LMFDB - Embedded newform 603.2.u.a.442.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(64,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("603.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (of order $11$, degree $10$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			442.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	603.442
Dual form			603.2.u.a.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.154861 + 0.178719i) q^{2} +(0.276671 - 1.92429i) q^{4} +(1.84125 + 0.540641i) q^{5} +(2.11435 + 2.44009i) q^{7} +(0.784630 - 0.504251i) q^{8} +O(q^{10})$	\(q+(0.154861 + 0.178719i) q^{2} +(0.276671 - 1.92429i) q^{4} +(1.84125 + 0.540641i) q^{5} +(2.11435 + 2.44009i) q^{7} +(0.784630 - 0.504251i) q^{8} +(0.188515 + 0.412791i) q^{10} +(1.71047 + 0.502239i) q^{11} +(1.19537 + 0.768216i) q^{13} +(-0.108660 + 0.755750i) q^{14} +(-3.51903 - 1.03328i) q^{16} +(-0.308705 - 2.14709i) q^{17} +(-3.09647 + 3.57352i) q^{19} +(1.54977 - 3.39353i) q^{20} +(0.175125 + 0.383470i) q^{22} +(-1.86779 + 4.08990i) q^{23} +(-1.10835 - 0.712290i) q^{25} +(0.0478208 + 0.332601i) q^{26} +(5.28043 - 3.39353i) q^{28} +7.97852 q^{29} +(8.25215 - 5.30334i) q^{31} +(-1.13520 - 2.48574i) q^{32} +(0.335919 - 0.387671i) q^{34} +(2.57385 + 5.63594i) q^{35} -5.11059 q^{37} -1.11818 q^{38} +(1.71732 - 0.504251i) q^{40} +(-1.31440 - 9.14184i) q^{41} +(-0.263933 - 1.83570i) q^{43} +(1.43969 - 3.15248i) q^{44} +(-1.02019 + 0.299555i) q^{46} +(-2.54645 + 5.57594i) q^{47} +(-0.487365 + 3.38969i) q^{49} +(-0.0443395 - 0.308388i) q^{50} +(1.80899 - 2.08769i) q^{52} +(-0.376741 + 2.62029i) q^{53} +(2.87787 + 1.84950i) q^{55} +(2.88940 + 0.848406i) q^{56} +(1.23556 + 1.42591i) q^{58} +(9.96996 - 6.40730i) q^{59} +(-8.04376 + 2.36186i) q^{61} +(2.22574 + 0.653536i) q^{62} +(-2.77870 + 6.08450i) q^{64} +(1.78565 + 2.06075i) q^{65} +(5.87551 - 5.69898i) q^{67} -4.21704 q^{68} +(-0.608660 + 1.33278i) q^{70} +(-1.09047 + 7.58435i) q^{71} +(-5.05565 + 1.48447i) q^{73} +(-0.791429 - 0.913358i) q^{74} +(6.01979 + 6.94720i) q^{76} +(2.39102 + 5.23561i) q^{77} +(-7.32594 - 4.70809i) q^{79} +(-5.92079 - 3.80506i) q^{80} +(1.43027 - 1.65062i) q^{82} +(-15.3495 - 4.50703i) q^{83} +(0.592401 - 4.12024i) q^{85} +(0.287201 - 0.331447i) q^{86} +(1.59534 - 0.468434i) q^{88} +(0.292424 + 0.640320i) q^{89} +(0.652910 + 4.54109i) q^{91} +(7.35338 + 4.72573i) q^{92} +(-1.39087 + 0.408396i) q^{94} +(-7.63338 + 4.90568i) q^{95} +1.26679 q^{97} +(-0.681276 + 0.437829i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$	0.154861	+	0.178719i	0.109503	+	0.126373i	0.807855	−	0.589381i	$-0.200628\pi$
$2$	0.154861	+	0.178719i	0.109503	+	0.126373i	−0.698352	+	0.715755i	$0.746083\pi$
$3$		0			0
$3$		0			0
$4$	0.276671	−	1.92429i	0.138336	−	0.962145i
$5$	1.84125	+	0.540641i	0.823434	+	0.241782i	0.666194	−	0.745779i	$-0.267922\pi$
$5$	1.84125	+	0.540641i	0.823434	+	0.241782i	0.157240	+	0.987560i	$0.449740\pi$
$6$		0			0
$7$	2.11435	+	2.44009i	0.799151	+	0.922269i	0.998334	−	0.0576932i	$-0.0183745\pi$
$7$	2.11435	+	2.44009i	0.799151	+	0.922269i	−0.199184	+	0.979962i	$0.563829\pi$
$8$	0.784630	−	0.504251i	0.277408	−	0.178280i
$9$		0			0
$10$	0.188515	+	0.412791i	0.0596137	+	0.130536i
$11$	1.71047	+	0.502239i	0.515726	+	0.151431i	0.529230	−	0.848478i	$-0.322481\pi$
$11$	1.71047	+	0.502239i	0.515726	+	0.151431i	−0.0135049	+	0.999909i	$0.504299\pi$
$12$		0			0
$13$	1.19537	+	0.768216i	0.331535	+	0.213065i	0.695809	−	0.718227i	$-0.255046\pi$
$13$	1.19537	+	0.768216i	0.331535	+	0.213065i	−0.364273	+	0.931292i	$0.618683\pi$
$14$	−0.108660	+	0.755750i	−0.0290407	+	0.201983i
$15$		0			0
$16$	−3.51903	−	1.03328i	−0.879758	−	0.258320i
$17$	−0.308705	−	2.14709i	−0.0748720	−	0.520746i	−0.992398	−	0.123070i	$-0.960726\pi$
$17$	−0.308705	−	2.14709i	−0.0748720	−	0.520746i	0.917526	−	0.397676i	$-0.130183\pi$
$18$		0			0
$19$	−3.09647	+	3.57352i	−0.710380	+	0.819822i	−0.990115	−	0.140255i	$-0.955208\pi$
$19$	−3.09647	+	3.57352i	−0.710380	+	0.819822i	0.279736	+	0.960077i	$0.409753\pi$
$20$	1.54977	−	3.39353i	0.346539	−	0.758815i
$21$		0			0
$22$	0.175125	+	0.383470i	0.0373367	+	0.0817561i
$23$	−1.86779	+	4.08990i	−0.389462	+	0.852803i	0.608769	+	0.793348i	$0.291664\pi$
$23$	−1.86779	+	4.08990i	−0.389462	+	0.852803i	−0.998231	+	0.0594552i	$0.981064\pi$
$24$		0			0
$25$	−1.10835	−	0.712290i	−0.221669	−	0.142458i
$26$	0.0478208	+	0.332601i	0.00937844	+	0.0652285i
$27$		0			0
$28$	5.28043	−	3.39353i	0.997907	−	0.641316i
$29$	7.97852			1.48157			0.740787	−	0.671740i	$-0.234453\pi$
$29$	7.97852			1.48157			0.740787	+	0.671740i	$0.234453\pi$
$30$		0			0
$31$	8.25215	−	5.30334i	1.48213	−	0.952507i	0.485185	−	0.874412i	$-0.338752\pi$
$31$	8.25215	−	5.30334i	1.48213	−	0.952507i	0.996946	−	0.0780957i	$-0.0248840\pi$
$32$	−1.13520	−	2.48574i	−0.200677	−	0.439421i
$33$		0			0
$34$	0.335919	−	0.387671i	0.0576097	−	0.0664851i
$35$	2.57385	+	5.63594i	0.435059	+	0.952647i
$36$		0			0
$37$	−5.11059			−0.840175			−0.420088	−	0.907484i	$-0.638001\pi$
$37$	−5.11059			−0.840175			−0.420088	+	0.907484i	$0.638001\pi$
$38$	−1.11818			−0.181392
$39$		0			0
$40$	1.71732	−	0.504251i	0.271532	−	0.0797291i
$41$	−1.31440	−	9.14184i	−0.205275	−	1.42772i	−0.788315	−	0.615272i	$-0.789046\pi$
$41$	−1.31440	−	9.14184i	−0.205275	−	1.42772i	0.583040	−	0.812443i	$-0.301863\pi$
$42$		0			0
$43$	−0.263933	−	1.83570i	−0.0402495	−	0.279941i	0.959750	−	0.280855i	$-0.0906181\pi$
$43$	−0.263933	−	1.83570i	−0.0402495	−	0.279941i	−1.00000		0.000914132i	$0.999709\pi$
$44$	1.43969	−	3.15248i	0.217041	−	0.475254i
$45$		0			0
$46$	−1.02019	+	0.299555i	−0.150419	+	0.0441669i
$47$	−2.54645	+	5.57594i	−0.371437	+	0.813334i	0.627947	+	0.778256i	$0.283895\pi$
$47$	−2.54645	+	5.57594i	−0.371437	+	0.813334i	−0.999385	+	0.0350783i	$0.988832\pi$
$48$		0			0
$49$	−0.487365	+	3.38969i	−0.0696235	+	0.484242i
$50$	−0.0443395	−	0.308388i	−0.00627055	−	0.0436127i
$51$		0			0
$52$	1.80899	−	2.08769i	0.250862	−	0.289511i
$53$	−0.376741	+	2.62029i	−0.0517494	+	0.359925i	0.947450	+	0.319905i	$0.103651\pi$
$53$	−0.376741	+	2.62029i	−0.0517494	+	0.359925i	−0.999199	+	0.0400195i	$0.987258\pi$
$54$		0			0
$55$	2.87787	+	1.84950i	0.388053	+	0.249386i
$56$	2.88940	+	0.848406i	0.386113	+	0.113373i
$57$		0			0
$58$	1.23556	+	1.42591i	0.162237	+	0.187231i
$59$	9.96996	−	6.40730i	1.29798	−	0.834160i	0.304988	−	0.952356i	$-0.401348\pi$
$59$	9.96996	−	6.40730i	1.29798	−	0.834160i	0.992990	+	0.118196i	$0.0377112\pi$
$60$		0			0
$61$	−8.04376	+	2.36186i	−1.02990	+	0.302405i	−0.752670	−	0.658398i	$-0.771234\pi$
$61$	−8.04376	+	2.36186i	−1.02990	+	0.302405i	−0.277229	+	0.960804i	$0.589416\pi$
$62$	2.22574	+	0.653536i	0.282669	+	0.0829992i
$63$		0			0
$64$	−2.77870	+	6.08450i	−0.347337	+	0.760562i
$65$	1.78565	+	2.06075i	0.221482	+	0.255604i
$66$		0			0
$67$	5.87551	−	5.69898i	0.717807	−	0.696242i
$67$	5.87551	−	5.69898i	0.717807	−	0.696242i
$68$	−4.21704			−0.511391
$69$		0			0
$70$	−0.608660	+	1.33278i	−0.0727488	+	0.159298i
$71$	−1.09047	+	7.58435i	−0.129414	+	0.900097i	0.816884	+	0.576802i	$0.195700\pi$
$71$	−1.09047	+	7.58435i	−0.129414	+	0.900097i	−0.946298	+	0.323295i	$0.895209\pi$
$72$		0			0
$73$	−5.05565	+	1.48447i	−0.591719	+	0.173744i	−0.563864	−	0.825868i	$-0.690686\pi$
$73$	−5.05565	+	1.48447i	−0.591719	+	0.173744i	−0.0278551	+	0.999612i	$0.508868\pi$
$74$	−0.791429	−	0.913358i	−0.0920018	−	0.106176i
$75$		0			0
$76$	6.01979	+	6.94720i	0.690517	+	0.796899i
$77$	2.39102	+	5.23561i	0.272483	+	0.596654i
$78$		0			0
$79$	−7.32594	−	4.70809i	−0.824232	−	0.529702i	0.0592081	−	0.998246i	$-0.481142\pi$
$79$	−7.32594	−	4.70809i	−0.824232	−	0.529702i	−0.883440	+	0.468544i	$0.844779\pi$
$80$	−5.92079	−	3.80506i	−0.661965	−	0.425419i
$81$		0			0
$82$	1.43027	−	1.65062i	0.157947	−	0.182280i
$83$	−15.3495	−	4.50703i	−1.68483	−	0.494710i	−0.707549	−	0.706664i	$-0.750199\pi$
$83$	−15.3495	−	4.50703i	−1.68483	−	0.494710i	−0.977280	+	0.211954i	$0.932017\pi$
$84$		0			0
$85$	0.592401	−	4.12024i	0.0642549	−	0.446902i
$86$	0.287201	−	0.331447i	0.0309696	−	0.0357409i
$87$		0			0
$88$	1.59534	−	0.468434i	0.170064	−	0.0499352i
$89$	0.292424	+	0.640320i	0.0309969	+	0.0678738i	0.924497	−	0.381189i	$-0.124485\pi$
$89$	0.292424	+	0.640320i	0.0309969	+	0.0678738i	−0.893500	+	0.449063i	$0.851758\pi$
$90$		0			0
$91$	0.652910	+	4.54109i	0.0684436	+	0.476036i
$92$	7.35338	+	4.72573i	0.766643	+	0.492692i
$93$		0			0
$94$	−1.39087	+	0.408396i	−0.143457	+	0.0421228i
$95$	−7.63338	+	4.90568i	−0.783169	+	0.503312i
$96$		0			0
$97$	1.26679			0.128623			0.0643113	−	0.997930i	$-0.479515\pi$
$97$	1.26679			0.128623			0.0643113	+	0.997930i	$0.479515\pi$
$98$	−0.681276	+	0.437829i	−0.0688193	+	0.0442274i
$99$		0			0
$100$	−1.67730	+	1.93571i	−0.167730	+	0.193571i
$101$	−8.31314	+	9.59388i	−0.827189	+	0.954627i	−0.999538	−	0.0304092i	$-0.990319\pi$
$101$	−8.31314	+	9.59388i	−0.827189	+	0.954627i	0.172349	+	0.985036i	$0.444864\pi$
$102$		0			0
$103$	−3.80839	+	2.44750i	−0.375252	+	0.241160i	−0.714649	−	0.699484i	$-0.753413\pi$
$103$	−3.80839	+	2.44750i	−0.375252	+	0.241160i	0.339397	+	0.940643i	$0.389777\pi$
$104$	1.32529			0.129956
$105$		0			0
$106$	−0.526638	+	0.338450i	−0.0511516	+	0.0328731i
$107$	−2.96797	+	0.871473i	−0.286924	+	0.0842485i	−0.422028	−	0.906583i	$-0.638681\pi$
$107$	−2.96797	+	0.871473i	−0.286924	+	0.0842485i	0.135104	+	0.990831i	$0.456863\pi$
$108$		0			0
$109$	12.6231	+	8.11236i	1.20907	+	0.777024i	0.980503	−	0.196504i	$-0.0629589\pi$
$109$	12.6231	+	8.11236i	1.20907	+	0.777024i	0.228569	+	0.973528i	$0.426595\pi$
$110$	0.115130	+	0.800745i	0.0109772	+	0.0763480i
$111$		0			0
$112$	−4.91917	−	10.7715i	−0.464818	−	1.01781i
$113$	−19.3534	+	5.68268i	−1.82062	+	0.534581i	−0.999353	−	0.0359674i	$-0.988549\pi$
$113$	−19.3534	+	5.68268i	−1.82062	+	0.534581i	−0.821264	+	0.570549i	$0.806731\pi$
$114$		0			0
$115$	−5.65025	+	6.52073i	−0.526888	+	0.608062i
$116$	2.20743	−	15.3530i	0.204954	−	1.42549i
$117$		0			0
$118$	2.68906	+	0.789580i	0.247548	+	0.0726867i
$119$	4.58639	−	5.29298i	0.420434	−	0.485207i
$120$		0			0
$121$	−6.58033	−	4.22892i	−0.598212	−	0.384447i
$122$	−1.66777	−	1.07181i	−0.150993	−	0.0970373i
$123$		0			0
$124$	−7.92202	−	17.3468i	−0.711419	−	1.55779i
$125$	−7.93899	−	9.16209i	−0.710085	−	0.819482i
$126$		0			0
$127$	−0.157828	−	0.182143i	−0.0140049	−	0.0161626i	0.748704	−	0.662905i	$-0.230676\pi$
$127$	−0.157828	−	0.182143i	−0.0140049	−	0.0161626i	−0.762709	+	0.646742i	$0.776131\pi$
$128$	−6.76172	+	1.98542i	−0.597657	+	0.175488i
$129$		0			0
$130$	−0.0917675	+	0.638257i	−0.00804854	+	0.0559789i
$131$	−1.43131	+	3.13414i	−0.125055	+	0.273831i	−0.961796	−	0.273767i	$-0.911730\pi$
$131$	−1.43131	+	3.13414i	−0.125055	+	0.273831i	0.836742	+	0.547598i	$0.184458\pi$
$132$		0			0
$133$	−15.2668			−1.32380
$134$	1.92840	+	0.167515i	0.166588	+	0.0144711i
$135$		0			0
$136$	−1.32489	−	1.52901i	−0.113609	−	0.131111i
$137$	8.91469	−	19.5204i	0.761633	−	1.66774i	0.0173777	−	0.999849i	$-0.494468\pi$
$137$	8.91469	−	19.5204i	0.761633	−	1.66774i	0.744255	−	0.667895i	$-0.232805\pi$
$138$		0			0
$139$	0.744984	+	0.218747i	0.0631887	+	0.0185539i	0.313174	−	0.949696i	$-0.398608\pi$
$139$	0.744984	+	0.218747i	0.0631887	+	0.0185539i	−0.249985	+	0.968250i	$0.580426\pi$
$140$	11.5573	−	3.39353i	0.976769	−	0.286805i
$141$		0			0
$142$	−1.52434	+	0.979632i	−0.127920	+	0.0822089i
$143$	1.65881	+	1.91437i	0.138717	+	0.160088i
$144$		0			0
$145$	14.6905	+	4.31352i	1.21998	+	0.358218i
$146$	−1.04823	−	0.673653i	−0.0867517	−	0.0557520i
$147$		0			0
$148$	−1.41395	+	9.83425i	−0.116226	+	0.808370i
$149$	5.87125	−	6.77578i	0.480991	−	0.555094i	−0.462445	−	0.886648i	$-0.653028\pi$
$149$	5.87125	−	6.77578i	0.480991	−	0.555094i	0.943436	+	0.331555i	$0.107573\pi$
$150$		0			0
$151$	−0.428448	−	2.97992i	−0.0348666	−	0.242502i	0.964934	−	0.262494i	$-0.0845451\pi$
$151$	−0.428448	−	2.97992i	−0.0348666	−	0.242502i	−0.999800	+	0.0199919i	$0.993636\pi$
$152$	−0.627634	+	4.36529i	−0.0509078	+	0.354072i
$153$		0			0
$154$	−0.565427	+	1.23811i	−0.0455634	+	0.0997699i
$155$	18.0615	−	5.30334i	1.45074	−	0.425974i
$156$		0			0
$157$	−6.05946	+	13.2684i	−0.483598	+	1.05893i	0.497861	+	0.867257i	$0.334119\pi$
$157$	−6.05946	+	13.2684i	−0.483598	+	1.05893i	−0.981459	+	0.191674i	$0.938608\pi$
$158$	−0.293075	−	2.03838i	−0.0233158	−	0.162165i
$159$		0			0
$160$	−0.746298	−	5.19062i	−0.0590001	−	0.410354i
$161$	−13.9289	+	4.08990i	−1.09775	+	0.322329i
$162$		0			0
$163$	16.0048			1.25359			0.626797	−	0.779182i	$-0.284365\pi$
$163$	16.0048			1.25359			0.626797	+	0.779182i	$0.284365\pi$
$164$	−17.9552			−1.40207
$165$		0			0
$166$	−1.57155	−	3.44121i	−0.121976	−	0.267090i
$167$	−4.29807	+	4.96024i	−0.332595	+	0.383835i	−0.897273	−	0.441476i	$-0.854455\pi$
$167$	−4.29807	+	4.96024i	−0.332595	+	0.383835i	0.564678	+	0.825311i	$0.309000\pi$
$168$		0			0
$169$	−4.56165	−	9.98861i	−0.350896	−	0.768355i
$170$	0.828104	−	0.532190i	0.0635126	−	0.0408171i
$171$		0			0
$172$	−3.60544			−0.274912
$173$	−10.4091	+	6.68954i	−0.791391	+	0.508596i	−0.872796	−	0.488085i	$-0.837696\pi$
$173$	−10.4091	+	6.68954i	−0.791391	+	0.508596i	0.0814049	+	0.996681i	$0.474059\pi$
$174$		0			0
$175$	−0.605379	−	4.21050i	−0.0457623	−	0.318284i
$176$	−5.50024	−	3.53479i	−0.414596	−	0.266445i
$177$		0			0
$178$	−0.0691521	+	0.151422i	−0.00518317	+	0.0113496i
$179$	−2.93161	−	6.41932i	−0.219119	−	0.479803i	0.767867	−	0.640609i	$-0.221318\pi$
$179$	−2.93161	−	6.41932i	−0.219119	−	0.479803i	−0.986986	+	0.160806i	$0.948591\pi$
$180$		0			0
$181$	6.31584	−	13.8298i	0.469453	−	1.02796i	−0.515778	−	0.856723i	$-0.672497\pi$
$181$	6.31584	−	13.8298i	0.469453	−	1.02796i	0.985230	−	0.171235i	$-0.0547758\pi$
$182$	−0.710468	+	0.819924i	−0.0526634	+	0.0607768i
$183$		0			0
$184$	0.596808	+	4.15089i	0.0439973	+	0.306008i
$185$	−9.40988	−	2.76299i	−0.691828	−	0.203139i
$186$		0			0
$187$	0.550322	−	3.82757i	0.0402435	−	0.279900i
$188$	10.0252	+	6.44280i	0.731162	+	0.469889i
$189$		0			0
$190$	−2.05885	−	0.604532i	−0.149365	−	0.0438574i
$191$	4.93548	+	10.8072i	0.357118	+	0.781980i	0.999873	+	0.0159086i	$0.00506407\pi$
$191$	4.93548	+	10.8072i	0.357118	+	0.781980i	−0.642755	+	0.766072i	$0.722209\pi$
$192$		0			0
$193$	−15.8871	+	10.2100i	−1.14358	+	0.734933i	−0.968350	−	0.249595i	$-0.919703\pi$
$193$	−15.8871	+	10.2100i	−1.14358	+	0.734933i	−0.175228	+	0.984528i	$0.556066\pi$
$194$	0.196175	+	0.226399i	0.0140846	+	0.0162545i
$195$		0			0
$196$	6.38792	+	1.87566i	0.456280	+	0.133976i
$197$	−3.75753	+	26.1342i	−0.267713	+	1.86199i	0.202297	+	0.979324i	$0.435159\pi$
$197$	−3.75753	+	26.1342i	−0.267713	+	1.86199i	−0.470010	+	0.882661i	$0.655750\pi$
$198$		0			0
$199$	8.09881	+	9.34653i	0.574109	+	0.662558i	0.966328	−	0.257315i	$-0.0828376\pi$
$199$	8.09881	+	9.34653i	0.574109	+	0.662558i	−0.392218	+	0.919872i	$0.628292\pi$
$200$	−1.22881			−0.0868903
$201$		0			0
$202$	−3.00199			−0.211219
$203$	16.8694	+	19.4683i	1.18400	+	1.36641i
$204$		0			0
$205$	2.52231	−	17.5431i	0.176166	−	1.22526i
$206$	−1.02719	−	0.301609i	−0.0715674	−	0.0210141i
$207$		0			0
$208$	−3.41275	−	3.93853i	−0.236632	−	0.273088i
$209$	−7.09118	+	4.55722i	−0.490507	+	0.315230i
$210$		0			0
$211$	−4.76325	−	10.4301i	−0.327916	−	0.718035i	0.671827	−	0.740708i	$-0.265510\pi$
$211$	−4.76325	−	10.4301i	−0.327916	−	0.718035i	−0.999743	+	0.0226727i	$0.992782\pi$
$212$	4.93797	+	1.44992i	0.339141	+	0.0995808i
$213$		0			0
$214$	−0.615370	−	0.395474i	−0.0420658	−	0.0270341i
$215$	0.506485	−	3.52268i	0.0345420	−	0.240245i
$216$		0			0
$217$	30.3886	+	8.92290i	2.06291	+	0.605726i
$218$	0.504988	+	3.51227i	0.0342021	+	0.237881i
$219$		0			0
$220$	4.35519	−	5.02616i	0.293627	−	0.338864i
$221$	1.28041	−	2.80372i	0.0861300	−	0.188598i
$222$		0			0
$223$	7.77300	+	17.0205i	0.520519	+	1.13978i	0.969243	+	0.246107i	$0.0791514\pi$
$223$	7.77300	+	17.0205i	0.520519	+	1.13978i	−0.448724	+	0.893670i	$0.648121\pi$
$224$	3.66523	−	8.02574i	0.244894	−	0.536242i
$225$		0			0
$226$	−4.01269	−	2.57880i	−0.266920	−	0.171539i
$227$	−0.433595	−	3.01572i	−0.0287787	−	0.200160i	0.970360	−	0.241666i	$-0.0776937\pi$
$227$	−0.433595	−	3.01572i	−0.0287787	−	0.200160i	−0.999138	+	0.0415054i	$0.986785\pi$
$228$		0			0
$229$	−1.20510	+	0.774471i	−0.0796353	+	0.0511785i	−0.579853	−	0.814721i	$-0.696890\pi$
$229$	−1.20510	+	0.774471i	−0.0796353	+	0.0511785i	0.500217	+	0.865900i	$0.333253\pi$
$230$	−2.04038			−0.134539
$231$		0			0
$232$	6.26019	−	4.02318i	0.411001	−	0.264135i
$233$	−1.00879	−	2.20895i	−0.0660882	−	0.144713i	0.873706	−	0.486455i	$-0.161710\pi$
$233$	−1.00879	−	2.20895i	−0.0660882	−	0.144713i	−0.939794	+	0.341742i	$0.888983\pi$
$234$		0			0
$235$	−7.70323	+	8.89000i	−0.502503	+	0.579920i
$236$	−9.57111	−	20.9578i	−0.623026	−	1.36424i
$237$		0			0
$238$	1.65621			0.107356
$239$	22.2984			1.44236			0.721181	−	0.692747i	$-0.243600\pi$
$239$	22.2984			1.44236			0.721181	+	0.692747i	$0.243600\pi$
$240$		0			0
$241$	−15.7065	+	4.61183i	−1.01174	+	0.297074i	−0.745266	−	0.666767i	$-0.767678\pi$
$241$	−15.7065	+	4.61183i	−1.01174	+	0.297074i	−0.266476	+	0.963841i	$0.585859\pi$
$242$	−0.263247	−	1.83092i	−0.0169222	−	0.117696i
$243$		0			0
$244$	2.31943	+	16.1320i	0.148486	+	1.03274i
$245$	−2.72997	+	5.97780i	−0.174411	+	0.381908i
$246$		0			0
$247$	−6.44666	+	1.89291i	−0.410191	+	0.120443i
$248$	3.80067	−	8.32231i	0.241343	−	0.528467i
$249$		0			0
$250$	0.407999	−	2.83770i	0.0258041	−	0.179472i
$251$	−0.885368	−	6.15787i	−0.0558839	−	0.388681i	−0.998498	−	0.0547958i	$-0.982549\pi$
$251$	−0.885368	−	6.15787i	−0.0558839	−	0.388681i	0.942614	−	0.333885i	$-0.108360\pi$
$252$		0			0
$253$	−5.24891	+	6.05756i	−0.329996	+	0.380836i
$254$	0.00811104	−	0.0564135i	0.000508932	−	0.00353970i
$255$		0			0
$256$	9.85227	+	6.33167i	0.615767	+	0.395729i
$257$	24.4129	+	7.16827i	1.52283	+	0.447144i	0.932848	−	0.360270i	$-0.117315\pi$
$257$	24.4129	+	7.16827i	1.52283	+	0.447144i	0.589985	+	0.807414i	$0.299134\pi$
$258$		0			0
$259$	−10.8056	−	12.4703i	−0.671426	−	0.774867i
$260$	4.45951	−	2.86595i	0.276567	−	0.177739i
$261$		0			0
$262$	−0.781785	+	0.229553i	−0.0482988	+	0.0141818i
$263$	23.6313	+	6.93878i	1.45717	+	0.427864i	0.911905	−	0.410400i	$-0.134611\pi$
$263$	23.6313	+	6.93878i	1.45717	+	0.427864i	0.545265	+	0.838264i	$0.316429\pi$
$264$		0			0
$265$	−2.11031	+	4.62094i	−0.129635	+	0.283862i
$266$	−2.36422	−	2.72846i	−0.144960	−	0.167293i
$267$		0			0
$268$	−9.34091	−	12.8829i	−0.570587	−	0.786950i
$269$	−6.18111			−0.376869			−0.188434	−	0.982086i	$-0.560341\pi$
$269$	−6.18111			−0.376869			−0.188434	+	0.982086i	$0.560341\pi$
$270$		0			0
$271$	−5.70261	+	12.4870i	−0.346409	+	0.758530i	0.653590	+	0.756849i	$0.273262\pi$
$271$	−5.70261	+	12.4870i	−0.346409	+	0.758530i	−0.999999	+	0.00168074i	$0.999465\pi$
$272$	−1.13220	+	7.87466i	−0.0686500	+	0.477471i
$273$		0			0
$274$	4.86921	−	1.42973i	0.294159	−	0.0863730i
$275$	−1.53805	−	1.77500i	−0.0927479	−	0.107037i
$276$		0			0
$277$	−6.40477	−	7.39150i	−0.384825	−	0.444112i	0.529978	−	0.848011i	$-0.322200\pi$
$277$	−6.40477	−	7.39150i	−0.384825	−	0.444112i	−0.914804	+	0.403899i	$0.867655\pi$
$278$	0.0762745	+	0.167018i	0.00457464	+	0.0100171i
$279$		0			0
$280$	4.86144	+	3.12426i	0.290527	+	0.186710i
$281$	−12.9563	−	8.32649i	−0.772906	−	0.496717i	0.0937661	−	0.995594i	$-0.470109\pi$
$281$	−12.9563	−	8.32649i	−0.772906	−	0.496717i	−0.866673	+	0.498877i	$0.833746\pi$
$282$		0			0
$283$	−9.67728	+	11.1682i	−0.575255	+	0.663879i	−0.966578	−	0.256374i	$-0.917472\pi$
$283$	−9.67728	+	11.1682i	−0.575255	+	0.663879i	0.391323	+	0.920253i	$0.372018\pi$
$284$	14.2928	+	4.19674i	0.848121	+	0.249031i
$285$		0			0
$286$	−0.0852492	+	0.592921i	−0.00504089	+	0.0350602i
$287$	19.5279	−	22.5363i	1.15269	−	1.33028i
$288$		0			0
$289$	11.7967	−	3.46382i	0.693922	−	0.203754i
$290$	1.50407	+	3.29346i	0.0883222	+	0.193399i
$291$		0			0
$292$	1.45780	+	10.1393i	0.0853115	+	0.593355i
$293$	−5.92535	−	3.80799i	−0.346163	−	0.222465i	0.355993	−	0.934489i	$-0.384143\pi$
$293$	−5.92535	−	3.80799i	−0.346163	−	0.222465i	−0.702156	+	0.712023i	$0.747779\pi$
$294$		0			0
$295$	21.8213	−	6.40730i	1.27048	−	0.373048i
$296$	−4.00992	+	2.57702i	−0.233072	+	0.149786i
$297$		0			0
$298$	2.12019			0.122819
$299$	−5.37463	+	3.45406i	−0.310823	+	0.199754i
$300$		0			0
$301$	3.92123	−	4.52534i	0.226016	−	0.260836i
$302$	0.466218	−	0.538044i	0.0268278	−	0.0309610i
$303$		0			0
$304$	14.5890	−	9.37580i	0.836739	−	0.537739i
$305$	−16.0875			−0.921169
$306$		0			0
$307$	6.10383	−	3.92269i	0.348364	−	0.223880i	−0.354743	−	0.934964i	$-0.615432\pi$
$307$	6.10383	−	3.92269i	0.348364	−	0.223880i	0.703107	+	0.711084i	$0.251795\pi$
$308$	10.7364	−	3.15248i	0.611761	−	0.179629i
$309$		0			0
$310$	3.74482	+	2.40665i	0.212692	+	0.136689i
$311$	0.237028	+	1.64857i	0.0134406	+	0.0934818i	0.995438	−	0.0954152i	$-0.0304179\pi$
$311$	0.237028	+	1.64857i	0.0134406	+	0.0934818i	−0.981997	+	0.188897i	$0.939509\pi$
$312$		0			0
$313$	−9.98524	−	21.8646i	−0.564399	−	1.23586i	−0.949726	−	0.313081i	$-0.898639\pi$
$313$	−9.98524	−	21.8646i	−0.564399	−	1.23586i	0.385327	−	0.922780i	$-0.374089\pi$
$314$	−3.30968	+	0.971810i	−0.186776	+	0.0548424i
$315$		0			0
$316$	−11.0866	+	12.7946i	−0.623671	+	0.719754i
$317$	2.61018	−	18.1542i	0.146602	−	1.01964i	−0.775127	−	0.631806i	$-0.782314\pi$
$317$	2.61018	−	18.1542i	0.146602	−	1.01964i	0.921729	−	0.387835i	$-0.126777\pi$
$318$		0			0
$319$	13.6470	+	4.00712i	0.764086	+	0.224356i
$320$	−8.40581	+	9.70082i	−0.469899	+	0.542292i
$321$		0			0
$322$	−2.88798	−	1.85599i	−0.160941	−	0.103431i
$323$	8.62857	+	5.54525i	0.480107	+	0.308546i
$324$		0			0
$325$	−0.777688	−	1.70290i	−0.0431383	−	0.0944598i
$326$	2.47852	+	2.86036i	0.137272	+	0.158421i
$327$		0			0
$328$	−5.64110	−	6.51017i	−0.311478	−	0.359464i
$329$	−18.9899	+	5.57594i	−1.04695	+	0.307411i
$330$		0			0
$331$	0.138411	−	0.962669i	0.00760775	−	0.0529131i	−0.985664	−	0.168721i	$-0.946036\pi$
$331$	0.138411	−	0.962669i	0.00760775	−	0.0529131i	0.993272	+	0.115807i	$0.0369456\pi$
$332$	−12.9196	+	28.2900i	−0.709055	+	1.55261i
$333$		0			0
$334$	−1.55209			−0.0849267
$335$	13.8994	−	7.31673i	0.759405	−	0.399756i
$336$		0			0
$337$	15.8021	+	18.2366i	0.860798	+	0.993413i	0.999995	+	0.00314875i	$0.00100228\pi$
$337$	15.8021	+	18.2366i	0.860798	+	0.993413i	−0.139197	+	0.990265i	$0.544452\pi$
$338$	1.07873	−	2.36210i	0.0586754	−	0.128481i
$339$		0			0
$340$	−7.76463	−	2.27990i	−0.421096	−	0.123645i
$341$	16.7786	−	4.92664i	0.908611	−	0.266792i
$342$		0			0
$343$	9.71150	−	6.24120i	0.524371	−	0.336993i
$344$	−1.13274	−	1.30725i	−0.0610734	−	0.0704824i
$345$		0			0
$346$	−2.80751	−	0.824360i	−0.150933	−	0.0443179i
$347$	14.3077	+	9.19501i	0.768078	+	0.493614i	0.865058	−	0.501672i	$-0.167282\pi$
$347$	14.3077	+	9.19501i	0.768078	+	0.493614i	−0.0969793	+	0.995286i	$0.530918\pi$
$348$		0			0
$349$	4.10754	−	28.5686i	0.219872	−	1.52924i	−0.518636	−	0.854995i	$-0.673560\pi$
$349$	4.10754	−	28.5686i	0.219872	−	1.52924i	0.738507	−	0.674245i	$-0.235531\pi$
$350$	0.658746	−	0.760234i	0.0352115	−	0.0406362i
$351$		0			0
$352$	−0.693288	−	4.82193i	−0.0369524	−	0.257010i
$353$	2.59765	−	18.0670i	0.138259	−	0.961611i	−0.796071	−	0.605203i	$-0.793092\pi$
$353$	2.59765	−	18.0670i	0.138259	−	0.961611i	0.934330	−	0.356408i	$-0.115999\pi$
$354$		0			0
$355$	−6.10823	+	13.3752i	−0.324191	+	0.709880i
$356$	1.31307	−	0.385551i	0.0695924	−	0.0204342i
$357$		0			0
$358$	0.693263	−	1.51803i	0.0366401	−	0.0802306i
$359$	−0.706929	−	4.91680i	−0.0373103	−	0.259499i	0.962625	−	0.270836i	$-0.0873002\pi$
$359$	−0.706929	−	4.91680i	−0.0373103	−	0.259499i	−0.999936	+	0.0113374i	$0.996391\pi$
$360$		0			0
$361$	−0.477922	−	3.32402i	−0.0251538	−	0.174948i
$362$	3.44971	−	1.01293i	0.181313	−	0.0532383i
$363$		0			0
$364$	8.91902			0.467483
$365$	−10.1113			−0.529250
$366$		0			0
$367$	3.53214	+	7.73431i	0.184376	+	0.403728i	0.979139	−	0.203193i	$-0.0651319\pi$
$367$	3.53214	+	7.73431i	0.184376	+	0.403728i	−0.794763	+	0.606921i	$0.792405\pi$
$368$	10.7988	−	12.4625i	0.562928	−	0.649654i
$369$		0			0
$370$	−0.963423	−	2.10960i	−0.0500860	−	0.109673i
$371$	−7.19032	+	4.62094i	−0.373303	+	0.239907i
$372$		0			0
$373$	13.9275			0.721141			0.360570	−	0.932732i	$-0.382582\pi$
$373$	13.9275			0.721141			0.360570	+	0.932732i	$0.382582\pi$
$374$	0.769283	−	0.494388i	0.0397787	−	0.0255642i
$375$		0			0
$376$	0.813655	+	5.65909i	0.0419610	+	0.291845i
$377$	9.53727	+	6.12923i	0.491194	+	0.315671i
$378$		0			0
$379$	0.396995	−	0.869298i	0.0203923	−	0.0446529i	−0.899162	−	0.437616i	$-0.855823\pi$
$379$	0.396995	−	0.869298i	0.0203923	−	0.0446529i	0.919554	+	0.392963i	$0.128550\pi$
$380$	7.32801	+	16.0461i	0.375919	+	0.823148i
$381$		0			0
$382$	−1.16714	+	2.55567i	−0.0597159	+	0.130759i
$383$	9.95541	−	11.4892i	0.508698	−	0.587069i	−0.442067	−	0.896982i	$-0.645755\pi$
$383$	9.95541	−	11.4892i	0.508698	−	0.587069i	0.950765	+	0.309913i	$0.100300\pi$
$384$		0			0
$385$	1.57190	+	10.9328i	0.0801113	+	0.557186i
$386$	−4.28501	−	1.25819i	−0.218101	−	0.0640403i
$387$		0			0
$388$	0.350483	−	2.43766i	0.0177931	−	0.123754i
$389$	−3.93265	−	2.52736i	−0.199393	−	0.128142i	0.437134	−	0.899396i	$-0.355993\pi$
$389$	−3.93265	−	2.52736i	−0.199393	−	0.128142i	−0.636527	+	0.771254i	$0.719630\pi$
$390$		0			0
$391$	9.35798	+	2.74775i	0.473253	+	0.138960i
$392$	1.32686	+	2.90541i	0.0670163	+	0.146745i
$393$		0			0
$394$	−5.25257	+	3.37562i	−0.264621	+	0.170061i
$395$	−10.9435	−	12.6295i	−0.550628	−	0.635459i
$396$		0			0
$397$	−6.71543	−	1.97183i	−0.337038	−	0.0989632i	0.108834	−	0.994060i	$-0.465288\pi$
$397$	−6.71543	−	1.97183i	−0.337038	−	0.0989632i	−0.445872	+	0.895097i	$0.647106\pi$
$398$	−0.416212	+	2.89482i	−0.0208628	+	0.145104i
$399$		0			0
$400$	3.16431	+	3.65180i	0.158215	+	0.182590i
$401$	−1.64631			−0.0822127			−0.0411063	−	0.999155i	$-0.513088\pi$
$401$	−1.64631			−0.0822127			−0.0411063	+	0.999155i	$0.513088\pi$
$402$		0			0
$403$	13.9385			0.694325
$404$	16.1614	+	18.6512i	0.804060	+	0.927934i
$405$		0			0
$406$	−0.866949	+	6.02977i	−0.0430260	+	0.299252i
$407$	−8.74149	−	2.56673i	−0.433300	−	0.127228i
$408$		0			0
$409$	6.03319	+	6.96267i	0.298322	+	0.344282i	0.885045	−	0.465506i	$-0.154128\pi$
$409$	6.03319	+	6.96267i	0.298322	+	0.344282i	−0.586723	+	0.809788i	$0.699582\pi$
$410$	3.52588	−	2.26595i	0.174131	−	0.111907i
$411$		0			0
$412$	3.65604	+	8.00560i	0.180120	+	0.394408i
$413$	36.7145	+	10.7803i	1.80660	+	0.530466i
$414$		0			0
$415$	−25.8257	−	16.5972i	−1.26773	−	0.814722i
$416$	0.552606	−	3.84346i	0.0270937	−	0.188441i
$417$		0			0
$418$	−1.91261	−	0.561592i	−0.0935487	−	0.0274684i
$419$	−1.69574	−	11.7941i	−0.0828422	−	0.576180i	−0.988390	−	0.151937i	$-0.951449\pi$
$419$	−1.69574	−	11.7941i	−0.0828422	−	0.576180i	0.905548	−	0.424244i	$-0.139460\pi$
$420$		0			0
$421$	−11.0413	+	12.7423i	−0.538119	+	0.621022i	−0.958073	−	0.286523i	$-0.907501\pi$
$421$	−11.0413	+	12.7423i	−0.538119	+	0.621022i	0.419955	+	0.907545i	$0.362046\pi$
$422$	1.12641	−	2.46649i	0.0548327	−	0.120067i
$423$		0			0
$424$	1.02568	+	2.24593i	0.0498115	+	0.109072i
$425$	−1.18720	+	2.59961i	−0.0575877	+	0.126099i
$426$		0			0
$427$	−22.7705	−	14.6337i	−1.10194	−	0.708176i
$428$	0.855817	+	5.95234i	0.0413675	+	0.287717i
$429$		0			0
$430$	0.708003	−	0.455006i	0.0341429	−	0.0219423i
$431$	−9.37815			−0.451729			−0.225865	−	0.974159i	$-0.572521\pi$
$431$	−9.37815			−0.451729			−0.225865	+	0.974159i	$0.572521\pi$
$432$		0			0
$433$	−16.9702	+	10.9061i	−0.815534	+	0.524112i	−0.880651	−	0.473766i	$-0.842894\pi$
$433$	−16.9702	+	10.9061i	−0.815534	+	0.524112i	0.0651170	+	0.997878i	$0.479258\pi$
$434$	3.11131	+	6.81282i	0.149348	+	0.327026i
$435$		0			0
$436$	19.1030	−	22.0460i	0.914867	−	1.05581i
$437$	−8.83176	−	19.3389i	−0.422480	−	0.925103i
$438$		0			0
$439$	−3.04620			−0.145387			−0.0726935	−	0.997354i	$-0.523159\pi$
$439$	−3.04620			−0.145387			−0.0726935	+	0.997354i	$0.523159\pi$
$440$	3.19068			0.152110
$441$		0			0
$442$	0.699363	−	0.205351i	0.0332653	−	0.00976757i
$443$	−5.23162	−	36.3867i	−0.248562	−	1.72878i	−0.606539	−	0.795054i	$-0.707443\pi$
$443$	−5.23162	−	36.3867i	−0.248562	−	1.72878i	0.357978	−	0.933730i	$-0.383466\pi$
$444$		0			0
$445$	0.192244	+	1.33709i	0.00911325	+	0.0633840i
$446$	−1.83815	+	4.02499i	−0.0870390	+	0.190589i
$447$		0			0
$448$	−20.7219	+	6.08450i	−0.979017	+	0.287465i
$449$	−4.13186	+	9.04750i	−0.194994	+	0.426978i	−0.981722	−	0.190323i	$-0.939047\pi$
$449$	−4.13186	+	9.04750i	−0.194994	+	0.426978i	0.786727	+	0.617301i	$0.211774\pi$
$450$		0			0
$451$	2.34315	−	16.2970i	0.110335	−	0.767394i
$452$	5.58059	+	38.8138i	0.262489	+	1.82565i
$453$		0			0
$454$	0.471819	−	0.544508i	0.0221436	−	0.0255550i
$455$	−1.25293	+	8.71429i	−0.0587381	+	0.408532i
$456$		0			0
$457$	0.0684070	+	0.0439625i	0.00319994	+	0.00205648i	0.542240	−	0.840224i	$-0.317576\pi$
$457$	0.0684070	+	0.0439625i	0.00319994	+	0.00205648i	−0.539040	+	0.842280i	$0.681213\pi$
$458$	−0.325035	−	0.0954390i	−0.0151879	−	0.00445957i
$459$		0			0
$460$	10.9845	+	12.6768i	0.512156	+	0.591059i
$461$	8.13928	−	5.23080i	0.379084	−	0.243623i	−0.337197	−	0.941434i	$-0.609479\pi$
$461$	8.13928	−	5.23080i	0.379084	−	0.243623i	0.716282	+	0.697811i	$0.245843\pi$
$462$		0			0
$463$	−6.50191	+	1.90913i	−0.302169	+	0.0887250i	−0.429303	−	0.903161i	$-0.641241\pi$
$463$	−6.50191	+	1.90913i	−0.302169	+	0.0887250i	0.127133	+	0.991886i	$0.459422\pi$
$464$	−28.0767	−	8.24405i	−1.30343	−	0.382721i
$465$		0			0
$466$	0.238558	−	0.522369i	0.0110510	−	0.0241983i
$467$	−3.18015	−	3.67009i	−0.147160	−	0.169831i	0.677384	−	0.735630i	$-0.263114\pi$
$467$	−3.18015	−	3.67009i	−0.147160	−	0.169831i	−0.824544	+	0.565798i	$0.808568\pi$
$468$		0			0
$469$	26.3290	+	2.28712i	1.21576	+	0.105610i
$470$	−2.78174			−0.128312
$471$		0			0
$472$	4.59184	−	10.0547i	0.211356	−	0.462806i
$473$	0.470509	−	3.27246i	0.0216340	−	0.150468i
$474$		0			0
$475$	5.97735	−	1.75511i	0.274260	−	0.0805299i
$476$	−8.91630	−	10.2900i	−0.408678	−	0.471640i
$477$		0			0
$478$	3.45314	+	3.98514i	0.157943	+	0.182276i
$479$	11.4608	+	25.0957i	0.523659	+	1.14665i	0.968035	+	0.250813i	$0.0806980\pi$
$479$	11.4608	+	25.0957i	0.523659	+	1.14665i	−0.444376	+	0.895840i	$0.646575\pi$
$480$		0			0
$481$	−6.10903	−	3.92603i	−0.278548	−	0.179012i
$482$	−3.25654	−	2.09285i	−0.148331	−	0.0953267i
$483$		0			0
$484$	−9.95826	+	11.4924i	−0.452648	+	0.522384i
$485$	2.33247	+	0.684876i	0.105912	+	0.0310986i
$486$		0			0
$487$	4.90188	−	34.0933i	0.222125	−	1.54492i	−0.507852	−	0.861444i	$-0.669560\pi$
$487$	4.90188	−	34.0933i	0.222125	−	1.54492i	0.729978	−	0.683471i	$-0.239530\pi$
$488$	−5.12040	+	5.90926i	−0.231790	+	0.267500i
$489$		0			0
$490$	−1.49111	+	0.437829i	−0.0673615	+	0.0197791i
$491$	2.01760	+	4.41792i	0.0910529	+	0.199378i	0.949679	−	0.313224i	$-0.101409\pi$
$491$	2.01760	+	4.41792i	0.0910529	+	0.199378i	−0.858626	+	0.512602i	$0.828682\pi$
$492$		0			0
$493$	−2.46301	−	17.1306i	−0.110928	−	0.771524i
$494$	−1.33663	−	0.859002i	−0.0601380	−	0.0386483i
$495$		0			0
$496$	−34.5194	+	10.1358i	−1.54997	+	0.455111i
$497$	−20.8122	+	13.3752i	−0.933553	+	0.599958i
$498$		0			0
$499$	4.61007			0.206375			0.103188	−	0.994662i	$-0.467096\pi$
$499$	4.61007			0.206375			0.103188	+	0.994662i	$0.467096\pi$
$500$	−19.8270	+	12.7420i	−0.886691	+	0.569841i
$501$		0			0
$502$	0.963418	−	1.11184i	0.0429995	−	0.0496240i
$503$	−10.4074	+	12.0108i	−0.464044	+	0.535535i	−0.938745	−	0.344612i	$-0.888011\pi$
$503$	−10.4074	+	12.0108i	−0.464044	+	0.535535i	0.474702	+	0.880147i	$0.342556\pi$
$504$		0			0
$505$	−20.4935	+	13.1703i	−0.911947	+	0.586072i
$506$	−1.89545			−0.0842630
$507$		0			0
$508$	−0.394162	+	0.253312i	−0.0174881	+	0.0112389i
$509$	−31.7841	+	9.33267i	−1.40881	+	0.413663i	−0.895699	−	0.444661i	$-0.853324\pi$
$509$	−31.7841	+	9.33267i	−1.40881	+	0.413663i	−0.513108	+	0.858324i	$0.671506\pi$
$510$		0			0
$511$	−14.3117	−	9.19757i	−0.633112	−	0.406876i
$512$	2.39998	+	16.6922i	0.106065	+	0.737699i
$513$		0			0
$514$	2.49949	+	5.47312i	0.110248	+	0.241409i
$515$	−8.33543	+	2.44750i	−0.367303	+	0.107850i
$516$		0			0
$517$	−7.15607	+	8.25854i	−0.314723	+	0.363210i
$518$	0.555318	−	3.86232i	0.0243993	−	0.169701i
$519$		0			0
$520$	2.44020	+	0.716508i	0.107010	+	0.0314210i
$521$	1.00230	−	1.15671i	0.0439115	−	0.0506765i	−0.733369	−	0.679831i	$-0.762053\pi$
$521$	1.00230	−	1.15671i	0.0439115	−	0.0506765i	0.777280	+	0.629154i	$0.216599\pi$
$522$		0			0
$523$	22.4182	+	14.4073i	0.980281	+	0.629988i	0.929539	−	0.368723i	$-0.120205\pi$
$523$	22.4182	+	14.4073i	0.980281	+	0.629988i	0.0507420	+	0.998712i	$0.483841\pi$
$524$	5.63499	+	3.62139i	0.246166	+	0.158201i
$525$		0			0
$526$	2.41947	+	5.29791i	0.105494	+	0.231000i
$527$	−13.9342	−	16.0810i	−0.606985	−	0.700497i
$528$		0			0
$529$	1.82318	+	2.10407i	0.0792689	+	0.0914812i
$530$	−1.15265	+	0.338450i	−0.0500681	+	0.0147013i
$531$		0			0
$532$	−4.22387	+	29.3777i	−0.183128	+	1.27368i
$533$	5.45172	−	11.9376i	0.236140	−	0.517075i
$534$		0			0
$535$	−5.93593			−0.256633
$536$	1.73638	−	7.43432i	0.0750002	−	0.321114i
$537$		0			0
$538$	−0.957211	−	1.10468i	−0.0412683	−	0.0476262i
$539$	−2.53606	+	5.55319i	−0.109236	+	0.239193i
$540$		0			0
$541$	0.788773	+	0.231605i	0.0339120	+	0.00995746i	0.298645	−	0.954364i	$-0.403465\pi$
$541$	0.788773	+	0.231605i	0.0339120	+	0.00995746i	−0.264733	+	0.964322i	$0.585284\pi$
$542$	−3.11477	+	0.914579i	−0.133791	+	0.0392845i
$543$		0			0
$544$	−4.98667	+	3.20474i	−0.213802	+	0.137402i
$545$	18.8564	+	21.7615i	0.807721	+	0.932159i
$546$		0			0
$547$	32.8253	+	9.63839i	1.40351	+	0.412108i	0.893888	−	0.448290i	$-0.147967\pi$
$547$	32.8253	+	9.63839i	1.40351	+	0.412108i	0.509622	+	0.860398i	$0.329785\pi$
$548$	−35.0966	−	22.5552i	−1.49925	−	0.963510i
$549$		0			0
$550$	0.0790431	−	0.549757i	0.00337041	−	0.0234417i
$551$	−24.7053	+	28.5114i	−1.05248	+	1.21463i
$552$		0			0
$553$	−4.00143	−	27.8305i	−0.170158	−	1.18348i
$554$	0.329153	−	2.28931i	0.0139844	−	0.0972633i
$555$		0			0
$556$	0.627048	−	1.37304i	0.0265928	−	0.0582300i
$557$	4.15428	−	1.21981i	0.176022	−	0.0516848i	−0.192534	−	0.981290i	$-0.561670\pi$
$557$	4.15428	−	1.21981i	0.176022	−	0.0516848i	0.368556	+	0.929606i	$0.379852\pi$
$558$		0			0
$559$	1.09471	−	2.39709i	0.0463015	−	0.101386i
$560$	−3.23394	−	22.4925i	−0.136659	−	0.950483i
$561$		0			0
$562$	−0.518317	−	3.60498i	−0.0218639	−	0.152067i
$563$	−5.39088	+	1.58291i	−0.227199	+	0.0667116i	−0.393350	−	0.919389i	$-0.628684\pi$
$563$	−5.39088	+	1.58291i	−0.227199	+	0.0667116i	0.166152	+	0.986100i	$0.446866\pi$
$564$		0			0
$565$	−38.7068			−1.62841
$566$	−3.49460			−0.146889
$567$		0			0
$568$	2.96881	+	6.50078i	0.124568	+	0.272767i
$569$	29.1536	−	33.6451i	1.22218	−	1.41048i	0.339436	−	0.940629i	$-0.389764\pi$
$569$	29.1536	−	33.6451i	1.22218	−	1.41048i	0.882748	−	0.469847i	$-0.155691\pi$
$570$		0			0
$571$	−14.8924	−	32.6097i	−0.623226	−	1.36468i	−0.913149	−	0.407625i	$-0.866357\pi$
$571$	−14.8924	−	32.6097i	−0.623226	−	1.36468i	0.289923	−	0.957050i	$-0.406370\pi$
$572$	4.14275	−	2.66238i	0.173217	−	0.111320i
$573$		0			0
$574$	7.05177			0.294335
$575$	4.98336	−	3.20261i	0.207820	−	0.133558i
$576$		0			0
$577$	−2.61567	−	18.1924i	−0.108892	−	0.757359i	−0.968967	−	0.247191i	$-0.920492\pi$
$577$	−2.61567	−	18.1924i	−0.108892	−	0.757359i	0.860075	−	0.510168i	$-0.170417\pi$
$578$	2.44589	+	1.57188i	0.101736	+	0.0653816i
$579$		0			0
$580$	12.3649	−	27.0753i	0.513424	−	1.12424i
$581$	−21.4567	−	46.9837i	−0.890176	−	1.94921i
$582$		0			0
$583$	−1.96042	+	4.29271i	−0.0811921	+	0.177786i
$584$	−3.21827	+	3.71408i	−0.133173	+	0.153690i
$585$		0			0
$586$	−0.237044	−	1.64868i	−0.00979221	−	0.0681063i
$587$	44.5520	+	13.0816i	1.83886	+	0.539937i	0.999990	−	0.00440002i	$-0.00140057\pi$
$587$	44.5520	+	13.0816i	1.83886	+	0.539937i	0.838867	+	0.544337i	$0.183219\pi$
$588$		0			0
$589$	−6.60099	+	45.9109i	−0.271989	+	1.89173i
$590$	4.52436	+	2.90763i	0.186265	+	0.119705i
$591$		0			0
$592$	17.9843	+	5.28067i	0.739150	+	0.217034i
$593$	−6.57249	−	14.3918i	−0.269900	−	0.590998i	0.725347	−	0.688384i	$-0.241679\pi$
$593$	−6.57249	−	14.3918i	−0.269900	−	0.590998i	−0.995247	+	0.0973852i	$0.968952\pi$
$594$		0			0
$595$	11.3063	−	7.26613i	0.463514	−	0.297882i
$596$	−11.4142	−	13.1726i	−0.467542	−	0.539573i
$597$		0			0
$598$	−1.44962	−	0.425648i	−0.0592796	−	0.0174060i
$599$	2.12770	−	14.7984i	0.0869353	−	0.604648i	−0.899054	−	0.437838i	$-0.855744\pi$
$599$	2.12770	−	14.7984i	0.0869353	−	0.604648i	0.985989	−	0.166810i	$-0.0533466\pi$
$600$		0			0
$601$	−10.4145	−	12.0190i	−0.424818	−	0.490266i	0.502481	−	0.864589i	$-0.332421\pi$
$601$	−10.4145	−	12.0190i	−0.424818	−	0.490266i	−0.927299	+	0.374322i	$0.877875\pi$
$602$	1.41601			0.0577121
$603$		0			0
$604$	−5.85277			−0.238146
$605$	−9.82973	−	11.3441i	−0.399635	−	0.461204i
$606$		0			0
$607$	−5.52844	+	38.4511i	−0.224392	+	1.56068i	0.496748	+	0.867895i	$0.334527\pi$
$607$	−5.52844	+	38.4511i	−0.224392	+	1.56068i	−0.721141	+	0.692789i	$0.756382\pi$
$608$	12.3980	+	3.64037i	0.502804	+	0.147637i
$609$		0			0
$610$	−2.49133	−	2.87514i	−0.100871	−	0.116411i
$611$	−7.32746	+	4.70908i	−0.296437	+	0.190509i
$612$		0			0
$613$	10.0620	+	22.0328i	0.406402	+	0.889896i	0.996581	+	0.0826235i	$0.0263299\pi$
$613$	10.0620	+	22.0328i	0.406402	+	0.889896i	−0.590179	+	0.807272i	$0.700943\pi$
$614$	1.64630	+	0.483398i	0.0664394	+	0.0195084i
$615$		0			0
$616$	4.51613	+	2.90234i	0.181960	+	0.116939i
$617$	−0.261885	+	1.82145i	−0.0105431	+	0.0733290i	−0.994414	−	0.105553i	$-0.966339\pi$
$617$	−0.261885	+	1.82145i	−0.0105431	+	0.0733290i	0.983871	+	0.178882i	$0.0572479\pi$
$618$		0			0
$619$	−27.0222	−	7.93444i	−1.08611	−	0.318912i	−0.310792	−	0.950478i	$-0.600594\pi$
$619$	−27.0222	−	7.93444i	−1.08611	−	0.318912i	−0.775322	+	0.631566i	$0.782413\pi$
$620$	−5.20806	−	36.2229i	−0.209161	−	1.45474i
$621$		0			0
$622$	−0.257924	+	0.297660i	−0.0103418	+	0.0119351i
$623$	−0.944152	+	2.06740i	−0.0378267	+	0.0828288i
$624$		0			0
$625$	−6.92777	−	15.1697i	−0.277111	−	0.606788i
$626$	2.36130	−	5.17052i	0.0943764	−	0.206656i
$627$		0			0
$628$	23.8557	+	15.3311i	0.951947	+	0.611779i
$629$	1.57766	+	10.9729i	0.0629056	+	0.437518i
$630$		0			0
$631$	2.18642	−	1.40513i	0.0870400	−	0.0559372i	−0.496397	−	0.868096i	$-0.665344\pi$
$631$	2.18642	−	1.40513i	0.0870400	−	0.0559372i	0.583437	+	0.812158i	$0.301708\pi$
$632$	−8.12221			−0.323084
$633$		0			0
$634$	3.64871	−	2.34488i	0.144909	−	0.0931272i
$635$	−0.192127	−	0.420699i	−0.00762432	−	0.0166949i
$636$		0			0
$637$	−3.18660	+	3.67753i	−0.126258	+	0.145709i
$638$	1.39724	+	3.05952i	0.0553172	+	0.121128i
$639$		0			0
$640$	−13.5234			−0.534561
$641$	−21.7800			−0.860257			−0.430129	−	0.902768i	$-0.641532\pi$
$641$	−21.7800			−0.860257			−0.430129	+	0.902768i	$0.641532\pi$
$642$		0			0
$643$	20.5691	−	6.03963i	0.811165	−	0.238180i	0.150258	−	0.988647i	$-0.451990\pi$
$643$	20.5691	−	6.03963i	0.811165	−	0.238180i	0.660908	+	0.750467i	$0.270171\pi$
$644$	4.01642	+	27.9348i	0.158269	+	1.10079i
$645$		0			0
$646$	0.345187	+	2.40083i	0.0135812	+	0.0944594i
$647$	7.93719	−	17.3800i	0.312043	−	0.683279i	−0.687016	−	0.726642i	$-0.741080\pi$
$647$	7.93719	−	17.3800i	0.312043	−	0.683279i	0.999059	+	0.0433627i	$0.0138071\pi$
$648$		0			0
$649$	20.2713	−	5.95219i	0.795718	−	0.233644i
$650$	0.183907	−	0.402699i	0.00721341	−	0.0157952i
$651$		0			0
$652$	4.42807	−	30.7979i	0.173417	−	1.20614i
$653$	−1.18630	−	8.25087i	−0.0464234	−	0.322882i	−0.999779	−	0.0210316i	$-0.993305\pi$
$653$	−1.18630	−	8.25087i	−0.0464234	−	0.322882i	0.953355	−	0.301850i	$-0.0976042\pi$
$654$		0			0
$655$	−4.32986	+	4.99692i	−0.169182	+	0.195246i
$656$	−4.82068	+	33.5286i	−0.188216	+	1.30907i
$657$		0			0
$658$	−3.93731	−	2.53036i	−0.153493	−	0.0986436i
$659$	3.12634	+	0.917978i	0.121785	+	0.0357593i	0.342057	−	0.939679i	$-0.388876\pi$
$659$	3.12634	+	0.917978i	0.121785	+	0.0357593i	−0.220272	+	0.975438i	$0.570695\pi$
$660$		0			0
$661$	−6.40434	−	7.39100i	−0.249100	−	0.287477i	0.617405	−	0.786646i	$-0.288184\pi$
$661$	−6.40434	−	7.39100i	−0.249100	−	0.287477i	−0.866505	+	0.499169i	$0.833639\pi$
$662$	0.193481	−	0.124343i	0.00751987	−	0.00483273i
$663$		0			0
$664$	−14.3164	+	4.20366i	−0.555583	+	0.163134i
$665$	−28.1100	−	8.25384i	−1.09006	−	0.320070i
$666$		0			0
$667$	−14.9022	+	32.6313i	−0.577017	+	1.26349i
$668$	8.35579	+	9.64310i	0.323295	+	0.373103i
$669$		0			0
$670$	3.46011	+	1.35101i	0.133676	+	0.0521941i
$671$	−14.9448			−0.576938
$672$		0			0
$673$	7.62659	−	16.6999i	0.293983	−	0.643734i	−0.703791	−	0.710407i	$-0.748511\pi$
$673$	7.62659	−	16.6999i	0.293983	−	0.643734i	0.997775	+	0.0666727i	$0.0212383\pi$
$674$	−0.812100	+	5.64828i	−0.0312809	+	0.217564i
$675$		0			0
$676$	−20.4831	+	6.01437i	−0.787810	+	0.231322i
$677$	−2.68545	−	3.09918i	−0.103210	−	0.119111i	0.701794	−	0.712380i	$-0.252383\pi$
$677$	−2.68545	−	3.09918i	−0.103210	−	0.119111i	−0.805004	+	0.593269i	$0.797837\pi$
$678$		0			0
$679$	2.67843	+	3.09108i	0.102789	+	0.118625i
$680$	−1.61282	−	3.53158i	−0.0618488	−	0.135430i
$681$		0			0
$682$	3.47883	+	2.23571i	0.133211	+	0.0856096i
$683$	12.3662	+	7.94729i	0.473181	+	0.304095i	0.755410	−	0.655252i	$-0.227438\pi$
$683$	12.3662	+	7.94729i	0.473181	+	0.304095i	−0.282230	+	0.959347i	$0.591074\pi$
$684$		0			0
$685$	26.9677	−	31.1224i	1.03038	−	1.18913i
$686$	2.61935	+	0.769110i	0.100007	+	0.0293648i
$687$		0			0
$688$	−0.968001	+	6.73259i	−0.0369047	+	0.256678i
$689$	−2.46329	+	2.84279i	−0.0938441	+	0.108302i
$690$		0			0
$691$	6.25576	−	1.83686i	0.237980	−	0.0698773i	−0.160568	−	0.987025i	$-0.551332\pi$
$691$	6.25576	−	1.83686i	0.237980	−	0.0698773i	0.398548	+	0.917148i	$0.369514\pi$
$692$	9.99271	+	21.8810i	0.379866	+	0.831790i
$693$		0			0
$694$	0.572382	+	3.98100i	0.0217273	+	0.151117i
$695$	1.25344	+	0.805537i	0.0475457	+	0.0305558i
$696$		0			0
$697$	−19.2226	+	5.64427i	−0.728108	+	0.213792i
$698$	5.74184	−	3.69006i	0.217332	−	0.139671i
$699$		0			0
$700$	−8.26972			−0.312566
$701$	34.4490	−	22.1390i	1.30112	−	0.836180i	0.307788	−	0.951455i	$-0.400411\pi$
$701$	34.4490	−	22.1390i	1.30112	−	0.836180i	0.993334	+	0.115275i	$0.0367749\pi$
$702$		0			0
$703$	15.8248	−	18.2628i	0.596843	−	0.688794i
$704$	−7.80874	+	9.01177i	−0.294303	+	0.339644i
$705$		0			0
$706$	3.63119	−	2.33363i	0.136662	−	0.0878271i
$707$	−40.9869			−1.54147
$708$		0			0
$709$	−24.3898	+	15.6744i	−0.915979	+	0.588664i	−0.911488	−	0.411326i	$-0.865066\pi$
$709$	−24.3898	+	15.6744i	−0.915979	+	0.588664i	−0.00449103	+	0.999990i	$0.501430\pi$
$710$	−3.33632	+	0.979632i	−0.125210	+	0.0367649i
$711$		0			0
$712$	0.552326	+	0.354959i	0.0206993	+	0.0133026i
$713$	6.27679	+	43.6560i	0.235067	+	1.63493i
$714$		0			0
$715$	2.01930	+	4.42166i	0.0755177	+	0.165361i
$716$	−13.1637	+	3.86522i	−0.491952	+	0.144450i
$717$		0			0
$718$	0.769249	−	0.887761i	0.0287081	−	0.0331309i
$719$	−3.27833	+	22.8013i	−0.122261	+	0.850344i	0.832724	+	0.553689i	$0.186780\pi$
$719$	−3.27833	+	22.8013i	−0.122261	+	0.850344i	−0.954985	+	0.296655i	$0.904129\pi$
$720$		0			0
$721$	−14.0244	−	4.11794i	−0.522297	−	0.153360i
$722$	0.520053	−	0.600174i	0.0193544	−	0.0223361i
$723$		0			0
$724$	−24.8651	−	15.9798i	−0.924102	−	0.593885i
$725$	−8.84296	−	5.68303i	−0.328419	−	0.211062i
$726$		0			0
$727$	7.34048	+	16.0734i	0.272244	+	0.596130i	0.995533	−	0.0944149i	$-0.0300980\pi$
$727$	7.34048	+	16.0734i	0.272244	+	0.596130i	−0.723289	+	0.690545i	$0.757371\pi$
$728$	2.80214	+	3.23384i	0.103854	+	0.119854i
$729$		0			0
$730$	−1.56584	−	1.80708i	−0.0579545	−	0.0668830i
$731$	−3.85993	+	1.13338i	−0.142765	+	0.0419195i
$732$		0			0
$733$	3.47351	−	24.1588i	0.128297	−	0.892325i	−0.819415	−	0.573200i	$-0.805702\pi$
$733$	3.47351	−	24.1588i	0.128297	−	0.892325i	0.947712	−	0.319125i	$-0.103389\pi$
$734$	−0.835277	+	1.82900i	−0.0308306	+	0.0675096i
$735$		0			0
$736$	12.2868			0.452896
$737$	12.9121	−	6.79702i	0.475624	−	0.250372i
$738$		0			0
$739$	−9.38260	−	10.8281i	−0.345145	−	0.398318i	0.556463	−	0.830872i	$-0.312158\pi$
$739$	−9.38260	−	10.8281i	−0.345145	−	0.398318i	−0.901608	+	0.432554i	$0.857612\pi$
$740$	−7.92024	+	17.3429i	−0.291154	+	0.637538i
$741$		0			0
$742$	−1.93935	−	0.569444i	−0.0711957	−	0.0209049i
$743$	−38.0800	+	11.1813i	−1.39702	+	0.410202i	−0.891659	−	0.452707i	$-0.850458\pi$
$743$	−38.0800	+	11.1813i	−1.39702	+	0.410202i	−0.505360	+	0.862909i	$0.668640\pi$
$744$		0			0
$745$	14.4737	−	9.30169i	0.530276	−	0.340788i
$746$	2.15683	+	2.48911i	0.0789671	+	0.0911329i
$747$		0			0
$748$	−7.21310	−	2.11796i	−0.263737	−	0.0774402i
$749$	−8.40181	−	5.39951i	−0.306995	−	0.197294i
$750$		0			0
$751$	−6.32058	+	43.9606i	−0.230641	+	1.60415i	0.464701	+	0.885468i	$0.346162\pi$
$751$	−6.32058	+	43.9606i	−0.230641	+	1.60415i	−0.695342	+	0.718679i	$0.744747\pi$
$752$	14.7225	−	16.9907i	0.536875	−	0.619587i
$753$		0			0
$754$	0.381540	+	2.65367i	0.0138949	+	0.0966408i
$755$	0.822185	−	5.71842i	0.0299224	−	0.208115i
$756$		0			0
$757$	16.5979	−	36.3444i	0.603262	−	1.32096i	−0.323826	−	0.946117i	$-0.604969\pi$
$757$	16.5979	−	36.3444i	0.603262	−	1.32096i	0.927088	−	0.374843i	$-0.122303\pi$
$758$	0.216839	−	0.0636697i	0.00787595	−	0.00231259i
$759$		0			0
$760$	−3.51569	+	7.69828i	−0.127527	+	0.279246i
$761$	3.05056	+	21.2171i	0.110583	+	0.769120i	0.967355	+	0.253425i	$0.0815571\pi$
$761$	3.05056	+	21.2171i	0.110583	+	0.769120i	−0.856772	+	0.515695i	$0.827534\pi$
$762$		0			0
$763$	6.89473	+	47.9539i	0.249606	+	1.73605i
$764$	22.1617	−	6.50725i	0.801781	−	0.235424i
$765$		0			0
$766$	3.59503			0.129894
$767$	16.8400			0.608056
$768$		0			0
$769$	6.09871	+	13.3543i	0.219925	+	0.481569i	0.987147	−	0.159812i	$-0.0510889\pi$
$769$	6.09871	+	13.3543i	0.219925	+	0.481569i	−0.767222	+	0.641381i	$0.778362\pi$
$770$	−1.71047	+	1.97399i	−0.0616410	+	0.0711375i
$771$		0			0
$772$	15.2515	+	33.3962i	0.548915	+	1.20196i
$773$	20.7339	−	13.3249i	0.745747	−	0.479262i	−0.111760	−	0.993735i	$-0.535649\pi$
$773$	20.7339	−	13.3249i	0.745747	−	0.479262i	0.857507	+	0.514473i	$0.172012\pi$
$774$		0			0
$775$	−12.9238			−0.464235
$776$	0.993958	−	0.638778i	0.0356810	−	0.0229308i
$777$		0			0
$778$	−0.157326	−	1.09423i	−0.00564041	−	0.0392299i
$779$	36.7386	+	23.6104i	1.31630	+	0.845932i
$780$		0			0
$781$	−5.67436	+	12.4251i	−0.203045	+	0.444606i
$782$	0.958109	+	2.09797i	0.0342619	+	0.0750231i
$783$		0			0
$784$	5.21756	−	11.4249i	0.186341	−	0.408031i
$785$	−18.3304	+	21.1544i	−0.654241	+	0.755035i
$786$		0			0
$787$	2.40269	+	16.7111i	0.0856465	+	0.595685i	0.986771	+	0.162123i	$0.0518342\pi$
$787$	2.40269	+	16.7111i	0.0856465	+	0.595685i	−0.901124	+	0.433561i	$0.857257\pi$
$788$	49.2502	+	14.4612i	1.75447	+	0.515158i
$789$		0			0
$790$	0.562407	−	3.91163i	0.0200095	−	0.139169i
$791$	−54.7862	−	35.2090i	−1.94797	−	1.25189i
$792$		0			0
$793$	−11.4297	−	3.35606i	−0.405880	−	0.119177i
$794$	−0.687554	−	1.50553i	−0.0244004	−	0.0534293i
$795$		0			0
$796$	20.2261	−	12.9985i	0.716896	−	0.460721i
$797$	14.8480	+	17.1355i	0.525942	+	0.606969i	0.955108	−	0.296256i	$-0.0957383\pi$
$797$	14.8480	+	17.1355i	0.525942	+	0.606969i	−0.429167	+	0.903225i	$0.641193\pi$
$798$		0			0
$799$	12.7581	+	3.74613i	0.451351	+	0.132529i
$800$	−0.512376	+	3.56365i	−0.0181152	+	0.125994i
$801$		0			0
$802$	−0.254948	−	0.294226i	−0.00900254	−	0.0103895i
$803$	−9.39309			−0.331475
$804$		0			0
$805$	−27.8578			−0.981859
$806$	2.15852	+	2.49107i	0.0760307	+	0.0877441i
$807$		0			0
$808$	−1.68502	+	11.7196i	−0.0592787	+	0.412292i
$809$	30.7049	+	9.01579i	1.07953	+	0.316978i	0.772690	−	0.634783i	$-0.218911\pi$
$809$	30.7049	+	9.01579i	1.07953	+	0.316978i	0.306838	+	0.951762i	$0.400729\pi$
$810$		0			0
$811$	−10.4919	−	12.1083i	−0.368421	−	0.425180i	0.541023	−	0.841008i	$-0.318037\pi$
$811$	−10.4919	−	12.1083i	−0.368421	−	0.425180i	−0.909443	+	0.415828i	$0.863492\pi$
$812$	42.1300	−	27.0753i	1.47847	−	0.950158i
$813$		0			0
$814$	−0.894990	−	1.95976i	−0.0313694	−	0.0686894i
$815$	29.4689	+	8.65286i	1.03225	+	0.303096i
$816$		0			0
$817$	7.37717	+	4.74102i	0.258094	+	0.165867i
$818$	−0.310056	+	2.15649i	−0.0108409	+	0.0753999i
$819$		0			0
$820$	−33.0601	−	9.70732i	−1.15451	−	0.338994i
$821$	−5.47646	−	38.0896i	−0.191130	−	1.32934i	−0.829024	−	0.559213i	$-0.811103\pi$
$821$	−5.47646	−	38.0896i	−0.191130	−	1.32934i	0.637894	−	0.770124i	$-0.279806\pi$
$822$		0			0
$823$	28.7034	−	33.1255i	1.00054	−	1.15468i	0.0125867	−	0.999921i	$-0.495993\pi$
$823$	28.7034	−	33.1255i	1.00054	−	1.15468i	0.987952	−	0.154762i	$-0.0494611\pi$
$824$	−1.75402	+	3.84077i	−0.0611042	+	0.133800i
$825$		0			0
$826$	3.75898	+	8.23101i	0.130792	+	0.286394i
$827$	1.77190	−	3.87991i	0.0616149	−	0.134918i	−0.876320	−	0.481730i	$-0.840009\pi$
$827$	1.77190	−	3.87991i	0.0616149	−	0.134918i	0.937935	+	0.346812i	$0.112736\pi$
$828$		0			0
$829$	33.4191	+	21.4771i	1.16069	+	0.745931i	0.971740	−	0.236055i	$-0.0758545\pi$
$829$	33.4191	+	21.4771i	1.16069	+	0.745931i	0.188952	+	0.981986i	$0.439491\pi$
$830$	−1.03316	−	7.18578i	−0.0358615	−	0.249422i
$831$		0			0
$832$	−7.99577	+	5.13857i	−0.277204	+	0.178148i
$833$	7.42843			0.257380
$834$		0			0
$835$	−10.5956	+	6.80935i	−0.366674	+	0.235647i
$836$	6.80750	+	14.9063i	0.235442	+	0.515547i
$837$		0			0
$838$	1.84523	−	2.12951i	0.0637423	−	0.0735626i
$839$	4.78745	+	10.4831i	0.165281	+	0.361915i	0.974091	−	0.226154i	$-0.0726154\pi$
$839$	4.78745	+	10.4831i	0.165281	+	0.361915i	−0.808810	+	0.588070i	$0.799888\pi$
$840$		0			0
$841$	34.6568			1.19506
$842$	−3.98715			−0.137406
$843$		0			0
$844$	−21.3883	+	6.28018i	−0.736216	+	0.216173i
$845$	−2.99890	−	20.8578i	−0.103165	−	0.717530i
$846$		0			0
$847$	−3.59418	−	24.9981i	−0.123497	−	0.858944i
$848$	4.03326	−	8.83161i	0.138503	−	0.303279i
$849$		0			0
$850$	−0.648449	+	0.190402i	−0.0222416	+	0.00653073i
$851$	9.54552	−	20.9018i	0.327216	−	0.716504i
$852$		0			0
$853$	−6.08173	+	42.2994i	−0.208235	+	1.44830i	0.570680	+	0.821173i	$0.306680\pi$
$853$	−6.08173	+	42.2994i	−0.208235	+	1.44830i	−0.778914	+	0.627131i	$0.784229\pi$
$854$	−0.910938	−	6.33571i	−0.0311716	−	0.216804i
$855$		0			0
$856$	−1.88931	+	2.18038i	−0.0645754	+	0.0745240i
$857$	−2.97102	+	20.6639i	−0.101488	+	0.705865i	0.874018	+	0.485893i	$0.161506\pi$
$857$	−2.97102	+	20.6639i	−0.101488	+	0.705865i	−0.975506	+	0.219972i	$0.929403\pi$
$858$		0			0
$859$	−23.4570	−	15.0749i	−0.800341	−	0.514348i	0.0753860	−	0.997154i	$-0.475981\pi$
$859$	−23.4570	−	15.0749i	−0.800341	−	0.514348i	−0.875727	+	0.482806i	$0.839617\pi$
$860$	−6.63852	−	1.94925i	−0.226372	−	0.0664687i
$861$		0			0
$862$	−1.45231	−	1.67605i	−0.0494658	−	0.0570865i
$863$	−31.7347	+	20.3947i	−1.08026	+	0.694242i	−0.954618	−	0.297833i	$-0.903736\pi$
$863$	−31.7347	+	20.3947i	−1.08026	+	0.694242i	−0.125644	+	0.992075i	$0.540100\pi$
$864$		0			0
$865$	−22.7825	+	6.68954i	−0.774628	+	0.227451i
$866$	−4.57713	−	1.34397i	−0.155537	−	0.0456698i
$867$		0			0
$868$	25.5779	−	56.0078i	0.868171	−	1.90103i
$869$	−10.1662	−	11.7324i	−0.344864	−	0.397995i
$870$		0			0
$871$	11.4014	−	2.29872i	0.386323	−	0.0778892i
$872$	13.9951			0.473934
$873$		0			0
$874$	2.08853	−	4.57323i	0.0706454	−	0.154692i
$875$	5.57052	−	38.7438i	0.188318	−	1.30978i
$876$		0			0
$877$	41.3045	−	12.1281i	1.39475	−	0.409537i	0.503875	−	0.863776i	$-0.331907\pi$
$877$	41.3045	−	12.1281i	1.39475	−	0.409537i	0.890880	+	0.454240i	$0.150089\pi$
$878$	−0.471736	−	0.544413i	−0.0159203	−	0.0183730i
$879$		0			0
$880$	−8.21628	−	9.48209i	−0.276971	−	0.319641i
$881$	3.83399	+	8.39526i	0.129170	+	0.282843i	0.963156	−	0.268942i	$-0.0866740\pi$
$881$	3.83399	+	8.39526i	0.129170	+	0.282843i	−0.833986	+	0.551785i	$0.813947\pi$
$882$		0			0
$883$	20.9352	+	13.4542i	0.704526	+	0.452771i	0.843223	−	0.537563i	$-0.180655\pi$
$883$	20.9352	+	13.4542i	0.704526	+	0.452771i	−0.138697	+	0.990335i	$0.544292\pi$
$884$	−5.04091	−	3.23959i	−0.169544	−	0.108959i
$885$		0			0
$886$	5.69281	−	6.56986i	0.191254	−	0.220719i
$887$	36.1886	+	10.6259i	1.21509	+	0.356784i	0.825606	−	0.564247i	$-0.190834\pi$
$887$	36.1886	+	10.6259i	1.21509	+	0.356784i	0.389489	+	0.921031i	$0.372652\pi$
$888$		0			0
$889$	0.110742	−	0.770228i	0.00371417	−	0.0258326i
$890$	−0.209192	+	0.241420i	−0.00701212	+	0.00809242i
$891$		0			0
$892$	34.9030	−	10.2484i	1.16864	−	0.343143i
$893$	−12.0407	−	26.3655i	−0.402928	−	0.882288i
$894$		0			0
$895$	−1.92728	−	13.4045i	−0.0644220	−	0.448065i
$896$	−19.1413	−	12.3014i	−0.639465	−	0.410959i
$897$		0			0
$898$	−2.25682	+	0.662662i	−0.0753111	+	0.0221133i
$899$	65.8400	−	42.3128i	2.19589	−	1.41121i
$900$		0			0
$901$	5.74231			0.191304
$902$	3.27544	−	2.10500i	0.109060	−	0.0700887i
$903$		0			0
$904$	−12.3198	+	14.2178i	−0.409750	+	0.472876i
$905$	19.1060	−	22.0495i	0.635105	−	0.732950i
$906$		0			0
$907$	28.7415	−	18.4710i	0.954346	−	0.613321i	0.0319180	−	0.999490i	$-0.489838\pi$
$907$	28.7415	−	18.4710i	0.954346	−	0.613321i	0.922428	+	0.386170i	$0.126202\pi$
$908$	−5.92308			−0.196564
$909$		0			0
$910$	−1.75144	+	1.12558i	−0.0580596	+	0.0373126i
$911$	9.11265	−	2.67571i	0.301915	−	0.0886504i	−0.127266	−	0.991869i	$-0.540620\pi$
$911$	9.11265	−	2.67571i	0.301915	−	0.0886504i	0.429182	+	0.903218i	$0.358802\pi$
$912$		0			0
$913$	−23.9913	−	15.4182i	−0.793995	−	0.510270i
$914$	0.00273663	+	0.0190337i	9.05197e−5	+	0.000629578i
$915$		0			0
$916$	1.15689	+	2.53324i	0.0382247	+	0.0837005i
$917$	−10.6739	+	3.13414i	−0.352483	+	0.103498i
$918$		0			0
$919$	29.5002	−	34.0451i	0.973123	−	1.12304i	−0.0192551	−	0.999815i	$-0.506129\pi$
$919$	29.5002	−	34.0451i	0.973123	−	1.12304i	0.992378	−	0.123229i	$-0.0393251\pi$
$920$	−1.14527	+	7.96550i	−0.0377583	+	0.262615i
$921$		0			0
$922$	2.19530	+	0.644598i	0.0722983	+	0.0212287i
$923$	−7.12993	+	8.22838i	−0.234685	+	0.270840i
$924$		0			0
$925$	5.66429	+	3.64022i	0.186241	+	0.119690i
$926$	−1.34809	−	0.866364i	−0.0443010	−	0.0284705i
$927$		0			0
$928$	−9.05723	−	19.8326i	−0.297318	−	0.651036i
$929$	34.7415	+	40.0938i	1.13983	+	1.31544i	0.942159	+	0.335167i	$0.108793\pi$
$929$	34.7415	+	40.0938i	1.13983	+	1.31544i	0.197672	+	0.980268i	$0.436662\pi$
$930$		0			0
$931$	−10.6040	−	12.2377i	−0.347533	−	0.401075i
$932$	−4.52976	+	1.33006i	−0.148377	+	0.0435675i
$933$		0			0
$934$	0.163433	−	1.13670i	0.00534771	−	0.0371941i
$935$	3.08263	−	6.75001i	0.100813	−	0.220749i
$936$		0			0
$937$	−15.2240			−0.497347			−0.248674	−	0.968587i	$-0.579995\pi$
$937$	−15.2240			−0.497347			−0.248674	+	0.968587i	$0.579995\pi$
$938$	3.66857	+	5.05967i	0.119783	+	0.165204i
$939$		0			0
$940$	14.9757	+	17.2829i	0.488453	+	0.563705i
$941$	12.0441	−	26.3729i	0.392626	−	0.859731i	−0.605339	−	0.795968i	$-0.706962\pi$
$941$	12.0441	−	26.3729i	0.392626	−	0.859731i	0.997965	−	0.0637634i	$-0.0203103\pi$
$942$		0			0
$943$	39.8442	+	11.6993i	1.29751	+	0.380982i
$944$	−41.7051	+	12.2457i	−1.35739	+	0.398565i
$945$		0			0
$946$	0.657713	−	0.422687i	0.0213841	−	0.0137427i
$947$	34.4313	+	39.7358i	1.11887	+	1.29124i	0.952284	+	0.305214i	$0.0987280\pi$
$947$	34.4313	+	39.7358i	1.11887	+	1.29124i	0.166583	+	0.986027i	$0.446727\pi$
$948$		0			0
$949$	−7.18376	−	2.10934i	−0.233195	−	0.0684721i
$950$	1.23933	+	0.796467i	0.0402091	+	0.0258408i
$951$		0			0
$952$	0.929630	−	6.46572i	0.0301295	−	0.209555i
$953$	−34.5781	+	39.9052i	−1.12009	+	1.29266i	−0.168361	+	0.985725i	$0.553848\pi$
$953$	−34.5781	+	39.9052i	−1.12009	+	1.29266i	−0.951732	+	0.306931i	$0.900698\pi$
$954$		0			0
$955$	3.24466	+	22.5671i	0.104995	+	0.730254i
$956$	6.16931	−	42.9085i	0.199530	−	1.38776i
$957$		0			0
$958$	−2.71025	+	5.93461i	−0.0875641	+	0.191739i
$959$	66.4805	−	19.5204i	2.14677	−	0.630348i
$960$		0			0
$961$	27.0948	−	59.3293i	0.874025	−	1.91385i
$962$	−0.244392	−	1.69979i	−0.00787953	−	0.0548033i
$963$		0			0
$964$	4.52898	+	31.4998i	0.145869	+	1.01454i
$965$	−34.7721	+	10.2100i	−1.11935	+	0.328672i
$966$		0			0
$967$	−4.72962			−0.152094			−0.0760471	−	0.997104i	$-0.524230\pi$
$967$	−4.72962			−0.152094			−0.0760471	+	0.997104i	$0.524230\pi$
$968$	−7.29556			−0.234488
$969$		0			0
$970$	0.238808	+	0.522918i	0.00766768	+	0.0167899i
$971$	−11.7939	+	13.6108i	−0.378483	+	0.436792i	−0.912747	−	0.408525i	$-0.866043\pi$
$971$	−11.7939	+	13.6108i	−0.378483	+	0.436792i	0.534264	+	0.845317i	$0.320589\pi$
$972$		0			0
$973$	1.04140	+	2.28034i	0.0333856	+	0.0731043i
$974$	6.85222	−	4.40366i	0.219559	−	0.141102i
$975$		0			0
$976$	30.7467			0.984178
$977$	0.216366	−	0.139050i	0.00692215	−	0.00444859i	−0.537175	−	0.843471i	$-0.680509\pi$
$977$	0.216366	−	0.139050i	0.00692215	−	0.00444859i	0.544097	+	0.839022i	$0.316872\pi$
$978$		0			0
$979$	0.178589	+	1.24211i	0.00570773	+	0.0396981i
$980$	10.7477	+	6.90714i	0.343323	+	0.220640i
$981$		0			0
$982$	−0.477119	+	1.04475i	−0.0152255	+	0.0333392i
$983$	−7.41473	−	16.2360i	−0.236493	−	0.517848i	0.753756	−	0.657154i	$-0.228240\pi$
$983$	−7.41473	−	16.2360i	−0.236493	−	0.517848i	−0.990249	+	0.139306i	$0.955513\pi$
$984$		0			0
$985$	−21.0478	+	46.0882i	−0.670638	+	1.46849i
$986$	2.68014	−	3.09305i	0.0853530	−	0.0985027i
$987$		0			0
$988$	1.85890	+	12.9290i	0.0591396	+	0.411325i
$989$	8.00079	+	2.34924i	0.254410	+	0.0747016i
$990$		0			0
$991$	−1.44835	+	10.0735i	−0.0460082	+	0.319994i	0.953801	+	0.300440i	$0.0971336\pi$
$991$	−1.44835	+	10.0735i	−0.0460082	+	0.319994i	−0.999809	+	0.0195538i	$0.993775\pi$
$992$	−22.5506	−	14.4924i	−0.715982	−	0.460133i
$993$		0			0
$994$	−5.61338	−	1.64824i	−0.178046	−	0.0522789i
$995$	9.85885	+	21.5879i	0.312547	+	0.684382i
$996$		0			0
$997$	7.08824	−	4.55534i	0.224487	−	0.144269i	−0.423563	−	0.905866i	$-0.639221\pi$
$997$	7.08824	−	4.55534i	0.224487	−	0.144269i	0.648050	+	0.761597i	$0.275585\pi$
$998$	0.713919	+	0.823906i	0.0225987	+	0.0260803i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.a.442.1		10
3.2	odd	2		67.2.e.b.40.1	✓	10
67.62	even	11	inner	603.2.u.a.397.1		10
201.14	odd	22		4489.2.a.i.1.2		5
201.53	even	22		4489.2.a.h.1.4		5
201.62	odd	22		67.2.e.b.62.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.b.40.1	✓	10	3.2	odd	2
67.2.e.b.62.1	yes	10	201.62	odd	22
603.2.u.a.397.1		10	67.62	even	11	inner
603.2.u.a.442.1		10	1.1	even	1	trivial
4489.2.a.h.1.4		5	201.53	even	22
4489.2.a.i.1.2		5	201.14	odd	22

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.154861 + 0.178719i) q^{2} +(0.276671 - 1.92429i) q^{4} +(1.84125 + 0.540641i) q^{5} +(2.11435 + 2.44009i) q^{7} +(0.784630 - 0.504251i) q^{8} +O(q^{10})\)	\(q+(0.154861 + 0.178719i) q^{2} +(0.276671 - 1.92429i) q^{4} +(1.84125 + 0.540641i) q^{5} +(2.11435 + 2.44009i) q^{7} +(0.784630 - 0.504251i) q^{8} +(0.188515 + 0.412791i) q^{10} +(1.71047 + 0.502239i) q^{11} +(1.19537 + 0.768216i) q^{13} +(-0.108660 + 0.755750i) q^{14} +(-3.51903 - 1.03328i) q^{16} +(-0.308705 - 2.14709i) q^{17} +(-3.09647 + 3.57352i) q^{19} +(1.54977 - 3.39353i) q^{20} +(0.175125 + 0.383470i) q^{22} +(-1.86779 + 4.08990i) q^{23} +(-1.10835 - 0.712290i) q^{25} +(0.0478208 + 0.332601i) q^{26} +(5.28043 - 3.39353i) q^{28} +7.97852 q^{29} +(8.25215 - 5.30334i) q^{31} +(-1.13520 - 2.48574i) q^{32} +(0.335919 - 0.387671i) q^{34} +(2.57385 + 5.63594i) q^{35} -5.11059 q^{37} -1.11818 q^{38} +(1.71732 - 0.504251i) q^{40} +(-1.31440 - 9.14184i) q^{41} +(-0.263933 - 1.83570i) q^{43} +(1.43969 - 3.15248i) q^{44} +(-1.02019 + 0.299555i) q^{46} +(-2.54645 + 5.57594i) q^{47} +(-0.487365 + 3.38969i) q^{49} +(-0.0443395 - 0.308388i) q^{50} +(1.80899 - 2.08769i) q^{52} +(-0.376741 + 2.62029i) q^{53} +(2.87787 + 1.84950i) q^{55} +(2.88940 + 0.848406i) q^{56} +(1.23556 + 1.42591i) q^{58} +(9.96996 - 6.40730i) q^{59} +(-8.04376 + 2.36186i) q^{61} +(2.22574 + 0.653536i) q^{62} +(-2.77870 + 6.08450i) q^{64} +(1.78565 + 2.06075i) q^{65} +(5.87551 - 5.69898i) q^{67} -4.21704 q^{68} +(-0.608660 + 1.33278i) q^{70} +(-1.09047 + 7.58435i) q^{71} +(-5.05565 + 1.48447i) q^{73} +(-0.791429 - 0.913358i) q^{74} +(6.01979 + 6.94720i) q^{76} +(2.39102 + 5.23561i) q^{77} +(-7.32594 - 4.70809i) q^{79} +(-5.92079 - 3.80506i) q^{80} +(1.43027 - 1.65062i) q^{82} +(-15.3495 - 4.50703i) q^{83} +(0.592401 - 4.12024i) q^{85} +(0.287201 - 0.331447i) q^{86} +(1.59534 - 0.468434i) q^{88} +(0.292424 + 0.640320i) q^{89} +(0.652910 + 4.54109i) q^{91} +(7.35338 + 4.72573i) q^{92} +(-1.39087 + 0.408396i) q^{94} +(-7.63338 + 4.90568i) q^{95} +1.26679 q^{97} +(-0.681276 + 0.437829i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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