LMFDB - Embedded newform 162.2.g.b.103.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

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("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			103.5
Character	$\chi$	$=$	162.103
Dual form			162.2.g.b.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686242 - 0.727374i) q^{2} +(1.72979 - 0.0885576i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.21262 - 0.258618i) q^{5} +(-1.25147 - 1.19743i) q^{6} +(-2.58863 - 1.30006i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.98432 - 0.306371i) q^{9} +O(q^{10})$	\(q+(-0.686242 - 0.727374i) q^{2} +(1.72979 - 0.0885576i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.21262 - 0.258618i) q^{5} +(-1.25147 - 1.19743i) q^{6} +(-2.58863 - 1.30006i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.98432 - 0.306371i) q^{9} +(-1.70650 - 1.43192i) q^{10} +(2.24105 + 5.19534i) q^{11} +(-0.0121703 + 1.73201i) q^{12} +(-3.63018 - 0.860369i) q^{13} +(0.830796 + 2.77505i) q^{14} +(3.80445 - 0.643297i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(1.29783 - 7.36037i) q^{17} +(-2.27081 - 1.96047i) q^{18} +(-0.140098 - 0.794532i) q^{19} +(0.129528 + 2.22391i) q^{20} +(-4.59290 - 2.01958i) q^{21} +(2.24105 - 5.19534i) q^{22} +(-4.42192 + 2.22077i) q^{23} +(1.26817 - 1.17972i) q^{24} +(-0.0364359 + 0.00863547i) q^{25} +(1.86537 + 3.23092i) q^{26} +(5.13509 - 0.794240i) q^{27} +(1.44837 - 2.50866i) q^{28} +(-1.91151 + 6.38489i) q^{29} +(-3.07869 - 2.32580i) q^{30} +(2.05098 + 1.34895i) q^{31} +(0.597159 + 0.802123i) q^{32} +(4.33662 + 8.78835i) q^{33} +(-6.24436 + 4.10698i) q^{34} +(-6.06386 - 2.20706i) q^{35} +(0.132330 + 2.99708i) q^{36} +(-6.41853 + 2.33615i) q^{37} +(-0.481781 + 0.647144i) q^{38} +(-6.35563 - 1.16677i) q^{39} +(1.52873 - 1.62036i) q^{40} +(2.55518 - 2.70834i) q^{41} +(1.68285 + 4.72667i) q^{42} +(-6.77615 + 9.10195i) q^{43} +(-5.31685 + 1.93518i) q^{44} +(6.52391 - 1.44968i) q^{45} +(4.64984 + 1.69240i) q^{46} +(3.20034 - 2.10490i) q^{47} +(-1.72837 - 0.112857i) q^{48} +(0.830731 + 1.11587i) q^{49} +(0.0312851 + 0.0205765i) q^{50} +(1.59315 - 12.8468i) q^{51} +(1.06999 - 3.57401i) q^{52} +(-1.66998 + 2.89249i) q^{53} +(-4.10162 - 3.19009i) q^{54} +(6.30219 + 10.9157i) q^{55} +(-2.81866 + 0.668036i) q^{56} +(-0.312700 - 1.36196i) q^{57} +(5.95596 - 2.99119i) q^{58} +(-1.15336 + 2.67379i) q^{59} +(0.421000 + 3.83542i) q^{60} +(-0.409169 - 7.02515i) q^{61} +(-0.426276 - 2.41753i) q^{62} +(-8.12358 - 3.08670i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-8.25471 - 0.964837i) q^{65} +(3.41645 - 9.18528i) q^{66} +(-0.117994 - 0.394126i) q^{67} +(7.27245 + 1.72360i) q^{68} +(-7.45231 + 4.23305i) q^{69} +(2.55591 + 5.92527i) q^{70} +(0.709941 + 0.595711i) q^{71} +(2.08919 - 2.15297i) q^{72} +(3.44620 - 2.89170i) q^{73} +(6.10392 + 3.06550i) q^{74} +(-0.0622616 + 0.0181642i) q^{75} +(0.801334 - 0.0936625i) q^{76} +(0.952994 - 16.3623i) q^{77} +(3.51282 + 5.42360i) q^{78} +(1.27120 + 1.34739i) q^{79} -2.22768 q^{80} +(8.81227 - 1.82862i) q^{81} -3.72345 q^{82} +(-2.38885 - 2.53203i) q^{83} +(2.28321 - 4.46770i) q^{84} +(0.968081 - 16.6213i) q^{85} +(11.2706 - 1.31734i) q^{86} +(-2.74107 + 11.2138i) q^{87} +(5.05624 + 2.53934i) q^{88} +(13.5689 - 11.3857i) q^{89} +(-5.53144 - 3.75049i) q^{90} +(8.27866 + 6.94662i) q^{91} +(-1.95990 - 4.54357i) q^{92} +(3.66721 + 2.15176i) q^{93} +(-3.72726 - 0.883376i) q^{94} +(-0.515462 - 1.72176i) q^{95} +(1.10399 + 1.33462i) q^{96} +(3.60360 + 0.421200i) q^{97} +(0.241569 - 1.37001i) q^{98} +(8.27970 + 14.8179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$3$	1.72979	−	0.0885576i	0.998692	−	0.0511287i
$3$	1.72979	−	0.0885576i	0.998692	−	0.0511287i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	2.21262	−	0.258618i	0.989512	−	0.115657i	0.394091	−	0.919071i	$-0.371059\pi$
$5$	2.21262	−	0.258618i	0.989512	−	0.115657i	0.595421	+	0.803414i	$0.296985\pi$
$6$	−1.25147	−	1.19743i	−0.510909	−	0.488848i
$7$	−2.58863	−	1.30006i	−0.978409	−	0.491376i	−0.113627	−	0.993523i	$-0.536247\pi$
$7$	−2.58863	−	1.30006i	−0.978409	−	0.491376i	−0.864782	+	0.502148i	$0.832543\pi$
$8$	0.766044	−	0.642788i	0.270838	−	0.227260i
$9$	2.98432	−	0.306371i	0.994772	−	0.102124i
$10$	−1.70650	−	1.43192i	−0.539643	−	0.452814i
$11$	2.24105	+	5.19534i	0.675702	+	1.56645i	0.817097	+	0.576500i	$0.195582\pi$
$11$	2.24105	+	5.19534i	0.675702	+	1.56645i	−0.141396	+	0.989953i	$0.545159\pi$
$12$	−0.0121703	+	1.73201i	−0.00351327	+	0.499988i
$13$	−3.63018	−	0.860369i	−1.00683	−	0.238623i	−0.306062	−	0.952012i	$-0.599012\pi$
$13$	−3.63018	−	0.860369i	−1.00683	−	0.238623i	−0.700769	+	0.713388i	$0.747160\pi$
$14$	0.830796	+	2.77505i	0.222040	+	0.741664i
$15$	3.80445	−	0.643297i	0.982305	−	0.166099i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	1.29783	−	7.36037i	0.314770	−	1.78515i	−0.258733	−	0.965949i	$-0.583305\pi$
$17$	1.29783	−	7.36037i	0.314770	−	1.78515i	0.573504	−	0.819203i	$-0.305584\pi$
$18$	−2.27081	−	1.96047i	−0.535234	−	0.462087i
$19$	−0.140098	−	0.794532i	−0.0321406	−	0.182278i	0.964511	−	0.264042i	$-0.0850558\pi$
$19$	−0.140098	−	0.794532i	−0.0321406	−	0.182278i	−0.996652	+	0.0817638i	$0.973945\pi$
$20$	0.129528	+	2.22391i	0.0289633	+	0.497281i
$21$	−4.59290	−	2.01958i	−1.00225	−	0.440708i
$22$	2.24105	−	5.19534i	0.477793	−	1.10765i
$23$	−4.42192	+	2.22077i	−0.922034	+	0.463063i	−0.845483	−	0.534003i	$-0.820687\pi$
$23$	−4.42192	+	2.22077i	−0.922034	+	0.463063i	−0.0765513	+	0.997066i	$0.524391\pi$
$24$	1.26817	−	1.17972i	0.258864	−	0.240810i
$25$	−0.0364359	+	0.00863547i	−0.00728718	+	0.00172709i
$26$	1.86537	+	3.23092i	0.365830	+	0.633635i
$27$	5.13509	−	0.794240i	0.988249	−	0.152852i
$28$	1.44837	−	2.50866i	0.273717	−	0.474091i
$29$	−1.91151	+	6.38489i	−0.354958	+	1.18564i	0.575054	+	0.818116i	$0.304981\pi$
$29$	−1.91151	+	6.38489i	−0.354958	+	1.18564i	−0.930012	+	0.367528i	$0.880204\pi$
$30$	−3.07869	−	2.32580i	−0.562089	−	0.424631i
$31$	2.05098	+	1.34895i	0.368366	+	0.242278i	0.720173	−	0.693794i	$-0.244062\pi$
$31$	2.05098	+	1.34895i	0.368366	+	0.242278i	−0.351807	+	0.936073i	$0.614433\pi$
$32$	0.597159	+	0.802123i	0.105564	+	0.141797i
$33$	4.33662	+	8.78835i	0.754909	+	1.52986i
$34$	−6.24436	+	4.10698i	−1.07090	+	0.704342i
$35$	−6.06386	−	2.20706i	−1.02498	−	0.373062i
$36$	0.132330	+	2.99708i	0.0220551	+	0.499513i
$37$	−6.41853	+	2.33615i	−1.05520	+	0.384061i	−0.810623	−	0.585569i	$-0.800871\pi$
$37$	−6.41853	+	2.33615i	−1.05520	+	0.384061i	−0.244577	+	0.969630i	$0.578649\pi$
$38$	−0.481781	+	0.647144i	−0.0781552	+	0.104981i
$39$	−6.35563	−	1.16677i	−1.01771	−	0.186833i
$40$	1.52873	−	1.62036i	0.241713	−	0.256201i
$41$	2.55518	−	2.70834i	0.399053	−	0.422971i	−0.496424	−	0.868080i	$-0.665354\pi$
$41$	2.55518	−	2.70834i	0.399053	−	0.422971i	0.895476	+	0.445109i	$0.146835\pi$
$42$	1.68285	+	4.72667i	0.259670	+	0.729341i
$43$	−6.77615	+	9.10195i	−1.03335	+	1.38803i	−0.114506	+	0.993423i	$0.536528\pi$
$43$	−6.77615	+	9.10195i	−1.03335	+	1.38803i	−0.918848	+	0.394612i	$0.870879\pi$
$44$	−5.31685	+	1.93518i	−0.801546	+	0.291739i
$45$	6.52391	−	1.44968i	0.972527	−	0.216105i
$46$	4.64984	+	1.69240i	0.685581	+	0.249531i
$47$	3.20034	−	2.10490i	0.466818	−	0.307031i	−0.294221	−	0.955738i	$-0.595060\pi$
$47$	3.20034	−	2.10490i	0.466818	−	0.307031i	0.761039	+	0.648706i	$0.224690\pi$
$48$	−1.72837	−	0.112857i	−0.249469	−	0.0162895i
$49$	0.830731	+	1.11587i	0.118676	+	0.159409i
$50$	0.0312851	+	0.0205765i	0.00442438	+	0.00290996i
$51$	1.59315	−	12.8468i	0.223086	−	1.79891i
$52$	1.06999	−	3.57401i	0.148381	−	0.495627i
$53$	−1.66998	+	2.89249i	−0.229389	+	0.397314i	−0.957627	−	0.288010i	$-0.907006\pi$
$53$	−1.66998	+	2.89249i	−0.229389	+	0.397314i	0.728238	+	0.685324i	$0.240340\pi$
$54$	−4.10162	−	3.19009i	−0.558160	−	0.434116i
$55$	6.30219	+	10.9157i	0.849787	+	1.47187i
$56$	−2.81866	+	0.668036i	−0.376660	+	0.0892700i
$57$	−0.312700	−	1.36196i	−0.0414182	−	0.180397i
$58$	5.95596	−	2.99119i	0.782055	−	0.392763i
$59$	−1.15336	+	2.67379i	−0.150155	+	0.348098i	−0.976647	−	0.214850i	$-0.931074\pi$
$59$	−1.15336	+	2.67379i	−0.150155	+	0.348098i	0.826492	+	0.562948i	$0.190333\pi$
$60$	0.421000	+	3.83542i	0.0543508	+	0.495150i
$61$	−0.409169	−	7.02515i	−0.0523887	−	0.899479i	−0.917460	−	0.397829i	$-0.869764\pi$
$61$	−0.409169	−	7.02515i	−0.0523887	−	0.899479i	0.865071	−	0.501650i	$-0.167273\pi$
$62$	−0.426276	−	2.41753i	−0.0541371	−	0.307027i
$63$	−8.12358	−	3.08670i	−1.02347	−	0.388888i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	−8.25471	−	0.964837i	−1.02387	−	0.119673i
$66$	3.41645	−	9.18528i	0.420536	−	1.13063i
$67$	−0.117994	−	0.394126i	−0.0144152	−	0.0481501i	0.950479	−	0.310788i	$-0.100593\pi$
$67$	−0.117994	−	0.394126i	−0.0144152	−	0.0481501i	−0.964895	+	0.262638i	$0.915408\pi$
$68$	7.27245	+	1.72360i	0.881915	+	0.209018i
$69$	−7.45231	+	4.23305i	−0.897152	+	0.509600i
$70$	2.55591	+	5.92527i	0.305490	+	0.708205i
$71$	0.709941	+	0.595711i	0.0842545	+	0.0706979i	0.683942	−	0.729536i	$-0.260264\pi$
$71$	0.709941	+	0.595711i	0.0842545	+	0.0706979i	−0.599688	+	0.800234i	$0.704709\pi$
$72$	2.08919	−	2.15297i	0.246213	−	0.253731i
$73$	3.44620	−	2.89170i	0.403347	−	0.338448i	−0.418439	−	0.908245i	$-0.637423\pi$
$73$	3.44620	−	2.89170i	0.403347	−	0.338448i	0.821786	+	0.569797i	$0.192978\pi$
$74$	6.10392	+	3.06550i	0.709566	+	0.356357i
$75$	−0.0622616	+	0.0181642i	−0.00718935	+	0.00209742i
$76$	0.801334	−	0.0936625i	0.0919193	−	0.0107438i
$77$	0.952994	−	16.3623i	0.108604	−	1.86466i
$78$	3.51282	+	5.42360i	0.397748	+	0.614102i
$79$	1.27120	+	1.34739i	0.143021	+	0.151593i	0.794924	−	0.606709i	$-0.207511\pi$
$79$	1.27120	+	1.34739i	0.143021	+	0.151593i	−0.651903	+	0.758302i	$0.726029\pi$
$80$	−2.22768			−0.249062
$81$	8.81227	−	1.82862i	0.979141	−	0.203180i
$82$	−3.72345			−0.411186
$83$	−2.38885	−	2.53203i	−0.262210	−	0.277927i	0.582871	−	0.812565i	$-0.301929\pi$
$83$	−2.38885	−	2.53203i	−0.262210	−	0.277927i	−0.845081	+	0.534638i	$0.820448\pi$
$84$	2.28321	−	4.46770i	0.249119	−	0.487466i
$85$	0.968081	−	16.6213i	0.105003	−	1.80283i
$86$	11.2706	−	1.31734i	1.21534	−	0.142053i
$87$	−2.74107	+	11.2138i	−0.293874	+	1.20224i
$88$	5.05624	+	2.53934i	0.538997	+	0.270695i
$89$	13.5689	−	11.3857i	1.43830	−	1.20688i	0.497709	−	0.867344i	$-0.334175\pi$
$89$	13.5689	−	11.3857i	1.43830	−	1.20688i	0.940593	−	0.339535i	$-0.110270\pi$
$90$	−5.53144	−	3.75049i	−0.583065	−	0.395336i
$91$	8.27866	+	6.94662i	0.867839	+	0.728203i
$92$	−1.95990	−	4.54357i	−0.204334	−	0.473699i
$93$	3.66721	+	2.15176i	0.380272	+	0.223127i
$94$	−3.72726	−	0.883376i	−0.384437	−	0.0911133i
$95$	−0.515462	−	1.72176i	−0.0528853	−	0.176649i
$96$	1.10399	+	1.33462i	0.112676	+	0.136214i
$97$	3.60360	+	0.421200i	0.365890	+	0.0427664i	0.297052	−	0.954861i	$-0.403997\pi$
$97$	3.60360	+	0.421200i	0.365890	+	0.0427664i	0.0688382	+	0.997628i	$0.478071\pi$
$98$	0.241569	−	1.37001i	0.0244022	−	0.138391i
$99$	8.27970	+	14.8179i	0.832141	+	1.48926i
$100$	−0.00650230	−	0.0368764i	−0.000650230	−	0.00368764i
$101$	−0.169381	−	2.90816i	−0.0168541	−	0.289373i	−0.996195	−	0.0871557i	$-0.972222\pi$
$101$	−0.169381	−	2.90816i	−0.0168541	−	0.289373i	0.979341	−	0.202218i	$-0.0648148\pi$
$102$	−10.4377	+	7.65719i	−1.03349	+	0.758174i
$103$	3.13961	−	7.27843i	0.309355	−	0.717165i	−0.690627	−	0.723211i	$-0.742665\pi$
$103$	3.13961	−	7.27843i	0.309355	−	0.717165i	0.999982	+	0.00604605i	$0.00192453\pi$
$104$	−3.33391	+	1.67435i	−0.326917	+	0.164184i
$105$	−10.6846	−	3.28075i	−1.04271	−	0.320168i
$106$	3.24993	−	0.770248i	0.315661	−	0.0748131i
$107$	−0.784150	−	1.35819i	−0.0758066	−	0.131301i	0.825630	−	0.564212i	$-0.190820\pi$
$107$	−0.784150	−	1.35819i	−0.0758066	−	0.131301i	−0.901437	+	0.432911i	$0.857486\pi$
$108$	0.494317	+	5.17259i	0.0475657	+	0.497732i
$109$	7.99151	−	13.8417i	0.765448	−	1.32579i	−0.174561	−	0.984646i	$-0.555851\pi$
$109$	7.99151	−	13.8417i	0.765448	−	1.32579i	0.940009	−	0.341149i	$-0.110816\pi$
$110$	3.61498	−	12.0749i	0.344674	−	1.15129i
$111$	−10.8958	+	4.60945i	−1.03418	+	0.437510i
$112$	2.42020	+	1.59179i	0.228687	+	0.150410i
$113$	2.55968	+	3.43825i	0.240794	+	0.323443i	0.906048	−	0.423174i	$-0.139084\pi$
$113$	2.55968	+	3.43825i	0.240794	+	0.323443i	−0.665254	+	0.746617i	$0.731677\pi$
$114$	−0.776069	+	1.16209i	−0.0726855	+	0.108839i
$115$	−9.20968	+	6.05730i	−0.858807	+	0.564846i
$116$	−6.26294	−	2.27952i	−0.581499	−	0.211648i
$117$	−11.0972	−	1.45543i	−1.02594	−	0.134554i
$118$	2.73633	−	0.995943i	0.251900	−	0.0916840i
$119$	−12.9285	+	17.3660i	−1.18515	+	1.59194i
$120$	2.50087	−	2.93825i	0.228297	−	0.268224i
$121$	−14.4206	+	15.2849i	−1.31096	+	1.38954i
$122$	−4.82912	+	5.11857i	−0.437208	+	0.463414i
$123$	4.18008	−	4.91112i	0.376905	−	0.442821i
$124$	−1.46592	+	1.96907i	−0.131643	+	0.176828i
$125$	−10.5451	+	3.83809i	−0.943178	+	0.343289i
$126$	3.32955	+	8.02710i	0.296620	+	0.715111i
$127$	11.7885	+	4.29066i	1.04606	+	0.380734i	0.807174	−	0.590314i	$-0.200996\pi$
$127$	11.7885	+	4.29066i	1.04606	+	0.380734i	0.238885	+	0.971048i	$0.423218\pi$
$128$	−0.835488	+	0.549509i	−0.0738474	+	0.0485702i
$129$	−10.9152	+	16.3445i	−0.961034	+	1.43905i
$130$	4.96293	+	6.66637i	0.435277	+	0.584679i
$131$	1.74145	+	1.14537i	0.152151	+	0.100071i	0.623302	−	0.781981i	$-0.285791\pi$
$131$	1.74145	+	1.14537i	0.152151	+	0.100071i	−0.471151	+	0.882053i	$0.656161\pi$
$132$	−9.02564	+	3.81829i	−0.785581	+	0.332339i
$133$	−0.670278	+	2.23888i	−0.0581204	+	0.194136i
$134$	−0.205705	+	0.356291i	−0.0177702	+	0.0307788i
$135$	11.1566	−	3.08538i	0.960206	−	0.265547i
$136$	−3.73696	−	6.47260i	−0.320441	−	0.555021i
$137$	6.61393	−	1.56753i	0.565066	−	0.133923i	0.0618529	−	0.998085i	$-0.480299\pi$
$137$	6.61393	−	1.56753i	0.565066	−	0.133923i	0.503214	+	0.864162i	$0.332151\pi$
$138$	8.19309	+	2.51571i	0.697443	+	0.214152i
$139$	−7.06707	+	3.54921i	−0.599421	+	0.301040i	−0.722516	−	0.691354i	$-0.757014\pi$
$139$	−7.06707	+	3.54921i	−0.599421	+	0.301040i	0.123095	+	0.992395i	$0.460718\pi$
$140$	2.55591	−	5.92527i	0.216014	−	0.500777i
$141$	5.34950	−	3.92444i	0.450509	−	0.330497i
$142$	−0.0538864	−	0.925194i	−0.00452205	−	0.0776405i
$143$	−3.66551	−	20.7881i	−0.306525	−	1.73839i
$144$	−2.99970	−	0.0421582i	−0.249975	−	0.00351318i
$145$	−2.57819	+	14.6217i	−0.214107	+	1.21426i
$146$	−4.46827	−	0.522266i	−0.369797	−	0.0432230i
$147$	1.53581	+	1.85664i	0.126671	+	0.153133i
$148$	−1.95900	−	6.54350i	−0.161029	−	0.537873i
$149$	10.0871	+	2.39068i	0.826364	+	0.195852i	0.621974	−	0.783038i	$-0.286331\pi$
$149$	10.0871	+	2.39068i	0.826364	+	0.195852i	0.204390	+	0.978890i	$0.434479\pi$
$150$	0.0559386	+	0.0328224i	0.00456737	+	0.00267994i
$151$	−8.51417	−	19.7381i	−0.692873	−	1.60626i	−0.791524	−	0.611138i	$-0.790712\pi$
$151$	−8.51417	−	19.7381i	−0.692873	−	1.60626i	0.0986508	−	0.995122i	$-0.468547\pi$
$152$	−0.618037	−	0.518594i	−0.0501294	−	0.0420635i
$153$	1.61813	−	22.3633i	0.130818	−	1.80796i
$154$	−12.5555	+	10.5353i	−1.01175	+	0.848958i
$155$	4.88688	+	2.45429i	0.392524	+	0.197133i
$156$	1.53435	−	6.27703i	0.122846	−	0.502565i
$157$	7.73541	−	0.904140i	0.617353	−	0.0721582i	0.198332	−	0.980135i	$-0.436448\pi$
$157$	7.73541	−	0.904140i	0.617353	−	0.0721582i	0.419021	+	0.907977i	$0.362373\pi$
$158$	0.107708	−	1.84927i	0.00856876	−	0.147120i
$159$	−2.63256	+	5.15128i	−0.208775	+	0.408523i
$160$	1.52873	+	1.62036i	0.120856	+	0.128100i
$161$	14.3338			1.12966
$162$	−7.37744	−	5.15494i	−0.579626	−	0.405011i
$163$	11.0833			0.868109			0.434054	−	0.900887i	$-0.357083\pi$
$163$	11.0833			0.868109			0.434054	+	0.900887i	$0.357083\pi$
$164$	2.55518	+	2.70834i	0.199526	+	0.211486i
$165$	11.8681	+	18.3237i	0.923931	+	1.42650i
$166$	−0.202406	+	3.47517i	−0.0157097	+	0.269726i
$167$	−8.41089	+	0.983092i	−0.650854	+	0.0760739i	−0.435112	−	0.900376i	$-0.643291\pi$
$167$	−8.41089	+	0.983092i	−0.650854	+	0.0760739i	−0.215742	+	0.976450i	$0.569217\pi$
$168$	−4.81652	+	1.40517i	−0.371603	+	0.108411i
$169$	0.820757	+	0.412200i	0.0631352	+	0.0317077i
$170$	−12.7542	+	10.7021i	−0.978206	+	0.820812i
$171$	−0.661517	−	2.32821i	−0.0505875	−	0.178043i
$172$	−8.69256	−	7.29392i	−0.662801	−	0.556156i
$173$	5.44260	+	12.6174i	0.413793	+	0.959280i	0.989882	+	0.141893i	$0.0453189\pi$
$173$	5.44260	+	12.6174i	0.413793	+	0.959280i	−0.576089	+	0.817387i	$0.695422\pi$
$174$	10.0376	−	5.70157i	0.760951	−	0.432235i
$175$	0.105546	+	0.0250148i	0.00797850	+	0.00189094i
$176$	−1.62275	−	5.42038i	−0.122320	−	0.408576i
$177$	−1.75828	+	4.72723i	−0.132161	+	0.355320i
$178$	−17.5932	−	2.05635i	−1.31867	−	0.154130i
$179$	−1.56628	+	8.88284i	−0.117070	+	0.663935i	0.868635	+	0.495452i	$0.164998\pi$
$179$	−1.56628	+	8.88284i	−0.117070	+	0.663935i	−0.985705	+	0.168482i	$0.946113\pi$
$180$	1.06789	+	6.59717i	0.0795962	+	0.491724i
$181$	1.98404	+	11.2521i	0.147473	+	0.836358i	0.965349	+	0.260964i	$0.0840404\pi$
$181$	1.98404	+	11.2521i	0.147473	+	0.836358i	−0.817876	+	0.575395i	$0.804849\pi$
$182$	−0.628372	−	10.7887i	−0.0465781	−	0.799714i
$183$	−1.32990	−	12.1158i	−0.0983094	−	0.895624i
$184$	−1.95990	+	4.54357i	−0.144486	+	0.334956i
$185$	−13.5976	+	6.82896i	−0.999713	+	0.502075i
$186$	−0.951456	−	4.14406i	−0.0697641	−	0.303857i
$187$	41.1481	−	9.75228i	3.00905	−	0.713157i
$188$	1.91525	+	3.31732i	0.139684	+	0.241940i
$189$	−14.3254	−	4.61992i	−1.04202	−	0.336050i
$190$	−0.898634	+	1.55648i	−0.0651938	+	0.112919i
$191$	6.03754	−	20.1668i	0.436861	−	1.45922i	−0.402388	−	0.915469i	$-0.631820\pi$
$191$	6.03754	−	20.1668i	0.436861	−	1.45922i	0.839249	−	0.543748i	$-0.182995\pi$
$192$	0.213162	−	1.71888i	0.0153836	−	0.124050i
$193$	−16.7511	−	11.0174i	−1.20577	−	0.793048i	−0.222453	−	0.974943i	$-0.571407\pi$
$193$	−16.7511	−	11.0174i	−1.20577	−	0.793048i	−0.983318	+	0.181895i	$0.941777\pi$
$194$	−2.16657	−	2.91021i	−0.155551	−	0.208941i
$195$	−14.3643	−	0.937944i	−1.02865	−	0.0671675i
$196$	−1.16228	+	0.764444i	−0.0830201	+	0.0546032i
$197$	18.6836	+	6.80027i	1.33115	+	0.484499i	0.907014	−	0.421100i	$-0.138356\pi$
$197$	18.6836	+	6.80027i	1.33115	+	0.484499i	0.424136	+	0.905599i	$0.360578\pi$
$198$	5.09630	−	16.1911i	0.362178	−	1.15065i
$199$	−21.2644	+	7.73960i	−1.50739	+	0.548646i	−0.957962	−	0.286894i	$-0.907377\pi$
$199$	−21.2644	+	7.73960i	−1.50739	+	0.548646i	−0.549430	+	0.835540i	$0.685155\pi$
$200$	−0.0223608	+	0.0300357i	−0.00158114	+	0.00212385i
$201$	−0.239006	−	0.671304i	−0.0168582	−	0.0473501i
$202$	−1.99909	+	2.11891i	−0.140655	+	0.149086i
$203$	13.2489	−	14.0430i	0.929891	−	0.985627i
$204$	12.7324	+	2.33743i	0.891448	+	0.163653i
$205$	4.95322	−	6.65333i	0.345948	−	0.464688i
$206$	−7.44867	+	2.71109i	−0.518973	+	0.188891i
$207$	−12.5160	+	7.98223i	−0.869924	+	0.554803i
$208$	3.50575	+	1.27599i	0.243080	+	0.0884740i
$209$	3.81390	−	2.50844i	0.263813	−	0.173512i
$210$	4.94591	+	10.0231i	0.341300	+	0.691659i
$211$	8.09444	+	10.8727i	0.557244	+	0.748508i	0.988083	−	0.153920i	$-0.0491899\pi$
$211$	8.09444	+	10.8727i	0.557244	+	0.748508i	−0.430839	+	0.902429i	$0.641782\pi$
$212$	−2.79050	−	1.83534i	−0.191652	−	0.126052i
$213$	1.28080	+	0.967582i	0.0877590	+	0.0662976i
$214$	−0.449793	+	1.50241i	−0.0307472	+	0.102703i
$215$	−12.6391	+	21.8916i	−0.861979	+	1.49299i
$216$	3.42318	−	3.90920i	0.232918	−	0.265987i
$217$	−3.55550	−	6.15831i	−0.241363	−	0.418053i
$218$	−15.5522	+	3.68594i	−1.05333	+	0.249643i
$219$	5.70510	−	5.30721i	0.385515	−	0.358628i
$220$	−11.2637	+	5.65683i	−0.759397	+	0.381384i
$221$	−11.0440	+	25.6029i	−0.742900	+	1.72223i
$222$	10.8299	+	4.76211i	0.726858	+	0.319612i
$223$	−1.52468	−	26.1777i	−0.102100	−	1.75299i	−0.528935	−	0.848662i	$-0.677409\pi$
$223$	−1.52468	−	26.1777i	−0.102100	−	1.75299i	0.426835	−	0.904329i	$-0.359628\pi$
$224$	−0.503015	−	2.85274i	−0.0336091	−	0.190607i
$225$	−0.106091	+	0.0369339i	−0.00707271	+	0.00246226i
$226$	0.744331	−	4.22131i	0.0495122	−	0.280797i
$227$	−5.59370	−	0.653809i	−0.371267	−	0.0433948i	−0.0715860	−	0.997434i	$-0.522806\pi$
$227$	−5.59370	−	0.653809i	−0.371267	−	0.0433948i	−0.299681	+	0.954040i	$0.596880\pi$
$228$	1.37784	−	0.232980i	0.0912498	−	0.0154295i
$229$	1.29122	+	4.31297i	0.0853261	+	0.285009i	0.989994	−	0.141108i	$-0.0450664\pi$
$229$	1.29122	+	4.31297i	0.0853261	+	0.285009i	−0.904668	+	0.426117i	$0.859881\pi$
$230$	10.7260	+	2.54211i	0.707251	+	0.167622i
$231$	0.199472	−	28.3876i	0.0131243	−	1.86777i
$232$	2.63982	+	6.11980i	0.173313	+	0.401785i
$233$	18.4568	+	15.4871i	1.20914	+	1.01459i	0.999321	+	0.0368530i	$0.0117333\pi$
$233$	18.4568	+	15.4871i	1.20914	+	1.01459i	0.209823	+	0.977739i	$0.432711\pi$
$234$	6.55672	+	9.07058i	0.428626	+	0.592963i
$235$	6.53677	−	5.48500i	0.426412	−	0.357802i
$236$	−2.60221	−	1.30688i	−0.169389	−	0.0850705i
$237$	2.31822	+	2.21812i	0.150584	+	0.144082i
$238$	21.5036	−	2.51342i	1.39387	−	0.162921i
$239$	−0.945595	+	16.2352i	−0.0611655	+	1.05017i	0.818478	+	0.574538i	$0.194818\pi$
$239$	−0.945595	+	16.2352i	−0.0611655	+	1.05017i	−0.879644	+	0.475633i	$0.842219\pi$
$240$	−3.85341	+	0.197278i	−0.248736	+	0.0127342i
$241$	−5.62866	−	5.96603i	−0.362574	−	0.384306i	0.520247	−	0.854016i	$-0.325840\pi$
$241$	−5.62866	−	5.96603i	−0.362574	−	0.384306i	−0.882821	+	0.469710i	$0.844358\pi$
$242$	21.0138			1.35082
$243$	15.0814	−	3.94351i	0.967473	−	0.252976i
$244$	7.03706			0.450501
$245$	2.12667	+	2.25414i	0.135868	+	0.144012i
$246$	−6.44076	+	0.329739i	−0.410648	+	0.0210234i
$247$	−0.175012	+	3.00483i	−0.0111357	+	0.191193i
$248$	2.43823	−	0.284988i	0.154827	−	0.0180967i
$249$	−4.35643	−	4.16832i	−0.276077	−	0.264157i
$250$	10.0282	+	5.03634i	0.634238	+	0.318526i
$251$	−9.58840	+	8.04563i	−0.605215	+	0.507835i	−0.893117	−	0.449824i	$-0.851487\pi$
$251$	−9.58840	+	8.04563i	−0.605215	+	0.507835i	0.287902	+	0.957660i	$0.407042\pi$
$252$	3.55382	−	7.93036i	0.223870	−	0.499566i
$253$	−21.4474	−	17.9965i	−1.34839	−	1.13143i
$254$	−4.96884	−	11.5191i	−0.311773	−	0.722770i
$255$	0.202629	−	28.8370i	0.0126892	−	1.80585i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	−3.76253	−	12.5677i	−0.234700	−	0.783953i	−0.991477	−	0.130280i	$-0.958412\pi$
$257$	−3.76253	−	12.5677i	−0.234700	−	0.783953i	0.756777	−	0.653673i	$-0.226773\pi$
$258$	19.3791	−	3.27682i	1.20649	−	0.204006i
$259$	19.6523	+	2.29703i	1.22114	+	0.142730i
$260$	1.44317	−	8.18464i	0.0895018	−	0.507590i
$261$	−3.74840	+	19.6401i	−0.232020	+	1.21569i
$262$	−0.361943	−	2.05268i	−0.0223609	−	0.126815i
$263$	0.388598	+	6.67197i	0.0239620	+	0.411411i	0.988866	+	0.148808i	$0.0475438\pi$
$263$	0.388598	+	6.67197i	0.0239620	+	0.411411i	−0.964904	+	0.262603i	$0.915419\pi$
$264$	8.97109	+	3.94474i	0.552132	+	0.242782i
$265$	−2.94698	+	6.83186i	−0.181031	+	0.419678i
$266$	2.08848	−	1.04887i	0.128053	−	0.0643105i
$267$	22.4630	−	20.8964i	1.37472	−	1.27884i
$268$	0.400320	−	0.0948775i	0.0244534	−	0.00579557i
$269$	0.548920	+	0.950757i	0.0334682	+	0.0579687i	0.882274	−	0.470736i	$-0.156011\pi$
$269$	0.548920	+	0.950757i	0.0334682	+	0.0579687i	−0.848806	+	0.528704i	$0.822678\pi$
$270$	−9.90034	−	5.99769i	−0.602515	−	0.365008i
$271$	4.63384	−	8.02605i	0.281486	−	0.487548i	−0.690265	−	0.723557i	$-0.742506\pi$
$271$	4.63384	−	8.02605i	0.281486	−	0.487548i	0.971751	+	0.236009i	$0.0758394\pi$
$272$	−2.14354	+	7.15993i	−0.129971	+	0.434135i
$273$	14.9355	+	11.2830i	0.903936	+	0.682879i
$274$	−5.67894	−	3.73510i	−0.343077	−	0.225645i
$275$	−0.126519	−	0.169944i	−0.00762938	−	0.0102480i
$276$	−3.79258	−	7.68583i	−0.228286	−	0.462633i
$277$	−20.7086	+	13.6203i	−1.24426	+	0.818363i	−0.988914	−	0.148486i	$-0.952560\pi$
$277$	−20.7086	+	13.6203i	−1.24426	+	0.818363i	−0.255346	+	0.966850i	$0.582190\pi$
$278$	7.43132	+	2.70478i	0.445701	+	0.162222i
$279$	6.53404	+	3.39733i	0.391182	+	0.203393i
$280$	−6.06386	+	2.20706i	−0.362385	+	0.131897i
$281$	−1.03043	+	1.38411i	−0.0614705	+	0.0825692i	−0.831795	−	0.555083i	$-0.812687\pi$
$281$	−1.03043	+	1.38411i	−0.0614705	+	0.0825692i	0.770325	+	0.637652i	$0.220094\pi$
$282$	−6.52558	−	1.19797i	−0.388593	−	0.0713383i
$283$	−7.88870	+	8.36154i	−0.468935	+	0.497042i	−0.918068	−	0.396423i	$-0.870251\pi$
$283$	−7.88870	+	8.36154i	−0.468935	+	0.497042i	0.449133	+	0.893465i	$0.351733\pi$
$284$	−0.635983	+	0.674102i	−0.0377386	+	0.0400006i
$285$	−1.04411	−	2.93263i	−0.0618480	−	0.173714i
$286$	−12.6053	+	16.9319i	−0.745368	+	1.00120i
$287$	−10.1354	+	3.68899i	−0.598274	+	0.217754i
$288$	2.02786	+	2.21084i	0.119493	+	0.130275i
$289$	−36.5159	−	13.2907i	−2.14799	−	0.781806i
$290$	12.4047	−	8.15868i	0.728427	−	0.479094i
$291$	6.27075	+	0.409460i	0.367598	+	0.0240030i
$292$	2.68643	+	3.60850i	0.157211	+	0.211172i
$293$	−9.63418	−	6.33650i	−0.562835	−	0.370182i	0.235981	−	0.971758i	$-0.424170\pi$
$293$	−9.63418	−	6.33650i	−0.562835	−	0.370182i	−0.798816	+	0.601575i	$0.794540\pi$
$294$	0.296538	−	2.39121i	0.0172945	−	0.139458i
$295$	−1.86046	+	6.21436i	−0.108320	+	0.361814i
$296$	−3.41523	+	5.91535i	−0.198506	+	0.343823i
$297$	15.6343	+	24.8986i	0.907197	+	1.44476i
$298$	−5.18324	−	8.97764i	−0.300257	−	0.520061i
$299$	17.9631	−	4.25732i	1.03883	−	0.246207i
$300$	−0.0145133	−	0.0632124i	−0.000837924	−	0.00364957i
$301$	29.3740	−	14.7522i	1.69309	−	0.850301i
$302$	−8.51417	+	19.7381i	−0.489935	+	1.13580i
$303$	−0.550533	−	5.01550i	−0.0316273	−	0.288133i
$304$	0.0469106	+	0.805424i	0.00269051	+	0.0461943i
$305$	−2.72216	−	15.4381i	−0.155871	−	0.883986i
$306$	−17.3769	+	14.1696i	−0.993371	+	0.810024i
$307$	3.50034	−	19.8514i	0.199775	−	1.13298i	−0.705677	−	0.708533i	$-0.749357\pi$
$307$	3.50034	−	19.8514i	0.199775	−	1.13298i	0.905452	−	0.424448i	$-0.139532\pi$
$308$	16.2792	+	1.90276i	0.927593	+	0.108420i
$309$	4.78629	−	12.8682i	0.272283	−	0.732044i
$310$	−1.56840	−	5.23882i	−0.0890792	−	0.297545i
$311$	−12.5976	−	2.98568i	−0.714343	−	0.169302i	−0.142654	−	0.989773i	$-0.545564\pi$
$311$	−12.5976	−	2.98568i	−0.714343	−	0.169302i	−0.571689	+	0.820470i	$0.693712\pi$
$312$	−5.61868	+	3.19152i	−0.318095	+	0.180684i
$313$	13.5386	+	31.3861i	0.765249	+	1.77405i	0.619921	+	0.784664i	$0.287165\pi$
$313$	13.5386	+	31.3861i	0.765249	+	1.77405i	0.145328	+	0.989383i	$0.453576\pi$
$314$	−5.96601	−	5.00607i	−0.336681	−	0.282509i
$315$	−18.7726	−	4.72878i	−1.05772	−	0.266437i
$316$	−1.41902	+	1.19070i	−0.0798263	+	0.0669822i
$317$	−4.45315	−	2.23645i	−0.250114	−	0.125612i	0.319326	−	0.947645i	$-0.396544\pi$
$317$	−4.45315	−	2.23645i	−0.250114	−	0.125612i	−0.569440	+	0.822033i	$0.692840\pi$
$318$	5.55347	−	1.62017i	0.311423	−	0.0908546i
$319$	−37.4554	+	4.37791i	−2.09710	+	0.245116i
$320$	0.129528	−	2.22391i	0.00724084	−	0.124320i
$321$	−1.47669	−	2.27993i	−0.0824207	−	0.127253i
$322$	−9.83647	−	10.4261i	−0.548165	−	0.581021i
$323$	−6.02987			−0.335511
$324$	1.31313	+	8.90369i	0.0729519	+	0.494649i
$325$	0.139699			0.00774909
$326$	−7.60580	−	8.06168i	−0.421246	−	0.446495i
$327$	12.5978	−	24.6509i	0.696661	−	1.36320i
$328$	0.216499	−	3.71715i	0.0119542	−	0.205245i
$329$	−11.0210	+	1.28817i	−0.607607	+	0.0710190i
$330$	5.18381	−	21.2071i	0.285359	−	1.16741i
$331$	−0.339951	−	0.170730i	−0.0186854	−	0.00938417i	0.439432	−	0.898276i	$-0.355180\pi$
$331$	−0.339951	−	0.170730i	−0.0186854	−	0.00938417i	−0.458117	+	0.888892i	$0.651476\pi$
$332$	2.66665	−	2.23758i	0.146351	−	0.122803i
$333$	−18.4392	+	8.93827i	−1.01046	+	0.489814i
$334$	6.48698	+	5.44322i	0.354952	+	0.297840i
$335$	−0.363002	−	0.841534i	−0.0198329	−	0.0459779i
$336$	4.32739	+	2.53913i	0.236078	+	0.138521i
$337$	10.7920	+	2.55776i	0.587879	+	0.139330i	0.513781	−	0.857921i	$-0.328244\pi$
$337$	10.7920	+	2.55776i	0.587879	+	0.139330i	0.0740974	+	0.997251i	$0.476392\pi$
$338$	−0.263415	−	0.879866i	−0.0143279	−	0.0478584i
$339$	4.73218	+	5.72075i	0.257017	+	0.310708i
$340$	16.5369	+	1.93289i	0.896840	+	0.104826i
$341$	−2.41190	+	13.6786i	−0.130612	+	0.740736i
$342$	−1.23952	+	2.07889i	−0.0670256	+	0.112413i
$343$	2.82134	+	16.0006i	0.152338	+	0.863952i
$344$	0.659788	+	11.3281i	0.0355734	+	0.610772i
$345$	−15.3944	+	11.2934i	−0.828804	+	0.608017i
$346$	5.44260	−	12.6174i	0.292596	−	0.678313i
$347$	−6.31802	+	3.17303i	−0.339169	+	0.170337i	−0.610228	−	0.792226i	$-0.708922\pi$
$347$	−6.31802	+	3.17303i	−0.339169	+	0.170337i	0.271059	+	0.962563i	$0.412626\pi$
$348$	−11.0354	−	3.38846i	−0.591560	−	0.181640i
$349$	−9.52680	+	2.25789i	−0.509958	+	0.120862i	−0.477536	−	0.878612i	$-0.658470\pi$
$349$	−9.52680	+	2.25789i	−0.509958	+	0.120862i	−0.0324218	+	0.999474i	$0.510322\pi$
$350$	−0.0542347	−	0.0939373i	−0.00289897	−	0.00502116i
$351$	−19.3247	−	1.53484i	−1.03147	−	0.0819236i
$352$	−2.82904	+	4.90004i	−0.150788	+	0.261173i
$353$	−3.61221	+	12.0656i	−0.192258	+	0.642188i	0.806446	+	0.591307i	$0.201388\pi$
$353$	−3.61221	+	12.0656i	−0.192258	+	0.642188i	−0.998705	+	0.0508805i	$0.983797\pi$
$354$	4.64507	−	1.96509i	0.246883	−	0.104443i
$355$	1.72489	+	1.13448i	0.0915475	+	0.0602118i
$356$	10.5774	+	14.2080i	0.560604	+	0.753021i
$357$	−20.8256	+	31.1844i	−1.10221	+	1.65045i
$358$	7.53599	−	4.95650i	0.398290	−	0.261959i
$359$	24.1126	+	8.77626i	1.27261	+	0.463193i	0.887982	−	0.459877i	$-0.152107\pi$
$359$	24.1126	+	8.77626i	1.27261	+	0.463193i	0.384630	+	0.923071i	$0.374329\pi$
$360$	4.06577	−	5.30401i	0.214285	−	0.279546i
$361$	17.2425	−	6.27576i	0.907500	−	0.330303i
$362$	6.82291	−	9.16477i	0.358604	−	0.481689i
$363$	−23.5909	+	27.7166i	−1.23820	+	1.45475i
$364$	−7.41623	+	7.86074i	−0.388716	+	0.412015i
$365$	6.87726	−	7.28947i	0.359972	−	0.381548i
$366$	−7.90006	+	9.28168i	−0.412943	+	0.485161i
$367$	−2.04913	+	2.75246i	−0.106964	+	0.143677i	−0.852382	−	0.522920i	$-0.824843\pi$
$367$	−2.04913	+	2.75246i	−0.106964	+	0.143677i	0.745418	+	0.666597i	$0.232250\pi$
$368$	4.64984	−	1.69240i	0.242389	−	0.0882226i
$369$	6.79572	−	8.86536i	0.353771	−	0.461512i
$370$	14.2984	+	5.20420i	0.743340	+	0.270553i
$371$	8.08336	−	5.31651i	0.419667	−	0.276020i
$372$	−2.36135	+	3.53589i	−0.122430	+	0.183327i
$373$	−2.47132	−	3.31955i	−0.127960	−	0.171880i	0.733526	−	0.679661i	$-0.237873\pi$
$373$	−2.47132	−	3.31955i	−0.127960	−	0.171880i	−0.861486	+	0.507781i	$0.830466\pi$
$374$	−35.3311	−	23.2376i	−1.82693	−	1.20159i
$375$	−17.9008	+	7.57291i	−0.924393	+	0.391063i
$376$	1.09860	−	3.66959i	0.0566561	−	0.189245i
$377$	12.4325	−	21.5337i	0.640306	−	1.10904i
$378$	6.47027	+	13.5903i	0.332795	+	0.699010i
$379$	−10.9856	−	19.0275i	−0.564290	−	0.977379i	−0.997115	−	0.0759015i	$-0.975817\pi$
$379$	−10.9856	−	19.0275i	−0.564290	−	0.977379i	0.432825	−	0.901478i	$-0.357517\pi$
$380$	1.74882	−	0.414479i	0.0897127	−	0.0212623i
$381$	20.7715	+	6.37796i	1.06416	+	0.326753i
$382$	−18.8120	+	9.44774i	−0.962505	+	0.483388i
$383$	4.12972	−	9.57376i	0.211019	−	0.489196i	−0.779529	−	0.626366i	$-0.784541\pi$
$383$	4.12972	−	9.57376i	0.211019	−	0.489196i	0.990548	+	0.137170i	$0.0438007\pi$
$384$	−1.39655	+	1.02452i	−0.0712675	+	0.0522824i
$385$	−2.12297	−	36.4499i	−0.108196	−	1.85766i
$386$	3.48156	+	19.7449i	0.177207	+	1.00499i
$387$	−17.4336	+	29.2391i	−0.886200	+	1.48631i
$388$	−0.630018	+	3.57301i	−0.0319843	+	0.181392i
$389$	10.8958	+	1.27354i	0.552439	+	0.0645708i	0.387733	−	0.921772i	$-0.373258\pi$
$389$	10.8958	+	1.27354i	0.552439	+	0.0645708i	0.164706	+	0.986343i	$0.447332\pi$
$390$	9.17515	+	11.0919i	0.464602	+	0.561659i
$391$	10.6068	+	35.4292i	0.536409	+	1.79173i
$392$	1.35364	+	0.320819i	0.0683692	+	0.0162038i
$393$	3.11376	+	1.82702i	0.157068	+	0.0921611i
$394$	−7.87512	−	18.2566i	−0.396743	−	0.919753i
$395$	3.16113	+	2.65250i	0.159054	+	0.133462i
$396$	−15.2743	+	7.40411i	−0.767561	+	0.372070i
$397$	−10.7858	+	9.05040i	−0.541326	+	0.454227i	−0.871991	−	0.489522i	$-0.837171\pi$
$397$	−10.7858	+	9.05040i	−0.541326	+	0.454227i	0.330665	+	0.943748i	$0.392727\pi$
$398$	20.2221	+	10.1559i	1.01364	+	0.509070i
$399$	−0.961166	+	3.93215i	−0.0481185	+	0.196853i
$400$	0.0371921	−	0.00434713i	0.00185960	−	0.000217356i
$401$	1.54726	−	26.5654i	0.0772664	−	1.32661i	−0.707452	−	0.706761i	$-0.750156\pi$
$401$	1.54726	−	26.5654i	0.0772664	−	1.32661i	0.784719	−	0.619852i	$-0.212807\pi$
$402$	−0.324273	+	0.634524i	−0.0161732	+	0.0316472i
$403$	−6.28482	−	6.66152i	−0.313069	−	0.331834i
$404$	2.91309			0.144932
$405$	19.0253	−	6.32504i	0.945373	−	0.314294i
$406$	−19.3065			−0.958164
$407$	−26.5213	−	28.1110i	−1.31461	−	1.39341i
$408$	−7.03733	−	10.8653i	−0.348400	−	0.537911i
$409$	−0.681583	+	11.7023i	−0.0337021	+	0.578643i	0.938613	+	0.344971i	$0.112111\pi$
$409$	−0.681583	+	11.7023i	−0.0337021	+	0.578643i	−0.972315	+	0.233672i	$0.924926\pi$
$410$	−8.23856	+	0.962949i	−0.406873	+	0.0475567i
$411$	11.3019	−	3.29721i	0.557480	−	0.162639i
$412$	7.08357	+	3.55750i	0.348982	+	0.175265i
$413$	6.46171	−	5.42202i	0.317960	−	0.266800i
$414$	14.3951	+	3.62608i	0.707480	+	0.178212i
$415$	−5.94044	−	4.98462i	−0.291605	−	0.244685i
$416$	−1.47767	−	3.42563i	−0.0724488	−	0.167955i
$417$	−11.9102	+	6.76522i	−0.583245	+	0.331294i
$418$	−4.44183	−	1.05273i	−0.217257	−	0.0514908i
$419$	6.43034	+	21.4788i	0.314143	+	1.04931i	0.958621	+	0.284687i	$0.0918896\pi$
$419$	6.43034	+	21.4788i	0.314143	+	1.04931i	−0.644478	+	0.764623i	$0.722925\pi$
$420$	3.89645	−	10.4758i	0.190127	−	0.511166i
$421$	15.9895	+	1.86891i	0.779283	+	0.0910851i	0.496428	−	0.868078i	$-0.334645\pi$
$421$	15.9895	+	1.86891i	0.779283	+	0.0910851i	0.282854	+	0.959163i	$0.408719\pi$
$422$	2.35379	−	13.3490i	0.114581	−	0.649819i
$423$	8.90595	−	7.26218i	0.433022	−	0.353099i
$424$	0.579978	+	3.28922i	0.0281662	+	0.159739i
$425$	0.0162726	+	0.279389i	0.000789336	+	0.0135524i
$426$	−0.175145	−	1.59561i	−0.00848580	−	0.0773078i
$427$	−8.07392	+	18.7174i	−0.390724	+	0.905801i
$428$	1.40148	−	0.703851i	0.0677433	−	0.0340219i
$429$	−8.18149	−	35.6344i	−0.395006	−	1.72045i
$430$	24.5968	−	5.82955i	1.18616	−	0.281126i
$431$	−1.78363	−	3.08934i	−0.0859146	−	0.148808i	0.819866	−	0.572555i	$-0.194048\pi$
$431$	−1.78363	−	3.08934i	−0.0859146	−	0.148808i	−0.905781	+	0.423747i	$0.860715\pi$
$432$	−5.19258	+	0.192722i	−0.249828	+	0.00927234i
$433$	−3.88735	+	6.73308i	−0.186814	+	0.323571i	−0.944186	−	0.329412i	$-0.893149\pi$
$433$	−3.88735	+	6.73308i	−0.186814	+	0.323571i	0.757372	+	0.652983i	$0.226483\pi$
$434$	−2.03946	+	6.81227i	−0.0978971	+	0.326999i
$435$	−3.16486	+	25.5206i	−0.151743	+	1.22362i
$436$	13.3536	+	8.78282i	0.639523	+	0.420621i
$437$	2.38398	+	3.20223i	0.114041	+	0.153184i
$438$	−7.77540	−	0.507709i	−0.371523	−	0.0242593i
$439$	−6.60977	+	4.34731i	−0.315467	+	0.207486i	−0.697361	−	0.716720i	$-0.745642\pi$
$439$	−6.60977	+	4.34731i	−0.315467	+	0.207486i	0.381894	+	0.924206i	$0.375272\pi$
$440$	11.8442	+	4.31095i	0.564652	+	0.205517i
$441$	2.82103	+	3.07558i	0.134335	+	0.146456i
$442$	26.2017	−	9.53664i	1.24629	−	0.453612i
$443$	20.4514	−	27.4710i	0.971676	−	1.30519i	0.0194437	−	0.999811i	$-0.493810\pi$
$443$	20.4514	−	27.4710i	0.971676	−	1.30519i	0.952232	−	0.305376i	$-0.0987821\pi$
$444$	−3.96812	−	11.1454i	−0.188319	−	0.528936i
$445$	27.0783	−	28.7013i	1.28363	−	1.36057i
$446$	−17.9947	+	19.0733i	−0.852074	+	0.903146i
$447$	17.6602	+	3.24207i	0.835297	+	0.153345i
$448$	−1.72982	+	2.32355i	−0.0817262	+	0.109777i
$449$	−21.6003	+	7.86187i	−1.01938	+	0.371024i	−0.797028	−	0.603942i	$-0.793596\pi$
$449$	−21.6003	+	7.86187i	−1.01938	+	0.371024i	−0.222353	+	0.974966i	$0.571374\pi$
$450$	0.0996685	+	0.0518219i	0.00469842	+	0.00244291i
$451$	19.7970	+	7.20552i	0.932205	+	0.339295i
$452$	−3.58126	+	2.35543i	−0.168448	+	0.110790i
$453$	−16.4756	−	33.3886i	−0.774093	−	1.56873i
$454$	3.36306	+	4.51738i	0.157836	+	0.212011i
$455$	20.1140	+	13.2292i	0.942959	+	0.620194i
$456$	−1.11500	−	0.842325i	−0.0522145	−	0.0394455i
$457$	−12.1517	+	40.5895i	−0.568432	+	1.89870i	−0.155835	+	0.987783i	$0.549807\pi$
$457$	−12.1517	+	40.5895i	−0.568432	+	1.89870i	−0.412597	+	0.910914i	$0.635378\pi$
$458$	2.25105	−	3.89894i	0.105185	−	0.182185i
$459$	0.818585	−	38.8270i	0.0382083	−	1.81229i
$460$	−5.51156	−	9.54630i	−0.256978	−	0.445099i
$461$	11.2787	−	2.67311i	0.525303	−	0.124499i	0.0405957	−	0.999176i	$-0.487074\pi$
$461$	11.2787	−	2.67311i	0.525303	−	0.124499i	0.484707	+	0.874677i	$0.338926\pi$
$462$	−20.7853	+	19.3357i	−0.967020	+	0.899577i
$463$	4.67961	−	2.35019i	0.217480	−	0.109222i	−0.336724	−	0.941603i	$-0.609319\pi$
$463$	4.67961	−	2.35019i	0.217480	−	0.109222i	0.554204	+	0.832381i	$0.313023\pi$
$464$	2.63982	−	6.11980i	0.122551	−	0.284105i
$465$	8.67061	+	3.81262i	0.402090	+	0.176806i
$466$	−1.40092	−	24.0529i	−0.0648963	−	1.11423i
$467$	−0.229543	−	1.30180i	−0.0106220	−	0.0602403i	0.979036	−	0.203687i	$-0.0652925\pi$
$467$	−0.229543	−	1.30180i	−0.0106220	−	0.0602403i	−0.989658	+	0.143447i	$0.954181\pi$
$468$	2.09821	−	10.9938i	0.0969898	−	0.508188i
$469$	−0.206945	+	1.17364i	−0.00955583	+	0.0541938i
$470$	−8.47545	−	0.990638i	−0.390943	−	0.0456947i
$471$	13.3005	−	2.24900i	0.612856	−	0.103628i
$472$	0.835155	+	2.78961i	0.0384411	+	0.128402i
$473$	−62.4734	−	14.8065i	−2.87253	−	0.680802i
$474$	0.0225443	−	3.20838i	0.00103550	−	0.147366i
$475$	0.0119657	+	0.0277397i	0.000549026	+	0.00127279i
$476$	−16.5849	−	13.9164i	−0.760167	−	0.637856i
$477$	−4.09757	+	9.14374i	−0.187615	+	0.418663i
$478$	12.4580	−	10.4535i	0.569816	−	0.478132i
$479$	−2.60074	−	1.30614i	−0.118831	−	0.0596790i	0.388391	−	0.921495i	$-0.373031\pi$
$479$	−2.60074	−	1.30614i	−0.118831	−	0.0596790i	−0.507221	+	0.861816i	$0.669327\pi$
$480$	2.78786	+	2.66749i	0.127248	+	0.121754i
$481$	25.3104	−	2.95836i	1.15405	−	0.134890i
$482$	−0.476913	+	8.18828i	−0.0217228	+	0.372966i
$483$	24.7945	−	1.26937i	1.12819	−	0.0577583i
$484$	−14.4206	−	15.2849i	−0.655480	−	0.694768i
$485$	8.08231			0.366999
$486$	−13.2179	−	8.26362i	−0.599576	−	0.374845i
$487$	22.5798			1.02319			0.511594	−	0.859227i	$-0.329055\pi$
$487$	22.5798			1.02319			0.511594	+	0.859227i	$0.329055\pi$
$488$	−4.82912	−	5.11857i	−0.218604	−	0.231707i
$489$	19.1717	−	0.981508i	0.866973	−	0.0443853i
$490$	0.180192	−	3.09377i	0.00814023	−	0.139762i
$491$	−24.4537	+	2.85823i	−1.10358	+	0.128990i	−0.648320	−	0.761368i	$-0.724528\pi$
$491$	−24.4537	+	2.85823i	−1.10358	+	0.128990i	−0.455261	+	0.890358i	$0.650454\pi$
$492$	4.65976	+	4.45856i	0.210078	+	0.201007i
$493$	44.5143	+	22.3559i	2.00482	+	1.00686i
$494$	2.30574	−	1.93474i	0.103740	−	0.0870482i
$495$	22.1520	+	30.6451i	0.995657	+	1.37740i
$496$	−1.88050	−	1.57793i	−0.0844371	−	0.0708512i
$497$	−1.06331	−	2.46504i	−0.0476961	−	0.110572i
$498$	−0.0423656	+	6.02923i	−0.00189845	+	0.270176i
$499$	9.64104	+	2.28497i	0.431592	+	0.102289i	0.440669	−	0.897670i	$-0.354741\pi$
$499$	9.64104	+	2.28497i	0.431592	+	0.102289i	−0.00907686	+	0.999959i	$0.502889\pi$
$500$	−3.21845	−	10.7504i	−0.143934	−	0.480772i
$501$	−14.4620	+	2.44539i	−0.646113	+	0.109252i
$502$	12.4321	+	1.45311i	0.554873	+	0.0648554i
$503$	6.64598	−	37.6912i	0.296330	−	1.68057i	−0.365419	−	0.930843i	$-0.619074\pi$
$503$	6.64598	−	37.6912i	0.296330	−	1.68057i	0.661749	−	0.749725i	$-0.269814\pi$
$504$	−8.20712	+	2.85719i	−0.365574	+	0.127269i
$505$	−1.12688	−	6.39085i	−0.0501455	−	0.284389i
$506$	1.62792	+	27.9502i	0.0723697	+	1.24254i
$507$	1.45624	+	0.640333i	0.0646738	+	0.0284382i
$508$	−4.96884	+	11.5191i	−0.220457	+	0.511076i
$509$	30.2138	−	15.1739i	1.33920	−	0.672572i	0.372393	−	0.928075i	$-0.378537\pi$
$509$	30.2138	−	15.1739i	1.33920	−	0.672572i	0.966808	+	0.255503i	$0.0822411\pi$
$510$	−21.1144	+	19.6418i	−0.934959	+	0.869753i
$511$	−12.6803	+	3.00528i	−0.560943	+	0.132946i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	−1.35046	−	3.96873i	−0.0596244	−	0.175224i
$514$	−6.55943	+	11.3613i	−0.289324	+	0.501124i
$515$	5.06442	−	16.9163i	0.223165	−	0.745423i
$516$	−15.6822	−	11.8471i	−0.690370	−	0.521541i
$517$	18.1078	+	11.9097i	0.796379	+	0.523787i
$518$	−11.8154	−	15.8709i	−0.519141	−	0.697327i
$519$	10.5319	+	21.3433i	0.462298	+	0.936868i
$520$	−6.94366	+	4.56691i	−0.304499	+	0.200272i
$521$	−40.7602	−	14.8355i	−1.78574	−	0.649955i	−0.999486	−	0.0320465i	$-0.989798\pi$
$521$	−40.7602	−	14.8355i	−1.78574	−	0.649955i	−0.786250	−	0.617908i	$-0.787980\pi$
$522$	16.8580	−	10.7514i	0.737856	−	0.470576i
$523$	−32.7107	+	11.9057i	−1.43034	+	0.520600i	−0.937028	−	0.349254i	$-0.886435\pi$
$523$	−32.7107	+	11.9057i	−1.43034	+	0.520600i	−0.493309	+	0.869854i	$0.664213\pi$
$524$	−1.24469	+	1.67190i	−0.0543744	+	0.0730374i
$525$	0.184787	+	0.0339233i	0.00806475	+	0.00148054i
$526$	4.58634	−	4.86124i	0.199974	−	0.211960i
$527$	12.5906	−	13.3452i	0.548454	−	0.581327i
$528$	−3.28703	−	9.23238i	−0.143050	−	0.401788i
$529$	0.886903	−	1.19132i	0.0385610	−	0.0517964i
$530$	6.99165	−	2.54475i	0.303698	−	0.110537i
$531$	−2.62282	+	8.33280i	−0.113821	+	0.361613i
$532$	−2.19612	−	0.799323i	−0.0952140	−	0.0346551i
$533$	−11.6059	+	7.63335i	−0.502709	+	0.330637i
$534$	−30.6146	−	1.99903i	−1.32482	−	0.0865066i
$535$	−2.08627	−	2.80235i	−0.0901975	−	0.121156i
$536$	−0.343727	−	0.226073i	−0.0148468	−	0.00976487i
$537$	−1.92269	+	15.5041i	−0.0829703	+	0.669052i
$538$	0.314864	−	1.05172i	0.0135747	−	0.0453428i
$539$	−3.93559	+	6.81664i	−0.169518	+	0.293613i
$540$	2.43146	+	11.3171i	0.104633	+	0.487011i
$541$	6.10522	+	10.5746i	0.262484	+	0.454636i	0.966901	−	0.255150i	$-0.0821250\pi$
$541$	6.10522	+	10.5746i	0.262484	+	0.454636i	−0.704417	+	0.709786i	$0.748792\pi$
$542$	−9.01787	+	2.13727i	−0.387351	+	0.0918038i
$543$	4.42842	+	19.2879i	0.190042	+	0.827724i
$544$	6.67893	−	3.35429i	0.286357	−	0.143814i
$545$	14.1024	−	32.6931i	0.604082	−	1.40042i
$546$	−2.04237	−	18.6066i	−0.0874055	−	0.796287i
$547$	−0.825872	−	14.1797i	−0.0353117	−	0.606279i	−0.968827	−	0.247740i	$-0.920312\pi$
$547$	−0.825872	−	14.1797i	−0.0353117	−	0.606279i	0.933515	−	0.358539i	$-0.116725\pi$
$548$	1.18031	+	6.69389i	0.0504205	+	0.285949i
$549$	−3.37339	−	20.8399i	−0.143973	−	0.889426i
$550$	−0.0367905	+	0.208649i	−0.00156875	+	0.00889684i
$551$	5.34080	+	0.624250i	0.227526	+	0.0265939i
$552$	−2.98784	+	8.03296i	−0.127171	+	0.341905i
$553$	−1.53897	−	5.14052i	−0.0654436	−	0.218597i
$554$	24.1182	+	5.71611i	1.02468	+	0.242854i
$555$	−22.9161	+	13.0168i	−0.972735	+	0.552532i
$556$	−3.13230	−	7.26148i	−0.132839	−	0.307955i
$557$	−1.35560	−	1.13749i	−0.0574388	−	0.0481969i	0.613616	−	0.789604i	$-0.289714\pi$
$557$	−1.35560	−	1.13749i	−0.0574388	−	0.0481969i	−0.671055	+	0.741407i	$0.734159\pi$
$558$	−2.01280	−	7.08407i	−0.0852087	−	0.299893i
$559$	32.4297	−	27.2117i	1.37163	−	1.15093i
$560$	5.76663	+	2.89611i	0.243685	+	0.122383i
$561$	70.3137	−	20.5133i	2.96865	−	0.866073i
$562$	1.71389	−	0.200325i	0.0722962	−	0.00845021i
$563$	−2.75169	+	47.2446i	−0.115970	+	1.99112i	0.0160148	+	0.999872i	$0.494902\pi$
$563$	−2.75169	+	47.2446i	−0.115970	+	1.99112i	−0.131985	+	0.991252i	$0.542135\pi$
$564$	3.60675	+	5.56864i	0.151872	+	0.234482i
$565$	6.55278	+	6.94554i	0.275678	+	0.292201i
$566$	11.4955			0.483193
$567$	−25.1890	−	6.72285i	−1.05784	−	0.282333i
$568$	0.926762			0.0388861
$569$	4.92644	+	5.22173i	0.206527	+	0.218906i	0.822355	−	0.568975i	$-0.192660\pi$
$569$	4.92644	+	5.22173i	0.206527	+	0.218906i	−0.615828	+	0.787881i	$0.711178\pi$
$570$	−1.41661	+	2.77196i	−0.0593351	+	0.116104i
$571$	2.55366	−	43.8446i	0.106867	−	1.83484i	−0.340217	−	0.940347i	$-0.610500\pi$
$571$	2.55366	−	43.8446i	0.106867	−	1.83484i	0.447084	−	0.894492i	$-0.352462\pi$
$572$	20.9661	−	2.45059i	0.876637	−	0.102464i
$573$	8.65772	−	35.4189i	0.361682	−	1.47964i
$574$	9.63861	+	4.84069i	0.402308	+	0.202047i
$575$	0.141939	−	0.119101i	0.00591928	−	0.00496686i
$576$	0.216504	−	2.99218i	0.00902100	−	0.124674i
$577$	7.74860	+	6.50185i	0.322578	+	0.270675i	0.789668	−	0.613535i	$-0.210253\pi$
$577$	7.74860	+	6.50185i	0.322578	+	0.270675i	−0.467089	+	0.884210i	$0.654697\pi$
$578$	15.3914	+	35.6813i	0.640199	+	1.48415i
$579$	−29.9515	−	17.5743i	−1.24474	−	0.730362i
$580$	−14.4470	−	3.42400i	−0.599879	−	0.142174i
$581$	2.89205	+	9.66013i	0.119983	+	0.400770i
$582$	−4.00542	−	4.84217i	−0.166030	−	0.200714i
$583$	−18.7700	−	2.19390i	−0.777373	−	0.0908619i
$584$	0.781189	−	4.43034i	0.0323258	−	0.183329i
$585$	−24.9302	−	0.350372i	−1.03074	−	0.0144861i
$586$	2.00237	+	11.3560i	0.0827173	+	0.469113i
$587$	−1.48734	−	25.5366i	−0.0613889	−	1.05401i	−0.878566	−	0.477621i	$-0.841499\pi$
$587$	−1.48734	−	25.5366i	−0.0613889	−	1.05401i	0.817177	−	0.576386i	$-0.195538\pi$
$588$	−1.94280	+	1.42525i	−0.0801197	+	0.0587764i
$589$	0.784446	−	1.81855i	0.0323225	−	0.0749321i
$590$	5.79688	−	2.91130i	0.238654	−	0.119856i
$591$	32.9208	+	10.1084i	1.35418	+	0.415805i
$592$	6.64634	−	1.57521i	0.273163	−	0.0647408i
$593$	2.85599	+	4.94672i	0.117281	+	0.203137i	0.918689	−	0.394981i	$-0.129249\pi$
$593$	2.85599	+	4.94672i	0.117281	+	0.203137i	−0.801408	+	0.598118i	$0.795915\pi$
$594$	7.38165	−	28.4585i	0.302873	−	1.16767i
$595$	−24.1147	+	41.7678i	−0.988605	+	1.71231i
$596$	−2.97314	+	9.93099i	−0.121785	+	0.406789i
$597$	−36.0974	+	15.2710i	−1.47737	+	0.624999i
$598$	−15.4237	−	10.1443i	−0.630720	−	0.414831i
$599$	19.1974	+	25.7866i	0.784384	+	1.05361i	0.997070	+	0.0764898i	$0.0243713\pi$
$599$	19.1974	+	25.7866i	0.784384	+	1.05361i	−0.212687	+	0.977120i	$0.568221\pi$
$600$	−0.0360194	+	0.0539356i	−0.00147049	+	0.00220191i
$601$	−32.3853	+	21.3001i	−1.32102	+	0.868850i	−0.997015	−	0.0772042i	$-0.975401\pi$
$601$	−32.3853	+	21.3001i	−1.32102	+	0.868850i	−0.324007	+	0.946055i	$0.605030\pi$
$602$	−30.8880	−	11.2423i	−1.25890	−	0.458202i
$603$	−0.472879	−	1.14005i	−0.0192571	−	0.0464263i
$604$	20.1997	−	7.35210i	0.821915	−	0.299153i
$605$	−27.9542	+	37.5490i	−1.13650	+	1.52659i
$606$	−3.27034	+	3.84229i	−0.132849	+	0.156082i
$607$	−8.65305	+	9.17170i	−0.351217	+	0.372268i	−0.878763	−	0.477258i	$-0.841631\pi$
$607$	−8.65305	+	9.17170i	−0.351217	+	0.372268i	0.527546	+	0.849526i	$0.323112\pi$
$608$	0.553652	−	0.586837i	0.0224536	−	0.0237994i
$609$	21.6741	−	25.4647i	0.878281	−	1.03188i
$610$	−9.36124	+	12.5743i	−0.379026	+	0.509120i
$611$	−13.4288	+	4.88769i	−0.543272	+	0.197735i
$612$	22.2314	+	2.91570i	0.898649	+	0.117860i
$613$	−20.3798	−	7.41766i	−0.823134	−	0.299596i	−0.104096	−	0.994567i	$-0.533195\pi$
$613$	−20.3798	−	7.41766i	−0.823134	−	0.299596i	−0.719038	+	0.694971i	$0.755417\pi$
$614$	−16.8415	+	11.0768i	−0.679667	+	0.447024i
$615$	7.97880	−	11.9475i	0.321736	−	0.481769i
$616$	−9.78744	−	13.1468i	−0.394347	−	0.529700i
$617$	34.5136	+	22.7000i	1.38947	+	0.913866i	0.999974	−	0.00716353i	$-0.00228024\pi$
$617$	34.5136	+	22.7000i	1.38947	+	0.913866i	0.389492	+	0.921030i	$0.372651\pi$
$618$	−12.6445	+	5.34925i	−0.508637	+	0.215178i
$619$	−1.30008	+	4.34256i	−0.0522545	+	0.174542i	−0.980133	−	0.198340i	$-0.936445\pi$
$619$	−1.30008	+	4.34256i	−0.0522545	+	0.174542i	0.927879	+	0.372882i	$0.121630\pi$
$620$	−2.73428	+	4.73591i	−0.109811	+	0.190199i
$621$	−20.9431	+	14.9159i	−0.840420	+	0.598556i
$622$	6.47328	+	11.2120i	0.259555	+	0.449562i
$623$	−49.9269	+	11.8329i	−2.00028	+	0.474075i
$624$	6.17720	+	1.89673i	0.247286	+	0.0759299i
$625$	−22.1723	+	11.1353i	−0.886890	+	0.445413i
$626$	13.5386	−	31.3861i	0.541113	−	1.25444i
$627$	6.37508	−	4.67681i	0.254596	−	0.186774i
$628$	0.452836	+	7.77489i	0.0180701	+	0.310252i
$629$	8.86478	+	50.2747i	0.353462	+	2.00458i
$630$	9.44298	+	16.8998i	0.376217	+	0.673305i
$631$	−3.35180	+	19.0090i	−0.133433	+	0.756735i	0.842505	+	0.538688i	$0.181080\pi$
$631$	−3.35180	+	19.0090i	−0.133433	+	0.756735i	−0.975938	+	0.218047i	$0.930031\pi$
$632$	1.83988	+	0.215051i	0.0731864	+	0.00855426i
$633$	14.9645	+	18.0906i	0.594785	+	0.719038i
$634$	1.42920	+	4.77385i	0.0567607	+	0.189594i
$635$	27.1930	+	6.44487i	1.07912	+	0.255757i
$636$	−4.98949	−	2.92762i	−0.197846	−	0.116088i
$637$	−2.05565	−	4.76553i	−0.0814478	−	0.188817i
$638$	28.8878	+	24.2398i	1.14368	+	0.959662i
$639$	2.30120	+	1.56028i	0.0910339	+	0.0617239i
$640$	−1.70650	+	1.43192i	−0.0674554	+	0.0566018i
$641$	−23.0721	−	11.5872i	−0.911293	−	0.457669i	−0.0695693	−	0.997577i	$-0.522163\pi$
$641$	−23.0721	−	11.5872i	−0.911293	−	0.457669i	−0.841724	+	0.539909i	$0.818459\pi$
$642$	−0.644996	+	2.63869i	−0.0254560	+	0.104141i
$643$	−18.4856	+	2.16066i	−0.729002	+	0.0852082i	−0.472494	−	0.881334i	$-0.656646\pi$
$643$	−18.4856	+	2.16066i	−0.729002	+	0.0852082i	−0.256508	+	0.966542i	$0.582572\pi$
$644$	−0.833438	+	14.3096i	−0.0328421	+	0.563877i
$645$	−19.9243	+	38.9870i	−0.784517	+	1.53511i
$646$	4.13795	+	4.38597i	0.162806	+	0.172564i
$647$	−27.0181			−1.06219			−0.531096	−	0.847311i	$-0.678220\pi$
$647$	−27.0181			−1.06219			−0.531096	+	0.847311i	$0.678220\pi$
$648$	5.57518	−	7.06522i	0.219014	−	0.277548i
$649$	−16.4760			−0.646739
$650$	−0.0958671	−	0.101613i	−0.00376022	−	0.00398560i
$651$	−6.69562	−	10.3377i	−0.262422	−	0.405166i
$652$	−0.644435	+	11.0645i	−0.0252380	+	0.433320i
$653$	−6.47720	+	0.757076i	−0.253472	+	0.0296267i	−0.241880	−	0.970306i	$-0.577764\pi$
$653$	−6.47720	+	0.757076i	−0.253472	+	0.0296267i	−0.0115922	+	0.999933i	$0.503690\pi$
$654$	−26.5756	+	7.75315i	−1.03919	+	0.303172i
$655$	4.14937	+	2.08389i	0.162129	+	0.0814243i
$656$	−2.85233	+	2.39339i	−0.111365	+	0.0934460i
$657$	9.39860	−	9.68556i	0.366674	−	0.377870i
$658$	8.50004	+	7.13238i	0.331366	+	0.278049i
$659$	−14.8284	−	34.3761i	−0.577633	−	1.33910i	−0.917165	−	0.398509i	$-0.869528\pi$
$659$	−14.8284	−	34.3761i	−0.577633	−	1.33910i	0.339532	−	0.940595i	$-0.389731\pi$
$660$	−18.9828	+	10.7826i	−0.738904	+	0.419712i
$661$	−30.2497	−	7.16931i	−1.17658	−	0.278854i	−0.404594	−	0.914497i	$-0.632587\pi$
$661$	−30.2497	−	7.16931i	−1.17658	−	0.278854i	−0.771983	+	0.635643i	$0.780735\pi$
$662$	0.109104	+	0.364434i	0.00424046	+	0.0141641i
$663$	−16.8364	+	45.2655i	−0.653872	+	1.75797i
$664$	−3.45753	−	0.404127i	−0.134178	−	0.0156832i
$665$	−0.904052	+	5.12714i	−0.0350576	+	0.198822i
$666$	19.1552	+	7.27836i	0.742249	+	0.282031i
$667$	−5.72683	−	32.4785i	−0.221744	−	1.25757i
$668$	−0.492379	−	8.45382i	−0.0190507	−	0.327088i
$669$	−4.95561	−	45.1469i	−0.191595	−	1.74548i
$670$	−0.363002	+	0.841534i	−0.0140240	+	0.0325113i
$671$	35.5811	−	17.8695i	1.37359	−	0.689844i
$672$	−1.12274	−	4.89008i	−0.0433106	−	0.188639i
$673$	−15.5065	+	3.67510i	−0.597730	+	0.141665i	−0.518333	−	0.855179i	$-0.673447\pi$
$673$	−15.5065	+	3.67510i	−0.597730	+	0.141665i	−0.0793963	+	0.996843i	$0.525299\pi$
$674$	−5.54549	−	9.60507i	−0.213604	−	0.369973i
$675$	−0.180243	+	0.0732828i	−0.00693756	+	0.00282066i
$676$	−0.459225	+	0.795401i	−0.0176625	+	0.0305924i
$677$	7.13321	−	23.8266i	0.274152	−	0.915730i	−0.704413	−	0.709790i	$-0.748790\pi$
$677$	7.13321	−	23.8266i	0.274152	−	0.915730i	0.978565	−	0.205940i	$-0.0660251\pi$
$678$	0.913704	−	7.36788i	0.0350906	−	0.282962i
$679$	−8.78078	−	5.77521i	−0.336976	−	0.221632i
$680$	−9.94238	−	13.3549i	−0.381273	−	0.512138i
$681$	−9.73379	−	0.635585i	−0.373000	−	0.0243557i
$682$	11.6046	−	7.63245i	0.444362	−	0.292262i
$683$	2.30415	+	0.838640i	0.0881657	+	0.0320897i	0.385726	−	0.922613i	$-0.373951\pi$
$683$	2.30415	+	0.838640i	0.0881657	+	0.0320897i	−0.297561	+	0.954703i	$0.596173\pi$
$684$	2.36274	−	0.525024i	0.0903415	−	0.0200748i
$685$	14.2287	−	5.17883i	0.543651	−	0.197873i
$686$	9.70230	−	13.0325i	0.370436	−	0.497581i
$687$	2.61548	+	7.34616i	0.0997866	+	0.280274i
$688$	7.78701	−	8.25375i	0.296877	−	0.314671i
$689$	8.55094	−	9.06347i	0.325765	−	0.345291i
$690$	18.7788	+	3.44743i	0.714896	+	0.131241i
$691$	2.72052	−	3.65429i	0.103493	−	0.139016i	−0.747359	−	0.664420i	$-0.768679\pi$
$691$	2.72052	−	3.65429i	0.103493	−	0.139016i	0.850853	+	0.525404i	$0.176086\pi$
$692$	−12.9125	+	4.69975i	−0.490858	+	0.178658i
$693$	−2.16890	−	49.1222i	−0.0823896	−	1.86600i
$694$	6.64367	+	2.41810i	0.252190	+	0.0917897i
$695$	−14.7188	+	9.68072i	−0.558317	+	0.367211i
$696$	5.10829	+	10.3522i	0.193629	+	0.392398i
$697$	−16.6182	−	22.3221i	−0.629458	−	0.845508i
$698$	8.18002	+	5.38009i	0.309618	+	0.203639i
$699$	33.2978	+	25.1548i	1.25944	+	0.951443i
$700$	−0.0311094	+	0.103913i	−0.00117582	+	0.00392753i
$701$	7.04420	−	12.2009i	0.266056	−	0.460822i	−0.701784	−	0.712390i	$-0.747613\pi$
$701$	7.04420	−	12.2009i	0.266056	−	0.460822i	0.967840	+	0.251568i	$0.0809462\pi$
$702$	12.1450	+	15.1095i	0.458383	+	0.570272i
$703$	2.75537	+	4.77244i	0.103921	+	0.179996i
$704$	5.50556	−	1.30484i	0.207499	−	0.0491781i
$705$	10.8215	−	10.0668i	0.407560	−	0.379136i
$706$	11.2551	−	5.65250i	0.423590	−	0.212735i
$707$	−3.34232	+	7.74836i	−0.125701	+	0.291407i
$708$	−4.61699	−	2.03017i	−0.173517	−	0.0762986i
$709$	−1.16016	−	19.9192i	−0.0435708	−	0.748082i	−0.947373	−	0.320131i	$-0.896273\pi$
$709$	−1.16016	−	19.9192i	−0.0435708	−	0.748082i	0.903802	−	0.427950i	$-0.140764\pi$
$710$	−0.358502	−	2.03316i	−0.0134543	−	0.0763033i
$711$	4.20645	+	3.63158i	0.157754	+	0.136195i
$712$	3.07582	−	17.4439i	0.115271	−	0.653736i
$713$	−12.0650	−	1.41019i	−0.451836	−	0.0528121i
$714$	36.9741	−	6.25198i	1.38372	−	0.233975i
$715$	−13.4866	−	45.0482i	−0.504368	−	1.68471i
$716$	−8.77674	−	2.08013i	−0.328002	−	0.0777379i
$717$	−0.197923	+	28.1672i	−0.00739157	+	1.05192i
$718$	−10.1634	−	23.5615i	−0.379296	−	0.879307i
$719$	10.6365	+	8.92511i	0.396676	+	0.332850i	0.819207	−	0.573498i	$-0.194414\pi$
$719$	10.6365	+	8.92511i	0.396676	+	0.332850i	−0.422531	+	0.906348i	$0.638858\pi$
$720$	−6.64810	+	0.682497i	−0.247760	+	0.0254352i
$721$	−17.5897	+	14.7595i	−0.655073	+	0.549672i
$722$	−16.3973	−	8.23506i	−0.610246	−	0.306477i
$723$	−10.2647	−	9.82149i	−0.381749	−	0.365265i
$724$	−11.3484	+	1.32644i	−0.421759	+	0.0492966i
$725$	0.0145111	−	0.249146i	0.000538929	−	0.00925305i
$726$	36.3494	−	1.86093i	1.34905	−	0.0690657i
$727$	−7.62974	−	8.08705i	−0.282971	−	0.299932i	0.570260	−	0.821464i	$-0.306842\pi$
$727$	−7.62974	−	8.08705i	−0.282971	−	0.299932i	−0.853232	+	0.521532i	$0.825361\pi$
$728$	10.8070			0.400535
$729$	25.7384	−	8.15700i	0.953273	−	0.302111i
$730$	−10.0216			−0.370917
$731$	58.1994	+	61.6878i	2.15258	+	2.28161i
$732$	12.1726	−	0.623185i	0.449912	−	0.0230336i
$733$	−0.218405	+	3.74987i	−0.00806698	+	0.138505i	0.991870	+	0.127257i	$0.0406173\pi$
$733$	−0.218405	+	3.74987i	−0.00806698	+	0.138505i	−0.999937	+	0.0112476i	$0.996420\pi$
$734$	3.40827	−	0.398369i	0.125801	−	0.0147041i
$735$	3.87831	+	3.71085i	0.143054	+	0.136877i
$736$	−4.42192	−	2.22077i	−0.162994	−	0.0818587i
$737$	1.78319	−	1.49627i	0.0656845	−	0.0551159i
$738$	−11.1119	+	1.14076i	−0.409036	+	0.0419918i
$739$	33.3929	+	28.0200i	1.22838	+	1.03073i	0.998343	+	0.0575483i	$0.0183283\pi$
$739$	33.3929	+	28.0200i	1.22838	+	1.03073i	0.230034	+	0.973183i	$0.426116\pi$
$740$	−6.02677	−	13.9716i	−0.221549	−	0.513608i
$741$	−0.0366317	+	5.21321i	−0.00134570	+	0.191512i
$742$	−9.41423	−	2.23121i	−0.345607	−	0.0819104i
$743$	2.21564	+	7.40074i	0.0812838	+	0.271507i	0.988964	−	0.148156i	$-0.0473337\pi$
$743$	2.21564	+	7.40074i	0.0812838	+	0.271507i	−0.907680	+	0.419662i	$0.862148\pi$
$744$	4.19237	−	0.708891i	0.153700	−	0.0259892i
$745$	22.9371	+	2.68096i	0.840349	+	0.0982227i
$746$	−0.718636	+	4.07558i	−0.0263111	+	0.149218i
$747$	−7.90482	−	6.82451i	−0.289222	−	0.249696i
$748$	7.34323	+	41.6455i	0.268495	+	1.52271i
$749$	0.264150	+	4.53528i	0.00965183	+	0.165716i
$750$	17.7926	+	7.82372i	0.649694	+	0.285682i
$751$	−3.44753	+	7.99226i	−0.125802	+	0.291642i	−0.969464	−	0.245232i	$-0.921136\pi$
$751$	−3.44753	+	7.99226i	−0.125802	+	0.291642i	0.843662	+	0.536874i	$0.180395\pi$
$752$	−3.42307	+	1.71913i	−0.124826	+	0.0626902i
$753$	−15.8734	+	14.7663i	−0.578458	+	0.538115i
$754$	−24.1947	+	5.73426i	−0.881120	+	0.208829i
$755$	−23.9432	−	41.4708i	−0.871382	−	1.50928i
$756$	5.44506	−	14.0325i	0.198035	−	0.510359i
$757$	19.1896	−	33.2373i	0.697457	−	1.20803i	−0.271888	−	0.962329i	$-0.587648\pi$
$757$	19.1896	−	33.2373i	0.697457	−	1.20803i	0.969345	−	0.245703i	$-0.0790187\pi$
$758$	−6.30139	+	21.0481i	−0.228877	+	0.764502i
$759$	−38.6931	−	29.2308i	−1.40447	−	1.06101i
$760$	−1.50160	−	0.987615i	−0.0544686	−	0.0358246i
$761$	−1.93402	−	2.59783i	−0.0701080	−	0.0941714i	0.765686	−	0.643215i	$-0.222400\pi$
$761$	−1.93402	−	2.59783i	−0.0701080	−	0.0941714i	−0.835794	+	0.549043i	$0.814992\pi$
$762$	−9.61512	−	19.4855i	−0.348319	−	0.705884i
$763$	−38.6821	+	25.4416i	−1.40038	+	0.921047i
$764$	19.7816	+	7.19992i	0.715673	+	0.260484i
$765$	−2.20323	−	49.8998i	−0.0796581	−	1.80413i
$766$	−9.79769	+	3.56607i	−0.354005	+	0.128847i
$767$	6.48736	−	8.71404i	0.234245	&

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686242 - 0.727374i) q^{2} +(1.72979 - 0.0885576i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.21262 - 0.258618i) q^{5} +(-1.25147 - 1.19743i) q^{6} +(-2.58863 - 1.30006i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.98432 - 0.306371i) q^{9} +O(q^{10})\)	\(q+(-0.686242 - 0.727374i) q^{2} +(1.72979 - 0.0885576i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(2.21262 - 0.258618i) q^{5} +(-1.25147 - 1.19743i) q^{6} +(-2.58863 - 1.30006i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.98432 - 0.306371i) q^{9} +(-1.70650 - 1.43192i) q^{10} +(2.24105 + 5.19534i) q^{11} +(-0.0121703 + 1.73201i) q^{12} +(-3.63018 - 0.860369i) q^{13} +(0.830796 + 2.77505i) q^{14} +(3.80445 - 0.643297i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(1.29783 - 7.36037i) q^{17} +(-2.27081 - 1.96047i) q^{18} +(-0.140098 - 0.794532i) q^{19} +(0.129528 + 2.22391i) q^{20} +(-4.59290 - 2.01958i) q^{21} +(2.24105 - 5.19534i) q^{22} +(-4.42192 + 2.22077i) q^{23} +(1.26817 - 1.17972i) q^{24} +(-0.0364359 + 0.00863547i) q^{25} +(1.86537 + 3.23092i) q^{26} +(5.13509 - 0.794240i) q^{27} +(1.44837 - 2.50866i) q^{28} +(-1.91151 + 6.38489i) q^{29} +(-3.07869 - 2.32580i) q^{30} +(2.05098 + 1.34895i) q^{31} +(0.597159 + 0.802123i) q^{32} +(4.33662 + 8.78835i) q^{33} +(-6.24436 + 4.10698i) q^{34} +(-6.06386 - 2.20706i) q^{35} +(0.132330 + 2.99708i) q^{36} +(-6.41853 + 2.33615i) q^{37} +(-0.481781 + 0.647144i) q^{38} +(-6.35563 - 1.16677i) q^{39} +(1.52873 - 1.62036i) q^{40} +(2.55518 - 2.70834i) q^{41} +(1.68285 + 4.72667i) q^{42} +(-6.77615 + 9.10195i) q^{43} +(-5.31685 + 1.93518i) q^{44} +(6.52391 - 1.44968i) q^{45} +(4.64984 + 1.69240i) q^{46} +(3.20034 - 2.10490i) q^{47} +(-1.72837 - 0.112857i) q^{48} +(0.830731 + 1.11587i) q^{49} +(0.0312851 + 0.0205765i) q^{50} +(1.59315 - 12.8468i) q^{51} +(1.06999 - 3.57401i) q^{52} +(-1.66998 + 2.89249i) q^{53} +(-4.10162 - 3.19009i) q^{54} +(6.30219 + 10.9157i) q^{55} +(-2.81866 + 0.668036i) q^{56} +(-0.312700 - 1.36196i) q^{57} +(5.95596 - 2.99119i) q^{58} +(-1.15336 + 2.67379i) q^{59} +(0.421000 + 3.83542i) q^{60} +(-0.409169 - 7.02515i) q^{61} +(-0.426276 - 2.41753i) q^{62} +(-8.12358 - 3.08670i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-8.25471 - 0.964837i) q^{65} +(3.41645 - 9.18528i) q^{66} +(-0.117994 - 0.394126i) q^{67} +(7.27245 + 1.72360i) q^{68} +(-7.45231 + 4.23305i) q^{69} +(2.55591 + 5.92527i) q^{70} +(0.709941 + 0.595711i) q^{71} +(2.08919 - 2.15297i) q^{72} +(3.44620 - 2.89170i) q^{73} +(6.10392 + 3.06550i) q^{74} +(-0.0622616 + 0.0181642i) q^{75} +(0.801334 - 0.0936625i) q^{76} +(0.952994 - 16.3623i) q^{77} +(3.51282 + 5.42360i) q^{78} +(1.27120 + 1.34739i) q^{79} -2.22768 q^{80} +(8.81227 - 1.82862i) q^{81} -3.72345 q^{82} +(-2.38885 - 2.53203i) q^{83} +(2.28321 - 4.46770i) q^{84} +(0.968081 - 16.6213i) q^{85} +(11.2706 - 1.31734i) q^{86} +(-2.74107 + 11.2138i) q^{87} +(5.05624 + 2.53934i) q^{88} +(13.5689 - 11.3857i) q^{89} +(-5.53144 - 3.75049i) q^{90} +(8.27866 + 6.94662i) q^{91} +(-1.95990 - 4.54357i) q^{92} +(3.66721 + 2.15176i) q^{93} +(-3.72726 - 0.883376i) q^{94} +(-0.515462 - 1.72176i) q^{95} +(1.10399 + 1.33462i) q^{96} +(3.60360 + 0.421200i) q^{97} +(0.241569 - 1.37001i) q^{98} +(8.27970 + 14.8179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more