LMFDB - Embedded newform 441.2.s.d.362.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (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			362.11
Character	$\chi$	$=$	441.362
Dual form			441.2.s.d.374.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.105953 + 0.0611722i) q^{2} +(-1.73002 + 0.0838860i) q^{3} +(-0.992516 + 1.71909i) q^{4} +0.529430 q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(2.98593 - 0.290249i) q^{9} +O(q^{10})$	\(q+(-0.105953 + 0.0611722i) q^{2} +(-1.73002 + 0.0838860i) q^{3} +(-0.992516 + 1.71909i) q^{4} +0.529430 q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(2.98593 - 0.290249i) q^{9} +(-0.0560949 + 0.0323864i) q^{10} +4.20449i q^{11} +(1.57286 - 3.05731i) q^{12} +(-1.74714 + 1.00871i) q^{13} +(-0.915923 + 0.0444117i) q^{15} +(-1.95521 - 3.38652i) q^{16} +(-2.19381 - 3.79979i) q^{17} +(-0.298614 + 0.213409i) q^{18} +(-4.54391 - 2.62343i) q^{19} +(-0.525467 + 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +6.27515i q^{23} +(0.0408983 + 0.843464i) q^{24} -4.71970 q^{25} +(0.123411 - 0.213753i) q^{26} +(-5.14136 + 0.752613i) q^{27} +(-7.27689 - 4.20131i) q^{29} +(0.0943284 - 0.0607346i) q^{30} +(-1.03204 - 0.595849i) q^{31} +(1.25878 + 0.726755i) q^{32} +(-0.352698 - 7.27385i) q^{33} +(0.464883 + 0.268400i) q^{34} +(-2.46462 + 5.42115i) q^{36} +(1.61626 - 2.79945i) q^{37} +0.641923 q^{38} +(2.93797 - 1.89165i) q^{39} -0.258122i q^{40} +(-0.0994958 - 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +(-7.22789 - 4.17303i) q^{44} +(1.58084 - 0.153666i) q^{45} +(-0.383865 - 0.664873i) q^{46} +(4.98595 + 8.63591i) q^{47} +(3.66663 + 5.69472i) q^{48} +(0.500069 - 0.288715i) q^{50} +(4.11408 + 6.38968i) q^{51} -4.00466i q^{52} +(-3.65249 + 2.10877i) q^{53} +(0.498706 - 0.394250i) q^{54} +2.22598i q^{55} +(8.08111 + 4.15740i) q^{57} +1.02802 q^{58} +(-6.71960 + 11.6387i) q^{59} +(0.832720 - 1.61863i) q^{60} +(-11.3564 + 6.55662i) q^{61} +0.145798 q^{62} +7.64300 q^{64} +(-0.924990 + 0.534043i) q^{65} +(0.482327 + 0.749114i) q^{66} +(3.29001 - 5.69847i) q^{67} +8.70956 q^{68} +(-0.526397 - 10.8561i) q^{69} +8.50587i q^{71} +(-0.141510 - 1.45578i) q^{72} +(4.86015 - 2.80601i) q^{73} +0.395481i q^{74} +(8.16517 - 0.395917i) q^{75} +(9.01980 - 5.20758i) q^{76} +(-0.195572 + 0.380150i) q^{78} +(-0.286342 - 0.495959i) q^{79} +(-1.03514 - 1.79292i) q^{80} +(8.83151 - 1.73332i) q^{81} +(0.0210838 + 0.0121728i) q^{82} +(5.42692 - 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +0.969724i q^{86} +(12.9416 + 6.65792i) q^{87} +2.04989 q^{88} +(-6.43688 + 11.1490i) q^{89} +(-0.158095 + 0.112985i) q^{90} +(-10.7875 - 6.22819i) q^{92} +(1.83543 + 0.944256i) q^{93} +(-1.05656 - 0.610003i) q^{94} +(-2.40568 - 1.38892i) q^{95} +(-2.23867 - 1.15171i) 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} - 8 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 8 * q^9	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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	$-0.680440\pi$
$2$	−0.105953	+	0.0611722i	−0.0749204	+	0.0432553i	0.462072	+	0.886842i	$0.347106\pi$
$3$	−1.73002	+	0.0838860i	−0.998827	+	0.0484316i
$3$	−1.73002	+	0.0838860i	−0.998827	+	0.0484316i
$4$	−0.992516	+	1.71909i	−0.496258	+	0.859544i
$5$	0.529430			0.236768			0.118384	−	0.992968i	$-0.462229\pi$
$5$	0.529430			0.236768			0.118384	+	0.992968i	$0.462229\pi$
$6$	0.178170	−	0.114717i	0.0727375	−	0.0468331i
$7$		0			0
$7$		0			0
$8$		−	0.487547i		−	0.172374i
$9$	2.98593	−	0.290249i	0.995309	−	0.0967496i
$10$	−0.0560949	+	0.0323864i	−0.0177388	+	0.0102415i
$11$			4.20449i			1.26770i	0.773455	+	0.633851i	$0.218527\pi$
$11$			4.20449i			1.26770i	−0.773455	+	0.633851i	$0.781473\pi$
$12$	1.57286	−	3.05731i	0.454046	−	0.882570i
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	−0.722319	−	0.691560i	$-0.756924\pi$
$13$	−1.74714	+	1.00871i	−0.484570	+	0.279767i	0.237749	+	0.971327i	$0.423590\pi$
$14$		0			0
$15$	−0.915923	+	0.0444117i	−0.236490	+	0.0114671i
$16$	−1.95521	−	3.38652i	−0.488802	−	0.846630i
$17$	−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	$-0.345255\pi$
$18$	−0.298614	+	0.213409i	−0.0703840	+	0.0503009i
$19$	−4.54391	−	2.62343i	−1.04244	−	0.601855i	−0.121919	−	0.992540i	$-0.538905\pi$
$19$	−4.54391	−	2.62343i	−1.04244	−	0.601855i	−0.920524	+	0.390685i	$0.872238\pi$
$20$	−0.525467	+	0.910136i	−0.117498	+	0.203513i
$21$		0			0
$22$	−0.257198	−	0.445480i	−0.0548348	−	0.0949767i
$23$			6.27515i			1.30846i	0.756296	+	0.654230i	$0.227007\pi$
$23$			6.27515i			1.30846i	−0.756296	+	0.654230i	$0.772993\pi$
$24$	0.0408983	+	0.843464i	0.00834834	+	0.172171i
$25$	−4.71970			−0.943941
$26$	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	−0.362855	−	0.931846i	$-0.618198\pi$
$29$	−7.27689	−	4.20131i	−1.35128	−	0.780164i	−0.988429	+	0.151681i	$0.951531\pi$
$30$	0.0943284	−	0.0607346i	0.0172219	−	0.0110886i
$31$	−1.03204	−	0.595849i	−0.185360	−	0.107018i	0.404449	−	0.914561i	$-0.367463\pi$
$31$	−1.03204	−	0.595849i	−0.185360	−	0.107018i	−0.589809	+	0.807543i	$0.700797\pi$
$32$	1.25878	+	0.726755i	0.222522	+	0.128473i
$33$	−0.352698	−	7.27385i	−0.0613969	−	1.26621i
$34$	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	$0.0810597\pi$
$38$	0.641923			0.104134
$39$	2.93797	−	1.89165i	0.470452	−	0.302907i
$40$		−	0.258122i		−	0.0408126i
$41$	−0.0994958	−	0.172332i	−0.0155386	−	0.0269137i	0.858152	−	0.513396i	$-0.171613\pi$
$41$	−0.0994958	−	0.172332i	−0.0155386	−	0.0269137i	−0.873690	+	0.486483i	$0.838280\pi$
$42$		0			0
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	−0.387786	−	0.921750i	$-0.626760\pi$
$43$	3.96309	−	6.86427i	0.604366	−	1.04679i	0.992151	−	0.125042i	$-0.0399067\pi$
$44$	−7.22789	−	4.17303i	−1.08965	−	0.629107i
$45$	1.58084	−	0.153666i	0.235657	−	0.0229072i
$46$	−0.383865	−	0.664873i	−0.0565978	−	0.0980302i
$47$	4.98595	+	8.63591i	0.727275	+	1.25968i	0.958031	+	0.286665i	$0.0925468\pi$
$47$	4.98595	+	8.63591i	0.727275	+	1.25968i	−0.230756	+	0.973012i	$0.574120\pi$
$48$	3.66663	+	5.69472i	0.529232	+	0.821963i
$49$		0			0
$50$	0.500069	−	0.288715i	0.0707204	−	0.0408304i
$51$	4.11408	+	6.38968i	0.576086	+	0.894734i
$52$		−	4.00466i		−	0.555346i
$53$	−3.65249	+	2.10877i	−0.501708	+	0.289661i	−0.729419	−	0.684068i	$-0.760209\pi$
$53$	−3.65249	+	2.10877i	−0.501708	+	0.289661i	0.227711	+	0.973729i	$0.426876\pi$
$54$	0.498706	−	0.394250i	0.0678652	−	0.0536507i
$55$			2.22598i			0.300152i
$56$		0			0
$57$	8.08111	+	4.15740i	1.07037	+	0.550662i
$58$	1.02802			0.134985
$59$	−6.71960	+	11.6387i	−0.874817	+	1.51523i	−0.0178590	+	0.999841i	$0.505685\pi$
$59$	−6.71960	+	11.6387i	−0.874817	+	1.51523i	−0.856958	+	0.515387i	$0.827648\pi$
$60$	0.832720	−	1.61863i	0.107504	−	0.208964i
$61$	−11.3564	+	6.55662i	−1.45404	+	0.839489i	−0.998707	−	0.0508335i	$-0.983812\pi$
$61$	−11.3564	+	6.55662i	−1.45404	+	0.839489i	−0.455330	+	0.890323i	$0.650479\pi$
$62$	0.145798			0.0185163
$63$		0			0
$64$	7.64300			0.955375
$65$	−0.924990	+	0.534043i	−0.114731	+	0.0662399i
$66$	0.482327	+	0.749114i	0.0593704	+	0.0922095i
$67$	3.29001	−	5.69847i	0.401939	−	0.696179i	−0.592021	−	0.805923i	$-0.701670\pi$
$67$	3.29001	−	5.69847i	0.401939	−	0.696179i	0.993960	+	0.109744i	$0.0350030\pi$
$68$	8.70956			1.05619
$69$	−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	$0.831592\pi$
$72$	−0.141510	−	1.45578i	−0.0166771	−	0.171565i
$73$	4.86015	−	2.80601i	0.568838	−	0.328419i	−0.187847	−	0.982198i	$-0.560151\pi$
$73$	4.86015	−	2.80601i	0.568838	−	0.328419i	0.756685	+	0.653780i	$0.226818\pi$
$74$			0.395481i			0.0459738i
$75$	8.16517	−	0.395917i	0.942833	−	0.0457166i
$76$	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	0.849468	−	0.527640i	$-0.176923\pi$
$79$	−0.286342	−	0.495959i	−0.0322160	−	0.0557997i	−0.881684	+	0.471841i	$0.843590\pi$
$80$	−1.03514	−	1.79292i	−0.115733	−	0.200455i
$81$	8.83151	−	1.73332i	0.981279	−	0.192591i
$82$	0.0210838	+	0.0121728i	0.00232832	+	0.00134426i
$83$	5.42692	−	9.39971i	0.595682	−	1.03175i	−0.397768	−	0.917486i	$-0.630215\pi$
$83$	5.42692	−	9.39971i	0.595682	−	1.03175i	0.993450	−	0.114266i	$-0.0364516\pi$
$84$		0			0
$85$	−1.16147	−	2.01172i	−0.125979	−	0.218202i
$86$			0.969724i			0.104568i
$87$	12.9416	+	6.65792i	1.38748	+	0.713804i
$88$	2.04989			0.218519
$89$	−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
$93$	1.83543	+	0.944256i	0.190326	+	0.0979148i
$94$	−1.05656	−	0.610003i	−0.108975	−	0.0629170i
$95$	−2.40568	−	1.38892i	−0.246817	−	0.142500i
$96$	−2.23867	−	1.15171i	−0.228484	−	0.117546i
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	0.524858	−	0.851190i	$-0.324118\pi$
$97$	0.493773	+	0.285080i	0.0501351	+	0.0289455i	−0.474723	+	0.880135i	$0.657452\pi$
$98$		0			0
$99$	1.22035	+	12.5543i	0.122650	+	1.26176i
$100$	4.68438	−	8.11359i	0.468438	−	0.811359i
$101$	11.6310			1.15733			0.578666	−	0.815564i	$-0.303573\pi$
$101$	11.6310			1.15733			0.578666	+	0.815564i	$0.303573\pi$
$102$	−0.826772	−	0.425340i	−0.0818626	−	0.0421150i
$103$			6.39705i			0.630320i	0.949038	+	0.315160i	$0.102058\pi$
$103$			6.39705i			0.630320i	−0.949038	+	0.315160i	$0.897942\pi$
$104$	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	0.489361	−	0.872081i	$-0.337230\pi$
$107$	−0.219332	−	0.126632i	−0.0212037	−	0.0122419i	−0.510564	+	0.859840i	$0.670563\pi$
$108$	3.80907	−	9.58543i	0.366528	−	0.922358i
$109$	−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	$-0.361026\pi$
$110$	−0.136168	−	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	$0.258544\pi$
$114$	−1.11054	+	0.0538484i	−0.104011	+	0.00504336i
$115$			3.32225i			0.309801i
$116$	14.4449	−	8.33974i	1.34117	−	0.774326i
$117$	−4.92406	+	3.51905i	−0.455230	+	0.325336i
$118$		−	1.64421i		−	0.151362i
$119$		0			0
$120$	0.0216528	+	0.446555i	0.00197662	+	0.0407647i
$121$	−6.67776			−0.607069
$122$	0.802166	−	1.38939i	0.0726247	−	0.125790i
$123$	0.186586	+	0.289791i	0.0168239	+	0.0261296i
$124$	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
$129$	−6.28040	+	12.2078i	−0.552959	+	1.07483i
$130$	0.0653372	−	0.113167i	0.00573045	−	0.00992543i
$131$	5.45673			0.476757			0.238379	−	0.971172i	$-0.423384\pi$
$131$	5.45673			0.476757			0.238379	+	0.971172i	$0.423384\pi$
$132$	12.8544	+	6.61309i	1.11884	+	0.575596i
$133$		0			0
$134$			0.805030i			0.0695440i
$135$	−2.72199	+	0.398456i	−0.234271	+	0.0342936i
$136$	−1.85257	+	1.06958i	−0.158857	+	0.0917161i
$137$			1.61654i			0.138110i	0.997613	+	0.0690551i	$0.0219984\pi$
$137$			1.61654i			0.138110i	−0.997613	+	0.0690551i	$0.978002\pi$
$138$	0.719867	+	1.11804i	0.0612791	+	0.0951741i
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	−0.854006	−	0.520262i	$-0.825834\pi$
$139$	−9.79085	+	5.65275i	−0.830449	+	0.479460i	0.0235572	+	0.999722i	$0.492501\pi$
$140$		0			0
$141$	−9.35021	−	14.5220i	−0.787430	−	1.22298i
$142$	−0.520323	−	0.901226i	−0.0436645	−	0.0756292i
$143$	−4.24113	−	7.34585i	−0.354661	−	0.614291i
$144$	−6.82104	−	9.54440i	−0.568420	−	0.795367i
$145$	−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
$149$			5.32808i			0.436494i	0.975894	+	0.218247i	$0.0700338\pi$
$149$			5.32808i			0.436494i	−0.975894	+	0.218247i	$0.929966\pi$
$150$	−0.840909	+	0.541431i	−0.0686599	+	0.0442076i
$151$	−2.64263			−0.215054			−0.107527	−	0.994202i	$-0.534293\pi$
$151$	−2.64263			−0.215054			−0.107527	+	0.994202i	$0.534293\pi$
$152$	−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
$156$	0.335935	+	6.92813i	0.0268963	+	0.554694i
$157$	11.3181	+	6.53448i	0.903279	+	0.521508i	0.878263	−	0.478179i	$-0.158703\pi$
$157$	11.3181	+	6.53448i	0.903279	+	0.521508i	0.0250163	+	0.999687i	$0.492036\pi$
$158$	0.0606778	+	0.0350324i	0.00482727	+	0.00278703i
$159$	6.14198	−	3.95460i	0.487091	−	0.313620i
$160$	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	$0.934319\pi$
$164$	0.395005			0.0308447
$165$	−0.186729	−	3.85099i	−0.0145368	−	0.299799i
$166$			1.32791i			0.103066i
$167$	10.6605	+	18.4645i	0.824932	+	1.42882i	0.901971	+	0.431796i	$0.142120\pi$
$167$	10.6605	+	18.4645i	0.824932	+	1.42882i	−0.0770396	+	0.997028i	$0.524547\pi$
$168$		0			0
$169$	−4.46499	+	7.73360i	−0.343461	+	0.594892i
$170$	0.246123	+	0.142099i	0.0188768	+	0.0108985i
$171$	−14.3292	−	6.51449i	−1.09578	−	0.498176i
$172$	7.86686	+	13.6258i	0.599842	+	1.03896i
$173$	−10.2433	−	17.7418i	−0.778781	−	1.34889i	−0.932645	−	0.360796i	$-0.882505\pi$
$173$	−10.2433	−	17.7418i	−0.778781	−	1.34889i	0.153864	−	0.988092i	$-0.450828\pi$
$174$	−1.77848	+	0.0862361i	−0.134827	+	0.00653754i
$175$		0			0
$176$	14.2386	−	8.22066i	1.07327	−	0.619655i
$177$	10.6487	−	20.6988i	0.800405	−	1.55582i
$178$		−	1.57503i		−	0.118054i
$179$	−12.4770	+	7.20357i	−0.932571	+	0.538420i	−0.887624	−	0.460569i	$-0.847645\pi$
$179$	−12.4770	+	7.20357i	−0.932571	+	0.538420i	−0.0449475	+	0.998989i	$0.514312\pi$
$180$	−1.30484	+	2.87012i	−0.0972571	+	0.213926i
$181$			6.97309i			0.518306i	0.965836	+	0.259153i	$0.0834434\pi$
$181$			6.97309i			0.518306i	−0.965836	+	0.259153i	$0.916557\pi$
$182$		0			0
$183$	19.0968	−	12.2957i	1.41167	−	0.908925i
$184$	3.05943			0.225544
$185$	0.855697	−	1.48211i	0.0629121	−	0.108967i
$186$	−0.252233	+	0.0122304i	−0.0184946	+	0.000896775i
$187$	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	$-0.538455\pi$
$191$	9.38310	−	5.41734i	0.678937	−	0.391985i	0.799455	+	0.600727i	$0.205122\pi$
$192$	−13.2225	+	0.641141i	−0.954254	+	0.0462704i
$193$	−5.26223	+	9.11444i	−0.378783	+	0.656072i	−0.990886	−	0.134707i	$-0.956991\pi$
$193$	−5.26223	+	9.11444i	−0.378783	+	0.656072i	0.612102	+	0.790779i	$0.290324\pi$
$194$	−0.0697560			−0.00500819
$195$	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	$0.813590\pi$
$198$	−0.897275	−	1.25552i	−0.0637666	−	0.0892259i
$199$	−10.8668	+	6.27394i	−0.770326	+	0.444748i	−0.832991	−	0.553287i	$-0.813373\pi$
$199$	−10.8668	+	6.27394i	−0.770326	+	0.444748i	0.0626651	+	0.998035i	$0.480040\pi$
$200$			2.30108i			0.162711i
$201$	−5.21376	+	10.1344i	−0.367750	+	0.714828i
$202$	−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
$206$	−0.391322	−	0.677790i	−0.0272647	−	0.0472238i
$207$	1.82135	+	18.7371i	0.126593	+	1.30232i
$208$	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	0.821852	−	0.569701i	$-0.192941\pi$
$211$	−1.19765	−	2.07438i	−0.0824494	−	0.142807i	−0.904302	+	0.426894i	$0.859608\pi$
$212$		−	8.37194i		−	0.574987i
$213$	−0.713523	−	14.7153i	−0.0488898	−	1.00828i
$214$	0.0309854			0.00211812
$215$	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
$219$	−8.17277	+	5.26215i	−0.552264	+	0.355583i
$220$	−3.82666	−	2.20932i	−0.257993	−	0.148953i
$221$	7.66580	+	4.42585i	0.515657	+	0.297715i
$222$	−0.0331754	−	0.684190i	−0.00222658	−	0.0459198i
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	0.416711	−	0.909039i	$-0.363183\pi$
$223$	−2.42193	−	1.39830i	−0.162184	−	0.0936370i	−0.578895	+	0.815402i	$0.696516\pi$
$224$		0			0
$225$	−14.0927	+	1.36989i	−0.939513	+	0.0913259i
$226$	−0.302770	+	0.524413i	−0.0201400	+	0.0348834i
$227$	2.84601			0.188896			0.0944480	−	0.995530i	$-0.469891\pi$
$227$	2.84601			0.188896			0.0944480	+	0.995530i	$0.469891\pi$
$228$	−15.1676	+	9.76585i	−1.00450	+	0.646759i
$229$		−	23.7245i		−	1.56776i	−0.620912	−	0.783880i	$-0.713238\pi$
$229$		−	23.7245i		−	1.56776i	0.620912	−	0.783880i	$-0.286762\pi$
$230$	−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	0.926161	−	0.377129i	$-0.123089\pi$
$233$	16.2205	+	9.36488i	1.06264	+	0.613514i	0.136477	+	0.990643i	$0.456422\pi$
$234$	0.306453	−	0.674071i	0.0200335	−	0.0440654i
$235$	2.63971	+	4.57211i	0.172196	+	0.298251i
$236$	−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	$0.196727\pi$
$240$	1.94122	+	3.01496i	0.125305	+	0.194615i
$241$		−	4.20405i		−	0.270807i	−0.990791	−	0.135403i	$-0.956767\pi$
$241$		−	4.20405i		−	0.270807i	0.990791	−	0.135403i	$-0.0432331\pi$
$242$	0.707531	−	0.408493i	0.0454818	−	0.0262590i
$243$	−15.1333	+	3.73952i	−0.970800	+	0.239890i
$244$		−	26.0302i		−	1.66641i
$245$		0			0
$246$	−0.0374965	−	0.0192905i	−0.00239069	−	0.00122991i
$247$	10.5851			0.673516
$248$	−0.290504	+	0.503168i	−0.0184470	+	0.0319512i
$249$	−8.60017	+	16.7169i	−0.545014	+	1.05939i
$250$	0.545226	−	0.314786i	0.0344831	−	0.0199088i
$251$	−7.50592			−0.473770			−0.236885	−	0.971538i	$-0.576126\pi$
$251$	−7.50592			−0.473770			−0.236885	+	0.971538i	$0.576126\pi$
$252$		0			0
$253$	−26.3838			−1.65874
$254$	0.390381	−	0.225387i	0.0244947	−	0.0141420i
$255$	2.17812	+	3.38288i	0.136399	+	0.211844i
$256$	−7.40797	+	12.8310i	−0.462998	+	0.801936i
$257$	−5.03921			−0.314337			−0.157169	−	0.987572i	$-0.550237\pi$
$257$	−5.03921			−0.314337			−0.157169	+	0.987572i	$0.550237\pi$
$258$	−0.0813463	−	1.67764i	−0.00506440	−	0.104445i
$259$		0			0
$260$		−	2.12018i		−	0.131488i
$261$	−22.9477	−	10.4327i	−1.42043	−	0.645768i
$262$	−0.578160	+	0.333801i	−0.0357188	+	0.0206223i
$263$		−	14.1444i		−	0.872182i	−0.899903	−	0.436091i	$-0.856363\pi$
$263$		−	14.1444i		−	0.872182i	0.899903	−	0.436091i	$-0.143637\pi$
$264$	−3.54634	+	0.171957i	−0.218262	+	0.0105832i
$265$	−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
$269$	−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	$0.993050\pi$
$270$	0.264030	−	0.208728i	0.0160683	−	0.0127028i
$271$	14.5560	+	8.40390i	0.884213	+	0.510501i	0.872045	−	0.489425i	$-0.162793\pi$
$271$	14.5560	+	8.40390i	0.884213	+	0.510501i	0.0121677	+	0.999926i	$0.496127\pi$
$272$	−8.57871	+	14.8588i	−0.520160	+	0.900944i
$273$		0			0
$274$	−0.0988873	−	0.171278i	−0.00597400	−	0.0103473i
$275$		−	19.8440i		−	1.19664i
$276$	19.1851	+	9.86995i	1.15481	+	0.594101i
$277$	17.8213			1.07078			0.535390	−	0.844605i	$-0.320165\pi$
$277$	17.8213			1.07078			0.535390	+	0.844605i	$0.320165\pi$
$278$	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	0.709199	−	0.705008i	$-0.249057\pi$
$281$	7.59774	+	4.38656i	0.453243	+	0.261680i	−0.255956	+	0.966688i	$0.582390\pi$
$282$	1.87903	+	0.966686i	0.111895	+	0.0575653i
$283$	−18.7047	−	10.7991i	−1.11188	−	0.641942i	−0.172562	−	0.984999i	$-0.555204\pi$
$283$	−18.7047	−	10.7991i	−1.11188	−	0.641942i	−0.939315	+	0.343056i	$0.888538\pi$
$284$	−14.6223	−	8.44221i	−0.867676	−	0.500953i
$285$	4.27838	+	2.20105i	0.253429	+	0.130379i
$286$	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
$290$	0.544262			0.0319601
$291$	−0.878151	−	0.451773i	−0.0514781	−	0.0264834i
$292$			11.1400i			0.651921i
$293$	9.79756	+	16.9699i	0.572379	+	0.991390i	0.996321	+	0.0857006i	$0.0273128\pi$
$293$	9.79756	+	16.9699i	0.572379	+	0.991390i	−0.423942	+	0.905690i	$0.639354\pi$
$294$		0			0
$295$	−3.55755	+	6.16186i	−0.207129	+	0.358758i
$296$	−1.36486	−	0.788003i	−0.0793309	−	0.0458017i
$297$	−3.16436	−	21.6168i	−0.183615	−	1.25433i
$298$	−0.325931	−	0.564529i	−0.0188807	−	0.0327023i
$299$	−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
$303$	−20.1219	+	0.975682i	−1.15597	+	0.0560515i
$304$			20.5174i			1.17675i
$305$	−6.01241	+	3.47127i	−0.344270	+	0.198764i
$306$	1.46601	+	0.666492i	0.0838062	+	0.0381008i
$307$			27.7677i			1.58478i	0.610012	+	0.792392i	$0.291165\pi$
$307$			27.7677i			1.58478i	−0.610012	+	0.792392i	$0.708835\pi$
$308$		0			0
$309$	−0.536623	−	11.0670i	−0.0305274	−	0.629581i
$310$	0.0771896			0.00438407
$311$	−10.0080	+	17.3344i	−0.567501	+	0.982941i	0.429311	+	0.903157i	$0.358756\pi$
$311$	−10.0080	+	17.3344i	−0.567501	+	0.982941i	−0.996812	+	0.0797841i	$0.974577\pi$
$312$	−0.922269	−	1.43240i	−0.0522132	−	0.0810936i
$313$	15.9654	−	9.21765i	0.902420	−	0.521012i	0.0244352	−	0.999701i	$-0.492221\pi$
$313$	15.9654	−	9.21765i	0.902420	−	0.521012i	0.877984	+	0.478689i	$0.158888\pi$
$314$	−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	$-0.532699\pi$
$317$	12.5992	−	7.27416i	0.707642	−	0.408558i	0.810187	+	0.586171i	$0.199365\pi$
$318$	−0.408852	+	0.794722i	−0.0229273	+	0.0445658i
$319$	17.6644	−	30.5956i	0.989016	−	1.71303i
$320$	4.04643			0.226202
$321$	0.390072	+	0.200676i	0.0217717	+	0.0112006i
$322$		0			0
$323$			23.0212i			1.28093i
$324$	−5.78568	+	16.9025i	−0.321427	+	0.939028i
$325$	8.24600	−	4.76083i	0.457406	−	0.264083i
$326$		−	2.08315i		−	0.115375i
$327$	11.2257	+	17.4349i	0.620781	+	0.964150i
$328$	−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	0.908658	+	0.417541i	$0.137108\pi$
$331$	14.8446	+	25.7115i	0.815930	+	1.41323i	−0.0927274	+	0.995692i	$0.529559\pi$
$332$	10.7726	+	18.6587i	0.591224	+	1.02403i
$333$	4.01350	−	8.82806i	0.219939	−	0.483775i
$334$	−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	0.712868	−	0.701298i	$-0.247396\pi$
$337$	−4.60606	−	7.97793i	−0.250908	−	0.434586i	−0.963776	+	0.266713i	$0.914063\pi$
$338$		−	1.09253i		−	0.0594260i
$339$	−7.20789	+	4.64090i	−0.391479	+	0.252059i
$340$	4.61110			0.250072
$341$	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
$345$	−0.278690	−	5.74755i	−0.0150042	−	0.309438i
$346$	2.17062	+	1.25321i	0.116693	+	0.0673728i
$347$	−15.7313	−	9.08247i	−0.844501	−	0.487573i	0.0142910	−	0.999898i	$-0.495451\pi$
$347$	−15.7313	−	9.08247i	−0.844501	−	0.487573i	−0.858791	+	0.512325i	$0.828784\pi$
$348$	−24.2903	+	15.6396i	−1.30210	+	0.838372i
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	0.339478	−	0.940614i	$-0.389750\pi$
$349$	−5.70494	−	3.29375i	−0.305378	−	0.176310i	−0.644856	+	0.764304i	$0.723083\pi$
$350$		0			0
$351$	8.22352	−	6.50108i	0.438939	−	0.347002i
$352$	−3.05564	+	5.29252i	−0.162866	+	0.282092i
$353$	20.9385			1.11444			0.557221	−	0.830364i	$-0.311868\pi$
$353$	20.9385			1.11444			0.557221	+	0.830364i	$0.311868\pi$
$354$	0.137926	+	2.84451i	0.00733070	+	0.151184i
$355$			4.50326i			0.239008i
$356$	−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	0.138302	−	0.990390i	$-0.455836\pi$
$359$	−12.3205	−	7.11324i	−0.650251	−	0.375422i	−0.788552	+	0.614968i	$0.789169\pi$
$360$	−0.0749195	−	0.770732i	−0.00394860	−	0.0406212i
$361$	4.26472	+	7.38671i	0.224459	+	0.388774i
$362$	−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
$366$	−1.27121	+	2.47096i	−0.0664473	+	0.129159i
$367$		−	12.3827i		−	0.646373i	−0.946335	−	0.323186i	$-0.895246\pi$
$367$		−	12.3827i		−	0.646373i	0.946335	−	0.323186i	$-0.104754\pi$
$368$	21.2509	−	12.2692i	1.10778	−	0.639577i
$369$	−0.347106	−	0.485691i	−0.0180696	−	0.0252841i
$370$			0.209380i			0.0108851i
$371$		0			0
$372$	−3.44496	+	2.21808i	−0.178613	+	0.115002i
$373$	−21.3117			−1.10348			−0.551740	−	0.834016i	$-0.686036\pi$
$373$	−21.3117			−1.10348			−0.551740	+	0.834016i	$0.686036\pi$
$374$	−1.12849	+	1.95460i	−0.0583527	+	0.101070i
$375$	8.90250	−	0.431669i	0.459723	−	0.0222913i
$376$	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
$381$	6.37419	−	0.309075i	0.326559	−	0.0158344i
$382$	−0.662781	+	1.14797i	−0.0339108	+	0.0587353i
$383$	−12.6435			−0.646052			−0.323026	−	0.946390i	$-0.604700\pi$
$383$	−12.6435			−0.646052			−0.323026	+	0.946390i	$0.604700\pi$
$384$	5.59524	−	3.60257i	0.285531	−	0.183843i
$385$		0			0
$386$		−	1.28761i		−	0.0655375i
$387$	9.84115	−	21.6465i	0.500254	−	1.10035i
$388$	−0.980156	+	0.565893i	−0.0497599	+	0.0287289i
$389$		−	13.2257i		−	0.670571i	−0.942117	−	0.335286i	$-0.891167\pi$
$389$		−	13.2257i		−	0.670571i	0.942117	−	0.335286i	$-0.108833\pi$
$390$	−0.103541	+	0.201262i	−0.00524302	+	0.0101913i
$391$	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
$395$	−0.151598	−	0.262575i	−0.00762772	−	0.0132116i
$396$	−22.7932	−	10.3625i	−1.14540	−	0.520733i
$397$	21.4672	+	12.3941i	1.07741	+	0.622043i	0.930197	−	0.367062i	$-0.119636\pi$
$397$	21.4672	+	12.3941i	1.07741	+	0.622043i	0.147214	+	0.989105i	$0.452970\pi$
$398$	0.767582	−	1.32949i	0.0384754	−	0.0666413i
$399$		0			0
$400$	9.22800	+	15.9834i	0.461400	+	0.799168i
$401$			3.69060i			0.184300i	0.995745	+	0.0921499i	$0.0293739\pi$
$401$			3.69060i			0.184300i	−0.995745	+	0.0921499i	$0.970626\pi$
$402$	−0.0675307	−	1.39272i	−0.00336813	−	0.0694624i
$403$	2.40416			0.119760
$404$	−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
$408$	3.11526	−	2.00581i	0.154229	−	0.0993022i
$409$	16.0535	+	9.26852i	0.793797	+	0.458299i	0.841297	−	0.540573i	$-0.181792\pi$
$409$	16.0535	+	9.26852i	0.793797	+	0.458299i	−0.0475008	+	0.998871i	$0.515126\pi$
$410$	0.0111624	+	0.00644462i	0.000551272	+	0.000318277i
$411$	−0.135605	−	2.79664i	−0.00668890	−	0.137948i
$412$	−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
$416$	−2.93235			−0.143770
$417$	16.4642	−	10.6007i	0.806254	−	0.519117i
$418$			2.69896i			0.132011i
$419$	1.46994	+	2.54600i	0.0718111	+	0.124380i	0.899695	−	0.436519i	$-0.143789\pi$
$419$	1.46994	+	2.54600i	0.0718111	+	0.124380i	−0.827884	+	0.560899i	$0.810455\pi$
$420$		0			0
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	0.285031	+	0.958518i	$0.407996\pi$
$421$	−14.1081	+	24.4359i	−0.687585	+	1.19093i	−0.972617	+	0.232415i	$0.925337\pi$
$422$	0.253790	+	0.146525i	0.0123543	+	0.00713275i
$423$	17.3942	+	24.3390i	0.845736	+	1.18340i
$424$	1.02812	+	1.78076i	0.0499300	+	0.0864813i
$425$	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
$429$	7.95345	+	12.3527i	0.383996	+	0.596393i
$430$			0.513401i			0.0247584i
$431$	5.85836	−	3.38232i	0.282187	−	0.162921i	−0.352226	−	0.935915i	$-0.614575\pi$
$431$	5.85836	−	3.38232i	0.282187	−	0.162921i	0.634413	+	0.772994i	$0.281242\pi$
$432$	12.6012	+	15.9398i	0.606274	+	0.766904i
$433$		−	28.3475i		−	1.36229i	−0.732146	−	0.681147i	$-0.761481\pi$
$433$		−	28.3475i		−	1.36229i	0.732146	−	0.681147i	$-0.238519\pi$
$434$		0			0
$435$	6.85166	+	3.52490i	0.328512	+	0.169006i
$436$	23.7649			1.13813
$437$	16.4624	−	28.5137i	0.787503	−	1.36399i
$438$	0.544035	−	1.05749i	0.0259950	−	0.0505288i
$439$	−22.8208	+	13.1756i	−1.08918	+	0.628837i	−0.933358	−	0.358948i	$-0.883136\pi$
$439$	−22.8208	+	13.1756i	−1.08918	+	0.628837i	−0.155821	+	0.987785i	$0.549802\pi$
$440$	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	$-0.624989\pi$
$443$	4.75958	−	2.74795i	0.226135	−	0.130559i	0.608788	+	0.793333i	$0.291656\pi$
$444$	−6.01663	−	9.34456i	−0.285536	−	0.443473i
$445$	−3.40787	+	5.90261i	−0.161549	+	0.279810i
$446$	0.342148			0.0162012
$447$	−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	$-0.0557412\pi$
$450$	1.40937	−	1.00723i	0.0664383	−	0.0474811i
$451$	0.724568	−	0.418329i	0.0341186	−	0.0196984i
$452$			9.82485i			0.462122i
$453$	4.57180	−	0.221680i	0.214802	−	0.0104154i
$454$	−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	−0.698991	−	0.715130i	$-0.746367\pi$
$457$	−20.7109	−	35.8724i	−0.968817	−	1.67804i	−0.269826	−	0.962909i	$-0.586966\pi$
$458$	1.45128	+	2.51369i	0.0678139	+	0.117457i
$459$	14.1389	+	17.8850i	0.659949	+	0.834800i
$460$	−5.71124	−	3.29739i	−0.266288	−	0.153741i
$461$	5.44638	−	9.43341i	0.253663	−	0.439357i	−0.710868	−	0.703325i	$-0.751698\pi$
$461$	5.44638	−	9.43341i	0.253663	−	0.439357i	0.964532	+	0.263968i	$0.0850312\pi$
$462$		0			0
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	0.791316	−	0.611407i	$-0.209396\pi$
$463$	−2.87980	−	4.98796i	−0.133836	−	0.231810i	−0.925152	+	0.379597i	$0.876063\pi$
$464$			32.8578i			1.52538i
$465$	0.971733	+	0.499917i	0.0450630	+	0.0231831i
$466$	−2.29148			−0.106151
$467$	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
$471$	−20.1286	−	10.3553i	−0.927476	−	0.477149i
$472$	5.67440	+	3.27612i	0.261185	+	0.150795i
$473$	28.8608	+	16.6628i	1.32702	+	0.766156i
$474$	−0.107912	−	0.0555166i	−0.00495658	−	0.00254996i
$475$	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
$479$	−1.89529			−0.0865980			−0.0432990	−	0.999062i	$-0.513787\pi$
$479$	−1.89529			−0.0865980			−0.0432990	+	0.999062i	$0.513787\pi$
$480$	−1.18522	−	0.609747i	−0.0540976	−	0.0278310i
$481$			6.52138i			0.297349i
$482$	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
$486$	1.37467	−	1.32195i	0.0623562	−	0.0599649i
$487$	−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	$-0.387523\pi$
$488$	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	$0.352441\pi$
$492$	−0.683365	+	0.0331354i	−0.0308085	+	0.00149386i
$493$			36.8675i			1.66043i
$494$	−1.12153	+	0.647517i	−0.0504601	+	0.0291332i
$495$	0.646089	+	6.64662i	0.0290395	+	0.298743i
$496$			4.66003i			0.209242i
$497$		0			0
$498$	−0.111393	−	2.29731i	−0.00499164	−	0.102945i
$499$	−12.5569			−0.562123			−0.281062	−	0.959690i	$-0.590687\pi$
$499$	−12.5569			−0.562123			−0.281062	+	0.959690i	$0.590687\pi$
$500$	5.10739	−	8.84625i	0.228409	−	0.395617i
$501$	−19.9917	−	31.0496i	−0.893164	−	1.38719i
$502$	0.795278	−	0.459154i	0.0354950	−	0.0204930i
$503$	18.1502			0.809278			0.404639	−	0.914476i	$-0.367397\pi$
$503$	18.1502			0.809278			0.404639	+	0.914476i	$0.367397\pi$
$504$		0			0
$505$	6.15782			0.274020
$506$	2.79546	−	1.61396i	0.124273	−	0.0717491i
$507$	7.07578	−	13.7538i	0.314246	−	0.610828i
$508$	3.65689	−	6.33391i	0.162248	−	0.281022i
$509$	−18.6765			−0.827823			−0.413912	−	0.910317i	$-0.635838\pi$
$509$	−18.6765			−0.827823			−0.413912	+	0.910317i	$0.635838\pi$
$510$	−0.437717	−	0.225188i	−0.0193825	−	0.00997149i
$511$		0			0
$512$		−	9.49685i		−	0.419705i
$513$	25.3363	+	10.0682i	1.11862	+	0.444521i
$514$	0.533921	−	0.308260i	0.0235503	−	0.0135967i
$515$			3.38679i			0.149240i
$516$	−14.7528	−	22.9130i	−0.649457	−	1.00869i
$517$	−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
$521$	−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	$0.962850\pi$
$522$	3.06958	−	0.298380i	0.134352	−	0.0130597i
$523$	−18.3024	−	10.5669i	−0.800308	−	0.462058i	0.0432710	−	0.999063i	$-0.486222\pi$
$523$	−18.3024	−	10.5669i	−0.800308	−	0.462058i	−0.843579	+	0.537005i	$0.819555\pi$
$524$	−5.41590	+	9.38061i	−0.236595	+	0.409794i
$525$		0			0
$526$	0.865245	+	1.49865i	0.0377265	+	0.0653442i
$527$			5.22872i			0.227766i
$528$	−23.9434	+	15.4163i	−1.04200	+	0.670908i
$529$	−16.3775			−0.712065
$530$	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
$534$	0.132123	+	2.72483i	0.00571753	+	0.117915i
$535$	−0.116121	−	0.0670425i	−0.00502035	−	0.00289850i
$536$	−2.77827	−	1.60403i	−0.120003	−	0.0692837i
$537$	20.9811	−	13.5090i	0.905400	−	0.582954i
$538$	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	$0.291454\pi$
$542$	−2.05634			−0.0883274
$543$	−0.584945	−	12.0636i	−0.0251024	−	0.517698i
$544$		−	6.37745i		−	0.273431i
$545$	−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	$-0.0402673\pi$
$548$	−2.77897	−	1.60444i	−0.118712	−	0.0685383i
$549$	−32.0063	+	22.8738i	−1.36600	+	0.976228i
$550$	1.21390	+	2.10254i	0.0517608	+	0.0896524i
$551$	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
$555$	−1.35604	+	2.63586i	−0.0575608	+	0.111886i
$556$		−	22.4418i		−	0.951744i
$557$	−10.1510	+	5.86069i	−0.430113	+	0.248326i	−0.699395	−	0.714736i	$-0.746547\pi$
$557$	−10.1510	+	5.86069i	−0.430113	+	0.248326i	0.269282	+	0.963061i	$0.413214\pi$
$558$	0.435341	−	0.0423176i	0.0184295	−	0.00179145i
$559$			15.9905i			0.676326i
$560$		0			0
$561$	−26.8653	+	17.2976i	−1.13426	+	0.730306i
$562$	−1.07334			−0.0452762
$563$	−18.3014	+	31.6990i	−0.771314	+	1.33595i	0.165529	+	0.986205i	$0.447067\pi$
$563$	−18.3014	+	31.6990i	−0.771314	+	1.33595i	−0.936843	+	0.349750i	$0.886267\pi$
$564$	34.2449	−	1.66048i	1.44197	−	0.0699190i
$565$	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	$-0.956677\pi$
$569$	−32.6468	+	18.8486i	−1.36862	+	0.790176i	−0.377872	+	0.925858i	$0.623344\pi$
$570$	−0.587952	+	0.0285089i	−0.0246266	+	0.00119411i
$571$	−14.1123	+	24.4432i	−0.590581	+	1.02292i	0.403574	+	0.914947i	$0.367768\pi$
$571$	−14.1123	+	24.4432i	−0.590581	+	1.02292i	−0.994154	+	0.107968i	$0.965565\pi$
$572$	16.8376			0.704013
$573$	−15.7785	+	10.1592i	−0.659156	+	0.424407i
$574$		0			0
$575$		−	29.6168i		−	1.23511i
$576$	22.8214	−	2.21837i	0.950893	−	0.0924321i
$577$	8.12775	−	4.69256i	0.338363	−	0.195354i	−0.321185	−	0.947016i	$-0.604081\pi$
$577$	8.12775	−	4.69256i	0.338363	−	0.195354i	0.659548	+	0.751663i	$0.270748\pi$
$578$		−	0.275422i		−	0.0114560i
$579$	8.33917	−	16.2096i	0.346564	−	0.673647i
$580$	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
$584$	−1.36806	−	2.36955i	−0.0566108	−	0.0980527i
$585$	−2.60695	+	1.86309i	−0.107784	+	0.0770293i
$586$	−2.07617	−	1.19868i	−0.0857657	−	0.0495169i
$587$	−23.1819	+	40.1523i	−0.956821	+	1.65726i	−0.226675	+	0.973971i	$0.572785\pi$
$587$	−23.1819	+	40.1523i	−0.956821	+	1.65726i	−0.730146	+	0.683291i	$0.760548\pi$
$588$		0			0
$589$	3.12633	+	5.41496i	0.128818	+	0.223120i
$590$		−	0.870494i		−	0.0358377i
$591$	−1.30154	−	26.8423i	−0.0535383	−	1.10414i
$592$	−12.6405			−0.519522
$593$	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
$597$	18.2734	−	11.7656i	0.747882	−	0.481534i
$598$	1.34133	+	0.774419i	0.0548512	+	0.0316684i
$599$	−6.02771	−	3.48010i	−0.246286	−	0.142193i	0.371777	−	0.928322i	$-0.378749\pi$
$599$	−6.02771	−	3.48010i	−0.246286	−	0.142193i	−0.618062	+	0.786129i	$0.712082\pi$
$600$	−0.193028	−	3.98090i	−0.00788034	−	0.162520i
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	0.541994	−	0.840383i	$-0.317670\pi$
$601$	2.08865	+	1.20588i	0.0851976	+	0.0491889i	−0.456796	+	0.889572i	$0.651003\pi$
$602$		0			0
$603$	8.16976	−	17.9701i	0.332698	−	0.731800i
$604$	2.62285	−	4.54292i	0.106722	−	0.184849i
$605$	−3.53540			−0.143735
$606$	2.07230	−	1.33428i	0.0841815	−	0.0542014i
$607$		−	12.7370i		−	0.516979i	−0.966014	−	0.258489i	$-0.916775\pi$
$607$		−	12.7370i		−	0.516979i	0.966014	−	0.258489i	$-0.0832247\pi$
$608$	−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
$612$	26.0061	−	2.52794i	1.05123	−	0.102186i
$613$	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	$0.766404\pi$
$614$	−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	$0.921752\pi$
$618$	0.733851	+	1.13976i	0.0295198	+	0.0458480i
$619$		−	40.7177i		−	1.63658i	−0.574804	−	0.818291i	$-0.694922\pi$
$619$		−	40.7177i		−	1.63658i	0.574804	−	0.818291i	$-0.305078\pi$
$620$	1.08461	−	0.626198i	0.0435589	−	0.0251487i
$621$	−4.72276	−	32.2628i	−0.189518	−	1.29466i
$622$		−	2.44884i		−	0.0981897i
$623$		0			0
$624$	−12.1505	−	6.25092i	−0.486408	−	0.250237i
$625$	20.8741			0.834965
$626$	−1.12773	+	1.95328i	−0.0450731	+	0.0780689i
$627$	−17.4798	+	33.9770i	−0.698075	+	1.35691i
$628$	−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
$633$	2.24596	+	3.48826i	0.0892690	+	0.138646i
$634$	−0.889953	+	1.54144i	−0.0353446	+	0.0612186i
$635$	−1.95066			−0.0774097
$636$	0.702288	+	14.4836i	0.0278475	+	0.574312i
$637$		0			0
$638$			4.32228i			0.171121i
$639$	2.46882	+	25.3979i	0.0976649	+	1.00473i
$640$	−1.76160	+	1.01706i	−0.0696334	+	0.0402029i
$641$			35.3134i			1.39480i	0.716684	+	0.697398i	$0.245659\pi$
$641$			35.3134i			1.39480i	−0.716684	+	0.697398i	$0.754341\pi$
$642$	−0.0536052	+	0.00259924i	−0.00211563	+	0.000102584i
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	−0.374998	−	0.927025i	$-0.622357\pi$
$643$	6.09416	−	3.51846i	0.240330	−	0.138755i	0.615328	+	0.788271i	$0.289023\pi$
$644$		0			0
$645$	−3.32503	+	6.46315i	−0.130923	+	0.254486i
$646$	−1.40826	−	2.43917i	−0.0554071	−	0.0959680i
$647$	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	$0.738100\pi$
$648$	−0.845075	−	4.30577i	−0.0331977	−	0.169147i
$649$	−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
$653$			4.79890i			0.187795i	0.995582	+	0.0938977i	$0.0299327\pi$
$653$			4.79890i			0.187795i	−0.995582	+	0.0938977i	$0.970067\pi$
$654$	−2.25593	−	1.16058i	−0.0882137	−	0.0453824i
$655$	2.88896			0.112881
$656$	−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	0.214464	−	0.976732i	$-0.431200\pi$
$659$	−13.4562	−	7.76893i	−0.524179	−	0.302635i	−0.738643	+	0.674097i	$0.764533\pi$
$660$	6.80552	+	3.50117i	0.264905	+	0.136283i
$661$	−18.2131	−	10.5154i	−0.708409	−	0.409000i	0.102062	−	0.994778i	$-0.467456\pi$
$661$	−18.2131	−	10.5154i	−0.708409	−	0.409000i	−0.810472	+	0.585778i	$0.800789\pi$
$662$	−3.14566	−	1.81615i	−0.122260	−	0.0705866i
$663$	−13.6332	−	7.01375i	−0.529471	−	0.272391i
$664$	−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
$668$	−42.3227			−1.63752
$669$	4.30727	+	2.21592i	0.166529	+	0.0856723i
$670$			0.426207i			0.0164658i
$671$	−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	$0.0310772\pi$
$674$	0.976056	+	0.563526i	0.0375963	+	0.0217062i
$675$	24.2657	−	3.55211i	0.933987	−	0.136721i
$676$	−8.86315	−	15.3514i	−0.340891	−	0.590440i
$677$	9.03150	+	15.6430i	0.347109	+	0.601210i	0.985735	−	0.168308i	$-0.0538302\pi$
$677$	9.03150	+	15.6430i	0.347109	+	0.601210i	−0.638626	+	0.769517i	$0.720497\pi$
$678$	0.479806	−	0.932642i	0.0184269	−	0.0358179i
$679$		0			0
$680$	−0.980808	+	0.566270i	−0.0376123	+	0.0217155i
$681$	−4.92364	+	0.238740i	−0.188674	+	0.00914854i
$682$			0.613005i			0.0234732i
$683$	−39.4602	+	22.7824i	−1.50990	+	0.871743i	−0.509970	+	0.860192i	$0.670343\pi$
$683$	−39.4602	+	22.7824i	−1.50990	+	0.871743i	−0.999933	+	0.0115508i	$0.996323\pi$
$684$	25.4210	−	18.1674i	0.971995	−	0.694650i
$685$			0.855844i			0.0327001i
$686$		0			0
$687$	1.99015	+	41.0438i	0.0759291	+	1.56592i
$688$	−30.9947			−1.18166
$689$	4.25428	−	7.36863i	0.162075	−	0.280723i
$690$	0.381119	+	0.591925i	0.0145089	+	0.0225342i
$691$	−3.33627	+	1.92620i	−0.126918	+	0.0732760i	−0.562115	−	0.827059i	$-0.690012\pi$
$691$	−3.33627	+	1.92620i	−0.126918	+	0.0732760i	0.435197	+	0.900335i	$0.356679\pi$
$692$	40.6664			1.54590
$693$		0			0
$694$	2.22238			0.0843604
$695$	−5.18357	+	2.99273i	−0.196624	+	0.113521i
$696$	3.24605	−	6.30962i	0.123041	−	0.239166i
$697$	−0.436550	+	0.756126i	−0.0165355	+	0.0286403i
$698$	0.805943			0.0305054
$699$	−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	$-0.341488\pi$
$702$	−0.473624	+	1.19186i	−0.0178758	+	0.0449840i
$703$	−14.6883	+	8.48028i	−0.553979	+	0.319840i
$704$			32.1349i			1.21113i
$705$	−4.95028	−	7.68840i	−0.186438	−	0.289562i
$706$	−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	0.998342	+	0.0575566i	$0.0183310\pi$
$709$	14.6187	+	25.3203i	0.549017	+	0.950925i	−0.449326	+	0.893368i	$0.648336\pi$
$710$	−0.275474	−	0.477136i	−0.0103384	−	0.0179066i
$711$	−0.998948	−	1.39779i	−0.0374635	−	0.0524211i
$712$	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
$716$		−	28.5986i		−	1.06878i
$717$	−18.7364	+	12.0637i	−0.699723	+	0.450526i
$718$	1.74053			0.0649560
$719$	−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
$723$	0.352661	+	7.27309i	0.0131156	+	0.270489i
$724$	−11.9874	−	6.92091i	−0.445507	−	0.257214i
$725$	34.3448	+	19.8290i	1.27553	+	0.736429i
$726$	−1.18978	+	0.766053i	−0.0441567	+	0.0284309i
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	0.417278	−	0.908779i	$-0.362984\pi$
$727$	−4.34397	−	2.50799i	−0.161109	−	0.0930164i	−0.578387	+	0.815763i	$0.696318\pi$
$728$		0			0
$729$	25.8671	−	7.73891i	0.958043	−	0.286626i
$730$	−0.181753	+	0.314806i	−0.00672698	+	0.0116515i
$731$	−34.7771			−1.28628
$732$	2.18357	+	45.0327i	0.0807070	+	1.66446i
$733$			22.7332i			0.839670i	0.907601	+	0.419835i	$0.137912\pi$
$733$			22.7332i			0.839670i	−0.907601	+	0.419835i	$0.862088\pi$
$734$	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
$738$	0.0664879	+	0.0302274i	0.00244745	+	0.00111269i
$739$	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	$0.819335\pi$
$740$	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	$0.610454\pi$
$744$	0.460369	−	0.894859i	0.0168779	−	0.0328071i
$745$			2.82085i			0.103348i
$746$	2.25805	−	1.30369i	0.0826732	−	0.0477314i
$747$	13.4761	−	29.6420i	0.493066	−	1.08454i
$748$			36.6193i			1.33893i
$749$		0			0
$750$	−0.916844	+	0.590323i	−0.0334784	+	0.0215555i
$751$	26.5421			0.968534			0.484267	−	0.874920i	$-0.339086\pi$
$751$	26.5421			0.968534			0.484267	+	0.874920i	$0.339086\pi$
$752$	19.4971	−	33.7700i	0.710987	−	1.23147i
$753$	12.9854	−	0.629642i	0.473214	−	0.0229454i
$754$	−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
$759$	45.6445	−	2.21323i	1.65679	−	0.0803353i
$760$	−0.677163	+	1.17288i	−0.0245633	+	0.0425448i
$761$	25.9156			0.939439			0.469720	−	0.882816i	$-0.344355\pi$
$761$	25.9156			0.939439			0.469720	+	0.882816i	$0.344355\pi$
$762$	−0.656460	+	0.422671i	−0.0237810	+	0.0153117i
$763$		0			0
$764$			21.5072i			0.778102i
$765$	−4.05196	−	5.66974i	−0.146499	−	0.204990i
$766$	1.33962	−	0.773430i	0.0484024	−	0.0279452i
$767$		−	27.1126i		−	0.978979i
$768$	11.7396	−	22.8193i	0.423616	−	0.823419i
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	−0.120532	−	0.992709i	$-0.538460\pi$
$769$	18.8269	−	10.8697i	0.678914	−	0.391971i	0.799446	+	0.600738i	$0.205127\pi$
$770$		0			0
$771$	8.71792	−	0.422719i	0.313968	−	0.0152239i
$772$	−10.4457	−	18.0925i	−0.375948	−	0.651162i
$773$	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	$0.714248\pi$
$774$	0.281461	+	2.89553i	0.0101169	+	0.104078i
$775$	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
$779$			1.04408i			0.0374080i
$780$	0.177854	+	3.66796i	0.00636819	+	0.131334i
$781$	−35.7629			−1.27970
$782$	−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
$786$	0.972226	−	0.625981i	0.0346781	−	0.0223280i
$787$	−16.4065	−	9.47232i	−0.584830	−	0.337652i	0.178221	−	0.983991i	$-0.442966\pi$
$787$	−16.4065	−	9.47232i	−0.584830	−	0.337652i	−0.763051	+	0.646339i	$0.776299\pi$
$788$	−26.6727	−	15.3995i	−0.950176	−	0.548584i
$789$	1.18652	+	24.4701i	0.0422412	+	0.871158i
$790$	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
$794$	−3.03270			−0.107627
$795$	3.25175	−	2.09368i	0.115328	−	0.0742552i
$796$		−	24.9079i		−	0.882838i
$797$	11.4342	+	19.8047i	0.405022	+	0.701518i	0.994324	−	0.106394i	$-0.0339306\pi$
$797$	11.4342	+	19.8047i	0.405022	+	0.701518i	−0.589302	+	0.807913i	$0.700597\pi$
$798$		0			0
$799$	21.8764	−	37.8911i	0.773932	−	1.34049i
$800$	−5.94106	−	3.43007i	−0.210048	−	0.121271i
$801$	−15.9841	+	35.1584i	−0.564769	+	1.24226i
$802$	−0.225762	−	0.391032i	−0.00797194	−	0.0138078i
$803$	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
$807$	14.7935	+	22.9762i	0.520757	+	0.808799i
$808$		−	5.67068i		−	0.199494i
$809$	10.3762	−	5.99072i	0.364809	−	0.210622i	−0.306379	−	0.951909i	$-0.599118\pi$
$809$	10.3762	−	5.99072i	0.364809	−	0.210622i	0.671188	+	0.741287i	$0.265784\pi$
$810$	−0.439267	+	0.383251i	−0.0154343	+	0.0134661i
$811$		−	36.9371i		−	1.29704i	−0.761199	−	0.648519i	$-0.775389\pi$
$811$		−	36.9371i		−	1.29704i	0.761199	−	0.648519i	$-0.224611\pi$
$812$		0			0
$813$	−25.8871	−	13.3179i	−0.907900	−	0.467078i
$814$	−1.66280			−0.0582811
$815$	−4.50728	+	7.80683i	−0.157883	+	0.273461i
$816$	13.5949	−	26.4256i	0.475916	−	0.925079i
$817$	−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	$-0.895563\pi$
$821$	−32.6907	+	18.8740i	−1.14091	+	0.658707i	−0.194257	+	0.980951i	$0.562229\pi$
$822$	0.185445	+	0.288019i	0.00646813	+	0.0100458i
$823$	10.5082	−	18.2008i	0.366293	−	0.634438i	−0.622690	−	0.782469i	$-0.713960\pi$
$823$	10.5082	−	18.2008i	0.366293	−	0.634438i	0.988983	+	0.148031i	$0.0472934\pi$
$824$	3.11886			0.108651
$825$	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	$-0.136472\pi$
$828$	−34.0185	−	15.4658i	−1.18222	−	0.537475i
$829$	21.7251	−	12.5430i	0.754542	−	0.435635i	−0.0727906	−	0.997347i	$-0.523190\pi$
$829$	21.7251	−	12.5430i	0.754542	−	0.435635i	0.827333	+	0.561712i	$0.189857\pi$
$830$			0.703034i			0.0244027i
$831$	−30.8312	+	1.49496i	−1.06952	+	0.0518596i
$832$	−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
$836$	21.8952	+	37.9237i	0.757263	+	1.31162i
$837$	5.75454	+	2.28675i	0.198906	+	0.0790415i
$838$	−0.311489	−	0.179838i	−0.0107602	−	0.00621242i
$839$	3.72840	−	6.45777i	0.128719	−	0.222947i	−0.794462	−	0.607314i	$-0.792247\pi$
$839$	3.72840	−	6.45777i	0.128719	−	0.222947i	0.923180	+	0.384367i	$0.125580\pi$
$840$		0			0
$841$	20.8021	+	36.0303i	0.717313	+	1.24242i
$842$		−	3.45209i		−	0.118967i
$843$	−13.5122	−	6.95148i	−0.465385	−	0.239422i
$844$	4.75473			0.163665
$845$	−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
$849$	33.2653	+	17.1137i	1.14166	+	0.587339i
$850$	−2.19411	−	1.26677i	−0.0752574	−	0.0434499i
$851$	17.5670	+	10.1423i	0.602187	+	0.347673i
$852$	26.0051	+	13.3786i	0.890920	+	0.458342i
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	0.462007	−	0.886876i	$-0.347130\pi$
$853$	−2.19184	−	1.26546i	−0.0750472	−	0.0433285i	−0.537054	+	0.843548i	$0.680463\pi$
$854$		0			0
$855$	−7.58631	−	3.44897i	−0.259446	−	0.117952i
$856$	−0.0617388	+	0.106935i	−0.00211019	+	0.00365495i
$857$	−19.0420			−0.650461			−0.325231	−	0.945635i	$-0.605442\pi$
$857$	−19.0420			−0.650461			−0.325231	+	0.945635i	$0.605442\pi$
$858$	−1.59834	−	0.822279i	−0.0545663	−	0.0280721i
$859$			10.2585i			0.350017i	0.984567	+	0.175008i	$0.0559952\pi$
$859$			10.2585i			0.350017i	−0.984567	+	0.175008i	$0.944005\pi$
$860$	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	0.433597	−	0.901107i	$-0.357244\pi$
$863$	−3.81858	−	2.20466i	−0.129986	−	0.0750475i	−0.563583	+	0.826059i	$0.690578\pi$
$864$	−7.01879	−	2.78914i	−0.238784	−	0.0948884i
$865$	−5.42309	−	9.39306i	−0.184390	−	0.319374i
$866$	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
$870$	−0.941583	+	0.0456559i	−0.0319226	+	0.00154788i
$871$			13.2747i			0.449797i
$872$	−5.05493	+	2.91847i	−0.171182	+	0.0988317i
$873$	1.55711	+	0.707911i	0.0527004	+	0.0239592i
$874$			4.02816i			0.136255i
$875$		0			0
$876$	−0.934493	−	19.2725i	−0.0315736	−	0.651156i
$877$	−50.1173			−1.69234			−0.846170	−	0.532913i	$-0.821097\pi$
$877$	−50.1173			−1.69234			−0.846170	+	0.532913i	$0.821097\pi$
$878$	1.61196	−	2.79200i	0.0544011	−	0.0942255i
$879$	−18.3735	−	28.5363i	−0.619722	−	0.962505i
$880$	7.53833	−	4.35226i	0.254117	−	0.146715i
$881$	−42.5809			−1.43459			−0.717294	−	0.696771i	$-0.754619\pi$
$881$	−42.5809			−1.43459			−0.717294	+	0.696771i	$0.754619\pi$
$882$		0			0
$883$	−15.6590			−0.526967			−0.263483	−	0.964664i	$-0.584871\pi$
$883$	−15.6590			−0.526967			−0.263483	+	0.964664i	$0.584871\pi$
$884$	−15.2169	+	8.78546i	−0.511798	+	0.295487i
$885$	5.63774	−	10.9586i	0.189510	−	0.368368i
$886$	−0.336196	+	0.582309i	−0.0112947	+	0.0195630i
$887$	−24.7838			−0.832159			−0.416080	−	0.909328i	$-0.636596\pi$
$887$	−24.7838			−0.832159			−0.416080	+	0.909328i	$0.636596\pi$
$888$	2.42734	+	1.24877i	0.0814561	+	0.0419059i
$889$		0			0
$890$		−	0.833869i		−	0.0279513i
$891$	7.28774	+	37.1320i	0.244149	+	1.24397i
$892$	4.80760	−	2.77567i	0.160970	−	0.0929363i
$893$		−	52.3210i		−	1.75086i
$894$	0.611222	+	0.949304i	0.0204423	+	0.0317495i
$895$	−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
$899$	5.00670	+	8.67186i	0.166983	+	0.289223i
$900$	11.6323	−	25.5862i	0.387742	−	0.852874i
$901$	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
$905$			3.69176i			0.122718i
$906$	−0.470837	+	0.303155i	−0.0156425	+	0.0100717i
$907$	44.1033			1.46443			0.732213	−	0.681076i	$-0.238487\pi$
$907$	44.1033			1.46443			0.732213	+	0.681076i	$0.238487\pi$
$908$	−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	0.821957	−	0.569549i	$-0.192882\pi$
$911$	22.3259	+	12.8899i	0.739691	+	0.427061i	−0.0822657	+	0.996610i	$0.526216\pi$
$912$	−1.72112	−	35.4954i	−0.0569920	−	1.17537i
$913$	39.5210	+	22.8175i	1.30795	+	0.755148i
$914$	4.38879	+	2.53387i	0.145168	+	0.0838129i
$915$	10.1104	−	6.50972i	0.334239	−	0.215205i
$916$	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	$0.831189\pi$
$920$	1.61975			0.0534016
$921$	−2.32932	−	48.0386i	−0.0767536	−	1.58292i
$922$			1.33267i			0.0438891i
$923$	−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
$927$	1.85674	+	19.1011i	0.0609832	+	0.627363i
$928$	−6.10666	−	10.5770i	−0.200461	−	0.347208i
$929$	1.69009	+	2.92732i	0.0554500	+	0.0960422i	0.892418	−	0.451210i	$-0.149007\pi$
$929$	1.69009	+	2.92732i	0.0554500	+	0.0960422i	−0.836968	+	0.547252i	$0.815674\pi$
$930$	−0.133539	+	0.00647513i	−0.00437893	+	0.000212328i
$931$		0			0
$932$	−32.1981	+	18.5896i	−1.05468	+	0.608922i
$933$	15.8599	−	30.8283i	0.519230	−	1.00927i
$934$			2.92259i			0.0956300i
$935$	8.45827	−	4.88338i	0.276615	−	0.159704i
$936$	1.71570	+	2.40071i	0.0560794	+	0.0784697i
$937$			8.26186i			0.269903i	0.990852	+	0.134952i	$0.0430879\pi$
$937$			8.26186i			0.269903i	−0.990852	+	0.134952i	$0.956912\pi$
$938$		0			0
$939$	−26.8473	+	17.2860i	−0.876127	+	0.564106i
$940$	−10.4798			−0.341814
$941$	26.1882	−	45.3592i	0.853710	−	1.47867i	−0.0241274	−	0.999709i	$-0.507681\pi$
$941$	26.1882	−	45.3592i	0.853710	−	1.47867i	0.877837	−	0.478960i	$-0.158986\pi$
$942$	2.76615	−	0.134127i	0.0901261	−	0.00437008i
$943$	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	$-0.627551\pi$
$947$	6.53348	−	3.77211i	0.212310	−	0.122577i	0.602384	+	0.798206i	$0.294217\pi$
$948$	−1.96668	+	0.0953613i	−0.0638747	+	0.00309719i
$949$	−5.66092	+	9.80500i	−0.183761	+	0.318284i
$950$	−3.02969			−0.0982960
$951$	−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	$-0.262056\pi$
$954$	0.640656	−	1.40918i	0.0207420	−	0.0456239i
$955$	4.96769	−	2.86810i	0.160751	−	0.0928095i
$956$			25.5390i			0.825989i
$957$	−27.9932	+	54.4128i	−0.904891	+	1.75892i
$958$	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
$962$	−0.398927	−	0.690963i	−0.0128619	−	0.0222775i
$963$	−0.691665	−	0.314452i	−0.0222886	−	0.0101331i
$964$	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	0.735193	−	0.677858i	$-0.237092\pi$
$967$	−6.82403	−	11.8196i	−0.219446	−	0.380092i	−0.954639	+	0.297766i	$0.903758\pi$
$968$			3.25572i			0.104643i
$969$	−1.93116	−	39.8271i	−0.0620376	−	1.27943i
$970$	−0.0369309			−0.00118578
$971$	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
$975$	−13.8664	+	8.92805i	−0.444079	+	0.285926i
$976$	44.4082	+	25.6391i	1.42147	+	0.820688i
$977$	2.21904	+	1.28116i	0.0709932	+	0.0409880i	0.535076	−	0.844804i	$-0.320283\pi$
$977$	2.21904	+	1.28116i	0.0709932	+	0.0409880i	−0.464083	+	0.885792i	$0.653616\pi$
$978$	0.174747	+	3.60388i	0.00558779	+	0.115239i
$979$	−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
$983$	39.1498			1.24869			0.624343	−	0.781150i	$-0.285367\pi$
$983$	39.1498			1.24869			0.624343	+	0.781150i	$0.285367\pi$
$984$	0.141286	−	0.0909692i	0.00450405	−	0.00289999i
$985$			8.21443i			0.261733i
$986$	−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
$990$	−0.475044	−	0.664710i	−0.0150979	−	0.0211259i
$991$	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	$0.750464\pi$
$992$	−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
$996$	−20.2020	−	31.3763i	−0.640126	−	0.994195i
$997$			24.8268i			0.786274i	0.919480	+	0.393137i	$0.128610\pi$
$997$			24.8268i			0.786274i	−0.919480	+	0.393137i	$0.871390\pi$
$998$	1.33044	−	0.768132i	0.0421145	−	0.0243148i
$999$	−6.20288	+	15.6094i	−0.196251	+	0.493859i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.13		48	9.5	odd	6
441.2.i.d.68.14		48	63.41	even	6
441.2.i.d.227.11		48	7.3	odd	6
441.2.i.d.227.12		48	7.4	even	3
441.2.o.e.146.13	✓	48	7.5	odd	6
441.2.o.e.146.14	yes	48	7.2	even	3
441.2.o.e.293.13	yes	48	63.23	odd	6
441.2.o.e.293.14	yes	48	63.5	even	6
441.2.s.d.362.11		48	1.1	even	1	trivial
441.2.s.d.362.12		48	7.6	odd	2	inner
441.2.s.d.374.11		48	63.59	even	6	inner
441.2.s.d.374.12		48	63.32	odd	6	inner
1323.2.i.d.521.11		48	21.11	odd	6
1323.2.i.d.521.12		48	21.17	even	6
1323.2.i.d.1097.11		48	63.13	odd	6
1323.2.i.d.1097.12		48	9.4	even	3
1323.2.o.e.440.11		48	21.5	even	6
1323.2.o.e.440.12		48	21.2	odd	6
1323.2.o.e.881.11		48	63.58	even	3
1323.2.o.e.881.12		48	63.40	odd	6
1323.2.s.d.656.13		48	21.20	even	2
1323.2.s.d.656.14		48	3.2	odd	2
1323.2.s.d.962.13		48	63.4	even	3
1323.2.s.d.962.14		48	63.31	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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.105953 + 0.0611722i) q^{2} +(-1.73002 + 0.0838860i) q^{3} +(-0.992516 + 1.71909i) q^{4} +0.529430 q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(2.98593 - 0.290249i) q^{9} +O(q^{10})\)	\(q+(-0.105953 + 0.0611722i) q^{2} +(-1.73002 + 0.0838860i) q^{3} +(-0.992516 + 1.71909i) q^{4} +0.529430 q^{5} +(0.178170 - 0.114717i) q^{6} -0.487547i q^{8} +(2.98593 - 0.290249i) q^{9} +(-0.0560949 + 0.0323864i) q^{10} +4.20449i q^{11} +(1.57286 - 3.05731i) q^{12} +(-1.74714 + 1.00871i) q^{13} +(-0.915923 + 0.0444117i) q^{15} +(-1.95521 - 3.38652i) q^{16} +(-2.19381 - 3.79979i) q^{17} +(-0.298614 + 0.213409i) q^{18} +(-4.54391 - 2.62343i) q^{19} +(-0.525467 + 0.910136i) q^{20} +(-0.257198 - 0.445480i) q^{22} +6.27515i q^{23} +(0.0408983 + 0.843464i) q^{24} -4.71970 q^{25} +(0.123411 - 0.213753i) q^{26} +(-5.14136 + 0.752613i) q^{27} +(-7.27689 - 4.20131i) q^{29} +(0.0943284 - 0.0607346i) q^{30} +(-1.03204 - 0.595849i) q^{31} +(1.25878 + 0.726755i) q^{32} +(-0.352698 - 7.27385i) q^{33} +(0.464883 + 0.268400i) q^{34} +(-2.46462 + 5.42115i) q^{36} +(1.61626 - 2.79945i) q^{37} +0.641923 q^{38} +(2.93797 - 1.89165i) q^{39} -0.258122i q^{40} +(-0.0994958 - 0.172332i) q^{41} +(3.96309 - 6.86427i) q^{43} +(-7.22789 - 4.17303i) q^{44} +(1.58084 - 0.153666i) q^{45} +(-0.383865 - 0.664873i) q^{46} +(4.98595 + 8.63591i) q^{47} +(3.66663 + 5.69472i) q^{48} +(0.500069 - 0.288715i) q^{50} +(4.11408 + 6.38968i) q^{51} -4.00466i q^{52} +(-3.65249 + 2.10877i) q^{53} +(0.498706 - 0.394250i) q^{54} +2.22598i q^{55} +(8.08111 + 4.15740i) q^{57} +1.02802 q^{58} +(-6.71960 + 11.6387i) q^{59} +(0.832720 - 1.61863i) q^{60} +(-11.3564 + 6.55662i) q^{61} +0.145798 q^{62} +7.64300 q^{64} +(-0.924990 + 0.534043i) q^{65} +(0.482327 + 0.749114i) q^{66} +(3.29001 - 5.69847i) q^{67} +8.70956 q^{68} +(-0.526397 - 10.8561i) q^{69} +8.50587i q^{71} +(-0.141510 - 1.45578i) q^{72} +(4.86015 - 2.80601i) q^{73} +0.395481i q^{74} +(8.16517 - 0.395917i) q^{75} +(9.01980 - 5.20758i) q^{76} +(-0.195572 + 0.380150i) q^{78} +(-0.286342 - 0.495959i) q^{79} +(-1.03514 - 1.79292i) q^{80} +(8.83151 - 1.73332i) q^{81} +(0.0210838 + 0.0121728i) q^{82} +(5.42692 - 9.39971i) q^{83} +(-1.16147 - 2.01172i) q^{85} +0.969724i q^{86} +(12.9416 + 6.65792i) q^{87} +2.04989 q^{88} +(-6.43688 + 11.1490i) q^{89} +(-0.158095 + 0.112985i) q^{90} +(-10.7875 - 6.22819i) q^{92} +(1.83543 + 0.944256i) q^{93} +(-1.05656 - 0.610003i) q^{94} +(-2.40568 - 1.38892i) q^{95} +(-2.23867 - 1.15171i) q^{96} +(0.493773 + 0.285080i) q^{97} +(1.22035 + 12.5543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 8 * q^9	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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