LMFDB - Embedded newform 196.2.p.a.103.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(3,196)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("196.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.p (of order $42$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$26$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			103.9
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.925869 + 1.06900i) q^{2} +(-0.318723 - 0.217301i) q^{3} +(-0.285533 - 1.97951i) q^{4} +(-2.23221 - 0.167281i) q^{5} +(0.527391 - 0.139523i) q^{6} +(2.62649 - 0.318706i) q^{7} +(2.38047 + 1.52753i) q^{8} +(-1.04166 - 2.65410i) q^{9} +O(q^{10})$	\(q+(-0.925869 + 1.06900i) q^{2} +(-0.318723 - 0.217301i) q^{3} +(-0.285533 - 1.97951i) q^{4} +(-2.23221 - 0.167281i) q^{5} +(0.527391 - 0.139523i) q^{6} +(2.62649 - 0.318706i) q^{7} +(2.38047 + 1.52753i) q^{8} +(-1.04166 - 2.65410i) q^{9} +(2.24556 - 2.23136i) q^{10} +(4.62345 + 1.81457i) q^{11} +(-0.339145 + 0.692962i) q^{12} +(4.05935 - 3.23722i) q^{13} +(-2.09108 + 3.10280i) q^{14} +(0.675106 + 0.538379i) q^{15} +(-3.83694 + 1.13043i) q^{16} +(-1.83646 - 1.97924i) q^{17} +(3.80168 + 1.34382i) q^{18} +(1.20408 - 2.08553i) q^{19} +(0.306236 + 4.46646i) q^{20} +(-0.906375 - 0.469160i) q^{21} +(-6.22048 + 3.26242i) q^{22} +(2.13014 - 2.29575i) q^{23} +(-0.426775 - 1.00414i) q^{24} +(0.0106413 + 0.00160391i) q^{25} +(-0.297826 + 7.33670i) q^{26} +(-0.502253 + 2.20051i) q^{27} +(-1.38083 - 5.10816i) q^{28} +(1.93620 + 8.48305i) q^{29} +(-1.20059 + 0.223222i) q^{30} +(0.0585377 + 0.101390i) q^{31} +(2.34407 - 5.14833i) q^{32} +(-1.07929 - 1.58303i) q^{33} +(3.81613 - 0.130670i) q^{34} +(-5.91619 + 0.272057i) q^{35} +(-4.95640 + 2.81981i) q^{36} +(-0.160245 - 0.0494289i) q^{37} +(1.11462 + 3.21809i) q^{38} +(-1.99726 + 0.149674i) q^{39} +(-5.05819 - 3.80799i) q^{40} +(-4.98272 - 10.3467i) q^{41} +(1.34072 - 0.534537i) q^{42} +(1.97048 - 4.09173i) q^{43} +(2.27181 - 9.67029i) q^{44} +(1.88122 + 6.09878i) q^{45} +(0.481927 + 4.40269i) q^{46} +(-10.2787 + 1.54926i) q^{47} +(1.46856 + 0.473478i) q^{48} +(6.79685 - 1.67415i) q^{49} +(-0.0115670 + 0.00989052i) q^{50} +(0.155231 + 1.02989i) q^{51} +(-7.56721 - 7.11120i) q^{52} +(2.75719 - 0.850480i) q^{53} +(-1.88734 - 2.57430i) q^{54} +(-10.0170 - 4.82392i) q^{55} +(6.73911 + 3.25338i) q^{56} +(-0.836956 + 0.403057i) q^{57} +(-10.8611 - 5.78439i) q^{58} +(0.758813 + 10.1257i) q^{59} +(0.872963 - 1.49011i) q^{60} +(-2.62620 + 8.51392i) q^{61} +(-0.162585 - 0.0312971i) q^{62} +(-3.58178 - 6.63898i) q^{63} +(3.33328 + 7.27250i) q^{64} +(-9.60287 + 6.54712i) q^{65} +(2.69154 + 0.311912i) q^{66} +(-5.07455 + 2.92979i) q^{67} +(-3.39355 + 4.20044i) q^{68} +(-1.17779 + 0.268824i) q^{69} +(5.18679 - 6.57631i) q^{70} +(9.49078 + 2.16621i) q^{71} +(1.57459 - 7.90919i) q^{72} +(1.11225 - 7.37932i) q^{73} +(0.201205 - 0.125537i) q^{74} +(-0.00304308 - 0.00282356i) q^{75} +(-4.47214 - 1.78801i) q^{76} +(12.7217 + 3.29242i) q^{77} +(1.68920 - 2.27365i) q^{78} +(11.9926 + 6.92396i) q^{79} +(8.75397 - 1.88152i) q^{80} +(-5.63197 + 5.22570i) q^{81} +(15.6740 + 4.25317i) q^{82} +(1.95783 - 2.45504i) q^{83} +(-0.669908 + 1.92814i) q^{84} +(3.76829 + 4.72528i) q^{85} +(2.54967 + 5.89485i) q^{86} +(1.22627 - 3.12448i) q^{87} +(8.23416 + 11.3820i) q^{88} +(-1.74456 + 0.684691i) q^{89} +(-8.26137 - 3.63564i) q^{90} +(9.63011 - 9.79626i) q^{91} +(-5.15269 - 3.56113i) q^{92} +(0.00337496 - 0.0450357i) q^{93} +(7.86055 - 12.4223i) q^{94} +(-3.03664 + 4.45393i) q^{95} +(-1.86585 + 1.13152i) q^{96} -1.56668i q^{97} +(-4.50332 + 8.81590i) q^{98} -14.1613i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{29}{42}\right)$

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 $

$2$	−0.925869	+	1.06900i	−0.654688	+	0.755899i
$2$	−0.925869	+	1.06900i	−0.654688	+	0.755899i
$3$	−0.318723	−	0.217301i	−0.184015	−	0.125459i	0.467809	−	0.883829i	$-0.345043\pi$
$3$	−0.318723	−	0.217301i	−0.184015	−	0.125459i	−0.651824	+	0.758370i	$0.725996\pi$
$4$	−0.285533	−	1.97951i	−0.142767	−	0.989756i
$5$	−2.23221	−	0.167281i	−0.998276	−	0.0748105i	−0.434443	−	0.900699i	$-0.643055\pi$
$5$	−2.23221	−	0.167281i	−0.998276	−	0.0748105i	−0.563833	+	0.825889i	$0.690674\pi$
$6$	0.527391	−	0.139523i	0.215306	−	0.0569599i
$7$	2.62649	−	0.318706i	0.992718	−	0.120459i
$7$	2.62649	−	0.318706i	0.992718	−	0.120459i
$8$	2.38047	+	1.52753i	0.841624	+	0.540065i
$9$	−1.04166	−	2.65410i	−0.347220	−	0.884701i
$10$	2.24556	−	2.23136i	0.710109	−	0.705619i
$11$	4.62345	+	1.81457i	1.39402	+	0.547113i	0.939170	−	0.343454i	$-0.111597\pi$
$11$	4.62345	+	1.81457i	1.39402	+	0.547113i	0.454852	+	0.890567i	$0.349692\pi$
$12$	−0.339145	+	0.692962i	−0.0979027	+	0.200041i
$13$	4.05935	−	3.23722i	1.12586	−	0.897845i	0.130255	−	0.991481i	$-0.458420\pi$
$13$	4.05935	−	3.23722i	1.12586	−	0.897845i	0.995606	+	0.0936360i	$0.0298490\pi$
$14$	−2.09108	+	3.10280i	−0.558866	+	0.829258i
$15$	0.675106	+	0.538379i	0.174312	+	0.139009i
$16$	−3.83694	+	1.13043i	−0.959235	+	0.282608i
$17$	−1.83646	−	1.97924i	−0.445408	−	0.480035i	0.469941	−	0.882698i	$-0.344275\pi$
$17$	−1.83646	−	1.97924i	−0.445408	−	0.480035i	−0.915348	+	0.402663i	$0.868085\pi$
$18$	3.80168	+	1.34382i	0.896065	+	0.316740i
$19$	1.20408	−	2.08553i	0.276235	−	0.478453i	−0.694211	−	0.719772i	$-0.744246\pi$
$19$	1.20408	−	2.08553i	0.276235	−	0.478453i	0.970446	+	0.241318i	$0.0775798\pi$
$20$	0.306236	+	4.46646i	0.0684765	+	0.998731i
$21$	−0.906375	−	0.469160i	−0.197787	−	0.102379i
$22$	−6.22048	+	3.26242i	−1.32621	+	0.695551i
$23$	2.13014	−	2.29575i	0.444165	−	0.478696i	−0.470794	−	0.882243i	$-0.656032\pi$
$23$	2.13014	−	2.29575i	0.444165	−	0.478696i	0.914959	+	0.403547i	$0.132223\pi$
$24$	−0.426775	−	1.00414i	−0.0871150	−	0.204969i
$25$	0.0106413	+	0.00160391i	0.00212825	+	0.000320782i
$26$	−0.297826	+	7.33670i	−0.0584084	+	1.43885i
$27$	−0.502253	+	2.20051i	−0.0966587	+	0.423489i
$28$	−1.38083	−	5.10816i	−0.260953	−	0.965352i
$29$	1.93620	+	8.48305i	0.359544	+	1.57526i	0.754333	+	0.656492i	$0.227960\pi$
$29$	1.93620	+	8.48305i	0.359544	+	1.57526i	−0.394790	+	0.918771i	$0.629183\pi$
$30$	−1.20059	+	0.223222i	−0.219197	+	0.0407545i
$31$	0.0585377	+	0.101390i	0.0105137	+	0.0182102i	0.871234	−	0.490867i	$-0.163320\pi$
$31$	0.0585377	+	0.101390i	0.0105137	+	0.0182102i	−0.860721	+	0.509077i	$0.829987\pi$
$32$	2.34407	−	5.14833i	0.414377	−	0.910105i
$33$	−1.07929	−	1.58303i	−0.187880	−	0.275569i
$34$	3.81613	−	0.130670i	0.654461	−	0.0224098i
$35$	−5.91619	+	0.272057i	−1.00002	+	0.0459861i
$36$	−4.95640	+	2.81981i	−0.826067	+	0.469969i
$37$	−0.160245	−	0.0494289i	−0.0263441	−	0.00812606i	0.281555	−	0.959545i	$-0.409150\pi$
$37$	−0.160245	−	0.0494289i	−0.0263441	−	0.00812606i	−0.307899	+	0.951419i	$0.599626\pi$
$38$	1.11462	+	3.21809i	0.180814	+	0.522044i
$39$	−1.99726	+	0.149674i	−0.319818	+	0.0239670i
$40$	−5.05819	−	3.80799i	−0.799770	−	0.602096i
$41$	−4.98272	−	10.3467i	−0.778171	−	1.61589i	−0.787797	−	0.615935i	$-0.788778\pi$
$41$	−4.98272	−	10.3467i	−0.778171	−	1.61589i	0.00962633	−	0.999954i	$-0.496936\pi$
$42$	1.34072	−	0.534537i	0.206877	−	0.0824808i
$43$	1.97048	−	4.09173i	0.300495	−	0.623984i	−0.694978	−	0.719031i	$-0.744586\pi$
$43$	1.97048	−	4.09173i	0.300495	−	0.623984i	0.995473	+	0.0950473i	$0.0303002\pi$
$44$	2.27181	−	9.67029i	0.342489	−	1.45785i
$45$	1.88122	+	6.09878i	0.280436	+	0.909152i
$46$	0.481927	+	4.40269i	0.0710563	+	0.649141i
$47$	−10.2787	+	1.54926i	−1.49930	+	0.225983i	−0.846843	−	0.531843i	$-0.821500\pi$
$47$	−10.2787	+	1.54926i	−1.49930	+	0.225983i	−0.652457	+	0.757826i	$0.726262\pi$
$48$	1.46856	+	0.473478i	0.211969	+	0.0683406i
$49$	6.79685	−	1.67415i	0.970979	−	0.239165i
$50$	−0.0115670	+	0.00989052i	−0.00163582	+	0.00139873i
$51$	0.155231	+	1.02989i	0.0217367	+	0.144214i
$52$	−7.56721	−	7.11120i	−1.04938	−	0.986146i
$53$	2.75719	−	0.850480i	0.378729	−	0.116822i	−0.0995451	−	0.995033i	$-0.531739\pi$
$53$	2.75719	−	0.850480i	0.378729	−	0.116822i	0.478274	+	0.878211i	$0.341263\pi$
$54$	−1.88734	−	2.57430i	−0.256834	−	0.350318i
$55$	−10.0170	−	4.82392i	−1.35069	−	0.650458i
$56$	6.73911	+	3.25338i	0.900551	+	0.434751i
$57$	−0.836956	+	0.403057i	−0.110858	+	0.0533862i
$58$	−10.8611	−	5.78439i	−1.42613	−	0.759528i
$59$	0.758813	+	10.1257i	0.0987890	+	1.31825i	0.797707	+	0.603046i	$0.206046\pi$
$59$	0.758813	+	10.1257i	0.0987890	+	1.31825i	−0.698918	+	0.715202i	$0.746335\pi$
$60$	0.872963	−	1.49011i	0.112699	−	0.192372i
$61$	−2.62620	+	8.51392i	−0.336250	+	1.09010i	0.616759	+	0.787152i	$0.288445\pi$
$61$	−2.62620	+	8.51392i	−0.336250	+	1.09010i	−0.953009	+	0.302943i	$0.902031\pi$
$62$	−0.162585	−	0.0312971i	−0.0206483	−	0.00397474i
$63$	−3.58178	−	6.63898i	−0.451262	−	0.836433i
$64$	3.33328	+	7.27250i	0.416660	+	0.909062i
$65$	−9.60287	+	6.54712i	−1.19109	+	0.812071i
$66$	2.69154	+	0.311912i	0.331305	+	0.0383937i
$67$	−5.07455	+	2.92979i	−0.619955	+	0.357931i	−0.776852	−	0.629684i	$-0.783184\pi$
$67$	−5.07455	+	2.92979i	−0.619955	+	0.357931i	0.156896	+	0.987615i	$0.449851\pi$
$68$	−3.39355	+	4.20044i	−0.411529	+	0.509378i
$69$	−1.17779	+	0.268824i	−0.141790	+	0.0323625i
$70$	5.18679	−	6.57631i	0.619940	−	0.786020i
$71$	9.49078	+	2.16621i	1.12635	+	0.257082i	0.744814	−	0.667273i	$-0.232538\pi$
$71$	9.49078	+	2.16621i	1.12635	+	0.257082i	0.381535	+	0.924354i	$0.375396\pi$
$72$	1.57459	−	7.90919i	0.185568	−	0.932106i
$73$	1.11225	−	7.37932i	0.130179	−	0.863684i	−0.824460	−	0.565920i	$-0.808521\pi$
$73$	1.11225	−	7.37932i	0.130179	−	0.863684i	0.954639	−	0.297764i	$-0.0962409\pi$
$74$	0.201205	−	0.125537i	0.0233896	−	0.0145934i
$75$	−0.00304308	−	0.00282356i	−0.000351384	−	0.000326037i
$76$	−4.47214	−	1.78801i	−0.512989	−	0.205098i
$77$	12.7217	+	3.29242i	1.44978	+	0.375206i
$78$	1.68920	−	2.27365i	0.191264	−	0.257441i
$79$	11.9926	+	6.92396i	1.34928	+	0.779006i	0.988147	−	0.153509i	$-0.0490575\pi$
$79$	11.9926	+	6.92396i	1.34928	+	0.779006i	0.361131	+	0.932515i	$0.382391\pi$
$80$	8.75397	−	1.88152i	0.978724	−	0.210360i
$81$	−5.63197	+	5.22570i	−0.625774	+	0.580634i
$82$	15.6740	+	4.25317i	1.73091	+	0.469685i
$83$	1.95783	−	2.45504i	0.214899	−	0.269475i	−0.662684	−	0.748899i	$-0.730583\pi$
$83$	1.95783	−	2.45504i	0.214899	−	0.269475i	0.877584	+	0.479424i	$0.159154\pi$
$84$	−0.669908	+	1.92814i	−0.0730930	+	0.210378i
$85$	3.76829	+	4.72528i	0.408728	+	0.512529i
$86$	2.54967	+	5.89485i	0.274938	+	0.635658i
$87$	1.22627	−	3.12448i	0.131470	−	0.334979i
$88$	8.23416	+	11.3820i	0.877765	+	1.21333i
$89$	−1.74456	+	0.684691i	−0.184923	+	0.0725771i	−0.455996	−	0.889982i	$-0.650717\pi$
$89$	−1.74456	+	0.684691i	−0.184923	+	0.0725771i	0.271073	+	0.962559i	$0.412622\pi$
$90$	−8.26137	−	3.63564i	−0.870825	−	0.383230i
$91$	9.63011	−	9.79626i	1.00951	−	1.02693i
$92$	−5.15269	−	3.56113i	−0.537205	−	0.371273i
$93$	0.00337496	−	0.0450357i	0.000349967	−	0.00466998i
$94$	7.86055	−	12.4223i	0.810753	−	1.28127i
$95$	−3.03664	+	4.45393i	−0.311552	+	0.456963i
$96$	−1.86585	+	1.13152i	−0.190432	+	0.115485i
$97$		−	1.56668i		−	0.159072i	−0.996832	−	0.0795360i	$-0.974656\pi$
$97$		−	1.56668i		−	0.159072i	0.996832	−	0.0795360i	$-0.0253439\pi$
$98$	−4.50332	+	8.81590i	−0.454904	+	0.890540i
$99$		−	14.1613i		−	1.42326i
$100$	0.000136529	−	0.0215225i	1.36529e−5	−	0.00215225i
$101$	−2.65201	+	3.88978i	−0.263885	+	0.387047i	−0.935198	−	0.354126i	$-0.884778\pi$
$101$	−2.65201	+	3.88978i	−0.263885	+	0.387047i	0.671313	+	0.741174i	$0.265731\pi$
$102$	−1.24468	−	0.787603i	−0.123242	−	0.0779843i
$103$	−1.18362	+	15.7943i	−0.116625	+	1.55626i	0.565331	+	0.824864i	$0.308748\pi$
$103$	−1.18362	+	15.7943i	−0.116625	+	1.55626i	−0.681957	+	0.731393i	$0.738871\pi$
$104$	14.6081	−	1.50532i	1.43245	−	0.147609i
$105$	1.94474	+	1.19889i	0.189787	+	0.116999i
$106$	−1.64363	+	3.73487i	−0.159643	+	0.362763i
$107$	−3.99573	+	1.56821i	−0.386281	+	0.151604i	−0.550531	−	0.834814i	$-0.685575\pi$
$107$	−3.99573	+	1.56821i	−0.386281	+	0.151604i	0.164250	+	0.986419i	$0.447480\pi$
$108$	4.49936	+	0.365896i	0.432951	+	0.0352084i
$109$	0.0952969	−	0.242812i	0.00912778	−	0.0232572i	−0.926237	−	0.376941i	$-0.876976\pi$
$109$	0.0952969	−	0.242812i	0.00912778	−	0.0232572i	0.935365	+	0.353684i	$0.115071\pi$
$110$	14.4312	−	6.24186i	1.37596	−	0.595138i
$111$	0.0403326	+	0.0505755i	0.00382820	+	0.00480041i
$112$	−9.71740	+	4.19192i	−0.918208	+	0.396100i
$113$	−2.75151	+	3.45029i	−0.258840	+	0.324576i	−0.894223	−	0.447622i	$-0.852271\pi$
$113$	−2.75151	+	3.45029i	−0.258840	+	0.324576i	0.635382	+	0.772198i	$0.280842\pi$
$114$	0.344043	−	1.26789i	0.0322226	−	0.118748i
$115$	−5.13897	+	4.76826i	−0.479211	+	0.444643i
$116$	16.2395	−	6.25493i	1.50780	−	0.580756i
$117$	−12.8204	−	7.40185i	−1.18525	−	0.684302i
$118$	−11.5269	−	8.56386i	−1.06114	−	0.788367i
$119$	−5.45424	−	4.61314i	−0.499989	−	0.422886i
$120$	0.784678	+	2.31284i	0.0716310	+	0.211133i
$121$	10.0200	+	9.29722i	0.910911	+	0.845202i
$122$	−6.66989	−	10.6902i	−0.603863	−	0.967844i
$123$	−0.660253	+	4.38049i	−0.0595330	+	0.394975i
$124$	0.183989	−	0.144826i	0.0165227	−	0.0130058i
$125$	10.8883	+	2.48518i	0.973876	+	0.222281i
$126$	10.4133	+	2.31790i	0.927695	+	0.206495i
$127$	−12.3552	+	2.82000i	−1.09635	+	0.250235i	−0.732189	−	0.681101i	$-0.761501\pi$
$127$	−12.3552	+	2.82000i	−1.09635	+	0.250235i	−0.364161	+	0.931336i	$0.618644\pi$
$128$	−10.8605	−	3.17009i	−0.959942	−	0.280199i
$129$	−1.51717	+	0.875941i	−0.133580	+	0.0771223i
$130$	1.89210	−	16.3273i	0.165948	−	1.43200i
$131$	−0.0396336	+	0.0270217i	−0.00346280	+	0.00236090i	−0.565050	−	0.825057i	$-0.691143\pi$
$131$	−0.0396336	+	0.0270217i	−0.00346280	+	0.00236090i	0.561587	+	0.827417i	$0.310191\pi$
$132$	−2.82545	+	2.58847i	−0.245923	+	0.225297i
$133$	2.49783	−	5.86136i	0.216589	−	0.508244i
$134$	1.56641	−	8.13731i	0.135317	−	0.702957i
$135$	1.48924	−	4.82800i	0.128173	−	0.415528i
$136$	−1.34830	−	7.51677i	−0.115615	−	0.644558i
$137$	0.234947	+	3.13515i	0.0200729	+	0.267854i	0.998206	+	0.0598738i	$0.0190698\pi$
$137$	0.234947	+	3.13515i	0.0200729	+	0.267854i	−0.978133	+	0.207980i	$0.933311\pi$
$138$	0.803109	−	1.50796i	0.0683652	−	0.128366i
$139$	−3.06434	+	1.47571i	−0.259914	+	0.125168i	−0.559303	−	0.828963i	$-0.688931\pi$
$139$	−3.06434	+	1.47571i	−0.259914	+	0.125168i	0.299390	+	0.954131i	$0.403217\pi$
$140$	2.22781	+	11.6335i	0.188284	+	0.983210i
$141$	3.61270	+	1.73979i	0.304245	+	0.146516i
$142$	−11.1029	+	8.14005i	−0.931735	+	0.683098i
$143$	24.6424	−	7.60116i	2.06070	−	0.635641i
$144$	6.99707	+	9.00611i	0.583089	+	0.750509i
$145$	−2.90296	−	19.2599i	−0.241078	−	1.59945i
$146$	6.85871	+	8.02129i	0.567631	+	0.663846i
$147$	−2.53011	−	0.943375i	−0.208680	−	0.0778083i
$148$	−0.0520900	+	0.331320i	−0.00428177	+	0.0272343i
$149$	−9.85202	+	1.48495i	−0.807109	+	0.121652i	−0.539620	−	0.841909i	$-0.681432\pi$
$149$	−9.85202	+	1.48495i	−0.807109	+	0.121652i	−0.267489	+	0.963561i	$0.586194\pi$
$150$	0.00583588		0.000638808i	0.000476498		5.21584e-5i
$151$	3.68923	+	11.9602i	0.300225	+	0.973305i	0.972480	+	0.232986i	$0.0748496\pi$
$151$	3.68923	+	11.9602i	0.300225	+	0.973305i	−0.672255	+	0.740319i	$0.734674\pi$
$152$	6.05200	−	3.12527i	0.490882	−	0.253493i
$153$	−3.34013	+	6.93585i	−0.270033	+	0.560730i
$154$	−15.2983	+	10.5512i	−1.23277	+	0.850241i
$155$	−0.113708	−	0.236117i	−0.00913324	−	0.0189654i
$156$	0.866566	+	3.91086i	0.0693808	+	0.313120i
$157$	−5.51812	+	0.413526i	−0.440394	+	0.0330030i	−0.293082	−	0.956087i	$-0.594681\pi$
$157$	−5.51812	+	0.413526i	−0.440394	+	0.0330030i	−0.147311	+	0.989090i	$0.547062\pi$
$158$	−18.5053	+	6.40949i	−1.47221	+	0.509912i
$159$	−1.06359	−	0.328074i	−0.0843480	−	0.0260179i
$160$	−6.09368	+	11.1001i	−0.481748	+	0.877537i
$161$	4.86312	−	6.70863i	0.383267	−	0.528714i
$162$	−0.371826	−	10.8589i	−0.0292134	−	0.853156i
$163$	0.118870	+	0.174351i	0.00931065	+	0.0136562i	0.830866	−	0.556473i	$-0.187846\pi$
$163$	0.118870	+	0.174351i	0.00931065	+	0.0136562i	−0.821555	+	0.570129i	$0.806893\pi$
$164$	−19.0588	+	12.8177i	−1.48824	+	1.00089i
$165$	2.14439	+	3.71420i	0.166941	+	0.289150i
$166$	0.811750	+	4.36597i	0.0630041	+	0.338865i
$167$	−2.35188	−	10.3042i	−0.181994	−	0.797366i	−0.980680	−	0.195619i	$-0.937329\pi$
$167$	−2.35188	−	10.3042i	−0.181994	−	0.797366i	0.798686	−	0.601747i	$-0.205529\pi$
$168$	−1.44094	−	2.50134i	−0.111171	−	0.192983i
$169$	3.10594	−	13.6080i	0.238918	−	1.04677i
$170$	−8.54028	−	0.346684i	−0.655010	−	0.0265894i
$171$	−6.78945	−	1.02335i	−0.519202	−	0.0782572i
$172$	−8.66228	−	2.73225i	−0.660492	−	0.208332i
$173$	13.1334	−	14.1544i	0.998511	−	1.07614i	0.00141437	−	0.999999i	$-0.499550\pi$
$173$	13.1334	−	14.1544i	0.998511	−	1.07614i	0.997097	−	0.0761404i	$-0.0242597\pi$
$174$	2.20471	+	4.20374i	0.167139	+	0.318685i
$175$	0.0284603		0.000821220i	0.00215139		6.20784e-5i
$176$	−19.7911	−	1.73589i	−1.49181	−	0.130848i
$177$	1.95847	−	3.39217i	0.147207	−	0.254971i
$178$	0.883301	−	2.49888i	0.0662062	−	0.187299i
$179$	−11.7479	−	12.6612i	−0.878076	−	0.946341i	0.120850	−	0.992671i	$-0.461438\pi$
$179$	−11.7479	−	12.6612i	−0.878076	−	0.946341i	−0.998926	+	0.0463299i	$0.985247\pi$
$180$	11.5355	−	5.46531i	0.859802	−	0.407360i
$181$	−5.72802	−	4.56794i	−0.425760	−	0.339532i	0.387052	−	0.922058i	$-0.373493\pi$
$181$	−5.72802	−	4.56794i	−0.425760	−	0.339532i	−0.812813	+	0.582525i	$0.802065\pi$
$182$	1.55601	+	19.3647i	0.115339	+	1.43540i
$183$	2.68711	−	2.14290i	0.198637	−	0.158408i
$184$	8.57757	−	2.21110i	0.632347	−	0.163004i
$185$	0.349432	+	0.137142i	0.0256907	+	0.0100829i
$186$	0.0450185	+	0.0453050i	0.00330091	+	0.00332192i
$187$	−4.89933	−	12.4833i	−0.358274	−	0.912868i
$188$	6.00169	+	19.9044i	0.437718	+	1.45168i
$189$	−0.617844	+	5.93969i	−0.0449415	+	0.432049i
$190$	−1.94973	−	7.36993i	−0.141448	−	0.534671i
$191$	8.12560	+	0.608929i	0.587947	+	0.0440606i	0.365383	−	0.930857i	$-0.380938\pi$
$191$	8.12560	+	0.608929i	0.587947	+	0.0440606i	0.222565	+	0.974918i	$0.428557\pi$
$192$	0.517931	−	3.04224i	0.0373785	−	0.219554i
$193$	−18.2779	−	12.4617i	−1.31567	−	0.897009i	−0.316994	−	0.948428i	$-0.602674\pi$
$193$	−18.2779	−	12.4617i	−1.31567	−	0.897009i	−0.998677	+	0.0514180i	$0.983626\pi$
$194$	1.67478	+	1.45054i	0.120242	+	0.104143i
$195$	4.48335			0.321059
$196$	−5.25473	−	12.9764i	−0.375338	−	0.926888i
$197$	−8.72284			−0.621476			−0.310738	−	0.950496i	$-0.600576\pi$
$197$	−8.72284			−0.621476			−0.310738	+	0.950496i	$0.600576\pi$
$198$	15.1384	+	13.1115i	1.07584	+	0.931792i
$199$	2.84823	+	1.94189i	0.201905	+	0.137657i	0.660052	−	0.751220i	$-0.270534\pi$
$199$	2.84823	+	1.94189i	0.201905	+	0.137657i	−0.458147	+	0.888877i	$0.651487\pi$
$200$	0.0228812	+	0.0200729i	0.00161794	+	0.00141937i
$201$	2.25402	+	0.168916i	0.158986	+	0.0119144i
$202$	−1.70277	−	6.43643i	−0.119807	−	0.452865i
$203$	7.78900	+	21.6635i	0.546681	+	1.52048i
$204$	1.99436	−	0.601351i	0.139633	−	0.0421030i
$205$	9.39169	+	23.9296i	0.655944	+	1.67132i
$206$	−15.7883	−	15.8887i	−1.10002	−	1.10702i
$207$	−8.31203	−	3.26223i	−0.577726	−	0.226741i
$208$	−11.9160	+	17.0099i	−0.826228	+	1.17942i
$209$	9.35134	−	7.45745i	0.646846	−	0.515842i
$210$	−3.08219	+	0.968923i	−0.212691	+	0.0668621i
$211$	16.4025	+	13.0806i	1.12919	+	0.900503i	0.995890	−	0.0905722i	$-0.0288696\pi$
$211$	16.4025	+	13.0806i	1.12919	+	0.900503i	0.133305	+	0.991075i	$0.457441\pi$
$212$	−2.47081	−	5.21505i	−0.169696	−	0.358171i
$213$	−2.55421	−	2.75278i	−0.175011	−	0.188617i
$214$	2.02310	−	5.72340i	0.138296	−	0.391243i
$215$	−5.08299	+	8.80400i	−0.346657	+	0.600428i
$216$	−4.55696	+	4.47105i	−0.310062	+	0.304217i
$217$	0.186062	+	0.247644i	0.0126307	+	0.0168111i
$218$	0.171335	+	0.326685i	0.0116043	+	0.0221259i
$219$	−1.95804	+	2.11026i	−0.132312	+	0.142598i
$220$	−6.68883	+	21.2061i	−0.450961	+	1.42972i
$221$	−13.8621	−	2.08937i	−0.932464	−	0.140546i
$222$	−0.0914080	−	0.00371061i	−0.00613490	−	0.000249040i
$223$	−1.54366	+	6.76320i	−0.103371	+	0.452897i	0.896579	+	0.442884i	$0.146045\pi$
$223$	−1.54366	+	6.76320i	−0.103371	+	0.452897i	−0.999950	+	0.0100134i	$0.996813\pi$
$224$	4.51586	−	14.2691i	0.301728	−	0.953394i
$225$	−0.00682761	−	0.0299137i	−0.000455174	−	0.00199425i
$226$	−1.14083	−	6.13589i	−0.0758866	−	0.408153i
$227$	7.76907	+	13.4564i	0.515651	+	0.893134i	0.999835	+	0.0181679i	$0.00578335\pi$
$227$	7.76907	+	13.4564i	0.515651	+	0.893134i	−0.484184	+	0.874966i	$0.660883\pi$
$228$	1.03683	+	1.54168i	0.0686661	+	0.102100i
$229$	14.3587	+	21.0603i	0.948850	+	1.39171i	0.919912	+	0.392125i	$0.128260\pi$
$229$	14.3587	+	21.0603i	0.948850	+	1.39171i	0.0289378	+	0.999581i	$0.490788\pi$
$230$	−0.339277	−	9.90836i	−0.0223713	−	0.653338i
$231$	−3.33925	−	3.81382i	−0.219707	−	0.250931i
$232$	−8.34907	+	23.1513i	−0.548144	+	1.51996i
$233$	−6.91974	−	2.13446i	−0.453327	−	0.139833i	0.0596795	−	0.998218i	$-0.480992\pi$
$233$	−6.91974	−	2.13446i	−0.453327	−	0.139833i	−0.513006	+	0.858385i	$0.671468\pi$
$234$	19.7826	−	6.85188i	1.29323	−	0.447922i
$235$	23.2034	−	1.73885i	1.51362	−	0.113430i
$236$	19.8272	−	4.39329i	1.29064	−	0.285979i
$237$	−2.31774	−	4.81284i	−0.150553	−	0.312627i
$238$	9.98137	−	1.55943i	0.646996	−	0.101083i
$239$	3.55856	−	7.38943i	0.230184	−	0.477982i	−0.753601	−	0.657332i	$-0.771685\pi$
$239$	3.55856	−	7.38943i	0.230184	−	0.477982i	0.983785	+	0.179349i	$0.0573993\pi$
$240$	−3.19895	−	1.30257i	−0.206491	−	0.0840803i
$241$	−1.33055	−	4.31355i	−0.0857085	−	0.277860i	0.902565	−	0.430553i	$-0.141682\pi$
$241$	−1.33055	−	4.31355i	−0.0857085	−	0.277860i	−0.988274	+	0.152693i	$0.951205\pi$
$242$	−19.2160	+	2.10342i	−1.23525	+	0.135213i
$243$	9.62627	−	1.45093i	0.617526	−	0.0930770i
$244$	17.6033	+	2.76758i	1.12693	+	0.177176i
$245$	−15.4521	+	2.60008i	−0.987197	+	0.166113i
$246$	−4.07145	−	4.76157i	−0.259586	−	0.303587i
$247$	−1.86354	−	12.3638i	−0.118574	−	0.786688i
$248$	−0.0155297	+	0.330775i	−0.000986139	+	0.0210042i
$249$	−1.15749	+	0.357037i	−0.0733527	+	0.0226263i
$250$	−12.7378	+	9.33864i	−0.805607	+	0.590627i
$251$	−23.7535	−	11.4391i	−1.49931	−	0.722027i	−0.508978	−	0.860779i	$-0.669977\pi$
$251$	−23.7535	−	11.4391i	−1.49931	−	0.722027i	−0.990327	+	0.138752i	$0.955691\pi$
$252$	−12.1192	+	8.98583i	−0.763440	+	0.566054i
$253$	14.0144	−	6.74897i	0.881077	−	0.424304i
$254$	8.42474	−	15.8187i	0.528615	−	0.992555i
$255$	−0.174228	−	2.32491i	−0.0109106	−	0.145591i
$256$	13.4442	−	8.67482i	0.840265	−	0.542176i
$257$	3.74970	−	12.1562i	0.233900	−	0.758284i	−0.760188	−	0.649703i	$-0.774893\pi$
$257$	3.74970	−	12.1562i	0.233900	−	0.758284i	0.994088	−	0.108581i	$-0.0346306\pi$
$258$	0.468321	−	2.43287i	0.0291564	−	0.151464i
$259$	−0.436633	−	0.0787535i	−0.0271311	−	0.00489350i
$260$	15.7021	+	17.1396i	0.973800	+	1.06295i
$261$	20.4980	−	13.9753i	1.26880	−	0.865051i
$262$	0.00780922	−	0.0673870i	0.000482455	−	0.00416318i
$263$	6.60660	−	3.81432i	0.407380	−	0.235201i	−0.282283	−	0.959331i	$-0.591092\pi$
$263$	6.60660	−	3.81432i	0.407380	−	0.235201i	0.689663	+	0.724130i	$0.257758\pi$
$264$	−0.151090	−	5.41699i	−0.00929896	−	0.333393i
$265$	−6.29690	+	1.43723i	−0.386816	+	0.0882882i
$266$	3.95315	+	8.09704i	0.242383	+	0.496461i
$267$	0.704816	+	0.160870i	0.0431341	+	0.00984507i
$268$	7.24852	+	9.20859i	0.442774	+	0.562504i
$269$	−2.44037	+	16.1908i	−0.148792	+	0.987169i	0.782436	+	0.622731i	$0.213977\pi$
$269$	−2.44037	+	16.1908i	−0.148792	+	0.987169i	−0.931228	+	0.364438i	$0.881261\pi$
$270$	3.78230	+	6.06210i	0.230184	+	0.368928i
$271$	8.84305	+	8.20516i	0.537177	+	0.498428i	0.901461	−	0.432860i	$-0.142496\pi$
$271$	8.84305	+	8.20516i	0.537177	+	0.498428i	−0.364284	+	0.931288i	$0.618686\pi$
$272$	9.28379	+	5.51821i	0.562913	+	0.334591i
$273$	−5.19807	+	1.02965i	−0.314602	+	0.0623175i
$274$	−3.56901	−	2.65158i	−0.215612	−	0.160188i
$275$	0.0462889	+	0.0267249i	0.00279132	+	0.00161157i
$276$	0.868439	+	2.25470i	0.0522739	+	0.135717i
$277$	3.13377	−	2.90772i	0.188290	−	0.174708i	−0.580395	−	0.814335i	$-0.697102\pi$
$277$	3.13377	−	2.90772i	0.188290	−	0.174708i	0.768685	+	0.639627i	$0.220911\pi$
$278$	1.25964	−	4.64210i	0.0755482	−	0.278414i
$279$	0.208124	−	0.260979i	0.0124600	−	0.0156244i
$280$	−14.4989	−	8.38956i	−0.866475	−	0.501372i
$281$	−1.91007	−	2.39515i	−0.113945	−	0.142883i	0.721588	−	0.692323i	$-0.243413\pi$
$281$	−1.91007	−	2.39515i	−0.113945	−	0.142883i	−0.835533	+	0.549440i	$0.814841\pi$
$282$	−5.20473	+	2.25118i	−0.309937	+	0.134056i
$283$	0.126189	−	0.321525i	0.00750117	−	0.0191127i	−0.927074	−	0.374878i	$-0.877685\pi$
$283$	0.126189	−	0.321525i	0.00750117	−	0.0191127i	0.934575	+	0.355765i	$0.115780\pi$
$284$	1.57810	−	19.4057i	0.0936432	−	1.15151i
$285$	1.93569	−	0.759702i	0.114660	−	0.0450009i
$286$	−14.6899	+	33.3804i	−0.868634	+	1.97383i
$287$	−16.3846	−	25.5875i	−0.967153	−	1.51038i
$288$	−16.1059	−	0.858592i	−0.949051	−	0.0505930i
$289$	0.725632	−	9.68288i	0.0426842	−	0.569581i
$290$	23.2766	+	14.7288i	1.36685	+	0.864908i
$291$	−0.340441	+	0.499336i	−0.0199570	+	0.0292716i
$292$	−14.9250	−	0.0946782i	−0.873422	−	0.00554062i
$293$			8.80258i			0.514252i	0.966378	+	0.257126i	$0.0827755\pi$
$293$			8.80258i			0.514252i	−0.966378	+	0.257126i	$0.917224\pi$
$294$	3.35102	−	1.83125i	0.195435	−	0.106801i
$295$		−	22.7296i		−	1.32337i
$296$	−0.305953	−	0.362443i	−0.0177832	−	0.0210666i
$297$	−6.31513	+	9.26259i	−0.366441	+	0.537470i
$298$	7.53426	−	11.9067i	0.436448	−	0.689737i
$299$	1.21515	−	16.2150i	0.0702737	−	0.937737i
$300$	−0.00472038	+	0.00683003i	−0.000272531	+	0.000394332i
$301$	3.87137	−	11.3749i	0.223142	−	0.655637i
$302$	−16.2012	−	7.12976i	−0.932274	−	0.410272i
$303$	1.69051	−	0.663476i	0.0971172	−	0.0381157i
$304$	−2.26244	+	9.36319i	−0.129760	+	0.537016i
$305$	7.28645	−	18.5656i	0.417221	−	1.06306i
$306$	−4.32192	−	9.99229i	−0.247068	−	0.571221i
$307$	19.2512	+	24.1402i	1.09872	+	1.37776i	0.919102	+	0.394019i	$0.128916\pi$
$307$	19.2512	+	24.1402i	1.09872	+	1.37776i	0.179621	+	0.983736i	$0.442513\pi$
$308$	2.88491	−	26.1229i	0.164383	−	1.48849i
$309$	3.80936	−	4.77679i	0.216707	−	0.271742i
$310$	0.357688	+	0.0970592i	0.0203153	+	0.00551259i
$311$	−20.9862	+	19.4723i	−1.19002	+	1.10417i	−0.197725	+	0.980258i	$0.563355\pi$
$311$	−20.9862	+	19.4723i	−1.19002	+	1.10417i	−0.992293	+	0.123917i	$0.960454\pi$
$312$	−4.98305	−	2.69459i	−0.282110	−	0.152551i
$313$	9.33603	+	5.39016i	0.527704	+	0.304670i	0.740081	−	0.672518i	$-0.234787\pi$
$313$	9.33603	+	5.39016i	0.527704	+	0.304670i	−0.212377	+	0.977188i	$0.568121\pi$
$314$	4.66699	−	6.28175i	0.263374	−	0.354500i
$315$	6.88472	+	15.4188i	0.387910	+	0.868751i
$316$	10.2818	−	25.7166i	0.578394	−	1.44667i
$317$	0.855108	+	0.793424i	0.0480276	+	0.0445631i	0.703822	−	0.710377i	$-0.251475\pi$
$317$	0.855108	+	0.793424i	0.0480276	+	0.0445631i	−0.655794	+	0.754940i	$0.727666\pi$
$318$	1.33546	−	0.833226i	0.0748886	−	0.0467250i
$319$	−6.44116	+	42.7343i	−0.360636	+	2.39266i
$320$	−6.22405	−	16.7914i	−0.347935	−	0.938666i
$321$	1.61430	+	0.368454i	0.0901015	+	0.0205651i
$322$	2.66894	+	11.4100i	0.148734	+	0.635855i
$323$	−6.33900	+	1.44684i	−0.352712	+	0.0805041i
$324$	11.9525	+	9.65644i	0.664026	+	0.536469i
$325$	0.0483888	−	0.0279373i	0.00268413	−	0.00154968i
$326$	−0.296440	−	0.0343533i	−0.0164183	−	0.00190265i
$327$	−0.0831367	+	0.0566817i	−0.00459747	+	0.00313450i
$328$	3.94375	−	32.2414i	0.217757	−	1.78023i
$329$	−26.5030	+	7.34499i	−1.46116	+	0.404942i
$330$	−5.95591	−	1.14650i	−0.327862	−	0.0631126i
$331$	1.29973	−	4.21361i	0.0714394	−	0.231601i	−0.912811	−	0.408383i	$-0.866093\pi$
$331$	1.29973	−	4.21361i	0.0714394	−	0.231601i	0.984250	+	0.176782i	$0.0565689\pi$
$332$	−5.41880	−	3.17455i	−0.297396	−	0.174226i
$333$	0.0357308	+	0.476794i	0.00195803	+	0.0261281i
$334$	13.1928	+	7.02622i	0.721877	+	0.384457i
$335$	11.8176	−	5.69105i	0.645664	−	0.310935i
$336$	4.00806	+	0.775543i	0.218658	+	0.0423093i
$337$	15.4478	+	7.43927i	0.841495	+	0.405243i	0.804414	−	0.594069i	$-0.202480\pi$
$337$	15.4478	+	7.43927i	0.841495	+	0.405243i	0.0370816	+	0.999312i	$0.488194\pi$
$338$	11.6713	+	15.9195i	0.634835	+	0.865905i
$339$	1.62672	−	0.501777i	0.0883513	−	0.0272528i
$340$	8.27779	−	8.80860i	0.448926	−	0.477713i
$341$	0.0866662	+	0.574993i	0.00469324	+	0.0311376i
$342$	7.38010	−	6.31046i	0.399070	−	0.341231i
$343$	17.3183	−	6.56333i	0.935099	−	0.354387i
$344$	10.9409	−	6.73029i	0.589895	−	0.362873i
$345$	2.67405	−	0.403049i	0.143966	−	0.0216994i
$346$	2.97132	+	27.1447i	0.159739	+	1.45931i
$347$	−6.81460	−	22.0924i	−0.365827	−	1.18598i	−0.932234	−	0.361856i	$-0.882143\pi$
$347$	−6.81460	−	22.0924i	−0.365827	−	1.18598i	0.566407	−	0.824126i	$-0.308333\pi$
$348$	−6.53509	−	1.53527i	−0.350317	−	0.0822991i
$349$	−11.6755	+	24.2445i	−0.624977	+	1.29778i	0.312562	+	0.949897i	$0.398813\pi$
$349$	−11.6755	+	24.2445i	−0.624977	+	1.29778i	−0.937539	+	0.347881i	$0.886901\pi$
$350$	−0.0272284	+	0.0296638i	−0.00145542	+	0.00158559i
$351$	5.08474	+	10.5586i	0.271403	+	0.563575i
$352$	20.1797	−	19.5496i	1.07558	−	1.04200i
$353$	−22.6879	+	1.70023i	−1.20756	+	0.0904939i	−0.663254	−	0.748395i	$-0.730825\pi$
$353$	−22.6879	+	1.70023i	−1.20756	+	0.0904939i	−0.544303	+	0.838889i	$0.683206\pi$
$354$	1.81295	+	5.23431i	0.0963572	+	0.278200i
$355$	−20.8231	−	6.42307i	−1.10517	−	0.340901i
$356$	1.85349	+	3.25789i	0.0982346	+	0.172668i
$357$	0.735946	+	2.65553i	0.0389504	+	0.140545i
$358$	24.4118	−	0.835898i	1.29020	−	0.0441786i
$359$	8.89416	+	13.0453i	0.469416	+	0.688506i	0.985814	−	0.167842i	$-0.0536800\pi$
$359$	8.89416	+	13.0453i	0.469416	+	0.688506i	−0.516398	+	0.856349i	$0.672728\pi$
$360$	−4.83789	+	17.3916i	−0.254979	+	0.916617i
$361$	6.60038	+	11.4322i	0.347388	+	0.601694i
$362$	10.1865	−	1.89395i	0.535392	−	0.0995438i
$363$	−1.17331	−	5.14060i	−0.0615827	−	0.269811i
$364$	−22.1415	−	16.2658i	−1.16053	−	0.852557i
$365$	−3.71721	+	16.2862i	−0.194568	+	0.852457i
$366$	−0.197148	+	4.85658i	−0.0103051	+	0.253857i
$367$	−7.19442	−	1.08438i	−0.375546	−	0.0566044i	−0.0414424	−	0.999141i	$-0.513195\pi$
$367$	−7.19442	−	1.08438i	−0.375546	−	0.0566044i	−0.334103	+	0.942536i	$0.608433\pi$
$368$	−5.57804	+	11.2166i	−0.290775	+	0.584707i
$369$	−22.2710	+	24.0024i	−1.15938	+	1.24952i
$370$	−0.470133	+	0.246568i	−0.0244411	+	0.0128185i
$371$	6.97066	−	3.11251i	0.361899	−	0.161593i
$372$	−0.0901123	+	0.00617841i	−0.00467211	+	0.000320336i
$373$	5.38922	−	9.33441i	0.279043	−	0.483317i	−0.692104	−	0.721798i	$-0.743316\pi$
$373$	5.38922	−	9.33441i	0.279043	−	0.483317i	0.971147	+	0.238481i	$0.0766493\pi$
$374$	17.8808	+	6.32049i	0.924594	+	0.326825i
$375$	−2.93030	−	3.15812i	−0.151320	−	0.163084i
$376$	−26.8346	−	12.0131i	−1.38389	−	0.619526i
$377$	35.3213	+	28.1678i	1.81914	+	1.45071i
$378$	−5.77750	−	6.15985i	−0.297163	−	0.316829i
$379$	−24.0797	+	19.2029i	−1.23689	+	0.986387i	−0.237001	+	0.971509i	$0.576164\pi$
$379$	−24.0797	+	19.2029i	−1.23689	+	0.986387i	−0.999889	+	0.0148777i	$0.995264\pi$
$380$	9.68367	+	4.73932i	0.496762	+	0.243122i
$381$	4.55068	+	1.78601i	0.233138	+	0.0915001i
$382$	−8.17418	+	8.12249i	−0.418228	+	0.415583i
$383$	−9.49472	−	24.1922i	−0.485158	−	1.23616i	−0.938641	−	0.344896i	$-0.887914\pi$
$383$	−9.49472	−	24.1922i	−0.485158	−	1.23616i	0.453483	−	0.891265i	$-0.350181\pi$
$384$	2.77262	+	3.37038i	0.141490	+	0.171994i
$385$	−27.8469	−	9.47749i	−1.41921	−	0.483018i
$386$	30.2445	−	8.00125i	1.53940	−	0.407253i
$387$	−12.9124	−	0.967654i	−0.656377	−	0.0491886i
$388$	−3.10126	+	0.447339i	−0.157443	+	0.0227102i
$389$	0.447822	+	0.305320i	0.0227055	+	0.0154803i	0.574620	−	0.818421i	$-0.305150\pi$
$389$	0.447822	+	0.305320i	0.0227055	+	0.0154803i	−0.551914	+	0.833901i	$0.686102\pi$
$390$	−4.15099	+	4.79271i	−0.210194	+	0.242688i
$391$	−8.45575			−0.427626
$392$	18.7370	+	6.39715i	0.946363	+	0.323105i
$393$	0.0185040			0.000933402
$394$	8.07620	−	9.32473i	0.406873	−	0.469773i
$395$	−25.6119	−	17.4619i	−1.28867	−	0.878603i
$396$	−28.0324	+	4.04351i	−1.40868	+	0.203194i
$397$	8.00894	+	0.600187i	0.401957	+	0.0301225i	0.274175	−	0.961680i	$-0.411595\pi$
$397$	8.00894	+	0.600187i	0.401957	+	0.0301225i	0.127782	+	0.991802i	$0.459214\pi$
$398$	−4.71297	+	1.24683i	−0.236240	+	0.0624979i
$399$	−2.06980	+	1.32537i	−0.103619	+	0.0663513i
$400$	−0.0426430	+	0.00587512i	−0.00213215	+	0.000293756i
$401$	1.25364	+	3.19422i	0.0626037	+	0.159512i	0.958753	−	0.284242i	$-0.0917418\pi$
$401$	1.25364	+	3.19422i	0.0626037	+	0.159512i	−0.896149	+	0.443753i	$0.853647\pi$
$402$	−2.26750	+	2.25316i	−0.113093	+	0.112377i
$403$	0.565848	+	0.222079i	0.0281869	+	0.0110625i
$404$	8.45710	+	4.13902i	0.420757	+	0.205924i
$405$	13.4459	−	10.7228i	0.668133	−	0.532819i
$406$	−30.3700	−	11.7311i	−1.50724	−	0.582206i
$407$	−0.651190	−	0.519307i	−0.0322783	−	0.0257411i
$408$	−1.20367	+	2.68875i	−0.0595906	+	0.133113i
$409$	25.5146	+	27.4982i	1.26162	+	1.35970i	0.904978	+	0.425459i	$0.139887\pi$
$409$	25.5146	+	27.4982i	1.26162	+	1.35970i	0.356640	+	0.934242i	$0.383922\pi$
$410$	−34.2763	−	12.1160i	−1.69279	−	0.598365i
$411$	0.606389	−	1.05030i	0.0299110	−	0.0518073i
$412$	31.6029	−	2.16681i	1.55697	−	0.106751i
$413$	5.22012	+	26.3531i	0.256865	+	1.29675i
$414$	11.1832	−	5.86518i	0.549624	−	0.288258i
$415$	−4.78097	+	5.15266i	−0.234689	+	0.252934i
$416$	−7.15092	−	28.4872i	−0.350603	−	1.39670i
$417$	1.29735	+	0.195544i	0.0635313	+	0.00957581i
$418$	−0.686087	+	16.9012i	−0.0335576	+	0.826666i
$419$	−2.22293	+	9.73931i	−0.108597	+	0.475796i	0.891158	+	0.453693i	$0.149894\pi$
$419$	−2.22293	+	9.73931i	−0.108597	+	0.475796i	−0.999756	+	0.0221037i	$0.992964\pi$
$420$	1.81792	−	4.19196i	0.0887054	−	0.204547i
$421$	−6.58417	−	28.8472i	−0.320893	−	1.40592i	−0.835968	−	0.548779i	$-0.815093\pi$
$421$	−6.58417	−	28.8472i	−0.320893	−	1.40592i	0.515074	−	0.857145i	$-0.327764\pi$
$422$	−29.1697	+	5.42344i	−1.41996	+	0.264009i
$423$	14.8188	+	25.6669i	0.720514	+	1.24797i
$424$	7.86254	+	2.18715i	0.381839	+	0.106218i
$425$	−0.0163677	−	0.0240071i	−0.000793952	−	0.00116451i
$426$	5.30759	−	0.181740i	0.257154	−	0.00880533i
$427$	−4.18423	+	23.1987i	−0.202489	+	1.12266i
$428$	4.24520	+	7.46182i	0.205199	+	0.360680i
$429$	−9.50582	−	2.93216i	−0.458945	−	0.141566i
$430$	−4.70532	−	13.5851i	−0.226910	−	0.655131i
$431$	0.396927	−	0.0297455i	0.0191193	−	0.00143279i	−0.0651670	−	0.997874i	$-0.520758\pi$
$431$	0.396927	−	0.0297455i	0.0191193	−	0.00143279i	0.0842863	+	0.996442i	$0.473139\pi$
$432$	−0.560420	−	9.01101i	−0.0269632	−	0.433542i
$433$	−3.88217	−	8.06141i	−0.186565	−	0.387406i	0.786617	−	0.617441i	$-0.211830\pi$
$433$	−3.88217	−	8.06141i	−0.186565	−	0.387406i	−0.973183	+	0.230034i	$0.926116\pi$
$434$	−0.437001	−	0.0303848i	−0.0209767	−	0.00145852i
$435$	−3.25996	+	6.76937i	−0.156303	+	0.324567i
$436$	−0.507861	−	0.119310i	−0.0243221	−	0.00571393i
$437$	−2.22298	−	7.20674i	−0.106340	−	0.344745i
$438$	−0.442990	−	4.04697i	−0.0211669	−	0.193372i
$439$	1.83712	−	0.276901i	0.0876809	−	0.0132158i	−0.105055	−	0.994466i	$-0.533502\pi$
$439$	1.83712	−	0.276901i	0.0876809	−	0.0132158i	0.192736	+	0.981251i	$0.438264\pi$
$440$	−16.4764	−	26.7845i	−0.785482	−	1.27690i
$441$	−11.5234	−	16.2957i	−0.548732	−	0.775984i
$442$	15.0680	−	12.8841i	0.716712	−	0.612835i
$443$	−3.70078	−	24.5531i	−0.175829	−	1.16655i	−0.886398	−	0.462924i	$-0.846800\pi$
$443$	−3.70078	−	24.5531i	−0.175829	−	1.16655i	0.710569	−	0.703628i	$-0.248438\pi$
$444$	0.0885985	−	0.0942799i	0.00420470	−	0.00447433i
$445$	4.00878	−	1.23654i	0.190034	−	0.0586178i
$446$	−5.80065	−	7.91201i	−0.274669	−	0.374644i
$447$	3.46274	+	1.66757i	0.163782	+	0.0788733i
$448$	11.0726	+	18.0388i	0.523131	+	0.852252i
$449$	−9.17598	+	4.41892i	−0.433041	+	0.208542i	−0.637689	−	0.770294i	$-0.720109\pi$
$449$	−9.17598	+	4.41892i	−0.433041	+	0.208542i	0.204648	+	0.978836i	$0.434395\pi$
$450$	0.0382993	+	0.0203974i	0.00180545	+	0.000961545i
$451$	−4.26250	−	56.8791i	−0.200713	−	2.67833i
$452$	7.61553	+	4.46148i	0.358205	+	0.209850i
$453$	1.42312	−	4.61365i	0.0668641	−	0.216768i
$454$	−21.5781	−	4.15373i	−1.01271	−	0.194944i
$455$	−23.1352	+	20.2564i	−1.08459	+	0.949635i
$456$	−2.60803	−	0.319013i	−0.122132	−	0.0149392i
$457$	−4.27692	+	2.91596i	−0.200066	+	0.136403i	−0.659209	−	0.751960i	$-0.729109\pi$
$457$	−4.27692	+	2.91596i	−0.200066	+	0.136403i	0.459143	+	0.888362i	$0.348156\pi$
$458$	−35.8078	−	4.14963i	−1.67319	−	0.193900i
$459$	5.27771	−	3.04709i	0.246342	−	0.142226i
$460$	10.9062	+	8.81115i	0.508504	+	0.410822i
$461$	5.80544	−	1.32505i	0.270386	−	0.0617139i	−0.0851780	−	0.996366i	$-0.527146\pi$
$461$	5.80544	−	1.32505i	0.270386	−	0.0617139i	0.355564	+	0.934652i	$0.384289\pi$
$462$	7.16869	−	0.0385765i	0.333518	−	0.00179474i
$463$	−24.4393	−	5.57811i	−1.13579	−	0.259237i	−0.387024	−	0.922070i	$-0.626497\pi$
$463$	−24.4393	−	5.57811i	−1.13579	−	0.259237i	−0.748767	+	0.662833i	$0.769354\pi$
$464$	−17.0186	−	30.3602i	−0.790069	−	1.40944i
$465$	−0.0150672	+	0.0999646i	−0.000698727	+	0.00463575i
$466$	8.68851	−	5.42099i	0.402487	−	0.251122i
$467$	20.6998	+	19.2066i	0.957871	+	0.888774i	0.993867	−	0.110578i	$-0.0352701\pi$
$467$	20.6998	+	19.2066i	0.957871	+	0.888774i	−0.0359966	+	0.999352i	$0.511461\pi$
$468$	−10.9914	+	27.4916i	−0.508078	+	1.27080i
$469$	−12.3945	+	9.31235i	−0.572325	+	0.430004i
$470$	−19.6244	+	26.4144i	−0.905208	+	1.21841i
$471$	1.84861	+	1.06729i	0.0851794	+	0.0491783i
$472$	−13.6609	+	25.2629i	−0.628796	+	1.16282i
$473$	16.5351	−	15.3423i	0.760286	−	0.705442i
$474$	7.29086	+	1.97839i	0.334880	+	0.0908703i
$475$	0.0161579	−	0.0202614i	0.000741377	−	0.000929657i
$476$	−7.57441	+	12.1139i	−0.347172	+	0.555241i
$477$	−5.12931	−	6.43195i	−0.234855	−	0.294499i
$478$	4.60456	+	10.6458i	0.210608	+	0.486926i
$479$	8.93940	−	22.7772i	0.408451	−	1.04072i	−0.567624	−	0.823288i	$-0.692137\pi$
$479$	8.93940	−	22.7772i	0.408451	−	1.04072i	0.976076	−	0.217430i	$-0.0697673\pi$
$480$	4.35425	−	2.21368i	0.198744	−	0.101040i
$481$	−0.810502	+	0.318098i	−0.0369557	+	0.0145040i
$482$	5.84311	+	2.57142i	0.266147	+	0.117125i
$483$	−3.00778	+	1.08143i	−0.136859	+	0.0492068i
$484$	15.5429	−	22.4894i	0.706496	−	1.02225i
$485$	−0.262076	+	3.49716i	−0.0119003	+	0.158798i
$486$	−7.36162	+	11.6339i	−0.333930	+	0.527724i
$487$	14.3263	−	21.0129i	0.649188	−	0.952183i	−0.350689	−	0.936492i	$-0.614053\pi$
$487$	14.3263	−	21.0129i	0.649188	−	0.952183i	0.999877	−	0.0156914i	$-0.00499494\pi$
$488$	−19.2569	+	16.2555i	−0.871718	+	0.735853i
$489$		−	0.0814002i		−	0.00368105i
$490$	11.5271	−	18.9257i	0.520742	−	0.854974i
$491$			14.8458i			0.669983i	0.942221	+	0.334992i	$0.108733\pi$
$491$			14.8458i			0.669983i	−0.942221	+	0.334992i	$0.891267\pi$
$492$	8.85976	+	0.0562025i	0.399429	+	0.00253381i
$493$	13.2342	−	19.4110i	0.596038	−	0.874228i
$494$	14.9423	+	9.45511i	0.672286	+	0.425405i
$495$	−2.36892	+	31.6110i	−0.106475	+	1.42081i
$496$	−0.339221	−	0.322855i	−0.0152315	−	0.0144966i
$497$	25.6178	+	2.66475i	1.14911	+	0.119530i
$498$	0.690007	−	1.56793i	0.0309200	−	0.0702605i
$499$	−33.9503	+	13.3245i	−1.51982	+	0.596487i	−0.970921	−	0.239399i	$-0.923050\pi$
$499$	−33.9503	+	13.3245i	−1.51982	+	0.596487i	−0.548903	+	0.835886i	$0.684954\pi$
$500$	1.81047	−	22.2631i	0.0809668	−	0.995634i
$501$	−1.48953	+	3.79526i	−0.0665473	+	0.169560i
$502$	34.2210	−	14.8014i	1.52736	−	0.660621i
$503$	19.0064	+	23.8332i	0.847453	+	1.06267i	0.997261	+	0.0739570i	$0.0235628\pi$
$503$	19.0064	+	23.8332i	0.847453	+	1.06267i	−0.149809	+	0.988715i	$0.547866\pi$
$504$	1.61494	−	21.2752i	0.0719354	−	0.947672i
$505$	6.57053	−	8.23919i	0.292385	−	0.366639i
$506$	−5.76081	+	21.2301i	−0.256099	+	0.943792i
$507$	−3.94697	+	3.66225i	−0.175291	+	0.162646i
$508$	9.11006	+	23.6521i	0.404194	+	1.04939i
$509$	−8.99626	−	5.19399i	−0.398752	−	0.230220i	0.287193	−	0.957873i	$-0.407278\pi$
$509$	−8.99626	−	5.19399i	−0.398752	−	0.230220i	−0.685945	+	0.727653i	$0.740611\pi$
$510$	2.64664	+	1.96631i	0.117195	+	0.0870697i
$511$	0.569486	−	19.7362i	0.0251926	−	0.873077i
$512$	−3.17420	+	22.4037i	−0.140281	+	0.990112i
$513$	3.98449	+	3.69706i	0.175919	+	0.163229i
$514$	9.52330	+	15.2635i	0.420055	+	0.673244i
$515$	5.28418	−	35.0582i	0.232849	−	1.54485i
$516$	2.16714	+	2.75315i	0.0954030	+	0.121201i
$517$	−50.3342	−	11.4884i	−2.21369	−	0.505261i
$518$	0.488453	−	0.393847i	0.0214614	−	0.0173046i
$519$	−7.26167	+	1.65743i	−0.318752	+	0.0727531i
$520$	−32.8603	+	0.916536i	−1.44102	+	0.0401928i
$521$	24.5873	−	14.1955i	1.07719	−	0.621915i	0.147052	−	0.989129i	$-0.453022\pi$
$521$	24.5873	−	14.1955i	1.07719	−	0.621915i	0.930137	+	0.367214i	$0.119688\pi$
$522$	−4.03884	+	34.8518i	−0.176775	+	1.52542i
$523$	12.5826	−	8.57868i	0.550199	−	0.375120i	−0.256079	−	0.966656i	$-0.582431\pi$
$523$	12.5826	−	8.57868i	0.550199	−	0.375120i	0.806278	+	0.591536i	$0.201478\pi$
$524$	0.0648066	+	0.0707396i	0.00283109	+	0.00309027i
$525$	−0.00889248	−	0.00644620i	−0.000388100	−	0.000281335i
$526$	−2.03932	+	10.5940i	−0.0889187	+	0.461922i
$527$	0.0931729	−	0.302059i	0.00405868	−	0.0131579i
$528$	5.93067	+	4.85391i	0.258099	+	0.211239i
$529$	0.985843	+	13.1552i	0.0428627	+	0.571963i
$530$	4.29371	−	8.06209i	0.186507	−	0.350195i
$531$	26.0841	−	12.5614i	1.13195	−	0.545120i
$532$	−12.3159	−	3.27087i	−0.533960	−	0.141810i
$533$	−53.7213	−	25.8708i	−2.32693	−	1.12059i
$534$	−0.824538	+	0.604506i	−0.0356812	+	0.0261595i
$535$	9.18165	−	2.83216i	0.396957	−	0.122445i
$536$	−16.5552	−	0.777259i	−0.715075	−	0.0335725i
$537$	0.993016	+	6.58823i	0.0428518	+	0.284303i
$538$	−15.0485	−	17.5993i	−0.648788	−	0.758760i
$539$	34.4628	+	4.59301i	1.48442	+	0.197835i
$540$	−9.98232	−	1.56942i	−0.429571	−	0.0675369i
$541$	−28.4631	+	4.29012i	−1.22372	+	0.184447i	−0.728945	−	0.684572i	$-0.759989\pi$
$541$	−28.4631	+	4.29012i	−1.22372	+	0.184447i	−0.494779	+	0.869019i	$0.664751\pi$
$542$	−16.9588	+	1.85635i	−0.728445	+	0.0797371i
$543$	0.833028	+	2.70061i	0.0357487	+	0.115894i
$544$	−14.4946	+	4.81526i	−0.621449	+	0.206452i
$545$	−0.253341	+	0.526068i	−0.0108519	+	0.0225343i
$546$	3.71203	−	6.51008i	0.158860	−	0.278606i
$547$	9.61599	+	19.9678i	0.411150	+	0.853762i	0.998996	+	0.0447895i	$0.0142617\pi$
$547$	9.61599	+	19.9678i	0.411150	+	0.853762i	−0.587846	+	0.808973i	$0.700024\pi$
$548$	6.13898	−	1.36027i	0.262244	−	0.0581078i
$549$	25.3324	−	1.89840i	1.08116	−	0.0810218i
$550$	−0.0714264	+	0.0247392i	−0.00304563	+	0.00105488i
$551$	20.0230	+	6.17628i	0.853008	+	0.263118i
$552$	−3.21434	−	1.15919i	−0.136811	−	0.0493385i
$553$	33.7052	+	14.3635i	1.43329	+	0.610800i
$554$	0.206894	+	6.04218i	0.00879006	+	0.256708i
$555$	−0.0815707	−	0.119642i	−0.00346248	−	0.00507853i
$556$	3.79615	+	5.64453i	0.160993	+	0.239381i
$557$	−6.06410	−	10.5033i	−0.256944	−	0.445040i	0.708478	−	0.705733i	$-0.249382\pi$
$557$	−6.06410	−	10.5033i	−0.256944	−	0.445040i	−0.965422	+	0.260693i	$0.916049\pi$
$558$	0.0862919	+	0.464117i	0.00365303	+	0.0196477i
$559$	−5.24701	−	22.9887i	−0.221925	−	0.972316i
$560$	22.3925	−	7.73173i	0.946257	−	0.326725i
$561$	−1.15111	+	5.04333i	−0.0485998	+	0.212930i
$562$	4.32890	+	0.175727i	0.182604	+	0.00741260i
$563$	0.204030	+	0.0307526i	0.00859885	+	0.00129607i	0.153340	−	0.988173i	$-0.450997\pi$
$563$	0.204030	+	0.0307526i	0.00859885	+	0.00129607i	−0.144741	+	0.989470i	$0.546235\pi$
$564$	2.41238	−	7.64816i	0.101580	−	0.322046i
$565$	6.71913	−	7.24150i	0.282676	−	0.304652i
$566$	0.226876	+	0.432587i	0.00953632	+	0.0181830i
$567$	−13.1268	+	15.5202i	−0.551275	+	0.651786i
$568$	19.2836	+	19.6541i	0.809121	+	0.824667i
$569$	19.4755	−	33.7325i	0.816454	−	1.41414i	−0.0918251	−	0.995775i	$-0.529270\pi$
$569$	19.4755	−	33.7325i	0.816454	−	1.41414i	0.908279	−	0.418365i	$-0.137397\pi$
$570$	−0.980071	+	2.77264i	−0.0410506	+	0.116133i
$571$	−1.63166	−	1.75852i	−0.0682831	−	0.0735916i	0.697986	−	0.716111i	$-0.254080\pi$
$571$	−1.63166	−	1.75852i	−0.0682831	−	0.0735916i	−0.766269	+	0.642520i	$0.777889\pi$
$572$	−22.0828	−	46.6095i	−0.923329	−	1.94884i
$573$	−2.45749	−	1.95978i	−0.102663	−	0.0818711i
$574$	42.5231	+	6.17550i	1.77488	+	0.257760i
$575$	0.0263495	−	0.0210131i	0.00109885	−	0.000876305i
$576$	15.8298	−	16.4223i	0.659576	−	0.684264i
$577$	−13.1810	−	5.17315i	−0.548731	−	0.215361i	0.0747462	−	0.997203i	$-0.476185\pi$
$577$	−13.1810	−	5.17315i	−0.548731	−	0.215361i	−0.623477	+	0.781842i	$0.714281\pi$
$578$	9.67919	+	9.74078i	0.402601	+	0.405163i
$579$	3.11764	+	7.94362i	0.129565	+	0.330126i
$580$	−37.2963	+	11.2458i	−1.54864	+	0.466956i
$581$	4.35977	−	7.07209i	0.180874	−	0.293400i
$582$	−0.218587	−	0.826252i	−0.00906073	−	0.0342492i
$583$	14.2910	+	1.07096i	0.591871	+	0.0443546i
$584$	13.9198	−	15.8673i	0.576007	−	0.656592i
$585$	27.3797	+	18.6671i	1.13201	+	0.771791i
$586$	−9.40998	−	8.15003i	−0.388723	−	0.336675i
$587$	43.9277			1.81309			0.906546	−	0.422108i	$-0.138710\pi$
$587$	43.9277			1.81309			0.906546	+	0.422108i	$0.138710\pi$
$588$	−1.14499	+	5.27774i	−0.0472188	+	0.217650i
$589$	0.281936			0.0116170
$590$	24.2980	+	21.0446i	1.00033	+	0.866392i
$591$	2.78016	+	1.89548i	0.114361	+	0.0779698i
$592$	0.670725	+	0.00850994i	0.0275666	+	0.000349756i
$593$	23.1037	+	1.73139i	0.948757	+	0.0710995i	0.540111	−	0.841594i	$-0.318382\pi$
$593$	23.1037	+	1.73139i	0.948757	+	0.0710995i	0.408646	+	0.912693i	$0.366001\pi$
$594$	−4.05475	−	15.3268i	−0.166369	−	0.628868i
$595$	11.4033	+	11.2099i	0.467491	+	0.459562i
$596$	5.75256	+	19.0782i	0.235634	+	0.781473i
$597$	−0.485819	−	1.23785i	−0.0198833	−	0.0506617i
$598$	16.2088	+	16.3119i	0.662827	+	0.667045i
$599$	−9.98255	−	3.91786i	−0.407876	−	0.160079i	0.152528	−	0.988299i	$-0.451259\pi$
$599$	−9.98255	−	3.91786i	−0.407876	−	0.160079i	−0.560404	+	0.828220i	$0.689354\pi$
$600$	−0.00293087	−	0.0113698i	−0.000119652	−	0.000464170i
$601$	−19.5056	+	15.5552i	−0.795652	+	0.634511i	−0.934565	−	0.355794i	$-0.884211\pi$
$601$	−19.5056	+	15.5552i	−0.795652	+	0.634511i	0.138913	+	0.990305i	$0.455639\pi$
$602$	8.57540	+	14.6701i	0.349507	+	0.597911i
$603$	13.0619	+	10.4165i	0.531923	+	0.424194i
$604$	22.6219	−	10.7179i	0.920473	−	0.436105i
$605$	−20.8116	−	22.4296i	−0.846111	−	0.911891i
$606$	−0.855932	+	2.42145i	−0.0347699	+	0.0983647i
$607$	18.1735	−	31.4775i	0.737642	−	1.27763i	−0.215913	−	0.976413i	$-0.569273\pi$
$607$	18.1735	−	31.4775i	0.737642	−	1.27763i	0.953555	−	0.301220i	$-0.0973939\pi$
$608$	−7.91455	−	11.0876i	−0.320978	−	0.449663i
$609$	2.22498	−	8.59722i	0.0901609	−	0.348377i
$610$	13.1003	+	24.9785i	0.530418	+	1.01135i
$611$	−36.7095	+	39.5634i	−1.48511	+	1.60056i
$612$	14.6833	+	4.63141i	0.593538	+	0.187214i
$613$	0.286758	+	0.0432218i	0.0115821	+	0.00174571i	0.154831	−	0.987941i	$-0.450517\pi$
$613$	0.286758	+	0.0432218i	0.0115821	+	0.00174571i	−0.143249	+	0.989687i	$0.545755\pi$
$614$	−43.6300	−	1.77111i	−1.76076	−	0.0714764i
$615$	2.20660	−	9.66774i	0.0889787	−	0.389841i
$616$	25.2544	+	27.2704i	1.01753	+	1.09875i
$617$	9.12140	+	39.9635i	0.367214	+	1.60887i	0.734397	+	0.678720i	$0.237465\pi$
$617$	9.12140	+	39.9635i	0.367214	+	1.60887i	−0.367183	+	0.930149i	$0.619678\pi$
$618$	1.57943	+	8.49490i	0.0635340	+	0.341715i
$619$	−2.36701	−	4.09978i	−0.0951381	−	0.164784i	0.814528	−	0.580124i	$-0.196996\pi$
$619$	−2.36701	−	4.09978i	−0.0951381	−	0.164784i	−0.909666	+	0.415340i	$0.863663\pi$
$620$	−0.434929	+	0.292505i	−0.0174672	+	0.0117473i
$621$	3.98195	+	5.84045i	0.159790	+	0.234369i
$622$	−1.38552	−	40.4631i	−0.0555543	−	1.62242i
$623$	−4.36386	+	2.35433i	−0.174834	+	0.0943244i
$624$	7.49417	−	2.83206i	0.300007	−	0.113373i
$625$	−23.9406	−	7.38471i	−0.957625	−	0.295388i
$626$	−14.4060	+	4.98966i	−0.575781	+	0.199427i
$627$	−4.60100	+	0.344797i	−0.183746	+	0.0137699i
$628$	2.39419	+	10.8051i	0.0955384	+	0.431171i
$629$	0.196452	+	0.407936i	0.00783304	+	0.0162655i
$630$	−22.8571	−	6.91600i	−0.910648	−	0.275540i
$631$	15.9695	−	33.1610i	0.635735	−	1.32012i	−0.295376	−	0.955381i	$-0.595445\pi$
$631$	15.9695	−	33.1610i	0.635735	−	1.32012i	0.931111	−	0.364737i	$-0.118841\pi$
$632$	17.9716	+	34.8014i	0.714870	+	1.38433i
$633$	−2.38542	−	7.73335i	−0.0948121	−	0.307373i
$634$	−1.63989	+	0.179506i	−0.0651284	+	0.00712908i
$635$	28.0513	−	4.22805i	1.11318	−	0.167785i
$636$	−0.345736	+	2.19906i	−0.0137093	+	0.0871985i
$637$	22.1712	−	28.7989i	0.878455	−	1.14105i
$638$	−39.7194	−	46.4520i	−1.57251	−	1.83905i
$639$	−4.13682	−	27.4460i	−0.163650	−	1.08575i
$640$	23.7127	+	8.89308i	0.937325	+	0.351530i
$641$	8.57532	−	2.64513i	0.338705	−	0.104477i	−0.120737	−	0.992685i	$-0.538526\pi$
$641$	8.57532	−	2.64513i	0.338705	−	0.104477i	0.459442	+	0.888208i	$0.348050\pi$
$642$	−1.88851	+	1.38455i	−0.0745335	+	0.0546439i
$643$	20.1996	+	9.72762i	0.796595	+	0.383620i	0.787481	−	0.616338i	$-0.211385\pi$
$643$	20.1996	+	9.72762i	0.796595	+	0.383620i	0.00911381	+	0.999958i	$0.497099\pi$
$644$	−14.6684	−	7.71107i	−0.578016	−	0.303859i
$645$	3.53319	−	1.70149i	0.139119	−	0.0669962i
$646$	4.32241	−	8.11599i	0.170063	−	0.319319i
$647$	0.668670	+	8.92279i	0.0262881	+	0.350791i	0.994802	+	0.101830i	$0.0324699\pi$
$647$	0.668670	+	8.92279i	0.0262881	+	0.350791i	−0.968514	+	0.248961i	$0.919911\pi$
$648$	−21.3892	+	3.83661i	−0.840246	+	0.150716i
$649$	−14.8654	+	48.1923i	−0.583517	+	1.89172i
$650$	−0.0149367	+	0.0775940i	−0.000585864	+	0.00304349i
$651$	−0.00548885	−	0.119361i	−0.000215125	−	0.00467813i
$652$	0.311188	−	0.285088i	0.0121871	−	0.0111649i
$653$	25.2057	−	17.1850i	0.986377	−	0.672500i	0.0412313	−	0.999150i	$-0.486872\pi$
$653$	25.2057	−	17.1850i	0.986377	−	0.672500i	0.945146	+	0.326649i	$0.105920\pi$
$654$	0.0163809	−	0.141353i	0.000640543	−	0.00552735i
$655$	0.0929909	−	0.0536883i	0.00363345	−	0.00209778i
$656$	30.8147	+	34.0672i	1.20311	+	1.33010i
$657$	−20.7441	+	4.73470i	−0.809303	+	0.184718i
$658$	16.6865	−	35.1323i	0.650509	−	1.36960i
$659$	20.6664	+	4.71697i	0.805049	+	0.183747i	0.605194	−	0.796078i	$-0.293096\pi$
$659$	20.6664	+	4.71697i	0.805049	+	0.183747i	0.199855	+	0.979825i	$0.435953\pi$
$660$	6.74000	−	5.30538i	0.262354	−	0.206512i
$661$	5.12776	−	34.0205i	0.199447	−	1.32324i	−0.635153	−	0.772386i	$-0.719063\pi$
$661$	5.12776	−	34.0205i	0.199447	−	1.32324i	0.834600	−	0.550857i	$-0.185699\pi$
$662$	3.30098	+	5.29066i	0.128296	+	0.205627i
$663$	3.96413	+	3.67818i	0.153954	+	0.142849i
$664$	8.41070	−	2.85350i	0.326399	−	0.110737i
$665$	−6.55619	+	12.6660i	−0.254238	+	0.491165i
$666$	−0.542776	−	0.403252i	−0.0210321	−	0.0156257i
$667$	23.5993	+	13.6251i	0.913769	+	0.527565i
$668$	−19.7258	+	7.59777i	−0.763216	+	0.293967i
$669$	1.96165	−	1.82014i	0.0758418	−	0.0703709i
$670$	−4.85779	+	17.9022i	−0.187673	+	0.691622i
$671$	−27.5912	+	34.5982i	−1.06515	+	1.33565i
$672$	−4.54000	+	3.56658i	−0.175134	+	0.137584i
$673$	−23.7840	−	29.8242i	−0.916805	−	1.14964i	−0.988350	−	0.152200i	$-0.951364\pi$
$673$	−23.7840	−	29.8242i	−0.916805	−	1.14964i	0.0715442	−	0.997437i	$-0.477207\pi$
$674$	−22.2552	+	9.62595i	−0.857240	+	0.370778i
$675$	−0.00887403	+	0.0226107i	−0.000341562	+	0.000870285i
$676$	−27.8241	−	2.26270i	−1.07016	−	0.0870271i
$677$	−24.5992	+	9.65448i	−0.945425	+	0.371052i	−0.787441	−	0.616390i	$-0.788595\pi$
$677$	−24.5992	+	9.65448i	−0.945425	+	0.371052i	−0.157984	+	0.987442i	$0.550499\pi$
$678$	−0.969729	+	2.20355i	−0.0372422	+	0.0846268i
$679$	−0.499309	−	4.11486i	−0.0191617	−	0.157914i
$680$	1.75227	+	17.0046i	0.0671965	+	0.652096i
$681$	0.447921	−	5.97710i	0.0171644	−	0.229043i
$682$	−0.694910	−	0.439722i	−0.0266095	−	0.0168378i
$683$	−12.5734	+	18.4417i	−0.481106	+	0.705654i	−0.987670	−	0.156549i	$-0.949963\pi$
$683$	−12.5734	+	18.4417i	−0.481106	+	0.705654i	0.506564	+	0.862203i	$0.330915\pi$
$684$	−0.0871100	+	13.7320i	−0.00333073	+	0.525056i
$685$		−	7.03762i		−	0.268894i
$686$	−9.01823	+	24.5901i	−0.344318	+	0.938853i
$687$		−	9.83257i		−	0.375136i
$688$	−2.93516	+	17.9272i	−0.111902	+	0.683469i
$689$	8.43920	−	12.3780i	0.321508	−	0.471566i
$690$	−2.04496	+	3.23174i	−0.0778504	+	0.123030i
$691$	1.40836	−	18.7932i	0.0535765	−	0.714929i	−0.904144	−	0.427228i	$-0.859490\pi$
$691$	1.40836	−	18.7932i	0.0535765	−	0.714929i	0.957720	−	0.287701i	$-0.0928908\pi$
$692$	−31.7688	−	21.9561i	−1.20767	−	0.834646i
$693$	−4.51328	−	37.1944i	−0.171445	−	1.41290i
$694$	29.9263	+	13.1698i	1.13599	+	0.499920i
$695$	7.08711	−	2.78149i	0.268830	−	0.105508i
$696$	7.69184	−	5.56457i	0.291558	−	0.210924i
$697$	−11.3280	+	28.8634i	−0.429080	+	1.09328i
$698$	−15.1074	−	34.9284i	−0.571824	−	1.32206i
$699$	1.74166	+	2.18397i	0.0658755	+	0.0826052i
$700$	−0.00650074	−	0.0565720i	−0.000245705	−	0.00213822i
$701$	−6.52176	+	8.17802i	−0.246323	+	0.308880i	−0.889588	−	0.456764i	$-0.849008\pi$
$701$	−6.52176	+	8.17802i	−0.246323	+	0.308880i	0.643264	+	0.765644i	$0.277580\pi$
$702$	−15.9949	−	4.34025i	−0.603690	−	0.163812i
$703$	−0.296033	+	0.274678i	−0.0111651	+	0.0103597i
$704$	2.21481	+	39.6725i	0.0834736	+	1.49521i
$705$	−7.77329	−	4.48791i	−0.292759	−	0.169025i
$706$	19.1885	−	25.8276i	0.722169	−	0.972036i
$707$	−5.72576	+	11.0617i	−0.215339	+	0.416016i
$708$	−7.27404	−	2.90824i	−0.273375	−	0.109298i
$709$	−5.50248	−	5.10556i	−0.206650	−	0.191743i	0.570057	−	0.821605i	$-0.306921\pi$
$709$	−5.50248	−	5.10556i	−0.206650	−	0.191743i	−0.776707	+	0.629862i	$0.783112\pi$
$710$	26.1457	−	16.3130i	0.981232	−	0.612217i
$711$	5.88465	−	39.0421i	0.220692	−	1.46419i
$712$	−5.19877	−	1.03499i	−0.194832	−	0.0387880i
$713$	0.357460	+	0.0815878i	0.0133870	+	0.00305549i
$714$	−3.52015	−	1.67194i	−0.131738	−	0.0625708i
$715$	−56.2785	+	12.8452i	−2.10470	+	0.480384i
$716$	−21.7086	+	26.8702i	−0.811287	+	1.00419i
$717$	−2.73993	+	1.58190i	−0.102324	+	0.0590770i
$718$	−22.1803	−	2.57039i	−0.827762	−	0.0959261i
$719$	−31.9071	+	21.7539i	−1.18993	+	0.811282i	−0.985843	−	0.167670i	$-0.946376\pi$
$719$	−31.9071	+	21.7539i	−1.18993	+	0.811282i	−0.204089	+	0.978952i	$0.565423\pi$
$720$	−14.1124	−	21.2741i	−0.525938	−	0.792837i
$721$	1.92497	+	41.8607i	0.0716897	+	1.55897i
$722$	−18.3321	−	3.52889i	−0.682251	−	0.131332i
$723$	−0.513263	+	1.66396i	−0.0190884	+	0.0618832i
$724$	−7.40676	+	12.6430i	−0.275270	+	0.469873i
$725$	0.00699755	+	0.0933758i	0.000259882	+	0.00346789i
$726$	6.58164	+	3.50525i	0.244268	+	0.130092i
$727$	−42.5423	+	20.4873i	−1.57781	+	0.759831i	−0.998472	−	0.0552600i	$-0.982401\pi$
$727$	−42.5423	+	20.4873i	−1.57781	+	0.759831i	−0.579333	+	0.815091i	$0.696687\pi$
$728$	37.8883	−	8.60941i	1.40423	−	0.319086i
$729$	17.3828	+	8.37111i	0.643807	+	0.310041i
$730$	−13.9683	−	19.0526i	−0.516990	−	0.705167i
$731$	−11.7172	+	3.61428i	−0.433377	+	0.133679i
$732$	−5.00916	−	4.70731i	−0.185144	−	0.173987i
$733$	0.134809	+	0.894400i	0.00497929	+	0.0330354i	0.991183	−	0.132504i	$-0.0423017\pi$
$733$	0.134809	+	0.894400i	0.00497929	+	0.0330354i	−0.986203	+	0.165539i	$0.947064\pi$
$734$	7.82030	−	6.68686i	0.288653	−	0.246816i
$735$	5.48993	+	2.52905i	0.202499	+	0.0932856i
$736$	−6.82607	−	16.3481i	−0.251612	−	0.602598i
$737$	−28.7782	+	4.33762i	−1.06006	+	0.159778i
$738$	−5.03863	−	46.0309i	−0.185475	−	1.69442i
$739$	−7.07532	−	22.9376i	−0.260270	−	0.843774i	−0.987533	−	0.157415i	$-0.949684\pi$
$739$	−7.07532	−	22.9376i	−0.260270	−	0.843774i	0.727263	−	0.686359i	$-0.240792\pi$
$740$	0.171700	−	0.730863i	0.00631180	−	0.0268671i
$741$	−2.09271	+	4.34556i	−0.0768777	+	0.159638i
$742$	−3.12664	+	10.3334i	−0.114783	+	0.379352i
$743$	−11.2574	−	23.3763i	−0.412994	−	0.857592i	−0.998885	−	0.0472019i	$-0.984970\pi$
$743$	−11.2574	−	23.3763i	−0.412994	−	0.857592i	0.585891	−	0.810390i	$-0.300745\pi$
$744$	0.0768275	−	0.102051i	0.00281663	−	0.00374136i
$745$	22.2402	−	1.66667i	0.814818	−	0.0610622i
$746$	4.98879	+	14.4035i	0.182653	+	0.527351i
$747$	−8.55531	−	2.63896i	−0.313023	−	0.0965547i
$748$	−23.3119	+	13.2627i	−0.852367	+	0.484931i
$749$	−9.99492	+	5.39233i	−0.365206	+	0.197032i
$750$	6.08911	−	0.208501i	0.222343	−	0.00761336i
$751$	−12.0092	−	17.6142i	−0.438221	−	0.642752i	0.542065	−	0.840337i	$-0.317643\pi$
$751$	−12.0092	−	17.6142i	−0.438221	−	0.642752i	−0.980286	+	0.197584i	$0.936690\pi$
$752$	37.6874	−	17.5638i	1.37432	−	0.640486i
$753$	5.08504	+	8.80755i	0.185309	+	0.320965i
$754$	−62.8143	+	11.6789i	−2.28756	+	0.425319i
$755$	−6.23443	−	27.3148i	−0.226894	−	0.994088i
$756$	11.9341	−	0.472950i	0.434039	−	0.0172010i
$757$	−2.43155	+	10.6533i	−0.0883762	+	0.387201i	−0.999700	−	0.0244887i	$-0.992204\pi$
$757$	−2.43155	+	10.6533i	−0.0883762	+	0.387201i	0.911324	+	0.411690i	$0.135061\pi$
$758$	1.76667	−	43.5206i	0.0641685	−	1.58074i
$759$	−5.93326	−	0.894295i	−0.215364	−	0.0324609i
$760$	−14.0321	+	5.96388i	−0.508999	+	0.216333i
$761$	22.0839	−	23.8008i	0.800542	−	0.862779i	−0.192407	−	0.981315i	$-0.561630\pi$
$761$	22.0839	−	23.8008i	0.800542	−	0.862779i	0.992950	+	0.118536i	$0.0378200\pi$
$762$	−6.12259	+	3.21108i	−0.221798	+	0.116325i
$763$	0.172910	−	0.668115i	0.00625977	−	0.0241874i
$764$	−1.11475	−	16.2586i	−0.0403301	−	0.588215i
$765$	8.61612	−	14.9236i	0.311516	−	0.539562i
$766$	34.6523	+	12.2489i	1.25204	+	0.442570i

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.925869 + 1.06900i) q^{2} +(-0.318723 - 0.217301i) q^{3} +(-0.285533 - 1.97951i) q^{4} +(-2.23221 - 0.167281i) q^{5} +(0.527391 - 0.139523i) q^{6} +(2.62649 - 0.318706i) q^{7} +(2.38047 + 1.52753i) q^{8} +(-1.04166 - 2.65410i) q^{9} +O(q^{10})\)	\(q+(-0.925869 + 1.06900i) q^{2} +(-0.318723 - 0.217301i) q^{3} +(-0.285533 - 1.97951i) q^{4} +(-2.23221 - 0.167281i) q^{5} +(0.527391 - 0.139523i) q^{6} +(2.62649 - 0.318706i) q^{7} +(2.38047 + 1.52753i) q^{8} +(-1.04166 - 2.65410i) q^{9} +(2.24556 - 2.23136i) q^{10} +(4.62345 + 1.81457i) q^{11} +(-0.339145 + 0.692962i) q^{12} +(4.05935 - 3.23722i) q^{13} +(-2.09108 + 3.10280i) q^{14} +(0.675106 + 0.538379i) q^{15} +(-3.83694 + 1.13043i) q^{16} +(-1.83646 - 1.97924i) q^{17} +(3.80168 + 1.34382i) q^{18} +(1.20408 - 2.08553i) q^{19} +(0.306236 + 4.46646i) q^{20} +(-0.906375 - 0.469160i) q^{21} +(-6.22048 + 3.26242i) q^{22} +(2.13014 - 2.29575i) q^{23} +(-0.426775 - 1.00414i) q^{24} +(0.0106413 + 0.00160391i) q^{25} +(-0.297826 + 7.33670i) q^{26} +(-0.502253 + 2.20051i) q^{27} +(-1.38083 - 5.10816i) q^{28} +(1.93620 + 8.48305i) q^{29} +(-1.20059 + 0.223222i) q^{30} +(0.0585377 + 0.101390i) q^{31} +(2.34407 - 5.14833i) q^{32} +(-1.07929 - 1.58303i) q^{33} +(3.81613 - 0.130670i) q^{34} +(-5.91619 + 0.272057i) q^{35} +(-4.95640 + 2.81981i) q^{36} +(-0.160245 - 0.0494289i) q^{37} +(1.11462 + 3.21809i) q^{38} +(-1.99726 + 0.149674i) q^{39} +(-5.05819 - 3.80799i) q^{40} +(-4.98272 - 10.3467i) q^{41} +(1.34072 - 0.534537i) q^{42} +(1.97048 - 4.09173i) q^{43} +(2.27181 - 9.67029i) q^{44} +(1.88122 + 6.09878i) q^{45} +(0.481927 + 4.40269i) q^{46} +(-10.2787 + 1.54926i) q^{47} +(1.46856 + 0.473478i) q^{48} +(6.79685 - 1.67415i) q^{49} +(-0.0115670 + 0.00989052i) q^{50} +(0.155231 + 1.02989i) q^{51} +(-7.56721 - 7.11120i) q^{52} +(2.75719 - 0.850480i) q^{53} +(-1.88734 - 2.57430i) q^{54} +(-10.0170 - 4.82392i) q^{55} +(6.73911 + 3.25338i) q^{56} +(-0.836956 + 0.403057i) q^{57} +(-10.8611 - 5.78439i) q^{58} +(0.758813 + 10.1257i) q^{59} +(0.872963 - 1.49011i) q^{60} +(-2.62620 + 8.51392i) q^{61} +(-0.162585 - 0.0312971i) q^{62} +(-3.58178 - 6.63898i) q^{63} +(3.33328 + 7.27250i) q^{64} +(-9.60287 + 6.54712i) q^{65} +(2.69154 + 0.311912i) q^{66} +(-5.07455 + 2.92979i) q^{67} +(-3.39355 + 4.20044i) q^{68} +(-1.17779 + 0.268824i) q^{69} +(5.18679 - 6.57631i) q^{70} +(9.49078 + 2.16621i) q^{71} +(1.57459 - 7.90919i) q^{72} +(1.11225 - 7.37932i) q^{73} +(0.201205 - 0.125537i) q^{74} +(-0.00304308 - 0.00282356i) q^{75} +(-4.47214 - 1.78801i) q^{76} +(12.7217 + 3.29242i) q^{77} +(1.68920 - 2.27365i) q^{78} +(11.9926 + 6.92396i) q^{79} +(8.75397 - 1.88152i) q^{80} +(-5.63197 + 5.22570i) q^{81} +(15.6740 + 4.25317i) q^{82} +(1.95783 - 2.45504i) q^{83} +(-0.669908 + 1.92814i) q^{84} +(3.76829 + 4.72528i) q^{85} +(2.54967 + 5.89485i) q^{86} +(1.22627 - 3.12448i) q^{87} +(8.23416 + 11.3820i) q^{88} +(-1.74456 + 0.684691i) q^{89} +(-8.26137 - 3.63564i) q^{90} +(9.63011 - 9.79626i) q^{91} +(-5.15269 - 3.56113i) q^{92} +(0.00337496 - 0.0450357i) q^{93} +(7.86055 - 12.4223i) q^{94} +(-3.03664 + 4.45393i) q^{95} +(-1.86585 + 1.13152i) q^{96} -1.56668i q^{97} +(-4.50332 + 8.81590i) q^{98} -14.1613i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

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