LMFDB - Embedded newform 588.2.x.b.559.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(55,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 9]))

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

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

chi := DirichletCharacter("588.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, degree $6$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			559.14
Character	$\chi$	$=$	588.559
Dual form			588.2.x.b.223.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0968063 - 1.41090i) q^{2} +(0.222521 + 0.974928i) q^{3} +(-1.98126 + 0.273167i) q^{4} +(-3.84631 + 0.877896i) q^{5} +(1.35398 - 0.408333i) q^{6} +(2.22982 - 1.42405i) q^{7} +(0.577209 + 2.76890i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})$	\(q+(-0.0968063 - 1.41090i) q^{2} +(0.222521 + 0.974928i) q^{3} +(-1.98126 + 0.273167i) q^{4} +(-3.84631 + 0.877896i) q^{5} +(1.35398 - 0.408333i) q^{6} +(2.22982 - 1.42405i) q^{7} +(0.577209 + 2.76890i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(1.61097 + 5.34176i) q^{10} +(0.211161 - 0.438481i) q^{11} +(-0.707190 - 1.87080i) q^{12} +(1.80566 - 3.74949i) q^{13} +(-2.22505 - 3.00818i) q^{14} +(-1.71177 - 3.55453i) q^{15} +(3.85076 - 1.08243i) q^{16} +(3.87770 + 3.09236i) q^{17} +(0.699384 + 1.22917i) q^{18} +1.26247 q^{19} +(7.38072 - 2.79002i) q^{20} +(1.88453 + 1.85703i) q^{21} +(-0.639093 - 0.255479i) q^{22} +(1.01756 - 0.811475i) q^{23} +(-2.57104 + 1.17888i) q^{24} +(9.51858 - 4.58391i) q^{25} +(-5.46495 - 2.18463i) q^{26} +(-0.623490 - 0.781831i) q^{27} +(-4.02884 + 3.43052i) q^{28} +(3.84838 - 4.82572i) q^{29} +(-4.84936 + 2.75923i) q^{30} +1.46864 q^{31} +(-1.89997 - 5.32824i) q^{32} +(0.474475 + 0.108296i) q^{33} +(3.98761 - 5.77039i) q^{34} +(-7.32641 + 7.43489i) q^{35} +(1.66653 - 1.10575i) q^{36} +(5.94597 - 7.45601i) q^{37} +(-0.122215 - 1.78122i) q^{38} +(4.05728 + 0.926049i) q^{39} +(-4.65094 - 10.1433i) q^{40} +(-0.785690 + 0.179329i) q^{41} +(2.43764 - 2.83864i) q^{42} +(-9.95871 - 2.27301i) q^{43} +(-0.298586 + 0.926427i) q^{44} +(3.08450 - 2.45981i) q^{45} +(-1.24341 - 1.35711i) q^{46} +(7.29098 + 3.51115i) q^{47} +(1.91217 + 3.51335i) q^{48} +(2.94417 - 6.35074i) q^{49} +(-7.38887 - 12.9860i) q^{50} +(-2.15196 + 4.46859i) q^{51} +(-2.55324 + 7.92196i) q^{52} +(4.02092 + 5.04208i) q^{53} +(-1.04273 + 0.955366i) q^{54} +(-0.427252 + 1.87191i) q^{55} +(5.23013 + 5.35218i) q^{56} +(0.280926 + 1.23082i) q^{57} +(-7.18114 - 4.96251i) q^{58} +(-0.246939 + 1.08191i) q^{59} +(4.36244 + 6.57483i) q^{60} +(4.52728 + 3.61038i) q^{61} +(-0.142173 - 2.07209i) q^{62} +(-1.39112 + 2.25051i) q^{63} +(-7.33366 + 3.19647i) q^{64} +(-3.65347 + 16.0069i) q^{65} +(0.106862 - 0.679919i) q^{66} +5.76579i q^{67} +(-8.52745 - 5.06750i) q^{68} +(1.01756 + 0.811475i) q^{69} +(11.1991 + 9.61706i) q^{70} +(-3.14148 + 2.50524i) q^{71} +(-1.72143 - 2.24425i) q^{72} +(6.35632 + 13.1990i) q^{73} +(-11.0953 - 7.66735i) q^{74} +(6.58706 + 8.25991i) q^{75} +(-2.50128 + 0.344866i) q^{76} +(-0.153568 - 1.27844i) q^{77} +(0.913788 - 5.81405i) q^{78} -17.2973i q^{79} +(-13.8610 + 7.54393i) q^{80} +(0.623490 - 0.781831i) q^{81} +(0.329074 + 1.09117i) q^{82} +(-4.95499 + 2.38620i) q^{83} +(-4.24101 - 3.16446i) q^{84} +(-17.6296 - 8.48997i) q^{85} +(-2.24292 + 14.2707i) q^{86} +(5.56108 + 2.67807i) q^{87} +(1.33600 + 0.331590i) q^{88} +(-6.19385 - 12.8617i) q^{89} +(-3.76914 - 4.11379i) q^{90} +(-1.31317 - 10.9320i) q^{91} +(-1.79437 + 1.88570i) q^{92} +(0.326802 + 1.43181i) q^{93} +(4.24806 - 10.6267i) q^{94} +(-4.85586 + 1.10832i) q^{95} +(4.77186 - 3.03798i) q^{96} +3.59515i q^{97} +(-9.24525 - 3.53912i) q^{98} +0.486678i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9	$ 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9} - 20 q^{10} + 14 q^{14} - 20 q^{16} - 12 q^{19} + 25 q^{20} + 2 q^{21} - 6 q^{22} - 27 q^{24} + 32 q^{25} - 6 q^{26} + 28 q^{27} + 6 q^{28} - 8 q^{30} + 4 q^{31} - 45 q^{32} - 44 q^{34} + 12 q^{35} - 10 q^{37} - 35 q^{38} - 14 q^{39} + 40 q^{40} + 7 q^{42} + 20 q^{44} + 28 q^{46} + 8 q^{47} - 8 q^{48} - 8 q^{49} + 114 q^{50} - 20 q^{52} - 8 q^{53} + 23 q^{56} + 12 q^{57} - 6 q^{58} - 20 q^{59} + 10 q^{60} - 14 q^{61} + 16 q^{62} + 12 q^{63} - 42 q^{64} - 8 q^{65} + 6 q^{66} + 16 q^{68} + 19 q^{70} - 28 q^{71} - 15 q^{72} + 22 q^{74} - 18 q^{75} - 49 q^{76} + 8 q^{77} + 6 q^{78} - 26 q^{80} - 28 q^{81} - 12 q^{82} - 10 q^{83} - 27 q^{84} - 24 q^{85} - 34 q^{86} + 94 q^{88} - 20 q^{90} + 16 q^{91} + 7 q^{92} - 4 q^{93} + 11 q^{94} + 10 q^{96} - 150 q^{98}+O(q^{100}) $ 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9 - 20 * q^10 + 14 * q^14 - 20 * q^16 - 12 * q^19 + 25 * q^20 + 2 * q^21 - 6 * q^22 - 27 * q^24 + 32 * q^25 - 6 * q^26 + 28 * q^27 + 6 * q^28 - 8 * q^30 + 4 * q^31 - 45 * q^32 - 44 * q^34 + 12 * q^35 - 10 * q^37 - 35 * q^38 - 14 * q^39 + 40 * q^40 + 7 * q^42 + 20 * q^44 + 28 * q^46 + 8 * q^47 - 8 * q^48 - 8 * q^49 + 114 * q^50 - 20 * q^52 - 8 * q^53 + 23 * q^56 + 12 * q^57 - 6 * q^58 - 20 * q^59 + 10 * q^60 - 14 * q^61 + 16 * q^62 + 12 * q^63 - 42 * q^64 - 8 * q^65 + 6 * q^66 + 16 * q^68 + 19 * q^70 - 28 * q^71 - 15 * q^72 + 22 * q^74 - 18 * q^75 - 49 * q^76 + 8 * q^77 + 6 * q^78 - 26 * q^80 - 28 * q^81 - 12 * q^82 - 10 * q^83 - 27 * q^84 - 24 * q^85 - 34 * q^86 + 94 * q^88 - 20 * q^90 + 16 * q^91 + 7 * q^92 - 4 * q^93 + 11 * q^94 + 10 * q^96 - 150 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{14}\right)$

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 $

$2$	−0.0968063	−	1.41090i	−0.0684524	−	0.997654i
$2$	−0.0968063	−	1.41090i	−0.0684524	−	0.997654i
$3$	0.222521	+	0.974928i	0.128473	+	0.562875i
$3$	0.222521	+	0.974928i	0.128473	+	0.562875i
$4$	−1.98126	+	0.273167i	−0.990629	+	0.136584i
$5$	−3.84631	+	0.877896i	−1.72012	+	0.392607i	−0.964850	−	0.262802i	$-0.915353\pi$
$5$	−3.84631	+	0.877896i	−1.72012	+	0.392607i	−0.755274	+	0.655409i	$0.772496\pi$
$6$	1.35398	−	0.408333i	0.552760	−	0.166701i
$7$	2.22982	−	1.42405i	0.842792	−	0.538240i
$7$	2.22982	−	1.42405i	0.842792	−	0.538240i
$8$	0.577209	+	2.76890i	0.204074	+	0.978955i
$9$	−0.900969	+	0.433884i	−0.300323	+	0.144628i
$10$	1.61097	+	5.34176i	0.509433	+	1.68921i
$11$	0.211161	−	0.438481i	0.0636676	−	0.132207i	−0.866707	−	0.498818i	$-0.833768\pi$
$11$	0.211161	−	0.438481i	0.0636676	−	0.132207i	0.930374	+	0.366611i	$0.119482\pi$
$12$	−0.707190	−	1.87080i	−0.204148	−	0.540053i
$13$	1.80566	−	3.74949i	0.500800	−	1.03992i	−0.485389	−	0.874299i	$-0.661322\pi$
$13$	1.80566	−	3.74949i	0.500800	−	1.03992i	0.986189	−	0.165624i	$-0.0529638\pi$
$14$	−2.22505	−	3.00818i	−0.594669	−	0.803971i
$15$	−1.71177	−	3.55453i	−0.441977	−	0.917775i
$16$	3.85076	−	1.08243i	0.962690	−	0.270607i
$17$	3.87770	+	3.09236i	0.940480	+	0.750007i	0.968348	−	0.249604i	$-0.0803005\pi$
$17$	3.87770	+	3.09236i	0.940480	+	0.750007i	−0.0278684	+	0.999612i	$0.508872\pi$
$18$	0.699384	+	1.22917i	0.164847	+	0.289718i
$19$	1.26247			0.289631			0.144815	−	0.989459i	$-0.453741\pi$
$19$	1.26247			0.289631			0.144815	+	0.989459i	$0.453741\pi$
$20$	7.38072	−	2.79002i	1.65038	−	0.623868i
$21$	1.88453	+	1.85703i	0.411237	+	0.405237i
$22$	−0.639093	−	0.255479i	−0.136255	−	0.0544683i
$23$	1.01756	−	0.811475i	0.212175	−	0.169204i	−0.511636	−	0.859203i	$-0.670960\pi$
$23$	1.01756	−	0.811475i	0.212175	−	0.169204i	0.723811	+	0.689998i	$0.242389\pi$
$24$	−2.57104	+	1.17888i	−0.524811	+	0.240637i
$25$	9.51858	−	4.58391i	1.90372	−	0.916781i
$26$	−5.46495	−	2.18463i	−1.07176	−	0.428440i
$27$	−0.623490	−	0.781831i	−0.119991	−	0.150464i
$28$	−4.02884	+	3.43052i	−0.761379	+	0.648307i
$29$	3.84838	−	4.82572i	0.714627	−	0.896114i	−0.283393	−	0.959004i	$-0.591460\pi$
$29$	3.84838	−	4.82572i	0.714627	−	0.896114i	0.998020	+	0.0628897i	$0.0200316\pi$
$30$	−4.84936	+	2.75923i	−0.885368	+	0.503764i
$31$	1.46864			0.263775			0.131887	−	0.991265i	$-0.457896\pi$
$31$	1.46864			0.263775			0.131887	+	0.991265i	$0.457896\pi$
$32$	−1.89997	−	5.32824i	−0.335871	−	0.941908i
$33$	0.474475	+	0.108296i	0.0825956	+	0.0188519i
$34$	3.98761	−	5.77039i	0.683870	−	0.989613i
$35$	−7.32641	+	7.43489i	−1.23839	+	1.25673i
$36$	1.66653	−	1.10575i	0.277755	−	0.184292i
$37$	5.94597	−	7.45601i	0.977511	−	1.22576i	0.00332925	−	0.999994i	$-0.498940\pi$
$37$	5.94597	−	7.45601i	0.977511	−	1.22576i	0.974182	−	0.225765i	$-0.0724883\pi$
$38$	−0.122215	−	1.78122i	−0.0198259	−	0.288951i
$39$	4.05728	+	0.926049i	0.649685	+	0.148286i
$40$	−4.65094	−	10.1433i	−0.735378	−	1.60380i
$41$	−0.785690	+	0.179329i	−0.122704	+	0.0280064i	−0.283432	−	0.958992i	$-0.591473\pi$
$41$	−0.785690	+	0.179329i	−0.122704	+	0.0280064i	0.160728	+	0.986999i	$0.448616\pi$
$42$	2.43764	−	2.83864i	0.376136	−	0.438012i
$43$	−9.95871	−	2.27301i	−1.51869	−	0.346631i	−0.619783	−	0.784773i	$-0.712779\pi$
$43$	−9.95871	−	2.27301i	−1.51869	−	0.346631i	−0.898906	+	0.438142i	$0.855637\pi$
$44$	−0.298586	+	0.926427i	−0.0450136	+	0.139664i
$45$	3.08450	−	2.45981i	0.459811	−	0.366687i
$46$	−1.24341	−	1.35711i	−0.183331	−	0.200095i
$47$	7.29098	+	3.51115i	1.06350	+	0.512154i	0.882006	−	0.471238i	$-0.156193\pi$
$47$	7.29098	+	3.51115i	1.06350	+	0.512154i	0.181493	+	0.983392i	$0.441907\pi$
$48$	1.91217	+	3.51335i	0.275997	+	0.507108i
$49$	2.94417	−	6.35074i	0.420595	−	0.907248i
$50$	−7.38887	−	12.9860i	−1.04494	−	1.83649i
$51$	−2.15196	+	4.46859i	−0.301335	+	0.625728i
$52$	−2.55324	+	7.92196i	−0.354071	+	1.09858i
$53$	4.02092	+	5.04208i	0.552316	+	0.692583i	0.977117	−	0.212704i	$-0.0682272\pi$
$53$	4.02092	+	5.04208i	0.552316	+	0.692583i	−0.424800	+	0.905287i	$0.639656\pi$
$54$	−1.04273	+	0.955366i	−0.141897	+	0.130009i
$55$	−0.427252	+	1.87191i	−0.0576107	+	0.252409i
$56$	5.23013	+	5.35218i	0.698905	+	0.715215i
$57$	0.280926	+	1.23082i	0.0372096	+	0.163026i
$58$	−7.18114	−	4.96251i	−0.942930	−	0.651610i
$59$	−0.246939	+	1.08191i	−0.0321487	+	0.140853i	−0.988455	−	0.151513i	$-0.951585\pi$
$59$	−0.246939	+	1.08191i	−0.0321487	+	0.140853i	0.956307	+	0.292366i	$0.0944425\pi$
$60$	4.36244	+	6.57483i	0.563188	+	0.848807i
$61$	4.52728	+	3.61038i	0.579659	+	0.462262i	0.868896	−	0.494995i	$-0.164830\pi$
$61$	4.52728	+	3.61038i	0.579659	+	0.462262i	−0.289237	+	0.957257i	$0.593402\pi$
$62$	−0.142173	−	2.07209i	−0.0180560	−	0.263156i
$63$	−1.39112	+	2.25051i	−0.175265	+	0.283537i
$64$	−7.33366	+	3.19647i	−0.916707	+	0.399559i
$65$	−3.65347	+	16.0069i	−0.453158	+	1.98541i
$66$	0.106862	−	0.679919i	0.0131538	−	0.0836923i
$67$			5.76579i			0.704404i	0.935924	+	0.352202i	$0.114567\pi$
$67$			5.76579i			0.704404i	−0.935924	+	0.352202i	$0.885433\pi$
$68$	−8.52745	−	5.06750i	−1.03410	−	0.614525i
$69$	1.01756	+	0.811475i	0.122500	+	0.0976901i
$70$	11.1991	+	9.61706i	1.33855	+	1.14946i
$71$	−3.14148	+	2.50524i	−0.372825	+	0.297318i	−0.791920	−	0.610624i	$-0.790919\pi$
$71$	−3.14148	+	2.50524i	−0.372825	+	0.297318i	0.419096	+	0.907942i	$0.362347\pi$
$72$	−1.72143	−	2.24425i	−0.202872	−	0.264488i
$73$	6.35632	+	13.1990i	0.743952	+	1.54483i	0.835785	+	0.549057i	$0.185013\pi$
$73$	6.35632	+	13.1990i	0.743952	+	1.54483i	−0.0918335	+	0.995774i	$0.529273\pi$
$74$	−11.0953	−	7.66735i	−1.28980	−	0.891312i
$75$	6.58706	+	8.25991i	0.760608	+	0.953772i
$76$	−2.50128	+	0.344866i	−0.286916	+	0.0395588i
$77$	−0.153568	−	1.27844i	−0.0175006	−	0.145691i
$78$	0.913788	−	5.81405i	0.103466	−	0.658312i
$79$		−	17.2973i		−	1.94610i	−0.230603	−	0.973048i	$-0.574070\pi$
$79$		−	17.2973i		−	1.94610i	0.230603	−	0.973048i	$-0.425930\pi$
$80$	−13.8610	+	7.54393i	−1.54970	+	0.843437i
$81$	0.623490	−	0.781831i	0.0692766	−	0.0868702i
$82$	0.329074	+	1.09117i	0.0363401	+	0.120499i
$83$	−4.95499	+	2.38620i	−0.543881	+	0.261919i	−0.685588	−	0.727989i	$-0.740455\pi$
$83$	−4.95499	+	2.38620i	−0.543881	+	0.261919i	0.141708	+	0.989909i	$0.454741\pi$
$84$	−4.24101	−	3.16446i	−0.462732	−	0.345271i
$85$	−17.6296	−	8.48997i	−1.91220	−	0.920867i
$86$	−2.24292	+	14.2707i	−0.241860	+	1.53885i
$87$	5.56108	+	2.67807i	0.596210	+	0.287120i
$88$	1.33600	+	0.331590i	0.142418	+	0.0353477i
$89$	−6.19385	−	12.8617i	−0.656547	−	1.36333i	−0.917404	−	0.397957i	$-0.869719\pi$
$89$	−6.19385	−	12.8617i	−0.656547	−	1.36333i	0.260857	−	0.965377i	$-0.415995\pi$
$90$	−3.76914	−	4.11379i	−0.397302	−	0.433631i
$91$	−1.31317	−	10.9320i	−0.137658	−	1.14599i
$92$	−1.79437	+	1.88570i	−0.187077	+	0.196598i
$93$	0.326802	+	1.43181i	0.0338878	+	0.148472i
$94$	4.24806	−	10.6267i	0.438154	−	1.09606i
$95$	−4.85586	+	1.10832i	−0.498200	+	0.113711i
$96$	4.77186	−	3.03798i	0.487026	−	0.310063i
$97$			3.59515i			0.365033i	0.983203	+	0.182516i	$0.0584242\pi$
$97$			3.59515i			0.365033i	−0.983203	+	0.182516i	$0.941576\pi$
$98$	−9.24525	−	3.53912i	−0.933911	−	0.357506i
$99$			0.486678i			0.0489129i
$100$	−17.6066	+	11.6821i	−1.76066	+	1.16821i
$101$	−9.20206	+	2.10031i	−0.915640	+	0.208989i	−0.654280	−	0.756253i	$-0.727028\pi$
$101$	−9.20206	+	2.10031i	−0.915640	+	0.208989i	−0.261360	+	0.965241i	$0.584171\pi$
$102$	6.51304	+	2.60360i	0.644887	+	0.257795i
$103$	3.13189	+	13.7217i	0.308595	+	1.35204i	0.856779	+	0.515684i	$0.172462\pi$
$103$	3.13189	+	13.7217i	0.308595	+	1.35204i	−0.548185	+	0.836357i	$0.684681\pi$
$104$	11.4242	+	2.83546i	1.12024	+	0.278040i
$105$	−8.87876	−	5.48830i	−0.866478	−	0.535603i
$106$	6.72460	−	6.16121i	0.653151	−	0.598430i
$107$	−7.50112	−	15.5762i	−0.725161	−	1.50581i	−0.857431	−	0.514598i	$-0.827941\pi$
$107$	−7.50112	−	15.5762i	−0.725161	−	1.50581i	0.132271	−	0.991214i	$-0.457773\pi$
$108$	1.44886	+	1.37869i	0.139417	+	0.132665i
$109$	−1.60357	−	0.772241i	−0.153595	−	0.0739672i	0.355507	−	0.934673i	$-0.384308\pi$
$109$	−1.60357	−	0.772241i	−0.153595	−	0.0739672i	−0.509102	+	0.860706i	$0.670022\pi$
$110$	2.68244	+	0.421595i	0.255760	+	0.0401975i
$111$	8.59217	+	4.13777i	0.815533	+	0.392740i
$112$	7.04506	−	7.89729i	0.665695	−	0.746224i
$113$	13.6982	−	6.59671i	1.28862	−	0.620566i	0.341028	−	0.940053i	$-0.389225\pi$
$113$	13.6982	−	6.59671i	1.28862	−	0.620566i	0.947591	+	0.319487i	$0.103511\pi$
$114$	1.70936	−	0.515509i	0.160096	−	0.0482818i
$115$	−3.20145	+	4.01450i	−0.298537	+	0.374354i
$116$	−6.30641	+	10.6122i	−0.585535	+	0.985323i
$117$			4.16162i			0.384742i
$118$	1.55037	+	0.243670i	0.142723	+	0.0224316i
$119$	13.0502	+	1.37337i	1.19631	+	0.125896i
$120$	8.85410	−	6.79143i	0.808265	−	0.619970i
$121$	6.71071	+	8.41497i	0.610065	+	0.764997i
$122$	4.65561	−	6.73703i	0.421499	−	0.609942i
$123$	−0.349665	−	0.726087i	−0.0315282	−	0.0654691i
$124$	−2.90975	+	0.401184i	−0.261303	+	0.0360274i
$125$	−17.1647	+	13.6884i	−1.53526	+	1.22433i
$126$	3.30990	+	1.74487i	0.294869	+	0.155445i
$127$	2.69476	+	2.14900i	0.239121	+	0.190693i	0.735717	−	0.677289i	$-0.236845\pi$
$127$	2.69476	+	2.14900i	0.239121	+	0.190693i	−0.496596	+	0.867982i	$0.665417\pi$
$128$	5.21984	+	10.0376i	0.461373	+	0.887206i
$129$		−	10.2148i		−	0.899364i
$130$	22.9378	+	3.60510i	2.01178	+	0.316188i
$131$	−0.220049	+	0.964099i	−0.0192258	+	0.0842338i	−0.983631	−	0.180196i	$-0.942327\pi$
$131$	−0.220049	+	0.964099i	−0.0192258	+	0.0842338i	0.964405	+	0.264430i	$0.0851838\pi$
$132$	−0.969641	−	0.0849509i	−0.0843964	−	0.00739402i
$133$	2.81508	−	1.79782i	0.244098	−	0.155891i
$134$	8.13494	−	0.558165i	0.702752	−	0.0482181i
$135$	3.08450	+	2.45981i	0.265472	+	0.211707i
$136$	−6.32421	+	12.5219i	−0.542296	+	1.07374i
$137$	4.05489	−	17.7656i	0.346432	−	1.51782i	−0.438781	−	0.898594i	$-0.644590\pi$
$137$	4.05489	−	17.7656i	0.346432	−	1.51782i	0.785213	−	0.619225i	$-0.212553\pi$
$138$	1.04640	−	1.51422i	0.0890756	−	0.128899i
$139$	2.69583	+	11.8112i	0.228657	+	1.00181i	0.950736	+	0.310002i	$0.100330\pi$
$139$	2.69583	+	11.8112i	0.228657	+	1.00181i	−0.722079	+	0.691811i	$0.756813\pi$
$140$	12.4845	−	16.7318i	1.05514	−	1.41409i
$141$	−1.80072	+	7.88948i	−0.151648	+	0.664414i
$142$	3.83876	+	4.18978i	0.322141	+	0.351598i
$143$	−1.26280	−	1.58350i	−0.105600	−	0.132419i
$144$	−2.99977	+	2.64602i	−0.249980	+	0.220501i
$145$	−10.5656	+	21.9397i	−0.877426	+	1.82199i
$146$	18.0072	−	10.2459i	1.49028	−	0.847954i
$147$	6.84665	+	1.45718i	0.564702	+	0.120186i
$148$	−9.74375	+	16.3965i	−0.800931	+	1.34778i
$149$	−6.45073	−	3.10651i	−0.528464	−	0.254495i	0.150573	−	0.988599i	$-0.451888\pi$
$149$	−6.45073	−	3.10651i	−0.528464	−	0.254495i	−0.679037	+	0.734104i	$0.737602\pi$
$150$	11.0162	−	10.0933i	0.899470	−	0.824112i
$151$	14.3752	−	11.4638i	1.16984	−	0.932915i	0.171208	−	0.985235i	$-0.445233\pi$
$151$	14.3752	−	11.4638i	1.16984	−	0.932915i	0.998630	+	0.0523203i	$0.0166617\pi$
$152$	0.728709	+	3.49566i	0.0591061	+	0.283535i
$153$	−4.83541	−	1.10365i	−0.390920	−	0.0892249i
$154$	−1.78888	+	0.340429i	−0.144152	+	0.0274325i
$155$	−5.64884	+	1.28931i	−0.453725	+	0.103560i
$156$	−8.29149	−	0.726423i	−0.663850	−	0.0581604i
$157$	−2.24926	−	0.513379i	−0.179511	−	0.0409721i	0.131821	−	0.991274i	$-0.457918\pi$
$157$	−2.24926	−	0.513379i	−0.179511	−	0.0409721i	−0.311331	+	0.950301i	$0.600775\pi$
$158$	−24.4047	+	1.67449i	−1.94153	+	0.133215i
$159$	−4.02092	+	5.04208i	−0.318880	+	0.399863i
$160$	11.9855	+	18.8261i	0.947539	+	1.48833i
$161$	1.11339	−	3.25849i	0.0877472	−	0.256805i
$162$	−1.16344	−	0.803993i	−0.0914086	−	0.0631677i
$163$	−20.1553	−	4.60033i	−1.57869	−	0.360325i	−0.658742	−	0.752369i	$-0.728911\pi$
$163$	−20.1553	−	4.60033i	−1.57869	−	0.360325i	−0.919947	+	0.392044i	$0.871768\pi$
$164$	1.50767	−	0.569921i	0.117729	−	0.0445034i
$165$	−1.92005			−0.149476
$166$	3.84635	+	6.75998i	0.298535	+	0.524676i
$167$	5.97855	−	7.49686i	0.462634	−	0.580124i	−0.494716	−	0.869054i	$-0.664728\pi$
$167$	5.97855	−	7.49686i	0.462634	−	0.580124i	0.957350	+	0.288930i	$0.0932995\pi$
$168$	−4.05417	+	6.28997i	−0.312786	+	0.485281i
$169$	−2.69293	−	3.37682i	−0.207148	−	0.259756i
$170$	−10.2718	+	25.6954i	−0.787812	+	1.97075i
$171$	−1.13745	+	0.547765i	−0.0869827	+	0.0418887i
$172$	20.3517	+	1.78302i	1.55180	+	0.135954i
$173$	14.8636	−	11.8533i	1.13006	−	0.901191i	0.134095	−	0.990968i	$-0.457187\pi$
$173$	14.8636	−	11.8533i	1.13006	−	0.901191i	0.995962	+	0.0897778i	$0.0286157\pi$
$174$	3.24014	−	8.10536i	0.245634	−	0.614466i
$175$	14.6970	−	23.7762i	1.11099	−	1.79731i
$176$	0.338507	−	1.91705i	0.0255159	−	0.144503i
$177$	−1.10973			−0.0834127
$178$	−17.5469	+	9.98398i	−1.31519	+	0.748331i
$179$	2.37352	+	1.89282i	0.177405	+	0.141476i	0.708167	−	0.706045i	$-0.249523\pi$
$179$	2.37352	+	1.89282i	0.177405	+	0.141476i	−0.530761	+	0.847521i	$0.678094\pi$
$180$	−5.43925	+	5.71610i	−0.405418	+	0.426053i
$181$	−6.09541	−	12.6573i	−0.453069	−	0.940806i	−0.994952	−	0.100353i	$-0.968003\pi$
$181$	−6.09541	−	12.6573i	−0.453069	−	0.940806i	0.541883	−	0.840454i	$-0.317711\pi$
$182$	−15.2968	+	2.91104i	−1.13388	+	0.215780i
$183$	−2.51245	+	5.21716i	−0.185726	+	0.385663i
$184$	2.83424	+	2.34913i	0.208943	+	0.173180i
$185$	−16.3245	+	33.8981i	−1.20020	+	2.49224i
$186$	1.98851	−	0.599693i	0.145804	−	0.0439716i
$187$	2.17476	−	1.04731i	0.159034	−	0.0765869i
$188$	−15.4044	−	4.96483i	−1.12348	−	0.362098i
$189$	−2.50363	−	0.855461i	−0.182113	−	0.0622256i
$190$	2.03380	+	6.74382i	0.147547	+	0.489248i
$191$	−12.8094	+	2.92366i	−0.926856	+	0.211549i	−0.659202	−	0.751966i	$-0.729106\pi$
$191$	−12.8094	+	2.92366i	−0.926856	+	0.211549i	−0.267654	+	0.963515i	$0.586248\pi$
$192$	−4.74822	−	6.43851i	−0.342674	−	0.464659i
$193$	1.21712	+	5.33255i	0.0876101	+	0.383845i	0.999656	−	0.0262441i	$-0.00835473\pi$
$193$	1.21712	+	5.33255i	0.0876101	+	0.383845i	−0.912045	+	0.410089i	$0.865498\pi$
$194$	5.07239	−	0.348034i	0.364176	−	0.0249874i
$195$	−16.4186			−1.17576
$196$	−4.09834	+	13.3867i	−0.292738	+	0.956193i
$197$	−5.42046			−0.386192			−0.193096	−	0.981180i	$-0.561853\pi$
$197$	−5.42046			−0.386192			−0.193096	+	0.981180i	$0.561853\pi$
$198$	0.686652	−	0.0471135i	0.0487982	−	0.00334821i
$199$	4.19586	+	18.3833i	0.297437	+	1.30316i	0.873929	+	0.486054i	$0.161564\pi$
$199$	4.19586	+	18.3833i	0.297437	+	1.30316i	−0.576492	+	0.817103i	$0.695579\pi$
$200$	18.1866	+	23.7102i	1.28599	+	1.67656i
$201$	−5.62123	+	1.28301i	−0.396491	+	0.0904966i
$202$	3.85414	+	12.7798i	0.271176	+	0.899186i
$203$	1.70913	−	16.2408i	0.119957	−	1.13988i
$204$	3.04291	−	9.44127i	0.213046	−	0.661021i
$205$	2.86458	−	1.37951i	0.200071	−	0.0963491i
$206$	19.0567	−	5.74712i	1.32775	−	0.400421i
$207$	−0.564702	+	1.17262i	−0.0392495	+	0.0815024i
$208$	2.89460	−	16.3929i	0.200705	−	1.13664i
$209$	0.266585	−	0.553570i	0.0184401	−	0.0382912i
$210$	−6.88390	+	13.0583i	−0.475035	+	0.901109i
$211$	10.0671	+	20.9046i	0.693048	+	1.43913i	0.888715	+	0.458459i	$0.151598\pi$
$211$	10.0671	+	20.9046i	0.693048	+	1.43913i	−0.195667	+	0.980670i	$0.562687\pi$
$212$	−9.34381	−	8.89127i	−0.641736	−	0.610655i
$213$	−3.14148	−	2.50524i	−0.215250	−	0.171657i
$214$	−21.2503	+	12.0912i	−1.45264	+	0.826536i
$215$	40.2998			2.74842
$216$	1.80493	−	2.17766i	0.122810	−	0.148171i
$217$	3.27479	−	2.09141i	0.222307	−	0.141974i
$218$	−0.934316	+	2.33724i	−0.0632798	+	0.158298i
$219$	−11.4537	+	9.13402i	−0.773969	+	0.617220i
$220$	0.335150	−	3.82545i	0.0225958	−	0.257912i
$221$	18.5966	−	8.95565i	1.25094	−	0.602422i
$222$	5.00619	−	12.5232i	0.335993	−	0.840504i
$223$	−9.77737	−	12.2604i	−0.654741	−	0.821019i	0.338018	−	0.941140i	$-0.390243\pi$
$223$	−9.77737	−	12.2604i	−0.654741	−	0.821019i	−0.992759	+	0.120120i	$0.961672\pi$
$224$	−11.8243	−	9.17534i	−0.790042	−	0.613053i
$225$	−6.58706	+	8.25991i	−0.439137	+	0.550661i
$226$	−10.6333	−	18.6881i	−0.707319	−	1.24312i
$227$	−5.31375			−0.352686			−0.176343	−	0.984329i	$-0.556427\pi$
$227$	−5.31375			−0.352686			−0.176343	+	0.984329i	$0.556427\pi$
$228$	−0.892806	−	2.36183i	−0.0591275	−	0.156416i
$229$	21.3557	+	4.87430i	1.41122	+	0.322103i	0.859164	−	0.511701i	$-0.170984\pi$
$229$	21.3557	+	4.87430i	1.41122	+	0.322103i	0.552061	+	0.833804i	$0.313842\pi$
$230$	5.97396	+	4.12829i	0.393911	+	0.272212i
$231$	1.21221	−	0.434196i	0.0797577	−	0.0285680i
$232$	15.5833	+	7.87036i	1.02309	+	0.516714i
$233$	2.34249	−	2.93739i	0.153462	−	0.192435i	−0.699157	−	0.714968i	$-0.746441\pi$
$233$	2.34249	−	2.93739i	0.153462	−	0.192435i	0.852619	+	0.522533i	$0.175013\pi$
$234$	5.87162	−	0.402872i	0.383840	−	0.0263365i
$235$	−31.1258	−	7.10426i	−2.03042	−	0.463431i
$236$	0.193707	−	2.21100i	0.0126093	−	0.143924i
$237$	16.8636	−	3.84901i	1.09541	−	0.250020i
$238$	0.674333	−	18.5455i	0.0437105	−	1.20212i
$239$	−6.92758	−	1.58118i	−0.448108	−	0.102278i	−0.00748909	−	0.999972i	$-0.502384\pi$
$239$	−6.92758	−	1.58118i	−0.448108	−	0.102278i	−0.440619	+	0.897694i	$0.645241\pi$
$240$	−10.4391	−	11.8348i	−0.673844	−	0.763930i
$241$	6.35072	−	5.06453i	0.409086	−	0.326235i	−0.397231	−	0.917718i	$-0.630029\pi$
$241$	6.35072	−	5.06453i	0.409086	−	0.326235i	0.806317	+	0.591484i	$0.201458\pi$
$242$	11.2230	−	10.2827i	0.721442	−	0.661000i
$243$	0.900969	+	0.433884i	0.0577972	+	0.0278337i
$244$	−9.95594	−	5.91639i	−0.637364	−	0.378758i
$245$	−5.74890	+	27.0116i	−0.367284	+	1.72571i
$246$	−0.990584	+	0.563631i	−0.0631573	+	0.0359358i
$247$	2.27959	−	4.73363i	0.145047	−	0.301193i
$248$	0.847710	+	4.06651i	0.0538297	+	0.258224i
$249$	−3.42896	−	4.29978i	−0.217301	−	0.272487i
$250$	20.9746	+	22.8925i	1.32655	+	1.44785i
$251$	0.449468	−	1.96925i	0.0283702	−	0.124298i	−0.958760	−	0.284217i	$-0.908266\pi$
$251$	0.449468	−	1.96925i	0.0283702	−	0.124298i	0.987130	+	0.159919i	$0.0511234\pi$
$252$	2.14141	−	4.83884i	0.134896	−	0.304818i
$253$	−0.140948	−	0.617532i	−0.00886131	−	0.0388239i
$254$	2.77115	−	4.01007i	0.173877	−	0.251614i
$255$	4.35415	−	19.0768i	0.272668	−	1.19463i
$256$	13.6567	−	8.33635i	0.853543	−	0.521022i
$257$	−5.51642	−	4.39920i	−0.344105	−	0.274414i	0.436153	−	0.899873i	$-0.356341\pi$
$257$	−5.51642	−	4.39920i	−0.344105	−	0.274414i	−0.780258	+	0.625458i	$0.784912\pi$
$258$	−14.4120	+	0.988859i	−0.897255	+	0.0615637i
$259$	2.64070	−	25.0929i	0.164085	−	1.55920i
$260$	2.86590	−	32.7118i	0.177736	−	2.02870i
$261$	−1.37347	+	6.01758i	−0.0850158	+	0.372479i
$262$	1.38155	+	0.217136i	0.0853522	+	0.0134147i
$263$			24.6901i			1.52246i	0.648483	+	0.761229i	$0.275404\pi$
$263$			24.6901i			1.52246i	−0.648483	+	0.761229i	$0.724596\pi$
$264$	−0.0259895	+	1.37629i	−0.00159954	+	0.0847046i
$265$	−19.8921	−	15.8635i	−1.22196	−	0.974484i
$266$	−2.80906	−	3.79774i	−0.172234	−	0.232855i
$267$	11.1609	−	8.90055i	0.683038	−	0.544705i
$268$	−1.57503	−	11.4235i	−0.0962101	−	0.697803i
$269$	3.38566	+	7.03040i	0.206428	+	0.428651i	0.978319	−	0.207103i	$-0.0664035\pi$
$269$	3.38566	+	7.03040i	0.206428	+	0.428651i	−0.771892	+	0.635754i	$0.780689\pi$
$270$	3.17194	−	4.59004i	0.193038	−	0.279341i
$271$	−16.4026	−	20.5683i	−0.996389	−	1.24943i	−0.968290	−	0.249828i	$-0.919626\pi$
$271$	−16.4026	−	20.5683i	−0.996389	−	1.24943i	−0.0280990	−	0.999605i	$-0.508945\pi$
$272$	18.2793	+	7.71060i	1.10835	+	0.467524i
$273$	10.3657	−	3.71285i	0.627363	−	0.224712i
$274$	−25.4580	−	4.00120i	−1.53797	−	0.241721i
$275$		−	5.14166i		−	0.310054i
$276$	−2.23771	−	1.32978i	−0.134694	−	0.0800432i
$277$	8.41073	−	10.5467i	0.505352	−	0.633691i	−0.462075	−	0.886841i	$-0.652895\pi$
$277$	8.41073	−	10.5467i	0.505352	−	0.633691i	0.967427	+	0.253149i	$0.0814664\pi$
$278$	16.4034	−	4.94693i	0.983811	−	0.296697i
$279$	−1.32320	+	0.637218i	−0.0792177	+	0.0381492i
$280$	−24.8154	−	15.9946i	−1.48300	−	0.955862i
$281$	2.69279	+	1.29678i	0.160638	+	0.0773594i	0.512475	−	0.858702i	$-0.328729\pi$
$281$	2.69279	+	1.29678i	0.160638	+	0.0773594i	−0.351837	+	0.936061i	$0.614443\pi$
$282$	11.3056	+	1.77688i	0.673237	+	0.105812i
$283$	−11.1751	−	5.38163i	−0.664289	−	0.319905i	0.0711795	−	0.997464i	$-0.477324\pi$
$283$	−11.1751	−	5.38163i	−0.664289	−	0.319905i	−0.735469	+	0.677559i	$0.763038\pi$
$284$	5.53972	−	5.82168i	0.328722	−	0.345453i
$285$	−2.16106	−	4.48749i	−0.128010	−	0.265816i
$286$	−2.11190	+	1.93497i	−0.124879	+	0.114417i
$287$	−1.49657	+	1.51873i	−0.0883399	+	0.0896479i
$288$	4.02365	+	3.97621i	0.237096	+	0.234300i
$289$	1.69099	+	7.40869i	0.0994697	+	0.435805i
$290$	31.9775	+	12.7831i	1.87778	+	0.750648i
$291$	−3.50502	+	0.799997i	−0.205468	+	0.0468967i
$292$	−16.1991	−	24.4144i	−0.947978	−	1.42874i
$293$		−	6.94236i		−	0.405577i	−0.979223	−	0.202788i	$-0.935000\pi$
$293$		−	6.94236i		−	0.405577i	0.979223	−	0.202788i	$-0.0650003\pi$
$294$	1.39313	−	9.80098i	0.0812490	−	0.571605i
$295$		−	4.37815i		−	0.254906i
$296$	24.0770	+	12.1601i	1.39945	+	0.706794i
$297$	−0.474475	+	0.108296i	−0.0275319	+	0.00628397i
$298$	−3.75849	+	9.40204i	−0.217723	+	0.544645i
$299$	−1.20526	−	5.28058i	−0.0697018	−	0.305384i
$300$	−15.3070	−	14.5656i	−0.883750	−	0.840948i
$301$	−25.4430	+	9.11329i	−1.46651	+	0.525281i
$302$	−17.5659	−	19.1722i	−1.01080	−	1.10323i
$303$	−4.09530	−	8.50399i	−0.235269	−	0.488541i
$304$	4.86147	−	1.36654i	0.278824	−	0.0783762i
$305$	−20.5829	−	9.91219i	−1.17857	−	0.567570i
$306$	−1.08904	+	6.92910i	−0.0622562	+	0.396110i
$307$	−9.88187	−	4.75886i	−0.563988	−	0.271602i	0.130090	−	0.991502i	$-0.458473\pi$
$307$	−9.88187	−	4.75886i	−0.563988	−	0.271602i	−0.694078	+	0.719900i	$0.744188\pi$
$308$	0.653484	+	2.49096i	0.0372357	+	0.141936i
$309$	−12.6808	+	6.10674i	−0.721384	+	0.347400i
$310$	2.36593	+	7.84511i	0.134376	+	0.445572i
$311$	−4.50930	+	5.65449i	−0.255699	+	0.320637i	−0.893068	−	0.449923i	$-0.851452\pi$
$311$	−4.50930	+	5.65449i	−0.255699	+	0.320637i	0.637368	+	0.770559i	$0.280023\pi$
$312$	−0.222239	+	11.7688i	−0.0125818	+	0.666275i
$313$			7.77323i			0.439369i	0.975571	+	0.219684i	$0.0705028\pi$
$313$			7.77323i			0.439369i	−0.975571	+	0.219684i	$0.929497\pi$
$314$	−0.506582	+	3.22317i	−0.0285881	+	0.181894i
$315$	3.37499	−	9.87741i	0.190159	−	0.556529i
$316$	4.72505	+	34.2704i	0.265805	+	1.92786i
$317$	7.45847	+	9.35262i	0.418909	+	0.525296i	0.945849	−	0.324607i	$-0.105232\pi$
$317$	7.45847	+	9.35262i	0.418909	+	0.525296i	−0.526940	+	0.849903i	$0.676661\pi$
$318$	7.50310	+	5.18500i	0.420753	+	0.290760i
$319$	−1.30336	−	2.70645i	−0.0729740	−	0.151532i
$320$	25.4014	−	18.7328i	1.41998	−	1.04720i
$321$	13.5166	−	10.7791i	0.754420	−	0.601630i
$322$	−4.70518	−	1.25543i	−0.262209	−	0.0699624i
$323$	4.89548	+	3.90401i	0.272392	+	0.217225i
$324$	−1.02172	+	1.71933i	−0.0567624	+	0.0955181i
$325$		−	43.9668i		−	2.43884i
$326$	−4.53942	+	28.8824i	−0.251415	+	1.59965i
$327$	0.396050	−	1.73521i	0.0219016	−	0.0959573i
$328$	−0.950052	−	2.07199i	−0.0524578	−	0.114407i
$329$	21.2576	−	2.55349i	1.17197	−	0.140778i
$330$	0.185873	+	2.70900i	0.0102320	+	0.149125i
$331$	14.2131	+	11.3346i	0.781222	+	0.623004i	0.930709	−	0.365760i	$-0.119191\pi$
$331$	14.2131	+	11.3346i	0.781222	+	0.623004i	−0.149487	+	0.988764i	$0.547762\pi$
$332$	9.16528	−	6.08121i	0.503010	−	0.333750i
$333$	−2.12209	+	9.29749i	−0.116290	+	0.509499i
$334$	−11.1561	−	7.70936i	−0.610432	−	0.421838i
$335$	−5.06177	−	22.1771i	−0.276554	−	1.21166i
$336$	9.26696	+	5.11111i	0.505554	+	0.278834i
$337$	−6.91159	+	30.2816i	−0.376498	+	1.64955i	0.331591	+	0.943423i	$0.392415\pi$
$337$	−6.91159	+	30.2816i	−0.376498	+	1.64955i	−0.708089	+	0.706123i	$0.750443\pi$
$338$	−4.50366	+	4.12634i	−0.244967	+	0.224443i
$339$	9.47945	+	11.8869i	0.514853	+	0.645605i
$340$	37.2480	+	12.0050i	2.02005	+	0.651061i
$341$	0.310119	−	0.643970i	0.0167939	−	0.0348729i
$342$	0.882952	+	1.55179i	0.0477446	+	0.0839113i
$343$	−2.47881	−	18.3536i	−0.133843	−	0.991003i
$344$	0.545490	−	28.8867i	0.0294109	−	1.55747i
$345$	−4.62624	−	2.22788i	−0.249068	−	0.119945i
$346$	−18.1627	−	19.8235i	−0.976432	−	1.06572i
$347$	−22.8895	+	18.2538i	−1.22877	+	0.979914i	−0.228794	+	0.973475i	$0.573478\pi$
$347$	−22.8895	+	18.2538i	−1.22877	+	0.979914i	−0.999979	+	0.00643910i	$0.997950\pi$
$348$	−11.7495	−	3.78685i	−0.629839	−	0.202996i
$349$	1.49584	+	0.341417i	0.0800707	+	0.0182756i	0.262369	−	0.964968i	$-0.415496\pi$
$349$	1.49584	+	0.341417i	0.0800707	+	0.0182756i	−0.182298	+	0.983243i	$0.558354\pi$
$350$	−34.9685	−	18.4342i	−1.86915	−	0.985351i
$351$	−4.05728	+	0.926049i	−0.216562	+	0.0494288i
$352$	−2.73753	−	0.292015i	−0.145911	−	0.0155645i
$353$	−32.2813	−	7.36800i	−1.71816	−	0.392159i	−0.753874	−	0.657020i	$-0.771817\pi$
$353$	−32.2813	−	7.36800i	−1.71816	−	0.392159i	−0.964287	+	0.264861i	$0.914674\pi$
$354$	0.107429	+	1.56572i	0.00570980	+	0.0832171i
$355$	9.88376	−	12.3938i	0.524576	−	0.657797i
$356$	15.7850	+	23.7903i	0.836604	+	1.26088i
$357$	1.56502	+	13.0286i	0.0828294	+	0.689548i
$358$	2.44080	−	3.53203i	0.129000	−	0.186673i
$359$	13.4995	+	3.08118i	0.712477	+	0.162618i	0.563372	−	0.826203i	$-0.309504\pi$
$359$	13.4995	+	3.08118i	0.712477	+	0.162618i	0.149105	+	0.988821i	$0.452361\pi$
$360$	8.59138	+	7.12087i	0.452805	+	0.375303i
$361$	−17.4062			−0.916114
$362$	−17.2680	+	9.82530i	−0.907586	+	0.516406i
$363$	−6.71071	+	8.41497i	−0.352221	+	0.441671i
$364$	5.58800	+	21.3005i	0.292891	+	1.11645i
$365$	−36.0358	−	45.1875i	−1.88620	−	2.36522i
$366$	7.60409	+	3.03975i	0.397472	+	0.158890i
$367$	−24.4659	+	11.7821i	−1.27711	+	0.615023i	−0.944645	−	0.328093i	$-0.893594\pi$
$367$	−24.4659	+	11.7821i	−1.27711	+	0.615023i	−0.332463	+	0.943116i	$0.607880\pi$
$368$	3.04000	−	4.22623i	0.158471	−	0.220307i
$369$	0.630075	−	0.502468i	0.0328004	−	0.0261574i
$370$	49.4070	+	19.7506i	2.56855	+	1.02678i
$371$	16.1461	+	5.51692i	0.838263	+	0.286424i
$372$	−1.03860	−	2.74752i	−0.0538491	−	0.142452i
$373$	8.11851			0.420361			0.210180	−	0.977663i	$-0.432595\pi$
$373$	8.11851			0.420361			0.210180	+	0.977663i	$0.432595\pi$
$374$	−1.68818	−	2.96698i	−0.0872935	−	0.153419i
$375$	−17.1647	−	13.6884i	−0.886382	−	0.706866i
$376$	−5.51362	+	22.2147i	−0.284343	+	1.14564i
$377$	−11.1451	−	23.1431i	−0.574004	−	1.19193i
$378$	−0.964599	+	3.61518i	−0.0496136	+	0.185945i
$379$	1.47164	−	3.05588i	0.0755928	−	0.156970i	−0.859747	−	0.510719i	$-0.829379\pi$
$379$	1.47164	−	3.05588i	0.0755928	−	0.156970i	0.935340	+	0.353749i	$0.115093\pi$
$380$	9.31794	−	3.52232i	0.478000	−	0.180691i
$381$	−1.49548	+	3.10540i	−0.0766157	+	0.159094i
$382$	5.36502	+	17.7897i	0.274498	+	0.910201i
$383$	2.98516	−	1.43758i	0.152534	−	0.0734567i	−0.356059	−	0.934463i	$-0.615880\pi$
$383$	2.98516	−	1.43758i	0.152534	−	0.0734567i	0.508594	+	0.861007i	$0.330166\pi$
$384$	−8.62441	+	7.32254i	−0.440112	+	0.373677i
$385$	1.71300	+	4.78245i	0.0873027	+	0.243736i
$386$	7.40584	−	2.23345i	0.376948	−	0.113680i
$387$	9.95871	−	2.27301i	0.506230	−	0.115544i
$388$	−0.982079	−	7.12293i	−0.0498575	−	0.361612i
$389$	−3.05499	−	13.3848i	−0.154894	−	0.678636i	−0.991421	−	0.130710i	$-0.958274\pi$
$389$	−3.05499	−	13.3848i	−0.154894	−	0.678636i	0.836526	−	0.547927i	$-0.184583\pi$
$390$	1.58942	+	23.1649i	0.0804834	+	1.17300i
$391$	6.45515			0.326451
$392$	19.2840	+	4.48641i	0.973988	+	0.226598i
$393$	−0.988893			−0.0498831
$394$	0.524734	+	7.64770i	0.0264357	+	0.385286i
$395$	15.1852	+	66.5307i	0.764051	+	3.34752i
$396$	−0.132944	−	0.964233i	−0.00668071	−	0.0484545i
$397$	−13.8667	+	3.16498i	−0.695949	+	0.158846i	−0.555839	−	0.831290i	$-0.687603\pi$
$397$	−13.8667	+	3.16498i	−0.695949	+	0.158846i	−0.140110	+	0.990136i	$0.544746\pi$
$398$	25.5307	−	7.69955i	1.27974	−	0.385943i
$399$	2.37916	+	2.34445i	0.119107	+	0.117369i
$400$	31.6920	−	27.9547i	1.58460	−	1.39774i
$401$	−1.13160	+	0.544952i	−0.0565096	+	0.0272136i	−0.461925	−	0.886919i	$-0.652841\pi$
$401$	−1.13160	+	0.544952i	−0.0565096	+	0.0272136i	0.405416	+	0.914133i	$0.367127\pi$
$402$	2.35437	+	7.80678i	0.117425	+	0.389367i
$403$	2.65186	−	5.50665i	0.132099	−	0.274306i
$404$	17.6579	−	6.67496i	0.878514	−	0.332092i
$405$	−1.71177	+	3.55453i	−0.0850585	+	0.176626i
$406$	−23.0795	−	0.839194i	−1.14542	−	0.0416485i
$407$	−2.01376	−	4.18162i	−0.0998184	−	0.207275i
$408$	−13.6152	−	3.37926i	−0.674054	−	0.167298i
$409$	3.43363	+	2.73823i	0.169782	+	0.135397i	0.704695	−	0.709511i	$-0.251084\pi$
$409$	3.43363	+	2.73823i	0.169782	+	0.135397i	−0.534912	+	0.844908i	$0.679655\pi$
$410$	−2.22365	−	3.90808i	−0.109818	−	0.193006i
$411$	18.2225			0.898849
$412$	−9.95341	−	26.3307i	−0.490369	−	1.29722i
$413$	0.990065	+	2.76412i	0.0487179	+	0.136013i
$414$	1.70911	+	0.683219i	0.0839980	+	0.0335784i
$415$	16.9636	−	13.5280i	0.832711	−	0.664065i
$416$	−23.4089	−	2.49705i	−1.14772	−	0.122428i
$417$	−10.9152	+	5.25648i	−0.534519	+	0.257411i
$418$	−0.806837	−	0.322535i	−0.0394637	−	0.0157757i
$419$	10.1665	+	12.7483i	0.496664	+	0.622797i	0.965473	−	0.260502i	$-0.0838882\pi$
$419$	10.1665	+	12.7483i	0.496664	+	0.622797i	−0.468809	+	0.883300i	$0.655317\pi$
$420$	19.0903	+	8.44835i	0.931512	+	0.412237i
$421$	−3.44855	+	4.32435i	−0.168072	+	0.210756i	−0.858733	−	0.512423i	$-0.828748\pi$
$421$	−3.44855	+	4.32435i	−0.168072	+	0.210756i	0.690661	+	0.723178i	$0.257320\pi$
$422$	28.5196	−	16.2273i	1.38831	−	0.789935i
$423$	−8.09238			−0.393465
$424$	−11.6401	+	14.0439i	−0.565294	+	0.682031i
$425$	51.0852	+	11.6599i	2.47800	+	0.565587i
$426$	−3.23053	+	4.67482i	−0.156519	+	0.226496i
$427$	15.2364	+	1.60343i	0.737340	+	0.0775954i
$428$	19.1166	+	28.8115i	0.924034	+	1.39265i
$429$	1.26280	−	1.58350i	0.0609684	−	0.0764520i
$430$	−3.90127	−	56.8588i	−0.188136	−	2.74197i
$431$	−26.8429	−	6.12673i	−1.29298	−	0.295114i	−0.479929	−	0.877307i	$-0.659338\pi$
$431$	−26.8429	−	6.12673i	−1.29298	−	0.295114i	−0.813050	+	0.582193i	$0.802195\pi$
$432$	−3.24719	−	2.33576i	−0.156230	−	0.112379i
$433$	9.19233	−	2.09809i	0.441755	−	0.100828i	0.00414277	−	0.999991i	$-0.498681\pi$
$433$	9.19233	−	2.09809i	0.441755	−	0.100828i	0.437613	+	0.899164i	$0.355824\pi$
$434$	−3.26778	−	4.41793i	−0.156859	−	0.212067i
$435$	−23.7407	−	5.41866i	−1.13828	−	0.259805i
$436$	3.38804	+	1.09196i	0.162258	+	0.0522956i
$437$	1.28464	−	1.02446i	0.0614525	−	0.0490067i
$438$	13.9959	+	15.2758i	0.668752	+	0.729904i
$439$	−21.0168	−	10.1212i	−1.00308	−	0.483057i	−0.141096	−	0.989996i	$-0.545063\pi$
$439$	−21.0168	−	10.1212i	−1.00308	−	0.483057i	−0.861982	+	0.506939i	$0.830777\pi$
$440$	−5.42976	−	0.102534i	−0.258854	−	0.00488814i
$441$	0.102878	+	6.99924i	0.00489897	+	0.333297i
$442$	−14.4358	−	25.3709i	−0.686639	−	1.20677i
$443$	9.55931	−	19.8501i	0.454176	−	0.943107i	−0.540624	−	0.841264i	$-0.681812\pi$
$443$	9.55931	−	19.8501i	0.454176	−	0.943107i	0.994801	−	0.101843i	$-0.0324738\pi$
$444$	−18.1536	−	5.85089i	−0.861532	−	0.277671i
$445$	35.1147	+	44.0324i	1.66460	+	2.08734i
$446$	−16.3517	+	14.9817i	−0.774275	+	0.709406i
$447$	1.59320	−	6.98026i	0.0753557	−	0.330155i
$448$	−11.8008	+	17.5710i	−0.557535	+	0.830154i
$449$	9.07246	+	39.7490i	0.428156	+	1.87587i	0.480085	+	0.877222i	$0.340606\pi$
$449$	9.07246	+	39.7490i	0.428156	+	1.87587i	−0.0519288	+	0.998651i	$0.516537\pi$
$450$	12.2915	+	8.49405i	0.579429	+	0.400413i
$451$	−0.0872752	+	0.382378i	−0.00410963	+	0.0180055i
$452$	−25.3377	+	16.8117i	−1.19178	+	0.790755i
$453$	14.3752	+	11.4638i	0.675406	+	0.538619i
$454$	0.514405	+	7.49715i	0.0241422	+	0.351859i
$455$	14.6481	+	40.8952i	0.686711	+	1.91720i
$456$	−3.24586	+	1.48830i	−0.152001	+	0.0696959i
$457$	5.51778	−	24.1750i	0.258111	−	1.13086i	−0.665158	−	0.746703i	$-0.731636\pi$
$457$	5.51778	−	24.1750i	0.258111	−	1.13086i	0.923269	−	0.384155i	$-0.125507\pi$
$458$	4.80976	−	30.6025i	0.224746	−	1.42996i
$459$		−	4.95976i		−	0.231502i
$460$	5.24627	−	8.82828i	0.244609	−	0.411621i
$461$	22.7659	+	18.1552i	1.06031	+	0.845572i	0.988405	−	0.151840i	$-0.0485197\pi$
$461$	22.7659	+	18.1552i	1.06031	+	0.845572i	0.0719082	+	0.997411i	$0.477091\pi$
$462$	−0.729956	−	1.66827i	−0.0339606	−	0.0776151i
$463$	−16.0344	+	12.7870i	−0.745180	+	0.594262i	−0.920726	−	0.390210i	$-0.872402\pi$
$463$	−16.0344	+	12.7870i	−0.745180	+	0.594262i	0.175546	+	0.984471i	$0.443831\pi$
$464$	9.59570	−	22.7483i	0.445469	−	1.05606i
$465$	−2.51397	−	5.22031i	−0.116583	−	0.242086i
$466$	−4.37113	−	3.02066i	−0.202489	−	0.139929i
$467$	1.47883	+	1.85440i	0.0684323	+	0.0858113i	0.814869	−	0.579645i	$-0.196809\pi$
$467$	1.47883	+	1.85440i	0.0684323	+	0.0858113i	−0.746437	+	0.665456i	$0.768237\pi$
$468$	−1.13682	−	8.24525i	−0.0525495	−	0.381137i
$469$	8.21078	+	12.8567i	0.379138	+	0.593666i
$470$	−7.01020	+	44.6030i	−0.323357	+	2.05738i
$471$		−	2.30711i		−	0.106306i
$472$	−3.13824	−	0.0592619i	−0.144449	−	0.00272775i
$473$	−3.09957	+	3.88673i	−0.142518	+	0.178712i
$474$	−7.06305	−	23.4202i	−0.324417	−	1.07572i
$475$	12.0169	−	5.78705i	0.551374	−	0.265528i
$476$	−26.2310	+	0.843905i	−1.20230	+	0.0386803i
$477$	−5.81040	−	2.79814i	−0.266040	−	0.128118i
$478$	−1.56024	+	9.92717i	−0.0713638	+	0.454058i
$479$	4.95680	+	2.38707i	0.226482	+	0.109068i	0.543684	−	0.839290i	$-0.317029\pi$
$479$	4.95680	+	2.38707i	0.226482	+	0.109068i	−0.317202	+	0.948358i	$0.602743\pi$
$480$	−15.6870	+	15.8742i	−0.716012	+	0.724556i
$481$	−17.2199	−	35.7574i	−0.785158	−	1.63040i
$482$	−7.76031	−	8.46992i	−0.353472	−	0.385794i
$483$	3.42455	+	0.360389i	0.155822	+	0.0163983i
$484$	−15.5943	−	14.8391i	−0.708834	−	0.674503i
$485$	−3.15617	−	13.8281i	−0.143314	−	0.627901i
$486$	0.524946	−	1.31318i	0.0238120	−	0.0595669i
$487$	−9.95959	+	2.27321i	−0.451312	+	0.103009i	−0.442134	−	0.896949i	$-0.645779\pi$
$487$	−9.95959	+	2.27321i	−0.451312	+	0.103009i	−0.00917788	+	0.999958i	$0.502921\pi$
$488$	−7.38362	+	14.6195i	−0.334241	+	0.661796i
$489$		−	20.6737i		−	0.934896i
$490$	38.6671	+	5.49621i	1.74680	+	0.248294i
$491$			27.1990i			1.22747i	0.789510	+	0.613737i	$0.210335\pi$
$491$			27.1990i			1.22747i	−0.789510	+	0.613737i	$0.789665\pi$
$492$	0.891120	+	1.34305i	0.0401748	+	0.0605493i
$493$	29.8457	−	6.81209i	1.34418	−	0.306801i
$494$	−6.89934	−	2.75803i	−0.310416	−	0.124089i
$495$	−0.427252	−	1.87191i	−0.0192036	−	0.0841363i
$496$	5.65537	−	1.58970i	0.253933	−	0.0713795i
$497$	−3.43733	+	10.0599i	−0.154185	+	0.451246i
$498$	−5.73460	+	5.25415i	−0.256973	+	0.235444i
$499$	17.7260	+	36.8083i	0.793523	+	1.64777i	0.761399	+	0.648283i	$0.224513\pi$
$499$	17.7260	+	36.8083i	0.793523	+	1.64777i	0.0321234	+	0.999484i	$0.489773\pi$
$500$	30.2685	−	31.8091i	1.35365	−	1.42255i
$501$	8.63925	+	4.16044i	0.385973	+	0.185875i
$502$	−2.82192	−	0.443518i	−0.125948	−	0.0197952i
$503$	16.8855	+	8.13161i	0.752885	+	0.362570i	0.770639	−	0.637272i	$-0.219937\pi$
$503$	16.8855	+	8.13161i	0.752885	+	0.362570i	−0.0177537	+	0.999842i	$0.505651\pi$
$504$	−7.03440	−	2.55288i	−0.313337	−	0.113714i
$505$	33.5502	−	16.1569i	1.49296	−	0.718973i
$506$	−0.857629	+	0.258644i	−0.0381263	+	0.0114981i
$507$	2.69293	−	3.37682i	0.119597	−	0.149970i
$508$	−5.92605	−	3.52160i	−0.262926	−	0.156246i
$509$		−	12.8302i		−	0.568688i	−0.958722	−	0.284344i	$-0.908224\pi$
$509$		−	12.8302i		−	0.568688i	0.958722	−	0.284344i	$-0.0917757\pi$
$510$	−27.3369	−	4.29650i	−1.21050	−	0.190252i
$511$	32.9695	+	20.3797i	1.45849	+	0.901546i
$512$	−13.0838	−	18.4612i	−0.578227	−	0.815876i
$513$	−0.787138	−	0.987039i	−0.0347530	−	0.0435788i
$514$	−5.67279	+	8.20897i	−0.250216	+	0.362082i
$515$	−24.0925	−	50.0285i	−1.06164	−	2.20452i
$516$	2.79035	+	20.2382i	0.122838	+	0.890936i
$517$	3.07915	−	2.45554i	0.135421	−	0.107994i
$518$	−35.6591	−	1.29660i	−1.56677	−	0.0569694i
$519$	14.8636	+	11.8533i	0.652439	+	0.520303i
$520$	−46.4304	−	0.876782i	−2.03611	−	0.0384494i
$521$			21.6112i			0.946802i	0.880847	+	0.473401i	$0.156974\pi$
$521$			21.6112i			0.946802i	−0.880847	+	0.473401i	$0.843026\pi$
$522$	8.62314	+	1.35529i	0.377424	+	0.0593193i
$523$	−2.90380	+	12.7224i	−0.126974	+	0.556310i	0.870919	+	0.491427i	$0.163525\pi$
$523$	−2.90380	+	12.7224i	−0.126974	+	0.556310i	−0.997893	+	0.0648831i	$0.979333\pi$
$524$	0.172614	−	1.97024i	0.00754067	−	0.0860703i
$525$	26.4505	+	9.03780i	1.15439	+	0.394442i
$526$	34.8352	−	2.39016i	1.51889	−	0.104216i
$527$	5.69493	+	4.54155i	0.248075	+	0.197833i
$528$	1.94431	−	0.0965648i	0.0846154	−	0.00420244i
$529$	−4.74105	+	20.7719i	−0.206133	+	0.903126i
$530$	−20.4560	+	29.6014i	−0.888552	+	1.28580i
$531$	−0.246939	−	1.08191i	−0.0107162	−	0.0469509i
$532$	−5.08629	+	4.33093i	−0.220519	+	0.187770i
$533$	−0.746299	+	3.26975i	−0.0323258	+	0.141629i
$534$	−13.6382	−	14.8853i	−0.590183	−	0.644150i
$535$	42.5260	+	53.3259i	1.83856	+	2.30548i
$536$	−15.9649	+	3.32807i	−0.689580	+	0.143751i
$537$	−1.31720	+	2.73520i	−0.0568416	+	0.118033i
$538$	9.59142	−	5.45741i	0.413515	−	0.235286i
$539$	−2.16299	−	2.63199i	−0.0931664	−	0.113368i
$540$	−6.78313	−	4.03093i	−0.291900	−	0.173464i
$541$	−10.6254	−	5.11694i	−0.456823	−	0.219994i	0.191298	−	0.981532i	$-0.438730\pi$
$541$	−10.6254	−	5.11694i	−0.456823	−	0.219994i	−0.648121	+	0.761538i	$0.724445\pi$
$542$	−27.4318	+	25.1336i	−1.17830	+	1.07958i
$543$	10.9836	−	8.75909i	0.471349	−	0.375889i
$544$	9.10930	−	26.5367i	0.390558	−	1.13775i
$545$	6.84580	+	1.56251i	0.293242	+	0.0669305i
$546$	−6.24192	−	14.2656i	−0.267130	−	0.610509i
$547$	−4.06595	+	0.928027i	−0.173848	+	0.0396796i	−0.308558	−	0.951205i	$-0.599847\pi$
$547$	−4.06595	+	0.928027i	−0.173848	+	0.0396796i	0.134711	+	0.990885i	$0.456989\pi$
$548$	−3.18078	+	36.3059i	−0.135876	+	1.55091i
$549$	−5.64542	−	1.28853i	−0.240941	−	0.0549932i
$550$	−7.25435	+	0.497745i	−0.309327	+	0.0212239i
$551$	4.85847	−	6.09233i	0.206978	−	0.259542i
$552$	−1.65955	+	3.28591i	−0.0706353	+	0.139858i
$553$	−24.6322	−	38.5698i	−1.04747	−	1.64015i
$554$	−15.6946	−	10.8457i	−0.666798	−	0.460789i
$555$	−36.6807	−	8.37213i	−1.55701	−	0.355377i
$556$	−8.56757	−	22.6646i	−0.363346	−	0.961194i
$557$	−4.99764			−0.211757			−0.105878	−	0.994379i	$-0.533765\pi$
$557$	−4.99764			−0.211757			−0.105878	+	0.994379i	$0.533765\pi$
$558$	1.02714	+	1.80521i	0.0434824	+	0.0764205i
$559$	−26.5047	+	33.2358i	−1.12103	+	1.40573i
$560$	−20.1645	+	36.5603i	−0.852105	+	1.54495i
$561$	1.50498	+	1.88719i	0.0635404	+	0.0796771i
$562$	1.56894	−	3.92479i	0.0661819	−	0.165557i
$563$	23.1339	−	11.1407i	0.974980	−	0.469525i	0.122604	−	0.992456i	$-0.460875\pi$
$563$	23.1339	−	11.1407i	0.974980	−	0.469525i	0.852376	+	0.522930i	$0.175161\pi$
$564$	1.41255	−	16.1230i	0.0594789	−	0.678901i
$565$	−46.8964	+	37.3986i	−1.97294	+	1.57337i
$566$	−6.51111	+	16.2878i	−0.273682	+	0.684629i
$567$	0.276902	−	2.63122i	0.0116288	−	0.110501i
$568$	−8.75007	−	7.25240i	−0.367145	−	0.304304i
$569$	41.5754			1.74293			0.871465	−	0.490458i	$-0.163170\pi$
$569$	41.5754			1.74293			0.871465	+	0.490458i	$0.163170\pi$
$570$	−6.12217	+	3.48345i	−0.256430	+	0.145906i
$571$	21.8240	+	17.4040i	0.913305	+	0.728337i	0.962737	−	0.270441i	$-0.0871694\pi$
$571$	21.8240	+	17.4040i	0.913305	+	0.728337i	−0.0494312	+	0.998778i	$0.515741\pi$
$572$	2.93449	+	2.79236i	0.122697	+	0.116754i
$573$	−5.70072	−	11.8377i	−0.238151	−	0.494526i
$574$	2.28765	+	1.96449i	0.0954847	+	0.0819961i
$575$	5.96598	−	12.3885i	0.248798	−	0.516635i
$576$	5.22050	−	6.06188i	0.217521	−	0.252578i
$577$	−10.9482	+	22.7343i	−0.455781	+	0.946439i	0.538796	+	0.842436i	$0.318879\pi$
$577$	−10.9482	+	22.7343i	−0.455781	+	0.946439i	−0.994577	+	0.104003i	$0.966835\pi$
$578$	10.2892	−	3.10301i	0.427974	−	0.129068i
$579$	−4.92801	+	2.37321i	−0.204801	+	0.0986271i
$580$	14.9400	−	46.3544i	0.620349	−	1.92476i
$581$	−7.65066	+	12.3769i	−0.317403	+	0.513482i
$582$	1.46802	+	4.86777i	0.0608514	+	0.201776i
$583$	3.05992	−	0.698407i	0.126729	−	0.0289251i
$584$	−32.8780	+	25.2187i	−1.36050	+	1.04356i
$585$	−3.65347	−	16.0069i	−0.151053	−	0.661804i
$586$	−9.79494	+	0.672064i	−0.404625	+	0.0277627i
$587$	−39.8734			−1.64575			−0.822875	−	0.568223i	$-0.807631\pi$
$587$	−39.8734			−1.64575			−0.822875	+	0.568223i	$0.807631\pi$
$588$	−13.9630	−	1.01676i	−0.575826	−	0.0419307i
$589$	1.85411			0.0763973
$590$	−6.17712	+	0.423833i	−0.254308	+	0.0174489i
$591$	−1.20616	−	5.28455i	−0.0496150	−	0.217378i
$592$	14.8259	−	35.1474i	0.609340	−	1.44455i
$593$	7.31927	−	1.67058i	0.300566	−	0.0686023i	−0.0695781	−	0.997577i	$-0.522165\pi$
$593$	7.31927	−	1.67058i	0.300566	−	0.0686023i	0.370144	+	0.928974i	$0.379308\pi$
$594$	0.198727	+	0.658952i	0.00815385	+	0.0270371i
$595$	−51.4009	+	6.17434i	−2.10723	+	0.253123i
$596$	13.6291	+	4.39266i	0.558271	+	0.179930i
$597$	−16.9887	+	8.18133i	−0.695301	+	0.334840i
$598$	−7.33367	+	2.21169i	−0.299896	+	0.0904426i
$599$	6.77195	−	14.0621i	0.276694	−	0.574562i	−0.715593	−	0.698517i	$-0.753844\pi$
$599$	6.77195	−	14.0621i	0.276694	−	0.574562i	0.992288	+	0.123955i	$0.0395579\pi$
$600$	−19.0688	+	23.0066i	−0.778480	+	0.939242i
$601$	5.39703	−	11.2070i	0.220149	−	0.457145i	−0.761418	−	0.648261i	$-0.775496\pi$
$601$	5.39703	−	11.2070i	0.220149	−	0.457145i	0.981567	+	0.191116i	$0.0612107\pi$
$602$	15.3210	+	35.0152i	0.624435	+	1.42711i
$603$	−2.50168	−	5.19480i	−0.101876	−	0.211549i
$604$	−25.3494	+	26.6397i	−1.03145	+	1.08395i
$605$	−33.1990	−	26.4753i	−1.34973	−	1.07637i
$606$	−11.6018	+	6.60129i	−0.471291	+	0.268159i
$607$	3.42482			0.139009			0.0695047	−	0.997582i	$-0.477858\pi$
$607$	3.42482			0.139009			0.0695047	+	0.997582i	$0.477858\pi$
$608$	−2.39866	−	6.72674i	−0.0972786	−	0.272805i
$609$	16.2139	−	1.94763i	0.657020	−	0.0789221i
$610$	−11.9925	+	29.9999i	−0.485563	+	1.21466i
$611$	26.3301	−	20.9975i	1.06520	−	0.849470i
$612$	9.88167	+	0.865739i	0.399443	+	0.0349954i
$613$	−4.55139	+	2.19183i	−0.183829	+	0.0885274i	−0.523534	−	0.852004i	$-0.675387\pi$
$613$	−4.55139	+	2.19183i	−0.183829	+	0.0885274i	0.339706	+	0.940532i	$0.389673\pi$
$614$	−5.75763	+	14.4030i	−0.232359	+	0.581257i
$615$	1.98235	+	2.48579i	0.0799361	+	0.100237i
$616$	3.45123	−	1.16314i	0.139054	−	0.0468642i
$617$	1.35133	−	1.69452i	0.0544025	−	0.0682186i	−0.753886	−	0.657005i	$-0.771823\pi$
$617$	1.35133	−	1.69452i	0.0544025	−	0.0682186i	0.808288	+	0.588787i	$0.200394\pi$
$618$	9.84355	+	17.3001i	0.395966	+	0.695912i
$619$	−45.4088			−1.82513			−0.912566	−	0.408930i	$-0.865902\pi$
$619$	−45.4088			−1.82513			−0.912566	+	0.408930i	$0.865902\pi$
$620$	10.8396	−	4.09753i	0.435329	−	0.164561i
$621$	−1.26887	−	0.289612i	−0.0509181	−	0.0116217i
$622$	8.41443	+	5.81477i	0.337388	+	0.233151i
$623$	−32.1268	−	19.8588i	−1.28713	−	0.795627i
$624$	16.6260	−	0.825734i	0.665573	−	0.0330558i
$625$	21.0686	−	26.4192i	0.842743	−	1.05677i
$626$	10.9672	−	0.752498i	0.438338	−	0.0300759i
$627$	0.599011	+	0.136720i	0.0239222	+	0.00546009i
$628$	4.59660	+	0.402711i	0.183424	+	0.0160699i
$629$	46.1133	−	10.5251i	1.83866	−	0.419662i
$630$	−14.2627	−	3.80556i	−0.568240	−	0.151617i
$631$	22.9974	+	5.24901i	0.915512	+	0.208960i	0.654224	−	0.756301i	$-0.272995\pi$
$631$	22.9974	+	5.24901i	0.915512	+	0.208960i	0.261288	+	0.965261i	$0.415853\pi$
$632$	47.8945	−	9.98415i	1.90514	−	0.397148i
$633$	−18.1403	+	14.4664i	−0.721012	+	0.574988i
$634$	12.4736	−	11.4285i	0.495388	−	0.453885i
$635$	−12.2515	−	5.90001i	−0.486186	−	0.234135i
$636$	6.58915	−	11.0880i	0.261277	−	0.439669i
$637$	−18.4959	−	22.5064i	−0.732834	−	0.891737i
$638$	−3.69235	+	2.10090i	−0.146181	+	0.0831756i
$639$	1.74339	−	3.62018i	0.0689674	−	0.143212i
$640$	−28.8891	−	34.0253i	−1.14194	−	1.34497i
$641$	9.17682	+	11.5074i	0.362463	+	0.454514i	0.929305	−	0.369312i	$-0.120407\pi$
$641$	9.17682	+	11.5074i	0.362463	+	0.454514i	−0.566843	+	0.823826i	$0.691835\pi$
$642$	−16.5167	−	18.0270i	−0.651861	−	0.711468i
$643$	4.95656	−	21.7161i	0.195468	−	0.856400i	−0.778125	−	0.628109i	$-0.783829\pi$
$643$	4.95656	−	21.7161i	0.195468	−	0.856400i	0.973593	−	0.228291i	$-0.0733137\pi$
$644$	−1.31579	+	6.76005i	−0.0518495	+	0.266383i
$645$	8.96754	+	39.2894i	0.353097	+	1.54702i
$646$	5.03424	−	7.28494i	0.198070	−	0.286622i
$647$	9.27536	−	40.6380i	0.364652	−	1.59765i	−0.376572	−	0.926387i	$-0.622897\pi$
$647$	9.27536	−	40.6380i	0.364652	−	1.59765i	0.741224	−	0.671258i	$-0.234246\pi$
$648$	2.52470	+	1.27510i	0.0991796	+	0.0500908i
$649$	0.422254	+	0.336736i	0.0165749	+	0.0132180i
$650$	−62.0326	+	4.25627i	−2.43312	+	0.166945i
$651$	2.76768	+	2.72730i	0.108474	+	0.106891i
$652$	41.1896	+	3.60865i	1.61311	+	0.141325i
$653$	−0.444252	+	1.94640i	−0.0173849	+	0.0761683i	−0.982876	−	0.184267i	$-0.941009\pi$
$653$	−0.444252	+	1.94640i	−0.0173849	+	0.0761683i	0.965491	+	0.260435i	$0.0838661\pi$
$654$	−2.48654	−	0.390807i	−0.0972314	−	0.0152817i
$655$		−	3.90141i		−	0.152441i
$656$	−2.83139	+	1.54101i	−0.110547	+	0.0601662i
$657$	−11.4537	−	9.13402i	−0.446851	−	0.356352i
$658$	−5.66058	−	29.7451i	−0.220672	−	1.15958i
$659$	0.189703	−	0.151283i	0.00738980	−	0.00589317i	−0.619788	−	0.784769i	$-0.712781\pi$
$659$	0.189703	−	0.151283i	0.00738980	−	0.00589317i	0.627178	+	0.778876i	$0.284210\pi$
$660$	3.80412	−	0.524496i	0.148075	−	0.0204160i
$661$	6.24063	+	12.9588i	0.242732	+	0.504039i	0.986370	−	0.164544i	$-0.0526154\pi$
$661$	6.24063	+	12.9588i	0.242732	+	0.504039i	−0.743637	+	0.668583i	$0.766901\pi$
$662$	14.6160	−	21.1505i	0.568066	−	0.822036i
$663$	12.8692	+	16.1375i	0.499800	+	0.626729i
$664$	−9.46722	−	12.3426i	−0.367399	−	0.478984i
$665$	−9.24937	+	9.38632i	−0.358675	+	0.363986i
$666$	13.3232	+	2.09399i	0.516264	+	0.0811407i
$667$		−	8.03332i		−	0.311051i
$668$	−9.79714	+	16.4863i	−0.379063	+	0.637876i
$669$	9.77737	−	12.2604i	0.378015	−	0.474016i
$670$	−30.7995	+	9.28851i	−1.18989	+	0.358846i
$671$	2.53907	−	1.22275i	0.0980198	−	0.0472039i
$672$	6.31414	−	13.5695i	0.243573	−	0.523455i
$673$	−17.6721	−	8.51045i	−0.681211	−	0.328054i	0.0610789	−	0.998133i	$-0.480546\pi$
$673$	−17.6721	−	8.51045i	−0.681211	−	0.328054i	−0.742290	+	0.670079i	$0.766260\pi$
$674$	43.3933	+	6.82008i	1.67145	+	0.262700i
$675$	−9.51858	−	4.58391i	−0.366370	−	0.176435i
$676$	6.25782	+	5.95474i	0.240685	+	0.229028i
$677$	12.5278	+	26.0143i	0.481484	+	0.999811i	0.990301	+	0.138937i	$0.0443685\pi$
$677$	12.5278	+	26.0143i	0.481484	+	0.999811i	−0.508818	+	0.860874i	$0.669917\pi$
$678$	15.8534	−	14.5252i	0.608848	−	0.557839i
$679$	5.11968	+	8.01654i	0.196475	+	0.307646i
$680$	13.3319	−	53.7152i	0.511257	−	2.05988i
$681$	−1.18242	−	5.18052i	−0.0453105	−	0.198518i
$682$	−0.938596	−	0.375206i	−0.0359407	−	0.0143674i
$683$	36.7231	−	8.38181i	1.40517	−	0.320721i	0.548313	−	0.836273i	$-0.315270\pi$
$683$	36.7231	−	8.38181i	1.40517	−	0.320721i	0.856858	+	0.515552i	$0.172413\pi$
$684$	2.10394	−	1.39598i	0.0804463	−	0.0533765i
$685$			71.8919i			2.74685i
$686$	−25.6551	+	5.27409i	−0.979516	+	0.201366i
$687$			21.9049i			0.835724i
$688$	−40.8090	+	2.02679i	−1.55583	+	0.0772705i
$689$	26.1657	−	5.97214i	0.996832	−	0.227520i
$690$	−2.69546	+	6.74281i	−0.102614	+	0.256694i
$691$	10.6364	+	46.6012i	0.404629	+	1.77279i	0.608251	+	0.793745i	$0.291871\pi$
$691$	10.6364	+	46.6012i	0.404629	+	1.77279i	−0.203622	+	0.979050i	$0.565271\pi$
$692$	−26.2106	+	27.5447i	−0.996379	+	1.04709i
$693$	0.693053	+	1.08520i	0.0263269	+	0.0412234i
$694$	27.9700	+	30.5276i	1.06173	+	1.15881i
$695$	−20.7380	−	43.0629i	−0.786637	−	1.63347i
$696$	−4.20542	+	16.9439i	−0.159406	+	0.642257i
$697$	−3.60122	−	1.73426i	−0.136406	−	0.0656896i
$698$	0.336896	−	2.14353i	0.0127517	−	0.0811339i
$699$	3.38500	+	1.63013i	0.128033	+	0.0616572i
$700$	−22.6236	+	51.1215i	−0.855092	+	1.93221i
$701$	15.9593	−	7.68557i	0.602773	−	0.290280i	−0.107502	−	0.994205i	$-0.534285\pi$
$701$	15.9593	−	7.68557i	0.602773	−	0.290280i	0.710275	+	0.703925i	$0.248571\pi$
$702$	1.69933	+	5.63476i	0.0641371	+	0.212670i
$703$	7.50661	−	9.41299i	0.283117	−	0.355018i
$704$	−0.146993	+	3.89064i	−0.00553999	+	0.146634i
$705$		−	31.9263i		−	1.20241i
$706$	−7.27044	+	46.2588i	−0.273627	+	1.74097i
$707$	−17.5280	+	17.7875i	−0.659207	+	0.668968i
$708$	2.19867	−	0.303143i	0.0826310	−	0.0113928i
$709$	−4.07602	−	5.11117i	−0.153078	−	0.191954i	0.699379	−	0.714751i	$-0.253460\pi$
$709$	−4.07602	−	5.11117i	−0.153078	−	0.191954i	−0.852457	+	0.522797i	$0.824889\pi$
$710$	−18.4432	−	12.7452i	−0.692163	−	0.478317i
$711$	7.50501	+	15.5843i	0.281460	+	0.584457i
$712$	32.0376	−	24.5741i	1.20066	−	0.920952i
$713$	1.49442	−	1.19176i	0.0559666	−	0.0446318i
$714$	18.2305	−	3.46933i	0.682261	−	0.129836i
$715$	6.24726	+	4.98202i	0.233634	+	0.186317i
$716$	−5.21961	−	3.10179i	−0.195066	−	0.115919i
$717$		−	7.10574i		−	0.265369i
$718$	3.04038	−	19.3447i	0.113466	−	0.721938i
$719$	−3.52189	+	15.4304i	−0.131344	+	0.575458i	0.865830	+	0.500338i	$0.166791\pi$
$719$	−3.52189	+	15.4304i	−0.131344	+	0.575458i	−0.997175	+	0.0751195i	$0.976066\pi$
$720$	9.21511	−	12.8109i	0.343427	−	0.477434i
$721$	26.5239	+	26.1370i	0.987803	+	0.973391i
$722$	1.68503	+	24.5583i	0.0627102	+	0.913965i
$723$	6.35072	+	5.06453i	0.236186	+	0.188352i
$724$	15.5341	+	23.4122i	0.577321	+	0.870108i
$725$	14.5105	−	63.5746i	0.538906	−	2.36110i
$726$	12.5223	+	8.65350i	0.464746	+	0.321161i
$727$	−4.18546	−	18.3377i	−0.155230	−	0.680108i	−0.991315	−	0.131508i	$-0.958018\pi$
$727$	−4.18546	−	18.3377i	−0.155230	−	0.680108i	0.836085	−	0.548600i	$-0.184839\pi$
$728$	29.5118	−	9.94611i	1.09378	−	0.368627i
$729$	−0.222521	+	0.974928i	−0.00824152	+	0.0361084i
$730$	−60.2663	+	55.2172i	−2.23056	+	2.04368i
$731$	−31.5879	−	39.6100i	−1.16832	−	1.46503i
$732$	3.55265	−	11.0228i	0.131310	−	0.407416i
$733$	−3.82154	+	7.93551i	−0.141152	+	0.293105i	−0.959546	−	0.281553i	$-0.909150\pi$
$733$	−3.82154	+	7.93551i	−0.141152	+	0.293105i	0.818394	+	0.574658i	$0.194865\pi$
$734$	18.9918	+	33.3782i	0.701002	+	1.23201i
$735$	−27.6136	+	0.405879i	−1.01854	+	0.0149711i
$736$	−6.25706	−	3.88001i	−0.230638	−	0.143019i
$737$	2.52819	+	1.21751i	0.0931272	+	0.0448477i
$738$	−0.769925	−	0.840328i	−0.0283413	−	0.0309329i
$739$	8.42770	−	6.72086i	0.310018	−	0.247231i	−0.456104	−	0.889927i	$-0.650755\pi$
$739$	8.42770	−	6.72086i	0.310018	−	0.247231i	0.766122	+	0.642696i	$0.222184\pi$
$740$	23.0831	−	71.6201i	0.848551	−	2.63281i
$741$	5.12220	+	1.16911i	0.188169	+	0.0429483i
$742$	6.22076	−	23.3145i	0.228371	−	0.855903i
$743$	−36.8536	+	8.41160i	−1.35203	+	0.308592i	−0.836352	−	0.548192i	$-0.815316\pi$
$743$	−36.8536	+	8.41160i	−1.35203	+	0.308592i	−0.515676	+	0.856784i	$0.672459\pi$
$744$	−3.77592	+	1.73134i	−0.138432	+	0.0634740i
$745$	27.5387	+	6.28553i	1.00894	+	0.230284i
$746$	−0.785923	−	11.4544i	−0.0287747	−	0.419375i
$747$	3.42896	−	4.29978i	0.125459	−	0.157321i
$748$	−4.02267	+	2.66906i	−0.147083	+	0.0975907i
$749$	−38.9075	−	24.0502i	−1.42165	−	0.878775i
$750$	−17.6513	+	25.5428i	−0.644533	+	0.932690i
$751$	−5.22211	−	1.19191i	−0.190558	−	0.0434935i	0.126177	−	0.992008i	$-0.459729\pi$
$751$	−5.22211	−	1.19191i	−0.190558	−	0.0434935i	−0.316735	+	0.948514i	$0.602586\pi$
$752$	31.8764	+	5.62862i	1.16241	+	0.205255i
$753$	2.01989			0.0736090
$754$	−31.5736	+	17.9650i	−1.14984	+	0.654248i
$755$	−45.2275	+	56.7135i	−1.64600	+	2.06401i
$756$	5.19403	+	1.01098i	0.188905	+	0.0367689i
$757$	−11.6979	−	14.6687i	−0.425167	−	0.533143i	0.522400	−	0.852701i	$-0.325037\pi$
$757$	−11.6979	−	14.6687i	−0.425167	−	0.533143i	−0.947567	+	0.319558i	$0.896465\pi$
$758$	−4.45400	−	1.78050i	−0.161776	−	0.0646705i
$759$	0.570686	−	0.274828i	0.0207146	−	0.00997561i
$760$	−5.87167	−	12.8057i	−0.212988	−	0.464510i
$761$	−32.3377	+	25.7884i	−1.17224	+	0.934830i	−0.998749	−	0.0500060i	$-0.984076\pi$
$761$	−32.3377	+	25.7884i	−1.17224	+	0.934830i	−0.173490	+	0.984836i	$0.555505\pi$
$762$	4.52616	+	1.80934i	0.163966	+	0.0655457i
$763$	−4.67539	+	0.561613i	−0.169260	+	0.0203318i
$764$	24.5801	−	9.29164i	0.889276	−	0.336160i
$765$	19.5674			0.707460
$766$	−2.31725	−	4.07258i	−0.0837258	−	0.147148i
$767$	3.61073	+	2.87946i	0.130376	+	0.103971i
$768$	11.1662	+	11.4593i	0.402927	+	0.413501i
$769$	−19.7651	−	41.0426i	−0.712746	−	1.48003i	−0.870300	−	0.492523i	$-0.836075\pi$
$769$	−19.7651	−	41.0426i	−0.712746	−	1.48003i	0.157553	−	0.987511i	$-0.449639\pi$
$770$	6.58172	−	2.87984i	0.237189	−	0.103782i
$771$	3.06138	−	6.35702i	0.110253	−	0.228943i
$772$	−3.86810	−	10.2327i	−0.139216	−	0.368282i
$773$	14.5155	−	30.1418i	0.522087	−	1.08413i	−0.458618	−	0.888633i	$-0.651655\pi$
$773$	14.5155	−	30.1418i	0.522087	−	1.08413i	0.980705	−	0.195492i	$-0.0626303\pi$
$774$	−4.17105	−	13.8307i	−0.149925	−	0.497133i
$775$	13.9793	−	6.73209i	0.502152	−	0.241824i
$776$	−9.95464	+	2.07516i	−0.357351	+	0.0744938i
$777$	25.0514	−	3.00920i	0.898713	−	0.107954i
$778$	−18.5888	+	5.60601i	−0.666441	+	0.200985i
$779$	−0.991911	+	0.226397i	−0.0355389	+	0.00811152i
$780$	32.5294	−	4.48501i	1.16474	−	0.160589i
$781$	0.435144	+	1.90649i	0.0155707	+	0.0682196i
$782$	−0.624900	−	9.10755i	−0.0223464	−	0.325685i
$783$	−6.17233			−0.220581
$784$	4.46305	−	27.6420i	0.159395	−	0.987215i
$785$	9.10206			0.324866
$786$	0.0957311	+	1.39523i	0.00341462	+	0.0497660i
$787$	−5.97033	−	26.1577i	−0.212819	−	0.932422i	−0.962641	−	0.270782i	$-0.912718\pi$
$787$	−5.97033	−	26.1577i	−0.212819	−	0.932422i	0.749822	−	0.661640i	$-0.230139\pi$
$788$	10.7393	−	1.48069i	0.382572	−	0.0527475i
$789$	−24.0711	+	5.49407i	−0.856954	+	0.195594i
$790$	92.3980	−	27.8654i	3.28737	−	0.991405i
$791$	21.1505	−	34.2164i	0.752023	−	1.21659i
$792$	−1.34756	+	0.280915i	−0.0478836	+	0.00998187i
$793$	21.7118	−	10.4559i	0.771010	−	0.371299i
$794$	5.80784	+	19.2581i	0.206113	+	0.683443i
$795$	11.0393	−	22.9234i	0.391524	−	0.813008i
$796$	−13.3348	−	35.2758i	−0.472639	−	1.25032i
$797$	−15.1041	+	31.3640i	−0.535015	+	1.11097i	0.441846	+	0.897091i	$0.354324\pi$
$797$	−15.1041	+	31.3640i	−0.535015	+	1.11097i	−0.976860	+	0.213878i	$0.931390\pi$
$798$	3.07745	−	3.58370i	0.108941	−	0.126862i
$799$	17.4145	+	36.1615i	0.616080	+	1.27930i
$800$	−42.5092	−	42.0079i	−1.50293	−	1.48520i
$801$	11.1609	+	8.90055i	0.394352	+	0.314486i
$802$	0.878417	+	1.54382i	0.0310180	+	0.0545142i
$803$	7.12974			0.251603
$804$	10.7866	−	4.07751i	0.380415	−	0.143803i
$805$	−1.42182	+	13.5106i	−0.0501125	+	0.476187i
$806$	−8.02602	−	3.20842i	−0.282705	−	0.113012i
$807$	−6.10076	+	4.86519i	−0.214757	+	0.171263i
$808$	−11.1271	−	24.2673i	−0.391449	−	0.853721i
$809$	−23.0258	+	11.0886i	−0.809543	+	0.389855i	−0.792403	−	0.609998i	$-0.791170\pi$
$809$	−23.0258	+	11.0886i	−0.809543	+	0.389855i	−0.0171397	+	0.999853i	$0.505456\pi$
$810$	5.18078	+	2.07103i	0.182034	+	0.0727686i
$811$	3.11922	+	3.91138i	0.109531	+	0.137347i	0.833575	−	0.552406i	$-0.186290\pi$
$811$	3.11922	+	3.91138i	0.109531	+	0.137347i	−0.724044	+	0.689754i	$0.757719\pi$
$812$	1.05022	+	32.6440i	0.0368557	+	1.14558i
$813$	16.4026	−	20.5683i	0.575266	−	0.721360i
$814$	−5.70488	+	3.24601i	−0.199956	+	0.113773i
$815$	81.5624			2.85701
$816$	−3.44974	+	19.5368i	−0.120765	+	0.683925i
$817$	−12.5726	−	2.86961i	−0.439859	−	0.100395i
$818$	3.53096	−	5.10958i	0.123457	−	0.178652i
$819$	5.92636	+	9.27966i	0.207084	+	0.324258i
$820$	−5.29863	+	3.51567i	−0.185036	+	0.122773i
$821$	3.04246	−	3.81513i	0.106183	−	0.133149i	−0.725901	−	0.687800i	$-0.758577\pi$
$821$	3.04246	−	3.81513i	0.106183	−	0.133149i	0.832083	+	0.554651i	$0.187148\pi$
$822$	−1.76405	−	25.7101i	−0.0615284	−	0.896741i
$823$	8.59591	+	1.96196i	0.299635	+	0.0683896i	0.369695	−	0.929153i	$-0.379462\pi$
$823$	8.59591	+	1.96196i	0.299635	+	0.0683896i	−0.0700606	+	0.997543i	$0.522319\pi$
$824$	−36.1864	+	16.5922i	−1.26061	+	0.578017i
$825$	5.01275	−	1.14413i	0.174522	−	0.0398334i
$826$	3.80404	−	1.66446i	0.132359	−	0.0579141i
$827$	−9.77035	−	2.23002i	−0.339748	−	0.0775453i	0.0492428	−	0.998787i	$-0.484319\pi$
$827$	−9.77035	−	2.23002i	−0.339748	−	0.0775453i	−0.388991	+	0.921242i	$0.627176\pi$
$828$	0.798499	−	2.47751i	0.0277498	−	0.0860995i
$829$	−12.3118	+	9.81837i	−0.427608	+	0.341006i	−0.813528	−	0.581526i	$-0.802456\pi$
$829$	−12.3118	+	9.81837i	−0.427608	+	0.341006i	0.385919	+	0.922532i	$0.373884\pi$
$830$	−20.7288	−	22.6243i	−0.719508	−	0.785301i
$831$	12.1539	+	5.85299i	0.421613	+	0.203038i
$832$	−1.25695	+	33.2693i	−0.0435768	+	1.15340i
$833$	31.0554	−	15.5218i	1.07600	−	0.537799i
$834$	8.47301	+	14.8913i	0.293396	+	0.515645i
$835$	−16.4139	+	34.0838i	−0.568026	+	1.17952i
$836$	−0.376956	+	1.16959i	−0.0130373	+	0.0404510i
$837$	−0.915680	−	1.14823i	−0.0316505	−	0.0396885i
$838$	17.0024	−	15.5779i	0.587338	−	0.538131i
$839$	−0.313744	+	1.37460i	−0.0108317	+	0.0474566i	−0.980055	−	0.198727i	$-0.936319\pi$
$839$	−0.313744	+	1.37460i	−0.0108317	+	0.0474566i	0.969223	+	0.246183i	$0.0791765\pi$
$840$	10.0717	−	27.7523i	0.347506	−	0.957546i
$841$	−2.02442	−	8.86956i	−0.0698076	−	0.305847i
$842$	6.43505	+	4.44693i	0.221767	+	0.153251i
$843$	−0.665065	+	2.91384i	−0.0229060	+	0.100358i
$844$	−25.6560	−	38.6673i	−0.883115	−	1.33098i
$845$	13.3223	+	10.6242i	0.458303	+	0.365484i
$846$	0.783393	+	11.4175i	0.0269336	+	0.392542i
$847$	26.9470	+	9.20745i	0.925909	+	0.316372i
$848$	20.9413	+	15.0635i	0.719127	+	0.517281i
$849$	2.76002	−	12.0924i	0.0947235	−	0.415011i
$850$	11.5055	−	73.2047i	0.394635	−	2.51090i
$851$		−	12.4119i		−	0.425475i
$852$	6.90843	+	4.10538i	0.236679	+	0.140648i
$853$	−19.3758	−	15.4516i	−0.663413	−	0.529054i	0.232886	−	0.972504i	$-0.425183\pi$
$853$	−19.3758	−	15.4516i	−0.663413	−	0.529054i	−0.896299	+	0.443450i	$0.853755\pi$
$854$	0.787295	−	21.6522i	0.0269407	−	0.740922i
$855$	3.89409	−	3.10544i	0.133175	−	0.106204i
$856$	38.7994	−	29.7606i	1.32614	−	1.01720i
$857$	1.44565	+	3.00192i	0.0493824	+	0.102544i	0.924200	−	0.381909i	$-0.124733\pi$
$857$	1.44565	+	3.00192i	0.0493824	+	0.102544i	−0.874818	+	0.484452i	$0.839019\pi$
$858$	−2.35640	−	1.62838i	−0.0804461	−	0.0555921i
$859$	18.1252	+	22.7283i	0.618424	+	0.775479i	0.988122	−	0.153673i	$-0.0491103\pi$
$859$	18.1252	+	22.7283i	0.618424	+	0.775479i	−0.369698	+	0.929152i	$0.620539\pi$
$860$	−79.8442	+	11.0086i	−2.72266	+	0.375390i
$861$	−1.81367	−	1.12110i	−0.0618098	−	0.0382070i
$862$	−6.04561	+	38.4657i	−0.205914	+	1.31015i
$863$			27.6905i			0.942594i	0.881974	+	0.471297i	$0.156214\pi$
$863$			27.6905i			0.942594i	−0.881974	+	0.471297i	$0.843786\pi$
$864$	−2.98117	+	4.80756i	−0.101421	+	0.163557i
$865$	−46.7640	+	58.6402i	−1.59002	+	1.99383i
$866$	−3.85006	−	12.7663i	−0.130830	−	0.433817i
$867$	−6.84666	+	3.29718i	−0.232525	+	0.111978i
$868$	−5.91690	+	5.03819i	−0.200833	+	0.171007i
$869$	−7.58453	−	3.65252i	−0.257288	−	0.123903i
$870$	−5.34692	+	34.0202i	−0.181278	+	1.15339i
$871$	21.6188	+	10.4111i	0.732526	+	0.352766i
$872$	1.21266	−	4.88589i	0.0410659	−	0.165457i
$873$	−1.55988	−	3.23912i	−0.0527939	−	0.109628i
$874$	−1.56977	−	1.71331i	−0.0530984	−	0.0579537i
$875$	−18.7812	+	54.9660i	−0.634921	+	1.85819i
$876$	20.1976	−	21.2256i	0.682414	−	0.717147i
$877$	0.173924	+	0.762012i	0.00587301	+	0.0257313i	0.977780	−	0.209636i	$-0.0672279\pi$
$877$	0.173924	+	0.762012i	0.00587301	+	0.0257313i	−0.971907	+	0.235367i	$0.924371\pi$
$878$	−12.2454	+	30.6324i	−0.413261	+	1.03379i
$879$	6.76830	−	1.54482i	0.228289	−	0.0521055i
$880$	0.380970	+	7.67076i	0.0128425	+	0.258581i
$881$			40.5201i			1.36516i	0.730813	+	0.682578i	$0.239141\pi$
$881$			40.5201i			1.36516i	−0.730813	+	0.682578i	$0.760859\pi$
$882$	9.86525	−	0.822722i	0.332180	−	0.0277025i
$883$			37.3098i			1.25557i	0.778386	+	0.627787i	$0.216039\pi$
$883$			37.3098i			1.25557i	−0.778386	+	0.627787i	$0.783961\pi$
$884$	−34.3982	+	22.8234i	−1.15694	+	0.767635i
$885$	4.26838	−	0.974231i	0.143480	−	0.0327484i
$886$	−28.9318	−	11.5656i	−0.971984	−	0.388553i
$887$	−4.46507	−	19.5627i	−0.149922	−	0.656852i	−0.992905	−	0.118912i	$-0.962059\pi$
$887$	−4.46507	−	19.5627i	−0.149922	−	0.656852i	0.842983	−	0.537941i	$-0.180798\pi$
$888$	−6.49761	+	26.1793i	−0.218046	+	0.878518i
$889$	9.06911	+	0.954405i	0.304168	+	0.0320097i
$890$	58.7259	−	53.8058i	1.96850	−	1.80358i
$891$	−0.211161	−	0.438481i	−0.00707417	−	0.0146897i
$892$	22.7206	+	21.6202i	0.760743	+	0.723898i
$893$	9.20465	+	4.43272i	0.308022	+	0.148335i
$894$	−10.0026	−	1.57210i	−0.334539	−	0.0525790i
$895$	−10.7910	−	5.19667i	−0.360703	−	0.173706i
$896$	25.9333	+	14.9487i	0.866371	+	0.499401i
$897$	4.87999	−	2.35008i	0.162938	−	0.0784668i
$898$	55.2035	−	16.6483i	1.84216	−	0.555560i
$899$	5.65188	−	7.08723i	0.188501	−	0.236372i
$900$	10.7943	−	18.1644i	0.359811	−	0.605479i
$901$			31.9858i			1.06560i
$902$	0.547944	+	0.0861197i	0.0182445	+	0.00286747i
$903$	−14.5464	−	22.7772i	−0.484074	−	0.757977i
$904$	26.1724	+	34.1213i	0.870480	+	1.13486i
$905$	34.5566	+	43.3326i	1.14870	+	1.44043i
$906$	14.7827	−	21.3917i	0.491122	−	0.710692i
$907$	−0.382040	−	0.793314i	−0.0126854	−	0.0263416i	0.894530	−	0.447008i	$-0.147511\pi$
$907$	−0.382040	−	0.793314i	−0.0126854	−	0.0263416i	−0.907215	+	0.420667i	$0.861796\pi$
$908$	10.5279	−	1.45154i	0.349381	−	0.0481712i
$909$	7.37948	−	5.88494i	0.244762	−	0.195191i
$910$	56.2809	−	24.6258i	1.86569	−	0.816337i
$911$	−6.07476	−	4.84446i	−0.201266	−	0.160504i	0.517670	−	0.855580i	$-0.326799\pi$
$911$	−6.07476	−	4.84446i	−0.201266	−	0.160504i	−0.718936	+	0.695076i	$0.755371\pi$
$912$	2.41405	+	4.43550i	0.0799373	+	0.146874i
$913$			2.67654i			0.0885806i
$914$	−34.6426	−	5.44473i	−1.14587	−	0.180096i
$915$	5.08355	−	22.2725i	0.168057	−	0.736306i
$916$	−43.6426	−	3.82356i	−1.44199	−	0.126334i
$917$	0.882255	+	2.46313i	0.0291346	+	0.0813396i
$918$	−6.99771	+	0.480136i	−0.230959	+	0.0158469i
$919$	14.7939	+	11.7978i	0.488007	+	0.389173i	0.836351	−	0.548194i	$-0.184685\pi$
$919$	14.7939	+	11.7978i	0.488007	+	0.389173i	−0.348344	+	0.937367i	$0.613256\pi$
$920$	−12.9637	−	6.54732i	−0.427399	−	0.215859i
$921$	2.44062	−	10.6931i	0.0804212	−	0.352348i
$922$	23.4112	−	33.8779i	0.771007	−	1.11571i
$923$	3.72096	+	16.3026i	0.122477	+	0.536606i
$924$	−2.28310	+	1.19139i	−0.0751083	+	0.0391939i
$925$	22.4195	−	98.2263i	0.737149	−	3.22966i
$926$	19.5933	+	21.3850i	0.643877	+	0.702754i
$927$	−8.77537	−	11.0040i	−0.288221	−	0.361418i
$928$	−33.0244	−	11.3364i	−1.08408	−	0.372134i
$929$	16.9738	−	35.2465i	0.556893	−	1.15640i	−0.412517	−	0.910950i	$-0.635350\pi$
$929$	16.9738	−	35.2465i	0.556893	−	1.15640i	0.969409	−	0.245450i	$-0.0789356\pi$
$930$	−7.12195	+	4.05231i	−0.233538	+	0.132880i
$931$	3.71693	−	8.01762i	0.121817	−	0.262767i
$932$	−3.83868	+	6.45963i	−0.125740	+	0.211592i
$933$	−6.51613	−	3.13800i	−0.213329	−	0.102734i
$934$	2.47320	−	2.26600i	0.0809257	−	0.0741457i
$935$	−7.44539	+	5.93750i	−0.243490	+	0.194177i
$936$	−11.5231	+	2.40213i	−0.376646	+	0.0785160i
$937$	−30.9970	−	7.07487i	−1.01263	−	0.231126i	−0.316155	−	0.948708i	$-0.602392\pi$
$937$	−30.9970	−	7.07487i	−1.01263	−	0.231126i	−0.696474	+	0.717582i	$0.745249\pi$
$938$	17.3446	−	12.8292i	0.566320	−	0.418887i
$939$	−7.57834	+	1.72971i	−0.247310	+	0.0564468i
$940$	63.6089	+	5.57282i	2.07469	+	0.181765i
$941$	−49.6590	−	11.3343i	−1.61884	−	0.369489i	−0.685382	−	0.728184i	$-0.740365\pi$
$941$	−49.6590	−	11.3343i	−1.61884	−	0.369489i	−0.933455	+	0.358695i	$0.883222\pi$
$942$	−3.25509	+	0.223342i	−0.106056	+	0.00727689i
$943$	−0.653964	+	0.820046i	−0.0212960	+	0.0267044i
$944$	0.220189	+	4.43347i	0.00716655	+	0.144297i
$945$	10.3808	+	1.09244i	0.337686	+	0.0355371i
$946$	5.78384	+	3.99691i	0.188049	+	0.129951i
$947$	−41.4233	−	9.45461i	−1.34608	−	0.307233i	−0.512050	−	0.858956i	$-0.671114\pi$
$947$	−41.4233	−	9.45461i	−1.34608	−	0.307233i	−0.834028	+	0.551722i	$0.813971\pi$
$948$	−32.3597	+	12.2325i	−1.05099	+	0.397292i
$949$	60.9671			1.97908
$950$	−9.32824	−	16.3944i	−0.302648	−	0.531905i
$951$	−7.45847	+	9.35262i	−0.241857	+	0.303280i
$952$	3.72999	+	36.9275i	0.120890	+	1.19683i
$953$	−6.79970	−	8.52656i	−0.220264	−	0.276202i	0.659406	−	0.751787i	$-0.270808\pi$
$953$	−6.79970	−	8.52656i	−0.220264	−	0.276202i	−0.879670	+	0.475585i	$0.842236\pi$
$954$	−3.38540	+	8.46875i	−0.109607	+	0.274186i
$955$	46.7023	−	22.4906i	1.51125	−	0.727780i
$956$	14.1572	+	1.24033i	0.457878	+	0.0401150i
$957$	2.34857	−	1.87292i	0.0759185	−	0.0605430i
$958$	2.88806	−	7.22461i	0.0933089	−	0.233417i
$959$	−16.2575	−	45.3884i	−0.524981	−	1.46567i
$960$	23.9155	+	20.5961i	0.771869	+	0.664735i
$961$	−28.8431			−0.930423
$962$	−48.7830	+	27.7570i	−1.57283	+	0.894921i
$963$	13.5166	+	10.7791i	0.435565	+	0.347351i
$964$	−11.1989	+	11.7689i	−0.360693	+	0.379052i
$965$	−9.36284	−	19.4421i	−0.301400	−	0.625864i
$966$	0.176954	−	4.86657i	0.00569339	−	0.156579i
$967$	25.0168	−	51.9480i	0.804487	−	1.67053i	0.0644956	−	0.997918i	$-0.479456\pi$
$967$	25.0168	−	51.9480i	0.804487	−	1.67053i	0.739991	−	0.672616i	$-0.234830\pi$
$968$	−19.4267	+	23.4385i	−0.624399	+	0.753342i
$969$	−2.71679	+	5.64146i	−0.0872757	+	0.181230i
$970$	−19.2045	+	5.79168i	−0.616618	+	0.185960i
$971$	−18.3674	+	8.84529i	−0.589439	+	0.283859i	−0.704733	−	0.709472i	$-0.748933\pi$
$971$	−18.3674	+	8.84529i	−0.589439	+	0.283859i	0.115294	+	0.993331i	$0.463219\pi$
$972$	−1.90357	−	0.613520i	−0.0610572	−	0.0196787i
$973$	22.8309	+	22.4978i	0.731926	+	0.721247i
$974$	4.17142	+	13.8319i	0.133661	+	0.443202i
$975$	42.8645	−	9.78354i	1.37276	−	0.313324i
$976$	21.3414	+	9.00226i	0.683123	+	0.288155i
$977$	−9.04987	−	39.6501i	−0.289531	−	1.26852i	−0.885170	−	0.465267i	$-0.845958\pi$
$977$	−9.04987	−	39.6501i	−0.289531	−	1.26852i	0.595639	−	0.803252i	$-0.296899\pi$
$978$	−29.1684	+	2.00134i	−0.932703	+	0.0639959i
$979$	−6.94750			−0.222043
$980$	4.01137	−	55.0873i	0.128139	−	1.75970i
$981$	1.77983			0.0568257
$982$	38.3750	−	2.63304i	1.22460	−	0.0840236i
$983$	2.85683	+	12.5166i	0.0911189	+	0.399218i	0.999834	−	0.0181981i	$-0.00579296\pi$
$983$	2.85683	+	12.5166i	0.0911189	+	0.399218i	−0.908716	+	0.417416i	$0.862936\pi$
$984$	1.80864	−	1.38729i	0.0576572	−	0.0442253i
$985$	20.8488	−	4.75860i	0.664297	−	0.151621i
$986$	−12.5004	−	41.4498i	−0.398094	−	1.32003i
$987$	7.21973	+	20.1564i	0.229807	+	0.641586i
$988$	−3.22339	+	10.0012i	−0.102550	+	0.318182i
$989$	−11.9781	+	5.76833i	−0.380880	+	0.183422i
$990$	−2.59972	+	0.784022i	−0.0826244	+	0.0249178i
$991$	−3.48812	+	7.24315i	−0.110804	+	0.230086i	−0.948996	−	0.315289i	$-0.897899\pi$
$991$	−3.48812	+	7.24315i	−0.110804	+	0.230086i	0.838192	+	0.545375i	$0.183613\pi$
$992$	−2.79037	−	7.82524i	−0.0885944	−	0.248452i
$993$	−7.88767	+	16.3789i	−0.250308	+	0.519769i
$994$	14.5262	+	3.87586i	0.460742	+	0.122935i
$995$	−32.2772	−	67.0243i	−1.02326	−	2.12481i
$996$	7.96821	+	7.58229i	0.252482	+	0.240254i
$997$	38.2141	+	30.4748i	1.21025	+	0.965145i	0.999922	−	0.0124847i	$-0.00397411\pi$
$997$	38.2141	+	30.4748i	1.21025	+	0.965145i	0.210332	+	0.977630i	$0.432546\pi$
$998$	50.2168	−	28.5728i	1.58958	−	0.904455i
$999$	−9.53659			−0.301724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.x.b.559.14	yes	168
4.3	odd	2		588.2.x.a.559.6	yes	168
49.27	odd	14		588.2.x.a.223.6	✓	168
196.27	even	14	inner	588.2.x.b.223.14	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.x.a.223.6	✓	168	49.27	odd	14
588.2.x.a.559.6	yes	168	4.3	odd	2
588.2.x.b.223.14	yes	168	196.27	even	14	inner
588.2.x.b.559.14	yes	168	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0968063 - 1.41090i) q^{2} +(0.222521 + 0.974928i) q^{3} +(-1.98126 + 0.273167i) q^{4} +(-3.84631 + 0.877896i) q^{5} +(1.35398 - 0.408333i) q^{6} +(2.22982 - 1.42405i) q^{7} +(0.577209 + 2.76890i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\)	\(q+(-0.0968063 - 1.41090i) q^{2} +(0.222521 + 0.974928i) q^{3} +(-1.98126 + 0.273167i) q^{4} +(-3.84631 + 0.877896i) q^{5} +(1.35398 - 0.408333i) q^{6} +(2.22982 - 1.42405i) q^{7} +(0.577209 + 2.76890i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(1.61097 + 5.34176i) q^{10} +(0.211161 - 0.438481i) q^{11} +(-0.707190 - 1.87080i) q^{12} +(1.80566 - 3.74949i) q^{13} +(-2.22505 - 3.00818i) q^{14} +(-1.71177 - 3.55453i) q^{15} +(3.85076 - 1.08243i) q^{16} +(3.87770 + 3.09236i) q^{17} +(0.699384 + 1.22917i) q^{18} +1.26247 q^{19} +(7.38072 - 2.79002i) q^{20} +(1.88453 + 1.85703i) q^{21} +(-0.639093 - 0.255479i) q^{22} +(1.01756 - 0.811475i) q^{23} +(-2.57104 + 1.17888i) q^{24} +(9.51858 - 4.58391i) q^{25} +(-5.46495 - 2.18463i) q^{26} +(-0.623490 - 0.781831i) q^{27} +(-4.02884 + 3.43052i) q^{28} +(3.84838 - 4.82572i) q^{29} +(-4.84936 + 2.75923i) q^{30} +1.46864 q^{31} +(-1.89997 - 5.32824i) q^{32} +(0.474475 + 0.108296i) q^{33} +(3.98761 - 5.77039i) q^{34} +(-7.32641 + 7.43489i) q^{35} +(1.66653 - 1.10575i) q^{36} +(5.94597 - 7.45601i) q^{37} +(-0.122215 - 1.78122i) q^{38} +(4.05728 + 0.926049i) q^{39} +(-4.65094 - 10.1433i) q^{40} +(-0.785690 + 0.179329i) q^{41} +(2.43764 - 2.83864i) q^{42} +(-9.95871 - 2.27301i) q^{43} +(-0.298586 + 0.926427i) q^{44} +(3.08450 - 2.45981i) q^{45} +(-1.24341 - 1.35711i) q^{46} +(7.29098 + 3.51115i) q^{47} +(1.91217 + 3.51335i) q^{48} +(2.94417 - 6.35074i) q^{49} +(-7.38887 - 12.9860i) q^{50} +(-2.15196 + 4.46859i) q^{51} +(-2.55324 + 7.92196i) q^{52} +(4.02092 + 5.04208i) q^{53} +(-1.04273 + 0.955366i) q^{54} +(-0.427252 + 1.87191i) q^{55} +(5.23013 + 5.35218i) q^{56} +(0.280926 + 1.23082i) q^{57} +(-7.18114 - 4.96251i) q^{58} +(-0.246939 + 1.08191i) q^{59} +(4.36244 + 6.57483i) q^{60} +(4.52728 + 3.61038i) q^{61} +(-0.142173 - 2.07209i) q^{62} +(-1.39112 + 2.25051i) q^{63} +(-7.33366 + 3.19647i) q^{64} +(-3.65347 + 16.0069i) q^{65} +(0.106862 - 0.679919i) q^{66} +5.76579i q^{67} +(-8.52745 - 5.06750i) q^{68} +(1.01756 + 0.811475i) q^{69} +(11.1991 + 9.61706i) q^{70} +(-3.14148 + 2.50524i) q^{71} +(-1.72143 - 2.24425i) q^{72} +(6.35632 + 13.1990i) q^{73} +(-11.0953 - 7.66735i) q^{74} +(6.58706 + 8.25991i) q^{75} +(-2.50128 + 0.344866i) q^{76} +(-0.153568 - 1.27844i) q^{77} +(0.913788 - 5.81405i) q^{78} -17.2973i q^{79} +(-13.8610 + 7.54393i) q^{80} +(0.623490 - 0.781831i) q^{81} +(0.329074 + 1.09117i) q^{82} +(-4.95499 + 2.38620i) q^{83} +(-4.24101 - 3.16446i) q^{84} +(-17.6296 - 8.48997i) q^{85} +(-2.24292 + 14.2707i) q^{86} +(5.56108 + 2.67807i) q^{87} +(1.33600 + 0.331590i) q^{88} +(-6.19385 - 12.8617i) q^{89} +(-3.76914 - 4.11379i) q^{90} +(-1.31317 - 10.9320i) q^{91} +(-1.79437 + 1.88570i) q^{92} +(0.326802 + 1.43181i) q^{93} +(4.24806 - 10.6267i) q^{94} +(-4.85586 + 1.10832i) q^{95} +(4.77186 - 3.03798i) q^{96} +3.59515i q^{97} +(-9.24525 - 3.53912i) q^{98} +0.486678i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9	\( 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9} - 20 q^{10} + 14 q^{14} - 20 q^{16} - 12 q^{19} + 25 q^{20} + 2 q^{21} - 6 q^{22} - 27 q^{24} + 32 q^{25} - 6 q^{26} + 28 q^{27} + 6 q^{28} - 8 q^{30} + 4 q^{31} - 45 q^{32} - 44 q^{34} + 12 q^{35} - 10 q^{37} - 35 q^{38} - 14 q^{39} + 40 q^{40} + 7 q^{42} + 20 q^{44} + 28 q^{46} + 8 q^{47} - 8 q^{48} - 8 q^{49} + 114 q^{50} - 20 q^{52} - 8 q^{53} + 23 q^{56} + 12 q^{57} - 6 q^{58} - 20 q^{59} + 10 q^{60} - 14 q^{61} + 16 q^{62} + 12 q^{63} - 42 q^{64} - 8 q^{65} + 6 q^{66} + 16 q^{68} + 19 q^{70} - 28 q^{71} - 15 q^{72} + 22 q^{74} - 18 q^{75} - 49 q^{76} + 8 q^{77} + 6 q^{78} - 26 q^{80} - 28 q^{81} - 12 q^{82} - 10 q^{83} - 27 q^{84} - 24 q^{85} - 34 q^{86} + 94 q^{88} - 20 q^{90} + 16 q^{91} + 7 q^{92} - 4 q^{93} + 11 q^{94} + 10 q^{96} - 150 q^{98}+O(q^{100}) \) 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9 - 20 * q^10 + 14 * q^14 - 20 * q^16 - 12 * q^19 + 25 * q^20 + 2 * q^21 - 6 * q^22 - 27 * q^24 + 32 * q^25 - 6 * q^26 + 28 * q^27 + 6 * q^28 - 8 * q^30 + 4 * q^31 - 45 * q^32 - 44 * q^34 + 12 * q^35 - 10 * q^37 - 35 * q^38 - 14 * q^39 + 40 * q^40 + 7 * q^42 + 20 * q^44 + 28 * q^46 + 8 * q^47 - 8 * q^48 - 8 * q^49 + 114 * q^50 - 20 * q^52 - 8 * q^53 + 23 * q^56 + 12 * q^57 - 6 * q^58 - 20 * q^59 + 10 * q^60 - 14 * q^61 + 16 * q^62 + 12 * q^63 - 42 * q^64 - 8 * q^65 + 6 * q^66 + 16 * q^68 + 19 * q^70 - 28 * q^71 - 15 * q^72 + 22 * q^74 - 18 * q^75 - 49 * q^76 + 8 * q^77 + 6 * q^78 - 26 * q^80 - 28 * q^81 - 12 * q^82 - 10 * q^83 - 27 * q^84 - 24 * q^85 - 34 * q^86 + 94 * q^88 - 20 * q^90 + 16 * q^91 + 7 * q^92 - 4 * q^93 + 11 * q^94 + 10 * q^96 - 150 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more