LMFDB - Embedded newform 169.2.g.a.27.2

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			27.2
Character	$\chi$	$=$	169.27
Dual form			169.2.g.a.144.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.814971 - 2.14890i) q^{2} +(0.722310 - 1.04645i) q^{3} +(-2.45658 + 2.17634i) q^{4} +(-0.370802 - 3.05383i) q^{5} +(-2.83737 - 0.699350i) q^{6} +(0.780099 + 0.409428i) q^{7} +(2.60879 + 1.36920i) q^{8} +(0.490496 + 1.29333i) q^{9} +O(q^{10})$	\(q+(-0.814971 - 2.14890i) q^{2} +(0.722310 - 1.04645i) q^{3} +(-2.45658 + 2.17634i) q^{4} +(-0.370802 - 3.05383i) q^{5} +(-2.83737 - 0.699350i) q^{6} +(0.780099 + 0.409428i) q^{7} +(2.60879 + 1.36920i) q^{8} +(0.490496 + 1.29333i) q^{9} +(-6.26019 + 3.28560i) q^{10} +(0.433436 - 1.14288i) q^{11} +(0.503012 + 4.14268i) q^{12} +(-3.33830 - 1.36225i) q^{13} +(0.244062 - 2.01003i) q^{14} +(-3.46351 - 1.81779i) q^{15} +(0.0249923 - 0.205830i) q^{16} +(5.12941 + 2.69212i) q^{17} +(2.37950 - 2.10805i) q^{18} +0.803292 q^{19} +(7.55709 + 6.69499i) q^{20} +(0.991918 - 0.520599i) q^{21} -2.80917 q^{22} -1.28618 q^{23} +(3.31715 - 1.74097i) q^{24} +(-4.33368 + 1.06816i) q^{25} +(-0.206723 + 8.28388i) q^{26} +(5.41143 + 1.33380i) q^{27} +(-2.80743 + 0.691970i) q^{28} +(-2.29000 - 6.03824i) q^{29} +(-1.08359 + 8.92418i) q^{30} +(-4.54890 - 1.12120i) q^{31} +(5.25863 - 1.29614i) q^{32} +(-0.882884 - 1.27908i) q^{33} +(1.60479 - 13.2166i) q^{34} +(0.961060 - 2.53411i) q^{35} +(-4.01967 - 2.10969i) q^{36} +(8.67654 + 2.13858i) q^{37} +(-0.654660 - 1.72620i) q^{38} +(-3.83681 + 2.50939i) q^{39} +(3.21396 - 8.47450i) q^{40} +(4.12633 - 5.97803i) q^{41} +(-1.92710 - 1.70726i) q^{42} +(3.22950 - 0.796001i) q^{43} +(1.42252 + 3.75087i) q^{44} +(3.76774 - 1.97746i) q^{45} +(1.04820 + 2.76387i) q^{46} +(-4.38657 - 3.88617i) q^{47} +(-0.197338 - 0.174826i) q^{48} +(-3.53553 - 5.12210i) q^{49} +(5.82719 + 8.44214i) q^{50} +(6.52219 - 3.42311i) q^{51} +(11.1655 - 3.91881i) q^{52} +(5.14307 + 2.69929i) q^{53} +(-1.54396 - 12.7156i) q^{54} +(-3.65087 - 0.899858i) q^{55} +(1.47453 + 2.13622i) q^{56} +(0.580226 - 0.840602i) q^{57} +(-11.1093 + 9.84198i) q^{58} +(0.450121 + 3.70708i) q^{59} +(12.4645 - 3.07223i) q^{60} +(-10.2717 + 5.39103i) q^{61} +(1.29787 + 10.6889i) q^{62} +(-0.146890 + 1.20975i) q^{63} +(-7.30647 - 10.5852i) q^{64} +(-2.92223 + 10.6997i) q^{65} +(-2.02909 + 2.93964i) q^{66} +(9.13908 + 8.09652i) q^{67} +(-18.4598 + 4.54994i) q^{68} +(-0.929019 + 1.34592i) q^{69} -6.22879 q^{70} +(-4.50356 + 6.52453i) q^{71} +(-0.491226 + 4.04561i) q^{72} +(-0.529407 + 1.39593i) q^{73} +(-2.47554 - 20.3879i) q^{74} +(-2.01249 + 5.30650i) q^{75} +(-1.97335 + 1.74824i) q^{76} +(0.806048 - 0.714096i) q^{77} +(8.51933 + 6.19986i) q^{78} +(12.7973 + 11.3374i) q^{79} -0.637837 q^{80} +(2.19842 - 1.94763i) q^{81} +(-16.2090 - 3.99517i) q^{82} +(8.22709 + 11.9190i) q^{83} +(-1.30373 + 3.43765i) q^{84} +(6.31929 - 16.6626i) q^{85} +(-4.34248 - 6.29117i) q^{86} +(-7.97279 - 1.96512i) q^{87} +(2.69557 - 2.38806i) q^{88} -11.6944 q^{89} +(-7.31997 - 6.48492i) q^{90} +(-2.04647 - 2.42949i) q^{91} +(3.15960 - 2.79916i) q^{92} +(-4.45899 + 3.95032i) q^{93} +(-4.77606 + 12.5934i) q^{94} +(-0.297862 - 2.45312i) q^{95} +(2.44202 - 6.43909i) q^{96} +(0.702735 - 5.78754i) q^{97} +(-8.12554 + 11.7719i) q^{98} +1.69072 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{13}\right)$

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 $

$2$	−0.814971	−	2.14890i	−0.576272	−	1.51950i	−0.833143	−	0.553058i	$-0.813461\pi$
$2$	−0.814971	−	2.14890i	−0.576272	−	1.51950i	0.256871	−	0.966446i	$-0.417308\pi$
$3$	0.722310	−	1.04645i	0.417026	−	0.604166i	−0.557025	−	0.830496i	$-0.688057\pi$
$3$	0.722310	−	1.04645i	0.417026	−	0.604166i	0.974051	+	0.226329i	$0.0726726\pi$
$4$	−2.45658	+	2.17634i	−1.22829	+	1.08817i
$5$	−0.370802	−	3.05383i	−0.165828	−	1.36571i	−0.803453	−	0.595368i	$-0.797006\pi$
$5$	−0.370802	−	3.05383i	−0.165828	−	1.36571i	0.637625	−	0.770347i	$-0.279917\pi$
$6$	−2.83737	−	0.699350i	−1.15835	−	0.285508i
$7$	0.780099	+	0.409428i	0.294850	+	0.154749i	0.605662	−	0.795722i	$-0.292909\pi$
$7$	0.780099	+	0.409428i	0.294850	+	0.154749i	−0.310812	+	0.950472i	$0.600601\pi$
$8$	2.60879	+	1.36920i	0.922346	+	0.484085i
$9$	0.490496	+	1.29333i	0.163499	+	0.431110i
$10$	−6.26019	+	3.28560i	−1.97965	+	1.03900i
$11$	0.433436	−	1.14288i	0.130686	−	0.344590i	−0.853662	−	0.520828i	$-0.825623\pi$
$11$	0.433436	−	1.14288i	0.130686	−	0.344590i	0.984348	+	0.176237i	$0.0563927\pi$
$12$	0.503012	+	4.14268i	0.145207	+	1.19589i
$13$	−3.33830	−	1.36225i	−0.925879	−	0.377820i
$13$	−3.33830	−	1.36225i	−0.925879	−	0.377820i
$14$	0.244062	−	2.01003i	0.0652282	−	0.537203i
$15$	−3.46351	−	1.81779i	−0.894273	−	0.469351i
$16$	0.0249923	−	0.205830i	0.00624807	−	0.0514575i
$17$	5.12941	+	2.69212i	1.24407	+	0.652936i	0.952769	−	0.303697i	$-0.0982209\pi$
$17$	5.12941	+	2.69212i	1.24407	+	0.652936i	0.291297	+	0.956633i	$0.405913\pi$
$18$	2.37950	−	2.10805i	0.560854	−	0.496873i
$19$	0.803292			0.184288			0.0921439	−	0.995746i	$-0.470628\pi$
$19$	0.803292			0.184288			0.0921439	+	0.995746i	$0.470628\pi$
$20$	7.55709	+	6.69499i	1.68982	+	1.49705i
$21$	0.991918	−	0.520599i	0.216454	−	0.113604i
$22$	−2.80917			−0.598916
$23$	−1.28618			−0.268187			−0.134093	−	0.990969i	$-0.542812\pi$
$23$	−1.28618			−0.268187			−0.134093	+	0.990969i	$0.542812\pi$
$24$	3.31715	−	1.74097i	0.677110	−	0.355375i
$25$	−4.33368	+	1.06816i	−0.866736	+	0.213631i
$26$	−0.206723	+	8.28388i	−0.0405417	+	1.62460i
$27$	5.41143	+	1.33380i	1.04143	+	0.256689i
$28$	−2.80743	+	0.691970i	−0.530555	+	0.130770i
$29$	−2.29000	−	6.03824i	−0.425243	−	1.12127i	−0.960914	−	0.276846i	$-0.910711\pi$
$29$	−2.29000	−	6.03824i	−0.425243	−	1.12127i	0.535672	−	0.844426i	$-0.320059\pi$
$30$	−1.08359	+	8.92418i	−0.197836	+	1.62932i
$31$	−4.54890	−	1.12120i	−0.817006	−	0.201374i	−0.191399	−	0.981512i	$-0.561302\pi$
$31$	−4.54890	−	1.12120i	−0.817006	−	0.201374i	−0.625607	+	0.780138i	$0.715149\pi$
$32$	5.25863	−	1.29614i	0.929603	−	0.229127i
$33$	−0.882884	−	1.27908i	−0.153690	−	0.222659i
$34$	1.60479	−	13.2166i	0.275219	−	2.26663i
$35$	0.961060	−	2.53411i	0.162449	−	0.428342i
$36$	−4.01967	−	2.10969i	−0.669945	−	0.351614i
$37$	8.67654	+	2.13858i	1.42642	+	0.351580i	0.875596	−	0.483045i	$-0.160469\pi$
$37$	8.67654	+	2.13858i	1.42642	+	0.351580i	0.550819	+	0.834624i	$0.314315\pi$
$38$	−0.654660	−	1.72620i	−0.106200	−	0.280026i
$39$	−3.83681	+	2.50939i	−0.614382	+	0.401824i
$40$	3.21396	−	8.47450i	0.508171	−	1.33994i
$41$	4.12633	−	5.97803i	0.644425	−	0.933611i	−0.355574	−	0.934648i	$-0.615715\pi$
$41$	4.12633	−	5.97803i	0.644425	−	0.933611i	0.999999	+	0.00103695i	$0.000330070\pi$
$42$	−1.92710	−	1.70726i	−0.297358	−	0.263436i
$43$	3.22950	−	0.796001i	0.492494	−	0.121389i	0.0147560	−	0.999891i	$-0.495303\pi$
$43$	3.22950	−	0.796001i	0.492494	−	0.121389i	0.477738	+	0.878502i	$0.341457\pi$
$44$	1.42252	+	3.75087i	0.214453	+	0.565466i
$45$	3.76774	−	1.97746i	0.561661	−	0.294782i
$46$	1.04820	+	2.76387i	0.154548	+	0.407510i
$47$	−4.38657	−	3.88617i	−0.639848	−	0.566856i	0.279576	−	0.960123i	$-0.409806\pi$
$47$	−4.38657	−	3.88617i	−0.639848	−	0.566856i	−0.919424	+	0.393268i	$0.871344\pi$
$48$	−0.197338	−	0.174826i	−0.0284833	−	0.0252340i
$49$	−3.53553	−	5.12210i	−0.505076	−	0.731728i
$50$	5.82719	+	8.44214i	0.824089	+	1.19390i
$51$	6.52219	−	3.42311i	0.913290	−	0.479331i
$52$	11.1655	−	3.91881i	1.54838	−	0.543441i
$53$	5.14307	+	2.69929i	0.706454	+	0.370776i	0.779371	−	0.626562i	$-0.215539\pi$
$53$	5.14307	+	2.69929i	0.706454	+	0.370776i	−0.0729171	+	0.997338i	$0.523231\pi$
$54$	−1.54396	−	12.7156i	−0.210106	−	1.73038i
$55$	−3.65087	−	0.899858i	−0.492283	−	0.121337i
$56$	1.47453	+	2.13622i	0.197042	+	0.285465i
$57$	0.580226	−	0.840602i	0.0768528	−	0.111340i
$58$	−11.1093	+	9.84198i	−1.45872	+	1.29232i
$59$	0.450121	+	3.70708i	0.0586008	+	0.482621i	0.992234	+	0.124389i	$0.0396971\pi$
$59$	0.450121	+	3.70708i	0.0586008	+	0.482621i	−0.933633	+	0.358232i	$0.883380\pi$
$60$	12.4645	−	3.07223i	1.60916	−	0.396623i
$61$	−10.2717	+	5.39103i	−1.31516	+	0.690250i	−0.968798	−	0.247850i	$-0.920276\pi$
$61$	−10.2717	+	5.39103i	−1.31516	+	0.690250i	−0.346364	+	0.938100i	$0.612584\pi$
$62$	1.29787	+	10.6889i	0.164829	+	1.35749i
$63$	−0.146890	+	1.20975i	−0.0185064	+	0.152414i
$64$	−7.30647	−	10.5852i	−0.913309	−	1.32316i
$65$	−2.92223	+	10.6997i	−0.362458	+	1.32714i
$66$	−2.02909	+	2.93964i	−0.249764	+	0.361845i
$67$	9.13908	+	8.09652i	1.11652	+	0.989147i	0.999992	−	0.00404056i	$-0.00128615\pi$
$67$	9.13908	+	8.09652i	1.11652	+	0.989147i	0.116525	+	0.993188i	$0.462825\pi$
$68$	−18.4598	+	4.54994i	−2.23858	+	0.551761i
$69$	−0.929019	+	1.34592i	−0.111841	+	0.162029i
$70$	−6.22879			−0.744483
$71$	−4.50356	+	6.52453i	−0.534474	+	0.774320i	−0.993467	−	0.114120i	$-0.963595\pi$
$71$	−4.50356	+	6.52453i	−0.534474	+	0.774320i	0.458993	+	0.888440i	$0.348210\pi$
$72$	−0.491226	+	4.04561i	−0.0578916	+	0.476780i
$73$	−0.529407	+	1.39593i	−0.0619624	+	0.163382i	−0.962422	−	0.271558i	$-0.912461\pi$
$73$	−0.529407	+	1.39593i	−0.0619624	+	0.163382i	0.900460	+	0.434940i	$0.143230\pi$
$74$	−2.47554	−	20.3879i	−0.287776	−	2.37005i
$75$	−2.01249	+	5.30650i	−0.232382	+	0.612742i
$76$	−1.97335	+	1.74824i	−0.226359	+	0.200537i
$77$	0.806048	−	0.714096i	0.0918577	−	0.0813788i
$78$	8.51933	+	6.19986i	0.964624	+	0.701996i
$79$	12.7973	+	11.3374i	1.43981	+	1.27556i	0.901481	+	0.432819i	$0.142481\pi$
$79$	12.7973	+	11.3374i	1.43981	+	1.27556i	0.538325	+	0.842738i	$0.319057\pi$
$80$	−0.637837			−0.0713124
$81$	2.19842	−	1.94763i	0.244269	−	0.216403i
$82$	−16.2090	−	3.99517i	−1.78999	−	0.441193i
$83$	8.22709	+	11.9190i	0.903040	+	1.30828i	0.950923	+	0.309427i	$0.100137\pi$
$83$	8.22709	+	11.9190i	0.903040	+	1.30828i	−0.0478829	+	0.998853i	$0.515247\pi$
$84$	−1.30373	+	3.43765i	−0.142248	+	0.375078i
$85$	6.31929	−	16.6626i	0.685424	−	1.80731i
$86$	−4.34248	−	6.29117i	−0.468262	−	0.678394i
$87$	−7.97279	−	1.96512i	−0.854772	−	0.210682i
$88$	2.69557	−	2.38806i	0.287348	−	0.254568i
$89$	−11.6944			−1.23961			−0.619804	−	0.784756i	$-0.712788\pi$
$89$	−11.6944			−1.23961			−0.619804	+	0.784756i	$0.712788\pi$
$90$	−7.31997	−	6.48492i	−0.771592	−	0.683571i
$91$	−2.04647	−	2.42949i	−0.214528	−	0.254679i
$92$	3.15960	−	2.79916i	0.329411	−	0.291833i
$93$	−4.45899	+	3.95032i	−0.462376	+	0.409629i
$94$	−4.77606	+	12.5934i	−0.492613	+	1.29891i
$95$	−0.297862	−	2.45312i	−0.0305600	−	0.251684i
$96$	2.44202	−	6.43909i	0.249238	−	0.657187i
$97$	0.702735	−	5.78754i	0.0713519	−	0.587636i	−0.912555	−	0.408954i	$-0.865894\pi$
$97$	0.702735	−	5.78754i	0.0713519	−	0.587636i	0.983907	−	0.178682i	$-0.0571833\pi$
$98$	−8.12554	+	11.7719i	−0.820803	+	1.18914i
$99$	1.69072			0.169923
$100$	8.32137	−	12.0556i	0.832137	−	1.20556i
$101$	−0.975608	+	0.240466i	−0.0970766	+	0.0239272i	−0.287555	−	0.957764i	$-0.592842\pi$
$101$	−0.975608	+	0.240466i	−0.0970766	+	0.0239272i	0.190478	+	0.981691i	$0.438996\pi$
$102$	−12.6713	−	11.2258i	−1.25465	−	1.11152i
$103$	−8.58119	+	12.4320i	−0.845530	+	1.22496i	0.126935	+	0.991911i	$0.459486\pi$
$103$	−8.58119	+	12.4320i	−0.845530	+	1.22496i	−0.972465	+	0.233050i	$0.925129\pi$
$104$	−6.84374	−	8.12463i	−0.671084	−	0.796685i
$105$	−1.95763	−	2.83611i	−0.191045	−	0.276776i
$106$	1.60906	−	13.2518i	0.156286	−	1.28713i
$107$	1.40532	+	11.5739i	0.135858	+	1.11889i	0.887985	+	0.459872i	$0.152105\pi$
$107$	1.40532	+	11.5739i	0.135858	+	1.11889i	−0.752127	+	0.659018i	$0.770972\pi$
$108$	−16.1964	+	8.50054i	−1.55850	+	0.817965i
$109$	4.14535	−	1.02174i	0.397053	−	0.0978648i	−0.0357332	−	0.999361i	$-0.511377\pi$
$109$	4.14535	−	1.02174i	0.397053	−	0.0978648i	0.432786	+	0.901497i	$0.357531\pi$
$110$	1.04165	+	8.57872i	0.0993170	+	0.817949i
$111$	8.50506	−	7.53483i	0.807265	−	0.715174i
$112$	0.103769	−	0.150335i	0.00980525	−	0.0142054i
$113$	−5.79105	−	8.38978i	−0.544776	−	0.789244i	0.449814	−	0.893122i	$-0.351490\pi$
$113$	−5.79105	−	8.38978i	−0.544776	−	0.789244i	−0.994590	+	0.103878i	$0.966875\pi$
$114$	−2.27924	−	0.561782i	−0.213470	−	0.0526157i
$115$	0.476917	+	3.92777i	0.0444728	+	0.366266i
$116$	18.7669	+	9.84960i	1.74246	+	0.914513i
$117$	0.124418	−	4.98571i	0.0115024	−	0.460929i
$118$	7.59932	−	3.98843i	0.699574	−	0.367165i
$119$	2.89922	+	4.20025i	0.265771	+	0.385036i
$120$	−6.54664	−	9.48445i	−0.597624	−	0.865808i
$121$	7.11532	+	6.30362i	0.646847	+	0.573057i
$122$	19.9560	+	17.6794i	1.80673	+	1.60062i
$123$	−3.27519	−	8.63598i	−0.295314	−	0.778680i
$124$	13.6149	−	7.14563i	1.22265	−	0.641697i
$125$	−0.585380	−	1.54352i	−0.0523580	−	0.138057i
$126$	2.71934	−	0.670258i	0.242258	−	0.0597113i
$127$	7.29059	+	6.45890i	0.646935	+	0.573134i	0.921473	−	0.388442i	$-0.126987\pi$
$127$	7.29059	+	6.45890i	0.646935	+	0.573134i	−0.274538	+	0.961576i	$0.588525\pi$
$128$	−10.6388	+	15.4130i	−0.940347	+	1.36233i
$129$	1.49973	−	3.95446i	0.132044	−	0.348171i
$130$	25.3742	−	2.44039i	2.22547	−	0.214036i
$131$	−1.90749	−	5.02965i	−0.166659	−	0.439442i	0.825504	−	0.564396i	$-0.190891\pi$
$131$	−1.90749	−	5.02965i	−0.166659	−	0.439442i	−0.992163	+	0.124954i	$0.960122\pi$
$132$	4.95259	+	1.22070i	0.431068	+	0.106249i
$133$	0.626647	+	0.328890i	0.0543372	+	0.0285184i
$134$	9.95054	−	26.2374i	0.859596	−	2.26657i
$135$	2.06662	−	17.0202i	0.177867	−	1.46486i
$136$	9.69551	+	14.0464i	0.831383	+	1.20447i
$137$	−5.26505	+	1.29772i	−0.449823	+	0.110871i	−0.457718	−	0.889097i	$-0.651333\pi$
$137$	−5.26505	+	1.29772i	−0.449823	+	0.110871i	0.00789491	+	0.999969i	$0.497487\pi$
$138$	3.64937	+	0.899488i	0.310655	+	0.0765695i
$139$	0.916034	−	7.54422i	0.0776970	−	0.639892i	−0.900888	−	0.434051i	$-0.857084\pi$
$139$	0.916034	−	7.54422i	0.0776970	−	0.639892i	0.978585	−	0.205841i	$-0.0659931\pi$
$140$	3.15416	+	8.31684i	0.266575	+	0.702901i
$141$	−7.23513	+	1.78330i	−0.609308	+	0.150181i
$142$	17.6909	+	4.36040i	1.48458	+	0.365917i
$143$	−3.00382	+	3.22482i	−0.251192	+	0.269673i
$144$	0.278465	−	0.0686354i	0.0232054	−	0.00571962i
$145$	−17.5906	+	9.23227i	−1.46082	+	0.766698i
$146$	3.43117			0.283966
$147$	−7.91375			−0.652715
$148$	−25.9689	+	13.6295i	−2.13463	+	1.12034i
$149$	0.784604	+	0.695098i	0.0642773	+	0.0569447i	0.694650	−	0.719348i	$-0.255559\pi$
$149$	0.784604	+	0.695098i	0.0642773	+	0.0569447i	−0.630372	+	0.776293i	$0.717098\pi$
$150$	13.0433			1.06498
$151$	−4.59340	+	4.06940i	−0.373805	+	0.331163i	−0.829020	−	0.559219i	$-0.811101\pi$
$151$	−4.59340	+	4.06940i	−0.373805	+	0.331163i	0.455214	+	0.890382i	$0.349563\pi$
$152$	2.09562	+	1.09987i	0.169977	+	0.0892109i
$153$	−0.965852	+	7.95450i	−0.0780845	+	0.643084i
$154$	−2.19143	−	1.15015i	−0.176590	−	0.0926818i
$155$	−1.73722	+	14.3073i	−0.139537	+	1.14919i
$156$	3.96416	−	14.5147i	0.317387	−	1.16211i
$157$	−2.57248	−	21.1863i	−0.205306	−	1.69085i	−0.622970	−	0.782246i	$-0.714074\pi$
$157$	−2.57248	−	21.1863i	−0.205306	−	1.69085i	0.417664	−	0.908602i	$-0.362849\pi$
$158$	13.9335	−	36.7397i	1.10849	−	2.92286i
$159$	6.53955	−	3.43222i	0.518620	−	0.272193i
$160$	−5.90809	−	15.5784i	−0.467076	−	1.23158i
$161$	−1.00335	−	0.526597i	−0.0790748	−	0.0415016i
$162$	−5.97692	−	3.13693i	−0.469591	−	0.246460i
$163$	−24.2657	−	5.98095i	−1.90063	−	0.468464i	−0.999381	−	0.0351676i	$-0.988803\pi$
$163$	−24.2657	−	5.98095i	−1.90063	−	0.468464i	−0.901252	−	0.433296i	$-0.857350\pi$
$164$	2.87355	+	23.6658i	0.224387	+	1.84799i
$165$	−3.57871	+	3.17046i	−0.278602	+	0.246820i
$166$	18.9079	−	27.3929i	1.46754	−	2.12610i
$167$	−3.21349	−	8.47329i	−0.248668	−	0.655683i	0.751323	−	0.659934i	$-0.229416\pi$
$167$	−3.21349	−	8.47329i	−0.248668	−	0.655683i	−0.999991	+	0.00425168i	$0.998647\pi$
$168$	3.30051			0.254640
$169$	9.28854	+	9.09522i	0.714503	+	0.699632i
$170$	−40.9564			−3.14121
$171$	0.394011	+	1.03892i	0.0301308	+	0.0794483i
$172$	−6.20117	+	8.98394i	−0.472835	+	0.685019i
$173$	14.5153	−	12.8594i	1.10357	−	0.977682i	0.103718	−	0.994607i	$-0.466926\pi$
$173$	14.5153	−	12.8594i	1.10357	−	0.977682i	0.999857	+	0.0169247i	$0.00538757\pi$
$174$	2.27475	+	18.7343i	0.172448	+	1.42024i
$175$	−3.81803	−	0.941061i	−0.288616	−	0.0711375i
$176$	−0.224406	−	0.117777i	−0.0169152	−	0.00887779i
$177$	4.20439	+	2.20663i	0.316021	+	0.165861i
$178$	9.53064	+	25.1302i	0.714352	+	1.88359i
$179$	7.18041	−	3.76857i	0.536689	−	0.281676i	−0.174524	−	0.984653i	$-0.555839\pi$
$179$	7.18041	−	3.76857i	0.536689	−	0.281676i	0.711213	+	0.702977i	$0.248146\pi$
$180$	−4.95212	+	13.0577i	−0.369109	+	0.973262i
$181$	1.58588	+	13.0609i	0.117878	+	0.970810i	0.924879	+	0.380261i	$0.124166\pi$
$181$	1.58588	+	13.0609i	0.117878	+	0.970810i	−0.807001	+	0.590549i	$0.798911\pi$
$182$	−3.55292	+	6.37762i	−0.263360	+	0.472740i
$183$	−1.77796	+	14.6428i	−0.131431	+	1.08243i
$184$	−3.35537	−	1.76103i	−0.247361	−	0.129825i
$185$	3.31357	−	27.2897i	0.243618	−	2.00638i
$186$	12.1228	+	6.36254i	0.888888	+	0.466524i
$187$	5.30004	−	4.69542i	0.387577	−	0.343363i
$188$	19.2336			1.40276
$189$	3.67536	+	3.25608i	0.267343	+	0.236845i
$190$	−5.02876	+	2.63930i	−0.364825	+	0.191475i
$191$	−10.6826			−0.772967			−0.386484	−	0.922296i	$-0.626310\pi$
$191$	−10.6826			−0.772967			−0.386484	+	0.922296i	$0.626310\pi$
$192$	−16.3544			−1.18028
$193$	−8.59036	+	4.50857i	−0.618348	+	0.324534i	−0.744647	−	0.667458i	$-0.767382\pi$
$193$	−8.59036	+	4.50857i	−0.618348	+	0.324534i	0.126300	+	0.991992i	$0.459690\pi$
$194$	−13.0096	+	3.20657i	−0.934033	+	0.230219i
$195$	9.08595	+	10.7865i	0.650658	+	0.772437i
$196$	19.8328	+	4.88834i	1.41663	+	0.349167i
$197$	5.61933	−	1.38504i	0.400360	−	0.0986800i	−0.0339940	−	0.999422i	$-0.510823\pi$
$197$	5.61933	−	1.38504i	0.400360	−	0.0986800i	0.434354	+	0.900742i	$0.356977\pi$
$198$	−1.37788	−	3.63318i	−0.0979220	−	0.258199i
$199$	−2.50163	+	20.6028i	−0.177336	+	1.46049i	0.583800	+	0.811898i	$0.301565\pi$
$199$	−2.50163	+	20.6028i	−0.177336	+	1.46049i	−0.761135	+	0.648593i	$0.775358\pi$
$200$	−12.7682	−	3.14707i	−0.902846	−	0.222532i
$201$	15.0738	−	3.71536i	1.06323	−	0.262062i
$202$	1.31183	+	1.90051i	0.0923000	+	0.133720i
$203$	0.685793	−	5.64802i	0.0481333	−	0.396413i
$204$	−8.57244	+	22.6037i	−0.600191	+	1.58257i
$205$	−19.7859	−	10.3845i	−1.38191	−	0.725282i
$206$	33.7086	+	8.30842i	2.34859	+	0.578875i
$207$	−0.630864	−	1.66345i	−0.0438481	−	0.115618i
$208$	−0.363824	+	0.653077i	−0.0252267	+	0.0452828i
$209$	0.348175	−	0.918063i	0.0240838	−	0.0635037i
$210$	−4.49912	+	6.51810i	−0.310469	+	0.449791i
$211$	6.04895	+	5.35890i	0.416427	+	0.368922i	0.845164	−	0.534507i	$-0.179503\pi$
$211$	6.04895	+	5.35890i	0.416427	+	0.368922i	−0.428737	+	0.903429i	$0.641041\pi$
$212$	−18.5089	+	4.56204i	−1.27120	+	0.313322i
$213$	3.57461	+	9.42547i	0.244928	+	0.645823i
$214$	23.7259	−	12.4523i	1.62187	−	0.851221i
$215$	−3.62836	−	9.56719i	−0.247452	−	0.652477i
$216$	12.2910	+	10.8889i	0.836300	+	0.740897i
$217$	−3.08954	−	2.73709i	−0.209732	−	0.185806i
$218$	−5.57396	−	8.07528i	−0.377516	−	0.546927i
$219$	1.07837	+	1.56229i	0.0728697	+	0.105570i
$220$	10.9271	−	5.73496i	0.736702	−	0.386651i
$221$	−13.4562	−	15.9747i	−0.905162	−	1.07457i
$222$	−23.1230	−	12.1359i	−1.55191	−	0.814507i
$223$	3.52450	+	29.0269i	0.236018	+	1.94378i	0.320240	+	0.947337i	$0.396237\pi$
$223$	3.52450	+	29.0269i	0.236018	+	1.94378i	−0.0842217	+	0.996447i	$0.526840\pi$
$224$	4.63293	+	1.14191i	0.309551	+	0.0762974i
$225$	−3.50713	−	5.08095i	−0.233809	−	0.338730i
$226$	−13.3093	+	19.2818i	−0.885320	+	1.28261i
$227$	10.1599	−	9.00089i	0.674336	−	0.597410i	−0.254868	−	0.966976i	$-0.582032\pi$
$227$	10.1599	−	9.00089i	0.674336	−	0.597410i	0.929205	+	0.369566i	$0.120494\pi$
$228$	0.404065	+	3.32778i	0.0267599	+	0.220387i
$229$	10.1532	−	2.50254i	0.670942	−	0.165372i	0.110894	−	0.993832i	$-0.464629\pi$
$229$	10.1532	−	2.50254i	0.670942	−	0.165372i	0.560049	+	0.828460i	$0.310782\pi$
$230$	8.05172	−	4.22587i	0.530915	−	0.278645i
$231$	−0.165047	−	1.35929i	−0.0108593	−	0.0894344i
$232$	2.29341	−	18.8880i	0.150570	−	1.24006i
$233$	−0.345291	−	0.500240i	−0.0226208	−	0.0327718i	0.811510	−	0.584338i	$-0.198646\pi$
$233$	−0.345291	−	0.500240i	−0.0226208	−	0.0327718i	−0.834131	+	0.551566i	$0.814030\pi$
$234$	−10.8152	+	3.79585i	−0.707012	+	0.248142i
$235$	−10.2411	+	14.8369i	−0.668058	+	0.967850i
$236$	−9.17364	−	8.12713i	−0.597153	−	0.529031i
$237$	21.1076	−	5.20255i	1.37108	−	0.337942i
$238$	6.66314	−	9.65323i	0.431907	−	0.625726i
$239$	−24.6496			−1.59445			−0.797225	−	0.603682i	$-0.793700\pi$
$239$	−24.6496			−1.59445			−0.797225	+	0.603682i	$0.793700\pi$
$240$	−0.460716	+	0.667463i	−0.0297391	+	0.0430845i
$241$	0.245379	−	2.02088i	0.0158062	−	0.130176i	−0.982670	−	0.185365i	$-0.940653\pi$
$241$	0.245379	−	2.02088i	0.0158062	−	0.130176i	0.998476	+	0.0551893i	$0.0175762\pi$
$242$	7.74709	−	20.4274i	0.498002	−	1.31312i
$243$	1.56524	+	12.8909i	0.100410	+	0.826953i
$244$	13.5007	−	35.5983i	0.864292	−	2.27895i
$245$	−14.3310	+	12.6962i	−0.915577	+	0.811130i
$246$	−15.8887	+	14.0761i	−1.01303	+	0.897463i
$247$	−2.68163	−	1.09428i	−0.170628	−	0.0696277i
$248$	−10.3320	−	9.15332i	−0.656081	−	0.581237i
$249$	18.4151			1.16701
$250$	−2.83981	+	2.51585i	−0.179605	+	0.159116i
$251$	−13.4167	−	3.30691i	−0.846852	−	0.208730i	−0.208066	−	0.978115i	$-0.566717\pi$
$251$	−13.4167	−	3.30691i	−0.846852	−	0.208730i	−0.638786	+	0.769384i	$0.720563\pi$
$252$	−2.27198	−	3.29153i	−0.143121	−	0.207347i
$253$	−0.557475	+	1.46994i	−0.0350482	+	0.0924144i
$254$	7.93792	−	20.9306i	0.498069	−	1.31330i
$255$	−12.8720	−	18.6484i	−0.806079	−	1.16781i
$256$	16.8148	+	4.14446i	1.05092	+	0.259029i
$257$	−12.7683	+	11.3118i	−0.796467	+	0.705608i	−0.959714	−	0.280977i	$-0.909341\pi$
$257$	−12.7683	+	11.3118i	−0.796467	+	0.705608i	0.163248	+	0.986585i	$0.447803\pi$
$258$	−9.71999			−0.605140
$259$	5.89297	+	5.22072i	0.366172	+	0.324400i
$260$	−16.1076	−	32.6446i	−0.998950	−	2.02453i
$261$	6.68620	−	5.92346i	0.413866	−	0.366653i
$262$	−9.25367	+	8.19804i	−0.571694	+	0.506476i
$263$	8.15071	−	21.4917i	0.502594	−	1.32523i	−0.408396	−	0.912805i	$-0.633912\pi$
$263$	8.15071	−	21.4917i	0.502594	−	1.32523i	0.910990	−	0.412428i	$-0.135319\pi$
$264$	−0.551947	−	4.54569i	−0.0339700	−	0.279768i
$265$	6.33611	−	16.7070i	0.389224	−	1.02630i
$266$	0.196053	−	1.61464i	0.0120208	−	0.0989999i
$267$	−8.44702	+	12.2376i	−0.516949	+	0.748930i
$268$	−40.0717			−2.44777
$269$	9.79082	−	14.1844i	0.596957	−	0.864841i	−0.401747	−	0.915751i	$-0.631597\pi$
$269$	9.79082	−	14.1844i	0.596957	−	0.864841i	0.998703	+	0.0509100i	$0.0162122\pi$
$270$	−38.2589	+	9.42998i	−2.32836	+	0.573890i
$271$	−20.8139	−	18.4395i	−1.26435	−	1.12012i	−0.987233	−	0.159283i	$-0.949082\pi$
$271$	−20.8139	−	18.4395i	−1.26435	−	1.12012i	−0.277119	−	0.960835i	$-0.589380\pi$
$272$	0.682316	−	0.988505i	0.0413715	−	0.0599369i
$273$	−4.02051	+	0.386675i	−0.243332	+	0.0234027i
$274$	7.07953	+	10.2565i	0.427690	+	0.619616i
$275$	−0.657601	+	5.41583i	−0.0396549	+	0.326587i
$276$	−0.646963	−	5.32822i	−0.0389426	−	0.320721i
$277$	−7.17511	+	3.76579i	−0.431111	+	0.226264i	−0.666298	−	0.745686i	$-0.732122\pi$
$277$	−7.17511	+	3.76579i	−0.431111	+	0.226264i	0.235187	+	0.971950i	$0.424430\pi$
$278$	−16.9583	+	4.17985i	−1.01709	+	0.250691i
$279$	−0.781129	−	6.43317i	−0.0467649	−	0.385144i
$280$	5.97690	−	5.29507i	0.357188	−	0.316441i
$281$	−7.21506	+	10.4528i	−0.430414	+	0.623563i	−0.976847	−	0.213940i	$-0.931370\pi$
$281$	−7.21506	+	10.4528i	−0.430414	+	0.623563i	0.546432	+	0.837503i	$0.315986\pi$
$282$	9.72856	+	14.0943i	0.579327	+	0.839301i
$283$	8.02894	+	1.97896i	0.477271	+	0.117637i	0.470610	−	0.882341i	$-0.344034\pi$
$283$	8.02894	+	1.97896i	0.477271	+	0.117637i	0.00666040	+	0.999978i	$0.497880\pi$
$284$	−3.13625	−	25.8293i	−0.186102	−	1.53269i
$285$	−2.78221	−	1.46021i	−0.164804	−	0.0864956i
$286$	9.37785	+	3.82679i	0.554524	+	0.226283i
$287$	5.66652	−	2.97402i	0.334484	−	0.175551i
$288$	4.25567	+	6.16540i	0.250768	+	0.363300i
$289$	9.40626	+	13.6273i	0.553309	+	0.801607i
$290$	34.1751	+	30.2765i	2.00683	+	1.77790i
$291$	−5.54876	−	4.91578i	−0.325274	−	0.288168i
$292$	−1.73749	−	4.58139i	−0.101679	−	0.268106i
$293$	−5.34316	+	2.80431i	−0.312151	+	0.163829i	−0.613522	−	0.789677i	$-0.710248\pi$
$293$	−5.34316	+	2.80431i	−0.312151	+	0.163829i	0.301371	+	0.953507i	$0.402556\pi$
$294$	6.44948	+	17.0059i	0.376141	+	0.991803i
$295$	11.1539	−	2.74919i	0.649405	−	0.160064i
$296$	19.7071	+	17.4590i	1.14545	+	1.01478i
$297$	3.86987	−	5.60648i	0.224553	−	0.325321i
$298$	0.854269	−	2.25252i	0.0494865	−	0.130485i
$299$	4.29365	+	1.75210i	0.248308	+	0.101326i
$300$	−6.60492	−	17.4157i	−0.381335	−	1.00550i
$301$	2.84524	+	0.701288i	0.163997	+	0.0404216i
$302$	12.4882	+	6.55432i	0.718616	+	0.377159i
$303$	−0.453057	+	1.19461i	−0.0260274	+	0.0686287i
$304$	0.0200761	−	0.165342i	0.00115144	−	0.00948299i
$305$	20.2721	+	29.3692i	1.16078	+	1.68167i
$306$	17.8806	−	4.40717i	1.02217	−	0.251941i
$307$	6.22983	+	1.53552i	0.355555	+	0.0876365i	0.413048	−	0.910709i	$-0.364464\pi$
$307$	6.22983	+	1.53552i	0.355555	+	0.0876365i	−0.0574922	+	0.998346i	$0.518310\pi$
$308$	−0.426006	+	3.50847i	−0.0242739	+	0.199914i
$309$	6.81115	+	17.9595i	0.387473	+	1.02168i
$310$	32.1608	−	7.92692i	1.82661	−	0.450219i
$311$	19.4180	+	4.78610i	1.10109	+	0.271395i	0.747671	−	0.664069i	$-0.231172\pi$
$311$	19.4180	+	4.78610i	1.10109	+	0.271395i	0.353421	+	0.935464i	$0.385018\pi$
$312$	−13.4453	+	1.29311i	−0.761190	+	0.0732080i
$313$	28.3679	−	6.99205i	1.60345	−	0.395214i	0.666729	−	0.745300i	$-0.267694\pi$
$313$	28.3679	−	6.99205i	1.60345	−	0.395214i	0.936718	+	0.350086i	$0.113848\pi$
$314$	−43.4307	+	22.7942i	−2.45094	+	1.28635i
$315$	3.74884			0.211223
$316$	−56.1116			−3.15652
$317$	−8.74615	+	4.59033i	−0.491233	+	0.257819i	−0.692103	−	0.721799i	$-0.743315\pi$
$317$	−8.74615	+	4.59033i	−0.491233	+	0.257819i	0.200870	+	0.979618i	$0.435623\pi$
$318$	−12.7051	−	11.2557i	−0.712464	−	0.631188i
$319$	−7.89353			−0.441953
$320$	−29.6163	+	26.2378i	−1.65560	+	1.46674i
$321$	13.1265	+	6.88934i	0.732652	+	0.384525i
$322$	−0.313907	+	2.58525i	−0.0174933	+	0.144071i
$323$	4.12042	+	2.16256i	0.229266	+	0.120328i
$324$	−1.16189	+	9.56903i	−0.0645495	+	0.531613i
$325$	15.9222	+	2.33773i	0.883207	+	0.129674i
$326$	6.92334	+	57.0188i	0.383448	+	3.15798i
$327$	1.92504	−	5.07591i	0.106455	−	0.280698i
$328$	18.9498	−	9.94565i	1.04633	−	0.549156i
$329$	−1.83086	−	4.82758i	−0.100939	−	0.266153i
$330$	9.72957	+	5.10647i	0.535595	+	0.281102i
$331$	−11.4100	−	5.98842i	−0.627149	−	0.329153i	0.121031	−	0.992649i	$-0.461380\pi$
$331$	−11.4100	−	5.98842i	−0.627149	−	0.329153i	−0.748180	+	0.663495i	$0.769072\pi$
$332$	−46.1503	−	11.3750i	−2.53283	−	0.624286i
$333$	1.48992	+	12.2706i	0.0816472	+	0.672425i
$334$	−15.5894	+	13.8110i	−0.853012	+	0.755703i
$335$	21.3366	−	30.9114i	1.16574	−	1.68887i
$336$	−0.0823645	−	0.217177i	−0.00449335	−	0.0118480i
$337$	14.2919			0.778530			0.389265	−	0.921126i	$-0.372729\pi$
$337$	14.2919			0.778530			0.389265	+	0.921126i	$0.372729\pi$
$338$	11.9748	−	27.3725i	0.651345	−	1.48887i
$339$	−12.9624			−0.704020
$340$	20.7397	+	54.6860i	1.12477	+	2.96577i
$341$	−3.25305	+	4.71286i	−0.176163	+	0.255215i
$342$	1.91143	−	1.69338i	0.103359	−	0.0915676i
$343$	−1.40430	−	11.5654i	−0.0758249	−	0.624474i
$344$	9.51497	+	2.34523i	0.513013	+	0.126446i
$345$	4.45468	+	2.33800i	0.239832	+	0.125874i
$346$	−39.4631	−	20.7118i	−2.12155	−	1.11348i
$347$	3.20215	+	8.44337i	0.171900	+	0.453264i	0.993085	−	0.117399i	$-0.0374556\pi$
$347$	3.20215	+	8.44337i	0.171900	+	0.453264i	−0.821184	+	0.570663i	$0.806686\pi$
$348$	23.8626	−	12.5240i	1.27917	−	0.671359i
$349$	0.970761	−	2.55969i	0.0519636	−	0.137017i	−0.906521	−	0.422160i	$-0.861272\pi$
$349$	0.970761	−	2.55969i	0.0519636	−	0.137017i	0.958485	+	0.285143i	$0.0920412\pi$
$350$	1.08934	+	8.97152i	0.0582276	+	0.479548i
$351$	−16.2480	−	11.8243i	−0.867256	−	0.631137i
$352$	0.797956	−	6.57175i	0.0425312	−	0.350276i
$353$	−30.7422	−	16.1348i	−1.63624	−	0.858767i	−0.995879	−	0.0906956i	$-0.971091\pi$
$353$	−30.7422	−	16.1348i	−1.63624	−	0.858767i	−0.640365	−	0.768071i	$-0.721217\pi$
$354$	1.31538	−	10.8332i	0.0699119	−	0.575776i
$355$	21.5947	+	11.3338i	1.14613	+	0.601536i
$356$	28.7284	−	25.4511i	1.52260	−	1.34891i
$357$	6.48948			0.343459
$358$	−13.9501	−	12.3587i	−0.737287	−	0.653179i
$359$	11.2468	−	5.90275i	0.593581	−	0.311535i	−0.141050	−	0.990003i	$-0.545048\pi$
$359$	11.2468	−	5.90275i	0.593581	−	0.311535i	0.734631	+	0.678467i	$0.237355\pi$
$360$	12.5368			0.660746
$361$	−18.3547			−0.966038
$362$	26.7742	−	14.0522i	1.40722	−	0.738566i
$363$	11.7359	−	2.89263i	0.615974	−	0.151824i
$364$	10.3147	+	1.51442i	0.540637	+	0.0793773i
$365$	4.45925	+	1.09911i	0.233408	+	0.0575298i
$366$	32.9150	−	8.11282i	1.72049	−	0.424064i
$367$	6.17017	+	16.2694i	0.322080	+	0.849256i	0.994075	+	0.108700i	$0.0346687\pi$
$367$	6.17017	+	16.2694i	0.322080	+	0.849256i	−0.671994	+	0.740556i	$0.734562\pi$
$368$	−0.0321445	+	0.264734i	−0.00167565	+	0.0138002i
$369$	9.75552	+	2.40452i	0.507852	+	0.125174i
$370$	−61.3433	+	15.1198i	−3.18909	+	0.786040i
$371$	2.90694	+	4.21143i	0.150921	+	0.218646i
$372$	2.35663	−	19.4086i	0.122186	−	1.00629i
$373$	7.43339	−	19.6002i	0.384886	−	1.01486i	−0.592903	−	0.805274i	$-0.702018\pi$
$373$	7.43339	−	19.6002i	0.384886	−	1.01486i	0.977790	−	0.209588i	$-0.0672123\pi$
$374$	−14.4094	−	7.56263i	−0.745091	−	0.391054i
$375$	−2.03804	−	0.502331i	−0.105244	−	0.0259403i
$376$	−6.12272	−	16.1443i	−0.315755	−	0.832578i
$377$	−0.580875	+	23.2770i	−0.0299166	+	1.19883i
$378$	4.00170	−	10.5516i	0.205825	−	0.542716i
$379$	−20.2811	+	29.3822i	−1.04177	+	1.50926i	−0.192502	+	0.981297i	$0.561660\pi$
$379$	−20.2811	+	29.3822i	−1.04177	+	1.50926i	−0.849266	+	0.527965i	$0.822955\pi$
$380$	6.07054	+	5.37803i	0.311412	+	0.275887i
$381$	12.0250	−	2.96389i	0.616057	−	0.151844i
$382$	8.70603	+	22.9559i	0.445439	+	1.17453i
$383$	−19.8457	+	10.4158i	−1.01407	+	0.532224i	−0.888022	−	0.459801i	$-0.847921\pi$
$383$	−19.8457	+	10.4158i	−1.01407	+	0.532224i	−0.126045	+	0.992024i	$0.540228\pi$
$384$	8.44435	+	22.2659i	0.430924	+	1.13625i
$385$	−2.47961	−	2.19675i	−0.126373	−	0.111957i
$386$	16.6894	+	14.7855i	0.849467	+	0.752562i
$387$	2.61355	+	3.78638i	0.132854	+	0.192472i
$388$	10.8693	+	15.7470i	0.551808	+	0.799431i
$389$	−32.7542	+	17.1908i	−1.66071	+	0.871606i	−0.668973	+	0.743287i	$0.733266\pi$
$389$	−32.7542	+	17.1908i	−1.66071	+	0.871606i	−0.991733	+	0.128319i	$0.959042\pi$
$390$	15.7743	−	28.3155i	0.798764	−	1.43381i
$391$	−6.59734	−	3.46255i	−0.333642	−	0.175109i
$392$	−2.21028	−	18.2033i	−0.111636	−	0.919406i
$393$	−6.64106	−	1.63687i	−0.334997	−	0.0825694i
$394$	−7.55590	−	10.9466i	−0.380661	−	0.551483i
$395$	29.8772	−	43.2846i	1.50329	−	2.17789i
$396$	−4.15338	+	3.67957i	−0.208715	+	0.184906i
$397$	−2.24283	−	18.4714i	−0.112565	−	0.927052i	−0.934129	−	0.356936i	$-0.883821\pi$
$397$	−2.24283	−	18.4714i	−0.112565	−	0.927052i	0.821564	−	0.570116i	$-0.193102\pi$
$398$	46.3121	−	11.4149i	2.32141	−	0.572177i
$399$	0.796799	−	0.418193i	0.0398899	−	0.0209358i
$400$	0.111550	+	0.918697i	0.00557750	+	0.0459348i
$401$	−3.21532	+	26.4805i	−0.160565	+	1.32237i	0.660192	+	0.751097i	$0.270475\pi$
$401$	−3.21532	+	26.4805i	−0.160565	+	1.32237i	−0.820757	+	0.571277i	$0.806448\pi$
$402$	−20.2687	−	29.3643i	−1.01091	−	1.46456i
$403$	13.6582	+	9.93965i	0.680365	+	0.495129i
$404$	1.87333	−	2.71398i	0.0932014	−	0.135026i
$405$	−6.76291	−	5.99142i	−0.336052	−	0.297716i
$406$	−12.6959	+	3.12927i	−0.630089	+	0.155303i
$407$	6.20485	−	8.98928i	0.307563	−	0.445582i
$408$	21.7019			1.07441
$409$	8.01160	−	11.6068i	0.396148	−	0.573920i	−0.573260	−	0.819374i	$-0.694322\pi$
$409$	8.01160	−	11.6068i	0.396148	−	0.573920i	0.969408	+	0.245454i	$0.0789369\pi$
$410$	−6.19023	+	50.9811i	−0.305713	+	2.51778i
$411$	−2.44500	+	6.44694i	−0.120603	+	0.318004i
$412$	−5.97588	−	49.2158i	−0.294411	−	2.42469i
$413$	−1.16664	+	3.07618i	−0.0574067	+	0.151369i
$414$	−3.06046	+	2.71133i	−0.150413	+	0.133255i
$415$	33.3480	−	29.5437i	1.63699	−	1.45024i
$416$	−19.3206	−	2.83668i	−0.947269	−	0.139080i
$417$	−7.23296	−	6.40785i	−0.354200	−	0.313794i
$418$	−2.25658			−0.110373
$419$	1.71952	−	1.52336i	0.0840042	−	0.0744212i	−0.620076	−	0.784542i	$-0.712898\pi$
$419$	1.71952	−	1.52336i	0.0840042	−	0.0744212i	0.704080	+	0.710121i	$0.251360\pi$
$420$	10.9814	+	2.70668i	0.535838	+	0.132072i
$421$	−8.11760	−	11.7604i	−0.395628	−	0.573166i	0.573660	−	0.819093i	$-0.305523\pi$
$421$	−8.11760	−	11.7604i	−0.395628	−	0.573166i	−0.969288	+	0.245927i	$0.920908\pi$
$422$	6.58604	−	17.3660i	0.320603	−	0.845362i
$423$	2.87450	−	7.57944i	0.139763	−	0.368525i
$424$	9.72131	+	14.0838i	0.472109	+	0.683968i
$425$	−25.1048	−	6.18779i	−1.21776	−	0.300152i
$426$	17.3412	−	15.3630i	0.840185	−	0.744339i
$427$	−10.2202			−0.494591
$428$	−28.6410	−	25.3737i	−1.38442	−	1.22649i
$429$	1.20491	+	5.47266i	0.0581736	+	0.264223i
$430$	−17.6020	+	15.5940i	−0.848842	+	0.752008i
$431$	26.5177	−	23.4926i	1.27731	−	1.13160i	0.292821	−	0.956167i	$-0.405406\pi$
$431$	26.5177	−	23.4926i	1.27731	−	1.13160i	0.984491	−	0.175433i	$-0.0561325\pi$
$432$	0.409780	−	1.08050i	0.0197155	−	0.0519856i
$433$	0.540165	+	4.44866i	0.0259587	+	0.213789i	0.999916	−	0.0129414i	$-0.00411948\pi$
$433$	0.540165	+	4.44866i	0.0259587	+	0.213789i	−0.973958	+	0.226730i	$0.927196\pi$
$434$	−3.36386	+	8.86977i	−0.161471	+	0.425763i
$435$	−3.04480	+	25.0762i	−0.145987	+	1.20231i
$436$	−7.95975	+	11.5317i	−0.381203	+	0.552268i
$437$	−1.03318			−0.0494235
$438$	2.47837	−	3.59054i	0.118421	−	0.171563i
$439$	−8.50768	+	2.09696i	−0.406050	+	0.100082i	−0.437050	−	0.899437i	$-0.643977\pi$
$439$	−8.50768	+	2.09696i	−0.406050	+	0.100082i	0.0310006	+	0.999519i	$0.490131\pi$
$440$	−8.29226	−	7.34631i	−0.395318	−	0.350221i
$441$	4.89041	−	7.08497i	0.232876	−	0.337380i
$442$	−23.3616	+	41.9350i	−1.11120	+	1.99464i
$443$	−0.647449	−	0.937992i	−0.0307612	−	0.0445653i	0.807302	−	0.590139i	$-0.200927\pi$
$443$	−0.647449	−	0.937992i	−0.0307612	−	0.0445653i	−0.838063	+	0.545574i	$0.816312\pi$
$444$	−4.49502	+	37.0198i	−0.213324	+	1.75688i
$445$	4.33633	+	35.7129i	0.205562	+	1.69295i
$446$	59.5036	−	31.2299i	2.81758	−	1.47878i
$447$	1.29411	−	0.318970i	0.0612093	−	0.0150867i
$448$	−1.36588	−	11.2490i	−0.0645317	−	0.531466i
$449$	6.33080	−	5.60860i	0.298769	−	0.264686i	−0.500398	−	0.865796i	$-0.666813\pi$
$449$	6.33080	−	5.60860i	0.298769	−	0.264686i	0.799167	+	0.601110i	$0.205274\pi$
$450$	−8.06026	+	11.6773i	−0.379965	+	0.550474i
$451$	−5.04364	−	7.30698i	−0.237496	−	0.344072i
$452$	32.4852	+	8.00688i	1.52798	+	0.376612i
$453$	0.940548	+	7.74611i	0.0441908	+	0.363944i
$454$	−27.6221	−	14.4972i	−1.29637	−	0.680386i
$455$	−6.66040	+	7.15042i	−0.312245	+	0.335217i
$456$	2.66464	−	1.39851i	0.124783	−	0.0654912i
$457$	−3.30534	−	4.78861i	−0.154617	−	0.224002i	0.738018	−	0.674781i	$-0.235762\pi$
$457$	−3.30534	−	4.78861i	−0.154617	−	0.224002i	−0.892636	+	0.450779i	$0.851146\pi$
$458$	−13.6523	−	19.7787i	−0.637929	−	0.924200i
$459$	24.1667	+	21.4098i	1.12801	+	0.999326i
$460$	−9.71976	−	8.61095i	−0.453186	−	0.401488i
$461$	−3.08829	−	8.14315i	−0.143836	−	0.379264i	0.843667	−	0.536868i	$-0.180393\pi$
$461$	−3.08829	−	8.14315i	−0.143836	−	0.379264i	−0.987503	+	0.157603i	$0.949623\pi$
$462$	−2.78646	+	1.46245i	−0.129638	+	0.0680393i
$463$	−10.2879	−	27.1270i	−0.478119	−	1.26070i	−0.929651	−	0.368442i	$-0.879891\pi$
$463$	−10.2879	−	27.1270i	−0.478119	−	1.26070i	0.451532	−	0.892255i	$-0.350878\pi$
$464$	−1.30008	+	0.320442i	−0.0603548	+	0.0148761i
$465$	13.7170	+	12.1522i	0.636112	+	0.563546i
$466$	−0.793565	+	1.14968i	−0.0367612	+	0.0532578i
$467$	−3.06508	+	8.08195i	−0.141835	+	0.373988i	−0.987044	−	0.160447i	$-0.948706\pi$
$467$	−3.06508	+	8.08195i	−0.141835	+	0.373988i	0.845210	+	0.534435i	$0.179476\pi$
$468$	10.5450	+	12.5186i	0.487441	+	0.578672i
$469$	3.81445	+	10.0579i	0.176135	+	0.464430i
$470$	40.2292	+	9.91560i	1.85563	+	0.457373i
$471$	−24.0284	−	12.6111i	−1.10717	−	0.581088i
$472$	−3.90146	+	10.2873i	−0.179579	+	0.473511i
$473$	0.490051	−	4.03594i	0.0225326	−	0.185573i
$474$	−28.3818	−	41.1182i	−1.30362	−	1.88862i
$475$	−3.48121	+	0.858041i	−0.159729	+	0.0393696i
$476$	−16.2634	−	4.00856i	−0.745430	−	0.183732i
$477$	−0.968422	+	7.97567i	−0.0443410	+	0.365181i
$478$	20.0887	+	52.9696i	0.918836	+	2.42277i
$479$	−11.2199	+	2.76547i	−0.512652	+	0.126357i	−0.487152	−	0.873317i	$-0.661964\pi$
$479$	−11.2199	+	2.76547i	−0.512652	+	0.126357i	−0.0255005	+	0.999675i	$0.508118\pi$
$480$	−20.5694	−	5.06990i	−0.938860	−	0.231408i
$481$	−26.0517	−	18.9588i	−1.18785	−	0.864449i
$482$	−4.54264	+	1.11966i	−0.206912	+	0.0509992i
$483$	−1.27578	+	0.669582i	−0.0580501	+	0.0304671i
$484$	−31.1982			−1.41810
$485$	−17.9348			−0.814375
$486$	26.4257	−	13.8693i	1.19869	−	0.629123i
$487$	8.03696	+	7.12012i	0.364189	+	0.322643i	0.825295	−	0.564702i	$-0.191009\pi$
$487$	8.03696	+	7.12012i	0.364189	+	0.322643i	−0.461106	+	0.887345i	$0.652547\pi$
$488$	−34.1782			−1.54717
$489$	−23.7861	+	21.0726i	−1.07564	+	0.952937i
$490$	38.9623	+	20.4490i	1.76014	+	0.923791i
$491$	2.97915	−	24.5355i	0.134447	−	1.10727i	−0.756766	−	0.653686i	$-0.773222\pi$
$491$	2.97915	−	24.5355i	0.134447	−	1.10727i	0.891213	−	0.453585i	$-0.149855\pi$
$492$	26.8406	+	14.0871i	1.21007	+	0.635093i
$493$	4.50932	−	37.1376i	0.203090	−	1.67259i
$494$	−0.166059	+	6.65438i	−0.00747134	+	0.299395i
$495$	−0.626921	−	5.16316i	−0.0281780	−	0.232067i
$496$	−0.344464	+	0.908278i	−0.0154669	+	0.0407829i
$497$	−6.18455	+	3.24590i	−0.277415	+	0.145599i
$498$	−15.0078	−	39.5723i	−0.672515	−	1.77328i
$499$	−9.25789	−	4.85891i	−0.414440	−	0.217515i	0.244598	−	0.969625i	$-0.421344\pi$
$499$	−9.25789	−	4.85891i	−0.414440	−	0.217515i	−0.659038	+	0.752110i	$0.729036\pi$
$500$	4.79726	+	2.51780i	0.214540	+	0.112599i
$501$	−11.1880	−	2.75759i	−0.499842	−	0.123200i
$502$	3.82797	+	31.5261i	0.170851	+	1.40708i
$503$	−11.1293	+	9.85966i	−0.496229	+	0.439621i	−0.873746	−	0.486382i	$-0.838316\pi$
$503$	−11.1293	+	9.85966i	−0.496229	+	0.439621i	0.377517	+	0.926003i	$0.376778\pi$
$504$	−2.03959	+	2.95486i	−0.0908506	+	0.131620i
$505$	1.09610	+	2.89018i	0.0487758	+	0.128611i
$506$	3.61309			0.160621
$507$	16.2269	−	3.15040i	0.720661	−	0.139914i
$508$	−31.9667			−1.41829
$509$	−3.55986	−	9.38657i	−0.157788	−	0.416052i	0.832687	−	0.553743i	$-0.186801\pi$
$509$	−3.55986	−	9.38657i	−0.157788	−	0.416052i	−0.990475	+	0.137691i	$0.956032\pi$
$510$	−29.5832	+	42.8587i	−1.30997	+	1.89781i
$511$	−0.984524	+	0.872212i	−0.0435528	+	0.0385844i
$512$	−0.282626	−	2.32764i	−0.0124904	−	0.102868i
$513$	4.34696	+	1.07143i	0.191923	+	0.0473047i
$514$	34.7137	+	18.2191i	1.53115	+	0.803612i
$515$	41.1471	+	21.5957i	1.81316	+	0.951620i
$516$	4.92205	+	12.9784i	0.216681	+	0.571341i
$517$	−6.34270	+	3.32891i	−0.278952	+	0.146405i
$518$	6.41621	−	16.9182i	0.281912	−	0.743341i
$519$	−2.97216	−	24.4779i	−0.130463	−	1.07446i
$520$	−22.2736	+	23.9123i	−0.976760	+	1.04862i
$521$	2.24441	−	18.4843i	0.0983292	−	0.809814i	−0.857214	−	0.514961i	$-0.827806\pi$
$521$	2.24441	−	18.4843i	0.0983292	−	0.809814i	0.955543	−	0.294853i	$-0.0952705\pi$
$522$	−18.1780	−	9.54055i	−0.795629	−	0.417579i
$523$	0.117230	−	0.965475i	0.00512610	−	0.0422173i	−0.989921	−	0.141618i	$-0.954770\pi$
$523$	0.117230	−	0.965475i	0.00512610	−	0.0422173i	0.995047	+	0.0994008i	$0.0316926\pi$
$524$	15.6321	+	8.20438i	0.682894	+	0.358410i
$525$	−3.74257	+	3.31563i	−0.163339	+	0.144706i
$526$	−52.8261			−2.30333
$527$	−20.3148	−	17.9973i	−0.884925	−	0.783975i
$528$	−0.285338	+	0.149757i	−0.0124177	+	0.00651733i
$529$	−21.3457			−0.928076
$530$	−41.0654			−1.78377
$531$	−4.57370	+	2.40046i	−0.198482	+	0.104171i
$532$	−2.25519	+	0.555854i	−0.0977748	+	0.0240993i
$533$	−21.9185	+	14.3354i	−0.949397	+	0.620934i
$534$	33.1815	+	8.17851i	1.43590	+	0.353919i
$535$	34.8236	−	8.58325i	1.50556	−	0.371086i
$536$	12.7562	+	33.6353i	0.550984	+	1.45282i
$537$	1.24288	−	10.2360i	0.0536340	−	0.441716i
$538$	−38.4602	−	9.47959i	−1.65814	−	0.408694i
$539$	−7.38635	+	1.82057i	−0.318153	+	0.0784176i
$540$	31.9649	+	46.3091i	1.37555	+	1.99283i
$541$	−1.32778	+	10.9353i	−0.0570859	+	0.470145i	0.935932	+	0.352181i	$0.114560\pi$
$541$	−1.32778	+	10.9353i	−0.0570859	+	0.470145i	−0.993018	+	0.117964i	$0.962363\pi$
$542$	−22.6619	+	59.7546i	−0.973413	+	2.56668i
$543$	14.8131	+	7.77449i	0.635689	+	0.333635i
$544$	30.4631	+	7.50847i	1.30609	+	0.321923i
$545$	−4.65732	−	12.2803i	−0.199498	−	0.526032i
$546$	4.10753	+	8.32455i	0.175786	+	0.356258i
$547$	2.00953	−	5.29869i	0.0859212	−	0.226556i	−0.885168	−	0.465271i	$-0.845957\pi$
$547$	2.00953	−	5.29869i	0.0859212	−	0.226556i	0.971090	+	0.238715i	$0.0767262\pi$
$548$	10.1097	−	14.6465i	0.431867	−	0.625667i
$549$	−12.0106	−	10.6405i	−0.512601	−	0.454125i
$550$	12.1740	−	3.00063i	0.519102	−	0.127947i
$551$	−1.83954	−	4.85047i	−0.0783670	−	0.206637i
$552$	−4.26644	+	2.23920i	−0.181592	+	0.0953067i
$553$	5.34130	+	14.0839i	0.227135	+	0.598906i
$554$	13.9398	+	12.3496i	0.592246	+	0.524685i
$555$	−26.1638	−	23.1791i	−1.11059	−	0.983897i
$556$	14.1685	+	20.5266i	0.600878	+	0.870522i
$557$	−2.95431	−	4.28005i	−0.125178	−	0.181352i	0.755384	−	0.655282i	$-0.227450\pi$
$557$	−2.95431	−	4.28005i	−0.125178	−	0.181352i	−0.880562	+	0.473930i	$0.842835\pi$
$558$	−13.1877	+	6.92142i	−0.558278	+	0.293007i
$559$	−11.8654	−	1.74210i	−0.501853	−	0.0736830i
$560$	−0.497576	−	0.261148i	−0.0210264	−	0.0110355i
$561$	−1.08524	−	8.93776i	−0.0458189	−	0.377352i
$562$	28.3422	+	6.98571i	1.19554	+	0.294675i
$563$	−12.9790	−	18.8034i	−0.547001	−	0.792467i	0.447819	−	0.894124i	$-0.352201\pi$
$563$	−12.9790	−	18.8034i	−0.547001	−	0.792467i	−0.994820	+	0.101657i	$0.967586\pi$
$564$	13.8926	−	20.1269i	0.584985	−	0.847497i
$565$	−23.4736	+	20.7958i	−0.987543	+	0.874887i
$566$	−2.29077	−	18.8662i	−0.0962883	−	0.793005i
$567$	2.51240	−	0.619251i	0.105511	−	0.0260061i
$568$	−20.6822	+	10.8549i	−0.867807	+	0.455460i
$569$	3.43029	+	28.2510i	0.143805	+	1.18434i	0.868649	+	0.495429i	$0.164989\pi$
$569$	3.43029	+	28.2510i	0.143805	+	1.18434i	−0.724843	+	0.688914i	$0.758088\pi$
$570$	−0.870440	+	7.16872i	−0.0364587	+	0.300265i
$571$	−0.384356	−	0.556836i	−0.0160848	−	0.0233028i	0.814859	−	0.579659i	$-0.196814\pi$
$571$	−0.384356	−	0.556836i	−0.0160848	−	0.0233028i	−0.830944	+	0.556356i	$0.812199\pi$
$572$	0.360832	−	14.4594i	0.0150871	−	0.604577i
$573$	−7.71617	+	11.1788i	−0.322347	+	0.467001i
$574$	−11.0089	−	9.75306i	−0.459504	−	0.407085i
$575$	5.57388	−	1.37384i	0.232447	−	0.0572930i
$576$	10.1064	−	14.6417i	0.421101	−	0.610071i
$577$	30.8111			1.28268			0.641342	−	0.767255i	$-0.278378\pi$
$577$	30.8111			1.28268			0.641342	+	0.767255i	$0.278378\pi$
$578$	21.6180	−	31.3190i	0.899188	−	1.30270i
$579$	−1.48693	+	12.2459i	−0.0617945	+	0.508924i
$580$	23.1202	−	60.9630i	0.960015	−	2.53135i
$581$	1.53798	+	12.6664i	0.0638061	+	0.525491i
$582$	−6.04144	+	15.9300i	−0.250426	+	0.660319i
$583$	5.31414	−	4.70792i	0.220089	−	0.194982i
$584$	−3.29242	+	2.91683i	−0.136241	+	0.120699i
$585$	−15.2716	+	1.46876i	−0.631405	+	0.0607258i
$586$	10.3807	+	9.19650i	0.428823	+	0.379904i
$587$	−3.65856			−0.151005			−0.0755026	−	0.997146i	$-0.524056\pi$
$587$	−3.65856			−0.151005			−0.0755026	+	0.997146i	$0.524056\pi$
$588$	19.4408	−	17.2230i	0.801724	−	0.710266i
$589$	−3.65409	−	0.900653i	−0.150564	−	0.0371107i
$590$	−14.9978	−	21.7281i	−0.617451	−	0.894533i
$591$	2.60953	−	6.88075i	0.107342	−	0.283036i
$592$	0.657030	−	1.73245i	0.0270038	−	0.0712031i
$593$	10.5955	+	15.3502i	0.435104	+	0.630357i	0.977792	−	0.209578i	$-0.0672089\pi$
$593$	10.5955	+	15.3502i	0.435104	+	0.630357i	−0.542688	+	0.839934i	$0.682593\pi$
$594$	−15.2016	−	3.74686i	−0.623730	−	0.153736i
$595$	11.7518	−	10.4112i	0.481777	−	0.426817i
$596$	−3.44022			−0.140917
$597$	19.7527	+	17.4994i	0.808426	+	0.716203i
$598$	0.265883	−	10.6545i	0.0108727	−	0.435697i
$599$	−11.6327	+	10.3057i	−0.475299	+	0.421078i	−0.866462	−	0.499243i	$-0.833611\pi$
$599$	−11.6327	+	10.3057i	−0.475299	+	0.421078i	0.391163	+	0.920322i	$0.372073\pi$
$600$	−12.5158	+	11.0881i	−0.510956	+	0.452668i
$601$	0.767354	−	2.02335i	0.0313010	−	0.0825340i	−0.918455	−	0.395526i	$-0.870562\pi$
$601$	0.767354	−	2.02335i	0.0313010	−	0.0825340i	0.949756	+	0.312992i	$0.101331\pi$
$602$	−0.811787	−	6.68567i	−0.0330860	−	0.272487i
$603$	−5.98880	+	15.7912i	−0.243883	+	0.643066i
$604$	2.42766	−	19.9936i	0.0987803	−	0.813529i
$605$	16.6118	−	24.0664i	0.675367	−	0.978437i
$606$	2.93633			0.119280
$607$	21.9437	−	31.7910i	0.890668	−	1.29035i	−0.0655951	−	0.997846i	$-0.520895\pi$
$607$	21.9437	−	31.7910i	0.890668	−	1.29035i	0.956263	−	0.292509i	$-0.0944900\pi$
$608$	4.22421	−	1.04118i	0.171315	−	0.0422252i
$609$	−5.41499	−	4.79727i	−0.219427	−	0.194395i
$610$	46.5903	−	67.4977i	1.88639	−	2.73290i
$611$	9.34978	+	18.9488i	0.378252	+	0.766587i
$612$	−14.9390	−	21.6429i	−0.603874	−	0.874863i
$613$	1.53832	−	12.6692i	0.0621322	−	0.511705i	−0.928106	−	0.372317i	$-0.878563\pi$
$613$	1.53832	−	12.6692i	0.0621322	−	0.511705i	0.990238	−	0.139388i	$-0.0445134\pi$
$614$	−1.77746	−	14.6387i	−0.0717325	−	0.590770i
$615$	−25.1584	+	13.2041i	−1.01448	+	0.532442i
$616$	3.08055	−	0.759287i	0.124119	−	0.0305926i
$617$	3.06239	+	25.2211i	0.123287	+	1.01536i	0.914715	+	0.404099i	$0.132415\pi$
$617$	3.06239	+	25.2211i	0.123287	+	1.01536i	−0.791428	+	0.611263i	$0.790662\pi$
$618$	33.0424	−	29.2730i	1.32916	−	1.17753i
$619$	−2.26243	+	3.27770i	−0.0909349	+	0.131742i	−0.865811	−	0.500371i	$-0.833197\pi$
$619$	−2.26243	+	3.27770i	−0.0909349	+	0.131742i	0.774876	+	0.632113i	$0.217812\pi$
$620$	−26.8700	−	38.9279i	−1.07912	−	1.56338i
$621$	−6.96006	−	1.71550i	−0.279298	−	0.0688407i
$622$	−5.54023	−	45.6279i	−0.222143	−	1.82951i
$623$	−9.12283	−	4.78803i	−0.365499	−	0.191828i
$624$	0.420617	+	0.852447i	0.0168382	+	0.0341252i
$625$	−24.2572	+	12.7312i	−0.970288	+	0.509247i
$626$	−38.1442	−	55.2615i	−1.52455	−	2.20869i
$627$	−0.709213	−	1.02747i	−0.0283233	−	0.0410333i
$628$	52.4281	+	46.4472i	2.09211	+	1.85345i
$629$	38.7483	+	34.3280i	1.54500	+	1.36875i
$630$	−3.05519	−	8.05588i	−0.121722	−	0.320954i
$631$	40.6517	−	21.3357i	1.61832	−	0.849360i	0.620442	−	0.784252i	$-0.286953\pi$
$631$	40.6517	−	21.3357i	1.61832	−	0.849360i	0.997878	−	0.0651079i	$-0.0207392\pi$
$632$	17.8622	+	47.0989i	0.710522	+	1.87349i
$633$	9.97703	−	2.45912i	0.396551	−	0.0977411i
$634$	16.9920	+	15.0536i	0.674840	+	0.597856i
$635$	17.0210	−	24.6592i	0.675458	−	0.978570i
$636$	−8.59526	+	22.6638i	−0.340824	+	0.898679i
$637$	4.82509	+	21.9154i	0.191177	+	0.868320i
$638$	6.43300	+	16.9624i	0.254685	+	0.671549i
$639$	−10.6474	−	2.62434i	−0.421203	−	0.103817i
$640$	51.0135	+	26.7740i	2.01649	+	1.05833i
$641$	−10.5919	+	27.9285i	−0.418354	+	1.10311i	0.545835	+	0.837893i	$0.316213\pi$
$641$	−10.5919	+	27.9285i	−0.418354	+	1.10311i	−0.964189	+	0.265217i	$0.914557\pi$
$642$	4.10677	−	33.8223i	0.162081	−	1.33486i
$643$	−15.5656	−	22.5507i	−0.613849	−	0.889313i	0.385595	−	0.922668i	$-0.373996\pi$
$643$	−15.5656	−	22.5507i	−0.613849	−	0.889313i	−0.999444	+	0.0333548i	$0.989381\pi$
$644$	3.61086	−	0.889996i	0.142288	−	0.0350708i
$645$	−12.6324	−	3.11360i	−0.497399	−	0.122598i
$646$	1.28911	−	10.6168i	0.0507195	−	0.417712i
$647$	15.0962	+	39.8053i	0.593492	+	1.56491i	0.808625	+	0.588325i	$0.200212\pi$
$647$	15.0962	+	39.8053i	0.593492	+	1.56491i	−0.215133	+	0.976585i	$0.569018\pi$
$648$	8.40191	−	2.07088i	0.330058	−	0.0813520i
$649$	4.43183	+	1.09235i	0.173965	+	0.0428784i
$650$	−7.95261	−	36.1205i	−0.311927	−	1.41676i
$651$	−5.09583	+	1.25601i	−0.199721	+	0.0492269i
$652$	72.6272	−	38.1177i	2.84430	−	1.49280i
$653$	−31.8636			−1.24692			−0.623460	−	0.781855i	$-0.714274\pi$
$653$	−31.8636			−1.24692			−0.623460	+	0.781855i	$0.714274\pi$
$654$	−12.4765			−0.487869
$655$	−14.6524	+	7.69017i	−0.572516	+	0.300480i
$656$	−1.12733	−	0.998728i	−0.0440149	−	0.0389938i
$657$	−2.06507			−0.0805662
$658$	−8.88190	+	7.86868i	−0.346253	+	0.306753i
$659$	−11.5601	−	6.06723i	−0.450319	−	0.236346i	0.224288	−	0.974523i	$-0.427995\pi$
$659$	−11.5601	−	6.06723i	−0.450319	−	0.236346i	−0.674607	+	0.738177i	$0.735687\pi$
$660$	1.89139	−	15.5770i	0.0736223	−	0.606334i
$661$	19.9106	+	10.4499i	0.774434	+	0.406454i	0.805148	−	0.593074i	$-0.202086\pi$
$661$	19.9106	+	10.4499i	0.774434	+	0.406454i	−0.0307142	+	0.999528i	$0.509778\pi$
$662$	−3.56972	+	29.3993i	−0.138741	+	1.14264i
$663$	−26.4362	+	2.54252i	−1.02670	+	0.0987433i
$664$	5.14327	+	42.3587i	0.199598	+	1.64384i
$665$	0.772012	−	2.03563i	0.0299373	−	0.0789383i
$666$	25.1541	−	13.2019i	0.974701	−	0.511563i
$667$	2.94535	+	7.76625i	0.114044	+	0.300710i
$668$	26.3350	+	13.8217i	1.01893	+	0.534776i
$669$	32.9209	+	17.2782i	1.27279	+	0.668014i
$670$	−83.8143	−	20.6584i	−3.23803	−	0.798103i
$671$	1.70914	+	14.0760i	0.0659804	+	0.543398i
$672$	4.54136	−	4.02330i	0.175187	−	0.155202i
$673$	15.5317	−	22.5016i	0.598704	−	0.867372i	−0.400090	−	0.916476i	$-0.631021\pi$
$673$	15.5317	−	22.5016i	0.598704	−	0.867372i	0.998794	+	0.0491035i	$0.0156364\pi$
$674$	−11.6475	−	30.7119i	−0.448645	−	1.18298i
$675$	−24.8761			−0.957482
$676$	−42.6124	−	2.12810i	−1.63894	−	0.0818498i
$677$	20.1441			0.774201			0.387101	−	0.922037i	$-0.373477\pi$
$677$	20.1441			0.774201			0.387101	+	0.922037i	$0.373477\pi$
$678$	10.5640	+	27.8549i	0.405707	+	1.06976i
$679$	2.91778	−	4.22714i	0.111974	−	0.162223i
$680$	39.3001	−	34.8169i	1.50709	−	1.33517i
$681$	−2.08035	−	17.1332i	−0.0797192	−	0.656547i
$682$	12.7786	+	3.14964i	0.489318	+	0.120606i
$683$	10.9384	+	5.74093i	0.418547	+	0.219671i	0.660831	−	0.750535i	$-0.270204\pi$
$683$	10.9384	+	5.74093i	0.418547	+	0.219671i	−0.242283	+	0.970206i	$0.577896\pi$
$684$	−3.22897	−	1.69469i	−0.123463	−	0.0647982i
$685$	5.91530	+	15.5974i	0.226012	+	0.595945i
$686$	−23.7085	+	12.4432i	−0.905195	+	0.475083i
$687$	4.71498	−	12.4324i	0.179888	−	0.474325i
$688$	−0.0831282	−	0.684622i	−0.00316923	−	0.0261010i
$689$	−13.4920	−	16.0172i	−0.514005	−	0.610206i
$690$	1.39369	−	11.4781i	0.0530569	−	0.436963i
$691$	−16.0695	−	8.43392i	−0.611312	−	0.320841i	0.130501	−	0.991448i	$-0.458342\pi$
$691$	−16.0695	−	8.43392i	−0.611312	−	0.320841i	−0.741813	+	0.670607i	$0.766034\pi$
$692$	−7.67148	+	63.1803i	−0.291626	+	2.40176i
$693$	1.31893	+	0.692226i	0.0501018	+	0.0262955i
$694$	15.5343	−	13.7622i	0.589675	−	0.522406i
$695$	−23.3784			−0.886794
$696$	−18.1087	−	16.0429i	−0.686408	−	0.608105i
$697$	37.2593	−	19.5552i	1.41130	−	0.740705i
$698$	−6.29166			−0.238143
$699$	−0.772882			−0.0292331
$700$	11.4274	−	5.99755i	0.431914	−	0.226686i
$701$	2.27517	−	0.560778i	0.0859319	−	0.0211803i	−0.196115	−	0.980581i	$-0.562833\pi$
$701$	2.27517	−	0.560778i	0.0859319	−	0.0211803i	0.282047	+	0.959401i	$0.408987\pi$
$702$	−12.1677	+	44.5519i	−0.459240	+	1.68150i
$703$	6.96980	+	1.71790i	0.262871	+	0.0647918i
$704$	−15.2645	+	3.76236i	−0.575303	+	0.141799i
$705$	8.12870	+	21.4336i	0.306145	+	0.807237i
$706$	−9.61801	+	79.2114i	−0.361978	+	2.98116i
$707$	−0.859525	−	0.211854i	−0.0323257	−	0.00796758i
$708$	−15.1308	+	3.72941i	−0.568651	+	0.140160i
$709$	17.1303	+	24.8175i	0.643342	+	0.932042i	0.999998	−	0.00219423i	$-0.000698446\pi$
$709$	17.1303	+	24.8175i	0.643342	+	0.932042i	−0.356656	+	0.934236i	$0.616083\pi$
$710$	6.75613	−	55.6417i	0.253553	−	2.08820i
$711$	−8.38599	+	22.1120i	−0.314499	+	0.829266i
$712$	−30.5084	−	16.0120i	−1.14335	−	0.600076i
$713$	5.85069	+	1.44207i	0.219110	+	0.0540058i
$714$	−5.28874	−	13.9452i	−0.197926	−	0.521888i
$715$	10.9619	+	7.97740i	0.409951	+	0.298338i
$716$	−9.43758	+	24.8848i	−0.352699	+	0.929990i
$717$	−17.8047	+	25.7945i	−0.664927	+	0.963313i
$718$	−21.8502	−	19.3576i	−0.815443	−	0.722420i
$719$	−17.6688	+	4.35497i	−0.658935	+	0.162413i	−0.554584	−	0.832128i	$-0.687123\pi$
$719$	−17.6688	+	4.35497i	−0.658935	+	0.162413i	−0.104351	+	0.994541i	$0.533276\pi$
$720$	−0.312856	−	0.824934i	−0.0116595	−	0.0307435i
$721$	−11.7842	+	6.18482i	−0.438866	+	0.230335i
$722$	14.9586	+	39.4425i	0.556700	+	1.46790i
$723$	−1.93750	−	1.71648i	−0.0720564	−	0.0638364i
$724$	−32.3209	−	28.6338i	−1.20120	−	1.06417i
$725$	16.3739	+	23.7217i	0.608112	+	0.881002i
$726$	−15.7804	−	22.8618i	−0.585665	−	0.848482i
$727$	−6.44684	+	3.38356i	−0.239100	+	0.125489i	−0.580018	−	0.814604i	$-0.696954\pi$
$727$	−6.44684	+	3.38356i	−0.239100	+	0.125489i	0.340918	+	0.940093i	$0.389262\pi$
$728$	−2.01235	−	9.14003i	−0.0745827	−	0.338752i
$729$	22.4222	+	11.7681i	0.830450	+	0.435854i
$730$	−1.27229	−	10.4782i	−0.0470895	−	0.387817i
$731$	18.7084	+	4.61120i	0.691955	+	0.170552i
$732$	−27.5001	−	39.8408i	−1.01643	−	1.47256i
$733$	−11.3217	+	16.4023i	−0.418176	+	0.605833i	−0.974297	−	0.225269i	$-0.927674\pi$
$733$	−11.3217	+	16.4023i	−0.418176	+	0.605833i	0.556120	+	0.831102i	$0.312289\pi$
$734$	29.9328	−	26.5182i	1.10484	−	0.978804i
$735$	2.93444	+	24.1673i	0.108238	+	0.891423i
$736$	−6.76353	+	1.66706i	−0.249307	+	0.0614487i
$737$	13.2145	−	6.93552i	0.486763	−	0.255473i
$738$	−2.78339	−	22.9233i	−0.102458	−	0.843817i
$739$	1.57358	−	12.9596i	0.0578851	−	0.476726i	−0.934724	−	0.355373i	$-0.884354\pi$
$739$	1.57358	−	12.9596i	0.0578851	−	0.476726i	0.992609	−	0.121353i	$-0.0387232\pi$
$740$	51.2516	+	74.2508i	1.88405	+	2.72951i
$741$	−3.08208	+	2.01577i	−0.113223	+	0.0740512i
$742$	6.68088	−	9.67892i	0.245263	−	0.355324i
$743$	16.6166	+	14.7210i	0.609602	+	0.540061i	0.910454	−	0.413610i	$-0.135732\pi$
$743$	16.6166	+	14.7210i	0.609602	+	0.540061i	−0.300852	+	0.953671i	$0.597271\pi$
$744$	−17.0413	+	4.20032i	−0.624766	+	0.153991i
$745$	1.83178	−	2.65379i	0.0671112	−	0.0972274i
$746$	−48.1770			−1.76389
$747$	−11.3799	+	16.4866i	−0.416367	+	0.603212i
$748$	−2.80113	+	23.0694i	−0.102419	+	0.843500i
$749$	−3.64238	+	9.60416i	−0.133090	+	0.350928i
$750$	0.581481	+	4.78893i	0.0212327	+	0.174867i
$751$	10.6282	−	28.0243i	0.387829	−	1.02262i	−0.588912	−	0.808197i	$-0.700444\pi$
$751$	10.6282	−	28.0243i	0.387829	−	1.02262i	0.976741	−	0.214423i	$-0.0687871\pi$
$752$	−0.909520	+	0.805765i	−0.0331668	+	0.0293832i
$753$	−13.1515	+	11.6512i	−0.479267	+	0.424594i
$754$	50.4935	−	17.7219i	1.83886	−	0.645392i
$755$	14.1305	+	12.5185i	0.514261	+	0.455596i
$756$	−16.1152			−0.586103
$757$	15.6171	−	13.8355i	0.567612	−	0.502860i	−0.329802	−	0.944050i	$-0.606982\pi$
$757$	15.6171	−	13.8355i	0.567612	−	0.502860i	0.897414	+	0.441190i	$0.145443\pi$
$758$	79.6679	+	19.6364i	2.89367	+	0.713226i
$759$	1.13555	+	1.64512i	0.0412177	+	0.0597141i
$760$	2.58174	−	6.80750i	0.0936497	−	0.246934i
$761$	−6.60147	+	17.4066i	−0.239303	+	0.630990i	−0.999832	−	0.0183136i	$-0.994170\pi$
$761$	−6.60147	+	17.4066i	−0.239303	+	0.630990i	0.760529	+	0.649304i	$0.224940\pi$
$762$	−16.1691	−	23.4250i	−0.585744	−	0.848597i
$763$	3.65212	+	0.900166i	0.132215	+	0.0325882i
$764$	26.2427	−	23.2490i	0.949429	−	0.841121i
$765$	24.6498			0.891217
$766$	38.5562	+	34.1579i	1.39309	+	1.23417i
$767$	3.54733	−	12.9885i	0.128087	−	0.468989i

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)

\(f(q)\)	\(=\)	\(q+(-0.814971 - 2.14890i) q^{2} +(0.722310 - 1.04645i) q^{3} +(-2.45658 + 2.17634i) q^{4} +(-0.370802 - 3.05383i) q^{5} +(-2.83737 - 0.699350i) q^{6} +(0.780099 + 0.409428i) q^{7} +(2.60879 + 1.36920i) q^{8} +(0.490496 + 1.29333i) q^{9} +O(q^{10})\)	\(q+(-0.814971 - 2.14890i) q^{2} +(0.722310 - 1.04645i) q^{3} +(-2.45658 + 2.17634i) q^{4} +(-0.370802 - 3.05383i) q^{5} +(-2.83737 - 0.699350i) q^{6} +(0.780099 + 0.409428i) q^{7} +(2.60879 + 1.36920i) q^{8} +(0.490496 + 1.29333i) q^{9} +(-6.26019 + 3.28560i) q^{10} +(0.433436 - 1.14288i) q^{11} +(0.503012 + 4.14268i) q^{12} +(-3.33830 - 1.36225i) q^{13} +(0.244062 - 2.01003i) q^{14} +(-3.46351 - 1.81779i) q^{15} +(0.0249923 - 0.205830i) q^{16} +(5.12941 + 2.69212i) q^{17} +(2.37950 - 2.10805i) q^{18} +0.803292 q^{19} +(7.55709 + 6.69499i) q^{20} +(0.991918 - 0.520599i) q^{21} -2.80917 q^{22} -1.28618 q^{23} +(3.31715 - 1.74097i) q^{24} +(-4.33368 + 1.06816i) q^{25} +(-0.206723 + 8.28388i) q^{26} +(5.41143 + 1.33380i) q^{27} +(-2.80743 + 0.691970i) q^{28} +(-2.29000 - 6.03824i) q^{29} +(-1.08359 + 8.92418i) q^{30} +(-4.54890 - 1.12120i) q^{31} +(5.25863 - 1.29614i) q^{32} +(-0.882884 - 1.27908i) q^{33} +(1.60479 - 13.2166i) q^{34} +(0.961060 - 2.53411i) q^{35} +(-4.01967 - 2.10969i) q^{36} +(8.67654 + 2.13858i) q^{37} +(-0.654660 - 1.72620i) q^{38} +(-3.83681 + 2.50939i) q^{39} +(3.21396 - 8.47450i) q^{40} +(4.12633 - 5.97803i) q^{41} +(-1.92710 - 1.70726i) q^{42} +(3.22950 - 0.796001i) q^{43} +(1.42252 + 3.75087i) q^{44} +(3.76774 - 1.97746i) q^{45} +(1.04820 + 2.76387i) q^{46} +(-4.38657 - 3.88617i) q^{47} +(-0.197338 - 0.174826i) q^{48} +(-3.53553 - 5.12210i) q^{49} +(5.82719 + 8.44214i) q^{50} +(6.52219 - 3.42311i) q^{51} +(11.1655 - 3.91881i) q^{52} +(5.14307 + 2.69929i) q^{53} +(-1.54396 - 12.7156i) q^{54} +(-3.65087 - 0.899858i) q^{55} +(1.47453 + 2.13622i) q^{56} +(0.580226 - 0.840602i) q^{57} +(-11.1093 + 9.84198i) q^{58} +(0.450121 + 3.70708i) q^{59} +(12.4645 - 3.07223i) q^{60} +(-10.2717 + 5.39103i) q^{61} +(1.29787 + 10.6889i) q^{62} +(-0.146890 + 1.20975i) q^{63} +(-7.30647 - 10.5852i) q^{64} +(-2.92223 + 10.6997i) q^{65} +(-2.02909 + 2.93964i) q^{66} +(9.13908 + 8.09652i) q^{67} +(-18.4598 + 4.54994i) q^{68} +(-0.929019 + 1.34592i) q^{69} -6.22879 q^{70} +(-4.50356 + 6.52453i) q^{71} +(-0.491226 + 4.04561i) q^{72} +(-0.529407 + 1.39593i) q^{73} +(-2.47554 - 20.3879i) q^{74} +(-2.01249 + 5.30650i) q^{75} +(-1.97335 + 1.74824i) q^{76} +(0.806048 - 0.714096i) q^{77} +(8.51933 + 6.19986i) q^{78} +(12.7973 + 11.3374i) q^{79} -0.637837 q^{80} +(2.19842 - 1.94763i) q^{81} +(-16.2090 - 3.99517i) q^{82} +(8.22709 + 11.9190i) q^{83} +(-1.30373 + 3.43765i) q^{84} +(6.31929 - 16.6626i) q^{85} +(-4.34248 - 6.29117i) q^{86} +(-7.97279 - 1.96512i) q^{87} +(2.69557 - 2.38806i) q^{88} -11.6944 q^{89} +(-7.31997 - 6.48492i) q^{90} +(-2.04647 - 2.42949i) q^{91} +(3.15960 - 2.79916i) q^{92} +(-4.45899 + 3.95032i) q^{93} +(-4.77606 + 12.5934i) q^{94} +(-0.297862 - 2.45312i) q^{95} +(2.44202 - 6.43909i) q^{96} +(0.702735 - 5.78754i) q^{97} +(-8.12554 + 11.7719i) q^{98} +1.69072 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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