LMFDB - Embedded newform 441.2.bb.e.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.e.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.502390 + 0.466150i) q^{2} +(-0.114360 + 1.52603i) q^{4} +(1.18268 - 3.01342i) q^{5} +(-2.63978 + 0.177638i) q^{7} +(-1.50851 - 1.89161i) q^{8} +O(q^{10})$	\(q+(-0.502390 + 0.466150i) q^{2} +(-0.114360 + 1.52603i) q^{4} +(1.18268 - 3.01342i) q^{5} +(-2.63978 + 0.177638i) q^{7} +(-1.50851 - 1.89161i) q^{8} +(0.810538 + 2.06522i) q^{10} +(-3.90713 - 1.20519i) q^{11} +(-1.27405 - 5.58196i) q^{13} +(1.24339 - 1.31978i) q^{14} +(-1.38679 - 0.209025i) q^{16} +(-1.70058 + 1.15943i) q^{17} +(2.71638 + 4.70491i) q^{19} +(4.46331 + 2.14942i) q^{20} +(2.52470 - 1.21583i) q^{22} +(-6.50703 - 4.43642i) q^{23} +(-4.01669 - 3.72695i) q^{25} +(3.24210 + 2.21043i) q^{26} +(0.0308041 - 4.04870i) q^{28} +(3.68397 + 1.77410i) q^{29} +(-1.48036 + 2.56406i) q^{31} +(4.79226 - 3.26731i) q^{32} +(0.313883 - 1.37521i) q^{34} +(-2.58671 + 8.16485i) q^{35} +(-0.396860 - 5.29573i) q^{37} +(-3.55788 - 1.09746i) q^{38} +(-7.48430 + 2.30860i) q^{40} +(-3.21159 - 4.02721i) q^{41} +(5.73640 - 7.19321i) q^{43} +(2.28597 - 5.82456i) q^{44} +(5.33711 - 0.804439i) q^{46} +(1.84012 - 1.70738i) q^{47} +(6.93689 - 0.937853i) q^{49} +3.75526 q^{50} +(8.66393 - 1.30588i) q^{52} +(-0.118564 + 1.58213i) q^{53} +(-8.25261 + 10.3484i) q^{55} +(4.31816 + 4.72548i) q^{56} +(-2.67779 + 0.825988i) q^{58} +(0.228719 + 0.582765i) q^{59} +(-0.503578 - 6.71978i) q^{61} +(-0.451517 - 1.97823i) q^{62} +(-0.260377 + 1.14079i) q^{64} +(-18.3275 - 2.76243i) q^{65} +(-6.35199 + 11.0020i) q^{67} +(-1.57485 - 2.72772i) q^{68} +(-2.50651 - 5.30774i) q^{70} +(-4.77259 + 2.29836i) q^{71} +(5.32261 + 4.93866i) q^{73} +(2.66798 + 2.47553i) q^{74} +(-7.49048 + 3.60723i) q^{76} +(10.5280 + 2.48738i) q^{77} +(-1.10217 - 1.90902i) q^{79} +(-2.27001 + 3.93178i) q^{80} +(3.49076 + 0.526147i) q^{82} +(-2.60748 + 11.4241i) q^{83} +(1.48262 + 6.49578i) q^{85} +(0.471207 + 6.28782i) q^{86} +(3.61419 + 9.20881i) q^{88} +(1.92178 - 0.592791i) q^{89} +(4.35477 + 14.5088i) q^{91} +(7.51425 - 9.42257i) q^{92} +(-0.128562 + 1.71554i) q^{94} +(17.3905 - 2.62119i) q^{95} +0.380496 q^{97} +(-3.04785 + 3.70480i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

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 $

$2$	−0.502390	+	0.466150i	−0.355244	+	0.329618i	−0.837526	−	0.546398i	$-0.815999\pi$
$2$	−0.502390	+	0.466150i	−0.355244	+	0.329618i	0.482282	+	0.876016i	$0.339808\pi$
$3$		0			0
$3$		0			0
$4$	−0.114360	+	1.52603i	−0.0571800	+	0.763014i
$5$	1.18268	−	3.01342i	0.528910	−	1.34764i	−0.377800	−	0.925887i	$-0.623319\pi$
$5$	1.18268	−	3.01342i	0.528910	−	1.34764i	0.906710	−	0.421754i	$-0.138585\pi$
$6$		0			0
$7$	−2.63978	+	0.177638i	−0.997743	+	0.0671410i
$7$	−2.63978	+	0.177638i	−0.997743	+	0.0671410i
$8$	−1.50851	−	1.89161i	−0.533339	−	0.668786i
$9$		0			0
$10$	0.810538	+	2.06522i	0.256315	+	0.653079i
$11$	−3.90713	−	1.20519i	−1.17804	−	0.363378i	−0.356923	−	0.934134i	$-0.616174\pi$
$11$	−3.90713	−	1.20519i	−1.17804	−	0.363378i	−0.821120	+	0.570756i	$0.806650\pi$
$12$		0			0
$13$	−1.27405	−	5.58196i	−0.353357	−	1.54816i	−0.769373	−	0.638799i	$-0.779431\pi$
$13$	−1.27405	−	5.58196i	−0.353357	−	1.54816i	0.416017	−	0.909357i	$-0.363426\pi$
$14$	1.24339	−	1.31978i	0.332311	−	0.352726i
$15$		0			0
$16$	−1.38679	−	0.209025i	−0.346698	−	0.0522564i
$17$	−1.70058	+	1.15943i	−0.412450	+	0.281204i	−0.751716	−	0.659487i	$-0.770774\pi$
$17$	−1.70058	+	1.15943i	−0.412450	+	0.281204i	0.339266	+	0.940690i	$0.389821\pi$
$18$		0			0
$19$	2.71638	+	4.70491i	0.623181	+	1.07938i	0.988890	+	0.148652i	$0.0474934\pi$
$19$	2.71638	+	4.70491i	0.623181	+	1.07938i	−0.365708	+	0.930729i	$0.619173\pi$
$20$	4.46331	+	2.14942i	0.998026	+	0.480624i
$21$		0			0
$22$	2.52470	−	1.21583i	0.538268	−	0.259216i
$23$	−6.50703	−	4.43642i	−1.35681	−	0.925057i	−0.356851	−	0.934161i	$-0.616150\pi$
$23$	−6.50703	−	4.43642i	−1.35681	−	0.925057i	−0.999959	+	0.00910410i	$0.997102\pi$
$24$		0			0
$25$	−4.01669	−	3.72695i	−0.803338	−	0.745389i
$26$	3.24210	+	2.21043i	0.635828	+	0.433500i
$27$		0			0
$28$	0.0308041	−	4.04870i	0.00582143	−	0.765132i
$29$	3.68397	+	1.77410i	0.684095	+	0.329443i	0.743448	−	0.668794i	$-0.233189\pi$
$29$	3.68397	+	1.77410i	0.684095	+	0.329443i	−0.0593524	+	0.998237i	$0.518904\pi$
$30$		0			0
$31$	−1.48036	+	2.56406i	−0.265880	+	0.460518i	−0.967794	−	0.251744i	$-0.918996\pi$
$31$	−1.48036	+	2.56406i	−0.265880	+	0.460518i	0.701914	+	0.712262i	$0.252329\pi$
$32$	4.79226	−	3.26731i	0.847160	−	0.577584i
$33$		0			0
$34$	0.313883	−	1.37521i	0.0538305	−	0.235847i
$35$	−2.58671	+	8.16485i	−0.437235	+	1.38011i
$36$		0			0
$37$	−0.396860	−	5.29573i	−0.0652434	−	0.870612i	−0.929797	−	0.368072i	$-0.880018\pi$
$37$	−0.396860	−	5.29573i	−0.0652434	−	0.870612i	0.864554	−	0.502540i	$-0.167601\pi$
$38$	−3.55788	−	1.09746i	−0.577165	−	0.178032i
$39$		0			0
$40$	−7.48430	+	2.30860i	−1.18337	+	0.365022i
$41$	−3.21159	−	4.02721i	−0.501566	−	0.628944i	0.465015	−	0.885303i	$-0.346049\pi$
$41$	−3.21159	−	4.02721i	−0.501566	−	0.628944i	−0.966582	+	0.256358i	$0.917477\pi$
$42$		0			0
$43$	5.73640	−	7.19321i	0.874792	−	1.09695i	−0.119769	−	0.992802i	$-0.538215\pi$
$43$	5.73640	−	7.19321i	0.874792	−	1.09695i	0.994561	−	0.104153i	$-0.0332132\pi$
$44$	2.28597	−	5.82456i	0.344623	−	0.878085i
$45$		0			0
$46$	5.33711	−	0.804439i	0.786914	−	0.118608i
$47$	1.84012	−	1.70738i	0.268408	−	0.249047i	−0.534473	−	0.845186i	$-0.679490\pi$
$47$	1.84012	−	1.70738i	0.268408	−	0.249047i	0.802881	+	0.596139i	$0.203299\pi$
$48$		0			0
$49$	6.93689	−	0.937853i	0.990984	−	0.133979i
$50$	3.75526			0.531075
$51$		0			0
$52$	8.66393	−	1.30588i	1.20147	−	0.181093i
$53$	−0.118564	+	1.58213i	−0.0162861	+	0.217323i	0.983123	+	0.182946i	$0.0585635\pi$
$53$	−0.118564	+	1.58213i	−0.0162861	+	0.217323i	−0.999409	+	0.0343762i	$0.989056\pi$
$54$		0			0
$55$	−8.25261	+	10.3484i	−1.11278	+	1.39538i
$56$	4.31816	+	4.72548i	0.577039	+	0.631468i
$57$		0			0
$58$	−2.67779	+	0.825988i	−0.351611	+	0.108458i
$59$	0.228719	+	0.582765i	0.0297766	+	0.0758696i	0.944989	−	0.327103i	$-0.106072\pi$
$59$	0.228719	+	0.582765i	0.0297766	+	0.0758696i	−0.915212	+	0.402972i	$0.867977\pi$
$60$		0			0
$61$	−0.503578	−	6.71978i	−0.0644766	−	0.860380i	−0.931878	−	0.362771i	$-0.881831\pi$
$61$	−0.503578	−	6.71978i	−0.0644766	−	0.860380i	0.867402	−	0.497609i	$-0.165788\pi$
$62$	−0.451517	−	1.97823i	−0.0573428	−	0.251235i
$63$		0			0
$64$	−0.260377	+	1.14079i	−0.0325471	+	0.142598i
$65$	−18.3275	−	2.76243i	−2.27325	−	0.342638i
$66$		0			0
$67$	−6.35199	+	11.0020i	−0.776019	+	1.34410i	0.158201	+	0.987407i	$0.449431\pi$
$67$	−6.35199	+	11.0020i	−0.776019	+	1.34410i	−0.934220	+	0.356698i	$0.883903\pi$
$68$	−1.57485	−	2.72772i	−0.190979	−	0.330785i
$69$		0			0
$70$	−2.50651	−	5.30774i	−0.299585	−	0.634396i
$71$	−4.77259	+	2.29836i	−0.566402	+	0.272765i	−0.695093	−	0.718920i	$-0.744637\pi$
$71$	−4.77259	+	2.29836i	−0.566402	+	0.272765i	0.128691	+	0.991685i	$0.458922\pi$
$72$		0			0
$73$	5.32261	+	4.93866i	0.622965	+	0.578027i	0.927198	−	0.374571i	$-0.122210\pi$
$73$	5.32261	+	4.93866i	0.622965	+	0.578027i	−0.304234	+	0.952597i	$0.598400\pi$
$74$	2.66798	+	2.47553i	0.310147	+	0.287774i
$75$		0			0
$76$	−7.49048	+	3.60723i	−0.859217	+	0.413777i
$77$	10.5280	+	2.48738i	1.19978	+	0.283463i
$78$		0			0
$79$	−1.10217	−	1.90902i	−0.124004	−	0.214782i	0.797339	−	0.603532i	$-0.206240\pi$
$79$	−1.10217	−	1.90902i	−0.124004	−	0.214782i	−0.921343	+	0.388750i	$0.872907\pi$
$80$	−2.27001	+	3.93178i	−0.253795	+	0.439586i
$81$		0			0
$82$	3.49076	+	0.526147i	0.385490	+	0.0581032i
$83$	−2.60748	+	11.4241i	−0.286208	+	1.25396i	0.603475	+	0.797382i	$0.293782\pi$
$83$	−2.60748	+	11.4241i	−0.286208	+	1.25396i	−0.889683	+	0.456579i	$0.849075\pi$
$84$		0			0
$85$	1.48262	+	6.49578i	0.160813	+	0.704567i
$86$	0.471207	+	6.28782i	0.0508116	+	0.678034i
$87$		0			0
$88$	3.61419	+	9.20881i	0.385274	+	0.981663i
$89$	1.92178	−	0.592791i	0.203708	−	0.0628357i	−0.191222	−	0.981547i	$-0.561245\pi$
$89$	1.92178	−	0.592791i	0.203708	−	0.0628357i	0.394930	+	0.918711i	$0.370769\pi$
$90$		0			0
$91$	4.35477	+	14.5088i	0.456504	+	1.52094i
$92$	7.51425	−	9.42257i	0.783414	−	0.982371i
$93$		0			0
$94$	−0.128562	+	1.71554i	−0.0132602	+	0.176945i
$95$	17.3905	−	2.62119i	1.78423	−	0.268929i
$96$		0			0
$97$	0.380496			0.0386336			0.0193168	−	0.999813i	$-0.493851\pi$
$97$	0.380496			0.0386336			0.0193168	+	0.999813i	$0.493851\pi$
$98$	−3.04785	+	3.70480i	−0.307879	+	0.374241i
$99$		0			0
$100$	6.14678	−	5.70337i	0.614678	−	0.570337i
$101$	−2.76905	+	0.417367i	−0.275531	+	0.0415296i	−0.285354	−	0.958422i	$-0.592111\pi$
$101$	−2.76905	+	0.417367i	−0.275531	+	0.0415296i	0.00982322	+	0.999952i	$0.496873\pi$
$102$		0			0
$103$	4.01007	−	10.2175i	0.395124	−	1.00676i	−0.585468	−	0.810696i	$-0.699089\pi$
$103$	4.01007	−	10.2175i	0.395124	−	1.00676i	0.980591	−	0.196063i	$-0.0628156\pi$
$104$	−8.63699	+	10.8304i	−0.846927	+	1.06201i
$105$		0			0
$106$	−0.677946	−	0.850117i	−0.0658479	−	0.0825706i
$107$	11.2550	−	3.47171i	1.08806	−	0.335623i	0.301709	−	0.953400i	$-0.402443\pi$
$107$	11.2550	−	3.47171i	1.08806	−	0.335623i	0.786353	+	0.617777i	$0.211967\pi$
$108$		0			0
$109$	−3.13858	−	0.968124i	−0.300621	−	0.0927294i	0.140775	−	0.990042i	$-0.455041\pi$
$109$	−3.13858	−	0.968124i	−0.300621	−	0.0927294i	−0.441396	+	0.897312i	$0.645517\pi$
$110$	−0.677898	−	9.04592i	−0.0646350	−	0.862494i
$111$		0			0
$112$	3.69796	+	0.305434i	0.349425	+	0.0288608i
$113$	−1.58539	+	6.94605i	−0.149141	+	0.653429i	0.843984	+	0.536369i	$0.180204\pi$
$113$	−1.58539	+	6.94605i	−0.149141	+	0.653429i	−0.993125	+	0.117061i	$0.962653\pi$
$114$		0			0
$115$	−21.0645	+	14.3615i	−1.96428	+	1.33922i
$116$	−3.12863	+	5.41895i	−0.290486	+	0.503137i
$117$		0			0
$118$	−0.386562	−	0.186159i	−0.0355859	−	0.0171373i
$119$	4.28319	−	3.36274i	0.392639	−	0.308262i
$120$		0			0
$121$	4.72452	+	3.22112i	0.429502	+	0.292830i
$122$	3.38542	+	3.14121i	0.306502	+	0.284392i
$123$		0			0
$124$	−3.74353	−	2.55230i	−0.336179	−	0.229203i
$125$	−1.39825	+	0.673364i	−0.125064	+	0.0602275i
$126$		0			0
$127$	−6.28782	−	3.02806i	−0.557954	−	0.268696i	0.133583	−	0.991038i	$-0.457352\pi$
$127$	−6.28782	−	3.02806i	−0.557954	−	0.268696i	−0.691537	+	0.722341i	$0.743066\pi$
$128$	5.39912	+	9.35156i	0.477220	+	0.826569i
$129$		0			0
$130$	10.4953	−	7.15557i	0.920498	−	0.627585i
$131$	−2.44022	−	0.367803i	−0.213203	−	0.0321351i	0.0415723	−	0.999135i	$-0.486763\pi$
$131$	−2.44022	−	0.367803i	−0.213203	−	0.0321351i	−0.254775	+	0.967000i	$0.582001\pi$
$132$		0			0
$133$	−8.00643	−	11.9374i	−0.694246	−	1.03510i
$134$	−1.93739	−	8.48827i	−0.167365	−	0.733275i
$135$		0			0
$136$	4.75854	+	1.46781i	0.408041	+	0.125864i
$137$	0.499980	+	1.27393i	0.0427162	+	0.108839i	0.950640	−	0.310297i	$-0.100428\pi$
$137$	0.499980	+	1.27393i	0.0427162	+	0.108839i	−0.907924	+	0.419136i	$0.862333\pi$
$138$		0			0
$139$	9.30010	+	11.6620i	0.788824	+	0.989154i	0.999932	+	0.0116913i	$0.00372153\pi$
$139$	9.30010	+	11.6620i	0.788824	+	0.989154i	−0.211108	+	0.977463i	$0.567707\pi$
$140$	−12.1640	−	4.88113i	−1.02804	−	0.412531i
$141$		0			0
$142$	1.32632	−	3.37942i	0.111303	−	0.283594i
$143$	−1.74946	+	23.3449i	−0.146297	+	1.95220i
$144$		0			0
$145$	9.70306	−	9.00313i	0.805796	−	0.747669i
$146$	−4.97619			−0.411832
$147$		0			0
$148$	8.12682			0.668020
$149$	−4.05685	+	3.76421i	−0.332351	+	0.308376i	−0.828641	−	0.559780i	$-0.810886\pi$
$149$	−4.05685	+	3.76421i	−0.332351	+	0.308376i	0.496291	+	0.868156i	$0.334695\pi$
$150$		0			0
$151$	1.23607	−	16.4942i	0.100590	−	1.34228i	−0.687261	−	0.726410i	$-0.741187\pi$
$151$	1.23607	−	16.4942i	0.100590	−	1.34228i	0.787851	−	0.615866i	$-0.211194\pi$
$152$	4.80218	−	12.2358i	0.389509	−	0.992451i
$153$		0			0
$154$	−6.44868	+	3.65801i	−0.519649	+	0.294771i
$155$	5.97578	+	7.49339i	0.479986	+	0.601884i
$156$		0			0
$157$	−5.59067	−	14.2448i	−0.446184	−	1.13686i	−0.960258	−	0.279113i	$-0.909960\pi$
$157$	−5.59067	−	14.2448i	−0.446184	−	1.13686i	0.514074	−	0.857746i	$-0.328136\pi$
$158$	1.44361	+	0.445296i	0.114848	+	0.0354258i
$159$		0			0
$160$	−4.17805	−	18.3053i	−0.330304	−	1.44716i
$161$	17.9652	+	10.5553i	1.41586	+	0.831872i
$162$		0			0
$163$	−10.3453	−	1.55930i	−0.810303	−	0.122133i	−0.269194	−	0.963086i	$-0.586757\pi$
$163$	−10.3453	−	1.55930i	−0.810303	−	0.122133i	−0.541109	+	0.840953i	$0.681995\pi$
$164$	6.51292	−	4.44043i	0.508573	−	0.346739i
$165$		0			0
$166$	−4.01538	−	6.95485i	−0.311654	−	0.539801i
$167$	−22.5144	−	10.8424i	−1.74222	−	0.839009i	−0.981885	−	0.189477i	$-0.939321\pi$
$167$	−22.5144	−	10.8424i	−1.74222	−	0.839009i	−0.760334	−	0.649532i	$-0.774965\pi$
$168$		0			0
$169$	−17.8224	+	8.58284i	−1.37096	+	0.660218i
$170$	−3.77286	−	2.57230i	−0.289366	−	0.197286i
$171$		0			0
$172$	10.3210	+	9.57652i	0.786972	+	0.730203i
$173$	−1.83718	−	1.25257i	−0.139678	−	0.0952308i	0.491465	−	0.870897i	$-0.336462\pi$
$173$	−1.83718	−	1.25257i	−0.139678	−	0.0952308i	−0.631143	+	0.775666i	$0.717414\pi$
$174$		0			0
$175$	11.2652	+	9.12480i	0.851572	+	0.689770i
$176$	5.16646	+	2.48804i	0.389437	+	0.187543i
$177$		0			0
$178$	−0.689155	+	1.19365i	−0.0516543	+	0.0894679i
$179$	4.56106	−	3.10968i	0.340910	−	0.232428i	−0.380747	−	0.924679i	$-0.624333\pi$
$179$	4.56106	−	3.10968i	0.340910	−	0.232428i	0.721657	+	0.692251i	$0.243381\pi$
$180$		0			0
$181$	−2.03515	+	8.91657i	−0.151271	+	0.662763i	0.841245	+	0.540654i	$0.181823\pi$
$181$	−2.03515	+	8.91657i	−0.151271	+	0.662763i	−0.992517	+	0.122110i	$0.961034\pi$
$182$	−8.95109	−	5.25912i	−0.663499	−	0.389832i
$183$		0			0
$184$	1.42394	+	19.0012i	0.104974	+	1.40079i
$185$	−16.4276	−	5.06724i	−1.20778	−	0.372551i
$186$		0			0
$187$	8.04170	−	2.48054i	0.588067	−	0.181395i
$188$	2.39507	+	3.00333i	0.174679	+	0.219040i
$189$		0			0
$190$	−7.51494	+	9.42344i	−0.545191	+	0.683648i
$191$	5.39558	−	13.7477i	0.390411	−	0.994750i	−0.591652	−	0.806194i	$-0.701524\pi$
$191$	5.39558	−	13.7477i	0.390411	−	0.994750i	0.982062	−	0.188557i	$-0.0603809\pi$
$192$		0			0
$193$	5.52182	−	0.832280i	0.397469	−	0.0599088i	0.0527335	−	0.998609i	$-0.483207\pi$
$193$	5.52182	−	0.832280i	0.397469	−	0.0599088i	0.344736	+	0.938700i	$0.387969\pi$
$194$	−0.191158	+	0.177369i	−0.0137243	+	0.0127343i
$195$		0			0
$196$	0.637888	+	10.6931i	0.0455634	+	0.763796i
$197$	8.04114			0.572908			0.286454	−	0.958094i	$-0.407523\pi$
$197$	8.04114			0.572908			0.286454	+	0.958094i	$0.407523\pi$
$198$		0			0
$199$	7.13784	−	1.07586i	0.505988	−	0.0762654i	0.108912	−	0.994051i	$-0.465263\pi$
$199$	7.13784	−	1.07586i	0.505988	−	0.0762654i	0.397076	+	0.917786i	$0.370025\pi$
$200$	−0.990715	+	13.2202i	−0.0700541	+	0.934807i
$201$		0			0
$202$	1.19659	−	1.50048i	0.0841917	−	0.105573i
$203$	−10.0400	−	4.02883i	−0.704671	−	0.282769i
$204$		0			0
$205$	−15.9339	+	4.91497i	−1.11287	+	0.343276i
$206$	2.74826	+	7.00246i	0.191481	+	0.487884i
$207$		0			0
$208$	0.600066	+	8.00733i	0.0416071	+	0.555208i
$209$	−4.94294	−	21.6564i	−0.341910	−	1.49801i
$210$		0			0
$211$	3.21625	−	14.0913i	0.221416	−	0.970085i	−0.734998	−	0.678069i	$-0.762817\pi$
$211$	3.21625	−	14.0913i	0.221416	−	0.970085i	0.956414	−	0.292016i	$-0.0943259\pi$
$212$	−2.40082	−	0.361865i	−0.164889	−	0.0248530i
$213$		0			0
$214$	−4.03607	+	6.99068i	−0.275900	+	0.477873i
$215$	−14.8918	−	25.7934i	−1.01561	−	1.75910i
$216$		0			0
$217$	3.45235	−	7.03152i	0.234361	−	0.477331i
$218$	2.02808	−	0.976674i	0.137359	−	0.0661487i
$219$		0			0
$220$	−14.8483	−	13.7772i	−1.00107	−	0.928857i
$221$	8.63852	+	8.01537i	0.581090	+	0.539172i
$222$		0			0
$223$	1.08117	−	0.520662i	0.0724003	−	0.0348661i	−0.397333	−	0.917674i	$-0.630064\pi$
$223$	1.08117	−	0.520662i	0.0724003	−	0.0348661i	0.469734	+	0.882808i	$0.344350\pi$
$224$	−12.0701	+	9.47627i	−0.806469	+	0.633160i
$225$		0			0
$226$	−2.44142	−	4.22866i	−0.162401	−	0.281286i
$227$	10.1636	−	17.6039i	0.674585	−	1.16841i	−0.302006	−	0.953306i	$-0.597656\pi$
$227$	10.1636	−	17.6039i	0.674585	−	1.16841i	0.976590	−	0.215109i	$-0.0690105\pi$
$228$		0			0
$229$	−13.0602	−	1.96851i	−0.863042	−	0.130083i	−0.297419	−	0.954747i	$-0.596126\pi$
$229$	−13.0602	−	1.96851i	−0.863042	−	0.130083i	−0.565623	+	0.824664i	$0.691364\pi$
$230$	3.88797	−	17.0343i	0.256365	−	1.12321i
$231$		0			0
$232$	−2.20138	−	9.64489i	−0.144528	−	0.633218i
$233$	−2.10876	−	28.1394i	−0.138149	−	1.84347i	−0.449623	−	0.893218i	$-0.648442\pi$
$233$	−2.10876	−	28.1394i	−0.138149	−	1.84347i	0.311474	−	0.950255i	$-0.399177\pi$
$234$		0			0
$235$	−2.96878	−	7.56432i	−0.193662	−	0.493442i
$236$	−0.915473	+	0.282386i	−0.0595922	+	0.0183818i
$237$		0			0
$238$	−0.584292	+	3.68602i	−0.0378741	+	0.238929i
$239$	2.39936	−	3.00870i	0.155201	−	0.194616i	−0.698152	−	0.715950i	$-0.745994\pi$
$239$	2.39936	−	3.00870i	0.155201	−	0.194616i	0.853353	+	0.521334i	$0.174565\pi$
$240$		0			0
$241$	1.29017	−	17.2161i	0.0831070	−	1.10899i	−0.787273	−	0.616605i	$-0.788508\pi$
$241$	1.29017	−	17.2161i	0.0831070	−	1.10899i	0.870380	−	0.492381i	$-0.163873\pi$
$242$	−3.87508	+	0.584075i	−0.249100	+	0.0375457i
$243$		0			0
$244$	10.3122			0.660169
$245$	5.37797	−	22.0129i	0.343586	−	1.40635i
$246$		0			0
$247$	22.8018	−	21.1570i	1.45085	−	1.34619i
$248$	7.08334	−	1.06764i	0.449793	−	0.0677953i
$249$		0			0
$250$	0.388581	−	0.990088i	0.0245760	−	0.0626187i
$251$	−10.3212	+	12.9424i	−0.651471	+	0.816919i	−0.992385	−	0.123176i	$-0.960692\pi$
$251$	−10.3212	+	12.9424i	−0.651471	+	0.816919i	0.340914	+	0.940094i	$0.389263\pi$
$252$		0			0
$253$	20.0771	+	25.1758i	1.26223	+	1.58279i
$254$	4.57047	−	1.40980i	0.286777	−	0.0884589i
$255$		0			0
$256$	−9.30798	−	2.87113i	−0.581748	−	0.179446i
$257$	1.39171	+	18.5711i	0.0868126	+	1.15843i	0.855147	+	0.518385i	$0.173467\pi$
$257$	1.39171	+	18.5711i	0.0868126	+	1.15843i	−0.768335	+	0.640048i	$0.778914\pi$
$258$		0			0
$259$	1.98835	+	13.9091i	0.123550	+	0.864267i
$260$	6.31149	−	27.6525i	0.391422	−	1.71493i
$261$		0			0
$262$	1.39739	−	0.952727i	0.0863312	−	0.0588596i
$263$	1.88445	−	3.26397i	0.116200	−	0.201265i	−0.802059	−	0.597245i	$-0.796262\pi$
$263$	1.88445	−	3.26397i	0.116200	−	0.201265i	0.918259	+	0.395980i	$0.129595\pi$
$264$		0			0
$265$	4.62740	+	2.22844i	0.284259	+	0.136892i
$266$	9.58698	+	2.26504i	0.587815	+	0.138879i
$267$		0			0
$268$	−16.0629	−	10.9515i	−0.981198	−	0.668970i
$269$	12.4531	+	11.5548i	0.759278	+	0.704507i	0.961492	−	0.274835i	$-0.0886231\pi$
$269$	12.4531	+	11.5548i	0.759278	+	0.704507i	−0.202214	+	0.979341i	$0.564814\pi$
$270$		0			0
$271$	9.56381	+	6.52049i	0.580960	+	0.396092i	0.817839	−	0.575447i	$-0.195172\pi$
$271$	9.56381	+	6.52049i	0.580960	+	0.396092i	−0.236879	+	0.971539i	$0.576124\pi$
$272$	2.60070	−	1.25243i	0.157691	−	0.0759398i
$273$		0			0
$274$	−0.845027	−	0.406944i	−0.0510500	−	0.0245844i
$275$	11.2020	+	19.4025i	0.675509	+	1.17002i
$276$		0			0
$277$	21.3132	−	14.5311i	1.28058	−	0.873088i	0.284260	−	0.958747i	$-0.408252\pi$
$277$	21.3132	−	14.5311i	1.28058	−	0.873088i	0.996324	+	0.0856595i	$0.0272997\pi$
$278$	−10.1085	−	1.52361i	−0.606268	−	0.0913802i
$279$		0			0
$280$	19.3468	−	7.42370i	1.15619	−	0.443651i
$281$	−4.59674	−	20.1396i	−0.274218	−	1.20143i	−0.904981	−	0.425453i	$-0.860115\pi$
$281$	−4.59674	−	20.1396i	−0.274218	−	1.20143i	0.630762	−	0.775976i	$-0.282742\pi$
$282$		0			0
$283$	1.47509	+	0.455006i	0.0876852	+	0.0270473i	0.338287	−	0.941043i	$-0.390152\pi$
$283$	1.47509	+	0.455006i	0.0876852	+	0.0270473i	−0.250602	+	0.968090i	$0.580629\pi$
$284$	−2.96157	−	7.54595i	−0.175737	−	0.447770i
$285$		0			0
$286$	−10.0033	−	12.5437i	−0.591508	−	0.741727i
$287$	9.19329	+	10.0604i	0.542663	+	0.593850i
$288$		0			0
$289$	−4.66312	+	11.8814i	−0.274301	+	0.698908i
$290$	−0.677917	+	9.04617i	−0.0398086	+	0.531209i
$291$		0			0
$292$	−8.14523	+	7.55767i	−0.476664	+	0.442279i
$293$	−10.5264			−0.614961			−0.307480	−	0.951554i	$-0.599486\pi$
$293$	−10.5264			−0.614961			−0.307480	+	0.951554i	$0.599486\pi$
$294$		0			0
$295$	2.02662			0.117994
$296$	−9.41880	+	8.73937i	−0.547457	+	0.507966i
$297$		0			0
$298$	0.283437	−	3.78221i	0.0164191	−	0.219097i
$299$	−16.4736	+	41.9742i	−0.952695	+	2.42743i
$300$		0			0
$301$	−13.8650	+	20.0075i	−0.799168	+	1.15321i
$302$	7.06777	+	8.86270i	0.406704	+	0.509991i
$303$		0			0
$304$	−2.78362	−	7.09254i	−0.159651	−	0.406785i
$305$	−20.8451	−	6.42985i	−1.19359	−	0.368172i
$306$		0			0
$307$	−2.95836	−	12.9614i	−0.168842	−	0.739747i	−0.986462	−	0.163988i	$-0.947564\pi$
$307$	−2.95836	−	12.9614i	−0.168842	−	0.739747i	0.817620	−	0.575758i	$-0.195293\pi$
$308$	−4.99980	+	15.7816i	−0.284890	+	0.899242i
$309$		0			0
$310$	−6.49522	−	0.978997i	−0.368904	−	0.0556033i
$311$	−3.56250	+	2.42887i	−0.202011	+	0.137729i	−0.660100	−	0.751177i	$-0.729486\pi$
$311$	−3.56250	+	2.42887i	−0.202011	+	0.137729i	0.458090	+	0.888906i	$0.348534\pi$
$312$		0			0
$313$	−0.805922	−	1.39590i	−0.0455534	−	0.0789008i	0.842350	−	0.538931i	$-0.181172\pi$
$313$	−0.805922	−	1.39590i	−0.0455534	−	0.0789008i	−0.887903	+	0.460031i	$0.847838\pi$
$314$	9.44891	+	4.55036i	0.533233	+	0.256791i
$315$		0			0
$316$	3.03927	−	1.46363i	0.170972	−	0.0823358i
$317$	−3.31043	−	2.25701i	−0.185932	−	0.126766i	0.466777	−	0.884375i	$-0.345415\pi$
$317$	−3.31043	−	2.25701i	−0.185932	−	0.126766i	−0.652709	+	0.757609i	$0.726368\pi$
$318$		0			0
$319$	−12.2556	−	11.3715i	−0.686181	−	0.636683i
$320$	3.12972	+	2.13381i	0.174957	+	0.119284i
$321$		0			0
$322$	−13.9459	+	3.07162i	−0.777174	+	0.171175i
$323$	−10.0745	−	4.85160i	−0.560558	−	0.269950i
$324$		0			0
$325$	−15.6862	+	27.1693i	−0.870114	+	1.50708i
$326$	5.92422	−	4.03907i	0.328112	−	0.223703i
$327$		0			0
$328$	−2.77320	+	12.1502i	−0.153124	+	0.670882i
$329$	−4.55421	+	4.83398i	−0.251082	+	0.266506i
$330$		0			0
$331$	0.906214	+	12.0926i	0.0498100	+	0.664669i	0.965101	+	0.261876i	$0.0843413\pi$
$331$	0.906214	+	12.0926i	0.0498100	+	0.664669i	−0.915291	+	0.402792i	$0.868040\pi$
$332$	−17.1354	−	5.28556i	−0.940425	−	0.290083i
$333$		0			0
$334$	16.3652	−	5.04800i	0.895465	−	0.276214i
$335$	25.6412	+	32.1530i	1.40093	+	1.75671i
$336$		0			0
$337$	20.9031	−	26.2117i	1.13867	−	1.42784i	0.250621	−	0.968085i	$-0.419365\pi$
$337$	20.9031	−	26.2117i	1.13867	−	1.42784i	0.888045	−	0.459757i	$-0.152063\pi$
$338$	4.95294	−	12.6199i	0.269404	−	0.686431i
$339$		0			0
$340$	−10.0823	+	1.51966i	−0.546790	+	0.0824153i
$341$	8.87412	−	8.23398i	0.480561	−	0.445895i
$342$		0			0
$343$	−18.1453	+	3.70799i	−0.979753	+	0.200212i
$344$	−22.2602			−1.20019
$345$		0			0
$346$	1.50686	−	0.227123i	0.0810095	−	0.0122102i
$347$	−0.285075	+	3.80406i	−0.0153036	+	0.204213i	0.984311	+	0.176444i	$0.0564593\pi$
$347$	−0.285075	+	3.80406i	−0.0153036	+	0.204213i	−0.999614	+	0.0277689i	$0.991160\pi$
$348$		0			0
$349$	−2.50423	+	3.14021i	−0.134049	+	0.168092i	−0.844325	−	0.535831i	$-0.819998\pi$
$349$	−2.50423	+	3.14021i	−0.134049	+	0.168092i	0.710277	+	0.703923i	$0.248570\pi$
$350$	−9.91308	+	0.667079i	−0.529876	+	0.0356569i
$351$		0			0
$352$	−22.6617	+	6.99020i	−1.20787	+	0.372579i
$353$	12.3719	+	31.5230i	0.658488	+	1.67780i	0.732695	+	0.680558i	$0.238262\pi$
$353$	12.3719	+	31.5230i	0.658488	+	1.67780i	−0.0742065	+	0.997243i	$0.523642\pi$
$354$		0			0
$355$	1.28147	+	17.1000i	0.0680133	+	0.907575i
$356$	0.684841	+	3.00048i	0.0362965	+	0.159025i
$357$		0			0
$358$	−0.841856	+	3.68841i	−0.0444935	+	0.194939i
$359$	11.1527	+	1.68100i	0.588617	+	0.0887198i	0.436596	−	0.899657i	$-0.356184\pi$
$359$	11.1527	+	1.68100i	0.588617	+	0.0887198i	0.152021	+	0.988377i	$0.451422\pi$
$360$		0			0
$361$	−5.25748	+	9.10622i	−0.276709	+	0.479275i
$362$	−3.13402	−	5.42828i	−0.164720	−	0.285304i
$363$		0			0
$364$	−22.6389	+	4.98628i	−1.18660	+	0.261352i
$365$	21.1772	−	10.1984i	1.10846	−	0.533808i
$366$		0			0
$367$	17.3373	+	16.0867i	0.905000	+	0.839717i	0.987620	−	0.156864i	$-0.0501384\pi$
$367$	17.3373	+	16.0867i	0.905000	+	0.839717i	−0.0826205	+	0.996581i	$0.526329\pi$
$368$	8.09658	+	7.51253i	0.422064	+	0.391618i
$369$		0			0
$370$	10.6152	−	5.11199i	0.551856	−	0.265760i
$371$	0.0319366	−	4.19754i	0.00165807	−	0.217926i
$372$		0			0
$373$	−8.76582	−	15.1828i	−0.453877	−	0.786138i	0.544746	−	0.838601i	$-0.316626\pi$
$373$	−8.76582	−	15.1828i	−0.453877	−	0.786138i	−0.998623	+	0.0524632i	$0.983293\pi$
$374$	−2.88377	+	4.99484i	−0.149116	+	0.258277i
$375$		0			0
$376$	−6.00553	−	0.905189i	−0.309712	−	0.0466815i
$377$	5.20943	−	22.8240i	0.268299	−	1.17550i
$378$		0			0
$379$	−4.66716	−	20.4482i	−0.239736	−	1.05035i	−0.941254	−	0.337700i	$-0.890351\pi$
$379$	−4.66716	−	20.4482i	−0.239736	−	1.05035i	0.701518	−	0.712652i	$-0.252506\pi$
$380$	2.01124	+	26.8381i	0.103174	+	1.37677i
$381$		0			0
$382$	3.69781	+	9.42188i	0.189197	+	0.482065i
$383$	19.4332	−	5.99435i	0.992990	−	0.306297i	0.244649	−	0.969612i	$-0.421327\pi$
$383$	19.4332	−	5.99435i	0.992990	−	0.306297i	0.748341	+	0.663315i	$0.230851\pi$
$384$		0			0
$385$	19.9468	−	28.7836i	1.01658	−	1.46695i
$386$	−2.38614	+	2.99213i	−0.121451	+	0.152295i
$387$		0			0
$388$	−0.0435136	+	0.580649i	−0.00220907	+	0.0294780i
$389$	8.24358	−	1.24252i	0.417966	−	0.0629982i	0.0633073	−	0.997994i	$-0.479835\pi$
$389$	8.24358	−	1.24252i	0.417966	−	0.0629982i	0.354659	+	0.934996i	$0.384597\pi$
$390$		0			0
$391$	16.2094			0.819746
$392$	−12.2384	−	11.7072i	−0.618134	−	0.591300i
$393$		0			0
$394$	−4.03979	+	3.74838i	−0.203522	+	0.188841i
$395$	−7.05620	+	1.06355i	−0.355036	+	0.0535130i
$396$		0			0
$397$	−8.45491	+	21.5428i	−0.424340	+	1.08120i	0.545641	+	0.838019i	$0.316286\pi$
$397$	−8.45491	+	21.5428i	−0.424340	+	1.08120i	−0.969981	+	0.243181i	$0.921809\pi$
$398$	−3.08447	+	3.86780i	−0.154611	+	0.193876i
$399$		0			0
$400$	4.79130	+	6.00810i	0.239565	+	0.300405i
$401$	−33.5608	+	10.3521i	−1.67594	+	0.516960i	−0.979636	−	0.200783i	$-0.935652\pi$
$401$	−33.5608	+	10.3521i	−1.67594	+	0.516960i	−0.696308	+	0.717743i	$0.745175\pi$
$402$		0			0
$403$	16.1985	+	4.99657i	0.806905	+	0.248897i
$404$	−0.320246	−	4.27338i	−0.0159328	−	0.212609i
$405$		0			0
$406$	6.92205	−	2.65611i	0.343535	−	0.131820i
$407$	−4.83177	+	21.1694i	−0.239502	+	1.04933i
$408$		0			0
$409$	6.55016	−	4.46582i	0.323884	−	0.220821i	−0.390452	−	0.920623i	$-0.627681\pi$
$409$	6.55016	−	4.46582i	0.323884	−	0.220821i	0.714336	+	0.699803i	$0.246729\pi$
$410$	5.71395	−	9.89685i	0.282192	−	0.488770i
$411$		0			0
$412$	15.1336	+	7.28795i	0.745578	+	0.359051i
$413$	−0.707289	−	1.49774i	−0.0348034	−	0.0736992i
$414$		0			0
$415$	31.3418	+	21.3685i	1.53851	+	1.04894i
$416$	−24.3435	−	22.5875i	−1.19354	−	1.10744i
$417$		0			0
$418$	12.5784	+	8.57584i	0.615232	+	0.419458i
$419$	16.3695	−	7.88314i	0.799703	−	0.385116i	0.0110372	−	0.999939i	$-0.496487\pi$
$419$	16.3695	−	7.88314i	0.799703	−	0.385116i	0.788665	+	0.614823i	$0.210772\pi$
$420$		0			0
$421$	−15.0700	−	7.25732i	−0.734466	−	0.353700i	0.0289732	−	0.999580i	$-0.490776\pi$
$421$	−15.0700	−	7.25732i	−0.734466	−	0.353700i	−0.763439	+	0.645880i	$0.776491\pi$
$422$	4.95285	+	8.57859i	0.241101	+	0.417599i
$423$		0			0
$424$	3.17164	−	2.16239i	0.154028	−	0.105015i
$425$	11.1518	+	1.68087i	0.540944	+	0.0815341i
$426$		0			0
$427$	2.52303	+	17.6493i	0.122098	+	0.854109i
$428$	4.01080	+	17.5725i	0.193870	+	0.849398i
$429$		0			0
$430$	19.5051	+	6.01653i	0.940621	+	0.290143i
$431$	2.96143	+	7.54561i	0.142647	+	0.363459i	0.984286	−	0.176582i	$-0.0565040\pi$
$431$	2.96143	+	7.54561i	0.142647	+	0.363459i	−0.841639	+	0.540041i	$0.818409\pi$
$432$		0			0
$433$	−3.63151	−	4.55377i	−0.174519	−	0.218840i	0.686877	−	0.726774i	$-0.258981\pi$
$433$	−3.63151	−	4.55377i	−0.174519	−	0.218840i	−0.861396	+	0.507933i	$0.830410\pi$
$434$	1.54332	+	5.14188i	0.0740816	+	0.246818i
$435$		0			0
$436$	1.83631	−	4.67885i	0.0879434	−	0.224076i
$437$	3.19738	−	42.6660i	0.152951	−	2.04099i
$438$		0			0
$439$	−4.62336	+	4.28986i	−0.220661	+	0.204744i	−0.782755	−	0.622330i	$-0.786186\pi$
$439$	−4.62336	+	4.28986i	−0.220661	+	0.204744i	0.562094	+	0.827073i	$0.309996\pi$
$440$	32.0244			1.52670
$441$		0			0
$442$	−8.07628			−0.384149
$443$	17.2704	−	16.0245i	0.820539	−	0.761349i	−0.153399	−	0.988164i	$-0.549022\pi$
$443$	17.2704	−	16.0245i	0.820539	−	0.761349i	0.973938	+	0.226815i	$0.0728314\pi$
$444$		0			0
$445$	0.486524	−	6.49221i	0.0230634	−	0.307760i
$446$	−0.300461	+	0.765562i	−0.0142272	+	0.0362504i
$447$		0			0
$448$	0.484691	−	3.05768i	0.0228995	−	0.144462i
$449$	−0.417358	−	0.523350i	−0.0196963	−	0.0246984i	0.771886	−	0.635761i	$-0.219314\pi$
$449$	−0.417358	−	0.523350i	−0.0196963	−	0.0246984i	−0.791582	+	0.611063i	$0.790742\pi$
$450$		0			0
$451$	7.69455	+	19.6054i	0.362322	+	0.923182i
$452$	−10.4186	−	3.21370i	−0.490048	−	0.151160i
$453$		0			0
$454$	3.09997	+	13.5818i	0.145489	+	0.637427i
$455$	48.8714	+	4.03654i	2.29113	+	0.189236i
$456$		0			0
$457$	1.46031	+	0.220107i	0.0683106	+	0.0102962i	0.183109	−	0.983093i	$-0.441384\pi$
$457$	1.46031	+	0.220107i	0.0683106	+	0.0102962i	−0.114798	+	0.993389i	$0.536622\pi$
$458$	7.47894	−	5.09905i	0.349468	−	0.238263i
$459$		0			0
$460$	−19.5072	−	33.7874i	−0.909527	−	1.57535i
$461$	−25.3460	−	12.2060i	−1.18048	−	0.568489i	−0.262428	−	0.964952i	$-0.584523\pi$
$461$	−25.3460	−	12.2060i	−1.18048	−	0.568489i	−0.918051	+	0.396463i	$0.870237\pi$
$462$		0			0
$463$	−6.13786	+	2.95584i	−0.285251	+	0.137369i	−0.571038	−	0.820924i	$-0.693459\pi$
$463$	−6.13786	+	2.95584i	−0.285251	+	0.137369i	0.285787	+	0.958293i	$0.407745\pi$
$464$	−4.73807	−	3.23036i	−0.219959	−	0.149966i
$465$		0			0
$466$	14.1766	+	13.1540i	0.656718	+	0.609346i
$467$	24.3805	+	16.6224i	1.12820	+	0.769191i	0.975700	−	0.219113i	$-0.0703162\pi$
$467$	24.3805	+	16.6224i	1.12820	+	0.769191i	0.152497	+	0.988304i	$0.451269\pi$
$468$		0			0
$469$	14.8135	−	30.1712i	0.684023	−	1.39317i
$470$	5.01759	+	2.41634i	0.231444	+	0.111458i
$471$		0			0
$472$	0.757342	−	1.31176i	0.0348595	−	0.0603784i
$473$	−31.0820	+	21.1913i	−1.42915	+	0.974379i
$474$		0			0
$475$	6.62408	−	29.0220i	0.303934	−	1.33162i
$476$	4.64181	+	6.92083i	0.212757	+	0.317216i
$477$		0			0
$478$	0.197091	+	2.63000i	0.00901475	+	0.120293i
$479$	−11.0089	−	3.39578i	−0.503008	−	0.155157i	0.0328589	−	0.999460i	$-0.489539\pi$
$479$	−11.0089	−	3.39578i	−0.503008	−	0.155157i	−0.535867	+	0.844303i	$0.680015\pi$
$480$		0			0
$481$	−29.0549	+	8.96225i	−1.32479	+	0.408643i
$482$	7.37712	+	9.25061i	0.336018	+	0.421354i
$483$		0			0
$484$	−5.45583	+	6.84139i	−0.247992	+	0.310972i
$485$	0.450005	−	1.14659i	0.0204337	−	0.0520642i
$486$		0			0
$487$	−36.9218	+	5.56507i	−1.67309	+	0.252177i	−0.916012	−	0.401151i	$-0.868610\pi$
$487$	−36.9218	+	5.56507i	−1.67309	+	0.252177i	−0.757075	+	0.653328i	$0.773372\pi$
$488$	−11.9516	+	11.0894i	−0.541022	+	0.501995i
$489$		0			0
$490$	7.55949	+	13.5660i	0.341503	+	0.612850i
$491$	−10.9414			−0.493777			−0.246888	−	0.969044i	$-0.579408\pi$
$491$	−10.9414			−0.493777			−0.246888	+	0.969044i	$0.579408\pi$
$492$		0			0
$493$	−8.32182	+	1.25431i	−0.374796	+	0.0564914i
$494$	−1.59308	+	21.2582i	−0.0716760	+	0.956450i
$495$		0			0
$496$	2.58891	−	3.24638i	0.116245	−	0.145767i
$497$	12.1903	−	6.91495i	0.546810	−	0.310178i
$498$		0			0
$499$	21.0497	−	6.49298i	0.942315	−	0.290666i	0.214722	−	0.976675i	$-0.431115\pi$
$499$	21.0497	−	6.49298i	0.942315	−	0.290666i	0.727593	+	0.686009i	$0.240639\pi$
$500$	−0.867668	−	2.21078i	−0.0388033	−	0.0988692i
$501$		0			0
$502$	−0.847822	−	11.3134i	−0.0378401	−	0.504942i
$503$	0.828981	+	3.63200i	0.0369624	+	0.161943i	0.990041	−	0.140781i	$-0.0449612\pi$
$503$	0.828981	+	3.63200i	0.0369624	+	0.161943i	−0.953078	+	0.302724i	$0.902104\pi$
$504$		0			0
$505$	−2.01720	+	8.83792i	−0.0897641	+	0.393282i
$506$	−21.8222	−	3.28917i	−0.970117	−	0.146222i
$507$		0			0
$508$	5.33998	−	9.24911i	0.236923	−	0.410363i
$509$	7.75438	+	13.4310i	0.343707	+	0.595318i	0.985118	−	0.171880i	$-0.0549840\pi$
$509$	7.75438	+	13.4310i	0.343707	+	0.595318i	−0.641411	+	0.767197i	$0.721651\pi$
$510$		0			0
$511$	−14.9278	−	12.0915i	−0.660368	−	0.534896i
$512$	−13.4432	+	6.47388i	−0.594109	+	0.286108i
$513$		0			0
$514$	−9.35610	−	8.68120i	−0.412680	−	0.382911i
$515$	−26.0469	−	24.1680i	−1.14776	−	1.06497i
$516$		0			0
$517$	−9.24728	+	4.45325i	−0.406695	+	0.195854i
$518$	−7.48264	−	6.06091i	−0.328768	−	0.266301i
$519$		0			0
$520$	22.4219	+	38.8358i	0.983264	+	1.70306i
$521$	9.77073	−	16.9234i	0.428064	−	0.741428i	−0.568637	−	0.822588i	$-0.692529\pi$
$521$	9.77073	−	16.9234i	0.428064	−	0.741428i	0.996701	+	0.0811604i	$0.0258626\pi$
$522$		0			0
$523$	−10.8415	−	1.63410i	−0.474068	−	0.0714542i	−0.0923370	−	0.995728i	$-0.529434\pi$
$523$	−10.8415	−	1.63410i	−0.474068	−	0.0714542i	−0.381731	+	0.924274i	$0.624672\pi$
$524$	0.840342	−	3.68178i	0.0367105	−	0.160839i
$525$		0			0
$526$	0.574768	+	2.51822i	0.0250611	+	0.109800i
$527$	−0.455390	−	6.07675i	−0.0198371	−	0.264707i
$528$		0			0
$529$	14.2568	+	36.3257i	0.619861	+	1.57938i
$530$	−3.36355	+	1.03752i	−0.146103	+	0.0450669i
$531$		0			0
$532$	19.1324	−	10.8529i	0.829497	−	0.470532i
$533$	−18.3880	+	23.0578i	−0.796472	+	0.998745i
$534$		0			0
$535$	2.84935	−	38.0219i	0.123188	−	1.64383i
$536$	30.3935	−	4.58109i	1.31280	−	0.197873i
$537$		0			0
$538$	−11.6426			−0.501947
$539$	−28.2336	−	4.69595i	−1.21611	−	0.202269i
$540$		0			0
$541$	32.2868	−	29.9578i	1.38812	−	1.28799i	0.475183	−	0.879887i	$-0.342382\pi$
$541$	32.2868	−	29.9578i	1.38812	−	1.28799i	0.912937	−	0.408100i	$-0.133809\pi$
$542$	−7.84430	+	1.18234i	−0.336941	+	0.0507857i
$543$		0			0
$544$	−4.36138	+	11.1126i	−0.186993	+	0.476449i
$545$	−6.62929	+	8.31287i	−0.283968	+	0.356084i
$546$		0			0
$547$	−16.8456	−	21.1237i	−0.720266	−	0.903185i	0.278087	−	0.960556i	$-0.410300\pi$
$547$	−16.8456	−	21.1237i	−0.720266	−	0.903185i	−0.998353	+	0.0573710i	$0.981728\pi$
$548$	−2.00123	+	0.617297i	−0.0854883	+	0.0263696i
$549$		0			0
$550$	−14.6723	−	4.52580i	−0.625628	−	0.192981i
$551$	1.66005	+	22.1519i	0.0707207	+	0.943702i
$552$		0			0
$553$	3.24861	+	4.84361i	0.138145	+	0.205971i
$554$	−3.93387	+	17.2354i	−0.167134	+	0.732263i
$555$		0			0
$556$	−18.8600	+	12.8586i	−0.799844	+	0.545324i
$557$	16.5688	−	28.6980i	0.702043	−	1.21597i	−0.265706	−	0.964054i	$-0.585605\pi$
$557$	16.5688	−	28.6980i	0.702043	−	1.21597i	0.967748	−	0.251919i	$-0.0810617\pi$
$558$		0			0
$559$	−47.4606	−	22.8558i	−2.00737	−	0.966699i
$560$	5.29390	−	10.7823i	0.223708	−	0.455634i
$561$		0			0
$562$	11.6974	+	7.97518i	0.493427	+	0.336413i
$563$	6.33720	+	5.88006i	0.267081	+	0.247815i	0.802332	−	0.596878i	$-0.203592\pi$
$563$	6.33720	+	5.88006i	0.267081	+	0.247815i	−0.535251	+	0.844693i	$0.679783\pi$
$564$		0			0
$565$	19.0563	+	12.9924i	0.801706	+	0.546594i
$566$	−0.953174	+	0.459024i	−0.0400649	+	0.0192942i
$567$		0			0
$568$	11.5471	+	5.56079i	0.484506	+	0.233326i
$569$	22.4137	+	38.8217i	0.939632	+	1.62749i	0.766158	+	0.642652i	$0.222166\pi$
$569$	22.4137	+	38.8217i	0.939632	+	1.62749i	0.173474	+	0.984839i	$0.444501\pi$
$570$		0			0
$571$	−28.4446	+	19.3932i	−1.19037	+	0.811579i	−0.985907	−	0.167296i	$-0.946497\pi$
$571$	−28.4446	+	19.3932i	−1.19037	+	0.811579i	−0.204461	+	0.978875i	$0.565544\pi$
$572$	−35.4249	−	5.33944i	−1.48119	−	0.223253i
$573$		0			0
$574$	−9.30830	−	0.768820i	−0.388521	−	0.0320899i
$575$	9.60245	+	42.0711i	0.400450	+	1.75449i
$576$		0			0
$577$	−26.6613	−	8.22391i	−1.10992	−	0.342366i	−0.315009	−	0.949089i	$-0.602008\pi$
$577$	−26.6613	−	8.22391i	−1.10992	−	0.342366i	−0.794914	+	0.606723i	$0.792484\pi$
$578$	−3.19583	−	8.14284i	−0.132929	−	0.338697i
$579$		0			0
$580$	12.6294	+	15.8368i	0.524407	+	0.657585i
$581$	4.85382	−	30.6204i	0.201370	−	1.27035i
$582$		0			0
$583$	2.37001	−	6.03870i	0.0981559	−	0.250097i
$584$	1.31282	−	17.5183i	0.0543248	−	0.724914i
$585$		0			0
$586$	5.28838	−	4.90690i	0.218461	−	0.202702i
$587$	35.7448			1.47535			0.737673	−	0.675158i	$-0.235925\pi$
$587$	35.7448			1.47535			0.737673	+	0.675158i	$0.235925\pi$
$588$		0			0
$589$	−16.0849			−0.662766
$590$	−1.01815	+	0.944707i	−0.0419167	+	0.0388930i
$591$		0			0
$592$	−0.556579	+	7.42703i	−0.0228753	+	0.305249i
$593$	16.7364	−	42.6436i	0.687281	−	1.75116i	0.0275969	−	0.999619i	$-0.491215\pi$
$593$	16.7364	−	42.6436i	0.687281	−	1.75116i	0.659684	−	0.751543i	$-0.270690\pi$
$594$		0			0
$595$	−5.06769	−	16.8841i	−0.207755	−	0.692180i
$596$	−5.28035	−	6.62135i	−0.216292	−	0.271221i
$597$		0			0
$598$	−11.2901	−	28.7666i	−0.461685	−	1.17635i
$599$	−12.6875	−	3.91357i	−0.518397	−	0.159904i	0.0245062	−	0.999700i	$-0.492199\pi$
$599$	−12.6875	−	3.91357i	−0.518397	−	0.159904i	−0.542903	+	0.839795i	$0.682675\pi$
$600$		0			0
$601$	4.45065	+	19.4996i	0.181546	+	0.795405i	0.980895	+	0.194538i	$0.0623207\pi$
$601$	4.45065	+	19.4996i	0.181546	+	0.795405i	−0.799349	+	0.600867i	$0.794822\pi$
$602$	−2.36084	−	16.5148i	−0.0962208	−	0.673092i
$603$		0			0
$604$	25.0292	+	3.77255i	1.01842	+	0.153503i
$605$	15.2942	−	10.4274i	0.621797	−	0.423934i
$606$		0			0
$607$	9.46011	+	16.3854i	0.383974	+	0.665062i	0.991626	−	0.129141i	$-0.0412219\pi$
$607$	9.46011	+	16.3854i	0.383974	+	0.665062i	−0.607652	+	0.794203i	$0.707889\pi$
$608$	28.3900	+	13.6719i	1.15137	+	0.554469i
$609$		0			0
$610$	13.4696	−	6.48664i	0.545370	−	0.262636i
$611$	−11.8749	−	8.09617i	−0.480407	−	0.327536i
$612$		0			0
$613$	5.66887	+	5.25994i	0.228963	+	0.212447i	0.786309	−	0.617834i	$-0.211990\pi$
$613$	5.66887	+	5.25994i	0.228963	+	0.212447i	−0.557345	+	0.830281i	$0.688180\pi$
$614$	7.52822	+	5.13265i	0.303814	+	0.207137i
$615$		0			0
$616$	−11.1765	−	23.6672i	−0.450315	−	0.953580i
$617$	−37.1455	−	17.8884i	−1.49542	−	0.720158i	−0.505641	−	0.862744i	$-0.668744\pi$
$617$	−37.1455	−	17.8884i	−1.49542	−	0.720158i	−0.989782	+	0.142586i	$0.954458\pi$
$618$		0			0
$619$	4.18785	−	7.25357i	0.168324	−	0.291546i	−0.769507	−	0.638639i	$-0.779498\pi$
$619$	4.18785	−	7.25357i	0.168324	−	0.291546i	0.937831	+	0.347093i	$0.112831\pi$
$620$	−12.1185	+	8.26227i	−0.486692	+	0.331821i
$621$		0			0
$622$	0.657547	−	2.88090i	0.0263652	−	0.115514i
$623$	−4.96778	+	1.90622i	−0.199030	+	0.0763711i
$624$		0			0
$625$	−1.67194	−	22.3106i	−0.0668778	−	0.892422i
$626$	1.05559	+	0.325605i	0.0421897	+	0.0130138i
$627$		0			0
$628$	22.3773	−	6.90249i	0.892952	−	0.275439i
$629$	6.81493	+	8.54566i	0.271729	+	0.340738i
$630$		0			0
$631$	−13.8472	+	17.3638i	−0.551247	+	0.691242i	−0.976913	−	0.213639i	$-0.931468\pi$
$631$	−13.8472	+	17.3638i	−0.551247	+	0.691242i	0.425666	+	0.904880i	$0.360040\pi$
$632$	−1.94849	+	4.96467i	−0.0775067	+	0.197484i
$633$		0			0
$634$	2.71523	−	0.409256i	0.107836	−	0.0162536i
$635$	−16.5613	+	15.3666i	−0.657214	+	0.609805i
$636$		0			0
$637$	−14.0730	−	37.5265i	−0.557591	−	1.48686i
$638$	11.4579			0.453624
$639$		0			0
$640$	34.5656	−	5.20992i	1.36632	−	0.205940i
$641$	2.78419	−	37.1524i	0.109969	−	1.46743i	−0.620350	−	0.784325i	$-0.713009\pi$
$641$	2.78419	−	37.1524i	0.109969	−	1.46743i	0.730319	−	0.683107i	$-0.239372\pi$
$642$		0			0
$643$	−19.8260	+	24.8610i	−0.781861	+	0.980422i	0.218129	+	0.975920i	$0.430005\pi$
$643$	−19.8260	+	24.8610i	−0.781861	+	0.980422i	−0.999990	+	0.00450227i	$0.998567\pi$
$644$	−18.1622	+	26.2083i	−0.715689	+	1.03275i
$645$		0			0
$646$	7.32288	−	2.25881i	0.288115	−	0.0888717i
$647$	−2.42483	−	6.17836i	−0.0953298	−	0.242896i	0.875252	−	0.483667i	$-0.160695\pi$
$647$	−2.42483	−	6.17836i	−0.0953298	−	0.242896i	−0.970582	+	0.240770i	$0.922600\pi$
$648$		0			0
$649$	−0.191290	−	2.55259i	−0.00750879	−	0.100198i
$650$	−4.78438	−	20.9617i	−0.187659	−	0.822186i
$651$		0			0
$652$	3.56261	−	15.6088i	0.139523	−	0.611289i
$653$	1.51706	+	0.228661i	0.0593673	+	0.00894818i	0.178659	−	0.983911i	$-0.442824\pi$
$653$	1.51706	+	0.228661i	0.0593673	+	0.00894818i	−0.119291	+	0.992859i	$0.538062\pi$
$654$		0			0
$655$	−3.99434	+	6.91840i	−0.156072	+	0.270324i
$656$	3.61203	+	6.25621i	0.141026	+	0.244264i
$657$		0			0
$658$	0.0346296	−	4.55149i	0.00135000	−	0.177436i
$659$	−26.1587	+	12.5974i	−1.01900	+	0.490724i	−0.867344	−	0.497709i	$-0.834175\pi$
$659$	−26.1587	+	12.5974i	−1.01900	+	0.490724i	−0.151655	+	0.988433i	$0.548460\pi$
$660$		0			0
$661$	19.8983	+	18.4629i	0.773953	+	0.718123i	0.964653	−	0.263525i	$-0.0848852\pi$
$661$	19.8983	+	18.4629i	0.773953	+	0.718123i	−0.190700	+	0.981648i	$0.561076\pi$
$662$	−6.09223	−	5.65277i	−0.236781	−	0.219701i
$663$		0			0
$664$	25.5434	−	12.3011i	0.991278	−	0.477374i
$665$	−45.4414	+	10.0086i	−1.76214	+	0.388117i
$666$		0			0
$667$	−16.1010	−	27.8878i	−0.623433	−	1.07982i
$668$	19.1205	−	33.1177i	0.739796	−	1.28136i
$669$		0			0
$670$	−27.8700	−	4.20073i	−1.07671	−	0.162288i
$671$	−6.13106	+	26.8619i	−0.236687	+	1.03699i
$672$		0			0
$673$	6.89539	+	30.2107i	0.265798	+	1.16454i	0.914850	+	0.403793i	$0.132308\pi$
$673$	6.89539	+	30.2107i	0.265798	+	1.16454i	−0.649053	+	0.760744i	$0.724834\pi$
$674$	1.71705	+	22.9125i	0.0661385	+	0.882557i
$675$		0			0
$676$	−11.0595	−	28.1791i	−0.425365	−	1.08381i
$677$	29.8472	−	9.20665i	1.14712	−	0.353840i	0.337807	−	0.941215i	$-0.390315\pi$
$677$	29.8472	−	9.20665i	1.14712	−	0.353840i	0.809315	+	0.587375i	$0.199839\pi$
$678$		0			0
$679$	−1.00443	+	0.0675908i	−0.0385464	+	0.00259390i
$680$	10.0510	−	12.6035i	0.385437	−	0.483322i
$681$		0			0
$682$	−0.620002	+	8.27335i	−0.0237411	+	0.316803i
$683$	−40.5567	+	6.11293i	−1.55186	+	0.233905i	−0.868318	−	0.496008i	$-0.834799\pi$
$683$	−40.5567	+	6.11293i	−1.55186	+	0.233905i	−0.683540	+	0.729913i	$0.739561\pi$
$684$		0			0
$685$	4.43019			0.169269
$686$	7.38753	−	10.3213i	0.282057	−	0.394068i
$687$		0			0
$688$	−9.45876	+	8.77645i	−0.360612	+	0.334599i
$689$	8.98245	−	1.35389i	0.342204	−	0.0515790i
$690$		0			0
$691$	14.6439	−	37.3119i	0.557078	−	1.41941i	−0.323825	−	0.946117i	$-0.604969\pi$
$691$	14.6439	−	37.3119i	0.557078	−	1.41941i	0.880904	−	0.473296i	$-0.156936\pi$
$692$	2.12155	−	2.66034i	0.0806493	−	0.101131i
$693$		0			0
$694$	−1.63004	−	2.04401i	−0.0618756	−	0.0775896i
$695$	46.1414	−	14.2327i	1.75024	−	0.539878i
$696$		0			0
$697$	10.1308	+	3.12495i	0.383733	+	0.118366i
$698$	−0.205706	−	2.74496i	−0.00778610	−	0.103898i
$699$		0			0
$700$	−15.2130	+	16.1476i	−0.574998	+	0.610321i
$701$	4.53943	−	19.8885i	0.171452	−	0.751179i	−0.813950	−	0.580935i	$-0.802687\pi$
$701$	4.53943	−	19.8885i	0.171452	−	0.751179i	0.985402	−	0.170244i	$-0.0544557\pi$
$702$		0			0
$703$	23.8379	−	16.2524i	0.899064	−	0.612972i
$704$	2.39219	−	4.14339i	0.0901590	−	0.156160i
$705$		0			0
$706$	−20.9100	−	10.0697i	−0.786957	−	0.378978i
$707$	7.23555	−	1.59365i	0.272121	−	0.0599353i
$708$		0			0
$709$	19.6566	+	13.4016i	0.738218	+	0.503308i	0.873093	−	0.487554i	$-0.162111\pi$
$709$	19.6566	+	13.4016i	0.738218	+	0.503308i	−0.134875	+	0.990863i	$0.543063\pi$
$710$	−8.61497	−	7.99353i	−0.323314	−	0.299992i
$711$		0			0
$712$	−4.02036	−	2.74103i	−0.150669	−	0.102725i
$713$	21.0080	−	10.1169i	0.786755	−	0.378881i
$714$		0			0
$715$	68.2788	+	32.8813i	2.55348	+	1.22969i
$716$	4.22386	+	7.31593i	0.157853	+	0.273409i
$717$		0			0
$718$	−6.38661	+	4.35432i	−0.238346	+	0.162502i
$719$	−20.3956	−	3.07414i	−0.760626	−	0.114646i	−0.242735	−	0.970093i	$-0.578045\pi$
$719$	−20.3956	−	3.07414i	−0.760626	−	0.114646i	−0.517891	+	0.855447i	$0.673283\pi$
$720$		0			0
$721$	−8.77068	+	27.6843i	−0.326637	+	1.03102i
$722$	−1.60356	−	7.02565i	−0.0596783	−	0.261468i
$723$		0			0
$724$	−13.3742	−	4.12539i	−0.497048	−	0.153319i
$725$	−8.18536	−	20.8560i	−0.303997	−	0.774571i
$726$		0			0
$727$	20.5614	+	25.7832i	0.762581	+	0.956247i	0.999885	−	0.0151890i	$-0.00483501\pi$
$727$	20.5614	+	25.7832i	0.762581	+	0.956247i	−0.237303	+	0.971436i	$0.576264\pi$
$728$	20.8759	−	30.1243i	0.773711	−	1.11648i
$729$		0			0
$730$	−5.88523	+	14.9953i	−0.217822	+	0.555002i
$731$	−1.41513	+	18.8836i	−0.0523404	+	0.698434i
$732$		0			0
$733$	−33.5306	+	31.1118i	−1.23848	+	1.14914i	−0.255230	+	0.966880i	$0.582151\pi$
$733$	−33.5306	+	31.1118i	−1.23848	+	1.14914i	−0.983250	+	0.182261i	$0.941658\pi$
$734$	−16.2089			−0.598281
$735$		0			0
$736$	−45.6785			−1.68373
$737$	38.0775	−	35.3307i	1.40260	−	1.30142i
$738$		0			0
$739$	−0.217533	+	2.90277i	−0.00800207	+	0.106780i	−0.999775	−	0.0212328i	$-0.993241\pi$
$739$	−0.217533	+	2.90277i	−0.00800207	+	0.106780i	0.991772	+	0.128013i	$0.0408599\pi$
$740$	9.61142	−	24.4895i	0.353323	−	0.900252i
$741$		0			0
$742$	1.94064	+	2.12369i	0.0712432	+	0.0779632i
$743$	−10.3714	−	13.0053i	−0.380489	−	0.477118i	0.554302	−	0.832316i	$-0.312985\pi$
$743$	−10.3714	−	13.0053i	−0.380489	−	0.477118i	−0.934791	+	0.355197i	$0.884414\pi$
$744$		0			0
$745$	6.54518	+	16.6768i	0.239797	+	0.610992i
$746$	11.4814	+	3.54153i	0.420362	+	0.129665i
$747$		0			0
$748$	2.86572	+	12.5555i	0.104781	+	0.459076i
$749$	−29.0940	+	11.1639i	−1.06307	+	0.407919i
$750$		0			0
$751$	−15.9219	−	2.39984i	−0.580997	−	0.0875712i	−0.148033	−	0.988982i	$-0.547294\pi$
$751$	−15.9219	−	2.39984i	−0.580997	−	0.0875712i	−0.432964	+	0.901411i	$0.642532\pi$
$752$	−2.90875	+	1.98315i	−0.106071	+	0.0723180i
$753$		0			0
$754$	8.02225	+	13.8949i	0.292153	+	0.506024i
$755$	−48.2419	−	23.2321i	−1.75570	−	0.845502i
$756$		0			0
$757$	−30.3539	+	14.6177i	−1.10323	+	0.531288i	−0.894673	−	0.446721i	$-0.852592\pi$
$757$	−30.3539	+	14.6177i	−1.10323	+	0.531288i	−0.208559	+	0.978010i	$0.566877\pi$
$758$	11.8766	+	8.09736i	0.431379	+	0.294109i
$759$		0			0
$760$	−31.1920	−	28.9420i	−1.13145	−	1.04984i
$761$	19.6123	+	13.3714i	0.710944	+	0.484713i	0.863992	−	0.503505i	$-0.167957\pi$
$761$	19.6123	+	13.3714i	0.710944	+	0.484713i	−0.153048	+	0.988219i	$0.548909\pi$
$762$		0			0
$763$	8.45714	+	1.99810i	0.306169	+	0.0723362i
$764$	20.3624	+	9.80601i	0.736685	+	0.354769i
$765$		0			0
$766$	−6.96879	+	12.0703i	−0.251792	+	0.436117i
$767$	2.96157	−	2.01917i	0.106936	−	0.0729079i
$768$		0			0
$769$	3.59221	−	15.7385i	0.129538	−	0.567544i	−0.867946	−	0.496658i	$-0.834560\pi$
$769$	3.59221	−	15.7385i	0.129538	−	0.567544i	0.997484	−	0.0708859i	$-0.0225826\pi$
$770$	3.39640	+	23.7588i	0.122398	+	0.856208i
$771$		0			0
$772$	0.638608	+	8.52163i	0.0229840	+	0.306700i
$773$	−1.88196	−	0.580507i	−0.0676893	−	0.0208794i	0.260726	−	0.965413i	$-0.416038\pi$
$773$	−1.88196	−	0.580507i	−0.0676893	−	0.0208794i	−0.328415	+	0.944534i	$0.606514\pi$
$774$		0			0
$775$	15.5022	−	4.78181i	0.556857	−	0.171768i
$776$	−0.573983	−	0.719752i	−0.0206048	−	0.0258376i
$777$		0			0
$778$	−3.56229	+	4.46698i	−0.127714	+	0.160149i
$779$	10.2238	−	26.0497i	0.366304	−	0.933328i
$780$		0			0
$781$	21.4171	−	3.22810i	0.766362	−	0.115511i
$782$	−8.14346	+	7.55603i	−0.291210	+	0.270203i
$783$		0			0
$784$	−9.81607	−	0.149378i	−0.350574	−	0.00533492i
$785$	−49.5375			−1.76807
$786$		0			0
$787$	5.76443	−	0.868848i	0.205480	−	0.0309711i	−0.0454958	−	0.998965i	$-0.514487\pi$
$787$	5.76443	−	0.868848i	0.205480	−	0.0309711i	0.250975	+	0.967993i	$0.419249\pi$
$788$	−0.919586	+	12.2710i	−0.0327589	+	0.437137i
$789$		0			0
$790$	3.04919	−	3.82357i	0.108485	−	0.136036i
$791$	2.95120	−	18.6177i	0.104933	−	0.661968i
$792$		0			0
$793$	−36.8679	+	11.3723i	−1.30922	+	0.403841i
$794$	−5.79449	−	14.7641i	−0.205639	−	0.523959i
$795$		0			0
$796$	0.825504	+	11.0156i	0.0292592	+	0.390437i
$797$	−1.30984	−	5.73879i	−0.0463969	−	0.203278i	0.946417	−	0.322948i	$-0.104674\pi$
$797$	−1.30984	−	5.73879i	−0.0463969	−	0.203278i	−0.992814	+	0.119669i	$0.961817\pi$
$798$		0			0
$799$	−1.14967	+	5.03702i	−0.0406723	+	0.178197i
$800$	−31.4261	−	4.73672i	−1.11108	−	0.167468i
$801$		0			0
$802$	12.0350	−	20.8452i	0.424969	−	0.736068i
$803$	−14.8441	−	25.7107i	−0.523837	−	0.907312i
$804$		0			0
$805$	53.0545	−	41.6532i	1.86993	−	1.46808i
$806$	−10.4671	+	5.04070i	−0.368689	+	0.177551i
$807$		0			0
$808$	4.96664	+	4.60837i	0.174726	+	0.162122i
$809$	21.8990	+	20.3193i	0.769929	+	0.714390i	0.963797	−	0.266638i	$-0.0859127\pi$
$809$	21.8990	+	20.3193i	0.769929	+	0.714390i	−0.193867	+	0.981028i	$0.562103\pi$
$810$		0			0
$811$	−0.174070	+	0.0838278i	−0.00611243	+	0.00294359i	−0.436937	−	0.899492i	$-0.643937\pi$
$811$	−0.174070	+	0.0838278i	−0.00611243	+	0.00294359i	0.430825	+	0.902435i	$0.358223\pi$
$812$	7.29629	−	14.8606i	0.256050	−	0.521505i
$813$		0			0
$814$	−7.44067	−	12.8876i	−0.260795	−	0.451711i
$815$	−16.9339	+	29.3304i	−0.593169	+	1.02740i
$816$		0			0
$817$	49.4257	+	7.44973i	1.72919	+	0.260633i
$818$	−1.20899	+	5.29694i	−0.0422714	+	0.185203i
$819$		0			0
$820$	−5.67818	−	24.8777i	−0.198291	−	0.868768i
$821$	3.41850	+	45.6167i	0.119306	+	1.59203i	0.660297	+	0.751005i	$0.270430\pi$
$821$	3.41850	+	45.6167i	0.119306	+	1.59203i	−0.540990	+	0.841029i	$0.681950\pi$
$822$		0			0
$823$	−17.1255	−	43.6350i	−0.596956	−	1.52102i	−0.835275	−	0.549833i	$-0.814692\pi$
$823$	−17.1255	−	43.6350i	−0.596956	−	1.52102i	0.238319	−	0.971187i	$-0.423404\pi$
$824$	−25.3768	+	7.82769i	−0.884041	+	0.272691i
$825$		0			0
$826$	1.05351	+	0.422750i	0.0366563	+	0.0147093i
$827$	−15.3468	+	19.2443i	−0.533662	+	0.669190i	−0.973447	−	0.228912i	$-0.926483\pi$
$827$	−15.3468	+	19.2443i	−0.533662	+	0.669190i	0.439786	+	0.898103i	$0.355054\pi$
$828$		0			0
$829$	−0.197593	+	2.63669i	−0.00686268	+	0.0915761i	−0.999583	−	0.0288632i	$-0.990811\pi$
$829$	−0.197593	+	2.63669i	−0.00686268	+	0.0915761i	0.992721	+	0.120439i	$0.0384303\pi$
$830$	−25.7068	+	3.87467i	−0.892295	+	0.134492i
$831$		0			0
$832$	6.69955			0.232265
$833$	−10.7093	+	9.63775i	−0.371056	+	0.333928i
$834$		0			0
$835$	−59.3000	+	55.0223i	−2.05216	+	1.90413i
$836$	33.6136	−	5.06644i	1.16255	−	0.175226i
$837$		0			0
$838$	−4.54916	+	11.5911i	−0.157148	+	0.400407i
$839$	11.1722	−	14.0095i	0.385708	−	0.483662i	−0.550637	−	0.834745i	$-0.685615\pi$
$839$	11.1722	−	14.0095i	0.385708	−	0.483662i	0.936344	+	0.351083i	$0.114186\pi$
$840$		0			0
$841$	−7.65705	−	9.60164i	−0.264036	−	0.331091i
$842$	10.9540	−	3.37886i	0.377500	−	0.116443i
$843$		0			0
$844$	21.1359	+	6.51957i	0.727528	+	0.224413i
$845$	4.78544	+	63.8572i	0.164624	+	2.19675i
$846$		0			0
$847$	−13.0439	−	7.66381i	−0.448194	−	0.263332i
$848$	0.495130	−	2.16931i	0.0170028	−	0.0744943i
$849$		0			0
$850$	−6.38611	+	4.35398i	−0.219042	+	0.149340i
$851$	−20.9117	+	36.2201i	−0.716843	+	1.24161i
$852$		0			0
$853$	−30.8079	−	14.8363i	−1.05484	−	0.507985i	−0.175650	−	0.984453i	$-0.556203\pi$
$853$	−30.8079	−	14.8363i	−1.05484	−	0.507985i	−0.879192	+	0.476467i	$0.841917\pi$
$854$	−9.49477	−	7.69073i	−0.324904	−	0.263171i
$855$		0			0
$856$	−23.5454	−	16.0530i	−0.804766	−	0.548680i
$857$	23.2473	+	21.5704i	0.794114	+	0.736830i	0.968813	−	0.247792i	$-0.0797049\pi$
$857$	23.2473	+	21.5704i	0.794114	+	0.736830i	−0.174699	+	0.984622i	$0.555895\pi$
$858$		0			0
$859$	−29.8491	−	20.3508i	−1.01844	−	0.694360i	−0.0656033	−	0.997846i	$-0.520897\pi$
$859$	−29.8491	−	20.3508i	−1.01844	−	0.694360i	−0.952836	+	0.303486i	$0.901850\pi$
$860$	41.0645	−	19.7756i	1.40029	−	0.674344i
$861$		0			0
$862$	−5.00518	−	2.41037i	−0.170477	−	0.0820975i
$863$	18.7146	+	32.4146i	0.637052	+	1.10341i	0.986076	+	0.166293i	$0.0531798\pi$
$863$	18.7146	+	32.4146i	0.637052	+	1.10341i	−0.349024	+	0.937114i	$0.613487\pi$
$864$		0			0
$865$	−5.94729	+	4.05480i	−0.202214	+	0.137867i
$866$	3.94718	+	0.594942i	0.134131	+	0.0202169i
$867$		0			0
$868$	10.3355	+	6.07251i	0.350809	+	0.206114i
$869$	2.00560	+	8.78711i	0.0680354	+	0.298082i
$870$		0			0
$871$	69.5052	+	21.4395i	2.35510	+	0.726451i
$872$	2.90327	+	7.39741i	0.0983171	+	0.250508i
$873$		0			0
$874$	18.2824	+	22.9255i	0.618413	+	0.775465i
$875$	3.57147	−	2.02592i	0.120738	−	0.0684885i
$876$		0			0
$877$	14.1558	−	36.0683i	0.478006	−	1.21794i	−0.465044	−	0.885287i	$-0.653962\pi$
$877$	14.1558	−	36.0683i	0.478006	−	1.21794i	0.943050	−	0.332651i	$-0.107943\pi$
$878$	0.323017	−	4.31036i	0.0109013	−	0.145468i
$879$		0			0
$880$	13.6078	−	12.6262i	0.458717	−	0.425627i
$881$	−22.1671			−0.746828			−0.373414	−	0.927665i	$-0.621813\pi$
$881$	−22.1671			−0.746828			−0.373414	+	0.927665i	$0.621813\pi$
$882$		0			0
$883$	9.82028			0.330479			0.165239	−	0.986254i	$-0.447160\pi$
$883$	9.82028			0.330479			0.165239	+	0.986254i	$0.447160\pi$
$884$	−13.2196	+	12.2660i	−0.444623	+	0.412550i
$885$		0			0
$886$	−1.20661	+	16.1012i	−0.0405370	+	0.540929i
$887$	17.7829	−	45.3101i	0.597092	−	1.52137i	−0.238005	−	0.971264i	$-0.576494\pi$
$887$	17.7829	−	45.3101i	0.597092	−	1.52137i	0.835098	−	0.550102i	$-0.185411\pi$
$888$		0			0
$889$	17.1364	+	6.87644i	0.574736	+	0.230629i
$890$	2.78192	+	3.48842i	0.0932501	+	0.116932i
$891$		0			0
$892$	0.670904	+	1.70943i	0.0224635	+	0.0572361i
$893$	13.0315	+	4.01969i	0.436083	+	0.134514i
$894$		0			0
$895$	−3.97649	−	17.4221i	−0.132919	−	0.582358i
$896$	−15.9137	−	23.7270i	−0.531639	−	0.792662i
$897$		0			0
$898$	0.453636	+	0.0683747i	0.0151380	+	0.00228169i
$899$	−10.0025	+	6.81959i	−0.333602	+	0.227446i
$900$		0			0
$901$	−1.63275	−	2.82800i	−0.0543948	−	0.0942145i
$902$	−13.0047	−	6.26274i	−0.433010	−	0.208527i
$903$		0			0
$904$	15.5308	−	7.47925i	0.516547	−	0.248756i
$905$	24.4624	+	16.6782i	0.813158	+	0.554402i
$906$		0			0
$907$	−40.7407	−	37.8019i	−1.35277	−	1.25519i	−0.938606	−	0.344990i	$-0.887882\pi$
$907$	−40.7407	−	37.8019i	−1.35277	−	1.25519i	−0.414167	−	0.910201i	$-0.635927\pi$
$908$	25.7018	+	17.5232i	0.852944	+	0.581528i
$909$		0			0
$910$	−26.4342	+	20.7535i	−0.876284	+	0.687972i
$911$	50.2396	+	24.1941i	1.66451	+	0.801587i	0.998448	+	0.0556935i	$0.0177370\pi$
$911$	50.2396	+	24.1941i	1.66451	+	0.801587i	0.666065	+	0.745894i	$0.267977\pi$
$912$		0			0
$913$	23.9560	−	41.4930i	0.792827	−	1.37322i
$914$	−0.836250	+	0.570146i	−0.0276607	+	0.0188587i
$915$		0			0
$916$	4.49756	−	19.7051i	0.148604	−	0.651075i
$917$	6.50697	+	0.537444i	0.214879	+	0.0177480i
$918$		0			0
$919$	1.50834	+	20.1274i	0.0497555	+	0.663942i	0.965203	+	0.261503i	$0.0842182\pi$
$919$	1.50834	+	20.1274i	0.0497555	+	0.663942i	−0.915447	+	0.402438i	$0.868163\pi$
$920$	58.9425	+	18.1814i	1.94328	+	0.599422i
$921$		0			0
$922$	18.4234	−	5.68286i	0.606742	−	0.187155i
$923$	18.9098	+	23.7122i	0.622424	+	0.780495i
$924$		0			0
$925$	−18.1428	+	22.7504i	−0.596532	+	0.748028i
$926$	1.70574	−	4.34615i	0.0560540	−	0.142823i
$927$		0			0
$928$	23.4511	−	3.53468i	0.769819	−	0.116032i
$929$	−37.5193	+	34.8128i	−1.23097	+	1.14217i	−0.246031	+	0.969262i	$0.579126\pi$
$929$	−37.5193	+	34.8128i	−1.23097	+	1.14217i	−0.984938	+	0.172910i	$0.944683\pi$
$930$		0			0
$931$	23.2558	+	30.0899i	0.762177	+	0.986157i
$932$	43.1827			1.41450
$933$		0			0
$934$	−19.9971	+	3.01407i	−0.654324	+	0.0986235i
$935$	2.03586	−	27.1667i	0.0665798	−	0.888445i
$936$		0			0
$937$	32.1809	−	40.3535i	1.05130	−	1.31829i	0.105191	−	0.994452i	$-0.466455\pi$
$937$	32.1809	−	40.3535i	1.05130	−	1.31829i	0.946112	−	0.323840i	$-0.104974\pi$
$938$	6.62213	+	22.0630i	0.216220	+	0.720383i
$939$		0			0
$940$	11.8829	−	3.66538i	0.387577	−	0.119552i
$941$	11.7509	+	29.9409i	0.383070	+	0.976046i	0.984226	+	0.176915i	$0.0566116\pi$
$941$	11.7509	+	29.9409i	0.383070	+	0.976046i	−0.601156	+	0.799131i	$0.705293\pi$
$942$		0			0
$943$	3.03154	+	40.4531i	0.0987207	+	1.31734i
$944$	−0.195373	−	0.855983i	−0.00635884	−	0.0278599i
$945$		0			0
$946$	5.73695	−	25.1352i	0.186524	−	0.817216i
$947$	−47.5270	−	7.16355i	−1.54442	−	0.232784i	−0.679116	−	0.734031i	$-0.737637\pi$
$947$	−47.5270	−	7.16355i	−1.54442	−	0.232784i	−0.865304	+	0.501247i	$0.832875\pi$
$948$		0			0
$949$	20.7861	−	36.0027i	0.674747	−	1.16870i
$950$	10.2007	+	17.6682i	0.330956	+	0.573232i
$951$		0			0
$952$	−12.8222	−	3.02941i	−0.415571	−	0.0981838i
$953$	4.23698	−	2.04042i	0.137249	−	0.0660958i	−0.363999	−	0.931399i	$-0.618589\pi$
$953$	4.23698	−	2.04042i	0.137249	−	0.0660958i	0.501248	+	0.865304i	$0.332874\pi$
$954$		0			0
$955$	−35.0464	−	32.5183i	−1.13407	−	1.05227i
$956$	4.31697	+	4.00556i	0.139621	+	0.129549i
$957$		0			0
$958$	7.11369	−	3.42577i	0.229833	−	0.110682i
$959$	−1.54614	−	3.27408i	−0.0499273	−	0.105725i
$960$		0			0
$961$	11.1171	+	19.2553i	0.358615	+	0.621140i
$962$	10.4192	−	18.0465i	0.335927	−	0.581842i
$963$		0			0
$964$	26.1247	+	3.93767i	0.841420	+	0.126824i
$965$	4.02253	−	17.6239i	0.129490	−	0.567332i
$966$		0			0
$967$	10.7569	+	47.1289i	0.345917	+	1.51556i	0.786353	+	0.617778i	$0.211967\pi$
$967$	10.7569	+	47.1289i	0.345917	+	1.51556i	−0.440436	+	0.897784i	$0.645176\pi$
$968$	−1.03387	−	13.7961i	−0.0332299	−	0.443423i
$969$		0			0
$970$	0.308407	+	0.785808i	0.00990235	+	0.0252308i
$971$	−41.8360	+	12.9047i	−1.34258	+	0.414132i	−0.881063	−	0.472999i	$-0.843172\pi$
$971$	−41.8360	+	12.9047i	−1.34258	+	0.414132i	−0.461519	+	0.887130i	$0.652695\pi$
$972$		0			0
$973$	−26.6218	−	29.1330i	−0.853457	−	0.933960i
$974$	15.9550	−	20.0069i	0.511231	−	0.641064i
$975$		0			0
$976$	−0.706247	+	9.42421i	−0.0226064	+	0.301662i
$977$	−49.6071	+	7.47706i	−1.58707	+	0.239212i	−0.882462	−	0.470384i	$-0.844116\pi$
$977$	−49.6071	+	7.47706i	−1.58707	+	0.239212i	−0.704609	+	0.709596i	$0.748877\pi$
$978$		0			0
$979$	−8.22306			−0.262810
$980$	32.9773	+	10.7243i	1.05342	+	0.342576i
$981$		0			0
$982$	5.49684	−	5.10032i	0.175411	−	0.162758i
$983$	13.9099	−	2.09658i	0.443656	−	0.0668704i	0.0765844	−	0.997063i	$-0.475599\pi$
$983$	13.9099	−	2.09658i	0.443656	−	0.0668704i	0.367071	+	0.930193i	$0.380360\pi$
$984$		0			0
$985$	9.51009	−	24.2313i	0.303017	−	0.772074i
$986$	3.59610	−	4.50937i	0.114523	−	0.143608i
$987$		0			0
$988$	29.6786	+	37.2158i	0.944201	+	1.18399i
$989$	−69.2390	+	21.3574i	−2.20167	+	0.679126i
$990$		0			0
$991$	29.3390	+	9.04987i	0.931983	+	0.287479i	0.723323	−	0.690510i	$-0.242614\pi$
$991$	29.3390	+	9.04987i	0.931983	+	0.287479i	0.208660	+	0.977988i	$0.433090\pi$
$992$	1.28330	+	17.1244i	0.0407447	+	0.543701i
$993$		0			0
$994$	−2.90089	+	9.15652i	−0.0920106	+	0.290427i
$995$	5.19977	−	22.7817i	0.164844	−	0.722228i
$996$		0			0
$997$	−28.4844	+	19.4204i	−0.902111	+	0.615049i	−0.923028	−	0.384732i	$-0.874294\pi$
$997$	−28.4844	+	19.4204i	−0.902111	+	0.615049i	0.0209169	+	0.999781i	$0.493341\pi$
$998$	−7.54848	+	13.0743i	−0.238943	+	0.413861i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.109.2		60
3.2	odd	2		147.2.m.b.109.4	yes	60
49.9	even	21	inner	441.2.bb.e.352.2		60
147.95	odd	42		7203.2.a.n.1.11		30
147.101	even	42		7203.2.a.m.1.11		30
147.107	odd	42		147.2.m.b.58.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.58.4	✓	60	147.107	odd	42
147.2.m.b.109.4	yes	60	3.2	odd	2
441.2.bb.e.109.2		60	1.1	even	1	trivial
441.2.bb.e.352.2		60	49.9	even	21	inner
7203.2.a.m.1.11		30	147.101	even	42
7203.2.a.n.1.11		30	147.95	odd	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.502390 + 0.466150i) q^{2} +(-0.114360 + 1.52603i) q^{4} +(1.18268 - 3.01342i) q^{5} +(-2.63978 + 0.177638i) q^{7} +(-1.50851 - 1.89161i) q^{8} +O(q^{10})\)	\(q+(-0.502390 + 0.466150i) q^{2} +(-0.114360 + 1.52603i) q^{4} +(1.18268 - 3.01342i) q^{5} +(-2.63978 + 0.177638i) q^{7} +(-1.50851 - 1.89161i) q^{8} +(0.810538 + 2.06522i) q^{10} +(-3.90713 - 1.20519i) q^{11} +(-1.27405 - 5.58196i) q^{13} +(1.24339 - 1.31978i) q^{14} +(-1.38679 - 0.209025i) q^{16} +(-1.70058 + 1.15943i) q^{17} +(2.71638 + 4.70491i) q^{19} +(4.46331 + 2.14942i) q^{20} +(2.52470 - 1.21583i) q^{22} +(-6.50703 - 4.43642i) q^{23} +(-4.01669 - 3.72695i) q^{25} +(3.24210 + 2.21043i) q^{26} +(0.0308041 - 4.04870i) q^{28} +(3.68397 + 1.77410i) q^{29} +(-1.48036 + 2.56406i) q^{31} +(4.79226 - 3.26731i) q^{32} +(0.313883 - 1.37521i) q^{34} +(-2.58671 + 8.16485i) q^{35} +(-0.396860 - 5.29573i) q^{37} +(-3.55788 - 1.09746i) q^{38} +(-7.48430 + 2.30860i) q^{40} +(-3.21159 - 4.02721i) q^{41} +(5.73640 - 7.19321i) q^{43} +(2.28597 - 5.82456i) q^{44} +(5.33711 - 0.804439i) q^{46} +(1.84012 - 1.70738i) q^{47} +(6.93689 - 0.937853i) q^{49} +3.75526 q^{50} +(8.66393 - 1.30588i) q^{52} +(-0.118564 + 1.58213i) q^{53} +(-8.25261 + 10.3484i) q^{55} +(4.31816 + 4.72548i) q^{56} +(-2.67779 + 0.825988i) q^{58} +(0.228719 + 0.582765i) q^{59} +(-0.503578 - 6.71978i) q^{61} +(-0.451517 - 1.97823i) q^{62} +(-0.260377 + 1.14079i) q^{64} +(-18.3275 - 2.76243i) q^{65} +(-6.35199 + 11.0020i) q^{67} +(-1.57485 - 2.72772i) q^{68} +(-2.50651 - 5.30774i) q^{70} +(-4.77259 + 2.29836i) q^{71} +(5.32261 + 4.93866i) q^{73} +(2.66798 + 2.47553i) q^{74} +(-7.49048 + 3.60723i) q^{76} +(10.5280 + 2.48738i) q^{77} +(-1.10217 - 1.90902i) q^{79} +(-2.27001 + 3.93178i) q^{80} +(3.49076 + 0.526147i) q^{82} +(-2.60748 + 11.4241i) q^{83} +(1.48262 + 6.49578i) q^{85} +(0.471207 + 6.28782i) q^{86} +(3.61419 + 9.20881i) q^{88} +(1.92178 - 0.592791i) q^{89} +(4.35477 + 14.5088i) q^{91} +(7.51425 - 9.42257i) q^{92} +(-0.128562 + 1.71554i) q^{94} +(17.3905 - 2.62119i) q^{95} +0.380496 q^{97} +(-3.04785 + 3.70480i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more