LMFDB - Embedded newform 855.2.bs.b.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.2
Root			$0.597039 - 1.03410i$ of defining polynomial
Character	$\chi$	$=$	855.271
Dual form			855.2.bs.b.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12207 + 0.408399i) q^{2} +(-0.439845 + 0.369074i) q^{4} +(0.766044 + 0.642788i) q^{5} +(1.09825 + 1.90222i) q^{7} +(1.53688 - 2.66196i) q^{8} +O(q^{10})$	\(q+(-1.12207 + 0.408399i) q^{2} +(-0.439845 + 0.369074i) q^{4} +(0.766044 + 0.642788i) q^{5} +(1.09825 + 1.90222i) q^{7} +(1.53688 - 2.66196i) q^{8} +(-1.12207 - 0.408399i) q^{10} +(-1.41324 + 2.44780i) q^{11} +(0.708694 + 4.01920i) q^{13} +(-2.00917 - 1.68589i) q^{14} +(-0.437935 + 2.48365i) q^{16} +(0.359555 - 0.130867i) q^{17} +(-2.75520 - 3.37770i) q^{19} -0.574177 q^{20} +(0.586069 - 3.32376i) q^{22} +(2.27970 - 1.91290i) q^{23} +(0.173648 + 0.984808i) q^{25} +(-2.43664 - 4.22038i) q^{26} +(-1.18512 - 0.431347i) q^{28} +(8.05787 + 2.93282i) q^{29} +(2.34622 + 4.06377i) q^{31} +(0.544580 + 3.08847i) q^{32} +(-0.349999 + 0.293684i) q^{34} +(-0.381417 + 2.16312i) q^{35} -10.7694 q^{37} +(4.47097 + 2.66478i) q^{38} +(2.88840 - 1.05129i) q^{40} +(-0.544445 + 3.08770i) q^{41} +(1.53900 + 1.29137i) q^{43} +(-0.281814 - 1.59824i) q^{44} +(-1.77675 + 3.07743i) q^{46} +(-10.2405 - 3.72722i) q^{47} +(1.08771 - 1.88398i) q^{49} +(-0.597039 - 1.03410i) q^{50} +(-1.79510 - 1.50627i) q^{52} +(-5.72676 + 4.80532i) q^{53} +(-2.65602 + 0.966713i) q^{55} +6.75150 q^{56} -10.2392 q^{58} +(-12.1961 + 4.43900i) q^{59} +(4.57784 - 3.84126i) q^{61} +(-4.29225 - 3.60163i) q^{62} +(-4.39435 - 7.61123i) q^{64} +(-2.04060 + 3.53443i) q^{65} +(-0.986138 - 0.358925i) q^{67} +(-0.109849 + 0.190264i) q^{68} +(-0.455441 - 2.58294i) q^{70} +(5.99626 + 5.03146i) q^{71} +(-2.44663 + 13.8755i) q^{73} +(12.0840 - 4.39822i) q^{74} +(2.45848 + 0.468792i) q^{76} -6.20833 q^{77} +(-2.33355 + 13.2342i) q^{79} +(-1.93194 + 1.62109i) q^{80} +(-0.650110 - 3.68695i) q^{82} +(-2.77807 - 4.81175i) q^{83} +(0.359555 + 0.130867i) q^{85} +(-2.25425 - 0.820481i) q^{86} +(4.34397 + 7.52398i) q^{88} +(1.13984 + 6.46435i) q^{89} +(-6.86708 + 5.76216i) q^{91} +(-0.296716 + 1.68276i) q^{92} +13.0127 q^{94} +(0.0605361 - 4.35848i) q^{95} +(-13.5750 + 4.94091i) q^{97} +(-0.451074 + 2.55817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.12207	+	0.408399i	−0.793421	+	0.288782i	−0.706757	−	0.707456i	$-0.749843\pi$
$2$	−1.12207	+	0.408399i	−0.793421	+	0.288782i	−0.0866635	+	0.996238i	$0.527620\pi$
$3$		0			0
$3$		0			0
$4$	−0.439845	+	0.369074i	−0.219923	+	0.184537i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$6$		0			0
$7$	1.09825	+	1.90222i	0.415098	+	0.718970i	0.995439	−	0.0954033i	$-0.0304141\pi$
$7$	1.09825	+	1.90222i	0.415098	+	0.718970i	−0.580341	+	0.814374i	$0.697081\pi$
$8$	1.53688	−	2.66196i	0.543371	−	0.941146i
$9$		0			0
$10$	−1.12207	−	0.408399i	−0.354829	−	0.129147i
$11$	−1.41324	+	2.44780i	−0.426108	+	0.738040i	−0.996523	−	0.0833161i	$-0.973449\pi$
$11$	−1.41324	+	2.44780i	−0.426108	+	0.738040i	0.570415	+	0.821356i	$0.306782\pi$
$12$		0			0
$13$	0.708694	+	4.01920i	0.196556	+	1.11473i	0.910185	+	0.414202i	$0.135939\pi$
$13$	0.708694	+	4.01920i	0.196556	+	1.11473i	−0.713628	+	0.700524i	$0.752949\pi$
$14$	−2.00917	−	1.68589i	−0.536972	−	0.450573i
$15$		0			0
$16$	−0.437935	+	2.48365i	−0.109484	+	0.620913i
$17$	0.359555	−	0.130867i	0.0872049	−	0.0317400i	−0.298049	−	0.954550i	$-0.596336\pi$
$17$	0.359555	−	0.130867i	0.0872049	−	0.0317400i	0.385254	+	0.922810i	$0.374114\pi$
$18$		0			0
$19$	−2.75520	−	3.37770i	−0.632087	−	0.774898i
$19$	−2.75520	−	3.37770i	−0.632087	−	0.774898i
$20$	−0.574177			−0.128390
$21$		0			0
$22$	0.586069	−	3.32376i	0.124950	−	0.708628i
$23$	2.27970	−	1.91290i	0.475351	−	0.398867i	−0.373391	−	0.927674i	$-0.621805\pi$
$23$	2.27970	−	1.91290i	0.475351	−	0.398867i	0.848742	+	0.528807i	$0.177361\pi$
$24$		0			0
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	−2.43664	−	4.22038i	−0.477864	−	0.827686i
$27$		0			0
$28$	−1.18512	−	0.431347i	−0.223966	−	0.0815170i
$29$	8.05787	+	2.93282i	1.49631	+	0.544612i	0.955102	−	0.296278i	$-0.0957454\pi$
$29$	8.05787	+	2.93282i	1.49631	+	0.544612i	0.541207	+	0.840889i	$0.317968\pi$
$30$		0			0
$31$	2.34622	+	4.06377i	0.421393	+	0.729874i	0.996076	−	0.0885019i	$-0.0282079\pi$
$31$	2.34622	+	4.06377i	0.421393	+	0.729874i	−0.574683	+	0.818376i	$0.694875\pi$
$32$	0.544580	+	3.08847i	0.0962691	+	0.545969i
$33$		0			0
$34$	−0.349999	+	0.293684i	−0.0600243	+	0.0503663i
$35$	−0.381417	+	2.16312i	−0.0644712	+	0.365634i
$36$		0			0
$37$	−10.7694			−1.77048			−0.885242	−	0.465131i	$-0.846007\pi$
$37$	−10.7694			−1.77048			−0.885242	+	0.465131i	$0.846007\pi$
$38$	4.47097	+	2.66478i	0.725287	+	0.432285i
$39$		0			0
$40$	2.88840	−	1.05129i	0.456696	−	0.166224i
$41$	−0.544445	+	3.08770i	−0.0850280	+	0.482218i	0.912323	+	0.409472i	$0.134287\pi$
$41$	−0.544445	+	3.08770i	−0.0850280	+	0.482218i	−0.997351	+	0.0727454i	$0.976824\pi$
$42$		0			0
$43$	1.53900	+	1.29137i	0.234695	+	0.196933i	0.752549	−	0.658537i	$-0.228824\pi$
$43$	1.53900	+	1.29137i	0.234695	+	0.196933i	−0.517853	+	0.855469i	$0.673269\pi$
$44$	−0.281814	−	1.59824i	−0.0424850	−	0.240944i
$45$		0			0
$46$	−1.77675	+	3.07743i	−0.261968	+	0.453742i
$47$	−10.2405	−	3.72722i	−1.49372	−	0.543671i	−0.539297	−	0.842115i	$-0.681310\pi$
$47$	−10.2405	−	3.72722i	−1.49372	−	0.543671i	−0.954427	+	0.298444i	$0.903532\pi$
$48$		0			0
$49$	1.08771	−	1.88398i	0.155388	−	0.269140i
$50$	−0.597039	−	1.03410i	−0.0844341	−	0.146244i
$51$		0			0
$52$	−1.79510	−	1.50627i	−0.248936	−	0.208882i
$53$	−5.72676	+	4.80532i	−0.786631	+	0.660062i	−0.944909	−	0.327333i	$-0.893850\pi$
$53$	−5.72676	+	4.80532i	−0.786631	+	0.660062i	0.158278	+	0.987395i	$0.449406\pi$
$54$		0			0
$55$	−2.65602	+	0.966713i	−0.358138	+	0.130352i
$56$	6.75150			0.902208
$57$		0			0
$58$	−10.2392			−1.34448
$59$	−12.1961	+	4.43900i	−1.58779	+	0.577909i	−0.976880	−	0.213789i	$-0.931419\pi$
$59$	−12.1961	+	4.43900i	−1.58779	+	0.577909i	−0.610912	+	0.791698i	$0.709197\pi$
$60$		0			0
$61$	4.57784	−	3.84126i	0.586132	−	0.491823i	−0.300822	−	0.953680i	$-0.597261\pi$
$61$	4.57784	−	3.84126i	0.586132	−	0.491823i	0.886954	+	0.461857i	$0.152817\pi$
$62$	−4.29225	−	3.60163i	−0.545116	−	0.457407i
$63$		0			0
$64$	−4.39435	−	7.61123i	−0.549294	−	0.951404i
$65$	−2.04060	+	3.53443i	−0.253106	+	0.438392i
$66$		0			0
$67$	−0.986138	−	0.358925i	−0.120476	−	0.0438496i	0.281079	−	0.959685i	$-0.409308\pi$
$67$	−0.986138	−	0.358925i	−0.120476	−	0.0438496i	−0.401555	+	0.915835i	$0.631530\pi$
$68$	−0.109849	+	0.190264i	−0.0133211	+	0.0230729i
$69$		0			0
$70$	−0.455441	−	2.58294i	−0.0544356	−	0.308720i
$71$	5.99626	+	5.03146i	0.711625	+	0.597124i	0.925055	−	0.379834i	$-0.124019\pi$
$71$	5.99626	+	5.03146i	0.711625	+	0.597124i	−0.213430	+	0.976958i	$0.568463\pi$
$72$		0			0
$73$	−2.44663	+	13.8755i	−0.286357	+	1.62401i	0.414042	+	0.910258i	$0.364117\pi$
$73$	−2.44663	+	13.8755i	−0.286357	+	1.62401i	−0.700399	+	0.713752i	$0.746995\pi$
$74$	12.0840	−	4.39822i	1.40474	−	0.511283i
$75$		0			0
$76$	2.45848	+	0.468792i	0.282008	+	0.0537741i
$77$	−6.20833			−0.707505
$78$		0			0
$79$	−2.33355	+	13.2342i	−0.262545	+	1.48897i	0.513390	+	0.858156i	$0.328390\pi$
$79$	−2.33355	+	13.2342i	−0.262545	+	1.48897i	−0.775935	+	0.630813i	$0.782722\pi$
$80$	−1.93194	+	1.62109i	−0.215997	+	0.181243i
$81$		0			0
$82$	−0.650110	−	3.68695i	−0.0717926	−	0.407156i
$83$	−2.77807	−	4.81175i	−0.304932	−	0.528158i	0.672314	−	0.740266i	$-0.265301\pi$
$83$	−2.77807	−	4.81175i	−0.304932	−	0.528158i	−0.977246	+	0.212108i	$0.931967\pi$
$84$		0			0
$85$	0.359555	+	0.130867i	0.0389992	+	0.0141946i
$86$	−2.25425	−	0.820481i	−0.243082	−	0.0884748i
$87$		0			0
$88$	4.34397	+	7.52398i	0.463069	+	0.802059i
$89$	1.13984	+	6.46435i	0.120823	+	0.685220i	0.983702	+	0.179809i	$0.0575479\pi$
$89$	1.13984	+	6.46435i	0.120823	+	0.685220i	−0.862879	+	0.505411i	$0.831341\pi$
$90$		0			0
$91$	−6.86708	+	5.76216i	−0.719865	+	0.604039i
$92$	−0.296716	+	1.68276i	−0.0309347	+	0.175440i
$93$		0			0
$94$	13.0127			1.34215
$95$	0.0605361	−	4.35848i	0.00621087	−	0.447170i
$96$		0			0
$97$	−13.5750	+	4.94091i	−1.37834	+	0.501673i	−0.921674	−	0.387966i	$-0.873178\pi$
$97$	−13.5750	+	4.94091i	−1.37834	+	0.501673i	−0.456663	+	0.889640i	$0.650955\pi$
$98$	−0.451074	+	2.55817i	−0.0455654	+	0.258414i
$99$		0			0
$100$	−0.439845	−	0.369074i	−0.0439845	−	0.0369074i
$101$	−0.738074	−	4.18582i	−0.0734411	−	0.416505i	−0.999257	−	0.0385313i	$-0.987732\pi$
$101$	−0.738074	−	4.18582i	−0.0734411	−	0.416505i	0.925816	−	0.377974i	$-0.123379\pi$
$102$		0			0
$103$	7.33528	−	12.7051i	0.722767	−	1.25187i	−0.237119	−	0.971481i	$-0.576203\pi$
$103$	7.33528	−	12.7051i	0.722767	−	1.25187i	0.959887	−	0.280389i	$-0.0904634\pi$
$104$	11.7882	+	4.29054i	1.15592	+	0.420722i
$105$		0			0
$106$	4.46332	−	7.73070i	0.433516	−	0.750872i
$107$	−3.09023	−	5.35244i	−0.298744	−	0.517439i	0.677105	−	0.735886i	$-0.263234\pi$
$107$	−3.09023	−	5.35244i	−0.298744	−	0.517439i	−0.975849	+	0.218447i	$0.929901\pi$
$108$		0			0
$109$	0.577493	+	0.484574i	0.0553138	+	0.0464138i	0.670025	−	0.742338i	$-0.266283\pi$
$109$	0.577493	+	0.484574i	0.0553138	+	0.0464138i	−0.614712	+	0.788752i	$0.710728\pi$
$110$	2.58543	−	2.16943i	0.246511	−	0.206847i
$111$		0			0
$112$	−5.20540	+	1.89461i	−0.491864	+	0.179024i
$113$	−0.870003			−0.0818430			−0.0409215	−	0.999162i	$-0.513029\pi$
$113$	−0.870003			−0.0818430			−0.0409215	+	0.999162i	$0.513029\pi$
$114$		0			0
$115$	2.97594			0.277508
$116$	−4.62665	+	1.68396i	−0.429573	+	0.156352i
$117$		0			0
$118$	11.8719	−	9.96171i	1.09290	−	0.917050i
$119$	0.643818	+	0.540227i	0.0590187	+	0.0495225i
$120$		0			0
$121$	1.50551	+	2.60762i	0.136864	+	0.237056i
$122$	−3.56787	+	6.17973i	−0.323020	+	0.559487i
$123$		0			0
$124$	−2.53180	−	0.921502i	−0.227363	−	0.0827533i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	−0.598116	−	3.39209i	−0.0530743	−	0.300999i	0.946703	−	0.322108i	$-0.104391\pi$
$127$	−0.598116	−	3.39209i	−0.0530743	−	0.300999i	−0.999777	+	0.0211090i	$0.993280\pi$
$128$	3.23436	+	2.71395i	0.285880	+	0.239882i
$129$		0			0
$130$	0.846236	−	4.79924i	0.0742198	−	0.420922i
$131$	9.67954	−	3.52307i	0.845706	−	0.307812i	0.117418	−	0.993083i	$-0.462538\pi$
$131$	9.67954	−	3.52307i	0.845706	−	0.307812i	0.728288	+	0.685271i	$0.240316\pi$
$132$		0			0
$133$	3.39923	−	8.95054i	0.294751	−	0.776110i
$134$	1.25310			0.108251
$135$		0			0
$136$	0.204231	−	1.15825i	0.0175126	−	0.0993191i
$137$	−1.12449	+	0.943562i	−0.0960720	+	0.0806140i	−0.689559	−	0.724230i	$-0.742195\pi$
$137$	−1.12449	+	0.943562i	−0.0960720	+	0.0806140i	0.593487	+	0.804844i	$0.297751\pi$
$138$		0			0
$139$	−1.27243	−	7.21629i	−0.107926	−	0.612078i	−0.990011	−	0.140988i	$-0.954972\pi$
$139$	−1.27243	−	7.21629i	−0.107926	−	0.612078i	0.882085	−	0.471090i	$-0.156139\pi$
$140$	−0.630588	−	1.09221i	−0.0532944	−	0.0923086i
$141$		0			0
$142$	−8.78304	−	3.19677i	−0.737057	−	0.268267i
$143$	−10.8398	−	3.94535i	−0.906467	−	0.329927i
$144$		0			0
$145$	4.28750	+	7.42617i	0.356058	+	0.616710i
$146$	−2.92147	−	16.5685i	−0.241783	−	1.37122i
$147$		0			0
$148$	4.73689	−	3.97472i	0.389370	−	0.326720i
$149$	−1.73507	+	9.84006i	−0.142142	+	0.806129i	0.827475	+	0.561503i	$0.189777\pi$
$149$	−1.73507	+	9.84006i	−0.142142	+	0.806129i	−0.969617	+	0.244627i	$0.921335\pi$
$150$		0			0
$151$	15.0689			1.22629			0.613144	−	0.789971i	$-0.289905\pi$
$151$	15.0689			1.22629			0.613144	+	0.789971i	$0.289905\pi$
$152$	−13.2257	+	2.14311i	−1.07275	+	0.173829i
$153$		0			0
$154$	6.96616	−	2.53548i	0.561349	−	0.204314i
$155$	−0.814833	+	4.62115i	−0.0654490	+	0.371179i
$156$		0			0
$157$	7.92438	+	6.64935i	0.632435	+	0.530676i	0.901684	−	0.432395i	$-0.142331\pi$
$157$	7.92438	+	6.64935i	0.632435	+	0.530676i	−0.269250	+	0.963070i	$0.586776\pi$
$158$	−2.78645	−	15.8027i	−0.221678	−	1.25720i
$159$		0			0
$160$	−1.56806	+	2.71595i	−0.123966	+	0.214715i
$161$	6.14242	+	2.23566i	0.484090	+	0.176194i
$162$		0			0
$163$	3.45005	−	5.97565i	0.270228	−	0.468049i	−0.698692	−	0.715423i	$-0.746234\pi$
$163$	3.45005	−	5.97565i	0.270228	−	0.468049i	0.968920	+	0.247373i	$0.0795674\pi$
$164$	−0.900118	−	1.55905i	−0.0702874	−	0.121741i
$165$		0			0
$166$	5.08229	+	4.26455i	0.394462	+	0.330993i
$167$	−9.08683	+	7.62476i	−0.703160	+	0.590022i	−0.922671	−	0.385589i	$-0.873998\pi$
$167$	−9.08683	+	7.62476i	−0.703160	+	0.590022i	0.219510	+	0.975610i	$0.429554\pi$
$168$		0			0
$169$	−3.43575	+	1.25051i	−0.264289	+	0.0961932i
$170$	−0.456891			−0.0350419
$171$		0			0
$172$	−1.15353			−0.0879561
$173$	23.8744	−	8.68955i	1.81513	−	0.660655i	0.818901	−	0.573935i	$-0.194584\pi$
$173$	23.8744	−	8.68955i	1.81513	−	0.660655i	0.996233	−	0.0867194i	$-0.0276384\pi$
$174$		0			0
$175$	−1.68261	+	1.41188i	−0.127193	+	0.106728i
$176$	−5.46058	−	4.58197i	−0.411607	−	0.345379i
$177$		0			0
$178$	−3.91901	−	6.78792i	−0.293742	−	0.508776i
$179$	−0.194400	+	0.336710i	−0.0145301	+	0.0251669i	−0.873199	−	0.487364i	$-0.837959\pi$
$179$	−0.194400	+	0.336710i	−0.0145301	+	0.0251669i	0.858669	+	0.512531i	$0.171292\pi$
$180$		0			0
$181$	−4.49536	−	1.63618i	−0.334137	−	0.121616i	0.169502	−	0.985530i	$-0.445784\pi$
$181$	−4.49536	−	1.63618i	−0.334137	−	0.121616i	−0.503640	+	0.863914i	$0.668006\pi$
$182$	5.35206	−	9.27003i	0.396721	−	0.687141i
$183$		0			0
$184$	−1.58842	−	9.00838i	−0.117100	−	0.664107i
$185$	−8.24986	−	6.92246i	−0.606542	−	0.508949i
$186$		0			0
$187$	−0.187800	+	1.06507i	−0.0137333	+	0.0778854i
$188$	5.87984	−	2.14009i	0.428831	−	0.156082i
$189$		0			0
$190$	1.71207	+	4.91523i	0.124207	+	0.356588i
$191$	23.8516			1.72584			0.862921	−	0.505338i	$-0.168632\pi$
$191$	23.8516			1.72584			0.862921	+	0.505338i	$0.168632\pi$
$192$		0			0
$193$	−1.94937	+	11.0554i	−0.140319	+	0.795787i	0.830688	+	0.556737i	$0.187947\pi$
$193$	−1.94937	+	11.0554i	−0.140319	+	0.795787i	−0.971007	+	0.239050i	$0.923164\pi$
$194$	13.2142	−	11.0881i	0.948727	−	0.796076i
$195$		0			0
$196$	0.216901	+	1.23011i	0.0154929	+	0.0878647i
$197$	−8.43639	−	14.6122i	−0.601068	−	1.04108i	−0.992660	−	0.120941i	$-0.961409\pi$
$197$	−8.43639	−	14.6122i	−0.601068	−	1.04108i	0.391592	−	0.920139i	$-0.371924\pi$
$198$		0			0
$199$	14.7743	+	5.37740i	1.04732	+	0.381194i	0.807651	−	0.589660i	$-0.200738\pi$
$199$	14.7743	+	5.37740i	1.04732	+	0.381194i	0.239670	+	0.970854i	$0.422961\pi$
$200$	2.88840	+	1.05129i	0.204241	+	0.0743375i
$201$		0			0
$202$	2.53765	+	4.39534i	0.178549	+	0.309255i
$203$	3.27065	+	18.5488i	0.229555	+	1.30187i
$204$		0			0
$205$	−2.40180	+	2.01535i	−0.167749	+	0.140758i
$206$	−3.04194	+	17.2517i	−0.211942	+	1.20198i
$207$		0			0
$208$	−10.2927			−0.713668
$209$	12.1617	−	1.97069i	0.841243	−	0.136316i
$210$		0			0
$211$	8.72857	−	3.17694i	0.600899	−	0.218709i	−0.0236172	−	0.999721i	$-0.507518\pi$
$211$	8.72857	−	3.17694i	0.600899	−	0.218709i	0.624517	+	0.781012i	$0.285296\pi$
$212$	0.745369	−	4.22720i	0.0511922	−	0.290325i
$213$		0			0
$214$	5.65337	+	4.74374i	0.386457	+	0.324276i
$215$	0.348863	+	1.97850i	0.0237922	+	0.134932i
$216$		0			0
$217$	−5.15344	+	8.92603i	−0.349839	+	0.605938i
$218$	−0.845885	−	0.307877i	−0.0572906	−	0.0208521i
$219$		0			0
$220$	0.811450	−	1.40547i	0.0547080	−	0.0947570i
$221$	0.780797	+	1.35238i	0.0525221	+	0.0909710i
$222$		0			0
$223$	−2.13799	−	1.79399i	−0.143170	−	0.120134i	0.568390	−	0.822759i	$-0.307567\pi$
$223$	−2.13799	−	1.79399i	−0.143170	−	0.120134i	−0.711560	+	0.702625i	$0.752011\pi$
$224$	−5.27685	+	4.42781i	−0.352575	+	0.295845i
$225$		0			0
$226$	0.976201	−	0.355308i	0.0649359	−	0.0236347i
$227$	0.844086			0.0560240			0.0280120	−	0.999608i	$-0.491082\pi$
$227$	0.844086			0.0560240			0.0280120	+	0.999608i	$0.491082\pi$
$228$		0			0
$229$	21.9559			1.45089			0.725444	−	0.688282i	$-0.241635\pi$
$229$	21.9559			1.45089			0.725444	+	0.688282i	$0.241635\pi$
$230$	−3.33920	+	1.21537i	−0.220180	+	0.0801391i
$231$		0			0
$232$	20.1911	−	16.9423i	1.32561	−	1.11232i
$233$	3.38242	+	2.83819i	0.221590	+	0.185936i	0.746824	−	0.665022i	$-0.231578\pi$
$233$	3.38242	+	2.83819i	0.221590	+	0.185936i	−0.525234	+	0.850958i	$0.676022\pi$
$234$		0			0
$235$	−5.44883	−	9.43766i	−0.355443	−	0.615645i
$236$	3.72606	−	6.45373i	0.242546	−	0.420102i
$237$		0			0
$238$	−0.943034	−	0.343236i	−0.0611278	−	0.0222487i
$239$	9.91358	−	17.1708i	0.641256	−	1.11069i	−0.343896	−	0.939008i	$-0.611747\pi$
$239$	9.91358	−	17.1708i	0.641256	−	1.11069i	0.985153	−	0.171681i	$-0.0549198\pi$
$240$		0			0
$241$	−3.62651	−	20.5670i	−0.233604	−	1.32484i	−0.845533	−	0.533923i	$-0.820717\pi$
$241$	−3.62651	−	20.5670i	−0.233604	−	1.32484i	0.611929	−	0.790913i	$-0.290394\pi$
$242$	−2.75423	−	2.31107i	−0.177049	−	0.148561i
$243$		0			0
$244$	−0.595830	+	3.37912i	−0.0381441	+	0.216326i
$245$	2.04424	−	0.744041i	0.130601	−	0.0475350i
$246$		0			0
$247$	11.6231	−	13.4675i	0.739558	−	0.856915i
$248$	14.4235			0.915891
$249$		0			0
$250$	0.207349	−	1.17594i	0.0131139	−	0.0743728i
$251$	−4.25499	+	3.57036i	−0.268573	+	0.225359i	−0.767121	−	0.641503i	$-0.778311\pi$
$251$	−4.25499	+	3.57036i	−0.268573	+	0.225359i	0.498548	+	0.866862i	$0.333867\pi$
$252$		0			0
$253$	1.46063	+	8.28364i	0.0918290	+	0.520788i
$254$	2.05645	+	3.56188i	0.129033	+	0.223492i
$255$		0			0
$256$	11.7798	+	4.28750i	0.736237	+	0.267969i
$257$	18.9036	+	6.88036i	1.17918	+	0.429185i	0.855911	−	0.517123i	$-0.172997\pi$
$257$	18.9036	+	6.88036i	1.17918	+	0.429185i	0.323266	+	0.946308i	$0.395219\pi$
$258$		0			0
$259$	−11.8275	−	20.4858i	−0.734924	−	1.27293i
$260$	−0.406916	−	2.30774i	−0.0252359	−	0.143120i
$261$		0			0
$262$	−9.42228	+	7.90623i	−0.582110	+	0.488448i
$263$	−2.03312	+	11.5304i	−0.125368	+	0.710995i	0.855721	+	0.517437i	$0.173114\pi$
$263$	−2.03312	+	11.5304i	−0.125368	+	0.710995i	−0.981089	+	0.193558i	$0.937997\pi$
$264$		0			0
$265$	−7.47576			−0.459232
$266$	−0.158773	+	11.4313i	−0.00973499	+	0.700900i
$267$		0			0
$268$	0.566218	−	0.206086i	0.0345873	−	0.0125887i
$269$	2.23756	−	12.6898i	0.136426	−	0.773712i	−0.837429	−	0.546545i	$-0.815943\pi$
$269$	2.23756	−	12.6898i	0.136426	−	0.773712i	0.973856	−	0.227167i	$-0.0729463\pi$
$270$		0			0
$271$	−11.8097	−	9.90953i	−0.717389	−	0.601961i	0.209273	−	0.977857i	$-0.432890\pi$
$271$	−11.8097	−	9.90953i	−0.717389	−	0.601961i	−0.926662	+	0.375896i	$0.877335\pi$
$272$	0.167567	+	0.950321i	0.0101603	+	0.0576217i
$273$		0			0
$274$	0.876407	−	1.51798i	0.0529457	−	0.0917046i
$275$	−2.65602	−	0.966713i	−0.160164	−	0.0582950i
$276$		0			0
$277$	−2.64855	+	4.58742i	−0.159136	+	0.275632i	−0.934557	−	0.355813i	$-0.884204\pi$
$277$	−2.64855	+	4.58742i	−0.159136	+	0.275632i	0.775421	+	0.631444i	$0.217537\pi$
$278$	4.37487	+	7.57750i	0.262387	+	0.454468i
$279$		0			0
$280$	5.17195	+	4.33978i	0.309083	+	0.259352i
$281$	4.12384	−	3.46031i	0.246008	−	0.206425i	−0.511443	−	0.859317i	$-0.670889\pi$
$281$	4.12384	−	3.46031i	0.246008	−	0.206425i	0.757451	+	0.652892i	$0.226445\pi$
$282$		0			0
$283$	−16.6106	+	6.04576i	−0.987397	+	0.359383i	−0.784712	−	0.619861i	$-0.787189\pi$
$283$	−16.6106	+	6.04576i	−0.987397	+	0.359383i	−0.202685	+	0.979244i	$0.564967\pi$
$284$	−4.49441			−0.266694
$285$		0			0
$286$	13.7742			0.814487
$287$	−6.47141	+	2.35540i	−0.381995	+	0.139035i
$288$		0			0
$289$	−12.9106	+	10.8333i	−0.759447	+	0.637252i
$290$	−7.84370	−	6.58165i	−0.460598	−	0.386488i
$291$		0			0
$292$	−4.04496	−	7.00608i	−0.236714	−	0.410000i
$293$	2.35524	−	4.07939i	0.137594	−	0.238320i	−0.788991	−	0.614405i	$-0.789396\pi$
$293$	2.35524	−	4.07939i	0.137594	−	0.238320i	0.926586	+	0.376084i	$0.122730\pi$
$294$		0			0
$295$	−12.1961	−	4.43900i	−0.710082	−	0.258449i
$296$	−16.5514	+	28.6678i	−0.962029	+	1.66628i
$297$		0			0
$298$	−2.07181	−	11.7498i	−0.120017	−	0.680648i
$299$	9.30394	+	7.80693i	0.538061	+	0.451486i
$300$		0			0
$301$	−0.766273	+	4.34575i	−0.0441673	+	0.250485i
$302$	−16.9083	+	6.15411i	−0.972962	+	0.354129i
$303$		0			0
$304$	9.59563	−	5.36375i	0.550347	−	0.307632i
$305$	5.97594			0.342181
$306$		0			0
$307$	2.05006	−	11.6265i	0.117003	−	0.663557i	−0.868736	−	0.495275i	$-0.835067\pi$
$307$	2.05006	−	11.6265i	0.117003	−	0.663557i	0.985739	−	0.168281i	$-0.0538217\pi$
$308$	2.73071	−	2.29134i	0.155596	−	0.130561i
$309$		0			0
$310$	−0.972974	−	5.51801i	−0.0552612	−	0.313402i
$311$	−4.47006	−	7.74236i	−0.253474	−	0.439029i	0.711006	−	0.703186i	$-0.248240\pi$
$311$	−4.47006	−	7.74236i	−0.253474	−	0.439029i	−0.964480	+	0.264157i	$0.914906\pi$
$312$		0			0
$313$	12.6205	+	4.59349i	0.713353	+	0.259639i	0.673101	−	0.739550i	$-0.264962\pi$
$313$	12.6205	+	4.59349i	0.713353	+	0.259639i	0.0402519	+	0.999190i	$0.487184\pi$
$314$	−11.6073	−	4.22470i	−0.655036	−	0.238414i
$315$		0			0
$316$	−3.85801	−	6.68227i	−0.217030	−	0.375907i
$317$	1.92013	+	10.8896i	0.107845	+	0.611622i	0.990046	+	0.140747i	$0.0449505\pi$
$317$	1.92013	+	10.8896i	0.107845	+	0.611622i	−0.882200	+	0.470875i	$0.843938\pi$
$318$		0			0
$319$	−18.5667	+	15.5793i	−1.03953	+	0.872273i
$320$	1.52614	−	8.65518i	0.0853139	−	0.483839i
$321$		0			0
$322$	−7.80524			−0.434969
$323$	−1.43268	−	0.853903i	−0.0797163	−	0.0475124i
$324$		0			0
$325$	−3.83508	+	1.39586i	−0.212732	+	0.0774281i
$326$	−1.43073	+	8.11408i	−0.0792408	+	0.449397i
$327$		0			0
$328$	7.38259	+	6.19473i	0.407635	+	0.342047i
$329$	−4.15655	−	23.5730i	−0.229158	−	1.29962i
$330$		0			0
$331$	1.42273	−	2.46424i	0.0782003	−	0.135447i	−0.824273	−	0.566192i	$-0.808416\pi$
$331$	1.42273	−	2.46424i	0.0782003	−	0.135447i	0.902473	+	0.430745i	$0.141749\pi$
$332$	2.99781	+	1.09111i	0.164526	+	0.0598827i
$333$		0			0
$334$	7.08209	−	12.2665i	0.387515	−	0.671195i
$335$	−0.524713	−	0.908829i	−0.0286681	−	0.0496547i
$336$		0			0
$337$	4.90717	+	4.11760i	0.267311	+	0.224300i	0.766584	−	0.642145i	$-0.221955\pi$
$337$	4.90717	+	4.11760i	0.267311	+	0.224300i	−0.499273	+	0.866445i	$0.666400\pi$
$338$	3.34444	−	2.80632i	0.181913	−	0.152643i
$339$		0			0
$340$	−0.206448	+	0.0751411i	−0.0111962	+	0.00407510i
$341$	−13.2631			−0.718235
$342$		0			0
$343$	20.1537			1.08820
$344$	5.80285	−	2.11206i	0.312869	−	0.113875i
$345$		0			0
$346$	−23.2398	+	19.5005i	−1.24938	+	1.04835i
$347$	−12.1057	−	10.1579i	−0.649869	−	0.545305i	0.257162	−	0.966368i	$-0.417213\pi$
$347$	−12.1057	−	10.1579i	−0.649869	−	0.545305i	−0.907031	+	0.421063i	$0.861657\pi$
$348$		0			0
$349$	13.7825	+	23.8721i	0.737763	+	1.27784i	0.953501	+	0.301391i	$0.0974510\pi$
$349$	13.7825	+	23.8721i	0.737763	+	1.27784i	−0.215738	+	0.976451i	$0.569216\pi$
$350$	1.31139	−	2.27140i	0.0700968	−	0.121411i
$351$		0			0
$352$	−8.32959	−	3.03172i	−0.443968	−	0.161591i
$353$	−2.11442	+	3.66228i	−0.112539	+	0.194924i	−0.916793	−	0.399362i	$-0.869232\pi$
$353$	−2.11442	+	3.66228i	−0.112539	+	0.194924i	0.804254	+	0.594285i	$0.202565\pi$
$354$		0			0
$355$	1.35924	+	7.70864i	0.0721410	+	0.409132i
$356$	−2.88718	−	2.42263i	−0.153020	−	0.128399i
$357$		0			0
$358$	0.0806174	−	0.457204i	0.00426076	−	0.0241640i
$359$	5.38553	−	1.96017i	0.284237	−	0.103454i	−0.195967	−	0.980610i	$-0.562785\pi$
$359$	5.38553	−	1.96017i	0.284237	−	0.103454i	0.480205	+	0.877157i	$0.340562\pi$
$360$		0			0
$361$	−3.81772	+	18.6125i	−0.200932	+	0.979605i
$362$	5.71231			0.300232
$363$		0			0
$364$	0.893788	−	5.06892i	0.0468472	−	0.265684i
$365$	−10.7933	+	9.05662i	−0.564945	+	0.474045i
$366$		0			0
$367$	−0.164205	−	0.931253i	−0.00857143	−	0.0486110i	0.980222	−	0.197901i	$-0.0634124\pi$
$367$	−0.164205	−	0.931253i	−0.00857143	−	0.0486110i	−0.988793	+	0.149290i	$0.952301\pi$
$368$	3.75261	+	6.49971i	0.195618	+	0.338821i
$369$		0			0
$370$	12.0840	+	4.39822i	0.628218	+	0.228653i
$371$	−15.4302	−	5.61612i	−0.801094	−	0.291574i
$372$		0			0
$373$	−0.336649	−	0.583094i	−0.0174310	−	0.0301915i	0.857178	−	0.515020i	$-0.172215\pi$
$373$	−0.336649	−	0.583094i	−0.0174310	−	0.0301915i	−0.874609	+	0.484828i	$0.838882\pi$
$374$	−0.224248	−	1.27177i	−0.0115956	−	0.0657618i
$375$		0			0
$376$	−25.6601	+	21.5314i	−1.32332	+	1.11040i
$377$	−6.07706	+	34.4647i	−0.312984	+	1.77502i
$378$		0			0
$379$	−34.7701			−1.78602			−0.893010	−	0.450037i	$-0.851411\pi$
$379$	−34.7701			−1.78602			−0.893010	+	0.450037i	$0.851411\pi$
$380$	1.58198	+	1.93940i	0.0811536	+	0.0994891i
$381$		0			0
$382$	−26.7631	+	9.74097i	−1.36932	+	0.498392i
$383$	−4.73308	+	26.8426i	−0.241849	+	1.37159i	0.585849	+	0.810420i	$0.300761\pi$
$383$	−4.73308	+	26.8426i	−0.241849	+	1.37159i	−0.827698	+	0.561174i	$0.810350\pi$
$384$		0			0
$385$	−4.75586	−	3.99064i	−0.242381	−	0.203382i
$386$	−2.32770	−	13.2010i	−0.118477	−	0.671916i
$387$		0			0
$388$	4.14736	−	7.18343i	0.210550	−	0.364684i
$389$	34.2998	+	12.4841i	1.73907	+	0.632969i	0.999208	−	0.0397915i	$-0.0126694\pi$
$389$	34.2998	+	12.4841i	1.73907	+	0.632969i	0.739860	+	0.672761i	$0.234892\pi$
$390$		0			0
$391$	0.569343	−	0.986131i	0.0287929	−	0.0498708i
$392$	−3.34338	−	5.79091i	−0.168866	−	0.292485i
$393$		0			0
$394$	15.4338	+	12.9505i	0.777544	+	0.652437i
$395$	−10.2944	+	8.63804i	−0.517968	+	0.434627i
$396$		0			0
$397$	13.0013	−	4.73209i	0.652517	−	0.237497i	0.00551465	−	0.999985i	$-0.498245\pi$
$397$	13.0013	−	4.73209i	0.652517	−	0.237497i	0.647002	+	0.762488i	$0.276022\pi$
$398$	−18.7739			−0.941048
$399$		0			0
$400$	−2.52197			−0.126098
$401$	22.8095	−	8.30199i	1.13905	−	0.414582i	0.297482	−	0.954727i	$-0.403853\pi$
$401$	22.8095	−	8.30199i	1.13905	−	0.414582i	0.841572	+	0.540145i	$0.181631\pi$
$402$		0			0
$403$	−14.6704	+	12.3099i	−0.730783	+	0.613200i
$404$	1.86952	+	1.56871i	0.0930120	+	0.0780463i
$405$		0			0
$406$	−11.2452	−	19.4772i	−0.558089	−	0.966638i
$407$	15.2198	−	26.3614i	0.754417	−	1.30669i
$408$		0			0
$409$	31.8875	+	11.6061i	1.57674	+	0.573885i	0.974491	−	0.224426i	$-0.0720509\pi$
$409$	31.8875	+	11.6061i	1.57674	+	0.573885i	0.602245	+	0.798311i	$0.294273\pi$
$410$	1.87192	−	3.24225i	0.0924473	−	0.160123i
$411$		0			0
$412$	1.46273	+	8.29554i	0.0720634	+	0.408692i
$413$	−21.8382	−	18.3244i	−1.07459	−	0.901686i
$414$		0			0
$415$	0.964812	−	5.47172i	0.0473608	−	0.268596i
$416$	−12.0272	+	4.37756i	−0.589684	+	0.214628i
$417$		0			0
$418$	−12.8414	+	7.17807i	−0.628094	+	0.351091i
$419$	−21.4325			−1.04705			−0.523523	−	0.852012i	$-0.675382\pi$
$419$	−21.4325			−1.04705			−0.523523	+	0.852012i	$0.675382\pi$
$420$		0			0
$421$	−1.27528	+	7.23247i	−0.0621533	+	0.352489i	0.937832	+	0.347089i	$0.112830\pi$
$421$	−1.27528	+	7.23247i	−0.0621533	+	0.352489i	−0.999985	+	0.00539967i	$0.998281\pi$
$422$	−8.49657	+	7.12947i	−0.413607	+	0.347057i
$423$		0			0
$424$	3.99022	+	22.6297i	0.193782	+	1.09899i
$425$	0.191315	+	0.331368i	0.00928015	+	0.0160737i
$426$		0			0
$427$	12.3345	+	4.48939i	0.596908	+	0.217257i
$428$	3.33467	+	1.21372i	0.161187	+	0.0586674i
$429$		0			0
$430$	−1.19946	−	2.07753i	−0.0578433	−	0.100187i
$431$	−0.0219443	−	0.124452i	−0.00105702	−	0.00599466i	0.984275	−	0.176645i	$-0.0565244\pi$
$431$	−0.0219443	−	0.124452i	−0.00105702	−	0.00599466i	−0.985332	+	0.170650i	$0.945413\pi$
$432$		0			0
$433$	4.45694	−	3.73982i	0.214187	−	0.179724i	−0.529382	−	0.848384i	$-0.677576\pi$
$433$	4.45694	−	3.73982i	0.214187	−	0.179724i	0.743569	+	0.668660i	$0.233132\pi$
$434$	2.13713	−	12.1203i	0.102585	−	0.581791i
$435$		0			0
$436$	−0.432852			−0.0207298
$437$	−12.7422	−	2.42973i	−0.609544	−	0.116230i
$438$		0			0
$439$	−17.3872	+	6.32841i	−0.829844	+	0.302039i	−0.721795	−	0.692107i	$-0.756683\pi$
$439$	−17.3872	+	6.32841i	−0.829844	+	0.302039i	−0.108049	+	0.994146i	$0.534460\pi$
$440$	−1.50865	+	8.55595i	−0.0719218	+	0.407889i
$441$		0			0
$442$	−1.42842	−	1.19858i	−0.0679429	−	0.0570108i
$443$	−3.84201	−	21.7891i	−0.182539	−	1.03523i	−0.929076	−	0.369889i	$-0.879396\pi$
$443$	−3.84201	−	21.7891i	−0.182539	−	1.03523i	0.746537	−	0.665344i	$-0.231715\pi$
$444$		0			0
$445$	−3.28204	+	5.68465i	−0.155583	+	0.269478i
$446$	3.13163	+	1.13982i	0.148287	+	0.0539720i
$447$		0			0
$448$	9.65214	−	16.7180i	0.456021	−	0.789851i
$449$	−10.2840	−	17.8124i	−0.485331	−	0.840617i	0.514527	−	0.857474i	$-0.327967\pi$
$449$	−10.2840	−	17.8124i	−0.485331	−	0.840617i	−0.999858	+	0.0168567i	$0.994634\pi$
$450$		0			0
$451$	−6.78865	−	5.69635i	−0.319665	−	0.268231i
$452$	0.382667	−	0.321096i	0.0179991	−	0.0151031i
$453$		0			0
$454$	−0.947121	+	0.344724i	−0.0444506	+	0.0161787i
$455$	−8.96433			−0.420254
$456$		0			0
$457$	20.3583			0.952323			0.476161	−	0.879358i	$-0.342028\pi$
$457$	20.3583			0.952323			0.476161	+	0.879358i	$0.342028\pi$
$458$	−24.6360	+	8.96676i	−1.15116	+	0.418989i
$459$		0			0
$460$	−1.30895	+	1.09834i	−0.0610303	+	0.0512105i
$461$	4.24592	+	3.56275i	0.197752	+	0.165934i	0.736287	−	0.676670i	$-0.236577\pi$
$461$	4.24592	+	3.56275i	0.197752	+	0.165934i	−0.538535	+	0.842603i	$0.681022\pi$
$462$		0			0
$463$	−16.3250	−	28.2757i	−0.758686	−	1.31408i	−0.943521	−	0.331313i	$-0.892508\pi$
$463$	−16.3250	−	28.2757i	−0.758686	−	1.31408i	0.184835	−	0.982770i	$-0.440825\pi$
$464$	−10.8129	+	18.7286i	−0.501978	+	0.869451i
$465$		0			0
$466$	−4.95442	−	1.80326i	−0.229509	−	0.0835344i
$467$	14.3306	−	24.8214i	0.663142	−	1.14860i	−0.316643	−	0.948545i	$-0.602556\pi$
$467$	14.3306	−	24.8214i	0.663142	−	1.14860i	0.979785	−	0.200051i	$-0.0641108\pi$
$468$		0			0
$469$	−0.400268	−	2.27003i	−0.0184827	−	0.104820i
$470$	9.96828	+	8.36438i	0.459803	+	0.385820i
$471$		0			0
$472$	−6.92748	+	39.2877i	−0.318863	+	1.80836i
$473$	−5.33600	+	1.94214i	−0.245350	+	0.0892999i
$474$		0			0
$475$	2.84795	−	3.29988i	0.130673	−	0.151409i
$476$	−0.482564			−0.0221183
$477$		0			0
$478$	−4.11115	+	23.3155i	−0.188040	+	1.06643i
$479$	−7.86922	+	6.60306i	−0.359554	+	0.301701i	−0.804613	−	0.593800i	$-0.797627\pi$
$479$	−7.86922	+	6.60306i	−0.359554	+	0.301701i	0.445059	+	0.895501i	$0.353183\pi$
$480$		0			0
$481$	−7.63223	−	43.2846i	−0.348000	−	1.97361i
$482$	12.4687	+	21.5964i	0.567934	+	0.983691i
$483$		0			0
$484$	−1.62460	−	0.591304i	−0.0738453	−	0.0268775i
$485$	−13.5750	−	4.94091i	−0.616411	−	0.224355i
$486$		0			0
$487$	−5.56223	−	9.63406i	−0.252049	−	0.436561i	0.712041	−	0.702138i	$-0.247771\pi$
$487$	−5.56223	−	9.63406i	−0.252049	−	0.436561i	−0.964090	+	0.265577i	$0.914438\pi$
$488$	−3.18968	−	18.0896i	−0.144390	−	0.818878i
$489$		0			0
$490$	−1.98990	+	1.66973i	−0.0898946	+	0.0754305i
$491$	−2.41105	+	13.6738i	−0.108809	+	0.617089i	0.880821	+	0.473450i	$0.156991\pi$
$491$	−2.41105	+	13.6738i	−0.108809	+	0.617089i	−0.989630	+	0.143639i	$0.954120\pi$
$492$		0			0
$493$	3.28106			0.147771
$494$	−7.54176	+	19.8583i	−0.339320	+	0.893465i
$495$		0			0
$496$	−11.1205	+	4.04752i	−0.499324	+	0.181739i
$497$	−2.98556	+	16.9320i	−0.133921	+	0.759502i
$498$		0			0
$499$	9.79608	+	8.21989i	0.438533	+	0.367973i	0.835160	−	0.550007i	$-0.185375\pi$
$499$	9.79608	+	8.21989i	0.438533	+	0.367973i	−0.396627	+	0.917980i	$0.629819\pi$
$500$	−0.0997049	−	0.565454i	−0.00445894	−	0.0252879i
$501$		0			0
$502$	3.31625	−	5.74392i	0.148012	−	0.256364i
$503$	9.83338	+	3.57906i	0.438449	+	0.159582i	0.551807	−	0.833972i	$-0.313939\pi$
$503$	9.83338	+	3.57906i	0.438449	+	0.159582i	−0.113358	+	0.993554i	$0.536161\pi$
$504$		0			0
$505$	2.12520	−	3.68095i	0.0945701	−	0.163800i
$506$	−5.02195	−	8.69828i	−0.223253	−	0.386686i
$507$		0			0
$508$	1.51501	+	1.27124i	0.0672177	+	0.0564024i
$509$	−21.4000	+	17.9567i	−0.948539	+	0.795919i	−0.979051	−	0.203616i	$-0.934731\pi$
$509$	−21.4000	+	17.9567i	−0.948539	+	0.795919i	0.0305117	+	0.999534i	$0.490286\pi$
$510$		0			0
$511$	−29.0813	+	10.5847i	−1.28648	+	0.468241i
$512$	−23.4130			−1.03472
$513$		0			0
$514$	−24.0211			−1.05952
$515$	13.7858	−	5.01763i	0.607476	−	0.221103i
$516$		0			0
$517$	23.5957	−	19.7992i	1.03774	−	0.870766i
$518$	21.6376	+	18.1561i	0.950701	+	0.797733i
$519$		0			0
$520$	6.27234	+	10.8640i	0.275060	+	0.476419i
$521$	−4.03138	+	6.98256i	−0.176618	+	0.305912i	−0.940720	−	0.339184i	$-0.889849\pi$
$521$	−4.03138	+	6.98256i	−0.176618	+	0.305912i	0.764102	+	0.645095i	$0.223182\pi$
$522$		0			0
$523$	10.8457	+	3.94751i	0.474249	+	0.172612i	0.568076	−	0.822976i	$-0.307688\pi$
$523$	10.8457	+	3.94751i	0.474249	+	0.172612i	−0.0938274	+	0.995588i	$0.529910\pi$
$524$	−2.95723	+	5.12207i	−0.129187	+	0.223759i
$525$		0			0
$526$	−2.42771	−	13.7682i	−0.105853	−	0.600322i
$527$	1.37541	+	1.15411i	0.0599138	+	0.0502736i
$528$		0			0
$529$	−2.45604	+	13.9289i	−0.106784	+	0.605605i
$530$	8.38830	−	3.05309i	0.364364	−	0.132618i
$531$		0			0
$532$	1.80828	+	5.19142i	0.0783987	+	0.225077i
$533$	−12.7959			−0.554254
$534$		0			0
$535$	1.07323	−	6.08657i	0.0463996	−	0.263145i
$536$	−2.47102	+	2.07343i	−0.106732	+	0.0895587i
$537$		0			0
$538$	2.67182	+	15.1526i	0.115190	+	0.653277i
$539$	3.07440	+	5.32502i	0.132424	+	0.229365i
$540$		0			0
$541$	−32.1819	−	11.7133i	−1.38361	−	0.503593i	−0.460339	−	0.887743i	$-0.652272\pi$
$541$	−32.1819	−	11.7133i	−1.38361	−	0.503593i	−0.923270	+	0.384151i	$0.874494\pi$
$542$	17.2983	+	6.29608i	0.743027	+	0.270440i
$543$		0			0
$544$	0.599987	+	1.03921i	0.0257242	+	0.0445556i
$545$	0.130907	+	0.742411i	0.00560744	+	0.0318014i
$546$		0			0
$547$	−21.2152	+	17.8017i	−0.907098	+	0.761146i	−0.971565	−	0.236774i	$-0.923910\pi$
$547$	−21.2152	+	17.8017i	−0.907098	+	0.761146i	0.0644666	+	0.997920i	$0.479465\pi$
$548$	0.146359	−	0.830043i	0.00625214	−	0.0354577i
$549$		0			0
$550$	3.37504			0.143912
$551$	−12.2949	−	35.2976i	−0.523779	−	1.50373i
$552$		0			0
$553$	−27.7372	+	10.0955i	−1.17951	+	0.429305i
$554$	1.09835	−	6.22906i	0.0466645	−	0.264647i
$555$		0			0
$556$	3.22302	+	2.70443i	0.136686	+	0.114694i
$557$	−2.36781	−	13.4285i	−0.100327	−	0.568985i	−0.992984	−	0.118248i	$-0.962272\pi$
$557$	−2.36781	−	13.4285i	−0.100327	−	0.568985i	0.892657	−	0.450737i	$-0.148839\pi$
$558$		0			0
$559$	−4.09961	+	7.10074i	−0.173395	+	0.300329i
$560$	−5.20540	−	1.89461i	−0.219968	−	0.0800619i
$561$		0			0
$562$	−3.21403	+	5.56687i	−0.135576	+	0.234824i
$563$	19.5093	+	33.7910i	0.822217	+	1.42412i	0.904028	+	0.427474i	$0.140596\pi$
$563$	19.5093	+	33.7910i	0.822217	+	1.42412i	−0.0818108	+	0.996648i	$0.526070\pi$
$564$		0			0
$565$	−0.666461	−	0.559227i	−0.0280382	−	0.0235269i
$566$	16.1691	−	13.5675i	0.679638	−	0.570284i
$567$		0			0
$568$	22.6091	−	8.22904i	0.948657	−	0.345283i
$569$	−8.86810			−0.371770			−0.185885	−	0.982572i	$-0.559515\pi$
$569$	−8.86810			−0.371770			−0.185885	+	0.982572i	$0.559515\pi$
$570$		0			0
$571$	35.4054			1.48167			0.740834	−	0.671688i	$-0.234431\pi$
$571$	35.4054			1.48167			0.740834	+	0.671688i	$0.234431\pi$
$572$	6.22395	−	2.26533i	0.260237	−	0.0947184i
$573$		0			0
$574$	6.29941	−	5.28583i	0.262932	−	0.220626i
$575$	2.27970	+	1.91290i	0.0950702	+	0.0797733i
$576$		0			0
$577$	13.0041	+	22.5238i	0.541368	+	0.937677i	0.998826	+	0.0484454i	$0.0154267\pi$
$577$	13.0041	+	22.5238i	0.541368	+	0.937677i	−0.457458	+	0.889231i	$0.651240\pi$
$578$	10.0623	−	17.4283i	0.418535	−	0.724923i
$579$		0			0
$580$	−4.62665	−	1.68396i	−0.192111	−	0.0699227i
$581$	6.10200	−	10.5690i	0.253153	−	0.438475i
$582$		0			0
$583$	−3.66920	−	20.8091i	−0.151963	−	0.861823i
$584$	33.1760	+	27.8379i	1.37283	+	1.15194i
$585$		0			0
$586$	−0.976714	+	5.53922i	−0.0403477	+	0.228823i
$587$	9.90499	−	3.60512i	0.408823	−	0.148799i	−0.129419	−	0.991590i	$-0.541311\pi$
$587$	9.90499	−	3.60512i	0.408823	−	0.148799i	0.538241	+	0.842791i	$0.319089\pi$
$588$		0			0
$589$	7.26189	−	19.1213i	0.299221	−	0.787880i
$590$	15.4977			0.638029
$591$		0			0
$592$	4.71631	−	26.7475i	0.193839	−	1.09932i
$593$	10.1307	−	8.50064i	0.416017	−	0.349080i	−0.410629	−	0.911803i	$-0.634691\pi$
$593$	10.1307	−	8.50064i	0.416017	−	0.349080i	0.826645	+	0.562723i	$0.190246\pi$
$594$		0			0
$595$	0.145942	+	0.827676i	0.00598302	+	0.0339314i
$596$	−2.86855	−	4.96848i	−0.117500	−	0.203517i
$597$		0			0
$598$	−13.6280	−	4.96018i	−0.557289	−	0.202837i
$599$	−3.49529	−	1.27218i	−0.142814	−	0.0519800i	0.269624	−	0.962966i	$-0.413100\pi$
$599$	−3.49529	−	1.27218i	−0.142814	−	0.0519800i	−0.412438	+	0.910986i	$0.635323\pi$
$600$		0			0
$601$	21.0672	+	36.4895i	0.859349	+	1.48844i	0.872550	+	0.488524i	$0.162465\pi$
$601$	21.0672	+	36.4895i	0.859349	+	1.48844i	−0.0132009	+	0.999913i	$0.504202\pi$
$602$	−0.914990	−	5.18917i	−0.0372922	−	0.211495i
$603$		0			0
$604$	−6.62798	+	5.56153i	−0.269689	+	0.226296i
$605$	−0.522858	+	2.96527i	−0.0212572	+	0.120556i
$606$		0			0
$607$	−27.1082			−1.10029			−0.550144	−	0.835070i	$-0.685427\pi$
$607$	−27.1082			−1.10029			−0.550144	+	0.835070i	$0.685427\pi$
$608$	8.93149	−	10.3488i	0.362220	−	0.419699i
$609$		0			0
$610$	−6.70540	+	2.44057i	−0.271494	+	0.0988157i
$611$	7.72311	−	43.8000i	0.312444	−	1.77196i
$612$		0			0
$613$	−8.61611	−	7.22977i	−0.348001	−	0.292008i	0.451986	−	0.892025i	$-0.350716\pi$
$613$	−8.61611	−	7.22977i	−0.348001	−	0.292008i	−0.799987	+	0.600017i	$0.795160\pi$
$614$	2.44793	+	13.8829i	0.0987904	+	0.560268i
$615$		0			0
$616$	−9.54149	+	16.5263i	−0.384438	+	0.665866i
$617$	28.8071	+	10.4849i	1.15973	+	0.422108i	0.849001	−	0.528391i	$-0.177204\pi$
$617$	28.8071	+	10.4849i	1.15973	+	0.422108i	0.310730	+	0.950498i	$0.399427\pi$
$618$		0			0
$619$	20.1384	−	34.8807i	0.809431	−	1.40198i	−0.103828	−	0.994595i	$-0.533109\pi$
$619$	20.1384	−	34.8807i	0.809431	−	1.40198i	0.913259	−	0.407380i	$-0.133558\pi$
$620$	−1.34715	−	2.33332i	−0.0541027	−	0.0937085i
$621$		0			0
$622$	8.17767	+	6.86188i	0.327895	+	0.275136i
$623$	−11.0448	+	9.26766i	−0.442499	+	0.371301i
$624$		0			0
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	−16.0370			−0.640968
$627$		0			0
$628$	−5.93960			−0.237016
$629$	−3.87220	+	1.40937i	−0.154395	+	0.0561951i
$630$		0			0
$631$	29.6279	−	24.8608i	1.17947	−	0.989692i	0.179487	−	0.983760i	$-0.442556\pi$
$631$	29.6279	−	24.8608i	1.17947	−	0.989692i	0.999982	−	0.00593154i	$-0.00188808\pi$
$632$	31.6426	+	26.5513i	1.25868	+	1.05616i
$633$		0			0
$634$	−6.60183	−	11.4347i	−0.262192	−	0.454130i
$635$	1.72221	−	2.98295i	0.0683437	−	0.118375i
$636$		0			0
$637$	8.34295	+	3.03658i	0.330560	+	0.120314i
$638$	14.4705	−	25.0636i	0.572892	−	0.992278i
$639$		0			0
$640$	0.733171	+	4.15802i	0.0289811	+	0.164360i
$641$	33.0725	+	27.7511i	1.30628	+	1.09610i	0.989023	+	0.147764i	$0.0472077\pi$
$641$	33.0725	+	27.7511i	1.30628	+	1.09610i	0.317261	+	0.948338i	$0.397237\pi$
$642$		0			0
$643$	0.760389	−	4.31238i	0.0299868	−	0.170064i	−0.966137	−	0.258032i	$-0.916926\pi$
$643$	0.760389	−	4.31238i	0.0299868	−	0.170064i	0.996123	+	0.0879678i	$0.0280373\pi$
$644$	−3.52684	+	1.28366i	−0.138977	+	0.0505834i
$645$		0			0
$646$	1.95629	+	0.373032i	0.0769693	+	0.0146768i
$647$	16.4916			0.648351			0.324176	−	0.945997i	$-0.394913\pi$
$647$	16.4916			0.648351			0.324176	+	0.945997i	$0.394913\pi$
$648$		0			0
$649$	6.37015	−	36.1269i	0.250050	−	1.41811i
$650$	3.73315	−	3.13248i	0.146426	−	0.122866i
$651$		0			0
$652$	0.687973	+	3.90169i	0.0269431	+	0.152802i
$653$	0.813059	+	1.40826i	0.0318175	+	0.0551095i	0.881496	−	0.472192i	$-0.156537\pi$
$653$	0.813059	+	1.40826i	0.0318175	+	0.0551095i	−0.849678	+	0.527302i	$0.823204\pi$
$654$		0			0
$655$	9.67954	+	3.52307i	0.378211	+	0.137658i
$656$	−7.43034	−	2.70442i	−0.290106	−	0.105590i
$657$		0			0
$658$	14.2911	+	24.7529i	0.557125	+	0.964969i
$659$	0.331134	+	1.87796i	0.0128992	+	0.0731548i	0.990578	−	0.136951i	$-0.0437303\pi$
$659$	0.331134	+	1.87796i	0.0128992	+	0.0731548i	−0.977679	+	0.210106i	$0.932619\pi$
$660$		0			0
$661$	5.07136	−	4.25538i	0.197253	−	0.165515i	−0.538811	−	0.842426i	$-0.681126\pi$
$661$	5.07136	−	4.25538i	0.197253	−	0.165515i	0.736064	+	0.676911i	$0.236682\pi$
$662$	−0.590004	+	3.34608i	−0.0229312	+	0.130049i
$663$		0			0
$664$	−17.0783			−0.662765
$665$	8.35725	−	4.67153i	0.324080	−	0.181154i
$666$		0			0
$667$	23.9797	−	8.72791i	0.928499	−	0.337946i
$668$	1.18270	−	6.70743i	0.0457601	−	0.259518i
$669$		0			0
$670$	0.959927	+	0.805475i	0.0370852	+	0.0311182i
$671$	2.93307	+	16.6343i	0.113230	+	0.642158i
$672$		0			0
$673$	6.22298	−	10.7785i	0.239878	−	0.415482i	−0.720801	−	0.693142i	$-0.756226\pi$
$673$	6.22298	−	10.7785i	0.239878	−	0.415482i	0.960679	+	0.277661i	$0.0895591\pi$
$674$	−7.18779	−	2.61614i	−0.276864	−	0.100770i
$675$		0			0
$676$	1.04967	−	1.81808i	0.0403719	−	0.0699261i
$677$	2.35303	+	4.07556i	0.0904342	+	0.156637i	0.907694	−	0.419633i	$-0.137841\pi$
$677$	2.35303	+	4.07556i	0.0904342	+	0.156637i	−0.817260	+	0.576270i	$0.804508\pi$
$678$		0			0
$679$	−24.3074	−	20.3963i	−0.932833	−	0.782739i
$680$	0.900959	−	0.755994i	0.0345502	−	0.0289910i
$681$		0			0
$682$	14.8820	−	5.41662i	0.569863	−	0.207413i
$683$	−17.6914			−0.676942			−0.338471	−	0.940977i	$-0.609910\pi$
$683$	−17.6914			−0.676942			−0.338471	+	0.940977i	$0.609910\pi$
$684$		0			0
$685$	−1.46792			−0.0560864
$686$	−22.6138	+	8.23076i	−0.863400	+	0.314252i
$687$		0			0
$688$	−3.88130	+	3.25680i	−0.147973	+	0.124164i
$689$	−23.3721	−	19.6115i	−0.890406	−	0.747140i
$690$		0			0
$691$	−13.0639	−	22.6273i	−0.496974	−	0.860784i	0.503020	−	0.864275i	$-0.332222\pi$
$691$	−13.0639	−	22.6273i	−0.496974	−	0.860784i	−0.999994	+	0.00349090i	$0.998889\pi$
$692$	−7.29394	+	12.6335i	−0.277274	+	0.480252i
$693$		0			0
$694$	17.7319	+	6.45388i	0.673093	+	0.244986i
$695$	3.66381	−	6.34590i	0.138976	−	0.240714i
$696$		0			0
$697$	0.208321	+	1.18145i	0.00789073	+	0.0447505i
$698$	−25.2143	−	21.1573i	−0.954374	−	0.800814i
$699$		0			0
$700$	0.219001	−	1.24202i	0.00827745	−	0.0469438i
$701$	−19.9867	+	7.27458i	−0.754889	+	0.274757i	−0.690661	−	0.723178i	$-0.742680\pi$
$701$	−19.9867	+	7.27458i	−0.754889	+	0.274757i	−0.0642272	+	0.997935i	$0.520458\pi$
$702$		0			0
$703$	29.6720	+	36.3759i	1.11910	+	1.37194i
$704$	24.8411			0.936233
$705$		0			0
$706$	0.876847	−	4.97285i	0.0330006	−	0.187156i
$707$	7.15176	−	6.00104i	0.268970	−	0.225692i
$708$		0			0
$709$	1.84788	+	10.4798i	0.0693985	+	0.393578i	0.999645	+	0.0266433i	$0.00848181\pi$
$709$	1.84788	+	10.4798i	0.0693985	+	0.393578i	−0.930247	+	0.366935i	$0.880407\pi$
$710$	−4.67336	−	8.09450i	−0.175388	−	0.303781i
$711$		0			0
$712$	18.9597	+	6.90075i	0.710543	+	0.258617i
$713$	13.1222	+	4.77611i	0.491432	+	0.178867i
$714$		0			0
$715$	−5.76772	−	9.98999i	−0.215701	−	0.373604i
$716$	−0.0387652	−	0.219848i	−0.00144872	−	0.00821612i
$717$		0			0
$718$	−5.24239	+	4.39889i	−0.195644	+	0.164165i
$719$	6.65775	−	37.7580i	0.248292	−	1.40813i	−0.564429	−	0.825481i	$-0.690904\pi$
$719$	6.65775	−	37.7580i	0.248292	−	1.40813i	0.812721	−	0.582653i	$-0.197985\pi$
$720$		0			0
$721$	32.2238			1.20008
$722$	−3.31759	−	22.4436i	−0.123468	−	0.835265i
$723$		0			0
$724$	2.58113	−	0.939456i	0.0959271	−	0.0349146i
$725$	−1.48903	+	8.44473i	−0.0553013	+	0.313629i
$726$		0			0
$727$	5.90339	+	4.95353i	0.218945	+	0.183716i	0.745663	−	0.666324i	$-0.232133\pi$
$727$	5.90339	+	4.95353i	0.218945	+	0.183716i	−0.526718	+	0.850040i	$0.676578\pi$
$728$	4.78475	+	27.1357i	0.177335	+	1.00572i
$729$		0			0
$730$	8.41204	−	14.5701i	0.311343	−	0.539263i
$731$	0.722353	+	0.262915i	0.0267172	+	0.00972427i
$732$		0			0
$733$	−2.04263	+	3.53795i	−0.0754464	+	0.130677i	−0.901280	−	0.433236i	$-0.857372\pi$
$733$	−2.04263	+	3.53795i	−0.0754464	+	0.130677i	0.825834	+	0.563913i	$0.190705\pi$
$734$	0.564571	+	0.977866i	0.0208387	+	0.0360937i
$735$		0			0
$736$	7.14941	+	5.99906i	0.263531	+	0.221128i
$737$	2.27223	−	1.90662i	0.0836985	−	0.0702314i
$738$		0			0
$739$	23.1521	−	8.42669i	0.851665	−	0.309981i	0.120946	−	0.992659i	$-0.461407\pi$
$739$	23.1521	−	8.42669i	0.851665	−	0.309981i	0.730719	+	0.682678i	$0.239185\pi$
$740$	6.18356			0.227312
$741$		0			0
$742$	19.6073			0.719806
$743$	−24.2217	+	8.81599i	−0.888610	+	0.323427i	−0.745679	−	0.666305i	$-0.767875\pi$
$743$	−24.2217	+	8.81599i	−0.888610	+	0.323427i	−0.142931	+	0.989733i	$0.545653\pi$
$744$		0			0
$745$	−7.65421	+	6.42264i	−0.280429	+	0.235307i
$746$	0.615878	+	0.516783i	0.0225489	+	0.0189208i
$747$		0			0
$748$	−0.310486	−	0.537777i	−0.0113525	−	0.0196631i
$749$	6.78766	−	11.7566i	0.248016	−	0.429576i
$750$		0			0
$751$	14.5890	+	5.30998i	0.532362	+	0.193764i	0.594193	−	0.804323i	$-0.297472\pi$
$751$	14.5890	+	5.30998i	0.532362	+	0.193764i	−0.0618308	+	0.998087i	$0.519694\pi$
$752$	13.7418	−	23.8014i	0.501111	−	0.867950i
$753$		0			0
$754$	−7.25648	−	41.1535i	−0.264265	−	1.49872i
$755$	11.5434	+	9.68609i	0.420108	+	0.352513i
$756$		0			0
$757$	−3.76351	+	21.3440i	−0.136787	+	0.775759i	0.836811	+	0.547492i	$0.184417\pi$
$757$	−3.76351	+	21.3440i	−0.136787	+	0.775759i	−0.973598	+	0.228268i	$0.926694\pi$
$758$	39.0143	−	14.2001i	1.41706	−	0.515769i
$759$		0			0
$760$	−11.5091	−	6.85962i	−0.417478	−	0.248825i
$761$	−1.91229			−0.0693204			−0.0346602	−	0.999399i	$-0.511035\pi$
$761$	−1.91229			−0.0693204			−0.0346602	+	0.999399i	$0.511035\pi$
$762$		0			0
$763$	−0.287536	+	1.63070i	−0.0104095	+	0.0590353i
$764$	−10.4910	+	8.80302i	−0.379552	+	0.318482i
$765$		0			0
$766$	−5.65167	−	32.0522i	−0.204203	−	1.15809i
$767$	−26.4845	−	45.8726i	−0.956301	−	1.65636i
$768$		0			0
$769$	−23.4461	−	8.53369i	−0.845489	−	0.307733i	−0.117289	−	0.993098i	$-0.537420\pi$
$769$	−23.4461	−	8.53369i	−0.845489	−	0.307733i	−0.728200	+	0.685365i	$0.759643\pi$
$770$	6.96616	+	2.53548i	0.251043	+	0.0913722i
$771$		0			0
$772$	−3.22285	−	5.58214i	−0.115993	−	0.200906i
$773$	3.03236	+	17.1974i	0.109067	+	0.618547i	0.989518	+	0.144410i	$0.0461286\pi$
$773$	3.03236	+	17.1974i	0.109067	+	0.618547i	−0.880451	+	0.474136i	$0.842760\pi$
$774$		0			0
$775$	−3.59461	+	3.01624i	−0.129122	+	0.108347i
$776$	−7.71075	+	43.7298i	−0.276800	+	1.56981i
$777$		0			0
$778$	−43.5851			−1.56260
$779$	11.9294	−	6.66827i	0.427414	−	0.238915i
$780$		0			0
$781$	−20.7902	+	7.56700i	−0.743931	+	0.270769i
$782$	−0.236106	+	1.33902i	−0.00844313	+	0.0478834i
$783$		0			0
$784$	4.20279	+	3.52656i	0.150100	+	0.125949i
$785$	1.79631	+	10.1874i	0.0641131	+	0.363604i
$786$		0			0
$787$	24.5804	−	42.5745i	0.876196	−	1.51762i	0.0207128	−	0.999785i	$-0.493406\pi$
$787$	24.5804	−	42.5745i	0.876196	−	1.51762i	0.855483	−	0.517831i	$-0.173260\pi$
$788$	9.10371	+	3.31348i	0.324306	+	0.118038i
$789$		0			0
$790$	8.02325	−	13.8967i	0.285454	−	0.494422i
$791$	−0.955477	−	1.65493i	−0.0339728	−	0.0588427i
$792$		0			0
$793$	18.6831	+	15.6770i	0.663456	+	0.556706i
$794$	−12.6558	+	10.6194i	−0.449136	+	0.376870i
$795$		0			0
$796$	−8.48306	+	3.08758i	−0.300674	+	0.109436i
$797$	35.4304			1.25501			0.627505	−	0.778613i	$-0.284076\pi$
$797$	35.4304			1.25501			0.627505	+	0.778613i	$0.284076\pi$
$798$		0			0
$799$	−4.16978			−0.147516
$800$	−2.94698	+	1.07261i	−0.104192	+	0.0379226i
$801$		0			0
$802$	−22.2033	+	18.6308i	−0.784026	+	0.657876i
$803$	−30.5069	−	25.5983i	−1.07657	−	0.903346i
$804$		0			0
$805$	3.26831	+	5.66088i	0.115193	+	0.199520i
$806$	11.4338	−	19.8039i	0.402738	−	0.697562i
$807$		0			0
$808$	−12.2768	−	4.46840i	−0.431898	−	0.157198i
$809$	−18.1503	+	31.4373i	−0.638131	+	1.10528i	0.347711	+	0.937602i	$0.386959\pi$
$809$	−18.1503	+	31.4373i	−0.638131	+	1.10528i	−0.985842	+	0.167674i	$0.946374\pi$
$810$		0			0
$811$	−1.04633	−	5.93406i	−0.0367418	−	0.208373i	0.960910	−	0.276860i	$-0.0892939\pi$
$811$	−1.04633	−	5.93406i	−0.0367418	−	0.208373i	−0.997652	+	0.0684872i	$0.978183\pi$
$812$	−8.28445	−	6.95148i	−0.290727	−	0.243949i
$813$		0			0
$814$	−6.31163	+	35.7950i	−0.221223	+	1.25462i
$815$	6.48397	−	2.35997i	0.227123	−	0.0826662i
$816$		0			0
$817$	0.121618	−	8.75627i	0.00425488	−	0.306343i
$818$	−40.5198			−1.41674
$819$		0			0
$820$	0.312608	−	1.77289i	0.0109167	−	0.0619119i
$821$	28.0570	−	23.5426i	0.979196	−	0.821643i	−0.00477169	−	0.999989i	$-0.501519\pi$
$821$	28.0570	−	23.5426i	0.979196	−	0.821643i	0.983968	+	0.178345i	$0.0570744\pi$
$822$		0			0
$823$	−2.65820	−	15.0754i	−0.0926590	−	0.525495i	−0.995440	−	0.0953939i	$-0.969589\pi$
$823$	−2.65820	−	15.0754i	−0.0926590	−	0.525495i	0.902781	−	0.430101i	$-0.141522\pi$
$824$	−22.5470	−	39.0525i	−0.785461	−	1.36046i
$825$		0			0
$826$	31.9876	+	11.6425i	1.11299	+	0.405096i
$827$	19.8223	+	7.21472i	0.689288	+	0.250880i	0.662831	−	0.748769i	$-0.269355\pi$
$827$	19.8223	+	7.21472i	0.689288	+	0.250880i	0.0264579	+	0.999650i	$0.491577\pi$
$828$		0			0
$829$	−20.0967	−	34.8085i	−0.697987	−	1.20895i	−0.969163	−	0.246419i	$-0.920746\pi$
$829$	−20.0967	−	34.8085i	−0.697987	−	1.20895i	0.271177	−	0.962530i	$-0.412587\pi$
$830$	1.15206	+	6.53366i	0.0399886	+	0.226787i
$831$		0			0
$832$	27.4769	−	23.0558i	0.952589	−	0.799317i
$833$	0.144542	−	0.819740i	0.00500809	−	0.0284023i
$834$		0			0
$835$	−11.8620			−0.410502
$836$	−4.62194	+	5.35537i	−0.159853	+	0.185219i
$837$		0			0
$838$	24.0487	−	8.75300i	0.830747	−	0.302367i
$839$	−4.84143	+	27.4571i	−0.167145	+	0.947925i	0.779681	+	0.626177i	$0.215381\pi$
$839$	−4.84143	+	27.4571i	−0.167145	+	0.947925i	−0.946825	+	0.321748i	$0.895730\pi$
$840$		0			0
$841$	34.1125	+	28.6238i	1.17629	+	0.987027i
$842$	−1.52278	−	8.63613i	−0.0524786	−	0.297621i
$843$		0			0
$844$	−2.66669	+	4.61885i	−0.0917914	+	0.158987i
$845$	−3.43575	−	1.25051i	−0.118194	−	0.0430189i
$846$		0			0
$847$	−3.30684	+	5.72761i	−0.113624	+	0.196803i
$848$	−9.42680	−	16.3277i	−0.323718	−	0.560696i
$849$		0			0
$850$	−0.349999	−	0.293684i	−0.0120049	−	0.0100733i
$851$	−24.5511	+	20.6008i	−0.841601	+	0.706187i
$852$		0			0
$853$	−18.9031	+	6.88015i	−0.647228	+	0.235572i	−0.644713	−	0.764425i	$-0.723023\pi$
$853$	−18.9031	+	6.88015i	−0.647228	+	0.235572i	−0.00251570	+	0.999997i	$0.500801\pi$
$854$	−15.6736			−0.536339
$855$		0			0
$856$	−18.9973			−0.649315
$857$	−4.08976	+	1.48855i	−0.139704	+	0.0508480i	−0.410926	−	0.911669i	$-0.634794\pi$
$857$	−4.08976	+	1.48855i	−0.139704	+	0.0508480i	0.271222	+	0.962517i	$0.412572\pi$
$858$		0			0
$859$	−4.22949	+	3.54896i	−0.144308	+	0.121089i	−0.712084	−	0.702094i	$-0.752249\pi$
$859$	−4.22949	+	3.54896i	−0.144308	+	0.121089i	0.567776	+	0.823183i	$0.307804\pi$
$860$	−0.883658	−	0.741477i	−0.0301325	−	0.0252842i
$861$		0			0
$862$	0.0754492	+	0.130682i	0.00256981	+	0.00445104i
$863$	17.9032	−	31.0093i	0.609433	−	1.05557i	−0.381901	−	0.924203i	$-0.624730\pi$
$863$	17.9032	−	31.0093i	0.609433	−	1.05557i	0.991334	−	0.131366i	$-0.0419364\pi$
$864$		0			0
$865$	23.8744	+	8.68955i	0.811752	+	0.295454i
$866$	−3.47365	+	6.01653i	−0.118039	+	0.204450i
$867$		0			0
$868$	−1.02765	−	5.82808i	−0.0348806	−	0.197818i
$869$	−29.0969	−	24.4152i	−0.987046	−	0.828230i
$870$		0			0
$871$	0.743722	−	4.21786i	0.0252001	−	0.142917i
$872$	2.17746	−	0.792530i	0.0737381	−	0.0268385i
$873$		0			0
$874$	15.2899	−	2.47759i	0.517190	−	0.0838059i
$875$	−2.19649			−0.0742549
$876$		0			0
$877$	−4.25763	+	24.1462i	−0.143770	+	0.815360i	0.824577	+	0.565750i	$0.191413\pi$
$877$	−4.25763	+	24.1462i	−0.143770	+	0.815360i	−0.968347	+	0.249610i	$0.919698\pi$
$878$	16.9250	−	14.2018i	0.571193	−	0.479288i
$879$		0			0
$880$	−1.23781	−	7.01999i	−0.0417267	−	0.236644i
$881$	−14.7421	−	25.5341i	−0.496675	−	0.860266i	0.503318	−	0.864101i	$-0.332113\pi$
$881$	−14.7421	−	25.5341i	−0.496675	−	0.860266i	−0.999993	+	0.00383530i	$0.998779\pi$
$882$		0			0
$883$	7.54441	+	2.74594i	0.253890	+	0.0924083i	0.465830	−	0.884874i	$-0.345756\pi$
$883$	7.54441	+	2.74594i	0.253890	+	0.0924083i	−0.211940	+	0.977283i	$0.567978\pi$
$884$	−0.842559	−	0.306666i	−0.0283383	−	0.0103143i
$885$		0			0
$886$	13.2096	+	22.8798i	0.443787	+	0.768661i
$887$	−3.63211	−	20.5987i	−0.121954	−	0.691638i	−0.983070	−	0.183229i	$-0.941345\pi$
$887$	−3.63211	−	20.5987i	−0.121954	−	0.691638i	0.861116	−	0.508409i	$-0.169766\pi$
$888$		0			0
$889$	5.79561	−	4.86309i	0.194378	−	0.163103i
$890$	1.36106	−	7.71894i	0.0456227	−	0.258739i
$891$		0			0
$892$	1.60250			0.0536556
$893$	15.6251	+	44.8585i	0.522874	+	1.50113i
$894$		0			0
$895$	−0.365352	+	0.132977i	−0.0122124	+	0.00444494i
$896$	−1.61040	+	9.13305i	−0.0537998	+	0.305114i
$897$		0			0
$898$	18.8138	+	15.7867i	0.627826	+	0.526809i
$899$	6.98720	+	39.6264i	0.233036	+	1.32161i
$900$		0			0
$901$	−1.43023	+	2.47723i	−0.0476478	+	0.0825283i
$902$	9.94370	+	3.61921i	0.331089	+	0.120506i
$903$		0			0
$904$	−1.33709	+	2.31591i	−0.0444711	+	0.0770262i
$905$	−2.39193	−	4.14295i	−0.0795105	−	0.137716i
$906$		0			0
$907$	−0.224543	−	0.188414i	−0.00745584	−	0.00625619i	0.639052	−	0.769163i	$-0.279327\pi$
$907$	−0.224543	−	0.188414i	−0.00745584	−	0.00625619i	−0.646508	+	0.762907i	$0.723771\pi$
$908$	−0.371267	+	0.311530i	−0.0123209	+	0.0103385i
$909$		0			0
$910$	10.0586	−	3.66102i	0.333439	−	0.121362i
$911$	22.0356			0.730073			0.365037	−	0.930993i	$-0.381056\pi$
$911$	22.0356			0.730073			0.365037	+	0.930993i	$0.381056\pi$
$912$		0			0
$913$	15.7043			0.519736
$914$	−22.8434	+	8.31432i	−0.755592	+	0.275013i
$915$		0			0
$916$	−9.65720	+	8.10336i	−0.319083	+	0.267742i
$917$	17.3321	+	14.5434i	0.572358	+	0.480265i
$918$		0			0
$919$	0.460757	+	0.798054i	0.0151990	+	0.0263254i	0.873525	−	0.486780i	$-0.161829\pi$
$919$	0.460757	+	0.798054i	0.0151990	+	0.0263254i	−0.858326	+	0.513105i	$0.828495\pi$
$920$	4.57368	−	7.92184i	0.150790	−	0.261175i
$921$		0			0
$922$	−6.21922	−	2.26361i	−0.204819	−	0.0745481i
$923$	−15.9729	+	27.6660i	−0.525756	+	0.910636i
$924$		0			0
$925$	−1.87009	−	10.6058i	−0.0614883	−	0.348717i
$926$	29.8655	+	25.0601i	0.981440	+	0.823526i
$927$		0			0
$928$	−4.66978	+	26.4836i	−0.153293	+	0.869368i
$929$	−22.0825	+	8.03737i	−0.724503	+	0.263697i	−0.677836	−	0.735213i	$-0.737082\pi$
$929$	−22.0825	+	8.03737i	−0.724503	+	0.263697i	−0.0466666	+	0.998911i	$0.514860\pi$
$930$		0			0
$931$	−9.36039	+	1.51677i	−0.306774	+	0.0497100i
$932$	−2.53525			−0.0830448
$933$		0			0
$934$	−5.94289	+	33.7038i	−0.194457	+	1.10282i
$935$	−0.828475	+	0.695173i	−0.0270940	+	0.0227346i
$936$		0			0
$937$	−9.25942	−	52.5128i	−0.302492	−	1.71552i	−0.635081	−	0.772445i	$-0.719033\pi$
$937$	−9.25942	−	52.5128i	−0.302492	−	1.71552i	0.332589	−	0.943072i	$-0.392078\pi$
$938$	1.37621	+	2.38366i	0.0449348	+	0.0778293i
$939$		0			0
$940$	5.87984	+	2.14009i	0.191779	+	0.0698019i
$941$	−3.88045	−	1.41237i	−0.126499	−	0.0460418i	0.277995	−	0.960583i	$-0.410330\pi$
$941$	−3.88045	−	1.41237i	−0.126499	−	0.0460418i	−0.404494	+	0.914541i	$0.632552\pi$
$942$		0			0
$943$	4.66528	+	8.08050i	0.151922	+	0.263137i
$944$	−5.68386	−	32.2348i	−0.184994	−	1.04915i
$945$		0			0
$946$	5.19418	−	4.35843i	0.168877	−	0.141705i
$947$	−1.46241	+	8.29375i	−0.0475220	+	0.269511i	−0.999306	−	0.0372596i	$-0.988137\pi$
$947$	−1.46241	+	8.29375i	−0.0475220	+	0.269511i	0.951784	+	0.306770i	$0.0992483\pi$
$948$		0			0
$949$	−57.5025			−1.86661
$950$	−1.84792	+	4.86578i	−0.0599545	+	0.157867i
$951$		0			0
$952$	2.42754	−	0.883552i	0.0786770	−	0.0286361i
$953$	3.29483	−	18.6859i	0.106730	−	0.605296i	−0.883785	−	0.467893i	$-0.845013\pi$
$953$	3.29483	−	18.6859i	0.106730	−	0.605296i	0.990515	−	0.137403i	$-0.0438755\pi$
$954$		0			0
$955$	18.2714	+	15.3315i	0.591249	+	0.496117i
$956$	1.97686	+	11.2114i	0.0639364	+	0.362601i
$957$		0			0
$958$	6.13311	−	10.6229i	0.198152	−	0.343209i
$959$	−3.02983	−	1.10277i	−0.0978383	−	0.0356102i
$960$		0			0
$961$	4.49052	−	7.77782i	0.144856	−	0.250897i
$962$	26.2412	+	45.4511i	0.846051	+	1.46540i
$963$		0			0
$964$	9.18584	+	7.70784i	0.295856	+	0.248253i
$965$	−8.59960	+	7.21592i	−0.276831	+	0.232289i
$966$		0			0
$967$	3.53205	−	1.28556i	0.113583	−	0.0413408i	−0.284603	−	0.958645i	$-0.591862\pi$
$967$	3.53205	−	1.28556i	0.113583	−	0.0413408i	0.398186	+	0.917305i	$0.369640\pi$
$968$	9.25517			0.297473
$969$		0			0
$970$	17.2500			0.553863
$971$	12.0598	−	4.38940i	0.387016	−	0.140862i	−0.141182	−	0.989984i	$-0.545090\pi$
$971$	12.0598	−	4.38940i	0.387016	−	0.140862i	0.528198	+	0.849121i	$0.322868\pi$
$972$		0			0
$973$	12.3295	−	10.3457i	0.395266	−	0.331668i
$974$	10.1757	+	8.53845i	0.326051	+	0.273590i
$975$		0			0
$976$	7.53556	+	13.0520i	0.241207	+	0.417783i
$977$	−13.7672	+	23.8455i	−0.440453	+	0.762887i	−0.997723	−	0.0674446i	$-0.978515\pi$
$977$	−13.7672	+	23.8455i	−0.440453	+	0.762887i	0.557270	+	0.830331i	$0.311849\pi$
$978$		0			0
$979$	−17.4343	−	6.34557i	−0.557203	−	0.202805i
$980$	−0.624541	+	1.08174i	−0.0199502	+	0.0345548i
$981$		0			0
$982$	−2.87899	−	16.3276i	−0.0918722	−	0.521033i
$983$	−36.9720	−	31.0232i	−1.17922	−	0.989486i	−0.999984	−	0.00568028i	$-0.998192\pi$
$983$	−36.9720	−	31.0232i	−1.17922	−	0.989486i	−0.179239	−	0.983805i	$-0.557364\pi$
$984$		0			0
$985$	2.92993	−	16.6164i	0.0933552	−	0.529444i
$986$	−3.68157	+	1.33998i	−0.117245	+	0.0426737i
$987$		0			0
$988$	−0.141856	+	10.2134i	−0.00451305	+	0.324931i
$989$	5.97872			0.190112
$990$		0			0
$991$	−7.57591	+	42.9651i	−0.240657	+	1.36483i	0.589710	+	0.807615i	$0.299242\pi$
$991$	−7.57591	+	42.9651i	−0.240657	+	1.36483i	−0.830367	+	0.557217i	$0.811869\pi$
$992$	−11.2731	+	9.45927i	−0.357922	+	0.300332i
$993$		0			0
$994$	−3.56499	−	20.2181i	−0.113075	−	0.641279i
$995$	7.86124	+	13.6161i	0.249218	+	0.431658i
$996$		0			0
$997$	−28.3767	−	10.3283i	−0.898698	−	0.327099i	−0.148967	−	0.988842i	$-0.547595\pi$
$997$	−28.3767	−	10.3283i	−0.898698	−	0.327099i	−0.749731	+	0.661743i	$0.769817\pi$
$998$	−14.3488	−	5.22255i	−0.454205	−	0.165317i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.b.271.2		18
3.2	odd	2		95.2.k.b.81.2	yes	18
15.2	even	4		475.2.u.c.24.4		36
15.8	even	4		475.2.u.c.24.3		36
15.14	odd	2		475.2.l.b.176.2		18
19.4	even	9	inner	855.2.bs.b.631.2		18
57.2	even	18		1805.2.a.u.1.6		9
57.17	odd	18		1805.2.a.t.1.4		9
57.23	odd	18		95.2.k.b.61.2	✓	18
285.23	even	36		475.2.u.c.99.4		36
285.59	even	18		9025.2.a.cd.1.4		9
285.74	odd	18		9025.2.a.ce.1.6		9
285.137	even	36		475.2.u.c.99.3		36
285.194	odd	18		475.2.l.b.251.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.2	✓	18	57.23	odd	18
95.2.k.b.81.2	yes	18	3.2	odd	2
475.2.l.b.176.2		18	15.14	odd	2
475.2.l.b.251.2		18	285.194	odd	18
475.2.u.c.24.3		36	15.8	even	4
475.2.u.c.24.4		36	15.2	even	4
475.2.u.c.99.3		36	285.137	even	36
475.2.u.c.99.4		36	285.23	even	36
855.2.bs.b.271.2		18	1.1	even	1	trivial
855.2.bs.b.631.2		18	19.4	even	9	inner
1805.2.a.t.1.4		9	57.17	odd	18
1805.2.a.u.1.6		9	57.2	even	18
9025.2.a.cd.1.4		9	285.59	even	18
9025.2.a.ce.1.6		9	285.74	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12207 + 0.408399i) q^{2} +(-0.439845 + 0.369074i) q^{4} +(0.766044 + 0.642788i) q^{5} +(1.09825 + 1.90222i) q^{7} +(1.53688 - 2.66196i) q^{8} +O(q^{10})\)	\(q+(-1.12207 + 0.408399i) q^{2} +(-0.439845 + 0.369074i) q^{4} +(0.766044 + 0.642788i) q^{5} +(1.09825 + 1.90222i) q^{7} +(1.53688 - 2.66196i) q^{8} +(-1.12207 - 0.408399i) q^{10} +(-1.41324 + 2.44780i) q^{11} +(0.708694 + 4.01920i) q^{13} +(-2.00917 - 1.68589i) q^{14} +(-0.437935 + 2.48365i) q^{16} +(0.359555 - 0.130867i) q^{17} +(-2.75520 - 3.37770i) q^{19} -0.574177 q^{20} +(0.586069 - 3.32376i) q^{22} +(2.27970 - 1.91290i) q^{23} +(0.173648 + 0.984808i) q^{25} +(-2.43664 - 4.22038i) q^{26} +(-1.18512 - 0.431347i) q^{28} +(8.05787 + 2.93282i) q^{29} +(2.34622 + 4.06377i) q^{31} +(0.544580 + 3.08847i) q^{32} +(-0.349999 + 0.293684i) q^{34} +(-0.381417 + 2.16312i) q^{35} -10.7694 q^{37} +(4.47097 + 2.66478i) q^{38} +(2.88840 - 1.05129i) q^{40} +(-0.544445 + 3.08770i) q^{41} +(1.53900 + 1.29137i) q^{43} +(-0.281814 - 1.59824i) q^{44} +(-1.77675 + 3.07743i) q^{46} +(-10.2405 - 3.72722i) q^{47} +(1.08771 - 1.88398i) q^{49} +(-0.597039 - 1.03410i) q^{50} +(-1.79510 - 1.50627i) q^{52} +(-5.72676 + 4.80532i) q^{53} +(-2.65602 + 0.966713i) q^{55} +6.75150 q^{56} -10.2392 q^{58} +(-12.1961 + 4.43900i) q^{59} +(4.57784 - 3.84126i) q^{61} +(-4.29225 - 3.60163i) q^{62} +(-4.39435 - 7.61123i) q^{64} +(-2.04060 + 3.53443i) q^{65} +(-0.986138 - 0.358925i) q^{67} +(-0.109849 + 0.190264i) q^{68} +(-0.455441 - 2.58294i) q^{70} +(5.99626 + 5.03146i) q^{71} +(-2.44663 + 13.8755i) q^{73} +(12.0840 - 4.39822i) q^{74} +(2.45848 + 0.468792i) q^{76} -6.20833 q^{77} +(-2.33355 + 13.2342i) q^{79} +(-1.93194 + 1.62109i) q^{80} +(-0.650110 - 3.68695i) q^{82} +(-2.77807 - 4.81175i) q^{83} +(0.359555 + 0.130867i) q^{85} +(-2.25425 - 0.820481i) q^{86} +(4.34397 + 7.52398i) q^{88} +(1.13984 + 6.46435i) q^{89} +(-6.86708 + 5.76216i) q^{91} +(-0.296716 + 1.68276i) q^{92} +13.0127 q^{94} +(0.0605361 - 4.35848i) q^{95} +(-13.5750 + 4.94091i) q^{97} +(-0.451074 + 2.55817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more