$384$		0			0
$385$		0			0
$386$	3240.00			0.427232
$387$		0			0
$388$	1872.00	−	3242.40i	0.244939	−	0.424247i
$389$	947.000	−	1640.25i	0.123431	−	0.213789i	−0.797687	−	0.603071i	$-0.793943\pi$
$389$	947.000	−	1640.25i	0.123431	−	0.213789i	0.921119	+	0.389282i	$0.127277\pi$
$390$		0			0
$391$	−1764.00			−0.228157
$392$		0			0
$393$		0			0
$394$	4924.00	+	8528.62i	0.629613	+	1.09052i
$395$	−2124.00	+	3678.88i	−0.270557	+	0.468619i
$396$		0			0
$397$	4608.00	+	7981.29i	0.582541	+	1.00899i	0.995177	+	0.0980950i	$0.0312749\pi$
$397$	4608.00	+	7981.29i	0.582541	+	1.00899i	−0.412636	+	0.910896i	$0.635392\pi$
$398$	−18144.0			−2.28512
$399$		0			0
$400$	−12736.0			−1.59200
$401$	−5825.00	−	10089.2i	−0.725403	−	1.25643i	−0.958808	−	0.284055i	$-0.908320\pi$
$401$	−5825.00	−	10089.2i	−0.725403	−	1.25643i	0.233405	−	0.972380i	$-0.425013\pi$
$402$		0			0
$403$	−648.000	+	1122.37i	−0.0800972	+	0.138732i
$404$	2664.00	+	4614.18i	0.328067	+	0.568228i
$405$		0			0
$406$		0			0
$407$	−8100.00			−0.986492
$408$		0			0
$409$	−3762.00	+	6515.98i	−0.454814	+	0.787761i	−0.998677	−	0.0514127i	$-0.983628\pi$
$409$	−3762.00	+	6515.98i	−0.454814	+	0.787761i	0.543863	+	0.839174i	$0.316961\pi$
$410$	−9720.00	+	16835.5i	−1.17082	+	2.02792i
$411$		0			0
$412$	2016.00			0.241071
$413$		0			0
$414$		0			0
$415$	−324.000	−	561.184i	−0.0383242	−	0.0663794i
$416$	−4608.00	+	7981.29i	−0.543091	+	0.940661i
$417$		0			0
$418$	7200.00	+	12470.8i	0.842496	+	1.45925i
$419$	−3852.00			−0.449123			−0.224561	−	0.974460i	$-0.572095\pi$
$419$	−3852.00			−0.449123			−0.224561	+	0.974460i	$0.572095\pi$
$420$		0			0
$421$	10402.0			1.20419			0.602093	−	0.798426i	$-0.294334\pi$
$421$	10402.0			1.20419			0.602093	+	0.798426i	$0.294334\pi$
$422$	5832.00	+	10101.3i	0.672742	+	1.16522i
$423$		0			0
$424$		0			0
$425$	−12537.0	−	21714.7i	−1.43090	−	2.47840i
$426$		0			0
$427$		0			0
$428$	−5360.00			−0.605340
$429$		0			0
$430$	−11664.0	+	20202.6i	−1.30811	+	2.26572i
$431$	−5195.00	+	8998.00i	−0.580590	+	1.00561i	0.414819	+	0.909904i	$0.363845\pi$
$431$	−5195.00	+	8998.00i	−0.580590	+	1.00561i	−0.995409	+	0.0957078i	$0.969489\pi$
$432$		0			0
$433$	−11232.0			−1.24659			−0.623297	−	0.781985i	$-0.714207\pi$
$433$	−11232.0			−1.24659			−0.623297	+	0.781985i	$0.714207\pi$
$434$		0			0
$435$		0			0
$436$	−648.000	−	1122.37i	−0.0711779	−	0.123284i
$437$	504.000	−	872.954i	0.0551707	−	0.0955584i
$438$		0			0
$439$	7308.00	+	12657.8i	0.794514	+	1.37614i	0.923147	+	0.384447i	$0.125608\pi$
$439$	7308.00	+	12657.8i	0.794514	+	1.37614i	−0.128633	+	0.991692i	$0.541059\pi$
$440$		0			0
$441$		0			0
$442$	−18144.0			−1.95254
$443$	5969.00	+	10338.6i	0.640171	+	1.10881i	0.985394	+	0.170288i	$0.0544698\pi$
$443$	5969.00	+	10338.6i	0.640171	+	1.10881i	−0.345223	+	0.938521i	$0.612197\pi$
$444$		0			0
$445$	−2106.00	+	3647.70i	−0.224346	+	0.388579i
$446$	2160.00	+	3741.23i	0.229325	+	0.397203i
$447$		0			0
$448$		0			0
$449$	−8186.00			−0.860404			−0.430202	−	0.902733i	$-0.641558\pi$
$449$	−8186.00			−0.860404			−0.430202	+	0.902733i	$0.641558\pi$
$450$		0			0
$451$	6750.00	−	11691.3i	0.704756	−	1.22067i
$452$	−5560.00	+	9630.20i	−0.578585	+	1.00214i
$453$		0			0
$454$	5328.00			0.550783
$455$		0			0
$456$		0			0
$457$	−1053.00	−	1823.85i	−0.107784	−	0.186687i	0.807088	−	0.590431i	$-0.201042\pi$
$457$	−1053.00	−	1823.85i	−0.107784	−	0.186687i	−0.914872	+	0.403744i	$0.867709\pi$
$458$	−3240.00	+	5611.84i	−0.330557	+	0.572542i
$459$		0			0
$460$	1008.00	+	1745.91i	0.102170	+	0.176964i
$461$	9486.00			0.958367			0.479183	−	0.877715i	$-0.340933\pi$
$461$	9486.00			0.958367			0.479183	+	0.877715i	$0.340933\pi$
$462$		0			0
$463$	−12652.0			−1.26995			−0.634977	−	0.772531i	$-0.718990\pi$
$463$	−12652.0			−1.26995			−0.634977	+	0.772531i	$0.718990\pi$
$464$	−5056.00	−	8757.25i	−0.505860	−	0.876175i
$465$		0			0
$466$	−13436.0	+	23271.8i	−1.33565	+	2.31341i
$467$	1854.00	+	3211.22i	0.183711	+	0.318196i	0.943141	−	0.332392i	$-0.107856\pi$
$467$	1854.00	+	3211.22i	0.183711	+	0.318196i	−0.759431	+	0.650588i	$0.774522\pi$
$468$		0			0
$469$		0			0
$470$	5184.00			0.508766
$471$		0			0
$472$		0			0
$473$	8100.00	−	14029.6i	0.787396	−	1.36381i
$474$		0			0
$475$	14328.0			1.38403
$476$		0			0
$477$		0			0
$478$	7156.00	+	12394.6i	0.684744	+	1.18601i
$479$	4032.00	−	6983.63i	0.384607	−	0.666159i	−0.607108	−	0.794620i	$-0.707670\pi$
$479$	4032.00	−	6983.63i	0.384607	−	0.666159i	0.991715	+	0.128461i	$0.0410036\pi$
$480$		0			0
$481$	2916.00	+	5050.66i	0.276420	+	0.478774i
$482$	−3024.00			−0.285766
$483$		0			0
$484$	9352.00			0.878287
$485$	4212.00	+	7295.40i	0.394344	+	0.683025i
$486$		0			0
$487$	5832.00	−	10101.3i	0.542655	−	0.939907i	−0.456095	−	0.889931i	$-0.650752\pi$
$487$	5832.00	−	10101.3i	0.542655	−	0.939907i	0.998750	−	0.0499756i	$-0.0159143\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9814.00			0.902036			0.451018	−	0.892515i	$-0.351061\pi$
$491$	9814.00			0.902036			0.451018	+	0.892515i	$0.351061\pi$
$492$		0			0
$493$	9954.00	−	17240.8i	0.909342	−	1.57503i
$494$	5184.00	−	8978.95i	0.472144	−	0.817778i
$495$		0			0
$496$	−2304.00			−0.208574
$497$		0			0
$498$		0			0
$499$	7614.00	+	13187.8i	0.683065	+	1.18310i	0.974041	+	0.226373i	$0.0726868\pi$
$499$	7614.00	+	13187.8i	0.683065	+	1.18310i	−0.290976	+	0.956730i	$0.593980\pi$
$500$	−5328.00	+	9228.37i	−0.476551	+	0.825410i
$501$		0			0
$502$	−13032.0	−	22572.1i	−1.15866	−	2.00686i
$503$	−11088.0			−0.982882			−0.491441	−	0.870911i	$-0.663530\pi$
$503$	−11088.0			−0.982882			−0.491441	+	0.870911i	$0.663530\pi$
$504$		0			0
$505$	−11988.0			−1.05635
$506$	−1400.00	−	2424.87i	−0.122999	−	0.213041i
$507$		0			0
$508$	−3664.00	+	6346.23i	−0.320007	+	0.554269i
$509$	2907.00	+	5035.07i	0.253144	+	0.438459i	0.964390	−	0.264485i	$-0.0852019\pi$
$509$	2907.00	+	5035.07i	0.253144	+	0.438459i	−0.711245	+	0.702944i	$0.751869\pi$
$510$		0			0
$511$		0			0
$512$	−16384.0			−1.41421
$513$		0			0
$514$	−12060.0	+	20888.5i	−1.03491	+	1.79252i
$515$	−2268.00	+	3928.29i	−0.194058	+	0.336119i
$516$		0			0
$517$	−3600.00			−0.306243
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5841.00	−	10116.9i	0.491169	−	0.850729i	−0.508780	−	0.860897i	$-0.669903\pi$
$521$	5841.00	−	10116.9i	0.491169	−	0.850729i	0.999948	+	0.0101677i	$0.00323655\pi$
$522$		0			0
$523$	−1494.00	−	2587.68i	−0.124910	−	0.216351i	0.796788	−	0.604259i	$-0.206531\pi$
$523$	−1494.00	−	2587.68i	−0.124910	−	0.216351i	−0.921698	+	0.387909i	$0.873198\pi$
$524$	18144.0			1.51264
$525$		0			0
$526$	2360.00			0.195629
$527$	−2268.00	−	3928.29i	−0.187468	−	0.324704i
$528$		0			0
$529$	5985.50	−	10367.2i	0.491945	−	0.852074i
$530$	792.000	+	1371.78i	0.0649100	+	0.112427i
$531$		0			0
$532$		0			0
$533$	−9720.00			−0.789906
$534$		0			0
$535$	6030.00	−	10444.3i	0.487289	−	0.844009i
$536$		0			0
$537$		0			0
$538$	3960.00			0.317338
$539$		0			0
$540$		0			0
$541$	−3565.00	−	6174.76i	−0.283311	−	0.490709i	0.688887	−	0.724869i	$-0.258100\pi$
$541$	−3565.00	−	6174.76i	−0.283311	−	0.490709i	−0.972198	+	0.234159i	$0.924766\pi$
$542$	6840.00	−	11847.2i	0.542072	−	0.938897i
$543$		0			0
$544$	−16128.0	−	27934.5i	−1.27111	−	2.20162i
$545$	2916.00			0.229188
$546$		0			0
$547$	−5488.00			−0.428976			−0.214488	−	0.976727i	$-0.568808\pi$
$547$	−5488.00			−0.428976			−0.214488	+	0.976727i	$0.568808\pi$
$548$	3224.00	+	5584.13i	0.251318	+	0.435296i
$549$		0			0
$550$	19900.0	−	34467.8i	1.54280	−	2.67220i
$551$	5688.00	+	9851.90i	0.439777	+	0.761716i
$552$		0			0
$553$		0			0
$554$	10936.0			0.838675
$555$		0			0
$556$	10512.0	−	18207.3i	0.801813	−	1.38878i
$557$	2873.00	−	4976.18i	0.218551	−	0.378541i	−0.735814	−	0.677183i	$-0.763200\pi$
$557$	2873.00	−	4976.18i	0.218551	−	0.378541i	0.954365	+	0.298642i	$0.0965337\pi$
$558$		0			0
$559$	−11664.0			−0.882531
$560$		0			0
$561$		0			0
$562$	−1196.00	−	2071.53i	−0.0897691	−	0.155485i
$563$	−6534.00	+	11317.2i	−0.489121	+	0.847183i	−0.999922	−	0.0125165i	$-0.996016\pi$
$563$	−6534.00	+	11317.2i	−0.489121	+	0.847183i	0.510800	+	0.859699i	$0.329349\pi$
$564$		0			0
$565$	−12510.0	−	21668.0i	−0.931504	−	1.61341i
$566$	14400.0			1.06939
$567$		0			0
$568$		0			0
$569$	−565.000	−	978.609i	−0.0416275	−	0.0721009i	0.844461	−	0.535617i	$-0.179921\pi$
$569$	−565.000	−	978.609i	−0.0416275	−	0.0721009i	−0.886088	+	0.463516i	$0.846588\pi$
$570$		0			0
$571$	−8432.00	+	14604.7i	−0.617983	+	1.07038i	0.371870	+	0.928285i	$0.378717\pi$
$571$	−8432.00	+	14604.7i	−0.617983	+	1.07038i	−0.989853	+	0.142093i	$0.954617\pi$
$572$	−7200.00	−	12470.8i	−0.526306	−	0.911589i
$573$		0			0
$574$		0			0
$575$	−2786.00			−0.202060
$576$		0			0
$577$	−1044.00	+	1808.26i	−0.0753246	+	0.130466i	−0.901227	−	0.433347i	$-0.857333\pi$
$577$	−1044.00	+	1808.26i	−0.0753246	+	0.130466i	0.825903	+	0.563813i	$0.190666\pi$
$578$	21926.0	−	37976.9i	1.57786	−	2.73293i
$579$		0			0
$580$	−22752.0			−1.62884
$581$		0			0
$582$		0			0
$583$	−550.000	−	952.628i	−0.0390715	−	0.0676738i
$584$		0			0
$585$		0			0
$586$	15804.0	+	27373.3i	1.11409	+	1.92966i
$587$	10260.0			0.721423			0.360712	−	0.932677i	$-0.382534\pi$
$587$	10260.0			0.721423			0.360712	+	0.932677i	$0.382534\pi$
$588$		0			0
$589$	2592.00			0.181327
$590$	16848.0	+	29181.6i	1.17563	+	2.03625i
$591$		0			0
$592$	−5184.00	+	8978.95i	−0.359900	+	0.623366i
$593$	−1791.00	−	3102.10i	−0.124026	−	0.214820i	0.797326	−	0.603549i	$-0.206247\pi$
$593$	−1791.00	−	3102.10i	−0.124026	−	0.214820i	−0.921352	+	0.388730i	$0.872914\pi$
$594$		0			0
$595$		0			0
$596$	19120.0			1.31407
$597$		0			0
$598$	−1008.00	+	1745.91i	−0.0689301	+	0.119390i
$599$	3517.00	−	6091.62i	0.239901	−	0.415521i	−0.720785	−	0.693159i	$-0.756218\pi$
$599$	3517.00	−	6091.62i	0.239901	−	0.415521i	0.960686	+	0.277638i	$0.0895517\pi$
$600$		0			0
$601$	18072.0			1.22658			0.613288	−	0.789859i	$-0.289846\pi$
$601$	18072.0			1.22658			0.613288	+	0.789859i	$0.289846\pi$
$602$		0			0
$603$		0			0
$604$	−12960.0	−	22447.4i	−0.873071	−	1.51220i
$605$	−10521.0	+	18222.9i	−0.707007	+	1.22457i
$606$		0			0
$607$	14292.0	+	24754.5i	0.955674	+	1.65528i	0.732817	+	0.680426i	$0.238205\pi$
$607$	14292.0	+	24754.5i	0.955674	+	1.65528i	0.222857	+	0.974851i	$0.428462\pi$
$608$	18432.0			1.22947
$609$		0			0
$610$	57024.0			3.78497
$611$	1296.00	+	2244.74i	0.0858110	+	0.148629i
$612$		0			0
$613$	5455.00	−	9448.34i	0.359421	−	0.622536i	−0.628443	−	0.777856i	$-0.716307\pi$
$613$	5455.00	−	9448.34i	0.359421	−	0.622536i	0.987864	+	0.155320i	$0.0496407\pi$
$614$	20448.0	+	35417.0i	1.34400	+	2.32787i
$615$		0			0
$616$		0			0
$617$	5522.00			0.360304			0.180152	−	0.983639i	$-0.442341\pi$
$617$	5522.00			0.360304			0.180152	+	0.983639i	$0.442341\pi$
$618$		0			0
$619$	1206.00	−	2088.85i	0.0783089	−	0.135635i	−0.824211	−	0.566282i	$-0.808381\pi$
$619$	1206.00	−	2088.85i	0.0783089	−	0.135635i	0.902520	+	0.430647i	$0.141715\pi$
$620$	−2592.00	+	4489.48i	−0.167899	+	0.290809i
$621$		0			0
$622$	−15552.0			−1.00254
$623$		0			0
$624$		0			0
$625$	449.500	+	778.557i	0.0287680	+	0.0498276i
$626$	−10224.0	+	17708.5i	−0.652769	+	1.13063i
$627$		0			0
$628$	12096.0	+	20950.9i	0.768603	+	1.33126i
$629$	−20412.0			−1.29393
$630$		0			0
$631$	24676.0			1.55679			0.778396	−	0.627773i	$-0.216034\pi$
$631$	24676.0			1.55679			0.778396	+	0.627773i	$0.216034\pi$
$632$		0			0
$633$		0			0
$634$	20204.0	−	34994.4i	1.26562	−	2.19212i
$635$	−8244.00	−	14279.0i	−0.515202	−	0.892356i
$636$		0			0
$637$		0			0
$638$	31600.0			1.96090
$639$		0			0
$640$		0			0
$641$	−13741.0	+	23800.1i	−0.846703	+	1.46653i	0.0374303	+	0.999299i	$0.488083\pi$
$641$	−13741.0	+	23800.1i	−0.846703	+	1.46653i	−0.884134	+	0.467234i	$0.845251\pi$
$642$		0			0
$643$	22752.0			1.39541			0.697707	−	0.716383i	$-0.254204\pi$
$643$	22752.0			1.39541			0.697707	+	0.716383i	$0.254204\pi$
$644$		0			0
$645$		0			0
$646$	18144.0	+	31426.3i	1.10506	+	1.91401i
$647$	−7416.00	+	12844.9i	−0.450623	+	0.780502i	−0.998425	−	0.0561063i	$-0.982131\pi$
$647$	−7416.00	+	12844.9i	−0.450623	+	0.780502i	0.547802	+	0.836608i	$0.315465\pi$
$648$		0			0
$649$	−11700.0	−	20265.0i	−0.707650	−	1.22569i
$650$	−28656.0			−1.72920
$651$		0			0
$652$	−14272.0			−0.857262
$653$	1411.00	+	2443.92i	0.0845585	+	0.146460i	0.905203	−	0.424979i	$-0.139719\pi$
$653$	1411.00	+	2443.92i	0.0845585	+	0.146460i	−0.820645	+	0.571439i	$0.806385\pi$
$654$		0			0
$655$	−20412.0	+	35354.6i	−1.21765	+	2.10904i
$656$	−8640.00	−	14964.9i	−0.514231	−	0.890674i
$657$		0			0
$658$		0			0
$659$	15826.0			0.935498			0.467749	−	0.883861i	$-0.345065\pi$
$659$	15826.0			0.935498			0.467749	+	0.883861i	$0.345065\pi$
$660$		0			0
$661$	−11916.0	+	20639.1i	−0.701178	+	1.21448i	0.266875	+	0.963731i	$0.414009\pi$
$661$	−11916.0	+	20639.1i	−0.701178	+	1.21448i	−0.968053	+	0.250745i	$0.919324\pi$
$662$	11016.0	−	19080.3i	0.646751	−	1.12021i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1106.00	−	1915.65i	−0.0642046	−	0.111206i
$668$	12096.0	−	20950.9i	0.700611	−	1.21349i
$669$		0			0
$670$	8352.00	+	14466.1i	0.481591	+	0.834140i
$671$	−39600.0			−2.27830
$672$		0			0
$673$	13770.0			0.788699			0.394350	−	0.918961i	$-0.370970\pi$
$673$	13770.0			0.788699			0.394350	+	0.918961i	$0.370970\pi$
$674$	−18468.0	−	31987.5i	−1.05543	−	1.82806i
$675$		0			0
$676$	3604.00	−	6242.31i	0.205052	−	0.355161i
$677$	−4167.00	−	7217.46i	−0.236560	−	0.409733i	0.723165	−	0.690675i	$-0.242687\pi$
$677$	−4167.00	−	7217.46i	−0.236560	−	0.409733i	−0.959725	+	0.280942i	$0.909353\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	3600.00	−	6235.38i	0.202128	−	0.350096i
$683$	−9299.00	+	16106.3i	−0.520961	+	0.902331i	0.478742	+	0.877956i	$0.341093\pi$
$683$	−9299.00	+	16106.3i	−0.520961	+	0.902331i	−0.999703	+	0.0243752i	$0.992240\pi$
$684$		0			0
$685$	−14508.0			−0.809229
$686$		0			0
$687$		0			0
$688$	−10368.0	−	17957.9i	−0.574529	−	0.995114i
$689$	−396.000	+	685.892i	−0.0218961	+	0.0379251i
$690$		0			0
$691$	4482.00	+	7763.05i	0.246749	+	0.427381i	0.962622	−	0.270849i	$-0.0873045\pi$
$691$	4482.00	+	7763.05i	0.246749	+	0.427381i	−0.715873	+	0.698230i	$0.753971\pi$
$692$	12528.0			0.688213
$693$		0			0
$694$	−25976.0			−1.42080
$695$	23652.0	+	40966.5i	1.29089	+	2.23589i
$696$		0			0
$697$	17010.0	−	29462.2i	0.924390	−	1.60109i
$698$	−20160.0	−	34918.1i	−1.09322	−	1.89351i
$699$		0			0
$700$		0			0
$701$	−3542.00			−0.190841			−0.0954205	−	0.995437i	$-0.530420\pi$
$701$	−3542.00			−0.190841			−0.0954205	+	0.995437i	$0.530420\pi$
$702$		0			0
$703$	5832.00	−	10101.3i	0.312885	−	0.541932i
$704$	12800.0	−	22170.3i	0.685253	−	1.18689i
$705$		0			0
$706$	2952.00			0.157365
$707$		0			0
$708$		0			0
$709$	243.000	+	420.888i	0.0128717	+	0.0222945i	0.872390	−	0.488811i	$-0.162569\pi$
$709$	243.000	+	420.888i	0.0128717	+	0.0222945i	−0.859518	+	0.511106i	$0.829236\pi$
$710$	26424.0	−	45767.7i	1.39673	−	2.41920i
$711$		0			0
$712$		0			0
$713$	−504.000			−0.0264726
$714$		0			0
$715$	32400.0			1.69467
$716$	15208.0	+	26341.0i	0.793784	+	1.37487i
$717$		0			0
$718$	−388.000	+	672.036i	−0.0201672	+	0.0349306i
$719$	13464.0	+	23320.3i	0.698362	+	1.20960i	0.969034	+	0.246927i	$0.0794209\pi$
$719$	13464.0	+	23320.3i	0.698362	+	1.20960i	−0.270672	+	0.962672i	$0.587246\pi$
$720$		0			0
$721$		0			0
$722$	6700.00			0.345358
$723$		0			0
$724$	−1872.00	+	3242.40i	−0.0960944	+	0.166440i
$725$	15721.0	−	27229.6i	0.805329	−	1.39487i
$726$		0			0
$727$	−20628.0			−1.05234			−0.526169	−	0.850380i	$-0.676372\pi$
$727$	−20628.0			−1.05234			−0.526169	+	0.850380i	$0.676372\pi$
$728$		0			0
$729$		0			0
$730$	−6480.00	−	11223.7i	−0.328542	−	0.569051i
$731$	20412.0	−	35354.6i	1.03278	−	1.78883i
$732$		0			0
$733$	−4878.00	−	8448.94i	−0.245802	−	0.425742i	0.716555	−	0.697531i	$-0.245718\pi$
$733$	−4878.00	−	8448.94i	−0.245802	−	0.425742i	−0.962357	+	0.271789i	$0.912385\pi$
$734$	−19008.0			−0.955856
$735$		0			0
$736$	−3584.00			−0.179495
$737$	−5800.00	−	10045.9i	−0.289886	−	0.502097i
$738$		0			0
$739$	−9532.00	+	16509.9i	−0.474479	+	0.821822i	−0.999573	−	0.0292221i	$-0.990697\pi$
$739$	−9532.00	+	16509.9i	−0.474479	+	0.821822i	0.525094	+	0.851045i	$0.324030\pi$
$740$	11664.0	+	20202.6i	0.579429	+	1.00360i
$741$		0			0
$742$		0			0
$743$	3766.00			0.185950			0.0929752	−	0.995668i	$-0.470362\pi$
$743$	3766.00			0.185950			0.0929752	+	0.995668i	$0.470362\pi$
$744$		0			0
$745$	−21510.0	+	37256.4i	−1.05781	+	1.83217i
$746$	−4612.00	+	7988.22i	−0.226350	+	0.392050i
$747$		0			0
$748$	50400.0			2.46365
$749$		0			0
$750$		0			0
$751$	5832.00	+	10101.3i	0.283372	+	0.490815i	0.972213	−	0.234097i	$-0.0752134\pi$
$751$	5832.00	+	10101.3i	0.283372	+	0.490815i	−0.688841	+	0.724913i	$0.741880\pi$
$752$	−2304.00	+	3990.65i	−0.111726	+	0.193516i
$753$		0			0
$754$	−11376.0	−	19703.8i	−0.549456	−	0.951685i
$755$	58320.0			2.81123
$756$		0			0
$757$	−34182.0			−1.64117			−0.820585	−	0.571524i	$-0.806352\pi$
$757$	−34182.0			−1.64117			−0.820585	+	0.571524i	$0.806352\pi$
$758$	−14904.0	−	25814.5i	−0.714166	−	1.23697i
$759$		0			0
$760$		0			0
$761$	2367.00	+	4099.76i	0.112751	+	0.195291i	0.916879	−	0.399166i	$-0.130700\pi$
$761$	2367.00	+	4099.76i	0.112751	+	0.195291i	−0.804127	+	0.594457i	$0.797367\pi$
$762$		0			0
$763$		0			0
$764$	−3856.00			−0.182598
$765$		0			0
$766$	−2304.00	+	3990.65i	−0.108677	+	0.188235i
$767$	−8424.00	+	14590.8i	−0.396575	+	0.686888i
$768$		0			0
$769$	30240.0			1.41805			0.709026	−	0.705182i	$-0.249135\pi$
$769$	30240.0			1.41805			0.709026	+	0.705182i	$0.249135\pi$
$770$		0			0
$771$		0			0
$772$	3240.00	+	5611.84i	0.151049	+	0.261625i
$773$	−13851.0	+	23990.6i	−0.644484	+	1.11628i	0.339937	+	0.940448i	$0.389594\pi$
$773$	−13851.0	+	23990.6i	−0.644484	+	1.11628i	−0.984421	+	0.175830i	$0.943739\pi$
$774$		0			0
$775$	−3582.00	−	6204.21i	−0.166025	−	0.287563i
$776$		0			0
$777$		0			0
$778$	7576.00			0.349117
$779$	9720.00	+	16835.5i	0.447054	+	0.774320i
$780$		0			0
$781$	−18350.0	+	31783.1i	−0.840736	+	1.45620i
$782$	−3528.00	−	6110.68i	−0.161331	−	0.279434i
$783$		0			0
$784$		0			0
$785$	−54432.0			−2.47486
$786$		0			0
$787$	−11322.0	+	19610.3i	−0.512815	+	0.888222i	0.487074	+	0.873361i	$0.338064\pi$
$787$	−11322.0	+	19610.3i	−0.512815	+	0.888222i	−0.999890	+	0.0148617i	$0.995269\pi$
$788$	−9848.00	+	17057.2i	−0.445204	+	0.771115i
$789$		0			0
$790$	−16992.0			−0.765251
$791$		0			0
$792$		0			0
$793$	14256.0	+	24692.1i	0.638393	+	1.10573i
$794$	−18432.0	+	31925.2i	−0.823838	+	1.42693i
$795$		0			0
$796$	−18144.0	−	31426.3i	−0.807911	−	1.39934i
$797$	30150.0			1.33998			0.669992	−	0.742368i	$-0.266297\pi$
$797$	30150.0			1.33998			0.669992	+	0.742368i	$0.266297\pi$
$798$		0			0
$799$	−9072.00			−0.401682
$800$	−25472.0	−	44118.8i	−1.12571	−	1.94979i
$801$		0			0
$802$	23300.0	−	40356.8i	1.02587	−	1.77687i
$803$	4500.00	+	7794.23i	0.197760	+	0.342531i
$804$		0			0
$805$		0			0
$806$	−5184.00			−0.226549
$807$		0			0
$808$		0			0
$809$	−5659.00	+	9801.68i	−0.245933	+	0.425969i	−0.962394	−	0.271659i	$-0.912428\pi$
$809$	−5659.00	+	9801.68i	−0.245933	+	0.425969i	0.716460	+	0.697628i	$0.245761\pi$
$810$		0			0
$811$	29628.0			1.28284			0.641418	−	0.767192i	$-0.278347\pi$
$811$	29628.0			1.28284			0.641418	+	0.767192i	$0.278347\pi$
$812$		0			0
$813$		0			0
$814$	−16200.0	−	28059.2i	−0.697555	−	1.20820i
$815$	16056.0	−	27809.8i	0.690082	−	1.19526i
$816$		0			0
$817$	11664.0	+	20202.6i	0.499476	+	0.865117i
$818$	−30096.0			−1.28641
$819$		0			0
$820$	−38880.0			−1.65579
$821$	8885.00	+	15389.3i	0.377696	+	0.654189i	0.990727	−	0.135870i	$-0.0433830\pi$
$821$	8885.00	+	15389.3i	0.377696	+	0.654189i	−0.613030	+	0.790059i	$0.710050\pi$
$822$		0			0
$823$	−3934.00	+	6813.89i	−0.166623	+	0.288599i	−0.937230	−	0.348711i	$-0.886620\pi$
$823$	−3934.00	+	6813.89i	−0.166623	+	0.288599i	0.770608	+	0.637310i	$0.219953\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−35726.0			−1.50219			−0.751097	−	0.660192i	$-0.770475\pi$
$827$	−35726.0			−1.50219			−0.751097	+	0.660192i	$0.770475\pi$
$828$		0			0
$829$	13554.0	−	23476.2i	0.567853	−	0.983550i	−0.428925	−	0.903340i	$-0.641108\pi$
$829$	13554.0	−	23476.2i	0.567853	−	0.983550i	0.996778	−	0.0802098i	$-0.0255590\pi$
$830$	1296.00	−	2244.74i	0.0541986	−	0.0938747i
$831$		0			0
$832$	−18432.0			−0.768046
$833$		0			0
$834$		0			0
$835$	27216.0	+	47139.5i	1.12796	+	1.95369i
$836$	−14400.0	+	24941.5i	−0.595735	+	1.03184i
$837$		0			0
$838$	−7704.00	−	13343.7i	−0.317578	−	0.550061i
$839$	23256.0			0.956956			0.478478	−	0.878099i	$-0.341189\pi$
$839$	23256.0			0.956956			0.478478	+	0.878099i	$0.341189\pi$
$840$		0			0
$841$	575.000			0.0235762
$842$	20804.0	+	36033.6i	0.851488	+	1.47482i
$843$		0			0
$844$	−11664.0	+	20202.6i	−0.475701	+	0.823938i
$845$	8109.00	+	14045.2i	0.330128	+	0.571798i
$846$		0			0
$847$		0			0
$848$	−1408.00			−0.0570176
$849$		0			0
$850$	50148.0	−	86858.9i	2.02360	−	3.50498i
$851$	−1134.00	+	1964.15i	−0.0456792	+	0.0791187i
$852$		0			0
$853$	−35280.0			−1.41614			−0.708068	−	0.706144i	$-0.750433\pi$
$853$	−35280.0			−1.41614			−0.708068	+	0.706144i	$0.750433\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9855.00	−	17069.4i	0.392813	−	0.680371i	−0.600007	−	0.799995i	$-0.704835\pi$
$857$	9855.00	−	17069.4i	0.392813	−	0.680371i	0.992819	+	0.119624i	$0.0381688\pi$
$858$		0			0
$859$	1944.00	+	3367.11i	0.0772159	+	0.133742i	0.902048	−	0.431636i	$-0.142064\pi$
$859$	1944.00	+	3367.11i	0.0772159	+	0.133742i	−0.824832	+	0.565378i	$0.808730\pi$
$860$	−46656.0			−1.84995
$861$		0			0
$862$	−41560.0			−1.64216
$863$	−18317.0	−	31726.0i	−0.722500	−	1.25141i	−0.959995	−	0.280019i	$-0.909659\pi$
$863$	−18317.0	−	31726.0i	−0.722500	−	1.25141i	0.237494	−	0.971389i	$-0.423674\pi$
$864$		0			0
$865$	−14094.0	+	24411.5i	−0.554000	+	0.959557i
$866$	−22464.0	−	38908.8i	−0.881476	−	1.52676i
$867$		0			0
$868$		0			0
$869$	11800.0			0.460630
$870$		0			0
$871$	−4176.00	+	7233.04i	−0.162455	+	0.281380i
$872$		0			0
$873$		0			0
$874$	4032.00			0.156046
$875$		0			0
$876$		0			0
$877$	−613.000	−	1061.75i	−0.0236027	−	0.0408810i	0.853983	−	0.520301i	$-0.174180\pi$
$877$	−613.000	−	1061.75i	−0.0236027	−	0.0408810i	−0.877585	+	0.479420i	$0.840847\pi$
$878$	−29232.0	+	50631.3i	−1.12361	+	1.94615i
$879$		0			0
$880$	28800.0	+	49883.1i	1.10324	+	1.91086i
$881$	−38538.0			−1.47376			−0.736878	−	0.676026i	$-0.763701\pi$
$881$	−38538.0			−1.47376			−0.736878	+	0.676026i	$0.763701\pi$
$882$		0			0
$883$	−37260.0			−1.42004			−0.710022	−	0.704180i	$-0.751315\pi$
$883$	−37260.0			−1.42004			−0.710022	+	0.704180i	$0.751315\pi$
$884$	−18144.0	−	31426.3i	−0.690327	−	1.19568i
$885$		0			0
$886$	−23876.0	+	41354.4i	−0.905338	+	1.56809i
$887$	−13320.0	−	23070.9i	−0.504219	−	0.873332i	−0.999988	−	0.00487800i	$-0.998447\pi$
$887$	−13320.0	−	23070.9i	−0.504219	−	0.873332i	0.495770	−	0.868454i	$-0.334886\pi$
$888$		0			0
$889$		0			0
$890$	−16848.0			−0.634546
$891$		0			0
$892$	−4320.00	+	7482.46i	−0.162157	+	0.280865i
$893$	2592.00	−	4489.48i	0.0971310	−	0.168236i
$894$		0			0
$895$	−68436.0			−2.55594
$896$		0			0
$897$		0			0
$898$	−16372.0	−	28357.1i	−0.608397	−	1.05377i
$899$	2844.00	−	4925.95i	0.105509	−	0.182747i
$900$		0			0
$901$	−1386.00	−	2400.62i	−0.0512479	−	0.0887640i
$902$	54000.0			1.99335
$903$		0			0
$904$		0			0
$905$	−4212.00	−	7295.40i	−0.154709	−	0.267964i
$906$		0			0
$907$	6318.00	−	10943.1i	0.231296	−	0.400617i	−0.726894	−	0.686750i	$-0.759037\pi$
$907$	6318.00	−	10943.1i	0.231296	−	0.400617i	0.958190	+	0.286133i	$0.0923700\pi$
$908$	5328.00	+	9228.37i	0.194731	+	0.337284i
$909$		0			0
$910$		0			0
$911$	33638.0			1.22336			0.611678	−	0.791107i	$-0.290495\pi$
$911$	33638.0			1.22336			0.611678	+	0.791107i	$0.290495\pi$
$912$		0			0
$913$	−900.000	+	1558.85i	−0.0326239	+	0.0565063i
$914$	4212.00	−	7295.40i	0.152430	−	0.264016i
$915$		0			0
$916$	−12960.0			−0.467479
$917$		0			0
$918$		0			0
$919$	−18468.0	−	31987.5i	−0.662898	−	1.14817i	−0.979851	−	0.199731i	$-0.935993\pi$
$919$	−18468.0	−	31987.5i	−0.662898	−	1.14817i	0.316953	−	0.948441i	$-0.397340\pi$
$920$		0			0
$921$		0			0
$922$	18972.0	+	32860.5i	0.677668	+	1.17375i
$923$	26424.0			0.942315
$924$		0			0
$925$	−32238.0			−1.14592
$926$	−25304.0	−	43827.8i	−0.897992	−	1.55537i
$927$		0			0
$928$	20224.0	−	35029.0i	0.715394	−	1.23910i
$929$	11151.0	+	19314.1i	0.393813	+	0.682104i	0.992949	−	0.118543i	$-0.0378224\pi$
$929$	11151.0	+	19314.1i	0.393813	+	0.682104i	−0.599136	+	0.800647i	$0.704489\pi$
$930$		0			0
$931$		0			0
$932$	−53744.0			−1.88889
$933$		0			0
$934$	−7416.00	+	12844.9i	−0.259806	+	0.449997i
$935$	−56700.0	+	98207.3i	−1.98320	+	3.43500i
$936$		0			0
$937$	−13824.0			−0.481975			−0.240987	−	0.970528i	$-0.577471\pi$
$937$	−13824.0			−0.481975			−0.240987	+	0.970528i	$0.577471\pi$
$938$		0			0
$939$		0			0
$940$	5184.00	+	8978.95i	0.179876	+	0.311554i
$941$	−6777.00	+	11738.1i	−0.234776	+	0.406643i	−0.959207	−	0.282703i	$-0.908769\pi$
$941$	−6777.00	+	11738.1i	−0.234776	+	0.406643i	0.724432	+	0.689346i	$0.242102\pi$
$942$		0			0
$943$	−1890.00	−	3273.58i	−0.0652671	−	0.113046i
$944$	−29952.0			−1.03268
$945$		0			0
$946$	64800.0			2.22709
$947$	22439.0	+	38865.5i	0.769978	+	1.33364i	0.937574	+	0.347786i	$0.113066\pi$
$947$	22439.0	+	38865.5i	0.769978	+	1.33364i	−0.167596	+	0.985856i	$0.553600\pi$
$948$		0			0
$949$	3240.00	−	5611.84i	0.110827	−	0.191958i
$950$	28656.0	+	49633.6i	0.978656	+	1.69508i
$951$		0			0
$952$		0			0
$953$	−38362.0			−1.30395			−0.651976	−	0.758239i	$-0.726060\pi$
$953$	−38362.0			−1.30395			−0.651976	+	0.758239i	$0.726060\pi$
$954$		0			0
$955$	4338.00	−	7513.64i	0.146989	−	0.254592i
$956$	−14312.0	+	24789.1i	−0.484187	+	0.838637i
$957$		0			0
$958$	32256.0			1.08783
$959$		0			0
$960$		0			0
$961$	14247.5	+	24677.4i	0.478248	+	0.828351i
$962$	−11664.0	+	20202.6i	−0.390917	+	0.677089i
$963$		0			0
$964$	−3024.00	−	5237.72i	−0.101034	−	0.174995i
$965$	−14580.0			−0.486370
$966$		0			0
$967$	26444.0			0.879402			0.439701	−	0.898144i	$-0.355084\pi$
$967$	26444.0			0.879402			0.439701	+	0.898144i	$0.355084\pi$
$968$		0			0
$969$		0			0
$970$	−16848.0	+	29181.6i	−0.557687	+	0.965943i
$971$	−8910.00	−	15432.6i	−0.294475	−	0.510046i	0.680387	−	0.732853i	$-0.261812\pi$
$971$	−8910.00	−	15432.6i	−0.294475	−	0.510046i	−0.974863	+	0.222806i	$0.928478\pi$
$972$		0			0
$973$		0			0
$974$	46656.0			1.53486
$975$		0			0
$976$	−25344.0	+	43897.1i	−0.831190	+	1.43966i
$977$	17219.0	−	29824.2i	0.563853	−	0.976622i	−0.433302	−	0.901249i	$-0.642652\pi$
$977$	17219.0	−	29824.2i	0.563853	−	0.976622i	0.997155	−	0.0753737i	$-0.0240150\pi$
$978$		0			0
$979$	11700.0			0.381955
$980$		0			0
$981$		0			0
$982$	19628.0	+	33996.7i	0.637836	+	1.10476i
$983$	−13032.0	+	22572.1i	−0.422845	+	0.732388i	−0.996216	−	0.0869069i	$-0.972302\pi$
$983$	−13032.0	+	22572.1i	−0.422845	+	0.732388i	0.573372	+	0.819295i	$0.305635\pi$
$984$		0			0
$985$	−22158.0	−	38378.8i	−0.716764	−	1.24147i
$986$	79632.0			2.57201
$987$		0			0
$988$	20736.0			0.667713
$989$	−2268.00	−	3928.29i	−0.0729203	−	0.126302i
$990$		0			0
$991$	−16848.0	+	29181.6i	−0.540055	+	0.935402i	0.458845	+	0.888516i	$0.348263\pi$
$991$	−16848.0	+	29181.6i	−0.540055	+	0.935402i	−0.998900	+	0.0468863i	$0.985070\pi$
$992$	−4608.00	−	7981.29i	−0.147484	−	0.255450i
$993$		0			0
$994$		0			0
$995$	81648.0			2.60142
$996$		0			0
$997$	18036.0	−	31239.3i	0.572925	−	0.992335i	−0.423339	−	0.905971i	$-0.639142\pi$
$997$	18036.0	−	31239.3i	0.572925	−	0.992335i	0.996264	−	0.0863632i	$-0.0275246\pi$
$998$	−30456.0	+	52751.3i	−0.966000	+	1.67316i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.l.361.1		2
3.2	odd	2		147.4.e.d.67.1		2
7.2	even	3	inner	441.4.e.l.226.1		2
7.3	odd	6		441.4.a.a.1.1		1
7.4	even	3		441.4.a.c.1.1		1
7.5	odd	6		441.4.e.o.226.1		2
7.6	odd	2		441.4.e.o.361.1		2
21.2	odd	6		147.4.e.d.79.1		2
21.5	even	6		147.4.e.a.79.1		2
21.11	odd	6		147.4.a.f.1.1	✓	1
21.17	even	6		147.4.a.h.1.1	yes	1
21.20	even	2		147.4.e.a.67.1		2
84.11	even	6		2352.4.a.t.1.1		1
84.59	odd	6		2352.4.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.f.1.1	✓	1	21.11	odd	6
147.4.a.h.1.1	yes	1	21.17	even	6
147.4.e.a.67.1		2	21.20	even	2
147.4.e.a.79.1		2	21.5	even	6
147.4.e.d.67.1		2	3.2	odd	2
147.4.e.d.79.1		2	21.2	odd	6
441.4.a.a.1.1		1	7.3	odd	6
441.4.a.c.1.1		1	7.4	even	3
441.4.e.l.226.1		2	7.2	even	3	inner
441.4.e.l.361.1		2	1.1	even	1	trivial
441.4.e.o.226.1		2	7.5	odd	6
441.4.e.o.361.1		2	7.6	odd	2
2352.4.a.s.1.1		1	84.59	odd	6
2352.4.a.t.1.1		1	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +(36.0000 - 62.3538i) q^{10} +(-25.0000 + 43.3013i) q^{11} +36.0000 q^{13} +(32.0000 + 55.4256i) q^{16} +(-63.0000 + 109.119i) q^{17} +(-36.0000 - 62.3538i) q^{19} +144.000 q^{20} -200.000 q^{22} +(7.00000 + 12.1244i) q^{23} +(-99.5000 + 172.339i) q^{25} +(72.0000 + 124.708i) q^{26} -158.000 q^{29} +(-18.0000 + 31.1769i) q^{31} +(-128.000 + 221.703i) q^{32} -504.000 q^{34} +(81.0000 + 140.296i) q^{37} +(144.000 - 249.415i) q^{38} -270.000 q^{41} -324.000 q^{43} +(-200.000 - 346.410i) q^{44} +(-28.0000 + 48.4974i) q^{46} +(36.0000 + 62.3538i) q^{47} -796.000 q^{50} +(-144.000 + 249.415i) q^{52} +(-11.0000 + 19.0526i) q^{53} +900.000 q^{55} +(-316.000 - 547.328i) q^{58} +(-234.000 + 405.300i) q^{59} +(396.000 + 685.892i) q^{61} -144.000 q^{62} -512.000 q^{64} +(-324.000 - 561.184i) q^{65} +(-116.000 + 200.918i) q^{67} +(-504.000 - 872.954i) q^{68} +734.000 q^{71} +(90.0000 - 155.885i) q^{73} +(-324.000 + 561.184i) q^{74} +576.000 q^{76} +(-118.000 - 204.382i) q^{79} +(576.000 - 997.661i) q^{80} +(-540.000 - 935.307i) q^{82} +36.0000 q^{83} +2268.00 q^{85} +(-648.000 - 1122.37i) q^{86} +(-117.000 - 202.650i) q^{89} -112.000 q^{92} +(-144.000 + 249.415i) q^{94} +(-648.000 + 1122.37i) q^{95} -468.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 8 q^{4} - 18 q^{5}+O(q^{10}) \) 2 * q + 4 * q^2 - 8 * q^4 - 18 * q^5	\( 2 q + 4 q^{2} - 8 q^{4} - 18 q^{5} + 72 q^{10} - 50 q^{11} + 72 q^{13} + 64 q^{16} - 126 q^{17} - 72 q^{19} + 288 q^{20} - 400 q^{22} + 14 q^{23} - 199 q^{25} + 144 q^{26} - 316 q^{29} - 36 q^{31} - 256 q^{32} - 1008 q^{34} + 162 q^{37} + 288 q^{38} - 540 q^{41} - 648 q^{43} - 400 q^{44} - 56 q^{46} + 72 q^{47} - 1592 q^{50} - 288 q^{52} - 22 q^{53} + 1800 q^{55} - 632 q^{58} - 468 q^{59} + 792 q^{61} - 288 q^{62} - 1024 q^{64} - 648 q^{65} - 232 q^{67} - 1008 q^{68} + 1468 q^{71} + 180 q^{73} - 648 q^{74} + 1152 q^{76} - 236 q^{79} + 1152 q^{80} - 1080 q^{82} + 72 q^{83} + 4536 q^{85} - 1296 q^{86} - 234 q^{89} - 224 q^{92} - 288 q^{94} - 1296 q^{95} - 936 q^{97}+O(q^{100}) \) 2 * q + 4 * q^2 - 8 * q^4 - 18 * q^5 + 72 * q^10 - 50 * q^11 + 72 * q^13 + 64 * q^16 - 126 * q^17 - 72 * q^19 + 288 * q^20 - 400 * q^22 + 14 * q^23 - 199 * q^25 + 144 * q^26 - 316 * q^29 - 36 * q^31 - 256 * q^32 - 1008 * q^34 + 162 * q^37 + 288 * q^38 - 540 * q^41 - 648 * q^43 - 400 * q^44 - 56 * q^46 + 72 * q^47 - 1592 * q^50 - 288 * q^52 - 22 * q^53 + 1800 * q^55 - 632 * q^58 - 468 * q^59 + 792 * q^61 - 288 * q^62 - 1024 * q^64 - 648 * q^65 - 232 * q^67 - 1008 * q^68 + 1468 * q^71 + 180 * q^73 - 648 * q^74 + 1152 * q^76 - 236 * q^79 + 1152 * q^80 - 1080 * q^82 + 72 * q^83 + 4536 * q^85 - 1296 * q^86 - 234 * q^89 - 224 * q^92 - 288 * q^94 - 1296 * q^95 - 936 * q^97

Introduction

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