LMFDB - Embedded newform 722.2.e.r.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			99.4
Character	$\chi$	$=$	722.99
Dual form			722.2.e.r.423.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.485104 + 2.75116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.79605 + 1.50706i) q^{5} +(0.485104 - 2.75116i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-4.51450 + 1.64314i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.485104 + 2.75116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.79605 + 1.50706i) q^{5} +(0.485104 - 2.75116i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-4.51450 + 1.64314i) q^{9} +(2.20318 - 0.801892i) q^{10} +(-2.87811 - 4.98503i) q^{11} +(-1.39680 + 2.41933i) q^{12} +(0.0528381 - 0.299660i) q^{13} +(-0.983662 + 0.825390i) q^{14} +(-5.01745 - 4.21014i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-3.93373 - 1.43176i) q^{17} +4.80423 q^{18} -2.34458 q^{20} +(3.37087 + 1.22690i) q^{21} +(0.999556 + 5.66877i) q^{22} +(-4.96154 - 4.16323i) q^{23} +(2.14003 - 1.79569i) q^{24} +(0.0863099 - 0.489488i) q^{25} +(-0.152141 + 0.263516i) q^{26} +(-2.52015 - 4.36502i) q^{27} +(1.20664 - 0.439181i) q^{28} +(2.93894 - 1.06969i) q^{29} +(3.27491 + 5.67231i) q^{30} +(-3.22123 + 5.57934i) q^{31} +(0.173648 - 0.984808i) q^{32} +(12.3184 - 10.3364i) q^{33} +(3.20681 + 2.69083i) q^{34} +(0.522789 + 2.96488i) q^{35} +(-4.51450 - 1.64314i) q^{36} -3.97980 q^{37} +0.850045 q^{39} +(2.20318 + 0.801892i) q^{40} +(-0.871225 - 4.94096i) q^{41} +(-2.74796 - 2.30581i) q^{42} +(-0.757908 + 0.635960i) q^{43} +(0.999556 - 5.66877i) q^{44} +(5.63194 - 9.75480i) q^{45} +(3.23842 + 5.60910i) q^{46} +(4.12943 - 1.50299i) q^{47} +(-2.62513 + 0.955469i) q^{48} +(2.67557 + 4.63422i) q^{49} +(-0.248520 + 0.430448i) q^{50} +(2.03074 - 11.5169i) q^{51} +(0.233094 - 0.195589i) q^{52} +(2.52078 + 2.11518i) q^{53} +(0.875238 + 4.96372i) q^{54} +(12.6820 + 4.61587i) q^{55} -1.28408 q^{56} -3.12756 q^{58} +(-3.11391 - 1.13337i) q^{59} +(-1.13736 - 6.45031i) q^{60} +(-8.39696 - 7.04589i) q^{61} +(4.93521 - 4.14114i) q^{62} +(-1.07124 + 6.07528i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.356707 + 0.617834i) q^{65} +(-15.1108 + 5.49989i) q^{66} +(4.11662 - 1.49833i) q^{67} +(-2.09310 - 3.62535i) q^{68} +(9.04686 - 15.6696i) q^{69} +(0.522789 - 2.96488i) q^{70} +(-3.38262 + 2.83835i) q^{71} +(3.68025 + 3.08810i) q^{72} +(-0.393642 - 2.23245i) q^{73} +(3.73979 + 1.36117i) q^{74} +1.38853 q^{75} -7.39144 q^{77} +(-0.798781 - 0.290732i) q^{78} +(1.48931 + 8.44629i) q^{79} +(-1.79605 - 1.50706i) q^{80} +(-0.254396 + 0.213463i) q^{81} +(-0.871225 + 4.94096i) q^{82} +(4.88232 - 8.45643i) q^{83} +(1.79360 + 3.10661i) q^{84} +(9.22294 - 3.35688i) q^{85} +(0.929712 - 0.338387i) q^{86} +(4.36858 + 7.56661i) q^{87} +(-2.87811 + 4.98503i) q^{88} +(-2.61801 + 14.8475i) q^{89} +(-8.62863 + 7.24028i) q^{90} +(-0.299311 - 0.251152i) q^{91} +(-1.12469 - 6.37844i) q^{92} +(-16.9123 - 6.15557i) q^{93} -4.39445 q^{94} +2.79360 q^{96} +(-16.3057 - 5.93480i) q^{97} +(-0.929216 - 5.26985i) q^{98} +(21.1843 + 17.7758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 6 * q^7 - 12 * q^8	$ 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	0.485104	+	2.75116i	0.280075	+	1.58838i	0.722364	+	0.691513i	$0.243055\pi$
$3$	0.485104	+	2.75116i	0.280075	+	1.58838i	−0.442289	+	0.896872i	$0.645834\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−1.79605	+	1.50706i	−0.803218	+	0.673980i	−0.948979	−	0.315340i	$-0.897881\pi$
$5$	−1.79605	+	1.50706i	−0.803218	+	0.673980i	0.145761	+	0.989320i	$0.453437\pi$
$6$	0.485104	−	2.75116i	0.198043	−	1.12316i
$7$	0.642040	−	1.11205i	0.242668	−	0.420314i	−0.718805	−	0.695211i	$-0.755311\pi$
$7$	0.642040	−	1.11205i	0.242668	−	0.420314i	0.961473	+	0.274898i	$0.0886441\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−4.51450	+	1.64314i	−1.50483	+	0.547714i
$10$	2.20318	−	0.801892i	0.696707	−	0.253581i
$11$	−2.87811	−	4.98503i	−0.867782	−	1.50304i	−0.864258	−	0.503049i	$-0.832212\pi$
$11$	−2.87811	−	4.98503i	−0.867782	−	1.50304i	−0.00352407	−	0.999994i	$-0.501122\pi$
$12$	−1.39680	+	2.41933i	−0.403222	+	0.698401i
$13$	0.0528381	−	0.299660i	0.0146547	−	0.0831107i	−0.976603	−	0.215049i	$-0.931009\pi$
$13$	0.0528381	−	0.299660i	0.0146547	−	0.0831107i	0.991258	+	0.131938i	$0.0421200\pi$
$14$	−0.983662	+	0.825390i	−0.262895	+	0.220595i
$15$	−5.01745	−	4.21014i	−1.29550	−	1.08705i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−3.93373	−	1.43176i	−0.954071	−	0.347253i	−0.182363	−	0.983231i	$-0.558375\pi$
$17$	−3.93373	−	1.43176i	−0.954071	−	0.347253i	−0.771707	+	0.635978i	$0.780597\pi$
$18$	4.80423			1.13237
$19$		0			0
$19$		0			0
$20$	−2.34458			−0.524263
$21$	3.37087	+	1.22690i	0.735585	+	0.267731i
$22$	0.999556	+	5.66877i	0.213106	+	1.20858i
$23$	−4.96154	−	4.16323i	−1.03455	−	0.868093i	−0.0431677	−	0.999068i	$-0.513745\pi$
$23$	−4.96154	−	4.16323i	−1.03455	−	0.868093i	−0.991386	+	0.130974i	$0.958189\pi$
$24$	2.14003	−	1.79569i	0.436831	−	0.366545i
$25$	0.0863099	−	0.489488i	0.0172620	−	0.0978976i
$26$	−0.152141	+	0.263516i	−0.0298374	+	0.0516798i
$27$	−2.52015	−	4.36502i	−0.485003	−	0.840049i
$28$	1.20664	−	0.439181i	0.228033	−	0.0829974i
$29$	2.93894	−	1.06969i	0.545748	−	0.198636i	−0.0544081	−	0.998519i	$-0.517327\pi$
$29$	2.93894	−	1.06969i	0.545748	−	0.198636i	0.600156	+	0.799883i	$0.295105\pi$
$30$	3.27491	+	5.67231i	0.597914	+	1.03562i
$31$	−3.22123	+	5.57934i	−0.578550	+	1.00208i	0.417096	+	0.908863i	$0.363048\pi$
$31$	−3.22123	+	5.57934i	−0.578550	+	1.00208i	−0.995646	+	0.0932159i	$0.970285\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	12.3184	−	10.3364i	2.14437	−	1.79934i
$34$	3.20681	+	2.69083i	0.549963	+	0.461474i
$35$	0.522789	+	2.96488i	0.0883675	+	0.501157i
$36$	−4.51450	−	1.64314i	−0.752416	−	0.273857i
$37$	−3.97980			−0.654275			−0.327137	−	0.944977i	$-0.606084\pi$
$37$	−3.97980			−0.654275			−0.327137	+	0.944977i	$0.606084\pi$
$38$		0			0
$39$	0.850045			0.136116
$40$	2.20318	+	0.801892i	0.348354	+	0.126790i
$41$	−0.871225	−	4.94096i	−0.136063	−	0.771649i	−0.974114	−	0.226058i	$-0.927416\pi$
$41$	−0.871225	−	4.94096i	−0.136063	−	0.771649i	0.838051	−	0.545591i	$-0.183695\pi$
$42$	−2.74796	−	2.30581i	−0.424020	−	0.355795i
$43$	−0.757908	+	0.635960i	−0.115580	+	0.0969830i	−0.698746	−	0.715370i	$-0.746258\pi$
$43$	−0.757908	+	0.635960i	−0.115580	+	0.0969830i	0.583166	+	0.812353i	$0.301814\pi$
$44$	0.999556	−	5.66877i	0.150689	−	0.854599i
$45$	5.63194	−	9.75480i	0.839560	−	1.45416i
$46$	3.23842	+	5.60910i	0.477479	+	0.827017i
$47$	4.12943	−	1.50299i	0.602340	−	0.219234i	−0.0228083	−	0.999740i	$-0.507261\pi$
$47$	4.12943	−	1.50299i	0.602340	−	0.219234i	0.625148	+	0.780506i	$0.285039\pi$
$48$	−2.62513	+	0.955469i	−0.378905	+	0.137910i
$49$	2.67557	+	4.63422i	0.382224	+	0.662032i
$50$	−0.248520	+	0.430448i	−0.0351460	+	0.0608746i
$51$	2.03074	−	11.5169i	0.284360	−	1.61269i
$52$	0.233094	−	0.195589i	0.0323243	−	0.0271233i
$53$	2.52078	+	2.11518i	0.346256	+	0.290543i	0.799284	−	0.600953i	$-0.205212\pi$
$53$	2.52078	+	2.11518i	0.346256	+	0.290543i	−0.453029	+	0.891496i	$0.649657\pi$
$54$	0.875238	+	4.96372i	0.119105	+	0.675477i
$55$	12.6820	+	4.61587i	1.71004	+	0.622403i
$56$	−1.28408			−0.171592
$57$		0			0
$58$	−3.12756			−0.410669
$59$	−3.11391	−	1.13337i	−0.405396	−	0.147552i	0.131270	−	0.991347i	$-0.458094\pi$
$59$	−3.11391	−	1.13337i	−0.405396	−	0.147552i	−0.536666	+	0.843794i	$0.680317\pi$
$60$	−1.13736	−	6.45031i	−0.146833	−	0.832732i
$61$	−8.39696	−	7.04589i	−1.07512	−	0.902134i	−0.0796145	−	0.996826i	$-0.525369\pi$
$61$	−8.39696	−	7.04589i	−1.07512	−	0.902134i	−0.995507	+	0.0946920i	$0.969813\pi$
$62$	4.93521	−	4.14114i	0.626773	−	0.525925i
$63$	−1.07124	+	6.07528i	−0.134963	+	0.765414i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.356707	+	0.617834i	0.0442440	+	0.0766329i
$66$	−15.1108	+	5.49989i	−1.86001	+	0.676989i
$67$	4.11662	−	1.49833i	0.502925	−	0.183050i	−0.0780842	−	0.996947i	$-0.524880\pi$
$67$	4.11662	−	1.49833i	0.502925	−	0.183050i	0.581009	+	0.813897i	$0.302658\pi$
$68$	−2.09310	−	3.62535i	−0.253825	−	0.439638i
$69$	9.04686	−	15.6696i	1.08911	−	1.88640i
$70$	0.522789	−	2.96488i	0.0624852	−	0.354371i
$71$	−3.38262	+	2.83835i	−0.401443	+	0.336851i	−0.821051	−	0.570855i	$-0.806612\pi$
$71$	−3.38262	+	2.83835i	−0.401443	+	0.336851i	0.419608	+	0.907705i	$0.362168\pi$
$72$	3.68025	+	3.08810i	0.433722	+	0.363936i
$73$	−0.393642	−	2.23245i	−0.0460723	−	0.261289i	0.953068	−	0.302758i	$-0.0979074\pi$
$73$	−0.393642	−	2.23245i	−0.0460723	−	0.261289i	−0.999140	+	0.0414689i	$0.986796\pi$
$74$	3.73979	+	1.36117i	0.434741	+	0.158233i
$75$	1.38853			0.160334
$76$		0			0
$77$	−7.39144			−0.842332
$78$	−0.798781	−	0.290732i	−0.0904441	−	0.0329190i
$79$	1.48931	+	8.44629i	0.167560	+	0.950282i	0.946385	+	0.323040i	$0.104705\pi$
$79$	1.48931	+	8.44629i	0.167560	+	0.950282i	−0.778825	+	0.627241i	$0.784184\pi$
$80$	−1.79605	−	1.50706i	−0.200804	−	0.168495i
$81$	−0.254396	+	0.213463i	−0.0282662	+	0.0237182i
$82$	−0.871225	+	4.94096i	−0.0962107	+	0.545638i
$83$	4.88232	−	8.45643i	0.535904	−	0.928214i	−0.463214	−	0.886246i	$-0.653304\pi$
$83$	4.88232	−	8.45643i	0.535904	−	0.928214i	0.999119	−	0.0419676i	$-0.0133626\pi$
$84$	1.79360	+	3.10661i	0.195698	+	0.338959i
$85$	9.22294	−	3.35688i	1.00037	−	0.364104i
$86$	0.929712	−	0.338387i	0.100253	−	0.0364892i
$87$	4.36858	+	7.56661i	0.468361	+	0.811225i
$88$	−2.87811	+	4.98503i	−0.306807	+	0.531406i
$89$	−2.61801	+	14.8475i	−0.277509	+	1.57383i	0.453370	+	0.891323i	$0.350222\pi$
$89$	−2.61801	+	14.8475i	−0.277509	+	1.57383i	−0.730878	+	0.682508i	$0.760889\pi$
$90$	−8.62863	+	7.24028i	−0.909537	+	0.763192i
$91$	−0.299311	−	0.251152i	−0.0313763	−	0.0263279i
$92$	−1.12469	−	6.37844i	−0.117257	−	0.664998i
$93$	−16.9123	−	6.15557i	−1.75372	−	0.638303i
$94$	−4.39445			−0.453253
$95$		0			0
$96$	2.79360			0.285121
$97$	−16.3057	−	5.93480i	−1.65559	−	0.602587i	−0.665933	−	0.746011i	$-0.731966\pi$
$97$	−16.3057	−	5.93480i	−1.65559	−	0.602587i	−0.989661	+	0.143424i	$0.954189\pi$
$98$	−0.929216	−	5.26985i	−0.0938650	−	0.532335i
$99$	21.1843	+	17.7758i	2.12910	+	1.78653i
$100$	0.380754	−	0.319491i	0.0380754	−	0.0319491i
$101$	0.638446	−	3.62081i	0.0635278	−	0.360284i	−0.936428	−	0.350860i	$-0.885889\pi$
$101$	0.638446	−	3.62081i	0.0635278	−	0.360284i	0.999956	−	0.00942370i	$-0.00299970\pi$
$102$	−5.84728	+	10.1278i	−0.578967	+	1.00280i
$103$	−9.50676	−	16.4662i	−0.936729	−	1.62246i	−0.771521	−	0.636204i	$-0.780504\pi$
$103$	−9.50676	−	16.4662i	−0.936729	−	1.62246i	−0.165208	−	0.986259i	$-0.552830\pi$
$104$	−0.285932	+	0.104071i	−0.0280379	+	0.0102050i
$105$	−7.90327	+	2.87656i	−0.771280	+	0.280723i
$106$	−1.64532	−	2.84978i	−0.159808	−	0.276795i
$107$	−5.01864	+	8.69254i	−0.485170	+	0.840339i	−0.999855	−	0.0170403i	$-0.994576\pi$
$107$	−5.01864	+	8.69254i	−0.485170	+	0.840339i	0.514685	+	0.857380i	$0.327909\pi$
$108$	0.875238	−	4.96372i	0.0842198	−	0.477634i
$109$	−6.77450	+	5.68448i	−0.648879	+	0.544474i	−0.906731	−	0.421710i	$-0.861430\pi$
$109$	−6.77450	+	5.68448i	−0.648879	+	0.544474i	0.257851	+	0.966185i	$0.416986\pi$
$110$	−10.3384	−	8.67499i	−0.985732	−	0.827128i
$111$	−1.93062	−	10.9491i	−0.183246	−	1.03924i
$112$	1.20664	+	0.439181i	0.114017	+	0.0414987i
$113$	−14.2502			−1.34055			−0.670275	−	0.742113i	$-0.733824\pi$
$113$	−14.2502			−1.34055			−0.670275	+	0.742113i	$0.733824\pi$
$114$		0			0
$115$	15.1854			1.41605
$116$	2.93894	+	1.06969i	0.272874	+	0.0993181i
$117$	0.253846	+	1.43963i	0.0234681	+	0.133094i
$118$	2.53848	+	2.13004i	0.233686	+	0.196086i
$119$	−4.11780	+	3.45524i	−0.377478	+	0.316741i
$120$	−1.13736	+	6.45031i	−0.103827	+	0.588830i
$121$	−11.0670	+	19.1686i	−1.00609	+	1.74260i
$122$	5.48073	+	9.49290i	0.496202	+	0.859447i
$123$	13.1708	−	4.79377i	1.18757	−	0.432239i
$124$	−6.05394	+	2.20345i	−0.543659	+	0.197876i
$125$	−5.27877	−	9.14309i	−0.472147	−	0.817783i
$126$	3.08450	−	5.34252i	0.274789	−	0.475949i
$127$	0.387261	−	2.19627i	0.0343638	−	0.194887i	−0.962793	−	0.270240i	$-0.912897\pi$
$127$	0.387261	−	2.19627i	0.0343638	−	0.194887i	0.997157	+	0.0753525i	$0.0240082\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−2.11729	−	1.77662i	−0.186417	−	0.156423i
$130$	−0.123883	−	0.702575i	−0.0108653	−	0.0616199i
$131$	−1.43083	−	0.520778i	−0.125012	−	0.0455006i	0.278757	−	0.960362i	$-0.410078\pi$
$131$	−1.43083	−	0.520778i	−0.125012	−	0.0455006i	−0.403769	+	0.914861i	$0.632300\pi$
$132$	16.0806			1.39964
$133$		0			0
$134$	−4.38081			−0.378445
$135$	11.1047	+	4.04177i	0.955739	+	0.347860i
$136$	0.726925	+	4.12259i	0.0623333	+	0.353510i
$137$	8.20568	+	6.88538i	0.701058	+	0.588258i	0.922075	−	0.387012i	$-0.126493\pi$
$137$	8.20568	+	6.88538i	0.701058	+	0.588258i	−0.221016	+	0.975270i	$0.570937\pi$
$138$	−13.8606	+	11.6304i	−1.17989	+	0.990047i
$139$	−1.87789	+	10.6500i	−0.159281	+	0.903325i	0.795487	+	0.605971i	$0.207215\pi$
$139$	−1.87789	+	10.6500i	−0.159281	+	0.903325i	−0.954767	+	0.297354i	$0.903896\pi$
$140$	−1.50531	+	2.60727i	−0.127222	+	0.220355i
$141$	6.13818	+	10.6316i	0.516928	+	0.895346i
$142$	4.14940	−	1.51026i	0.348210	−	0.126738i
$143$	−1.64589	+	0.599054i	−0.137636	+	0.0500954i
$144$	−2.40211	−	4.16058i	−0.200176	−	0.346715i
$145$	−3.66640	+	6.35039i	−0.304478	+	0.527371i
$146$	−0.393642	+	2.23245i	−0.0325780	+	0.184759i
$147$	−11.4516	+	9.60901i	−0.944510	+	0.792538i
$148$	−3.04870	−	2.55816i	−0.250602	−	0.210280i
$149$	−1.62080	−	9.19204i	−0.132781	−	0.753041i	−0.976379	−	0.216065i	$-0.930678\pi$
$149$	−1.62080	−	9.19204i	−0.132781	−	0.753041i	0.843597	−	0.536976i	$-0.180433\pi$
$150$	−1.30479	−	0.474905i	−0.106536	−	0.0387759i
$151$	19.8232			1.61319			0.806593	−	0.591107i	$-0.201309\pi$
$151$	19.8232			1.61319			0.806593	+	0.591107i	$0.201309\pi$
$152$		0			0
$153$	20.1114			1.62591
$154$	6.94568	+	2.52802i	0.559699	+	0.203714i
$155$	−2.62293	−	14.8754i	−0.210679	−	1.19482i
$156$	0.651172	+	0.546398i	0.0521355	+	0.0437469i
$157$	10.6232	−	8.91394i	0.847825	−	0.711410i	−0.111484	−	0.993766i	$-0.535561\pi$
$157$	10.6232	−	8.91394i	0.847825	−	0.711410i	0.959310	+	0.282356i	$0.0911161\pi$
$158$	1.48931	−	8.44629i	0.118483	−	0.671951i
$159$	−4.59638	+	7.96116i	−0.364517	+	0.631361i
$160$	1.17229	+	2.03046i	0.0926775	+	0.160522i
$161$	−7.81521	+	2.84450i	−0.615925	+	0.224178i
$162$	0.312063	−	0.113582i	0.0245180	−	0.00892381i
$163$	−7.12480	−	12.3405i	−0.558057	−	0.966583i	−0.997659	−	0.0683904i	$-0.978214\pi$
$163$	−7.12480	−	12.3405i	−0.558057	−	0.966583i	0.439601	−	0.898193i	$-0.355120\pi$
$164$	2.50859	−	4.34501i	0.195888	−	0.339288i
$165$	−6.54691	+	37.1294i	−0.509676	+	2.89052i
$166$	−7.48015	+	6.27659i	−0.580572	+	0.487158i
$167$	8.87854	+	7.44998i	0.687042	+	0.576497i	0.918055	−	0.396454i	$-0.129759\pi$
$167$	8.87854	+	7.44998i	0.687042	+	0.576497i	−0.231012	+	0.972951i	$0.574204\pi$
$168$	−0.622912	−	3.53271i	−0.0480587	−	0.272555i
$169$	12.1290	+	4.41459i	0.933000	+	0.339584i
$170$	−9.81485			−0.752764
$171$		0			0
$172$	−0.989378			−0.0754394
$173$	−3.74329	−	1.36245i	−0.284597	−	0.103585i	0.195777	−	0.980648i	$-0.437277\pi$
$173$	−3.74329	−	1.36245i	−0.284597	−	0.103585i	−0.480374	+	0.877064i	$0.659499\pi$
$174$	−1.51719	−	8.60443i	−0.115018	−	0.652300i
$175$	−0.488918	−	0.410251i	−0.0369587	−	0.0310121i
$176$	4.40952	−	3.70002i	0.332380	−	0.278900i
$177$	1.60752	−	9.11667i	0.120828	−	0.685251i
$178$	7.53827	−	13.0567i	0.565017	−	0.978638i
$179$	4.22545	+	7.31869i	0.315825	+	0.547024i	0.979612	−	0.200897i	$-0.0643855\pi$
$179$	4.22545	+	7.31869i	0.315825	+	0.547024i	−0.663788	+	0.747921i	$0.731052\pi$
$180$	10.5846	−	3.85247i	0.788928	−	0.287146i
$181$	−7.97354	+	2.90213i	−0.592669	+	0.215714i	−0.620903	−	0.783888i	$-0.713234\pi$
$181$	−7.97354	+	2.90213i	−0.592669	+	0.215714i	0.0282341	+	0.999601i	$0.491012\pi$
$182$	0.195361	+	0.338376i	0.0144811	+	0.0250821i
$183$	15.3110	−	26.5194i	1.13182	−	1.96037i
$184$	−1.12469	+	6.37844i	−0.0829133	+	0.470225i
$185$	7.14791	−	5.99781i	0.525525	−	0.440968i
$186$	13.7870	+	11.5687i	1.01091	+	0.848258i
$187$	4.18433	+	23.7305i	0.305989	+	1.73535i
$188$	4.12943	+	1.50299i	0.301170	+	0.109617i
$189$	−6.47214			−0.470779
$190$		0			0
$191$	−22.3790			−1.61929			−0.809644	−	0.586921i	$-0.800340\pi$
$191$	−22.3790			−1.61929			−0.809644	+	0.586921i	$0.800340\pi$
$192$	−2.62513	−	0.955469i	−0.189452	−	0.0689550i
$193$	1.28988	+	7.31526i	0.0928475	+	0.526564i	0.995386	+	0.0959545i	$0.0305903\pi$
$193$	1.28988	+	7.31526i	0.0928475	+	0.526564i	−0.902538	+	0.430610i	$0.858299\pi$
$194$	13.2925	+	11.1538i	0.954349	+	0.800794i
$195$	−1.52672	+	1.28107i	−0.109331	+	0.0917395i
$196$	−0.929216	+	5.26985i	−0.0663726	+	0.376418i
$197$	−4.26777	+	7.39199i	−0.304066	+	0.526658i	−0.977053	−	0.212997i	$-0.931678\pi$
$197$	−4.26777	+	7.39199i	−0.304066	+	0.526658i	0.672987	+	0.739654i	$0.265011\pi$
$198$	−13.8271	−	23.9492i	−0.982648	−	1.70200i
$199$	5.97575	−	2.17499i	0.423609	−	0.154181i	−0.121414	−	0.992602i	$-0.538743\pi$
$199$	5.97575	−	2.17499i	0.423609	−	0.154181i	0.545024	+	0.838421i	$0.316521\pi$
$200$	−0.467064	+	0.169997i	−0.0330264	+	0.0120206i
$201$	6.11913	+	10.5986i	0.431610	+	0.747571i
$202$	−1.83833	+	3.18409i	−0.129345	+	0.224032i
$203$	0.697377	−	3.95502i	0.0489463	−	0.277588i
$204$	8.95856	−	7.51712i	0.627224	−	0.526304i
$205$	9.01112	+	7.56122i	0.629364	+	0.528099i
$206$	3.30166	+	18.7247i	0.230038	+	1.30461i
$207$	29.2396	+	10.6424i	2.03230	+	0.739695i
$208$	0.304282			0.0210982
$209$		0			0
$210$	8.41049			0.580379
$211$	13.1160	+	4.77385i	0.902945	+	0.328645i	0.751432	−	0.659810i	$-0.229363\pi$
$211$	13.1160	+	4.77385i	0.902945	+	0.328645i	0.151513	+	0.988455i	$0.451585\pi$
$212$	0.571414	+	3.24065i	0.0392449	+	0.222569i
$213$	−9.44970	−	7.92924i	−0.647483	−	0.543303i
$214$	7.68900	−	6.45184i	0.525609	−	0.441039i
$215$	0.402807	−	2.28443i	0.0274712	−	0.155797i
$216$	−2.52015	+	4.36502i	−0.171474	+	0.297002i
$217$	4.13632	+	7.16431i	0.280791	+	0.486345i
$218$	8.31015	−	3.02465i	0.562835	−	0.204855i
$219$	5.95089	−	2.16595i	0.402124	−	0.146361i
$220$	6.74794	+	11.6878i	0.454946	+	0.787990i
$221$	−0.636892	+	1.10313i	−0.0428420	+	0.0742046i
$222$	−1.93062	+	10.9491i	−0.129574	+	0.734853i
$223$	6.83618	−	5.73624i	0.457784	−	0.384127i	−0.384531	−	0.923112i	$-0.625637\pi$
$223$	6.83618	−	5.73624i	0.457784	−	0.384127i	0.842315	+	0.538985i	$0.181192\pi$
$224$	−0.983662	−	0.825390i	−0.0657237	−	0.0551487i
$225$	0.414652	+	2.35161i	0.0276435	+	0.156774i
$226$	13.3908	+	4.87387i	0.890746	+	0.324205i
$227$	−0.659796			−0.0437922			−0.0218961	−	0.999760i	$-0.506970\pi$
$227$	−0.659796			−0.0437922			−0.0218961	+	0.999760i	$0.506970\pi$
$228$		0			0
$229$	−6.97208			−0.460728			−0.230364	−	0.973105i	$-0.573992\pi$
$229$	−6.97208			−0.460728			−0.230364	+	0.973105i	$0.573992\pi$
$230$	−14.2696	−	5.19373i	−0.940912	−	0.342464i
$231$	−3.58562	−	20.3350i	−0.235916	−	1.33795i
$232$	−2.39585	−	2.01036i	−0.157295	−	0.131986i
$233$	−22.6823	+	19.0327i	−1.48597	+	1.24688i	−0.586458	+	0.809980i	$0.699478\pi$
$233$	−22.6823	+	19.0327i	−1.48597	+	1.24688i	−0.899512	+	0.436897i	$0.856077\pi$
$234$	0.253846	−	1.43963i	0.0165944	−	0.0941118i
$235$	−5.15156	+	8.92277i	−0.336051	+	0.582057i
$236$	−1.65688	−	2.86979i	−0.107853	−	0.186808i
$237$	−22.5147	+	8.19466i	−1.46248	+	0.532301i
$238$	5.05123	−	1.83850i	0.327422	−	0.119172i
$239$	12.3517	+	21.3938i	0.798965	+	1.38385i	0.920291	+	0.391235i	$0.127952\pi$
$239$	12.3517	+	21.3938i	0.798965	+	1.38385i	−0.121326	+	0.992613i	$0.538715\pi$
$240$	3.27491	−	5.67231i	0.211395	−	0.366146i
$241$	4.78551	−	27.1400i	0.308262	−	1.74824i	−0.299478	−	0.954103i	$-0.596813\pi$
$241$	4.78551	−	27.1400i	0.308262	−	1.74824i	0.607740	−	0.794136i	$-0.292076\pi$
$242$	16.9556	−	14.2275i	1.08995	−	0.914576i
$243$	−12.2939	−	10.3158i	−0.788657	−	0.661762i
$244$	−1.90344	−	10.7949i	−0.121855	−	0.691075i
$245$	−11.7895	−	4.29104i	−0.753206	−	0.274144i
$246$	−14.0160			−0.893630
$247$		0			0
$248$	6.44246			0.409097
$249$	25.6335	+	9.32982i	1.62445	+	0.591253i
$250$	1.83330	+	10.3971i	0.115948	+	0.657573i
$251$	−2.28936	−	1.92101i	−0.144503	−	0.121253i	0.567670	−	0.823256i	$-0.307845\pi$
$251$	−2.28936	−	1.92101i	−0.144503	−	0.121253i	−0.712174	+	0.702003i	$0.752289\pi$
$252$	−4.72573	+	3.96536i	−0.297693	+	0.249794i
$253$	−6.47396	+	36.7157i	−0.407014	+	2.30829i
$254$	−1.11507	+	1.93136i	−0.0699659	+	0.121185i
$255$	13.7094	+	23.7454i	0.858516	+	1.48699i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−13.2800	+	4.83352i	−0.828382	+	0.301507i	−0.721195	−	0.692732i	$-0.756407\pi$
$257$	−13.2800	+	4.83352i	−0.828382	+	0.301507i	−0.107188	+	0.994239i	$0.534185\pi$
$258$	1.38197	+	2.39364i	0.0860374	+	0.149021i
$259$	−2.55519	+	4.42571i	−0.158772	+	0.275000i
$260$	−0.123883	+	0.702575i	−0.00768290	+	0.0435719i
$261$	−11.5102	+	9.65821i	−0.712464	+	0.597828i
$262$	1.16642	+	0.978743i	0.0720617	+	0.0604670i
$263$	1.31432	+	7.45388i	0.0810445	+	0.459626i	0.998140	+	0.0609591i	$0.0194159\pi$
$263$	1.31432	+	7.45388i	0.0810445	+	0.459626i	−0.917096	+	0.398667i	$0.869473\pi$
$264$	−15.1108	−	5.49989i	−0.930006	−	0.338495i
$265$	−7.71517			−0.473939
$266$		0			0
$267$	−42.1179			−2.57757
$268$	4.11662	+	1.49833i	0.251462	+	0.0915249i
$269$	−1.33201	−	7.55421i	−0.0812141	−	0.460588i	−0.998110	−	0.0614606i	$-0.980424\pi$
$269$	−1.33201	−	7.55421i	−0.0812141	−	0.460588i	0.916895	−	0.399128i	$-0.130687\pi$
$270$	−9.05262	−	7.59605i	−0.550925	−	0.462281i
$271$	8.93583	−	7.49805i	0.542813	−	0.455474i	−0.329686	−	0.944091i	$-0.606943\pi$
$271$	8.93583	−	7.49805i	0.542813	−	0.455474i	0.872499	+	0.488617i	$0.162498\pi$
$272$	0.726925	−	4.12259i	0.0440763	−	0.249969i
$273$	0.545762	−	0.945288i	0.0330310	−	0.0572114i
$274$	−5.35588	−	9.27665i	−0.323560	−	0.560423i
$275$	−2.68852	+	0.978541i	−0.162124	+	0.0590083i
$276$	17.0025	−	6.18842i	1.02343	−	0.372499i
$277$	−13.7202	−	23.7642i	−0.824370	−	1.42785i	−0.902400	−	0.430899i	$-0.858197\pi$
$277$	−13.7202	−	23.7642i	−0.824370	−	1.42785i	0.0780307	−	0.996951i	$-0.475137\pi$
$278$	5.40717	−	9.36549i	0.324300	−	0.561705i
$279$	5.37459	−	30.4808i	0.321769	−	1.82484i
$280$	2.30627	−	1.93519i	0.137826	−	0.115650i
$281$	12.4647	+	10.4591i	0.743580	+	0.623938i	0.933797	−	0.357804i	$-0.116474\pi$
$281$	12.4647	+	10.4591i	0.743580	+	0.623938i	−0.190216	+	0.981742i	$0.560919\pi$
$282$	−2.13177	−	12.0899i	−0.126945	−	0.719940i
$283$	−3.18907	−	1.16073i	−0.189571	−	0.0689981i	0.245490	−	0.969399i	$-0.421051\pi$
$283$	−3.18907	−	1.16073i	−0.189571	−	0.0689981i	−0.435061	+	0.900401i	$0.643273\pi$
$284$	−4.41570			−0.262023
$285$		0			0
$286$	1.75152			0.103569
$287$	−6.05394	−	2.20345i	−0.357353	−	0.130066i
$288$	0.834245	+	4.73124i	0.0491584	+	0.278791i
$289$	0.401564	+	0.336952i	0.0236214	+	0.0198207i
$290$	5.61725	−	4.71343i	0.329856	−	0.276782i
$291$	8.41762	−	47.7387i	0.493450	−	2.79849i
$292$	1.13345	−	1.96319i	0.0663299	−	0.114887i
$293$	−11.6892	−	20.2462i	−0.682888	−	1.18280i	−0.974096	−	0.226136i	$-0.927391\pi$
$293$	−11.6892	−	20.2462i	−0.682888	−	1.18280i	0.291208	−	0.956660i	$-0.405943\pi$
$294$	14.0474	−	5.11285i	0.819263	−	0.298187i
$295$	7.30080	−	2.65727i	0.425069	−	0.154712i
$296$	1.98990	+	3.44660i	0.115660	+	0.200330i
$297$	−14.5065	+	25.1260i	−0.841753	+	1.45796i
$298$	−1.62080	+	9.19204i	−0.0938907	+	0.532481i
$299$	−1.50971	+	1.26680i	−0.0873088	+	0.0732608i
$300$	1.06368	+	0.892530i	0.0614114	+	0.0515303i
$301$	0.220610	+	1.25114i	0.0127157	+	0.0721145i
$302$	−18.6277	−	6.77992i	−1.07190	−	0.390141i
$303$	10.2712			0.590062
$304$		0			0
$305$	25.7000			1.47158
$306$	−18.8985	−	6.87851i	−1.08036	−	0.393218i
$307$	−0.241027	−	1.36693i	−0.0137562	−	0.0780150i	0.977157	−	0.212519i	$-0.0681669\pi$
$307$	−0.241027	−	1.36693i	−0.0137562	−	0.0780150i	−0.990913	+	0.134504i	$0.957056\pi$
$308$	−5.66217	−	4.75112i	−0.322632	−	0.270720i
$309$	40.6894	−	34.1425i	2.31474	−	1.94230i
$310$	−2.62293	+	14.8754i	−0.148972	+	0.844864i
$311$	6.09512	−	10.5571i	0.345623	−	0.598636i	−0.639844	−	0.768505i	$-0.721001\pi$
$311$	6.09512	−	10.5571i	0.345623	−	0.598636i	0.985467	+	0.169869i	$0.0543343\pi$
$312$	−0.425022	−	0.736160i	−0.0240622	−	0.0416769i
$313$	−15.5344	+	5.65408i	−0.878059	+	0.319587i	−0.741426	−	0.671035i	$-0.765850\pi$
$313$	−15.5344	+	5.65408i	−0.878059	+	0.319587i	−0.136633	+	0.990622i	$0.543628\pi$
$314$	−13.0313	+	4.74301i	−0.735399	+	0.267663i
$315$	−7.23185	−	12.5259i	−0.407469	−	0.705757i
$316$	−4.28829	+	7.42754i	−0.241235	+	0.417832i
$317$	0.466786	−	2.64727i	0.0262173	−	0.148686i	−0.968889	−	0.247496i	$-0.920392\pi$
$317$	0.466786	−	2.64727i	0.0262173	−	0.148686i	0.995106	+	0.0988098i	$0.0315035\pi$
$318$	7.04206	−	5.90899i	0.394899	−	0.331360i
$319$	−13.7910	−	11.5720i	−0.772149	−	0.647910i
$320$	−0.407131	−	2.30896i	−0.0227593	−	0.129075i
$321$	−26.3492	−	9.59031i	−1.47067	−	0.535279i
$322$	8.31677			0.463475
$323$		0			0
$324$	−0.332090			−0.0184495
$325$	−0.142119	−	0.0517272i	−0.00788336	−	0.00286931i
$326$	2.47442	+	14.0331i	0.137045	+	0.777222i
$327$	−18.9253	−	15.8802i	−1.04657	−	0.878176i
$328$	−3.84339	+	3.22499i	−0.212216	+	0.178070i
$329$	0.979866	−	5.55710i	0.0540218	−	0.306373i
$330$	18.8511	−	32.6510i	1.03772	−	1.79738i
$331$	−2.60651	−	4.51462i	−0.143267	−	0.248146i	0.785458	−	0.618915i	$-0.212427\pi$
$331$	−2.60651	−	4.51462i	−0.143267	−	0.248146i	−0.928725	+	0.370769i	$0.879094\pi$
$332$	9.17576	−	3.33971i	0.503585	−	0.183290i
$333$	17.9668	−	6.53937i	0.984573	−	0.358355i
$334$	−5.79506	−	10.0373i	−0.317091	−	0.549218i
$335$	−5.13558	+	8.89508i	−0.280587	+	0.485990i
$336$	−0.622912	+	3.53271i	−0.0339827	+	0.192725i
$337$	−20.4744	+	17.1801i	−1.11531	+	0.935859i	−0.998358	−	0.0572783i	$-0.981758\pi$
$337$	−20.4744	+	17.1801i	−1.11531	+	0.935859i	−0.116955	+	0.993137i	$0.537313\pi$
$338$	−9.88765	−	8.29672i	−0.537817	−	0.451282i
$339$	−6.91285	−	39.2047i	−0.375455	−	2.12931i
$340$	9.22294	+	3.35688i	0.500184	+	0.182052i
$341$	37.0842			2.00822
$342$		0			0
$343$	15.8598			0.856351
$344$	0.929712	+	0.338387i	0.0501267	+	0.0182446i
$345$	7.36652	+	41.7776i	0.396600	+	2.24923i
$346$	3.05156	+	2.56056i	0.164053	+	0.137657i
$347$	−25.0253	+	20.9987i	−1.34343	+	1.12727i	−0.362697	+	0.931907i	$0.618144\pi$
$347$	−25.0253	+	20.9987i	−1.34343	+	1.12727i	−0.980731	+	0.195363i	$0.937412\pi$
$348$	−1.51719	+	8.60443i	−0.0813301	+	0.461246i
$349$	14.5529	−	25.2063i	0.778998	−	1.34926i	−0.153521	−	0.988145i	$-0.549061\pi$
$349$	14.5529	−	25.2063i	0.778998	−	1.34926i	0.932520	−	0.361119i	$-0.117605\pi$
$350$	0.319119	+	0.552730i	0.0170576	+	0.0295447i
$351$	−1.44118	+	0.524547i	−0.0769246	+	0.0279983i
$352$	−5.40907	+	1.96874i	−0.288305	+	0.104934i
$353$	7.15244	+	12.3884i	0.380686	+	0.659368i	0.991160	−	0.132668i	$-0.0423545\pi$
$353$	7.15244	+	12.3884i	0.380686	+	0.659368i	−0.610474	+	0.792036i	$0.709021\pi$
$354$	−4.62866	+	8.01707i	−0.246010	+	0.426102i
$355$	1.79777	−	10.1957i	0.0954156	−	0.541129i
$356$	−11.5493	+	9.69101i	−0.612111	+	0.513622i
$357$	−11.5035	−	9.65258i	−0.608830	−	0.510869i
$358$	−1.46748	−	8.32250i	−0.0775588	−	0.439858i
$359$	−18.4844	−	6.72778i	−0.975570	−	0.355078i	−0.195454	−	0.980713i	$-0.562618\pi$
$359$	−18.4844	−	6.72778i	−0.975570	−	0.355078i	−0.780116	+	0.625634i	$0.784840\pi$
$360$	−11.2639			−0.593658
$361$		0			0
$362$	8.48526			0.445976
$363$	−58.1046	−	21.1484i	−3.04970	−	1.11000i
$364$	−0.0678483	−	0.384787i	−0.00355622	−	0.0201683i
$365$	4.07145	+	3.41635i	0.213110	+	0.178820i
$366$	−23.4578	+	19.6834i	−1.22616	+	1.02887i
$367$	1.65843	−	9.40544i	0.0865695	−	0.490960i	−0.910437	−	0.413647i	$-0.864255\pi$
$367$	1.65843	−	9.40544i	0.0865695	−	0.490960i	0.997007	−	0.0773130i	$-0.0246341\pi$
$368$	3.23842	−	5.60910i	0.168814	−	0.292395i
$369$	12.0518	+	20.8744i	0.627394	+	1.08668i
$370$	−8.76821	+	3.19137i	−0.455838	+	0.165911i
$371$	3.97062	−	1.44519i	0.206144	−	0.0750304i
$372$	−8.99885	−	15.5865i	−0.466569	−	0.808120i
$373$	−1.82005	+	3.15242i	−0.0942387	+	0.163226i	−0.909291	−	0.416162i	$-0.863375\pi$
$373$	−1.82005	+	3.15242i	−0.0942387	+	0.163226i	0.815052	+	0.579388i	$0.196708\pi$
$374$	4.18433	−	23.7305i	0.216367	−	1.22708i
$375$	22.5934	−	18.9581i	1.16672	−	0.978993i
$376$	−3.36635	−	2.82470i	−0.173606	−	0.145673i
$377$	−0.165254	−	0.937204i	−0.00851103	−	0.0482684i
$378$	6.08182	+	2.21360i	0.312815	+	0.113855i
$379$	8.34741			0.428778			0.214389	−	0.976748i	$-0.431224\pi$
$379$	8.34741			0.428778			0.214389	+	0.976748i	$0.431224\pi$
$380$		0			0
$381$	6.23015			0.319180
$382$	21.0294	+	7.65408i	1.07596	+	0.391617i
$383$	−1.64717	−	9.34155i	−0.0841663	−	0.477331i	−0.997533	−	0.0701939i	$-0.977638\pi$
$383$	−1.64717	−	9.34155i	−0.0841663	−	0.477331i	0.913367	−	0.407137i	$-0.133473\pi$
$384$	2.14003	+	1.79569i	0.109208	+	0.0916361i
$385$	13.2754	−	11.1394i	0.676576	−	0.567715i
$386$	1.28988	−	7.31526i	0.0656531	−	0.372337i
$387$	2.37660	−	4.11639i	0.120809	−	0.209248i
$388$	−8.67609	−	15.0274i	−0.440462	−	0.762902i
$389$	−33.8740	+	12.3291i	−1.71748	+	0.625112i	−0.997616	−	0.0690033i	$-0.978018\pi$
$389$	−33.8740	+	12.3291i	−1.71748	+	0.625112i	−0.719864	+	0.694115i	$0.755796\pi$
$390$	1.87280	−	0.681645i	0.0948331	−	0.0345164i
$391$	13.5566	+	23.4808i	0.685589	+	1.18747i
$392$	2.67557	−	4.63422i	0.135137	−	0.234064i
$393$	0.738646	−	4.18907i	0.0372598	−	0.211311i
$394$	6.53860	−	5.48654i	0.329410	−	0.276408i
$395$	−15.4040	−	12.9255i	−0.775058	−	0.650351i
$396$	4.80209	+	27.2340i	0.241314	+	1.36856i
$397$	6.02255	+	2.19203i	0.302263	+	0.110015i	0.488699	−	0.872452i	$-0.337472\pi$
$397$	6.02255	+	2.19203i	0.302263	+	0.110015i	−0.186436	+	0.982467i	$0.559694\pi$
$398$	−6.35926			−0.318761
$399$		0			0
$400$	0.497039			0.0248520
$401$	−0.176343	−	0.0641834i	−0.00880612	−	0.00320517i	0.337613	−	0.941285i	$-0.390380\pi$
$401$	−0.176343	−	0.0641834i	−0.00880612	−	0.00320517i	−0.346419	+	0.938080i	$0.612603\pi$
$402$	−2.12515	−	12.0523i	−0.105993	−	0.601116i
$403$	1.50170	+	1.26008i	0.0748050	+	0.0627688i
$404$	2.81649	−	2.36332i	0.140126	−	0.117579i
$405$	0.135204	−	0.766782i	0.00671836	−	0.0381017i
$406$	−2.00802	+	3.47799i	−0.0996562	+	0.172610i
$407$	11.4543	+	19.8394i	0.567768	+	0.983402i
$408$	−10.9893	+	3.99978i	−0.544051	+	0.198018i
$409$	−16.2250	+	5.90541i	−0.802274	+	0.292004i	−0.710428	−	0.703769i	$-0.751499\pi$
$409$	−16.2250	+	5.90541i	−0.802274	+	0.292004i	−0.0918455	+	0.995773i	$0.529277\pi$
$410$	−5.88159	−	10.1872i	−0.290471	−	0.503110i
$411$	−14.9622	+	25.9153i	−0.738031	+	1.27831i
$412$	3.30166	−	18.7247i	0.162661	−	0.922498i
$413$	−3.25961	+	2.73514i	−0.160395	+	0.134587i
$414$	−23.8364	−	20.0011i	−1.17149	−	0.983000i
$415$	3.97549	+	22.5461i	0.195149	+	1.10675i
$416$	−0.285932	−	0.104071i	−0.0140190	−	0.00510249i
$417$	−30.2110			−1.47944
$418$		0			0
$419$	−1.72572			−0.0843068			−0.0421534	−	0.999111i	$-0.513422\pi$
$419$	−1.72572			−0.0843068			−0.0421534	+	0.999111i	$0.513422\pi$
$420$	−7.90327	−	2.87656i	−0.385640	−	0.140362i
$421$	5.68777	+	32.2569i	0.277205	+	1.57211i	0.731870	+	0.681444i	$0.238648\pi$
$421$	5.68777	+	32.2569i	0.277205	+	1.57211i	−0.454665	+	0.890663i	$0.650241\pi$
$422$	−10.6923	−	8.97190i	−0.520493	−	0.436745i
$423$	−16.1727	+	13.5705i	−0.786343	+	0.659820i
$424$	0.571414	−	3.24065i	0.0277503	−	0.157380i
$425$	−1.04035	+	1.80194i	−0.0504644	+	0.0874069i
$426$	6.16785	+	10.6830i	0.298833	+	0.517595i
$427$	−13.2265	+	4.81406i	−0.640077	+	0.232969i
$428$	−9.43195	+	3.43295i	−0.455911	+	0.165938i
$429$	−2.44652	−	4.23750i	−0.118119	−	0.204588i
$430$	−1.15984	+	2.00890i	−0.0559323	+	0.0968776i
$431$	−4.43010	+	25.1243i	−0.213390	+	1.21020i	0.670288	+	0.742101i	$0.266171\pi$
$431$	−4.43010	+	25.1243i	−0.213390	+	1.21020i	−0.883678	+	0.468095i	$0.844940\pi$
$432$	3.86109	−	3.23984i	0.185767	−	0.155877i
$433$	18.7554	+	15.7376i	0.901326	+	0.756302i	0.970449	−	0.241306i	$-0.0775758\pi$
$433$	18.7554	+	15.7376i	0.901326	+	0.756302i	−0.0691234	+	0.997608i	$0.522020\pi$
$434$	−1.43653	−	8.14695i	−0.0689555	−	0.391066i
$435$	−19.2496	−	7.00627i	−0.922946	−	0.335925i
$436$	−8.84348			−0.423526
$437$		0			0
$438$	−6.33280			−0.302593
$439$	28.9790	+	10.5475i	1.38309	+	0.503404i	0.923114	−	0.384526i	$-0.125635\pi$
$439$	28.9790	+	10.5475i	1.38309	+	0.503404i	0.459978	+	0.887930i	$0.347857\pi$
$440$	−2.34354	−	13.2909i	−0.111724	−	0.633617i
$441$	−19.6935	−	16.5248i	−0.937788	−	0.786897i
$442$	0.975776	−	0.818773i	0.0464129	−	0.0389451i
$443$	1.85885	−	10.5420i	0.0883165	−	0.500868i	−0.908275	−	0.418374i	$-0.862600\pi$
$443$	1.85885	−	10.5420i	0.0883165	−	0.500868i	0.996592	−	0.0824942i	$-0.0262886\pi$
$444$	5.55899	−	9.62845i	0.263818	−	0.456946i
$445$	−17.6740	−	30.6123i	−0.837830	−	1.45116i
$446$	−8.38582	+	3.05219i	−0.397080	+	0.144525i
$447$	24.5025	−	8.91820i	1.15893	−	0.421816i
$448$	0.642040	+	1.11205i	0.0303335	+	0.0525392i
$449$	−1.15781	+	2.00538i	−0.0546403	+	0.0946399i	−0.892052	−	0.451933i	$-0.850735\pi$
$449$	−1.15781	+	2.00538i	−0.0546403	+	0.0946399i	0.837411	+	0.546573i	$0.184068\pi$
$450$	0.414652	−	2.35161i	0.0195469	−	0.110856i
$451$	−22.1234	+	18.5637i	−1.04175	+	0.874131i
$452$	−10.9163	−	9.15988i	−0.513460	−	0.430844i
$453$	9.61630	+	54.5368i	0.451813	+	2.56236i
$454$	0.620005	+	0.225663i	0.0290983	+	0.0105909i
$455$	0.916079			0.0429465
$456$		0			0
$457$	−0.0521810			−0.00244092			−0.00122046	−	0.999999i	$-0.500388\pi$
$457$	−0.0521810			−0.00244092			−0.00122046	+	0.999999i	$0.500388\pi$
$458$	6.55161	+	2.38459i	0.306137	+	0.111425i
$459$	3.66391	+	20.7791i	0.171017	+	0.969885i
$460$	11.6327	+	9.76101i	0.542378	+	0.455109i
$461$	30.2373	−	25.3721i	1.40829	−	1.18170i	0.451019	−	0.892514i	$-0.351061\pi$
$461$	30.2373	−	25.3721i	1.40829	−	1.18170i	0.957274	−	0.289183i	$-0.0933837\pi$
$462$	−3.58562	+	20.3350i	−0.166818	+	0.946072i
$463$	3.09528	−	5.36119i	0.143850	−	0.249155i	−0.785093	−	0.619377i	$-0.787385\pi$
$463$	3.09528	−	5.36119i	0.143850	−	0.249155i	0.928943	+	0.370222i	$0.120718\pi$
$464$	1.56378	+	2.70855i	0.0725967	+	0.125741i
$465$	39.6522	−	14.4322i	1.83883	−	0.669278i
$466$	27.8240	−	10.1271i	1.28892	−	0.469129i
$467$	10.4981	+	18.1832i	0.485793	+	0.841418i	0.999867	−	0.0163277i	$-0.00519750\pi$
$467$	10.4981	+	18.1832i	0.485793	+	0.841418i	−0.514074	+	0.857746i	$0.671864\pi$
$468$	−0.730921	+	1.26599i	−0.0337868	+	0.0585205i
$469$	0.976825	−	5.53985i	0.0451056	−	0.255806i
$470$	7.89266	−	6.62272i	0.364061	−	0.305483i
$471$	29.6771	+	24.9020i	1.36745	+	1.14742i
$472$	0.575427	+	3.26341i	0.0264862	+	0.150211i
$473$	5.35162	+	1.94783i	0.246068	+	0.0895613i
$474$	23.9596			1.10050
$475$		0			0
$476$	−5.37540			−0.246381
$477$	−14.8556	−	5.40699i	−0.680191	−	0.247569i
$478$	−4.28970	−	24.3281i	−0.196206	−	1.11274i
$479$	11.8913	+	9.97795i	0.543326	+	0.455904i	0.872673	−	0.488304i	$-0.162384\pi$
$479$	11.8913	+	9.97795i	0.543326	+	0.455904i	−0.329348	+	0.944209i	$0.606829\pi$
$480$	−5.01745	+	4.21014i	−0.229014	+	0.192166i
$481$	−0.210285	+	1.19258i	−0.00958817	+	0.0543772i
$482$	−13.7793	+	23.8665i	−0.627631	+	1.08709i
$483$	−11.6169	−	20.1210i	−0.528586	−	0.915539i
$484$	−20.7992	+	7.57028i	−0.945417	+	0.344104i
$485$	38.2300	−	13.9146i	1.73593	−	0.631829i
$486$	8.02431	+	13.8985i	0.363990	+	0.630449i
$487$	14.3033	−	24.7740i	0.648143	−	1.12262i	−0.335423	−	0.942068i	$-0.608879\pi$
$487$	14.3033	−	24.7740i	0.648143	−	1.12262i	0.983566	−	0.180549i	$-0.0577875\pi$
$488$	−1.90344	+	10.7949i	−0.0861646	+	0.488663i
$489$	30.4945	−	25.5879i	1.37901	−	1.15713i
$490$	9.61092	+	8.06452i	0.434177	+	0.364318i
$491$	−5.27002	−	29.8878i	−0.237833	−	1.34882i	−0.836565	−	0.547867i	$-0.815440\pi$
$491$	−5.27002	−	29.8878i	−0.237833	−	1.34882i	0.598733	−	0.800949i	$-0.295671\pi$
$492$	13.1708	+	4.79377i	0.593784	+	0.216120i
$493$	−13.0926			−0.589659
$494$		0			0
$495$	−64.8373			−2.91422
$496$	−6.05394	−	2.20345i	−0.271830	−	0.0989379i
$497$	0.984603	+	5.58396i	0.0441655	+	0.250475i
$498$	−20.8966	−	17.5343i	−0.936398	−	0.785732i
$499$	6.72299	−	5.64126i	0.300962	−	0.252537i	−0.479782	−	0.877387i	$-0.659284\pi$
$499$	6.72299	−	5.64126i	0.300962	−	0.252537i	0.780745	+	0.624850i	$0.214840\pi$
$500$	1.83330	−	10.3971i	0.0819875	−	0.464974i
$501$	−16.1891	+	28.0403i	−0.723275	+	1.25275i
$502$	1.49428	+	2.58816i	0.0666928	+	0.115515i
$503$	19.8316	−	7.21811i	0.884247	−	0.321840i	0.140325	−	0.990106i	$-0.455185\pi$
$503$	19.8316	−	7.21811i	0.884247	−	0.321840i	0.743922	+	0.668266i	$0.232963\pi$
$504$	5.79697	−	2.10992i	0.258218	−	0.0939835i
$505$	4.31011	+	7.46533i	0.191798	+	0.332203i
$506$	18.6410	−	32.2872i	0.828695	−	1.43534i
$507$	−6.26144	+	35.5104i	−0.278080	+	1.57707i
$508$	1.70839	−	1.43351i	0.0757976	−	0.0636017i
$509$	17.0224	+	14.2835i	0.754505	+	0.633105i	0.936690	−	0.350160i	$-0.113873\pi$
$509$	17.0224	+	14.2835i	0.754505	+	0.633105i	−0.182185	+	0.983264i	$0.558317\pi$
$510$	−4.76123	−	27.0022i	−0.210831	−	1.19568i
$511$	−2.73532	−	0.995576i	−0.121004	−	0.0440417i
$512$	1.00000			0.0441942
$513$		0			0
$514$	14.1323			0.623347
$515$	41.8902	+	15.2468i	1.84590	+	0.671854i
$516$	−0.479952	−	2.72194i	−0.0211287	−	0.119827i
$517$	−19.3774	−	16.2596i	−0.852218	−	0.715095i
$518$	3.91477	−	3.28488i	0.172005	−	0.144330i
$519$	1.93243	−	10.9593i	0.0848241	−	0.481061i
$520$	0.356707	−	0.617834i	0.0156426	−	0.0270938i
$521$	−5.01661	−	8.68902i	−0.219782	−	0.380673i	0.734959	−	0.678111i	$-0.237201\pi$
$521$	−5.01661	−	8.68902i	−0.219782	−	0.380673i	−0.954741	+	0.297438i	$0.903868\pi$
$522$	14.1194	−	5.13902i	0.617987	−	0.224929i
$523$	−27.5163	+	10.0151i	−1.20321	+	0.437931i	−0.864342	−	0.502904i	$-0.832265\pi$
$523$	−27.5163	+	10.0151i	−1.20321	+	0.437931i	−0.338864	+	0.940835i	$0.610043\pi$
$524$	−0.761327	−	1.31866i	−0.0332587	−	0.0576058i
$525$	0.891491	−	1.54411i	0.0389079	−	0.0673904i
$526$	1.31432	−	7.45388i	0.0573071	−	0.325005i
$527$	20.6598	−	17.3356i	0.899953	−	0.755150i
$528$	12.3184	+	10.3364i	0.536092	+	0.449834i
$529$	3.29053	+	18.6615i	0.143066	+	0.811370i
$530$	7.24988	+	2.63874i	0.314915	+	0.114620i
$531$	15.9200			0.690870
$532$		0			0
$533$	−1.52664			−0.0661262
$534$	39.5778	+	14.4052i	1.71270	+	0.623372i
$535$	−4.08649	−	23.1756i	−0.176674	−	1.00197i
$536$	−3.35590	−	2.81593i	−0.144953	−	0.121630i
$537$	−18.0851	+	15.1752i	−0.780431	+	0.654859i
$538$	−1.33201	+	7.55421i	−0.0574271	+	0.325685i
$539$	15.4012	−	26.6756i	0.663375	−	1.14900i
$540$	5.90868	+	10.2341i	0.254269	+	0.440407i
$541$	35.5583	−	12.9422i	1.52877	−	0.556427i	0.565451	−	0.824782i	$-0.308702\pi$
$541$	35.5583	−	12.9422i	1.52877	−	0.556427i	0.963320	+	0.268355i	$0.0864801\pi$
$542$	−10.9614	+	3.98963i	−0.470833	+	0.171369i
$543$	−11.8522	−	20.5287i	−0.508628	−	0.880970i
$544$	−2.09310	+	3.62535i	−0.0897408	+	0.155436i
$545$	3.60046	−	20.4192i	0.154227	−	0.874663i
$546$	−0.836157	+	0.701619i	−0.0357842	+	0.0300265i
$547$	−11.1058	−	9.31886i	−0.474849	−	0.398446i	0.373711	−	0.927545i	$-0.378085\pi$
$547$	−11.1058	−	9.31886i	−0.474849	−	0.398446i	−0.848560	+	0.529100i	$0.822530\pi$
$548$	1.86008	+	10.5490i	0.0794585	+	0.450632i
$549$	49.4855	+	18.0112i	2.11199	+	0.768701i
$550$	2.86106			0.121996
$551$		0			0
$552$	−18.0937			−0.770120
$553$	10.3489	+	3.76667i	0.440078	+	0.160175i
$554$	4.76499	+	27.0236i	0.202445	+	1.14812i
$555$	19.9684	+	16.7555i	0.847613	+	0.711232i
$556$	−8.28426	+	6.95132i	−0.351331	+	0.294802i
$557$	−0.753288	+	4.27211i	−0.0319178	+	0.181015i	−0.996599	−	0.0824058i	$-0.973740\pi$
$557$	−0.753288	+	4.27211i	−0.0319178	+	0.181015i	0.964681	+	0.263421i	$0.0848508\pi$
$558$	−15.4755	+	26.8044i	−0.655131	+	1.13472i
$559$	0.150525	+	0.260717i	0.00636654	+	0.0110272i
$560$	−2.82906	+	1.02969i	−0.119550	+	0.0435125i
$561$	−63.2568	+	23.0236i	−2.67070	+	0.972056i
$562$	−8.13574	−	14.0915i	−0.343185	−	0.594415i
$563$	13.6468	−	23.6370i	0.575144	−	0.996179i	−0.420882	−	0.907116i	$-0.638279\pi$
$563$	13.6468	−	23.6370i	0.575144	−	0.996179i	0.996026	−	0.0890637i	$-0.0283875\pi$
$564$	−2.13177	+	12.0899i	−0.0897636	+	0.509075i
$565$	25.5941	−	21.4760i	1.07675	−	0.903503i
$566$	2.59976	+	2.18145i	0.109276	+	0.0916934i
$567$	0.0740488	+	0.419952i	0.00310976	+	0.0176363i
$568$	4.14940	+	1.51026i	0.174105	+	0.0633690i
$569$	−7.19043			−0.301439			−0.150719	−	0.988577i	$-0.548159\pi$
$569$	−7.19043			−0.301439			−0.150719	+	0.988577i	$0.548159\pi$
$570$		0			0
$571$	42.0134			1.75821			0.879103	−	0.476631i	$-0.158142\pi$
$571$	42.0134			1.75821			0.879103	+	0.476631i	$0.158142\pi$
$572$	−1.64589	−	0.599054i	−0.0688180	−	0.0250477i
$573$	−10.8562	−	61.5683i	−0.453523	−	2.57205i
$574$	4.93521	+	4.14114i	0.205992	+	0.172848i
$575$	−2.46608	+	2.06929i	−0.102843	+	0.0862953i
$576$	0.834245	−	4.73124i	0.0347602	−	0.197135i
$577$	−10.8357	+	18.7679i	−0.451095	+	0.781319i	−0.998454	−	0.0555783i	$-0.982300\pi$
$577$	−10.8357	+	18.7679i	−0.451095	+	0.781319i	0.547359	+	0.836898i	$0.315633\pi$
$578$	−0.262102	−	0.453974i	−0.0109020	−	0.0188828i
$579$	−19.4998	+	7.09733i	−0.810382	+	0.294955i
$580$	−6.89058	+	2.50797i	−0.286116	+	0.104138i
$581$	−6.26929	−	10.8587i	−0.260094	−	0.450496i
$582$	−24.2376	+	41.9807i	−1.00468	+	1.74016i
$583$	3.28918	−	18.6539i	0.136224	−	0.772565i
$584$	−1.73654	+	1.45713i	−0.0718586	+	0.0602965i
$585$	−2.62554	−	2.20309i	−0.108553	−	0.0910866i
$586$	4.05960	+	23.0231i	0.167701	+	0.951077i
$587$	1.19214	+	0.433902i	0.0492047	+	0.0179091i	0.366505	−	0.930416i	$-0.380554\pi$
$587$	1.19214	+	0.433902i	0.0492047	+	0.0179091i	−0.317301	+	0.948325i	$0.602776\pi$
$588$	−14.9490			−0.616485
$589$		0			0
$590$	−7.76934			−0.319859
$591$	−22.4069	−	8.15544i	−0.921696	−	0.335470i
$592$	−0.691084	−	3.91933i	−0.0284034	−	0.161084i
$593$	16.5159	+	13.8585i	0.678227	+	0.569100i	0.915488	−	0.402346i	$-0.131805\pi$
$593$	16.5159	+	13.8585i	0.678227	+	0.569100i	−0.237260	+	0.971446i	$0.576249\pi$
$594$	22.2253	−	18.6492i	0.911913	−	0.765186i
$595$	2.18849	−	12.4116i	0.0897195	−	0.508825i
$596$	4.66692	−	8.08334i	0.191165	−	0.331107i
$597$	8.88262	+	15.3852i	0.363542	+	0.629672i
$598$	1.85193	−	0.674049i	0.0757312	−	0.0275639i
$599$	26.9144	−	9.79605i	1.09969	−	0.400256i	0.272491	−	0.962158i	$-0.412153\pi$
$599$	26.9144	−	9.79605i	1.09969	−	0.400256i	0.827203	+	0.561903i	$0.189930\pi$
$600$	−0.694265	−	1.20250i	−0.0283433	−	0.0490920i
$601$	−3.77932	+	6.54598i	−0.154162	+	0.267016i	−0.932754	−	0.360515i	$-0.882601\pi$
$601$	−3.77932	+	6.54598i	−0.154162	+	0.267016i	0.778592	+	0.627531i	$0.215934\pi$
$602$	0.220610	−	1.25114i	0.00899138	−	0.0509926i
$603$	−16.1225	+	13.5284i	−0.656559	+	0.550918i
$604$	15.1854	+	12.7421i	0.617886	+	0.518468i
$605$	−9.01145	−	51.1065i	−0.366368	−	2.07777i
$606$	−9.65173	−	3.51294i	−0.392075	−	0.142703i
$607$	1.72737			0.0701117			0.0350558	−	0.999385i	$-0.488839\pi$
$607$	1.72737			0.0701117			0.0350558	+	0.999385i	$0.488839\pi$
$608$		0			0
$609$	11.2192			0.454625
$610$	−24.1501	−	8.78991i	−0.977808	−	0.355893i
$611$	−0.232195	−	1.31684i	−0.00939358	−	0.0532737i
$612$	15.4062	+	12.9274i	0.622760	+	0.522558i
$613$	−21.0026	+	17.6233i	−0.848287	+	0.711797i	−0.959412	−	0.282009i	$-0.908999\pi$
$613$	−21.0026	+	17.6233i	−0.848287	+	0.711797i	0.111125	+	0.993806i	$0.464555\pi$
$614$	−0.241027	+	1.36693i	−0.00972707	+	0.0551649i
$615$	−16.4308	+	28.4590i	−0.662555	+	1.14758i
$616$	3.69572	+	6.40117i	0.148905	+	0.257911i
$617$	−9.98659	+	3.63482i	−0.402045	+	0.146332i	−0.535125	−	0.844773i	$-0.679735\pi$
$617$	−9.98659	+	3.63482i	−0.402045	+	0.146332i	0.133080	+	0.991105i	$0.457513\pi$
$618$	−49.9130	+	18.1668i	−2.00779	+	0.730777i
$619$	−4.18004	−	7.24004i	−0.168010	−	0.291002i	0.769710	−	0.638394i	$-0.220401\pi$
$619$	−4.18004	−	7.24004i	−0.168010	−	0.291002i	−0.937720	+	0.347392i	$0.887067\pi$
$620$	7.55242	−	13.0812i	0.303313	−	0.525353i
$621$	−5.66877	+	32.1492i	−0.227480	+	1.29010i
$622$	−9.33827	+	7.83574i	−0.374431	+	0.314185i
$623$	14.8302	+	12.4440i	0.594160	+	0.498559i
$624$	0.147609	+	0.837131i	0.00590908	+	0.0335121i
$625$	25.5955	+	9.31600i	1.02382	+	0.372640i
$626$	16.5314			0.660728
$627$		0			0
$628$	13.8676			0.553379
$629$	15.6555	+	5.69812i	0.624224	+	0.227199i
$630$	2.51160	+	14.2440i	0.100064	+	0.567493i
$631$	18.7912	+	15.7677i	0.748065	+	0.627701i	0.934990	−	0.354673i	$-0.115408\pi$
$631$	18.7912	+	15.7677i	0.748065	+	0.627701i	−0.186925	+	0.982374i	$0.559852\pi$
$632$	6.57005	−	5.51292i	0.261342	−	0.219292i
$633$	−6.77099	+	38.4002i	−0.269123	+	1.52627i
$634$	−1.34406	+	2.32797i	−0.0533793	+	0.0924557i
$635$	2.61437	+	4.52823i	0.103748	+	0.179697i
$636$	−8.63837	+	3.14411i	−0.342533	+	0.124672i
$637$	1.53006	−	0.556897i	0.0606233	−	0.0220651i
$638$	9.00145	+	15.5910i	0.356371	+	0.617253i
$639$	10.6070	−	18.3719i	0.419606	−	0.726780i
$640$	−0.407131	+	2.30896i	−0.0160933	+	0.0912695i
$641$	−5.34140	+	4.48197i	−0.210973	+	0.177027i	−0.742150	−	0.670233i	$-0.766194\pi$
$641$	−5.34140	+	4.48197i	−0.210973	+	0.177027i	0.531178	+	0.847260i	$0.321750\pi$
$642$	21.4800	+	18.0239i	0.847749	+	0.711346i
$643$	−1.57850	−	8.95214i	−0.0622501	−	0.353038i	−0.999984	−	0.00568299i	$-0.998191\pi$
$643$	−1.57850	−	8.95214i	−0.0622501	−	0.353038i	0.937734	−	0.347355i	$-0.112920\pi$
$644$	−7.81521	−	2.84450i	−0.307962	−	0.112089i
$645$	6.48025			0.255160
$646$		0			0
$647$	30.0074			1.17971			0.589856	−	0.807509i	$-0.299185\pi$
$647$	30.0074			1.17971			0.589856	+	0.807509i	$0.299185\pi$
$648$	0.312063	+	0.113582i	0.0122590	+	0.00446190i
$649$	3.31228	+	18.7849i	0.130018	+	0.737371i
$650$	0.115857	+	0.0972154i	0.00454428	+	0.00381310i
$651$	−17.7036	+	14.8551i	−0.693860	+	0.582218i
$652$	2.47442	−	14.0331i	0.0969056	−	0.549579i
$653$	−5.20956	+	9.02323i	−0.203866	+	0.353106i	−0.949771	−	0.312946i	$-0.898684\pi$
$653$	−5.20956	+	9.02323i	−0.203866	+	0.353106i	0.745905	+	0.666053i	$0.232017\pi$
$654$	12.3526	+	21.3953i	0.483025	+	0.836623i
$655$	3.35468	−	1.22101i	0.131078	−	0.0477086i
$656$	4.71461	−	1.71598i	0.184075	−	0.0669977i
$657$	5.44533	+	9.43159i	0.212443	+	0.367962i
$658$	−2.82141	+	4.88683i	−0.109990	+	0.190508i
$659$	−4.58008	+	25.9749i	−0.178414	+	1.01184i	0.755714	+	0.654902i	$0.227290\pi$
$659$	−4.58008	+	25.9749i	−0.178414	+	1.01184i	−0.934129	+	0.356937i	$0.883821\pi$
$660$	−28.8815	+	24.2345i	−1.12421	+	0.943326i
$661$	−18.9167	−	15.8730i	−0.735773	−	0.617387i	0.195926	−	0.980619i	$-0.437229\pi$
$661$	−18.9167	−	15.8730i	−0.735773	−	0.617387i	−0.931699	+	0.363232i	$0.881673\pi$
$662$	0.905233	+	5.13383i	0.0351829	+	0.199532i
$663$	−3.34385	−	1.21706i	−0.129864	−	0.0472668i
$664$	−9.76464			−0.378942
$665$		0			0
$666$	−19.1198			−0.740879
$667$	−19.0351	−	6.92820i	−0.737040	−	0.268261i
$668$	2.01260	+	11.4140i	0.0778699	+	0.441622i
$669$	19.0976	+	16.0248i	0.738355	+	0.619554i
$670$	7.86816	−	6.60217i	0.303974	−	0.255064i
$671$	−10.9566	+	62.1379i	−0.422975	+	2.39881i
$672$	1.79360	−	3.10661i	0.0691898	−	0.119840i
$673$	4.88690	+	8.46436i	0.188376	+	0.326277i	0.944709	−	0.327910i	$-0.106344\pi$
$673$	4.88690	+	8.46436i	0.188376	+	0.326277i	−0.756333	+	0.654187i	$0.773011\pi$
$674$	25.1156	−	9.14133i	0.967417	−	0.352111i
$675$	−2.35414	+	0.856837i	−0.0906109	+	0.0329797i
$676$	6.45371	+	11.1781i	0.248219	+	0.429929i
$677$	10.7874	−	18.6843i	0.414592	−	0.718094i	−0.580794	−	0.814051i	$-0.697258\pi$
$677$	10.7874	−	18.6843i	0.414592	−	0.718094i	0.995386	+	0.0959565i	$0.0305910\pi$
$678$	−6.91285	+	39.2047i	−0.265486	+	1.50565i
$679$	−17.0687	+	14.3223i	−0.655036	+	0.549640i
$680$	−7.51861	−	6.30886i	−0.288326	−	0.241934i
$681$	−0.320070	−	1.81521i	−0.0122651	−	0.0695588i
$682$	−34.8478	−	12.6835i	−1.33439	−	0.485678i
$683$	33.2509			1.27231			0.636155	−	0.771561i	$-0.280524\pi$
$683$	33.2509			1.27231			0.636155	+	0.771561i	$0.280524\pi$
$684$		0			0
$685$	−25.1145			−0.959576
$686$	−14.9034	−	5.42439i	−0.569014	−	0.207104i
$687$	−3.38219	−	19.1813i	−0.129038	−	0.731813i
$688$	−0.757908	−	0.635960i	−0.0288950	−	0.0242458i
$689$	0.767029	−	0.643614i	0.0292215	−	0.0245197i
$690$	7.36652	−	41.7776i	0.280439	−	1.59045i
$691$	−2.40466	+	4.16500i	−0.0914776	+	0.158444i	−0.908133	−	0.418682i	$-0.862492\pi$
$691$	−2.40466	+	4.16500i	−0.0914776	+	0.158444i	0.816655	+	0.577126i	$0.195826\pi$
$692$	−1.99176	−	3.44983i	−0.0757155	−	0.131143i
$693$	33.3686	−	12.1452i	1.26757	−	0.461357i
$694$	30.6981	−	11.1732i	1.16528	−	0.424128i
$695$	−12.6775	−	21.9581i	−0.480886	−	0.832919i
$696$	4.36858	−	7.56661i	0.165591	−	0.286811i
$697$	−3.64712	+	20.6838i	−0.138144	+	0.783456i
$698$	−22.2963	+	18.7088i	−0.843928	+	0.708140i
$699$	−63.3655	−	53.1700i	−2.39670	−	2.01107i
$700$	−0.110829	−	0.628541i	−0.00418893	−	0.0237566i
$701$	−3.25572	−	1.18499i	−0.122967	−	0.0447563i	0.279804	−	0.960057i	$-0.409731\pi$
$701$	−3.25572	−	1.18499i	−0.122967	−	0.0447563i	−0.402771	+	0.915301i	$0.631953\pi$
$702$	1.53367			0.0578848
$703$		0			0
$704$	5.75621			0.216946
$705$	−27.0471	−	9.84432i	−1.01865	−	0.370759i
$706$	−2.48402	−	14.0876i	−0.0934872	−	0.530192i
$707$	−3.61660	−	3.03468i	−0.136016	−	0.114131i
$708$	7.09151	−	5.95048i	0.266515	−	0.223633i
$709$	3.57269	−	20.2617i	0.134175	−	0.760945i	−0.841255	−	0.540638i	$-0.818183\pi$
$709$	3.57269	−	20.2617i	0.134175	−	0.760945i	0.975431	−	0.220307i	$-0.0707060\pi$
$710$	−5.17647	+	8.96591i	−0.194269	+	0.336484i
$711$	−20.6019	−	35.6836i	−0.772633	−	1.33824i
$712$	14.1673	−	5.15648i	0.530942	−	0.193247i
$713$	39.2103	−	14.2714i	1.46844	−	0.534468i
$714$	7.50837	+	13.0049i	0.280994	+	0.486696i
$715$	2.05328	−	3.55639i	0.0767884	−	0.133001i
$716$	−1.46748	+	8.32250i	−0.0548424	+	0.311027i
$717$	−52.8659	+	44.3597i	−1.97431	+	1.65664i
$718$	15.0686	+	12.6441i	0.562356	+	0.471873i
$719$	4.20030	+	23.8211i	0.156645	+	0.888376i	0.957267	+	0.289206i	$0.0933914\pi$
$719$	4.20030	+	23.8211i	0.156645	+	0.888376i	−0.800622	+	0.599170i	$0.795498\pi$
$720$	10.5846	+	3.85247i	0.394464	+	0.143573i
$721$	−24.4149			−0.909257
$722$		0			0
$723$	76.9880			2.86321
$724$	−7.97354	−	2.90213i	−0.296334	−	0.107857i
$725$	−0.269939	−	1.53090i	−0.0100253	−	0.0568563i
$726$	47.3673	+	39.7459i	1.75797	+	1.47511i
$727$	13.8866	−	11.6522i	0.515024	−	0.432157i	−0.347869	−	0.937543i	$-0.613095\pi$
$727$	13.8866	−	11.6522i	0.515024	−	0.432157i	0.862893	+	0.505387i	$0.168650\pi$
$728$	−0.0678483	+	0.384787i	−0.00251463	+	0.0142611i
$729$	21.9186	−	37.9641i	0.811800	−	1.40608i
$730$	−2.65745	−	4.60284i	−0.0983567	−	0.170359i
$731$	3.89195	−	1.41655i	0.143949	−	0.0523932i
$732$	28.7752	−	10.4733i	1.06356	−	0.387106i
$733$	−11.3682	−	19.6902i	−0.419893	−	0.727275i	0.576036	−	0.817425i	$-0.304599\pi$
$733$	−11.3682	−	19.6902i	−0.419893	−	0.727275i	−0.995928	+	0.0901491i	$0.971266\pi$
$734$	−4.77527	+	8.27100i	−0.176258	+	0.305288i
$735$	6.08620	−	34.5165i	0.224493	−	1.27316i
$736$	−4.96154	+	4.16323i	−0.182885	+	0.153459i
$737$	−19.3173	−	16.2091i	−0.711561	−	0.597070i
$738$	−4.18556	−	23.7375i	−0.154073	−	0.873790i
$739$	−14.2633	−	5.19141i	−0.524683	−	0.190969i	0.0660797	−	0.997814i	$-0.478951\pi$
$739$	−14.2633	−	5.19141i	−0.524683	−	0.190969i	−0.590763	+	0.806845i	$0.701173\pi$
$740$	9.33094			0.343012
$741$		0			0
$742$	−4.22545			−0.155121
$743$	3.07867	+	1.12054i	0.112945	+	0.0411087i	0.397875	−	0.917440i	$-0.369748\pi$
$743$	3.07867	+	1.12054i	0.112945	+	0.0411087i	−0.284929	+	0.958549i	$0.591970\pi$
$744$	3.12527	+	17.7243i	0.114578	+	0.649803i
$745$	16.7640	+	14.0667i	0.614187	+	0.515364i
$746$	2.78848	−	2.33981i	0.102094	−	0.0856666i
$747$	−8.14611	+	46.1989i	−0.298050	+	1.69033i
$748$	−12.0483	+	20.8683i	−0.440530	+	0.763020i
$749$	6.44433	+	11.1619i	0.235471	+	0.407847i
$750$	−27.7149	+	10.0874i	−1.01201	+	0.368340i
$751$	−49.0823	+	17.8645i	−1.79104	+	0.651885i	−0.791889	+	0.610665i	$0.790902\pi$
$751$	−49.0823	+	17.8645i	−1.79104	+	0.651885i	−0.999150	+	0.0412203i	$0.986875\pi$
$752$	2.19723	+	3.80571i	0.0801246	+	0.138780i
$753$	4.17442	−	7.23030i	0.152124	−	0.263487i
$754$	−0.165254	+	0.937204i	−0.00601821	+	0.0341309i
$755$	−35.6034	+	29.8748i	−1.29574	+	1.08725i
$756$	−4.95794	−	4.16021i	−0.180319	−	0.151305i
$757$	−4.20823	−	23.8660i	−0.152951	−	0.867426i	−0.960636	−	0.277812i	$-0.910391\pi$
$757$	−4.20823	−	23.8660i	−0.152951	−	0.867426i	0.807685	−	0.589614i	$-0.200720\pi$
$758$	−7.84400	−	2.85498i	−0.284907	−	0.103698i
$759$	−104.151			−3.78045
$760$		0			0
$761$	−24.8054			−0.899195			−0.449597	−	0.893231i	$-0.648433\pi$
$761$	−24.8054			−0.899195			−0.449597	+	0.893231i	$0.648433\pi$
$762$	−5.85442	−	2.13084i	−0.212083	−	0.0771920i
$763$	1.97190	+	11.1832i	0.0713876	+	0.404859i
$764$	−17.1433	−	14.3850i	−0.620224	−	0.520429i
$765$	−36.1211	+	30.3092i	−1.30596	+	1.09583i
$766$	−1.64717	+	9.34155i	−0.0595146	+	0.337524i
$767$	−0.504158	+	0.873228i	−0.0182041	+	0.0315304i
$768$	−1.39680	−	2.41933i	−0.0504028	−	0.0873001i
$769$	−9.06136	+	3.29806i	−0.326761	+	0.118931i	−0.500191	−	0.865915i	$-0.666737\pi$
$769$	−9.06136	+	3.29806i	−0.326761	+	0.118931i	0.173431	+	0.984846i	$0.444515\pi$
$770$	−16.2847	+	5.92714i	−0.586859	+	0.213599i
$771$	−19.7400	−	34.1906i	−0.710918	−	1.23135i
$772$	−3.71406	+	6.43293i	−0.133672	+	0.231526i
$773$	0.223539	−	1.26775i	0.00804015	−	0.0455979i	−0.980524	−	0.196401i	$-0.937075\pi$
$773$	0.223539	−	1.26775i	0.00804015	−	0.0455979i	0.988564	+	0.150803i	$0.0481858\pi$
$774$	−3.64116	+	3.05530i	−0.130879	+	0.109820i
$775$	2.45299	+	2.05831i	0.0881141	+	0.0739365i
$776$	3.01317	+	17.0886i	0.108167	+	0.613444i
$777$	−13.4154	−	4.88280i	−0.481275	−	0.175170i
$778$	36.0480			1.29238
$779$		0			0
$780$	−1.99300			−0.0713607
$781$	23.8848	+	8.69336i	0.854666	+	0.311073i
$782$	−4.70817	−	26.7014i	−0.168364	−	0.954839i
$783$	−12.0758	−	10.1328i	−0.431553	−	0.362116i
$784$	−4.09921	+	3.43965i	−0.146400	+	0.122845i
$785$	−5.64595	+	32.0198i	−0.201513	+	1.14283i
$786$	−2.12685	+	3.68381i	−0.0758621	+	0.131397i
$787$	8.17232	+	14.1549i	0.291312	+	0.504567i	0.974120	−	0.226031i	$-0.0725749\pi$
$787$	8.17232	+	14.1549i	0.291312	+	0.504567i	−0.682808	+	0.730598i	$0.739242\pi$
$788$	−8.02078	+	2.91933i	−0.285729	+	0.103997i
$789$	−19.8693	+	7.23182i	−0.707365	+	0.257460i
$790$	10.0542	+	17.4144i	0.357714	+	0.619578i
$791$	−9.14922	+	15.8469i	−0.325309	+	0.563451i
$792$	4.80209	−	27.2340i	0.170635	−	0.967719i
$793$	−2.55505	+	2.14394i	−0.0907324	+	0.0761336i
$794$	−4.90963	−	4.11967i	−0.174236	−	0.146201i
$795$	−3.74266	−	21.2257i	−0.132738	−	0.752797i
$796$	5.97575	+	2.17499i	0.211805	+	0.0770906i
$797$	−15.6884			−0.555712			−0.277856	−	0.960623i	$-0.589624\pi$
$797$	−15.6884			−0.555712			−0.277856	+	0.960623i	$0.589624\pi$
$798$		0			0
$799$	−18.3960			−0.650804
$800$	−0.467064	−	0.169997i	−0.0165132	−	0.00601031i
$801$	−12.5775	−	71.3307i	−0.444405	−	2.52035i
$802$	0.143756	+	0.120625i	0.00507619	+	0.00425943i
$803$	−9.99590	+	8.38756i	−0.352748	+	0.295990i
$804$	−2.12515	+	12.0523i	−0.0749483	+	0.425053i
$805$	9.74965	−	16.8869i	0.343630	−	0.595185i
$806$	−0.980164	−	1.69769i	−0.0345248	−	0.0597987i
$807$	20.1367	−	7.32916i	0.708845	−	0.257999i
$808$	−3.45494	+	1.25749i	−0.121544	+	0.0442385i
$809$	5.76242	+	9.98080i	0.202596	+	0.350906i	0.949364	−	0.314178i	$-0.101729\pi$
$809$	5.76242	+	9.98080i	0.202596	+	0.350906i	−0.746768	+	0.665084i	$0.768396\pi$
$810$	−0.389305	+	0.674297i	−0.0136788	+	0.0236924i
$811$	−1.44146	+	8.17491i	−0.0506164	+	0.287060i	−0.999600	−	0.0282641i	$-0.991002\pi$
$811$	−1.44146	+	8.17491i	−0.0506164	+	0.287060i	0.948984	+	0.315324i	$0.102113\pi$
$812$	3.07646	−	2.58146i	0.107963	−	0.0905914i
$813$	24.9632	+	20.9466i	0.875496	+	0.734629i
$814$	−3.97803	−	22.5605i	−0.139430	−	0.790746i
$815$	31.3944	+	11.4266i	1.09970	+	0.400258i
$816$	11.6946			0.409392
$817$		0			0
$818$	17.2663			0.603701
$819$	1.76392	+	0.642013i	0.0616362	+	0.0224337i
$820$	2.04265	+	11.5845i	0.0713326	+	0.404547i
$821$	−25.8243	−	21.6692i	−0.901275	−	0.756259i	0.0691645	−	0.997605i	$-0.477967\pi$
$821$	−25.8243	−	21.6692i	−0.901275	−	0.756259i	−0.970439	+	0.241346i	$0.922411\pi$
$822$	22.9234	−	19.2350i	0.799546	−	0.670899i
$823$	3.79730	−	21.5355i	0.132365	−	0.750682i	−0.844293	−	0.535882i	$-0.819979\pi$
$823$	3.79730	−	21.5355i	0.132365	−	0.750682i	0.976658	−	0.214799i	$-0.0689098\pi$
$824$	−9.50676	+	16.4662i	−0.331184	+	0.573627i
$825$	−3.99634	−	6.92186i	−0.139135	−	0.240988i
$826$	3.99850	−	1.45534i	0.139126	−	0.0506376i
$827$	−36.8073	+	13.3968i	−1.27991	+	0.465851i	−0.890404	−	0.455171i	$-0.849578\pi$
$827$	−36.8073	+	13.3968i	−1.27991	+	0.465851i	−0.389511	+	0.921022i	$0.627356\pi$
$828$	15.5581	+	26.9474i	0.540681	+	0.936487i
$829$	7.20878	−	12.4860i	0.250371	−	0.433656i	−0.713257	−	0.700903i	$-0.752781\pi$
$829$	7.20878	−	12.4860i	0.250371	−	0.433656i	0.963628	+	0.267247i	$0.0861140\pi$
$830$	3.97549	−	22.5461i	0.137991	−	0.782588i
$831$	58.7233	−	49.2747i	2.03709	−	1.70932i
$832$	0.233094	+	0.195589i	0.00808108	+	0.00678083i
$833$	−3.88988	−	22.0606i	−0.134776	−	0.764354i
$834$	28.3890	+	10.3328i	0.983032	+	0.357794i
$835$	−27.1739			−0.940392
$836$		0			0
$837$	32.4719			1.12239
$838$	1.62164	+	0.590230i	0.0560188	+	0.0203892i
$839$	3.63849	+	20.6349i	0.125615	+	0.712395i	0.980941	+	0.194306i	$0.0622454\pi$
$839$	3.63849	+	20.6349i	0.125615	+	0.712395i	−0.855326	+	0.518089i	$0.826643\pi$
$840$	6.44281	+	5.40616i	0.222298	+	0.186530i
$841$	−14.7221	+	12.3533i	−0.507660	+	0.425977i
$842$	5.68777	−	32.2569i	0.196013	−	1.11165i
$843$	−22.7280	+	39.3661i	−0.782795	+	1.35584i
$844$	6.97890	+	12.0878i	0.240224	+	0.416079i
$845$	−28.4374	+	10.3504i	−0.978275	+	0.356063i
$846$	19.8387	−	7.22071i	0.682070	−	0.248253i
$847$	14.2109	+	24.6140i	0.488293	+	0.845748i
$848$	−1.64532	+	2.84978i	−0.0565006	+	0.0978619i
$849$	1.64632	−	9.33673i	0.0565015	−	0.320436i
$850$	1.59391	−	1.33745i	0.0546706	−	0.0458741i
$851$	19.7459	+	16.5688i	0.676882	+	0.567971i
$852$	−2.14207	−	12.1483i	−0.0733862	−	0.416194i
$853$	−48.8220	−	17.7698i	−1.67163	−	0.608425i	−0.679508	−	0.733668i	$-0.737807\pi$
$853$	−48.8220	−	17.7698i	−1.67163	−	0.608425i	−0.992126	+	0.125243i	$0.960029\pi$
$854$	14.0754			0.481650
$855$		0			0
$856$	10.0373			0.343067
$857$	−27.4235	−	9.98133i	−0.936768	−	0.340956i	−0.171879	−	0.985118i	$-0.554984\pi$
$857$	−27.4235	−	9.98133i	−0.936768	−	0.340956i	−0.764889	+	0.644162i	$0.777206\pi$
$858$	0.849668	+	4.81870i	0.0290072	+	0.164508i
$859$	16.8463	+	14.1358i	0.574790	+	0.482306i	0.883231	−	0.468937i	$-0.155363\pi$
$859$	16.8463	+	14.1358i	0.574790	+	0.482306i	−0.308442	+	0.951243i	$0.599807\pi$
$860$	1.77697	−	1.49106i	0.0605943	−	0.0508446i
$861$	3.12527	−	17.7243i	0.106509	−	0.604041i
$862$	12.7560	−	22.0940i	0.434470	−	0.752524i
$863$	17.9079	+	31.0173i	0.609590	+	1.05584i	0.991308	+	0.131562i	$0.0419994\pi$
$863$	17.9079	+	31.0173i	0.609590	+	1.05584i	−0.381717	+	0.924279i	$0.624667\pi$
$864$	−4.73633	+	1.72388i	−0.161133	+	0.0586477i
$865$	8.77643	−	3.19436i	0.298408	−	0.108611i
$866$	−12.2417	−	21.2032i	−0.415990	−	0.720516i
$867$	−0.732209	+	1.26822i	−0.0248671	+	0.0430711i
$868$	−1.43653	+	8.14695i	−0.0487589	+	0.276526i
$869$	37.8186	−	31.7336i	1.28291	−	1.07649i
$870$	15.6924	+	13.1675i	0.532022	+	0.446419i
$871$	−0.231474	−	1.31275i	−0.00784319	−	0.0444810i
$872$	8.31015	+	3.02465i	0.281417	+	0.102428i
$873$	83.3638			2.82144
$874$		0			0
$875$	−13.5567			−0.458300
$876$	5.95089	+	2.16595i	0.201062	+	0.0731805i
$877$	1.35877	+	7.70595i	0.0458823	+	0.260211i	0.999117	−	0.0420204i	$-0.0133794\pi$
$877$	1.35877	+	7.70595i	0.0458823	+	0.260211i	−0.953234	+	0.302232i	$0.902268\pi$
$878$	−23.6239	−	19.8228i	−0.797268	−	0.668987i
$879$	50.0302	−	41.9803i	1.68748	−	1.41596i
$880$	−2.34354	+	13.2909i	−0.0790006	+	0.448035i
$881$	7.24145	−	12.5426i	0.243970	−	0.422569i	−0.717871	−	0.696176i	$-0.754883\pi$
$881$	7.24145	−	12.5426i	0.243970	−	0.422569i	0.961842	+	0.273607i	$0.0882167\pi$
$882$	12.8540	+	22.2639i	0.432818	+	0.749663i
$883$	22.1325	−	8.05558i	0.744818	−	0.271092i	0.0583947	−	0.998294i	$-0.481402\pi$
$883$	22.1325	−	8.05558i	0.744818	−	0.271092i	0.686424	+	0.727202i	$0.259180\pi$
$884$	−1.19697	+	0.435660i	−0.0402583	+	0.0146528i
$885$	10.8522	+	18.7966i	0.364794	+	0.631842i
$886$	−5.35234	+	9.27052i	−0.179815	+	0.311449i
$887$	−2.75642	+	15.6324i	−0.0925514	+	0.524885i	0.902919	+	0.429811i	$0.141420\pi$
$887$	−2.75642	+	15.6324i	−0.0925514	+	0.524885i	−0.995470	+	0.0950740i	$0.969691\pi$
$888$	−8.51686	+	7.14650i	−0.285807	+	0.239821i
$889$	−2.19371	−	1.84074i	−0.0735746	−	0.0617365i
$890$	6.13813	+	34.8111i	0.205751	+	1.16687i
$891$	1.79630	+	0.653800i	0.0601783	+	0.0219031i
$892$	8.92400			0.298798
$893$		0			0
$894$	−26.0751			−0.872081
$895$	−18.6188	−	6.77671i	−0.622359	−	0.226520i
$896$	−0.222978	−	1.26457i	−0.00744917	−	0.0422464i
$897$	−4.21754	−	3.53893i	−0.140819	−	0.118162i
$898$	1.77387	−	1.48845i	0.0591946	−	0.0496702i
$899$	−3.49887	+	19.8431i	−0.116694	+	0.661804i
$900$	−1.19394	+	2.06797i	−0.0397981	+	0.0689324i
$901$	−6.88763	−	11.9297i	−0.229460	−	0.397437i
$902$	27.1383	−	9.87754i	0.903607	−	0.328886i
$903$	−3.33507	+	1.21387i	−0.110984	+	0.0403949i
$904$	7.12512	+	12.3411i	0.236978	+	0.410458i
$905$	9.94718	−	17.2290i	0.330655	−	0.572712i
$906$	9.61630	−	54.5368i	0.319480	−	1.81186i
$907$	34.4817	−	28.9336i	1.14495	−	0.960725i	0.145358	−	0.989379i	$-0.453567\pi$
$907$	34.4817	−	28.9336i	1.14495	−	0.960725i	0.999589	+	0.0286545i	$0.00912227\pi$
$908$	−0.505433	−	0.424109i	−0.0167734	−	0.0140745i
$909$	3.06724	+	17.3952i	0.101734	+	0.576962i
$910$	−0.860833	−	0.313318i	−0.0285363	−	0.0103864i
$911$	−2.75901			−0.0914100			−0.0457050	−	0.998955i	$-0.514553\pi$
$911$	−2.75901			−0.0914100			−0.0457050	+	0.998955i	$0.514553\pi$
$912$		0			0
$913$	−56.2074			−1.86019
$914$	0.0490341	+	0.0178469i	0.00162190	+	0.000590324i
$915$	12.4672	+	70.7048i	0.412152	+	2.33743i
$916$	−5.34092	−	4.48157i	−0.176469	−	0.148075i
$917$	−1.49778	+	1.25678i	−0.0494609	+	0.0415027i
$918$	3.66391	−	20.7791i	0.120927	−	0.685812i
$919$	19.6542	−	34.0420i	0.648331	−	1.12294i	−0.335191	−	0.942150i	$-0.608801\pi$
$919$	19.6542	−	34.0420i	0.648331	−	1.12294i	0.983521	−	0.180792i	$-0.0578660\pi$
$920$	−7.59272	−	13.1510i	−0.250325	−	0.433575i
$921$	3.64373	−	1.32621i	0.120065	−	0.0437001i
$922$	−37.0916	+	13.5002i	−1.22155	+	0.444606i
$923$	0.671809	+	1.16361i	0.0221129	+	0.0383006i
$924$	10.3244	−	17.8823i	0.339647	−	0.588286i
$925$	−0.343496	+	1.94806i	−0.0112941	+	0.0640519i
$926$	−4.74225	+	3.97922i	−0.155840	+	0.130765i
$927$	69.9745	+	58.7156i	2.29827	+	1.92847i
$928$	−0.543095	−	3.08004i	−0.0178280	−	0.101107i
$929$	27.9481	+	10.1723i	0.916947	+	0.333741i	0.757023	−	0.653388i	$-0.226653\pi$
$929$	27.9481	+	10.1723i	0.916947	+	0.333741i	0.159924	+	0.987129i	$0.448875\pi$
$930$	−42.1970			−1.38369
$931$		0			0
$932$	−29.6097			−0.969898
$933$	32.0010	+	11.6474i	1.04767	+	0.381319i
$934$	−3.64594	−	20.6772i	−0.119299	−	0.676578i
$935$	−43.2787	−	36.3152i	−1.41537	−	1.18763i
$936$	1.11984	−	0.939654i	0.0366030	−	0.0307135i
$937$	6.55020	−	37.1480i	0.213986	−	1.21357i	−0.668672	−	0.743557i	$-0.733137\pi$
$937$	6.55020	−	37.1480i	0.213986	−	1.21357i	0.882658	−	0.470016i	$-0.155752\pi$
$938$	−2.81266	+	4.87166i	−0.0918365	+	0.159065i
$939$	−23.0911	−	39.9950i	−0.753550	−	1.30519i
$940$	−9.68178	+	3.52388i	−0.315785	+	0.114936i
$941$	6.08594	−	2.21510i	0.198396	−	0.0722102i	−0.240911	−	0.970547i	$-0.577446\pi$
$941$	6.08594	−	2.21510i	0.198396	−	0.0722102i	0.439307	+	0.898337i	$0.355224\pi$
$942$	−19.3703	−	33.5504i	−0.631120	−	1.09313i
$943$	−16.2477	+	28.1419i	−0.529099	+	0.916427i
$944$	0.575427	−	3.26341i	0.0187286	−	0.106215i
$945$	11.6243	−	9.75393i	0.378138	−	0.317295i
$946$	−4.36268	−	3.66072i	−0.141843	−	0.119020i
$947$	2.82895	+	16.0438i	0.0919286	+	0.521353i	0.995645	+	0.0932221i	$0.0297167\pi$
$947$	2.82895	+	16.0438i	0.0919286	+	0.521353i	−0.903717	+	0.428131i	$0.859172\pi$
$948$	−22.5147	−	8.19466i	−0.731242	−	0.266150i
$949$	−0.689776			−0.0223911
$950$		0			0
$951$	7.50953			0.243513
$952$	5.05123	+	1.83850i	0.163711	+	0.0595860i
$953$	−6.01193	−	34.0954i	−0.194746	−	1.10446i	−0.912781	−	0.408450i	$-0.866069\pi$
$953$	−6.01193	−	34.0954i	−0.194746	−	1.10446i	0.718035	−	0.696007i	$-0.245042\pi$
$954$	12.1104	+	10.1618i	0.392088	+	0.329001i
$955$	40.1938	−	33.7266i	1.30064	−	1.09137i
$956$	−4.28970	+	24.3281i	−0.138739	+	0.786827i
$957$	25.1465	−	43.5550i	0.812871	−	1.40793i
$958$	−7.76147	−	13.4433i	−0.250762	−	0.434332i
$959$	12.9252	−	4.70440i	0.417377	−	0.151913i
$960$	6.15482	−	2.24017i	0.198646	−	0.0723012i
$961$	−5.25267	−	9.09789i	−0.169441	−	0.293480i
$962$	0.605491	−	1.04874i	0.0195218	−	0.0338128i
$963$	8.37355	−	47.4888i	0.269834	−	1.53030i
$964$	21.1111	−	17.7144i	0.679944	−	0.570541i
$965$	−13.3413	−	11.1946i	−0.429470	−	0.360368i
$966$	4.03450	+	22.8808i	0.129808	+	0.736177i
$967$	45.9608	+	16.7284i	1.47800	+	0.537948i	0.950260	−	0.311457i	$-0.100817\pi$
$967$	45.9608	+	16.7284i	1.47800	+	0.537948i	0.527741	+	0.849406i	$0.323039\pi$
$968$	22.1340			0.711414
$969$		0			0
$970$	−40.6835			−1.30627
$971$	−5.70950	−	2.07809i	−0.183226	−	0.0666890i	0.248778	−	0.968561i	$-0.419971\pi$
$971$	−5.70950	−	2.07809i	−0.183226	−	0.0666890i	−0.432004	+	0.901872i	$0.642193\pi$
$972$	−2.78681	−	15.8048i	−0.0893870	−	0.506939i
$973$	10.6376	+	8.92605i	0.341027	+	0.286156i
$974$	−21.9139	+	18.3879i	−0.702166	+	0.589187i
$975$	0.0733673	−	0.416087i	0.00234963	−	0.0133254i
$976$	5.48073	−	9.49290i	0.175434	−	0.303860i
$977$	−28.5239	−	49.4048i	−0.912559	−	1.58060i	−0.810436	−	0.585828i	$-0.800770\pi$
$977$	−28.5239	−	49.4048i	−0.912559	−	1.58060i	−0.102124	−	0.994772i	$-0.532564\pi$
$978$	−37.4070	+	13.6150i	−1.19614	+	0.435361i
$979$	81.5501	−	29.6818i	2.60635	−	0.948634i
$980$	−6.27308	−	10.8653i	−0.200386	−	0.347079i
$981$	21.2430	−	36.7940i	0.678238	−	1.17474i
$982$	−5.27002	+	29.8878i	−0.168173	+	0.953757i
$983$	0.142882	−	0.119892i	0.00455723	−	0.00382397i	−0.640506	−	0.767953i	$-0.721275\pi$
$983$	0.142882	−	0.119892i	0.00455723	−	0.00382397i	0.645063	+	0.764129i	$0.276831\pi$
$984$	−10.7369	−	9.00933i	−0.342280	−	0.287207i
$985$	−3.47509	−	19.7082i	−0.110725	−	0.627955i
$986$	12.3030	+	4.47792i	0.391807	+	0.142606i
$987$	15.7638			0.501768
$988$		0			0
$989$	6.40804			0.203764
$990$	60.9271	+	22.1757i	1.93639	+	0.704789i
$991$	−8.02946	−	45.5373i	−0.255064	−	1.44654i	−0.795908	−	0.605418i	$-0.793006\pi$
$991$	−8.02946	−	45.5373i	−0.255064	−	1.44654i	0.540843	−	0.841123i	$-0.318105\pi$
$992$	4.93521	+	4.14114i	0.156693	+	0.131481i
$993$	11.1560	−	9.36101i	0.354025	−	0.297063i
$994$	0.984603	−	5.58396i	0.0312297	−	0.177112i
$995$	−7.45488	+	12.9122i	−0.236336	+	0.409345i
$996$	13.6393	+	23.6239i	0.432177	+	0.748553i
$997$	19.5917	−	7.13078i	0.620474	−	0.225834i	−0.0126059	−	0.999921i	$-0.504013\pi$
$997$	19.5917	−	7.13078i	0.620474	−	0.225834i	0.633080	+	0.774086i	$0.281790\pi$
$998$	−8.24696	+	3.00165i	−0.261053	+	0.0950156i
$999$	10.0297	+	17.3719i	0.317325	+	0.549623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.r.99.4		24
19.2	odd	18		722.2.e.s.415.4		24
19.3	odd	18		722.2.e.s.245.1		24
19.4	even	9		722.2.c.m.653.1		8
19.5	even	9	inner	722.2.e.r.423.4		24
19.6	even	9		722.2.c.m.429.1		8
19.7	even	3	inner	722.2.e.r.595.1		24
19.8	odd	6		722.2.e.s.389.1		24
19.9	even	9		722.2.a.n.1.4	yes	4
19.10	odd	18		722.2.a.m.1.1	✓	4
19.11	even	3	inner	722.2.e.r.389.4		24
19.12	odd	6		722.2.e.s.595.4		24
19.13	odd	18		722.2.c.n.429.4		8
19.14	odd	18		722.2.e.s.423.1		24
19.15	odd	18		722.2.c.n.653.4		8
19.16	even	9	inner	722.2.e.r.245.4		24
19.17	even	9	inner	722.2.e.r.415.1		24
19.18	odd	2		722.2.e.s.99.1		24
57.29	even	18		6498.2.a.ca.1.3		4
57.47	odd	18		6498.2.a.bx.1.3		4
76.47	odd	18		5776.2.a.bt.1.1		4
76.67	even	18		5776.2.a.bv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.1	✓	4	19.10	odd	18
722.2.a.n.1.4	yes	4	19.9	even	9
722.2.c.m.429.1		8	19.6	even	9
722.2.c.m.653.1		8	19.4	even	9
722.2.c.n.429.4		8	19.13	odd	18
722.2.c.n.653.4		8	19.15	odd	18
722.2.e.r.99.4		24	1.1	even	1	trivial
722.2.e.r.245.4		24	19.16	even	9	inner
722.2.e.r.389.4		24	19.11	even	3	inner
722.2.e.r.415.1		24	19.17	even	9	inner
722.2.e.r.423.4		24	19.5	even	9	inner
722.2.e.r.595.1		24	19.7	even	3	inner
722.2.e.s.99.1		24	19.18	odd	2
722.2.e.s.245.1		24	19.3	odd	18
722.2.e.s.389.1		24	19.8	odd	6
722.2.e.s.415.4		24	19.2	odd	18
722.2.e.s.423.1		24	19.14	odd	18
722.2.e.s.595.4		24	19.12	odd	6
5776.2.a.bt.1.1		4	76.47	odd	18
5776.2.a.bv.1.4		4	76.67	even	18
6498.2.a.bx.1.3		4	57.47	odd	18
6498.2.a.ca.1.3		4	57.29	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.485104 + 2.75116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.79605 + 1.50706i) q^{5} +(0.485104 - 2.75116i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-4.51450 + 1.64314i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.485104 + 2.75116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.79605 + 1.50706i) q^{5} +(0.485104 - 2.75116i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-4.51450 + 1.64314i) q^{9} +(2.20318 - 0.801892i) q^{10} +(-2.87811 - 4.98503i) q^{11} +(-1.39680 + 2.41933i) q^{12} +(0.0528381 - 0.299660i) q^{13} +(-0.983662 + 0.825390i) q^{14} +(-5.01745 - 4.21014i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-3.93373 - 1.43176i) q^{17} +4.80423 q^{18} -2.34458 q^{20} +(3.37087 + 1.22690i) q^{21} +(0.999556 + 5.66877i) q^{22} +(-4.96154 - 4.16323i) q^{23} +(2.14003 - 1.79569i) q^{24} +(0.0863099 - 0.489488i) q^{25} +(-0.152141 + 0.263516i) q^{26} +(-2.52015 - 4.36502i) q^{27} +(1.20664 - 0.439181i) q^{28} +(2.93894 - 1.06969i) q^{29} +(3.27491 + 5.67231i) q^{30} +(-3.22123 + 5.57934i) q^{31} +(0.173648 - 0.984808i) q^{32} +(12.3184 - 10.3364i) q^{33} +(3.20681 + 2.69083i) q^{34} +(0.522789 + 2.96488i) q^{35} +(-4.51450 - 1.64314i) q^{36} -3.97980 q^{37} +0.850045 q^{39} +(2.20318 + 0.801892i) q^{40} +(-0.871225 - 4.94096i) q^{41} +(-2.74796 - 2.30581i) q^{42} +(-0.757908 + 0.635960i) q^{43} +(0.999556 - 5.66877i) q^{44} +(5.63194 - 9.75480i) q^{45} +(3.23842 + 5.60910i) q^{46} +(4.12943 - 1.50299i) q^{47} +(-2.62513 + 0.955469i) q^{48} +(2.67557 + 4.63422i) q^{49} +(-0.248520 + 0.430448i) q^{50} +(2.03074 - 11.5169i) q^{51} +(0.233094 - 0.195589i) q^{52} +(2.52078 + 2.11518i) q^{53} +(0.875238 + 4.96372i) q^{54} +(12.6820 + 4.61587i) q^{55} -1.28408 q^{56} -3.12756 q^{58} +(-3.11391 - 1.13337i) q^{59} +(-1.13736 - 6.45031i) q^{60} +(-8.39696 - 7.04589i) q^{61} +(4.93521 - 4.14114i) q^{62} +(-1.07124 + 6.07528i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.356707 + 0.617834i) q^{65} +(-15.1108 + 5.49989i) q^{66} +(4.11662 - 1.49833i) q^{67} +(-2.09310 - 3.62535i) q^{68} +(9.04686 - 15.6696i) q^{69} +(0.522789 - 2.96488i) q^{70} +(-3.38262 + 2.83835i) q^{71} +(3.68025 + 3.08810i) q^{72} +(-0.393642 - 2.23245i) q^{73} +(3.73979 + 1.36117i) q^{74} +1.38853 q^{75} -7.39144 q^{77} +(-0.798781 - 0.290732i) q^{78} +(1.48931 + 8.44629i) q^{79} +(-1.79605 - 1.50706i) q^{80} +(-0.254396 + 0.213463i) q^{81} +(-0.871225 + 4.94096i) q^{82} +(4.88232 - 8.45643i) q^{83} +(1.79360 + 3.10661i) q^{84} +(9.22294 - 3.35688i) q^{85} +(0.929712 - 0.338387i) q^{86} +(4.36858 + 7.56661i) q^{87} +(-2.87811 + 4.98503i) q^{88} +(-2.61801 + 14.8475i) q^{89} +(-8.62863 + 7.24028i) q^{90} +(-0.299311 - 0.251152i) q^{91} +(-1.12469 - 6.37844i) q^{92} +(-16.9123 - 6.15557i) q^{93} -4.39445 q^{94} +2.79360 q^{96} +(-16.3057 - 5.93480i) q^{97} +(-0.929216 - 5.26985i) q^{98} +(21.1843 + 17.7758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 6 * q^7 - 12 * q^8	\( 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Introduction

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