LMFDB - Embedded newform 462.2.ba.b.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			61.3
Character	$\chi$	$=$	462.61
Dual form			462.2.ba.b.409.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.131864 - 0.118731i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.17519 - 2.37043i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.131864 - 0.118731i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.17519 - 2.37043i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.0887206 + 0.153669i) q^{10} +(3.00345 - 1.40687i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(1.93838 + 5.96571i) q^{13} +(2.56296 - 0.656669i) q^{14} +(0.143553 - 0.104297i) q^{15} +(0.669131 + 0.743145i) q^{16} +(4.95293 - 1.05278i) q^{17} +(-0.406737 + 0.913545i) q^{18} +(4.82010 - 2.14605i) q^{19} +(-0.168757 + 0.0548323i) q^{20} +(-0.920974 - 2.48028i) q^{21} +(0.751673 + 3.23032i) q^{22} +(0.243079 - 0.421026i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.519351 + 4.94130i) q^{25} +(-6.23835 + 0.655677i) q^{26} +(0.951057 + 0.309017i) q^{27} +(0.109449 + 2.64349i) q^{28} +(-3.42738 - 4.71738i) q^{29} +(0.0721718 + 0.162101i) q^{30} +(-0.863720 - 0.777697i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.13406 - 1.08522i) q^{33} +5.06358i q^{34} +(-0.436410 - 0.173044i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.164754 + 1.56753i) q^{37} +(1.09700 + 5.16096i) q^{38} +(1.30417 + 6.13564i) q^{39} +(-0.0185477 - 0.176469i) q^{40} +(-3.11587 - 2.26381i) q^{41} +(2.61756 - 0.385169i) q^{42} -3.10113i q^{43} +(-3.31601 + 0.0636253i) q^{44} +(0.153669 - 0.0887206i) q^{45} +(0.361286 + 0.325304i) q^{46} +(-2.52068 - 5.66154i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-4.23786 + 5.57140i) q^{49} +(-4.72534 - 1.53536i) q^{50} +(5.03584 - 0.529288i) q^{51} +(0.655677 - 6.23835i) q^{52} +(0.0562900 - 0.0625164i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.229009 - 0.542120i) q^{55} +(-2.60848 - 0.442555i) q^{56} +(5.01802 - 1.63045i) q^{57} +(5.32689 - 2.37168i) q^{58} +(-2.20745 + 4.95801i) q^{59} +(-0.173564 + 0.0368921i) q^{60} +(-5.97248 - 6.63311i) q^{61} +(0.940280 - 0.683153i) q^{62} +(-0.656669 - 2.56296i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.963919 + 0.556519i) q^{65} +(0.409895 + 3.29120i) q^{66} +(6.50383 + 11.2650i) q^{67} +(-4.95293 - 1.05278i) q^{68} +(0.285757 - 0.393311i) q^{69} +(0.259997 - 0.390895i) q^{70} +(-1.55851 + 4.79660i) q^{71} +(0.743145 - 0.669131i) q^{72} +(2.73723 + 1.21869i) q^{73} +(-1.56753 - 0.164754i) q^{74} +(-1.03301 + 4.85994i) q^{75} -5.27626 q^{76} +(-6.86451 - 5.46613i) q^{77} -6.27271 q^{78} +(-2.21581 + 10.4246i) q^{79} +(0.176469 + 0.0185477i) q^{80} +(0.913545 + 0.406737i) q^{81} +(2.86217 - 2.57710i) q^{82} +(0.869462 - 2.67593i) q^{83} +(-0.167471 + 2.64045i) q^{84} +(0.528117 - 0.726891i) q^{85} +(3.03337 + 0.644762i) q^{86} +(-2.91550 - 5.04980i) q^{87} +(0.627203 - 3.25678i) q^{88} +(-8.73396 - 5.04256i) q^{89} +(0.0548323 + 0.168757i) q^{90} +(11.8633 - 11.6056i) q^{91} +(-0.393311 + 0.285757i) q^{92} +(-0.777697 - 0.863720i) q^{93} +(6.06190 - 1.28850i) q^{94} +(0.380797 - 0.855284i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-14.0191 + 4.55507i) q^{97} +(-4.56855 - 5.30361i) q^{98} +(3.23032 - 0.751673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	0.131864	−	0.118731i	0.0589716	−	0.0530983i	−0.639118	−	0.769109i	$-0.720700\pi$
$5$	0.131864	−	0.118731i	0.0589716	−	0.0530983i	0.698089	+	0.716011i	$0.254034\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	−1.17519	−	2.37043i	−0.444180	−	0.895938i
$7$	−1.17519	−	2.37043i	−0.444180	−	0.895938i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.978148	+	0.207912i	0.326049	+	0.0693039i
$10$	0.0887206	+	0.153669i	0.0280559	+	0.0485943i
$11$	3.00345	−	1.40687i	0.905575	−	0.424187i
$11$	3.00345	−	1.40687i	0.905575	−	0.424187i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	1.93838	+	5.96571i	0.537609	+	1.65459i	0.737944	+	0.674862i	$0.235797\pi$
$13$	1.93838	+	5.96571i	0.537609	+	1.65459i	−0.200336	+	0.979727i	$0.564203\pi$
$14$	2.56296	−	0.656669i	0.684981	−	0.175502i
$15$	0.143553	−	0.104297i	0.0370652	−	0.0269294i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	4.95293	−	1.05278i	1.20126	−	0.255336i	0.436533	−	0.899688i	$-0.356206\pi$
$17$	4.95293	−	1.05278i	1.20126	−	0.255336i	0.764729	+	0.644353i	$0.222873\pi$
$18$	−0.406737	+	0.913545i	−0.0958687	+	0.215325i
$19$	4.82010	−	2.14605i	1.10581	−	0.492337i	0.229120	−	0.973398i	$-0.426415\pi$
$19$	4.82010	−	2.14605i	1.10581	−	0.492337i	0.876687	+	0.481061i	$0.159749\pi$
$20$	−0.168757	+	0.0548323i	−0.0377351	+	0.0122609i
$21$	−0.920974	−	2.48028i	−0.200973	−	0.541242i
$22$	0.751673	+	3.23032i	0.160257	+	0.688707i
$23$	0.243079	−	0.421026i	0.0506855	−	0.0877899i	−0.839570	−	0.543252i	$-0.817193\pi$
$23$	0.243079	−	0.421026i	0.0506855	−	0.0877899i	0.890255	+	0.455462i	$0.150526\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.519351	+	4.94130i	−0.103870	+	0.988259i
$26$	−6.23835	+	0.655677i	−1.22344	+	0.128589i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	0.109449	+	2.64349i	0.0206838	+	0.499572i
$29$	−3.42738	−	4.71738i	−0.636448	−	0.875996i	0.361972	−	0.932189i	$-0.382104\pi$
$29$	−3.42738	−	4.71738i	−0.636448	−	0.875996i	−0.998420	+	0.0561931i	$0.982104\pi$
$30$	0.0721718	+	0.162101i	0.0131767	+	0.0295954i
$31$	−0.863720	−	0.777697i	−0.155129	−	0.139678i	0.587912	−	0.808925i	$-0.299950\pi$
$31$	−0.863720	−	0.777697i	−0.155129	−	0.139678i	−0.743040	+	0.669247i	$0.766617\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.13406	−	1.08522i	0.545569	−	0.188912i
$34$			5.06358i			0.868396i
$35$	−0.436410	−	0.173044i	−0.0737667	−	0.0292497i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	0.164754	+	1.56753i	0.0270854	+	0.257701i	0.999682	+	0.0252029i	$0.00802317\pi$
$37$	0.164754	+	1.56753i	0.0270854	+	0.257701i	−0.972597	+	0.232498i	$0.925310\pi$
$38$	1.09700	+	5.16096i	0.177956	+	0.837218i
$39$	1.30417	+	6.13564i	0.208834	+	0.982489i
$40$	−0.0185477	−	0.176469i	−0.00293264	−	0.0279022i
$41$	−3.11587	−	2.26381i	−0.486617	−	0.353548i	0.317265	−	0.948337i	$-0.397236\pi$
$41$	−3.11587	−	2.26381i	−0.486617	−	0.353548i	−0.803882	+	0.594789i	$0.797236\pi$
$42$	2.61756	−	0.385169i	0.403899	−	0.0594328i
$43$		−	3.10113i		−	0.472918i	−0.971641	−	0.236459i	$-0.924013\pi$
$43$		−	3.10113i		−	0.472918i	0.971641	−	0.236459i	$-0.0759869\pi$
$44$	−3.31601	+	0.0636253i	−0.499908	+	0.00959187i
$45$	0.153669	−	0.0887206i	0.0229076	−	0.0132257i
$46$	0.361286	+	0.325304i	0.0532687	+	0.0479634i
$47$	−2.52068	−	5.66154i	−0.367679	−	0.825821i	−0.998745	−	0.0500911i	$-0.984049\pi$
$47$	−2.52068	−	5.66154i	−0.367679	−	0.825821i	0.631066	−	0.775729i	$-0.282618\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	−4.23786	+	5.57140i	−0.605409	+	0.795915i
$50$	−4.72534	−	1.53536i	−0.668264	−	0.217132i
$51$	5.03584	−	0.529288i	0.705158	−	0.0741151i
$52$	0.655677	−	6.23835i	0.0909261	−	0.865104i
$53$	0.0562900	−	0.0625164i	0.00773203	−	0.00858729i	−0.739266	−	0.673413i	$-0.764828\pi$
$53$	0.0562900	−	0.0625164i	0.00773203	−	0.00858729i	0.746998	+	0.664826i	$0.231494\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.229009	−	0.542120i	0.0308796	−	0.0730994i
$56$	−2.60848	−	0.442555i	−0.348572	−	0.0591389i
$57$	5.01802	−	1.63045i	0.664653	−	0.215959i
$58$	5.32689	−	2.37168i	0.699455	−	0.311417i
$59$	−2.20745	+	4.95801i	−0.287385	+	0.645478i	−0.998330	−	0.0577703i	$-0.981601\pi$
$59$	−2.20745	+	4.95801i	−0.287385	+	0.645478i	0.710945	+	0.703248i	$0.248268\pi$
$60$	−0.173564	+	0.0368921i	−0.0224070	+	0.00476275i
$61$	−5.97248	−	6.63311i	−0.764698	−	0.849283i	0.227523	−	0.973773i	$-0.426937\pi$
$61$	−5.97248	−	6.63311i	−0.764698	−	0.849283i	−0.992221	+	0.124489i	$0.960271\pi$
$62$	0.940280	−	0.683153i	0.119416	−	0.0867605i
$63$	−0.656669	−	2.56296i	−0.0827325	−	0.322903i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.963919	+	0.556519i	0.119559	+	0.0690277i
$66$	0.409895	+	3.29120i	0.0504545	+	0.405119i
$67$	6.50383	+	11.2650i	0.794569	+	1.37623i	0.923113	+	0.384530i	$0.125636\pi$
$67$	6.50383	+	11.2650i	0.794569	+	1.37623i	−0.128544	+	0.991704i	$0.541030\pi$
$68$	−4.95293	−	1.05278i	−0.600631	−	0.127668i
$69$	0.285757	−	0.393311i	0.0344011	−	0.0473490i
$70$	0.259997	−	0.390895i	0.0310756	−	0.0467209i
$71$	−1.55851	+	4.79660i	−0.184961	+	0.569251i	−0.999948	−	0.0102284i	$-0.996744\pi$
$71$	−1.55851	+	4.79660i	−0.184961	+	0.569251i	0.814987	+	0.579480i	$0.196744\pi$
$72$	0.743145	−	0.669131i	0.0875805	−	0.0788578i
$73$	2.73723	+	1.21869i	0.320368	+	0.142637i	0.560619	−	0.828074i	$-0.310563\pi$
$73$	2.73723	+	1.21869i	0.320368	+	0.142637i	−0.240251	+	0.970711i	$0.577230\pi$
$74$	−1.56753	−	0.164754i	−0.182222	−	0.0191523i
$75$	−1.03301	+	4.85994i	−0.119282	+	0.561178i
$76$	−5.27626			−0.605228
$77$	−6.86451	−	5.46613i	−0.782283	−	0.622923i
$78$	−6.27271			−0.710245
$79$	−2.21581	+	10.4246i	−0.249298	+	1.17286i	0.658215	+	0.752830i	$0.271312\pi$
$79$	−2.21581	+	10.4246i	−0.249298	+	1.17286i	−0.907513	+	0.420025i	$0.862021\pi$
$80$	0.176469	+	0.0185477i	0.0197298	+	0.00207369i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	2.86217	−	2.57710i	0.316073	−	0.284594i
$83$	0.869462	−	2.67593i	0.0954358	−	0.293721i	−0.891931	−	0.452171i	$-0.850650\pi$
$83$	0.869462	−	2.67593i	0.0954358	−	0.293721i	0.987367	+	0.158450i	$0.0506496\pi$
$84$	−0.167471	+	2.64045i	−0.0182725	+	0.288096i
$85$	0.528117	−	0.726891i	0.0572824	−	0.0788424i
$86$	3.03337	+	0.644762i	0.327096	+	0.0695264i
$87$	−2.91550	−	5.04980i	−0.312575	−	0.541395i
$88$	0.627203	−	3.25678i	0.0668601	−	0.347174i
$89$	−8.73396	−	5.04256i	−0.925798	−	0.534510i	−0.0403179	−	0.999187i	$-0.512837\pi$
$89$	−8.73396	−	5.04256i	−0.925798	−	0.534510i	−0.885480	+	0.464677i	$0.846170\pi$
$90$	0.0548323	+	0.168757i	0.00577984	+	0.0177885i
$91$	11.8633	−	11.6056i	1.24361	−	1.21660i
$92$	−0.393311	+	0.285757i	−0.0410055	+	0.0297922i
$93$	−0.777697	−	0.863720i	−0.0806434	−	0.0895636i
$94$	6.06190	−	1.28850i	0.625237	−	0.132898i
$95$	0.380797	−	0.855284i	0.0390690	−	0.0877503i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	−14.0191	+	4.55507i	−1.42342	+	0.462497i	−0.916687	−	0.399606i	$-0.869147\pi$
$97$	−14.0191	+	4.55507i	−1.42342	+	0.462497i	−0.506733	+	0.862103i	$0.669147\pi$
$98$	−4.56855	−	5.30361i	−0.461494	−	0.535746i
$99$	3.23032	−	0.751673i	0.324660	−	0.0755460i
$100$	2.48426	−	4.30286i	0.248426	−	0.430286i
$101$	9.62392	−	10.6884i	0.957615	−	1.06354i	−0.0403119	−	0.999187i	$-0.512835\pi$
$101$	9.62392	−	10.6884i	0.957615	−	1.06354i	0.997927	−	0.0643525i	$-0.0204982\pi$
$102$	−0.529288	+	5.03584i	−0.0524073	+	0.498622i
$103$	−9.65874	+	1.01517i	−0.951704	+	0.100028i	−0.567639	−	0.823278i	$-0.692143\pi$
$103$	−9.65874	+	1.01517i	−0.951704	+	0.100028i	−0.384065	+	0.923306i	$0.625476\pi$
$104$	5.96571	+	1.93838i	0.584986	+	0.190073i
$105$	−0.415931	−	0.217713i	−0.0405907	−	0.0212466i
$106$	0.0494469	+	0.0680578i	0.00480271	+	0.00661036i
$107$	−7.72985	−	17.3615i	−0.747273	−	1.67840i	−0.734616	−	0.678483i	$-0.762638\pi$
$107$	−7.72985	−	17.3615i	−0.747273	−	1.67840i	−0.0126571	−	0.999920i	$-0.504029\pi$
$108$	−0.743145	−	0.669131i	−0.0715091	−	0.0643871i
$109$	−11.2794	+	6.51214i	−1.08037	+	0.623750i	−0.930995	−	0.365031i	$-0.881058\pi$
$109$	−11.2794	+	6.51214i	−1.08037	+	0.623750i	−0.149371	+	0.988781i	$0.547725\pi$
$110$	0.482659	+	0.336718i	0.0460198	+	0.0321048i
$111$			1.57617i			0.149603i
$112$	0.975217	−	2.45946i	0.0921493	−	0.232397i
$113$	4.60486	+	3.34563i	0.433189	+	0.314730i	0.782923	−	0.622119i	$-0.213728\pi$
$113$	4.60486	+	3.34563i	0.433189	+	0.314730i	−0.349734	+	0.936849i	$0.613728\pi$
$114$	0.551519	+	5.24735i	0.0516545	+	0.491460i
$115$	−0.0179354	−	0.0843794i	−0.00167249	−	0.00786842i
$116$	1.21233	+	5.70358i	0.112562	+	0.529565i
$117$	0.655677	+	6.23835i	0.0606174	+	0.576736i
$118$	−4.39071	−	3.19004i	−0.404197	−	0.293667i
$119$	−8.31616	−	10.5033i	−0.762341	−	0.962840i
$120$		−	0.177441i		−	0.0161981i
$121$	7.04144	−	8.45093i	0.640131	−	0.768266i
$122$	7.72991	−	4.46287i	0.699834	−	0.404049i
$123$	−2.86217	−	2.57710i	−0.258073	−	0.232370i
$124$	0.472729	+	1.06177i	0.0424524	+	0.0953496i
$125$	1.03969	+	1.43101i	0.0929926	+	0.127993i
$126$	2.64349	−	0.109449i	0.235500	−	0.00975045i
$127$	2.98151	+	0.968751i	0.264566	+	0.0859627i	0.438296	−	0.898831i	$-0.355582\pi$
$127$	2.98151	+	0.968751i	0.264566	+	0.0859627i	−0.173730	+	0.984793i	$0.555582\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	0.324157	−	3.08414i	0.0285404	−	0.271544i
$130$	−0.744768	+	0.827148i	−0.0653204	+	0.0725457i
$131$	2.16679	−	3.75299i	0.189313	−	0.327900i	−0.755708	−	0.654909i	$-0.772707\pi$
$131$	2.16679	−	3.75299i	0.189313	−	0.327900i	0.945022	+	0.327008i	$0.106040\pi$
$132$	−3.30450	−	0.283341i	−0.287620	−	0.0246617i
$133$	−10.7516	−	8.90369i	−0.932280	−	0.772048i
$134$	−12.3710	+	4.01959i	−1.06869	+	0.347239i
$135$	0.162101	−	0.0721718i	0.0139514	−	0.00621156i
$136$	2.05954	−	4.62581i	0.176604	−	0.396660i
$137$	−0.444633	+	0.0945096i	−0.0379876	+	0.00807450i	−0.226866	−	0.973926i	$-0.572848\pi$
$137$	−0.444633	+	0.0945096i	−0.0379876	+	0.00807450i	0.188879	+	0.982000i	$0.439515\pi$
$138$	0.325304	+	0.361286i	0.0276917	+	0.0307547i
$139$	13.3962	−	9.73294i	1.13625	−	0.825537i	0.149662	−	0.988737i	$-0.452182\pi$
$139$	13.3962	−	9.73294i	1.13625	−	0.825537i	0.986593	+	0.163200i	$0.0521816\pi$
$140$	0.328297	+	0.335587i	0.0277462	+	0.0283623i
$141$	−1.91508	−	5.89401i	−0.161279	−	0.496365i
$142$	−4.36775	−	2.52172i	−0.366533	−	0.211618i
$143$	14.2148	+	15.1907i	1.18870	+	1.27031i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−1.01205	−	0.215118i	−0.0840462	−	0.0178646i
$146$	−1.76116	+	2.42403i	−0.145755	+	0.200614i
$147$	−4.79702	+	5.09790i	−0.395651	+	0.420468i
$148$	0.487062	−	1.49902i	0.0400363	−	0.123219i
$149$	−18.0958	+	16.2935i	−1.48246	+	1.33482i	−0.693244	+	0.720703i	$0.743819\pi$
$149$	−18.0958	+	16.2935i	−1.48246	+	1.33482i	−0.789218	+	0.614113i	$0.789514\pi$
$150$	−4.53896	−	2.02088i	−0.370605	−	0.165004i
$151$	11.2925	+	1.18689i	0.918974	+	0.0965881i	0.552190	−	0.833718i	$-0.313792\pi$
$151$	11.2925	+	1.18689i	0.918974	+	0.0965881i	0.366784	+	0.930306i	$0.380459\pi$
$152$	1.09700	−	5.16096i	0.0889781	−	0.418609i
$153$	5.06358			0.409366
$154$	6.77389	−	5.57803i	0.545856	−	0.449490i
$155$	−0.206231			−0.0165649
$156$	1.30417	−	6.13564i	0.104417	−	0.491244i
$157$	11.4351	+	1.20188i	0.912621	+	0.0959203i	0.549187	−	0.835700i	$-0.314938\pi$
$157$	11.4351	+	1.20188i	0.912621	+	0.0959203i	0.363434	+	0.931620i	$0.381604\pi$
$158$	−9.73607	−	4.33478i	−0.774560	−	0.344856i
$159$	0.0625164	−	0.0562900i	0.00495787	−	0.00446409i
$160$	−0.0548323	+	0.168757i	−0.00433488	+	0.0133414i
$161$	−1.28368	−	0.0814173i	−0.101168	−	0.00641658i
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−16.3050	−	3.46573i	−1.27710	−	0.271457i	−0.481055	−	0.876690i	$-0.659746\pi$
$163$	−16.3050	−	3.46573i	−1.27710	−	0.271457i	−0.796048	+	0.605234i	$0.793080\pi$
$164$	1.92571	+	3.33543i	0.150373	+	0.260453i
$165$	0.284422	−	0.515212i	0.0221422	−	0.0401092i
$166$	2.43668	+	1.40682i	0.189123	+	0.109190i
$167$	−2.01262	−	6.19419i	−0.155741	−	0.479321i	0.842494	−	0.538705i	$-0.181086\pi$
$167$	−2.01262	−	6.19419i	−0.155741	−	0.479321i	−0.998235	+	0.0593841i	$0.981086\pi$
$168$	−2.54793	−	0.712791i	−0.196577	−	0.0549930i
$169$	−21.3151	+	15.4863i	−1.63963	+	1.19126i
$170$	0.601205	+	0.667706i	0.0461103	+	0.0512107i
$171$	5.16096	−	1.09700i	0.394668	−	0.0838893i
$172$	−1.26134	+	2.83303i	−0.0961766	+	0.216016i
$173$	3.22430	−	1.43555i	0.245139	−	0.109143i	−0.280489	−	0.959857i	$-0.590497\pi$
$173$	3.22430	−	1.43555i	0.245139	−	0.109143i	0.525629	+	0.850714i	$0.323830\pi$
$174$	5.54562	−	1.80188i	0.420412	−	0.136600i
$175$	12.3233	−	4.57587i	0.931556	−	0.345903i
$176$	3.05521	+	1.29062i	0.230295	+	0.0972841i
$177$	−2.71361	+	4.70011i	−0.203967	+	0.353282i
$178$	6.74826	−	7.49470i	0.505803	−	0.561751i
$179$	−1.53551	+	14.6094i	−0.114769	+	1.09195i	0.773869	+	0.633346i	$0.218319\pi$
$179$	−1.53551	+	14.6094i	−0.114769	+	1.09195i	−0.888638	+	0.458609i	$0.848348\pi$
$180$	−0.176469	+	0.0185477i	−0.0131532	+	0.00138246i
$181$	−15.8353	−	5.14518i	−1.17702	−	0.382439i	−0.345764	−	0.938321i	$-0.612380\pi$
$181$	−15.8353	−	5.14518i	−1.17702	−	0.382439i	−0.831261	+	0.555883i	$0.812380\pi$
$182$	8.88548	+	14.0170i	0.658635	+	1.03901i
$183$	−5.24642	−	7.22107i	−0.387826	−	0.533797i
$184$	−0.197738	−	0.444128i	−0.0145775	−	0.0327415i
$185$	0.207840	+	0.187140i	0.0152807	+	0.0137588i
$186$	1.00654	−	0.581125i	0.0738029	−	0.0426101i
$187$	13.3948	−	10.1301i	0.979521	−	0.740785i
$188$			6.19733i			0.451987i
$189$	−0.385169	−	2.61756i	−0.0280169	−	0.190400i
$190$	0.757422	+	0.550299i	0.0549492	+	0.0399229i
$191$	1.16120	+	11.0481i	0.0840218	+	0.799414i	0.952674	+	0.303993i	$0.0983198\pi$
$191$	1.16120	+	11.0481i	0.0840218	+	0.799414i	−0.868653	+	0.495422i	$0.835014\pi$
$192$	−0.207912	−	0.978148i	−0.0150047	−	0.0705917i
$193$	1.44316	+	6.78952i	0.103881	+	0.488720i	0.999073	+	0.0430408i	$0.0137045\pi$
$193$	1.44316	+	6.78952i	0.103881	+	0.488720i	−0.895193	+	0.445679i	$0.852962\pi$
$194$	−1.54080	−	14.6598i	−0.110623	−	1.05251i
$195$	0.900466	+	0.654227i	0.0644837	+	0.0468502i
$196$	6.13757	−	3.36604i	0.438398	−	0.240431i
$197$			15.8046i			1.12603i	0.826447	+	0.563015i	$0.190359\pi$
$197$			15.8046i			1.12603i	−0.826447	+	0.563015i	$0.809641\pi$
$198$	0.0636253	+	3.31601i	0.00452165	+	0.235659i
$199$	−23.8497	+	13.7696i	−1.69066	+	0.976102i	−0.736672	+	0.676250i	$0.763604\pi$
$199$	−23.8497	+	13.7696i	−1.69066	+	0.976102i	−0.953986	+	0.299852i	$0.903063\pi$
$200$	3.69233	+	3.32459i	0.261087	+	0.235084i
$201$	5.29069	+	11.8831i	0.373176	+	0.838168i
$202$	8.45395	+	11.6359i	0.594818	+	0.818696i
$203$	−7.15440	+	13.6682i	−0.502140	+	0.959318i
$204$	−4.81575	−	1.56473i	−0.337170	−	0.109553i
$205$	−0.679657	+	0.0714348i	−0.0474693	+	0.00498923i
$206$	1.01517	−	9.65874i	0.0707306	−	0.672956i
$207$	0.325304	−	0.361286i	0.0226102	−	0.0251111i
$208$	−3.13636	+	5.43233i	−0.217467	+	0.376664i
$209$	11.4577	−	13.2268i	0.792548	−	0.914917i
$210$	0.299432	−	0.361577i	0.0206628	−	0.0249512i
$211$	−5.59996	+	1.81954i	−0.385517	+	0.125262i	−0.495362	−	0.868687i	$-0.664965\pi$
$211$	−5.59996	+	1.81954i	−0.385517	+	0.125262i	0.109845	+	0.993949i	$0.464965\pi$
$212$	−0.0768512	+	0.0342164i	−0.00527816	+	0.00234999i
$213$	−2.05135	+	4.60741i	−0.140556	+	0.315695i
$214$	18.5893	−	3.95127i	1.27074	−	0.270103i
$215$	−0.368201	−	0.408929i	−0.0251111	−	0.0278887i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	−0.828440	+	2.96133i	−0.0562382	+	0.201028i
$218$	−4.02472	−	12.3868i	−0.272589	−	0.838942i
$219$	2.59485	+	1.49813i	0.175343	+	0.101235i
$220$	−0.429710	+	0.402105i	−0.0289711	+	0.0271099i
$221$	15.8812	+	27.5070i	1.06828	+	1.85032i
$222$	−1.54172	−	0.327703i	−0.103474	−	0.0219940i
$223$	7.68505	−	10.5776i	0.514629	−	0.708326i	−0.470062	−	0.882633i	$-0.655769\pi$
$223$	7.68505	−	10.5776i	0.514629	−	0.708326i	0.984691	+	0.174307i	$0.0557686\pi$
$224$	2.20296	+	1.46526i	0.147191	+	0.0979016i
$225$	−1.53536	+	4.72534i	−0.102357	+	0.315023i
$226$	−4.22992	+	3.80864i	−0.281370	+	0.253347i
$227$	19.0283	+	8.47193i	1.26295	+	0.562302i	0.925395	−	0.379004i	$-0.123733\pi$
$227$	19.0283	+	8.47193i	1.26295	+	0.562302i	0.337555	+	0.941306i	$0.390400\pi$
$228$	−5.24735	−	0.551519i	−0.347514	−	0.0365252i
$229$	−2.42040	+	11.3871i	−0.159944	+	0.752480i	0.822921	+	0.568156i	$0.192343\pi$
$229$	−2.42040	+	11.3871i	−0.159944	+	0.752480i	−0.982866	+	0.184324i	$0.940990\pi$
$230$	0.0862645			0.00568811
$231$	−6.25553	−	6.15372i	−0.411584	−	0.404885i
$232$	−5.83101			−0.382824
$233$	−2.62920	+	12.3694i	−0.172244	+	0.810346i	0.804163	+	0.594409i	$0.202614\pi$
$233$	−2.62920	+	12.3694i	−0.172244	+	0.810346i	−0.976407	+	0.215937i	$0.930719\pi$
$234$	−6.23835	−	0.655677i	−0.407814	−	0.0428630i
$235$	−1.00459	−	0.447272i	−0.0655322	−	0.0291768i
$236$	4.03321	−	3.63152i	0.262539	−	0.236392i
$237$	−3.29333	+	10.1358i	−0.213925	+	0.658394i
$238$	12.0028	−	5.95066i	0.778029	−	0.385724i
$239$	15.0830	−	20.7600i	0.975641	−	1.34285i	0.0364959	−	0.999334i	$-0.488380\pi$
$239$	15.0830	−	20.7600i	0.975641	−	1.34285i	0.939145	−	0.343521i	$-0.111620\pi$
$240$	0.173564	+	0.0368921i	0.0112035	+	0.00238137i
$241$	−12.6544	−	21.9180i	−0.815139	−	1.41186i	−0.909228	−	0.416298i	$-0.863327\pi$
$241$	−12.6544	−	21.9180i	−0.815139	−	1.41186i	0.0940898	−	0.995564i	$-0.470006\pi$
$242$	6.80226	+	8.64461i	0.437266	+	0.555697i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.75820	+	8.48888i	0.176576	+	0.543445i
$245$	0.102677	+	1.23784i	0.00655976	+	0.0790825i
$246$	3.11587	−	2.26381i	0.198660	−	0.144335i
$247$	22.1458	+	24.5955i	1.40911	+	1.56497i
$248$	−1.13685	+	0.241645i	−0.0721901	+	0.0153445i
$249$	1.14441	−	2.57039i	0.0725240	−	0.162892i
$250$	−1.61590	+	0.719446i	−0.102199	+	0.0455017i
$251$	15.2627	−	4.95917i	0.963376	−	0.313020i	0.215237	−	0.976562i	$-0.430948\pi$
$251$	15.2627	−	4.95917i	0.963376	−	0.313020i	0.748139	+	0.663542i	$0.230948\pi$
$252$	−0.442555	+	2.60848i	−0.0278783	+	0.164319i
$253$	0.137749	−	1.60651i	0.00866019	−	0.101000i
$254$	−1.56747	+	2.71494i	−0.0983519	+	0.170351i
$255$	0.601205	−	0.667706i	0.0376489	−	0.0418134i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	21.1509	−	2.22305i	1.31936	−	0.138670i	0.581457	−	0.813577i	$-0.302483\pi$
$257$	21.1509	−	2.22305i	1.31936	−	0.138670i	0.737903	+	0.674907i	$0.235816\pi$
$258$	2.94935	+	0.958303i	0.183619	+	0.0596613i
$259$	3.52210	−	2.23268i	0.218853	−	0.138732i
$260$	−0.654227	−	0.900466i	−0.0405734	−	0.0558446i
$261$	−2.37168	−	5.32689i	−0.146804	−	0.329726i
$262$	3.22048	+	2.89973i	0.198962	+	0.179146i
$263$	6.75291	−	3.89879i	0.416402	−	0.240410i	−0.277135	−	0.960831i	$-0.589385\pi$
$263$	6.75291	−	3.89879i	0.416402	−	0.240410i	0.693537	+	0.720421i	$0.256051\pi$
$264$	0.964194	−	3.17338i	0.0593420	−	0.195308i
$265$		−	0.0149271i		−	0.000916963i
$266$	10.9445	−	8.66545i	0.671051	−	0.531313i
$267$	−8.15903	−	5.92788i	−0.499324	−	0.362780i
$268$	−1.35967	−	12.9364i	−0.0830550	−	0.790216i
$269$	−1.18219	−	5.56176i	−0.0720794	−	0.339107i	0.927301	−	0.374318i	$-0.122123\pi$
$269$	−1.18219	−	5.56176i	−0.0720794	−	0.339107i	−0.999380	+	0.0352109i	$0.988790\pi$
$270$	0.0368921	+	0.173564i	0.00224518	+	0.0105627i
$271$	1.10844	+	10.5461i	0.0673329	+	0.640630i	0.975193	+	0.221357i	$0.0710485\pi$
$271$	1.10844	+	10.5461i	0.0673329	+	0.640630i	−0.907860	+	0.419273i	$0.862285\pi$
$272$	4.09652	+	2.97630i	0.248388	+	0.180464i
$273$	13.0114	−	10.3020i	0.787489	−	0.623504i
$274$		−	0.454566i		−	0.0274614i
$275$	5.39191	+	15.5716i	0.325145	+	0.939003i
$276$	−0.421026	+	0.243079i	−0.0253428	+	0.0146317i
$277$	8.28275	+	7.45782i	0.497662	+	0.448097i	0.879337	−	0.476200i	$-0.157986\pi$
$277$	8.28275	+	7.45782i	0.497662	+	0.448097i	−0.381675	+	0.924297i	$0.624653\pi$
$278$	6.73502	+	15.1271i	0.403940	+	0.907263i
$279$	−0.683153	−	0.940280i	−0.0408993	−	0.0562931i
$280$	−0.396510	+	0.251350i	−0.0236960	+	0.0150211i
$281$	−14.5191	−	4.71754i	−0.866136	−	0.281425i	−0.157947	−	0.987448i	$-0.550488\pi$
$281$	−14.5191	−	4.71754i	−0.866136	−	0.281425i	−0.708189	+	0.706023i	$0.750488\pi$
$282$	6.16338	−	0.647797i	0.367024	−	0.0385758i
$283$	−0.354062	+	3.36868i	−0.0210468	+	0.200247i	−0.999992	−	0.00387388i	$-0.998767\pi$
$283$	−0.354062	+	3.36868i	−0.0210468	+	0.200247i	0.978946	+	0.204121i	$0.0654336\pi$
$284$	3.37472	−	3.74801i	0.200253	−	0.222403i
$285$	0.468113	−	0.810795i	0.0277286	−	0.0480273i
$286$	−17.8141	+	10.7458i	−1.05337	+	0.635415i
$287$	−1.70447	+	10.0463i	−0.100611	+	0.593017i
$288$	−0.951057	+	0.309017i	−0.0560415	+	0.0182090i
$289$	7.89287	−	3.51413i	0.464286	−	0.206714i
$290$	0.420834	−	0.945209i	0.0247122	−	0.0555046i
$291$	−14.4184	+	3.06473i	−0.845221	+	0.179657i
$292$	−2.00490	−	2.22666i	−0.117328	−	0.130306i
$293$	−22.8616	+	16.6099i	−1.33559	+	0.970363i	−0.335996	+	0.941863i	$0.609073\pi$
$293$	−22.8616	+	16.6099i	−1.33559	+	0.970363i	−0.999594	+	0.0284997i	$0.990927\pi$
$294$	−3.98915	−	5.75210i	−0.232652	−	0.335470i
$295$	0.297587	+	0.915878i	0.0173262	+	0.0533245i
$296$	1.36500	+	0.788083i	0.0793390	+	0.0458064i
$297$	3.29120	−	0.409895i	0.190975	−	0.0237845i
$298$	−12.1751	−	21.0879i	−0.705286	−	1.22159i
$299$	2.98289	+	0.634034i	0.172505	+	0.0366671i
$300$	2.92042	−	4.01961i	0.168611	−	0.232072i
$301$	−7.35101	+	3.64442i	−0.423705	+	0.210061i
$302$	−3.50881	+	10.7990i	−0.201909	+	0.621413i
$303$	10.6884	−	9.62392i	0.614035	−	0.552879i
$304$	4.82010	+	2.14605i	0.276452	+	0.123084i
$305$	−1.57512	−	0.165551i	−0.0901909	−	0.00947945i
$306$	−1.05278	+	4.95293i	−0.0601833	+	0.283140i
$307$	−7.38011			−0.421205			−0.210603	−	0.977572i	$-0.567543\pi$
$307$	−7.38011			−0.421205			−0.210603	+	0.977572i	$0.567543\pi$
$308$	4.04776	+	7.78560i	0.230643	+	0.443626i
$309$	−9.71195			−0.552493
$310$	0.0428778	−	0.201724i	0.00243530	−	0.0114572i
$311$	14.9237	+	1.56854i	0.846243	+	0.0889438i	0.517718	−	0.855551i	$-0.326782\pi$
$311$	14.9237	+	1.56854i	0.846243	+	0.0889438i	0.328525	+	0.944495i	$0.393448\pi$
$312$	5.73041	+	2.55134i	0.324421	+	0.144441i
$313$	0.862164	−	0.776296i	0.0487324	−	0.0438789i	−0.644405	−	0.764685i	$-0.722895\pi$
$313$	0.862164	−	0.776296i	0.0487324	−	0.0438789i	0.693137	+	0.720806i	$0.256228\pi$
$314$	−3.55311	+	10.9353i	−0.200513	+	0.617117i
$315$	−0.390895	−	0.259997i	−0.0220245	−	0.0146492i
$316$	6.26430	−	8.62206i	0.352394	−	0.485029i
$317$	−30.9013	−	6.56828i	−1.73559	−	0.368911i	−0.771861	−	0.635791i	$-0.780674\pi$
$317$	−30.9013	−	6.56828i	−1.73559	−	0.368911i	−0.963730	+	0.266880i	$0.914007\pi$
$318$	0.0420621	+	0.0728536i	0.00235872	+	0.00408543i
$319$	−16.9307	−	9.34656i	−0.947938	−	0.523307i
$320$	−0.153669	−	0.0887206i	−0.00859033	−	0.00495963i
$321$	−5.87273	−	18.0744i	−0.327784	−	1.00882i
$322$	0.346529	−	1.23870i	0.0193113	−	0.0690298i
$323$	21.6143	−	15.7037i	1.20265	−	0.873777i
$324$	−0.669131	−	0.743145i	−0.0371739	−	0.0412858i
$325$	−30.4850	+	6.47979i	−1.69100	+	0.359434i
$326$	6.77998	−	15.2281i	0.375509	−	0.843406i
$327$	−11.8983	+	5.29745i	−0.657976	+	0.292950i
$328$	−3.66292	+	1.19016i	−0.202251	+	0.0657153i
$329$	−10.4580	+	12.6285i	−0.576568	+	0.696230i
$330$	0.444819	+	0.385325i	0.0244865	+	0.0212114i
$331$	−4.74747	+	8.22286i	−0.260945	+	0.451969i	−0.966493	−	0.256692i	$-0.917367\pi$
$331$	−4.74747	+	8.22286i	−0.260945	+	0.451969i	0.705549	+	0.708661i	$0.250701\pi$
$332$	−1.88269	+	2.09094i	−0.103326	+	0.114755i
$333$	−0.164754	+	1.56753i	−0.00902848	+	0.0859002i
$334$	6.47728	−	0.680790i	0.354421	−	0.0372512i
$335$	2.19513	+	0.713240i	0.119933	+	0.0389685i
$336$	1.22696	−	2.34405i	0.0669361	−	0.127878i
$337$	18.1468	+	24.9769i	0.988519	+	1.36058i	0.932111	+	0.362172i	$0.117965\pi$
$337$	18.1468	+	24.9769i	0.988519	+	1.36058i	0.0564073	+	0.998408i	$0.482035\pi$
$338$	−10.7163	−	24.0691i	−0.582888	−	1.30919i
$339$	4.22992	+	3.80864i	0.229738	+	0.206857i
$340$	−0.778113	+	0.449244i	−0.0421991	+	0.0243637i
$341$	−3.68826	−	1.12063i	−0.199730	−	0.0606857i
$342$			5.27626i			0.285307i
$343$	18.1869	+	3.49810i	0.982000	+	0.188879i
$344$	−2.50887	−	1.82280i	−0.135269	−	0.0982788i
$345$	−0.00901710	−	0.0857920i	−0.000485464	−	0.00461888i
$346$	0.733812	+	3.45231i	0.0394500	+	0.185597i
$347$	−7.59862	−	35.7487i	−0.407915	−	1.91909i	−0.393816	−	0.919189i	$-0.628845\pi$
$347$	−7.59862	−	35.7487i	−0.407915	−	1.91909i	−0.0140994	−	0.999901i	$-0.504488\pi$
$348$	0.609506	+	5.79906i	0.0326730	+	0.310862i
$349$	−20.5146	−	14.9047i	−1.09812	−	0.797832i	−0.117369	−	0.993088i	$-0.537446\pi$
$349$	−20.5146	−	14.9047i	−1.09812	−	0.797832i	−0.980752	+	0.195257i	$0.937446\pi$
$350$	1.91372	+	13.0054i	0.102292	+	0.695168i
$351$			6.27271i			0.334813i
$352$	−1.89763	+	2.72011i	−0.101144	+	0.144982i
$353$	21.4502	−	12.3843i	1.14168	−	0.659148i	0.194833	−	0.980836i	$-0.437584\pi$
$353$	21.4502	−	12.3843i	1.14168	−	0.659148i	0.946846	+	0.321688i	$0.104250\pi$
$354$	−4.03321	−	3.63152i	−0.214362	−	0.193013i
$355$	0.363994	+	0.817544i	0.0193188	+	0.0433907i
$356$	5.92788	+	8.15903i	0.314177	+	0.432427i
$357$	−7.17270	−	11.3151i	−0.379620	−	0.598858i
$358$	−13.9709	−	4.53941i	−0.738383	−	0.239915i
$359$	−34.3803	+	3.61352i	−1.81453	+	0.190714i	−0.950079	−	0.312010i	$-0.898998\pi$
$359$	−34.3803	+	3.61352i	−1.81453	+	0.190714i	−0.864447	+	0.502725i	$0.832331\pi$
$360$	0.0185477	−	0.176469i	0.000977547	−	0.00930074i
$361$	5.91437	−	6.56857i	0.311283	−	0.345714i
$362$	8.32508	−	14.4195i	0.437557	−	0.757870i
$363$	7.88623	−	7.66860i	0.413920	−	0.402497i
$364$	−15.5581	+	5.77701i	−0.815467	+	0.302797i
$365$	0.505640	−	0.164292i	0.0264664	−	0.00859946i
$366$	8.15407	−	3.63042i	0.426220	−	0.189765i
$367$	15.0816	−	33.8739i	0.787254	−	1.76820i	0.163559	−	0.986534i	$-0.447703\pi$
$367$	15.0816	−	33.8739i	0.787254	−	1.76820i	0.623695	−	0.781668i	$-0.285631\pi$
$368$	0.475535	−	0.101078i	0.0247890	−	0.00526906i
$369$	−2.57710	−	2.86217i	−0.134159	−	0.148998i
$370$	−0.226263	+	0.164390i	−0.0117629	+	0.00854622i
$371$	−0.214342	−	0.0599629i	−0.0111281	−	0.00311312i
$372$	0.359155	+	1.10536i	0.0186213	+	0.0573105i
$373$	6.30005	+	3.63733i	0.326204	+	0.188334i	0.654155	−	0.756361i	$-0.273025\pi$
$373$	6.30005	+	3.63733i	0.326204	+	0.188334i	−0.327951	+	0.944695i	$0.606358\pi$
$374$	7.12379	+	15.2082i	0.368362	+	0.786398i
$375$	0.884412	+	1.53185i	0.0456709	+	0.0791042i
$376$	−6.06190	−	1.28850i	−0.312619	−	0.0664492i
$377$	21.4990	−	29.5908i	1.10725	−	1.52400i
$378$	2.64045	+	0.167471i	0.135810	+	0.00861376i
$379$	6.80861	−	20.9547i	0.349735	−	1.07637i	−0.609265	−	0.792967i	$-0.708535\pi$
$379$	6.80861	−	20.9547i	0.349735	−	1.07637i	0.959000	−	0.283406i	$-0.0914645\pi$
$380$	−0.695751	+	0.626457i	−0.0356913	+	0.0321366i
$381$	2.86391	+	1.27510i	0.146723	+	0.0653252i
$382$	−11.0481	−	1.16120i	−0.565271	−	0.0594124i
$383$	−0.197813	+	0.930638i	−0.0101078	+	0.0475534i	−0.982912	−	0.184074i	$-0.941072\pi$
$383$	−0.197813	+	0.930638i	−0.0101078	+	0.0475534i	0.972805	+	0.231627i	$0.0744049\pi$
$384$	1.00000			0.0510310
$385$	−1.55419	+	0.0942435i	−0.0792086	+	0.00480309i
$386$	−6.94120			−0.353298
$387$	0.644762	−	3.03337i	0.0327751	−	0.154195i
$388$	14.6598	+	1.54080i	0.744237	+	0.0782224i
$389$	9.67739	+	4.30865i	0.490663	+	0.218457i	0.637127	−	0.770759i	$-0.280123\pi$
$389$	9.67739	+	4.30865i	0.490663	+	0.218457i	−0.146464	+	0.989216i	$0.546789\pi$
$390$	−0.827148	+	0.744768i	−0.0418843	+	0.0377128i
$391$	0.760708	−	2.34122i	0.0384706	−	0.118400i
$392$	2.01641	+	6.70329i	0.101844	+	0.338567i
$393$	2.54721	−	3.50594i	0.128490	−	0.176851i
$394$	−15.4592	−	3.28596i	−0.778824	−	0.165544i
$395$	0.945536	+	1.63772i	0.0475751	+	0.0824024i
$396$	−3.25678	−	0.627203i	−0.163659	−	0.0315181i
$397$	−10.8585	−	6.26913i	−0.544970	−	0.314639i	0.202121	−	0.979361i	$-0.435217\pi$
$397$	−10.8585	−	6.26913i	−0.544970	−	0.314639i	−0.747091	+	0.664722i	$0.768550\pi$
$398$	−8.51009	−	26.1914i	−0.426572	−	1.31285i
$399$	−9.76199	−	9.97876i	−0.488711	−	0.499563i
$400$	−4.01961	+	2.92042i	−0.200981	+	0.146021i
$401$	−5.42276	−	6.02258i	−0.270800	−	0.300753i	0.592372	−	0.805665i	$-0.298192\pi$
$401$	−5.42276	−	6.02258i	−0.270800	−	0.300753i	−0.863171	+	0.504912i	$0.831525\pi$
$402$	−12.7234	+	2.70444i	−0.634586	+	0.134885i
$403$	2.96530	−	6.66017i	0.147712	−	0.331766i
$404$	−13.1393	+	5.84998i	−0.653703	+	0.291047i
$405$	0.168757	−	0.0548323i	0.00838558	−	0.00272464i
$406$	−11.8820	−	9.83983i	−0.589694	−	0.488343i
$407$	2.70014	+	4.47622i	0.133841	+	0.221878i
$408$	2.53179	−	4.38519i	0.125342	−	0.217099i
$409$	−12.2271	+	13.5796i	−0.604592	+	0.671467i	−0.965279	−	0.261219i	$-0.915875\pi$
$409$	−12.2271	+	13.5796i	−0.604592	+	0.671467i	0.360688	+	0.932687i	$0.382542\pi$
$410$	0.0714348	−	0.679657i	0.00352792	−	0.0335659i
$411$	−0.452076	+	0.0475151i	−0.0222993	+	0.00234375i
$412$	9.23661	+	3.00116i	0.455055	+	0.147856i
$413$	14.3468	−	0.594001i	0.705958	−	0.0292289i
$414$	0.285757	+	0.393311i	0.0140442	+	0.0193302i
$415$	−0.203065	−	0.456092i	−0.00996808	−	0.0223887i
$416$	−4.66154	−	4.19727i	−0.228551	−	0.205788i
$417$	14.3402	−	8.27933i	0.702244	−	0.405441i
$418$	10.5556	+	13.9574i	0.516290	+	0.682677i
$419$			14.8532i			0.725625i	0.931862	+	0.362812i	$0.118183\pi$
$419$			14.8532i			0.725625i	−0.931862	+	0.362812i	$0.881817\pi$
$420$	0.291420	+	0.368065i	0.0142198	+	0.0179597i
$421$	−5.80923	−	4.22065i	−0.283125	−	0.205702i	0.437154	−	0.899386i	$-0.355986\pi$
$421$	−5.80923	−	4.22065i	−0.283125	−	0.205702i	−0.720279	+	0.693684i	$0.755986\pi$
$422$	−0.615479	−	5.85589i	−0.0299610	−	0.285060i
$423$	−1.28850	−	6.06190i	−0.0626489	−	0.294740i
$424$	−0.0174904	−	0.0822858i	−0.000849408	−	0.00399615i
$425$	2.62978	+	25.0206i	0.127563	+	1.21368i
$426$	−4.08023	−	2.96446i	−0.197688	−	0.143629i
$427$	−8.70453	+	21.9525i	−0.421242	+	1.06236i
$428$			19.0046i			0.918620i
$429$	12.5491	+	16.5933i	0.605874	+	0.801132i
$430$	0.476546	−	0.275134i	0.0229811	−	0.0132682i
$431$	−11.0867	−	9.98251i	−0.534027	−	0.480840i	0.357433	−	0.933939i	$-0.383652\pi$
$431$	−11.0867	−	9.98251i	−0.534027	−	0.480840i	−0.891461	+	0.453098i	$0.850319\pi$
$432$	0.406737	+	0.913545i	0.0195691	+	0.0439530i
$433$	1.19231	+	1.64107i	0.0572988	+	0.0788650i	0.836705	−	0.547654i	$-0.184479\pi$
$433$	1.19231	+	1.64107i	0.0572988	+	0.0788650i	−0.779406	+	0.626519i	$0.784479\pi$
$434$	−2.72437	−	1.42603i	−0.130774	−	0.0684517i
$435$	−0.984021	−	0.319728i	−0.0471802	−	0.0153298i
$436$	12.9529	−	1.36141i	0.620333	−	0.0651996i
$437$	0.268126	−	2.55105i	0.0128262	−	0.122033i
$438$	−2.00490	+	2.22666i	−0.0957976	+	0.106394i
$439$	3.67315	−	6.36208i	0.175310	−	0.303645i	−0.764959	−	0.644079i	$-0.777241\pi$
$439$	3.67315	−	6.36208i	0.175310	−	0.303645i	0.940268	+	0.340434i	$0.110574\pi$
$440$	−0.303976	−	0.503922i	−0.0144915	−	0.0240236i
$441$	−5.30361	+	4.56855i	−0.252553	+	0.217550i
$442$	−30.2078	+	9.81511i	−1.43684	+	0.466857i
$443$	−8.65809	+	3.85483i	−0.411358	+	0.183148i	−0.601973	−	0.798516i	$-0.705619\pi$
$443$	−8.65809	+	3.85483i	−0.411358	+	0.183148i	0.190615	+	0.981665i	$0.438952\pi$
$444$	0.641085	−	1.43990i	0.0304245	−	0.0683346i
$445$	−1.75041	+	0.372061i	−0.0829773	+	0.0176374i
$446$	8.74861	+	9.71631i	0.414259	+	0.460081i
$447$	−19.6998	+	14.3127i	−0.931767	+	0.676968i
$448$	−1.89126	+	1.85017i	−0.0893535	+	0.0874125i
$449$	5.72092	+	17.6072i	0.269987	+	0.830934i	0.990502	+	0.137495i	$0.0439052\pi$
$449$	5.72092	+	17.6072i	0.269987	+	0.830934i	−0.720516	+	0.693439i	$0.756095\pi$
$450$	−4.30286	−	2.48426i	−0.202839	−	0.117109i
$451$	−12.5432	−	2.41563i	−0.590638	−	0.113747i
$452$	−2.84596	−	4.92935i	−0.133863	−	0.231857i
$453$	11.1066	+	2.36078i	0.521834	+	0.110919i
$454$	−12.2430	+	16.8510i	−0.574592	+	0.790858i
$455$	0.186401	−	2.93892i	0.00873862	−	0.137778i
$456$	1.63045	−	5.01802i	0.0763530	−	0.234990i
$457$	12.5932	−	11.3389i	0.589084	−	0.530414i	−0.319788	−	0.947489i	$-0.603612\pi$
$457$	12.5932	−	11.3389i	0.589084	−	0.530414i	0.908872	+	0.417076i	$0.136945\pi$
$458$	−10.6350	−	4.73502i	−0.496942	−	0.221253i
$459$	5.03584	+	0.529288i	0.235053	+	0.0247050i
$460$	−0.0179354	+	0.0843794i	−0.000836243	+	0.00393421i
$461$	29.8874			1.39199			0.695996	−	0.718045i	$-0.254963\pi$
$461$	29.8874			1.39199			0.695996	+	0.718045i	$0.254963\pi$
$462$	7.31985	−	4.83941i	0.340550	−	0.225150i
$463$	27.6872			1.28673			0.643367	−	0.765558i	$-0.277537\pi$
$463$	27.6872			1.28673			0.643367	+	0.765558i	$0.277537\pi$
$464$	1.21233	−	5.70358i	0.0562812	−	0.264782i
$465$	−0.205101	−	0.0215570i	−0.00951134	−	0.000999682i
$466$	−11.5525	−	5.14348i	−0.535157	−	0.238267i
$467$	−9.92540	+	8.93687i	−0.459293	+	0.413549i	−0.866027	−	0.499997i	$-0.833334\pi$
$467$	−9.92540	+	8.93687i	−0.459293	+	0.413549i	0.406734	+	0.913547i	$0.366668\pi$
$468$	1.93838	−	5.96571i	0.0896014	−	0.275765i
$469$	19.0595	−	28.6553i	0.880088	−	1.32318i
$470$	0.646364	−	0.889644i	0.0298146	−	0.0410362i
$471$	11.2468	+	2.39059i	0.518227	+	0.110152i
$472$	2.71361	+	4.70011i	0.124904	+	0.216340i
$473$	−4.36289	−	9.31410i	−0.200606	−	0.428263i
$474$	−9.22963	−	5.32873i	−0.423931	−	0.244757i
$475$	8.10093	+	24.9321i	0.371696	+	1.14396i
$476$	3.32509	+	12.9778i	0.152405	+	0.594835i
$477$	0.0680578	−	0.0494469i	0.00311615	−	0.00226402i
$478$	17.1704	+	19.0697i	0.785357	+	0.872228i
$479$	−24.9236	+	5.29768i	−1.13879	+	0.242057i	−0.738449	−	0.674309i	$-0.764442\pi$
$479$	−24.9236	+	5.29768i	−1.13879	+	0.242057i	−0.400341	+	0.916366i	$0.631108\pi$
$480$	−0.0721718	+	0.162101i	−0.00329418	+	0.00739884i
$481$	−9.03208	+	4.02134i	−0.411827	+	0.183357i
$482$	24.0700	−	7.82082i	1.09636	−	0.356229i
$483$	−1.26813	−	0.215152i	−0.0577020	−	0.00978975i
$484$	−9.86998	+	4.85629i	−0.448635	+	0.220741i
$485$	−1.30779	+	2.26515i	−0.0593835	+	0.102855i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	1.41297	−	13.4435i	0.0640279	−	0.609185i	−0.914716	−	0.404098i	$-0.867586\pi$
$487$	1.41297	−	13.4435i	0.0640279	−	0.609185i	0.978744	−	0.205087i	$-0.0657477\pi$
$488$	−8.87684	+	0.932993i	−0.401836	+	0.0422346i
$489$	−15.8534	−	5.15107i	−0.716914	−	0.232940i
$490$	−1.23213	−	0.156928i	−0.0556622	−	0.00708928i
$491$	0.0556181	+	0.0765518i	0.00251001	+	0.00345473i	0.810270	−	0.586057i	$-0.199320\pi$
$491$	0.0556181	+	0.0765518i	0.00251001	+	0.00345473i	−0.807760	+	0.589511i	$0.799320\pi$
$492$	1.56651	+	3.51845i	0.0706239	+	0.158624i
$493$	−21.9419	−	19.7566i	−0.988214	−	0.889792i
$494$	−28.6624	+	16.5482i	−1.28958	+	0.744540i
$495$	0.336718	−	0.482659i	0.0151343	−	0.0216939i
$496$		−	1.16225i		−	0.0521865i
$497$	13.2015	−	1.94257i	0.592169	−	0.0871364i
$498$	2.27628	+	1.65381i	0.102003	+	0.0741092i
$499$	−2.63314	−	25.0526i	−0.117875	−	1.12151i	−0.880295	−	0.474426i	$-0.842655\pi$
$499$	−2.63314	−	25.0526i	−0.117875	−	1.12151i	0.762420	−	0.647083i	$-0.224011\pi$
$500$	−0.367759	−	1.73017i	−0.0164467	−	0.0773756i
$501$	−1.35412	−	6.37064i	−0.0604976	−	0.284619i
$502$	1.67749	+	15.9603i	0.0748702	+	0.712342i
$503$	−18.3777	−	13.3522i	−0.819423	−	0.595346i	0.0971241	−	0.995272i	$-0.469036\pi$
$503$	−18.3777	−	13.3522i	−0.819423	−	0.595346i	−0.916547	+	0.399927i	$0.869036\pi$
$504$	−2.45946	−	0.975217i	−0.109553	−	0.0434396i
$505$		−	2.55209i		−	0.113566i
$506$	1.54277	+	0.468751i	0.0685843	+	0.0208385i
$507$	−22.8171	+	13.1735i	−1.01334	+	0.585054i
$508$	−2.32972	−	2.09769i	−0.103364	−	0.0930698i
$509$	−13.0912	−	29.4034i	−0.580259	−	1.30328i	−0.930386	−	0.366580i	$-0.880529\pi$
$509$	−13.0912	−	29.4034i	−0.580259	−	1.30328i	0.350128	−	0.936702i	$-0.386138\pi$
$510$	0.528117	+	0.726891i	0.0233854	+	0.0321873i
$511$	−0.327937	−	7.92060i	−0.0145071	−	0.350387i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	5.24735	−	0.551519i	0.231676	−	0.0243502i
$514$	−2.22305	+	21.1509i	−0.0980547	+	0.932928i
$515$	−1.15311	+	1.28066i	−0.0508122	+	0.0564326i
$516$	−1.55057	+	2.68566i	−0.0682599	+	0.118230i
$517$	−15.5358	−	13.4579i	−0.683263	−	0.591877i
$518$	1.45161	+	3.90934i	0.0637800	+	0.171767i
$519$	3.35670	−	1.09066i	0.147343	−	0.0478745i
$520$	1.01681	−	0.452713i	0.0445901	−	0.0198528i
$521$	−3.53895	+	7.94861i	−0.155044	+	0.348235i	−0.974321	−	0.225163i	$-0.927708\pi$
$521$	−3.53895	+	7.94861i	−0.155044	+	0.348235i	0.819277	+	0.573398i	$0.194375\pi$
$522$	5.70358	−	1.21233i	0.249639	−	0.0530624i
$523$	10.0990	+	11.2161i	0.441600	+	0.490446i	0.922320	−	0.386428i	$-0.126291\pi$
$523$	10.0990	+	11.2161i	0.441600	+	0.490446i	−0.480720	+	0.876874i	$0.659625\pi$
$524$	−3.50594	+	2.54721i	−0.153158	+	0.111276i
$525$	12.7341	−	3.26267i	0.555763	−	0.142394i
$526$	2.40959	+	7.41595i	0.105063	+	0.323351i
$527$	−5.09668	−	2.94257i	−0.222015	−	0.128180i
$528$	2.90357	+	1.60291i	0.126361	+	0.0697575i
$529$	11.3818	+	19.7139i	0.494862	+	0.857126i
$530$	0.0146009	+	0.00310351i	0.000634222	+	0.000134808i
$531$	−3.19004	+	4.39071i	−0.138436	+	0.190541i
$532$	6.20060	+	12.5070i	0.268830	+	0.542247i
$533$	7.46550	−	22.9765i	0.323367	−	0.995221i
$534$	7.49470	−	6.74826i	0.324327	−	0.292026i
$535$	−3.08065	−	1.37159i	−0.133188	−	0.0592992i
$536$	12.9364	+	1.35967i	0.558767	+	0.0587288i
$537$	−3.05419	+	14.3688i	−0.131798	+	0.620061i
$538$	5.68602			0.245142
$539$	−4.88998	+	22.6956i	−0.210626	+	0.977567i
$540$	−0.177441			−0.00763585
$541$	0.233413	−	1.09812i	0.0100352	−	0.0472119i	−0.972845	−	0.231457i	$-0.925651\pi$
$541$	0.233413	−	1.09812i	0.0100352	−	0.0472119i	0.982880	+	0.184245i	$0.0589840\pi$
$542$	−10.5461	−	1.10844i	−0.452994	−	0.0476116i
$543$	−15.2107	−	6.77223i	−0.652753	−	0.290624i
$544$	−3.76297	+	3.38819i	−0.161336	+	0.145268i
$545$	−0.714152	+	2.19793i	−0.0305909	+	0.0941491i
$546$	7.37163	+	14.8690i	0.315476	+	0.636335i
$547$	14.8320	−	20.4144i	0.634169	−	0.872859i	−0.364119	−	0.931353i	$-0.618630\pi$
$547$	14.8320	−	20.4144i	0.634169	−	0.872859i	0.998288	+	0.0584938i	$0.0186298\pi$
$548$	0.444633	+	0.0945096i	0.0189938	+	0.00403725i
$549$	−4.46287	−	7.72991i	−0.190471	−	0.329905i
$550$	−16.3524	+	2.03657i	−0.697267	+	0.0868395i
$551$	−26.6440	−	15.3829i	−1.13507	−	0.655335i
$552$	−0.150231	−	0.462364i	−0.00639427	−	0.0196795i
$553$	27.3147	−	6.99842i	1.16154	−	0.297603i
$554$	−9.01693	+	6.55118i	−0.383093	+	0.278333i
$555$	0.187140	+	0.207840i	0.00794366	+	0.00882233i
$556$	−16.1968	+	3.44274i	−0.686898	+	0.146005i
$557$	14.7798	−	33.1961i	0.626242	−	1.40656i	−0.269941	−	0.962877i	$-0.587004\pi$
$557$	14.7798	−	33.1961i	0.626242	−	1.40656i	0.896183	−	0.443685i	$-0.146329\pi$
$558$	1.06177	−	0.472729i	0.0449482	−	0.0200122i
$559$	18.5004	−	6.01116i	0.782485	−	0.254245i
$560$	−0.163419	−	0.440104i	−0.00690570	−	0.0185978i
$561$	14.3803	−	8.67446i	0.607135	−	0.366236i
$562$	7.63314	−	13.2210i	0.321984	−	0.557693i
$563$	−25.1277	+	27.9071i	−1.05900	+	1.17614i	−0.0751507	+	0.997172i	$0.523944\pi$
$563$	−25.1277	+	27.9071i	−1.05900	+	1.17614i	−0.983854	+	0.178972i	$0.942723\pi$
$564$	−0.647797	+	6.16338i	−0.0272772	+	0.259525i
$565$	1.00445	−	0.105572i	0.0422574	−	0.00444144i
$566$	−3.22145	−	1.04671i	−0.135408	−	0.0439966i
$567$	−0.109449	−	2.64349i	−0.00459641	−	0.111016i
$568$	2.96446	+	4.08023i	0.124386	+	0.171203i
$569$	15.4738	+	34.7546i	0.648694	+	1.45699i	0.875582	+	0.483069i	$0.160478\pi$
$569$	15.4738	+	34.7546i	0.648694	+	1.45699i	−0.226889	+	0.973921i	$0.572855\pi$
$570$	0.695751	+	0.626457i	0.0291418	+	0.0262394i
$571$	−30.6383	+	17.6891i	−1.28218	+	0.740264i	−0.977246	−	0.212111i	$-0.931966\pi$
$571$	−30.6383	+	17.6891i	−1.28218	+	0.740264i	−0.304929	+	0.952375i	$0.598633\pi$
$572$	−6.80725	−	19.6590i	−0.284625	−	0.821986i
$573$			11.1090i			0.464084i
$574$	−9.47243	−	3.75597i	−0.395371	−	0.156771i
$575$	1.95417	+	1.41979i	0.0814945	+	0.0592092i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	4.46316	+	20.9975i	0.185804	+	0.874138i	0.967970	+	0.251068i	$0.0807817\pi$
$577$	4.46316	+	20.9975i	0.185804	+	0.874138i	−0.782166	+	0.623070i	$0.785885\pi$
$578$	1.79632	+	8.45102i	0.0747170	+	0.351516i
$579$	0.725553	+	6.90318i	0.0301530	+	0.286886i
$580$	0.837058	+	0.608158i	0.0347569	+	0.0252524i
$581$	−7.36488	+	1.08372i	−0.305547	+	0.0449605i
$582$		−	14.7405i		−	0.611014i
$583$	0.0811119	−	0.266958i	0.00335931	−	0.0110563i
$584$	2.59485	−	1.49813i	0.107375	−	0.0619933i
$585$	0.827148	+	0.744768i	0.0341984	+	0.0307923i
$586$	−11.4938	−	25.8154i	−0.474803	−	1.06643i
$587$	8.63209	+	11.8811i	0.356285	+	0.490384i	0.949109	−	0.314948i	$-0.101987\pi$
$587$	8.63209	+	11.8811i	0.356285	+	0.490384i	−0.592824	+	0.805332i	$0.701987\pi$
$588$	6.45580	−	2.70605i	0.266233	−	0.111595i
$589$	−5.83219	−	1.89499i	−0.240311	−	0.0780818i
$590$	−0.957736	+	0.100662i	−0.0394294	+	0.00414419i
$591$	−1.65203	+	15.7180i	−0.0679554	+	0.646553i
$592$	−1.05466	+	1.17132i	−0.0433463	+	0.0481409i
$593$	23.8853	−	41.3706i	0.980852	−	1.69889i	0.321764	−	0.946820i	$-0.395724\pi$
$593$	23.8853	−	41.3706i	0.980852	−	1.69889i	0.659088	−	0.752066i	$-0.270942\pi$
$594$	−0.283341	+	3.30450i	−0.0116256	+	0.135585i
$595$	−2.34368	−	0.397630i	−0.0960816	−	0.0163012i
$596$	23.1585	−	7.52464i	0.948608	−	0.308221i
$597$	−25.1583	+	11.2012i	−1.02966	+	0.458435i
$598$	−1.24036	+	2.78589i	−0.0507220	+	0.113923i
$599$	−32.1489	+	6.83346i	−1.31357	+	0.279208i	−0.810856	−	0.585245i	$-0.800998\pi$
$599$	−32.1489	+	6.83346i	−1.31357	+	0.279208i	−0.502713	+	0.864453i	$0.667665\pi$
$600$	3.32459	+	3.69233i	0.135726	+	0.150739i
$601$	26.4768	−	19.2366i	1.08001	−	0.784675i	0.102328	−	0.994751i	$-0.467371\pi$
$601$	26.4768	−	19.2366i	1.08001	−	0.784675i	0.977685	+	0.210075i	$0.0673709\pi$
$602$	−2.03642	−	7.94809i	−0.0829981	−	0.323940i
$603$	4.01959	+	12.3710i	0.163690	+	0.503787i
$604$	−9.83350	−	5.67737i	−0.400119	−	0.231009i
$605$	−0.0748739	−	1.95042i	−0.00304406	−	0.0792957i
$606$	7.19136	+	12.4558i	0.292129	+	0.505982i
$607$	40.7556	+	8.66287i	1.65422	+	0.351615i	0.938100	−	0.346364i	$-0.112584\pi$
$607$	40.7556	+	8.66287i	1.65422	+	0.351615i	0.716118	+	0.697979i	$0.245917\pi$
$608$	−3.10131	+	4.26858i	−0.125775	+	0.173114i
$609$	−8.54392	+	12.8455i	−0.346217	+	0.520524i
$610$	0.489419	−	1.50628i	0.0198160	−	0.0609874i
$611$	28.8891	−	26.0118i	1.16873	−	1.05233i
$612$	−4.62581	−	2.05954i	−0.186987	−	0.0832521i
$613$	33.4491	+	3.51564i	1.35100	+	0.141995i	0.752215	−	0.658918i	$-0.228985\pi$
$613$	33.4491	+	3.51564i	1.35100	+	0.141995i	0.598781	+	0.800913i	$0.295652\pi$
$614$	1.53441	−	7.21884i	0.0619238	−	0.291329i
$615$	−0.683401			−0.0275574
$616$	−8.45705	+	2.34059i	−0.340744	+	0.0943051i
$617$	39.0051			1.57028			0.785142	−	0.619315i	$-0.212590\pi$
$617$	39.0051			1.57028			0.785142	+	0.619315i	$0.212590\pi$
$618$	2.01923	−	9.49972i	0.0812252	−	0.382135i
$619$	−14.2699	−	1.49983i	−0.573557	−	0.0602833i	−0.186690	−	0.982419i	$-0.559776\pi$
$619$	−14.2699	−	1.49983i	−0.573557	−	0.0602833i	−0.386867	+	0.922136i	$0.626443\pi$
$620$	0.188401	+	0.0838817i	0.00756638	+	0.00336877i
$621$	0.361286	−	0.325304i	0.0144979	−	0.0130540i
$622$	−4.63707	+	14.2714i	−0.185930	+	0.572232i
$623$	−1.68896	+	26.6292i	−0.0676668	+	1.06688i
$624$	−3.68701	+	5.07473i	−0.147598	+	0.203152i
$625$	−23.9927	−	5.09981i	−0.959708	−	0.203992i
$626$	0.580078	+	1.00473i	0.0231846	+	0.0401569i
$627$	12.7775	−	11.9567i	0.510286	−	0.477504i
$628$	−9.95764	−	5.74905i	−0.397353	−	0.229412i
$629$	2.46628	+	7.59042i	0.0983369	+	0.302650i
$630$	0.335587	−	0.328297i	0.0133701	−	0.0130797i
$631$	23.3644	−	16.9752i	0.930122	−	0.675773i	−0.0159007	−	0.999874i	$-0.505062\pi$
$631$	23.3644	−	16.9752i	0.930122	−	0.675773i	0.946023	+	0.324100i	$0.105062\pi$
$632$	7.13123	+	7.92003i	0.283665	+	0.315042i
$633$	−5.75947	+	1.22421i	−0.228919	+	0.0486581i
$634$	12.8495	−	28.8604i	0.510319	−	1.14619i
$635$	0.508176	−	0.226255i	0.0201664	−	0.00897864i
$636$	−0.0800068	+	0.0259958i	−0.00317247	+	0.00103080i
$637$	−41.4519	−	14.4824i	−1.64238	−	0.573812i
$638$	12.6624	−	14.6175i	0.501309	−	0.578711i
$639$	−2.52172	+	4.36775i	−0.0997577	+	0.172785i
$640$	0.118731	−	0.131864i	0.00469327	−	0.00521240i
$641$	−1.10036	+	10.4692i	−0.0434617	+	0.413510i	0.951062	+	0.309000i	$0.0999942\pi$
$641$	−1.10036	+	10.4692i	−0.0434617	+	0.413510i	−0.994524	+	0.104510i	$0.966672\pi$
$642$	18.9005	−	1.98652i	0.745942	−	0.0784016i
$643$	−3.67079	−	1.19271i	−0.144762	−	0.0470360i	0.235740	−	0.971816i	$-0.424249\pi$
$643$	−3.67079	−	1.19271i	−0.144762	−	0.0470360i	−0.380502	+	0.924780i	$0.624249\pi$
$644$	1.13958	+	0.596496i	0.0449058	+	0.0235052i
$645$	−0.323440	−	0.445177i	−0.0127354	−	0.0175288i
$646$	10.8667	+	24.4070i	0.427544	+	0.960279i
$647$	13.8533	+	12.4735i	0.544629	+	0.490386i	0.894903	−	0.446261i	$-0.147245\pi$
$647$	13.8533	+	12.4735i	0.544629	+	0.490386i	−0.350274	+	0.936647i	$0.613912\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	0.345308	+	17.9967i	0.0135545	+	0.706433i
$650$		−	31.1661i		−	1.22243i
$651$	−1.13345	+	2.85851i	−0.0444232	+	0.112034i
$652$	13.4857	+	9.79792i	0.528140	+	0.383716i
$653$	−1.55457	−	14.7907i	−0.0608349	−	0.578805i	−0.981900	−	0.189398i	$-0.939346\pi$
$653$	−1.55457	−	14.7907i	−0.0608349	−	0.578805i	0.921066	−	0.389407i	$-0.127320\pi$
$654$	−2.70790	−	12.7397i	−0.105887	−	0.498160i
$655$	−0.159875	−	0.752152i	−0.00624683	−	0.0293890i
$656$	−0.402583	−	3.83032i	−0.0157182	−	0.149549i
$657$	2.42403	+	1.76116i	0.0945705	+	0.0687095i
$658$	−10.1782	−	12.8551i	−0.396786	−	0.501143i
$659$			26.6879i			1.03961i	0.854284	+	0.519806i	$0.173996\pi$
$659$			26.6879i			1.03961i	−0.854284	+	0.519806i	$0.826004\pi$
$660$	−0.469388	+	0.354985i	−0.0182709	+	0.0138178i
$661$	24.4507	−	14.1166i	0.951022	−	0.549073i	0.0576235	−	0.998338i	$-0.481648\pi$
$661$	24.4507	−	14.1166i	0.951022	−	0.549073i	0.893398	+	0.449266i	$0.148314\pi$
$662$	−7.05611	−	6.35335i	−0.274244	−	0.246930i
$663$	12.9189	+	29.0164i	0.501729	+	1.12690i
$664$	−1.65381	−	2.27628i	−0.0641804	−	0.0883368i
$665$	−2.47490	+	0.102468i	−0.0959724	+	0.00397356i
$666$	−1.49902	−	0.487062i	−0.0580860	−	0.0188733i
$667$	−2.81926	+	0.296317i	−0.109162	+	0.0114734i
$668$	−0.680790	+	6.47728i	−0.0263405	+	0.250614i
$669$	8.74861	−	9.71631i	0.338241	−	0.375654i
$670$	−1.15405	+	1.99887i	−0.0445847	+	0.0772230i
$671$	−27.2700	−	11.5197i	−1.05275	−	0.444714i
$672$	2.03773	+	1.68750i	0.0786071	+	0.0650968i
$673$	5.98003	−	1.94303i	0.230513	−	0.0748982i	−0.191483	−	0.981496i	$-0.561330\pi$
$673$	5.98003	−	1.94303i	0.230513	−	0.0748982i	0.421996	+	0.906598i	$0.361330\pi$
$674$	−28.2040	+	12.5572i	−1.08638	+	0.483687i
$675$	−2.02088	+	4.53896i	−0.0777836	+	0.174705i
$676$	25.7712	−	5.47784i	0.991200	−	0.210686i
$677$	−19.9470	−	22.1534i	−0.766627	−	0.851425i	0.225811	−	0.974171i	$-0.427497\pi$
$677$	−19.9470	−	22.1534i	−0.766627	−	0.851425i	−0.992438	+	0.122746i	$0.960830\pi$
$678$	−4.60486	+	3.34563i	−0.176849	+	0.128488i
$679$	27.2725	+	27.8781i	1.04662	+	1.06986i
$680$	−0.277648	−	0.854512i	−0.0106473	−	0.0327690i
$681$	18.0385	+	10.4145i	0.691235	+	0.399085i
$682$	1.86298	−	3.37467i	0.0713371	−	0.129223i
$683$	−6.40710	−	11.0974i	−0.245161	−	0.424631i	0.717016	−	0.697057i	$-0.245507\pi$
$683$	−6.40710	−	11.0974i	−0.245161	−	0.424631i	−0.962177	+	0.272426i	$0.912174\pi$
$684$	−5.16096	−	1.09700i	−0.197334	−	0.0419447i
$685$	−0.0474100	+	0.0652543i	−0.00181144	+	0.00249324i
$686$	−7.20292	+	17.0622i	−0.275009	+	0.651437i
$687$	−3.59741	+	11.0717i	−0.137250	+	0.422412i
$688$	2.30459	−	2.07506i	0.0878617	−	0.0791110i
$689$	0.482066	+	0.214629i	0.0183652	+	0.00817673i
$690$	0.0857920	+	0.00901710i	0.00326604	+	0.000343275i
$691$	0.153724	−	0.723215i	0.00584794	−	0.0275124i	−0.975127	−	0.221647i	$-0.928857\pi$
$691$	0.153724	−	0.723215i	0.00584794	−	0.0275124i	0.980975	+	0.194135i	$0.0621900\pi$
$692$	−3.52944			−0.134169
$693$	−5.57803	−	6.77389i	−0.211892	−	0.257319i
$694$	36.5473			1.38732
$695$	0.610884	−	2.87398i	0.0231721	−	0.109016i
$696$	−5.79906	−	0.609506i	−0.219813	−	0.0231033i
$697$	−17.8159	−	7.93217i	−0.674827	−	0.300452i
$698$	18.8442	−	16.9674i	0.713265	−	0.642227i
$699$	−3.90775	+	12.0268i	−0.147805	+	0.454896i
$700$	−13.1191	−	0.832080i	−0.495855	−	0.0314497i
$701$	−16.6756	+	22.9520i	−0.629830	+	0.866887i	−0.998022	−	0.0628632i	$-0.979977\pi$
$701$	−16.6756	+	22.9520i	−0.629830	+	0.866887i	0.368192	+	0.929750i	$0.379977\pi$
$702$	−6.13564	−	1.30417i	−0.231575	−	0.0492227i
$703$	4.15813	+	7.20209i	0.156827	+	0.271632i
$704$	−2.26613	−	2.42171i	−0.0854080	−	0.0912715i
$705$	−0.952334	−	0.549830i	−0.0358670	−	0.0207078i
$706$	7.65390	+	23.5563i	0.288058	+	0.886553i
$707$	−36.6461	−	10.2519i	−1.37822	−	0.385561i
$708$	4.39071	−	3.19004i	0.165013	−	0.119889i
$709$	7.66950	+	8.51784i	0.288034	+	0.319894i	0.869745	−	0.493501i	$-0.164283\pi$
$709$	7.66950	+	8.51784i	0.288034	+	0.319894i	−0.581711	+	0.813396i	$0.697617\pi$
$710$	−0.875358	+	0.186063i	−0.0328516	+	0.00698282i
$711$	−4.33478	+	9.73607i	−0.162567	+	0.365131i
$712$	−9.21321	+	4.10198i	−0.345280	+	0.153728i
$713$	−0.537383	+	0.174606i	−0.0201251	+	0.00653905i
$714$	12.5591	−	4.66342i	0.470013	−	0.174524i
$715$	3.67803	+	0.315369i	0.137551	+	0.0117941i
$716$	7.34492	−	12.7218i	0.274492	−	0.475435i
$717$	17.1704	−	19.0697i	0.641242	−	0.712171i
$718$	3.61352	−	34.3803i	0.134855	−	1.28306i
$719$	9.35376	−	0.983120i	0.348836	−	0.0366642i	0.0715098	−	0.997440i	$-0.477218\pi$
$719$	9.35376	−	0.983120i	0.348836	−	0.0366642i	0.277327	+	0.960776i	$0.410552\pi$
$720$	0.168757	+	0.0548323i	0.00628919	+	0.00204348i
$721$	13.7572	+	21.7023i	0.512347	+	0.808237i
$722$	5.19537	+	7.15081i	0.193352	+	0.266126i
$723$	−10.2940	−	23.1207i	−0.382837	−	0.859866i
$724$	12.3735	+	11.1411i	0.459857	+	0.414057i
$725$	25.0900	−	14.4857i	0.931819	−	0.537986i
$726$	5.86138	+	9.30829i	0.217536	+	0.345463i
$727$		−	9.89238i		−	0.366888i	−0.983030	−	0.183444i	$-0.941275\pi$
$727$		−	9.89238i		−	0.366888i	0.983030	−	0.183444i	$-0.0587246\pi$
$728$	−2.41605	−	16.4192i	−0.0895448	−	0.608537i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	0.0555738	+	0.528749i	0.00205688	+	0.0195699i
$731$	−3.26480	−	15.3597i	−0.120753	−	0.568098i
$732$	1.85576	+	8.73069i	0.0685910	+	0.322695i
$733$	3.52246	+	33.5140i	0.130105	+	1.23787i	0.843510	+	0.537114i	$0.180485\pi$
$733$	3.52246	+	33.5140i	0.130105	+	1.23787i	−0.713405	+	0.700752i	$0.752848\pi$
$734$	29.9980	+	21.7948i	1.10725	+	0.804461i
$735$	−0.0272751	+	1.24179i	−0.00100606	+	0.0458041i
$736$			0.486159i			0.0179200i
$737$	35.3822	+	24.6837i	1.30332	+	0.909236i
$738$	3.33543	−	1.92571i	0.122779	−	0.0708864i
$739$	12.7932	+	11.5191i	0.470607	+	0.423736i	0.870006	−	0.493041i	$-0.164115\pi$
$739$	12.7932	+	11.5191i	0.470607	+	0.423736i	−0.399400	+	0.916777i	$0.630781\pi$
$740$	−0.113755	−	0.255497i	−0.00418171	−	0.00939227i
$741$	19.4536	+	26.7756i	0.714646	+	0.983626i
$742$	0.103217	−	0.197191i	0.00378921	−	0.00723912i
$743$	−20.9537	−	6.80827i	−0.768717	−	0.249771i	−0.101701	−	0.994815i	$-0.532429\pi$
$743$	−20.9537	−	6.80827i	−0.768717	−	0.249771i	−0.667016	+	0.745044i	$0.732429\pi$
$744$	−1.15588	+	0.121488i	−0.0423767	+	0.00445397i
$745$	−0.451640	+	4.29707i	−0.0165468	+	0.157432i
$746$	−4.86770	+	5.40613i	−0.178219	+	0.197932i
$747$	1.40682	−	2.43668i	0.0514728	−	0.0891535i
$748$	−16.3570	+	3.80615i	−0.598071	+	0.139167i
$749$	−32.0702	+	38.7261i	−1.17182	+	1.41502i
$750$	−1.68225	+	0.546597i	−0.0614272	+	0.0199589i
$751$	27.9727	−	12.4542i	1.02074	−	0.454462i	0.173025	−	0.984917i	$-0.444646\pi$
$751$	27.9727	−	12.4542i	1.02074	−	0.454462i	0.847713	+	0.530455i	$0.177979\pi$
$752$	2.52068	−	5.66154i	0.0919197	−	0.206455i
$753$	15.6975	−	3.33661i	0.572049	−	0.121593i
$754$	24.4743	+	27.1814i	0.891301	+	0.989890i
$755$	1.63001	−	1.18427i	0.0593220	−	0.0431000i
$756$	−0.712791	+	2.54793i	−0.0259239	+	0.0926672i
$757$	5.85764	+	18.0280i	0.212900	+	0.655237i	0.999296	+	0.0375153i	$0.0119443\pi$
$757$	5.85764	+	18.0280i	0.212900	+	0.655237i	−0.786397	+	0.617722i	$0.788056\pi$
$758$	19.0812	+	11.0166i	0.693062	+	0.400140i
$759$	0.304920	−	1.58331i	0.0110679	−	0.0574706i
$760$	−0.468113	−	0.810795i	−0.0169802	−	0.0294106i
$761$	−26.9400	−	5.72627i	−0.976574	−	0.207577i	−0.308134	−	0.951343i	$-0.599704\pi$
$761$	−26.9400	−	5.72627i	−0.976574	−	0.207577i	−0.668440	+	0.743766i	$0.733038\pi$
$762$	−1.84267	+	2.53622i	−0.0667530	+	0.0918777i
$763$	28.6919	+	19.0839i	1.03872	+	0.690884i
$764$	3.43286	−	10.5653i	0.124197	−	0.382238i
$765$	0.667706	−	0.601205i	0.0241410	−	0.0217366i
$766$	−0.869174	−	0.386981i	−0.0314045	−	0.0139822i
$767$	−33.8569	−	3.55850i	−1.22250	−	0.128490i
$768$	−0.207912	+	0.978148i	−0.00750237	+	0.0352959i
$769$	43.8771			1.58225			0.791124	−	0.611655i	$-0.209496\pi$
$769$	43.8771			1.58225			0.791124	+	0.611655i	$0.209496\pi$
$770$	0.230949	−	1.53982i	0.00832283	−	0.0554911i
$771$	21.2674			0.765928
$772$	1.44316	−	6.78952i	0.0519403	−	0.244360i
$773$	−18.1287	−	1.90540i	−0.652043	−	0.0685325i	−0.227269	−	0.973832i	$-0.572980\pi$
$773$	−18.1287	−	1.90540i	−0.652043	−	0.0685325i	−0.424774	+	0.905299i	$0.639646\pi$
$774$	2.83303	+	1.26134i	0.101831	+	0.0453381i
$775$	4.29140	−	3.86400i	0.154152	−	0.138799i
$776$	−4.55507	+	14.0191i	−0.163517	+	0.503255i
$777$	3.73619	−	1.85229i	0.134035	−	0.0664506i
$778$	−6.22654	+	8.57010i	−0.223232	+	0.307253i
$779$	−19.8770	−	4.22499i	−0.712169	−	0.151376i
$780$	−0.556519	−	0.963919i	−0.0199266	−	0.0345138i
$781$	2.06728	+	16.5990i	0.0739730	+	0.593957i
$782$	2.13190	+	1.23085i	0.0762364	+	0.0440151i
$783$	−1.80188	−	5.54562i	−0.0643939	−	0.198184i
$784$	−6.97604	+	0.578651i	−0.249144	+	0.0206661i
$785$	1.65058	−	1.19922i	0.0589119	−	0.0428020i
$786$	2.89973	+	3.22048i	0.103430	+	0.114871i
$787$	5.49443	−	1.16788i	0.195855	−	0.0416303i	−0.108940	−	0.994048i	$-0.534745\pi$
$787$	5.49443	−	1.16788i	0.195855	−	0.0416303i	0.304795	+	0.952418i	$0.401412\pi$
$788$	6.42831	−	14.4382i	0.228999	−	0.514340i
$789$	7.12345	−	3.17156i	0.253602	−	0.112911i
$790$	−1.79852	+	0.584373i	−0.0639883	+	0.0207911i
$791$	2.51899	−	14.8472i	0.0895649	−	0.527907i
$792$	1.29062	−	3.05521i	0.0458602	−	0.108562i
$793$	27.9943	−	48.4875i	0.994107	−	1.72184i
$794$	8.38974	−	9.31775i	0.297741	−	0.330674i
$795$	0.00156030	−	0.0148453i	5.53383e−5	−	0.000526509i
$796$	27.3884	−	2.87863i	0.970755	−	0.102030i
$797$	1.81895	+	0.591013i	0.0644305	+	0.0209347i	0.341055	−	0.940043i	$-0.389216\pi$
$797$	1.81895	+	0.591013i	0.0644305	+	0.0209347i	−0.276624	+	0.960978i	$0.589216\pi$
$798$	11.7903	−	7.47397i	0.417373	−	0.264576i
$799$	−18.4451	−	25.3875i	−0.652540	−	0.898144i
$800$	−2.02088	−	4.53896i	−0.0714488	−	0.160477i
$801$	−7.49470	−	6.74826i	−0.264812	−	0.238438i
$802$	7.01843	−	4.05209i	0.247829	−	0.143084i
$803$	9.93567	−	0.190638i	0.350622	−	0.00672749i
$804$		−	13.0077i		−	0.458744i
$805$	−0.178938	+	0.141676i	−0.00630673	+	0.00499344i
$806$	5.89811	+	4.28522i	0.207752	+	0.150941i
$807$	−0.594351	−	5.65487i	−0.0209221	−	0.199061i
$808$	−2.99033	−	14.0684i	−0.105200	−	0.494925i
$809$	−5.50662	−	25.9066i	−0.193603	−	0.910828i	−0.962463	−	0.271412i	$-0.912509\pi$
$809$	−5.50662	−	25.9066i	−0.193603	−	0.910828i	0.768861	−	0.639416i	$-0.220824\pi$
$810$	0.0185477	+	0.176469i	0.000651698	+	0.00620049i
$811$	−21.2634	−	15.4488i	−0.746660	−	0.542480i	0.148130	−	0.988968i	$-0.452675\pi$
$811$	−21.2634	−	15.4488i	−0.746660	−	0.542480i	−0.894790	+	0.446488i	$0.852675\pi$
$812$	12.0952	−	9.57654i	0.424459	−	0.336071i
$813$			10.6042i			0.371905i
$814$	−4.93979	+	1.71048i	−0.173140	+	0.0599523i
$815$	−2.56154	+	1.47890i	−0.0897267	+	0.0518037i
$816$	3.76297	+	3.38819i	0.131730	+	0.118611i
$817$	−6.65518	−	14.9478i	−0.232835	−	0.522956i
$818$	−10.7407	−	14.7833i	−0.375539	−	0.516885i
$819$	14.0170	−	8.88548i	0.489794	−	0.310484i
$820$	0.649953	+	0.211182i	0.0226973	+	0.00737481i
$821$	−36.1213	+	3.79650i	−1.26064	+	0.132499i	−0.711173	−	0.703017i	$-0.751836\pi$
$821$	−36.1213	+	3.79650i	−1.26064	+	0.132499i	−0.549467	+	0.835515i	$0.685169\pi$
$822$	0.0475151	−	0.452076i	0.00165728	−	0.0157680i
$823$	2.96507	−	3.29304i	0.103356	−	0.114788i	−0.689247	−	0.724526i	$-0.742059\pi$
$823$	2.96507	−	3.29304i	0.103356	−	0.114788i	0.792603	+	0.609738i	$0.208725\pi$
$824$	−4.85597	+	8.41079i	−0.169166	+	0.293004i
$825$	3.73470	+	16.0499i	0.130026	+	0.558786i
$826$	−2.40184	+	14.1568i	−0.0835707	+	0.492577i
$827$	−8.43100	+	2.73940i	−0.293175	+	0.0952582i	−0.451912	−	0.892063i	$-0.649258\pi$
$827$	−8.43100	+	2.73940i	−0.293175	+	0.0952582i	0.158737	+	0.987321i	$0.449258\pi$
$828$	−0.444128	+	0.197738i	−0.0154345	+	0.00687189i
$829$	−2.46300	+	5.53200i	−0.0855437	+	0.192134i	−0.951252	−	0.308414i	$-0.900202\pi$
$829$	−2.46300	+	5.53200i	−0.0855437	+	0.192134i	0.865708	+	0.500549i	$0.166868\pi$
$830$	0.488345	−	0.103801i	0.0169507	−	0.00360298i
$831$	7.45782	+	8.28275i	0.258709	+	0.287325i
$832$	5.07473	−	3.68701i	0.175935	−	0.127824i
$833$	−15.1244	+	32.0563i	−0.524028	+	1.11068i
$834$	5.11691	+	15.7482i	0.177184	+	0.545317i
$835$	−1.00084	−	0.577834i	−0.0346354	−	0.0199968i
$836$	−15.8470	+	7.42300i	−0.548079	+	0.256730i
$837$	−0.581125	−	1.00654i	−0.0200866	−	0.0347910i
$838$	−14.5286	−	3.08815i	−0.501882	−	0.106678i
$839$	−2.16892	+	2.98526i	−0.0748793	+	0.103062i	−0.844814	−	0.535060i	$-0.820289\pi$
$839$	−2.16892	+	2.98526i	−0.0748793	+	0.103062i	0.769935	+	0.638123i	$0.220289\pi$
$840$	−0.420612	+	0.208527i	−0.0145125	+	0.00719486i
$841$	−1.54528	+	4.75588i	−0.0532855	+	0.163996i
$842$	5.33623	−	4.80476i	0.183899	−	0.165583i
$843$	−13.9464	−	6.20935i	−0.480341	−	0.213861i
$844$	5.85589	+	0.615479i	0.201568	+	0.0211856i
$845$	−0.971994	+	4.57287i	−0.0334376	+	0.157312i
$846$	6.19733			0.213069
$847$	−28.3073	−	6.75979i	−0.972652	−	0.232269i
$848$	0.0841241			0.00288883
$849$	−0.704245	+	3.31321i	−0.0241696	+	0.113709i
$850$	−25.0206	−	2.62978i	−0.858201	−	0.0902005i
$851$	0.700019	+	0.311669i	0.0239964	+	0.0106839i
$852$	3.74801	−	3.37472i	0.128405	−	0.115616i
$853$	6.72374	−	20.6935i	0.230216	−	0.708533i	−0.767504	−	0.641045i	$-0.778501\pi$
$853$	6.72374	−	20.6935i	0.230216	−	0.708533i	0.997720	−	0.0674887i	$-0.0214987\pi$
$854$	−19.6630	−	13.0785i	−0.672855	−	0.447537i
$855$	0.550299	−	0.757422i	0.0188198	−	0.0259033i
$856$	−18.5893	−	3.95127i	−0.635368	−	0.135052i
$857$	−0.502910	−	0.871065i	−0.0171791	−	0.0297550i	0.857308	−	0.514804i	$-0.172135\pi$
$857$	−0.502910	−	0.871065i	−0.0171791	−	0.0297550i	−0.874487	+	0.485049i	$0.838802\pi$
$858$	−18.8398	+	8.82489i	−0.643180	+	0.301277i
$859$	−38.7850	−	22.3925i	−1.32333	−	0.764023i	−0.339069	−	0.940761i	$-0.610112\pi$
$859$	−38.7850	−	22.3925i	−1.32333	−	0.764023i	−0.984258	+	0.176738i	$0.943445\pi$
$860$	0.170042	+	0.523336i	0.00579839	+	0.0178456i
$861$	−2.74526	+	9.81314i	−0.0935581	+	0.334431i
$862$	12.0694	−	8.76895i	0.411086	−	0.298672i
$863$	9.04885	+	10.0498i	0.308027	+	0.342098i	0.877205	−	0.480116i	$-0.159405\pi$
$863$	9.04885	+	10.0498i	0.308027	+	0.342098i	−0.569179	+	0.822214i	$0.692739\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	0.254726	−	0.572124i	0.00866095	−	0.0194528i
$866$	−1.85311	+	0.825057i	−0.0629712	+	0.0280366i
$867$	8.21696	−	2.66985i	0.279062	−	0.0906729i
$868$	1.96130	−	2.36835i	0.0665708	−	0.0803870i
$869$	8.01092	+	34.4270i	0.271752	+	1.16786i
$870$	0.517330	−	0.896042i	0.0175391	−	0.0303787i
$871$	−54.5966	+	60.6356i	−1.84993	+	2.05456i
$872$	−1.36141	+	12.9529i	−0.0461031	+	0.438642i
$873$	−14.6598	+	1.54080i	−0.496158	+	0.0521483i
$874$	2.43955	+	0.792659i	0.0825191	+	0.0268121i
$875$	2.17027	−	4.14621i	0.0733686	−	0.140168i
$876$	−1.76116	−	2.42403i	−0.0595042	−	0.0819005i
$877$	20.0780	+	45.0958i	0.677984	+	1.52278i	0.843821	+	0.536625i	$0.180301\pi$
$877$	20.0780	+	45.0958i	0.677984	+	1.52278i	−0.165837	+	0.986153i	$0.553032\pi$
$878$	5.45936	+	4.91563i	0.184244	+	0.165894i
$879$	−24.4726	+	14.1293i	−0.825440	+	0.476568i
$880$	0.556110	−	0.192562i	0.0187465	−	0.00649126i
$881$		−	11.9752i		−	0.403456i	−0.979442	−	0.201728i	$-0.935344\pi$
$881$		−	11.9752i		−	0.403456i	0.979442	−	0.201728i	$-0.0646557\pi$
$882$	−3.36604	−	6.13757i	−0.113340	−	0.206663i
$883$	8.54379	+	6.20743i	0.287521	+	0.208897i	0.722191	−	0.691693i	$-0.243135\pi$
$883$	8.54379	+	6.20743i	0.287521	+	0.208897i	−0.434670	+	0.900590i	$0.643135\pi$
$884$	−3.32007	−	31.5884i	−0.111666	−	1.06243i
$885$	0.200221	+	0.941967i	0.00673036	+	0.0316639i
$886$	−1.97047	−	9.27035i	−0.0661994	−	0.311444i
$887$	0.596252	+	5.67296i	0.0200202	+	0.190479i	0.999961	−	0.00880834i	$-0.00280382\pi$
$887$	0.596252	+	5.67296i	0.0200202	+	0.190479i	−0.979941	+	0.199288i	$0.936137\pi$
$888$	1.27515	+	0.926447i	0.0427911	+	0.0310895i
$889$	−1.20748	−	8.20592i	−0.0404976	−	0.275218i
$890$		−	1.78951i		−	0.0599846i
$891$	3.31601	−	0.0636253i	0.111091	−	0.00213153i
$892$	−11.3229	+	6.53729i	−0.379120	+	0.218885i
$893$	−24.2999	−	21.8797i	−0.813164	−	0.732176i
$894$	−9.90414	−	22.2451i	−0.331244	−	0.743986i
$895$	1.53211	+	2.10877i	0.0512128	+	0.0704884i
$896$	−1.41653	−	2.23460i	−0.0473229	−	0.0746528i
$897$	2.90028	+	0.942358i	0.0968375	+	0.0314644i
$898$	−18.4119	+	1.93516i	−0.614412	+	0.0645773i
$899$	−0.708398	+	6.73996i	−0.0236264	+	0.224790i
$900$	3.32459	−	3.69233i	0.110820	−	0.123078i
$901$	0.212984	−	0.368900i	0.00709554	−	0.0122898i
$902$	4.97072	−	11.7669i	0.165507	−	0.391795i
$903$	−7.69169	+	2.85606i	−0.255963	+	0.0950438i
$904$	5.41334	−	1.75890i	0.180045	−	0.0585001i
$905$	−2.69900	+	1.20167i	−0.0897178	+	0.0399450i
$906$	−4.61839	+	10.3731i	−0.153436	+	0.344622i
$907$	−49.2073	+	10.4593i	−1.63390	+	0.347296i	−0.931290	−	0.364278i	$-0.881316\pi$
$907$	−49.2073	+	10.4593i	−1.63390	+	0.347296i	−0.702610	+	0.711575i	$0.747982\pi$
$908$	−13.9373	−	15.4790i	−0.462527	−	0.513688i
$909$	11.6359	−	8.45395i	0.385937	−	0.280400i
$910$	2.83594	+	0.793363i	0.0940104	+	0.0262997i
$911$	16.4827	+	50.7286i	0.546097	+	1.68071i	0.718366	+	0.695665i	$0.244890\pi$
$911$	16.4827	+	50.7286i	0.546097	+	1.68071i	−0.172269	+	0.985050i	$0.555110\pi$
$912$	4.56937	+	2.63813i	0.151307	+	0.0873572i
$913$	−1.15329	−	9.26024i	−0.0381685	−	0.306469i
$914$	8.47289	+	14.6755i	0.280258	+	0.485422i
$915$	−1.54918	−	0.329289i	−0.0512144	−	0.0108860i
$916$	6.84269	−	9.41815i	0.226089	−	0.311185i
$917$	−11.4426	−	0.725748i	−0.377867	−	0.0239663i
$918$	−1.56473	+	4.81575i	−0.0516438	+	0.158943i
$919$	24.1810	−	21.7727i	0.797657	−	0.718213i	−0.165776	−	0.986163i	$-0.553013\pi$
$919$	24.1810	−	21.7727i	0.797657	−	0.718213i	0.963433	+	0.267950i	$0.0863462\pi$
$920$	−0.0788066	−	0.0350869i	−0.00259818	−	0.00115678i
$921$	−7.33968	−	0.771432i	−0.241851	−	0.0254195i
$922$	−6.21393	+	29.2342i	−0.204645	+	0.962778i
$923$	−31.6361			−1.04131
$924$	3.21177	+	8.16606i	0.105660	+	0.268644i
$925$	−7.83120			−0.257488
$926$	−5.75649	+	27.0822i	−0.189170	+	0.889975i
$927$	−9.65874	−	1.01517i	−0.317235	−	0.0333427i
$928$	5.32689	+	2.37168i	0.174864	+	0.0778543i
$929$	11.5851	−	10.4313i	0.380095	−	0.342239i	−0.456833	−	0.889553i	$-0.651016\pi$
$929$	11.5851	−	10.4313i	0.380095	−	0.342239i	0.836928	+	0.547314i	$0.184350\pi$
$930$	0.0637289	−	0.196137i	0.00208975	−	0.00643159i
$931$	−8.47043	+	35.9494i	−0.277607	+	1.17819i
$932$	7.43297	−	10.2306i	0.243475	−	0.335115i
$933$	14.6780	+	3.11990i	0.480535	+	0.102141i
$934$	−6.67797	−	11.5666i	−0.218510	−	0.378470i
$935$	0.563534	−	2.92617i	0.0184295	−	0.0956961i
$936$	5.43233	+	3.13636i	0.177561	+	0.102515i
$937$	9.51847	+	29.2948i	0.310955	+	0.957021i	0.977388	+	0.211456i	$0.0678203\pi$
$937$	9.51847	+	29.2948i	0.310955	+	0.957021i	−0.666433	+	0.745565i	$0.732180\pi$
$938$	24.0664	+	24.6008i	0.785796	+	0.803245i
$939$	0.938586	−	0.681923i	0.0306296	−	0.0222537i
$940$	0.735817	+	0.817207i	0.0239997	+	0.0266544i
$941$	35.7809	−	7.60547i	1.16642	−	0.247931i	0.416300	−	0.909228i	$-0.363327\pi$
$941$	35.7809	−	7.60547i	1.16642	−	0.247931i	0.750125	+	0.661296i	$0.229993\pi$
$942$	−4.67670	+	10.5040i	−0.152375	+	0.342240i
$943$	−1.71052	+	0.761575i	−0.0557023	+	0.0248003i
$944$	−5.16159	+	1.67710i	−0.167995	+	0.0545850i
$945$	−0.361577	−	0.299432i	−0.0117621	−	0.00974053i
$946$	10.0177	−	2.33104i	0.325702	−	0.0757886i
$947$	21.4365	−	37.1291i	0.696592	−	1.20653i	−0.273049	−	0.962000i	$-0.588032\pi$
$947$	21.4365	−	37.1291i	0.696592	−	1.20653i	0.969641	−	0.244532i	$-0.0786344\pi$
$948$	7.13123	−	7.92003i	0.231612	−	0.257231i
$949$	−1.96459	+	18.6918i	−0.0637731	+	0.606761i
$950$	−26.0716	+	2.74023i	−0.845873	+	0.0889048i
$951$	−30.0455	−	9.76237i	−0.974291	−	0.316566i
$952$	−13.3855	+	0.554201i	−0.433827	+	0.0179618i
$953$	−6.58898	−	9.06895i	−0.213438	−	0.293772i	0.688852	−	0.724902i	$-0.258115\pi$
$953$	−6.58898	−	9.06895i	−0.213438	−	0.293772i	−0.902290	+	0.431130i	$0.858115\pi$
$954$	0.0342164	+	0.0768512i	0.00110780	+	0.00248815i
$955$	1.46488	+	1.31898i	0.0474024	+	0.0426813i
$956$	−22.2229	+	12.8304i	−0.718740	+	0.414965i
$957$	−15.8610	−	11.0651i	−0.512713	−	0.357684i
$958$		−	25.4805i		−	0.823236i
$959$	0.746556	+	0.942904i	0.0241076	+	0.0304479i
$960$	−0.143553	−	0.104297i	−0.00463315	−	0.00336618i
$961$	−3.09918	−	29.4868i	−0.0999736	−	0.951186i
$962$	−2.05559	−	9.67079i	−0.0662749	−	0.311799i
$963$	−3.95127	−	18.5893i	−0.127328	−	0.599031i
$964$	2.64548	+	25.1701i	0.0852052	+	0.810673i
$965$	0.996429	+	0.723948i	0.0320762	+	0.0233047i
$966$	0.474110	−	1.19569i	0.0152542	−	0.0384706i
$967$		−	7.01538i		−	0.225599i	−0.993618	−	0.112800i	$-0.964018\pi$
$967$		−	7.01538i		−	0.225599i	0.993618	−	0.112800i	$-0.0359818\pi$
$968$	−2.69809	−	10.6640i	−0.0867199	−	0.342753i
$969$	23.1374	−	13.3584i	0.743279	−	0.429133i
$970$	−1.94375	−	1.75016i	−0.0624101	−	0.0561943i
$971$	−8.01443	−	18.0007i	−0.257195	−	0.577670i	0.738085	−	0.674707i	$-0.235730\pi$
$971$	−8.01443	−	18.0007i	−0.257195	−	0.577670i	−0.995281	+	0.0970370i	$0.969063\pi$
$972$	−0.587785	−	0.809017i	−0.0188532	−	0.0259492i
$973$	−38.8144	−	20.3168i	−1.24433	−	0.651326i
$974$	12.8560	+	4.17716i	0.411932	+	0.133845i
$975$	−30.9953	+	3.25774i	−0.992645	+	0.104331i
$976$	0.932993	−	8.87684i	0.0298644	−	0.284141i
$977$	22.3919	−	24.8687i	0.716379	−	0.795620i	−0.269514	−	0.962997i	$-0.586863\pi$
$977$	22.3919	−	24.8687i	0.716379	−	0.795620i	0.985893	+	0.167377i	$0.0535296\pi$
$978$	8.33461	−	14.4360i	0.266512	−	0.461611i
$979$	−33.3262	−	2.85753i	−1.06511	−	0.0913270i
$980$	0.409674	−	1.17258i	0.0130866	−	0.0374568i
$981$	−12.3868	+	4.02472i	−0.395481	+	0.128500i
$982$	−0.0864426	+	0.0384867i	−0.00275849	+	0.00122816i
$983$	7.72528	−	17.3513i	0.246398	−	0.553419i	−0.747431	−	0.664339i	$-0.768713\pi$
$983$	7.72528	−	17.3513i	0.246398	−	0.553419i	0.993829	+	0.110920i	$0.0353797\pi$
$984$	−3.76726	+	0.800756i	−0.120096	+	0.0255272i
$985$	1.87650	+	2.08406i	0.0597902	+	0.0664038i
$986$	23.8868	−	17.3548i	0.760712	−	0.552689i
$987$	−11.7207	+	11.4661i	−0.373075	+	0.364971i
$988$	−10.2274	−	31.4766i	−0.325376	−	1.00140i
$989$	−1.30566	−	0.753821i	−0.0415175	−	0.0239701i
$990$	0.402105	+	0.429710i	0.0127797	+	0.0136571i
$991$	17.2956	+	29.9569i	0.549414	+	0.951612i	0.998315	+	0.0580308i	$0.0184821\pi$
$991$	17.2956	+	29.9569i	0.549414	+	0.951612i	−0.448901	+	0.893581i	$0.648185\pi$
$992$	1.13685	+	0.241645i	0.0360951	+	0.00767224i
$993$	−5.58098	+	7.68157i	−0.177107	+	0.243767i
$994$	−0.844628	+	13.3169i	−0.0267900	+	0.422387i
$995$	−1.51004	+	4.64742i	−0.0478715	+	0.147333i
$996$	−2.09094	+	1.88269i	−0.0662540	+	0.0596553i
$997$	−42.4324	−	18.8921i	−1.34385	−	0.598319i	−0.396355	−	0.918097i	$-0.629725\pi$
$997$	−42.4324	−	18.8921i	−1.34385	−	0.598319i	−0.947493	+	0.319778i	$0.896392\pi$
$998$	25.0526	+	2.63314i	0.793027	+	0.0833505i
$999$	−0.327703	+	1.54172i	−0.0103681	+	0.0487780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.61.3	yes	64
7.3	odd	6		462.2.ba.a.325.2	yes	64
11.2	odd	10		462.2.ba.a.145.2	✓	64
77.24	even	30	inner	462.2.ba.b.409.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.145.2	✓	64	11.2	odd	10
462.2.ba.a.325.2	yes	64	7.3	odd	6
462.2.ba.b.61.3	yes	64	1.1	even	1	trivial
462.2.ba.b.409.3	yes	64	77.24	even	30	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.131864 - 0.118731i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.17519 - 2.37043i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.131864 - 0.118731i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.17519 - 2.37043i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.0887206 + 0.153669i) q^{10} +(3.00345 - 1.40687i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(1.93838 + 5.96571i) q^{13} +(2.56296 - 0.656669i) q^{14} +(0.143553 - 0.104297i) q^{15} +(0.669131 + 0.743145i) q^{16} +(4.95293 - 1.05278i) q^{17} +(-0.406737 + 0.913545i) q^{18} +(4.82010 - 2.14605i) q^{19} +(-0.168757 + 0.0548323i) q^{20} +(-0.920974 - 2.48028i) q^{21} +(0.751673 + 3.23032i) q^{22} +(0.243079 - 0.421026i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.519351 + 4.94130i) q^{25} +(-6.23835 + 0.655677i) q^{26} +(0.951057 + 0.309017i) q^{27} +(0.109449 + 2.64349i) q^{28} +(-3.42738 - 4.71738i) q^{29} +(0.0721718 + 0.162101i) q^{30} +(-0.863720 - 0.777697i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.13406 - 1.08522i) q^{33} +5.06358i q^{34} +(-0.436410 - 0.173044i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.164754 + 1.56753i) q^{37} +(1.09700 + 5.16096i) q^{38} +(1.30417 + 6.13564i) q^{39} +(-0.0185477 - 0.176469i) q^{40} +(-3.11587 - 2.26381i) q^{41} +(2.61756 - 0.385169i) q^{42} -3.10113i q^{43} +(-3.31601 + 0.0636253i) q^{44} +(0.153669 - 0.0887206i) q^{45} +(0.361286 + 0.325304i) q^{46} +(-2.52068 - 5.66154i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-4.23786 + 5.57140i) q^{49} +(-4.72534 - 1.53536i) q^{50} +(5.03584 - 0.529288i) q^{51} +(0.655677 - 6.23835i) q^{52} +(0.0562900 - 0.0625164i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.229009 - 0.542120i) q^{55} +(-2.60848 - 0.442555i) q^{56} +(5.01802 - 1.63045i) q^{57} +(5.32689 - 2.37168i) q^{58} +(-2.20745 + 4.95801i) q^{59} +(-0.173564 + 0.0368921i) q^{60} +(-5.97248 - 6.63311i) q^{61} +(0.940280 - 0.683153i) q^{62} +(-0.656669 - 2.56296i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.963919 + 0.556519i) q^{65} +(0.409895 + 3.29120i) q^{66} +(6.50383 + 11.2650i) q^{67} +(-4.95293 - 1.05278i) q^{68} +(0.285757 - 0.393311i) q^{69} +(0.259997 - 0.390895i) q^{70} +(-1.55851 + 4.79660i) q^{71} +(0.743145 - 0.669131i) q^{72} +(2.73723 + 1.21869i) q^{73} +(-1.56753 - 0.164754i) q^{74} +(-1.03301 + 4.85994i) q^{75} -5.27626 q^{76} +(-6.86451 - 5.46613i) q^{77} -6.27271 q^{78} +(-2.21581 + 10.4246i) q^{79} +(0.176469 + 0.0185477i) q^{80} +(0.913545 + 0.406737i) q^{81} +(2.86217 - 2.57710i) q^{82} +(0.869462 - 2.67593i) q^{83} +(-0.167471 + 2.64045i) q^{84} +(0.528117 - 0.726891i) q^{85} +(3.03337 + 0.644762i) q^{86} +(-2.91550 - 5.04980i) q^{87} +(0.627203 - 3.25678i) q^{88} +(-8.73396 - 5.04256i) q^{89} +(0.0548323 + 0.168757i) q^{90} +(11.8633 - 11.6056i) q^{91} +(-0.393311 + 0.285757i) q^{92} +(-0.777697 - 0.863720i) q^{93} +(6.06190 - 1.28850i) q^{94} +(0.380797 - 0.855284i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-14.0191 + 4.55507i) q^{97} +(-4.56855 - 5.30361i) q^{98} +(3.23032 - 0.751673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Introduction

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