LMFDB - Embedded newform 128.2.k.a.109.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	128.109
Dual form			128.2.k.a.101.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.399184 - 1.35671i) q^{2} +(-0.135634 - 0.0724978i) q^{3} +(-1.68130 + 1.08315i) q^{4} +(2.12942 - 2.59470i) q^{5} +(-0.0442153 + 0.212955i) q^{6} +(-1.11060 - 0.742082i) q^{7} +(2.14067 + 1.84866i) q^{8} +(-1.65357 - 2.47474i) q^{9} +(-4.37028 - 1.85323i) q^{10} +(-0.181497 - 0.0550566i) q^{11} +(0.306568 - 0.0250213i) q^{12} +(0.374137 - 0.307046i) q^{13} +(-0.563451 + 1.80299i) q^{14} +(-0.476932 + 0.197552i) q^{15} +(1.65356 - 3.64222i) q^{16} +(1.79255 + 0.742500i) q^{17} +(-2.69742 + 3.23129i) q^{18} +(-0.487163 + 4.94625i) q^{19} +(-0.769739 + 6.66897i) q^{20} +(0.0968362 + 0.181168i) q^{21} +(-0.00224473 + 0.268216i) q^{22} +(5.40603 + 1.07533i) q^{23} +(-0.156324 - 0.405934i) q^{24} +(-1.22261 - 6.14649i) q^{25} +(-0.565921 - 0.385026i) q^{26} +(0.0900899 + 0.914698i) q^{27} +(2.67105 + 0.0447117i) q^{28} +(2.45765 + 8.10178i) q^{29} +(0.458403 + 0.568197i) q^{30} +(3.30297 - 3.30297i) q^{31} +(-5.60149 - 0.789483i) q^{32} +(0.0206257 + 0.0206257i) q^{33} +(0.291795 - 2.72836i) q^{34} +(-4.29042 + 1.30149i) q^{35} +(5.46068 + 2.36973i) q^{36} +(8.32789 - 0.820226i) q^{37} +(6.90508 - 1.31353i) q^{38} +(-0.0730059 + 0.0145218i) q^{39} +(9.35510 - 1.61784i) q^{40} +(0.580168 - 2.91670i) q^{41} +(0.207136 - 0.203698i) q^{42} +(-8.36535 + 4.47137i) q^{43} +(0.364787 - 0.104022i) q^{44} +(-9.94237 - 0.979238i) q^{45} +(-0.699102 - 7.76365i) q^{46} +(-3.57155 + 8.62250i) q^{47} +(-0.488332 + 0.374128i) q^{48} +(-1.99603 - 4.81884i) q^{49} +(-7.85094 + 4.11231i) q^{50} +(-0.189301 - 0.230664i) q^{51} +(-0.296460 + 0.921485i) q^{52} +(-3.12341 + 10.2965i) q^{53} +(1.20501 - 0.487359i) q^{54} +(-0.529339 + 0.353693i) q^{55} +(-1.00558 - 3.64168i) q^{56} +(0.424668 - 0.635561i) q^{57} +(10.0107 - 6.56841i) q^{58} +(-10.8483 - 8.90293i) q^{59} +(0.587888 - 0.848734i) q^{60} +(0.339850 - 0.635815i) q^{61} +(-5.79966 - 3.16267i) q^{62} +3.97554i q^{63} +(1.16493 + 7.91473i) q^{64} -1.62460i q^{65} +(0.0197495 - 0.0362165i) q^{66} +(-0.0570291 + 0.106694i) q^{67} +(-3.81807 + 0.693240i) q^{68} +(-0.655283 - 0.537776i) q^{69} +(3.47840 + 5.30131i) q^{70} +(8.81399 - 13.1911i) q^{71} +(1.03520 - 8.35449i) q^{72} +(-1.93431 + 1.29247i) q^{73} +(-4.43717 - 10.9711i) q^{74} +(-0.279780 + 0.922310i) q^{75} +(-4.53848 - 8.84383i) q^{76} +(0.160715 + 0.195832i) q^{77} +(0.0488446 + 0.0932506i) q^{78} +(-3.11404 - 7.51796i) q^{79} +(-5.92934 - 12.0463i) q^{80} +(-3.36290 + 8.11876i) q^{81} +(-4.18870 + 0.377184i) q^{82} +(14.1505 + 1.39370i) q^{83} +(-0.359043 - 0.199710i) q^{84} +(5.74366 - 3.07005i) q^{85} +(9.40566 + 9.56442i) q^{86} +(0.254021 - 1.27705i) q^{87} +(-0.286745 - 0.453384i) q^{88} +(-1.57448 + 0.313183i) q^{89} +(2.64030 + 13.8798i) q^{90} +(-0.643371 + 0.0633666i) q^{91} +(-10.2539 + 4.04761i) q^{92} +(-0.687453 + 0.208537i) q^{93} +(13.1239 + 1.40358i) q^{94} +(11.7967 + 11.7967i) q^{95} +(0.702516 + 0.513177i) q^{96} +(-11.0877 + 11.0877i) q^{97} +(-5.74097 + 4.63163i) q^{98} +(0.163868 + 0.540199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) $ 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{23}{32}\right)$	$1$

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 $

$2$	−0.399184	−	1.35671i	−0.282266	−	0.959336i
$2$	−0.399184	−	1.35671i	−0.282266	−	0.959336i
$3$	−0.135634	−	0.0724978i	−0.0783083	−	0.0418566i	0.431778	−	0.901980i	$-0.357886\pi$
$3$	−0.135634	−	0.0724978i	−0.0783083	−	0.0418566i	−0.510086	+	0.860123i	$0.670386\pi$
$4$	−1.68130	+	1.08315i	−0.840652	+	0.541576i
$5$	2.12942	−	2.59470i	0.952305	−	1.16039i	−0.0346516	−	0.999399i	$-0.511032\pi$
$5$	2.12942	−	2.59470i	0.952305	−	1.16039i	0.986956	−	0.160987i	$-0.0514678\pi$
$6$	−0.0442153	+	0.212955i	−0.0180508	+	0.0869387i
$7$	−1.11060	−	0.742082i	−0.419769	−	0.280480i	0.327694	−	0.944784i	$-0.393728\pi$
$7$	−1.11060	−	0.742082i	−0.419769	−	0.280480i	−0.747463	+	0.664303i	$0.768728\pi$
$8$	2.14067	+	1.84866i	0.756841	+	0.653599i
$9$	−1.65357	−	2.47474i	−0.551190	−	0.824914i
$10$	−4.37028	−	1.85323i	−1.38200	−	0.586043i
$11$	−0.181497	−	0.0550566i	−0.0547235	−	0.0166002i	0.262804	−	0.964849i	$-0.415353\pi$
$11$	−0.181497	−	0.0550566i	−0.0547235	−	0.0166002i	−0.317528	+	0.948249i	$0.602853\pi$
$12$	0.306568	−	0.0250213i	0.0884985	−	0.00722303i
$13$	0.374137	−	0.307046i	0.103767	−	0.0851593i	−0.581079	−	0.813847i	$-0.697369\pi$
$13$	0.374137	−	0.307046i	0.103767	−	0.0851593i	0.684846	+	0.728688i	$0.259869\pi$
$14$	−0.563451	+	1.80299i	−0.150589	+	0.481869i
$15$	−0.476932	+	0.197552i	−0.123143	+	0.0510076i
$16$	1.65356	−	3.64222i	0.413391	−	0.910554i
$17$	1.79255	+	0.742500i	0.434758	+	0.180083i	0.589319	−	0.807901i	$-0.299396\pi$
$17$	1.79255	+	0.742500i	0.434758	+	0.180083i	−0.154561	+	0.987983i	$0.549396\pi$
$18$	−2.69742	+	3.23129i	−0.635788	+	0.761622i
$19$	−0.487163	+	4.94625i	−0.111763	+	1.13475i	0.761724	+	0.647901i	$0.224353\pi$
$19$	−0.487163	+	4.94625i	−0.111763	+	1.13475i	−0.873487	+	0.486847i	$0.838147\pi$
$20$	−0.769739	+	6.66897i	−0.172119	+	1.49123i
$21$	0.0968362	+	0.181168i	0.0211314	+	0.0395340i
$22$	−0.00224473	+	0.268216i	−0.000478577	+	0.0571839i
$23$	5.40603	+	1.07533i	1.12724	+	0.224221i	0.723278	−	0.690557i	$-0.242634\pi$
$23$	5.40603	+	1.07533i	1.12724	+	0.224221i	0.403958	+	0.914778i	$0.367634\pi$
$24$	−0.156324	−	0.405934i	−0.0319094	−	0.0828610i
$25$	−1.22261	−	6.14649i	−0.244523	−	1.22930i
$26$	−0.565921	−	0.385026i	−0.110986	−	0.0755098i
$27$	0.0900899	+	0.914698i	0.0173378	+	0.176034i
$28$	2.67105	+	0.0447117i	0.504781	+	0.00844971i
$29$	2.45765	+	8.10178i	0.456374	+	1.50446i	0.819695	+	0.572800i	$0.194143\pi$
$29$	2.45765	+	8.10178i	0.456374	+	1.50446i	−0.363321	+	0.931664i	$0.618357\pi$
$30$	0.458403	+	0.568197i	0.0836926	+	0.103738i
$31$	3.30297	−	3.30297i	0.593232	−	0.593232i	−0.345271	−	0.938503i	$-0.612213\pi$
$31$	3.30297	−	3.30297i	0.593232	−	0.593232i	0.938503	+	0.345271i	$0.112213\pi$
$32$	−5.60149	−	0.789483i	−0.990213	−	0.139562i
$33$	0.0206257	+	0.0206257i	0.00359047	+	0.00359047i
$34$	0.291795	−	2.72836i	0.0500424	−	0.467910i
$35$	−4.29042	+	1.30149i	−0.725214	+	0.219991i
$36$	5.46068	+	2.36973i	0.910113	+	0.394954i
$37$	8.32789	−	0.820226i	1.36910	−	0.134844i	0.613404	−	0.789770i	$-0.289800\pi$
$37$	8.32789	−	0.820226i	1.36910	−	0.134844i	0.755694	+	0.654925i	$0.227300\pi$
$38$	6.90508	−	1.31353i	1.12015	−	0.213083i
$39$	−0.0730059	+	0.0145218i	−0.0116903	+	0.00232534i
$40$	9.35510	−	1.61784i	1.47917	−	0.255803i
$41$	0.580168	−	2.91670i	0.0906070	−	0.455512i	−0.908671	−	0.417513i	$-0.862902\pi$
$41$	0.580168	−	2.91670i	0.0906070	−	0.455512i	0.999278	−	0.0379988i	$-0.0120983\pi$
$42$	0.207136	−	0.203698i	0.0319618	−	0.0314312i
$43$	−8.36535	+	4.47137i	−1.27570	+	0.681878i	−0.963391	−	0.268101i	$-0.913604\pi$
$43$	−8.36535	+	4.47137i	−1.27570	+	0.681878i	−0.312313	+	0.949979i	$0.601104\pi$
$44$	0.364787	−	0.104022i	0.0549937	−	0.0156820i
$45$	−9.94237	−	0.979238i	−1.48212	−	0.145976i
$46$	−0.699102	−	7.76365i	−0.103077	−	1.14469i
$47$	−3.57155	+	8.62250i	−0.520965	+	1.25772i	0.416340	+	0.909209i	$0.363313\pi$
$47$	−3.57155	+	8.62250i	−0.520965	+	1.25772i	−0.937305	+	0.348511i	$0.886687\pi$
$48$	−0.488332	+	0.374128i	−0.0704846	+	0.0540007i
$49$	−1.99603	−	4.81884i	−0.285147	−	0.688406i
$50$	−7.85094	+	4.11231i	−1.11029	+	0.581569i
$51$	−0.189301	−	0.230664i	−0.0265075	−	0.0322995i
$52$	−0.296460	+	0.921485i	−0.0411116	+	0.127787i
$53$	−3.12341	+	10.2965i	−0.429033	+	1.41433i	0.430194	+	0.902737i	$0.358445\pi$
$53$	−3.12341	+	10.2965i	−0.429033	+	1.41433i	−0.859227	+	0.511595i	$0.829055\pi$
$54$	1.20501	−	0.487359i	0.163982	−	0.0663212i
$55$	−0.529339	+	0.353693i	−0.0713761	+	0.0476920i
$56$	−1.00558	−	3.64168i	−0.134376	−	0.486640i
$57$	0.424668	−	0.635561i	0.0562487	−	0.0841822i
$58$	10.0107	−	6.56841i	1.31447	−	0.862475i
$59$	−10.8483	−	8.90293i	−1.41232	−	1.15906i	−0.964227	−	0.265077i	$-0.914603\pi$
$59$	−10.8483	−	8.90293i	−1.41232	−	1.15906i	−0.448095	−	0.893986i	$-0.647897\pi$
$60$	0.587888	−	0.848734i	0.0758961	−	0.109571i
$61$	0.339850	−	0.635815i	0.0435134	−	0.0814078i	−0.859225	−	0.511598i	$-0.829054\pi$
$61$	0.339850	−	0.635815i	0.0435134	−	0.0814078i	0.902738	+	0.430190i	$0.141554\pi$
$62$	−5.79966	−	3.16267i	−0.736558	−	0.401659i
$63$			3.97554i			0.500871i
$64$	1.16493	+	7.91473i	0.145617	+	0.989341i
$65$		−	1.62460i		−	0.201507i
$66$	0.0197495	−	0.0362165i	0.00243100	−	0.00445794i
$67$	−0.0570291	+	0.106694i	−0.00696721	+	0.0130347i	−0.885381	−	0.464866i	$-0.846102\pi$
$67$	−0.0570291	+	0.106694i	−0.00696721	+	0.0130347i	0.878414	+	0.477901i	$0.158602\pi$
$68$	−3.81807	+	0.693240i	−0.463009	+	0.0840677i
$69$	−0.655283	−	0.537776i	−0.0788867	−	0.0647407i
$70$	3.47840	+	5.30131i	0.415749	+	0.633628i
$71$	8.81399	−	13.1911i	1.04603	−	1.56549i	0.242567	−	0.970135i	$-0.422011\pi$
$71$	8.81399	−	13.1911i	1.04603	−	1.56549i	0.803461	−	0.595357i	$-0.202989\pi$
$72$	1.03520	−	8.35449i	0.122000	−	0.984586i
$73$	−1.93431	+	1.29247i	−0.226394	+	0.151272i	−0.663595	−	0.748092i	$-0.730970\pi$
$73$	−1.93431	+	1.29247i	−0.226394	+	0.151272i	0.437200	+	0.899364i	$0.355970\pi$
$74$	−4.43717	−	10.9711i	−0.515811	−	1.27536i
$75$	−0.279780	+	0.922310i	−0.0323062	+	0.106499i
$76$	−4.53848	−	8.84383i	−0.520599	−	1.01446i
$77$	0.160715	+	0.195832i	0.0183152	+	0.0223171i
$78$	0.0488446	+	0.0932506i	0.00553056	+	0.0105586i
$79$	−3.11404	−	7.51796i	−0.350357	−	0.845837i	−0.996576	−	0.0826847i	$-0.973651\pi$
$79$	−3.11404	−	7.51796i	−0.350357	−	0.845837i	0.646219	−	0.763152i	$-0.276349\pi$
$80$	−5.92934	−	12.0463i	−0.662921	−	1.34682i
$81$	−3.36290	+	8.11876i	−0.373656	+	0.902085i
$82$	−4.18870	+	0.377184i	−0.462565	+	0.0416530i
$83$	14.1505	+	1.39370i	1.55322	+	0.152979i	0.837903	−	0.545820i	$-0.183782\pi$
$83$	14.1505	+	1.39370i	1.55322	+	0.152979i	0.715318	+	0.698799i	$0.246282\pi$
$84$	−0.359043	−	0.199710i	−0.0391748	−	0.0217901i
$85$	5.74366	−	3.07005i	0.622988	−	0.332994i
$86$	9.40566	+	9.56442i	1.01424	+	1.03136i
$87$	0.254021	−	1.27705i	0.0272339	−	0.136914i
$88$	−0.286745	−	0.453384i	−0.0305671	−	0.0483309i
$89$	−1.57448	+	0.313183i	−0.166894	+	0.0331974i	−0.277830	−	0.960630i	$-0.589615\pi$
$89$	−1.57448	+	0.313183i	−0.166894	+	0.0331974i	0.110936	+	0.993828i	$0.464615\pi$
$90$	2.64030	+	13.8798i	0.278312	+	1.46306i
$91$	−0.643371	+	0.0633666i	−0.0674437	+	0.00664262i
$92$	−10.2539	+	4.04761i	−1.06905	+	0.421992i
$93$	−0.687453	+	0.208537i	−0.0712856	+	0.0216243i
$94$	13.1239	+	1.40358i	1.35363	+	0.144769i
$95$	11.7967	+	11.7967i	1.21031	+	1.21031i
$96$	0.702516	+	0.513177i	0.0717003	+	0.0523759i
$97$	−11.0877	+	11.0877i	−1.12578	+	1.12578i	−0.134927	+	0.990856i	$0.543080\pi$
$97$	−11.0877	+	11.0877i	−1.12578	+	1.12578i	−0.990856	+	0.134927i	$0.956920\pi$
$98$	−5.74097	+	4.63163i	−0.579925	+	0.467865i
$99$	0.163868	+	0.540199i	0.0164693	+	0.0542920i
$100$	8.71317	+	9.00984i	0.871317	+	0.900984i
$101$	0.150952	+	1.53264i	0.0150203	+	0.152504i	0.999769	−	0.0214772i	$-0.00683695\pi$
$101$	0.150952	+	1.53264i	0.0150203	+	0.152504i	−0.984749	+	0.173981i	$0.944337\pi$
$102$	−0.237378	+	0.348904i	−0.0235039	+	0.0345466i
$103$	−2.60627	−	13.1026i	−0.256804	−	1.29104i	−0.866808	−	0.498642i	$-0.833832\pi$
$103$	−2.60627	−	13.1026i	−0.256804	−	1.29104i	0.610004	−	0.792398i	$-0.291168\pi$
$104$	1.36853	+	0.0343664i	0.134195	+	0.00336991i
$105$	0.676281	+	0.134521i	0.0659983	+	0.0131279i
$106$	15.2161	+	0.127345i	1.47792	+	0.0123689i
$107$	2.08456	+	3.89993i	0.201522	+	0.377021i	0.962300	−	0.271992i	$-0.0876823\pi$
$107$	2.08456	+	3.89993i	0.201522	+	0.377021i	−0.760778	+	0.649012i	$0.775182\pi$
$108$	−1.14223	−	1.44030i	−0.109911	−	0.138593i
$109$	−0.181097	+	1.83871i	−0.0173459	+	0.176116i	−0.999954	−	0.00957465i	$-0.996952\pi$
$109$	−0.181097	+	1.83871i	−0.0173459	+	0.176116i	0.982608	+	0.185691i	$0.0594522\pi$
$110$	0.691162	+	0.576969i	0.0658997	+	0.0550118i
$111$	−1.18901	−	0.492504i	−0.112856	−	0.0467464i
$112$	−4.53927	+	2.81798i	−0.428921	+	0.266274i
$113$	3.84674	−	1.59337i	0.361871	−	0.149892i	−0.194337	−	0.980935i	$-0.562256\pi$
$113$	3.84674	−	1.59337i	0.361871	−	0.149892i	0.556208	+	0.831043i	$0.312256\pi$
$114$	−1.03179	−	0.322444i	−0.0966361	−	0.0301997i
$115$	14.3019	−	11.7372i	1.33366	−	1.09450i
$116$	−12.9075	−	10.9595i	−1.19843	−	1.01757i
$117$	−1.37852	−	0.418170i	−0.127444	−	0.0386599i
$118$	−7.74821	+	18.2718i	−0.713280	+	1.68206i
$119$	−1.43982	−	2.15484i	−0.131988	−	0.197534i
$120$	−1.38616	−	0.458791i	−0.126538	−	0.0418817i
$121$	−9.11626	−	6.09129i	−0.828751	−	0.553753i
$122$	−0.998278	−	0.207270i	−0.0903798	−	0.0187653i
$123$	−0.290145	+	0.353543i	−0.0261615	+	0.0318779i
$124$	−1.97568	+	9.13092i	−0.177421	+	0.819981i
$125$	−3.75040	−	2.00463i	−0.335446	−	0.179300i
$126$	5.39364	−	1.58697i	0.480504	−	0.141379i
$127$	−8.79384			−0.780328			−0.390164	−	0.920745i	$-0.627582\pi$
$127$	−8.79384			−0.780328			−0.390164	+	0.920745i	$0.627582\pi$
$128$	10.2729	−	4.73991i	0.908008	−	0.418953i
$129$	1.45879			0.128439
$130$	−2.20411	+	0.648517i	−0.193313	+	0.0568787i
$131$	12.3982	+	6.62696i	1.08323	+	0.579000i	0.913644	−	0.406515i	$-0.133256\pi$
$131$	12.3982	+	6.62696i	1.08323	+	0.579000i	0.169589	+	0.985515i	$0.445756\pi$
$132$	−0.0570188	−	0.0123373i	−0.00496285	−	0.00107382i
$133$	4.21157	−	5.13181i	0.365189	−	0.444985i
$134$	0.167517	+	0.0347811i	0.0144713	+	0.00300463i
$135$	2.56521	+	1.71402i	0.220778	+	0.147519i
$136$	2.46464	+	4.90326i	0.211341	+	0.420451i
$137$	5.95510	+	8.91243i	0.508778	+	0.761440i	0.993574	−	0.113187i	$-0.0361060\pi$
$137$	5.95510	+	8.91243i	0.508778	+	0.761440i	−0.484796	+	0.874628i	$0.661106\pi$
$138$	−0.468026	+	1.10370i	−0.0398410	+	0.0939530i
$139$	−0.316667	−	0.0960600i	−0.0268594	−	0.00814770i	0.276826	−	0.960920i	$-0.410717\pi$
$139$	−0.316667	−	0.0960600i	−0.0268594	−	0.00814770i	−0.303686	+	0.952772i	$0.598217\pi$
$140$	5.80379	−	6.83537i	0.490510	−	0.577694i
$141$	1.10954	−	0.910573i	0.0934398	−	0.0766840i
$142$	−21.4148	−	6.69232i	−1.79709	−	0.561607i
$143$	−0.0848098	+	0.0351294i	−0.00709215	+	0.00293766i
$144$	−11.7478	+	1.93052i	−0.978986	+	0.160876i
$145$	26.2551	+	10.8752i	2.18037	+	0.903137i
$146$	2.52565	+	2.10836i	0.209024	+	0.174489i
$147$	−0.0786262	+	0.798306i	−0.00648498	+	0.0658431i
$148$	−13.1133	+	10.3994i	−1.07791	+	0.854827i
$149$	0.739789	+	1.38405i	0.0606059	+	0.113386i	0.910400	−	0.413729i	$-0.135774\pi$
$149$	0.739789	+	1.38405i	0.0606059	+	0.113386i	−0.849794	+	0.527115i	$0.823274\pi$
$150$	1.36299	+	0.0114070i	0.111287	+	0.000931375i
$151$	−12.0809	−	2.40303i	−0.983126	−	0.195556i	−0.322745	−	0.946486i	$-0.604606\pi$
$151$	−12.0809	−	2.40303i	−0.983126	−	0.195556i	−0.660382	+	0.750930i	$0.729606\pi$
$152$	−10.1868	+	9.68770i	−0.826257	+	0.785776i
$153$	−1.12662	−	5.66388i	−0.0910815	−	0.457898i
$154$	0.201531	−	0.296216i	0.0162399	−	0.0238698i
$155$	−1.53683	−	15.6036i	−0.123441	−	1.25332i
$156$	0.107016	−	0.103492i	0.00856811	−	0.00828599i
$157$	2.19799	+	7.24581i	0.175419	+	0.578278i	0.999923	+	0.0124222i	$0.00395422\pi$
$157$	2.19799	+	7.24581i	0.175419	+	0.578278i	−0.824504	+	0.565856i	$0.808546\pi$
$158$	−8.95659	+	7.22590i	−0.712548	+	0.574861i
$159$	1.17011	−	1.17011i	0.0927960	−	0.0927960i
$160$	−13.9764	+	12.8531i	−1.10493	+	1.01612i
$161$	−5.20598	−	5.20598i	−0.410289	−	0.410289i
$162$	12.3572	+	1.32159i	0.970873	+	0.103834i
$163$	−15.2055	+	4.61255i	−1.19099	+	0.361283i	−0.822726	−	0.568439i	$-0.807548\pi$
$163$	−15.2055	+	4.61255i	−1.19099	+	0.361283i	−0.368264	+	0.929721i	$0.620048\pi$
$164$	2.18379	+	5.53227i	0.170526	+	0.431998i
$165$	0.0974383	−	0.00959683i	0.00758556	−	0.000747113i
$166$	−3.75782	−	19.7544i	−0.291663	−	1.53324i
$167$	14.9692	−	2.97756i	1.15835	−	0.230410i	0.421733	−	0.906720i	$-0.361422\pi$
$167$	14.9692	−	2.97756i	1.15835	−	0.230410i	0.736618	+	0.676310i	$0.236422\pi$
$168$	−0.127623	+	0.566837i	−0.00984632	+	0.0437324i
$169$	−2.49047	+	12.5205i	−0.191575	+	0.963112i
$170$	−6.45794	−	6.56695i	−0.495301	−	0.503662i
$171$	13.0463	−	6.97337i	0.997673	−	0.533267i
$172$	9.22152	−	16.5787i	0.703134	−	1.26411i
$173$	−15.3857	−	1.51536i	−1.16975	−	0.115210i	−0.505572	−	0.862784i	$-0.668719\pi$
$173$	−15.3857	−	1.51536i	−1.16975	−	0.115210i	−0.664179	+	0.747574i	$0.731219\pi$
$174$	−1.83398	+	0.165147i	−0.139034	+	0.0125197i
$175$	−3.20336	+	7.73360i	−0.242151	+	0.584605i
$176$	−0.500645	+	0.570012i	−0.0377375	+	0.0429663i
$177$	0.825948	+	1.99401i	0.0620820	+	0.149879i
$178$	1.05341	+	2.01109i	0.0789561	+	0.150737i
$179$	−8.70051	−	10.6016i	−0.650307	−	0.792401i	0.338601	−	0.940930i	$-0.390046\pi$
$179$	−8.70051	−	10.6016i	−0.650307	−	0.792401i	−0.988908	+	0.148529i	$0.952546\pi$
$180$	17.7768	−	9.12270i	1.32500	−	0.679966i
$181$	2.43393	−	8.02359i	0.180913	−	0.596389i	−0.818837	−	0.574026i	$-0.805381\pi$
$181$	2.43393	−	8.02359i	0.180913	−	0.596389i	0.999750	−	0.0223633i	$-0.00711904\pi$
$182$	0.342794	+	0.847571i	0.0254096	+	0.0628261i
$183$	−0.0921905	+	0.0615997i	−0.00681492	+	0.00455358i
$184$	9.58462	+	12.2958i	0.706588	+	0.906460i
$185$	15.6053	−	23.3550i	1.14733	−	1.71710i
$186$	0.557344	+	0.849428i	0.0408664	+	0.0622831i
$187$	−0.284464	−	0.233454i	−0.0208021	−	0.0170718i
$188$	−3.33461	−	18.3656i	−0.243201	−	1.33945i
$189$	0.578727	−	1.08272i	0.0420962	−	0.0787564i
$190$	11.2956	−	20.7137i	0.819468	−	1.50273i
$191$			5.63943i			0.408055i	0.978965	+	0.204027i	$0.0654032\pi$
$191$			5.63943i			0.408055i	−0.978965	+	0.204027i	$0.934597\pi$
$192$	0.415796	−	1.15796i	0.0300075	−	0.0835686i
$193$			2.21104i			0.159154i	0.996829	+	0.0795769i	$0.0253569\pi$
$193$			2.21104i			0.159154i	−0.996829	+	0.0795769i	$0.974643\pi$
$194$	19.4687	+	10.6167i	1.39777	+	0.762234i
$195$	−0.117780	+	0.220351i	−0.00843442	+	0.0157797i
$196$	8.57547	+	5.93993i	0.612533	+	0.424281i
$197$	−6.53350	−	5.36190i	−0.465493	−	0.382020i	0.372208	−	0.928149i	$-0.378601\pi$
$197$	−6.53350	−	5.36190i	−0.465493	−	0.382020i	−0.837701	+	0.546129i	$0.816101\pi$
$198$	0.667478	−	0.437959i	0.0474356	−	0.0311244i
$199$	−7.32240	+	10.9587i	−0.519071	+	0.776845i	−0.994702	−	0.102800i	$-0.967220\pi$
$199$	−7.32240	+	10.9587i	−0.519071	+	0.776845i	0.475631	+	0.879645i	$0.342220\pi$
$200$	8.74555	−	15.4178i	0.618404	−	1.09020i
$201$	0.0154701	−	0.0103368i	0.00109118	−	0.000729103i
$202$	2.01909	−	0.816604i	0.142062	−	0.0574561i
$203$	3.28271	−	10.8216i	0.230401	−	0.759531i
$204$	0.568118	+	0.182775i	0.0397762	+	0.0127968i
$205$	−6.33255	−	7.71624i	−0.442285	−	0.538926i
$206$	−16.7360	+	8.76631i	−1.16605	+	0.610778i
$207$	−6.27810	−	15.1567i	−0.436358	−	1.05346i
$208$	−0.499670	−	1.87041i	−0.0346459	−	0.129689i
$209$	0.360743	−	0.870910i	0.0249531	−	0.0602421i
$210$	−0.0874559	−	0.971214i	−0.00603503	−	0.0670201i
$211$	−5.77547	−	0.568835i	−0.397600	−	0.0391602i	−0.102758	−	0.994706i	$-0.532767\pi$
$211$	−5.77547	−	0.568835i	−0.397600	−	0.0391602i	−0.294842	+	0.955546i	$0.595267\pi$
$212$	−5.90127	−	20.6947i	−0.405301	−	1.42131i
$213$	−2.15180	+	1.15016i	−0.147439	+	0.0788077i
$214$	4.45894	−	4.38492i	0.304807	−	0.299747i
$215$	−6.21144	+	31.2270i	−0.423617	+	2.12967i
$216$	−1.49811	+	2.12461i	−0.101934	+	0.144562i
$217$	−6.11937	+	1.21722i	−0.415410	+	0.0826302i
$218$	2.56687	−	0.488288i	0.173851	−	0.0330710i
$219$	0.356060	−	0.0350688i	0.0240603	−	0.00236973i
$220$	0.506876	−	1.16802i	0.0341736	−	0.0787479i
$221$	0.898642	−	0.272600i	0.0604492	−	0.0183371i
$222$	−0.193549	+	1.80974i	−0.0129901	+	0.121462i
$223$	1.95160	+	1.95160i	0.130689	+	0.130689i	0.769425	−	0.638737i	$-0.220543\pi$
$223$	1.95160	+	1.95160i	0.130689	+	0.130689i	−0.638737	+	0.769425i	$0.720543\pi$
$224$	5.63518	+	5.03357i	0.376516	+	0.336319i
$225$	−13.1893	+	13.1893i	−0.879287	+	0.879287i
$226$	−3.69730	−	4.58285i	−0.245941	−	0.304847i
$227$	4.38810	+	14.4656i	0.291248	+	0.960117i	0.973440	+	0.228944i	$0.0735271\pi$
$227$	4.38810	+	14.4656i	0.291248	+	0.960117i	−0.682191	+	0.731174i	$0.738973\pi$
$228$	−0.0255870	+	1.52855i	−0.00169454	+	0.101231i
$229$	0.0144057	+	0.146264i	0.000951955	+	0.00966536i	0.995649	−	0.0931833i	$-0.0297043\pi$
$229$	0.0144057	+	0.146264i	0.000951955	+	0.00966536i	−0.994697	+	0.102849i	$0.967204\pi$
$230$	−21.6331	−	14.7181i	−1.42644	−	0.970483i
$231$	−0.00760102	−	0.0382129i	−0.000500111	−	0.00251423i
$232$	−9.71641	+	21.8866i	−0.637913	+	1.43693i
$233$	−20.2728	−	4.03251i	−1.32811	−	0.264178i	−0.520486	−	0.853870i	$-0.674249\pi$
$233$	−20.2728	−	4.03251i	−1.32811	−	0.264178i	−0.807628	+	0.589692i	$0.799249\pi$
$234$	−0.0170493	+	2.03718i	−0.00111455	+	0.133174i
$235$	14.7675	+	27.6280i	0.963325	+	1.80225i
$236$	27.8824	+	3.21822i	1.81499	+	0.209488i
$237$	−0.122666	+	1.24545i	−0.00796803	+	0.0809008i
$238$	−2.34874	+	2.81359i	−0.152246	+	0.182378i
$239$	−12.4323	−	5.14962i	−0.804177	−	0.333101i	−0.0575490	−	0.998343i	$-0.518329\pi$
$239$	−12.4323	−	5.14962i	−0.804177	−	0.333101i	−0.746628	+	0.665242i	$0.768329\pi$
$240$	−0.0691112	+	2.06375i	−0.00446111	+	0.133215i
$241$	16.5636	−	6.86086i	1.06695	−	0.441947i	0.221039	−	0.975265i	$-0.429055\pi$
$241$	16.5636	−	6.86086i	1.06695	−	0.441947i	0.845915	+	0.533318i	$0.179055\pi$
$242$	−4.62502	+	14.7996i	−0.297308	+	0.951356i
$243$	3.17619	−	2.60664i	0.203753	−	0.167216i
$244$	0.117293	+	1.43711i	0.00750892	+	0.0920014i
$245$	−16.7538	−	5.08222i	−1.07036	−	0.324691i
$246$	0.595475	+	0.252513i	0.0379661	+	0.0160996i
$247$	1.33646	+	2.00016i	0.0850371	+	0.127267i
$248$	13.1766	−	0.964509i	0.836717	−	0.0612464i
$249$	−1.81825	−	1.21492i	−0.115227	−	0.0769921i
$250$	−1.22259	+	5.88841i	−0.0773236	+	0.372416i
$251$	−10.4175	+	12.6937i	−0.657546	+	0.801222i	−0.989875	−	0.141941i	$-0.954666\pi$
$251$	−10.4175	+	12.6937i	−0.657546	+	0.801222i	0.332329	+	0.943164i	$0.392166\pi$
$252$	−4.30612	−	6.68409i	−0.271260	−	0.421058i
$253$	−0.921976	−	0.492807i	−0.0579642	−	0.0309825i
$254$	3.51037	+	11.9307i	0.220260	+	0.748596i
$255$	−1.00161			−0.0627231
$256$	−10.5315	−	12.0453i	−0.658216	−	0.752829i
$257$	4.49360			0.280303			0.140152	−	0.990130i	$-0.455241\pi$
$257$	4.49360			0.280303			0.140152	+	0.990130i	$0.455241\pi$
$258$	−0.582326	−	1.97915i	−0.0362541	−	0.123216i
$259$	−9.85766	−	5.26903i	−0.612525	−	0.327402i
$260$	1.75969	+	2.73145i	0.109132	+	0.169398i
$261$	15.9859	−	19.4789i	0.989504	−	1.20571i
$262$	4.04168	−	19.4660i	0.249696	−	1.20262i
$263$	14.2440	+	9.51756i	0.878325	+	0.586878i	0.910916	−	0.412591i	$-0.135376\pi$
$263$	14.2440	+	9.51756i	0.878325	+	0.586878i	−0.0325916	+	0.999469i	$0.510376\pi$
$264$	0.00602296	+	0.0822826i	0.000370687	+	0.00506415i
$265$	20.0653	+	30.0299i	1.23260	+	1.84472i
$266$	−8.64355	−	3.66532i	−0.529970	−	0.224735i
$267$	0.236258	+	0.0716680i	0.0144587	+	0.00438601i
$268$	−0.0196825	−	0.241156i	−0.00120230	−	0.0147309i
$269$	11.4987	−	9.43672i	0.701087	−	0.575367i	−0.214870	−	0.976643i	$-0.568933\pi$
$269$	11.4987	−	9.43672i	0.701087	−	0.575367i	0.915957	+	0.401275i	$0.131433\pi$
$270$	1.30143	−	4.16445i	0.0792024	−	0.253440i
$271$	−11.5173	+	4.77061i	−0.699624	+	0.289794i	−0.704003	−	0.710197i	$-0.748606\pi$
$271$	−11.5173	+	4.77061i	−0.699624	+	0.289794i	0.00437943	+	0.999990i	$0.498606\pi$
$272$	5.66844	−	5.30109i	0.343700	−	0.321426i
$273$	0.0918569	+	0.0380484i	0.00555943	+	0.00230279i
$274$	9.71437	−	11.6370i	0.586866	−	0.703018i
$275$	−0.116504	+	1.18288i	−0.00702545	+	0.0713306i
$276$	1.68422	+	0.194395i	0.101378	+	0.0117012i
$277$	5.09008	+	9.52286i	0.305833	+	0.572173i	0.987146	−	0.159819i	$-0.0510909\pi$
$277$	5.09008	+	9.52286i	0.305833	+	0.572173i	−0.681313	+	0.731992i	$0.738591\pi$
$278$	−0.00391649	+	0.467970i	−0.000234895	+	0.0280670i
$279$	−13.6357	−	2.71231i	−0.816348	−	0.162382i
$280$	−11.5904	−	5.14547i	−0.692657	−	0.307501i
$281$	5.00511	+	25.1624i	0.298580	+	1.50106i	0.780671	+	0.624942i	$0.214877\pi$
$281$	5.00511	+	25.1624i	0.298580	+	1.50106i	−0.482091	+	0.876121i	$0.660123\pi$
$282$	−1.67829	−	1.14183i	−0.0999407	−	0.0679949i
$283$	−1.47858	−	15.0123i	−0.0878928	−	0.892390i	−0.933498	−	0.358582i	$-0.883260\pi$
$283$	−1.47858	−	15.0123i	−0.0878928	−	0.892390i	0.845606	−	0.533808i	$-0.179240\pi$
$284$	−0.531058	+	31.7251i	−0.0315125	+	1.88254i
$285$	−0.744796	−	2.45526i	−0.0441179	−	0.145437i
$286$	0.0815150	+	0.101039i	0.00482008	+	0.00597455i
$287$	−2.80877	+	2.80877i	−0.165796	+	0.165796i
$288$	7.30869	+	15.1677i	0.430669	+	0.893766i
$289$	−9.35887	−	9.35887i	−0.550522	−	0.550522i
$290$	4.27385	−	39.9617i	0.250969	−	2.34663i
$291$	2.30770	−	0.700032i	0.135280	−	0.0410366i
$292$	1.85223	−	4.26819i	0.108394	−	0.249777i
$293$	0.107888	−	0.0106261i	0.00630290	−	0.000620782i	−0.0948652	−	0.995490i	$-0.530242\pi$
$293$	0.107888	−	0.0106261i	0.00630290	−	0.000620782i	0.101168	+	0.994869i	$0.467742\pi$
$294$	1.11445	−	0.211999i	0.0649962	−	0.0123640i
$295$	−46.2009	+	9.18994i	−2.68992	+	0.535059i
$296$	19.3436	+	13.6396i	1.12432	+	0.792785i
$297$	0.0340091	−	0.170975i	0.00197341	−	0.00992099i
$298$	1.58244	−	1.55617i	0.0916680	−	0.0901464i
$299$	2.35277	−	1.25758i	0.136064	−	0.0727279i
$300$	−0.528607	−	1.85373i	−0.0305192	−	0.107025i
$301$	12.6087	+	1.24185i	0.726754	+	0.0715790i
$302$	1.56228	+	17.3494i	0.0898993	+	0.998348i
$303$	0.0906390	−	0.218822i	0.00520707	−	0.0125710i
$304$	17.2098	+	9.95329i	0.987048	+	0.570861i
$305$	−0.926069	−	2.23573i	−0.0530266	−	0.128017i
$306$	−7.23450	+	3.78942i	−0.413569	+	0.216627i
$307$	11.1702	+	13.6110i	0.637518	+	0.776818i	0.987103	−	0.160087i	$-0.0511773\pi$
$307$	11.1702	+	13.6110i	0.637518	+	0.776818i	−0.349585	+	0.936905i	$0.613677\pi$
$308$	−0.482326	−	0.155174i	−0.0274831	−	0.00884185i
$309$	−0.596413	+	1.96611i	−0.0339287	+	0.111848i
$310$	−20.5561	+	8.31376i	−1.16751	+	0.472190i
$311$	18.5250	−	12.3780i	1.05045	−	0.701891i	0.0945355	−	0.995521i	$-0.469863\pi$
$311$	18.5250	−	12.3780i	1.05045	−	0.701891i	0.955919	+	0.293630i	$0.0948634\pi$
$312$	−0.183127	−	0.103877i	−0.0103675	−	0.00588085i
$313$	8.47932	−	12.6902i	0.479279	−	0.717292i	−0.510503	−	0.859876i	$-0.670541\pi$
$313$	8.47932	−	12.6902i	0.479279	−	0.717292i	0.989783	+	0.142583i	$0.0455409\pi$
$314$	8.95303	−	5.87444i	0.505249	−	0.331514i
$315$	10.3154	+	8.46559i	0.581204	+	0.476982i
$316$	13.3788	+	9.26700i	0.752614	+	0.521309i
$317$	0.174406	−	0.326290i	0.00979561	−	0.0183263i	−0.876976	−	0.480534i	$-0.840443\pi$
$317$	0.174406	−	0.326290i	0.00979561	−	0.0183263i	0.886771	+	0.462208i	$0.152943\pi$
$318$	−2.05459	−	1.12041i	−0.115216	−	0.0628294i
$319$		−	1.60576i		−	0.0899054i
$320$	23.0170	+	13.8311i	1.28669	+	0.773183i
$321$		−	0.680089i		−	0.0379589i
$322$	−4.98484	+	9.14113i	−0.277794	+	0.509415i
$323$	−4.54586	+	8.50470i	−0.252938	+	0.473214i
$324$	−3.13980	−	17.2926i	−0.174433	−	0.960702i
$325$	−2.34468	−	1.92423i	−0.130060	−	0.106737i
$326$	12.3277	+	18.7882i	0.682767	+	1.04058i
$327$	0.157865	−	0.236262i	0.00872995	−	0.0130653i
$328$	6.63393	−	5.17116i	0.366297	−	0.285530i
$329$	10.3652	−	6.92579i	0.571451	−	0.381831i
$330$	−0.0519159	−	0.128364i	−0.00285788	−	0.00706622i
$331$	−2.83863	+	9.35771i	−0.156025	+	0.514346i	−0.999748	−	0.0224324i	$-0.992859\pi$
$331$	−2.83863	+	9.35771i	−0.156025	+	0.514346i	0.843723	+	0.536779i	$0.180359\pi$
$332$	−25.3009	+	12.9839i	−1.38857	+	0.712585i
$333$	−15.8006	−	19.2531i	−0.865868	−	1.05506i
$334$	−10.0151	−	19.1202i	−0.548004	−	1.04621i
$335$	0.155400	+	0.375169i	0.00849042	+	0.0204977i
$336$	0.819977	−	0.0531260i	0.0447334	−	0.00289826i
$337$	1.79808	−	4.34094i	0.0979475	−	0.236466i	−0.867309	−	0.497770i	$-0.834152\pi$
$337$	1.79808	−	4.34094i	0.0979475	−	0.236466i	0.965257	+	0.261304i	$0.0841524\pi$
$338$	17.9807	−	1.61913i	0.978023	−	0.0880691i
$339$	−0.637265	−	0.0627651i	−0.0346115	−	0.00340893i
$340$	−6.33151	+	11.3829i	−0.343374	+	0.617327i
$341$	−0.781331	+	0.417630i	−0.0423114	+	0.0226159i
$342$	−14.6687	−	14.9163i	−0.793192	−	0.806580i
$343$	−3.18327	+	16.0034i	−0.171880	+	0.864100i
$344$	−26.1735	−	5.89293i	−1.41118	−	0.317726i
$345$	−2.79074	+	0.555113i	−0.150248	+	0.0298863i
$346$	4.08583	+	21.4787i	0.219656	+	1.15470i
$347$	20.0724	−	1.97696i	1.07754	−	0.106129i	0.456360	−	0.889795i	$-0.349153\pi$
$347$	20.0724	−	1.97696i	1.07754	−	0.106129i	0.621182	+	0.783666i	$0.286653\pi$
$348$	0.956154	+	2.42225i	0.0512552	+	0.129846i
$349$	27.5367	−	8.35317i	1.47401	−	0.447135i	0.551847	−	0.833946i	$-0.313923\pi$
$349$	27.5367	−	8.35317i	1.47401	−	0.447135i	0.922159	+	0.386811i	$0.126423\pi$
$350$	11.7710	+	1.25889i	0.629184	+	0.0672904i
$351$	0.314561	+	0.314561i	0.0167900	+	0.0167900i
$352$	0.973189	+	0.451688i	0.0518712	+	0.0240751i
$353$	12.0137	−	12.0137i	0.639425	−	0.639425i	−0.310989	−	0.950414i	$-0.600660\pi$
$353$	12.0137	−	12.0137i	0.639425	−	0.639425i	0.950414	+	0.310989i	$0.100660\pi$
$354$	2.37559	−	1.91655i	0.126261	−	0.101863i
$355$	−15.4582	−	50.9590i	−0.820438	−	2.70462i
$356$	2.30795	−	2.23196i	0.122321	−	0.118293i
$357$	0.0390670	+	0.396654i	0.00206764	+	0.0209931i
$358$	−10.9102	+	16.0360i	−0.576619	+	0.847531i
$359$	−6.61583	−	33.2600i	−0.349170	−	1.75540i	−0.612290	−	0.790633i	$-0.709752\pi$
$359$	−6.61583	−	33.2600i	−0.349170	−	1.75540i	0.263120	−	0.964763i	$-0.415248\pi$
$360$	−19.4730	−	20.4763i	−1.02632	−	1.07919i
$361$	−5.59318	−	1.11255i	−0.294378	−	0.0585554i
$362$	−11.8572	−	0.0992344i	−0.623203	−	0.00521565i
$363$	0.794868	+	1.48709i	0.0417198	+	0.0780522i
$364$	1.01307	−	0.803408i	0.0530991	−	0.0421100i
$365$	−0.765394	+	7.77117i	−0.0400625	+	0.406762i
$366$	0.120374	+	0.100486i	0.00629203	+	0.00525247i
$367$	22.3629	+	9.26301i	1.16733	+	0.483525i	0.880310	−	0.474399i	$-0.157334\pi$
$367$	22.3629	+	9.26301i	1.16733	+	0.483525i	0.287023	+	0.957924i	$0.407334\pi$
$368$	12.8558	−	17.9118i	0.670154	−	0.933718i
$369$	−8.17743	+	3.38720i	−0.425700	+	0.176331i
$370$	−37.9153	−	11.8489i	−1.97112	−	0.615994i
$371$	11.1097	−	9.11750i	0.576787	−	0.473357i
$372$	0.929941	−	1.09523i	0.0482152	−	0.0567850i
$373$	−31.7137	−	9.62025i	−1.64207	−	0.498118i	−0.671923	−	0.740621i	$-0.734532\pi$
$373$	−31.7137	−	9.62025i	−1.64207	−	0.498118i	−0.970151	+	0.242503i	$0.922032\pi$
$374$	−0.203174	+	0.479125i	−0.0105059	+	0.0247750i
$375$	0.363350	+	0.543792i	0.0187633	+	0.0280813i
$376$	−23.5856	+	11.8553i	−1.21633	+	0.611392i
$377$	3.40712	+	2.27657i	0.175476	+	0.117249i
$378$	−1.69995	−	0.352956i	−0.0874362	−	0.0181541i
$379$	−3.38631	+	4.12623i	−0.173943	+	0.211950i	−0.852683	−	0.522428i	$-0.825026\pi$
$379$	−3.38631	+	4.12623i	−0.173943	+	0.211950i	0.678740	+	0.734379i	$0.262526\pi$
$380$	−32.6114	−	7.05620i	−1.67293	−	0.361976i
$381$	1.19274	+	0.637535i	0.0611061	+	0.0326619i
$382$	7.65105	−	2.25117i	0.391462	−	0.115180i
$383$	13.1180			0.670298			0.335149	−	0.942165i	$-0.391213\pi$
$383$	13.1180			0.670298			0.335149	+	0.942165i	$0.391213\pi$
$384$	−1.73699	−	0.101874i	−0.0886405	−	0.00519871i
$385$	0.850355			0.0433381
$386$	2.99973	−	0.882611i	0.152682	−	0.0449237i
$387$	24.8982	+	13.3084i	1.26565	+	0.676502i
$388$	6.63211	−	30.6514i	0.336694	−	1.55609i
$389$	−0.145657	+	0.177483i	−0.00738509	+	0.00899876i	−0.776690	−	0.629883i	$-0.783103\pi$
$389$	−0.145657	+	0.177483i	−0.00738509	+	0.00899876i	0.769305	+	0.638882i	$0.220603\pi$
$390$	0.345968	+	0.0718324i	0.0175188	+	0.00363737i
$391$	8.89217	+	5.94156i	0.449697	+	0.300478i
$392$	4.63555	−	14.0055i	0.234130	−	0.707385i
$393$	−1.20117	−	1.79768i	−0.0605911	−	0.0906810i
$394$	−4.66646	+	11.0044i	−0.235093	+	0.554395i
$395$	−26.1380	−	7.92887i	−1.31515	−	0.398945i
$396$	−0.860629	−	0.730745i	−0.0432482	−	0.0367213i
$397$	14.6428	−	12.0170i	0.734899	−	0.603116i	−0.190688	−	0.981651i	$-0.561072\pi$
$397$	14.6428	−	12.0170i	0.734899	−	0.603116i	0.925587	+	0.378535i	$0.123572\pi$
$398$	17.7908	+	5.55978i	0.891771	+	0.278687i
$399$	−0.943277	+	0.390718i	−0.0472229	+	0.0195604i
$400$	−24.4085	−	5.71059i	−1.22043	−	0.285530i
$401$	−31.8230	−	13.1815i	−1.58917	−	0.658254i	−0.599334	−	0.800499i	$-0.704568\pi$
$401$	−31.8230	−	13.1815i	−1.58917	−	0.658254i	−0.989831	+	0.142245i	$0.954568\pi$
$402$	−0.0201995	−	0.0168621i	−0.00100746	−	0.000841007i
$403$	0.221599	−	2.24993i	0.0110386	−	0.112077i
$404$	−1.91388	−	2.41333i	−0.0952191	−	0.120068i
$405$	13.9048	+	26.0140i	0.690933	+	1.29265i
$406$	−15.9922	−	0.133840i	−0.793680	−	0.00664238i
$407$	−1.55665	−	0.309637i	−0.0771602	−	0.0153481i
$408$	0.0211877	−	0.843729i	0.00104895	−	0.0417708i
$409$	5.18514	+	26.0675i	0.256389	+	1.28895i	0.867511	+	0.497418i	$0.165718\pi$
$409$	5.18514	+	26.0675i	0.256389	+	1.28895i	−0.611122	+	0.791536i	$0.709282\pi$
$410$	−7.94081	+	11.6716i	−0.392169	+	0.576420i
$411$	−0.161581	−	1.64056i	−0.00797020	−	0.0809228i
$412$	18.5741	+	19.2065i	0.915079	+	0.946236i
$413$	5.44141	+	17.9379i	0.267754	+	0.882667i
$414$	−18.0570	+	14.5678i	−0.887455	+	0.715970i
$415$	33.7486	−	33.7486i	1.65665	−	1.65665i
$416$	−2.33813	+	1.42454i	−0.114636	+	0.0698440i
$417$	0.0359867	+	0.0359867i	0.00176228	+	0.00176228i
$418$	−1.32557	−	0.141768i	−0.0648358	−	0.00693410i
$419$	−21.7315	+	6.59218i	−1.06165	+	0.322049i	−0.772356	−	0.635190i	$-0.780922\pi$
$419$	−21.7315	+	6.59218i	−1.06165	+	0.322049i	−0.289298	+	0.957239i	$0.593422\pi$
$420$	−1.28274	+	0.506345i	−0.0625913	+	0.0247071i
$421$	−29.7632	+	2.93141i	−1.45057	+	0.142868i	−0.792399	−	0.610003i	$-0.791168\pi$
$421$	−29.7632	+	2.93141i	−1.45057	+	0.142868i	−0.658168	+	0.752871i	$0.728668\pi$
$422$	1.53374	+	8.06269i	0.0746612	+	0.392486i
$423$	27.2443	−	5.41922i	1.32466	−	0.263492i
$424$	−25.7209	+	16.2673i	−1.24912	+	0.790009i
$425$	2.37217	−	11.9257i	0.115067	−	0.578482i
$426$	2.41940	+	2.46023i	0.117220	+	0.119199i
$427$	−0.849266	+	0.453942i	−0.0410989	+	0.0219678i
$428$	−7.72899	−	4.29908i	−0.373595	−	0.207804i
$429$	0.0140499	+	0.00138379i	0.000678335	+	6.68101e-5i
$430$	44.8454	−	4.03824i	2.16264	−	0.194741i
$431$	5.85086	−	14.1252i	0.281826	−	0.680388i	−0.718052	−	0.695989i	$-0.754966\pi$
$431$	5.85086	−	14.1252i	0.281826	−	0.680388i	0.999878	+	0.0156011i	$0.00496618\pi$
$432$	3.48050	+	1.18438i	0.167456	+	0.0569837i
$433$	−11.6465	−	28.1171i	−0.559694	−	1.35122i	−0.910009	−	0.414589i	$-0.863925\pi$
$433$	−11.6465	−	28.1171i	−0.559694	−	1.35122i	0.350315	−	0.936632i	$-0.386075\pi$
$434$	4.09417	+	7.81629i	0.196526	+	0.375194i
$435$	−2.77265	−	3.37848i	−0.132938	−	0.161986i
$436$	−1.68712	−	3.28758i	−0.0807984	−	0.157446i
$437$	−7.95246	+	26.2158i	−0.380418	+	1.25407i
$438$	−0.189712	−	0.469069i	−0.00906477	−	0.0224130i
$439$	1.85148	−	1.23712i	0.0883664	−	0.0590445i	−0.510602	−	0.859817i	$-0.670577\pi$
$439$	1.85148	−	1.23712i	0.0883664	−	0.0590445i	0.598968	+	0.800773i	$0.295577\pi$
$440$	−1.78700	−	0.221427i	−0.0851918	−	0.0105561i
$441$	−8.62481	+	12.9079i	−0.410705	+	0.614664i
$442$	−0.728563	−	1.11038i	−0.0346542	−	0.0528152i
$443$	−16.0609	−	13.1808i	−0.763075	−	0.626239i	0.170197	−	0.985410i	$-0.445560\pi$
$443$	−16.0609	−	13.1808i	−0.763075	−	0.626239i	−0.933272	+	0.359171i	$0.883060\pi$
$444$	2.53254	−	0.459830i	0.120189	−	0.0218225i
$445$	−2.54011	+	4.75221i	−0.120413	+	0.225276i
$446$	1.86870	−	3.42679i	0.0884854	−	0.162263i
$447$		−	0.241357i		−	0.0114158i
$448$	4.57960	−	9.65460i	0.216366	−	0.456137i
$449$		−	12.0240i		−	0.567447i	−0.958906	−	0.283724i	$-0.908430\pi$
$449$		−	12.0240i		−	0.567447i	0.958906	−	0.283724i	$-0.0915698\pi$
$450$	23.1590	+	12.6291i	1.09173	+	0.595339i
$451$	−0.265882	+	0.497431i	−0.0125199	+	0.0234231i
$452$	−4.74168	+	6.84555i	−0.223030	+	0.321988i
$453$	1.46436	+	1.20177i	0.0688016	+	0.0564640i
$454$	17.8739	−	11.7278i	0.838866	−	0.550414i
$455$	−1.20559	+	1.80429i	−0.0565189	+	0.0845865i
$456$	2.08401	−	0.575460i	0.0975927	−	0.0269484i
$457$	9.55723	−	6.38594i	0.447068	−	0.298722i	−0.311582	−	0.950219i	$-0.600859\pi$
$457$	9.55723	−	6.38594i	0.447068	−	0.298722i	0.758651	+	0.651498i	$0.225859\pi$
$458$	0.192686	−	0.0779304i	0.00900363	−	0.00364145i
$459$	−0.517672	+	1.70654i	−0.0241629	+	0.0796543i
$460$	−11.3326	+	35.2249i	−0.528383	+	1.64237i
$461$	8.79720	+	10.7194i	0.409727	+	0.499253i	0.936459	−	0.350778i	$-0.114083\pi$
$461$	8.79720	+	10.7194i	0.409727	+	0.499253i	−0.526732	+	0.850031i	$0.676583\pi$
$462$	−0.0488095	+	0.0255664i	−0.00227082	+	0.00118945i
$463$	−3.77259	−	9.10783i	−0.175327	−	0.423277i	0.811649	−	0.584146i	$-0.198570\pi$
$463$	−3.77259	−	9.10783i	−0.175327	−	0.423277i	−0.986976	+	0.160869i	$0.948570\pi$
$464$	33.5723	+	4.44552i	1.55856	+	0.206378i
$465$	−0.922785	+	2.22780i	−0.0427931	+	0.103312i
$466$	2.62165	+	29.1139i	0.121446	+	1.34868i
$467$	−29.6180	−	2.91712i	−1.37056	−	0.134988i	−0.614202	−	0.789149i	$-0.710522\pi$
$467$	−29.6180	−	2.91712i	−1.37056	−	0.134988i	−0.756356	+	0.654161i	$0.773022\pi$
$468$	2.77066	−	0.790079i	0.128074	−	0.0365214i
$469$	0.142512	−	0.0761744i	0.00658060	−	0.00351741i
$470$	31.5882	−	31.0638i	1.45705	−	1.43287i
$471$	0.227183	−	1.14213i	0.0104680	−	0.0526264i
$472$	−6.76406	−	39.1129i	−0.311341	−	1.80032i
$473$	1.76447	−	0.350974i	0.0811303	−	0.0161378i
$474$	1.73868	−	0.330743i	0.0798602	−	0.0151915i
$475$	30.9977	−	3.05301i	1.42227	−	0.140082i
$476$	4.75480	+	2.06340i	0.217936	+	0.0945759i
$477$	30.6459	−	9.29634i	1.40318	−	0.425650i
$478$	−2.02375	+	18.9226i	−0.0925640	+	0.865499i
$479$	−1.25772	−	1.25772i	−0.0574668	−	0.0574668i	0.677789	−	0.735256i	$-0.262938\pi$
$479$	−1.25772	−	1.25772i	−0.0574668	−	0.0574668i	−0.735256	+	0.677789i	$0.762938\pi$
$480$	2.82749	−	0.730054i	0.129057	−	0.0333223i
$481$	2.86393	−	2.86393i	0.130584	−	0.130584i
$482$	−15.9201	−	19.7332i	−0.725141	−	0.898821i
$483$	0.328685	+	1.08353i	0.0149557	+	0.0493023i
$484$	21.9250	+	0.367010i	0.996590	+	0.0166823i
$485$	5.15893	+	52.3795i	0.234255	+	2.37843i
$486$	−4.80433	−	3.26863i	−0.217929	−	0.148268i
$487$	2.68056	+	13.4761i	0.121468	+	0.610661i	0.992782	+	0.119935i	$0.0382685\pi$
$487$	2.68056	+	13.4761i	0.121468	+	0.610661i	−0.871314	+	0.490726i	$0.836732\pi$
$488$	1.90291	−	0.732804i	0.0861408	−	0.0331725i
$489$	2.39679	+	0.476750i	0.108386	+	0.0215594i
$490$	−0.207209	+	24.7588i	−0.00936073	+	1.11849i
$491$	14.1771	+	26.5235i	0.639804	+	1.19699i	0.967659	+	0.252261i	$0.0811740\pi$
$491$	14.1771	+	26.5235i	0.639804	+	1.19699i	−0.327856	+	0.944728i	$0.606326\pi$
$492$	0.104881	−	0.908683i	0.00472841	−	0.0409666i
$493$	−1.61011	+	16.3477i	−0.0725155	+	0.736263i
$494$	2.18013	−	2.61162i	0.0980888	−	0.117502i
$495$	1.75060	+	0.725122i	0.0786836	+	0.0325918i
$496$	−6.56847	−	17.4918i	−0.294933	−	0.785406i
$497$	−19.5777	+	8.10935i	−0.878180	+	0.363754i
$498$	−0.922466	+	2.95180i	−0.0413367	+	0.132274i
$499$	−3.93306	+	3.22778i	−0.176068	+	0.144495i	−0.718300	−	0.695734i	$-0.755079\pi$
$499$	−3.93306	+	3.22778i	−0.176068	+	0.144495i	0.542232	+	0.840229i	$0.317579\pi$
$500$	8.47689	−	0.691862i	0.379098	−	0.0309410i
$501$	−2.24620	−	0.681376i	−0.100353	−	0.0304416i
$502$	21.3802	+	9.06632i	0.954244	+	0.404650i
$503$	8.17711	+	12.2379i	0.364599	+	0.545661i	0.967733	−	0.251979i	$-0.0810814\pi$
$503$	8.17711	+	12.2379i	0.364599	+	0.545661i	−0.603134	+	0.797640i	$0.706081\pi$
$504$	−7.34941	+	8.51032i	−0.327369	+	0.379080i
$505$	4.29819	+	2.87196i	0.191267	+	0.127800i
$506$	−0.300555	+	1.44757i	−0.0133613	+	0.0643524i
$507$	1.24550	−	1.51764i	0.0553145	−	0.0674009i
$508$	14.7851	−	9.52507i	0.655984	−	0.422607i
$509$	−14.7190	−	7.86746i	−0.652407	−	0.348719i	0.111762	−	0.993735i	$-0.464351\pi$
$509$	−14.7190	−	7.86746i	−0.652407	−	0.348719i	−0.764169	+	0.645016i	$0.776851\pi$
$510$	0.399826	+	1.35889i	0.0177046	+	0.0601725i
$511$	3.10737			0.137462
$512$	−12.1379	+	19.0964i	−0.536424	+	0.843949i
$513$	−4.56822			−0.201692
$514$	−1.79378	−	6.09650i	−0.0791200	−	0.268905i
$515$	−39.5473	−	21.1385i	−1.74266	−	0.931472i
$516$	−2.45267	+	1.58009i	−0.107973	+	0.0695596i
$517$	1.12295	−	1.36832i	0.0493874	−	0.0601787i
$518$	−3.21350	+	15.4773i	−0.141193	+	0.680032i
$519$	1.97696	+	1.32096i	0.0867789	+	0.0579838i
$520$	3.00334	−	3.47774i	0.131705	−	0.152509i
$521$	−5.06833	−	7.58529i	−0.222047	−	0.332317i	0.703674	−	0.710523i	$-0.251541\pi$
$521$	−5.06833	−	7.58529i	−0.222047	−	0.332317i	−0.925722	+	0.378205i	$0.876541\pi$
$522$	−32.8085	−	13.9125i	−1.43599	−	0.608935i
$523$	1.12932	+	0.342577i	0.0493819	+	0.0149798i	0.314879	−	0.949132i	$-0.398036\pi$
$523$	1.12932	+	0.342577i	0.0493819	+	0.0149798i	−0.265497	+	0.964112i	$0.585536\pi$
$524$	−28.0231	+	2.28717i	−1.22419	+	0.0999156i
$525$	0.995153	−	0.816701i	0.0434320	−	0.0356438i
$526$	7.22653	−	23.1242i	0.315092	−	1.00826i
$527$	8.37321	−	3.46830i	0.364743	−	0.151081i
$528$	0.109229	−	0.0410173i	0.00475359	−	0.00178505i
$529$	6.81964	+	2.82479i	0.296506	+	0.122817i
$530$	32.7319	−	39.2102i	1.42178	−	1.70318i
$531$	−4.09412	+	41.5683i	−0.177669	+	1.80391i
$532$	−1.52239	+	13.1899i	−0.0660041	+	0.571855i
$533$	−0.678500	−	1.26938i	−0.0293891	−	0.0549831i
$534$	0.00292200	−	0.349141i	0.000126447	−	0.0151088i
$535$	14.5581	+	2.89578i	0.629400	+	0.125195i
$536$	−0.319321	+	0.122969i	−0.0137926	+	0.00531146i
$537$	0.411491	+	2.06870i	0.0177571	+	0.0892712i
$538$	−17.3930	−	11.8333i	−0.749864	−	0.510171i
$539$	0.0969649	+	0.984501i	0.00417657	+	0.0424054i
$540$	−6.16944	−	0.103273i	−0.265490	−	0.00444414i
$541$	5.23802	+	17.2674i	0.225200	+	0.742386i	0.994615	+	0.103636i	$0.0330478\pi$
$541$	5.23802	+	17.2674i	0.225200	+	0.742386i	−0.769415	+	0.638749i	$0.779452\pi$
$542$	11.0698	+	13.7212i	0.475490	+	0.589376i
$543$	−0.911816	+	0.911816i	−0.0391298	+	0.0391298i
$544$	−9.45478	−	5.57430i	−0.405370	−	0.238996i
$545$	4.38527	+	4.38527i	0.187844	+	0.187844i
$546$	0.0149526	−	0.139811i	0.000639913	−	0.00598337i
$547$	0.760300	−	0.230635i	0.0325081	−	0.00986122i	−0.273989	−	0.961733i	$-0.588343\pi$
$547$	0.760300	−	0.230635i	0.0325081	−	0.00986122i	0.306497	+	0.951872i	$0.400843\pi$
$548$	−19.6658	−	8.53423i	−0.840083	−	0.364564i
$549$	−2.13545	+	0.210323i	−0.0911386	+	0.00897637i
$550$	1.65133	−	0.314128i	0.0704131	−	0.0133944i
$551$	−41.2708	+	8.20926i	−1.75819	+	0.349726i
$552$	−0.408579	−	2.36259i	−0.0173903	−	0.100559i
$553$	−2.12048	+	10.6604i	−0.0901718	+	0.453324i
$554$	10.8878	−	10.7071i	0.462580	−	0.454902i
$555$	−3.80980	+	2.03638i	−0.161717	+	0.0864395i
$556$	0.636462	−	0.181493i	0.0269920	−	0.00769702i
$557$	−18.2234	−	1.79485i	−0.772152	−	0.0760504i	−0.295735	−	0.955270i	$-0.595565\pi$
$557$	−18.2234	−	1.79485i	−0.772152	−	0.0760504i	−0.476417	+	0.879220i	$0.658065\pi$
$558$	1.76335	+	19.5824i	0.0746487	+	0.828987i
$559$	−1.75687	+	4.24146i	−0.0743076	+	0.179395i
$560$	−2.35419	+	17.7787i	−0.0994828	+	0.751288i
$561$	0.0216581	+	0.0522872i	0.000914405	+	0.00220757i
$562$	32.1400	−	16.8349i	1.35574	−	0.710138i
$563$	−9.14512	−	11.1434i	−0.385421	−	0.469637i	0.543771	−	0.839233i	$-0.316996\pi$
$563$	−9.14512	−	11.1434i	−0.385421	−	0.469637i	−0.929192	+	0.369597i	$0.879496\pi$
$564$	−0.879178	+	2.73275i	−0.0370201	+	0.115069i
$565$	4.05700	−	13.3741i	0.170679	−	0.562654i
$566$	−19.7771	+	7.99869i	−0.831293	+	0.336210i
$567$	9.75964	−	6.52118i	0.409866	−	0.273864i
$568$	43.2536	−	11.9437i	1.81488	−	0.501145i
$569$	0.0300548	−	0.0449802i	0.00125996	−	0.00188567i	−0.830839	−	0.556513i	$-0.812139\pi$
$569$	0.0300548	−	0.0449802i	0.00125996	−	0.00188567i	0.832099	+	0.554627i	$0.187139\pi$
$570$	−3.03376	+	1.99057i	−0.127070	+	0.0833760i
$571$	19.2334	+	15.7845i	0.804893	+	0.660559i	0.944083	−	0.329707i	$-0.106950\pi$
$571$	19.2334	+	15.7845i	0.804893	+	0.660559i	−0.139190	+	0.990266i	$0.544450\pi$
$572$	0.104541	−	0.150925i	0.00437106	−	0.00631049i
$573$	0.408846	−	0.764898i	0.0170798	−	0.0319541i
$574$	4.93189	+	2.68945i	0.205853	+	0.112256i
$575$		−	34.5429i		−	1.44054i
$576$	17.6606	−	15.9705i	0.735859	−	0.665436i
$577$		−	8.94718i		−	0.372476i	−0.982505	−	0.186238i	$-0.940370\pi$
$577$		−	8.94718i		−	0.372476i	0.982505	−	0.186238i	$-0.0596295\pi$
$578$	−8.96133	+	16.4332i	−0.372742	+	0.683529i
$579$	0.160295	−	0.299891i	0.00666164	−	0.0124631i
$580$	−55.9223	+	10.1537i	−2.32205	+	0.421610i
$581$	−14.6814	−	12.0487i	−0.609086	−	0.499864i
$582$	−1.87093	−	2.85142i	−0.0775527	−	0.118195i
$583$	1.13378	−	1.69682i	0.0469563	−	0.0702751i
$584$	−6.53005	−	0.809138i	−0.270216	−	0.0334824i
$585$	−4.02048	+	2.68640i	−0.166226	+	0.111069i
$586$	−0.0574838	−	0.142131i	−0.00237463	−	0.00587138i
$587$	7.89764	−	26.0350i	0.325971	−	1.07458i	−0.628882	−	0.777501i	$-0.716487\pi$
$587$	7.89764	−	26.0350i	0.325971	−	1.07458i	0.954853	−	0.297080i	$-0.0960128\pi$
$588$	−0.732492	−	1.42736i	−0.0302075	−	0.0588633i
$589$	14.7283	+	17.9464i	0.606867	+	0.739470i
$590$	30.9107	+	59.0126i	1.27258	+	2.42951i
$591$	0.497438	+	1.20092i	0.0204618	+	0.0493993i
$592$	10.7833	−	31.6883i	0.443189	−	1.30238i
$593$	−1.82052	+	4.39513i	−0.0747599	+	0.180486i	−0.956841	−	0.290610i	$-0.906142\pi$
$593$	−1.82052	+	4.39513i	−0.0747599	+	0.180486i	0.882082	+	0.471097i	$0.156142\pi$
$594$	−0.245539	+	0.0221103i	−0.0100746	+	0.000907198i
$595$	−8.65716	−	0.852656i	−0.354909	−	0.0349555i
$596$	−2.74295	−	1.52570i	−0.112355	−	0.0624952i
$597$	1.78765	−	0.955519i	0.0731637	−	0.0391068i
$598$	−2.64536	−	2.69001i	−0.108177	−	0.110003i
$599$	−2.80655	+	14.1095i	−0.114672	+	0.576497i	0.880135	+	0.474723i	$0.157452\pi$
$599$	−2.80655	+	14.1095i	−0.114672	+	0.576497i	−0.994808	+	0.101774i	$0.967548\pi$
$600$	−2.30395	+	1.45714i	−0.0940584	+	0.0594876i
$601$	−42.4056	+	8.43499i	−1.72976	+	0.344070i	−0.956880	−	0.290483i	$-0.906184\pi$
$601$	−42.4056	+	8.43499i	−1.72976	+	0.344070i	−0.772879	+	0.634554i	$0.781184\pi$
$602$	−3.34838	−	17.6020i	−0.136470	−	0.717406i
$603$	0.358341	−	0.0352936i	0.0145928	−	0.00143726i
$604$	22.9144	−	9.04518i	0.932375	−	0.368043i
$605$	−35.2174	+	10.6831i	−1.43179	+	0.434329i
$606$	−0.333059	−	0.0356202i	−0.0135296	−	0.00144697i
$607$	−16.1357	−	16.1357i	−0.654930	−	0.654930i	0.299246	−	0.954176i	$-0.403265\pi$
$607$	−16.1357	−	16.1357i	−0.654930	−	0.654930i	−0.954176	+	0.299246i	$0.903265\pi$
$608$	6.63383	−	27.3218i	0.269037	−	1.10805i
$609$	−1.22979	+	1.22979i	−0.0498337	+	0.0498337i
$610$	−2.66355	+	2.14887i	−0.107844	+	0.0870053i
$611$	1.31125	+	4.32263i	0.0530477	+	0.174875i
$612$	8.02903	+	8.30241i	0.324554	+	0.335605i
$613$	−0.498594	−	5.06231i	−0.0201380	−	0.204465i	−0.999989	−	0.00473379i	$-0.998493\pi$
$613$	−0.498594	−	5.06231i	−0.0201380	−	0.204465i	0.979851	−	0.199731i	$-0.0640068\pi$
$614$	14.0071	−	20.5880i	0.565280	−	0.830864i
$615$	0.299498	+	1.50568i	0.0120769	+	0.0607149i
$616$	−0.0179882	+	0.716318i	−0.000724764	+	0.0288613i
$617$	−29.6709	−	5.90191i	−1.19451	−	0.237602i	−0.442506	−	0.896766i	$-0.645910\pi$
$617$	−29.6709	−	5.90191i	−1.19451	−	0.237602i	−0.752000	+	0.659164i	$0.770910\pi$
$618$	2.90551	+	0.0243165i	0.116877	+	0.000978153i
$619$	−8.63894	−	16.1623i	−0.347228	−	0.649618i	0.646315	−	0.763071i	$-0.276309\pi$
$619$	−8.63894	−	16.1623i	−0.347228	−	0.649618i	−0.993543	+	0.113452i	$0.963809\pi$
$620$	19.4850	+	24.5699i	0.782536	+	0.986749i
$621$	−0.496571	+	5.04177i	−0.0199267	+	0.202319i
$622$	−24.1882	−	20.1918i	−0.969857	−	0.809619i
$623$	1.98103	+	0.820570i	0.0793683	+	0.0328754i
$624$	−0.0678284	+	0.289916i	−0.00271531	+	0.0116059i
$625$	15.7617	−	6.52873i	0.630470	−	0.261149i
$626$	−20.6017	−	6.43822i	−0.823409	−	0.257323i
$627$	−0.112068	+	0.0919718i	−0.00447556	+	0.00367300i
$628$	−11.5438	−	9.80164i	−0.460648	−	0.391128i
$629$	15.5372	+	4.71316i	0.619509	+	0.187926i
$630$	7.36759	−	17.3742i	0.293532	−	0.692206i
$631$	−18.9104	−	28.3014i	−0.752812	−	1.12666i	−0.987961	−	0.154703i	$-0.950558\pi$
$631$	−18.9104	−	28.3014i	−0.752812	−	1.12666i	0.235149	−	0.971959i	$-0.424442\pi$
$632$	7.23200	−	21.8503i	0.287674	−	0.869157i
$633$	0.742111	+	0.495863i	0.0294963	+	0.0197088i
$634$	−0.512300	−	0.106367i	−0.0203460	−	0.00422439i
$635$	−18.7258	+	22.8174i	−0.743110	+	0.905482i
$636$	−0.699905	+	3.23473i	−0.0277530	+	0.128265i
$637$	−2.22640	−	1.19003i	−0.0882130	−	0.0471508i
$638$	−2.17855	+	0.640995i	−0.0862495	+	0.0253772i
$639$	−47.2190			−1.86796
$640$	9.57673	−	36.7485i	0.378553	−	1.45261i
$641$	11.0097			0.434858			0.217429	−	0.976076i	$-0.430233\pi$
$641$	11.0097			0.434858			0.217429	+	0.976076i	$0.430233\pi$
$642$	−0.922681	+	0.271481i	−0.0364153	+	0.0107145i
$643$	42.0290	+	22.4650i	1.65746	+	0.885932i	0.989964	+	0.141321i	$0.0451348\pi$
$643$	42.0290	+	22.4650i	1.65746	+	0.885932i	0.667498	+	0.744611i	$0.267365\pi$
$644$	14.3917	+	3.11396i	0.567112	+	0.122707i
$645$	3.10637	−	3.78513i	0.122313	−	0.149039i
$646$	13.3530	+	2.77245i	0.525368	+	0.109081i
$647$	29.4587	+	19.6837i	1.15814	+	0.773846i	0.977755	−	0.209750i	$-0.0672650\pi$
$647$	29.4587	+	19.6837i	1.15814	+	0.773846i	0.180387	+	0.983596i	$0.442265\pi$
$648$	−22.2077	+	11.1627i	−0.872400	+	0.438514i
$649$	1.47876	+	2.21313i	0.0580465	+	0.0868728i
$650$	−1.67466	+	3.94917i	−0.0656854	+	0.154899i
$651$	0.918240	+	0.278545i	0.0359886	+	0.0109170i
$652$	20.5690	−	24.2250i	0.805545	−	0.948724i
$653$	3.90577	−	3.20538i	0.152844	−	0.125436i	−0.554863	−	0.831942i	$-0.687229\pi$
$653$	3.90577	−	3.20538i	0.152844	−	0.125436i	0.707708	+	0.706505i	$0.249729\pi$
$654$	−0.383555	−	0.119864i	−0.0149982	−	0.00468707i
$655$	43.5959	−	18.0580i	1.70343	−	0.705584i
$656$	−9.66391	−	6.93604i	−0.377312	−	0.270807i
$657$	6.39705	+	2.64974i	0.249573	+	0.103376i
$658$	−13.5339	−	11.2978i	−0.527606	−	0.440435i
$659$	2.04620	−	20.7754i	0.0797086	−	0.809295i	−0.869350	−	0.494197i	$-0.835462\pi$
$659$	2.04620	−	20.7754i	0.0797086	−	0.809295i	0.949059	−	0.315099i	$-0.102038\pi$
$660$	−0.153429	+	0.121676i	−0.00597220	+	0.00473622i
$661$	−17.0403	−	31.8801i	−0.662789	−	1.23999i	−0.958603	−	0.284746i	$-0.908091\pi$
$661$	−17.0403	−	31.8801i	−0.662789	−	1.23999i	0.295813	−	0.955246i	$-0.404409\pi$
$662$	13.8288	+	0.115735i	0.537471	+	0.00449815i
$663$	−0.141649	−	0.0281758i	−0.00550120	−	0.00109426i
$664$	27.7151	+	29.1429i	1.07555	+	1.13096i
$665$	−4.34734	−	21.8555i	−0.168583	−	0.847522i
$666$	−19.8134	+	29.1223i	−0.767755	+	1.12847i
$667$	4.57407	+	46.4413i	0.177109	+	1.79821i
$668$	−21.9426	+	21.2201i	−0.848985	+	0.821030i
$669$	−0.123216	−	0.406189i	−0.00476381	−	0.0157042i
$670$	0.446961	−	0.360594i	0.0172676	−	0.0139310i
$671$	−0.0966877	+	0.0966877i	−0.00373259	+	0.00373259i
$672$	−0.399398	−	1.09126i	−0.0154071	−	0.0420963i
$673$	−18.7729	−	18.7729i	−0.723642	−	0.723642i	0.245703	−	0.969345i	$-0.420981\pi$
$673$	−18.7729	−	18.7729i	−0.723642	−	0.723642i	−0.969345	+	0.245703i	$0.920981\pi$
$674$	−6.60715	−	0.706626i	−0.254498	−	0.0272182i
$675$	5.51204	−	1.67206i	0.212159	−	0.0643576i
$676$	−9.37432	−	23.7482i	−0.360551	−	0.913394i
$677$	27.0517	−	2.66436i	1.03968	−	0.102400i	0.436259	−	0.899821i	$-0.356303\pi$
$677$	27.0517	−	2.66436i	1.03968	−	0.102400i	0.603423	+	0.797421i	$0.293803\pi$
$678$	0.169232	+	0.889636i	0.00649933	+	0.0341663i
$679$	20.5420	−	4.08605i	0.788328	−	0.156808i
$680$	17.9708	+	4.04610i	0.689147	+	0.155161i
$681$	0.453551	−	2.28016i	0.0173801	−	0.0873758i
$682$	0.878497	+	0.893325i	0.0336394	+	0.0342072i
$683$	8.04037	−	4.29767i	0.307656	−	0.164446i	−0.310342	−	0.950625i	$-0.600444\pi$
$683$	8.04037	−	4.29767i	0.307656	−	0.164446i	0.617999	+	0.786179i	$0.287944\pi$
$684$	−14.3815	+	25.8554i	−0.549891	+	0.988608i
$685$	35.8060	+	3.52658i	1.36808	+	0.134744i
$686$	22.9826	−	2.06954i	0.877479	−	0.0790153i
$687$	0.00864988	−	0.0208827i	0.000330014	−	0.000796724i
$688$	2.45307	+	37.8621i	0.0935224	+	1.44348i
$689$	1.99292	+	4.81133i	0.0759241	+	0.183297i
$690$	1.86715	+	3.56462i	0.0710810	+	0.135703i
$691$	−24.5094	−	29.8648i	−0.932382	−	1.13611i	−0.990460	−	0.137798i	$-0.955997\pi$
$691$	−24.5094	−	29.8648i	−0.932382	−	1.13611i	0.0580785	−	0.998312i	$-0.481503\pi$
$692$	27.5093	−	14.1173i	1.04575	−	0.536657i
$693$	0.218880	−	0.721550i	0.00831456	−	0.0274094i
$694$	−10.6947	−	26.4432i	−0.405967	−	1.00377i
$695$	−0.923565	+	0.617106i	−0.0350328	+	0.0234082i
$696$	2.90460	−	2.26415i	0.110099	−	0.0858222i
$697$	3.20563	−	4.79757i	0.121422	−	0.181721i
$698$	−22.3250	−	34.0248i	−0.845014	−	1.28786i
$699$	2.45733	+	2.01668i	0.0929447	+	0.0762778i
$700$	−2.99084	−	16.4722i	−0.113043	−	0.622593i
$701$	14.6991	−	27.5000i	0.555176	−	1.03866i	−0.435210	−	0.900329i	$-0.643326\pi$
$701$	14.6991	−	27.5000i	0.555176	−	1.03866i	0.990386	−	0.138332i	$-0.0441740\pi$
$702$	0.301199	−	0.552334i	0.0113680	−	0.0208465i
$703$			41.5915i			1.56865i
$704$	0.224326	−	1.50064i	0.00845460	−	0.0565574i
$705$		−	4.81791i		−	0.181453i
$706$	−21.0947	−	11.5034i	−0.793911	−	0.432935i
$707$	0.969697	−	1.81418i	0.0364692	−	0.0682291i
$708$	−3.54849	−	2.45792i	−0.133360	−	0.0923741i
$709$	2.31868	+	1.90289i	0.0870797	+	0.0714645i	0.676926	−	0.736051i	$-0.263312\pi$
$709$	2.31868	+	1.90289i	0.0870797	+	0.0714645i	−0.589846	+	0.807516i	$0.700812\pi$
$710$	−62.9657	+	41.3143i	−2.36306	+	1.55050i
$711$	−13.4557	+	20.1379i	−0.504630	+	0.755232i
$712$	−3.94941	−	2.24025i	−0.148010	−	0.0839569i
$713$	21.4078	−	14.3042i	0.801727	−	0.535697i
$714$	0.522548	−	0.211340i	0.0195559	−	0.00790922i
$715$	−0.0894452	+	0.294861i	−0.00334506	+	0.0110272i
$716$	26.1113	+	8.40054i	0.975827	+	0.313943i
$717$	1.31290	+	1.59978i	0.0490312	+	0.0597447i
$718$	−42.4831	+	22.2526i	−1.58546	+	0.830460i
$719$	−6.09932	−	14.7251i	−0.227466	−	0.549152i	0.768401	−	0.639968i	$-0.221052\pi$
$719$	−6.09932	−	14.7251i	−0.227466	−	0.549152i	−0.995868	+	0.0908161i	$0.971052\pi$
$720$	−20.0069	+	34.5930i	−0.745614	+	1.28921i
$721$	−6.82868	+	16.4859i	−0.254313	+	0.613967i
$722$	0.723303	+	8.03241i	0.0269186	+	0.298935i
$723$	−2.74398	−	0.270259i	−0.102050	−	0.0100510i
$724$	4.59860	+	16.1264i	0.170905	+	0.599333i
$725$	46.7928	−	25.0113i	1.73784	−	0.928895i
$726$	1.70025	−	1.67203i	0.0631022	−	0.0620548i
$727$	6.02809	−	30.3052i	0.223569	−	1.12396i	−0.692031	−	0.721868i	$-0.743284\pi$
$727$	6.02809	−	30.3052i	0.223569	−	1.12396i	0.915600	−	0.402091i	$-0.131716\pi$
$728$	−1.49439	−	1.05373i	−0.0553857	−	0.0390537i
$729$	25.2367	−	5.01990i	0.934694	−	0.185922i
$730$	10.8487	−	2.06372i	0.401530	−	0.0763816i
$731$	−18.3153	+	1.80390i	−0.677417	+	0.0667197i
$732$	0.0882783	−	0.203424i	0.00326286	−	0.00751877i
$733$	−16.5818	+	5.03003i	−0.612463	+	0.185789i	−0.581251	−	0.813724i	$-0.697437\pi$
$733$	−16.5818	+	5.03003i	−0.612463	+	0.185789i	−0.0312116	+	0.999513i	$0.509937\pi$
$734$	3.64027	−	34.0375i	0.134365	−	1.25635i
$735$	1.90394	+	1.90394i	0.0702278	+	0.0702278i
$736$	−29.4329	−	10.2914i	−1.08491	−	0.379346i
$737$	0.0162248	−	0.0162248i	0.000597649	−	0.000597649i
$738$	7.85974	+	9.74225i	0.289321	+	0.358617i
$739$	5.77788	+	19.0471i	0.212543	+	0.700660i	0.996779	+	0.0801974i	$0.0255551\pi$
$739$	5.77788	+	19.0471i	0.212543	+	0.700660i	−0.784236	+	0.620462i	$0.786945\pi$
$740$	−0.940247	+	56.1698i	−0.0345642	+	2.06484i
$741$	−0.0362626	−	0.368180i	−0.00133214	−	0.0135254i
$742$	−16.8046	−	11.4330i	−0.616916	−	0.419720i
$743$	7.74710	+	38.9473i	0.284213	+	1.42884i	0.814078	+	0.580755i	$0.197243\pi$
$743$	7.74710	+	38.9473i	0.284213	+	1.42884i	−0.529865	+	0.848082i	$0.677757\pi$
$744$	−1.85712	−	0.824458i	−0.0680855	−	0.0302261i
$745$	5.16652	+	1.02768i	0.189287	+	0.0376514i
$746$	−0.392230	+	46.8664i	−0.0143606	+	1.71590i
$747$	−19.9498	−	37.3235i	−0.729925	−	1.36559i
$748$	0.731136	+	0.0843885i	0.0267330	+	0.00308555i
$749$	0.578951	−	5.87819i	0.0211544	−	0.214784i
$750$	0.592722	−	0.710033i	0.0216432	−	0.0259267i
$751$	30.2032	+	12.5106i	1.10213	+	0.456518i	0.858221	−	0.513280i	$-0.171570\pi$
$751$	30.2032	+	12.5106i	1.10213	+	0.456518i	0.243910	+	0.969798i	$0.421570\pi$
$752$	25.4992	+	27.2662i	0.929860	+	0.994296i
$753$	2.33323	−	0.966457i	0.0850278	−	0.0352196i
$754$	1.72856	−	5.53123i	0.0629505	−	0.201436i
$755$	−31.9604	+	26.2292i	−1.16316	+	0.954578i
$756$	0.199737	+	2.44723i	0.00726436	+	0.0890050i
$757$	17.5361	+	5.31953i	0.637362	+	0.193342i	0.592396	−	0.805647i	$-0.298182\pi$
$757$	17.5361	+	5.31953i	0.637362	+	0.193342i	0.0449660	+	0.998989i	$0.485682\pi$
$758$	6.94985	+	2.94710i	0.252430	+	0.107044i
$759$	0.0893238	+	0.133683i	0.00324225	+	0.00485237i
$760$	3.44478	+	47.0608i	0.124955	+	1.70708i
$761$	10.7889	+	7.20891i	0.391097	+	0.261323i	0.735536	−	0.677486i	$-0.236931\pi$
$761$	10.7889	+	7.20891i	0.391097	+	0.261323i	−0.344438	+	0.938809i	$0.611931\pi$
$762$	0.388822	−	1.87270i	0.0140856	−	0.0678406i
$763$	1.56560	−	1.90768i	0.0566784	−	0.0690628i
$764$	−6.10836	−	9.48159i	−0.220993	−	0.343032i
$765$	−17.0951	−	9.13754i	−0.618076	−	0.330368i
$766$	−5.23650	−	17.7973i	−0.189202	−	0.643041i
$767$	−6.79235			−0.245257
$768$	0.555168	+	2.39725i	0.0200329	+	0.0865034i
$769$	55.4296			1.99884			0.999422	−	0.0339985i	$-0.0108241\pi$
$769$	55.4296			1.99884			0.999422	+	0.0339985i	$0.0108241\pi$
$770$	−0.339449	−	1.15368i	−0.0122329	−	0.0415758i
$771$	−0.609484	−	0.325776i	−0.0219500	−	0.0117325i
$772$	−2.39489	−	3.71742i	−0.0861939	−	0.133793i
$773$	−29.5336	+	35.9867i	−1.06225	+	1.29435i	−0.108386	+	0.994109i	$0.534568\pi$
$773$	−29.5336	+	35.9867i	−1.06225	+	1.29435i	−0.953862	+	0.300244i	$0.902932\pi$
$774$	8.11656	−	39.0920i	0.291744	−	1.40513i
$775$	−24.3400	−	16.2634i	−0.874317	−	0.584200i
$776$	−44.2324	+	3.23774i	−1.58785	+	0.116228i
$777$	0.955040	+	1.42932i	0.0342619	+	0.0512765i
$778$	0.298937	+	0.126765i	0.0107174	+	0.00454474i
$779$	14.1441	+	4.29057i	0.506765	+	0.153726i
$780$	−0.0406497	−	0.498052i	−0.00145549	−	0.0178331i
$781$	−2.32597	+	1.90887i	−0.0832297	+	0.0683049i
$782$	4.51133	−	14.4358i	0.161325	−	0.516225i
$783$	−7.18928	+	2.97790i	−0.256924	+	0.106421i
$784$	−20.8518	−	0.698288i	−0.744707	−	0.0249389i
$785$	23.4812	+	9.72622i	0.838079	+	0.347144i
$786$	−1.95943	+	2.34724i	−0.0698907	+	0.0837234i
$787$	−2.46437	+	25.0212i	−0.0878455	+	0.891910i	0.845750	+	0.533580i	$0.179154\pi$
$787$	−2.46437	+	25.0212i	−0.0878455	+	0.891910i	−0.933595	+	0.358330i	$0.883346\pi$
$788$	16.7926	+	1.93821i	0.598210	+	0.0690460i
$789$	−1.24197	−	2.32357i	−0.0442154	−	0.0827211i
$790$	−0.323270	+	38.6267i	−0.0115014	+	1.37427i
$791$	−5.45462	−	1.08499i	−0.193944	−	0.0385779i
$792$	−0.647856	+	1.45932i	−0.0230206	+	0.0518548i
$793$	−0.0680742	−	0.342232i	−0.00241738	−	0.0121530i
$794$	−22.1487	−	15.0689i	−0.786028	−	0.534776i
$795$	−0.544437	−	5.52776i	−0.0193092	−	0.196049i
$796$	0.441187	−	26.3562i	0.0156375	−	0.934172i
$797$	−6.23492	−	20.5538i	−0.220852	−	0.728052i	−0.995423	−	0.0955650i	$-0.969534\pi$
$797$	−6.23492	−	20.5538i	−0.220852	−	0.728052i	0.774571	−	0.632487i	$-0.217966\pi$
$798$	0.906631	+	1.12378i	0.0320944	+	0.0397814i
$799$	−12.8044	+	12.8044i	−0.452987	+	0.452987i
$800$	1.99591	+	35.3948i	0.0705660	+	1.25139i
$801$	3.37856	+	3.37856i	0.119376	+	0.119376i
$802$	−5.18020	+	48.4363i	−0.182919	+	1.71035i
$803$	0.422231	−	0.128082i	0.0149002	−	0.00451993i
$804$	−0.0148137	+	0.0341359i	−0.000522438	+	0.00120388i
$805$	−24.5937	+	2.42227i	−0.866814	+	0.0853737i
$806$	−3.14095	+	0.597493i	−0.110635	+	0.0210458i
$807$	−2.24375	+	0.446310i	−0.0789838	+	0.0157109i
$808$	−2.51019	+	3.55994i	−0.0883082	+	0.125238i
$809$	7.10502	−	35.7193i	0.249799	−	1.25582i	−0.628537	−	0.777780i	$-0.716346\pi$
$809$	7.10502	−	35.7193i	0.249799	−	1.25582i	0.878336	−	0.478045i	$-0.158654\pi$
$810$	29.7428	−	29.2491i	1.04505	−	1.02771i
$811$	−5.53266	+	2.95727i	−0.194278	+	0.103844i	−0.565667	−	0.824633i	$-0.691381\pi$
$811$	−5.53266	+	2.95727i	−0.194278	+	0.103844i	0.371390	+	0.928477i	$0.378881\pi$
$812$	6.20226	+	21.7501i	0.217657	+	0.763281i
$813$	1.90799	+	0.187921i	0.0669161	+	0.00659066i
$814$	0.201304	+	2.23552i	0.00705570	+	0.0783548i
$815$	−20.4107	+	49.2759i	−0.714957	+	1.72606i
$816$	−1.15315	+	0.308058i	−0.0403684	+	0.0107842i
$817$	−18.0413	−	43.5554i	−0.631183	−	1.52381i
$818$	33.2961	−	17.4405i	1.16417	−	0.609791i
$819$	1.22068	+	1.48740i	0.0426539	+	0.0519739i
$820$	19.0048	+	6.11422i	0.663677	+	0.213518i
$821$	8.45214	−	27.8630i	0.294982	−	0.972424i	−0.676725	−	0.736235i	$-0.736602\pi$
$821$	8.45214	−	27.8630i	0.294982	−	0.972424i	0.971707	−	0.236189i	$-0.0758984\pi$
$822$	−2.16126	+	0.874104i	−0.0753825	+	0.0304879i
$823$	−11.9092	+	7.95748i	−0.415129	+	0.277380i	−0.745545	−	0.666455i	$-0.767811\pi$
$823$	−11.9092	+	7.95748i	−0.415129	+	0.277380i	0.330416	+	0.943835i	$0.392811\pi$
$824$	18.6431	−	32.8665i	0.649463	−	1.14496i
$825$	0.101558	−	0.151993i	0.00353581	−	0.00529171i
$826$	22.1644	−	14.5429i	0.771197	−	0.506013i
$827$	−22.9146	−	18.8055i	−0.796819	−	0.653933i	0.145234	−	0.989397i	$-0.453607\pi$
$827$	−22.9146	−	18.8055i	−0.796819	−	0.653933i	−0.942053	+	0.335465i	$0.891107\pi$
$828$	26.9724	+	18.6828i	0.937355	+	0.649273i
$829$	8.94431	−	16.7336i	0.310649	−	0.581183i	−0.677347	−	0.735664i	$-0.736870\pi$
$829$	8.94431	−	16.7336i	0.310649	−	0.581183i	0.987996	+	0.154481i	$0.0493705\pi$
$830$	−59.2589	−	32.3150i	−2.05691	−	1.12167i
$831$		−	1.66064i		−	0.0576070i
$832$	2.86603	+	2.60351i	0.0993618	+	0.0902603i
$833$		−	10.1201i		−	0.350640i
$834$	0.0344580	−	0.0631887i	0.00119318	−	0.00218805i
$835$	24.1498	−	45.1811i	0.835738	−	1.56356i
$836$	0.336810	+	1.85500i	0.0116488	+	0.0641566i
$837$	3.31879	+	2.72366i	0.114714	+	0.0941435i
$838$	17.6185	+	26.8518i	0.608622	+	0.927579i
$839$	7.42607	−	11.1139i	0.256376	−	0.383694i	−0.680846	−	0.732427i	$-0.738388\pi$
$839$	7.42607	−	11.1139i	0.256376	−	0.383694i	0.937222	+	0.348732i	$0.113388\pi$
$840$	1.19901	+	1.53818i	0.0413699	+	0.0530721i
$841$	−35.4862	+	23.7111i	−1.22366	+	0.817626i
$842$	15.8581	+	39.2097i	0.546505	+	1.35125i
$843$	1.14536	−	3.77573i	0.0394482	−	0.130043i
$844$	10.3265	−	5.29933i	0.355451	−	0.182411i
$845$	27.1836	+	33.1233i	0.935145	+	1.13948i
$846$	−18.2278	−	34.7992i	−0.626684	−	1.19642i
$847$	5.60431	+	13.5300i	0.192567	+	0.464897i
$848$	32.3373	+	28.4020i	1.11047	+	0.975329i
$849$	−0.887815	+	2.14337i	−0.0304697	+	0.0735604i
$850$	−17.1266	+	1.54222i	−0.587438	+	0.0528977i
$851$	45.9029	+	4.52104i	1.57353	+	0.154979i
$852$	2.37203	−	4.26450i	0.0812644	−	0.146099i
$853$	−11.2584	+	6.01773i	−0.385479	+	0.206043i	−0.652741	−	0.757581i	$-0.726381\pi$
$853$	−11.2584	+	6.01773i	−0.385479	+	0.206043i	0.267262	+	0.963624i	$0.413881\pi$
$854$	0.954880	+	0.970998i	0.0326753	+	0.0332269i
$855$	9.68711	−	48.7004i	0.331292	−	1.66552i
$856$	−2.74729	+	12.2021i	−0.0939004	+	0.417059i
$857$	36.9270	−	7.34524i	1.26140	−	0.250909i	0.481298	−	0.876557i	$-0.340166\pi$
$857$	36.9270	−	7.34524i	1.26140	−	0.250909i	0.780105	+	0.625649i	$0.215166\pi$
$858$	−0.00373109	−	0.0196139i	−0.000127377	−	0.000669609i
$859$	−14.8740	+	1.46496i	−0.507494	+	0.0499838i	−0.348524	−	0.937300i	$-0.613317\pi$
$859$	−14.8740	+	1.46496i	−0.507494	+	0.0499838i	−0.158970	+	0.987283i	$0.550817\pi$
$860$	−23.3803	−	59.2301i	−0.797262	−	2.01973i
$861$	0.584593	−	0.177334i	0.0199229	−	0.00604354i
$862$	−21.4993	−	2.29933i	−0.732271	−	0.0783154i
$863$	38.0460	+	38.0460i	1.29510	+	1.29510i	0.931590	+	0.363511i	$0.118422\pi$
$863$	38.0460	+	38.0460i	1.29510	+	1.29510i	0.363511	+	0.931590i	$0.381578\pi$
$864$	0.217501	−	5.19480i	0.00739953	−	0.176731i
$865$	−36.6944	+	36.6944i	−1.24765	+	1.24765i
$866$	−33.4975	+	27.0248i	−1.13829	+	0.918338i
$867$	0.590882	+	1.94788i	0.0200674	+	0.0661534i
$868$	8.97009	−	8.67472i	0.304465	−	0.294439i
$869$	0.151277	+	1.53594i	0.00513171	+	0.0521031i
$870$	−3.47681	+	5.11031i	−0.117875	+	0.173256i
$871$	0.0114233	+	0.0574287i	0.000387063	+	0.00194590i
$872$	−3.78680	+	3.60128i	−0.128237	+	0.121955i
$873$	45.7734	+	9.10489i	1.54919	+	0.308154i
$874$	38.7416	+	0.324232i	1.31045	+	0.0109673i
$875$	2.67761	+	5.00946i	0.0905198	+	0.169351i
$876$	−0.560659	+	0.444628i	−0.0189429	+	0.0150226i
$877$	0.261117	−	2.65116i	0.00881729	−	0.0895234i	−0.989769	−	0.142680i	$-0.954428\pi$
$877$	0.261117	−	2.65116i	0.00881729	−	0.0895234i	0.998586	+	0.0531562i	$0.0169281\pi$
$878$	−2.41749	−	2.01808i	−0.0815864	−	0.0681068i
$879$	−0.0154037	−	0.00638041i	−0.000519553	−	0.000215206i
$880$	0.412931	+	2.51282i	0.0139199	+	0.0847072i
$881$	−20.2346	+	8.38144i	−0.681720	+	0.282378i	−0.696546	−	0.717512i	$-0.745281\pi$
$881$	−20.2346	+	8.38144i	−0.681720	+	0.282378i	0.0148256	+	0.999890i	$0.495281\pi$
$882$	20.9552	+	6.54869i	0.705598	+	0.220506i
$883$	11.5623	−	9.48892i	0.389102	−	0.319328i	−0.419422	−	0.907792i	$-0.637767\pi$
$883$	11.5623	−	9.48892i	0.389102	−	0.319328i	0.808523	+	0.588464i	$0.200267\pi$
$884$	−1.21562	+	1.43169i	−0.0408858	+	0.0481530i
$885$	6.93266	+	2.10300i	0.233039	+	0.0706916i
$886$	−11.4712	+	27.0515i	−0.385384	+	0.908811i
$887$	3.14343	+	4.70448i	0.105546	+	0.157961i	0.880483	−	0.474078i	$-0.157218\pi$
$887$	3.14343	+	4.70448i	0.105546	+	0.157961i	−0.774937	+	0.632039i	$0.782218\pi$
$888$	−1.63481	−	3.25236i	−0.0548605	−	0.109142i
$889$	9.76648	+	6.52575i	0.327557	+	0.218867i
$890$	7.46132	+	1.54917i	0.250104	+	0.0519284i
$891$	1.05735	−	1.28838i	0.0354225	−	0.0431625i
$892$	−5.39511	−	1.16735i	−0.180642	−	0.0390858i
$893$	−40.9091	−	21.8664i	−1.36897	−	0.731730i
$894$	−0.327451	+	0.0963460i	−0.0109516	+	0.00322229i
$895$	−46.0350			−1.53878
$896$	−14.9266	−	2.35920i	−0.498661	−	0.0788153i
$897$	−0.410288			−0.0136991
$898$	−16.3130	+	4.79979i	−0.544373	+	0.160171i
$899$	34.8775	+	18.6424i	1.16323	+	0.621760i
$900$	7.88920	−	36.4613i	0.262973	−	1.21538i
$901$	−13.2440	+	16.1379i	−0.441222	+	0.537631i
$902$	0.781004	+	0.162158i	0.0260046	+	0.00539926i
$903$	−1.62014	−	1.08254i	−0.0539148	−	0.0360247i
$904$	11.1802	+	3.70043i	0.371848	+	0.123074i
$905$	−15.6360	−	23.4009i	−0.519758	−	0.777873i
$906$	1.04590	−	2.46643i	0.0347476	−	0.0819417i
$907$	6.34426	+	1.92451i	0.210658	+	0.0639023i	0.393850	−	0.919175i	$-0.371143\pi$
$907$	6.34426	+	1.92451i	0.210658	+	0.0639023i	−0.183192	+	0.983077i	$0.558643\pi$
$908$	−23.0462	−	19.5681i	−0.764815	−	0.649391i
$909$	3.54328	−	2.90790i	0.117523	−	0.0964489i
$910$	2.92915	+	0.915385i	0.0971003	+	0.0303447i
$911$	8.63355	−	3.57614i	0.286042	−	0.118483i	−0.235049	−	0.971984i	$-0.575525\pi$
$911$	8.63355	−	3.57614i	0.286042	−	0.118483i	0.521091	+	0.853501i	$0.325525\pi$
$912$	−1.61263	−	2.59767i	−0.0533997	−	0.0860176i
$913$	−2.49155	−	1.03203i	−0.0824582	−	0.0341553i
$914$	−12.4789	−	10.4172i	−0.412767	−	0.344570i
$915$	−0.0364791	+	0.370378i	−0.00120596	+	0.0122443i
$916$	−0.182646	−	0.230310i	−0.00603479	−	0.00760965i
$917$	−8.85170	−	16.5604i	−0.292309	−	0.546872i
$918$	2.52192	+	0.0211062i	0.0832357	+	0.000696607i
$919$	−9.57985	−	1.90555i	−0.316010	−	0.0628583i	0.0345370	−	0.999403i	$-0.489004\pi$
$919$	−9.57985	−	1.90555i	−0.316010	−	0.0628583i	−0.350547	+	0.936545i	$0.614004\pi$
$920$	52.3137	+	1.31370i	1.72473	+	0.0433114i
$921$	−0.528296	−	2.65592i	−0.0174079	−	0.0875156i
$922$	11.0314	−	16.2142i	0.363300	−	0.533988i
$923$	−0.752629	−	7.64157i	−0.0247731	−	0.251525i
$924$	0.0541700	+	0.0560145i	0.00178206	+	0.00184274i
$925$	−15.2233	−	50.1845i	−0.500539	−	1.65006i
$926$	−10.8507	+	8.75399i	−0.356576	+	0.287674i
$927$	−28.1160	+	28.1160i	−0.923450	+	0.923450i
$928$	−7.37028	−	47.3224i	−0.241941	−	1.55343i
$929$	39.9272	+	39.9272i	1.30997	+	1.30997i	0.921434	+	0.388534i	$0.127018\pi$
$929$	39.9272	+	39.9272i	1.30997	+	1.30997i	0.388534	+	0.921434i	$0.372982\pi$
$930$	3.39083	+	0.362645i	0.111190	+	0.0118916i
$931$	24.8076	−	7.52530i	0.813036	−	0.246632i
$932$	38.4525	−	15.1786i	1.25955	−	0.497193i
$933$	−3.40999	+	0.335855i	−0.111638	+	0.0109954i
$934$	7.86537	+	41.3474i	0.257363	+	1.35293i
$935$	−1.21149	+	0.240979i	−0.0396198	+	0.00788087i
$936$	−2.17791	−	3.44358i	−0.0711871	−	0.112557i
$937$	−1.71770	+	8.63545i	−0.0561147	+	0.282108i	−0.998647	−	0.0520083i	$-0.983438\pi$
$937$	−1.71770	+	8.63545i	−0.0561147	+	0.282108i	0.942532	+	0.334116i	$0.108438\pi$
$938$	−0.160235	−	0.162940i	−0.00523186	−	0.00532017i
$939$	−2.07009	+	1.10649i	−0.0675550	+	0.0361089i
$940$	−54.7540	−	30.4557i	−1.78588	−	0.993354i
$941$	−25.7216	−	2.53336i	−0.838502	−	0.0825852i	−0.330356	−	0.943856i	$-0.607169\pi$
$941$	−25.7216	−	2.53336i	−0.838502	−	0.0825852i	−0.508146	+	0.861271i	$0.669669\pi$
$942$	−1.64022	+	0.147698i	−0.0534412	+	0.00481228i
$943$	6.27281	−	15.1439i	0.204271	−	0.493154i
$944$	−50.3647	+	24.7901i	−1.63923	+	0.806850i
$945$	−1.57699	−	3.80719i	−0.0512995	−	0.123848i
$946$	−1.18052	−	2.25376i	−0.0383819	−	0.0732760i
$947$	−3.75302	−	4.57307i	−0.121957	−	0.148605i	0.708453	−	0.705758i	$-0.249393\pi$
$947$	−3.75302	−	4.57307i	−0.121957	−	0.148605i	−0.830410	+	0.557154i	$0.811893\pi$
$948$	−1.14277	−	2.22685i	−0.0371156	−	0.0723247i
$949$	−0.326851	+	1.07748i	−0.0106100	+	0.0349766i
$950$	−16.5158	−	40.8361i	−0.535845	−	1.32490i
$951$	−0.0473107	+	0.0316120i	−0.00153415	+	0.00102509i
$952$	0.901388	−	7.27454i	0.0292141	−	0.235769i
$953$	−11.0052	+	16.4704i	−0.356492	+	0.533528i	−0.965760	−	0.259436i	$-0.916463\pi$
$953$	−11.0052	+	16.4704i	−0.356492	+	0.533528i	0.609268	+	0.792964i	$0.291463\pi$
$954$	−24.8458	−	37.8666i	−0.804412	−	1.22598i
$955$	14.6326	+	12.0087i	0.473501	+	0.388593i
$956$	26.4803	−	4.80798i	0.856433	−	0.155501i
$957$	−0.116414	+	0.217796i	−0.00376314	+	0.00704033i
$958$	−1.20430	+	2.20842i	−0.0389090	+	0.0713509i
$959$		−	14.3173i		−	0.462331i
$960$	−2.11916	−	3.54465i	−0.0683956	−	0.114403i
$961$			9.18073i			0.296153i
$962$	−5.02874	−	2.74227i	−0.162133	−	0.0884144i
$963$	6.20437	−	11.6076i	0.199933	−	0.374048i
$964$	−20.4171	+	29.4761i	−0.657589	+	0.949360i
$965$	5.73698	+	4.70822i	0.184680	+	0.151563i
$966$	1.33883	−	0.878457i	0.0430760	−	0.0282639i
$967$	−7.85147	+	11.7506i	−0.252486	+	0.377872i	−0.935962	−	0.352101i	$-0.885467\pi$
$967$	−7.85147	+	11.7506i	−0.252486	+	0.377872i	0.683476	+	0.729973i	$0.260467\pi$
$968$	−8.25419	−	29.8923i	−0.265300	−	0.960774i
$969$	1.23315	−	0.823961i	0.0396143	−	0.0264694i
$970$	69.0043	−	27.9083i	2.21559	−	0.896080i
$971$	4.95320	−	16.3285i	0.158956	−	0.524007i	−0.840897	−	0.541196i	$-0.817972\pi$
$971$	4.95320	−	16.3285i	0.158956	−	0.524007i	0.999852	+	0.0171891i	$0.00547172\pi$
$972$	−2.51676	+	7.82285i	−0.0807252	+	0.250918i
$973$	0.280408	+	0.341678i	0.00898946	+	0.0109537i
$974$	17.2131	−	9.01619i	0.551543	−	0.288897i
$975$	0.178516	+	0.430975i	0.00571708	+	0.0138023i
$976$	−1.75381	−	2.28917i	−0.0561382	−	0.0732745i
$977$	−15.1737	+	36.6326i	−0.485450	+	1.17198i	0.471536	+	0.881847i	$0.343700\pi$
$977$	−15.1737	+	36.6326i	−0.485450	+	1.17198i	−0.956986	+	0.290133i	$0.906300\pi$
$978$	−0.309950	−	3.44205i	−0.00991109	−	0.110064i
$979$	0.303006	+	0.0298435i	0.00968413	+	0.000953804i
$980$	33.6731	−	9.60220i	1.07565	−	0.306731i
$981$	4.84978	−	2.59226i	0.154842	−	0.0827645i
$982$	30.3253	−	29.8219i	0.967719	−	0.951656i
$983$	1.18564	−	5.96062i	0.0378161	−	0.190114i	−0.957260	−	0.289229i	$-0.906601\pi$
$983$	1.18564	−	5.96062i	0.0378161	−	0.190114i	0.995076	+	0.0991147i	$0.0316011\pi$
$984$	−1.27468	+	0.220439i	−0.0406354	+	0.00702735i
$985$	−27.8251	+	5.53476i	−0.886582	+	0.176352i
$986$	22.8217	−	4.34130i	0.726792	−	0.138255i
$987$	−1.90797	+	0.187919i	−0.0607315	+	0.00598153i
$988$	−4.41348	−	1.91528i	−0.140411	−	0.0609332i
$989$	−50.0316	+	15.1769i	−1.59091	+	0.482598i
$990$	0.284965	−	2.66451i	0.00905679	−	0.0846835i
$991$	−15.6471	−	15.6471i	−0.497048	−	0.497048i	0.413470	−	0.910518i	$-0.364317\pi$
$991$	−15.6471	−	15.6471i	−0.497048	−	0.497048i	−0.910518	+	0.413470i	$0.864317\pi$
$992$	−21.1092	+	15.8939i	−0.670218	+	0.504633i
$993$	1.06343	−	1.06343i	0.0337469	−	0.0337469i
$994$	18.8171	+	23.3241i	0.596843	+	0.739794i
$995$	12.8422	+	42.3352i	0.407127	+	1.34212i
$996$	4.37297	+	0.0732007i	0.138563	+	0.00231945i
$997$	−4.19514	−	42.5940i	−0.132861	−	1.34896i	−0.798186	−	0.602411i	$-0.794207\pi$
$997$	−4.19514	−	42.5940i	−0.132861	−	1.34896i	0.665325	−	0.746554i	$-0.268293\pi$
$998$	5.94916	+	4.04752i	0.188317	+	0.128122i
$999$	1.50052	+	7.54362i	0.0474743	+	0.238669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.k.a.109.8	yes	240
4.3	odd	2		512.2.k.a.273.8		240
128.27	odd	32		512.2.k.a.497.8		240
128.101	even	32	inner	128.2.k.a.101.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.8	✓	240	128.101	even	32	inner
128.2.k.a.109.8	yes	240	1.1	even	1	trivial
512.2.k.a.273.8		240	4.3	odd	2
512.2.k.a.497.8		240	128.27	odd	32

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.399184 - 1.35671i) q^{2} +(-0.135634 - 0.0724978i) q^{3} +(-1.68130 + 1.08315i) q^{4} +(2.12942 - 2.59470i) q^{5} +(-0.0442153 + 0.212955i) q^{6} +(-1.11060 - 0.742082i) q^{7} +(2.14067 + 1.84866i) q^{8} +(-1.65357 - 2.47474i) q^{9} +(-4.37028 - 1.85323i) q^{10} +(-0.181497 - 0.0550566i) q^{11} +(0.306568 - 0.0250213i) q^{12} +(0.374137 - 0.307046i) q^{13} +(-0.563451 + 1.80299i) q^{14} +(-0.476932 + 0.197552i) q^{15} +(1.65356 - 3.64222i) q^{16} +(1.79255 + 0.742500i) q^{17} +(-2.69742 + 3.23129i) q^{18} +(-0.487163 + 4.94625i) q^{19} +(-0.769739 + 6.66897i) q^{20} +(0.0968362 + 0.181168i) q^{21} +(-0.00224473 + 0.268216i) q^{22} +(5.40603 + 1.07533i) q^{23} +(-0.156324 - 0.405934i) q^{24} +(-1.22261 - 6.14649i) q^{25} +(-0.565921 - 0.385026i) q^{26} +(0.0900899 + 0.914698i) q^{27} +(2.67105 + 0.0447117i) q^{28} +(2.45765 + 8.10178i) q^{29} +(0.458403 + 0.568197i) q^{30} +(3.30297 - 3.30297i) q^{31} +(-5.60149 - 0.789483i) q^{32} +(0.0206257 + 0.0206257i) q^{33} +(0.291795 - 2.72836i) q^{34} +(-4.29042 + 1.30149i) q^{35} +(5.46068 + 2.36973i) q^{36} +(8.32789 - 0.820226i) q^{37} +(6.90508 - 1.31353i) q^{38} +(-0.0730059 + 0.0145218i) q^{39} +(9.35510 - 1.61784i) q^{40} +(0.580168 - 2.91670i) q^{41} +(0.207136 - 0.203698i) q^{42} +(-8.36535 + 4.47137i) q^{43} +(0.364787 - 0.104022i) q^{44} +(-9.94237 - 0.979238i) q^{45} +(-0.699102 - 7.76365i) q^{46} +(-3.57155 + 8.62250i) q^{47} +(-0.488332 + 0.374128i) q^{48} +(-1.99603 - 4.81884i) q^{49} +(-7.85094 + 4.11231i) q^{50} +(-0.189301 - 0.230664i) q^{51} +(-0.296460 + 0.921485i) q^{52} +(-3.12341 + 10.2965i) q^{53} +(1.20501 - 0.487359i) q^{54} +(-0.529339 + 0.353693i) q^{55} +(-1.00558 - 3.64168i) q^{56} +(0.424668 - 0.635561i) q^{57} +(10.0107 - 6.56841i) q^{58} +(-10.8483 - 8.90293i) q^{59} +(0.587888 - 0.848734i) q^{60} +(0.339850 - 0.635815i) q^{61} +(-5.79966 - 3.16267i) q^{62} +3.97554i q^{63} +(1.16493 + 7.91473i) q^{64} -1.62460i q^{65} +(0.0197495 - 0.0362165i) q^{66} +(-0.0570291 + 0.106694i) q^{67} +(-3.81807 + 0.693240i) q^{68} +(-0.655283 - 0.537776i) q^{69} +(3.47840 + 5.30131i) q^{70} +(8.81399 - 13.1911i) q^{71} +(1.03520 - 8.35449i) q^{72} +(-1.93431 + 1.29247i) q^{73} +(-4.43717 - 10.9711i) q^{74} +(-0.279780 + 0.922310i) q^{75} +(-4.53848 - 8.84383i) q^{76} +(0.160715 + 0.195832i) q^{77} +(0.0488446 + 0.0932506i) q^{78} +(-3.11404 - 7.51796i) q^{79} +(-5.92934 - 12.0463i) q^{80} +(-3.36290 + 8.11876i) q^{81} +(-4.18870 + 0.377184i) q^{82} +(14.1505 + 1.39370i) q^{83} +(-0.359043 - 0.199710i) q^{84} +(5.74366 - 3.07005i) q^{85} +(9.40566 + 9.56442i) q^{86} +(0.254021 - 1.27705i) q^{87} +(-0.286745 - 0.453384i) q^{88} +(-1.57448 + 0.313183i) q^{89} +(2.64030 + 13.8798i) q^{90} +(-0.643371 + 0.0633666i) q^{91} +(-10.2539 + 4.04761i) q^{92} +(-0.687453 + 0.208537i) q^{93} +(13.1239 + 1.40358i) q^{94} +(11.7967 + 11.7967i) q^{95} +(0.702516 + 0.513177i) q^{96} +(-11.0877 + 11.0877i) q^{97} +(-5.74097 + 4.63163i) q^{98} +(0.163868 + 0.540199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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