LMFDB - Embedded newform 169.2.g.a.14.4

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			14.4
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.885893 + 1.28344i) q^{2} +(-1.70070 + 0.892595i) q^{3} +(-0.153196 - 0.403946i) q^{4} +(2.77189 + 2.45568i) q^{5} +(0.361046 - 2.97348i) q^{6} +(3.26613 + 0.805028i) q^{7} +(-2.37420 - 0.585188i) q^{8} +(0.391453 - 0.567117i) q^{9} +O(q^{10})$	\(q+(-0.885893 + 1.28344i) q^{2} +(-1.70070 + 0.892595i) q^{3} +(-0.153196 - 0.403946i) q^{4} +(2.77189 + 2.45568i) q^{5} +(0.361046 - 2.97348i) q^{6} +(3.26613 + 0.805028i) q^{7} +(-2.37420 - 0.585188i) q^{8} +(0.391453 - 0.567117i) q^{9} +(-5.60732 + 1.38208i) q^{10} +(-1.53597 - 2.22524i) q^{11} +(0.621101 + 0.550247i) q^{12} +(-3.49393 + 0.890203i) q^{13} +(-3.92664 + 3.47870i) q^{14} +(-6.90608 - 1.70220i) q^{15} +(3.50108 - 3.10169i) q^{16} +(-3.27833 - 0.808035i) q^{17} +(0.381074 + 1.00481i) q^{18} +7.55032 q^{19} +(0.567318 - 1.49590i) q^{20} +(-6.27326 + 1.54622i) q^{21} +4.21667 q^{22} +1.76869 q^{23} +(4.56013 - 1.12397i) q^{24} +(1.05033 + 8.65023i) q^{25} +(1.95273 - 5.27287i) q^{26} +(0.535009 - 4.40619i) q^{27} +(-0.175171 - 1.44266i) q^{28} +(-1.72976 + 2.50599i) q^{29} +(8.30271 - 7.35556i) q^{30} +(0.836152 - 6.88633i) q^{31} +(0.289754 + 2.38634i) q^{32} +(4.59846 + 2.41346i) q^{33} +(3.94131 - 3.49170i) q^{34} +(7.07646 + 10.2520i) q^{35} +(-0.289054 - 0.0712453i) q^{36} +(-0.445358 + 3.66786i) q^{37} +(-6.68878 + 9.69037i) q^{38} +(5.14753 - 4.63263i) q^{39} +(-5.14399 - 7.45236i) q^{40} +(-1.42618 + 0.748516i) q^{41} +(3.57296 - 9.42112i) q^{42} +(0.0744845 + 0.613435i) q^{43} +(-0.663571 + 0.961348i) q^{44} +(2.47772 - 0.610704i) q^{45} +(-1.56687 + 2.27000i) q^{46} +(-2.47961 + 6.53820i) q^{47} +(-3.18573 + 8.40008i) q^{48} +(3.82131 + 2.00558i) q^{49} +(-12.0325 - 6.31515i) q^{50} +(6.29669 - 1.55199i) q^{51} +(0.894851 + 1.27498i) q^{52} +(12.9219 + 3.18497i) q^{53} +(5.18111 + 4.59007i) q^{54} +(1.20693 - 9.93999i) q^{55} +(-7.28334 - 3.82259i) q^{56} +(-12.8408 + 6.73938i) q^{57} +(-1.68390 - 4.44008i) q^{58} +(-2.43331 - 2.15572i) q^{59} +(0.370392 + 3.05045i) q^{60} +(13.6795 - 3.37169i) q^{61} +(8.09744 + 7.17370i) q^{62} +(1.73508 - 1.53715i) q^{63} +(4.96386 + 2.60523i) q^{64} +(-11.8708 - 6.11243i) q^{65} +(-7.17127 + 3.76377i) q^{66} +(-3.14424 + 8.29068i) q^{67} +(0.175825 + 1.44805i) q^{68} +(-3.00800 + 1.57872i) q^{69} -19.4268 q^{70} +(4.18318 - 2.19550i) q^{71} +(-1.26126 + 1.11738i) q^{72} +(-3.56058 - 5.15839i) q^{73} +(-4.31293 - 3.82092i) q^{74} +(-9.50744 - 13.7739i) q^{75} +(-1.15668 - 3.04992i) q^{76} +(-3.22530 - 8.50442i) q^{77} +(1.38553 + 10.7105i) q^{78} +(3.79832 - 10.0153i) q^{79} +17.3214 q^{80} +(3.75613 + 9.90410i) q^{81} +(0.302768 - 2.49352i) q^{82} +(3.97704 + 2.08731i) q^{83} +(1.58563 + 2.29718i) q^{84} +(-7.10289 - 10.2903i) q^{85} +(-0.853291 - 0.447842i) q^{86} +(0.704964 - 5.80590i) q^{87} +(2.34452 + 6.18200i) q^{88} -9.93317 q^{89} +(-1.41120 + 3.72102i) q^{90} +(-12.1282 + 0.0948039i) q^{91} +(-0.270956 - 0.714453i) q^{92} +(4.72466 + 12.4579i) q^{93} +(-6.19470 - 8.97458i) q^{94} +(20.9287 + 18.5412i) q^{95} +(-2.62282 - 3.79980i) q^{96} +(-1.36959 + 1.21335i) q^{97} +(-5.95932 + 3.12769i) q^{98} -1.86323 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 $

$2$	−0.885893	+	1.28344i	−0.626421	+	0.907528i	−0.999797	−	0.0201525i	$-0.993585\pi$
$2$	−0.885893	+	1.28344i	−0.626421	+	0.907528i	0.373376	+	0.927680i	$0.378200\pi$
$3$	−1.70070	+	0.892595i	−0.981898	+	0.515340i	−0.877697	−	0.479216i	$-0.840921\pi$
$3$	−1.70070	+	0.892595i	−0.981898	+	0.515340i	−0.104201	+	0.994556i	$0.533229\pi$
$4$	−0.153196	−	0.403946i	−0.0765982	−	0.201973i
$5$	2.77189	+	2.45568i	1.23963	+	1.09821i	0.991584	+	0.129466i	$0.0413262\pi$
$5$	2.77189	+	2.45568i	1.23963	+	1.09821i	0.248044	+	0.968749i	$0.420212\pi$
$6$	0.361046	−	2.97348i	0.147397	−	1.21392i
$7$	3.26613	+	0.805028i	1.23448	+	0.304272i	0.801974	−	0.597359i	$-0.203783\pi$
$7$	3.26613	+	0.805028i	1.23448	+	0.304272i	0.432506	+	0.901631i	$0.357630\pi$
$8$	−2.37420	−	0.585188i	−0.839406	−	0.206895i
$9$	0.391453	−	0.567117i	0.130484	−	0.189039i
$10$	−5.60732	+	1.38208i	−1.77319	+	0.437052i
$11$	−1.53597	−	2.22524i	−0.463113	−	0.670935i	0.519951	−	0.854196i	$-0.325950\pi$
$11$	−1.53597	−	2.22524i	−0.463113	−	0.670935i	−0.983064	+	0.183261i	$0.941335\pi$
$12$	0.621101	+	0.550247i	0.179296	+	0.158843i
$13$	−3.49393	+	0.890203i	−0.969042	+	0.246898i
$13$	−3.49393	+	0.890203i	−0.969042	+	0.246898i
$14$	−3.92664	+	3.47870i	−1.04944	+	0.929722i
$15$	−6.90608	−	1.70220i	−1.78314	−	0.439505i
$16$	3.50108	−	3.10169i	0.875271	−	0.775422i
$17$	−3.27833	−	0.808035i	−0.795111	−	0.195977i	−0.179220	−	0.983809i	$-0.557357\pi$
$17$	−3.27833	−	0.808035i	−0.795111	−	0.195977i	−0.615890	+	0.787832i	$0.711204\pi$
$18$	0.381074	+	1.00481i	0.0898201	+	0.236836i
$19$	7.55032			1.73216			0.866081	−	0.499903i	$-0.166631\pi$
$19$	7.55032			1.73216			0.866081	+	0.499903i	$0.166631\pi$
$20$	0.567318	−	1.49590i	0.126856	−	0.334492i
$21$	−6.27326	+	1.54622i	−1.36894	+	0.337413i
$22$	4.21667			0.898996
$23$	1.76869			0.368797			0.184398	−	0.982852i	$-0.440966\pi$
$23$	1.76869			0.368797			0.184398	+	0.982852i	$0.440966\pi$
$24$	4.56013	−	1.12397i	0.930833	−	0.229430i
$25$	1.05033	+	8.65023i	0.210065	+	1.73005i
$26$	1.95273	−	5.27287i	0.382962	−	1.03409i
$27$	0.535009	−	4.40619i	0.102962	−	0.847972i
$28$	−0.175171	−	1.44266i	−0.0331042	−	0.272638i
$29$	−1.72976	+	2.50599i	−0.321208	+	0.465350i	−0.950012	−	0.312214i	$-0.898930\pi$
$29$	−1.72976	+	2.50599i	−0.321208	+	0.465350i	0.628804	+	0.777564i	$0.283545\pi$
$30$	8.30271	−	7.35556i	1.51586	−	1.34294i
$31$	0.836152	−	6.88633i	0.150177	−	1.23682i	−0.701467	−	0.712702i	$-0.747471\pi$
$31$	0.836152	−	6.88633i	0.150177	−	1.23682i	0.851645	−	0.524120i	$-0.175606\pi$
$32$	0.289754	+	2.38634i	0.0512217	+	0.421849i
$33$	4.59846	+	2.41346i	0.800490	+	0.420129i
$34$	3.94131	−	3.49170i	0.675929	−	0.598821i
$35$	7.07646	+	10.2520i	1.19614	+	1.73291i
$36$	−0.289054	−	0.0712453i	−0.0481756	−	0.0118742i
$37$	−0.445358	+	3.66786i	−0.0732165	+	0.602992i	0.909209	+	0.416339i	$0.136687\pi$
$37$	−0.445358	+	3.66786i	−0.0732165	+	0.602992i	−0.982426	+	0.186653i	$0.940236\pi$
$38$	−6.68878	+	9.69037i	−1.08506	+	1.57199i
$39$	5.14753	−	4.63263i	0.824264	−	0.741814i
$40$	−5.14399	−	7.45236i	−0.813336	−	1.17832i
$41$	−1.42618	+	0.748516i	−0.222732	+	0.116899i	−0.572399	−	0.819975i	$-0.693987\pi$
$41$	−1.42618	+	0.748516i	−0.222732	+	0.116899i	0.349667	+	0.936874i	$0.386295\pi$
$42$	3.57296	−	9.42112i	0.551320	−	1.45371i
$43$	0.0744845	+	0.613435i	0.0113588	+	0.0935479i	0.997286	−	0.0736288i	$-0.0234580\pi$
$43$	0.0744845	+	0.613435i	0.0113588	+	0.0935479i	−0.985927	+	0.167177i	$0.946535\pi$
$44$	−0.663571	+	0.961348i	−0.100037	+	0.144929i
$45$	2.47772	−	0.610704i	0.369357	−	0.0910384i
$46$	−1.56687	+	2.27000i	−0.231022	+	0.334693i
$47$	−2.47961	+	6.53820i	−0.361689	+	0.953695i	0.623439	+	0.781872i	$0.285735\pi$
$47$	−2.47961	+	6.53820i	−0.361689	+	0.953695i	−0.985128	+	0.171823i	$0.945034\pi$
$48$	−3.18573	+	8.40008i	−0.459821	+	1.21245i
$49$	3.82131	+	2.00558i	0.545902	+	0.286512i
$50$	−12.0325	−	6.31515i	−1.70165	−	0.893097i
$51$	6.29669	−	1.55199i	0.881713	−	0.217323i
$52$	0.894851	+	1.27498i	0.124093	+	0.176808i
$53$	12.9219	+	3.18497i	1.77496	+	0.437490i	0.984553	−	0.175086i	$-0.0560205\pi$
$53$	12.9219	+	3.18497i	1.77496	+	0.437490i	0.790412	+	0.612576i	$0.209867\pi$
$54$	5.18111	+	4.59007i	0.705060	+	0.624629i
$55$	1.20693	−	9.93999i	0.162743	−	1.34031i
$56$	−7.28334	−	3.82259i	−0.973278	−	0.510816i
$57$	−12.8408	+	6.73938i	−1.70081	+	0.892653i
$58$	−1.68390	−	4.44008i	−0.221107	−	0.583011i
$59$	−2.43331	−	2.15572i	−0.316790	−	0.280651i	0.489710	−	0.871885i	$-0.337103\pi$
$59$	−2.43331	−	2.15572i	−0.316790	−	0.280651i	−0.806500	+	0.591234i	$0.798641\pi$
$60$	0.370392	+	3.05045i	0.0478174	+	0.393811i
$61$	13.6795	−	3.37169i	1.75148	−	0.431701i	0.772392	−	0.635146i	$-0.219060\pi$
$61$	13.6795	−	3.37169i	1.75148	−	0.431701i	0.979086	+	0.203445i	$0.0652139\pi$
$62$	8.09744	+	7.17370i	1.02838	+	0.911061i
$63$	1.73508	−	1.53715i	0.218599	−	0.193662i
$64$	4.96386	+	2.60523i	0.620482	+	0.325654i
$65$	−11.8708	−	6.11243i	−1.47240	−	0.758154i
$66$	−7.17127	+	3.76377i	−0.882723	+	0.463289i
$67$	−3.14424	+	8.29068i	−0.384130	+	1.01287i	0.593925	+	0.804521i	$0.297578\pi$
$67$	−3.14424	+	8.29068i	−0.384130	+	1.01287i	−0.978055	+	0.208347i	$0.933192\pi$
$68$	0.175825	+	1.44805i	0.0213220	+	0.175602i
$69$	−3.00800	+	1.57872i	−0.362121	+	0.190056i
$70$	−19.4268			−2.32195
$71$	4.18318	−	2.19550i	0.496452	−	0.260558i	−0.197863	−	0.980230i	$-0.563400\pi$
$71$	4.18318	−	2.19550i	0.496452	−	0.260558i	0.694314	+	0.719672i	$0.255708\pi$
$72$	−1.26126	+	1.11738i	−0.148641	+	0.131684i
$73$	−3.56058	−	5.15839i	−0.416735	−	0.603744i	0.557254	−	0.830342i	$-0.311855\pi$
$73$	−3.56058	−	5.15839i	−0.416735	−	0.603744i	−0.973988	+	0.226598i	$0.927240\pi$
$74$	−4.31293	−	3.82092i	−0.501367	−	0.444173i
$75$	−9.50744	−	13.7739i	−1.09782	−	1.59047i
$76$	−1.15668	−	3.04992i	−0.132681	−	0.349850i
$77$	−3.22530	−	8.50442i	−0.367557	−	0.969168i
$78$	1.38553	+	10.7105i	0.156881	+	1.21273i
$79$	3.79832	−	10.0153i	0.427344	−	1.12681i	−0.532537	−	0.846407i	$-0.678761\pi$
$79$	3.79832	−	10.0153i	0.427344	−	1.12681i	0.959881	−	0.280408i	$-0.0904696\pi$
$80$	17.3214			1.93659
$81$	3.75613	+	9.90410i	0.417348	+	1.10046i
$82$	0.302768	−	2.49352i	0.0334351	−	0.275363i
$83$	3.97704	+	2.08731i	0.436537	+	0.229112i	0.668651	−	0.743576i	$-0.266872\pi$
$83$	3.97704	+	2.08731i	0.436537	+	0.229112i	−0.232114	+	0.972689i	$0.574564\pi$
$84$	1.58563	+	2.29718i	0.173006	+	0.250643i
$85$	−7.10289	−	10.2903i	−0.770416	−	1.11614i
$86$	−0.853291	−	0.447842i	−0.0920127	−	0.0482920i
$87$	0.704964	−	5.80590i	0.0755801	−	0.622458i
$88$	2.34452	+	6.18200i	0.249927	+	0.659003i
$89$	−9.93317			−1.05291			−0.526457	−	0.850202i	$-0.676480\pi$
$89$	−9.93317			−1.05291			−0.526457	+	0.850202i	$0.676480\pi$
$90$	−1.41120	+	3.72102i	−0.148753	+	0.392230i
$91$	−12.1282	+	0.0948039i	−1.27139	+	0.00993815i
$92$	−0.270956	−	0.714453i	−0.0282491	−	0.0744869i
$93$	4.72466	+	12.4579i	0.489925	+	1.29183i
$94$	−6.19470	−	8.97458i	−0.638935	−	0.925657i
$95$	20.9287	+	18.5412i	2.14724	+	1.90229i
$96$	−2.62282	−	3.79980i	−0.267690	−	0.387816i
$97$	−1.36959	+	1.21335i	−0.139061	+	0.123197i	−0.729786	−	0.683676i	$-0.760380\pi$
$97$	−1.36959	+	1.21335i	−0.139061	+	0.123197i	0.590725	+	0.806873i	$0.298842\pi$
$98$	−5.95932	+	3.12769i	−0.601982	+	0.315944i
$99$	−1.86323			−0.187262
$100$	3.33331	−	1.74946i	0.333331	−	0.174946i
$101$	0.502063	+	4.13486i	0.0499571	+	0.411434i	0.996138	+	0.0877969i	$0.0279826\pi$
$101$	0.502063	+	4.13486i	0.0499571	+	0.411434i	−0.946181	+	0.323637i	$0.895094\pi$
$102$	−3.58631	+	9.45631i	−0.355097	+	0.936314i
$103$	−5.31284	+	2.78839i	−0.523489	+	0.274748i	−0.705700	−	0.708511i	$-0.749367\pi$
$103$	−5.31284	+	2.78839i	−0.523489	+	0.274748i	0.182210	+	0.983260i	$0.441675\pi$
$104$	8.81622	−	0.0689145i	0.864502	−	0.00675762i
$105$	−21.1858	−	11.1192i	−2.06752	−	1.08512i
$106$	−15.5352	+	13.7630i	−1.50891	+	1.33678i
$107$	−2.87378	−	2.54595i	−0.277819	−	0.246126i	0.512694	−	0.858571i	$-0.328647\pi$
$107$	−2.87378	−	2.54595i	−0.277819	−	0.246126i	−0.790513	+	0.612445i	$0.790186\pi$
$108$	−1.86182	+	0.458898i	−0.179154	+	0.0441575i
$109$	0.505270	+	4.16128i	0.0483961	+	0.398578i	0.996697	+	0.0812062i	$0.0258772\pi$
$109$	0.505270	+	4.16128i	0.0483961	+	0.398578i	−0.948301	+	0.317372i	$0.897200\pi$
$110$	11.6881	+	10.3548i	1.11442	+	0.987291i
$111$	−2.51649	−	6.63544i	−0.238855	−	0.629808i
$112$	13.9319	−	7.31204i	1.31644	−	0.690923i
$113$	0.520380	+	0.273117i	0.0489533	+	0.0256927i	0.489022	−	0.872271i	$-0.337354\pi$
$113$	0.520380	+	0.273117i	0.0489533	+	0.0256927i	−0.440069	+	0.897964i	$0.645046\pi$
$114$	2.72602	−	22.4508i	0.255315	−	2.10271i
$115$	4.90261	+	4.34333i	0.457170	+	0.405018i
$116$	1.27728	+	0.314820i	0.118592	+	0.0292303i
$117$	−0.862859	+	2.32994i	−0.0797713	+	0.215403i
$118$	4.92239	−	1.21326i	0.453142	−	0.111690i
$119$	−10.0569	−	5.27829i	−0.921918	−	0.483860i
$120$	15.4003	+	8.08271i	1.40585	+	0.737847i
$121$	1.30817	−	3.44936i	0.118925	−	0.313578i
$122$	−7.79121	+	20.5437i	−0.705383	+	1.85994i
$123$	1.75738	−	2.54600i	0.158457	−	0.229565i
$124$	−2.90980	+	0.717201i	−0.261308	+	0.0644065i
$125$	−7.81249	+	11.3184i	−0.698771	+	1.01234i
$126$	0.435736	+	3.58861i	0.0388185	+	0.319699i
$127$	4.88700	−	12.8860i	0.433651	−	1.14344i	−0.523032	−	0.852313i	$-0.675199\pi$
$127$	4.88700	−	12.8860i	0.433651	−	1.14344i	0.956683	−	0.291131i	$-0.0940315\pi$
$128$	−11.9981	+	6.29711i	−1.06050	+	0.556591i
$129$	−0.674224	−	0.976783i	−0.0593621	−	0.0860009i
$130$	18.3612	−	9.82053i	1.61039	−	0.861318i
$131$	−1.32597	+	1.92101i	−0.115851	+	0.167839i	−0.876620	−	0.481184i	$-0.840207\pi$
$131$	−1.32597	+	1.92101i	−0.115851	+	0.167839i	0.760769	+	0.649023i	$0.224822\pi$
$132$	0.270439	−	2.22726i	0.0235387	−	0.193858i
$133$	24.6603	+	6.07822i	2.13832	+	0.527048i
$134$	−7.85511	−	11.3801i	−0.678578	−	0.983091i
$135$	12.3032	−	10.8997i	1.05889	−	0.938095i
$136$	7.31055	+	3.83687i	0.626874	+	0.329009i
$137$	−1.93213	−	15.9125i	−0.165073	−	1.35950i	−0.806008	−	0.591905i	$-0.798376\pi$
$137$	−1.93213	−	15.9125i	−0.165073	−	1.35950i	0.640935	−	0.767595i	$-0.278547\pi$
$138$	0.638578	−	5.25916i	0.0543593	−	0.447689i
$139$	−13.7274	+	12.1614i	−1.16434	+	1.03152i	−0.165370	+	0.986232i	$0.552882\pi$
$139$	−13.7274	+	12.1614i	−1.16434	+	1.03152i	−0.998974	+	0.0452872i	$0.985580\pi$
$140$	3.05717	−	4.42907i	0.258378	−	0.374325i
$141$	−1.61889	−	13.3328i	−0.136335	−	1.12282i
$142$	−0.888059	+	7.31383i	−0.0745243	+	0.613763i
$143$	7.34749	+	6.40751i	0.614428	+	0.535823i
$144$	−0.388512	−	3.19969i	−0.0323760	−	0.266641i
$145$	−10.9486	+	2.69859i	−0.909233	+	0.224106i
$146$	9.77477			0.808966
$147$	−8.28907			−0.683671
$148$	1.54984	−	0.382002i	0.127396	−	0.0314003i
$149$	0.891019	−	2.34942i	0.0729951	−	0.192472i	−0.893553	−	0.448958i	$-0.851795\pi$
$149$	0.891019	−	2.34942i	0.0729951	−	0.192472i	0.966548	+	0.256485i	$0.0825646\pi$
$150$	26.1005			2.13110
$151$	−7.82248	−	20.6262i	−0.636584	−	1.67853i	−0.730464	−	0.682951i	$-0.760696\pi$
$151$	−7.82248	−	20.6262i	−0.636584	−	1.67853i	0.0938801	−	0.995584i	$-0.470073\pi$
$152$	−17.9260	−	4.41836i	−1.45399	−	0.358376i
$153$	−1.74156	+	1.54289i	−0.140797	+	0.124735i
$154$	13.7722	+	3.39453i	1.10979	+	0.273539i
$155$	19.2284	−	17.0348i	1.54446	−	1.36827i
$156$	−2.65991	−	1.36962i	−0.212963	−	0.109657i
$157$	10.5366	+	9.33465i	0.840916	+	0.744986i	0.969075	−	0.246767i	$-0.0793683\pi$
$157$	10.5366	+	9.33465i	0.840916	+	0.744986i	−0.128159	+	0.991754i	$0.540907\pi$
$158$	9.48917	+	13.7474i	0.754918	+	1.09369i
$159$	−24.8192	+	6.11738i	−1.96829	+	0.485140i
$160$	−5.05692	+	7.32621i	−0.399784	+	0.579188i
$161$	5.77675	+	1.42384i	0.455272	+	0.112214i
$162$	−16.0388	−	3.95322i	−1.26013	−	0.310594i
$163$	−1.22408	+	10.0812i	−0.0958775	+	0.789622i	0.862882	+	0.505405i	$0.168657\pi$
$163$	−1.22408	+	10.0812i	−0.0958775	+	0.789622i	−0.958760	+	0.284217i	$0.908266\pi$
$164$	0.520845	+	0.461428i	0.0406712	+	0.0360315i
$165$	6.81975	+	17.9822i	0.530917	+	1.39991i
$166$	−6.20217	+	3.25515i	−0.481382	+	0.252649i
$167$	4.42166	−	6.40587i	0.342158	−	0.495701i	−0.613696	−	0.789542i	$-0.710318\pi$
$167$	4.42166	−	6.40587i	0.342158	−	0.495701i	0.955854	+	0.293841i	$0.0949335\pi$
$168$	15.7988			1.21890
$169$	11.4151	−	6.22061i	0.878083	−	0.478508i
$170$	19.4994			1.49553
$171$	2.95559	−	4.28192i	0.226020	−	0.327446i
$172$	0.236384	−	0.124064i	0.0180241	−	0.00945976i
$173$	−4.63440	−	12.2199i	−0.352347	−	0.929062i	−0.987633	−	0.156785i	$-0.949887\pi$
$173$	−4.63440	−	12.2199i	−0.352347	−	0.929062i	0.635286	−	0.772277i	$-0.280882\pi$
$174$	6.82699	+	6.04819i	0.517553	+	0.458512i
$175$	−3.53317	+	29.0983i	−0.267082	+	2.19962i
$176$	−12.2796	−	3.02664i	−0.925608	−	0.228142i
$177$	6.06251	+	1.49427i	0.455686	+	0.112317i
$178$	8.79972	−	12.7486i	0.659567	−	0.955548i
$179$	17.4846	−	4.30958i	1.30686	−	0.322113i	0.476421	−	0.879217i	$-0.341934\pi$
$179$	17.4846	−	4.30958i	1.30686	−	0.322113i	0.830442	+	0.557104i	$0.188088\pi$
$180$	−0.626269	−	0.907308i	−0.0466794	−	0.0676267i
$181$	2.00697	+	1.77802i	0.149177	+	0.132159i	0.734411	−	0.678705i	$-0.237459\pi$
$181$	2.00697	+	1.77802i	0.149177	+	0.132159i	−0.585233	+	0.810865i	$0.698997\pi$
$182$	10.6227	−	15.6498i	0.787404	−	1.16004i
$183$	−20.2551	+	17.9445i	−1.49730	+	1.32649i
$184$	−4.19921	−	1.03501i	−0.309570	−	0.0763022i
$185$	−10.2416	+	9.07324i	−0.752975	+	0.667078i
$186$	−20.1745	−	4.97257i	−1.47927	−	0.364606i
$187$	3.23735	+	8.53618i	0.236738	+	0.624227i
$188$	3.02095			0.220325
$189$	5.29451	−	13.9605i	0.385119	−	1.01548i
$190$	−42.3370	+	10.4351i	−3.07145	+	0.757045i
$191$	−6.73859			−0.487587			−0.243794	−	0.969827i	$-0.578392\pi$
$191$	−6.73859			−0.487587			−0.243794	+	0.969827i	$0.578392\pi$
$192$	−10.7674			−0.777073
$193$	−7.68211	+	1.89347i	−0.552970	+	0.136295i	−0.505893	−	0.862596i	$-0.668837\pi$
$193$	−7.68211	+	1.89347i	−0.552970	+	0.136295i	−0.0470773	+	0.998891i	$0.514991\pi$
$194$	−0.343951	−	2.83269i	−0.0246942	−	0.203375i
$195$	25.6447	−	0.200459i	1.83645	−	0.0143551i
$196$	0.224734	−	1.85085i	0.0160524	−	0.132204i
$197$	−2.14266	−	17.6464i	−0.152659	−	1.25726i	−0.844638	−	0.535339i	$-0.820184\pi$
$197$	−2.14266	−	17.6464i	−0.152659	−	1.25726i	0.691979	−	0.721918i	$-0.256739\pi$
$198$	1.65062	−	2.39134i	0.117305	−	0.169945i
$199$	−6.46059	+	5.72359i	−0.457979	+	0.405734i	−0.860319	−	0.509756i	$-0.829736\pi$
$199$	−6.46059	+	5.72359i	−0.457979	+	0.405734i	0.402339	+	0.915491i	$0.368197\pi$
$200$	2.56832	−	21.1520i	0.181608	−	1.49567i
$201$	−2.05282	−	16.9065i	−0.144795	−	1.19249i
$202$	−5.75161	−	3.01868i	−0.404682	−	0.212393i
$203$	−7.66700	+	6.79237i	−0.538118	+	0.476731i
$204$	−1.59155	−	2.30576i	−0.111431	−	0.161435i
$205$	−5.79133	−	1.42743i	−0.404484	−	0.0996963i
$206$	1.12788	−	9.28892i	0.0785830	−	0.647189i
$207$	0.692357	−	1.00305i	0.0481221	−	0.0697169i
$208$	−9.47140	+	13.9538i	−0.656724	+	0.967519i
$209$	−11.5971	−	16.8013i	−0.802187	−	1.16217i
$210$	33.0391	−	17.3403i	2.27992	−	1.19659i
$211$	−2.24615	+	5.92261i	−0.154631	+	0.407729i	−0.989837	−	0.142209i	$-0.954579\pi$
$211$	−2.24615	+	5.92261i	−0.154631	+	0.407729i	0.835205	+	0.549938i	$0.185349\pi$
$212$	−0.693039	−	5.70769i	−0.0475981	−	0.392006i
$213$	−5.15463	+	7.46776i	−0.353189	+	0.511683i
$214$	5.81342	−	1.43288i	0.397397	−	0.0979497i
$215$	−1.29994	+	1.88328i	−0.0886550	+	0.128439i
$216$	−3.84867	+	10.1481i	−0.261869	+	0.690491i
$217$	8.27466	−	21.8185i	0.561721	−	1.48114i
$218$	−5.78835	−	3.03796i	−0.392037	−	0.205757i
$219$	10.6598	+	5.59471i	0.720325	+	0.378055i
$220$	−4.20011	+	1.03523i	−0.283171	+	0.0697955i
$221$	12.1736	−	0.0951580i	0.818882	−	0.00640102i
$222$	10.7455	+	2.64853i	0.721192	+	0.177758i
$223$	−6.24367	−	5.53141i	−0.418107	−	0.370411i	0.427681	−	0.903930i	$-0.359331\pi$
$223$	−6.24367	−	5.53141i	−0.418107	−	0.370411i	−0.845788	+	0.533519i	$0.820869\pi$
$224$	−0.974695	+	8.02733i	−0.0651245	+	0.536349i
$225$	5.31684	+	2.79049i	0.354456	+	0.186033i
$226$	−0.811530	+	0.425924i	−0.0539821	+	0.0283320i
$227$	−7.43374	−	19.6012i	−0.493395	−	1.30097i	−0.918353	−	0.395762i	$-0.870480\pi$
$227$	−7.43374	−	19.6012i	−0.493395	−	1.30097i	0.424958	−	0.905213i	$-0.360289\pi$
$228$	4.68951	+	4.15454i	0.310570	+	0.275141i
$229$	2.49840	+	20.5761i	0.165099	+	1.35971i	0.805922	+	0.592021i	$0.201670\pi$
$229$	2.49840	+	20.5761i	0.165099	+	1.35971i	−0.640824	+	0.767688i	$0.721407\pi$
$230$	−9.91758	+	2.44446i	−0.653946	+	0.161183i
$231$	13.0763	+	11.5846i	0.860355	+	0.762208i
$232$	5.57327	−	4.93748i	0.365903	−	0.324162i
$233$	3.34995	+	1.75819i	0.219462	+	0.115183i	0.570872	−	0.821039i	$-0.306605\pi$
$233$	3.34995	+	1.75819i	0.219462	+	0.115183i	−0.351410	+	0.936222i	$0.614298\pi$
$234$	−2.22593	−	3.17150i	−0.145514	−	0.207328i
$235$	−22.9290	+	12.0340i	−1.49572	+	0.785015i
$236$	−0.498021	+	1.31317i	−0.0324184	+	0.0854803i
$237$	2.47985	+	20.4234i	0.161084	+	1.32664i
$238$	15.6837	−	8.23145i	1.01662	−	0.533566i
$239$	−3.99585			−0.258470			−0.129235	−	0.991614i	$-0.541252\pi$
$239$	−3.99585			−0.258470			−0.129235	+	0.991614i	$0.541252\pi$
$240$	−29.4584	+	15.4610i	−1.90153	+	0.998002i
$241$	−17.2294	+	15.2639i	−1.10984	+	0.983235i	−0.999943	−	0.0107078i	$-0.996592\pi$
$241$	−17.2294	+	15.2639i	−1.10984	+	0.983235i	−0.109900	+	0.993943i	$0.535053\pi$
$242$	3.26814	+	4.73472i	0.210084	+	0.304359i
$243$	−5.26148	−	4.66126i	−0.337524	−	0.299020i
$244$	−3.45763	−	5.00924i	−0.221352	−	0.320684i
$245$	5.66720	+	14.9432i	0.362064	+	0.954685i
$246$	1.71078	+	4.51097i	0.109076	+	0.287609i
$247$	−26.3803	+	6.72132i	−1.67854	+	0.427667i
$248$	−6.01499	+	15.8602i	−0.381952	+	1.00713i
$249$	−8.62687			−0.546705
$250$	−7.60537	−	20.0537i	−0.481006	−	1.26831i
$251$	−0.527679	+	4.34583i	−0.0333068	+	0.274306i	0.966535	+	0.256534i	$0.0825805\pi$
$251$	−0.527679	+	4.34583i	−0.0333068	+	0.274306i	−0.999842	+	0.0177723i	$0.994343\pi$
$252$	−0.886731	−	0.465392i	−0.0558588	−	0.0293170i
$253$	−2.71665	−	3.93575i	−0.170795	−	0.247439i
$254$	12.2090	+	17.6877i	0.766059	+	1.10983i
$255$	21.2649	+	11.1607i	1.33166	+	0.698910i
$256$	1.19567	−	9.84719i	0.0747291	−	0.615449i
$257$	2.62178	+	6.91306i	0.163542	+	0.431225i	0.991588	−	0.129436i	$-0.0413166\pi$
$257$	2.62178	+	6.91306i	0.163542	+	0.431225i	−0.828046	+	0.560660i	$0.810547\pi$
$258$	1.85093			0.115234
$259$	−4.40732	+	11.6212i	−0.273858	+	0.722103i
$260$	−0.650520	+	5.73158i	−0.0403435	+	0.355457i
$261$	0.744070	+	1.96195i	0.0460568	+	0.121442i
$262$	−1.29082	−	3.40361i	−0.0797471	−	0.210276i
$263$	−3.03730	−	4.40028i	−0.187288	−	0.271333i	0.718081	−	0.695960i	$-0.245021\pi$
$263$	−3.03730	−	4.40028i	−0.187288	−	0.271333i	−0.905369	+	0.424627i	$0.860405\pi$
$264$	−9.50535	−	8.42100i	−0.585014	−	0.518277i
$265$	27.9969	+	40.5606i	1.71984	+	2.49162i
$266$	−29.6474	+	26.2653i	−1.81780	+	1.61043i
$267$	16.8933	−	8.86629i	1.03385	−	0.542608i
$268$	3.83067			0.233995
$269$	−12.0061	+	6.30127i	−0.732023	+	0.384195i	−0.789174	−	0.614170i	$-0.789491\pi$
$269$	−12.0061	+	6.30127i	−0.732023	+	0.384195i	0.0571506	+	0.998366i	$0.481798\pi$
$270$	3.08974	+	25.4463i	0.188036	+	1.54861i
$271$	9.73656	−	25.6732i	0.591454	−	1.55954i	−0.220236	−	0.975447i	$-0.570683\pi$
$271$	9.73656	−	25.6732i	0.591454	−	1.55954i	0.811690	−	0.584089i	$-0.198548\pi$
$272$	−13.9840	+	7.33935i	−0.847902	+	0.445013i
$273$	20.5419	−	10.9868i	1.24325	−	0.664954i
$274$	22.1344	+	11.6170i	1.33719	+	0.701811i
$275$	17.6356	−	15.6237i	1.06346	−	0.942147i
$276$	1.09853	+	0.973214i	0.0661238	+	0.0585806i
$277$	−0.180912	+	0.0445908i	−0.0108699	+	0.00267920i	−0.244747	−	0.969587i	$-0.578705\pi$
$277$	−0.180912	+	0.0445908i	−0.0108699	+	0.00267920i	0.233877	+	0.972266i	$0.424859\pi$
$278$	−3.44741	−	28.3920i	−0.206762	−	1.70284i
$279$	−3.57804	−	3.16987i	−0.214212	−	0.189775i
$280$	−10.8016	−	28.4814i	−0.645517	−	1.70209i
$281$	19.4773	−	10.2225i	1.16192	−	0.609822i	0.230250	−	0.973132i	$-0.426046\pi$
$281$	19.4773	−	10.2225i	1.16192	−	0.609822i	0.931668	+	0.363310i	$0.118353\pi$
$282$	18.5460	+	9.73368i	1.10440	+	0.579632i
$283$	2.27728	−	18.7551i	0.135370	−	1.11487i	−0.753738	−	0.657175i	$-0.771751\pi$
$283$	2.27728	−	18.7551i	0.135370	−	1.11487i	0.889108	−	0.457697i	$-0.151326\pi$
$284$	−1.52771	−	1.35343i	−0.0906529	−	0.0803115i
$285$	−52.1431	−	12.8521i	−3.08869	−	0.761294i
$286$	−14.7327	+	3.75369i	−0.871165	+	0.221960i
$287$	−5.26065	+	1.29663i	−0.310526	+	0.0765379i
$288$	1.46676	+	0.769813i	0.0864295	+	0.0453617i
$289$	−4.95825	−	2.60229i	−0.291662	−	0.153076i
$290$	6.23583	−	16.4425i	0.366181	−	0.965539i
$291$	1.24623	−	3.28604i	0.0730553	−	0.192631i
$292$	−1.53824	+	2.22853i	−0.0900188	+	0.130415i
$293$	−3.01610	+	0.743402i	−0.176202	+	0.0434300i	−0.326430	−	0.945222i	$-0.605846\pi$
$293$	−3.01610	+	0.743402i	−0.176202	+	0.0434300i	0.150227	+	0.988651i	$0.451999\pi$
$294$	7.34323	−	10.6385i	0.428266	−	0.620451i
$295$	−1.45110	−	11.9509i	−0.0844861	−	0.695806i
$296$	3.20375	−	8.44761i	0.186214	−	0.491007i
$297$	−10.6266	+	5.57727i	−0.616618	+	0.323626i
$298$	2.22599	+	3.22491i	0.128948	+	0.186814i
$299$	−6.17966	+	1.57449i	−0.357379	+	0.0910550i
$300$	−4.10740	+	5.95060i	−0.237141	+	0.343558i
$301$	−0.250556	+	2.06352i	−0.0144418	+	0.118939i
$302$	33.4023	+	8.23293i	1.92209	+	0.473752i
$303$	−4.54461	−	6.58401i	−0.261081	−	0.378241i
$304$	26.4343	−	23.4188i	1.51611	−	1.34316i
$305$	46.1978	+	24.2465i	2.64528	+	1.38835i
$306$	−0.437364	−	3.60202i	−0.0250024	−	0.205914i
$307$	2.24485	−	18.4880i	0.128120	−	1.05516i	−0.776849	−	0.629687i	$-0.783183\pi$
$307$	2.24485	−	18.4880i	0.128120	−	1.05516i	0.904969	−	0.425477i	$-0.139894\pi$
$308$	−2.94122	+	2.60569i	−0.167591	+	0.148473i
$309$	6.54663	−	9.48443i	0.372425	−	0.539550i
$310$	4.82889	+	39.7695i	0.274262	+	2.25875i
$311$	2.31976	−	19.1049i	0.131541	−	1.08334i	−0.766133	−	0.642682i	$-0.777822\pi$
$311$	2.31976	−	19.1049i	0.131541	−	1.08334i	0.897674	−	0.440659i	$-0.145255\pi$
$312$	−14.9322	+	7.98652i	−0.845370	+	0.452148i
$313$	−0.502927	−	4.14197i	−0.0284271	−	0.234118i	0.971569	−	0.236755i	$-0.0760838\pi$
$313$	−0.502927	−	4.14197i	−0.0284271	−	0.234118i	−0.999997	+	0.00263666i	$0.999161\pi$
$314$	−21.3148	+	5.25362i	−1.20286	+	0.296479i
$315$	8.58419			0.483664
$316$	−4.62754			−0.260320
$317$	2.68886	−	0.662745i	0.151022	−	0.0372235i	−0.163080	−	0.986613i	$-0.552143\pi$
$317$	2.68886	−	0.662745i	0.151022	−	0.0372235i	0.314102	+	0.949389i	$0.398297\pi$
$318$	14.1359	−	37.2733i	0.792701	−	2.09018i
$319$	8.23329			0.460976
$320$	7.36165	+	19.4111i	0.411529	+	1.08511i
$321$	7.15993	+	1.76476i	0.399628	+	0.0984995i
$322$	−6.94500	+	6.15273i	−0.387029	+	0.342878i
$323$	−24.7524	−	6.10092i	−1.37726	−	0.339464i
$324$	3.42529	−	3.03454i	0.190294	−	0.168586i
$325$	−11.3702	−	29.2883i	−0.630706	−	1.62462i
$326$	−11.8542	−	10.5019i	−0.656544	−	0.581647i
$327$	−4.57365	−	6.62607i	−0.252923	−	0.366423i
$328$	3.82405	−	0.942545i	0.211148	−	0.0520433i
$329$	−13.3622	+	19.3584i	−0.736680	+	1.06726i
$330$	−29.1206	−	7.17759i	−1.60304	−	0.395113i
$331$	−8.44747	−	2.08211i	−0.464315	−	0.114443i	0.000216573	−	1.00000i	$-0.499931\pi$
$331$	−8.44747	−	2.08211i	−0.464315	−	0.114443i	−0.464531	+	0.885557i	$0.653777\pi$
$332$	0.233892	−	1.92628i	0.0128365	−	0.105718i
$333$	1.90577	+	1.68836i	0.104435	+	0.0925217i
$334$	4.30443	+	11.3498i	0.235528	+	0.621036i
$335$	−29.0748	+	15.2596i	−1.58852	+	0.833722i
$336$	−17.1673	+	24.8711i	−0.936553	+	1.35683i
$337$	−20.3370			−1.10783			−0.553913	−	0.832575i	$-0.686866\pi$
$337$	−20.3370			−1.10783			−0.553913	+	0.832575i	$0.686866\pi$
$338$	−2.12878	+	20.1613i	−0.115790	+	1.09663i
$339$	−1.12879			−0.0613076
$340$	−3.06859	+	4.44562i	−0.166418	+	0.241098i
$341$	−16.6080	+	8.71658i	−0.899376	+	0.472029i
$342$	2.87723	+	7.58664i	0.155583	+	0.410239i
$343$	−6.75892	−	5.98788i	−0.364948	−	0.323315i
$344$	0.182133	−	1.50000i	0.00981998	−	0.0808748i
$345$	−12.2147	−	3.01065i	−0.657617	−	0.162088i
$346$	19.7891	+	4.87757i	1.06387	+	0.262220i
$347$	6.02599	−	8.73016i	0.323492	−	0.468659i	−0.627172	−	0.778881i	$-0.715788\pi$
$347$	6.02599	−	8.73016i	0.323492	−	0.468659i	0.950664	+	0.310221i	$0.100403\pi$
$348$	−2.45327	+	0.604676i	−0.131509	+	0.0324140i
$349$	−1.38151	−	2.00147i	−0.0739508	−	0.107136i	0.784263	−	0.620428i	$-0.213041\pi$
$349$	−1.38151	−	2.00147i	−0.0739508	−	0.107136i	−0.858214	+	0.513292i	$0.828426\pi$
$350$	−34.2158	−	30.3126i	−1.82891	−	1.62027i
$351$	2.05312	+	15.8712i	0.109588	+	0.847141i
$352$	4.86512	−	4.31012i	0.259312	−	0.229730i
$353$	20.3890	+	5.02544i	1.08520	+	0.267477i	0.741058	−	0.671441i	$-0.234324\pi$
$353$	20.3890	+	5.02544i	1.08520	+	0.267477i	0.344140	+	0.938918i	$0.388171\pi$
$354$	−7.28854	+	6.45709i	−0.387382	+	0.343190i
$355$	16.9868	+	4.18686i	0.901564	+	0.222215i
$356$	1.52172	+	4.01246i	0.0806513	+	0.212660i
$357$	21.8152			1.15458
$358$	−9.95845	+	26.2583i	−0.526321	+	1.38779i
$359$	16.4961	−	4.06592i	0.870630	−	0.214591i	0.221400	−	0.975183i	$-0.428937\pi$
$359$	16.4961	−	4.06592i	0.870630	−	0.214591i	0.649230	+	0.760592i	$0.275091\pi$
$360$	−6.23999			−0.328876
$361$	38.0074			2.00039
$362$	−4.05995	+	1.00069i	−0.213386	+	0.0525950i
$363$	0.854081	+	7.03399i	0.0448276	+	0.369189i
$364$	1.89630	+	4.88463i	0.0993931	+	0.256024i
$365$	2.79783	−	23.0422i	0.146445	−	1.20608i
$366$	−5.08674	−	41.8931i	−0.265888	−	2.18979i
$367$	−6.53370	+	9.46569i	−0.341056	+	0.494105i	−0.955555	−	0.294812i	$-0.904743\pi$
$367$	−6.53370	+	9.46569i	−0.341056	+	0.494105i	0.614499	+	0.788918i	$0.289358\pi$
$368$	6.19232	−	5.48591i	0.322797	−	0.285973i
$369$	−0.133785	+	1.10182i	−0.00696457	+	0.0573584i
$370$	−2.57200	−	21.1823i	−0.133712	−	1.10122i
$371$	39.6407	+	20.8050i	2.05804	+	1.08014i
$372$	4.30852	−	3.81701i	0.223386	−	0.197903i
$373$	18.5146	+	26.8230i	0.958648	+	1.38884i	0.921005	+	0.389550i	$0.127369\pi$
$373$	18.5146	+	26.8230i	0.958648	+	1.38884i	0.0376422	+	0.999291i	$0.488015\pi$
$374$	−13.8236	−	3.40721i	−0.714802	−	0.176183i
$375$	3.18399	−	26.2225i	0.164420	−	1.35412i
$376$	9.71317	−	14.0720i	0.500919	−	0.725706i
$377$	3.81282	−	10.2956i	0.196370	−	0.530249i
$378$	13.2270	+	19.1627i	0.680325	+	0.985622i
$379$	9.19514	−	4.82598i	0.472323	−	0.247894i	−0.211728	−	0.977329i	$-0.567909\pi$
$379$	9.19514	−	4.82598i	0.472323	−	0.247894i	0.684050	+	0.729435i	$0.260217\pi$
$380$	4.28344	−	11.2945i	0.219736	−	0.579395i
$381$	3.19063	+	26.2772i	0.163461	+	1.34622i
$382$	5.96967	−	8.64856i	0.305435	−	0.442499i
$383$	−15.1494	+	3.73398i	−0.774096	+	0.190798i	−0.606527	−	0.795063i	$-0.707438\pi$
$383$	−15.1494	+	3.73398i	−0.774096	+	0.190798i	−0.167569	+	0.985860i	$0.553592\pi$
$384$	14.7844	−	21.4189i	0.754465	−	1.09303i
$385$	11.9440	−	31.4936i	0.608720	−	1.60506i
$386$	4.37538	−	11.5369i	0.222701	−	0.587214i
$387$	0.377046	+	0.197889i	0.0191663	+	0.0100593i
$388$	0.699945	+	0.367360i	0.0355343	+	0.0186499i
$389$	27.3855	−	6.74991i	1.38850	−	0.342234i	0.526945	−	0.849900i	$-0.323338\pi$
$389$	27.3855	−	6.74991i	1.38850	−	0.342234i	0.861554	+	0.507665i	$0.169491\pi$
$390$	−22.4611	+	33.0909i	−1.13736	+	1.67562i
$391$	−5.79833	−	1.42916i	−0.293234	−	0.0722757i
$392$	−7.89892	−	6.99784i	−0.398956	−	0.353444i
$393$	0.540402	−	4.45061i	0.0272597	−	0.224503i
$394$	24.5463	+	12.8829i	1.23662	+	0.649030i
$395$	35.1230	−	18.4340i	1.76723	−	0.927515i
$396$	0.285440	+	0.752644i	0.0143439	+	0.0378218i
$397$	−24.6269	−	21.8176i	−1.23599	−	1.09499i	−0.992134	−	0.125180i	$-0.960049\pi$
$397$	−24.6269	−	21.8176i	−1.23599	−	1.09499i	−0.243856	−	0.969811i	$-0.578413\pi$
$398$	−1.62247	−	13.3623i	−0.0813272	−	0.669790i
$399$	−47.3651	+	11.6745i	−2.37122	+	0.584454i
$400$	30.5076	+	27.0274i	1.52538	+	1.35137i
$401$	2.35932	−	2.09017i	0.117819	−	0.104378i	−0.602156	−	0.798378i	$-0.705692\pi$
$401$	2.35932	−	2.09017i	0.117819	−	0.104378i	0.719975	+	0.694000i	$0.244153\pi$
$402$	23.5170	+	12.3427i	1.17292	+	0.615596i
$403$	3.20877	+	24.8047i	0.159840	+	1.23561i
$404$	1.59334	−	0.836252i	0.0792719	−	0.0416051i
$405$	−13.9097	+	36.6770i	−0.691180	+	1.82249i
$406$	−1.92544	−	15.8574i	−0.0955580	−	0.786991i
$407$	8.84592	−	4.64270i	0.438476	−	0.230130i
$408$	−15.8578			−0.785078
$409$	−26.6215	+	13.9720i	−1.31635	+	0.690872i	−0.969046	−	0.246882i	$-0.920594\pi$
$409$	−26.6215	+	13.9720i	−1.31635	+	0.690872i	−0.347301	+	0.937754i	$0.612902\pi$
$410$	6.96252	−	6.16825i	0.343854	−	0.304628i
$411$	17.4894	+	25.3378i	0.862690	+	1.24982i
$412$	1.94027	+	1.71893i	0.0955901	+	0.0846854i
$413$	−6.21207	−	8.99974i	−0.305676	−	0.442848i
$414$	0.674001	+	1.77719i	0.0331253	+	0.0873443i
$415$	5.89815	+	15.5521i	0.289529	+	0.763425i
$416$	−3.13670	−	8.07975i	−0.153789	−	0.396142i
$417$	12.4910	−	32.9359i	0.611685	−	1.61288i
$418$	31.8372			1.55721
$419$	−3.84817	−	10.1468i	−0.187995	−	0.495703i	0.807570	−	0.589771i	$-0.200782\pi$
$419$	−3.84817	−	10.1468i	−0.187995	−	0.495703i	−0.995566	+	0.0940680i	$0.970013\pi$
$420$	−1.24595	+	10.2613i	−0.0607962	+	0.500702i
$421$	−29.7333	−	15.6052i	−1.44911	−	0.760552i	−0.457426	−	0.889248i	$-0.651229\pi$
$421$	−29.7333	−	15.6052i	−1.44911	−	0.760552i	−0.991684	+	0.128696i	$0.958921\pi$
$422$	−5.61145	−	8.12959i	−0.273161	−	0.395742i
$423$	2.73727	+	3.96563i	0.133091	+	0.192815i
$424$	−28.8155	−	15.1235i	−1.39940	−	0.734463i
$425$	3.54637	−	29.2070i	0.172024	−	1.41675i
$426$	−5.01796	−	13.2313i	−0.243121	−	0.641058i
$427$	47.3932			2.29352
$428$	−0.588171	+	1.55088i	−0.0284303	+	0.0749646i
$429$	−18.2152	−	4.33889i	−0.879437	−	0.209484i
$430$	−1.26547	−	3.33678i	−0.0610265	−	0.160914i
$431$	9.96556	+	26.2770i	0.480024	+	1.26572i	0.928303	+	0.371826i	$0.121268\pi$
$431$	9.96556	+	26.2770i	0.480024	+	1.26572i	−0.448278	+	0.893894i	$0.647963\pi$
$432$	−11.7935	−	17.0859i	−0.567416	−	0.822045i
$433$	4.15913	+	3.68467i	0.199875	+	0.177074i	0.757123	−	0.653272i	$-0.226604\pi$
$433$	4.15913	+	3.68467i	0.199875	+	0.177074i	−0.557248	+	0.830346i	$0.688143\pi$
$434$	20.6722	+	29.9489i	0.992298	+	1.43759i
$435$	16.2115	−	14.3622i	0.777284	−	0.688613i
$436$	1.60352	−	0.841594i	0.0767948	−	0.0403050i
$437$	13.3541			0.638816
$438$	−16.6239	+	8.72491i	−0.794322	+	0.416893i
$439$	4.00239	+	32.9626i	0.191023	+	1.57322i	0.701082	+	0.713080i	$0.252701\pi$
$439$	4.00239	+	32.9626i	0.191023	+	1.57322i	−0.510059	+	0.860140i	$0.670376\pi$
$440$	−8.68226	+	22.8932i	−0.413910	+	1.09139i
$441$	2.63326	−	1.38204i	0.125393	−	0.0658116i
$442$	−10.6623	+	15.7083i	−0.507156	+	0.747168i
$443$	10.0329	+	5.26565i	0.476676	+	0.250179i	0.685909	−	0.727687i	$-0.259405\pi$
$443$	10.0329	+	5.26565i	0.476676	+	0.250179i	−0.209234	+	0.977866i	$0.567097\pi$
$444$	−2.29484	+	2.03305i	−0.108908	+	0.0964843i
$445$	−27.5337	−	24.3927i	−1.30522	−	1.15632i
$446$	12.6305	−	3.11313i	0.598069	−	0.147411i
$447$	0.581730	+	4.79098i	0.0275149	+	0.226606i
$448$	14.1153	+	12.5051i	0.666885	+	0.590809i
$449$	11.7526	+	30.9891i	0.554641	+	1.46247i	0.860032	+	0.510241i	$0.170444\pi$
$449$	11.7526	+	30.9891i	0.554641	+	1.46247i	−0.305391	+	0.952227i	$0.598787\pi$
$450$	−8.29158	+	4.35176i	−0.390869	+	0.205144i
$451$	3.85620	+	2.02389i	0.181581	+	0.0953012i
$452$	0.0306039	−	0.252046i	0.00143949	−	0.0118552i
$453$	31.7145	+	28.0966i	1.49008	+	1.32009i
$454$	31.7424	+	7.82379i	1.48974	+	0.367189i
$455$	−33.8510	−	29.5203i	−1.58696	−	1.38393i
$456$	34.4305	−	8.48635i	1.61235	−	0.397410i
$457$	−7.94663	−	4.17071i	−0.371727	−	0.195098i	0.268506	−	0.963278i	$-0.413470\pi$
$457$	−7.94663	−	4.17071i	−0.371727	−	0.195098i	−0.640233	+	0.768180i	$0.721162\pi$
$458$	−28.6215	−	15.0217i	−1.33740	−	0.701919i
$459$	−5.31429	+	14.0126i	−0.248050	+	0.654053i
$460$	1.00341	−	2.64577i	0.0467841	−	0.123360i
$461$	−1.18100	+	1.71097i	−0.0550044	+	0.0796877i	−0.849521	−	0.527555i	$-0.823109\pi$
$461$	−1.18100	+	1.71097i	−0.0550044	+	0.0796877i	0.794517	+	0.607242i	$0.207724\pi$
$462$	−26.4522	+	6.51989i	−1.23067	+	0.303333i
$463$	−4.32852	+	6.27095i	−0.201163	+	0.291436i	−0.910562	−	0.413372i	$-0.864351\pi$
$463$	−4.32852	+	6.27095i	−0.201163	+	0.291436i	0.709399	+	0.704807i	$0.248966\pi$
$464$	1.71677	+	14.1388i	0.0796989	+	0.656380i
$465$	−17.4964	+	46.1343i	−0.811377	+	2.13942i
$466$	−5.22422	+	2.74188i	−0.242007	+	0.127015i
$467$	−17.0726	−	24.7339i	−0.790024	−	1.14455i	−0.986455	−	0.164029i	$-0.947551\pi$
$467$	−17.0726	−	24.7339i	−0.790024	−	1.14455i	0.196432	−	0.980517i	$-0.437065\pi$
$468$	1.07336	−	0.00839019i	0.0496159	−	0.000387837i
$469$	−16.9437	+	24.5472i	−0.782388	+	1.13348i
$470$	4.86766	−	40.0888i	0.224528	−	1.84916i
$471$	−26.2517	−	6.47047i	−1.20962	−	0.298143i
$472$	4.51566	+	6.54206i	0.207850	+	0.301123i
$473$	1.25063	−	1.10796i	0.0575042	−	0.0509443i
$474$	−28.4091	−	14.9102i	−1.30487	−	0.684850i
$475$	7.93031	+	65.3120i	0.363868	+	2.99672i
$476$	−0.591455	+	4.87107i	−0.0271093	+	0.223265i
$477$	6.86458	−	6.08149i	0.314307	−	0.278452i
$478$	3.53989	−	5.12842i	0.161911	−	0.234569i
$479$	1.52668	+	12.5733i	0.0697556	+	0.574489i	0.985121	+	0.171864i	$0.0549791\pi$
$479$	1.52668	+	12.5733i	0.0697556	+	0.574489i	−0.915365	+	0.402625i	$0.868098\pi$
$480$	2.06095	−	16.9734i	0.0940690	−	0.774728i
$481$	−1.70908	−	13.2117i	−0.0779275	−	0.602401i
$482$	−4.32688	−	35.6351i	−0.197084	−	1.62313i
$483$	−11.0954	+	2.73478i	−0.504859	+	0.124437i
$484$	−1.59376			−0.0724437
$485$	−6.77597			−0.307681
$486$	10.6435	−	2.62340i	0.482801	−	0.119000i
$487$	−2.56149	+	6.75408i	−0.116072	+	0.306057i	−0.980445	−	0.196795i	$-0.936947\pi$
$487$	−2.56149	+	6.75408i	−0.116072	+	0.306057i	0.864373	+	0.502852i	$0.167716\pi$
$488$	−34.4509			−1.55952
$489$	−6.91665	−	18.2377i	−0.312782	−	0.824738i
$490$	−24.1992	−	5.96456i	−1.09321	−	0.269452i
$491$	−13.4841	+	11.9458i	−0.608528	+	0.539109i	−0.910129	−	0.414326i	$-0.864017\pi$
$491$	−13.4841	+	11.9458i	−0.608528	+	0.539109i	0.301601	+	0.953434i	$0.402479\pi$
$492$	−1.29767	−	0.319847i	−0.0585034	−	0.0144198i
$493$	7.69564	−	6.81774i	0.346594	−	0.307056i
$494$	14.7437	−	39.8118i	0.663352	−	1.79122i
$495$	−5.16468	−	4.57551i	−0.232135	−	0.205654i
$496$	−18.4318	−	26.7031i	−0.827613	−	1.19900i
$497$	15.4302	−	3.80321i	0.692140	−	0.170597i
$498$	7.64248	−	11.0720i	0.342468	−	0.496150i
$499$	11.9213	+	2.93835i	0.533673	+	0.131539i	0.496937	−	0.867787i	$-0.334458\pi$
$499$	11.9213	+	2.93835i	0.533673	+	0.131539i	0.0367355	+	0.999325i	$0.488304\pi$
$500$	5.76884	+	1.42189i	0.257991	+	0.0635890i
$501$	−1.80205	+	14.8412i	−0.0805096	+	0.663056i
$502$	−5.11013	−	4.52718i	−0.228076	−	0.202058i
$503$	−8.83831	−	23.3047i	−0.394081	−	1.03911i	−0.974421	−	0.224731i	$-0.927850\pi$
$503$	−8.83831	−	23.3047i	−0.394081	−	1.03911i	0.580340	−	0.814374i	$-0.302920\pi$
$504$	−5.01894	+	2.63414i	−0.223561	+	0.117334i
$505$	−8.76224	+	12.6943i	−0.389914	+	0.564889i
$506$	7.45796			0.331547
$507$	−13.8611	+	20.7684i	−0.615594	+	0.922358i
$508$	−5.95390			−0.264161
$509$	−24.0029	+	34.7742i	−1.06391	+	1.54134i	−0.243212	+	0.969973i	$0.578201\pi$
$509$	−24.0029	+	34.7742i	−1.06391	+	1.54134i	−0.820696	+	0.571364i	$0.806414\pi$
$510$	−33.1625	+	17.4050i	−1.46846	+	0.770708i
$511$	−7.47666	−	19.7143i	−0.330748	−	0.872111i
$512$	−8.70596	−	7.71280i	−0.384753	−	0.340861i
$513$	4.03949	−	33.2682i	0.178348	−	1.46883i
$514$	−11.1951	−	2.75934i	−0.493794	−	0.121709i
$515$	−21.5740	−	5.31752i	−0.950665	−	0.234318i
$516$	−0.291278	+	0.421989i	−0.0128228	+	0.0185771i
$517$	18.3577	−	4.52476i	0.807370	−	0.198999i
$518$	−11.0106	−	15.9516i	−0.483778	−	0.700874i
$519$	18.7891	+	16.6457i	0.824752	+	0.730666i
$520$	24.6068	+	21.4588i	1.07908	+	0.941031i
$521$	−9.09156	+	8.05442i	−0.398309	+	0.352871i	−0.838374	−	0.545095i	$-0.816494\pi$
$521$	−9.09156	+	8.05442i	−0.398309	+	0.352871i	0.440066	+	0.897966i	$0.354955\pi$
$522$	−3.17721	−	0.783112i	−0.139063	−	0.0342759i
$523$	6.07148	−	5.37886i	0.265487	−	0.235201i	−0.519868	−	0.854247i	$-0.674019\pi$
$523$	6.07148	−	5.37886i	0.265487	−	0.235201i	0.785355	+	0.619046i	$0.212480\pi$
$524$	0.979116	+	0.241330i	0.0427729	+	0.0105426i
$525$	−19.9641	−	52.6410i	−0.871305	−	2.29744i
$526$	8.33821			0.363563
$527$	−8.30557	+	21.9000i	−0.361796	+	0.953979i
$528$	23.5854	−	5.81328i	1.02642	−	0.252991i
$529$	−19.8718			−0.863989
$530$	−76.8593			−3.33855
$531$	−2.17507	+	0.536107i	−0.0943901	+	0.0232651i
$532$	−1.32260	−	10.8926i	−0.0573419	−	0.472253i
$533$	4.31663	−	3.88485i	0.186974	−	0.168271i
$534$	−3.58633	+	29.5361i	−0.155196	+	1.27815i
$535$	−1.71377	−	14.1142i	−0.0740928	−	0.610209i
$536$	12.3167	−	17.8438i	0.531999	−	0.770733i
$537$	−25.8894	+	22.9360i	−1.11721	+	0.989761i
$538$	2.54880	−	20.9913i	0.109887	−	0.904999i
$539$	−1.40654	−	11.5839i	−0.0605838	−	0.498952i
$540$	−6.28768	−	3.30003i	−0.270579	−	0.142011i
$541$	12.0094	−	10.6394i	0.516324	−	0.457423i	−0.364271	−	0.931293i	$-0.618682\pi$
$541$	12.0094	−	10.6394i	0.516324	−	0.457423i	0.880595	+	0.473870i	$0.157143\pi$
$542$	24.3244	+	35.2400i	1.04482	+	1.51369i
$543$	−5.00031	−	1.23247i	−0.214584	−	0.0528902i
$544$	0.978335	−	8.05732i	0.0419458	−	0.345455i
$545$	−8.81821	+	12.7754i	−0.377731	+	0.547238i
$546$	−4.09696	+	36.0974i	−0.175334	+	1.54483i
$547$	1.16137	+	1.68253i	0.0496565	+	0.0719399i	0.847026	−	0.531552i	$-0.178391\pi$
$547$	1.16137	+	1.68253i	0.0496565	+	0.0719399i	−0.797369	+	0.603492i	$0.793776\pi$
$548$	−6.13180	+	3.21822i	−0.261938	+	0.137476i
$549$	3.44273	−	9.07772i	0.146932	−	0.387428i
$550$	4.42888	+	36.4751i	0.188848	+	1.55530i
$551$	−13.0602	+	18.9210i	−0.556385	+	0.806063i
$552$	8.06544	−	1.98795i	0.343288	−	0.0846129i
$553$	20.4684	−	29.6536i	0.870406	−	1.26100i
$554$	0.103039	−	0.271692i	0.00437771	−	0.0115431i
$555$	9.31909	−	24.5724i	0.395573	−	1.04304i
$556$	7.01554	+	3.68204i	0.297525	+	0.156153i
$557$	−3.97499	−	2.08624i	−0.168426	−	0.0883967i	0.378404	−	0.925641i	$-0.376473\pi$
$557$	−3.97499	−	2.08624i	−0.168426	−	0.0883967i	−0.546830	+	0.837244i	$0.684165\pi$
$558$	7.23809	−	1.78403i	0.306413	−	0.0755240i
$559$	−0.806325	−	2.07699i	−0.0341039	−	0.0878474i
$560$	56.5738	+	13.9442i	2.39068	+	0.589250i
$561$	−13.1251	−	11.6278i	−0.554142	−	0.490927i
$562$	−4.13489	+	34.0539i	−0.174420	+	1.43648i
$563$	26.7369	+	14.0326i	1.12683	+	0.591405i	0.921921	−	0.387377i	$-0.126619\pi$
$563$	26.7369	+	14.0326i	1.12683	+	0.591405i	0.204906	+	0.978782i	$0.434311\pi$
$564$	−5.13771	+	2.69648i	−0.216337	+	0.113542i
$565$	0.771750	+	2.03494i	0.0324678	+	0.0856105i
$566$	22.0535	+	19.5377i	0.926979	+	0.821231i
$567$	4.29492	+	35.3718i	0.180370	+	1.48548i
$568$	−11.2165	+	2.76461i	−0.470633	+	0.116001i
$569$	−13.1151	−	11.6189i	−0.549812	−	0.487091i	0.341874	−	0.939746i	$-0.388938\pi$
$569$	−13.1151	−	11.6189i	−0.549812	−	0.487091i	−0.891686	+	0.452655i	$0.850477\pi$
$570$	62.6882	−	55.5369i	2.62572	−	2.32618i
$571$	3.54419	+	1.86013i	0.148320	+	0.0778441i	0.537250	−	0.843423i	$-0.319463\pi$
$571$	3.54419	+	1.86013i	0.148320	+	0.0778441i	−0.388931	+	0.921267i	$0.627155\pi$
$572$	1.46267	−	3.94959i	0.0611575	−	0.165141i
$573$	11.4603	−	6.01483i	0.478761	−	0.251273i
$574$	2.99623	−	7.90040i	0.125060	−	0.329756i
$575$	1.85770	+	15.2995i	0.0774714	+	0.638035i
$576$	3.42059	−	1.79526i	0.142524	−	0.0748026i
$577$	−16.7774			−0.698454			−0.349227	−	0.937038i	$-0.613556\pi$
$577$	−16.7774			−0.698454			−0.349227	+	0.937038i	$0.613556\pi$
$578$	7.73236	−	4.05826i	0.321624	−	0.168801i
$579$	11.3748	−	10.0772i	0.472722	−	0.418795i
$580$	2.76737	+	4.00923i	0.114909	+	0.166474i
$581$	11.3092	+	10.0190i	0.469183	+	0.415660i
$582$	3.11340	+	4.51054i	0.129055	+	0.186968i
$583$	−12.7604	−	33.6465i	−0.528482	−	1.39349i
$584$	5.43491	+	14.3307i	0.224898	+	0.593007i
$585$	−8.11334	+	4.33943i	−0.335445	+	0.179413i
$586$	1.71783	−	4.52955i	0.0709630	−	0.187114i
$587$	−24.5712			−1.01416			−0.507081	−	0.861898i	$-0.669276\pi$
$587$	−24.5712			−1.01416			−0.507081	+	0.861898i	$0.669276\pi$
$588$	1.26986	+	3.34833i	0.0523680	+	0.138083i
$589$	6.31322	−	51.9940i	0.260132	−	2.14238i
$590$	16.6237	+	8.72479i	0.684387	+	0.359194i
$591$	19.3951	+	28.0987i	0.797810	+	1.15583i
$592$	9.81731	+	14.2228i	0.403489	+	0.584555i
$593$	−21.4740	−	11.2704i	−0.881832	−	0.462821i	−0.0379065	−	0.999281i	$-0.512069\pi$
$593$	−21.4740	−	11.2704i	−0.881832	−	0.462821i	−0.843926	+	0.536460i	$0.819761\pi$
$594$	2.25595	−	18.5794i	0.0925629	−	0.762324i
$595$	−14.9149	−	39.3275i	−0.611453	−	1.61227i
$596$	−1.08554			−0.0444655
$597$	5.87867	−	15.5008i	0.240598	−	0.634405i
$598$	3.45376	−	9.32604i	0.141235	−	0.381370i
$599$	14.3955	+	37.9578i	0.588185	+	1.55092i	0.816511	+	0.577330i	$0.195906\pi$
$599$	14.3955	+	37.9578i	0.588185	+	1.55092i	−0.228326	+	0.973585i	$0.573325\pi$
$600$	14.5122	+	38.2656i	0.592460	+	1.56219i
$601$	6.02351	+	8.72656i	0.245704	+	0.355964i	0.926360	−	0.376640i	$-0.122920\pi$
$601$	6.02351	+	8.72656i	0.245704	+	0.355964i	−0.680656	+	0.732603i	$0.738305\pi$
$602$	−2.42643	−	2.14963i	−0.0988939	−	0.0876123i
$603$	3.47097	+	5.02856i	0.141349	+	0.204779i
$604$	−7.13348	+	6.31971i	−0.290257	+	0.257145i
$605$	12.0966	−	6.34881i	0.491798	−	0.258116i
$606$	12.4762			0.506811
$607$	6.15708	−	3.23148i	0.249908	−	0.131162i	−0.335118	−	0.942176i	$-0.608776\pi$
$607$	6.15708	−	3.23148i	0.249908	−	0.131162i	0.585027	+	0.811014i	$0.301084\pi$
$608$	2.18773	+	18.0176i	0.0887243	+	0.730710i
$609$	6.97641	−	18.3953i	0.282699	−	0.745415i
$610$	−72.0452	+	37.8123i	−2.91703	+	1.53097i
$611$	2.84327	−	25.0514i	0.115026	−	1.01347i
$612$	0.890043	+	0.467131i	0.0359779	+	0.0188826i
$613$	23.8150	−	21.0983i	0.961880	−	0.852152i	−0.0271850	−	0.999630i	$-0.508654\pi$
$613$	23.8150	−	21.0983i	0.961880	−	0.852152i	0.989065	+	0.147479i	$0.0471158\pi$
$614$	21.7395	+	19.2595i	0.877334	+	0.777250i
$615$	11.1234	−	2.74168i	0.448539	−	0.110555i
$616$	2.68083	+	22.0786i	0.108014	+	0.889572i
$617$	6.73636	+	5.96789i	0.271196	+	0.240258i	0.787749	−	0.615997i	$-0.211247\pi$
$617$	6.73636	+	5.96789i	0.271196	+	0.240258i	−0.516553	+	0.856255i	$0.672785\pi$
$618$	6.37306	+	16.8044i	0.256362	+	0.675971i
$619$	−4.68457	+	2.45865i	−0.188289	+	0.0988215i	−0.556233	−	0.831026i	$-0.687754\pi$
$619$	−4.68457	+	2.45865i	−0.188289	+	0.0988215i	0.367945	+	0.929848i	$0.380062\pi$
$620$	−9.82686	−	5.15754i	−0.394656	−	0.207132i
$621$	0.946262	−	7.79317i	0.0379722	−	0.312729i
$622$	22.4649	+	19.9022i	0.900762	+	0.798006i
$623$	−32.4430	−	7.99647i	−1.29980	−	0.320372i
$624$	3.65294	−	32.1852i	0.146235	−	1.28844i
$625$	−7.14690	+	1.76155i	−0.285876	+	0.0704621i
$626$	5.76150	+	3.02387i	0.230276	+	0.120858i
$627$	34.7199	+	18.2224i	1.38658	+	0.727733i
$628$	2.15652	−	5.68627i	0.0860544	−	0.226907i
$629$	4.42378	−	11.6646i	0.176388	−	0.465097i
$630$	−7.60468	+	11.0173i	−0.302978	+	0.438939i
$631$	−8.33861	+	2.05528i	−0.331955	+	0.0818195i	−0.401771	−	0.915740i	$-0.631605\pi$
$631$	−8.33861	+	2.05528i	−0.331955	+	0.0818195i	0.0698156	+	0.997560i	$0.477759\pi$
$632$	−14.8788	+	21.5557i	−0.591848	+	0.857440i
$633$	−1.46647	−	12.0775i	−0.0582869	−	0.480036i
$634$	−1.53145	+	4.03811i	−0.0608218	+	0.160374i
$635$	45.1900	−	23.7176i	1.79331	−	0.941203i
$636$	6.27330	+	9.08845i	0.248753	+	0.360380i
$637$	−15.1368	−	3.60561i	−0.599741	−	0.142860i
$638$	−7.29382	+	10.5669i	−0.288765	+	0.418348i
$639$	0.392410	−	3.23178i	0.0155235	−	0.127847i
$640$	−48.7212	−	12.0087i	−1.92587	−	0.474686i
$641$	−4.30755	−	6.24056i	−0.170138	−	0.246487i	0.728635	−	0.684903i	$-0.240155\pi$
$641$	−4.30755	−	6.24056i	−0.170138	−	0.246487i	−0.898773	+	0.438415i	$0.855540\pi$
$642$	−8.60789	+	7.62593i	−0.339727	+	0.300971i
$643$	−15.9800	−	8.38696i	−0.630191	−	0.330750i	0.119207	−	0.992869i	$-0.461965\pi$
$643$	−15.9800	−	8.38696i	−0.630191	−	0.330750i	−0.749398	+	0.662120i	$0.769657\pi$
$644$	−0.309823	−	2.55162i	−0.0122087	−	0.100548i
$645$	0.529790	−	4.36322i	0.0208605	−	0.171801i
$646$	29.7582	−	26.3634i	1.17082	−	1.03726i
$647$	−26.6493	+	38.6082i	−1.04769	+	1.51784i	−0.205505	+	0.978656i	$0.565884\pi$
$647$	−26.6493	+	38.6082i	−1.04769	+	1.51784i	−0.842186	+	0.539187i	$0.818732\pi$
$648$	−3.12205	−	25.7124i	−0.122646	−	1.01008i
$649$	−1.05951	+	8.72583i	−0.0415893	+	0.342519i
$650$	47.6625	+	11.3533i	1.86948	+	0.445313i
$651$	5.40238	+	44.4926i	0.211736	+	1.74380i
$652$	4.25979	−	1.04994i	0.166826	−	0.0411190i
$653$	18.6754			0.730824			0.365412	−	0.930846i	$-0.380928\pi$
$653$	18.6754			0.730824			0.365412	+	0.930846i	$0.380928\pi$
$654$	12.5559			0.490975
$655$	−8.39283	+	2.06865i	−0.327935	+	0.0808288i
$656$	−2.67150	+	7.04418i	−0.104305	+	0.275029i
$657$	−4.31921			−0.168509
$658$	−13.0079	−	34.2990i	−0.507101	−	1.33711i
$659$	−4.68282	−	1.15421i	−0.182417	−	0.0449617i	0.147049	−	0.989129i	$-0.453022\pi$
$659$	−4.68282	−	1.15421i	−0.182417	−	0.0449617i	−0.329466	+	0.944168i	$0.606869\pi$
$660$	6.21907	−	5.50962i	0.242077	−	0.214462i
$661$	−25.8270	−	6.36579i	−1.00455	−	0.247600i	−0.297471	−	0.954731i	$-0.596143\pi$
$661$	−25.8270	−	6.36579i	−1.00455	−	0.247600i	−0.707083	+	0.707130i	$0.749989\pi$
$662$	10.1558	−	8.99727i	0.394717	−	0.349689i
$663$	−20.6186	+	11.0279i	−0.800760	+	0.428288i
$664$	−8.22082	−	7.28301i	−0.319030	−	0.282636i
$665$	53.4295	+	77.4060i	2.07191	+	3.00168i
$666$	−3.85521	+	0.950225i	−0.149387	+	0.0368205i
$667$	−3.05940	+	4.43231i	−0.118460	+	0.171620i
$668$	−3.26501	−	0.804752i	−0.126327	−	0.0311368i
$669$	15.5559	+	3.83419i	0.601426	+	0.148238i
$670$	6.17237	−	50.8341i	0.238460	−	1.96389i
$671$	−28.5141	−	25.2613i	−1.10078	−	0.975202i
$672$	−5.50750	−	14.5221i	−0.212456	−	0.560201i
$673$	41.3359	−	21.6947i	1.59338	−	0.836271i	0.593884	−	0.804551i	$-0.297594\pi$
$673$	41.3359	−	21.6947i	1.59338	−	0.836271i	0.999497	−	0.0317196i	$-0.0100983\pi$
$674$	18.0164	−	26.1012i	0.693965	−	1.00538i
$675$	38.6765			1.48866
$676$	−4.26154	−	3.65810i	−0.163905	−	0.140696i
$677$	44.3162			1.70321			0.851604	−	0.524185i	$-0.175630\pi$
$677$	44.3162			1.70321			0.851604	+	0.524185i	$0.175630\pi$
$678$	0.999989	−	1.44873i	0.0384044	−	0.0556383i
$679$	−5.45004	+	2.86040i	−0.209154	+	0.109772i
$680$	10.8419	+	28.5878i	0.415768	+	1.09629i
$681$	30.1384	+	26.7003i	1.15491	+	1.02316i
$682$	3.52577	−	29.0374i	0.135009	−	1.11190i
$683$	10.0984	+	2.48902i	0.386403	+	0.0952397i	0.427731	−	0.903906i	$-0.359313\pi$
$683$	10.0984	+	2.48902i	0.386403	+	0.0952397i	−0.0413287	+	0.999146i	$0.513159\pi$
$684$	−2.18245	−	0.537925i	−0.0834480	−	0.0205681i
$685$	33.7205	−	48.8525i	1.28839	−	1.86656i
$686$	13.6728	−	3.37003i	0.522028	−	0.128668i
$687$	−22.6152	−	32.7637i	−0.862823	−	1.25001i
$688$	2.16346	+	1.91666i	0.0824811	+	0.0730719i
$689$	−47.9836	+	0.375078i	−1.82803	+	0.0142893i
$690$	14.6849	−	13.0097i	0.559044	−	0.495270i
$691$	−16.8349	−	4.14942i	−0.640428	−	0.157851i	−0.0942878	−	0.995545i	$-0.530057\pi$
$691$	−16.8349	−	4.14942i	−0.640428	−	0.157851i	−0.546140	+	0.837694i	$0.683904\pi$
$692$	−4.22620	+	3.74409i	−0.160656	+	0.142329i
$693$	−6.08555	−	1.49995i	−0.231171	−	0.0569785i
$694$	5.86623	+	15.4680i	0.222679	+	0.587156i
$695$	−67.9155			−2.57618
$696$	−5.07127	+	13.3718i	−0.192226	+	0.506858i
$697$	5.28030	−	1.30148i	0.200006	−	0.0492970i
$698$	3.79263			0.143553
$699$	−7.26659			−0.274848
$700$	12.2954	−	3.03054i	0.464722	−	0.114544i
$701$	−3.12223	−	25.7139i	−0.117925	−	0.971200i	−0.924794	−	0.380469i	$-0.875763\pi$
$701$	−3.12223	−	25.7139i	−0.117925	−	0.971200i	0.806869	−	0.590731i	$-0.201161\pi$
$702$	−22.1885	−	11.4251i	−0.837452	−	0.431214i
$703$	−3.36260	+	27.6935i	−0.126823	+	1.04448i
$704$	−1.82708	−	15.0473i	−0.0688606	−	0.567118i
$705$	28.2537	−	40.9326i	1.06410	−	1.54161i
$706$	−24.5123	+	21.7160i	−0.922534	+	0.817294i
$707$	−1.68888	+	13.9091i	−0.0635167	+	0.523107i
$708$	−0.325149	−	2.67784i	−0.0122198	−	0.100639i
$709$	−9.96521	−	5.23015i	−0.374251	−	0.196422i	0.267101	−	0.963668i	$-0.413934\pi$
$709$	−9.96521	−	5.23015i	−0.374251	−	0.196422i	−0.641353	+	0.767246i	$0.721626\pi$
$710$	−20.4220	+	18.0923i	−0.766425	+	0.678993i
$711$	−4.19301	−	6.07463i	−0.157250	−	0.227816i
$712$	23.5833	+	5.81277i	0.883822	+	0.217843i
$713$	1.47889	−	12.1798i	0.0553849	−	0.456135i
$714$	−19.3259	+	27.9984i	−0.723254	+	1.04781i
$715$	4.63166	+	35.8040i	0.173214	+	1.33899i
$716$	−4.41942	−	6.40263i	−0.165161	−	0.239278i
$717$	6.79573	−	3.56667i	0.253791	−	0.133200i
$718$	−9.39542	+	24.7737i	−0.350634	+	0.924545i
$719$	3.41344	+	28.1122i	0.127300	+	1.04841i	0.906669	+	0.421843i	$0.138617\pi$
$719$	3.41344	+	28.1122i	0.127300	+	1.04841i	−0.779369	+	0.626565i	$0.784460\pi$
$720$	6.78050	−	9.82325i	0.252694	−	0.366091i
$721$	−19.5971	+	4.83026i	−0.729835	+	0.179888i
$722$	−33.6705	+	48.7801i	−1.25309	+	1.81541i
$723$	15.6775	−	41.3382i	0.583052	−	1.53738i
$724$	0.410764	−	1.08310i	0.0152659	−	0.0402529i
$725$	−23.4942	−	12.3307i	−0.872552	−	0.457951i
$726$	−9.78431	−	5.13520i	−0.363130	−	0.190585i
$727$	26.2617	−	6.47292i	0.973991	−	0.240067i	0.279960	−	0.960012i	$-0.409679\pi$
$727$	26.2617	−	6.47292i	0.973991	−	0.240067i	0.694032	+	0.719945i	$0.255833\pi$
$728$	28.8504	+	6.87222i	1.06927	+	0.254701i
$729$	−17.7451	−	4.37378i	−0.657227	−	0.161992i
$730$	27.0946	+	24.0037i	1.00282	+	0.888418i
$731$	0.251492	−	2.07122i	0.00930178	−	0.0766070i
$732$	10.3516	+	5.43294i	0.382606	+	0.200807i
$733$	−20.6521	+	10.8391i	−0.762803	+	0.400350i	−0.800803	−	0.598928i	$-0.795594\pi$
$733$	−20.6521	+	10.8391i	−0.762803	+	0.400350i	0.0379998	+	0.999278i	$0.487901\pi$
$734$	−6.36047	−	16.7712i	−0.234769	−	0.619036i
$735$	−22.9764	−	20.3553i	−0.847498	−	0.750817i
$736$	0.512483	+	4.22068i	0.0188904	+	0.155576i
$737$	23.2782	−	5.73757i	0.857464	−	0.211346i
$738$	−1.29560	−	1.14780i	−0.0476915	−	0.0422510i
$739$	−36.8832	+	32.6757i	−1.35677	+	1.20199i	−0.398145	+	0.917322i	$0.630346\pi$
$739$	−36.8832	+	32.6757i	−1.35677	+	1.20199i	−0.958625	+	0.284671i	$0.908116\pi$
$740$	5.23407	+	2.74705i	0.192408	+	0.100984i
$741$	38.8655	−	34.9778i	1.42776	−	1.28494i
$742$	−61.8194	+	32.4453i	−2.26946	+	1.19111i
$743$	11.3772	−	29.9991i	0.417388	−	1.10056i	−0.547247	−	0.836971i	$-0.684324\pi$
$743$	11.3772	−	29.9991i	0.417388	−	1.10056i	0.964635	−	0.263590i	$-0.0849067\pi$
$744$	−3.92708	−	32.3424i	−0.143974	−	1.18573i
$745$	8.23925	−	4.32429i	0.301863	−	0.158430i
$746$	−50.8275			−1.86093
$747$	2.74057	−	1.43836i	0.100272	−	0.0526270i
$748$	2.95220	−	2.61542i	0.107943	−	0.0956294i
$749$	−7.33656	−	10.6288i	−0.268072	−	0.388370i
$750$	30.8343	+	27.3168i	1.12591	+	0.997468i
$751$	−23.3044	−	33.7623i	−0.850391	−	1.23200i	−0.970946	−	0.239297i	$-0.923083\pi$
$751$	−23.3044	−	33.7623i	−0.850391	−	1.23200i	0.120555	−	0.992707i	$-0.461532\pi$
$752$	11.5981	+	30.5818i	0.422941	+	1.11520i
$753$	−2.98164	−	7.86194i	−0.108657	−	0.286505i
$754$	9.83599	+	14.0143i	0.358206	+	0.510371i
$755$	28.9683	−	76.3830i	1.05426	−	2.77986i
$756$	−6.45037			−0.234598
$757$	11.5756	+	30.5224i	0.420723	+	1.10936i	0.963082	+	0.269209i	$0.0867623\pi$
$757$	11.5756	+	30.5224i	0.420723	+	1.10936i	−0.542358	+	0.840147i	$0.682469\pi$
$758$	−1.95206	+	16.0767i	−0.0709022	+	0.583932i
$759$	8.13324	+	4.26865i	0.295218	+	0.154942i
$760$	−38.8388	−	56.2677i	−1.40883	−	2.04104i
$761$	18.1757	+	26.3321i	0.658869	+	0.954537i	0.999895	+	0.0144832i	$0.00461031\pi$
$761$	18.1757	+	26.3321i	0.658869	+	0.954537i	−0.341026	+	0.940054i	$0.610774\pi$
$762$	−36.5518	−	19.1838i	−1.32413	−	0.694957i
$763$	−1.69967	+	13.9980i	−0.0615320	+	0.506762i
$764$	1.03233	+	2.72202i	0.0373483	+	0.0984793i
$765$	−8.61625			−0.311521
$766$	8.62838	−	22.7512i	0.311756	−	0.822033i
$767$	10.4208	+	5.36580i	0.376275	+	0.193748i
$768$	6.75609

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)

\(f(q)\)	\(=\)	\(q+(-0.885893 + 1.28344i) q^{2} +(-1.70070 + 0.892595i) q^{3} +(-0.153196 - 0.403946i) q^{4} +(2.77189 + 2.45568i) q^{5} +(0.361046 - 2.97348i) q^{6} +(3.26613 + 0.805028i) q^{7} +(-2.37420 - 0.585188i) q^{8} +(0.391453 - 0.567117i) q^{9} +O(q^{10})\)	\(q+(-0.885893 + 1.28344i) q^{2} +(-1.70070 + 0.892595i) q^{3} +(-0.153196 - 0.403946i) q^{4} +(2.77189 + 2.45568i) q^{5} +(0.361046 - 2.97348i) q^{6} +(3.26613 + 0.805028i) q^{7} +(-2.37420 - 0.585188i) q^{8} +(0.391453 - 0.567117i) q^{9} +(-5.60732 + 1.38208i) q^{10} +(-1.53597 - 2.22524i) q^{11} +(0.621101 + 0.550247i) q^{12} +(-3.49393 + 0.890203i) q^{13} +(-3.92664 + 3.47870i) q^{14} +(-6.90608 - 1.70220i) q^{15} +(3.50108 - 3.10169i) q^{16} +(-3.27833 - 0.808035i) q^{17} +(0.381074 + 1.00481i) q^{18} +7.55032 q^{19} +(0.567318 - 1.49590i) q^{20} +(-6.27326 + 1.54622i) q^{21} +4.21667 q^{22} +1.76869 q^{23} +(4.56013 - 1.12397i) q^{24} +(1.05033 + 8.65023i) q^{25} +(1.95273 - 5.27287i) q^{26} +(0.535009 - 4.40619i) q^{27} +(-0.175171 - 1.44266i) q^{28} +(-1.72976 + 2.50599i) q^{29} +(8.30271 - 7.35556i) q^{30} +(0.836152 - 6.88633i) q^{31} +(0.289754 + 2.38634i) q^{32} +(4.59846 + 2.41346i) q^{33} +(3.94131 - 3.49170i) q^{34} +(7.07646 + 10.2520i) q^{35} +(-0.289054 - 0.0712453i) q^{36} +(-0.445358 + 3.66786i) q^{37} +(-6.68878 + 9.69037i) q^{38} +(5.14753 - 4.63263i) q^{39} +(-5.14399 - 7.45236i) q^{40} +(-1.42618 + 0.748516i) q^{41} +(3.57296 - 9.42112i) q^{42} +(0.0744845 + 0.613435i) q^{43} +(-0.663571 + 0.961348i) q^{44} +(2.47772 - 0.610704i) q^{45} +(-1.56687 + 2.27000i) q^{46} +(-2.47961 + 6.53820i) q^{47} +(-3.18573 + 8.40008i) q^{48} +(3.82131 + 2.00558i) q^{49} +(-12.0325 - 6.31515i) q^{50} +(6.29669 - 1.55199i) q^{51} +(0.894851 + 1.27498i) q^{52} +(12.9219 + 3.18497i) q^{53} +(5.18111 + 4.59007i) q^{54} +(1.20693 - 9.93999i) q^{55} +(-7.28334 - 3.82259i) q^{56} +(-12.8408 + 6.73938i) q^{57} +(-1.68390 - 4.44008i) q^{58} +(-2.43331 - 2.15572i) q^{59} +(0.370392 + 3.05045i) q^{60} +(13.6795 - 3.37169i) q^{61} +(8.09744 + 7.17370i) q^{62} +(1.73508 - 1.53715i) q^{63} +(4.96386 + 2.60523i) q^{64} +(-11.8708 - 6.11243i) q^{65} +(-7.17127 + 3.76377i) q^{66} +(-3.14424 + 8.29068i) q^{67} +(0.175825 + 1.44805i) q^{68} +(-3.00800 + 1.57872i) q^{69} -19.4268 q^{70} +(4.18318 - 2.19550i) q^{71} +(-1.26126 + 1.11738i) q^{72} +(-3.56058 - 5.15839i) q^{73} +(-4.31293 - 3.82092i) q^{74} +(-9.50744 - 13.7739i) q^{75} +(-1.15668 - 3.04992i) q^{76} +(-3.22530 - 8.50442i) q^{77} +(1.38553 + 10.7105i) q^{78} +(3.79832 - 10.0153i) q^{79} +17.3214 q^{80} +(3.75613 + 9.90410i) q^{81} +(0.302768 - 2.49352i) q^{82} +(3.97704 + 2.08731i) q^{83} +(1.58563 + 2.29718i) q^{84} +(-7.10289 - 10.2903i) q^{85} +(-0.853291 - 0.447842i) q^{86} +(0.704964 - 5.80590i) q^{87} +(2.34452 + 6.18200i) q^{88} -9.93317 q^{89} +(-1.41120 + 3.72102i) q^{90} +(-12.1282 + 0.0948039i) q^{91} +(-0.270956 - 0.714453i) q^{92} +(4.72466 + 12.4579i) q^{93} +(-6.19470 - 8.97458i) q^{94} +(20.9287 + 18.5412i) q^{95} +(-2.62282 - 3.79980i) q^{96} +(-1.36959 + 1.21335i) q^{97} +(-5.95932 + 3.12769i) q^{98} -1.86323 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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