LMFDB - Embedded newform 169.2.g.a.14.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, degree $12$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			14.13
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39315 - 2.01832i) q^{2} +(0.422612 - 0.221804i) q^{3} +(-1.42355 - 3.75360i) q^{4} +(1.09172 + 0.967184i) q^{5} +(0.141089 - 1.16197i) q^{6} +(0.0247635 + 0.00610365i) q^{7} +(-4.79682 - 1.18231i) q^{8} +(-1.57479 + 2.28148i) q^{9} +O(q^{10})$	\(q+(1.39315 - 2.01832i) q^{2} +(0.422612 - 0.221804i) q^{3} +(-1.42355 - 3.75360i) q^{4} +(1.09172 + 0.967184i) q^{5} +(0.141089 - 1.16197i) q^{6} +(0.0247635 + 0.00610365i) q^{7} +(-4.79682 - 1.18231i) q^{8} +(-1.57479 + 2.28148i) q^{9} +(3.47302 - 0.856022i) q^{10} +(-0.525155 - 0.760819i) q^{11} +(-1.43417 - 1.27057i) q^{12} +(-1.67528 + 3.19272i) q^{13} +(0.0468182 - 0.0414773i) q^{14} +(0.675901 + 0.166595i) q^{15} +(-3.05920 + 2.71021i) q^{16} +(-3.00961 - 0.741802i) q^{17} +(2.41084 + 6.35686i) q^{18} +0.108296 q^{19} +(2.07629 - 5.47473i) q^{20} +(0.0118191 - 0.00291316i) q^{21} -2.26719 q^{22} +7.06888 q^{23} +(-2.28943 + 0.564295i) q^{24} +(-0.346265 - 2.85175i) q^{25} +(4.11001 + 7.82917i) q^{26} +(-0.332074 + 2.73488i) q^{27} +(-0.0123414 - 0.101641i) q^{28} +(-2.26582 + 3.28261i) q^{29} +(1.27787 - 1.13209i) q^{30} +(-0.280618 + 2.31110i) q^{31} +(0.0171754 + 0.141452i) q^{32} +(-0.390689 - 0.205050i) q^{33} +(-5.69002 + 5.04092i) q^{34} +(0.0211315 + 0.0306143i) q^{35} +(10.8055 + 2.66333i) q^{36} +(0.673803 - 5.54927i) q^{37} +(0.150872 - 0.218575i) q^{38} +(0.000163142 + 1.72086i) q^{39} +(-4.09330 - 5.93016i) q^{40} +(4.78352 - 2.51058i) q^{41} +(0.0105861 - 0.0279133i) q^{42} +(-0.311275 - 2.56358i) q^{43} +(-2.10822 + 3.05429i) q^{44} +(-3.92585 + 0.967634i) q^{45} +(9.84798 - 14.2673i) q^{46} +(-1.52449 + 4.01975i) q^{47} +(-0.691718 + 1.82391i) q^{48} +(-6.19762 - 3.25276i) q^{49} +(-6.23814 - 3.27403i) q^{50} +(-1.43643 + 0.354049i) q^{51} +(14.3690 + 1.74333i) q^{52} +(-9.34209 - 2.30262i) q^{53} +(5.05723 + 4.48032i) q^{54} +(0.162527 - 1.33853i) q^{55} +(-0.111569 - 0.0585562i) q^{56} +(0.0457670 - 0.0240204i) q^{57} +(3.46874 + 9.14631i) q^{58} +(5.67571 + 5.02824i) q^{59} +(-0.336851 - 2.77422i) q^{60} +(7.46070 - 1.83890i) q^{61} +(4.27360 + 3.78608i) q^{62} +(-0.0529226 + 0.0468853i) q^{63} +(-6.92838 - 3.63629i) q^{64} +(-4.91689 + 1.86526i) q^{65} +(-0.958143 + 0.502872i) q^{66} +(0.0996988 - 0.262884i) q^{67} +(1.49991 + 12.3529i) q^{68} +(2.98739 - 1.56790i) q^{69} +0.0912288 q^{70} +(-11.3135 + 5.93776i) q^{71} +(10.2514 - 9.08195i) q^{72} +(6.09344 + 8.82787i) q^{73} +(-10.2615 - 9.09089i) q^{74} +(-0.778864 - 1.12838i) q^{75} +(-0.154165 - 0.406498i) q^{76} +(-0.00836090 - 0.0220459i) q^{77} +(3.47348 + 2.39708i) q^{78} +(0.343366 - 0.905382i) q^{79} -5.96108 q^{80} +(-2.48284 - 6.54672i) q^{81} +(1.59698 - 13.1523i) q^{82} +(-10.2775 - 5.39407i) q^{83} +(-0.0277600 - 0.0402173i) q^{84} +(-2.56821 - 3.72069i) q^{85} +(-5.60778 - 2.94319i) q^{86} +(-0.229468 + 1.88984i) q^{87} +(1.61955 + 4.27041i) q^{88} -16.1273 q^{89} +(-3.51628 + 9.27167i) q^{90} +(-0.0609730 + 0.0688374i) q^{91} +(-10.0629 - 26.5337i) q^{92} +(0.394018 + 1.03894i) q^{93} +(5.98930 + 8.67700i) q^{94} +(0.118229 + 0.104742i) q^{95} +(0.0386332 + 0.0559698i) q^{96} +(-1.43126 + 1.26798i) q^{97} +(-15.1993 + 7.97721i) q^{98} +2.56280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

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 $

$2$	1.39315	−	2.01832i	0.985103	−	1.42717i	0.0825511	−	0.996587i	$-0.473693\pi$
$2$	1.39315	−	2.01832i	0.985103	−	1.42717i	0.902552	−	0.430581i	$-0.141691\pi$
$3$	0.422612	−	0.221804i	0.243995	−	0.128058i	−0.338294	−	0.941041i	$-0.609850\pi$
$3$	0.422612	−	0.221804i	0.243995	−	0.128058i	0.582289	+	0.812982i	$0.302157\pi$
$4$	−1.42355	−	3.75360i	−0.711776	−	1.87680i
$5$	1.09172	+	0.967184i	0.488234	+	0.432538i	0.870982	−	0.491315i	$-0.163484\pi$
$5$	1.09172	+	0.967184i	0.488234	+	0.432538i	−0.382748	+	0.923853i	$0.625022\pi$
$6$	0.141089	−	1.16197i	0.0575993	−	0.474373i
$7$	0.0247635	+	0.00610365i	0.00935971	+	0.00230696i	0.243993	−	0.969777i	$-0.421543\pi$
$7$	0.0247635	+	0.00610365i	0.00935971	+	0.00230696i	−0.234633	+	0.972084i	$0.575389\pi$
$8$	−4.79682	−	1.18231i	−1.69593	−	0.418010i
$9$	−1.57479	+	2.28148i	−0.524930	+	0.760493i
$10$	3.47302	−	0.856022i	1.09827	−	0.270698i
$11$	−0.525155	−	0.760819i	−0.158340	−	0.229396i	0.735782	−	0.677219i	$-0.236815\pi$
$11$	−0.525155	−	0.760819i	−0.158340	−	0.229396i	−0.894122	+	0.447823i	$0.852199\pi$
$12$	−1.43417	−	1.27057i	−0.414010	−	0.366781i
$13$	−1.67528	+	3.19272i	−0.464639	+	0.885500i
$13$	−1.67528	+	3.19272i	−0.464639	+	0.885500i
$14$	0.0468182	−	0.0414773i	0.0125127	−	0.0110853i
$15$	0.675901	+	0.166595i	0.174517	+	0.0430145i
$16$	−3.05920	+	2.71021i	−0.764800	+	0.677554i
$17$	−3.00961	−	0.741802i	−0.729938	−	0.179914i	−0.143204	−	0.989693i	$-0.545740\pi$
$17$	−3.00961	−	0.741802i	−0.729938	−	0.179914i	−0.586734	+	0.809780i	$0.699587\pi$
$18$	2.41084	+	6.35686i	0.568241	+	1.49833i
$19$	0.108296			0.0248447			0.0124224	−	0.999923i	$-0.496046\pi$
$19$	0.108296			0.0248447			0.0124224	+	0.999923i	$0.496046\pi$
$20$	2.07629	−	5.47473i	0.464273	−	1.22419i
$21$	0.0118191	−	0.00291316i	0.00257915	−	0.000635703i
$22$	−2.26719			−0.483367
$23$	7.06888			1.47396			0.736981	−	0.675913i	$-0.236251\pi$
$23$	7.06888			1.47396			0.736981	+	0.675913i	$0.236251\pi$
$24$	−2.28943	+	0.564295i	−0.467329	+	0.115186i
$25$	−0.346265	−	2.85175i	−0.0692530	−	0.570349i
$26$	4.11001	+	7.82917i	0.806040	+	1.53543i
$27$	−0.332074	+	2.73488i	−0.0639077	+	0.526328i
$28$	−0.0123414	−	0.101641i	−0.00233231	−	0.0192083i
$29$	−2.26582	+	3.28261i	−0.420752	+	0.609565i	−0.974843	−	0.222891i	$-0.928451\pi$
$29$	−2.26582	+	3.28261i	−0.420752	+	0.609565i	0.554091	+	0.832456i	$0.313066\pi$
$30$	1.27787	−	1.13209i	0.233306	−	0.206691i
$31$	−0.280618	+	2.31110i	−0.0504006	+	0.415086i	0.945571	+	0.325416i	$0.105504\pi$
$31$	−0.280618	+	2.31110i	−0.0504006	+	0.415086i	−0.995972	+	0.0896700i	$0.971419\pi$
$32$	0.0171754	+	0.141452i	0.00303621	+	0.0250055i
$33$	−0.390689	−	0.205050i	−0.0680103	−	0.0356945i
$34$	−5.69002	+	5.04092i	−0.975831	+	0.864511i
$35$	0.0211315	+	0.0306143i	0.00357188	+	0.00517476i
$36$	10.8055	+	2.66333i	1.80092	+	0.443888i
$37$	0.673803	−	5.54927i	0.110773	−	0.912294i	−0.826317	−	0.563205i	$-0.809568\pi$
$37$	0.673803	−	5.54927i	0.110773	−	0.912294i	0.937090	−	0.349089i	$-0.113509\pi$
$38$	0.150872	−	0.218575i	0.0244746	−	0.0354576i
$39$	0.000163142		1.72086i	2.61237e−5		0.275559i
$40$	−4.09330	−	5.93016i	−0.647207	−	0.937641i
$41$	4.78352	−	2.51058i	0.747060	−	0.392087i	−0.0478183	−	0.998856i	$-0.515227\pi$
$41$	4.78352	−	2.51058i	0.747060	−	0.392087i	0.794879	+	0.606769i	$0.207535\pi$
$42$	0.0105861	−	0.0279133i	0.00163347	−	0.00430711i
$43$	−0.311275	−	2.56358i	−0.0474690	−	0.390942i	−0.997008	−	0.0772944i	$-0.975372\pi$
$43$	−0.311275	−	2.56358i	−0.0474690	−	0.390942i	0.949539	−	0.313648i	$-0.101551\pi$
$44$	−2.10822	+	3.05429i	−0.317826	+	0.460451i
$45$	−3.92585	+	0.967634i	−0.585231	+	0.144246i
$46$	9.84798	−	14.2673i	1.45200	−	2.10359i
$47$	−1.52449	+	4.01975i	−0.222370	+	0.586340i	−0.999051	−	0.0435530i	$-0.986132\pi$
$47$	−1.52449	+	4.01975i	−0.222370	+	0.586340i	0.776681	+	0.629894i	$0.216901\pi$
$48$	−0.691718	+	1.82391i	−0.0998409	+	0.263259i
$49$	−6.19762	−	3.25276i	−0.885374	−	0.464680i
$50$	−6.23814	−	3.27403i	−0.882206	−	0.463017i
$51$	−1.43643	+	0.354049i	−0.201141	+	0.0495767i
$52$	14.3690	+	1.74333i	1.99262	+	0.241757i
$53$	−9.34209	−	2.30262i	−1.28323	−	0.316289i	−0.462000	−	0.886880i	$-0.652868\pi$
$53$	−9.34209	−	2.30262i	−1.28323	−	0.316289i	−0.821235	+	0.570591i	$0.806714\pi$
$54$	5.05723	+	4.48032i	0.688202	+	0.609694i
$55$	0.162527	−	1.33853i	0.0219151	−	0.180487i
$56$	−0.111569	−	0.0585562i	−0.0149091	−	0.00782490i
$57$	0.0457670	−	0.0240204i	0.00606199	−	0.00318158i
$58$	3.46874	+	9.14631i	0.455467	+	1.20097i
$59$	5.67571	+	5.02824i	0.738915	+	0.654621i	0.946172	−	0.323665i	$-0.104915\pi$
$59$	5.67571	+	5.02824i	0.738915	+	0.654621i	−0.207257	+	0.978287i	$0.566454\pi$
$60$	−0.336851	−	2.77422i	−0.0434872	−	0.358150i
$61$	7.46070	−	1.83890i	0.955245	−	0.235447i	0.269264	−	0.963066i	$-0.413219\pi$
$61$	7.46070	−	1.83890i	0.955245	−	0.235447i	0.685981	+	0.727619i	$0.259373\pi$
$62$	4.27360	+	3.78608i	0.542748	+	0.480832i
$63$	−0.0529226	+	0.0468853i	−0.00666762	+	0.00590700i
$64$	−6.92838	−	3.63629i	−0.866047	−	0.454537i
$65$	−4.91689	+	1.86526i	−0.609865	+	0.231357i
$66$	−0.958143	+	0.502872i	−0.117939	+	0.0618993i
$67$	0.0996988	−	0.262884i	0.0121802	−	0.0321164i	−0.928788	−	0.370611i	$-0.879148\pi$
$67$	0.0996988	−	0.262884i	0.0121802	−	0.0321164i	0.940968	+	0.338494i	$0.109918\pi$
$68$	1.49991	+	12.3529i	0.181891	+	1.49800i
$69$	2.98739	−	1.56790i	0.359639	−	0.188753i
$70$	0.0912288			0.0109039
$71$	−11.3135	+	5.93776i	−1.34266	+	0.704682i	−0.974354	−	0.225022i	$-0.927755\pi$
$71$	−11.3135	+	5.93776i	−1.34266	+	0.704682i	−0.368307	+	0.929704i	$0.620062\pi$
$72$	10.2514	−	9.08195i	1.20814	−	1.07032i
$73$	6.09344	+	8.82787i	0.713183	+	1.03322i	0.997228	+	0.0744125i	$0.0237082\pi$
$73$	6.09344	+	8.82787i	0.713183	+	1.03322i	−0.284045	+	0.958811i	$0.591676\pi$
$74$	−10.2615	−	9.09089i	−1.19287	−	1.05679i
$75$	−0.778864	−	1.12838i	−0.0899354	−	0.130294i
$76$	−0.154165	−	0.406498i	−0.0176839	−	0.0466286i
$77$	−0.00836090	−	0.0220459i	−0.000952813	−	0.00251236i
$78$	3.47348	+	2.39708i	0.393294	+	0.271416i
$79$	0.343366	−	0.905382i	0.0386317	−	0.101863i	−0.914312	−	0.405010i	$-0.867268\pi$
$79$	0.343366	−	0.905382i	0.0386317	−	0.101863i	0.952944	+	0.303147i	$0.0980372\pi$
$80$	−5.96108			−0.666469
$81$	−2.48284	−	6.54672i	−0.275871	−	0.727413i
$82$	1.59698	−	13.1523i	0.176357	−	1.45243i
$83$	−10.2775	−	5.39407i	−1.12811	−	0.592076i	−0.205823	−	0.978589i	$-0.565987\pi$
$83$	−10.2775	−	5.39407i	−1.12811	−	0.592076i	−0.922284	+	0.386513i	$0.873680\pi$
$84$	−0.0277600	−	0.0402173i	−0.00302886	−	0.00438806i
$85$	−2.56821	−	3.72069i	−0.278561	−	0.403566i
$86$	−5.60778	−	2.94319i	−0.604702	−	0.317372i
$87$	−0.229468	+	1.88984i	−0.0246015	+	0.202612i
$88$	1.61955	+	4.27041i	0.172645	+	0.455227i
$89$	−16.1273			−1.70949			−0.854744	−	0.519051i	$-0.826286\pi$
$89$	−16.1273			−1.70949			−0.854744	+	0.519051i	$0.826286\pi$
$90$	−3.51628	+	9.27167i	−0.370649	+	0.977320i
$91$	−0.0609730	+	0.0688374i	−0.00639170	+	0.00721612i
$92$	−10.0629	−	26.5337i	−1.04913	−	2.76633i
$93$	0.394018	+	1.03894i	0.0408578	+	0.107733i
$94$	5.98930	+	8.67700i	0.617749	+	0.894965i
$95$	0.118229	+	0.104742i	0.0121300	+	0.0107463i
$96$	0.0386332	+	0.0559698i	0.00394298	+	0.00571240i
$97$	−1.43126	+	1.26798i	−0.145322	+	0.128744i	−0.732652	−	0.680604i	$-0.761718\pi$
$97$	−1.43126	+	1.26798i	−0.145322	+	0.128744i	0.587330	+	0.809348i	$0.300179\pi$
$98$	−15.1993	+	7.97721i	−1.53536	+	0.805819i
$99$	2.56280			0.257571
$100$	−10.2114	+	5.35935i	−1.02114	+	0.535935i
$101$	0.187725	+	1.54605i	0.0186793	+	0.153838i	0.999064	−	0.0432553i	$-0.0137729\pi$
$101$	0.187725	+	1.54605i	0.0186793	+	0.153838i	−0.980385	+	0.197093i	$0.936850\pi$
$102$	−1.28658	+	3.39242i	−0.127390	+	0.335900i
$103$	14.4513	−	7.58461i	1.42393	−	0.747334i	0.435665	−	0.900109i	$-0.356513\pi$
$103$	14.4513	−	7.58461i	1.42393	−	0.747334i	0.988261	+	0.152774i	$0.0488208\pi$
$104$	11.8108	−	13.3342i	1.15814	−	1.30752i
$105$	0.0157208	+	0.00825092i	0.00153419	+	0.000805207i
$106$	−17.6623	+	15.6474i	−1.71552	+	1.51981i
$107$	11.6112	+	10.2866i	1.12249	+	0.994444i	0.999998	+	0.00197468i	$0.000628559\pi$
$107$	11.6112	+	10.2866i	1.12249	+	0.994444i	0.122497	+	0.992469i	$0.460910\pi$
$108$	10.7384	−	2.64677i	1.03330	−	0.254685i
$109$	−1.19278	−	9.82345i	−0.114248	−	0.940916i	−0.931275	−	0.364317i	$-0.881303\pi$
$109$	−1.19278	−	9.82345i	−0.114248	−	0.940916i	0.817027	−	0.576599i	$-0.195621\pi$
$110$	−2.47515	−	2.19279i	−0.235997	−	0.209075i
$111$	−0.946092	−	2.49464i	−0.0897990	−	0.236781i
$112$	−0.0922986	+	0.0484420i	−0.00872139	+	0.00457734i
$113$	5.51437	+	2.89417i	0.518749	+	0.272260i	0.703712	−	0.710485i	$-0.251524\pi$
$113$	5.51437	+	2.89417i	0.518749	+	0.272260i	−0.184964	+	0.982745i	$0.559217\pi$
$114$	0.0152793	−	0.125836i	0.00143104	−	0.0117857i
$115$	7.71727	+	6.83690i	0.719639	+	0.637544i
$116$	15.5471	+	3.83202i	1.44351	+	0.355794i
$117$	−4.64589	−	8.84997i	−0.429513	−	0.818180i
$118$	18.0557	−	4.45033i	1.66216	−	0.409686i
$119$	−0.0700007	−	0.0367392i	−0.00641695	−	0.00336788i
$120$	−3.04521	−	1.59825i	−0.277988	−	0.145899i
$121$	3.59760	−	9.48608i	0.327054	−	0.862371i
$122$	6.68236	−	17.6199i	0.604993	−	1.59524i
$123$	1.46471	−	2.12201i	0.132069	−	0.191335i
$124$	9.07442	−	2.23664i	0.814907	−	0.200856i
$125$	6.52283	−	9.44996i	0.583420	−	0.845230i
$126$	0.0209007	+	0.172133i	0.00186198	+	0.0153348i
$127$	6.71663	−	17.7103i	0.596004	−	1.57153i	−0.208777	−	0.977963i	$-0.566948\pi$
$127$	6.71663	−	17.7103i	0.596004	−	1.57153i	0.804781	−	0.593571i	$-0.202283\pi$
$128$	−17.2438	+	9.05024i	−1.52415	+	0.799936i
$129$	−0.700160	−	1.01436i	−0.0616457	−	0.0893092i
$130$	−3.08525	+	12.5224i	−0.270594	+	1.09829i
$131$	−1.83905	+	2.66432i	−0.160679	+	0.232783i	−0.895051	−	0.445963i	$-0.852861\pi$
$131$	−1.83905	+	2.66432i	−0.160679	+	0.232783i	0.734373	+	0.678747i	$0.237477\pi$
$132$	−0.213507	+	1.75839i	−0.0185834	+	0.153048i
$133$	0.00268178		0.000660998i	0.000232539		5.73158e-5i
$134$	−0.391690	−	0.567460i	−0.0338368	−	0.0490211i
$135$	−3.00766	+	2.66456i	−0.258858	+	0.229329i
$136$	13.5595	+	7.11659i	1.16272	+	0.610242i
$137$	2.15788	+	17.7718i	0.184360	+	1.51834i	0.731812	+	0.681506i	$0.238675\pi$
$137$	2.15788	+	17.7718i	0.184360	+	1.51834i	−0.547452	+	0.836837i	$0.684402\pi$
$138$	0.997339	−	8.21383i	0.0848992	−	0.699207i
$139$	8.37428	−	7.41897i	0.710297	−	0.629268i	−0.228578	−	0.973526i	$-0.573408\pi$
$139$	8.37428	−	7.41897i	0.710297	−	0.629268i	0.938875	+	0.344257i	$0.111869\pi$
$140$	0.0848320	−	0.122900i	0.00716961	−	0.0103870i
$141$	0.247328	+	2.03693i	0.0208288	+	0.171540i
$142$	−3.77699	+	31.1063i	−0.316958	+	2.61039i
$143$	3.30886	−	0.402087i	0.276701	−	0.0336242i
$144$	−1.36570	−	11.2475i	−0.113808	−	0.937293i
$145$	−5.64854	+	1.39224i	−0.469086	+	0.115619i
$146$	26.3065			2.17714
$147$	−3.34066			−0.275533
$148$	−21.7889	+	5.37049i	−1.79104	+	0.441451i
$149$	−2.47333	+	6.52163i	−0.202623	+	0.534273i	−0.997355	−	0.0726880i	$-0.976842\pi$
$149$	−2.47333	+	6.52163i	−0.202623	+	0.534273i	0.794732	+	0.606961i	$0.207611\pi$
$150$	−3.36250			−0.274547
$151$	2.85793	+	7.53575i	0.232575	+	0.613251i	0.999597	−	0.0283699i	$-0.00903163\pi$
$151$	2.85793	+	7.53575i	0.232575	+	0.613251i	−0.767022	+	0.641621i	$0.778262\pi$
$152$	−0.519475	−	0.128039i	−0.0421350	−	0.0103853i
$153$	6.43191	−	5.69818i	0.519989	−	0.460670i
$154$	−0.0561436	−	0.0138382i	−0.00452418	−	0.00111511i
$155$	−2.54162	+	2.25168i	−0.204148	+	0.180859i
$156$	6.45919	−	2.45035i	0.517149	−	0.196185i
$157$	15.8162	+	14.0119i	1.26227	+	1.11827i	0.987642	+	0.156724i	$0.0500932\pi$
$157$	15.8162	+	14.0119i	1.26227	+	1.11827i	0.274628	+	0.961551i	$0.411445\pi$
$158$	−1.34899	−	1.95435i	−0.107320	−	0.155480i
$159$	−4.45881	+	1.09900i	−0.353606	+	0.0871561i
$160$	−0.118060	+	0.171039i	−0.00933343	+	0.0135218i
$161$	0.175050	+	0.0431459i	0.0137959	+	0.00340037i
$162$	−16.6723	−	4.10936i	−1.30990	−	0.322862i
$163$	−2.94538	+	24.2574i	−0.230700	+	1.89998i	0.172725	+	0.984970i	$0.444743\pi$
$163$	−2.94538	+	24.2574i	−0.230700	+	1.89998i	−0.403425	+	0.915013i	$0.632180\pi$
$164$	−16.2333	−	14.3815i	−1.26761	−	1.12300i
$165$	−0.228205	−	0.601726i	−0.0177657	−	0.0468443i
$166$	−25.2051	+	13.2287i	−1.95629	+	1.02674i
$167$	8.48042	−	12.2860i	0.656235	−	0.950720i	−0.343698	−	0.939080i	$-0.611680\pi$
$167$	8.48042	−	12.2860i	0.656235	−	0.950720i	0.999932	−	0.0116396i	$-0.00370509\pi$
$168$	−0.0601386			−0.00463979
$169$	−7.38687	−	10.6974i	−0.568221	−	0.822876i
$170$	−11.0874			−0.850367
$171$	−0.170543	+	0.247074i	−0.0130418	+	0.0188942i
$172$	−9.17954	+	4.81779i	−0.699933	+	0.367353i
$173$	−1.62914	−	4.29568i	−0.123861	−	0.326595i	0.858716	−	0.512452i	$-0.171263\pi$
$173$	−1.62914	−	4.29568i	−0.123861	−	0.326595i	−0.982577	+	0.185858i	$0.940494\pi$
$174$	3.49461	+	3.09596i	0.264926	+	0.234704i
$175$	0.00883134	−	0.0727326i	0.000667586	−	0.00549807i
$176$	3.66854	+	0.904213i	0.276526	+	0.0681576i
$177$	3.51391	+	0.866100i	0.264121	+	0.0651001i
$178$	−22.4676	+	32.5500i	−1.68402	+	2.43973i
$179$	4.56485	−	1.12513i	0.341193	−	0.0840965i	−0.0649962	−	0.997886i	$-0.520704\pi$
$179$	4.56485	−	1.12513i	0.341193	−	0.0840965i	0.406189	+	0.913789i	$0.366857\pi$
$180$	9.22075	+	13.3586i	0.687274	+	0.995689i
$181$	−12.6308	−	11.1899i	−0.938839	−	0.831739i	0.0470923	−	0.998891i	$-0.485004\pi$
$181$	−12.6308	−	11.1899i	−0.938839	−	0.831739i	−0.985931	+	0.167152i	$0.946543\pi$
$182$	0.0539917	+	0.218963i	0.00400213	+	0.0162307i
$183$	2.74511	−	2.43195i	0.202924	−	0.179775i
$184$	−33.9081	−	8.35760i	−2.49974	−	0.616131i
$185$	6.10277	−	5.40658i	0.448685	−	0.397500i
$186$	2.64584	+	0.652141i	0.194002	+	0.0478173i
$187$	1.01614	+	2.67933i	0.0743072	+	0.195932i
$188$	17.2587			1.25872
$189$	−0.0249160	+	0.0656982i	−0.00181238	+	0.00477884i
$190$	0.376113	−	0.0927035i	0.0272861	−	0.00672542i
$191$	24.1049			1.74417			0.872084	−	0.489356i	$-0.162768\pi$
$191$	24.1049			1.74417			0.872084	+	0.489356i	$0.162768\pi$
$192$	−3.73456			−0.269518
$193$	2.65839	−	0.655235i	0.191355	−	0.0471649i	−0.142473	−	0.989799i	$-0.545505\pi$
$193$	2.65839	−	0.655235i	0.191355	−	0.0471649i	0.333829	+	0.942634i	$0.391659\pi$
$194$	0.565246	+	4.65522i	0.0405823	+	0.334225i
$195$	−1.66421	+	1.87887i	−0.119177	+	0.134548i
$196$	−3.38692	+	27.8938i	−0.241923	+	1.99242i
$197$	0.609568	+	5.02024i	0.0434299	+	0.357678i	0.998182	+	0.0602743i	$0.0191975\pi$
$197$	0.609568	+	5.02024i	0.0434299	+	0.357678i	−0.954752	+	0.297403i	$0.903879\pi$
$198$	3.57036	−	5.17255i	0.253734	−	0.367597i
$199$	2.09017	−	1.85173i	0.148168	−	0.131266i	−0.585782	−	0.810468i	$-0.699213\pi$
$199$	2.09017	−	1.85173i	0.148168	−	0.131266i	0.733951	+	0.679203i	$0.237674\pi$
$200$	−1.71068	+	14.0887i	−0.120963	+	0.996222i
$201$	−0.0161748	−	0.133212i	−0.00114088	−	0.00939602i
$202$	3.38196	+	1.77499i	0.237954	+	0.124888i
$203$	−0.0761455	+	0.0674590i	−0.00534436	+	0.00473469i
$204$	3.37379	+	4.88778i	0.236213	+	0.342213i
$205$	7.65048	+	1.88568i	0.534333	+	0.131701i
$206$	4.82455	−	39.7338i	0.336143	−	2.76838i
$207$	−11.1320	+	16.1275i	−0.773727	+	1.12094i
$208$	−3.52793	−	14.3075i	−0.244618	−	0.992048i
$209$	−0.0568721	−	0.0823934i	−0.00393392	−	0.00569927i
$210$	0.0385544	−	0.0202349i	0.00266050	−	0.00139634i
$211$	4.83865	−	12.7585i	0.333106	−	0.878329i	−0.658910	−	0.752222i	$-0.728982\pi$
$211$	4.83865	−	12.7585i	0.333106	−	0.878329i	0.992017	−	0.126108i	$-0.0402485\pi$
$212$	4.65585	+	38.3443i	0.319765	+	2.63350i
$213$	−3.46418	+	5.01873i	−0.237362	+	0.343878i
$214$	36.9377	−	9.10433i	2.52501	−	0.622359i
$215$	2.13963	−	3.09979i	0.145921	−	0.211404i
$216$	4.82638	−	12.7261i	0.328393	−	0.865902i
$217$	−0.0210552	+	0.0555181i	−0.00142932	+	0.00376881i
$218$	−21.4886	−	11.2781i	−1.45539	−	0.763848i
$219$	4.53321	+	2.37921i	0.306326	+	0.160772i
$220$	−5.25566	+	1.29540i	−0.354336	+	0.0873360i
$221$	7.41031	−	8.36611i	0.498471	−	0.562765i
$222$	−6.35302	−	1.56588i	−0.426387	−	0.105095i
$223$	10.1401	+	8.98337i	0.679033	+	0.601571i	0.930499	−	0.366296i	$-0.119374\pi$
$223$	10.1401	+	8.98337i	0.679033	+	0.601571i	−0.251466	+	0.967866i	$0.580913\pi$
$224$	−0.000438052		0.00360768i	−2.92686e−5		0.000241048i
$225$	7.05149	+	3.70091i	0.470099	+	0.246727i
$226$	13.5237	−	7.09778i	0.899582	−	0.472137i
$227$	7.27430	+	19.1807i	0.482812	+	1.27307i	0.926299	+	0.376790i	$0.122972\pi$
$227$	7.27430	+	19.1807i	0.482812	+	1.27307i	−0.443487	+	0.896281i	$0.646259\pi$
$228$	−0.155315	−	0.137597i	−0.0102860	−	0.00911257i
$229$	1.19807	+	9.86698i	0.0791706	+	0.652028i	0.977234	+	0.212163i	$0.0680508\pi$
$229$	1.19807	+	9.86698i	0.0791706	+	0.652028i	−0.898064	+	0.439865i	$0.855026\pi$
$230$	24.5503	−	6.05111i	1.61880	−	0.398999i
$231$	−0.00842327	−	0.00746237i	−0.000554210	−	0.000490988i
$232$	14.7498	−	13.0672i	0.968372	−	0.857902i
$233$	−19.1746	−	10.0636i	−1.25617	−	0.659288i	−0.300514	−	0.953777i	$-0.597158\pi$
$233$	−19.1746	−	10.0636i	−1.25617	−	0.659288i	−0.955655	+	0.294489i	$0.904851\pi$
$234$	−24.3345	−	2.95240i	−1.59080	−	0.193005i
$235$	−5.55216	+	2.91400i	−0.362183	+	0.190088i
$236$	10.7943	−	28.4623i	0.702651	−	1.85274i
$237$	−0.0557066	−	0.458785i	−0.00361853	−	0.0298013i
$238$	−0.171673	+	0.0901008i	−0.0111279	+	0.00584036i
$239$	−5.26681			−0.340682			−0.170341	−	0.985385i	$-0.554487\pi$
$239$	−5.26681			−0.340682			−0.170341	+	0.985385i	$0.554487\pi$
$240$	−2.51922	+	1.32219i	−0.162615	+	0.0853470i
$241$	5.97086	−	5.28972i	0.384617	−	0.340741i	−0.448555	−	0.893755i	$-0.648061\pi$
$241$	5.97086	−	5.28972i	0.384617	−	0.340741i	0.833171	+	0.553015i	$0.186523\pi$
$242$	−14.1340	−	20.4766i	−0.908566	−	1.31629i
$243$	−8.68773	−	7.69665i	−0.557318	−	0.493741i
$244$	−17.5232	−	25.3867i	−1.12181	−	1.62522i
$245$	−3.62007	−	9.54535i	−0.231278	−	0.609830i
$246$	−2.24233	−	5.91253i	−0.142965	−	0.376969i
$247$	−0.181426	+	0.345757i	−0.0115438	+	0.0220000i
$248$	4.07851	−	10.7542i	0.258986	−	0.682890i
$249$	−5.53984			−0.351073
$250$	−9.98578	−	26.3303i	−0.631556	−	1.66528i
$251$	−1.28299	+	10.5663i	−0.0809814	+	0.666942i	0.894532	+	0.447003i	$0.147509\pi$
$251$	−1.28299	+	10.5663i	−0.0809814	+	0.666942i	−0.975514	+	0.219939i	$0.929414\pi$
$252$	0.251327	+	0.131906i	0.0158321	+	0.00830932i
$253$	−3.71226	−	5.37813i	−0.233388	−	0.338120i
$254$	−26.3878	−	38.2293i	−1.65572	−	2.39872i
$255$	−1.91062	−	1.00277i	−0.119648	−	0.0627959i
$256$	−3.87052	+	31.8766i	−0.241908	+	1.99229i
$257$	9.03665	+	23.8277i	0.563691	+	1.48633i	0.849262	+	0.527972i	$0.177048\pi$
$257$	9.03665	+	23.8277i	0.563691	+	1.48633i	−0.285571	+	0.958358i	$0.592183\pi$
$258$	−3.02272			−0.188187
$259$	0.0505565	−	0.133306i	0.00314143	−	0.00828326i
$260$	14.0009	+	15.8007i	0.868298	+	0.979919i
$261$	−3.92101	−	10.3388i	−0.242704	−	0.639958i
$262$	2.81539	+	7.42359i	0.173936	+	0.458631i
$263$	−11.3087	−	16.3835i	−0.697323	−	1.01025i	−0.998394	−	0.0566452i	$-0.981960\pi$
$263$	−11.3087	−	16.3835i	−0.697323	−	1.01025i	0.301071	−	0.953602i	$-0.402656\pi$
$264$	1.63163	+	1.44550i	0.100420	+	0.0889645i
$265$	−7.97194	−	11.5493i	−0.489712	−	0.709471i
$266$	0.00507021	−	0.00449182i	0.000310875	−	0.000275411i
$267$	−6.81557	+	3.57709i	−0.417106	+	0.218914i
$268$	−1.12869			−0.0689456
$269$	5.54987	−	2.91280i	0.338382	−	0.177596i	−0.286970	−	0.957940i	$-0.592648\pi$
$269$	5.54987	−	2.91280i	0.338382	−	0.177596i	0.625351	+	0.780343i	$0.284956\pi$
$270$	1.18782	+	9.78255i	0.0722882	+	0.595347i
$271$	11.3515	−	29.9315i	0.689556	−	1.81821i	0.126184	−	0.992007i	$-0.459727\pi$
$271$	11.3515	−	29.9315i	0.689556	−	1.81821i	0.563372	−	0.826203i	$-0.309504\pi$
$272$	11.2174	−	5.88737i	0.680157	−	0.356974i
$273$	−0.0104995	+	0.0426155i	−0.000635458	+	0.00257921i
$274$	38.8753	+	20.4033i	2.34854	+	1.23261i
$275$	−1.98782	+	1.76106i	−0.119870	+	0.106196i
$276$	−10.1380	−	8.98147i	−0.610235	−	0.540621i
$277$	−22.6751	+	5.58891i	−1.36242	+	0.335805i	−0.851738	−	0.523968i	$-0.824451\pi$
$277$	−22.6751	+	5.58891i	−1.36242	+	0.335805i	−0.510677	+	0.859773i	$0.670605\pi$
$278$	−3.30725	−	27.2377i	−0.198356	−	1.63361i
$279$	−4.83081	−	4.27972i	−0.289213	−	0.256220i
$280$	−0.0651686	−	0.171835i	−0.00389457	−	0.0102691i
$281$	−1.53027	+	0.803145i	−0.0912880	+	0.0479116i	−0.509749	−	0.860323i	$-0.670262\pi$
$281$	−1.53027	+	0.803145i	−0.0912880	+	0.0479116i	0.418461	+	0.908235i	$0.362570\pi$
$282$	4.45574	+	2.33855i	0.265336	+	0.139259i
$283$	1.23543	−	10.1747i	0.0734386	−	0.604822i	−0.908806	−	0.417218i	$-0.863005\pi$
$283$	1.23543	−	10.1747i	0.0734386	−	0.604822i	0.982245	−	0.187603i	$-0.0600719\pi$
$284$	38.3933	+	34.0135i	2.27822	+	2.01833i
$285$	0.0731971	+	0.0180415i	0.00433582	+	0.00106868i
$286$	3.79819	−	7.23851i	0.224591	−	0.428022i
$287$	0.133780	−	0.0329739i	0.00789680	−	0.00194639i
$288$	−0.349768	−	0.183572i	−0.0206103	−	0.0108171i
$289$	−6.54527	−	3.43522i	−0.385016	−	0.202072i
$290$	−5.05925	+	13.3402i	−0.297090	+	0.783361i
$291$	−0.323623	+	0.853323i	−0.0189711	+	0.0500227i
$292$	24.4619	−	35.4392i	1.43153	−	2.07392i
$293$	−28.4753	+	7.01853i	−1.66355	+	0.410027i	−0.955229	−	0.295868i	$-0.904391\pi$
$293$	−28.4753	+	7.01853i	−1.66355	+	0.410027i	−0.708317	+	0.705895i	$0.750545\pi$
$294$	−4.65403	+	6.74252i	−0.271428	+	0.393232i
$295$	1.33308	+	10.9789i	0.0776150	+	0.639217i
$296$	−9.79307	+	25.8222i	−0.569211	+	1.50089i
$297$	2.25514	−	1.18359i	0.130856	−	0.0686787i
$298$	9.71703	+	14.0776i	0.562893	+	0.815491i
$299$	−11.8423	+	22.5689i	−0.684861	+	1.30519i
$300$	−3.12673	+	4.52985i	−0.180522	+	0.261531i
$301$	0.00793894	−	0.0653831i	0.000457593	−	0.00376862i
$302$	19.1911	+	4.73018i	1.10432	+	0.272191i
$303$	0.422255	+	0.611742i	0.0242579	+	0.0351437i
$304$	−0.331298	+	0.293504i	−0.0190012	+	0.0168336i
$305$	9.92359	+	5.20830i	0.568223	+	0.298226i
$306$	−2.54015	−	20.9201i	−0.145211	−	1.19592i
$307$	−0.584046	+	4.81005i	−0.0333332	+	0.274524i	0.966507	+	0.256641i	$0.0826157\pi$
$307$	−0.584046	+	4.81005i	−0.0333332	+	0.274524i	−0.999840	+	0.0178831i	$0.994307\pi$
$308$	−0.0708492	+	0.0627669i	−0.00403701	+	0.00357647i
$309$	4.42498	−	6.41069i	0.251728	−	0.364692i
$310$	1.00376	+	8.26671i	0.0570098	+	0.469518i
$311$	0.232710	−	1.91654i	0.0131958	−	0.108677i	−0.984623	−	0.174694i	$-0.944106\pi$
$311$	0.232710	−	1.91654i	0.0131958	−	0.108677i	0.997818	+	0.0660175i	$0.0210293\pi$
$312$	2.03381	−	8.25486i	0.115142	−	0.467340i
$313$	−0.213781	−	1.76065i	−0.0120836	−	0.0995178i	0.985419	−	0.170144i	$-0.0544233\pi$
$313$	−0.213781	−	1.76065i	−0.0120836	−	0.0995178i	−0.997503	+	0.0706263i	$0.977500\pi$
$314$	50.3149	−	12.4015i	2.83943	−	0.699857i
$315$	−0.103124			−0.00581036
$316$	−3.88724			−0.218674
$317$	−21.0204	+	5.18107i	−1.18063	+	0.290998i	−0.780318	−	0.625383i	$-0.784943\pi$
$317$	−21.0204	+	5.18107i	−1.18063	+	0.290998i	−0.400307	+	0.916381i	$0.631097\pi$
$318$	−3.99364	+	10.5304i	−0.223952	+	0.590514i
$319$	3.68738			0.206454
$320$	−4.04692	−	10.6708i	−0.226230	−	0.596519i
$321$	7.18863	+	1.77184i	0.401230	+	0.0988943i
$322$	0.330952	−	0.293198i	0.0184432	−	0.0163393i
$323$	−0.325928	−	0.0803340i	−0.0181351	−	0.00446990i
$324$	−21.0393	+	18.6392i	−1.16885	+	1.03551i
$325$	9.68491	+	3.67195i	0.537222	+	0.203683i
$326$	44.8558	+	39.7388i	2.48433	+	2.20093i
$327$	−2.68296	−	3.88694i	−0.148368	−	0.214948i
$328$	−25.9140	+	6.38722i	−1.43086	+	0.352675i
$329$	−0.0622868	+	0.0902379i	−0.00343398	+	0.00497498i
$330$	−1.53240	−	0.377702i	−0.0843558	−	0.0207918i
$331$	−19.2453	−	4.74354i	−1.05782	−	0.260728i	−0.328217	−	0.944602i	$-0.606448\pi$
$331$	−19.2453	−	4.74354i	−1.05782	−	0.260728i	−0.729600	+	0.683874i	$0.760294\pi$
$332$	−5.61656	+	46.2565i	−0.308249	+	2.53866i
$333$	11.5994	+	10.2762i	0.635645	+	0.563133i
$334$	−12.9826	−	34.2324i	−0.710379	−	1.87311i
$335$	0.363101	−	0.190570i	0.0198383	−	0.0104120i
$336$	−0.0282618	+	0.0409443i	−0.00154181	+	0.00223370i
$337$	−13.6958			−0.746059			−0.373030	−	0.927819i	$-0.621681\pi$
$337$	−13.6958			−0.746059			−0.373030	+	0.927819i	$0.621681\pi$
$338$	−31.8817	+	0.00604495i	−1.73414	+	0.000328802i
$339$	2.97238			0.161437
$340$	−10.3100	+	14.9366i	−0.559138	+	0.810052i
$341$	1.90570	−	1.00019i	0.103199	−	0.0541632i
$342$	0.261084	+	0.688421i	0.0141178	+	0.0372255i
$343$	−0.267254	−	0.236766i	−0.0144304	−	0.0127842i
$344$	−1.53782	+	12.6651i	−0.0829135	+	0.682854i
$345$	4.77786	+	1.17764i	0.257231	+	0.0634018i
$346$	−10.9397	−	2.69639i	−0.588121	−	0.144959i
$347$	−11.5169	+	16.6851i	−0.618259	+	0.895703i	−0.999587	−	0.0287367i	$-0.990852\pi$
$347$	−11.5169	+	16.6851i	−0.618259	+	0.895703i	0.381328	+	0.924440i	$0.375467\pi$
$348$	7.42035	−	1.82895i	0.397772	−	0.0980421i
$349$	−1.02770	−	1.48888i	−0.0550114	−	0.0796978i	0.794513	−	0.607247i	$-0.207726\pi$
$349$	−1.02770	−	1.48888i	−0.0550114	−	0.0796978i	−0.849524	+	0.527550i	$0.823111\pi$
$350$	−0.134494	−	0.119152i	−0.00718903	−	0.00636892i
$351$	−8.17537	−	5.64191i	−0.436369	−	0.301143i
$352$	0.0985998	−	0.0873518i	0.00525539	−	0.00465587i
$353$	−11.4418	−	2.82014i	−0.608984	−	0.150101i	−0.0772490	−	0.997012i	$-0.524614\pi$
$353$	−11.4418	−	2.82014i	−0.608984	−	0.150101i	−0.531735	+	0.846911i	$0.678460\pi$
$354$	6.64345	−	5.88558i	0.353095	−	0.312815i
$355$	−18.0941	−	4.45979i	−0.960334	−	0.236701i
$356$	22.9580	+	60.5353i	1.21677	+	3.20836i
$357$	−0.0377320			−0.00199699
$358$	4.08862	−	10.7808i	0.216090	−	0.569784i
$359$	3.45603	−	0.851836i	0.182402	−	0.0449582i	−0.147056	−	0.989128i	$-0.546980\pi$
$359$	3.45603	−	0.851836i	0.182402	−	0.0449582i	0.329459	+	0.944170i	$0.393134\pi$
$360$	19.9756			1.05281
$361$	−18.9883			−0.999383
$362$	−40.1813	+	9.90381i	−2.11188	+	0.520533i
$363$	−0.583662	−	4.80689i	−0.0306343	−	0.252296i
$364$	0.345186	+	0.130874i	0.0180927	+	0.00685968i
$365$	−1.88581	+	15.5311i	−0.0987080	+	0.812933i
$366$	−1.08412	−	8.92857i	−0.0566681	−	0.466704i
$367$	1.21314	−	1.75753i	0.0633252	−	0.0917424i	−0.790042	−	0.613053i	$-0.789941\pi$
$367$	1.21314	−	1.75753i	0.0633252	−	0.0917424i	0.853367	+	0.521310i	$0.174557\pi$
$368$	−21.6251	+	19.1582i	−1.12729	+	0.998688i
$369$	−1.80520	+	14.8671i	−0.0939748	+	0.773952i
$370$	−2.41017	−	19.8495i	−0.125299	−	1.03193i
$371$	−0.217288	−	0.114042i	−0.0112810	−	0.00592075i
$372$	3.33886	−	2.95797i	0.173112	−	0.153364i
$373$	7.81206	+	11.3177i	0.404493	+	0.586010i	0.971305	−	0.237838i	$-0.0764386\pi$
$373$	7.81206	+	11.3177i	0.404493	+	0.586010i	−0.566812	+	0.823847i	$0.691823\pi$
$374$	6.82337	+	1.68181i	0.352828	+	0.0869643i
$375$	0.660590	−	5.44045i	0.0341127	−	0.280944i
$376$	12.0653	−	17.4796i	0.622220	−	0.901441i
$377$	−6.68455	−	12.7334i	−0.344272	−	0.655804i
$378$	0.0978883	+	0.141816i	0.00503483	+	0.00729421i
$379$	−7.78442	+	4.08558i	−0.399859	+	0.209862i	−0.652651	−	0.757658i	$-0.726343\pi$
$379$	−7.78442	+	4.08558i	−0.399859	+	0.209862i	0.252792	+	0.967521i	$0.418651\pi$
$380$	0.224853	−	0.592890i	0.0115347	−	0.0304146i
$381$	−1.08968	−	8.97435i	−0.0558262	−	0.459770i
$382$	33.5816	−	48.6514i	1.71819	−	2.48922i
$383$	22.7532	−	5.60817i	1.16264	−	0.286564i	0.389635	−	0.920969i	$-0.372601\pi$
$383$	22.7532	−	5.60817i	1.16264	−	0.286564i	0.773001	+	0.634405i	$0.218755\pi$
$384$	−5.28005	+	7.64947i	−0.269446	+	0.390361i
$385$	0.0121946	−	0.0321545i	0.000621495	−	0.00163875i
$386$	2.38106	−	6.27833i	0.121193	−	0.319559i
$387$	6.33895	+	3.32694i	0.322227	+	0.169118i
$388$	6.79697	+	3.56732i	0.345064	+	0.181103i
$389$	13.8606	−	3.41634i	0.702762	−	0.173215i	0.128287	−	0.991737i	$-0.459052\pi$
$389$	13.8606	−	3.41634i	0.702762	−	0.173215i	0.574475	+	0.818522i	$0.305206\pi$
$390$	1.47366	+	5.97645i	0.0746219	+	0.302629i
$391$	−21.2746	−	5.24371i	−1.07590	−	0.265186i
$392$	25.8831	+	22.9304i	1.30729	+	1.15816i
$393$	−0.186247	+	1.53388i	−0.00939493	+	0.0773742i
$394$	10.9817	+	5.76363i	0.553249	+	0.290367i
$395$	1.25053	−	0.656330i	0.0629211	−	0.0330236i
$396$	−3.64828	−	9.61972i	−0.183333	−	0.483409i
$397$	21.8117	+	19.3235i	1.09470	+	0.969817i	0.999671	−	0.0256580i	$-0.00816808\pi$
$397$	21.8117	+	19.3235i	1.09470	+	0.969817i	0.0950261	+	0.995475i	$0.469707\pi$
$398$	−0.825472	−	6.79837i	−0.0413772	−	0.340772i
$399$	0.00127996		0.000315482i	6.40783e−5		1.57939e-5i
$400$	8.78814	+	7.78561i	0.439407	+	0.389281i
$401$	0.135520	−	0.120060i	0.00676756	−	0.00599553i	−0.659732	−	0.751501i	$-0.729330\pi$
$401$	0.135520	−	0.120060i	0.00676756	−	0.00599553i	0.666500	+	0.745505i	$0.267792\pi$
$402$	−0.291397	−	0.152937i	−0.0145336	−	0.00762781i
$403$	−6.90857	−	4.76768i	−0.344141	−	0.237495i
$404$	5.53603	−	2.90553i	0.275428	−	0.144556i
$405$	3.62130	−	9.54858i	0.179944	−	0.474473i
$406$	0.0300721	+	0.247666i	0.00149245	+	0.0122915i
$407$	−4.57584	+	2.40159i	−0.226816	+	0.119042i
$408$	7.30890			0.361844
$409$	−15.6750	+	8.22687i	−0.775079	+	0.406793i	−0.805388	−	0.592748i	$-0.798043\pi$
$409$	−15.6750	+	8.22687i	−0.775079	+	0.406793i	0.0303093	+	0.999541i	$0.490351\pi$
$410$	14.4641	−	12.8141i	0.714333	−	0.632844i
$411$	4.85379	+	7.03192i	0.239420	+	0.346859i
$412$	−49.0417	−	43.4472i	−2.41611	−	2.14049i
$413$	0.109860	+	0.159159i	0.00540584	+	0.00783171i
$414$	17.0419	+	44.9359i	0.837565	+	2.20848i
$415$	−6.00319	−	15.8291i	−0.294685	−	0.777021i
$416$	−0.480391	−	0.182136i	−0.0235531	−	0.00892996i
$417$	1.89352	−	4.99279i	0.0927258	−	0.244498i
$418$	−0.245527			−0.0120091
$419$	14.3357	+	37.8002i	0.700347	+	1.84666i	0.497532	+	0.867446i	$0.334240\pi$
$419$	14.3357	+	37.8002i	0.700347	+	1.84666i	0.202815	+	0.979217i	$0.434991\pi$
$420$	0.00859124	−	0.0707552i	0.000419209	−	0.00345250i
$421$	17.1644	+	9.00858i	0.836542	+	0.439051i	0.827876	−	0.560911i	$-0.189549\pi$
$421$	17.1644	+	9.00858i	0.836542	+	0.439051i	0.00866633	+	0.999962i	$0.497241\pi$
$422$	−19.0097	−	27.5404i	−0.925379	−	1.34064i
$423$	−6.77021	−	9.80835i	−0.329179	−	0.476898i
$424$	42.0899	+	22.0905i	2.04407	+	1.07281i
$425$	−1.07331	+	8.83951i	−0.0520632	+	0.428779i
$426$	5.30330	+	13.9837i	0.256946	+	0.677510i
$427$	0.195977			0.00948399
$428$	22.0827	−	58.2272i	1.06741	−	2.81452i
$429$	1.30918	−	0.903844i	0.0632078	−	0.0436380i
$430$	−3.27555	−	8.63691i	−0.157961	−	0.416509i
$431$	−12.9266	−	34.0846i	−0.622652	−	1.64180i	−0.758964	−	0.651132i	$-0.774294\pi$
$431$	−12.9266	−	34.0846i	−0.622652	−	1.64180i	0.136313	−	0.990666i	$-0.456475\pi$
$432$	−6.39622	−	9.26653i	−0.307738	−	0.445836i
$433$	11.7377	+	10.3987i	0.564077	+	0.499728i	0.896285	−	0.443478i	$-0.146255\pi$
$433$	11.7377	+	10.3987i	0.564077	+	0.499728i	−0.332209	+	0.943206i	$0.607794\pi$
$434$	0.0827202	+	0.119841i	0.00397070	+	0.00575255i
$435$	−2.07833	+	1.84124i	−0.0996485	+	0.0882809i
$436$	−35.1753	+	18.4614i	−1.68459	+	0.884141i
$437$	0.765529			0.0366202
$438$	11.1174	−	5.83488i	0.531212	−	0.278801i
$439$	−2.17473	−	17.9105i	−0.103794	−	0.854822i	−0.947883	−	0.318618i	$-0.896781\pi$
$439$	−2.17473	−	17.9105i	−0.103794	−	0.854822i	0.844089	−	0.536203i	$-0.180142\pi$
$440$	−2.36216	+	6.22851i	−0.112612	+	0.296933i
$441$	17.1810	−	9.01731i	0.818145	−	0.429396i
$442$	−6.56184	−	26.6116i	−0.312115	−	1.26578i
$443$	−5.44350	−	2.85697i	−0.258629	−	0.135739i	0.330426	−	0.943832i	$-0.392808\pi$
$443$	−5.44350	−	2.85697i	−0.258629	−	0.135739i	−0.589055	+	0.808093i	$0.700500\pi$
$444$	−8.01706	+	7.10249i	−0.380473	+	0.337069i
$445$	−17.6065	−	15.5980i	−0.834630	−	0.739418i
$446$	32.2580	−	7.95088i	1.52746	−	0.376485i
$447$	0.401265	+	3.30471i	0.0189792	+	0.156307i
$448$	−0.149376	−	0.132336i	−0.00705735	−	0.00625227i
$449$	3.17661	+	8.37603i	0.149913	+	0.395289i	0.988845	−	0.148948i	$-0.0475886\pi$
$449$	3.17661	+	8.37603i	0.149913	+	0.395289i	−0.838932	+	0.544237i	$0.816819\pi$
$450$	17.2934	−	9.07627i	0.815218	−	0.427859i
$451$	−4.42219	−	2.32095i	−0.208233	−	0.109289i
$452$	3.01354	−	24.8187i	0.141745	−	1.16738i
$453$	2.87925	+	2.55080i	0.135279	+	0.119847i
$454$	48.8471	+	12.0397i	2.29251	+	0.565052i
$455$	−0.133144	+	0.0161794i	−0.00624189	+	0.000758503i
$456$	−0.247936	+	0.0611107i	−0.0116107	+	0.00286177i
$457$	20.5869	+	10.8048i	0.963013	+	0.505428i	0.871511	−	0.490377i	$-0.163141\pi$
$457$	20.5869	+	10.8048i	0.963013	+	0.505428i	0.0915023	+	0.995805i	$0.470833\pi$
$458$	21.5838	+	11.3281i	1.00855	+	0.529325i
$459$	3.02815	−	7.98459i	0.141342	−	0.372689i
$460$	14.6770	−	38.7002i	0.684321	−	1.80441i
$461$	−7.76067	+	11.2433i	−0.361450	+	0.523651i	−0.960949	−	0.276724i	$-0.910751\pi$
$461$	−7.76067	+	11.2433i	−0.361450	+	0.523651i	0.599499	+	0.800376i	$0.295367\pi$
$462$	−0.0267963	+	0.00660469i	−0.00124668	+	0.000307278i
$463$	−4.76588	+	6.90458i	−0.221489	+	0.320883i	−0.917938	−	0.396724i	$-0.870147\pi$
$463$	−4.76588	+	6.90458i	−0.221489	+	0.320883i	0.696449	+	0.717607i	$0.254762\pi$
$464$	−1.96497	−	16.1830i	−0.0912216	−	0.751278i
$465$	−0.574687	+	1.51532i	−0.0266505	+	0.0702715i
$466$	−47.0246	+	24.6804i	−2.17837	+	1.14330i
$467$	17.9189	+	25.9601i	0.829189	+	1.20129i	0.977204	+	0.212303i	$0.0680964\pi$
$467$	17.9189	+	25.9601i	0.829189	+	1.20129i	−0.148014	+	0.988985i	$0.547288\pi$
$468$	−26.6056	+	30.0372i	−1.22984	+	1.38847i
$469$	0.00407344	−	0.00590140i	0.000188094	−	0.000272501i
$470$	−1.85359	+	15.2657i	−0.0854996	+	0.704152i
$471$	9.79201	+	2.41351i	0.451192	+	0.111209i
$472$	−21.2804	−	30.8300i	−0.979511	−	1.41907i
$473$	−1.78695	+	1.58310i	−0.0821642	+	0.0727911i
$474$	−1.00358	−	0.526721i	−0.0460961	−	0.0241931i
$475$	−0.0374990	−	0.308832i	−0.00172057	−	0.0141702i
$476$	−0.0382545	+	0.315055i	−0.00175339	+	0.0144405i
$477$	19.9652	−	17.6876i	0.914144	−	0.809861i
$478$	−7.33744	+	10.6301i	−0.335607	+	0.486210i
$479$	−0.523648	−	4.31263i	−0.0239261	−	0.197049i	0.975845	−	0.218466i	$-0.0701053\pi$
$479$	−0.523648	−	4.31263i	−0.0239261	−	0.197049i	−0.999771	+	0.0214171i	$0.993182\pi$
$480$	−0.0119563	+	0.0984691i	−0.000545728	+	0.00449448i
$481$	16.5884	+	11.4478i	0.756367	+	0.521977i
$482$	−2.35807	−	19.4204i	−0.107407	−	0.884577i
$483$	0.0835480	−	0.0205927i	0.00380157	−	0.000937002i
$484$	−40.7283			−1.85129
$485$	−2.78891			−0.126638
$486$	−27.6376	+	6.81205i	−1.25367	+	0.309001i
$487$	−1.28338	+	3.38401i	−0.0581557	+	0.153344i	−0.960945	−	0.276739i	$-0.910746\pi$
$487$	−1.28338	+	3.38401i	−0.0581557	+	0.153344i	0.902789	+	0.430083i	$0.141516\pi$
$488$	−37.9618			−1.71845
$489$	4.13562	+	10.9047i	0.187019	+	0.493129i
$490$	−24.3089	−	5.99160i	−1.09816	−	0.270673i
$491$	5.70427	−	5.05354i	0.257430	−	0.228063i	−0.524529	−	0.851392i	$-0.675759\pi$
$491$	5.70427	−	5.05354i	0.257430	−	0.228063i	0.781960	+	0.623329i	$0.214220\pi$
$492$	−10.0503	−	2.47716i	−0.453100	−	0.111679i
$493$	9.25429	−	8.19858i	0.416792	−	0.369246i
$494$	0.445097	+	0.847866i	0.0200258	+	0.0381473i
$495$	2.79787	+	2.47870i	0.125755	+	0.111409i
$496$	−5.40511	−	7.83065i	−0.242697	−	0.351607i
$497$	−0.316402	+	0.0779862i	−0.0141926	+	0.00349816i
$498$	−7.71780	+	11.1812i	−0.345843	+	0.501040i
$499$	−16.5533	−	4.08001i	−0.741026	−	0.182646i	−0.149307	−	0.988791i	$-0.547704\pi$
$499$	−16.5533	−	4.08001i	−0.741026	−	0.182646i	−0.591719	+	0.806144i	$0.701550\pi$
$500$	−44.7569	−	11.0316i	−2.00159	−	0.493348i
$501$	0.858842	−	7.07320i	0.0383702	−	0.316007i
$502$	19.5389	+	17.3099i	0.872063	+	0.772581i
$503$	−12.3816	−	32.6475i	−0.552067	−	1.45568i	−0.862978	−	0.505242i	$-0.831403\pi$
$503$	−12.3816	−	32.6475i	−0.552067	−	1.45568i	0.310911	−	0.950439i	$-0.399366\pi$
$504$	0.309293	−	0.162330i	0.0137770	−	0.00723073i
$505$	−1.29037	+	1.86943i	−0.0574209	+	0.0831885i
$506$	−16.0265			−0.712465
$507$	−5.49450	−	2.88241i	−0.244019	−	0.128012i
$508$	−76.0388			−3.37368
$509$	−2.23524	+	3.23831i	−0.0990754	+	0.143535i	−0.869386	−	0.494133i	$-0.835486\pi$
$509$	−2.23524	+	3.23831i	−0.0990754	+	0.143535i	0.770311	+	0.637668i	$0.220101\pi$
$510$	−4.68568	+	2.45923i	−0.207485	+	0.108897i
$511$	0.0970124	+	0.255801i	0.00429158	+	0.0113160i
$512$	29.7913	+	26.3928i	1.31660	+	1.16641i
$513$	−0.0359622	+	0.296176i	−0.00158777	+	0.0130765i
$514$	60.6813	+	14.9566i	2.67654	+	0.659707i
$515$	23.1125	+	5.69673i	1.01846	+	0.251028i
$516$	−2.81078	+	4.07211i	−0.123737	+	0.179265i
$517$	3.85889	−	0.951132i	0.169714	−	0.0418307i
$518$	−0.198623	−	0.287755i	−0.00872698	−	0.0126432i
$519$	−1.64129	−	1.45406i	−0.0720447	−	0.0638260i
$520$	25.7908	−	3.13405i	1.13100	−	0.137437i
$521$	−0.451377	+	0.399885i	−0.0197752	+	0.0175193i	−0.672952	−	0.739686i	$-0.734974\pi$
$521$	−0.451377	+	0.399885i	−0.0197752	+	0.0175193i	0.653177	+	0.757205i	$0.273436\pi$
$522$	−26.3296	−	6.48967i	−1.15242	−	0.284045i
$523$	−17.5004	+	15.5040i	−0.765241	+	0.677944i	−0.952559	−	0.304355i	$-0.901559\pi$
$523$	−17.5004	+	15.5040i	−0.765241	+	0.677944i	0.187318	+	0.982299i	$0.440021\pi$
$524$	12.6188	+	3.11025i	0.551254	+	0.135872i
$525$	−0.0124001	−	0.0326965i	−0.000541186	−	0.00142699i
$526$	−48.8217			−2.12873
$527$	2.55893	−	6.74735i	0.111469	−	0.293919i
$528$	1.75092	−	0.431564i	0.0761992	−	0.0187814i
$529$	26.9690			1.17257
$530$	−34.4164			−1.49495
$531$	−20.4099	+	5.03058i	−0.885714	+	0.218309i
$532$	−0.00133653	−	0.0110073i	−5.79457e−5	−	0.000477226i
$533$	0.00184660	+	19.4784i	7.99852e−5	+	0.843701i
$534$	−2.27538	+	18.7394i	−0.0984652	+	0.810934i
$535$	2.72717	+	22.4603i	0.117906	+	0.971043i
$536$	−0.789048	+	1.14313i	−0.0340817	+	0.0493758i
$537$	1.67960	−	1.48800i	0.0724801	−	0.0642118i
$538$	1.85282	−	15.2594i	0.0798809	−	0.657878i
$539$	0.779950	+	6.42347i	0.0335948	+	0.276678i
$540$	14.2832	+	7.49642i	0.614653	+	0.322595i
$541$	25.2677	−	22.3852i	1.08634	−	0.962416i	0.0869140	−	0.996216i	$-0.472299\pi$
$541$	25.2677	−	22.3852i	1.08634	−	0.962416i	0.999429	+	0.0338003i	$0.0107610\pi$
$542$	−44.5971	−	64.6100i	−1.91561	−	2.77524i
$543$	−7.81988	−	1.92743i	−0.335583	−	0.0827138i
$544$	0.0532383	−	0.438457i	0.00228258	−	0.0187987i
$545$	8.19889	−	11.8781i	0.351202	−	0.508804i
$546$	0.0713844	+	0.0805610i	0.00305497	+	0.00344769i
$547$	−19.5974	−	28.3917i	−0.837924	−	1.21394i	−0.974739	−	0.223346i	$-0.928302\pi$
$547$	−19.5974	−	28.3917i	−0.837924	−	1.21394i	0.136816	−	0.990597i	$-0.456313\pi$
$548$	63.6361	−	33.3988i	2.71840	−	1.42673i
$549$	−7.55364	+	19.9173i	−0.322382	+	0.850050i
$550$	0.785050	+	6.46546i	0.0334746	+	0.275688i
$551$	−0.245379	+	0.355492i	−0.0104535	+	0.0151445i
$552$	−16.1837	+	3.98893i	−0.688825	+	0.169780i
$553$	0.0140291	−	0.0203246i	0.000596577	−	0.000864291i
$554$	−20.3095	+	53.5518i	−0.862869	+	2.27520i
$555$	1.37990	−	3.63850i	0.0585736	−	0.154446i
$556$	−39.7690	−	20.8724i	−1.68658	−	0.885187i
$557$	25.9275	+	13.6078i	1.09858	+	0.576580i	0.913786	−	0.406196i	$-0.133145\pi$
$557$	25.9275	+	13.6078i	1.09858	+	0.576580i	0.184796	+	0.982777i	$0.440837\pi$
$558$	−15.3679	+	3.78784i	−0.650574	+	0.160352i
$559$	8.70626	+	3.30090i	0.368236	+	0.139613i
$560$	−0.147617	−	0.0363843i	−0.00623796	−	0.00153752i
$561$	1.02372	+	0.906934i	0.0432213	+	0.0382908i
$562$	−0.510879	+	4.20747i	−0.0215501	+	0.177481i
$563$	6.55969	+	3.44279i	0.276458	+	0.145096i	0.597254	−	0.802052i	$-0.296258\pi$
$563$	6.55969	+	3.44279i	0.276458	+	0.145096i	−0.320797	+	0.947148i	$0.603951\pi$
$564$	7.29373	−	3.82805i	0.307122	−	0.161190i
$565$	3.22099	+	8.49305i	0.135508	+	0.357305i
$566$	−18.8146	−	16.6683i	−0.790837	−	0.700621i
$567$	−0.0215249	−	0.177274i	−0.000903962	−	0.00744480i
$568$	61.2889	−	15.1064i	2.57162	−	0.633849i
$569$	17.7821	+	15.7536i	0.745466	+	0.660426i	0.947791	−	0.318893i	$-0.103311\pi$
$569$	17.7821	+	15.7536i	0.745466	+	0.660426i	−0.202324	+	0.979319i	$0.564850\pi$
$570$	0.138388	−	0.122601i	0.00579643	−	0.00513519i
$571$	17.8664	+	9.37703i	0.747687	+	0.392417i	0.795115	−	0.606458i	$-0.207410\pi$
$571$	17.8664	+	9.37703i	0.747687	+	0.392417i	−0.0474282	+	0.998875i	$0.515103\pi$
$572$	−6.21961	−	11.8477i	−0.260055	−	0.495379i
$573$	10.1870	−	5.34656i	0.425568	−	0.223356i
$574$	0.119824	−	0.315949i	0.00500134	−	0.0131874i
$575$	−2.44770	−	20.1586i	−0.102076	−	0.840674i
$576$	19.2069	−	10.0805i	0.800286	−	0.420023i
$577$	41.3183			1.72010			0.860051	−	0.510208i	$-0.170431\pi$
$577$	41.3183			1.72010			0.860051	+	0.510208i	$0.170431\pi$
$578$	−16.0519	+	8.42468i	−0.667671	+	0.350421i
$579$	0.978135	−	0.866552i	0.0406499	−	0.0360127i
$580$	13.2669	+	19.2204i	0.550878	+	0.798084i
$581$	−0.221584	−	0.196306i	−0.00919286	−	0.00814416i
$582$	1.27143	+	1.84198i	0.0527023	+	0.0763524i
$583$	3.15417	+	8.31687i	0.130633	+	0.344450i
$584$	−18.7918	−	49.5500i	−0.777612	−	2.05039i
$585$	3.48751	−	14.1552i	0.144191	−	0.585244i
$586$	−25.5046	+	67.2501i	−1.05359	+	2.77808i
$587$	27.3815			1.13016			0.565079	−	0.825037i	$-0.308846\pi$
$587$	27.3815			1.13016			0.565079	+	0.825037i	$0.308846\pi$
$588$	4.75560	+	12.5395i	0.196118	+	0.517120i
$589$	−0.0303898	+	0.250282i	−0.00125219	+	0.0103127i
$590$	24.0161	+	12.6046i	0.988729	+	0.518925i
$591$	1.37112	+	1.98641i	0.0564003	+	0.0817100i
$592$	12.9784	+	18.8025i	0.533409	+	0.772777i
$593$	−6.43115	−	3.37533i	−0.264096	−	0.138608i	0.327479	−	0.944859i	$-0.393801\pi$
$593$	−6.43115	−	3.37533i	−0.264096	−	0.138608i	−0.591574	+	0.806250i	$0.701493\pi$
$594$	0.752877	−	6.20050i	0.0308909	−	0.254410i
$595$	−0.0408879	−	0.107813i	−0.00167624	−	0.00441989i
$596$	28.0005			1.14694
$597$	0.472611	−	1.24617i	0.0193427	−	0.0510024i
$598$	29.0532	+	55.3434i	1.18807	+	2.26316i
$599$	−15.7538	−	41.5393i	−0.643682	−	1.69725i	−0.714386	−	0.699751i	$-0.753294\pi$
$599$	−15.7538	−	41.5393i	−0.643682	−	1.69725i	0.0707048	−	0.997497i	$-0.477475\pi$
$600$	2.40198	+	6.33349i	0.0980603	+	0.258564i
$601$	−2.31620	−	3.35560i	−0.0944799	−	0.136878i	0.772893	−	0.634536i	$-0.218809\pi$
$601$	−2.31620	−	3.35560i	−0.0944799	−	0.136878i	−0.867373	+	0.497658i	$0.834193\pi$
$602$	−0.120904	−	0.107111i	−0.00492767	−	0.00436554i
$603$	0.442760	+	0.641448i	0.0180306	+	0.0261218i
$604$	24.2178	−	21.4551i	0.985407	−	0.872994i
$605$	13.1024	−	6.87665i	0.532687	−	0.279576i
$606$	1.82295			0.0740525
$607$	−15.4512	+	8.10940i	−0.627144	+	0.329150i	−0.748178	−	0.663498i	$-0.769071\pi$
$607$	−15.4512	+	8.10940i	−0.627144	+	0.329150i	0.121035	+	0.992648i	$0.461379\pi$
$608$	0.00186002	+	0.0153187i	7.54339e−5	+	0.000621254i
$609$	−0.0172173	+	0.0453983i	−0.000697681	+	0.00183963i
$610$	24.3370	−	12.7731i	0.985378	−	0.517166i
$611$	−10.2800	−	11.6015i	−0.415883	−	0.469345i
$612$	−30.5448	−	16.0312i	−1.23470	−	0.648021i
$613$	−25.1779	+	22.3056i	−1.01692	+	0.900916i	−0.995103	−	0.0988457i	$-0.968485\pi$
$613$	−25.1779	+	22.3056i	−1.01692	+	0.900916i	−0.0218214	+	0.999762i	$0.506947\pi$
$614$	8.89456	+	7.87989i	0.358955	+	0.318006i
$615$	3.65143	−	0.899998i	0.147240	−	0.0362914i
$616$	0.0140407	+	0.115635i	0.000565714	+	0.00465908i
$617$	−9.37213	−	8.30298i	−0.377308	−	0.334265i	0.453061	−	0.891479i	$-0.350332\pi$
$617$	−9.37213	−	8.30298i	−0.377308	−	0.334265i	−0.830369	+	0.557214i	$0.811870\pi$
$618$	−6.77419	−	17.8621i	−0.272498	−	0.718518i
$619$	−36.9876	+	19.4126i	−1.48666	+	0.780259i	−0.995850	−	0.0910084i	$-0.970991\pi$
$619$	−36.9876	+	19.4126i	−1.48666	+	0.780259i	−0.490809	+	0.871267i	$0.663299\pi$
$620$	12.0700	+	6.33483i	0.484743	+	0.254413i
$621$	−2.34739	+	19.3325i	−0.0941976	+	0.775787i
$622$	−3.54399	−	3.13970i	−0.142101	−	0.125891i
$623$	−0.399367	−	0.0984351i	−0.0160003	−	0.00394372i
$624$	−4.66441	−	5.26402i	−0.186726	−	0.210729i
$625$	2.31490	−	0.570571i	0.0925959	−	0.0228228i
$626$	−3.85138	−	2.02136i	−0.153932	−	0.0807899i
$627$	−0.0423100	−	0.0222060i	−0.00168970	−	0.000886822i
$628$	30.0800	−	79.3144i	1.20032	−	3.16499i
$629$	−6.14435	+	16.2013i	−0.244991	+	0.645989i
$630$	−0.143666	+	0.208137i	−0.00572380	+	0.00829236i
$631$	13.2938	−	3.27662i	0.529216	−	0.130440i	0.0343511	−	0.999410i	$-0.489064\pi$
$631$	13.2938	−	3.27662i	0.529216	−	0.130440i	0.494865	+	0.868970i	$0.335217\pi$
$632$	−2.71751	+	3.93699i	−0.108097	+	0.156605i
$633$	−0.785006	−	6.46511i	−0.0312012	−	0.256965i
$634$	−18.8275	+	49.6440i	−0.747734	+	1.97161i
$635$	24.4618	−	12.8386i	0.970738	−	0.509483i
$636$	10.4725	+	15.1721i	0.415263	+	0.601612i
$637$	20.7679	−	14.3379i	0.822854	−	0.568090i
$638$	5.13706	−	7.44231i	0.203378	−	0.294644i
$639$	4.26946	−	35.1621i	0.168897	−	1.39099i
$640$	−27.5787	−	6.79754i	−1.09014	−	0.268696i
$641$	−9.95870	−	14.4277i	−0.393345	−	0.569858i	0.575414	−	0.817862i	$-0.304841\pi$
$641$	−9.95870	−	14.4277i	−0.393345	−	0.569858i	−0.968759	+	0.248004i	$0.920225\pi$
$642$	13.5909	−	12.0405i	0.536392	−	0.475202i
$643$	−7.25606	−	3.80828i	−0.286151	−	0.150184i	0.315541	−	0.948912i	$-0.397814\pi$
$643$	−7.25606	−	3.80828i	−0.286151	−	0.150184i	−0.601692	+	0.798728i	$0.705506\pi$
$644$	−0.0872401	−	0.718487i	−0.00343774	−	0.0283124i
$645$	0.216688	−	1.78458i	0.00853207	−	0.0702679i
$646$	−0.616205	+	0.545910i	−0.0242443	+	0.0214785i
$647$	5.22698	−	7.57259i	0.205494	−	0.297709i	−0.706663	−	0.707550i	$-0.749800\pi$
$647$	5.22698	−	7.57259i	0.205494	−	0.297709i	0.912157	+	0.409841i	$0.134416\pi$
$648$	4.16950	+	34.3389i	0.163793	+	1.34896i
$649$	0.844951	−	6.95880i	0.0331672	−	0.273157i
$650$	20.9037	−	14.4317i	0.819909	−	0.566057i
$651$	0.00341593	+	0.0281327i	0.000133881	+	0.00110261i
$652$	95.2452	−	23.4758i	3.73009	−	0.919385i
$653$	−20.6758			−0.809108			−0.404554	−	0.914514i	$-0.632573\pi$
$653$	−20.6758			−0.809108			−0.404554	+	0.914514i	$0.632573\pi$
$654$	−11.5829			−0.452925
$655$	−4.58463	+	1.13001i	−0.179136	+	0.0441531i
$656$	−7.82952	+	20.6447i	−0.305691	+	0.806042i
$657$	−29.7365			−1.16013
$658$	0.0953545	+	0.251429i	0.00371731	+	0.00980173i
$659$	−13.4242	−	3.30878i	−0.522934	−	0.128892i	−0.0309921	−	0.999520i	$-0.509867\pi$
$659$	−13.4242	−	3.30878i	−0.522934	−	0.128892i	−0.491942	+	0.870628i	$0.663713\pi$
$660$	−1.93378	+	1.71318i	−0.0752721	+	0.0666853i
$661$	−31.4628	−	7.75488i	−1.22376	−	0.301630i	−0.426067	−	0.904692i	$-0.640101\pi$
$661$	−31.4628	−	7.75488i	−1.22376	−	0.301630i	−0.797694	+	0.603062i	$0.793947\pi$
$662$	−36.3855	+	32.2347i	−1.41416	+	1.25284i
$663$	1.27605	−	5.17925i	0.0495576	−	0.201145i
$664$	42.9221	+	38.0256i	1.66570	+	1.47568i
$665$	0.00228845	+	0.00331540i	8.87425e−5	+	0.000128566i
$666$	36.9004	−	9.09513i	1.42986	−	0.352429i
$667$	−16.0168	+	23.2044i	−0.620173	+	0.898476i
$668$	−58.1891	−	14.3423i	−2.25140	−	0.554921i
$669$	6.27788	+	1.54736i	0.242717	+	0.0598243i
$670$	0.121221	−	0.998346i	0.00468318	−	0.0385695i
$671$	−5.31710	−	4.71054i	−0.205264	−	0.181848i
$672$	0.000615072		0.00162181i	2.37269e−5		6.25627e-5i
$673$	3.59862	−	1.88870i	0.138717	−	0.0728041i	−0.393937	−	0.919137i	$-0.628887\pi$
$673$	3.59862	−	1.88870i	0.138717	−	0.0728041i	0.532654	+	0.846333i	$0.321195\pi$
$674$	−19.0803	+	27.6426i	−0.734945	+	1.06475i
$675$	7.91417			0.304616
$676$	−29.6381	+	42.9556i	−1.13993	+	1.65214i
$677$	−6.10595			−0.234671			−0.117335	−	0.993092i	$-0.537435\pi$
$677$	−6.10595			−0.234671			−0.117335	+	0.993092i	$0.537435\pi$
$678$	4.14095	−	5.99921i	0.159032	−	0.230398i
$679$	−0.0431822	+	0.0226638i	−0.00165718	+	0.000869756i
$680$	7.92022	+	20.8839i	0.303727	+	0.800861i
$681$	7.32857	+	6.49254i	0.280831	+	0.248795i
$682$	0.636216	−	5.23971i	0.0243620	−	0.200639i
$683$	38.3974	+	9.46411i	1.46924	+	0.362134i	0.891100	−	0.453807i	$-0.149934\pi$
$683$	38.3974	+	9.46411i	1.46924	+	0.362134i	0.578135	+	0.815941i	$0.303781\pi$
$684$	1.17019	+	0.288427i	0.0447435	+	0.0110283i
$685$	−14.8327	+	21.4889i	−0.566730	+	0.821050i
$686$	−0.850194	+	0.209554i	−0.0324606	+	0.00800081i
$687$	2.69485	+	3.90417i	0.102815	+	0.148953i
$688$	7.90011	+	6.99888i	0.301189	+	0.266830i
$689$	23.0022	−	25.9691i	0.876315	−	0.989344i
$690$	9.03310	−	8.00263i	0.343884	−	0.304655i
$691$	−31.9230	−	7.86831i	−1.21441	−	0.299325i	−0.420460	−	0.907311i	$-0.638131\pi$
$691$	−31.9230	−	7.86831i	−1.21441	−	0.299325i	−0.793947	+	0.607987i	$0.791977\pi$
$692$	−13.8051	+	12.2303i	−0.524791	+	0.464924i
$693$	0.0634638	+	0.0156424i	0.00241079	+	0.000594207i
$694$	17.6312	+	46.4896i	0.669270	+	1.76472i
$695$	16.3179			0.618974
$696$	3.33509	−	8.79390i	0.126416	−	0.333332i
$697$	−16.2589	+	4.00746i	−0.615849	+	0.151793i
$698$	−4.43677			−0.167934
$699$	−10.3356			−0.390926
$700$	−0.285581	+	0.0703894i	−0.0107939	+	0.00266047i
$701$	−3.15929	−	26.0191i	−0.119325	−	0.982727i	−0.922236	−	0.386628i	$-0.873640\pi$
$701$	−3.15929	−	26.0191i	−0.119325	−	0.982727i	0.802911	−	0.596099i	$-0.203283\pi$
$702$	−22.7767	+	8.64052i	−0.859650	+	0.326115i
$703$	0.0729700	−	0.600962i	0.00275212	−	0.0226657i
$704$	0.871914	+	7.18086i	0.0328615	+	0.270639i
$705$	−1.70007	+	2.46298i	−0.0640284	+	0.0927612i
$706$	−21.6320	+	19.1643i	−0.814131	+	0.721258i
$707$	−0.00478784	+	0.0394314i	−0.000180065	+	0.00148297i
$708$	−1.75124	−	14.4227i	−0.0658155	−	0.542039i
$709$	−11.0173	−	5.78233i	−0.413764	−	0.217160i	0.244979	−	0.969528i	$-0.421219\pi$
$709$	−11.0173	−	5.78233i	−0.413764	−	0.217160i	−0.658742	+	0.752368i	$0.728911\pi$
$710$	−34.2090	+	30.3065i	−1.28384	+	1.13738i
$711$	1.52488	+	2.20917i	0.0571875	+	0.0828504i
$712$	77.3596	+	19.0674i	2.89917	+	0.714582i
$713$	−1.98366	+	16.3369i	−0.0742885	+	0.611821i
$714$	−0.0525662	+	0.0761553i	−0.00196724	+	0.00285004i
$715$	4.00126	+	2.76131i	0.149639	+	0.103267i
$716$	−10.7216	−	15.5329i	−0.400685	−	0.580493i
$717$	−2.22582	+	1.16820i	−0.0831247	+	0.0436272i
$718$	3.09548	−	8.16211i	0.115522	−	0.304607i
$719$	−2.24669	−	18.5032i	−0.0837874	−	0.690051i	−0.972715	−	0.232004i	$-0.925472\pi$
$719$	−2.24669	−	18.5032i	−0.0837874	−	0.690051i	0.888928	−	0.458048i	$-0.151451\pi$
$720$	9.38745	−	13.6001i	0.349850	−	0.506845i
$721$	0.404157	−	0.0996159i	0.0150516	−	0.00370989i
$722$	−26.4534	+	38.3244i	−0.984495	+	1.42629i
$723$	1.35007	−	3.55985i	0.0502098	−	0.132392i
$724$	−24.0218	+	63.3403i	−0.892763	+	2.35402i
$725$	10.1457	+	5.32490i	0.376803	+	0.197762i
$726$	−10.5150	−	5.51868i	−0.390247	−	0.204818i
$727$	−39.3920	+	9.70926i	−1.46097	+	0.360097i	−0.888138	−	0.459577i	$-0.848001\pi$
$727$	−39.3920	+	9.70926i	−1.46097	+	0.360097i	−0.572831	+	0.819673i	$0.694155\pi$
$728$	0.373863	−	0.258112i	0.0138563	−	0.00956625i
$729$	15.0161	+	3.70113i	0.556151	+	0.137079i
$730$	28.7195	+	25.4432i	1.06296	+	0.941696i
$731$	−0.964854	+	7.94629i	−0.0356864	+	0.293904i
$732$	−13.0364	−	6.84202i	−0.481838	−	0.252888i
$733$	35.4871	−	18.6251i	1.31075	−	0.687933i	0.342876	−	0.939381i	$-0.388599\pi$
$733$	35.4871	−	18.6251i	1.31075	−	0.687933i	0.967871	+	0.251447i	$0.0809066\pi$
$734$	−1.85719	−	4.89700i	−0.0685500	−	0.180751i
$735$	−3.64708	−	3.23103i	−0.134525	−	0.119178i
$736$	0.121411	+	0.999909i	0.00447527	+	0.0368571i
$737$	−0.252365	+	0.0622023i	−0.00929597	+	0.00229125i
$738$	27.4917	+	24.3556i	1.01199	+	0.896541i
$739$	−2.67804	+	2.37254i	−0.0985134	+	0.0872753i	−0.710942	−	0.703251i	$-0.751731\pi$
$739$	−2.67804	+	2.37254i	−0.0985134	+	0.0872753i	0.612429	+	0.790526i	$0.290193\pi$
$740$	−28.9818	−	15.2108i	−1.06539	−	0.559160i
$741$	1.76676e−5		0.186362i	6.49036e−7		0.00684618i
$742$	−0.532887	+	0.279680i	−0.0195629	+	0.0102674i
$743$	4.52773	−	11.9387i	0.166106	−	0.437987i	−0.825956	−	0.563735i	$-0.809364\pi$
$743$	4.52773	−	11.9387i	0.166106	−	0.437987i	0.992062	+	0.125748i	$0.0401331\pi$
$744$	−0.661684	−	5.44946i	−0.0242585	−	0.199787i
$745$	−9.00781	+	4.72766i	−0.330021	+	0.173208i
$746$	33.7261			1.23480
$747$	28.4914	−	14.9535i	1.04245	−	0.547119i
$748$	8.61060	−	7.62833i	0.314835	−	0.278919i
$749$	0.224747	+	0.325602i	0.00821208	+	0.0118973i
$750$	−10.0603	−	8.91263i	−0.367349	−	0.325443i
$751$	14.4117	+	20.8789i	0.525890	+	0.761883i	0.992456	−	0.122603i	$-0.0391242\pi$
$751$	14.4117	+	20.8789i	0.525890	+	0.761883i	−0.466566	+	0.884487i	$0.654509\pi$
$752$	−6.23066	−	16.4289i	−0.227209	−	0.599100i
$753$	1.80145	+	4.75003i	0.0656485	+	0.173101i
$754$	−35.0127	−	4.24794i	−1.27509	−	0.154701i
$755$	−4.16838	+	10.9911i	−0.151703	+	0.400008i
$756$	0.282074			0.0102589
$757$	1.93751	+	5.10878i	0.0704198	+	0.185682i	0.965606	−	0.260012i	$-0.0837264\pi$
$757$	1.93751	+	5.10878i	0.0704198	+	0.185682i	−0.895186	+	0.445693i	$0.852957\pi$
$758$	−2.59883	+	21.4033i	−0.0943937	+	0.777402i
$759$	−2.76173	−	1.44947i	−0.100245	−	0.0526124i
$760$	−0.443286	−	0.642211i	−0.0160797	−	0.0232954i
$761$	−23.2473	−	33.6795i	−0.842713	−	1.22088i	−0.973321	−	0.229446i	$-0.926308\pi$
$761$	−23.2473	−	33.6795i	−0.842713	−	1.22088i	0.130608	−	0.991434i	$-0.458307\pi$
$762$	−19.6312	−	10.3033i	−0.711164	−	0.373247i
$763$	0.0304214	−	0.250543i	0.00110133	−	0.00907026i
$764$	−34.3146	−	90.4801i	−1.24146	−	3.27345i
$765$	12.5331			0.453134
$766$	20.3795	−	53.7363i	0.736341	−	1.94157i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39315 - 2.01832i) q^{2} +(0.422612 - 0.221804i) q^{3} +(-1.42355 - 3.75360i) q^{4} +(1.09172 + 0.967184i) q^{5} +(0.141089 - 1.16197i) q^{6} +(0.0247635 + 0.00610365i) q^{7} +(-4.79682 - 1.18231i) q^{8} +(-1.57479 + 2.28148i) q^{9} +O(q^{10})\)	\(q+(1.39315 - 2.01832i) q^{2} +(0.422612 - 0.221804i) q^{3} +(-1.42355 - 3.75360i) q^{4} +(1.09172 + 0.967184i) q^{5} +(0.141089 - 1.16197i) q^{6} +(0.0247635 + 0.00610365i) q^{7} +(-4.79682 - 1.18231i) q^{8} +(-1.57479 + 2.28148i) q^{9} +(3.47302 - 0.856022i) q^{10} +(-0.525155 - 0.760819i) q^{11} +(-1.43417 - 1.27057i) q^{12} +(-1.67528 + 3.19272i) q^{13} +(0.0468182 - 0.0414773i) q^{14} +(0.675901 + 0.166595i) q^{15} +(-3.05920 + 2.71021i) q^{16} +(-3.00961 - 0.741802i) q^{17} +(2.41084 + 6.35686i) q^{18} +0.108296 q^{19} +(2.07629 - 5.47473i) q^{20} +(0.0118191 - 0.00291316i) q^{21} -2.26719 q^{22} +7.06888 q^{23} +(-2.28943 + 0.564295i) q^{24} +(-0.346265 - 2.85175i) q^{25} +(4.11001 + 7.82917i) q^{26} +(-0.332074 + 2.73488i) q^{27} +(-0.0123414 - 0.101641i) q^{28} +(-2.26582 + 3.28261i) q^{29} +(1.27787 - 1.13209i) q^{30} +(-0.280618 + 2.31110i) q^{31} +(0.0171754 + 0.141452i) q^{32} +(-0.390689 - 0.205050i) q^{33} +(-5.69002 + 5.04092i) q^{34} +(0.0211315 + 0.0306143i) q^{35} +(10.8055 + 2.66333i) q^{36} +(0.673803 - 5.54927i) q^{37} +(0.150872 - 0.218575i) q^{38} +(0.000163142 + 1.72086i) q^{39} +(-4.09330 - 5.93016i) q^{40} +(4.78352 - 2.51058i) q^{41} +(0.0105861 - 0.0279133i) q^{42} +(-0.311275 - 2.56358i) q^{43} +(-2.10822 + 3.05429i) q^{44} +(-3.92585 + 0.967634i) q^{45} +(9.84798 - 14.2673i) q^{46} +(-1.52449 + 4.01975i) q^{47} +(-0.691718 + 1.82391i) q^{48} +(-6.19762 - 3.25276i) q^{49} +(-6.23814 - 3.27403i) q^{50} +(-1.43643 + 0.354049i) q^{51} +(14.3690 + 1.74333i) q^{52} +(-9.34209 - 2.30262i) q^{53} +(5.05723 + 4.48032i) q^{54} +(0.162527 - 1.33853i) q^{55} +(-0.111569 - 0.0585562i) q^{56} +(0.0457670 - 0.0240204i) q^{57} +(3.46874 + 9.14631i) q^{58} +(5.67571 + 5.02824i) q^{59} +(-0.336851 - 2.77422i) q^{60} +(7.46070 - 1.83890i) q^{61} +(4.27360 + 3.78608i) q^{62} +(-0.0529226 + 0.0468853i) q^{63} +(-6.92838 - 3.63629i) q^{64} +(-4.91689 + 1.86526i) q^{65} +(-0.958143 + 0.502872i) q^{66} +(0.0996988 - 0.262884i) q^{67} +(1.49991 + 12.3529i) q^{68} +(2.98739 - 1.56790i) q^{69} +0.0912288 q^{70} +(-11.3135 + 5.93776i) q^{71} +(10.2514 - 9.08195i) q^{72} +(6.09344 + 8.82787i) q^{73} +(-10.2615 - 9.09089i) q^{74} +(-0.778864 - 1.12838i) q^{75} +(-0.154165 - 0.406498i) q^{76} +(-0.00836090 - 0.0220459i) q^{77} +(3.47348 + 2.39708i) q^{78} +(0.343366 - 0.905382i) q^{79} -5.96108 q^{80} +(-2.48284 - 6.54672i) q^{81} +(1.59698 - 13.1523i) q^{82} +(-10.2775 - 5.39407i) q^{83} +(-0.0277600 - 0.0402173i) q^{84} +(-2.56821 - 3.72069i) q^{85} +(-5.60778 - 2.94319i) q^{86} +(-0.229468 + 1.88984i) q^{87} +(1.61955 + 4.27041i) q^{88} -16.1273 q^{89} +(-3.51628 + 9.27167i) q^{90} +(-0.0609730 + 0.0688374i) q^{91} +(-10.0629 - 26.5337i) q^{92} +(0.394018 + 1.03894i) q^{93} +(5.98930 + 8.67700i) q^{94} +(0.118229 + 0.104742i) q^{95} +(0.0386332 + 0.0559698i) q^{96} +(-1.43126 + 1.26798i) q^{97} +(-15.1993 + 7.97721i) q^{98} +2.56280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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