LMFDB - Embedded newform 169.2.g.a.14.8

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			14.8
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0291084 - 0.0421708i) q^{2} +(2.28283 - 1.19812i) q^{3} +(0.708279 + 1.86758i) q^{4} +(-2.44658 - 2.16748i) q^{5} +(0.0159238 - 0.131144i) q^{6} +(1.95389 + 0.481590i) q^{7} +(0.198879 + 0.0490192i) q^{8} +(2.07162 - 3.00127i) q^{9} +O(q^{10})$	\(q+(0.0291084 - 0.0421708i) q^{2} +(2.28283 - 1.19812i) q^{3} +(0.708279 + 1.86758i) q^{4} +(-2.44658 - 2.16748i) q^{5} +(0.0159238 - 0.131144i) q^{6} +(1.95389 + 0.481590i) q^{7} +(0.198879 + 0.0490192i) q^{8} +(2.07162 - 3.00127i) q^{9} +(-0.162620 + 0.0400823i) q^{10} +(-0.973026 - 1.40967i) q^{11} +(3.85447 + 3.41476i) q^{12} +(0.791320 + 3.51764i) q^{13} +(0.0771835 - 0.0683786i) q^{14} +(-8.18203 - 2.01669i) q^{15} +(-2.98226 + 2.64205i) q^{16} +(-3.06904 - 0.756451i) q^{17} +(-0.0662641 - 0.174724i) q^{18} -3.47634 q^{19} +(2.31508 - 6.10435i) q^{20} +(5.03740 - 1.24161i) q^{21} -0.0877702 q^{22} +5.13219 q^{23} +(0.512737 - 0.126378i) q^{24} +(0.685095 + 5.64227i) q^{25} +(0.171376 + 0.0690223i) q^{26} +(0.201003 - 1.65541i) q^{27} +(0.484490 + 3.99014i) q^{28} +(-4.23710 + 6.13850i) q^{29} +(-0.323211 + 0.286340i) q^{30} +(0.953821 - 7.85543i) q^{31} +(0.0739878 + 0.609344i) q^{32} +(-3.91021 - 2.05224i) q^{33} +(-0.121235 + 0.107405i) q^{34} +(-3.73650 - 5.41326i) q^{35} +(7.07239 + 1.74319i) q^{36} +(-0.254397 + 2.09515i) q^{37} +(-0.101191 + 0.146600i) q^{38} +(6.02101 + 7.08209i) q^{39} +(-0.380324 - 0.550995i) q^{40} +(-6.52287 + 3.42347i) q^{41} +(0.0942710 - 0.248572i) q^{42} +(-0.847945 - 6.98346i) q^{43} +(1.94350 - 2.81564i) q^{44} +(-11.5736 + 2.85263i) q^{45} +(0.149390 - 0.216428i) q^{46} +(-1.14272 + 3.01309i) q^{47} +(-3.64249 + 9.60445i) q^{48} +(-2.61245 - 1.37112i) q^{49} +(0.257881 + 0.135346i) q^{50} +(-7.91243 + 1.95024i) q^{51} +(-6.00900 + 3.96932i) q^{52} +(2.86347 + 0.705782i) q^{53} +(-0.0639591 - 0.0566628i) q^{54} +(-0.674849 + 5.55788i) q^{55} +(0.364979 + 0.191556i) q^{56} +(-7.93591 + 4.16508i) q^{57} +(0.135530 + 0.357364i) q^{58} +(4.47563 + 3.96506i) q^{59} +(-2.02883 - 16.7089i) q^{60} +(13.2261 - 3.25994i) q^{61} +(-0.303505 - 0.268882i) q^{62} +(5.49310 - 4.86646i) q^{63} +(-7.02791 - 3.68853i) q^{64} +(5.68839 - 10.3214i) q^{65} +(-0.200364 + 0.105159i) q^{66} +(-2.93446 + 7.73754i) q^{67} +(-0.761007 - 6.26745i) q^{68} +(11.7159 - 6.14899i) q^{69} -0.337045 q^{70} +(8.57507 - 4.50054i) q^{71} +(0.559122 - 0.495339i) q^{72} +(-4.85564 - 7.03461i) q^{73} +(0.0809489 + 0.0717145i) q^{74} +(8.32408 + 12.0595i) q^{75} +(-2.46222 - 6.49234i) q^{76} +(-1.22230 - 3.22294i) q^{77} +(0.473919 - 0.0477628i) q^{78} +(2.94795 - 7.77311i) q^{79} +13.0229 q^{80} +(2.35500 + 6.20963i) q^{81} +(-0.0455000 + 0.374726i) q^{82} +(-10.8397 - 5.68913i) q^{83} +(5.88668 + 8.52832i) q^{84} +(5.86906 + 8.50280i) q^{85} +(-0.319180 - 0.167519i) q^{86} +(-2.31791 + 19.0897i) q^{87} +(-0.124413 - 0.328051i) q^{88} +15.2083 q^{89} +(-0.216590 + 0.571102i) q^{90} +(-0.147912 + 7.25417i) q^{91} +(3.63502 + 9.58476i) q^{92} +(-7.23435 - 19.0754i) q^{93} +(0.0938019 + 0.135895i) q^{94} +(8.50515 + 7.53490i) q^{95} +(0.898970 + 1.30238i) q^{96} +(11.1691 - 9.89497i) q^{97} +(-0.133865 + 0.0702579i) q^{98} -6.24655 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 $

$2$	0.0291084	−	0.0421708i	0.0205827	−	0.0298192i	−0.812557	−	0.582881i	$-0.801925\pi$
$2$	0.0291084	−	0.0421708i	0.0205827	−	0.0298192i	0.833140	+	0.553062i	$0.186541\pi$
$3$	2.28283	−	1.19812i	1.31799	−	0.691736i	0.348605	−	0.937270i	$-0.386656\pi$
$3$	2.28283	−	1.19812i	1.31799	−	0.691736i	0.969388	+	0.245534i	$0.0789632\pi$
$4$	0.708279	+	1.86758i	0.354139	+	0.933789i
$5$	−2.44658	−	2.16748i	−1.09414	−	0.969326i	−0.0944861	−	0.995526i	$-0.530121\pi$
$5$	−2.44658	−	2.16748i	−1.09414	−	0.969326i	−0.999657	+	0.0262002i	$0.991659\pi$
$6$	0.0159238	−	0.131144i	0.00650086	−	0.0535394i
$7$	1.95389	+	0.481590i	0.738500	+	0.182024i	0.590584	−	0.806976i	$-0.298897\pi$
$7$	1.95389	+	0.481590i	0.738500	+	0.182024i	0.147916	+	0.989000i	$0.452744\pi$
$8$	0.198879	+	0.0490192i	0.0703142	+	0.0173309i
$9$	2.07162	−	3.00127i	0.690542	−	1.00042i
$10$	−0.162620	+	0.0400823i	−0.0514250	+	0.0126751i
$11$	−0.973026	−	1.40967i	−0.293378	−	0.425032i	0.648383	−	0.761315i	$-0.275446\pi$
$11$	−0.973026	−	1.40967i	−0.293378	−	0.425032i	−0.941761	+	0.336283i	$0.890830\pi$
$12$	3.85447	+	3.41476i	1.11269	+	0.985756i
$13$	0.791320	+	3.51764i	0.219473	+	0.975619i
$13$	0.791320	+	3.51764i	0.219473	+	0.975619i
$14$	0.0771835	−	0.0683786i	0.0206282	−	0.0182750i
$15$	−8.18203	−	2.01669i	−2.11259	−	0.520707i
$16$	−2.98226	+	2.64205i	−0.745564	+	0.660512i
$17$	−3.06904	−	0.756451i	−0.744352	−	0.183466i	−0.151140	−	0.988512i	$-0.548294\pi$
$17$	−3.06904	−	0.756451i	−0.744352	−	0.183466i	−0.593212	+	0.805046i	$0.702141\pi$
$18$	−0.0662641	−	0.174724i	−0.0156186	−	0.0411829i
$19$	−3.47634			−0.797528			−0.398764	−	0.917054i	$-0.630561\pi$
$19$	−3.47634			−0.797528			−0.398764	+	0.917054i	$0.630561\pi$
$20$	2.31508	−	6.10435i	0.517667	−	1.36497i
$21$	5.03740	−	1.24161i	1.09925	−	0.270941i
$22$	−0.0877702			−0.0187127
$23$	5.13219			1.07014			0.535068	−	0.844809i	$-0.320286\pi$
$23$	5.13219			1.07014			0.535068	+	0.844809i	$0.320286\pi$
$24$	0.512737	−	0.126378i	0.104662	−	0.0257969i
$25$	0.685095	+	5.64227i	0.137019	+	1.12845i
$26$	0.171376	+	0.0690223i	0.0336096	+	0.0135364i
$27$	0.201003	−	1.65541i	0.0386831	−	0.318584i
$28$	0.484490	+	3.99014i	0.0915600	+	0.754065i
$29$	−4.23710	+	6.13850i	−0.786810	+	1.13989i	0.200283	+	0.979738i	$0.435814\pi$
$29$	−4.23710	+	6.13850i	−0.786810	+	1.13989i	−0.987092	+	0.160153i	$0.948801\pi$
$30$	−0.323211	+	0.286340i	−0.0590100	+	0.0522783i
$31$	0.953821	−	7.85543i	0.171311	−	1.41088i	−0.612791	−	0.790245i	$-0.709953\pi$
$31$	0.953821	−	7.85543i	0.171311	−	1.41088i	0.784103	−	0.620631i	$-0.213124\pi$
$32$	0.0739878	+	0.609344i	0.0130793	+	0.107718i
$33$	−3.91021	−	2.05224i	−0.680681	−	0.357249i
$34$	−0.121235	+	0.107405i	−0.0207916	+	0.0184198i
$35$	−3.73650	−	5.41326i	−0.631584	−	0.915007i
$36$	7.07239	+	1.74319i	1.17873	+	0.290531i
$37$	−0.254397	+	2.09515i	−0.0418226	+	0.344440i	0.956745	+	0.290929i	$0.0939643\pi$
$37$	−0.254397	+	2.09515i	−0.0418226	+	0.344440i	−0.998567	+	0.0535111i	$0.982959\pi$
$38$	−0.101191	+	0.146600i	−0.0164153	+	0.0237817i
$39$	6.02101	+	7.08209i	0.964134	+	1.13404i
$40$	−0.380324	−	0.550995i	−0.0601345	−	0.0871199i
$41$	−6.52287	+	3.42347i	−1.01870	+	0.534656i	−0.889487	−	0.456961i	$-0.848938\pi$
$41$	−6.52287	+	3.42347i	−1.01870	+	0.534656i	−0.129215	+	0.991617i	$0.541246\pi$
$42$	0.0942710	−	0.248572i	0.0145463	−	0.0383555i
$43$	−0.847945	−	6.98346i	−0.129310	−	1.06497i	−0.902469	−	0.430755i	$-0.858247\pi$
$43$	−0.847945	−	6.98346i	−0.129310	−	1.06497i	0.773159	−	0.634213i	$-0.218676\pi$
$44$	1.94350	−	2.81564i	0.292993	−	0.424474i
$45$	−11.5736	+	2.85263i	−1.72529	+	0.425245i
$46$	0.149390	−	0.216428i	0.0220263	−	0.0319106i
$47$	−1.14272	+	3.01309i	−0.166682	+	0.439505i	−0.992167	−	0.124920i	$-0.960133\pi$
$47$	−1.14272	+	3.01309i	−0.166682	+	0.439505i	0.825485	+	0.564425i	$0.190902\pi$
$48$	−3.64249	+	9.60445i	−0.525748	+	1.38628i
$49$	−2.61245	−	1.37112i	−0.373207	−	0.195874i
$50$	0.257881	+	0.135346i	0.0364698	+	0.0191409i
$51$	−7.91243	+	1.95024i	−1.10796	+	0.273088i
$52$	−6.00900	+	3.96932i	−0.833298	+	0.550446i
$53$	2.86347	+	0.705782i	0.393328	+	0.0969466i	0.431019	−	0.902343i	$-0.358154\pi$
$53$	2.86347	+	0.705782i	0.393328	+	0.0969466i	−0.0376912	+	0.999289i	$0.512000\pi$
$54$	−0.0639591	−	0.0566628i	−0.00870373	−	0.00771083i
$55$	−0.674849	+	5.55788i	−0.0909967	+	0.749425i
$56$	0.364979	+	0.191556i	0.0487724	+	0.0255977i
$57$	−7.93591	+	4.16508i	−1.05114	+	0.551679i
$58$	0.135530	+	0.357364i	0.0177960	+	0.0469241i
$59$	4.47563	+	3.96506i	0.582677	+	0.516207i	0.902169	−	0.431382i	$-0.141974\pi$
$59$	4.47563	+	3.96506i	0.582677	+	0.516207i	−0.319492	+	0.947589i	$0.603512\pi$
$60$	−2.02883	−	16.7089i	−0.261921	−	2.15712i
$61$	13.2261	−	3.25994i	1.69343	−	0.417392i	0.729590	−	0.683885i	$-0.239711\pi$
$61$	13.2261	−	3.25994i	1.69343	−	0.417392i	0.963837	+	0.266493i	$0.0858649\pi$
$62$	−0.303505	−	0.268882i	−0.0385452	−	0.0341481i
$63$	5.49310	−	4.86646i	0.692066	−	0.613117i
$64$	−7.02791	−	3.68853i	−0.878489	−	0.461067i
$65$	5.68839	−	10.3214i	0.705558	−	1.28021i
$66$	−0.200364	+	0.105159i	−0.0246632	+	0.0129442i
$67$	−2.93446	+	7.73754i	−0.358501	+	0.945291i	0.627509	+	0.778609i	$0.284074\pi$
$67$	−2.93446	+	7.73754i	−0.358501	+	0.945291i	−0.986011	+	0.166682i	$0.946695\pi$
$68$	−0.761007	−	6.26745i	−0.0922856	−	0.760040i
$69$	11.7159	−	6.14899i	1.41043	−	0.740251i
$70$	−0.337045			−0.0402845
$71$	8.57507	−	4.50054i	1.01767	−	0.534116i	0.128511	−	0.991708i	$-0.458980\pi$
$71$	8.57507	−	4.50054i	1.01767	−	0.534116i	0.889162	+	0.457592i	$0.151288\pi$
$72$	0.559122	−	0.495339i	0.0658931	−	0.0583762i
$73$	−4.85564	−	7.03461i	−0.568309	−	0.823338i	0.428468	−	0.903557i	$-0.359054\pi$
$73$	−4.85564	−	7.03461i	−0.568309	−	0.823338i	−0.996777	+	0.0802187i	$0.974438\pi$
$74$	0.0809489	+	0.0717145i	0.00941012	+	0.00833664i
$75$	8.32408	+	12.0595i	0.961182	+	1.39251i
$76$	−2.46222	−	6.49234i	−0.282436	−	0.744723i
$77$	−1.22230	−	3.22294i	−0.139294	−	0.367288i
$78$	0.473919	−	0.0477628i	0.0536608	−	0.00540807i
$79$	2.94795	−	7.77311i	0.331670	−	0.874543i	−0.660633	−	0.750709i	$-0.729712\pi$
$79$	2.94795	−	7.77311i	0.331670	−	0.874543i	0.992303	−	0.123834i	$-0.0395189\pi$
$80$	13.0229			1.45601
$81$	2.35500	+	6.20963i	0.261667	+	0.689959i
$82$	−0.0455000	+	0.374726i	−0.00502464	+	0.0413816i
$83$	−10.8397	−	5.68913i	−1.18982	−	0.624463i	−0.250700	−	0.968065i	$-0.580661\pi$
$83$	−10.8397	−	5.68913i	−1.18982	−	0.624463i	−0.939116	+	0.343601i	$0.888353\pi$
$84$	5.88668	+	8.52832i	0.642289	+	0.930517i
$85$	5.86906	+	8.50280i	0.636589	+	0.922258i
$86$	−0.319180	−	0.167519i	−0.0344181	−	0.0180640i
$87$	−2.31791	+	19.0897i	−0.248506	+	2.04663i
$88$	−0.124413	−	0.328051i	−0.0132625	−	0.0349703i
$89$	15.2083			1.61208			0.806038	−	0.591863i	$-0.201607\pi$
$89$	15.2083			1.61208			0.806038	+	0.591863i	$0.201607\pi$
$90$	−0.216590	+	0.571102i	−0.0228306	+	0.0601994i
$91$	−0.147912	+	7.25417i	−0.0155053	+	0.760444i
$92$	3.63502	+	9.58476i	0.378977	+	0.999281i
$93$	−7.23435	−	19.0754i	−0.750167	−	1.97803i
$94$	0.0938019	+	0.135895i	0.00967492	+	0.0140165i
$95$	8.50515	+	7.53490i	0.872610	+	0.773065i
$96$	0.898970	+	1.30238i	0.0917508	+	0.132924i
$97$	11.1691	−	9.89497i	1.13405	−	1.00468i	0.134146	−	0.990962i	$-0.457171\pi$
$97$	11.1691	−	9.89497i	1.13405	−	1.00468i	0.999906	−	0.0137205i	$-0.00436751\pi$
$98$	−0.133865	+	0.0702579i	−0.0135224	+	0.00709712i
$99$	−6.24655			−0.627801
$100$	−10.0521	+	5.27576i	−1.00521	+	0.527576i
$101$	−1.47123	−	12.1166i	−0.146393	−	1.20565i	−0.861912	−	0.507058i	$-0.830733\pi$
$101$	−1.47123	−	12.1166i	−0.146393	−	1.20565i	0.715519	−	0.698593i	$-0.246190\pi$
$102$	−0.148075	+	0.390441i	−0.0146616	+	0.0386595i
$103$	10.6432	−	5.58597i	1.04870	−	0.550402i	0.149876	−	0.988705i	$-0.452112\pi$
$103$	10.6432	−	5.58597i	1.04870	−	0.550402i	0.898828	+	0.438303i	$0.144420\pi$
$104$	−0.0150554	+	0.738374i	−0.00147630	+	0.0724035i
$105$	−15.0155	−	7.88076i	−1.46537	−	0.769084i
$106$	0.113114	−	0.100211i	0.0109866	−	0.00973331i
$107$	8.99305	+	7.96715i	0.869391	+	0.770213i	0.974533	−	0.224244i	$-0.0719912\pi$
$107$	8.99305	+	7.96715i	0.869391	+	0.770213i	−0.105142	+	0.994457i	$0.533530\pi$
$108$	3.23397	−	0.797103i	0.311189	−	0.0767013i
$109$	1.48178	+	12.2036i	0.141929	+	1.16889i	0.873395	+	0.487013i	$0.161913\pi$
$109$	1.48178	+	12.2036i	0.141929	+	1.16889i	−0.731466	+	0.681878i	$0.761163\pi$
$110$	0.214737	+	0.190240i	0.0204743	+	0.0181387i
$111$	1.92950	+	5.08766i	0.183140	+	0.482900i
$112$	−7.09938	+	3.72604i	−0.670828	+	0.352078i
$113$	−13.6566	−	7.16752i	−1.28470	−	0.674263i	−0.322492	−	0.946572i	$-0.604520\pi$
$113$	−13.6566	−	7.16752i	−1.28470	−	0.674263i	−0.962210	+	0.272309i	$0.912213\pi$
$114$	−0.0553566	+	0.455902i	−0.00518462	+	0.0426992i
$115$	−12.5563	−	11.1239i	−1.17088	−	1.03731i
$116$	−14.4652	−	3.56534i	−1.34306	−	0.331034i
$117$	12.1967	+	4.91227i	1.12759	+	0.454140i
$118$	0.297488	−	0.0733242i	0.0273860	−	0.00675004i
$119$	−5.63226	−	2.95604i	−0.516309	−	0.270980i
$120$	−1.52837	−	0.802153i	−0.139521	−	0.0732262i
$121$	2.86026	−	7.54188i	0.260024	−	0.685626i
$122$	0.247516	−	0.652646i	0.0224090	−	0.0590878i
$123$	−10.7889	+	15.6304i	−0.972801	+	1.40935i
$124$	15.3462	−	3.78250i	1.37813	−	0.339678i
$125$	1.26949	−	1.83917i	0.113546	−	0.164500i
$126$	−0.0453272	−	0.373303i	−0.00403807	−	0.0332565i
$127$	−3.82809	+	10.0939i	−0.339688	+	0.895684i	0.650944	+	0.759126i	$0.274373\pi$
$127$	−3.82809	+	10.0939i	−0.339688	+	0.895684i	−0.990632	+	0.136558i	$0.956396\pi$
$128$	−1.44714	+	0.759518i	−0.127910	+	0.0671325i
$129$	−10.3028	−	14.9261i	−0.907107	−	1.31417i
$130$	−0.269680	−	0.540322i	−0.0236525	−	0.0473894i
$131$	8.68094	−	12.5765i	0.758458	−	1.09882i	−0.233514	−	0.972353i	$-0.575022\pi$
$131$	8.68094	−	12.5765i	0.758458	−	1.09882i	0.991971	−	0.126462i	$-0.0403622\pi$
$132$	1.06319	−	8.75618i	0.0925390	−	0.762128i
$133$	−6.79239	−	1.67417i	−0.588975	−	0.145169i
$134$	0.240881	+	0.348976i	0.0208089	+	0.0301469i
$135$	−4.07984	+	3.61442i	−0.351137	+	0.311080i
$136$	−0.573287	−	0.300884i	−0.0491589	−	0.0258006i
$137$	−1.57337	−	12.9579i	−0.134422	−	1.10707i	−0.891270	−	0.453474i	$-0.850184\pi$
$137$	−1.57337	−	12.9579i	−0.134422	−	1.10707i	0.756847	−	0.653592i	$-0.226739\pi$
$138$	0.0817239	−	0.673057i	0.00695680	−	0.0572944i
$139$	−10.0227	+	8.87938i	−0.850118	+	0.753139i	−0.970886	−	0.239542i	$-0.923003\pi$
$139$	−10.0227	+	8.87938i	−0.850118	+	0.753139i	0.120768	+	0.992681i	$0.461464\pi$
$140$	7.46319	−	10.8123i	0.630755	−	0.913806i
$141$	1.00143	+	8.24749i	0.0843354	+	0.694564i
$142$	0.0598150	−	0.492621i	0.00501957	−	0.0413398i
$143$	4.18875	−	4.53826i	0.350281	−	0.379508i
$144$	1.75138	+	14.4239i	0.145948	+	1.20199i
$145$	23.6715	−	5.83449i	1.96581	−	0.484528i
$146$	−0.437995			−0.0362487
$147$	−7.60654			−0.627377
$148$	−4.09303	+	1.00884i	−0.336445	+	0.0829263i
$149$	−3.60740	+	9.51192i	−0.295529	+	0.779247i	0.702205	+	0.711975i	$0.252199\pi$
$149$	−3.60740	+	9.51192i	−0.295529	+	0.779247i	−0.997735	+	0.0672725i	$0.978570\pi$
$150$	0.750859			0.0613074
$151$	4.20103	+	11.0772i	0.341875	+	0.901449i	0.990146	+	0.140040i	$0.0447230\pi$
$151$	4.20103	+	11.0772i	0.341875	+	0.901449i	−0.648271	+	0.761409i	$0.724508\pi$
$152$	−0.691371	−	0.170408i	−0.0560776	−	0.0138219i
$153$	−8.62822	+	7.64393i	−0.697550	+	0.617975i
$154$	−0.171493	−	0.0422692i	−0.0138193	−	0.00340615i
$155$	−19.3601	+	17.1515i	−1.55504	+	1.37764i
$156$	−8.96179	+	16.2608i	−0.717517	+	1.30191i
$157$	−9.34712	−	8.28083i	−0.745982	−	0.660882i	0.201936	−	0.979399i	$-0.435277\pi$
$157$	−9.34712	−	8.28083i	−0.745982	−	0.660882i	−0.947917	+	0.318517i	$0.896815\pi$
$158$	−0.241988	−	0.350580i	−0.0192515	−	0.0278906i
$159$	7.38243	−	1.81961i	0.585465	−	0.144304i
$160$	1.13972	−	1.65118i	0.0901031	−	0.130537i
$161$	10.0277	+	2.47161i	0.790295	+	0.194790i
$162$	0.330415	+	0.0814401i	0.0259599	+	0.00639854i
$163$	−1.50104	+	12.3622i	−0.117571	+	0.968281i	0.807863	+	0.589371i	$0.200624\pi$
$163$	−1.50104	+	12.3622i	−0.117571	+	0.968281i	−0.925433	+	0.378910i	$0.876299\pi$
$164$	−11.0136	−	9.75720i	−0.860018	−	0.761910i
$165$	5.11846	+	13.4963i	0.398471	+	1.05068i
$166$	−0.555442	+	0.291519i	−0.0431107	+	0.0226262i
$167$	2.45113	−	3.55108i	0.189674	−	0.274791i	−0.716597	−	0.697488i	$-0.754301\pi$
$167$	2.45113	−	3.55108i	0.189674	−	0.274791i	0.906271	+	0.422697i	$0.138917\pi$
$168$	1.06269			0.0819886
$169$	−11.7476	+	5.56716i	−0.903663	+	0.428243i
$170$	0.529409			0.0406038
$171$	−7.20168	+	10.4334i	−0.550726	+	0.797865i
$172$	12.4416	−	6.52984i	0.948661	−	0.497896i
$173$	−0.745801	−	1.96652i	−0.0567022	−	0.149511i	0.903672	−	0.428225i	$-0.140861\pi$
$173$	−0.745801	−	1.96652i	−0.0567022	−	0.149511i	−0.960374	+	0.278714i	$0.910092\pi$
$174$	0.737557	+	0.653419i	0.0559141	+	0.0495356i
$175$	−1.37866	+	11.3543i	−0.104217	+	0.858303i
$176$	6.62623	+	1.63322i	0.499471	+	0.123109i
$177$	14.9677	+	3.68921i	1.12504	+	0.277298i
$178$	0.442689	−	0.641346i	0.0331810	−	0.0480709i
$179$	−8.76364	+	2.16004i	−0.655025	+	0.161449i	−0.552803	−	0.833312i	$-0.686442\pi$
$179$	−8.76364	+	2.16004i	−0.655025	+	0.161449i	−0.102223	+	0.994762i	$0.532595\pi$
$180$	−13.5248	−	19.5941i	−1.00808	−	1.46046i
$181$	12.5001	+	11.0741i	0.929126	+	0.823134i	0.984509	−	0.175331i	$-0.0560997\pi$
$181$	12.5001	+	11.0741i	0.929126	+	0.823134i	−0.0553836	+	0.998465i	$0.517638\pi$
$182$	0.301608	+	0.217395i	0.0223567	+	0.0161144i
$183$	26.2871	−	23.2883i	1.94320	−	1.72152i
$184$	1.02068	+	0.251576i	0.0752458	+	0.0185464i
$185$	5.16359	−	4.57454i	0.379635	−	0.336327i
$186$	−1.01500	−	0.250176i	−0.0744237	−	0.0183438i
$187$	1.91991	+	5.06239i	0.140398	+	0.370199i
$188$	−6.43655			−0.469433
$189$	1.18997	−	3.13769i	0.0865574	−	0.228233i
$190$	0.565324	−	0.139340i	0.0410129	−	0.0101088i
$191$	−16.2634			−1.17678			−0.588388	−	0.808579i	$-0.700237\pi$
$191$	−16.2634			−1.17678			−0.588388	+	0.808579i	$0.700237\pi$
$192$	−20.4628			−1.47678
$193$	2.71363	−	0.668851i	0.195332	−	0.0481449i	−0.140436	−	0.990090i	$-0.544850\pi$
$193$	2.71363	−	0.668851i	0.195332	−	0.0481449i	0.335768	+	0.941945i	$0.391004\pi$
$194$	−0.0921638	−	0.759037i	−0.00661697	−	0.0544957i
$195$	0.619389	−	30.3773i	0.0443554	−	2.17536i
$196$	0.710328	−	5.85008i	0.0507377	−	0.417863i
$197$	0.945956	+	7.79065i	0.0673966	+	0.555061i	0.986824	+	0.161800i	$0.0517299\pi$
$197$	0.945956	+	7.79065i	0.0673966	+	0.555061i	−0.919427	+	0.393261i	$0.871347\pi$
$198$	−0.181827	+	0.263422i	−0.0129219	+	0.0187206i
$199$	2.34615	−	2.07851i	0.166314	−	0.147342i	−0.575860	−	0.817548i	$-0.695333\pi$
$199$	2.34615	−	2.07851i	0.166314	−	0.147342i	0.742175	+	0.670206i	$0.233794\pi$
$200$	−0.140329	+	1.15571i	−0.00992273	+	0.0817210i
$201$	2.57164	+	21.1793i	0.181389	+	1.49387i
$202$	−0.553793	−	0.290653i	−0.0389648	−	0.0204503i
$203$	−11.2351	+	9.95339i	−0.788546	+	0.698591i
$204$	−9.24642	−	13.3958i	−0.647379	−	0.937890i
$205$	23.3790	+	5.76241i	1.63286	+	0.402464i
$206$	0.0742410	−	0.611430i	0.00517262	−	0.0426003i
$207$	10.6320	−	15.4031i	0.738973	−	1.07059i
$208$	−11.6537	−	8.39981i	−0.808039	−	0.582422i
$209$	3.38257	+	4.90050i	0.233978	+	0.338975i
$210$	−0.769416	+	0.403821i	−0.0530947	+	0.0278663i
$211$	−3.86656	+	10.1953i	−0.266185	+	0.701873i	0.733567	+	0.679617i	$0.237854\pi$
$211$	−3.86656	+	10.1953i	−0.266185	+	0.701873i	−0.999752	+	0.0222558i	$0.992915\pi$
$212$	0.710032	+	5.84764i	0.0487652	+	0.401618i
$213$	14.1832	−	20.5480i	0.971819	−	1.40792i
$214$	0.597754	−	0.147333i	0.0408616	−	0.0100715i
$215$	−13.0619	+	18.9235i	−0.890817	+	1.29057i
$216$	0.121122	−	0.319373i	0.00824132	−	0.0217306i
$217$	5.64675	−	14.8893i	0.383327	−	1.01075i
$218$	0.557767	+	0.292738i	0.0377767	+	0.0198268i
$219$	−19.5129	−	10.2412i	−1.31856	−	0.692034i
$220$	−10.8578	+	2.67620i	−0.732030	+	0.180429i
$221$	0.232330	−	11.3944i	0.0156282	−	0.766470i
$222$	0.270715	+	0.0667253i	0.0181692	+	0.00447831i
$223$	−9.55007	−	8.46063i	−0.639520	−	0.566565i	0.279809	−	0.960056i	$-0.409729\pi$
$223$	−9.55007	−	8.46063i	−0.639520	−	0.566565i	−0.919329	+	0.393490i	$0.871267\pi$
$224$	−0.148890	+	1.22622i	−0.00994815	+	0.0819304i
$225$	18.3532	+	9.63250i	1.22355	+	0.642167i
$226$	−0.699780	+	0.367273i	−0.0465487	+	0.0244306i
$227$	4.94423	+	13.0369i	0.328160	+	0.865287i	0.992980	+	0.118283i	$0.0377391\pi$
$227$	4.94423	+	13.0369i	0.328160	+	0.865287i	−0.664820	+	0.747004i	$0.731492\pi$
$228$	−13.3995	−	11.8709i	−0.887400	−	0.786168i
$229$	−1.15497	−	9.51206i	−0.0763227	−	0.628574i	−0.979806	−	0.199951i	$-0.935922\pi$
$229$	−1.15497	−	9.51206i	−0.0763227	−	0.628574i	0.903483	−	0.428624i	$-0.141001\pi$
$230$	−0.834598	+	0.205710i	−0.0550317	+	0.0135641i
$231$	−6.65178	−	5.89296i	−0.437655	−	0.387728i
$232$	−1.14357	+	1.01312i	−0.0750793	+	0.0665144i
$233$	5.24980	+	2.75531i	0.343926	+	0.180506i	0.627838	−	0.778344i	$-0.283940\pi$
$233$	5.24980	+	2.75531i	0.343926	+	0.180506i	−0.283912	+	0.958850i	$0.591632\pi$
$234$	0.562181	−	0.371356i	0.0367509	−	0.0242763i
$235$	9.32656	−	4.89495i	0.608398	−	0.319312i
$236$	−4.23506	+	11.1669i	−0.275679	+	0.726906i
$237$	−2.58346	−	21.2767i	−0.167814	−	1.38207i
$238$	−0.288605	+	0.151471i	−0.0187075	+	0.00981843i
$239$	−4.88638			−0.316073			−0.158037	−	0.987433i	$-0.550516\pi$
$239$	−4.88638			−0.316073			−0.158037	+	0.987433i	$0.550516\pi$
$240$	29.7291	−	15.6030i	1.91900	−	1.00717i
$241$	−13.0923	+	11.5987i	−0.843347	+	0.747141i	−0.969558	−	0.244863i	$-0.921257\pi$
$241$	−13.0923	+	11.5987i	−0.843347	+	0.747141i	0.126210	+	0.992004i	$0.459719\pi$
$242$	−0.234790	−	0.340151i	−0.0150928	−	0.0218658i
$243$	16.5606	+	14.6714i	1.06236	+	0.941169i
$244$	15.4559	+	22.3918i	0.989465	+	1.43349i
$245$	3.41968	+	9.01697i	0.218476	+	0.576073i
$246$	0.345099	+	0.909951i	0.0220027	+	0.0580164i
$247$	−2.75090	−	12.2285i	−0.175036	−	0.778083i
$248$	0.574762	−	1.51552i	0.0364974	−	0.0962357i
$249$	−31.5616			−2.00013
$250$	−0.0406065	−	0.107071i	−0.00256818	−	0.00677174i
$251$	−1.80105	+	14.8330i	−0.113681	+	0.936251i	0.818562	+	0.574418i	$0.194772\pi$
$251$	−1.80105	+	14.8330i	−0.113681	+	0.936251i	−0.932243	+	0.361832i	$0.882151\pi$
$252$	12.9791	+	6.81198i	0.817609	+	0.429114i
$253$	−4.99375	−	7.23470i	−0.313955	−	0.454842i
$254$	0.314236	+	0.455249i	0.0197169	+	0.0285649i
$255$	23.5855	+	12.3786i	1.47698	+	0.775178i
$256$	1.90332	−	15.6752i	0.118957	−	0.979702i
$257$	−1.92618	−	5.07893i	−0.120152	−	0.316815i	0.861424	−	0.507886i	$-0.169573\pi$
$257$	−1.92618	−	5.07893i	−0.120152	−	0.316815i	−0.981576	+	0.191072i	$0.938804\pi$
$258$	−0.929342			−0.0578583
$259$	−1.50606	+	3.97117i	−0.0935823	+	0.246756i
$260$	23.3049	+	3.31311i	1.44531	+	0.205471i
$261$	9.64559	+	25.4333i	0.597047	+	1.57428i
$262$	−0.277673	−	0.732164i	−0.0171547	−	0.0452333i
$263$	4.39580	+	6.36842i	0.271057	+	0.392694i	0.934747	−	0.355314i	$-0.115626\pi$
$263$	4.39580	+	6.36842i	0.271057	+	0.392694i	−0.663690	+	0.748008i	$0.731011\pi$
$264$	−0.677059	−	0.599822i	−0.0416701	−	0.0369165i
$265$	−5.47593	−	7.93326i	−0.336384	−	0.487336i
$266$	−0.268317	+	0.237708i	−0.0164515	+	0.0145748i
$267$	34.7180	−	18.2214i	2.12471	−	1.11513i
$268$	−16.5289			−1.00966
$269$	16.0188	−	8.40729i	0.976681	−	0.512602i	0.100684	−	0.994918i	$-0.467897\pi$
$269$	16.0188	−	8.40729i	0.976681	−	0.512602i	0.875997	+	0.482317i	$0.160205\pi$
$270$	0.0336655	+	0.277260i	0.00204881	+	0.0168735i
$271$	−5.97535	+	15.7557i	−0.362977	+	0.957091i	0.621786	+	0.783187i	$0.286407\pi$
$271$	−5.97535	+	15.7557i	−0.362977	+	0.957091i	−0.984763	+	0.173904i	$0.944362\pi$
$272$	11.1513	−	5.85263i	0.676144	−	0.354868i
$273$	8.35372	+	16.7373i	0.505590	+	1.01298i
$274$	−0.592242	−	0.310832i	−0.0357786	−	0.0187781i
$275$	7.28713	−	6.45583i	0.439430	−	0.389301i
$276$	19.7818	+	17.5252i	1.19073	+	1.05489i
$277$	−8.88048	+	2.18884i	−0.533576	+	0.131515i	−0.496892	−	0.867812i	$-0.665526\pi$
$277$	−8.88048	+	2.18884i	−0.533576	+	0.131515i	−0.0366840	+	0.999327i	$0.511679\pi$
$278$	0.0827043	+	0.681131i	0.00496027	+	0.0408515i
$279$	−21.6003	−	19.1362i	−1.29317	−	1.14565i
$280$	−0.477757	−	1.25974i	−0.0285514	−	0.0752840i
$281$	−7.08249	+	3.71718i	−0.422506	+	0.221748i	−0.662556	−	0.749012i	$-0.730528\pi$
$281$	−7.08249	+	3.71718i	−0.422506	+	0.221748i	0.240050	+	0.970760i	$0.422836\pi$
$282$	0.376953	+	0.197840i	0.0224472	+	0.0117812i
$283$	0.653097	−	5.37874i	0.0388226	−	0.319733i	−0.960341	−	0.278830i	$-0.910053\pi$
$283$	0.653097	−	5.37874i	0.0388226	−	0.319733i	0.999163	−	0.0409030i	$-0.0130234\pi$
$284$	14.4787	+	12.8270i	0.859150	+	0.761141i
$285$	28.4435	+	7.01070i	1.68485	+	0.415278i
$286$	−0.0694543	−	0.308744i	−0.00410692	−	0.0182564i
$287$	−14.3937	+	3.54772i	−0.849631	+	0.209415i
$288$	1.98208	+	1.04028i	0.116795	+	0.0612988i
$289$	−6.20595	−	3.25713i	−0.365056	−	0.191596i
$290$	0.442993	−	1.16808i	0.0260134	−	0.0685918i
$291$	13.6418	−	35.9705i	0.799697	−	2.10863i
$292$	9.69853	−	14.0507i	0.567563	−	0.822257i
$293$	−24.1987	+	5.96444i	−1.41370	+	0.348447i	−0.870919	−	0.491426i	$-0.836476\pi$
$293$	−24.1987	+	5.96444i	−1.41370	+	0.348447i	−0.542784	+	0.839873i	$0.682630\pi$
$294$	−0.221414	+	0.320774i	−0.0129131	+	0.0187079i
$295$	−2.35579	−	19.4016i	−0.137159	−	1.12961i
$296$	−0.153297	+	0.404210i	−0.00891018	+	0.0234942i
$297$	−2.52917	+	1.32741i	−0.146757	+	0.0770241i
$298$	0.296120	+	0.429003i	0.0171538	+	0.0248515i
$299$	4.06120	+	18.0532i	0.234866	+	1.04404i
$300$	−16.6263	+	24.0874i	−0.959920	+	1.39068i
$301$	1.70637	−	14.0533i	0.0983538	−	0.810016i
$302$	0.589419	+	0.145279i	0.0339172	+	0.00835985i
$303$	−17.8758	−	25.8975i	−1.02694	−	1.48777i
$304$	10.3674	−	9.18467i	0.594608	−	0.526777i
$305$	−39.4245	−	20.6916i	−2.25744	−	1.18480i
$306$	0.0711971	+	0.586361i	0.00407007	+	0.0335200i
$307$	−0.382375	+	3.14914i	−0.0218233	+	0.179731i	−0.999545	−	0.0301762i	$-0.990393\pi$
$307$	−0.382375	+	3.14914i	−0.0218233	+	0.179731i	0.977721	+	0.209907i	$0.0673162\pi$
$308$	5.15336	−	4.56548i	0.293640	−	0.260142i
$309$	17.6039	−	25.5037i	1.00145	−	1.45085i
$310$	0.159753	+	1.31568i	0.00907335	+	0.0747257i
$311$	−0.350654	+	2.88790i	−0.0198838	+	0.163758i	−0.999268	−	0.0382472i	$-0.987823\pi$
$311$	−0.350654	+	2.88790i	−0.0198838	+	0.163758i	0.979385	+	0.202005i	$0.0647457\pi$
$312$	0.850293	+	1.70362i	0.0481384	+	0.0964486i
$313$	−2.81738	−	23.2032i	−0.159248	−	1.31152i	−0.824908	−	0.565267i	$-0.808773\pi$
$313$	−2.81738	−	23.2032i	−0.159248	−	1.31152i	0.665661	−	0.746255i	$-0.268150\pi$
$314$	−0.621289	+	0.153134i	−0.0350613	+	0.00864184i
$315$	−23.9873			−1.35153
$316$	16.6049			0.934096
$317$	−27.3623	+	6.74421i	−1.53682	+	0.378792i	−0.914702	−	0.404130i	$-0.867574\pi$
$317$	−27.3623	+	6.74421i	−1.53682	+	0.378792i	−0.622119	+	0.782922i	$0.713728\pi$
$318$	0.138156	−	0.364289i	0.00774743	−	0.0204283i
$319$	12.7761			0.715323
$320$	9.19952	+	24.2571i	0.514269	+	1.35601i
$321$	30.0752	+	7.41288i	1.67864	+	0.413747i
$322$	0.396120	−	0.350932i	0.0220749	−	0.0195567i
$323$	10.6691	+	2.62969i	0.593642	+	0.146320i
$324$	−9.92897	+	8.79630i	−0.551610	+	0.488683i
$325$	−19.3053	+	6.87476i	−1.07087	+	0.381343i
$326$	0.477630	+	0.423143i	0.0264535	+	0.0234357i
$327$	18.0040	+	26.0833i	0.995625	+	1.44241i
$328$	−1.46508	+	0.361109i	−0.0808953	+	0.0199389i
$329$	−3.68381	+	5.33692i	−0.203095	+	0.294234i
$330$	0.718138	+	0.177005i	0.0395322	+	0.00974381i
$331$	10.3507	+	2.55122i	0.568926	+	0.140228i	0.513278	−	0.858223i	$-0.328431\pi$
$331$	10.3507	+	2.55122i	0.568926	+	0.140228i	0.0556487	+	0.998450i	$0.482277\pi$
$332$	2.94734	−	24.2735i	0.161756	−	1.33218i
$333$	5.76108	+	5.10387i	0.315705	+	0.279690i
$334$	−0.0784033	−	0.206732i	−0.00429004	−	0.0113119i
$335$	23.9503	−	12.5701i	1.30855	−	0.686778i
$336$	−11.7424	+	17.0118i	−0.640602	+	0.928072i
$337$	−3.26539			−0.177877			−0.0889385	−	0.996037i	$-0.528347\pi$
$337$	−3.26539			−0.177877			−0.0889385	+	0.996037i	$0.528347\pi$
$338$	−0.107183	+	0.657458i	−0.00582998	+	0.0357610i
$339$	−39.7632			−2.15964
$340$	−11.7227	+	16.9833i	−0.635753	+	0.921048i
$341$	−12.0017	+	6.29896i	−0.649927	+	0.341108i
$342$	0.230357	+	0.607401i	0.0124563	+	0.0328445i
$343$	−14.9880	−	13.2782i	−0.809278	−	0.716958i
$344$	0.173685	−	1.43043i	0.00936448	−	0.0771235i
$345$	−41.9917	−	10.3500i	−2.26076	−	0.557227i
$346$	−0.104639	−	0.0257911i	−0.00562540	−	0.00138654i
$347$	−5.93814	+	8.60289i	−0.318776	+	0.461827i	−0.949313	−	0.314332i	$-0.898219\pi$
$347$	−5.93814	+	8.60289i	−0.318776	+	0.461827i	0.630537	+	0.776159i	$0.282835\pi$
$348$	−37.2932	+	9.19196i	−1.99913	+	0.492741i
$349$	0.465781	+	0.674800i	0.0249327	+	0.0361212i	0.835252	−	0.549867i	$-0.185322\pi$
$349$	0.465781	+	0.674800i	0.0249327	+	0.0361212i	−0.810319	+	0.585989i	$0.800706\pi$
$350$	0.438688	+	0.388644i	0.0234489	+	0.0207739i
$351$	5.98220	−	0.602902i	0.319306	−	0.0321805i
$352$	0.786983	−	0.697206i	0.0419464	−	0.0371612i
$353$	7.84864	+	1.93452i	0.417741	+	0.102964i	0.442583	−	0.896727i	$-0.354062\pi$
$353$	7.84864	+	1.93452i	0.417741	+	0.102964i	−0.0248421	+	0.999691i	$0.507908\pi$
$354$	0.591263	−	0.523813i	0.0314253	−	0.0278404i
$355$	−30.7344	−	7.57535i	−1.63121	−	0.402058i
$356$	10.7717	+	28.4027i	0.570900	+	1.50534i
$357$	−16.3992			−0.867938
$358$	−0.164005	+	0.432445i	−0.00866792	+	0.0228554i
$359$	26.3709	−	6.49984i	1.39180	−	0.343048i	0.529013	−	0.848613i	$-0.322562\pi$
$359$	26.3709	−	6.49984i	1.39180	−	0.343048i	0.862788	+	0.505565i	$0.168716\pi$
$360$	−2.44157			−0.128682
$361$	−6.91503			−0.363949
$362$	0.830863	−	0.204789i	0.0436692	−	0.0107635i
$363$	−2.50661	−	20.6438i	−0.131563	−	1.08352i
$364$	−13.6525	+	4.86174i	−0.715585	+	0.254824i
$365$	−3.36766	+	27.7352i	−0.176272	+	1.45173i
$366$	−0.216912	−	1.78643i	−0.0113382	−	0.0933784i
$367$	−7.71738	+	11.1806i	−0.402844	+	0.583620i	−0.970934	−	0.239346i	$-0.923067\pi$
$367$	−7.71738	+	11.1806i	−0.402844	+	0.583620i	0.568091	+	0.822966i	$0.307682\pi$
$368$	−15.3055	+	13.5595i	−0.797855	+	0.706837i
$369$	−3.23821	+	26.6690i	−0.168574	+	1.38833i
$370$	−0.0426082	−	0.350910i	−0.00221509	−	0.0182429i
$371$	5.25500	+	2.75804i	0.272826	+	0.143190i
$372$	30.5009	−	27.0214i	1.58140	−	1.40099i
$373$	5.36910	+	7.77848i	0.278001	+	0.402754i	0.936967	−	0.349419i	$-0.113621\pi$
$373$	5.36910	+	7.77848i	0.278001	+	0.402754i	−0.658965	+	0.752173i	$0.729006\pi$
$374$	0.269370	+	0.0663938i	0.0139288	+	0.00343314i
$375$	0.694475	−	5.71951i	0.0358625	−	0.295354i
$376$	−0.374961	+	0.543225i	−0.0193371	+	0.0280147i
$377$	−24.9460	−	10.0471i	−1.28478	−	0.517451i
$378$	−0.0976806	−	0.141515i	−0.00502415	−	0.00727874i
$379$	13.6734	−	7.17637i	0.702357	−	0.368625i	−0.0754319	−	0.997151i	$-0.524034\pi$
$379$	13.6734	−	7.17637i	0.702357	−	0.368625i	0.777789	+	0.628526i	$0.216341\pi$
$380$	−8.04800	+	21.2208i	−0.412854	+	1.08861i
$381$	3.35478	+	27.6291i	0.171870	+	1.41548i
$382$	−0.473400	+	0.685839i	−0.0242213	+	0.0350906i
$383$	−4.15529	+	1.02419i	−0.212326	+	0.0523336i	−0.344044	−	0.938954i	$-0.611797\pi$
$383$	−4.15529	+	1.02419i	−0.212326	+	0.0523336i	0.131718	+	0.991287i	$0.457951\pi$
$384$	−2.39358	+	3.46770i	−0.122147	+	0.176960i
$385$	−3.99520	+	10.5345i	−0.203614	+	0.536887i
$386$	0.0507835	−	0.133905i	0.00258481	−	0.00681560i
$387$	−22.7158	−	11.9222i	−1.15471	−	0.606039i
$388$	26.3905	+	13.8508i	1.33977	+	0.703167i
$389$	34.8144	−	8.58098i	1.76516	−	0.435073i	0.782831	−	0.622234i	$-0.213775\pi$
$389$	34.8144	−	8.58098i	1.76516	−	0.435073i	0.982329	+	0.187161i	$0.0599286\pi$
$390$	−1.26300	−	0.910354i	−0.0639547	−	0.0460976i
$391$	−15.7509	−	3.88225i	−0.796558	−	0.196334i
$392$	−0.452349	−	0.400746i	−0.0228471	−	0.0202407i
$393$	4.74892	−	39.1109i	0.239551	−	1.97288i
$394$	0.356073	+	0.186881i	0.0179387	+	0.00941495i
$395$	−24.0604	+	12.6279i	−1.21061	+	0.635378i
$396$	−4.42429	−	11.6659i	−0.222329	−	0.586234i
$397$	8.72191	+	7.72694i	0.437740	+	0.387804i	0.853010	−	0.521894i	$-0.174774\pi$
$397$	8.72191	+	7.72694i	0.437740	+	0.387804i	−0.415270	+	0.909698i	$0.636313\pi$
$398$	−0.0193597	−	0.159441i	−0.000970412	−	0.00799206i
$399$	−17.5117	+	4.31625i	−0.876683	+	0.216083i
$400$	−16.9503	−	15.0166i	−0.847513	−	0.750831i
$401$	9.69753	−	8.59126i	0.484272	−	0.429027i	−0.385332	−	0.922778i	$-0.625913\pi$
$401$	9.69753	−	8.59126i	0.484272	−	0.429027i	0.869603	+	0.493751i	$0.164375\pi$
$402$	0.968005	+	0.508048i	0.0482797	+	0.0253391i
$403$	28.3874	−	2.86095i	1.41408	−	0.142514i
$404$	21.5867	−	11.3296i	1.07398	−	0.563668i
$405$	7.69755	−	20.2968i	0.382494	−	1.00855i
$406$	0.0927079	+	0.763518i	0.00460102	+	0.0378928i
$407$	3.20100	−	1.68002i	0.158668	−	0.0832753i
$408$	−1.66921			−0.0826383
$409$	27.1453	−	14.2469i	1.34225	−	0.704466i	0.367975	−	0.929836i	$-0.380051\pi$
$409$	27.1453	−	14.2469i	1.34225	−	0.704466i	0.974273	+	0.225370i	$0.0723590\pi$
$410$	0.923531	−	0.818177i	0.0456099	−	0.0404069i
$411$	−19.1168	−	27.6955i	−0.942964	−	1.36612i
$412$	17.9706	+	15.9205i	0.885347	+	0.784349i
$413$	6.83534	+	9.90269i	0.336345	+	0.487280i
$414$	−0.340080	−	0.896717i	−0.0167140	−	0.0440712i
$415$	14.1892	+	37.4138i	0.696520	+	1.83657i
$416$	−2.08491	+	0.742449i	−0.102221	+	0.0364016i
$417$	−12.2416	+	32.2786i	−0.599476	+	1.58069i
$418$	0.305119			0.0149239
$419$	−5.47164	−	14.4275i	−0.267307	−	0.704831i	−0.999713	−	0.0239627i	$-0.992372\pi$
$419$	−5.47164	−	14.4275i	−0.267307	−	0.704831i	0.732406	−	0.680869i	$-0.238398\pi$
$420$	4.08275	−	33.6245i	0.199218	−	1.64071i
$421$	17.6470	+	9.26187i	0.860063	+	0.451396i	0.836268	−	0.548321i	$-0.184733\pi$
$421$	17.6470	+	9.26187i	0.860063	+	0.451396i	0.0237953	+	0.999717i	$0.492425\pi$
$422$	0.317394	+	0.459825i	0.0154505	+	0.0223839i
$423$	6.67582	+	9.67159i	0.324589	+	0.470249i
$424$	0.534886	+	0.280730i	0.0259764	+	0.0136335i
$425$	2.16551	−	17.8346i	0.105043	−	0.865105i
$426$	−0.453672	−	1.19624i	−0.0219805	−	0.0579578i
$427$	27.4122			1.32657
$428$	−8.50968	+	22.4382i	−0.411331	+	1.08459i
$429$	4.12481	−	15.3787i	0.199148	−	0.742491i
$430$	0.417806	+	1.10166i	0.0201484	+	0.0531269i
$431$	8.39126	+	22.1259i	0.404193	+	1.06577i	0.970399	+	0.241505i	$0.0776412\pi$
$431$	8.39126	+	22.1259i	0.404193	+	1.06577i	−0.566207	+	0.824263i	$0.691590\pi$
$432$	3.77423	+	5.46792i	0.181588	+	0.263075i
$433$	1.49922	+	1.32819i	0.0720477	+	0.0638287i	0.698378	−	0.715729i	$-0.253905\pi$
$433$	1.49922	+	1.32819i	0.0720477	+	0.0638287i	−0.626330	+	0.779558i	$0.715444\pi$
$434$	−0.463524	−	0.671530i	−0.0222499	−	0.0322345i
$435$	47.0475	−	41.6804i	2.25575	−	1.99842i
$436$	−21.7416	+	11.4109i	−1.04123	+	0.546482i
$437$	−17.8413			−0.853463
$438$	−0.999867	+	0.524771i	−0.0477755	+	0.0250745i
$439$	−1.26677	−	10.4328i	−0.0604596	−	0.497929i	−0.991212	−	0.132280i	$-0.957770\pi$
$439$	−1.26677	−	10.4328i	−0.0604596	−	0.497929i	0.930753	−	0.365649i	$-0.119153\pi$
$440$	−0.406656	+	1.07226i	−0.0193866	+	0.0511182i
$441$	−9.52710	+	5.00021i	−0.453671	+	0.238105i
$442$	−0.473748	−	0.341470i	−0.0225339	−	0.0162421i
$443$	9.75928	+	5.12206i	0.463677	+	0.243357i	0.680349	−	0.732888i	$-0.261828\pi$
$443$	9.75928	+	5.12206i	0.463677	+	0.243357i	−0.216672	+	0.976244i	$0.569520\pi$
$444$	−8.13498	+	7.20697i	−0.386069	+	0.342028i
$445$	−37.2083	−	32.9637i	−1.76384	−	1.56263i
$446$	−0.634778	+	0.156459i	−0.0300576	+	0.00740854i
$447$	3.16137	+	26.0362i	0.149528	+	1.23147i
$448$	−11.9554	−	10.5915i	−0.564839	−	0.500404i
$449$	0.315101	+	0.830852i	0.0148705	+	0.0392103i	0.942246	−	0.334922i	$-0.108710\pi$
$449$	0.315101	+	0.830852i	0.0148705	+	0.0392103i	−0.927375	+	0.374132i	$0.877941\pi$
$450$	0.940442	−	0.493582i	0.0443329	−	0.0232677i
$451$	11.1729	+	5.86399i	0.526111	+	0.276124i
$452$	3.71324	−	30.5813i	0.174656	−	1.43842i
$453$	22.8621	+	20.2540i	1.07415	+	0.951617i
$454$	0.693693	+	0.170980i	0.0325566	+	0.00802449i
$455$	16.0851	−	17.4273i	0.754083	−	0.817004i
$456$	−1.78245	+	0.439335i	−0.0834710	+	0.0205737i
$457$	4.11746	+	2.16101i	0.192607	+	0.101088i	0.558270	−	0.829659i	$-0.311465\pi$
$457$	4.11746	+	2.16101i	0.192607	+	0.101088i	−0.365663	+	0.930747i	$0.619158\pi$
$458$	−0.434750	−	0.228174i	−0.0203145	−	0.0106619i
$459$	−1.86913	+	4.92848i	−0.0872433	+	0.230042i
$460$	11.8814	−	31.3287i	0.553973	−	1.46071i
$461$	−1.28579	+	1.86279i	−0.0598854	+	0.0867590i	−0.851783	−	0.523896i	$-0.824478\pi$
$461$	−1.28579	+	1.86279i	−0.0598854	+	0.0867590i	0.791897	+	0.610655i	$0.209094\pi$
$462$	−0.442133	+	0.108976i	−0.0205699	+	0.00507002i
$463$	8.23333	−	11.9280i	0.382635	−	0.554343i	−0.583588	−	0.812050i	$-0.698352\pi$
$463$	8.23333	−	11.9280i	0.382635	−	0.554343i	0.966223	+	0.257707i	$0.0829670\pi$
$464$	−3.58209	−	29.5012i	−0.166295	−	1.36956i
$465$	−23.6461	+	62.3497i	−1.09656	+	2.89140i
$466$	0.269006	−	0.141185i	0.0124615	−	0.00654029i
$467$	−9.05213	−	13.1143i	−0.418882	−	0.606856i	0.555565	−	0.831473i	$-0.312502\pi$
$467$	−9.05213	−	13.1143i	−0.418882	−	0.606856i	−0.974447	+	0.224617i	$0.927887\pi$
$468$	−0.535388	+	26.2575i	−0.0247483	+	1.21376i
$469$	−9.45993	+	13.7051i	−0.436819	+	0.632841i
$470$	0.0650570	−	0.535792i	0.00300085	−	0.0247143i
$471$	−31.2593	−	7.70473i	−1.44035	−	0.355015i
$472$	0.695743	+	1.00796i	0.0320242	+	0.0463950i
$473$	−9.01931	+	7.99041i	−0.414708	+	0.367400i
$474$	−0.972455	−	0.510384i	−0.0446663	−	0.0234427i
$475$	−2.38163	−	19.6145i	−0.109277	−	0.899973i
$476$	1.53142	−	12.6124i	0.0701926	−	0.578088i
$477$	8.05027	−	7.13192i	0.368597	−	0.326548i
$478$	−0.142234	+	0.206062i	−0.00650565	+	0.00942507i
$479$	2.02795	+	16.7017i	0.0926594	+	0.763118i	0.962781	+	0.270282i	$0.0871169\pi$
$479$	2.02795	+	16.7017i	0.0926594	+	0.763118i	−0.870122	+	0.492837i	$0.835960\pi$
$480$	0.623488	−	5.13488i	0.0284582	−	0.234374i
$481$	−7.57129	+	0.763054i	−0.345221	+	0.0347923i
$482$	0.108033	+	0.889732i	0.00492077	+	0.0405262i
$483$	25.8529	−	6.37216i	1.17635	−	0.289943i
$484$	16.1109			0.732314
$485$	−48.7732			−2.21468
$486$	1.10075	−	0.271311i	0.0499312	−	0.0123069i
$487$	1.61906	−	4.26912i	0.0733668	−	0.193452i	−0.893316	−	0.449429i	$-0.851628\pi$
$487$	1.61906	−	4.26912i	0.0733668	−	0.193452i	0.966683	+	0.255976i	$0.0823969\pi$
$488$	2.79019			0.126306
$489$	11.3848	+	30.0192i	0.514837	+	1.35751i
$490$	0.479794	+	0.118259i	0.0216749	+	0.00534238i
$491$	18.9793	−	16.8142i	0.856525	−	0.758815i	−0.115596	−	0.993296i	$-0.536878\pi$
$491$	18.9793	−	16.8142i	0.856525	−	0.758815i	0.972121	+	0.234482i	$0.0753393\pi$
$492$	−36.8325	−	9.07840i	−1.66054	−	0.409286i
$493$	17.6473	−	15.6342i	0.794795	−	0.704127i
$494$	−0.595761	−	0.239945i	−0.0268046	−	0.0107957i
$495$	15.2827	+	13.5393i	0.686904	+	0.608544i
$496$	17.9099	+	25.9469i	0.804177	+	1.16505i
$497$	18.9221	−	4.66389i	0.848774	−	0.209204i
$498$	−0.918706	+	1.33098i	−0.0411682	+	0.0596424i
$499$	−2.27085	−	0.559714i	−0.101657	−	0.0250562i	0.188159	−	0.982139i	$-0.439748\pi$
$499$	−2.27085	−	0.559714i	−0.101657	−	0.0250562i	−0.289816	+	0.957082i	$0.593594\pi$
$500$	4.33394	+	1.06822i	0.193820	+	0.0477723i
$501$	1.34090	−	11.0433i	0.0599068	−	0.493377i
$502$	0.573093	+	0.507716i	0.0255784	+	0.0226605i
$503$	11.9929	+	31.6226i	0.534735	+	1.40998i	0.881570	+	0.472054i	$0.156487\pi$
$503$	11.9929	+	31.6226i	0.534735	+	1.40998i	−0.346835	+	0.937926i	$0.612744\pi$
$504$	1.33101	−	0.698568i	0.0592879	−	0.0311167i
$505$	−22.6631	+	32.8332i	−1.00849	+	1.46106i
$506$	−0.450453			−0.0200251
$507$	−20.1477	+	26.7840i	−0.894791	+	1.18952i
$508$	−21.5624			−0.956677
$509$	−3.33365	+	4.82963i	−0.147761	+	0.214069i	−0.889875	−	0.456205i	$-0.849208\pi$
$509$	−3.33365	+	4.82963i	−0.147761	+	0.214069i	0.742113	+	0.670275i	$0.233824\pi$
$510$	1.20855	−	0.634296i	0.0535155	−	0.0280871i
$511$	−6.09957	−	16.0833i	−0.269829	−	0.711481i
$512$	−3.05228	−	2.70409i	−0.134893	−	0.119505i
$513$	−0.698757	+	5.75478i	−0.0308509	+	0.254080i
$514$	−0.270250	−	0.0666107i	−0.0119202	−	0.00293807i
$515$	−38.1468	−	9.40235i	−1.68095	−	0.414317i
$516$	20.5784	−	29.8130i	0.905916	−	1.31245i
$517$	5.35936	−	1.32096i	0.235705	−	0.0580960i
$518$	0.123628	+	0.179106i	0.00543190	+	0.00786947i
$519$	−4.05866	−	3.59566i	−0.178155	−	0.157832i
$520$	1.63724	−	1.77386i	0.0717979	−	0.0777888i
$521$	17.3790	−	15.3964i	0.761388	−	0.674531i	−0.190256	−	0.981735i	$-0.560932\pi$
$521$	17.3790	−	15.3964i	0.761388	−	0.674531i	0.951644	+	0.307204i	$0.0993934\pi$
$522$	1.35331	+	0.333561i	0.0592328	+	0.0145996i
$523$	6.41277	−	5.68122i	0.280411	−	0.248423i	−0.511180	−	0.859474i	$-0.670791\pi$
$523$	6.41277	−	5.68122i	0.280411	−	0.248423i	0.791591	+	0.611051i	$0.209253\pi$
$524$	29.6361	+	7.30465i	1.29466	+	0.319105i
$525$	10.4566	+	27.5717i	0.456362	+	1.20333i
$526$	0.396516			0.0172889
$527$	−8.86957	+	23.3871i	−0.386364	+	1.01876i
$528$	17.0834	−	4.21067i	0.743458	−	0.183246i
$529$	3.33937			0.145190
$530$	−0.493947			−0.0214557
$531$	21.1720	−	5.21843i	0.918787	−	0.226461i
$532$	−1.68425	−	13.8711i	−0.0730217	−	0.601388i
$533$	−17.2042	−	20.2361i	−0.745198	−	0.876522i
$534$	0.242174	−	1.99448i	0.0104799	−	0.0863096i
$535$	−4.73358	−	38.9845i	−0.204650	−	1.68545i
$536$	−0.962890	+	1.39499i	−0.0415905	+	0.0602542i
$537$	−17.4179	+	15.4309i	−0.751639	+	0.665894i
$538$	0.111738	−	0.920246i	0.00481737	−	0.0396746i
$539$	0.609153	+	5.01682i	0.0262381	+	0.216090i
$540$	−9.63988	−	5.05940i	−0.414834	−	0.217722i
$541$	−4.73982	+	4.19911i	−0.203781	+	0.180534i	−0.758841	−	0.651276i	$-0.774234\pi$
$541$	−4.73982	+	4.19911i	−0.203781	+	0.180534i	0.555060	+	0.831810i	$0.312695\pi$
$542$	0.490498	+	0.710609i	0.0210687	+	0.0305233i
$543$	41.8038	+	10.3037i	1.79397	+	0.442174i
$544$	0.233868	−	1.92607i	0.0100270	−	0.0825797i
$545$	22.8257	−	33.0687i	0.977745	−	1.41651i
$546$	0.948986	+	0.134912i	0.0406129	+	0.00577368i
$547$	6.06986	+	8.79371i	0.259528	+	0.375992i	0.930988	−	0.365049i	$-0.118948\pi$
$547$	6.06986	+	8.79371i	0.259528	+	0.375992i	−0.671460	+	0.741041i	$0.734332\pi$
$548$	23.0854	−	12.1162i	0.986161	−	0.517577i
$549$	17.6155	−	46.4484i	0.751813	−	1.98237i
$550$	−0.0601309	−	0.495223i	−0.00256399	−	0.0211164i
$551$	14.7296	−	21.3395i	0.627503	−	0.909095i
$552$	2.63147	−	0.648598i	0.112003	−	0.0276062i
$553$	9.50341	−	13.7681i	0.404126	−	0.585478i
$554$	−0.166191	+	0.438210i	−0.00706079	+	0.0186178i
$555$	6.30674	−	16.6295i	0.267706	−	0.705883i
$556$	−23.6818	−	12.4292i	−1.00433	−	0.527115i
$557$	−25.0788	−	13.1624i	−1.06262	−	0.557707i	−0.159548	−	0.987190i	$-0.551004\pi$
$557$	−25.0788	−	13.1624i	−1.06262	−	0.557707i	−0.903075	+	0.429483i	$0.858696\pi$
$558$	−1.43574	+	0.353877i	−0.0607796	+	0.0149808i
$559$	23.8943	−	8.50892i	1.01062	−	0.359889i
$560$	25.4453	+	6.27170i	1.07526	+	0.265028i
$561$	10.4482	+	9.25629i	0.441123	+	0.390801i
$562$	−0.0494036	+	0.406875i	−0.00208396	+	0.0171630i
$563$	−26.4346	−	13.8739i	−1.11408	−	0.584716i	−0.195802	−	0.980643i	$-0.562731\pi$
$563$	−26.4346	−	13.8739i	−1.11408	−	0.584716i	−0.918282	+	0.395927i	$0.870423\pi$
$564$	−14.6935	+	7.71177i	−0.618710	+	0.324724i
$565$	17.8764	+	47.1362i	0.752066	+	1.98303i
$566$	−0.207815	−	0.184108i	−0.00873511	−	0.00773863i
$567$	1.61091	+	13.2671i	0.0676520	+	0.557164i
$568$	1.92601	−	0.474719i	0.0808137	−	0.0199188i
$569$	−2.88930	−	2.55970i	−0.121126	−	0.107308i	0.600386	−	0.799711i	$-0.295014\pi$
$569$	−2.88930	−	2.55970i	−0.121126	−	0.107308i	−0.721511	+	0.692403i	$0.756552\pi$
$570$	1.12359	−	0.995416i	0.0470621	−	0.0416934i
$571$	−41.5409	−	21.8024i	−1.73843	−	0.912400i	−0.957812	−	0.287395i	$-0.907211\pi$
$571$	−41.5409	−	21.8024i	−1.73843	−	0.912400i	−0.780621	−	0.625005i	$-0.785097\pi$
$572$	11.4424	+	4.60846i	0.478429	+	0.192689i
$573$	−37.1265	+	19.4855i	−1.55098	+	0.814018i
$574$	−0.269366	+	0.710261i	−0.0112431	+	0.0296457i
$575$	3.51604	+	28.9572i	0.146629	+	1.20760i
$576$	−25.6295	+	13.4514i	−1.06789	+	0.560474i
$577$	47.4624			1.97589			0.987943	−	0.154819i	$-0.0494794\pi$
$577$	47.4624			1.97589			0.987943	+	0.154819i	$0.0494794\pi$
$578$	−0.318001	+	0.166900i	−0.0132271	+	0.00694211i
$579$	5.39340	−	4.77814i	0.224142	−	0.198573i
$580$	27.6624	+	40.0758i	1.14862	+	1.66406i
$581$	−18.4398	−	16.3362i	−0.765011	−	0.677741i
$582$	−1.11981	−	1.62233i	−0.0464177	−	0.0672477i
$583$	−1.79131	−	4.72330i	−0.0741885	−	0.195619i
$584$	−0.620852	−	1.63705i	−0.0256910	−	0.0677417i
$585$	−19.1929	−	38.4544i	−0.793530	−	1.58989i
$586$	−0.452860	+	1.19409i	−0.0187075	+	0.0493275i
$587$	−4.60901			−0.190234			−0.0951170	−	0.995466i	$-0.530323\pi$
$587$	−4.60901			−0.190234			−0.0951170	+	0.995466i	$0.530323\pi$
$588$	−5.38755	−	14.2058i	−0.222179	−	0.585837i
$589$	−3.31581	+	27.3082i	−0.136626	+	1.12521i
$590$	−0.886756	−	0.465405i	−0.0365072	−	0.0191604i
$591$	11.4936	+	16.6514i	0.472784	+	0.684945i
$592$	−4.77680	−	6.92039i	−0.196325	−	0.284426i
$593$	−7.13185	−	3.74308i	−0.292870	−	0.153710i	0.311889	−	0.950119i	$-0.399038\pi$
$593$	−7.13185	−	3.74308i	−0.292870	−	0.153710i	−0.604759	+	0.796409i	$0.706731\pi$
$594$	−0.0176421	+	0.145296i	−0.000723864	+	0.00596156i
$595$	7.37262	+	19.4400i	0.302248	+	0.796962i
$596$	−20.3193			−0.832311
$597$	2.86556	−	7.55586i	0.117280	−	0.309241i
$598$	0.879533	+	0.354236i	0.0359668	+	0.0144858i
$599$	8.26948	+	21.8048i	0.337882	+	0.890921i	0.991024	+	0.133686i	$0.0426813\pi$
$599$	8.26948	+	21.8048i	0.337882	+	0.890921i	−0.653142	+	0.757236i	$0.726549\pi$
$600$	1.06433	+	2.80642i	0.0434513	+	0.114572i
$601$	12.2836	+	17.7959i	0.501060	+	0.725910i	0.989154	−	0.146880i	$-0.0469233\pi$
$601$	12.2836	+	17.7959i	0.501060	+	0.725910i	−0.488095	+	0.872791i	$0.662308\pi$
$602$	−0.542967	−	0.481027i	−0.0221297	−	0.0196052i
$603$	17.1433	+	24.8364i	0.698130	+	1.01142i
$604$	−17.7120	+	15.6915i	−0.720692	+	0.638477i
$605$	−23.3447	+	12.2523i	−0.949098	+	0.498125i
$606$	−1.61245			−0.0655015
$607$	−11.3659	+	5.96531i	−0.461329	+	0.242124i	−0.679342	−	0.733822i	$-0.737735\pi$
$607$	−11.3659	+	5.96531i	−0.461329	+	0.242124i	0.218013	+	0.975946i	$0.430043\pi$
$608$	−0.257207	−	2.11829i	−0.0104311	−	0.0859081i
$609$	−13.7224	+	36.1829i	−0.556058	+	1.46620i
$610$	−2.02016	+	1.06026i	−0.0817940	+	0.0429288i
$611$	−11.5032	−	1.63534i	−0.465371	−	0.0661590i
$612$	−20.3868	−	10.6998i	−0.824088	−	0.432515i
$613$	3.76904	−	3.33908i	0.152230	−	0.134864i	−0.583570	−	0.812063i	$-0.698345\pi$
$613$	3.76904	−	3.33908i	0.152230	−	0.134864i	0.735800	+	0.677199i	$0.236806\pi$
$614$	0.121672	+	0.107792i	0.00491026	+	0.00435011i
$615$	60.2744	−	14.8563i	2.43050	−	0.599064i
$616$	−0.0851035	−	0.700890i	−0.00342892	−	0.0282397i
$617$	−5.67750	−	5.02982i	−0.228567	−	0.202493i	0.541064	−	0.840981i	$-0.318022\pi$
$617$	−5.67750	−	5.02982i	−0.228567	−	0.202493i	−0.769632	+	0.638488i	$0.779560\pi$
$618$	−0.563088	−	1.48474i	−0.0226507	−	0.0597250i
$619$	−21.5490	+	11.3098i	−0.866127	+	0.454578i	−0.838412	−	0.545038i	$-0.816515\pi$
$619$	−21.5490	+	11.3098i	−0.866127	+	0.454578i	−0.0277150	+	0.999616i	$0.508823\pi$
$620$	−45.7441	−	24.0084i	−1.83713	−	0.964199i
$621$	1.03159	−	8.49588i	0.0413962	−	0.340928i
$622$	0.111578	+	0.0988494i	0.00447387	+	0.00396350i
$623$	29.7153	+	7.32417i	1.19052	+	0.293436i
$624$	−36.6674	−	5.21278i	−1.46787	−	0.208678i
$625$	20.5005	−	5.05291i	0.820019	−	0.202117i
$626$	−1.06051	−	0.556596i	−0.0423863	−	0.0222461i
$627$	13.5932	+	7.13429i	0.542862	+	0.284916i
$628$	8.84472	−	23.3216i	0.352943	−	0.930633i
$629$	2.36563	−	6.23766i	0.0943239	−	0.248712i
$630$	−0.698230	+	1.01156i	−0.0278182	+	0.0403016i
$631$	39.0147	−	9.61626i	1.55315	−	0.382817i	0.632927	−	0.774211i	$-0.281853\pi$
$631$	39.0147	−	9.61626i	1.55315	−	0.382817i	0.920223	+	0.391394i	$0.128007\pi$
$632$	0.967316	−	1.40140i	0.0384778	−	0.0557447i
$633$	3.38849	+	27.9067i	0.134680	+	1.10919i
$634$	−0.512065	+	1.35020i	−0.0203367	+	0.0536234i
$635$	31.2439	−	16.3981i	1.23988	−	0.650738i
$636$	8.62707	+	12.4985i	0.342086	+	0.495597i
$637$	2.75582	−	10.2746i	0.109190	−	0.407096i
$638$	0.371891	−	0.538777i	0.0147233	−	0.0213304i
$639$	4.25700	−	35.0595i	0.168404	−	1.38693i
$640$	5.18678	+	1.27843i	0.205025	+	0.0505342i
$641$	2.27226	+	3.29194i	0.0897491	+	0.130024i	0.865287	−	0.501278i	$-0.167136\pi$
$641$	2.27226	+	3.29194i	0.0897491	+	0.130024i	−0.775537	+	0.631302i	$0.782521\pi$
$642$	1.18805	−	1.05252i	0.0468885	−	0.0415396i
$643$	−15.2888	−	8.02419i	−0.602932	−	0.316443i	0.135493	−	0.990778i	$-0.456738\pi$
$643$	−15.2888	−	8.02419i	−0.602932	−	0.316443i	−0.738426	+	0.674335i	$0.764430\pi$
$644$	2.48650	+	20.4781i	0.0979817	+	0.806951i
$645$	−7.14555	+	58.8489i	−0.281356	+	2.31717i
$646$	0.421455	−	0.373376i	0.0165819	−	0.0146903i
$647$	−12.9884	+	18.8170i	−0.510629	+	0.739773i	−0.990492	−	0.137570i	$-0.956071\pi$
$647$	−12.9884	+	18.8170i	−0.510629	+	0.739773i	0.479863	+	0.877343i	$0.340686\pi$
$648$	0.163969	+	1.35040i	0.00644130	+	0.0530489i
$649$	1.23453	−	10.1673i	0.0484595	−	0.399100i
$650$	−0.272034	+	1.01423i	−0.0106700	+	0.0397816i
$651$	−4.94857	−	40.7552i	−0.193950	−	1.59732i
$652$	−24.1505	+	5.95256i	−0.945806	+	0.233120i
$653$	−0.299520			−0.0117211			−0.00586056	−	0.999983i	$-0.501865\pi$
$653$	−0.299520			−0.0117211			−0.00586056	+	0.999983i	$0.501865\pi$
$654$	1.62402			0.0635043
$655$	−48.4979	+	11.9537i	−1.89497	+	0.467068i
$656$	10.4079	−	27.4434i	0.406361	−	1.07149i
$657$	−31.1718			−1.21613
$658$	0.117832	+	0.310698i	0.00459358	+	0.0121123i
$659$	−4.53077	−	1.11674i	−0.176494	−	0.0435018i	0.150078	−	0.988674i	$-0.452047\pi$
$659$	−4.53077	−	1.11674i	−0.176494	−	0.0435018i	−0.326572	+	0.945172i	$0.605894\pi$
$660$	−21.5800	+	19.1182i	−0.840001	+	0.744176i
$661$	−31.5846	−	7.78490i	−1.22850	−	0.302798i	−0.428910	−	0.903347i	$-0.641102\pi$
$661$	−31.5846	−	7.78490i	−1.22850	−	0.302798i	−0.799588	+	0.600549i	$0.794949\pi$
$662$	0.408879	−	0.362235i	0.0158915	−	0.0140787i
$663$	−13.1215	−	26.2898i	−0.509597	−	1.02101i
$664$	−1.87692	−	1.66280i	−0.0728385	−	0.0645292i
$665$	12.9894	+	18.8183i	0.503706	+	0.729744i
$666$	0.382930	−	0.0943837i	0.0148382	−	0.00365730i
$667$	−21.7456	+	31.5039i	−0.841993	+	1.21984i
$668$	8.36800	+	2.06253i	0.323768	+	0.0798016i
$669$	−31.9381	−	7.87202i	−1.23480	−	0.304350i
$670$	0.167064	−	1.37590i	0.00645426	−	0.0531556i
$671$	−17.4648	−	15.4724i	−0.674220	−	0.597307i
$672$	1.12927	+	2.97765i	0.0435626	+	0.114865i
$673$	−34.7535	+	18.2400i	−1.33965	+	0.703102i	−0.973764	−	0.227558i	$-0.926926\pi$
$673$	−34.7535	+	18.2400i	−1.33965	+	0.703102i	−0.365884	+	0.930660i	$0.619233\pi$
$674$	−0.0950502	+	0.137704i	−0.00366120	+	0.00530416i
$675$	9.47798			0.364807
$676$	−18.7177	−	17.9965i	−0.719912	−	0.692173i
$677$	11.9279			0.458426			0.229213	−	0.973376i	$-0.426385\pi$
$677$	11.9279			0.458426			0.229213	+	0.973376i	$0.426385\pi$
$678$	−1.15744	+	1.67684i	−0.0444513	+	0.0643988i
$679$	26.5885	−	13.9547i	1.02037	−	0.535533i
$680$	0.750431	+	1.97872i	0.0287777	+	0.0758806i
$681$	26.9066	+	23.8372i	1.03106	+	0.913442i
$682$	−0.0837171	+	0.689472i	−0.00320569	+	0.0264013i
$683$	−16.6921	−	4.11423i	−0.638705	−	0.157427i	−0.0933519	−	0.995633i	$-0.529758\pi$
$683$	−16.6921	−	4.11423i	−0.638705	−	0.157427i	−0.545353	+	0.838207i	$0.683604\pi$
$684$	−24.5861	−	6.05992i	−0.940071	−	0.231707i
$685$	−24.2365	+	35.1127i	−0.926030	+	1.34159i
$686$	−0.996231	+	0.245549i	−0.0380363	+	0.00937510i
$687$	−14.0332	−	20.3306i	−0.535400	−	0.775661i
$688$	20.9794	+	18.5862i	0.799833	+	0.708590i
$689$	−0.216768	+	10.6312i	−0.00825821	+	0.405015i
$690$	−1.65878	+	1.46955i	−0.0631487	+	0.0559448i
$691$	−18.0230	−	4.44227i	−0.685626	−	0.168992i	−0.118910	−	0.992905i	$-0.537940\pi$
$691$	−18.0230	−	4.44227i	−0.685626	−	0.168992i	−0.566716	+	0.823913i	$0.691786\pi$
$692$	3.14438	−	2.78568i	0.119532	−	0.105896i
$693$	−12.2050	−	3.00827i	−0.463631	−	0.114275i
$694$	0.189941	+	0.500832i	0.00721005	+	0.0190113i
$695$	43.7673			1.66019
$696$	−1.39675	+	3.68292i	−0.0529435	+	0.139601i
$697$	22.6087	−	5.57254i	0.856364	−	0.211075i
$698$	0.0420150			0.00159029
$699$	15.2856			0.578154
$700$	−22.1815	+	5.46724i	−0.838381	+	0.206642i
$701$	−0.980348	−	8.07389i	−0.0370272	−	0.304947i	−0.999443	−	0.0333670i	$-0.989377\pi$
$701$	−0.980348	−	8.07389i	−0.0370272	−	0.304947i	0.962416	−	0.271580i	$-0.0875461\pi$
$702$	0.148707	−	0.269824i	0.00561260	−	0.0101838i
$703$	0.884371	−	7.28345i	0.0333547	−	0.274701i
$704$	1.63872	+	13.4961i	0.0617616	+	0.508653i
$705$	15.4262	−	22.3487i	0.580984	−	0.841701i
$706$	0.310041	−	0.274673i	0.0116686	−	0.0103374i
$707$	2.96064	−	24.3831i	0.111346	−	0.917020i
$708$	3.71143	+	30.5664i	0.139484	+	1.14875i
$709$	−15.8731	−	8.33084i	−0.596126	−	0.312871i	0.139539	−	0.990217i	$-0.455438\pi$
$709$	−15.8731	−	8.33084i	−0.596126	−	0.312871i	−0.735665	+	0.677345i	$0.763130\pi$
$710$	−1.21409	+	1.07559i	−0.0455639	+	0.0403661i
$711$	−17.2221	−	24.9506i	−0.645880	−	0.935719i
$712$	3.02461	+	0.745499i	0.113352	+	0.0279387i
$713$	4.89519	−	40.3155i	0.183326	−	1.50983i
$714$	−0.477354	+	0.691567i	−0.0178645	+	0.0258812i
$715$	−20.0847	+	2.02419i	−0.751124	+	0.0757003i
$716$	−10.2412	−	14.8369i	−0.382730	−	0.554480i
$717$	−11.1548	+	5.85447i	−0.416582	+	0.218639i
$718$	0.493511	−	1.30128i	0.0184177	−	0.0485634i
$719$	4.79936	+	39.5263i	0.178986	+	1.47408i	0.754506	+	0.656293i	$0.227877\pi$
$719$	4.79936	+	39.5263i	0.178986	+	1.47408i	−0.575520	+	0.817788i	$0.695200\pi$
$720$	26.9786	−	39.0852i	1.00543	−	1.45662i
$721$	23.4857	−	5.78871i	0.874654	−	0.215583i
$722$	−0.201285	+	0.291612i	−0.00749106	+	0.0108527i
$723$	−15.9907	+	42.1641i	−0.594702	+	1.56810i
$724$	−11.8282	+	31.1885i	−0.439593	+	1.15911i
$725$	−37.5379	−	19.7014i	−1.39412	−	0.731691i
$726$	−0.943528	−	0.495202i	−0.0350176	−	0.0183787i
$727$	−41.7957	+	10.3017i	−1.55011	+	0.382069i	−0.919203	−	0.393785i	$-0.871165\pi$
$727$	−41.7957	+	10.3017i	−1.55011	+	0.382069i	−0.630912	+	0.775854i	$0.717319\pi$
$728$	−0.385010	+	1.43545i	−0.0142694	+	0.0532013i
$729$	36.0384	+	8.88266i	1.33475	+	0.328987i
$730$	1.07159	+	0.949344i	0.0396612	+	0.0351368i
$731$	−2.68026	+	22.0740i	−0.0991332	+	0.816435i
$732$	62.1114	+	32.5986i	2.29570	+	1.20488i
$733$	4.78419	−	2.51094i	0.176708	−	0.0927436i	−0.374050	−	0.927409i	$-0.622031\pi$
$733$	4.78419	−	2.51094i	0.176708	−	0.0927436i	0.550758	+	0.834665i	$0.314339\pi$
$734$	0.246852	+	0.650896i	0.00911148	+	0.0240250i
$735$	18.6100	+	16.4870i	0.686440	+	0.608132i
$736$	0.379719	+	3.12727i	0.0139966	+	0.115273i
$737$	13.7627	−	3.39220i	0.506955	−	0.124953i
$738$	1.03039	+	0.912850i	0.0379294	+	0.0336025i
$739$	33.4939	−	29.6730i	1.23209	−	1.09154i	0.239393	−	0.970923i	$-0.423051\pi$
$739$	33.4939	−	29.6730i	1.23209	−	1.09154i	0.992699	−	0.120616i	$-0.0384870\pi$
$740$	12.2006	+	6.40335i	0.448502	+	0.235392i
$741$	−20.9311	−	24.6198i	−0.768924	−	0.904430i
$742$	0.269273	−	0.141325i	0.00988533	−	0.00518822i
$743$	−5.42588	+	14.3069i	−0.199056	+	0.524868i	−0.996960	−	0.0779170i	$-0.975173\pi$
$743$	−5.42588	+	14.3069i	−0.199056	+	0.524868i	0.797904	+	0.602785i	$0.205942\pi$
$744$	−0.503696	−	4.14831i	−0.0184664	−	0.152085i
$745$	29.4427	−	15.4527i	1.07870	−	0.566143i
$746$	0.484310			0.0177319
$747$	−39.5305	+	20.7472i	−1.44634	+	0.759100i
$748$	−8.09457	+	7.17117i	−0.295967	+	0.262204i
$749$	13.7345	+	19.8979i	0.501848	+	0.727053i
$750$	−0.220981	−	0.195772i	−0.00806910	−	0.00714860i
$751$	−22.7411	−	32.9462i	−0.829836	−	1.20223i	−0.977027	−	0.213117i	$-0.931638\pi$
$751$	−22.7411	−	32.9462i	−0.829836	−	1.20223i	0.147190	−	0.989108i	$-0.452977\pi$
$752$	−4.55287	−	12.0049i	−0.166026	−	0.437775i
$753$	13.6602	+	36.0191i	0.497807	+	1.31261i
$754$	−1.14983	+	0.759536i	−0.0418743	+	0.0276607i
$755$	13.7314	−	36.2068i	0.499738	−	1.31770i
$756$	6.70270			0.243775
$757$	−8.55795	−	22.5655i	−0.311044	−	0.820156i	−0.995815	−	0.0913969i	$-0.970867\pi$
$757$	−8.55795	−	22.5655i	−0.311044	−	0.820156i	0.684771	−	0.728759i	$-0.259902\pi$
$758$	0.0953784	−	0.785512i	0.00346430	−	0.0285311i
$759$	−20.0680	−	10.5325i	−0.728420	−	0.382305i
$760$	1.32214	+	1.91545i	0.0479590	+	0.0694806i
$761$	−3.73132	−	5.40575i	−0.135260	−	0.195958i	0.749501	−	0.662004i	$-0.230294\pi$
$761$	−3.73132	−	5.40575i	−0.135260	−	0.195958i	−0.884761	+	0.466046i	$0.845678\pi$
$762$	1.26279	+	0.662764i	0.0457461	+	0.0240094i
$763$	−2.98188	+	24.5580i	−0.107951	+	0.889060i
$764$	−11.5190	−	30.3731i	−0.416743	−	1.09886i
$765$	37.6777			1.36224
$766$	−0.0777631	+	0.205044i	−0.00280969	+	0.00740856i
$767$	−10.4060	+	18.8813i	−0.375739

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)

\(f(q)\)	\(=\)	\(q+(0.0291084 - 0.0421708i) q^{2} +(2.28283 - 1.19812i) q^{3} +(0.708279 + 1.86758i) q^{4} +(-2.44658 - 2.16748i) q^{5} +(0.0159238 - 0.131144i) q^{6} +(1.95389 + 0.481590i) q^{7} +(0.198879 + 0.0490192i) q^{8} +(2.07162 - 3.00127i) q^{9} +O(q^{10})\)	\(q+(0.0291084 - 0.0421708i) q^{2} +(2.28283 - 1.19812i) q^{3} +(0.708279 + 1.86758i) q^{4} +(-2.44658 - 2.16748i) q^{5} +(0.0159238 - 0.131144i) q^{6} +(1.95389 + 0.481590i) q^{7} +(0.198879 + 0.0490192i) q^{8} +(2.07162 - 3.00127i) q^{9} +(-0.162620 + 0.0400823i) q^{10} +(-0.973026 - 1.40967i) q^{11} +(3.85447 + 3.41476i) q^{12} +(0.791320 + 3.51764i) q^{13} +(0.0771835 - 0.0683786i) q^{14} +(-8.18203 - 2.01669i) q^{15} +(-2.98226 + 2.64205i) q^{16} +(-3.06904 - 0.756451i) q^{17} +(-0.0662641 - 0.174724i) q^{18} -3.47634 q^{19} +(2.31508 - 6.10435i) q^{20} +(5.03740 - 1.24161i) q^{21} -0.0877702 q^{22} +5.13219 q^{23} +(0.512737 - 0.126378i) q^{24} +(0.685095 + 5.64227i) q^{25} +(0.171376 + 0.0690223i) q^{26} +(0.201003 - 1.65541i) q^{27} +(0.484490 + 3.99014i) q^{28} +(-4.23710 + 6.13850i) q^{29} +(-0.323211 + 0.286340i) q^{30} +(0.953821 - 7.85543i) q^{31} +(0.0739878 + 0.609344i) q^{32} +(-3.91021 - 2.05224i) q^{33} +(-0.121235 + 0.107405i) q^{34} +(-3.73650 - 5.41326i) q^{35} +(7.07239 + 1.74319i) q^{36} +(-0.254397 + 2.09515i) q^{37} +(-0.101191 + 0.146600i) q^{38} +(6.02101 + 7.08209i) q^{39} +(-0.380324 - 0.550995i) q^{40} +(-6.52287 + 3.42347i) q^{41} +(0.0942710 - 0.248572i) q^{42} +(-0.847945 - 6.98346i) q^{43} +(1.94350 - 2.81564i) q^{44} +(-11.5736 + 2.85263i) q^{45} +(0.149390 - 0.216428i) q^{46} +(-1.14272 + 3.01309i) q^{47} +(-3.64249 + 9.60445i) q^{48} +(-2.61245 - 1.37112i) q^{49} +(0.257881 + 0.135346i) q^{50} +(-7.91243 + 1.95024i) q^{51} +(-6.00900 + 3.96932i) q^{52} +(2.86347 + 0.705782i) q^{53} +(-0.0639591 - 0.0566628i) q^{54} +(-0.674849 + 5.55788i) q^{55} +(0.364979 + 0.191556i) q^{56} +(-7.93591 + 4.16508i) q^{57} +(0.135530 + 0.357364i) q^{58} +(4.47563 + 3.96506i) q^{59} +(-2.02883 - 16.7089i) q^{60} +(13.2261 - 3.25994i) q^{61} +(-0.303505 - 0.268882i) q^{62} +(5.49310 - 4.86646i) q^{63} +(-7.02791 - 3.68853i) q^{64} +(5.68839 - 10.3214i) q^{65} +(-0.200364 + 0.105159i) q^{66} +(-2.93446 + 7.73754i) q^{67} +(-0.761007 - 6.26745i) q^{68} +(11.7159 - 6.14899i) q^{69} -0.337045 q^{70} +(8.57507 - 4.50054i) q^{71} +(0.559122 - 0.495339i) q^{72} +(-4.85564 - 7.03461i) q^{73} +(0.0809489 + 0.0717145i) q^{74} +(8.32408 + 12.0595i) q^{75} +(-2.46222 - 6.49234i) q^{76} +(-1.22230 - 3.22294i) q^{77} +(0.473919 - 0.0477628i) q^{78} +(2.94795 - 7.77311i) q^{79} +13.0229 q^{80} +(2.35500 + 6.20963i) q^{81} +(-0.0455000 + 0.374726i) q^{82} +(-10.8397 - 5.68913i) q^{83} +(5.88668 + 8.52832i) q^{84} +(5.86906 + 8.50280i) q^{85} +(-0.319180 - 0.167519i) q^{86} +(-2.31791 + 19.0897i) q^{87} +(-0.124413 - 0.328051i) q^{88} +15.2083 q^{89} +(-0.216590 + 0.571102i) q^{90} +(-0.147912 + 7.25417i) q^{91} +(3.63502 + 9.58476i) q^{92} +(-7.23435 - 19.0754i) q^{93} +(0.0938019 + 0.135895i) q^{94} +(8.50515 + 7.53490i) q^{95} +(0.898970 + 1.30238i) q^{96} +(11.1691 - 9.89497i) q^{97} +(-0.133865 + 0.0702579i) q^{98} -6.24655 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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