LMFDB - Embedded newform 225.2.q.a.106.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.14
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.160864 + 0.0341926i) q^{2} +(1.48677 + 0.888545i) q^{3} +(-1.80238 - 0.802473i) q^{4} +(0.278910 - 2.21861i) q^{5} +(0.208786 + 0.193771i) q^{6} +(2.06663 - 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(1.42098 + 2.64213i) q^{9} +O(q^{10})$	\(q+(0.160864 + 0.0341926i) q^{2} +(1.48677 + 0.888545i) q^{3} +(-1.80238 - 0.802473i) q^{4} +(0.278910 - 2.21861i) q^{5} +(0.208786 + 0.193771i) q^{6} +(2.06663 - 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(1.42098 + 2.64213i) q^{9} +(0.120726 - 0.347356i) q^{10} +(0.350384 + 0.0744764i) q^{11} +(-1.96670 - 2.79459i) q^{12} +(-1.80589 + 0.383854i) q^{13} +(0.454839 - 0.505150i) q^{14} +(2.38601 - 3.05073i) q^{15} +(2.56843 + 2.85253i) q^{16} +(3.22940 + 2.34629i) q^{17} +(0.138242 + 0.473609i) q^{18} +(-0.0599095 - 0.0435268i) q^{19} +(-2.28307 + 3.77496i) q^{20} +(6.25317 - 3.48562i) q^{21} +(0.0538175 + 0.0239611i) q^{22} +(-2.92946 + 3.25349i) q^{23} +(-0.444658 - 1.04067i) q^{24} +(-4.84442 - 1.23758i) q^{25} -0.303627 q^{26} +(-0.234983 + 5.19084i) q^{27} +(-6.59733 + 4.79324i) q^{28} +(0.679330 + 6.46339i) q^{29} +(0.488134 - 0.409168i) q^{30} +(0.566578 - 5.39063i) q^{31} +(0.969013 + 1.67838i) q^{32} +(0.454765 + 0.422061i) q^{33} +(0.439267 + 0.487855i) q^{34} +(-7.36512 - 5.58341i) q^{35} +(-0.440908 - 5.90242i) q^{36} +(2.37480 - 7.30889i) q^{37} +(-0.00814896 - 0.00905033i) q^{38} +(-3.02602 - 1.03391i) q^{39} +(-0.999482 + 1.06563i) q^{40} +(-4.60199 + 0.978183i) q^{41} +(1.12509 - 0.346897i) q^{42} +(1.55061 - 2.68574i) q^{43} +(-0.571760 - 0.415408i) q^{44} +(6.25816 - 2.41567i) q^{45} +(-0.582489 + 0.423203i) q^{46} +(1.35210 + 12.8643i) q^{47} +(1.28406 + 6.52322i) q^{48} +(-5.04195 - 8.73292i) q^{49} +(-0.736974 - 0.364726i) q^{50} +(2.71659 + 6.35787i) q^{51} +(3.56294 + 0.757326i) q^{52} +(1.53179 - 1.11291i) q^{53} +(-0.215288 + 0.826982i) q^{54} +(0.262959 - 0.756591i) q^{55} +(-2.46712 + 1.09843i) q^{56} +(-0.0503961 - 0.117947i) q^{57} +(-0.111721 + 1.06295i) q^{58} +(-4.84033 + 1.02884i) q^{59} +(-6.74863 + 3.58388i) q^{60} +(-8.90148 - 1.89207i) q^{61} +(0.275461 - 0.847783i) q^{62} +(12.3942 + 0.373904i) q^{63} +(-2.27380 - 6.99805i) q^{64} +(0.347939 + 4.11362i) q^{65} +(0.0587237 + 0.0834439i) q^{66} +(-1.50633 + 14.3317i) q^{67} +(-3.93777 - 6.82042i) q^{68} +(-7.24631 + 2.23424i) q^{69} +(-0.993869 - 1.15000i) q^{70} +(10.8652 - 7.89400i) q^{71} +(0.263580 - 1.94234i) q^{72} +(4.15877 + 12.7994i) q^{73} +(0.631930 - 1.09453i) q^{74} +(-6.10289 - 6.14449i) q^{75} +(0.0730507 + 0.126528i) q^{76} +(0.990704 - 1.10029i) q^{77} +(-0.451424 - 0.269786i) q^{78} +(0.626261 + 5.95848i) q^{79} +(7.04499 - 4.90273i) q^{80} +(-4.96166 + 7.50879i) q^{81} -0.773739 q^{82} +(-2.63648 + 1.17384i) q^{83} +(-14.0677 + 1.26443i) q^{84} +(6.10621 - 6.51035i) q^{85} +(0.341269 - 0.379018i) q^{86} +(-4.73301 + 10.2132i) q^{87} +(-0.156609 - 0.173932i) q^{88} +(2.21408 + 6.81425i) q^{89} +(1.08931 - 0.174610i) q^{90} +(-2.35810 + 7.25750i) q^{91} +(7.89085 - 3.51323i) q^{92} +(5.63219 - 7.51120i) q^{93} +(-0.222362 + 2.11564i) q^{94} +(-0.113278 + 0.120775i) q^{95} +(-0.0506157 + 3.35638i) q^{96} +(-1.10503 - 10.5137i) q^{97} +(-0.512465 - 1.57721i) q^{98} +(0.301111 + 1.03159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.160864	+	0.0341926i	0.113748	+	0.0241778i	0.264434	−	0.964404i	$-0.414815\pi$
$2$	0.160864	+	0.0341926i	0.113748	+	0.0241778i	−0.150686	+	0.988582i	$0.548148\pi$
$3$	1.48677	+	0.888545i	0.858388	+	0.513002i
$3$	1.48677	+	0.888545i	0.858388	+	0.513002i
$4$	−1.80238	−	0.802473i	−0.901191	−	0.401236i
$5$	0.278910	−	2.21861i	0.124733	−	0.992190i
$5$	0.278910	−	2.21861i	0.124733	−	0.992190i
$6$	0.208786	+	0.193771i	0.0852364	+	0.0791067i
$7$	2.06663	−	3.57951i	0.781114	−	1.35293i	−0.150179	−	0.988659i	$-0.547985\pi$
$7$	2.06663	−	3.57951i	0.781114	−	1.35293i	0.931293	−	0.364271i	$-0.118682\pi$
$8$	−0.528597	−	0.384048i	−0.186887	−	0.135782i
$9$	1.42098	+	2.64213i	0.473658	+	0.880709i
$10$	0.120726	−	0.347356i	0.0381771	−	0.109844i
$11$	0.350384	+	0.0744764i	0.105645	+	0.0224555i	0.260431	−	0.965493i	$-0.416135\pi$
$11$	0.350384	+	0.0744764i	0.105645	+	0.0224555i	−0.154786	+	0.987948i	$0.549469\pi$
$12$	−1.96670	−	2.79459i	−0.567737	−	0.806729i
$13$	−1.80589	+	0.383854i	−0.500864	+	0.106462i	−0.451414	−	0.892315i	$-0.649080\pi$
$13$	−1.80589	+	0.383854i	−0.500864	+	0.106462i	−0.0494500	+	0.998777i	$0.515747\pi$
$14$	0.454839	−	0.505150i	0.121561	−	0.135007i
$15$	2.38601	−	3.05073i	0.616064	−	0.787696i
$16$	2.56843	+	2.85253i	0.642107	+	0.713132i
$17$	3.22940	+	2.34629i	0.783244	+	0.569060i	0.905951	−	0.423383i	$-0.139157\pi$
$17$	3.22940	+	2.34629i	0.783244	+	0.569060i	−0.122707	+	0.992443i	$0.539157\pi$
$18$	0.138242	+	0.473609i	0.0325840	+	0.111631i
$19$	−0.0599095	−	0.0435268i	−0.0137442	−	0.00998573i	0.580892	−	0.813981i	$-0.302704\pi$
$19$	−0.0599095	−	0.0435268i	−0.0137442	−	0.00998573i	−0.594636	+	0.803995i	$0.702704\pi$
$20$	−2.28307	+	3.77496i	−0.510511	+	0.844106i
$21$	6.25317	−	3.48562i	1.36455	−	0.760625i
$22$	0.0538175	+	0.0239611i	0.0114739	+	0.00510852i
$23$	−2.92946	+	3.25349i	−0.610834	+	0.678400i	−0.966634	−	0.256162i	$-0.917542\pi$
$23$	−2.92946	+	3.25349i	−0.610834	+	0.678400i	0.355799	+	0.934562i	$0.384209\pi$
$24$	−0.444658	−	1.04067i	−0.0907655	−	0.212427i
$25$	−4.84442	−	1.23758i	−0.968884	−	0.247517i
$26$	−0.303627			−0.0595462
$27$	−0.234983	+	5.19084i	−0.0452225	+	0.998977i
$28$	−6.59733	+	4.79324i	−1.24678	+	0.905837i
$29$	0.679330	+	6.46339i	0.126148	+	1.20022i	0.856132	+	0.516757i	$0.172861\pi$
$29$	0.679330	+	6.46339i	0.126148	+	1.20022i	−0.729984	+	0.683465i	$0.760472\pi$
$30$	0.488134	−	0.409168i	0.0891207	−	0.0747035i
$31$	0.566578	−	5.39063i	0.101760	−	0.968186i	−0.817871	−	0.575402i	$-0.804846\pi$
$31$	0.566578	−	5.39063i	0.101760	−	0.968186i	0.919631	−	0.392783i	$-0.128488\pi$
$32$	0.969013	+	1.67838i	0.171299	+	0.296698i
$33$	0.454765	+	0.422061i	0.0791644	+	0.0734714i
$34$	0.439267	+	0.487855i	0.0753336	+	0.0836664i
$35$	−7.36512	−	5.58341i	−1.24493	−	0.943768i
$36$	−0.440908	−	5.90242i	−0.0734847	−	0.983736i
$37$	2.37480	−	7.30889i	0.390415	−	1.20157i	−0.542060	−	0.840340i	$-0.682355\pi$
$37$	2.37480	−	7.30889i	0.390415	−	1.20157i	0.932475	−	0.361235i	$-0.117645\pi$
$38$	−0.00814896	−	0.00905033i	−0.00132194	−	0.00146816i
$39$	−3.02602	−	1.03391i	−0.484550	−	0.165558i
$40$	−0.999482	+	1.06563i	−0.158032	+	0.168491i
$41$	−4.60199	+	0.978183i	−0.718710	+	0.152767i	−0.552727	−	0.833362i	$-0.686413\pi$
$41$	−4.60199	+	0.978183i	−0.718710	+	0.152767i	−0.165983	+	0.986129i	$0.553080\pi$
$42$	1.12509	−	0.346897i	0.173605	−	0.0535274i
$43$	1.55061	−	2.68574i	0.236466	−	0.409571i	−0.723232	−	0.690605i	$-0.757344\pi$
$43$	1.55061	−	2.68574i	0.236466	−	0.409571i	0.959698	+	0.281034i	$0.0906775\pi$
$44$	−0.571760	−	0.415408i	−0.0861961	−	0.0626252i
$45$	6.25816	−	2.41567i	0.932911	−	0.360106i
$46$	−0.582489	+	0.423203i	−0.0858833	+	0.0623979i
$47$	1.35210	+	12.8643i	0.197224	+	1.87646i	0.428463	+	0.903560i	$0.359055\pi$
$47$	1.35210	+	12.8643i	0.197224	+	1.87646i	−0.231239	+	0.972897i	$0.574278\pi$
$48$	1.28406	+	6.52322i	0.185339	+	0.941545i
$49$	−5.04195	−	8.73292i	−0.720279	−	1.24756i
$50$	−0.736974	−	0.364726i	−0.104224	−	0.0515800i
$51$	2.71659	+	6.35787i	0.380398	+	0.890280i
$52$	3.56294	+	0.757326i	0.494091	+	0.105022i
$53$	1.53179	−	1.11291i	0.210408	−	0.152870i	−0.477590	−	0.878583i	$-0.658490\pi$
$53$	1.53179	−	1.11291i	0.210408	−	0.152870i	0.687998	+	0.725712i	$0.258490\pi$
$54$	−0.215288	+	0.826982i	−0.0292971	+	0.112538i
$55$	0.262959	−	0.756591i	0.0354574	−	0.102019i
$56$	−2.46712	+	1.09843i	−0.329683	+	0.146784i
$57$	−0.0503961	−	0.117947i	−0.00667513	−	0.0156224i
$58$	−0.111721	+	1.06295i	−0.0146697	+	0.139573i
$59$	−4.84033	+	1.02884i	−0.630157	+	0.133944i	−0.511909	−	0.859040i	$-0.671061\pi$
$59$	−4.84033	+	1.02884i	−0.630157	+	0.133944i	−0.118249	+	0.992984i	$0.537728\pi$
$60$	−6.74863	+	3.58388i	−0.871244	+	0.462678i
$61$	−8.90148	−	1.89207i	−1.13972	−	0.242255i	−0.400876	−	0.916133i	$-0.631294\pi$
$61$	−8.90148	−	1.89207i	−1.13972	−	0.242255i	−0.738843	+	0.673878i	$0.764627\pi$
$62$	0.275461	−	0.847783i	0.0349836	−	0.107669i
$63$	12.3942	+	0.373904i	1.56152	+	0.0471075i
$64$	−2.27380	−	6.99805i	−0.284226	−	0.874756i
$65$	0.347939	+	4.11362i	0.0431565	+	0.510232i
$66$	0.0587237	+	0.0834439i	0.00722839	+	0.0102712i
$67$	−1.50633	+	14.3317i	−0.184027	+	1.75090i	0.379857	+	0.925045i	$0.375973\pi$
$67$	−1.50633	+	14.3317i	−0.184027	+	1.75090i	−0.563884	+	0.825854i	$0.690693\pi$
$68$	−3.93777	−	6.82042i	−0.477525	−	0.827098i
$69$	−7.24631	+	2.23424i	−0.872353	+	0.268971i
$70$	−0.993869	−	1.15000i	−0.118790	−	0.137451i
$71$	10.8652	−	7.89400i	1.28946	−	0.936845i	0.289662	−	0.957129i	$-0.406457\pi$
$71$	10.8652	−	7.89400i	1.28946	−	0.936845i	0.999794	+	0.0202841i	$0.00645707\pi$
$72$	0.263580	−	1.94234i	0.0310632	−	0.228907i
$73$	4.15877	+	12.7994i	0.486747	+	1.49805i	0.829435	+	0.558603i	$0.188663\pi$
$73$	4.15877	+	12.7994i	0.486747	+	1.49805i	−0.342688	+	0.939449i	$0.611337\pi$
$74$	0.631930	−	1.09453i	0.0734603	−	0.127237i
$75$	−6.10289	−	6.14449i	−0.704701	−	0.709504i
$76$	0.0730507	+	0.126528i	0.00837950	+	0.0145137i
$77$	0.990704	−	1.10029i	0.112901	−	0.125390i
$78$	−0.451424	−	0.269786i	−0.0511137	−	0.0305473i
$79$	0.626261	+	5.95848i	0.0704599	+	0.670381i	0.971564	+	0.236778i	$0.0760913\pi$
$79$	0.626261	+	5.95848i	0.0704599	+	0.670381i	−0.901104	+	0.433603i	$0.857242\pi$
$80$	7.04499	−	4.90273i	0.787654	−	0.548141i
$81$	−4.96166	+	7.50879i	−0.551295	+	0.834310i
$82$	−0.773739			−0.0854452
$83$	−2.63648	+	1.17384i	−0.289391	+	0.128845i	−0.546298	−	0.837591i	$-0.683963\pi$
$83$	−2.63648	+	1.17384i	−0.289391	+	0.128845i	0.256907	+	0.966436i	$0.417297\pi$
$84$	−14.0677	+	1.26443i	−1.53491	+	0.137960i
$85$	6.10621	−	6.51035i	0.662312	−	0.706147i
$86$	0.341269	−	0.379018i	0.0368000	−	0.0408705i
$87$	−4.73301	+	10.2132i	−0.507432	+	1.09497i
$88$	−0.156609	−	0.173932i	−0.0166946	−	0.0185412i
$89$	2.21408	+	6.81425i	0.234692	+	0.722309i	0.997162	+	0.0752851i	$0.0239867\pi$
$89$	2.21408	+	6.81425i	0.234692	+	0.722309i	−0.762470	+	0.647024i	$0.776013\pi$
$90$	1.08931	−	0.174610i	0.114823	−	0.0184055i
$91$	−2.35810	+	7.25750i	−0.247196	+	0.760792i
$92$	7.89085	−	3.51323i	0.822678	−	0.366280i
$93$	5.63219	−	7.51120i	0.584031	−	0.778875i
$94$	−0.222362	+	2.11564i	−0.0229349	+	0.218211i
$95$	−0.113278	+	0.120775i	−0.0116221	+	0.0123913i
$96$	−0.0506157	+	3.35638i	−0.00516594	+	0.342559i
$97$	−1.10503	−	10.5137i	−0.112199	−	1.06750i	−0.895256	−	0.445552i	$-0.853008\pi$
$97$	−1.10503	−	10.5137i	−0.112199	−	1.06750i	0.783057	−	0.621950i	$-0.213659\pi$
$98$	−0.512465	−	1.57721i	−0.0517668	−	0.159322i
$99$	0.301111	+	1.03159i	0.0302628	+	0.103678i
$100$	7.73837	+	6.11811i	0.773837	+	0.611811i
$101$	8.75862	−	15.1704i	0.871516	−	1.50951i	0.0110870	−	0.999939i	$-0.496471\pi$
$101$	8.75862	−	15.1704i	0.871516	−	1.50951i	0.860429	−	0.509571i	$-0.170196\pi$
$102$	0.219608	+	1.11564i	0.0217444	+	0.110465i
$103$	10.9302	+	4.86646i	1.07699	+	0.479506i	0.867057	−	0.498210i	$-0.166009\pi$
$103$	10.9302	+	4.86646i	1.07699	+	0.479506i	0.209932	+	0.977716i	$0.432676\pi$
$104$	1.10201	+	0.490645i	0.108061	+	0.0481117i
$105$	−5.98914	−	14.8455i	−0.584481	−	1.44877i
$106$	0.284463	−	0.126651i	0.0276295	−	0.0123014i
$107$	−8.49063			−0.820820			−0.410410	−	0.911901i	$-0.634614\pi$
$107$	−8.49063			−0.820820			−0.410410	+	0.911901i	$0.634614\pi$
$108$	4.58903	−	9.16731i	0.441580	−	0.882125i
$109$	2.49526	−	7.67961i	0.239002	−	0.735573i	−0.757563	−	0.652762i	$-0.773610\pi$
$109$	2.49526	−	7.67961i	0.239002	−	0.735573i	0.996565	−	0.0828110i	$-0.0263898\pi$
$110$	0.0681704	−	0.112717i	0.00649979	−	0.0107471i
$111$	10.0251	−	8.75653i	0.951538	−	0.831133i
$112$	15.5187	−	3.29859i	1.46638	−	0.311688i
$113$	−8.69849	+	1.84892i	−0.818285	+	0.173932i	−0.597992	−	0.801502i	$-0.704035\pi$
$113$	−8.69849	+	1.84892i	−0.818285	+	0.173932i	−0.220293	+	0.975434i	$0.570701\pi$
$114$	−0.00407400	−	0.0206965i	−0.000381565	−	0.00193840i
$115$	6.40116	+	7.40675i	0.596911	+	0.690683i
$116$	3.96228	−	12.1946i	0.367889	−	1.13224i
$117$	−3.58032	−	4.22594i	−0.331000	−	0.390689i
$118$	−0.813812			−0.0749175
$119$	15.0726	−	6.71074i	1.38170	−	0.615173i
$120$	−2.43286	+	0.696267i	−0.222089	+	0.0635602i
$121$	−9.93178	−	4.42191i	−0.902889	−	0.401992i
$122$	−1.36723	−	0.608730i	−0.123783	−	0.0551118i
$123$	−7.71126	−	2.63474i	−0.695301	−	0.237567i
$124$	−5.34702	+	9.26131i	−0.480177	+	0.831691i
$125$	−4.09687	+	10.4027i	−0.366435	+	0.930444i
$126$	1.98099	+	0.483936i	0.176480	+	0.0431125i
$127$	−1.00273	−	3.08608i	−0.0889778	−	0.273845i	0.896660	−	0.442720i	$-0.145987\pi$
$127$	−1.00273	−	3.08608i	−0.0889778	−	0.273845i	−0.985637	+	0.168875i	$0.945987\pi$
$128$	−0.531648	−	5.05830i	−0.0469915	−	0.447094i
$129$	4.69180	−	2.61529i	0.413090	−	0.230263i
$130$	−0.0846847	+	0.673628i	−0.00742734	+	0.0590811i
$131$	0.899383	−	8.55705i	0.0785794	−	0.747633i	−0.882304	−	0.470680i	$-0.844009\pi$
$131$	0.899383	−	8.55705i	0.0785794	−	0.747633i	0.960883	−	0.276953i	$-0.0893247\pi$
$132$	−0.480968	−	1.12565i	−0.0418629	−	0.0979754i
$133$	−0.279616	+	0.124493i	−0.0242458	+	0.0107949i
$134$	−0.732352	+	2.25395i	−0.0632656	+	0.194711i
$135$	11.4509	+	1.96911i	0.985535	+	0.169474i
$136$	−0.805959	−	2.48049i	−0.0691105	−	0.212700i
$137$	−3.83481	−	4.25899i	−0.327630	−	0.363870i	0.556715	−	0.830703i	$-0.312061\pi$
$137$	−3.83481	−	4.25899i	−0.327630	−	0.363870i	−0.884345	+	0.466833i	$0.845395\pi$
$138$	−1.24206	+	0.111638i	−0.105731	+	0.00950328i
$139$	11.0972	−	12.3247i	0.941256	−	1.04537i	−0.0576371	−	0.998338i	$-0.518357\pi$
$139$	11.0972	−	12.3247i	0.941256	−	1.04537i	0.998893	−	0.0470333i	$-0.0149767\pi$
$140$	8.79424	+	15.9738i	0.743249	+	1.35003i
$141$	−9.42029	+	20.3277i	−0.793331	+	1.71190i
$142$	2.01772	−	0.898349i	0.169324	−	0.0753877i
$143$	−0.661343			−0.0553043
$144$	−3.88706	+	10.8395i	−0.323922	+	0.903290i
$145$	14.5292	+	0.295542i	1.20658	+	0.0245434i
$146$	0.231350	+	2.20115i	0.0191467	+	0.182169i
$147$	0.263363	−	17.4638i	0.0217218	−	1.44039i
$148$	−10.1455	+	11.2677i	−0.833954	+	0.926200i
$149$	−3.50472	−	6.07035i	−0.287118	−	0.497302i	0.686003	−	0.727599i	$-0.259364\pi$
$149$	−3.50472	−	6.07035i	−0.287118	−	0.497302i	−0.973120	+	0.230297i	$0.926030\pi$
$150$	−0.771637	−	1.19710i	−0.0630039	−	0.0977427i
$151$	2.35416	−	4.07752i	0.191579	−	0.331824i	−0.754195	−	0.656651i	$-0.771973\pi$
$151$	2.35416	−	4.07752i	0.191579	−	0.331824i	0.945774	+	0.324827i	$0.105306\pi$
$152$	0.0149516	+	0.0460162i	0.00121273	+	0.00373241i
$153$	−1.61031	+	11.8665i	−0.130186	+	0.959350i
$154$	0.196990	−	0.143122i	0.0158739	−	0.0115331i
$155$	−11.8017	−	2.76051i	−0.947932	−	0.221730i
$156$	4.62435	+	4.29180i	0.370245	+	0.343619i
$157$	8.51816	+	14.7539i	0.679823	+	1.17749i	0.975034	+	0.222057i	$0.0712770\pi$
$157$	8.51816	+	14.7539i	0.679823	+	1.17749i	−0.295210	+	0.955432i	$0.595390\pi$
$158$	−0.102993	+	0.979915i	−0.00819370	+	0.0779579i
$159$	3.26630	−	0.293579i	0.259034	−	0.0232823i
$160$	3.99393	−	1.68174i	0.315748	−	0.132953i
$161$	5.59181	+	17.2098i	0.440696	+	1.35632i
$162$	−1.05490	+	1.03824i	−0.0828804	+	0.0815718i
$163$	0.313473	−	0.964770i	0.0245531	−	0.0755666i	−0.938029	−	0.346556i	$-0.887351\pi$
$163$	0.313473	−	0.964770i	0.0245531	−	0.0755666i	0.962582	+	0.270990i	$0.0873509\pi$
$164$	9.07951	+	1.92991i	0.708991	+	0.150701i
$165$	1.06323	−	0.891226i	0.0827720	−	0.0693819i
$166$	−0.464250	+	0.0986794i	−0.0360328	+	0.00765901i
$167$	−0.400647	+	3.81190i	−0.0310030	+	0.294974i	0.968024	+	0.250860i	$0.0807132\pi$
$167$	−0.400647	+	3.81190i	−0.0310030	+	0.294974i	−0.999026	+	0.0441142i	$0.985953\pi$
$168$	−4.64405	−	0.559030i	−0.358296	−	0.0431301i
$169$	−8.76220	+	3.90118i	−0.674015	+	0.300091i
$170$	1.20487	−	0.838491i	0.0924096	−	0.0643094i
$171$	0.0298733	−	0.220139i	0.00228447	−	0.0168344i
$172$	−4.95002	+	3.59640i	−0.377436	+	0.274223i
$173$	−21.6977	−	4.61198i	−1.64964	−	0.350642i	−0.713064	−	0.701099i	$-0.752693\pi$
$173$	−21.6977	−	4.61198i	−1.64964	−	0.350642i	−0.936579	+	0.350456i	$0.886026\pi$
$174$	−1.11058	+	1.48110i	−0.0841932	+	0.112282i
$175$	−14.4416	+	14.7830i	−1.09168	+	1.11749i
$176$	0.687489	+	1.19077i	0.0518215	+	0.0897574i
$177$	−8.11064	−	2.77120i	−0.609633	−	0.208296i
$178$	0.123169	+	1.17187i	0.00923187	+	0.0878354i
$179$	11.8426	−	8.60413i	0.885156	−	0.643103i	−0.0494548	−	0.998776i	$-0.515748\pi$
$179$	11.8426	−	8.60413i	0.885156	−	0.643103i	0.934610	+	0.355673i	$0.115748\pi$
$180$	−13.2181	−	0.668044i	−0.985219	−	0.0497930i
$181$	−13.9341	−	10.1237i	−1.03571	−	0.752489i	−0.0662678	−	0.997802i	$-0.521109\pi$
$181$	−13.9341	−	10.1237i	−1.03571	−	0.752489i	−0.969444	+	0.245313i	$0.921109\pi$
$182$	−0.627486	+	1.08684i	−0.0465123	+	0.0805617i
$183$	−11.5533	−	10.7224i	−0.854043	−	0.792626i
$184$	2.79800	−	0.594733i	0.206271	−	0.0438443i
$185$	−15.5532	−	7.30728i	−1.14349	−	0.537242i
$186$	1.16284	−	1.01570i	0.0852637	−	0.0744747i
$187$	0.956785	+	1.06262i	0.0699671	+	0.0777063i
$188$	7.88628	−	24.2715i	0.575166	−	1.77018i
$189$	18.0951	+	11.5687i	1.31622	+	0.841498i
$190$	−0.0223519	+	0.0155551i	−0.00162158	+	0.00112848i
$191$	0.389712	+	0.432819i	0.0281986	+	0.0313177i	0.757079	−	0.653323i	$-0.226626\pi$
$191$	0.389712	+	0.432819i	0.0281986	+	0.0313177i	−0.728881	+	0.684641i	$0.759959\pi$
$192$	2.83746	−	12.4249i	0.204776	−	0.896688i
$193$	−4.64632	−	8.04765i	−0.334449	−	0.579283i	0.648930	−	0.760848i	$-0.275217\pi$
$193$	−4.64632	−	8.04765i	−0.334449	−	0.579283i	−0.983379	+	0.181565i	$0.941884\pi$
$194$	0.181731	−	1.72905i	0.0130475	−	0.124139i
$195$	−3.13783	+	6.42517i	−0.224705	+	0.460116i
$196$	2.07960	+	19.7861i	0.148543	+	1.41329i
$197$	−3.47512	+	2.52482i	−0.247592	+	0.179886i	−0.704659	−	0.709546i	$-0.748900\pi$
$197$	−3.47512	+	2.52482i	−0.247592	+	0.179886i	0.457067	+	0.889432i	$0.348900\pi$
$198$	0.0131651	+	0.176241i	0.000935603	+	0.0125249i
$199$	−3.20175			−0.226966			−0.113483	−	0.993540i	$-0.536201\pi$
$199$	−3.20175			−0.226966			−0.113483	+	0.993540i	$0.536201\pi$
$200$	2.08545	+	2.51467i	0.147464	+	0.177814i
$201$	−14.9739	+	19.9696i	−1.05618	+	1.40854i
$202$	1.92766	−	2.14088i	0.135630	−	0.150632i
$203$	24.5397	+	10.9258i	1.72235	+	0.766840i
$204$	0.205687	−	13.6393i	0.0144009	−	0.954942i
$205$	0.886660	+	10.4828i	0.0619270	+	0.732152i
$206$	1.59188	+	1.15657i	0.110912	+	0.0805820i
$207$	−12.7588	−	3.11686i	−0.886800	−	0.216637i
$208$	−5.73325	−	4.16545i	−0.397529	−	0.288822i
$209$	−0.0177496	−	0.0197129i	−0.00122776	−	0.00136357i
$210$	−0.455829	−	2.59288i	−0.0314552	−	0.178926i
$211$	−4.85666	+	5.39387i	−0.334347	+	0.371329i	−0.886751	−	0.462246i	$-0.847044\pi$
$211$	−4.85666	+	5.39387i	−0.334347	+	0.371329i	0.552405	+	0.833576i	$0.313710\pi$
$212$	−3.65396	+	0.776673i	−0.250955	+	0.0533421i
$213$	23.1682	−	2.08239i	1.58746	−	0.142683i
$214$	−1.36583	−	0.290317i	−0.0933665	−	0.0198457i
$215$	−5.52611	−	4.18927i	−0.376877	−	0.285706i
$216$	2.11774	−	2.65362i	0.144094	−	0.180556i
$217$	−18.1249	−	13.1685i	−1.23040	−	0.893938i
$218$	0.663982	−	1.15005i	0.0449705	−	0.0778912i
$219$	−5.18968	+	22.7250i	−0.350686	+	1.53561i
$220$	−1.08110	+	1.15265i	−0.0728875	+	0.0777116i
$221$	−6.73257	−	2.99753i	−0.452882	−	0.201636i
$222$	1.91208	−	1.06582i	0.128330	−	0.0715334i
$223$	0.581978	+	0.123703i	0.0389721	+	0.00828378i	0.227357	−	0.973812i	$-0.426992\pi$
$223$	0.581978	+	0.123703i	0.0389721	+	0.00828378i	−0.188384	+	0.982095i	$0.560325\pi$
$224$	8.01038			0.535216
$225$	−3.61395	−	14.5581i	−0.240930	−	0.970543i
$226$	−1.46249			−0.0972834
$227$	9.03312	+	1.92005i	0.599549	+	0.127438i	0.497682	−	0.867360i	$-0.334185\pi$
$227$	9.03312	+	1.92005i	0.599549	+	0.127438i	0.101868	+	0.994798i	$0.467518\pi$
$228$	−0.00381575	+	0.253026i	−0.000252704	+	0.0167571i
$229$	2.38530	+	1.06200i	0.157625	+	0.0701793i	0.484033	−	0.875050i	$-0.339172\pi$
$229$	2.38530	+	1.06200i	0.157625	+	0.0701793i	−0.326408	+	0.945229i	$0.605838\pi$
$230$	0.776458	+	1.41035i	0.0511981	+	0.0929956i
$231$	2.45061	−	0.755592i	0.161238	−	0.0497143i
$232$	2.12316	−	3.67742i	0.139392	−	0.241435i
$233$	5.35177	+	3.88829i	0.350606	+	0.254730i	0.749123	−	0.662431i	$-0.230475\pi$
$233$	5.35177	+	3.88829i	0.350606	+	0.254730i	−0.398517	+	0.917161i	$0.630475\pi$
$234$	−0.431446	−	0.802221i	−0.0282045	−	0.0524428i
$235$	28.9180	+	0.588229i	1.88640	+	0.0383718i
$236$	9.54975	+	2.02986i	0.621636	+	0.132133i
$237$	−4.36327	+	9.41535i	−0.283425	+	0.611593i
$238$	2.65409	−	0.564144i	0.172039	−	0.0365680i
$239$	11.0538	−	12.2765i	0.715013	−	0.794102i	−0.270677	−	0.962670i	$-0.587248\pi$
$239$	11.0538	−	12.2765i	0.715013	−	0.794102i	0.985690	+	0.168568i	$0.0539143\pi$
$240$	14.8306	−	1.02944i	0.957310	−	0.0664499i
$241$	5.03131	+	5.58784i	0.324095	+	0.359944i	0.883071	−	0.469240i	$-0.155472\pi$
$241$	5.03131	+	5.58784i	0.324095	+	0.359944i	−0.558975	+	0.829184i	$0.688805\pi$
$242$	−1.44646	−	1.05092i	−0.0929823	−	0.0675556i
$243$	−14.0487	+	6.75520i	−0.901228	+	0.433346i
$244$	14.5256	+	10.5534i	0.929903	+	0.675614i
$245$	−20.7811	+	8.75040i	−1.32766	+	0.559042i
$246$	−1.15037	−	0.687502i	−0.0733451	−	0.0438335i
$247$	0.124898	+	0.0556081i	0.00794706	+	0.00353826i
$248$	−2.36975	+	2.63188i	−0.150479	+	0.167124i
$249$	−4.96285	−	0.597405i	−0.314508	−	0.0378590i
$250$	−1.01473	+	1.53333i	−0.0641773	+	0.0969763i
$251$	−19.2136			−1.21275			−0.606377	−	0.795177i	$-0.707378\pi$
$251$	−19.2136			−1.21275			−0.606377	+	0.795177i	$0.707378\pi$
$252$	−22.0390	−	10.6199i	−1.38833	−	0.668991i
$253$	−1.26874	+	0.921796i	−0.0797652	+	0.0579528i
$254$	−0.0557813	−	0.530724i	−0.00350003	−	0.0333006i
$255$	14.8633	−	4.25376i	0.930775	−	0.266381i
$256$	−1.45085	+	13.8039i	−0.0906779	+	0.862742i
$257$	−9.44838	−	16.3651i	−0.589374	−	1.02083i	−0.994315	−	0.106483i	$-0.966041\pi$
$257$	−9.44838	−	16.3651i	−0.589374	−	1.02083i	0.404941	−	0.914343i	$-0.367292\pi$
$258$	0.844163	−	0.260280i	0.0525553	−	0.0162043i
$259$	−21.2544	−	23.6055i	−1.32069	−	1.46677i
$260$	2.67395	−	7.69353i	0.165831	−	0.477132i
$261$	−16.1118	+	10.9792i	−0.997294	+	0.679595i
$262$	0.437266	−	1.34577i	0.0270144	−	0.0831417i
$263$	10.8268	+	12.0244i	0.667611	+	0.741457i	0.977874	−	0.209194i	$-0.0670840\pi$
$263$	10.8268	+	12.0244i	0.667611	+	0.741457i	−0.310264	+	0.950651i	$0.600417\pi$
$264$	−0.0782955	−	0.397752i	−0.00481875	−	0.0244799i
$265$	−2.04188	−	3.70885i	−0.125432	−	0.227833i
$266$	−0.0492367	+	0.0104656i	−0.00301890	+	0.000641686i
$267$	−2.76293	+	12.0985i	−0.169089	+	0.740419i
$268$	14.2158	−	24.6225i	0.868368	−	1.50406i
$269$	−1.72574	−	1.25382i	−0.105220	−	0.0764469i	0.533931	−	0.845528i	$-0.320714\pi$
$269$	−1.72574	−	1.25382i	−0.105220	−	0.0764469i	−0.639151	+	0.769081i	$0.720714\pi$
$270$	1.77470	+	0.708294i	0.108005	+	0.0431054i
$271$	−13.1625	+	9.56310i	−0.799563	+	0.580917i	−0.910786	−	0.412879i	$-0.864523\pi$
$271$	−13.1625	+	9.56310i	−0.799563	+	0.580917i	0.111223	+	0.993796i	$0.464523\pi$
$272$	1.60160	+	15.2382i	0.0971114	+	0.923954i
$273$	−9.95457	+	8.69495i	−0.602478	+	0.526242i
$274$	−0.471256	−	0.816239i	−0.0284696	−	0.0493108i
$275$	−1.60523	−	0.794424i	−0.0967993	−	0.0479056i
$276$	14.8535	+	1.78800i	0.894078	+	0.107625i
$277$	8.33504	+	1.77167i	0.500804	+	0.106449i	0.451386	−	0.892329i	$-0.350930\pi$
$277$	8.33504	+	1.77167i	0.500804	+	0.106449i	0.0494184	+	0.998778i	$0.484263\pi$
$278$	2.20656	−	1.60316i	0.132341	−	0.0961511i
$279$	15.0478	−	6.16298i	0.900889	−	0.368968i
$280$	1.74888	+	5.77993i	0.104516	+	0.345417i
$281$	−7.58966	+	3.37913i	−0.452761	+	0.201582i	−0.620431	−	0.784261i	$-0.713042\pi$
$281$	−7.58966	+	3.37913i	−0.452761	+	0.201582i	0.167670	+	0.985843i	$0.446376\pi$
$282$	−2.21044	+	2.94789i	−0.131630	+	0.175544i
$283$	−0.547146	+	5.20574i	−0.0325244	+	0.309449i	0.966150	+	0.257980i	$0.0830570\pi$
$283$	−0.547146	+	5.20574i	−0.0325244	+	0.309449i	−0.998675	+	0.0514690i	$0.983610\pi$
$284$	−25.9179	+	5.50902i	−1.53794	+	0.326900i
$285$	−0.275733	+	0.0789126i	−0.0163330	+	0.00467438i
$286$	−0.106386	−	0.0226130i	−0.00629073	−	0.00133714i
$287$	−6.00921	+	18.4944i	−0.354712	+	1.09169i
$288$	−3.05755	+	4.94519i	−0.180168	+	0.291398i
$289$	−0.329378	−	1.01372i	−0.0193752	−	0.0596307i
$290$	2.32711	+	0.544333i	0.136653	+	0.0319643i
$291$	7.69894	−	16.6133i	0.451320	−	0.973888i
$292$	2.77545	−	26.4067i	0.162421	−	1.54533i
$293$	−10.1972	−	17.6621i	−0.595728	−	1.03183i	−0.993444	−	0.114323i	$-0.963530\pi$
$293$	−10.1972	−	17.6621i	−0.595728	−	1.03183i	0.397715	−	0.917509i	$-0.369803\pi$
$294$	0.639500	−	2.80029i	0.0372964	−	0.163316i
$295$	0.932580	+	11.0257i	0.0542969	+	0.641943i
$296$	−4.06228	+	2.95142i	−0.236115	+	0.171548i
$297$	−0.468929	+	1.80128i	−0.0272100	+	0.104521i
$298$	−0.356220	−	1.09633i	−0.0206353	−	0.0635089i
$299$	4.04142	−	6.99994i	0.233721	−	0.404817i
$300$	6.06896	+	15.9721i	0.350392	+	0.922151i
$301$	−6.40909	−	11.1009i	−0.369414	−	0.639843i
$302$	0.518120	−	0.575430i	0.0298144	−	0.0331123i
$303$	26.5016	−	14.7725i	1.52248	−	0.848655i
$304$	−0.0297118	−	0.282689i	−0.00170409	−	0.0162133i
$305$	−6.68047	+	19.2212i	−0.382523	+	1.10060i
$306$	−0.664787	+	1.85383i	−0.0380034	+	0.105976i
$307$	8.63664			0.492919			0.246459	−	0.969153i	$-0.420733\pi$
$307$	8.63664			0.492919			0.246459	+	0.969153i	$0.420733\pi$
$308$	−2.66858	+	1.18813i	−0.152056	+	0.0676999i
$309$	11.9267	+	16.9473i	0.678486	+	0.964100i
$310$	−1.80407	−	0.847596i	−0.102464	−	0.0481402i
$311$	−9.01162	+	10.0084i	−0.511002	+	0.567525i	−0.942337	−	0.334667i	$-0.891376\pi$
$311$	−9.01162	+	10.0084i	−0.511002	+	0.567525i	0.431334	+	0.902192i	$0.358043\pi$
$312$	1.20247	+	1.70866i	0.0680765	+	0.0967337i
$313$	−4.88783	−	5.42848i	−0.276276	−	0.306836i	0.588998	−	0.808134i	$-0.299523\pi$
$313$	−4.88783	−	5.42848i	−0.276276	−	0.306836i	−0.865274	+	0.501299i	$0.832856\pi$
$314$	0.865788	+	2.66462i	0.0488593	+	0.150373i
$315$	4.28641	−	27.3935i	0.241512	−	1.54345i
$316$	3.65275	−	11.2420i	0.205483	−	0.632413i
$317$	−21.2233	+	9.44920i	−1.19202	+	0.530720i	−0.904259	−	0.426983i	$-0.859576\pi$
$317$	−21.2233	+	9.44920i	−1.19202	+	0.530720i	−0.287757	+	0.957703i	$0.592910\pi$
$318$	0.535467	+	0.0644571i	0.0300275	+	0.00361457i
$319$	−0.243344	+	2.31526i	−0.0136246	+	0.129630i
$320$	−16.1601	+	3.09285i	−0.903377	+	0.172895i
$321$	−12.6236	−	7.54431i	−0.704582	−	0.421082i
$322$	0.311070	+	2.95963i	0.0173353	+	0.164934i
$323$	−0.0913448	−	0.281131i	−0.00508256	−	0.0156425i
$324$	14.9684	−	9.55212i	0.831578	−	0.530674i
$325$	9.22354	+	0.375392i	0.511630	+	0.0208230i
$326$	0.0834143	−	0.144478i	0.00461989	−	0.00800189i
$327$	10.5336	−	9.20067i	0.582507	−	0.508798i
$328$	2.80827	+	1.25032i	0.155061	+	0.0690374i
$329$	48.8424	+	21.7460i	2.69277	+	1.19890i
$330$	0.201508	−	0.107011i	0.0110926	−	0.00589078i
$331$	24.5649	−	10.9370i	1.35021	−	0.601152i	0.401082	−	0.916042i	$-0.368634\pi$
$331$	24.5649	−	10.9370i	1.35021	−	0.601152i	0.949128	+	0.314890i	$0.101968\pi$
$332$	5.69392			0.312494
$333$	22.6856	−	4.11123i	1.24316	−	0.225294i
$334$	−0.194788	+	0.599497i	−0.0106583	+	0.0328030i
$335$	31.3763	+	7.33921i	1.71427	+	0.400984i
$336$	26.0036	+	8.88478i	1.41862	+	0.484704i
$337$	−8.43475	+	1.79286i	−0.459470	+	0.0976634i	−0.431831	−	0.901955i	$-0.642132\pi$
$337$	−8.43475	+	1.79286i	−0.459470	+	0.0976634i	−0.0276393	+	0.999618i	$0.508799\pi$
$338$	−1.54291	+	0.327956i	−0.0839232	+	0.0178384i
$339$	−14.5755	−	4.98008i	−0.791633	−	0.270481i
$340$	−16.2301	+	6.83408i	−0.880202	+	0.370630i
$341$	0.599994	−	1.84659i	0.0324915	−	0.0999986i
$342$	0.0123327	−	0.0343909i	0.000666874	−	0.00185965i
$343$	−12.7466			−0.688251
$344$	−1.85110	+	0.824163i	−0.0998046	+	0.0444359i
$345$	2.93583	+	16.6999i	0.158060	+	0.899090i
$346$	−3.33267	−	1.48380i	−0.179165	−	0.0797696i
$347$	32.0841	+	14.2848i	1.72236	+	0.766846i	0.996908	+	0.0785773i	$0.0250377\pi$
$347$	32.0841	+	14.2848i	1.72236	+	0.766846i	0.725456	+	0.688269i	$0.241629\pi$
$348$	16.7265	−	14.6100i	0.896635	−	0.783177i
$349$	10.5156	−	18.2135i	0.562886	−	0.974946i	−0.434357	−	0.900741i	$-0.643025\pi$
$349$	10.5156	−	18.2135i	0.562886	−	0.974946i	0.997243	−	0.0742057i	$-0.0236421\pi$
$350$	−2.82860	+	1.88426i	−0.151195	+	0.100718i
$351$	−1.56817	−	9.46428i	−0.0837027	−	0.505166i
$352$	0.214527	+	0.660245i	0.0114343	+	0.0351912i
$353$	−2.05945	−	19.5943i	−0.109613	−	1.04290i	−0.901662	−	0.432443i	$-0.857652\pi$
$353$	−2.05945	−	19.5943i	−0.109613	−	1.04290i	0.792048	−	0.610459i	$-0.209015\pi$
$354$	−1.20995	−	0.723108i	−0.0643082	−	0.0384328i
$355$	−14.4833	−	26.3072i	−0.768691	−	1.39624i
$356$	1.47762	−	14.0586i	0.0783138	−	0.745106i
$357$	28.3723	+	3.41533i	1.50162	+	0.180758i
$358$	2.19924	−	0.979164i	0.116233	−	0.0517504i
$359$	−0.938606	+	2.88873i	−0.0495377	+	0.152461i	−0.972765	−	0.231792i	$-0.925541\pi$
$359$	−0.938606	+	2.88873i	−0.0495377	+	0.152461i	0.923228	+	0.384253i	$0.125541\pi$
$360$	−4.23578	−	1.12652i	−0.223245	−	0.0593728i
$361$	−5.86963	−	18.0649i	−0.308928	−	0.950782i
$362$	−1.89533	−	2.10498i	−0.0996163	−	0.110635i
$363$	−10.8372	−	15.3992i	−0.568806	−	0.808249i
$364$	10.0741	−	11.1885i	0.528029	−	0.586435i
$365$	29.5567	−	5.65678i	1.54707	−	0.296090i
$366$	−1.49187	−	2.11989i	−0.0779815	−	0.110808i
$367$	−6.63569	+	2.95440i	−0.346380	+	0.154218i	−0.572551	−	0.819869i	$-0.694046\pi$
$367$	−6.63569	+	2.95440i	−0.346380	+	0.154218i	0.226170	+	0.974088i	$0.427379\pi$
$368$	−16.8048			−0.876010
$369$	−9.12380	−	10.7691i	−0.474966	−	0.560615i
$370$	−2.25209	−	1.70728i	−0.117080	−	0.0887572i
$371$	−0.818032	−	7.78306i	−0.0424701	−	0.404076i
$372$	−16.1789	+	9.01838i	−0.838836	+	0.467581i
$373$	7.06598	−	7.84757i	0.365863	−	0.406332i	−0.531903	−	0.846805i	$-0.678523\pi$
$373$	7.06598	−	7.84757i	0.365863	−	0.406332i	0.897765	+	0.440474i	$0.145190\pi$
$374$	0.117578	+	0.203651i	0.00607983	+	0.0105306i
$375$	−15.3344	+	11.8261i	−0.791862	+	0.610699i
$376$	4.22581	−	7.31932i	0.217930	−	0.377465i
$377$	−3.70779	−	11.4114i	−0.190961	−	0.587718i
$378$	2.51527	+	2.47970i	0.129372	+	0.127542i
$379$	−28.5159	+	20.7180i	−1.46476	+	1.06421i	−0.482673	+	0.875801i	$0.660334\pi$
$379$	−28.5159	+	20.7180i	−1.46476	+	1.06421i	−0.982090	+	0.188412i	$0.939666\pi$
$380$	0.301089	−	0.126781i	0.0154456	−	0.00650372i
$381$	1.25129	−	5.47927i	0.0641058	−	0.280711i
$382$	0.0478913	+	0.0829501i	0.00245033	+	0.00424410i
$383$	0.652307	−	6.20628i	0.0333313	−	0.317126i	−0.965134	−	0.261754i	$-0.915699\pi$
$383$	0.652307	−	6.20628i	0.0333313	−	0.317126i	0.998466	−	0.0553718i	$-0.0176344\pi$
$384$	3.70408	−	7.99292i	0.189023	−	0.407887i
$385$	−2.16479	−	2.50486i	−0.110328	−	0.127660i
$386$	−0.472253	−	1.45344i	−0.0240370	−	0.0739784i
$387$	9.29943	+	0.280543i	0.472717	+	0.0142608i
$388$	−6.44524	+	19.8364i	−0.327208	+	1.00704i
$389$	−27.8772	−	5.92548i	−1.41343	−	0.300434i	−0.562972	−	0.826476i	$-0.690342\pi$
$389$	−27.8772	−	5.92548i	−1.41343	−	0.300434i	−0.850459	+	0.526042i	$0.823676\pi$
$390$	−0.724456	+	0.926285i	−0.0366843	+	0.0469043i
$391$	−17.0940	+	3.63345i	−0.864483	+	0.183752i
$392$	−0.688700	+	6.55254i	−0.0347846	+	0.330953i
$393$	8.94050	−	11.9232i	0.450989	−	0.601448i
$394$	−0.645351	+	0.287329i	−0.0325123	+	0.0144754i
$395$	13.3942	+	0.272455i	0.673934	+	0.0137087i
$396$	0.285103	−	2.10095i	0.0143270	−	0.105577i
$397$	−4.87063	+	3.53872i	−0.244450	+	0.177603i	−0.703263	−	0.710929i	$-0.748275\pi$
$397$	−4.87063	+	3.53872i	−0.244450	+	0.177603i	0.458814	+	0.888533i	$0.348275\pi$
$398$	−0.515045	−	0.109476i	−0.0258169	−	0.00548755i
$399$	−0.526342	−	0.0633587i	−0.0263501	−	0.00317190i
$400$	−8.91229	−	16.9975i	−0.445615	−	0.849874i
$401$	13.2682	+	22.9812i	0.662583	+	1.14763i	0.979934	+	0.199320i	$0.0638733\pi$
$401$	13.2682	+	22.9812i	0.662583	+	1.14763i	−0.317351	+	0.948308i	$0.602793\pi$
$402$	−3.09157	+	2.70038i	−0.154194	+	0.134683i
$403$	1.04604	+	9.95237i	0.0521068	+	0.495763i
$404$	−27.9602	+	20.3143i	−1.39107	+	1.01067i
$405$	15.2752	+	13.1022i	0.759030	+	0.651056i
$406$	3.57397	+	2.59664i	0.177373	+	0.128869i
$407$	1.37643	−	2.38405i	0.0682272	−	0.118173i
$408$	1.00575	−	4.40405i	0.0497920	−	0.218033i
$409$	26.7098	−	5.67735i	1.32072	−	0.280727i	0.506978	−	0.861959i	$-0.330762\pi$
$409$	26.7098	−	5.67735i	1.32072	−	0.280727i	0.813738	+	0.581232i	$0.197429\pi$
$410$	−0.215804	+	1.71662i	−0.0106578	+	0.0847779i
$411$	−1.91718	−	9.73954i	−0.0945676	−	0.480416i
$412$	−15.7953	−	17.5424i	−0.778178	−	0.864254i
$413$	−6.32043	+	19.4523i	−0.311008	+	0.957184i
$414$	−1.94586	−	0.937648i	−0.0956337	−	0.0460829i
$415$	1.86894	+	6.17670i	0.0917425	+	0.303202i
$416$	−2.39418	−	2.65901i	−0.117384	−	0.130369i
$417$	27.4502	−	8.46366i	1.34424	−	0.414467i
$418$	−0.00218123	−	0.00377800i	−0.000106687	−	0.000184788i
$419$	1.23627	−	11.7624i	0.0603960	−	0.574629i	−0.921918	−	0.387386i	$-0.873378\pi$
$419$	1.23627	−	11.7624i	0.0603960	−	0.574629i	0.982314	−	0.187243i	$-0.0599553\pi$
$420$	−1.11837	+	31.5634i	−0.0545710	+	1.54014i
$421$	−0.191178	−	1.81894i	−0.00931746	−	0.0886497i	0.988875	−	0.148749i	$-0.0475248\pi$
$421$	−0.191178	−	1.81894i	−0.00931746	−	0.0886497i	−0.998192	+	0.0600998i	$0.980858\pi$
$422$	−0.965691	+	0.701616i	−0.0470091	+	0.0341541i
$423$	−32.0679	+	21.8523i	−1.55919	+	1.06250i
$424$	−1.23711			−0.0600795
$425$	−12.7408	−	15.3631i	−0.618020	−	0.745219i
$426$	3.79812	+	0.457200i	0.184019	+	0.0221514i
$427$	−25.1688	+	27.9528i	−1.21800	+	1.35273i
$428$	15.3034	+	6.81350i	0.739716	+	0.329343i
$429$	−0.983265	−	0.587633i	−0.0474725	−	0.0283712i
$430$	−0.745707	−	0.862853i	−0.0359612	−	0.0416105i
$431$	28.5016	+	20.7076i	1.37288	+	0.997452i	0.997506	+	0.0705766i	$0.0224839\pi$
$431$	28.5016	+	20.7076i	1.37288	+	0.997452i	0.375369	+	0.926876i	$0.377516\pi$
$432$	−15.4105	+	12.6620i	−0.741440	+	0.609200i
$433$	3.17805	+	2.30899i	0.152727	+	0.110963i	0.661525	−	0.749923i	$-0.269910\pi$
$433$	3.17805	+	2.30899i	0.152727	+	0.110963i	−0.508797	+	0.860886i	$0.669910\pi$
$434$	−2.46537	−	2.73808i	−0.118342	−	0.131432i
$435$	21.3390	+	13.3492i	1.02313	+	0.640047i
$436$	−10.6601	+	11.8392i	−0.510525	+	0.566996i
$437$	0.317116	−	0.0674052i	0.0151697	−	0.00322443i
$438$	−1.61186	+	3.47817i	−0.0770175	+	0.166194i
$439$	−18.8943	−	4.01611i	−0.901777	−	0.191679i	−0.266384	−	0.963867i	$-0.585829\pi$
$439$	−18.8943	−	4.01611i	−0.901777	−	0.191679i	−0.635394	+	0.772188i	$0.719162\pi$
$440$	−0.429567	+	0.298943i	−0.0204788	+	0.0142515i
$441$	15.9090	−	25.7307i	0.757570	−	1.22527i
$442$	−0.980532	−	0.712398i	−0.0466392	−	0.0338853i
$443$	−2.24077	+	3.88113i	−0.106462	+	0.184398i	−0.914335	−	0.404959i	$-0.867286\pi$
$443$	−2.24077	+	3.88113i	−0.106462	+	0.184398i	0.807872	+	0.589357i	$0.200619\pi$
$444$	−25.0959	+	7.73778i	−1.19100	+	0.367219i
$445$	15.7357	−	3.01161i	0.745942	−	0.142764i
$446$	0.0893894	+	0.0397987i	0.00423271	+	0.00188452i
$447$	0.183066	−	12.1393i	0.00865874	−	0.574170i
$448$	−29.7487	−	6.32329i	−1.40550	−	0.298747i
$449$	−11.2399			−0.530445			−0.265222	−	0.964187i	$-0.585445\pi$
$449$	−11.2399			−0.530445			−0.265222	+	0.964187i	$0.585445\pi$
$450$	−0.0835716	−	2.46545i	−0.00393961	−	0.116222i
$451$	−1.68531			−0.0793583
$452$	17.1617	+	3.64784i	0.807219	+	0.171580i
$453$	7.12316	−	3.97057i	0.334675	−	0.186554i
$454$	1.38745	+	0.617732i	0.0651162	+	0.0289916i
$455$	15.4438	+	7.25589i	0.724017	+	0.340161i
$456$	−0.0186579	+	0.0817007i	−0.000873737	+	0.00382599i
$457$	7.48417	−	12.9630i	0.350095	−	0.606381i	−0.636171	−	0.771548i	$-0.719483\pi$
$457$	7.48417	−	12.9630i	0.350095	−	0.606381i	0.986266	+	0.165166i	$0.0528161\pi$
$458$	0.347396	+	0.252398i	0.0162327	+	0.0117938i
$459$	−12.9381	+	16.2119i	−0.603898	+	0.756708i
$460$	−5.59363	−	18.4866i	−0.260805	−	0.861940i
$461$	−29.4933	−	6.26900i	−1.37364	−	0.291976i	−0.538784	−	0.842444i	$-0.681116\pi$
$461$	−29.4933	−	6.26900i	−1.37364	−	0.291976i	−0.834856	+	0.550468i	$0.814449\pi$
$462$	0.420049	−	0.0377546i	0.0195424	−	0.00175650i
$463$	27.0421	−	5.74797i	1.25675	−	0.267131i	0.469041	−	0.883176i	$-0.344599\pi$
$463$	27.0421	−	5.74797i	1.25675	−	0.267131i	0.787711	+	0.616045i	$0.211266\pi$
$464$	−16.6922	+	18.5386i	−0.774915	+	0.860631i
$465$	−15.0935	−	14.5906i	−0.699945	−	0.676621i
$466$	0.727954	+	0.808474i	0.0337218	+	0.0374519i
$467$	−23.9054	−	17.3683i	−1.10621	−	0.803709i	−0.124147	−	0.992264i	$-0.539620\pi$
$467$	−23.9054	−	17.3683i	−1.10621	−	0.803709i	−0.982063	+	0.188555i	$0.939620\pi$
$468$	3.06190	+	10.4899i	0.141536	+	0.484894i
$469$	48.1876	+	35.0103i	2.22510	+	1.61663i
$470$	4.63174	+	1.08341i	0.213646	+	0.0499738i
$471$	−0.444940	+	29.5044i	−0.0205018	+	1.35949i
$472$	2.95371	+	1.31508i	0.135955	+	0.0605313i
$473$	0.743333	−	0.825554i	0.0341785	−	0.0379590i
$474$	−1.02383	+	1.36540i	−0.0470259	+	0.0627147i
$475$	0.236358	+	0.285005i	0.0108449	+	0.0130769i
$476$	−32.5517			−1.49201
$477$	5.11709	+	2.46577i	0.234296	+	0.112900i
$478$	2.19793	−	1.59689i	0.100531	−	0.0730399i
$479$	1.40083	+	13.3280i	0.0640056	+	0.608973i	0.978767	+	0.204977i	$0.0657121\pi$
$479$	1.40083	+	13.3280i	0.0640056	+	0.608973i	−0.914761	+	0.403995i	$0.867621\pi$
$480$	7.43236	+	1.04842i	0.339239	+	0.0478538i
$481$	−1.48309	+	14.1106i	−0.0676230	+	0.643390i
$482$	0.618292	+	1.07091i	0.0281624	+	0.0487788i
$483$	−6.97796	+	30.5556i	−0.317508	+	1.39033i
$484$	14.3524	+	15.9400i	0.652382	+	0.724544i
$485$	−23.6339	−	0.480743i	−1.07316	−	0.0218294i
$486$	−2.49091	+	0.606302i	−0.112990	+	0.0275024i
$487$	0.825534	−	2.54073i	0.0374085	−	0.115132i	−0.930608	−	0.366016i	$-0.880721\pi$
$487$	0.825534	−	2.54073i	0.0374085	−	0.115132i	0.968017	+	0.250885i	$0.0807215\pi$
$488$	3.97865	+	4.41874i	0.180105	+	0.200027i
$489$	1.32330	−	1.15586i	0.0598418	−	0.0522697i
$490$	−3.64213	+	0.697059i	−0.164535	+	0.0314899i
$491$	17.5164	−	3.72322i	0.790503	−	0.168027i	0.205070	−	0.978747i	$-0.434258\pi$
$491$	17.5164	−	3.72322i	0.790503	−	0.168027i	0.585433	+	0.810721i	$0.300925\pi$
$492$	11.7843	+	10.9369i	0.531279	+	0.493073i
$493$	−12.9712	+	22.4668i	−0.584193	+	1.01185i
$494$	0.0181901	+	0.0132159i	0.000818413	+	0.000594612i
$495$	2.37267	−	0.380326i	0.106643	−	0.0170944i
$496$	16.8321	−	12.2293i	0.755785	−	0.549110i
$497$	−5.80238	−	55.2060i	−0.260272	−	2.47633i
$498$	−0.777914	−	0.265793i	−0.0348592	−	0.0119105i
$499$	−10.2734	−	17.7940i	−0.459899	−	0.796568i	0.539057	−	0.842270i	$-0.318781\pi$
$499$	−10.2734	−	17.7940i	−0.459899	−	0.796568i	−0.998955	+	0.0457019i	$0.985448\pi$
$500$	15.7320	−	15.4620i	0.703556	−	0.691481i
$501$	−3.98272	+	5.31143i	−0.177935	+	0.237297i
$502$	−3.09077	−	0.656964i	−0.137948	−	0.0293218i
$503$	−32.2593	+	23.4377i	−1.43837	+	1.04504i	−0.449990	+	0.893034i	$0.648572\pi$
$503$	−32.2593	+	23.4377i	−1.43837	+	1.04504i	−0.988380	+	0.152003i	$0.951428\pi$
$504$	−6.40792	−	4.95760i	−0.285431	−	0.220829i
$505$	−31.2142	−	23.6631i	−1.38901	−	1.05299i
$506$	−0.235613	+	0.104902i	−0.0104743	+	0.00466345i
$507$	−16.4938	−	1.98544i	−0.732513	−	0.0881766i
$508$	−0.669195	+	6.36696i	−0.0296907	+	0.282488i
$509$	−19.4228	+	4.12845i	−0.860902	+	0.182990i	−0.617148	−	0.786847i	$-0.711712\pi$
$509$	−19.4228	+	4.12845i	−0.860902	+	0.182990i	−0.243754	+	0.969837i	$0.578379\pi$
$510$	2.53641	−	0.176060i	0.112314	−	0.00779607i
$511$	54.4102	+	11.5652i	2.40696	+	0.511616i
$512$	−3.84880	+	11.8454i	−0.170094	+	0.523497i
$513$	0.240018	−	0.300752i	0.0105971	−	0.0132785i
$514$	−0.960336	−	2.95561i	−0.0423586	−	0.130366i
$515$	13.8453	−	22.8926i	0.610097	−	1.00877i
$516$	−10.5551	+	0.948708i	−0.464663	+	0.0417645i
$517$	−0.484337	+	4.60815i	−0.0213011	+	0.202666i
$518$	−2.61193	−	4.52400i	−0.114762	−	0.198773i
$519$	−28.1615	−	26.1363i	−1.23615	−	1.14726i
$520$	1.39591	−	2.30807i	0.0612146	−	0.101216i
$521$	8.76012	−	6.36460i	0.383788	−	0.278838i	−0.379117	−	0.925349i	$-0.623772\pi$
$521$	8.76012	−	6.36460i	0.383788	−	0.278838i	0.762905	+	0.646510i	$0.223772\pi$
$522$	−2.96721	+	1.21525i	−0.129871	+	0.0531900i
$523$	4.62026	+	14.2197i	0.202030	+	0.621785i	0.999822	+	0.0188521i	$0.00600116\pi$
$523$	4.62026	+	14.2197i	0.202030	+	0.621785i	−0.797792	+	0.602932i	$0.793999\pi$
$524$	−8.48783	+	14.7014i	−0.370793	+	0.642232i
$525$	−34.6067	+	9.14698i	−1.51036	+	0.399207i
$526$	1.33050	+	2.30449i	0.0580124	+	0.100480i
$527$	14.4777	−	16.0791i	0.630659	−	0.700418i
$528$	−0.0359105	+	2.38126i	−0.00156280	+	0.103631i
$529$	0.400662	+	3.81205i	0.0174201	+	0.165741i
$530$	−0.201649	−	0.666436i	−0.00875908	−	0.0289481i
$531$	−9.59632	−	11.3268i	−0.416445	−	0.491541i
$532$	0.603877			0.0261814
$533$	7.93521	−	3.53298i	0.343712	−	0.153030i
$534$	−0.858136	+	1.85174i	−0.0371352	+	0.0801328i
$535$	−2.36813	+	18.8374i	−0.102383	+	0.814410i
$536$	6.30031	−	6.99721i	0.272132	−	0.302233i
$537$	25.2524	−	2.26972i	1.08972	−	0.0979454i
$538$	−0.234737	−	0.260702i	−0.0101202	−	0.0112397i
$539$	−1.11622	−	3.43538i	−0.0480791	−	0.147972i
$540$	−19.0587	−	12.7381i	−0.820156	−	0.548161i
$541$	11.4490	−	35.2363i	0.492230	−	1.51493i	−0.329000	−	0.944330i	$-0.606712\pi$
$541$	11.4490	−	35.2363i	0.492230	−	1.51493i	0.821230	−	0.570597i	$-0.193288\pi$
$542$	−2.44435	+	1.08829i	−0.104994	+	0.0467463i
$543$	−11.7214	−	27.4327i	−0.503014	−	1.17725i
$544$	−0.808645	+	7.69374i	−0.0346704	+	0.329867i
$545$	−16.3421	−	7.67791i	−0.700017	−	0.328885i
$546$	−1.89863	+	1.05833i	−0.0812539	+	0.0452923i
$547$	2.23082	+	21.2248i	0.0953828	+	0.907507i	0.932667	+	0.360739i	$0.117475\pi$
$547$	2.23082	+	21.2248i	0.0953828	+	0.907507i	−0.837284	+	0.546768i	$0.815858\pi$
$548$	3.49408	+	10.7537i	0.149260	+	0.459374i
$549$	−7.64971	−	26.2074i	−0.326482	−	1.11851i
$550$	−0.231060	−	0.182681i	−0.00985245	−	0.00778955i
$551$	0.240632	−	0.416787i	0.0102513	−	0.0177557i
$552$	4.68843	+	1.60192i	0.199553	+	0.0681821i
$553$	22.6227	+	10.0723i	0.962015	+	0.428317i
$554$	1.28023	+	0.569994i	0.0543916	+	0.0242167i
$555$	−16.6312	−	24.6840i	−0.705955	−	1.04778i
$556$	−29.8918	+	13.3087i	−1.26769	+	0.564413i
$557$	38.6947			1.63955			0.819773	−	0.572689i	$-0.194100\pi$
$557$	38.6947			1.63955			0.819773	+	0.572689i	$0.194100\pi$
$558$	2.63137	−	0.476875i	0.111395	−	0.0201877i
$559$	−1.76930	+	5.44535i	−0.0748335	+	0.230314i
$560$	−2.98996	−	35.3498i	−0.126349	−	1.49380i
$561$	0.478337	+	2.43002i	0.0201954	+	0.102595i
$562$	−1.33644	+	0.284069i	−0.0563744	+	0.0119827i
$563$	−13.3515	+	2.83794i	−0.562697	+	0.119605i	−0.480474	−	0.877009i	$-0.659535\pi$
$563$	−13.3515	+	2.83794i	−0.562697	+	0.119605i	−0.0822233	+	0.996614i	$0.526202\pi$
$564$	33.2914	−	29.0788i	1.40182	−	1.22444i
$565$	1.67593	+	19.8142i	0.0705068	+	0.833590i
$566$	−0.266014	+	0.818707i	−0.0111814	+	0.0344128i
$567$	16.6239	+	33.2783i	0.698138	+	1.39756i
$568$	−8.77496			−0.368189
$569$	21.2151	−	9.44557i	0.889383	−	0.395979i	0.0893962	−	0.995996i	$-0.471506\pi$
$569$	21.2151	−	9.44557i	0.889383	−	0.395979i	0.799987	+	0.600017i	$0.204840\pi$
$570$	−0.0470536	+	0.00326614i	−0.00197086	+	0.000136804i
$571$	23.2475	+	10.3505i	0.972879	+	0.433154i	0.830720	−	0.556690i	$-0.187929\pi$
$571$	23.2475	+	10.3505i	0.972879	+	0.433154i	0.142159	+	0.989844i	$0.454596\pi$
$572$	1.19199	+	0.530709i	0.0498397	+	0.0221901i
$573$	0.194833	+	0.989780i	0.00813928	+	0.0413486i
$574$	−1.59904	+	2.76961i	−0.0667425	+	0.115601i
$575$	18.2180	−	12.1358i	0.759743	−	0.506099i
$576$	15.2587	−	15.9517i	0.635780	−	0.664656i
$577$	9.47834	+	29.1713i	0.394588	+	1.21442i	0.929282	+	0.369372i	$0.120427\pi$
$577$	9.47834	+	29.1713i	0.394588	+	1.21442i	−0.534693	+	0.845046i	$0.679573\pi$
$578$	−0.0183232	−	0.174333i	−0.000762143	−	0.00725131i
$579$	0.242697	−	16.0935i	0.0100861	−	0.668822i
$580$	−25.9500	−	12.1920i	−1.07751	−	0.506243i
$581$	−1.24687	+	11.8632i	−0.0517290	+	0.492169i
$582$	1.80653	−	2.40923i	0.0748831	−	0.0998656i
$583$	0.619601	−	0.275864i	0.0256612	−	0.0114251i
$584$	2.71726	−	8.36287i	0.112441	−	0.346058i
$585$	−10.3743	+	6.76465i	−0.428924	+	0.279684i
$586$	−1.03645	−	3.18986i	−0.0428153	−	0.131772i
$587$	−9.90751	−	11.0034i	−0.408927	−	0.454159i	0.503138	−	0.864206i	$-0.332179\pi$
$587$	−9.90751	−	11.0034i	−0.408927	−	0.454159i	−0.912064	+	0.410047i	$0.865512\pi$
$588$	−14.4889	+	31.2652i	−0.597514	+	1.28935i
$589$	−0.268580	+	0.298288i	−0.0110666	+	0.0122908i
$590$	−0.226981	+	1.80553i	−0.00934464	+	0.0743324i
$591$	−7.41013	+	0.666032i	−0.304812	+	0.0273969i
$592$	26.9483	−	11.9982i	1.10757	−	0.493122i
$593$	29.3262			1.20428			0.602140	−	0.798390i	$-0.294315\pi$
$593$	29.3262			1.20428			0.602140	+	0.798390i	$0.294315\pi$
$594$	−0.137024	+	0.273727i	−0.00562217	+	0.0112312i
$595$	−10.6846	−	35.3118i	−0.438026	−	1.44764i
$596$	1.44555	+	13.7535i	0.0592122	+	0.563366i
$597$	−4.76027	−	2.84490i	−0.194825	−	0.116434i
$598$	0.889463	−	0.987849i	0.0363728	−	0.0403961i
$599$	2.03948	+	3.53249i	0.0833310	+	0.144334i	0.904679	−	0.426094i	$-0.140111\pi$
$599$	2.03948	+	3.53249i	0.0833310	+	0.144334i	−0.821348	+	0.570428i	$0.806777\pi$
$600$	0.866190	+	5.59176i	0.0353621	+	0.228283i
$601$	−8.15219	+	14.1200i	−0.332535	+	0.575967i	−0.983008	−	0.183562i	$-0.941237\pi$
$601$	−8.15219	+	14.1200i	−0.332535	+	0.575967i	0.650474	+	0.759529i	$0.274570\pi$
$602$	−0.651421	−	2.00487i	−0.0265500	−	0.0817124i
$603$	−40.0067	+	16.3851i	−1.62920	+	0.667254i
$604$	−7.51520	+	5.46011i	−0.305789	+	0.222169i
$605$	−12.5806	+	20.8014i	−0.511472	+	0.845696i
$606$	4.76826	−	1.47019i	0.193697	−	0.0597224i
$607$	9.93751	+	17.2123i	0.403351	+	0.698625i	0.994128	−	0.108210i	$-0.0345120\pi$
$607$	9.93751	+	17.2123i	0.403351	+	0.698625i	−0.590777	+	0.806835i	$0.701179\pi$
$608$	0.0150014	−	0.142729i	0.000608387	−	0.00578842i
$609$	26.7769	+	38.0488i	1.08505	+	1.54182i
$610$	−1.73187	+	2.86356i	−0.0701212	+	0.115942i
$611$	−7.37976	−	22.7126i	−0.298553	−	0.918852i
$612$	12.4249	−	20.0958i	0.502248	−	0.812323i
$613$	1.01670	−	3.12907i	0.0410639	−	0.126382i	−0.928423	−	0.371525i	$-0.878835\pi$
$613$	1.01670	−	3.12907i	0.0410639	−	0.126382i	0.969487	+	0.245143i	$0.0788350\pi$
$614$	1.38932	+	0.295309i	0.0560684	+	0.0119177i
$615$	−7.99620	+	16.3734i	−0.322438	+	0.660239i
$616$	−0.946247	+	0.201131i	−0.0381254	+	0.00810380i
$617$	−4.59814	+	43.7484i	−0.185114	+	1.76124i	0.369589	+	0.929195i	$0.379499\pi$
$617$	−4.59814	+	43.7484i	−0.185114	+	1.76124i	−0.554703	+	0.832048i	$0.687168\pi$
$618$	1.33910	+	3.13401i	0.0538665	+	0.126068i
$619$	−10.3474	+	4.60696i	−0.415897	+	0.185169i	−0.604008	−	0.796978i	$-0.706430\pi$
$619$	−10.3474	+	4.60696i	−0.415897	+	0.185169i	0.188110	+	0.982148i	$0.439764\pi$
$620$	19.0559	+	14.4460i	0.765302	+	0.580166i
$621$	−16.2000	−	15.9709i	−0.650083	−	0.640888i
$622$	−1.79186	+	1.30186i	−0.0718469	+	0.0521998i
$623$	28.9674	+	6.15721i	1.16055	+	0.246684i
$624$	−4.82284	−	11.2873i	−0.193068	−	0.451855i
$625$	21.9368	+	11.9907i	0.877471	+	0.479630i
$626$	−0.600659	−	1.04037i	−0.0240072	−	0.0415817i
$627$	−0.00887376	−	0.0450799i	−0.000354384	−	0.00180032i
$628$	−3.51340	−	33.4278i	−0.140200	−	1.33391i
$629$	24.8180	−	18.0313i	0.989559	−	0.718956i
$630$	1.62618	−	4.26005i	0.0647886	−	0.169724i
$631$	19.7944	+	14.3815i	0.788005	+	0.572519i	0.907371	−	0.420331i	$-0.138086\pi$
$631$	19.7944	+	14.3815i	0.788005	+	0.572519i	−0.119366	+	0.992850i	$0.538086\pi$
$632$	1.95730	−	3.39015i	0.0778573	−	0.134853i
$633$	−12.0134	+	3.70409i	−0.477492	+	0.147224i
$634$	−3.73714	+	0.794354i	−0.148421	+	0.0315478i
$635$	−7.12647	+	1.36392i	−0.282805	+	0.0541255i
$636$	−6.12271	−	2.09197i	−0.242781	−	0.0829521i
$637$	12.4574	+	13.8353i	0.493579	+	0.548175i
$638$	−0.118310	+	0.364121i	−0.00468394	+	0.0144157i
$639$	36.2960	+	17.4899i	1.43585	+	0.691891i
$640$	−11.3706	−	0.231293i	−0.449464	−	0.00914267i
$641$	19.5816	+	21.7476i	0.773426	+	0.858977i	0.993182	−	0.116578i	$-0.0371925\pi$
$641$	19.5816	+	21.7476i	0.773426	+	0.858977i	−0.219755	+	0.975555i	$0.570526\pi$
$642$	−1.77272	−	1.64524i	−0.0699638	−	0.0649324i
$643$	−3.57430	−	6.19087i	−0.140957	−	0.244144i	0.786900	−	0.617080i	$-0.211685\pi$
$643$	−3.57430	−	6.19087i	−0.140957	−	0.244144i	−0.927857	+	0.372936i	$0.878351\pi$
$644$	3.73183	−	35.5060i	0.147055	−	1.39913i
$645$	−4.49370	−	11.1387i	−0.176939	−	0.438585i
$646$	−0.00508147	−	0.0483470i	−0.000199928	−	0.00190219i
$647$	25.5288	−	18.5478i	1.00364	−	0.729188i	0.0407758	−	0.999168i	$-0.487017\pi$
$647$	25.5288	−	18.5478i	1.00364	−	0.729188i	0.962866	+	0.269980i	$0.0870171\pi$
$648$	5.50645	−	2.06361i	0.216314	−	0.0810662i
$649$	−1.77260			−0.0695805
$650$	1.47090	+	0.375764i	0.0576933	+	0.0147387i
$651$	−15.2468	−	35.6834i	−0.597568	−	1.39854i
$652$	−1.33920	+	1.48733i	−0.0524471	+	0.0582484i
$653$	−2.13507	−	0.950593i	−0.0835516	−	0.0371996i	0.364535	−	0.931190i	$-0.381228\pi$
$653$	−2.13507	−	0.950593i	−0.0835516	−	0.0371996i	−0.448087	+	0.893990i	$0.647895\pi$
$654$	2.00906	−	1.11988i	0.0785605	−	0.0437909i
$655$	−18.7339	−	4.38203i	−0.731993	−	0.171220i
$656$	−14.6102	−	10.6149i	−0.570431	−	0.414443i
$657$	−27.9080	+	29.1756i	−1.08880	+	1.13825i
$658$	7.11341	+	5.16819i	0.277309	+	0.201477i
$659$	−28.6007	−	31.7643i	−1.11413	−	1.23736i	−0.968764	−	0.247984i	$-0.920232\pi$
$659$	−28.6007	−	31.7643i	−1.11413	−	1.23736i	−0.145362	−	0.989379i	$-0.546435\pi$
$660$	−2.63152	+	0.753122i	−0.102432	+	0.0293152i
$661$	3.82599	−	4.24920i	0.148814	−	0.165275i	−0.664129	−	0.747618i	$-0.731197\pi$
$661$	3.82599	−	4.24920i	0.148814	−	0.165275i	0.812943	+	0.582343i	$0.197864\pi$
$662$	4.32557	−	0.919428i	0.168118	−	0.0357346i
$663$	−7.34635	−	10.4388i	−0.285309	−	0.405411i
$664$	1.84444	+	0.392049i	0.0715783	+	0.0152144i
$665$	0.198213	+	0.655079i	0.00768637	+	0.0254029i
$666$	3.78985	+	0.114331i	0.146854	+	0.00443025i
$667$	−23.0187	−	16.7240i	−0.891287	−	0.647558i
$668$	3.78106	−	6.54900i	0.146294	−	0.253388i
$669$	0.755352	+	0.701032i	0.0292036	+	0.0271035i
$670$	4.79636	+	2.25345i	0.185300	+	0.0870584i
$671$	−2.97802	−	1.32590i	−0.114965	−	0.0511858i
$672$	11.9096	+	7.11758i	0.459423	+	0.274567i
$673$	1.93341	+	0.410959i	0.0745275	+	0.0158413i	0.245025	−	0.969517i	$-0.421204\pi$
$673$	1.93341	+	0.410959i	0.0745275	+	0.0158413i	−0.170497	+	0.985358i	$0.554537\pi$
$674$	−1.41815			−0.0546250
$675$	7.56245	−	24.8558i	0.291079	−	0.956699i
$676$	18.9234			0.727824
$677$	10.1510	+	2.15766i	0.390134	+	0.0829254i	0.398802	−	0.917037i	$-0.369426\pi$
$677$	10.1510	+	2.15766i	0.390134	+	0.0829254i	−0.00866862	+	0.999962i	$0.502759\pi$
$678$	−2.17439	−	1.29949i	−0.0835068	−	0.0499065i
$679$	−39.9175	−	17.7724i	−1.53189	−	0.682043i
$680$	−5.72801	+	1.09627i	−0.219659	+	0.0420401i
$681$	11.7241	+	10.8810i	0.449270	+	0.416961i
$682$	0.159657	−	0.276534i	0.00611358	−	0.0105890i
$683$	19.2932	+	14.0174i	0.738235	+	0.536359i	0.892158	−	0.451724i	$-0.149191\pi$
$683$	19.2932	+	14.0174i	0.738235	+	0.536359i	−0.153923	+	0.988083i	$0.549191\pi$
$684$	−0.230499	+	0.372802i	−0.00881333	+	0.0142544i
$685$	−10.5186	+	7.32006i	−0.401894	+	0.279685i
$686$	−2.05046	−	0.435839i	−0.0782870	−	0.0166404i
$687$	2.60276	+	3.69841i	0.0993014	+	0.141103i
$688$	11.6438	−	2.47496i	0.443914	−	0.0943569i
$689$	−2.33905	+	2.59778i	−0.0891108	+	0.0989676i
$690$	−0.0987429	+	2.78678i	−0.00375908	+	0.106091i
$691$	−0.688270	−	0.764401i	−0.0261830	−	0.0290792i	0.729911	−	0.683542i	$-0.239561\pi$
$691$	−0.688270	−	0.764401i	−0.0261830	−	0.0290792i	−0.756094	+	0.654463i	$0.772895\pi$
$692$	35.4065	+	25.7243i	1.34595	+	0.977893i
$693$	4.31487	+	1.05408i	0.163908	+	0.0400413i
$694$	4.67273	+	3.39494i	0.177374	+	0.128870i
$695$	−24.2486	−	28.0579i	−0.919802	−	1.06430i
$696$	6.42421	−	3.58096i	0.243509	−	0.135736i
$697$	−17.1568	−	7.63868i	−0.649859	−	0.289336i
$698$	2.31434	−	2.57033i	0.0875990	−	0.0972886i
$699$	4.50193	+	10.5363i	0.170279	+	0.398518i
$700$	37.8923	−	15.0557i	1.43219	−	0.569052i
$701$	14.7743			0.558019			0.279009	−	0.960288i	$-0.409994\pi$
$701$	14.7743			0.558019			0.279009	+	0.960288i	$0.409994\pi$
$702$	0.0713471	−	1.57608i	0.00269282	−	0.0594852i
$703$	−0.460406	+	0.334504i	−0.0173645	+	0.0126161i
$704$	−0.275515	−	2.62135i	−0.0103839	−	0.0987958i
$705$	42.4718	+	26.5695i	1.59958	+	1.00067i
$706$	0.338691	−	3.22243i	0.0127468	−	0.121278i
$707$	−36.2017	−	62.7032i	−1.36151	−	2.35820i
$708$	12.3947	+	11.5033i	0.465820	+	0.432321i
$709$	−7.87589	−	8.74706i	−0.295785	−	0.328503i	0.576873	−	0.816834i	$-0.304273\pi$
$709$	−7.87589	−	8.74706i	−0.295785	−	0.328503i	−0.872659	+	0.488331i	$0.837606\pi$
$710$	−1.43032	−	4.72709i	−0.0536788	−	0.177405i
$711$	−14.8531	+	10.1215i	−0.557036	+	0.379586i
$712$	1.44664	−	4.45231i	0.0542152	−	0.166857i
$713$	15.8786	+	17.6350i	0.594659	+	0.660435i
$714$	4.44729	+	1.51952i	0.166436	+	0.0568668i
$715$	−0.184455	+	1.46726i	−0.00689824	+	0.0548723i
$716$	−28.2494	+	6.00460i	−1.05573	+	0.224403i
$717$	27.3428	−	8.43055i	1.02113	−	0.314845i
$718$	−0.249761	+	0.432599i	−0.00932099	+	0.0161444i
$719$	−37.9326	−	27.5596i	−1.41465	−	1.02780i	−0.992626	−	0.121213i	$-0.961321\pi$
$719$	−37.9326	−	27.5596i	−1.41465	−	1.02780i	−0.422019	−	0.906587i	$-0.638679\pi$
$720$	22.9644	+	11.6471i	0.855832	+	0.434062i
$721$	40.0084	−	29.0678i	1.48999	−	1.08254i
$722$	−0.326525	−	3.10668i	−0.0121520	−	0.115619i
$723$	2.51536	+	12.7784i	0.0935473	+	0.475233i
$724$	16.9905	+	29.4285i	0.631449	+	1.09370i
$725$	4.70803	−	32.1521i	0.174852	−	1.19410i
$726$	−1.21677	−	2.84772i	−0.0451587	−	0.105689i
$727$	30.7754	+	6.54152i	1.14140	+	0.242611i	0.739554	−	0.673097i	$-0.235036\pi$
$727$	30.7754	+	6.54152i	1.14140	+	0.242611i	0.401843	+	0.915709i	$0.368370\pi$
$728$	4.03371	−	2.93066i	0.149499	−	0.108618i
$729$	−26.8896	−	2.43952i	−0.995910	−	0.0903524i
$730$	4.94801	+	0.100649i	0.183134	+	0.00372518i
$731$	11.3091	−	5.03512i	0.418281	−	0.186231i
$732$	12.2190	+	28.5971i	0.451626	+	1.05698i
$733$	4.73859	−	45.0847i	0.175024	−	1.66524i	−0.456378	−	0.889786i	$-0.650854\pi$
$733$	4.73859	−	45.0847i	0.175024	−	1.66524i	0.631402	−	0.775455i	$-0.282480\pi$
$734$	−1.16846	+	0.248364i	−0.0431286	+	0.00916727i
$735$	−38.6719	−	5.45514i	−1.42644	−	0.201216i
$736$	−8.29928	−	1.76407i	−0.305916	−	0.0650244i
$737$	−1.59517	+	4.90942i	−0.0587587	+	0.180841i
$738$	−1.09946	−	2.04432i	−0.0404719	−	0.0752523i
$739$	12.0961	+	37.2280i	0.444963	+	1.36945i	0.882524	+	0.470267i	$0.155842\pi$
$739$	12.0961	+	37.2280i	0.444963	+	1.36945i	−0.437562	+	0.899188i	$0.644158\pi$
$740$	22.1689	+	25.6515i	0.814946	+	0.942969i
$741$	0.136284	+	0.193654i	0.00500652	+	0.00711405i
$742$	0.134531	−	1.27998i	0.00493881	−	0.0469896i
$743$	24.2958	+	42.0815i	0.891325	+	1.54382i	0.838288	+	0.545228i	$0.183557\pi$
$743$	24.2958	+	42.0815i	0.891325	+	1.54382i	0.0530375	+	0.998593i	$0.483110\pi$
$744$	−5.86182	+	1.80737i	−0.214905	+	0.0662612i
$745$	−14.4452	+	6.08250i	−0.529231	+	0.222846i
$746$	1.40499	−	1.02078i	0.0514403	−	0.0373735i
$747$	−6.84779	−	5.29792i	−0.250548	−	0.193841i
$748$	−0.871772	−	2.68304i	−0.0318751	−	0.0981016i
$749$	−17.5470	+	30.3923i	−0.641154	+	1.11051i
$750$	−2.87111	+	1.37807i	−0.104838	+	0.0503202i
$751$	9.62073	+	16.6636i	0.351066	+	0.608063i	0.986436	−	0.164144i	$-0.0524861\pi$
$751$	9.62073	+	16.6636i	0.351066	+	0.608063i	−0.635371	+	0.772207i	$0.719153\pi$
$752$	−33.2231	+	36.8980i	−1.21152	+	1.34553i
$753$	−28.5663	−	17.0722i	−1.04101	−	0.622145i
$754$	−0.206263	−	1.96246i	−0.00751165	−	0.0714686i
$755$	−8.38982	−	6.36021i	−0.305337	−	0.231472i
$756$	−23.3307	−	35.3720i	−0.848528	−	1.28647i
$757$	−21.2374			−0.771886			−0.385943	−	0.922523i	$-0.626124\pi$
$757$	−21.2374			−0.771886			−0.385943	+	0.922523i	$0.626124\pi$
$758$	−5.29557	+	2.35774i	−0.192344	+	0.0856370i
$759$	−2.70539	+	0.243164i	−0.0981994	+	0.00882629i
$760$	0.106262	−	0.0203372i	0.00385453	−	0.000737710i
$761$	22.6915	−	25.2015i	0.822566	−	0.913552i	−0.174908	−	0.984585i	$-0.555963\pi$
$761$	22.6915	−	25.2015i	0.822566	−	0.913552i	0.997474	+	0.0710326i	$0.0226294\pi$
$762$	0.388638	−	0.838629i	0.0140789	−	0.0303803i
$763$	−22.3325	−	24.8027i	−0.808490	−	0.897919i
$764$	−0.355085	−	1.09284i	−0.0128465	−	0.0395375i
$765$	25.8780	+	6.88234i	0.935619	+	0.248831i
$766$

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.160864 + 0.0341926i) q^{2} +(1.48677 + 0.888545i) q^{3} +(-1.80238 - 0.802473i) q^{4} +(0.278910 - 2.21861i) q^{5} +(0.208786 + 0.193771i) q^{6} +(2.06663 - 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(1.42098 + 2.64213i) q^{9} +O(q^{10})\)	\(q+(0.160864 + 0.0341926i) q^{2} +(1.48677 + 0.888545i) q^{3} +(-1.80238 - 0.802473i) q^{4} +(0.278910 - 2.21861i) q^{5} +(0.208786 + 0.193771i) q^{6} +(2.06663 - 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(1.42098 + 2.64213i) q^{9} +(0.120726 - 0.347356i) q^{10} +(0.350384 + 0.0744764i) q^{11} +(-1.96670 - 2.79459i) q^{12} +(-1.80589 + 0.383854i) q^{13} +(0.454839 - 0.505150i) q^{14} +(2.38601 - 3.05073i) q^{15} +(2.56843 + 2.85253i) q^{16} +(3.22940 + 2.34629i) q^{17} +(0.138242 + 0.473609i) q^{18} +(-0.0599095 - 0.0435268i) q^{19} +(-2.28307 + 3.77496i) q^{20} +(6.25317 - 3.48562i) q^{21} +(0.0538175 + 0.0239611i) q^{22} +(-2.92946 + 3.25349i) q^{23} +(-0.444658 - 1.04067i) q^{24} +(-4.84442 - 1.23758i) q^{25} -0.303627 q^{26} +(-0.234983 + 5.19084i) q^{27} +(-6.59733 + 4.79324i) q^{28} +(0.679330 + 6.46339i) q^{29} +(0.488134 - 0.409168i) q^{30} +(0.566578 - 5.39063i) q^{31} +(0.969013 + 1.67838i) q^{32} +(0.454765 + 0.422061i) q^{33} +(0.439267 + 0.487855i) q^{34} +(-7.36512 - 5.58341i) q^{35} +(-0.440908 - 5.90242i) q^{36} +(2.37480 - 7.30889i) q^{37} +(-0.00814896 - 0.00905033i) q^{38} +(-3.02602 - 1.03391i) q^{39} +(-0.999482 + 1.06563i) q^{40} +(-4.60199 + 0.978183i) q^{41} +(1.12509 - 0.346897i) q^{42} +(1.55061 - 2.68574i) q^{43} +(-0.571760 - 0.415408i) q^{44} +(6.25816 - 2.41567i) q^{45} +(-0.582489 + 0.423203i) q^{46} +(1.35210 + 12.8643i) q^{47} +(1.28406 + 6.52322i) q^{48} +(-5.04195 - 8.73292i) q^{49} +(-0.736974 - 0.364726i) q^{50} +(2.71659 + 6.35787i) q^{51} +(3.56294 + 0.757326i) q^{52} +(1.53179 - 1.11291i) q^{53} +(-0.215288 + 0.826982i) q^{54} +(0.262959 - 0.756591i) q^{55} +(-2.46712 + 1.09843i) q^{56} +(-0.0503961 - 0.117947i) q^{57} +(-0.111721 + 1.06295i) q^{58} +(-4.84033 + 1.02884i) q^{59} +(-6.74863 + 3.58388i) q^{60} +(-8.90148 - 1.89207i) q^{61} +(0.275461 - 0.847783i) q^{62} +(12.3942 + 0.373904i) q^{63} +(-2.27380 - 6.99805i) q^{64} +(0.347939 + 4.11362i) q^{65} +(0.0587237 + 0.0834439i) q^{66} +(-1.50633 + 14.3317i) q^{67} +(-3.93777 - 6.82042i) q^{68} +(-7.24631 + 2.23424i) q^{69} +(-0.993869 - 1.15000i) q^{70} +(10.8652 - 7.89400i) q^{71} +(0.263580 - 1.94234i) q^{72} +(4.15877 + 12.7994i) q^{73} +(0.631930 - 1.09453i) q^{74} +(-6.10289 - 6.14449i) q^{75} +(0.0730507 + 0.126528i) q^{76} +(0.990704 - 1.10029i) q^{77} +(-0.451424 - 0.269786i) q^{78} +(0.626261 + 5.95848i) q^{79} +(7.04499 - 4.90273i) q^{80} +(-4.96166 + 7.50879i) q^{81} -0.773739 q^{82} +(-2.63648 + 1.17384i) q^{83} +(-14.0677 + 1.26443i) q^{84} +(6.10621 - 6.51035i) q^{85} +(0.341269 - 0.379018i) q^{86} +(-4.73301 + 10.2132i) q^{87} +(-0.156609 - 0.173932i) q^{88} +(2.21408 + 6.81425i) q^{89} +(1.08931 - 0.174610i) q^{90} +(-2.35810 + 7.25750i) q^{91} +(7.89085 - 3.51323i) q^{92} +(5.63219 - 7.51120i) q^{93} +(-0.222362 + 2.11564i) q^{94} +(-0.113278 + 0.120775i) q^{95} +(-0.0506157 + 3.35638i) q^{96} +(-1.10503 - 10.5137i) q^{97} +(-0.512465 - 1.57721i) q^{98} +(0.301111 + 1.03159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

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