LMFDB - Embedded newform 54.2.e.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,2,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, 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:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Root			$0.500000 + 1.80139i$ of defining polynomial
Character	$\chi$	$=$	54.43
Dual form			54.2.e.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-1.36085 + 1.07149i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.696050 + 0.253341i) q^{5} +(-1.73121 - 0.0539310i) q^{6} +(0.717657 - 4.07003i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.703829 - 2.91627i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-1.36085 + 1.07149i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.696050 + 0.253341i) q^{5} +(-1.73121 - 0.0539310i) q^{6} +(0.717657 - 4.07003i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.703829 - 2.91627i) q^{9} +(0.370360 + 0.641483i) q^{10} +(-4.27215 + 1.55493i) q^{11} +(-1.29152 - 1.15411i) q^{12} +(0.662744 - 0.556108i) q^{13} +(3.16592 - 2.65653i) q^{14} +(-1.21867 + 0.401049i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.17975 + 3.77544i) q^{17} +(2.41371 - 1.78158i) q^{18} +(-0.777964 + 1.34747i) q^{19} +(-0.128625 + 0.729467i) q^{20} +(3.38437 + 6.30767i) q^{21} +(-4.27215 - 1.55493i) q^{22} +(-0.608539 - 3.45119i) q^{23} +(-0.247510 - 1.71428i) q^{24} +(-3.40992 - 2.86126i) q^{25} +0.865150 q^{26} +(2.16694 + 4.72275i) q^{27} +4.13282 q^{28} +(-2.50318 - 2.10042i) q^{29} +(-1.19135 - 0.476126i) q^{30} +(1.85778 + 10.5360i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(4.14766 - 6.69359i) q^{33} +(-0.757019 + 4.29327i) q^{34} +(1.53063 - 2.65113i) q^{35} +(2.99418 + 0.186732i) q^{36} +(0.880842 + 1.52566i) q^{37} +(-1.46209 + 0.532159i) q^{38} +(-0.306033 + 1.46690i) q^{39} +(-0.567425 + 0.476126i) q^{40} +(-1.97401 + 1.65639i) q^{41} +(-1.46192 + 7.00738i) q^{42} +(2.58757 - 0.941797i) q^{43} +(-2.27316 - 3.93723i) q^{44} +(1.22871 - 1.85156i) q^{45} +(1.75222 - 3.03493i) q^{46} +(1.68378 - 9.54918i) q^{47} +(0.912311 - 1.47231i) q^{48} +(-9.47229 - 3.44763i) q^{49} +(-0.772966 - 4.38371i) q^{50} +(-7.01165 - 2.80223i) q^{51} +(0.662744 + 0.556108i) q^{52} +4.00839 q^{53} +(-1.37575 + 5.01072i) q^{54} -3.36756 q^{55} +(3.16592 + 2.65653i) q^{56} +(-0.385108 - 2.66729i) q^{57} +(-0.567425 - 3.21803i) q^{58} +(-1.34517 - 0.489601i) q^{59} +(-0.606576 - 1.13052i) q^{60} +(-0.751711 + 4.26317i) q^{61} +(-5.34926 + 9.26519i) q^{62} +(-11.3642 - 4.95749i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.602188 - 0.219178i) q^{65} +(7.47985 - 2.46152i) q^{66} +(10.0444 - 8.42825i) q^{67} +(-3.33957 + 2.80223i) q^{68} +(4.52604 + 4.04452i) q^{69} +(2.87665 - 1.04701i) q^{70} +(2.54213 + 4.40310i) q^{71} +(2.17365 + 2.06767i) q^{72} +(0.286636 - 0.496469i) q^{73} +(-0.305913 + 1.73492i) q^{74} +(7.70620 + 0.240065i) q^{75} +(-1.46209 - 0.532159i) q^{76} +(3.26270 + 18.5037i) q^{77} +(-1.17734 + 0.926998i) q^{78} +(5.17820 + 4.34502i) q^{79} -0.740720 q^{80} +(-8.00925 - 4.10511i) q^{81} -2.57689 q^{82} +(7.06556 + 5.92871i) q^{83} +(-5.62415 + 4.42826i) q^{84} +(0.560740 + 3.18011i) q^{85} +(2.58757 + 0.941797i) q^{86} +(5.65702 + 0.176229i) q^{87} +(0.789461 - 4.47725i) q^{88} +(6.19947 - 10.7378i) q^{89} +(2.13141 - 0.628576i) q^{90} +(-1.78776 - 3.09648i) q^{91} +(3.29309 - 1.19859i) q^{92} +(-13.8173 - 12.3473i) q^{93} +(7.42794 - 6.23278i) q^{94} +(-0.882872 + 0.740818i) q^{95} +(1.64525 - 0.541430i) q^{96} +(-5.40770 + 1.96824i) q^{97} +(-5.04010 - 8.72971i) q^{98} +(1.52774 + 13.5531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−1.36085	+	1.07149i	−0.785688	+	0.618624i
$3$	−1.36085	+	1.07149i	−0.785688	+	0.618624i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.696050	+	0.253341i	0.311283	+	0.113298i	0.492938	−	0.870065i	$-0.335923\pi$
$5$	0.696050	+	0.253341i	0.311283	+	0.113298i	−0.181655	+	0.983362i	$0.558145\pi$
$6$	−1.73121	−	0.0539310i	−0.706764	−	0.0220172i
$7$	0.717657	−	4.07003i	0.271249	−	1.53833i	−0.479382	−	0.877606i	$-0.659139\pi$
$7$	0.717657	−	4.07003i	0.271249	−	1.53833i	0.750631	−	0.660722i	$-0.229750\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.703829	−	2.91627i	0.234610	−	0.972090i
$10$	0.370360	+	0.641483i	0.117118	+	0.202855i
$11$	−4.27215	+	1.55493i	−1.28810	+	0.468830i	−0.893103	−	0.449852i	$-0.851477\pi$
$11$	−4.27215	+	1.55493i	−1.28810	+	0.468830i	−0.394998	+	0.918682i	$0.629255\pi$
$12$	−1.29152	−	1.15411i	−0.372829	−	0.333164i
$13$	0.662744	−	0.556108i	0.183812	−	0.154237i	−0.546239	−	0.837630i	$-0.683941\pi$
$13$	0.662744	−	0.556108i	0.183812	−	0.154237i	0.730051	+	0.683393i	$0.239496\pi$
$14$	3.16592	−	2.65653i	0.846129	−	0.709986i
$15$	−1.21867	+	0.401049i	−0.314660	+	0.103550i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.17975	+	3.77544i	0.528667	+	0.915678i	0.999441	+	0.0334246i	$0.0106414\pi$
$17$	2.17975	+	3.77544i	0.528667	+	0.915678i	−0.470774	+	0.882254i	$0.656025\pi$
$18$	2.41371	−	1.78158i	0.568916	−	0.419922i
$19$	−0.777964	+	1.34747i	−0.178477	+	0.309132i	−0.941359	−	0.337406i	$-0.890450\pi$
$19$	−0.777964	+	1.34747i	−0.178477	+	0.309132i	0.762882	+	0.646538i	$0.223784\pi$
$20$	−0.128625	+	0.729467i	−0.0287614	+	0.163114i
$21$	3.38437	+	6.30767i	0.738529	+	1.37645i
$22$	−4.27215	−	1.55493i	−0.910825	−	0.331513i
$23$	−0.608539	−	3.45119i	−0.126889	−	0.719624i	−0.980168	−	0.198169i	$-0.936501\pi$
$23$	−0.608539	−	3.45119i	−0.126889	−	0.719624i	0.853279	−	0.521455i	$-0.174611\pi$
$24$	−0.247510	−	1.71428i	−0.0505228	−	0.349925i
$25$	−3.40992	−	2.86126i	−0.681984	−	0.572252i
$26$	0.865150			0.169670
$27$	2.16694	+	4.72275i	0.417028	+	0.908894i
$28$	4.13282			0.781029
$29$	−2.50318	−	2.10042i	−0.464829	−	0.390038i	0.380075	−	0.924956i	$-0.375898\pi$
$29$	−2.50318	−	2.10042i	−0.464829	−	0.390038i	−0.844904	+	0.534918i	$0.820343\pi$
$30$	−1.19135	−	0.476126i	−0.217509	−	0.0869283i
$31$	1.85778	+	10.5360i	0.333667	+	1.89232i	0.440016	+	0.897990i	$0.354973\pi$
$31$	1.85778	+	10.5360i	0.333667	+	1.89232i	−0.106350	+	0.994329i	$0.533916\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	4.14766	−	6.69359i	0.722015	−	1.16520i
$34$	−0.757019	+	4.29327i	−0.129828	+	0.736290i
$35$	1.53063	−	2.65113i	0.258724	−	0.448123i
$36$	2.99418	+	0.186732i	0.499030	+	0.0311220i
$37$	0.880842	+	1.52566i	0.144810	+	0.250817i	0.929302	−	0.369321i	$-0.120410\pi$
$37$	0.880842	+	1.52566i	0.144810	+	0.250817i	−0.784492	+	0.620139i	$0.787076\pi$
$38$	−1.46209	+	0.532159i	−0.237183	+	0.0863275i
$39$	−0.306033	+	1.46690i	−0.0490044	+	0.234892i
$40$	−0.567425	+	0.476126i	−0.0897177	+	0.0752821i
$41$	−1.97401	+	1.65639i	−0.308289	+	0.258685i	−0.783784	−	0.621033i	$-0.786713\pi$
$41$	−1.97401	+	1.65639i	−0.308289	+	0.258685i	0.475495	+	0.879718i	$0.342269\pi$
$42$	−1.46192	+	7.00738i	−0.225579	+	1.08126i
$43$	2.58757	−	0.941797i	0.394600	−	0.143623i	−0.137096	−	0.990558i	$-0.543777\pi$
$43$	2.58757	−	0.941797i	0.394600	−	0.143623i	0.531696	+	0.846935i	$0.321555\pi$
$44$	−2.27316	−	3.93723i	−0.342692	−	0.593560i
$45$	1.22871	−	1.85156i	0.183166	−	0.276014i
$46$	1.75222	−	3.03493i	0.258350	−	0.447476i
$47$	1.68378	−	9.54918i	0.245604	−	1.39289i	−0.573481	−	0.819219i	$-0.694407\pi$
$47$	1.68378	−	9.54918i	0.245604	−	1.39289i	0.819085	−	0.573672i	$-0.194481\pi$
$48$	0.912311	−	1.47231i	0.131681	−	0.212509i
$49$	−9.47229	−	3.44763i	−1.35318	−	0.492519i
$50$	−0.772966	−	4.38371i	−0.109314	−	0.619950i
$51$	−7.01165	−	2.80223i	−0.981827	−	0.392391i
$52$	0.662744	+	0.556108i	0.0919060	+	0.0771183i
$53$	4.00839			0.550595			0.275297	−	0.961359i	$-0.411224\pi$
$53$	4.00839			0.550595			0.275297	+	0.961359i	$0.411224\pi$
$54$	−1.37575	+	5.01072i	−0.187216	+	0.681872i
$55$	−3.36756			−0.454081
$56$	3.16592	+	2.65653i	0.423064	+	0.354993i
$57$	−0.385108	−	2.66729i	−0.0510088	−	0.353291i
$58$	−0.567425	−	3.21803i	−0.0745065	−	0.422548i
$59$	−1.34517	−	0.489601i	−0.175126	−	0.0637406i	0.252969	−	0.967474i	$-0.418593\pi$
$59$	−1.34517	−	0.489601i	−0.175126	−	0.0637406i	−0.428095	+	0.903734i	$0.640815\pi$
$60$	−0.606576	−	1.13052i	−0.0783086	−	0.145949i
$61$	−0.751711	+	4.26317i	−0.0962468	+	0.545843i	0.898111	+	0.439768i	$0.144939\pi$
$61$	−0.751711	+	4.26317i	−0.0962468	+	0.545843i	−0.994358	+	0.106075i	$0.966172\pi$
$62$	−5.34926	+	9.26519i	−0.679357	+	1.17668i
$63$	−11.3642	−	4.95749i	−1.43175	−	0.624585i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.602188	−	0.219178i	0.0746922	−	0.0271857i
$66$	7.47985	−	2.46152i	0.920705	−	0.302992i
$67$	10.0444	−	8.42825i	1.22712	−	1.02967i	0.228697	−	0.973498i	$-0.426554\pi$
$67$	10.0444	−	8.42825i	1.22712	−	1.02967i	0.998421	−	0.0561764i	$-0.0178909\pi$
$68$	−3.33957	+	2.80223i	−0.404983	+	0.339821i
$69$	4.52604	+	4.04452i	0.544871	+	0.486903i
$70$	2.87665	−	1.04701i	0.343825	−	0.125142i
$71$	2.54213	+	4.40310i	0.301695	+	0.522551i	0.976520	−	0.215427i	$-0.0691142\pi$
$71$	2.54213	+	4.40310i	0.301695	+	0.522551i	−0.674825	+	0.737978i	$0.735781\pi$
$72$	2.17365	+	2.06767i	0.256167	+	0.243677i
$73$	0.286636	−	0.496469i	0.0335483	−	0.0581073i	−0.848764	−	0.528772i	$-0.822653\pi$
$73$	0.286636	−	0.496469i	0.0335483	−	0.0581073i	0.882312	+	0.470665i	$0.155986\pi$
$74$	−0.305913	+	1.73492i	−0.0355617	+	0.201680i
$75$	7.70620	+	0.240065i	0.889835	+	0.0277203i
$76$	−1.46209	−	0.532159i	−0.167714	−	0.0610428i
$77$	3.26270	+	18.5037i	0.371819	+	2.10869i
$78$	−1.17734	+	0.926998i	−0.133308	+	0.104962i
$79$	5.17820	+	4.34502i	0.582593	+	0.488853i	0.885797	−	0.464072i	$-0.153612\pi$
$79$	5.17820	+	4.34502i	0.582593	+	0.488853i	−0.303205	+	0.952925i	$0.598057\pi$
$80$	−0.740720			−0.0828151
$81$	−8.00925	−	4.10511i	−0.889916	−	0.456124i
$82$	−2.57689			−0.284570
$83$	7.06556	+	5.92871i	0.775546	+	0.650761i	0.942123	−	0.335268i	$-0.108827\pi$
$83$	7.06556	+	5.92871i	0.775546	+	0.650761i	−0.166577	+	0.986029i	$0.553271\pi$
$84$	−5.62415	+	4.42826i	−0.613645	+	0.483163i
$85$	0.560740	+	3.18011i	0.0608208	+	0.344932i
$86$	2.58757	+	0.941797i	0.279024	+	0.101557i
$87$	5.65702	+	0.176229i	0.606497	+	0.0188937i
$88$	0.789461	−	4.47725i	0.0841568	−	0.477277i
$89$	6.19947	−	10.7378i	0.657142	−	1.13820i	−0.324210	−	0.945985i	$-0.605098\pi$
$89$	6.19947	−	10.7378i	0.657142	−	1.13820i	0.981352	−	0.192219i	$-0.0615683\pi$
$90$	2.13141	−	0.628576i	0.224670	−	0.0662577i
$91$	−1.78776	−	3.09648i	−0.187408	−	0.324600i
$92$	3.29309	−	1.19859i	0.343329	−	0.124961i
$93$	−13.8173	−	12.3473i	−1.43279	−	1.28036i
$94$	7.42794	−	6.23278i	0.766134	−	0.642862i
$95$	−0.882872	+	0.740818i	−0.0905808	+	0.0760063i
$96$	1.64525	−	0.541430i	0.167918	−	0.0552595i
$97$	−5.40770	+	1.96824i	−0.549069	+	0.199845i	−0.601633	−	0.798773i	$-0.705483\pi$
$97$	−5.40770	+	1.96824i	−0.549069	+	0.199845i	0.0525637	+	0.998618i	$0.483261\pi$
$98$	−5.04010	−	8.72971i	−0.509127	−	0.881834i
$99$	1.52774	+	13.5531i	0.153544	+	1.36214i
$100$	2.22567	−	3.85497i	0.222567	−	0.385497i
$101$	−1.91700	+	10.8718i	−0.190748	+	1.08179i	0.727596	+	0.686006i	$0.240637\pi$
$101$	−1.91700	+	10.8718i	−0.190748	+	1.08179i	−0.918345	+	0.395782i	$0.870474\pi$
$102$	−3.56999	−	6.65364i	−0.353482	−	0.658808i
$103$	6.03419	+	2.19627i	0.594567	+	0.216405i	0.621737	−	0.783226i	$-0.286427\pi$
$103$	6.03419	+	2.19627i	0.594567	+	0.216405i	−0.0271702	+	0.999631i	$0.508650\pi$
$104$	0.150232	+	0.852007i	0.0147314	+	0.0835461i
$105$	0.757693	+	5.24785i	0.0739433	+	0.512138i
$106$	3.07060	+	2.57654i	0.298243	+	0.250256i
$107$	−17.2923			−1.67171			−0.835854	−	0.548952i	$-0.815027\pi$
$107$	−17.2923			−1.67171			−0.835854	+	0.548952i	$0.815027\pi$
$108$	−4.27472	+	2.95411i	−0.411335	+	0.284260i
$109$	−9.94570			−0.952626			−0.476313	−	0.879276i	$-0.658027\pi$
$109$	−9.94570			−0.952626			−0.476313	+	0.879276i	$0.658027\pi$
$110$	−2.57970	−	2.16462i	−0.245964	−	0.206389i
$111$	−2.83342	−	1.13239i	−0.268937	−	0.107482i
$112$	0.717657	+	4.07003i	0.0678122	+	0.384582i
$113$	−2.30350	−	0.838405i	−0.216695	−	0.0788705i	0.231392	−	0.972861i	$-0.425672\pi$
$113$	−2.30350	−	0.838405i	−0.216695	−	0.0788705i	−0.448087	+	0.893990i	$0.647894\pi$
$114$	1.41949	−	2.29080i	0.132947	−	0.214553i
$115$	0.450757	−	2.55637i	0.0420333	−	0.238383i
$116$	1.63383	−	2.82988i	0.151698	−	0.262748i
$117$	−1.15530	−	2.32414i	−0.106808	−	0.214867i
$118$	−0.715749	−	1.23971i	−0.0658900	−	0.114125i
$119$	16.9305	−	6.16219i	1.55201	−	0.564887i
$120$	0.262018	−	1.25592i	0.0239188	−	0.114650i
$121$	7.40693	−	6.21515i	0.673357	−	0.565014i
$122$	−3.31616	+	2.78258i	−0.300231	+	0.251923i
$123$	0.911532	−	4.36924i	0.0821901	−	0.393961i
$124$	−10.0533	+	3.65911i	−0.902815	+	0.328598i
$125$	−3.50040	−	6.06287i	−0.313085	−	0.542279i
$126$	−5.51887	−	11.1024i	−0.491660	−	0.989083i
$127$	−4.05136	+	7.01715i	−0.359500	+	0.622672i	−0.987877	−	0.155237i	$-0.950386\pi$
$127$	−4.05136	+	7.01715i	−0.359500	+	0.622672i	0.628378	+	0.777908i	$0.283719\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−2.51217	+	4.05419i	−0.221184	+	0.356951i
$130$	0.602188	+	0.219178i	0.0528153	+	0.0192232i
$131$	−2.76007	−	15.6532i	−0.241149	−	1.36762i	−0.829269	−	0.558849i	$-0.811243\pi$
$131$	−2.76007	−	15.6532i	−0.241149	−	1.36762i	0.588120	−	0.808773i	$-0.299868\pi$
$132$	7.31213	+	2.92232i	0.636439	+	0.254355i
$133$	4.92595	+	4.13336i	0.427134	+	0.358408i
$134$	13.1120			1.13271
$135$	0.311829	+	3.83624i	0.0268379	+	0.330171i
$136$	−4.35950			−0.373824
$137$	−9.46551	−	7.94250i	−0.808693	−	0.678574i	0.141603	−	0.989924i	$-0.454775\pi$
$137$	−9.46551	−	7.94250i	−0.808693	−	0.678574i	−0.950295	+	0.311350i	$0.899219\pi$
$138$	0.867382	+	6.00756i	0.0738365	+	0.511398i
$139$	−0.761169	−	4.31680i	−0.0645615	−	0.366146i	−0.999922	−	0.0124519i	$-0.996036\pi$
$139$	−0.761169	−	4.31680i	−0.0645615	−	0.366146i	0.935361	−	0.353695i	$-0.115075\pi$
$140$	2.87665	+	1.04701i	0.243121	+	0.0884888i
$141$	7.94045	+	14.7992i	0.668707	+	1.24631i
$142$	−0.882872	+	5.00702i	−0.0740890	+	0.420179i
$143$	−1.96663	+	3.40630i	−0.164458	+	0.284849i
$144$	0.336039	+	2.98112i	0.0280033	+	0.248427i
$145$	−1.21021	−	2.09615i	−0.100503	−	0.174076i
$146$	0.538700	−	0.196071i	0.0445832	−	0.0162269i
$147$	16.5845	−	5.45773i	1.36786	−	0.450146i
$148$	−1.34953	+	1.13239i	−0.110931	+	0.0930818i
$149$	5.23476	−	4.39248i	0.428848	−	0.359846i	−0.402669	−	0.915346i	$-0.631917\pi$
$149$	5.23476	−	4.39248i	0.428848	−	0.359846i	0.831517	+	0.555499i	$0.187473\pi$
$150$	5.74898	+	5.13735i	0.469402	+	0.419463i
$151$	4.89254	−	1.78074i	0.398149	−	0.144915i	−0.135182	−	0.990821i	$-0.543162\pi$
$151$	4.89254	−	1.78074i	0.398149	−	0.144915i	0.533332	+	0.845906i	$0.320940\pi$
$152$	−0.777964	−	1.34747i	−0.0631012	−	0.109295i
$153$	12.5444	−	3.69947i	1.01415	−	0.299085i
$154$	−9.39457	+	16.2719i	−0.757036	+	1.31122i
$155$	−1.37609	+	7.80422i	−0.110531	+	0.626850i
$156$	−1.49776	−	0.0466584i	−0.119917	−	0.00373567i
$157$	−3.73260	−	1.35856i	−0.297894	−	0.108424i	0.188749	−	0.982025i	$-0.439557\pi$
$157$	−3.73260	−	1.35856i	−0.297894	−	0.108424i	−0.486643	+	0.873601i	$0.661779\pi$
$158$	1.17380	+	6.65696i	0.0933826	+	0.529599i
$159$	−5.45482	+	4.29494i	−0.432595	+	0.340611i
$160$	−0.567425	−	0.476126i	−0.0448589	−	0.0376411i
$161$	−14.4832			−1.14144
$162$	−3.49672	−	8.29294i	−0.274729	−	0.651555i
$163$	2.34707			0.183837			0.0919184	−	0.995767i	$-0.470700\pi$
$163$	2.34707			0.183837			0.0919184	+	0.995767i	$0.470700\pi$
$164$	−1.97401	−	1.65639i	−0.154145	−	0.129343i
$165$	4.58274	−	3.60829i	0.356766	−	0.280905i
$166$	1.60163	+	9.08331i	0.124311	+	0.705002i
$167$	0.989141	+	0.360018i	0.0765420	+	0.0278590i	0.380007	−	0.924983i	$-0.375921\pi$
$167$	0.989141	+	0.360018i	0.0765420	+	0.0278590i	−0.303465	+	0.952842i	$0.598144\pi$
$168$	−7.15478	−	0.222887i	−0.552003	−	0.0171961i
$169$	−2.12745	+	12.0654i	−0.163650	+	0.928107i
$170$	−1.61459	+	2.79654i	−0.123833	+	0.214485i
$171$	3.38204	+	3.21714i	0.258631	+	0.246021i
$172$	1.37682	+	2.38471i	0.104981	+	0.181833i
$173$	−6.42081	+	2.33699i	−0.488166	+	0.177678i	−0.574364	−	0.818600i	$-0.694750\pi$
$173$	−6.42081	+	2.33699i	−0.488166	+	0.177678i	0.0861981	+	0.996278i	$0.472528\pi$
$174$	4.22025	+	3.77126i	0.319937	+	0.285899i
$175$	−14.0926	+	11.8251i	−1.06530	+	0.893892i
$176$	3.48269	−	2.92232i	0.262517	−	0.220278i
$177$	2.35517	−	0.775057i	0.177026	−	0.0582568i
$178$	11.6512	−	4.24069i	0.873294	−	0.317853i
$179$	1.09877	+	1.90312i	0.0821258	+	0.142246i	0.904163	−	0.427188i	$-0.140496\pi$
$179$	1.09877	+	1.90312i	0.0821258	+	0.142246i	−0.822037	+	0.569434i	$0.807162\pi$
$180$	2.03679	+	0.888525i	0.151814	+	0.0662267i
$181$	7.86998	−	13.6312i	0.584971	−	1.01320i	−0.409908	−	0.912127i	$-0.634439\pi$
$181$	7.86998	−	13.6312i	0.584971	−	1.01320i	0.994879	−	0.101073i	$-0.0322275\pi$
$182$	0.620881	−	3.52119i	0.0460228	−	0.261008i
$183$	−3.54496	−	6.60698i	−0.262051	−	0.488402i
$184$	3.29309	+	1.19859i	0.242770	+	0.0883610i
$185$	0.226596	+	1.28509i	0.0166597	+	0.0944818i
$186$	−2.64799	−	18.3402i	−0.194160	−	1.34477i
$187$	−15.1828	−	12.7399i	−1.11027	−	0.931631i
$188$	9.69649			0.707189
$189$	20.7769	−	5.43020i	1.51129	−	0.394989i
$190$	−1.15251			−0.0836117
$191$	6.00686	+	5.04036i	0.434641	+	0.364707i	0.833700	−	0.552218i	$-0.186218\pi$
$191$	6.00686	+	5.04036i	0.434641	+	0.364707i	−0.399058	+	0.916926i	$0.630663\pi$
$192$	1.60836	+	0.642788i	0.116073	+	0.0463892i
$193$	−2.87224	−	16.2893i	−0.206748	−	1.17253i	−0.894665	−	0.446738i	$-0.852586\pi$
$193$	−2.87224	−	16.2893i	−0.206748	−	1.17253i	0.687916	−	0.725790i	$-0.258526\pi$
$194$	−5.40770	−	1.96824i	−0.388251	−	0.141312i
$195$	−0.584641	+	0.943505i	−0.0418670	+	0.0675658i
$196$	1.75041	−	9.92706i	0.125029	−	0.709075i
$197$	5.68810	−	9.85208i	0.405260	−	0.701931i	−0.589091	−	0.808066i	$-0.700514\pi$
$197$	5.68810	−	9.85208i	0.405260	−	0.701931i	0.994352	+	0.106135i	$0.0338476\pi$
$198$	−7.54147	+	11.3643i	−0.535949	+	0.807627i
$199$	−0.936258	−	1.62165i	−0.0663696	−	0.114955i	0.830931	−	0.556375i	$-0.187808\pi$
$199$	−0.936258	−	1.62165i	−0.0663696	−	0.114955i	−0.897301	+	0.441420i	$0.854475\pi$
$200$	4.18288	−	1.52245i	0.295775	−	0.107653i
$201$	−4.63816	+	22.2320i	−0.327151	+	1.56813i
$202$	−8.45678	+	7.09608i	−0.595017	+	0.499279i
$203$	−10.3452	+	8.68065i	−0.726090	+	0.609262i
$204$	1.54210	−	7.39173i	0.107969	−	0.517525i
$205$	−1.79364	+	0.652833i	−0.125274	+	0.0455958i
$206$	3.21073	+	5.56114i	0.223702	+	0.387463i
$207$	−10.4929	−	0.654390i	−0.729308	−	0.0454832i
$208$	−0.432575	+	0.749242i	−0.0299937	+	0.0519506i
$209$	1.22834	−	6.96629i	0.0849663	−	0.481868i
$210$	−2.79283	+	4.50712i	−0.192723	+	0.311021i
$211$	−5.14025	−	1.87090i	−0.353870	−	0.128798i	0.158968	−	0.987284i	$-0.449183\pi$
$211$	−5.14025	−	1.87090i	−0.353870	−	0.128798i	−0.512837	+	0.858486i	$0.671406\pi$
$212$	0.696050	+	3.94749i	0.0478049	+	0.271115i
$213$	−8.17732	−	3.26810i	−0.560301	−	0.223926i
$214$	−13.2467	−	11.1153i	−0.905522	−	0.759824i
$215$	2.03967			0.139104
$216$	−5.17349	−	0.484752i	−0.352012	−	0.0329832i
$217$	44.2150			3.00151
$218$	−7.61885	−	6.39297i	−0.516014	−	0.432987i
$219$	0.141891	+	0.982747i	0.00958809	+	0.0664079i
$220$	−0.584770	−	3.31639i	−0.0394252	−	0.223591i
$221$	3.54417	+	1.28997i	0.238407	+	0.0867729i
$222$	−1.44264	−	2.68875i	−0.0968239	−	0.180457i
$223$	−0.219638	+	1.24563i	−0.0147080	+	0.0834134i	−0.991278	−	0.131786i	$-0.957929\pi$
$223$	−0.219638	+	1.24563i	−0.0147080	+	0.0834134i	0.976570	+	0.215199i	$0.0690400\pi$
$224$	−2.06641	+	3.57913i	−0.138068	+	0.239140i
$225$	−10.7442	+	7.93040i	−0.716281	+	0.528693i
$226$	−1.22567	−	2.12292i	−0.0815301	−	0.141214i
$227$	−9.34189	+	3.40017i	−0.620043	+	0.225677i	−0.632892	−	0.774240i	$-0.718132\pi$
$227$	−9.34189	+	3.40017i	−0.620043	+	0.225677i	0.0128486	+	0.999917i	$0.495910\pi$
$228$	2.55989	−	0.842427i	0.169533	−	0.0557911i
$229$	−7.64692	+	6.41653i	−0.505323	+	0.424016i	−0.859480	−	0.511170i	$-0.829212\pi$
$229$	−7.64692	+	6.41653i	−0.505323	+	0.424016i	0.354157	+	0.935186i	$0.384768\pi$
$230$	1.98850	−	1.66855i	0.131118	−	0.110021i
$231$	−24.2665	−	21.6848i	−1.59662	−	1.42676i
$232$	3.07060	−	1.11761i	0.201595	−	0.0733746i
$233$	13.5765	+	23.5152i	0.889428	+	1.54053i	0.840553	+	0.541729i	$0.182230\pi$
$233$	13.5765	+	23.5152i	0.889428	+	1.54053i	0.0488748	+	0.998805i	$0.484436\pi$
$234$	0.608918	−	2.52301i	0.0398062	−	0.164934i
$235$	3.59119	−	6.22013i	0.234264	−	0.405757i
$236$	0.248577	−	1.40975i	0.0161810	−	0.0917669i
$237$	−11.7024	−	0.364555i	−0.760152	−	0.0236804i
$238$	16.9305	+	6.16219i	1.09744	+	0.399435i
$239$	−3.39241	−	19.2393i	−0.219437	−	1.24449i	−0.873039	−	0.487651i	$-0.837854\pi$
$239$	−3.39241	−	19.2393i	−0.219437	−	1.24449i	0.653602	−	0.756839i	$-0.273257\pi$
$240$	1.00801	−	0.793673i	0.0650668	−	0.0512313i
$241$	12.4216	+	10.4229i	0.800144	+	0.671400i	0.948234	−	0.317573i	$-0.102868\pi$
$241$	12.4216	+	10.4229i	0.800144	+	0.671400i	−0.148090	+	0.988974i	$0.547312\pi$
$242$	9.66906			0.621551
$243$	15.2980	−	2.99536i	0.981365	−	0.192153i
$244$	−4.32893			−0.277132
$245$	−5.71975	−	4.79944i	−0.365422	−	0.306625i
$246$	3.50676	−	2.76111i	0.223583	−	0.176042i
$247$	0.233750	+	1.32566i	0.0148731	+	0.0843498i
$248$	−10.0533	−	3.65911i	−0.638386	−	0.232354i
$249$	−15.9677	−	0.497429i	−1.01191	−	0.0315233i
$250$	1.21568	−	6.89444i	0.0768861	−	0.436043i
$251$	−11.7303	+	20.3174i	−0.740408	+	1.28242i	0.211902	+	0.977291i	$0.432034\pi$
$251$	−11.7303	+	20.3174i	−0.740408	+	1.28242i	−0.952310	+	0.305133i	$0.901299\pi$
$252$	2.90880	−	12.0524i	0.183237	−	0.759231i
$253$	7.96615	+	13.7978i	0.500827	+	0.867458i
$254$	−7.61406	+	2.77129i	−0.477749	+	0.173886i
$255$	−4.17053	−	3.72683i	−0.261169	−	0.233383i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	16.8456	−	14.1352i	1.05080	−	0.881728i	0.0576244	−	0.998338i	$-0.481647\pi$
$257$	16.8456	−	14.1352i	1.05080	−	0.881728i	0.993178	+	0.116611i	$0.0372030\pi$
$258$	−4.53041	+	1.49090i	−0.282051	+	0.0928193i
$259$	6.84164	−	2.49015i	0.425119	−	0.154731i
$260$	0.320417	+	0.554979i	0.0198714	+	0.0344183i
$261$	−7.88719	+	5.82161i	−0.488205	+	0.360349i
$262$	7.94732	−	13.7652i	0.490987	−	0.850414i
$263$	−4.07773	+	23.1260i	−0.251444	+	1.42601i	0.553595	+	0.832786i	$0.313255\pi$
$263$	−4.07773	+	23.1260i	−0.251444	+	1.42601i	−0.805039	+	0.593222i	$0.797856\pi$
$264$	3.72298	+	6.93877i	0.229134	+	0.427052i
$265$	2.79004	+	1.01549i	0.171391	+	0.0623811i
$266$	1.11662	+	6.33268i	0.0684645	+	0.388281i
$267$	3.06886	+	21.2552i	0.187811	+	1.30080i
$268$	10.0444	+	8.42825i	0.613559	+	0.514837i
$269$	18.3001			1.11578			0.557888	−	0.829916i	$-0.311612\pi$
$269$	18.3001			1.11578			0.557888	+	0.829916i	$0.311612\pi$
$270$	−2.22702	+	3.13917i	−0.135532	+	0.191044i
$271$	−16.4825			−1.00124			−0.500620	−	0.865667i	$-0.666895\pi$
$271$	−16.4825			−1.00124			−0.500620	+	0.865667i	$0.666895\pi$
$272$	−3.33957	−	2.80223i	−0.202491	−	0.169910i
$273$	5.75071	+	2.29829i	0.348049	+	0.139099i
$274$	−2.14566	−	12.1686i	−0.129624	−	0.735133i
$275$	19.0167	+	6.92153i	1.14675	+	0.417384i
$276$	−3.19713	+	5.15960i	−0.192445	+	0.310572i
$277$	1.95736	−	11.1008i	0.117606	−	0.666980i	−0.867820	−	0.496878i	$-0.834479\pi$
$277$	1.95736	−	11.1008i	0.117606	−	0.666980i	0.985427	−	0.170101i	$-0.0544094\pi$
$278$	2.19170	−	3.79613i	0.131449	−	0.227677i
$279$	32.0333	+	1.99776i	1.91778	+	0.119602i
$280$	1.53063	+	2.65113i	0.0914728	+	0.158435i
$281$	0.681601	−	0.248083i	0.0406609	−	0.0147994i	−0.321610	−	0.946872i	$-0.604224\pi$
$281$	0.681601	−	0.248083i	0.0406609	−	0.0147994i	0.362271	+	0.932073i	$0.382002\pi$
$282$	−3.42997	+	16.4408i	−0.204252	+	0.979037i
$283$	−16.9589	+	14.2302i	−1.00810	+	0.845897i	−0.988086	−	0.153903i	$-0.950816\pi$
$283$	−16.9589	+	14.2302i	−1.00810	+	0.845897i	−0.0200144	+	0.999800i	$0.506371\pi$
$284$	−3.89477	+	3.26810i	−0.231112	+	0.193926i
$285$	0.407680	−	1.95413i	0.0241489	−	0.115753i
$286$	−3.69605	+	1.34525i	−0.218552	+	0.0795464i
$287$	5.32491	+	9.22302i	0.314320	+	0.544418i
$288$	−1.65881	+	2.49967i	−0.0977461	+	0.147295i
$289$	−1.00263	+	1.73660i	−0.0589780	+	0.102153i
$290$	0.420303	−	2.38366i	0.0246811	−	0.139973i
$291$	5.25013	−	8.47277i	0.307768	−	0.496683i
$292$	0.538700	+	0.196071i	0.0315251	+	0.0114742i
$293$	−1.13889	−	6.45895i	−0.0665344	−	0.377336i	−0.999834	−	0.0182360i	$-0.994195\pi$
$293$	−1.13889	−	6.45895i	−0.0665344	−	0.377336i	0.933299	−	0.359100i	$-0.116916\pi$
$294$	16.2126	+	6.47943i	0.945538	+	0.377888i
$295$	−0.812267	−	0.681573i	−0.0472920	−	0.0396827i
$296$	−1.76168			−0.102396
$297$	−16.6010	−	16.8068i	−0.963290	−	0.975232i
$298$	6.83349			0.395854
$299$	−2.32254	−	1.94884i	−0.134316	−	0.112705i
$300$	1.10175	+	7.63081i	0.0636095	+	0.440565i
$301$	−1.97616	−	11.2074i	−0.113904	−	0.645982i
$302$	4.89254	+	1.78074i	0.281534	+	0.102470i
$303$	−9.04028	−	16.8490i	−0.519351	−	0.967948i
$304$	0.270184	−	1.53229i	0.0154961	−	0.0878829i
$305$	−1.60326	+	2.77694i	−0.0918027	+	0.159007i
$306$	11.9875	+	5.22940i	0.685281	+	0.298945i
$307$	−3.98740	−	6.90639i	−0.227573	−	0.394168i	0.729515	−	0.683965i	$-0.239746\pi$
$307$	−3.98740	−	6.90639i	−0.227573	−	0.394168i	−0.957088	+	0.289796i	$0.906412\pi$
$308$	−17.6560	+	6.42626i	−1.00604	+	0.366170i
$309$	−10.5649	+	3.47677i	−0.601016	+	0.197787i
$310$	−6.07060	+	5.09384i	−0.344787	+	0.289311i
$311$	10.8380	−	9.09419i	0.614569	−	0.515684i	−0.281522	−	0.959555i	$-0.590839\pi$
$311$	10.8380	−	9.09419i	0.614569	−	0.515684i	0.896091	+	0.443870i	$0.146395\pi$
$312$	−1.11736	−	0.998483i	−0.0632579	−	0.0565279i
$313$	−22.5917	+	8.22270i	−1.27696	+	0.464774i	−0.889425	−	0.457082i	$-0.848895\pi$
$313$	−22.5917	+	8.22270i	−1.27696	+	0.464774i	−0.387532	+	0.921856i	$0.626672\pi$
$314$	−1.98607	−	3.43998i	−0.112081	−	0.194129i
$315$	−6.65411	−	6.32968i	−0.374917	−	0.356637i
$316$	−3.37983	+	5.85403i	−0.190130	+	0.329315i
$317$	3.15913	−	17.9163i	0.177435	−	1.00628i	−0.757862	−	0.652415i	$-0.773756\pi$
$317$	3.15913	−	17.9163i	0.177435	−	1.00628i	0.935296	−	0.353866i	$-0.115133\pi$
$318$	−6.93937	−	0.216177i	−0.389140	−	0.0121226i
$319$	13.9600	+	5.08101i	0.781608	+	0.284482i
$320$	−0.128625	−	0.729467i	−0.00719034	−	0.0407785i
$321$	23.5322	−	18.5285i	1.31344	−	1.03416i
$322$	−11.0948	−	9.30962i	−0.618287	−	0.518805i
$323$	−6.78307			−0.377420
$324$	2.65195	−	8.60041i	0.147331	−	0.477801i
$325$	−3.85107			−0.213619
$326$	1.79796	+	1.50867i	0.0995798	+	0.0835574i
$327$	13.5346	−	10.6567i	0.748466	−	0.589317i
$328$	−0.447473	−	2.53774i	−0.0247075	−	0.140123i
$329$	−37.6571	−	13.7061i	−2.07610	−	0.755640i
$330$	5.82995	+	0.181616i	0.320928	+	0.00999761i
$331$	3.11884	−	17.6878i	0.171427	−	0.972212i	−0.770760	−	0.637125i	$-0.780123\pi$
$331$	3.11884	−	17.6878i	0.171427	−	0.972212i	0.942187	−	0.335086i	$-0.108766\pi$
$332$	−4.61172	+	7.98773i	−0.253101	+	0.438384i
$333$	5.06921	−	1.49497i	0.277791	−	0.0819236i
$334$	0.526311	+	0.911597i	0.0287985	+	0.0498804i
$335$	9.12662	−	3.32182i	0.498640	−	0.181490i
$336$	−5.33761	−	4.76975i	−0.291191	−	0.260211i
$337$	−17.9989	+	15.1029i	−0.980462	+	0.822705i	−0.984159	−	0.177288i	$-0.943268\pi$
$337$	−17.9989	+	15.1029i	−0.980462	+	0.822705i	0.00369714	+	0.999993i	$0.498823\pi$
$338$	−9.38520	+	7.87512i	−0.510488	+	0.428350i
$339$	4.03306	−	1.32723i	0.219046	−	0.0720850i
$340$	−3.03443	+	1.10444i	−0.164565	+	0.0598968i
$341$	−24.3195	−	42.1225i	−1.31697	−	2.28106i
$342$	0.522853	+	4.63841i	0.0282727	+	0.250816i
$343$	−6.36495	+	11.0244i	−0.343675	+	0.595263i
$344$	−0.478163	+	2.71180i	−0.0257808	+	0.146210i
$345$	2.12571	+	3.96182i	0.114444	+	0.213297i
$346$	−6.42081	−	2.33699i	−0.345185	−	0.125637i
$347$	1.44691	+	8.20582i	0.0776741	+	0.440512i	0.998698	+	0.0510063i	$0.0162429\pi$
$347$	1.44691	+	8.20582i	0.0776741	+	0.440512i	−0.921024	+	0.389505i	$0.872646\pi$
$348$	0.808781	+	5.60168i	0.0433552	+	0.300282i
$349$	−4.05619	−	3.40354i	−0.217123	−	0.182188i	0.527739	−	0.849407i	$-0.323040\pi$
$349$	−4.05619	−	3.40354i	−0.217123	−	0.182188i	−0.744861	+	0.667219i	$0.767484\pi$
$350$	−18.3966			−0.983337
$351$	4.06248	+	1.92492i	0.216839	+	0.102745i
$352$	4.54632			0.242320
$353$	26.4759	+	22.2159i	1.40917	+	1.18243i	0.956852	+	0.290577i	$0.0938473\pi$
$353$	26.4759	+	22.2159i	1.40917	+	1.18243i	0.452318	+	0.891857i	$0.350597\pi$
$354$	2.30237	+	0.920149i	0.122369	+	0.0489054i
$355$	0.653961	+	3.70880i	0.0347087	+	0.196843i
$356$	11.6512	+	4.24069i	0.617512	+	0.224756i
$357$	−16.4371	+	26.5266i	−0.869946	+	1.40394i
$358$	−0.381598	+	2.16415i	−0.0201681	+	0.114379i
$359$	12.8489	−	22.2549i	0.678138	−	1.17457i	−0.297403	−	0.954752i	$-0.596120\pi$
$359$	12.8489	−	22.2549i	0.678138	−	1.17457i	0.975541	−	0.219818i	$-0.0705462\pi$
$360$	0.989141	+	1.98987i	0.0521323	+	0.104876i
$361$	8.28954	+	14.3579i	0.436292	+	0.755680i
$362$	14.7907	−	5.38339i	0.777384	−	0.282944i
$363$	−3.42027	+	16.3943i	−0.179518	+	0.860479i
$364$	2.73900	−	2.29829i	0.143563	−	0.120463i
$365$	0.325289	−	0.272950i	0.0170264	−	0.0142869i
$366$	1.53129	−	7.33990i	0.0800417	−	0.383663i
$367$	−10.6739	+	3.88499i	−0.557174	+	0.202795i	−0.605231	−	0.796050i	$-0.706919\pi$
$367$	−10.6739	+	3.88499i	−0.557174	+	0.202795i	0.0480573	+	0.998845i	$0.484697\pi$
$368$	1.75222	+	3.03493i	0.0913406	+	0.158207i
$369$	3.44112	+	6.92257i	0.179138	+	0.360375i
$370$	−0.652458	+	1.13009i	−0.0339197	+	0.0587506i
$371$	2.87665	−	16.3143i	0.149348	−	0.846995i
$372$	9.76038	−	15.7515i	0.506052	−	0.816678i
$373$	26.9731	+	9.81739i	1.39661	+	0.508325i	0.927171	−	0.374639i	$-0.122233\pi$
$373$	26.9731	+	9.81739i	1.39661	+	0.508325i	0.469441	+	0.882964i	$0.344455\pi$
$374$	−3.44166	−	19.5186i	−0.177964	−	1.00928i
$375$	11.2598	+	4.50002i	0.581454	+	0.232380i
$376$	7.42794	+	6.23278i	0.383067	+	0.321431i
$377$	−2.82703			−0.145599
$378$	19.4065	+	9.19534i	0.998161	+	0.472957i
$379$	−23.0493			−1.18396			−0.591981	−	0.805952i	$-0.701654\pi$
$379$	−23.0493			−1.18396			−0.591981	+	0.805952i	$0.701654\pi$
$380$	−0.882872	−	0.740818i	−0.0452904	−	0.0380031i
$381$	−2.00550	−	13.8903i	−0.102745	−	0.711620i
$382$	1.36165	+	7.72227i	0.0696678	+	0.395106i
$383$	23.1212	+	8.41541i	1.18144	+	0.430007i	0.856709	−	0.515800i	$-0.172505\pi$
$383$	23.1212	+	8.41541i	1.18144	+	0.430007i	0.324727	+	0.945808i	$0.394728\pi$
$384$	0.818900	+	1.52624i	0.0417893	+	0.0778855i
$385$	−2.41675	+	13.7061i	−0.123169	+	0.698525i
$386$	8.27028	−	14.3246i	0.420946	−	0.729101i
$387$	−0.925328	−	8.20890i	−0.0470371	−	0.417282i
$388$	−2.87738	−	4.98377i	−0.146077	−	0.253012i
$389$	−34.8878	+	12.6981i	−1.76888	+	0.643820i	−0.768891	+	0.639380i	$0.779191\pi$
$389$	−34.8878	+	12.6981i	−1.76888	+	0.643820i	−0.999990	+	0.00444021i	$0.998587\pi$
$390$	−1.05433	+	0.346967i	−0.0533883	+	0.0175694i
$391$	11.7033	−	9.82024i	0.591862	−	0.496631i
$392$	7.72188	−	6.47943i	0.390014	−	0.327260i
$393$	20.5282	+	18.3442i	1.03551	+	0.925344i
$394$	10.6901	−	3.89089i	0.538561	−	0.196020i
$395$	2.50351	+	4.33620i	0.125965	+	0.218178i
$396$	−13.0819	+	3.85801i	−0.657392	+	0.193872i
$397$	−3.19629	+	5.53614i	−0.160417	+	0.277851i	−0.935018	−	0.354599i	$-0.884617\pi$
$397$	−3.19629	+	5.53614i	−0.160417	+	0.277851i	0.774601	+	0.632450i	$0.217951\pi$
$398$	0.325159	−	1.84407i	0.0162987	−	0.0924348i
$399$	−11.1323	−	0.346796i	−0.557313	−	0.0173615i
$400$	4.18288	+	1.52245i	0.209144	+	0.0761223i
$401$	5.67599	+	32.1901i	0.283445	+	1.60750i	0.710787	+	0.703407i	$0.248339\pi$
$401$	5.67599	+	32.1901i	0.283445	+	1.60750i	−0.427342	+	0.904090i	$0.640550\pi$
$402$	−17.8435	+	14.0494i	−0.889953	+	0.700719i
$403$	7.09038	+	5.94953i	0.353197	+	0.296367i
$404$	−11.0395			−0.549238
$405$	−4.53484	−	4.88643i	−0.225338	−	0.242809i
$406$	−13.5047			−0.670226
$407$	−6.13539	−	5.14821i	−0.304120	−	0.255187i
$408$	5.93263	−	4.67115i	0.293709	−	0.231256i
$409$	−3.79522	−	21.5238i	−0.187662	−	1.06428i	−0.922488	−	0.386027i	$-0.873847\pi$
$409$	−3.79522	−	21.5238i	−0.187662	−	1.06428i	0.734826	−	0.678256i	$-0.237264\pi$
$410$	−1.79364	−	0.652833i	−0.0885818	−	0.0322411i
$411$	21.3914	+	0.666390i	1.05516	+	0.0328706i
$412$	−1.11507	+	6.32390i	−0.0549357	+	0.311556i
$413$	−2.95806	+	5.12351i	−0.145557	+	0.252112i
$414$	−7.61741	−	7.24601i	−0.374375	−	0.356122i
$415$	3.41599	+	5.91668i	0.167685	+	0.290438i
$416$	−0.812975	+	0.295899i	−0.0398594	+	0.0145076i
$417$	5.66124	+	5.05894i	0.277232	+	0.247737i
$418$	5.41881	−	4.54692i	0.265043	−	0.222397i
$419$	−20.0021	+	16.7838i	−0.977168	+	0.819941i	−0.983660	−	0.180037i	$-0.942378\pi$
$419$	−20.0021	+	16.7838i	−0.977168	+	0.819941i	0.00649160	+	0.999979i	$0.497934\pi$
$420$	−5.03655	+	1.65746i	−0.245758	+	0.0808758i
$421$	35.2362	−	12.8249i	1.71731	−	0.625049i	0.719707	−	0.694278i	$-0.244276\pi$
$421$	35.2362	−	12.8249i	1.71731	−	0.625049i	0.997601	+	0.0692288i	$0.0220539\pi$
$422$	−2.73507	−	4.73728i	−0.133141	−	0.230607i
$423$	−26.6629	−	11.6313i	−1.29639	−	0.565535i
$424$	−2.00419	+	3.47137i	−0.0973323	+	0.168584i
$425$	3.36975	−	19.1108i	0.163457	−	0.927009i
$426$	−4.16350	−	7.75979i	−0.201722	−	0.375963i
$427$	16.8118	+	6.11898i	0.813578	+	0.296118i
$428$	−3.00277	−	17.0296i	−0.145144	−	0.823155i
$429$	−0.973519	−	6.74268i	−0.0470020	−	0.325540i
$430$	1.56248	+	1.31107i	0.0753494	+	0.0632256i
$431$	6.13162			0.295350			0.147675	−	0.989036i	$-0.452821\pi$
$431$	6.13162			0.295350			0.147675	+	0.989036i	$0.452821\pi$
$432$	−3.65153	−	3.69680i	−0.175684	−	0.177862i
$433$	−20.9401			−1.00632			−0.503158	−	0.864195i	$-0.667829\pi$
$433$	−20.9401			−1.00632			−0.503158	+	0.864195i	$0.667829\pi$
$434$	33.8707	+	28.4209i	1.62585	+	1.36425i
$435$	3.89292	+	1.55582i	0.186651	+	0.0745960i
$436$	−1.72705	−	9.79461i	−0.0827109	−	0.469077i
$437$	5.12381	+	1.86492i	0.245105	+	0.0892110i
$438$	−0.523003	+	0.844034i	−0.0249901	+	0.0403295i
$439$	−4.98629	+	28.2787i	−0.237983	+	1.34967i	0.598258	+	0.801304i	$0.295860\pi$
$439$	−4.98629	+	28.2787i	−0.237983	+	1.34967i	−0.836240	+	0.548363i	$0.815251\pi$
$440$	1.68378	−	2.91639i	0.0802709	−	0.139033i
$441$	−16.7211	+	25.1972i	−0.796243	+	1.19987i
$442$	1.88581	+	3.26632i	0.0896989	+	0.155363i
$443$	14.2882	−	5.20050i	0.678855	−	0.247083i	0.0204992	−	0.999790i	$-0.493474\pi$
$443$	14.2882	−	5.20050i	0.678855	−	0.247083i	0.658356	+	0.752707i	$0.271252\pi$
$444$	0.623166	−	2.98701i	0.0295742	−	0.141757i
$445$	7.03547	−	5.90346i	0.333513	−	0.279851i
$446$	−0.968926	+	0.813026i	−0.0458800	+	0.0384979i
$447$	−2.41723	+	11.5865i	−0.114331	+	0.548022i
$448$	−3.88358	+	1.41351i	−0.183482	+	0.0667820i
$449$	6.21048	+	10.7569i	0.293091	+	0.507648i	0.974539	−	0.224218i	$-0.0719828\pi$
$449$	6.21048	+	10.7569i	0.293091	+	0.507648i	−0.681448	+	0.731866i	$0.738649\pi$
$450$	−13.3281	−	0.831206i	−0.628293	−	0.0391834i
$451$	5.85769	−	10.1458i	0.275828	−	0.477748i
$452$	0.425670	−	2.41409i	0.0200218	−	0.113549i
$453$	−4.74998	+	7.66562i	−0.223173	+	0.360162i
$454$	−9.34189	−	3.40017i	−0.438437	−	0.159578i
$455$	−0.459899	−	2.60822i	−0.0215604	−	0.122275i
$456$	2.50249	+	1.00013i	0.117190	+	0.0468354i
$457$	−8.30728	−	6.97064i	−0.388598	−	0.326073i	0.427468	−	0.904030i	$-0.359405\pi$
$457$	−8.30728	−	6.97064i	−0.388598	−	0.326073i	−0.816067	+	0.577957i	$0.803850\pi$
$458$	−9.98234			−0.466444
$459$	−13.1071	+	18.4756i	−0.611786	+	0.862365i
$460$	2.59581			0.121030
$461$	−6.28283	−	5.27192i	−0.292621	−	0.245538i	0.484644	−	0.874711i	$-0.338949\pi$
$461$	−6.28283	−	5.27192i	−0.292621	−	0.245538i	−0.777265	+	0.629173i	$0.783394\pi$
$462$	−4.65050	−	32.2097i	−0.216361	−	1.49853i
$463$	−5.84350	−	33.1401i	−0.271571	−	1.54015i	−0.749649	−	0.661836i	$-0.769778\pi$
$463$	−5.84350	−	33.1401i	−0.271571	−	1.54015i	0.478078	−	0.878317i	$-0.341333\pi$
$464$	3.07060	+	1.11761i	0.142549	+	0.0518837i
$465$	−6.48946	−	12.0948i	−0.300942	−	0.560885i
$466$	−4.71508	+	26.7405i	−0.218422	+	1.23873i
$467$	−5.43426	+	9.41241i	−0.251467	+	0.435554i	−0.963930	−	0.266156i	$-0.914246\pi$
$467$	−5.43426	+	9.41241i	−0.251467	+	0.435554i	0.712463	+	0.701710i	$0.247580\pi$
$468$	2.08822	−	1.54133i	0.0965280	−	0.0712482i
$469$	−27.0948	−	46.9296i	−1.25112	−	2.16701i
$470$	6.74924	−	2.45652i	0.311319	−	0.113311i
$471$	6.53519	−	2.15064i	0.301125	−	0.0990964i
$472$	1.09659	−	0.920149i	0.0504747	−	0.0423533i
$473$	−9.59003	+	8.04699i	−0.440950	+	0.370001i
$474$	−8.73022	−	7.80142i	−0.400992	−	0.358331i
$475$	6.50827	−	2.36882i	0.298620	−	0.108689i
$476$	9.00852	+	15.6032i	0.412905	+	0.715172i
$477$	2.82122	−	11.6895i	0.129175	−	0.535227i
$478$	9.76807	−	16.9188i	0.446781	−	0.773847i
$479$	−3.26943	+	18.5418i	−0.149384	+	0.847198i	0.814358	+	0.580363i	$0.197089\pi$
$479$	−3.26943	+	18.5418i	−0.149384	+	0.847198i	−0.963742	+	0.266836i	$0.914022\pi$
$480$	1.28234	+	0.0399478i	0.0585307	+	0.00182336i
$481$	1.43221	+	0.521280i	0.0653030	+	0.0237683i
$482$	2.81574	+	15.9689i	0.128254	+	0.727362i
$483$	19.7095	−	15.5186i	0.896812	−	0.706119i
$484$	7.40693	+	6.21515i	0.336679	+	0.282507i
$485$	−4.26267			−0.193558
$486$	13.6443	+	7.53876i	0.618918	+	0.341965i
$487$	32.9521			1.49320			0.746601	−	0.665272i	$-0.231685\pi$
$487$	32.9521			1.49320			0.746601	+	0.665272i	$0.231685\pi$
$488$	−3.31616	−	2.78258i	−0.150115	−	0.125962i
$489$	−3.19401	+	2.51486i	−0.144438	+	0.113726i
$490$	−1.29656	−	7.35317i	−0.0585727	−	0.332183i
$491$	−32.5492	−	11.8469i	−1.46892	−	0.534645i	−0.521116	−	0.853486i	$-0.674484\pi$
$491$	−32.5492	−	11.8469i	−1.46892	−	0.534645i	−0.947808	+	0.318841i	$0.896706\pi$
$492$	4.46114	+	0.138974i	0.201124	+	0.00626545i
$493$	2.47369	−	14.0290i	0.111409	−	0.631834i
$494$	−0.673056	+	1.16577i	−0.0302822	+	0.0524503i
$495$	−2.37018	+	9.82070i	−0.106532	+	0.441407i
$496$	−5.34926	−	9.26519i	−0.240189	−	0.416019i
$497$	19.7451	−	7.18664i	0.885690	−	0.322365i
$498$	−11.9122	−	10.6449i	−0.533800	−	0.477009i
$499$	18.1706	−	15.2470i	0.813428	−	0.682547i	−0.137995	−	0.990433i	$-0.544066\pi$
$499$	18.1706	−	15.2470i	0.813428	−	0.682547i	0.951423	+	0.307886i	$0.0996214\pi$
$500$	5.36292	−	4.50002i	0.239837	−	0.201247i
$501$	−1.73183	+	0.569921i	−0.0773724	+	0.0254622i
$502$	−22.0457	+	8.02398i	−0.983948	+	0.358128i
$503$	−16.0067	−	27.7243i	−0.713701	−	1.23617i	−0.963458	−	0.267858i	$-0.913684\pi$
$503$	−16.0067	−	27.7243i	−0.713701	−	1.23617i	0.249757	−	0.968309i	$-0.419649\pi$
$504$	9.97541	−	7.36294i	0.444340	−	0.327972i
$505$	−4.08861	+	7.08168i	−0.181941	+	0.315131i
$506$	−2.76661	+	15.6902i	−0.122991	+	0.697517i
$507$	−10.0328	−	18.6987i	−0.445571	−	0.830440i
$508$	−7.61406	−	2.77129i	−0.337819	−	0.122956i
$509$	6.91488	+	39.2162i	0.306497	+	1.73823i	0.616376	+	0.787452i	$0.288600\pi$
$509$	6.91488	+	39.2162i	0.306497	+	1.73823i	−0.309879	+	0.950776i	$0.600289\pi$
$510$	−0.799252	−	5.53569i	−0.0353915	−	0.245124i
$511$	−1.81494	−	1.52291i	−0.0802881	−	0.0673697i
$512$	1.00000			0.0441942
$513$	−8.04958	−	0.754239i	−0.355398	−	0.0333005i
$514$	21.9904			0.969956
$515$	3.64369	+	3.05742i	0.160560	+	0.134726i
$516$	−4.42883	−	1.77000i	−0.194968	−	0.0779199i
$517$	7.65500	+	43.4136i	0.336666	+	1.90933i
$518$	6.84164	+	2.49015i	0.300604	+	0.109411i
$519$	6.23372	−	10.0601i	0.273630	−	0.441590i
$520$	−0.111280	+	0.631099i	−0.00487994	+	0.0276755i
$521$	−1.81609	+	3.14555i	−0.0795642	+	0.137809i	−0.903062	−	0.429510i	$-0.858686\pi$
$521$	−1.81609	+	3.14555i	−0.0795642	+	0.137809i	0.823498	+	0.567319i	$0.192020\pi$
$522$	−9.78400	−	0.610178i	−0.428234	−	0.0267068i
$523$	−6.50104	−	11.2601i	−0.284270	−	0.492371i	0.688162	−	0.725558i	$-0.258418\pi$
$523$	−6.50104	−	11.2601i	−0.284270	−	0.492371i	−0.972432	+	0.233187i	$0.925085\pi$
$524$	14.9361	−	5.43628i	0.652485	−	0.237485i
$525$	6.50748	−	31.1922i	0.284010	−	1.36134i
$526$	−17.9888	+	15.0944i	−0.784349	+	0.658147i
$527$	−35.7285	+	29.9797i	−1.55636	+	1.30594i
$528$	−1.60819	+	7.70850i	−0.0699873	+	0.335469i
$529$	10.0725	−	3.66609i	0.437935	−	0.159395i
$530$	1.48455	+	2.57131i	0.0644847	+	0.111691i
$531$	−2.37458	+	3.57828i	−0.103048	+	0.155284i
$532$	−3.21518	+	5.56886i	−0.139396	+	0.241441i
$533$	−0.387131	+	2.19553i	−0.0167685	+	0.0950989i
$534$	−11.3117	+	18.2550i	−0.489505	+	0.789973i
$535$	−12.0363	−	4.38085i	−0.520374	−	0.189401i
$536$	2.27688	+	12.9128i	0.0983462	+	0.557749i
$537$	−3.53443	−	1.41255i	−0.152522	−	0.0609560i
$538$	14.0187	+	11.7631i	0.604388	+	0.507142i
$539$	45.8278			1.97394
$540$	−3.72381	+	0.973248i	−0.160247	+	0.0418819i
$541$	−31.1320			−1.33847			−0.669235	−	0.743051i	$-0.733378\pi$
$541$	−31.1320			−1.33847			−0.669235	+	0.743051i	$0.733378\pi$
$542$	−12.6263	−	10.5947i	−0.542347	−	0.455083i
$543$	3.89580	+	26.9826i	0.167185	+	1.15794i
$544$	−0.757019	−	4.29327i	−0.0324569	−	0.184072i
$545$	−6.92270	−	2.51966i	−0.296536	−	0.107930i
$546$	2.92799	+	5.45708i	0.125306	+	0.233541i
$547$	3.35773	−	19.0426i	0.143566	−	0.814204i	−0.824941	−	0.565219i	$-0.808792\pi$
$547$	3.35773	−	19.0426i	0.143566	−	0.814204i	0.968507	−	0.248985i	$-0.0800970\pi$
$548$	6.17817	−	10.7009i	0.263918	−	0.457120i
$549$	11.9035	+	5.19274i	0.508027	+	0.221621i
$550$	10.1186	+	17.5259i	0.431459	+	0.747308i
$551$	4.77764	−	1.73892i	0.203534	−	0.0740804i
$552$	−5.76568	+	1.89741i	−0.245404	+	0.0807590i
$553$	21.4005	−	17.9572i	0.910044	−	0.763617i
$554$	8.63485	−	7.24550i	0.366860	−	0.307832i
$555$	−1.68532	−	1.50602i	−0.0715380	−	0.0639271i
$556$	4.11905	−	1.49921i	0.174686	−	0.0635807i
$557$	0.618509	+	1.07129i	0.0262070	+	0.0453919i	0.878831	−	0.477132i	$-0.158324\pi$
$557$	0.618509	+	1.07129i	0.0262070	+	0.0453919i	−0.852624	+	0.522524i	$0.824990\pi$
$558$	23.2548	+	22.1210i	0.984455	+	0.936456i
$559$	1.19115	−	2.06314i	0.0503804	−	0.0872614i
$560$	−0.531583	+	3.01476i	−0.0224635	+	0.127397i
$561$	34.3121	+	1.06890i	1.44866	+	0.0451289i
$562$	0.681601	+	0.248083i	0.0287516	+	0.0104647i
$563$	−3.63180	−	20.5969i	−0.153062	−	0.868057i	−0.960536	−	0.278155i	$-0.910277\pi$
$563$	−3.63180	−	20.5969i	−0.153062	−	0.868057i	0.807474	−	0.589903i	$-0.200834\pi$
$564$	−13.1955	+	10.3897i	−0.555630	+	0.437484i
$565$	−1.39095	−	1.16714i	−0.0585176	−	0.0491021i
$566$	−22.1382			−0.930539
$567$	−22.4558	+	29.6518i	−0.943056	+	1.24526i
$568$	−5.08426			−0.213331
$569$	−4.70347	−	3.94668i	−0.197180	−	0.165453i	0.538852	−	0.842400i	$-0.318858\pi$
$569$	−4.70347	−	3.94668i	−0.197180	−	0.165453i	−0.736032	+	0.676947i	$0.763303\pi$
$570$	1.56839	−	1.23490i	0.0656927	−	0.0517242i
$571$	2.98710	+	16.9407i	0.125006	+	0.708946i	0.981304	+	0.192464i	$0.0616478\pi$
$571$	2.98710	+	16.9407i	0.125006	+	0.708946i	−0.856298	+	0.516483i	$0.827241\pi$
$572$	−3.69605	−	1.34525i	−0.154540	−	0.0562478i
$573$	−13.5751	−	0.422895i	−0.567109	−	0.0176667i
$574$	−1.84932	+	10.4880i	−0.0771893	+	0.437762i
$575$	−7.79970	+	13.5095i	−0.325270	+	0.563384i
$576$	−2.87748	+	0.848600i	−0.119895	+	0.0353583i
$577$	7.08481	+	12.2713i	0.294945	+	0.510859i	0.974972	−	0.222328i	$-0.0713655\pi$
$577$	7.08481	+	12.2713i	0.294945	+	0.510859i	−0.680027	+	0.733187i	$0.738032\pi$
$578$	−1.88432	+	0.685836i	−0.0783773	+	0.0285270i
$579$	21.3624	+	19.0897i	0.887793	+	0.793341i
$580$	1.85416	−	1.55582i	0.0769897	−	0.0646020i
$581$	29.2007	−	24.5023i	1.21145	−	1.01653i
$582$	9.46803	−	3.11580i	0.392462	−	0.129154i
$583$	−17.1244	+	6.23278i	−0.709221	+	0.258135i
$584$	0.286636	+	0.496469i	0.0118611	+	0.0205440i
$585$	−0.215346	−	1.91040i	−0.00890345	−	0.0789855i
$586$	3.27929	−	5.67990i	0.135466	−	0.234635i
$587$	5.83795	−	33.1087i	0.240958	−	1.36654i	−0.588737	−	0.808324i	$-0.700375\pi$
$587$	5.83795	−	33.1087i	0.240958	−	1.36654i	0.829695	−	0.558217i	$-0.188514\pi$
$588$	8.25467	+	15.3848i	0.340417	+	0.634458i
$589$	−15.6422	−	5.69331i	−0.644527	−	0.234589i
$590$	−0.184126	−	1.04423i	−0.00758035	−	0.0429903i
$591$	2.81572	+	19.5019i	0.115823	+	0.802202i
$592$	−1.34953	−	1.13239i	−0.0554653	−	0.0465409i
$593$	6.82673			0.280340			0.140170	−	0.990127i	$-0.455235\pi$
$593$	6.82673			0.280340			0.140170	+	0.990127i	$0.455235\pi$
$594$	−1.91391	−	23.5457i	−0.0785288	−	0.966093i
$595$	13.3456			0.547116
$596$	5.23476	+	4.39248i	0.214424	+	0.179923i
$597$	3.01168	+	1.20363i	0.123260	+	0.0492613i
$598$	−0.526477	−	2.98580i	−0.0215293	−	0.122099i
$599$	27.5399	+	10.0237i	1.12525	+	0.409557i	0.836565	−	0.547867i	$-0.184560\pi$
$599$	27.5399	+	10.0237i	1.12525	+	0.409557i	0.288684	+	0.957424i	$0.406782\pi$
$600$	−4.06100	+	6.55373i	−0.165790	+	0.267555i
$601$	−0.803257	+	4.55550i	−0.0327655	+	0.185823i	−0.996798	−	0.0799624i	$-0.974520\pi$
$601$	−0.803257	+	4.55550i	−0.0327655	+	0.185823i	0.964032	+	0.265785i	$0.0856311\pi$
$602$	5.69013	−	9.85559i	0.231912	−	0.401684i
$603$	−17.5095	−	35.2242i	−0.713042	−	1.43444i
$604$	2.60327	+	4.50899i	0.105925	+	0.183468i
$605$	6.73014	−	2.44957i	0.273619	−	0.0995893i
$606$	3.90506	−	18.7180i	0.158632	−	0.760369i
$607$	−10.3745	+	8.70526i	−0.421089	+	0.353335i	−0.828577	−	0.559875i	$-0.810849\pi$
$607$	−10.3745	+	8.70526i	−0.421089	+	0.353335i	0.407488	+	0.913210i	$0.366405\pi$
$608$	1.19191	−	1.00013i	0.0483383	−	0.0405607i
$609$	4.77706	−	22.8978i	0.193576	−	0.927866i
$610$	−3.01315	+	1.09670i	−0.121999	+	0.0444040i
$611$	−4.19446	−	7.26502i	−0.169690	−	0.293911i
$612$	5.82158	+	11.7114i	0.235323	+	0.473405i
$613$	−14.9136	+	25.8311i	−0.602354	+	1.04331i	0.390110	+	0.920768i	$0.372437\pi$
$613$	−14.9136	+	25.8311i	−0.602354	+	1.04331i	−0.992464	+	0.122539i	$0.960896\pi$
$614$	1.38481	−	7.85365i	0.0558864	−	0.316948i
$615$	1.74138	−	2.81028i	0.0702192	−	0.113321i
$616$	−17.6560	−	6.42626i	−0.711381	−	0.258922i
$617$	−5.84851	−	33.1685i	−0.235452	−	1.33531i	−0.841660	−	0.540008i	$-0.818421\pi$
$617$	−5.84851	−	33.1685i	−0.235452	−	1.33531i	0.606208	−	0.795306i	$-0.292690\pi$
$618$	−10.3280	−	4.12763i	−0.415454	−	0.166038i
$619$	27.2839	+	22.8939i	1.09663	+	0.920182i	0.997194	−	0.0748615i	$-0.0238515\pi$
$619$	27.2839	+	22.8939i	1.09663	+	0.920182i	0.0994367	+	0.995044i	$0.468296\pi$
$620$	−7.92461			−0.318260
$621$	14.9805	−	10.3525i	0.601145	−	0.415432i
$622$	14.1480			0.567285
$623$	−39.2541	−	32.9381i	−1.57268	−	1.31964i
$624$	−0.214133	−	1.48311i	−0.00857219	−	0.0593717i
$625$	2.96435	+	16.8117i	0.118574	+	0.672467i
$626$	−22.5917	−	8.22270i	−0.902945	−	0.328645i
$627$	5.79269	+	10.7962i	0.231338	+	0.431160i
$628$	0.689756	−	3.91180i	0.0275243	−	0.156098i
$629$	−3.84003	+	6.65113i	−0.153112	+	0.265198i
$630$	−1.02871	−	9.12600i	−0.0409846	−	0.363588i
$631$	19.6546	+	34.0427i	0.782436	+	1.35522i	0.930519	+	0.366243i	$0.119356\pi$
$631$	19.6546	+	34.0427i	0.782436	+	1.35522i	−0.148083	+	0.988975i	$0.547310\pi$
$632$	−6.35200	+	2.31194i	−0.252669	+	0.0919640i
$633$	8.99976	−	2.96170i	0.357708	−	0.117717i
$634$	13.9364	−	11.6941i	0.553486	−	0.464430i
$635$	−4.59768	+	3.85791i	−0.182453	+	0.153097i
$636$	−5.17691	−	4.62614i	−0.205278	−	0.183438i
$637$	−8.19495	+	2.98272i	−0.324696	+	0.118180i
$638$	7.42794	+	12.8656i	0.294075	+	0.509353i
$639$	14.6298	−	4.31450i	0.578747	−	0.170679i
$640$	0.370360	−	0.641483i	0.0146398	−	0.0253568i
$641$	−4.79194	+	27.1764i	−0.189270	+	1.07340i	0.731075	+	0.682297i	$0.239019\pi$
$641$	−4.79194	+	27.1764i	−0.189270	+	1.07340i	−0.920345	+	0.391107i	$0.872092\pi$
$642$	29.9366	+	0.932590i	1.18150	+	0.0368064i
$643$	−30.6010	−	11.1378i	−1.20678	−	0.439234i	−0.341197	−	0.939992i	$-0.610832\pi$
$643$	−30.6010	−	11.1378i	−1.20678	−	0.439234i	−0.865587	+	0.500758i	$0.833055\pi$
$644$	−2.51498	−	14.2632i	−0.0991041	−	0.562047i
$645$	−2.77569	+	2.18548i	−0.109293	+	0.0860532i
$646$	−5.19613	−	4.36007i	−0.204439	−	0.171545i
$647$	−11.8337			−0.465232			−0.232616	−	0.972569i	$-0.574728\pi$
$647$	−11.8337			−0.465232			−0.232616	+	0.972569i	$0.574728\pi$
$648$	7.55976	−	4.88366i	0.296975	−	0.191848i
$649$	6.50805			0.255463
$650$	−2.95009	−	2.47542i	−0.115712	−	0.0970940i
$651$	−60.1701	+	47.3759i	−2.35825	+	1.85681i
$652$	0.407565	+	2.31141i	0.0159615	+	0.0905219i
$653$	1.90882	+	0.694752i	0.0746978	+	0.0271878i	0.379099	−	0.925356i	$-0.376234\pi$
$653$	1.90882	+	0.694752i	0.0746978	+	0.0271878i	−0.304401	+	0.952544i	$0.598456\pi$
$654$	17.2181	+	0.536382i	0.673281	+	0.0209742i
$655$	2.04444	−	11.5946i	0.0798830	−	0.453039i
$656$	1.28845	−	2.23165i	0.0503054	−	0.0871314i
$657$	−1.24609	−	1.18534i	−0.0486147	−	0.0462445i
$658$	−20.0369	−	34.7050i	−0.781120	−	1.35294i
$659$	−45.4410	+	16.5392i	−1.77013	+	0.644275i	−0.770151	+	0.637861i	$0.779819\pi$
$659$	−45.4410	+	16.5392i	−1.77013	+	0.644275i	−0.999979	+	0.00641394i	$0.997958\pi$
$660$	4.34926	+	3.88654i	0.169295	+	0.151284i
$661$	−13.0788	+	10.9744i	−0.508706	+	0.426855i	−0.860673	−	0.509157i	$-0.829957\pi$
$661$	−13.0788	+	10.9744i	−0.508706	+	0.426855i	0.351968	+	0.936012i	$0.385513\pi$
$662$	13.7587	−	11.5449i	0.534747	−	0.448706i
$663$	−6.20527	+	2.04207i	−0.240993	+	0.0793075i
$664$	−8.66720	+	3.15460i	−0.336352	+	0.122422i
$665$	2.38155	+	4.12497i	0.0923527	+	0.159960i
$666$	4.84418	+	2.11321i	0.187708	+	0.0818854i
$667$	−5.72567	+	9.91715i	−0.221699	+	0.383993i
$668$	−0.182786	+	1.03663i	−0.00707220	+	0.0401084i
$669$	−1.03578	−	1.93045i	−0.0400456	−	0.0746356i
$670$	9.12662	+	3.32182i	0.352592	+	0.128333i
$671$	−3.41752	−	19.3817i	−0.131932	−	0.748224i
$672$	−1.02291	−	7.08479i	−0.0394598	−	0.273302i
$673$	−22.8356	−	19.1613i	−0.880247	−	0.738615i	0.0859825	−	0.996297i	$-0.472597\pi$
$673$	−22.8356	−	19.1613i	−0.880247	−	0.738615i	−0.966230	+	0.257681i	$0.917042\pi$
$674$	−23.4959			−0.905027
$675$	6.12394	−	22.3044i	0.235711	−	0.858496i
$676$	−12.2515			−0.471212
$677$	6.10334	+	5.12131i	0.234570	+	0.196828i	0.752494	−	0.658599i	$-0.228851\pi$
$677$	6.10334	+	5.12131i	0.234570	+	0.196828i	−0.517924	+	0.855427i	$0.673295\pi$
$678$	3.94263	+	1.57569i	0.151416	+	0.0605139i
$679$	4.12994	+	23.4221i	0.158493	+	0.898856i
$680$	−3.03443	−	1.10444i	−0.116365	−	0.0423534i
$681$	9.06968	−	14.6368i	0.347551	−	0.560885i
$682$	8.44606	−	47.9000i	0.323416	−	1.83419i
$683$	15.1593	−	26.2566i	0.580054	−	1.00468i	−0.415419	−	0.909630i	$-0.636365\pi$
$683$	15.1593	−	26.2566i	0.580054	−	1.00468i	0.995472	−	0.0950521i	$-0.0303018\pi$
$684$	−2.58098	+	3.88931i	−0.0986863	+	0.148711i
$685$	−4.57630	−	7.92638i	−0.174851	−	0.302851i
$686$	−11.9622	+	4.35388i	−0.456719	+	0.166232i
$687$	3.53109	−	16.9255i	0.134719	−	0.645748i
$688$	−2.10940	+	1.77000i	−0.0804202	+	0.0674806i
$689$	2.65653	−	2.22910i	0.101206	−	0.0849218i
$690$	−0.918223	+	4.40131i	−0.0349562	+	0.167555i
$691$	−24.9197	+	9.07005i	−0.947992	+	0.345041i	−0.769317	−	0.638867i	$-0.779403\pi$
$691$	−24.9197	+	9.07005i	−0.947992	+	0.345041i	−0.178675	+	0.983908i	$0.557181\pi$
$692$	−3.41644	−	5.91745i	−0.129874	−	0.224948i
$693$	56.2581	+	3.50853i	2.13707	+	0.133278i
$694$	−4.16620	+	7.21608i	−0.158147	+	0.273919i
$695$	0.563813	−	3.19754i	0.0213867	−	0.121290i
$696$	−2.98113	+	4.81101i	−0.112999	+	0.182361i
$697$	−10.5565	−	3.84224i	−0.399855	−	0.145535i
$698$	−0.919463	−	5.21453i	−0.0348022	−	0.197373i
$699$	−43.6719	−	17.4536i	−1.65182	−	0.660158i
$700$	−14.0926	−	11.8251i	−0.532649	−	0.446946i
$701$	46.2262			1.74594			0.872971	−	0.487773i	$-0.162191\pi$
$701$	46.2262			1.74594			0.872971	+	0.487773i	$0.162191\pi$
$702$	1.87473	+	4.08589i	0.0707570	+	0.154212i
$703$	−2.74105			−0.103381
$704$	3.48269	+	2.92232i	0.131259	+	0.110139i
$705$	1.77771	+	12.3126i	0.0669525	+	0.463719i
$706$	6.00160	+	34.0368i	0.225873	+	1.28099i
$707$	42.8730	+	15.6045i	1.61240	+	0.586867i
$708$	1.17225	+	2.18481i	0.0440560	+	0.0821101i
$709$	5.30328	−	30.0764i	0.199169	−	1.12954i	−0.707186	−	0.707027i	$-0.750036\pi$
$709$	5.30328	−	30.0764i	0.199169	−	1.12954i	0.906355	−	0.422516i	$-0.138853\pi$
$710$	−1.88301	+	3.26146i	−0.0706680	+	0.122401i
$711$	16.3158	−	12.0429i	0.611891	−	0.451642i
$712$	6.19947	+	10.7378i	0.232335	+	0.402416i
$713$	35.2312	−	12.8231i	1.31942	−	0.480229i
$714$	−29.6426	+	9.75497i	−1.10934	+	0.365071i
$715$	−2.23183	+	1.87272i	−0.0834656	+	0.0700359i
$716$	−1.68341	+	1.41255i	−0.0629120	+	0.0527894i
$717$	25.2313	+	22.5469i	0.942279	+	0.842031i
$718$	24.1480	−	8.78915i	0.901195	−	0.328008i
$719$	−3.46256	−	5.99733i	−0.129132	−	0.223663i	0.794209	−	0.607645i	$-0.207886\pi$
$719$	−3.46256	−	5.99733i	−0.129132	−	0.223663i	−0.923340	+	0.383982i	$0.874552\pi$
$720$	−0.521341	+	2.16014i	−0.0194292	+	0.0805037i
$721$	13.2694	−	22.9832i	0.494177	−	0.855939i
$722$	−2.87893	+	16.3272i	−0.107143	+	0.607636i
$723$	−28.0720	−	0.874503i	−1.04401	−	0.0325231i
$724$	14.7907	+	5.38339i	0.549693	+	0.200072i
$725$	2.52580	+	14.3245i	0.0938057	+	0.531999i
$726$	−13.1581	+	10.3603i	−0.488345	+	0.384506i
$727$	−16.6231	−	13.9485i	−0.616517	−	0.517319i	0.280189	−	0.959945i	$-0.409603\pi$
$727$	−16.6231	−	13.9485i	−0.616517	−	0.517319i	−0.896707	+	0.442625i	$0.854047\pi$
$728$	3.57551			0.132517
$729$	−17.6088	+	20.4678i	−0.652176	+	0.758067i
$730$	0.424635			0.0157164
$731$	9.19595	+	7.71631i	0.340124	+	0.285398i
$732$	5.89103	−	4.63840i	0.217739	−	0.171440i
$733$	6.80782	+	38.6090i	0.251452	+	1.42606i	0.805017	+	0.593251i	$0.202156\pi$
$733$	6.80782	+	38.6090i	0.251452	+	1.42606i	−0.553565	+	0.832806i	$0.686733\pi$
$734$	−10.6739	−	3.88499i	−0.393981	−	0.143397i
$735$	12.9263	+	0.402682i	0.476793	+	0.0148531i
$736$	−0.608539	+	3.45119i	−0.0224310	+	0.127213i
$737$	−29.8057	+	51.6251i	−1.09791	+	1.90163i
$738$	−1.81369	+	7.51491i	−0.0667629	+	0.276628i
$739$	15.4039	+	26.6804i	0.566643	+	0.981454i	0.996895	+	0.0787451i	$0.0250913\pi$
$739$	15.4039	+	26.6804i	0.566643	+	0.981454i	−0.430252	+	0.902709i	$0.641575\pi$
$740$	−1.22622	+	0.446307i	−0.0450767	+	0.0164066i
$741$	−1.73853	−	1.55357i	−0.0638664	−	0.0570717i
$742$	12.6903	−	10.6484i	0.465874	−	0.390915i
$743$	24.4602	−	20.5245i	0.897357	−	0.752972i	−0.0723153	−	0.997382i	$-0.523039\pi$
$743$	24.4602	−	20.5245i	0.897357	−	0.752972i	0.969672	+	0.244410i	$0.0785943\pi$
$744$	17.6018	−	5.79250i	0.645312	−	0.212363i
$745$	4.75645	−	1.73121i	0.174263	−	0.0634265i
$746$	14.3521	+	24.8585i	0.525466	+	0.910134i
$747$	22.2627	−	16.4323i	0.814548	−	0.601226i
$748$	9.90985	−	17.1644i	0.362340	−	0.627591i
$749$	−12.4099	+	70.3801i	−0.453448	+	2.57163i
$750$	5.73295	+	10.6849i	0.209338	+	0.390157i
$751$	−2.85191	−	1.03801i	−0.104068	−	0.0378776i	0.289462	−	0.957190i	$-0.406524\pi$
$751$	−2.85191	−	1.03801i	−0.104068	−	0.0378776i	−0.393529	+	0.919312i	$0.628746\pi$
$752$	1.68378	+	9.54918i	0.0614010	+	0.348223i
$753$	−5.80672	−	40.2178i	−0.211609	−	1.46562i
$754$	−2.16563	−	1.81718i	−0.0788675	−	0.0661777i
$755$	3.85659			0.140356
$756$	8.95557	+	19.5183i	0.325711	+	0.709873i
$757$	10.7254			0.389823			0.194912	−	0.980821i	$-0.437558\pi$
$757$	10.7254			0.389823			0.194912	+	0.980821i	$0.437558\pi$
$758$	−17.6568	−	14.8158i	−0.641323	−	0.538134i
$759$	−25.6249	−	10.2411i	−0.930124	−	0.371728i
$760$	−0.200131	−	1.13500i	−0.00725951	−	0.0411707i
$761$	−25.4656	−	9.26871i	−0.923126	−	0.335990i	−0.163645	−	0.986519i	$-0.552325\pi$
$761$	−25.4656	−	9.26871i	−0.923126	−	0.335990i	−0.759481	+	0.650529i	$0.774547\pi$
$762$	7.39219	−	11.9297i	0.267791	−	0.432167i
$763$	−7.13760	+	40.4793i	−0.258398	+	1.46545i
$764$	−3.92070	+	6.79085i	−0.141846	+	0.245684i
$765$	9.66873	+	0.602990i	0.349574	+	0.0218011i
$766$	12.3025	+	21.3086i	0.444508	+	0.769910i
$767$	−1.16377	+	0.423579i	−0.0420214	+	0.0152945i
$768$	−0.353733	+	1.69554i	−0.0127643	+	0.0611827i
$769$	20.6292	−	17.3100i	0.743910	−	0.624214i	−0.189975	−	0.981789i	$-0.560841\pi$
$769$	20.6292	−	17.3100i	0.743910	−	0.624214i	0.933885	+	0.357575i	$0.116396\pi$
$770$	−10.6614	+	8.94599i	−0.384211	+	0.322391i
$771$	−7.77874	+	37.2857i	−0.280145	+	1.34281i
$772$	15.5431	−	5.65721i	0.559407	−	0.203607i
$773$	7.19832	+	12.4679i	0.258906	+	0.448438i	0.965949	−	0.258733i	$-0.0833048\pi$
$773$	7.19832	+	12.4679i	0.258906	+	0.448438i	−0.707043	+	0.707170i	$0.749971\pi$
$774$	4.56774	−	6.88317i	0.164184	−	0.247411i
$775$	23.8113	−	41.2424i	0.855328	−	1.48147i
$776$	0.999303	−	5.66733i	0.0358729	−	0.203445i
$777$	−6.64228	+	10.7195i	−0.238291	+	0.384559i
$778$	−34.8878	−	12.6981i	−1.25079	−	0.455250i
$779$	−0.696235	−	3.94855i	−0.0249452	−	0.141471i
$780$	−1.03069	−	0.411921i	−0.0369047	−	0.0147491i
$781$	−17.7069	−	14.8578i	−0.633602	−	0.531655i
$782$	15.2776			0.546325
$783$	4.49551	−	16.3734i	0.160656	−	0.585137i
$784$	10.0802			0.360007
$785$	−2.25390	−	1.89124i	−0.0804450	−	0.0675014i
$786$	3.93408	+	27.2478i	0.140324	+	0.971896i
$787$	−1.54500	−	8.76212i	−0.0550732	−	0.312336i	0.944810	−	0.327619i	$-0.106246\pi$
$787$	−1.54500	−	8.76212i	−0.0550732	−	0.312336i	−0.999883	+	0.0152831i	$0.995135\pi$
$788$	10.6901	+	3.89089i	0.380820	+	0.138607i
$789$	−19.2300	−	35.8402i	−0.684606	−	1.27595i
$790$	−0.869459	+	4.93095i	−0.0309340	+	0.175435i
$791$	−5.06546	+	8.77363i	−0.180107	+	0.311954i
$792$	−12.5012	−	5.45350i	−0.444212	−	0.193782i
$793$	1.87259	+	3.24342i	0.0664976	+	0.115177i
$794$	−6.00706	+	2.18639i	−0.213183	+	0.0775921i
$795$	−4.88491	+	1.60756i	−0.173250	+	0.0570142i
$796$	1.43443	−	1.20363i	0.0508420	−	0.0426615i
$797$	23.0251	−	19.3204i	0.815592	−	0.684363i	−0.136344	−	0.990662i	$-0.543535\pi$
$797$	23.0251	−	19.3204i	0.815592	−	0.684363i	0.951935	+	0.306299i	$0.0990907\pi$
$798$	−8.30494	−	7.42138i	−0.293992	−	0.262714i
$799$	39.7225	−	14.4578i	1.40528	−	0.511481i
$800$	2.22567	+	3.85497i	0.0786892	+	0.136294i
$801$	−26.9509	−	25.6369i	−0.952264	−	0.905835i
$802$	−16.3433	+	28.3075i	−0.577104	+	0.999573i
$803$	−0.452577	+	2.56669i	−0.0159711	+	0.0905765i
$804$	−22.6997	−	0.707145i	−0.800556	−	0.0249391i
$805$	−10.0810	−	3.66919i	−0.355309	−	0.129322i
$806$	1.60726	+	9.11521i	0.0566132	+	0.321070i
$807$	−24.9037	+	19.6083i	−0.876651	+	0.690245i
$808$	−8.45678	−	7.09608i	−0.297509	−	0.249639i
$809$	−22.4607			−0.789676			−0.394838	−	0.918751i	$-0.629199\pi$
$809$	−22.4607			−0.789676			−0.394838	+	0.918751i	$0.629199\pi$
$810$	−0.332949	−	6.65816i	−0.0116986	−	0.233944i
$811$	21.1008			0.740949			0.370474	−	0.928843i	$-0.379195\pi$
$811$	21.1008			0.740949			0.370474	+	0.928843i	$0.379195\pi$
$812$	−10.3452	−	8.68065i	−0.363045	−	0.304631i
$813$	22.4302	−	17.6608i	0.786662	−	0.619391i
$814$	−1.39078	−	7.88751i	−0.0487468	−	0.276457i
$815$	1.63368	+	0.594610i	0.0572252	+	0.0208283i
$816$	7.54722	+	0.235112i	0.264205	+	0.00823058i
$817$	−0.743987	+	4.21936i	−0.0260288	+	0.147617i
$818$	10.9279	−	18.9277i	0.382085	−	0.661791i
$819$	−10.2885	+	3.03418i	−0.359508	+	0.106023i
$820$	−0.954378	−	1.65303i	−0.0333283	−	0.0577264i
$821$	6.32803	−	2.30322i	0.220850	−	0.0803828i	−0.229226	−	0.973373i	$-0.573619\pi$
$821$	6.32803	−	2.30322i	0.220850	−	0.0803828i	0.450075	+	0.892991i	$0.351397\pi$
$822$	15.9584	+	14.2606i	0.556615	+	0.497397i
$823$	23.1807	−	19.4509i	0.808030	−	0.678017i	−0.142107	−	0.989851i	$-0.545388\pi$
$823$	23.1807	−	19.4509i	0.808030	−	0.678017i	0.950137	+	0.311834i	$0.100943\pi$
$824$	−4.91912	+	4.12763i	−0.171366	+	0.143793i
$825$	−33.2953	+	10.9570i	−1.15919	+	0.381475i
$826$	−5.55934	+	2.02343i	−0.193434	+	0.0704042i
$827$	−2.82370	−	4.89079i	−0.0981897	−	0.170070i	0.812746	−	0.582619i	$-0.197972\pi$
$827$	−2.82370	−	4.89079i	−0.0981897	−	0.170070i	−0.910935	+	0.412549i	$0.864639\pi$
$828$	−1.17763	−	10.4471i	−0.0409254	−	0.363063i
$829$	−11.3107	+	19.5907i	−0.392837	+	0.680413i	−0.992822	−	0.119597i	$-0.961840\pi$
$829$	−11.3107	+	19.5907i	−0.392837	+	0.680413i	0.599986	+	0.800011i	$0.295173\pi$
$830$	−1.18636	+	6.72820i	−0.0411792	+	0.233539i
$831$	9.23064	+	17.2038i	0.320207	+	0.596792i
$832$	−0.812975	−	0.295899i	−0.0281849	−	0.0102584i
$833$	−7.63091	−	43.2770i	−0.264395	−	1.49946i
$834$	1.08493	+	7.51435i	0.0375682	+	0.260201i
$835$	0.597284	+	0.501181i	0.0206699	+	0.0173441i
$836$	7.07375			0.244651
$837$	−45.7331	+	31.6047i	−1.58077	+	1.09242i
$838$	−26.1109			−0.901987
$839$	−8.13447	−	6.82563i	−0.280833	−	0.235647i	0.491480	−	0.870889i	$-0.336456\pi$
$839$	−8.13447	−	6.82563i	−0.280833	−	0.235647i	−0.772313	+	0.635242i	$0.780900\pi$
$840$	−4.92362	−	1.96774i	−0.169881	−	0.0678936i
$841$	−3.18164	−	18.0440i	−0.109712	−	0.622206i
$842$	35.2362	+	12.8249i	1.21432	+	0.441976i
$843$	−0.661740	+	1.06793i	−0.0227915	+	0.0367815i
$844$	0.949880	−	5.38704i	0.0326962	−	0.185430i
$845$	−4.53747	+	7.85914i	−0.156094	+	0.270362i
$846$	−12.9485	−	26.0487i	−0.445177	−	0.895572i
$847$	−19.9802	−	34.6068i	−0.686529	−	1.18910i
$848$	−3.76665	+	1.37095i	−0.129347	+	0.0470786i
$849$	7.83103	−	37.5364i	0.268760	−	1.28825i
$850$	14.8655	−	12.4737i	0.509884	−	0.427843i
$851$	4.72933	−	3.96838i	0.162119	−	0.136034i
$852$	1.79847	−	8.62059i	0.0616146	−	0.295336i
$853$	16.0795	−	5.85246i	0.550551	−	0.200384i	−0.0517401	−	0.998661i	$-0.516477\pi$
$853$	16.0795	−	5.85246i	0.550551	−	0.200384i	0.602291	+	0.798276i	$0.294255\pi$
$854$	8.94535	+	15.4938i	0.306104	+	0.530187i
$855$	1.53903	+	3.09610i	0.0526338	+	0.105884i
$856$	8.64614	−	14.9755i	0.295519	−	0.511854i
$857$	5.77848	−	32.7714i	0.197389	−	1.11945i	−0.711586	−	0.702599i	$-0.752023\pi$
$857$	5.77848	−	32.7714i	0.197389	−	1.11945i	0.908975	−	0.416850i	$-0.136866\pi$
$858$	3.58835	−	5.79096i	0.122504	−	0.197700i
$859$	0.698231	+	0.254135i	0.0238233	+	0.00867098i	0.353904	−	0.935282i	$-0.384854\pi$
$859$	0.698231	+	0.254135i	0.0238233	+	0.00867098i	−0.330081	+	0.943953i	$0.607076\pi$
$860$	0.354185	+	2.00868i	0.0120776	+	0.0684955i
$861$	−17.1288	−	6.84558i	−0.583747	−	0.233297i
$862$	4.69710	+	3.94133i	0.159984	+	0.134242i
$863$	14.4375			0.491457			0.245728	−	0.969339i	$-0.420973\pi$
$863$	14.4375			0.491457			0.245728	+	0.969339i	$0.420973\pi$
$864$	−0.420980	−	5.17907i	−0.0143220	−	0.176196i
$865$	−5.06126			−0.172088
$866$	−16.0410	−	13.4600i	−0.545096	−	0.457390i
$867$	−0.496319	−	3.43755i	−0.0168559	−	0.116745i
$868$	7.67786	+	43.5433i	0.260604	+	1.47796i
$869$	−28.8782	−	10.5108i	−0.979627	−	0.356555i
$870$	1.98209	+	3.69415i	0.0671991	+	0.125243i
$871$	1.96984	−	11.1715i	0.0667456	−	0.378533i
$872$	4.97285	−	8.61323i	0.168402	−	0.291681i
$873$	1.93383	+	17.1556i	0.0654501	+	0.580630i
$874$	2.72632	+	4.72213i	0.0922193	+	0.159728i
$875$	−27.1882	+	9.89568i	−0.919127	+	0.334535i
$876$	−0.943178	+	0.310387i	−0.0318670	+	0.0104870i
$877$	−22.3924	+	18.7895i	−0.756139	+	0.634476i	−0.937119	−	0.349011i	$-0.886518\pi$
$877$	−22.3924	+	18.7895i	−0.756139	+	0.634476i	0.180979	+	0.983487i	$0.442073\pi$
$878$	−21.9969	+	18.4576i	−0.742359	+	0.622913i
$879$	8.47053	+	7.56936i	0.285704	+	0.255308i
$880$	3.16447	−	1.15177i	0.106674	−	0.0388262i
$881$	3.02765	+	5.24404i	0.102004	+	0.176676i	0.912510	−	0.409054i	$-0.134141\pi$
$881$	3.02765	+	5.24404i	0.102004	+	0.176676i	−0.810506	+	0.585730i	$0.800808\pi$
$882$	−29.0055	+	8.55406i	−0.976667	+	0.288030i
$883$	−3.06634	+	5.31105i	−0.103190	+	0.178731i	−0.912997	−	0.407965i	$-0.866238\pi$
$883$	−3.06634	+	5.31105i	−0.103190	+	0.178731i	0.809807	+	0.586696i	$0.199572\pi$
$884$	−0.654936	+	3.71432i	−0.0220279	+	0.124926i
$885$	1.83567	+	0.0571852i	0.0617054	+	0.00192226i
$886$	14.2882	+	5.20050i	0.480023	+	0.174714i
$887$	9.46864	+	53.6993i	0.317926	+	1.80305i	0.555325	+	0.831634i	$0.312594\pi$
$887$	9.46864	+	53.6993i	0.317926	+	1.80305i	−0.237399	+	0.971412i	$0.576295\pi$
$888$	2.39739	−	1.88762i	0.0804511	−	0.0633445i
$889$	25.6526	+	21.5251i	0.860359	+	0.721927i
$890$	9.18415			0.307853
$891$	40.5999	+	5.08379i	1.36015	+	0.170313i
$892$	−1.26484			−0.0423501
$893$	11.5573	+	9.69776i	0.386752	+	0.324523i
$894$	−9.29936	+	7.32200i	−0.311017	+	0.244884i
$895$	0.282658	+	1.60303i	0.00944820	+	0.0535834i
$896$	−3.88358	−	1.41351i	−0.129741	−	0.0472220i
$897$	5.24879	+	0.163511i	0.175252	+	0.00545949i
$898$	−2.15688	+	12.2323i	−0.0719760	+	0.408196i
$899$	17.4796	−	30.2756i	0.582978	−	1.00975i
$900$	−9.67563	−	9.20388i	−0.322521	−	0.306796i
$901$	8.73729	+	15.1334i	0.291081	+	0.504168i
$902$	11.0089	−	4.00690i	0.366555	−	0.133415i
$903$	14.6978	+	13.1341i	0.489113	+	0.437076i
$904$	1.87783	−	1.57569i	0.0624557	−	0.0524066i
$905$	8.93125	−	7.49421i	0.296885	−	0.249116i
$906$	−8.56606	+	2.81898i	−0.284588	+	0.0936542i
$907$	3.63868	−	1.32437i	0.120820	−	0.0439750i	−0.280902	−	0.959736i	$-0.590634\pi$
$907$	3.63868	−	1.32437i	0.120820	−	0.0439750i	0.401723	+	0.915761i	$0.368412\pi$
$908$	−4.97072	−	8.60954i	−0.164959	−	0.285717i
$909$	30.3559	+	13.2424i	1.00684	+	0.439222i
$910$	1.32423	−	2.29363i	0.0438977	−	0.0760330i
$911$	−0.755948	+	4.28719i	−0.0250457	+	0.142041i	−0.994766	−	0.102175i	$-0.967420\pi$
$911$	−0.755948	+	4.28719i	−0.0250457	+	0.142041i	0.969721	+	0.244217i	$0.0785308\pi$
$912$	1.27415	+	2.37472i	0.0421913	+	0.0786347i
$913$	−39.4039	−	14.3418i	−1.30408	−	0.474646i
$914$	−1.88311	−	10.6796i	−0.0622877	−	0.353251i
$915$	−0.793648	−	5.49687i	−0.0262372	−	0.181721i
$916$	−7.64692	−	6.41653i	−0.252661	−	0.212008i
$917$	−65.6896			−2.16926
$918$	−21.9165	+	5.72804i	−0.723351	+	0.189053i
$919$	23.4247			0.772710			0.386355	−	0.922350i	$-0.373734\pi$
$919$	23.4247			0.772710			0.386355	+	0.922350i	$0.373734\pi$
$920$	1.98850	+	1.66855i	0.0655590	+	0.0550105i
$921$	12.8264	+	5.12611i	0.422643	+	0.168911i
$922$	−1.42420	−	8.07705i	−0.0469036	−	0.266004i
$923$	4.13338	+	1.50443i	0.136052	+	0.0495188i
$924$	17.1415	−	27.6634i	0.563915	−	0.910058i
$925$	1.36172	−	7.72271i	0.0447731	−	0.253921i
$926$	16.8257	−	29.1429i	0.552926	−	0.957697i
$927$	10.6519	−	16.0515i	0.349856	−	0.527201i
$928$	1.63383	+	2.82988i	0.0536332	+	0.0928955i
$929$	38.3287	−	13.9505i	1.25752	−	0.457701i	0.374586	−	0.927192i	$-0.377785\pi$
$929$	38.3287	−	13.9505i	1.25752	−	0.457701i	0.882937	+	0.469492i	$0.155563\pi$
$930$	2.80320	−	13.4365i	0.0919205	−	0.440601i
$931$	12.0147	−	10.0815i	0.393765	−	0.330408i
$932$	−20.8004	+	17.4536i	−0.681341	+	0.571713i
$933$	−5.00464	+	23.9887i	−0.163844	+	0.785353i
$934$	−10.2131	+	3.71725i	−0.334182	+	0.121632i
$935$	−7.34043	−	12.7140i	−0.240058	−	0.415792i
$936$	2.59042	+	0.161551i	0.0846705	+	0.00528047i
$937$	10.2480	−	17.7501i	0.334789	−	0.579871i	−0.648656	−	0.761082i	$-0.724668\pi$
$937$	10.2480	−	17.7501i	0.334789	−	0.579871i	0.983444	+	0.181211i	$0.0580017\pi$
$938$	9.40993	−	53.3664i	0.307245	−	1.74247i
$939$	21.9334	−	35.3965i	0.715769	−	1.15512i
$940$	6.74924	+	2.45652i	0.220136	+	0.0801229i
$941$	1.49514	+	8.47935i	0.0487401	+	0.276419i	0.999431	−	0.0337201i	$-0.0107355\pi$
$941$	1.49514	+	8.47935i	0.0487401	+	0.276419i	−0.950691	+	0.310139i	$0.899624\pi$
$942$	6.38865	+	2.55325i	0.208153	+	0.0831893i
$943$	6.91780	+	5.80472i	0.225275	+	0.189028i
$944$	1.43150			0.0465913
$945$	15.8374	+	1.48395i	0.515191	+	0.0482730i
$946$	−12.5189			−0.407024
$947$	31.4937	+	26.4264i	1.02341	+	0.858741i	0.990052	−	0.140702i	$-0.0449360\pi$
$947$	31.4937	+	26.4264i	1.02341	+	0.858741i	0.0333562	+	0.999444i	$0.489380\pi$
$948$	−1.67308	−	11.5879i	−0.0543392	−	0.376358i
$949$	−0.0861238	−	0.488432i	−0.00279570	−	0.0158552i
$950$	6.50827	+	2.36882i	0.211156	+	0.0768545i
$951$	14.8980	+	27.7664i	0.483101	+	0.900388i
$952$	−3.12862	+	17.7433i	−0.101399	+	0.575064i
$953$	−13.8375	+	23.9672i	−0.448240	+	0.776374i	−0.998272	−	0.0587696i	$-0.981282\pi$
$953$	−13.8375	+	23.9672i	−0.448240	+	0.776374i	0.550032	+	0.835144i	$0.314616\pi$
$954$	9.67507	−	7.14126i	0.313242	−	0.231207i
$955$	2.90414	+	5.03012i	0.0939759	+	0.162771i
$956$	18.3580	−	6.68175i	0.593739	−	0.216103i
$957$	−24.4417	+	8.04343i	−0.790087	+	0.260007i
$958$	−14.4230	+	12.1023i	−0.465986	+	0.391009i
$959$	−39.1192	+	32.8249i	−1.26323	+	1.05997i
$960$	0.956654	+	0.854876i	0.0308759	+	0.0275910i
$961$	−78.4251	+	28.5444i	−2.52984	+	0.920788i
$962$	0.762061	+	1.31993i	0.0245698	+	0.0425562i
$963$	−12.1708	+	50.4289i	−0.392199	+	1.62505i
$964$	−8.10761	+	14.0428i	−0.261128	+	0.452288i
$965$	2.12753	−	12.0658i	0.0684875	−	0.388412i
$966$	25.0735	+	0.781094i	0.806726	+	0.0251313i
$967$	−56.1727	−	20.4452i	−1.80639	−	0.657474i	−0.997589	−	0.0693962i	$-0.977893\pi$
$967$	−56.1727	−	20.4452i	−1.80639	−	0.657474i	−0.808805	−	0.588077i	$-0.799885\pi$
$968$	1.67901	+	9.52216i	0.0539656	+	0.306054i
$969$	9.23075	−	7.26797i	0.296534	−	0.233481i
$970$	−3.26539	−	2.73999i	−0.104845	−	0.0879758i
$971$	−3.80514			−0.122113			−0.0610564	−	0.998134i	$-0.519447\pi$
$971$	−3.80514			−0.122113			−0.0610564	+	0.998134i	$0.519447\pi$
$972$	5.60632	+	14.5454i	0.179823	+	0.466544i
$973$	−18.1158			−0.580765
$974$	25.2428	+	21.1812i	0.808830	+	0.678689i
$975$	5.24074	−	4.12638i	0.167838	−	0.132150i
$976$	−0.751711	−	4.26317i	−0.0240617	−	0.136461i
$977$	−26.6685	−	9.70654i	−0.853201	−	0.310540i	−0.121856	−	0.992548i	$-0.538885\pi$
$977$	−26.6685	−	9.70654i	−0.853201	−	0.310540i	−0.731345	+	0.682008i	$0.761107\pi$
$978$	−4.06328	−	0.126580i	−0.129929	−	0.00404758i
$979$	−9.78848	+	55.5132i	−0.312841	+	1.77421i
$980$	3.73330	−	6.46627i	0.119256	−	0.206558i
$981$	−7.00008	+	29.0043i	−0.223495	+	0.926037i
$982$	−17.3191	−	29.9975i	−0.552673	−	0.957258i
$983$	−16.6680	+	6.06666i	−0.531627	+	0.193496i	−0.593865	−	0.804565i	$-0.702399\pi$
$983$	−16.6680	+	6.06666i	−0.531627	+	0.193496i	0.0622377	+	0.998061i	$0.480176\pi$
$984$	3.32810	+	2.97403i	0.106096	+	0.0948086i
$985$	6.45514	−	5.41650i	0.205678	−	0.172584i
$986$	10.9126	−	9.15677i	0.347528	−	0.291611i
$987$	65.9315	−	21.6972i	2.09862	−	0.690629i
$988$	−1.26493	+	0.460397i	−0.0402428	+	0.0146472i
$989$	−4.82496	−	8.35707i	−0.153425	−	0.265739i
$990$	−8.12829	+	5.99956i	−0.258334	+	0.190679i
$991$	6.59603	−	11.4247i	0.209530	−	0.362916i	−0.742037	−	0.670359i	$-0.766140\pi$
$991$	6.59603	−	11.4247i	0.209530	−	0.362916i	0.951566	+	0.307443i	$0.0994734\pi$
$992$	1.85778	−	10.5360i	0.0589845	−	0.334518i
$993$	14.7080	+	27.4123i	0.466745	+	0.869904i
$994$	19.7451	+	7.18664i	0.626277	+	0.227946i
$995$	−0.240852	−	1.36594i	−0.00763552	−	0.0433032i
$996$	−2.28289	−	15.8115i	−0.0723362	−	0.501007i
$997$	45.1830	+	37.9130i	1.43096	+	1.20072i	0.945143	+	0.326656i	$0.105922\pi$
$997$	45.1830	+	37.9130i	1.43096	+	1.20072i	0.485816	+	0.874061i	$0.338523\pi$
$998$	23.7200			0.750845
$999$	−5.29660	+	7.46602i	−0.167577	+	0.236214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.2.e.b.43.1	✓	12
3.2	odd	2		162.2.e.b.127.1		12
4.3	odd	2		432.2.u.b.97.2		12
9.2	odd	6		486.2.e.g.217.2		12
9.4	even	3		486.2.e.h.55.1		12
9.5	odd	6		486.2.e.e.55.2		12
9.7	even	3		486.2.e.f.217.1		12
27.2	odd	18		1458.2.c.g.973.3		12
27.4	even	9		486.2.e.f.271.1		12
27.5	odd	18		162.2.e.b.37.1		12
27.7	even	9		1458.2.a.g.1.3		6
27.11	odd	18		1458.2.c.g.487.3		12
27.13	even	9		486.2.e.h.433.1		12
27.14	odd	18		486.2.e.e.433.2		12
27.16	even	9		1458.2.c.f.487.4		12
27.20	odd	18		1458.2.a.f.1.4		6
27.22	even	9	inner	54.2.e.b.49.1	yes	12
27.23	odd	18		486.2.e.g.271.2		12
27.25	even	9		1458.2.c.f.973.4		12
108.103	odd	18		432.2.u.b.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.1	✓	12	1.1	even	1	trivial
54.2.e.b.49.1	yes	12	27.22	even	9	inner
162.2.e.b.37.1		12	27.5	odd	18
162.2.e.b.127.1		12	3.2	odd	2
432.2.u.b.49.2		12	108.103	odd	18
432.2.u.b.97.2		12	4.3	odd	2
486.2.e.e.55.2		12	9.5	odd	6
486.2.e.e.433.2		12	27.14	odd	18
486.2.e.f.217.1		12	9.7	even	3
486.2.e.f.271.1		12	27.4	even	9
486.2.e.g.217.2		12	9.2	odd	6
486.2.e.g.271.2		12	27.23	odd	18
486.2.e.h.55.1		12	9.4	even	3
486.2.e.h.433.1		12	27.13	even	9
1458.2.a.f.1.4		6	27.20	odd	18
1458.2.a.g.1.3		6	27.7	even	9
1458.2.c.f.487.4		12	27.16	even	9
1458.2.c.f.973.4		12	27.25	even	9
1458.2.c.g.487.3		12	27.11	odd	18
1458.2.c.g.973.3		12	27.2	odd	18

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.36085 + 1.07149i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.696050 + 0.253341i) q^{5} +(-1.73121 - 0.0539310i) q^{6} +(0.717657 - 4.07003i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.703829 - 2.91627i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.36085 + 1.07149i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.696050 + 0.253341i) q^{5} +(-1.73121 - 0.0539310i) q^{6} +(0.717657 - 4.07003i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.703829 - 2.91627i) q^{9} +(0.370360 + 0.641483i) q^{10} +(-4.27215 + 1.55493i) q^{11} +(-1.29152 - 1.15411i) q^{12} +(0.662744 - 0.556108i) q^{13} +(3.16592 - 2.65653i) q^{14} +(-1.21867 + 0.401049i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(2.17975 + 3.77544i) q^{17} +(2.41371 - 1.78158i) q^{18} +(-0.777964 + 1.34747i) q^{19} +(-0.128625 + 0.729467i) q^{20} +(3.38437 + 6.30767i) q^{21} +(-4.27215 - 1.55493i) q^{22} +(-0.608539 - 3.45119i) q^{23} +(-0.247510 - 1.71428i) q^{24} +(-3.40992 - 2.86126i) q^{25} +0.865150 q^{26} +(2.16694 + 4.72275i) q^{27} +4.13282 q^{28} +(-2.50318 - 2.10042i) q^{29} +(-1.19135 - 0.476126i) q^{30} +(1.85778 + 10.5360i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(4.14766 - 6.69359i) q^{33} +(-0.757019 + 4.29327i) q^{34} +(1.53063 - 2.65113i) q^{35} +(2.99418 + 0.186732i) q^{36} +(0.880842 + 1.52566i) q^{37} +(-1.46209 + 0.532159i) q^{38} +(-0.306033 + 1.46690i) q^{39} +(-0.567425 + 0.476126i) q^{40} +(-1.97401 + 1.65639i) q^{41} +(-1.46192 + 7.00738i) q^{42} +(2.58757 - 0.941797i) q^{43} +(-2.27316 - 3.93723i) q^{44} +(1.22871 - 1.85156i) q^{45} +(1.75222 - 3.03493i) q^{46} +(1.68378 - 9.54918i) q^{47} +(0.912311 - 1.47231i) q^{48} +(-9.47229 - 3.44763i) q^{49} +(-0.772966 - 4.38371i) q^{50} +(-7.01165 - 2.80223i) q^{51} +(0.662744 + 0.556108i) q^{52} +4.00839 q^{53} +(-1.37575 + 5.01072i) q^{54} -3.36756 q^{55} +(3.16592 + 2.65653i) q^{56} +(-0.385108 - 2.66729i) q^{57} +(-0.567425 - 3.21803i) q^{58} +(-1.34517 - 0.489601i) q^{59} +(-0.606576 - 1.13052i) q^{60} +(-0.751711 + 4.26317i) q^{61} +(-5.34926 + 9.26519i) q^{62} +(-11.3642 - 4.95749i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.602188 - 0.219178i) q^{65} +(7.47985 - 2.46152i) q^{66} +(10.0444 - 8.42825i) q^{67} +(-3.33957 + 2.80223i) q^{68} +(4.52604 + 4.04452i) q^{69} +(2.87665 - 1.04701i) q^{70} +(2.54213 + 4.40310i) q^{71} +(2.17365 + 2.06767i) q^{72} +(0.286636 - 0.496469i) q^{73} +(-0.305913 + 1.73492i) q^{74} +(7.70620 + 0.240065i) q^{75} +(-1.46209 - 0.532159i) q^{76} +(3.26270 + 18.5037i) q^{77} +(-1.17734 + 0.926998i) q^{78} +(5.17820 + 4.34502i) q^{79} -0.740720 q^{80} +(-8.00925 - 4.10511i) q^{81} -2.57689 q^{82} +(7.06556 + 5.92871i) q^{83} +(-5.62415 + 4.42826i) q^{84} +(0.560740 + 3.18011i) q^{85} +(2.58757 + 0.941797i) q^{86} +(5.65702 + 0.176229i) q^{87} +(0.789461 - 4.47725i) q^{88} +(6.19947 - 10.7378i) q^{89} +(2.13141 - 0.628576i) q^{90} +(-1.78776 - 3.09648i) q^{91} +(3.29309 - 1.19859i) q^{92} +(-13.8173 - 12.3473i) q^{93} +(7.42794 - 6.23278i) q^{94} +(-0.882872 + 0.740818i) q^{95} +(1.64525 - 0.541430i) q^{96} +(-5.40770 + 1.96824i) q^{97} +(-5.04010 - 8.72971i) q^{98} +(1.52774 + 13.5531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Introduction

L-functions

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