LMFDB - Embedded newform 169.2.g.a.14.9

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			14.9
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.481559 - 0.697658i) q^{2} +(1.04345 - 0.547645i) q^{3} +(0.454382 + 1.19811i) q^{4} +(0.674379 + 0.597448i) q^{5} +(0.120414 - 0.991695i) q^{6} +(-0.515253 - 0.126998i) q^{7} +(2.70085 + 0.665700i) q^{8} +(-0.915320 + 1.32607i) q^{9} +O(q^{10})$	\(q+(0.481559 - 0.697658i) q^{2} +(1.04345 - 0.547645i) q^{3} +(0.454382 + 1.19811i) q^{4} +(0.674379 + 0.597448i) q^{5} +(0.120414 - 0.991695i) q^{6} +(-0.515253 - 0.126998i) q^{7} +(2.70085 + 0.665700i) q^{8} +(-0.915320 + 1.32607i) q^{9} +(0.741567 - 0.182780i) q^{10} +(-1.47414 - 2.13566i) q^{11} +(1.13026 + 1.00132i) q^{12} +(-0.909072 - 3.48907i) q^{13} +(-0.336726 + 0.298313i) q^{14} +(1.03087 + 0.254087i) q^{15} +(-0.153197 + 0.135721i) q^{16} +(-5.78443 - 1.42573i) q^{17} +(0.484363 + 1.27716i) q^{18} +4.91931 q^{19} +(-0.409380 + 1.07945i) q^{20} +(-0.607191 + 0.149659i) q^{21} -2.19985 q^{22} -4.70766 q^{23} +(3.18277 - 0.784483i) q^{24} +(-0.504840 - 4.15773i) q^{25} +(-2.87195 - 1.04597i) q^{26} +(-0.655009 + 5.39448i) q^{27} +(-0.0819639 - 0.675033i) q^{28} +(4.17327 - 6.04603i) q^{29} +(0.673691 - 0.596838i) q^{30} +(-0.345381 + 2.84446i) q^{31} +(0.691502 + 5.69503i) q^{32} +(-2.70778 - 1.42115i) q^{33} +(-3.78021 + 3.34898i) q^{34} +(-0.271601 - 0.393482i) q^{35} +(-2.00468 - 0.494108i) q^{36} +(-1.35384 + 11.1499i) q^{37} +(2.36894 - 3.43200i) q^{38} +(-2.85934 - 3.14282i) q^{39} +(1.42368 + 2.06255i) q^{40} +(3.38243 - 1.77523i) q^{41} +(-0.187987 + 0.495682i) q^{42} +(1.21336 + 9.99294i) q^{43} +(1.88893 - 2.73659i) q^{44} +(-1.40953 + 0.347418i) q^{45} +(-2.26702 + 3.28434i) q^{46} +(-0.266006 + 0.701399i) q^{47} +(-0.0855268 + 0.225516i) q^{48} +(-5.94884 - 3.12219i) q^{49} +(-3.14379 - 1.64999i) q^{50} +(-6.81656 + 1.68013i) q^{51} +(3.76721 - 2.67453i) q^{52} +(-1.63193 - 0.402235i) q^{53} +(3.44808 + 3.05473i) q^{54} +(0.281817 - 2.32097i) q^{55} +(-1.30708 - 0.686007i) q^{56} +(5.13306 - 2.69404i) q^{57} +(-2.20838 - 5.82303i) q^{58} +(-5.96165 - 5.28156i) q^{59} +(0.163986 + 1.35054i) q^{60} +(9.58018 - 2.36130i) q^{61} +(1.81814 + 1.61073i) q^{62} +(0.640030 - 0.567017i) q^{63} +(3.94373 + 2.06983i) q^{64} +(1.47148 - 2.89608i) q^{65} +(-2.29543 + 1.20474i) q^{66} +(0.427860 - 1.12817i) q^{67} +(-0.920158 - 7.57818i) q^{68} +(-4.91222 + 2.57813i) q^{69} -0.405307 q^{70} +(6.99334 - 3.67039i) q^{71} +(-3.35490 + 2.97219i) q^{72} +(0.746804 + 1.08193i) q^{73} +(7.12685 + 6.31384i) q^{74} +(-2.80374 - 4.06192i) q^{75} +(2.23524 + 5.89385i) q^{76} +(0.488330 + 1.28762i) q^{77} +(-3.56956 + 0.481391i) q^{78} +(-0.912716 + 2.40664i) q^{79} -0.184399 q^{80} +(0.556675 + 1.46783i) q^{81} +(0.390330 - 3.21466i) q^{82} +(5.18384 + 2.72069i) q^{83} +(-0.455204 - 0.659477i) q^{84} +(-3.04909 - 4.41738i) q^{85} +(7.55596 + 3.96567i) q^{86} +(1.04353 - 8.59420i) q^{87} +(-2.55973 - 6.74944i) q^{88} +13.4789 q^{89} +(-0.436392 + 1.15067i) q^{90} +(0.0252958 + 1.91320i) q^{91} +(-2.13908 - 5.64028i) q^{92} +(1.19737 + 3.15721i) q^{93} +(0.361240 + 0.523346i) q^{94} +(3.31748 + 2.93903i) q^{95} +(3.84041 + 5.56379i) q^{96} +(2.08113 - 1.84372i) q^{97} +(-5.04293 + 2.64674i) q^{98} +4.18135 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 $

$2$	0.481559	−	0.697658i	0.340513	−	0.493319i	−0.614894	−	0.788610i	$-0.710801\pi$
$2$	0.481559	−	0.697658i	0.340513	−	0.493319i	0.955407	+	0.295291i	$0.0954166\pi$
$3$	1.04345	−	0.547645i	0.602437	−	0.316183i	−0.135788	−	0.990738i	$-0.543357\pi$
$3$	1.04345	−	0.547645i	0.602437	−	0.316183i	0.738225	+	0.674555i	$0.235664\pi$
$4$	0.454382	+	1.19811i	0.227191	+	0.599053i
$5$	0.674379	+	0.597448i	0.301591	+	0.267187i	0.800322	−	0.599570i	$-0.204662\pi$
$5$	0.674379	+	0.597448i	0.301591	+	0.267187i	−0.498731	+	0.866757i	$0.666200\pi$
$6$	0.120414	−	0.991695i	0.0491587	−	0.404858i
$7$	−0.515253	−	0.126998i	−0.194747	−	0.0480009i	0.140736	−	0.990047i	$-0.455053\pi$
$7$	−0.515253	−	0.126998i	−0.194747	−	0.0480009i	−0.335483	+	0.942046i	$0.608899\pi$
$8$	2.70085	+	0.665700i	0.954894	+	0.235360i
$9$	−0.915320	+	1.32607i	−0.305107	+	0.442023i
$10$	0.741567	−	0.182780i	0.234504	−	0.0578001i
$11$	−1.47414	−	2.13566i	−0.444471	−	0.643927i	0.535156	−	0.844753i	$-0.320253\pi$
$11$	−1.47414	−	2.13566i	−0.444471	−	0.643927i	−0.979627	+	0.200826i	$0.935637\pi$
$12$	1.13026	+	1.00132i	0.326279	+	0.289058i
$13$	−0.909072	−	3.48907i	−0.252131	−	0.967693i
$13$	−0.909072	−	3.48907i	−0.252131	−	0.967693i
$14$	−0.336726	+	0.298313i	−0.0899938	+	0.0797276i
$15$	1.03087	+	0.254087i	0.266170	+	0.0656049i
$16$	−0.153197	+	0.135721i	−0.0382993	+	0.0339302i
$17$	−5.78443	−	1.42573i	−1.40293	−	0.345791i	−0.535998	−	0.844219i	$-0.680065\pi$
$17$	−5.78443	−	1.42573i	−1.40293	−	0.345791i	−0.866931	+	0.498428i	$0.833911\pi$
$18$	0.484363	+	1.27716i	0.114165	+	0.301030i
$19$	4.91931			1.12857			0.564284	−	0.825581i	$-0.309152\pi$
$19$	4.91931			1.12857			0.564284	+	0.825581i	$0.309152\pi$
$20$	−0.409380	+	1.07945i	−0.0915402	+	0.241372i
$21$	−0.607191	+	0.149659i	−0.132500	+	0.0326583i
$22$	−2.19985			−0.469009
$23$	−4.70766			−0.981616			−0.490808	−	0.871268i	$-0.663298\pi$
$23$	−4.70766			−0.981616			−0.490808	+	0.871268i	$0.663298\pi$
$24$	3.18277	−	0.784483i	0.649680	−	0.160132i
$25$	−0.504840	−	4.15773i	−0.100968	−	0.831546i
$26$	−2.87195	−	1.04597i	−0.563235	−	0.205131i
$27$	−0.655009	+	5.39448i	−0.126057	+	1.03817i
$28$	−0.0819639	−	0.675033i	−0.0154897	−	0.127569i
$29$	4.17327	−	6.04603i	0.774957	−	1.12272i	−0.214334	−	0.976760i	$-0.568758\pi$
$29$	4.17327	−	6.04603i	0.774957	−	1.12272i	0.989291	−	0.145958i	$-0.0466266\pi$
$30$	0.673691	−	0.596838i	0.122998	−	0.108967i
$31$	−0.345381	+	2.84446i	−0.0620322	+	0.510881i	0.928265	+	0.371918i	$0.121300\pi$
$31$	−0.345381	+	2.84446i	−0.0620322	+	0.510881i	−0.990298	+	0.138963i	$0.955623\pi$
$32$	0.691502	+	5.69503i	0.122241	+	1.00675i
$33$	−2.70778	−	1.42115i	−0.471364	−	0.247391i
$34$	−3.78021	+	3.34898i	−0.648301	+	0.574345i
$35$	−0.271601	−	0.393482i	−0.0459089	−	0.0665106i
$36$	−2.00468	−	0.494108i	−0.334113	−	0.0823514i
$37$	−1.35384	+	11.1499i	−0.222570	+	1.83303i	0.270123	+	0.962826i	$0.412936\pi$
$37$	−1.35384	+	11.1499i	−0.222570	+	1.83303i	−0.492693	+	0.870203i	$0.663988\pi$
$38$	2.36894	−	3.43200i	0.384292	−	0.556743i
$39$	−2.85934	−	3.14282i	−0.457861	−	0.503254i
$40$	1.42368	+	2.06255i	0.225103	+	0.326118i
$41$	3.38243	−	1.77523i	0.528246	−	0.277245i	−0.179444	−	0.983768i	$-0.557430\pi$
$41$	3.38243	−	1.77523i	0.528246	−	0.277245i	0.707690	+	0.706523i	$0.249737\pi$
$42$	−0.187987	+	0.495682i	−0.0290071	+	0.0764853i
$43$	1.21336	+	9.99294i	0.185036	+	1.52391i	0.728833	+	0.684692i	$0.240063\pi$
$43$	1.21336	+	9.99294i	0.185036	+	1.52391i	−0.543796	+	0.839217i	$0.683014\pi$
$44$	1.88893	−	2.73659i	0.284767	−	0.412556i
$45$	−1.40953	+	0.347418i	−0.210120	+	0.0517900i
$46$	−2.26702	+	3.28434i	−0.334253	+	0.484250i
$47$	−0.266006	+	0.701399i	−0.0388009	+	0.102310i	−0.953016	−	0.302919i	$-0.902039\pi$
$47$	−0.266006	+	0.701399i	−0.0388009	+	0.102310i	0.914215	+	0.405229i	$0.132808\pi$
$48$	−0.0855268	+	0.225516i	−0.0123447	+	0.0325504i
$49$	−5.94884	−	3.12219i	−0.849834	−	0.446027i
$50$	−3.14379	−	1.64999i	−0.444598	−	0.233343i
$51$	−6.81656	+	1.68013i	−0.954509	+	0.235265i
$52$	3.76721	−	2.67453i	0.522418	−	0.370891i
$53$	−1.63193	−	0.402235i	−0.224163	−	0.0552513i	0.125634	−	0.992077i	$-0.459903\pi$
$53$	−1.63193	−	0.402235i	−0.224163	−	0.0552513i	−0.349797	+	0.936825i	$0.613750\pi$
$54$	3.44808	+	3.05473i	0.469224	+	0.415696i
$55$	0.281817	−	2.32097i	0.0380002	−	0.312960i
$56$	−1.30708	−	0.686007i	−0.174666	−	0.0916716i
$57$	5.13306	−	2.69404i	0.679890	−	0.356834i
$58$	−2.20838	−	5.82303i	−0.289975	−	0.764602i
$59$	−5.96165	−	5.28156i	−0.776140	−	0.687600i	0.178969	−	0.983855i	$-0.442724\pi$
$59$	−5.96165	−	5.28156i	−0.776140	−	0.687600i	−0.955109	+	0.296255i	$0.904262\pi$
$60$	0.163986	+	1.35054i	0.0211705	+	0.174355i
$61$	9.58018	−	2.36130i	1.22662	−	0.302334i	0.427780	−	0.903883i	$-0.359296\pi$
$61$	9.58018	−	2.36130i	1.22662	−	0.302334i	0.798836	+	0.601549i	$0.205450\pi$
$62$	1.81814	+	1.61073i	0.230904	+	0.204563i
$63$	0.640030	−	0.567017i	0.0806362	−	0.0714374i
$64$	3.94373	+	2.06983i	0.492967	+	0.258729i
$65$	1.47148	−	2.89608i	0.182514	−	0.359214i
$66$	−2.29543	+	1.20474i	−0.282549	+	0.148293i
$67$	0.427860	−	1.12817i	0.0522715	−	0.137829i	−0.906337	−	0.422555i	$-0.861133\pi$
$67$	0.427860	−	1.12817i	0.0522715	−	0.137829i	0.958609	+	0.284726i	$0.0919027\pi$
$68$	−0.920158	−	7.57818i	−0.111586	−	0.918989i
$69$	−4.91222	+	2.57813i	−0.591361	+	0.310370i
$70$	−0.405307			−0.0484435
$71$	6.99334	−	3.67039i	0.829957	−	0.435595i	0.00445199	−	0.999990i	$-0.498583\pi$
$71$	6.99334	−	3.67039i	0.829957	−	0.435595i	0.825505	+	0.564395i	$0.190891\pi$
$72$	−3.35490	+	2.97219i	−0.395379	+	0.350275i
$73$	0.746804	+	1.08193i	0.0874068	+	0.126631i	0.864248	−	0.503066i	$-0.167795\pi$
$73$	0.746804	+	1.08193i	0.0874068	+	0.126631i	−0.776841	+	0.629696i	$0.783179\pi$
$74$	7.12685	+	6.31384i	0.828480	+	0.733969i
$75$	−2.80374	−	4.06192i	−0.323748	−	0.469030i
$76$	2.23524	+	5.89385i	0.256400	+	0.676071i
$77$	0.488330	+	1.28762i	0.0556504	+	0.146738i
$78$	−3.56956	+	0.481391i	−0.404173	+	0.0545068i
$79$	−0.912716	+	2.40664i	−0.102689	+	0.270768i	−0.976507	−	0.215484i	$-0.930867\pi$
$79$	−0.912716	+	2.40664i	−0.102689	+	0.270768i	0.873819	+	0.486252i	$0.161636\pi$
$80$	−0.184399			−0.0206164
$81$	0.556675	+	1.46783i	0.0618527	+	0.163092i
$82$	0.390330	−	3.21466i	0.0431047	−	0.354999i
$83$	5.18384	+	2.72069i	0.569001	+	0.298635i	0.724582	−	0.689188i	$-0.242033\pi$
$83$	5.18384	+	2.72069i	0.569001	+	0.298635i	−0.155581	+	0.987823i	$0.549725\pi$
$84$	−0.455204	−	0.659477i	−0.0496668	−	0.0719548i
$85$	−3.04909	−	4.41738i	−0.330721	−	0.479132i
$86$	7.55596	+	3.96567i	0.814780	+	0.427630i
$87$	1.04353	−	8.59420i	0.111878	−	0.921395i
$88$	−2.55973	−	6.74944i	−0.272868	−	0.719493i
$89$	13.4789			1.42876			0.714381	−	0.699757i	$-0.246708\pi$
$89$	13.4789			1.42876			0.714381	+	0.699757i	$0.246708\pi$
$90$	−0.436392	+	1.15067i	−0.0459998	+	0.121291i
$91$	0.0252958	+	1.91320i	0.00265172	+	0.200558i
$92$	−2.13908	−	5.64028i	−0.223014	−	0.588040i
$93$	1.19737	+	3.15721i	0.124162	+	0.327387i
$94$	0.361240	+	0.523346i	0.0372590	+	0.0539790i
$95$	3.31748	+	2.93903i	0.340366	+	0.301538i
$96$	3.84041	+	5.56379i	0.391960	+	0.567852i
$97$	2.08113	−	1.84372i	0.211307	−	0.187202i	−0.550830	−	0.834618i	$-0.685689\pi$
$97$	2.08113	−	1.84372i	0.211307	−	0.187202i	0.762137	+	0.647416i	$0.224150\pi$
$98$	−5.04293	+	2.64674i	−0.509413	+	0.267361i
$99$	4.18135			0.420242
$100$	4.75201	−	2.49405i	0.475201	−	0.249405i
$101$	−0.650664	−	5.35870i	−0.0647435	−	0.533211i	−0.988610	−	0.150497i	$-0.951913\pi$
$101$	−0.650664	−	5.35870i	−0.0647435	−	0.533211i	0.923867	−	0.382714i	$-0.125010\pi$
$102$	−2.11042	+	5.56471i	−0.208962	+	0.550988i
$103$	7.23426	−	3.79683i	0.712813	−	0.374113i	−0.0690083	−	0.997616i	$-0.521983\pi$
$103$	7.23426	−	3.79683i	0.712813	−	0.374113i	0.781821	+	0.623503i	$0.214291\pi$
$104$	−0.132595	−	10.0286i	−0.0130020	−	0.983386i
$105$	−0.498891	−	0.261838i	−0.0486867	−	0.0255528i
$106$	−1.06649	+	0.944831i	−0.103587	+	0.0917701i
$107$	−4.28960	−	3.80025i	−0.414691	−	0.367384i	0.429827	−	0.902911i	$-0.358575\pi$
$107$	−4.28960	−	3.80025i	−0.414691	−	0.367384i	−0.844518	+	0.535527i	$0.820113\pi$
$108$	−6.76079	+	1.66638i	−0.650557	+	0.160348i
$109$	0.647619	+	5.33363i	0.0620307	+	0.510869i	0.990299	+	0.138956i	$0.0443748\pi$
$109$	0.647619	+	5.33363i	0.0620307	+	0.510869i	−0.928268	+	0.371912i	$0.878702\pi$
$110$	−1.48353	−	1.31429i	−0.141449	−	0.125313i
$111$	4.69351	+	12.3758i	0.445489	+	1.17466i
$112$	0.0961716	−	0.0504747i	0.00908736	−	0.00476941i
$113$	−12.1681	−	6.38632i	−1.14468	−	0.600774i	−0.217749	−	0.976005i	$-0.569871\pi$
$113$	−12.1681	−	6.38632i	−1.14468	−	0.600774i	−0.926932	+	0.375230i	$0.877564\pi$
$114$	0.592352	−	4.87846i	0.0554788	−	0.456909i
$115$	−3.17475	−	2.81258i	−0.296047	−	0.262275i
$116$	9.14004	+	2.25282i	0.848631	+	0.209169i
$117$	5.45884	+	1.98812i	0.504670	+	0.183802i
$118$	−6.55560	+	1.61581i	−0.603492	+	0.148747i
$119$	2.79938	+	1.46923i	0.256618	+	0.134684i
$120$	2.61508	+	1.37250i	0.238723	+	0.125292i
$121$	1.51269	−	3.98863i	0.137517	−	0.362603i
$122$	2.96604	−	7.82079i	0.268532	−	0.708061i
$123$	2.55720	−	3.70474i	0.230575	−	0.334045i
$124$	−3.56490	+	0.878670i	−0.320138	+	0.0789069i
$125$	4.70259	−	6.81288i	0.420613	−	0.609363i
$126$	−0.0873721	−	0.719574i	−0.00778373	−	0.0641047i
$127$	−5.48017	+	14.4500i	−0.486287	+	1.28223i	0.437463	+	0.899236i	$0.355877\pi$
$127$	−5.48017	+	14.4500i	−0.486287	+	1.28223i	−0.923750	+	0.382996i	$0.874892\pi$
$128$	−6.81630	+	3.57747i	−0.602482	+	0.316207i
$129$	6.73867	+	9.76265i	0.593307	+	0.859553i
$130$	−1.31187	−	2.42122i	−0.115059	−	0.212355i
$131$	−11.5160	+	16.6838i	−1.00616	+	1.45767i	−0.120848	+	0.992671i	$0.538561\pi$
$131$	−11.5160	+	16.6838i	−1.00616	+	1.45767i	−0.885310	+	0.465001i	$0.846054\pi$
$132$	0.472326	−	3.88996i	0.0411107	−	0.338577i
$133$	−2.53469	−	0.624745i	−0.219785	−	0.0541722i
$134$	−0.581041	−	0.841783i	−0.0501943	−	0.0727189i
$135$	−3.66465	+	3.24659i	−0.315402	+	0.279422i
$136$	−14.6737	−	7.70138i	−1.25826	−	0.660388i
$137$	−0.00404005	−	0.0332728i	−0.000345165	−	0.00284269i	0.992535	−	0.121958i	$-0.0389173\pi$
$137$	−0.00404005	−	0.0332728i	−0.000345165	−	0.00284269i	−0.992880	+	0.119115i	$0.961994\pi$
$138$	−0.566867	+	4.66857i	−0.0482549	+	0.397415i
$139$	−3.67828	+	3.25868i	−0.311988	+	0.276397i	−0.804556	−	0.593877i	$-0.797597\pi$
$139$	−3.67828	+	3.25868i	−0.311988	+	0.276397i	0.492568	+	0.870274i	$0.336058\pi$
$140$	0.348022	−	0.504197i	0.0294133	−	0.0426125i
$141$	0.106554	+	0.877553i	0.00897348	+	0.0739033i
$142$	0.807027	−	6.64647i	0.0677242	−	0.557759i
$143$	−6.11137	+	7.08485i	−0.511059	+	0.592465i
$144$	−0.0397509	−	0.327378i	−0.00331257	−	0.0272815i
$145$	6.42655	−	1.58400i	0.533696	−	0.131544i
$146$	1.11445			0.0922324
$147$	−7.91717			−0.652997
$148$	−13.9739	+	3.44426i	−1.14865	+	0.283116i
$149$	6.09715	−	16.0769i	0.499498	−	1.31707i	−0.414019	−	0.910268i	$-0.635875\pi$
$149$	6.09715	−	16.0769i	0.499498	−	1.31707i	0.913517	−	0.406800i	$-0.133355\pi$
$150$	−4.18399			−0.341622
$151$	3.49663	+	9.21985i	0.284552	+	0.750301i	0.998732	+	0.0503395i	$0.0160303\pi$
$151$	3.49663	+	9.21985i	0.284552	+	0.750301i	−0.714180	+	0.699962i	$0.753200\pi$
$152$	13.2863	+	3.27478i	1.07766	+	0.265620i
$153$	7.18522	−	6.36555i	0.580891	−	0.514624i
$154$	1.13348	+	0.279377i	0.0913383	+	0.0225129i
$155$	−1.93234	+	1.71190i	−0.155209	+	0.137503i
$156$	2.46620	−	4.85384i	0.197454	−	0.388618i
$157$	10.9811	+	9.72842i	0.876389	+	0.776413i	0.975807	−	0.218633i	$-0.0701598\pi$
$157$	10.9811	+	9.72842i	0.876389	+	0.776413i	−0.0994184	+	0.995046i	$0.531698\pi$
$158$	1.23948	+	1.79570i	0.0986079	+	0.142858i
$159$	−1.92312	+	0.474008i	−0.152514	+	0.0375912i
$160$	−2.93615	+	4.25375i	−0.232123	+	0.336288i
$161$	2.42564	+	0.597866i	0.191167	+	0.0471184i
$162$	1.29212	+	0.318478i	0.101518	+	0.0250220i
$163$	2.40334	−	19.7933i	0.188244	−	1.55033i	−0.526033	−	0.850464i	$-0.676321\pi$
$163$	2.40334	−	19.7933i	0.188244	−	1.55033i	0.714276	−	0.699864i	$-0.246756\pi$
$164$	3.66383	+	3.24587i	0.286097	+	0.253460i
$165$	−0.977006	−	2.57615i	−0.0760598	−	0.200553i
$166$	4.39444	−	2.30638i	0.341074	−	0.179010i
$167$	−10.0602	+	14.5747i	−0.778481	+	1.12782i	0.210180	+	0.977663i	$0.432595\pi$
$167$	−10.0602	+	14.5747i	−0.778481	+	1.12782i	−0.988661	+	0.150162i	$0.952021\pi$
$168$	−1.73956			−0.134210
$169$	−11.3472	+	6.34362i	−0.872860	+	0.487971i
$170$	−4.55014			−0.348979
$171$	−4.50274	+	6.52335i	−0.344333	+	0.498853i
$172$	−11.4213	+	5.99435i	−0.870864	+	0.457065i
$173$	−2.85385	−	7.52498i	−0.216974	−	0.572114i	0.781697	−	0.623659i	$-0.214355\pi$
$173$	−2.85385	−	7.52498i	−0.216974	−	0.572114i	−0.998671	+	0.0515453i	$0.983585\pi$
$174$	−5.49330	−	4.86664i	−0.416446	−	0.368939i
$175$	−0.267905	+	2.20640i	−0.0202517	+	0.166788i
$176$	0.515688	+	0.127106i	0.0388715	+	0.00958096i
$177$	−9.11310	−	2.24618i	−0.684983	−	0.168833i
$178$	6.49089	−	9.40368i	0.486513	−	0.704836i
$179$	−15.6888	+	3.86695i	−1.17264	+	0.289029i	−0.777074	−	0.629409i	$-0.783297\pi$
$179$	−15.6888	+	3.86695i	−1.17264	+	0.289029i	−0.395564	+	0.918439i	$0.629451\pi$
$180$	−1.05671	−	1.53091i	−0.0787623	−	0.114107i
$181$	8.47043	+	7.50415i	0.629602	+	0.557779i	0.916426	−	0.400204i	$-0.131061\pi$
$181$	8.47043	+	7.50415i	0.629602	+	0.557779i	−0.286823	+	0.957983i	$0.592599\pi$
$182$	1.34694	+	0.903671i	0.0998420	+	0.0669846i
$183$	8.70329	−	7.71044i	0.643366	−	0.569972i
$184$	−12.7147	−	3.13389i	−0.937339	−	0.231033i
$185$	−7.57447	+	6.71040i	−0.556886	+	0.493358i
$186$	2.77925	+	0.685025i	0.203785	+	0.0502284i
$187$	5.48218	+	14.4553i	0.400897	+	1.05708i
$188$	−0.961219			−0.0701041
$189$	1.02259	−	2.69634i	0.0743822	−	0.196130i
$190$	3.64800	−	0.899151i	0.264654	−	0.0652313i
$191$	16.0522			1.16150			0.580750	−	0.814082i	$-0.302759\pi$
$191$	16.0522			1.16150			0.580750	+	0.814082i	$0.302759\pi$
$192$	5.24863			0.378787
$193$	−14.2683	+	3.51681i	−1.02705	+	0.253146i	−0.716630	−	0.697453i	$-0.754316\pi$
$193$	−14.2683	+	3.51681i	−1.02705	+	0.253146i	−0.310422	+	0.950599i	$0.600470\pi$
$194$	−0.284101	−	2.33978i	−0.0203973	−	0.167987i
$195$	−0.0506095	−	3.82776i	−0.00362422	−	0.274112i
$196$	1.03767	−	8.54600i	0.0741194	−	0.610429i
$197$	−0.193350	−	1.59238i	−0.0137756	−	0.113452i	0.984199	−	0.177066i	$-0.0566606\pi$
$197$	−0.193350	−	1.59238i	−0.0137756	−	0.113452i	−0.997975	+	0.0636136i	$0.979737\pi$
$198$	2.01357	−	2.91715i	0.143098	−	0.207313i
$199$	−6.25815	+	5.54424i	−0.443629	+	0.393021i	−0.855151	−	0.518379i	$-0.826536\pi$
$199$	−6.25815	+	5.54424i	−0.443629	+	0.393021i	0.411522	+	0.911400i	$0.364997\pi$
$200$	1.40430	−	11.5655i	0.0992992	−	0.817803i
$201$	−0.171388	−	1.41151i	−0.0120888	−	0.0995603i
$202$	−4.05188	−	2.12659i	−0.285089	−	0.149626i
$203$	−2.91813	+	2.58523i	−0.204812	+	0.181448i
$204$	−5.11029	−	7.40354i	−0.357792	−	0.518351i
$205$	3.34165	+	0.823642i	0.233391	+	0.0575257i
$206$	0.834829	−	6.87543i	0.0581653	−	0.479034i
$207$	4.30902	−	6.24269i	0.299497	−	0.433897i
$208$	0.612806	+	0.411135i	0.0424905	+	0.0285071i
$209$	−7.25176	−	10.5060i	−0.501615	−	0.726715i
$210$	−0.422918	+	0.221965i	−0.0291841	+	0.0153170i
$211$	1.65131	−	4.35415i	0.113681	−	0.299752i	−0.866086	−	0.499896i	$-0.833372\pi$
$211$	1.65131	−	4.35415i	0.113681	−	0.299752i	0.979767	+	0.200144i	$0.0641409\pi$
$212$	−0.259600	−	2.13800i	−0.0178294	−	0.146838i
$213$	5.28714	−	7.65974i	0.362269	−	0.524837i
$214$	−4.71697	+	1.16263i	−0.322446	+	0.0794757i
$215$	−5.15199	+	7.46395i	−0.351363	+	0.509037i
$216$	−5.36018	+	14.1336i	−0.364714	+	0.961673i
$217$	0.539201	−	1.42176i	0.0366033	−	0.0965151i
$218$	4.03291	+	2.11664i	0.273143	+	0.143357i
$219$	1.37177	+	0.719959i	0.0926955	+	0.0486503i
$220$	2.90882	−	0.716960i	0.196113	−	0.0483374i
$221$	0.283980	+	21.4783i	0.0191026	+	1.44479i
$222$	10.8943	+	2.68519i	0.731175	+	0.180218i
$223$	17.2670	+	15.2972i	1.15628	+	1.02438i	0.999324	+	0.0367732i	$0.0117079\pi$
$223$	17.2670	+	15.2972i	1.15628	+	1.02438i	0.156960	+	0.987605i	$0.449831\pi$
$224$	0.366962	−	3.02220i	0.0245187	−	0.201929i
$225$	5.97553	+	3.13620i	0.398369	+	0.209080i
$226$	−10.3151	+	5.41380i	−0.686152	+	0.360120i
$227$	2.29148	+	6.04214i	0.152091	+	0.401031i	0.989308	−	0.145839i	$-0.0465883\pi$
$227$	2.29148	+	6.04214i	0.152091	+	0.401031i	−0.837217	+	0.546870i	$0.815819\pi$
$228$	5.56011	+	4.92583i	0.368227	+	0.326221i
$229$	−1.63135	−	13.4354i	−0.107803	−	0.887834i	−0.941825	−	0.336103i	$-0.890891\pi$
$229$	−1.63135	−	13.4354i	−0.107803	−	0.887834i	0.834023	−	0.551730i	$-0.186032\pi$
$230$	−3.49105	+	0.860466i	−0.230193	+	0.0567375i
$231$	1.21471	+	1.07614i	0.0799219	+	0.0708047i
$232$	15.2962	−	13.5513i	1.00425	−	0.889684i
$233$	−9.03432	−	4.74158i	−0.591858	−	0.310631i	0.142072	−	0.989856i	$-0.454624\pi$
$233$	−9.03432	−	4.74158i	−0.591858	−	0.310631i	−0.733930	+	0.679225i	$0.762316\pi$
$234$	4.01578	−	2.85101i	0.262520	−	0.186376i
$235$	−0.598438	+	0.314085i	−0.0390378	+	0.0204886i
$236$	3.61900	−	9.54252i	0.235577	−	0.621165i
$237$	0.365608	+	3.01105i	0.0237488	+	0.195589i
$238$	2.37308	−	1.24549i	0.153824	−	0.0807331i
$239$	21.0349			1.36064			0.680318	−	0.732917i	$-0.261842\pi$
$239$	21.0349			1.36064			0.680318	+	0.732917i	$0.261842\pi$
$240$	−0.192411	+	0.100985i	−0.0124201	+	0.00651857i
$241$	13.0847	−	11.5920i	0.842859	−	0.746708i	−0.126602	−	0.991954i	$-0.540407\pi$
$241$	13.0847	−	11.5920i	0.842859	−	0.746708i	0.969461	+	0.245246i	$0.0788687\pi$
$242$	−2.05425	−	2.97610i	−0.132052	−	0.191311i
$243$	−10.8177	−	9.58368i	−0.693958	−	0.614794i
$244$	7.18215	+	10.4051i	0.459790	+	0.666121i
$245$	−2.14642	−	5.65966i	−0.137130	−	0.361582i
$246$	−1.35320	−	3.56810i	−0.0862770	−	0.227494i
$247$	−4.47201	−	17.1638i	−0.284547	−	1.09211i
$248$	−2.82638	+	7.45255i	−0.179475	+	0.473237i
$249$	6.89906			0.437210
$250$	−2.48849	−	6.56161i	−0.157386	−	0.414992i
$251$	0.428634	−	3.53012i	0.0270552	−	0.222819i	−0.972910	−	0.231185i	$-0.925740\pi$
$251$	0.428634	−	3.53012i	0.0270552	−	0.222819i	0.999965	+	0.00836550i	$0.00266285\pi$
$252$	0.970164	+	0.509181i	0.0611146	+	0.0320754i
$253$	6.93977	+	10.0540i	0.436299	+	0.632089i
$254$	7.44215	+	10.7818i	0.466962	+	0.676512i
$255$	−5.60074	−	2.93949i	−0.350732	−	0.184078i
$256$	−1.86031	+	15.3211i	−0.116270	+	0.957567i
$257$	2.44686	+	6.45184i	0.152631	+	0.402455i	0.989422	−	0.145068i	$-0.0463401\pi$
$257$	2.44686	+	6.45184i	0.152631	+	0.402455i	−0.836791	+	0.547523i	$0.815571\pi$
$258$	10.0561			0.626063
$259$	2.11359	−	5.57307i	0.131332	−	0.346294i
$260$	4.13842	+	0.447060i	0.256654	+	0.0277255i
$261$	4.19757	+	11.0681i	0.259823	+	0.685098i
$262$	6.09397	+	16.0685i	0.376487	+	0.992714i
$263$	−7.20289	−	10.4352i	−0.444149	−	0.643461i	0.535416	−	0.844588i	$-0.320155\pi$
$263$	−7.20289	−	10.4352i	−0.444149	−	0.643461i	−0.979565	+	0.201127i	$0.935539\pi$
$264$	−6.36725	−	5.64089i	−0.391877	−	0.347173i
$265$	−0.860227	−	1.24625i	−0.0528433	−	0.0765567i
$266$	−1.65646	+	1.46749i	−0.101564	+	0.0899779i
$267$	14.0646	−	7.38167i	0.860739	−	0.451751i
$268$	1.54608			0.0944422
$269$	−2.95497	+	1.55089i	−0.180168	+	0.0945593i	−0.552396	−	0.833582i	$-0.686286\pi$
$269$	−2.95497	+	1.55089i	−0.180168	+	0.0945593i	0.372228	+	0.928141i	$0.378594\pi$
$270$	0.500270	+	4.12009i	0.0304455	+	0.250741i
$271$	−0.403342	+	1.06353i	−0.0245013	+	0.0646046i	−0.946709	−	0.322091i	$-0.895614\pi$
$271$	−0.403342	+	1.06353i	−0.0245013	+	0.0646046i	0.922207	+	0.386696i	$0.126384\pi$
$272$	1.07966	−	0.566649i	0.0654639	−	0.0343581i
$273$	1.07415	+	1.98248i	0.0650106	+	0.119985i
$274$	−0.0251586	−	0.0132042i	−0.00151988	−	0.000797697i
$275$	−8.13531	+	7.20726i	−0.490578	+	0.434614i
$276$	−5.32089	−	4.71390i	−0.320280	−	0.283743i
$277$	18.3410	−	4.52065i	1.10200	−	0.271619i	0.353954	−	0.935263i	$-0.384837\pi$
$277$	18.3410	−	4.52065i	1.10200	−	0.271619i	0.748049	+	0.663644i	$0.230991\pi$
$278$	0.502132	+	4.13543i	0.0301159	+	0.248026i
$279$	−3.45582	−	3.06159i	−0.206895	−	0.183293i
$280$	−0.471612	−	1.24354i	−0.0281842	−	0.0743157i
$281$	−6.32219	+	3.31814i	−0.377150	+	0.197944i	−0.642637	−	0.766171i	$-0.722160\pi$
$281$	−6.32219	+	3.31814i	−0.377150	+	0.197944i	0.265487	+	0.964115i	$0.414467\pi$
$282$	0.663544	+	0.348255i	0.0395135	+	0.0207383i
$283$	1.55567	−	12.8121i	0.0924750	−	0.761600i	−0.870530	−	0.492116i	$-0.836224\pi$
$283$	1.55567	−	12.8121i	0.0924750	−	0.761600i	0.963005	−	0.269484i	$-0.0868532\pi$
$284$	7.57516	+	6.71100i	0.449503	+	0.398225i
$285$	5.07117	+	1.24993i	0.300390	+	0.0740396i
$286$	1.99982	+	7.67542i	0.118252	+	0.453857i
$287$	−1.96826	+	0.485132i	−0.116183	+	0.0286364i
$288$	−8.18496	−	4.29580i	−0.482303	−	0.253132i
$289$	16.3741	+	8.59379i	0.963183	+	0.505517i
$290$	1.98967	−	5.24633i	0.116837	−	0.308075i
$291$	1.16185	−	3.06356i	0.0681091	−	0.179589i
$292$	−0.956935	+	1.38636i	−0.0560004	+	0.0811306i
$293$	20.8199	−	5.13164i	1.21631	−	0.299794i	0.421600	−	0.906782i	$-0.361469\pi$
$293$	20.8199	−	5.13164i	1.21631	−	0.299794i	0.794711	+	0.606988i	$0.207623\pi$
$294$	−3.81258	+	5.52348i	−0.222354	+	0.322136i
$295$	−0.864955	−	7.12354i	−0.0503596	−	0.414749i
$296$	−11.0790	+	29.2129i	−0.643953	+	1.69796i
$297$	12.4864	−	6.55336i	0.724533	−	0.380264i
$298$	−8.28002	−	11.9957i	−0.479649	−	0.694891i
$299$	4.27960	+	16.4254i	0.247496	+	0.949903i
$300$	3.59264	−	5.20484i	0.207421	−	0.300501i
$301$	0.643899	−	5.30299i	0.0371137	−	0.305659i
$302$	8.11614	+	2.00045i	0.467031	+	0.115113i
$303$	−3.61361	−	5.23521i	−0.207596	−	0.300755i
$304$	−0.753624	+	0.667653i	−0.0432233	+	0.0382925i
$305$	7.87143	+	4.13124i	0.450717	+	0.236554i
$306$	−0.980872	−	8.07821i	−0.0560727	−	0.461801i
$307$	1.45510	−	11.9838i	0.0830468	−	0.683952i	−0.890423	−	0.455135i	$-0.849591\pi$
$307$	1.45510	−	11.9838i	0.0830468	−	0.683952i	0.973469	−	0.228817i	$-0.0734858\pi$
$308$	−1.32082	+	1.17014i	−0.0752606	+	0.0666751i
$309$	5.46928	−	7.92361i	0.311136	−	0.450759i
$310$	0.263788	+	2.17249i	0.0149822	+	0.123389i
$311$	−1.36613	+	11.2511i	−0.0774660	+	0.637990i	0.901327	+	0.433139i	$0.142594\pi$
$311$	−1.36613	+	11.2511i	−0.0774660	+	0.637990i	−0.978793	+	0.204851i	$0.934329\pi$
$312$	−5.63048	−	10.3917i	−0.318763	−	0.588317i
$313$	−3.60250	−	29.6692i	−0.203625	−	1.67700i	−0.633211	−	0.773979i	$-0.718264\pi$
$313$	−3.60250	−	29.6692i	−0.203625	−	1.67700i	0.429586	−	0.903026i	$-0.358659\pi$
$314$	12.0752	−	2.97626i	0.681441	−	0.167960i
$315$	0.770386			0.0434063
$316$	−3.29813			−0.185534
$317$	−25.6712	+	6.32738i	−1.44184	+	0.355381i	−0.881225	−	0.472697i	$-0.843281\pi$
$317$	−25.6712	+	6.32738i	−1.44184	+	0.355381i	−0.560613	+	0.828078i	$0.689435\pi$
$318$	−0.595402	+	1.56995i	−0.0333885	+	0.0880382i
$319$	−19.0643			−1.06739
$320$	1.42296	+	3.75203i	0.0795456	+	0.209745i
$321$	−6.55718	−	1.61620i	−0.365986	−	0.0902075i
$322$	1.58519	−	1.40436i	0.0883393	−	0.0782618i
$323$	−28.4554	−	7.01362i	−1.58330	−	0.390248i
$324$	−1.50567	+	1.33391i	−0.0836485	+	0.0741061i
$325$	−14.0477	+	5.54110i	−0.779225	+	0.307365i
$326$	−12.6516	−	11.2083i	−0.700706	−	0.620772i
$327$	3.59669	+	5.21071i	0.198898	+	0.288153i
$328$	10.3172	−	2.54296i	0.569672	−	0.140411i
$329$	0.226137	−	0.327616i	0.0124673	−	0.0180620i
$330$	−2.26776	−	0.558953i	−0.124836	−	0.0307693i
$331$	−32.0888	−	7.90918i	−1.76376	−	0.434728i	−0.781756	−	0.623585i	$-0.785676\pi$
$331$	−32.0888	−	7.90918i	−1.76376	−	0.434728i	−0.982005	+	0.188857i	$0.939522\pi$
$332$	−0.904233	+	7.44703i	−0.0496262	+	0.408709i
$333$	−13.5463	−	12.0010i	−0.742334	−	0.657650i
$334$	5.32359	+	14.0371i	0.291294	+	0.768079i
$335$	0.962566	−	0.505193i	0.0525906	−	0.0276017i
$336$	0.0727081	−	0.105336i	0.00396655	−	0.00574654i
$337$	−21.7472			−1.18464			−0.592322	−	0.805701i	$-0.701789\pi$
$337$	−21.7472			−1.18464			−0.592322	+	0.805701i	$0.701789\pi$
$338$	−1.03865	+	10.9713i	−0.0564951	+	0.596759i
$339$	−16.1943			−0.879552
$340$	3.90703	−	5.66031i	0.211889	−	0.306974i
$341$	6.58396	−	3.45553i	0.356542	−	0.187127i
$342$	2.38273	+	6.28275i	0.128843	+	0.339732i
$343$	5.44914	+	4.82752i	0.294226	+	0.260662i
$344$	−3.37519	+	27.7972i	−0.181978	+	1.49872i
$345$	−4.85299	−	1.19616i	−0.261276	−	0.0643988i
$346$	−6.62416	−	1.63271i	−0.356117	−	0.0877750i
$347$	−14.1415	+	20.4874i	−0.759153	+	1.09982i	0.232714	+	0.972545i	$0.425239\pi$
$347$	−14.1415	+	20.4874i	−0.759153	+	1.09982i	−0.991867	+	0.127278i	$0.959376\pi$
$348$	10.7709	−	2.65479i	0.577382	−	0.142312i
$349$	−15.7510	−	22.8193i	−0.843131	−	1.22149i	−0.973195	−	0.229981i	$-0.926134\pi$
$349$	−15.7510	−	22.8193i	−0.843131	−	1.22149i	0.130064	−	0.991506i	$-0.458482\pi$
$350$	1.41030	+	1.24942i	0.0753837	+	0.0667841i
$351$	19.4172	−	2.61860i	1.03641	−	0.139771i
$352$	11.1433	−	9.87211i	0.593940	−	0.526185i
$353$	−28.0563	−	6.91525i	−1.49328	−	0.368061i	−0.593656	−	0.804719i	$-0.702316\pi$
$353$	−28.0563	−	6.91525i	−1.49328	−	0.368061i	−0.899628	+	0.436658i	$0.856162\pi$
$354$	−5.95556	+	5.27616i	−0.316534	+	0.280425i
$355$	6.90903	+	1.70292i	0.366693	+	0.0903817i
$356$	6.12457	+	16.1492i	0.324602	+	0.855905i
$357$	3.72563			0.197181
$358$	−4.85728	+	12.8076i	−0.256715	+	0.676902i
$359$	16.6169	−	4.09570i	0.877006	−	0.216163i	0.224984	−	0.974362i	$-0.427767\pi$
$359$	16.6169	−	4.09570i	0.877006	−	0.216163i	0.652022	+	0.758200i	$0.273921\pi$
$360$	−4.03820			−0.212832
$361$	5.19961			0.273663
$362$	9.31434	−	2.29578i	0.489551	−	0.120663i
$363$	−0.605939	−	4.99036i	−0.0318036	−	0.261926i
$364$	−2.28073	+	0.899631i	−0.119542	+	0.0471535i
$365$	−0.142769	+	1.17581i	−0.00747287	+	0.0615446i
$366$	−1.18811	−	9.78495i	−0.0621034	−	0.511468i
$367$	−8.47069	+	12.2719i	−0.442166	+	0.640589i	−0.979182	−	0.202984i	$-0.934936\pi$
$367$	−8.47069	+	12.2719i	−0.442166	+	0.640589i	0.537016	+	0.843572i	$0.319552\pi$
$368$	0.721201	−	0.638928i	0.0375952	−	0.0333064i
$369$	−0.741917	+	6.11024i	−0.0386227	+	0.318086i
$370$	1.03401	+	8.51584i	0.0537556	+	0.442717i
$371$	0.789775	+	0.414506i	0.0410031	+	0.0215201i
$372$	−3.23860	+	2.86915i	−0.167914	+	0.148759i
$373$	−16.3700	−	23.7161i	−0.847607	−	1.22797i	−0.971822	−	0.235716i	$-0.924257\pi$
$373$	−16.3700	−	23.7161i	−0.847607	−	1.22797i	0.124215	−	0.992255i	$-0.460359\pi$
$374$	12.7249	+	3.13640i	0.657987	+	0.162179i
$375$	1.17588	−	9.68426i	0.0607223	−	0.500093i
$376$	−1.18536	+	1.71729i	−0.0611304	+	0.0885627i
$377$	−24.8888	−	9.06455i	−1.28184	−	0.466848i
$378$	−1.38869	−	2.01186i	−0.0714263	−	0.103479i
$379$	14.6354	−	7.68125i	0.751770	−	0.394559i	−0.0448861	−	0.998992i	$-0.514292\pi$
$379$	14.6354	−	7.68125i	0.751770	−	0.394559i	0.796656	+	0.604433i	$0.206600\pi$
$380$	−2.01387	+	5.31013i	−0.103309	+	0.272404i
$381$	2.19520	+	18.0791i	0.112463	+	0.926220i
$382$	7.73010	−	11.1990i	0.395506	−	0.572990i
$383$	20.9564	−	5.16528i	1.07082	−	0.263933i	0.335769	−	0.941945i	$-0.391004\pi$
$383$	20.9564	−	5.16528i	1.07082	−	0.263933i	0.735052	+	0.678011i	$0.237158\pi$
$384$	−5.15329	+	7.46583i	−0.262978	+	0.380989i
$385$	−0.439966	+	1.16010i	−0.0224228	+	0.0591240i
$386$	−4.41747	+	11.6479i	−0.224843	+	0.592864i
$387$	−14.3619	−	7.53773i	−0.730059	−	0.383164i
$388$	3.15461	+	1.65567i	0.160151	+	0.0840537i
$389$	−25.9506	+	6.39625i	−1.31575	+	0.324303i	−0.833882	−	0.551943i	$-0.813887\pi$
$389$	−25.9506	+	6.39625i	−1.31575	+	0.324303i	−0.481865	+	0.876245i	$0.660040\pi$
$390$	−2.69484	−	1.80798i	−0.136459	−	0.0915508i
$391$	27.2311	+	6.71187i	1.37714	+	0.339434i
$392$	−13.9885	−	12.3927i	−0.706524	−	0.625926i
$393$	−2.87958	+	23.7154i	−0.145255	+	1.19629i
$394$	−1.20405	−	0.631932i	−0.0606589	−	0.0318363i
$395$	−2.05336	+	1.07768i	−0.103316	+	0.0542242i
$396$	1.89993	+	5.00970i	0.0954750	+	0.251747i
$397$	24.5471	+	21.7469i	1.23199	+	1.09144i	0.992714	+	0.120491i	$0.0384468\pi$
$397$	24.5471	+	21.7469i	1.23199	+	1.09144i	0.239271	+	0.970953i	$0.423092\pi$
$398$	0.854316	+	7.03593i	0.0428230	+	0.352679i
$399$	−2.98696	+	0.736220i	−0.149535	+	0.0368571i
$400$	0.641631	+	0.568435i	0.0320815	+	0.0284218i
$401$	−4.74061	+	4.19981i	−0.236735	+	0.209729i	−0.773146	−	0.634228i	$-0.781318\pi$
$401$	−4.74061	+	4.19981i	−0.236735	+	0.209729i	0.536411	+	0.843957i	$0.319780\pi$
$402$	−1.06729	−	0.560155i	−0.0532314	−	0.0279380i
$403$	10.2385	−	1.38077i	0.510016	−	0.0687809i
$404$	6.12464	−	3.21446i	0.304712	−	0.159925i
$405$	−0.501542	+	1.32246i	−0.0249218	+	0.0657135i
$406$	0.398361	+	3.28080i	0.0197703	+	0.162823i
$407$	25.8082	−	13.5452i	1.27926	−	0.671409i
$408$	−19.5290			−0.966828
$409$	3.84116	−	2.01600i	0.189933	−	0.0996846i	−0.367076	−	0.930191i	$-0.619641\pi$
$409$	3.84116	−	2.01600i	0.189933	−	0.0996846i	0.557009	+	0.830506i	$0.311949\pi$
$410$	2.18382	−	1.93470i	0.107851	−	0.0955478i
$411$	−0.0224373	−	0.0325060i	−0.00110675	−	0.00160340i
$412$	7.83612	+	6.94220i	0.386058	+	0.342017i
$413$	2.40101	+	3.47846i	0.118146	+	0.171164i
$414$	−2.28022	−	6.01244i	−0.112067	−	0.295495i
$415$	1.87040	+	4.93185i	0.0918146	+	0.242095i
$416$	19.2417	−	7.58989i	0.943403	−	0.372125i
$417$	−2.05351	+	5.41466i	−0.100561	+	0.265157i
$418$	−10.8217			−0.529309
$419$	3.61637	+	9.53559i	0.176671	+	0.465844i	0.993876	−	0.110504i	$-0.0352465\pi$
$419$	3.61637	+	9.53559i	0.176671	+	0.465844i	−0.817204	+	0.576348i	$0.804477\pi$
$420$	0.0870229	−	0.716698i	0.00424628	−	0.0349713i
$421$	−17.7029	−	9.29120i	−0.862786	−	0.452825i	−0.0255545	−	0.999673i	$-0.508135\pi$
$421$	−17.7029	−	9.29120i	−0.862786	−	0.452825i	−0.837232	+	0.546848i	$0.815827\pi$
$422$	−2.24250	−	3.24883i	−0.109163	−	0.158150i
$423$	−0.686624	−	0.994747i	−0.0333848	−	0.0483662i
$424$	−4.13984	−	2.17275i	−0.201048	−	0.105518i
$425$	−3.00761	+	24.7699i	−0.145890	+	1.20151i
$426$	−2.79781	−	7.37723i	−0.135554	−	0.357428i
$427$	−5.23610			−0.253392
$428$	2.60399	−	6.86616i	0.125869	−	0.331888i
$429$	−2.49693	+	10.7396i	−0.120553	+	0.518511i
$430$	2.72630	+	7.18866i	0.131474	+	0.346668i
$431$	−12.6122	−	33.2558i	−0.607511	−	1.60187i	−0.786203	−	0.617969i	$-0.787956\pi$
$431$	−12.6122	−	33.2558i	−0.607511	−	1.60187i	0.178692	−	0.983905i	$-0.442813\pi$
$432$	−0.631798	−	0.915317i	−0.0303974	−	0.0440382i
$433$	18.9895	+	16.8233i	0.912579	+	0.808475i	0.981955	−	0.189116i	$-0.0605622\pi$
$433$	18.9895	+	16.8233i	0.912579	+	0.808475i	−0.0693754	+	0.997591i	$0.522101\pi$
$434$	−0.732243	−	1.06084i	−0.0351488	−	0.0509218i
$435$	5.83832	−	5.17230i	0.279926	−	0.247993i
$436$	−6.09598	+	3.19942i	−0.291945	+	0.153224i
$437$	−23.1585			−1.10782
$438$	1.16287	−	0.610322i	0.0555642	−	0.0291623i
$439$	1.26781	+	10.4414i	0.0605094	+	0.498339i	0.991184	+	0.132492i	$0.0422978\pi$
$439$	1.26781	+	10.4414i	0.0605094	+	0.498339i	−0.930675	+	0.365848i	$0.880779\pi$
$440$	2.30621	−	6.08098i	0.109944	−	0.289900i
$441$	9.58533	−	5.03077i	0.456444	−	0.239560i
$442$	15.1213	+	10.1450i	0.719246	+	0.482546i
$443$	6.31561	+	3.31469i	0.300064	+	0.157486i	0.608035	−	0.793910i	$-0.291958\pi$
$443$	6.31561	+	3.31469i	0.300064	+	0.157486i	−0.307972	+	0.951396i	$0.599650\pi$
$444$	−12.6948	+	11.2467i	−0.602471	+	0.533742i
$445$	9.08990	+	8.05295i	0.430903	+	0.381746i
$446$	18.9873	−	4.67995i	0.899075	−	0.221602i
$447$	−2.44234	−	20.1145i	−0.115519	−	0.951383i
$448$	−1.76915	−	1.56733i	−0.0835847	−	0.0740496i
$449$	0.976287	+	2.57426i	0.0460738	+	0.121487i	0.956078	−	0.293112i	$-0.0946910\pi$
$449$	0.976287	+	2.57426i	0.0460738	+	0.121487i	−0.910004	+	0.414599i	$0.863922\pi$
$450$	5.06557	−	2.65861i	0.238793	−	0.125328i
$451$	−8.77748	−	4.60678i	−0.413315	−	0.216925i
$452$	2.12252	−	17.4805i	0.0998349	−	0.822214i
$453$	8.69777	+	7.70555i	0.408657	+	0.362038i
$454$	5.31883	+	1.31097i	0.249625	+	0.0615270i
$455$	−1.12598	+	1.30534i	−0.0527867	+	0.0611951i
$456$	15.6570	−	3.85911i	0.733208	−	0.180719i
$457$	0.534493	+	0.280523i	0.0250025	+	0.0131223i	0.477178	−	0.878807i	$-0.341660\pi$
$457$	0.534493	+	0.280523i	0.0250025	+	0.0131223i	−0.452176	+	0.891929i	$0.649352\pi$
$458$	−10.1589	−	5.33179i	−0.474693	−	0.249138i
$459$	11.4799	−	30.2701i	0.535838	−	1.41289i
$460$	1.92722	−	5.08167i	0.0898573	−	0.236934i
$461$	−6.56010	+	9.50395i	−0.305534	+	0.442643i	−0.945433	−	0.325816i	$-0.894361\pi$
$461$	−6.56010	+	9.50395i	−0.305534	+	0.442643i	0.639899	+	0.768459i	$0.278976\pi$
$462$	1.33573	−	0.329228i	0.0621438	−	0.0153171i
$463$	20.0158	−	28.9978i	0.930211	−	1.34764i	−0.00740597	−	0.999973i	$-0.502357\pi$
$463$	20.0158	−	28.9978i	0.930211	−	1.34764i	0.937617	−	0.347670i	$-0.113027\pi$
$464$	0.181238	+	1.49263i	0.00841379	+	0.0692938i
$465$	−1.07878	+	2.84452i	−0.0500274	+	0.131911i
$466$	−7.65856	+	4.01952i	−0.354776	+	0.186201i
$467$	0.527115	+	0.763658i	0.0243920	+	0.0353379i	0.834990	−	0.550265i	$-0.185473\pi$
$467$	0.527115	+	0.763658i	0.0243920	+	0.0353379i	−0.810598	+	0.585603i	$0.800858\pi$
$468$	0.0984174	+	7.44363i	0.00454935	+	0.344082i
$469$	−0.363733	+	0.526958i	−0.0167956	+	0.0243327i
$470$	−0.0690594	+	0.568755i	−0.00318547	+	0.0262347i
$471$	16.7860	+	4.13737i	0.773457	+	0.190640i
$472$	−12.5856	−	18.2334i	−0.579298	−	0.839258i
$473$	19.5529	−	17.3224i	0.899043	−	0.796483i
$474$	2.27675	+	1.19493i	0.104574	+	0.0548849i
$475$	−2.48346	−	20.4532i	−0.113949	−	0.938456i
$476$	−0.488303	+	4.02154i	−0.0223813	+	0.184327i
$477$	2.02713	−	1.79588i	0.0928160	−	0.0822278i
$478$	10.1295	−	14.6752i	0.463315	−	0.671227i
$479$	1.38833	+	11.4339i	0.0634344	+	0.522429i	0.989443	+	0.144926i	$0.0462943\pi$
$479$	1.38833	+	11.4339i	0.0634344	+	0.522429i	−0.926008	+	0.377503i	$0.876783\pi$
$480$	−0.734183	+	6.04655i	−0.0335107	+	0.275986i
$481$	40.1334	−	5.41240i	1.82993	−	0.246784i
$482$	−1.78622	−	14.7109i	−0.0813603	−	0.670062i
$483$	2.85845	−	0.704545i	0.130064	−	0.0320579i
$484$	5.46614			0.248461
$485$	2.50500			0.113746
$486$	−11.8955	+	2.93198i	−0.539591	+	0.132997i
$487$	−3.89068	+	10.2589i	−0.176303	+	0.464874i	−0.993816	−	0.111036i	$-0.964583\pi$
$487$	−3.89068	+	10.2589i	−0.176303	+	0.464874i	0.817513	+	0.575910i	$0.195352\pi$
$488$	27.4465			1.24245
$489$	−8.33192	−	21.9695i	−0.376783	−	0.993494i
$490$	−4.98214	−	1.22799i	−0.225070	−	0.0554748i
$491$	−19.2786	+	17.0793i	−0.870031	+	0.770780i	−0.974651	−	0.223732i	$-0.928176\pi$
$491$	−19.2786	+	17.0793i	−0.870031	+	0.770780i	0.104620	+	0.994512i	$0.466637\pi$
$492$	5.60061	+	1.38043i	0.252495	+	0.0622345i
$493$	−32.7600	+	29.0228i	−1.47544	+	1.30712i
$494$	−14.1280	−	5.14545i	−0.635649	−	0.231505i
$495$	2.81982	+	2.49814i	0.126741	+	0.112283i
$496$	−0.333142	−	0.482639i	−0.0149585	−	0.0216711i
$497$	−4.06947	+	1.00303i	−0.182541	+	0.0449923i
$498$	3.32230	−	4.81319i	0.148876	−	0.215684i
$499$	−10.0100	−	2.46725i	−0.448111	−	0.110449i	0.00880104	−	0.999961i	$-0.497199\pi$
$499$	−10.0100	−	2.46725i	−0.448111	−	0.110449i	−0.456912	+	0.889512i	$0.651045\pi$
$500$	10.2993	+	2.53856i	0.460600	+	0.113528i
$501$	−2.51555	+	20.7174i	−0.112386	+	0.925585i
$502$	−2.25641	−	1.99900i	−0.100708	−	0.0892198i
$503$	2.48262	+	6.54612i	0.110694	+	0.291877i	0.978904	−	0.204320i	$-0.0654984\pi$
$503$	2.48262	+	6.54612i	0.110694	+	0.291877i	−0.868210	+	0.496198i	$0.834729\pi$
$504$	2.10609	−	1.10536i	0.0938126	−	0.0492366i
$505$	2.76275	−	4.00254i	0.122941	−	0.178110i
$506$	10.3562			0.460387
$507$	−8.36617	+	12.8335i	−0.371555	+	0.569955i
$508$	−19.8028			−0.878605
$509$	−17.2451	+	24.9839i	−0.764378	+	1.10739i	0.226681	+	0.973969i	$0.427212\pi$
$509$	−17.2451	+	24.9839i	−0.764378	+	1.10739i	−0.991059	+	0.133423i	$0.957403\pi$
$510$	−4.74784	+	2.49186i	−0.210238	+	0.110341i
$511$	−0.247389	−	0.652311i	−0.0109438	−	0.0288566i
$512$	−1.73116	−	1.53367i	−0.0765072	−	0.0677795i
$513$	−3.22219	+	26.5371i	−0.142263	+	1.17164i
$514$	5.67949	+	1.39987i	0.250511	+	0.0617455i
$515$	7.14704	+	1.76159i	0.314936	+	0.0776248i
$516$	−8.63476	+	12.5096i	−0.380124	+	0.550705i
$517$	1.89008	−	0.465864i	0.0831258	−	0.0204887i
$518$	−2.87028	−	4.15832i	−0.126113	−	0.182706i
$519$	−7.09887	−	6.28905i	−0.311606	−	0.276059i
$520$	5.90215	−	6.84230i	0.258826	−	0.300055i
$521$	10.6607	−	9.44456i	0.467054	−	0.413774i	−0.396496	−	0.918036i	$-0.629774\pi$
$521$	10.6607	−	9.44456i	0.467054	−	0.413774i	0.863550	+	0.504263i	$0.168236\pi$
$522$	9.74312	+	2.40146i	0.426445	+	0.105109i
$523$	16.9972	−	15.0582i	0.743235	−	0.658449i	−0.204006	−	0.978970i	$-0.565396\pi$
$523$	16.9972	−	15.0582i	0.743235	−	0.658449i	0.947241	+	0.320521i	$0.103858\pi$
$524$	−25.2216	−	6.21658i	−1.10181	−	0.271572i
$525$	0.928777	+	2.44898i	0.0405352	+	0.106882i
$526$	−10.7488			−0.468670
$527$	6.05327	−	15.9612i	0.263685	−	0.695280i
$528$	0.607704	−	0.149786i	0.0264469	−	0.00651858i
$529$	−0.837897			−0.0364303
$530$	−1.28371			−0.0557607
$531$	12.4605	−	3.07124i	0.540741	−	0.133281i
$532$	−0.403206	−	3.32070i	−0.0174812	−	0.143971i
$533$	−9.26878	−	10.1877i	−0.401475	−	0.441278i
$534$	1.62305	−	13.3670i	0.0702361	−	0.578446i
$535$	−0.622363	−	5.12562i	−0.0269071	−	0.221600i
$536$	1.90661	−	2.76220i	0.0823531	−	0.119309i
$537$	−14.2528	+	12.6269i	−0.615054	+	0.544890i
$538$	−0.341002	+	2.80840i	−0.0147016	+	0.121079i
$539$	2.10148	+	17.3073i	0.0905173	+	0.745477i
$540$	−5.55491	−	2.91544i	−0.239045	−	0.125461i
$541$	13.9195	−	12.3316i	0.598447	−	0.530177i	−0.308609	−	0.951189i	$-0.599863\pi$
$541$	13.9195	−	12.3316i	0.598447	−	0.530177i	0.907055	+	0.421012i	$0.138325\pi$
$542$	0.547745	+	0.793545i	0.0235277	+	0.0340857i
$543$	12.9481	+	3.19142i	0.555656	+	0.136957i
$544$	4.11965	−	33.9284i	0.176629	−	1.45467i
$545$	−2.74982	+	3.98380i	−0.117789	+	0.170647i
$546$	1.90036	+	0.205290i	0.0813279	+	0.00878560i
$547$	5.66841	+	8.21211i	0.242364	+	0.351124i	0.925222	−	0.379427i	$-0.123879\pi$
$547$	5.66841	+	8.21211i	0.242364	+	0.351124i	−0.682858	+	0.730551i	$0.739263\pi$
$548$	0.0380286	−	0.0199590i	0.00162450	−	0.000852604i
$549$	−5.63768	+	14.8653i	−0.240610	+	0.634437i
$550$	1.11057	+	9.14638i	0.0473550	+	0.390003i
$551$	20.5296	−	29.7423i	0.874591	−	1.26706i
$552$	−14.9834	+	3.69308i	−0.637737	+	0.157188i
$553$	0.775919	−	1.12411i	0.0329954	−	0.0478021i
$554$	5.67839	−	14.9727i	0.241252	−	0.636129i
$555$	−4.22867	+	11.1501i	−0.179497	+	0.473295i
$556$	−5.57558	−	2.92629i	−0.236457	−	0.124102i
$557$	−10.7554	−	5.64488i	−0.455722	−	0.239181i	0.221211	−	0.975226i	$-0.428999\pi$
$557$	−10.7554	−	5.64488i	−0.455722	−	0.239181i	−0.676933	+	0.736045i	$0.736691\pi$
$558$	−3.80013	+	0.936647i	−0.160872	+	0.0396514i
$559$	33.7630	−	13.3178i	1.42802	−	0.563283i
$560$	0.0950121	+	0.0234184i	0.00401499	+	0.000989607i
$561$	13.6368	+	12.0811i	0.575745	+	0.510066i
$562$	−0.729577	+	6.00861i	−0.0307754	+	0.253458i
$563$	32.4696	+	17.0413i	1.36843	+	0.718207i	0.979193	−	0.202931i	$-0.0650468\pi$
$563$	32.4696	+	17.0413i	1.36843	+	0.718207i	0.389236	+	0.921138i	$0.372739\pi$
$564$	−1.00298	+	0.526407i	−0.0422333	+	0.0221657i
$565$	−4.39043	−	11.5766i	−0.184707	−	0.487032i
$566$	−8.18931	−	7.25510i	−0.344223	−	0.304955i
$567$	−0.100416	−	0.827001i	−0.00421708	−	0.0347308i
$568$	21.3313	−	5.25770i	0.895043	−	0.220608i
$569$	6.12811	+	5.42903i	0.256904	+	0.227597i	0.781737	−	0.623608i	$-0.214334\pi$
$569$	6.12811	+	5.42903i	0.256904	+	0.227597i	−0.524833	+	0.851205i	$0.675872\pi$
$570$	3.31409	−	2.93603i	0.138812	−	0.122977i
$571$	−36.7530	−	19.2895i	−1.53807	−	0.807240i	−0.538689	−	0.842505i	$-0.681080\pi$
$571$	−36.7530	−	19.2895i	−1.53807	−	0.807240i	−0.999378	+	0.0352652i	$0.988772\pi$
$572$	−11.2653	−	4.10285i	−0.471026	−	0.171549i
$573$	16.7497	−	8.79094i	0.699730	−	0.367247i
$574$	−0.609375	+	1.60679i	−0.0254348	+	0.0670661i
$575$	2.37662	+	19.5732i	0.0991118	+	0.816259i
$576$	−6.35452	+	3.33511i	−0.264772	+	0.138963i
$577$	−17.9677			−0.748004			−0.374002	−	0.927428i	$-0.622015\pi$
$577$	−17.9677			−0.748004			−0.374002	+	0.927428i	$0.622015\pi$
$578$	13.8806	−	7.28511i	0.577358	−	0.303021i
$579$	−12.9623	+	11.4836i	−0.538693	+	0.477241i
$580$	4.81791	+	6.97995i	0.200053	+	0.289826i
$581$	−2.32547	−	2.06018i	−0.0964766	−	0.0854708i
$582$	−1.57782	−	2.28586i	−0.0654026	−	0.0947520i
$583$	1.54666	+	4.07821i	0.0640562	+	0.168902i
$584$	1.29676	+	3.41928i	0.0536604	+	0.141491i
$585$	2.49353	+	4.60212i	0.103095	+	0.190274i
$586$	6.44586	−	16.9963i	0.266276	−	0.702112i
$587$	−26.7302			−1.10327			−0.551636	−	0.834085i	$-0.685996\pi$
$587$	−26.7302			−1.10327			−0.551636	+	0.834085i	$0.685996\pi$
$588$	−3.59742	−	9.48561i	−0.148355	−	0.391180i
$589$	−1.69903	+	13.9928i	−0.0700075	+	0.576563i
$590$	−5.38632	−	2.82696i	−0.221751	−	0.116384i
$591$	−1.07381	−	1.55568i	−0.0441707	−	0.0639922i
$592$	−1.30587	−	1.89187i	−0.0536708	−	0.0777555i
$593$	34.2801	+	17.9916i	1.40771	+	0.738825i	0.985818	−	0.167819i	$-0.0536725\pi$
$593$	34.2801	+	17.9916i	1.40771	+	0.738825i	0.421896	+	0.906644i	$0.361365\pi$
$594$	1.44092	−	11.8671i	0.0591217	−	0.486911i
$595$	1.01005	+	2.66330i	0.0414082	+	0.109184i
$596$	22.0322			0.902475
$597$	−3.49380	+	9.21239i	−0.142992	+	0.377038i
$598$	13.5202	+	4.92407i	0.552881	+	0.201360i
$599$	−4.50198	−	11.8707i	−0.183946	−	0.485025i	0.811046	−	0.584982i	$-0.198899\pi$
$599$	−4.50198	−	11.8707i	−0.183946	−	0.485025i	−0.994992	+	0.0999574i	$0.968129\pi$
$600$	−4.86846	−	12.8371i	−0.198754	−	0.524071i
$601$	17.8228	+	25.8208i	0.727008	+	1.05325i	0.995933	+	0.0900917i	$0.0287160\pi$
$601$	17.8228	+	25.8208i	0.727008	+	1.05325i	−0.268926	+	0.963161i	$0.586669\pi$
$602$	−3.38960	−	3.00292i	−0.138150	−	0.122390i
$603$	1.10441	+	1.60001i	0.0449750	+	0.0651576i
$604$	−9.45756	+	8.37866i	−0.384823	+	0.340923i
$605$	3.40312	−	1.78610i	0.138357	−	0.0726152i
$606$	−5.39255			−0.219057
$607$	3.64861	−	1.91494i	0.148092	−	0.0777248i	−0.389049	−	0.921217i	$-0.627196\pi$
$607$	3.64861	−	1.91494i	0.148092	−	0.0777248i	0.537142	+	0.843492i	$0.319504\pi$
$608$	3.40171	+	28.0156i	0.137958	+	1.13618i
$609$	−1.62913	+	4.29566i	−0.0660157	+	0.174069i
$610$	6.67275	−	3.50213i	0.270172	−	0.141797i
$611$	2.68905	+	0.290489i	0.108787	+	0.0117519i
$612$	10.8914	+	5.71627i	0.440260	+	0.231066i
$613$	−28.0155	+	24.8195i	−1.13153	+	1.00245i	−0.131596	+	0.991303i	$0.542010\pi$
$613$	−28.0155	+	24.8195i	−1.13153	+	1.00245i	−0.999938	+	0.0111478i	$0.996451\pi$
$614$	−7.65988	−	6.78606i	−0.309128	−	0.273863i
$615$	3.93791	−	0.970607i	0.158792	−	0.0391387i
$616$	0.461738	+	3.80275i	0.0186039	+	0.153217i
$617$	1.86028	+	1.64806i	0.0748920	+	0.0663485i	0.699738	−	0.714399i	$-0.253300\pi$
$617$	1.86028	+	1.64806i	0.0748920	+	0.0663485i	−0.624846	+	0.780748i	$0.714838\pi$
$618$	−2.89420	−	7.63137i	−0.116422	−	0.306979i
$619$	−11.6745	+	6.12726i	−0.469238	+	0.246275i	−0.682732	−	0.730669i	$-0.739208\pi$
$619$	−11.6745	+	6.12726i	−0.469238	+	0.246275i	0.213493	+	0.976945i	$0.431516\pi$
$620$	−2.92906	−	1.53729i	−0.117634	−	0.0617389i
$621$	3.08356	−	25.3954i	0.123739	−	1.01908i
$622$	7.19154	+	6.37115i	0.288354	+	0.255460i
$623$	−6.94505	−	1.71180i	−0.278248	−	0.0685819i
$624$	0.864589	+	0.0933989i	0.0346113	+	0.00373895i
$625$	−13.0912	+	3.22668i	−0.523646	+	0.129067i
$626$	−22.4338	−	11.7742i	−0.896635	−	0.470590i
$627$	−13.3204	−	6.99109i	−0.531966	−	0.279197i
$628$	−6.66606	+	17.5770i	−0.266005	+	0.701397i
$629$	23.7279	−	62.5654i	0.946095	−	2.49465i
$630$	0.370986	−	0.537466i	0.0147804	−	0.0214132i
$631$	10.1128	−	2.49259i	0.402585	−	0.0992284i	−0.0328235	−	0.999461i	$-0.510450\pi$
$631$	10.1128	−	2.49259i	0.402585	−	0.0992284i	0.435409	+	0.900233i	$0.356604\pi$
$632$	−4.06720	+	5.89236i	−0.161785	+	0.234386i
$633$	−0.661467	−	5.44767i	−0.0262910	−	0.216526i
$634$	−7.94784	+	20.9567i	−0.315649	+	0.832298i
$635$	−12.3288	+	6.47068i	−0.489255	+	0.256781i
$636$	−1.44174	−	2.08873i	−0.0571688	−	0.0828234i
$637$	−5.48561	+	23.5942i	−0.217348	+	0.934835i
$638$	−9.18057	+	13.3003i	−0.363462	+	0.526566i
$639$	−1.53395	+	12.6332i	−0.0606822	+	0.499763i
$640$	−6.73412	−	1.65981i	−0.266190	−	0.0656098i
$641$	−14.9255	−	21.6234i	−0.589523	−	0.854072i	0.408760	−	0.912642i	$-0.365961\pi$
$641$	−14.9255	−	21.6234i	−0.589523	−	0.854072i	−0.998283	+	0.0585700i	$0.981346\pi$
$642$	−4.28522	+	3.79637i	−0.169124	+	0.149831i
$643$	−30.6162	−	16.0686i	−1.20738	−	0.633684i	−0.263723	−	0.964598i	$-0.584951\pi$
$643$	−30.6162	−	16.0686i	−1.20738	−	0.633684i	−0.943661	+	0.330915i	$0.892643\pi$
$644$	0.385858	+	3.17783i	0.0152050	+	0.125224i
$645$	−1.28825	+	10.6097i	−0.0507250	+	0.417758i
$646$	−18.5960	+	16.4747i	−0.731651	+	0.648187i
$647$	18.9778	−	27.4941i	0.746095	−	1.08091i	−0.247608	−	0.968860i	$-0.579645\pi$
$647$	18.9778	−	27.4941i	0.746095	−	1.08091i	0.993703	−	0.112045i	$-0.0357401\pi$
$648$	0.526360	+	4.33497i	0.0206774	+	0.170294i
$649$	−2.49132	+	20.5178i	−0.0977927	+	0.805396i
$650$	−2.89899	+	12.4688i	−0.113708	+	0.489068i
$651$	−0.215988	−	1.77882i	−0.00846525	−	0.0697176i
$652$	24.8065	−	6.11424i	0.971496	−	0.239452i
$653$	−5.72647			−0.224094			−0.112047	−	0.993703i	$-0.535741\pi$
$653$	−5.72647			−0.224094			−0.112047	+	0.993703i	$0.535741\pi$
$654$	5.36731			0.209879
$655$	−17.7339	+	4.37100i	−0.692919	+	0.170789i
$656$	−0.277242	+	0.731026i	−0.0108245	+	0.0285418i
$657$	−2.11828			−0.0826420
$658$	−0.119666	−	0.315532i	−0.00466505	−	0.0123007i
$659$	42.4559	+	10.4644i	1.65385	+	0.407637i	0.952343	−	0.305029i	$-0.0986662\pi$
$659$	42.4559	+	10.4644i	1.65385	+	0.407637i	0.701504	+	0.712666i	$0.252512\pi$
$660$	2.64257	−	2.34111i	0.102862	−	0.0911277i
$661$	12.7635	+	3.14592i	0.496442	+	0.122362i	0.479584	−	0.877496i	$-0.340788\pi$
$661$	12.7635	+	3.14592i	0.496442	+	0.122362i	0.0168581	+	0.999858i	$0.494634\pi$
$662$	−20.9705	+	18.5783i	−0.815043	+	0.722065i
$663$	12.0588	+	22.2561i	0.468326	+	0.864354i
$664$	12.1896	+	10.7991i	0.473049	+	0.419085i
$665$	−1.33609	−	1.93566i	−0.0518113	−	0.0750616i
$666$	−14.8959	+	3.67152i	−0.577206	+	0.142268i
$667$	−19.6464	+	28.4627i	−0.760710	+	1.10208i
$668$	−22.0332	−	5.43070i	−0.852490	−	0.210120i
$669$	26.3947	+	6.50571i	1.02048	+	0.251525i
$670$	0.111079	−	0.914822i	0.00429138	−	0.0353427i
$671$	−19.1655	−	16.9791i	−0.739876	−	0.655473i
$672$	−1.27219	−	3.35448i	−0.0490757	−	0.129402i
$673$	−2.78435	+	1.46134i	−0.107329	+	0.0563306i	−0.517533	−	0.855663i	$-0.673150\pi$
$673$	−2.78435	+	1.46134i	−0.107329	+	0.0563306i	0.410204	+	0.911994i	$0.365457\pi$
$674$	−10.4725	+	15.1721i	−0.403387	+	0.584407i
$675$	22.7595			0.876013
$676$	−12.7563	−	10.7127i	−0.490626	−	0.412027i
$677$	−5.13633			−0.197405			−0.0987026	−	0.995117i	$-0.531469\pi$
$677$	−5.13633			−0.197405			−0.0987026	+	0.995117i	$0.531469\pi$
$678$	−7.79849	+	11.2981i	−0.299499	+	0.433900i
$679$	−1.30646	+	0.685683i	−0.0501374	+	0.0263141i
$680$	−5.29450	−	13.9604i	−0.203035	−	0.535359i
$681$	5.70000	+	5.04976i	0.218424	+	0.193507i
$682$	0.759785	−	6.25739i	0.0290937	−	0.239608i
$683$	15.8218	+	3.89971i	0.605403	+	0.149218i	0.530090	−	0.847942i	$-0.322158\pi$
$683$	15.8218	+	3.89971i	0.605403	+	0.149218i	0.0753131	+	0.997160i	$0.476004\pi$
$684$	−9.86162	−	2.43067i	−0.377069	−	0.0929391i
$685$	0.0171542	−	0.0248522i	0.000655430	−	0.000949554i
$686$	5.99204	−	1.47691i	0.228777	−	0.0563885i
$687$	−9.06004	−	13.1257i	−0.345662	−	0.500778i
$688$	−1.54213	−	1.36621i	−0.0587933	−	0.0520863i
$689$	0.0801180	+	6.05958i	0.00305225	+	0.230852i
$690$	−3.17151	+	2.80971i	−0.120737	+	0.106964i
$691$	−45.0037	−	11.0924i	−1.71202	−	0.421975i	−0.743067	−	0.669217i	$-0.766630\pi$
$691$	−45.0037	−	11.0924i	−1.71202	−	0.421975i	−0.968954	+	0.247241i	$0.920476\pi$
$692$	7.71899	−	6.83843i	0.293432	−	0.259958i
$693$	−2.15445	−	0.531025i	−0.0818409	−	0.0201720i
$694$	7.48329	+	19.7318i	0.284062	+	0.749009i
$695$	−4.42745			−0.167943
$696$	8.53956	−	22.5170i	0.323691	−	0.853504i
$697$	−22.0964	+	5.44627i	−0.836961	+	0.206292i
$698$	−23.5051			−0.889680
$699$	−12.0236			−0.454773
$700$	−2.76523	+	0.681568i	−0.104516	+	0.0257608i
$701$	3.88706	+	32.0128i	0.146812	+	1.20911i	0.860797	+	0.508948i	$0.169965\pi$
$701$	3.88706	+	32.0128i	0.146812	+	1.20911i	−0.713985	+	0.700161i	$0.753112\pi$
$702$	7.52361	−	14.8076i	0.283960	−	0.558875i
$703$	−6.65996	+	54.8497i	−0.251185	+	2.06870i
$704$	−1.39316	−	11.4737i	−0.0525067	−	0.432432i
$705$	−0.452434	+	0.655464i	−0.0170396	+	0.0246862i
$706$	−18.3352	+	16.2436i	−0.690055	+	0.611335i
$707$	−0.345290	+	2.84372i	−0.0129860	+	0.106949i
$708$	−1.44967	−	11.9391i	−0.0544818	−	0.448698i
$709$	−11.6631	−	6.12127i	−0.438017	−	0.229889i	0.231275	−	0.972888i	$-0.425710\pi$
$709$	−11.6631	−	6.12127i	−0.438017	−	0.229889i	−0.669292	+	0.742999i	$0.733403\pi$
$710$	4.51516	−	4.00008i	0.169451	−	0.150120i
$711$	−2.35594	−	3.41317i	−0.0883546	−	0.128004i
$712$	36.4045	+	8.97291i	1.36432	+	0.336274i
$713$	1.62594	−	13.3908i	0.0608918	−	0.501489i
$714$	1.79411	−	2.59921i	0.0671428	−	0.0972731i
$715$	−8.35421	+	1.12665i	−0.312430	+	0.0421343i
$716$	−11.7617	−	17.0398i	−0.439556	−	0.636807i
$717$	21.9489	−	11.5197i	0.819697	−	0.430210i
$718$	5.14461	−	13.5652i	0.191995	−	0.506250i
$719$	−1.33856	−	11.0240i	−0.0499199	−	0.411128i	−0.996152	−	0.0876397i	$-0.972068\pi$
$719$	−1.33856	−	11.0240i	−0.0499199	−	0.411128i	0.946232	−	0.323488i	$-0.104855\pi$
$720$	0.168784	−	0.244526i	0.00629021	−	0.00911294i
$721$	−4.20966	+	1.03759i	−0.156776	+	0.0386418i
$722$	2.50392	−	3.62755i	0.0931861	−	0.135003i
$723$	7.30491	−	19.2615i	0.271673	−	0.716342i
$724$	−5.14196	+	13.5582i	−0.191099	+	0.503887i
$725$	−27.2446	−	14.2991i	−1.01184	−	0.531054i
$726$	−3.77336	−	1.98041i	−0.140043	−	0.0735000i
$727$	43.0686	−	10.6154i	1.59732	−	0.393705i	0.662570	−	0.749000i	$-0.269466\pi$
$727$	43.0686	−	10.6154i	1.59732	−	0.393705i	0.934754	+	0.355294i	$0.115619\pi$
$728$	−1.20530	+	5.18411i	−0.0446713	+	0.192136i
$729$	−21.1089	−	5.20288i	−0.781812	−	0.192699i
$730$	0.751561	+	0.665825i	0.0278165	+	0.0246433i
$731$	7.22866	−	59.5333i	0.267362	−	2.20192i
$732$	13.1925	+	6.92398i	0.487610	+	0.255918i
$733$	−0.895816	+	0.470160i	−0.0330877	+	0.0173658i	−0.481186	−	0.876619i	$-0.659794\pi$
$733$	−0.895816	+	0.470160i	−0.0330877	+	0.0173658i	0.448098	+	0.893984i	$0.352101\pi$
$734$	4.48247	+	11.8193i	0.165451	+	0.436258i
$735$	−5.33917	−	4.73009i	−0.196938	−	0.174472i
$736$	−3.25536	−	26.8103i	−0.119994	−	0.988241i
$737$	−3.04013	+	0.749325i	−0.111985	+	0.0276017i
$738$	3.90558	+	3.46004i	0.143766	+	0.127366i
$739$	38.1169	−	33.7686i	1.40215	−	1.24220i	0.468767	−	0.883322i	$-0.344698\pi$
$739$	38.1169	−	33.7686i	1.40215	−	1.24220i	0.933385	−	0.358876i	$-0.116840\pi$
$740$	−11.4815	−	6.02594i	−0.422067	−	0.221518i
$741$	−14.0660	−	15.4605i	−0.516727	−	0.567956i
$742$	0.669506	−	0.351384i	0.0245783	−	0.0128997i
$743$	−2.48687	+	6.55734i	−0.0912345	+	0.240566i	−0.972864	−	0.231376i	$-0.925677\pi$
$743$	−2.48687	+	6.55734i	−0.0912345	+	0.240566i	0.881630	+	0.471941i	$0.156447\pi$
$744$	1.13217	+	9.32423i	0.0415072	+	0.341843i
$745$	13.7169	−	7.19917i	0.502548	−	0.263757i
$746$	−24.4288			−0.894403
$747$	−8.35270	+	4.38384i	−0.305609	+	0.160396i
$748$	−14.8280	+	13.1365i	−0.542166	+	0.480317i
$749$	1.72760	+	2.50286i	0.0631252	+	0.0914527i
$750$	−6.19005	−	5.48391i	−0.226029	−	0.200244i
$751$	−0.851381	−	1.23344i	−0.0310673	−	0.0450088i	0.807142	−	0.590357i	$-0.201013\pi$
$751$	−0.851381	−	1.23344i	−0.0310673	−	0.0450088i	−0.838210	+	0.545348i	$0.816398\pi$
$752$	−0.0544432	−	0.143555i	−0.00198534	−	0.00523491i
$753$	−1.48600	−	3.91825i	−0.0541527	−	0.142789i
$754$	−18.3094	+	12.9988i	−0.666788	+	0.473387i
$755$	−3.15033	+	8.30673i	−0.114652	+	0.302313i
$756$	3.69514			0.134391
$757$	9.97467	+	26.3010i	0.362536	+	0.955928i	0.984888	+	0.173191i	$0.0554077\pi$
$757$	9.97467	+	26.3010i	0.362536	+	0.955928i	−0.622353	+	0.782737i	$0.713823\pi$
$758$	1.68892	−	13.9095i	0.0613442	−	0.505215i
$759$	12.7473	+	6.69031i	0.462699	+	0.242843i
$760$	7.00350	+	10.1463i	0.254044	+	0.368046i
$761$	−2.11283	−	3.06096i	−0.0765900	−	0.110960i	0.782817	−	0.622252i	$-0.213782\pi$
$761$	−2.11283	−	3.06096i	−0.0765900	−	0.110960i	−0.859407	+	0.511293i	$0.829167\pi$
$762$	13.6701	+	7.17464i	0.495217	+	0.259910i
$763$	0.343674	−	2.83041i	0.0124418	−	0.102468i
$764$	7.29385	+	19.2323i	0.263882	+	0.695800i
$765$	8.64864			0.312692
$766$	6.48812	−	17.1078i	0.234425	−	0.618129i
$767$	−13.0081	+	25.6019i	−0.469697 <

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)

\(f(q)\)	\(=\)	\(q+(0.481559 - 0.697658i) q^{2} +(1.04345 - 0.547645i) q^{3} +(0.454382 + 1.19811i) q^{4} +(0.674379 + 0.597448i) q^{5} +(0.120414 - 0.991695i) q^{6} +(-0.515253 - 0.126998i) q^{7} +(2.70085 + 0.665700i) q^{8} +(-0.915320 + 1.32607i) q^{9} +O(q^{10})\)	\(q+(0.481559 - 0.697658i) q^{2} +(1.04345 - 0.547645i) q^{3} +(0.454382 + 1.19811i) q^{4} +(0.674379 + 0.597448i) q^{5} +(0.120414 - 0.991695i) q^{6} +(-0.515253 - 0.126998i) q^{7} +(2.70085 + 0.665700i) q^{8} +(-0.915320 + 1.32607i) q^{9} +(0.741567 - 0.182780i) q^{10} +(-1.47414 - 2.13566i) q^{11} +(1.13026 + 1.00132i) q^{12} +(-0.909072 - 3.48907i) q^{13} +(-0.336726 + 0.298313i) q^{14} +(1.03087 + 0.254087i) q^{15} +(-0.153197 + 0.135721i) q^{16} +(-5.78443 - 1.42573i) q^{17} +(0.484363 + 1.27716i) q^{18} +4.91931 q^{19} +(-0.409380 + 1.07945i) q^{20} +(-0.607191 + 0.149659i) q^{21} -2.19985 q^{22} -4.70766 q^{23} +(3.18277 - 0.784483i) q^{24} +(-0.504840 - 4.15773i) q^{25} +(-2.87195 - 1.04597i) q^{26} +(-0.655009 + 5.39448i) q^{27} +(-0.0819639 - 0.675033i) q^{28} +(4.17327 - 6.04603i) q^{29} +(0.673691 - 0.596838i) q^{30} +(-0.345381 + 2.84446i) q^{31} +(0.691502 + 5.69503i) q^{32} +(-2.70778 - 1.42115i) q^{33} +(-3.78021 + 3.34898i) q^{34} +(-0.271601 - 0.393482i) q^{35} +(-2.00468 - 0.494108i) q^{36} +(-1.35384 + 11.1499i) q^{37} +(2.36894 - 3.43200i) q^{38} +(-2.85934 - 3.14282i) q^{39} +(1.42368 + 2.06255i) q^{40} +(3.38243 - 1.77523i) q^{41} +(-0.187987 + 0.495682i) q^{42} +(1.21336 + 9.99294i) q^{43} +(1.88893 - 2.73659i) q^{44} +(-1.40953 + 0.347418i) q^{45} +(-2.26702 + 3.28434i) q^{46} +(-0.266006 + 0.701399i) q^{47} +(-0.0855268 + 0.225516i) q^{48} +(-5.94884 - 3.12219i) q^{49} +(-3.14379 - 1.64999i) q^{50} +(-6.81656 + 1.68013i) q^{51} +(3.76721 - 2.67453i) q^{52} +(-1.63193 - 0.402235i) q^{53} +(3.44808 + 3.05473i) q^{54} +(0.281817 - 2.32097i) q^{55} +(-1.30708 - 0.686007i) q^{56} +(5.13306 - 2.69404i) q^{57} +(-2.20838 - 5.82303i) q^{58} +(-5.96165 - 5.28156i) q^{59} +(0.163986 + 1.35054i) q^{60} +(9.58018 - 2.36130i) q^{61} +(1.81814 + 1.61073i) q^{62} +(0.640030 - 0.567017i) q^{63} +(3.94373 + 2.06983i) q^{64} +(1.47148 - 2.89608i) q^{65} +(-2.29543 + 1.20474i) q^{66} +(0.427860 - 1.12817i) q^{67} +(-0.920158 - 7.57818i) q^{68} +(-4.91222 + 2.57813i) q^{69} -0.405307 q^{70} +(6.99334 - 3.67039i) q^{71} +(-3.35490 + 2.97219i) q^{72} +(0.746804 + 1.08193i) q^{73} +(7.12685 + 6.31384i) q^{74} +(-2.80374 - 4.06192i) q^{75} +(2.23524 + 5.89385i) q^{76} +(0.488330 + 1.28762i) q^{77} +(-3.56956 + 0.481391i) q^{78} +(-0.912716 + 2.40664i) q^{79} -0.184399 q^{80} +(0.556675 + 1.46783i) q^{81} +(0.390330 - 3.21466i) q^{82} +(5.18384 + 2.72069i) q^{83} +(-0.455204 - 0.659477i) q^{84} +(-3.04909 - 4.41738i) q^{85} +(7.55596 + 3.96567i) q^{86} +(1.04353 - 8.59420i) q^{87} +(-2.55973 - 6.74944i) q^{88} +13.4789 q^{89} +(-0.436392 + 1.15067i) q^{90} +(0.0252958 + 1.91320i) q^{91} +(-2.13908 - 5.64028i) q^{92} +(1.19737 + 3.15721i) q^{93} +(0.361240 + 0.523346i) q^{94} +(3.31748 + 2.93903i) q^{95} +(3.84041 + 5.56379i) q^{96} +(2.08113 - 1.84372i) q^{97} +(-5.04293 + 2.64674i) q^{98} +4.18135 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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