LMFDB - Embedded newform 441.2.o.e.146.13

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			146.13
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.13

$q$-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	0.919127	−	0.393960i	$-0.128895\pi$
$5$	0.264715	+	0.458500i	0.118384	+	0.205047i	−0.800743	+	0.599008i	$0.795562\pi$
$6$	−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	−0.237749	−	0.971327i	$-0.576410\pi$
$13$	1.74714	−	1.00871i	0.484570	−	0.279767i	0.722319	+	0.691560i	$0.243076\pi$
$14$		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	$-0.678588\pi$
$17$	−4.38762			−1.06415			−0.532077	+	0.846696i	$0.678588\pi$
$18$	−0.0355103	−	0.365312i	−0.00836986	−	0.0861048i
$19$		−	5.24685i		−	1.20371i	−0.798605	−	0.601855i	$-0.794428\pi$
$19$		−	5.24685i		−	1.20371i	0.798605	−	0.601855i	$-0.205572\pi$
$20$	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	−0.589809	−	0.807543i	$-0.700797\pi$
$31$	−1.03204	+	0.595849i	−0.185360	+	0.107018i	0.404449	+	0.914561i	$0.367463\pi$
$32$	−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	0.873690	−	0.486483i	$-0.161720\pi$
$41$	0.0994958	+	0.172332i	0.0155386	+	0.0269137i	−0.858152	+	0.513396i	$0.828387\pi$
$42$		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	$0.425880\pi$
$47$	−4.98595	+	8.63591i	−0.727275	+	1.25968i	−0.958031	+	0.286665i	$0.907453\pi$
$48$	−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	$0.172352\pi$
$59$	6.71960	+	11.6387i	0.874817	+	1.51523i	0.0178590	+	0.999841i	$0.494315\pi$
$60$	0.985416	+	1.53047i	0.127217	+	0.197583i
$61$	−11.3564	−	6.55662i	−1.45404	−	0.839489i	−0.455330	−	0.890323i	$-0.650479\pi$
$61$	−11.3564	−	6.55662i	−1.45404	−	0.839489i	−0.998707	+	0.0508335i	$0.983812\pi$
$62$	−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	$-0.893484\pi$
$73$		−	5.61202i		−	0.656837i	0.944532	−	0.328419i	$-0.106516\pi$
$74$	−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	$0.369785\pi$
$83$	−5.42692	+	9.39971i	−0.595682	+	1.03175i	−0.993450	+	0.114266i	$0.963548\pi$
$84$		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	$-0.739023\pi$
$89$	−12.8738			−1.36461			−0.682307	+	0.731065i	$0.739023\pi$
$90$	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	0.474723	−	0.880135i	$-0.342548\pi$
$97$	−0.493773	−	0.285080i	−0.0501351	−	0.0289455i	−0.524858	+	0.851190i	$0.675882\pi$
$98$		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	$-0.636907\pi$
$101$	5.81552	−	10.0728i	0.578666	−	1.00228i	0.995633	−	0.0933576i	$-0.0297600\pi$
$102$	0.781741	−	0.503335i	0.0774039	−	0.0498376i
$103$	−5.54001	+	3.19853i	−0.545874	+	0.315160i	−0.747456	−	0.664311i	$-0.768725\pi$
$103$	−5.54001	+	3.19853i	−0.545874	+	0.315160i	0.201582	+	0.979472i	$0.435392\pi$
$104$	−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	0.960249	−	0.279144i	$-0.0900508\pi$
$131$	2.72837	+	4.72567i	0.238379	+	0.412884i	−0.721871	+	0.692028i	$0.756717\pi$
$132$	−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	−0.0235572	−	0.999722i	$-0.507499\pi$
$139$	9.79085	−	5.65275i	0.830449	−	0.479460i	0.854006	+	0.520262i	$0.174166\pi$
$140$		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	0.0250163	−	0.999687i	$-0.492036\pi$
$157$	11.3181	−	6.53448i	0.903279	−	0.521508i	0.878263	+	0.478179i	$0.158703\pi$
$158$	−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	$-0.857880\pi$
$167$	−10.6605	−	18.4645i	−0.824932	−	1.42882i	0.0770396	−	0.997028i	$-0.475453\pi$
$168$		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	$-0.549172\pi$
$173$	10.2433	−	17.7418i	0.778781	−	1.34889i	0.932645	−	0.360796i	$-0.117495\pi$
$174$	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	$-0.916557\pi$
$181$		−	6.97309i		−	0.518306i	0.965836	−	0.259153i	$-0.0834434\pi$
$182$		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	$0.146707\pi$
$199$			12.5479i			0.889495i	−0.895656	+	0.444748i	$0.853293\pi$
$200$	−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	0.578895	−	0.815402i	$-0.303484\pi$
$223$	2.42193	+	1.39830i	0.162184	+	0.0936370i	−0.416711	+	0.909039i	$0.636817\pi$
$224$		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	−0.814930	−	0.579559i	$-0.803225\pi$
$227$	1.42300	−	2.46471i	0.0944480	−	0.163589i	0.909378	+	0.415970i	$0.136558\pi$
$228$	−0.873687	−	18.0184i	−0.0578613	−	1.19330i
$229$	20.5460	−	11.8623i	1.35772	−	0.783880i	0.368404	−	0.929666i	$-0.379904\pi$
$229$	20.5460	−	11.8623i	1.35772	−	0.783880i	0.989316	+	0.145786i	$0.0465711\pi$
$230$	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	0.378132	−	0.925752i	$-0.376566\pi$
$241$	−3.64082	−	2.10203i	−0.234526	−	0.135403i	−0.612658	+	0.790348i	$0.709900\pi$
$242$			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	$-0.423874\pi$
$251$	7.50592			0.473770			0.236885	+	0.971538i	$0.423874\pi$
$252$		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	0.776678	−	0.629898i	$-0.216903\pi$
$257$	−2.51960	−	4.36408i	−0.157169	−	0.272224i	−0.933847	+	0.357674i	$0.883570\pi$
$258$	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	$-0.659717\pi$
$269$	−15.7771			−0.961948			−0.480974	+	0.876735i	$0.659717\pi$
$270$	0.0487488	+	0.333020i	0.00296676	+	0.0202670i
$271$			16.8078i			1.02100i	0.859877	+	0.510501i	$0.170540\pi$
$271$			16.8078i			1.02100i	−0.859877	+	0.510501i	$0.829460\pi$
$272$	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	−0.939315	−	0.343056i	$-0.888538\pi$
$283$	−18.7047	+	10.7991i	−1.11188	+	0.641942i	−0.172562	+	0.984999i	$0.555204\pi$
$284$	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	$-0.972687\pi$
$293$	−9.79756	−	16.9699i	−0.572379	−	0.991390i	0.423942	−	0.905690i	$-0.360646\pi$
$294$		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	$-0.708835\pi$
$307$		−	27.7677i		−	1.58478i	0.610012	−	0.792392i	$-0.291165\pi$
$308$		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	$0.0254231\pi$
$311$	10.0080	+	17.3344i	0.567501	+	0.982941i	−0.429311	+	0.903157i	$0.641244\pi$
$312$	1.70163	−	0.0825094i	0.0963357	−	0.00467118i
$313$	15.9654	+	9.21765i	0.902420	+	0.521012i	0.877984	−	0.478689i	$-0.158888\pi$
$313$	15.9654	+	9.21765i	0.902420	+	0.521012i	0.0244352	+	0.999701i	$0.492221\pi$
$314$	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	0.644856	−	0.764304i	$-0.276917\pi$
$349$	5.70494	+	3.29375i	0.305378	+	0.176310i	−0.339478	+	0.940614i	$0.610250\pi$
$350$		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	$-0.645201\pi$
$353$	10.4692	−	18.1332i	0.557221	−	0.965135i	0.997727	−	0.0673857i	$-0.0214658\pi$
$354$	−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	0.193280	−	0.981144i	$-0.438087\pi$
$367$	−10.7237	−	6.19136i	−0.559775	−	0.323186i	−0.753055	+	0.657957i	$0.771421\pi$
$368$			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	0.658085	−	0.752944i	$-0.271367\pi$
$383$	−6.32174	−	10.9496i	−0.323026	−	0.559497i	−0.981111	+	0.193446i	$0.938033\pi$
$384$	−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	$0.213697\pi$
$397$			24.7882i			1.24409i	−0.782983	+	0.622043i	$0.786303\pi$
$398$	−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	−0.0475008	−	0.998871i	$-0.515126\pi$
$409$	16.0535	−	9.26852i	0.793797	−	0.458299i	0.841297	+	0.540573i	$0.181792\pi$
$410$	−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	0.827884	−	0.560899i	$-0.189545\pi$
$419$	−1.46994	−	2.54600i	−0.0718111	−	0.124380i	−0.899695	+	0.436519i	$0.856211\pi$
$420$		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	$0.238519\pi$
$433$			28.3475i			1.36229i	−0.732146	+	0.681147i	$0.761481\pi$
$434$		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	−0.155821	−	0.987785i	$-0.549802\pi$
$439$	−22.8208	−	13.1756i	−1.08918	−	0.628837i	−0.933358	+	0.358948i	$0.883136\pi$
$440$	−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	−0.964532	−	0.263968i	$-0.914969\pi$
$461$	−5.44638	+	9.43341i	−0.253663	+	0.439357i	0.710868	+	0.703325i	$0.248302\pi$
$462$		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	$-0.313595\pi$
$467$	23.8882			1.10541			0.552707	+	0.833376i	$0.313595\pi$
$468$	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	−0.886863	−	0.462033i	$-0.847120\pi$
$479$	−0.947645	+	1.64137i	−0.0432990	+	0.0749961i	0.843564	+	0.537029i	$0.180453\pi$
$480$	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	$-0.632603\pi$
$503$	−18.1502			−0.809278			−0.404639	+	0.914476i	$0.632603\pi$
$504$		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	0.581402	−	0.813617i	$-0.302504\pi$
$509$	−9.33827	−	16.1744i	−0.413912	−	0.716916i	−0.995314	+	0.0967005i	$0.969171\pi$
$510$	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	$-0.629517\pi$
$521$	−18.0665			−0.791508			−0.395754	+	0.918357i	$0.629517\pi$
$522$	−1.27638	+	2.80752i	−0.0558658	+	0.122882i
$523$		−	21.1338i		−	0.924116i	−0.886850	−	0.462058i	$-0.847111\pi$
$523$		−	21.1338i		−	0.924116i	0.886850	−	0.462058i	$-0.152889\pi$
$524$	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	$0.113733\pi$
$563$	18.3014	+	31.6990i	0.771314	+	1.33595i	−0.165529	+	0.986205i	$0.552933\pi$
$564$	−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	$-0.937414\pi$
$577$		−	9.38512i		−	0.390708i	0.980733	−	0.195354i	$-0.0625855\pi$
$578$	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	$-0.427215\pi$
$587$	23.1819	−	40.1523i	0.956821	−	1.65726i	0.730146	−	0.683291i	$-0.239452\pi$
$588$		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	$-0.378503\pi$
$593$	18.1416			0.744986			0.372493	+	0.928035i	$0.378503\pi$
$594$	−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	0.456796	−	0.889572i	$-0.348997\pi$
$601$	−2.08865	−	1.20588i	−0.0851976	−	0.0491889i	−0.541994	+	0.840383i	$0.682330\pi$
$602$		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	−0.259149	−	0.965837i	$-0.583442\pi$
$607$	11.0306	−	6.36850i	0.447717	−	0.258489i	0.706865	+	0.707348i	$0.250109\pi$
$608$	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	−0.421259	−	0.906940i	$-0.638412\pi$
$619$	−35.2626	−	20.3588i	−1.41732	−	0.818291i	−0.996063	+	0.0886491i	$0.971745\pi$
$620$			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	−0.615328	−	0.788271i	$-0.710977\pi$
$643$	−6.09416	+	3.51846i	−0.240330	+	0.138755i	0.374998	+	0.927025i	$0.377643\pi$
$644$		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	$-0.404767\pi$
$647$	14.9942			0.589482			0.294741	+	0.955577i	$0.404767\pi$
$648$	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	−0.810472	−	0.585778i	$-0.800789\pi$
$661$	−18.2131	+	10.5154i	−0.708409	+	0.409000i	0.102062	+	0.994778i	$0.467456\pi$
$662$	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	−0.985735	−	0.168308i	$-0.946170\pi$
$677$	−9.03150	+	15.6430i	−0.347109	+	0.601210i	0.638626	+	0.769517i	$0.279503\pi$
$678$	−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	0.435197	−	0.900335i	$-0.356679\pi$
$691$	−3.33627	−	1.92620i	−0.126918	−	0.0732760i	−0.562115	+	0.827059i	$0.690012\pi$
$692$	−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	$-0.520023\pi$
$719$	−3.37122			−0.125725			−0.0628627	+	0.998022i	$0.520023\pi$
$720$	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	0.578387	−	0.815763i	$-0.303682\pi$
$727$	4.34397	+	2.50799i	0.161109	+	0.0930164i	−0.417278	+	0.908779i	$0.637016\pi$
$728$		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	−0.817388	−	0.576088i	$-0.804579\pi$
$733$	−19.6875	+	11.3666i	−0.727175	+	0.419835i	0.0902126	+	0.995923i	$0.471245\pi$
$734$	−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	0.999401	−	0.0346186i	$-0.0110217\pi$
$761$	12.9578	+	22.4436i	0.469720	+	0.813578i	−0.529681	+	0.848197i	$0.677688\pi$
$762$	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	−0.799446	−	0.600738i	$-0.794873\pi$
$769$	−18.8269	+	10.8697i	−0.678914	+	0.391971i	0.120532	+	0.992709i	$0.461540\pi$
$770$		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	$-0.380914\pi$
$773$	20.3213			0.730905			0.365453	+	0.930830i	$0.380914\pi$
$774$	−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	−0.763051	−	0.646339i	$-0.776299\pi$
$787$	−16.4065	+	9.47232i	−0.584830	+	0.337652i	0.178221	+	0.983991i	$0.442966\pi$
$788$	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	0.589302	−	0.807913i	$-0.299403\pi$
$797$	−11.4342	−	19.8047i	−0.405022	−	0.701518i	−0.994324	+	0.106394i	$0.966069\pi$
$798$		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	$0.224611\pi$
$811$			36.9371i			1.29704i	−0.761199	+	0.648519i	$0.775389\pi$
$812$		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	$-0.856524\pi$
$829$		−	25.0859i		−	0.871270i	0.900123	−	0.435635i	$-0.143476\pi$
$830$	−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	−0.923180	−	0.384367i	$-0.874420\pi$
$839$	−3.72840	+	6.45777i	−0.128719	+	0.222947i	0.794462	+	0.607314i	$0.207753\pi$
$840$		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	0.537054	−	0.843548i	$-0.319537\pi$
$853$	2.19184	+	1.26546i	0.0750472	+	0.0433285i	−0.462007	+	0.886876i	$0.652870\pi$
$854$		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	−0.981559	−	0.191159i	$-0.938775\pi$
$857$	−9.52098	+	16.4908i	−0.325231	+	0.563316i	0.656328	+	0.754475i	$0.272109\pi$
$858$	1.51128	−	0.973060i	0.0515943	−	0.0332197i
$859$	−8.88415	+	5.12927i	−0.303123	+	0.175008i	−0.643845	−	0.765156i	$-0.722662\pi$
$859$	−8.88415	+	5.12927i	−0.303123	+	0.175008i	0.340722	+	0.940164i	$0.389329\pi$
$860$	−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	$-0.245381\pi$
$881$	42.5809			1.43459			0.717294	+	0.696771i	$0.245381\pi$
$882$		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	0.579461	−	0.815000i	$-0.303263\pi$
$887$	−12.3919	−	21.4634i	−0.416080	−	0.720671i	−0.995541	+	0.0943286i	$0.969930\pi$
$888$	−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	−0.892418	−	0.451210i	$-0.850993\pi$
$929$	−1.69009	+	2.92732i	−0.0554500	+	0.0960422i	0.836968	+	0.547252i	$0.184326\pi$
$930$	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	$-0.956912\pi$
$937$		−	8.26186i		−	0.269903i	0.990852	−	0.134952i	$-0.0430879\pi$
$938$		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	$-0.841014\pi$
$941$	−26.1882	−	45.3592i	−0.853710	−	1.47867i	0.0241274	−	0.999709i	$-0.492319\pi$
$942$	−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	$-0.482262\pi$
$971$	3.47104			0.111391			0.0556955	+	0.998448i	$0.482262\pi$
$972$	−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	$-0.618700\pi$
$983$	19.5749	−	33.9047i	0.624343	−	1.08139i	0.988668	−	0.150122i	$-0.0479665\pi$
$984$	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	0.800207	−	0.599725i	$-0.204723\pi$
$997$	21.5007	+	12.4134i	0.680933	+	0.393137i	−0.119273	+	0.992861i	$0.538057\pi$
$998$			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.146.13	✓	48
3.2	odd	2		1323.2.o.e.440.11		48
7.2	even	3		441.2.i.d.227.11		48
7.3	odd	6		441.2.s.d.362.11		48
7.4	even	3		441.2.s.d.362.12		48
7.5	odd	6		441.2.i.d.227.12		48
7.6	odd	2	inner	441.2.o.e.146.14	yes	48
9.4	even	3		1323.2.o.e.881.12		48
9.5	odd	6	inner	441.2.o.e.293.14	yes	48
21.2	odd	6		1323.2.i.d.521.12		48
21.5	even	6		1323.2.i.d.521.11		48
21.11	odd	6		1323.2.s.d.656.13		48
21.17	even	6		1323.2.s.d.656.14		48
21.20	even	2		1323.2.o.e.440.12		48
63.4	even	3		1323.2.i.d.1097.11		48
63.5	even	6		441.2.s.d.374.12		48
63.13	odd	6		1323.2.o.e.881.11		48
63.23	odd	6		441.2.s.d.374.11		48
63.31	odd	6		1323.2.i.d.1097.12		48
63.32	odd	6		441.2.i.d.68.14		48
63.40	odd	6		1323.2.s.d.962.13		48
63.41	even	6	inner	441.2.o.e.293.13	yes	48
63.58	even	3		1323.2.s.d.962.14		48
63.59	even	6		441.2.i.d.68.13		48

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

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

L-functions

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