LMFDB - Embedded newform 538.2.e.a.191.6

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			191.6
Character	$\chi$	$=$	538.191
Dual form			538.2.e.a.369.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.186460 - 0.982463i) q^{2} +(0.411524 - 0.00964984i) q^{3} +(-0.930465 + 0.366380i) q^{4} +(0.415669 - 1.57591i) q^{5} +(-0.0862134 - 0.402508i) q^{6} +(-0.208350 - 0.464053i) q^{7} +(0.533449 + 0.845832i) q^{8} +(-2.82744 + 0.132675i) q^{9} +(-1.62577 - 0.114536i) q^{10} +(-0.181259 - 0.203857i) q^{11} +(-0.379374 + 0.159753i) q^{12} +(0.295322 - 4.19192i) q^{13} +(-0.417066 + 0.291224i) q^{14} +(0.155851 - 0.652534i) q^{15} +(0.731531 - 0.681808i) q^{16} +(-2.44559 - 2.17449i) q^{17} +(0.657553 + 2.75312i) q^{18} +(-2.59527 - 1.72313i) q^{19} +(0.190614 + 1.61862i) q^{20} +(-0.0902193 - 0.188959i) q^{21} +(-0.166484 + 0.216091i) q^{22} +(-0.141295 - 6.02564i) q^{23} +(0.227689 + 0.342933i) q^{24} +(2.03884 + 1.15597i) q^{25} +(-4.17347 + 0.491482i) q^{26} +(-2.39414 + 0.168668i) q^{27} +(0.363883 + 0.355450i) q^{28} +(3.87775 + 6.83934i) q^{29} +(-0.670151 - 0.0314460i) q^{30} +(-4.64579 - 0.547105i) q^{31} +(-0.806252 - 0.591572i) q^{32} +(-0.0765596 - 0.0821430i) q^{33} +(-1.68035 + 2.80816i) q^{34} +(-0.817908 + 0.135448i) q^{35} +(2.58223 - 1.15937i) q^{36} +(3.47141 - 6.47173i) q^{37} +(-1.20899 + 2.87105i) q^{38} +(0.0810809 - 1.72793i) q^{39} +(1.55469 - 0.489079i) q^{40} +(-2.28854 - 0.434338i) q^{41} +(-0.168822 + 0.123870i) q^{42} +(-3.06891 + 1.74000i) q^{43} +(0.243344 + 0.123272i) q^{44} +(-0.966200 + 4.51093i) q^{45} +(-5.89362 + 1.26236i) q^{46} +(-3.54763 - 1.02527i) q^{47} +(0.294464 - 0.287640i) q^{48} +(4.47936 - 5.03782i) q^{49} +(0.755539 - 2.21862i) q^{50} +(-1.02740 - 0.871257i) q^{51} +(1.26105 + 4.00863i) q^{52} +(-2.96734 - 4.04418i) q^{53} +(0.612122 + 2.32070i) q^{54} +(-0.396603 + 0.200910i) q^{55} +(0.281367 - 0.423778i) q^{56} +(-1.08465 - 0.684064i) q^{57} +(5.99635 - 5.08500i) q^{58} +(4.59329 + 11.6652i) q^{59} +(0.0940617 + 0.664261i) q^{60} +(-6.85556 - 8.47945i) q^{61} +(0.328745 + 4.66633i) q^{62} +(0.650667 + 1.28444i) q^{63} +(-0.430864 + 0.902417i) q^{64} +(-6.48331 - 2.20785i) q^{65} +(-0.0664272 + 0.0905334i) q^{66} +(6.35855 + 2.50374i) q^{67} +(3.07223 + 1.12727i) q^{68} +(-0.116293 - 2.47834i) q^{69} +(0.285579 + 0.778309i) q^{70} +(3.21472 - 4.60385i) q^{71} +(-1.62052 - 2.32077i) q^{72} +(0.0380800 - 0.103782i) q^{73} +(-7.00551 - 2.20381i) q^{74} +(0.850186 + 0.456037i) q^{75} +(3.04613 + 0.652453i) q^{76} +(-0.0568352 + 0.126587i) q^{77} +(-1.71274 + 0.242530i) q^{78} +(11.4662 + 8.83394i) q^{79} +(-0.770389 - 1.43623i) q^{80} +(7.47073 - 0.702658i) q^{81} +2.32939i q^{82} +(0.934924 + 9.94021i) q^{83} +(0.153177 + 0.142765i) q^{84} +(-4.44335 + 2.95015i) q^{85} +(2.28171 + 2.69065i) q^{86} +(1.66179 + 2.77713i) q^{87} +(0.0757365 - 0.262062i) q^{88} +(2.53101 + 15.2837i) q^{89} +(4.61198 + 0.108146i) q^{90} +(-2.00680 + 0.736342i) q^{91} +(2.33915 + 5.55488i) q^{92} +(-1.91714 - 0.180316i) q^{93} +(-0.345800 + 3.67658i) q^{94} +(-3.79426 + 3.37365i) q^{95} +(-0.337501 - 0.235666i) q^{96} +(6.09500 - 7.53873i) q^{97} +(-5.78470 - 3.46146i) q^{98} +(0.539546 + 0.552346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

$n$	$271$
$\chi(n)$	$e\left(\frac{59}{134}\right)$

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 $

$2$	−0.186460	−	0.982463i	−0.131847	−	0.694706i
$2$	−0.186460	−	0.982463i	−0.131847	−	0.694706i
$3$	0.411524	−	0.00964984i	0.237594	−	0.00557134i	0.0955203	−	0.995427i	$-0.469549\pi$
$3$	0.411524	−	0.00964984i	0.237594	−	0.00557134i	0.142073	+	0.989856i	$0.454623\pi$
$4$	−0.930465	+	0.366380i	−0.465233	+	0.183190i
$5$	0.415669	−	1.57591i	0.185893	−	0.704766i	−0.807486	−	0.589886i	$-0.799173\pi$
$5$	0.415669	−	1.57591i	0.185893	−	0.704766i	0.993379	−	0.114880i	$-0.0366483\pi$
$6$	−0.0862134	−	0.402508i	−0.0351965	−	0.164323i
$7$	−0.208350	−	0.464053i	−0.0787490	−	0.175396i	0.868670	−	0.495391i	$-0.164975\pi$
$7$	−0.208350	−	0.464053i	−0.0787490	−	0.175396i	−0.947419	+	0.319996i	$0.896319\pi$
$8$	0.533449	+	0.845832i	0.188603	+	0.299047i
$9$	−2.82744	+	0.132675i	−0.942481	+	0.0442248i
$10$	−1.62577	−	0.114536i	−0.514115	−	0.0362196i
$11$	−0.181259	−	0.203857i	−0.0546516	−	0.0614652i	0.719356	−	0.694642i	$-0.244437\pi$
$11$	−0.181259	−	0.203857i	−0.0546516	−	0.0614652i	−0.774007	+	0.633177i	$0.781751\pi$
$12$	−0.379374	+	0.159753i	−0.109516	+	0.0461168i
$13$	0.295322	−	4.19192i	0.0819076	−	1.16263i	−0.769685	−	0.638424i	$-0.779587\pi$
$13$	0.295322	−	4.19192i	0.0819076	−	1.16263i	0.851592	−	0.524205i	$-0.175637\pi$
$14$	−0.417066	+	0.291224i	−0.111466	+	0.0778328i
$15$	0.155851	−	0.652534i	0.0402405	−	0.168484i
$16$	0.731531	−	0.681808i	0.182883	−	0.170452i
$17$	−2.44559	−	2.17449i	−0.593144	−	0.527392i	0.313335	−	0.949643i	$-0.398554\pi$
$17$	−2.44559	−	2.17449i	−0.593144	−	0.527392i	−0.906479	+	0.422251i	$0.861240\pi$
$18$	0.657553	+	2.75312i	0.154987	+	0.648916i
$19$	−2.59527	−	1.72313i	−0.595396	−	0.395312i	0.218912	−	0.975745i	$-0.429749\pi$
$19$	−2.59527	−	1.72313i	−0.595396	−	0.395312i	−0.814308	+	0.580432i	$0.802884\pi$
$20$	0.190614	+	1.61862i	0.0426226	+	0.361934i
$21$	−0.0902193	−	0.188959i	−0.0196875	−	0.0412341i
$22$	−0.166484	+	0.216091i	−0.0354946	+	0.0460708i
$23$	−0.141295	−	6.02564i	−0.0294621	−	1.25643i	−0.792416	−	0.609981i	$-0.791177\pi$
$23$	−0.141295	−	6.02564i	−0.0294621	−	1.25643i	0.762954	−	0.646453i	$-0.223748\pi$
$24$	0.227689	+	0.342933i	0.0464769	+	0.0700008i
$25$	2.03884	+	1.15597i	0.407767	+	0.231195i
$26$	−4.17347	+	0.491482i	−0.818484	+	0.0963876i
$27$	−2.39414	+	0.168668i	−0.460753	+	0.0324602i
$28$	0.363883	+	0.355450i	0.0687673	+	0.0671737i
$29$	3.87775	+	6.83934i	0.720079	+	1.27003i	0.954591	+	0.297919i	$0.0962927\pi$
$29$	3.87775	+	6.83934i	0.720079	+	1.27003i	−0.234512	+	0.972113i	$0.575349\pi$
$30$	−0.670151	−	0.0314460i	−0.122352	−	0.00574123i
$31$	−4.64579	−	0.547105i	−0.834409	−	0.0982629i	−0.311069	−	0.950387i	$-0.600687\pi$
$31$	−4.64579	−	0.547105i	−0.834409	−	0.0982629i	−0.523339	+	0.852124i	$0.675314\pi$
$32$	−0.806252	−	0.591572i	−0.142527	−	0.104576i
$33$	−0.0765596	−	0.0821430i	−0.0133273	−	0.0142993i
$34$	−1.68035	+	2.80816i	−0.288178	+	0.481596i
$35$	−0.817908	+	0.135448i	−0.138252	+	0.0228948i
$36$	2.58223	−	1.15937i	0.430371	−	0.193228i
$37$	3.47141	−	6.47173i	0.570697	−	1.06395i	−0.417197	−	0.908816i	$-0.636988\pi$
$37$	3.47141	−	6.47173i	0.570697	−	1.06395i	0.987894	−	0.155130i	$-0.0495796\pi$
$38$	−1.20899	+	2.87105i	−0.196124	+	0.465746i
$39$	0.0810809	−	1.72793i	0.0129833	−	0.276690i
$40$	1.55469	−	0.489079i	0.245818	−	0.0773302i
$41$	−2.28854	−	0.434338i	−0.357410	−	0.0678323i	0.00464463	−	0.999989i	$-0.498522\pi$
$41$	−2.28854	−	0.434338i	−0.357410	−	0.0678323i	−0.362054	+	0.932157i	$0.617925\pi$
$42$	−0.168822	+	0.123870i	−0.0260499	+	0.0191136i
$43$	−3.06891	+	1.74000i	−0.468004	+	0.265348i	−0.709040	−	0.705169i	$-0.750871\pi$
$43$	−3.06891	+	1.74000i	−0.468004	+	0.265348i	0.241035	+	0.970516i	$0.422513\pi$
$44$	0.243344	+	0.123272i	0.0366855	+	0.0185840i
$45$	−0.966200	+	4.51093i	−0.144033	+	0.672450i
$46$	−5.89362	+	1.26236i	−0.868967	+	0.186125i
$47$	−3.54763	−	1.02527i	−0.517474	−	0.149551i	0.00864378	−	0.999963i	$-0.497249\pi$
$47$	−3.54763	−	1.02527i	−0.517474	−	0.149551i	−0.526118	+	0.850411i	$0.676353\pi$
$48$	0.294464	−	0.287640i	0.0425022	−	0.0415172i
$49$	4.47936	−	5.03782i	0.639909	−	0.719689i
$50$	0.755539	−	2.21862i	0.106849	−	0.313761i
$51$	−1.02740	−	0.871257i	−0.143865	−	0.122000i
$52$	1.26105	+	4.00863i	0.174876	+	0.555898i
$53$	−2.96734	−	4.04418i	−0.407595	−	0.555511i	0.553100	−	0.833115i	$-0.313445\pi$
$53$	−2.96734	−	4.04418i	−0.407595	−	0.555511i	−0.960696	+	0.277604i	$0.910460\pi$
$54$	0.612122	+	2.32070i	0.0832992	+	0.315808i
$55$	−0.396603	+	0.200910i	−0.0534780	+	0.0270907i
$56$	0.281367	−	0.423778i	0.0375992	−	0.0566297i
$57$	−1.08465	−	0.684064i	−0.143665	−	0.0906065i
$58$	5.99635	−	5.08500i	0.787359	−	0.667694i
$59$	4.59329	+	11.6652i	0.597995	+	1.51868i	0.836742	+	0.547598i	$0.184458\pi$
$59$	4.59329	+	11.6652i	0.597995	+	1.51868i	−0.238746	+	0.971082i	$0.576736\pi$
$60$	0.0940617	+	0.664261i	0.0121433	+	0.0857558i
$61$	−6.85556	−	8.47945i	−0.877765	−	1.08568i	−0.995698	−	0.0926612i	$-0.970463\pi$
$61$	−6.85556	−	8.47945i	−0.877765	−	1.08568i	0.117933	−	0.993022i	$-0.462373\pi$
$62$	0.328745	+	4.66633i	0.0417506	+	0.592624i
$63$	0.650667	+	1.28444i	0.0819763	+	0.161824i
$64$	−0.430864	+	0.902417i	−0.0538580	+	0.112802i
$65$	−6.48331	−	2.20785i	−0.804155	−	0.273850i
$66$	−0.0664272	+	0.0905334i	−0.00817662	+	0.0111439i
$67$	6.35855	+	2.50374i	0.776821	+	0.305881i	0.721342	−	0.692579i	$-0.243525\pi$
$67$	6.35855	+	2.50374i	0.776821	+	0.305881i	0.0554789	+	0.998460i	$0.482331\pi$
$68$	3.07223	+	1.12727i	0.372563	+	0.136702i
$69$	−0.116293	−	2.47834i	−0.0140000	−	0.298356i
$70$	0.285579	+	0.778309i	0.0341333	+	0.0930257i
$71$	3.21472	−	4.60385i	0.381517	−	0.546376i	−0.582289	−	0.812982i	$-0.697843\pi$
$71$	3.21472	−	4.60385i	0.381517	−	0.546376i	0.963806	+	0.266606i	$0.0859023\pi$
$72$	−1.62052	−	2.32077i	−0.190980	−	0.273505i
$73$	0.0380800	−	0.103782i	0.00445693	−	0.0121468i	−0.936550	−	0.350533i	$-0.886000\pi$
$73$	0.0380800	−	0.103782i	0.00445693	−	0.0121468i	0.941007	+	0.338386i	$0.109881\pi$
$74$	−7.00551	−	2.20381i	−0.814374	−	0.256188i
$75$	0.850186	+	0.456037i	0.0981710	+	0.0526586i
$76$	3.04613	+	0.652453i	0.349415	+	0.0748415i
$77$	−0.0568352	+	0.126587i	−0.00647697	+	0.0144260i
$78$	−1.71274	+	0.242530i	−0.193930	+	0.0274611i
$79$	11.4662	+	8.83394i	1.29004	+	0.993896i	0.999312	+	0.0370909i	$0.0118091\pi$
$79$	11.4662	+	8.83394i	1.29004	+	0.993896i	0.290732	+	0.956805i	$0.406101\pi$
$80$	−0.770389	−	1.43623i	−0.0861321	−	0.160575i
$81$	7.47073	−	0.702658i	0.830081	−	0.0780731i
$82$			2.32939i			0.257238i
$83$	0.934924	+	9.94021i	0.102621	+	1.09108i	0.884148	+	0.467208i	$0.154740\pi$
$83$	0.934924	+	9.94021i	0.102621	+	1.09108i	−0.781526	+	0.623872i	$0.785559\pi$
$84$	0.153177	+	0.142765i	0.0167129	+	0.0155769i
$85$	−4.44335	+	2.95015i	−0.481949	+	0.319989i
$86$	2.28171	+	2.69065i	0.246044	+	0.290140i
$87$	1.66179	+	2.77713i	0.178162	+	0.297740i
$88$	0.0757365	−	0.262062i	0.00807354	−	0.0279359i
$89$	2.53101	+	15.2837i	0.268287	+	1.62007i	0.697308	+	0.716771i	$0.254381\pi$
$89$	2.53101	+	15.2837i	0.268287	+	1.62007i	−0.429021	+	0.903294i	$0.641142\pi$
$90$	4.61198	+	0.108146i	0.486145	+	0.0113996i
$91$	−2.00680	+	0.736342i	−0.210370	+	0.0771896i
$92$	2.33915	+	5.55488i	0.243873	+	0.579137i
$93$	−1.91714	−	0.180316i	−0.198798	−	0.0186979i
$94$	−0.345800	+	3.67658i	−0.0356665	+	0.379210i
$95$	−3.79426	+	3.37365i	−0.389283	+	0.346129i
$96$	−0.337501	−	0.235666i	−0.0344460	−	0.0240526i
$97$	6.09500	−	7.53873i	0.618853	−	0.765442i	−0.367511	−	0.930019i	$-0.619790\pi$
$97$	6.09500	−	7.53873i	0.618853	−	0.765442i	0.986364	+	0.164577i	$0.0526258\pi$
$98$	−5.78470	−	3.46146i	−0.584343	−	0.349660i
$99$	0.539546	+	0.552346i	0.0542264	+	0.0555129i
$100$	−2.32059	−	0.328604i	−0.232059	−	0.0328604i
$101$	−2.00775	+	3.18346i	−0.199778	+	0.316766i	−0.930760	−	0.365630i	$-0.880853\pi$
$101$	−2.00775	+	3.18346i	−0.199778	+	0.316766i	0.730982	+	0.682397i	$0.239062\pi$
$102$	−0.664407	+	1.17184i	−0.0657861	+	0.116030i
$103$	11.9544	−	3.45486i	1.17791	−	0.340417i	0.369606	−	0.929188i	$-0.379493\pi$
$103$	11.9544	−	3.45486i	1.17791	−	0.340417i	0.808300	+	0.588771i	$0.200388\pi$
$104$	3.70320	−	1.98638i	0.363128	−	0.194781i
$105$	−0.335282	+	0.0636327i	−0.0327202	+	0.00620991i
$106$	−3.41996	+	3.66938i	−0.332176	+	0.356401i
$107$	−2.14939	−	7.43729i	−0.207790	−	0.718990i	−0.994782	−	0.102027i	$-0.967467\pi$
$107$	−2.14939	−	7.43729i	−0.207790	−	0.718990i	0.786992	−	0.616963i	$-0.211637\pi$
$108$	2.16587	−	1.03411i	0.208411	−	0.0995068i
$109$	10.4719	−	8.46646i	1.00303	−	0.810939i	0.0210206	−	0.999779i	$-0.493308\pi$
$109$	10.4719	−	8.46646i	1.00303	−	0.810939i	0.982008	+	0.188840i	$0.0604726\pi$
$110$	0.271337	+	0.352186i	0.0258710	+	0.0335796i
$111$	1.36612	−	2.69677i	0.129666	−	0.255966i
$112$	−0.468810	−	0.197414i	−0.0442984	−	0.0186539i
$113$	−3.10807	−	9.12679i	−0.292383	−	0.858576i	−0.989870	−	0.141979i	$-0.954654\pi$
$113$	−3.10807	−	9.12679i	−0.292383	−	0.858576i	0.697487	−	0.716598i	$-0.254302\pi$
$114$	−0.469824	+	1.19317i	−0.0440031	+	0.111751i
$115$	−9.55457	−	2.28201i	−0.890969	−	0.212798i
$116$	−6.11390	−	4.94304i	−0.567662	−	0.458949i
$117$	−0.278846	+	11.8916i	−0.0257793	+	1.09938i
$118$	10.6042	−	6.68783i	0.976192	−	0.615665i
$119$	−0.499539	+	1.58794i	−0.0457927	+	0.145566i
$120$	0.635073	−	0.216270i	0.0579740	−	0.0197427i
$121$	1.27781	−	10.8506i	0.116164	−	0.986419i
$122$	−7.05246	+	8.31641i	−0.638499	+	0.752932i
$123$	−0.945981	−	0.156657i	−0.0852962	−	0.0141253i
$124$	4.52320	−	1.19306i	0.406195	−	0.107140i
$125$	8.36347	−	8.56188i	0.748051	−	0.765798i
$126$	1.14059	−	0.878753i	0.101612	−	0.0782855i
$127$	18.9186	+	8.49404i	1.67875	+	0.753724i	0.999809	+	0.0195311i	$0.00621735\pi$
$127$	18.9186	+	8.49404i	1.67875	+	0.753724i	0.678941	+	0.734193i	$0.262439\pi$
$128$	0.966930	+	0.255043i	0.0854653	+	0.0225428i
$129$	−1.24614	+	0.745667i	−0.109716	+	0.0656523i
$130$	−0.960254	+	6.78128i	−0.0842198	+	0.594758i
$131$	1.83515	−	0.438306i	0.160338	−	0.0382950i	−0.151346	−	0.988481i	$-0.548361\pi$
$131$	1.83515	−	0.438306i	0.160338	−	0.0382950i	0.311684	+	0.950186i	$0.399107\pi$
$132$	0.101332	+	0.0483813i	0.00881979	+	0.00421105i
$133$	−0.258896	+	1.56336i	−0.0224491	+	0.135560i
$134$	1.27422	−	6.71389i	0.110076	−	0.579992i
$135$	−0.729366	+	3.84305i	−0.0627738	+	0.330757i
$136$	0.534655	−	3.22854i	0.0458463	−	0.276845i
$137$	−12.1924	−	5.82131i	−1.04166	−	0.497348i	−0.168973	−	0.985621i	$-0.554045\pi$
$137$	−12.1924	−	5.82131i	−1.04166	−	0.497348i	−0.872691	+	0.488273i	$0.837627\pi$
$138$	−2.41319	+	0.576364i	−0.205424	+	0.0490634i
$139$	−0.153646	+	1.08504i	−0.0130321	+	0.0920321i	−0.995569	−	0.0940373i	$-0.970023\pi$
$139$	−0.153646	+	1.08504i	−0.0130321	+	0.0920321i	0.982537	+	0.186069i	$0.0595749\pi$
$140$	0.711410	−	0.425695i	0.0601251	−	0.0359778i
$141$	−1.46983	−	0.387690i	−0.123782	−	0.0326494i
$142$	−5.12252	−	2.29991i	−0.429873	−	0.193004i
$143$	−0.908082	+	0.699619i	−0.0759376	+	0.0585051i
$144$	−1.97791	+	2.02483i	−0.164825	+	0.168736i
$145$	12.3900	−	3.26806i	1.02893	−	0.271397i
$146$	−0.109062	−	0.0180610i	−0.00902606	−	0.00149474i
$147$	1.79475	−	2.11641i	0.148029	−	0.174559i
$148$	−0.858917	+	7.29358i	−0.0706026	+	0.599528i
$149$	14.0475	−	4.78380i	1.15082	−	0.391904i	0.319437	−	0.947607i	$-0.396506\pi$
$149$	14.0475	−	4.78380i	1.15082	−	0.391904i	0.831381	+	0.555703i	$0.187551\pi$
$150$	0.289513	−	0.920308i	0.0236387	−	0.0751428i
$151$	6.15447	−	3.88150i	0.500844	−	0.315872i	−0.259112	−	0.965847i	$-0.583430\pi$
$151$	6.15447	−	3.88150i	0.500844	−	0.315872i	0.759955	+	0.649975i	$0.225221\pi$
$152$	0.0730288	−	3.11436i	0.00592342	−	0.252608i
$153$	7.20328	+	5.82379i	0.582351	+	0.470825i
$154$	0.134965	+	0.0322349i	0.0108758	+	0.00259756i
$155$	−2.79330	+	7.09391i	−0.224363	+	0.569797i
$156$	0.557635	+	1.63748i	0.0446465	+	0.131103i
$157$	3.96144	+	1.66815i	0.316157	+	0.133133i	0.540419	−	0.841396i	$-0.318266\pi$
$157$	3.96144	+	1.66815i	0.316157	+	0.133133i	−0.224262	+	0.974529i	$0.571997\pi$
$158$	6.54103	−	12.9122i	0.520377	−	1.02724i
$159$	−1.26016	−	1.63564i	−0.0999370	−	0.129715i
$160$	−1.26740	+	1.02468i	−0.100196	+	0.0810079i
$161$	−2.76678	+	1.32101i	−0.218053	+	0.104110i
$162$	−2.08333	−	7.20870i	−0.163682	−	0.566369i
$163$	−5.01564	+	5.38142i	−0.392855	+	0.421506i	−0.896943	−	0.442147i	$-0.854217\pi$
$163$	−5.01564	+	5.38142i	−0.392855	+	0.421506i	0.504088	+	0.863653i	$0.331829\pi$
$164$	2.28854	−	0.434338i	0.178705	−	0.0339161i
$165$	−0.161273	+	0.0865064i	−0.0125551	+	0.00673451i
$166$	9.59156	−	2.77198i	0.744449	−	0.215147i
$167$	−3.33049	+	5.87412i	−0.257721	+	0.454553i	−0.968552	−	0.248809i	$-0.919961\pi$
$167$	−3.33049	+	5.87412i	−0.257721	+	0.454553i	0.710831	+	0.703363i	$0.248319\pi$
$168$	0.111700	−	0.177110i	0.00861783	−	0.0136643i
$169$	−4.61337	−	0.653269i	−0.354874	−	0.0502515i
$170$	3.72692	+	3.81534i	0.285842	+	0.292623i
$171$	7.56660	+	4.52771i	0.578632	+	0.346243i
$172$	2.21801	−	2.74340i	0.169122	−	0.209182i
$173$	2.38457	+	1.66507i	0.181296	+	0.126593i	0.659647	−	0.751575i	$-0.270706\pi$
$173$	2.38457	+	1.66507i	0.181296	+	0.126593i	−0.478351	+	0.878169i	$0.658765\pi$
$174$	2.41857	−	2.15047i	0.183352	−	0.163026i
$175$	0.111641	−	1.18698i	0.00843924	−	0.0897269i
$176$	−0.271588	−	0.0255441i	−0.0204717	−	0.00192546i
$177$	2.00282	+	4.75619i	0.150541	+	0.357497i
$178$	14.5437	−	5.33642i	1.09010	−	0.399982i
$179$	−11.9898	−	0.281149i	−0.896158	−	0.0210140i	−0.427123	−	0.904193i	$-0.640473\pi$
$179$	−11.9898	−	0.281149i	−0.896158	−	0.0210140i	−0.469035	+	0.883179i	$0.655398\pi$
$180$	−0.753700	−	4.55126i	−0.0561775	−	0.339231i
$181$	−3.89335	+	13.4717i	−0.289390	+	1.00134i	0.675209	+	0.737626i	$0.264053\pi$
$181$	−3.89335	+	13.4717i	−0.289390	+	1.00134i	−0.964600	+	0.263718i	$0.915051\pi$
$182$	1.09762	+	1.83431i	0.0813608	+	0.135968i
$183$	−2.90305	−	3.42335i	−0.214600	−	0.253061i
$184$	5.02131	−	3.33389i	0.370176	−	0.245777i
$185$	−8.75587	−	8.16072i	−0.643744	−	0.599988i
$186$	0.180316	+	1.91714i	0.0132214	+	0.140571i
$187$			0.892698i			0.0652805i
$188$	3.67658	−	0.345800i	0.268142	−	0.0252201i
$189$	0.577091	+	1.07587i	0.0419772	+	0.0782577i
$190$	4.02196	+	3.09867i	0.291784	+	0.224801i
$191$	−10.5440	+	1.49307i	−0.762937	+	0.108035i	−0.510850	−	0.859670i	$-0.670669\pi$
$191$	−10.5440	+	1.49307i	−0.762937	+	0.108035i	−0.252087	+	0.967705i	$0.581117\pi$
$192$	−0.168603	+	0.375524i	−0.0121679	+	0.0271011i
$193$	−4.01929	−	0.860895i	−0.289315	−	0.0619686i	0.0624782	−	0.998046i	$-0.480100\pi$
$193$	−4.01929	−	0.860895i	−0.289315	−	0.0619686i	−0.351793	+	0.936078i	$0.614428\pi$
$194$	−8.54300	−	4.58243i	−0.613351	−	0.329000i
$195$	−2.68934	−	0.846022i	−0.192588	−	0.0605849i
$196$	−2.32214	+	6.32867i	−0.165867	+	0.452048i
$197$	−6.22919	−	8.92092i	−0.443812	−	0.635589i	0.533898	−	0.845549i	$-0.320726\pi$
$197$	−6.22919	−	8.92092i	−0.443812	−	0.635589i	−0.977710	+	0.209960i	$0.932667\pi$
$198$	0.442056	−	0.633074i	0.0314155	−	0.0449906i
$199$	2.58595	+	7.04767i	0.183313	+	0.499596i	0.996612	−	0.0822507i	$-0.0262108\pi$
$199$	2.58595	+	7.04767i	0.183313	+	0.499596i	−0.813298	+	0.581847i	$0.802330\pi$
$200$	0.109856	+	2.34117i	0.00776803	+	0.165545i
$201$	2.64086	+	0.968993i	0.186272	+	0.0683475i
$202$	3.50200	+	1.37895i	0.246400	+	0.0970223i
$203$	2.36589	−	3.22446i	0.166053	−	0.226313i
$204$	1.27518	+	0.434253i	0.0892801	+	0.0304038i
$205$	−1.63575	+	3.42598i	−0.114246	+	0.239281i
$206$	−5.62329	−	11.1006i	−0.391793	−	0.773415i
$207$	1.19895	+	17.0184i	0.0833331	+	1.18286i
$208$	−2.64204	−	3.26787i	−0.183193	−	0.226586i
$209$	0.119145	+	0.841397i	0.00824142	+	0.0582006i
$210$	0.125033	+	0.317537i	0.00862813	+	0.0219121i
$211$	−10.2018	+	8.65133i	−0.702323	+	0.595582i	−0.925297	−	0.379242i	$-0.876185\pi$
$211$	−10.2018	+	8.65133i	−0.702323	+	0.595582i	0.222974	+	0.974824i	$0.428423\pi$
$212$	4.24271	+	2.67579i	0.291391	+	0.183774i
$213$	1.27851	−	1.92562i	0.0876020	−	0.131941i
$214$	−6.90609	+	3.49846i	−0.472090	+	0.239150i
$215$	1.46642	+	5.55957i	0.100009	+	0.379160i
$216$	−1.41982	−	1.93506i	−0.0966063	−	0.131664i
$217$	0.714066	+	2.26988i	0.0484740	+	0.154090i
$218$	−10.2706	−	8.70962i	−0.695611	−	0.589890i
$219$	0.0146694	−	0.0430763i	0.000991264	−	0.00291082i
$220$	0.295416	−	0.332247i	0.0199170	−	0.0224001i
$221$	−9.83753	+	9.60955i	−0.661744	+	0.646409i
$222$	−2.90420	−	0.839321i	−0.194917	−	0.0563315i
$223$	4.98958	−	1.06872i	0.334127	−	0.0715669i	−0.0392973	−	0.999228i	$-0.512512\pi$
$223$	4.98958	−	1.06872i	0.334127	−	0.0715669i	0.373424	+	0.927661i	$0.378184\pi$
$224$	−0.106538	+	0.497398i	−0.00711837	+	0.0332338i
$225$	−5.91806	−	2.99795i	−0.394537	−	0.199863i
$226$	−8.38720	+	4.75535i	−0.557908	+	0.316321i
$227$	13.7204	−	10.0671i	0.910652	−	0.668174i	−0.0328786	−	0.999459i	$-0.510467\pi$
$227$	13.7204	−	10.0671i	0.910652	−	0.668174i	0.943530	+	0.331286i	$0.107482\pi$
$228$	1.25985	+	0.239105i	0.0834358	+	0.0158351i
$229$	−13.9297	+	4.38205i	−0.920501	+	0.289574i	−0.723096	−	0.690748i	$-0.757281\pi$
$229$	−13.9297	+	4.38205i	−0.920501	+	0.289574i	−0.197405	+	0.980322i	$0.563252\pi$
$230$	−0.460441	+	9.81252i	−0.0303606	+	0.647018i
$231$	−0.0221675	+	0.0526423i	−0.00145851	+	0.00346361i
$232$	−3.71635	+	6.92836i	−0.243990	+	0.454869i
$233$	18.2955	−	8.21431i	1.19858	−	0.538137i	0.290475	−	0.956883i	$-0.406187\pi$
$233$	18.2955	−	8.21431i	1.19858	−	0.538137i	0.908104	+	0.418745i	$0.137530\pi$
$234$	11.7350	−	1.94335i	0.767143	−	0.127041i
$235$	−3.09037	+	5.16455i	−0.201593	+	0.336898i
$236$	−8.54779	−	9.17117i	−0.556414	−	0.596993i
$237$	4.80385	+	3.52473i	0.312043	+	0.228956i
$238$	1.65324	+	0.194691i	0.107163	+	0.0126199i
$239$	−15.1300	−	0.709958i	−0.978680	−	0.0459234i	−0.448477	−	0.893794i	$-0.648033\pi$
$239$	−15.1300	−	0.709958i	−0.978680	−	0.0459234i	−0.530203	+	0.847871i	$0.677884\pi$
$240$	−0.330893	−	0.583610i	−0.0213591	−	0.0376718i
$241$	−13.1632	−	12.8582i	−0.847916	−	0.828267i	0.138867	−	0.990311i	$-0.455654\pi$
$241$	−13.1632	−	12.8582i	−0.847916	−	0.828267i	−0.986783	+	0.162044i	$0.948191\pi$
$242$	−10.8986	+	0.767809i	−0.700587	+	0.0493566i
$243$	10.2184	−	1.20336i	0.655512	−	0.0771954i
$244$	9.48556	+	5.37810i	0.607251	+	0.344297i
$245$	−6.07720	−	9.15312i	−0.388258	−	0.584772i
$246$	0.0224782	+	0.958601i	0.00143316	+	0.0611182i
$247$	−7.98964	+	10.3703i	−0.508369	+	0.659846i
$248$	−2.01554	−	4.22141i	−0.127987	−	0.268060i
$249$	0.480666	+	4.08162i	0.0304609	+	0.258662i
$250$	−9.97118	−	6.62035i	−0.630633	−	0.418707i
$251$	−2.14076	−	8.96318i	−0.135124	−	0.565751i	−0.998161	−	0.0606117i	$-0.980695\pi$
$251$	−2.14076	−	8.96318i	−0.135124	−	0.565751i	0.863038	−	0.505139i	$-0.168559\pi$
$252$	−1.07602	−	0.956737i	−0.0677827	−	0.0602687i
$253$	−1.20276	+	1.12101i	−0.0756168	+	0.0704770i
$254$	4.81752	−	20.1706i	0.302278	−	1.26561i
$255$	−1.80008	+	1.25694i	−0.112725	+	0.0787125i
$256$	0.0702762	−	0.997528i	0.00439226	−	0.0623455i
$257$	−26.7501	+	11.2644i	−1.66863	+	0.702654i	−0.999191	−	0.0402157i	$-0.987195\pi$
$257$	−26.7501	+	11.2644i	−1.66863	+	0.702654i	−0.669436	+	0.742870i	$0.733464\pi$
$258$	0.964945	+	1.08525i	0.0600749	+	0.0675646i
$259$	−3.72650	−	0.262533i	−0.231553	−	0.0163130i
$260$	6.84141	−	0.321025i	0.424286	−	0.0199091i
$261$	−11.8715	−	18.8234i	−0.734828	−	1.16514i
$262$	−0.772802	−	1.72124i	−0.0477439	−	0.106339i
$263$	4.60780	+	21.5126i	0.284129	+	1.32652i	0.860548	+	0.509369i	$0.170121\pi$
$263$	4.60780	+	21.5126i	0.284129	+	1.32652i	−0.576419	+	0.817154i	$0.695550\pi$
$264$	0.0286385	−	0.108576i	0.00176258	−	0.00668237i
$265$	−7.60667	+	2.99520i	−0.467274	+	0.183994i
$266$	1.58421	−	0.0371483i	0.0971344	−	0.00227771i
$267$	1.18906	+	6.26518i	0.0727692	+	0.383423i
$268$	−6.83374			−0.417437
$269$	−14.9373	+	6.77323i	−0.910744	+	0.412971i
$269$	−14.9373	+	6.77323i	−0.910744	+	0.412971i
$270$	3.91165			0.238055
$271$	−0.429959	−	2.26546i	−0.0261181	−	0.137617i	0.966991	−	0.254811i	$-0.0820132\pi$
$271$	−0.429959	−	2.26546i	−0.0261181	−	0.137617i	−0.993109	+	0.117194i	$0.962610\pi$
$272$	−3.27161	+	0.0767161i	−0.198371	+	0.00465160i
$273$	−0.818742	+	0.322388i	−0.0495525	+	0.0195118i
$274$	−3.44583	+	13.0640i	−0.208170	+	0.789224i
$275$	−0.133904	−	0.625162i	−0.00807471	−	0.0376987i
$276$	1.01622	+	2.26340i	0.0611692	+	0.136241i
$277$	1.69066	+	2.68070i	0.101582	+	0.161068i	0.892780	−	0.450492i	$-0.148751\pi$
$277$	1.69066	+	2.68070i	0.101582	+	0.161068i	−0.791198	+	0.611560i	$0.790542\pi$
$278$	1.09466	−	0.0513658i	0.0656535	−	0.00308072i
$279$	13.2083	+	0.930530i	0.790760	+	0.0557093i
$280$	−0.550879	−	0.619559i	−0.0329213	−	0.0370257i
$281$	9.21373	−	3.87988i	0.549645	−	0.231454i	−0.0956131	−	0.995419i	$-0.530481\pi$
$281$	9.21373	−	3.87988i	0.549645	−	0.231454i	0.645258	+	0.763965i	$0.276750\pi$
$282$	−0.106827	+	1.51634i	−0.00636144	+	0.0902967i
$283$	0.499710	−	0.348932i	0.0297047	−	0.0207418i	−0.557563	−	0.830135i	$-0.688263\pi$
$283$	0.499710	−	0.348932i	0.0297047	−	0.0207418i	0.587267	+	0.809393i	$0.300204\pi$
$284$	−1.30443	+	5.46153i	−0.0774035	+	0.324082i
$285$	−1.52887	+	1.42495i	−0.0905627	+	0.0844070i
$286$	0.856670	+	0.761706i	0.0506560	+	0.0450406i
$287$	0.275262	+	1.15250i	0.0162482	+	0.0680298i
$288$	2.35812	+	1.56567i	0.138953	+	0.0922579i
$289$	−0.735725	−	6.24748i	−0.0432780	−	0.367499i
$290$	−5.52098	−	11.5634i	−0.324203	−	0.679023i
$291$	2.43549	−	3.16119i	0.142771	−	0.185312i
$292$	0.00259152	+	0.110517i	0.000151657	+	0.00646753i
$293$	−4.51469	−	6.79977i	−0.263751	−	0.397247i	0.677195	−	0.735804i	$-0.263195\pi$
$293$	−4.51469	−	6.79977i	−0.263751	−	0.397247i	−0.940946	+	0.338557i	$0.890061\pi$
$294$	−2.41395	−	1.36865i	−0.140784	−	0.0798214i
$295$	20.2925	−	2.38972i	1.18148	−	0.139135i
$296$	7.32582	−	0.516107i	0.425805	−	0.0299981i
$297$	0.468343	+	0.457490i	0.0271760	+	0.0265463i
$298$	−7.31921	−	12.9092i	−0.423990	−	0.747808i
$299$	−25.3007	−	1.18721i	−1.46318	−	0.0686580i
$300$	−0.958151	−	0.112835i	−0.0553189	−	0.00651454i
$301$	1.44686	+	1.06161i	0.0833957	+	0.0611900i
$302$	−4.96099	−	5.32279i	−0.285473	−	0.306292i
$303$	−0.795516	+	1.32945i	−0.0457012	+	0.0763747i
$304$	−3.07336	+	0.508957i	−0.176269	+	0.0291907i
$305$	−16.2125	+	7.27906i	−0.928323	+	0.416798i
$306$	4.37853	−	8.16286i	0.250304	−	0.466639i
$307$	7.44705	−	17.6849i	0.425025	−	1.00933i	−0.558654	−	0.829401i	$-0.688682\pi$
$307$	7.44705	−	17.6849i	0.425025	−	1.00933i	0.983680	−	0.179928i	$-0.0575865\pi$
$308$	0.00650404	−	0.138609i	0.000370602	−	0.00789795i
$309$	4.88620	−	1.53712i	0.277966	−	0.0874435i
$310$	7.49034	+	1.42158i	0.425423	+	0.0807403i
$311$	−17.6179	+	12.9268i	−0.999021	+	0.733013i	−0.963871	−	0.266369i	$-0.914176\pi$
$311$	−17.6179	+	12.9268i	−0.999021	+	0.733013i	−0.0351498	+	0.999382i	$0.511191\pi$
$312$	1.50479	−	0.853180i	0.0851918	−	0.0483018i
$313$	−10.1130	−	5.12300i	−0.571620	−	0.289569i	0.142269	−	0.989828i	$-0.454560\pi$
$313$	−10.1130	−	5.12300i	−0.571620	−	0.289569i	−0.713889	+	0.700259i	$0.753068\pi$
$314$	0.900245	−	4.20301i	0.0508038	−	0.237190i
$315$	2.29462	−	0.491486i	0.129287	−	0.0276921i
$316$	−13.9054	−	4.01870i	−0.782242	−	0.226070i
$317$	11.0875	−	10.8305i	0.622734	−	0.608302i	−0.317736	−	0.948179i	$-0.602923\pi$
$317$	11.0875	−	10.8305i	0.622734	−	0.608302i	0.940470	+	0.339877i	$0.110385\pi$
$318$	−1.37199	+	1.54304i	−0.0769373	+	0.0865294i
$319$	0.691371	−	2.03020i	0.0387094	−	0.113669i
$320$	1.24303	+	1.05411i	0.0694873	+	0.0589264i
$321$	−0.956296	−	3.03989i	−0.0533752	−	0.169670i
$322$	1.81374	+	2.47194i	0.101076	+	0.137756i
$323$	2.60006	+	9.85747i	0.144671	+	0.548484i
$324$	−6.69382	+	3.39093i	−0.371879	+	0.188385i
$325$	5.44786	−	8.20525i	0.302193	−	0.455145i
$326$	6.22226	+	3.92426i	0.344619	+	0.217344i
$327$	4.22775	−	3.58520i	0.233795	−	0.198262i
$328$	−0.853442	−	2.16742i	−0.0471235	−	0.119676i
$329$	0.263369	+	1.85990i	0.0145200	+	0.102540i
$330$	0.115060	+	0.142315i	0.00633386	+	0.00783417i
$331$	−1.52718	−	21.6775i	−0.0839417	−	1.19150i	−0.842060	−	0.539384i	$-0.818657\pi$
$331$	−1.52718	−	21.6775i	−0.0839417	−	1.19150i	0.758118	−	0.652117i	$-0.226119\pi$
$332$	−4.51181	−	8.90648i	−0.247618	−	0.488807i
$333$	−8.95659	+	18.7590i	−0.490818	+	1.02799i
$334$	6.39211	+	2.17679i	0.349761	+	0.119109i
$335$	6.58872	−	8.97975i	0.359980	−	0.490616i
$336$	−0.194832	−	0.0767169i	−0.0106289	−	0.00418525i
$337$	1.43531	+	0.526647i	0.0781862	+	0.0286883i	0.383261	−	0.923640i	$-0.374801\pi$
$337$	1.43531	+	0.526647i	0.0781862	+	0.0286883i	−0.305075	+	0.952328i	$0.598682\pi$
$338$	0.218396	+	4.65427i	0.0118792	+	0.253159i
$339$	−1.36712	−	3.72590i	−0.0742518	−	0.202363i
$340$	3.05351	−	4.37297i	0.165600	−	0.237158i
$341$	0.730560	+	1.04625i	0.0395620	+	0.0566574i
$342$	3.03744	−	8.27814i	0.164246	−	0.447631i
$343$	−6.66775	−	2.09756i	−0.360025	−	0.113258i
$344$	−3.10886	−	1.66758i	−0.167618	−	0.0899099i
$345$	−3.95396	−	0.846902i	−0.212874	−	0.0455956i
$346$	1.19124	−	2.65322i	0.0640416	−	0.142638i
$347$	−31.1031	+	4.40431i	−1.66970	+	0.236436i	−0.910229	−	0.414105i	$-0.864095\pi$
$347$	−31.1031	+	4.40431i	−1.66970	+	0.236436i	−0.759471	+	0.650541i	$0.774542\pi$
$348$	−2.56372	−	1.97518i	−0.137430	−	0.105881i
$349$	6.59096	+	12.2875i	0.352806	+	0.657734i	0.993968	−	0.109672i	$-0.0349801\pi$
$349$	6.59096	+	12.2875i	0.352806	+	0.657734i	−0.641162	+	0.767406i	$0.721547\pi$
$350$	−1.18698	+	0.111641i	−0.0634465	+	0.00596745i
$351$			10.0859i			0.538343i
$352$	0.0255441	+	0.271588i	0.00136151	+	0.0144757i
$353$	7.37781	+	6.87633i	0.392681	+	0.365990i	0.853132	−	0.521695i	$-0.174700\pi$
$353$	7.37781	+	6.87633i	0.392681	+	0.365990i	−0.460451	+	0.887685i	$0.652312\pi$
$354$	4.29933	−	2.85453i	0.228507	−	0.151717i
$355$	−5.91896	−	6.97977i	−0.314146	−	0.370448i
$356$	−7.95465	−	13.2936i	−0.421596	−	0.704560i
$357$	−0.190249	+	0.658297i	−0.0100691	+	0.0348408i
$358$	1.95940	+	11.8319i	0.103557	+	0.625337i
$359$	−23.3924	−	0.548530i	−1.23461	−	0.0289503i	−0.598863	−	0.800851i	$-0.704381\pi$
$359$	−23.3924	−	0.548530i	−1.23461	−	0.0289503i	−0.635743	+	0.771901i	$0.719306\pi$
$360$	−4.33091	+	1.58911i	−0.228259	+	0.0837535i
$361$	−3.60747	−	8.56683i	−0.189867	−	0.450886i
$362$	13.9614	+	1.31314i	0.733795	+	0.0690169i
$363$	0.421141	−	4.47762i	0.0221042	−	0.235014i
$364$	1.59748	−	1.42039i	0.0837307	−	0.0744488i
$365$	−0.147722	−	0.103149i	−0.00773211	−	0.00539909i
$366$	−2.82201	+	3.49046i	−0.147509	+	0.182449i
$367$	23.8800	+	14.2893i	1.24653	+	0.745898i	0.976200	−	0.216871i	$-0.0695851\pi$
$367$	23.8800	+	14.2893i	1.24653	+	0.745898i	0.270325	+	0.962769i	$0.412869\pi$
$368$	−4.21169	−	4.31161i	−0.219550	−	0.224758i
$369$	6.52834	+	0.924436i	0.339852	+	0.0481242i
$370$	−6.38498	+	10.1240i	−0.331939	+	0.526320i
$371$	−1.25847	+	2.21961i	−0.0653364	+	0.115236i
$372$	1.84989	−	0.534623i	0.0959124	−	0.0277189i
$373$	16.0261	−	8.59633i	0.829798	−	0.445101i	−0.00212091	−	0.999998i	$-0.500675\pi$
$373$	16.0261	−	8.59633i	0.829798	−	0.445101i	0.831919	+	0.554897i	$0.187242\pi$
$374$	0.877042	−	0.166452i	0.0453508	−	0.00860705i
$375$	3.35915	−	3.60413i	0.173466	−	0.186116i
$376$	−1.02527	−	3.54763i	−0.0528743	−	0.182955i
$377$	29.8151	−	14.2354i	1.53556	−	0.733160i
$378$	0.949394	−	0.767576i	0.0488315	−	0.0394799i
$379$	5.86833	+	7.61690i	0.301436	+	0.391254i	0.918345	−	0.395780i	$-0.129526\pi$
$379$	5.86833	+	7.61690i	0.301436	+	0.391254i	−0.616909	+	0.787034i	$0.711615\pi$
$380$	2.29439	−	4.52921i	0.117700	−	0.232343i
$381$	7.86741	+	3.31294i	0.403060	+	0.169727i
$382$	3.43292	+	10.0807i	0.175643	+	0.515773i
$383$	−9.82109	+	24.9418i	−0.501834	+	1.27447i	0.427094	+	0.904207i	$0.359537\pi$
$383$	−9.82109	+	24.9418i	−0.501834	+	1.27447i	−0.928928	+	0.370260i	$0.879268\pi$
$384$	0.400376	+	0.0956256i	0.0204316	+	0.00487987i
$385$	0.175865	+	0.142185i	0.00896292	+	0.00724644i
$386$	−0.0963597	+	4.10933i	−0.00490458	+	0.209159i
$387$	8.44631	−	5.32692i	0.429350	−	0.270783i
$388$	−2.90914	+	9.24761i	−0.147689	+	0.469476i
$389$	27.3845	−	9.32561i	1.38845	−	0.472827i	0.475072	−	0.879947i	$-0.342422\pi$
$389$	27.3845	−	9.32561i	1.38845	−	0.472827i	0.913375	+	0.407120i	$0.133467\pi$
$390$	−0.329729	+	2.79993i	−0.0166965	+	0.141780i
$391$	−12.7572	+	15.0435i	−0.645157	+	0.760784i
$392$	6.65067	+	1.10137i	0.335909	+	0.0556274i
$393$	0.750980	−	0.198083i	0.0378819	−	0.00999195i
$394$	−7.60297	+	7.78334i	−0.383032	+	0.392119i
$395$	18.6876	−	14.3976i	0.940274	−	0.724421i
$396$	−0.704397	−	0.316260i	−0.0353973	−	0.0158927i
$397$	−24.5261	−	6.46915i	−1.23093	−	0.324677i	−0.418760	−	0.908097i	$-0.637535\pi$
$397$	−24.5261	−	6.46915i	−1.23093	−	0.324677i	−0.812171	+	0.583419i	$0.801714\pi$
$398$	6.44190	−	3.85471i	0.322903	−	0.193219i
$399$	−0.0914558	+	0.645858i	−0.00457852	+	0.0323333i
$400$	2.27962	−	0.544464i	0.113981	−	0.0272232i
$401$	1.87800	+	0.896661i	0.0937829	+	0.0447771i	0.477173	−	0.878809i	$-0.341661\pi$
$401$	1.87800	+	0.896661i	0.0937829	+	0.0447771i	−0.383390	+	0.923586i	$0.625244\pi$
$402$	0.459584	−	2.77522i	0.0229220	−	0.138416i
$403$	−3.66542	+	19.3132i	−0.182588	+	0.962059i
$404$	0.701781	−	3.69770i	0.0349149	−	0.183967i
$405$	1.99803	−	12.0652i	0.0992831	−	0.599527i
$406$	−3.60905	−	1.72316i	−0.179114	−	0.0855190i
$407$	−1.94853	+	0.465386i	−0.0965852	+	0.0230683i
$408$	0.188868	−	1.33378i	0.00935038	−	0.0660321i
$409$	−14.2017	+	8.49801i	−0.702227	+	0.420199i	−0.819636	−	0.572884i	$-0.805825\pi$
$409$	−14.2017	+	8.49801i	−0.702227	+	0.420199i	0.117410	+	0.993084i	$0.462541\pi$
$410$	3.67090	+	0.968257i	0.181293	+	0.0478188i
$411$	−5.07363	−	2.27795i	−0.250264	−	0.112363i
$412$	−9.85740	+	7.59449i	−0.485639	+	0.374154i
$413$	4.45626	−	4.56198i	0.219278	−	0.224480i
$414$	16.4964	−	4.35118i	0.810754	−	0.213849i
$415$	16.0535	+	2.65849i	0.788033	+	0.130500i
$416$	−2.71793	+	3.20504i	−0.133257	+	0.157140i
$417$	−0.0527585	+	0.448004i	−0.00258360	+	0.0219389i
$418$	0.804425	−	0.273942i	0.0393457	−	0.0133989i
$419$	4.94184	−	15.7092i	0.241425	−	0.767444i	−0.752618	−	0.658457i	$-0.771209\pi$
$419$	4.94184	−	15.7092i	0.241425	−	0.767444i	0.994043	−	0.108987i	$-0.0347607\pi$
$420$	0.288655	−	0.182049i	0.0140849	−	0.00888307i
$421$	0.583308	−	24.8756i	0.0284287	−	1.21236i	−0.780767	−	0.624822i	$-0.785171\pi$
$421$	0.583308	−	24.8756i	0.0284287	−	1.21236i	0.809196	−	0.587539i	$-0.199903\pi$
$422$	10.4018	+	8.40979i	0.506354	+	0.409382i
$423$	10.1667	+	2.42822i	0.494324	+	0.118064i
$424$	1.83777	−	4.66723i	0.0892500	−	0.226661i
$425$	−2.47251	−	7.26047i	−0.119934	−	0.352185i
$426$	−2.13024	−	0.897036i	−0.103210	−	0.0434616i
$427$	−2.50656	+	4.94804i	−0.121301	+	0.239452i
$428$	4.72481	+	6.13265i	0.228382	+	0.296433i
$429$	−0.366947	+	0.296673i	−0.0177164	+	0.0143235i
$430$	5.18864	−	2.47735i	0.250219	−	0.119468i
$431$	−0.115693	−	0.400317i	−0.00557271	−	0.0192826i	0.957850	−	0.287267i	$-0.0927468\pi$
$431$	−0.115693	−	0.400317i	−0.00557271	−	0.0192826i	−0.963423	+	0.267985i	$0.913642\pi$
$432$	−1.63639	+	1.75573i	−0.0787308	+	0.0844726i
$433$	32.4897	−	6.16616i	1.56135	−	0.296327i	0.667473	−	0.744634i	$-0.267376\pi$
$433$	32.4897	−	6.16616i	1.56135	−	0.296327i	0.893880	+	0.448307i	$0.147973\pi$
$434$	2.09693	−	1.12479i	0.100656	−	0.0539915i
$435$	5.06725	−	1.46445i	0.242956	−	0.0702148i
$436$	−6.64182	+	11.7144i	−0.318086	+	0.561020i
$437$	−10.0162	+	15.8817i	−0.479142	+	0.759723i
$438$	−0.0450561	−	0.00638010i	−0.00215286	−	0.000304853i
$439$	16.7735	+	17.1714i	0.800555	+	0.819547i	0.986628	−	0.162989i	$-0.0521134\pi$
$439$	16.7735	+	17.1714i	0.800555	+	0.819547i	−0.186073	+	0.982536i	$0.559576\pi$
$440$	−0.381504	−	0.228285i	−0.0181875	−	0.0108830i
$441$	−11.9968	+	14.8385i	−0.571274	+	0.706593i
$442$	11.2753	+	7.87321i	0.536313	+	0.374490i
$443$	18.6217	−	16.5574i	0.884745	−	0.786668i	−0.0931749	−	0.995650i	$-0.529702\pi$
$443$	18.6217	−	16.5574i	0.884745	−	0.786668i	0.977919	+	0.208982i	$0.0670150\pi$
$444$	−0.283083	+	3.00977i	−0.0134345	+	0.142837i
$445$	25.1377	+	2.36432i	1.19164	+	0.112079i
$446$	−1.98034	−	4.70280i	−0.0937716	−	0.222684i
$447$	5.73473	−	2.10421i	0.271244	−	0.0995255i
$448$	0.508540	+	0.0119248i	0.0240263	+	0.000563392i
$449$	−1.74757	−	10.5528i	−0.0824729	−	0.498017i	−0.995858	−	0.0909210i	$-0.971019\pi$
$449$	−1.74757	−	10.5528i	−0.0824729	−	0.498017i	0.913385	−	0.407096i	$-0.133459\pi$
$450$	−1.84189	+	6.37327i	−0.0868275	+	0.300439i
$451$	0.326275	+	0.545263i	0.0153637	+	0.0256754i
$452$	6.23583	+	7.35343i	0.293309	+	0.345876i
$453$	2.49526	−	1.65672i	0.117237	−	0.0778396i
$454$	−12.4488	−	11.6026i	−0.584251	−	0.544538i
$455$	0.326239	+	3.46861i	0.0152943	+	0.162611i
$456$		−	1.28234i		−	0.0600511i
$457$	33.0262	−	3.10627i	1.54490	−	0.145305i	0.713370	−	0.700787i	$-0.247168\pi$
$457$	33.0262	−	3.10627i	1.54490	−	0.145305i	0.831528	+	0.555482i	$0.187466\pi$
$458$	6.90253	+	12.8683i	0.322534	+	0.601298i
$459$	6.22186	+	4.79355i	0.290412	+	0.223744i
$460$	9.72628	−	1.37728i	0.453490	−	0.0642158i
$461$	−7.60008	+	16.9275i	−0.353971	+	0.788390i	0.645721	+	0.763573i	$0.276557\pi$
$461$	−7.60008	+	16.9275i	−0.353971	+	0.788390i	−0.999692	+	0.0248167i	$0.992100\pi$
$462$	0.0558524	+	0.0119631i	0.00259849	+	0.000556572i
$463$	−28.4894	−	15.2816i	−1.32402	−	0.710197i	−0.350015	−	0.936744i	$-0.613824\pi$
$463$	−28.4894	−	15.2816i	−1.32402	−	0.710197i	−0.974000	+	0.226547i	$0.927256\pi$
$464$	7.49981	+	2.35931i	0.348170	+	0.109528i
$465$	−1.08106	+	2.94627i	−0.0501327	+	0.136630i
$466$	−11.4816	−	16.4430i	−0.531877	−	0.761708i
$467$	−8.28043	+	11.8585i	−0.383172	+	0.548747i	−0.964213	−	0.265128i	$-0.914586\pi$
$467$	−8.28043	+	11.8585i	−0.383172	+	0.548747i	0.581041	+	0.813874i	$0.302646\pi$
$468$	−4.09739	−	11.1669i	−0.189402	−	0.516189i
$469$	−0.162937	−	3.47236i	−0.00752371	−	0.160339i
$470$	5.65020	+	2.07319i	0.260625	+	0.0956292i
$471$	1.64633	+	0.648257i	0.0758587	+	0.0298701i
$472$	−7.41651	+	10.1079i	−0.341373	+	0.465256i
$473$	0.910979	+	0.310228i	0.0418868	+	0.0142643i
$474$	2.56719	−	5.37682i	0.117915	−	0.246966i
$475$	−3.29945	−	6.51324i	−0.151389	−	0.298848i
$476$	−0.116986	−	1.66055i	−0.00536205	−	0.0761110i
$477$	8.92654	+	11.0410i	0.408718	+	0.505532i
$478$	2.12364	+	14.9971i	0.0971329	+	0.685949i
$479$	3.45699	+	8.77944i	0.157954	+	0.401143i	0.987568	−	0.157195i	$-0.0502452\pi$
$479$	3.45699	+	8.77944i	0.157954	+	0.401143i	−0.829614	+	0.558338i	$0.811439\pi$
$480$	−0.511676	+	0.433910i	−0.0233547	+	0.0198052i
$481$	−26.1038	−	16.4631i	−1.19023	−	0.750654i
$482$	−10.1782	+	15.3299i	−0.463606	+	0.698257i
$483$	−1.12585	+	0.570328i	−0.0512279	+	0.0259508i
$484$	2.78649	+	10.5643i	0.126659	+	0.480194i
$485$	−9.34682	−	12.7388i	−0.424417	−	0.578437i
$486$	−3.08758	−	9.81483i	−0.140055	−	0.445210i
$487$	30.5828	+	25.9348i	1.38584	+	1.17522i	0.963157	+	0.268938i	$0.0866727\pi$
$487$	30.5828	+	25.9348i	1.38584	+	1.17522i	0.422683	+	0.906278i	$0.361089\pi$
$488$	3.51510	−	10.3220i	0.159121	−	0.467255i
$489$	−2.01213	+	2.26299i	−0.0909915	+	0.102336i
$490$	−7.85945	+	7.67731i	−0.355054	+	0.346826i
$491$	−18.9413	−	5.47407i	−0.854808	−	0.247041i	−0.178755	−	0.983894i	$-0.557207\pi$
$491$	−18.9413	−	5.47407i	−0.854808	−	0.247041i	−0.676054	+	0.736852i	$0.736311\pi$
$492$	0.937598	−	0.200825i	0.0422702	−	0.00905388i
$493$	5.38869	−	25.1584i	0.242694	−	1.13308i
$494$	11.6782	+	5.91588i	0.525426	+	0.266168i
$495$	1.09472	−	0.620680i	0.0492039	−	0.0278975i
$496$	−3.77156	+	2.76731i	−0.169348	+	0.124256i
$497$	−2.80622	−	0.532588i	−0.125876	−	0.0238898i
$498$	3.92041	−	1.23329i	0.175678	−	0.0552652i
$499$	1.42548	−	30.3785i	0.0638131	−	1.35993i	−0.699839	−	0.714301i	$-0.746745\pi$
$499$	1.42548	−	30.3785i	0.0638131	−	1.35993i	0.763652	−	0.645628i	$-0.223404\pi$
$500$	−4.64501	+	11.0307i	−0.207731	+	0.493310i
$501$	−1.31389	+	2.44948i	−0.0587005	+	0.109435i
$502$	−8.40682	+	3.77449i	−0.375215	+	0.168464i
$503$	−18.0017	+	2.98113i	−0.802658	+	0.132922i	−0.550578	−	0.834784i	$-0.685592\pi$
$503$	−18.0017	+	2.98113i	−0.802658	+	0.132922i	−0.252081	+	0.967706i	$0.581115\pi$
$504$	−0.739324	+	1.23554i	−0.0329321	+	0.0550353i
$505$	4.18228	+	4.48729i	0.186109	+	0.199682i
$506$	1.32561	+	0.972643i	0.0589307	+	0.0432393i
$507$	−1.90482	−	0.224318i	−0.0845959	−	0.00996231i
$508$	−20.7151	−	0.972032i	−0.919084	−	0.0431269i
$509$	−10.9135	−	19.2485i	−0.483731	−	0.853176i	0.516263	−	0.856430i	$-0.327323\pi$
$509$	−10.9135	−	19.2485i	−0.483731	−	0.853176i	−0.999995	+	0.00325351i	$0.998964\pi$
$510$	1.57054	+	1.53414i	0.0695445	+	0.0679329i
$511$	−0.0560943	+	0.00395187i	−0.00248147	+	0.000174820i
$512$	−0.993137	+	0.116955i	−0.0438909	+	0.00516874i
$513$	6.50408	+	3.68767i	0.287162	+	0.162814i
$514$	16.0547	+	24.1806i	0.708142	+	1.06656i
$515$	−0.475432	−	20.2751i	−0.0209500	−	0.893429i
$516$	0.886292	−	1.15038i	0.0390168	−	0.0506426i
$517$	0.434030	+	0.909048i	0.0190886	+	0.0399799i
$518$	0.436914	+	3.71009i	0.0191969	+	0.163012i
$519$	0.997377	+	0.662207i	0.0437800	+	0.0290676i
$520$	−1.59104	−	6.66157i	−0.0697719	−	0.292129i
$521$	17.8841	+	15.9016i	0.783517	+	0.696661i	0.957610	−	0.288068i	$-0.0930129\pi$
$521$	17.8841	+	15.9016i	0.783517	+	0.696661i	−0.174093	+	0.984729i	$0.555699\pi$
$522$	−16.2797	+	15.1731i	−0.712542	+	0.664109i
$523$	−2.00196	+	8.38205i	−0.0875397	+	0.366521i	−0.998992	−	0.0448840i	$-0.985708\pi$
$523$	−2.00196	+	8.38205i	−0.0875397	+	0.366521i	0.911453	+	0.411405i	$0.134962\pi$
$524$	−1.54696	+	1.08019i	−0.0675792	+	0.0471884i
$525$	0.0344887	−	0.489547i	0.00150521	−	0.0213656i
$526$	20.2761	−	8.53823i	0.884082	−	0.372284i
$527$	10.1720	+	11.4402i	0.443101	+	0.498344i
$528$	−0.112012	−	0.00789125i	−0.00487468	−	0.000343423i
$529$	−13.3137	+	0.624730i	−0.578856	+	0.0271622i
$530$	4.36102	+	6.91479i	0.189430	+	0.300359i
$531$	−14.5349	−	32.3733i	−0.630763	−	1.40488i
$532$	−0.331889	−	1.54950i	−0.0143892	−	0.0671795i
$533$	−2.49657	+	9.46510i	−0.108138	+	0.409979i
$534$	5.93359	−	2.33641i	0.256772	−	0.101106i
$535$	−12.6139	+	0.295784i	−0.545347	+	0.0127878i
$536$	1.27422	+	6.71389i	0.0550379	+	0.289996i
$537$	−4.93680			−0.213039
$538$	9.43965	+	13.4124i	0.406972	+	0.578250i
$539$	−1.83892			−0.0792079
$540$	−0.729366	−	3.84305i	−0.0313869	−	0.165378i
$541$	17.6787	−	0.414548i	0.760067	−	0.0178228i	0.358351	−	0.933587i	$-0.383339\pi$
$541$	17.6787	−	0.414548i	0.760067	−	0.0178228i	0.401716	+	0.915764i	$0.368414\pi$
$542$	−2.14556	+	0.844836i	−0.0921598	+	0.0362888i
$543$	−1.47221	+	5.58150i	−0.0631785	+	0.239525i
$544$	0.685396	+	3.19993i	0.0293861	+	0.137196i
$545$	−8.98947	−	20.0220i	−0.385067	−	0.857649i
$546$	0.469397	+	0.744271i	0.0200883	+	0.0318519i
$547$	−6.08063	+	0.285326i	−0.259989	+	0.0121997i	−0.176468	−	0.984306i	$-0.556467\pi$
$547$	−6.08063	+	0.285326i	−0.259989	+	0.0121997i	−0.0835207	+	0.996506i	$0.526616\pi$
$548$	13.4774	+	0.949486i	0.575725	+	0.0405600i
$549$	20.5087	+	23.0656i	0.875291	+	0.984417i
$550$	−0.589230	+	0.248123i	−0.0251249	+	0.0105800i
$551$	1.72123	−	24.4318i	0.0733268	−	1.04083i
$552$	2.03422	−	1.42043i	0.0865821	−	0.0604575i
$553$	1.71044	−	7.16146i	0.0727352	−	0.304536i
$554$	2.31845	−	2.16086i	0.0985013	−	0.0918060i
$555$	−3.68200	−	3.27384i	−0.156292	−	0.138967i
$556$	−0.254576	−	1.06589i	−0.0107964	−	0.0452037i
$557$	16.1137	+	10.6986i	0.682759	+	0.453316i	0.845939	−	0.533280i	$-0.179041\pi$
$557$	16.1137	+	10.6986i	0.682759	+	0.453316i	−0.163180	+	0.986596i	$0.552175\pi$
$558$	−1.54861	−	13.1502i	−0.0655579	−	0.556691i
$559$	6.38762	+	13.3785i	0.270168	+	0.565849i
$560$	−0.505976	+	0.656741i	−0.0213814	+	0.0277524i
$561$	0.00861439	+	0.367367i	0.000363700	+	0.0155102i
$562$	−5.52983	−	8.32870i	−0.233262	−	0.351325i
$563$	18.6904	+	10.5970i	0.787706	+	0.446611i	0.833623	−	0.552334i	$-0.186263\pi$
$563$	18.6904	+	10.5970i	0.787706	+	0.446611i	−0.0459170	+	0.998945i	$0.514621\pi$
$564$	1.50967	−	0.177784i	0.0635684	−	0.00748604i
$565$	−15.6749	+	1.10430i	−0.659448	+	0.0464583i
$566$	−0.435988	−	0.425885i	−0.0183260	−	0.0179013i
$567$	−1.88260	−	3.32042i	−0.0790618	−	0.139444i
$568$	5.60897	+	0.263194i	0.235347	+	0.0110434i
$569$	14.8878	+	1.75323i	0.624127	+	0.0734994i	0.423095	−	0.906085i	$-0.360944\pi$
$569$	14.8878	+	1.75323i	0.624127	+	0.0734994i	0.201032	+	0.979585i	$0.435570\pi$
$570$	1.68504	+	1.23636i	0.0705785	+	0.0517856i
$571$	−24.2480	−	26.0163i	−1.01475	−	1.08875i	−0.996038	−	0.0889252i	$-0.971657\pi$
$571$	−24.2480	−	26.0163i	−1.01475	−	1.08875i	−0.0187075	−	0.999825i	$-0.505955\pi$
$572$	0.588613	−	0.983674i	0.0246111	−	0.0411295i
$573$	−4.32470	+	0.716181i	−0.180667	+	0.0299189i
$574$	1.08096	−	0.485329i	0.0451184	−	0.0202573i
$575$	6.67740	−	12.4486i	0.278467	−	0.519144i
$576$	1.09852	−	2.60870i	0.0457715	−	0.108696i
$577$	−0.274434	+	5.84851i	−0.0114249	+	0.243476i	0.985742	+	0.168261i	$0.0538152\pi$
$577$	−0.274434	+	5.84851i	−0.0114249	+	0.243476i	−0.997167	+	0.0752154i	$0.976036\pi$
$578$	−6.00073	+	1.88773i	−0.249598	+	0.0785192i
$579$	−1.66234	−	0.315494i	−0.0690847	−	0.0131115i
$580$	−10.3311	+	7.58026i	−0.428976	+	0.314753i
$581$	4.41799	−	2.50490i	0.183289	−	0.103921i
$582$	−3.55987	−	1.80334i	−0.147561	−	0.0747510i
$583$	−0.286578	+	1.33796i	−0.0118688	+	0.0554125i
$584$	0.108096	−	0.0231531i	0.00447304	−	0.000958083i
$585$	18.6241	+	5.38241i	0.770012	+	0.222535i
$586$	−5.83871	+	5.70340i	−0.241195	+	0.235605i
$587$	10.2222	−	11.4966i	0.421915	−	0.474517i	−0.497693	−	0.867353i	$-0.665819\pi$
$587$	10.2222	−	11.4966i	0.421915	−	0.474517i	0.919609	+	0.392836i	$0.128506\pi$
$588$	−0.894544	+	2.62681i	−0.0368904	+	0.108328i
$589$	11.1144	+	9.42517i	0.457959	+	0.388357i
$590$	−6.13156	−	19.4911i	−0.252432	−	0.802435i
$591$	−2.64955	−	3.61106i	−0.108988	−	0.148539i
$592$	−1.87303	−	7.10111i	−0.0769810	−	0.291854i
$593$	14.2938	−	7.24091i	0.586977	−	0.297348i	−0.133255	−	0.991082i	$-0.542543\pi$
$593$	14.2938	−	7.24091i	0.586977	−	0.297348i	0.720232	+	0.693733i	$0.244035\pi$
$594$	0.362139	−	0.545434i	0.0148588	−	0.0223794i
$595$	2.29480	+	1.44729i	0.0940777	+	0.0593329i
$596$	−11.3180	+	9.59789i	−0.463605	+	0.393145i
$597$	1.13219	+	2.87533i	0.0463375	+	0.117680i
$598$	3.55119	+	25.0784i	0.145219	+	1.02553i
$599$	18.9430	+	23.4301i	0.773991	+	0.957328i	0.999858	−	0.0168302i	$-0.00535749\pi$
$599$	18.9430	+	23.4301i	0.773991	+	0.957328i	−0.225868	+	0.974158i	$0.572522\pi$
$600$	0.0678005	+	0.962387i	0.00276794	+	0.0392893i
$601$	15.4526	+	30.5040i	0.630325	+	1.24428i	0.954478	+	0.298280i	$0.0964131\pi$
$601$	15.4526	+	30.5040i	0.630325	+	1.24428i	−0.324154	+	0.946004i	$0.605079\pi$
$602$	0.773207	−	1.61943i	0.0315136	−	0.0660032i
$603$	−18.3106	−	6.23558i	−0.745667	−	0.253932i
$604$	−4.30442	+	5.86648i	−0.175144	+	0.238704i
$605$	−16.5684	−	6.52397i	−0.673601	−	0.265237i
$606$	1.45446	+	0.533676i	0.0590835	+	0.0216791i
$607$	0.0837830	+	1.78551i	0.00340065	+	0.0724717i	0.999944	−	0.0106056i	$-0.00337593\pi$
$607$	0.0837830	+	1.78551i	0.00340065	+	0.0724717i	−0.996543	+	0.0830772i	$0.973525\pi$
$608$	1.07309	+	2.92456i	0.0435196	+	0.118607i
$609$	0.942504	−	1.34977i	0.0381922	−	0.0546956i
$610$	10.1744	+	14.5709i	0.411949	+	0.589958i
$611$	−5.34554	+	14.5686i	−0.216258	+	0.589381i
$612$	−8.83612	−	2.77969i	−0.357179	−	0.112362i
$613$	−23.0753	−	12.3775i	−0.932004	−	0.499924i	−0.0648117	−	0.997898i	$-0.520645\pi$
$613$	−23.0753	−	12.3775i	−0.932004	−	0.499924i	−0.867192	+	0.497974i	$0.834078\pi$
$614$	−18.7633	−	4.01892i	−0.757225	−	0.162191i
$615$	−0.640091	+	1.42566i	−0.0258110	+	0.0574881i
$616$	−0.137390	+	0.0194550i	−0.00553562	+	0.000783863i
$617$	28.7032	+	22.1140i	1.15555	+	0.890276i	0.995304	−	0.0968011i	$-0.0308611\pi$
$617$	28.7032	+	22.1140i	1.15555	+	0.890276i	0.160245	+	0.987077i	$0.448772\pi$
$618$	−2.42124	−	4.51390i	−0.0973966	−	0.181576i
$619$	−25.0184	+	2.35310i	−1.00558	+	0.0945792i	−0.583612	−	0.812033i	$-0.698361\pi$
$619$	−25.0184	+	2.35310i	−1.00558	+	0.0945792i	−0.421965	+	0.906612i	$0.638659\pi$
$620$		−	7.62405i		−	0.306189i
$621$	1.35461	+	14.4024i	0.0543588	+	0.577949i
$622$	15.9852	+	14.8986i	0.640946	+	0.597380i
$623$	6.56510	−	4.35888i	0.263025	−	0.174635i
$624$	−1.11880	−	1.31931i	−0.0447878	−	0.0528148i
$625$	−3.99902	−	6.68306i	−0.159961	−	0.267322i
$626$	−3.14748	+	10.8909i	−0.125799	+	0.435287i
$627$	0.0571503	+	0.345105i	0.00228236	+	0.0137822i
$628$	−4.29716	−	0.100764i	−0.171475	−	0.00402093i
$629$	−22.5624	+	8.27866i	−0.899621	+	0.330092i
$630$	−0.910722	−	2.16274i	−0.0362840	−	0.0861654i
$631$	39.0411	+	3.67200i	1.55420	+	0.146180i	0.835638	−	0.549281i	$-0.185098\pi$
$631$	39.0411	+	3.67200i	1.55420	+	0.146180i	0.718564	+	0.695461i	$0.244800\pi$
$632$	−1.35541	+	14.4109i	−0.0539155	+	0.573235i
$633$	−4.11482	+	3.65868i	−0.163549	+	0.145419i
$634$	−12.7079	−	8.87355i	−0.504697	−	0.352414i
$635$	21.2497	−	26.2831i	0.843267	−	1.04301i
$636$	1.77180	+	1.06021i	0.0702564	+	0.0420402i
$637$	−19.7953	−	20.2649i	−0.784318	−	0.802925i
$638$	−2.12351	−	0.300696i	−0.0840704	−	0.0119047i
$639$	−8.47862	+	13.4436i	−0.335409	+	0.531822i
$640$	0.803846	−	1.41778i	0.0317748	−	0.0560425i
$641$	−26.1792	+	7.56583i	−1.03401	+	0.298832i	−0.751013	−	0.660287i	$-0.770435\pi$
$641$	−26.1792	+	7.56583i	−1.03401	+	0.298832i	−0.283002	+	0.959119i	$0.591330\pi$
$642$	−2.80826	+	1.50634i	−0.110833	+	0.0594506i
$643$	16.8870	−	3.20496i	0.665958	−	0.126391i	0.157555	−	0.987510i	$-0.449639\pi$
$643$	16.8870	−	3.20496i	0.665958	−	0.126391i	0.508403	+	0.861119i	$0.330236\pi$
$644$	2.09040	−	2.24285i	0.0823733	−	0.0883807i
$645$	0.657118	+	2.27375i	0.0258740	+	0.0895288i
$646$	9.19978	−	4.39248i	0.361961	−	0.172820i
$647$	17.6856	−	14.2987i	0.695294	−	0.562139i	−0.214741	−	0.976671i	$-0.568891\pi$
$647$	17.6856	−	14.2987i	0.695294	−	0.562139i	0.910035	+	0.414532i	$0.136055\pi$
$648$	4.57959	+	5.94415i	0.179903	+	0.233508i
$649$	1.54546	−	3.05080i	0.0606646	−	0.119754i
$650$	−9.07716	−	3.82237i	−0.356035	−	0.149925i
$651$	0.315760	+	0.927221i	0.0123756	+	0.0363407i
$652$	2.69523	−	6.84486i	0.105553	−	0.268065i
$653$	28.0494	+	6.69931i	1.09766	+	0.262164i	0.740619	−	0.671925i	$-0.234532\pi$
$653$	28.0494	+	6.69931i	1.09766	+	0.262164i	0.357040	+	0.934089i	$0.383786\pi$
$654$	−4.31064	−	3.48511i	−0.168559	−	0.136279i
$655$	0.0720873	−	3.07422i	0.00281669	−	0.120120i
$656$	−1.97027	+	1.24261i	−0.0769263	+	0.0485158i
$657$	−0.0938998	+	0.298490i	−0.00366338	+	0.0116452i
$658$	1.77818	−	0.605547i	0.0693205	−	0.0236067i
$659$	−5.61198	+	47.6547i	−0.218612	+	1.85636i	0.243965	+	0.969784i	$0.421552\pi$
$659$	−5.61198	+	47.6547i	−0.218612	+	1.85636i	−0.462577	+	0.886579i	$0.653075\pi$
$660$	0.118365	−	0.139578i	0.00460735	−	0.00543308i
$661$	−10.1600	−	1.68252i	−0.395179	−	0.0654426i	−0.0375223	−	0.999296i	$-0.511947\pi$
$661$	−10.1600	−	1.68252i	−0.395179	−	0.0654426i	−0.357657	+	0.933853i	$0.616424\pi$
$662$	−21.0125	+	5.54238i	−0.816675	+	0.215411i
$663$	−3.95565	+	4.04950i	−0.153625	+	0.157269i
$664$	−7.90902	+	6.09339i	−0.306929	+	0.236469i
$665$	2.35609	+	1.05784i	0.0913652	+	0.0410211i
$666$	20.1001	+	5.30171i	0.778862	+	0.205437i
$667$	40.6635	−	24.3323i	1.57450	−	0.942150i
$668$	0.946746	−	6.68589i	0.0366307	−	0.258685i
$669$	2.04302	−	0.487954i	0.0789877	−	0.0188654i
$670$	−10.0508	−	4.79881i	−0.388296	−	0.185394i
$671$	−0.485966	+	2.93453i	−0.0187605	+	0.113286i
$672$	−0.0390432	+	0.205719i	−0.00150612	+	0.00793580i
$673$	2.62075	−	13.8088i	0.101023	−	0.532290i	−0.895216	−	0.445633i	$-0.852979\pi$
$673$	2.62075	−	13.8088i	0.101023	−	0.532290i	0.996238	−	0.0866569i	$-0.0276184\pi$
$674$	0.249784	−	1.50833i	0.00962131	−	0.0580989i
$675$	−5.07624	−	2.42368i	−0.195384	−	0.0932873i
$676$	4.53192	−	1.08240i	0.174305	−	0.0416308i
$677$	−4.37662	+	30.9075i	−0.168207	+	1.18787i	0.708097	+	0.706115i	$0.249554\pi$
$677$	−4.37662	+	30.9075i	−0.168207	+	1.18787i	−0.876304	+	0.481758i	$0.839998\pi$
$678$	−3.40565	+	2.03788i	−0.130793	+	0.0782642i
$679$	−4.76827	−	1.25770i	−0.182989	−	0.0482663i
$680$	−4.86564	−	2.18457i	−0.186589	−	0.0837745i
$681$	5.54911	−	4.27524i	0.212642	−	0.163827i
$682$	0.891677	−	0.912831i	0.0341441	−	0.0349541i
$683$	6.19602	−	1.63430i	0.237084	−	0.0625346i	−0.134577	−	0.990903i	$-0.542967\pi$
$683$	6.19602	−	1.63430i	0.237084	−	0.0625346i	0.371661	+	0.928369i	$0.378788\pi$
$684$	−8.69932	−	1.44063i	−0.332627	−	0.0550838i
$685$	−14.2418	+	16.7943i	−0.544152	+	0.641676i
$686$	−0.817505	+	6.94192i	−0.0312125	+	0.265044i
$687$	−5.69013	+	1.93774i	−0.217092	+	0.0739293i
$688$	−1.05866	+	3.36527i	−0.0403609	+	0.128300i
$689$	−17.8292	+	11.2445i	−0.679238	+	0.428382i
$690$	−0.0947934	+	4.04253i	−0.00360872	+	0.153897i
$691$	−19.8728	−	16.0670i	−0.755997	−	0.611217i	0.171440	−	0.985194i	$-0.445158\pi$
$691$	−19.8728	−	16.0670i	−0.755997	−	0.611217i	−0.927438	+	0.373978i	$0.877994\pi$
$692$	−2.82881	−	0.675631i	−0.107535	−	0.0256836i
$693$	0.143903	−	0.365459i	0.00546644	−	0.0138827i
$694$	10.1265	+	29.7364i	0.384398	+	1.12878i
$695$	1.64606	+	0.693151i	0.0624386	+	0.0262927i
$696$	−1.46251	+	2.88705i	−0.0554363	+	0.109433i
$697$	4.65237	+	6.03863i	0.176221	+	0.228729i
$698$	10.8430	−	8.76650i	0.410415	−	0.331817i
$699$	7.44978	−	3.55694i	0.281777	−	0.134536i
$700$	0.331006	+	1.14534i	0.0125109	+	0.0432899i
$701$	9.32819	−	10.0085i	0.352321	−	0.378015i	−0.530532	−	0.847665i	$-0.678008\pi$
$701$	9.32819	−	10.0085i	0.352321	−	0.378015i	0.882853	+	0.469650i	$0.155620\pi$
$702$	9.90897	−	1.88061i	0.373990	−	0.0709790i
$703$	−20.1609	+	10.8142i	−0.760381	+	0.407866i
$704$	0.262062	−	0.0757365i	0.00987684	−	0.00285443i
$705$	−1.22193	+	2.15516i	−0.0460204	+	0.0811680i
$706$	5.38007	−	8.53059i	0.202482	−	0.321053i
$707$	1.89561	+	0.268425i	0.0712918	+	0.0100952i
$708$	−3.60612	−	3.69168i	−0.135526	−	0.138742i
$709$	−34.8085	−	20.8288i	−1.30726	−	0.782241i	−0.320944	−	0.947098i	$-0.604000\pi$
$709$	−34.8085	−	20.8288i	−1.30726	−	0.782241i	−0.986317	+	0.164857i	$0.947284\pi$
$710$	−5.75371	+	7.11661i	−0.215933	+	0.267082i
$711$	−33.5920	−	23.4562i	−1.25980	−	0.879676i
$712$	−11.5772	+	10.2939i	−0.433876	+	0.385779i
$713$	−2.64023	+	28.0712i	−0.0988773	+	1.05127i
$714$	0.682226	+	0.0641666i	0.0255317	+	0.00240137i
$715$	0.725071	+	1.72186i	0.0271161	+	0.0643940i
$716$	11.2591	−	4.13122i	0.420772	−	0.154391i
$717$	−6.23322	−	0.146163i	−0.232784	−	0.00545855i
$718$	3.82285	+	23.0845i	0.142667	+	0.861505i
$719$	9.98781	−	34.5596i	0.372482	−	1.28886i	−0.526239	−	0.850337i	$-0.676398\pi$
$719$	9.98781	−	34.5596i	0.372482	−	1.28886i	0.898721	−	0.438521i	$-0.144497\pi$
$720$	2.36878	+	3.95865i	0.0882793	+	0.147530i
$721$	−4.09395	−	4.82767i	−0.152467	−	0.179792i
$722$	−7.74394	+	5.14157i	−0.288200	+	0.191350i
$723$	−5.54106	−	5.16442i	−0.206074	−	0.192067i
$724$	−1.31314	−	13.9614i	−0.0488023	−	0.518871i
$725$			18.4269i			0.684356i
$726$	−4.47762	+	0.421141i	−0.166180	+	0.0156300i
$727$	−23.3443	−	43.5205i	−0.865791	−	1.61409i	−0.786797	−	0.617212i	$-0.788262\pi$
$727$	−23.3443	−	43.5205i	−0.865791	−	1.61409i	−0.0789937	−	0.996875i	$-0.525171\pi$
$728$	−1.69335	−	1.30462i	−0.0627597	−	0.0483523i
$729$	−18.0952	+	2.56235i	−0.670194	+	0.0949019i
$730$	−0.0737963	+	0.164364i	−0.00273132	+	0.00608340i
$731$	11.2889	+	2.41798i	0.417536	+	0.0894323i
$732$	3.95544	+	2.12168i	0.146197	+	0.0784197i
$733$	16.9104	+	5.31974i	0.624602	+	0.196489i	0.595848	−	0.803097i	$-0.296816\pi$
$733$	16.9104	+	5.31974i	0.624602	+	0.196489i	0.0287540	+	0.999587i	$0.490846\pi$
$734$	9.58608	−	26.1256i	0.353829	−	0.964313i
$735$	−2.58924	−	3.70809i	−0.0955056	−	0.136775i
$736$	−3.45068	+	4.94177i	−0.127194	+	0.182156i
$737$	−0.642139	−	1.75006i	−0.0236535	−	0.0644644i
$738$	−0.309051	−	6.58622i	−0.0113763	−	0.242442i
$739$	−12.3824	−	4.54339i	−0.455494	−	0.167131i	0.106430	−	0.994320i	$-0.466058\pi$
$739$	−12.3824	−	4.54339i	−0.455494	−	0.167131i	−0.561924	+	0.827189i	$0.689939\pi$
$740$	11.1370	+	4.38529i	0.409403	+	0.161206i
$741$	−3.18786	+	4.34473i	−0.117109	+	0.159607i
$742$	2.41534	+	0.822528i	0.0886698	+	0.0301960i
$743$	1.73750	−	3.63909i	0.0637428	−	0.133505i	−0.868073	−	0.496436i	$-0.834642\pi$
$743$	1.73750	−	3.63909i	0.0637428	−	0.133505i	0.931816	+	0.362931i	$0.118224\pi$
$744$	−0.870178	−	1.71776i	−0.0319023	−	0.0629763i
$745$	−1.69969	−	24.1260i	−0.0622718	−	0.883910i
$746$	−11.4338	−	14.1421i	−0.418621	−	0.517780i
$747$	−3.96226	−	27.9813i	−0.144971	−	1.02378i
$748$	−0.327067	−	0.830624i	−0.0119587	−	0.0303706i
$749$	−3.00347	+	2.54699i	−0.109744	+	0.0930652i
$750$	−4.16727	−	2.62821i	−0.152167	−	0.0959688i
$751$	13.2466	−	19.9513i	0.483376	−	0.728034i	−0.507670	−	0.861552i	$-0.669493\pi$
$751$	13.2466	−	19.9513i	0.483376	−	0.728034i	0.991046	+	0.133518i	$0.0426274\pi$
$752$	−3.29424	+	1.66878i	−0.120128	+	0.0608542i
$753$	−0.967468	−	3.66791i	−0.0352565	−	0.133666i
$754$	−19.5451	−	26.6379i	−0.711789	−	0.970095i
$755$	−3.55865	−	11.3123i	−0.129513	−	0.411696i
$756$	−0.931139	−	0.789621i	−0.0338652	−	0.0287183i
$757$	−8.12024	+	23.8449i	−0.295135	+	0.866657i	0.694043	+	0.719934i	$0.255828\pi$
$757$	−8.12024	+	23.8449i	−0.295135	+	0.866657i	−0.989178	+	0.146723i	$0.953127\pi$
$758$	6.38911	−	7.18567i	0.232063	−	0.260995i
$759$	−0.484147	+	0.472928i	−0.0175734	+	0.0171662i
$760$	−4.87759	−	1.40963i	−0.176929	−	0.0511328i
$761$	19.7984	−	4.24064i	0.717692	−	0.153723i	0.164019	−	0.986457i	$-0.447554\pi$
$761$	19.7984	−	4.24064i	0.717692	−	0.153723i	0.553673	+	0.832734i	$0.313226\pi$
$762$	1.78789	−	8.34717i	0.0647683	−	0.302386i
$763$	−6.11071	−	3.09554i	−0.221223	−	0.112066i
$764$	9.26379	−	5.25236i	0.335152	−	0.190024i
$765$	12.1719	−	8.93091i	0.440077	−	0.322898i
$766$	26.3357	+	4.99820i	0.951546	+	0.180592i
$767$	50.2561	−	15.8097i	1.81464	−	0.570855i
$768$	0.0192944	−	0.411185i	0.000696226	−	0.0148374i
$769$

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+(-0.186460 - 0.982463i) q^{2} +(0.411524 - 0.00964984i) q^{3} +(-0.930465 + 0.366380i) q^{4} +(0.415669 - 1.57591i) q^{5} +(-0.0862134 - 0.402508i) q^{6} +(-0.208350 - 0.464053i) q^{7} +(0.533449 + 0.845832i) q^{8} +(-2.82744 + 0.132675i) q^{9} +(-1.62577 - 0.114536i) q^{10} +(-0.181259 - 0.203857i) q^{11} +(-0.379374 + 0.159753i) q^{12} +(0.295322 - 4.19192i) q^{13} +(-0.417066 + 0.291224i) q^{14} +(0.155851 - 0.652534i) q^{15} +(0.731531 - 0.681808i) q^{16} +(-2.44559 - 2.17449i) q^{17} +(0.657553 + 2.75312i) q^{18} +(-2.59527 - 1.72313i) q^{19} +(0.190614 + 1.61862i) q^{20} +(-0.0902193 - 0.188959i) q^{21} +(-0.166484 + 0.216091i) q^{22} +(-0.141295 - 6.02564i) q^{23} +(0.227689 + 0.342933i) q^{24} +(2.03884 + 1.15597i) q^{25} +(-4.17347 + 0.491482i) q^{26} +(-2.39414 + 0.168668i) q^{27} +(0.363883 + 0.355450i) q^{28} +(3.87775 + 6.83934i) q^{29} +(-0.670151 - 0.0314460i) q^{30} +(-4.64579 - 0.547105i) q^{31} +(-0.806252 - 0.591572i) q^{32} +(-0.0765596 - 0.0821430i) q^{33} +(-1.68035 + 2.80816i) q^{34} +(-0.817908 + 0.135448i) q^{35} +(2.58223 - 1.15937i) q^{36} +(3.47141 - 6.47173i) q^{37} +(-1.20899 + 2.87105i) q^{38} +(0.0810809 - 1.72793i) q^{39} +(1.55469 - 0.489079i) q^{40} +(-2.28854 - 0.434338i) q^{41} +(-0.168822 + 0.123870i) q^{42} +(-3.06891 + 1.74000i) q^{43} +(0.243344 + 0.123272i) q^{44} +(-0.966200 + 4.51093i) q^{45} +(-5.89362 + 1.26236i) q^{46} +(-3.54763 - 1.02527i) q^{47} +(0.294464 - 0.287640i) q^{48} +(4.47936 - 5.03782i) q^{49} +(0.755539 - 2.21862i) q^{50} +(-1.02740 - 0.871257i) q^{51} +(1.26105 + 4.00863i) q^{52} +(-2.96734 - 4.04418i) q^{53} +(0.612122 + 2.32070i) q^{54} +(-0.396603 + 0.200910i) q^{55} +(0.281367 - 0.423778i) q^{56} +(-1.08465 - 0.684064i) q^{57} +(5.99635 - 5.08500i) q^{58} +(4.59329 + 11.6652i) q^{59} +(0.0940617 + 0.664261i) q^{60} +(-6.85556 - 8.47945i) q^{61} +(0.328745 + 4.66633i) q^{62} +(0.650667 + 1.28444i) q^{63} +(-0.430864 + 0.902417i) q^{64} +(-6.48331 - 2.20785i) q^{65} +(-0.0664272 + 0.0905334i) q^{66} +(6.35855 + 2.50374i) q^{67} +(3.07223 + 1.12727i) q^{68} +(-0.116293 - 2.47834i) q^{69} +(0.285579 + 0.778309i) q^{70} +(3.21472 - 4.60385i) q^{71} +(-1.62052 - 2.32077i) q^{72} +(0.0380800 - 0.103782i) q^{73} +(-7.00551 - 2.20381i) q^{74} +(0.850186 + 0.456037i) q^{75} +(3.04613 + 0.652453i) q^{76} +(-0.0568352 + 0.126587i) q^{77} +(-1.71274 + 0.242530i) q^{78} +(11.4662 + 8.83394i) q^{79} +(-0.770389 - 1.43623i) q^{80} +(7.47073 - 0.702658i) q^{81} +2.32939i q^{82} +(0.934924 + 9.94021i) q^{83} +(0.153177 + 0.142765i) q^{84} +(-4.44335 + 2.95015i) q^{85} +(2.28171 + 2.69065i) q^{86} +(1.66179 + 2.77713i) q^{87} +(0.0757365 - 0.262062i) q^{88} +(2.53101 + 15.2837i) q^{89} +(4.61198 + 0.108146i) q^{90} +(-2.00680 + 0.736342i) q^{91} +(2.33915 + 5.55488i) q^{92} +(-1.91714 - 0.180316i) q^{93} +(-0.345800 + 3.67658i) q^{94} +(-3.79426 + 3.37365i) q^{95} +(-0.337501 - 0.235666i) q^{96} +(6.09500 - 7.53873i) q^{97} +(-5.78470 - 3.46146i) q^{98} +(0.539546 + 0.552346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38}+ \cdots + 18 q^{99}+O(q^{100}) \) 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

Introduction

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