LMFDB - Embedded newform 441.2.i.d.68.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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			68.14
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.122344i q^{2} +(0.937657 - 1.45630i) q^{3} +1.98503 q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 + 0.114717i) q^{6} +0.487547i q^{8} +(-1.24160 - 2.73101i) q^{9} +O(q^{10})$	\(q+0.122344i q^{2} +(0.937657 - 1.45630i) q^{3} +1.98503 q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 + 0.114717i) q^{6} +0.487547i q^{8} +(-1.24160 - 2.73101i) q^{9} +(0.0560949 - 0.0323864i) q^{10} +(3.64120 + 2.10225i) q^{11} +(1.86128 - 2.89080i) q^{12} +(-1.74714 - 1.00871i) q^{13} +(-0.915923 - 0.0444117i) q^{15} +3.91042 q^{16} +(-2.19381 - 3.79979i) q^{17} +(0.334124 - 0.151903i) q^{18} +(4.54391 + 2.62343i) q^{19} +(-0.525467 - 0.910136i) q^{20} +(-0.257198 + 0.445480i) q^{22} +(-5.43444 + 3.13757i) q^{23} +(0.710012 + 0.457151i) q^{24} +(2.35985 - 4.08738i) q^{25} +(0.123411 - 0.213753i) q^{26} +(-5.14136 - 0.752613i) q^{27} +(-7.27689 + 4.20131i) q^{29} +(0.00543353 - 0.112058i) q^{30} -1.19170i q^{31} +1.45351i q^{32} +(6.47569 - 3.33148i) q^{33} +(0.464883 - 0.268400i) q^{34} +(-2.46462 - 5.42115i) q^{36} +(1.61626 - 2.79945i) q^{37} +(-0.320962 + 0.555922i) q^{38} +(-3.10721 + 1.59853i) q^{39} +(0.223540 - 0.129061i) q^{40} +(-0.0994958 + 0.172332i) q^{41} +(3.96309 + 6.86427i) q^{43} +(7.22789 + 4.17303i) q^{44} +(-0.923498 + 1.29221i) q^{45} +(-0.383865 - 0.664873i) q^{46} -9.97189 q^{47} +(3.66663 - 5.69472i) q^{48} +(0.500069 + 0.288715i) q^{50} +(-7.59066 - 0.368060i) q^{51} +(-3.46814 - 2.00233i) q^{52} +(3.65249 - 2.10877i) q^{53} +(0.0920780 - 0.629017i) q^{54} -2.22598i q^{55} +(8.08111 - 4.15740i) q^{57} +(-0.514008 - 0.890287i) q^{58} +13.4392 q^{59} +(-1.81814 - 0.0881587i) q^{60} +13.1132i q^{61} +0.145798 q^{62} +7.64300 q^{64} +1.06809i q^{65} +(0.407588 + 0.792264i) q^{66} -6.58003 q^{67} +(-4.35478 - 7.54270i) q^{68} +(-0.526397 + 10.8561i) q^{69} -8.50587i q^{71} +(1.33150 - 0.605338i) q^{72} +(-4.86015 + 2.80601i) q^{73} +(0.342497 + 0.197741i) q^{74} +(-3.73971 - 7.26921i) q^{75} +(9.01980 + 5.20758i) q^{76} +(-0.195572 - 0.380150i) q^{78} +0.572684 q^{79} +(-1.03514 - 1.79292i) q^{80} +(-5.91686 + 6.78165i) q^{81} +(-0.0210838 - 0.0121728i) q^{82} +(5.42692 + 9.39971i) q^{83} +(-1.16147 + 2.01172i) q^{85} +(-0.839806 + 0.484862i) q^{86} +(-0.704863 + 14.5367i) q^{87} +(-1.02494 + 1.77525i) q^{88} +(-6.43688 + 11.1490i) q^{89} +(-0.158095 - 0.112985i) q^{90} +(-10.7875 + 6.22819i) q^{92} +(-1.73547 - 1.11740i) q^{93} -1.22001i q^{94} -2.77784i q^{95} +(2.11674 + 1.36289i) q^{96} +(0.493773 - 0.285080i) q^{97} +(1.22035 - 12.5543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^9	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			0.122344i			0.0865106i	0.999064	+	0.0432553i	$0.0137729\pi$
$2$			0.122344i			0.0865106i	−0.999064	+	0.0432553i	$0.986227\pi$
$3$	0.937657	−	1.45630i	0.541356	−	0.840793i
$3$	0.937657	−	1.45630i	0.541356	−	0.840793i
$4$	1.98503			0.992516
$5$	−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
$9$	−1.24160	−	2.73101i	−0.413867	−	0.910337i
$10$	0.0560949	−	0.0323864i	0.0177388	−	0.0102415i
$11$	3.64120	+	2.10225i	1.09786	+	0.633851i	0.935659	−	0.352906i	$-0.114807\pi$
$11$	3.64120	+	2.10225i	1.09786	+	0.633851i	0.162204	+	0.986757i	$0.448140\pi$
$12$	1.86128	−	2.89080i	0.537305	−	0.834501i
$13$	−1.74714	−	1.00871i	−0.484570	−	0.279767i	0.237749	−	0.971327i	$-0.423590\pi$
$13$	−1.74714	−	1.00871i	−0.484570	−	0.279767i	−0.722319	+	0.691560i	$0.756924\pi$
$14$		0			0
$15$	−0.915923	−	0.0444117i	−0.236490	−	0.0114671i
$16$	3.91042			0.977604
$17$	−2.19381	−	3.79979i	−0.532077	−	0.921584i	−0.999299	−	0.0374442i	$-0.988078\pi$
$17$	−2.19381	−	3.79979i	−0.532077	−	0.921584i	0.467222	−	0.884140i	$-0.345255\pi$
$18$	0.334124	−	0.151903i	0.0787538	−	0.0358039i
$19$	4.54391	+	2.62343i	1.04244	+	0.601855i	0.920524	−	0.390685i	$-0.127762\pi$
$19$	4.54391	+	2.62343i	1.04244	+	0.601855i	0.121919	+	0.992540i	$0.461095\pi$
$20$	−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	−0.944727	−	0.327857i	$-0.893674\pi$
$23$	−5.43444	+	3.13757i	−1.13316	+	0.654230i	−0.188431	+	0.982086i	$0.560340\pi$
$24$	0.710012	+	0.457151i	0.144931	+	0.0933156i
$25$	2.35985	−	4.08738i	0.471970	−	0.817477i
$26$	0.123411	−	0.213753i	0.0242028	−	0.0419205i
$27$	−5.14136	−	0.752613i	−0.989455	−	0.144840i
$28$		0			0
$29$	−7.27689	+	4.20131i	−1.35128	+	0.780164i	−0.988429	−	0.151681i	$-0.951531\pi$
$29$	−7.27689	+	4.20131i	−1.35128	+	0.780164i	−0.362855	+	0.931846i	$0.618198\pi$
$30$	0.00543353	−	0.112058i	0.000992023	−	0.0204589i
$31$		−	1.19170i		−	0.214035i	−0.994257	−	0.107018i	$-0.965870\pi$
$31$		−	1.19170i		−	0.214035i	0.994257	−	0.107018i	$-0.0341301\pi$
$32$			1.45351i			0.256947i
$33$	6.47569	−	3.33148i	1.12727	−	0.579936i
$34$	0.464883	−	0.268400i	0.0797268	−	0.0460303i
$35$		0			0
$36$	−2.46462	−	5.42115i	−0.410769	−	0.903524i
$37$	1.61626	−	2.79945i	0.265712	−	0.460226i	−0.702038	−	0.712139i	$-0.747726\pi$
$37$	1.61626	−	2.79945i	0.265712	−	0.460226i	0.967750	+	0.251913i	$0.0810597\pi$
$38$	−0.320962	+	0.555922i	−0.0520668	+	0.0901824i
$39$	−3.10721	+	1.59853i	−0.497551	+	0.255970i
$40$	0.223540	−	0.129061i	0.0353448	−	0.0204063i
$41$	−0.0994958	+	0.172332i	−0.0155386	+	0.0269137i	−0.873690	−	0.486483i	$-0.838280\pi$
$41$	−0.0994958	+	0.172332i	−0.0155386	+	0.0269137i	0.858152	+	0.513396i	$0.171613\pi$
$42$		0			0
$43$	3.96309	+	6.86427i	0.604366	+	1.04679i	0.992151	+	0.125042i	$0.0399067\pi$
$43$	3.96309	+	6.86427i	0.604366	+	1.04679i	−0.387786	+	0.921750i	$0.626760\pi$
$44$	7.22789	+	4.17303i	1.08965	+	0.629107i
$45$	−0.923498	+	1.29221i	−0.137667	+	0.192632i
$46$	−0.383865	−	0.664873i	−0.0565978	−	0.0980302i
$47$	−9.97189			−1.45455			−0.727275	−	0.686346i	$-0.759213\pi$
$47$	−9.97189			−1.45455			−0.727275	+	0.686346i	$0.759213\pi$
$48$	3.66663	−	5.69472i	0.529232	−	0.821963i
$49$		0			0
$50$	0.500069	+	0.288715i	0.0707204	+	0.0408304i
$51$	−7.59066	−	0.368060i	−1.06291	−	0.0515387i
$52$	−3.46814	−	2.00233i	−0.480944	−	0.277673i
$53$	3.65249	−	2.10877i	0.501708	−	0.289661i	−0.227711	−	0.973729i	$-0.573124\pi$
$53$	3.65249	−	2.10877i	0.501708	−	0.289661i	0.729419	+	0.684068i	$0.239791\pi$
$54$	0.0920780	−	0.629017i	0.0125302	−	0.0855983i
$55$		−	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
$59$	13.4392			1.74963			0.874817	−	0.484454i	$-0.160982\pi$
$59$	13.4392			1.74963			0.874817	+	0.484454i	$0.160982\pi$
$60$	−1.81814	−	0.0881587i	−0.234720	−	0.0113812i
$61$			13.1132i			1.67898i	0.543377	+	0.839489i	$0.317146\pi$
$61$			13.1132i			1.67898i	−0.543377	+	0.839489i	$0.682854\pi$
$62$	0.145798			0.0185163
$63$		0			0
$64$	7.64300			0.955375
$65$			1.06809i			0.132480i
$66$	0.407588	+	0.792264i	0.0501706	+	0.0975210i
$67$	−6.58003			−0.803878			−0.401939	−	0.915666i	$-0.631664\pi$
$67$	−6.58003			−0.803878			−0.401939	+	0.915666i	$0.631664\pi$
$68$	−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	$-0.831592\pi$
$71$		−	8.50587i		−	1.00946i	0.863277	−	0.504730i	$-0.168408\pi$
$72$	1.33150	−	0.605338i	0.156918	−	0.0713398i
$73$	−4.86015	+	2.80601i	−0.568838	+	0.328419i	−0.756685	−	0.653780i	$-0.773182\pi$
$73$	−4.86015	+	2.80601i	−0.568838	+	0.328419i	0.187847	+	0.982198i	$0.439849\pi$
$74$	0.342497	+	0.197741i	0.0398145	+	0.0229869i
$75$	−3.73971	−	7.26921i	−0.431825	−	0.839376i
$76$	9.01980	+	5.20758i	1.03464	+	0.597351i
$77$		0			0
$78$	−0.195572	−	0.380150i	−0.0221441	−	0.0430435i
$79$	0.572684			0.0644320			0.0322160	−	0.999481i	$-0.489744\pi$
$79$	0.572684			0.0644320			0.0322160	+	0.999481i	$0.489744\pi$
$80$	−1.03514	−	1.79292i	−0.115733	−	0.200455i
$81$	−5.91686	+	6.78165i	−0.657429	+	0.753517i
$82$	−0.0210838	−	0.0121728i	−0.00232832	−	0.00134426i
$83$	5.42692	+	9.39971i	0.595682	+	1.03175i	0.993450	+	0.114266i	$0.0364516\pi$
$83$	5.42692	+	9.39971i	0.595682	+	1.03175i	−0.397768	+	0.917486i	$0.630215\pi$
$84$		0			0
$85$	−1.16147	+	2.01172i	−0.125979	+	0.218202i
$86$	−0.839806	+	0.484862i	−0.0905586	+	0.0522840i
$87$	−0.704863	+	14.5367i	−0.0755692	+	1.55850i
$88$	−1.02494	+	1.77525i	−0.109259	+	0.189243i
$89$	−6.43688	+	11.1490i	−0.682307	+	1.18179i	0.291968	+	0.956428i	$0.405690\pi$
$89$	−6.43688	+	11.1490i	−0.682307	+	1.18179i	−0.974275	+	0.225363i	$0.927643\pi$
$90$	−0.158095	−	0.112985i	−0.0166647	−	0.0119096i
$91$		0			0
$92$	−10.7875	+	6.22819i	−1.12468	+	0.649333i
$93$	−1.73547	−	1.11740i	−0.179959	−	0.115869i
$94$		−	1.22001i		−	0.125834i
$95$		−	2.77784i		−	0.285000i
$96$	2.11674	+	1.36289i	0.216039	+	0.139100i
$97$	0.493773	−	0.285080i	0.0501351	−	0.0289455i	−0.474723	−	0.880135i	$-0.657452\pi$
$97$	0.493773	−	0.285080i	0.0501351	−	0.0289455i	0.524858	+	0.851190i	$0.324118\pi$
$98$		0			0
$99$	1.22035	−	12.5543i	0.122650	−	1.26176i
$100$	4.68438	−	8.11359i	0.468438	−	0.811359i
$101$	−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	$0.970240\pi$
$102$	0.0450301	−	0.928675i	0.00445864	−	0.0919526i
$103$	−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
$107$	0.219332	+	0.126632i	0.0212037	+	0.0122419i	0.510564	−	0.859840i	$-0.329437\pi$
$107$	0.219332	+	0.126632i	0.0212037	+	0.0122419i	−0.489361	+	0.872081i	$0.662770\pi$
$108$	−10.2058	−	1.49396i	−0.982050	−	0.143756i
$109$	−5.98602	−	10.3681i	−0.573357	−	0.993084i	−0.996218	−	0.0868891i	$-0.972307\pi$
$109$	−5.98602	−	10.3681i	−0.573357	−	0.993084i	0.422861	−	0.906195i	$-0.361026\pi$
$110$	0.272337			0.0259663
$111$	−2.56133	−	4.97868i	−0.243110	−	0.472555i
$112$		0			0
$113$	4.28636	+	2.47473i	0.403227	+	0.232803i	0.687875	−	0.725829i	$-0.258544\pi$
$113$	4.28636	+	2.47473i	0.403227	+	0.232803i	−0.284648	+	0.958632i	$0.591877\pi$
$114$	0.508635	+	0.988679i	0.0476381	+	0.0925983i
$115$	2.87715	+	1.66113i	0.268296	+	0.154901i
$116$	−14.4449	+	8.33974i	−1.34117	+	0.774326i
$117$	−0.585556	+	6.02389i	−0.0541346	+	0.556909i
$118$			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
$122$	−1.60433			−0.145249
$123$	0.157673	+	0.306483i	0.0142169	+	0.0276347i
$124$		−	2.36556i		−	0.212433i
$125$	−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	$0.552269\pi$
$128$			3.84210i			0.339597i
$129$	13.7124	+	0.664896i	1.20731	+	0.0585408i
$130$	−0.130674			−0.0114609
$131$	−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
$135$	1.01592	+	2.55654i	0.0874366	+	0.220032i
$136$	1.85257	−	1.06958i	0.158857	−	0.0917161i
$137$	1.39996	+	0.808270i	0.119607	+	0.0690551i	0.558610	−	0.829431i	$-0.311335\pi$
$137$	1.39996	+	0.808270i	0.119607	+	0.0690551i	−0.439003	+	0.898486i	$0.644668\pi$
$138$	−1.32819	−	0.0644018i	−0.113063	−	0.00548224i
$139$	−9.79085	−	5.65275i	−0.830449	−	0.479460i	0.0235572	−	0.999722i	$-0.492501\pi$
$139$	−9.79085	−	5.65275i	−0.830449	−	0.479460i	−0.854006	+	0.520262i	$0.825834\pi$
$140$		0			0
$141$	−9.35021	+	14.5220i	−0.787430	+	1.22298i
$142$	1.04065			0.0873291
$143$	−4.24113	−	7.34585i	−0.354661	−	0.614291i
$144$	−4.85517	−	10.6794i	−0.404598	−	0.889949i
$145$	3.85260	+	2.22430i	0.319941	+	0.184718i
$146$	−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	−0.676954	−	0.736025i	$-0.736700\pi$
$149$	−4.61426	+	2.66404i	−0.378015	+	0.218247i	0.298939	+	0.954272i	$0.403367\pi$
$150$	0.889347	−	0.457533i	0.0726149	−	0.0373574i
$151$	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	$0.132373\pi$
$152$	−1.27904	+	2.21537i	−0.103744	+	0.179690i
$153$	−7.65344	+	10.7091i	−0.618744	+	0.865783i
$154$		0			0
$155$	−0.546393	+	0.315460i	−0.0438873	+	0.0253384i
$156$	−6.16790	+	3.17314i	−0.493828	+	0.254054i
$157$			13.0690i			1.04302i	0.853246	+	0.521508i	$0.174630\pi$
$157$			13.0690i			1.04302i	−0.853246	+	0.521508i	$0.825370\pi$
$158$			0.0700647i			0.00557405i
$159$	0.353792	−	7.29641i	0.0280575	−	0.578643i
$160$	0.666434	−	0.384766i	0.0526862	−	0.0304184i
$161$		0			0
$162$	−0.829698	−	0.723895i	−0.0651872	−	0.0568745i
$163$	−8.51345	+	14.7457i	−0.666825	+	1.15498i	0.311962	+	0.950095i	$0.399014\pi$
$163$	−8.51345	+	14.7457i	−0.666825	+	1.15498i	−0.978787	+	0.204880i	$0.934319\pi$
$164$	−0.197502	+	0.342084i	−0.0154223	+	0.0267123i
$165$	−3.24169	−	2.08721i	−0.252365	−	0.162489i
$166$	−1.15000	+	0.663954i	−0.0892575	+	0.0515328i
$167$	10.6605	−	18.4645i	0.824932	−	1.42882i	−0.0770396	−	0.997028i	$-0.524547\pi$
$167$	10.6605	−	18.4645i	0.824932	−	1.42882i	0.901971	−	0.431796i	$-0.142120\pi$
$168$		0			0
$169$	−4.46499	−	7.73360i	−0.343461	−	0.594892i
$170$	−0.246123	−	0.142099i	−0.0188768	−	0.0108985i
$171$	1.52289	−	15.6667i	0.116458	−	1.19806i
$172$	7.86686	+	13.6258i	0.599842	+	1.03896i
$173$	20.4865			1.55756			0.778781	−	0.627296i	$-0.215838\pi$
$173$	20.4865			1.55756			0.778781	+	0.627296i	$0.215838\pi$
$174$	−1.77848	−	0.0862361i	−0.134827	−	0.00653754i
$175$		0			0
$176$	14.2386	+	8.22066i	1.07327	+	0.619655i
$177$	12.6013	−	19.5714i	0.947175	−	1.47108i
$178$	−1.36402	−	0.787516i	−0.102237	−	0.0590268i
$179$	12.4770	−	7.20357i	0.932571	−	0.538420i	0.0449475	−	0.998989i	$-0.485688\pi$
$179$	12.4770	−	7.20357i	0.932571	−	0.538420i	0.887624	+	0.460569i	$0.152355\pi$
$180$	−1.83317	+	2.56508i	−0.136637	+	0.191190i
$181$		−	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
$185$	−1.71139			−0.125824
$186$	0.136708	−	0.212325i	0.0100239	−	0.0155684i
$187$		−	18.4477i		−	1.34903i
$188$	−19.7945			−1.44366
$189$		0			0
$190$	0.339853			0.0246555
$191$		−	10.8347i		−	0.783969i	−0.919972	−	0.391985i	$-0.871789\pi$
$191$		−	10.8347i		−	0.783969i	0.919972	−	0.391985i	$-0.128211\pi$
$192$	7.16651	−	11.1305i	0.517198	−	0.803273i
$193$	10.5245			0.757567			0.378783	−	0.925485i	$-0.376343\pi$
$193$	10.5245			0.757567			0.378783	+	0.925485i	$0.376343\pi$
$194$	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	$-0.813590\pi$
$197$		−	15.5156i		−	1.10544i	0.833366	−	0.552721i	$-0.186410\pi$
$198$	1.53595	+	0.149303i	0.109155	+	0.0106105i
$199$	10.8668	−	6.27394i	0.770326	−	0.444748i	−0.0626651	−	0.998035i	$-0.519960\pi$
$199$	10.8668	−	6.27394i	0.770326	−	0.444748i	0.832991	+	0.553287i	$0.186627\pi$
$200$	1.99279	+	1.15054i	0.140912	+	0.0813553i
$201$	−6.16980	+	9.58247i	−0.435184	+	0.675895i
$202$	−1.23235	−	0.711497i	−0.0867078	−	0.0500608i
$203$		0			0
$204$	−15.0677	−	0.730611i	−1.05495	−	0.0511530i
$205$	0.105352			0.00735810
$206$	−0.391322	−	0.677790i	−0.0272647	−	0.0472238i
$207$	15.3162	+	10.9459i	1.06455	+	0.760793i
$208$	−6.83206	−	3.94449i	−0.473718	−	0.273501i
$209$	11.0302	+	19.1048i	0.762973	+	1.32151i
$210$		0			0
$211$	−1.19765	+	2.07438i	−0.0824494	+	0.142807i	−0.904302	−	0.426894i	$-0.859608\pi$
$211$	−1.19765	+	2.07438i	−0.0824494	+	0.142807i	0.821852	+	0.569701i	$0.192941\pi$
$212$	7.25031	−	4.18597i	0.497953	−	0.287493i
$213$	−12.3871	−	7.97558i	−0.848748	−	0.546478i
$214$	−0.0154927	+	0.0268341i	−0.00105906	+	0.00183434i
$215$	2.09818	−	3.63415i	0.143095	−	0.247847i
$216$	0.366934	−	2.50665i	0.0249667	−	0.170556i
$217$		0			0
$218$	1.26848	−	0.732357i	0.0859123	−	0.0496015i
$219$	−0.470770	+	9.70890i	−0.0318117	+	0.656066i
$220$		−	4.41865i		−	0.297905i
$221$			8.85170i			0.595430i
$222$	0.609114	−	0.313364i	0.0408810	−	0.0210316i
$223$	−2.42193	+	1.39830i	−0.162184	+	0.0936370i	−0.578895	−	0.815402i	$-0.696516\pi$
$223$	−2.42193	+	1.39830i	−0.162184	+	0.0936370i	0.416711	+	0.909039i	$0.363183\pi$
$224$		0			0
$225$	−14.0927	−	1.36989i	−0.939513	−	0.0913259i
$226$	−0.302770	+	0.524413i	−0.0201400	+	0.0348834i
$227$	−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	$0.196775\pi$
$228$	16.0413	−	8.25258i	1.06236	−	0.546540i
$229$	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
$233$	−16.2205	−	9.36488i	−1.06264	−	0.613514i	−0.136477	−	0.990643i	$-0.543578\pi$
$233$	−16.2205	−	9.36488i	−1.06264	−	0.613514i	−0.926161	+	0.377129i	$0.876911\pi$
$234$	−0.736990	−	0.0716395i	−0.0481785	−	0.00468322i
$235$	2.63971	+	4.57211i	0.172196	+	0.298251i
$236$	26.6772			1.73654
$237$	0.536981	−	0.833998i	0.0348807	−	0.0541740i
$238$		0			0
$239$	11.1421	+	6.43288i	0.720721	+	0.416109i	0.815018	−	0.579436i	$-0.196727\pi$
$239$	11.1421	+	6.43288i	0.720721	+	0.416109i	−0.0942969	+	0.995544i	$0.530060\pi$
$240$	−3.58164	−	0.173668i	−0.231194	−	0.0112102i
$241$	−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	$0.709900\pi$
$242$	−0.707531	+	0.408493i	−0.0454818	+	0.0262590i
$243$	4.32812	+	14.9756i	0.277649	+	0.960683i
$244$			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
$248$	0.581008			0.0368941
$249$	18.7774	+	0.910486i	1.18997	+	0.0576997i
$250$		−	0.629572i		−	0.0398177i
$251$	−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
$254$		−	0.450774i		−	0.0282840i
$255$	1.84061	+	3.57775i	0.115263	+	0.224047i
$256$	14.8159			0.925996
$257$	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
$261$	20.5088	+	14.6569i	1.26946	+	0.907241i
$262$	0.578160	−	0.333801i	0.0357188	−	0.0206223i
$263$	−12.2494	−	7.07220i	−0.755331	−	0.436091i	0.0722856	−	0.997384i	$-0.476971\pi$
$263$	−12.2494	−	7.07220i	−0.755331	−	0.436091i	−0.827617	+	0.561293i	$0.810304\pi$
$264$	1.62425	+	3.15720i	0.0999658	+	0.194312i
$265$	−1.93374	−	1.11644i	−0.118789	−	0.0685826i
$266$		0			0
$267$	10.2007	+	19.8279i	0.624271	+	1.21345i
$268$	−13.0616			−0.797862
$269$	−7.88856	−	13.6634i	−0.480974	−	0.833071i	0.518788	−	0.854903i	$-0.326384\pi$
$269$	−7.88856	−	13.6634i	−0.480974	−	0.833071i	−0.999762	+	0.0218318i	$0.993050\pi$
$270$	−0.312778	+	0.124292i	−0.0190351	+	0.00756419i
$271$	−14.5560	−	8.40390i	−0.884213	−	0.510501i	−0.0121677	−	0.999926i	$-0.503873\pi$
$271$	−14.5560	−	8.40390i	−0.884213	−	0.510501i	−0.872045	+	0.489425i	$0.837207\pi$
$272$	−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
$276$	−1.04492	+	21.5497i	−0.0628965	+	1.29714i
$277$	−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	$0.986831\pi$
$278$	0.691583	−	1.19786i	0.0414784	−	0.0718427i
$279$	−3.25454	+	1.47961i	−0.194844	+	0.0885821i
$280$		0			0
$281$	7.59774	−	4.38656i	0.453243	−	0.261680i	−0.255956	−	0.966688i	$-0.582390\pi$
$281$	7.59774	−	4.38656i	0.453243	−	0.261680i	0.709199	+	0.705008i	$0.249057\pi$
$282$	−1.77669	−	1.14395i	−0.105800	−	0.0681210i
$283$		−	21.5983i		−	1.28388i	−0.766753	−	0.641942i	$-0.778129\pi$
$283$		−	21.5983i		−	1.28388i	0.766753	−	0.641942i	$-0.221871\pi$
$284$		−	16.8844i		−	1.00191i
$285$	−4.04536	−	2.60466i	−0.239626	−	0.154287i
$286$	0.898724	−	0.518879i	0.0531427	−	0.0306819i
$287$		0			0
$288$	3.96956	−	1.80468i	0.233908	−	0.106342i
$289$	−1.12560	+	1.94960i	−0.0662118	+	0.114682i
$290$	−0.272131	+	0.471344i	−0.0159801	+	0.0276783i
$291$	0.0478285	−	0.986388i	0.00280376	−	0.0578231i
$292$	−9.64756	+	5.57002i	−0.564581	+	0.325961i
$293$	9.79756	−	16.9699i	0.572379	−	0.991390i	−0.423942	−	0.905690i	$-0.639354\pi$
$293$	9.79756	−	16.9699i	0.572379	−	0.991390i	0.996321	−	0.0857006i	$-0.0273128\pi$
$294$		0			0
$295$	−3.55755	−	6.16186i	−0.207129	−	0.358758i
$296$	1.36486	+	0.788003i	0.0793309	+	0.0458017i
$297$	−17.1385	−	13.5488i	−0.994478	−	0.786182i
$298$	−0.325931	−	0.564529i	−0.0188807	−	0.0327023i
$299$	12.6597			0.732127
$300$	−7.42345	−	14.4296i	−0.428593	−	0.833094i
$301$		0			0
$302$	0.279996	+	0.161656i	0.0161120	+	0.00930224i
$303$	9.21600	+	17.9139i	0.529445	+	1.02913i
$304$	17.7686	+	10.2587i	1.01910	+	0.588376i
$305$	6.01241	−	3.47127i	0.344270	−	0.198764i
$306$	−1.31020	−	0.936356i	−0.0748994	−	0.0535279i
$307$		−	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
$311$	20.0160			1.13500			0.567501	−	0.823373i	$-0.307910\pi$
$311$	20.0160			1.13500			0.567501	+	0.823373i	$0.307910\pi$
$312$	−0.779359	−	1.51491i	−0.0441225	−	0.0857648i
$313$		−	18.4353i		−	1.04202i	−0.853549	−	0.521012i	$-0.825555\pi$
$313$		−	18.4353i		−	1.04202i	0.853549	−	0.521012i	$-0.174445\pi$
$314$	−1.59891			−0.0902320
$315$		0			0
$316$	1.13680			0.0639498
$317$		−	14.5483i		−	0.817115i	−0.912733	−	0.408558i	$-0.866032\pi$
$317$		−	14.5483i		−	0.817115i	0.912733	−	0.408558i	$-0.133968\pi$
$318$	0.892675	+	0.0432845i	0.0500587	+	0.00242727i
$319$	−35.3288			−1.97803
$320$	−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
$324$	−11.7451	+	13.4618i	−0.652508	+	0.747878i
$325$	−8.24600	+	4.76083i	−0.457406	+	0.264083i
$326$	−1.80406	−	1.04157i	−0.0999176	−	0.0576874i
$327$	−20.7119	−	1.00429i	−1.14537	−	0.0555372i
$328$	−0.0840197	−	0.0485088i	−0.00463921	−	0.00267845i
$329$		0			0
$330$	0.255358	−	0.396603i	0.0140570	−	0.0218323i
$331$	−29.6891			−1.63186			−0.815930	−	0.578150i	$-0.803775\pi$
$331$	−29.6891			−1.63186			−0.815930	+	0.578150i	$0.803775\pi$
$332$	10.7726	+	18.6587i	0.591224	+	1.02403i
$333$	−9.65208	−	0.938236i	−0.528931	−	0.0514150i
$334$	2.25903	+	1.30425i	0.123608	+	0.0713653i
$335$	1.74183	+	3.01694i	0.0951664	+	0.164833i
$336$		0			0
$337$	−4.60606	+	7.97793i	−0.250908	+	0.434586i	−0.963776	−	0.266713i	$-0.914063\pi$
$337$	−4.60606	+	7.97793i	−0.250908	+	0.434586i	0.712868	+	0.701298i	$0.247396\pi$
$338$	0.946163	−	0.546267i	0.0514645	−	0.0297130i
$339$	7.62308	−	3.92177i	0.414029	−	0.213001i
$340$	−2.30555	+	3.99333i	−0.125036	+	0.216569i
$341$	2.50524	−	4.33921i	0.135667	−	0.234981i
$342$	1.91674	+	0.186317i	0.103645	+	0.0100749i
$343$		0			0
$344$	−3.34665	+	1.93219i	−0.180439	+	0.104177i
$345$	5.11687	−	2.63242i	0.275483	−	0.141725i
$346$			2.50641i			0.134746i
$347$		−	18.1649i		−	0.975145i	−0.873082	−	0.487573i	$-0.837882\pi$
$347$		−	18.1649i		−	0.975145i	0.873082	−	0.487573i	$-0.162118\pi$
$348$	−1.39918	+	28.8558i	−0.0750037	+	1.54683i
$349$	−5.70494	+	3.29375i	−0.305378	+	0.176310i	−0.644856	−	0.764304i	$-0.723083\pi$
$349$	−5.70494	+	3.29375i	−0.305378	+	0.176310i	0.339478	+	0.940614i	$0.389750\pi$
$350$		0			0
$351$	8.22352	+	6.50108i	0.438939	+	0.347002i
$352$	−3.05564	+	5.29252i	−0.162866	+	0.282092i
$353$	−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	$0.978534\pi$
$354$	2.39446	+	1.54170i	0.127264	+	0.0819407i
$355$	−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
$359$	12.3205	+	7.11324i	0.650251	+	0.375422i	0.788552	−	0.614968i	$-0.210831\pi$
$359$	12.3205	+	7.11324i	0.650251	+	0.375422i	−0.138302	+	0.990390i	$0.544164\pi$
$360$	−0.630014	−	0.450248i	−0.0332046	−	0.0237302i
$361$	4.26472	+	7.38671i	0.224459	+	0.388774i
$362$	0.853120			0.0448390
$363$	11.5526	+	0.560171i	0.606357	+	0.0294013i
$364$		0			0
$365$	2.57311	+	1.48559i	0.134683	+	0.0777591i
$366$	−1.50431	+	2.33638i	−0.0786317	+	0.122125i
$367$	−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	$0.771421\pi$
$368$	−21.2509	+	12.2692i	−1.10778	+	0.639577i
$369$	0.594174	+	0.0577570i	0.0309315	+	0.00300671i
$370$		−	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	$0.647297\pi$
$374$	2.25698			0.116705
$375$	−4.82509	+	7.49396i	−0.249166	+	0.386986i
$376$		−	4.86176i		−	0.250726i
$377$	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	$0.412234\pi$
$380$		−	5.51410i		−	0.282867i
$381$	−3.45476	+	5.36567i	−0.176993	+	0.274892i
$382$	1.32556			0.0678217
$383$	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
$387$	13.8258	−	19.3459i	0.702807	−	0.983409i
$388$	0.980156	−	0.565893i	0.0497599	−	0.0287289i
$389$	−11.4538	−	6.61286i	−0.580732	−	0.335286i	0.180692	−	0.983540i	$-0.442166\pi$
$389$	−11.4538	−	6.61286i	−0.580732	−	0.335286i	−0.761424	+	0.648254i	$0.775499\pi$
$390$	−0.122528	+	0.190301i	−0.00620443	+	0.00963625i
$391$	23.8442	+	13.7665i	1.20586	+	0.696201i
$392$		0			0
$393$	−9.44025	−	0.457744i	−0.476198	−	0.0230901i
$394$	1.89825			0.0956324
$395$	−0.151598	−	0.262575i	−0.00762772	−	0.0132116i
$396$	2.42243	−	24.9207i	0.121732	−	1.25231i
$397$	−21.4672	−	12.3941i	−1.07741	−	0.622043i	−0.147214	−	0.989105i	$-0.547030\pi$
$397$	−21.4672	−	12.3941i	−1.07741	−	0.622043i	−0.930197	+	0.367062i	$0.880364\pi$
$398$	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	−0.577677	−	0.816266i	$-0.696041\pi$
$401$	−3.19615	+	1.84530i	−0.159608	+	0.0921499i	0.418068	+	0.908416i	$0.362707\pi$
$402$	−1.17236	−	0.754841i	−0.0584721	−	0.0376481i
$403$	−1.20208	+	2.08207i	−0.0598800	+	0.103715i
$404$	−11.5440	+	19.9948i	−0.574336	+	0.994778i
$405$	4.67566	+	0.917672i	0.232336	+	0.0455995i
$406$		0			0
$407$	11.7703	−	6.79556i	0.583430	−	0.336843i
$408$	0.179446	−	3.70080i	0.00888392	−	0.183217i
$409$			18.5370i			0.916597i	0.888798	+	0.458299i	$0.151541\pi$
$409$			18.5370i			0.916597i	−0.888798	+	0.458299i	$0.848459\pi$
$410$			0.0128892i			0.000636554i
$411$	2.48977	−	1.28088i	0.122811	−	0.0631813i
$412$	−10.9971	+	6.34918i	−0.541788	+	0.312802i
$413$		0			0
$414$	−1.33917	+	1.87385i	−0.0658167	+	0.0920945i
$415$	2.87317	−	4.97648i	0.141039	−	0.244286i
$416$	1.46618	−	2.53949i	0.0718852	−	0.124509i
$417$	−17.4125	+	8.95805i	−0.852696	+	0.438677i
$418$	−2.33737	+	1.34948i	−0.114324	+	0.0660053i
$419$	1.46994	−	2.54600i	0.0718111	−	0.124380i	−0.827884	−	0.560899i	$-0.810455\pi$
$419$	1.46994	−	2.54600i	0.0718111	−	0.124380i	0.899695	+	0.436519i	$0.143789\pi$
$420$		0			0
$421$	−14.1081	−	24.4359i	−0.687585	−	1.19093i	−0.972617	−	0.232415i	$-0.925337\pi$
$421$	−14.1081	−	24.4359i	−0.687585	−	1.19093i	0.285031	−	0.958518i	$-0.407996\pi$
$422$	−0.253790	−	0.146525i	−0.0123543	−	0.00713275i
$423$	12.3811	+	27.2334i	0.601990	+	1.32413i
$424$	1.02812	+	1.78076i	0.0499300	+	0.0864813i
$425$	−20.7083			−1.00450
$426$	0.975768	−	1.51549i	0.0472761	−	0.0734257i
$427$		0			0
$428$	0.435382	+	0.251368i	0.0210450	+	0.0121503i
$429$	−14.6745	−	0.711543i	−0.708490	−	0.0343536i
$430$	0.444618	+	0.256700i	0.0214414	+	0.0123792i
$431$	−5.85836	+	3.38232i	−0.282187	+	0.162921i	−0.634413	−	0.772994i	$-0.718758\pi$
$431$	−5.85836	+	3.38232i	−0.282187	+	0.162921i	0.352226	+	0.935915i	$0.385425\pi$
$432$	−20.1048	−	2.94303i	−0.967295	−	0.141597i
$433$			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
$437$	−32.9248			−1.57501
$438$	−1.18783	−	0.0575961i	−0.0567567	−	0.00275205i
$439$			26.3512i			1.25767i	0.777537	+	0.628837i	$0.216469\pi$
$439$			26.3512i			1.25767i	−0.777537	+	0.628837i	$0.783531\pi$
$440$	1.08527			0.0517382
$441$		0			0
$442$	−1.08296			−0.0515110
$443$		−	5.49589i		−	0.261118i	−0.991441	−	0.130559i	$-0.958323\pi$
$443$		−	5.49589i		−	0.261118i	0.991441	−	0.130559i	$-0.0416772\pi$
$444$	−5.08432	−	9.88283i	−0.241291	−	0.469018i
$445$	6.81575			0.323097
$446$	−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	$0.0557412\pi$
$449$			7.38342i			0.348445i	−0.984706	+	0.174223i	$0.944259\pi$
$450$	0.167598	−	1.72416i	0.00790065	−	0.0812778i
$451$	−0.724568	+	0.418329i	−0.0341186	+	0.0196984i
$452$	8.50857	+	4.91242i	0.400209	+	0.231061i
$453$	−2.09392	−	4.07014i	−0.0983810	−	0.191232i
$454$	−0.301544	−	0.174097i	−0.0141522	−	0.00817076i
$455$		0			0
$456$	2.02693	+	3.93992i	0.0949196	+	0.184504i
$457$	41.4219			1.93763			0.968817	−	0.247779i	$-0.0797006\pi$
$457$	41.4219			1.93763			0.968817	+	0.247779i	$0.0797006\pi$
$458$	1.45128	+	2.51369i	0.0678139	+	0.117457i
$459$	8.41939	+	21.1872i	0.392984	+	0.988933i
$460$	5.71124	+	3.29739i	0.266288	+	0.153741i
$461$	5.44638	+	9.43341i	0.253663	+	0.439357i	0.964532	−	0.263968i	$-0.0850312\pi$
$461$	5.44638	+	9.43341i	0.253663	+	0.439357i	−0.710868	+	0.703325i	$0.751698\pi$
$462$		0			0
$463$	−2.87980	+	4.98796i	−0.133836	+	0.231810i	−0.925152	−	0.379597i	$-0.876063\pi$
$463$	−2.87980	+	4.98796i	−0.133836	+	0.231810i	0.791316	+	0.611407i	$0.209396\pi$
$464$	−28.4557	+	16.4289i	−1.32102	+	0.762692i
$465$	−0.0529254	+	1.09150i	−0.00245436	+	0.0506173i
$466$	1.14574	−	1.98448i	0.0530755	−	0.0919294i
$467$	11.9441	−	20.6878i	0.552707	−	0.957316i	−0.445371	−	0.895346i	$-0.646928\pi$
$467$	11.9441	−	20.6878i	0.552707	−	0.957316i	0.998078	−	0.0619701i	$-0.0197383\pi$
$468$	−1.16235	+	11.9576i	−0.0537295	+	0.552741i
$469$		0			0
$470$	−0.559372	+	0.322954i	−0.0258019	+	0.0148967i
$471$	19.0323	+	12.2542i	0.876961	+	0.564643i
$472$			6.55223i			0.301591i
$473$			33.3256i			1.53231i
$474$	0.102035	+	0.0656967i	0.00468662	+	0.00301755i
$475$	21.4459	−	12.3818i	0.984005	−	0.568116i
$476$		0			0
$477$	−10.2940	−	7.35675i	−0.471330	−	0.336842i
$478$	−0.787028	+	1.36317i	−0.0359978	+	0.0623500i
$479$	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	$0.152880\pi$
$480$	0.0645529	−	1.33130i	0.00294643	−	0.0607654i
$481$	−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
$485$	−0.261418	−	0.150930i	−0.0118704	−	0.00685337i
$486$	−1.83218	+	0.529521i	−0.0831092	+	0.0240196i
$487$	−14.1124	−	24.4434i	−0.639494	−	1.10764i	−0.985544	−	0.169420i	$-0.945811\pi$
$487$	−14.1124	−	24.4434i	−0.639494	−	1.10764i	0.346050	−	0.938216i	$-0.387523\pi$
$488$	−6.39331			−0.289412
$489$	13.4915	+	26.2245i	0.610105	+	1.18592i
$490$		0			0
$491$	−2.30250	−	1.32935i	−0.103910	−	0.0599927i	0.447144	−	0.894462i	$-0.352441\pi$
$491$	−2.30250	−	1.32935i	−0.103910	−	0.0599927i	−0.551055	+	0.834469i	$0.685774\pi$
$492$	0.312986	+	0.608379i	0.0141105	+	0.0274279i
$493$	31.9282	+	18.4338i	1.43797	+	0.830215i
$494$	1.12153	−	0.647517i	0.0504601	−	0.0291332i
$495$	−6.07919	+	2.76378i	−0.273239	+	0.124223i
$496$		−	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	$0.742647\pi$
$500$	−10.2148			−0.456819
$501$	−16.8939	−	32.8381i	−0.754763	−	1.46710i
$502$		−	0.918308i		−	0.0409861i
$503$	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
$506$		−	3.22791i		−	0.143498i
$507$	−15.4490	−	0.749101i	−0.686116	−	0.0332687i
$508$	−7.31377			−0.324496
$509$	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
$513$	−21.3874	−	16.9078i	−0.944278	−	0.746496i
$514$	−0.533921	+	0.308260i	−0.0235503	+	0.0135967i
$515$	2.93305	+	1.69340i	0.129245	+	0.0746199i
$516$	27.2196	+	1.31984i	1.19828	+	0.0581027i
$517$	−36.3096	−	20.9634i	−1.59690	−	0.921968i
$518$		0			0
$519$	19.2093	−	29.8345i	0.843196	−	1.30959i
$520$	−0.520742			−0.0228360
$521$	−9.03326	−	15.6461i	−0.395754	−	0.685466i	0.597443	−	0.801911i	$-0.296183\pi$
$521$	−9.03326	−	15.6461i	−0.395754	−	0.685466i	−0.993197	+	0.116445i	$0.962850\pi$
$522$	−1.79319	+	2.50914i	−0.0784859	+	0.109822i
$523$	18.3024	+	10.5669i	0.800308	+	0.462058i	0.843579	−	0.537005i	$-0.180445\pi$
$523$	18.3024	+	10.5669i	0.800308	+	0.462058i	−0.0432710	+	0.999063i	$0.513778\pi$
$524$	−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
$528$	25.3226	−	13.0275i	1.10203	−	0.566948i
$529$	8.18875	−	14.1833i	0.356033	−	0.616666i
$530$	0.136591	−	0.236582i	0.00593312	−	0.0102765i
$531$	−16.6861	−	36.7026i	−0.724115	−	1.59276i
$532$		0			0
$533$	0.347667	−	0.200725i	0.0150591	−	0.00869439i
$534$	−2.42584	+	1.24800i	−0.104976	+	0.0540060i
$535$		−	0.134085i		−	0.00579700i
$536$		−	3.20807i		−	0.138567i
$537$	1.20856	−	24.9246i	0.0521531	−	1.07558i
$538$	1.67164	−	0.965122i	0.0720695	−	0.0416093i
$539$		0			0
$540$	2.01664	+	5.07481i	0.0867822	+	0.218385i
$541$	−8.88661	+	15.3921i	−0.382065	+	0.661757i	−0.991357	−	0.131189i	$-0.958120\pi$
$541$	−8.88661	+	15.3921i	−0.382065	+	0.661757i	0.609292	+	0.792946i	$0.291454\pi$
$542$	1.02817	−	1.78084i	0.0441637	−	0.0764938i
$543$	−10.1549	−	6.53837i	−0.435788	−	0.280588i
$544$	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	0.992009	+	0.126166i	$0.0402673\pi$
$547$	14.1560	+	24.5190i	0.605268	+	1.04835i	−0.386741	+	0.922188i	$0.626399\pi$
$548$	2.77897	+	1.60444i	0.118712	+	0.0685383i
$549$	35.8124	−	16.2814i	1.52844	−	0.694873i
$550$	1.21390	+	2.10254i	0.0517608	+	0.0896524i
$551$	−44.0873			−1.87818
$552$	−5.29287	−	0.256643i	−0.225279	−	0.0109235i
$553$		0			0
$554$	−1.88823	−	1.09017i	−0.0802232	−	0.0463169i
$555$	−1.60470	+	2.49230i	−0.0681157	+	0.105792i
$556$	−19.4352	−	11.2209i	−0.824234	−	0.475872i
$557$	10.1510	−	5.86069i	0.430113	−	0.248326i	−0.269282	−	0.963061i	$-0.586786\pi$
$557$	10.1510	−	5.86069i	0.430113	−	0.248326i	0.699395	+	0.714736i	$0.253453\pi$
$558$	−0.181022	−	0.398175i	−0.00766329	−	0.0168561i
$559$		−	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
$563$	36.6029			1.54263			0.771314	−	0.636455i	$-0.219600\pi$
$563$	36.6029			1.54263			0.771314	+	0.636455i	$0.219600\pi$
$564$	−18.5605	+	28.8267i	−0.781536	+	1.21382i
$565$		−	2.62039i		−	0.110241i
$566$	2.64243			0.111070
$567$		0			0
$568$	4.14701			0.174005
$569$			37.6973i			1.58035i	0.612880	+	0.790176i	$0.290011\pi$
$569$			37.6973i			1.58035i	−0.612880	+	0.790176i	$0.709989\pi$
$570$	0.318666	−	0.494927i	0.0133474	−	0.0207302i
$571$	28.2246			1.18116			0.590581	−	0.806979i	$-0.298899\pi$
$571$	28.2246			1.18116			0.590581	+	0.806979i	$0.298899\pi$
$572$	−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
$576$	−9.48955	−	20.8731i	−0.395398	−	0.869714i
$577$	−8.12775	+	4.69256i	−0.338363	+	0.195354i	−0.659548	−	0.751663i	$-0.729252\pi$
$577$	−8.12775	+	4.69256i	−0.338363	+	0.195354i	0.321185	+	0.947016i	$0.395919\pi$
$578$	−0.238523	−	0.137711i	−0.00992123	−	0.00572802i
$579$	9.86832	−	15.3267i	0.410113	−	0.636957i
$580$	7.64754	+	4.41531i	0.317547	+	0.183336i
$581$		0			0
$582$	0.120679	+	0.00585155i	0.00500231	+	0.000242555i
$583$	17.7326			0.734409
$584$	−1.36806	−	2.36955i	−0.0566108	−	0.0980527i
$585$	2.91696	−	1.32614i	0.120601	−	0.0548290i
$586$	2.07617	+	1.19868i	0.0857657	+	0.0495169i
$587$	−23.1819	−	40.1523i	−0.956821	−	1.65726i	−0.730146	−	0.683291i	$-0.760548\pi$
$587$	−23.1819	−	40.1523i	−0.956821	−	1.65726i	−0.226675	−	0.973971i	$-0.572785\pi$
$588$		0			0
$589$	3.12633	−	5.41496i	0.128818	−	0.223120i
$590$	0.753870	−	0.435247i	0.0310363	−	0.0179188i
$591$	−22.5953	−	14.5483i	−0.929448	−	0.598438i
$592$	6.32025	−	10.9470i	0.259761	−	0.449919i
$593$	9.07080	−	15.7111i	0.372493	−	0.645177i	−0.617455	−	0.786606i	$-0.711836\pi$
$593$	9.07080	−	15.7111i	0.372493	−	0.645177i	0.989948	+	0.141429i	$0.0451697\pi$
$594$	1.65762	−	2.09680i	0.0680131	−	0.0860329i
$595$		0			0
$596$	−9.15945	+	5.28821i	−0.375186	+	0.216613i
$597$	1.05259	−	21.7081i	0.0430797	−	0.888452i
$598$			1.54884i			0.0633367i
$599$		−	6.96020i		−	0.284386i	−0.989839	−	0.142193i	$-0.954585\pi$
$599$		−	6.96020i		−	0.284386i	0.989839	−	0.142193i	$-0.0454154\pi$
$600$	3.54408	−	1.82328i	0.144686	−	0.0744353i
$601$	2.08865	−	1.20588i	0.0851976	−	0.0491889i	−0.456796	−	0.889572i	$-0.651003\pi$
$601$	2.08865	−	1.20588i	0.0851976	−	0.0491889i	0.541994	+	0.840383i	$0.317670\pi$
$602$		0			0
$603$	8.16976	+	17.9701i	0.332698	+	0.731800i
$604$	2.62285	−	4.54292i	0.106722	−	0.184849i
$605$	1.76770	−	3.06175i	0.0718673	−	0.124478i
$606$	−2.19167	+	1.12753i	−0.0890306	+	0.0458026i
$607$	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
$611$	17.4223	+	10.0588i	0.704832	+	0.406935i
$612$	−15.1923	+	21.2580i	−0.614113	+	0.859303i
$613$	5.16761	+	8.95057i	0.208718	+	0.361510i	0.951311	−	0.308233i	$-0.0997376\pi$
$613$	5.16761	+	8.95057i	0.208718	+	0.361510i	−0.742593	+	0.669743i	$0.766404\pi$
$614$	3.39722			0.137101
$615$	0.0987840	−	0.153424i	0.00398336	−	0.00618665i
$616$		0			0
$617$	−41.3741	−	23.8873i	−1.66566	−	0.961668i	−0.969937	−	0.243355i	$-0.921752\pi$
$617$	−41.3741	−	23.8873i	−1.66566	−	0.961668i	−0.695721	−	0.718313i	$-0.744915\pi$
$618$	−1.35399	−	0.0656529i	−0.0544654	−	0.00264095i
$619$	−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	$0.971745\pi$
$620$	−1.08461	+	0.626198i	−0.0435589	+	0.0251487i
$621$	30.3018	−	12.0414i	1.21597	−	0.483203i
$622$			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
$626$	2.25546			0.0901462
$627$	38.1648	+	1.85055i	1.52416	+	0.0739040i
$628$			25.9423i			1.03521i
$629$	−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	$0.426627\pi$
$632$			0.279210i			0.0111064i
$633$	1.89794	+	3.68919i	0.0754363	+	0.146632i
$634$	1.77991			0.0706891
$635$	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
$639$	−23.2296	+	10.5609i	−0.918950	+	0.417782i
$640$	1.76160	−	1.01706i	0.0696334	−	0.0402029i
$641$	30.5823	+	17.6567i	1.20793	+	0.697398i	0.962306	−	0.271968i	$-0.0876744\pi$
$641$	30.5823	+	17.6567i	1.20793	+	0.697398i	0.245622	+	0.969366i	$0.421008\pi$
$642$	0.0245516	+	0.0477231i	0.000968975	+	0.00188348i
$643$	6.09416	+	3.51846i	0.240330	+	0.138755i	0.615328	−	0.788271i	$-0.289023\pi$
$643$	6.09416	+	3.51846i	0.240330	+	0.138755i	−0.374998	+	0.927025i	$0.622357\pi$
$644$		0			0
$645$	−3.32503	−	6.46315i	−0.130923	−	0.254486i
$646$	2.81651			0.110814
$647$	7.49709	+	12.9853i	0.294741	+	0.510507i	0.974925	−	0.222535i	$-0.0714333\pi$
$647$	7.49709	+	12.9853i	0.294741	+	0.510507i	−0.680184	+	0.733042i	$0.738100\pi$
$648$	−3.30637	−	2.88474i	−0.129887	−	0.113323i
$649$	48.9347	+	28.2525i	1.92086	+	1.10901i
$650$	−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	−0.579109	−	0.815250i	$-0.696599\pi$
$653$	−4.15597	+	2.39945i	−0.162636	+	0.0938977i	0.416473	+	0.909148i	$0.363266\pi$
$654$	0.122869	−	2.53398i	0.00480456	−	0.0990865i
$655$	−1.44448	+	2.50191i	−0.0564405	+	0.0977577i
$656$	−0.389070	+	0.673889i	−0.0151906	+	0.0263109i
$657$	13.6976	+	9.78919i	0.534395	+	0.381913i
$658$		0			0
$659$	−13.4562	+	7.76893i	−0.524179	+	0.302635i	−0.738643	−	0.674097i	$-0.764533\pi$
$659$	−13.4562	+	7.76893i	−0.524179	+	0.302635i	0.214464	+	0.976732i	$0.431200\pi$
$660$	−6.43486	−	4.14317i	−0.250477	−	0.161273i
$661$		−	21.0307i		−	0.818001i	−0.912534	−	0.409000i	$-0.865877\pi$
$661$		−	21.0307i		−	0.818001i	0.912534	−	0.409000i	$-0.134123\pi$
$662$		−	3.63230i		−	0.141173i
$663$	12.8907	+	8.29986i	0.500634	+	0.322340i
$664$	−4.58280	+	2.64588i	−0.177847	+	0.102680i
$665$		0			0
$666$	0.114788	−	1.18088i	0.00444794	−	0.0457581i
$667$	26.3639	−	45.6636i	1.02081	−	1.76810i
$668$	21.1614	−	36.6526i	0.818758	−	1.41813i
$669$	−0.234596	+	4.83817i	−0.00906999	+	0.187054i
$670$	−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	0.995238	−	0.0974770i	$-0.0310772\pi$
$673$	10.7194	+	18.5665i	0.413201	+	0.715686i	−0.582036	+	0.813163i	$0.697744\pi$
$674$	−0.976056	−	0.563526i	−0.0375963	−	0.0217062i
$675$	−15.2091	+	19.2387i	−0.585397	+	0.740496i
$676$	−8.86315	−	15.3514i	−0.340891	−	0.590440i
$677$	−18.0630			−0.694217			−0.347109	−	0.937825i	$-0.612836\pi$
$677$	−18.0630			−0.694217			−0.347109	+	0.937825i	$0.612836\pi$
$678$	0.479806	+	0.932642i	0.0184269	+	0.0358179i
$679$		0			0
$680$	−0.980808	−	0.566270i	−0.0376123	−	0.0217155i
$681$	2.25507	+	4.38337i	0.0864143	+	0.167971i
$682$	0.530878	+	0.306503i	0.0203284	+	0.0117366i
$683$	39.4602	−	22.7824i	1.50990	−	0.871743i	0.509970	−	0.860192i	$-0.329657\pi$
$683$	39.4602	−	22.7824i	1.50990	−	0.871743i	0.999933	−	0.0115508i	$-0.00367681\pi$
$684$	3.02299	−	31.0989i	0.115587	−	1.18910i
$685$		−	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
$689$	−8.50857			−0.324151
$690$	0.322062	+	0.626021i	0.0122607	+	0.0238322i
$691$			3.85240i			0.146552i	0.997312	+	0.0732760i	$0.0233454\pi$
$691$			3.85240i			0.146552i	−0.997312	+	0.0732760i	$0.976655\pi$
$692$	40.6664			1.54590
$693$		0			0
$694$	2.22238			0.0843604
$695$			5.98547i			0.227042i
$696$	−7.08732	−	0.343654i	−0.268644	−	0.0130262i
$697$	0.873099			0.0330710
$698$	−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	$0.341488\pi$
$701$			46.5216i			1.75710i	−0.477653	+	0.878549i	$0.658512\pi$
$702$	−0.795371	+	1.00610i	−0.0300194	+	0.0379729i
$703$	14.6883	−	8.48028i	0.553979	−	0.319840i
$704$	27.8297	+	16.0675i	1.04887	+	0.605566i
$705$	9.13348	+	0.442869i	0.343987	+	0.0166794i
$706$	−2.21850	−	1.28085i	−0.0834944	−	0.0482055i
$707$		0			0
$708$	25.0141	−	38.8499i	0.940086	−	1.46007i
$709$	−29.2374			−1.09803			−0.549017	−	0.835811i	$-0.684998\pi$
$709$	−29.2374			−1.09803			−0.549017	+	0.835811i	$0.684998\pi$
$710$	−0.275474	−	0.477136i	−0.0103384	−	0.0179066i
$711$	−0.711045	−	1.56401i	−0.0266663	−	0.0586549i
$712$	−5.43565	−	3.13828i	−0.203710	−	0.117612i
$713$	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
$717$	19.8156	−	10.1943i	0.740028	−	0.380715i
$718$	−0.870265	+	1.50734i	−0.0324780	+	0.0562536i
$719$	−1.68561	+	2.91956i	−0.0628627	+	0.108881i	−0.895744	−	0.444570i	$-0.853356\pi$
$719$	−1.68561	+	2.91956i	−0.0628627	+	0.108881i	0.832881	+	0.553452i	$0.186690\pi$
$720$	−3.61126	+	5.05309i	−0.134584	+	0.188317i
$721$		0			0
$722$	−0.903723	+	0.521765i	−0.0336331	+	0.0194181i
$723$	−6.47501	+	3.33113i	−0.240808	+	0.123886i
$724$		−	13.8418i		−	0.514427i
$725$			39.6579i			1.47286i
$726$	−0.0685338	+	1.41340i	−0.00254353	+	0.0524563i
$727$	−4.34397	+	2.50799i	−0.161109	+	0.0930164i	−0.578387	−	0.815763i	$-0.696318\pi$
$727$	−4.34397	+	2.50799i	−0.161109	+	0.0930164i	0.417278	+	0.908779i	$0.362984\pi$
$728$		0			0
$729$	25.8671	+	7.73891i	0.958043	+	0.286626i
$730$	−0.181753	+	0.314806i	−0.00672698	+	0.0116515i
$731$	17.3885	−	30.1178i	0.643138	−	1.11395i
$732$	37.9077	+	24.4074i	1.40111	+	0.902123i
$733$	−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
$737$	−23.9592	−	13.8328i	−0.882547	−	0.509539i
$738$	−0.00706625	+	0.0726939i	−0.000260112	+	0.00267590i
$739$	1.19511	+	2.06999i	0.0439628	+	0.0761458i	0.887170	−	0.461444i	$-0.152668\pi$
$739$	1.19511	+	2.06999i	0.0439628	+	0.0761458i	−0.843207	+	0.537589i	$0.819335\pi$
$740$	−3.39717			−0.124883
$741$	−18.3125	−	0.887945i	−0.672726	−	0.0326195i
$742$		0			0
$743$	−36.1039	−	20.8446i	−1.32453	−	0.764715i	−0.340078	−	0.940397i	$-0.610454\pi$
$743$	−36.1039	−	20.8446i	−1.32453	−	0.764715i	−0.984447	+	0.175682i	$0.943787\pi$
$744$	0.544786	−	0.846120i	0.0199728	−	0.0310203i
$745$	2.44292	+	1.41042i	0.0895018	+	0.0516739i
$746$	−2.25805	+	1.30369i	−0.0826732	+	0.0477314i
$747$	18.9326	−	26.4917i	0.692709	−	0.969280i
$748$		−	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	$0.994247\pi$
$752$	−38.9942			−1.42197
$753$	−7.03798	+	10.9309i	−0.256478	+	0.398342i
$754$			2.07395i			0.0755287i
$755$	−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	$0.379371\pi$
$758$			1.29686i			0.0471041i
$759$	−24.7390	+	38.4227i	−0.897967	+	1.39465i
$760$	1.35433			0.0491266
$761$	−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
$765$	6.93612	+	0.674229i	0.250776	+	0.0243768i
$766$	−1.33962	+	0.773430i	−0.0484024	+	0.0279452i
$767$	−23.4802	−	13.5563i	−0.847821	−	0.489489i
$768$	13.8923	−	21.5764i	0.501294	−	0.778572i
$769$	18.8269	+	10.8697i	0.678914	+	0.391971i	0.799446	−	0.600738i	$-0.205127\pi$
$769$	18.8269	+	10.8697i	0.678914	+	0.391971i	−0.120532	+	0.992709i	$0.538460\pi$
$770$		0			0
$771$	8.71792	+	0.422719i	0.313968	+	0.0152239i
$772$	20.8914			0.751897
$773$	10.1606	+	17.5987i	0.365453	+	0.632982i	0.988849	−	0.148924i	$-0.0475809\pi$
$773$	10.1606	+	17.5987i	0.365453	+	0.632982i	−0.623396	+	0.781906i	$0.714248\pi$
$774$	2.36687	+	1.69152i	0.0850753	+	0.0608003i
$775$	−4.87093	−	2.81223i	−0.174969	−	0.101018i
$776$	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
$780$	3.08762	+	1.98800i	0.110554	+	0.0711820i
$781$	17.8814	−	30.9715i	0.639848	−	1.10825i
$782$	−1.68425	+	2.91721i	−0.0602288	+	0.104319i
$783$	40.5751	−	16.1238i	1.45003	−	0.576217i
$784$		0			0
$785$	5.99211	−	3.45955i	0.213868	−	0.123477i
$786$	0.0560024	−	1.15496i	0.00199754	−	0.0411961i
$787$		−	18.9446i		−	0.675303i	−0.941271	−	0.337652i	$-0.890367\pi$
$787$		−	18.9446i		−	0.675303i	0.941271	−	0.337652i	$-0.109633\pi$
$788$		−	30.7990i		−	1.09717i
$789$	−21.7850	+	11.2075i	−0.775566	+	0.398997i
$790$	0.0321246	−	0.0185472i	0.00114294	−	0.000659879i
$791$		0			0
$792$	6.12081	+	0.594977i	0.217493	+	0.0211416i
$793$	13.2275	−	22.9107i	0.469722	−	0.813583i
$794$	1.51635	−	2.62640i	0.0538133	−	0.0932074i
$795$	−3.43905	+	1.76925i	−0.121971	+	0.0627490i
$796$	21.5709	−	12.4540i	0.764560	−	0.441419i
$797$	11.4342	−	19.8047i	0.405022	−	0.701518i	−0.589302	−	0.807913i	$-0.700597\pi$
$797$	11.4342	−	19.8047i	0.405022	−	0.701518i	0.994324	+	0.106394i	$0.0339306\pi$
$798$		0			0
$799$	21.8764	+	37.8911i	0.773932	+	1.34049i
$800$	5.94106	+	3.43007i	0.210048	+	0.121271i
$801$	38.4401	+	3.73659i	1.35821	+	0.132026i
$802$	−0.225762	−	0.391032i	−0.00797194	−	0.0138078i
$803$	−23.5957			−0.832674
$804$	−12.2473	+	19.0215i	−0.431927	+	0.670837i
$805$		0			0
$806$	−0.254729	−	0.147068i	−0.00897246	−	0.00518025i
$807$	−27.2947	−	1.32348i	−0.960819	−	0.0465887i
$808$	−4.91095	−	2.83534i	−0.172767	−	0.0997469i
$809$	−10.3762	+	5.99072i	−0.364809	+	0.210622i	−0.671188	−	0.741287i	$-0.734216\pi$
$809$	−10.3762	+	5.99072i	−0.364809	+	0.210622i	0.306379	+	0.951909i	$0.400882\pi$
$810$	−0.112272	+	0.572042i	−0.00394484	+	0.0200995i
$811$			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
$815$	9.01455			0.315766
$816$	−29.6826	−	1.43927i	−1.03910	−	0.0503844i
$817$			41.5875i			1.45496i
$818$	−2.26790			−0.0792954
$819$		0			0
$820$	0.209127			0.00730304
$821$			37.7480i			1.31741i	0.752400	+	0.658707i	$0.228896\pi$
$821$			37.7480i			1.31741i	−0.752400	+	0.658707i	$0.771104\pi$
$822$	0.156709	+	0.304609i	0.00546586	+	0.0106245i
$823$	−21.0164			−0.732586			−0.366293	−	0.930499i	$-0.619373\pi$
$823$	−21.0164			−0.732586			−0.366293	+	0.930499i	$0.619373\pi$
$824$	−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	$0.136472\pi$
$827$			23.9104i			0.831447i	−0.909491	+	0.415724i	$0.863528\pi$
$828$	30.4031	+	21.7280i	1.05658	+	0.755099i
$829$	−21.7251	+	12.5430i	−0.754542	+	0.435635i	−0.827333	−	0.561712i	$-0.810143\pi$
$829$	−21.7251	+	12.5430i	−0.754542	+	0.435635i	0.0727906	+	0.997347i	$0.476810\pi$
$830$	0.608845	+	0.351517i	0.0211333	+	0.0122013i
$831$	14.1209	+	27.4481i	0.489850	+	0.952164i
$832$	−13.3534	−	7.70960i	−0.462946	−	0.267282i
$833$		0			0
$834$	−1.09597	−	2.13033i	−0.0379502	−	0.0737672i
$835$	−11.2879			−0.390635
$836$	21.8952	+	37.9237i	0.757263	+	1.31162i
$837$	−0.896887	+	6.12695i	−0.0310010	+	0.211778i
$838$	0.311489	+	0.179838i	0.0107602	+	0.00621242i
$839$	3.72840	+	6.45777i	0.128719	+	0.222947i	0.923180	−	0.384367i	$-0.125580\pi$
$839$	3.72840	+	6.45777i	0.128719	+	0.222947i	−0.794462	+	0.607314i	$0.792247\pi$
$840$		0			0
$841$	20.8021	−	36.0303i	0.717313	−	1.24242i
$842$	2.98960	−	1.72604i	0.103028	−	0.0594834i
$843$	0.735941	−	15.1776i	0.0253472	−	0.522746i
$844$	−2.37737	+	4.11772i	−0.0818323	+	0.141738i
$845$	−2.36390	+	4.09439i	−0.0813206	+	0.140851i
$846$	−3.33185	+	1.51476i	−0.114551	+	0.0520785i
$847$		0			0
$848$	14.2828	−	8.24615i	0.490472	−	0.283174i
$849$	−31.4535	−	20.2518i	−1.07948	−	0.695039i
$850$		−	2.53354i		−	0.0868998i
$851$			20.2846i			0.695346i
$852$	−24.5887	−	15.8318i	−0.842396	−	0.542388i
$853$	−2.19184	+	1.26546i	−0.0750472	+	0.0433285i	−0.537054	−	0.843548i	$-0.680463\pi$
$853$	−2.19184	+	1.26546i	−0.0750472	+	0.0433285i	0.462007	+	0.886876i	$0.347130\pi$
$854$		0			0
$855$	−7.58631	+	3.44897i	−0.259446	+	0.117952i
$856$	−0.0617388	+	0.106935i	−0.00211019	+	0.00365495i
$857$	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	$0.0612247\pi$
$858$	0.0870533	−	1.79534i	0.00297195	−	0.0612919i
$859$	−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
$863$	3.81858	+	2.20466i	0.129986	+	0.0750475i	0.563583	−	0.826059i	$-0.309422\pi$
$863$	3.81858	+	2.20466i	0.129986	+	0.0750475i	−0.433597	+	0.901107i	$0.642756\pi$
$864$	1.09393	−	7.47302i	0.0372163	−	0.254237i
$865$	−5.42309	−	9.39306i	−0.184390	−	0.319374i
$866$	−3.46816			−0.117853
$867$	1.78377	+	3.46726i	0.0605799	+	0.117754i
$868$		0			0
$869$	2.08526	+	1.20392i	0.0707375	+	0.0408403i
$870$	0.431252	+	0.838262i	0.0146208	+	0.0284198i
$871$	11.4962	+	6.63736i	0.389535	+	0.224898i
$872$	5.05493	−	2.91847i	0.171182	−	0.0988317i
$873$	−1.39163	−	0.994545i	−0.0470994	−	0.0336603i
$874$		−	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	$0.512236\pi$
$878$	−3.22392			−0.108802
$879$	−15.5264	−	30.1801i	−0.523693	−	1.01795i
$880$		−	8.70452i		−	0.293429i
$881$	−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	$0.584871\pi$
$884$			17.5709i			0.590974i
$885$	−12.3093	−	0.596858i	−0.413771	−	0.0200632i
$886$	0.672392			0.0225895
$887$	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
$891$	−35.8011	+	12.2546i	−1.19938	+	0.410546i
$892$	−4.80760	+	2.77567i	−0.160970	+	0.0929363i
$893$	−45.3113	−	26.1605i	−1.51629	−	0.875428i
$894$	−1.12773	−	0.0546821i	−0.0377170	−	0.00182884i
$895$	−6.60567	−	3.81379i	−0.220803	−	0.127481i
$896$		0			0
$897$	11.8704	−	18.4362i	0.396341	−	0.615567i
$898$	−0.903321			−0.0301442
$899$	5.00670	+	8.67186i	0.166983	+	0.289223i
$900$	−27.9744	−	2.71927i	−0.932481	−	0.0906424i
$901$	−16.0257	−	9.25246i	−0.533895	−	0.308244i
$902$	−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
$906$	0.497959	−	0.256180i	0.0165436	−	0.00851100i
$907$	−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	$0.905154\pi$
$908$	−2.82471	+	4.89254i	−0.0937412	+	0.162365i
$909$	34.7295	+	3.37590i	1.15190	+	0.111971i
$910$		0			0
$911$	22.3259	−	12.8899i	0.739691	−	0.427061i	−0.0822657	−	0.996610i	$-0.526216\pi$
$911$	22.3259	−	12.8899i	0.739691	−	0.427061i	0.821957	+	0.569549i	$0.192882\pi$
$912$	31.6005	−	16.2572i	1.04640	−	0.538329i
$913$			45.6349i			1.51030i
$914$			5.06774i			0.167626i
$915$	0.582382	−	12.0107i	0.0192529	−	0.397062i
$916$	40.7845	−	23.5470i	1.34756	−	0.778013i
$917$		0			0
$918$	−2.59213	+	1.03007i	−0.0855531	+	0.0339972i
$919$	−26.3551	+	45.6484i	−0.869375	+	1.50580i	−0.00673776	+	0.999977i	$0.502145\pi$
$919$	−26.3551	+	45.6484i	−0.869375	+	1.50580i	−0.862637	+	0.505824i	$0.831189\pi$
$920$	−0.809876	+	1.40275i	−0.0267008	+	0.0462472i
$921$	−40.4380	−	26.0365i	−1.33248	−	0.857933i
$922$	−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
$926$	−0.610249	−	0.352327i	−0.0200540	−	0.0115782i
$927$	15.6137	+	11.1585i	0.512821	+	0.366495i
$928$	−6.10666	−	10.5770i	−0.200461	−	0.347208i
$929$	−3.38018			−0.110900			−0.0554500	−	0.998461i	$-0.517659\pi$
$929$	−3.38018			−0.110900			−0.0554500	+	0.998461i	$0.517659\pi$
$930$	−0.133539	−	0.00647513i	−0.00437893	−	0.000212328i
$931$		0			0
$932$	−32.1981	−	18.5896i	−1.05468	−	0.608922i
$933$	18.7681	−	29.1492i	0.614441	−	0.954302i
$934$	2.53103	+	1.46129i	0.0828180	+	0.0478150i
$935$	−8.45827	+	4.88338i	−0.276615	+	0.159704i
$936$	−2.93693	−	0.285486i	−0.0959965	−	0.00933139i
$937$		−	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
$941$	−52.3763			−1.70742			−0.853710	−	0.520749i	$-0.825653\pi$
$941$	−52.3763			−1.70742			−0.853710	+	0.520749i	$0.825653\pi$
$942$	−1.49923	+	2.32849i	−0.0488476	+	0.0758664i
$943$		−	1.24870i		−	0.0406633i
$944$	52.5528			1.71045
$945$		0			0
$946$	−4.07720			−0.132561
$947$		−	7.54421i		−	0.245154i	−0.992459	−	0.122577i	$-0.960884\pi$
$947$		−	7.54421i		−	0.245154i	0.992459	−	0.122577i	$-0.0391158\pi$
$948$	1.06592	−	1.65551i	0.0346196	−	0.0537685i
$949$	11.3218			0.367523
$950$	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	$0.262056\pi$
$953$			45.2795i			1.46675i	−0.679825	+	0.733374i	$0.737944\pi$
$954$	0.900058	−	1.25941i	0.0291404	−	0.0407750i
$955$	−4.96769	+	2.86810i	−0.160751	+	0.0928095i
$956$	22.1174	+	12.7695i	0.715327	+	0.412994i
$957$	−33.1263	+	51.4492i	−1.07082	+	1.66312i
$958$	0.200812	+	0.115939i	0.00648795	+	0.00374582i
$959$		0			0
$960$	−7.00040	−	0.339439i	−0.225937	−	0.0109553i
$961$	29.5799			0.954189
$962$	−0.398927	−	0.690963i	−0.0128619	−	0.0222775i
$963$	0.0735093	−	0.756225i	0.00236880	−	0.0243690i
$964$	−7.22714	−	4.17259i	−0.232770	−	0.134390i
$965$	−2.78598	−	4.82546i	−0.0896838	−	0.155337i
$966$		0			0
$967$	−6.82403	+	11.8196i	−0.219446	+	0.380092i	−0.954639	−	0.297766i	$-0.903758\pi$
$967$	−6.82403	+	11.8196i	−0.219446	+	0.380092i	0.735193	+	0.677858i	$0.237092\pi$
$968$	−2.81954	+	1.62786i	−0.0906233	+	0.0523214i
$969$	−33.5257	−	21.5860i	−1.07700	−	0.693441i
$970$	0.0184654	−	0.0319831i	0.000592889	−	0.00102691i
$971$	1.73552	−	3.00601i	0.0556955	−	0.0964675i	−0.836833	−	0.547458i	$-0.815596\pi$
$971$	1.73552	−	3.00601i	0.0556955	−	0.0964675i	0.892529	+	0.450990i	$0.148929\pi$
$972$	8.59145	+	29.7270i	0.275571	+	0.953493i
$973$		0			0
$974$	2.99051	−	1.72657i	0.0958222	−	0.0553230i
$975$	−0.798734	+	16.4726i	−0.0255800	+	0.527547i
$976$			51.2782i			1.64138i
$977$			2.56232i			0.0819759i	0.999160	+	0.0409880i	$0.0130505\pi$
$977$			2.56232i			0.0819759i	−0.999160	+	0.0409880i	$0.986949\pi$
$978$	−3.20843	+	1.65061i	−0.102594	+	0.0527806i
$979$	−46.8759	+	27.0638i	−1.49816	+	0.864963i
$980$		0			0
$981$	−20.8832	+	29.2209i	−0.666748	+	0.932953i
$982$	0.162638	−	0.281698i	0.00519000	−	0.00898935i
$983$	−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	$0.952033\pi$
$984$	−0.149425	+	0.0768731i	−0.00476349	+	0.00245062i
$985$	−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
$989$	−43.0743	−	24.8690i	−1.36968	−	0.790788i
$990$	−0.338133	−	0.743755i	−0.0107466	−	0.0236381i
$991$	8.10333	+	14.0354i	0.257411	+	0.445848i	0.965547	−	0.260227i	$-0.0837974\pi$
$991$	8.10333	+	14.0354i	0.257411	+	0.445848i	−0.708137	+	0.706075i	$0.750464\pi$
$992$	1.73215			0.0549957
$993$	−27.8382	+	43.2361i	−0.883418	+	1.37206i
$994$		0			0
$995$	−5.75320	−	3.32161i	−0.182389	−	0.105302i
$996$	37.2736	+	1.80734i	1.18106	+	0.0572679i
$997$	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	$0.538057\pi$
$998$	−1.33044	+	0.768132i	−0.0421145	+	0.0243148i
$999$	−10.4167	+	13.1765i	−0.329569	+	0.416887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.14		48
3.2	odd	2		1323.2.i.d.1097.11		48
7.2	even	3		441.2.o.e.293.14	yes	48
7.3	odd	6		441.2.s.d.374.12		48
7.4	even	3		441.2.s.d.374.11		48
7.5	odd	6		441.2.o.e.293.13	yes	48
7.6	odd	2	inner	441.2.i.d.68.13		48
9.2	odd	6		441.2.s.d.362.12		48
9.7	even	3		1323.2.s.d.656.13		48
21.2	odd	6		1323.2.o.e.881.12		48
21.5	even	6		1323.2.o.e.881.11		48
21.11	odd	6		1323.2.s.d.962.14		48
21.17	even	6		1323.2.s.d.962.13		48
21.20	even	2		1323.2.i.d.1097.12		48
63.2	odd	6		441.2.o.e.146.13	✓	48
63.11	odd	6	inner	441.2.i.d.227.11		48
63.16	even	3		1323.2.o.e.440.11		48
63.20	even	6		441.2.s.d.362.11		48
63.25	even	3		1323.2.i.d.521.12		48
63.34	odd	6		1323.2.s.d.656.14		48
63.38	even	6	inner	441.2.i.d.227.12		48
63.47	even	6		441.2.o.e.146.14	yes	48
63.52	odd	6		1323.2.i.d.521.11		48
63.61	odd	6		1323.2.o.e.440.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.13		48	7.6	odd	2	inner
441.2.i.d.68.14		48	1.1	even	1	trivial
441.2.i.d.227.11		48	63.11	odd	6	inner
441.2.i.d.227.12		48	63.38	even	6	inner
441.2.o.e.146.13	✓	48	63.2	odd	6
441.2.o.e.146.14	yes	48	63.47	even	6
441.2.o.e.293.13	yes	48	7.5	odd	6
441.2.o.e.293.14	yes	48	7.2	even	3
441.2.s.d.362.11		48	63.20	even	6
441.2.s.d.362.12		48	9.2	odd	6
441.2.s.d.374.11		48	7.4	even	3
441.2.s.d.374.12		48	7.3	odd	6
1323.2.i.d.521.11		48	63.52	odd	6
1323.2.i.d.521.12		48	63.25	even	3
1323.2.i.d.1097.11		48	3.2	odd	2
1323.2.i.d.1097.12		48	21.20	even	2
1323.2.o.e.440.11		48	63.16	even	3
1323.2.o.e.440.12		48	63.61	odd	6
1323.2.o.e.881.11		48	21.5	even	6
1323.2.o.e.881.12		48	21.2	odd	6
1323.2.s.d.656.13		48	9.7	even	3
1323.2.s.d.656.14		48	63.34	odd	6
1323.2.s.d.962.13		48	21.17	even	6
1323.2.s.d.962.14		48	21.11	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.122344i q^{2} +(0.937657 - 1.45630i) q^{3} +1.98503 q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 + 0.114717i) q^{6} +0.487547i q^{8} +(-1.24160 - 2.73101i) q^{9} +O(q^{10})\)	\(q+0.122344i q^{2} +(0.937657 - 1.45630i) q^{3} +1.98503 q^{4} +(-0.264715 - 0.458500i) q^{5} +(0.178170 + 0.114717i) q^{6} +0.487547i q^{8} +(-1.24160 - 2.73101i) q^{9} +(0.0560949 - 0.0323864i) q^{10} +(3.64120 + 2.10225i) q^{11} +(1.86128 - 2.89080i) q^{12} +(-1.74714 - 1.00871i) q^{13} +(-0.915923 - 0.0444117i) q^{15} +3.91042 q^{16} +(-2.19381 - 3.79979i) q^{17} +(0.334124 - 0.151903i) q^{18} +(4.54391 + 2.62343i) q^{19} +(-0.525467 - 0.910136i) q^{20} +(-0.257198 + 0.445480i) q^{22} +(-5.43444 + 3.13757i) q^{23} +(0.710012 + 0.457151i) q^{24} +(2.35985 - 4.08738i) q^{25} +(0.123411 - 0.213753i) q^{26} +(-5.14136 - 0.752613i) q^{27} +(-7.27689 + 4.20131i) q^{29} +(0.00543353 - 0.112058i) q^{30} -1.19170i q^{31} +1.45351i q^{32} +(6.47569 - 3.33148i) q^{33} +(0.464883 - 0.268400i) q^{34} +(-2.46462 - 5.42115i) q^{36} +(1.61626 - 2.79945i) q^{37} +(-0.320962 + 0.555922i) q^{38} +(-3.10721 + 1.59853i) q^{39} +(0.223540 - 0.129061i) q^{40} +(-0.0994958 + 0.172332i) q^{41} +(3.96309 + 6.86427i) q^{43} +(7.22789 + 4.17303i) q^{44} +(-0.923498 + 1.29221i) q^{45} +(-0.383865 - 0.664873i) q^{46} -9.97189 q^{47} +(3.66663 - 5.69472i) q^{48} +(0.500069 + 0.288715i) q^{50} +(-7.59066 - 0.368060i) q^{51} +(-3.46814 - 2.00233i) q^{52} +(3.65249 - 2.10877i) q^{53} +(0.0920780 - 0.629017i) q^{54} -2.22598i q^{55} +(8.08111 - 4.15740i) q^{57} +(-0.514008 - 0.890287i) q^{58} +13.4392 q^{59} +(-1.81814 - 0.0881587i) q^{60} +13.1132i q^{61} +0.145798 q^{62} +7.64300 q^{64} +1.06809i q^{65} +(0.407588 + 0.792264i) q^{66} -6.58003 q^{67} +(-4.35478 - 7.54270i) q^{68} +(-0.526397 + 10.8561i) q^{69} -8.50587i q^{71} +(1.33150 - 0.605338i) q^{72} +(-4.86015 + 2.80601i) q^{73} +(0.342497 + 0.197741i) q^{74} +(-3.73971 - 7.26921i) q^{75} +(9.01980 + 5.20758i) q^{76} +(-0.195572 - 0.380150i) q^{78} +0.572684 q^{79} +(-1.03514 - 1.79292i) q^{80} +(-5.91686 + 6.78165i) q^{81} +(-0.0210838 - 0.0121728i) q^{82} +(5.42692 + 9.39971i) q^{83} +(-1.16147 + 2.01172i) q^{85} +(-0.839806 + 0.484862i) q^{86} +(-0.704863 + 14.5367i) q^{87} +(-1.02494 + 1.77525i) q^{88} +(-6.43688 + 11.1490i) q^{89} +(-0.158095 - 0.112985i) q^{90} +(-10.7875 + 6.22819i) q^{92} +(-1.73547 - 1.11740i) q^{93} -1.22001i q^{94} -2.77784i q^{95} +(2.11674 + 1.36289i) q^{96} +(0.493773 - 0.285080i) q^{97} +(1.22035 - 12.5543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^9	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more