LMFDB - Embedded newform 441.2.o.e.146.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(146,441)]

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([1, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("441.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.14
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.105953 + 0.0611722i) q^{2} +(0.792362 - 1.54018i) q^{3} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(-1.74433 - 2.44076i) q^{9} +O(q^{10})$	\(q+(0.105953 + 0.0611722i) q^{2} +(0.792362 - 1.54018i) q^{3} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(-1.74433 - 2.44076i) q^{9} -0.0647728i q^{10} +(-3.64120 - 2.10225i) q^{11} +(-3.43414 + 0.166516i) q^{12} +(-1.74714 + 1.00871i) q^{13} +(-0.915923 + 0.0444117i) q^{15} +(-1.95521 + 3.38652i) q^{16} +4.38762 q^{17} +(-0.0355103 - 0.365312i) q^{18} +5.24685i q^{19} +(-0.525467 + 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(5.43444 - 3.13757i) q^{23} +(-0.750911 - 0.386313i) q^{24} +(2.35985 - 4.08738i) q^{25} -0.246821 q^{26} +(-5.14136 + 0.752613i) q^{27} +(-7.27689 - 4.20131i) q^{29} +(-0.0997619 - 0.0513235i) q^{30} +(1.03204 - 0.595849i) q^{31} +(-1.25878 + 0.726755i) q^{32} +(-6.12299 + 3.94237i) q^{33} +(0.464883 + 0.268400i) q^{34} +(-2.46462 + 5.42115i) q^{36} -3.23252 q^{37} +(-0.320962 + 0.555922i) q^{38} +(0.169234 + 3.49019i) q^{39} +(-0.223540 + 0.129061i) q^{40} +(-0.0994958 - 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +8.34605i q^{44} +(-0.657340 + 1.44588i) q^{45} +0.767730 q^{46} +(4.98595 - 8.63591i) q^{47} +(3.66663 + 5.69472i) q^{48} +(0.500069 - 0.288715i) q^{50} +(3.47658 - 6.75774i) q^{51} +(3.46814 + 2.00233i) q^{52} -4.21753i q^{53} +(-0.590784 - 0.234767i) q^{54} +2.22598i q^{55} +(8.08111 + 4.15740i) q^{57} +(-0.514008 - 0.890287i) q^{58} +(-6.71960 - 11.6387i) q^{59} +(0.985416 + 1.53047i) q^{60} +(11.3564 + 6.55662i) q^{61} +0.145798 q^{62} +7.64300 q^{64} +(0.924990 + 0.534043i) q^{65} +(-0.889915 + 0.0431507i) q^{66} +(3.29001 + 5.69847i) q^{67} +(-4.35478 - 7.54270i) q^{68} +(-0.526397 - 10.8561i) q^{69} +8.50587i q^{71} +(-1.18999 + 0.850440i) q^{72} +5.61202i q^{73} +(-0.342497 - 0.197741i) q^{74} +(-4.42546 - 6.87329i) q^{75} +(9.01980 - 5.20758i) q^{76} +(-0.195572 + 0.380150i) q^{78} +(-0.286342 + 0.495959i) q^{79} +2.07029 q^{80} +(-2.91465 + 8.51497i) q^{81} -0.0243455i q^{82} +(5.42692 - 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(0.839806 - 0.484862i) q^{86} +(-12.2367 + 7.87878i) q^{87} +(-1.02494 + 1.77525i) q^{88} +12.8738 q^{89} +(-0.158095 + 0.112985i) q^{90} +(-10.7875 - 6.22819i) q^{92} +(-0.0999668 - 2.06166i) q^{93} +(1.05656 - 0.610003i) q^{94} +(2.40568 - 1.38892i) q^{95} +(0.121929 + 2.51460i) q^{96} +(0.493773 + 0.285080i) q^{97} +(1.22035 + 12.5543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 + 16 * q^9	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.105953	+	0.0611722i	0.0749204	+	0.0432553i	0.536992	−	0.843587i	$-0.319560\pi$
$2$	0.105953	+	0.0611722i	0.0749204	+	0.0432553i	−0.462072	+	0.886842i	$0.652894\pi$
$3$	0.792362	−	1.54018i	0.457470	−	0.889225i
$3$	0.792362	−	1.54018i	0.457470	−	0.889225i
$4$	−0.992516	−	1.71909i	−0.496258	−	0.859544i
$5$	−0.264715	−	0.458500i	−0.118384	−	0.205047i	0.800743	−	0.599008i	$-0.204438\pi$
$5$	−0.264715	−	0.458500i	−0.118384	−	0.205047i	−0.919127	+	0.393960i	$0.871105\pi$
$6$	0.178170	−	0.114717i	0.0727375	−	0.0468331i
$7$		0			0
$7$		0			0
$8$		−	0.487547i		−	0.172374i
$9$	−1.74433	−	2.44076i	−0.581442	−	0.813588i
$10$		−	0.0647728i		−	0.0204830i
$11$	−3.64120	−	2.10225i	−1.09786	−	0.633851i	−0.162204	−	0.986757i	$-0.551860\pi$
$11$	−3.64120	−	2.10225i	−1.09786	−	0.633851i	−0.935659	+	0.352906i	$0.885193\pi$
$12$	−3.43414	+	0.166516i	−0.991351	+	0.0480691i
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	−0.722319	−	0.691560i	$-0.756924\pi$
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	0.237749	+	0.971327i	$0.423590\pi$
$14$		0			0
$15$	−0.915923	+	0.0444117i	−0.236490	+	0.0114671i
$16$	−1.95521	+	3.38652i	−0.488802	+	0.846630i
$17$	4.38762			1.06415			0.532077	−	0.846696i	$-0.321412\pi$
$17$	4.38762			1.06415			0.532077	+	0.846696i	$0.321412\pi$
$18$	−0.0355103	−	0.365312i	−0.00836986	−	0.0861048i
$19$			5.24685i			1.20371i	0.798605	+	0.601855i	$0.205572\pi$
$19$			5.24685i			1.20371i	−0.798605	+	0.601855i	$0.794428\pi$
$20$	−0.525467	+	0.910136i	−0.117498	+	0.203513i
$21$		0			0
$22$	−0.257198	−	0.445480i	−0.0548348	−	0.0949767i
$23$	5.43444	−	3.13757i	1.13316	−	0.654230i	0.188431	−	0.982086i	$-0.439660\pi$
$23$	5.43444	−	3.13757i	1.13316	−	0.654230i	0.944727	+	0.327857i	$0.106326\pi$
$24$	−0.750911	−	0.386313i	−0.153279	−	0.0788559i
$25$	2.35985	−	4.08738i	0.471970	−	0.817477i
$26$	−0.246821			−0.0484056
$27$	−5.14136	+	0.752613i	−0.989455	+	0.144840i
$28$		0			0
$29$	−7.27689	−	4.20131i	−1.35128	−	0.780164i	−0.362855	−	0.931846i	$-0.618198\pi$
$29$	−7.27689	−	4.20131i	−1.35128	−	0.780164i	−0.988429	+	0.151681i	$0.951531\pi$
$30$	−0.0997619	−	0.0513235i	−0.0182140	−	0.00937034i
$31$	1.03204	−	0.595849i	0.185360	−	0.107018i	−0.404449	−	0.914561i	$-0.632537\pi$
$31$	1.03204	−	0.595849i	0.185360	−	0.107018i	0.589809	+	0.807543i	$0.299203\pi$
$32$	−1.25878	+	0.726755i	−0.222522	+	0.128473i
$33$	−6.12299	+	3.94237i	−1.06588	+	0.686279i
$34$	0.464883	+	0.268400i	0.0797268	+	0.0460303i
$35$		0			0
$36$	−2.46462	+	5.42115i	−0.410769	+	0.903524i
$37$	−3.23252			−0.531424			−0.265712	−	0.964053i	$-0.585607\pi$
$37$	−3.23252			−0.531424			−0.265712	+	0.964053i	$0.585607\pi$
$38$	−0.320962	+	0.555922i	−0.0520668	+	0.0901824i
$39$	0.169234	+	3.49019i	0.0270991	+	0.558877i
$40$	−0.223540	+	0.129061i	−0.0353448	+	0.0204063i
$41$	−0.0994958	−	0.172332i	−0.0155386	−	0.0269137i	0.858152	−	0.513396i	$-0.171613\pi$
$41$	−0.0994958	−	0.172332i	−0.0155386	−	0.0269137i	−0.873690	+	0.486483i	$0.838280\pi$
$42$		0			0
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	−0.387786	−	0.921750i	$-0.626760\pi$
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	0.992151	−	0.125042i	$-0.0399067\pi$
$44$			8.34605i			1.25821i
$45$	−0.657340	+	1.44588i	−0.0979905	+	0.215539i
$46$	0.767730			0.113196
$47$	4.98595	−	8.63591i	0.727275	−	1.25968i	−0.230756	−	0.973012i	$-0.574120\pi$
$47$	4.98595	−	8.63591i	0.727275	−	1.25968i	0.958031	−	0.286665i	$-0.0925468\pi$
$48$	3.66663	+	5.69472i	0.529232	+	0.821963i
$49$		0			0
$50$	0.500069	−	0.288715i	0.0707204	−	0.0408304i
$51$	3.47658	−	6.75774i	0.486819	−	0.946272i
$52$	3.46814	+	2.00233i	0.480944	+	0.277673i
$53$		−	4.21753i		−	0.579323i	−0.957129	−	0.289661i	$-0.906457\pi$
$53$		−	4.21753i		−	0.579323i	0.957129	−	0.289661i	$-0.0935427\pi$
$54$	−0.590784	−	0.234767i	−0.0803955	−	0.0319477i
$55$			2.22598i			0.300152i
$56$		0			0
$57$	8.08111	+	4.15740i	1.07037	+	0.550662i
$58$	−0.514008	−	0.890287i	−0.0674925	−	0.116900i
$59$	−6.71960	−	11.6387i	−0.874817	−	1.51523i	−0.856958	−	0.515387i	$-0.827648\pi$
$59$	−6.71960	−	11.6387i	−0.874817	−	1.51523i	−0.0178590	−	0.999841i	$-0.505685\pi$
$60$	0.985416	+	1.53047i	0.127217	+	0.197583i
$61$	11.3564	+	6.55662i	1.45404	+	0.839489i	0.998707	−	0.0508335i	$-0.0161878\pi$
$61$	11.3564	+	6.55662i	1.45404	+	0.839489i	0.455330	+	0.890323i	$0.349521\pi$
$62$	0.145798			0.0185163
$63$		0			0
$64$	7.64300			0.955375
$65$	0.924990	+	0.534043i	0.114731	+	0.0662399i
$66$	−0.889915	+	0.0431507i	−0.109541	+	0.00531148i
$67$	3.29001	+	5.69847i	0.401939	+	0.696179i	0.993960	−	0.109744i	$-0.0350030\pi$
$67$	3.29001	+	5.69847i	0.401939	+	0.696179i	−0.592021	+	0.805923i	$0.701670\pi$
$68$	−4.35478	−	7.54270i	−0.528095	−	0.914687i
$69$	−0.526397	−	10.8561i	−0.0633708	−	1.30692i
$70$		0			0
$71$			8.50587i			1.00946i	0.863277	+	0.504730i	$0.168408\pi$
$71$			8.50587i			1.00946i	−0.863277	+	0.504730i	$0.831592\pi$
$72$	−1.18999	+	0.850440i	−0.140241	+	0.100225i
$73$			5.61202i			0.656837i	0.944532	+	0.328419i	$0.106516\pi$
$73$			5.61202i			0.656837i	−0.944532	+	0.328419i	$0.893484\pi$
$74$	−0.342497	−	0.197741i	−0.0398145	−	0.0229869i
$75$	−4.42546	−	6.87329i	−0.511008	−	0.793659i
$76$	9.01980	−	5.20758i	1.03464	−	0.597351i
$77$		0			0
$78$	−0.195572	+	0.380150i	−0.0221441	+	0.0430435i
$79$	−0.286342	+	0.495959i	−0.0322160	+	0.0557997i	−0.881684	−	0.471841i	$-0.843590\pi$
$79$	−0.286342	+	0.495959i	−0.0322160	+	0.0557997i	0.849468	+	0.527640i	$0.176923\pi$
$80$	2.07029			0.231465
$81$	−2.91465	+	8.51497i	−0.323851	+	0.946108i
$82$		−	0.0243455i		−	0.00268851i
$83$	5.42692	−	9.39971i	0.595682	−	1.03175i	−0.397768	−	0.917486i	$-0.630215\pi$
$83$	5.42692	−	9.39971i	0.595682	−	1.03175i	0.993450	−	0.114266i	$-0.0364516\pi$
$84$		0			0
$85$	−1.16147	−	2.01172i	−0.125979	−	0.218202i
$86$	0.839806	−	0.484862i	0.0905586	−	0.0522840i
$87$	−12.2367	+	7.87878i	−1.31191	+	0.844694i
$88$	−1.02494	+	1.77525i	−0.109259	+	0.189243i
$89$	12.8738			1.36461			0.682307	−	0.731065i	$-0.260977\pi$
$89$	12.8738			1.36461			0.682307	+	0.731065i	$0.260977\pi$
$90$	−0.158095	+	0.112985i	−0.0166647	+	0.0119096i
$91$		0			0
$92$	−10.7875	−	6.22819i	−1.12468	−	0.649333i
$93$	−0.0999668	−	2.06166i	−0.0103661	−	0.213784i
$94$	1.05656	−	0.610003i	0.108975	−	0.0629170i
$95$	2.40568	−	1.38892i	0.246817	−	0.142500i
$96$	0.121929	+	2.51460i	0.0124443	+	0.256645i
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	0.524858	−	0.851190i	$-0.324118\pi$
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	−0.474723	+	0.880135i	$0.657452\pi$
$98$		0			0
$99$	1.22035	+	12.5543i	0.122650	+	1.26176i
$100$	−9.36876			−0.936876
$101$	−5.81552	+	10.0728i	−0.578666	+	1.00228i	0.416966	+	0.908922i	$0.363093\pi$
$101$	−5.81552	+	10.0728i	−0.578666	+	1.00228i	−0.995633	+	0.0933576i	$0.970240\pi$
$102$	0.781741	−	0.503335i	0.0774039	−	0.0498376i
$103$	5.54001	−	3.19853i	0.545874	−	0.315160i	−0.201582	−	0.979472i	$-0.564608\pi$
$103$	5.54001	−	3.19853i	0.545874	−	0.315160i	0.747456	+	0.664311i	$0.231275\pi$
$104$	0.491795	+	0.851814i	0.0482245	+	0.0835272i
$105$		0			0
$106$	0.257996	−	0.446862i	0.0250588	−	0.0434031i
$107$			0.253263i			0.0244839i	0.999925	+	0.0122419i	$0.00389683\pi$
$107$			0.253263i			0.0244839i	−0.999925	+	0.0122419i	$0.996103\pi$
$108$	6.39669	+	8.09147i	0.615522	+	0.778602i
$109$	11.9720			1.14671			0.573357	−	0.819306i	$-0.305641\pi$
$109$	11.9720			1.14671			0.573357	+	0.819306i	$0.305641\pi$
$110$	−0.136168	+	0.235851i	−0.0129831	+	0.0224875i
$111$	−2.56133	+	4.97868i	−0.243110	+	0.472555i
$112$		0			0
$113$	4.28636	−	2.47473i	0.403227	−	0.232803i	−0.284648	−	0.958632i	$-0.591877\pi$
$113$	4.28636	−	2.47473i	0.403227	−	0.232803i	0.687875	+	0.725829i	$0.258544\pi$
$114$	0.601903	+	0.934831i	0.0563734	+	0.0875549i
$115$	−2.87715	−	1.66113i	−0.268296	−	0.154901i
$116$			16.6795i			1.54865i
$117$	5.50962	+	2.50484i	0.509364	+	0.231572i
$118$		−	1.64421i		−	0.151362i
$119$		0			0
$120$	0.0216528	+	0.446555i	0.00197662	+	0.0407647i
$121$	3.33888	+	5.78311i	0.303535	+	0.525737i
$122$	0.802166	+	1.38939i	0.0726247	+	0.125790i
$123$	−0.344259	+	0.0166926i	−0.0310408	+	0.00150512i
$124$	−2.04863	−	1.18278i	−0.183973	−	0.106217i
$125$	−5.14590			−0.460263
$126$		0			0
$127$	−3.68446			−0.326943			−0.163472	−	0.986548i	$-0.552269\pi$
$127$	−3.68446			−0.326943			−0.163472	+	0.986548i	$0.552269\pi$
$128$	3.32736	+	1.92105i	0.294100	+	0.169798i
$129$	−7.43204	−	11.5429i	−0.654354	−	1.01629i
$130$	0.0653372	+	0.113167i	0.00573045	+	0.00992543i
$131$	−2.72837	−	4.72567i	−0.238379	−	0.412884i	0.721871	−	0.692028i	$-0.243283\pi$
$131$	−2.72837	−	4.72567i	−0.238379	−	0.412884i	−0.960249	+	0.279144i	$0.909949\pi$
$132$	12.8544	+	6.61309i	1.11884	+	0.575596i
$133$		0			0
$134$			0.805030i			0.0695440i
$135$	1.70607	+	2.15808i	0.146835	+	0.185738i
$136$		−	2.13917i		−	0.183432i
$137$	−1.39996	−	0.808270i	−0.119607	−	0.0690551i	0.439003	−	0.898486i	$-0.355332\pi$
$137$	−1.39996	−	0.808270i	−0.119607	−	0.0690551i	−0.558610	+	0.829431i	$0.688665\pi$
$138$	0.608320	−	1.18244i	0.0517836	−	0.100656i
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	−0.854006	−	0.520262i	$-0.825834\pi$
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	0.0235572	+	0.999722i	$0.492501\pi$
$140$		0			0
$141$	−9.35021	−	14.5220i	−0.787430	−	1.22298i
$142$	−0.520323	+	0.901226i	−0.0436645	+	0.0756292i
$143$	8.48226			0.709322
$144$	11.6762	−	1.13499i	0.973018	−	0.0945827i
$145$			4.44860i			0.369436i
$146$	−0.343300	+	0.594613i	−0.0284117	+	0.0492105i
$147$		0			0
$148$	3.20833	+	5.55699i	0.263723	+	0.456782i
$149$	4.61426	−	2.66404i	0.378015	−	0.218247i	−0.298939	−	0.954272i	$-0.596633\pi$
$149$	4.61426	−	2.66404i	0.378015	−	0.218247i	0.676954	+	0.736025i	$0.263300\pi$
$150$	−0.0484383	−	0.998964i	−0.00395497	−	0.0815651i
$151$	1.32132	−	2.28859i	0.107527	−	0.186243i	−0.807241	−	0.590222i	$-0.799040\pi$
$151$	1.32132	−	2.28859i	0.107527	−	0.186243i	0.914768	+	0.403980i	$0.132373\pi$
$152$	2.55808			0.207488
$153$	−7.65344	−	10.7091i	−0.618744	−	0.865783i
$154$		0			0
$155$	−0.546393	−	0.315460i	−0.0438873	−	0.0253384i
$156$	5.83197	−	3.75499i	0.466931	−	0.300640i
$157$	−11.3181	+	6.53448i	−0.903279	+	0.521508i	−0.878263	−	0.478179i	$-0.841297\pi$
$157$	−11.3181	+	6.53448i	−0.903279	+	0.521508i	−0.0250163	+	0.999687i	$0.507964\pi$
$158$	−0.0606778	+	0.0350324i	−0.00482727	+	0.00278703i
$159$	−6.49577	−	3.34181i	−0.515148	−	0.265023i
$160$	0.666434	+	0.384766i	0.0526862	+	0.0304184i
$161$		0			0
$162$	−0.829698	+	0.723895i	−0.0651872	+	0.0568745i
$163$	17.0269			1.33365			0.666825	−	0.745214i	$-0.267653\pi$
$163$	17.0269			1.33365			0.666825	+	0.745214i	$0.267653\pi$
$164$	−0.197502	+	0.342084i	−0.0154223	+	0.0267123i
$165$	3.42842	+	1.76378i	0.266902	+	0.137310i
$166$	1.15000	−	0.663954i	0.0892575	−	0.0515328i
$167$	10.6605	+	18.4645i	0.824932	+	1.42882i	0.901971	+	0.431796i	$0.142120\pi$
$167$	10.6605	+	18.4645i	0.824932	+	1.42882i	−0.0770396	+	0.997028i	$0.524547\pi$
$168$		0			0
$169$	−4.46499	+	7.73360i	−0.343461	+	0.594892i
$170$		−	0.284198i		−	0.0217970i
$171$	12.8063	−	9.15222i	0.979324	−	0.699888i
$172$	−15.7337			−1.19968
$173$	−10.2433	+	17.7418i	−0.778781	+	1.34889i	0.153864	+	0.988092i	$0.450828\pi$
$173$	−10.2433	+	17.7418i	−0.778781	+	1.34889i	−0.932645	+	0.360796i	$0.882505\pi$
$174$	−1.77848	+	0.0862361i	−0.134827	+	0.00653754i
$175$		0			0
$176$	14.2386	−	8.22066i	1.07327	−	0.619655i
$177$	−23.2500	+	1.12736i	−1.74758	+	0.0847376i
$178$	1.36402	+	0.787516i	0.102237	+	0.0590268i
$179$		−	14.4071i		−	1.07684i	−0.842676	−	0.538420i	$-0.819021\pi$
$179$		−	14.4071i		−	1.07684i	0.842676	−	0.538420i	$-0.180979\pi$
$180$	3.13801	−	0.305032i	0.233894	−	0.0227358i
$181$			6.97309i			0.518306i	0.965836	+	0.259153i	$0.0834434\pi$
$181$			6.97309i			0.518306i	−0.965836	+	0.259153i	$0.916557\pi$
$182$		0			0
$183$	19.0968	−	12.2957i	1.41167	−	0.908925i
$184$	−1.52971	−	2.64954i	−0.112772	−	0.195327i
$185$	0.855697	+	1.48211i	0.0629121	+	0.108967i
$186$	0.115524	−	0.224555i	0.00847067	−	0.0164652i
$187$	−15.9762	−	9.22386i	−1.16829	−	0.674515i
$188$	−19.7945			−1.44366
$189$		0			0
$190$	0.339853			0.0246555
$191$	−9.38310	−	5.41734i	−0.678937	−	0.391985i	0.120517	−	0.992711i	$-0.461545\pi$
$191$	−9.38310	−	5.41734i	−0.678937	−	0.391985i	−0.799455	+	0.600727i	$0.794878\pi$
$192$	6.05602	−	11.7716i	0.437056	−	0.849543i
$193$	−5.26223	−	9.11444i	−0.378783	−	0.656072i	0.612102	−	0.790779i	$-0.290324\pi$
$193$	−5.26223	−	9.11444i	−0.378783	−	0.656072i	−0.990886	+	0.134707i	$0.956991\pi$
$194$	0.0348780	+	0.0604104i	0.00250409	+	0.00433722i
$195$	1.55545	−	1.00150i	0.111388	−	0.0717187i
$196$		0			0
$197$			15.5156i			1.10544i	0.833366	+	0.552721i	$0.186410\pi$
$197$			15.5156i			1.10544i	−0.833366	+	0.552721i	$0.813590\pi$
$198$	−0.638675	+	1.40482i	−0.0453886	+	0.0998364i
$199$		−	12.5479i		−	0.889495i	−0.895656	−	0.444748i	$-0.853293\pi$
$199$		−	12.5479i		−	0.889495i	0.895656	−	0.444748i	$-0.146707\pi$
$200$	−1.99279	−	1.15054i	−0.140912	−	0.0813553i
$201$	11.3836	−	0.551972i	0.802935	−	0.0389331i
$202$	−1.23235	+	0.711497i	−0.0867078	+	0.0500608i
$203$		0			0
$204$	−15.0677	+	0.730611i	−1.05495	+	0.0511530i
$205$	−0.0526760	+	0.0912375i	−0.00367905	+	0.00637231i
$206$	0.782644			0.0545294
$207$	−17.1375	−	7.79123i	−1.19114	−	0.541528i
$208$		−	7.88898i		−	0.547002i
$209$	11.0302	−	19.1048i	0.762973	−	1.32151i
$210$		0			0
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	0.821852	−	0.569701i	$-0.192941\pi$
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	−0.904302	+	0.426894i	$0.859608\pi$
$212$	−7.25031	+	4.18597i	−0.497953	+	0.287493i
$213$	13.1006	+	6.73972i	0.897638	+	0.461798i
$214$	−0.0154927	+	0.0268341i	−0.00105906	+	0.00183434i
$215$	−4.19636			−0.286189
$216$	0.366934	+	2.50665i	0.0249667	+	0.170556i
$217$		0			0
$218$	1.26848	+	0.732357i	0.0859123	+	0.0496015i
$219$	8.64354	+	4.44675i	0.584076	+	0.300484i
$220$	3.82666	−	2.20932i	0.257993	−	0.148953i
$221$	−7.66580	+	4.42585i	−0.515657	+	0.297715i
$222$	−0.575938	+	0.370826i	−0.0386544	+	0.0248882i
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	0.416711	−	0.909039i	$-0.363183\pi$
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	−0.578895	+	0.815402i	$0.696516\pi$
$224$		0			0
$225$	−14.0927	+	1.36989i	−0.939513	+	0.0913259i
$226$	0.605540			0.0402799
$227$	−1.42300	+	2.46471i	−0.0944480	+	0.163589i	−0.909378	−	0.415970i	$-0.863442\pi$
$227$	−1.42300	+	2.46471i	−0.0944480	+	0.163589i	0.814930	+	0.579559i	$0.196775\pi$
$228$	−0.873687	−	18.0184i	−0.0578613	−	1.19330i
$229$	−20.5460	+	11.8623i	−1.35772	+	0.783880i	−0.989316	−	0.145786i	$-0.953429\pi$
$229$	−20.5460	+	11.8623i	−1.35772	+	0.783880i	−0.368404	+	0.929666i	$0.620096\pi$
$230$	−0.203229	−	0.352004i	−0.0134006	−	0.0232104i
$231$		0			0
$232$	−2.04834	+	3.54782i	−0.134480	+	0.232926i
$233$		−	18.7298i		−	1.22703i	−0.789684	−	0.613514i	$-0.789755\pi$
$233$		−	18.7298i		−	1.22703i	0.789684	−	0.613514i	$-0.210245\pi$
$234$	0.430536	+	0.602432i	0.0281450	+	0.0393822i
$235$	−5.27942			−0.344391
$236$	−13.3386	+	23.1032i	−0.868270	+	1.50389i
$237$	0.536981	+	0.833998i	0.0348807	+	0.0541740i
$238$		0			0
$239$	11.1421	−	6.43288i	0.720721	−	0.416109i	−0.0942969	−	0.995544i	$-0.530060\pi$
$239$	11.1421	−	6.43288i	0.720721	−	0.416109i	0.815018	+	0.579436i	$0.196727\pi$
$240$	1.64042	−	3.18862i	0.105889	−	0.205825i
$241$	3.64082	+	2.10203i	0.234526	+	0.135403i	0.612658	−	0.790348i	$-0.290100\pi$
$241$	3.64082	+	2.10203i	0.234526	+	0.135403i	−0.378132	+	0.925752i	$0.623434\pi$
$242$			0.816987i			0.0525179i
$243$	10.8052	+	11.2360i	0.693151	+	0.720792i
$244$		−	26.0302i		−	1.66641i
$245$		0			0
$246$	−0.0374965	−	0.0192905i	−0.00239069	−	0.00122991i
$247$	−5.29257	−	9.16700i	−0.336758	−	0.583282i
$248$	−0.290504	−	0.503168i	−0.0184470	−	0.0319512i
$249$	−10.1772	−	15.8064i	−0.644953	−	1.00169i
$250$	−0.545226	−	0.314786i	−0.0344831	−	0.0199088i
$251$	−7.50592			−0.473770			−0.236885	−	0.971538i	$-0.576126\pi$
$251$	−7.50592			−0.473770			−0.236885	+	0.971538i	$0.576126\pi$
$252$		0			0
$253$	−26.3838			−1.65874
$254$	−0.390381	−	0.225387i	−0.0244947	−	0.0141420i
$255$	−4.01872	+	0.194862i	−0.251662	+	0.0122027i
$256$	−7.40797	−	12.8310i	−0.462998	−	0.801936i
$257$	2.51960	+	4.36408i	0.157169	+	0.272224i	0.933847	−	0.357674i	$-0.116430\pi$
$257$	2.51960	+	4.36408i	0.157169	+	0.272224i	−0.776678	+	0.629898i	$0.783097\pi$
$258$	−0.0813463	−	1.67764i	−0.00506440	−	0.104445i
$259$		0			0
$260$		−	2.12018i		−	0.131488i
$261$	2.43885	+	25.0896i	0.150961	+	1.55301i
$262$		−	0.667601i		−	0.0412445i
$263$	12.2494	+	7.07220i	0.755331	+	0.436091i	0.827617	−	0.561293i	$-0.189696\pi$
$263$	12.2494	+	7.07220i	0.755331	+	0.436091i	−0.0722856	+	0.997384i	$0.523029\pi$
$264$	1.92209	+	2.98524i	0.118296	+	0.183729i
$265$	−1.93374	+	1.11644i	−0.118789	+	0.0685826i
$266$		0			0
$267$	10.2007	−	19.8279i	0.624271	−	1.21345i
$268$	6.53078	−	11.3116i	0.398931	−	0.690969i
$269$	15.7771			0.961948			0.480974	−	0.876735i	$-0.340283\pi$
$269$	15.7771			0.961948			0.480974	+	0.876735i	$0.340283\pi$
$270$	0.0487488	+	0.333020i	0.00296676	+	0.0202670i
$271$		−	16.8078i		−	1.02100i	−0.859877	−	0.510501i	$-0.829460\pi$
$271$		−	16.8078i		−	1.02100i	0.859877	−	0.510501i	$-0.170540\pi$
$272$	−8.57871	+	14.8588i	−0.520160	+	0.900944i
$273$		0			0
$274$	−0.0988873	−	0.171278i	−0.00597400	−	0.0103473i
$275$	−17.1854	+	9.92198i	−1.03632	+	0.598318i
$276$	−18.1402	+	11.6798i	−1.09191	+	0.703041i
$277$	−8.91066	+	15.4337i	−0.535390	+	0.927322i	0.463755	+	0.885964i	$0.346502\pi$
$277$	−8.91066	+	15.4337i	−0.535390	+	0.927322i	−0.999144	+	0.0413586i	$0.986831\pi$
$278$	−1.38317			−0.0829568
$279$	−3.25454	−	1.47961i	−0.194844	−	0.0885821i
$280$		0			0
$281$	7.59774	+	4.38656i	0.453243	+	0.261680i	0.709199	−	0.705008i	$-0.249057\pi$
$281$	7.59774	+	4.38656i	0.453243	+	0.261680i	−0.255956	+	0.966688i	$0.582390\pi$
$282$	−0.102341	−	2.11063i	−0.00609434	−	0.125686i
$283$	18.7047	−	10.7991i	1.11188	−	0.641942i	0.172562	−	0.984999i	$-0.444796\pi$
$283$	18.7047	−	10.7991i	1.11188	−	0.641942i	0.939315	+	0.343056i	$0.111462\pi$
$284$	14.6223	−	8.44221i	0.867676	−	0.500953i
$285$	−0.233022	−	4.80571i	−0.0138030	−	0.284666i
$286$	0.898724	+	0.518879i	0.0531427	+	0.0306819i
$287$		0			0
$288$	3.96956	+	1.80468i	0.233908	+	0.106342i
$289$	2.25120			0.132424
$290$	−0.272131	+	0.471344i	−0.0159801	+	0.0276783i
$291$	0.830323	−	0.534615i	0.0486744	−	0.0313397i
$292$	9.64756	−	5.57002i	0.564581	−	0.325961i
$293$	9.79756	+	16.9699i	0.572379	+	0.991390i	0.996321	+	0.0857006i	$0.0273128\pi$
$293$	9.79756	+	16.9699i	0.572379	+	0.991390i	−0.423942	+	0.905690i	$0.639354\pi$
$294$		0			0
$295$	−3.55755	+	6.16186i	−0.207129	+	0.358758i
$296$			1.57601i			0.0916035i
$297$	20.3029	+	8.06799i	1.17809	+	0.468152i
$298$	0.651862			0.0377613
$299$	−6.32983	+	10.9636i	−0.366063	+	0.634040i
$300$	−7.42345	+	14.4296i	−0.428593	+	0.833094i
$301$		0			0
$302$	0.279996	−	0.161656i	0.0161120	−	0.00930224i
$303$	10.9059	+	16.9383i	0.626529	+	0.973078i
$304$	−17.7686	−	10.2587i	−1.01910	−	0.588376i
$305$		−	6.94254i		−	0.397529i
$306$	−0.155806	−	1.60285i	−0.00890682	−	0.0916287i
$307$			27.7677i			1.58478i	0.610012	+	0.792392i	$0.291165\pi$
$307$			27.7677i			1.58478i	−0.610012	+	0.792392i	$0.708835\pi$
$308$		0			0
$309$	−0.536623	−	11.0670i	−0.0305274	−	0.629581i
$310$	−0.0385948	−	0.0668482i	−0.00219204	−	0.00379672i
$311$	−10.0080	−	17.3344i	−0.567501	−	0.982941i	−0.996812	−	0.0797841i	$-0.974577\pi$
$311$	−10.0080	−	17.3344i	−0.567501	−	0.982941i	0.429311	−	0.903157i	$-0.358756\pi$
$312$	1.70163	−	0.0825094i	0.0963357	−	0.00467118i
$313$	−15.9654	−	9.21765i	−0.902420	−	0.521012i	−0.0244352	−	0.999701i	$-0.507779\pi$
$313$	−15.9654	−	9.21765i	−0.902420	−	0.521012i	−0.877984	+	0.478689i	$0.841112\pi$
$314$	−1.59891			−0.0902320
$315$		0			0
$316$	1.13680			0.0639498
$317$	−12.5992	−	7.27416i	−0.707642	−	0.408558i	0.102545	−	0.994728i	$-0.467301\pi$
$317$	−12.5992	−	7.27416i	−0.707642	−	0.408558i	−0.810187	+	0.586171i	$0.800635\pi$
$318$	−0.483823	−	0.751437i	−0.0271314	−	0.0421385i
$319$	17.6644	+	30.5956i	0.989016	+	1.71303i
$320$	−2.02322	−	3.50431i	−0.113101	−	0.195897i
$321$	0.390072	+	0.200676i	0.0217717	+	0.0112006i
$322$		0			0
$323$			23.0212i			1.28093i
$324$	17.5308	−	3.44070i	0.973935	−	0.191150i
$325$			9.52166i			0.528167i
$326$	1.80406	+	1.04157i	0.0999176	+	0.0576874i
$327$	9.48619	−	18.4391i	0.524588	−	1.01969i
$328$	−0.0840197	+	0.0485088i	−0.00463921	+	0.00267845i
$329$		0			0
$330$	0.255358	+	0.396603i	0.0140570	+	0.0218323i
$331$	14.8446	−	25.7115i	0.815930	−	1.41323i	−0.0927274	−	0.995692i	$-0.529559\pi$
$331$	14.8446	−	25.7115i	0.815930	−	1.41323i	0.908658	−	0.417541i	$-0.137108\pi$
$332$	−21.5452			−1.18245
$333$	5.63857	+	7.88983i	0.308992	+	0.432360i
$334$			2.60850i			0.142731i
$335$	1.74183	−	3.01694i	0.0951664	−	0.164833i
$336$		0			0
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	0.712868	−	0.701298i	$-0.247396\pi$
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	−0.963776	+	0.266713i	$0.914063\pi$
$338$	−0.946163	+	0.546267i	−0.0514645	+	0.0297130i
$339$	−0.415191	−	8.56267i	−0.0225501	−	0.465060i
$340$	−2.30555	+	3.99333i	−0.125036	+	0.216569i
$341$	−5.01049			−0.271333
$342$	1.91674	−	0.186317i	0.103645	−	0.0100749i
$343$		0			0
$344$	−3.34665	−	1.93219i	−0.180439	−	0.104177i
$345$	−4.83818	+	3.11513i	−0.260479	+	0.167713i
$346$	−2.17062	+	1.25321i	−0.116693	+	0.0673728i
$347$	15.7313	−	9.08247i	0.844501	−	0.487573i	−0.0142910	−	0.999898i	$-0.504549\pi$
$347$	15.7313	−	9.08247i	0.844501	−	0.487573i	0.858791	+	0.512325i	$0.171216\pi$
$348$	25.6895	+	13.2162i	1.37710	+	0.708462i
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	0.339478	−	0.940614i	$-0.389750\pi$
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	−0.644856	+	0.764304i	$0.723083\pi$
$350$		0			0
$351$	8.22352	−	6.50108i	0.438939	−	0.347002i
$352$	6.11128			0.325732
$353$	−10.4692	+	18.1332i	−0.557221	+	0.965135i	0.440506	+	0.897750i	$0.354799\pi$
$353$	−10.4692	+	18.1332i	−0.557221	+	0.965135i	−0.997727	+	0.0673857i	$0.978534\pi$
$354$	−2.53238	−	1.30281i	−0.134595	−	0.0692435i
$355$	3.89994	−	2.25163i	0.206987	−	0.119504i
$356$	−12.7774	−	22.1311i	−0.677201	−	1.17295i
$357$		0			0
$358$	0.881317	−	1.52649i	0.0465791	−	0.0806773i
$359$			14.2265i			0.750845i	0.926854	+	0.375422i	$0.122502\pi$
$359$			14.2265i			0.750845i	−0.926854	+	0.375422i	$0.877498\pi$
$360$	0.704933	+	0.320484i	0.0371532	+	0.0168910i
$361$	−8.52944			−0.448918
$362$	−0.426560	+	0.738823i	−0.0224195	+	0.0388317i
$363$	11.5526	−	0.560171i	0.606357	−	0.0294013i
$364$		0			0
$365$	2.57311	−	1.48559i	0.134683	−	0.0777591i
$366$	2.77552	−	0.134581i	0.145079	−	0.00703466i
$367$	10.7237	+	6.19136i	0.559775	+	0.323186i	0.753055	−	0.657957i	$-0.228579\pi$
$367$	10.7237	+	6.19136i	0.559775	+	0.323186i	−0.193280	+	0.981144i	$0.561913\pi$
$368$			24.5384i			1.27915i
$369$	−0.247068	+	0.543448i	−0.0128618	+	0.0282908i
$370$			0.209380i			0.0108851i
$371$		0			0
$372$	−3.44496	+	2.21808i	−0.178613	+	0.115002i
$373$	10.6559	+	18.4565i	0.551740	+	0.955642i	0.998149	+	0.0608130i	$0.0193693\pi$
$373$	10.6559	+	18.4565i	0.551740	+	0.955642i	−0.446409	+	0.894829i	$0.647297\pi$
$374$	−1.12849	−	1.95460i	−0.0583527	−	0.101070i
$375$	−4.07741	+	7.92563i	−0.210557	+	0.409278i
$376$	−4.21041	−	2.43088i	−0.217135	−	0.125363i
$377$	16.9517			0.873057
$378$		0			0
$379$	10.6001			0.544489			0.272244	−	0.962228i	$-0.412234\pi$
$379$	10.6001			0.544489			0.272244	+	0.962228i	$0.412234\pi$
$380$	−4.77535	−	2.75705i	−0.244970	−	0.141434i
$381$	−2.91943	+	5.67475i	−0.149567	+	0.290726i
$382$	−0.662781	−	1.14797i	−0.0339108	−	0.0587353i
$383$	6.32174	+	10.9496i	0.323026	+	0.559497i	0.981111	−	0.193446i	$-0.0619666\pi$
$383$	6.32174	+	10.9496i	0.323026	+	0.559497i	−0.658085	+	0.752944i	$0.728633\pi$
$384$	5.59524	−	3.60257i	0.285531	−	0.183843i
$385$		0			0
$386$		−	1.28761i		−	0.0655375i
$387$	−23.6670	+	2.30056i	−1.20306	+	0.116944i
$388$		−	1.13179i		−	0.0574578i
$389$	11.4538	+	6.61286i	0.580732	+	0.335286i	0.761424	−	0.648254i	$-0.224501\pi$
$389$	11.4538	+	6.61286i	0.580732	+	0.335286i	−0.180692	+	0.983540i	$0.557834\pi$
$390$	0.226069	−	0.0109618i	0.0114475	−	0.000555070i
$391$	23.8442	−	13.7665i	1.20586	−	0.696201i
$392$		0			0
$393$	−9.44025	+	0.457744i	−0.476198	+	0.0230901i
$394$	−0.949125	+	1.64393i	−0.0478162	+	0.0828201i
$395$	0.303196			0.0152554
$396$	20.3707	−	14.5582i	1.02367	−	0.731579i
$397$		−	24.7882i		−	1.24409i	−0.782983	−	0.622043i	$-0.786303\pi$
$397$		−	24.7882i		−	1.24409i	0.782983	−	0.622043i	$-0.213697\pi$
$398$	0.767582	−	1.32949i	0.0384754	−	0.0666413i
$399$		0			0
$400$	9.22800	+	15.9834i	0.461400	+	0.799168i
$401$	3.19615	−	1.84530i	0.159608	−	0.0921499i	−0.418068	−	0.908416i	$-0.637293\pi$
$401$	3.19615	−	1.84530i	0.159608	−	0.0921499i	0.577677	+	0.816266i	$0.303959\pi$
$402$	1.23989	+	0.637875i	0.0618402	+	0.0318143i
$403$	−1.20208	+	2.08207i	−0.0598800	+	0.103715i
$404$	23.0880			1.14867
$405$	4.67566	−	0.917672i	0.232336	−	0.0455995i
$406$		0			0
$407$	11.7703	+	6.79556i	0.583430	+	0.336843i
$408$	−3.29471	−	1.69500i	−0.163112	−	0.0839148i
$409$	−16.0535	+	9.26852i	−0.793797	+	0.458299i	−0.841297	−	0.540573i	$-0.818208\pi$
$409$	−16.0535	+	9.26852i	−0.793797	+	0.458299i	0.0475008	+	0.998871i	$0.484874\pi$
$410$	−0.0111624	+	0.00644462i	−0.000551272	+	0.000318277i
$411$	−2.35416	+	1.51576i	−0.116122	+	0.0747669i
$412$	−10.9971	−	6.34918i	−0.541788	−	0.312802i
$413$		0			0
$414$	−1.33917	−	1.87385i	−0.0658167	−	0.0920945i
$415$	−5.74635			−0.282077
$416$	1.46618	−	2.53949i	0.0718852	−	0.124509i
$417$	0.948373	+	19.5587i	0.0464420	+	0.957795i
$418$	2.33737	−	1.34948i	0.114324	−	0.0660053i
$419$	1.46994	+	2.54600i	0.0718111	+	0.124380i	0.899695	−	0.436519i	$-0.143789\pi$
$419$	1.46994	+	2.54600i	0.0718111	+	0.124380i	−0.827884	+	0.560899i	$0.810455\pi$
$420$		0			0
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	0.285031	+	0.958518i	$0.407996\pi$
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	−0.972617	+	0.232415i	$0.925337\pi$
$422$		−	0.293051i		−	0.0142655i
$423$	−29.7753	+	2.89433i	−1.44773	+	0.140727i
$424$	−2.05624			−0.0998600
$425$	10.3541	−	17.9339i	0.502249	−	0.869921i
$426$	0.975768	+	1.51549i	0.0472761	+	0.0734257i
$427$		0			0
$428$	0.435382	−	0.251368i	0.0210450	−	0.0121503i
$429$	6.72102	−	13.0642i	0.324494	−	0.630747i
$430$	−0.444618	−	0.256700i	−0.0214414	−	0.0123792i
$431$			6.76465i			0.325842i	0.986639	+	0.162921i	$0.0520915\pi$
$431$			6.76465i			0.325842i	−0.986639	+	0.162921i	$0.947908\pi$
$432$	7.50369	−	18.8828i	0.361021	−	0.908500i
$433$		−	28.3475i		−	1.36229i	−0.732146	−	0.681147i	$-0.761481\pi$
$433$		−	28.3475i		−	1.36229i	0.732146	−	0.681147i	$-0.238519\pi$
$434$		0			0
$435$	6.85166	+	3.52490i	0.328512	+	0.169006i
$436$	−11.8824	−	20.5810i	−0.569066	−	0.985651i
$437$	16.4624	+	28.5137i	0.787503	+	1.36399i
$438$	0.643795	+	0.999893i	0.0307617	+	0.0477767i
$439$	22.8208	+	13.1756i	1.08918	+	0.628837i	0.933358	−	0.358948i	$-0.116864\pi$
$439$	22.8208	+	13.1756i	1.08918	+	0.628837i	0.155821	+	0.987785i	$0.450198\pi$
$440$	1.08527			0.0517382
$441$		0			0
$442$	−1.08296			−0.0515110
$443$	−4.75958	−	2.74795i	−0.226135	−	0.130559i	0.382653	−	0.923892i	$-0.375011\pi$
$443$	−4.75958	−	2.74795i	−0.226135	−	0.130559i	−0.608788	+	0.793333i	$0.708344\pi$
$444$	11.1009	−	0.538268i	0.526827	−	0.0255451i
$445$	−3.40787	−	5.90261i	−0.161549	−	0.279810i
$446$	−0.171074	−	0.296309i	−0.00810060	−	0.0140306i
$447$	−0.446952	−	9.21768i	−0.0211401	−	0.435981i
$448$		0			0
$449$		−	7.38342i		−	0.348445i	−0.984706	−	0.174223i	$-0.944259\pi$
$449$		−	7.38342i		−	0.348445i	0.984706	−	0.174223i	$-0.0557412\pi$
$450$	−1.57697	−	0.716937i	−0.0743390	−	0.0337967i
$451$			0.836659i			0.0393967i
$452$	−8.50857	−	4.91242i	−0.400209	−	0.231061i
$453$	−2.47788	−	3.84846i	−0.116421	−	0.180816i
$454$	−0.301544	+	0.174097i	−0.0141522	+	0.00817076i
$455$		0			0
$456$	2.02693	−	3.93992i	0.0949196	−	0.184504i
$457$	−20.7109	+	35.8724i	−0.968817	+	1.67804i	−0.269826	+	0.962909i	$0.586966\pi$
$457$	−20.7109	+	35.8724i	−0.968817	+	1.67804i	−0.698991	+	0.715130i	$0.746367\pi$
$458$	−2.90256			−0.135628
$459$	−22.5583	+	3.30218i	−1.05293	+	0.154133i
$460$			6.59477i			0.307483i
$461$	5.44638	−	9.43341i	0.253663	−	0.439357i	−0.710868	−	0.703325i	$-0.751698\pi$
$461$	5.44638	−	9.43341i	0.253663	−	0.439357i	0.964532	+	0.263968i	$0.0850312\pi$
$462$		0			0
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	0.791316	−	0.611407i	$-0.209396\pi$
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	−0.925152	+	0.379597i	$0.876063\pi$
$464$	28.4557	−	16.4289i	1.32102	−	0.762692i
$465$	−0.918807	+	0.591587i	−0.0426087	+	0.0274342i
$466$	1.14574	−	1.98448i	0.0530755	−	0.0919294i
$467$	−23.8882			−1.10541			−0.552707	−	0.833376i	$-0.686405\pi$
$467$	−23.8882			−1.10541			−0.552707	+	0.833376i	$0.686405\pi$
$468$	−1.16235	−	11.9576i	−0.0537295	−	0.552741i
$469$		0			0
$470$	−0.559372	−	0.322954i	−0.0258019	−	0.0148967i
$471$	1.09630	+	22.6095i	0.0505150	+	1.04179i
$472$	−5.67440	+	3.27612i	−0.261185	+	0.150795i
$473$	−28.8608	+	16.6628i	−1.32702	+	0.766156i
$474$	0.00587745	+	0.121213i	0.000269960	+	0.00556751i
$475$	21.4459	+	12.3818i	0.984005	+	0.568116i
$476$		0			0
$477$	−10.2940	+	7.35675i	−0.471330	+	0.336842i
$478$	1.57406			0.0719956
$479$	0.947645	−	1.64137i	0.0432990	−	0.0749961i	−0.843564	−	0.537029i	$-0.819547\pi$
$479$	0.947645	−	1.64137i	0.0432990	−	0.0749961i	0.886863	+	0.462033i	$0.152880\pi$
$480$	1.12067	−	0.721556i	0.0511512	−	0.0329344i
$481$	5.64768	−	3.26069i	0.257512	−	0.148675i
$482$	0.257171	+	0.445434i	0.0117138	+	0.0202890i
$483$		0			0
$484$	6.62778	−	11.4797i	0.301263	−	0.521803i
$485$		−	0.301860i		−	0.0137067i
$486$	0.457509	+	1.85147i	0.0207531	+	0.0839845i
$487$	28.2248			1.27899			0.639494	−	0.768796i	$-0.279144\pi$
$487$	28.2248			1.27899			0.639494	+	0.768796i	$0.279144\pi$
$488$	3.19666	−	5.53677i	0.144706	−	0.250638i
$489$	13.4915	−	26.2245i	0.610105	−	1.18592i
$490$		0			0
$491$	−2.30250	+	1.32935i	−0.103910	+	0.0599927i	−0.551055	−	0.834469i	$-0.685774\pi$
$491$	−2.30250	+	1.32935i	−0.103910	+	0.0599927i	0.447144	+	0.894462i	$0.352441\pi$
$492$	0.370379	+	0.575244i	0.0166980	+	0.0259340i
$493$	−31.9282	−	18.4338i	−1.43797	−	0.830215i
$494$		−	1.29503i		−	0.0582663i
$495$	5.43310	−	3.88284i	0.244200	−	0.174521i
$496$			4.66003i			0.209242i
$497$		0			0
$498$	−0.111393	−	2.29731i	−0.00499164	−	0.102945i
$499$	6.27844	+	10.8746i	0.281062	+	0.486813i	0.971646	−	0.236438i	$-0.0759801\pi$
$499$	6.27844	+	10.8746i	0.281062	+	0.486813i	−0.690585	+	0.723251i	$0.742647\pi$
$500$	5.10739	+	8.84625i	0.228409	+	0.395617i
$501$	36.8856	−	1.78853i	1.64793	−	0.0799056i
$502$	−0.795278	−	0.459154i	−0.0354950	−	0.0204930i
$503$	18.1502			0.809278			0.404639	−	0.914476i	$-0.367397\pi$
$503$	18.1502			0.809278			0.404639	+	0.914476i	$0.367397\pi$
$504$		0			0
$505$	6.15782			0.274020
$506$	−2.79546	−	1.61396i	−0.124273	−	0.0717491i
$507$	8.37326	+	13.0047i	0.371870	+	0.577559i
$508$	3.65689	+	6.33391i	0.162248	+	0.281022i
$509$	9.33827	+	16.1744i	0.413912	+	0.716916i	0.995314	−	0.0967005i	$-0.0308289\pi$
$509$	9.33827	+	16.1744i	0.413912	+	0.716916i	−0.581402	+	0.813617i	$0.697496\pi$
$510$	−0.437717	−	0.225188i	−0.0193825	−	0.00997149i
$511$		0			0
$512$		−	9.49685i		−	0.419705i
$513$	−3.94885	−	26.9759i	−0.174346	−	1.19102i
$514$			0.616519i			0.0271935i
$515$	−2.93305	−	1.69340i	−0.129245	−	0.0746199i
$516$	−12.4668	+	24.2328i	−0.548820	+	1.06679i
$517$	−36.3096	+	20.9634i	−1.59690	+	0.921968i
$518$		0			0
$519$	19.2093	+	29.8345i	0.843196	+	1.30959i
$520$	0.260371	−	0.450975i	0.0114180	−	0.0197766i
$521$	18.0665			0.791508			0.395754	−	0.918357i	$-0.370483\pi$
$521$	18.0665			0.791508			0.395754	+	0.918357i	$0.370483\pi$
$522$	−1.27638	+	2.80752i	−0.0558658	+	0.122882i
$523$			21.1338i			0.924116i	0.886850	+	0.462058i	$0.152889\pi$
$523$			21.1338i			0.924116i	−0.886850	+	0.462058i	$0.847111\pi$
$524$	−5.41590	+	9.38061i	−0.236595	+	0.409794i
$525$		0			0
$526$	0.865245	+	1.49865i	0.0377265	+	0.0653442i
$527$	4.52820	−	2.61436i	0.197252	−	0.113883i
$528$	−1.37920	−	28.4438i	−0.0600218	−	1.23786i
$529$	8.18875	−	14.1833i	0.356033	−	0.616666i
$530$	−0.273181			−0.0118662
$531$	−16.6861	+	36.7026i	−0.724115	+	1.59276i
$532$		0			0
$533$	0.347667	+	0.200725i	0.0150591	+	0.00869439i
$534$	2.29371	−	1.47684i	0.0992587	−	0.0639091i
$535$	0.116121	−	0.0670425i	0.00502035	−	0.00289850i
$536$	2.77827	−	1.60403i	0.120003	−	0.0692837i
$537$	−22.1896	−	11.4157i	−0.957554	−	0.492623i
$538$	1.67164	+	0.965122i	0.0720695	+	0.0416093i
$539$		0			0
$540$	2.01664	−	5.07481i	0.0867822	−	0.218385i
$541$	17.7732			0.764131			0.382065	−	0.924135i	$-0.375213\pi$
$541$	17.7732			0.764131			0.382065	+	0.924135i	$0.375213\pi$
$542$	1.02817	−	1.78084i	0.0441637	−	0.0764938i
$543$	10.7398	+	5.52521i	0.460891	+	0.237110i
$544$	−5.52304	+	3.18873i	−0.236798	+	0.136715i
$545$	−3.16918	−	5.48918i	−0.135753	−	0.235131i
$546$		0			0
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	−0.386741	−	0.922188i	$-0.626399\pi$
$547$	14.1560	−	24.5190i	0.605268	−	1.04835i	0.992009	−	0.126166i	$-0.0402673\pi$
$548$			3.20888i			0.137077i
$549$	−3.80610	−	39.1552i	−0.162440	−	1.67110i
$550$	−2.42780			−0.103522
$551$	22.0437	−	38.1808i	0.939092	−	1.62655i
$552$	−5.29287	+	0.256643i	−0.225279	+	0.0109235i
$553$		0			0
$554$	−1.88823	+	1.09017i	−0.0802232	+	0.0463169i
$555$	2.96074	−	0.143562i	0.125677	−	0.00609387i
$556$	19.4352	+	11.2209i	0.824234	+	0.475872i
$557$		−	11.7214i		−	0.496651i	−0.968677	−	0.248326i	$-0.920120\pi$
$557$		−	11.7214i		−	0.496651i	0.968677	−	0.248326i	$-0.0798803\pi$
$558$	−0.254319	−	0.355858i	−0.0107662	−	0.0150647i
$559$			15.9905i			0.676326i
$560$		0			0
$561$	−26.8653	+	17.2976i	−1.13426	+	0.730306i
$562$	0.536671	+	0.929541i	0.0226381	+	0.0392103i
$563$	−18.3014	−	31.6990i	−0.771314	−	1.33595i	−0.936843	−	0.349750i	$-0.886267\pi$
$563$	−18.3014	−	31.6990i	−0.771314	−	1.33595i	0.165529	−	0.986205i	$-0.447067\pi$
$564$	−15.6844	+	30.4872i	−0.660433	+	1.28374i
$565$	−2.26933	−	1.31020i	−0.0954713	−	0.0551204i
$566$	2.64243			0.111070
$567$		0			0
$568$	4.14701			0.174005
$569$	32.6468	+	18.8486i	1.36862	+	0.790176i	0.990752	−	0.135682i	$-0.0433225\pi$
$569$	32.6468	+	18.8486i	1.36862	+	0.790176i	0.377872	+	0.925858i	$0.376656\pi$
$570$	0.269287	−	0.523436i	0.0112792	−	0.0219243i
$571$	−14.1123	−	24.4432i	−0.590581	−	1.02292i	−0.994154	−	0.107968i	$-0.965565\pi$
$571$	−14.1123	−	24.4432i	−0.590581	−	1.02292i	0.403574	−	0.914947i	$-0.367768\pi$
$572$	−8.41878	−	14.5817i	−0.352007	−	0.609694i
$573$	−15.7785	+	10.1592i	−0.659156	+	0.424407i
$574$		0			0
$575$		−	29.6168i		−	1.23511i
$576$	−13.3319	−	18.6548i	−0.555495	−	0.777282i
$577$			9.38512i			0.390708i	0.980733	+	0.195354i	$0.0625855\pi$
$577$			9.38512i			0.390708i	−0.980733	+	0.195354i	$0.937414\pi$
$578$	0.238523	+	0.137711i	0.00992123	+	0.00572802i
$579$	−18.2075	+	0.882854i	−0.756678	+	0.0366902i
$580$	7.64754	−	4.41531i	0.317547	−	0.183336i
$581$		0			0
$582$	0.120679	−	0.00585155i	0.00500231	−	0.000242555i
$583$	−8.86629	+	15.3569i	−0.367204	+	0.636017i
$584$	2.73612			0.113222
$585$	−0.310011	−	3.18923i	−0.0128174	−	0.131858i
$586$			2.39735i			0.0990338i
$587$	−23.1819	+	40.1523i	−0.956821	+	1.65726i	−0.226675	+	0.973971i	$0.572785\pi$
$587$	−23.1819	+	40.1523i	−0.956821	+	1.65726i	−0.730146	+	0.683291i	$0.760548\pi$
$588$		0			0
$589$	3.12633	+	5.41496i	0.128818	+	0.223120i
$590$	−0.753870	+	0.435247i	−0.0310363	+	0.0179188i
$591$	23.8969	+	12.2940i	0.982986	+	0.505707i
$592$	6.32025	−	10.9470i	0.259761	−	0.449919i
$593$	−18.1416			−0.744986			−0.372493	−	0.928035i	$-0.621497\pi$
$593$	−18.1416			−0.744986			−0.372493	+	0.928035i	$0.621497\pi$
$594$	1.65762	+	2.09680i	0.0680131	+	0.0860329i
$595$		0			0
$596$	−9.15945	−	5.28821i	−0.375186	−	0.216613i
$597$	−19.3260	−	9.94246i	−0.790961	−	0.406918i
$598$	−1.34133	+	0.774419i	−0.0548512	+	0.0316684i
$599$	6.02771	−	3.48010i	0.246286	−	0.142193i	−0.371777	−	0.928322i	$-0.621251\pi$
$599$	6.02771	−	3.48010i	0.246286	−	0.142193i	0.618062	+	0.786129i	$0.287918\pi$
$600$	−3.35105	+	2.15762i	−0.136806	+	0.0880844i
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	0.541994	−	0.840383i	$-0.317670\pi$
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	−0.456796	+	0.889572i	$0.651003\pi$
$602$		0			0
$603$	8.16976	−	17.9701i	0.332698	−	0.731800i
$604$	−5.24571			−0.213445
$605$	1.76770	−	3.06175i	0.0718673	−	0.124478i
$606$	0.119369	+	2.46181i	0.00484905	+	0.100004i
$607$	−11.0306	+	6.36850i	−0.447717	+	0.258489i	−0.706865	−	0.707348i	$-0.749891\pi$
$607$	−11.0306	+	6.36850i	−0.447717	+	0.258489i	0.259149	+	0.965837i	$0.416558\pi$
$608$	−3.81318	−	6.60462i	−0.154645	−	0.267853i
$609$		0			0
$610$	0.424690	−	0.735585i	0.0171952	−	0.0297830i
$611$			20.1176i			0.813870i
$612$	−10.8138	+	23.7859i	−0.437122	+	0.961489i
$613$	−10.3352			−0.417436			−0.208718	−	0.977976i	$-0.566929\pi$
$613$	−10.3352			−0.417436			−0.208718	+	0.977976i	$0.566929\pi$
$614$	−1.69861	+	2.94208i	−0.0685503	+	0.118733i
$615$	0.0987840	+	0.153424i	0.00398336	+	0.00618665i
$616$		0			0
$617$	−41.3741	+	23.8873i	−1.66566	+	0.961668i	−0.695721	+	0.718313i	$0.744915\pi$
$617$	−41.3741	+	23.8873i	−1.66566	+	0.961668i	−0.969937	+	0.243355i	$0.921752\pi$
$618$	0.620137	−	1.20541i	0.0249456	−	0.0484889i
$619$	35.2626	+	20.3588i	1.41732	+	0.818291i	0.996063	−	0.0886491i	$-0.0282550\pi$
$619$	35.2626	+	20.3588i	1.41732	+	0.818291i	0.421259	+	0.906940i	$0.361588\pi$
$620$			1.25240i			0.0502975i
$621$	−25.5790	+	20.2214i	−1.02645	+	0.811458i
$622$		−	2.44884i		−	0.0981897i
$623$		0			0
$624$	−12.1505	−	6.25092i	−0.486408	−	0.250237i
$625$	−10.4371	−	18.0775i	−0.417483	−	0.723101i
$626$	−1.12773	−	1.95328i	−0.0450731	−	0.0780689i
$627$	−20.6850	−	32.1264i	−0.826080	−	1.28301i
$628$	22.4667	+	12.9711i	0.896519	+	0.517605i
$629$	−14.1831			−0.565517
$630$		0			0
$631$	11.4782			0.456942			0.228471	−	0.973551i	$-0.426627\pi$
$631$	11.4782			0.456942			0.228471	+	0.973551i	$0.426627\pi$
$632$	0.241803	+	0.139605i	0.00961841	+	0.00555319i
$633$	−4.14390	+	0.200932i	−0.164705	+	0.00798631i
$634$	−0.889953	−	1.54144i	−0.0353446	−	0.0612186i
$635$	0.975332	+	1.68932i	0.0387049	+	0.0670388i
$636$	0.702288	+	14.4836i	0.0278475	+	0.574312i
$637$		0			0
$638$			4.32228i			0.171121i
$639$	20.7608	−	14.8370i	0.821285	−	0.586943i
$640$		−	2.03412i		−	0.0804057i
$641$	−30.5823	−	17.6567i	−1.20793	−	0.697398i	−0.245622	−	0.969366i	$-0.578992\pi$
$641$	−30.5823	−	17.6567i	−1.20793	−	0.697398i	−0.962306	+	0.271968i	$0.912326\pi$
$642$	0.0290536	+	0.0451239i	0.00114665	+	0.00178090i
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	−0.374998	−	0.927025i	$-0.622357\pi$
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	0.615328	+	0.788271i	$0.289023\pi$
$644$		0			0
$645$	−3.32503	+	6.46315i	−0.130923	+	0.254486i
$646$	−1.40826	+	2.43917i	−0.0554071	+	0.0959680i
$647$	−14.9942			−0.589482			−0.294741	−	0.955577i	$-0.595233\pi$
$647$	−14.9942			−0.589482			−0.294741	+	0.955577i	$0.595233\pi$
$648$	4.15145	+	1.42103i	0.163084	+	0.0558233i
$649$			56.5050i			2.21801i
$650$	−0.582461	+	1.00885i	−0.0228460	+	0.0395704i
$651$		0			0
$652$	−16.8995	−	29.2708i	−0.661835	−	1.14633i
$653$	4.15597	−	2.39945i	0.162636	−	0.0938977i	−0.416473	−	0.909148i	$-0.636734\pi$
$653$	4.15597	−	2.39945i	0.162636	−	0.0938977i	0.579109	+	0.815250i	$0.303401\pi$
$654$	2.13306	−	1.37340i	0.0834092	−	0.0537041i
$655$	−1.44448	+	2.50191i	−0.0564405	+	0.0977577i
$656$	0.778140			0.0303812
$657$	13.6976	−	9.78919i	0.534395	−	0.381913i
$658$		0			0
$659$	−13.4562	−	7.76893i	−0.524179	−	0.302635i	0.214464	−	0.976732i	$-0.431200\pi$
$659$	−13.4562	−	7.76893i	−0.524179	−	0.302635i	−0.738643	+	0.674097i	$0.764533\pi$
$660$	−0.370663	−	7.64434i	−0.0144280	−	0.297556i
$661$	18.2131	−	10.5154i	0.708409	−	0.409000i	−0.102062	−	0.994778i	$-0.532544\pi$
$661$	18.2131	−	10.5154i	0.708409	−	0.409000i	0.810472	+	0.585778i	$0.199211\pi$
$662$	3.14566	−	1.81615i	0.122260	−	0.0705866i
$663$	0.742534	+	15.3136i	0.0288376	+	0.594731i
$664$	−4.58280	−	2.64588i	−0.177847	−	0.102680i
$665$		0			0
$666$	0.114788	+	1.18088i	0.00444794	+	0.0457581i
$667$	−52.7277			−2.04163
$668$	21.1614	−	36.6526i	0.818758	−	1.41813i
$669$	−4.07268	+	2.62225i	−0.157459	+	0.101382i
$670$	0.369106	−	0.213103i	0.0142598	−	0.00823290i
$671$	−27.5673	−	47.7479i	−1.06422	−	1.84329i
$672$		0			0
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	−0.582036	−	0.813163i	$-0.697744\pi$
$673$	10.7194	−	18.5665i	0.413201	−	0.715686i	0.995238	+	0.0974770i	$0.0310772\pi$
$674$		−	1.12705i		−	0.0434124i
$675$	−9.05663	+	22.7908i	−0.348590	+	0.877217i
$676$	17.7263			0.681781
$677$	9.03150	−	15.6430i	0.347109	−	0.601210i	−0.638626	−	0.769517i	$-0.720497\pi$
$677$	9.03150	−	15.6430i	0.347109	−	0.601210i	0.985735	+	0.168308i	$0.0538302\pi$
$678$	0.479806	−	0.932642i	0.0184269	−	0.0358179i
$679$		0			0
$680$	−0.980808	+	0.566270i	−0.0376123	+	0.0217155i
$681$	2.66858	+	4.14463i	0.102260	+	0.158823i
$682$	−0.530878	−	0.306503i	−0.0203284	−	0.0117366i
$683$		−	45.5647i		−	1.74349i	−0.489963	−	0.871743i	$-0.662990\pi$
$683$		−	45.5647i		−	1.74349i	0.489963	−	0.871743i	$-0.337010\pi$
$684$	−28.4439	−	12.9315i	−1.08758	−	0.494447i
$685$			0.855844i			0.0327001i
$686$		0			0
$687$	1.99015	+	41.0438i	0.0759291	+	1.56592i
$688$	15.4973	+	26.8422i	0.590830	+	1.02335i
$689$	4.25428	+	7.36863i	0.162075	+	0.280723i
$690$	−0.703181	+	0.0340962i	−0.0267697	+	0.00129802i
$691$	3.33627	+	1.92620i	0.126918	+	0.0732760i	0.562115	−	0.827059i	$-0.309988\pi$
$691$	3.33627	+	1.92620i	0.126918	+	0.0732760i	−0.435197	+	0.900335i	$0.643321\pi$
$692$	40.6664			1.54590
$693$		0			0
$694$	2.22238			0.0843604
$695$	5.18357	+	2.99273i	0.196624	+	0.113521i
$696$	3.84127	+	5.96597i	0.145603	+	0.226140i
$697$	−0.436550	−	0.756126i	−0.0165355	−	0.0286403i
$698$	−0.402972	−	0.697967i	−0.0152527	−	0.0264185i
$699$	−28.8473	−	14.8407i	−1.09110	−	0.561329i
$700$		0			0
$701$		−	46.5216i		−	1.75710i	−0.477653	−	0.878549i	$-0.658512\pi$
$701$		−	46.5216i		−	1.75710i	0.477653	−	0.878549i	$-0.341488\pi$
$702$	1.26900	−	0.185761i	0.0478952	−	0.00701109i
$703$		−	16.9606i		−	0.639680i
$704$	−27.8297	−	16.0675i	−1.04887	−	0.605566i
$705$	−4.18321	+	8.13126i	−0.157549	+	0.306241i
$706$	−2.21850	+	1.28085i	−0.0834944	+	0.0482055i
$707$		0			0
$708$	25.0141	+	38.8499i	0.940086	+	1.46007i
$709$	14.6187	−	25.3203i	0.549017	−	0.950925i	−0.449326	−	0.893368i	$-0.648336\pi$
$709$	14.6187	−	25.3203i	0.549017	−	0.950925i	0.998342	−	0.0575566i	$-0.0183310\pi$
$710$	0.550949			0.0206767
$711$	1.70999	−	0.166221i	0.0641297	−	0.00623377i
$712$		−	6.27655i		−	0.235224i
$713$	3.73904	−	6.47621i	0.140028	−	0.242536i
$714$		0			0
$715$	−2.24538	−	3.88911i	−0.0839724	−	0.145445i
$716$	−24.7672	+	14.2993i	−0.925592	+	0.534391i
$717$	−1.07926	−	22.2580i	−0.0403056	−	0.831241i
$718$	−0.870265	+	1.50734i	−0.0324780	+	0.0562536i
$719$	3.37122			0.125725			0.0628627	−	0.998022i	$-0.479977\pi$
$719$	3.37122			0.125725			0.0628627	+	0.998022i	$0.479977\pi$
$720$	−3.61126	−	5.05309i	−0.134584	−	0.188317i
$721$		0			0
$722$	−0.903723	−	0.521765i	−0.0336331	−	0.0194181i
$723$	6.12235	−	3.94196i	0.227693	−	0.146603i
$724$	11.9874	−	6.92091i	0.445507	−	0.257214i
$725$	−34.3448	+	19.8290i	−1.27553	+	0.736429i
$726$	1.25831	+	0.647349i	0.0467002	+	0.0240254i
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	0.417278	−	0.908779i	$-0.362984\pi$
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	−0.578387	+	0.815763i	$0.696318\pi$
$728$		0			0
$729$	25.8671	−	7.73891i	0.958043	−	0.286626i
$730$	0.363506			0.0134540
$731$	17.3885	−	30.1178i	0.643138	−	1.11395i
$732$	−40.0913	−	20.6253i	−1.48182	−	0.762334i
$733$	19.6875	−	11.3666i	0.727175	−	0.419835i	−0.0902126	−	0.995923i	$-0.528755\pi$
$733$	19.6875	−	11.3666i	0.727175	−	0.419835i	0.817388	+	0.576088i	$0.195421\pi$
$734$	0.757478	+	1.31199i	0.0279590	+	0.0484265i
$735$		0			0
$736$	−4.56050	+	7.89901i	−0.168102	+	0.291162i
$737$		−	27.6657i		−	1.01908i
$738$	−0.0594216	+	0.0424665i	−0.00218734	+	0.00156321i
$739$	−2.39022			−0.0879256			−0.0439628	−	0.999033i	$-0.513998\pi$
$739$	−2.39022			−0.0879256			−0.0439628	+	0.999033i	$0.513998\pi$
$740$	1.69859	−	2.94204i	0.0624413	−	0.108151i
$741$	−18.3125	+	0.887945i	−0.672726	+	0.0326195i
$742$		0			0
$743$	−36.1039	+	20.8446i	−1.32453	+	0.764715i	−0.984447	−	0.175682i	$-0.943787\pi$
$743$	−36.1039	+	20.8446i	−1.32453	+	0.764715i	−0.340078	+	0.940397i	$0.610454\pi$
$744$	−1.00515	+	0.0487385i	−0.0368508	+	0.00178684i
$745$	−2.44292	−	1.41042i	−0.0895018	−	0.0516739i
$746$			2.60737i			0.0954627i
$747$	−32.4088	+	3.15031i	−1.18578	+	0.115264i
$748$			36.6193i			1.33893i
$749$		0			0
$750$	−0.916844	+	0.590323i	−0.0334784	+	0.0215555i
$751$	−13.2710	−	22.9861i	−0.484267	−	0.838775i	0.515570	−	0.856848i	$-0.327580\pi$
$751$	−13.2710	−	22.9861i	−0.484267	−	0.838775i	−0.999837	+	0.0180728i	$0.994247\pi$
$752$	19.4971	+	33.7700i	0.710987	+	1.23147i
$753$	−5.94741	+	11.5605i	−0.216736	+	0.421288i
$754$	1.79609	+	1.03697i	0.0654097	+	0.0377643i
$755$	−1.39909			−0.0509180
$756$		0			0
$757$	20.3580			0.739923			0.369961	−	0.929047i	$-0.379371\pi$
$757$	20.3580			0.739923			0.369961	+	0.929047i	$0.379371\pi$
$758$	1.12311	+	0.648430i	0.0407933	+	0.0235520i
$759$	−20.9055	+	40.6359i	−0.758823	+	1.47499i
$760$	−0.677163	−	1.17288i	−0.0245633	−	0.0425448i
$761$	−12.9578	−	22.4436i	−0.469720	−	0.813578i	0.529681	−	0.848197i	$-0.322312\pi$
$761$	−12.9578	−	22.4436i	−0.469720	−	0.813578i	−0.999401	+	0.0346186i	$0.988978\pi$
$762$	−0.656460	+	0.422671i	−0.0237810	+	0.0153117i
$763$		0			0
$764$			21.5072i			0.778102i
$765$	−2.88416	+	6.34397i	−0.104277	+	0.229367i
$766$			1.54686i			0.0558903i
$767$	23.4802	+	13.5563i	0.847821	+	0.489489i
$768$	−25.6319	+	1.24285i	−0.924910	+	0.0448475i
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	−0.120532	−	0.992709i	$-0.538460\pi$
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	0.799446	+	0.600738i	$0.205127\pi$
$770$		0			0
$771$	8.71792	−	0.422719i	0.313968	−	0.0152239i
$772$	−10.4457	+	18.0925i	−0.375948	+	0.651162i
$773$	−20.3213			−0.730905			−0.365453	−	0.930830i	$-0.619086\pi$
$773$	−20.3213			−0.730905			−0.365453	+	0.930830i	$0.619086\pi$
$774$	−2.64833	−	1.20401i	−0.0951922	−	0.0432772i
$775$		−	5.62446i		−	0.202037i
$776$	0.138990	−	0.240738i	0.00498945	−	0.00864197i
$777$		0			0
$778$	0.809047	+	1.40131i	0.0290058	+	0.0502394i
$779$	0.904199	−	0.522039i	0.0323963	−	0.0187040i
$780$	−3.26547	−	1.67995i	−0.116923	−	0.0601520i
$781$	17.8814	−	30.9715i	0.639848	−	1.10825i
$782$	3.36851			0.120458
$783$	40.5751	+	16.1238i	1.45003	+	0.576217i
$784$		0			0
$785$	5.99211	+	3.45955i	0.213868	+	0.123477i
$786$	−1.02823	−	0.528982i	−0.0366757	−	0.0188682i
$787$	16.4065	−	9.47232i	0.584830	−	0.337652i	−0.178221	−	0.983991i	$-0.557034\pi$
$787$	16.4065	−	9.47232i	0.584830	−	0.337652i	0.763051	+	0.646339i	$0.223701\pi$
$788$	26.6727	−	15.3995i	0.950176	−	0.548584i
$789$	20.5985	−	13.2626i	0.733324	−	0.472161i
$790$	0.0321246	+	0.0185472i	0.00114294	+	0.000659879i
$791$		0			0
$792$	6.12081	−	0.594977i	0.217493	−	0.0211416i
$793$	−26.4550			−0.939445
$794$	1.51635	−	2.62640i	0.0538133	−	0.0932074i
$795$	0.187308	+	3.86294i	0.00664313	+	0.137004i
$796$	−21.5709	+	12.4540i	−0.764560	+	0.441419i
$797$	11.4342	+	19.8047i	0.405022	+	0.701518i	0.994324	−	0.106394i	$-0.0339306\pi$
$797$	11.4342	+	19.8047i	0.405022	+	0.701518i	−0.589302	+	0.807913i	$0.700597\pi$
$798$		0			0
$799$	21.8764	−	37.8911i	0.773932	−	1.34049i
$800$			6.86014i			0.242543i
$801$	−22.4560	−	31.4218i	−0.793444	−	1.11023i
$802$	0.451525			0.0159439
$803$	11.7978	−	20.4345i	0.416337	−	0.721117i
$804$	−12.2473	−	19.0215i	−0.431927	−	0.670837i
$805$		0			0
$806$	−0.254729	+	0.147068i	−0.00897246	+	0.00518025i
$807$	12.5012	−	24.2996i	0.440063	−	0.855388i
$808$	4.91095	+	2.83534i	0.172767	+	0.0997469i
$809$			11.9814i			0.421245i	0.977568	+	0.210622i	$0.0675490\pi$
$809$			11.9814i			0.421245i	−0.977568	+	0.210622i	$0.932451\pi$
$810$	0.551539	+	0.188790i	0.0193791	+	0.00663342i
$811$		−	36.9371i		−	1.29704i	−0.761199	−	0.648519i	$-0.775389\pi$
$811$		−	36.9371i		−	1.29704i	0.761199	−	0.648519i	$-0.224611\pi$
$812$		0			0
$813$	−25.8871	−	13.3179i	−0.907900	−	0.467078i
$814$	0.831399	+	1.44003i	0.0291405	+	0.0504729i
$815$	−4.50728	−	7.80683i	−0.157883	−	0.273461i
$816$	16.0878	+	24.9863i	0.563184	+	0.874695i
$817$	36.0158	+	20.7937i	1.26003	+	0.727481i
$818$	−2.26790			−0.0792954
$819$		0			0
$820$	0.209127			0.00730304
$821$	32.6907	+	18.8740i	1.14091	+	0.658707i	0.946657	−	0.322244i	$-0.104437\pi$
$821$	32.6907	+	18.8740i	1.14091	+	0.658707i	0.194257	+	0.980951i	$0.437771\pi$
$822$	−0.342154	+	0.0165905i	−0.0119340	+	0.000578661i
$823$	10.5082	+	18.2008i	0.366293	+	0.634438i	0.988983	−	0.148031i	$-0.0472934\pi$
$823$	10.5082	+	18.2008i	0.366293	+	0.634438i	−0.622690	+	0.782469i	$0.713960\pi$
$824$	−1.55943	−	2.70101i	−0.0543253	−	0.0940943i
$825$	1.66463	+	34.3304i	0.0579550	+	1.19523i
$826$		0			0
$827$		−	23.9104i		−	0.831447i	−0.909491	−	0.415724i	$-0.863528\pi$
$827$		−	23.9104i		−	0.831447i	0.909491	−	0.415724i	$-0.136472\pi$
$828$	3.61544	+	37.1938i	0.125645	+	1.29257i
$829$			25.0859i			0.871270i	0.900123	+	0.435635i	$0.143476\pi$
$829$			25.0859i			0.871270i	−0.900123	+	0.435635i	$0.856524\pi$
$830$	−0.608845	−	0.351517i	−0.0211333	−	0.0122013i
$831$	16.7103	+	25.9531i	0.579673	+	0.900304i
$832$	−13.3534	+	7.70960i	−0.462946	+	0.267282i
$833$		0			0
$834$	−1.09597	+	2.13033i	−0.0379502	+	0.0737672i
$835$	5.64397	−	9.77564i	0.195318	−	0.338300i
$836$	−43.7905			−1.51453
$837$	−4.85765	+	3.84020i	−0.167905	+	0.132737i
$838$			0.359677i			0.0124248i
$839$	3.72840	−	6.45777i	0.128719	−	0.222947i	−0.794462	−	0.607314i	$-0.792247\pi$
$839$	3.72840	−	6.45777i	0.128719	−	0.222947i	0.923180	+	0.384367i	$0.125580\pi$
$840$		0			0
$841$	20.8021	+	36.0303i	0.717313	+	1.24242i
$842$	−2.98960	+	1.72604i	−0.103028	+	0.0594834i
$843$	12.7763	−	8.22617i	0.440038	−	0.283324i
$844$	−2.37737	+	4.11772i	−0.0818323	+	0.141738i
$845$	4.72780			0.162641
$846$	−3.33185	−	1.51476i	−0.114551	−	0.0520785i
$847$		0			0
$848$	14.2828	+	8.24615i	0.490472	+	0.283174i
$849$	−1.81179	−	37.3654i	−0.0621806	−	1.28238i
$850$	2.19411	−	1.26677i	0.0752574	−	0.0434499i
$851$	−17.5670	+	10.1423i	−0.602187	+	0.347673i
$852$	−1.41637	−	29.2104i	−0.0485239	−	1.00073i
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	0.462007	−	0.886876i	$-0.347130\pi$
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	−0.537054	+	0.843548i	$0.680463\pi$
$854$		0			0
$855$	−7.58631	−	3.44897i	−0.259446	−	0.117952i
$856$	0.123478			0.00422038
$857$	9.52098	−	16.4908i	0.325231	−	0.563316i	−0.656328	−	0.754475i	$-0.727891\pi$
$857$	9.52098	−	16.4908i	0.325231	−	0.563316i	0.981559	+	0.191159i	$0.0612247\pi$
$858$	1.51128	−	0.973060i	0.0515943	−	0.0332197i
$859$	8.88415	−	5.12927i	0.303123	−	0.175008i	−0.340722	−	0.940164i	$-0.610671\pi$
$859$	8.88415	−	5.12927i	0.303123	−	0.175008i	0.643845	+	0.765156i	$0.277338\pi$
$860$	4.16495	+	7.21390i	0.142024	+	0.245992i
$861$		0			0
$862$	−0.413809	+	0.716738i	−0.0140944	+	0.0244122i
$863$			4.40932i			0.150095i	0.997180	+	0.0750475i	$0.0239108\pi$
$863$			4.40932i			0.150095i	−0.997180	+	0.0750475i	$0.976089\pi$
$864$	5.92486	−	4.68388i	0.201568	−	0.159349i
$865$	10.8462			0.368781
$866$	1.73408	−	3.00352i	0.0589265	−	0.102064i
$867$	1.78377	−	3.46726i	0.0605799	−	0.117754i
$868$		0			0
$869$	2.08526	−	1.20392i	0.0707375	−	0.0408403i
$870$	0.510331	+	0.792607i	0.0173018	+	0.0268719i
$871$	−11.4962	−	6.63736i	−0.389535	−	0.224898i
$872$		−	5.83693i		−	0.197663i
$873$	−0.165488	−	1.70246i	−0.00560093	−	0.0576194i
$874$			4.02816i			0.136255i
$875$		0			0
$876$	−0.934493	−	19.2725i	−0.0315736	−	0.651156i
$877$	25.0586	+	43.4028i	0.846170	+	1.46561i	0.884601	+	0.466349i	$0.154431\pi$
$877$	25.0586	+	43.4028i	0.846170	+	1.46561i	−0.0384307	+	0.999261i	$0.512236\pi$
$878$	1.61196	+	2.79200i	0.0544011	+	0.0942255i
$879$	33.8999	−	1.64376i	1.14342	−	0.0554425i
$880$	−7.53833	−	4.35226i	−0.254117	−	0.146715i
$881$	−42.5809			−1.43459			−0.717294	−	0.696771i	$-0.754619\pi$
$881$	−42.5809			−1.43459			−0.717294	+	0.696771i	$0.754619\pi$
$882$		0			0
$883$	−15.6590			−0.526967			−0.263483	−	0.964664i	$-0.584871\pi$
$883$	−15.6590			−0.526967			−0.263483	+	0.964664i	$0.584871\pi$
$884$	15.2169	+	8.78546i	0.511798	+	0.295487i
$885$	6.67153	+	10.3617i	0.224261	+	0.348305i
$886$	−0.336196	−	0.582309i	−0.0112947	−	0.0195630i
$887$	12.3919	+	21.4634i	0.416080	+	0.720671i	0.995541	−	0.0943286i	$-0.0300704\pi$
$887$	12.3919	+	21.4634i	0.416080	+	0.720671i	−0.579461	+	0.815000i	$0.696737\pi$
$888$	2.42734	+	1.24877i	0.0814561	+	0.0419059i
$889$		0			0
$890$		−	0.833869i		−	0.0279513i
$891$	28.5134	−	24.8774i	0.955235	−	0.833424i
$892$			5.55134i			0.185873i
$893$	45.3113	+	26.1605i	1.51629	+	0.875428i
$894$	0.516510	−	1.00399i	0.0172747	−	0.0335783i
$895$	−6.60567	+	3.81379i	−0.220803	+	0.127481i
$896$		0			0
$897$	11.8704	+	18.4362i	0.396341	+	0.615567i
$898$	0.451660	−	0.782299i	0.0150721	−	0.0261056i
$899$	−10.0134			−0.333965
$900$	16.3422	+	22.8669i	0.544739	+	0.762231i
$901$		−	18.5049i		−	0.616488i
$902$	−0.0511803	+	0.0886468i	−0.00170412	+	0.00295162i
$903$		0			0
$904$	−1.20655	−	2.08980i	−0.0401292	−	0.0695058i
$905$	3.19716	−	1.84588i	0.106277	−	0.0613592i
$906$	−0.0271213	−	0.559335i	−0.000901045	−	0.0185826i
$907$	−22.0517	+	38.1946i	−0.732213	+	1.26823i	0.223722	+	0.974653i	$0.428179\pi$
$907$	−22.0517	+	38.1946i	−0.732213	+	1.26823i	−0.955935	+	0.293577i	$0.905154\pi$
$908$	5.64941			0.187482
$909$	34.7295	−	3.37590i	1.15190	−	0.111971i
$910$		0			0
$911$	22.3259	+	12.8899i	0.739691	+	0.427061i	0.821957	−	0.569549i	$-0.192882\pi$
$911$	22.3259	+	12.8899i	0.739691	+	0.427061i	−0.0822657	+	0.996610i	$0.526216\pi$
$912$	−29.8794	+	19.2382i	−0.989405	+	0.637042i
$913$	−39.5210	+	22.8175i	−1.30795	+	0.755148i
$914$	−4.38879	+	2.53387i	−0.145168	+	0.0838129i
$915$	−10.6928	−	5.50100i	−0.353492	−	0.181857i
$916$	40.7845	+	23.5470i	1.34756	+	0.778013i
$917$		0			0
$918$	−2.59213	−	1.03007i	−0.0855531	−	0.0339972i
$919$	52.7102			1.73875			0.869375	−	0.494154i	$-0.164522\pi$
$919$	52.7102			1.73875			0.869375	+	0.494154i	$0.164522\pi$
$920$	−0.809876	+	1.40275i	−0.0267008	+	0.0462472i
$921$	42.7673	+	22.0020i	1.40923	+	0.724992i
$922$	1.15412	−	0.666334i	0.0380091	−	0.0219446i
$923$	−8.57999	−	14.8610i	−0.282414	−	0.489155i
$924$		0			0
$925$	−7.62828	+	13.2126i	−0.250816	+	0.434426i
$926$		−	0.704655i		−	0.0231564i
$927$	−17.4704	−	7.94258i	−0.573804	−	0.260869i
$928$	12.2133			0.400922
$929$	1.69009	−	2.92732i	0.0554500	−	0.0960422i	−0.836968	−	0.547252i	$-0.815674\pi$
$929$	1.69009	−	2.92732i	0.0554500	−	0.0960422i	0.892418	+	0.451210i	$0.149007\pi$
$930$	−0.133539	+	0.00647513i	−0.00437893	+	0.000212328i
$931$		0			0
$932$	−32.1981	+	18.5896i	−1.05468	+	0.608922i
$933$	−34.6280	+	1.67906i	−1.13367	+	0.0549700i
$934$	−2.53103	−	1.46129i	−0.0828180	−	0.0478150i
$935$			9.76677i			0.319407i
$936$	1.22123	−	2.68620i	0.0399170	−	0.0878011i
$937$			8.26186i			0.269903i	0.990852	+	0.134952i	$0.0430879\pi$
$937$			8.26186i			0.269903i	−0.990852	+	0.134952i	$0.956912\pi$
$938$		0			0
$939$	−26.8473	+	17.2860i	−0.876127	+	0.564106i
$940$	5.23990	+	9.07578i	0.170907	+	0.296019i
$941$	26.1882	+	45.3592i	0.853710	+	1.47867i	0.877837	+	0.478960i	$0.158986\pi$
$941$	26.1882	+	45.3592i	0.853710	+	1.47867i	−0.0241274	+	0.999709i	$0.507681\pi$
$942$	−1.26692	+	2.46262i	−0.0412784	+	0.0802365i
$943$	−1.08141	−	0.624351i	−0.0352155	−	0.0203317i
$944$	52.5528			1.71045
$945$		0			0
$946$	−4.07720			−0.132561
$947$	−6.53348	−	3.77211i	−0.212310	−	0.122577i	0.390075	−	0.920783i	$-0.372449\pi$
$947$	−6.53348	−	3.77211i	−0.212310	−	0.122577i	−0.602384	+	0.798206i	$0.705783\pi$
$948$	0.900754	−	1.75087i	0.0292551	−	0.0568657i
$949$	−5.66092	−	9.80500i	−0.183761	−	0.318284i
$950$	1.51484	+	2.62379i	0.0491480	+	0.0851269i
$951$	−21.1867	+	13.6413i	−0.687025	+	0.442350i
$952$		0			0
$953$		−	45.2795i		−	1.46675i	−0.679825	−	0.733374i	$-0.737944\pi$
$953$		−	45.2795i		−	1.46675i	0.679825	−	0.733374i	$-0.262056\pi$
$954$	−1.54071	+	0.149766i	−0.0498824	+	0.00484885i
$955$			5.73620i			0.185619i
$956$	−22.1174	−	12.7695i	−0.715327	−	0.412994i
$957$	61.1195	−	2.96359i	1.97571	−	0.0957993i
$958$	0.200812	−	0.115939i	0.00648795	−	0.00374582i
$959$		0			0
$960$	−7.00040	+	0.339439i	−0.225937	+	0.0109553i
$961$	−14.7899	+	25.6169i	−0.477094	+	0.826352i
$962$	0.797855			0.0257239
$963$	0.618156	−	0.441774i	0.0199198	−	0.0142360i
$964$		−	8.34518i		−	0.268780i
$965$	−2.78598	+	4.82546i	−0.0896838	+	0.155337i
$966$		0			0
$967$	−6.82403	−	11.8196i	−0.219446	−	0.380092i	0.735193	−	0.677858i	$-0.237092\pi$
$967$	−6.82403	−	11.8196i	−0.219446	−	0.380092i	−0.954639	+	0.297766i	$0.903758\pi$
$968$	2.81954	−	1.62786i	0.0906233	−	0.0523214i
$969$	35.4568	+	18.2411i	1.13904	+	0.585989i
$970$	0.0184654	−	0.0319831i	0.000592889	−	0.00102691i
$971$	−3.47104			−0.111391			−0.0556955	−	0.998448i	$-0.517738\pi$
$971$	−3.47104			−0.111391			−0.0556955	+	0.998448i	$0.517738\pi$
$972$	8.59145	−	29.7270i	0.275571	−	0.953493i
$973$		0			0
$974$	2.99051	+	1.72657i	0.0958222	+	0.0553230i
$975$	14.6651	+	7.54460i	0.469659	+	0.241621i
$976$	−44.4082	+	25.6391i	−1.42147	+	0.820688i
$977$	−2.21904	+	1.28116i	−0.0709932	+	0.0409880i	−0.535076	−	0.844804i	$-0.679717\pi$
$977$	−2.21904	+	1.28116i	−0.0709932	+	0.0409880i	0.464083	+	0.885792i	$0.346384\pi$
$978$	3.03368	−	1.95328i	0.0970064	−	0.0624589i
$979$	−46.8759	−	27.0638i	−1.49816	−	0.864963i
$980$		0			0
$981$	−20.8832	−	29.2209i	−0.666748	−	0.932953i
$982$	−0.325277			−0.0103800
$983$	−19.5749	+	33.9047i	−0.624343	+	1.08139i	0.364325	+	0.931272i	$0.381300\pi$
$983$	−19.5749	+	33.9047i	−0.624343	+	1.08139i	−0.988668	+	0.150122i	$0.952033\pi$
$984$	0.00813842	+	0.167842i	0.000259443	+	0.00535062i
$985$	7.11390	−	4.10721i	0.226668	−	0.130867i
$986$	−2.25527	−	3.90624i	−0.0718224	−	0.124400i
$987$		0			0
$988$	−10.5059	+	18.1968i	−0.334238	+	0.578917i
$989$		−	49.7380i		−	1.58158i
$990$	0.813177	−	0.0790454i	0.0258445	−	0.00251223i
$991$	−16.2067			−0.514821			−0.257411	−	0.966302i	$-0.582869\pi$
$991$	−16.2067			−0.514821			−0.257411	+	0.966302i	$0.582869\pi$
$992$	−0.866073	+	1.50008i	−0.0274978	+	0.0476277i
$993$	−27.8382	−	43.2361i	−0.883418	−	1.37206i
$994$		0			0
$995$	−5.75320	+	3.32161i	−0.182389	+	0.105302i
$996$	−17.0716	+	33.1836i	−0.540935	+	1.05146i
$997$	−21.5007	−	12.4134i	−0.680933	−	0.393137i	0.119273	−	0.992861i	$-0.461943\pi$
$997$	−21.5007	−	12.4134i	−0.680933	−	0.393137i	−0.800207	+	0.599725i	$0.795277\pi$
$998$			1.53626i			0.0486296i
$999$	16.6196	−	2.43284i	0.525820	−	0.0769716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.146.14	yes	48
3.2	odd	2		1323.2.o.e.440.12		48
7.2	even	3		441.2.i.d.227.12		48
7.3	odd	6		441.2.s.d.362.12		48
7.4	even	3		441.2.s.d.362.11		48
7.5	odd	6		441.2.i.d.227.11		48
7.6	odd	2	inner	441.2.o.e.146.13	✓	48
9.4	even	3		1323.2.o.e.881.11		48
9.5	odd	6	inner	441.2.o.e.293.13	yes	48
21.2	odd	6		1323.2.i.d.521.11		48
21.5	even	6		1323.2.i.d.521.12		48
21.11	odd	6		1323.2.s.d.656.14		48
21.17	even	6		1323.2.s.d.656.13		48
21.20	even	2		1323.2.o.e.440.11		48
63.4	even	3		1323.2.i.d.1097.12		48
63.5	even	6		441.2.s.d.374.11		48
63.13	odd	6		1323.2.o.e.881.12		48
63.23	odd	6		441.2.s.d.374.12		48
63.31	odd	6		1323.2.i.d.1097.11		48
63.32	odd	6		441.2.i.d.68.13		48
63.40	odd	6		1323.2.s.d.962.14		48
63.41	even	6	inner	441.2.o.e.293.14	yes	48
63.58	even	3		1323.2.s.d.962.13		48
63.59	even	6		441.2.i.d.68.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.13		48	63.32	odd	6
441.2.i.d.68.14		48	63.59	even	6
441.2.i.d.227.11		48	7.5	odd	6
441.2.i.d.227.12		48	7.2	even	3
441.2.o.e.146.13	✓	48	7.6	odd	2	inner
441.2.o.e.146.14	yes	48	1.1	even	1	trivial
441.2.o.e.293.13	yes	48	9.5	odd	6	inner
441.2.o.e.293.14	yes	48	63.41	even	6	inner
441.2.s.d.362.11		48	7.4	even	3
441.2.s.d.362.12		48	7.3	odd	6
441.2.s.d.374.11		48	63.5	even	6
441.2.s.d.374.12		48	63.23	odd	6
1323.2.i.d.521.11		48	21.2	odd	6
1323.2.i.d.521.12		48	21.5	even	6
1323.2.i.d.1097.11		48	63.31	odd	6
1323.2.i.d.1097.12		48	63.4	even	3
1323.2.o.e.440.11		48	21.20	even	2
1323.2.o.e.440.12		48	3.2	odd	2
1323.2.o.e.881.11		48	9.4	even	3
1323.2.o.e.881.12		48	63.13	odd	6
1323.2.s.d.656.13		48	21.17	even	6
1323.2.s.d.656.14		48	21.11	odd	6
1323.2.s.d.962.13		48	63.58	even	3
1323.2.s.d.962.14		48	63.40	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.105953 + 0.0611722i) q^{2} +(0.792362 - 1.54018i) q^{3} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(-1.74433 - 2.44076i) q^{9} +O(q^{10})\)	\(q+(0.105953 + 0.0611722i) q^{2} +(0.792362 - 1.54018i) q^{3} +(-0.992516 - 1.71909i) q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(-1.74433 - 2.44076i) q^{9} -0.0647728i q^{10} +(-3.64120 - 2.10225i) q^{11} +(-3.43414 + 0.166516i) q^{12} +(-1.74714 + 1.00871i) q^{13} +(-0.915923 + 0.0444117i) q^{15} +(-1.95521 + 3.38652i) q^{16} +4.38762 q^{17} +(-0.0355103 - 0.365312i) q^{18} +5.24685i q^{19} +(-0.525467 + 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +(5.43444 - 3.13757i) q^{23} +(-0.750911 - 0.386313i) q^{24} +(2.35985 - 4.08738i) q^{25} -0.246821 q^{26} +(-5.14136 + 0.752613i) q^{27} +(-7.27689 - 4.20131i) q^{29} +(-0.0997619 - 0.0513235i) q^{30} +(1.03204 - 0.595849i) q^{31} +(-1.25878 + 0.726755i) q^{32} +(-6.12299 + 3.94237i) q^{33} +(0.464883 + 0.268400i) q^{34} +(-2.46462 + 5.42115i) q^{36} -3.23252 q^{37} +(-0.320962 + 0.555922i) q^{38} +(0.169234 + 3.49019i) q^{39} +(-0.223540 + 0.129061i) q^{40} +(-0.0994958 - 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +8.34605i q^{44} +(-0.657340 + 1.44588i) q^{45} +0.767730 q^{46} +(4.98595 - 8.63591i) q^{47} +(3.66663 + 5.69472i) q^{48} +(0.500069 - 0.288715i) q^{50} +(3.47658 - 6.75774i) q^{51} +(3.46814 + 2.00233i) q^{52} -4.21753i q^{53} +(-0.590784 - 0.234767i) q^{54} +2.22598i q^{55} +(8.08111 + 4.15740i) q^{57} +(-0.514008 - 0.890287i) q^{58} +(-6.71960 - 11.6387i) q^{59} +(0.985416 + 1.53047i) q^{60} +(11.3564 + 6.55662i) q^{61} +0.145798 q^{62} +7.64300 q^{64} +(0.924990 + 0.534043i) q^{65} +(-0.889915 + 0.0431507i) q^{66} +(3.29001 + 5.69847i) q^{67} +(-4.35478 - 7.54270i) q^{68} +(-0.526397 - 10.8561i) q^{69} +8.50587i q^{71} +(-1.18999 + 0.850440i) q^{72} +5.61202i q^{73} +(-0.342497 - 0.197741i) q^{74} +(-4.42546 - 6.87329i) q^{75} +(9.01980 - 5.20758i) q^{76} +(-0.195572 + 0.380150i) q^{78} +(-0.286342 + 0.495959i) q^{79} +2.07029 q^{80} +(-2.91465 + 8.51497i) q^{81} -0.0243455i q^{82} +(5.42692 - 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +(0.839806 - 0.484862i) q^{86} +(-12.2367 + 7.87878i) q^{87} +(-1.02494 + 1.77525i) q^{88} +12.8738 q^{89} +(-0.158095 + 0.112985i) q^{90} +(-10.7875 - 6.22819i) q^{92} +(-0.0999668 - 2.06166i) q^{93} +(1.05656 - 0.610003i) q^{94} +(2.40568 - 1.38892i) q^{95} +(0.121929 + 2.51460i) q^{96} +(0.493773 + 0.285080i) q^{97} +(1.22035 + 12.5543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 + 16 * q^9	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

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