LMFDB - Embedded newform 507.2.q.b.16.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.7
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.529051 - 0.0427094i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.69603 - 0.275632i) q^{4} +(0.694311 + 0.615105i) q^{5} +(0.424322 + 0.318857i) q^{6} +(0.272511 - 0.283714i) q^{7} +(1.91621 + 0.472304i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.341055 - 0.355076i) q^{10} +(0.976689 - 2.05833i) q^{11} +(1.28615 + 1.13943i) q^{12} +(-2.75005 - 2.33179i) q^{13} +(-0.156290 + 0.138460i) q^{14} +(-0.258072 - 0.890966i) q^{15} +(2.26610 + 0.756536i) q^{16} +(-1.60118 + 1.66701i) q^{17} +(-0.188214 - 0.496281i) q^{18} +(-1.92987 + 3.34263i) q^{19} +(-1.00803 - 1.23461i) q^{20} +(-0.381959 + 0.0941444i) q^{21} +(-0.604629 + 1.04725i) q^{22} +(-4.02629 - 6.97374i) q^{23} +(-1.36713 - 1.42334i) q^{24} +(-0.498971 - 4.10940i) q^{25} +(1.35533 + 1.35109i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.540387 + 0.406075i) q^{28} +(-6.52498 - 0.526751i) q^{29} +(0.0984804 + 0.482389i) q^{30} +(-0.423082 + 3.48439i) q^{31} +(-4.79784 - 2.04417i) q^{32} +(-1.92559 + 1.21767i) q^{33} +(0.918304 - 0.813546i) q^{34} +(0.363721 - 0.0293626i) q^{35} +(-0.478056 - 1.65044i) q^{36} +(-2.40244 + 1.02358i) q^{37} +(1.16376 - 1.68600i) q^{38} +(1.07805 + 3.44061i) q^{39} +(1.03993 + 1.50660i) q^{40} +(-8.81955 - 5.57715i) q^{41} +(0.206097 - 0.0334940i) q^{42} +(-3.74018 - 1.59354i) q^{43} +(-2.22383 + 3.22178i) q^{44} +(-0.258072 + 0.890966i) q^{45} +(1.83227 + 3.86143i) q^{46} +(0.285052 - 0.751620i) q^{47} +(-1.51094 - 1.85057i) q^{48} +(0.275630 + 6.83969i) q^{49} +(0.0884713 + 2.19539i) q^{50} +(2.24426 - 0.553160i) q^{51} +(4.02145 + 4.71278i) q^{52} +(-8.85701 - 2.18306i) q^{53} +(-0.106168 + 0.520046i) q^{54} +(1.94422 - 0.828353i) q^{55} +(0.656188 - 0.414948i) q^{56} +(3.41762 - 1.79371i) q^{57} +(3.42955 + 0.557357i) q^{58} +(10.8754 - 3.63075i) q^{59} +(0.192118 + 1.58224i) q^{60} +(3.85538 - 13.3103i) q^{61} +(0.372648 - 1.82535i) q^{62} +(0.373145 + 0.124574i) q^{63} +(-1.77980 - 0.934110i) q^{64} +(-0.475091 - 3.31055i) q^{65} +(1.07074 - 0.561970i) q^{66} +(-0.342708 + 0.0556955i) q^{67} +(3.17513 - 2.38595i) q^{68} +(-0.324245 + 8.04605i) q^{69} -0.193681 q^{70} +(0.144463 - 3.58480i) q^{71} +(0.394763 + 1.93368i) q^{72} +(9.66031 + 13.9954i) q^{73} +(1.31473 - 0.438921i) q^{74} +(-1.77461 + 3.73990i) q^{75} +(4.19444 - 5.13726i) q^{76} +(-0.317818 - 0.838018i) q^{77} +(-0.423398 - 1.86630i) q^{78} +(-3.22236 + 8.49666i) q^{79} +(1.10803 + 1.91916i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(4.42780 + 3.32727i) q^{82} +(3.28304 + 1.72307i) q^{83} +(0.673763 - 0.0543917i) q^{84} +(-2.13710 + 0.172525i) q^{85} +(1.91069 + 1.00281i) q^{86} +(5.23332 + 3.93258i) q^{87} +(2.84370 - 3.48290i) q^{88} +(-7.02896 - 12.1745i) q^{89} +(0.174586 - 0.460345i) q^{90} +(-1.41098 + 0.144789i) q^{91} +(4.90652 + 12.9374i) q^{92} +(2.21987 - 2.71885i) q^{93} +(-0.182908 + 0.385471i) q^{94} +(-3.39599 + 1.13375i) q^{95} +(2.96255 + 4.29200i) q^{96} +(-1.68932 - 8.27485i) q^{97} +(0.146297 - 3.63032i) q^{98} +2.27830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	−0.529051	−	0.0427094i	−0.374096	−	0.0302001i	−0.108011	−	0.994150i	$-0.534448\pi$
$2$	−0.529051	−	0.0427094i	−0.374096	−	0.0302001i	−0.266085	+	0.963950i	$0.585730\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	−1.69603	−	0.275632i	−0.848015	−	0.137816i
$5$	0.694311	+	0.615105i	0.310505	+	0.275084i	0.803954	−	0.594691i	$-0.202726\pi$
$5$	0.694311	+	0.615105i	0.310505	+	0.275084i	−0.493449	+	0.869775i	$0.664264\pi$
$6$	0.424322	+	0.318857i	0.173229	+	0.130173i
$7$	0.272511	−	0.283714i	0.102999	−	0.107234i	−0.667707	−	0.744424i	$-0.732724\pi$
$7$	0.272511	−	0.283714i	0.102999	−	0.107234i	0.770706	+	0.637190i	$0.219904\pi$
$8$	1.91621	+	0.472304i	0.677483	+	0.166985i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−0.341055	−	0.355076i	−0.107851	−	0.112285i
$11$	0.976689	−	2.05833i	0.294483	−	0.620610i	−0.701248	−	0.712918i	$-0.747373\pi$
$11$	0.976689	−	2.05833i	0.294483	−	0.620610i	0.995730	+	0.0923082i	$0.0294245\pi$
$12$	1.28615	+	1.13943i	0.371280	+	0.328925i
$13$	−2.75005	−	2.33179i	−0.762726	−	0.646722i
$13$	−2.75005	−	2.33179i	−0.762726	−	0.646722i
$14$	−0.156290	+	0.138460i	−0.0417701	+	0.0370051i
$15$	−0.258072	−	0.890966i	−0.0666338	−	0.230047i
$16$	2.26610	+	0.756536i	0.566525	+	0.189134i
$17$	−1.60118	+	1.66701i	−0.388343	+	0.404308i	−0.886463	−	0.462800i	$-0.846845\pi$
$17$	−1.60118	+	1.66701i	−0.388343	+	0.404308i	0.498119	+	0.867109i	$0.334024\pi$
$18$	−0.188214	−	0.496281i	−0.0443626	−	0.116975i
$19$	−1.92987	+	3.34263i	−0.442742	+	0.766851i	−0.997892	−	0.0648991i	$-0.979327\pi$
$19$	−1.92987	+	3.34263i	−0.442742	+	0.766851i	0.555150	+	0.831750i	$0.312661\pi$
$20$	−1.00803	−	1.23461i	−0.225402	−	0.276067i
$21$	−0.381959	+	0.0941444i	−0.0833503	+	0.0205440i
$22$	−0.604629	+	1.04725i	−0.128907	+	0.223274i
$23$	−4.02629	−	6.97374i	−0.839539	−	1.45413i	−0.890280	−	0.455413i	$-0.849492\pi$
$23$	−4.02629	−	6.97374i	−0.839539	−	1.45413i	0.0507407	−	0.998712i	$-0.483842\pi$
$24$	−1.36713	−	1.42334i	−0.279065	−	0.290537i
$25$	−0.498971	−	4.10940i	−0.0997942	−	0.821879i
$26$	1.35533	+	1.35109i	0.265801	+	0.264970i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−0.540387	+	0.406075i	−0.102124	+	0.0767409i
$29$	−6.52498	−	0.526751i	−1.21166	−	0.0978152i	−0.541932	−	0.840423i	$-0.682307\pi$
$29$	−6.52498	−	0.526751i	−1.21166	−	0.0978152i	−0.669727	+	0.742607i	$0.733589\pi$
$30$	0.0984804	+	0.482389i	0.0179800	+	0.0880718i
$31$	−0.423082	+	3.48439i	−0.0759877	+	0.625815i	0.904110	+	0.427300i	$0.140535\pi$
$31$	−0.423082	+	3.48439i	−0.0759877	+	0.625815i	−0.980098	+	0.198516i	$0.936388\pi$
$32$	−4.79784	−	2.04417i	−0.848147	−	0.361362i
$33$	−1.92559	+	1.21767i	−0.335203	+	0.211970i
$34$	0.918304	−	0.813546i	0.157488	−	0.139522i
$35$	0.363721	−	0.0293626i	0.0614801	−	0.00496319i
$36$	−0.478056	−	1.65044i	−0.0796759	−	0.275073i
$37$	−2.40244	+	1.02358i	−0.394958	+	0.168276i	−0.580309	−	0.814397i	$-0.697068\pi$
$37$	−2.40244	+	1.02358i	−0.394958	+	0.168276i	0.185351	+	0.982672i	$0.440658\pi$
$38$	1.16376	−	1.68600i	0.188787	−	0.273505i
$39$	1.07805	+	3.44061i	0.172626	+	0.550939i
$40$	1.03993	+	1.50660i	0.164427	+	0.238214i
$41$	−8.81955	−	5.57715i	−1.37738	−	0.871004i	−0.378866	−	0.925452i	$-0.623686\pi$
$41$	−8.81955	−	5.57715i	−1.37738	−	0.871004i	−0.998517	+	0.0544475i	$0.982660\pi$
$42$	0.206097	−	0.0334940i	0.0318014	−	0.00516823i
$43$	−3.74018	−	1.59354i	−0.570372	−	0.243013i	0.0874721	−	0.996167i	$-0.472121\pi$
$43$	−3.74018	−	1.59354i	−0.570372	−	0.243013i	−0.657844	+	0.753154i	$0.728531\pi$
$44$	−2.22383	+	3.22178i	−0.335256	+	0.485702i
$45$	−0.258072	+	0.890966i	−0.0384710	+	0.132817i
$46$	1.83227	+	3.86143i	0.270153	+	0.569336i
$47$	0.285052	−	0.751620i	0.0415791	−	0.109635i	−0.912618	−	0.408812i	$-0.865943\pi$
$47$	0.285052	−	0.751620i	0.0415791	−	0.109635i	0.954197	+	0.299177i	$0.0967123\pi$
$48$	−1.51094	−	1.85057i	−0.218086	−	0.267107i
$49$	0.275630	+	6.83969i	0.0393757	+	0.977099i
$50$	0.0884713	+	2.19539i	0.0125117	+	0.310475i
$51$	2.24426	−	0.553160i	0.314259	−	0.0774579i
$52$	4.02145	+	4.71278i	0.557674	+	0.653545i
$53$	−8.85701	−	2.18306i	−1.21660	−	0.299866i	−0.421775	−	0.906700i	$-0.638593\pi$
$53$	−8.85701	−	2.18306i	−1.21660	−	0.299866i	−0.794828	+	0.606835i	$0.792439\pi$
$54$	−0.106168	+	0.520046i	−0.0144477	+	0.0707693i
$55$	1.94422	−	0.828353i	0.262158	−	0.111695i
$56$	0.656188	−	0.414948i	0.0876868	−	0.0554498i
$57$	3.41762	−	1.79371i	0.452675	−	0.237582i
$58$	3.42955	+	0.557357i	0.450322	+	0.0731845i
$59$	10.8754	−	3.63075i	1.41586	−	0.472684i	0.497167	−	0.867655i	$-0.334374\pi$
$59$	10.8754	−	3.63075i	1.41586	−	0.472684i	0.918694	+	0.394971i	$0.129245\pi$
$60$	0.192118	+	1.58224i	0.0248024	+	0.204266i
$61$	3.85538	−	13.3103i	0.493631	−	1.70421i	−0.196479	−	0.980508i	$-0.562951\pi$
$61$	3.85538	−	13.3103i	0.493631	−	1.70421i	0.690110	−	0.723704i	$-0.257562\pi$
$62$	0.372648	−	1.82535i	0.0473264	−	0.231820i
$63$	0.373145	+	0.124574i	0.0470118	+	0.0156949i
$64$	−1.77980	−	0.934110i	−0.222475	−	0.116764i
$65$	−0.475091	−	3.31055i	−0.0589278	−	0.410624i
$66$	1.07074	−	0.561970i	0.131800	−	0.0691737i
$67$	−0.342708	+	0.0556955i	−0.0418685	+	0.00680429i	−0.181309	−	0.983426i	$-0.558034\pi$
$67$	−0.342708	+	0.0556955i	−0.0418685	+	0.00680429i	0.139441	+	0.990230i	$0.455469\pi$
$68$	3.17513	−	2.38595i	0.385041	−	0.289340i
$69$	−0.324245	+	8.04605i	−0.0390345	+	0.968630i
$70$	−0.193681			−0.0231493
$71$	0.144463	−	3.58480i	0.0171446	−	0.425438i	−0.967711	−	0.252062i	$-0.918891\pi$
$71$	0.144463	−	3.58480i	0.0171446	−	0.425438i	0.984856	−	0.173376i	$-0.0554676\pi$
$72$	0.394763	+	1.93368i	0.0465232	+	0.227886i
$73$	9.66031	+	13.9954i	1.13065	+	1.63803i	0.646031	+	0.763311i	$0.276428\pi$
$73$	9.66031	+	13.9954i	1.13065	+	1.63803i	0.484622	+	0.874724i	$0.338957\pi$
$74$	1.31473	−	0.438921i	0.152834	−	0.0510235i
$75$	−1.77461	+	3.73990i	−0.204914	+	0.431847i
$76$	4.19444	−	5.13726i	0.481136	−	0.589284i
$77$	−0.317818	−	0.838018i	−0.0362187	−	0.0955010i
$78$	−0.423398	−	1.86630i	−0.0479404	−	0.211317i
$79$	−3.22236	+	8.49666i	−0.362544	+	0.955949i	0.622342	+	0.782745i	$0.286181\pi$
$79$	−3.22236	+	8.49666i	−0.362544	+	0.955949i	−0.984886	+	0.173204i	$0.944588\pi$
$80$	1.10803	+	1.91916i	0.123881	+	0.214569i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	4.42780	+	3.32727i	0.488969	+	0.367436i
$83$	3.28304	+	1.72307i	0.360360	+	0.189132i	0.635180	−	0.772364i	$-0.280926\pi$
$83$	3.28304	+	1.72307i	0.360360	+	0.189132i	−0.274820	+	0.961496i	$0.588618\pi$
$84$	0.673763	−	0.0543917i	0.0735135	−	0.00593463i
$85$	−2.13710	+	0.172525i	−0.231801	+	0.0187129i
$86$	1.91069	+	1.00281i	0.206035	+	0.108135i
$87$	5.23332	+	3.93258i	0.561071	+	0.421617i
$88$	2.84370	−	3.48290i	0.303140	−	0.371279i
$89$	−7.02896	−	12.1745i	−0.745068	−	1.29050i	−0.950163	−	0.311754i	$-0.899083\pi$
$89$	−7.02896	−	12.1745i	−0.745068	−	1.29050i	0.205094	−	0.978742i	$-0.434250\pi$
$90$	0.174586	−	0.460345i	0.0184030	−	0.0485246i
$91$	−1.41098	+	0.144789i	−0.147911	+	0.0151780i
$92$	4.90652	+	12.9374i	0.511540	+	1.34882i
$93$	2.21987	−	2.71885i	0.230190	−	0.281932i
$94$	−0.182908	+	0.385471i	−0.0188655	+	0.0397583i
$95$	−3.39599	+	1.13375i	−0.348422	+	0.116320i
$96$	2.96255	+	4.29200i	0.302364	+	0.438050i
$97$	−1.68932	−	8.27485i	−0.171525	−	0.840184i	−0.970925	−	0.239385i	$-0.923054\pi$
$97$	−1.68932	−	8.27485i	−0.171525	−	0.840184i	0.799400	−	0.600799i	$-0.205151\pi$
$98$	0.146297	−	3.63032i	0.0147782	−	0.366718i
$99$	2.27830			0.228978
$100$	−0.286410	+	7.10719i	−0.0286410	+	0.710719i
$101$	−5.74266	+	4.31533i	−0.571416	+	0.429391i	−0.846776	−	0.531950i	$-0.821459\pi$
$101$	−5.74266	+	4.31533i	−0.571416	+	0.429391i	0.275360	+	0.961341i	$0.411203\pi$
$102$	−1.21095	+	0.196799i	−0.119902	+	0.0194860i
$103$	16.2904	−	8.54984i	1.60514	−	0.842441i	0.606250	−	0.795274i	$-0.292673\pi$
$103$	16.2904	−	8.54984i	1.60514	−	0.842441i	0.998887	−	0.0471670i	$-0.0150193\pi$
$104$	−4.16836	−	5.76706i	−0.408742	−	0.565507i
$105$	−0.323107	−	0.169580i	−0.0315320	−	0.0165493i
$106$	4.59257	+	1.53323i	0.446070	+	0.148920i
$107$	1.79411	−	8.78815i	0.173444	−	0.849583i	−0.796195	−	0.605040i	$-0.793157\pi$
$107$	1.79411	−	8.78815i	0.173444	−	0.849583i	0.969639	−	0.244543i	$-0.0786378\pi$
$108$	−0.478056	+	1.65044i	−0.0460009	+	0.158814i
$109$	0.910394	+	7.49777i	0.0872000	+	0.718156i	0.969091	+	0.246703i	$0.0793473\pi$
$109$	0.910394	+	7.49777i	0.0872000	+	0.718156i	−0.881891	+	0.471453i	$0.843730\pi$
$110$	−1.06397	+	0.355205i	−0.101445	+	0.0338674i
$111$	2.57759	+	0.418898i	0.244654	+	0.0397601i
$112$	0.832177	−	0.436760i	0.0786333	−	0.0412699i
$113$	2.43829	−	1.54188i	0.229375	−	0.145048i	−0.414835	−	0.909897i	$-0.636161\pi$
$113$	2.43829	−	1.54188i	0.229375	−	0.145048i	0.644210	+	0.764849i	$0.277186\pi$
$114$	−1.88471	+	0.802998i	−0.176519	+	0.0752077i
$115$	1.49409	−	7.31853i	0.139325	−	0.682457i
$116$	10.9214	+	2.69188i	1.01402	+	0.249934i
$117$	0.927731	−	3.48415i	0.0857687	−	0.322110i
$118$	−5.90873	+	1.45637i	−0.543943	+	0.134070i
$119$	0.0366135	+	0.908555i	0.00335635	+	0.0832871i
$120$	−0.0737130	−	1.82917i	−0.00672905	−	0.166980i
$121$	3.67410	+	4.49996i	0.334009	+	0.409087i
$122$	−2.60817	+	6.87718i	−0.236133	+	0.622631i
$123$	4.47340	+	9.42750i	0.403353	+	0.850049i
$124$	1.67797	−	5.79302i	0.150686	−	0.520228i
$125$	4.81592	−	6.97707i	0.430749	−	0.624048i
$126$	−0.192092	−	0.0818429i	−0.0171129	−	0.00729114i
$127$	−13.6044	+	2.21093i	−1.20720	+	0.196188i	−0.730520	−	0.682891i	$-0.760722\pi$
$127$	−13.6044	+	2.21093i	−1.20720	+	0.196188i	−0.476675	+	0.879080i	$0.658158\pi$
$128$	9.71732	+	6.14486i	0.858898	+	0.543134i
$129$	2.30947	+	3.34584i	0.203337	+	0.294585i
$130$	0.109956	+	1.77174i	0.00964375	+	0.155392i
$131$	−3.29466	+	4.77314i	−0.287856	+	0.417031i	−0.940058	−	0.341013i	$-0.889230\pi$
$131$	−3.29466	+	4.77314i	−0.287856	+	0.417031i	0.652202	+	0.758045i	$0.273845\pi$
$132$	3.60149	−	1.53445i	0.313470	−	0.133557i
$133$	0.422440	+	1.45843i	0.0366302	+	0.126462i
$134$	0.183689	−	0.0148289i	0.0158683	−	0.00128102i
$135$	0.694311	−	0.615105i	0.0597567	−	0.0529399i
$136$	−3.85554	+	2.43809i	−0.330610	+	0.209065i
$137$	−3.44295	−	1.46690i	−0.294151	−	0.125326i	0.239850	−	0.970810i	$-0.422902\pi$
$137$	−3.44295	−	1.46690i	−0.294151	−	0.125326i	−0.534001	+	0.845484i	$0.679312\pi$
$138$	0.515184	−	4.24292i	0.0438554	−	0.361182i
$139$	2.25981	+	11.0693i	0.191675	+	0.938884i	0.955845	+	0.293870i	$0.0949433\pi$
$139$	2.25981	+	11.0693i	0.191675	+	0.938884i	−0.764171	+	0.645014i	$0.776852\pi$
$140$	−0.624975	−	0.0504532i	−0.0528200	−	0.00426407i
$141$	−0.642638	+	0.482911i	−0.0541199	+	0.0406684i
$142$	−0.229533	+	1.89037i	−0.0192620	+	0.158637i
$143$	−7.48553	+	3.38307i	−0.625972	+	0.282907i
$144$	0.287968	+	2.37163i	0.0239973	+	0.197636i
$145$	−4.20636	−	4.37928i	−0.349319	−	0.363679i
$146$	−4.51306	−	7.81686i	−0.373504	−	0.646928i
$147$	3.42262	−	5.92816i	0.282293	−	0.488946i
$148$	4.35673	−	1.07384i	0.358121	−	0.0882690i
$149$	−5.77987	−	7.07906i	−0.473506	−	0.579939i	0.481530	−	0.876429i	$-0.340081\pi$
$149$	−5.77987	−	7.07906i	−0.473506	−	0.579939i	−0.955036	+	0.296490i	$0.904184\pi$
$150$	1.09859	−	1.90281i	0.0896992	−	0.155364i
$151$	3.77792	+	9.96155i	0.307443	+	0.810660i	0.996314	+	0.0857764i	$0.0273371\pi$
$151$	3.77792	+	9.96155i	0.307443	+	0.810660i	−0.688872	+	0.724883i	$0.741894\pi$
$152$	−5.27677	+	5.49370i	−0.428003	+	0.445598i
$153$	−2.19247	−	0.731955i	−0.177251	−	0.0591750i
$154$	0.132351	+	0.456928i	0.0106651	+	0.0368203i
$155$	−2.43702	+	2.15901i	−0.195746	+	0.173416i
$156$	−0.880066	−	6.13252i	−0.0704617	−	0.490995i
$157$	−9.13253	−	8.09072i	−0.728855	−	0.645710i	0.214793	−	0.976660i	$-0.431092\pi$
$157$	−9.13253	−	8.09072i	−0.728855	−	0.645710i	−0.943648	+	0.330950i	$0.892631\pi$
$158$	2.06768	−	4.35755i	0.164496	−	0.346668i
$159$	6.31909	+	6.57887i	0.501136	+	0.521738i
$160$	−2.07381	−	4.37047i	−0.163949	−	0.345516i
$161$	−3.07575	−	0.758105i	−0.242403	−	0.0597471i
$162$	0.367679	−	0.382794i	0.0288876	−	0.0300752i
$163$	−7.33599	−	5.51264i	−0.574599	−	0.431783i	0.273309	−	0.961926i	$-0.411882\pi$
$163$	−7.33599	−	5.51264i	−0.574599	−	0.431783i	−0.847908	+	0.530143i	$0.822138\pi$
$164$	13.4210	+	11.8900i	1.04800	+	0.928449i
$165$	−2.08596	−	0.339001i	−0.162392	−	0.0263912i
$166$	−1.66330	−	1.05181i	−0.129097	−	0.0816362i
$167$	23.6502	+	1.90924i	1.83011	+	0.147742i	0.946961	−	0.321350i	$-0.104137\pi$
$167$	23.6502	+	1.90924i	1.83011	+	0.147742i	0.883150	+	0.469092i	$0.155419\pi$
$168$	−0.776379			−0.0598990
$169$	2.12552	+	12.8251i	0.163502	+	0.986543i
$170$	1.13800			0.0872810
$171$	−3.84722	−	0.310579i	−0.294204	−	0.0237506i
$172$	5.90422	+	3.73360i	0.450193	+	0.284685i
$173$	6.24062	+	1.01420i	0.474466	+	0.0771082i	0.392942	−	0.919563i	$-0.371457\pi$
$173$	6.24062	+	1.01420i	0.474466	+	0.0771082i	0.0815236	+	0.996671i	$0.474021\pi$
$174$	−2.60074	−	2.30405i	−0.197161	−	0.174670i
$175$	−1.30187	−	0.978290i	−0.0984120	−	0.0739518i
$176$	3.77048	−	3.92548i	0.284210	−	0.295894i
$177$	−11.1323	−	2.74387i	−0.836757	−	0.206242i
$178$	3.19871	+	6.74115i	0.239754	+	0.505270i
$179$	13.3103	+	13.8575i	0.994857	+	1.03576i	0.999360	+	0.0357661i	$0.0113871\pi$
$179$	13.3103	+	13.8575i	0.994857	+	1.03576i	−0.00450306	+	0.999990i	$0.501433\pi$
$180$	0.683275	−	1.43997i	0.0509283	−	0.107329i
$181$	−10.9115	−	9.66672i	−0.811043	−	0.718521i	0.151850	−	0.988403i	$-0.451477\pi$
$181$	−10.9115	−	9.66672i	−0.811043	−	0.718521i	−0.962893	+	0.269882i	$0.913015\pi$
$182$	0.752664	−	0.0163387i	0.0557912	−	0.00121110i
$183$	−10.3724	+	9.18918i	−0.766753	+	0.679284i
$184$	−4.42150	−	15.2648i	−0.325958	−	1.12534i
$185$	−2.29765	−	0.767068i	−0.168926	−	0.0563959i
$186$	−1.29055	+	1.34360i	−0.0946275	+	0.0985177i
$187$	1.86739	+	4.92390i	0.136557	+	0.360072i
$188$	−0.690626	+	1.19620i	−0.0503691	+	0.0872418i
$189$	−0.248798	−	0.304722i	−0.0180974	−	0.0221653i
$190$	1.84508	−	0.454771i	0.133856	−	0.0329925i
$191$	1.30825	−	2.26596i	0.0946618	−	0.163959i	−0.814806	−	0.579734i	$-0.803156\pi$
$191$	1.30825	−	2.26596i	0.0946618	−	0.163959i	0.909467	+	0.415775i	$0.136490\pi$
$192$	1.00502	+	1.74074i	0.0725309	+	0.125627i
$193$	−12.5255	−	13.0404i	−0.901605	−	0.938670i	0.0967899	−	0.995305i	$-0.469143\pi$
$193$	−12.5255	−	13.0404i	−0.901605	−	0.938670i	−0.998395	+	0.0566345i	$0.981963\pi$
$194$	0.540324	+	4.44997i	0.0387930	+	0.319489i
$195$	−1.36784	+	3.05197i	−0.0979528	+	0.218556i
$196$	1.41776	−	11.6763i	0.101268	−	0.834021i
$197$	−14.6446	+	11.0047i	−1.04338	+	0.784052i	−0.976892	−	0.213734i	$-0.931437\pi$
$197$	−14.6446	+	11.0047i	−1.04338	+	0.784052i	−0.0664925	+	0.997787i	$0.521181\pi$
$198$	−1.20534	−	0.0973048i	−0.0856595	−	0.00691515i
$199$	2.71281	+	13.2882i	0.192306	+	0.941977i	0.955315	+	0.295589i	$0.0955160\pi$
$199$	2.71281	+	13.2882i	0.192306	+	0.941977i	−0.763009	+	0.646388i	$0.776279\pi$
$200$	0.984750	−	8.11014i	0.0696323	−	0.573474i
$201$	0.319421	+	0.136093i	0.0225302	+	0.00959923i
$202$	3.22246	−	2.03776i	0.226732	−	0.143377i
$203$	−1.92758	+	1.70768i	−0.135289	+	0.119856i
$204$	−3.95880	+	0.319587i	−0.277171	+	0.0223756i
$205$	−2.69297	−	9.29723i	−0.188086	−	0.649346i
$206$	−8.98360	+	3.82755i	−0.625917	+	0.266678i
$207$	4.57439	−	6.62714i	0.317942	−	0.460618i
$208$	−4.46780	−	7.36458i	−0.309786	−	0.510642i
$209$	4.99535	+	7.23701i	0.345535	+	0.500594i
$210$	0.163697	+	0.103516i	0.0112962	+	0.00714328i
$211$	20.1373	−	3.27263i	1.38631	−	0.225297i	0.578954	−	0.815361i	$-0.303461\pi$
$211$	20.1373	−	3.27263i	1.38631	−	0.225297i	0.807357	+	0.590063i	$0.200897\pi$
$212$	14.4200	+	6.14380i	0.990371	+	0.421958i
$213$	−2.03805	+	2.95263i	−0.139645	+	0.202311i
$214$	−1.32452	+	4.57276i	−0.0905420	+	0.312587i
$215$	−1.61665	−	3.40702i	−0.110255	−	0.232357i
$216$	0.699834	−	1.84531i	0.0476177	−	0.125558i
$217$	0.873276	+	1.06957i	0.0592818	+	0.0726071i
$218$	−0.161420	−	4.00559i	−0.0109327	−	0.271293i
$219$	−0.684748	−	16.9919i	−0.0462710	−	1.14820i
$220$	−3.52577	+	0.869023i	−0.237707	+	0.0585895i
$221$	8.29043	−	0.850730i	0.557675	−	0.0572263i
$222$	−1.34578	−	0.331706i	−0.0903231	−	0.0222626i
$223$	2.61348	−	12.8017i	0.175012	−	0.857264i	−0.793553	−	0.608502i	$-0.791771\pi$
$223$	2.61348	−	12.8017i	0.175012	−	0.857264i	0.968564	−	0.248763i	$-0.0800239\pi$
$224$	−1.88742	+	0.804156i	−0.126109	+	0.0537299i
$225$	3.49873	−	2.21246i	0.233249	−	0.147498i
$226$	−1.35583	+	0.711597i	−0.0901888	+	0.0473347i
$227$	−25.2887	−	4.10981i	−1.67847	−	0.272778i	−0.754797	−	0.655959i	$-0.772265\pi$
$227$	−25.2887	−	4.10981i	−1.67847	−	0.272778i	−0.923673	+	0.383181i	$0.874829\pi$
$228$	−6.29079	+	2.10017i	−0.416618	+	0.139087i
$229$	−1.29897	−	10.6979i	−0.0858381	−	0.706940i	−0.970566	−	0.240833i	$-0.922579\pi$
$229$	−1.29897	−	10.6979i	−0.0858381	−	0.706940i	0.884728	−	0.466107i	$-0.154344\pi$
$230$	−1.10302	+	3.80807i	−0.0727310	+	0.251097i
$231$	−0.179275	+	0.878147i	−0.0117954	+	0.0577778i
$232$	−12.2545	−	4.09114i	−0.804545	−	0.268597i
$233$	17.6120	+	9.24351i	1.15380	+	0.605563i	0.929451	−	0.368946i	$-0.120281\pi$
$233$	17.6120	+	9.24351i	1.15380	+	0.605563i	0.224352	+	0.974508i	$0.427973\pi$
$234$	−0.639623	+	1.80367i	−0.0418135	+	0.117910i
$235$	0.660240	−	0.346521i	0.0430693	−	0.0226045i
$236$	−19.4458	+	3.16025i	−1.26581	+	0.205715i
$237$	7.26468	−	5.45905i	0.471892	−	0.354604i
$238$	0.0194334	−	0.482236i	0.00125968	−	0.0312587i
$239$	−6.13013			−0.396525			−0.198262	−	0.980149i	$-0.563530\pi$
$239$	−6.13013			−0.396525			−0.198262	+	0.980149i	$0.563530\pi$
$240$	0.0892316	−	2.21426i	0.00575988	−	0.142930i
$241$	−3.57210	−	17.4973i	−0.230099	−	1.12710i	−0.916549	−	0.399922i	$-0.869037\pi$
$241$	−3.57210	−	17.4973i	−0.230099	−	1.12710i	0.686450	−	0.727177i	$-0.259168\pi$
$242$	−1.75160	−	2.53763i	−0.112597	−	0.163125i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−10.2076	+	21.5120i	−0.653474	+	1.37717i
$245$	−4.01576	+	4.91841i	−0.256557	+	0.314226i
$246$	−1.96402	−	5.17869i	−0.125221	−	0.330181i
$247$	13.1015	−	4.69234i	0.833630	−	0.298567i
$248$	−2.45641	+	6.47701i	−0.155982	+	0.411291i
$249$	−1.85387	−	3.21099i	−0.117484	−	0.203488i
$250$	−2.84586	+	3.48554i	−0.179988	+	0.220445i
$251$	−2.20873	−	1.65975i	−0.139414	−	0.104763i	0.528747	−	0.848779i	$-0.322662\pi$
$251$	−2.20873	−	1.65975i	−0.139414	−	0.104763i	−0.668161	+	0.744017i	$0.732918\pi$
$252$	−0.598528	−	0.314132i	−0.0377037	−	0.0197884i
$253$	−18.2867	+	1.47625i	−1.14967	+	0.0928113i
$254$	7.29185	−	0.588659i	0.457531	−	0.0369358i
$255$	1.89847	+	0.996391i	0.118887	+	0.0623965i
$256$	−1.66470	−	1.25094i	−0.104044	−	0.0781838i
$257$	8.02955	−	9.83441i	0.500869	−	0.613454i	−0.460854	−	0.887476i	$-0.652457\pi$
$257$	8.02955	−	9.83441i	0.500869	−	0.613454i	0.961723	+	0.274022i	$0.0883542\pi$
$258$	−1.07893	−	1.86876i	−0.0671711	−	0.116344i
$259$	−0.364286	+	0.960542i	−0.0226356	+	0.0596852i
$260$	−0.106725	+	5.74575i	−0.00661881	+	0.356336i
$261$	−2.32132	−	6.12081i	−0.143686	−	0.378869i
$262$	1.94690	−	2.38452i	0.120280	−	0.147316i
$263$	7.26041	−	15.3010i	0.447696	−	0.943499i	−0.546655	−	0.837358i	$-0.684099\pi$
$263$	7.26041	−	15.3010i	0.447696	−	0.943499i	0.994351	−	0.106142i	$-0.0338497\pi$
$264$	−4.26496	+	1.42385i	−0.262490	+	0.0876321i
$265$	−4.80670	−	6.96371i	−0.295273	−	0.427777i
$266$	−0.161204	−	0.789627i	−0.00988403	−	0.0484152i
$267$	−0.566056	+	14.0465i	−0.0346420	+	0.859633i
$268$	0.596595			0.0364428
$269$	−0.208830	+	5.18207i	−0.0127326	+	0.315956i	0.980255	+	0.197738i	$0.0633594\pi$
$269$	−0.208830	+	5.18207i	−0.0127326	+	0.315956i	−0.992988	+	0.118219i	$0.962282\pi$
$270$	−0.393597	+	0.295769i	−0.0239535	+	0.0179999i
$271$	−10.3054	+	1.67479i	−0.626007	+	0.101736i	−0.465136	−	0.885239i	$-0.653995\pi$
$271$	−10.3054	+	1.67479i	−0.626007	+	0.101736i	−0.160871	+	0.986975i	$0.551430\pi$
$272$	−4.88959	+	2.56625i	−0.296475	+	0.155602i
$273$	1.26993	+	0.631746i	0.0768597	+	0.0382350i
$274$	1.75885	+	0.923113i	0.106256	+	0.0557673i
$275$	−8.94583	−	2.98656i	−0.539454	−	0.180096i
$276$	2.76767	−	13.5570i	0.166594	−	0.816033i
$277$	−4.54224	+	15.6816i	−0.272917	+	0.942217i	0.700591	+	0.713563i	$0.252920\pi$
$277$	−4.54224	+	15.6816i	−0.272917	+	0.942217i	−0.973508	+	0.228654i	$0.926567\pi$
$278$	−0.722792	−	5.95273i	−0.0433502	−	0.357021i
$279$	−3.32935	+	1.11150i	−0.199323	+	0.0665437i
$280$	0.710835	+	0.115522i	0.0424805	+	0.00690376i
$281$	−6.25585	+	3.28332i	−0.373193	+	0.195867i	−0.640883	−	0.767638i	$-0.721432\pi$
$281$	−6.25585	+	3.28332i	−0.373193	+	0.195867i	0.267691	+	0.963505i	$0.413740\pi$
$282$	0.360613	−	0.228038i	0.0214742	−	0.0135795i
$283$	−16.7033	+	7.11662i	−0.992909	+	0.423039i	−0.826450	−	0.563009i	$-0.809643\pi$
$283$	−16.7033	+	7.11662i	−0.992909	+	0.423039i	−0.166459	+	0.986048i	$0.553233\pi$
$284$	−1.23310	+	6.04011i	−0.0731709	+	0.358415i
$285$	3.47621	+	0.856809i	0.205913	+	0.0507530i
$286$	4.10472	−	1.47011i	0.242717	−	0.0869297i
$287$	−3.98574	+	0.982396i	−0.235271	+	0.0579890i
$288$	−0.209993	−	5.21093i	−0.0123740	−	0.307057i
$289$	0.469393	+	11.6479i	0.0276113	+	0.685168i
$290$	2.03834	+	2.49652i	0.119696	+	0.146600i
$291$	−2.99483	+	7.89671i	−0.175560	+	0.462913i
$292$	−12.5266	−	26.3992i	−0.733064	−	1.54490i
$293$	8.47333	−	29.2533i	0.495017	−	1.70900i	−0.191155	−	0.981560i	$-0.561223\pi$
$293$	8.47333	−	29.2533i	0.495017	−	1.70900i	0.686173	−	0.727439i	$-0.259289\pi$
$294$	−2.06393	+	2.99012i	−0.120371	+	0.174387i
$295$	9.78423	+	4.16867i	0.569660	+	0.242709i
$296$	−5.08702	+	0.826721i	−0.295677	+	0.0480522i
$297$	−1.92559	−	1.21767i	−0.111734	−	0.0706565i
$298$	2.75551	+	3.99204i	0.159622	+	0.231253i
$299$	−5.18880	+	28.5666i	−0.300076	+	1.65205i
$300$	4.04062	−	5.85385i	0.233285	−	0.337972i
$301$	−1.47135	+	0.626883i	−0.0848072	+	0.0361330i
$302$	−1.57326	−	5.43152i	−0.0905310	−	0.312549i
$303$	7.16003	−	0.578017i	0.411333	−	0.0332062i
$304$	−6.90209	+	6.11471i	−0.395862	+	0.350703i
$305$	10.8641	−	6.87003i	0.622076	−	0.393377i
$306$	1.12867	+	0.480881i	0.0645217	+	0.0274901i
$307$	1.04294	−	8.58938i	0.0595237	−	0.490222i	−0.932211	−	0.361916i	$-0.882123\pi$
$307$	1.04294	−	8.58938i	0.0595237	−	0.490222i	0.991735	−	0.128306i	$-0.0409540\pi$
$308$	0.308045	+	1.50890i	0.0175525	+	0.0859777i
$309$	−18.3381	−	1.48040i	−1.04322	−	0.0842170i
$310$	1.38152	−	1.03814i	0.0784649	−	0.0589626i
$311$	−1.29478	+	10.6635i	−0.0734203	+	0.604671i	0.908840	+	0.417146i	$0.136970\pi$
$311$	−1.29478	+	10.6635i	−0.0734203	+	0.604671i	−0.982260	+	0.187525i	$0.939953\pi$
$312$	0.440762	+	7.10211i	0.0249532	+	0.402078i
$313$	−0.912426	−	7.51450i	−0.0515734	−	0.424745i	−0.995513	−	0.0946263i	$-0.969834\pi$
$313$	−0.912426	−	7.51450i	−0.0515734	−	0.424745i	0.943940	−	0.330118i	$-0.107089\pi$
$314$	4.48603	+	4.67045i	0.253161	+	0.263569i
$315$	0.182452	+	0.316017i	0.0102800	+	0.0178055i
$316$	7.80717	−	13.5224i	0.439187	−	0.760695i
$317$	−11.3456	+	2.79645i	−0.637235	+	0.157064i	−0.544681	−	0.838643i	$-0.683349\pi$
$317$	−11.3456	+	2.79645i	−0.637235	+	0.157064i	−0.0925541	+	0.995708i	$0.529503\pi$
$318$	−3.06214	−	3.75044i	−0.171716	−	0.210314i
$319$	−7.45711	+	12.9161i	−0.417518	+	0.723162i
$320$	−0.661156	−	1.74333i	−0.0369597	−	0.0974549i
$321$	−6.21333	+	6.46877i	−0.346795	+	0.361051i
$322$	1.59485	+	0.532440i	0.0888777	+	0.0296717i
$323$	−2.48211	−	8.56925i	−0.138108	−	0.476806i
$324$	1.28615	−	1.13943i	0.0714529	−	0.0633017i
$325$	−8.21005	+	12.4645i	−0.455412	+	0.691408i
$326$	3.64567	+	3.22978i	0.201915	+	0.178881i
$327$	3.23785	−	6.82362i	0.179053	−	0.377347i
$328$	−14.2660	−	14.8525i	−0.787710	−	0.820093i
$329$	−0.135565	−	0.285698i	−0.00747395	−	0.0157510i
$330$	1.08910	+	0.268439i	0.0599530	+	0.0147771i
$331$	3.67077	−	3.82167i	0.201764	−	0.210058i	−0.612632	−	0.790368i	$-0.709889\pi$
$331$	3.67077	−	3.82167i	0.201764	−	0.210058i	0.814396	+	0.580310i	$0.197069\pi$
$332$	−5.09319	−	3.82729i	−0.279525	−	0.210050i
$333$	−1.95466	−	1.73168i	−0.107115	−	0.0948955i
$334$	−12.4306	−	2.02018i	−0.680175	−	0.110539i
$335$	−0.272205	−	0.172132i	−0.0148721	−	0.00940456i
$336$	−0.936781	−	0.0756248i	−0.0511056	−	0.00412567i
$337$	17.3646			0.945911			0.472955	−	0.881086i	$-0.343187\pi$
$337$	17.3646			0.945911			0.472955	+	0.881086i	$0.343187\pi$
$338$	−0.576760	−	6.87589i	−0.0313716	−	0.373999i
$339$	−2.88490			−0.156686
$340$	3.67214	+	0.296446i	0.199150	+	0.0160770i
$341$	6.75881	+	4.27401i	0.366010	+	0.231451i
$342$	2.02211	+	0.328625i	0.109343	+	0.0177700i
$343$	4.07683	+	3.61175i	0.220128	+	0.195016i
$344$	−6.41434	−	4.82007i	−0.345838	−	0.259881i
$345$	−5.17430	+	5.38701i	−0.278575	+	0.290027i
$346$	−3.25829	−	0.803097i	−0.175167	−	0.0431748i
$347$	−0.475588	−	1.00228i	−0.0255309	−	0.0538052i	0.890284	−	0.455405i	$-0.150506\pi$
$347$	−0.475588	−	1.00228i	−0.0255309	−	0.0538052i	−0.915815	+	0.401600i	$0.868454\pi$
$348$	−7.79192	−	8.11225i	−0.417691	−	0.434862i
$349$	2.12268	−	4.47345i	0.113624	−	0.239458i	−0.838670	−	0.544641i	$-0.816666\pi$
$349$	2.12268	−	4.47345i	0.113624	−	0.239458i	0.952294	+	0.305182i	$0.0987174\pi$
$350$	0.646973	+	0.573168i	0.0345821	+	0.0306371i
$351$	−2.64627	+	2.44893i	−0.141247	+	0.130714i
$352$	−8.89358	+	7.87902i	−0.474029	+	0.419953i
$353$	0.207113	+	0.715036i	0.0110235	+	0.0380576i	0.965841	−	0.259134i	$-0.0834372\pi$
$353$	0.207113	+	0.715036i	0.0110235	+	0.0380576i	−0.954818	+	0.297192i	$0.903950\pi$
$354$	5.77238	+	1.92710i	0.306799	+	0.102424i
$355$	2.30533	−	2.40011i	0.122354	−	0.127384i
$356$	8.56564	+	22.5857i	0.453978	+	1.19704i
$357$	0.454646	−	0.787470i	0.0240624	−	0.0416773i
$358$	−6.44998	−	7.89979i	−0.340892	−	0.417517i
$359$	15.1720	−	3.73956i	0.800747	−	0.197366i	0.182351	−	0.983233i	$-0.441629\pi$
$359$	15.1720	−	3.73956i	0.800747	−	0.197366i	0.618396	+	0.785867i	$0.287783\pi$
$360$	−0.915327	+	1.58539i	−0.0482420	+	0.0835575i
$361$	2.05123	+	3.55284i	0.107960	+	0.186992i
$362$	5.35987	+	5.58021i	0.281708	+	0.293289i
$363$	−0.700241	−	5.76700i	−0.0367531	−	0.302689i
$364$	2.43297	+	0.143344i	0.127522	+	0.00751327i
$365$	−1.90138	+	15.6592i	−0.0995226	+	0.819642i
$366$	5.88002	−	4.41855i	0.307353	−	0.230961i
$367$	23.7977	+	1.92115i	1.24223	+	0.100283i	0.684048	−	0.729437i	$-0.260218\pi$
$367$	23.7977	+	1.92115i	1.24223	+	0.100283i	0.558180	+	0.829720i	$0.311500\pi$
$368$	−3.84810	−	18.8492i	−0.200596	−	0.982584i
$369$	1.25780	−	10.3589i	0.0654784	−	0.539263i
$370$	1.18281	+	0.503949i	0.0614915	+	0.0261991i
$371$	−3.03299	+	1.91795i	−0.157465	+	0.0995750i
$372$	−4.51437	+	3.99938i	−0.234059	+	0.207358i
$373$	15.1613	−	1.22395i	0.785025	−	0.0633737i	0.318547	−	0.947907i	$-0.396805\pi$
$373$	15.1613	−	1.22395i	0.785025	−	0.0633737i	0.466477	+	0.884533i	$0.345523\pi$
$374$	−0.777648	−	2.68475i	−0.0402112	−	0.138825i
$375$	−7.79938	+	3.32300i	−0.402758	+	0.171599i
$376$	0.901213	−	1.30563i	0.0464765	−	0.0673328i
$377$	16.7157	+	16.6635i	0.860904	+	0.858212i
$378$	0.118612	+	0.171840i	0.00610076	+	0.00883847i
$379$	24.7832	+	15.6719i	1.27303	+	0.805013i	0.988141	−	0.153548i	$-0.0490700\pi$
$379$	24.7832	+	15.6719i	1.27303	+	0.805013i	0.284886	+	0.958562i	$0.408044\pi$
$380$	6.07220	−	0.986829i	0.311497	−	0.0506233i
$381$	12.6800	+	5.40243i	0.649614	+	0.276775i
$382$	−0.788911	+	1.14293i	−0.0403642	+	0.0584776i
$383$	4.41332	−	15.2365i	0.225510	−	0.778551i	−0.765345	−	0.643620i	$-0.777432\pi$
$383$	4.41332	−	15.2365i	0.225510	−	0.778551i	0.990855	−	0.134931i	$-0.0430811\pi$
$384$	−4.92876	−	10.3871i	−0.251520	−	0.530067i
$385$	0.294805	−	0.777336i	0.0150246	−	0.0396167i
$386$	6.06968	+	7.43401i	0.308939	+	0.378381i
$387$	−0.163701	−	4.06221i	−0.00832140	−	0.206494i
$388$	0.584331	+	14.5000i	0.0296649	+	0.736127i
$389$	−0.260707	+	0.0642586i	−0.0132184	+	0.00325804i	−0.245919	−	0.969290i	$-0.579090\pi$
$389$	−0.260707	+	0.0642586i	−0.0132184	+	0.00325804i	0.232701	+	0.972548i	$0.425244\pi$
$390$	0.854003	−	1.55623i	0.0432441	−	0.0788027i
$391$	18.0721	+	4.45437i	0.913944	+	0.225267i
$392$	−2.70225	+	13.2365i	−0.136484	+	0.668544i
$393$	5.33570	−	2.27333i	0.269150	−	0.114674i
$394$	8.21775	−	5.19659i	0.414004	−	0.261800i
$395$	−7.46366	+	3.91723i	−0.375538	+	0.197097i
$396$	−3.86406	−	0.627971i	−0.194176	−	0.0315567i
$397$	33.3316	−	11.1277i	1.67287	−	0.558485i	0.687094	−	0.726569i	$-0.258886\pi$
$397$	33.3316	−	11.1277i	1.67287	−	0.558485i	0.985773	+	0.168084i	$0.0537580\pi$
$398$	−0.867683	−	7.14601i	−0.0434930	−	0.358197i
$399$	0.422440	−	1.45843i	0.0211484	−	0.0730129i
$400$	1.97819	−	9.68979i	0.0989093	−	0.484490i
$401$	5.47357	+	1.82735i	0.273337	+	0.0912533i	0.450032	−	0.893012i	$-0.351412\pi$
$401$	5.47357	+	1.82735i	0.273337	+	0.0912533i	−0.176695	+	0.984266i	$0.556541\pi$
$402$	−0.163178	−	0.0856422i	−0.00813856	−	0.00427145i
$403$	9.28836	−	8.59571i	0.462686	−	0.428183i
$404$	10.9292	−	5.73606i	0.543746	−	0.285380i
$405$	−0.915577	+	0.148796i	−0.0454954	+	0.00739372i
$406$	1.09272	−	0.821126i	0.0542308	−	0.0407518i
$407$	−0.239564	+	5.94473i	−0.0118748	+	0.294669i
$408$	4.56174			0.225840
$409$	−1.40072	+	34.7584i	−0.0692610	+	1.71869i	0.475174	+	0.879892i	$0.342385\pi$
$409$	−1.40072	+	34.7584i	−0.0692610	+	1.71869i	−0.544436	+	0.838803i	$0.683256\pi$
$410$	1.02764	+	5.03373i	0.0507516	+	0.248598i
$411$	2.12594	+	3.07995i	0.104865	+	0.151923i
$412$	−29.9855	+	10.0106i	−1.47728	+	0.493189i
$413$	1.93358	−	4.07493i	0.0951452	−	0.200514i
$414$	−2.70313	+	3.31073i	−0.132851	+	0.162713i
$415$	1.21958	+	3.21576i	0.0598667	+	0.157855i
$416$	8.42772	+	16.8091i	0.413203	+	0.824135i
$417$	4.00618	−	10.5634i	0.196184	−	0.517294i
$418$	−2.33371	−	4.04210i	−0.114145	−	0.197705i
$419$	−7.08485	+	8.67737i	−0.346118	+	0.423917i	−0.918100	−	0.396349i	$-0.870277\pi$
$419$	−7.08485	+	8.67737i	−0.346118	+	0.423917i	0.571982	+	0.820266i	$0.306175\pi$
$420$	0.501257	+	0.376670i	0.0244588	+	0.0183796i
$421$	9.22890	+	4.84370i	0.449789	+	0.236068i	0.674378	−	0.738386i	$-0.264412\pi$
$421$	9.22890	+	4.84370i	0.449789	+	0.236068i	−0.224589	+	0.974454i	$0.572104\pi$
$422$	−10.7935	+	0.871337i	−0.525417	+	0.0424160i
$423$	0.801251	−	0.0646836i	0.0389581	−	0.00314503i
$424$	−15.9408	−	8.36640i	−0.774156	−	0.406308i
$425$	7.64933	+	5.74810i	0.371047	+	0.278824i
$426$	1.20434	−	1.47505i	0.0583504	−	0.0714663i
$427$	−2.72569	−	4.72103i	−0.131905	−	0.228467i
$428$	−5.46516	+	14.4105i	−0.264169	+	0.696555i
$429$	8.13483	+	1.14142i	0.392753	+	0.0551084i
$430$	0.709779	+	1.87153i	0.0342286	+	0.0902533i
$431$	15.2881	−	18.7245i	0.736400	−	0.901927i	−0.261597	−	0.965177i	$-0.584249\pi$
$431$	15.2881	−	18.7245i	0.736400	−	0.901927i	0.997998	+	0.0632505i	$0.0201467\pi$
$432$	1.02417	−	2.15839i	0.0492753	−	0.103845i
$433$	−18.1408	+	6.05628i	−0.871790	+	0.291046i	−0.717145	−	0.696924i	$-0.754552\pi$
$433$	−18.1408	+	6.05628i	−0.871790	+	0.291046i	−0.154645	+	0.987970i	$0.549423\pi$
$434$	−0.416327	−	0.603154i	−0.0199843	−	0.0289523i
$435$	1.21459	+	5.94948i	0.0582354	+	0.285256i
$436$	0.522567	−	12.9674i	0.0250264	−	0.621025i
$437$	31.0808			1.48680
$438$	−0.363446	+	9.01881i	−0.0173661	+	0.430935i
$439$	−21.9784	+	16.5157i	−1.04897	+	0.788252i	−0.977869	−	0.209217i	$-0.932909\pi$
$439$	−21.9784	+	16.5157i	−1.04897	+	0.788252i	−0.0711038	+	0.997469i	$0.522652\pi$
$440$	4.11676	−	0.669039i	0.196259	−	0.0318952i
$441$	−6.06116	+	3.18114i	−0.288627	+	0.151483i
$442$	−4.42240	+	0.0960003i	−0.210352	+	0.00456627i
$443$	−12.8590	−	6.74895i	−0.610951	−	0.320652i	0.130716	−	0.991420i	$-0.458272\pi$
$443$	−12.8590	−	6.74895i	−0.610951	−	0.320652i	−0.741667	+	0.670768i	$0.765965\pi$
$444$	−4.25620	−	1.42093i	−0.201990	−	0.0674343i
$445$	2.60833	−	12.7765i	0.123647	−	0.605662i
$446$	−1.92942	+	6.66113i	−0.0913606	+	0.315414i
$447$	1.10158	+	9.07229i	0.0521028	+	0.429105i
$448$	−0.750034	+	0.250398i	−0.0354358	+	0.0118302i
$449$	−5.10988	−	0.830437i	−0.241150	−	0.0391907i	0.0386347	−	0.999253i	$-0.487699\pi$
$449$	−5.10988	−	0.830437i	−0.241150	−	0.0391907i	−0.279785	+	0.960063i	$0.590263\pi$
$450$	−1.94550	+	1.02108i	−0.0917118	+	0.0481341i
$451$	−20.0936	+	12.7064i	−0.946169	+	0.598321i
$452$	−4.56041	+	1.94301i	−0.214504	+	0.0913914i
$453$	2.13105	−	10.4386i	0.100125	−	0.490447i
$454$	13.2035	+	3.25437i	0.619671	+	0.152735i
$455$	−1.06872	−	0.767372i	−0.0501023	−	0.0359750i
$456$	7.39607	−	1.82297i	0.346353	−	0.0853682i
$457$	−0.927638	−	23.0191i	−0.0433931	−	1.07679i	−0.863427	−	0.504474i	$-0.831687\pi$
$457$	−0.927638	−	23.0191i	−0.0433931	−	1.07679i	0.820034	−	0.572315i	$-0.193954\pi$
$458$	0.230316	+	5.71524i	0.0107620	+	0.267056i
$459$	1.46185	+	1.79044i	0.0682333	+	0.0835707i
$460$	−4.55124	+	12.0006i	−0.212203	+	0.559532i
$461$	−4.00053	−	8.43094i	−0.186323	−	0.392668i	0.788698	−	0.614781i	$-0.210756\pi$
$461$	−4.00053	−	8.43094i	−0.186323	−	0.392668i	−0.975021	+	0.222113i	$0.928705\pi$
$462$	0.132351	−	0.456928i	0.00615752	−	0.0212582i
$463$	6.59891	−	9.56018i	0.306678	−	0.444299i	−0.639095	−	0.769127i	$-0.720691\pi$
$463$	6.59891	−	9.56018i	0.306678	−	0.444299i	0.945773	+	0.324828i	$0.105307\pi$
$464$	−14.3878	−	6.13005i	−0.667935	−	0.284581i
$465$	3.21366	−	0.522271i	0.149030	−	0.0242197i
$466$	−8.92289	−	5.64249i	−0.413345	−	0.261383i
$467$	−3.03555	−	4.39776i	−0.140469	−	0.203504i	0.746435	−	0.665458i	$-0.231764\pi$
$467$	−3.03555	−	4.39776i	−0.140469	−	0.203504i	−0.886904	+	0.461954i	$0.847148\pi$
$468$	−2.53380	+	5.65351i	−0.117125	+	0.261334i
$469$	−0.0775901	+	0.112409i	−0.00358278	+	0.00519055i
$470$	−0.364100	+	0.155129i	−0.0167947	+	0.00715555i
$471$	3.39451	+	11.7192i	0.156411	+	0.539993i
$472$	22.5545	−	1.82078i	1.03815	−	0.0838084i
$473$	−6.93303	+	6.14212i	−0.318781	+	0.282415i
$474$	−4.07654	+	2.57785i	−0.187242	+	0.118405i
$475$	14.6991	+	6.26271i	0.674442	+	0.287353i
$476$	0.188329	−	1.55103i	0.00863204	−	0.0710912i
$477$	−1.82465	−	8.93773i	−0.0835450	−	0.409230i
$478$	3.24315	+	0.261814i	0.148338	+	0.0119751i
$479$	18.8487	−	14.1639i	0.861221	−	0.647166i	−0.0755370	−	0.997143i	$-0.524067\pi$
$479$	18.8487	−	14.1639i	0.861221	−	0.647166i	0.936758	+	0.349977i	$0.113811\pi$
$480$	−0.583100	+	4.80226i	−0.0266147	+	0.219192i
$481$	8.99359	+	2.78707i	0.410073	+	0.127080i
$482$	1.14252	+	9.40952i	0.0520405	+	0.428592i
$483$	2.19442	+	2.28463i	0.0998494	+	0.103954i
$484$	−4.99105	−	8.64476i	−0.226866	−	0.392944i
$485$	3.91699	−	6.78443i	0.177861	−	0.308065i
$486$	−0.515349	+	0.127022i	−0.0233767	+	0.00576184i
$487$	16.3928	+	20.0776i	0.742829	+	0.909801i	0.998374	−	0.0569963i	$-0.0181523\pi$
$487$	16.3928	+	20.0776i	0.742829	+	0.909801i	−0.255545	+	0.966797i	$0.582255\pi$
$488$	13.6742	−	23.6845i	0.619004	−	1.07215i
$489$	3.25399	+	8.58006i	0.147150	+	0.388004i
$490$	2.33461	−	2.43058i	0.105467	−	0.109802i
$491$	13.5626	+	4.52786i	0.612071	+	0.204339i	0.605769	−	0.795641i	$-0.292866\pi$
$491$	13.5626	+	4.52786i	0.612071	+	0.204339i	0.00630227	+	0.999980i	$0.497994\pi$
$492$	−4.98851	−	17.2223i	−0.224899	−	0.776442i
$493$	11.3258	−	10.0338i	0.510087	−	0.451898i
$494$	−7.13178	+	1.92293i	−0.320874	+	0.0865167i
$495$	1.58185	+	1.40139i	0.0710987	+	0.0629880i
$496$	−3.59481	+	7.57591i	−0.161412	+	0.340168i
$497$	−0.977690	−	1.01788i	−0.0438554	−	0.0456583i
$498$	0.843651	+	1.77796i	0.0378049	+	0.0796722i
$499$	−16.1381	−	3.97770i	−0.722443	−	0.178066i	−0.139084	−	0.990281i	$-0.544416\pi$
$499$	−16.1381	−	3.97770i	−0.722443	−	0.178066i	−0.583359	+	0.812215i	$0.698262\pi$
$500$	−10.0911	+	10.5059i	−0.451286	+	0.469838i
$501$	−18.9685	−	14.2539i	−0.847451	−	0.636818i
$502$	1.09765	+	0.972429i	0.0489903	+	0.0434016i
$503$	36.3331	+	5.90471i	1.62001	+	0.263278i	0.901674	−	0.432415i	$-0.142339\pi$
$503$	36.3331	+	5.90471i	1.62001	+	0.263278i	0.718339	+	0.695693i	$0.244903\pi$
$504$	0.656188	+	0.414948i	0.0292289	+	0.0184833i
$505$	−6.64157	−	0.536163i	−0.295546	−	0.0238589i
$506$	9.73764			0.432891
$507$	5.05808	−	11.9756i	0.224637	−	0.531857i
$508$	23.6829			1.05076
$509$	−38.5241	−	3.10999i	−1.70755	−	0.137848i	−0.812250	−	0.583309i	$-0.801758\pi$
$509$	−38.5241	−	3.10999i	−1.70755	−	0.137848i	−0.895301	+	0.445461i	$0.853040\pi$
$510$	−0.961830	−	0.608225i	−0.0425906	−	0.0269326i
$511$	6.60322	+	1.07313i	0.292109	+	0.0474724i
$512$	−16.3843	−	14.5152i	−0.724089	−	0.641487i
$513$	3.08563	+	2.31870i	0.136234	+	0.102373i
$514$	−4.66806	+	4.85997i	−0.205899	+	0.214364i
$515$	16.5696	+	4.08405i	0.730145	+	0.179965i
$516$	−2.99471	−	6.31121i	−0.131835	−	0.277836i
$517$	−1.26867	−	1.32083i	−0.0557962	−	0.0580900i
$518$	0.233750	−	0.492618i	0.0102704	−	0.0216444i
$519$	−4.73246	−	4.19259i	−0.207732	−	0.184034i
$520$	0.653213	−	6.56811i	0.0286453	−	0.288031i
$521$	−29.3549	+	26.0061i	−1.28606	+	1.13935i	−0.303615	+	0.952795i	$0.598194\pi$
$521$	−29.3549	+	26.0061i	−1.28606	+	1.13935i	−0.982445	+	0.186555i	$0.940268\pi$
$522$	0.966680	+	3.33737i	0.0423104	+	0.146073i
$523$	15.5337	+	5.18590i	0.679240	+	0.226764i	0.635294	−	0.772270i	$-0.280879\pi$
$523$	15.5337	+	5.18590i	0.679240	+	0.226764i	0.0439457	+	0.999034i	$0.486007\pi$
$524$	6.90347	−	7.18728i	0.301580	−	0.313978i
$525$	0.577463	+	1.52265i	0.0252026	+	0.0664537i
$526$	−4.49463	+	7.78492i	−0.195975	+	0.339439i
$527$	−5.13107	−	6.28442i	−0.223513	−	0.273754i
$528$	−5.28480	+	1.30259i	−0.229992	+	0.0566878i
$529$	−20.9220	+	36.2380i	−0.909653	+	1.57557i
$530$	2.24558	+	3.88945i	0.0975416	+	0.168947i
$531$	7.94242	+	8.26894i	0.344672	+	0.358841i
$532$	−0.314481	−	2.58998i	−0.0136345	−	0.112290i
$533$	11.2495	+	35.9028i	0.487268	+	1.55512i
$534$	0.899391	−	7.40715i	0.0389205	−	0.320539i
$535$	6.65131	−	4.99814i	0.287561	−	0.216088i
$536$	−0.683007	−	0.0551380i	−0.0295014	−	0.00238160i
$537$	−3.84337	−	18.8261i	−0.165854	−	0.812406i
$538$	0.331805	−	2.73266i	0.0143051	−	0.117813i
$539$	14.3475	+	6.11292i	0.617993	+	0.263302i
$540$	−1.34711	+	0.851863i	−0.0579705	+	0.0366583i
$541$	10.6677	−	9.45074i	0.458639	−	0.406319i	−0.401915	−	0.915677i	$-0.631655\pi$
$541$	10.6677	−	9.45074i	0.458639	−	0.406319i	0.860555	+	0.509358i	$0.170117\pi$
$542$	5.52361	−	0.445911i	0.237259	−	0.0191535i
$543$	4.05573	+	14.0020i	0.174048	+	0.600884i
$544$	11.0899	−	4.72495i	0.475474	−	0.202580i
$545$	−3.97982	+	5.76577i	−0.170477	+	0.246978i
$546$	−0.644877	−	0.388464i	−0.0275982	−	0.0166247i
$547$	−20.0217	−	29.0064i	−0.856064	−	1.24022i	−0.969109	−	0.246633i	$-0.920676\pi$
$547$	−20.0217	−	29.0064i	−0.856064	−	1.24022i	0.113045	−	0.993590i	$-0.463940\pi$
$548$	5.43502	+	3.43690i	0.232172	+	0.146817i
$549$	13.6780	−	2.22289i	0.583762	−	0.0948706i
$550$	4.60525	+	1.96211i	0.196368	+	0.0836648i
$551$	14.3531	−	20.7940i	0.611461	−	0.885855i
$552$	−4.42150	+	15.2648i	−0.188192	+	0.649713i
$553$	1.53249	+	3.22966i	0.0651683	+	0.137339i
$554$	3.07283	−	8.10239i	0.130552	−	0.344237i
$555$	1.53198	+	1.87633i	0.0650288	+	0.0796459i
$556$	−0.781660	−	19.3967i	−0.0331498	−	0.822603i
$557$	0.0720331	+	1.78748i	0.00305214	+	0.0757381i	0.999997	−	0.00236797i	$-0.000753750\pi$
$557$	0.0720331	+	1.78748i	0.00305214	+	0.0757381i	−0.996945	+	0.0781060i	$0.975113\pi$
$558$	1.80887	−	0.445846i	0.0765754	−	0.0188742i
$559$	6.56987	+	13.1036i	0.277876	+	0.554224i
$560$	0.846443	+	0.208629i	0.0357687	+	0.00881620i
$561$	1.05336	−	5.15969i	0.0444728	−	0.217842i
$562$	3.44990	−	1.46986i	0.145525	−	0.0620024i
$563$	15.3820	−	9.72701i	0.648275	−	0.409944i	−0.169461	−	0.985537i	$-0.554203\pi$
$563$	15.3820	−	9.72701i	0.648275	−	0.409944i	0.817737	+	0.575592i	$0.195228\pi$
$564$	1.22304	−	0.641900i	0.0514992	−	0.0270289i
$565$	2.64135	+	0.429262i	0.111123	+	0.0180592i
$566$	9.14086	−	3.05167i	0.384219	−	0.128271i
$567$	0.0474179	+	0.390522i	0.00199137	+	0.0164004i
$568$	1.96994	−	6.80101i	0.0826567	−	0.285364i
$569$	−0.914530	+	4.47967i	−0.0383391	+	0.187797i	−0.994450	−	0.105206i	$-0.966450\pi$
$569$	−0.914530	+	4.47967i	−0.0383391	+	0.187797i	0.956111	+	0.293004i	$0.0946548\pi$
$570$	−1.80250	−	0.601763i	−0.0754984	−	0.0252051i
$571$	−26.3960	−	13.8537i	−1.10464	−	0.579758i	−0.189086	−	0.981960i	$-0.560553\pi$
$571$	−26.3960	−	13.8537i	−1.10464	−	0.579758i	−0.915551	+	0.402202i	$0.868245\pi$
$572$	13.6282	−	3.67454i	0.569822	−	0.153640i
$573$	−2.31680	+	1.21595i	−0.0967857	+	0.0507971i
$574$	2.15062	−	0.349509i	0.0897650	−	0.0145882i
$575$	−26.6489	+	20.0253i	−1.11133	+	0.835113i
$576$	0.0809359	−	2.00840i	0.00337233	−	0.0836835i
$577$	−29.4049			−1.22414			−0.612072	−	0.790802i	$-0.709664\pi$
$577$	−29.4049			−1.22414			−0.612072	+	0.790802i	$0.709664\pi$
$578$	0.249141	−	6.18236i	0.0103629	−	0.257152i
$579$	3.61677	+	17.7161i	0.150308	+	0.736256i
$580$	5.92704	+	8.58679i	0.246107	+	0.356547i
$581$	1.38352	−	0.461888i	0.0573982	−	0.0191623i
$582$	1.92168	−	4.04986i	0.0796562	−	0.167872i
$583$	−13.1440	+	16.0985i	−0.544369	+	0.666731i
$584$	11.9011	+	31.3807i	0.492472	+	1.29854i
$585$	2.78725	−	1.84843i	0.115239	−	0.0764232i
$586$	−5.73222	+	15.1146i	−0.236796	+	0.624379i
$587$	−3.58123	−	6.20288i	−0.147813	−	0.256020i	0.782606	−	0.622518i	$-0.213890\pi$
$587$	−3.58123	−	6.20288i	−0.147813	−	0.256020i	−0.930419	+	0.366498i	$0.880557\pi$
$588$	−7.43885	+	9.11094i	−0.306773	+	0.375729i
$589$	−10.8305	−	8.13861i	−0.446264	−	0.335346i
$590$	−4.99832	−	2.62332i	−0.205777	−	0.108000i
$591$	18.2591	−	1.47403i	0.751079	−	0.0606334i
$592$	−6.21854	+	0.502012i	−0.255580	+	0.0206326i
$593$	−8.28266	−	4.34708i	−0.340128	−	0.178513i	0.286007	−	0.958228i	$-0.407672\pi$
$593$	−8.28266	−	4.34708i	−0.340128	−	0.178513i	−0.626135	+	0.779714i	$0.715364\pi$
$594$	0.966732	+	0.726452i	0.0396655	+	0.0298067i
$595$	−0.533436	+	0.653340i	−0.0218687	+	0.0267843i
$596$	7.85162	+	13.5994i	0.321615	+	0.557053i
$597$	4.80926	−	12.6810i	0.196830	−	0.518998i
$598$	3.96520	−	14.8916i	0.162149	−	0.608962i
$599$	0.306358	+	0.807800i	0.0125175	+	0.0330058i	0.941129	−	0.338047i	$-0.109766\pi$
$599$	0.306358	+	0.807800i	0.0125175	+	0.0330058i	−0.928612	+	0.371053i	$0.878997\pi$
$600$	−5.16689	+	6.32830i	−0.210938	+	0.258352i
$601$	4.38565	−	9.24256i	0.178894	−	0.377012i	−0.794118	−	0.607763i	$-0.792067\pi$
$601$	4.38565	−	9.24256i	0.178894	−	0.377012i	0.973013	+	0.230751i	$0.0741183\pi$
$602$	0.805193	−	0.268813i	0.0328172	−	0.0109560i
$603$	−0.197235	−	0.285744i	−0.00803201	−	0.0116364i
$604$	−3.66174	−	17.9364i	−0.148994	−	0.729822i
$605$	−0.216981	+	5.38433i	−0.00882153	+	0.218904i
$606$	−3.81271			−0.154881
$607$	0.344765	−	8.55526i	0.0139936	−	0.347247i	−0.976992	−	0.213277i	$-0.931586\pi$
$607$	0.344765	−	8.55526i	0.0139936	−	0.347247i	0.990985	−	0.133970i	$-0.0427727\pi$
$608$	16.0921	−	12.0924i	0.652620	−	0.490412i
$609$	2.54187	−	0.413093i	0.103002	−	0.0167394i
$610$	−6.04107	+	3.17060i	−0.244596	+	0.128374i
$611$	−2.53652	+	1.40231i	−0.102617	+	0.0567314i
$612$	3.51675	+	1.84573i	0.142156	+	0.0746092i
$613$	−18.0416	−	6.02317i	−0.728693	−	0.243273i	−0.0719714	−	0.997407i	$-0.522929\pi$
$613$	−18.0416	−	6.02317i	−0.728693	−	0.243273i	−0.656721	+	0.754133i	$0.728057\pi$
$614$	−0.918616	+	4.49968i	−0.0370723	+	0.181592i
$615$	−2.69297	+	9.29723i	−0.108591	+	0.374900i
$616$	−0.213208	−	1.75593i	−0.00859040	−	0.0707483i
$617$	33.6848	−	11.2456i	1.35610	−	0.452732i	0.456606	−	0.889669i	$-0.349065\pi$
$617$	33.6848	−	11.2456i	1.35610	−	0.452732i	0.899492	+	0.436937i	$0.143937\pi$
$618$	9.63854	+	1.56642i	0.387719	+	0.0630105i
$619$	−20.6398	+	10.8326i	−0.829583	+	0.435399i	−0.825370	−	0.564592i	$-0.809033\pi$
$619$	−20.6398	+	10.8326i	−0.829583	+	0.435399i	−0.00421341	+	0.999991i	$0.501341\pi$
$620$	4.72835	−	2.99003i	0.189895	−	0.120082i
$621$	−7.40821	+	3.15634i	−0.297281	+	0.126660i
$622$	1.14044	−	5.58623i	0.0457274	−	0.223987i
$623$	−5.36955	−	1.32348i	−0.215126	−	0.0530239i
$624$	−0.159971	+	8.61236i	−0.00640397	+	0.344770i
$625$	−12.4611	+	3.07138i	−0.498443	+	0.122855i
$626$	0.161780	+	4.01453i	0.00646602	+	0.160453i
$627$	−0.354083	−	8.78649i	−0.0141407	−	0.350899i
$628$	13.2590	+	16.2393i	0.529091	+	0.648019i
$629$	2.14042	−	5.64382i	0.0853440	−	0.225034i
$630$	−0.0830297	−	0.174981i	−0.00330798	−	0.00697142i
$631$	−10.9348	+	37.7512i	−0.435306	+	1.50285i	0.380640	+	0.924723i	$0.375704\pi$
$631$	−10.9348	+	37.7512i	−0.435306	+	1.50285i	−0.815946	+	0.578128i	$0.803783\pi$
$632$	−10.1877	+	14.7595i	−0.405246	+	0.587101i
$633$	−18.7690	−	7.99671i	−0.746000	−	0.317841i
$634$	6.12187	−	0.994900i	0.243130	−	0.0395125i
$635$	−10.8056	−	6.83307i	−0.428808	−	0.271162i
$636$	−8.90401	−	12.8997i	−0.353067	−	0.511506i
$637$	15.1907	−	19.4522i	0.601878	−	0.770724i
$638$	4.49683	−	6.51478i	0.178031	−	0.257923i
$639$	3.30062	−	1.40626i	0.130571	−	0.0556309i
$640$	2.96710	+	10.2436i	0.117285	+	0.404914i
$641$	−15.9426	+	1.28702i	−0.629694	+	0.0508341i	−0.391194	−	0.920308i	$-0.627938\pi$
$641$	−15.9426	+	1.28702i	−0.629694	+	0.0508341i	−0.238500	+	0.971142i	$0.576656\pi$
$642$	3.56345	−	3.15694i	0.140638	−	0.124595i
$643$	13.4202	−	8.48641i	0.529240	−	0.334671i	−0.242975	−	0.970033i	$-0.578123\pi$
$643$	13.4202	−	8.48641i	0.529240	−	0.334671i	0.772215	+	0.635361i	$0.219149\pi$
$644$	5.00761	+	2.13354i	0.197328	+	0.0840734i
$645$	−0.454558	+	3.74362i	−0.0178982	+	0.147405i
$646$	0.947177	+	4.63958i	0.0372662	+	0.182542i
$647$	−8.18695	−	0.660919i	−0.321862	−	0.0259834i	−0.0815202	−	0.996672i	$-0.525978\pi$
$647$	−8.18695	−	0.660919i	−0.321862	−	0.0259834i	−0.240342	+	0.970688i	$0.577260\pi$
$648$	−1.57775	+	1.18560i	−0.0619798	+	0.0465748i
$649$	3.14864	−	25.9313i	0.123595	−	1.01789i
$650$	4.87589	−	6.24373i	0.191248	−	0.244899i
$651$	−0.166436	−	1.37073i	−0.00652315	−	0.0537230i
$652$	10.9226	+	11.3716i	0.427762	+	0.445347i
$653$	−24.2657	−	42.0294i	−0.949589	−	1.64474i	−0.746291	−	0.665619i	$-0.768167\pi$
$653$	−24.2657	−	42.0294i	−0.949589	−	1.64474i	−0.203297	−	0.979117i	$-0.565166\pi$
$654$	−2.00442	+	3.47176i	−0.0783790	+	0.135756i
$655$	−5.22350	+	1.28748i	−0.204099	+	0.0503059i
$656$	−15.7667	−	19.3107i	−0.615586	−	0.753955i
$657$	−8.50282	+	14.7273i	−0.331727	+	0.574568i
$658$	0.0595190	+	0.156939i	0.00232029	+	0.00611810i
$659$	2.86748	−	2.98536i	0.111701	−	0.116293i	−0.663004	−	0.748616i	$-0.730719\pi$
$659$	2.86748	−	2.98536i	0.111701	−	0.116293i	0.774705	+	0.632323i	$0.217898\pi$
$660$	3.44441	+	1.14991i	0.134073	+	0.0447603i
$661$	−2.77585	−	9.58336i	−0.107968	−	0.372750i	0.888279	−	0.459305i	$-0.151901\pi$
$661$	−2.77585	−	9.58336i	−0.107968	−	0.372750i	−0.996247	+	0.0865550i	$0.972414\pi$
$662$	−2.10525	+	1.86508i	−0.0818227	+	0.0724886i
$663$	−7.46167	−	3.71192i	−0.289787	−	0.144159i
$664$	5.47718	+	4.85236i	0.212556	+	0.188308i
$665$	−0.603785	+	1.27245i	−0.0234138	+	0.0493435i
$666$	0.960158	+	0.999630i	0.0372054	+	0.0387349i
$667$	22.5980	+	47.6244i	0.875000	+	1.84402i
$668$	−39.5852	−	9.75689i	−1.53160	−	0.377505i
$669$	−9.05095	+	9.42304i	−0.349930	+	0.364316i
$670$	0.136658	+	0.102692i	0.00527958	+	0.00396735i
$671$	−23.6315	−	20.9357i	−0.912284	−	0.808214i
$672$	2.02503	+	0.329099i	0.0781171	+	0.0126953i
$673$	26.5976	+	16.8193i	1.02526	+	0.648336i	0.937565	−	0.347811i	$-0.113075\pi$
$673$	26.5976	+	16.8193i	1.02526	+	0.648336i	0.0876974	+	0.996147i	$0.472049\pi$
$674$	−9.18677	−	0.741633i	−0.353861	−	0.0285666i
$675$	−4.13958			−0.159332
$676$	−0.0699588	−	22.3375i	−0.00269072	−	0.859136i
$677$	−28.6473			−1.10101			−0.550503	−	0.834833i	$-0.685564\pi$
$677$	−28.6473			−1.10101			−0.550503	+	0.834833i	$0.685564\pi$
$678$	1.52626	+	0.123213i	0.0586157	+	0.00473195i
$679$	−2.80805	−	1.77570i	−0.107763	−	0.0681452i
$680$	−4.17662	−	0.678768i	−0.160166	−	0.0260295i
$681$	19.1772	+	16.9895i	0.734872	+	0.651040i
$682$	−3.39321	−	2.54984i	−0.129933	−	0.0976382i
$683$	12.2700	−	12.7744i	0.469499	−	0.488800i	−0.443779	−	0.896136i	$-0.646363\pi$
$683$	12.2700	−	12.7744i	0.469499	−	0.488800i	0.913278	+	0.407336i	$0.133542\pi$
$684$	6.43939	+	1.58717i	0.246216	+	0.0606868i
$685$	−1.48817	−	3.13626i	−0.0568602	−	0.119830i
$686$	−2.00259	−	2.08492i	−0.0764594	−	0.0796026i
$687$	−4.61981	+	9.73605i	−0.176257	+	0.371454i
$688$	−7.27005	−	6.44070i	−0.277168	−	0.245550i
$689$	19.2668	+	26.6562i	0.734005	+	1.01552i
$690$	2.96754	−	2.62901i	0.112972	−	0.100085i
$691$	3.34214	+	11.5384i	0.127141	+	0.438942i	0.998679	−	0.0513866i	$-0.0163641\pi$
$691$	3.34214	+	11.5384i	0.127141	+	0.438942i	−0.871538	+	0.490328i	$0.836877\pi$
$692$	−10.3047	−	3.44022i	−0.391727	−	0.130778i
$693$	0.620861	−	0.646385i	0.0235846	−	0.0245541i
$694$	0.208803	+	0.550569i	0.00792607	+	0.0208993i
$695$	−5.23976	+	9.07554i	−0.198756	+	0.344255i
$696$	8.17078	+	10.0074i	0.309713	+	0.379329i
$697$	23.4188	−	5.77222i	0.887052	−	0.218639i
$698$	−1.31406	+	2.27603i	−0.0497381	+	0.0861489i
$699$	−9.94518	−	17.2256i	−0.376161	−	0.651530i
$700$	1.93836	+	2.01804i	0.0732631	+	0.0762749i
$701$	−2.47657	−	20.3964i	−0.0935389	−	0.770362i	−0.961705	−	0.274088i	$-0.911624\pi$
$701$	−2.47657	−	20.3964i	−0.0935389	−	0.770362i	0.868166	−	0.496274i	$-0.165299\pi$
$702$	1.50460	−	1.18259i	0.0567876	−	0.0446340i
$703$	1.21493	−	10.0058i	0.0458218	−	0.377377i
$704$	−3.66101	+	2.75107i	−0.137980	+	0.103685i
$705$	−0.743231	−	0.0599998i	−0.0279917	−	0.00225972i
$706$	−0.0790345	−	0.387137i	−0.00297450	−	0.0145701i
$707$	−0.340618	+	2.80525i	−0.0128103	+	0.105502i
$708$	18.1244	+	7.72211i	0.681159	+	0.290215i
$709$	20.6663	−	13.0686i	0.776138	−	0.490800i	−0.0867285	−	0.996232i	$-0.527641\pi$
$709$	20.6663	−	13.0686i	0.776138	−	0.490800i	0.862866	+	0.505432i	$0.168667\pi$
$710$	−1.32215	+	1.17132i	−0.0496193	+	0.0439588i
$711$	−9.05772	+	0.731214i	−0.339691	+	0.0274227i
$712$	−7.71891	−	26.6488i	−0.289278	−	0.998705i
$713$	26.0027	−	11.0787i	0.973808	−	0.414901i
$714$	−0.274163	+	0.397194i	−0.0102603	+	0.0148646i
$715$	−7.27823	−	2.25549i	−0.272190	−	0.0843505i
$716$	−18.7551	−	27.1714i	−0.700910	−	1.01544i
$717$	5.18112	+	3.27634i	0.193493	+	0.122357i
$718$	−8.18648	+	1.33043i	−0.305517	+	0.0496513i
$719$	−35.0660	−	14.9402i	−1.30774	−	0.557176i	−0.378141	−	0.925748i	$-0.623437\pi$
$719$	−35.0660	−	14.9402i	−1.30774	−	0.557176i	−0.929599	+	0.368572i	$0.879847\pi$
$720$	−1.25886	+	1.82378i	−0.0469151	+	0.0679682i
$721$	2.01359	−	6.95173i	0.0749901	−	0.258896i
$722$	−0.933468	−	1.96724i	−0.0347401	−	0.0732132i
$723$	−6.33260	+	16.6977i	−0.235512	+	0.620994i
$724$	15.8417	+	19.4026i	0.588753	+	0.721091i
$725$	1.09115	+	27.0766i	0.0405242	+	1.00560i
$726$	0.124158	+	3.08095i	0.00460793	+	0.114345i
$727$	−3.22966	+	0.796041i	−0.119782	+	0.0295235i	−0.298751	−	0.954331i	$-0.596570\pi$
$727$	−3.22966	+	0.796041i	−0.119782	+	0.0295235i	0.178969	+	0.983855i	$0.442724\pi$
$728$	−2.77212	−	0.388965i	−0.102742	−	0.0144160i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	1.67472	−	8.20334i	0.0619843	−	0.303619i
$731$	8.64515	−	3.68335i	0.319752	−	0.136234i
$732$	20.1248	−	12.7261i	0.743834	−	0.470372i
$733$	1.09103	−	0.572616i	0.0402980	−	0.0211500i	−0.444454	−	0.895802i	$-0.646602\pi$
$733$	1.09103	−	0.572616i	0.0402980	−	0.0211500i	0.484752	+	0.874652i	$0.338910\pi$
$734$	−12.5081	−	2.03277i	−0.461684	−	0.0750309i
$735$	6.02280	−	2.01071i	0.222154	−	0.0741661i
$736$	5.06200	+	41.6893i	0.186588	+	1.53669i
$737$	−0.220080	+	0.759803i	−0.00810674	+	0.0279877i
$738$	−1.10786	+	5.42667i	−0.0407810	+	0.199759i
$739$	−40.8936	−	13.6523i	−1.50430	−	0.502208i	−0.559209	−	0.829027i	$-0.688895\pi$
$739$	−40.8936	−	13.6523i	−1.50430	−	0.502208i	−0.945087	+	0.326819i	$0.894023\pi$
$740$	3.68545	+	1.93427i	0.135480	+	0.0711053i
$741$	−13.5812	−	3.03639i	−0.498917	−	0.111545i
$742$	1.68652	−	0.885156i	0.0619143	−	0.0324951i
$743$	−42.9514	+	6.98029i	−1.57574	+	0.256082i	−0.884497	−	0.466545i	$-0.845499\pi$
$743$	−42.9514	+	6.98029i	−1.57574	+	0.256082i	−0.691238	+	0.722627i	$0.742934\pi$
$744$	5.53787	−	4.16144i	0.203028	−	0.152566i
$745$	0.341341	−	8.47030i	0.0125058	−	0.310328i
$746$	−8.07340			−0.295588
$747$	−0.149295	+	3.70473i	−0.00546243	+	0.135549i
$748$	−1.80997	−	8.86580i	−0.0661789	−	0.324166i
$749$	−2.00441	−	2.90388i	−0.0732394	−	0.106106i
$750$	4.26819	−	1.42493i	0.155852	−	0.0520312i
$751$	−0.0377225	+	0.0794984i	−0.00137651	+	0.00290094i	−0.904138	−	0.427242i	$-0.859485\pi$
$751$	−0.0377225	+	0.0794984i	−0.00137651	+	0.00290094i	0.902761	+	0.430142i	$0.141537\pi$
$752$	1.21458	−	1.48759i	0.0442913	−	0.0542470i
$753$	0.979717	+	2.58330i	0.0357029	+	0.0941407i
$754$	−8.13180	−	9.52975i	−0.296143	−	0.347053i
$755$	−3.50436	+	9.24023i	−0.127537	+	0.336286i
$756$	0.337977	+	0.585394i	0.0122921	+	0.0212906i
$757$	−29.9021	+	36.6234i	−1.08681	+	1.33110i	−0.147104	+	0.989121i	$0.546995\pi$
$757$	−29.9021	+	36.6234i	−1.08681	+	1.33110i	−0.939707	+	0.341981i	$0.888902\pi$
$758$	−12.4422	−	9.34973i	−0.451922	−	0.339598i
$759$	16.2447	+	8.52589i	0.589646	+	0.309470i
$760$	−7.04292	+	0.568563i	−0.255474	+	0.0206240i
$761$	−18.6204	+	1.50320i	−0.674990	+	0.0544908i	−0.413209	−	0.910636i	$-0.635592\pi$
$761$	−18.6204	+	1.50320i	−0.674990	+	0.0544908i	−0.261781	+	0.965127i	$0.584310\pi$
$762$	−6.47762	−	3.39972i	−0.234659	−	0.123159i
$763$	2.37531	+	1.78493i	0.0859922	+	0.0646189i
$764$	−2.84341	+	3.48254i	−0.102871	+	0.125994i
$765$	−1.07203	−	1.85681i	−0.0387592	−	0.0671329i
$766$	−2.98561	+	7.87242i	−0.107875	+	0.284442i
$767$	−38.3741	−	15.3745i	−1.38561	−	0.555140i
$768$	0.738403	+	1.94701i	0.0266448	+	0.0702566i

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.529051 - 0.0427094i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.69603 - 0.275632i) q^{4} +(0.694311 + 0.615105i) q^{5} +(0.424322 + 0.318857i) q^{6} +(0.272511 - 0.283714i) q^{7} +(1.91621 + 0.472304i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.341055 - 0.355076i) q^{10} +(0.976689 - 2.05833i) q^{11} +(1.28615 + 1.13943i) q^{12} +(-2.75005 - 2.33179i) q^{13} +(-0.156290 + 0.138460i) q^{14} +(-0.258072 - 0.890966i) q^{15} +(2.26610 + 0.756536i) q^{16} +(-1.60118 + 1.66701i) q^{17} +(-0.188214 - 0.496281i) q^{18} +(-1.92987 + 3.34263i) q^{19} +(-1.00803 - 1.23461i) q^{20} +(-0.381959 + 0.0941444i) q^{21} +(-0.604629 + 1.04725i) q^{22} +(-4.02629 - 6.97374i) q^{23} +(-1.36713 - 1.42334i) q^{24} +(-0.498971 - 4.10940i) q^{25} +(1.35533 + 1.35109i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.540387 + 0.406075i) q^{28} +(-6.52498 - 0.526751i) q^{29} +(0.0984804 + 0.482389i) q^{30} +(-0.423082 + 3.48439i) q^{31} +(-4.79784 - 2.04417i) q^{32} +(-1.92559 + 1.21767i) q^{33} +(0.918304 - 0.813546i) q^{34} +(0.363721 - 0.0293626i) q^{35} +(-0.478056 - 1.65044i) q^{36} +(-2.40244 + 1.02358i) q^{37} +(1.16376 - 1.68600i) q^{38} +(1.07805 + 3.44061i) q^{39} +(1.03993 + 1.50660i) q^{40} +(-8.81955 - 5.57715i) q^{41} +(0.206097 - 0.0334940i) q^{42} +(-3.74018 - 1.59354i) q^{43} +(-2.22383 + 3.22178i) q^{44} +(-0.258072 + 0.890966i) q^{45} +(1.83227 + 3.86143i) q^{46} +(0.285052 - 0.751620i) q^{47} +(-1.51094 - 1.85057i) q^{48} +(0.275630 + 6.83969i) q^{49} +(0.0884713 + 2.19539i) q^{50} +(2.24426 - 0.553160i) q^{51} +(4.02145 + 4.71278i) q^{52} +(-8.85701 - 2.18306i) q^{53} +(-0.106168 + 0.520046i) q^{54} +(1.94422 - 0.828353i) q^{55} +(0.656188 - 0.414948i) q^{56} +(3.41762 - 1.79371i) q^{57} +(3.42955 + 0.557357i) q^{58} +(10.8754 - 3.63075i) q^{59} +(0.192118 + 1.58224i) q^{60} +(3.85538 - 13.3103i) q^{61} +(0.372648 - 1.82535i) q^{62} +(0.373145 + 0.124574i) q^{63} +(-1.77980 - 0.934110i) q^{64} +(-0.475091 - 3.31055i) q^{65} +(1.07074 - 0.561970i) q^{66} +(-0.342708 + 0.0556955i) q^{67} +(3.17513 - 2.38595i) q^{68} +(-0.324245 + 8.04605i) q^{69} -0.193681 q^{70} +(0.144463 - 3.58480i) q^{71} +(0.394763 + 1.93368i) q^{72} +(9.66031 + 13.9954i) q^{73} +(1.31473 - 0.438921i) q^{74} +(-1.77461 + 3.73990i) q^{75} +(4.19444 - 5.13726i) q^{76} +(-0.317818 - 0.838018i) q^{77} +(-0.423398 - 1.86630i) q^{78} +(-3.22236 + 8.49666i) q^{79} +(1.10803 + 1.91916i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(4.42780 + 3.32727i) q^{82} +(3.28304 + 1.72307i) q^{83} +(0.673763 - 0.0543917i) q^{84} +(-2.13710 + 0.172525i) q^{85} +(1.91069 + 1.00281i) q^{86} +(5.23332 + 3.93258i) q^{87} +(2.84370 - 3.48290i) q^{88} +(-7.02896 - 12.1745i) q^{89} +(0.174586 - 0.460345i) q^{90} +(-1.41098 + 0.144789i) q^{91} +(4.90652 + 12.9374i) q^{92} +(2.21987 - 2.71885i) q^{93} +(-0.182908 + 0.385471i) q^{94} +(-3.39599 + 1.13375i) q^{95} +(2.96255 + 4.29200i) q^{96} +(-1.68932 - 8.27485i) q^{97} +(0.146297 - 3.63032i) q^{98} +2.27830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

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