LMFDB - Embedded newform 405.2.r.a.8.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			8.10
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.807333 - 0.565301i) q^{2} +(-0.351818 + 0.966613i) q^{4} +(2.04189 + 0.911409i) q^{5} +(-0.275357 + 0.590505i) q^{7} +(0.772562 + 2.88324i) q^{8} +O(q^{10})$	\(q+(0.807333 - 0.565301i) q^{2} +(-0.351818 + 0.966613i) q^{4} +(2.04189 + 0.911409i) q^{5} +(-0.275357 + 0.590505i) q^{7} +(0.772562 + 2.88324i) q^{8} +(2.16371 - 0.418474i) q^{10} +(-0.890417 + 1.06116i) q^{11} +(-2.93770 + 4.19546i) q^{13} +(0.111508 + 0.632393i) q^{14} +(0.677632 + 0.568601i) q^{16} +(1.18168 - 4.41009i) q^{17} +(0.00652973 + 0.00376994i) q^{19} +(-1.59936 + 1.65307i) q^{20} +(-0.118990 + 1.36006i) q^{22} +(6.70560 - 3.12687i) q^{23} +(3.33867 + 3.72200i) q^{25} +5.04782i q^{26} +(-0.473914 - 0.473914i) q^{28} +(0.586508 - 3.32625i) q^{29} +(3.73277 + 1.35862i) q^{31} +(-5.07868 - 0.444327i) q^{32} +(-1.53902 - 4.22842i) q^{34} +(-1.10044 + 0.954786i) q^{35} +(1.60572 + 0.430252i) q^{37} +(0.00740282 - 0.000647662i) q^{38} +(-1.05032 + 6.59139i) q^{40} +(1.90299 - 0.335548i) q^{41} +(-0.929732 - 10.6269i) q^{43} +(-0.712464 - 1.23402i) q^{44} +(3.64603 - 6.31511i) q^{46} +(-6.61847 - 3.08624i) q^{47} +(4.22664 + 5.03711i) q^{49} +(4.79947 + 1.11755i) q^{50} +(-3.02186 - 4.31566i) q^{52} +(1.18766 - 1.18766i) q^{53} +(-2.78529 + 1.35524i) q^{55} +(-1.91530 - 0.337719i) q^{56} +(-1.40682 - 3.01694i) q^{58} +(7.77643 - 6.52520i) q^{59} +(-9.02437 + 3.28460i) q^{61} +(3.78162 - 1.01328i) q^{62} +(-5.88351 + 3.39685i) q^{64} +(-9.82225 + 5.88925i) q^{65} +(-12.3176 - 8.62489i) q^{67} +(3.84712 + 2.69378i) q^{68} +(-0.348682 + 1.39291i) q^{70} +(-5.41550 + 3.12664i) q^{71} +(12.1662 - 3.25991i) q^{73} +(1.53958 - 0.560360i) q^{74} +(-0.00594135 + 0.00498539i) q^{76} +(-0.381436 - 0.817993i) q^{77} +(-0.782046 - 0.137896i) q^{79} +(0.865425 + 1.77862i) q^{80} +(1.34666 - 1.34666i) q^{82} +(-5.32053 - 7.59850i) q^{83} +(6.43227 - 7.92795i) q^{85} +(-6.75799 - 8.05386i) q^{86} +(-3.74748 - 1.74748i) q^{88} +(-5.89645 + 10.2130i) q^{89} +(-1.66853 - 2.88997i) q^{91} +(0.663323 + 7.58182i) q^{92} +(-7.08796 + 1.24980i) q^{94} +(0.00989706 + 0.0136491i) q^{95} +(-2.18091 + 0.190805i) q^{97} +(6.25979 + 1.67731i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	0.807333	−	0.565301i	0.570871	−	0.399728i	−0.252193	−	0.967677i	$-0.581152\pi$
$2$	0.807333	−	0.565301i	0.570871	−	0.399728i	0.823064	+	0.567949i	$0.192263\pi$
$3$		0			0
$3$		0			0
$4$	−0.351818	+	0.966613i	−0.175909	+	0.483307i
$5$	2.04189	+	0.911409i	0.913163	+	0.407595i
$5$	2.04189	+	0.911409i	0.913163	+	0.407595i
$6$		0			0
$7$	−0.275357	+	0.590505i	−0.104075	+	0.223190i	−0.951449	−	0.307807i	$-0.900405\pi$
$7$	−0.275357	+	0.590505i	−0.104075	+	0.223190i	0.847374	+	0.530997i	$0.178183\pi$
$8$	0.772562	+	2.88324i	0.273142	+	1.01938i
$9$		0			0
$10$	2.16371	−	0.418474i	0.684225	−	0.132333i
$11$	−0.890417	+	1.06116i	−0.268471	+	0.319951i	−0.883390	−	0.468639i	$-0.844744\pi$
$11$	−0.890417	+	1.06116i	−0.268471	+	0.319951i	0.614919	+	0.788591i	$0.289189\pi$
$12$		0			0
$13$	−2.93770	+	4.19546i	−0.814770	+	1.16361i	0.169253	+	0.985573i	$0.445864\pi$
$13$	−2.93770	+	4.19546i	−0.814770	+	1.16361i	−0.984023	+	0.178040i	$0.943024\pi$
$14$	0.111508	+	0.632393i	0.0298018	+	0.169014i
$15$		0			0
$16$	0.677632	+	0.568601i	0.169408	+	0.142150i
$17$	1.18168	−	4.41009i	0.286600	−	1.06961i	−0.661063	−	0.750331i	$-0.729894\pi$
$17$	1.18168	−	4.41009i	0.286600	−	1.06961i	0.947662	−	0.319274i	$-0.103439\pi$
$18$		0			0
$19$	0.00652973	+	0.00376994i	0.00149802	+	0.000864884i	0.500749	−	0.865593i	$-0.333058\pi$
$19$	0.00652973	+	0.00376994i	0.00149802	+	0.000864884i	−0.499251	+	0.866458i	$0.666391\pi$
$20$	−1.59936	+	1.65307i	−0.357627	+	0.369638i
$21$		0			0
$22$	−0.118990	+	1.36006i	−0.0253687	+	0.289966i
$23$	6.70560	−	3.12687i	1.39822	−	0.651998i	0.430164	−	0.902751i	$-0.358456\pi$
$23$	6.70560	−	3.12687i	1.39822	−	0.651998i	0.968051	+	0.250752i	$0.0806780\pi$
$24$		0			0
$25$	3.33867	+	3.72200i	0.667733	+	0.744401i
$26$			5.04782i			0.989959i
$27$		0			0
$28$	−0.473914	−	0.473914i	−0.0895613	−	0.0895613i
$29$	0.586508	−	3.32625i	0.108912	−	0.617669i	−0.880674	−	0.473723i	$-0.842910\pi$
$29$	0.586508	−	3.32625i	0.108912	−	0.617669i	0.989586	−	0.143946i	$-0.0459791\pi$
$30$		0			0
$31$	3.73277	+	1.35862i	0.670426	+	0.244015i	0.654731	−	0.755862i	$-0.272782\pi$
$31$	3.73277	+	1.35862i	0.670426	+	0.244015i	0.0156946	+	0.999877i	$0.495004\pi$
$32$	−5.07868	−	0.444327i	−0.897792	−	0.0785466i
$33$		0			0
$34$	−1.53902	−	4.22842i	−0.263940	−	0.725168i
$35$	−1.10044	+	0.954786i	−0.186008	+	0.161388i
$36$		0			0
$37$	1.60572	+	0.430252i	0.263979	+	0.0707331i	0.388381	−	0.921499i	$-0.373034\pi$
$37$	1.60572	+	0.430252i	0.263979	+	0.0707331i	−0.124402	+	0.992232i	$0.539701\pi$
$38$	0.00740282		0.000647662i	0.00120090		0.000105065i
$39$		0			0
$40$	−1.05032	+	6.59139i	−0.166070	+	1.04219i
$41$	1.90299	−	0.335548i	0.297197	−	0.0524038i	−0.0230615	−	0.999734i	$-0.507341\pi$
$41$	1.90299	−	0.335548i	0.297197	−	0.0524038i	0.320258	+	0.947330i	$0.396230\pi$
$42$		0			0
$43$	−0.929732	−	10.6269i	−0.141783	−	1.62058i	−0.650400	−	0.759592i	$-0.725399\pi$
$43$	−0.929732	−	10.6269i	−0.141783	−	1.62058i	0.508617	−	0.860993i	$-0.330157\pi$
$44$	−0.712464	−	1.23402i	−0.107408	−	0.186036i
$45$		0			0
$46$	3.64603	−	6.31511i	0.537578	−	0.931113i
$47$	−6.61847	−	3.08624i	−0.965403	−	0.450175i	−0.125012	−	0.992155i	$-0.539897\pi$
$47$	−6.61847	−	3.08624i	−0.965403	−	0.450175i	−0.840391	+	0.541980i	$0.817675\pi$
$48$		0			0
$49$	4.22664	+	5.03711i	0.603806	+	0.719587i
$50$	4.79947	+	1.11755i	0.678747	+	0.158045i
$51$		0			0
$52$	−3.02186	−	4.31566i	−0.419056	−	0.598474i
$53$	1.18766	−	1.18766i	0.163138	−	0.163138i	−0.620817	−	0.783955i	$-0.713199\pi$
$53$	1.18766	−	1.18766i	0.163138	−	0.163138i	0.783955	+	0.620817i	$0.213199\pi$
$54$		0			0
$55$	−2.78529	+	1.35524i	−0.375568	+	0.182740i
$56$	−1.91530	−	0.337719i	−0.255942	−	0.0451295i
$57$		0			0
$58$	−1.40682	−	3.01694i	−0.184725	−	0.396144i
$59$	7.77643	−	6.52520i	1.01240	−	0.849508i	0.0237505	−	0.999718i	$-0.492439\pi$
$59$	7.77643	−	6.52520i	1.01240	−	0.849508i	0.988654	+	0.150210i	$0.0479948\pi$
$60$		0			0
$61$	−9.02437	+	3.28460i	−1.15545	+	0.420550i	−0.847471	−	0.530842i	$-0.821876\pi$
$61$	−9.02437	+	3.28460i	−1.15545	+	0.420550i	−0.307981	+	0.951392i	$0.599653\pi$
$62$	3.78162	−	1.01328i	0.480266	−	0.128687i
$63$		0			0
$64$	−5.88351	+	3.39685i	−0.735439	+	0.424606i
$65$	−9.82225	+	5.88925i	−1.21830	+	0.730472i
$66$		0			0
$67$	−12.3176	−	8.62489i	−1.50484	−	1.05370i	−0.979178	−	0.203002i	$-0.934930\pi$
$67$	−12.3176	−	8.62489i	−1.50484	−	1.05370i	−0.525658	−	0.850696i	$-0.676181\pi$
$68$	3.84712	+	2.69378i	0.466532	+	0.326669i
$69$		0			0
$70$	−0.348682	+	1.39291i	−0.0416754	+	0.166485i
$71$	−5.41550	+	3.12664i	−0.642702	+	0.371064i	−0.785654	−	0.618666i	$-0.787674\pi$
$71$	−5.41550	+	3.12664i	−0.642702	+	0.371064i	0.142953	+	0.989730i	$0.454340\pi$
$72$		0			0
$73$	12.1662	−	3.25991i	1.42394	−	0.381544i	0.537061	−	0.843543i	$-0.319534\pi$
$73$	12.1662	−	3.25991i	1.42394	−	0.381544i	0.886880	+	0.461999i	$0.152868\pi$
$74$	1.53958	−	0.560360i	0.178972	−	0.0651405i
$75$		0			0
$76$	−0.00594135	+	0.00498539i	−0.000681520	+	0.000571863i
$77$	−0.381436	−	0.817993i	−0.0434687	−	0.0932189i
$78$		0			0
$79$	−0.782046	−	0.137896i	−0.0879871	−	0.0155145i	0.129481	−	0.991582i	$-0.458669\pi$
$79$	−0.782046	−	0.137896i	−0.0879871	−	0.0155145i	−0.217468	+	0.976067i	$0.569780\pi$
$80$	0.865425	+	1.77862i	0.0967575	+	0.198856i
$81$		0			0
$82$	1.34666	−	1.34666i	0.148714	−	0.148714i
$83$	−5.32053	−	7.59850i	−0.584004	−	0.834044i	0.413053	−	0.910707i	$-0.364462\pi$
$83$	−5.32053	−	7.59850i	−0.584004	−	0.834044i	−0.997057	+	0.0766627i	$0.975574\pi$
$84$		0			0
$85$	6.43227	−	7.92795i	0.697678	−	0.859907i
$86$	−6.75799	−	8.05386i	−0.728733	−	0.868470i
$87$		0			0
$88$	−3.74748	−	1.74748i	−0.399482	−	0.186282i
$89$	−5.89645	+	10.2130i	−0.625023	+	1.08257i	0.363514	+	0.931589i	$0.381577\pi$
$89$	−5.89645	+	10.2130i	−0.625023	+	1.08257i	−0.988537	+	0.150982i	$0.951756\pi$
$90$		0			0
$91$	−1.66853	−	2.88997i	−0.174909	−	0.302951i
$92$	0.663323	+	7.58182i	0.0691562	+	0.790459i
$93$		0			0
$94$	−7.08796	+	1.24980i	−0.731068	+	0.128907i
$95$	0.00989706	+	0.0136491i	0.00101542	+	0.00140037i
$96$		0			0
$97$	−2.18091	+	0.190805i	−0.221438	+	0.0193733i	−0.197335	−	0.980336i	$-0.563229\pi$
$97$	−2.18091	+	0.190805i	−0.221438	+	0.0193733i	−0.0241031	+	0.999709i	$0.507673\pi$
$98$	6.25979	+	1.67731i	0.632334	+	0.169433i
$99$		0			0
$100$	−4.77234	+	1.91773i	−0.477234	+	0.191773i
$101$	−2.19882	−	6.04120i	−0.218790	−	0.601122i	0.780934	−	0.624614i	$-0.214744\pi$
$101$	−2.19882	−	6.04120i	−0.218790	−	0.601122i	−0.999724	+	0.0234923i	$0.992521\pi$
$102$		0			0
$103$	9.32840	+	0.816129i	0.919154	+	0.0804156i	0.536904	−	0.843643i	$-0.319594\pi$
$103$	9.32840	+	0.816129i	0.919154	+	0.0804156i	0.382250	+	0.924059i	$0.375149\pi$
$104$	−14.3661	−	5.22883i	−1.40871	−	0.512729i
$105$		0			0
$106$	0.287452	−	1.63022i	0.0279198	−	0.158341i
$107$	−2.45371	−	2.45371i	−0.237210	−	0.237210i	0.578484	−	0.815694i	$-0.303644\pi$
$107$	−2.45371	−	2.45371i	−0.237210	−	0.237210i	−0.815694	+	0.578484i	$0.803644\pi$
$108$		0			0
$109$			11.1343i			1.06647i	0.845967	+	0.533235i	$0.179024\pi$
$109$			11.1343i			1.06647i	−0.845967	+	0.533235i	$0.820976\pi$
$110$	−1.48254	+	2.66865i	−0.141354	+	0.254446i
$111$		0			0
$112$	−0.522352	+	0.243577i	−0.0493576	+	0.0230158i
$113$	−0.776537	+	8.87586i	−0.0730505	+	0.834971i	0.867969	+	0.496619i	$0.165425\pi$
$113$	−0.776537	+	8.87586i	−0.0730505	+	0.834971i	−0.941019	+	0.338353i	$0.890130\pi$
$114$		0			0
$115$	16.5420	−	0.273199i	1.54255	−	0.0254760i
$116$	3.00885	+	1.73716i	0.279365	+	0.161291i
$117$		0			0
$118$	2.58947	−	9.66403i	0.238380	−	0.889646i
$119$	2.27880	+	1.91214i	0.208897	+	0.175285i
$120$		0			0
$121$	1.57692	+	8.94314i	0.143356	+	0.813013i
$122$	−5.42888	+	7.75325i	−0.491508	+	0.701946i
$123$		0			0
$124$	−2.62652	+	3.13016i	−0.235868	+	0.281097i
$125$	3.42494	+	10.6428i	0.306336	+	0.951924i
$126$		0			0
$127$	0.737710	+	2.75317i	0.0654611	+	0.244304i	0.990902	−	0.134589i	$-0.0429714\pi$
$127$	0.737710	+	2.75317i	0.0654611	+	0.244304i	−0.925440	+	0.378893i	$0.876305\pi$
$128$	1.47937	−	3.17252i	0.130759	−	0.280413i
$129$		0			0
$130$	−4.60063	+	10.3071i	−0.403502	+	0.903994i
$131$	−2.22104	+	6.10227i	−0.194053	+	0.533158i	−0.998114	−	0.0613901i	$-0.980447\pi$
$131$	−2.22104	+	6.10227i	−0.194053	+	0.533158i	0.804060	+	0.594548i	$0.202669\pi$
$132$		0			0
$133$	−0.00402417	+	0.00281776i	−0.000348940	+	0.000244330i
$134$	−14.8201			−1.28026
$135$		0			0
$136$	13.6283			1.16862
$137$	15.1709	−	10.6228i	1.29614	−	0.907567i	0.297256	−	0.954798i	$-0.403929\pi$
$137$	15.1709	−	10.6228i	1.29614	−	0.907567i	0.998884	+	0.0472310i	$0.0150397\pi$
$138$		0			0
$139$	6.75787	−	18.5671i	0.573195	−	1.57484i	−0.226229	−	0.974074i	$-0.572640\pi$
$139$	6.75787	−	18.5671i	0.573195	−	1.57484i	0.799424	−	0.600767i	$-0.205138\pi$
$140$	−0.535753	−	1.39961i	−0.0452794	−	0.118289i
$141$		0			0
$142$	−2.60462	+	5.58563i	−0.218575	+	0.468735i
$143$	−1.83628	−	6.85307i	−0.153557	−	0.573083i
$144$		0			0
$145$	4.22916	−	6.25730i	0.351213	−	0.519641i
$146$	7.97931	−	9.50937i	0.660373	−	0.787001i
$147$		0			0
$148$	−0.980811	+	1.40074i	−0.0806222	+	0.115140i
$149$	−2.60422	−	14.7692i	−0.213346	−	1.20994i	−0.883754	−	0.467952i	$-0.844992\pi$
$149$	−2.60422	−	14.7692i	−0.213346	−	1.20994i	0.670408	−	0.741992i	$-0.266119\pi$
$150$		0			0
$151$	0.694966	+	0.583146i	0.0565555	+	0.0474557i	0.670627	−	0.741794i	$-0.266025\pi$
$151$	0.694966	+	0.583146i	0.0565555	+	0.0474557i	−0.614072	+	0.789250i	$0.710469\pi$
$152$	−0.00582502	+	0.0217393i	−0.000472472	+	0.00176329i
$153$		0			0
$154$	−0.770358	−	0.444766i	−0.0620772	−	0.0358403i
$155$	6.38367	+	6.17624i	0.512749	+	0.496087i
$156$		0			0
$157$	0.403811	−	4.61558i	0.0322276	−	0.368363i	−0.962907	−	0.269835i	$-0.913031\pi$
$157$	0.403811	−	4.61558i	0.0322276	−	0.368363i	0.995134	−	0.0985286i	$-0.0314136\pi$
$158$	−0.709324	+	0.330763i	−0.0564308	+	0.0263141i
$159$		0			0
$160$	−9.96516	−	5.53602i	−0.787815	−	0.437661i
$161$			4.82070i			0.379924i
$162$		0			0
$163$	−7.94001	−	7.94001i	−0.621909	−	0.621909i	0.324110	−	0.946019i	$-0.394935\pi$
$163$	−7.94001	−	7.94001i	−0.621909	−	0.621909i	−0.946019	+	0.324110i	$0.894935\pi$
$164$	−0.345161	+	1.95751i	−0.0269526	+	0.152856i
$165$		0			0
$166$	−8.59088	−	3.12682i	−0.666782	−	0.242689i
$167$	−0.896457	−	0.0784299i	−0.0693700	−	0.00606908i	0.0524179	−	0.998625i	$-0.483307\pi$
$167$	−0.896457	−	0.0784299i	−0.0693700	−	0.00606908i	−0.121788	+	0.992556i	$0.538863\pi$
$168$		0			0
$169$	−4.52560	−	12.4340i	−0.348123	−	0.956461i
$170$	0.711306	−	10.0367i	0.0545547	−	0.769777i
$171$		0			0
$172$	10.5992	+	2.84004i	0.808180	+	0.216551i
$173$	13.3057	−	1.16409i	1.01161	−	0.0885045i	0.430720	−	0.902486i	$-0.358260\pi$
$173$	13.3057	−	1.16409i	1.01161	−	0.0885045i	0.580891	+	0.813981i	$0.302704\pi$
$174$		0			0
$175$	−3.11718	+	0.946619i	−0.235637	+	0.0715577i
$176$	−1.20675	+	0.212783i	−0.0909622	+	0.0160391i
$177$		0			0
$178$	1.01299	+	11.5785i	0.0759268	+	0.867847i
$179$	3.72605	+	6.45370i	0.278498	+	0.482372i	0.971012	−	0.239032i	$-0.0768302\pi$
$179$	3.72605	+	6.45370i	0.278498	+	0.482372i	−0.692514	+	0.721405i	$0.743497\pi$
$180$		0			0
$181$	−13.1147	+	22.7153i	−0.974806	+	1.68841i	−0.294232	+	0.955734i	$0.595064\pi$
$181$	−13.1147	+	22.7153i	−0.974806	+	1.68841i	−0.680574	+	0.732679i	$0.738270\pi$
$182$	−2.98076	−	1.38995i	−0.220949	−	0.103030i
$183$		0			0
$184$	14.1960	+	16.9182i	1.04655	+	1.24722i
$185$	2.88658	+	2.34200i	0.212226	+	0.172187i
$186$		0			0
$187$	3.62762	+	5.18077i	0.265278	+	0.378856i
$188$	5.31170	−	5.31170i	0.387396	−	0.387396i
$189$		0			0
$190$	0.0157061	+	0.00542454i	0.00113944	+	0.000393537i
$191$	1.57094	+	0.276999i	0.113669	+	0.0200430i	0.230193	−	0.973145i	$-0.426064\pi$
$191$	1.57094	+	0.276999i	0.113669	+	0.0200430i	−0.116524	+	0.993188i	$0.537175\pi$
$192$		0			0
$193$	−3.55560	−	7.62500i	−0.255937	−	0.548860i	0.735792	−	0.677208i	$-0.236810\pi$
$193$	−3.55560	−	7.62500i	−0.255937	−	0.548860i	−0.991729	+	0.128348i	$0.959032\pi$
$194$	−1.65286	+	1.38691i	−0.118668	+	0.0995745i
$195$		0			0
$196$	−6.35595	+	2.31338i	−0.453996	+	0.165241i
$197$	10.9609	−	2.93696i	0.780931	−	0.209250i	0.153736	−	0.988112i	$-0.450869\pi$
$197$	10.9609	−	2.93696i	0.780931	−	0.209250i	0.627195	+	0.778862i	$0.284203\pi$
$198$		0			0
$199$	−21.0022	+	12.1256i	−1.48881	+	0.859563i	−0.999918	−	0.0127826i	$-0.995931\pi$
$199$	−21.0022	+	12.1256i	−1.48881	+	0.859563i	−0.488889	+	0.872346i	$0.662598\pi$
$200$	−8.15210	+	12.5017i	−0.576441	+	0.884001i
$201$		0			0
$202$	−5.19027	−	3.63427i	−0.365186	−	0.255706i
$203$	1.80267	+	1.26224i	0.126522	+	0.0885920i
$204$		0			0
$205$	4.19153	+	1.04925i	0.292749	+	0.0732826i
$206$	7.99248	−	4.61446i	0.556863	−	0.321505i
$207$		0			0
$208$	−4.37622	+	1.17261i	−0.303436	+	0.0813055i
$209$	−0.00981468	+	0.00357225i	−0.000678896	+	0.000247098i
$210$		0			0
$211$	6.98736	−	5.86309i	0.481029	−	0.403632i	−0.369769	−	0.929124i	$-0.620563\pi$
$211$	6.98736	−	5.86309i	0.481029	−	0.403632i	0.850799	+	0.525492i	$0.176119\pi$
$212$	0.730167	+	1.56585i	0.0501481	+	0.107543i
$213$		0			0
$214$	−3.36805	−	0.593878i	−0.230235	−	0.0405967i
$215$	7.78703	−	22.5463i	0.531071	−	1.53765i
$216$		0			0
$217$	−1.83011	+	1.83011i	−0.124236	+	0.124236i
$218$	6.29421	+	8.98907i	0.426298	+	0.608817i
$219$		0			0
$220$	−0.330076	−	3.16909i	−0.0222537	−	0.213660i
$221$	15.0310	+	17.9132i	1.01109	+	1.20497i
$222$		0			0
$223$	14.8136	+	6.90768i	0.991990	+	0.462572i	0.849708	−	0.527254i	$-0.176778\pi$
$223$	14.8136	+	6.90768i	0.991990	+	0.462572i	0.142282	+	0.989826i	$0.454556\pi$
$224$	1.66083	−	2.87663i	0.110969	−	0.192203i
$225$		0			0
$226$	4.39061	+	7.60476i	0.292059	+	0.505861i
$227$	−1.10129	−	12.5878i	−0.0730949	−	0.835479i	−0.940924	−	0.338617i	$-0.890041\pi$
$227$	−1.10129	−	12.5878i	−0.0730949	−	0.835479i	0.867830	−	0.496862i	$-0.165515\pi$
$228$		0			0
$229$	8.89322	−	1.56812i	0.587681	−	0.103624i	0.128102	−	0.991761i	$-0.459112\pi$
$229$	8.89322	−	1.56812i	0.587681	−	0.103624i	0.459579	+	0.888137i	$0.348000\pi$
$230$	13.2005	−	9.57177i	0.870413	−	0.631144i
$231$		0			0
$232$	10.0435	−	0.878692i	0.659388	−	0.0576889i
$233$	−20.6198	−	5.52507i	−1.35085	−	0.361959i	−0.490402	−	0.871496i	$-0.663150\pi$
$233$	−20.6198	−	5.52507i	−1.35085	−	0.361959i	−0.860449	+	0.509537i	$0.829817\pi$
$234$		0			0
$235$	−10.7014	−	12.3339i	−0.698081	−	0.804576i
$236$	3.57145	+	9.81248i	0.232482	+	0.638738i
$237$		0			0
$238$	2.92068	+	0.255527i	0.189320	+	0.0165633i
$239$	5.43398	+	1.97781i	0.351495	+	0.127934i	0.511733	−	0.859145i	$-0.329004\pi$
$239$	5.43398	+	1.97781i	0.351495	+	0.127934i	−0.160238	+	0.987078i	$0.551226\pi$
$240$		0			0
$241$	−4.00297	+	22.7020i	−0.257854	+	1.46236i	0.530784	+	0.847507i	$0.321897\pi$
$241$	−4.00297	+	22.7020i	−0.257854	+	1.46236i	−0.788639	+	0.614857i	$0.789214\pi$
$242$	6.32866	+	6.32866i	0.406822	+	0.406822i
$243$		0			0
$244$		−	9.87866i		−	0.632416i
$245$	4.03948	+	14.1374i	0.258073	+	0.903208i
$246$		0			0
$247$	−0.0349990	+	0.0163203i	−0.00222693	+	0.00103844i
$248$	−1.03342	+	11.8121i	−0.0656225	+	0.750069i
$249$		0			0
$250$	8.78146	+	6.65619i	0.555389	+	0.420974i
$251$	2.17404	+	1.25518i	0.137224	+	0.0792266i	0.567041	−	0.823690i	$-0.308088\pi$
$251$	2.17404	+	1.25518i	0.137224	+	0.0792266i	−0.429816	+	0.902916i	$0.641422\pi$
$252$		0			0
$253$	−2.65268	+	9.89993i	−0.166772	+	0.622403i
$254$	2.15195	+	1.80570i	0.135025	+	0.113300i
$255$		0			0
$256$	−2.95851	−	16.7785i	−0.184907	−	1.04866i
$257$	−7.24292	+	10.3440i	−0.451801	+	0.645238i	−0.978846	−	0.204599i	$-0.934411\pi$
$257$	−7.24292	+	10.3440i	−0.451801	+	0.645238i	0.527045	+	0.849837i	$0.323300\pi$
$258$		0			0
$259$	−0.696213	+	0.829715i	−0.0432606	+	0.0515560i
$260$	−2.23698	−	11.5663i	−0.138732	−	0.717309i
$261$		0			0
$262$	1.65649	+	6.18212i	0.102339	+	0.381933i
$263$	−7.09675	+	15.2190i	−0.437604	+	0.938445i	0.556584	+	0.830791i	$0.312112\pi$
$263$	−7.09675	+	15.2190i	−0.437604	+	0.938445i	−0.994188	+	0.107654i	$0.965666\pi$
$264$		0			0
$265$	3.50752	−	1.34263i	0.215465	−	0.0824772i
$266$	−0.00165597	+	0.00454974i	−0.000101534	+	0.000278962i
$267$		0			0
$268$	12.6705	−	8.87198i	0.773974	−	0.541942i
$269$	3.27377			0.199605			0.0998027	−	0.995007i	$-0.468179\pi$
$269$	3.27377			0.199605			0.0998027	+	0.995007i	$0.468179\pi$
$270$		0			0
$271$	8.46872			0.514438			0.257219	−	0.966353i	$-0.417194\pi$
$271$	8.46872			0.514438			0.257219	+	0.966353i	$0.417194\pi$
$272$	3.30833	−	2.31652i	0.200597	−	0.140459i
$273$		0			0
$274$	6.24292	−	17.1523i	0.377148	−	1.03621i
$275$	−6.92244	+	0.228717i	−0.417439	+	0.0137922i
$276$		0			0
$277$	−1.04261	+	2.23589i	−0.0626445	+	0.134342i	−0.935137	−	0.354285i	$-0.884724\pi$
$277$	−1.04261	+	2.23589i	−0.0626445	+	0.134342i	0.872493	+	0.488627i	$0.162502\pi$
$278$	−5.04014	−	18.8101i	−0.302288	−	1.12815i
$279$		0			0
$280$	−3.60304	−	2.43521i	−0.215323	−	0.145531i
$281$	12.4917	−	14.8870i	0.745190	−	0.888082i	−0.251626	−	0.967825i	$-0.580965\pi$
$281$	12.4917	−	14.8870i	0.745190	−	0.888082i	0.996816	+	0.0797423i	$0.0254097\pi$
$282$		0			0
$283$	−10.8099	+	15.4382i	−0.642583	+	0.917703i	−0.999867	−	0.0162923i	$-0.994814\pi$
$283$	−10.8099	+	15.4382i	−0.642583	+	0.917703i	0.357285	+	0.933996i	$0.383703\pi$
$284$	−1.11698	−	6.33470i	−0.0662805	−	0.375896i
$285$		0			0
$286$	−5.35653	−	4.49466i	−0.316738	−	0.265775i
$287$	−0.325858	+	1.21612i	−0.0192348	+	0.0717853i
$288$		0			0
$289$	−3.33013	−	1.92265i	−0.195890	−	0.113097i
$290$	−0.122916	−	7.44248i	−0.00721789	−	0.437037i
$291$		0			0
$292$	−1.12920	+	12.9069i	−0.0660817	+	0.755317i
$293$	−3.65580	+	1.70473i	−0.213574	+	0.0995913i	−0.526461	−	0.850199i	$-0.676482\pi$
$293$	−3.65580	+	1.70473i	−0.213574	+	0.0995913i	0.312887	+	0.949790i	$0.398704\pi$
$294$		0			0
$295$	21.8258	−	6.23626i	1.27075	−	0.363089i
$296$			4.96208i			0.288415i
$297$		0			0
$298$	−10.4515	−	10.4515i	−0.605441	−	0.605441i
$299$	−6.58033	+	37.3189i	−0.380551	+	2.15821i
$300$		0			0
$301$	6.53123	+	2.37717i	0.376454	+	0.137018i
$302$	0.890722	+	0.0779280i	0.0512553	+	0.00448426i
$303$		0			0
$304$	0.00228116	+	0.00626744i	0.000130834	+	0.000359462i
$305$	−21.4204	−	1.51808i	−1.22653	−	0.0869251i
$306$		0			0
$307$	8.60536	+	2.30580i	0.491134	+	0.131599i	0.495882	−	0.868390i	$-0.334845\pi$
$307$	8.60536	+	2.30580i	0.491134	+	0.131599i	−0.00474824	+	0.999989i	$0.501511\pi$
$308$	0.924879	−	0.0809164i	0.0526999	−	0.00461064i
$309$		0			0
$310$	8.64518	+	1.37759i	0.491013	+	0.0782417i
$311$	−26.8272	+	4.73035i	−1.52123	+	0.268234i	−0.870916	−	0.491433i	$-0.836473\pi$
$311$	−26.8272	+	4.73035i	−1.52123	+	0.268234i	−0.650313	+	0.759666i	$0.725362\pi$
$312$		0			0
$313$	1.36924	+	15.6505i	0.0773941	+	0.884618i	0.931315	+	0.364215i	$0.118663\pi$
$313$	1.36924	+	15.6505i	0.0773941	+	0.884618i	−0.853921	+	0.520403i	$0.825782\pi$
$314$	−2.28318	−	3.95459i	−0.128847	−	0.223170i
$315$		0			0
$316$	0.408430	−	0.707422i	0.0229760	−	0.0397956i
$317$	−12.8207	−	5.97838i	−0.720081	−	0.335779i	0.0277988	−	0.999614i	$-0.491150\pi$
$317$	−12.8207	−	5.97838i	−0.720081	−	0.335779i	−0.747880	+	0.663834i	$0.768928\pi$
$318$		0			0
$319$	3.00744	+	3.58413i	0.168384	+	0.200673i
$320$	−15.1094	+	1.57372i	−0.844643	+	0.0879735i
$321$		0			0
$322$	2.72514	+	3.89191i	0.151866	+	0.216888i
$323$	0.0243419	−	0.0243419i	0.00135442	−	0.00135442i
$324$		0			0
$325$	−25.4235	+	3.07315i	−1.41024	+	0.170467i
$326$	−10.8987	−	1.92174i	−0.603624	−	0.106435i
$327$		0			0
$328$	2.43764	+	5.22754i	0.134596	+	0.288643i
$329$	3.64488	−	3.05842i	0.200949	−	0.168616i
$330$		0			0
$331$	15.8479	−	5.76816i	0.871078	−	0.317047i	0.132475	−	0.991186i	$-0.457708\pi$
$331$	15.8479	−	5.76816i	0.871078	−	0.317047i	0.738604	+	0.674140i	$0.235485\pi$
$332$	9.21668	−	2.46960i	0.505831	−	0.135537i
$333$		0			0
$334$	−0.768076	+	0.443449i	−0.0420273	+	0.0242645i
$335$	−17.2905	−	28.8375i	−0.944680	−	1.57556i
$336$		0			0
$337$	−16.0410	−	11.2321i	−0.873811	−	0.611849i	0.0482752	−	0.998834i	$-0.484628\pi$
$337$	−16.0410	−	11.2321i	−0.873811	−	0.611849i	−0.922086	+	0.386985i	$0.873516\pi$
$338$	−10.6826	−	7.48005i	−0.581058	−	0.406861i
$339$		0			0
$340$	5.40027	+	9.00672i	0.292871	+	0.488458i
$341$	−4.76543	+	2.75132i	−0.258063	+	0.148993i
$342$		0			0
$343$	−8.54371	+	2.28928i	−0.461317	+	0.123610i
$344$	29.9216	−	10.8906i	1.61326	−	0.587180i
$345$		0			0
$346$	10.0840	−	8.46151i	0.542121	−	0.454894i
$347$	−4.69183	−	10.0617i	−0.251871	−	0.540138i	0.739199	−	0.673488i	$-0.235205\pi$
$347$	−4.69183	−	10.0617i	−0.251871	−	0.540138i	−0.991069	+	0.133349i	$0.957427\pi$
$348$		0			0
$349$	−5.91569	−	1.04309i	−0.316659	−	0.0558356i	0.0130596	−	0.999915i	$-0.495843\pi$
$349$	−5.91569	−	1.04309i	−0.316659	−	0.0558356i	−0.329719	+	0.944079i	$0.606954\pi$
$350$	−1.98148	+	2.52638i	−0.105915	+	0.135041i
$351$		0			0
$352$	4.99364	−	4.99364i	0.266162	−	0.266162i
$353$	−6.60297	−	9.43001i	−0.351440	−	0.501909i	0.604044	−	0.796951i	$-0.293555\pi$
$353$	−6.60297	−	9.43001i	−0.351440	−	0.501909i	−0.955484	+	0.295042i	$0.904666\pi$
$354$		0			0
$355$	−13.9075	+	1.44853i	−0.738135	+	0.0768802i
$356$	−7.79749	−	9.29269i	−0.413266	−	0.492512i
$357$		0			0
$358$	6.65644	+	3.10395i	0.351804	+	0.164049i
$359$	−7.64807	+	13.2468i	−0.403649	+	0.699141i	−0.994163	−	0.107886i	$-0.965592\pi$
$359$	−7.64807	+	13.2468i	−0.403649	+	0.699141i	0.590514	+	0.807028i	$0.298925\pi$
$360$		0			0
$361$	−9.49997	−	16.4544i	−0.499999	−	0.866023i
$362$	2.25305	+	25.7525i	0.118418	+	1.35352i
$363$		0			0
$364$	3.38050	−	0.596074i	0.177187	−	0.0312428i
$365$	27.8131	+	4.43195i	1.45581	+	0.231979i
$366$		0			0
$367$	−12.8423	+	1.12355i	−0.670361	+	0.0586490i	−0.417255	−	0.908790i	$-0.637008\pi$
$367$	−12.8423	+	1.12355i	−0.670361	+	0.0586490i	−0.253106	+	0.967439i	$0.581452\pi$
$368$	6.32188	+	1.69394i	0.329551	+	0.0883028i
$369$		0			0
$370$	3.65437	+	0.258988i	0.189982	+	0.0134641i
$371$	0.374288	+	1.02835i	0.0194321	+	0.0533892i
$372$		0			0
$373$	−16.1018	−	1.40873i	−0.833720	−	0.0729411i	−0.337702	−	0.941253i	$-0.609650\pi$
$373$	−16.1018	−	1.40873i	−0.833720	−	0.0729411i	−0.496018	+	0.868312i	$0.665205\pi$
$374$	5.85739	+	2.13192i	0.302878	+	0.110239i
$375$		0			0
$376$	3.78520	−	21.4670i	0.195207	−	1.10707i
$377$	12.2322	+	12.2322i	0.629989	+	0.629989i
$378$		0			0
$379$		−	9.64380i		−	0.495369i	−0.968841	−	0.247684i	$-0.920330\pi$
$379$		−	9.64380i		−	0.495369i	0.968841	−	0.247684i	$-0.0796696\pi$
$380$	−0.0166753	+	0.00476463i	−0.000855427	+	0.000244420i
$381$		0			0
$382$	1.42486	−	0.664424i	0.0729023	−	0.0339949i
$383$	1.26741	−	14.4866i	0.0647619	−	0.740232i	−0.892507	−	0.451033i	$-0.851056\pi$
$383$	1.26741	−	14.4866i	0.0647619	−	0.740232i	0.957269	−	0.289199i	$-0.0933888\pi$
$384$		0			0
$385$	−0.0333266	−	2.01790i	−0.00169848	−	0.102842i
$386$	−7.18097	−	4.14594i	−0.365502	−	0.211023i
$387$		0			0
$388$	0.582850	−	2.17522i	0.0295897	−	0.110430i
$389$	12.6045	+	10.5764i	0.639073	+	0.536246i	0.903733	−	0.428096i	$-0.140815\pi$
$389$	12.6045	+	10.5764i	0.639073	+	0.536246i	−0.264660	+	0.964342i	$0.585260\pi$
$390$		0			0
$391$	−5.86593	−	33.2673i	−0.296653	−	1.68240i
$392$	−11.2579	+	16.0779i	−0.568608	+	0.812056i
$393$		0			0
$394$	7.18883	−	8.56731i	0.362168	−	0.431615i
$395$	−1.47118	−	0.994333i	−0.0740229	−	0.0500303i
$396$		0			0
$397$	−5.64123	−	21.0533i	−0.283125	−	1.05664i	−0.950199	−	0.311645i	$-0.899120\pi$
$397$	−5.64123	−	21.0533i	−0.283125	−	1.05664i	0.667073	−	0.744992i	$-0.267547\pi$
$398$	−10.1012	+	21.6620i	−0.506325	+	1.08582i
$399$		0			0
$400$	0.146054	+	4.42052i	0.00730270	+	0.221026i
$401$	−9.14946	+	25.1379i	−0.456902	+	1.25533i	0.470877	+	0.882199i	$0.343938\pi$
$401$	−9.14946	+	25.1379i	−0.456902	+	1.25533i	−0.927779	+	0.373130i	$0.878285\pi$
$402$		0			0
$403$	−16.6658	+	11.6695i	−0.830182	+	0.581300i
$404$	6.61309			0.329013
$405$		0			0
$406$	2.16890			0.107641
$407$	−1.88633	+	1.32082i	−0.0935019	+	0.0654707i
$408$		0			0
$409$	−6.85481	+	18.8334i	−0.338949	+	0.931253i	0.646745	+	0.762706i	$0.276130\pi$
$409$	−6.85481	+	18.8334i	−0.338949	+	0.931253i	−0.985694	+	0.168547i	$0.946092\pi$
$410$	3.97710	−	1.52238i	0.196415	−	0.0751850i
$411$		0			0
$412$	−4.07078	+	8.72982i	−0.200553	+	0.430088i
$413$	1.71187	+	6.38878i	0.0842355	+	0.314371i
$414$		0			0
$415$	−3.93862	−	20.3645i	−0.193339	−	0.999655i
$416$	16.7838	−	20.0021i	0.822892	−	0.980684i
$417$		0			0
$418$	−0.00590432	+	0.00843224i	−0.000288790	+	0.000412435i
$419$	−0.389697	−	2.21008i	−0.0190379	−	0.107969i	0.973808	−	0.227372i	$-0.0730133\pi$
$419$	−0.389697	−	2.21008i	−0.0190379	−	0.107969i	−0.992846	+	0.119402i	$0.961902\pi$
$420$		0			0
$421$	−17.9696	−	15.0783i	−0.875786	−	0.734872i	0.0895219	−	0.995985i	$-0.471466\pi$
$421$	−17.9696	−	15.0783i	−0.875786	−	0.734872i	−0.965308	+	0.261113i	$0.915911\pi$
$422$	2.32672	−	8.68342i	0.113263	−	0.422702i
$423$		0			0
$424$	4.34185	+	2.50677i	0.210859	+	0.121739i
$425$	20.3596	−	10.3256i	0.987587	−	0.500866i
$426$		0			0
$427$	0.545349	−	6.23337i	0.0263913	−	0.301654i
$428$	3.23505	−	1.50853i	0.156372	−	0.0729176i
$429$		0			0
$430$	−6.45874	−	22.6044i	−0.311468	−	1.09008i
$431$		−	15.7591i		−	0.759089i	−0.925173	−	0.379545i	$-0.876081\pi$
$431$		−	15.7591i		−	0.759089i	0.925173	−	0.379545i	$-0.123919\pi$
$432$		0			0
$433$	14.0286	+	14.0286i	0.674170	+	0.674170i	0.958675	−	0.284505i	$-0.0918291\pi$
$433$	14.0286	+	14.0286i	0.674170	+	0.674170i	−0.284505	+	0.958675i	$0.591829\pi$
$434$	−0.442947	+	2.51208i	−0.0212621	+	0.120584i
$435$		0			0
$436$	−10.7625	−	3.91724i	−0.515432	−	0.187602i
$437$	0.0555739	+	0.00486209i	0.00265846	+	0.000232585i
$438$		0			0
$439$	1.43394	+	3.93972i	0.0684382	+	0.188033i	0.969197	−	0.246288i	$-0.0792108\pi$
$439$	1.43394	+	3.93972i	0.0684382	+	0.188033i	−0.900759	+	0.434320i	$0.856989\pi$
$440$	−6.05928	−	6.98365i	−0.288865	−	0.332932i
$441$		0			0
$442$	22.2614	+	5.96491i	1.05886	+	0.283722i
$443$	−21.2489	+	1.85904i	−1.00957	+	0.0883257i	−0.579922	−	0.814672i	$-0.696917\pi$
$443$	−21.2489	+	1.85904i	−1.00957	+	0.0883257i	−0.429646	+	0.902998i	$0.641361\pi$
$444$		0			0
$445$	−21.3481	+	15.4797i	−1.01200	+	0.733808i
$446$	15.8644	−	2.79732i	0.751201	−	0.132457i
$447$		0			0
$448$	−0.385789	−	4.40959i	−0.0182268	−	0.208333i
$449$	−9.32000	−	16.1427i	−0.439838	−	0.761822i	0.557839	−	0.829949i	$-0.311631\pi$
$449$	−9.32000	−	16.1427i	−0.439838	−	0.761822i	−0.997677	+	0.0681276i	$0.978297\pi$
$450$		0			0
$451$	−1.33838	+	2.31815i	−0.0630221	+	0.109157i
$452$	−8.30633	−	3.87330i	−0.390697	−	0.182185i
$453$		0			0
$454$	−8.00497	−	9.53996i	−0.375692	−	0.447732i
$455$	−0.773008	−	7.42173i	−0.0362392	−	0.347936i
$456$		0			0
$457$	8.19900	+	11.7094i	0.383533	+	0.547742i	0.963780	−	0.266699i	$-0.0859328\pi$
$457$	8.19900	+	11.7094i	0.383533	+	0.547742i	−0.580247	+	0.814441i	$0.697044\pi$
$458$	6.29334	−	6.29334i	0.294068	−	0.294068i
$459$		0			0
$460$	−5.55570	+	16.0858i	−0.259036	+	0.750006i
$461$	−24.9949	−	4.40727i	−1.16413	−	0.205267i	−0.441992	−	0.897019i	$-0.645728\pi$
$461$	−24.9949	−	4.40727i	−1.16413	−	0.205267i	−0.722135	+	0.691752i	$0.756839\pi$
$462$		0			0
$463$	−5.43841	−	11.6627i	−0.252744	−	0.542012i	0.738469	−	0.674288i	$-0.235549\pi$
$463$	−5.43841	−	11.6627i	−0.252744	−	0.542012i	−0.991213	+	0.132276i	$0.957772\pi$
$464$	2.28875	−	1.92049i	0.106252	−	0.0891563i
$465$		0			0
$466$	−19.7704	+	7.19584i	−0.915846	+	0.333341i
$467$	−26.2781	+	7.04119i	−1.21600	+	0.325828i	−0.809115	−	0.587650i	$-0.800053\pi$
$467$	−26.2781	+	7.04119i	−1.21600	+	0.325828i	−0.406890	+	0.913477i	$0.633387\pi$
$468$		0			0
$469$	8.48478	−	4.89869i	0.391791	−	0.226200i
$470$	−15.6120	−	3.90808i	−0.720126	−	0.180266i
$471$		0			0
$472$	24.8215	+	17.3802i	1.14250	+	0.799988i
$473$	12.1047	+	8.47577i	0.556572	+	0.389716i
$474$		0			0
$475$	0.00776886	+	0.0368902i	0.000356460	+	0.00169264i
$476$	−2.65002	+	1.52999i	−0.121464	+	0.0701270i
$477$		0			0
$478$	5.50508	−	1.47508i	0.251797	−	0.0674687i
$479$	17.2415	−	6.27539i	0.787784	−	0.286730i	0.0833693	−	0.996519i	$-0.473432\pi$
$479$	17.2415	−	6.27539i	0.787784	−	0.286730i	0.704415	+	0.709789i	$0.251210\pi$
$480$		0			0
$481$	−6.52224	+	5.47281i	−0.297388	+	0.249538i
$482$	9.60172	+	20.5910i	0.437346	+	0.937892i
$483$		0			0
$484$	−9.19935	−	1.62209i	−0.418152	−	0.0737315i
$485$	−4.62709	−	1.59810i	−0.210105	−	0.0725659i
$486$		0			0
$487$	4.34114	−	4.34114i	0.196716	−	0.196716i	−0.601875	−	0.798591i	$-0.705579\pi$
$487$	4.34114	−	4.34114i	0.196716	−	0.196716i	0.798591	+	0.601875i	$0.205579\pi$
$488$	−16.4422	−	23.4819i	−0.744302	−	1.06297i
$489$		0			0
$490$	11.2531	+	9.13011i	0.508364	+	0.412456i
$491$	−17.5435	−	20.9075i	−0.791728	−	0.943544i	0.207672	−	0.978199i	$-0.433411\pi$
$491$	−17.5435	−	20.9075i	−0.791728	−	0.943544i	−0.999399	+	0.0346544i	$0.988967\pi$
$492$		0			0
$493$	−13.9760	−	6.51712i	−0.629448	−	0.293516i
$494$	−0.0190300	+	0.0329609i	−0.000856199	+	0.00148298i
$495$		0			0
$496$	1.75694	+	3.04310i	0.0788887	+	0.136639i
$497$	−0.355101	−	4.05882i	−0.0159284	−	0.182063i
$498$		0			0
$499$	43.3225	−	7.63893i	1.93938	−	0.341965i	0.939382	−	0.342871i	$-0.111399\pi$
$499$	43.3225	−	7.63893i	1.93938	−	0.341965i	1.00000		0.000905893i	$0.000288355\pi$
$500$	−11.4925	−	0.433752i	−0.513958	−	0.0193980i
$501$		0			0
$502$	2.46473	−	0.215636i	0.110006	−	0.00962432i
$503$	4.03331	+	1.08072i	0.179836	+	0.0481870i	0.347613	−	0.937638i	$-0.386992\pi$
$503$	4.03331	+	1.08072i	0.179836	+	0.0481870i	−0.167777	+	0.985825i	$0.553659\pi$
$504$		0			0
$505$	1.01625	−	14.3395i	0.0452226	−	0.638100i
$506$	3.45484	+	9.49210i	0.153586	+	0.421975i
$507$		0			0
$508$	−2.92079	−	0.255536i	−0.129589	−	0.0113376i
$509$	1.50937	+	0.549366i	0.0669017	+	0.0243502i	0.375254	−	0.926922i	$-0.377555\pi$
$509$	1.50937	+	0.549366i	0.0669017	+	0.0243502i	−0.308353	+	0.951272i	$0.599778\pi$
$510$		0			0
$511$	−1.42504	+	8.08181i	−0.0630401	+	0.357518i
$512$	−6.92298	−	6.92298i	−0.305956	−	0.305956i
$513$		0			0
$514$			12.4454i			0.548945i
$515$	18.3038	+	10.1684i	0.806561	+	0.448075i
$516$		0			0
$517$	9.16819	−	4.27520i	0.403216	−	0.188023i
$518$	−0.0930377	+	1.06343i	−0.00408784	+	0.0467242i
$519$		0			0
$520$	−24.5684	−	23.7701i	−1.07740	−	1.04239i
$521$	28.3338	+	16.3586i	1.24133	+	0.716681i	0.969365	−	0.245626i	$-0.0789936\pi$
$521$	28.3338	+	16.3586i	1.24133	+	0.716681i	0.271964	+	0.962308i	$0.412327\pi$
$522$		0			0
$523$	−10.7572	+	40.1466i	−0.470381	+	1.75549i	0.168021	+	0.985783i	$0.446262\pi$
$523$	−10.7572	+	40.1466i	−0.470381	+	1.75549i	−0.638402	+	0.769703i	$0.720404\pi$
$524$	−5.11713	−	4.29378i	−0.223543	−	0.187575i
$525$		0			0
$526$	2.87389	+	16.2986i	0.125307	+	0.710654i
$527$	10.4026	−	14.8564i	0.453144	−	0.647156i
$528$		0			0
$529$	20.4037	−	24.3162i	0.887116	−	1.05722i
$530$	2.07275	−	3.06676i	0.0900344	−	0.133211i
$531$		0			0
$532$	−0.00130790	−	0.00488116i	−5.67048e−5	−	0.000211625i
$533$	−4.18262	+	8.96966i	−0.181169	+	0.388519i
$534$		0			0
$535$	−2.77389	−	7.24656i	−0.119926	−	0.313296i
$536$	15.3515	−	42.1779i	0.663084	−	1.82181i
$537$		0			0
$538$	2.64303	−	1.85067i	0.113949	−	0.0797879i
$539$	−9.10864			−0.392337
$540$		0			0
$541$	14.5826			0.626954			0.313477	−	0.949596i	$-0.398506\pi$
$541$	14.5826			0.626954			0.313477	+	0.949596i	$0.398506\pi$
$542$	6.83708	−	4.78737i	0.293678	−	0.205635i
$543$		0			0
$544$	−7.96090	+	21.8724i	−0.341321	+	0.937771i
$545$	−10.1479	+	22.7350i	−0.434687	+	0.973861i
$546$		0			0
$547$	5.97161	−	12.8062i	0.255327	−	0.547551i	−0.736304	−	0.676651i	$-0.763431\pi$
$547$	5.97161	−	12.8062i	0.255327	−	0.547551i	0.991632	+	0.129099i	$0.0412085\pi$
$548$	4.93072	+	18.4017i	0.210630	+	0.786082i
$549$		0			0
$550$	−5.45942	+	4.09791i	−0.232790	+	0.174735i
$551$	0.0163695	−	0.0195084i	0.000697364	−	0.000831086i
$552$		0			0
$553$	0.296770	−	0.423831i	0.0126199	−	0.0180231i
$554$	0.422214	+	2.39450i	0.0179382	+	0.101732i
$555$		0			0
$556$	15.5697	+	13.0645i	0.660301	+	0.554058i
$557$	−6.98848	+	26.0814i	−0.296111	+	1.10510i	0.644220	+	0.764841i	$0.277182\pi$
$557$	−6.98848	+	26.0814i	−0.296111	+	1.10510i	−0.940331	+	0.340262i	$0.889484\pi$
$558$		0			0
$559$	47.3160	+	27.3179i	2.00125	+	1.15542i
$560$	−1.28859	+	0.0212816i	−0.0544527	+	0.000899314i
$561$		0			0
$562$	1.66931	−	19.0803i	0.0704155	−	0.804853i
$563$	−4.52364	+	2.10941i	−0.190649	+	0.0889009i	−0.515598	−	0.856830i	$-0.672430\pi$
$563$	−4.52364	+	2.10941i	−0.190649	+	0.0889009i	0.324950	+	0.945731i	$0.394653\pi$
$564$		0			0
$565$	−9.67515	+	17.4158i	−0.407037	+	0.732690i
$566$			18.5746i			0.780748i
$567$		0			0
$568$	−13.1987	−	13.1987i	−0.553804	−	0.553804i
$569$	2.39518	−	13.5837i	0.100411	−	0.569459i	−0.892543	−	0.450962i	$-0.851081\pi$
$569$	2.39518	−	13.5837i	0.100411	−	0.569459i	0.992954	−	0.118497i	$-0.0378077\pi$
$570$		0			0
$571$	4.72552	+	1.71995i	0.197757	+	0.0719776i	0.439000	−	0.898487i	$-0.355333\pi$
$571$	4.72552	+	1.71995i	0.197757	+	0.0719776i	−0.241243	+	0.970465i	$0.577555\pi$
$572$	7.27031	+	0.636069i	0.303987	+	0.0265954i
$573$		0			0
$574$	0.424397	+	1.16602i	0.0177140	+	0.0486688i
$575$	34.0260	+	14.5187i	1.41898	+	0.605471i
$576$		0			0
$577$	−2.65137	−	0.710433i	−0.110378	−	0.0295757i	0.203207	−	0.979136i	$-0.434863\pi$
$577$	−2.65137	−	0.710433i	−0.110378	−	0.0295757i	−0.313585	+	0.949560i	$0.601530\pi$
$578$	−3.77540	+	0.330305i	−0.157036	+	0.0137389i
$579$		0			0
$580$	4.56050	+	6.28940i	0.189364	+	0.261153i
$581$	5.95200	−	1.04950i	0.246930	−	0.0435405i
$582$		0			0
$583$	0.202782	+	2.31781i	0.00839837	+	0.0959938i
$584$	18.7982	+	32.5595i	0.777876	+	1.34732i
$585$		0			0
$586$	−1.98777	+	3.44291i	−0.0821138	+	0.142225i
$587$	−18.7722	−	8.75362i	−0.774811	−	0.361300i	−0.00534328	−	0.999986i	$-0.501701\pi$
$587$	−18.7722	−	8.75362i	−0.774811	−	0.361300i	−0.769468	+	0.638685i	$0.779479\pi$
$588$		0			0
$589$	0.0192521	+	0.0229437i	0.000793268	+	0.000945380i
$590$	14.0953	−	17.3729i	0.580295	−	0.715229i
$591$		0			0
$592$	0.843448	+	1.20457i	0.0346655	+	0.0495075i
$593$	−33.2020	+	33.2020i	−1.36344	+	1.36344i	−0.493956	+	0.869487i	$0.664450\pi$
$593$	−33.2020	+	33.2020i	−1.36344	+	1.36344i	−0.869487	+	0.493956i	$0.835550\pi$
$594$		0			0
$595$	2.91032	+	5.98130i	0.119312	+	0.245209i
$596$	15.1924	+	2.67882i	0.622303	+	0.109729i
$597$		0			0
$598$	15.7839	+	33.8487i	0.645452	+	1.38418i
$599$	9.01503	−	7.56451i	0.368344	−	0.309078i	−0.439762	−	0.898114i	$-0.644937\pi$
$599$	9.01503	−	7.56451i	0.368344	−	0.309078i	0.808106	+	0.589037i	$0.200493\pi$
$600$		0			0
$601$	13.4574	−	4.89809i	0.548938	−	0.199797i	−0.0526366	−	0.998614i	$-0.516763\pi$
$601$	13.4574	−	4.89809i	0.548938	−	0.199797i	0.601575	+	0.798817i	$0.294540\pi$
$602$	6.61670	−	1.77294i	0.269677	−	0.0722596i
$603$		0			0
$604$	−0.808178	+	0.466602i	−0.0328843	+	0.0189858i
$605$	−4.93096	+	19.6982i	−0.200472	+	0.800844i
$606$		0			0
$607$	16.7167	+	11.7051i	0.678509	+	0.475097i	0.861328	−	0.508049i	$-0.169633\pi$
$607$	16.7167	+	11.7051i	0.678509	+	0.475097i	−0.182819	+	0.983147i	$0.558522\pi$
$608$	−0.0314873	−	0.0220476i	−0.00127698	−	0.000894150i
$609$		0			0
$610$	−18.1516	+	10.8834i	−0.734936	+	0.440655i
$611$	32.3913	−	18.7011i	1.31041	−	0.756566i
$612$		0			0
$613$	32.1941	−	8.62637i	1.30031	−	0.348416i	0.458740	−	0.888571i	$-0.348301\pi$
$613$	32.1941	−	8.62637i	1.30031	−	0.348416i	0.841566	+	0.540155i	$0.181634\pi$
$614$	8.25087	−	3.00307i	0.332978	−	0.121194i
$615$		0			0
$616$	2.06379	−	1.73172i	0.0831523	−	0.0697731i
$617$	0.373483	+	0.800937i	0.0150359	+	0.0322445i	0.913682	−	0.406429i	$-0.133226\pi$
$617$	0.373483	+	0.800937i	0.0150359	+	0.0322445i	−0.898646	+	0.438674i	$0.855448\pi$
$618$		0			0
$619$	−11.2863	−	1.99007i	−0.453633	−	0.0799877i	−0.0578365	−	0.998326i	$-0.518420\pi$
$619$	−11.2863	−	1.99007i	−0.453633	−	0.0799877i	−0.395796	+	0.918338i	$0.629531\pi$
$620$	−8.21593	+	3.99763i	−0.329960	+	0.160549i
$621$		0			0
$622$	−18.9844	+	18.9844i	−0.761204	+	0.761204i
$623$	−4.40717	−	6.29409i	−0.176569	−	0.252167i
$624$		0			0
$625$	−2.70661	+	24.8531i	−0.108264	+	0.994122i
$626$	9.95267	+	11.8611i	0.397789	+	0.474066i
$627$		0			0
$628$	4.31941	+	2.01418i	0.172363	+	0.0803744i
$629$	3.79491	−	6.57297i	0.151313	−	0.262082i
$630$		0			0
$631$	0.493720	+	0.855149i	0.0196547	+	0.0340429i	0.875685	−	0.482882i	$-0.160410\pi$
$631$	0.493720	+	0.855149i	0.0196547	+	0.0340429i	−0.856031	+	0.516925i	$0.827077\pi$
$632$	−0.206592	−	2.36136i	−0.00821780	−	0.0939299i
$633$		0			0
$634$	−13.7301	+	2.42099i	−0.545293	+	0.0961500i
$635$	−1.00294	+	6.29404i	−0.0398004	+	0.249771i
$636$		0			0
$637$	−33.5496	+	2.93521i	−1.32928	+	0.116297i
$638$	4.45412	+	1.19348i	0.176340	+	0.0472502i
$639$		0			0
$640$	5.91217	−	5.12963i	0.233699	−	0.202766i
$641$	9.55555	+	26.2536i	0.377421	+	1.03696i	0.972421	+	0.233231i	$0.0749298\pi$
$641$	9.55555	+	26.2536i	0.377421	+	1.03696i	−0.595000	+	0.803726i	$0.702848\pi$
$642$		0			0
$643$	−29.9171	−	2.61741i	−1.17982	−	0.103221i	−0.519677	−	0.854363i	$-0.673948\pi$
$643$	−29.9171	−	2.61741i	−1.17982	−	0.103221i	−0.660140	+	0.751142i	$0.729503\pi$
$644$	−4.65975	−	1.69601i	−0.183620	−	0.0668322i
$645$		0			0
$646$	0.00589152	−	0.0334124i	0.000231799	−	0.00131460i
$647$	22.0995	+	22.0995i	0.868820	+	0.868820i	0.992342	−	0.123522i	$-0.0394188\pi$
$647$	22.0995	+	22.0995i	0.868820	+	0.868820i	−0.123522	+	0.992342i	$0.539419\pi$
$648$		0			0
$649$			14.0622i			0.551988i
$650$	−18.7880	+	16.8530i	−0.736926	+	0.661028i
$651$		0			0
$652$	10.4684	−	4.88147i	0.409972	−	0.191173i
$653$	0.292733	−	3.34596i	0.0114555	−	0.130937i	−0.988313	−	0.152436i	$-0.951288\pi$
$653$	0.292733	−	3.34596i	0.0114555	−	0.130937i	0.999769	+	0.0214986i	$0.00684375\pi$
$654$		0			0
$655$	−10.0968	+	10.4359i	−0.394515	+	0.407765i
$656$	1.48032	+	0.854663i	0.0577968	+	0.0333690i
$657$		0			0
$658$	1.21371	−	4.52962i	0.0473152	−	0.176583i
$659$	−19.8580	−	16.6629i	−0.773560	−	0.649094i	0.168058	−	0.985777i	$-0.446250\pi$
$659$	−19.8580	−	16.6629i	−0.773560	−	0.649094i	−0.941618	+	0.336683i	$0.890695\pi$
$660$		0			0
$661$	6.41723	+	36.3939i	0.249601	+	1.41556i	0.809559	+	0.587038i	$0.199706\pi$
$661$	6.41723	+	36.3939i	0.249601	+	1.41556i	−0.559958	+	0.828521i	$0.689183\pi$
$662$	9.53378	−	13.6156i	0.370541	−	0.529187i
$663$		0			0
$664$	17.7979	−	21.2107i	0.690692	−	0.823134i
$665$	−0.0107851	+	0.00208589i	−0.000418227	+	8.08875e-5i
$666$		0			0
$667$	−6.46788	−	24.1385i	−0.250437	−	0.934645i
$668$	0.391202	−	0.838935i	0.0151360	−	0.0324594i
$669$		0			0
$670$	−30.2610	−	13.5072i	−1.16909	−	0.521827i
$671$	4.54997	−	12.5009i	0.175650	−	0.482593i
$672$		0			0
$673$	−4.90829	+	3.43682i	−0.189201	+	0.132480i	−0.664339	−	0.747431i	$-0.731287\pi$
$673$	−4.90829	+	3.43682i	−0.189201	+	0.132480i	0.475138	+	0.879911i	$0.342398\pi$
$674$	−19.2999			−0.743406
$675$		0			0
$676$	13.6111			0.523502
$677$	28.2910	−	19.8096i	1.08731	−	0.761345i	0.114613	−	0.993410i	$-0.463437\pi$
$677$	28.2910	−	19.8096i	1.08731	−	0.761345i	0.972700	+	0.232066i	$0.0745484\pi$
$678$		0			0
$679$	0.487857	−	1.34038i	0.0187222	−	0.0514389i
$680$	27.8275	+	12.4209i	1.06714	+	0.476321i
$681$		0			0
$682$	−2.29197	+	4.91514i	−0.0877639	+	0.188210i
$683$	0.984841	+	3.67548i	0.0376839	+	0.140638i	0.982205	−	0.187813i	$-0.0601399\pi$
$683$	0.984841	+	3.67548i	0.0376839	+	0.140638i	−0.944521	+	0.328451i	$0.893473\pi$
$684$		0			0
$685$	40.6591	−	7.86371i	1.55351	−	0.300457i
$686$	−5.60349	+	6.67798i	−0.213942	+	0.254966i
$687$		0			0
$688$	5.41244	−	7.72977i	0.206347	−	0.294695i
$689$	1.49380	+	8.47177i	0.0569093	+	0.322749i
$690$		0			0
$691$	0.658559	+	0.552596i	0.0250528	+	0.0210218i	0.655228	−	0.755431i	$-0.272573\pi$
$691$	0.658559	+	0.552596i	0.0250528	+	0.0210218i	−0.630175	+	0.776453i	$0.717017\pi$
$692$	−3.55595	+	13.2710i	−0.135177	+	0.504487i
$693$		0			0
$694$	−9.47573	−	5.47082i	−0.359694	−	0.207669i
$695$	30.7211	−	31.7529i	1.16532	−	1.20446i
$696$		0			0
$697$	0.768927	−	8.78887i	0.0291252	−	0.332902i
$698$	−5.36559	+	2.50202i	−0.203091	+	0.0947027i
$699$		0			0
$700$	0.181668	−	3.34615i	0.00686641	−	0.126473i
$701$		−	28.2369i		−	1.06649i	−0.845960	−	0.533246i	$-0.820972\pi$
$701$		−	28.2369i		−	1.06649i	0.845960	−	0.533246i	$-0.179028\pi$
$702$		0			0
$703$	0.00886291	+	0.00886291i	0.000334271	+	0.000334271i
$704$	1.63419	−	9.26794i	0.0615908	−	0.349299i
$705$		0			0
$706$	−10.6616	−	3.88050i	−0.401254	−	0.146045i
$707$	4.17282	+	0.365074i	0.156935	+	0.0137300i
$708$		0			0
$709$	−2.66301	−	7.31657i	−0.100012	−	0.274780i	0.879589	−	0.475735i	$-0.157818\pi$
$709$	−2.66301	−	7.31657i	−0.100012	−	0.274780i	−0.979600	+	0.200955i	$0.935596\pi$
$710$	−10.4092	+	9.03139i	−0.390649	+	0.338942i
$711$		0			0
$712$	−34.0018	−	9.11075i	−1.27427	−	0.341440i
$713$	29.2787	−	2.56156i	1.09650	−	0.0959310i
$714$		0			0
$715$	2.49647	−	15.6668i	0.0933628	−	0.585907i
$716$	−7.54913	+	1.33111i	−0.282124	+	0.0497461i
$717$		0			0
$718$	1.31391	+	15.0181i	0.0490347	+	0.560469i
$719$	5.23184	+	9.06182i	0.195115	+	0.337949i	0.946938	−	0.321416i	$-0.104159\pi$
$719$	5.23184	+	9.06182i	0.195115	+	0.337949i	−0.751823	+	0.659365i	$0.770825\pi$
$720$		0			0
$721$	−3.05057	+	5.28374i	−0.113609	+	0.196777i
$722$	−16.9713	−	7.91387i	−0.631608	−	0.294524i
$723$		0			0
$724$	−17.3429	−	20.6685i	−0.644544	−	0.768138i
$725$	14.3385	−	8.92226i	0.532517	−	0.331364i
$726$		0			0
$727$	10.3885	+	14.8363i	0.385289	+	0.550250i	0.964212	−	0.265133i	$-0.0854157\pi$
$727$	10.3885	+	14.8363i	0.385289	+	0.550250i	−0.578923	+	0.815382i	$0.696527\pi$
$728$	7.04345	−	7.04345i	0.261048	−	0.261048i
$729$		0			0
$730$	24.9598	−	12.1447i	0.923805	−	0.449496i
$731$	−47.9642	−	8.45739i	−1.77402	−	0.312808i
$732$		0			0
$733$	12.7723	+	27.3902i	0.471755	+	1.01168i	0.987887	+	0.155173i	$0.0495934\pi$
$733$	12.7723	+	27.3902i	0.471755	+	1.01168i	−0.516133	+	0.856509i	$0.672629\pi$
$734$	−9.73284	+	8.16683i	−0.359246	+	0.301443i
$735$		0			0
$736$	−35.4450	+	12.9009i	−1.30652	+	0.475534i
$737$	20.1202	−	5.39119i	0.741137	−	0.198587i
$738$		0			0
$739$	−3.17194	+	1.83132i	−0.116682	+	0.0673663i	−0.557205	−	0.830375i	$-0.688126\pi$
$739$	−3.17194	+	1.83132i	−0.116682	+	0.0673663i	0.440523	+	0.897741i	$0.354793\pi$
$740$	−3.27936	+	1.96625i	−0.120552	+	0.0722808i
$741$		0			0
$742$	0.883502	+	0.618635i	0.0324344	+	0.0227108i
$743$	−26.5204	−	18.5698i	−0.972939	−	0.681259i	−0.0249919	−	0.999688i	$-0.507956\pi$
$743$	−26.5204	−	18.5698i	−0.972939	−	0.681259i	−0.947947	+	0.318429i	$0.896845\pi$
$744$		0			0
$745$	8.14329	−	32.5308i	0.298347	−	1.19183i
$746$	−13.7959	+	7.96506i	−0.505103	+	0.291621i
$747$		0			0
$748$	−6.28407	+	1.68381i	−0.229768	+	0.0615662i
$749$	2.12458	−	0.773283i	0.0776303	−	0.0282551i
$750$		0			0
$751$	−16.4509	+	13.8040i	−0.600303	+	0.503714i	−0.891543	−	0.452936i	$-0.850377\pi$
$751$	−16.4509	+	13.8040i	−0.600303	+	0.503714i	0.291240	+	0.956650i	$0.405932\pi$
$752$	−2.73005	−	5.85460i	−0.0995546	−	0.213495i
$753$		0			0
$754$	16.7903	+	2.96058i	0.611467	+	0.107818i
$755$	0.887563	+	1.82412i	0.0323017	+	0.0663865i
$756$		0			0
$757$	20.3709	−	20.3709i	0.740395	−	0.740395i	−0.232259	−	0.972654i	$-0.574612\pi$
$757$	20.3709	−	20.3709i	0.740395	−	0.740395i	0.972654	+	0.232259i	$0.0746118\pi$
$758$	−5.45165	−	7.78576i	−0.198013	−	0.282792i
$759$		0			0
$760$	−0.0317075	+	0.0390804i	−0.00115015	+	0.00141759i
$761$	−20.6946	−	24.6629i	−0.750179	−	0.894028i	0.247006	−	0.969014i	$-0.420553\pi$
$761$	−20.6946	−	24.6629i	−0.750179	−	0.894028i	−0.997185	+	0.0749859i	$0.976109\pi$
$762$		0			0
$763$	−6.57484	−	3.06590i	−0.238025	−	0.110993i
$764$	−0.820438	+	1.42104i	−0.0296824	+	0.0514114i
$765$		0			0
$766$	−7.16607	−	12.4120i	−0.258921	−	0.448464i
$767$	4.53146	+	51.7948i	0.163621	+	1.87020i
$768$		0			0
$769$	−3.27352	+	0.577210i	−0.118046	+	0.0208147i	−0.232359	−	0.972630i	$-0.574644\pi$
$769$	−3.27352	+	0.577210i	−0.118046	+	0.0208147i	0.114313	+	0.993445i	$0.463533\pi$
$770$	−1.16763	−	1.61028i	−0.0420783	−	0.0580304i
$771$		0			0
$772$	8.62135	−	0.754271i	0.310289	−	0.0271468i
$773$	3.47814	+	0.931964i	0.125100	+	0.0335204i	0.320826	−	0.947138i	$-0.396040\pi$
$773$	3.47814	+	0.931964i	0.125100	+	0.0335204i	−0.195726	+	0.980659i	$0.562706\pi$
$774$		0			0
$775$	7.40570	+	18.4294i	0.266021	+	0.662002i
$776$	−2.23502	−	6.14068i	−0.0802327	−	0.220437i
$777$		0			0
$778$	16.1549	+	1.41337i	0.579181	+	0.0506718i
$779$	0.0136910	+	0.00498312i	0.000490531	+	0.000178539i
$780$		0			0
$781$	1.50420	−	8.53071i	0.0538243	−	0.305253i
$782$	−23.5418	−	23.5418i	−0.841853	−	0.841853i
$783$		0			0
$784$			5.81658i			0.207735i
$785$	5.03122	−	9.05649i	0.179572	−	0.323240i
$786$		0			0
$787$	−33.8637	+	15.7909i	−1.20711	+	0.562886i	−0.918828	−	0.394659i	$-0.870863\pi$
$787$	−33.8637	+	15.7909i	−1.20711	+	0.562886i	−0.288285	+	0.957545i	$0.593085\pi$
$788$	−1.01734	+	11.6282i	−0.0362412	+	0.414238i
$789$		0			0
$790$	−1.74983	+	0.0288993i	−0.0622560	+	0.00102819i
$791$	−5.02741	−	2.90258i	−0.178754	−	0.103204i
$792$		0			0
$793$	12.7304	−	47.5106i	0.452070	−	1.68715i
$794$	−16.4558	−	13.8081i	−0.583995	−	0.490030i
$795$		0			0
$796$	−4.33183	−	24.5670i	−0.153538	−	0.870756i
$797$	11.3609	−	16.2250i	0.402423	−	0.574719i	−0.565884	−	0.824485i	$-0.691465\pi$
$797$	11.3609	−	16.2250i	0.402423	−	0.574719i	0.968306	+	0.249766i	$0.0803537\pi$
$798$		0			0
$799$	−21.4315	+	25.5411i	−0.758194	+	0.903580i
$800$	−15.3022	−	20.3863i	−0.541015	−	0.720765i
$801$		0			0
$802$	6.82383	+	25.4669i	0.240958	+	0.899267i
$803$	−7.37368	+	15.8129i	−0.260211	+	0.558025i
$804$		0			0
$805$	−4.39363	+	9.84336i	−0.154855	+	0.346933i
$806$	−6.85806	+	18.8424i	−0.241565	+	0.663694i
$807$		0			0
$808$	15.7195	−	11.0069i	0.553010	−	0.387222i
$809$	−0.320020			−0.0112513			−0.00562564	−	0.999984i	$-0.501791\pi$
$809$	−0.320020			−0.0112513			−0.00562564	+	0.999984i	$0.501791\pi$
$810$		0			0
$811$	−25.9979			−0.912910			−0.456455	−	0.889747i	$-0.650881\pi$
$811$	−25.9979			−0.912910			−0.456455	+	0.889747i	$0.650881\pi$
$812$	−1.85431	+	1.29840i	−0.0650736	+	0.0455650i
$813$		0			0
$814$	−0.776235	+	2.13269i	−0.0272070	+	0.0747506i
$815$	−8.97606	−	23.4493i	−0.314418	−	0.821391i
$816$		0			0
$817$	0.0339918	−	0.0728957i	0.00118922	−	0.00255030i
$818$	5.11244	+	19.0799i	0.178752	+	0.667112i
$819$		0			0
$820$	−2.48887	+	3.68244i	−0.0869152	+	0.128596i
$821$	−3.59136	+	4.28001i	−0.125339	+	0.149373i	−0.825064	−	0.565039i	$-0.808861\pi$
$821$	−3.59136	+	4.28001i	−0.125339	+	0.149373i	0.699725	+	0.714412i	$0.253306\pi$
$822$		0			0
$823$	21.2514	−	30.3501i	0.740776	−	1.05794i	−0.255073	−	0.966922i	$-0.582100\pi$
$823$	21.2514	−	30.3501i	0.740776	−	1.05794i	0.995849	−	0.0910165i	$-0.0290116\pi$
$824$	4.85367	+	27.5265i	0.169086	+	0.958932i
$825$		0			0
$826$	4.99363	+	4.19015i	0.173750	+	0.145794i
$827$	3.37514	−	12.5962i	0.117365	−	0.438013i	−0.882088	−	0.471085i	$-0.843863\pi$
$827$	3.37514	−	12.5962i	0.117365	−	0.438013i	0.999453	+	0.0330724i	$0.0105292\pi$
$828$		0			0
$829$	−22.2366	−	12.8383i	−0.772309	−	0.445893i	0.0613890	−	0.998114i	$-0.480447\pi$
$829$	−22.2366	−	12.8383i	−0.772309	−	0.445893i	−0.833698	+	0.552221i	$0.813780\pi$
$830$	−14.6919	−	14.2145i	−0.509962	−	0.493391i
$831$		0			0
$832$	3.03262	−	34.6630i	0.105137	−	1.20172i
$833$	27.2087	−	12.6876i	0.942725	−	0.439600i
$834$		0			0
$835$	−1.75899	−	0.977185i	−0.0608724	−	0.0338169i
$836$		−	0.0107438i		−	0.000371582i
$837$		0			0
$838$	−1.56397	−	1.56397i	−0.0540266	−	0.0540266i
$839$	−1.09940	+	6.23500i	−0.0379555	+	0.215256i	−0.997887	−	0.0649800i	$-0.979302\pi$
$839$	−1.09940	+	6.23500i	−0.0379555	+	0.215256i	0.959931	+	0.280236i	$0.0904128\pi$
$840$		0			0
$841$	16.5311	+	6.01684i	0.570039	+	0.207477i
$842$	−23.0313	−	2.01497i	−0.793710	−	0.0694406i
$843$		0			0
$844$	3.20906	+	8.81681i	0.110460	+	0.303487i
$845$	2.09165	−	29.5136i	0.0719549	−	1.01530i
$846$		0			0
$847$	−5.71518	−	1.53138i	−0.196376	−	0.0526188i
$848$	1.48010	−	0.129492i	0.0508269	−	0.00444678i
$849$		0			0
$850$	10.5999	−	19.8455i	0.363574	−	0.680696i
$851$	12.1127	−	2.13579i	0.415218	−	0.0732141i
$852$		0			0
$853$	−4.29982	−	49.1472i	−0.147223	−	1.68277i	−0.606975	−	0.794721i	$-0.707617\pi$
$853$	−4.29982	−	49.1472i	−0.147223	−	1.68277i	0.459752	−	0.888047i	$-0.347938\pi$
$854$	−3.08345	−	5.34069i	−0.105513	−	0.182755i
$855$		0			0
$856$	5.17900	−	8.97029i	0.177015	−	0.306598i
$857$	−50.2090	−	23.4128i	−1.71511	−	0.799768i	−0.994298	−	0.106634i	$-0.965993\pi$
$857$	−50.2090	−	23.4128i	−1.71511	−	0.799768i	−0.720809	−	0.693134i	$-0.756229\pi$
$858$		0			0
$859$	−10.5665	−	12.5926i	−0.360523	−	0.429655i	0.555043	−	0.831821i	$-0.312702\pi$
$859$	−10.5665	−	12.5926i	−0.360523	−	0.429655i	−0.915566	+	0.402167i	$0.868257\pi$
$860$	19.0540	+	15.4593i	0.649735	+	0.527156i
$861$		0			0
$862$	−8.90863	−	12.7228i	−0.303429	−	0.433342i
$863$	13.7094	−	13.7094i	0.466672	−	0.466672i	−0.434162	−	0.900835i	$-0.642956\pi$
$863$	13.7094	−	13.7094i	0.466672	−	0.466672i	0.900835	+	0.434162i	$0.142956\pi$
$864$		0			0
$865$	28.2297	+	9.74994i	0.959839	+	0.331508i
$866$	19.2561	+	3.39537i	0.654348	+	0.115379i
$867$		0			0
$868$	−1.12515	−	2.41288i	−0.0381899	−	0.0818985i
$869$	0.842676	−	0.707089i	0.0285858	−	0.0239864i
$870$		0			0
$871$	72.3708	−	26.3408i	2.45219	−	0.892525i
$872$	−32.1028	+	8.60192i	−1.08714	+	0.291298i
$873$		0			0
$874$	0.0476152	−	0.0274906i	0.00161061	−	0.000929885i
$875$	−7.22772	−	0.908134i	−0.244342	−	0.0307005i
$876$		0			0
$877$	24.0198	+	16.8189i	0.811093	+	0.567933i	0.903896	−	0.427751i	$-0.140694\pi$
$877$	24.0198	+	16.8189i	0.811093	+	0.567933i	−0.0928040	+	0.995684i	$0.529583\pi$
$878$	3.38479	+	2.37006i	0.114231	+	0.0799856i
$879$		0			0
$880$	−2.65799	−	0.665364i	−0.0896008	−	0.0224294i
$881$	−24.7559	+	14.2928i	−0.834048	+	0.481538i	−0.855237	−	0.518237i	$-0.826588\pi$
$881$	−24.7559	+	14.2928i	−0.834048	+	0.481538i	0.0211883	+	0.999776i	$0.493255\pi$
$882$		0			0
$883$	−31.2423	+	8.37134i	−1.05139	+	0.281718i	−0.742825	−	0.669486i	$-0.766514\pi$
$883$	−31.2423	+	8.37134i	−1.05139	+	0.281718i	−0.308562	+	0.951204i	$0.599848\pi$
$884$	−22.6033	+	8.22694i	−0.760232	+	0.276702i
$885$		0			0
$886$	−16.1041	+	13.5129i	−0.541026	+	0.453975i
$887$	9.85973	+	21.1443i	0.331057	+	0.709955i	0.999426	−	0.0338753i	$-0.0107849\pi$
$887$	9.85973	+	21.1443i	0.331057	+	0.709955i	−0.668369	+	0.743830i	$0.733007\pi$
$888$		0			0
$889$	−1.82889	−	0.322483i	−0.0613391	−	0.0108157i
$890$	−8.48435	+	24.5654i	−0.284396	+	0.823433i
$891$		0			0
$892$	−11.8887	+	11.8887i	−0.398064	+	0.398064i
$893$	−0.0315819	−	0.0451036i	−0.00105685	−	0.00150933i
$894$		0			0
$895$	1.72623	+	16.5737i	0.0577016	+	0.553999i
$896$	1.46603	+	1.74715i	0.0489767	+	0.0583681i
$897$		0			0
$898$	−16.6498	−	7.76395i	−0.555612	−	0.259086i
$899$	6.70840	−	11.6193i	0.223738	−	0.387525i
$900$		0			0
$901$	−3.83426	−	6.64113i	−0.127738	−	0.221248i
$902$	0.229930	+	2.62811i	0.00765582	+	0.0875064i
$903$		0			0
$904$	−26.1912	+	4.61821i	−0.871105	+	0.153599i
$905$	−47.4817	+	34.4294i	−1.57834	+	1.14447i
$906$		0			0
$907$	8.44305	−	0.738671i	0.280347	−	0.0245272i	0.0538847	−	0.998547i	$-0.482840\pi$
$907$	8.44305	−	0.738671i	0.280347	−	0.0245272i	0.226462	+	0.974020i	$0.427284\pi$
$908$	12.5549	+	3.36409i	0.416650	+	0.111641i
$909$		0			0
$910$	−4.81958	−	5.55483i	−0.159768	−	0.184141i
$911$	14.3752	+	39.4954i	0.476270	+	1.30854i	0.912636	+	0.408773i	$0.134043\pi$
$911$	14.3752	+	39.4954i	0.476270	+	1.30854i	−0.436366	+	0.899769i	$0.643735\pi$
$912$		0			0
$913$	12.8007	+	1.11992i	0.423641	+	0.0370638i
$914$	13.2386	+	4.81847i	0.437896	+	0.159381i
$915$		0			0
$916$	−1.61304	+	9.14800i	−0.0532963	+	0.302258i
$917$	−2.99184	−	2.99184i	−0.0987992	−	0.0987992i
$918$		0			0
$919$		−	49.1112i		−	1.62003i	−0.586409	−	0.810015i	$-0.699459\pi$
$919$		−	49.1112i		−	1.62003i	0.586409	−	0.810015i	$-0.300541\pi$
$920$	13.5674	+	47.4835i	0.447305	+	1.56548i
$921$		0			0
$922$	−22.6706	+	10.5715i	−0.746617	+	0.348153i
$923$	2.79138	−	31.9057i	0.0918795	−	1.05019i
$924$		0			0
$925$	3.75958	+	7.41298i	0.123614	+	0.243737i
$926$	−10.9835	−	6.34135i	−0.360942	−	0.208390i
$927$		0			0
$928$	−4.45662	+	16.6324i	−0.146296	+	0.545984i
$929$	−0.315673	−	0.264881i	−0.0103569	−	0.00869047i	0.637594	−	0.770372i	$-0.279930\pi$
$929$	−0.315673	−	0.264881i	−0.0103569	−	0.00869047i	−0.647951	+	0.761682i	$0.724374\pi$
$930$		0			0
$931$	0.00860919	+	0.0488251i	0.000282155	+	0.00160018i
$932$	12.5950	−	17.9876i	0.412564	−	0.589203i
$933$		0			0
$934$	−17.2348	+	20.5396i	−0.563939	+	0.672077i
$935$	2.68541	+	13.8848i	0.0878222	+	0.454083i
$936$		0			0
$937$	−0.474207	−	1.76977i	−0.0154917	−	0.0578157i	0.957747	−	0.287611i	$-0.0928610\pi$
$937$	−0.474207	−	1.76977i	−0.0154917	−	0.0578157i	−0.973239	+	0.229795i	$0.926194\pi$
$938$	4.08081	−	8.75132i	0.133243	−	0.285741i
$939$		0			0
$940$	15.6871	−	6.00480i	0.511656	−	0.195855i
$941$	−2.52471	+	6.93657i	−0.0823031	+	0.226126i	−0.974018	−	0.226473i	$-0.927281\pi$
$941$	−2.52471	+	6.93657i	−0.0823031	+	0.226126i	0.891714	+	0.452598i	$0.149503\pi$
$942$		0			0
$943$	11.7115	−	8.20046i	0.381378	−	0.267044i
$944$	8.97979			0.292267
$945$		0			0
$946$	14.5638			0.473511
$947$	37.0964	−	25.9752i	1.20547	−	0.844080i	0.214313	−	0.976765i	$-0.431249\pi$
$947$	37.0964	−	25.9752i	1.20547	−	0.844080i	0.991158	+	0.132685i	$0.0423598\pi$
$948$		0			0
$949$	−22.0636	+	60.6193i	−0.716216	+	1.96779i
$950$	0.0271261	+	0.0253910i	0.000880088	+	0.000823792i
$951$		0			0
$952$	−3.75264	+	8.04757i	−0.121624	+	0.260823i
$953$	−15.2575	−	56.9417i	−0.494238	−	1.84452i	−0.534256	−	0.845323i	$-0.679408\pi$
$953$	−15.2575	−	56.9417i	−0.494238	−	1.84452i	0.0400176	−	0.999199i	$-0.487259\pi$
$954$		0			0
$955$	2.95524	+	1.99737i	0.0956293	+	0.0646335i
$956$	−3.82355	+	4.55672i	−0.123662	+	0.147375i
$957$		0			0
$958$	10.3721	−	14.8130i	0.335109	−	0.478585i
$959$	2.09539	+	11.8836i	0.0676638	+	0.383740i
$960$		0			0
$961$	−11.6596	−	9.78359i	−0.376117	−	0.315600i
$962$	−2.17184	+	8.10540i	−0.0700228	+	0.261329i
$963$		0			0
$964$	−20.5357	−	11.8563i	−0.661411	−	0.381866i
$965$	−0.310658	−	18.8101i	−0.0100004	−	0.605517i
$966$		0			0
$967$	−3.13774	+	35.8645i	−0.100903	+	1.15332i	0.761869	+	0.647731i	$0.224282\pi$
$967$	−3.13774	+	35.8645i	−0.100903	+	1.15332i	−0.862772	+	0.505593i	$0.831274\pi$
$968$	−24.5670	+	11.4558i	−0.789612	+	0.368202i
$969$		0			0
$970$	−4.63901	+	1.32550i	−0.148950	+	0.0425592i
$971$			28.3419i			0.909536i	0.890610	+	0.454768i	$0.150278\pi$
$971$			28.3419i			0.909536i	−0.890610	+	0.454768i	$0.849722\pi$
$972$		0			0
$973$	9.10313	+	9.10313i	0.291833	+	0.291833i
$974$	1.05070	−	5.95880i	0.0336665	−	0.190932i
$975$		0			0
$976$	−7.98283	−	2.90551i	−0.255524	−	0.0930032i
$977$	−0.127935	−	0.0111928i	−0.00409300	−	0.000358091i	0.0851091	−	0.996372i	$-0.472876\pi$
$977$	−0.127935	−	0.0111928i	−0.00409300	−	0.000358091i	−0.0892021	+	0.996014i	$0.528432\pi$
$978$		0			0
$979$	−5.58725	−	15.3509i	−0.178569	−	0.490615i
$980$	−15.0866	−	1.06920i	−0.481924	−	0.0341543i
$981$		0			0
$982$	−25.9825	−	6.96199i	−0.829135	−	0.222166i
$983$	42.4506	−	3.71395i	1.35396	−	0.118457i	0.613044	−	0.790049i	$-0.289945\pi$
$983$	42.4506	−	3.71395i	1.35396	−	0.118457i	0.740921	+	0.671592i	$0.234389\pi$
$984$		0			0
$985$	25.0578	+	3.99289i	0.798407	+	0.127224i
$986$	−14.9674	+	2.63916i	−0.476660	+	0.0840480i
$987$		0			0
$988$	−0.00346213	−	0.0395723i	−0.000110145	−	0.00125896i
$989$	−39.4634	−	68.3525i	−1.25486	−	2.17348i
$990$		0			0
$991$	−9.60146	+	16.6302i	−0.305001	+	0.528276i	−0.977261	−	0.212038i	$-0.931990\pi$
$991$	−9.60146	+	16.6302i	−0.305001	+	0.528276i	0.672261	+	0.740314i	$0.265323\pi$
$992$	−18.3539	−	8.55855i	−0.582736	−	0.271734i
$993$		0			0
$994$	−2.58114	−	3.07608i	−0.0818688	−	0.0975674i
$995$	−53.9357	+	5.61766i	−1.70988	+	0.178092i
$996$		0			0
$997$	−17.0633	−	24.3689i	−0.540400	−	0.771771i	0.452367	−	0.891832i	$-0.350580\pi$
$997$	−17.0633	−	24.3689i	−0.540400	−	0.771771i	−0.992766	+	0.120061i	$0.961691\pi$
$998$	30.6574	−	30.6574i	0.970443	−	0.970443i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.8.10		192
3.2	odd	2		135.2.q.a.83.7	yes	192
5.2	odd	4	inner	405.2.r.a.332.10		192
15.2	even	4		135.2.q.a.2.7	✓	192
15.8	even	4		675.2.ba.b.407.10		192
15.14	odd	2		675.2.ba.b.218.10		192
27.13	even	9		135.2.q.a.68.7	yes	192
27.14	odd	18	inner	405.2.r.a.233.10		192
135.13	odd	36		675.2.ba.b.257.10		192
135.67	odd	36		135.2.q.a.122.7	yes	192
135.94	even	18		675.2.ba.b.68.10		192
135.122	even	36	inner	405.2.r.a.152.10		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.7	✓	192	15.2	even	4
135.2.q.a.68.7	yes	192	27.13	even	9
135.2.q.a.83.7	yes	192	3.2	odd	2
135.2.q.a.122.7	yes	192	135.67	odd	36
405.2.r.a.8.10		192	1.1	even	1	trivial
405.2.r.a.152.10		192	135.122	even	36	inner
405.2.r.a.233.10		192	27.14	odd	18	inner
405.2.r.a.332.10		192	5.2	odd	4	inner
675.2.ba.b.68.10		192	135.94	even	18
675.2.ba.b.218.10		192	15.14	odd	2
675.2.ba.b.257.10		192	135.13	odd	36
675.2.ba.b.407.10		192	15.8	even	4

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.807333 - 0.565301i) q^{2} +(-0.351818 + 0.966613i) q^{4} +(2.04189 + 0.911409i) q^{5} +(-0.275357 + 0.590505i) q^{7} +(0.772562 + 2.88324i) q^{8} +O(q^{10})\)	\(q+(0.807333 - 0.565301i) q^{2} +(-0.351818 + 0.966613i) q^{4} +(2.04189 + 0.911409i) q^{5} +(-0.275357 + 0.590505i) q^{7} +(0.772562 + 2.88324i) q^{8} +(2.16371 - 0.418474i) q^{10} +(-0.890417 + 1.06116i) q^{11} +(-2.93770 + 4.19546i) q^{13} +(0.111508 + 0.632393i) q^{14} +(0.677632 + 0.568601i) q^{16} +(1.18168 - 4.41009i) q^{17} +(0.00652973 + 0.00376994i) q^{19} +(-1.59936 + 1.65307i) q^{20} +(-0.118990 + 1.36006i) q^{22} +(6.70560 - 3.12687i) q^{23} +(3.33867 + 3.72200i) q^{25} +5.04782i q^{26} +(-0.473914 - 0.473914i) q^{28} +(0.586508 - 3.32625i) q^{29} +(3.73277 + 1.35862i) q^{31} +(-5.07868 - 0.444327i) q^{32} +(-1.53902 - 4.22842i) q^{34} +(-1.10044 + 0.954786i) q^{35} +(1.60572 + 0.430252i) q^{37} +(0.00740282 - 0.000647662i) q^{38} +(-1.05032 + 6.59139i) q^{40} +(1.90299 - 0.335548i) q^{41} +(-0.929732 - 10.6269i) q^{43} +(-0.712464 - 1.23402i) q^{44} +(3.64603 - 6.31511i) q^{46} +(-6.61847 - 3.08624i) q^{47} +(4.22664 + 5.03711i) q^{49} +(4.79947 + 1.11755i) q^{50} +(-3.02186 - 4.31566i) q^{52} +(1.18766 - 1.18766i) q^{53} +(-2.78529 + 1.35524i) q^{55} +(-1.91530 - 0.337719i) q^{56} +(-1.40682 - 3.01694i) q^{58} +(7.77643 - 6.52520i) q^{59} +(-9.02437 + 3.28460i) q^{61} +(3.78162 - 1.01328i) q^{62} +(-5.88351 + 3.39685i) q^{64} +(-9.82225 + 5.88925i) q^{65} +(-12.3176 - 8.62489i) q^{67} +(3.84712 + 2.69378i) q^{68} +(-0.348682 + 1.39291i) q^{70} +(-5.41550 + 3.12664i) q^{71} +(12.1662 - 3.25991i) q^{73} +(1.53958 - 0.560360i) q^{74} +(-0.00594135 + 0.00498539i) q^{76} +(-0.381436 - 0.817993i) q^{77} +(-0.782046 - 0.137896i) q^{79} +(0.865425 + 1.77862i) q^{80} +(1.34666 - 1.34666i) q^{82} +(-5.32053 - 7.59850i) q^{83} +(6.43227 - 7.92795i) q^{85} +(-6.75799 - 8.05386i) q^{86} +(-3.74748 - 1.74748i) q^{88} +(-5.89645 + 10.2130i) q^{89} +(-1.66853 - 2.88997i) q^{91} +(0.663323 + 7.58182i) q^{92} +(-7.08796 + 1.24980i) q^{94} +(0.00989706 + 0.0136491i) q^{95} +(-2.18091 + 0.190805i) q^{97} +(6.25979 + 1.67731i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

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