LMFDB - Embedded newform 841.2.d.m.645.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			645.1
Character	$\chi$	$=$	841.645
Dual form			841.2.d.m.605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.504621 - 2.21089i) q^{2} +(-2.55926 - 1.23248i) q^{3} +(-2.83146 + 1.36356i) q^{4} +(-0.0128801 - 0.0564316i) q^{5} +(-1.43341 + 6.28018i) q^{6} +(1.40728 + 0.677709i) q^{7} +(1.61565 + 2.02596i) q^{8} +(3.16036 + 3.96297i) q^{9} +(-0.118264 + 0.0569531i) q^{10} +(-2.47705 + 3.10613i) q^{11} +8.92699 q^{12} +(0.252504 - 0.316631i) q^{13} +(0.788198 - 3.45332i) q^{14} +(-0.0365869 + 0.160298i) q^{15} +(-0.254963 + 0.319714i) q^{16} +5.16843 q^{17} +(7.16690 - 8.98701i) q^{18} +(3.10914 - 1.49728i) q^{19} +(0.113417 + 0.142221i) q^{20} +(-2.76633 - 3.46887i) q^{21} +(8.11728 + 3.90908i) q^{22} +(-0.0512209 + 0.224414i) q^{23} +(-1.63793 - 7.17623i) q^{24} +(4.50183 - 2.16797i) q^{25} +(-0.827455 - 0.398481i) q^{26} +(-1.30768 - 5.72931i) q^{27} -4.90874 q^{28} +0.372863 q^{30} +(-0.960917 - 4.21005i) q^{31} +(5.50488 + 2.65101i) q^{32} +(10.1677 - 4.89649i) q^{33} +(-2.60810 - 11.4268i) q^{34} +(0.0201183 - 0.0881438i) q^{35} +(-14.3522 - 6.91164i) q^{36} +(3.34857 + 4.19898i) q^{37} +(-4.87927 - 6.11841i) q^{38} +(-1.03647 + 0.499135i) q^{39} +(0.0935185 - 0.117269i) q^{40} -1.46294 q^{41} +(-6.27335 + 7.86653i) q^{42} +(-1.44264 + 6.32061i) q^{43} +(2.77829 - 12.1725i) q^{44} +(0.182931 - 0.229388i) q^{45} +0.522001 q^{46} +(-5.96928 + 7.48524i) q^{47} +(1.04656 - 0.503996i) q^{48} +(-2.84329 - 3.56537i) q^{49} +(-7.06485 - 8.85904i) q^{50} +(-13.2274 - 6.36997i) q^{51} +(-0.283211 + 1.24083i) q^{52} +(0.398044 + 1.74395i) q^{53} +(-12.0070 + 5.78226i) q^{54} +(0.207188 + 0.0997767i) q^{55} +(0.900657 + 3.94604i) q^{56} -9.80247 q^{57} -1.05216 q^{59} +(-0.114981 - 0.503764i) q^{60} +(2.87352 + 1.38382i) q^{61} +(-8.82307 + 4.24897i) q^{62} +(1.76177 + 7.71880i) q^{63} +(2.90123 - 12.7111i) q^{64} +(-0.0211203 - 0.0101710i) q^{65} +(-15.9564 - 20.0087i) q^{66} +(6.77893 + 8.50052i) q^{67} +(-14.6342 + 7.04745i) q^{68} +(0.407672 - 0.511205i) q^{69} -0.205028 q^{70} +(8.38773 - 10.5179i) q^{71} +(-2.92279 + 12.8056i) q^{72} +(1.56113 - 6.83974i) q^{73} +(7.59372 - 9.52223i) q^{74} -14.1933 q^{75} +(-6.76176 + 8.47898i) q^{76} +(-5.59095 + 2.69246i) q^{77} +(1.62656 + 2.03964i) q^{78} +(2.98318 + 3.74078i) q^{79} +(0.0213259 + 0.0102700i) q^{80} +(-0.330785 + 1.44926i) q^{81} +(0.738232 + 3.23440i) q^{82} +(-7.58927 + 3.65480i) q^{83} +(12.5628 + 6.04990i) q^{84} +(-0.0665701 - 0.291662i) q^{85} +14.7022 q^{86} -10.2950 q^{88} +(0.252043 + 1.10427i) q^{89} +(-0.599462 - 0.288686i) q^{90} +(0.569927 - 0.274462i) q^{91} +(-0.160971 - 0.705260i) q^{92} +(-2.72955 + 11.9589i) q^{93} +(19.5613 + 9.42022i) q^{94} +(-0.124540 - 0.156168i) q^{95} +(-10.8211 - 13.5693i) q^{96} +(15.5085 - 7.46850i) q^{97} +(-6.44786 + 8.08536i) q^{98} -20.1379 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} + 2 q^{5} + 6 q^{6} - 22 q^{7} + 6 q^{9} - 18 q^{13} + 18 q^{16} - 22 q^{20} + 8 q^{22} - 10 q^{23} - 50 q^{24} + 26 q^{25} - 24 q^{28} + 4 q^{30} + 34 q^{33} + 26 q^{34} - 38 q^{35} - 80 q^{36}+ \cdots - 60 q^{96}+O(q^{100}) $ 24 * q + 2 * q^4 + 2 * q^5 + 6 * q^6 - 22 * q^7 + 6 * q^9 - 18 * q^13 + 18 * q^16 - 22 * q^20 + 8 * q^22 - 10 * q^23 - 50 * q^24 + 26 * q^25 - 24 * q^28 + 4 * q^30 + 34 * q^33 + 26 * q^34 - 38 * q^35 - 80 * q^36 - 56 * q^38 - 100 * q^42 + 32 * q^45 + 26 * q^49 - 40 * q^51 - 12 * q^52 - 20 * q^53 - 76 * q^54 + 28 * q^57 + 88 * q^59 - 74 * q^62 + 26 * q^63 + 52 * q^64 - 12 * q^65 + 74 * q^67 + 42 * q^71 + 34 * q^78 + 12 * q^80 + 2 * q^81 + 44 * q^82 + 10 * q^83 + 88 * q^86 - 132 * q^88 + 6 * q^91 + 12 * q^92 - 38 * q^93 + 132 * q^94 - 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

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 $

$2$	−0.504621	−	2.21089i	−0.356821	−	1.56334i	−0.761060	−	0.648682i	$-0.775321\pi$
$2$	−0.504621	−	2.21089i	−0.356821	−	1.56334i	0.404239	−	0.914654i	$-0.367537\pi$
$3$	−2.55926	−	1.23248i	−1.47759	−	0.711571i	−0.490457	−	0.871465i	$-0.663170\pi$
$3$	−2.55926	−	1.23248i	−1.47759	−	0.711571i	−0.987134	+	0.159895i	$0.948885\pi$
$4$	−2.83146	+	1.36356i	−1.41573	+	0.681779i
$5$	−0.0128801	−	0.0564316i	−0.00576017	−	0.0252370i	0.971966	−	0.235121i	$-0.0755486\pi$
$5$	−0.0128801	−	0.0564316i	−0.00576017	−	0.0252370i	−0.977726	+	0.209884i	$0.932691\pi$
$6$	−1.43341	+	6.28018i	−0.585188	+	2.56387i
$7$	1.40728	+	0.677709i	0.531901	+	0.256150i	0.680501	−	0.732747i	$-0.261762\pi$
$7$	1.40728	+	0.677709i	0.531901	+	0.256150i	−0.148600	+	0.988897i	$0.547477\pi$
$8$	1.61565	+	2.02596i	0.571220	+	0.716287i
$9$	3.16036	+	3.96297i	1.05345	+	1.32099i
$10$	−0.118264	+	0.0569531i	−0.0373985	+	0.0180102i
$11$	−2.47705	+	3.10613i	−0.746860	+	0.936533i	−0.999519	−	0.0310229i	$-0.990124\pi$
$11$	−2.47705	+	3.10613i	−0.746860	+	0.936533i	0.252659	+	0.967555i	$0.418695\pi$
$12$	8.92699			2.57700
$13$	0.252504	−	0.316631i	0.0700321	−	0.0878175i	−0.745581	−	0.666415i	$-0.767828\pi$
$13$	0.252504	−	0.316631i	0.0700321	−	0.0878175i	0.815614	+	0.578597i	$0.196400\pi$
$14$	0.788198	−	3.45332i	0.210655	−	0.922939i
$15$	−0.0365869	+	0.160298i	−0.00944670	+	0.0413887i
$16$	−0.254963	+	0.319714i	−0.0637408	+	0.0799285i
$17$	5.16843			1.25353			0.626764	−	0.779209i	$-0.284379\pi$
$17$	5.16843			1.25353			0.626764	+	0.779209i	$0.284379\pi$
$18$	7.16690	−	8.98701i	1.68926	−	2.11826i
$19$	3.10914	−	1.49728i	0.713286	−	0.343500i	−0.0418005	−	0.999126i	$-0.513309\pi$
$19$	3.10914	−	1.49728i	0.713286	−	0.343500i	0.755086	+	0.655626i	$0.227595\pi$
$20$	0.113417	+	0.142221i	0.0253609	+	0.0318015i
$21$	−2.76633	−	3.46887i	−0.603663	−	0.756970i
$22$	8.11728	+	3.90908i	1.73061	+	0.833418i
$23$	−0.0512209	+	0.224414i	−0.0106803	+	0.0467935i	−0.979987	−	0.199060i	$-0.936211\pi$
$23$	−0.0512209	+	0.224414i	−0.0106803	+	0.0467935i	0.969307	+	0.245854i	$0.0790682\pi$
$24$	−1.63793	−	7.17623i	−0.334341	−	1.46484i
$25$	4.50183	−	2.16797i	0.900365	−	0.433593i
$26$	−0.827455	−	0.398481i	−0.162277	−	0.0781486i
$27$	−1.30768	−	5.72931i	−0.251663	−	1.10261i
$28$	−4.90874			−0.927664
$29$		0			0
$29$		0			0
$30$	0.372863			0.0680752
$31$	−0.960917	−	4.21005i	−0.172586	−	0.756148i	−0.984928	−	0.172967i	$-0.944665\pi$
$31$	−0.960917	−	4.21005i	−0.172586	−	0.756148i	0.812342	−	0.583182i	$-0.198192\pi$
$32$	5.50488	+	2.65101i	0.973135	+	0.468637i
$33$	10.1677	−	4.89649i	1.76996	−	0.852369i
$34$	−2.60810	−	11.4268i	−0.447285	−	1.95968i
$35$	0.0201183	−	0.0881438i	0.00340061	−	0.0148990i
$36$	−14.3522	−	6.91164i	−2.39203	−	1.15194i
$37$	3.34857	+	4.19898i	0.550502	+	0.690308i	0.976770	−	0.214289i	$-0.0687434\pi$
$37$	3.34857	+	4.19898i	0.550502	+	0.690308i	−0.426268	+	0.904597i	$0.640172\pi$
$38$	−4.87927	−	6.11841i	−0.791521	−	0.992536i
$39$	−1.03647	+	0.499135i	−0.165967	+	0.0799256i
$40$	0.0935185	−	0.117269i	0.0147866	−	0.0185418i
$41$	−1.46294			−0.228473			−0.114237	−	0.993454i	$-0.536442\pi$
$41$	−1.46294			−0.228473			−0.114237	+	0.993454i	$0.536442\pi$
$42$	−6.27335	+	7.86653i	−0.967998	+	1.21383i
$43$	−1.44264	+	6.32061i	−0.220000	+	0.963884i	0.737476	+	0.675373i	$0.236017\pi$
$43$	−1.44264	+	6.32061i	−0.220000	+	0.963884i	−0.957477	+	0.288511i	$0.906840\pi$
$44$	2.77829	−	12.1725i	0.418842	−	1.83507i
$45$	0.182931	−	0.229388i	0.0272697	−	0.0341951i
$46$	0.522001			0.0769648
$47$	−5.96928	+	7.48524i	−0.870709	+	1.09184i	0.124319	+	0.992242i	$0.460325\pi$
$47$	−5.96928	+	7.48524i	−0.870709	+	1.09184i	−0.995028	+	0.0995928i	$0.968246\pi$
$48$	1.04656	−	0.503996i	0.151058	−	0.0727455i
$49$	−2.84329	−	3.56537i	−0.406184	−	0.509339i
$50$	−7.06485	−	8.85904i	−0.999121	−	1.25286i
$51$	−13.2274	−	6.36997i	−1.85220	−	0.891974i
$52$	−0.283211	+	1.24083i	−0.0392743	+	0.172072i
$53$	0.398044	+	1.74395i	0.0546756	+	0.239549i	0.994880	−	0.101061i	$-0.0322236\pi$
$53$	0.398044	+	1.74395i	0.0546756	+	0.239549i	−0.940205	+	0.340610i	$0.889366\pi$
$54$	−12.0070	+	5.78226i	−1.63394	+	0.786866i
$55$	0.207188	+	0.0997767i	0.0279373	+	0.0134539i
$56$	0.900657	+	3.94604i	0.120355	+	0.527311i
$57$	−9.80247			−1.29837
$58$		0			0
$59$	−1.05216			−0.136980			−0.0684900	−	0.997652i	$-0.521818\pi$
$59$	−1.05216			−0.136980			−0.0684900	+	0.997652i	$0.521818\pi$
$60$	−0.114981	−	0.503764i	−0.0148440	−	0.0650357i
$61$	2.87352	+	1.38382i	0.367917	+	0.177179i	0.608702	−	0.793399i	$-0.291691\pi$
$61$	2.87352	+	1.38382i	0.367917	+	0.177179i	−0.240785	+	0.970578i	$0.577405\pi$
$62$	−8.82307	+	4.24897i	−1.12053	+	0.539619i
$63$	1.76177	+	7.71880i	0.221962	+	0.972478i
$64$	2.90123	−	12.7111i	0.362653	−	1.58889i
$65$	−0.0211203	−	0.0101710i	−0.00261964	−	0.00126155i
$66$	−15.9564	−	20.0087i	−1.96410	−	2.46290i
$67$	6.77893	+	8.50052i	0.828179	+	1.03850i	0.998588	+	0.0531298i	$0.0169197\pi$
$67$	6.77893	+	8.50052i	0.828179	+	1.03850i	−0.170409	+	0.985373i	$0.554509\pi$
$68$	−14.6342	+	7.04745i	−1.77465	+	0.854628i
$69$	0.407672	−	0.511205i	0.0490780	−	0.0615418i
$70$	−0.205028			−0.0245056
$71$	8.38773	−	10.5179i	0.995440	−	1.24824i	0.0268346	−	0.999640i	$-0.491457\pi$
$71$	8.38773	−	10.5179i	0.995440	−	1.24824i	0.968606	−	0.248603i	$-0.0799713\pi$
$72$	−2.92279	+	12.8056i	−0.344454	+	1.50915i
$73$	1.56113	−	6.83974i	0.182716	−	0.800531i	−0.797615	−	0.603167i	$-0.793905\pi$
$73$	1.56113	−	6.83974i	0.182716	−	0.800531i	0.980330	−	0.197363i	$-0.0632378\pi$
$74$	7.59372	−	9.52223i	0.882752	−	1.10694i
$75$	−14.1933			−1.63890
$76$	−6.76176	+	8.47898i	−0.775627	+	0.972605i
$77$	−5.59095	+	2.69246i	−0.637148	+	0.306834i
$78$	1.62656	+	2.03964i	0.184171	+	0.230943i
$79$	2.98318	+	3.74078i	0.335634	+	0.420871i	0.920796	−	0.390045i	$-0.127541\pi$
$79$	2.98318	+	3.74078i	0.335634	+	0.420871i	−0.585162	+	0.810916i	$0.698969\pi$
$80$	0.0213259	+	0.0102700i	0.00238431	+	0.00114822i
$81$	−0.330785	+	1.44926i	−0.0367539	+	0.161029i
$82$	0.738232	+	3.23440i	0.0815241	+	0.357180i
$83$	−7.58927	+	3.65480i	−0.833030	+	0.401166i	−0.801251	−	0.598329i	$-0.795832\pi$
$83$	−7.58927	+	3.65480i	−0.833030	+	0.401166i	−0.0317796	+	0.999495i	$0.510117\pi$
$84$	12.5628	+	6.04990i	1.37071	+	0.660099i
$85$	−0.0665701	−	0.291662i	−0.00722054	−	0.0316352i
$86$	14.7022			1.58537
$87$		0			0
$88$	−10.2950			−1.09745
$89$	0.252043	+	1.10427i	0.0267165	+	0.117053i	0.986528	−	0.163593i	$-0.0523085\pi$
$89$	0.252043	+	1.10427i	0.0267165	+	0.117053i	−0.959811	+	0.280646i	$0.909451\pi$
$90$	−0.599462	−	0.288686i	−0.0631888	−	0.0304301i
$91$	0.569927	−	0.274462i	0.0597446	−	0.0287715i
$92$	−0.160971	−	0.705260i	−0.0167824	−	0.0735284i
$93$	−2.72955	+	11.9589i	−0.283041	+	1.24009i
$94$	19.5613	+	9.42022i	2.01759	+	0.971621i
$95$	−0.124540	−	0.156168i	−0.0127775	−	0.0160225i
$96$	−10.8211	−	13.5693i	−1.10443	−	1.38491i
$97$	15.5085	−	7.46850i	1.57465	−	0.758311i	0.576383	−	0.817180i	$-0.304464\pi$
$97$	15.5085	−	7.46850i	1.57465	−	0.758311i	0.998266	+	0.0588689i	$0.0187494\pi$
$98$	−6.44786	+	8.08536i	−0.651332	+	0.816745i
$99$	−20.1379			−2.02393
$100$	−9.79057	+	12.2770i	−0.979057	+	1.22770i
$101$	1.38844	−	6.08315i	0.138155	−	0.605296i	−0.857685	−	0.514175i	$-0.828098\pi$
$101$	1.38844	−	6.08315i	0.138155	−	0.605296i	0.995840	−	0.0911203i	$-0.0290448\pi$
$102$	−7.40848	+	32.4587i	−0.733549	+	3.21389i
$103$	8.23659	−	10.3284i	0.811576	−	1.01768i	−0.187795	−	0.982208i	$-0.560134\pi$
$103$	8.23659	−	10.3284i	0.811576	−	1.01768i	0.999371	−	0.0354755i	$-0.0112946\pi$
$104$	1.04944			0.102906
$105$	−0.160123	+	0.200788i	−0.0156264	+	0.0195949i
$106$	3.65481	−	1.76006i	0.354987	−	0.170953i
$107$	5.77864	+	7.24619i	0.558642	+	0.700516i	0.978306	−	0.207164i	$-0.0664234\pi$
$107$	5.77864	+	7.24619i	0.558642	+	0.700516i	−0.419664	+	0.907680i	$0.637852\pi$
$108$	11.5149	+	14.4392i	1.10802	+	1.38941i
$109$	5.18545	+	2.49718i	0.496676	+	0.239187i	0.665414	−	0.746474i	$-0.268255\pi$
$109$	5.18545	+	2.49718i	0.496676	+	0.239187i	−0.168738	+	0.985661i	$0.553969\pi$
$110$	0.116044	−	0.508420i	0.0110643	−	0.0484760i
$111$	−3.39474	−	14.8733i	−0.322215	−	1.41171i
$112$	−0.575477	+	0.277135i	−0.0543775	+	0.0261868i
$113$	−7.26385	−	3.49809i	−0.683326	−	0.329072i	0.0598131	−	0.998210i	$-0.480950\pi$
$113$	−7.26385	−	3.49809i	−0.683326	−	0.329072i	−0.743139	+	0.669137i	$0.766664\pi$
$114$	4.94654	+	21.6722i	0.463286	+	2.02979i
$115$	0.0133237			0.00124245
$116$		0			0
$117$	2.05280			0.189782
$118$	0.530944	+	2.32622i	0.0488774	+	0.214146i
$119$	7.27341	+	3.50269i	0.666753	+	0.321091i
$120$	−0.383869	+	0.184862i	−0.0350423	+	0.0168755i
$121$	−1.06450	−	4.66388i	−0.0967727	−	0.423989i
$122$	1.60942	−	7.05135i	0.145710	−	0.638399i
$123$	3.74405	+	1.80304i	0.337590	+	0.162575i
$124$	8.46144	+	10.6103i	0.759860	+	0.952834i
$125$	−0.360772	−	0.452394i	−0.0322685	−	0.0404634i
$126$	16.1764	−	7.79014i	1.44111	−	0.694001i
$127$	10.9570	−	13.7396i	0.972277	−	1.21920i	−0.00340252	−	0.999994i	$-0.501083\pi$
$127$	10.9570	−	13.7396i	0.972277	−	1.21920i	0.975679	−	0.219202i	$-0.0703455\pi$
$128$	−17.3469			−1.53327
$129$	11.4821	−	14.3981i	1.01094	−	1.26768i
$130$	−0.0118292	+	0.0518270i	−0.00103749	+	0.00454553i
$131$	−0.744983	+	3.26398i	−0.0650895	+	0.285176i	−0.996989	−	0.0775403i	$-0.975293\pi$
$131$	−0.744983	+	3.26398i	−0.0650895	+	0.285176i	0.931900	+	0.362716i	$0.118150\pi$
$132$	−22.1126	+	27.7284i	−1.92466	+	2.41345i
$133$	5.39014			0.467385
$134$	15.3729	−	19.2770i	1.32802	−	1.66528i
$135$	−0.306471	+	0.147589i	−0.0263768	+	0.0127024i
$136$	8.35039	+	10.4711i	0.716040	+	0.897885i
$137$	−3.44204	−	4.31618i	−0.294073	−	0.368756i	0.612743	−	0.790282i	$-0.290066\pi$
$137$	−3.44204	−	4.31618i	−0.294073	−	0.368756i	−0.906816	+	0.421526i	$0.861495\pi$
$138$	−1.33594	−	0.643354i	−0.113723	−	0.0547659i
$139$	0.132958	−	0.582528i	0.0112774	−	0.0494094i	−0.968976	−	0.247154i	$-0.920505\pi$
$139$	0.132958	−	0.582528i	0.0112774	−	0.0494094i	0.980254	+	0.197745i	$0.0633617\pi$
$140$	0.0632252	+	0.277008i	0.00534351	+	0.0234114i
$141$	24.5024	−	11.7997i	2.06347	−	0.993715i
$142$	−27.4865	−	13.2368i	−2.30662	−	1.11081i
$143$	0.358028	+	1.56862i	0.0299398	+	0.131175i
$144$	−2.07279			−0.172733
$145$		0			0
$146$	−15.9097			−1.31669
$147$	2.88249	+	12.6290i	0.237744	+	1.04162i
$148$	−15.2069	−	7.32325i	−1.25000	−	0.601968i
$149$	−4.60312	+	2.21675i	−0.377102	+	0.181603i	−0.612827	−	0.790217i	$-0.709968\pi$
$149$	−4.60312	+	2.21675i	−0.377102	+	0.181603i	0.235725	+	0.971820i	$0.424254\pi$
$150$	7.16225	+	31.3799i	0.584796	+	2.56216i
$151$	1.73572	−	7.60469i	0.141251	−	0.618861i	−0.853894	−	0.520446i	$-0.825766\pi$
$151$	1.73572	−	7.60469i	0.141251	−	0.618861i	0.995145	−	0.0984149i	$-0.0313772\pi$
$152$	8.05673	+	3.87992i	0.653487	+	0.314703i
$153$	16.3341	+	20.4823i	1.32053	+	1.65590i
$154$	8.77405	+	11.0023i	0.707033	+	0.886591i
$155$	−0.225203	+	0.108452i	−0.0180888	+	0.00871109i
$156$	2.25411	−	2.82656i	0.180473	−	0.226306i
$157$	18.8577			1.50501			0.752504	−	0.658588i	$-0.228846\pi$
$157$	18.8577			1.50501			0.752504	+	0.658588i	$0.228846\pi$
$158$	6.76509	−	8.48315i	0.538202	−	0.674884i
$159$	1.13067	−	4.95380i	0.0896681	−	0.392862i
$160$	0.0786971	−	0.344795i	0.00622155	−	0.0272584i
$161$	−0.224169	+	0.281099i	−0.0176670	+	0.0221537i
$162$	3.37109			0.264858
$163$	−1.41033	+	1.76850i	−0.110466	+	0.138520i	−0.833991	−	0.551779i	$-0.813949\pi$
$163$	−1.41033	+	1.76850i	−0.110466	+	0.138520i	0.723525	+	0.690298i	$0.242521\pi$
$164$	4.14226	−	1.99481i	0.323456	−	0.155768i
$165$	−0.407277	−	0.510710i	−0.0317065	−	0.0397587i
$166$	11.9101	+	14.9347i	0.924400	+	1.15916i
$167$	−10.5728	−	5.09159i	−0.818147	−	0.393999i	−0.0224905	−	0.999747i	$-0.507160\pi$
$167$	−10.5728	−	5.09159i	−0.818147	−	0.393999i	−0.795656	+	0.605748i	$0.792874\pi$
$168$	2.55838	−	11.2090i	0.197383	−	0.864792i
$169$	2.85628	+	12.5142i	0.219714	+	0.962628i
$170$	−0.611241	+	0.294358i	−0.0468801	+	0.0225762i
$171$	15.7597	+	7.58947i	1.20517	+	0.580381i
$172$	−4.53375	−	19.8636i	−0.345695	−	1.51459i
$173$	19.2889			1.46651			0.733254	−	0.679954i	$-0.238000\pi$
$173$	19.2889			1.46651			0.733254	+	0.679954i	$0.238000\pi$
$174$		0			0
$175$	7.80457			0.589970
$176$	−0.361514	−	1.58390i	−0.0272501	−	0.119391i
$177$	2.69276	+	1.29677i	0.202401	+	0.0974710i
$178$	2.31424	−	1.11448i	0.173460	−	0.0835337i
$179$	−0.202580	−	0.887562i	−0.0151416	−	0.0663395i	0.966793	−	0.255562i	$-0.0822604\pi$
$179$	−0.202580	−	0.887562i	−0.0151416	−	0.0663395i	−0.981934	+	0.189222i	$0.939403\pi$
$180$	−0.205177	+	0.898938i	−0.0152930	+	0.0670029i
$181$	−4.74107	−	2.28318i	−0.352401	−	0.169707i	0.249305	−	0.968425i	$-0.419798\pi$
$181$	−4.74107	−	2.28318i	−0.352401	−	0.169707i	−0.601706	+	0.798718i	$0.705512\pi$
$182$	−0.894404	−	1.12155i	−0.0662976	−	0.0831346i
$183$	−5.64858	−	7.08310i	−0.417555	−	0.523598i
$184$	−0.537409	+	0.258803i	−0.0396183	+	0.0190792i
$185$	0.193825	−	0.243049i	0.0142503	−	0.0178693i
$186$	27.8173			2.03966
$187$	−12.8025	+	16.0538i	−0.936210	+	1.17397i
$188$	6.69520	−	29.3336i	0.488298	−	2.13937i
$189$	2.04254	−	8.94895i	0.148573	−	0.650940i
$190$	−0.282426	+	0.354150i	−0.0204893	+	0.0256928i
$191$	−10.3088			−0.745920			−0.372960	−	0.927847i	$-0.621657\pi$
$191$	−10.3088			−0.745920			−0.372960	+	0.927847i	$0.621657\pi$
$192$	−23.0911	+	28.9554i	−1.66646	+	2.08967i
$193$	2.44160	−	1.17581i	0.175750	−	0.0846368i	−0.343940	−	0.938992i	$-0.611762\pi$
$193$	2.44160	−	1.17581i	0.175750	−	0.0846368i	0.519690	+	0.854355i	$0.326047\pi$
$194$	−24.3379	−	30.5188i	−1.74736	−	2.19112i
$195$	0.0415168	+	0.0520604i	0.00297308	+	0.00372812i
$196$	12.9122	+	6.21820i	0.922302	+	0.444157i
$197$	3.28855	−	14.4081i	0.234300	−	1.02653i	−0.711730	−	0.702453i	$-0.752088\pi$
$197$	3.28855	−	14.4081i	0.234300	−	1.02653i	0.946030	−	0.324080i	$-0.105055\pi$
$198$	10.1620	+	44.5226i	0.722182	+	3.16409i
$199$	−13.5173	+	6.50959i	−0.958216	+	0.461453i	−0.846560	−	0.532294i	$-0.821330\pi$
$199$	−13.5173	+	6.50959i	−0.958216	+	0.461453i	−0.111657	+	0.993747i	$0.535616\pi$
$200$	11.6656	+	5.61786i	0.824883	+	0.397243i
$201$	−6.87240	−	30.1099i	−0.484741	−	2.12379i
$202$	−14.1498			−0.995577
$203$		0			0
$204$	46.1385			3.23034
$205$	0.0188429	+	0.0825561i	0.00131604	+	0.00576597i
$206$	−26.9912	−	12.9983i	−1.88057	−	0.905634i
$207$	−1.05122	+	0.506241i	−0.0730649	+	0.0351862i
$208$	0.0368518	+	0.161458i	0.00255521	+	0.0111951i
$209$	−3.05076	+	13.3662i	−0.211025	+	0.924562i
$210$	0.524722	+	0.252693i	0.0362093	+	0.0174375i
$211$	−7.46505	−	9.36088i	−0.513916	−	0.644430i	0.455389	−	0.890293i	$-0.349500\pi$
$211$	−7.46505	−	9.36088i	−0.513916	−	0.644430i	−0.969305	+	0.245863i	$0.920929\pi$
$212$	−3.50501	−	4.39515i	−0.240725	−	0.301860i
$213$	−34.4294	+	16.5803i	−2.35907	+	1.13607i
$214$	13.1045	−	16.4325i	0.895805	−	1.12330i
$215$	0.375263			0.0255927
$216$	9.49462	−	11.9059i	0.646027	−	0.810093i
$217$	1.50091	−	6.57594i	0.101889	−	0.446404i
$218$	2.90430	−	12.7246i	0.196704	−	0.861818i
$219$	−12.4251	+	15.5806i	−0.839613	+	1.05284i
$220$	−0.722696			−0.0487241
$221$	1.30505	−	1.63648i	0.0877872	−	0.110082i
$222$	−31.1703	+	15.0108i	−2.09201	+	1.00746i
$223$	8.33685	+	10.4541i	0.558277	+	0.700057i	0.978238	−	0.207485i	$-0.0665279\pi$
$223$	8.33685	+	10.4541i	0.558277	+	0.700057i	−0.419962	+	0.907542i	$0.637956\pi$
$224$	5.95028	+	7.46142i	0.397570	+	0.498537i
$225$	22.8190	+	10.9890i	1.52127	+	0.732603i
$226$	−4.06839	+	17.8248i	−0.270625	+	1.18569i
$227$	0.472258	+	2.06910i	0.0313448	+	0.137331i	0.988179	−	0.153303i	$-0.0489910\pi$
$227$	0.472258	+	2.06910i	0.0313448	+	0.137331i	−0.956834	+	0.290634i	$0.906134\pi$
$228$	27.7553	−	13.3662i	1.83814	−	0.885200i
$229$	24.6772	+	11.8839i	1.63072	+	0.785312i	0.999956	+	0.00933352i	$0.00297099\pi$
$229$	24.6772	+	11.8839i	1.63072	+	0.785312i	0.630760	+	0.775978i	$0.282743\pi$
$230$	−0.00672344	−	0.0294573i	−0.000443331	−	0.00194236i
$231$	17.6271			1.15978
$232$		0			0
$233$	17.4774			1.14498			0.572492	−	0.819910i	$-0.305977\pi$
$233$	17.4774			1.14498			0.572492	+	0.819910i	$0.305977\pi$
$234$	−1.03589	−	4.53852i	−0.0677181	−	0.296692i
$235$	0.499289	+	0.240445i	0.0325700	+	0.0156849i
$236$	2.97915	−	1.43468i	0.193926	−	0.0933900i
$237$	−3.02431	−	13.2503i	−0.196450	−	0.860703i
$238$	4.07375	−	17.8482i	0.264062	−	1.15693i
$239$	−15.5439	−	7.48555i	−1.00545	−	0.484200i	−0.142667	−	0.989771i	$-0.545568\pi$
$239$	−15.5439	−	7.48555i	−1.00545	−	0.484200i	−0.862785	+	0.505571i	$0.831282\pi$
$240$	−0.0419211	−	0.0525674i	−0.00270599	−	0.00339321i
$241$	13.7085	+	17.1899i	0.883040	+	1.10730i	0.993547	+	0.113422i	$0.0361811\pi$
$241$	13.7085	+	17.1899i	0.883040	+	1.10730i	−0.110507	+	0.993875i	$0.535247\pi$
$242$	−9.77415	+	4.70698i	−0.628306	+	0.302576i
$243$	−8.35934	+	10.4823i	−0.536252	+	0.672439i
$244$	−10.0232			−0.641667
$245$	−0.164578	+	0.206374i	−0.0105145	+	0.0131847i
$246$	2.09700	−	9.18755i	0.133700	−	0.585777i
$247$	0.310986	−	1.36252i	0.0197876	−	0.0866950i
$248$	6.97691	−	8.74877i	0.443034	−	0.555548i
$249$	23.9274			1.51634
$250$	−0.818141	+	1.02592i	−0.0517438	+	0.0648846i
$251$	8.80311	−	4.23936i	0.555648	−	0.267586i	−0.134917	−	0.990857i	$-0.543077\pi$
$251$	8.80311	−	4.23936i	0.555648	−	0.267586i	0.690564	+	0.723271i	$0.257362\pi$
$252$	−15.5134	−	19.4532i	−0.977252	−	1.22544i
$253$	−0.570180	−	0.714983i	−0.0358469	−	0.0449506i
$254$	−35.9060	−	17.2914i	−2.25294	−	1.08496i
$255$	−0.189097	+	0.828487i	−0.0118417	+	0.0518819i
$256$	2.95119	+	12.9300i	0.184449	+	0.808124i
$257$	13.8769	−	6.68278i	0.865620	−	0.416861i	0.0522684	−	0.998633i	$-0.483355\pi$
$257$	13.8769	−	6.68278i	0.865620	−	0.416861i	0.813352	+	0.581772i	$0.197641\pi$
$258$	−37.6267	−	18.1201i	−2.34254	−	1.12811i
$259$	1.86669	+	8.17849i	0.115990	+	0.508187i
$260$	0.0736698			0.00456880
$261$		0			0
$262$	7.59225			0.469050
$263$	6.89666	+	30.2162i	0.425266	+	1.86321i	0.500026	+	0.866010i	$0.333324\pi$
$263$	6.89666	+	30.2162i	0.425266	+	1.86321i	−0.0747599	+	0.997202i	$0.523819\pi$
$264$	26.3475	+	12.6883i	1.62158	+	0.780911i
$265$	0.0932867	−	0.0449245i	0.00573056	−	0.00275969i
$266$	−2.71998	−	11.9170i	−0.166773	−	0.730679i
$267$	0.715945	−	3.13676i	0.0438151	−	0.191967i
$268$	−30.7852	−	14.8254i	−1.88050	−	0.905603i
$269$	−8.63841	−	10.8322i	−0.526693	−	0.660453i	0.445322	−	0.895371i	$-0.353089\pi$
$269$	−8.63841	−	10.8322i	−0.526693	−	0.660453i	−0.972015	+	0.234918i	$0.924518\pi$
$270$	0.480954	+	0.603097i	0.0292699	+	0.0367033i
$271$	24.1804	−	11.6447i	1.46885	−	0.707362i	0.483100	−	0.875565i	$-0.339511\pi$
$271$	24.1804	−	11.6447i	1.46885	−	0.707362i	0.985752	+	0.168203i	$0.0537963\pi$
$272$	−1.31776	+	1.65242i	−0.0799009	+	0.100193i
$273$	−1.79686			−0.108751
$274$	−7.80567	+	9.78800i	−0.471558	+	0.591315i
$275$	−4.41729	+	19.3534i	−0.266373	+	1.16705i
$276$	−0.457249	+	2.00334i	−0.0275232	+	0.120587i
$277$	−14.0636	+	17.6352i	−0.845002	+	1.05960i	0.152454	+	0.988311i	$0.451283\pi$
$277$	−14.0636	+	17.6352i	−0.845002	+	1.05960i	−0.997456	+	0.0712885i	$0.977289\pi$
$278$	−1.35500			−0.0812675
$279$	13.6475	−	17.1134i	0.817053	−	1.02455i
$280$	0.211080	−	0.101651i	0.0126145	−	0.00607481i
$281$	−2.05756	−	2.58010i	−0.122744	−	0.153916i	0.716663	−	0.697420i	$-0.245669\pi$
$281$	−2.05756	−	2.58010i	−0.122744	−	0.153916i	−0.839406	+	0.543504i	$0.817097\pi$
$282$	−38.4523	−	48.2176i	−2.28980	−	2.87132i
$283$	15.9189	+	7.66611i	0.946277	+	0.455703i	0.842380	−	0.538885i	$-0.181154\pi$
$283$	15.9189	+	7.66611i	0.946277	+	0.455703i	0.103898	+	0.994588i	$0.466868\pi$
$284$	−9.40775	+	41.2180i	−0.558247	+	2.44584i
$285$	0.126257	+	0.553169i	0.00747883	+	0.0327669i
$286$	3.28738	−	1.58312i	0.194387	−	0.0936118i
$287$	−2.05877	−	0.991449i	−0.121525	−	0.0585234i
$288$	6.89155	+	30.1938i	0.406088	+	1.77919i
$289$	9.71265			0.571332
$290$		0			0
$291$	−48.8951			−2.86628
$292$	4.90611	+	21.4951i	0.287109	+	1.25790i
$293$	−12.1939	−	5.87226i	−0.712374	−	0.343061i	0.0423508	−	0.999103i	$-0.486515\pi$
$293$	−12.1939	−	5.87226i	−0.712374	−	0.343061i	−0.754725	+	0.656042i	$0.772230\pi$
$294$	26.4668	−	12.7457i	1.54357	−	0.743346i
$295$	0.0135520	+	0.0593752i	0.000789028	+	0.00345696i
$296$	−3.09685	+	13.5682i	−0.180001	+	0.788635i
$297$	21.0351	+	10.1300i	1.22058	+	0.587802i
$298$	7.22382	+	9.05838i	0.418464	+	0.524738i
$299$	0.0581227	+	0.0728835i	0.00336132	+	0.00421496i
$300$	40.1878	−	19.3534i	2.32024	−	1.11737i
$301$	−6.31373	+	7.91716i	−0.363917	+	0.456338i
$302$	−17.6890			−1.01789
$303$	−11.0507	+	13.8572i	−0.634847	+	0.796073i
$304$	−0.314014	+	1.37579i	−0.0180100	+	0.0789068i
$305$	0.0410795	−	0.179981i	0.00235221	−	0.0103057i
$306$	37.0416	−	46.4487i	2.11753	−	2.65530i
$307$	6.51865			0.372039			0.186020	−	0.982546i	$-0.440441\pi$
$307$	6.51865			0.372039			0.186020	+	0.982546i	$0.440441\pi$
$308$	12.1592	−	15.2472i	0.692835	−	0.868788i
$309$	−33.8091	+	16.2816i	−1.92333	+	0.926227i
$310$	0.353418	+	0.443172i	0.0200728	+	0.0251705i
$311$	15.3042	+	19.1908i	0.867820	+	1.08821i	0.995345	+	0.0963761i	$0.0307252\pi$
$311$	15.3042	+	19.1908i	0.867820	+	1.08821i	−0.127525	+	0.991835i	$0.540703\pi$
$312$	−2.68580	−	1.29341i	−0.152053	−	0.0732251i
$313$	−0.439360	+	1.92496i	−0.0248341	+	0.108805i	−0.985826	−	0.167772i	$-0.946343\pi$
$313$	−0.439360	+	1.92496i	−0.0248341	+	0.108805i	0.960992	+	0.276577i	$0.0892001\pi$
$314$	−9.51599	−	41.6923i	−0.537019	−	2.35283i
$315$	0.412892	−	0.198838i	0.0232638	−	0.0112033i
$316$	−13.5475	−	6.52413i	−0.762107	−	0.367011i
$317$	6.60459	+	28.9366i	0.370951	+	1.62524i	0.724114	+	0.689680i	$0.242249\pi$
$317$	6.60459	+	28.9366i	0.370951	+	1.62524i	−0.353163	+	0.935562i	$0.614894\pi$
$318$	−11.5229			−0.646170
$319$		0			0
$320$	−0.754675			−0.0421876
$321$	−5.85831	−	25.6669i	−0.326979	−	1.43259i
$322$	0.734600	+	0.353765i	0.0409377	+	0.0197145i
$323$	16.0694	−	7.73860i	0.894123	−	0.430587i
$324$	−1.03955	−	4.55457i	−0.0577529	−	0.253032i
$325$	0.450287	−	1.97284i	0.0249774	−	0.109433i
$326$	4.62165	+	2.22567i	0.255969	+	0.123268i
$327$	−10.1932	−	12.7819i	−0.563686	−	0.706840i
$328$	−2.36361	−	2.96387i	−0.130508	−	0.163652i
$329$	−13.4733	+	6.48838i	−0.742805	+	0.357716i
$330$	−0.923602	+	1.15816i	−0.0508426	+	0.0637546i
$331$	−28.3740			−1.55958			−0.779788	−	0.626044i	$-0.784673\pi$
$331$	−28.3740			−1.55958			−0.779788	+	0.626044i	$0.784673\pi$
$332$	16.5051	−	20.6968i	0.905838	−	1.13588i
$333$	−6.05772	+	26.5406i	−0.331961	+	1.45442i
$334$	−5.92168	+	25.9446i	−0.324020	+	1.41963i
$335$	0.392384	−	0.492034i	0.0214382	−	0.0268827i
$336$	1.81436			0.0989814
$337$	−2.50472	+	3.14082i	−0.136441	+	0.171091i	−0.845358	−	0.534201i	$-0.820613\pi$
$337$	−2.50472	+	3.14082i	−0.136441	+	0.171091i	0.708917	+	0.705292i	$0.249184\pi$
$338$	26.2261	−	12.6298i	1.42651	−	0.686972i
$339$	14.2788	+	17.9051i	0.775518	+	0.972469i
$340$	0.586189	+	0.735057i	0.0317905	+	0.0398641i
$341$	15.4572	+	7.44380i	0.837055	+	0.403104i
$342$	8.82681	−	38.6728i	0.477299	−	2.09118i
$343$	−4.01799	−	17.6040i	−0.216951	−	0.950525i
$344$	−15.1361	+	7.28918i	−0.816086	+	0.393006i
$345$	−0.0340990	−	0.0164212i	−0.00183583	−	0.000884088i
$346$	−9.73360	−	42.6457i	−0.523281	−	2.29265i
$347$	−3.55272			−0.190720			−0.0953601	−	0.995443i	$-0.530400\pi$
$347$	−3.55272			−0.190720			−0.0953601	+	0.995443i	$0.530400\pi$
$348$		0			0
$349$	3.34203			0.178895			0.0894473	−	0.995992i	$-0.471490\pi$
$349$	3.34203			0.178895			0.0894473	+	0.995992i	$0.471490\pi$
$350$	−3.93835	−	17.2550i	−0.210514	−	0.922321i
$351$	−2.14427	−	1.03263i	−0.114453	−	0.0551175i
$352$	−21.8703	+	10.5322i	−1.16569	+	0.561366i
$353$	−2.78493	−	12.2016i	−0.148227	−	0.649424i	−0.993378	−	0.114896i	$-0.963347\pi$
$353$	−2.78493	−	12.2016i	−0.148227	−	0.649424i	0.845151	−	0.534528i	$-0.179511\pi$
$354$	1.50818	−	6.60778i	0.0801590	−	0.351200i
$355$	−0.701575	−	0.337861i	−0.0372358	−	0.0179318i
$356$	−2.21939	−	2.78302i	−0.117627	−	0.147500i
$357$	−14.2976	−	17.9286i	−0.756709	−	0.948883i
$358$	−1.86008	+	0.895765i	−0.0983080	+	0.0473426i
$359$	11.4697	−	14.3825i	0.605346	−	0.759080i	−0.380855	−	0.924635i	$-0.624370\pi$
$359$	11.4697	−	14.3825i	0.605346	−	0.759080i	0.986201	+	0.165555i	$0.0529416\pi$
$360$	0.760284			0.0400705
$361$	−4.42141	+	5.54428i	−0.232706	+	0.291804i
$362$	−2.65541	+	11.6341i	−0.139566	+	0.611476i
$363$	−3.02378	+	13.2481i	−0.158708	+	0.695343i
$364$	−1.23948	+	1.55426i	−0.0649663	+	0.0814652i
$365$	−0.406084			−0.0212554
$366$	−12.8096	+	16.0627i	−0.669566	+	0.839609i
$367$	−8.85669	+	4.26516i	−0.462316	+	0.222639i	−0.650518	−	0.759491i	$-0.725448\pi$
$367$	−8.85669	+	4.26516i	−0.462316	+	0.222639i	0.188202	+	0.982130i	$0.439734\pi$
$368$	−0.0586887	−	0.0735933i	−0.00305936	−	0.00383631i
$369$	−4.62343	−	5.79760i	−0.240686	−	0.301811i
$370$	−0.635162	−	0.305878i	−0.0330205	−	0.0159018i
$371$	−0.621729	+	2.72397i	−0.0322786	+	0.141422i
$372$	−8.57810	−	37.5831i	−0.444754	−	1.94859i
$373$	−19.9832	+	9.62338i	−1.03469	+	0.498280i	−0.872569	−	0.488491i	$-0.837547\pi$
$373$	−19.9832	+	9.62338i	−1.03469	+	0.498280i	−0.162120	+	0.986771i	$0.551833\pi$
$374$	41.9536	+	20.2038i	2.16937	+	1.04471i
$375$	0.365746	+	1.60244i	0.0188871	+	0.0827496i
$376$	−24.8091			−1.27943
$377$		0			0
$378$	−20.8159			−1.07065
$379$	−1.93598	−	8.48209i	−0.0994447	−	0.435696i	−1.00000		0.000953214i	$-0.999697\pi$
$379$	−1.93598	−	8.48209i	−0.0994447	−	0.435696i	0.900555	−	0.434742i	$-0.143161\pi$
$380$	0.565574	+	0.272366i	0.0290134	+	0.0139721i
$381$	−44.9757	+	21.6591i	−2.30417	+	1.10963i
$382$	5.20205	+	22.7917i	0.266160	+	1.16612i
$383$	−1.13179	+	4.95869i	−0.0578317	+	0.253377i	−0.995577	−	0.0939456i	$-0.970052\pi$
$383$	−1.13179	+	4.95869i	−0.0578317	+	0.253377i	0.937746	+	0.347323i	$0.112909\pi$
$384$	44.3954	+	21.3797i	2.26554	+	1.09103i
$385$	0.223952	+	0.280827i	0.0114136	+	0.0143123i
$386$	−3.83167	−	4.80477i	−0.195027	−	0.244556i
$387$	−29.6076	+	14.2583i	−1.50504	+	0.724790i
$388$	−33.7279	+	42.2934i	−1.71227	+	2.14712i
$389$	29.8408			1.51299			0.756494	−	0.654000i	$-0.226910\pi$
$389$	29.8408			1.51299			0.756494	+	0.654000i	$0.226910\pi$
$390$	0.0941496	−	0.118060i	0.00476745	−	0.00597819i
$391$	−0.264732	+	1.15987i	−0.0133881	+	0.0586569i
$392$	2.62955	−	11.5208i	0.132812	−	0.581888i
$393$	5.92939	−	7.43522i	0.299098	−	0.375057i
$394$	−33.5142			−1.68842
$395$	0.172675	−	0.216527i	0.00868820	−	0.0108947i
$396$	57.0195	−	27.4591i	2.86534	−	1.37987i
$397$	−1.82220	−	2.28497i	−0.0914537	−	0.114679i	0.733999	−	0.679150i	$-0.237652\pi$
$397$	−1.82220	−	2.28497i	−0.0914537	−	0.114679i	−0.825453	+	0.564471i	$0.809080\pi$
$398$	21.2131	+	26.6004i	1.06332	+	1.33336i
$399$	−13.7948	−	6.64322i	−0.690604	−	0.332577i
$400$	−0.454672	+	1.99205i	−0.0227336	+	0.0996024i
$401$	4.54850	+	19.9283i	0.227141	+	0.995171i	0.951958	+	0.306229i	$0.0990674\pi$
$401$	4.54850	+	19.9283i	0.227141	+	0.995171i	−0.724817	+	0.688942i	$0.758075\pi$
$402$	−63.1018	+	30.3882i	−3.14723	+	1.51563i
$403$	−1.57567	−	0.758802i	−0.0784896	−	0.0377986i
$404$	4.36341	+	19.1174i	0.217088	+	0.951125i
$405$	0.0860448			0.00427560
$406$		0			0
$407$	−21.3372			−1.05764
$408$	−8.46551	−	37.0898i	−0.419105	−	1.83622i
$409$	30.2833	+	14.5837i	1.49741	+	0.721116i	0.990063	−	0.140625i	$-0.0449112\pi$
$409$	30.2833	+	14.5837i	1.49741	+	0.721116i	0.507349	+	0.861741i	$0.330626\pi$
$410$	0.173014	−	0.0833192i	0.00854455	−	0.00411484i
$411$	3.48949	+	15.2885i	0.172124	+	0.754124i
$412$	−9.23824	+	40.4754i	−0.455135	+	1.99408i
$413$	−1.48069	−	0.713061i	−0.0728598	−	0.0350874i
$414$	1.64971	+	2.06867i	0.0810789	+	0.101670i
$415$	0.303997	+	0.381200i	0.0149226	+	0.0187124i
$416$	2.22940	−	1.07362i	0.109305	−	0.0526387i
$417$	−1.05823	+	1.32698i	−0.0518216	+	0.0649823i
$418$	31.0907			1.52070
$419$	−4.69488	+	5.88719i	−0.229360	+	0.287608i	−0.883173	−	0.469048i	$-0.844597\pi$
$419$	−4.69488	+	5.88719i	−0.229360	+	0.287608i	0.653813	+	0.756656i	$0.273168\pi$
$420$	0.179596	−	0.786859i	0.00876336	−	0.0383948i
$421$	4.53398	−	19.8646i	0.220972	−	0.968144i	−0.735775	−	0.677226i	$-0.763182\pi$
$421$	4.53398	−	19.8646i	0.220972	−	0.968144i	0.956748	−	0.290918i	$-0.0939607\pi$
$422$	−16.9289	+	21.2281i	−0.824084	+	1.03337i
$423$	−48.5289			−2.35956
$424$	−2.89007	+	3.62403i	−0.140354	+	0.175999i
$425$	23.2674	−	11.2050i	1.12863	−	0.543521i
$426$	54.0312	+	67.7529i	2.61782	+	3.28264i
$427$	3.10602	+	3.89482i	0.150311	+	0.188484i
$428$	−26.2426	−	12.6378i	−1.26848	−	0.610869i
$429$	1.01700	−	4.45578i	0.0491013	−	0.215127i
$430$	−0.189366	−	0.829666i	−0.00913203	−	0.0400100i
$431$	−10.6631	+	5.13509i	−0.513625	+	0.247349i	−0.672697	−	0.739918i	$-0.734864\pi$
$431$	−10.6631	+	5.13509i	−0.513625	+	0.247349i	0.159072	+	0.987267i	$0.449150\pi$
$432$	2.16515	+	1.04268i	0.104171	+	0.0501660i
$433$	3.80447	+	16.6685i	0.182831	+	0.801037i	0.980274	+	0.197642i	$0.0633284\pi$
$433$	3.80447	+	16.6685i	0.182831	+	0.801037i	−0.797443	+	0.603394i	$0.793814\pi$
$434$	−15.2961			−0.734235
$435$		0			0
$436$	−18.0874			−0.866230
$437$	0.176758	+	0.774425i	0.00845546	+	0.0370458i
$438$	40.7171	+	19.6083i	1.94554	+	0.936921i
$439$	−16.8940	+	8.13573i	−0.806308	+	0.388297i	−0.791176	−	0.611588i	$-0.790531\pi$
$439$	−16.8940	+	8.13573i	−0.806308	+	0.388297i	−0.0151314	+	0.999886i	$0.504817\pi$
$440$	0.132601	+	0.580961i	0.00632148	+	0.0276962i
$441$	5.14363	−	22.5357i	0.244935	−	1.07313i
$442$	−4.27664	−	2.05952i	−0.203419	−	0.0979614i
$443$	2.12225	+	2.66122i	0.100831	+	0.126438i	0.829687	−	0.558229i	$-0.188519\pi$
$443$	2.12225	+	2.66122i	0.100831	+	0.126438i	−0.728856	+	0.684667i	$0.759948\pi$
$444$	29.8927	+	37.4843i	1.41864	+	1.77892i
$445$	0.0590695	−	0.0284464i	0.00280016	−	0.00134849i
$446$	18.9059	−	23.7072i	0.895219	−	1.12257i
$447$	14.5127			0.686427
$448$	12.6973	−	15.9219i	0.599889	−	0.752237i
$449$	−0.0309934	+	0.135791i	−0.00146267	+	0.00640836i	−0.975654	−	0.219316i	$-0.929618\pi$
$449$	−0.0309934	+	0.135791i	−0.00146267	+	0.00640836i	0.974191	+	0.225724i	$0.0724747\pi$
$450$	12.7806	−	55.9956i	0.602484	−	2.63966i
$451$	3.62379	−	4.54408i	0.170637	−	0.213973i
$452$	25.3371			1.19176
$453$	−13.8148	+	17.3232i	−0.649075	+	0.813914i
$454$	4.33623	−	2.08822i	0.203509	−	0.0980050i
$455$	−0.0228291	−	0.0286268i	−0.00107024	−	0.00134204i
$456$	−15.8374	−	19.8595i	−0.741654	−	0.930005i
$457$	−28.9026	−	13.9188i	−1.35201	−	0.651093i	−0.389169	−	0.921166i	$-0.627238\pi$
$457$	−28.9026	−	13.9188i	−1.35201	−	0.651093i	−0.962840	+	0.270073i	$0.912952\pi$
$458$	13.8214	−	60.5555i	0.645831	−	2.82957i
$459$	−6.75864	−	29.6115i	−0.315466	−	1.38215i
$460$	−0.0377256	+	0.0181677i	−0.00175896	+	0.000847073i
$461$	0.653661	+	0.314786i	0.0304440	+	0.0146611i	0.449044	−	0.893510i	$-0.351765\pi$
$461$	0.653661	+	0.314786i	0.0304440	+	0.0146611i	−0.418600	+	0.908171i	$0.637479\pi$
$462$	−8.89502	−	38.9716i	−0.413834	−	1.81312i
$463$	−9.14813			−0.425150			−0.212575	−	0.977145i	$-0.568185\pi$
$463$	−9.14813			−0.425150			−0.212575	+	0.977145i	$0.568185\pi$
$464$		0			0
$465$	0.710019			0.0329263
$466$	−8.81948	−	38.6407i	−0.408554	−	1.78999i
$467$	−27.6274	−	13.3047i	−1.27844	−	0.615667i	−0.333455	−	0.942766i	$-0.608215\pi$
$467$	−27.6274	−	13.3047i	−1.27844	−	0.615667i	−0.944990	+	0.327099i	$0.893929\pi$
$468$	−5.81242	+	2.79911i	−0.268679	+	0.129389i
$469$	3.77897	+	16.5567i	0.174496	+	0.764519i
$470$	0.279646	−	1.22521i	0.0128991	−	0.0565146i
$471$	−48.2618	−	23.2417i	−2.22379	−	1.07092i
$472$	−1.69993	−	2.13165i	−0.0782457	−	0.0981170i
$473$	−16.0591	−	20.1375i	−0.738399	−	0.925924i
$474$	−27.7689	+	13.3728i	−1.27547	+	0.614234i
$475$	10.7507	−	13.4810i	0.493278	−	0.618551i
$476$	−25.3705			−1.16285
$477$	−5.65324	+	7.08894i	−0.258844	+	0.324580i
$478$	−8.70595	+	38.1433i	−0.398201	+	1.74463i
$479$	−1.17876	+	5.16447i	−0.0538588	+	0.235971i	−0.994692	−	0.102900i	$-0.967188\pi$
$479$	−1.17876	+	5.16447i	−0.0538588	+	0.235971i	0.940833	+	0.338871i	$0.110045\pi$
$480$	−0.626358	+	0.785428i	−0.0285892	+	0.0358497i
$481$	2.17506			0.0991740
$482$	31.0873	−	38.9823i	1.41599	−	1.77559i
$483$	0.920156	−	0.443124i	0.0418686	−	0.0201628i
$484$	9.37355	+	11.7541i	0.426070	+	0.534275i
$485$	−0.621210	−	0.778973i	−0.0282077	−	0.0353713i
$486$	27.3935	+	13.1920i	1.24259	+	0.598401i
$487$	0.774725	−	3.39429i	0.0351062	−	0.153810i	−0.954337	−	0.298733i	$-0.903436\pi$
$487$	0.774725	−	3.39429i	0.0351062	−	0.153810i	0.989443	+	0.144922i	$0.0462933\pi$
$488$	1.83905	+	8.05742i	0.0832500	+	0.364742i
$489$	5.78905	−	2.78786i	0.261790	−	0.126071i
$490$	0.539319	+	0.259722i	0.0243639	+	0.0117331i
$491$	−1.30210	−	5.70489i	−0.0587631	−	0.257458i	0.937010	−	0.349302i	$-0.113581\pi$
$491$	−1.30210	−	5.70489i	−0.0587631	−	0.257458i	−0.995773	+	0.0918437i	$0.970724\pi$
$492$	−13.0597			−0.588776
$493$		0			0
$494$	−3.16931			−0.142594
$495$	0.259379	+	1.13641i	0.0116582	+	0.0510779i
$496$	1.59101	+	0.766191i	0.0714385	+	0.0344030i
$497$	18.9319	−	9.11713i	0.849213	−	0.408959i
$498$	−12.0743	−	52.9008i	−0.541061	−	2.37054i
$499$	5.27783	−	23.1237i	0.236268	−	1.03516i	−0.708060	−	0.706152i	$-0.750429\pi$
$499$	5.27783	−	23.1237i	0.236268	−	1.03516i	0.944328	−	0.329005i	$-0.106713\pi$
$500$	1.63838	+	0.789001i	0.0732704	+	0.0352852i
$501$	20.7833	+	26.0614i	0.928529	+	1.16434i
$502$	−13.8150	−	17.3234i	−0.616593	−	0.773183i
$503$	17.4212	−	8.38962i	0.776774	−	0.374075i	−0.00311266	−	0.999995i	$-0.500991\pi$
$503$	17.4212	−	8.38962i	0.776774	−	0.374075i	0.779887	+	0.625920i	$0.215277\pi$
$504$	−12.7916	+	16.0402i	−0.569784	+	0.714487i
$505$	−0.361165			−0.0160716
$506$	−1.29302	+	1.62140i	−0.0574819	+	0.0720801i
$507$	8.11345	−	35.5473i	0.360331	−	1.57871i
$508$	−12.2895	+	53.8437i	−0.545257	+	2.38893i
$509$	24.2136	−	30.3629i	1.07325	−	1.34581i	0.138555	−	0.990355i	$-0.455754\pi$
$509$	24.2136	−	30.3629i	1.07325	−	1.34581i	0.934693	−	0.355456i	$-0.115674\pi$
$510$	1.92712			0.0853342
$511$	6.83229	−	8.56742i	0.302243	−	0.379000i
$512$	−4.16055	+	2.00362i	−0.183872	+	0.0885482i
$513$	−12.6441	−	15.8553i	−0.558253	−	0.700027i
$514$	−21.7775	−	27.3081i	−0.960565	−	1.20451i
$515$	−0.688934	−	0.331773i	−0.0303581	−	0.0146197i
$516$	−12.8784	+	56.4240i	−0.566941	+	2.48393i
$517$	−8.46389	−	37.0827i	−0.372241	−	1.63090i
$518$	17.1398	−	8.25408i	0.753078	−	0.362663i
$519$	−49.3654	−	23.7731i	−2.16690	−	1.04352i
$520$	−0.0135170	−	0.0592216i	−0.000592758	−	0.00259704i
$521$	−33.3472			−1.46097			−0.730484	−	0.682930i	$-0.760706\pi$
$521$	−33.3472			−1.46097			−0.730484	+	0.682930i	$0.760706\pi$
$522$		0			0
$523$	31.8103			1.39097			0.695484	−	0.718542i	$-0.255190\pi$
$523$	31.8103			1.39097			0.695484	+	0.718542i	$0.255190\pi$
$524$	−2.34124	−	10.2577i	−0.102278	−	0.448108i
$525$	−19.9739	−	9.61894i	−0.871734	−	0.419805i
$526$	63.3246	−	30.4955i	2.76108	−	1.32967i
$527$	−4.96643	−	21.7594i	−0.216341	−	0.947853i
$528$	−1.02691	+	4.49917i	−0.0446903	+	0.195801i
$529$	20.6745	+	9.95634i	0.898893	+	0.432884i
$530$	−0.146398	−	0.183577i	−0.00635911	−	0.00797407i
$531$	−3.32522	−	4.16969i	−0.144302	−	0.180949i
$532$	−15.2620	+	7.34977i	−0.661689	+	0.318653i
$533$	−0.369399	+	0.463212i	−0.0160005	+	0.0200640i
$534$	−7.29632			−0.315742
$535$	0.334484	−	0.419430i	0.0144610	−	0.0181335i
$536$	−6.26934	+	27.4678i	−0.270794	+	1.18643i
$537$	−0.575443	+	2.52118i	−0.0248322	+	0.108797i
$538$	−19.5897	+	24.5648i	−0.844574	+	1.05906i
$539$	18.1175			0.780375
$540$	0.666513	−	0.835781i	0.0286821	−	0.0359663i
$541$	−34.9037	+	16.8087i	−1.50063	+	0.722664i	−0.990510	−	0.137441i	$-0.956112\pi$
$541$	−34.9037	+	16.8087i	−1.50063	+	0.722664i	−0.510117	+	0.860105i	$0.670398\pi$
$542$	−37.9470	−	47.5840i	−1.62996	−	2.04391i
$543$	9.31969	+	11.6865i	0.399946	+	0.501517i
$544$	28.4516	+	13.7016i	1.21985	+	0.587450i
$545$	0.0741305	−	0.324787i	0.00317540	−	0.0139123i
$546$	0.906735	+	3.97267i	0.0388047	+	0.170014i
$547$	−5.39730	+	2.59920i	−0.230772	+	0.111134i	−0.545697	−	0.837983i	$-0.683735\pi$
$547$	−5.39730	+	2.59920i	−0.230772	+	0.111134i	0.314925	+	0.949117i	$0.398021\pi$
$548$	15.6313	+	7.52765i	0.667737	+	0.321565i
$549$	3.59735	+	15.7610i	0.153531	+	0.672665i
$550$	45.0173			1.91954
$551$		0			0
$552$	1.69434			0.0721159
$553$	1.66299	+	7.28605i	0.0707176	+	0.309834i
$554$	46.0864	+	22.1940i	1.95802	+	0.942934i
$555$	−0.795601	+	0.383141i	−0.0337714	+	0.0162634i
$556$	0.417845	+	1.83070i	0.0177206	+	0.0776389i
$557$	−0.417760	+	1.83032i	−0.0177010	+	0.0775533i	−0.983007	−	0.183568i	$-0.941235\pi$
$557$	−0.417760	+	1.83032i	−0.0177010	+	0.0775533i	0.965306	+	0.261122i	$0.0840923\pi$
$558$	−44.7226	−	21.5373i	−1.89326	−	0.911746i
$559$	1.63703	+	2.05277i	0.0692388	+	0.0868227i
$560$	0.0230514	+	0.0289055i	0.000974099	+	0.00122148i
$561$	52.5508	−	25.3071i	2.21870	−	1.06847i
$562$	−4.66602	+	5.85101i	−0.196824	+	0.246810i
$563$	26.4739			1.11574			0.557872	−	0.829927i	$-0.311618\pi$
$563$	26.4739			1.11574			0.557872	+	0.829927i	$0.311618\pi$
$564$	−53.2877	+	66.8207i	−2.24382	+	2.81366i
$565$	−0.103843	+	0.454966i	−0.00436871	+	0.0191406i
$566$	8.91595	−	39.0633i	0.374765	−	1.64195i
$567$	−1.44769	+	1.81534i	−0.0607971	+	0.0762372i
$568$	34.8605			1.46271
$569$	−7.97139	+	9.99580i	−0.334178	+	0.419046i	−0.920322	−	0.391161i	$-0.872074\pi$
$569$	−7.97139	+	9.99580i	−0.334178	+	0.419046i	0.586144	+	0.810207i	$0.300645\pi$
$570$	1.15928	−	0.558282i	0.0485570	−	0.0233838i
$571$	−23.7265	−	29.7521i	−0.992924	−	1.24509i	−0.969431	−	0.245363i	$-0.921093\pi$
$571$	−23.7265	−	29.7521i	−0.992924	−	1.24509i	−0.0234924	−	0.999724i	$-0.507479\pi$
$572$	−3.15264	−	3.95329i	−0.131819	−	0.165295i
$573$	26.3830	+	12.7054i	1.10216	+	0.530775i
$574$	−1.15309	+	5.05201i	−0.0481290	+	0.210867i
$575$	0.255933	+	1.12132i	0.0106731	+	0.0467621i
$576$	59.5426	−	28.6742i	2.48094	−	1.19476i
$577$	−0.0921290	−	0.0443670i	−0.00383538	−	0.00184702i	0.431965	−	0.901890i	$-0.357820\pi$
$577$	−0.0921290	−	0.0443670i	−0.00383538	−	0.00184702i	−0.435800	+	0.900043i	$0.643535\pi$
$578$	−4.90121	−	21.4736i	−0.203863	−	0.893184i
$579$	−7.69786			−0.319912
$580$		0			0
$581$	−13.1571			−0.545848
$582$	24.6735	+	108.102i	1.02275	+	4.48096i
$583$	−6.40289	−	3.08347i	−0.265181	−	0.127704i
$584$	16.3793	−	7.88785i	0.677780	−	0.326402i
$585$	−0.0264404	−	0.115843i	−0.00109318	−	0.00478951i
$586$	−6.82964	+	29.9226i	−0.282130	+	1.23609i
$587$	0.662492	+	0.319039i	0.0273440	+	0.0131682i	0.447506	−	0.894281i	$-0.352312\pi$
$587$	0.662492	+	0.319039i	0.0273440	+	0.0131682i	−0.420162	+	0.907449i	$0.638027\pi$
$588$	−25.3820	−	31.8280i	−1.04674	−	1.31257i
$589$	−9.29127	−	11.6509i	−0.382840	−	0.480066i
$590$	0.124433	−	0.0599240i	0.00512285	−	0.00246703i
$591$	−26.1739	+	32.8210i	−1.07665	+	1.35008i
$592$	−2.19624			−0.0902647
$593$	27.9046	−	34.9913i	1.14590	−	1.43692i	0.264607	−	0.964356i	$-0.414758\pi$
$593$	27.9046	−	34.9913i	1.14590	−	1.43692i	0.881297	−	0.472562i	$-0.156671\pi$
$594$	11.7815	−	51.6182i	0.483402	−	2.11792i
$595$	0.103980	−	0.455565i	0.00426275	−	0.0186763i
$596$	10.0109	−	12.5532i	0.410061	−	0.514201i
$597$	42.6173			1.74421
$598$	0.131808	−	0.165281i	0.00539001	−	0.00675886i
$599$	−3.65797	+	1.76159i	−0.149461	+	0.0719764i	−0.507119	−	0.861876i	$-0.669290\pi$
$599$	−3.65797	+	1.76159i	−0.149461	+	0.0719764i	0.357658	+	0.933853i	$0.383575\pi$
$600$	−22.9315	−	28.7552i	−0.936174	−	1.17393i
$601$	−27.7036	−	34.7392i	−1.13005	−	1.41704i	−0.895570	−	0.444921i	$-0.853232\pi$
$601$	−27.7036	−	34.7392i	−1.13005	−	1.41704i	−0.234483	−	0.972120i	$-0.575340\pi$
$602$	20.6900	+	9.96379i	0.843262	+	0.406094i
$603$	−12.2634	+	53.7294i	−0.499404	+	2.18803i
$604$	5.45481	+	23.8991i	0.221953	+	0.972441i
$605$	−0.249479	+	0.120143i	−0.0101428	+	0.00488450i
$606$	36.2131	+	17.4393i	1.47106	+	0.708423i
$607$	2.15884	+	9.45849i	0.0876246	+	0.383908i	0.999656	−	0.0262110i	$-0.00834417\pi$
$607$	2.15884	+	9.45849i	0.0876246	+	0.383908i	−0.912032	+	0.410119i	$0.865487\pi$
$608$	21.0848			0.855100
$609$		0			0
$610$	−0.418648			−0.0169506
$611$	0.862787	+	3.78012i	0.0349046	+	0.152927i
$612$	−74.1781	−	35.7223i	−2.99847	−	1.44399i
$613$	1.60828	−	0.774505i	0.0649576	−	0.0312820i	−0.401123	−	0.916024i	$-0.631380\pi$
$613$	1.60828	−	0.774505i	0.0649576	−	0.0312820i	0.466081	+	0.884742i	$0.345666\pi$
$614$	−3.28945	−	14.4120i	−0.132751	−	0.581622i
$615$	0.0535245	−	0.234506i	0.00215832	−	0.00945621i
$616$	−14.4879	−	6.97699i	−0.583733	−	0.281111i
$617$	5.43065	+	6.80982i	0.218630	+	0.274153i	0.879036	−	0.476756i	$-0.158187\pi$
$617$	5.43065	+	6.80982i	0.218630	+	0.274153i	−0.660406	+	0.750909i	$0.729616\pi$
$618$	53.0576	+	66.5321i	2.13429	+	2.67631i
$619$	−12.7975	+	6.16293i	−0.514373	+	0.247709i	−0.673017	−	0.739627i	$-0.735002\pi$
$619$	−12.7975	+	6.16293i	−0.514373	+	0.247709i	0.158644	+	0.987336i	$0.449288\pi$
$620$	0.489772	−	0.614155i	0.0196697	−	0.0246651i
$621$	1.35272			0.0542826
$622$	34.7060	−	43.5199i	1.39158	−	1.74499i
$623$	−0.393681	+	1.72483i	−0.0157725	+	0.0691038i
$624$	0.104680	−	0.458633i	0.00419056	−	0.0183600i
$625$	15.5559	−	19.5065i	0.622237	−	0.780260i
$626$	4.47759			0.178961
$627$	24.2813	−	30.4477i	0.969700	−	1.21597i
$628$	−53.3947	+	25.7135i	−2.13068	+	1.02608i
$629$	17.3069	+	21.7021i	0.690070	+	0.865320i
$630$	−0.647964	−	0.812522i	−0.0258155	−	0.0323716i
$631$	−14.9293	−	7.18958i	−0.594327	−	0.286213i	0.112441	−	0.993658i	$-0.464133\pi$
$631$	−14.9293	−	7.18958i	−0.594327	−	0.286213i	−0.706768	+	0.707446i	$0.749847\pi$
$632$	−2.75892	+	12.0876i	−0.109744	+	0.480820i
$633$	7.56798	+	33.1575i	0.300800	+	1.31789i
$634$	60.6429	−	29.2041i	2.40844	−	1.15984i
$635$	−0.916478	−	0.441352i	−0.0363693	−	0.0175145i
$636$	3.55334	+	15.5682i	0.140899	+	0.617319i
$637$	−1.84685			−0.0731748
$638$		0			0
$639$	68.1903			2.69757
$640$	0.223431	+	0.978915i	0.00883189	+	0.0386950i
$641$	6.57486	+	3.16628i	0.259691	+	0.125061i	0.559200	−	0.829033i	$-0.311108\pi$
$641$	6.57486	+	3.16628i	0.259691	+	0.125061i	−0.299509	+	0.954094i	$0.596823\pi$
$642$	−53.7906	+	25.9042i	−2.12294	+	1.02236i
$643$	7.53691	+	33.0214i	0.297227	+	1.30224i	0.874237	+	0.485499i	$0.161362\pi$
$643$	7.53691	+	33.0214i	0.297227	+	1.30224i	−0.577010	+	0.816737i	$0.695781\pi$
$644$	0.251430	−	1.10159i	0.00990774	−	0.0434086i
$645$	−0.960398	−	0.462503i	−0.0378156	−	0.0182110i
$646$	−25.2181	−	31.6225i	−0.992194	−	1.24417i
$647$	20.8525	+	26.1482i	0.819795	+	1.02799i	0.999023	+	0.0441829i	$0.0140684\pi$
$647$	20.8525	+	26.1482i	0.819795	+	1.02799i	−0.179228	+	0.983807i	$0.557360\pi$
$648$	−3.47059	+	1.67135i	−0.136338	+	0.0656568i
$649$	2.60627	−	3.26815i	0.102305	−	0.128286i
$650$	−4.58895			−0.179993
$651$	−11.9459	+	14.9797i	−0.468198	+	0.587101i
$652$	1.58184	−	6.93051i	0.0619497	−	0.271420i
$653$	−5.28615	+	23.1601i	−0.206863	+	0.906326i	0.759776	+	0.650184i	$0.225308\pi$
$653$	−5.28615	+	23.1601i	−0.206863	+	0.906326i	−0.966639	+	0.256141i	$0.917549\pi$
$654$	−23.1156	+	28.9861i	−0.903893	+	1.13345i
$655$	0.193787			0.00757189
$656$	0.372997	−	0.467723i	0.0145631	−	0.0182615i
$657$	32.0394	−	15.4294i	1.24998	−	0.601956i
$658$	21.1440	+	26.5137i	0.824278	+	1.03361i
$659$	−3.07458	−	3.85540i	−0.119769	−	0.150185i	0.718333	−	0.695700i	$-0.244906\pi$
$659$	−3.07458	−	3.85540i	−0.119769	−	0.150185i	−0.838101	+	0.545515i	$0.816334\pi$
$660$	1.84957	+	0.890706i	0.0719944	+	0.0346707i
$661$	5.22326	−	22.8846i	0.203161	−	0.890107i	−0.765836	−	0.643036i	$-0.777675\pi$
$661$	5.22326	−	22.8846i	0.203161	−	0.890107i	0.968997	−	0.247071i	$-0.0794682\pi$
$662$	14.3181	+	62.7318i	0.556489	+	2.43814i
$663$	−5.35690	+	2.57975i	−0.208045	+	0.100189i
$664$	−19.6661	−	9.47070i	−0.763193	−	0.367535i
$665$	−0.0694258	−	0.304174i	−0.00269222	−	0.0117954i
$666$	61.7352			2.39219
$667$		0			0
$668$	36.8790			1.42689
$669$	−8.45179	−	37.0297i	−0.326765	−	1.43165i
$670$	−1.28584	−	0.619227i	−0.0496762	−	0.0239228i
$671$	−11.4162	+	5.49774i	−0.440717	+	0.212238i
$672$	−6.03232	−	26.4293i	−0.232702	−	1.01953i
$673$	−6.65990	+	29.1789i	−0.256720	+	1.12477i	0.668013	+	0.744150i	$0.267145\pi$
$673$	−6.65990	+	29.1789i	−0.256720	+	1.12477i	−0.924733	+	0.380616i	$0.875712\pi$
$674$	8.20794	+	3.95274i	0.316158	+	0.152254i
$675$	−18.3079	−	22.9573i	−0.704670	−	0.883629i
$676$	−25.1512	−	31.5386i	−0.967353	−	1.21302i
$677$	−19.8360	+	9.55250i	−0.762358	+	0.367132i	−0.774318	−	0.632796i	$-0.781907\pi$
$677$	−19.8360	+	9.55250i	−0.762358	+	0.367132i	0.0119603	+	0.999928i	$0.496193\pi$
$678$	32.3807	−	40.6041i	1.24357	−	1.55939i
$679$	26.8862			1.03180
$680$	0.483344	−	0.606094i	0.0185354	−	0.0232426i
$681$	1.34148	−	5.87741i	0.0514056	−	0.225223i
$682$	8.65739	−	37.9305i	0.331508	−	1.45243i
$683$	−2.87871	+	3.60979i	−0.110151	+	0.138125i	−0.833851	−	0.551990i	$-0.813869\pi$
$683$	−2.87871	+	3.60979i	−0.110151	+	0.138125i	0.723700	+	0.690115i	$0.242440\pi$
$684$	−54.9715			−2.10189
$685$	−0.199235	+	0.249832i	−0.00761237	+	0.00954561i
$686$	−36.8929	+	17.7667i	−1.40858	+	0.678335i
$687$	−48.5088	−	60.8282i	−1.85073	−	2.32074i
$688$	−1.65297	−	2.07275i	−0.0630188	−	0.0790230i
$689$	0.652694	+	0.314321i	0.0248657	+	0.0119747i
$690$	−0.0190984	+	0.0836756i	−0.000727064	+	0.00318547i
$691$	7.95421	+	34.8497i	0.302592	+	1.32574i	0.866199	+	0.499700i	$0.166556\pi$
$691$	7.95421	+	34.8497i	0.302592	+	1.32574i	−0.563606	+	0.826044i	$0.690586\pi$
$692$	−54.6157	+	26.3015i	−2.07618	+	0.999834i
$693$	−28.3396	−	13.6476i	−1.07653	−	0.518430i
$694$	1.79278	+	7.85468i	0.0680530	+	0.298160i
$695$	−0.0345855			−0.00131190
$696$		0			0
$697$	−7.56111			−0.286398
$698$	−1.68646	−	7.38886i	−0.0638334	−	0.279672i
$699$	−44.7293	−	21.5405i	−1.69182	−	0.814737i
$700$	−22.0983	+	10.6420i	−0.835237	+	0.402229i
$701$	0.811010	+	3.55327i	0.0306314	+	0.134205i	0.987932	−	0.154891i	$-0.0495025\pi$
$701$	0.811010	+	3.55327i	0.0306314	+	0.134205i	−0.957300	+	0.289096i	$0.906645\pi$
$702$	−1.20098	+	5.26183i	−0.0453280	+	0.198595i
$703$	16.6982	+	8.04145i	0.629786	+	0.303289i
$704$	32.2958	+	40.4976i	1.21719	+	1.52631i
$705$	−0.981470	−	1.23072i	−0.0369643	−	0.0463518i
$706$	−25.5710	+	12.3143i	−0.962377	+	0.463457i
$707$	6.07652	−	7.61972i	0.228531	−	0.286569i
$708$	−9.39266			−0.352998
$709$	−13.0877	+	16.4114i	−0.491518	+	0.616344i	−0.964293	−	0.264839i	$-0.914681\pi$
$709$	−13.0877	+	16.4114i	−0.491518	+	0.616344i	0.472774	+	0.881184i	$0.343253\pi$
$710$	−0.392944	+	1.72160i	−0.0147469	+	0.0646104i
$711$	−5.39670	+	23.6445i	−0.202392	+	0.886737i
$712$	−1.83000	+	2.29475i	−0.0685822	+	0.0859994i
$713$	0.994013			0.0372261
$714$	−32.4233	+	40.6576i	−1.21341	+	1.52157i
$715$	0.0839083	−	0.0404081i	0.00313799	−	0.00151118i
$716$	1.78384	+	2.23686i	0.0666651	+	0.0835954i
$717$	30.5552	+	38.3150i	1.14110	+	1.43090i
$718$	−37.5860	−	18.1005i	−1.40270	−	0.675503i
$719$	−5.39677	+	23.6448i	−0.201266	+	0.881803i	0.768902	+	0.639367i	$0.220803\pi$
$719$	−5.39677	+	23.6448i	−0.201266	+	0.881803i	−0.970167	+	0.242436i	$0.922054\pi$
$720$	0.0266979	+	0.116971i	0.000994970	+	0.00435925i
$721$	18.5908	−	8.95286i	0.692357	−	0.333422i
$722$	14.4889	+	6.97750i	0.539222	+	0.259676i
$723$	−13.8975	−	60.8888i	−0.516852	−	2.26448i
$724$	16.5374			0.614607
$725$		0			0
$726$	30.8159			1.14368
$727$	−6.88385	−	30.1601i	−0.255308	−	1.11858i	−0.926203	−	0.377025i	$-0.876947\pi$
$727$	−6.88385	−	30.1601i	−0.255308	−	1.11858i	0.670895	−	0.741552i	$-0.265910\pi$
$728$	1.47686	+	0.711216i	0.0547359	+	0.0263594i
$729$	38.3309	−	18.4592i	1.41966	−	0.683673i
$730$	0.204919	+	0.897808i	0.00758439	+	0.0332294i
$731$	−7.45617	+	32.6676i	−0.275776	+	1.20826i
$732$	25.6519	+	12.3533i	0.948122	+	0.456591i
$733$	−11.5408	−	14.4717i	−0.426268	−	0.534523i	0.521598	−	0.853191i	$-0.325336\pi$
$733$	−11.5408	−	14.4717i	−0.426268	−	0.534523i	−0.947866	+	0.318668i	$0.896765\pi$
$734$	13.8991	+	17.4289i	0.513024	+	0.643312i
$735$	0.675548	−	0.325327i	0.0249180	−	0.0119999i
$736$	−0.876889	+	1.09958i	−0.0323225	+	0.0405312i
$737$	−43.1955			−1.59113
$738$	−10.4848	+	13.1475i	−0.385950	+	0.483966i
$739$	7.57663	−	33.1954i	0.278711	−	1.22111i	−0.620714	−	0.784037i	$-0.713157\pi$
$739$	7.57663	−	33.1954i	0.278711	−	1.22111i	0.899425	−	0.437075i	$-0.143986\pi$
$740$	−0.217396	+	0.952473i	−0.00799163	+	0.0350136i
$741$	−2.47517	+	3.10376i	−0.0909276	+	0.114020i
$742$	6.33614			0.232607
$743$	−21.7142	+	27.2288i	−0.796618	+	0.998927i	0.203187	+	0.979140i	$0.434870\pi$
$743$	−21.7142	+	27.2288i	−0.796618	+	0.998927i	−0.999804	+	0.0197868i	$0.993701\pi$
$744$	−28.6384	+	13.7915i	−1.04994	+	0.505622i
$745$	0.184383	+	0.231209i	0.00675528	+	0.00847086i
$746$	31.3602	+	39.3244i	1.14818	+	1.43977i
$747$	−38.4687	−	18.5255i	−1.40750	−	0.677814i
$748$	14.3594	−	62.9125i	0.525030	−	2.30031i
$749$	3.22135	+	14.1136i	0.117705	+	0.515701i
$750$	3.35826	−	1.61725i	0.122626	−	0.0590536i
$751$	43.7769	+	21.0818i	1.59744	+	0.769287i	0.999480	−	0.0322376i	$-0.0102633\pi$
$751$	43.7769	+	21.0818i	1.59744	+	0.769287i	0.597961	+	0.801525i	$0.295978\pi$
$752$	−0.871188	−	3.81692i	−0.0317690	−	0.139189i
$753$	−27.7544			−1.01143
$754$		0			0
$755$	−0.451501			−0.0164318
$756$	6.41904	+	28.1237i	0.233458	+	1.02285i
$757$	27.1118	+	13.0563i	0.985394	+	0.474541i	0.855957	−	0.517047i	$-0.172969\pi$
$757$	27.1118	+	13.0563i	0.985394	+	0.474541i	0.129437	+	0.991588i	$0.458683\pi$
$758$	−17.7760	+	8.56048i	−0.645654	+	0.310931i
$759$	0.578041	+	2.53256i	0.0209816	+	0.0919262i
$760$	0.115178	−	0.504628i	0.00417795	−	0.0183048i
$761$	8.85531	+	4.26449i	0.321005	+	0.154588i	0.587446	−	0.809263i	$-0.300133\pi$
$761$	8.85531	+	4.26449i	0.321005	+	0.154588i	−0.266441	+	0.963851i	$0.585848\pi$
$762$	70.5816	+	88.5066i	2.55690	+	3.20625i
$763$	5.60500	+	7.02845i	0.202915	+	0.254447i
$764$	29.1890	−	14.0567i	1.05602	−	0.508552i
$765$	0.945464	−	1.18557i	0.0341833	−	0.0428645i
$766$	11.5342			0.416749
$767$	−0.265676	+	0.333147i	−0.00959300	+	0.0120292i
$768$	8.38305	−	36.7285i	0.302497	−	1.32533i
$769$	−6.67010	+	29.2236i	−0.240530	+	1.05383i	0.700006	+	0.714137i	$0.253181\pi$
$769$	−6.67010	+	29.2236i	−0.240530	+	1.05383i	−0.940536	+	0.339694i	$0.889677\pi$
$770$	0.507867	−	0.636844i	0.0183022	−	0.0229503i
$771$	−43.7511			−1.57566
$772$	−5.30999	+	6.65852i	−0.191111	+	0.239645i
$773$	15.2398	−	7.33911i	0.548138	−	0.263969i	−0.139253	−	0.990257i	$-0.544470\pi$
$773$	15.2398	−	7.33911i	0.548138	−	0.263969i	0.687391	+	0.726287i	$0.258756\pi$
$774$	46.4642	+	58.2642i	1.67012	+	2.09426i
$775$	−13.4531	−	16.8697i	−0.483251	−	0.605977i
$776$	40.1872	+	19.3532i	1.44264	+	0.694738i
$777$	5.30245	−	23.2316i	0.190224	−	0.833427i
$778$	−15.0583	−	65.9747i	−0.539866	−	2.36531i
$779$	−4.54849	+	2.19044i	−0.162967	+	0.0784806i
$780$	−0.188540	−	0.0907962i	−0.00675083	−	0.00325103i
$781$	11.8930	+	52.1067i	0.425565	+	1.86452i
$782$	2.69792			0.0964776
$783$		0			0
$784$	1.86483			0.0666012
$785$	−0.242890	−	1.06417i	−0.00866910	−	0.0379818i
$786$	−19.4306	−	9.35726i	−0.693065	−	0.333763i
$787$	18.0155	−	8.67579i	0.642182	−	0.309259i	−0.0843036	−	0.996440i	$-0.526867\pi$
$787$	18.0155	−	8.67579i	0.642182	−	0.309259i	0.726486	+	0.687181i	$0.241152\pi$
$788$	10.3349	+	45.2800i	0.368164	+	1.61303i
$789$	19.5904	−	85.8312i	0.697437	−	3.05567i
$790$	−0.565853	−	0.272500i	−0.0201321	−	0.00969513i
$791$	−7.85157	−	9.84556i	−0.279170	−	0.350068i
$792$	−32.5358	−	40.7986i	−1.15611	−	1.44972i
$793$	1.16374	−	0.560425i	0.0413255	−	0.0199013i
$794$	−4.13230	+	5.18173i	−0.146650	+	0.183893i
$795$	−0.294114			−0.0104311
$796$	29.3975	−	36.8632i	1.04197	−	1.30658i
$797$	−8.96777	+	39.2904i	−0.317655	+	1.39174i	0.523999	+	0.851719i	$0.324440\pi$
$797$	−8.96777	+	39.2904i	−0.317655	+	1.39174i	−0.841654	+	0.540017i	$0.818418\pi$
$798$	−7.72629	+	33.8511i	−0.273508	+	1.19832i
$799$	−30.8518	+	38.6869i	−1.09146	+	1.36865i
$800$	30.5293			1.07937
$801$	−3.57965	+	4.48874i	−0.126481	+	0.158602i
$802$	41.7640	−	20.1125i	1.47474	−	0.710196i
$803$	17.3781	+	21.7914i	0.613260	+	0.769003i
$804$	60.5155	+	75.8840i	2.13422	+	2.67622i
$805$	0.0187502	+	0.00902962i	0.000660858	+	0.000318252i
$806$	−0.882512	+	3.86654i	−0.0310851	+	0.136193i
$807$	8.75751	+	38.3692i	0.308279	+	1.35066i
$808$	14.5675	−	7.01532i	0.512482	−	0.246798i
$809$	−45.1522	−	21.7442i	−1.58747	−	0.764484i	−0.588439	−	0.808542i	$-0.700257\pi$
$809$	−45.1522	−	21.7442i	−1.58747	−	0.764484i	−0.999029	+	0.0440579i	$0.985971\pi$
$810$	−0.0434201	−	0.190236i	−0.00152563	−	0.00668420i
$811$	−24.7764			−0.870017			−0.435009	−	0.900426i	$-0.643255\pi$
$811$	−24.7764			−0.870017			−0.435009	+	0.900426i	$0.643255\pi$
$812$		0			0
$813$	−76.2357			−2.67370
$814$	10.7672	+	47.1741i	0.377390	+	1.65345i
$815$	0.117965	+	0.0568088i	0.00413212	+	0.00198992i
$816$	5.40906	−	2.60487i	0.189355	−	0.0911885i
$817$	4.97838	+	21.8117i	0.174171	+	0.763095i
$818$	16.9613	−	74.3122i	0.593037	−	2.59827i
$819$	2.88886	+	1.39120i	0.100945	+	0.0486126i
$820$	−0.165923	−	0.208061i	−0.00579428	−	0.00726579i
$821$	−22.1885	−	27.8235i	−0.774384	−	0.971047i	0.225611	−	0.974218i	$-0.427562\pi$
$821$	−22.1885	−	27.8235i	−0.774384	−	0.971047i	−0.999995	+	0.00317052i	$0.998991\pi$
$822$	32.0402	−	15.4298i	1.11753	−	0.538175i
$823$	−9.60419	+	12.0433i	−0.334781	+	0.419802i	−0.920519	−	0.390699i	$-0.872233\pi$
$823$	−9.60419	+	12.0433i	−0.334781	+	0.419802i	0.585738	+	0.810501i	$0.300805\pi$
$824$	34.2324			1.19254
$825$	35.1576	−	44.0863i	1.22403	−	1.53489i
$826$	−0.829313	+	3.63346i	−0.0288555	+	0.126424i
$827$	9.21841	−	40.3885i	0.320556	−	1.40445i	−0.516012	−	0.856581i	$-0.672584\pi$
$827$	9.21841	−	40.3885i	0.320556	−	1.40445i	0.836567	−	0.547864i	$-0.184559\pi$
$828$	2.28620	−	2.86680i	0.0794508	−	0.0996282i
$829$	−4.64043			−0.161169			−0.0805844	−	0.996748i	$-0.525679\pi$
$829$	−4.64043			−0.161169			−0.0805844	+	0.996748i	$0.525679\pi$
$830$	0.689388	−	0.864465i	0.0239290	−	0.0300060i
$831$	57.7276	−	27.8001i	2.00255	−	0.964376i
$832$	−3.29215	−	4.12823i	−0.114135	−	0.143120i
$833$	−14.6953	−	18.4274i	−0.509163	−	0.638470i
$834$	3.46780	+	1.67000i	0.120080	+	0.0578275i
$835$	−0.151147	+	0.662219i	−0.00523067	+	0.0229170i
$836$	−9.58754	−	42.0058i	−0.331592	−	1.45280i
$837$	−22.8641	+	11.0108i	−0.790300	+	0.380588i
$838$	15.3851	+	7.40906i	0.531468	+	0.255942i
$839$	−7.88295	−	34.5374i	−0.272150	−	1.19237i	−0.907470	−	0.420117i	$-0.861989\pi$
$839$	−7.88295	−	34.5374i	−0.272150	−	1.19237i	0.635321	−	0.772248i	$-0.280868\pi$
$840$	−0.665493			−0.0229617
$841$		0			0
$842$	−46.2065			−1.59238
$843$	2.08593	+	9.13904i	0.0718431	+	0.314765i
$844$	33.9011	+	16.3259i	1.16692	+	0.561960i
$845$	0.669404	−	0.322368i	0.0230282	−	0.0110898i
$846$	24.4887	+	107.292i	0.841939	+	3.68878i
$847$	1.66271	−	7.28479i	0.0571313	−	0.250308i
$848$	−0.659050	−	0.317382i	−0.0226319	−	0.0108989i
$849$	−31.2922	−	39.2392i	−1.07395	−	1.34669i
$850$	−36.5142	−	45.7873i	−1.25243	−	1.57049i
$851$	−1.11383	+	0.536390i	−0.0381814	+	0.0183872i
$852$	74.8772	−	93.8930i	2.56525	−	3.21672i
$853$	−25.5045			−0.873256			−0.436628	−	0.899642i	$-0.643827\pi$
$853$	−25.5045			−0.873256			−0.436628	+	0.899642i	$0.643827\pi$
$854$	7.04367	−	8.83248i	0.241029	−	0.302241i
$855$	0.225299	−	0.987098i	0.00770505	−	0.0337580i
$856$	−5.34424	+	23.4147i	−0.182662	+	0.800296i
$857$	−22.3127	+	27.9793i	−0.762189	+	0.955754i	−0.999879	−	0.0155868i	$-0.995038\pi$
$857$	−22.3127	+	27.9793i	−0.762189	+	0.955754i	0.237690	+	0.971341i	$0.423610\pi$
$858$	−10.3644			−0.353836
$859$	18.4402	−	23.1233i	0.629171	−	0.788956i	−0.360431	−	0.932786i	$-0.617370\pi$
$859$	18.4402	−	23.1233i	0.629171	−	0.788956i	0.989602	+	0.143830i	$0.0459419\pi$
$860$	−1.06254	+	0.511693i	−0.0362324	+	0.0174486i
$861$	4.04699	+	5.07476i	0.137921	+	0.172947i
$862$	16.7340	+	20.9837i	0.569961	+	0.714709i
$863$	36.2241	+	17.4446i	1.23308	+	0.593822i	0.932926	−	0.360068i	$-0.117246\pi$
$863$	36.2241	+	17.4446i	1.23308	+	0.593822i	0.300158	+	0.953890i	$0.402961\pi$
$864$	7.98986	−	35.0058i	0.271820	−	1.19092i
$865$	−0.248444	−	1.08850i	−0.00844734	−	0.0370102i
$866$	34.9324	−	16.8225i	1.18705	−	0.571654i
$867$	−24.8572	−	11.9706i	−0.844196	−	0.406543i
$868$	4.71689	+	20.6661i	0.160102	+	0.701452i
$869$	−19.0088			−0.644831
$870$		0			0
$871$	4.40323			0.149198
$872$	3.31869	+	14.5401i	0.112385	+	0.492390i
$873$	78.6099	+	37.8565i	2.66054	+	1.28125i
$874$	1.62297	−	0.781583i	0.0548979	−	0.0264374i
$875$	−0.201115	−	0.881143i	−0.00679893	−	0.0297881i
$876$	13.9362	−	61.0583i	0.470859	−	2.06297i
$877$	46.9427	+	22.6064i	1.58514	+	0.763364i	0.998905	−	0.0467750i	$-0.0148944\pi$
$877$	46.9427	+	22.6064i	1.58514	+	0.763364i	0.586237	+	0.810139i	$0.300609\pi$
$878$	26.5123	+	33.2454i	0.894747	+	1.12198i
$879$	23.9699	+	30.0573i	0.808485	+	1.01381i
$880$	−0.0847254	+	0.0408016i	−0.00285609	+	0.00137542i
$881$	−28.2196	+	35.3863i	−0.950743	+	1.19219i	0.0305225	+	0.999534i	$0.490283\pi$
$881$	−28.2196	+	35.3863i	−0.950743	+	1.19219i	−0.981266	+	0.192660i	$0.938289\pi$
$882$	−52.4196			−1.76506
$883$	−21.1350	+	26.5025i	−0.711251	+	0.891880i	−0.997808	−	0.0661830i	$-0.978918\pi$
$883$	−21.1350	+	26.5025i	−0.711251	+	0.891880i	0.286557	+	0.958063i	$0.407489\pi$
$884$	−1.46376	+	6.41314i	−0.0492315	+	0.215697i
$885$	0.0384954	−	0.168659i	0.00129401	−	0.00566942i
$886$	4.81273	−	6.03497i	0.161687	−	0.202749i
$887$	30.4108			1.02110			0.510548	−	0.859850i	$-0.329443\pi$
$887$	30.4108			1.02110			0.510548	+	0.859850i	$0.329443\pi$
$888$	24.6481	−	30.9078i	0.827137	−	1.03720i
$889$	24.7310	−	11.9098i	0.829452	−	0.399443i
$890$	−0.0926995	−	0.116241i	−0.00310729	−	0.00389642i
$891$	−3.68223	−	4.61737i	−0.123359	−	0.154688i
$892$	−37.8601	−	18.2325i	−1.26765	−	0.610469i
$893$	−7.35181	+	32.2104i	−0.246019	+	1.07788i
$894$	−7.32341	−	32.0860i	−0.244932	−	1.07312i
$895$	−0.0474772	+	0.0228638i	−0.00158699	+	0.000764254i
$896$	−24.4120	−	11.7562i	−0.815546	−	0.392746i
$897$	−0.0589240	−	0.258163i	−0.00196742	−	0.00861981i
$898$	0.315858			0.0105403
$899$		0			0
$900$	−79.5951			−2.65317
$901$	2.05726	+	9.01346i	0.0685374	+	0.300282i
$902$	−11.8751	−	5.71875i	−0.395398	−	0.190414i
$903$	25.9162	−	12.4806i	0.862437	−	0.415328i
$904$	−4.64886	−	20.3680i	−0.154619	−	0.677430i
$905$	−0.0677778	+	0.296954i	−0.00225301	+	0.00987108i
$906$	45.2709	+	21.8013i	1.50402	+	0.724300i
$907$	9.90255	+	12.4174i	0.328809	+	0.412313i	0.918566	−	0.395267i	$-0.129348\pi$
$907$	9.90255	+	12.4174i	0.328809	+	0.412313i	−0.589757	+	0.807580i	$0.700777\pi$
$908$	−4.15851	−	5.21460i	−0.138005	−	0.173053i
$909$	28.4953	−	13.7226i	0.945129	−	0.455150i
$910$	−0.0517706	+	0.0649183i	−0.00171618	+	0.00215202i
$911$	−24.9672			−0.827199			−0.413600	−	0.910459i	$-0.635729\pi$
$911$	−24.9672			−0.827199			−0.413600	+	0.910459i	$0.635729\pi$
$912$	2.49927	−	3.13399i	0.0827591	−	0.103777i
$913$	7.44675	−	32.6264i	0.246452	−	1.07977i
$914$	−16.1880	+	70.9243i	−0.535452	+	2.34597i
$915$	−0.326956	+	0.409990i	−0.0108088	+	0.0135538i
$916$	−86.0768			−2.84406
$917$	−3.26043	+	4.08845i	−0.107669	+	0.135012i
$918$	−62.0573	+	29.8852i	−2.04819	+	0.986359i
$919$	8.39456	+	10.5264i	0.276911	+	0.347236i	0.900766	−	0.434305i	$-0.143006\pi$
$919$	8.39456	+	10.5264i	0.276911	+	0.347236i	−0.623855	+	0.781540i	$0.714434\pi$
$920$	0.0215265	+	0.0269934i	0.000709709	+	0.000889947i
$921$	−16.6830	−	8.03409i	−0.549722	−	0.264732i
$922$	0.366107	−	1.60402i	0.0120571	−	0.0528256i
$923$	−1.21234	−	5.31162i	−0.0399048	−	0.174834i
$924$	−49.9104	+	24.0356i	−1.64193	+	0.790712i
$925$	24.1779	+	11.6435i	0.794966	+	0.382835i
$926$	4.61634	+	20.2255i	0.151702	+	0.664651i
$927$	66.9616			2.19931
$928$		0			0
$929$	7.53667			0.247270			0.123635	−	0.992328i	$-0.460545\pi$
$929$	7.53667			0.247270			0.123635	+	0.992328i	$0.460545\pi$
$930$	−0.358291	−	1.56977i	−0.0117488	−	0.0514749i
$931$	−14.1785	−	6.82803i	−0.464683	−	0.223780i
$932$	−49.4865	+	23.8315i	−1.62099	+	0.780625i
$933$	−15.5152	−	67.9764i	−0.507944	−	2.22545i
$934$	−15.4738	+	67.7950i	−0.506317	+	2.21832i
$935$	1.07084	+	0.515689i	0.0350202	+	0.0168648i
$936$	3.31662	+	4.15891i	0.108407	+	0.135938i
$937$	−22.7346	−	28.5083i	−0.742708	−	0.931326i	0.256674	−	0.966498i	$-0.417373\pi$
$937$	−22.7346	−	28.5083i	−0.742708	−	0.931326i	−0.999381	+	0.0351723i	$0.988802\pi$
$938$	34.6982	−	16.7098i	1.13294	−	0.545593i
$939$	3.49691	−	4.38499i	0.114117	−	0.143099i
$940$	−1.74158			−0.0568039
$941$	−21.9323	+	27.5023i	−0.714973	+	0.896548i	−0.998042	−	0.0625515i	$-0.980076\pi$
$941$	−21.9323	+	27.5023i	−0.714973	+	0.896548i	0.283068	+	0.959100i	$0.408648\pi$
$942$	−27.0308	+	118.430i	−0.880712	+	3.85865i
$943$	0.0749333	−	0.328304i	0.00244016	−	0.0106911i
$944$	0.268263	−	0.336391i	0.00873122	−	0.0109486i
$945$	−0.531311			−0.0172836
$946$	−36.4180	+	45.6668i	−1.18405	+	1.48476i
$947$	9.36711	−	4.51096i	0.304390	−	0.146587i	−0.275453	−	0.961314i	$-0.588828\pi$
$947$	9.36711	−	4.51096i	0.304390	−	0.146587i	0.579843	+	0.814728i	$0.303114\pi$
$948$	26.6308	+	33.3940i	0.864928	+	1.08459i
$949$	−1.77148	−	2.22136i	−0.0575046	−	0.0721085i
$950$	−35.2301	−	16.9659i	−1.14302	−	0.550447i
$951$	18.7608	−	82.1964i	0.608361	−	2.66540i
$952$	4.65498	+	20.3948i	0.150869	+	0.660999i
$953$	−48.4858	+	23.3495i	−1.57061	+	0.756366i	−0.997985	−	0.0634519i	$-0.979789\pi$
$953$	−48.4858	+	23.3495i	−1.57061	+	0.756366i	−0.572625	+	0.819818i	$0.694075\pi$
$954$	18.5256	+	8.92146i	0.599789	+	0.288843i
$955$	0.132779	+	0.581743i	0.00429663	+	0.0188248i
$956$	54.2189			1.75356
$957$		0			0
$958$	12.0129			0.388119
$959$	−1.91879	−	8.40676i	−0.0619609	−	0.271468i
$960$	1.93141	+	0.930120i	0.0623361	+	0.0300195i
$961$	11.1288	−	5.35937i	0.358995	−	0.172883i
$962$	−1.09758	−	4.80881i	−0.0353874	−	0.155042i
$963$	−10.4538	+	45.8012i	−0.336870	+	1.47592i
$964$	−62.2543	−	29.9801i	−2.00508	−	0.965594i
$965$	−0.0978010	−	0.122639i	−0.00314833	−	0.00394788i
$966$	−1.44403	−	1.81075i	−0.0464609	−	0.0582601i
$967$	10.7168	−	5.16092i	0.344628	−	0.165964i	−0.253561	−	0.967319i	$-0.581602\pi$
$967$	10.7168	−	5.16092i	0.344628	−	0.165964i	0.598188	+	0.801356i	$0.295887\pi$
$968$	7.72899	−	9.69185i	0.248419	−	0.311508i
$969$	−50.6634			−1.62754
$970$	−1.40875	+	1.76651i	−0.0452322	+	0.0567194i
$971$	11.1461	−	48.8341i	0.357694	−	1.56716i	−0.401226	−	0.915979i	$-0.631416\pi$
$971$	11.1461	−	48.8341i	0.357694	−	1.56716i	0.758921	−	0.651183i	$-0.225727\pi$
$972$	9.37591	−	41.0785i	0.300732	−	1.31759i
$973$	0.581894	−	0.729672i	0.0186547	−	0.0233922i
$974$	−7.89535			−0.252983
$975$	−3.58388	+	4.49404i	−0.114776	+	0.143924i
$976$	−1.17507	+	0.565883i	−0.0376130	+	0.0181135i
$977$	8.61138	+	10.7983i	0.275502	+	0.345469i	0.900262	−	0.435348i	$-0.143375\pi$
$977$	8.61138	+	10.7983i	0.275502	+	0.345469i	−0.624760	+	0.780817i	$0.714803\pi$
$978$	−9.08493	−	11.3921i	−0.290504	−	0.364281i
$979$	−4.05433	−	1.95246i	−0.129577	−	0.0624010i
$980$	0.184592	−	0.808749i	0.00589656	−	0.0258345i
$981$	6.49165	+	28.4418i	0.207262	+	0.908076i
$982$	−11.9558	+	5.75762i	−0.381525	+	0.183733i
$983$	−10.5011	−	5.05705i	−0.334932	−	0.161295i	0.258857	−	0.965916i	$-0.416654\pi$
$983$	−10.5011	−	5.05705i	−0.334932	−	0.161295i	−0.593789	+	0.804621i	$0.702369\pi$
$984$	2.39619	+	10.4984i	0.0763879	+	0.334677i
$985$	−0.855428			−0.0272562
$986$		0			0
$987$	42.4784			1.35210
$988$	0.977329	+	4.28196i	0.0310930	+	0.136227i
$989$	−1.34454	−	0.647495i	−0.0427538	−	0.0205891i
$990$	2.38159	−	1.14692i	0.0756920	−	0.0364514i
$991$	−1.54324	−	6.76136i	−0.0490225	−	0.214782i	0.944484	−	0.328558i	$-0.106563\pi$
$991$	−1.54324	−	6.76136i	−0.0490225	−	0.214782i	−0.993506	+	0.113776i	$0.963705\pi$
$992$	5.87117	−	25.7233i	0.186410	−	0.816715i
$993$	72.6165	+	34.9703i	2.30442	+	1.10975i
$994$	−29.7104	−	37.2557i	−0.942358	−	1.18168i
$995$	0.541451	+	0.678958i	0.0171652	+	0.0215244i
$996$	−67.7493	+	32.6264i	−2.14672	+	1.03381i
$997$	14.9450	−	18.7405i	0.473314	−	0.593516i	−0.486665	−	0.873588i	$-0.661787\pi$
$997$	14.9450	−	18.7405i	0.473314	−	0.593516i	0.959979	+	0.280072i	$0.0903583\pi$
$998$	−53.7872			−1.70260
$999$	19.6784	−	24.6759i	0.622597	−	0.780712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.m.645.1		24
29.2	odd	28		841.2.b.e.840.2		12
29.3	odd	28		841.2.e.e.63.2		12
29.4	even	14	inner	841.2.d.m.605.4		24
29.5	even	14		841.2.a.k.1.2		12
29.6	even	14		841.2.d.l.571.4		24
29.7	even	7		841.2.d.k.778.4		24
29.8	odd	28		841.2.e.h.651.2		12
29.9	even	14		841.2.d.l.190.4		24
29.10	odd	28		29.2.e.a.4.1	✓	12
29.11	odd	28		841.2.e.f.267.1		12
29.12	odd	4		841.2.e.i.196.2		12
29.13	even	14		841.2.d.k.574.1		24
29.14	odd	28		841.2.e.h.270.2		12
29.15	odd	28		841.2.e.a.270.1		12
29.16	even	7		841.2.d.k.574.4		24
29.17	odd	4		29.2.e.a.22.1	yes	12
29.18	odd	28		841.2.e.e.267.2		12
29.19	odd	28		841.2.e.i.236.2		12
29.20	even	7		841.2.d.l.190.1		24
29.21	odd	28		841.2.e.a.651.1		12
29.22	even	14		841.2.d.k.778.1		24
29.23	even	7		841.2.d.l.571.1		24
29.24	even	7		841.2.a.k.1.11		12
29.25	even	7	inner	841.2.d.m.605.1		24
29.26	odd	28		841.2.e.f.63.1		12
29.27	odd	28		841.2.b.e.840.11		12
29.28	even	2	inner	841.2.d.m.645.4		24
87.5	odd	14		7569.2.a.bp.1.11		12
87.17	even	4		261.2.o.a.109.2		12
87.53	odd	14		7569.2.a.bp.1.2		12
87.68	even	28		261.2.o.a.91.2		12
116.39	even	28		464.2.y.d.33.2		12
116.75	even	4		464.2.y.d.225.2		12
145.17	even	4		725.2.p.a.399.1		24
145.39	odd	28		725.2.q.a.526.2		12
145.68	even	28		725.2.p.a.149.1		24
145.97	even	28		725.2.p.a.149.4		24
145.104	odd	4		725.2.q.a.51.2		12
145.133	even	4		725.2.p.a.399.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.4.1	✓	12	29.10	odd	28
29.2.e.a.22.1	yes	12	29.17	odd	4
261.2.o.a.91.2		12	87.68	even	28
261.2.o.a.109.2		12	87.17	even	4
464.2.y.d.33.2		12	116.39	even	28
464.2.y.d.225.2		12	116.75	even	4
725.2.p.a.149.1		24	145.68	even	28
725.2.p.a.149.4		24	145.97	even	28
725.2.p.a.399.1		24	145.17	even	4
725.2.p.a.399.4		24	145.133	even	4
725.2.q.a.51.2		12	145.104	odd	4
725.2.q.a.526.2		12	145.39	odd	28
841.2.a.k.1.2		12	29.5	even	14
841.2.a.k.1.11		12	29.24	even	7
841.2.b.e.840.2		12	29.2	odd	28
841.2.b.e.840.11		12	29.27	odd	28
841.2.d.k.574.1		24	29.13	even	14
841.2.d.k.574.4		24	29.16	even	7
841.2.d.k.778.1		24	29.22	even	14
841.2.d.k.778.4		24	29.7	even	7
841.2.d.l.190.1		24	29.20	even	7
841.2.d.l.190.4		24	29.9	even	14
841.2.d.l.571.1		24	29.23	even	7
841.2.d.l.571.4		24	29.6	even	14
841.2.d.m.605.1		24	29.25	even	7	inner
841.2.d.m.605.4		24	29.4	even	14	inner
841.2.d.m.645.1		24	1.1	even	1	trivial
841.2.d.m.645.4		24	29.28	even	2	inner
841.2.e.a.270.1		12	29.15	odd	28
841.2.e.a.651.1		12	29.21	odd	28
841.2.e.e.63.2		12	29.3	odd	28
841.2.e.e.267.2		12	29.18	odd	28
841.2.e.f.63.1		12	29.26	odd	28
841.2.e.f.267.1		12	29.11	odd	28
841.2.e.h.270.2		12	29.14	odd	28
841.2.e.h.651.2		12	29.8	odd	28
841.2.e.i.196.2		12	29.12	odd	4
841.2.e.i.236.2		12	29.19	odd	28
7569.2.a.bp.1.2		12	87.53	odd	14
7569.2.a.bp.1.11		12	87.5	odd	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.504621 - 2.21089i) q^{2} +(-2.55926 - 1.23248i) q^{3} +(-2.83146 + 1.36356i) q^{4} +(-0.0128801 - 0.0564316i) q^{5} +(-1.43341 + 6.28018i) q^{6} +(1.40728 + 0.677709i) q^{7} +(1.61565 + 2.02596i) q^{8} +(3.16036 + 3.96297i) q^{9} +(-0.118264 + 0.0569531i) q^{10} +(-2.47705 + 3.10613i) q^{11} +8.92699 q^{12} +(0.252504 - 0.316631i) q^{13} +(0.788198 - 3.45332i) q^{14} +(-0.0365869 + 0.160298i) q^{15} +(-0.254963 + 0.319714i) q^{16} +5.16843 q^{17} +(7.16690 - 8.98701i) q^{18} +(3.10914 - 1.49728i) q^{19} +(0.113417 + 0.142221i) q^{20} +(-2.76633 - 3.46887i) q^{21} +(8.11728 + 3.90908i) q^{22} +(-0.0512209 + 0.224414i) q^{23} +(-1.63793 - 7.17623i) q^{24} +(4.50183 - 2.16797i) q^{25} +(-0.827455 - 0.398481i) q^{26} +(-1.30768 - 5.72931i) q^{27} -4.90874 q^{28} +0.372863 q^{30} +(-0.960917 - 4.21005i) q^{31} +(5.50488 + 2.65101i) q^{32} +(10.1677 - 4.89649i) q^{33} +(-2.60810 - 11.4268i) q^{34} +(0.0201183 - 0.0881438i) q^{35} +(-14.3522 - 6.91164i) q^{36} +(3.34857 + 4.19898i) q^{37} +(-4.87927 - 6.11841i) q^{38} +(-1.03647 + 0.499135i) q^{39} +(0.0935185 - 0.117269i) q^{40} -1.46294 q^{41} +(-6.27335 + 7.86653i) q^{42} +(-1.44264 + 6.32061i) q^{43} +(2.77829 - 12.1725i) q^{44} +(0.182931 - 0.229388i) q^{45} +0.522001 q^{46} +(-5.96928 + 7.48524i) q^{47} +(1.04656 - 0.503996i) q^{48} +(-2.84329 - 3.56537i) q^{49} +(-7.06485 - 8.85904i) q^{50} +(-13.2274 - 6.36997i) q^{51} +(-0.283211 + 1.24083i) q^{52} +(0.398044 + 1.74395i) q^{53} +(-12.0070 + 5.78226i) q^{54} +(0.207188 + 0.0997767i) q^{55} +(0.900657 + 3.94604i) q^{56} -9.80247 q^{57} -1.05216 q^{59} +(-0.114981 - 0.503764i) q^{60} +(2.87352 + 1.38382i) q^{61} +(-8.82307 + 4.24897i) q^{62} +(1.76177 + 7.71880i) q^{63} +(2.90123 - 12.7111i) q^{64} +(-0.0211203 - 0.0101710i) q^{65} +(-15.9564 - 20.0087i) q^{66} +(6.77893 + 8.50052i) q^{67} +(-14.6342 + 7.04745i) q^{68} +(0.407672 - 0.511205i) q^{69} -0.205028 q^{70} +(8.38773 - 10.5179i) q^{71} +(-2.92279 + 12.8056i) q^{72} +(1.56113 - 6.83974i) q^{73} +(7.59372 - 9.52223i) q^{74} -14.1933 q^{75} +(-6.76176 + 8.47898i) q^{76} +(-5.59095 + 2.69246i) q^{77} +(1.62656 + 2.03964i) q^{78} +(2.98318 + 3.74078i) q^{79} +(0.0213259 + 0.0102700i) q^{80} +(-0.330785 + 1.44926i) q^{81} +(0.738232 + 3.23440i) q^{82} +(-7.58927 + 3.65480i) q^{83} +(12.5628 + 6.04990i) q^{84} +(-0.0665701 - 0.291662i) q^{85} +14.7022 q^{86} -10.2950 q^{88} +(0.252043 + 1.10427i) q^{89} +(-0.599462 - 0.288686i) q^{90} +(0.569927 - 0.274462i) q^{91} +(-0.160971 - 0.705260i) q^{92} +(-2.72955 + 11.9589i) q^{93} +(19.5613 + 9.42022i) q^{94} +(-0.124540 - 0.156168i) q^{95} +(-10.8211 - 13.5693i) q^{96} +(15.5085 - 7.46850i) q^{97} +(-6.44786 + 8.08536i) q^{98} -20.1379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} + 2 q^{5} + 6 q^{6} - 22 q^{7} + 6 q^{9} - 18 q^{13} + 18 q^{16} - 22 q^{20} + 8 q^{22} - 10 q^{23} - 50 q^{24} + 26 q^{25} - 24 q^{28} + 4 q^{30} + 34 q^{33} + 26 q^{34} - 38 q^{35} - 80 q^{36}+ \cdots - 60 q^{96}+O(q^{100}) \) 24 * q + 2 * q^4 + 2 * q^5 + 6 * q^6 - 22 * q^7 + 6 * q^9 - 18 * q^13 + 18 * q^16 - 22 * q^20 + 8 * q^22 - 10 * q^23 - 50 * q^24 + 26 * q^25 - 24 * q^28 + 4 * q^30 + 34 * q^33 + 26 * q^34 - 38 * q^35 - 80 * q^36 - 56 * q^38 - 100 * q^42 + 32 * q^45 + 26 * q^49 - 40 * q^51 - 12 * q^52 - 20 * q^53 - 76 * q^54 + 28 * q^57 + 88 * q^59 - 74 * q^62 + 26 * q^63 + 52 * q^64 - 12 * q^65 + 74 * q^67 + 42 * q^71 + 34 * q^78 + 12 * q^80 + 2 * q^81 + 44 * q^82 + 10 * q^83 + 88 * q^86 - 132 * q^88 + 6 * q^91 + 12 * q^92 - 38 * q^93 + 132 * q^94 - 60 * q^96

Introduction

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