LMFDB - Embedded newform 196.2.p.a.103.13

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			103.13
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.109851 + 1.40994i) q^{2} +(-1.32314 - 0.902103i) q^{3} +(-1.97587 - 0.309768i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(1.41726 - 1.76645i) q^{6} +(-1.28165 - 2.31460i) q^{7} +(0.653806 - 2.75182i) q^{8} +(-0.159109 - 0.405403i) q^{9} +O(q^{10})$	\(q+(-0.109851 + 1.40994i) q^{2} +(-1.32314 - 0.902103i) q^{3} +(-1.97587 - 0.309768i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(1.41726 - 1.76645i) q^{6} +(-1.28165 - 2.31460i) q^{7} +(0.653806 - 2.75182i) q^{8} +(-0.159109 - 0.405403i) q^{9} +(-0.0697296 + 0.453528i) q^{10} +(-2.61131 - 1.02486i) q^{11} +(2.33491 + 2.19230i) q^{12} +(2.01211 - 1.60461i) q^{13} +(3.40424 - 1.55279i) q^{14} +(-0.406234 - 0.323961i) q^{15} +(3.80809 + 1.22412i) q^{16} +(-0.295026 - 0.317962i) q^{17} +(0.589072 - 0.179800i) q^{18} +(3.19321 - 5.53080i) q^{19} +(-0.631787 - 0.148135i) q^{20} +(-0.392197 + 4.21872i) q^{21} +(1.73185 - 3.56920i) q^{22} +(-3.32097 + 3.57916i) q^{23} +(-3.34751 + 3.05125i) q^{24} +(-4.84006 - 0.729521i) q^{25} +(2.04137 + 3.01323i) q^{26} +(-1.22423 + 5.36370i) q^{27} +(1.81539 + 4.97035i) q^{28} +(-0.987821 - 4.32793i) q^{29} +(0.501391 - 0.537178i) q^{30} +(1.28102 + 2.21879i) q^{31} +(-2.14426 + 5.23471i) q^{32} +(2.53060 + 3.71170i) q^{33} +(0.480717 - 0.381041i) q^{34} +(-0.358561 - 0.779973i) q^{35} +(0.188797 + 0.850308i) q^{36} +(-8.40044 - 2.59119i) q^{37} +(7.44732 + 5.10980i) q^{38} +(-4.10983 + 0.307989i) q^{39} +(0.278265 - 0.874510i) q^{40} +(3.27984 + 6.81065i) q^{41} +(-5.90507 - 1.01641i) q^{42} +(2.17288 - 4.51203i) q^{43} +(4.84212 + 2.83389i) q^{44} +(-0.0416505 - 0.135028i) q^{45} +(-4.68158 - 5.07555i) q^{46} +(5.45444 - 0.822124i) q^{47} +(-3.93436 - 5.05497i) q^{48} +(-3.71473 + 5.93302i) q^{49} +(1.56027 - 6.74405i) q^{50} +(0.103526 + 0.686853i) q^{51} +(-4.47272 + 2.54720i) q^{52} +(5.41768 - 1.67113i) q^{53} +(-7.42801 - 2.31530i) q^{54} +(-0.820048 - 0.394914i) q^{55} +(-7.20732 + 2.01359i) q^{56} +(-9.21441 + 4.43743i) q^{57} +(6.21063 - 0.917341i) q^{58} +(-0.182304 - 2.43268i) q^{59} +(0.702311 + 0.765941i) q^{60} +(2.02445 - 6.56311i) q^{61} +(-3.26908 + 1.56242i) q^{62} +(-0.734423 + 0.887859i) q^{63} +(-7.14508 - 3.59832i) q^{64} +(0.689933 - 0.470389i) q^{65} +(-5.51127 + 3.16026i) q^{66} +(-0.882664 + 0.509607i) q^{67} +(0.484437 + 0.719641i) q^{68} +(7.62288 - 1.73987i) q^{69} +(1.13910 - 0.419869i) q^{70} +(11.9497 + 2.72743i) q^{71} +(-1.21962 + 0.172785i) q^{72} +(1.03556 - 6.87048i) q^{73} +(4.57623 - 11.5595i) q^{74} +(5.74597 + 5.33149i) q^{75} +(-8.02261 + 9.93896i) q^{76} +(0.974644 + 7.35764i) q^{77} +(0.0172239 - 5.82845i) q^{78} +(9.00457 + 5.19879i) q^{79} +(1.20244 + 0.488403i) q^{80} +(5.50068 - 5.10389i) q^{81} +(-9.96291 + 3.87622i) q^{82} +(-3.97658 + 4.98647i) q^{83} +(2.08175 - 8.21414i) q^{84} +(-0.0877471 - 0.110031i) q^{85} +(6.12301 + 3.55929i) q^{86} +(-2.59721 + 6.61758i) q^{87} +(-4.52753 + 6.51580i) q^{88} +(12.6725 - 4.97359i) q^{89} +(0.194956 - 0.0438917i) q^{90} +(-6.29285 - 2.60068i) q^{91} +(7.67050 - 6.04320i) q^{92} +(0.306607 - 4.09138i) q^{93} +(0.559969 + 7.78075i) q^{94} +(1.16728 - 1.71208i) q^{95} +(7.55940 - 4.99192i) q^{96} +8.05557i q^{97} +(-7.95714 - 5.88930i) q^{98} +1.22170i 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 $

$2$	−0.109851	+	1.40994i	−0.0776766	+	0.996979i
$2$	−0.109851	+	1.40994i	−0.0776766	+	0.996979i
$3$	−1.32314	−	0.902103i	−0.763916	−	0.520829i	0.117555	−	0.993066i	$-0.462494\pi$
$3$	−1.32314	−	0.902103i	−0.763916	−	0.520829i	−0.881472	+	0.472237i	$0.843447\pi$
$4$	−1.97587	−	0.309768i	−0.987933	−	0.154884i
$5$	0.323554	+	0.0242470i	0.144698	+	0.0108436i	0.146882	−	0.989154i	$-0.453076\pi$
$5$	0.323554	+	0.0242470i	0.144698	+	0.0108436i	−0.00218437	+	0.999998i	$0.500695\pi$
$6$	1.41726	−	1.76645i	0.578594	−	0.721152i
$7$	−1.28165	−	2.31460i	−0.484419	−	0.874836i
$7$	−1.28165	−	2.31460i	−0.484419	−	0.874836i
$8$	0.653806	−	2.75182i	0.231155	−	0.972917i
$9$	−0.159109	−	0.405403i	−0.0530363	−	0.135134i
$10$	−0.0697296	+	0.453528i	−0.0220504	+	0.143418i
$11$	−2.61131	−	1.02486i	−0.787339	−	0.309008i	−0.0626064	−	0.998038i	$-0.519941\pi$
$11$	−2.61131	−	1.02486i	−0.787339	−	0.309008i	−0.724732	+	0.689031i	$0.758037\pi$
$12$	2.33491	+	2.19230i	0.674030	+	0.632862i
$13$	2.01211	−	1.60461i	0.558060	−	0.445038i	−0.303400	−	0.952863i	$-0.598122\pi$
$13$	2.01211	−	1.60461i	0.558060	−	0.445038i	0.861460	+	0.507825i	$0.169550\pi$
$14$	3.40424	−	1.55279i	0.909821	−	0.415001i
$15$	−0.406234	−	0.323961i	−0.104889	−	0.0836463i
$16$	3.80809	+	1.22412i	0.952022	+	0.306030i
$17$	−0.295026	−	0.317962i	−0.0715543	−	0.0771172i	0.696260	−	0.717790i	$-0.254846\pi$
$17$	−0.295026	−	0.317962i	−0.0715543	−	0.0771172i	−0.767814	+	0.640673i	$0.778656\pi$
$18$	0.589072	−	0.179800i	0.138846	−	0.0423793i
$19$	3.19321	−	5.53080i	0.732572	−	1.26885i	−0.223209	−	0.974771i	$-0.571653\pi$
$19$	3.19321	−	5.53080i	0.732572	−	1.26885i	0.955780	−	0.294081i	$-0.0950136\pi$
$20$	−0.631787	−	0.148135i	−0.141272	−	0.0331241i
$21$	−0.392197	+	4.21872i	−0.0855844	+	0.920601i
$22$	1.73185	−	3.56920i	0.369232	−	0.760957i
$23$	−3.32097	+	3.57916i	−0.692470	+	0.746306i	−0.977204	−	0.212301i	$-0.931904\pi$
$23$	−3.32097	+	3.57916i	−0.692470	+	0.746306i	0.284734	+	0.958607i	$0.408095\pi$
$24$	−3.34751	+	3.05125i	−0.683307	+	0.622834i
$25$	−4.84006	−	0.729521i	−0.968011	−	0.145904i
$26$	2.04137	+	3.01323i	0.400345	+	0.590943i
$27$	−1.22423	+	5.36370i	−0.235603	+	1.03224i
$28$	1.81539	+	4.97035i	0.343076	+	0.939308i
$29$	−0.987821	−	4.32793i	−0.183434	−	0.803676i	−0.979980	−	0.199098i	$-0.936199\pi$
$29$	−0.987821	−	4.32793i	−0.183434	−	0.803676i	0.796546	−	0.604578i	$-0.206658\pi$
$30$	0.501391	−	0.537178i	0.0915410	−	0.0980749i
$31$	1.28102	+	2.21879i	0.230078	+	0.398506i	0.957831	−	0.287333i	$-0.0927686\pi$
$31$	1.28102	+	2.21879i	0.230078	+	0.398506i	−0.727753	+	0.685839i	$0.759435\pi$
$32$	−2.14426	+	5.23471i	−0.379055	+	0.925374i
$33$	2.53060	+	3.71170i	0.440520	+	0.646125i
$34$	0.480717	−	0.381041i	0.0824423	−	0.0653479i
$35$	−0.358561	−	0.779973i	−0.0606079	−	0.131839i
$36$	0.188797	+	0.850308i	0.0314662	+	0.141718i
$37$	−8.40044	−	2.59119i	−1.38102	−	0.425989i	−0.486762	−	0.873535i	$-0.661822\pi$
$37$	−8.40044	−	2.59119i	−1.38102	−	0.425989i	−0.894261	+	0.447545i	$0.852298\pi$
$38$	7.44732	+	5.10980i	1.20811	+	0.828919i
$39$	−4.10983	+	0.307989i	−0.658099	+	0.0493177i
$40$	0.278265	−	0.874510i	0.0439975	−	0.138272i
$41$	3.27984	+	6.81065i	0.512224	+	1.06364i	0.983374	+	0.181592i	$0.0581249\pi$
$41$	3.27984	+	6.81065i	0.512224	+	1.06364i	−0.471150	+	0.882053i	$0.656161\pi$
$42$	−5.90507	−	1.01641i	−0.911171	−	0.156835i
$43$	2.17288	−	4.51203i	0.331361	−	0.688079i	−0.667015	−	0.745044i	$-0.732428\pi$
$43$	2.17288	−	4.51203i	0.331361	−	0.688079i	0.998376	+	0.0569657i	$0.0181426\pi$
$44$	4.84212	+	2.83389i	0.729977	+	0.427225i
$45$	−0.0416505	−	0.135028i	−0.00620889	−	0.0201287i
$46$	−4.68158	−	5.07555i	−0.690262	−	0.748349i
$47$	5.45444	−	0.822124i	0.795612	−	0.119919i	0.261356	−	0.965242i	$-0.415830\pi$
$47$	5.45444	−	0.822124i	0.795612	−	0.119919i	0.534255	+	0.845323i	$0.320592\pi$
$48$	−3.93436	−	5.05497i	−0.567876	−	0.729622i
$49$	−3.71473	+	5.93302i	−0.530676	+	0.847575i
$50$	1.56027	−	6.74405i	0.220655	−	0.953753i
$51$	0.103526	+	0.686853i	0.0144966	+	0.0961787i
$52$	−4.47272	+	2.54720i	−0.620255	+	0.353233i
$53$	5.41768	−	1.67113i	0.744175	−	0.229548i	0.100596	−	0.994927i	$-0.467925\pi$
$53$	5.41768	−	1.67113i	0.744175	−	0.229548i	0.643579	+	0.765380i	$0.277449\pi$
$54$	−7.42801	−	2.31530i	−1.01082	−	0.315072i
$55$	−0.820048	−	0.394914i	−0.110575	−	0.0532502i
$56$	−7.20732	+	2.01359i	−0.963119	+	0.269077i
$57$	−9.21441	+	4.43743i	−1.22048	+	0.587751i
$58$	6.21063	−	0.917341i	0.815496	−	0.120453i
$59$	−0.182304	−	2.43268i	−0.0237340	−	0.316708i	−0.996417	−	0.0845721i	$-0.973048\pi$
$59$	−0.182304	−	2.43268i	−0.0237340	−	0.316708i	0.972683	−	0.232136i	$-0.0745714\pi$
$60$	0.702311	+	0.765941i	0.0906679	+	0.0988826i
$61$	2.02445	−	6.56311i	0.259204	−	0.840320i	−0.728643	−	0.684894i	$-0.759849\pi$
$61$	2.02445	−	6.56311i	0.259204	−	0.840320i	0.987847	−	0.155426i	$-0.0496752\pi$
$62$	−3.26908	+	1.56242i	−0.415174	+	0.198428i
$63$	−0.734423	+	0.887859i	−0.0925286	+	0.111860i
$64$	−7.14508	−	3.59832i	−0.893135	−	0.449790i
$65$	0.689933	−	0.470389i	0.0855757	−	0.0583445i
$66$	−5.51127	+	3.16026i	−0.678391	+	0.389001i
$67$	−0.882664	+	0.509607i	−0.107835	+	0.0622583i	−0.552947	−	0.833216i	$-0.686497\pi$
$67$	−0.882664	+	0.509607i	−0.107835	+	0.0622583i	0.445113	+	0.895475i	$0.353164\pi$
$68$	0.484437	+	0.719641i	0.0587466	+	0.0872692i
$69$	7.62288	−	1.73987i	0.917687	−	0.209456i
$70$	1.13910	−	0.419869i	0.136149	−	0.0501840i
$71$	11.9497	+	2.72743i	1.41816	+	0.323687i	0.861799	−	0.507251i	$-0.169338\pi$
$71$	11.9497	+	2.72743i	1.41816	+	0.323687i	0.556366	+	0.830937i	$0.312195\pi$
$72$	−1.21962	+	0.172785i	−0.143734	+	0.0203629i
$73$	1.03556	−	6.87048i	0.121203	−	0.804128i	−0.842798	−	0.538230i	$-0.819093\pi$
$73$	1.03556	−	6.87048i	0.121203	−	0.804128i	0.964001	−	0.265899i	$-0.0856686\pi$
$74$	4.57623	−	11.5595i	0.531975	−	1.34376i
$75$	5.74597	+	5.33149i	0.663488	+	0.615627i
$76$	−8.02261	+	9.93896i	−0.920256	+	1.14008i
$77$	0.974644	+	7.35764i	0.111071	+	0.838481i
$78$	0.0172239	−	5.82845i	0.00195022	−	0.659942i
$79$	9.00457	+	5.19879i	1.01309	+	0.584910i	0.912096	−	0.409977i	$-0.134463\pi$
$79$	9.00457	+	5.19879i	1.01309	+	0.584910i	0.100997	+	0.994887i	$0.467797\pi$
$80$	1.20244	+	0.488403i	0.134437	+	0.0546051i
$81$	5.50068	−	5.10389i	0.611187	−	0.567098i
$82$	−9.96291	+	3.87622i	−1.10022	+	0.428056i
$83$	−3.97658	+	4.98647i	−0.436486	+	0.547336i	−0.950613	−	0.310378i	$-0.899544\pi$
$83$	−3.97658	+	4.98647i	−0.436486	+	0.547336i	0.514127	+	0.857714i	$0.328116\pi$
$84$	2.08175	−	8.21414i	0.227138	−	0.896236i
$85$	−0.0877471	−	0.110031i	−0.00951751	−	0.0119346i
$86$	6.12301	+	3.55929i	0.660261	+	0.383808i
$87$	−2.59721	+	6.61758i	−0.278450	+	0.709479i
$88$	−4.52753	+	6.51580i	−0.482636	+	0.694586i
$89$	12.6725	−	4.97359i	1.34328	−	0.527200i	0.418681	−	0.908133i	$-0.362493\pi$
$89$	12.6725	−	4.97359i	1.34328	−	0.527200i	0.924602	+	0.380934i	$0.124397\pi$
$90$	0.194956	−	0.0438917i	0.0205502	−	0.00462660i
$91$	−6.29285	−	2.60068i	−0.659670	−	0.272626i
$92$	7.67050	−	6.04320i	0.799705	−	0.630047i
$93$	0.306607	−	4.09138i	0.0317936	−	0.424257i
$94$	0.559969	+	7.78075i	0.0577564	+	0.802523i
$95$	1.16728	−	1.71208i	0.119760	−	0.175656i
$96$	7.55940	−	4.99192i	0.771528	−	0.509485i
$97$			8.05557i			0.817919i	0.912553	+	0.408960i	$0.134108\pi$
$97$			8.05557i			0.817919i	−0.912553	+	0.408960i	$0.865892\pi$
$98$	−7.95714	−	5.88930i	−0.803793	−	0.594909i
$99$			1.22170i			0.122785i
$100$	9.33732	+	2.94073i	0.933732	+	0.294073i
$101$	8.36578	−	12.2704i	0.832427	−	1.22095i	−0.140557	−	0.990073i	$-0.544889\pi$
$101$	8.36578	−	12.2704i	0.832427	−	1.22095i	0.972984	−	0.230873i	$-0.0741582\pi$
$102$	−0.979794	+	0.0705144i	−0.0970141	+	0.00698197i
$103$	0.641180	−	8.55595i	0.0631773	−	0.843043i	−0.872145	−	0.489247i	$-0.837272\pi$
$103$	0.641180	−	8.55595i	0.0631773	−	0.843043i	0.935323	−	0.353796i	$-0.115109\pi$
$104$	−3.10006	−	6.58608i	−0.303986	−	0.645819i
$105$	−0.229188	+	1.35547i	−0.0223665	+	0.132281i
$106$	1.76106	+	7.82218i	0.171049	+	0.759757i
$107$	2.95157	−	1.15841i	0.285339	−	0.111987i	−0.218355	−	0.975869i	$-0.570069\pi$
$107$	2.95157	−	1.15841i	0.285339	−	0.111987i	0.503694	+	0.863882i	$0.331974\pi$
$108$	4.08041	−	10.2187i	0.392638	−	0.983296i
$109$	6.02790	−	15.3588i	0.577368	−	1.47111i	−0.281829	−	0.959465i	$-0.590941\pi$
$109$	6.02790	−	15.3588i	0.577368	−	1.47111i	0.859197	−	0.511645i	$-0.170964\pi$
$110$	0.646889	−	1.11284i	0.0616784	−	0.106105i
$111$	8.77744	+	11.0066i	0.833118	+	1.04470i
$112$	−2.04730	−	10.3831i	−0.193452	−	0.981110i
$113$	−11.0022	+	13.7963i	−1.03500	+	1.29785i	−0.0814256	+	0.996679i	$0.525947\pi$
$113$	−11.0022	+	13.7963i	−1.03500	+	1.29785i	−0.953572	+	0.301166i	$0.902624\pi$
$114$	−5.24429	−	13.4792i	−0.491173	−	1.26245i
$115$	−1.16130	+	1.07753i	−0.108291	+	0.100480i
$116$	0.611149	+	8.85740i	0.0567438	+	0.822389i
$117$	−0.970657	−	0.560409i	−0.0897373	−	0.0518099i
$118$	3.44996	+	0.0101951i	0.317595	+	0.000938537i
$119$	−0.357834	+	1.09038i	−0.0328026	+	0.0999554i
$120$	−1.15708	+	0.906077i	−0.105627	+	0.0827131i
$121$	−2.29499	−	2.12944i	−0.208636	−	0.193586i
$122$	9.03121	+	3.57532i	0.817647	+	0.323695i
$123$	1.80422	−	11.9702i	0.162681	−	1.07932i
$124$	−1.84381	−	4.78085i	−0.165579	−	0.429333i
$125$	−3.12996	−	0.714393i	−0.279952	−	0.0638972i
$126$	−1.17115	−	1.13302i	−0.104334	−	0.100938i
$127$	−6.86346	+	1.56654i	−0.609034	+	0.139008i	−0.515905	−	0.856646i	$-0.672544\pi$
$127$	−6.86346	+	1.56654i	−0.609034	+	0.139008i	−0.0931292	+	0.995654i	$0.529687\pi$
$128$	5.85831	−	9.67885i	0.517806	−	0.855498i
$129$	−6.94535	+	4.00990i	−0.611504	+	0.353052i
$130$	0.587430	+	1.02444i	0.0515210	+	0.0898491i
$131$	−14.5953	+	9.95088i	−1.27519	+	0.869413i	−0.995871	−	0.0907844i	$-0.971063\pi$
$131$	−14.5953	+	9.95088i	−1.27519	+	0.869413i	−0.279324	+	0.960197i	$0.590110\pi$
$132$	−3.85035	−	8.11772i	−0.335130	−	0.706557i
$133$	−16.8942	−	0.302430i	−1.46491	−	0.0262240i
$134$	−0.621553	−	1.30049i	−0.0536940	−	0.112345i
$135$	−0.526157	+	1.70576i	−0.0452844	+	0.146808i
$136$	−1.06787	+	0.603974i	−0.0915688	+	0.0517904i
$137$	0.772969	+	10.3146i	0.0660392	+	0.881232i	0.927599	+	0.373577i	$0.121869\pi$
$137$	0.772969	+	10.3146i	0.0660392	+	0.881232i	−0.861560	+	0.507655i	$0.830512\pi$
$138$	1.61573	+	10.9389i	0.137540	+	0.931184i
$139$	12.9510	−	6.23687i	1.09849	−	0.529004i	0.205305	−	0.978698i	$-0.434181\pi$
$139$	12.9510	−	6.23687i	1.09849	−	0.529004i	0.893183	+	0.449694i	$0.148467\pi$
$140$	0.466859	+	1.65219i	0.0394567	+	0.139636i
$141$	−7.95863	−	3.83268i	−0.670238	−	0.322770i
$142$	−5.15821	+	16.5487i	−0.432867	+	1.38874i
$143$	−6.89874	+	2.12798i	−0.576902	+	0.177951i
$144$	−0.109639	−	1.73858i	−0.00913662	−	0.144882i
$145$	−0.214674	−	1.42427i	−0.0178277	−	0.118279i
$146$	9.57321	+	2.21481i	0.792284	+	0.183299i
$147$	10.2673	−	4.49916i	0.846833	−	0.371084i
$148$	15.7955	+	7.72203i	1.29838	+	0.634747i
$149$	2.76780	−	0.417179i	0.226747	−	0.0341766i	−0.0346858	−	0.999398i	$-0.511043\pi$
$149$	2.76780	−	0.417179i	0.226747	−	0.0341766i	0.261433	+	0.965222i	$0.415805\pi$
$150$	−8.14828	+	7.51581i	−0.665304	+	0.613663i
$151$	−2.74206	−	8.88954i	−0.223146	−	0.723420i	−0.996042	−	0.0888877i	$-0.971669\pi$
$151$	−2.74206	−	8.88954i	−0.223146	−	0.723420i	0.772896	−	0.634533i	$-0.218807\pi$
$152$	−13.1320	−	12.4032i	−1.06515	−	1.00603i
$153$	−0.0819616	+	0.170195i	−0.00662621	+	0.0137595i
$154$	−10.4809	+	0.565943i	−0.844576	+	0.0456050i
$155$	0.360679	+	0.748958i	0.0289705	+	0.0601578i
$156$	8.21587	+	0.664548i	0.657796	+	0.0532064i
$157$	−11.9883	+	0.898398i	−0.956770	+	0.0717000i	−0.543955	−	0.839115i	$-0.683074\pi$
$157$	−11.9883	+	0.898398i	−0.956770	+	0.0717000i	−0.412815	+	0.910815i	$0.635455\pi$
$158$	−8.31915	+	12.1248i	−0.661836	+	0.964598i
$159$	−8.67589	−	2.67616i	−0.688043	−	0.212233i
$160$	−0.820708	+	1.64172i	−0.0648827	+	0.129789i
$161$	12.5406	+	3.09948i	0.988341	+	0.244273i
$162$	6.59192	+	8.31630i	0.517910	+	0.653390i
$163$	−6.04539	−	8.86696i	−0.473511	−	0.694514i	0.512966	−	0.858409i	$-0.328547\pi$
$163$	−6.04539	−	8.86696i	−0.473511	−	0.694514i	−0.986478	+	0.163895i	$0.947594\pi$
$164$	−4.37080	−	14.4729i	−0.341302	−	1.13014i
$165$	0.728786	+	1.26229i	0.0567359	+	0.0982695i
$166$	−6.59379	−	6.15451i	−0.511778	−	0.477682i
$167$	−5.31218	−	23.2742i	−0.411069	−	1.80101i	−0.579131	−	0.815235i	$-0.696608\pi$
$167$	−5.31218	−	23.2742i	−0.411069	−	1.80101i	0.168062	−	0.985777i	$-0.446249\pi$
$168$	11.3528	+	3.83748i	0.875885	+	0.296068i
$169$	−1.41894	+	6.21676i	−0.109149	+	0.478213i
$170$	0.164777	−	0.111631i	0.0126378	−	0.00856172i
$171$	−2.75027	−	0.414536i	−0.210318	−	0.0317004i
$172$	−5.69100	+	8.24208i	−0.433935	+	0.628453i
$173$	0.831907	−	0.896582i	0.0632487	−	0.0681659i	−0.700635	−	0.713520i	$-0.747100\pi$
$173$	0.831907	−	0.896582i	0.0632487	−	0.0681659i	0.763883	+	0.645354i	$0.223290\pi$
$174$	−9.04508	−	4.38886i	−0.685706	−	0.332718i
$175$	4.51472	+	12.1378i	0.341281	+	0.917530i
$176$	−8.68953	−	7.09932i	−0.654998	−	0.535131i
$177$	−1.95331	+	3.38324i	−0.146820	+	0.254300i
$178$	5.62038	+	18.4138i	0.421265	+	1.38018i
$179$	10.6604	+	11.4891i	0.796793	+	0.858738i	0.992540	−	0.121916i	$-0.0389039\pi$
$179$	10.6604	+	11.4891i	0.796793	+	0.858738i	−0.195748	+	0.980654i	$0.562713\pi$
$180$	0.0404686	+	0.279698i	0.00301635	+	0.0208475i
$181$	20.0404	+	15.9817i	1.48959	+	1.18791i	0.934421	+	0.356170i	$0.115918\pi$
$181$	20.0404	+	15.9817i	1.48959	+	1.18791i	0.555169	+	0.831738i	$0.312654\pi$
$182$	4.35809	−	8.58686i	0.323043	−	0.636500i
$183$	−8.59923	+	6.85766i	−0.635674	+	0.506933i
$184$	7.67794	+	11.4788i	0.566025	+	0.846229i
$185$	−2.65516	−	1.04207i	−0.195211	−	0.0766148i
$186$	5.73493	+	0.881741i	0.420505	+	0.0646524i
$187$	0.444536	+	1.13266i	0.0325077	+	0.0828282i
$188$	−11.0319	−	0.0652023i	−0.804584	−	0.00475537i
$189$	13.9838	−	4.04080i	1.01717	−	0.293925i
$190$	2.28571	+	1.83387i	0.165823	+	0.133043i
$191$	1.00074	+	0.0749955i	0.0724114	+	0.00542648i	0.110886	−	0.993833i	$-0.464631\pi$
$191$	1.00074	+	0.0749955i	0.0724114	+	0.00542648i	−0.0384751	+	0.999260i	$0.512250\pi$
$192$	6.20790	+	11.2067i	0.448016	+	0.808772i
$193$	−4.45048	−	3.03428i	−0.320352	−	0.218413i	0.392457	−	0.919770i	$-0.371625\pi$
$193$	−4.45048	−	3.03428i	−0.320352	−	0.218413i	−0.712809	+	0.701358i	$0.752578\pi$
$194$	−11.3579	−	0.884915i	−0.815448	−	0.0635332i
$195$	−1.33722			−0.0957602
$196$	9.17767	−	10.5722i	0.655548	−	0.755154i
$197$	4.43186			0.315757			0.157878	−	0.987459i	$-0.449535\pi$
$197$	4.43186			0.315757			0.157878	+	0.987459i	$0.449535\pi$
$198$	−1.72252	−	0.134205i	−0.122414	−	0.00953753i
$199$	−13.8341	−	9.43193i	−0.980673	−	0.668612i	−0.0369393	−	0.999318i	$-0.511761\pi$
$199$	−13.8341	−	9.43193i	−0.980673	−	0.668612i	−0.943734	+	0.330706i	$0.892713\pi$
$200$	−5.17197	+	12.8420i	−0.365713	+	0.908068i
$201$	1.62761	+	0.121972i	0.114803	+	0.00860326i
$202$	16.3815	+	13.1432i	1.15260	+	0.924751i
$203$	−8.75137	+	7.83331i	−0.614226	+	0.549791i
$204$	0.00821063	−	1.38920i	0.000574859	−	0.0972633i
$205$	0.896065	+	2.28314i	0.0625839	+	0.159461i
$206$	11.9929	+	1.84391i	0.835588	+	0.128471i
$207$	1.97940	+	0.776856i	0.137578	+	0.0539952i
$208$	9.62653	−	3.64742i	0.667480	−	0.252903i
$209$	−14.0067	+	11.1700i	−0.968867	+	0.772646i
$210$	−1.88596	−	0.472042i	−0.130144	−	0.0325740i
$211$	0.173155	+	0.138087i	0.0119205	+	0.00950629i	0.629432	−	0.777056i	$-0.283288\pi$
$211$	0.173155	+	0.138087i	0.0119205	+	0.00950629i	−0.617511	+	0.786562i	$0.711859\pi$
$212$	−11.2223	+	1.62371i	−0.770748	+	0.111517i
$213$	−13.3507	−	14.3886i	−0.914773	−	0.985891i
$214$	1.30905	+	4.28880i	0.0894849	+	0.293176i
$215$	0.812447	−	1.40720i	0.0554084	−	0.0959702i
$216$	13.9595	+	6.87568i	0.949827	+	0.467831i
$217$	3.49379	−	5.80876i	0.237174	−	0.394324i
$218$	20.9929	+	10.1862i	1.42182	+	0.689894i
$219$	−7.56806	+	8.15643i	−0.511402	+	0.551161i
$220$	1.49797	+	1.03432i	0.100993	+	0.0697340i
$221$	−1.10383	−	0.166376i	−0.0742517	−	0.0111916i
$222$	−16.4828	+	11.1666i	−1.10625	+	0.749452i
$223$	3.71159	−	16.2616i	0.248547	−	1.08895i	−0.684447	−	0.729062i	$-0.739956\pi$
$223$	3.71159	−	16.2616i	0.248547	−	1.08895i	0.932994	−	0.359892i	$-0.117187\pi$
$224$	14.8644	−	1.74598i	0.993172	−	0.116658i
$225$	0.474346	+	2.07825i	0.0316231	+	0.138550i
$226$	−18.2433	−	17.0280i	−1.21353	−	1.13268i
$227$	7.02786	+	12.1726i	0.466456	+	0.807925i	0.999266	−	0.0383097i	$-0.0121973\pi$
$227$	7.02786	+	12.1726i	0.466456	+	0.807925i	−0.532810	+	0.846235i	$0.678864\pi$
$228$	19.5810	−	5.91343i	1.29678	−	0.391626i
$229$	7.98099	+	11.7060i	0.527399	+	0.773552i	0.993819	−	0.111011i	$-0.0354090\pi$
$229$	7.98099	+	11.7060i	0.527399	+	0.773552i	−0.466420	+	0.884563i	$0.654457\pi$
$230$	−1.39168	−	1.75573i	−0.0917645	−	0.115769i
$231$	5.34776	−	10.6144i	0.351857	−	0.698378i
$232$	−12.5555	−	0.111313i	−0.824312	−	0.00730805i
$233$	−25.4093	−	7.83773i	−1.66462	−	0.513467i	−0.687504	−	0.726181i	$-0.741294\pi$
$233$	−25.4093	−	7.83773i	−1.66462	−	0.513467i	−0.977114	+	0.212714i	$0.931770\pi$
$234$	0.896772	−	1.30701i	0.0586238	−	0.0854418i
$235$	1.78474	−	0.133748i	0.116423	−	0.00872473i
$236$	−0.393357	+	4.86312i	−0.0256054	+	0.316562i
$237$	−7.22447	−	15.0018i	−0.469280	−	0.974470i
$238$	−1.49807	−	0.624305i	−0.0971054	−	0.0404677i
$239$	3.72072	−	7.72616i	0.240674	−	0.499764i	−0.745287	−	0.666744i	$-0.767687\pi$
$239$	3.72072	−	7.72616i	0.240674	−	0.499764i	0.985960	+	0.166980i	$0.0534016\pi$
$240$	−1.15041	−	1.73095i	−0.0742585	−	0.111732i
$241$	8.99671	+	29.1666i	0.579529	+	1.87879i	0.464863	+	0.885383i	$0.346103\pi$
$241$	8.99671	+	29.1666i	0.579529	+	1.87879i	0.114666	+	0.993404i	$0.463420\pi$
$242$	3.25449	−	3.00188i	0.209207	−	0.192968i
$243$	4.43815	−	0.668943i	0.284707	−	0.0429127i
$244$	−6.03308	+	12.3407i	−0.386229	+	0.790033i
$245$	−1.34577	+	1.82958i	−0.0859783	+	0.116888i
$246$	16.6791	+	3.85878i	1.06342	+	0.246027i
$247$	−2.44966	−	16.2524i	−0.155868	−	1.03412i
$248$	6.94326	−	2.07448i	0.440897	−	0.131730i
$249$	9.75988	−	3.01052i	0.618507	−	0.190784i
$250$	1.35108	−	4.33458i	0.0854499	−	0.274143i
$251$	−17.5508	−	8.45200i	−1.10779	−	0.533485i	−0.211693	−	0.977336i	$-0.567898\pi$
$251$	−17.5508	−	8.45200i	−1.10779	−	0.533485i	−0.896101	+	0.443851i	$0.853612\pi$
$252$	1.72615	−	1.52679i	0.108737	−	0.0961787i
$253$	12.3402	−	5.94274i	0.775823	−	0.373617i
$254$	−1.45477	−	9.84916i	−0.0912803	−	0.617991i
$255$	0.0168422	+	0.224744i	0.00105470	+	0.0140740i
$256$	13.0031	+	9.32310i	0.812692	+	0.582694i
$257$	−2.89364	+	9.38097i	−0.180501	+	0.585169i	0.819428	+	0.573183i	$0.194291\pi$
$257$	−2.89364	+	9.38097i	−0.180501	+	0.585169i	−0.999928	+	0.0119858i	$0.996185\pi$
$258$	−4.89076	−	10.2330i	−0.304485	−	0.637080i
$259$	4.76888	+	22.7646i	0.296324	+	1.41453i
$260$	−1.50893	+	0.715705i	−0.0935797	+	0.0443862i
$261$	−1.59738	+	1.08908i	−0.0988755	+	0.0674122i
$262$	−12.4268	−	21.6716i	−0.767733	−	1.33887i
$263$	−10.2462	+	5.91566i	−0.631809	+	0.364775i	−0.781452	−	0.623965i	$-0.785521\pi$
$263$	−10.2462	+	5.91566i	−0.631809	+	0.364775i	0.149643	+	0.988740i	$0.452187\pi$
$264$	11.8685	−	4.53703i	0.730454	−	0.279235i
$265$	1.79343	−	0.409339i	0.110169	−	0.0251455i
$266$	2.28225	−	23.7865i	0.139934	−	1.45845i
$267$	−21.2542	−	4.85114i	−1.30074	−	0.296885i
$268$	1.90189	−	0.733493i	0.116176	−	0.0448052i
$269$	4.01084	−	26.6102i	0.244545	−	1.62245i	−0.443147	−	0.896449i	$-0.646138\pi$
$269$	4.01084	−	26.6102i	0.244545	−	1.62245i	0.687692	−	0.726002i	$-0.258624\pi$
$270$	−2.34722	−	0.929230i	−0.142847	−	0.0565511i
$271$	−4.26861	−	3.96069i	−0.259300	−	0.240595i	0.539800	−	0.841793i	$-0.318500\pi$
$271$	−4.26861	−	3.96069i	−0.259300	−	0.240595i	−0.799100	+	0.601198i	$0.794690\pi$
$272$	−0.734261	−	1.57198i	−0.0445211	−	0.0953150i
$273$	5.98025	+	9.11787i	0.361941	+	0.551839i
$274$	−14.6278	−	0.0432273i	−0.883699	−	0.00261146i
$275$	11.8912	+	6.86539i	0.717067	+	0.413999i
$276$	−15.6007	+	1.07643i	−0.939054	+	0.0647936i
$277$	0.0461258	−	0.0427985i	0.00277143	−	0.00257151i	−0.678786	−	0.734336i	$-0.737494\pi$
$277$	0.0461258	−	0.0427985i	0.00277143	−	0.00257151i	0.681557	+	0.731765i	$0.261303\pi$
$278$	7.37093	+	18.9452i	0.442079	+	1.13626i
$279$	0.695682	−	0.872358i	0.0416494	−	0.0522267i
$280$	−2.38078	+	0.476747i	−0.142279	+	0.0284911i
$281$	−12.4213	−	15.5758i	−0.740992	−	0.929174i	0.258328	−	0.966057i	$-0.416829\pi$
$281$	−12.4213	−	15.5758i	−0.740992	−	0.929174i	−0.999320	+	0.0368830i	$0.988257\pi$
$282$	6.27811	−	10.8002i	0.373856	−	0.643141i
$283$	5.63043	−	14.3461i	0.334695	−	0.852788i	−0.660127	−	0.751154i	$-0.729498\pi$
$283$	5.63043	−	14.3461i	0.334695	−	0.852788i	0.994822	−	0.101634i	$-0.0324071\pi$
$284$	−22.7661	−	9.09066i	−1.35092	−	0.539432i
$285$	−3.08895	+	1.21232i	−0.182974	+	0.0718118i
$286$	−2.24249	−	9.96058i	−0.132601	−	0.588982i
$287$	11.5603	−	16.3204i	0.682383	−	0.963362i
$288$	2.46334	+	0.0364001i	0.145153	+	0.00214490i
$289$	1.25635	−	16.7649i	0.0739030	−	0.986168i
$290$	2.03172	−	0.146220i	0.119306	−	0.00858631i
$291$	7.26695	−	10.6587i	0.425996	−	0.624821i
$292$	−4.17437	+	13.2544i	−0.244287	+	0.775652i
$293$		−	1.53780i		−	0.0898392i	−0.998991	−	0.0449196i	$-0.985697\pi$
$293$		−	1.53780i		−	0.0898392i	0.998991	−	0.0449196i	$-0.0143032\pi$
$294$	5.21567	+	14.9705i	0.304184	+	0.873099i
$295$		−	0.791523i		−	0.0460842i
$296$	−12.6228	+	21.4224i	−0.733683	+	1.24515i
$297$	8.69389	−	12.7516i	0.504470	−	0.739922i
$298$	0.284151	+	3.94827i	0.0164604	+	0.228717i
$299$	−0.939033	+	12.5305i	−0.0543057	+	0.724659i
$300$	−9.70175	−	12.3142i	−0.560131	−	0.710962i
$301$	−13.2284	+	0.753514i	−0.762474	+	0.0434318i
$302$	12.8349	−	2.88961i	0.738568	−	0.166279i
$303$	−22.1382	+	8.68862i	−1.27181	+	0.499148i
$304$	18.9304	−	17.1529i	1.08573	−	0.983786i
$305$	0.814154	−	2.07443i	0.0466183	−	0.118782i
$306$	−0.230961	−	0.134257i	−0.0132032	−	0.00767497i
$307$	7.98188	+	10.0090i	0.455550	+	0.571242i	0.955567	−	0.294774i	$-0.0952444\pi$
$307$	7.98188	+	10.0090i	0.455550	+	0.571242i	−0.500017	+	0.866016i	$0.666673\pi$
$308$	0.353396	−	14.8396i	0.0201366	−	0.845566i
$309$	−8.56672	+	10.7423i	−0.487343	+	0.611109i
$310$	−1.09561	+	0.426262i	−0.0622263	+	0.0242101i
$311$	3.29414	−	3.05651i	0.186793	−	0.173319i	−0.581233	−	0.813737i	$-0.697429\pi$
$311$	3.29414	−	3.05651i	0.186793	−	0.173319i	0.768026	+	0.640418i	$0.221239\pi$
$312$	−1.83950	+	11.5109i	−0.104141	+	0.651676i
$313$	12.3942	+	7.15578i	0.700560	+	0.404468i	0.807556	−	0.589791i	$-0.200790\pi$
$313$	12.3942	+	7.15578i	0.700560	+	0.404468i	−0.106996	+	0.994259i	$0.534123\pi$
$314$	0.0502418	−	17.0015i	0.00283531	−	0.959449i
$315$	−0.259153	+	0.269463i	−0.0146016	+	0.0151825i
$316$	−16.1814	−	13.0614i	−0.910275	−	0.734763i
$317$	12.1199	+	11.2457i	0.680723	+	0.631619i	0.942773	−	0.333436i	$-0.108208\pi$
$317$	12.1199	+	11.2457i	0.680723	+	0.631619i	−0.262050	+	0.965054i	$0.584398\pi$
$318$	4.72628	−	11.9385i	0.265037	−	0.669478i
$319$	−1.85603	+	12.3139i	−0.103917	+	0.689447i
$320$	−2.22457	−	1.33750i	−0.124357	−	0.0747682i
$321$	−4.95035	−	1.12989i	−0.276302	−	0.0630640i
$322$	−5.74769	+	17.3411i	−0.320306	+	0.966381i
$323$	−2.70066	+	0.616409i	−0.150269	+	0.0342979i
$324$	−12.4496	+	8.38066i	−0.691646	+	0.465592i
$325$	−10.9093	+	6.29851i	−0.605141	+	0.349378i
$326$	13.1660	−	7.54959i	0.729196	−	0.418133i
$327$	−21.8310	+	14.8841i	−1.20726	+	0.823094i
$328$	20.8861	−	4.57269i	1.15324	−	0.252485i
$329$	−8.89358	−	11.5712i	−0.490319	−	0.637939i
$330$	−1.85982	+	0.888880i	−0.102380	+	0.0489313i
$331$	6.88703	−	22.3272i	0.378545	−	1.22721i	−0.543261	−	0.839564i	$-0.682811\pi$
$331$	6.88703	−	22.3272i	0.378545	−	1.22721i	0.921806	−	0.387650i	$-0.126713\pi$
$332$	9.40183	−	8.62078i	0.515992	−	0.473126i
$333$	0.286108	+	3.81784i	0.0156786	+	0.209217i
$334$	33.3988	−	4.93316i	1.82750	−	0.269931i
$335$	−0.297946	+	0.143483i	−0.0162785	+	0.00783932i
$336$	−6.65774	+	15.5852i	−0.363209	+	0.850241i
$337$	30.4120	+	14.6457i	1.65665	+	0.797800i	0.999011	+	0.0444660i	$0.0141586\pi$
$337$	30.4120	+	14.6457i	1.65665	+	0.797800i	0.657638	+	0.753334i	$0.271556\pi$
$338$	−8.60940	−	2.68353i	−0.468289	−	0.145965i
$339$	27.0031	−	8.32935i	1.46661	−	0.452388i
$340$	0.139292	+	0.244588i	0.00755418	+	0.0132647i
$341$	−1.07118	−	7.10681i	−0.0580076	−	0.384855i
$342$	0.886592	−	3.83218i	0.0479414	−	0.207221i
$343$	18.4936	+	0.994035i	0.998559	+	0.0536728i
$344$	−10.9957	−	8.92938i	−0.592847	−	0.481440i
$345$	2.50860	−	0.378110i	0.135058	−	0.0203568i
$346$	1.17274	+	1.27143i	0.0630470	+	0.0683525i
$347$	10.1148	+	32.7915i	0.542994	+	1.76034i	0.643543	+	0.765410i	$0.277464\pi$
$347$	10.1148	+	32.7915i	0.542994	+	1.76034i	−0.100550	+	0.994932i	$0.532060\pi$
$348$	7.18164	−	12.2709i	0.384976	−	0.657790i
$349$	5.40347	−	11.2204i	0.289241	−	0.600615i	−0.704827	−	0.709380i	$-0.748975\pi$
$349$	5.40347	−	11.2204i	0.289241	−	0.600615i	0.994068	+	0.108765i	$0.0346895\pi$
$350$	−17.6095	+	5.03214i	−0.941267	+	0.268979i
$351$	6.14334	+	12.7568i	0.327907	+	0.680906i
$352$	10.9642	−	11.4719i	0.584392	−	0.611452i
$353$	4.86426	−	0.364526i	0.258898	−	0.0194017i	0.0553514	−	0.998467i	$-0.482372\pi$
$353$	4.86426	−	0.364526i	0.258898	−	0.0194017i	0.203547	+	0.979065i	$0.434753\pi$
$354$	−4.55559	−	3.12571i	−0.242127	−	0.166129i
$355$	3.80023	+	1.17221i	0.201695	+	0.0622147i
$356$	−26.5798	+	5.90162i	−1.40873	+	0.312785i
$357$	1.45710	−	1.11993i	0.0771181	−	0.0592729i
$358$	−17.3701	+	13.7684i	−0.918036	+	0.727681i
$359$	12.4421	+	18.2492i	0.656667	+	0.963154i	0.999716	+	0.0238363i	$0.00758804\pi$
$359$	12.4421	+	18.2492i	0.656667	+	0.963154i	−0.343049	+	0.939318i	$0.611460\pi$
$360$	−0.398803	+	0.0263330i	−0.0210188	+	0.00138787i
$361$	−10.8931	−	18.8675i	−0.573323	−	0.993025i
$362$	−24.7347	+	26.5001i	−1.30003	+	1.39282i
$363$	1.11562	+	4.88787i	0.0585551	+	0.256547i
$364$	11.6282	+	7.08793i	0.609484	+	0.371508i
$365$	0.501647	−	2.19786i	0.0262574	−	0.115041i
$366$	−8.72426	−	12.8777i	−0.456024	−	0.673130i
$367$	16.6152	+	2.50434i	0.867307	+	0.130725i	0.567599	−	0.823305i	$-0.307873\pi$
$367$	16.6152	+	2.50434i	0.867307	+	0.130725i	0.299708	+	0.954031i	$0.403111\pi$
$368$	−17.0279	+	9.56448i	−0.887639	+	0.498583i
$369$	2.23921	−	2.41329i	0.116568	−	0.125631i
$370$	1.76094	−	3.62915i	0.0915467	−	0.188670i
$371$	−10.8116	−	10.3979i	−0.561309	−	0.539834i
$372$	−1.87319	+	7.98904i	−0.0971205	+	0.414213i
$373$	−11.4975	+	19.9143i	−0.595318	+	1.03112i	0.398184	+	0.917306i	$0.369641\pi$
$373$	−11.4975	+	19.9143i	−0.595318	+	1.03112i	−0.993502	+	0.113816i	$0.963693\pi$
$374$	−1.64581	+	0.502345i	−0.0851030	+	0.0259756i
$375$	3.49692	+	3.76879i	0.180580	+	0.194619i
$376$	1.30380	−	15.5472i	0.0672384	−	0.801784i
$377$	−8.93223	−	7.12321i	−0.460033	−	0.366864i
$378$	4.16114	+	20.1603i	0.214026	+	1.03693i
$379$	−10.1114	+	8.06357i	−0.519388	+	0.414198i	−0.847784	−	0.530342i	$-0.822063\pi$
$379$	−10.1114	+	8.06357i	−0.519388	+	0.414198i	0.328396	+	0.944540i	$0.393492\pi$
$380$	−2.83673	+	3.02126i	−0.145521	+	0.154987i
$381$	10.4945	+	4.11879i	0.537650	+	0.211012i
$382$	−0.215672	+	1.40275i	−0.0110348	+	0.0717711i
$383$	−5.60580	−	14.2834i	−0.286443	−	0.729845i	−0.999584	−	0.0288249i	$-0.990823\pi$
$383$	−5.60580	−	14.2834i	−0.286443	−	0.729845i	0.713141	−	0.701020i	$-0.247272\pi$
$384$	−16.4827	+	7.52170i	−0.841129	+	0.383840i
$385$	0.136949	+	2.40422i	0.00697956	+	0.122531i
$386$	4.76705	−	5.94159i	0.242637	−	0.302419i
$387$	−2.17492	−	0.162987i	−0.110557	−	0.00828512i
$388$	2.49536	−	15.9167i	0.126682	−	0.808049i
$389$	22.0218	+	15.0142i	1.11655	+	0.761252i	0.973551	−	0.228471i	$-0.0733725\pi$
$389$	22.0218	+	15.0142i	1.11655	+	0.761252i	0.143001	+	0.989723i	$0.454325\pi$
$390$	0.146895	−	1.88540i	0.00743833	−	0.0954708i
$391$	2.11781			0.107102
$392$	13.8979	+	14.1013i	0.701951	+	0.712225i
$393$	28.2883			1.42696
$394$	−0.486845	+	6.24865i	−0.0245269	+	0.314803i
$395$	2.78741	+	1.90042i	0.140250	+	0.0956205i
$396$	0.378442	−	2.41391i	0.0190174	−	0.121303i
$397$	−17.0918	−	1.28085i	−0.857811	−	0.0642840i	−0.361441	−	0.932395i	$-0.617715\pi$
$397$	−17.0918	−	1.28085i	−0.857811	−	0.0642840i	−0.496370	+	0.868111i	$0.665334\pi$
$398$	14.8182	−	18.4691i	0.742767	−	0.925775i
$399$	22.0805	+	15.6404i	1.10541	+	0.783000i
$400$	−17.5383	−	8.70288i	−0.876917	−	0.435144i
$401$	2.59459	+	6.61090i	0.129567	+	0.330132i	0.980905	−	0.194485i	$-0.0623036\pi$
$401$	2.59459	+	6.61090i	0.129567	+	0.330132i	−0.851338	+	0.524618i	$0.824208\pi$
$402$	−0.350769	+	2.28143i	−0.0174947	+	0.113787i
$403$	6.13784	+	2.40892i	0.305748	+	0.119997i
$404$	−20.3306	+	21.6531i	−1.01149	+	1.07728i
$405$	1.90352	−	1.51801i	0.0945866	−	0.0754303i
$406$	−10.0832	−	13.1994i	−0.500418	−	0.655076i
$407$	19.2805	+	15.3757i	0.955699	+	0.762144i
$408$	1.95779	+	0.164182i	0.0969248	+	0.00812821i
$409$	8.81344	+	9.49863i	0.435797	+	0.469677i	0.912316	−	0.409487i	$-0.134292\pi$
$409$	8.81344	+	9.49863i	0.435797	+	0.469677i	−0.476519	+	0.879164i	$0.658102\pi$
$410$	−3.31752	+	1.01259i	−0.163841	+	0.0500084i
$411$	8.28204	−	14.3449i	0.408523	−	0.707582i
$412$	−3.91724	+	16.7068i	−0.192989	+	0.823084i
$413$	−5.39703	+	3.53981i	−0.265570	+	0.174183i
$414$	−1.31276	+	2.70549i	−0.0645187	+	0.132968i
$415$	−1.40754	+	1.51697i	−0.0690935	+	0.0744651i
$416$	4.08515	+	13.9735i	0.200291	+	0.685108i
$417$	−22.7623	−	3.43086i	−1.11467	−	0.168010i
$418$	−14.2104	−	20.9757i	−0.695053	−	1.02596i
$419$	−0.955920	+	4.18816i	−0.0466997	+	0.204605i	−0.992895	−	0.118990i	$-0.962034\pi$
$419$	−0.955920	+	4.18816i	−0.0466997	+	0.204605i	0.946196	+	0.323595i	$0.104891\pi$
$420$	0.872727	−	2.60724i	0.0425847	−	0.127220i
$421$	−6.63466	−	29.0684i	−0.323354	−	1.41671i	−0.831543	−	0.555460i	$-0.812542\pi$
$421$	−6.63466	−	29.0684i	−0.323354	−	1.41671i	0.508189	−	0.861245i	$-0.330315\pi$
$422$	−0.213716	+	0.228970i	−0.0104035	+	0.0111461i
$423$	−1.20114	−	2.08044i	−0.0584015	−	0.101154i
$424$	−1.05655	−	16.0011i	−0.0513108	−	0.777082i
$425$	1.19598	+	1.75418i	0.0580136	+	0.0850904i
$426$	21.7537	−	17.2430i	1.05397	−	0.835428i
$427$	−17.7856	+	3.72584i	−0.860706	+	0.180306i
$428$	−6.19075	+	1.37455i	−0.299241	+	0.0664416i
$429$	11.0477	+	3.40776i	0.533387	+	0.164528i
$430$	1.89482	+	1.30008i	0.0913763	+	0.0626956i
$431$	−25.6682	+	1.92357i	−1.23639	+	0.0926549i	−0.676835	−	0.736135i	$-0.736649\pi$
$431$	−25.6682	+	1.92357i	−1.23639	+	0.0926549i	−0.559560	+	0.828790i	$0.689030\pi$
$432$	−11.2278	+	18.9268i	−0.540196	+	0.910617i
$433$	−14.9846	−	31.1159i	−0.720115	−	1.49533i	−0.862789	−	0.505564i	$-0.831284\pi$
$433$	−14.9846	−	31.1159i	−0.720115	−	1.49533i	0.142674	−	0.989770i	$-0.454430\pi$
$434$	7.80621	+	5.56413i	0.374710	+	0.267087i
$435$	−1.00079	+	2.07817i	−0.0479843	+	0.0996404i
$436$	−16.6680	+	28.4797i	−0.798252	+	1.36393i
$437$	9.19104	+	29.7966i	0.439667	+	1.42537i
$438$	−10.6687	−	11.5665i	−0.509771	−	0.552669i
$439$	27.4680	−	4.14014i	1.31098	−	0.197598i	0.543899	−	0.839151i	$-0.316948\pi$
$439$	27.4680	−	4.14014i	1.31098	−	0.197598i	0.767079	+	0.641553i	$0.221709\pi$
$440$	−1.62289	+	1.99843i	−0.0773681	+	0.0952714i
$441$	2.99631	+	0.561966i	0.142682	+	0.0267603i
$442$	0.355837	−	1.53806i	0.0169254	−	0.0731580i
$443$	−5.61834	−	37.2752i	−0.266935	−	1.77100i	−0.573555	−	0.819167i	$-0.694436\pi$
$443$	−5.61834	−	37.2752i	−0.266935	−	1.77100i	0.306619	−	0.951832i	$-0.400802\pi$
$444$	−13.9336	−	24.4665i	−0.661258	−	1.16113i
$445$	4.22083	−	1.30195i	0.200087	−	0.0617185i
$446$	22.5201	+	7.01948i	1.06636	+	0.332382i
$447$	−4.03853	−	1.94485i	−0.191016	−	0.0919885i
$448$	0.828849	+	21.1498i	0.0391595	+	0.999233i
$449$	−7.93063	+	3.81919i	−0.374270	+	0.180239i	−0.611556	−	0.791201i	$-0.709456\pi$
$449$	−7.93063	+	3.81919i	−0.374270	+	0.180239i	0.237287	+	0.971440i	$0.423742\pi$
$450$	−2.98231	+	0.440502i	−0.140587	+	0.0207654i
$451$	−1.58468	−	21.1461i	−0.0746196	−	0.995730i
$452$	26.0125	−	23.8515i	1.22352	−	1.12188i
$453$	−4.39114	+	14.2357i	−0.206314	+	0.668853i
$454$	−17.9347	+	8.57169i	−0.841717	+	0.402290i
$455$	−1.97302	−	0.994044i	−0.0924964	−	0.0466015i
$456$	6.18658	+	28.2577i	0.289713	+	1.32329i
$457$	0.367781	−	0.250749i	0.0172041	−	0.0117295i	−0.554687	−	0.832059i	$-0.687162\pi$
$457$	0.367781	−	0.250749i	0.0172041	−	0.0117295i	0.571892	+	0.820329i	$0.306210\pi$
$458$	−17.3814	+	9.96681i	−0.812181	+	0.465718i
$459$	2.06663	−	1.19317i	0.0964622	−	0.0556925i
$460$	2.62835	−	1.76931i	0.122547	−	0.0824946i
$461$	−7.14998	+	1.63194i	−0.333008	+	0.0760068i	−0.385756	−	0.922601i	$-0.626059\pi$
$461$	−7.14998	+	1.63194i	−0.333008	+	0.0760068i	0.0527478	+	0.998608i	$0.483202\pi$
$462$	14.3783	+	8.70603i	0.668937	+	0.405041i
$463$	19.2117	+	4.38494i	0.892842	+	0.203785i	0.644243	−	0.764821i	$-0.277173\pi$
$463$	19.2117	+	4.38494i	0.892842	+	0.203785i	0.248599	+	0.968606i	$0.420030\pi$
$464$	1.53619	−	17.6903i	0.0713157	−	0.821253i
$465$	0.198407	−	1.31635i	0.00920093	−	0.0610441i
$466$	13.8420	−	34.9646i	0.641217	−	1.61970i
$467$	4.23062	+	3.92544i	0.195770	+	0.181648i	0.771966	−	0.635663i	$-0.219273\pi$
$467$	4.23062	+	3.92544i	0.195770	+	0.181648i	−0.576197	+	0.817311i	$0.695464\pi$
$468$	1.74429	+	1.40797i	0.0806299	+	0.0650835i
$469$	2.31080	+	1.38987i	0.106703	+	0.0641785i
$470$	−0.00747966	+	2.53107i	−0.000345011	+	0.116749i
$471$	16.6727	+	9.62596i	0.768235	+	0.443541i
$472$	−6.81350	−	1.08883i	−0.313617	−	0.0501175i
$473$	−10.2983	+	9.55540i	−0.473515	+	0.439358i
$474$	21.9452	−	8.53812i	1.00798	−	0.392169i
$475$	−19.4901	+	24.4398i	−0.894268	+	1.12138i
$476$	1.04480	−	2.04361i	0.0478883	−	0.0936686i
$477$	−1.53948	−	1.93045i	−0.0704881	−	0.0883893i
$478$	10.4847	+	6.09473i	0.479559	+	0.278766i
$479$	−9.11656	+	23.2286i	−0.416546	+	1.06134i	0.556523	+	0.830832i	$0.312135\pi$
$479$	−9.11656	+	23.2286i	−0.416546	+	1.06134i	−0.973070	+	0.230511i	$0.925960\pi$
$480$	2.56691	−	1.43186i	0.117163	−	0.0653552i
$481$	−21.0605	+	8.26563i	−0.960275	+	0.376880i
$482$	−42.1115	+	9.48083i	−1.91813	+	0.431840i
$483$	−13.7970	−	15.4140i	−0.627785	−	0.701361i
$484$	3.87496	+	4.91840i	0.176135	+	0.223564i
$485$	−0.195323	+	2.60641i	−0.00886917	+	0.118351i
$486$	0.455633	+	6.33101i	0.0206680	+	0.287180i
$487$	−6.37880	+	9.35598i	−0.289051	+	0.423960i	−0.943109	−	0.332485i	$-0.892113\pi$
$487$	−6.37880	+	9.35598i	−0.289051	+	0.423960i	0.654058	+	0.756445i	$0.273065\pi$
$488$	−16.7369	−	9.86193i	−0.757645	−	0.446429i
$489$			17.1858i			0.777169i
$490$	−2.43176	−	2.09844i	−0.109856	−	0.0947979i
$491$		−	17.5121i		−	0.790311i	−0.918614	−	0.395156i	$-0.870691\pi$
$491$		−	17.5121i		−	0.790311i	0.918614	−	0.395156i	$-0.129309\pi$
$492$	−7.27287	+	23.0926i	−0.327886	+	1.04110i
$493$	−1.08469	+	1.59094i	−0.0488518	+	0.0716524i
$494$	23.1841	−	1.66852i	1.04310	−	0.0750704i
$495$	−0.0296225	+	0.395284i	−0.00133143	+	0.0177667i
$496$	2.16217	+	10.0175i	0.0970843	+	0.449797i
$497$	−9.00241	−	31.1543i	−0.403813	−	1.39746i
$498$	3.17252	+	14.0916i	0.142164	+	0.631458i
$499$	−40.0936	+	15.7356i	−1.79484	+	0.704422i	−0.800354	+	0.599528i	$0.795355\pi$
$499$	−40.0936	+	15.7356i	−1.79484	+	0.704422i	−0.994483	+	0.104893i	$0.966550\pi$
$500$	5.96308	+	2.38110i	0.266677	+	0.106486i
$501$	−13.9669	+	35.5872i	−0.623997	+	1.58992i
$502$	13.8448	−	23.8171i	0.617923	−	1.06301i
$503$	13.2908	+	16.6661i	0.592606	+	0.743104i	0.984205	−	0.177032i	$-0.0566495\pi$
$503$	13.2908	+	16.6661i	0.592606	+	0.743104i	−0.391599	+	0.920136i	$0.628078\pi$
$504$	1.96306	+	2.60149i	0.0874418	+	0.115880i
$505$	3.00430	−	3.76727i	0.133690	−	0.167641i
$506$	7.02332	+	18.0518i	0.312224	+	0.802500i
$507$	7.48561	−	6.94563i	0.332448	−	0.308466i
$508$	14.0465	−	0.969194i	0.623215	−	0.0430010i
$509$	−33.0528	−	19.0831i	−1.46504	−	0.845841i	−0.465803	−	0.884888i	$-0.654234\pi$
$509$	−33.0528	−	19.0831i	−1.46504	−	0.845841i	−0.999237	+	0.0390471i	$0.987568\pi$
$510$	−0.318726		0.000941880i	−0.0141134		4.17072e-5i
$511$	−17.2296	+	6.40867i	−0.762193	+	0.283503i
$512$	−14.5734	+	17.3094i	−0.644061	+	0.764974i
$513$	25.7563	+	23.8984i	1.13717	+	1.05514i
$514$	−12.9087	−	5.11038i	−0.569380	−	0.225409i
$515$	0.414912	−	2.75276i	0.0182832	−	0.121301i
$516$	14.9652	−	5.77157i	0.658806	−	0.254079i
$517$	−15.0858	−	3.44323i	−0.663472	−	0.151433i
$518$	−32.6207	+	4.22311i	−1.43327	+	0.185553i
$519$	−1.90954	+	0.435840i	−0.0838195	+	0.0191312i
$520$	−0.843344	−	2.20612i	−0.0369831	−	0.0967447i
$521$	−18.1119	+	10.4569i	−0.793496	+	0.458125i	−0.841192	−	0.540737i	$-0.818146\pi$
$521$	−18.1119	+	10.4569i	−0.793496	+	0.458125i	0.0476958	+	0.998862i	$0.484812\pi$
$522$	−1.36006	−	2.37185i	−0.0595282	−	0.103813i
$523$	11.6723	−	7.95803i	0.510394	−	0.347980i	−0.280580	−	0.959831i	$-0.590527\pi$
$523$	11.6723	−	7.95803i	0.510394	−	0.347980i	0.790974	+	0.611850i	$0.209574\pi$
$524$	31.9207	−	15.1405i	1.39446	−	0.661414i
$525$	4.97590	−	20.1327i	0.217166	−	0.878665i
$526$	−7.21517	−	15.0964i	−0.314596	−	0.658235i
$527$	0.327558	−	1.06192i	0.0142686	−	0.0462578i
$528$	5.09317	+	17.2322i	0.221652	+	0.749937i
$529$	−0.0627145	−	0.836867i	−0.00272672	−	0.0363855i
$530$	0.380132	+	2.57360i	0.0165119	+	0.111790i
$531$	−0.957209	+	0.460968i	−0.0415393	+	0.0200043i
$532$	33.2869	+	5.83083i	1.44317	+	0.252798i
$533$	17.5278	+	8.44095i	0.759214	+	0.365618i
$534$	9.17462	−	29.4343i	0.397024	−	1.27375i
$535$	0.983080	−	0.303240i	0.0425023	−	0.0131102i
$536$	0.825257	+	2.76212i	0.0356457	+	0.119305i
$537$	−3.74078	−	24.8185i	−0.161427	−	1.07100i
$538$	37.0782	+	8.57821i	1.59855	+	0.369833i
$539$	15.7808	−	11.6859i	0.679729	−	0.503345i
$540$	1.56800	−	3.20736i	0.0674762	−	0.138023i
$541$	3.02017	−	0.455218i	0.129847	−	0.0195714i	−0.0837970	−	0.996483i	$-0.526705\pi$
$541$	3.02017	−	0.455218i	0.129847	−	0.0195714i	0.213644	+	0.976911i	$0.431467\pi$
$542$	6.05325	−	5.58340i	0.260010	−	0.239828i
$543$	−12.0992	−	39.2245i	−0.519224	−	1.68328i
$544$	2.29705	−	0.862581i	0.0984853	−	0.0369829i
$545$	2.32275	−	4.82325i	0.0994958	−	0.206605i
$546$	−13.5126	+	7.43018i	−0.578286	+	0.317982i
$547$	−9.01528	−	18.7204i	−0.385465	−	0.800427i	−0.999934	−	0.0114858i	$-0.996344\pi$
$547$	−9.01528	−	18.7204i	−0.385465	−	0.800427i	0.614469	−	0.788941i	$-0.289370\pi$
$548$	1.66783	−	20.6196i	0.0712463	−	0.880826i
$549$	−2.98281	+	0.223531i	−0.127303	+	0.00954007i
$550$	−10.9861	+	16.0117i	−0.468447	+	0.682742i
$551$	−27.0912	−	8.35653i	−1.15412	−	0.356000i
$552$	0.196058	−	22.1144i	0.00834478	−	0.941250i
$553$	0.492380	−	27.5050i	0.0209381	−	1.16963i
$554$	0.0552764	+	0.0697362i	0.00234847	+	0.00296281i
$555$	2.57310	+	3.77404i	0.109222	+	0.160199i
$556$	−27.5214	+	8.31141i	−1.16717	+	0.352482i
$557$	4.16650	+	7.21659i	0.176540	+	0.305777i	0.940693	−	0.339258i	$-0.110176\pi$
$557$	4.16650	+	7.21659i	0.176540	+	0.305777i	−0.764153	+	0.645035i	$0.776843\pi$
$558$	1.15355	+	1.07670i	0.0488337	+	0.0455804i
$559$	−2.86796	−	12.5653i	−0.121302	−	0.531457i
$560$	−0.410654	−	3.40913i	−0.0173533	−	0.144062i
$561$	0.433590	−	1.89968i	0.0183062	−	0.0802047i
$562$	23.3254	−	15.8023i	0.983925	−	0.666578i
$563$	−16.5135	−	2.48902i	−0.695963	−	0.104900i	−0.208473	−	0.978028i	$-0.566849\pi$
$563$	−16.5135	−	2.48902i	−0.695963	−	0.104900i	−0.487490	+	0.873129i	$0.662087\pi$
$564$	14.5379	+	10.0382i	0.612158	+	0.422684i
$565$	−3.89431	+	4.19707i	−0.163835	+	0.176572i
$566$	19.6087	+	9.51452i	0.824213	+	0.399925i
$567$	−18.8634	−	6.19046i	−0.792189	−	0.259975i
$568$	15.3182	−	31.1002i	0.642736	−	1.30493i
$569$	13.3698	−	23.1571i	0.560490	−	0.970797i	−0.436964	−	0.899479i	$-0.643946\pi$
$569$	13.3698	−	23.1571i	0.560490	−	0.970797i	0.997454	−	0.0713179i	$-0.0227205\pi$
$570$	−1.36998	−	4.48841i	−0.0573821	−	0.187999i
$571$	−11.5472	−	12.4449i	−0.483235	−	0.520804i	0.443624	−	0.896213i	$-0.353693\pi$
$571$	−11.5472	−	12.4449i	−0.483235	−	0.520804i	−0.926859	+	0.375409i	$0.877502\pi$
$572$	14.2902	−	2.06759i	0.597502	−	0.0864505i
$573$	−1.25647	−	1.00200i	−0.0524899	−	0.0418593i
$574$	21.7409	+	18.0922i	0.907446	+	0.755152i
$575$	18.6848	−	14.9006i	0.779208	−	0.621398i
$576$	−0.321923	+	3.46916i	−0.0134135	+	0.144548i
$577$	17.1308	+	6.72335i	0.713166	+	0.279897i	0.694057	−	0.719921i	$-0.255822\pi$
$577$	17.1308	+	6.72335i	0.713166	+	0.279897i	0.0191091	+	0.999817i	$0.493917\pi$
$578$	23.4994	+	3.61302i	0.977448	+	0.150282i
$579$	3.15138	+	8.02957i	0.130967	+	0.333698i
$580$	−0.0170257	+	2.88066i	−0.000706953	+	0.119613i
$581$	16.6383	+	2.81325i	0.690271	+	0.116713i
$582$	14.2298	+	11.4168i	0.589844	+	0.473243i
$583$	−15.8599	−	1.18854i	−0.656850	−	0.0492241i
$584$	−18.2293	−	7.34163i	−0.754333	−	0.303799i
$585$	−0.300471	−	0.204858i	−0.0124230	−	0.00846984i
$586$	2.16821	+	0.168929i	0.0895678	+	0.00697841i
$587$	−0.140687			−0.00580676			−0.00290338	−	0.999996i	$-0.500924\pi$
$587$	−0.140687			−0.00580676			−0.00290338	+	0.999996i	$0.500924\pi$
$588$	−21.6805	+	5.70925i	−0.894089	+	0.235446i
$589$	16.3622			0.674194
$590$	1.11600	+	0.0869498i	0.0459450	+	0.00357967i
$591$	−5.86397	−	3.99799i	−0.241212	−	0.164455i
$592$	−28.8177	−	20.1506i	−1.18440	−	0.828185i
$593$	11.4042	+	0.854624i	0.468313	+	0.0350952i	0.306797	−	0.951775i	$-0.400743\pi$
$593$	11.4042	+	0.854624i	0.468313	+	0.0350952i	0.161516	+	0.986870i	$0.448362\pi$
$594$	17.0239	+	13.6586i	0.698501	+	0.560421i
$595$	−0.142217	+	0.344121i	−0.00583033	+	0.0141076i
$596$	−5.59803	−	0.0330863i	−0.229304	−	0.00135527i
$597$	9.79590	+	24.9595i	0.400920	+	1.02153i
$598$	−17.5641	−	2.70047i	−0.718251	−	0.110431i
$599$	0.952438	+	0.373804i	0.0389156	+	0.0152732i	0.384719	−	0.923034i	$-0.374298\pi$
$599$	0.952438	+	0.373804i	0.0389156	+	0.0152732i	−0.345803	+	0.938307i	$0.612394\pi$
$600$	18.4281	−	12.3262i	0.752322	−	0.503213i
$601$	22.9737	−	18.3209i	0.937118	−	0.747327i	−0.0305556	−	0.999533i	$-0.509728\pi$
$601$	22.9737	−	18.3209i	0.937118	−	0.747327i	0.967673	+	0.252207i	$0.0811562\pi$
$602$	0.390750	−	18.7341i	0.0159258	−	0.763544i
$603$	0.347036	+	0.276752i	0.0141324	+	0.0112702i
$604$	2.66425	+	18.4139i	0.108407	+	0.749252i
$605$	−0.690920	−	0.744635i	−0.0280899	−	0.0302737i
$606$	−9.81852	−	32.1681i	−0.398850	−	1.30674i
$607$	2.38773	−	4.13568i	0.0969151	−	0.167862i	−0.813491	−	0.581577i	$-0.802436\pi$
$607$	2.38773	−	4.13568i	0.0969151	−	0.167862i	0.910406	+	0.413715i	$0.135769\pi$
$608$	22.1050	+	28.5750i	0.896478	+	1.15887i
$609$	18.6457	−	2.46994i	0.755564	−	0.100087i
$610$	2.83539	+	1.37579i	0.114802	+	0.0557040i
$611$	9.65576	−	10.4064i	0.390630	−	0.420999i
$612$	0.214666	−	0.310894i	0.00867736	−	0.0125671i
$613$	6.55547	+	0.988078i	0.264773	+	0.0399081i	0.280087	−	0.959975i	$-0.409637\pi$
$613$	6.55547	+	0.988078i	0.264773	+	0.0399081i	−0.0153140	+	0.999883i	$0.504875\pi$
$614$	−14.9889	+	10.1545i	−0.604901	+	0.409801i
$615$	0.874003	−	3.82926i	0.0352432	−	0.154410i
$616$	20.8842	+	2.12842i	0.841447	+	0.0857565i
$617$	−6.33896	−	27.7728i	−0.255197	−	1.11809i	−0.926318	−	0.376743i	$-0.877044\pi$
$617$	−6.33896	−	27.7728i	−0.255197	−	1.11809i	0.671121	−	0.741348i	$-0.265813\pi$
$618$	−14.2050	−	13.2586i	−0.571408	−	0.533340i
$619$	12.9733	+	22.4704i	0.521440	+	0.903160i	0.999689	+	0.0249362i	$0.00793828\pi$
$619$	12.9733	+	22.4704i	0.521440	+	0.903160i	−0.478249	+	0.878224i	$0.658728\pi$
$620$	−0.480651	−	1.59157i	−0.0193034	−	0.0639189i
$621$	−15.1319	−	22.1944i	−0.607221	−	0.890630i
$622$	3.94764	+	4.98030i	0.158286	+	0.199692i
$623$	−27.7536	−	22.9573i	−1.11193	−	0.919767i
$624$	−16.0276	−	3.85807i	−0.641618	−	0.154446i
$625$	22.3909	+	6.90669i	0.895638	+	0.276268i
$626$	−11.4507	+	16.6890i	−0.457664	+	0.667026i
$627$	28.6094	−	2.14398i	1.14255	−	0.0856222i
$628$	23.9655	+	1.93847i	0.956329	+	0.0773535i
$629$	1.65445	+	3.43549i	0.0659671	+	0.136982i
$630$	−0.351458	−	0.394991i	−0.0140024	−	0.0157368i
$631$	−8.78688	+	18.2461i	−0.349800	+	0.726367i	−0.999426	−	0.0338871i	$-0.989211\pi$
$631$	−8.78688	+	18.2461i	−0.349800	+	0.726367i	0.649626	+	0.760254i	$0.274926\pi$
$632$	20.1934	−	21.3800i	0.803250	−	0.850450i
$633$	−0.104541	−	0.338912i	−0.00415511	−	0.0134706i
$634$	−17.1871	+	15.8530i	−0.682587	+	0.629604i
$635$	−2.25868	+	0.340442i	−0.0896331	+	0.0135100i
$636$	16.3134	+	7.97524i	0.646868	+	0.316239i
$637$	2.04571	+	17.8986i	0.0810539	+	0.709168i
$638$	−17.1580	−	3.96959i	−0.679292	−	0.157157i
$639$	−0.795589	−	5.27839i	−0.0314730	−	0.208810i
$640$	2.13016	−	2.98958i	0.0842020	−	0.118174i
$641$	−26.1774	+	8.07467i	−1.03395	+	0.318930i	−0.764867	−	0.644188i	$-0.777196\pi$
$641$	−26.1774	+	8.07467i	−1.03395	+	0.318930i	−0.269079	+	0.963118i	$0.586719\pi$
$642$	2.13687	−	6.85558i	0.0843357	−	0.270568i
$643$	−19.8762	−	9.57187i	−0.783841	−	0.377478i	−0.00123806	−	0.999999i	$-0.500394\pi$
$643$	−19.8762	−	9.57187i	−0.783841	−	0.377478i	−0.782603	+	0.622521i	$0.786108\pi$
$644$	−23.8185	−	10.0088i	−0.938580	−	0.394404i
$645$	−2.34442	+	1.12901i	−0.0923114	+	0.0444548i
$646$	−0.572429	−	3.87549i	−0.0225219	−	0.152479i
$647$	0.839488	+	11.2022i	0.0330037	+	0.440404i	0.989089	+	0.147316i	$0.0470636\pi$
$647$	0.839488	+	11.2022i	0.0330037	+	0.440404i	−0.956086	+	0.293087i	$0.905317\pi$
$648$	−10.4486	−	18.4739i	−0.410461	−	0.725722i
$649$	−2.01711	+	6.53931i	−0.0791785	+	0.256690i
$650$	−7.68211	−	16.0734i	−0.301317	−	0.630451i
$651$	−9.86287	+	4.53406i	−0.386556	+	0.177704i
$652$	9.19818	+	19.3926i	0.360228	+	0.759472i
$653$	26.7162	−	18.2148i	1.04549	−	0.712800i	0.0864994	−	0.996252i	$-0.472432\pi$
$653$	26.7162	−	18.2148i	1.04549	−	0.712800i	0.958987	+	0.283452i	$0.0914796\pi$
$654$	−18.5876	−	32.4155i	−0.726832	−	1.26754i
$655$	−4.96363	+	2.86575i	−0.193945	+	0.111974i
$656$	4.15286	+	29.9505i	0.162142	+	1.16937i
$657$	−2.95008	+	0.673336i	−0.115093	+	0.0262693i
$658$	17.2916	−	11.2683i	0.674097	−	0.439285i
$659$	−16.8638	−	3.84906i	−0.656921	−	0.149938i	−0.118949	−	0.992900i	$-0.537952\pi$
$659$	−16.8638	−	3.84906i	−0.656921	−	0.149938i	−0.537972	+	0.842962i	$0.680810\pi$
$660$	−1.04897	−	2.71988i	−0.0408309	−	0.105871i
$661$	−6.17484	+	40.9674i	−0.240174	+	1.59345i	0.465590	+	0.885000i	$0.345842\pi$
$661$	−6.17484	+	40.9674i	−0.240174	+	1.59345i	−0.705764	+	0.708447i	$0.749396\pi$
$662$	30.7235	+	12.1630i	1.19410	+	0.472728i
$663$	1.31044	+	1.21591i	0.0508931	+	0.0472219i
$664$	11.1220	+	14.2030i	0.431616	+	0.551184i
$665$	−5.45883	−	0.507485i	−0.211684	−	0.0196794i
$666$	−5.41436	−	0.0160002i	−0.209802	−	0.000619996i
$667$	18.7709	+	10.8374i	0.726810	+	0.419624i
$668$	3.28656	+	47.6322i	0.127161	+	1.84295i
$669$	−19.5806	+	18.1681i	−0.757028	+	0.702419i
$670$	−0.169573	−	0.435848i	−0.00655117	−	0.0168383i
$671$	−12.0127	+	15.0635i	−0.463747	+	0.581520i
$672$	−21.2428	−	11.0991i	−0.819459	−	0.428156i
$673$	8.66067	+	10.8601i	0.333844	+	0.418628i	0.920214	−	0.391416i	$-0.128015\pi$
$673$	8.66067	+	10.8601i	0.333844	+	0.418628i	−0.586369	+	0.810044i	$0.699443\pi$
$674$	−23.9903	+	41.2703i	−0.924073	+	1.58967i
$675$	9.83826	−	25.0675i	0.378675	−	0.964848i
$676$	4.72938	−	11.8439i	0.181899	−	0.455536i
$677$	−10.0195	+	3.93237i	−0.385081	+	0.151133i	−0.549981	−	0.835177i	$-0.685365\pi$
$677$	−10.0195	+	3.93237i	−0.385081	+	0.151133i	0.164900	+	0.986310i	$0.447270\pi$
$678$	8.77757	+	38.9878i	0.337100	+	1.49732i
$679$	18.6454	−	10.3244i	0.715545	−	0.396216i
$680$	−0.360157	+	0.169525i	−0.0138114	+	0.00650101i
$681$	1.68209	−	22.4459i	0.0644579	−	0.860131i
$682$	10.1378	−	0.729606i	0.388198	−	0.0279381i
$683$	2.45241	−	3.59702i	0.0938387	−	0.137636i	−0.776448	−	0.630181i	$-0.782981\pi$
$683$	2.45241	−	3.59702i	0.0938387	−	0.137636i	0.870287	+	0.492545i	$0.163933\pi$
$684$	5.30575	+	1.67101i	0.202870	+	0.0638928i
$685$			3.35605i			0.128228i
$686$	−3.43307	+	25.9656i	−0.131075	+	0.991372i
$687$		−	22.6883i		−	0.865613i
$688$	13.7978	−	14.5224i	0.526036	−	0.553660i
$689$	8.21947	−	12.0558i	0.313137	−	0.459288i
$690$	0.257540	+	3.57851i	0.00980439	+	0.136232i
$691$	−3.68409	+	49.1608i	−0.140149	+	1.87016i	0.276388	+	0.961046i	$0.410863\pi$
$691$	−3.68409	+	49.1608i	−0.140149	+	1.87016i	−0.416537	+	0.909119i	$0.636757\pi$
$692$	−1.92147	+	1.51383i	−0.0730433	+	0.0575471i
$693$	2.82774	−	1.56579i	0.107417	−	0.0594795i
$694$	−47.3452	+	10.6591i	−1.79720	+	0.404616i
$695$	4.34156	−	1.70394i	0.164685	−	0.0646341i
$696$	16.5123	+	11.4737i	0.625899	+	0.434908i
$697$	1.19789	−	3.05218i	0.0453735	−	0.115610i
$698$	15.2265	+	8.85115i	0.576333	+	0.335021i
$699$	26.5497	+	33.2922i	1.00420	+	1.25923i
$700$	−5.16059	−	25.3811i	−0.195052	−	0.959316i
$701$	−1.03090	+	1.29271i	−0.0389367	+	0.0488250i	−0.800919	−	0.598773i	$-0.795655\pi$
$701$	−1.03090	+	1.29271i	−0.0389367	+	0.0488250i	0.761982	+	0.647598i	$0.224226\pi$
$702$	−18.6611	+	7.26039i	−0.704319	+	0.274026i
$703$	−41.1557	+	38.1869i	−1.55222	+	1.44025i
$704$	14.9702	+	16.7190i	0.564211	+	0.630122i
$705$	−2.48211	−	1.43305i	−0.0934818	−	0.0539717i
$706$	−0.0203856	+	6.89836i	−0.000767224	+	0.259623i
$707$	−39.1230	−	3.63710i	−1.47137	−	0.136787i
$708$	4.90750	−	6.07975i	0.184435	−	0.228491i
$709$	−16.0924	−	14.9315i	−0.604362	−	0.560766i	0.317513	−	0.948254i	$-0.397152\pi$
$709$	−16.0924	−	14.9315i	−0.604362	−	0.560766i	−0.921875	+	0.387488i	$0.873343\pi$
$710$	−2.07021	+	5.22932i	−0.0776937	+	0.196253i
$711$	0.674897	−	4.47765i	0.0253106	−	0.167925i
$712$	−5.40110	−	38.1243i	−0.202415	−	1.42877i
$713$	−12.1956	−	2.78357i	−0.456730	−	0.104246i
$714$	1.41897	+	2.17746i	0.0531036	+	0.0814892i
$715$	−2.28371	+	0.521242i	−0.0854059	+	0.0194933i
$716$	−17.5045	−	26.0032i	−0.654173	−	0.971786i
$717$	−11.8928	+	6.86633i	−0.444146	+	0.256428i
$718$	−27.0970	+	15.5379i	−1.01125	+	0.579869i
$719$	29.1133	−	19.8491i	1.08574	−	0.740246i	0.118208	−	0.992989i	$-0.462285\pi$
$719$	29.1133	−	19.8491i	1.08574	−	0.740246i	0.967534	+	0.252743i	$0.0813326\pi$
$720$	0.00668106	−	0.565182i	0.000248989	−	0.0210631i
$721$	−20.6254	+	9.48168i	−0.768128	+	0.353116i
$722$	27.7986	−	13.2861i	1.03456	−	0.494456i
$723$	14.4074	−	46.7075i	0.535815	−	1.73707i
$724$	−34.6465	−	37.7855i	−1.28763	−	1.40429i
$725$	1.62380	+	21.6680i	0.0603062	+	0.804731i
$726$	−7.01416	+	1.03602i	−0.260320	+	0.0384505i
$727$	30.5126	−	14.6941i	1.13165	−	0.544974i	0.228178	−	0.973620i	$-0.426723\pi$
$727$	30.5126	−	14.6941i	1.13165	−	0.544974i	0.903473	+	0.428645i	$0.141009\pi$
$728$	−11.2709	+	15.6165i	−0.417728	+	0.578785i
$729$	−26.7578	−	12.8859i	−0.991031	−	0.477256i
$730$	3.04374	+	0.948730i	0.112654	+	0.0351141i
$731$	−2.07571	+	0.640273i	−0.0767730	+	0.0236813i
$732$	19.1152	−	10.8860i	0.706518	−	0.402360i
$733$	3.34355	+	22.1830i	0.123497	+	0.819347i	0.961723	+	0.274024i	$0.0883549\pi$
$733$	3.34355	+	22.1830i	0.123497	+	0.819347i	−0.838226	+	0.545323i	$0.816407\pi$
$734$	−5.35617	+	23.1513i	−0.197700	+	0.854532i
$735$	3.43112	−	1.20677i	0.126559	−	0.0445123i
$736$	−11.6148	−	25.0590i	−0.428128	−	0.923685i
$737$	2.82718	−	0.426129i	0.104141	−	0.0156967i
$738$	3.15662	+	3.42225i	0.116197	+	0.125975i
$739$	2.38810	+	7.74202i	0.0878476	+	0.284795i	0.988827	−	0.149067i	$-0.0476269\pi$
$739$	2.38810	+	7.74202i	0.0878476	+	0.284795i	−0.900980	+	0.433861i	$0.857151\pi$
$740$	4.92344	+	2.88148i	0.180989	+	0.105925i
$741$	−11.4201	+	23.7141i	−0.419528	+	0.871159i
$742$	15.8481	−	14.1015i	0.581804	−	0.517681i
$743$	3.74567	+	7.77796i	0.137415	+	0.285346i	0.958308	−	0.285736i	$-0.0922382\pi$
$743$	3.74567	+	7.77796i	0.137415	+	0.285346i	−0.820893	+	0.571082i	$0.806524\pi$
$744$	−11.0583	−	3.51870i	−0.405417	−	0.129002i
$745$	0.905648	−	0.0678689i	0.0331804	−	0.00248653i
$746$	−26.8149	−	18.3984i	−0.981764	−	0.673614i
$747$	2.65424	+	0.818724i	0.0971135	+	0.0299555i
$748$	−0.527482	−	2.37568i	−0.0192866	−	0.0868636i
$749$	−6.46414	−	5.34703i	−0.236195	−	0.195376i
$750$	−5.69791	+	4.51645i	−0.208058	+	0.164917i
$751$	19.7777	+	29.0085i	0.721697	+	1.05854i	0.995314	+	0.0966964i	$0.0308276\pi$
$751$	19.7777	+	29.0085i	0.721697	+	1.05854i	−0.273617	+	0.961839i	$0.588220\pi$
$752$	21.7774	+	3.54616i	0.794139	+	0.129315i
$753$	15.5976	+	27.0158i	0.568407	+	0.984509i
$754$	11.0245	−	11.8114i	0.401490	−	0.430146i
$755$	−0.671659	−	2.94273i	−0.0244442	−	0.107097i
$756$	−28.8819	+	3.65233i	−1.05042	+	0.132834i
$757$	0.191320	−	0.838227i	0.00695364	−	0.0304659i	−0.971332	−	0.237727i	$-0.923598\pi$
$757$	0.191320	−	0.838227i	0.00695364	−	0.0304659i	0.978286	+	0.207261i	$0.0664549\pi$
$758$	−10.2584	−	15.1423i	−0.372602	−	0.549992i
$759$	−21.6888	−	3.26906i	−0.787254	−	0.118659i
$760$	−3.94818	−	4.33152i	−0.143216	−	0.157121i
$761$	−6.46148	+	6.96382i	−0.234228	+	0.252438i	−0.839218	−	0.543795i	$-0.816987\pi$
$761$	−6.46148	+	6.96382i	−0.234228	+	0.252438i	0.604989	+	0.796233i	$0.293177\pi$
$762$	−6.96009	+	14.3442i	−0.252137	+	0.519635i
$763$	−43.2752	+	5.73253i	−1.56667	+	0.207532i
$764$	−1.95411	−	0.458179i	−0.0706971	−	0.0165763i
$765$	−0.0306457	+	0.0530799i	−0.00110800	+	0.00191911i
$766$	20.7545	−	6.33480i	0.749890	−	0.228886i
$767$

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)

\(f(q)\)	\(=\)	\(q+(-0.109851 + 1.40994i) q^{2} +(-1.32314 - 0.902103i) q^{3} +(-1.97587 - 0.309768i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(1.41726 - 1.76645i) q^{6} +(-1.28165 - 2.31460i) q^{7} +(0.653806 - 2.75182i) q^{8} +(-0.159109 - 0.405403i) q^{9} +O(q^{10})\)	\(q+(-0.109851 + 1.40994i) q^{2} +(-1.32314 - 0.902103i) q^{3} +(-1.97587 - 0.309768i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(1.41726 - 1.76645i) q^{6} +(-1.28165 - 2.31460i) q^{7} +(0.653806 - 2.75182i) q^{8} +(-0.159109 - 0.405403i) q^{9} +(-0.0697296 + 0.453528i) q^{10} +(-2.61131 - 1.02486i) q^{11} +(2.33491 + 2.19230i) q^{12} +(2.01211 - 1.60461i) q^{13} +(3.40424 - 1.55279i) q^{14} +(-0.406234 - 0.323961i) q^{15} +(3.80809 + 1.22412i) q^{16} +(-0.295026 - 0.317962i) q^{17} +(0.589072 - 0.179800i) q^{18} +(3.19321 - 5.53080i) q^{19} +(-0.631787 - 0.148135i) q^{20} +(-0.392197 + 4.21872i) q^{21} +(1.73185 - 3.56920i) q^{22} +(-3.32097 + 3.57916i) q^{23} +(-3.34751 + 3.05125i) q^{24} +(-4.84006 - 0.729521i) q^{25} +(2.04137 + 3.01323i) q^{26} +(-1.22423 + 5.36370i) q^{27} +(1.81539 + 4.97035i) q^{28} +(-0.987821 - 4.32793i) q^{29} +(0.501391 - 0.537178i) q^{30} +(1.28102 + 2.21879i) q^{31} +(-2.14426 + 5.23471i) q^{32} +(2.53060 + 3.71170i) q^{33} +(0.480717 - 0.381041i) q^{34} +(-0.358561 - 0.779973i) q^{35} +(0.188797 + 0.850308i) q^{36} +(-8.40044 - 2.59119i) q^{37} +(7.44732 + 5.10980i) q^{38} +(-4.10983 + 0.307989i) q^{39} +(0.278265 - 0.874510i) q^{40} +(3.27984 + 6.81065i) q^{41} +(-5.90507 - 1.01641i) q^{42} +(2.17288 - 4.51203i) q^{43} +(4.84212 + 2.83389i) q^{44} +(-0.0416505 - 0.135028i) q^{45} +(-4.68158 - 5.07555i) q^{46} +(5.45444 - 0.822124i) q^{47} +(-3.93436 - 5.05497i) q^{48} +(-3.71473 + 5.93302i) q^{49} +(1.56027 - 6.74405i) q^{50} +(0.103526 + 0.686853i) q^{51} +(-4.47272 + 2.54720i) q^{52} +(5.41768 - 1.67113i) q^{53} +(-7.42801 - 2.31530i) q^{54} +(-0.820048 - 0.394914i) q^{55} +(-7.20732 + 2.01359i) q^{56} +(-9.21441 + 4.43743i) q^{57} +(6.21063 - 0.917341i) q^{58} +(-0.182304 - 2.43268i) q^{59} +(0.702311 + 0.765941i) q^{60} +(2.02445 - 6.56311i) q^{61} +(-3.26908 + 1.56242i) q^{62} +(-0.734423 + 0.887859i) q^{63} +(-7.14508 - 3.59832i) q^{64} +(0.689933 - 0.470389i) q^{65} +(-5.51127 + 3.16026i) q^{66} +(-0.882664 + 0.509607i) q^{67} +(0.484437 + 0.719641i) q^{68} +(7.62288 - 1.73987i) q^{69} +(1.13910 - 0.419869i) q^{70} +(11.9497 + 2.72743i) q^{71} +(-1.21962 + 0.172785i) q^{72} +(1.03556 - 6.87048i) q^{73} +(4.57623 - 11.5595i) q^{74} +(5.74597 + 5.33149i) q^{75} +(-8.02261 + 9.93896i) q^{76} +(0.974644 + 7.35764i) q^{77} +(0.0172239 - 5.82845i) q^{78} +(9.00457 + 5.19879i) q^{79} +(1.20244 + 0.488403i) q^{80} +(5.50068 - 5.10389i) q^{81} +(-9.96291 + 3.87622i) q^{82} +(-3.97658 + 4.98647i) q^{83} +(2.08175 - 8.21414i) q^{84} +(-0.0877471 - 0.110031i) q^{85} +(6.12301 + 3.55929i) q^{86} +(-2.59721 + 6.61758i) q^{87} +(-4.52753 + 6.51580i) q^{88} +(12.6725 - 4.97359i) q^{89} +(0.194956 - 0.0438917i) q^{90} +(-6.29285 - 2.60068i) q^{91} +(7.67050 - 6.04320i) q^{92} +(0.306607 - 4.09138i) q^{93} +(0.559969 + 7.78075i) q^{94} +(1.16728 - 1.71208i) q^{95} +(7.55940 - 4.99192i) q^{96} +8.05557i q^{97} +(-7.95714 - 5.88930i) q^{98} +1.22170i 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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