LMFDB - Embedded newform 538.2.e.a.103.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(9,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([109]))

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

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

chi := DirichletCharacter("538.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.e (of order $134$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$1452$
Relative dimension:	$22$ over $\Q(\zeta_{134})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{134}]$

Embedding invariants

Embedding label			103.6
Character	$\chi$	$=$	538.103
Dual form			538.2.e.a.491.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366380 - 0.930465i) q^{2} +(0.0594714 + 1.26740i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(3.62229 + 2.05376i) q^{5} +(1.15749 - 0.519687i) q^{6} +(-2.31918 - 2.06209i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.38404 - 0.130176i) q^{9} +O(q^{10})$	\(q+(-0.366380 - 0.930465i) q^{2} +(0.0594714 + 1.26740i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(3.62229 + 2.05376i) q^{5} +(1.15749 - 0.519687i) q^{6} +(-2.31918 - 2.06209i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.38404 - 0.130176i) q^{9} +(0.583814 - 4.12287i) q^{10} +(0.568300 - 4.82578i) q^{11} +(-0.907631 - 0.886597i) q^{12} +(3.30337 + 0.467769i) q^{13} +(-1.06900 + 2.91342i) q^{14} +(-2.38752 + 4.71305i) q^{15} +(0.0702762 - 0.997528i) q^{16} +(0.156542 - 0.0184350i) q^{17} +(-0.628210 - 1.24011i) q^{18} +(-3.73375 + 1.57227i) q^{19} +(-4.05009 + 0.967320i) q^{20} +(2.47557 - 3.06197i) q^{21} +(-4.69843 + 1.23928i) q^{22} +(6.62547 - 0.310893i) q^{23} +(-0.492410 + 1.16935i) q^{24} +(6.33572 + 10.5881i) q^{25} +(-0.775045 - 3.24505i) q^{26} +(0.780971 + 5.51520i) q^{27} +(3.10250 - 0.0727505i) q^{28} +(4.30501 + 2.57604i) q^{29} +(5.26006 + 0.494734i) q^{30} +(-1.92648 + 8.06600i) q^{31} +(-0.953913 + 0.300085i) q^{32} +(6.15000 + 0.433270i) q^{33} +(-0.0745071 - 0.138903i) q^{34} +(-4.16571 - 12.2325i) q^{35} +(-0.923716 + 1.03888i) q^{36} +(-5.42167 - 8.16581i) q^{37} +(2.83091 + 2.89807i) q^{38} +(-0.396396 + 4.21452i) q^{39} +(2.38393 + 3.41406i) q^{40} +(-3.01192 - 1.18597i) q^{41} +(-3.75605 - 1.18159i) q^{42} +(-4.08202 + 6.82176i) q^{43} +(2.87452 + 3.91768i) q^{44} +(5.28076 + 2.37095i) q^{45} +(-2.71672 - 6.05087i) q^{46} +(-2.00749 - 1.26608i) q^{47} +(1.26845 + 0.0297439i) q^{48} +(0.307684 + 2.61273i) q^{49} +(7.53057 - 9.77443i) q^{50} +(0.0326743 + 0.197306i) q^{51} +(-2.73545 + 1.91007i) q^{52} +(-0.340238 + 1.08155i) q^{53} +(4.84557 - 2.74732i) q^{54} +(11.9695 - 16.3132i) q^{55} +(-1.20438 - 2.86011i) q^{56} +(-2.21475 - 4.63866i) q^{57} +(0.819646 - 4.94948i) q^{58} +(-5.07905 - 5.44946i) q^{59} +(-1.46685 - 5.07557i) q^{60} +(1.96608 - 9.17909i) q^{61} +(8.21096 - 1.16270i) q^{62} +(-3.47827 - 2.55212i) q^{63} +(0.628713 + 0.777638i) q^{64} +(11.0051 + 8.47871i) q^{65} +(-1.85010 - 5.88110i) q^{66} +(8.97398 + 8.36400i) q^{67} +(-0.101947 + 0.120218i) q^{68} +(0.788053 + 8.37866i) q^{69} +(-9.85569 + 8.35779i) q^{70} +(0.00841757 - 0.00308860i) q^{71} +(1.30507 + 0.478861i) q^{72} +(-3.83019 - 3.24806i) q^{73} +(-5.61161 + 8.03647i) q^{74} +(-13.0426 + 8.65960i) q^{75} +(1.65937 - 3.69586i) q^{76} +(-11.2692 + 10.0199i) q^{77} +(4.06669 - 1.17528i) q^{78} +(-3.55032 - 13.4601i) q^{79} +(2.30324 - 3.46901i) q^{80} +(-2.84622 + 0.540179i) q^{81} +3.23700i q^{82} +(0.183595 + 0.967364i) q^{83} +(0.276714 + 3.92779i) q^{84} +(0.604903 + 0.254723i) q^{85} +(7.84298 + 1.29882i) q^{86} +(-3.00886 + 5.60939i) q^{87} +(2.59210 - 4.11000i) q^{88} +(4.94186 - 1.68292i) q^{89} +(0.271325 - 5.78223i) q^{90} +(-6.69651 - 7.89667i) q^{91} +(-4.63477 + 4.74473i) q^{92} +(-10.3374 - 1.96193i) q^{93} +(-0.442542 + 2.33177i) q^{94} +(-16.7538 - 1.97298i) q^{95} +(-0.437059 - 1.19115i) q^{96} +(-0.0510617 - 0.238394i) q^{97} +(2.31832 - 1.24354i) q^{98} +(0.158353 - 6.75306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38} + 24 q^{41} + 14 q^{43} - 2 q^{44} - 42 q^{45} - 402 q^{47} + 22 q^{49} + 12 q^{51} + 10 q^{52} - 10 q^{53} - 8 q^{54} - 4 q^{55} - 12 q^{56} + 16 q^{57} - 18 q^{58} - 268 q^{60} - 2 q^{61} + 4 q^{62} + 22 q^{64} + 16 q^{65} + 40 q^{66} + 6 q^{67} - 106 q^{73} + 40 q^{78} + 40 q^{79} - 2 q^{80} - 14 q^{81} - 402 q^{83} - 12 q^{84} - 100 q^{87} + 4 q^{92} - 340 q^{93} + 2 q^{96} - 64 q^{97} + 18 q^{99}+O(q^{100}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{51}{134}\right)$

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 $

$2$	−0.366380	−	0.930465i	−0.259070	−	0.657938i
$2$	−0.366380	−	0.930465i	−0.259070	−	0.657938i
$3$	0.0594714	+	1.26740i	0.0343358	+	0.731736i	0.946654	+	0.322253i	$0.104440\pi$
$3$	0.0594714	+	1.26740i	0.0343358	+	0.731736i	−0.912318	+	0.409483i	$0.865709\pi$
$4$	−0.731531	+	0.681808i	−0.365766	+	0.340904i
$5$	3.62229	+	2.05376i	1.61994	+	0.918468i	0.989878	+	0.141922i	$0.0453282\pi$
$5$	3.62229	+	2.05376i	1.61994	+	0.918468i	0.630061	+	0.776546i	$0.283030\pi$
$6$	1.15749	−	0.519687i	0.472542	−	0.212162i
$7$	−2.31918	−	2.06209i	−0.876566	−	0.779396i	0.0999157	−	0.994996i	$-0.468143\pi$
$7$	−2.31918	−	2.06209i	−0.876566	−	0.779396i	−0.976482	+	0.215600i	$0.930829\pi$
$8$	0.902417	+	0.430864i	0.319053	+	0.152333i
$9$	1.38404	−	0.130176i	0.461348	−	0.0433920i
$10$	0.583814	−	4.12287i	0.184618	−	1.30377i
$11$	0.568300	−	4.82578i	0.171349	−	1.45503i	−0.590378	−	0.807127i	$-0.701021\pi$
$11$	0.568300	−	4.82578i	0.171349	−	1.45503i	0.761726	−	0.647899i	$-0.224352\pi$
$12$	−0.907631	−	0.886597i	−0.262010	−	0.255939i
$13$	3.30337	+	0.467769i	0.916189	+	0.129736i	0.582391	−	0.812909i	$-0.302117\pi$
$13$	3.30337	+	0.467769i	0.916189	+	0.129736i	0.333798	+	0.942645i	$0.391670\pi$
$14$	−1.06900	+	2.91342i	−0.285703	+	0.778644i
$15$	−2.38752	+	4.71305i	−0.616454	+	1.21690i
$16$	0.0702762	−	0.997528i	0.0175690	−	0.249382i
$17$	0.156542	−	0.0184350i	0.0379671	−	0.00447114i	−0.0979504	−	0.995191i	$-0.531229\pi$
$17$	0.156542	−	0.0184350i	0.0379671	−	0.00447114i	0.135917	+	0.990720i	$0.456602\pi$
$18$	−0.628210	−	1.24011i	−0.148071	−	0.292297i
$19$	−3.73375	+	1.57227i	−0.856580	+	0.360703i	−0.771930	−	0.635707i	$-0.780709\pi$
$19$	−3.73375	+	1.57227i	−0.856580	+	0.360703i	−0.0846500	+	0.996411i	$0.526977\pi$
$20$	−4.05009	+	0.967320i	−0.905627	+	0.216299i
$21$	2.47557	−	3.06197i	0.540214	−	0.668176i
$22$	−4.69843	+	1.23928i	−1.00171	+	0.264216i
$23$	6.62547	−	0.310893i	1.38151	−	0.0648256i	0.656894	−	0.753983i	$-0.271870\pi$
$23$	6.62547	−	0.310893i	1.38151	−	0.0648256i	0.724612	+	0.689157i	$0.242019\pi$
$24$	−0.492410	+	1.16935i	−0.100513	+	0.238693i
$25$	6.33572	+	10.5881i	1.26714	+	2.11762i
$26$	−0.775045	−	3.24505i	−0.151999	−	0.636407i
$27$	0.780971	+	5.51520i	0.150298	+	1.06140i
$28$	3.10250	−	0.0727505i	0.586317	−	0.0137486i
$29$	4.30501	+	2.57604i	0.799421	+	0.478359i	0.854077	−	0.520146i	$-0.174123\pi$
$29$	4.30501	+	2.57604i	0.799421	+	0.478359i	−0.0546560	+	0.998505i	$0.517406\pi$
$30$	5.26006	+	0.494734i	0.960352	+	0.0903257i
$31$	−1.92648	+	8.06600i	−0.346006	+	1.44870i	0.476115	+	0.879383i	$0.342045\pi$
$31$	−1.92648	+	8.06600i	−0.346006	+	1.44870i	−0.822121	+	0.569313i	$0.807209\pi$
$32$	−0.953913	+	0.300085i	−0.168630	+	0.0530480i
$33$	6.15000	+	0.433270i	1.07058	+	0.0754226i
$34$	−0.0745071	−	0.138903i	−0.0127779	−	0.0238217i
$35$	−4.16571	−	12.2325i	−0.704133	−	2.06767i
$36$	−0.923716	+	1.03888i	−0.153953	+	0.173147i
$37$	−5.42167	−	8.16581i	−0.891317	−	1.34245i	−0.939118	−	0.343594i	$-0.888356\pi$
$37$	−5.42167	−	8.16581i	−0.891317	−	1.34245i	0.0478010	−	0.998857i	$-0.484779\pi$
$38$	2.83091	+	2.89807i	0.459235	+	0.470130i
$39$	−0.396396	+	4.21452i	−0.0634741	+	0.674863i
$40$	2.38393	+	3.41406i	0.376932	+	0.539810i
$41$	−3.01192	−	1.18597i	−0.470383	−	0.185218i	0.119291	−	0.992859i	$-0.461938\pi$
$41$	−3.01192	−	1.18597i	−0.470383	−	0.185218i	−0.589674	+	0.807641i	$0.700744\pi$
$42$	−3.75605	−	1.18159i	−0.579572	−	0.182323i
$43$	−4.08202	+	6.82176i	−0.622502	+	1.04031i	0.371232	+	0.928540i	$0.378935\pi$
$43$	−4.08202	+	6.82176i	−0.622502	+	1.04031i	−0.993734	+	0.111769i	$0.964348\pi$
$44$	2.87452	+	3.91768i	0.433350	+	0.590612i
$45$	5.28076	+	2.37095i	0.787209	+	0.353441i
$46$	−2.71672	−	6.05087i	−0.400558	−	0.892152i
$47$	−2.00749	−	1.26608i	−0.292822	−	0.184677i	0.378986	−	0.925403i	$-0.376273\pi$
$47$	−2.00749	−	1.26608i	−0.292822	−	0.184677i	−0.671808	+	0.740725i	$0.734482\pi$
$48$	1.26845	+	0.0297439i	0.183085	+	0.00429316i
$49$	0.307684	+	2.61273i	0.0439548	+	0.373247i
$50$	7.53057	−	9.77443i	1.06498	−	1.38231i
$51$	0.0326743	+	0.197306i	0.00457532	+	0.0276284i
$52$	−2.73545	+	1.91007i	−0.379338	+	0.264880i
$53$	−0.340238	+	1.08155i	−0.0467353	+	0.148563i	−0.974384	−	0.224892i	$-0.927797\pi$
$53$	−0.340238	+	1.08155i	−0.0467353	+	0.148563i	0.927648	+	0.373455i	$0.121827\pi$
$54$	4.84557	−	2.74732i	0.659398	−	0.373864i
$55$	11.9695	−	16.3132i	1.61397	−	2.19967i
$56$	−1.20438	−	2.86011i	−0.160943	−	0.382198i
$57$	−2.21475	−	4.63866i	−0.293351	−	0.614405i
$58$	0.819646	−	4.94948i	0.107625	−	0.649898i
$59$	−5.07905	−	5.44946i	−0.661237	−	0.709460i	0.309151	−	0.951013i	$-0.399955\pi$
$59$	−5.07905	−	5.44946i	−0.661237	−	0.709460i	−0.970388	+	0.241553i	$0.922343\pi$
$60$	−1.46685	−	5.07557i	−0.189369	−	0.655253i
$61$	1.96608	−	9.17909i	0.251730	−	1.17526i	−0.655688	−	0.755032i	$-0.727621\pi$
$61$	1.96608	−	9.17909i	0.251730	−	1.17526i	0.907418	−	0.420230i	$-0.138051\pi$
$62$	8.21096	−	1.16270i	1.04279	−	0.147663i
$63$	−3.47827	−	2.55212i	−0.438221	−	0.321537i
$64$	0.628713	+	0.777638i	0.0785891	+	0.0972047i
$65$	11.0051	+	8.47871i	1.36501	+	1.05165i
$66$	−1.85010	−	5.88110i	−0.227731	−	0.723914i
$67$	8.97398	+	8.36400i	1.09635	+	1.02183i	0.999649	+	0.0265116i	$0.00843988\pi$
$67$	8.97398	+	8.36400i	1.09635	+	1.02183i	0.0966975	+	0.995314i	$0.469172\pi$
$68$	−0.101947	+	0.120218i	−0.0123628	+	0.0145785i
$69$	0.788053	+	8.37866i	0.0948704	+	1.00867i
$70$	−9.85569	+	8.35779i	−1.17798	+	0.998947i
$71$	0.00841757	−	0.00308860i	0.000998981	−	0.000366549i	−0.343967	−	0.938982i	$-0.611771\pi$
$71$	0.00841757	−	0.00308860i	0.000998981	−	0.000366549i	0.344966	+	0.938615i	$0.387890\pi$
$72$	1.30507	+	0.478861i	0.153804	+	0.0564343i
$73$	−3.83019	−	3.24806i	−0.448290	−	0.380157i	0.394063	−	0.919083i	$-0.371069\pi$
$73$	−3.83019	−	3.24806i	−0.448290	−	0.380157i	−0.842353	+	0.538926i	$0.818830\pi$
$74$	−5.61161	+	8.03647i	−0.652336	+	0.934220i
$75$	−13.0426	+	8.65960i	−1.50603	+	0.999924i
$76$	1.65937	−	3.69586i	0.190342	−	0.423944i
$77$	−11.2692	+	10.0199i	−1.28424	+	1.14188i
$78$	4.06669	−	1.17528i	0.460462	−	0.133075i
$79$	−3.55032	−	13.4601i	−0.399442	−	1.51438i	−0.801064	−	0.598578i	$-0.795733\pi$
$79$	−3.55032	−	13.4601i	−0.399442	−	1.51438i	0.401622	−	0.915805i	$-0.368446\pi$
$80$	2.30324	−	3.46901i	0.257510	−	0.387847i
$81$	−2.84622	+	0.540179i	−0.316246	+	0.0600199i
$82$			3.23700i			0.357467i
$83$	0.183595	+	0.967364i	0.0201521	+	0.106182i	0.991103	−	0.133097i	$-0.0424921\pi$
$83$	0.183595	+	0.967364i	0.0201521	+	0.106182i	−0.970951	+	0.239279i	$0.923089\pi$
$84$	0.276714	+	3.92779i	0.0301920	+	0.428557i
$85$	0.604903	+	0.254723i	0.0656110	+	0.0276286i
$86$	7.84298	+	1.29882i	0.845731	+	0.140055i
$87$	−3.00886	+	5.60939i	−0.322583	+	0.601390i
$88$	2.59210	−	4.11000i	0.276318	−	0.438128i
$89$	4.94186	−	1.68292i	0.523836	−	0.178389i	−0.0478610	−	0.998854i	$-0.515240\pi$
$89$	4.94186	−	1.68292i	0.523836	−	0.178389i	0.571697	+	0.820465i	$0.306285\pi$
$90$	0.271325	−	5.78223i	0.0286001	−	0.609501i
$91$	−6.69651	−	7.89667i	−0.701985	−	0.827796i
$92$	−4.63477	+	4.74473i	−0.483208	+	0.494672i
$93$	−10.3374	−	1.96193i	−1.07194	−	0.203442i
$94$	−0.442542	+	2.33177i	−0.0456448	+	0.240503i
$95$	−16.7538	−	1.97298i	−1.71890	−	0.202424i
$96$	−0.437059	−	1.19115i	−0.0446071	−	0.121571i
$97$	−0.0510617	−	0.238394i	−0.00518453	−	0.0242052i	0.975154	−	0.221527i	$-0.0711040\pi$
$97$	−0.0510617	−	0.238394i	−0.00518453	−	0.0242052i	−0.980339	+	0.197322i	$0.936776\pi$
$98$	2.31832	−	1.24354i	0.234186	−	0.125617i
$99$	0.158353	−	6.75306i	0.0159150	−	0.678708i
$100$	−11.8538	−	3.42578i	−1.18538	−	0.342578i
$101$	−14.1412	+	6.75177i	−1.40710	+	0.671826i	−0.973375	−	0.229220i	$-0.926383\pi$
$101$	−14.1412	+	6.75177i	−1.40710	+	0.671826i	−0.433723	+	0.901046i	$0.642800\pi$
$102$	0.171615	−	0.102691i	0.0169924	−	0.0101680i
$103$	3.47001	−	2.18847i	0.341910	−	0.215636i	−0.351485	−	0.936194i	$-0.614323\pi$
$103$	3.47001	−	2.18847i	0.341910	−	0.215636i	0.693395	+	0.720558i	$0.256114\pi$
$104$	2.77947	+	1.84542i	0.272549	+	0.180959i
$105$	15.2558	−	6.00712i	1.48881	−	0.586235i
$106$	1.13100	−	0.0796796i	0.109853	−	0.00773917i
$107$	1.70504	+	2.70350i	0.164832	+	0.261357i	0.918093	−	0.396366i	$-0.129729\pi$
$107$	1.70504	+	2.70350i	0.164832	+	0.261357i	−0.753260	+	0.657723i	$0.771520\pi$
$108$	−4.33161	−	3.50207i	−0.416809	−	0.336986i
$109$	−10.0444	−	2.15142i	−0.962079	−	0.206068i	−0.298696	−	0.954348i	$-0.596552\pi$
$109$	−10.0444	−	2.15142i	−0.962079	−	0.206068i	−0.663383	+	0.748280i	$0.730880\pi$
$110$	−19.5643	−	5.16038i	−1.86538	−	0.492023i
$111$	10.0269	−	7.35708i	0.951715	−	0.698303i
$112$	−2.21997	+	2.16853i	−0.209768	+	0.204906i
$113$	−1.43799	−	1.86646i	−0.135275	−	0.175582i	0.719645	−	0.694342i	$-0.244304\pi$
$113$	−1.43799	−	1.86646i	−0.135275	−	0.175582i	−0.854920	+	0.518760i	$0.826394\pi$
$114$	−3.50467	+	3.76026i	−0.328242	+	0.352181i
$115$	24.6379	+	12.4810i	2.29750	+	1.16386i
$116$	−4.90562	+	1.05074i	−0.455475	+	0.0975586i
$117$	4.63290	+	0.217393i	0.428311	+	0.0200980i
$118$	−3.20967	+	6.72246i	−0.295474	+	0.618852i
$119$	−0.401064	−	0.280050i	−0.0367654	−	0.0256721i
$120$	−4.18522	+	3.22444i	−0.382056	+	0.294350i
$121$	−12.2661	−	2.92962i	−1.11510	−	0.266329i
$122$	−9.26116	+	1.53367i	−0.838466	+	0.138852i
$123$	1.32398	−	3.88785i	0.119380	−	0.350555i
$124$	−4.09018	−	7.21402i	−0.367309	−	0.647838i
$125$	0.716388	+	30.5509i	0.0640757	+	2.73255i
$126$	−1.10029	+	4.17146i	−0.0980213	+	0.371623i
$127$	−3.60905	−	4.05900i	−0.320251	−	0.360178i	0.565164	−	0.824978i	$-0.308813\pi$
$127$	−3.60905	−	4.05900i	−0.320251	−	0.360178i	−0.885416	+	0.464800i	$0.846126\pi$
$128$	0.493217	−	0.869906i	0.0435946	−	0.0768896i
$129$	−8.88869	−	4.76786i	−0.782605	−	0.419787i
$130$	3.85710	−	13.3463i	0.338290	−	1.17055i
$131$	−9.48055	+	4.80262i	−0.828319	+	0.419606i	−0.814405	−	0.580297i	$-0.802937\pi$
$131$	−9.48055	+	4.80262i	−0.828319	+	0.419606i	−0.0139141	+	0.999903i	$0.504429\pi$
$132$	−4.79433	+	3.87617i	−0.417293	+	0.337377i
$133$	11.9014	+	4.05294i	1.03198	+	0.351435i
$134$	4.49453	−	11.4144i	0.388268	−	0.986052i
$135$	−8.49796	+	21.5816i	−0.731388	+	1.85745i
$136$	0.149209	+	0.0508124i	0.0127946	+	0.00435713i
$137$	−9.64731	+	7.79976i	−0.824225	+	0.666379i	−0.945278	−	0.326267i	$-0.894209\pi$
$137$	−9.64731	+	7.79976i	−0.824225	+	0.666379i	0.121052	+	0.992646i	$0.461373\pi$
$138$	7.50732	−	3.80303i	0.639066	−	0.323735i
$139$	−0.0327551	+	0.113339i	−0.00277825	+	0.00961327i	−0.962062	−	0.272830i	$-0.912040\pi$
$139$	−0.0327551	+	0.113339i	−0.00277825	+	0.00961327i	0.959284	+	0.282443i	$0.0911449\pi$
$140$	11.3876	+	6.10825i	0.962425	+	0.516241i
$141$	1.48525	−	2.61959i	0.125081	−	0.220610i
$142$	−0.00595786	−	0.00670065i	−0.000499973	−	0.000562306i
$143$	4.13465	−	15.6755i	0.345757	−	1.31085i
$144$	−0.0325887	−	1.38977i	−0.00271573	−	0.115814i
$145$	10.3035	+	18.1726i	0.855656	+	1.50915i
$146$	−1.61891	+	4.75388i	−0.133982	+	0.393434i
$147$	−3.29308	+	0.545342i	−0.271609	+	0.0449791i
$148$	9.53363	+	2.27701i	0.783660	+	0.187169i
$149$	1.47514	−	1.13650i	0.120848	−	0.0931055i	−0.548108	−	0.836407i	$-0.684652\pi$
$149$	1.47514	−	1.13650i	0.120848	−	0.0931055i	0.668956	+	0.743302i	$0.266741\pi$
$150$	12.8360	+	8.96297i	1.04806	+	0.731824i
$151$	4.78899	−	10.0302i	0.389723	−	0.816250i	−0.609993	−	0.792407i	$-0.708828\pi$
$151$	4.78899	−	10.0302i	0.389723	−	0.816250i	0.999716	−	0.0238428i	$-0.00759013\pi$
$152$	−4.04683	−	0.189893i	−0.328241	−	0.0154023i
$153$	0.214262	−	0.0458928i	0.0173220	−	0.00371022i
$154$	13.4520	+	6.81446i	1.08399	+	0.549125i
$155$	−23.5439	+	25.2609i	−1.89109	+	2.02900i
$156$	−2.58352	−	3.35332i	−0.206847	−	0.268480i
$157$	−12.9426	+	12.6427i	−1.03293	+	1.00900i	−0.0329796	+	0.999456i	$0.510500\pi$
$157$	−12.9426	+	12.6427i	−1.03293	+	1.00900i	−0.999954	+	0.00954071i	$0.996963\pi$
$158$	−11.2234	+	8.23497i	−0.892888	+	0.655139i
$159$	−1.39100	−	0.366897i	−0.110313	−	0.0290969i
$160$	−4.07165	−	0.872110i	−0.321892	−	0.0689463i
$161$	−16.0067	−	12.9413i	−1.26151	−	1.01992i
$162$	1.54542	+	2.45040i	0.121419	+	0.192521i
$163$	17.7046	−	1.24729i	1.38673	−	0.0976956i	0.642841	−	0.766000i	$-0.277756\pi$
$163$	17.7046	−	1.24729i	1.38673	−	0.0976956i	0.743888	+	0.668304i	$0.232980\pi$
$164$	3.01192	−	1.18597i	0.235191	−	0.0926089i
$165$	21.3873	+	14.2000i	1.66500	+	1.10547i
$166$	0.832834	−	0.525251i	0.0646404	−	0.0407674i
$167$	19.7869	−	11.8401i	1.53115	−	0.916213i	0.533641	−	0.845711i	$-0.320823\pi$
$167$	19.7869	−	11.8401i	1.53115	−	0.916213i	0.997512	−	0.0705021i	$-0.0224601\pi$
$168$	3.55329	−	1.69654i	0.274142	−	0.130891i
$169$	−1.79548	−	0.518897i	−0.138114	−	0.0399152i
$170$	0.0153865	−	0.656167i	0.00118009	−	0.0503257i
$171$	−4.96299	+	2.66213i	−0.379530	+	0.203578i
$172$	−1.66501	−	7.77348i	−0.126956	−	0.592723i
$173$	3.10672	+	8.46695i	0.236199	+	0.643730i	0.999999	−	0.00172392i	$-0.000548742\pi$
$173$	3.10672	+	8.46695i	0.236199	+	0.643730i	−0.763799	+	0.645454i	$0.776668\pi$
$174$	6.32173	+	0.744469i	0.479249	+	0.0564381i
$175$	7.13993	−	37.6204i	0.539728	−	2.84384i
$176$	−4.77391	−	0.906032i	−0.359847	−	0.0682948i
$177$	6.60461	−	6.76130i	0.496433	−	0.508210i
$178$	−3.37650	−	3.98164i	−0.253079	−	0.298437i
$179$	0.916444	−	19.5305i	0.0684982	−	1.45978i	−0.647709	−	0.761888i	$-0.724273\pi$
$179$	0.916444	−	19.5305i	0.0684982	−	1.45978i	0.716207	−	0.697887i	$-0.245876\pi$
$180$	−5.47958	+	1.86604i	−0.408423	+	0.139086i
$181$	−4.05780	+	6.43401i	−0.301614	+	0.478237i	−0.962136	−	0.272570i	$-0.912126\pi$
$181$	−4.05780	+	6.43401i	−0.301614	+	0.478237i	0.660522	+	0.750807i	$0.270335\pi$
$182$	−4.89411	+	9.12405i	−0.362776	+	0.676320i
$183$	11.7505	+	1.94592i	0.868625	+	0.143846i
$184$	6.11289	+	2.57412i	0.450648	+	0.189767i
$185$	−2.86830	−	40.7137i	−0.210881	−	2.99333i
$186$	1.96193	+	10.3374i	0.143856	+	0.757978i
$187$		−	0.765915i		−	0.0560092i
$188$	2.33177	−	0.442542i	0.170062	−	0.0322757i
$189$	9.56161	−	14.4011i	0.695505	−	1.04753i
$190$	4.30246	+	16.3117i	0.312133	+	1.18337i
$191$	−17.9596	+	5.19035i	−1.29951	+	0.375561i	−0.854260	−	0.519846i	$-0.825989\pi$
$191$	−17.9596	+	5.19035i	−1.29951	+	0.375561i	−0.445249	+	0.895407i	$0.646885\pi$
$192$	−0.948190	+	0.843080i	−0.0684297	+	0.0608441i
$193$	10.3871	−	23.1349i	0.747680	−	1.66529i	0.00109332	−	0.999999i	$-0.499652\pi$
$193$	10.3871	−	23.1349i	0.747680	−	1.66529i	0.746587	−	0.665288i	$-0.231691\pi$
$194$	−0.203109	+	0.134854i	−0.0145824	+	0.00968194i
$195$	−10.0915	+	14.4521i	−0.722664	+	1.03494i
$196$	−2.00646	−	1.70151i	−0.143318	−	0.121536i
$197$	−15.9873	−	5.86611i	−1.13905	−	0.417943i	−0.295684	−	0.955286i	$-0.595547\pi$
$197$	−15.9873	−	5.86611i	−1.13905	−	0.417943i	−0.843364	+	0.537343i	$0.819428\pi$
$198$	−6.34151	+	2.32684i	−0.450671	+	0.165362i
$199$	−1.49553	+	1.26824i	−0.106015	+	0.0899028i	−0.698214	−	0.715889i	$-0.746021\pi$
$199$	−1.49553	+	1.26824i	−0.106015	+	0.0899028i	0.592198	+	0.805792i	$0.298260\pi$
$200$	1.15543	+	12.2847i	0.0817016	+	0.868660i
$201$	−10.0669	+	11.8711i	−0.710062	+	0.837321i
$202$	11.4633	+	10.6841i	0.806557	+	0.751734i
$203$	−4.67206	−	14.8516i	−0.327915	−	1.04238i
$204$	−0.158427	−	0.122058i	−0.0110921	−	0.00854576i
$205$	−8.47435	−	10.4817i	−0.591874	−	0.732073i
$206$	−3.30763	−	2.42691i	−0.230454	−	0.169091i
$207$	9.12947	−	1.29277i	0.634542	−	0.0898534i
$208$	0.698760	−	3.26233i	0.0484503	−	0.226202i
$209$	5.46553	+	18.9117i	0.378059	+	1.30815i
$210$	−11.1788	−	11.9941i	−0.771412	−	0.827671i
$211$	1.92759	−	11.6399i	0.132701	−	0.801323i	−0.835192	−	0.549959i	$-0.814643\pi$
$211$	1.92759	−	11.6399i	0.132701	−	0.801323i	0.967893	−	0.251364i	$-0.0808790\pi$
$212$	−0.488516	−	1.02317i	−0.0335514	−	0.0702714i
$213$	0.00441511	+	0.0104848i	0.000302518	+	0.000718405i
$214$	1.89082	−	2.57699i	0.129254	−	0.176159i
$215$	−28.7965	+	16.3270i	−1.96391	+	1.11349i
$216$	−1.67154	+	5.31350i	−0.113734	+	0.361538i
$217$	21.1006	−	14.7339i	1.43240	−	1.00020i
$218$	1.67825	+	10.1342i	0.113665	+	0.686375i
$219$	3.88882	−	5.04756i	0.262782	−	0.341083i
$220$	2.36640	+	20.0945i	0.159543	+	1.35477i
$221$	0.525740	+	0.0123281i	0.0353651	+	0.000829277i
$222$	−10.5192	−	6.63423i	−0.706001	−	0.445261i
$223$	11.3174	+	25.2069i	0.757869	+	1.68798i	0.725223	+	0.688514i	$0.241737\pi$
$223$	11.3174	+	25.2069i	0.757869	+	1.68798i	0.0326456	+	0.999467i	$0.489607\pi$
$224$	2.83109	+	1.27110i	0.189160	+	0.0849291i
$225$	10.1472	+	13.8296i	0.676481	+	0.921974i
$226$	−1.20983	+	2.02183i	−0.0804766	+	0.134490i
$227$	−5.34115	−	1.68024i	−0.354505	−	0.111521i	0.117606	−	0.993060i	$-0.462478\pi$
$227$	−5.34115	−	1.68024i	−0.354505	−	0.111521i	−0.472111	+	0.881539i	$0.656508\pi$
$228$	4.78283	+	1.88329i	0.316751	+	0.124724i
$229$	−14.9014	−	21.3405i	−0.984713	−	1.41022i	−0.910749	−	0.412960i	$-0.864495\pi$
$229$	−14.9014	−	21.3405i	−0.984713	−	1.41022i	−0.0739635	−	0.997261i	$-0.523565\pi$
$230$	2.58627	−	27.4975i	0.170534	−	1.81313i
$231$	−13.3695	−	13.6867i	−0.879648	−	0.900517i
$232$	2.77500	+	4.17954i	0.182187	+	0.274400i
$233$	−11.0350	+	12.4108i	−0.722929	+	0.813059i	−0.988530	−	0.151024i	$-0.951743\pi$
$233$	−11.0350	+	12.4108i	−0.722929	+	0.813059i	0.265601	+	0.964083i	$0.414430\pi$
$234$	−1.49512	−	4.39040i	−0.0977393	−	0.287009i
$235$	−4.67149	−	8.70902i	−0.304734	−	0.568114i
$236$	7.43097	+	0.523515i	0.483715	+	0.0340779i
$237$	16.8483	−	5.30018i	1.09441	−	0.344284i
$238$	−0.113635	+	0.475781i	−0.00736587	+	0.0308403i
$239$	−5.83231	−	0.548556i	−0.377261	−	0.0354832i	−0.0966849	−	0.995315i	$-0.530824\pi$
$239$	−5.83231	−	0.548556i	−0.377261	−	0.0354832i	−0.280576	+	0.959832i	$0.590525\pi$
$240$	4.53361	+	2.71283i	0.292643	+	0.175112i
$241$	23.1660	−	0.543220i	1.49225	−	0.0349919i	0.730524	−	0.682887i	$-0.239276\pi$
$241$	23.1660	−	0.543220i	1.49225	−	0.0349919i	0.761730	+	0.647895i	$0.224350\pi$
$242$	1.76813	+	12.4865i	0.113660	+	0.802663i
$243$	3.02808	+	12.6783i	0.194251	+	0.813314i
$244$	4.82013	+	8.05528i	0.308577	+	0.515686i
$245$	−4.25138	+	10.0960i	−0.271611	+	0.645008i
$246$	−4.10259	+	0.192509i	−0.261571	+	0.0122739i
$247$	−13.0694	+	3.44726i	−0.831586	+	0.219344i
$248$	−5.21383	+	6.44885i	−0.331079	+	0.409502i
$249$	−1.21512	+	0.290219i	−0.0770052	+	0.0183919i
$250$	28.1641	−	11.8598i	1.78125	−	0.750080i
$251$	4.21220	+	8.31504i	0.265872	+	0.524841i	0.985533	−	0.169485i	$-0.0542103\pi$
$251$	4.21220	+	8.31504i	0.265872	+	0.524841i	−0.719661	+	0.694325i	$0.755703\pi$
$252$	4.28452	−	0.504560i	0.269899	−	0.0317843i
$253$	2.26496	−	32.1497i	0.142397	−	2.02124i
$254$	−2.45448	+	4.84523i	−0.154008	+	0.304017i
$255$	−0.286862	+	0.781805i	−0.0179640	+	0.0489585i
$256$	−0.990123	−	0.140205i	−0.0618827	−	0.00876280i
$257$	−11.9147	−	11.6386i	−0.743220	−	0.725997i	0.225475	−	0.974249i	$-0.427607\pi$
$257$	−11.9147	−	11.6386i	−0.743220	−	0.725997i	−0.968695	+	0.248252i	$0.920144\pi$
$258$	−1.17969	+	10.0175i	−0.0734444	+	0.623660i
$259$	−4.26480	+	30.1179i	−0.265002	+	1.87144i
$260$	−13.8314	+	1.30091i	−0.857788	+	0.0806790i
$261$	6.29366	+	3.00494i	0.389568	+	0.186001i
$262$	7.94215	+	7.06174i	0.490668	+	0.436276i
$263$	−20.7245	+	9.30489i	−1.27793	+	0.573764i	−0.931305	−	0.364240i	$-0.881329\pi$
$263$	−20.7245	+	9.30489i	−1.27793	+	0.573764i	−0.346625	+	0.938004i	$0.612672\pi$
$264$	5.36319	+	3.04080i	0.330081	+	0.187148i
$265$	−3.45369	+	3.21893i	−0.212158	+	0.197738i
$266$	−0.589304	−	12.5587i	−0.0361325	−	0.770025i
$267$	2.42684	+	6.16325i	0.148520	+	0.377185i
$268$	−12.2674			−0.749350
$269$	16.2600	+	2.14798i	0.991387	+	0.130965i
$269$	16.2600	+	2.14798i	0.991387	+	0.130965i
$270$	23.1944			1.41157
$271$	−0.514371	−	1.30631i	−0.0312458	−	0.0793525i	0.913996	−	0.405723i	$-0.132980\pi$
$271$	−0.514371	−	1.30631i	−0.0312458	−	0.0793525i	−0.945242	+	0.326371i	$0.894174\pi$
$272$	−0.00738820	−	0.157451i	−0.000447975	−	0.00954686i
$273$	9.61002	−	8.95681i	0.581625	−	0.542091i
$274$	10.7920	+	6.11881i	0.651968	+	0.369651i
$275$	54.6963	−	24.5575i	3.29831	−	1.48088i
$276$	−6.28912	−	5.59195i	−0.378560	−	0.336596i
$277$	6.77264	+	3.23363i	0.406928	+	0.194290i	0.623234	−	0.782036i	$-0.285819\pi$
$277$	6.77264	+	3.23363i	0.406928	+	0.194290i	−0.216305	+	0.976326i	$0.569401\pi$
$278$	0.117459	−	0.0110475i	0.00704470	−	0.000662588i
$279$	−1.61633	+	11.4145i	−0.0967672	+	0.683367i
$280$	1.51134	−	12.8337i	0.0903198	−	0.766959i
$281$	−20.0042	−	19.5406i	−1.19335	−	1.16570i	−0.982119	−	0.188262i	$-0.939715\pi$
$281$	−20.0042	−	19.5406i	−1.19335	−	1.16570i	−0.211233	−	0.977436i	$-0.567748\pi$
$282$	−2.98161	−	0.422206i	−0.177552	−	0.0251420i
$283$	6.63195	−	18.0745i	0.394228	−	1.07442i	−0.572788	−	0.819703i	$-0.694138\pi$
$283$	6.63195	−	18.0745i	0.394228	−	1.07442i	0.967017	−	0.254714i	$-0.0819812\pi$
$284$	−0.00405188	+	0.00799857i	−0.000240435	+	0.000474628i
$285$	1.50420	−	21.3511i	0.0891009	−	1.26473i
$286$	−16.1003	+	1.89603i	−0.952033	+	0.112115i
$287$	4.53959	+	8.96132i	0.267963	+	0.528970i
$288$	−1.28119	+	0.539506i	−0.0754950	+	0.0317907i
$289$	−16.5108	+	3.94342i	−0.971221	+	0.231966i
$290$	13.1340	−	16.2451i	0.771256	−	0.953945i
$291$	0.299104	−	0.0788934i	0.0175338	−	0.00462481i
$292$	5.01646	−	0.235391i	0.293566	−	0.0137752i
$293$	−11.3833	+	27.0325i	−0.665021	+	1.57926i	0.142749	+	0.989759i	$0.454406\pi$
$293$	−11.3833	+	27.0325i	−0.665021	+	1.57926i	−0.807770	+	0.589498i	$0.799325\pi$
$294$	1.71394	+	2.86430i	0.0999591	+	0.167049i
$295$	−7.20595	−	30.1707i	−0.419547	−	1.75661i
$296$	−1.37426	−	9.70497i	−0.0798771	−	0.564090i
$297$	27.0589	−	0.634505i	1.57012	−	0.0368177i
$298$	−1.59793	−	0.956173i	−0.0925657	−	0.0553896i
$299$	22.0318	+	2.07219i	1.27413	+	0.119838i
$300$	3.63688	−	15.2273i	0.209975	−	0.879149i
$301$	23.5340	−	7.40339i	1.35648	−	0.426724i
$302$	−11.0874	−	0.781110i	−0.638007	−	0.0449478i
$303$	−9.39821	−	17.5210i	−0.539913	−	1.00656i
$304$	1.30599	+	3.83501i	0.0749036	+	0.219953i
$305$	25.9733	−	29.2115i	1.48723	−	1.67265i
$306$	−0.121203	−	0.182549i	−0.00692871	−	0.0104356i
$307$	−0.585808	−	0.599706i	−0.0334338	−	0.0342270i	0.698425	−	0.715683i	$-0.253884\pi$
$307$	−0.585808	−	0.599706i	−0.0334338	−	0.0342270i	−0.731859	+	0.681456i	$0.761347\pi$
$308$	1.41207	−	15.0133i	0.0804603	−	0.855462i
$309$	2.98004	+	4.26775i	0.169528	+	0.242784i
$310$	32.1304	+	12.6517i	1.82488	+	0.718566i
$311$	8.32087	+	2.61760i	0.471833	+	0.148431i	0.526679	−	0.850064i	$-0.323437\pi$
$311$	8.32087	+	2.61760i	0.471833	+	0.148431i	−0.0548461	+	0.998495i	$0.517467\pi$
$312$	−2.17360	+	3.63246i	−0.123056	+	0.205648i
$313$	5.73818	+	7.82055i	0.324341	+	0.442043i	0.937536	−	0.347888i	$-0.113101\pi$
$313$	5.73818	+	7.82055i	0.324341	+	0.442043i	−0.613195	+	0.789932i	$0.710116\pi$
$314$	16.5055	+	7.41063i	0.931460	+	0.418206i
$315$	−7.35790	−	16.3880i	−0.414571	−	0.923362i
$316$	11.7744	+	7.42587i	0.662362	+	0.417738i
$317$	16.3784	+	0.384057i	0.919901	+	0.0215708i	0.480765	−	0.876850i	$-0.340359\pi$
$317$	16.3784	+	0.384057i	0.919901	+	0.0215708i	0.439136	+	0.898420i	$0.355285\pi$
$318$	0.168249	+	1.42870i	0.00943492	+	0.0801175i
$319$	14.8779	−	19.3111i	0.833005	−	1.08121i
$320$	0.680304	+	4.10805i	0.0380301	+	0.229647i
$321$	−3.32502	+	2.32175i	−0.185584	+	0.129588i
$322$	−6.17688	+	19.6351i	−0.344224	+	1.09422i
$323$	−0.555505	+	0.314958i	−0.0309091	+	0.0175247i
$324$	1.71380	−	2.33573i	0.0952110	−	0.129763i
$325$	15.9764	+	37.9400i	0.886213	+	2.10453i
$326$	−7.64716	−	16.0165i	−0.423537	−	0.887072i
$327$	2.12936	−	12.8583i	0.117754	−	0.711063i
$328$	−2.20701	−	2.36797i	−0.121862	−	0.130749i
$329$	2.04495	+	7.07589i	0.112742	+	0.390106i
$330$	5.37677	−	25.1027i	0.295982	−	1.38186i
$331$	−21.3225	+	3.01935i	−1.17199	+	0.165958i	−0.699009	−	0.715113i	$-0.746375\pi$
$331$	−21.3225	+	3.01935i	−1.17199	+	0.165958i	−0.472984	+	0.881071i	$0.656823\pi$
$332$	−0.793862	−	0.582481i	−0.0435688	−	0.0319678i
$333$	−8.56682	−	10.5961i	−0.469459	−	0.580661i
$334$	−18.2663	−	14.0730i	−0.999487	−	0.770041i
$335$	15.3288	+	48.7272i	0.837499	+	2.66225i
$336$	−2.88042	−	2.68463i	−0.157140	−	0.146459i
$337$	8.44529	−	9.95887i	0.460044	−	0.542494i	−0.482799	−	0.875731i	$-0.660380\pi$
$337$	8.44529	−	9.95887i	0.460044	−	0.542494i	0.942843	+	0.333237i	$0.108141\pi$
$338$	0.175012	+	1.86074i	0.00951939	+	0.101211i
$339$	2.28004	−	1.93351i	0.123835	−	0.105014i
$340$	−0.616178	+	0.226090i	−0.0334169	+	0.0122614i
$341$	37.8299	+	13.8807i	2.04860	+	0.751680i
$342$	4.29536	+	3.64254i	0.232267	+	0.196966i
$343$	−7.76277	+	11.1172i	−0.419150	+	0.600271i
$344$	−6.62293	+	4.39728i	−0.357085	+	0.237086i
$345$	−14.3532	+	31.9684i	−0.772748	+	1.72112i
$346$	6.73996	−	5.99282i	0.362343	−	0.322176i
$347$	−8.99519	+	2.59963i	−0.482887	+	0.139555i	−0.510172	−	0.860072i	$-0.670418\pi$
$347$	−8.99519	+	2.59963i	−0.482887	+	0.139555i	0.0272850	+	0.999628i	$0.491314\pi$
$348$	−1.62345	−	6.15491i	−0.0870262	−	0.329938i
$349$	−13.6191	+	20.5123i	−0.729013	+	1.09800i	0.262109	+	0.965038i	$0.415582\pi$
$349$	−13.6191	+	20.5123i	−0.729013	+	1.09800i	−0.991122	+	0.132958i	$0.957552\pi$
$350$	−37.6204	+	7.13993i	−2.01090	+	0.381645i
$351$			18.5840i			0.991942i
$352$	0.906032	+	4.77391i	0.0482917	+	0.254450i
$353$	−1.09691	−	15.5699i	−0.0583825	−	0.828704i	−0.936591	−	0.350425i	$-0.886037\pi$
$353$	−1.09691	−	15.5699i	−0.0583825	−	0.828704i	0.878208	−	0.478279i	$-0.158739\pi$
$354$	−8.71095	−	3.66816i	−0.462982	−	0.194960i
$355$	0.0368341	+	0.00609982i	0.00195495	+	0.000323745i
$356$	−2.46770	+	4.60051i	−0.130788	+	0.243826i
$357$	0.331085	−	0.524965i	0.0175229	−	0.0277841i
$358$	−18.5082	+	6.30285i	−0.978188	+	0.333116i
$359$	−0.923274	+	19.6760i	−0.0487285	+	1.03846i	0.828984	+	0.559272i	$0.188919\pi$
$359$	−0.923274	+	19.6760i	−0.0487285	+	1.03846i	−0.877713	+	0.479187i	$0.840931\pi$
$360$	3.74389	+	4.41488i	0.197320	+	0.232684i
$361$	−1.80779	+	1.85068i	−0.0951468	+	0.0974041i
$362$	7.47333	+	1.41835i	0.392789	+	0.0745469i
$363$	2.98353	−	15.7203i	0.156595	−	0.825101i
$364$	10.2827	+	1.21093i	0.538961	+	0.0634699i
$365$	−7.20333	−	19.6317i	−0.377039	−	1.02757i
$366$	−2.49455	−	11.6464i	−0.130392	−	0.608768i
$367$	−7.54186	+	4.04543i	−0.393682	+	0.211170i	−0.657586	−	0.753379i	$-0.728422\pi$
$367$	−7.54186	+	4.04543i	−0.393682	+	0.211170i	0.263904	+	0.964549i	$0.414990\pi$
$368$	0.155489	−	6.63094i	0.00810542	−	0.345662i
$369$	−4.32301	−	1.24936i	−0.225047	−	0.0650390i
$370$	−36.8318	+	17.5856i	−1.91480	+	0.914229i
$371$	3.01933	−	1.80671i	0.156756	−	0.0937997i
$372$	8.89982	−	5.61294i	0.461434	−	0.291017i
$373$	24.9585	+	16.5712i	1.29230	+	0.858022i	0.995299	−	0.0968538i	$-0.0308779\pi$
$373$	24.9585	+	16.5712i	1.29230	+	0.858022i	0.297005	+	0.954876i	$0.404012\pi$
$374$	−0.712657	+	0.280616i	−0.0368506	+	0.0145103i
$375$	−38.6777	+	2.72486i	−1.99731	+	0.140711i
$376$	−1.26608	−	2.00749i	−0.0652932	−	0.103528i
$377$	13.0161	+	10.5234i	0.670361	+	0.541981i
$378$	−16.9029	−	3.62045i	−0.869394	−	0.186216i
$379$	−23.1036	−	6.09392i	−1.18675	−	0.313024i	−0.392003	−	0.919964i	$-0.628218\pi$
$379$	−23.1036	−	6.09392i	−1.18675	−	0.313024i	−0.794747	+	0.606940i	$0.792397\pi$
$380$	13.6011	−	9.97956i	0.697722	−	0.511941i
$381$	4.92976	−	4.81552i	0.252559	−	0.246706i
$382$	11.4095	+	14.8091i	0.583759	+	0.757700i
$383$	13.7337	−	14.7353i	0.701761	−	0.752940i	−0.276342	−	0.961059i	$-0.589122\pi$
$383$	13.7337	−	14.7353i	0.701761	−	0.752940i	0.978103	+	0.208120i	$0.0667343\pi$
$384$	1.13185	+	0.573370i	0.0577597	+	0.0292597i
$385$	−61.3987	+	13.1510i	−3.12917	+	0.670239i
$386$	−25.3319	−	1.18867i	−1.28936	−	0.0605016i
$387$	−4.76166	+	9.97300i	−0.242049	+	0.506956i
$388$	0.199892	+	0.139578i	0.0101480	+	0.00708601i
$389$	3.50736	−	2.70220i	0.177830	−	0.137007i	−0.517538	−	0.855660i	$-0.673152\pi$
$389$	3.50736	−	2.70220i	0.177830	−	0.137007i	0.695369	+	0.718653i	$0.255241\pi$
$390$	17.1445	+	4.09478i	0.868146	+	0.207347i
$391$	1.03144	−	0.170808i	0.0521619	−	0.00863814i
$392$	−0.848070	+	2.49034i	−0.0428340	+	0.125781i
$393$	−6.65067	−	11.7301i	−0.335482	−	0.591703i
$394$	0.399216	+	17.0248i	0.0201122	+	0.857699i
$395$	14.7835	−	56.0480i	0.743841	−	2.82008i
$396$	4.48845	+	5.04804i	0.225553	+	0.253674i
$397$	−11.1931	+	19.7418i	−0.561768	+	0.990812i	0.434176	+	0.900828i	$0.357040\pi$
$397$	−11.1931	+	19.7418i	−0.561768	+	0.990812i	−0.995943	+	0.0899839i	$0.971318\pi$
$398$	1.72798	+	0.926883i	0.0866159	+	0.0464605i
$399$	−4.42892	+	15.3249i	−0.221723	+	0.767203i
$400$	11.0072	−	5.57596i	0.550358	−	0.278798i
$401$	−1.55888	+	1.26034i	−0.0778470	+	0.0629386i	−0.666848	−	0.745194i	$-0.732357\pi$
$401$	−1.55888	+	1.26034i	−0.0778470	+	0.0629386i	0.589001	+	0.808132i	$0.299521\pi$
$402$	14.7339	+	5.01755i	0.734861	+	0.250253i
$403$	−10.1369	+	25.7438i	−0.504954	+	1.28239i
$404$	5.74129	−	14.5807i	0.285640	−	0.725416i
$405$	−11.4192	−	3.88875i	−0.567426	−	0.193234i
$406$	−12.1072	+	9.78853i	−0.600868	+	0.485796i
$407$	−42.4875	+	21.5231i	−2.10603	+	1.06686i
$408$	−0.0555261	+	0.192130i	−0.00274895	+	0.00951187i
$409$	−4.47480	−	2.40027i	−0.221265	−	0.118686i	0.358316	−	0.933600i	$-0.383351\pi$
$409$	−4.47480	−	2.40027i	−0.221265	−	0.118686i	−0.579581	+	0.814915i	$0.696784\pi$
$410$	−6.64801	+	11.7254i	−0.328322	+	0.579075i
$411$	−10.4592	−	11.7632i	−0.515914	−	0.580235i
$412$	−1.04631	+	3.96681i	−0.0515479	+	0.195431i
$413$	0.541947	+	23.1117i	0.0266675	+	1.13725i
$414$	−4.54773	−	8.02101i	−0.223509	−	0.394211i
$415$	−1.32170	+	3.88114i	−0.0648796	+	0.190517i
$416$	−3.29149	+	0.545079i	−0.161379	+	0.0267247i
$417$	−0.145594	−	0.0347736i	−0.00712977	−	0.00170287i
$418$	15.5943	−	12.0144i	0.762740	−	0.587642i
$419$	22.0489	+	15.3961i	1.07716	+	0.752147i	0.970246	−	0.242121i	$-0.0778431\pi$
$419$	22.0489	+	15.3961i	1.07716	+	0.752147i	0.106915	+	0.994268i	$0.465903\pi$
$420$	−7.06438	+	14.7959i	−0.344707	+	0.721966i
$421$	−0.438703	−	0.0205856i	−0.0213811	−	0.00100328i	0.0361790	−	0.999345i	$-0.488481\pi$
$421$	−0.438703	−	0.0205856i	−0.0213811	−	0.00100328i	−0.0575601	+	0.998342i	$0.518332\pi$
$422$	−11.5367	+	2.47106i	−0.561600	+	0.120289i
$423$	−2.94327	−	1.49099i	−0.143106	−	0.0724943i
$424$	−0.773039	+	0.829415i	−0.0375421	+	0.0402800i
$425$	1.18700	+	1.54069i	0.0575779	+	0.0747342i
$426$	0.00813811	−	0.00794951i	0.000394293	−	0.000385155i
$427$	−23.4878	+	17.2337i	−1.13665	+	0.833997i
$428$	−3.09055	−	0.815182i	−0.149388	−	0.0394033i
$429$	20.1130	+	4.30803i	0.971067	+	0.207994i
$430$	25.7421	+	20.8123i	1.24140	+	1.00366i
$431$	−6.91443	−	10.9634i	−0.333056	−	0.528091i	0.637034	−	0.770836i	$-0.280161\pi$
$431$	−6.91443	−	10.9634i	−0.333056	−	0.528091i	−0.970090	+	0.242745i	$0.921952\pi$
$432$	5.55644	−	0.391454i	0.267335	−	0.0188338i
$433$	17.8746	−	7.03831i	0.858999	−	0.338240i	0.104488	−	0.994526i	$-0.466680\pi$
$433$	17.8746	−	7.03831i	0.858999	−	0.338240i	0.754512	+	0.656287i	$0.227874\pi$
$434$	−21.4402	−	14.2352i	−1.02916	−	0.683312i
$435$	−22.4193	+	14.1394i	−1.07492	+	0.677932i
$436$	8.81465	−	5.27452i	0.422145	−	0.252604i
$437$	−24.2490	+	11.5778i	−1.15999	+	0.553842i
$438$	−6.12137	−	1.76909i	−0.292490	−	0.0845303i
$439$	−0.187818	+	8.00963i	−0.00896406	+	0.382279i	0.976801	+	0.214150i	$0.0686980\pi$
$439$	−0.187818	+	8.00963i	−0.00896406	+	0.382279i	−0.985765	+	0.168129i	$0.946227\pi$
$440$	17.8303	−	9.56410i	0.850025	−	0.455950i
$441$	0.765962	+	3.57607i	0.0364744	+	0.170289i
$442$	−0.181150	−	0.493700i	−0.00861642	−	0.0234829i
$443$	14.1276	+	1.66372i	0.671223	+	0.0790456i	0.445687	−	0.895189i	$-0.352960\pi$
$443$	14.1276	+	1.66372i	0.671223	+	0.0790456i	0.225537	+	0.974235i	$0.427586\pi$
$444$	−2.31891	+	12.2184i	−0.110050	+	0.579859i
$445$	21.3572	+	4.05335i	1.01243	+	0.192147i
$446$	19.3077	−	19.7658i	0.914246	−	0.935936i
$447$	1.52813	+	1.80200i	0.0722780	+	0.0852318i
$448$	0.145461	−	3.09994i	0.00687239	−	0.146458i
$449$	−10.6317	+	3.62056i	−0.501740	+	0.170865i	−0.561708	−	0.827336i	$-0.689855\pi$
$449$	−10.6317	+	3.62056i	−0.501740	+	0.170865i	0.0599676	+	0.998200i	$0.480900\pi$
$450$	9.15024	−	14.5085i	0.431346	−	0.683939i
$451$	−7.43491	+	13.8609i	−0.350096	+	0.652682i
$452$	2.32450	+	0.384943i	0.109335	+	0.0181062i
$453$	12.9972	+	5.47307i	0.610660	+	0.257147i
$454$	0.393491	+	5.58536i	0.0184674	+	0.262134i
$455$	−8.03888	−	42.3571i	−0.376869	−	1.98573i
$456$		−	5.14026i		−	0.240715i
$457$	37.3690	−	7.09220i	1.74805	−	0.331759i	0.788868	−	0.614563i	$-0.210667\pi$
$457$	37.3690	−	7.09220i	1.74805	−	0.331759i	0.959178	+	0.282804i	$0.0912645\pi$
$458$	−14.3970	+	21.6840i	−0.672729	+	1.01323i
$459$	0.223928	+	0.848964i	0.0104520	+	0.0396263i
$460$	−26.5330	+	7.66809i	−1.23711	+	0.357527i
$461$	−8.27084	+	7.35399i	−0.385211	+	0.342509i	−0.834629	−	0.550812i	$-0.814318\pi$
$461$	−8.27084	+	7.35399i	−0.385211	+	0.342509i	0.449418	+	0.893322i	$0.351631\pi$
$462$	−7.83666	+	17.4544i	−0.364594	+	0.812051i
$463$	−23.6133	+	15.6780i	−1.09740	+	0.728618i	−0.964914	−	0.262567i	$-0.915431\pi$
$463$	−23.6133	+	15.6780i	−1.09740	+	0.728618i	−0.132488	+	0.991185i	$0.542297\pi$
$464$	2.87221	−	4.11334i	0.133339	−	0.190957i
$465$	−33.4159	−	28.3373i	−1.54963	−	1.31411i
$466$	15.5908	+	5.72064i	0.722232	+	0.265003i
$467$	21.8655	−	8.02295i	1.01181	−	0.371258i	0.215736	−	0.976452i	$-0.430785\pi$
$467$	21.8655	−	8.02295i	1.01181	−	0.371258i	0.796078	+	0.605194i	$0.206904\pi$
$468$	−3.53733	+	2.99971i	−0.163513	+	0.138662i
$469$	−3.56493	−	37.9027i	−0.164613	−	1.75018i
$470$	−6.39190	+	7.53747i	−0.294836	+	0.347677i
$471$	−16.7931	−	15.6517i	−0.773786	−	0.721190i
$472$	−2.23545	−	7.10607i	−0.102895	−	0.327083i
$473$	30.6005	+	23.5757i	1.40701	+	1.08401i
$474$	−11.1045	−	13.7349i	−0.510047	−	0.630863i
$475$	−40.3033	−	29.5718i	−1.84924	−	1.35685i
$476$	0.484331	−	0.0685830i	0.0221993	−	0.00314350i
$477$	−0.330112	+	1.54121i	−0.0151148	+	0.0705670i
$478$	1.62643	+	5.62774i	0.0743911	+	0.257407i
$479$	11.1406	+	11.9530i	0.509026	+	0.546148i	0.933165	−	0.359449i	$-0.117035\pi$
$479$	11.1406	+	11.9530i	0.509026	+	0.546148i	−0.424139	+	0.905597i	$0.639423\pi$
$480$	0.863168	−	5.21229i	0.0393981	−	0.237907i
$481$	−14.0901	−	29.5108i	−0.642452	−	1.34557i
$482$	−8.99301	−	21.3561i	−0.409620	−	0.972746i
$483$	15.4499	−	21.0566i	0.702994	−	0.958109i
$484$	10.9705	−	6.21999i	0.498657	−	0.282727i
$485$	0.304642	−	0.968400i	0.0138331	−	0.0439728i
$486$	10.6873	−	7.46260i	0.484786	−	0.338511i
$487$	−2.21732	−	13.3894i	−0.100476	−	0.606731i	−0.989002	−	0.147904i	$-0.952747\pi$
$487$	−2.21732	−	13.3894i	−0.100476	−	0.606731i	0.888525	−	0.458827i	$-0.151730\pi$
$488$	5.72916	−	7.43626i	0.259347	−	0.336624i
$489$	2.63374	+	22.3647i	0.119102	+	1.01136i
$490$	10.9516	+	0.256804i	0.494742	+	0.0116012i
$491$	−5.68338	−	3.58440i	−0.256487	−	0.161761i	0.399038	−	0.916934i	$-0.369344\pi$
$491$	−5.68338	−	3.58440i	−0.256487	−	0.161761i	−0.655526	+	0.755173i	$0.727553\pi$
$492$	1.68223	+	3.74678i	0.0758408	+	0.168918i
$493$	0.721406	+	0.323897i	0.0324905	+	0.0145876i
$494$	7.99592	+	10.8976i	0.359753	+	0.490307i
$495$	14.4427	−	24.1363i	0.649153	−	1.08485i
$496$	7.91067	+	2.48856i	0.355200	+	0.111740i
$497$	−0.0258908	−	0.0101948i	−0.00116136	−	0.000457297i
$498$	0.715235	+	1.02430i	0.0320505	+	0.0458999i
$499$	−2.32598	+	24.7301i	−0.104125	+	1.10707i	0.775482	+	0.631369i	$0.217507\pi$
$499$	−2.32598	+	24.7301i	−0.104125	+	1.10707i	−0.879608	+	0.475700i	$0.842195\pi$
$500$	−21.3539	−	21.8605i	−0.954975	−	0.977631i
$501$	16.1829	+	24.3738i	0.722999	+	1.08894i
$502$	6.19359	−	6.96577i	0.276434	−	0.310898i
$503$	4.80970	+	14.1236i	0.214454	+	0.629740i	0.999941	+	0.0108615i	$0.00345738\pi$
$503$	4.80970	+	14.1236i	0.214454	+	0.629740i	−0.785487	+	0.618878i	$0.787587\pi$
$504$	−2.03924	−	3.80174i	−0.0908349	−	0.169343i
$505$	−65.0899	−	4.58561i	−2.89646	−	0.204057i
$506$	−30.7440	+	9.67155i	−1.36674	+	0.429953i
$507$	0.550872	−	2.30646i	0.0244651	−	0.102433i
$508$	5.40759	+	0.508610i	0.239923	+	0.0225659i
$509$	−18.5452	−	11.0971i	−0.822002	−	0.491871i	0.0397447	−	0.999210i	$-0.487346\pi$
$509$	−18.5452	−	11.0971i	−0.822002	−	0.491871i	−0.861746	+	0.507339i	$0.830629\pi$
$510$	0.832543	−	0.0195223i	0.0368656	−	0.000864463i
$511$	2.18509	+	15.4310i	0.0966625	+	0.682628i
$512$	0.232305	+	0.972643i	0.0102665	+	0.0429851i
$513$	−11.5873	−	19.3644i	−0.511593	−	0.854961i
$514$	−6.46401	+	15.3504i	−0.285115	+	0.677077i
$515$	17.0640	−	0.800707i	0.751928	−	0.0352834i
$516$	9.75312	−	2.57254i	0.429357	−	0.113250i
$517$	−7.25069	+	8.96818i	−0.318885	+	0.394420i
$518$	29.5862	−	7.06635i	1.29994	−	0.310478i
$519$	−10.5463	+	4.44101i	−0.462930	+	0.194939i
$520$	6.27800	+	12.3930i	0.275309	+	0.543470i
$521$	−3.93587	+	0.463501i	−0.172433	+	0.0203064i	−0.202730	−	0.979235i	$-0.564982\pi$
$521$	−3.93587	+	0.463501i	−0.172433	+	0.0203064i	0.0302971	+	0.999541i	$0.490355\pi$
$522$	0.490122	−	6.95699i	0.0214521	−	0.304499i
$523$	4.83004	−	9.53468i	0.211203	−	0.416922i	−0.761768	−	0.647850i	$-0.775668\pi$
$523$	4.83004	−	9.53468i	0.211203	−	0.416922i	0.972971	+	0.230927i	$0.0741759\pi$
$524$	3.66086	−	9.97717i	0.159925	−	0.435855i
$525$	48.1049	+	6.81183i	2.09947	+	0.297292i
$526$	16.2509	+	15.8743i	0.708575	+	0.692154i
$527$	−0.152879	+	1.29818i	−0.00665951	+	0.0565498i
$528$	0.864397	−	6.10435i	0.0376181	−	0.265658i
$529$	20.9013	−	1.96586i	0.908751	−	0.0854724i
$530$	4.26047	+	2.03418i	0.185063	+	0.0883593i
$531$	−7.73902	−	6.88112i	−0.335845	−	0.298615i
$532$	−11.4696	+	5.14960i	−0.497268	+	0.223263i
$533$	−9.39471	−	5.32658i	−0.406930	−	0.230720i
$534$	4.84554	−	4.51618i	0.209687	−	0.195434i
$535$	0.623833	+	13.2946i	0.0269707	+	0.574775i
$536$	4.49453	+	11.4144i	0.194134	+	0.493026i
$537$	24.8075			1.07052
$538$	−3.95870	−	15.9163i	−0.170672	−	0.686201i
$539$	12.7833			0.550615
$540$	−8.49796	−	21.5816i	−0.365694	−	0.928723i
$541$	−1.28646	−	27.4160i	−0.0553094	−	1.17871i	−0.834169	−	0.551508i	$-0.814053\pi$
$541$	−1.28646	−	27.4160i	−0.0553094	−	1.17871i	0.778860	−	0.627198i	$-0.215798\pi$
$542$	−1.02702	+	0.957209i	−0.0441142	+	0.0411157i
$543$	−8.39582	−	4.76023i	−0.360299	−	0.204281i
$544$	−0.143796	+	0.0645613i	−0.00616519	+	0.00276804i
$545$	−31.9653	−	28.4218i	−1.36924	−	1.21746i
$546$	−11.8549	−	5.66019i	−0.507344	−	0.242234i
$547$	23.1880	−	2.18094i	0.991448	−	0.0932504i	0.414515	−	0.910042i	$-0.363951\pi$
$547$	23.1880	−	2.18094i	0.991448	−	0.0932504i	0.576932	+	0.816792i	$0.304250\pi$
$548$	1.73937	−	12.2834i	0.0743022	−	0.524720i
$549$	1.52624	−	12.9602i	0.0651382	−	0.553128i
$550$	−42.8896	−	41.8956i	−1.82882	−	1.78644i
$551$	−20.1241	−	2.84964i	−0.857314	−	0.121399i
$552$	−2.89891	+	7.90058i	−0.123386	+	0.336271i
$553$	−19.5222	+	38.5375i	−0.830167	+	1.63878i
$554$	0.527423	−	7.48644i	0.0224080	−	0.318068i
$555$	51.4302	−	6.05660i	2.18309	−	0.257088i
$556$	−0.0533138	−	0.105244i	−0.00226101	−	0.00446332i
$557$	4.34825	−	1.83103i	0.184241	−	0.0775834i	−0.294028	−	0.955797i	$-0.594996\pi$
$557$	4.34825	−	1.83103i	0.184241	−	0.0775834i	0.478269	+	0.878213i	$0.341264\pi$
$558$	11.2130	−	2.67810i	0.474683	−	0.113373i
$559$	−16.6754	+	20.6254i	−0.705295	+	0.872359i
$560$	−12.4950	+	3.29575i	−0.528011	+	0.139271i
$561$	0.970723	−	0.0455500i	0.0409840	−	0.00192312i
$562$	−10.8527	+	25.7725i	−0.457795	+	1.08715i
$563$	7.06892	+	11.8134i	0.297919	+	0.497875i	0.970163	−	0.242455i	$-0.0779527\pi$
$563$	7.06892	+	11.8134i	0.297919	+	0.497875i	−0.672243	+	0.740330i	$0.734669\pi$
$564$	0.699553	+	2.92897i	0.0294565	+	0.123332i
$565$	−1.37556	−	9.71415i	−0.0578702	−	0.408678i
$566$	−19.2475	+	0.451335i	−0.809033	+	0.0189710i
$567$	7.71478	+	4.61638i	0.323990	+	0.193870i
$568$	0.00892692		0.000839620i	0.000374565		3.52297e-5i
$569$	−6.17592	+	25.8580i	−0.258908	+	1.08403i	0.678170	+	0.734905i	$0.262773\pi$
$569$	−6.17592	+	25.8580i	−0.258908	+	1.08403i	−0.937078	+	0.349120i	$0.886480\pi$
$570$	−20.4176	+	6.42303i	−0.855199	+	0.269031i
$571$	−23.0815	−	1.62610i	−0.965933	−	0.0680503i	−0.421476	−	0.906839i	$-0.638488\pi$
$571$	−23.0815	−	1.62610i	−0.965933	−	0.0680503i	−0.544456	+	0.838789i	$0.683264\pi$
$572$	7.66304	+	14.2861i	0.320408	+	0.597333i
$573$	−7.64635	−	22.4533i	−0.319431	−	0.938002i
$574$	6.67498	−	7.50718i	0.278608	−	0.313344i
$575$	45.2689	+	68.1814i	1.88784	+	2.84336i
$576$	0.971395	+	0.994441i	0.0404748	+	0.0414350i
$577$	3.73015	−	39.6594i	0.155288	−	1.65104i	−0.478905	−	0.877867i	$-0.658966\pi$
$577$	3.73015	−	39.6594i	0.155288	−	1.65104i	0.634193	−	0.773175i	$-0.281332\pi$
$578$	9.71843	+	13.9179i	0.404233	+	0.578908i
$579$	29.9390	+	11.7888i	1.24422	+	0.489925i
$580$	−19.9275	−	6.26887i	−0.827446	−	0.260300i
$581$	1.56900	−	2.62208i	0.0650932	−	0.108782i
$582$	−0.182993	−	0.249401i	−0.00758532	−	0.0103380i
$583$	5.02597	+	2.25656i	0.208155	+	0.0934571i
$584$	−2.05695	−	4.58140i	−0.0851173	−	0.189580i
$585$	16.3352	+	10.3023i	0.675379	+	0.425948i
$586$	29.3235	+	0.687606i	1.21134	+	0.0284048i
$587$	1.17707	+	9.99519i	0.0485828	+	0.412546i	0.995771	+	0.0918680i	$0.0292838\pi$
$587$	1.17707	+	9.99519i	0.0485828	+	0.412546i	−0.947188	+	0.320678i	$0.896089\pi$
$588$	2.03717	−	2.64418i	0.0840116	−	0.109044i
$589$	−5.48895	−	33.1453i	−0.226168	−	1.36573i
$590$	−25.4327	+	17.7588i	−1.04705	+	0.731119i
$591$	6.48394	−	20.6112i	0.266714	−	0.847832i
$592$	−8.52663	+	4.83441i	−0.350442	+	0.198693i
$593$	4.25065	−	5.79320i	0.174553	−	0.237898i	−0.710153	−	0.704048i	$-0.751374\pi$
$593$	4.25065	−	5.79320i	0.174553	−	0.237898i	0.884706	+	0.466150i	$0.154359\pi$
$594$	−10.5042	−	24.9449i	−0.430994	−	1.02350i
$595$	−0.877616	−	1.83811i	−0.0359787	−	0.0753552i
$596$	−0.304235	+	1.83714i	−0.0124620	+	0.0752523i
$597$	−1.69631	−	1.82002i	−0.0694252	−	0.0744883i
$598$	−6.14390	−	21.2590i	−0.251243	−	0.869346i
$599$	−2.88752	+	13.4811i	−0.117981	+	0.550822i	0.879244	+	0.476372i	$0.158048\pi$
$599$	−2.88752	+	13.4811i	−0.117981	+	0.550822i	−0.997225	+	0.0744500i	$0.976280\pi$
$600$	−15.5010	+	2.19499i	−0.632824	+	0.0896101i
$601$	15.1518	+	11.1173i	0.618054	+	0.453485i	0.855420	−	0.517935i	$-0.173299\pi$
$601$	15.1518	+	11.1173i	0.618054	+	0.453485i	−0.237366	+	0.971420i	$0.576284\pi$
$602$	−15.5110	−	19.1851i	−0.632180	−	0.781926i
$603$	13.5092	+	10.4079i	0.550136	+	0.423844i
$604$	3.33540	+	10.6026i	0.135716	+	0.431414i
$605$	−38.4146	−	35.8035i	−1.56177	−	1.45562i
$606$	−12.8594	+	15.1641i	−0.522377	+	0.615998i
$607$	0.418045	+	4.44470i	0.0169679	+	0.180405i	0.999995	−	0.00305402i	$-0.000972125\pi$
$607$	0.418045	+	4.44470i	0.0169679	+	0.180405i	−0.983027	+	0.183459i	$0.941271\pi$
$608$	3.08985	−	2.62025i	0.125310	−	0.106265i
$609$	18.5451	−	6.80464i	0.751486	−	0.275738i
$610$	−36.6964	−	13.4648i	−1.48579	−	0.545172i
$611$	−6.03924	−	5.12138i	−0.244322	−	0.207189i
$612$	−0.125449	+	0.179657i	−0.00507097	+	0.00726221i
$613$	8.97643	−	5.95988i	0.362555	−	0.240717i	−0.358600	−	0.933491i	$-0.616746\pi$
$613$	8.97643	−	5.95988i	0.362555	−	0.240717i	0.721155	+	0.692774i	$0.243612\pi$
$614$	−0.343377	+	0.764794i	−0.0138576	+	0.0308646i
$615$	12.7805	−	11.3638i	0.515361	−	0.458232i
$616$	−14.4867	+	4.18669i	−0.583686	+	0.168686i
$617$	9.61678	+	36.4596i	0.387157	+	1.46781i	0.823133	+	0.567849i	$0.192224\pi$
$617$	9.61678	+	36.4596i	0.387157	+	1.46781i	−0.435976	+	0.899958i	$0.643597\pi$
$618$	2.87917	−	4.33644i	0.115817	−	0.174437i
$619$	22.0361	−	4.18219i	0.885704	−	0.168096i	0.276409	−	0.961040i	$-0.410856\pi$
$619$	22.0361	−	4.18219i	0.885704	−	0.168096i	0.609295	+	0.792944i	$0.291453\pi$
$620$		−	34.5315i		−	1.38682i
$621$	6.88894	+	36.2980i	0.276443	+	1.45659i
$622$	−0.613011	−	8.70131i	−0.0245795	−	0.348891i
$623$	−14.9314	−	6.28756i	−0.598213	−	0.251906i
$624$	4.17624	+	0.691596i	0.167183	+	0.0276860i
$625$	−30.9868	+	57.7684i	−1.23947	+	2.31074i
$626$	5.17439	−	8.20447i	0.206810	−	0.327917i
$627$	−23.6438	+	8.05174i	−0.944241	+	0.321556i
$628$	0.848050	−	18.0729i	0.0338409	−	0.721188i
$629$	−0.999258	−	1.17835i	−0.0398430	−	0.0469837i
$630$	−12.5527	+	12.8505i	−0.500112	+	0.511977i
$631$	38.3127	+	7.27131i	1.52520	+	0.289466i	0.880159	−	0.474679i	$-0.157436\pi$
$631$	38.3127	+	7.27131i	1.52520	+	0.289466i	0.645045	+	0.764145i	$0.276839\pi$
$632$	2.59562	−	13.6764i	0.103248	−	0.544016i
$633$	14.8671	+	1.75080i	0.590913	+	0.0695880i
$634$	−5.64336	−	15.3802i	−0.224126	−	0.610826i
$635$	−4.73683	−	22.1150i	−0.187975	−	0.877608i
$636$	1.26771	−	0.679997i	0.0502681	−	0.0269636i
$637$	−0.205759	+	8.77472i	−0.00815245	+	0.347667i
$638$	−23.4193	−	6.76821i	−0.927177	−	0.267956i
$639$	0.0112482	−	0.00537052i	0.000444973	−	0.000212454i
$640$	3.57315	−	2.13811i	0.141241	−	0.0845161i
$641$	38.2949	−	24.1518i	1.51256	−	0.953938i	0.517388	−	0.855751i	$-0.326905\pi$
$641$	38.2949	−	24.1518i	1.51256	−	0.953938i	0.995168	−	0.0981874i	$-0.0313044\pi$
$642$	3.37853	+	2.24317i	0.133340	+	0.0885308i
$643$	26.1859	−	10.3109i	1.03267	−	0.406624i	0.211542	−	0.977369i	$-0.432151\pi$
$643$	26.1859	−	10.3109i	1.03267	−	0.406624i	0.821127	+	0.570745i	$0.193345\pi$
$644$	20.5329	−	1.44655i	0.809109	−	0.0570020i
$645$	−22.4054	−	35.5258i	−0.882212	−	1.39883i
$646$	0.496584	+	0.401483i	0.0195378	+	0.0157961i
$647$	2.80042	+	0.599823i	0.110096	+	0.0235815i	0.264156	−	0.964480i	$-0.414907\pi$
$647$	2.80042	+	0.599823i	0.110096	+	0.0235815i	−0.154060	+	0.988061i	$0.549235\pi$
$648$	−2.80122	−	0.738865i	−0.110042	−	0.0290254i
$649$	−29.1843	+	21.4134i	−1.14558	+	0.840551i
$650$	29.4484	−	28.7660i	1.15506	−	1.12829i
$651$	19.9287	+	25.8668i	0.781067	+	1.01380i
$652$	−12.1010	+	12.9835i	−0.473913	+	0.508475i
$653$	−33.3405	−	16.8895i	−1.30472	−	0.660937i	−0.344130	−	0.938922i	$-0.611826\pi$
$653$	−33.3405	−	16.8895i	−1.30472	−	0.660937i	−0.960586	+	0.277985i	$0.910334\pi$
$654$	−12.7443	+	2.72971i	−0.498342	+	0.106740i
$655$	−44.2047	−	2.07426i	−1.72722	−	0.0810478i
$656$	−1.39471	+	2.92113i	−0.0544542	+	0.114051i
$657$	−5.72397	−	3.99686i	−0.223313	−	0.155932i
$658$	5.83464	−	4.49522i	0.227458	−	0.175242i
$659$	−2.69144	−	0.642821i	−0.104843	−	0.0250407i	0.179546	−	0.983750i	$-0.442537\pi$
$659$	−2.69144	−	0.642821i	−0.104843	−	0.0250407i	−0.284389	+	0.958709i	$0.591791\pi$
$660$	−25.3272	+	4.19424i	−0.985858	+	0.163261i
$661$	5.35577	−	15.7271i	0.208315	−	0.611714i	−0.791684	−	0.610930i	$-0.790795\pi$
$661$	5.35577	−	15.7271i	0.208315	−	0.611714i	1.00000		0.000783182i	$-0.000249294\pi$
$662$	10.6216	+	18.7337i	0.412818	+	0.728104i
$663$	0.0156419	+	0.667058i	0.000607479	+	0.0259064i
$664$	−0.251123	+	0.952070i	−0.00974548	+	0.0369475i
$665$	34.7865	+	39.1235i	1.34896	+	1.51714i
$666$	−6.72056	+	11.8533i	−0.260416	+	0.459307i
$667$	29.3236	+	15.7291i	1.13542	+	0.609033i
$668$	−6.40204	+	22.1522i	−0.247702	+	0.857095i
$669$	−31.2743	+	15.8428i	−1.20913	+	0.612518i
$670$	39.7228	−	32.1156i	1.53463	−	1.24073i
$671$	−43.1789	−	14.7043i	−1.66690	−	0.567654i
$672$	−1.44263	+	3.66373i	−0.0556507	+	0.141331i
$673$	−13.6224	+	34.5956i	−0.525103	+	1.33356i	0.386423	+	0.922322i	$0.373710\pi$
$673$	−13.6224	+	34.5956i	−0.525103	+	1.33356i	−0.911527	+	0.411241i	$0.865096\pi$
$674$	−12.3606	−	4.20932i	−0.476111	−	0.162137i
$675$	−53.4474	+	43.2117i	−2.05719	+	1.66322i
$676$	1.66724	−	0.844582i	0.0641245	−	0.0324839i
$677$	1.46966	−	5.08530i	0.0564837	−	0.195444i	−0.927460	−	0.373922i	$-0.878013\pi$
$677$	1.46966	−	5.08530i	0.0564837	−	0.195444i	0.983944	+	0.178478i	$0.0571173\pi$
$678$	−2.63443	−	1.41310i	−0.101175	−	0.0542697i
$679$	−0.373168	+	0.658170i	−0.0143209	+	0.0252583i
$680$	0.436124	+	0.490497i	0.0167246	+	0.0188097i
$681$	1.81189	−	6.86932i	0.0694318	−	0.263233i
$682$	−0.944644	−	40.2850i	−0.0361723	−	1.54259i
$683$	−1.44764	−	2.55326i	−0.0553924	−	0.0976977i	0.840838	−	0.541288i	$-0.182063\pi$
$683$	−1.44764	−	2.55326i	−0.0553924	−	0.0976977i	−0.896230	+	0.443590i	$0.853705\pi$
$684$	1.81552	−	5.33124i	0.0694183	−	0.203845i
$685$	−50.9642	+	8.43980i	−1.94724	+	0.322468i
$686$	13.1883	+	3.14988i	0.503531	+	0.120263i
$687$	26.1608	−	20.1552i	0.998098	−	0.768971i
$688$	6.51803	+	4.55133i	0.248497	+	0.173518i
$689$	−1.62985	+	3.41361i	−0.0620923	+	0.130048i
$690$	35.0042	+	1.64253i	1.33259	+	0.0625301i
$691$	−9.23416	+	1.97787i	−0.351284	+	0.0752418i	−0.381676	−	0.924296i	$-0.624653\pi$
$691$	−9.23416	+	1.97787i	−0.351284	+	0.0752418i	0.0303916	+	0.999538i	$0.490325\pi$
$692$	−8.04549	−	4.07565i	−0.305844	−	0.154933i
$693$	−14.2926	+	15.3350i	−0.542933	+	0.582528i
$694$	5.71452	+	7.41726i	0.216920	+	0.281555i
$695$	−0.351419	+	0.343275i	−0.0133301	+	0.0130212i
$696$	−5.13213	+	3.76560i	−0.194533	+	0.142735i
$697$	−0.493356	−	0.130130i	−0.0186872	−	0.00492904i
$698$	24.0757	+	5.15679i	0.911279	+	0.195188i
$699$	−16.3858	−	13.2477i	−0.619767	−	0.501076i
$700$	20.4268	+	32.3886i	0.772062	+	1.22417i
$701$	38.7402	−	2.72926i	1.46320	−	0.103083i	0.683826	−	0.729645i	$-0.260315\pi$
$701$	38.7402	−	2.72926i	1.46320	−	0.103083i	0.779371	+	0.626562i	$0.215539\pi$
$702$	17.2918	−	6.80882i	0.652637	−	0.256982i
$703$	33.0820	+	21.9647i	1.24771	+	0.828415i
$704$	4.11000	−	2.59210i	0.154902	−	0.0976933i
$705$	10.7600	−	6.43860i	0.405246	−	0.242492i
$706$	−14.0854	+	6.72515i	−0.530111	+	0.253104i
$707$	46.7186	+	13.5018i	1.75703	+	0.507786i
$708$	−0.221574	+	9.44918i	−0.00832726	+	0.355122i
$709$	24.9186	−	13.3663i	0.935840	−	0.501981i	0.0673724	−	0.997728i	$-0.478538\pi$
$709$	24.9186	−	13.3663i	0.935840	−	0.501981i	0.868467	+	0.495747i	$0.165106\pi$
$710$	−0.00781962	−	0.0365077i	−0.000293465	−	0.00137011i
$711$	−6.66598	−	18.1672i	−0.249994	−	0.681325i
$712$	5.18473	+	0.610572i	0.194306	+	0.0228821i
$713$	−10.2562	+	54.0400i	−0.384096	+	2.02381i
$714$	−0.609764	−	0.115726i	−0.0228198	−	0.00433094i
$715$	47.1705	−	48.2896i	1.76408	−	1.80593i
$716$	12.6456	+	14.9120i	0.472589	+	0.557287i
$717$	0.348387	−	7.42451i	0.0130107	−	0.277273i
$718$	18.6461	−	6.34982i	0.695866	−	0.236973i
$719$	−2.38076	+	3.77492i	−0.0887875	+	0.140781i	−0.887292	−	0.461209i	$-0.847416\pi$
$719$	−2.38076	+	3.77492i	−0.0887875	+	0.140781i	0.798504	+	0.601989i	$0.205625\pi$
$720$	2.73620	−	5.10108i	0.101972	−	0.190106i
$721$	−12.5604	−	2.08003i	−0.467773	−	0.0774643i
$722$	2.38433	+	1.00403i	0.0887356	+	0.0373663i
$723$	2.06620	+	29.3284i	0.0768426	+	1.09073i
$724$	−1.41835	−	7.47333i	−0.0527126	−	0.277744i
$725$			61.9030i			2.29902i
$726$	−15.7203	+	2.98353i	−0.583435	+	0.110729i
$727$	24.5729	−	37.0103i	0.911358	−	1.37263i	−0.0165652	−	0.999863i	$-0.505273\pi$
$727$	24.5729	−	37.0103i	0.911358	−	1.37263i	0.927923	−	0.372772i	$-0.121593\pi$
$728$	−2.64066	−	10.0114i	−0.0978692	−	0.371046i
$729$	−24.2378	+	7.00478i	−0.897698	+	0.259436i
$730$	−15.6275	+	13.8951i	−0.578399	+	0.514281i
$731$	−0.513249	+	1.14315i	−0.0189832	+	0.0422808i
$732$	−9.92263	+	6.58811i	−0.366751	+	0.243503i
$733$	−18.4846	+	26.4720i	−0.682743	+	0.977766i	0.316828	+	0.948483i	$0.397382\pi$
$733$	−18.4846	+	26.4720i	−0.682743	+	0.977766i	−0.999571	+	0.0292834i	$0.990677\pi$
$734$	6.52732	+	5.53527i	0.240928	+	0.204311i
$735$	−13.0485	−	4.78780i	−0.481301	−	0.176601i
$736$	−6.22683	+	2.28477i	−0.229524	+	0.0842176i
$737$	45.4627	−	38.5531i	1.67464	−	1.42012i
$738$	0.421380	+	4.48015i	0.0155112	+	0.164917i
$739$	26.2224	−	30.9220i	0.964605	−	1.13748i	−0.0258523	−	0.999666i	$-0.508230\pi$
$739$	26.2224	−	30.9220i	0.964605	−	1.13748i	0.990458	−	0.137818i	$-0.0440088\pi$
$740$	29.8572	+	27.8278i	1.09757	+	1.02297i
$741$	−5.14632	−	16.3592i	−0.189055	−	0.600970i
$742$	−2.78730	−	2.14744i	−0.102325	−	0.0788349i
$743$	−5.75175	−	7.11418i	−0.211011	−	0.260994i	0.661104	−	0.750294i	$-0.270088\pi$
$743$	−5.75175	−	7.11418i	−0.211011	−	0.260994i	−0.872115	+	0.489300i	$0.837252\pi$
$744$	−8.48336	−	6.22451i	−0.311015	−	0.228202i
$745$	7.67746	−	1.08716i	0.281280	−	0.0398303i
$746$	6.27458	−	29.2944i	0.229729	−	1.07254i
$747$	0.380030	+	1.31497i	0.0139046	+	0.0481124i
$748$	0.522207	+	0.560291i	0.0190938	+	0.0204863i
$749$	1.62056	−	9.78582i	0.0592138	−	0.357566i
$750$	16.7061	+	34.9899i	0.610021	+	1.27765i
$751$	−14.2031	−	33.7288i	−0.518279	−	1.23078i	−0.945200	−	0.326493i	$-0.894133\pi$
$751$	−14.2031	−	33.7288i	−0.518279	−	1.23078i	0.426921	−	0.904289i	$-0.359598\pi$
$752$	−1.40403	+	1.91355i	−0.0511998	+	0.0697800i
$753$	−10.2880	+	5.83306i	−0.374916	+	0.212569i
$754$	5.02280	−	15.9665i	0.182920	−	0.581467i
$755$	37.9468	−	26.4971i	1.38103	−	0.964326i
$756$	2.82419	+	17.0541i	0.102715	+	0.620250i
$757$	−23.5601	+	30.5802i	−0.856307	+	1.11146i	0.136370	+	0.990658i	$0.456456\pi$
$757$	−23.5601	+	30.5802i	−0.856307	+	1.11146i	−0.992677	+	0.120800i	$0.961454\pi$
$758$	2.79450	+	23.7298i	0.101501	+	0.861903i
$759$	40.8814	+	0.958628i	1.48390	+	0.0347960i
$760$	−14.2688	−	8.99905i	−0.517584	−	0.326430i
$761$	8.09920	+	18.0391i	0.293596	+	0.653918i	0.998463	−	0.0554215i	$-0.0176502\pi$
$761$	8.09920	+	18.0391i	0.293596	+	0.653918i	−0.704867	+	0.709339i	$0.748994\pi$
$762$	−6.28684	−	2.82266i	−0.227748	−	0.102254i
$763$	18.8583	+	25.7020i	0.682717	+	0.930473i
$764$	9.59917	−	16.0419i	0.347286	−	0.580375i
$765$	0.870371	+	0.273804i	0.0314683	+	0.00989940i
$766$	−18.7425	−	7.38004i	−0.677193	−	0.266652i
$767$	−14.2289	−	20.3774i	−0.513776	−	0.735785i
$768$

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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366380 - 0.930465i) q^{2} +(0.0594714 + 1.26740i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(3.62229 + 2.05376i) q^{5} +(1.15749 - 0.519687i) q^{6} +(-2.31918 - 2.06209i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.38404 - 0.130176i) q^{9} +O(q^{10})\)	\(q+(-0.366380 - 0.930465i) q^{2} +(0.0594714 + 1.26740i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(3.62229 + 2.05376i) q^{5} +(1.15749 - 0.519687i) q^{6} +(-2.31918 - 2.06209i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.38404 - 0.130176i) q^{9} +(0.583814 - 4.12287i) q^{10} +(0.568300 - 4.82578i) q^{11} +(-0.907631 - 0.886597i) q^{12} +(3.30337 + 0.467769i) q^{13} +(-1.06900 + 2.91342i) q^{14} +(-2.38752 + 4.71305i) q^{15} +(0.0702762 - 0.997528i) q^{16} +(0.156542 - 0.0184350i) q^{17} +(-0.628210 - 1.24011i) q^{18} +(-3.73375 + 1.57227i) q^{19} +(-4.05009 + 0.967320i) q^{20} +(2.47557 - 3.06197i) q^{21} +(-4.69843 + 1.23928i) q^{22} +(6.62547 - 0.310893i) q^{23} +(-0.492410 + 1.16935i) q^{24} +(6.33572 + 10.5881i) q^{25} +(-0.775045 - 3.24505i) q^{26} +(0.780971 + 5.51520i) q^{27} +(3.10250 - 0.0727505i) q^{28} +(4.30501 + 2.57604i) q^{29} +(5.26006 + 0.494734i) q^{30} +(-1.92648 + 8.06600i) q^{31} +(-0.953913 + 0.300085i) q^{32} +(6.15000 + 0.433270i) q^{33} +(-0.0745071 - 0.138903i) q^{34} +(-4.16571 - 12.2325i) q^{35} +(-0.923716 + 1.03888i) q^{36} +(-5.42167 - 8.16581i) q^{37} +(2.83091 + 2.89807i) q^{38} +(-0.396396 + 4.21452i) q^{39} +(2.38393 + 3.41406i) q^{40} +(-3.01192 - 1.18597i) q^{41} +(-3.75605 - 1.18159i) q^{42} +(-4.08202 + 6.82176i) q^{43} +(2.87452 + 3.91768i) q^{44} +(5.28076 + 2.37095i) q^{45} +(-2.71672 - 6.05087i) q^{46} +(-2.00749 - 1.26608i) q^{47} +(1.26845 + 0.0297439i) q^{48} +(0.307684 + 2.61273i) q^{49} +(7.53057 - 9.77443i) q^{50} +(0.0326743 + 0.197306i) q^{51} +(-2.73545 + 1.91007i) q^{52} +(-0.340238 + 1.08155i) q^{53} +(4.84557 - 2.74732i) q^{54} +(11.9695 - 16.3132i) q^{55} +(-1.20438 - 2.86011i) q^{56} +(-2.21475 - 4.63866i) q^{57} +(0.819646 - 4.94948i) q^{58} +(-5.07905 - 5.44946i) q^{59} +(-1.46685 - 5.07557i) q^{60} +(1.96608 - 9.17909i) q^{61} +(8.21096 - 1.16270i) q^{62} +(-3.47827 - 2.55212i) q^{63} +(0.628713 + 0.777638i) q^{64} +(11.0051 + 8.47871i) q^{65} +(-1.85010 - 5.88110i) q^{66} +(8.97398 + 8.36400i) q^{67} +(-0.101947 + 0.120218i) q^{68} +(0.788053 + 8.37866i) q^{69} +(-9.85569 + 8.35779i) q^{70} +(0.00841757 - 0.00308860i) q^{71} +(1.30507 + 0.478861i) q^{72} +(-3.83019 - 3.24806i) q^{73} +(-5.61161 + 8.03647i) q^{74} +(-13.0426 + 8.65960i) q^{75} +(1.65937 - 3.69586i) q^{76} +(-11.2692 + 10.0199i) q^{77} +(4.06669 - 1.17528i) q^{78} +(-3.55032 - 13.4601i) q^{79} +(2.30324 - 3.46901i) q^{80} +(-2.84622 + 0.540179i) q^{81} +3.23700i q^{82} +(0.183595 + 0.967364i) q^{83} +(0.276714 + 3.92779i) q^{84} +(0.604903 + 0.254723i) q^{85} +(7.84298 + 1.29882i) q^{86} +(-3.00886 + 5.60939i) q^{87} +(2.59210 - 4.11000i) q^{88} +(4.94186 - 1.68292i) q^{89} +(0.271325 - 5.78223i) q^{90} +(-6.69651 - 7.89667i) q^{91} +(-4.63477 + 4.74473i) q^{92} +(-10.3374 - 1.96193i) q^{93} +(-0.442542 + 2.33177i) q^{94} +(-16.7538 - 1.97298i) q^{95} +(-0.437059 - 1.19115i) q^{96} +(-0.0510617 - 0.238394i) q^{97} +(2.31832 - 1.24354i) q^{98} +(0.158353 - 6.75306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38} + 24 q^{41} + 14 q^{43} - 2 q^{44} - 42 q^{45} - 402 q^{47} + 22 q^{49} + 12 q^{51} + 10 q^{52} - 10 q^{53} - 8 q^{54} - 4 q^{55} - 12 q^{56} + 16 q^{57} - 18 q^{58} - 268 q^{60} - 2 q^{61} + 4 q^{62} + 22 q^{64} + 16 q^{65} + 40 q^{66} + 6 q^{67} - 106 q^{73} + 40 q^{78} + 40 q^{79} - 2 q^{80} - 14 q^{81} - 402 q^{83} - 12 q^{84} - 100 q^{87} + 4 q^{92} - 340 q^{93} + 2 q^{96} - 64 q^{97} + 18 q^{99}+O(q^{100}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

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