LMFDB - Embedded newform 196.2.p.a.103.11

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			103.11
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.520558 - 1.31492i) q^{2} +(1.32314 + 0.902103i) q^{3} +(-1.45804 + 1.36899i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(0.497422 - 2.20942i) q^{6} +(1.28165 + 2.31460i) q^{7} +(2.55910 + 1.20457i) q^{8} +(-0.159109 - 0.405403i) q^{9} +O(q^{10})$	\(q+(-0.520558 - 1.31492i) q^{2} +(1.32314 + 0.902103i) q^{3} +(-1.45804 + 1.36899i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(0.497422 - 2.20942i) q^{6} +(1.28165 + 2.31460i) q^{7} +(2.55910 + 1.20457i) q^{8} +(-0.159109 - 0.405403i) q^{9} +(-0.136546 - 0.438070i) q^{10} +(2.61131 + 1.02486i) q^{11} +(-3.16416 + 0.496063i) q^{12} +(2.01211 - 1.60461i) q^{13} +(2.37634 - 2.89016i) q^{14} +(0.406234 + 0.323961i) q^{15} +(0.251751 - 3.99207i) q^{16} +(-0.295026 - 0.317962i) q^{17} +(-0.450248 + 0.420252i) q^{18} +(-3.19321 + 5.53080i) q^{19} +(-0.504947 + 0.407588i) q^{20} +(-0.392197 + 4.21872i) q^{21} +(-0.0117235 - 3.96716i) q^{22} +(3.32097 - 3.57916i) q^{23} +(2.29941 + 3.90239i) q^{24} +(-4.84006 - 0.729521i) q^{25} +(-3.15735 - 1.81048i) q^{26} +(1.22423 - 5.36370i) q^{27} +(-5.03735 - 1.62021i) q^{28} +(-0.987821 - 4.32793i) q^{29} +(0.214515 - 0.702806i) q^{30} +(-1.28102 - 2.21879i) q^{31} +(-5.38031 + 1.74707i) q^{32} +(2.53060 + 3.71170i) q^{33} +(-0.264517 + 0.553454i) q^{34} +(0.358561 + 0.779973i) q^{35} +(0.786978 + 0.373275i) q^{36} +(-8.40044 - 2.59119i) q^{37} +(8.93481 + 1.31972i) q^{38} +(4.10983 - 0.307989i) q^{39} +(0.798800 + 0.451793i) q^{40} +(3.27984 + 6.81065i) q^{41} +(5.75145 - 1.68038i) q^{42} +(-2.17288 + 4.51203i) q^{43} +(-5.21041 + 2.08056i) q^{44} +(-0.0416505 - 0.135028i) q^{45} +(-6.43507 - 2.50366i) 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} +(-0.737052 + 5.09413i) q^{52} +(5.41768 - 1.67113i) q^{53} +(-7.69012 + 1.18235i) q^{54} +(0.820048 + 0.394914i) q^{55} +(0.491791 + 7.46714i) q^{56} +(-9.21441 + 4.43743i) q^{57} +(-5.17667 + 3.55185i) q^{58} +(0.182304 + 2.43268i) q^{59} +(-1.03580 + 0.0837817i) q^{60} +(2.02445 - 6.56311i) q^{61} +(-2.25069 + 2.83945i) q^{62} +(0.734423 - 0.887859i) q^{63} +(5.09803 + 6.16523i) q^{64} +(0.689933 - 0.470389i) q^{65} +(3.56328 - 5.25969i) q^{66} +(0.882664 - 0.509607i) q^{67} +(0.865446 + 0.0597147i) q^{68} +(7.62288 - 1.73987i) q^{69} +(0.838951 - 0.877501i) q^{70} +(-11.9497 - 2.72743i) q^{71} +(0.0811594 - 1.22913i) q^{72} +(1.03556 - 6.87048i) q^{73} +(0.965703 + 12.3948i) q^{74} +(-5.74597 - 5.33149i) q^{75} +(-2.91577 - 12.4356i) q^{76} +(0.974644 + 7.35764i) q^{77} +(-2.54439 - 5.24378i) q^{78} +(-9.00457 - 5.19879i) q^{79} +(0.178251 - 1.28554i) q^{80} +(5.50068 - 5.10389i) q^{81} +(7.24813 - 7.85807i) q^{82} +(3.97658 - 4.98647i) q^{83} +(-5.20354 - 6.68797i) q^{84} +(-0.0877471 - 0.110031i) q^{85} +(7.06408 + 0.508392i) q^{86} +(2.59721 - 6.61758i) q^{87} +(5.44809 + 5.76823i) q^{88} +(12.6725 - 4.97359i) q^{89} +(-0.155869 + 0.125057i) q^{90} +(6.29285 + 2.60068i) q^{91} +(0.0577139 + 9.76491i) q^{92} +(0.306607 - 4.09138i) q^{93} +(3.92038 + 6.74420i) q^{94} +(-1.16728 + 1.71208i) q^{95} +(-8.69495 - 2.54197i) q^{96} +8.05557i q^{97} +(9.73520 + 1.79610i) 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 $

$2$	−0.520558	−	1.31492i	−0.368090	−	0.929790i
$2$	−0.520558	−	1.31492i	−0.368090	−	0.929790i
$3$	1.32314	+	0.902103i	0.763916	+	0.520829i	0.881472	−	0.472237i	$-0.156553\pi$
$3$	1.32314	+	0.902103i	0.763916	+	0.520829i	−0.117555	+	0.993066i	$0.537506\pi$
$4$	−1.45804	+	1.36899i	−0.729019	+	0.684493i
$5$	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	$0.500695\pi$
$6$	0.497422	−	2.20942i	0.203072	−	0.901994i
$7$	1.28165	+	2.31460i	0.484419	+	0.874836i
$7$	1.28165	+	2.31460i	0.484419	+	0.874836i
$8$	2.55910	+	1.20457i	0.904780	+	0.425879i
$9$	−0.159109	−	0.405403i	−0.0530363	−	0.135134i
$10$	−0.136546	−	0.438070i	−0.0431795	−	0.138530i
$11$	2.61131	+	1.02486i	0.787339	+	0.309008i	0.724732	−	0.689031i	$-0.241963\pi$
$11$	2.61131	+	1.02486i	0.787339	+	0.309008i	0.0626064	+	0.998038i	$0.480059\pi$
$12$	−3.16416	+	0.496063i	−0.913413	+	0.143201i
$13$	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	$0.169550\pi$
$14$	2.37634	−	2.89016i	0.635104	−	0.772427i
$15$	0.406234	+	0.323961i	0.104889	+	0.0836463i
$16$	0.251751	−	3.99207i	0.0629377	−	0.998017i
$17$	−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	$0.778656\pi$
$18$	−0.450248	+	0.420252i	−0.106124	+	0.0990543i
$19$	−3.19321	+	5.53080i	−0.732572	+	1.26885i	0.223209	+	0.974771i	$0.428347\pi$
$19$	−3.19321	+	5.53080i	−0.732572	+	1.26885i	−0.955780	+	0.294081i	$0.904986\pi$
$20$	−0.504947	+	0.407588i	−0.112910	+	0.0911394i
$21$	−0.392197	+	4.21872i	−0.0855844	+	0.920601i
$22$	−0.0117235	−	3.96716i	−0.00249947	−	0.845802i
$23$	3.32097	−	3.57916i	0.692470	−	0.746306i	−0.284734	−	0.958607i	$-0.591905\pi$
$23$	3.32097	−	3.57916i	0.692470	−	0.746306i	0.977204	+	0.212301i	$0.0680957\pi$
$24$	2.29941	+	3.90239i	0.469366	+	0.796572i
$25$	−4.84006	−	0.729521i	−0.968011	−	0.145904i
$26$	−3.15735	−	1.81048i	−0.619208	−	0.355064i
$27$	1.22423	−	5.36370i	0.235603	−	1.03224i
$28$	−5.03735	−	1.62021i	−0.951970	−	0.306190i
$29$	−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	$-0.206658\pi$
$30$	0.214515	−	0.702806i	0.0391648	−	0.128314i
$31$	−1.28102	−	2.21879i	−0.230078	−	0.398506i	0.727753	−	0.685839i	$-0.240565\pi$
$31$	−1.28102	−	2.21879i	−0.230078	−	0.398506i	−0.957831	+	0.287333i	$0.907231\pi$
$32$	−5.38031	+	1.74707i	−0.951113	+	0.308842i
$33$	2.53060	+	3.71170i	0.440520	+	0.646125i
$34$	−0.264517	+	0.553454i	−0.0453644	+	0.0949166i
$35$	0.358561	+	0.779973i	0.0606079	+	0.131839i
$36$	0.786978	+	0.373275i	0.131163	+	0.0622125i
$37$	−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	$0.852298\pi$
$38$	8.93481	+	1.31972i	1.44942	+	0.214086i
$39$	4.10983	−	0.307989i	0.658099	−	0.0493177i
$40$	0.798800	+	0.451793i	0.126301	+	0.0714348i
$41$	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	$0.656161\pi$
$42$	5.75145	−	1.68038i	0.887468	−	0.259289i
$43$	−2.17288	+	4.51203i	−0.331361	+	0.688079i	−0.998376	−	0.0569657i	$-0.981857\pi$
$43$	−2.17288	+	4.51203i	−0.331361	+	0.688079i	0.667015	+	0.745044i	$0.267572\pi$
$44$	−5.21041	+	2.08056i	−0.785498	+	0.313656i
$45$	−0.0416505	−	0.135028i	−0.00620889	−	0.0201287i
$46$	−6.43507	−	2.50366i	−0.948799	−	0.369144i
$47$	−5.45444	+	0.822124i	−0.795612	+	0.119919i	−0.534255	−	0.845323i	$-0.679408\pi$
$47$	−5.45444	+	0.822124i	−0.795612	+	0.119919i	−0.261356	+	0.965242i	$0.584170\pi$
$48$	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
$52$	−0.737052	+	5.09413i	−0.102211	+	0.706429i
$53$	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	$0.277449\pi$
$54$	−7.69012	+	1.18235i	−1.04649	+	0.160898i
$55$	0.820048	+	0.394914i	0.110575	+	0.0532502i
$56$	0.491791	+	7.46714i	0.0657183	+	0.997838i
$57$	−9.21441	+	4.43743i	−1.22048	+	0.587751i
$58$	−5.17667	+	3.55185i	−0.679730	+	0.466380i
$59$	0.182304	+	2.43268i	0.0237340	+	0.316708i	0.996417	+	0.0845721i	$0.0269523\pi$
$59$	0.182304	+	2.43268i	0.0237340	+	0.316708i	−0.972683	+	0.232136i	$0.925429\pi$
$60$	−1.03580	+	0.0837817i	−0.133722	+	0.0108162i
$61$	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	$-0.0496752\pi$
$62$	−2.25069	+	2.83945i	−0.285838	+	0.360610i
$63$	0.734423	−	0.887859i	0.0925286	−	0.111860i
$64$	5.09803	+	6.16523i	0.637254	+	0.770654i
$65$	0.689933	−	0.470389i	0.0855757	−	0.0583445i
$66$	3.56328	−	5.25969i	0.438609	−	0.647424i
$67$	0.882664	−	0.509607i	0.107835	−	0.0622583i	−0.445113	−	0.895475i	$-0.646836\pi$
$67$	0.882664	−	0.509607i	0.107835	−	0.0622583i	0.552947	+	0.833216i	$0.313503\pi$
$68$	0.865446	+	0.0597147i	0.104951	+	0.00724147i
$69$	7.62288	−	1.73987i	0.917687	−	0.209456i
$70$	0.838951	−	0.877501i	0.100274	−	0.104881i
$71$	−11.9497	−	2.72743i	−1.41816	−	0.323687i	−0.556366	−	0.830937i	$-0.687805\pi$
$71$	−11.9497	−	2.72743i	−1.41816	−	0.323687i	−0.861799	+	0.507251i	$0.830662\pi$
$72$	0.0811594	−	1.22913i	0.00956472	−	0.144854i
$73$	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	$-0.0856686\pi$
$74$	0.965703	+	12.3948i	0.112261	+	1.44086i
$75$	−5.74597	−	5.33149i	−0.663488	−	0.615627i
$76$	−2.91577	−	12.4356i	−0.334462	−	1.42646i
$77$	0.974644	+	7.35764i	0.111071	+	0.838481i
$78$	−2.54439	−	5.24378i	−0.288095	−	0.593741i
$79$	−9.00457	−	5.19879i	−1.01309	−	0.584910i	−0.100997	−	0.994887i	$-0.532203\pi$
$79$	−9.00457	−	5.19879i	−1.01309	−	0.584910i	−0.912096	+	0.409977i	$0.865537\pi$
$80$	0.178251	−	1.28554i	0.0199290	−	0.143728i
$81$	5.50068	−	5.10389i	0.611187	−	0.567098i
$82$	7.24813	−	7.85807i	0.800422	−	0.867779i
$83$	3.97658	−	4.98647i	0.436486	−	0.547336i	−0.514127	−	0.857714i	$-0.671884\pi$
$83$	3.97658	−	4.98647i	0.436486	−	0.547336i	0.950613	+	0.310378i	$0.100456\pi$
$84$	−5.20354	−	6.68797i	−0.567753	−	0.729718i
$85$	−0.0877471	−	0.110031i	−0.00951751	−	0.0119346i
$86$	7.06408	+	0.508392i	0.761740	+	0.0548213i
$87$	2.59721	−	6.61758i	0.278450	−	0.709479i
$88$	5.44809	+	5.76823i	0.580768	+	0.614895i
$89$	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	$0.124397\pi$
$90$	−0.155869	+	0.125057i	−0.0164300	+	0.0131821i
$91$	6.29285	+	2.60068i	0.659670	+	0.272626i
$92$	0.0577139	+	9.76491i	0.00601709	+	1.01806i
$93$	0.306607	−	4.09138i	0.0317936	−	0.424257i
$94$	3.92038	+	6.74420i	0.404357	+	0.695611i
$95$	−1.16728	+	1.71208i	−0.119760	+	0.175656i
$96$	−8.69495	−	2.54197i	−0.887425	−	0.259438i
$97$			8.05557i			0.817919i	0.912553	+	0.408960i	$0.134108\pi$
$97$			8.05557i			0.817919i	−0.912553	+	0.408960i	$0.865892\pi$
$98$	9.73520	+	1.79610i	0.983403	+	0.181433i
$99$		−	1.22170i		−	0.122785i
$100$	8.05569	−	5.56230i	0.805569	−	0.556230i
$101$	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	$-0.0741582\pi$
$102$	−0.849266	+	0.493676i	−0.0840899	+	0.0488812i
$103$	−0.641180	+	8.55595i	−0.0631773	+	0.843043i	0.872145	+	0.489247i	$0.162728\pi$
$103$	−0.641180	+	8.55595i	−0.0631773	+	0.843043i	−0.935323	+	0.353796i	$0.884891\pi$
$104$	7.08207	−	1.68263i	0.694454	−	0.164995i
$105$	−0.229188	+	1.35547i	−0.0223665	+	0.132281i
$106$	−5.01763	−	6.25390i	−0.487355	−	0.607433i
$107$	−2.95157	+	1.15841i	−0.285339	+	0.111987i	−0.503694	−	0.863882i	$-0.668026\pi$
$107$	−2.95157	+	1.15841i	−0.285339	+	0.111987i	0.218355	+	0.975869i	$0.429931\pi$
$108$	5.55786	+	9.49643i	0.534805	+	0.913794i
$109$	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	$-0.170964\pi$
$110$	0.0923986	−	1.28387i	0.00880986	−	0.122413i
$111$	−8.77744	−	11.0066i	−0.833118	−	1.04470i
$112$	9.56270	−	4.53375i	0.903590	−	0.428399i
$113$	−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	$0.902624\pi$
$114$	10.6315	+	9.80629i	0.995732	+	0.918443i
$115$	1.16130	−	1.07753i	0.108291	−	0.100480i
$116$	7.36516	+	4.95797i	0.683838	+	0.460336i
$117$	−0.970657	−	0.560409i	−0.0897373	−	0.0518099i
$118$	3.10388	−	1.50607i	0.285736	−	0.138645i
$119$	0.357834	−	1.09038i	0.0328026	−	0.0999554i
$120$	0.649362	+	1.31839i	0.0592784	+	0.120352i
$121$	−2.29499	−	2.12944i	−0.208636	−	0.193586i
$122$	−9.68382	+	0.754486i	−0.876732	+	0.0683080i
$123$	−1.80422	+	11.9702i	−0.162681	+	1.07932i
$124$	4.90527	+	1.48138i	0.440506	+	0.133032i
$125$	−3.12996	−	0.714393i	−0.279952	−	0.0638972i
$126$	−1.54978	−	0.503526i	−0.138065	−	0.0448576i
$127$	6.86346	−	1.56654i	0.609034	−	0.139008i	0.0931292	−	0.995654i	$-0.470313\pi$
$127$	6.86346	−	1.56654i	0.609034	−	0.139008i	0.515905	+	0.856646i	$0.327456\pi$
$128$	5.45298	−	9.91287i	0.481980	−	0.876182i
$129$	−6.94535	+	4.00990i	−0.611504	+	0.353052i
$130$	−0.977675	−	0.662344i	−0.0857477	−	0.0580914i
$131$	14.5953	−	9.95088i	1.27519	−	0.869413i	0.279324	−	0.960197i	$-0.409890\pi$
$131$	14.5953	−	9.95088i	1.27519	−	0.869413i	0.995871	+	0.0907844i	$0.0289374\pi$
$132$	−8.77098	−	1.94745i	−0.763416	−	0.169504i
$133$	−16.8942	−	0.302430i	−1.46491	−	0.0262240i
$134$	−1.12957	−	0.895355i	−0.0975801	−	0.0773469i
$135$	0.526157	−	1.70576i	0.0452844	−	0.146808i
$136$	−0.371995	−	1.16908i	−0.0318983	−	0.100248i
$137$	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	$0.830512\pi$
$138$	−6.25595	−	9.11779i	−0.532542	−	0.776158i
$139$	−12.9510	+	6.23687i	−1.09849	+	0.529004i	−0.893183	−	0.449694i	$-0.851533\pi$
$139$	−12.9510	+	6.23687i	−1.09849	+	0.529004i	−0.205305	+	0.978698i	$0.565819\pi$
$140$	−1.59057	−	0.646364i	−0.134428	−	0.0546278i
$141$	−7.95863	−	3.83268i	−0.670238	−	0.322770i
$142$	2.63414	+	17.1327i	0.221052	+	1.43774i
$143$	6.89874	−	2.12798i	0.576902	−	0.177951i
$144$	−1.65845	+	0.533114i	−0.138204	+	0.0444261i
$145$	−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	$0.415805\pi$
$150$	−4.01937	+	10.3309i	−0.328180	+	0.843511i
$151$	2.74206	+	8.88954i	0.223146	+	0.723420i	0.996042	+	0.0888877i	$0.0283312\pi$
$151$	2.74206	+	8.88954i	0.223146	+	0.723420i	−0.772896	+	0.634533i	$0.781193\pi$
$152$	−14.8340	+	10.3074i	−1.20319	+	0.836044i
$153$	−0.0819616	+	0.170195i	−0.00662621	+	0.0137595i
$154$	9.16737	−	5.11166i	0.738727	−	0.411910i
$155$	−0.360679	−	0.748958i	−0.0289705	−	0.0601578i
$156$	−5.57066	+	6.07536i	−0.446009	+	0.486418i
$157$	−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	$0.635455\pi$
$158$	−2.14860	+	14.5466i	−0.170933	+	1.15726i
$159$	8.67589	+	2.67616i	0.688043	+	0.212233i
$160$	−1.78318	+	0.434815i	−0.140973	+	0.0343752i
$161$	12.5406	+	3.09948i	0.988341	+	0.244273i
$162$	−9.57464	−	4.57609i	−0.752254	−	0.359532i
$163$	6.04539	+	8.86696i	0.473511	+	0.694514i	0.986478	−	0.163895i	$-0.0524058\pi$
$163$	6.04539	+	8.86696i	0.473511	+	0.694514i	−0.512966	+	0.858409i	$0.671453\pi$
$164$	−14.1058	−	5.44014i	−1.10148	−	0.424803i
$165$	0.728786	+	1.26229i	0.0567359	+	0.0982695i
$166$	−8.62685	−	2.63314i	−0.669574	−	0.204371i
$167$	5.31218	+	23.2742i	0.411069	+	1.80101i	0.579131	+	0.815235i	$0.303392\pi$
$167$	5.31218	+	23.2742i	0.411069	+	1.80101i	−0.168062	+	0.985777i	$0.553751\pi$
$168$	−6.08541	+	10.3237i	−0.469500	+	0.796493i
$169$	−1.41894	+	6.21676i	−0.109149	+	0.478213i
$170$	−0.0990052	+	0.172658i	−0.00759335	+	0.0132423i
$171$	2.75027	+	0.414536i	0.210318	+	0.0317004i
$172$	−3.00877	−	9.55336i	−0.229417	−	0.728437i
$173$	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	$0.223290\pi$
$174$	−10.0536	+	0.0297098i	−0.762161	+	0.00225229i
$175$	−4.51472	−	12.1378i	−0.341281	−	0.917530i
$176$	4.74872	−	10.1665i	0.357948	−	0.766329i
$177$	−1.95331	+	3.38324i	−0.146820	+	0.254300i
$178$	−13.1367	−	14.0743i	−0.984635	−	1.05491i
$179$	−10.6604	−	11.4891i	−0.796793	−	0.858738i	0.195748	−	0.980654i	$-0.437287\pi$
$179$	−10.6604	−	11.4891i	−0.796793	−	0.858738i	−0.992540	+	0.121916i	$0.961096\pi$
$180$	0.245579	+	0.139856i	0.0183044	+	0.0104243i
$181$	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	$0.312654\pi$
$182$	0.143902	−	9.62841i	0.0106667	−	0.713705i
$183$	8.59923	−	6.85766i	0.635674	−	0.506933i
$184$	12.8101	−	5.15910i	0.944370	−	0.380334i
$185$	−2.65516	−	1.04207i	−0.195211	−	0.0766148i
$186$	−5.53945	+	1.72664i	−0.406173	+	0.126603i
$187$	−0.444536	−	1.13266i	−0.0325077	−	0.0828282i
$188$	6.82730	−	8.66574i	0.497932	−	0.632014i
$189$	13.9838	−	4.04080i	1.01717	−	0.293925i
$190$	2.85889	+	0.643641i	0.207406	+	0.0466946i
$191$	−1.00074	−	0.0749955i	−0.0724114	−	0.00542648i	0.0384751	−	0.999260i	$-0.487750\pi$
$191$	−1.00074	−	0.0749955i	−0.0724114	−	0.00542648i	−0.110886	+	0.993833i	$0.535369\pi$
$192$	1.18374	+	12.7564i	0.0854291	+	0.920615i
$193$	−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	$0.752578\pi$
$194$	10.5924	−	4.19339i	0.760493	−	0.301068i
$195$	1.33722			0.0957602
$196$	−2.70601	−	13.7360i	−0.193286	−	0.981142i
$197$	4.43186			0.315757			0.157878	−	0.987459i	$-0.449535\pi$
$197$	4.43186			0.315757			0.157878	+	0.987459i	$0.449535\pi$
$198$	−1.60643	+	0.635964i	−0.114164	+	0.0451960i
$199$	13.8341	+	9.43193i	0.980673	+	0.668612i	0.943734	−	0.330706i	$-0.107287\pi$
$199$	13.8341	+	9.43193i	0.980673	+	0.668612i	0.0369393	+	0.999318i	$0.488239\pi$
$200$	−11.5074	−	7.69710i	−0.813699	−	0.544267i
$201$	1.62761	+	0.121972i	0.114803	+	0.00860326i
$202$	−20.4894	−	4.61292i	−1.44163	−	0.324564i
$203$	8.75137	−	7.83331i	0.614226	−	0.549791i
$204$	1.09124	+	0.859732i	0.0764019	+	0.0601932i
$205$	0.896065	+	2.28314i	0.0625839	+	0.159461i
$206$	11.5842	−	3.61077i	0.807108	−	0.251574i
$207$	−1.97940	−	0.776856i	−0.137578	−	0.0539952i
$208$	−5.89915	−	8.43646i	−0.409033	−	0.584963i
$209$	−14.0067	+	11.1700i	−0.968867	+	0.772646i
$210$	1.90165	−	0.404239i	0.131226	−	0.0278951i
$211$	−0.173155	−	0.138087i	−0.0119205	−	0.00950629i	0.617511	−	0.786562i	$-0.288141\pi$
$211$	−0.173155	−	0.138087i	−0.0119205	−	0.00950629i	−0.629432	+	0.777056i	$0.716712\pi$
$212$	−5.61142	+	9.85331i	−0.385394	+	0.676728i
$213$	−13.3507	−	14.3886i	−0.914773	−	0.985891i
$214$	3.05968	+	3.27807i	0.209155	+	0.224084i
$215$	−0.812447	+	1.40720i	−0.0554084	+	0.0959702i
$216$	9.59387	−	12.2516i	0.652780	−	0.833615i
$217$	3.49379	−	5.80876i	0.237174	−	0.394324i
$218$	−23.3335	+	0.0689539i	−1.58035	+	0.00467015i
$219$	7.56806	−	8.15643i	0.511402	−	0.551161i
$220$	−1.73629	+	0.546835i	−0.117061	+	0.0368676i
$221$	−1.10383	−	0.166376i	−0.0742517	−	0.0111916i
$222$	−9.90360	+	17.2712i	−0.664686	+	1.15917i
$223$	−3.71159	+	16.2616i	−0.248547	+	1.08895i	0.684447	+	0.729062i	$0.260044\pi$
$223$	−3.71159	+	16.2616i	−0.248547	+	1.08895i	−0.932994	+	0.359892i	$0.882813\pi$
$224$	−10.9395	−	10.2141i	−0.730924	−	0.682459i
$225$	0.474346	+	2.07825i	0.0316231	+	0.138550i
$226$	23.8683	+	7.28522i	1.58770	+	0.484606i
$227$	−7.02786	−	12.1726i	−0.466456	−	0.807925i	0.532810	−	0.846235i	$-0.321136\pi$
$227$	−7.02786	−	12.1726i	−0.466456	−	0.807925i	−0.999266	+	0.0383097i	$0.987803\pi$
$228$	7.36018	−	19.0843i	0.487440	−	1.26389i
$229$	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	$0.654457\pi$
$230$	−2.02138	−	0.966099i	−0.133286	−	0.0637027i
$231$	−5.34776	+	10.6144i	−0.351857	+	0.698378i
$232$	2.68535	−	12.2655i	0.176302	−	0.805270i
$233$	−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	$0.931770\pi$
$234$	−0.231611	+	1.56806i	−0.0151409	+	0.102508i
$235$	−1.78474	+	0.133748i	−0.116423	+	0.00872473i
$236$	−3.59611	−	3.29737i	−0.234087	−	0.214640i
$237$	−7.22447	−	15.0018i	−0.469280	−	0.974470i
$238$	−1.62004	+	0.0970843i	−0.105012	+	0.00629304i
$239$	−3.72072	+	7.72616i	−0.240674	+	0.499764i	−0.985960	−	0.166980i	$-0.946598\pi$
$239$	−3.72072	+	7.72616i	−0.240674	+	0.499764i	0.745287	+	0.666744i	$0.232313\pi$
$240$	1.39554	−	1.54016i	0.0900819	−	0.0994167i
$241$	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	$0.463420\pi$
$242$	−1.60537	+	4.12623i	−0.103197	+	0.265244i
$243$	−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
$248$	−0.605576	−	7.22119i	−0.0384541	−	0.458546i
$249$	9.75988	−	3.01052i	0.618507	−	0.190784i
$250$	0.689955	+	4.48753i	0.0436366	+	0.283817i
$251$	17.5508	+	8.45200i	1.10779	+	0.533485i	0.896101	−	0.443851i	$-0.146388\pi$
$251$	17.5508	+	8.45200i	1.10779	+	0.533485i	0.211693	+	0.977336i	$0.432102\pi$
$252$	0.144651	+	2.29995i	0.00911217	+	0.144883i
$253$	12.3402	−	5.94274i	0.775823	−	0.373617i
$254$	−5.63271	−	8.20944i	−0.353428	−	0.515106i
$255$	−0.0168422	−	0.224744i	−0.00105470	−	0.0140740i
$256$	−15.8732	−	2.01001i	−0.992078	−	0.125626i
$257$	−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	$0.996185\pi$
$258$	8.88816	+	7.04520i	0.553352	+	0.438615i
$259$	−4.76888	−	22.7646i	−0.296324	−	1.41453i
$260$	−0.361993	+	1.63035i	−0.0224499	+	0.101110i
$261$	−1.59738	+	1.08908i	−0.0988755	+	0.0674122i
$262$	−20.6823	−	14.0116i	−1.27776	−	0.865640i
$263$	10.2462	−	5.91566i	0.631809	−	0.364775i	−0.149643	−	0.988740i	$-0.547813\pi$
$263$	10.2462	−	5.91566i	0.631809	−	0.364775i	0.781452	+	0.623965i	$0.214479\pi$
$264$	2.00506	+	12.5469i	0.123403	+	0.772209i
$265$	1.79343	−	0.409339i	0.110169	−	0.0251455i
$266$	8.39672	+	22.3719i	0.514836	+	1.37171i
$267$	21.2542	+	4.85114i	1.30074	+	0.296885i
$268$	−0.589314	+	1.95138i	−0.0359981	+	0.119200i
$269$	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	$-0.258624\pi$
$270$	−2.51684	+	0.196092i	−0.153170	+	0.0119338i
$271$	4.26861	+	3.96069i	0.259300	+	0.240595i	0.799100	−	0.601198i	$-0.205310\pi$
$271$	4.26861	+	3.96069i	0.259300	+	0.240595i	−0.539800	+	0.841793i	$0.681500\pi$
$272$	−1.34360	+	1.09772i	−0.0814678	+	0.0665589i
$273$	5.98025	+	9.11787i	0.361941	+	0.551839i
$274$	13.1605	−	6.38572i	0.795052	−	0.385776i
$275$	−11.8912	−	6.86539i	−0.717067	−	0.413999i
$276$	−8.73259	+	12.9724i	−0.525640	+	0.780848i
$277$	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	$0.261303\pi$
$278$	14.9427	+	13.7829i	0.896206	+	0.826642i
$279$	−0.695682	+	0.872358i	−0.0416494	+	0.0522267i
$280$	−0.0219350	+	2.42794i	−0.00131087	+	0.145097i
$281$	−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	$0.988257\pi$
$282$	−0.896736	+	12.4601i	−0.0533999	+	0.741989i
$283$	−5.63043	+	14.3461i	−0.334695	+	0.852788i	0.660127	+	0.751154i	$0.270502\pi$
$283$	−5.63043	+	14.3461i	−0.334695	+	0.852788i	−0.994822	+	0.101634i	$0.967593\pi$
$284$	21.1569	−	12.3822i	1.25543	−	0.734750i
$285$	−3.08895	+	1.21232i	−0.182974	+	0.0718118i
$286$	−6.38933	−	7.96357i	−0.377809	−	0.470896i
$287$	−11.5603	+	16.3204i	−0.682383	+	0.963362i
$288$	1.56432	+	1.90322i	0.0921787	+	0.112148i
$289$	1.25635	−	16.7649i	0.0739030	−	0.986168i
$290$	−1.76105	+	1.02369i	−0.103412	+	0.0601134i
$291$	−7.26695	+	10.6587i	−0.425996	+	0.624821i
$292$	7.89571	+	11.4351i	0.462061	+	0.669187i
$293$		−	1.53780i		−	0.0898392i	−0.998991	−	0.0449196i	$-0.985697\pi$
$293$		−	1.53780i		−	0.0898392i	0.998991	−	0.0449196i	$-0.0143032\pi$
$294$	11.2608	+	11.1586i	0.656742	+	0.650785i
$295$			0.791523i			0.0460842i
$296$	−18.3763	−	16.7500i	−1.06810	−	0.973576i
$297$	8.69389	−	12.7516i	0.504470	−	0.739922i
$298$	−1.98936	−	3.42228i	−0.115241	−	0.198247i
$299$	0.939033	−	12.5305i	0.0543057	−	0.724659i
$300$	15.6766	−	0.0926539i	0.905088	−	0.00534938i
$301$	−13.2284	+	0.753514i	−0.762474	+	0.0434318i
$302$	10.2616	−	8.23312i	0.590491	−	0.473763i
$303$	22.1382	−	8.68862i	1.27181	−	0.499148i
$304$	21.2754	+	14.1399i	1.22023	+	0.810978i
$305$	0.814154	−	2.07443i	0.0466183	−	0.118782i
$306$	0.266459	+	0.0191767i	0.0152324	+	0.00109626i
$307$	−7.98188	−	10.0090i	−0.455550	−	0.571242i	0.500017	−	0.866016i	$-0.333327\pi$
$307$	−7.98188	−	10.0090i	−0.455550	−	0.571242i	−0.955567	+	0.294774i	$0.904756\pi$
$308$	−11.4936	−	9.39345i	−0.654908	−	0.535242i
$309$	−8.56672	+	10.7423i	−0.487343	+	0.611109i
$310$	−0.797067	+	0.864141i	−0.0452704	+	0.0490799i
$311$	−3.29414	+	3.05651i	−0.186793	+	0.173319i	−0.768026	−	0.640418i	$-0.778761\pi$
$311$	−3.29414	+	3.05651i	−0.186793	+	0.173319i	0.581233	+	0.813737i	$0.302571\pi$
$312$	10.8885	+	4.16240i	0.616439	+	0.235649i
$313$	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	$0.534123\pi$
$314$	7.42193	+	15.2960i	0.418844	+	0.863203i
$315$	0.259153	−	0.269463i	0.0146016	−	0.0151825i
$316$	20.2461	−	4.74710i	1.13893	−	0.267045i
$317$	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	$0.584398\pi$
$318$	−0.997368	−	12.8012i	−0.0559296	−	0.717856i
$319$	1.85603	−	12.3139i	0.103917	−	0.689447i
$320$	1.50000	+	2.11840i	0.0838524	+	0.118422i
$321$	−4.95035	−	1.12989i	−0.276302	−	0.0630640i
$322$	−2.45256	−	18.1034i	−0.136676	−	1.00886i
$323$	2.70066	−	0.616409i	0.150269	−	0.0342979i
$324$	−1.03305	+	14.9720i	−0.0573917	+	0.831779i
$325$	−10.9093	+	6.29851i	−0.605141	+	0.349378i
$326$	8.51238	−	12.5650i	0.471457	−	0.695910i
$327$	21.8310	−	14.8841i	1.20726	−	0.823094i
$328$	0.189547	+	21.3800i	0.0104660	+	1.18051i
$329$	−8.89358	−	11.5712i	−0.490319	−	0.637939i
$330$	1.28044	−	1.61539i	0.0704861	−	0.0889245i
$331$	−6.88703	+	22.3272i	−0.378545	+	1.22721i	0.543261	+	0.839564i	$0.317189\pi$
$331$	−6.88703	+	22.3272i	−0.378545	+	1.22721i	−0.921806	+	0.387650i	$0.873287\pi$
$332$	1.02841	+	12.7143i	0.0564413	+	0.697790i
$333$	0.286108	+	3.81784i	0.0156786	+	0.209217i
$334$	27.8384	−	19.1007i	1.52325	−	1.04514i
$335$	0.297946	−	0.143483i	0.0162785	−	0.00783932i
$336$	16.7427	+	2.62774i	0.913389	+	0.143355i
$337$	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	$0.271556\pi$
$338$	8.91320	−	1.37040i	0.484814	−	0.0745398i
$339$	−27.0031	+	8.32935i	−1.46661	+	0.452388i
$340$	0.278570	+	0.0403053i	0.0151076	+	0.00218586i
$341$	−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
$346$	−1.61199	−	0.627169i	−0.0866612	−	0.0337168i
$347$	−10.1148	−	32.7915i	−0.542994	−	1.76034i	−0.643543	−	0.765410i	$-0.722536\pi$
$347$	−10.1148	−	32.7915i	−0.542994	−	1.76034i	0.100550	−	0.994932i	$-0.467940\pi$
$348$	5.27255	+	13.2042i	0.282638	+	0.707820i
$349$	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	$0.0346895\pi$
$350$	−13.6100	+	12.2549i	−0.727488	+	0.655053i
$351$	−6.14334	−	12.7568i	−0.327907	−	0.680906i
$352$	−15.8401	−	0.951935i	−0.844283	−	0.0507383i
$353$	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	$0.434753\pi$
$354$	5.46550	+	0.807281i	0.290488	+	0.0429065i
$355$	−3.80023	−	1.17221i	−0.201695	−	0.0622147i
$356$	−11.6682	+	24.6002i	−0.618414	+	1.30381i
$357$	1.45710	−	1.11993i	0.0771181	−	0.0592729i
$358$	−9.55797	+	19.9983i	−0.505155	+	1.05694i
$359$	−12.4421	−	18.2492i	−0.656667	−	0.963154i	−0.999716	−	0.0238363i	$-0.992412\pi$
$359$	−12.4421	−	18.2492i	−0.656667	−	0.963154i	0.343049	−	0.939318i	$-0.388540\pi$
$360$	0.0560620	−	0.395720i	0.00295473	−	0.0208563i
$361$	−10.8931	−	18.8675i	−0.573323	−	0.993025i
$362$	10.5825	−	34.6709i	0.556202	−	1.82226i
$363$	−1.11562	−	4.88787i	−0.0585551	−	0.256547i
$364$	−12.7355	+	4.82293i	−0.667523	+	0.252790i
$365$	0.501647	−	2.19786i	0.0262574	−	0.115041i
$366$	−13.4937	−	7.73751i	−0.705326	−	0.404446i
$367$	−16.6152	−	2.50434i	−0.867307	−	0.130725i	−0.299708	−	0.954031i	$-0.596889\pi$
$367$	−16.6152	−	2.50434i	−0.867307	−	0.130725i	−0.567599	+	0.823305i	$0.692127\pi$
$368$	−13.4522	−	14.1586i	−0.701244	−	0.738068i
$369$	2.23921	−	2.41329i	0.116568	−	0.125631i
$370$	0.0119204	+	4.03379i	0.000619714	+	0.209707i
$371$	10.8116	+	10.3979i	0.561309	+	0.539834i
$372$	5.15400	+	6.38513i	0.267223	+	0.331054i
$373$	−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	$0.963693\pi$
$374$	−1.25795	+	1.17414i	−0.0650471	+	0.0607136i
$375$	−3.49692	−	3.76879i	−0.180580	−	0.194619i
$376$	−14.9488	−	4.46634i	−0.770925	−	0.230334i
$377$	−8.93223	−	7.12321i	−0.460033	−	0.366864i
$378$	−12.5927	−	16.2842i	−0.647700	−	0.837568i
$379$	10.1114	−	8.06357i	0.519388	−	0.414198i	−0.328396	−	0.944540i	$-0.606508\pi$
$379$	10.1114	−	8.06357i	0.519388	−	0.414198i	0.847784	+	0.530342i	$0.177937\pi$
$380$	−0.641883	−	4.09427i	−0.0329279	−	0.210032i
$381$	10.4945	+	4.11879i	0.537650	+	0.211012i
$382$	0.422333	+	1.35494i	0.0216084	+	0.0693248i
$383$	5.60580	+	14.2834i	0.286443	+	0.729845i	0.999584	+	0.0288249i	$0.00917653\pi$
$383$	5.60580	+	14.2834i	0.286443	+	0.729845i	−0.713141	+	0.701020i	$0.752728\pi$
$384$	16.1575	−	8.19699i	0.824533	−	0.418301i
$385$	0.136949	+	2.40422i	0.00697956	+	0.122531i
$386$	−1.67311	+	7.43155i	−0.0851592	+	0.378256i
$387$	2.17492	+	0.162987i	0.110557	+	0.00828512i
$388$	−11.0280	−	11.7453i	−0.559860	−	0.596279i
$389$	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	$0.454325\pi$
$390$	−0.696100	−	1.75834i	−0.0352484	−	0.0890369i
$391$	−2.11781			−0.107102
$392$	−16.6531	+	10.7086i	−0.841110	+	0.540865i
$393$	28.2883			1.42696
$394$	−2.30704	−	5.82754i	−0.116227	−	0.293587i
$395$	−2.78741	−	1.90042i	−0.140250	−	0.0956205i
$396$	1.67249	+	1.78128i	0.0840456	+	0.0895127i
$397$	−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	$0.665334\pi$
$398$	5.20079	−	23.1006i	0.260692	−	1.15793i
$399$	−22.0805	−	15.6404i	−1.10541	−	0.783000i
$400$	−4.13079	+	19.1382i	−0.206539	+	0.956909i
$401$	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	$0.824208\pi$
$402$	−0.686880	−	2.20367i	−0.0342585	−	0.109909i
$403$	−6.13784	−	2.40892i	−0.305748	−	0.119997i
$404$	4.60032	+	29.3433i	0.228874	+	1.45988i
$405$	1.90352	−	1.51801i	0.0945866	−	0.0754303i
$406$	−14.8558	−	7.42967i	−0.737280	−	0.368728i
$407$	−19.2805	−	15.3757i	−0.955699	−	0.762144i
$408$	0.562427	−	1.88243i	0.0278443	−	0.0931943i
$409$	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	$0.658102\pi$
$410$	2.53569	−	2.36676i	0.125229	−	0.116886i
$411$	−8.28204	+	14.3449i	−0.408523	+	0.707582i
$412$	−10.7781	−	13.3527i	−0.531000	−	0.657839i
$413$	−5.39703	+	3.53981i	−0.265570	+	0.174183i
$414$	0.00888656	+	3.00715i	0.000436751	+	0.147793i
$415$	1.40754	−	1.51697i	0.0690935	−	0.0744651i
$416$	−8.02243	+	12.1486i	−0.393332	+	0.595634i
$417$	−22.7623	−	3.43086i	−1.11467	−	0.168010i
$418$	21.9790	+	12.6031i	1.07503	+	0.616440i
$419$	0.955920	−	4.18816i	0.0466997	−	0.204605i	−0.946196	−	0.323595i	$-0.895109\pi$
$419$	0.955920	−	4.18816i	0.0466997	−	0.204605i	0.992895	+	0.118990i	$0.0379656\pi$
$420$	−1.52146	−	2.29009i	−0.0742397	−	0.111745i
$421$	−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	$-0.330315\pi$
$422$	−0.0914359	+	0.299568i	−0.00445103	+	0.0145827i
$423$	1.20114	+	2.08044i	0.0584015	+	0.101154i
$424$	15.8774	+	2.24936i	0.771075	+	0.109239i
$425$	1.19598	+	1.75418i	0.0580136	+	0.0850904i
$426$	−11.9701	+	25.0452i	−0.579952	+	1.21344i
$427$	17.7856	−	3.72584i	0.860706	−	0.180306i
$428$	2.71766	−	5.72967i	0.131363	−	0.276954i
$429$	11.0477	+	3.40776i	0.533387	+	0.164528i
$430$	2.27328	+	0.335775i	0.109627	+	0.0161925i
$431$	25.6682	−	1.92357i	1.23639	−	0.0926549i	0.559560	−	0.828790i	$-0.310970\pi$
$431$	25.6682	−	1.92357i	1.23639	−	0.0926549i	0.676835	+	0.736135i	$0.263351\pi$
$432$	−21.1040	−	6.23752i	−1.01537	−	0.300103i
$433$	−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	$-0.454430\pi$
$434$	−9.45679	−	1.57026i	−0.453940	−	0.0753747i
$435$	1.00079	−	2.07817i	0.0479843	−	0.0996404i
$436$	12.2371	+	30.6459i	0.586052	+	1.46767i
$437$	9.19104	+	29.7966i	0.439667	+	1.42537i
$438$	−14.6647	−	5.70551i	−0.700706	−	0.272620i
$439$	−27.4680	+	4.14014i	−1.31098	+	0.197598i	−0.767079	−	0.641553i	$-0.778291\pi$
$439$	−27.4680	+	4.14014i	−1.31098	+	0.197598i	−0.543899	+	0.839151i	$0.683052\pi$
$440$	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	$0.305564\pi$
$443$	5.61834	+	37.2752i	0.266935	+	1.77100i	−0.306619	+	0.951832i	$0.599198\pi$
$444$	27.8657	+	4.03179i	1.32245	+	0.191340i
$445$	4.22083	−	1.30195i	0.200087	−	0.0617185i
$446$	23.3148	−	3.58463i	1.10399	−	0.169737i
$447$	4.03853	+	1.94485i	0.191016	+	0.0919885i
$448$	−7.73614	+	19.7016i	−0.365498	+	0.930812i
$449$	−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	$0.423742\pi$
$450$	2.48581	−	1.70558i	0.117182	−	0.0804016i
$451$	1.58468	+	21.1461i	0.0746196	+	0.995730i
$452$	−2.84535	−	35.1773i	−0.133834	−	1.65460i
$453$	−4.39114	+	14.2357i	−0.206314	+	0.668853i
$454$	−12.3476	+	15.5776i	−0.579503	+	0.731095i
$455$	1.97302	+	0.994044i	0.0924964	+	0.0466015i
$456$	−28.9258	+	0.256446i	−1.35458	+	0.0120092i
$457$	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	$0.306210\pi$
$458$	11.2379	−	16.5880i	0.525110	−	0.775107i
$459$	−2.06663	+	1.19317i	−0.0964622	+	0.0556925i
$460$	−0.218096	+	3.16087i	−0.0101688	+	0.147376i
$461$	−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	$0.483202\pi$
$462$	16.7410	+	1.50645i	0.778860	+	0.0700865i
$463$	−19.2117	−	4.38494i	−0.892842	−	0.203785i	−0.248599	−	0.968606i	$-0.579970\pi$
$463$	−19.2117	−	4.38494i	−0.892842	−	0.203785i	−0.644243	+	0.764821i	$0.722827\pi$
$464$	−17.5261	+	2.85389i	−0.813627	+	0.132489i
$465$	0.198407	−	1.31635i	0.00920093	−	0.0610441i
$466$	2.92102	+	37.4912i	0.135314	+	1.73675i
$467$	−4.23062	−	3.92544i	−0.195770	−	0.181648i	0.576197	−	0.817311i	$-0.304536\pi$
$467$	−4.23062	−	3.92544i	−0.195770	−	0.181648i	−0.771966	+	0.635663i	$0.780727\pi$
$468$	2.18245	−	0.511719i	0.100884	−	0.0236542i
$469$	2.31080	+	1.38987i	0.106703	+	0.0641785i
$470$	1.10493	+	2.27717i	0.0509665	+	0.105038i
$471$	−16.6727	−	9.62596i	−0.768235	−	0.443541i
$472$	−2.46379	+	6.44508i	−0.113405	+	0.296659i
$473$	−10.2983	+	9.55540i	−0.473515	+	0.439358i
$474$	−15.9654	+	17.3089i	−0.733315	+	0.795025i
$475$	19.4901	−	24.4398i	0.894268	−	1.12138i
$476$	0.970985	+	2.07969i	0.0445050	+	0.0953225i
$477$	−1.53948	−	1.93045i	−0.0704881	−	0.0883893i
$478$	12.0962	+	0.870543i	0.553265	+	0.0398177i
$479$	9.11656	−	23.2286i	0.416546	−	1.06134i	−0.556523	−	0.830832i	$-0.687865\pi$
$479$	9.11656	−	23.2286i	0.416546	−	1.06134i	0.973070	−	0.230511i	$-0.0740397\pi$
$480$	−2.75165	−	1.03329i	−0.125595	−	0.0471630i
$481$	−21.0605	+	8.26563i	−0.960275	+	0.376880i
$482$	33.6685	−	27.0129i	1.53356	−	1.23040i
$483$	13.7970	+	15.4140i	0.627785	+	0.701361i
$484$	6.26136	−	0.0370068i	0.284607	−	0.00168213i
$485$	−0.195323	+	2.60641i	−0.00886917	+	0.118351i
$486$	3.18992	+	5.48759i	0.144698	+	0.248922i
$487$	6.37880	−	9.35598i	0.289051	−	0.423960i	−0.654058	−	0.756445i	$-0.726935\pi$
$487$	6.37880	−	9.35598i	0.289051	−	0.423960i	0.943109	+	0.332485i	$0.107887\pi$
$488$	13.0865	−	14.3571i	0.592398	−	0.649915i
$489$			17.1858i			0.777169i
$490$	3.10631	+	0.817183i	0.140329	+	0.0369166i
$491$			17.5121i			0.790311i	0.918614	+	0.395156i	$0.129309\pi$
$491$			17.5121i			0.790311i	−0.918614	+	0.395156i	$0.870691\pi$
$492$	−13.7564	−	19.9230i	−0.620188	−	0.898196i
$493$	−1.08469	+	1.59094i	−0.0488518	+	0.0716524i
$494$	20.0955	−	11.6814i	0.904138	−	0.525573i
$495$	0.0296225	−	0.395284i	0.00133143	−	0.0177667i
$496$	−9.18006	+	4.55534i	−0.412197	+	0.204541i
$497$	−9.00241	−	31.1543i	−0.403813	−	1.39746i
$498$	−9.03919	−	11.2663i	−0.405056	−	0.504856i
$499$	40.0936	−	15.7356i	1.79484	−	0.704422i	0.800354	−	0.599528i	$-0.204645\pi$
$499$	40.0936	−	15.7356i	1.79484	−	0.704422i	0.994483	−	0.104893i	$-0.0334501\pi$
$500$	5.54159	−	3.24326i	0.247828	−	0.145043i
$501$	−13.9669	+	35.5872i	−0.623997	+	1.58992i
$502$	1.97752	−	27.4776i	0.0882613	−	1.22639i
$503$	−13.2908	−	16.6661i	−0.592606	−	0.743104i	0.391599	−	0.920136i	$-0.371922\pi$
$503$	−13.2908	−	16.6661i	−0.592606	−	0.743104i	−0.984205	+	0.177032i	$0.943351\pi$
$504$	2.94895	−	1.38746i	0.131357	−	0.0618025i
$505$	3.00430	−	3.76727i	0.133690	−	0.167641i
$506$	−14.2380	−	13.1329i	−0.632958	−	0.583828i
$507$	−7.48561	+	6.94563i	−0.332448	+	0.308466i
$508$	−7.86262	+	11.6801i	−0.348847	+	0.518219i
$509$	−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	$0.987568\pi$
$510$	−0.286753	+	0.139139i	−0.0126977	+	0.00616116i
$511$	17.2296	−	6.40867i	0.762193	−	0.283503i
$512$	5.61994	+	21.9184i	0.248369	+	0.968666i
$513$	25.7563	+	23.8984i	1.13717	+	1.05514i
$514$	13.8415	−	1.07842i	0.610524	−	0.0475672i
$515$	−0.414912	+	2.75276i	−0.0182832	+	0.121301i
$516$	4.63708	−	15.3547i	0.204136	−	0.675952i
$517$	−15.0858	−	3.44323i	−0.663472	−	0.151433i
$518$	−27.4512	+	18.1210i	−1.20614	+	0.796192i
$519$	1.90954	−	0.435840i	0.0838195	−	0.0191312i
$520$	2.33223	−	0.372701i	0.102275	−	0.0163440i
$521$	−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	$0.484812\pi$
$522$	2.26358	+	1.53351i	0.0990743	+	0.0671197i
$523$	−11.6723	+	7.95803i	−0.510394	+	0.347980i	−0.790974	−	0.611850i	$-0.790426\pi$
$523$	−11.6723	+	7.95803i	−0.510394	+	0.347980i	0.280580	+	0.959831i	$0.409473\pi$
$524$	−7.65783	+	34.4895i	−0.334534	+	1.50668i
$525$	4.97590	−	20.1327i	0.217166	−	0.878665i
$526$	−13.1124	−	10.3935i	−0.571727	−	0.453180i
$527$	−0.327558	+	1.06192i	−0.0142686	+	0.0462578i
$528$	15.4545	−	9.16790i	0.672569	−	0.398981i
$529$	−0.0627145	−	0.836867i	−0.00272672	−	0.0363855i
$530$	−1.47183	−	2.14513i	−0.0639323	−	0.0931787i
$531$	0.957209	−	0.460968i	0.0415393	−	0.0200043i
$532$	25.0463	−	22.6869i	1.08590	−	0.983603i
$533$	17.5278	+	8.44095i	0.759214	+	0.365618i
$534$	−4.68519	−	30.4729i	−0.202748	−	1.31869i
$535$	−0.983080	+	0.303240i	−0.0425023	+	0.0131102i
$536$	2.87269	−	0.240906i	0.124081	−	0.0104056i
$537$	−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	$0.431467\pi$
$542$	2.98594	−	7.67466i	0.128257	−	0.329655i
$543$	12.0992	+	39.2245i	0.519224	+	1.68328i
$544$	2.14283	+	1.19530i	0.0918733	+	0.0512483i
$545$	2.32275	−	4.82325i	0.0994958	−	0.206605i
$546$	8.87622	−	12.6099i	0.379867	−	0.539656i
$547$	9.01528	+	18.7204i	0.385465	+	0.800427i	0.999934	+	0.0114858i	$0.00365613\pi$
$547$	9.01528	+	18.7204i	0.385465	+	0.800427i	−0.614469	+	0.788941i	$0.710630\pi$
$548$	−15.2475	−	13.9808i	−0.651341	−	0.597232i
$549$	−2.98281	+	0.223531i	−0.127303	+	0.00954007i
$550$	−2.83739	+	19.2098i	−0.120987	+	0.819111i
$551$	27.0912	+	8.35653i	1.15412	+	0.356000i
$552$	21.6035	+	4.72977i	0.919508	+	0.201312i
$553$	0.492380	−	27.5050i	0.0209381	−	1.16963i
$554$	−0.0802879	−	0.0383727i	−0.00341110	−	0.00163030i
$555$	−2.57310	−	3.77404i	−0.109222	−	0.160199i
$556$	10.3448	−	26.8233i	0.438719	−	1.13756i
$557$	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	$0.776843\pi$
$558$	1.50923	+	0.460655i	0.0638906	+	0.0195011i
$559$	2.86796	+	12.5653i	0.121302	+	0.531457i
$560$	3.20397	−	1.23504i	0.135393	−	0.0521901i
$561$	0.433590	−	1.89968i	0.0183062	−	0.0802047i
$562$	−14.0150	+	24.4411i	−0.591185	+	1.03099i
$563$	16.5135	+	2.48902i	0.695963	+	0.104900i	0.487490	−	0.873129i	$-0.337913\pi$
$563$	16.5135	+	2.48902i	0.695963	+	0.104900i	0.208473	+	0.978028i	$0.433151\pi$
$564$	16.8509	−	5.30708i	0.709550	−	0.223468i
$565$	−3.89431	+	4.19707i	−0.163835	+	0.176572i
$566$	21.7950	−	0.0644073i	0.916111	−	0.00270724i
$567$	18.8634	+	6.19046i	0.792189	+	0.259975i
$568$	−27.2951	−	21.3740i	−1.14528	−	0.896832i
$569$	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	$-0.0227205\pi$
$570$	3.20209	+	3.43064i	0.134121	+	0.143694i
$571$	11.5472	+	12.4449i	0.483235	+	0.520804i	0.926859	−	0.375409i	$-0.122498\pi$
$571$	11.5472	+	12.4449i	0.483235	+	0.520804i	−0.443624	+	0.896213i	$0.646307\pi$
$572$	−7.14546	+	12.5470i	−0.298766	+	0.524615i
$573$	−1.25647	−	1.00200i	−0.0524899	−	0.0418593i
$574$	27.4779	+	6.70519i	1.14690	+	0.279869i
$575$	−18.6848	+	14.9006i	−0.779208	+	0.621398i
$576$	1.68826	−	3.04770i	0.0703443	−	0.126987i
$577$	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	$0.493917\pi$
$578$	−22.6985	+	7.07508i	−0.944132	+	0.294284i
$579$	−3.15138	−	8.02957i	−0.130967	−	0.333698i
$580$	2.26281	+	1.78275i	0.0939579	+	0.0740247i
$581$	16.6383	+	2.81325i	0.690271	+	0.116713i
$582$	17.7982	+	4.00702i	0.737758	+	0.166096i
$583$	15.8599	+	1.18854i	0.656850	+	0.0492241i
$584$	10.9261	−	16.3349i	0.452124	−	0.675941i
$585$	−0.300471	−	0.204858i	−0.0124230	−	0.00846984i
$586$	−2.02209	+	0.800514i	−0.0835316	+	0.0330689i
$587$	0.140687			0.00580676			0.00290338	−	0.999996i	$-0.499076\pi$
$587$	0.140687			0.00580676			0.00290338	+	0.999996i	$0.499076\pi$
$588$	8.81084	−	20.6158i	0.363353	−	0.850180i
$589$	16.3622			0.674194
$590$	1.04079	−	0.412034i	0.0428487	−	0.0169632i
$591$	5.86397	+	3.99799i	0.241212	+	0.164455i
$592$	−12.4590	+	32.8828i	−0.512063	+	1.35147i
$593$	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	$0.448362\pi$
$594$	−21.2930	−	4.79383i	−0.873663	−	0.196693i
$595$	0.142217	−	0.344121i	0.00583033	−	0.0141076i
$596$	−3.46445	+	4.39735i	−0.141909	+	0.180122i
$597$	9.79590	+	24.9595i	0.400920	+	1.02153i
$598$	−16.9655	+	5.28811i	−0.693770	+	0.216247i
$599$	−0.952438	−	0.373804i	−0.0389156	−	0.0152732i	0.345803	−	0.938307i	$-0.387606\pi$
$599$	−0.952438	−	0.373804i	−0.0389156	−	0.0152732i	−0.384719	+	0.923034i	$0.625702\pi$
$600$	−8.28241	−	20.5652i	−0.338128	−	0.839573i
$601$	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	$0.0811562\pi$
$602$	7.87698	+	17.0021i	0.321042	+	0.692954i
$603$	−0.347036	−	0.276752i	−0.0141324	−	0.0112702i
$604$	−16.1677	−	9.20744i	−0.657854	−	0.374646i
$605$	−0.690920	−	0.744635i	−0.0280899	−	0.0302737i
$606$	−22.9491	−	24.5871i	−0.932243	−	0.998783i
$607$	−2.38773	+	4.13568i	−0.0969151	+	0.167862i	−0.910406	−	0.413715i	$-0.864231\pi$
$607$	−2.38773	+	4.13568i	−0.0969151	+	0.167862i	0.813491	+	0.581577i	$0.197564\pi$
$608$	7.51774	−	35.3362i	0.304885	−	1.43307i
$609$	18.6457	−	2.46994i	0.755564	−	0.100087i
$610$	−3.15153	+	0.00931322i	−0.127602	+	0.000377081i
$611$	−9.65576	+	10.4064i	−0.390630	+	0.420999i
$612$	−0.113492	−	0.360355i	−0.00458763	−	0.0145665i
$613$	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	$0.504875\pi$
$614$	−9.00597	+	15.7058i	−0.363451	+	0.633834i
$615$	−0.874003	+	3.82926i	−0.0352432	+	0.154410i
$616$	−6.36857	+	20.0030i	−0.256597	+	0.805944i
$617$	−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	$-0.265813\pi$
$618$	18.5848	+	5.67256i	0.747590	+	0.228184i
$619$	−12.9733	−	22.4704i	−0.521440	−	0.903160i	−0.999689	−	0.0249362i	$-0.992062\pi$
$619$	−12.9733	−	22.4704i	−0.521440	−	0.903160i	0.478249	−	0.878224i	$-0.341272\pi$
$620$	1.55120	+	0.598245i	0.0622976	+	0.0240261i
$621$	−15.1319	−	22.1944i	−0.607221	−	0.890630i
$622$	5.73387	+	2.74044i	0.229907	+	0.109882i
$623$	27.7536	+	22.9573i	1.11193	+	0.919767i
$624$	−0.194862	−	16.4843i	−0.00780072	−	0.659899i
$625$	22.3909	+	6.90669i	0.895638	+	0.276268i
$626$	2.95740	−	20.0224i	0.118201	−	0.800255i
$627$	−28.6094	+	2.14398i	−1.14255	+	0.0856222i
$628$	16.2495	−	17.7217i	0.648425	−	0.707173i
$629$	1.65445	+	3.43549i	0.0659671	+	0.136982i
$630$	−0.489226	−	0.200495i	−0.0194912	−	0.00798791i
$631$	8.78688	−	18.2461i	0.349800	−	0.726367i	−0.649626	−	0.760254i	$-0.725074\pi$
$631$	8.78688	−	18.2461i	0.349800	−	0.726367i	0.999426	+	0.0338871i	$0.0107887\pi$
$632$	−16.7813	−	24.1509i	−0.667525	−	0.960670i
$633$	−0.104541	−	0.338912i	−0.00415511	−	0.0134706i
$634$	8.47802	−	21.7908i	0.336705	−	0.865422i
$635$	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
$640$	2.00469	−	3.07513i	0.0792423	−	0.121555i
$641$	−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	$0.586719\pi$
$642$	1.09124	+	7.09749i	0.0430676	+	0.280116i
$643$	19.8762	+	9.57187i	0.783841	+	0.377478i	0.782603	−	0.622521i	$-0.213892\pi$
$643$	19.8762	+	9.57187i	0.783841	+	0.377478i	0.00123806	+	0.999999i	$0.499606\pi$
$644$	−22.5279	+	12.6488i	−0.887723	+	0.498433i
$645$	−2.34442	+	1.12901i	−0.0923114	+	0.0444548i
$646$	−2.21638	−	3.23029i	−0.0872024	−	0.127094i
$647$	−0.839488	−	11.2022i	−0.0330037	−	0.440404i	−0.989089	−	0.147316i	$-0.952936\pi$
$647$	−0.839488	−	11.2022i	−0.0330037	−	0.440404i	0.956086	−	0.293087i	$-0.0946826\pi$
$648$	20.2248	−	6.43543i	0.794505	−	0.252808i
$649$	−2.01711	+	6.53931i	−0.0791785	+	0.256690i
$650$	13.9610	+	11.0662i	0.547595	+	0.434051i
$651$	9.86287	−	4.53406i	0.386556	−	0.177704i
$652$	−20.9532	−	4.65230i	−0.820589	−	0.182198i
$653$	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	$0.0914796\pi$
$654$	−30.9358	−	20.9580i	−1.20968	−	0.819523i
$655$	4.96363	−	2.86575i	0.193945	−	0.111974i
$656$	28.0143	−	11.3788i	1.09377	−	0.444266i
$657$	−2.95008	+	0.673336i	−0.115093	+	0.0262693i
$658$	−10.5855	+	17.7178i	−0.412667	+	0.690713i
$659$	16.8638	+	3.84906i	0.656921	+	0.149938i	0.537972	−	0.842962i	$-0.319190\pi$
$659$	16.8638	+	3.84906i	0.656921	+	0.149938i	0.118949	+	0.992900i	$0.462048\pi$
$660$	−2.79066	−	0.842775i	−0.108626	−	0.0328050i
$661$	−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	$0.749396\pi$
$662$	32.9436	−	2.56671i	1.28039	−	0.0997578i
$663$	−1.31044	−	1.21591i	−0.0508931	−	0.0472219i
$664$	16.1830	−	7.97083i	0.628023	−	0.309328i
$665$	−5.45883	−	0.507485i	−0.211684	−	0.0196794i
$666$	4.87123	−	2.36362i	0.188756	−	0.0915884i
$667$	−18.7709	−	10.8374i	−0.726810	−	0.419624i
$668$	−39.6074	−	26.6624i	−1.53246	−	1.03160i
$669$	−19.5806	+	18.1681i	−0.757028	+	0.702419i
$670$	−0.343767	−	0.317084i	−0.0132809	−	0.0122500i
$671$	12.0127	−	15.0635i	0.463747	−	0.581520i
$672$	−5.26027	−	23.3832i	−0.202919	−	0.902028i
$673$	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	$0.699443\pi$
$674$	3.42667	−	47.6134i	0.131990	−	1.83400i
$675$	−9.83826	+	25.0675i	−0.378675	+	0.964848i
$676$	−6.44180	−	11.0068i	−0.247762	−	0.423338i
$677$	−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	$0.447270\pi$
$678$	25.0091	+	31.1710i	0.960470	+	1.19712i
$679$	−18.6454	+	10.3244i	−0.715545	+	0.396216i
$680$	−0.0920136	−	0.387279i	−0.00352856	−	0.0148515i
$681$	1.68209	−	22.4459i	0.0644579	−	0.860131i
$682$	−8.78729	+	5.10802i	−0.336483	+	0.195596i
$683$	−2.45241	+	3.59702i	−0.0938387	+	0.137636i	−0.870287	−	0.492545i	$-0.836067\pi$
$683$	−2.45241	+	3.59702i	−0.0938387	+	0.137636i	0.776448	+	0.630181i	$0.217019\pi$
$684$	−4.57749	+	3.16067i	−0.175025	+	0.120851i
$685$			3.35605i			0.128228i
$686$	8.31990	+	24.8350i	0.317655	+	0.948206i
$687$			22.6883i			0.865613i
$688$	17.4653	+	9.81020i	0.665859	+	0.374010i
$689$	8.21947	−	12.0558i	0.313137	−	0.459288i
$690$	−1.80306	−	3.10178i	−0.0686412	−	0.118083i
$691$	3.68409	−	49.1608i	0.140149	−	1.87016i	−0.276388	−	0.961046i	$-0.589137\pi$
$691$	3.68409	−	49.1608i	0.140149	−	1.87016i	0.416537	−	0.909119i	$-0.363243\pi$
$692$	0.0144574	+	2.44612i	0.000549588	+	0.0929875i
$693$	2.82774	−	1.56579i	0.107417	−	0.0594795i
$694$	−37.8529	+	30.3701i	−1.43688	+	1.15283i
$695$	−4.34156	+	1.70394i	−0.164685	+	0.0646341i
$696$	14.6178	−	13.8066i	0.554088	−	0.523336i
$697$	1.19789	−	3.05218i	0.0453735	−	0.115610i
$698$	−17.5668	−	1.26426i	−0.664913	−	0.0478528i
$699$	−26.5497	−	33.2922i	−1.00420	−	1.25923i
$700$	23.1991	+	11.5167i	0.876843	+	0.435292i
$701$	−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	$0.224226\pi$
$702$	−13.5762	+	14.7186i	−0.512400	+	0.555519i
$703$	41.1557	−	38.1869i	1.55222	−	1.44025i
$704$	6.99400	+	21.3241i	0.263596	+	0.803682i
$705$	−2.48211	−	1.43305i	−0.0934818	−	0.0539717i
$706$	−3.01145	−	6.20636i	−0.113338	−	0.233580i
$707$	39.1230	+	3.63710i	1.47137	+	0.136787i
$708$	−1.78360	−	7.60695i	−0.0670318	−	0.285887i
$709$	−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	$0.873343\pi$
$710$	0.436869	+	5.60720i	0.0163954	+	0.210435i
$711$	−0.674897	+	4.47765i	−0.0253106	+	0.167925i
$712$	38.4213	+	2.53696i	1.43990	+	0.0950767i
$713$	−12.1956	−	2.78357i	−0.456730	−	0.104246i
$714$	−2.23113	−	1.33299i	−0.0834978	−	0.0498859i
$715$	2.28371	−	0.521242i	0.0854059	−	0.0194933i
$716$	31.2717	+	2.15771i	1.16868	+	0.0806373i
$717$	−11.8928	+	6.86633i	−0.444146	+	0.256428i
$718$	−17.5194	+	25.8601i	−0.653818	+	0.965090i
$719$	−29.1133	+	19.8491i	−1.08574	+	0.740246i	−0.967534	−	0.252743i	$-0.918667\pi$
$719$	−29.1133	+	19.8491i	−1.08574	+	0.740246i	−0.118208	+	0.992989i	$0.537715\pi$
$720$	−0.549525	+	0.132278i	−0.0204796	+	0.00492972i
$721$	−20.6254	+	9.48168i	−0.768128	+	0.353116i
$722$	−19.1387	+	24.1452i	−0.712270	+	0.898593i
$723$	−14.4074	+	46.7075i	−0.535815	+	1.73707i
$724$	−51.0983	+	4.13313i	−1.89905	+	0.153607i
$725$	1.62380	+	21.6680i	0.0603062	+	0.804731i
$726$	−5.84642	+	4.01138i	−0.216981	+	0.148876i
$727$	−30.5126	+	14.6941i	−1.13165	+	0.544974i	−0.903473	−	0.428645i	$-0.858991\pi$
$727$	−30.5126	+	14.6941i	−1.13165	+	0.544974i	−0.228178	+	0.973620i	$0.573277\pi$
$728$	12.9714	+	14.2356i	0.480750	+	0.527606i
$729$	−26.7578	−	12.8859i	−0.991031	−	0.477256i
$730$	−3.15115	+	0.484487i	−0.116629	+	0.0179317i
$731$	2.07571	−	0.640273i	0.0767730	−	0.0236813i
$732$	−3.14997	+	21.7710i	−0.116426	+	0.804678i
$733$	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
$738$	−4.33893	−	1.68812i	−0.159718	−	0.0621407i
$739$	−2.38810	−	7.74202i	−0.0878476	−	0.284795i	0.900980	−	0.433861i	$-0.142849\pi$
$739$	−2.38810	−	7.74202i	−0.0878476	−	0.284795i	−0.988827	+	0.149067i	$0.952373\pi$
$740$	5.29792	−	2.11550i	0.194755	−	0.0777673i
$741$	−11.4201	+	23.7141i	−0.419528	+	0.871159i
$742$	8.04442	−	19.6291i	0.295320	−	0.720608i
$743$	−3.74567	−	7.77796i	−0.137415	−	0.285346i	0.820893	−	0.571082i	$-0.193476\pi$
$743$	−3.74567	−	7.77796i	−0.137415	−	0.285346i	−0.958308	+	0.285736i	$0.907762\pi$
$744$	5.71299	−	10.1009i	0.209448	−	0.370319i
$745$	0.905648	−	0.0678689i	0.0331804	−	0.00248653i
$746$	32.1708	+	4.75179i	1.17786	+	0.173975i
$747$	−2.65424	−	0.818724i	−0.0971135	−	0.0299555i
$748$	2.19874	+	1.04290i	0.0803941	+	0.0381320i
$749$	−6.46414	−	5.34703i	−0.236195	−	0.195376i
$750$	−3.13531	+	6.56005i	−0.114485	+	0.239539i
$751$	−19.7777	−	29.0085i	−0.721697	−	1.05854i	−0.995314	−	0.0966964i	$-0.969172\pi$
$751$	−19.7777	−	29.0085i	−0.721697	−	1.05854i	0.273617	−	0.961839i	$-0.411780\pi$
$752$	1.90882	+	21.9815i	0.0696075	+	0.801582i
$753$	15.5976	+	27.0158i	0.568407	+	0.984509i
$754$	−4.71672	+	15.4532i	−0.171773	+	0.562773i
$755$	0.671659	+	2.94273i	0.0244442	+	0.107097i
$756$	−14.8572	+	25.0353i	−0.540350	+	0.910526i
$757$	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	$0.0664549\pi$
$758$	−15.8665	−	9.09814i	−0.576299	−	0.330459i
$759$	21.6888	+	3.26906i	0.787254	+	0.118659i
$760$	−5.04951	+	2.97533i	−0.183165	+	0.107927i
$761$	−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	$0.293177\pi$
$762$	−0.0471154	−	15.9435i	−0.00170681	−	0.577573i
$763$	43.2752	−	5.73253i	1.56667	−	0.207532i
$764$	1.56179	−	1.26066i	0.0565036	−	0.0456091i
$765$	−0.0306457	+	0.0530799i	−0.00110800	+	0.00191911i
$766$	15.8633	−	14.8065i	0.573166	−	0.534981i

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)

\(f(q)\)	\(=\)	\(q+(-0.520558 - 1.31492i) q^{2} +(1.32314 + 0.902103i) q^{3} +(-1.45804 + 1.36899i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(0.497422 - 2.20942i) q^{6} +(1.28165 + 2.31460i) q^{7} +(2.55910 + 1.20457i) q^{8} +(-0.159109 - 0.405403i) q^{9} +O(q^{10})\)	\(q+(-0.520558 - 1.31492i) q^{2} +(1.32314 + 0.902103i) q^{3} +(-1.45804 + 1.36899i) q^{4} +(0.323554 + 0.0242470i) q^{5} +(0.497422 - 2.20942i) q^{6} +(1.28165 + 2.31460i) q^{7} +(2.55910 + 1.20457i) q^{8} +(-0.159109 - 0.405403i) q^{9} +(-0.136546 - 0.438070i) q^{10} +(2.61131 + 1.02486i) q^{11} +(-3.16416 + 0.496063i) q^{12} +(2.01211 - 1.60461i) q^{13} +(2.37634 - 2.89016i) q^{14} +(0.406234 + 0.323961i) q^{15} +(0.251751 - 3.99207i) q^{16} +(-0.295026 - 0.317962i) q^{17} +(-0.450248 + 0.420252i) q^{18} +(-3.19321 + 5.53080i) q^{19} +(-0.504947 + 0.407588i) q^{20} +(-0.392197 + 4.21872i) q^{21} +(-0.0117235 - 3.96716i) q^{22} +(3.32097 - 3.57916i) q^{23} +(2.29941 + 3.90239i) q^{24} +(-4.84006 - 0.729521i) q^{25} +(-3.15735 - 1.81048i) q^{26} +(1.22423 - 5.36370i) q^{27} +(-5.03735 - 1.62021i) q^{28} +(-0.987821 - 4.32793i) q^{29} +(0.214515 - 0.702806i) q^{30} +(-1.28102 - 2.21879i) q^{31} +(-5.38031 + 1.74707i) q^{32} +(2.53060 + 3.71170i) q^{33} +(-0.264517 + 0.553454i) q^{34} +(0.358561 + 0.779973i) q^{35} +(0.786978 + 0.373275i) q^{36} +(-8.40044 - 2.59119i) q^{37} +(8.93481 + 1.31972i) q^{38} +(4.10983 - 0.307989i) q^{39} +(0.798800 + 0.451793i) q^{40} +(3.27984 + 6.81065i) q^{41} +(5.75145 - 1.68038i) q^{42} +(-2.17288 + 4.51203i) q^{43} +(-5.21041 + 2.08056i) q^{44} +(-0.0416505 - 0.135028i) q^{45} +(-6.43507 - 2.50366i) 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} +(-0.737052 + 5.09413i) q^{52} +(5.41768 - 1.67113i) q^{53} +(-7.69012 + 1.18235i) q^{54} +(0.820048 + 0.394914i) q^{55} +(0.491791 + 7.46714i) q^{56} +(-9.21441 + 4.43743i) q^{57} +(-5.17667 + 3.55185i) q^{58} +(0.182304 + 2.43268i) q^{59} +(-1.03580 + 0.0837817i) q^{60} +(2.02445 - 6.56311i) q^{61} +(-2.25069 + 2.83945i) q^{62} +(0.734423 - 0.887859i) q^{63} +(5.09803 + 6.16523i) q^{64} +(0.689933 - 0.470389i) q^{65} +(3.56328 - 5.25969i) q^{66} +(0.882664 - 0.509607i) q^{67} +(0.865446 + 0.0597147i) q^{68} +(7.62288 - 1.73987i) q^{69} +(0.838951 - 0.877501i) q^{70} +(-11.9497 - 2.72743i) q^{71} +(0.0811594 - 1.22913i) q^{72} +(1.03556 - 6.87048i) q^{73} +(0.965703 + 12.3948i) q^{74} +(-5.74597 - 5.33149i) q^{75} +(-2.91577 - 12.4356i) q^{76} +(0.974644 + 7.35764i) q^{77} +(-2.54439 - 5.24378i) q^{78} +(-9.00457 - 5.19879i) q^{79} +(0.178251 - 1.28554i) q^{80} +(5.50068 - 5.10389i) q^{81} +(7.24813 - 7.85807i) q^{82} +(3.97658 - 4.98647i) q^{83} +(-5.20354 - 6.68797i) q^{84} +(-0.0877471 - 0.110031i) q^{85} +(7.06408 + 0.508392i) q^{86} +(2.59721 - 6.61758i) q^{87} +(5.44809 + 5.76823i) q^{88} +(12.6725 - 4.97359i) q^{89} +(-0.155869 + 0.125057i) q^{90} +(6.29285 + 2.60068i) q^{91} +(0.0577139 + 9.76491i) q^{92} +(0.306607 - 4.09138i) q^{93} +(3.92038 + 6.74420i) q^{94} +(-1.16728 + 1.71208i) q^{95} +(-8.69495 - 2.54197i) q^{96} +8.05557i q^{97} +(9.73520 + 1.79610i) 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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