LMFDB - Embedded newform 169.2.h.a.12.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, 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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.8
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.197515 - 0.136335i) q^{2} +(1.40158 + 0.735608i) q^{3} +(-0.688785 + 1.81618i) q^{4} +(-0.369290 - 0.416842i) q^{5} +(0.377124 - 0.0457911i) q^{6} +(0.397115 + 1.61116i) q^{7} +(0.226434 + 0.918678i) q^{8} +(-0.280874 - 0.406917i) q^{9} +O(q^{10})$	\(q+(0.197515 - 0.136335i) q^{2} +(1.40158 + 0.735608i) q^{3} +(-0.688785 + 1.81618i) q^{4} +(-0.369290 - 0.416842i) q^{5} +(0.377124 - 0.0457911i) q^{6} +(0.397115 + 1.61116i) q^{7} +(0.226434 + 0.918678i) q^{8} +(-0.280874 - 0.406917i) q^{9} +(-0.129771 - 0.0319856i) q^{10} +(3.54807 + 2.44906i) q^{11} +(-2.30138 + 2.03885i) q^{12} +(0.00632121 - 3.60555i) q^{13} +(0.298093 + 0.264088i) q^{14} +(-0.210959 - 0.855893i) q^{15} +(-2.73784 - 2.42552i) q^{16} +(-3.12757 + 0.770877i) q^{17} +(-0.110954 - 0.0420793i) q^{18} -1.72532i q^{19} +(1.01142 - 0.383581i) q^{20} +(-0.628591 + 2.55029i) q^{21} +1.03469 q^{22} +7.98168 q^{23} +(-0.358421 + 1.45417i) q^{24} +(0.565301 - 4.65567i) q^{25} +(-0.490313 - 0.713012i) q^{26} +(-0.666729 - 5.49101i) q^{27} +(-3.19967 - 0.388510i) q^{28} +(-0.395697 - 0.573266i) q^{29} +(-0.158356 - 0.140291i) q^{30} +(-4.11400 + 0.499530i) q^{31} +(-2.75000 - 0.333910i) q^{32} +(3.17137 + 6.04255i) q^{33} +(-0.512646 + 0.578657i) q^{34} +(0.524948 - 0.760518i) q^{35} +(0.932494 - 0.229839i) q^{36} +(-1.44710 + 0.175710i) q^{37} +(-0.235221 - 0.340776i) q^{38} +(2.66113 - 5.04883i) q^{39} +(0.299324 - 0.433646i) q^{40} +(-0.456082 + 0.868992i) q^{41} +(0.223538 + 0.589421i) q^{42} +(0.325001 - 2.67662i) q^{43} +(-6.89177 + 4.75705i) q^{44} +(-0.0658960 + 0.267350i) q^{45} +(1.57650 - 1.08818i) q^{46} +(-11.5975 + 4.39834i) q^{47} +(-2.05309 - 5.41355i) q^{48} +(3.76006 - 1.97343i) q^{49} +(-0.523075 - 0.996637i) q^{50} +(-4.95062 - 1.22022i) q^{51} +(6.54395 + 2.49493i) q^{52} +(-1.84470 + 0.454678i) q^{53} +(-0.880305 - 0.993659i) q^{54} +(-0.289397 - 2.38340i) q^{55} +(-1.39021 + 0.729641i) q^{56} +(1.26916 - 2.41818i) q^{57} +(-0.156312 - 0.0592815i) q^{58} +(3.10092 + 3.50021i) q^{59} +(1.69976 + 0.206388i) q^{60} +(-9.59120 - 2.36402i) q^{61} +(-0.744474 + 0.659546i) q^{62} +(0.544067 - 0.614125i) q^{63} +(5.88881 - 3.09069i) q^{64} +(-1.50528 + 1.32886i) q^{65} +(1.45021 + 0.761127i) q^{66} +(-4.31198 + 1.63532i) q^{67} +(0.754175 - 6.21119i) q^{68} +(11.1870 + 5.87139i) q^{69} -0.221783i q^{70} +(3.75186 - 7.14856i) q^{71} +(0.310226 - 0.350173i) q^{72} +(10.7947 + 7.45108i) q^{73} +(-0.261869 + 0.231995i) q^{74} +(4.21707 - 6.10948i) q^{75} +(3.13348 + 1.18837i) q^{76} +(-2.53682 + 6.68905i) q^{77} +(-0.162718 - 1.36003i) q^{78} +(4.76293 + 12.5588i) q^{79} +2.03697i q^{80} +(2.57876 - 6.79963i) q^{81} +(0.0283908 + 0.233819i) q^{82} +(4.25995 + 8.11666i) q^{83} +(-4.19882 - 2.89824i) q^{84} +(1.47632 + 1.01903i) q^{85} +(-0.300724 - 0.572983i) q^{86} +(-0.132903 - 1.09456i) q^{87} +(-1.44649 + 3.81408i) q^{88} +14.9265i q^{89} +(0.0234338 + 0.0617897i) q^{90} +(5.81161 - 1.42163i) q^{91} +(-5.49766 + 14.4961i) q^{92} +(-6.13357 - 2.32616i) q^{93} +(-1.69103 + 2.44988i) q^{94} +(-0.719184 + 0.637142i) q^{95} +(-3.60873 - 2.49092i) q^{96} +(3.54411 - 4.00048i) q^{97} +(0.473622 - 0.902412i) q^{98} -2.13164i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	0.197515	−	0.136335i	0.139664	−	0.0964034i	−0.496184	−	0.868217i	$-0.665266\pi$
$2$	0.197515	−	0.136335i	0.139664	−	0.0964034i	0.635848	+	0.771814i	$0.280650\pi$
$3$	1.40158	+	0.735608i	0.809205	+	0.424704i	0.817972	−	0.575258i	$-0.195098\pi$
$3$	1.40158	+	0.735608i	0.809205	+	0.424704i	−0.00876680	+	0.999962i	$0.502791\pi$
$4$	−0.688785	+	1.81618i	−0.344392	+	0.908088i
$5$	−0.369290	−	0.416842i	−0.165152	−	0.186418i	0.660109	−	0.751170i	$-0.270510\pi$
$5$	−0.369290	−	0.416842i	−0.165152	−	0.186418i	−0.825260	+	0.564752i	$0.808972\pi$
$6$	0.377124	−	0.0457911i	0.153960	−	0.0186941i
$7$	0.397115	+	1.61116i	0.150095	+	0.608960i	0.997013	+	0.0772361i	$0.0246095\pi$
$7$	0.397115	+	1.61116i	0.150095	+	0.608960i	−0.846918	+	0.531724i	$0.821544\pi$
$8$	0.226434	+	0.918678i	0.0800564	+	0.324802i
$9$	−0.280874	−	0.406917i	−0.0936247	−	0.135639i
$10$	−0.129771	−	0.0319856i	−0.0410371	−	0.0101147i
$11$	3.54807	+	2.44906i	1.06978	+	0.738418i	0.966612	−	0.256245i	$-0.0824855\pi$
$11$	3.54807	+	2.44906i	1.06978	+	0.738418i	0.103172	+	0.994664i	$0.467101\pi$
$12$	−2.30138	+	2.03885i	−0.664352	+	0.588565i
$13$	0.00632121	−	3.60555i	0.00175319	−	0.999998i
$13$	0.00632121	−	3.60555i	0.00175319	−	0.999998i
$14$	0.298093	+	0.264088i	0.0796688	+	0.0705804i
$15$	−0.210959	−	0.855893i	−0.0544693	−	0.220991i
$16$	−2.73784	−	2.42552i	−0.684461	−	0.606379i
$17$	−3.12757	+	0.770877i	−0.758548	+	0.186965i	−0.599576	−	0.800318i	$-0.704664\pi$
$17$	−3.12757	+	0.770877i	−0.758548	+	0.186965i	−0.158972	+	0.987283i	$0.550818\pi$
$18$	−0.110954	−	0.0420793i	−0.0261521	−	0.00991818i
$19$		−	1.72532i		−	0.395814i	−0.980221	−	0.197907i	$-0.936586\pi$
$19$		−	1.72532i		−	0.395814i	0.980221	−	0.197907i	$-0.0634145\pi$
$20$	1.01142	−	0.383581i	0.226160	−	0.0857713i
$21$	−0.628591	+	2.55029i	−0.137170	+	0.556520i
$22$	1.03469			0.220597
$23$	7.98168			1.66429			0.832147	−	0.554555i	$-0.187111\pi$
$23$	7.98168			1.66429			0.832147	+	0.554555i	$0.187111\pi$
$24$	−0.358421	+	1.45417i	−0.0731624	+	0.296832i
$25$	0.565301	−	4.65567i	0.113060	−	0.931135i
$26$	−0.490313	−	0.713012i	−0.0961584	−	0.139833i
$27$	−0.666729	−	5.49101i	−0.128312	−	1.05674i
$28$	−3.19967	−	0.388510i	−0.604681	−	0.0734216i
$29$	−0.395697	−	0.573266i	−0.0734791	−	0.106453i	0.784521	−	0.620102i	$-0.212909\pi$
$29$	−0.395697	−	0.573266i	−0.0734791	−	0.106453i	−0.858000	+	0.513649i	$0.828293\pi$
$30$	−0.158356	−	0.140291i	−0.0289117	−	0.0256135i
$31$	−4.11400	+	0.499530i	−0.738896	+	0.0897182i	−0.481326	−	0.876542i	$-0.659845\pi$
$31$	−4.11400	+	0.499530i	−0.738896	+	0.0897182i	−0.257570	+	0.966260i	$0.582922\pi$
$32$	−2.75000	−	0.333910i	−0.486135	−	0.0590275i
$33$	3.17137	+	6.04255i	0.552065	+	1.05187i
$34$	−0.512646	+	0.578657i	−0.0879180	+	0.0992389i
$35$	0.524948	−	0.760518i	0.0887324	−	0.128551i
$36$	0.932494	−	0.229839i	0.155416	−	0.0383065i
$37$	−1.44710	+	0.175710i	−0.237901	+	0.0288865i	−0.238619	−	0.971113i	$-0.576695\pi$
$37$	−1.44710	+	0.175710i	−0.237901	+	0.0288865i	0.000717505		1.00000i	$0.499772\pi$
$38$	−0.235221	−	0.340776i	−0.0381579	−	0.0552812i
$39$	2.66113	−	5.04883i	0.426122	−	0.808459i
$40$	0.299324	−	0.433646i	0.0473273	−	0.0685654i
$41$	−0.456082	+	0.868992i	−0.0712280	+	0.135714i	−0.918466	−	0.395500i	$-0.870571\pi$
$41$	−0.456082	+	0.868992i	−0.0712280	+	0.135714i	0.847238	+	0.531213i	$0.178264\pi$
$42$	0.223538	+	0.589421i	0.0344927	+	0.0909496i
$43$	0.325001	−	2.67662i	0.0495621	−	0.408181i	−0.946722	−	0.322052i	$-0.895627\pi$
$43$	0.325001	−	2.67662i	0.0495621	−	0.408181i	0.996284	−	0.0861286i	$-0.0274496\pi$
$44$	−6.89177	+	4.75705i	−1.03897	+	0.717152i
$45$	−0.0658960	+	0.267350i	−0.00982319	+	0.0398543i
$46$	1.57650	−	1.08818i	0.232443	−	0.160444i
$47$	−11.5975	+	4.39834i	−1.69167	+	0.641564i	−0.996973	−	0.0777432i	$-0.975229\pi$
$47$	−11.5975	+	4.39834i	−1.69167	+	0.641564i	−0.694692	+	0.719307i	$0.744459\pi$
$48$	−2.05309	−	5.41355i	−0.296338	−	0.781378i
$49$	3.76006	−	1.97343i	0.537152	−	0.281919i
$50$	−0.523075	−	0.996637i	−0.0739740	−	0.140946i
$51$	−4.95062	−	1.22022i	−0.693225	−	0.170865i
$52$	6.54395	+	2.49493i	0.907483	+	0.345984i
$53$	−1.84470	+	0.454678i	−0.253389	+	0.0624549i	−0.363964	−	0.931413i	$-0.618577\pi$
$53$	−1.84470	+	0.454678i	−0.253389	+	0.0624549i	0.110575	+	0.993868i	$0.464731\pi$
$54$	−0.880305	−	0.993659i	−0.119794	−	0.135220i
$55$	−0.289397	−	2.38340i	−0.0390223	−	0.321377i
$56$	−1.39021	+	0.729641i	−0.185775	+	0.0975024i
$57$	1.26916	−	2.41818i	0.168104	−	0.320295i
$58$	−0.156312	−	0.0592815i	−0.0205248	−	0.00778404i
$59$	3.10092	+	3.50021i	0.403705	+	0.455689i	0.914843	−	0.403810i	$-0.132314\pi$
$59$	3.10092	+	3.50021i	0.403705	+	0.455689i	−0.511138	+	0.859499i	$0.670776\pi$
$60$	1.69976	+	0.206388i	0.219438	+	0.0266446i
$61$	−9.59120	−	2.36402i	−1.22803	−	0.302681i	−0.428627	−	0.903481i	$-0.641003\pi$
$61$	−9.59120	−	2.36402i	−1.22803	−	0.302681i	−0.799399	+	0.600800i	$0.794849\pi$
$62$	−0.744474	+	0.659546i	−0.0945483	+	0.0837625i
$63$	0.544067	−	0.614125i	0.0685460	−	0.0773725i
$64$	5.88881	−	3.09069i	0.736101	−	0.386336i
$65$	−1.50528	+	1.32886i	−0.186707	+	0.164824i
$66$	1.45021	+	0.761127i	0.178508	+	0.0936882i
$67$	−4.31198	+	1.63532i	−0.526792	+	0.199786i	−0.603640	−	0.797257i	$-0.706284\pi$
$67$	−4.31198	+	1.63532i	−0.526792	+	0.199786i	0.0768479	+	0.997043i	$0.475514\pi$
$68$	0.754175	−	6.21119i	0.0914571	−	0.753217i
$69$	11.1870	+	5.87139i	1.34676	+	0.706832i
$70$		−	0.221783i		−	0.0265081i
$71$	3.75186	−	7.14856i	0.445263	−	0.848378i	−0.554604	−	0.832114i	$-0.687130\pi$
$71$	3.75186	−	7.14856i	0.445263	−	0.848378i	0.999868	−	0.0162643i	$-0.00517731\pi$
$72$	0.310226	−	0.350173i	0.0365605	−	0.0412682i
$73$	10.7947	+	7.45108i	1.26343	+	0.872082i	0.995810	−	0.0914423i	$-0.0291477\pi$
$73$	10.7947	+	7.45108i	1.26343	+	0.872082i	0.267619	+	0.963525i	$0.413763\pi$
$74$	−0.261869	+	0.231995i	−0.0304416	+	0.0269689i
$75$	4.21707	−	6.10948i	0.486945	−	0.705462i
$76$	3.13348	+	1.18837i	0.359434	+	0.136315i
$77$	−2.53682	+	6.68905i	−0.289098	+	0.762288i
$78$	−0.162718	−	1.36003i	−0.0184242	−	0.153993i
$79$	4.76293	+	12.5588i	0.535871	+	1.41298i	0.880414	+	0.474206i	$0.157265\pi$
$79$	4.76293	+	12.5588i	0.535871	+	1.41298i	−0.344543	+	0.938771i	$0.611966\pi$
$80$			2.03697i			0.227740i
$81$	2.57876	−	6.79963i	0.286529	−	0.755515i
$82$	0.0283908	+	0.233819i	0.00313524	+	0.0258210i
$83$	4.25995	+	8.11666i	0.467590	+	0.890919i	0.999039	+	0.0438283i	$0.0139555\pi$
$83$	4.25995	+	8.11666i	0.467590	+	0.890919i	−0.531449	+	0.847090i	$0.678352\pi$
$84$	−4.19882	−	2.89824i	−0.458129	−	0.316223i
$85$	1.47632	+	1.01903i	0.160129	+	0.110529i
$86$	−0.300724	−	0.572983i	−0.0324280	−	0.0617863i
$87$	−0.132903	−	1.09456i	−0.0142487	−	0.117349i
$88$	−1.44649	+	3.81408i	−0.154196	+	0.406583i
$89$			14.9265i			1.58221i	0.611682	+	0.791104i	$0.290493\pi$
$89$			14.9265i			1.58221i	−0.611682	+	0.791104i	$0.709507\pi$
$90$	0.0234338	+	0.0617897i	0.00247013	+	0.00651321i
$91$	5.81161	−	1.42163i	0.609222	−	0.149027i
$92$	−5.49766	+	14.4961i	−0.573170	+	1.51133i
$93$	−6.13357	−	2.32616i	−0.636022	−	0.241211i
$94$	−1.69103	+	2.44988i	−0.174417	+	0.252686i
$95$	−0.719184	+	0.637142i	−0.0737867	+	0.0653694i
$96$	−3.60873	−	2.49092i	−0.368314	−	0.254229i
$97$	3.54411	−	4.00048i	0.359850	−	0.406187i	−0.540506	−	0.841340i	$-0.681767\pi$
$97$	3.54411	−	4.00048i	0.359850	−	0.406187i	0.900356	+	0.435153i	$0.143306\pi$
$98$	0.473622	−	0.902412i	0.0478431	−	0.0911574i
$99$		−	2.13164i		−	0.214238i
$100$	8.06615	+	4.23344i	0.806615	+	0.423344i
$101$	−0.825756	+	6.80071i	−0.0821658	+	0.676696i	0.892186	+	0.451668i	$0.149171\pi$
$101$	−0.825756	+	6.80071i	−0.0821658	+	0.676696i	−0.974352	+	0.225029i	$0.927752\pi$
$102$	−1.14418	+	0.433931i	−0.113291	+	0.0429656i
$103$	−16.0297	−	8.41305i	−1.57946	−	0.828962i	−0.999902	−	0.0140288i	$-0.995534\pi$
$103$	−16.0297	−	8.41305i	−1.57946	−	0.828962i	−0.579554	−	0.814934i	$-0.696773\pi$
$104$	3.31377	−	0.810610i	0.324942	−	0.0794869i
$105$	1.29520	−	0.679775i	0.126399	−	0.0663392i
$106$	−0.302368	+	0.341303i	−0.0293686	+	0.0331503i
$107$	7.69082	−	6.81347i	0.743500	−	0.658683i	−0.203807	−	0.979011i	$-0.565332\pi$
$107$	7.69082	−	6.81347i	0.743500	−	0.658683i	0.947307	+	0.320328i	$0.103793\pi$
$108$	10.4319	+	2.57122i	1.00381	+	0.247416i
$109$	−1.86701	−	0.226696i	−0.178827	−	0.0217135i	0.0306332	−	0.999531i	$-0.490248\pi$
$109$	−1.86701	−	0.226696i	−0.178827	−	0.0217135i	−0.209460	+	0.977817i	$0.567171\pi$
$110$	−0.382101	−	0.431303i	−0.0364319	−	0.0411231i
$111$	−2.15748	−	0.818226i	−0.204779	−	0.0776625i
$112$	2.82065	−	5.37430i	0.266527	−	0.507824i
$113$	−0.607740	+	0.318966i	−0.0571713	+	0.0300058i	−0.493067	−	0.869992i	$-0.664124\pi$
$113$	−0.607740	+	0.318966i	−0.0571713	+	0.0300058i	0.435895	+	0.899997i	$0.356432\pi$
$114$	−0.0790041	−	0.650657i	−0.00739941	−	0.0609396i
$115$	−2.94755	−	3.32710i	−0.274861	−	0.310254i
$116$	1.31370	−	0.323798i	0.121974	−	0.0300639i
$117$	−1.46893	+	1.01013i	−0.135803	+	0.0933868i
$118$	1.08968	+	0.268582i	0.100313	+	0.0247250i
$119$	−2.48401	−	4.73288i	−0.227709	−	0.433863i
$120$	0.738522	−	0.387606i	0.0674175	−	0.0353834i
$121$	2.69027	+	7.09366i	0.244570	+	0.644879i
$122$	−2.21671	+	0.840686i	−0.200691	+	0.0761121i
$123$	−1.27847	+	0.882468i	−0.115276	+	0.0795694i
$124$	1.92642	−	7.81581i	0.172998	−	0.701881i
$125$	−4.44102	+	3.06542i	−0.397217	+	0.274179i
$126$	0.0237349	−	0.195474i	0.00211447	−	0.0174143i
$127$	−1.80359	−	4.75567i	−0.160043	−	0.421998i	0.830876	−	0.556457i	$-0.187840\pi$
$127$	−1.80359	−	4.75567i	−0.160043	−	0.421998i	−0.990919	+	0.134459i	$0.957070\pi$
$128$	3.31651	−	6.31908i	0.293141	−	0.558533i
$129$	2.42446	−	3.51244i	0.213462	−	0.309253i
$130$	−0.116146	+	0.467692i	−0.0101867	+	0.0410193i
$131$	6.38184	+	9.24569i	0.557584	+	0.807800i	0.995847	−	0.0910473i	$-0.0290214\pi$
$131$	6.38184	+	9.24569i	0.557584	+	0.807800i	−0.438263	+	0.898847i	$0.644406\pi$
$132$	−13.1587	+	1.59776i	−1.14532	+	0.139067i
$133$	2.77975	−	0.685148i	0.241035	−	0.0594098i
$134$	−0.628731	+	0.910874i	−0.0543141	+	0.0786876i
$135$	−2.04267	+	2.30569i	−0.175805	+	0.198443i
$136$	−1.41638	−	2.69868i	−0.121453	−	0.231410i
$137$	−7.48201	−	0.908481i	−0.639231	−	0.0776167i	−0.205497	−	0.978658i	$-0.565881\pi$
$137$	−7.48201	−	0.908481i	−0.639231	−	0.0776167i	−0.433734	+	0.901041i	$0.642804\pi$
$138$	3.01008	−	0.365490i	0.256235	−	0.0311126i
$139$	−12.2456	−	10.8487i	−1.03866	−	0.920171i	−0.0417805	−	0.999127i	$-0.513303\pi$
$139$	−12.2456	−	10.8487i	−1.03866	−	0.920171i	−0.996878	+	0.0789555i	$0.974841\pi$
$140$	1.01966	+	1.47723i	0.0861769	+	0.124849i
$141$	−19.4903	−	2.36655i	−1.64138	−	0.199300i
$142$	−0.233550	−	1.92346i	−0.0195991	−	0.161413i
$143$	8.85261	−	12.7772i	0.740293	−	1.06849i
$144$	−0.217994	+	1.79534i	−0.0181661	+	0.149612i
$145$	−0.0928345	+	0.376644i	−0.00770949	+	0.0312786i
$146$	3.14797			0.260528
$147$	6.72172			0.554398
$148$	0.677620	−	2.74921i	0.0557000	−	0.225984i
$149$	−10.0204	+	3.80024i	−0.820904	+	0.311328i	−0.729063	−	0.684446i	$-0.760044\pi$
$149$	−10.0204	+	3.80024i	−0.820904	+	0.311328i	−0.0918402	+	0.995774i	$0.529275\pi$
$150$		−	1.78165i		−	0.145471i
$151$	−15.2399	−	5.77971i	−1.24020	−	0.470346i	−0.354699	−	0.934981i	$-0.615417\pi$
$151$	−15.2399	−	5.77971i	−1.24020	−	0.470346i	−0.885503	+	0.464634i	$0.846186\pi$
$152$	1.58501	−	0.390670i	0.128561	−	0.0316875i
$153$	1.19214	+	1.05614i	0.0963786	+	0.0853839i
$154$	0.410891	+	1.66705i	0.0331105	+	0.134335i
$155$	1.72748	+	1.53042i	0.138755	+	0.122926i
$156$	7.33661	+	8.31063i	0.587399	+	0.665383i
$157$	3.14097	−	2.78265i	0.250676	−	0.222080i	−0.528422	−	0.848982i	$-0.677216\pi$
$157$	3.14097	−	2.78265i	0.250676	−	0.222080i	0.779098	+	0.626902i	$0.215677\pi$
$158$	2.65296	+	1.83120i	0.211058	+	0.145683i
$159$	−2.91997	−	0.719709i	−0.231569	−	0.0570766i
$160$	0.876358	+	1.26962i	0.0692822	+	0.100373i
$161$	3.16964	+	12.8597i	0.249803	+	1.01349i
$162$	−0.417683	−	1.69461i	−0.0328163	−	0.133141i
$163$	22.9675	−	2.78876i	1.79896	−	0.218433i	0.848479	−	0.529229i	$-0.177519\pi$
$163$	22.9675	−	2.78876i	1.79896	−	0.218433i	0.950477	+	0.310796i	$0.100596\pi$
$164$	−1.26410	−	1.42687i	−0.0987096	−	0.111420i
$165$	1.34763	−	3.55342i	0.104913	−	0.276633i
$166$	1.94799	+	1.02238i	0.151193	+	0.0793524i
$167$	−6.90583	+	4.76675i	−0.534389	+	0.368862i	−0.804487	−	0.593971i	$-0.797560\pi$
$167$	−6.90583	+	4.76675i	−0.534389	+	0.368862i	0.270097	+	0.962833i	$0.412944\pi$
$168$	−2.48523			−0.191740
$169$	−12.9999	−	0.0455828i	−0.999994	−	0.00350637i
$170$	0.430524			0.0330197
$171$	−0.702059	+	0.484597i	−0.0536878	+	0.0370580i
$172$	4.63736	+	2.43387i	0.353595	+	0.185581i
$173$	3.11163	−	8.20468i	0.236572	−	0.623790i	−0.763177	−	0.646190i	$-0.776361\pi$
$173$	3.11163	−	8.20468i	0.236572	−	0.623790i	0.999749	+	0.0223996i	$0.00713060\pi$
$174$	−0.175477	−	0.198073i	−0.0133029	−	0.0150159i
$175$	7.72551	−	0.938047i	0.583994	−	0.0709097i
$176$	−3.77383	−	15.3110i	−0.284463	−	1.15411i
$177$	1.77141	+	7.18690i	0.133147	+	0.540201i
$178$	2.03501	+	2.94821i	0.152530	+	0.220978i
$179$	−14.9596	−	3.68722i	−1.11814	−	0.275596i	−0.363405	−	0.931631i	$-0.618386\pi$
$179$	−14.9596	−	3.68722i	−1.11814	−	0.275596i	−0.754730	+	0.656035i	$0.772232\pi$
$180$	−0.440167	−	0.303826i	−0.0328081	−	0.0226458i
$181$	−12.6262	+	11.1858i	−0.938496	+	0.831435i	−0.985882	−	0.167442i	$-0.946449\pi$
$181$	−12.6262	+	11.1858i	−0.938496	+	0.831435i	0.0473863	+	0.998877i	$0.484911\pi$
$182$	0.954064	−	1.07312i	0.0707199	−	0.0795449i
$183$	−11.7039	−	10.3687i	−0.865176	−	0.766479i
$184$	1.80732	+	7.33259i	0.133238	+	0.540566i
$185$	0.607642	+	0.538324i	0.0446747	+	0.0395784i
$186$	−1.52861	+	0.376769i	−0.112083	+	0.0276260i
$187$	−12.9848	−	4.92447i	−0.949540	−	0.360113i
$188$		−	24.0926i		−	1.75713i
$189$	8.58211	−	3.25476i	0.624256	−	0.236749i
$190$	−0.0551852	+	0.223895i	−0.00400356	+	0.0162431i
$191$	−8.05542			−0.582870			−0.291435	−	0.956591i	$-0.594133\pi$
$191$	−8.05542			−0.582870			−0.291435	+	0.956591i	$0.594133\pi$
$192$	10.5272			0.759735
$193$	−1.39477	+	5.65879i	−0.100398	+	0.407329i	−0.999540	−	0.0303272i	$-0.990345\pi$
$193$	−1.39477	+	5.65879i	−0.100398	+	0.407329i	0.899143	+	0.437656i	$0.144191\pi$
$194$	0.154612	−	1.27334i	0.0111005	−	0.0914206i
$195$	−3.08729	+	0.755211i	−0.221086	+	0.0540817i
$196$	0.994229	+	8.18821i	0.0710163	+	0.584872i
$197$	23.4056	+	2.84196i	1.66758	+	0.202481i	0.899208	−	0.437521i	$-0.144143\pi$
$197$	23.4056	+	2.84196i	1.66758	+	0.202481i	0.768373	+	0.640002i	$0.221066\pi$
$198$	−0.290618	−	0.421033i	−0.0206533	−	0.0299215i
$199$	1.79999	+	1.59465i	0.127598	+	0.113042i	0.724508	−	0.689266i	$-0.242067\pi$
$199$	1.79999	+	1.59465i	0.127598	+	0.113042i	−0.596911	+	0.802308i	$0.703605\pi$
$200$	4.40507	−	0.534872i	0.311485	−	0.0378212i
$201$	−7.24656	−	0.879892i	−0.511133	−	0.0620628i
$202$	0.764076	+	1.45582i	0.0537602	+	0.102431i
$203$	0.766484	−	0.865182i	0.0537967	−	0.0607239i
$204$	5.62604	−	8.15073i	0.393902	−	0.570665i
$205$	0.530659	−	0.130796i	0.0370628	−	0.00913517i
$206$	−4.31311	+	0.523706i	−0.300509	+	0.0364883i
$207$	−2.24185	−	3.24788i	−0.155819	−	0.225743i
$208$	−8.76262	+	9.85609i	−0.607578	+	0.683397i
$209$	4.22539	−	6.12154i	0.292277	−	0.423436i
$210$	0.163145	−	0.310847i	0.0112581	−	0.0214505i
$211$	1.48788	+	3.92321i	0.102430	+	0.270085i	0.976428	−	0.215845i	$-0.0692505\pi$
$211$	1.48788	+	3.92321i	0.102430	+	0.270085i	−0.873998	+	0.485929i	$0.838481\pi$
$212$	0.444827	−	3.66348i	0.0305508	−	0.251609i
$213$	10.5171	−	7.25942i	0.720619	−	0.497407i
$214$	0.590140	−	2.39429i	0.0403411	−	0.163670i
$215$	−1.23575	+	0.852976i	−0.0842773	+	0.0581724i
$216$	4.89350	−	1.85586i	0.332960	−	0.126275i
$217$	−2.43855	−	6.42993i	−0.165539	−	0.436492i
$218$	−0.399670	+	0.209763i	−0.0270690	+	0.0142069i
$219$	9.64868	+	18.3840i	0.651997	+	1.24228i
$220$	4.52800	+	1.11605i	0.305278	+	0.0752442i
$221$	2.75966	+	11.2815i	0.185635	+	0.758874i
$222$	−0.537689	+	0.132528i	−0.0360873	+	0.00889472i
$223$	−8.35446	−	9.43024i	−0.559456	−	0.631495i	0.398926	−	0.916983i	$-0.369383\pi$
$223$	−8.35446	−	9.43024i	−0.559456	−	0.631495i	−0.958382	+	0.285488i	$0.907844\pi$
$224$	−0.554082	−	4.56328i	−0.0370212	−	0.304897i
$225$	−2.05325	+	1.07763i	−0.136883	+	0.0718419i
$226$	−0.0765516	+	0.145857i	−0.00509214	+	0.00970226i
$227$	7.88313	+	2.98968i	0.523221	+	0.198432i	0.602053	−	0.798456i	$-0.294350\pi$
$227$	7.88313	+	2.98968i	0.523221	+	0.198432i	−0.0788314	+	0.996888i	$0.525119\pi$
$228$	3.51766	+	3.97061i	0.232963	+	0.262960i
$229$	−14.3964	−	1.74804i	−0.951339	−	0.115513i	−0.369871	−	0.929083i	$-0.620598\pi$
$229$	−14.3964	−	1.74804i	−0.951339	−	0.115513i	−0.581468	+	0.813570i	$0.697521\pi$
$230$	−1.03579	−	0.255299i	−0.0682978	−	0.0168339i
$231$	−8.47610	+	7.50917i	−0.557686	+	0.494067i
$232$	0.437048	−	0.493325i	0.0286936	−	0.0323884i
$233$	5.44707	−	2.85884i	0.356850	−	0.187289i	−0.276766	−	0.960937i	$-0.589263\pi$
$233$	5.44707	−	2.85884i	0.356850	−	0.187289i	0.633615	+	0.773648i	$0.281570\pi$
$234$	−0.152420	+	0.399783i	−0.00996401	+	0.0261347i
$235$	6.11625	+	3.21005i	0.398980	+	0.209401i
$236$	−8.49286	+	3.22092i	−0.552838	+	0.209664i
$237$	−2.56272	+	21.1059i	−0.166466	+	1.37097i
$238$	−1.13589	−	0.596160i	−0.0736286	−	0.0386433i
$239$		−	5.08882i		−	0.329169i	−0.986363	−	0.164584i	$-0.947372\pi$
$239$		−	5.08882i		−	0.329169i	0.986363	−	0.164584i	$-0.0526283\pi$
$240$	−1.49841	+	2.85498i	−0.0967220	+	0.184288i
$241$	−7.28882	+	8.22738i	−0.469514	+	0.529972i	−0.934793	−	0.355192i	$-0.884415\pi$
$241$	−7.28882	+	8.22738i	−0.469514	+	0.529972i	0.465279	+	0.885164i	$0.345954\pi$
$242$	1.49848	+	1.03433i	0.0963262	+	0.0664892i
$243$	−3.80458	+	3.37056i	−0.244064	+	0.216221i
$244$	10.8997	−	15.7910i	0.697784	−	1.01092i
$245$	−2.21117	−	0.838584i	−0.141266	−	0.0535752i
$246$	−0.132207	+	0.348602i	−0.00842922	+	0.0222260i
$247$	−6.22070	−	0.0109061i	−0.395814	−	0.000693937i
$248$	−1.39046	−	3.66633i	−0.0882940	−	0.232812i
$249$			14.5098i			0.919523i
$250$	−0.459246	+	1.21093i	−0.0290453	+	0.0765861i
$251$	−0.0213620	−	0.175932i	−0.00134836	−	0.0111047i	0.992019	−	0.126087i	$-0.0402419\pi$
$251$	−0.0213620	−	0.175932i	−0.00134836	−	0.0111047i	−0.993368	+	0.114982i	$0.963319\pi$
$252$	0.740614	+	1.41112i	0.0466543	+	0.0888923i
$253$	28.3195	+	19.5476i	1.78043	+	1.22895i
$254$	−1.00460	−	0.693426i	−0.0630343	−	0.0435094i
$255$	1.31958	+	2.51424i	0.0826351	+	0.157448i
$256$	1.39683	+	11.5039i	0.0873020	+	0.718996i
$257$	−0.0818334	+	0.215777i	−0.00510463	+	0.0134598i	−0.937544	−	0.347866i	$-0.886906\pi$
$257$	−0.0818334	+	0.215777i	−0.00510463	+	0.0134598i	0.932440	+	0.361326i	$0.117676\pi$
$258$		−	1.02430i		−	0.0637701i
$259$	−0.857759	−	2.26173i	−0.0532986	−	0.140537i
$260$	−1.37663	−	3.64915i	−0.0853747	−	0.226310i
$261$	−0.122130	+	0.322031i	−0.00755968	+	0.0199332i
$262$	2.52102	+	0.956097i	0.155749	+	0.0590679i
$263$	14.3348	−	20.7676i	0.883922	−	1.28058i	−0.0750785	−	0.997178i	$-0.523921\pi$
$263$	14.3348	−	20.7676i	0.883922	−	1.28058i	0.959000	−	0.283404i	$-0.0914639\pi$
$264$	−4.83305	+	4.28171i	−0.297454	+	0.263521i
$265$	0.870760	+	0.601042i	0.0534903	+	0.0369217i
$266$	0.455634	−	0.514305i	0.0279367	−	0.0315341i
$267$	−10.9801	+	20.9208i	−0.671969	+	1.28033i
$268$		−	8.95770i		−	0.547179i
$269$	11.5785	+	6.07688i	0.705955	+	0.370514i	0.779179	−	0.626802i	$-0.215636\pi$
$269$	11.5785	+	6.07688i	0.705955	+	0.370514i	−0.0732239	+	0.997316i	$0.523329\pi$
$270$	−0.0891112	+	0.733897i	−0.00542314	+	0.0446635i
$271$	23.4179	−	8.88123i	1.42254	−	0.539497i	0.481093	−	0.876670i	$-0.340240\pi$
$271$	23.4179	−	8.88123i	1.42254	−	0.539497i	0.941443	+	0.337173i	$0.109471\pi$
$272$	10.4326	+	5.47544i	0.632568	+	0.331997i
$273$	9.19123	+	2.28253i	0.556278	+	0.138145i
$274$	−1.60167	+	0.840621i	−0.0967604	+	0.0507838i
$275$	13.4077	−	15.1342i	0.808517	−	0.912627i
$276$	−18.3689	+	16.2734i	−1.10568	+	0.979546i
$277$	7.63895	+	1.88283i	0.458980	+	0.113128i	0.462025	−	0.886867i	$-0.347123\pi$
$277$	7.63895	+	1.88283i	0.458980	+	0.113128i	−0.00304474	+	0.999995i	$0.500969\pi$
$278$	−3.89775	−	0.473272i	−0.233771	−	0.0283850i
$279$	1.35878	+	1.53375i	0.0813482	+	0.0918231i
$280$	0.817538	+	0.310051i	0.0488572	+	0.0185291i
$281$	−7.72110	+	14.7113i	−0.460602	+	0.877604i	0.538780	+	0.842447i	$0.318886\pi$
$281$	−7.72110	+	14.7113i	−0.460602	+	0.877604i	−0.999382	+	0.0351573i	$0.988807\pi$
$282$	−4.17228	+	2.18978i	−0.248455	+	0.130399i
$283$	0.931127	+	7.66852i	0.0553497	+	0.455846i	0.993864	+	0.110606i	$0.0352793\pi$
$283$	0.931127	+	7.66852i	0.0553497	+	0.455846i	−0.938515	+	0.345240i	$0.887798\pi$
$284$	10.3988	+	11.7379i	0.617057	+	0.696513i
$285$	−1.47668	+	0.363970i	−0.0874712	+	0.0215597i
$286$	0.00654050	−	3.73062i	0.000386748	−	0.220596i
$287$	−1.58120	−	0.389730i	−0.0933352	−	0.0230051i
$288$	0.636529	+	1.21281i	0.0375079	+	0.0714652i
$289$	−5.86530	+	3.07835i	−0.345018	+	0.181079i
$290$	0.0330136	+	0.0870496i	0.00193862	+	0.00511173i
$291$	7.91016	−	2.99993i	0.463702	−	0.175859i
$292$	−20.9677	+	14.4730i	−1.22704	+	0.846967i
$293$	−3.14068	+	12.7422i	−0.183480	+	0.744410i	0.805027	+	0.593238i	$0.202151\pi$
$293$	−3.14068	+	12.7422i	−0.183480	+	0.744410i	−0.988508	+	0.151171i	$0.951695\pi$
$294$	1.32764	−	0.916406i	0.0774297	−	0.0534459i
$295$	0.313898	−	2.58519i	0.0182759	−	0.150515i
$296$	−0.489092	−	1.28963i	−0.0284279	−	0.0749583i
$297$	11.0822	−	21.1153i	0.643053	−	1.22524i
$298$	−1.46108	+	2.11674i	−0.0846380	+	0.122619i
$299$	0.0504539	−	28.7783i	0.00291782	−	1.66429i
$300$	8.19124	+	11.8671i	0.472921	+	0.685145i
$301$	4.44152	−	0.539298i	0.256005	−	0.0310846i
$302$	−3.79808	+	0.936143i	−0.218555	+	0.0538690i
$303$	−6.16003	+	8.92434i	−0.353884	+	0.512690i
$304$	−4.18478	+	4.72364i	−0.240014	+	0.270919i
$305$	2.55651	+	4.87102i	0.146385	+	0.278914i
$306$	0.379454	+	0.0460741i	0.0216920	+	0.00263388i
$307$	22.1430	−	2.68865i	1.26377	−	0.153450i	0.538921	−	0.842356i	$-0.318832\pi$
$307$	22.1430	−	2.68865i	1.26377	−	0.153450i	0.724850	+	0.688907i	$0.241909\pi$
$308$	−10.4012	−	9.21464i	−0.592662	−	0.525053i
$309$	−16.2783	−	23.5832i	−0.926041	−	1.34160i
$310$	0.549854	+	0.0667643i	0.0312296	+	0.00379196i
$311$	−0.971247	−	7.99894i	−0.0550743	−	0.453578i	−0.993993	−	0.109440i	$-0.965094\pi$
$311$	−0.971247	−	7.99894i	−0.0550743	−	0.453578i	0.938919	−	0.344138i	$-0.111829\pi$
$312$	5.24082	+	1.30150i	0.296703	+	0.0736827i
$313$	3.62562	−	29.8596i	0.204932	−	1.68777i	−0.420346	−	0.907364i	$-0.638091\pi$
$313$	3.62562	−	29.8596i	0.204932	−	1.68777i	0.625278	−	0.780402i	$-0.284986\pi$
$314$	0.241016	−	0.977840i	0.0136013	−	0.0551827i
$315$	−0.456912			−0.0257441
$316$	−26.0896			−1.46766
$317$	7.38724	−	29.9712i	0.414909	−	1.68335i	−0.276601	−	0.960985i	$-0.589208\pi$
$317$	7.38724	−	29.9712i	0.414909	−	1.68335i	0.691510	−	0.722367i	$-0.256946\pi$
$318$	−0.674861	+	0.255941i	−0.0378443	+	0.0143525i
$319$		−	3.00307i		−	0.168140i
$320$	−3.46301	−	1.31335i	−0.193588	−	0.0734183i
$321$	15.7914	−	3.89223i	0.881389	−	0.217243i
$322$	2.37928	+	2.10786i	0.132592	+	0.117467i
$323$	1.33001	+	5.39605i	0.0740035	+	0.300244i
$324$	10.5731	+	9.36696i	0.587395	+	0.520387i
$325$	−16.7827	−	2.06765i	−0.930935	−	0.114692i
$326$	4.15623	−	3.68210i	0.230192	−	0.203933i
$327$	−2.45001	−	1.69112i	−0.135486	−	0.0935192i
$328$	−0.901596	−	0.222223i	−0.0497823	−	0.0122702i
$329$	−11.6919	−	16.9387i	−0.644598	−	0.933861i
$330$	−0.218277	−	0.885584i	−0.0120157	−	0.0487498i
$331$	3.02809	+	12.2855i	0.166439	+	0.675270i	0.993566	+	0.113255i	$0.0361276\pi$
$331$	3.02809	+	12.2855i	0.166439	+	0.675270i	−0.827127	+	0.562015i	$0.810026\pi$
$332$	−17.6755	+	2.14619i	−0.970067	+	0.117787i
$333$	0.477952	+	0.539496i	0.0261916	+	0.0295642i
$334$	−0.714133	+	1.88301i	−0.0390756	+	0.103034i
$335$	2.27404	+	1.19351i	0.124244	+	0.0652084i
$336$	7.90677	−	5.45765i	0.431349	−	0.297739i
$337$	2.70315			0.147250			0.0736251	−	0.997286i	$-0.476543\pi$
$337$	2.70315			0.147250			0.0736251	+	0.997286i	$0.476543\pi$
$338$	−2.57390	+	1.76334i	−0.140002	+	0.0959131i
$339$	−1.08643			−0.0590069
$340$	−2.86760	+	1.97936i	−0.155517	+	0.107346i
$341$	−15.8201	−	8.30304i	−0.856708	−	0.449635i
$342$	−0.0726000	+	0.191430i	−0.00392576	+	0.0103514i
$343$	12.3753	+	13.9688i	0.668202	+	0.754244i
$344$	2.53254	−	0.307507i	0.136546	−	0.0165796i
$345$	−1.68380	−	6.83146i	−0.0906529	−	0.367793i
$346$	−0.503991	−	2.04477i	−0.0270947	−	0.109928i
$347$	13.6074	+	19.7137i	0.730481	+	1.05829i	0.995567	+	0.0940601i	$0.0299846\pi$
$347$	13.6074	+	19.7137i	0.730481	+	1.05829i	−0.265085	+	0.964225i	$0.585400\pi$
$348$	2.07945	+	0.512539i	0.111470	+	0.0274750i
$349$	−25.6253	−	17.6879i	−1.37169	−	0.946809i	−0.999828	−	0.0185209i	$-0.994104\pi$
$349$	−25.6253	−	17.6879i	−1.37169	−	0.946809i	−0.371861	−	0.928288i	$-0.621280\pi$
$350$	1.39802	−	1.23854i	0.0747272	−	0.0662025i
$351$	−19.8023	+	2.36921i	−1.05697	+	0.126459i
$352$	−8.93941	−	7.91963i	−0.476472	−	0.422118i
$353$	−2.50653	−	10.1694i	−0.133409	−	0.541263i	−0.999167	−	0.0408001i	$-0.987009\pi$
$353$	−2.50653	−	10.1694i	−0.133409	−	0.541263i	0.865758	−	0.500463i	$-0.166837\pi$
$354$	1.32971	+	1.17802i	0.0706731	+	0.0626109i
$355$	−4.36535	+	1.07596i	−0.231689	+	0.0571061i
$356$	−27.1092	−	10.2812i	−1.43678	−	0.544900i
$357$		−	8.46079i		−	0.447793i
$358$	−3.45745	+	1.31124i	−0.182732	+	0.0693011i
$359$	−3.83730	+	15.5685i	−0.202525	+	0.821676i	0.778476	+	0.627674i	$0.215993\pi$
$359$	−3.83730	+	15.5685i	−0.202525	+	0.821676i	−0.981001	+	0.194002i	$0.937853\pi$
$360$	−0.260530			−0.0137311
$361$	16.0233			0.843331
$362$	−0.968845	+	3.93076i	−0.0509213	+	0.206596i
$363$	−1.44751	+	11.9214i	−0.0759748	+	0.625709i
$364$	−1.42102	+	11.5341i	−0.0744816	+	0.604551i
$365$	−0.880469	−	7.25131i	−0.0460859	−	0.379551i
$366$	−3.72532	−	0.452335i	−0.194725	−	0.0236440i
$367$	1.87734	+	2.71980i	0.0979963	+	0.141972i	0.868915	−	0.494962i	$-0.164818\pi$
$367$	1.87734	+	2.71980i	0.0979963	+	0.141972i	−0.770919	+	0.636934i	$0.780202\pi$
$368$	−21.8526	−	19.3597i	−1.13914	−	1.00919i
$369$	0.481709	−	0.0584900i	0.0250768	−	0.00304487i
$370$	0.193411	+	0.0234843i	0.0100550	+	0.00122089i
$371$	−1.46512	−	2.79155i	−0.0760651	−	0.144930i
$372$	8.44942	−	9.53743i	0.438082	−	0.494493i
$373$	−14.3439	+	20.7807i	−0.742698	+	1.07598i	0.251440	+	0.967873i	$0.419096\pi$
$373$	−14.3439	+	20.7807i	−0.742698	+	1.07598i	−0.994139	+	0.108112i	$0.965520\pi$
$374$	−3.23607	+	0.797619i	−0.167333	+	0.0412439i
$375$	−8.47941	+	1.02959i	−0.437875	+	0.0531677i
$376$	−6.66672	−	9.65841i	−0.343810	−	0.498095i
$377$	−2.06944	+	1.42308i	−0.106581	+	0.0732923i
$378$	1.25136	−	1.81291i	0.0643630	−	0.0932459i
$379$	10.0303	−	19.1111i	0.515220	−	0.981671i	−0.479352	−	0.877623i	$-0.659128\pi$
$379$	10.0303	−	19.1111i	0.515220	−	0.981671i	0.994572	−	0.104048i	$-0.0331795\pi$
$380$	−0.661798	−	1.74502i	−0.0339495	−	0.0895176i
$381$	0.970431	−	7.99222i	0.0497167	−	0.409454i
$382$	−1.59107	+	1.09824i	−0.0814061	+	0.0561906i
$383$	0.890815	−	3.61418i	0.0455185	−	0.184676i	−0.943782	−	0.330569i	$-0.892759\pi$
$383$	0.890815	−	3.61418i	0.0455185	−	0.184676i	0.989300	+	0.145893i	$0.0466055\pi$
$384$	9.29673	−	6.41707i	0.474422	−	0.327470i
$385$	3.72510	−	1.41275i	0.189849	−	0.0720002i
$386$	0.496003	+	1.30785i	0.0252459	+	0.0665680i
$387$	−1.18045	+	0.619546i	−0.0600054	+	0.0314933i
$388$	4.82444	+	9.19220i	0.244924	+	0.466663i
$389$	25.5320	+	6.29307i	1.29452	+	0.319071i	0.825644	−	0.564191i	$-0.190812\pi$
$389$	25.5320	+	6.29307i	1.29452	+	0.319071i	0.468879	+	0.883262i	$0.344658\pi$
$390$	−0.506826	+	0.570072i	−0.0256641	+	0.0288667i
$391$	−24.9633	+	6.15289i	−1.26245	+	0.311165i
$392$	2.66436	+	3.00744i	0.134570	+	0.151899i
$393$	2.14348	+	17.6532i	0.108124	+	0.890484i
$394$	5.01043	−	2.62968i	0.252422	−	0.132481i
$395$	3.47614	−	6.62323i	0.174904	−	0.333251i
$396$	3.87144	+	1.46824i	0.194547	+	0.0737821i
$397$	−0.00134083	−	0.00151348i	−6.72942e−5	−	7.59595e-5i	0.748477	−	0.663161i	$-0.230785\pi$
$397$	−0.00134083	−	0.00151348i	−6.72942e−5	−	7.59595e-5i	−0.748544	+	0.663085i	$0.769247\pi$
$398$	0.572931	+	0.0695665i	0.0287185	+	0.00348705i
$399$	4.40006	+	1.08452i	0.220279	+	0.0542938i
$400$	−12.8401	+	11.3754i	−0.642006	+	0.568768i
$401$	20.9686	−	23.6687i	1.04712	−	1.18196i	0.0642017	−	0.997937i	$-0.479550\pi$
$401$	20.9686	−	23.6687i	1.04712	−	1.18196i	0.982922	−	0.184022i	$-0.0589116\pi$
$402$	−1.55127	+	0.814168i	−0.0773702	+	0.0406070i
$403$	1.77507	+	14.8364i	0.0884226	+	0.739052i
$404$	−11.7825	−	6.18395i	−0.586202	−	0.307663i
$405$	−3.78668	+	1.43610i	−0.188162	+	0.0713604i
$406$	0.0334378	−	0.275385i	0.00165949	−	0.0136671i
$407$	−5.56473	−	2.92059i	−0.275833	−	0.144768i
$408$		−	4.82433i		−	0.238840i
$409$	−7.71261	+	14.6952i	−0.381364	+	0.726629i	−0.998169	−	0.0604874i	$-0.980734\pi$
$409$	−7.71261	+	14.6952i	−0.381364	+	0.726629i	0.616805	+	0.787116i	$0.288427\pi$
$410$	0.0869812	−	0.0981815i	0.00429570	−	0.00484884i
$411$	−9.81839	−	6.77714i	−0.484305	−	0.334292i
$412$	26.3206	−	23.3180i	1.29672	−	1.14880i
$413$	−4.40797	+	6.38605i	−0.216902	+	0.314237i
$414$	−0.885598	−	0.335863i	−0.0435248	−	0.0165068i
$415$	1.81021	−	4.77313i	0.0888596	−	0.234304i
$416$	−1.22131	+	9.91313i	−0.0598797	+	0.486031i
$417$	−9.18289	−	24.2133i	−0.449688	−	1.18573i
$418$		−	1.78517i		−	0.0873153i
$419$	−3.15503	+	8.31912i	−0.154133	+	0.406416i	−0.989734	−	0.142921i	$-0.954350\pi$
$419$	−3.15503	+	8.31912i	−0.154133	+	0.406416i	0.835601	+	0.549337i	$0.185120\pi$
$420$	0.342475	+	2.82053i	0.0167111	+	0.137628i
$421$	18.3578	+	34.9778i	0.894702	+	1.70471i	0.687187	+	0.726480i	$0.258845\pi$
$421$	18.3578	+	34.9778i	0.894702	+	1.70471i	0.207515	+	0.978232i	$0.433462\pi$
$422$	0.828749	+	0.572044i	0.0403429	+	0.0278467i
$423$	5.04719	+	3.48382i	0.245403	+	0.169389i
$424$	−0.835406	−	1.59173i	−0.0405709	−	0.0773014i
$425$	1.82093	+	14.9967i	0.0883282	+	0.727448i
$426$	1.08757	−	2.86769i	0.0526931	−	0.138940i
$427$		−	16.3917i		−	0.793250i
$428$	7.07714	+	18.6609i	0.342087	+	0.902008i
$429$	21.8067	−	11.3963i	1.05284	−	0.550220i
$430$	−0.127789	+	0.336951i	−0.00616252	+	0.0162492i
$431$	30.7522	+	11.6628i	1.48128	+	0.561775i	0.957081	−	0.289821i	$-0.0935958\pi$
$431$	30.7522	+	11.6628i	1.48128	+	0.561775i	0.524198	+	0.851596i	$0.324365\pi$
$432$	−11.4931	+	16.6507i	−0.552964	+	0.801106i
$433$	25.3859	−	22.4900i	1.21997	−	1.08080i	0.225668	−	0.974204i	$-0.427544\pi$
$433$	25.3859	−	22.4900i	1.21997	−	1.08080i	0.994303	−	0.106595i	$-0.0339948\pi$
$434$	−1.35827	−	0.937549i	−0.0651993	−	0.0450038i
$435$	−0.407178	+	0.459609i	−0.0195227	+	0.0220366i
$436$	1.69769	−	3.23467i	0.0813045	−	0.154913i
$437$		−	13.7709i		−	0.658752i
$438$	4.41215	+	2.31567i	0.210821	+	0.110647i
$439$	−3.50693	+	28.8822i	−0.167377	+	1.37847i	0.630751	+	0.775985i	$0.282747\pi$
$439$	−3.50693	+	28.8822i	−0.167377	+	1.37847i	−0.798128	+	0.602487i	$0.794176\pi$
$440$	2.12405	−	0.805544i	0.101260	−	0.0384028i
$441$	−1.85913	−	0.975746i	−0.0885299	−	0.0464641i
$442$	2.08314	+	1.85203i	0.0990846	+	0.0880919i
$443$	26.1806	−	13.7406i	1.24388	−	0.652836i	0.291153	−	0.956677i	$-0.405961\pi$
$443$	26.1806	−	13.7406i	1.24388	−	0.652836i	0.952723	+	0.303840i	$0.0982689\pi$
$444$	2.97208	−	3.35479i	0.141049	−	0.159211i
$445$	6.22200	−	5.51221i	0.294951	−	0.261304i
$446$	−2.93580	−	0.723611i	−0.139014	−	0.0342640i
$447$	−16.8399	−	2.04474i	−0.796502	−	0.0967128i
$448$	7.31811	+	8.26044i	0.345748	+	0.390269i
$449$	−30.9127	−	11.7236i	−1.45886	−	0.553272i	−0.507580	−	0.861604i	$-0.669460\pi$
$449$	−30.9127	−	11.7236i	−1.45886	−	0.553272i	−0.951279	+	0.308332i	$0.900229\pi$
$450$	−0.258630	+	0.492778i	−0.0121919	+	0.0232298i
$451$	−3.74642	+	1.96627i	−0.176412	+	0.0925882i
$452$	−0.160697	−	1.32346i	−0.00755856	−	0.0622504i
$453$	−17.1083	−	19.3113i	−0.803820	−	0.907325i
$454$	1.96464	−	0.484239i	0.0922049	−	0.0227265i
$455$	−2.73877	−	1.89753i	−0.128395	−	0.0889576i
$456$	2.50890	+	0.618389i	0.117490	+	0.0289587i
$457$	−3.52467	−	6.71570i	−0.164877	−	0.314147i	0.788974	−	0.614426i	$-0.210613\pi$
$457$	−3.52467	−	6.71570i	−0.164877	−	0.314147i	−0.953851	+	0.300279i	$0.902920\pi$
$458$	−3.08182	+	1.61746i	−0.144004	+	0.0755792i
$459$	6.31813	+	16.6595i	0.294905	+	0.777601i
$460$	8.07283	−	3.06162i	0.376398	−	0.142749i
$461$	−24.5876	+	16.9716i	−1.14516	+	0.790445i	−0.980619	−	0.195926i	$-0.937229\pi$
$461$	−24.5876	+	16.9716i	−1.14516	+	0.790445i	−0.164538	+	0.986371i	$0.552613\pi$
$462$	−0.650397	+	2.63876i	−0.0302592	+	0.122766i
$463$	2.31745	−	1.59962i	0.107701	−	0.0743405i	−0.512997	−	0.858390i	$-0.671465\pi$
$463$	2.31745	−	1.59962i	0.107701	−	0.0743405i	0.620698	+	0.784050i	$0.286849\pi$
$464$	−0.307110	+	2.52928i	−0.0142572	+	0.117419i
$465$	1.29543	+	3.41576i	0.0600740	+	0.158402i
$466$	0.686120	−	1.30729i	0.0317839	−	0.0605591i
$467$	15.7770	−	22.8569i	0.730073	−	1.05769i	−0.265538	−	0.964101i	$-0.585549\pi$
$467$	15.7770	−	22.8569i	0.730073	−	1.05769i	0.995611	−	0.0935928i	$-0.0298352\pi$
$468$	−0.822801	−	3.36360i	−0.0380340	−	0.155483i
$469$	−4.34711	−	6.29787i	−0.200731	−	0.290809i
$470$	1.64569	−	0.199824i	0.0759102	−	0.00921717i
$471$	6.44927	−	1.58960i	0.297167	−	0.0732450i
$472$	−2.51341	+	3.64131i	−0.115689	+	0.167605i
$473$	7.70832	−	8.70089i	0.354429	−	0.400068i
$474$	2.37129	+	4.51812i	0.108917	+	0.207524i
$475$	−8.03250	−	0.975322i	−0.368557	−	0.0447509i
$476$	10.3067	−	1.25146i	0.472407	−	0.0573605i
$477$	0.703146	+	0.622933i	0.0321948	+	0.0285221i
$478$	−0.693785	−	1.00512i	−0.0317330	−	0.0459731i
$479$	−18.9410	−	2.29985i	−0.865434	−	0.105083i	−0.324234	−	0.945977i	$-0.605107\pi$
$479$	−18.9410	−	2.29985i	−0.865434	−	0.105083i	−0.541200	+	0.840894i	$0.682030\pi$
$480$	0.294344	+	2.42414i	0.0134349	+	0.110646i
$481$	0.624381	+	5.21869i	0.0284693	+	0.237952i
$482$	−0.317974	+	2.61875i	−0.0144833	+	0.119281i
$483$	−5.01721	+	20.3556i	−0.228291	+	0.926213i
$484$	−14.7364			−0.669835
$485$	−2.97637			−0.135150
$486$	−0.291937	+	1.18443i	−0.0132425	+	0.0537270i
$487$	−28.4360	+	10.7844i	−1.28856	+	0.488686i	−0.901264	−	0.433270i	$-0.857360\pi$
$487$	−28.4360	+	10.7844i	−1.28856	+	0.488686i	−0.387294	+	0.921956i	$0.626590\pi$
$488$		−	9.34652i		−	0.423097i
$489$	34.2424	+	12.9864i	1.54849	+	0.587266i
$490$	−0.551067	+	0.135826i	−0.0248947	+	0.00613599i
$491$	21.8631	+	19.3690i	0.986669	+	0.874112i	0.992046	−	0.125873i	$-0.0401732\pi$
$491$	21.8631	+	19.3690i	0.986669	+	0.874112i	−0.00537737	+	0.999986i	$0.501712\pi$
$492$	−0.722122	−	2.92977i	−0.0325558	−	0.132084i
$493$	1.67949	+	1.48790i	0.0756403	+	0.0670115i
$494$	−1.23017	+	0.845945i	−0.0553480	+	0.0380609i
$495$	−0.888560	+	0.787195i	−0.0399378	+	0.0353818i
$496$	12.4751	+	8.61094i	0.560148	+	0.386642i
$497$	13.0074	+	3.20603i	0.583461	+	0.143810i
$498$	1.97820	+	2.86591i	0.0886452	+	0.128425i
$499$	7.92848	+	32.1671i	0.354927	+	1.44000i	0.828870	+	0.559441i	$0.188984\pi$
$499$	7.92848	+	32.1671i	0.354927	+	1.44000i	−0.473943	+	0.880556i	$0.657170\pi$
$500$	−2.50843	−	10.1771i	−0.112180	−	0.455133i
$501$	−13.1856	+	1.60102i	−0.589088	+	0.0715282i
$502$	−0.0282050	−	0.0318369i	−0.00125885	−	0.00142095i
$503$	−12.9208	+	34.0693i	−0.576109	+	1.51907i	0.257251	+	0.966345i	$0.417183\pi$
$503$	−12.9208	+	34.0693i	−0.576109	+	1.51907i	−0.833360	+	0.552730i	$0.813586\pi$
$504$	0.687378	+	0.360764i	0.0306183	+	0.0160697i
$505$	3.13977	−	2.16723i	0.139718	−	0.0964403i
$506$	8.25856			0.367138
$507$	−18.1870	−	9.62674i	−0.807711	−	0.427538i
$508$	9.87943			0.438329
$509$	1.80828	−	1.24816i	0.0801504	−	0.0553238i	−0.527316	−	0.849669i	$-0.676801\pi$
$509$	1.80828	−	1.24816i	0.0801504	−	0.0553238i	0.607466	+	0.794346i	$0.292186\pi$
$510$	0.603416	+	0.316697i	0.0267197	+	0.0140236i
$511$	−7.71810	+	20.3510i	−0.341429	+	0.900274i
$512$	11.3091	+	12.7653i	0.499795	+	0.564152i
$513$	−9.47372	+	1.15032i	−0.418275	+	0.0507878i
$514$	0.0132546	+	0.0537760i	0.000584635	+	0.00237196i
$515$	2.41270	+	9.78872i	0.106316	+	0.431343i
$516$	4.70927	+	6.82256i	0.207314	+	0.300347i
$517$	−51.9204	−	12.7972i	−2.28346	−	0.562822i
$518$	−0.477773	−	0.329783i	−0.0209921	−	0.0144898i
$519$	10.3966	−	9.21062i	0.456362	−	0.404301i
$520$	−1.56164	−	1.08197i	−0.0684824	−	0.0474474i
$521$	3.70576	+	3.28302i	0.162352	+	0.143832i	0.740388	−	0.672180i	$-0.234642\pi$
$521$	3.70576	+	3.28302i	0.162352	+	0.143832i	−0.578035	+	0.816012i	$0.696180\pi$
$522$	0.0197815	+	0.0802567i	0.000865813	+	0.00351274i
$523$	−4.67843	−	4.14473i	−0.204573	−	0.181236i	0.554615	−	0.832107i	$-0.312866\pi$
$523$	−4.67843	−	4.14473i	−0.204573	−	0.181236i	−0.759189	+	0.650871i	$0.774404\pi$
$524$	−21.1875	+	5.22225i	−0.925581	+	0.228135i
$525$	11.5180	+	4.36820i	0.502686	+	0.190644i
$526$		−	6.05624i		−	0.264065i
$527$	12.4817	−	4.73370i	0.543713	−	0.206203i
$528$	5.97358	−	24.2358i	0.259967	−	1.05473i
$529$	40.7072			1.76988
$530$	0.253931			0.0110301
$531$	0.553326	−	2.24493i	0.0240123	−	0.0974218i
$532$	−0.670303	+	5.52044i	−0.0290613	+	0.239341i
$533$	3.13031	+	1.64992i	0.135589	+	0.0714659i
$534$	0.683501	+	5.62914i	0.0295780	+	0.243597i
$535$	−5.68029	−	0.689712i	−0.245580	−	0.0298188i
$536$	−2.47871	−	3.59103i	−0.107064	−	0.155109i
$537$	−18.2548	−	16.1724i	−0.787755	−	0.697890i
$538$	3.11543	−	0.378281i	0.134316	−	0.0163089i
$539$	18.1740	+	2.20673i	0.782811	+	0.0950504i
$540$	−2.78059	−	5.29797i	−0.119658	−	0.227988i
$541$	24.5778	−	27.7426i	1.05668	−	1.19275i	0.0760081	−	0.997107i	$-0.475783\pi$
$541$	24.5778	−	27.7426i	1.05668	−	1.19275i	0.980675	−	0.195642i	$-0.0626790\pi$
$542$	3.41457	−	4.94686i	0.146668	−	0.212486i
$543$	−25.9250	+	6.38994i	−1.11255	+	0.274219i
$544$	8.85821	−	1.07558i	0.379793	−	0.0461152i
$545$	0.594972	+	0.861965i	0.0254858	+	0.0369225i
$546$	2.12660	−	0.802250i	0.0910100	−	0.0343331i
$547$	−15.5987	+	22.5986i	−0.666950	+	0.966244i	0.332780	+	0.943005i	$0.392013\pi$
$547$	−15.5987	+	22.5986i	−0.666950	+	0.966244i	−0.999730	+	0.0232397i	$0.992602\pi$
$548$	6.80346	−	12.9629i	0.290629	−	0.553748i
$549$	1.73196	+	4.56681i	0.0739183	+	0.194907i
$550$	0.584911	−	4.81718i	0.0249407	−	0.205405i
$551$	−0.989064	+	0.682702i	−0.0421356	+	0.0290841i
$552$	−2.86080	+	11.6067i	−0.121764	+	0.494015i
$553$	−18.3428	+	12.6611i	−0.780015	+	0.538405i
$554$	1.76551	−	0.669568i	0.0750092	−	0.0284472i
$555$	0.455666	+	1.20149i	0.0193420	+	0.0510005i
$556$	28.1377	−	14.7678i	1.19330	−	0.626294i
$557$	17.3154	+	32.9918i	0.733679	+	1.39791i	0.910435	+	0.413653i	$0.135747\pi$
$557$	17.3154	+	32.9918i	0.733679	+	1.39791i	−0.176756	+	0.984255i	$0.556560\pi$
$558$	0.477484	+	0.117689i	0.0202135	+	0.00498218i
$559$	−9.64863	−	1.18872i	−0.408093	−	0.0502777i
$560$	−3.28188	+	0.808910i	−0.138685	+	0.0341827i
$561$	−14.5768	−	16.4538i	−0.615431	−	0.694679i
$562$	0.480633	+	3.95837i	0.0202743	+	0.166974i
$563$	34.5743	−	18.1460i	1.45713	−	0.764763i	0.464461	−	0.885593i	$-0.346248\pi$
$563$	34.5743	−	18.1460i	1.45713	−	0.764763i	0.992673	+	0.120830i	$0.0385557\pi$
$564$	17.7227	−	33.7678i	0.746260	−	1.42188i
$565$	0.357391	+	0.135540i	0.0150355	+	0.00570223i
$566$	1.22940	+	1.38770i	0.0516755	+	0.0583296i
$567$	11.9793	+	1.45456i	0.503085	+	0.0610856i
$568$	7.41678	+	1.82807i	0.311201	+	0.0767042i
$569$	−34.5847	+	30.6393i	−1.44986	+	1.28447i	−0.559805	+	0.828624i	$0.689124\pi$
$569$	−34.5847	+	30.6393i	−1.44986	+	1.28447i	−0.890060	+	0.455844i	$0.849338\pi$
$570$	−0.242046	+	0.273213i	−0.0101382	+	0.0114436i
$571$	9.29620	−	4.87902i	0.389034	−	0.204181i	−0.258854	−	0.965916i	$-0.583345\pi$
$571$	9.29620	−	4.87902i	0.389034	−	0.204181i	0.647888	+	0.761736i	$0.275653\pi$
$572$	17.1082	+	24.8787i	0.715329	+	1.04023i
$573$	−11.2904	−	5.92563i	−0.471661	−	0.247547i
$574$	−0.365445	+	0.138595i	−0.0152534	+	0.00578484i
$575$	4.51205	−	37.1601i	0.188166	−	1.54968i
$576$	−2.91167	−	1.52816i	−0.121319	−	0.0636734i
$577$		−	26.4188i		−	1.09983i	−0.835221	−	0.549915i	$-0.814660\pi$
$577$		−	26.4188i		−	1.09983i	0.835221	−	0.549915i	$-0.185340\pi$
$578$	−0.738800	+	1.40767i	−0.0307300	+	0.0585512i
$579$	−6.11754	+	6.90527i	−0.254236	+	0.286973i
$580$	−0.620110	−	0.428031i	−0.0257487	−	0.0177730i
$581$	−11.3855	+	10.0867i	−0.472351	+	0.418466i
$582$	1.15338	−	1.67096i	0.0478092	−	0.0692636i
$583$	−7.65867	−	2.90455i	−0.317190	−	0.120294i
$584$	−4.40084	+	11.6041i	−0.182108	+	0.480180i
$585$	0.963528	+	0.239281i	0.0398370	+	0.00989305i
$586$	1.11688	+	2.94497i	0.0461379	+	0.121656i
$587$			12.3709i			0.510603i	0.966861	+	0.255302i	$0.0821748\pi$
$587$			12.3709i			0.510603i	−0.966861	+	0.255302i	$0.917825\pi$
$588$	−4.62982	+	12.2078i	−0.190931	+	0.503443i
$589$	0.861846	+	7.09794i	0.0355118	+	0.292466i
$590$	−0.290451	−	0.553409i	−0.0119577	−	0.0227835i
$591$	30.7144	+	21.2006i	1.26342	+	0.872077i
$592$	4.38811	+	3.02890i	0.180350	+	0.124487i
$593$	−12.9357	−	24.6469i	−0.531205	−	1.01213i	−0.992192	−	0.124720i	$-0.960197\pi$
$593$	−12.9357	−	24.6469i	−0.531205	−	1.01213i	0.460987	−	0.887407i	$-0.347496\pi$
$594$	−0.689858	−	5.68149i	−0.0283052	−	0.233114i
$595$	−1.05555	+	2.78325i	−0.0432732	+	0.114102i
$596$		−	20.8164i		−	0.852672i
$597$	1.34980	+	3.55912i	0.0552435	+	0.145665i
$598$	−3.91352	−	5.69103i	−0.160036	−	0.232724i
$599$	−0.495046	+	1.30533i	−0.0202270	+	0.0533343i	−0.944749	−	0.327794i	$-0.893695\pi$
$599$	−0.495046	+	1.30533i	−0.0202270	+	0.0533343i	0.924522	+	0.381128i	$0.124464\pi$
$600$	6.56753	+	2.49074i	0.268118	+	0.101684i
$601$	−12.9670	+	18.7859i	−0.528934	+	0.766293i	−0.992822	−	0.119601i	$-0.961839\pi$
$601$	−12.9670	+	18.7859i	−0.528934	+	0.766293i	0.463888	+	0.885894i	$0.346454\pi$
$602$	0.803743	−	0.712054i	0.0327581	−	0.0290212i
$603$	1.87656	+	1.29530i	0.0764195	+	0.0527486i
$604$	20.9940	−	23.6973i	0.854232	−	0.964228i
$605$	1.96345	−	3.74104i	0.0798255	−	0.152095i
$606$			2.60252i			0.105720i
$607$	−16.7340	−	8.78267i	−0.679212	−	0.356478i	0.0895777	−	0.995980i	$-0.471448\pi$
$607$	−16.7340	−	8.78267i	−0.679212	−	0.356478i	−0.768789	+	0.639502i	$0.779141\pi$
$608$	−0.576100	+	4.74461i	−0.0233639	+	0.192419i
$609$	1.71073	−	0.648794i	0.0693222	−	0.0262904i
$610$	1.16904	+	0.613560i	0.0473331	+	0.0248423i
$611$	15.7851	+	41.8430i	0.638597	+	1.69279i
$612$	−2.73926	+	1.43768i	−0.110728	+	0.0581146i
$613$	14.3628	−	16.2123i	0.580108	−	0.654807i	−0.383055	−	0.923726i	$-0.625128\pi$
$613$	14.3628	−	16.2123i	0.580108	−	0.654807i	0.963163	+	0.268919i	$0.0866664\pi$
$614$	4.00703	−	3.54992i	0.161711	−	0.143263i
$615$	0.839978	+	0.207036i	0.0338712	+	0.00834849i
$616$	−6.71951	−	0.815896i	−0.270737	−	0.0328734i
$617$	−8.05131	−	9.08805i	−0.324134	−	0.365871i	0.563745	−	0.825949i	$-0.309360\pi$
$617$	−8.05131	−	9.08805i	−0.324134	−	0.365871i	−0.887879	+	0.460078i	$0.847822\pi$
$618$	−6.43043	−	2.43874i	−0.258670	−	0.0981005i
$619$	2.47064	−	4.70742i	0.0993036	−	0.189207i	−0.830736	−	0.556667i	$-0.812080\pi$
$619$	2.47064	−	4.70742i	0.0993036	−	0.189207i	0.930040	+	0.367460i	$0.119772\pi$
$620$	−3.96937	+	2.08329i	−0.159414	+	0.0836668i
$621$	−5.32161	−	43.8274i	−0.213549	−	1.75873i
$622$	−1.28237	−	1.44750i	−0.0514184	−	0.0580394i
$623$	−24.0490	+	5.92754i	−0.963501	+	0.237482i
$624$	−19.5318	+	7.36828i	−0.781897	+	0.294967i
$625$	−19.8501	−	4.89262i	−0.794005	−	0.195705i
$626$	−3.35480	−	6.39203i	−0.134085	−	0.255477i
$627$	10.4253	−	5.47162i	0.416346	−	0.218515i
$628$	2.89034	+	7.62120i	0.115337	+	0.304119i
$629$	4.39045	−	1.66508i	0.175059	−	0.0663910i
$630$	−0.0902471	+	0.0622931i	−0.00359553	+	0.00248182i
$631$	9.27985	−	37.6498i	0.369425	−	1.49882i	−0.432633	−	0.901570i	$-0.642415\pi$
$631$	9.27985	−	37.6498i	0.369425	−	1.49882i	0.802058	−	0.597247i	$-0.203739\pi$
$632$	−10.4590	+	7.21934i	−0.416037	+	0.287170i
$633$	−0.800560	+	6.59320i	−0.0318194	+	0.262056i
$634$	−2.62703	−	6.92691i	−0.104333	−	0.275103i
$635$	−1.31632	+	2.50804i	−0.0522365	+	0.0995283i
$636$	3.31835	−	4.80746i	0.131581	−	0.190628i
$637$	−7.09154	−	13.5696i	−0.280977	−	0.537646i
$638$	−0.409424	−	0.593152i	−0.0162092	−	0.0234831i
$639$	−3.96267	+	0.481155i	−0.156761	+	0.0190342i
$640$	−3.85881	+	0.951112i	−0.152533	+	0.0375960i
$641$	−8.42826	+	12.2104i	−0.332896	+	0.482284i	−0.953311	−	0.301990i	$-0.902349\pi$
$641$	−8.42826	+	12.2104i	−0.332896	+	0.482284i	0.620415	+	0.784274i	$0.286964\pi$
$642$	2.58839	−	2.92169i	0.102156	−	0.115310i
$643$	5.91504	+	11.2702i	0.233266	+	0.444452i	0.973749	−	0.227623i	$-0.0730954\pi$
$643$	5.91504	+	11.2702i	0.233266	+	0.444452i	−0.740483	+	0.672075i	$0.765403\pi$
$644$	−25.5387	−	3.10097i	−1.00637	−	0.122195i
$645$	−2.35946	+	0.286491i	−0.0929037	+	0.0112806i
$646$	0.998366	+	0.884475i	0.0392802	+	0.0347992i
$647$	−2.24407	−	3.25110i	−0.0882235	−	0.127814i	0.776387	−	0.630256i	$-0.217050\pi$
$647$	−2.24407	−	3.25110i	−0.0882235	−	0.127814i	−0.864611	+	0.502443i	$0.832435\pi$
$648$	6.83059	+	0.829384i	0.268331	+	0.0325813i
$649$	2.43006	+	20.0133i	0.0953880	+	0.785591i
$650$	−3.59673	+	1.87967i	−0.141075	+	0.0737268i
$651$	1.31207	−	10.8059i	0.0514242	−	0.423517i
$652$	−10.7548	+	43.6339i	−0.421190	+	1.70884i
$653$	12.8275			0.501979			0.250990	−	0.967990i	$-0.419244\pi$
$653$	12.8275			0.501979			0.250990	+	0.967990i	$0.419244\pi$
$654$	−0.714474			−0.0279381
$655$	1.49724	−	6.07456i	0.0585022	−	0.237353i
$656$	3.35643	−	1.27293i	0.131047	−	0.0496995i
$657$		−	6.48538i		−	0.253019i
$658$	−4.61868	−	1.75163i	−0.180055	−	0.0682858i
$659$	−32.9940	+	8.13229i	−1.28526	+	0.316789i	−0.822029	−	0.569446i	$-0.807158\pi$
$659$	−32.9940	+	8.13229i	−1.28526	+	0.316789i	−0.463235	+	0.886235i	$0.653312\pi$
$660$	5.52540	+	4.89508i	0.215076	+	0.190541i
$661$	−8.11244	−	32.9135i	−0.315537	−	1.28019i	−0.887843	−	0.460146i	$-0.847797\pi$
$661$	−8.11244	−	32.9135i	−0.315537	−	1.28019i	0.572306	−	0.820040i	$-0.306049\pi$
$662$	2.27303	+	2.01373i	0.0883439	+	0.0782659i
$663$	−4.43085	+	17.8420i	−0.172080	+	0.692925i
$664$	−6.49200	+	5.75141i	−0.251938	+	0.223198i
$665$	−1.31213	−	0.905701i	−0.0508824	−	0.0351216i
$666$	0.167955	+	0.0413972i	0.00650812	+	0.00160411i
$667$	−3.15832	−	4.57562i	−0.122291	−	0.177169i
$668$	−3.90063	−	15.8255i	−0.150920	−	0.612306i
$669$	−4.77252	−	19.3629i	−0.184516	−	0.748612i
$670$	0.611875	−	0.0742951i	0.0236388	−	0.00287027i
$671$	−28.2406	−	31.8771i	−1.09022	−	1.23060i
$672$	2.58019	−	6.80341i	0.0995330	−	0.262447i
$673$	−23.8716	−	12.5288i	−0.920181	−	0.482948i	−0.0630291	−	0.998012i	$-0.520076\pi$
$673$	−23.8716	−	12.5288i	−0.920181	−	0.482948i	−0.857152	+	0.515063i	$0.827768\pi$
$674$	0.533914	−	0.368535i	0.0205656	−	0.0141954i
$675$	−25.9412			−0.998478
$676$	9.03693	−	23.5787i	0.347574	−	0.906875i
$677$	31.5499			1.21256			0.606280	−	0.795251i	$-0.292661\pi$
$677$	31.5499			1.21256			0.606280	+	0.795251i	$0.292661\pi$
$678$	−0.214587	+	0.148119i	−0.00824117	+	0.00568847i
$679$	7.85281	+	4.12147i	0.301363	+	0.158168i
$680$	−0.601870	+	1.58700i	−0.0230807	+	0.0608587i
$681$	8.84964	+	9.98918i	0.339119	+	0.382786i
$682$	−4.25671	+	0.516858i	−0.162998	+	0.0197915i
$683$	2.46175	+	9.98773i	0.0941964	+	0.382170i	0.999051	−	0.0435504i	$-0.0138669\pi$
$683$	2.46175	+	9.98773i	0.0941964	+	0.382170i	−0.904855	+	0.425720i	$0.860021\pi$
$684$	−0.396545	−	1.60885i	−0.0151623	−	0.0615158i
$685$	2.38434	+	3.45431i	0.0911009	+	0.131982i
$686$	4.34874	+	1.07187i	0.166036	+	0.0409241i
$687$	−18.8919	−	13.0401i	−0.720769	−	0.497511i
$688$	−7.38199	+	6.53987i	−0.281436	+	0.249330i
$689$	1.62770	+	6.65403i	0.0620105	+	0.253499i
$690$	−1.26394	−	1.11976i	−0.0481175	−	0.0426284i
$691$	3.18022	+	12.9027i	0.120981	+	0.490841i	0.999904	+	0.0138760i	$0.00441702\pi$
$691$	3.18022	+	12.9027i	0.120981	+	0.490841i	−0.878922	+	0.476965i	$0.841737\pi$
$692$	12.7579	+	11.3025i	0.484983	+	0.429657i
$693$	3.43442	−	0.846507i	0.130463	−	0.0321562i
$694$	5.37532	+	2.03859i	0.204045	+	0.0773839i
$695$			9.11079i			0.345592i
$696$	0.975453	−	0.369941i	0.0369745	−	0.0140226i
$697$	0.756543	−	3.06942i	0.0286561	−	0.116262i
$698$	−7.47286			−0.282852
$699$	9.73752			0.368307
$700$	−3.61756	+	14.6770i	−0.136731	+	0.554738i
$701$	−0.0933761	+	0.769021i	−0.00352677	+	0.0290455i	−0.994366	−	0.106001i	$-0.966195\pi$
$701$	−0.0933761	+	0.769021i	−0.00352677	+	0.0290455i	0.990839	+	0.135047i	$0.0431184\pi$
$702$	−3.58825	+	3.16770i	−0.135430	+	0.119557i
$703$	0.303154	+	2.49670i	0.0114337	+	0.0941648i
$704$	28.4632	+	3.45606i	1.07275	+	0.130255i
$705$	6.21109	+	8.99832i	0.233923	+	0.338896i
$706$	−1.88153	−	1.66689i	−0.0708121	−	0.0627341i
$707$	−11.2849	+	1.37024i	−0.424414	+	0.0515332i
$708$	−14.2728	−	1.73303i	−0.536405	−	0.0651313i
$709$	14.8538	+	28.3016i	0.557847	+	1.06289i	0.987160	+	0.159733i	$0.0510633\pi$
$709$	14.8538	+	28.3016i	0.557847	+	1.06289i	−0.429313	+	0.903156i	$0.641244\pi$
$710$	−0.715532	+	0.807668i	−0.0268534	+	0.0303112i
$711$	3.77260	−	5.46556i	0.141484	−	0.204974i
$712$	−13.7127	+	3.37987i	−0.513904	+	0.126666i
$713$	−32.8366	+	3.98708i	−1.22974	+	0.149317i
$714$	−1.15350	−	1.67114i	−0.0431687	−	0.0625407i
$715$	−8.59528	+	1.02837i	−0.321445	+	0.0384588i
$716$	17.0006	−	24.6296i	0.635342	−	0.920452i
$717$	3.74338	−	7.13242i	0.139799	−	0.266365i
$718$	1.36461	+	3.59818i	0.0509268	+	0.134283i
$719$	4.72083	−	38.8795i	0.176057	−	1.44996i	−0.590111	−	0.807322i	$-0.700916\pi$
$719$	4.72083	−	38.8795i	0.176057	−	1.44996i	0.766168	−	0.642640i	$-0.222161\pi$
$720$	0.828876	−	0.572132i	0.0308904	−	0.0213221i
$721$	7.18911	−	29.1674i	0.267736	−	1.08625i
$722$	3.16484	−	2.18453i	0.117783	−	0.0813000i
$723$	−16.2680	+	6.16965i	−0.605015	+	0.229452i
$724$	−11.6187	−	30.6360i	−0.431805	−	1.13858i
$725$	−2.89263	+	1.51817i	−0.107429	+	0.0563833i
$726$	1.33939	+	2.55200i	0.0497095	+	0.0947135i
$727$	6.98098	+	1.72066i	0.258910	+	0.0638156i	0.366634	−	0.930365i	$-0.380510\pi$
$727$	6.98098	+	1.72066i	0.258910	+	0.0638156i	−0.107724	+	0.994181i	$0.534356\pi$
$728$	2.62197	+	5.01709i	0.0971765	+	0.185946i
$729$	−28.9945	+	7.14651i	−1.07387	+	0.264685i
$730$	−1.16251	−	1.31221i	−0.0430266	−	0.0485670i
$731$	1.04688	+	8.62186i	0.0387204	+	0.318891i
$732$	26.8929	−	14.1145i	0.993990	−	0.521686i
$733$	12.3260	−	23.4853i	0.455272	−	0.867449i	−0.544319	−	0.838878i	$-0.683212\pi$
$733$	12.3260	−	23.4853i	0.455272	−	0.867449i	0.999592	−	0.0285710i	$-0.00909566\pi$
$734$	0.741606	+	0.281254i	0.0273732	+	0.0103813i
$735$	−2.48227	−	2.80190i	−0.0915597	−	0.103350i
$736$	−21.9496	−	2.66516i	−0.809072	−	0.0982392i
$737$	−19.3042	−	4.75806i	−0.711079	−	0.175265i
$738$	0.0871706	−	0.0772264i	0.00320879	−	0.00284274i
$739$	−9.35995	+	10.5652i	−0.344311	+	0.388647i	−0.895002	−	0.446062i	$-0.852826\pi$
$739$	−9.35995	+	10.5652i	−0.344311	+	0.388647i	0.550690	+	0.834710i	$0.314364\pi$
$740$	−1.39623	+	0.732796i	−0.0513263	+	0.0269381i
$741$	−8.71082	−	4.59129i	−0.320000	−	0.168665i
$742$	−0.669968	−	0.351627i	−0.0245953	−	0.0129086i
$743$	−18.2721	+	6.92968i	−0.670337	+	0.254225i	−0.666208	−	0.745766i	$-0.732084\pi$
$743$	−18.2721	+	6.92968i	−0.670337	+	0.254225i	−0.00412915	+	0.999991i	$0.501314\pi$
$744$	0.748142	−	6.16150i	0.0274282	−	0.225892i
$745$	5.28454	+	2.77354i	0.193610	+	0.101615i
$746$			6.06008i			0.221875i
$747$	2.10629	−	4.01320i	0.0770652	−	0.146835i
$748$	17.8874	−	20.1907i	0.654029	−	0.738246i
$749$	14.0317	+	9.68539i	0.512707	+	0.353896i
$750$	−1.53445	+	1.35940i	−0.0560300	+	0.0496383i
$751$	21.8243	−	31.6180i	0.796381	−	1.15376i	−0.188763	−	0.982023i	$-0.560448\pi$
$751$	21.8243	−	31.6180i	0.796381	−	1.15376i	0.985143	−	0.171734i	$-0.0549369\pi$
$752$	42.4203	+	16.0879i	1.54691	+	0.586666i
$753$	0.0994764	−	0.262298i	0.00362512	−	0.00955866i
$754$	−0.214730	+	0.563217i	−0.00782001	+	0.0205111i
$755$	3.21870	+	8.48700i	0.117140	+	0.308874i
$756$			17.8284i			0.648414i
$757$	1.97638	−	5.21129i	0.0718328	−	0.189407i	−0.894291	−	0.447485i	$-0.852320\pi$
$757$	1.97638	−	5.21129i	0.0718328	−	0.189407i	0.966124	+	0.258078i	$0.0830890\pi$
$758$	−0.624377	−	5.14221i	−0.0226784	−	0.186773i
$759$	25.3129	+	48.2297i	0.918800	+	1.75063i
$760$	−0.748176	−	0.516428i	−0.0271392	−	0.0187328i
$761$	−22.9787	−	15.8611i	−0.832979	−	0.574964i	0.0734614	−	0.997298i	$-0.476595\pi$
$761$	−22.9787	−	15.8611i	−0.832979	−	0.574964i	−0.906440	+	0.422334i	$0.861211\pi$
$762$	−0.897944	−	1.71089i	−0.0325291	−	0.0619790i
$763$	−0.376174	−	3.09807i	−0.0136184	−	0.112158i
$764$	5.54845	−	14.6301i	0.200736	−	0.529297i
$765$		−	0.886955i		−	0.0320679i
$766$	−0.316789	−	0.835305i	−0.0114461	−	0.0301808i

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.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.197515 - 0.136335i) q^{2} +(1.40158 + 0.735608i) q^{3} +(-0.688785 + 1.81618i) q^{4} +(-0.369290 - 0.416842i) q^{5} +(0.377124 - 0.0457911i) q^{6} +(0.397115 + 1.61116i) q^{7} +(0.226434 + 0.918678i) q^{8} +(-0.280874 - 0.406917i) q^{9} +O(q^{10})\)	\(q+(0.197515 - 0.136335i) q^{2} +(1.40158 + 0.735608i) q^{3} +(-0.688785 + 1.81618i) q^{4} +(-0.369290 - 0.416842i) q^{5} +(0.377124 - 0.0457911i) q^{6} +(0.397115 + 1.61116i) q^{7} +(0.226434 + 0.918678i) q^{8} +(-0.280874 - 0.406917i) q^{9} +(-0.129771 - 0.0319856i) q^{10} +(3.54807 + 2.44906i) q^{11} +(-2.30138 + 2.03885i) q^{12} +(0.00632121 - 3.60555i) q^{13} +(0.298093 + 0.264088i) q^{14} +(-0.210959 - 0.855893i) q^{15} +(-2.73784 - 2.42552i) q^{16} +(-3.12757 + 0.770877i) q^{17} +(-0.110954 - 0.0420793i) q^{18} -1.72532i q^{19} +(1.01142 - 0.383581i) q^{20} +(-0.628591 + 2.55029i) q^{21} +1.03469 q^{22} +7.98168 q^{23} +(-0.358421 + 1.45417i) q^{24} +(0.565301 - 4.65567i) q^{25} +(-0.490313 - 0.713012i) q^{26} +(-0.666729 - 5.49101i) q^{27} +(-3.19967 - 0.388510i) q^{28} +(-0.395697 - 0.573266i) q^{29} +(-0.158356 - 0.140291i) q^{30} +(-4.11400 + 0.499530i) q^{31} +(-2.75000 - 0.333910i) q^{32} +(3.17137 + 6.04255i) q^{33} +(-0.512646 + 0.578657i) q^{34} +(0.524948 - 0.760518i) q^{35} +(0.932494 - 0.229839i) q^{36} +(-1.44710 + 0.175710i) q^{37} +(-0.235221 - 0.340776i) q^{38} +(2.66113 - 5.04883i) q^{39} +(0.299324 - 0.433646i) q^{40} +(-0.456082 + 0.868992i) q^{41} +(0.223538 + 0.589421i) q^{42} +(0.325001 - 2.67662i) q^{43} +(-6.89177 + 4.75705i) q^{44} +(-0.0658960 + 0.267350i) q^{45} +(1.57650 - 1.08818i) q^{46} +(-11.5975 + 4.39834i) q^{47} +(-2.05309 - 5.41355i) q^{48} +(3.76006 - 1.97343i) q^{49} +(-0.523075 - 0.996637i) q^{50} +(-4.95062 - 1.22022i) q^{51} +(6.54395 + 2.49493i) q^{52} +(-1.84470 + 0.454678i) q^{53} +(-0.880305 - 0.993659i) q^{54} +(-0.289397 - 2.38340i) q^{55} +(-1.39021 + 0.729641i) q^{56} +(1.26916 - 2.41818i) q^{57} +(-0.156312 - 0.0592815i) q^{58} +(3.10092 + 3.50021i) q^{59} +(1.69976 + 0.206388i) q^{60} +(-9.59120 - 2.36402i) q^{61} +(-0.744474 + 0.659546i) q^{62} +(0.544067 - 0.614125i) q^{63} +(5.88881 - 3.09069i) q^{64} +(-1.50528 + 1.32886i) q^{65} +(1.45021 + 0.761127i) q^{66} +(-4.31198 + 1.63532i) q^{67} +(0.754175 - 6.21119i) q^{68} +(11.1870 + 5.87139i) q^{69} -0.221783i q^{70} +(3.75186 - 7.14856i) q^{71} +(0.310226 - 0.350173i) q^{72} +(10.7947 + 7.45108i) q^{73} +(-0.261869 + 0.231995i) q^{74} +(4.21707 - 6.10948i) q^{75} +(3.13348 + 1.18837i) q^{76} +(-2.53682 + 6.68905i) q^{77} +(-0.162718 - 1.36003i) q^{78} +(4.76293 + 12.5588i) q^{79} +2.03697i q^{80} +(2.57876 - 6.79963i) q^{81} +(0.0283908 + 0.233819i) q^{82} +(4.25995 + 8.11666i) q^{83} +(-4.19882 - 2.89824i) q^{84} +(1.47632 + 1.01903i) q^{85} +(-0.300724 - 0.572983i) q^{86} +(-0.132903 - 1.09456i) q^{87} +(-1.44649 + 3.81408i) q^{88} +14.9265i q^{89} +(0.0234338 + 0.0617897i) q^{90} +(5.81161 - 1.42163i) q^{91} +(-5.49766 + 14.4961i) q^{92} +(-6.13357 - 2.32616i) q^{93} +(-1.69103 + 2.44988i) q^{94} +(-0.719184 + 0.637142i) q^{95} +(-3.60873 - 2.49092i) q^{96} +(3.54411 - 4.00048i) q^{97} +(0.473622 - 0.902412i) q^{98} -2.13164i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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