LMFDB - Embedded newform 129.2.m.a.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [129,2,Mod(10,129)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(129, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("129.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 129 = 3 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	129.m (of order $21$, 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:	$1.03007018607$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	129.103
Dual form			129.2.m.a.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.287052 - 1.25766i) q^{2} +(-0.955573 + 0.294755i) q^{3} +(0.302640 - 0.145744i) q^{4} +(0.224531 - 0.572095i) q^{5} +(0.644999 + 1.11717i) q^{6} +(1.20831 - 2.09285i) q^{7} +(-1.87877 - 2.35590i) q^{8} +(0.826239 - 0.563320i) q^{9} +O(q^{10})$	\(q+(-0.287052 - 1.25766i) q^{2} +(-0.955573 + 0.294755i) q^{3} +(0.302640 - 0.145744i) q^{4} +(0.224531 - 0.572095i) q^{5} +(0.644999 + 1.11717i) q^{6} +(1.20831 - 2.09285i) q^{7} +(-1.87877 - 2.35590i) q^{8} +(0.826239 - 0.563320i) q^{9} +(-0.783950 - 0.118161i) q^{10} +(-1.65422 - 0.796629i) q^{11} +(-0.246236 + 0.228473i) q^{12} +(0.533238 - 0.0803727i) q^{13} +(-2.97894 - 0.918880i) q^{14} +(-0.0459275 + 0.612860i) q^{15} +(-2.00474 + 2.51387i) q^{16} +(0.615740 + 1.56888i) q^{17} +(-0.945636 - 0.877422i) q^{18} +(3.17956 + 2.16779i) q^{19} +(-0.0154273 - 0.205862i) q^{20} +(-0.537749 + 2.35603i) q^{21} +(-0.527039 + 2.30911i) q^{22} +(-0.00961601 - 0.128317i) q^{23} +(2.48972 + 1.69746i) q^{24} +(3.38838 + 3.14396i) q^{25} +(-0.254148 - 0.647559i) q^{26} +(-0.623490 + 0.781831i) q^{27} +(0.0606624 - 0.809484i) q^{28} +(6.23167 + 1.92221i) q^{29} +(0.783950 - 0.118161i) q^{30} +(-4.18482 + 3.88294i) q^{31} +(-1.69276 - 0.815189i) q^{32} +(1.81554 + 0.273648i) q^{33} +(1.79636 - 1.22474i) q^{34} +(-0.926008 - 1.16118i) q^{35} +(0.167952 - 0.290902i) q^{36} +(0.191060 + 0.330925i) q^{37} +(1.81363 - 4.62106i) q^{38} +(-0.485858 + 0.233977i) q^{39} +(-1.76964 + 0.545862i) q^{40} +(2.19588 + 9.62078i) q^{41} +3.11744 q^{42} +(-4.90043 - 4.35726i) q^{43} -0.616736 q^{44} +(-0.136757 - 0.599169i) q^{45} +(-0.158618 + 0.0489271i) q^{46} +(5.30472 - 2.55462i) q^{47} +(1.17470 - 2.99309i) q^{48} +(0.579974 + 1.00454i) q^{49} +(2.98138 - 5.16389i) q^{50} +(-1.05082 - 1.31769i) q^{51} +(0.149665 - 0.102040i) q^{52} +(-4.74489 - 0.715178i) q^{53} +(1.16225 + 0.559709i) q^{54} +(-0.827170 + 0.767502i) q^{55} +(-7.20070 + 1.08533i) q^{56} +(-3.67727 - 1.13429i) q^{57} +(0.628673 - 8.38906i) q^{58} +(-4.57796 + 5.74058i) q^{59} +(0.0754209 + 0.192169i) q^{60} +(-7.99323 - 7.41663i) q^{61} +(6.08466 + 4.14845i) q^{62} +(-0.180594 - 2.40986i) q^{63} +(-1.97029 + 8.63239i) q^{64} +(0.0737475 - 0.323109i) q^{65} +(-0.176998 - 2.36187i) q^{66} +(-10.3932 - 7.08599i) q^{67} +(0.415002 + 0.385065i) q^{68} +(0.0470108 + 0.119782i) q^{69} +(-1.19455 + 1.49792i) q^{70} +(0.389707 - 5.20028i) q^{71} +(-2.87944 - 0.888190i) q^{72} +(11.3353 - 1.70852i) q^{73} +(0.361346 - 0.335280i) q^{74} +(-4.16454 - 2.00554i) q^{75} +(1.27820 + 0.192658i) q^{76} +(-3.66604 + 2.49946i) q^{77} +(0.433728 + 0.543878i) q^{78} +(0.784744 - 1.35922i) q^{79} +(0.988045 + 1.71134i) q^{80} +(0.365341 - 0.930874i) q^{81} +(11.4693 - 5.52332i) q^{82} +(5.89686 - 1.81894i) q^{83} +(0.180632 + 0.791402i) q^{84} +1.03580 q^{85} +(-4.07326 + 7.41382i) q^{86} -6.52139 q^{87} +(1.23111 + 5.39386i) q^{88} +(13.3477 - 4.11722i) q^{89} +(-0.714292 + 0.343985i) q^{90} +(0.476109 - 1.21311i) q^{91} +(-0.0216115 - 0.0374322i) q^{92} +(2.85438 - 4.94393i) q^{93} +(-4.73556 - 5.93820i) q^{94} +(1.95409 - 1.33228i) q^{95} +(1.85783 + 0.280023i) q^{96} +(6.57955 + 3.16854i) q^{97} +(1.09689 - 1.01776i) q^{98} +(-1.81554 + 0.273648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 3 q^{3} - 6 q^{4} + 3 q^{5} + q^{6} - 11 q^{7} - 14 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 3 * q^3 - 6 * q^4 + 3 * q^5 + q^6 - 11 * q^7 - 14 * q^8 + 3 * q^9	\( 36 q + 2 q^{2} - 3 q^{3} - 6 q^{4} + 3 q^{5} + q^{6} - 11 q^{7} - 14 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + 4 q^{12} - 8 q^{13} - 70 q^{14} - 10 q^{15} + 10 q^{16} - 3 q^{17} - q^{18} - 3 q^{19} + 13 q^{20} + 13 q^{21} - 8 q^{22} - 32 q^{23} + 7 q^{24} + 12 q^{25} + 11 q^{26} + 6 q^{27} + 35 q^{28} + 8 q^{29} + 2 q^{30} - 24 q^{31} + 40 q^{32} + 17 q^{33} + 54 q^{34} - 14 q^{35} - 11 q^{36} + 2 q^{37} + 44 q^{38} + 12 q^{39} - 66 q^{40} + 55 q^{41} + 28 q^{42} - 23 q^{43} - 10 q^{44} + 8 q^{45} + 30 q^{46} + 26 q^{47} + 5 q^{48} - q^{49} + 19 q^{50} - 6 q^{51} - 64 q^{52} - 59 q^{53} - 2 q^{54} + 19 q^{55} - 11 q^{56} - 39 q^{57} - 69 q^{58} + 16 q^{59} - 48 q^{60} - 87 q^{61} - 67 q^{62} + 3 q^{63} + 18 q^{64} - 19 q^{65} + 10 q^{66} - 29 q^{67} + 3 q^{68} + 4 q^{69} - 83 q^{70} + 34 q^{71} + 8 q^{73} - 70 q^{74} - 32 q^{75} + 99 q^{76} + 101 q^{77} - 20 q^{78} - 10 q^{79} + 42 q^{80} + 3 q^{81} + 134 q^{82} - 33 q^{83} + 21 q^{84} + 92 q^{85} + 15 q^{86} + 16 q^{87} + 16 q^{88} + 80 q^{89} + 18 q^{90} - 22 q^{91} + 75 q^{92} - 4 q^{93} + 54 q^{94} - 69 q^{95} - 50 q^{96} + 91 q^{97} + 165 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 3 * q^3 - 6 * q^4 + 3 * q^5 + q^6 - 11 * q^7 - 14 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + 4 * q^12 - 8 * q^13 - 70 * q^14 - 10 * q^15 + 10 * q^16 - 3 * q^17 - q^18 - 3 * q^19 + 13 * q^20 + 13 * q^21 - 8 * q^22 - 32 * q^23 + 7 * q^24 + 12 * q^25 + 11 * q^26 + 6 * q^27 + 35 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 40 * q^32 + 17 * q^33 + 54 * q^34 - 14 * q^35 - 11 * q^36 + 2 * q^37 + 44 * q^38 + 12 * q^39 - 66 * q^40 + 55 * q^41 + 28 * q^42 - 23 * q^43 - 10 * q^44 + 8 * q^45 + 30 * q^46 + 26 * q^47 + 5 * q^48 - q^49 + 19 * q^50 - 6 * q^51 - 64 * q^52 - 59 * q^53 - 2 * q^54 + 19 * q^55 - 11 * q^56 - 39 * q^57 - 69 * q^58 + 16 * q^59 - 48 * q^60 - 87 * q^61 - 67 * q^62 + 3 * q^63 + 18 * q^64 - 19 * q^65 + 10 * q^66 - 29 * q^67 + 3 * q^68 + 4 * q^69 - 83 * q^70 + 34 * q^71 + 8 * q^73 - 70 * q^74 - 32 * q^75 + 99 * q^76 + 101 * q^77 - 20 * q^78 - 10 * q^79 + 42 * q^80 + 3 * q^81 + 134 * q^82 - 33 * q^83 + 21 * q^84 + 92 * q^85 + 15 * q^86 + 16 * q^87 + 16 * q^88 + 80 * q^89 + 18 * q^90 - 22 * q^91 + 75 * q^92 - 4 * q^93 + 54 * q^94 - 69 * q^95 - 50 * q^96 + 91 * q^97 + 165 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/129\mathbb{Z}\right)^\times$.

$n$	$44$	$46$
$\chi(n)$	$1$	$e\left(\frac{19}{21}\right)$

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 $

$2$	−0.287052	−	1.25766i	−0.202976	−	0.889297i	−0.969113	−	0.246619i	$-0.920680\pi$
$2$	−0.287052	−	1.25766i	−0.202976	−	0.889297i	0.766136	−	0.642678i	$-0.222177\pi$
$3$	−0.955573	+	0.294755i	−0.551700	+	0.170177i
$3$	−0.955573	+	0.294755i	−0.551700	+	0.170177i
$4$	0.302640	−	0.145744i	0.151320	−	0.0728718i
$5$	0.224531	−	0.572095i	0.100413	−	0.255849i	−0.871835	−	0.489799i	$-0.837070\pi$
$5$	0.224531	−	0.572095i	0.100413	−	0.255849i	0.972249	+	0.233951i	$0.0751654\pi$
$6$	0.644999	+	1.11717i	0.263320	+	0.456083i
$7$	1.20831	−	2.09285i	0.456698	−	0.791025i	−0.542086	−	0.840323i	$-0.682365\pi$
$7$	1.20831	−	2.09285i	0.456698	−	0.791025i	0.998784	+	0.0492985i	$0.0156986\pi$
$8$	−1.87877	−	2.35590i	−0.664245	−	0.832937i
$9$	0.826239	−	0.563320i	0.275413	−	0.187773i
$10$	−0.783950	−	0.118161i	−0.247907	−	0.0373659i
$11$	−1.65422	−	0.796629i	−0.498765	−	0.240193i	0.167549	−	0.985864i	$-0.446415\pi$
$11$	−1.65422	−	0.796629i	−0.498765	−	0.240193i	−0.666314	+	0.745671i	$0.732129\pi$
$12$	−0.246236	+	0.228473i	−0.0710821	+	0.0659545i
$13$	0.533238	−	0.0803727i	0.147894	−	0.0222914i	−0.0746781	−	0.997208i	$-0.523793\pi$
$13$	0.533238	−	0.0803727i	0.147894	−	0.0222914i	0.222572	+	0.974916i	$0.428555\pi$
$14$	−2.97894	−	0.918880i	−0.796154	−	0.245581i
$15$	−0.0459275	+	0.612860i	−0.0118584	+	0.158240i
$16$	−2.00474	+	2.51387i	−0.501186	+	0.628467i
$17$	0.615740	+	1.56888i	0.149339	+	0.380509i	0.985893	−	0.167374i	$-0.0535288\pi$
$17$	0.615740	+	1.56888i	0.149339	+	0.380509i	−0.836554	+	0.547884i	$0.815434\pi$
$18$	−0.945636	−	0.877422i	−0.222888	−	0.206810i
$19$	3.17956	+	2.16779i	0.729442	+	0.497325i	0.870188	−	0.492721i	$-0.163998\pi$
$19$	3.17956	+	2.16779i	0.729442	+	0.497325i	−0.140745	+	0.990046i	$0.544950\pi$
$20$	−0.0154273	−	0.205862i	−0.00344964	−	0.0460322i
$21$	−0.537749	+	2.35603i	−0.117346	+	0.514128i
$22$	−0.527039	+	2.30911i	−0.112365	+	0.492304i
$23$	−0.00961601	−	0.128317i	−0.00200508	−	0.0267559i	0.996112	−	0.0881013i	$-0.0280799\pi$
$23$	−0.00961601	−	0.128317i	−0.00200508	−	0.0267559i	−0.998117	+	0.0613454i	$0.980461\pi$
$24$	2.48972	+	1.69746i	0.508211	+	0.346492i
$25$	3.38838	+	3.14396i	0.677676	+	0.628792i
$26$	−0.254148	−	0.647559i	−0.0498425	−	0.126997i
$27$	−0.623490	+	0.781831i	−0.119991	+	0.150464i
$28$	0.0606624	−	0.809484i	0.0114641	−	0.152978i
$29$	6.23167	+	1.92221i	1.15719	+	0.356946i	0.813176	−	0.582018i	$-0.197737\pi$
$29$	6.23167	+	1.92221i	1.15719	+	0.356946i	0.344015	+	0.938964i	$0.388213\pi$
$30$	0.783950	−	0.118161i	0.143129	−	0.0215732i
$31$	−4.18482	+	3.88294i	−0.751615	+	0.697397i	−0.959798	−	0.280693i	$-0.909436\pi$
$31$	−4.18482	+	3.88294i	−0.751615	+	0.697397i	0.208183	+	0.978090i	$0.433245\pi$
$32$	−1.69276	−	0.815189i	−0.299240	−	0.144106i
$33$	1.81554	+	0.273648i	0.316044	+	0.0476360i
$34$	1.79636	−	1.22474i	0.308074	−	0.210041i
$35$	−0.926008	−	1.16118i	−0.156524	−	0.196275i
$36$	0.167952	−	0.290902i	0.0279921	−	0.0484837i
$37$	0.191060	+	0.330925i	0.0314100	+	0.0544037i	0.881303	−	0.472551i	$-0.156667\pi$
$37$	0.191060	+	0.330925i	0.0314100	+	0.0544037i	−0.849893	+	0.526955i	$0.823334\pi$
$38$	1.81363	−	4.62106i	0.294210	−	0.749636i
$39$	−0.485858	+	0.233977i	−0.0777995	+	0.0374663i
$40$	−1.76964	+	0.545862i	−0.279805	+	0.0863084i
$41$	2.19588	+	9.62078i	0.342939	+	1.50251i	0.792837	+	0.609433i	$0.208603\pi$
$41$	2.19588	+	9.62078i	0.342939	+	1.50251i	−0.449899	+	0.893080i	$0.648540\pi$
$42$	3.11744			0.481031
$43$	−4.90043	−	4.35726i	−0.747309	−	0.664477i
$43$	−4.90043	−	4.35726i	−0.747309	−	0.664477i
$44$	−0.616736			−0.0929764
$45$	−0.136757	−	0.599169i	−0.0203865	−	0.0893189i
$46$	−0.158618	+	0.0489271i	−0.0233869	+	0.00721391i
$47$	5.30472	−	2.55462i	0.773773	−	0.372630i	−0.00495766	−	0.999988i	$-0.501578\pi$
$47$	5.30472	−	2.55462i	0.773773	−	0.372630i	0.778731	+	0.627358i	$0.215864\pi$
$48$	1.17470	−	2.99309i	0.169554	−	0.432016i
$49$	0.579974	+	1.00454i	0.0828534	+	0.143506i
$50$	2.98138	−	5.16389i	0.421630	−	0.730285i
$51$	−1.05082	−	1.31769i	−0.147144	−	0.184513i
$52$	0.149665	−	0.102040i	0.0207548	−	0.0141504i
$53$	−4.74489	−	0.715178i	−0.651761	−	0.0982372i	−0.185165	−	0.982707i	$-0.559282\pi$
$53$	−4.74489	−	0.715178i	−0.651761	−	0.0982372i	−0.466596	+	0.884470i	$0.654520\pi$
$54$	1.16225	+	0.559709i	0.158162	+	0.0761668i
$55$	−0.827170	+	0.767502i	−0.111536	+	0.103490i
$56$	−7.20070	+	1.08533i	−0.962234	+	0.145033i
$57$	−3.67727	−	1.13429i	−0.487067	−	0.150240i
$58$	0.628673	−	8.38906i	0.0825488	−	1.10154i
$59$	−4.57796	+	5.74058i	−0.596000	+	0.747360i	−0.984749	−	0.173984i	$-0.944336\pi$
$59$	−4.57796	+	5.74058i	−0.596000	+	0.747360i	0.388749	+	0.921344i	$0.372907\pi$
$60$	0.0754209	+	0.192169i	0.00973680	+	0.0248090i
$61$	−7.99323	−	7.41663i	−1.02343	−	0.949603i	−0.0246837	−	0.999695i	$-0.507858\pi$
$61$	−7.99323	−	7.41663i	−1.02343	−	0.949603i	−0.998745	+	0.0500926i	$0.984048\pi$
$62$	6.08466	+	4.14845i	0.772752	+	0.526854i
$63$	−0.180594	−	2.40986i	−0.0227527	−	0.303614i
$64$	−1.97029	+	8.63239i	−0.246286	+	1.07905i
$65$	0.0737475	−	0.323109i	0.00914725	−	0.0400767i
$66$	−0.176998	−	2.36187i	−0.0217869	−	0.290726i
$67$	−10.3932	−	7.08599i	−1.26974	−	0.865692i	−0.274349	−	0.961630i	$-0.588462\pi$
$67$	−10.3932	−	7.08599i	−1.26974	−	0.865692i	−0.995387	+	0.0959382i	$0.969415\pi$
$68$	0.415002	+	0.385065i	0.0503264	+	0.0466960i
$69$	0.0470108	+	0.119782i	0.00565943	+	0.0144200i
$70$	−1.19455	+	1.49792i	−0.142776	+	0.179035i
$71$	0.389707	−	5.20028i	0.0462498	−	0.617160i	−0.925133	−	0.379642i	$-0.876047\pi$
$71$	0.389707	−	5.20028i	0.0462498	−	0.617160i	0.971383	−	0.237518i	$-0.0763339\pi$
$72$	−2.87944	−	0.888190i	−0.339345	−	0.104674i
$73$	11.3353	−	1.70852i	1.32669	−	0.199967i	0.552816	−	0.833303i	$-0.313553\pi$
$73$	11.3353	−	1.70852i	1.32669	−	0.199967i	0.773877	+	0.633336i	$0.218315\pi$
$74$	0.361346	−	0.335280i	0.0420056	−	0.0389755i
$75$	−4.16454	−	2.00554i	−0.480880	−	0.231580i
$76$	1.27820	+	0.192658i	0.146620	+	0.0220994i
$77$	−3.66604	+	2.49946i	−0.417784	+	0.284840i
$78$	0.433728	+	0.543878i	0.0491101	+	0.0615821i
$79$	0.784744	−	1.35922i	0.0882906	−	0.152924i	−0.818498	−	0.574509i	$-0.805193\pi$
$79$	0.784744	−	1.35922i	0.0882906	−	0.152924i	0.906789	+	0.421585i	$0.138526\pi$
$80$	0.988045	+	1.71134i	0.110467	+	0.191334i
$81$	0.365341	−	0.930874i	0.0405934	−	0.103430i
$82$	11.4693	−	5.52332i	1.26657	−	0.609948i
$83$	5.89686	−	1.81894i	0.647264	−	0.199655i	0.0462964	−	0.998928i	$-0.485258\pi$
$83$	5.89686	−	1.81894i	0.647264	−	0.199655i	0.600968	+	0.799273i	$0.294782\pi$
$84$	0.180632	+	0.791402i	0.0197086	+	0.0863490i
$85$	1.03580			0.112348
$86$	−4.07326	+	7.41382i	−0.439231	+	0.799452i
$87$	−6.52139			−0.699167
$88$	1.23111	+	5.39386i	0.131237	+	0.574987i
$89$	13.3477	−	4.11722i	1.41485	−	0.436425i	0.509276	−	0.860603i	$-0.329913\pi$
$89$	13.3477	−	4.11722i	1.41485	−	0.436425i	0.905579	+	0.424178i	$0.139437\pi$
$90$	−0.714292	+	0.343985i	−0.0752930	+	0.0362592i
$91$	0.476109	−	1.21311i	0.0499098	−	0.127168i
$92$	−0.0216115	−	0.0374322i	−0.00225316	−	0.00390258i
$93$	2.85438	−	4.94393i	0.295985	−	0.512662i
$94$	−4.73556	−	5.93820i	−0.488436	−	0.612479i
$95$	1.95409	−	1.33228i	0.200486	−	0.136689i
$96$	1.85783	+	0.280023i	0.189614	+	0.0285798i
$97$	6.57955	+	3.16854i	0.668052	+	0.321717i	0.736990	−	0.675904i	$-0.236247\pi$
$97$	6.57955	+	3.16854i	0.668052	+	0.321717i	−0.0689375	+	0.997621i	$0.521961\pi$
$98$	1.09689	−	1.01776i	0.110802	−	0.102810i
$99$	−1.81554	+	0.273648i	−0.182468	+	0.0275027i
$100$	1.48367	+	0.457652i	0.148367	+	0.0457652i
$101$	−0.688877	+	9.19243i	−0.0685458	+	0.914681i	0.851873	+	0.523748i	$0.175467\pi$
$101$	−0.688877	+	9.19243i	−0.0685458	+	0.914681i	−0.920419	+	0.390933i	$0.872152\pi$
$102$	−1.35556	+	1.69981i	−0.134220	+	0.168307i
$103$	−6.48775	−	16.5305i	−0.639257	−	1.62880i	−0.770493	−	0.637448i	$-0.779990\pi$
$103$	−6.48775	−	16.5305i	−0.639257	−	1.62880i	0.131236	−	0.991351i	$-0.458105\pi$
$104$	−1.19118	−	1.10526i	−0.116805	−	0.108379i
$105$	1.22713	+	0.836644i	0.119756	+	0.0816481i
$106$	0.462582	+	6.17273i	0.0449300	+	0.599549i
$107$	−2.07235	+	9.07954i	−0.200341	+	0.877752i	0.770388	+	0.637575i	$0.220063\pi$
$107$	−2.07235	+	9.07954i	−0.200341	+	0.877752i	−0.970729	+	0.240177i	$0.922795\pi$
$108$	−0.0747458	+	0.327483i	−0.00719242	+	0.0315121i
$109$	0.0619705	+	0.826939i	0.00593570	+	0.0792064i	0.999385	−	0.0350679i	$-0.0111648\pi$
$109$	0.0619705	+	0.826939i	0.00593570	+	0.0792064i	−0.993449	+	0.114274i	$0.963546\pi$
$110$	1.20269	+	0.819982i	0.114672	+	0.0781822i
$111$	−0.280113	−	0.259907i	−0.0265872	−	0.0246693i
$112$	2.83881	+	7.23317i	0.268242	+	0.683470i
$113$	−9.13505	+	11.4550i	−0.859353	+	1.07759i	0.136855	+	0.990591i	$0.456301\pi$
$113$	−9.13505	+	11.4550i	−0.859353	+	1.07759i	−0.996208	+	0.0870033i	$0.972271\pi$
$114$	−0.370977	+	4.95034i	−0.0347452	+	0.463642i
$115$	−0.0755684	−	0.0233098i	−0.00704679	−	0.00217365i
$116$	2.16610	−	0.326487i	0.201117	−	0.0303136i
$117$	0.395307	−	0.366791i	0.0365461	−	0.0339098i
$118$	8.53378	+	4.10965i	0.785599	+	0.378324i
$119$	4.02744	+	0.607040i	0.369195	+	0.0556472i
$120$	1.53013	−	1.04322i	0.139681	−	0.0952327i
$121$	−4.75657	−	5.96455i	−0.432415	−	0.542232i
$122$	−7.03310	+	12.1817i	−0.636747	+	1.10288i
$123$	−4.93410	−	8.54611i	−0.444892	−	0.770576i
$124$	−0.700577	+	1.78504i	−0.0629137	+	0.160301i
$125$	5.32802	−	2.56584i	0.476552	−	0.229495i
$126$	−2.97894	+	0.918880i	−0.265385	+	0.0818604i
$127$	4.72784	+	20.7140i	0.419528	+	1.83807i	0.535123	+	0.844774i	$0.320265\pi$
$127$	4.72784	+	20.7140i	0.419528	+	1.83807i	−0.115595	+	0.993296i	$0.536877\pi$
$128$	7.66451			0.677453
$129$	5.96705	+	2.71926i	0.525369	+	0.239417i
$130$	−0.427529			−0.0374968
$131$	2.08583	+	9.13863i	0.182240	+	0.798446i	0.980561	+	0.196214i	$0.0628647\pi$
$131$	2.08583	+	9.13863i	0.182240	+	0.798446i	−0.798321	+	0.602232i	$0.794278\pi$
$132$	0.589336	−	0.181786i	0.0512951	−	0.0158224i
$133$	8.37877	−	4.03500i	0.726532	−	0.349879i
$134$	−5.92834	+	15.1052i	−0.512131	+	1.30489i
$135$	0.307289	+	0.532240i	0.0264472	+	0.0458080i
$136$	2.53930	−	4.39819i	0.217743	−	0.377142i
$137$	−11.7020	−	14.6738i	−0.999768	−	1.25367i	−0.967151	−	0.254202i	$-0.918187\pi$
$137$	−11.7020	−	14.6738i	−0.999768	−	1.25367i	−0.0326170	−	0.999468i	$-0.510384\pi$
$138$	0.137149	−	0.0935069i	0.0116749	−	0.00795983i
$139$	−14.9502	−	2.25338i	−1.26806	−	0.191130i	−0.519659	−	0.854374i	$-0.673941\pi$
$139$	−14.9502	−	2.25338i	−1.26806	−	0.191130i	−0.748403	+	0.663244i	$0.769179\pi$
$140$	−0.449481	−	0.216459i	−0.0379881	−	0.0182941i
$141$	−4.31606	+	4.00472i	−0.363478	+	0.337258i
$142$	−6.65203	+	1.00263i	−0.558226	+	0.0841390i
$143$	−0.946120	−	0.291839i	−0.0791185	−	0.0244048i
$144$	−0.240284	+	3.20637i	−0.0200237	+	0.267197i
$145$	2.49889	−	3.13351i	0.207521	−	0.260224i
$146$	−5.40253	−	13.7654i	−0.447117	−	1.13924i
$147$	−0.850302	−	0.788965i	−0.0701317	−	0.0650727i
$148$	0.106052	+	0.0723053i	0.00871745	+	0.00594346i
$149$	−1.54182	−	20.5741i	−0.126310	−	1.68550i	−0.596251	−	0.802798i	$-0.703344\pi$
$149$	−1.54182	−	20.5741i	−0.126310	−	1.68550i	0.469941	−	0.882698i	$-0.344275\pi$
$150$	−1.32684	+	5.81325i	−0.108336	+	0.474650i
$151$	−1.31593	+	5.76547i	−0.107089	+	0.469187i	0.892738	+	0.450576i	$0.148781\pi$
$151$	−1.31593	+	5.76547i	−0.107089	+	0.469187i	−0.999827	+	0.0186107i	$0.994076\pi$
$152$	−0.866566	−	11.5635i	−0.0702878	−	0.937926i
$153$	1.39253	+	0.949411i	0.112579	+	0.0767553i
$154$	4.19580	+	3.89314i	0.338107	+	0.313718i
$155$	1.28179	+	3.26595i	0.102956	+	0.262327i
$156$	−0.112939	+	0.141621i	−0.00904237	+	0.0113388i
$157$	−1.04864	+	13.9931i	−0.0836904	+	1.11677i	0.784364	+	0.620301i	$0.212990\pi$
$157$	−1.04864	+	13.9931i	−0.0836904	+	1.11677i	−0.868054	+	0.496470i	$0.834629\pi$
$158$	−1.93469	−	0.596772i	−0.153916	−	0.0474766i
$159$	4.74489	−	0.715178i	0.376295	−	0.0567173i
$160$	−0.846441	+	0.785383i	−0.0669170	+	0.0620899i
$161$	−0.280167	−	0.134921i	−0.0220803	−	0.0106333i
$162$	−1.27559	−	0.192264i	−0.100220	−	0.0151057i
$163$	−2.99295	+	2.04056i	−0.234426	+	0.159829i	−0.674836	−	0.737968i	$-0.735786\pi$
$163$	−2.99295	+	2.04056i	−0.234426	+	0.159829i	0.440410	+	0.897797i	$0.354833\pi$
$164$	2.06673	+	2.59159i	0.161384	+	0.202369i
$165$	0.564196	−	0.977216i	0.0439226	−	0.0760762i
$166$	−3.98030	−	6.89409i	−0.308931	−	0.535085i
$167$	4.05131	−	10.3226i	0.313500	−	0.798785i	−0.684090	−	0.729398i	$-0.739800\pi$
$167$	4.05131	−	10.3226i	0.313500	−	0.798785i	0.997590	−	0.0693871i	$-0.0221044\pi$
$168$	6.56088	−	3.15956i	0.506183	−	0.243765i
$169$	−12.1446	+	3.74610i	−0.934197	+	0.288162i
$170$	−0.297328	−	1.30268i	−0.0228040	−	0.0999110i
$171$	3.84824			0.294282
$172$	−2.11811	−	0.604474i	−0.161504	−	0.0460907i
$173$	1.41416			0.107516			0.0537581	−	0.998554i	$-0.482880\pi$
$173$	1.41416			0.107516			0.0537581	+	0.998554i	$0.482880\pi$
$174$	1.87198	+	8.20166i	0.141914	+	0.621767i
$175$	10.6741	−	3.29251i	0.806883	−	0.248890i
$176$	5.31890	−	2.56145i	0.400927	−	0.193077i
$177$	2.68251	−	6.83492i	0.201630	−	0.513744i
$178$	−9.00953	−	15.6050i	−0.675293	−	1.16964i
$179$	6.98976	−	12.1066i	0.522439	−	0.904891i	−0.477220	−	0.878784i	$-0.658355\pi$
$179$	6.98976	−	12.1066i	0.522439	−	0.904891i	0.999659	−	0.0261074i	$-0.00831120\pi$
$180$	−0.128713	−	0.161401i	−0.00959370	−	0.0120301i
$181$	0.787267	−	0.536750i	0.0585171	−	0.0398963i	−0.533708	−	0.845669i	$-0.679202\pi$
$181$	0.787267	−	0.536750i	0.0585171	−	0.0398963i	0.592225	+	0.805772i	$0.298250\pi$
$182$	−1.66234	−	0.250557i	−0.123221	−	0.0185725i
$183$	9.82421	+	4.73109i	0.726226	+	0.349732i
$184$	−0.284235	+	0.263732i	−0.0209541	+	0.0194426i
$185$	0.232219	−	0.0350014i	0.0170731	−	0.00257336i
$186$	−7.03711	−	2.17066i	−0.515986	−	0.159161i
$187$	0.231248	−	3.08579i	0.0169105	−	0.225655i
$188$	1.23310	−	1.54626i	0.0899330	−	0.112772i
$189$	0.882890	+	2.24957i	0.0642208	+	0.163632i
$190$	−2.23647	−	2.07514i	−0.162251	−	0.150547i
$191$	7.44129	+	5.07339i	0.538433	+	0.367097i	0.801795	−	0.597600i	$-0.203879\pi$
$191$	7.44129	+	5.07339i	0.538433	+	0.367097i	−0.263362	+	0.964697i	$0.584831\pi$
$192$	−0.661689	−	8.82963i	−0.0477533	−	0.637224i
$193$	−0.392080	+	1.71781i	−0.0282225	+	0.123651i	−0.987077	−	0.160248i	$-0.948771\pi$
$193$	−0.392080	+	1.71781i	−0.0282225	+	0.123651i	0.958854	+	0.283898i	$0.0916279\pi$
$194$	2.09627	−	9.18434i	0.150503	−	0.659397i
$195$	0.0247669	+	0.330492i	0.00177360	+	0.0236670i
$196$	0.321929	+	0.219487i	0.0229949	+	0.0156777i
$197$	−5.55415	−	5.15350i	−0.395717	−	0.367172i	0.457070	−	0.889431i	$-0.348899\pi$
$197$	−5.55415	−	5.15350i	−0.395717	−	0.367172i	−0.852787	+	0.522259i	$0.825089\pi$
$198$	0.865308	+	2.20477i	0.0614947	+	0.156686i
$199$	−1.24650	+	1.56306i	−0.0883621	+	0.110803i	−0.824047	−	0.566521i	$-0.808289\pi$
$199$	−1.24650	+	1.56306i	−0.0883621	+	0.110803i	0.735685	+	0.677324i	$0.236860\pi$
$200$	1.04087	−	13.8895i	0.0736008	−	0.982134i
$201$	12.0201	+	3.70772i	0.847835	+	0.261522i
$202$	11.7586	−	1.77233i	0.827336	−	0.124701i
$203$	11.5527	−	10.7193i	0.810840	−	0.752350i
$204$	−0.510064	−	0.245634i	−0.0357116	−	0.0171978i
$205$	5.99704	+	0.903908i	0.418851	+	0.0631317i
$206$	−18.9274	+	12.9045i	−1.31873	+	0.899096i
$207$	−0.0802285	−	0.100603i	−0.00557626	−	0.00699241i
$208$	−0.866959	+	1.50162i	−0.0601128	+	0.104118i
$209$	−3.53277	−	6.11893i	−0.244367	−	0.423255i
$210$	0.699960	−	1.78347i	0.0483018	−	0.123071i
$211$	−19.4539	+	9.36849i	−1.33926	+	0.644953i	−0.959912	−	0.280301i	$-0.909566\pi$
$211$	−19.4539	+	9.36849i	−1.33926	+	0.644953i	−0.379347	+	0.925254i	$0.623851\pi$
$212$	−1.54023	+	0.475097i	−0.105783	+	0.0326298i
$213$	1.16042	+	5.08412i	0.0795105	+	0.348358i
$214$	12.0138			0.821247
$215$	−3.59307	+	1.82517i	−0.245045	+	0.124476i
$216$	3.01331			0.205030
$217$	3.06988	+	13.4500i	0.208397	+	0.913046i
$218$	1.02222	−	0.315312i	0.0692332	−	0.0213556i
$219$	−10.3281	+	4.97374i	−0.697907	+	0.336094i
$220$	−0.138476	+	0.352831i	−0.00933605	+	0.0237879i
$221$	0.454432	+	0.787099i	0.0305684	+	0.0529460i
$222$	−0.246467	+	0.426893i	−0.0165418	+	0.0286512i
$223$	−8.84349	−	11.0894i	−0.592204	−	0.742600i	0.391936	−	0.919992i	$-0.371805\pi$
$223$	−8.84349	−	11.0894i	−0.592204	−	0.742600i	−0.984140	+	0.177392i	$0.943234\pi$
$224$	−3.75145	+	2.55769i	−0.250654	+	0.170893i
$225$	4.57067	+	0.688917i	0.304711	+	0.0459278i
$226$	17.0287	+	8.20057i	1.13273	+	0.545494i
$227$	−14.2098	+	13.1847i	−0.943136	+	0.875102i	−0.992321	−	0.123688i	$-0.960528\pi$
$227$	−14.2098	+	13.1847i	−0.943136	+	0.875102i	0.0491855	+	0.998790i	$0.484337\pi$
$228$	−1.27820	+	0.192658i	−0.0846511	+	0.0127591i
$229$	−3.77742	−	1.16518i	−0.249619	−	0.0769973i	0.167421	−	0.985886i	$-0.446456\pi$
$229$	−3.77742	−	1.16518i	−0.249619	−	0.0769973i	−0.417040	+	0.908888i	$0.636932\pi$
$230$	−0.00762362	+	0.101730i	−0.000502686	+	0.00670788i
$231$	2.76644	−	3.46900i	0.182018	−	0.228244i
$232$	−7.17932	−	18.2926i	−0.471345	−	1.20097i
$233$	−14.7291	−	13.6666i	−0.964932	−	0.895326i	0.0296204	−	0.999561i	$-0.490570\pi$
$233$	−14.7291	−	13.6666i	−0.964932	−	0.895326i	−0.994553	+	0.104235i	$0.966761\pi$
$234$	−0.574770	−	0.391871i	−0.0375739	−	0.0256174i
$235$	−0.270412	−	3.60839i	−0.0176397	−	0.235386i
$236$	−0.548820	+	2.40454i	−0.0357251	+	0.156522i
$237$	−0.349244	+	1.53014i	−0.0226858	+	0.0993931i
$238$	−0.392638	−	5.23939i	−0.0254509	−	0.339619i
$239$	−0.0511442	−	0.0348695i	−0.00330824	−	0.00225552i	0.561665	−	0.827365i	$-0.310161\pi$
$239$	−0.0511442	−	0.0348695i	−0.00330824	−	0.00225552i	−0.564973	+	0.825109i	$0.691113\pi$
$240$	−1.44858	−	1.34408i	−0.0935052	−	0.0867601i
$241$	7.93544	+	20.2192i	0.511166	+	1.30243i	0.920748	+	0.390157i	$0.127579\pi$
$241$	7.93544	+	20.2192i	0.511166	+	1.30243i	−0.409582	+	0.912273i	$0.634325\pi$
$242$	−6.13597	+	7.69426i	−0.394435	+	0.494606i
$243$	−0.0747301	+	0.997204i	−0.00479394	+	0.0639707i
$244$	−3.50000	−	1.07961i	−0.224064	−	0.0691147i
$245$	0.704916	−	0.106249i	0.0450355	−	0.00678800i
$246$	−9.33171	+	8.65856i	−0.594968	+	0.552050i
$247$	1.86970	+	0.900399i	0.118966	+	0.0572910i
$248$	17.0101	+	2.56387i	1.08014	+	0.162806i
$249$	−5.09874	+	3.47626i	−0.323119	+	0.220299i
$250$	−4.75635	−	5.96428i	−0.300818	−	0.377214i
$251$	0.762113	−	1.32002i	0.0481041	−	0.0833188i	−0.840971	−	0.541081i	$-0.818015\pi$
$251$	0.762113	−	1.32002i	0.0481041	−	0.0833188i	0.889075	+	0.457762i	$0.151349\pi$
$252$	−0.405877	−	0.703000i	−0.0255678	−	0.0442848i
$253$	−0.0863139	+	0.219924i	−0.00542651	+	0.0138265i
$254$	24.6939	−	11.8920i	1.54944	−	0.746169i
$255$	−0.989783	+	0.305308i	−0.0619826	+	0.0191191i
$256$	1.74046	+	7.62547i	0.108779	+	0.476592i
$257$	−17.3946			−1.08505			−0.542523	−	0.840041i	$-0.682531\pi$
$257$	−17.3946			−1.08505			−0.542523	+	0.840041i	$0.682531\pi$
$258$	1.70704	−	8.28505i	0.106275	−	0.515805i
$259$	0.923437			0.0573796
$260$	−0.0247721	−	0.108534i	−0.00153630	−	0.00673098i
$261$	6.23167	−	1.92221i	0.385730	−	0.118982i
$262$	10.8945	−	5.24652i	0.673065	−	0.324131i
$263$	−5.44076	+	13.8628i	−0.335491	+	0.854818i	0.659205	+	0.751963i	$0.270893\pi$
$263$	−5.44076	+	13.8628i	−0.335491	+	0.854818i	−0.994696	+	0.102855i	$0.967202\pi$
$264$	−2.76629	−	4.79135i	−0.170253	−	0.294887i
$265$	−1.47452	+	2.55395i	−0.0905792	+	0.156888i
$266$	−7.47978	−	9.37935i	−0.458615	−	0.575085i
$267$	−11.5411	+	7.86861i	−0.706306	+	0.481551i
$268$	−4.17815	−	0.629754i	−0.255221	−	0.0384684i
$269$	−9.19692	−	4.42900i	−0.560746	−	0.270041i	0.131967	−	0.991254i	$-0.457871\pi$
$269$	−9.19692	−	4.42900i	−0.560746	−	0.270041i	−0.692713	+	0.721213i	$0.743585\pi$
$270$	0.581167	−	0.539244i	0.0353687	−	0.0328174i
$271$	30.8188	−	4.64518i	1.87211	−	0.282175i	0.888012	−	0.459821i	$-0.152086\pi$
$271$	30.8188	−	4.64518i	1.87211	−	0.282175i	0.984094	+	0.177647i	$0.0568484\pi$
$272$	−5.17836	−	1.59731i	−0.313984	−	0.0968513i
$273$	−0.0973875	+	1.29955i	−0.00589416	+	0.0786521i
$274$	−15.0955	+	18.9292i	−0.911955	+	1.14356i
$275$	−3.10055	−	7.90008i	−0.186970	−	0.476393i
$276$	0.0316847	+	0.0293991i	0.00190720	+	0.00176962i
$277$	9.22724	+	6.29103i	0.554411	+	0.377991i	0.807875	−	0.589354i	$-0.200618\pi$
$277$	9.22724	+	6.29103i	0.554411	+	0.377991i	−0.253464	+	0.967345i	$0.581570\pi$
$278$	1.45751	+	19.4491i	0.0874154	+	1.16648i
$279$	−1.27032	+	5.56563i	−0.0760519	+	0.333205i
$280$	−0.995865	+	4.36317i	−0.0595143	+	0.260749i
$281$	0.626740	+	8.36326i	0.0373881	+	0.498910i	0.984193	+	0.177101i	$0.0566719\pi$
$281$	0.626740	+	8.36326i	0.0373881	+	0.498910i	−0.946805	+	0.321809i	$0.895709\pi$
$282$	6.27549	+	4.27856i	0.373700	+	0.254784i
$283$	3.21334	+	2.98155i	0.191013	+	0.177235i	0.769882	−	0.638186i	$-0.220315\pi$
$283$	3.21334	+	2.98155i	0.191013	+	0.177235i	−0.578868	+	0.815421i	$0.696506\pi$
$284$	−0.639967	−	1.63061i	−0.0379751	−	0.0967589i
$285$	−1.47458	+	1.84907i	−0.0873466	+	0.109529i
$286$	−0.0954480	+	1.27367i	−0.00564396	+	0.0753134i
$287$	22.7882	+	7.02922i	1.34514	+	0.414922i
$288$	−1.85783	+	0.280023i	−0.109474	+	0.0165005i
$289$	10.3796	−	9.63089i	0.610567	−	0.566523i
$290$	−4.65818	−	2.24326i	−0.273538	−	0.131729i
$291$	−7.22118	−	1.08842i	−0.423313	−	0.0638042i
$292$	3.18150	−	2.16911i	0.186183	−	0.126937i
$293$	12.1815	+	15.2751i	0.711648	+	0.892378i	0.997833	−	0.0657960i	$-0.0209587\pi$
$293$	12.1815	+	15.2751i	0.711648	+	0.892378i	−0.286185	+	0.958174i	$0.592387\pi$
$294$	−0.748165	+	1.29586i	−0.0436339	+	0.0755761i
$295$	2.25626	+	3.90796i	0.131365	+	0.227530i
$296$	0.420670	−	1.07185i	0.0244510	−	0.0623000i
$297$	1.65422	−	0.796629i	0.0959875	−	0.0462251i
$298$	−25.4325	+	7.84490i	−1.47327	+	0.454443i
$299$	−0.0154408	−	0.0676505i	−0.000892964	−	0.00391233i
$300$	−1.55265			−0.0896423
$301$	−15.0404	+	4.99097i	−0.866912	+	0.287675i
$302$	7.62871			0.438983
$303$	−2.05124	−	8.98708i	−0.117841	−	0.516294i
$304$	−11.8238	+	3.64714i	−0.678139	+	0.209178i
$305$	−6.03774	+	2.90762i	−0.345720	+	0.166490i
$306$	0.794304	−	2.02385i	0.0454073	−	0.115696i
$307$	5.14716	+	8.91514i	0.293764	+	0.508814i	0.974697	−	0.223532i	$-0.0717588\pi$
$307$	5.14716	+	8.91514i	0.293764	+	0.508814i	−0.680933	+	0.732346i	$0.738425\pi$
$308$	−0.745208	+	1.29074i	−0.0424622	+	0.0735466i
$309$	11.0720	+	13.8838i	0.629862	+	0.789822i
$310$	3.73950	−	2.54955i	0.212389	−	0.144805i
$311$	14.0527	+	2.11811i	0.796856	+	0.120107i	0.534836	−	0.844956i	$-0.320373\pi$
$311$	14.0527	+	2.11811i	0.796856	+	0.120107i	0.262020	+	0.965062i	$0.415611\pi$
$312$	1.46404	+	0.705045i	0.0828850	+	0.0399153i
$313$	15.5112	−	14.3923i	0.876744	−	0.813499i	−0.106779	−	0.994283i	$-0.534054\pi$
$313$	15.5112	−	14.3923i	0.876744	−	0.813499i	0.983523	+	0.180784i	$0.0578634\pi$
$314$	17.8995	−	2.69792i	1.01013	−	0.152252i
$315$	−1.41922	−	0.437771i	−0.0799639	−	0.0246656i
$316$	0.0393976	−	0.525724i	0.00221629	−	0.0295743i
$317$	−21.4665	+	26.9181i	−1.20568	+	1.51187i	−0.403282	+	0.915076i	$0.632131\pi$
$317$	−21.4665	+	26.9181i	−1.20568	+	1.51187i	−0.802394	+	0.596795i	$0.796441\pi$
$318$	−2.26148	−	5.76215i	−0.126817	−	0.323125i
$319$	−8.77724	−	8.14409i	−0.491431	−	0.455981i
$320$	4.49616	+	3.06543i	0.251343	+	0.171363i
$321$	−0.695964	−	9.28700i	−0.0388449	−	0.518350i
$322$	−0.0892622	+	0.391083i	−0.00497439	+	0.0217942i
$323$	−1.44322	+	6.32315i	−0.0803028	+	0.351830i
$324$	−0.0251022	−	0.334965i	−0.00139457	−	0.0186092i
$325$	2.05950	+	1.40415i	0.114241	+	0.0778880i
$326$	3.42545	+	3.17835i	0.189718	+	0.176033i
$327$	−0.302962	−	0.771934i	−0.0167538	−	0.0426881i
$328$	18.5401	−	23.2485i	1.02370	−	1.28368i
$329$	1.06330	−	14.1888i	0.0586217	−	0.782253i
$330$	−1.39095	−	0.429053i	−0.0765695	−	0.0236186i
$331$	11.3019	−	1.70349i	0.621208	−	0.0936321i	0.169106	−	0.985598i	$-0.445912\pi$
$331$	11.3019	−	1.70349i	0.621208	−	0.0936321i	0.452103	+	0.891966i	$0.350674\pi$
$332$	1.51952	−	1.40991i	0.0833947	−	0.0773790i
$333$	0.344278	+	0.165795i	0.0188663	+	0.00908553i
$334$	−14.1452	−	2.13204i	−0.773990	−	0.116660i
$335$	−6.38746	+	4.35490i	−0.348984	+	0.237933i
$336$	−4.84470	−	6.07507i	−0.264300	−	0.331422i
$337$	4.78225	−	8.28310i	0.260506	−	0.451209i	−0.705871	−	0.708341i	$-0.749444\pi$
$337$	4.78225	−	8.28310i	0.260506	−	0.451209i	0.966376	+	0.257132i	$0.0827774\pi$
$338$	8.19742	+	14.1983i	0.445881	+	0.772288i
$339$	5.35279	−	13.6387i	0.290723	−	0.740751i
$340$	0.313474	−	0.150961i	0.0170005	−	0.00818703i
$341$	10.0159	−	3.08948i	0.542389	−	0.167305i
$342$	−1.10464	−	4.83976i	−0.0597323	−	0.261704i
$343$	19.7195			1.06475
$344$	−1.05850	+	19.7312i	−0.0570708	+	1.06384i
$345$	0.0790818			0.00425762
$346$	−0.405936	−	1.77852i	−0.0218232	−	0.0956138i
$347$	4.36727	−	1.34713i	0.234448	−	0.0723175i	−0.175305	−	0.984514i	$-0.556091\pi$
$347$	4.36727	−	1.34713i	0.234448	−	0.0723175i	0.409753	+	0.912197i	$0.365615\pi$
$348$	−1.97363	+	0.950451i	−0.105798	+	0.0509495i
$349$	3.05231	−	7.77717i	0.163387	−	0.416302i	−0.825610	−	0.564241i	$-0.809169\pi$
$349$	3.05231	−	7.77717i	0.163387	−	0.416302i	0.988996	+	0.147939i	$0.0472640\pi$
$350$	−7.20485	−	12.4792i	−0.385115	−	0.667040i
$351$	−0.269631	+	0.467014i	−0.0143918	+	0.0249274i
$352$	2.15079	+	2.69700i	0.114637	+	0.143751i
$353$	−18.3113	+	12.4844i	−0.974612	+	0.664479i	−0.942220	−	0.334996i	$-0.891265\pi$
$353$	−18.3113	+	12.4844i	−0.974612	+	0.664479i	−0.0323925	+	0.999475i	$0.510313\pi$
$354$	−9.36599	−	1.41170i	−0.497797	−	0.0750308i
$355$	−2.88755	−	1.39057i	−0.153255	−	0.0738039i
$356$	3.43949	−	3.19138i	0.182292	−	0.169143i
$357$	−4.02744	+	0.607040i	−0.213155	+	0.0321279i
$358$	−17.2324	−	5.31548i	−0.910759	−	0.280932i
$359$	0.823893	−	10.9941i	0.0434834	−	0.580246i	−0.932325	−	0.361620i	$-0.882224\pi$
$359$	0.823893	−	10.9941i	0.0434834	−	0.580246i	0.975809	−	0.218625i	$-0.0701573\pi$
$360$	−1.15465	+	1.44789i	−0.0608555	+	0.0763103i
$361$	−1.53116	−	3.90134i	−0.0805875	−	0.205334i
$362$	−0.901032	−	0.836036i	−0.0473572	−	0.0439411i
$363$	6.30333	+	4.29754i	0.330839	+	0.225562i
$364$	−0.0327129	−	0.436524i	−0.00171462	−	0.0228800i
$365$	1.56768	−	6.86846i	0.0820562	−	0.359512i
$366$	3.13002	−	13.7135i	0.163609	−	0.716818i
$367$	1.10326	+	14.7220i	0.0575899	+	0.768484i	0.948998	+	0.315282i	$0.102099\pi$
$367$	1.10326	+	14.7220i	0.0575899	+	0.768484i	−0.891408	+	0.453202i	$0.850282\pi$
$368$	0.341849	+	0.233069i	0.0178201	+	0.0121495i
$369$	7.23390	+	6.71208i	0.376582	+	0.349417i
$370$	−0.110679	−	0.282004i	−0.00575391	−	0.0146607i
$371$	−7.23006	+	9.06621i	−0.375366	+	0.470694i
$372$	0.143302	−	1.91224i	0.00742988	−	0.0991448i
$373$	5.81713	+	1.79435i	0.301200	+	0.0929078i	0.441671	−	0.897177i	$-0.354386\pi$
$373$	5.81713	+	1.79435i	0.301200	+	0.0929078i	−0.140472	+	0.990085i	$0.544862\pi$
$374$	−3.94724	+	0.594950i	−0.204107	+	0.0307641i
$375$	−4.33501	+	4.02231i	−0.223859	+	0.207711i
$376$	−15.9848	−	7.69787i	−0.824352	−	0.396987i
$377$	3.47746	+	0.524142i	0.179098	+	0.0269947i
$378$	2.57575	−	1.75611i	0.132482	−	0.0903248i
$379$	−20.4728	−	25.6721i	−1.05162	−	1.31869i	−0.945960	−	0.324282i	$-0.894877\pi$
$379$	−20.4728	−	25.6721i	−1.05162	−	1.31869i	−0.105656	−	0.994403i	$-0.533694\pi$
$380$	0.397215	−	0.687996i	0.0203767	−	0.0352935i
$381$	−10.6234	−	18.4002i	−0.544251	−	0.942670i
$382$	4.24454	−	10.8149i	0.217169	−	0.553339i
$383$	15.4844	−	7.45691i	0.791218	−	0.381030i	0.00578957	−	0.999983i	$-0.498157\pi$
$383$	15.4844	−	7.45691i	0.791218	−	0.381030i	0.785428	+	0.618953i	$0.212443\pi$
$384$	−7.32400	+	2.25915i	−0.373751	+	0.115287i
$385$	0.606791	+	2.65853i	0.0309250	+	0.135491i
$386$	2.27296			0.115691
$387$	−6.50346	−	0.839628i	−0.330590	−	0.0426807i
$388$	2.45303			0.124534
$389$	−6.48565	−	28.4155i	−0.328836	−	1.44072i	−0.821353	−	0.570421i	$-0.806780\pi$
$389$	−6.48565	−	28.4155i	−0.328836	−	1.44072i	0.492517	−	0.870303i	$-0.336077\pi$
$390$	0.408535	−	0.126016i	0.0206870	−	0.00638109i
$391$	0.195393	−	0.0940961i	0.00988143	−	0.00475865i
$392$	1.27697	−	3.25367i	0.0644968	−	0.164335i
$393$	−4.68683	−	8.11782i	−0.236419	−	0.409490i
$394$	−4.88700	+	8.46453i	−0.246203	+	0.426437i
$395$	−0.601402	−	0.754134i	−0.0302598	−	0.0379446i
$396$	−0.509571	+	0.347420i	−0.0256069	+	0.0174585i
$397$	−22.3804	−	3.37330i	−1.12324	−	0.169301i	−0.438950	−	0.898511i	$-0.644650\pi$
$397$	−22.3804	−	3.37330i	−1.12324	−	0.169301i	−0.684290	+	0.729210i	$0.739888\pi$
$398$	2.32360	+	1.11899i	0.116472	+	0.0560898i
$399$	−6.81719	+	6.32543i	−0.341286	+	0.316667i
$400$	−14.6963	+	2.21512i	−0.734817	+	0.110756i
$401$	−12.4414	−	3.83766i	−0.621294	−	0.191644i	−0.0319018	−	0.999491i	$-0.510156\pi$
$401$	−12.4414	−	3.83766i	−0.621294	−	0.191644i	−0.589392	+	0.807847i	$0.700633\pi$
$402$	1.21264	−	16.1815i	0.0604807	−	0.807059i
$403$	−1.91942	+	2.40688i	−0.0956132	+	0.119895i
$404$	1.13126	+	2.88239i	0.0562821	+	0.143404i
$405$	−0.450518	−	0.418019i	−0.0223864	−	0.0207715i
$406$	−16.7975	−	11.4523i	−0.833644	−	0.568369i
$407$	−0.0524297	−	0.699626i	−0.00259884	−	0.0346792i
$408$	−1.13009	+	4.95126i	−0.0559479	+	0.245124i
$409$	4.52973	−	19.8460i	0.223981	−	0.981323i	−0.730468	−	0.682947i	$-0.760698\pi$
$409$	4.52973	−	19.8460i	0.223981	−	0.981323i	0.954448	−	0.298376i	$-0.0964449\pi$
$410$	−0.584655	−	7.80167i	−0.0288740	−	0.385297i
$411$	15.5073	+	10.5727i	0.764918	+	0.521512i
$412$	−4.37267	−	4.05724i	−0.215426	−	0.199886i
$413$	6.48261	+	16.5174i	0.318988	+	0.812769i
$414$	−0.103495	+	0.129778i	−0.00508648	+	0.00637825i
$415$	0.283419	−	3.78197i	0.0139125	−	0.185650i
$416$	−0.968162	−	0.298638i	−0.0474680	−	0.0146420i
$417$	14.9502	−	2.25338i	0.732116	−	0.110349i
$418$	−6.68142	+	6.19945i	−0.326799	+	0.303225i
$419$	−3.95128	−	1.90284i	−0.193033	−	0.0929597i	0.334871	−	0.942264i	$-0.391307\pi$
$419$	−3.95128	−	1.90284i	−0.193033	−	0.0929597i	−0.527903	+	0.849304i	$0.677022\pi$
$420$	0.493314	+	0.0743551i	0.0240713	+	0.00362816i
$421$	12.8787	−	8.78057i	0.627671	−	0.427939i	−0.207266	−	0.978285i	$-0.566457\pi$
$421$	12.8787	−	8.78057i	0.627671	−	0.427939i	0.834937	+	0.550346i	$0.185504\pi$
$422$	17.3666	+	21.7770i	0.845393	+	1.06009i
$423$	2.94390	−	5.09898i	0.143137	−	0.247921i
$424$	7.22967	+	12.5222i	0.351104	+	0.608130i
$425$	−2.84613	+	7.25183i	−0.138058	+	0.351765i
$426$	6.06097	−	2.91881i	0.293655	−	0.141417i
$427$	−25.1802	+	7.76707i	−1.21856	+	0.375875i
$428$	0.696111	+	3.04986i	0.0336478	+	0.147421i
$429$	0.990107			0.0478028
$430$	3.32683	+	3.99492i	0.160434	+	0.192652i
$431$	32.3082			1.55623			0.778116	−	0.628120i	$-0.216175\pi$
$431$	32.3082			1.55623			0.778116	+	0.628120i	$0.216175\pi$
$432$	−0.715485	−	3.13474i	−0.0344238	−	0.150820i
$433$	−31.5162	+	9.72147i	−1.51457	+	0.467184i	−0.937052	−	0.349191i	$-0.886456\pi$
$433$	−31.5162	+	9.72147i	−1.51457	+	0.467184i	−0.577522	+	0.816375i	$0.695980\pi$
$434$	16.0343	−	7.72169i	0.769669	−	0.370653i
$435$	−1.46425	+	3.73085i	−0.0702055	+	0.178881i
$436$	0.139276	+	0.241233i	0.00667010	+	0.0115530i
$437$	0.247589	−	0.428837i	0.0118438	−	0.0205140i
$438$	9.21995	+	11.5614i	0.440546	+	0.552427i
$439$	−20.4560	+	13.9467i	−0.976313	+	0.665639i	−0.942646	−	0.333794i	$-0.891671\pi$
$439$	−20.4560	+	13.9467i	−0.976313	+	0.665639i	−0.0336669	+	0.999433i	$0.510719\pi$
$440$	3.36222	+	0.506773i	0.160288	+	0.0241595i
$441$	1.04508	+	0.503282i	0.0497656	+	0.0239658i
$442$	0.859453	−	0.797456i	0.0408800	−	0.0379311i
$443$	27.8394	−	4.19612i	1.32269	−	0.199364i	0.550544	−	0.834806i	$-0.314420\pi$
$443$	27.8394	−	4.19612i	1.32269	−	0.199364i	0.772148	+	0.635443i	$0.219182\pi$
$444$	−0.122653	−	0.0378335i	−0.00582086	−	0.00179550i
$445$	0.641528	−	8.56060i	0.0304114	−	0.405811i
$446$	−11.4081	+	14.3053i	−0.540189	+	0.677375i
$447$	7.53764	+	19.2056i	0.356518	+	0.908393i
$448$	15.6856	+	14.5541i	0.741076	+	0.687618i
$449$	−31.9454	−	21.7800i	−1.50760	−	1.02786i	−0.984459	−	0.175615i	$-0.943809\pi$
$449$	−31.9454	−	21.7800i	−1.50760	−	1.02786i	−0.523138	−	0.852248i	$-0.675239\pi$
$450$	−0.445597	−	5.94608i	−0.0210056	−	0.280301i
$451$	4.03173	−	17.6642i	0.189847	−	0.831773i
$452$	−1.09514	+	4.79811i	−0.0515109	+	0.225684i
$453$	−0.441934	−	5.89720i	−0.0207639	−	0.277075i
$454$	20.6608	+	14.0863i	0.969659	+	0.661102i
$455$	−0.587110	−	0.544759i	−0.0275241	−	0.0255387i
$456$	4.23648	+	10.7944i	0.198391	+	0.505492i
$457$	17.2640	−	21.6484i	0.807577	−	1.01267i	−0.191934	−	0.981408i	$-0.561476\pi$
$457$	17.2640	−	21.6484i	0.807577	−	1.01267i	0.999511	−	0.0312620i	$-0.00995263\pi$
$458$	−0.381080	+	5.08516i	−0.0178067	+	0.237614i
$459$	−1.61051	−	0.496776i	−0.0751721	−	0.0231875i
$460$	−0.0262672	+	0.00395915i	−0.00122472	+	0.000184596i
$461$	3.89569	−	3.61467i	0.181440	−	0.168352i	−0.584224	−	0.811593i	$-0.698601\pi$
$461$	3.89569	−	3.61467i	0.181440	−	0.168352i	0.765664	+	0.643241i	$0.222410\pi$
$462$	−5.15692	−	2.48344i	−0.239922	−	0.115540i
$463$	18.5213	+	2.79163i	0.860756	+	0.129738i	0.564563	−	0.825390i	$-0.309045\pi$
$463$	18.5213	+	2.79163i	0.860756	+	0.129738i	0.296193	+	0.955128i	$0.404283\pi$
$464$	−17.3251	+	11.8120i	−0.804297	+	0.548360i
$465$	−2.18750	−	2.74304i	−0.101443	−	0.127205i
$466$	−12.9598	+	22.4471i	−0.600352	+	1.03984i
$467$	−6.42848	−	11.1345i	−0.297475	−	0.515241i	0.678083	−	0.734985i	$-0.262811\pi$
$467$	−6.42848	−	11.1345i	−0.297475	−	0.515241i	−0.975558	+	0.219744i	$0.929478\pi$
$468$	0.0661780	−	0.168619i	0.00305908	−	0.00779441i
$469$	−27.3882	+	13.1895i	−1.26467	+	0.609033i
$470$	−4.46049	+	1.37588i	−0.205747	+	0.0634646i
$471$	−3.12249	−	13.6805i	−0.143877	−	0.630365i
$472$	22.1252			1.01839
$473$	4.63526	+	11.1117i	0.213130	+	0.510916i
$474$	2.02464			0.0929947
$475$	3.95813	+	17.3417i	0.181612	+	0.795693i
$476$	1.30734	−	0.403260i	0.0599217	−	0.0184834i
$477$	−4.32329	+	2.08199i	−0.197950	+	0.0953276i
$478$	−0.0291728	+	0.0743311i	−0.00133433	+	0.00339983i
$479$	11.8295	+	20.4893i	0.540503	+	0.936178i	0.998875	+	0.0474179i	$0.0150993\pi$
$479$	11.8295	+	20.4893i	0.540503	+	0.936178i	−0.458372	+	0.888760i	$0.651567\pi$
$480$	0.577341	−	0.999983i	0.0263519	−	0.0456428i
$481$	0.128478	+	0.161106i	0.00585808	+	0.00734580i
$482$	23.1509	−	15.7840i	1.05449	−	0.718941i
$483$	0.307489	+	0.0463465i	0.0139912	+	0.00210884i
$484$	−2.30882	−	1.11187i	−0.104946	−	0.0505395i
$485$	3.29002	−	3.05269i	0.149392	−	0.138616i
$486$	1.27559	−	0.192264i	0.0578619	−	0.00872128i
$487$	34.6712	+	10.6946i	1.57110	+	0.484621i	0.953379	−	0.301776i	$-0.0975794\pi$
$487$	34.6712	+	10.6946i	1.57110	+	0.484621i	0.617722	+	0.786396i	$0.288056\pi$
$488$	−2.45543	+	32.7654i	−0.111152	+	1.48322i
$489$	2.25852	−	2.83209i	0.102134	−	0.128071i
$490$	−0.335972	−	0.856043i	−0.0151777	−	0.0386721i
$491$	−21.5454	−	19.9912i	−0.972331	−	0.902192i	0.0228996	−	0.999738i	$-0.492710\pi$
$491$	−21.5454	−	19.9912i	−0.972331	−	0.902192i	−0.995231	+	0.0975461i	$0.968901\pi$
$492$	−2.73879	−	1.86728i	−0.123474	−	0.0841834i
$493$	0.821363	+	10.9603i	0.0369923	+	0.493628i
$494$	0.595692	−	2.60990i	0.0268014	−	0.117425i
$495$	−0.251091	+	1.10010i	−0.0112857	+	0.0494459i
$496$	−1.37172	−	18.3044i	−0.0615922	−	0.821891i
$497$	−10.4125	−	7.09916i	−0.467067	−	0.318441i
$498$	5.83554	+	5.41459i	0.261497	+	0.242633i
$499$	9.60195	+	24.4654i	0.429842	+	1.09522i	0.967682	+	0.252173i	$0.0811452\pi$
$499$	9.60195	+	24.4654i	0.429842	+	1.09522i	−0.537840	+	0.843047i	$0.680760\pi$
$500$	1.23851	−	1.55305i	0.0553881	−	0.0694544i
$501$	−0.828691	+	11.0581i	−0.0370232	+	0.494040i
$502$	−1.87889	−	0.579562i	−0.0838591	−	0.0258671i
$503$	−36.1054	+	5.44201i	−1.60986	+	0.242647i	−0.891499	−	0.453023i	$-0.850345\pi$
$503$	−36.1054	+	5.44201i	−1.60986	+	0.242647i	−0.718361	+	0.695671i	$0.755107\pi$
$504$	−5.33811	+	4.95304i	−0.237778	+	0.220626i
$505$	5.10427	+	2.45808i	0.227137	+	0.109383i
$506$	0.301365	+	0.0454235i	0.0133973	+	0.00201932i
$507$	10.5008	−	7.15935i	0.466358	−	0.317958i
$508$	4.44976	+	5.57983i	0.197426	+	0.247565i
$509$	19.3865	−	33.5783i	0.859290	−	1.48833i	−0.0133176	−	0.999911i	$-0.504239\pi$
$509$	19.3865	−	33.5783i	0.859290	−	1.48833i	0.872607	−	0.488422i	$-0.162427\pi$
$510$	0.668091	+	1.15717i	0.0295836	+	0.0512402i
$511$	10.1208	−	25.7875i	0.447720	−	1.14077i
$512$	22.9016	−	11.0288i	1.01212	−	0.487410i
$513$	−3.67727	+	1.13429i	−0.162356	+	0.0500801i
$514$	4.99315	+	21.8764i	0.220238	+	0.964927i
$515$	−10.9137			−0.480916
$516$	2.20218	−	0.0467044i	0.0969455	−	0.00205604i
$517$	−10.8103			−0.475434
$518$	−0.265074	−	1.16137i	−0.0116467	−	0.0510275i
$519$	−1.35133	+	0.416830i	−0.0593167	+	0.0182968i
$520$	−0.899768	+	0.433305i	−0.0394574	+	0.0190017i
$521$	−10.3740	+	26.4325i	−0.454493	+	1.15803i	0.501635	+	0.865079i	$0.332732\pi$
$521$	−10.3740	+	26.4325i	−0.454493	+	1.15803i	−0.956128	+	0.292949i	$0.905363\pi$
$522$	−4.20629	−	7.28551i	−0.184104	−	0.318878i
$523$	1.18071	−	2.04505i	0.0516288	−	0.0894237i	−0.839056	−	0.544045i	$-0.816892\pi$
$523$	1.18071	−	2.04505i	0.0516288	−	0.0894237i	0.890685	+	0.454621i	$0.150225\pi$
$524$	1.96315	+	2.46172i	0.0857607	+	0.107541i
$525$	−9.22936	+	6.29247i	−0.402802	+	0.274626i
$526$	18.9964	+	2.86325i	0.828283	+	0.124844i
$527$	−8.66863	−	4.17459i	−0.377611	−	0.181848i
$528$	−4.32760	+	4.01543i	−0.188335	+	0.174749i
$529$	22.7267	−	3.42550i	0.988119	−	0.148935i
$530$	3.63525	+	1.12133i	0.157905	+	0.0487073i
$531$	−0.548704	+	7.32195i	−0.0238117	+	0.317746i
$532$	1.94767	−	2.44230i	0.0844423	−	0.105887i
$533$	1.94418	+	4.95368i	0.0842116	+	0.214568i
$534$	13.2089	+	12.2561i	0.571605	+	0.530372i
$535$	4.72905	+	3.22421i	0.204455	+	0.139395i
$536$	2.83260	+	37.7984i	0.122350	+	1.63264i
$537$	−3.11074	+	13.6290i	−0.134238	+	0.588136i
$538$	−2.93017	+	12.8379i	−0.126329	+	0.553482i
$539$	−0.159154	−	2.12376i	−0.00685524	−	0.0914768i
$540$	0.170568	+	0.116292i	0.00734010	+	0.00500439i
$541$	−10.9480	−	10.1583i	−0.470691	−	0.436737i	0.408821	−	0.912615i	$-0.365940\pi$
$541$	−10.9480	−	10.1583i	−0.470691	−	0.436737i	−0.879512	+	0.475877i	$0.842131\pi$
$542$	−14.6886	−	37.4260i	−0.630930	−	1.60758i
$543$	−0.594081	+	0.744954i	−0.0254945	+	0.0319691i
$544$	0.236635	−	3.15768i	0.0101457	−	0.135384i
$545$	0.487002	+	0.150220i	0.0208609	+	0.00643472i
$546$	1.66234	−	0.250557i	0.0711414	−	0.0107228i
$547$	−6.28961	+	5.83590i	−0.268924	+	0.249525i	−0.803094	−	0.595852i	$-0.796815\pi$
$547$	−6.28961	+	5.83590i	−0.268924	+	0.249525i	0.534170	+	0.845377i	$0.320624\pi$
$548$	−5.68010	−	2.73539i	−0.242642	−	0.116850i
$549$	−10.7823	−	1.62516i	−0.460175	−	0.0693603i
$550$	−9.04555	+	6.16715i	−0.385704	+	0.262968i
$551$	15.6470	+	19.6208i	0.666586	+	0.835872i
$552$	0.193871	−	0.335795i	0.00825171	−	0.0142924i
$553$	−1.89643	−	3.28471i	−0.0806443	−	0.139680i
$554$	5.26325	−	13.4105i	0.223614	−	0.569759i
$555$	−0.211586	+	0.101894i	−0.00898130	+	0.00432517i
$556$	−4.85295	+	1.49694i	−0.205811	+	0.0634842i
$557$	−6.26418	−	27.4452i	−0.265422	−	1.16289i	−0.915275	−	0.402829i	$-0.868027\pi$
$557$	−6.26418	−	27.4452i	−0.265422	−	1.16289i	0.649854	−	0.760059i	$-0.274830\pi$
$558$	7.36429			0.311755
$559$	−2.96330	−	1.92960i	−0.125334	−	0.0816133i
$560$	4.77546			0.201800
$561$	0.688578	+	3.01686i	0.0290718	+	0.127372i
$562$	10.3382	−	3.18891i	0.436090	−	0.134516i
$563$	−39.8628	+	19.1969i	−1.68002	+	0.809053i	−0.683121	+	0.730305i	$0.739378\pi$
$563$	−39.8628	+	19.1969i	−1.68002	+	0.809053i	−0.996895	+	0.0787483i	$0.974908\pi$
$564$	−0.722549	+	1.84102i	−0.0304248	+	0.0775211i
$565$	4.50224	+	7.79811i	0.189411	+	0.328069i
$566$	2.82736	−	4.89714i	0.118843	−	0.205842i
$567$	−1.50674	−	1.88939i	−0.0632770	−	0.0793469i
$568$	−12.9835	+	8.85202i	−0.544777	+	0.371423i
$569$	−27.2019	−	4.10003i	−1.14036	−	0.171882i	−0.448413	−	0.893827i	$-0.648011\pi$
$569$	−27.2019	−	4.10003i	−1.14036	−	0.171882i	−0.691951	+	0.721944i	$0.743249\pi$
$570$	2.74877	+	1.32374i	0.115133	+	0.0554453i
$571$	−11.4074	+	10.5845i	−0.477385	+	0.442948i	−0.881798	−	0.471628i	$-0.843666\pi$
$571$	−11.4074	+	10.5845i	−0.477385	+	0.442948i	0.404413	+	0.914577i	$0.367476\pi$
$572$	−0.328867	+	0.0495687i	−0.0137506	+	0.00207257i
$573$	−8.60610	−	2.65463i	−0.359525	−	0.110899i
$574$	2.29896	−	30.6774i	0.0959566	−	1.28045i
$575$	0.370840	−	0.465018i	0.0154651	−	0.0193926i
$576$	3.23487	+	8.24232i	0.134786	+	0.343430i
$577$	−12.7719	−	11.8506i	−0.531702	−	0.493347i	0.368016	−	0.929819i	$-0.380037\pi$
$577$	−12.7719	−	11.8506i	−0.531702	−	0.493347i	−0.899718	+	0.436472i	$0.856228\pi$
$578$	−15.0918	−	10.2894i	−0.627737	−	0.427984i
$579$	−0.131674	−	1.75706i	−0.00547217	−	0.0730210i
$580$	0.299574	−	1.31252i	0.0124391	−	0.0544994i
$581$	3.31846	−	14.5391i	0.137673	−	0.603184i
$582$	0.703997	+	9.39419i	0.0291816	+	0.389402i
$583$	7.27936	+	4.96298i	0.301480	+	0.205546i
$584$	−25.3215	−	23.4949i	−1.04781	−	0.972225i
$585$	−0.121081	−	0.308509i	−0.00500607	−	0.0127553i
$586$	15.7140	−	19.7048i	0.649141	−	0.813998i
$587$	1.82048	−	24.2926i	0.0751391	−	1.00266i	−0.824453	−	0.565931i	$-0.808517\pi$
$587$	1.82048	−	24.2926i	0.0751391	−	1.00266i	0.899592	−	0.436731i	$-0.143864\pi$
$588$	−0.372322	−	0.114846i	−0.0153543	−	0.00473617i
$589$	−21.7233	+	3.27426i	−0.895093	+	0.134914i
$590$	4.26721	−	3.95939i	0.175678	−	0.163006i
$591$	6.82641	+	3.28743i	0.280801	+	0.135227i
$592$	−1.21493	−	0.183121i	−0.0499332	−	0.00752622i
$593$	−20.0347	+	13.6595i	−0.822728	+	0.560927i	−0.899903	−	0.436091i	$-0.856363\pi$
$593$	−20.0347	+	13.6595i	−0.822728	+	0.560927i	0.0771742	+	0.997018i	$0.475410\pi$
$594$	−1.47673	−	1.85176i	−0.0605910	−	0.0759787i
$595$	1.25157	−	2.16778i	0.0513093	−	0.0888703i
$596$	−3.46516	−	6.00183i	−0.141938	−	0.245844i
$597$	0.730401	−	1.86103i	0.0298933	−	0.0761670i
$598$	−0.0806487	+	0.0388384i	−0.00329797	+	0.00158822i
$599$	42.4291	−	13.0876i	1.73361	−	0.534747i	0.742738	−	0.669582i	$-0.233527\pi$
$599$	42.4291	−	13.0876i	1.73361	−	0.534747i	0.990868	+	0.134835i	$0.0430505\pi$
$600$	3.09936	+	13.5792i	0.126531	+	0.554369i
$601$	7.43076			0.303107			0.151554	−	0.988449i	$-0.451572\pi$
$601$	7.43076			0.303107			0.151554	+	0.988449i	$0.451572\pi$
$602$	10.5943	+	17.4829i	0.431790	+	0.712551i
$603$	−12.5790			−0.512256
$604$	0.442027	+	1.93665i	0.0179858	+	0.0788011i
$605$	−4.48028	+	1.38198i	−0.182149	+	0.0561856i
$606$	−10.7138	+	5.15951i	−0.435220	+	0.209591i
$607$	1.53201	−	3.90349i	0.0621822	−	0.158438i	−0.896406	−	0.443235i	$-0.853831\pi$
$607$	1.53201	−	3.90349i	0.0621822	−	0.158438i	0.958588	+	0.284797i	$0.0919261\pi$
$608$	−3.61507	−	6.26149i	−0.146611	−	0.253937i
$609$	−7.87986	+	13.6483i	−0.319308	+	0.553058i
$610$	5.38993	+	6.75876i	0.218232	+	0.273654i
$611$	2.62336	−	1.78858i	0.106130	−	0.0723580i
$612$	0.559806	+	0.0843771i	0.0226288	+	0.00341074i
$613$	10.0954	+	4.86170i	0.407750	+	0.196362i	0.626504	−	0.779418i	$-0.284485\pi$
$613$	10.0954	+	4.86170i	0.407750	+	0.196362i	−0.218754	+	0.975780i	$0.570199\pi$
$614$	9.73467	−	9.03245i	0.392859	−	0.364520i
$615$	−5.99704	+	0.903908i	−0.241824	+	0.0364491i
$616$	12.7761	+	3.94091i	0.514765	+	0.158784i
$617$	−0.976427	+	13.0295i	−0.0393095	+	0.524548i	0.942441	+	0.334373i	$0.108525\pi$
$617$	−0.976427	+	13.0295i	−0.0393095	+	0.524548i	−0.981750	+	0.190175i	$0.939094\pi$
$618$	14.2828	−	17.9101i	0.574539	−	0.720449i
$619$	6.67346	+	17.0037i	0.268229	+	0.683436i	0.999998	+	0.00188370i	$0.000599601\pi$
$619$	6.67346	+	17.0037i	0.268229	+	0.683436i	−0.731769	+	0.681552i	$0.761305\pi$
$620$	0.863912	+	0.801593i	0.0346955	+	0.0321928i
$621$	0.106317	+	0.0724860i	0.00426637	+	0.00290876i
$622$	−1.37001	−	18.2815i	−0.0549323	−	0.733020i
$623$	7.51142	−	32.9097i	0.300939	−	1.31850i
$624$	0.385833	−	1.69045i	0.0154457	−	0.0676720i
$625$	1.45552	+	19.4226i	0.0582209	+	0.776904i
$626$	−22.5530	−	15.3764i	−0.901400	−	0.614564i
$627$	5.17940	+	4.80578i	0.206845	+	0.191925i
$628$	1.72205	+	4.38770i	0.0687171	+	0.175088i
$629$	−0.401539	+	0.503514i	−0.0160104	+	0.0200764i
$630$	−0.143176	+	1.91055i	−0.00570427	+	0.0761182i
$631$	−28.4423	−	8.77330i	−1.13227	−	0.349259i	−0.328680	−	0.944441i	$-0.606604\pi$
$631$	−28.4423	−	8.77330i	−1.13227	−	0.349259i	−0.803591	+	0.595182i	$0.797080\pi$
$632$	−4.67654	+	0.704874i	−0.186023	+	0.0280384i
$633$	15.8282	−	14.6864i	0.629114	−	0.583732i
$634$	40.0156	+	19.2705i	1.58922	+	0.765330i
$635$	12.9119	+	1.94616i	0.512394	+	0.0772310i
$636$	1.33176	−	0.907979i	0.0528077	−	0.0360037i
$637$	0.390002	+	0.489047i	0.0154524	+	0.0193768i
$638$	−7.72294	+	13.3765i	−0.305754	+	0.529581i
$639$	−2.60743	−	4.51621i	−0.103148	−	0.178658i
$640$	1.72092	−	4.38483i	0.0680252	−	0.173325i
$641$	−2.52134	+	1.21421i	−0.0995868	+	0.0479585i	−0.483014	−	0.875613i	$-0.660458\pi$
$641$	−2.52134	+	1.21421i	−0.0995868	+	0.0479585i	0.383427	+	0.923571i	$0.374744\pi$
$642$	−11.4801	+	3.54113i	−0.453082	+	0.139757i
$643$	−8.16308	−	35.7648i	−0.321920	−	1.41042i	−0.834132	−	0.551565i	$-0.814031\pi$
$643$	−8.16308	−	35.7648i	−0.321920	−	1.41042i	0.512211	−	0.858859i	$-0.328826\pi$
$644$	−0.104454			−0.00411605
$645$	2.89546	−	2.80316i	0.114008	−	0.110374i
$646$	8.36663			0.329181
$647$	1.54930	+	6.78794i	0.0609094	+	0.266861i	0.996209	−	0.0869963i	$-0.0277268\pi$
$647$	1.54930	+	6.78794i	0.0609094	+	0.266861i	−0.935299	+	0.353858i	$0.884870\pi$
$648$	−2.87944	+	0.888190i	−0.113115	+	0.0348914i
$649$	12.1461	−	5.84924i	0.476775	−	0.229603i
$650$	1.17475	−	2.99321i	0.0460774	−	0.117403i
$651$	−6.89795	−	11.9476i	−0.270352	−	0.468263i
$652$	−0.608387	+	1.05376i	−0.0238263	+	0.0412683i
$653$	−5.53532	−	6.94108i	−0.216614	−	0.271625i	0.661638	−	0.749823i	$-0.269862\pi$
$653$	−5.53532	−	6.94108i	−0.216614	−	0.271625i	−0.878252	+	0.478198i	$0.841290\pi$
$654$	−0.883862	+	0.602607i	−0.0345617	+	0.0235638i
$655$	5.69650	+	0.858609i	0.222581	+	0.0335486i
$656$	−28.5875	−	13.7670i	−1.11616	−	0.537512i
$657$	8.40320	−	7.79703i	0.327840	−	0.304191i
$658$	−18.1498	+	2.73564i	−0.707554	+	0.106647i
$659$	8.26978	+	2.55089i	0.322145	+	0.0993685i	0.451610	−	0.892215i	$-0.350850\pi$
$659$	8.26978	+	2.55089i	0.322145	+	0.0993685i	−0.129465	+	0.991584i	$0.541326\pi$
$660$	0.0283251	−	0.377972i	0.00110255	−	0.0147126i
$661$	21.1140	−	26.4761i	0.821238	−	1.02980i	−0.177717	−	0.984082i	$-0.556871\pi$
$661$	21.1140	−	26.4761i	0.821238	−	1.02980i	0.998954	−	0.0457177i	$-0.0145575\pi$
$662$	−5.38663	−	13.7249i	−0.209357	−	0.533433i
$663$	−0.666244	−	0.618184i	−0.0258748	−	0.0240083i
$664$	−15.3641	−	10.4751i	−0.596242	−	0.406511i
$665$	−0.427113	−	5.69943i	−0.0165627	−	0.221015i
$666$	0.109688	−	0.480574i	0.00425032	−	0.0186219i
$667$	0.186728	−	0.818111i	0.00723015	−	0.0316774i
$668$	−0.278361	−	3.71447i	−0.0107701	−	0.143717i
$669$	11.7193	+	7.99005i	0.453093	+	0.308913i
$670$	7.31049	+	6.78314i	0.282429	+	0.262056i
$671$	7.31424	+	18.6364i	0.282363	+	0.719449i
$672$	2.83089	−	3.54982i	0.109204	−	0.136937i
$673$	−0.856883	+	11.4343i	−0.0330304	+	0.440760i	0.956032	+	0.293263i	$0.0947410\pi$
$673$	−0.856883	+	11.4343i	−0.0330304	+	0.440760i	−0.989062	+	0.147498i	$0.952878\pi$
$674$	−11.7900	−	3.63674i	−0.454135	−	0.140082i
$675$	−4.57067	+	0.688917i	−0.175925	+	0.0265164i
$676$	−3.12946	+	2.90371i	−0.120364	+	0.111681i
$677$	28.9852	+	13.9585i	1.11399	+	0.536470i	0.898031	−	0.439933i	$-0.144998\pi$
$677$	28.9852	+	13.9585i	1.11399	+	0.536470i	0.215960	+	0.976402i	$0.430712\pi$
$678$	−18.6893	−	2.81696i	−0.717757	−	0.108185i
$679$	14.5814	−	9.94146i	0.559584	−	0.381518i
$680$	−1.94603	−	2.44025i	−0.0746269	−	0.0935792i
$681$	9.69220	−	16.7874i	0.371406	−	0.643294i
$682$	−6.76057	−	11.7097i	−0.258876	−	0.448386i
$683$	−7.62456	+	19.4271i	−0.291746	+	0.743355i	0.707580	+	0.706633i	$0.249787\pi$
$683$	−7.62456	+	19.4271i	−0.291746	+	0.743355i	−0.999326	+	0.0367222i	$0.988308\pi$
$684$	1.16463	−	0.560856i	0.0445307	−	0.0214449i
$685$	−11.0223	+	3.39992i	−0.421139	+	0.129904i
$686$	−5.66051	−	24.8003i	−0.216119	−	0.946881i
$687$	3.95305			0.150818
$688$	20.7777	−	3.58385i	0.792142	−	0.136633i
$689$	−2.58764			−0.0985812
$690$	−0.0227005	−	0.0994576i	−0.000864195	−	0.00378629i
$691$	0.763343	−	0.235460i	0.0290389	−	0.00895733i	−0.280202	−	0.959941i	$-0.590401\pi$
$691$	0.763343	−	0.235460i	0.0290389	−	0.00895733i	0.309241	+	0.950984i	$0.399925\pi$
$692$	0.427979	−	0.206104i	0.0162693	−	0.00783490i
$693$	−1.62103	+	4.13030i	−0.0615777	+	0.156897i
$694$	−2.94785	−	5.10583i	−0.111899	−	0.193815i
$695$	−4.64593	+	8.04699i	−0.176230	+	0.305240i
$696$	12.2522	+	15.3638i	0.464418	+	0.582362i
$697$	−13.7418	+	9.36897i	−0.520506	+	0.354875i
$698$	−10.6572	−	1.60631i	−0.403380	−	0.0607997i
$699$	18.1030	+	8.71793i	0.684717	+	0.329742i
$700$	2.75053	−	2.55212i	0.103960	−	0.0964611i
$701$	26.9460	−	4.06145i	1.01774	−	0.153399i	0.381076	−	0.924544i	$-0.375554\pi$
$701$	26.9460	−	4.06145i	1.01774	−	0.153399i	0.636660	+	0.771145i	$0.280316\pi$
$702$	0.664741	+	0.205045i	0.0250890	+	0.00773894i
$703$	−0.109890	+	1.46637i	−0.00414456	+	0.0553054i
$704$	10.1361	−	12.7103i	0.382019	−	0.479036i
$705$	1.32199	+	3.36838i	0.0497891	+	0.126860i
$706$	20.9574	+	19.4456i	0.788742	+	0.731846i
$707$	18.4060	+	12.5490i	0.692230	+	0.471955i
$708$	−0.184312	−	2.45948i	−0.00692688	−	0.0924328i
$709$	4.66242	−	20.4274i	0.175101	−	0.767167i	−0.808746	−	0.588158i	$-0.799853\pi$
$709$	4.66242	−	20.4274i	0.175101	−	0.767167i	0.983847	−	0.179010i	$-0.0572894\pi$
$710$	−0.919984	+	4.03071i	−0.0345264	+	0.151270i
$711$	−0.117288	−	1.56510i	−0.00439864	−	0.0586958i
$712$	−34.7771	−	23.7106i	−1.30333	−	0.888592i
$713$	0.538487	+	0.499643i	0.0201665	+	0.0187118i
$714$	1.91953	+	4.89088i	0.0718366	+	0.183037i
$715$	−0.379393	+	0.475743i	−0.0141885	+	0.0177918i
$716$	0.350917	−	4.68266i	0.0131144	−	0.174999i
$717$	0.0591500	+	0.0182454i	0.00220900	+	0.000681385i
$718$	−14.0633	+	2.11970i	−0.524837	+	0.0791064i
$719$	28.0994	−	26.0724i	1.04793	−	0.972338i	0.0482823	−	0.998834i	$-0.484625\pi$
$719$	28.0994	−	26.0724i	1.04793	−	0.972338i	0.999649	+	0.0264956i	$0.00843481\pi$
$720$	1.78040	+	0.857393i	0.0663514	+	0.0319532i
$721$	−42.4352	−	6.39607i	−1.58037	−	0.238202i
$722$	−4.46702	+	3.04556i	−0.166245	+	0.113344i
$723$	−13.5426	−	16.9819i	−0.503654	−	0.631563i
$724$	0.160030	−	0.277181i	0.00594748	−	0.0103013i
$725$	15.0719	+	26.1053i	0.559756	+	0.969526i
$726$	3.59544	−	9.16103i	0.133439	−	0.339998i
$727$	−25.6311	+	12.3433i	−0.950604	+	0.457787i	−0.843898	−	0.536504i	$-0.819745\pi$
$727$	−25.6311	+	12.3433i	−0.950604	+	0.457787i	−0.106706	+	0.994291i	$0.534030\pi$
$728$	−3.75246	+	1.15748i	−0.139075	+	0.0428990i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−9.08817			−0.336368
$731$	3.81863	−	10.3711i	0.141237	−	0.383590i
$732$	3.66272			0.135378
$733$	7.43886	+	32.5918i	0.274761	+	1.20380i	0.904321	+	0.426853i	$0.140378\pi$
$733$	7.43886	+	32.5918i	0.274761	+	1.20380i	−0.629560	+	0.776952i	$0.716765\pi$
$734$	18.1986	−	5.61351i	0.671721	−	0.207198i
$735$	−0.642281	+	0.309306i	−0.0236909	+	0.0114089i
$736$	−0.0883248	+	0.225048i	−0.00325569	+	0.00829537i
$737$	11.5478	+	20.0013i	0.425368	+	0.736759i
$738$	6.36498	−	11.0245i	0.234298	−	0.405816i
$739$	22.2113	+	27.8521i	0.817057	+	1.02456i	0.999148	+	0.0412748i	$0.0131419\pi$
$739$	22.2113	+	27.8521i	0.817057	+	1.02456i	−0.182091	+	0.983282i	$0.558287\pi$
$740$	0.0651775	−	0.0444373i	0.00239597	−	0.00163355i
$741$	−2.05203	−	0.309294i	−0.0753832	−	0.0113622i
$742$	13.4776	+	6.49046i	0.494777	+	0.238272i
$743$	1.84764	−	1.71436i	0.0677833	−	0.0628937i	−0.645554	−	0.763715i	$-0.723373\pi$
$743$	1.84764	−	1.71436i	0.0677833	−	0.0628937i	0.713337	+	0.700821i	$0.247183\pi$
$744$	−17.0101	+	2.56387i	−0.623622	+	0.0939959i
$745$	−12.1165	−	3.73745i	−0.443915	−	0.136930i
$746$	0.586854	−	7.83102i	0.0214862	−	0.286714i
$747$	3.84757	−	4.82470i	0.140775	−	0.176526i
$748$	−0.379749	−	0.967585i	−0.0138850	−	0.0353784i
$749$	16.4981	+	15.3080i	0.602828	+	0.559343i
$750$	6.30305	+	4.29734i	0.230155	+	0.156917i
$751$	1.12398	+	14.9985i	0.0410148	+	0.547304i	0.979429	+	0.201791i	$0.0646762\pi$
$751$	1.12398	+	14.9985i	0.0410148	+	0.547304i	−0.938414	+	0.345513i	$0.887705\pi$
$752$	−4.21263	+	18.4567i	−0.153619	+	0.673048i
$753$	−0.339172	+	1.48601i	−0.0123601	+	0.0541532i
$754$	−0.339019	−	4.52390i	−0.0123464	−	0.164751i
$755$	3.00293	+	2.04736i	0.109288	+	0.0745111i
$756$	0.595058	+	0.552133i	0.0216420	+	0.0200809i
$757$	−0.372499	−	0.949111i	−0.0135387	−	0.0344960i	0.923945	−	0.382526i	$-0.124946\pi$
$757$	−0.372499	−	0.949111i	−0.0135387	−	0.0344960i	−0.937483	+	0.348030i	$0.886851\pi$
$758$	−26.4099	+	33.1169i	−0.959249	+	1.20286i
$759$	0.0176554	−	0.235595i	0.000640851	−	0.00855156i
$760$	−6.81000	−	2.10061i	−0.247025	−	0.0761971i
$761$	−9.38837	+	1.41507i	−0.340328	+	0.0512962i	−0.316983	−	0.948431i	$-0.602670\pi$
$761$	−9.38837	+	1.41507i	−0.340328	+	0.0512962i	−0.0233452	+	0.999727i	$0.507432\pi$
$762$	−20.0916	+	18.6423i	−0.727843	+	0.675340i
$763$	1.80554	+	0.869503i	0.0653650	+	0.0314781i
$764$	2.99144	+	0.450888i	0.108227	+	0.0163125i
$765$	0.855819	−	0.583488i	0.0309422	−	0.0210960i
$766$	−13.8231	−	17.3336i	−0.499447	−	0.626287i
$767$	−1.97976	+	3.42904i	−0.0714849	+	0.123816i
$768$	−3.91079	−	6.77368i	−0.141118	−	0.244424i
$769$	−14.1556	+	36.0679i	−0.510465	+	1.30064i	0.410806	+	0.911723i	$0.365247\pi$
$769$	−14.1556	+	36.0679i	−0.510465	+	1.30064i	−0.921271	+	0.388921i	$0.872848\pi$
$770$	3.16933	−	1.52627i	0.114215	−	0.0550029i
$771$	16.6218	−	5.12715i	0.598620	−	0.184650i
$772$	0.131701	+	0.577021i	0.00474004	+	0.0207675i
$773$	1.88684			0.0678651			0.0339325	−	0.999424i	$-0.489197\pi$
$773$	1.88684			0.0678651			0.0339325	+	0.999424i	$0.489197\pi$
$774$	0.810866	+	8.42013i	0.0291460	+	0.302655i
$775$	−26.3876			−0.947869
$776$	−4.89668	−	21.4537i	−0.175780	−	0.770145i
$777$	−0.882411	+	0.272188i	−0.0316563	+	0.00976469i
$778$	−33.8752	+	16.3134i	−1.21448	+	0.584865i
$779$	−13.8739	+	35.3501i	−0.497084	+	1.26655i
$780$	0.0556625	+	0.0964102i	0.00199304	+	0.00345204i
$781$	−4.78736	+	8.29195i	−0.171305	+	0.296709i
$782$	−0.174428	−	0.218726i	−0.00623754	−	0.00782163i
$783$	−5.38823	+	3.67363i	−0.192560	+	0.131285i
$784$	−3.68799	−	0.555875i	−0.131714	−	0.0198527i
$785$	7.76993	+	3.74180i	0.277321	+	0.133551i
$786$	−8.86406	+	8.22464i	−0.316171	+	0.293363i
$787$	−4.09419	+	0.617100i	−0.145942	+	0.0219972i	−0.221607	−	0.975136i	$-0.571130\pi$
$787$	−4.09419	+	0.617100i	−0.145942	+	0.0219972i	0.0756648	+	0.997133i	$0.475892\pi$
$788$	−2.43200	−	0.750171i	−0.0866362	−	0.0267237i
$789$	1.11290	−	14.8506i	0.0396203	−	0.528696i
$790$	−0.775807	+	0.972831i	−0.0276020	+	0.0346118i
$791$	12.9356	+	32.9595i	0.459939	+	1.17190i
$792$	4.05566	+	3.76311i	0.144112	+	0.133716i
$793$	−4.85839	−	3.31240i	−0.172527	−	0.117627i
$794$	2.18188	+	29.1151i	0.0774319	+	1.03326i
$795$	0.656225	−	2.87511i	0.0232739	−	0.101970i
$796$	−0.149434	+	0.654714i	−0.00529656	+	0.0232057i
$797$	0.0224640	+	0.299762i	0.000795716	+	0.0106181i	0.997588	−	0.0694200i	$-0.0221149\pi$
$797$	0.0224640	+	0.299762i	0.000795716	+	0.0106181i	−0.996792	+	0.0800381i	$0.974496\pi$
$798$	9.91209	+	6.75795i	0.350884	+	0.239229i
$799$	7.27422	+	6.74949i	0.257344	+	0.238780i
$800$	−3.17279	−	8.08413i	−0.112175	−	0.285817i
$801$	8.70908	−	10.9208i	0.307720	−	0.385869i
$802$	−1.25513	+	16.7486i	−0.0443203	+	0.591413i
$803$	−20.1121	−	6.20375i	−0.709739	−	0.218926i
$804$	4.17815	−	0.629754i	0.147352	−	0.0222097i
$805$	−0.140094	+	0.129988i	−0.00493766	+	0.00458148i
$806$	3.57800	+	1.72307i	0.126030	+	0.0606926i
$807$	10.0938	+	1.52140i	0.355319	+	0.0535557i
$808$	22.9507	−	15.6475i	0.807403	−	0.550478i
$809$	11.0738	+	13.8861i	0.389334	+	0.488210i	0.937414	−	0.348216i	$-0.113212\pi$
$809$	11.0738	+	13.8861i	0.389334	+	0.488210i	−0.548080	+	0.836426i	$0.684641\pi$
$810$	−0.396402	+	0.686589i	−0.0139282	+	0.0241243i
$811$	−4.54526	−	7.87263i	−0.159606	−	0.276445i	0.775121	−	0.631813i	$-0.217689\pi$
$811$	−4.54526	−	7.87263i	−0.159606	−	0.276445i	−0.934727	+	0.355368i	$0.884356\pi$
$812$	1.93403	−	4.92783i	0.0678712	−	0.172933i
$813$	−28.0804	+	13.5228i	−0.984822	+	0.474265i
$814$	−0.864838	+	0.266767i	−0.0303126	+	0.00935019i
$815$	0.495384	+	2.17042i	0.0173525	+	0.0760264i
$816$	5.41912			0.189707
$817$	−6.13561	−	24.4773i	−0.214658	−	0.856353i
$818$	−26.2597			−0.918150
$819$	−0.289987	−	1.27052i	−0.0101330	−	0.0443954i
$820$	1.94668	−	0.600471i	0.0679810	−	0.0209694i
$821$	22.7193	−	10.9411i	0.792910	−	0.381845i	0.00683511	−	0.999977i	$-0.497824\pi$
$821$	22.7193	−	10.9411i	0.792910	−	0.381845i	0.786075	+	0.618131i	$0.212110\pi$
$822$	8.84541	−	22.5377i	0.308519	−	0.786094i
$823$	0.0106058	+	0.0183698i	0.000369695	+	0.000640331i	0.866210	−	0.499680i	$-0.166549\pi$
$823$	0.0106058	+	0.0183698i	0.000369695	+	0.000640331i	−0.865840	+	0.500320i	$0.833216\pi$
$824$	−26.7553	+	46.3415i	−0.932065	+	1.61438i
$825$	5.29139	+	6.63519i	0.184223	+	0.231008i
$826$	18.9124	−	12.8942i	0.658045	−	0.448648i
$827$	54.3224	+	8.18779i	1.88898	+	0.284717i	0.988620	−	0.150435i	$-0.0480675\pi$
$827$	54.3224	+	8.18779i	1.88898	+	0.284717i	0.900357	+	0.435153i	$0.143306\pi$
$828$	−0.0389426	−	0.0187538i	−0.00135335	−	0.000651739i
$829$	5.99693	−	5.56434i	0.208282	−	0.193257i	−0.569133	−	0.822246i	$-0.692721\pi$
$829$	5.99693	−	5.56434i	0.208282	−	0.193257i	0.777415	+	0.628988i	$0.216531\pi$
$830$	−4.83777	+	0.729177i	−0.167921	+	0.0253101i
$831$	−10.6716	−	3.29176i	−0.370194	−	0.114190i
$832$	−0.356824	+	4.76148i	−0.0123706	+	0.165075i
$833$	−1.21890	+	1.52845i	−0.0422323	+	0.0529576i
$834$	−7.12547	−	18.1554i	−0.246735	−	0.628670i
$835$	−4.99585	−	4.63547i	−0.172888	−	0.160417i
$836$	−1.96095	−	1.33695i	−0.0678209	−	0.0462395i
$837$	−0.426616	−	5.69279i	−0.0147460	−	0.196772i
$838$	−1.25889	+	5.51557i	−0.0434877	+	0.190532i
$839$	2.07001	−	9.06932i	0.0714648	−	0.313108i	−0.926544	−	0.376187i	$-0.877235\pi$
$839$	2.07001	−	9.06932i	0.0714648	−	0.313108i	0.998009	+	0.0630794i	$0.0200921\pi$
$840$	−0.334445	−	4.46286i	−0.0115395	−	0.153983i
$841$	11.1778	+	7.62091i	0.385442	+	0.262790i
$842$	−14.7398	−	13.6765i	−0.507967	−	0.471324i
$843$	−3.06401	−	7.80697i	−0.105530	−	0.268886i
$844$	−4.52212	+	5.67055i	−0.155658	+	0.195188i
$845$	−0.583702	+	7.78896i	−0.0200799	+	0.267948i
$846$	−7.25781	−	2.23874i	−0.249529	−	0.0769694i
$847$	−18.2303	+	2.74778i	−0.626402	+	0.0944149i
$848$	11.3102	−	10.4943i	0.388392	−	0.360375i
$849$	−3.94941	−	1.90194i	−0.135543	−	0.0652743i
$850$	9.93729	+	1.49780i	0.340846	+	0.0513743i
$851$	0.0406260	−	0.0276983i	0.00139264	−	0.000949486i
$852$	1.09217	+	1.36953i	0.0374170	+	0.0469194i
$853$	17.0816	−	29.5863i	0.584864	−	1.01301i	−0.410028	−	0.912073i	$-0.634481\pi$
$853$	17.0816	−	29.5863i	0.584864	−	1.01301i	0.994892	−	0.100941i	$-0.0321854\pi$
$854$	16.9963	+	29.4385i	0.581602	+	1.00736i
$855$	0.864048	−	2.20156i	0.0295498	−	0.0752917i
$856$	25.2840	−	12.1761i	0.864188	−	0.416171i
$857$	39.5166	−	12.1892i	1.34986	−	0.416377i	0.466272	−	0.884642i	$-0.345597\pi$
$857$	39.5166	−	12.1892i	1.34986	−	0.416377i	0.883588	+	0.468265i	$0.155121\pi$
$858$	−0.284212	−	1.24521i	−0.00970283	−	0.0425109i
$859$	14.3965			0.491203			0.245602	−	0.969371i	$-0.421014\pi$
$859$	14.3965			0.491203			0.245602	+	0.969371i	$0.421014\pi$
$860$	−0.821397	+	1.07604i	−0.0280094	+	0.0366925i
$861$	−23.8477			−0.812726
$862$	−9.27413	−	40.6326i	−0.315878	−	1.38395i
$863$	−13.4661	+	4.15374i	−0.458391	+	0.141395i	−0.515347	−	0.856982i	$-0.672337\pi$
$863$	−13.4661	+	4.15374i	−0.458391	+	0.141395i	0.0569554	+	0.998377i	$0.481861\pi$
$864$	1.69276	−	0.815189i	0.0575888	−	0.0277333i
$865$	0.317521	−	0.809031i	0.0107960	−	0.0275079i
$866$	21.2730	+	36.8460i	0.722888	+	1.25208i
$867$	−7.07974	+	12.2625i	−0.240441	+	0.416455i
$868$	2.88932	+	3.62309i	0.0980698	+	0.122976i
$869$	−2.38093	+	1.62329i	−0.0807675	+	0.0550664i
$870$	5.11245	+	0.770577i	0.173328	+	0.0261250i
$871$	−6.11160	−	2.94319i	−0.207084	−	0.0997262i
$872$	1.83176	−	1.69962i	0.0620312	−	0.0575566i
$873$	7.22118	−	1.08842i	0.244400	−	0.0368374i
$874$	−0.610400	−	0.188283i	−0.0206471	−	0.00636878i
$875$	1.06797	−	14.2511i	0.0361040	−	0.481775i
$876$	−2.40080	+	3.01050i	−0.0811154	+	0.101715i
$877$	2.44479	+	6.22922i	0.0825546	+	0.210346i	0.966191	−	0.257829i	$-0.0830071\pi$
$877$	2.44479	+	6.22922i	0.0825546	+	0.210346i	−0.883636	+	0.468175i	$0.844912\pi$
$878$	23.4121	+	21.7232i	0.790119	+	0.733123i
$879$	−16.1427	−	11.0059i	−0.544479	−	0.371219i
$880$	−0.271135	−	3.61804i	−0.00913995	−	0.121964i
$881$	8.31312	−	36.4222i	0.280076	−	1.22709i	−0.617619	−	0.786477i	$-0.711903\pi$
$881$	8.31312	−	36.4222i	0.280076	−	1.22709i	0.897695	−	0.440616i	$-0.145240\pi$
$882$	0.332965	−	1.45881i	0.0112115	−	0.0491208i
$883$	−0.534208	−	7.12852i	−0.0179775	−	0.239894i	−0.998952	−	0.0457593i	$-0.985429\pi$
$883$	−0.534208	−	7.12852i	−0.0179775	−	0.239894i	0.980975	−	0.194134i	$-0.0621898\pi$
$884$	0.252244	+	0.171977i	0.00848387	+	0.00578420i
$885$	−3.30792	−	3.06930i	−0.111194	−	0.103173i
$886$	−13.2686	−	33.8079i	−0.445768	−	1.13580i
$887$	−25.0205	+	31.3747i	−0.840107	+	1.05346i	0.157714	+	0.987485i	$0.449588\pi$
$887$	−25.0205	+	31.3747i	−0.840107	+	1.05346i	−0.997821	+	0.0659760i	$0.978984\pi$
$888$	−0.0860476	+	1.14823i	−0.00288757	+	0.0385319i
$889$	49.0641	+	15.1343i	1.64556	+	0.507587i
$890$	−10.9504	+	1.65051i	−0.367059	+	0.0553253i
$891$	−1.34592	+	1.24883i	−0.0450899	+	0.0418373i
$892$	−4.29260	−	2.06721i	−0.143727	−	0.0692152i
$893$	22.4046	+	3.37695i	0.749741	+	0.113005i
$894$	21.9903	−	14.9927i	0.735466	−	0.501432i
$895$	−5.35672	−	6.71711i	−0.179055	−	0.224528i
$896$	9.26110	−	16.0407i	0.309392	−	0.535882i
$897$	0.0346951	+	0.0600937i	0.00115844	+	0.00200647i
$898$	−18.2218	+	46.4283i	−0.608068	+	1.54933i
$899$	−33.5422	+	16.1531i	−1.11870	+	0.538735i
$900$	1.48367	−	0.457652i	0.0494557	−	0.0152551i
$901$	−1.79959	−	7.88454i	−0.0599532	−	0.262672i
$902$	−23.3727			−0.778227
$903$	12.9010	−	9.20246i	0.429320	−	0.306239i
$904$	44.1495			1.46839
$905$	−0.130306	−	0.570908i	−0.00433152	−	0.0189776i
$906$	−7.28979	+	2.24860i	−0.242187	+	0.0747048i
$907$	−8.29516	+	3.99474i	−0.275436	+	0.132643i	−0.566503	−	0.824060i	$-0.691704\pi$
$907$	−8.29516	+	3.99474i	−0.275436	+	0.132643i	0.291067	+	0.956703i	$0.405990\pi$
$908$	−2.37885	+	6.06121i	−0.0789449	+	0.201148i
$909$	4.60910	+	7.98320i	0.152874	+	0.264786i
$910$	−0.516588	+	0.894756i	−0.0171247	+	0.0296609i
$911$	−15.5425	−	19.4897i	−0.514946	−	0.645722i	0.454581	−	0.890705i	$-0.349789\pi$
$911$	−15.5425	−	19.4897i	−0.514946	−	0.645722i	−0.969527	+	0.244983i	$0.921218\pi$
$912$	10.2234	−	6.97022i	0.338532	−	0.230807i
$913$	−11.2037	−	1.68869i	−0.370789	−	0.0558874i
$914$	−32.1819	−	15.4980i	−1.06448	−	0.512628i
$915$	4.91247	−	4.55810i	0.162401	−	0.150686i
$916$	−1.31302	+	0.197905i	−0.0433833	+	0.00653897i
$917$	21.6462	+	6.67696i	0.714819	+	0.220493i
$918$	−0.162474	+	2.16806i	−0.00536244	+	0.0715568i
$919$	22.4665	−	28.1721i	0.741103	−	0.929313i	−0.258221	−	0.966086i	$-0.583136\pi$
$919$	22.4665	−	28.1721i	0.741103	−	0.929313i	0.999324	+	0.0367725i	$0.0117077\pi$
$920$	0.0870601	+	0.221825i	0.00287029	+	0.00731337i
$921$	−7.54627	−	7.00191i	−0.248658	−	0.230721i
$922$	−5.66428	−	3.86184i	−0.186543	−	0.127183i
$923$	−0.210154	−	2.80431i	−0.00691731	−	0.0923051i
$924$	0.331649	−	1.45305i	0.0109104	−	0.0478018i
$925$	−0.393031	+	1.72198i	−0.0129228	+	0.0566185i
$926$	−1.80565	−	24.0947i	−0.0593373	−	0.791801i
$927$	−14.6724	−	10.0035i	−0.481905	−	0.328557i
$928$	−8.98173	−	8.33383i	−0.294840	−	0.273571i
$929$	−2.05332	−	5.23178i	−0.0673674	−	0.171649i	0.893225	−	0.449610i	$-0.148437\pi$
$929$	−2.05332	−	5.23178i	−0.0673674	−	0.171649i	−0.960593	+	0.277960i	$0.910342\pi$
$930$	−2.82187	+	3.53851i	−0.0925328	+	0.116032i
$931$	−0.333577	+	4.45128i	−0.0109325	+	0.145885i
$932$	−6.44941	−	1.98938i	−0.211257	−	0.0651643i
$933$	−14.0527	+	2.11811i	−0.460065	+	0.0693437i
$934$	−12.1580	+	11.2810i	−0.397822	+	0.369125i
$935$	−1.71344	−	0.825150i	−0.0560355	−	0.0269853i
$936$	−1.60681	−	0.242188i	−0.0525203	−	0.00791617i
$937$	20.7823	−	14.1691i	0.678928	−	0.462885i	−0.174115	−	0.984725i	$-0.555707\pi$
$937$	20.7823	−	14.1691i	0.678928	−	0.462885i	0.853043	+	0.521840i	$0.174754\pi$
$938$	24.4496	+	30.6589i	0.798309	+	1.00105i
$939$	−10.5799	+	18.3249i	−0.345261	+	0.598009i
$940$	−0.607738	−	1.05263i	−0.0198222	−	0.0343331i
$941$	−14.5919	+	37.1794i	−0.475681	+	1.21202i	0.468758	+	0.883327i	$0.344702\pi$
$941$	−14.5919	+	37.1794i	−0.475681	+	1.21202i	−0.944438	+	0.328688i	$0.893393\pi$
$942$	−16.3091	+	7.85403i	−0.531378	+	0.255898i
$943$	1.21339	−	0.374281i	0.0395134	−	0.0121883i
$944$	−5.25343	−	23.0168i	−0.170985	−	0.749133i
$945$	1.48520			0.0483136
$946$	12.6441	−	9.01919i	0.411096	−	0.293239i
$947$	6.76907			0.219965			0.109983	−	0.993934i	$-0.464920\pi$
$947$	6.76907			0.219965			0.109983	+	0.993934i	$0.464920\pi$
$948$	0.117313	+	0.513980i	0.00381014	+	0.0166933i
$949$	5.90708	−	1.82209i	0.191752	−	0.0591477i
$950$	20.6737	−	9.95594i	0.670744	−	0.323013i
$951$	12.5785	−	32.0495i	0.407886	−	1.03928i
$952$	−6.13651	−	10.6288i	−0.198886	−	0.344480i
$953$	23.8385	−	41.2895i	0.772205	−	1.33750i	−0.164147	−	0.986436i	$-0.552487\pi$
$953$	23.8385	−	41.2895i	0.772205	−	1.33750i	0.936352	−	0.351063i	$-0.114180\pi$
$954$	3.85943	+	4.83957i	0.124954	+	0.156687i
$955$	4.57326	−	3.11799i	0.147987	−	0.100896i
$956$	−0.0205603	−	0.00309896i	−0.000664967	−	0.000100228i
$957$	10.7878	+	5.19513i	0.348720	+	0.167935i
$958$	22.3728	−	20.7589i	0.722831	−	0.670689i
$959$	−44.8498	+	6.76002i	−1.44828	+	0.218292i
$960$	−5.19996	−	1.60397i	−0.167828	−	0.0517680i
$961$	0.118814	−	1.58546i	0.00383271	−	0.0511439i
$962$	0.165736	−	0.207826i	0.00534354	−	0.00670059i
$963$	3.40243	+	8.66926i	0.109642	+	0.279363i
$964$	5.34839	+	4.96258i	0.172260	+	0.159834i
$965$	0.894718	+	0.610008i	0.0288020	+	0.0196369i
$966$	−0.0299773	−	0.400019i	−0.000964503	−	0.0128704i
$967$	1.57680	−	6.90843i	0.0507066	−	0.222160i	−0.943226	−	0.332152i	$-0.892225\pi$
$967$	1.57680	−	6.90843i	0.0507066	−	0.222160i	0.993932	+	0.109992i	$0.0350825\pi$
$968$	−5.11540	+	22.4120i	−0.164415	+	0.720350i
$969$	−0.484682	−	6.46763i	−0.0155702	−	0.207770i
$970$	−4.78364	−	3.26143i	−0.153593	−	0.104718i
$971$	−14.1943	−	13.1704i	−0.455518	−	0.422659i	0.418751	−	0.908101i	$-0.362468\pi$
$971$	−14.1943	−	13.1704i	−0.455518	−	0.422659i	−0.874269	+	0.485442i	$0.838659\pi$
$972$	0.122720	+	0.312685i	0.00393624	+	0.0100294i
$973$	−22.7805	+	28.5659i	−0.730310	+	0.915780i
$974$	3.49776	−	46.6743i	0.112075	−	1.49554i
$975$	−2.38188	−	0.734714i	−0.0762813	−	0.0235297i
$976$	34.6688	−	5.22548i	1.10972	−	0.167264i
$977$	1.41695	−	1.31474i	0.0453322	−	0.0420621i	−0.657181	−	0.753732i	$-0.728251\pi$
$977$	1.41695	−	1.31474i	0.0453322	−	0.0420621i	0.702514	+	0.711670i	$0.252061\pi$
$978$	−4.21010	−	2.02748i	−0.134624	−	0.0648316i
$979$	−25.3599	−	3.82239i	−0.810507	−	0.122164i
$980$	0.197851	−	0.134892i	0.00632010	−	0.00430897i
$981$	0.517034	+	0.648340i	0.0165076	+	0.0206999i
$982$	−18.9574	+	32.8352i	−0.604956	+	1.04781i
$983$	3.63262	+	6.29188i	0.115863	+	0.200680i	0.918124	−	0.396293i	$-0.129703\pi$
$983$	3.63262	+	6.29188i	0.115863	+	0.200680i	−0.802262	+	0.596973i	$0.796370\pi$
$984$	−10.8638	+	27.6804i	−0.346324	+	0.882419i
$985$	−4.19537	+	2.02038i	−0.133675	+	0.0643747i
$986$	13.5485	−	4.17917i	0.431473	−	0.133092i
$987$	3.16615	+	13.8718i	0.100780	+	0.441545i
$988$	0.697072			0.0221768
$989$	−0.511987	+	0.670707i	−0.0162802	+	0.0213272i
$990$	1.45562			0.0462628
$991$	−9.30054	−	40.7483i	−0.295441	−	1.29441i	−0.876835	−	0.480791i	$-0.840350\pi$
$991$	−9.30054	−	40.7483i	−0.295441	−	1.29441i	0.581394	−	0.813622i	$-0.302508\pi$
$992$	10.2492	−	3.16146i	0.325413	−	0.100376i
$993$	−10.2977	+	4.95910i	−0.326787	+	0.157372i
$994$	−5.93935	+	15.1332i	−0.188385	+	0.479997i
$995$	0.614342	+	1.06407i	0.0194760	+	0.0337333i
$996$	−1.03644	+	1.79516i	−0.0328408	+	0.0568819i
$997$	−1.99688	−	2.50401i	−0.0632419	−	0.0793028i	0.749204	−	0.662339i	$-0.230436\pi$
$997$	−1.99688	−	2.50401i	−0.0632419	−	0.0793028i	−0.812446	+	0.583036i	$0.801865\pi$
$998$	28.0127	−	19.0988i	0.886728	−	0.604561i
$999$	−0.377851	−	0.0569519i	−0.0119547	−	0.00180188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	129.2.m.a.103.1	✓	36
3.2	odd	2		387.2.y.b.361.3		36
43.9	even	21		5547.2.a.z.1.15		18
43.34	odd	42		5547.2.a.y.1.4		18
43.38	even	21	inner	129.2.m.a.124.1	yes	36
129.38	odd	42		387.2.y.b.253.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.2.m.a.103.1	✓	36	1.1	even	1	trivial
129.2.m.a.124.1	yes	36	43.38	even	21	inner
387.2.y.b.253.3		36	129.38	odd	42
387.2.y.b.361.3		36	3.2	odd	2
5547.2.a.y.1.4		18	43.34	odd	42
5547.2.a.z.1.15		18	43.9	even	21

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:	\( N \)	\(=\)	\( 129 = 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	129.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.287052 - 1.25766i) q^{2} +(-0.955573 + 0.294755i) q^{3} +(0.302640 - 0.145744i) q^{4} +(0.224531 - 0.572095i) q^{5} +(0.644999 + 1.11717i) q^{6} +(1.20831 - 2.09285i) q^{7} +(-1.87877 - 2.35590i) q^{8} +(0.826239 - 0.563320i) q^{9} +O(q^{10})\)	\(q+(-0.287052 - 1.25766i) q^{2} +(-0.955573 + 0.294755i) q^{3} +(0.302640 - 0.145744i) q^{4} +(0.224531 - 0.572095i) q^{5} +(0.644999 + 1.11717i) q^{6} +(1.20831 - 2.09285i) q^{7} +(-1.87877 - 2.35590i) q^{8} +(0.826239 - 0.563320i) q^{9} +(-0.783950 - 0.118161i) q^{10} +(-1.65422 - 0.796629i) q^{11} +(-0.246236 + 0.228473i) q^{12} +(0.533238 - 0.0803727i) q^{13} +(-2.97894 - 0.918880i) q^{14} +(-0.0459275 + 0.612860i) q^{15} +(-2.00474 + 2.51387i) q^{16} +(0.615740 + 1.56888i) q^{17} +(-0.945636 - 0.877422i) q^{18} +(3.17956 + 2.16779i) q^{19} +(-0.0154273 - 0.205862i) q^{20} +(-0.537749 + 2.35603i) q^{21} +(-0.527039 + 2.30911i) q^{22} +(-0.00961601 - 0.128317i) q^{23} +(2.48972 + 1.69746i) q^{24} +(3.38838 + 3.14396i) q^{25} +(-0.254148 - 0.647559i) q^{26} +(-0.623490 + 0.781831i) q^{27} +(0.0606624 - 0.809484i) q^{28} +(6.23167 + 1.92221i) q^{29} +(0.783950 - 0.118161i) q^{30} +(-4.18482 + 3.88294i) q^{31} +(-1.69276 - 0.815189i) q^{32} +(1.81554 + 0.273648i) q^{33} +(1.79636 - 1.22474i) q^{34} +(-0.926008 - 1.16118i) q^{35} +(0.167952 - 0.290902i) q^{36} +(0.191060 + 0.330925i) q^{37} +(1.81363 - 4.62106i) q^{38} +(-0.485858 + 0.233977i) q^{39} +(-1.76964 + 0.545862i) q^{40} +(2.19588 + 9.62078i) q^{41} +3.11744 q^{42} +(-4.90043 - 4.35726i) q^{43} -0.616736 q^{44} +(-0.136757 - 0.599169i) q^{45} +(-0.158618 + 0.0489271i) q^{46} +(5.30472 - 2.55462i) q^{47} +(1.17470 - 2.99309i) q^{48} +(0.579974 + 1.00454i) q^{49} +(2.98138 - 5.16389i) q^{50} +(-1.05082 - 1.31769i) q^{51} +(0.149665 - 0.102040i) q^{52} +(-4.74489 - 0.715178i) q^{53} +(1.16225 + 0.559709i) q^{54} +(-0.827170 + 0.767502i) q^{55} +(-7.20070 + 1.08533i) q^{56} +(-3.67727 - 1.13429i) q^{57} +(0.628673 - 8.38906i) q^{58} +(-4.57796 + 5.74058i) q^{59} +(0.0754209 + 0.192169i) q^{60} +(-7.99323 - 7.41663i) q^{61} +(6.08466 + 4.14845i) q^{62} +(-0.180594 - 2.40986i) q^{63} +(-1.97029 + 8.63239i) q^{64} +(0.0737475 - 0.323109i) q^{65} +(-0.176998 - 2.36187i) q^{66} +(-10.3932 - 7.08599i) q^{67} +(0.415002 + 0.385065i) q^{68} +(0.0470108 + 0.119782i) q^{69} +(-1.19455 + 1.49792i) q^{70} +(0.389707 - 5.20028i) q^{71} +(-2.87944 - 0.888190i) q^{72} +(11.3353 - 1.70852i) q^{73} +(0.361346 - 0.335280i) q^{74} +(-4.16454 - 2.00554i) q^{75} +(1.27820 + 0.192658i) q^{76} +(-3.66604 + 2.49946i) q^{77} +(0.433728 + 0.543878i) q^{78} +(0.784744 - 1.35922i) q^{79} +(0.988045 + 1.71134i) q^{80} +(0.365341 - 0.930874i) q^{81} +(11.4693 - 5.52332i) q^{82} +(5.89686 - 1.81894i) q^{83} +(0.180632 + 0.791402i) q^{84} +1.03580 q^{85} +(-4.07326 + 7.41382i) q^{86} -6.52139 q^{87} +(1.23111 + 5.39386i) q^{88} +(13.3477 - 4.11722i) q^{89} +(-0.714292 + 0.343985i) q^{90} +(0.476109 - 1.21311i) q^{91} +(-0.0216115 - 0.0374322i) q^{92} +(2.85438 - 4.94393i) q^{93} +(-4.73556 - 5.93820i) q^{94} +(1.95409 - 1.33228i) q^{95} +(1.85783 + 0.280023i) q^{96} +(6.57955 + 3.16854i) q^{97} +(1.09689 - 1.01776i) q^{98} +(-1.81554 + 0.273648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 3 q^{3} - 6 q^{4} + 3 q^{5} + q^{6} - 11 q^{7} - 14 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 3 * q^3 - 6 * q^4 + 3 * q^5 + q^6 - 11 * q^7 - 14 * q^8 + 3 * q^9	\( 36 q + 2 q^{2} - 3 q^{3} - 6 q^{4} + 3 q^{5} + q^{6} - 11 q^{7} - 14 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + 4 q^{12} - 8 q^{13} - 70 q^{14} - 10 q^{15} + 10 q^{16} - 3 q^{17} - q^{18} - 3 q^{19} + 13 q^{20} + 13 q^{21} - 8 q^{22} - 32 q^{23} + 7 q^{24} + 12 q^{25} + 11 q^{26} + 6 q^{27} + 35 q^{28} + 8 q^{29} + 2 q^{30} - 24 q^{31} + 40 q^{32} + 17 q^{33} + 54 q^{34} - 14 q^{35} - 11 q^{36} + 2 q^{37} + 44 q^{38} + 12 q^{39} - 66 q^{40} + 55 q^{41} + 28 q^{42} - 23 q^{43} - 10 q^{44} + 8 q^{45} + 30 q^{46} + 26 q^{47} + 5 q^{48} - q^{49} + 19 q^{50} - 6 q^{51} - 64 q^{52} - 59 q^{53} - 2 q^{54} + 19 q^{55} - 11 q^{56} - 39 q^{57} - 69 q^{58} + 16 q^{59} - 48 q^{60} - 87 q^{61} - 67 q^{62} + 3 q^{63} + 18 q^{64} - 19 q^{65} + 10 q^{66} - 29 q^{67} + 3 q^{68} + 4 q^{69} - 83 q^{70} + 34 q^{71} + 8 q^{73} - 70 q^{74} - 32 q^{75} + 99 q^{76} + 101 q^{77} - 20 q^{78} - 10 q^{79} + 42 q^{80} + 3 q^{81} + 134 q^{82} - 33 q^{83} + 21 q^{84} + 92 q^{85} + 15 q^{86} + 16 q^{87} + 16 q^{88} + 80 q^{89} + 18 q^{90} - 22 q^{91} + 75 q^{92} - 4 q^{93} + 54 q^{94} - 69 q^{95} - 50 q^{96} + 91 q^{97} + 165 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 3 * q^3 - 6 * q^4 + 3 * q^5 + q^6 - 11 * q^7 - 14 * q^8 + 3 * q^9 - 2 * q^10 - q^11 + 4 * q^12 - 8 * q^13 - 70 * q^14 - 10 * q^15 + 10 * q^16 - 3 * q^17 - q^18 - 3 * q^19 + 13 * q^20 + 13 * q^21 - 8 * q^22 - 32 * q^23 + 7 * q^24 + 12 * q^25 + 11 * q^26 + 6 * q^27 + 35 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 40 * q^32 + 17 * q^33 + 54 * q^34 - 14 * q^35 - 11 * q^36 + 2 * q^37 + 44 * q^38 + 12 * q^39 - 66 * q^40 + 55 * q^41 + 28 * q^42 - 23 * q^43 - 10 * q^44 + 8 * q^45 + 30 * q^46 + 26 * q^47 + 5 * q^48 - q^49 + 19 * q^50 - 6 * q^51 - 64 * q^52 - 59 * q^53 - 2 * q^54 + 19 * q^55 - 11 * q^56 - 39 * q^57 - 69 * q^58 + 16 * q^59 - 48 * q^60 - 87 * q^61 - 67 * q^62 + 3 * q^63 + 18 * q^64 - 19 * q^65 + 10 * q^66 - 29 * q^67 + 3 * q^68 + 4 * q^69 - 83 * q^70 + 34 * q^71 + 8 * q^73 - 70 * q^74 - 32 * q^75 + 99 * q^76 + 101 * q^77 - 20 * q^78 - 10 * q^79 + 42 * q^80 + 3 * q^81 + 134 * q^82 - 33 * q^83 + 21 * q^84 + 92 * q^85 + 15 * q^86 + 16 * q^87 + 16 * q^88 + 80 * q^89 + 18 * q^90 - 22 * q^91 + 75 * q^92 - 4 * q^93 + 54 * q^94 - 69 * q^95 - 50 * q^96 + 91 * q^97 + 165 * q^98 - 17 * q^99

Introduction

L-functions

Modular forms

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