LMFDB - Embedded newform 722.2.e.s.245.1

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			245.1
Character	$\chi$	$=$	722.245
Dual form			722.2.e.s.389.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-2.14003 - 1.79569i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20318 - 0.801892i) q^{5} +(2.14003 - 1.79569i) q^{6} +(0.642040 + 1.11205i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.834245 + 4.73124i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-2.14003 - 1.79569i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20318 - 0.801892i) q^{5} +(2.14003 - 1.79569i) q^{6} +(0.642040 + 1.11205i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.834245 + 4.73124i) q^{9} +(0.407131 + 2.30896i) q^{10} +(-2.87811 + 4.98503i) q^{11} +(1.39680 + 2.41933i) q^{12} +(-0.233094 + 0.195589i) q^{13} +(-1.20664 + 0.439181i) q^{14} +(-6.15482 - 2.24017i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.726925 - 4.12259i) q^{17} -4.80423 q^{18} -2.34458 q^{20} +(0.622912 - 3.53271i) q^{21} +(-4.40952 - 3.70002i) q^{22} +(6.08623 + 2.21521i) q^{23} +(-2.62513 + 0.955469i) q^{24} +(0.380754 - 0.319491i) q^{25} +(-0.152141 - 0.263516i) q^{26} +(2.52015 - 4.36502i) q^{27} +(-0.222978 - 1.26457i) q^{28} +(0.543095 + 3.08004i) q^{29} +(3.27491 - 5.67231i) q^{30} +(3.22123 + 5.57934i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(15.1108 - 5.49989i) q^{33} +(3.93373 + 1.43176i) q^{34} +(2.30627 + 1.93519i) q^{35} +(0.834245 - 4.73124i) q^{36} +3.97980 q^{37} +0.850045 q^{39} +(0.407131 - 2.30896i) q^{40} +(3.84339 + 3.22499i) q^{41} +(3.37087 + 1.22690i) q^{42} +(0.929712 - 0.338387i) q^{43} +(4.40952 - 3.70002i) q^{44} +(5.63194 + 9.75480i) q^{45} +(-3.23842 + 5.60910i) q^{46} +(-0.763089 - 4.32769i) q^{47} +(-0.485104 - 2.75116i) q^{48} +(2.67557 - 4.63422i) q^{49} +(0.248520 + 0.430448i) q^{50} +(-8.95856 + 7.51712i) q^{51} +(0.285932 - 0.104071i) q^{52} +(3.09219 + 1.12547i) q^{53} +(3.86109 + 3.23984i) q^{54} +(-2.34354 + 13.2909i) q^{55} +1.28408 q^{56} -3.12756 q^{58} +(-0.575427 + 3.26341i) q^{59} +(5.01745 + 4.21014i) q^{60} +(10.3004 + 3.74904i) q^{61} +(-6.05394 + 2.20345i) q^{62} +(-4.72573 + 3.96536i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.356707 + 0.617834i) q^{65} +(2.79236 + 15.8363i) q^{66} +(0.760720 + 4.31426i) q^{67} +(-2.09310 + 3.62535i) q^{68} +(-9.04686 - 15.6696i) q^{69} +(-2.30627 + 1.93519i) q^{70} +(-4.14940 + 1.51026i) q^{71} +(4.51450 + 1.64314i) q^{72} +(-1.73654 - 1.45713i) q^{73} +(-0.691084 + 3.91933i) q^{74} -1.38853 q^{75} -7.39144 q^{77} +(-0.147609 + 0.837131i) q^{78} +(-6.57005 - 5.51292i) q^{79} +(2.20318 + 0.801892i) q^{80} +(0.312063 - 0.113582i) q^{81} +(-3.84339 + 3.22499i) q^{82} +(4.88232 + 8.45643i) q^{83} +(-1.79360 + 3.10661i) q^{84} +(-1.70433 - 9.66574i) q^{85} +(0.171804 + 0.974348i) q^{86} +(4.36858 - 7.56661i) q^{87} +(2.87811 + 4.98503i) q^{88} +(11.5493 - 9.69101i) q^{89} +(-10.5846 + 3.85247i) q^{90} +(-0.367159 - 0.133635i) q^{91} +(-4.96154 - 4.16323i) q^{92} +(3.12527 - 17.7243i) q^{93} +4.39445 q^{94} +2.79360 q^{96} +(-3.01317 + 17.0886i) q^{97} +(4.09921 + 3.43965i) q^{98} +(-25.9864 - 9.45828i) 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 $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−2.14003	−	1.79569i	−1.23554	−	1.03674i	−0.997859	−	0.0654024i	$-0.979167\pi$
$3$	−2.14003	−	1.79569i	−1.23554	−	1.03674i	−0.237685	−	0.971342i	$-0.576389\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	2.20318	−	0.801892i	0.985293	−	0.358617i	0.201397	−	0.979510i	$-0.435452\pi$
$5$	2.20318	−	0.801892i	0.985293	−	0.358617i	0.783896	+	0.620893i	$0.213230\pi$
$6$	2.14003	−	1.79569i	0.873662	−	0.733089i
$7$	0.642040	+	1.11205i	0.242668	+	0.420314i	0.961473	−	0.274898i	$-0.0886441\pi$
$7$	0.642040	+	1.11205i	0.242668	+	0.420314i	−0.718805	+	0.695211i	$0.755311\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.834245	+	4.73124i	0.278082	+	1.57708i
$10$	0.407131	+	2.30896i	0.128746	+	0.730156i
$11$	−2.87811	+	4.98503i	−0.867782	+	1.50304i	−0.00352407	+	0.999994i	$0.501122\pi$
$11$	−2.87811	+	4.98503i	−0.867782	+	1.50304i	−0.864258	+	0.503049i	$0.832212\pi$
$12$	1.39680	+	2.41933i	0.403222	+	0.698401i
$13$	−0.233094	+	0.195589i	−0.0646486	+	0.0542466i	−0.674539	−	0.738239i	$-0.735658\pi$
$13$	−0.233094	+	0.195589i	−0.0646486	+	0.0542466i	0.609891	+	0.792485i	$0.291213\pi$
$14$	−1.20664	+	0.439181i	−0.322488	+	0.117376i
$15$	−6.15482	−	2.24017i	−1.58917	−	0.578409i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.726925	−	4.12259i	0.176305	−	0.999876i	−0.760322	−	0.649547i	$-0.774959\pi$
$17$	0.726925	−	4.12259i	0.176305	−	0.999876i	0.936627	−	0.350329i	$-0.113930\pi$
$18$	−4.80423			−1.13237
$19$		0			0
$19$		0			0
$20$	−2.34458			−0.524263
$21$	0.622912	−	3.53271i	0.135931	−	0.770901i
$22$	−4.40952	−	3.70002i	−0.940112	−	0.788848i
$23$	6.08623	+	2.21521i	1.26907	+	0.461903i	0.886802	−	0.462150i	$-0.152922\pi$
$23$	6.08623	+	2.21521i	1.26907	+	0.461903i	0.382266	+	0.924052i	$0.375144\pi$
$24$	−2.62513	+	0.955469i	−0.535852	+	0.195034i
$25$	0.380754	−	0.319491i	0.0761508	−	0.0638981i
$26$	−0.152141	−	0.263516i	−0.0298374	−	0.0516798i
$27$	2.52015	−	4.36502i	0.485003	−	0.840049i
$28$	−0.222978	−	1.26457i	−0.0421389	−	0.238981i
$29$	0.543095	+	3.08004i	0.100850	+	0.571950i	0.992797	+	0.119809i	$0.0382283\pi$
$29$	0.543095	+	3.08004i	0.100850	+	0.571950i	−0.891947	+	0.452141i	$0.850661\pi$
$30$	3.27491	−	5.67231i	0.597914	−	1.03562i
$31$	3.22123	+	5.57934i	0.578550	+	1.00208i	0.995646	+	0.0932159i	$0.0297147\pi$
$31$	3.22123	+	5.57934i	0.578550	+	1.00208i	−0.417096	+	0.908863i	$0.636952\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	15.1108	−	5.49989i	2.63045	−	0.957407i
$34$	3.93373	+	1.43176i	0.674630	+	0.245545i
$35$	2.30627	+	1.93519i	0.389831	+	0.327107i
$36$	0.834245	−	4.73124i	0.139041	−	0.788540i
$37$	3.97980			0.654275			0.327137	−	0.944977i	$-0.393916\pi$
$37$	3.97980			0.654275			0.327137	+	0.944977i	$0.393916\pi$
$38$		0			0
$39$	0.850045			0.136116
$40$	0.407131	−	2.30896i	0.0643731	−	0.365078i
$41$	3.84339	+	3.22499i	0.600236	+	0.503658i	0.891522	−	0.452978i	$-0.149638\pi$
$41$	3.84339	+	3.22499i	0.600236	+	0.503658i	−0.291285	+	0.956636i	$0.594083\pi$
$42$	3.37087	+	1.22690i	0.520137	+	0.189314i
$43$	0.929712	−	0.338387i	0.141780	−	0.0516036i	−0.270156	−	0.962817i	$-0.587075\pi$
$43$	0.929712	−	0.338387i	0.141780	−	0.0516036i	0.411935	+	0.911213i	$0.364853\pi$
$44$	4.40952	−	3.70002i	0.664760	−	0.557800i
$45$	5.63194	+	9.75480i	0.839560	+	1.45416i
$46$	−3.23842	+	5.60910i	−0.477479	+	0.827017i
$47$	−0.763089	−	4.32769i	−0.111308	−	0.631259i	−0.988512	−	0.151141i	$-0.951705\pi$
$47$	−0.763089	−	4.32769i	−0.111308	−	0.631259i	0.877204	−	0.480117i	$-0.159406\pi$
$48$	−0.485104	−	2.75116i	−0.0700188	−	0.397096i
$49$	2.67557	−	4.63422i	0.382224	−	0.662032i
$50$	0.248520	+	0.430448i	0.0351460	+	0.0608746i
$51$	−8.95856	+	7.51712i	−1.25445	+	1.05261i
$52$	0.285932	−	0.104071i	0.0396516	−	0.0144320i
$53$	3.09219	+	1.12547i	0.424745	+	0.154595i	0.545544	−	0.838082i	$-0.316323\pi$
$53$	3.09219	+	1.12547i	0.424745	+	0.154595i	−0.120798	+	0.992677i	$0.538545\pi$
$54$	3.86109	+	3.23984i	0.525428	+	0.440886i
$55$	−2.34354	+	13.2909i	−0.316002	+	1.79214i
$56$	1.28408			0.171592
$57$		0			0
$58$	−3.12756			−0.410669
$59$	−0.575427	+	3.26341i	−0.0749142	+	0.424860i	0.924166	+	0.381990i	$0.124761\pi$
$59$	−0.575427	+	3.26341i	−0.0749142	+	0.424860i	−0.999081	+	0.0428696i	$0.986350\pi$
$60$	5.01745	+	4.21014i	0.647750	+	0.543527i
$61$	10.3004	+	3.74904i	1.31883	+	0.480015i	0.903084	−	0.429465i	$-0.141298\pi$
$61$	10.3004	+	3.74904i	1.31883	+	0.480015i	0.415748	+	0.909480i	$0.363520\pi$
$62$	−6.05394	+	2.20345i	−0.768851	+	0.279839i
$63$	−4.72573	+	3.96536i	−0.595386	+	0.499588i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.356707	+	0.617834i	−0.0442440	+	0.0766329i
$66$	2.79236	+	15.8363i	0.343716	+	1.94931i
$67$	0.760720	+	4.31426i	0.0929368	+	0.527071i	0.995360	+	0.0962201i	$0.0306753\pi$
$67$	0.760720	+	4.31426i	0.0929368	+	0.527071i	−0.902423	+	0.430851i	$0.858214\pi$
$68$	−2.09310	+	3.62535i	−0.253825	+	0.439638i
$69$	−9.04686	−	15.6696i	−1.08911	−	1.88640i
$70$	−2.30627	+	1.93519i	−0.275652	+	0.231299i
$71$	−4.14940	+	1.51026i	−0.492443	+	0.179235i	−0.576292	−	0.817244i	$-0.695501\pi$
$71$	−4.14940	+	1.51026i	−0.492443	+	0.179235i	0.0838491	+	0.996478i	$0.473279\pi$
$72$	4.51450	+	1.64314i	0.532038	+	0.193646i
$73$	−1.73654	−	1.45713i	−0.203247	−	0.170544i	0.535483	−	0.844546i	$-0.320130\pi$
$73$	−1.73654	−	1.45713i	−0.203247	−	0.170544i	−0.738730	+	0.674002i	$0.764574\pi$
$74$	−0.691084	+	3.91933i	−0.0803369	+	0.455613i
$75$	−1.38853			−0.160334
$76$		0			0
$77$	−7.39144			−0.842332
$78$	−0.147609	+	0.837131i	−0.0167134	+	0.0947864i
$79$	−6.57005	−	5.51292i	−0.739188	−	0.620252i	0.193431	−	0.981114i	$-0.438038\pi$
$79$	−6.57005	−	5.51292i	−0.739188	−	0.620252i	−0.932619	+	0.360861i	$0.882483\pi$
$80$	2.20318	+	0.801892i	0.246323	+	0.0896543i
$81$	0.312063	−	0.113582i	0.0346736	−	0.0126202i
$82$	−3.84339	+	3.22499i	−0.424431	+	0.356140i
$83$	4.88232	+	8.45643i	0.535904	+	0.928214i	0.999119	+	0.0419676i	$0.0133626\pi$
$83$	4.88232	+	8.45643i	0.535904	+	0.928214i	−0.463214	+	0.886246i	$0.653304\pi$
$84$	−1.79360	+	3.10661i	−0.195698	+	0.338959i
$85$	−1.70433	−	9.66574i	−0.184861	−	1.04840i
$86$	0.171804	+	0.974348i	0.0185261	+	0.105067i
$87$	4.36858	−	7.56661i	0.468361	−	0.811225i
$88$	2.87811	+	4.98503i	0.306807	+	0.531406i
$89$	11.5493	−	9.69101i	1.22422	−	1.02724i	0.225630	−	0.974213i	$-0.427556\pi$
$89$	11.5493	−	9.69101i	1.22422	−	1.02724i	0.998593	−	0.0530316i	$-0.0168884\pi$
$90$	−10.5846	+	3.85247i	−1.11571	+	0.406086i
$91$	−0.367159	−	0.133635i	−0.0384888	−	0.0140088i
$92$	−4.96154	−	4.16323i	−0.517277	−	0.434047i
$93$	3.12527	−	17.7243i	0.324075	−	1.83792i
$94$	4.39445			0.453253
$95$		0			0
$96$	2.79360			0.285121
$97$	−3.01317	+	17.0886i	−0.305942	+	1.73508i	0.313098	+	0.949721i	$0.398633\pi$
$97$	−3.01317	+	17.0886i	−0.305942	+	1.73508i	−0.619040	+	0.785360i	$0.712478\pi$
$98$	4.09921	+	3.43965i	0.414083	+	0.347457i
$99$	−25.9864	−	9.45828i	−2.61173	−	0.950593i
$100$	−0.467064	+	0.169997i	−0.0467064	+	0.0169997i
$101$	2.81649	−	2.36332i	0.280251	−	0.235159i	−0.491817	−	0.870699i	$-0.663667\pi$
$101$	2.81649	−	2.36332i	0.280251	−	0.235159i	0.772068	+	0.635540i	$0.219223\pi$
$102$	−5.84728	−	10.1278i	−0.578967	−	1.00280i
$103$	9.50676	−	16.4662i	0.936729	−	1.62246i	0.165208	−	0.986259i	$-0.447170\pi$
$103$	9.50676	−	16.4662i	0.936729	−	1.62246i	0.771521	−	0.636204i	$-0.219496\pi$
$104$	0.0528381	+	0.299660i	0.00518120	+	0.0293841i
$105$	−1.46047	−	8.28271i	−0.142527	−	0.808310i
$106$	−1.64532	+	2.84978i	−0.159808	+	0.276795i
$107$	5.01864	+	8.69254i	0.485170	+	0.840339i	0.999855	−	0.0170403i	$-0.00542435\pi$
$107$	5.01864	+	8.69254i	0.485170	+	0.840339i	−0.514685	+	0.857380i	$0.672091\pi$
$108$	−3.86109	+	3.23984i	−0.371533	+	0.311754i
$109$	−8.31015	+	3.02465i	−0.795968	+	0.289709i	−0.707815	−	0.706398i	$-0.750319\pi$
$109$	−8.31015	+	3.02465i	−0.795968	+	0.289709i	−0.0881536	+	0.996107i	$0.528097\pi$
$110$	−12.6820	−	4.61587i	−1.20918	−	0.440105i
$111$	−8.51686	−	7.14650i	−0.808385	−	0.678316i
$112$	−0.222978	+	1.26457i	−0.0210694	+	0.119491i
$113$	14.2502			1.34055			0.670275	−	0.742113i	$-0.266176\pi$
$113$	14.2502			1.34055			0.670275	+	0.742113i	$0.266176\pi$
$114$		0			0
$115$	15.1854			1.41605
$116$	0.543095	−	3.08004i	0.0504251	−	0.285975i
$117$	−1.11984	−	0.939654i	−0.103529	−	0.0868710i
$118$	−3.11391	−	1.13337i	−0.286658	−	0.104335i
$119$	5.05123	−	1.83850i	0.463045	−	0.168535i
$120$	−5.01745	+	4.21014i	−0.458029	+	0.384332i
$121$	−11.0670	−	19.1686i	−1.00609	−	1.74260i
$122$	−5.48073	+	9.49290i	−0.496202	+	0.859447i
$123$	−2.43386	−	13.8031i	−0.219454	−	1.24458i
$124$	−1.11872	−	6.34459i	−0.100464	−	0.569761i
$125$	−5.27877	+	9.14309i	−0.472147	+	0.817783i
$126$	−3.08450	−	5.34252i	−0.274789	−	0.475949i
$127$	−1.70839	+	1.43351i	−0.151595	+	0.127203i	−0.715431	−	0.698684i	$-0.753770\pi$
$127$	−1.70839	+	1.43351i	−0.151595	+	0.127203i	0.563836	+	0.825887i	$0.309325\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−2.59725	−	0.945320i	−0.228675	−	0.0832308i
$130$	−0.546506	−	0.458573i	−0.0479318	−	0.0402195i
$131$	0.264406	−	1.49952i	0.0231013	−	0.131014i	−0.971076	−	0.238771i	$-0.923256\pi$
$131$	0.264406	−	1.49952i	0.0231013	−	0.131014i	0.994177	+	0.107757i	$0.0343667\pi$
$132$	−16.0806			−1.39964
$133$		0			0
$134$	−4.38081			−0.378445
$135$	2.05206	−	11.6378i	0.176613	−	1.00162i
$136$	−3.20681	−	2.69083i	−0.274982	−	0.230737i
$137$	−10.0658	−	3.66363i	−0.859975	−	0.313005i	−0.125875	−	0.992046i	$-0.540174\pi$
$137$	−10.0658	−	3.66363i	−0.859975	−	0.313005i	−0.734101	+	0.679041i	$0.762396\pi$
$138$	17.0025	−	6.18842i	1.44735	−	0.526793i
$139$	−8.28426	+	6.95132i	−0.702662	+	0.589603i	−0.922530	−	0.385926i	$-0.873882\pi$
$139$	−8.28426	+	6.95132i	−0.702662	+	0.589603i	0.219868	+	0.975530i	$0.429437\pi$
$140$	−1.50531	−	2.60727i	−0.127222	−	0.220355i
$141$	−6.13818	+	10.6316i	−0.516928	+	0.895346i
$142$	−0.766777	−	4.34861i	−0.0643465	−	0.364927i
$143$	−0.304147	−	1.72491i	−0.0254341	−	0.144244i
$144$	−2.40211	+	4.16058i	−0.200176	+	0.346715i
$145$	3.66640	+	6.35039i	0.304478	+	0.527371i
$146$	1.73654	−	1.45713i	0.143717	−	0.120593i
$147$	−14.0474	+	5.11285i	−1.15861	+	0.421701i
$148$	−3.73979	−	1.36117i	−0.307408	−	0.111888i
$149$	−7.15014	−	5.99968i	−0.585762	−	0.491513i	0.301072	−	0.953602i	$-0.402656\pi$
$149$	−7.15014	−	5.99968i	−0.585762	−	0.491513i	−0.886834	+	0.462089i	$0.847100\pi$
$150$	0.241116	−	1.36744i	0.0196870	−	0.111651i
$151$	−19.8232			−1.61319			−0.806593	−	0.591107i	$-0.798691\pi$
$151$	−19.8232			−1.61319			−0.806593	+	0.591107i	$0.798691\pi$
$152$		0			0
$153$	20.1114			1.62591
$154$	1.28351	−	7.27914i	0.103428	−	0.586570i
$155$	11.5710	+	9.70921i	0.929404	+	0.779862i
$156$	−0.798781	−	0.290732i	−0.0639537	−	0.0232772i
$157$	−13.0313	+	4.74301i	−1.04001	+	0.378533i	−0.804885	−	0.593431i	$-0.797773\pi$
$157$	−13.0313	+	4.74301i	−1.04001	+	0.378533i	−0.235127	+	0.971965i	$0.575551\pi$
$158$	6.57005	−	5.51292i	0.522685	−	0.438585i
$159$	−4.59638	−	7.96116i	−0.364517	−	0.631361i
$160$	−1.17229	+	2.03046i	−0.0926775	+	0.160522i
$161$	1.44419	+	8.19042i	0.113818	+	0.645495i
$162$	0.0576668	+	0.327045i	0.00453074	+	0.0256951i
$163$	−7.12480	+	12.3405i	−0.558057	+	0.966583i	0.439601	+	0.898193i	$0.355120\pi$
$163$	−7.12480	+	12.3405i	−0.558057	+	0.966583i	−0.997659	+	0.0683904i	$0.978214\pi$
$164$	−2.50859	−	4.34501i	−0.195888	−	0.339288i
$165$	28.8815	−	24.2345i	2.24842	−	1.88665i
$166$	−9.17576	+	3.33971i	−0.712177	+	0.259211i
$167$	10.8911	+	3.96405i	0.842782	+	0.306748i	0.727094	−	0.686538i	$-0.240870\pi$
$167$	10.8911	+	3.96405i	0.842782	+	0.306748i	0.115688	+	0.993286i	$0.463093\pi$
$168$	−2.74796	−	2.30581i	−0.212010	−	0.177897i
$169$	−2.24135	+	12.7113i	−0.172411	+	0.977794i
$170$	9.81485			0.752764
$171$		0			0
$172$	−0.989378			−0.0754394
$173$	−0.691732	+	3.92301i	−0.0525914	+	0.298261i	−0.999746	−	0.0225153i	$-0.992833\pi$
$173$	−0.691732	+	3.92301i	−0.0525914	+	0.298261i	0.947155	+	0.320776i	$0.103944\pi$
$174$	6.69306	+	5.61614i	0.507399	+	0.425759i
$175$	0.599747	+	0.218290i	0.0453366	+	0.0165012i
$176$	−5.40907	+	1.96874i	−0.407724	+	0.148399i
$177$	7.09151	−	5.95048i	0.533031	−	0.447266i
$178$	7.53827	+	13.0567i	0.565017	+	0.978638i
$179$	−4.22545	+	7.31869i	−0.315825	+	0.547024i	−0.979612	−	0.200897i	$-0.935614\pi$
$179$	−4.22545	+	7.31869i	−0.315825	+	0.547024i	0.663788	+	0.747921i	$0.268948\pi$
$180$	−1.95595	−	11.0928i	−0.145788	−	0.826805i
$181$	−1.47345	−	8.35635i	−0.109521	−	0.621123i	−0.989318	−	0.145774i	$-0.953433\pi$
$181$	−1.47345	−	8.35635i	−0.109521	−	0.621123i	0.879797	−	0.475349i	$-0.157678\pi$
$182$	0.195361	−	0.338376i	0.0144811	−	0.0250821i
$183$	−15.3110	−	26.5194i	−1.13182	−	1.96037i
$184$	4.96154	−	4.16323i	0.365770	−	0.306917i
$185$	8.76821	−	3.19137i	0.644652	−	0.234634i
$186$	16.9123	+	6.15557i	1.24007	+	0.451349i
$187$	18.4591	+	15.4890i	1.34986	+	1.13267i
$188$	−0.763089	+	4.32769i	−0.0556540	+	0.315629i
$189$	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	$0.800340\pi$
$192$	−0.485104	+	2.75116i	−0.0350094	+	0.198548i
$193$	−5.69026	−	4.77470i	−0.409594	−	0.343690i	0.414594	−	0.910007i	$-0.363924\pi$
$193$	−5.69026	−	4.77470i	−0.409594	−	0.343690i	−0.824188	+	0.566316i	$0.808368\pi$
$194$	−16.3057	−	5.93480i	−1.17068	−	0.426093i
$195$	1.87280	−	0.681645i	0.134114	−	0.0488136i
$196$	−4.09921	+	3.43965i	−0.292801	+	0.245689i
$197$	−4.26777	−	7.39199i	−0.304066	−	0.526658i	0.672987	−	0.739654i	$-0.265011\pi$
$197$	−4.26777	−	7.39199i	−0.304066	−	0.526658i	−0.977053	+	0.212997i	$0.931678\pi$
$198$	13.8271	−	23.9492i	0.982648	−	1.70200i
$199$	−1.10427	−	6.26264i	−0.0782798	−	0.443947i	−0.998605	−	0.0527939i	$-0.983187\pi$
$199$	−1.10427	−	6.26264i	−0.0782798	−	0.443947i	0.920326	−	0.391153i	$-0.127924\pi$
$200$	−0.0863099	−	0.489488i	−0.00610303	−	0.0346120i
$201$	6.11913	−	10.5986i	0.431610	−	0.747571i
$202$	1.83833	+	3.18409i	0.129345	+	0.224032i
$203$	−3.07646	+	2.58146i	−0.215925	+	0.181183i
$204$	10.9893	−	3.99978i	0.769405	−	0.280040i
$205$	11.0538	+	4.02324i	0.772029	+	0.280996i
$206$	14.5652	+	12.2217i	1.01481	+	0.851523i
$207$	−5.40327	+	30.6435i	−0.375553	+	2.12987i
$208$	−0.304282			−0.0210982
$209$		0			0
$210$	8.41049			0.580379
$211$	2.42375	−	13.7457i	0.166858	−	0.946296i	−0.780271	−	0.625442i	$-0.784919\pi$
$211$	2.42375	−	13.7457i	0.166858	−	0.946296i	0.947128	−	0.320855i	$-0.103970\pi$
$212$	−2.52078	−	2.11518i	−0.173128	−	0.145271i
$213$	11.5918	+	4.21906i	0.794255	+	0.289085i
$214$	−9.43195	+	3.43295i	−0.644755	+	0.234672i
$215$	1.77697	−	1.49106i	0.121189	−	0.101689i
$216$	−2.52015	−	4.36502i	−0.171474	−	0.297002i
$217$	−4.13632	+	7.16431i	−0.280791	+	0.486345i
$218$	−1.53565	−	8.70913i	−0.104008	−	0.589857i
$219$	1.09968	+	6.23659i	0.0743095	+	0.421430i
$220$	6.74794	−	11.6878i	0.454946	−	0.787990i
$221$	0.636892	+	1.10313i	0.0428420	+	0.0742046i
$222$	8.51686	−	7.14650i	0.571615	−	0.479642i
$223$	8.38582	−	3.05219i	0.561556	−	0.204390i	−0.0456176	−	0.998959i	$-0.514526\pi$
$223$	8.38582	−	3.05219i	0.561556	−	0.204390i	0.607173	+	0.794569i	$0.292303\pi$
$224$	−1.20664	−	0.439181i	−0.0806220	−	0.0293440i
$225$	1.82923	+	1.53490i	0.121949	+	0.102327i
$226$	−2.47453	+	14.0337i	−0.164603	+	0.933511i
$227$	0.659796			0.0437922			0.0218961	−	0.999760i	$-0.493030\pi$
$227$	0.659796			0.0437922			0.0218961	+	0.999760i	$0.493030\pi$
$228$		0			0
$229$	−6.97208			−0.460728			−0.230364	−	0.973105i	$-0.573992\pi$
$229$	−6.97208			−0.460728			−0.230364	+	0.973105i	$0.573992\pi$
$230$	−2.63692	+	14.9547i	−0.173874	+	0.986086i
$231$	15.8179	+	13.2728i	1.04074	+	0.873283i
$232$	2.93894	+	1.06969i	0.192951	+	0.0702285i
$233$	27.8240	−	10.1271i	1.82281	−	0.663449i	0.828120	−	0.560551i	$-0.189411\pi$
$233$	27.8240	−	10.1271i	1.82281	−	0.663449i	0.994692	−	0.102898i	$-0.0328115\pi$
$234$	1.11984	−	0.939654i	0.0732060	−	0.0614271i
$235$	−5.15156	−	8.92277i	−0.336051	−	0.582057i
$236$	1.65688	−	2.86979i	0.107853	−	0.186808i
$237$	4.16054	+	23.5956i	0.270256	+	1.53270i
$238$	0.933429	+	5.29374i	0.0605052	+	0.343142i
$239$	12.3517	−	21.3938i	0.798965	−	1.38385i	−0.121326	−	0.992613i	$-0.538715\pi$
$239$	12.3517	−	21.3938i	0.798965	−	1.38385i	0.920291	−	0.391235i	$-0.127952\pi$
$240$	−3.27491	−	5.67231i	−0.211395	−	0.366146i
$241$	−21.1111	+	17.7144i	−1.35989	+	1.14108i	−0.383872	+	0.923386i	$0.625410\pi$
$241$	−21.1111	+	17.7144i	−1.35989	+	1.14108i	−0.976017	+	0.217696i	$0.930146\pi$
$242$	20.7992	−	7.57028i	1.33702	−	0.486636i
$243$	−15.0808	−	5.48895i	−0.967431	−	0.352116i
$244$	−8.39696	−	7.04589i	−0.537561	−	0.451067i
$245$	2.17862	−	12.3556i	0.139187	−	0.789367i
$246$	14.0160			0.893630
$247$		0			0
$248$	6.44246			0.409097
$249$	4.73687	−	26.8641i	0.300187	−	1.70245i
$250$	−8.08754	−	6.78625i	−0.511501	−	0.429200i
$251$	2.80832	+	1.02215i	0.177260	+	0.0645172i	0.429125	−	0.903245i	$-0.358822\pi$
$251$	2.80832	+	1.02215i	0.177260	+	0.0645172i	−0.251866	+	0.967762i	$0.581044\pi$
$252$	5.79697	−	2.10992i	0.365175	−	0.132913i
$253$	−28.5597	+	23.9644i	−1.79553	+	1.50663i
$254$	−1.11507	−	1.93136i	−0.0699659	−	0.121185i
$255$	−13.7094	+	23.7454i	−0.858516	+	1.48699i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.45404	−	13.9176i	−0.153079	−	0.868153i	−0.960521	−	0.278207i	$-0.910260\pi$
$257$	−2.45404	−	13.9176i	−0.153079	−	0.868153i	0.807442	−	0.589947i	$-0.200851\pi$
$258$	1.38197	−	2.39364i	0.0860374	−	0.149021i
$259$	2.55519	+	4.42571i	0.158772	+	0.275000i
$260$	0.546506	−	0.458573i	0.0338929	−	0.0284395i
$261$	−14.1194	+	5.13902i	−0.873966	+	0.318098i
$262$	1.43083	+	0.520778i	0.0883968	+	0.0321738i
$263$	5.79809	+	4.86518i	0.357526	+	0.300000i	0.803804	−	0.594895i	$-0.202806\pi$
$263$	5.79809	+	4.86518i	0.357526	+	0.300000i	−0.446278	+	0.894894i	$0.647251\pi$
$264$	2.79236	−	15.8363i	0.171858	−	0.974656i
$265$	7.71517			0.473939
$266$		0			0
$267$	−42.1179			−2.57757
$268$	0.760720	−	4.31426i	0.0464684	−	0.263535i
$269$	5.87613	+	4.93066i	0.358274	+	0.300628i	0.804102	−	0.594491i	$-0.202646\pi$
$269$	5.87613	+	4.93066i	0.358274	+	0.300628i	−0.445828	+	0.895118i	$0.647091\pi$
$270$	11.1047	+	4.04177i	0.675809	+	0.245975i
$271$	−10.9614	+	3.98963i	−0.665858	+	0.242353i	−0.652764	−	0.757562i	$-0.726391\pi$
$271$	−10.9614	+	3.98963i	−0.665858	+	0.242353i	−0.0130948	+	0.999914i	$0.504168\pi$
$272$	3.20681	−	2.69083i	0.194441	−	0.163156i
$273$	0.545762	+	0.945288i	0.0330310	+	0.0572114i
$274$	5.35588	−	9.27665i	0.323560	−	0.560423i
$275$	0.496818	+	2.81760i	0.0299593	+	0.169908i
$276$	3.14194	+	17.8188i	0.189123	+	1.07257i
$277$	−13.7202	+	23.7642i	−0.824370	+	1.42785i	0.0780307	+	0.996951i	$0.475137\pi$
$277$	−13.7202	+	23.7642i	−0.824370	+	1.42785i	−0.902400	+	0.430899i	$0.858197\pi$
$278$	−5.40717	−	9.36549i	−0.324300	−	0.561705i
$279$	−23.7099	+	19.8950i	−1.41947	+	1.19108i
$280$	2.82906	−	1.02969i	0.169069	−	0.0615359i
$281$	15.2902	+	5.56517i	0.912136	+	0.331990i	0.755106	−	0.655603i	$-0.227586\pi$
$281$	15.2902	+	5.56517i	0.912136	+	0.331990i	0.157031	+	0.987594i	$0.449808\pi$
$282$	−9.40424	−	7.89109i	−0.560014	−	0.469908i
$283$	0.589317	−	3.34218i	0.0350312	−	0.198672i	−0.962269	−	0.272099i	$-0.912282\pi$
$283$	0.589317	−	3.34218i	0.0350312	−	0.198672i	0.997301	+	0.0734265i	$0.0233934\pi$
$284$	4.41570			0.262023
$285$		0			0
$286$	1.75152			0.103569
$287$	−1.11872	+	6.34459i	−0.0660361	+	0.374509i
$288$	−3.68025	−	3.08810i	−0.216861	−	0.181968i
$289$	−0.492591	−	0.179288i	−0.0289759	−	0.0105464i
$290$	−6.89058	+	2.50797i	−0.404629	+	0.147273i
$291$	37.1341	−	31.1592i	2.17684	−	1.82659i
$292$	1.13345	+	1.96319i	0.0663299	+	0.114887i
$293$	11.6892	−	20.2462i	0.682888	−	1.18280i	−0.291208	−	0.956660i	$-0.594057\pi$
$293$	11.6892	−	20.2462i	0.682888	−	1.18280i	0.974096	−	0.226136i	$-0.0726095\pi$
$294$	−2.59586	−	14.7219i	−0.151394	−	0.858596i
$295$	1.34913	+	7.65131i	0.0785495	+	0.445477i
$296$	1.98990	−	3.44660i	0.115660	−	0.200330i
$297$	14.5065	+	25.1260i	0.841753	+	1.45796i
$298$	7.15014	−	5.99968i	0.414196	−	0.347552i
$299$	−1.85193	+	0.674049i	−0.107100	+	0.0389813i
$300$	1.30479	+	0.474905i	0.0753322	+	0.0274187i
$301$	0.973214	+	0.816623i	0.0560951	+	0.0470694i
$302$	3.44226	−	19.5220i	0.198080	−	1.12337i
$303$	−10.2712			−0.590062
$304$		0			0
$305$	25.7000			1.47158
$306$	−3.49231	+	19.8059i	−0.199642	+	1.13223i
$307$	1.06329	+	0.892202i	0.0606849	+	0.0509207i	0.672626	−	0.739983i	$-0.265166\pi$
$307$	1.06329	+	0.892202i	0.0606849	+	0.0509207i	−0.611941	+	0.790904i	$0.709611\pi$
$308$	6.94568	+	2.52802i	0.395767	+	0.144047i
$309$	−49.9130	+	18.1668i	−2.83945	+	1.03348i
$310$	−11.5710	+	9.70921i	−0.657188	+	0.551446i
$311$	6.09512	+	10.5571i	0.345623	+	0.598636i	0.985467	−	0.169869i	$-0.0543343\pi$
$311$	6.09512	+	10.5571i	0.345623	+	0.598636i	−0.639844	+	0.768505i	$0.721001\pi$
$312$	0.425022	−	0.736160i	0.0240622	−	0.0416769i
$313$	2.87065	+	16.2803i	0.162259	+	0.920215i	0.951846	+	0.306577i	$0.0991836\pi$
$313$	2.87065	+	16.2803i	0.162259	+	0.920215i	−0.789587	+	0.613638i	$0.789705\pi$
$314$	−2.40809	−	13.6569i	−0.135896	−	0.770706i
$315$	−7.23185	+	12.5259i	−0.407469	+	0.705757i
$316$	4.28829	+	7.42754i	0.241235	+	0.417832i
$317$	−2.05921	+	1.72789i	−0.115657	+	0.0970477i	−0.698782	−	0.715335i	$-0.746274\pi$
$317$	−2.05921	+	1.72789i	−0.115657	+	0.0970477i	0.583125	+	0.812382i	$0.301830\pi$
$318$	8.63837	−	3.14411i	0.484415	−	0.176313i
$319$	−16.9172	−	6.15736i	−0.947181	−	0.344746i
$320$	−1.79605	−	1.50706i	−0.100402	−	0.0842475i
$321$	4.86913	−	27.6142i	0.271768	−	1.54127i
$322$	−8.31677			−0.463475
$323$		0			0
$324$	−0.332090			−0.0184495
$325$	−0.0262626	+	0.148943i	−0.00145679	+	0.00826185i
$326$	−10.9158	−	9.15946i	−0.604571	−	0.507296i
$327$	23.2153	+	8.44967i	1.28381	+	0.467268i
$328$	4.71461	−	1.71598i	0.260321	−	0.0947491i
$329$	4.32265	−	3.62714i	0.238316	−	0.199971i
$330$	18.8511	+	32.6510i	1.03772	+	1.79738i
$331$	2.60651	−	4.51462i	0.143267	−	0.248146i	−0.785458	−	0.618915i	$-0.787573\pi$
$331$	2.60651	−	4.51462i	0.143267	−	0.248146i	0.928725	+	0.370769i	$0.120906\pi$
$332$	−1.69561	−	9.61630i	−0.0930588	−	0.527763i
$333$	3.32013	+	18.8294i	0.181942	+	1.03184i
$334$	−5.79506	+	10.0373i	−0.317091	+	0.549218i
$335$	5.13558	+	8.89508i	0.280587	+	0.485990i
$336$	2.74796	−	2.30581i	0.149914	−	0.125792i
$337$	−25.1156	+	9.14133i	−1.36813	+	0.497960i	−0.918560	−	0.395283i	$-0.870647\pi$
$337$	−25.1156	+	9.14133i	−1.36813	+	0.497960i	−0.449575	+	0.893243i	$0.648424\pi$
$338$	−12.1290	−	4.41459i	−0.659731	−	0.240122i
$339$	−30.4959	−	25.5891i	−1.65631	−	1.38981i
$340$	−1.70433	+	9.66574i	−0.0924303	+	0.524198i
$341$	−37.0842			−2.00822
$342$		0			0
$343$	15.8598			0.856351
$344$	0.171804	−	0.974348i	0.00926304	−	0.0525333i
$345$	−32.4972	−	27.2684i	−1.74959	−	1.46808i
$346$	−3.74329	−	1.36245i	−0.201241	−	0.0732456i
$347$	30.6981	−	11.1732i	1.64796	−	0.599808i	0.659555	−	0.751657i	$-0.270745\pi$
$347$	30.6981	−	11.1732i	1.64796	−	0.599808i	0.988404	+	0.151849i	$0.0485227\pi$
$348$	−6.69306	+	5.61614i	−0.358785	+	0.301057i
$349$	14.5529	+	25.2063i	0.778998	+	1.34926i	0.932520	+	0.361119i	$0.117605\pi$
$349$	14.5529	+	25.2063i	0.778998	+	1.34926i	−0.153521	+	0.988145i	$0.549061\pi$
$350$	−0.319119	+	0.552730i	−0.0170576	+	0.0295447i
$351$	0.266320	+	1.51037i	0.0142151	+	0.0806178i
$352$	−0.999556	−	5.66877i	−0.0532765	−	0.302146i
$353$	7.15244	−	12.3884i	0.380686	−	0.659368i	−0.610474	−	0.792036i	$-0.709021\pi$
$353$	7.15244	−	12.3884i	0.380686	−	0.659368i	0.991160	+	0.132668i	$0.0423545\pi$
$354$	4.62866	+	8.01707i	0.246010	+	0.426102i
$355$	−7.93081	+	6.65474i	−0.420924	+	0.353197i
$356$	−14.1673	+	5.15648i	−0.750866	+	0.273293i
$357$	−14.1111	−	5.13603i	−0.746840	−	0.271828i
$358$	−6.47376	−	5.43213i	−0.342149	−	0.287097i
$359$	3.41578	−	19.3719i	0.180278	−	1.02241i	−0.751595	−	0.659624i	$-0.770715\pi$
$359$	3.41578	−	19.3719i	0.180278	−	1.02241i	0.931874	−	0.362783i	$-0.118173\pi$
$360$	11.2639			0.593658
$361$		0			0
$362$	8.48526			0.445976
$363$	−10.7373	+	60.8943i	−0.563562	+	3.19612i
$364$	0.299311	+	0.251152i	0.0156882	+	0.0131639i
$365$	−4.99438	−	1.81780i	−0.261418	−	0.0951482i
$366$	28.7752	−	10.4733i	1.50411	−	0.547450i
$367$	7.31613	−	6.13896i	0.381899	−	0.320451i	−0.431548	−	0.902090i	$-0.642033\pi$
$367$	7.31613	−	6.13896i	0.381899	−	0.320451i	0.813447	+	0.581638i	$0.197588\pi$
$368$	3.23842	+	5.60910i	0.168814	+	0.292395i
$369$	−12.0518	+	20.8744i	−0.627394	+	1.08668i
$370$	1.62030	+	9.18918i	0.0842354	+	0.477723i
$371$	0.733741	+	4.16125i	0.0380939	+	0.216041i
$372$	−8.99885	+	15.5865i	−0.466569	+	0.808120i
$373$	1.82005	+	3.15242i	0.0942387	+	0.163226i	0.909291	−	0.416162i	$-0.136625\pi$
$373$	1.82005	+	3.15242i	0.0942387	+	0.163226i	−0.815052	+	0.579388i	$0.803292\pi$
$374$	−18.4591	+	15.4890i	−0.954496	+	0.800918i
$375$	27.7149	−	10.0874i	1.43119	−	0.520911i
$376$	−4.12943	−	1.50299i	−0.212959	−	0.0775109i
$377$	−0.729015	−	0.611716i	−0.0375462	−	0.0315050i
$378$	−1.12387	+	6.37381i	−0.0578059	+	0.327833i
$379$	−8.34741			−0.428778			−0.214389	−	0.976748i	$-0.568776\pi$
$379$	−8.34741			−0.428778			−0.214389	+	0.976748i	$0.568776\pi$
$380$		0			0
$381$	6.23015			0.319180
$382$	3.88608	−	22.0390i	0.198829	−	1.12761i
$383$	7.26644	+	6.09727i	0.371298	+	0.311556i	0.809275	−	0.587430i	$-0.199860\pi$
$383$	7.26644	+	6.09727i	0.371298	+	0.311556i	−0.437977	+	0.898986i	$0.644305\pi$
$384$	−2.62513	−	0.955469i	−0.133963	−	0.0487586i
$385$	−16.2847	+	5.92714i	−0.829944	+	0.302075i
$386$	5.69026	−	4.77470i	0.289627	−	0.243026i
$387$	2.37660	+	4.11639i	0.120809	+	0.209248i
$388$	8.67609	−	15.0274i	0.440462	−	0.762902i
$389$	6.25966	+	35.5003i	0.317378	+	1.79994i	0.558567	+	0.829460i	$0.311351\pi$
$389$	6.25966	+	35.5003i	0.317378	+	1.79994i	−0.241189	+	0.970478i	$0.577537\pi$
$390$	0.346080	+	1.96272i	0.0175244	+	0.0993860i
$391$	13.5566	−	23.4808i	0.685589	−	1.18747i
$392$	−2.67557	−	4.63422i	−0.135137	−	0.234064i
$393$	−3.25852	+	2.73422i	−0.164371	+	0.137923i
$394$	8.02078	−	2.91933i	0.404081	−	0.147074i
$395$	−18.8958	−	6.87750i	−0.950750	−	0.346045i
$396$	21.1843	+	17.7758i	1.06455	+	0.893265i
$397$	−1.11292	+	6.31169i	−0.0558559	+	0.316775i	−0.999915	−	0.0130002i	$-0.995862\pi$
$397$	−1.11292	+	6.31169i	−0.0558559	+	0.316775i	0.944060	+	0.329775i	$0.106973\pi$
$398$	6.35926			0.318761
$399$		0			0
$400$	0.497039			0.0248520
$401$	−0.0325868	+	0.184809i	−0.00162731	+	0.00922891i	−0.985611	−	0.169032i	$-0.945936\pi$
$401$	−0.0325868	+	0.184809i	−0.00162731	+	0.00922891i	0.983983	+	0.178261i	$0.0570470\pi$
$402$	9.37505	+	7.86660i	0.467585	+	0.392350i
$403$	−1.84211	−	0.670472i	−0.0917619	−	0.0333986i
$404$	−3.45494	+	1.25749i	−0.171890	+	0.0625627i
$405$	0.596450	−	0.500481i	0.0296379	−	0.0248691i
$406$	−2.00802	−	3.47799i	−0.0996562	−	0.172610i
$407$	−11.4543	+	19.8394i	−0.567768	+	0.983402i
$408$	2.03074	+	11.5169i	0.100537	+	0.570171i
$409$	−2.99826	−	17.0040i	−0.148254	−	0.840792i	−0.964696	−	0.263364i	$-0.915168\pi$
$409$	−2.99826	−	17.0040i	−0.148254	−	0.840792i	0.816442	−	0.577427i	$-0.195943\pi$
$410$	−5.88159	+	10.1872i	−0.290471	+	0.503110i
$411$	14.9622	+	25.9153i	0.738031	+	1.27831i
$412$	−14.5652	+	12.2217i	−0.717576	+	0.602118i
$413$	−3.99850	+	1.45534i	−0.196754	+	0.0716124i
$414$	−29.2396	−	10.6424i	−1.43705	−	0.523044i
$415$	17.5378	+	14.7160i	0.860896	+	0.722378i
$416$	0.0528381	−	0.299660i	0.00259060	−	0.0146920i
$417$	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	$0.513422\pi$
$420$	−1.46047	+	8.28271i	−0.0712634	+	0.404155i
$421$	−25.0914	−	21.0542i	−1.22288	−	1.02612i	−0.998669	−	0.0515798i	$-0.983574\pi$
$421$	−25.0914	−	21.0542i	−1.22288	−	1.02612i	−0.224213	−	0.974540i	$-0.571981\pi$
$422$	13.1160	+	4.77385i	0.638479	+	0.232387i
$423$	19.8387	−	7.22071i	0.964592	−	0.351083i
$424$	2.52078	−	2.11518i	0.122420	−	0.102722i
$425$	−1.04035	−	1.80194i	−0.0504644	−	0.0874069i
$426$	−6.16785	+	10.6830i	−0.298833	+	0.517595i
$427$	2.44416	+	13.8615i	0.118281	+	0.670807i
$428$	−1.74295	−	9.88479i	−0.0842489	−	0.477799i
$429$	−2.44652	+	4.23750i	−0.118119	+	0.204588i
$430$	1.15984	+	2.00890i	0.0559323	+	0.0968776i
$431$	19.5433	−	16.3987i	0.941366	−	0.789900i	−0.0364565	−	0.999335i	$-0.511607\pi$
$431$	19.5433	−	16.3987i	0.941366	−	0.789900i	0.977822	+	0.209435i	$0.0671626\pi$
$432$	4.73633	−	1.72388i	0.227877	−	0.0829403i
$433$	23.0069	+	8.37382i	1.10564	+	0.402420i	0.829392	−	0.558667i	$-0.188687\pi$
$433$	23.0069	+	8.37382i	1.10564	+	0.402420i	0.276247	+	0.961087i	$0.410909\pi$
$434$	−6.33720	−	5.31755i	−0.304196	−	0.255250i
$435$	3.55717	−	20.1737i	0.170553	−	0.967257i
$436$	8.84348			0.423526
$437$		0			0
$438$	−6.33280			−0.302593
$439$	5.35510	−	30.3703i	0.255585	−	1.44949i	−0.538981	−	0.842318i	$-0.681191\pi$
$439$	5.35510	−	30.3703i	0.255585	−	1.44949i	0.794566	−	0.607177i	$-0.207698\pi$
$440$	10.3384	+	8.67499i	0.492866	+	0.413564i
$441$	24.1577	+	8.79269i	1.15037	+	0.418699i
$442$	−1.19697	+	0.435660i	−0.0569339	+	0.0207222i
$443$	8.20026	−	6.88083i	0.389606	−	0.326918i	−0.426854	−	0.904321i	$-0.640378\pi$
$443$	8.20026	−	6.88083i	0.389606	−	0.326918i	0.816460	+	0.577402i	$0.195934\pi$
$444$	5.55899	+	9.62845i	0.263818	+	0.456946i
$445$	17.6740	−	30.6123i	0.837830	−	1.45116i
$446$	1.54964	+	8.78842i	0.0733774	+	0.416144i
$447$	4.52789	+	25.6789i	0.214162	+	1.21457i
$448$	0.642040	−	1.11205i	0.0303335	−	0.0525392i
$449$	1.15781	+	2.00538i	0.0546403	+	0.0946399i	0.892052	−	0.451933i	$-0.149265\pi$
$449$	1.15781	+	2.00538i	0.0546403	+	0.0946399i	−0.837411	+	0.546573i	$0.815932\pi$
$450$	−1.82923	+	1.53490i	−0.0862306	+	0.0723561i
$451$	−27.1383	+	9.87754i	−1.27789	+	0.465115i
$452$	−13.3908	−	4.87387i	−0.629852	−	0.229247i
$453$	42.4221	+	35.5963i	1.99316	+	1.67246i
$454$	−0.114572	+	0.649772i	−0.00537715	+	0.0304953i
$455$	−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	$0.500388\pi$
$458$	1.21069	−	6.86616i	0.0565718	−	0.320834i
$459$	−16.1633	−	13.5626i	−0.754436	−	0.633047i
$460$	−14.2696	−	5.19373i	−0.665326	−	0.242159i
$461$	−37.0916	+	13.5002i	−1.72753	+	0.628768i	−0.998450	−	0.0556634i	$-0.982273\pi$
$461$	−37.0916	+	13.5002i	−1.72753	+	0.628768i	−0.729077	+	0.684432i	$0.760050\pi$
$462$	−15.8179	+	13.2728i	−0.735913	+	0.617505i
$463$	3.09528	+	5.36119i	0.143850	+	0.249155i	0.928943	−	0.370222i	$-0.120718\pi$
$463$	3.09528	+	5.36119i	0.143850	+	0.249155i	−0.785093	+	0.619377i	$0.787385\pi$
$464$	−1.56378	+	2.70855i	−0.0725967	+	0.125741i
$465$	−7.32743	−	41.5559i	−0.339801	−	1.92711i
$466$	5.14167	+	29.1599i	0.238183	+	1.35080i
$467$	10.4981	−	18.1832i	0.485793	−	0.841418i	−0.514074	−	0.857746i	$-0.671864\pi$
$467$	10.4981	−	18.1832i	0.485793	−	0.841418i	0.999867	+	0.0163277i	$0.00519750\pi$
$468$	0.730921	+	1.26599i	0.0337868	+	0.0585205i
$469$	−4.30924	+	3.61588i	−0.198982	+	0.166966i
$470$	9.68178	−	3.52388i	0.446587	−	0.162544i
$471$	36.4043	+	13.2501i	1.67742	+	0.610532i
$472$	2.53848	+	2.13004i	0.116843	+	0.0980430i
$473$	−0.988939	+	5.60855i	−0.0454715	+	0.257882i
$474$	−23.9596			−1.10050
$475$		0			0
$476$	−5.37540			−0.246381
$477$	−2.74520	+	15.5688i	−0.125694	+	0.712847i
$478$	18.9239	+	15.8790i	0.865559	+	0.726290i
$479$	−14.5868	−	5.30916i	−0.666487	−	0.242582i	−0.0134527	−	0.999910i	$-0.504282\pi$
$479$	−14.5868	−	5.30916i	−0.666487	−	0.242582i	−0.653035	+	0.757328i	$0.726504\pi$
$480$	6.15482	−	2.24017i	0.280928	−	0.102249i
$481$	−0.927666	+	0.778404i	−0.0422979	+	0.0354922i
$482$	−13.7793	−	23.8665i	−0.627631	−	1.08709i
$483$	11.6169	−	20.1210i	0.528586	−	0.915539i
$484$	3.84353	+	21.7977i	0.174706	+	0.990807i
$485$	7.06462	+	40.0654i	0.320788	+	1.81928i
$486$	8.02431	−	13.8985i	0.363990	−	0.630449i
$487$	−14.3033	−	24.7740i	−0.648143	−	1.12262i	−0.983566	−	0.180549i	$-0.942213\pi$
$487$	−14.3033	−	24.7740i	−0.648143	−	1.12262i	0.335423	−	0.942068i	$-0.391121\pi$
$488$	8.39696	−	7.04589i	0.380113	−	0.318952i
$489$	37.4070	−	13.6150i	1.69160	−	0.615694i
$490$	11.7895	+	4.29104i	0.532597	+	0.193849i
$491$	−23.2486	−	19.5079i	−1.04919	−	0.880377i	−0.0561842	−	0.998420i	$-0.517893\pi$
$491$	−23.2486	−	19.5079i	−1.04919	−	0.880377i	−0.993008	+	0.118043i	$0.962338\pi$
$492$	−2.43386	+	13.8031i	−0.109727	+	0.622292i
$493$	13.0926			0.589659
$494$		0			0
$495$	−64.8373			−2.91422
$496$	−1.11872	+	6.34459i	−0.0502321	+	0.284880i
$497$	−4.34355	−	3.64467i	−0.194835	−	0.163486i
$498$	25.6335	+	9.32982i	1.14866	+	0.418079i
$499$	−8.24696	+	3.00165i	−0.369185	+	0.134372i	−0.519949	−	0.854198i	$-0.674049\pi$
$499$	−8.24696	+	3.00165i	−0.369185	+	0.134372i	0.150764	+	0.988570i	$0.451827\pi$
$500$	8.08754	−	6.78625i	0.361686	−	0.303490i
$501$	−16.1891	−	28.0403i	−0.723275	−	1.25275i
$502$	−1.49428	+	2.58816i	−0.0666928	+	0.115515i
$503$	−3.66473	−	20.7837i	−0.163402	−	0.926700i	−0.950697	−	0.310123i	$-0.899630\pi$
$503$	−3.66473	−	20.7837i	−0.163402	−	0.926700i	0.787294	−	0.616577i	$-0.211481\pi$
$504$	1.07124	+	6.07528i	0.0477167	+	0.270615i
$505$	4.31011	−	7.46533i	0.191798	−	0.332203i
$506$	−18.6410	−	32.2872i	−0.828695	−	1.43534i
$507$	27.6222	−	23.1778i	1.22674	−	1.02936i
$508$	2.09565	−	0.762755i	0.0929795	−	0.0338418i
$509$	20.8811	+	7.60009i	0.925537	+	0.336868i	0.760439	−	0.649409i	$-0.224984\pi$
$509$	20.8811	+	7.60009i	0.925537	+	0.336868i	0.165098	+	0.986277i	$0.447206\pi$
$510$	−21.0040	−	17.6245i	−0.930074	−	0.780424i
$511$	0.505467	−	2.86665i	0.0223606	−	0.126813i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	14.1323			0.623347
$515$	7.74100	−	43.9014i	0.341109	−	1.93453i
$516$	2.11729	+	1.77662i	0.0932087	+	0.0782114i
$517$	23.7699	+	8.65154i	1.04540	+	0.380494i
$518$	−4.80218	+	1.74785i	−0.210996	+	0.0767961i
$519$	8.52485	−	7.15320i	0.374199	−	0.313990i
$520$	0.356707	+	0.617834i	0.0156426	+	0.0270938i
$521$	5.01661	−	8.68902i	0.219782	−	0.380673i	−0.734959	−	0.678111i	$-0.762799\pi$
$521$	5.01661	−	8.68902i	0.219782	−	0.380673i	0.954741	+	0.297438i	$0.0961322\pi$
$522$	−2.60915	−	14.7972i	−0.114199	−	0.647657i
$523$	−5.08482	−	28.8374i	−0.222343	−	1.26097i	−0.867699	−	0.497090i	$-0.834402\pi$
$523$	−5.08482	−	28.8374i	−0.222343	−	1.26097i	0.645356	−	0.763882i	$-0.276709\pi$
$524$	−0.761327	+	1.31866i	−0.0332587	+	0.0576058i
$525$	−0.891491	−	1.54411i	−0.0389079	−	0.0673904i
$526$	−5.79809	+	4.86518i	−0.252809	+	0.212132i
$527$	25.3429	−	9.22407i	1.10396	−	0.401807i
$528$	15.1108	+	5.49989i	0.657614	+	0.239352i
$529$	14.5161	+	12.1804i	0.631134	+	0.529584i
$530$	−1.33972	+	7.59795i	−0.0581939	+	0.330034i
$531$	−15.9200			−0.690870
$532$		0			0
$533$	−1.52664			−0.0661262
$534$	7.31369	−	41.4780i	0.316494	−	1.79493i
$535$	18.0274	+	15.1268i	0.779395	+	0.653990i
$536$	4.11662	+	1.49833i	0.177811	+	0.0647178i
$537$	22.1847	−	8.07457i	0.957340	−	0.348443i
$538$	−5.87613	+	4.93066i	−0.253338	+	0.212576i
$539$	15.4012	+	26.6756i	0.663375	+	1.14900i
$540$	−5.90868	+	10.2341i	−0.254269	+	0.440407i
$541$	−6.57091	−	37.2655i	−0.282505	−	1.60217i	−0.714062	−	0.700082i	$-0.753147\pi$
$541$	−6.57091	−	37.2655i	−0.282505	−	1.60217i	0.431557	−	0.902086i	$-0.357964\pi$
$542$	−2.02559	−	11.4877i	−0.0870064	−	0.493438i
$543$	−11.8522	+	20.5287i	−0.508628	+	0.880970i
$544$	2.09310	+	3.62535i	0.0897408	+	0.155436i
$545$	−15.8833	+	13.3277i	−0.680367	+	0.570896i
$546$	−1.02570	+	0.373323i	−0.0438958	+	0.0159768i
$547$	−13.6233	−	4.95846i	−0.582488	−	0.212008i	0.0339340	−	0.999424i	$-0.489196\pi$
$547$	−13.6233	−	4.95846i	−0.582488	−	0.212008i	−0.616422	+	0.787416i	$0.711419\pi$
$548$	8.20568	+	6.88538i	0.350529	+	0.294129i
$549$	−9.14454	+	51.8613i	−0.390280	+	2.21339i
$550$	−2.86106			−0.121996
$551$		0			0
$552$	−18.0937			−0.770120
$553$	1.91239	−	10.8457i	0.0813231	−	0.461206i
$554$	−21.0206	−	17.6384i	−0.893081	−	0.749384i
$555$	−24.4949	−	8.91542i	−1.03975	−	0.378439i
$556$	10.1622	−	3.69872i	0.430971	−	0.156861i
$557$	−3.32311	+	2.78842i	−0.140805	+	0.118149i	−0.710470	−	0.703728i	$-0.751517\pi$
$557$	−3.32311	+	2.78842i	−0.140805	+	0.118149i	0.569665	+	0.821877i	$0.307073\pi$
$558$	−15.4755	−	26.8044i	−0.655131	−	1.13472i
$559$	−0.150525	+	0.260717i	−0.00636654	+	0.0110272i
$560$	0.522789	+	2.96488i	0.0220919	+	0.125289i
$561$	−11.6894	−	66.2937i	−0.493526	−	2.79892i
$562$	−8.13574	+	14.0915i	−0.343185	+	0.594415i
$563$	−13.6468	−	23.6370i	−0.575144	−	0.996179i	−0.996026	−	0.0890637i	$-0.971613\pi$
$563$	−13.6468	−	23.6370i	−0.575144	−	0.996179i	0.420882	−	0.907116i	$-0.361721\pi$
$564$	9.40424	−	7.89109i	0.395990	−	0.332275i
$565$	31.3959	−	11.4272i	1.32083	−	0.480744i
$566$	3.18907	+	1.16073i	0.134047	+	0.0487890i
$567$	0.326664	+	0.274104i	0.0137186	+	0.0115113i
$568$	−0.766777	+	4.34861i	−0.0321733	+	0.182464i
$569$	7.19043			0.301439			0.150719	−	0.988577i	$-0.451841\pi$
$569$	7.19043			0.301439			0.150719	+	0.988577i	$0.451841\pi$
$570$		0			0
$571$	42.0134			1.75821			0.879103	−	0.476631i	$-0.158142\pi$
$571$	42.0134			1.75821			0.879103	+	0.476631i	$0.158142\pi$
$572$	−0.304147	+	1.72491i	−0.0127170	+	0.0721219i
$573$	47.8917	+	40.1859i	2.00070	+	1.67879i
$574$	−6.05394	−	2.20345i	−0.252686	−	0.0919703i
$575$	3.02510	−	1.10104i	0.126155	−	0.0459168i
$576$	3.68025	−	3.08810i	0.153344	−	0.128671i
$577$	−10.8357	−	18.7679i	−0.451095	−	0.781319i	0.547359	−	0.836898i	$-0.315633\pi$
$577$	−10.8357	−	18.7679i	−0.451095	−	0.781319i	−0.998454	+	0.0555783i	$0.982300\pi$
$578$	0.262102	−	0.453974i	0.0109020	−	0.0188828i
$579$	3.60341	+	20.4360i	0.149753	+	0.849289i
$580$	−1.27333	−	7.22140i	−0.0528721	−	0.299852i
$581$	−6.26929	+	10.8587i	−0.260094	+	0.450496i
$582$	24.2376	+	41.9807i	1.00468	+	1.74016i
$583$	−14.5101	+	12.1755i	−0.600949	+	0.504256i
$584$	−2.13018	+	0.775323i	−0.0881476	+	0.0320831i
$585$	−3.22070	−	1.17224i	−0.133160	−	0.0484662i
$586$	17.9088	+	15.0273i	0.739807	+	0.620771i
$587$	−0.220298	+	1.24937i	−0.00909267	+	0.0515671i	−0.989017	−	0.147805i	$-0.952779\pi$
$587$	−0.220298	+	1.24937i	−0.00909267	+	0.0515671i	0.979924	+	0.199372i	$0.0638903\pi$
$588$	14.9490			0.616485
$589$		0			0
$590$	−7.76934			−0.319859
$591$	−4.14063	+	23.4827i	−0.170323	+	0.965948i
$592$	3.04870	+	2.55816i	0.125301	+	0.105140i
$593$	−20.2598	−	7.37395i	−0.831969	−	0.302812i	−0.109302	−	0.994009i	$-0.534862\pi$
$593$	−20.2598	−	7.37395i	−0.831969	−	0.302812i	−0.722667	+	0.691197i	$0.757084\pi$
$594$	−27.2633	+	9.92304i	−1.11863	+	0.407147i
$595$	9.65449	−	8.10108i	0.395795	−	0.332112i
$596$	4.66692	+	8.08334i	0.191165	+	0.331107i
$597$	−8.88262	+	15.3852i	−0.363542	+	0.629672i
$598$	−0.342224	−	1.94085i	−0.0139946	−	0.0793671i
$599$	4.97359	+	28.2066i	0.203215	+	1.15249i	0.900224	+	0.435428i	$0.143403\pi$
$599$	4.97359	+	28.2066i	0.203215	+	1.15249i	−0.697008	+	0.717063i	$0.745486\pi$
$600$	−0.694265	+	1.20250i	−0.0283433	+	0.0490920i
$601$	3.77932	+	6.54598i	0.154162	+	0.267016i	0.932754	−	0.360515i	$-0.117399\pi$
$601$	3.77932	+	6.54598i	0.154162	+	0.267016i	−0.778592	+	0.627531i	$0.784066\pi$
$602$	−0.973214	+	0.816623i	−0.0396652	+	0.0332831i
$603$	−19.7772	+	7.19830i	−0.805388	+	0.293137i
$604$	18.6277	+	6.77992i	0.757950	+	0.275871i
$605$	−39.7538	−	33.3574i	−1.61622	−	1.35617i
$606$	1.78357	−	10.1151i	0.0724525	−	0.410898i
$607$	−1.72737			−0.0701117			−0.0350558	−	0.999385i	$-0.511161\pi$
$607$	−1.72737			−0.0701117			−0.0350558	+	0.999385i	$0.511161\pi$
$608$		0			0
$609$	11.2192			0.454625
$610$	−4.46275	+	25.3095i	−0.180692	+	1.02475i
$611$	1.02432	+	0.859507i	0.0414396	+	0.0347719i
$612$	−18.8985	−	6.87851i	−0.763928	−	0.278047i
$613$	25.7635	−	9.37714i	1.04058	−	0.378739i	0.235479	−	0.971880i	$-0.424334\pi$
$613$	25.7635	−	9.37714i	1.04058	−	0.378739i	0.805099	+	0.593140i	$0.202112\pi$
$614$	−1.06329	+	0.892202i	−0.0429107	+	0.0360064i
$615$	−16.4308	−	28.4590i	−0.662555	−	1.14758i
$616$	−3.69572	+	6.40117i	−0.148905	+	0.257911i
$617$	1.84545	+	10.4660i	0.0742949	+	0.421347i	0.999157	+	0.0410453i	$0.0130688\pi$
$617$	1.84545	+	10.4660i	0.0742949	+	0.421347i	−0.924862	+	0.380302i	$0.875820\pi$
$618$	−9.22354	−	52.3093i	−0.371025	−	2.10419i
$619$	−4.18004	+	7.24004i	−0.168010	+	0.291002i	−0.937720	−	0.347392i	$-0.887067\pi$
$619$	−4.18004	+	7.24004i	−0.168010	+	0.291002i	0.769710	+	0.638394i	$0.220401\pi$
$620$	−7.55242	−	13.0812i	−0.303313	−	0.525353i
$621$	25.0076	−	20.9839i	1.00352	−	0.842055i
$622$	−11.4551	+	4.16931i	−0.459307	+	0.167174i
$623$	18.1919	+	6.62132i	0.728845	+	0.265278i
$624$	0.651172	+	0.546398i	0.0260677	+	0.0218734i
$625$	−4.72985	+	26.8243i	−0.189194	+	1.07297i
$626$	−16.5314			−0.660728
$627$		0			0
$628$	13.8676			0.553379
$629$	2.89301	−	16.4071i	0.115352	−	0.654193i
$630$	−11.0798	−	9.29709i	−0.441431	−	0.370405i
$631$	−23.0508	−	8.38980i	−0.917638	−	0.333993i	−0.160339	−	0.987062i	$-0.551259\pi$
$631$	−23.0508	−	8.38980i	−0.917638	−	0.333993i	−0.757298	+	0.653069i	$0.773481\pi$
$632$	−8.05936	+	2.93337i	−0.320584	+	0.116683i
$633$	−29.8700	+	25.0639i	−1.18723	+	0.996202i
$634$	−1.34406	−	2.32797i	−0.0533793	−	0.0924557i
$635$	−2.61437	+	4.52823i	−0.103748	+	0.179697i
$636$	1.59631	+	9.05310i	0.0632976	+	0.358979i
$637$	0.282744	+	1.60352i	0.0112027	+	0.0635338i
$638$	9.00145	−	15.5910i	0.356371	−	0.617253i
$639$	−10.6070	−	18.3719i	−0.419606	−	0.726780i
$640$	1.79605	−	1.50706i	0.0709951	−	0.0595720i
$641$	−6.55220	+	2.38480i	−0.258796	+	0.0941941i	−0.468160	−	0.883644i	$-0.655083\pi$
$641$	−6.55220	+	2.38480i	−0.258796	+	0.0941941i	0.209364	+	0.977838i	$0.432861\pi$
$642$	26.3492	+	9.59031i	1.03992	+	0.378499i
$643$	−6.96353	−	5.84309i	−0.274615	−	0.230429i	0.495070	−	0.868853i	$-0.335142\pi$
$643$	−6.96353	−	5.84309i	−0.274615	−	0.230429i	−0.769685	+	0.638424i	$0.779587\pi$
$644$	1.44419	−	8.19042i	0.0569091	−	0.322748i
$645$	−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	$0.299185\pi$
$648$	0.0576668	−	0.327045i	0.00226537	−	0.0128475i
$649$	−14.6120	−	12.2610i	−0.573573	−	0.481285i
$650$	−0.142119	−	0.0517272i	−0.00557438	−	0.00202891i
$651$	21.7167	−	7.90424i	0.851146	−	0.309792i
$652$	10.9158	−	9.15946i	0.427497	−	0.358712i
$653$	−5.20956	−	9.02323i	−0.203866	−	0.353106i	0.745905	−	0.666053i	$-0.232017\pi$
$653$	−5.20956	−	9.02323i	−0.203866	−	0.353106i	−0.949771	+	0.312946i	$0.898684\pi$
$654$	−12.3526	+	21.3953i	−0.483025	+	0.836623i
$655$	−0.619920	−	3.51574i	−0.0242223	−	0.137371i
$656$	0.871225	+	4.94096i	0.0340156	+	0.192912i
$657$	5.44533	−	9.43159i	0.212443	−	0.367962i
$658$	2.82141	+	4.88683i	0.109990	+	0.190508i
$659$	20.2049	−	16.9539i	0.787071	−	0.660431i	−0.157948	−	0.987447i	$-0.550488\pi$
$659$	20.2049	−	16.9539i	0.787071	−	0.660431i	0.945019	+	0.327017i	$0.106043\pi$
$660$	−35.4285	+	12.8949i	−1.37905	+	0.501933i
$661$	−23.2047	−	8.44583i	−0.902559	−	0.328505i	−0.151281	−	0.988491i	$-0.548340\pi$
$661$	−23.2047	−	8.44583i	−0.902559	−	0.328505i	−0.751278	+	0.659986i	$0.770562\pi$
$662$	3.99341	+	3.35087i	0.155208	+	0.130235i
$663$	0.617919	−	3.50439i	0.0239980	−	0.136099i
$664$	9.76464			0.378942
$665$		0			0
$666$	−19.1198			−0.740879
$667$	−3.51754	+	19.9489i	−0.136200	+	0.772426i
$668$	−8.87854	−	7.44998i	−0.343521	−	0.288248i
$669$	−23.4267	−	8.52660i	−0.905727	−	0.329658i
$670$	−9.65173	+	3.51294i	−0.372879	+	0.135717i
$671$	−48.3347	+	40.5577i	−1.86594	+	1.56571i
$672$	1.79360	+	3.10661i	0.0691898	+	0.119840i
$673$	−4.88690	+	8.46436i	−0.188376	+	0.326277i	−0.944709	−	0.327910i	$-0.893656\pi$
$673$	−4.88690	+	8.46436i	−0.188376	+	0.326277i	0.756333	+	0.654187i	$0.226989\pi$
$674$	−4.64118	−	26.3214i	−0.178771	−	1.01386i
$675$	−0.435027	−	2.46716i	−0.0167442	−	0.0949611i
$676$	6.45371	−	11.1781i	0.248219	−	0.429929i
$677$	−10.7874	−	18.6843i	−0.414592	−	0.718094i	0.580794	−	0.814051i	$-0.302742\pi$
$677$	−10.7874	−	18.6843i	−0.414592	−	0.718094i	−0.995386	+	0.0959565i	$0.969409\pi$
$678$	30.4959	−	25.5891i	1.17119	−	0.982742i
$679$	−20.9378	+	7.62075i	−0.803520	+	0.292457i
$680$	−9.22294	−	3.35688i	−0.353684	−	0.128730i
$681$	−1.41198	−	1.18479i	−0.0541072	−	0.0454013i
$682$	6.43960	−	36.5208i	0.246585	−	1.39845i
$683$	−33.2509			−1.27231			−0.636155	−	0.771561i	$-0.719476\pi$
$683$	−33.2509			−1.27231			−0.636155	+	0.771561i	$0.719476\pi$
$684$		0			0
$685$	−25.1145			−0.959576
$686$	−2.75403	+	15.6189i	−0.105149	+	0.596332i
$687$	14.9204	+	12.5197i	0.569250	+	0.477657i
$688$	0.929712	+	0.338387i	0.0354449	+	0.0129009i
$689$	−0.940900	+	0.342460i	−0.0358454	+	0.0130467i
$690$	32.4972	−	27.2684i	1.23715	−	1.03809i
$691$	−2.40466	−	4.16500i	−0.0914776	−	0.158444i	0.816655	−	0.577126i	$-0.195826\pi$
$691$	−2.40466	−	4.16500i	−0.0914776	−	0.158444i	−0.908133	+	0.418682i	$0.862492\pi$
$692$	1.99176	−	3.44983i	0.0757155	−	0.131143i
$693$	−6.16627	−	34.9706i	−0.234237	−	1.32843i
$694$	5.67277	+	32.1719i	0.215335	+	1.22123i
$695$	−12.6775	+	21.9581i	−0.480886	+	0.832919i
$696$	−4.36858	−	7.56661i	−0.165591	−	0.286811i
$697$	16.0892	−	13.5004i	0.609420	−	0.511364i
$698$	−27.3505	+	9.95476i	−1.03523	+	0.376793i
$699$	−77.7293	−	28.2911i	−2.93999	−	1.07007i
$700$	−0.488918	−	0.410251i	−0.0184794	−	0.0155060i
$701$	0.601633	−	3.41203i	0.0227234	−	0.128871i	−0.971336	−	0.237711i	$-0.923603\pi$
$701$	0.601633	−	3.41203i	0.0227234	−	0.128871i	0.994059	+	0.108841i	$0.0347139\pi$
$702$	−1.53367			−0.0578848
$703$		0			0
$704$	5.75621			0.216946
$705$	−4.99809	+	28.3456i	−0.188239	+	1.06756i
$706$	10.9582	+	9.19500i	0.412416	+	0.346058i
$707$	4.43641	+	1.61472i	0.166848	+	0.0607279i
$708$	−8.69903	+	3.16619i	−0.326929	+	0.118993i
$709$	15.7608	−	13.2249i	0.591910	−	0.496672i	−0.296924	−	0.954901i	$-0.595961\pi$
$709$	15.7608	−	13.2249i	0.591910	−	0.496672i	0.888834	+	0.458230i	$0.151516\pi$
$710$	−5.17647	−	8.96591i	−0.194269	−	0.336484i
$711$	20.6019	−	35.6836i	0.772633	−	1.33824i
$712$	−2.61801	−	14.8475i	−0.0981142	−	0.556433i
$713$	7.24578	+	41.0929i	0.271357	+	1.53894i
$714$	7.50837	−	13.0049i	0.280994	−	0.486696i
$715$	−2.05328	−	3.55639i	−0.0767884	−	0.133001i
$716$	6.47376	−	5.43213i	0.241936	−	0.203008i
$717$	−64.8496	+	23.6033i	−2.42185	+	0.881482i
$718$	18.4844	+	6.72778i	0.689832	+	0.251078i
$719$	18.5295	+	15.5481i	0.691034	+	0.579846i	0.919207	−	0.393774i	$-0.128831\pi$
$719$	18.5295	+	15.5481i	0.691034	+	0.579846i	−0.228173	+	0.973621i	$0.573275\pi$
$720$	−1.95595	+	11.0928i	−0.0728940	+	0.413402i
$721$	24.4149			0.909257
$722$		0			0
$723$	76.9880			2.86321
$724$	−1.47345	+	8.35635i	−0.0547604	+	0.310561i
$725$	1.19083	+	0.999226i	0.0442263	+	0.0371103i
$726$	−58.1046	−	21.1484i	−2.15647	−	0.784889i
$727$	−17.0344	+	6.20001i	−0.631771	+	0.229946i	−0.638002	−	0.770035i	$-0.720239\pi$
$727$	−17.0344	+	6.20001i	−0.631771	+	0.229946i	0.00623100	+	0.999981i	$0.498017\pi$
$728$	−0.299311	+	0.251152i	−0.0110932	+	0.00930830i
$729$	21.9186	+	37.9641i	0.811800	+	1.40608i
$730$	2.65745	−	4.60284i	0.0983567	−	0.170359i
$731$	−0.719204	−	4.07881i	−0.0266007	−	0.150860i
$732$	5.31745	+	30.1568i	0.196539	+	1.11463i
$733$	−11.3682	+	19.6902i	−0.419893	+	0.727275i	−0.995928	−	0.0901491i	$-0.971266\pi$
$733$	−11.3682	+	19.6902i	−0.419893	+	0.727275i	0.576036	+	0.817425i	$0.304599\pi$
$734$	4.77527	+	8.27100i	0.176258	+	0.305288i
$735$	−26.8491	+	22.5291i	−0.990344	+	0.830997i
$736$	−6.08623	+	2.21521i	−0.224342	+	0.0816537i
$737$	−23.6961	−	8.62469i	−0.872858	−	0.317695i
$738$	−18.4645	−	15.4936i	−0.679688	−	0.570326i
$739$	2.63575	−	14.9481i	0.0969575	−	0.549873i	−0.897172	−	0.441680i	$-0.854383\pi$
$739$	2.63575	−	14.9481i	0.0969575	−	0.549873i	0.994130	−	0.108193i	$-0.0345064\pi$
$740$	−9.33094			−0.343012
$741$		0			0
$742$	−4.22545			−0.155121
$743$	0.568915	−	3.22648i	0.0208715	−	0.118368i	−0.972592	−	0.232518i	$-0.925303\pi$
$743$	0.568915	−	3.22648i	0.0208715	−	0.118368i	0.993463	+	0.114150i	$0.0364146\pi$
$744$	−13.7870	−	11.5687i	−0.505457	−	0.424129i
$745$	−20.5641	−	7.48474i	−0.753412	−	0.274220i
$746$	−3.42058	+	1.24499i	−0.125236	+	0.0455823i
$747$	−35.9363	+	30.1542i	−1.31484	+	1.10328i
$748$	−12.0483	−	20.8683i	−0.440530	−	0.763020i
$749$	−6.44433	+	11.1619i	−0.235471	+	0.407847i
$750$	5.12151	+	29.0455i	0.187011	+	1.06059i
$751$	−9.07005	−	51.4388i	−0.330971	−	1.87703i	−0.463877	−	0.885899i	$-0.653542\pi$
$751$	−9.07005	−	51.4388i	−0.330971	−	1.87703i	0.132907	−	0.991129i	$-0.457569\pi$
$752$	2.19723	−	3.80571i	0.0801246	−	0.138780i
$753$	−4.17442	−	7.23030i	−0.152124	−	0.263487i
$754$	0.729015	−	0.611716i	0.0265492	−	0.0222774i
$755$	−43.6740	+	15.8960i	−1.58946	+	0.578516i
$756$	−6.08182	−	2.21360i	−0.221194	−	0.0805079i
$757$	−18.5645	−	15.5774i	−0.674737	−	0.566172i	0.239726	−	0.970841i	$-0.422942\pi$
$757$	−18.5645	−	15.5774i	−0.674737	−	0.566172i	−0.914463	+	0.404669i	$0.867387\pi$
$758$	1.44951	−	8.22060i	0.0526487	−	0.298585i
$759$	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	$0.648433\pi$
$762$	−1.08185	+	6.13550i	−0.0391914	+	0.222266i
$763$	−8.69899	−	7.29932i	−0.314925	−	0.264253i
$764$	21.0294	+	7.65408i	0.760817	+	0.276915i
$765$	44.3091	−	16.1272i	1.60200	−	0.583080i
$766$	−7.26644	+	6.09727i	−0.262547	+	0.220303i
$767$	−0.504158	−	0.873228i	−0.0182041	−	0.0315304i
$768$	1.39680	−	2.41933i	0.0504028	−	0.0873001i
$769$	1.67447	+	9.49640i	0.0603830	+	0.342449i	1.00000		0.000221010i	$7.03495e-5\pi$
$769$	1.67447	+	9.49640i	0.0603830	+	0.342449i	−0.939617	+	0.342228i	$0.888819\pi$
$770$	−3.00929	−	17.0665i	−0.108447	−	0.615034i
$771$	−19.7400	+	34.1906i	−0.710918	+	1.23135i
$772$	3.71406	+	6.43293i	0.133672	+	0.231526i
$773$	−0.986137	+	0.827468i	−0.0354689	+	0.0297619i	−0.660350	−	0.750958i	$-0.729592\pi$
$773$	−0.986137	+	0.827468i	−0.0354689	+	0.0297619i	0.624881	+	0.780720i	$0.285148\pi$
$774$	−4.46654	+	1.62569i	−0.160547	+	0.0584342i
$775$	3.00904	+	1.09520i	0.108088	+	0.0393408i
$776$	13.2925	+	11.1538i	0.477174	+	0.400397i
$777$	2.47906	−	14.0595i	0.0889359	−	0.504381i
$778$	−36.0480			−1.29238
$779$		0			0
$780$	−1.99300			−0.0713607
$781$	4.41374	−	25.0315i	0.157936	−	0.895699i
$782$	20.7700	+	17.4281i	0.742733	+	0.623227i
$783$	14.8131	+	5.39154i	0.529379	+	0.192678i
$784$	5.02843	−	1.83020i	0.179587	−	0.0653642i
$785$	−24.9070	+	20.8994i	−0.888967	+	0.745932i
$786$	−2.12685	−	3.68381i	−0.0758621	−	0.131397i
$787$	−8.17232	+	14.1549i	−0.291312	+	0.504567i	−0.974120	−	0.226031i	$-0.927425\pi$
$787$	−8.17232	+	14.1549i	−0.291312	+	0.504567i	0.682808	+	0.730598i	$0.260758\pi$
$788$	1.48218	+	8.40586i	0.0528005	+	0.299447i
$789$	−3.67169	−	20.8232i	−0.130716	−	0.741326i
$790$	10.0542	−	17.4144i	0.357714	−	0.619578i
$791$	9.14922	+	15.8469i	0.325309	+	0.563451i
$792$	−21.1843	+	17.7758i	−0.752752	+	0.631634i
$793$	−3.13423	+	1.14077i	−0.111300	+	0.0405098i
$794$	−6.02255	−	2.19203i	−0.213732	−	0.0777922i
$795$	−16.5106	−	13.8541i	−0.585572	−	0.491354i
$796$	−1.10427	+	6.26264i	−0.0391399	+	0.221974i
$797$	15.6884			0.555712			0.277856	−	0.960623i	$-0.410376\pi$
$797$	15.6884			0.555712			0.277856	+	0.960623i	$0.410376\pi$
$798$		0			0
$799$	−18.3960			−0.650804
$800$	−0.0863099	+	0.489488i	−0.00305152	+	0.0173060i
$801$	55.4854	+	46.5578i	1.96048	+	1.64504i
$802$	−0.176343	−	0.0641834i	−0.00622687	−	0.00226640i
$803$	12.2618	−	4.46293i	0.432709	−	0.157493i
$804$	−9.37505	+	7.86660i	−0.330633	+	0.277434i
$805$	9.74965	+	16.8869i	0.343630	+	0.595185i
$806$	0.980164	−	1.69769i	0.0345248	−	0.0597987i
$807$	−3.72111	−	21.1035i	−0.130989	−	0.742877i
$808$	−0.638446	−	3.62081i	−0.0224605	−	0.127380i
$809$	5.76242	−	9.98080i	0.202596	−	0.350906i	−0.746768	−	0.665084i	$-0.768396\pi$
$809$	5.76242	−	9.98080i	0.202596	−	0.350906i	0.949364	+	0.314178i	$0.101729\pi$
$810$	0.389305	+	0.674297i	0.0136788	+	0.0236924i
$811$	6.35895	−	5.33579i	0.223293	−	0.187365i	−0.524278	−	0.851547i	$-0.675665\pi$
$811$	6.35895	−	5.33579i	0.223293	−	0.187365i	0.747571	+	0.664182i	$0.231220\pi$
$812$	3.77384	−	1.37356i	0.132436	−	0.0482027i
$813$	30.6219	+	11.1454i	1.07396	+	0.390888i
$814$	−17.5490	−	14.7253i	−0.615091	−	0.516123i
$815$	−5.80146	+	32.9017i	−0.203216	+	1.15250i
$816$	−11.6946			−0.409392
$817$		0			0
$818$	17.2663			0.603701
$819$	0.325959	−	1.84860i	0.0113899	−	0.0645954i
$820$	−9.01112	−	7.56122i	−0.314682	−	0.264049i
$821$	31.6782	+	11.5299i	1.10558	+	0.402397i	0.829369	−	0.558701i	$-0.188700\pi$
$821$	31.6782	+	11.5299i	1.10558	+	0.402397i	0.276208	+	0.961098i	$0.410922\pi$
$822$	−28.1197	+	10.2347i	−0.980788	+	0.356978i
$823$	16.7517	−	14.0563i	0.583927	−	0.489973i	−0.302307	−	0.953211i	$-0.597757\pi$
$823$	16.7517	−	14.0563i	0.583927	−	0.489973i	0.886234	+	0.463238i	$0.153312\pi$
$824$	−9.50676	−	16.4662i	−0.331184	−	0.573627i
$825$	3.99634	−	6.92186i	0.139135	−	0.240988i
$826$	−0.738894	−	4.19047i	−0.0257094	−	0.145805i
$827$	−6.80171	−	38.5744i	−0.236519	−	1.34136i	−0.839392	−	0.543527i	$-0.817089\pi$
$827$	−6.80171	−	38.5744i	−0.236519	−	1.34136i	0.602873	−	0.797837i	$-0.294023\pi$
$828$	15.5581	−	26.9474i	0.540681	−	0.936487i
$829$	−7.20878	−	12.4860i	−0.250371	−	0.433656i	0.713257	−	0.700903i	$-0.247219\pi$
$829$	−7.20878	−	12.4860i	−0.250371	−	0.433656i	−0.963628	+	0.267247i	$0.913886\pi$
$830$	−17.5378	+	14.7160i	−0.608745	+	0.510798i
$831$	72.0348	−	26.2185i	2.49886	−	0.909511i
$832$	0.285932	+	0.104071i	0.00991291	+	0.00360800i
$833$	−17.1601	−	14.3990i	−0.594562	−	0.498897i
$834$	−5.24608	+	29.7520i	−0.181657	+	1.03023i
$835$	27.1739			0.940392
$836$		0			0
$837$	32.4719			1.12239
$838$	0.299668	−	1.69950i	0.0103518	−	0.0587082i
$839$	−16.0511	−	13.4685i	−0.554145	−	0.464983i	0.322197	−	0.946673i	$-0.395579\pi$
$839$	−16.0511	−	13.4685i	−0.554145	−	0.464983i	−0.876342	+	0.481690i	$0.840023\pi$
$840$	−7.90327	−	2.87656i	−0.272689	−	0.0992506i
$841$	18.0594	−	6.57307i	0.622737	−	0.226658i
$842$	25.0914	−	21.0542i	0.864708	−	0.725576i
$843$	−22.7280	−	39.3661i	−0.782795	−	1.35584i
$844$	−6.97890	+	12.0878i	−0.240224	+	0.416079i
$845$	5.25501	+	29.8027i	0.180778	+	1.02524i
$846$	3.66605	+	20.7912i	0.126041	+	0.714816i
$847$	14.2109	−	24.6140i	0.488293	−	0.845748i
$848$	1.64532	+	2.84978i	0.0565006	+	0.0978619i
$849$	−7.26269	+	6.09412i	−0.249255	+	0.209150i
$850$	1.95522	−	0.711642i	0.0670635	−	0.0244091i
$851$	24.2220	+	8.81608i	0.830319	+	0.302211i
$852$	−9.44970	−	7.92924i	−0.323741	−	0.271651i
$853$	9.02194	−	51.1660i	0.308906	−	1.75189i	−0.295621	−	0.955305i	$-0.595527\pi$
$853$	9.02194	−	51.1660i	0.308906	−	1.75189i	0.604527	−	0.796585i	$-0.293362\pi$
$854$	−14.0754			−0.481650
$855$		0			0
$856$	10.0373			0.343067
$857$	−5.06765	+	28.7401i	−0.173108	+	0.981743i	0.767198	+	0.641411i	$0.221651\pi$
$857$	−5.06765	+	28.7401i	−0.173108	+	0.981743i	−0.940305	+	0.340332i	$0.889461\pi$
$858$	−3.74829	−	3.14519i	−0.127964	−	0.107375i
$859$	−20.6651	−	7.52148i	−0.705084	−	0.256630i	−0.0355042	−	0.999370i	$-0.511304\pi$
$859$	−20.6651	−	7.52148i	−0.705084	−	0.256630i	−0.669580	+	0.742740i	$0.733526\pi$
$860$	−2.17978	+	0.793375i	−0.0743299	+	0.0270539i
$861$	13.7870	−	11.5687i	0.469861	−	0.394260i
$862$	12.7560	+	22.0940i	0.434470	+	0.752524i
$863$	−17.9079	+	31.0173i	−0.609590	+	1.05584i	0.381717	+	0.924279i	$0.375333\pi$
$863$	−17.9079	+	31.0173i	−0.609590	+	1.05584i	−0.991308	+	0.131562i	$0.958001\pi$
$864$	0.875238	+	4.96372i	0.0297762	+	0.168869i
$865$	1.62182	+	9.19779i	0.0551435	+	0.312734i
$866$	−12.2417	+	21.2032i	−0.415990	+	0.720516i
$867$	0.732209	+	1.26822i	0.0248671	+	0.0430711i
$868$	6.33720	−	5.31755i	0.215099	−	0.180489i
$869$	46.3914	−	16.8851i	1.57372	−	0.572787i
$870$	19.2496	+	7.00627i	0.652621	+	0.237535i
$871$	−1.02114	−	0.856839i	−0.0346000	−	0.0290329i
$872$	−1.53565	+	8.70913i	−0.0520038	+	0.294928i
$873$	−83.3638			−2.82144
$874$		0			0
$875$	−13.5567			−0.458300
$876$	1.09968	−	6.23659i	0.0371547	−	0.210715i
$877$	−5.99416	−	5.02970i	−0.202409	−	0.169841i	0.535949	−	0.844250i	$-0.319954\pi$
$877$	−5.99416	−	5.02970i	−0.202409	−	0.169841i	−0.738358	+	0.674409i	$0.764398\pi$
$878$	28.9790	+	10.5475i	0.977994	+	0.355961i
$879$	−61.3711	+	22.3372i	−2.07000	+	0.753417i
$880$	−10.3384	+	8.67499i	−0.348509	+	0.292434i
$881$	7.24145	+	12.5426i	0.243970	+	0.422569i	0.961842	−	0.273607i	$-0.0882167\pi$
$881$	7.24145	+	12.5426i	0.243970	+	0.422569i	−0.717871	+	0.696176i	$0.754883\pi$
$882$	−12.8540	+	22.2639i	−0.432818	+	0.749663i
$883$	−4.08992	−	23.1951i	−0.137637	−	0.780577i	−0.972987	−	0.230859i	$-0.925846\pi$
$883$	−4.08992	−	23.1951i	−0.137637	−	0.780577i	0.835350	−	0.549718i	$-0.185265\pi$
$884$	−0.221190	−	1.25443i	−0.00743944	−	0.0421912i
$885$	10.8522	−	18.7966i	0.364794	−	0.631842i
$886$	5.35234	+	9.27052i	0.179815	+	0.311449i
$887$	12.1599	−	10.2033i	0.408288	−	0.342594i	−0.415399	−	0.909639i	$-0.636358\pi$
$887$	12.1599	−	10.2033i	0.408288	−	0.342594i	0.823687	+	0.567045i	$0.191913\pi$
$888$	−10.4475	+	3.80257i	−0.350595	+	0.127606i
$889$	−2.69098	−	0.979438i	−0.0902527	−	0.0328493i
$890$	27.0782	+	22.7213i	0.907663	+	0.761620i
$891$	−0.331943	+	1.88254i	−0.0111205	+	0.0630675i
$892$	−8.92400			−0.298798
$893$		0			0
$894$	−26.0751			−0.872081
$895$	−3.44062	+	19.5127i	−0.115007	+	0.652239i
$896$	0.983662	+	0.825390i	0.0328618	+	0.0275743i
$897$	5.17357	+	1.88303i	0.172741	+	0.0628724i
$898$	−2.17597	+	0.791987i	−0.0726130	+	0.0264290i
$899$	−15.4352	+	12.9516i	−0.514792	+	0.431962i
$900$	−1.19394	−	2.06797i	−0.0397981	−	0.0689324i
$901$	6.88763	−	11.9297i	0.229460	−	0.397437i
$902$	−5.01496	−	28.4412i	−0.166980	−	0.946990i
$903$	−0.616296	−	3.49519i	−0.0205090	−	0.116313i
$904$	7.12512	−	12.3411i	0.236978	−	0.410458i
$905$	−9.94718	−	17.2290i	−0.330655	−	0.572712i
$906$	−42.4221	+	35.5963i	−1.40938	+	1.18261i
$907$	42.2981	−	15.3953i	1.40449	−	0.511191i	0.474979	−	0.879997i	$-0.342456\pi$
$907$	42.2981	−	15.3953i	1.40449	−	0.511191i	0.929506	+	0.368806i	$0.120233\pi$
$908$	−0.620005	−	0.225663i	−0.0205756	−	0.00748890i
$909$	13.5311	+	11.3539i	0.448797	+	0.376585i
$910$	0.159076	−	0.902162i	0.00527330	−	0.0299064i
$911$	2.75901			0.0914100			0.0457050	−	0.998955i	$-0.485447\pi$
$911$	2.75901			0.0914100			0.0457050	+	0.998955i	$0.485447\pi$
$912$		0			0
$913$	−56.2074			−1.86019
$914$	0.00906113	−	0.0513882i	0.000299716	−	0.00169977i
$915$	−54.9986	−	46.1493i	−1.81820	−	1.52565i
$916$	6.55161	+	2.38459i	0.216471	+	0.0787891i
$917$	1.83730	−	0.668721i	0.0606728	−	0.0220831i
$918$	16.1633	−	13.5626i	0.533467	−	0.447632i
$919$	19.6542	+	34.0420i	0.648331	+	1.12294i	0.983521	+	0.180792i	$0.0578660\pi$
$919$	19.6542	+	34.0420i	0.648331	+	1.12294i	−0.335191	+	0.942150i	$0.608801\pi$
$920$	7.59272	−	13.1510i	0.250325	−	0.433575i
$921$	−0.673335	−	3.81867i	−0.0221871	−	0.125829i
$922$	−6.85424	−	38.8724i	−0.225733	−	1.28019i
$923$	0.671809	−	1.16361i	0.0221129	−	0.0383006i
$924$	−10.3244	−	17.8823i	−0.339647	−	0.588286i
$925$	1.51532	−	1.27151i	0.0498235	−	0.0418069i
$926$	−5.81723	+	2.11730i	−0.191166	+	0.0695787i
$927$	85.8365	+	31.2419i	2.81924	+	1.02612i
$928$	−2.39585	−	2.01036i	−0.0786476	−	0.0659932i
$929$	−5.16460	+	29.2899i	−0.169445	+	0.960970i	0.774917	+	0.632063i	$0.217792\pi$
$929$	−5.16460	+	29.2899i	−0.169445	+	0.960970i	−0.944362	+	0.328907i	$0.893320\pi$
$930$	42.1970			1.38369
$931$		0			0
$932$	−29.6097			−0.969898
$933$	5.91354	−	33.5374i	0.193601	−	1.09796i
$934$	16.0840	+	13.4961i	0.526284	+	0.441605i
$935$	53.0892	+	19.3229i	1.73620	+	0.631926i
$936$	−1.37368	+	0.499979i	−0.0449002	+	0.0163423i
$937$	28.8960	−	24.2467i	0.943993	−	0.792104i	−0.0342830	−	0.999412i	$-0.510915\pi$
$937$	28.8960	−	24.2467i	0.943993	−	0.792104i	0.978276	+	0.207308i	$0.0664703\pi$
$938$	−2.81266	−	4.87166i	−0.0918365	−	0.159065i
$939$	23.0911	−	39.9950i	0.753550	−	1.30519i
$940$	1.78912	+	10.1466i	0.0583547	+	0.330946i
$941$	1.12464	+	6.37813i	0.0366621	+	0.207921i	0.997636	−	0.0687174i	$-0.0218907\pi$
$941$	1.12464	+	6.37813i	0.0366621	+	0.207921i	−0.960974	+	0.276638i	$0.910780\pi$
$942$	−19.3703	+	33.5504i	−0.631120	+	1.09313i
$943$	16.2477	+	28.1419i	0.529099	+	0.916427i
$944$	−2.53848	+	2.13004i	−0.0826205	+	0.0693268i
$945$	14.2593	−	5.18996i	0.463855	−	0.168829i
$946$	−5.35162	−	1.94783i	−0.173996	−	0.0633294i
$947$	12.4798	+	10.4718i	0.405541	+	0.340289i	0.822631	−	0.568576i	$-0.192506\pi$
$947$	12.4798	+	10.4718i	0.405541	+	0.340289i	−0.417090	+	0.908865i	$0.636950\pi$
$948$	4.16054	−	23.5956i	0.135128	−	0.766349i
$949$	0.689776			0.0223911
$950$		0			0
$951$	7.50953			0.243513
$952$	0.933429	−	5.29374i	0.0302526	−	0.171571i
$953$	26.5215	+	22.2542i	0.859115	+	0.720883i	0.961777	−	0.273833i	$-0.0882916\pi$
$953$	26.5215	+	22.2542i	0.859115	+	0.720883i	−0.102662	+	0.994716i	$0.532736\pi$
$954$	−14.8556	−	5.40699i	−0.480968	−	0.175058i
$955$	−49.3050	+	17.9456i	−1.59547	+	0.580705i
$956$	−18.9239	+	15.8790i	−0.612043	+	0.513565i
$957$	25.1465	+	43.5550i	0.812871	+	1.40793i
$958$	7.76147	−	13.4433i	0.250762	−	0.434332i
$959$	−2.38848	−	13.5458i	−0.0771282	−	0.437416i
$960$	1.13736	+	6.45031i	0.0367083	+	0.208183i
$961$	−5.25267	+	9.09789i	−0.169441	+	0.293480i
$962$	−0.605491	−	1.04874i	−0.0195218	−	0.0338128i
$963$	−36.9397	+	30.9961i	−1.19037	+	0.998835i
$964$	25.8967	−	9.42561i	0.834075	−	0.303579i
$965$	−16.3655	−	5.95655i	−0.526823	−	0.191748i
$966$	17.7981	+	14.9344i	0.572644	+	0.480506i
$967$	−8.49322	+	48.1674i	−0.273124	+	1.54896i	0.471736	+	0.881740i	$0.343627\pi$
$967$	−8.49322	+	48.1674i	−0.273124	+	1.54896i	−0.744860	+	0.667221i	$0.767484\pi$
$968$	−22.1340			−0.711414
$969$		0			0
$970$	−40.6835			−1.30627
$971$	−1.05507	+	5.98361i	−0.0338589	+	0.192023i	−0.997046	−	0.0768093i	$-0.975527\pi$
$971$	−1.05507	+	5.98361i	−0.0338589	+	0.192023i	0.963187	+	0.268833i	$0.0866378\pi$
$972$	12.2939	+	10.3158i	0.394329	+	0.330881i
$973$	−13.0490	−	4.74945i	−0.418332	−	0.152260i
$974$	26.8814	−	9.78401i	0.861334	−	0.313500i
$975$	0.323658	−	0.271581i	0.0103654	−	0.00869756i
$976$	5.48073	+	9.49290i	0.175434	+	0.303860i
$977$	28.5239	−	49.4048i	0.912559	−	1.58060i	0.102124	−	0.994772i	$-0.467436\pi$
$977$	28.5239	−	49.4048i	0.912559	−	1.58060i	0.810436	−	0.585828i	$-0.199230\pi$
$978$	6.91254	+	39.2030i	0.221039	+	1.25357i
$979$	15.0698	+	85.4653i	0.481634	+	2.73148i
$980$	−6.27308	+	10.8653i	−0.200386	+	0.347079i
$981$	−21.2430	−	36.7940i	−0.678238	−	1.17474i
$982$	23.2486	−	19.5079i	0.741891	−	0.622521i
$983$	0.175271	−	0.0637934i	0.00559028	−	0.00203469i	−0.339223	−	0.940706i	$-0.610164\pi$
$983$	0.175271	−	0.0637934i	0.00559028	−	0.00203469i	0.344814	+	0.938671i	$0.387942\pi$
$984$	−13.1708	−	4.79377i	−0.419869	−	0.152820i
$985$	−15.3303	−	12.8636i	−0.488462	−	0.409869i
$986$	−2.27350	+	12.8937i	−0.0724030	+	0.410618i
$987$	−15.7638			−0.501768
$988$		0			0
$989$	6.40804			0.203764
$990$	11.2589	−	63.8523i	0.357831	−	2.02936i
$991$	35.4218	+	29.7224i	1.12521	+	0.944163i	0.998856	−	0.0478224i	$-0.0152282\pi$
$991$	35.4218	+	29.7224i	1.12521	+	0.944163i	0.126354	+	0.991985i	$0.459673\pi$
$992$	−6.05394	−	2.20345i	−0.192213	−	0.0699597i
$993$	−13.6849	+	4.98089i	−0.434276	+	0.158064i
$994$	4.34355	−	3.64467i	0.137769	−	0.115602i
$995$	−7.45488	−	12.9122i	−0.236336	−	0.409345i
$996$	−13.6393	+	23.6239i	−0.432177	+	0.748553i
$997$	−3.62039	−	20.5323i	−0.114659	−	0.650263i	−0.986918	−	0.161220i	$-0.948457\pi$
$997$	−3.62039	−	20.5323i	−0.114659	−	0.650263i	0.872260	−	0.489043i	$-0.162654\pi$
$998$	−1.52398	−	8.64291i	−0.0482407	−	0.273586i
$999$	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.s.245.1		24
19.2	odd	18		722.2.c.m.429.1		8
19.3	odd	18		722.2.a.n.1.4	yes	4
19.4	even	9	inner	722.2.e.s.595.4		24
19.5	even	9		722.2.c.n.653.4		8
19.6	even	9	inner	722.2.e.s.99.1		24
19.7	even	3	inner	722.2.e.s.415.4		24
19.8	odd	6		722.2.e.r.423.4		24
19.9	even	9	inner	722.2.e.s.389.1		24
19.10	odd	18		722.2.e.r.389.4		24
19.11	even	3	inner	722.2.e.s.423.1		24
19.12	odd	6		722.2.e.r.415.1		24
19.13	odd	18		722.2.e.r.99.4		24
19.14	odd	18		722.2.c.m.653.1		8
19.15	odd	18		722.2.e.r.595.1		24
19.16	even	9		722.2.a.m.1.1	✓	4
19.17	even	9		722.2.c.n.429.4		8
19.18	odd	2		722.2.e.r.245.4		24
57.35	odd	18		6498.2.a.ca.1.3		4
57.41	even	18		6498.2.a.bx.1.3		4
76.3	even	18		5776.2.a.bt.1.1		4
76.35	odd	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	19.16	even	9
722.2.a.n.1.4	yes	4	19.3	odd	18
722.2.c.m.429.1		8	19.2	odd	18
722.2.c.m.653.1		8	19.14	odd	18
722.2.c.n.429.4		8	19.17	even	9
722.2.c.n.653.4		8	19.5	even	9
722.2.e.r.99.4		24	19.13	odd	18
722.2.e.r.245.4		24	19.18	odd	2
722.2.e.r.389.4		24	19.10	odd	18
722.2.e.r.415.1		24	19.12	odd	6
722.2.e.r.423.4		24	19.8	odd	6
722.2.e.r.595.1		24	19.15	odd	18
722.2.e.s.99.1		24	19.6	even	9	inner
722.2.e.s.245.1		24	1.1	even	1	trivial
722.2.e.s.389.1		24	19.9	even	9	inner
722.2.e.s.415.4		24	19.7	even	3	inner
722.2.e.s.423.1		24	19.11	even	3	inner
722.2.e.s.595.4		24	19.4	even	9	inner
5776.2.a.bt.1.1		4	76.3	even	18
5776.2.a.bv.1.4		4	76.35	odd	18
6498.2.a.bx.1.3		4	57.41	even	18
6498.2.a.ca.1.3		4	57.35	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-2.14003 - 1.79569i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20318 - 0.801892i) q^{5} +(2.14003 - 1.79569i) q^{6} +(0.642040 + 1.11205i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.834245 + 4.73124i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-2.14003 - 1.79569i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20318 - 0.801892i) q^{5} +(2.14003 - 1.79569i) q^{6} +(0.642040 + 1.11205i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.834245 + 4.73124i) q^{9} +(0.407131 + 2.30896i) q^{10} +(-2.87811 + 4.98503i) q^{11} +(1.39680 + 2.41933i) q^{12} +(-0.233094 + 0.195589i) q^{13} +(-1.20664 + 0.439181i) q^{14} +(-6.15482 - 2.24017i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.726925 - 4.12259i) q^{17} -4.80423 q^{18} -2.34458 q^{20} +(0.622912 - 3.53271i) q^{21} +(-4.40952 - 3.70002i) q^{22} +(6.08623 + 2.21521i) q^{23} +(-2.62513 + 0.955469i) q^{24} +(0.380754 - 0.319491i) q^{25} +(-0.152141 - 0.263516i) q^{26} +(2.52015 - 4.36502i) q^{27} +(-0.222978 - 1.26457i) q^{28} +(0.543095 + 3.08004i) q^{29} +(3.27491 - 5.67231i) q^{30} +(3.22123 + 5.57934i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(15.1108 - 5.49989i) q^{33} +(3.93373 + 1.43176i) q^{34} +(2.30627 + 1.93519i) q^{35} +(0.834245 - 4.73124i) q^{36} +3.97980 q^{37} +0.850045 q^{39} +(0.407131 - 2.30896i) q^{40} +(3.84339 + 3.22499i) q^{41} +(3.37087 + 1.22690i) q^{42} +(0.929712 - 0.338387i) q^{43} +(4.40952 - 3.70002i) q^{44} +(5.63194 + 9.75480i) q^{45} +(-3.23842 + 5.60910i) q^{46} +(-0.763089 - 4.32769i) q^{47} +(-0.485104 - 2.75116i) q^{48} +(2.67557 - 4.63422i) q^{49} +(0.248520 + 0.430448i) q^{50} +(-8.95856 + 7.51712i) q^{51} +(0.285932 - 0.104071i) q^{52} +(3.09219 + 1.12547i) q^{53} +(3.86109 + 3.23984i) q^{54} +(-2.34354 + 13.2909i) q^{55} +1.28408 q^{56} -3.12756 q^{58} +(-0.575427 + 3.26341i) q^{59} +(5.01745 + 4.21014i) q^{60} +(10.3004 + 3.74904i) q^{61} +(-6.05394 + 2.20345i) q^{62} +(-4.72573 + 3.96536i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.356707 + 0.617834i) q^{65} +(2.79236 + 15.8363i) q^{66} +(0.760720 + 4.31426i) q^{67} +(-2.09310 + 3.62535i) q^{68} +(-9.04686 - 15.6696i) q^{69} +(-2.30627 + 1.93519i) q^{70} +(-4.14940 + 1.51026i) q^{71} +(4.51450 + 1.64314i) q^{72} +(-1.73654 - 1.45713i) q^{73} +(-0.691084 + 3.91933i) q^{74} -1.38853 q^{75} -7.39144 q^{77} +(-0.147609 + 0.837131i) q^{78} +(-6.57005 - 5.51292i) q^{79} +(2.20318 + 0.801892i) q^{80} +(0.312063 - 0.113582i) q^{81} +(-3.84339 + 3.22499i) q^{82} +(4.88232 + 8.45643i) q^{83} +(-1.79360 + 3.10661i) q^{84} +(-1.70433 - 9.66574i) q^{85} +(0.171804 + 0.974348i) q^{86} +(4.36858 - 7.56661i) q^{87} +(2.87811 + 4.98503i) q^{88} +(11.5493 - 9.69101i) q^{89} +(-10.5846 + 3.85247i) q^{90} +(-0.367159 - 0.133635i) q^{91} +(-4.96154 - 4.16323i) q^{92} +(3.12527 - 17.7243i) q^{93} +4.39445 q^{94} +2.79360 q^{96} +(-3.01317 + 17.0886i) q^{97} +(4.09921 + 3.43965i) q^{98} +(-25.9864 - 9.45828i) 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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