LMFDB - Embedded newform 1950.2.y.i.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.i.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.758819 + 1.31431i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.758819 + 1.31431i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.45680 + 2.57313i) q^{11} -1.00000i q^{12} +(-1.86250 - 3.08725i) q^{13} +1.51764 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.15307 - 2.39778i) q^{17} -1.00000 q^{18} +(1.39778 + 0.807007i) q^{19} -1.51764i q^{21} +(4.45680 + 2.57313i) q^{22} +(4.71329 - 2.72122i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.74238 + 3.15660i) q^{26} +1.00000i q^{27} +(-0.758819 - 1.31431i) q^{28} +(4.93684 + 8.55085i) q^{29} -9.88072i q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.57313 - 4.45680i) q^{33} +4.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(-4.36981 - 7.56873i) q^{37} -1.61401i q^{38} +(3.15660 + 1.74238i) q^{39} +(1.10418 - 0.637499i) q^{41} +(-1.31431 + 0.758819i) q^{42} +(-2.04965 - 1.18336i) q^{43} -5.14626i q^{44} +(-4.71329 - 2.72122i) q^{46} +6.84909 q^{47} +(0.866025 + 0.500000i) q^{48} +(2.34839 + 4.06753i) q^{49} +4.79555 q^{51} +(3.60488 - 0.0693504i) q^{52} +0.881964i q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.758819 + 1.31431i) q^{56} -1.61401 q^{57} +(4.93684 - 8.55085i) q^{58} +(8.04354 + 4.64394i) q^{59} +(-6.24056 + 10.8090i) q^{61} +(-8.55695 + 4.94036i) q^{62} +(0.758819 + 1.31431i) q^{63} +1.00000 q^{64} -5.14626 q^{66} +(5.76733 + 9.98930i) q^{67} +(4.15307 - 2.39778i) q^{68} +(-2.72122 + 4.71329i) q^{69} +(13.7133 + 7.91737i) q^{71} +(0.500000 - 0.866025i) q^{72} -4.39355 q^{73} +(-4.36981 + 7.56873i) q^{74} +(-1.39778 + 0.807007i) q^{76} -7.81017i q^{77} +(-0.0693504 - 3.60488i) q^{78} +11.0382 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.10418 - 0.637499i) q^{82} -0.979336 q^{83} +(1.31431 + 0.758819i) q^{84} +2.36673i q^{86} +(-8.55085 - 4.93684i) q^{87} +(-4.45680 + 2.57313i) q^{88} +(3.54146 - 2.04466i) q^{89} +(5.47091 - 0.105249i) q^{91} +5.44244i q^{92} +(4.94036 + 8.55695i) q^{93} +(-3.42455 - 5.93149i) q^{94} -1.00000i q^{96} +(2.85898 - 4.95189i) q^{97} +(2.34839 - 4.06753i) q^{98} +5.14626i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9} - 12 q^{11} + 8 q^{14} - 4 q^{16} - 8 q^{18} - 12 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{28} - 4 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{36} - 16 q^{37} + 24 q^{43} + 12 q^{46} + 32 q^{47} + 16 q^{49} - 8 q^{51} - 4 q^{56} - 4 q^{58} + 12 q^{59} - 16 q^{61} - 24 q^{62} + 4 q^{63} + 8 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{69} + 60 q^{71} + 4 q^{72} - 24 q^{73} - 16 q^{74} + 12 q^{76} + 8 q^{79} - 4 q^{81} - 8 q^{83} - 12 q^{87} - 12 q^{88} - 24 q^{89} + 8 q^{91} + 4 q^{93} - 16 q^{94} + 16 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9 - 12 * q^11 + 8 * q^14 - 4 * q^16 - 8 * q^18 - 12 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^28 - 4 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^36 - 16 * q^37 + 24 * q^43 + 12 * q^46 + 32 * q^47 + 16 * q^49 - 8 * q^51 - 4 * q^56 - 4 * q^58 + 12 * q^59 - 16 * q^61 - 24 * q^62 + 4 * q^63 + 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^69 + 60 * q^71 + 4 * q^72 - 24 * q^73 - 16 * q^74 + 12 * q^76 + 8 * q^79 - 4 * q^81 - 8 * q^83 - 12 * q^87 - 12 * q^88 - 24 * q^89 + 8 * q^91 + 4 * q^93 - 16 * q^94 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−0.758819	+	1.31431i	−0.286807	+	0.496764i	−0.973046	−	0.230612i	$-0.925927\pi$
$7$	−0.758819	+	1.31431i	−0.286807	+	0.496764i	0.686239	+	0.727376i	$0.259260\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−4.45680	+	2.57313i	−1.34377	+	0.775829i	−0.987359	−	0.158499i	$-0.949335\pi$
$11$	−4.45680	+	2.57313i	−1.34377	+	0.775829i	−0.356415	+	0.934328i	$0.616001\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−1.86250	−	3.08725i	−0.516565	−	0.856248i
$13$	−1.86250	−	3.08725i	−0.516565	−	0.856248i
$14$	1.51764			0.405606
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.15307	−	2.39778i	−1.00727	−	0.581546i	−0.0968774	−	0.995296i	$-0.530885\pi$
$17$	−4.15307	−	2.39778i	−1.00727	−	0.581546i	−0.910391	+	0.413750i	$0.864219\pi$
$18$	−1.00000			−0.235702
$19$	1.39778	+	0.807007i	0.320672	+	0.185140i	0.651692	−	0.758484i	$-0.274059\pi$
$19$	1.39778	+	0.807007i	0.320672	+	0.185140i	−0.331020	+	0.943624i	$0.607393\pi$
$20$		0			0
$21$		−	1.51764i		−	0.331176i
$22$	4.45680	+	2.57313i	0.950192	+	0.548594i
$23$	4.71329	−	2.72122i	0.982789	−	0.567414i	0.0796783	−	0.996821i	$-0.474611\pi$
$23$	4.71329	−	2.72122i	0.982789	−	0.567414i	0.903111	+	0.429407i	$0.141277\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	−1.74238	+	3.15660i	−0.341709	+	0.619060i
$27$			1.00000i			0.192450i
$28$	−0.758819	−	1.31431i	−0.143403	−	0.248382i
$29$	4.93684	+	8.55085i	0.916747	+	1.58785i	0.804323	+	0.594193i	$0.202528\pi$
$29$	4.93684	+	8.55085i	0.916747	+	1.58785i	0.112425	+	0.993660i	$0.464138\pi$
$30$		0			0
$31$		−	9.88072i		−	1.77463i	−0.461164	−	0.887315i	$-0.652568\pi$
$31$		−	9.88072i		−	1.77463i	0.461164	−	0.887315i	$-0.347432\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.57313	−	4.45680i	0.447925	−	0.775829i
$34$			4.79555i			0.822431i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−4.36981	−	7.56873i	−0.718392	−	1.24429i	−0.961637	−	0.274326i	$-0.911545\pi$
$37$	−4.36981	−	7.56873i	−0.718392	−	1.24429i	0.243245	−	0.969965i	$-0.421788\pi$
$38$		−	1.61401i		−	0.261828i
$39$	3.15660	+	1.74238i	0.505460	+	0.279005i
$40$		0			0
$41$	1.10418	−	0.637499i	0.172444	−	0.0995606i	−0.411294	−	0.911503i	$-0.634923\pi$
$41$	1.10418	−	0.637499i	0.172444	−	0.0995606i	0.583738	+	0.811942i	$0.301590\pi$
$42$	−1.31431	+	0.758819i	−0.202803	+	0.117088i
$43$	−2.04965	−	1.18336i	−0.312568	−	0.180461i	0.335507	−	0.942038i	$-0.391092\pi$
$43$	−2.04965	−	1.18336i	−0.312568	−	0.180461i	−0.648075	+	0.761576i	$0.724426\pi$
$44$		−	5.14626i		−	0.775829i
$45$		0			0
$46$	−4.71329	−	2.72122i	−0.694937	−	0.401222i
$47$	6.84909			0.999043			0.499521	−	0.866302i	$-0.333509\pi$
$47$	6.84909			0.999043			0.499521	+	0.866302i	$0.333509\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	2.34839	+	4.06753i	0.335484	+	0.581075i
$50$		0			0
$51$	4.79555			0.671512
$52$	3.60488	−	0.0693504i	0.499908	−	0.00961716i
$53$			0.881964i			0.121147i	0.998164	+	0.0605735i	$0.0192930\pi$
$53$			0.881964i			0.121147i	−0.998164	+	0.0605735i	$0.980707\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−0.758819	+	1.31431i	−0.101401	+	0.175632i
$57$	−1.61401			−0.213781
$58$	4.93684	−	8.55085i	0.648238	−	1.12278i
$59$	8.04354	+	4.64394i	1.04718	+	0.604590i	0.921859	−	0.387526i	$-0.126670\pi$
$59$	8.04354	+	4.64394i	1.04718	+	0.604590i	0.125322	+	0.992116i	$0.460004\pi$
$60$		0			0
$61$	−6.24056	+	10.8090i	−0.799022	+	1.38395i	0.121232	+	0.992624i	$0.461315\pi$
$61$	−6.24056	+	10.8090i	−0.799022	+	1.38395i	−0.920254	+	0.391322i	$0.872018\pi$
$62$	−8.55695	+	4.94036i	−1.08673	+	0.627426i
$63$	0.758819	+	1.31431i	0.0956022	+	0.165588i
$64$	1.00000			0.125000
$65$		0			0
$66$	−5.14626			−0.633461
$67$	5.76733	+	9.98930i	0.704591	+	1.22039i	0.966839	+	0.255387i	$0.0822029\pi$
$67$	5.76733	+	9.98930i	0.704591	+	1.22039i	−0.262248	+	0.965001i	$0.584464\pi$
$68$	4.15307	−	2.39778i	0.503634	−	0.290773i
$69$	−2.72122	+	4.71329i	−0.327596	+	0.567414i
$70$		0			0
$71$	13.7133	+	7.91737i	1.62747	+	0.939619i	0.984845	+	0.173437i	$0.0554874\pi$
$71$	13.7133	+	7.91737i	1.62747	+	0.939619i	0.642623	+	0.766182i	$0.277846\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−4.39355			−0.514226			−0.257113	−	0.966381i	$-0.582771\pi$
$73$	−4.39355			−0.514226			−0.257113	+	0.966381i	$0.582771\pi$
$74$	−4.36981	+	7.56873i	−0.507980	+	0.879847i
$75$		0			0
$76$	−1.39778	+	0.807007i	−0.160336	+	0.0925701i
$77$		−	7.81017i		−	0.890051i
$78$	−0.0693504	−	3.60488i	−0.00785238	−	0.408173i
$79$	11.0382			1.24189			0.620947	−	0.783853i	$-0.286748\pi$
$79$	11.0382			1.24189			0.620947	+	0.783853i	$0.286748\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.10418	−	0.637499i	−0.121936	−	0.0704000i
$83$	−0.979336			−0.107496			−0.0537480	−	0.998555i	$-0.517117\pi$
$83$	−0.979336			−0.107496			−0.0537480	+	0.998555i	$0.517117\pi$
$84$	1.31431	+	0.758819i	0.143403	+	0.0827939i
$85$		0			0
$86$			2.36673i			0.255211i
$87$	−8.55085	−	4.93684i	−0.916747	−	0.529284i
$88$	−4.45680	+	2.57313i	−0.475096	+	0.274297i
$89$	3.54146	−	2.04466i	0.375394	−	0.216734i	−0.300418	−	0.953808i	$-0.597126\pi$
$89$	3.54146	−	2.04466i	0.375394	−	0.216734i	0.675812	+	0.737074i	$0.263793\pi$
$90$		0			0
$91$	5.47091	−	0.105249i	0.573507	−	0.0110331i
$92$			5.44244i			0.567414i
$93$	4.94036	+	8.55695i	0.512291	+	0.887315i
$94$	−3.42455	−	5.93149i	−0.353215	−	0.611786i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	2.85898	−	4.95189i	0.290285	−	0.502789i	−0.683592	−	0.729864i	$-0.739583\pi$
$97$	2.85898	−	4.95189i	0.290285	−	0.502789i	0.973877	+	0.227076i	$0.0729165\pi$
$98$	2.34839	−	4.06753i	0.237223	−	0.410882i
$99$			5.14626i			0.517219i
$100$		0			0
$101$	−3.92687	−	6.80153i	−0.390738	−	0.676778i	0.601809	−	0.798640i	$-0.294447\pi$
$101$	−3.92687	−	6.80153i	−0.390738	−	0.676778i	−0.992547	+	0.121862i	$0.961113\pi$
$102$	−2.39778	−	4.15307i	−0.237415	−	0.411215i
$103$			3.17449i			0.312792i	0.987694	+	0.156396i	$0.0499876\pi$
$103$			3.17449i			0.312792i	−0.987694	+	0.156396i	$0.950012\pi$
$104$	−1.86250	−	3.08725i	−0.182633	−	0.302729i
$105$		0			0
$106$	0.763803	−	0.440982i	0.0741871	−	0.0428319i
$107$	11.9106	−	6.87662i	1.15145	−	0.664787i	0.202207	−	0.979343i	$-0.435189\pi$
$107$	11.9106	−	6.87662i	1.15145	−	0.664787i	0.949239	+	0.314555i	$0.101855\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$		−	16.7895i		−	1.60814i	−0.594533	−	0.804071i	$-0.702663\pi$
$109$		−	16.7895i		−	1.60814i	0.594533	−	0.804071i	$-0.297337\pi$
$110$		0			0
$111$	7.56873	+	4.36981i	0.718392	+	0.414764i
$112$	1.51764			0.143403
$113$	8.36308	+	4.82843i	0.786732	+	0.454220i	0.838811	−	0.544423i	$-0.183251\pi$
$113$	8.36308	+	4.82843i	0.786732	+	0.454220i	−0.0520785	+	0.998643i	$0.516585\pi$
$114$	0.807007	+	1.39778i	0.0755831	+	0.130914i
$115$		0			0
$116$	−9.87367			−0.916747
$117$	−3.60488	+	0.0693504i	−0.333272	+	0.00641144i
$118$		−	9.28788i		−	0.855019i
$119$	6.30286	−	3.63896i	0.577782	−	0.333583i
$120$		0			0
$121$	7.74202	−	13.4096i	0.703820	−	1.21905i
$122$	12.4811			1.12999
$123$	−0.637499	+	1.10418i	−0.0574813	+	0.0995606i
$124$	8.55695	+	4.94036i	0.768437	+	0.443657i
$125$		0			0
$126$	0.758819	−	1.31431i	0.0676010	−	0.117088i
$127$	10.3843	−	5.99536i	0.921454	−	0.532002i	0.0373555	−	0.999302i	$-0.488107\pi$
$127$	10.3843	−	5.99536i	0.921454	−	0.532002i	0.884099	+	0.467300i	$0.154773\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.36673			0.208379
$130$		0			0
$131$	−20.3524			−1.77820			−0.889098	−	0.457717i	$-0.848667\pi$
$131$	−20.3524			−1.77820			−0.889098	+	0.457717i	$0.848667\pi$
$132$	2.57313	+	4.45680i	0.223962	+	0.387914i
$133$	−2.12132	+	1.22474i	−0.183942	+	0.106199i
$134$	5.76733	−	9.98930i	0.498221	−	0.862944i
$135$		0			0
$136$	−4.15307	−	2.39778i	−0.356123	−	0.205608i
$137$	−3.94148	+	6.82684i	−0.336743	+	0.583257i	−0.983818	−	0.179170i	$-0.942659\pi$
$137$	−3.94148	+	6.82684i	−0.336743	+	0.583257i	0.647075	+	0.762427i	$0.275992\pi$
$138$	5.44244			0.463291
$139$	2.05852	−	3.56546i	0.174601	−	0.302419i	−0.765422	−	0.643529i	$-0.777470\pi$
$139$	2.05852	−	3.56546i	0.174601	−	0.302419i	0.940023	+	0.341110i	$0.110803\pi$
$140$		0			0
$141$	−5.93149	+	3.42455i	−0.499521	+	0.288399i
$142$		−	15.8347i		−	1.32882i
$143$	16.2447	+	8.96676i	1.35845	+	0.749838i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	2.19677	+	3.80493i	0.181806	+	0.314898i
$147$	−4.06753	−	2.34839i	−0.335484	−	0.193692i
$148$	8.73961			0.718392
$149$	8.00644	+	4.62252i	0.655913	+	0.378692i	0.790718	−	0.612180i	$-0.209707\pi$
$149$	8.00644	+	4.62252i	0.655913	+	0.378692i	−0.134805	+	0.990872i	$0.543041\pi$
$150$		0			0
$151$		−	17.1479i		−	1.39548i	−0.716351	−	0.697740i	$-0.754189\pi$
$151$		−	17.1479i		−	1.39548i	0.716351	−	0.697740i	$-0.245811\pi$
$152$	1.39778	+	0.807007i	0.113375	+	0.0654569i
$153$	−4.15307	+	2.39778i	−0.335756	+	0.193849i
$154$	−6.76380	+	3.90508i	−0.545043	+	0.314681i
$155$		0			0
$156$	−3.08725	+	1.86250i	−0.247178	+	0.149119i
$157$		−	18.2791i		−	1.45883i	−0.684072	−	0.729415i	$-0.739793\pi$
$157$		−	18.2791i		−	1.45883i	0.684072	−	0.729415i	$-0.260207\pi$
$158$	−5.51910	−	9.55936i	−0.439076	−	0.760502i
$159$	−0.440982	−	0.763803i	−0.0349721	−	0.0605735i
$160$		0			0
$161$			8.25966i			0.650952i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	0.851911	−	1.47555i	0.0667269	−	0.115574i	−0.830732	−	0.556673i	$-0.812078\pi$
$163$	0.851911	−	1.47555i	0.0667269	−	0.115574i	0.897459	+	0.441098i	$0.145411\pi$
$164$			1.27500i			0.0995606i
$165$		0			0
$166$	0.489668	+	0.848130i	0.0380056	+	0.0658276i
$167$	−2.66717	−	4.61967i	−0.206392	−	0.357481i	0.744184	−	0.667975i	$-0.232839\pi$
$167$	−2.66717	−	4.61967i	−0.206392	−	0.357481i	−0.950575	+	0.310494i	$0.899505\pi$
$168$		−	1.51764i		−	0.117088i
$169$	−6.06218	+	11.5000i	−0.466321	+	0.884615i
$170$		0			0
$171$	1.39778	−	0.807007i	0.106891	−	0.0617134i
$172$	2.04965	−	1.18336i	0.156284	−	0.0902307i
$173$	15.3085	+	8.83839i	1.16389	+	0.671971i	0.952233	−	0.305374i	$-0.0987814\pi$
$173$	15.3085	+	8.83839i	1.16389	+	0.671971i	0.211655	+	0.977344i	$0.432115\pi$
$174$			9.87367i			0.748521i
$175$		0			0
$176$	4.45680	+	2.57313i	0.335944	+	0.193957i
$177$	−9.28788			−0.698120
$178$	−3.54146	−	2.04466i	−0.265444	−	0.153254i
$179$	10.7700	+	18.6542i	0.804987	+	1.39428i	0.916300	+	0.400493i	$0.131161\pi$
$179$	10.7700	+	18.6542i	0.804987	+	1.39428i	−0.111313	+	0.993785i	$0.535506\pi$
$180$		0			0
$181$	4.08328			0.303507			0.151754	−	0.988418i	$-0.451508\pi$
$181$	4.08328			0.303507			0.151754	+	0.988418i	$0.451508\pi$
$182$	−2.82660	−	4.68532i	−0.209522	−	0.347299i
$183$		−	12.4811i		−	0.922631i
$184$	4.71329	−	2.72122i	0.347469	−	0.200611i
$185$		0			0
$186$	4.94036	−	8.55695i	0.362245	−	0.627426i
$187$	24.6792			1.80472
$188$	−3.42455	+	5.93149i	−0.249761	+	0.432598i
$189$	−1.31431	−	0.758819i	−0.0956022	−	0.0551960i
$190$		0			0
$191$	6.47822	−	11.2206i	0.468747	−	0.811894i	−0.530615	−	0.847613i	$-0.678039\pi$
$191$	6.47822	−	11.2206i	0.468747	−	0.811894i	0.999362	+	0.0357192i	$0.0113722\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−4.32843	−	7.49706i	−0.311567	−	0.539650i	0.667135	−	0.744937i	$-0.267521\pi$
$193$	−4.32843	−	7.49706i	−0.311567	−	0.539650i	−0.978702	+	0.205287i	$0.934187\pi$
$194$	−5.71795			−0.410525
$195$		0			0
$196$	−4.69677			−0.335484
$197$	2.17415	+	3.76574i	0.154902	+	0.268298i	0.933023	−	0.359816i	$-0.117160\pi$
$197$	2.17415	+	3.76574i	0.154902	+	0.268298i	−0.778121	+	0.628114i	$0.783827\pi$
$198$	4.45680	−	2.57313i	0.316731	−	0.182865i
$199$	3.73351	−	6.46663i	0.264662	−	0.458407i	−0.702813	−	0.711374i	$-0.748073\pi$
$199$	3.73351	−	6.46663i	0.264662	−	0.458407i	0.967475	+	0.252967i	$0.0814064\pi$
$200$		0			0
$201$	−9.98930	−	5.76733i	−0.704591	−	0.406796i
$202$	−3.92687	+	6.80153i	−0.276293	+	0.478554i
$203$	−14.9847			−1.05172
$204$	−2.39778	+	4.15307i	−0.167878	+	0.290773i
$205$		0			0
$206$	2.74919	−	1.58725i	0.191545	−	0.110589i
$207$		−	5.44244i		−	0.378276i
$208$	−1.74238	+	3.15660i	−0.120813	+	0.218871i
$209$	−8.30614			−0.574548
$210$		0			0
$211$	−6.74384	−	11.6807i	−0.464265	−	0.804131i	0.534903	−	0.844914i	$-0.320348\pi$
$211$	−6.74384	−	11.6807i	−0.464265	−	0.804131i	−0.999168	+	0.0407826i	$0.987015\pi$
$212$	−0.763803	−	0.440982i	−0.0524582	−	0.0302868i
$213$	−15.8347			−1.08498
$214$	−11.9106	−	6.87662i	−0.814195	−	0.470076i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	12.9864	+	7.49768i	0.881571	+	0.508976i
$218$	−14.5401	+	8.39475i	−0.984782	+	0.568564i
$219$	3.80493	−	2.19677i	0.257113	−	0.148444i
$220$		0			0
$221$	0.332573	+	17.2874i	0.0223713	+	1.16288i
$222$		−	8.73961i		−	0.586565i
$223$	3.51047	+	6.08030i	0.235078	+	0.407167i	0.959295	−	0.282405i	$-0.0911321\pi$
$223$	3.51047	+	6.08030i	0.235078	+	0.407167i	−0.724217	+	0.689572i	$0.757799\pi$
$224$	−0.758819	−	1.31431i	−0.0507007	−	0.0878162i
$225$		0			0
$226$		−	9.65685i		−	0.642364i
$227$	4.29762	−	7.44370i	0.285243	−	0.494055i	−0.687425	−	0.726255i	$-0.741259\pi$
$227$	4.29762	−	7.44370i	0.285243	−	0.494055i	0.972668	+	0.232200i	$0.0745924\pi$
$228$	0.807007	−	1.39778i	0.0534454	−	0.0925701i
$229$		−	16.4086i		−	1.08431i	−0.840279	−	0.542155i	$-0.817609\pi$
$229$		−	16.4086i		−	1.08431i	0.840279	−	0.542155i	$-0.182391\pi$
$230$		0			0
$231$	3.90508	+	6.76380i	0.256936	+	0.445026i
$232$	4.93684	+	8.55085i	0.324119	+	0.561391i
$233$			6.94230i			0.454805i	0.973801	+	0.227403i	$0.0730233\pi$
$233$			6.94230i			0.454805i	−0.973801	+	0.227403i	$0.926977\pi$
$234$	1.86250	+	3.08725i	0.121756	+	0.201820i
$235$		0			0
$236$	−8.04354	+	4.64394i	−0.523590	+	0.302295i
$237$	−9.55936	+	5.51910i	−0.620947	+	0.358504i
$238$	−6.30286	−	3.63896i	−0.408554	−	0.235879i
$239$		−	18.3056i		−	1.18409i	−0.805904	−	0.592046i	$-0.798320\pi$
$239$		−	18.3056i		−	1.18409i	0.805904	−	0.592046i	$-0.201680\pi$
$240$		0			0
$241$	12.4906	+	7.21147i	0.804592	+	0.464532i	0.845074	−	0.534649i	$-0.179556\pi$
$241$	12.4906	+	7.21147i	0.804592	+	0.464532i	−0.0404822	+	0.999180i	$0.512889\pi$
$242$	−15.4840			−0.995352
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−6.24056	−	10.8090i	−0.399511	−	0.691973i
$245$		0			0
$246$	1.27500			0.0812909
$247$	−0.111932	−	5.81834i	−0.00712209	−	0.370212i
$248$		−	9.88072i		−	0.627426i
$249$	0.848130	−	0.489668i	0.0537480	−	0.0310314i
$250$		0			0
$251$	−3.88222	+	6.72420i	−0.245044	+	0.424428i	−0.962144	−	0.272542i	$-0.912136\pi$
$251$	−3.88222	+	6.72420i	−0.245044	+	0.424428i	0.717100	+	0.696970i	$0.245469\pi$
$252$	−1.51764			−0.0956022
$253$	−14.0041	+	24.2558i	−0.880432	+	1.52495i
$254$	−10.3843	−	5.99536i	−0.651566	−	0.376182i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−16.7841	+	9.69031i	−1.04696	+	0.604465i	−0.921798	−	0.387671i	$-0.873280\pi$
$257$	−16.7841	+	9.69031i	−1.04696	+	0.604465i	−0.125166	+	0.992136i	$0.539946\pi$
$258$	−1.18336	−	2.04965i	−0.0736731	−	0.127606i
$259$	13.2636			0.824158
$260$		0			0
$261$	9.87367			0.611165
$262$	10.1762	+	17.6257i	0.628687	+	1.08892i
$263$	1.64019	−	0.946961i	0.101138	−	0.0583921i	−0.448578	−	0.893744i	$-0.648069\pi$
$263$	1.64019	−	0.946961i	0.101138	−	0.0583921i	0.549716	+	0.835352i	$0.314736\pi$
$264$	2.57313	−	4.45680i	0.158365	−	0.274297i
$265$		0			0
$266$	2.12132	+	1.22474i	0.130066	+	0.0750939i
$267$	−2.04466	+	3.54146i	−0.125131	+	0.216734i
$268$	−11.5347			−0.704591
$269$	−2.30104	+	3.98551i	−0.140297	+	0.243001i	−0.927608	−	0.373554i	$-0.878139\pi$
$269$	−2.30104	+	3.98551i	−0.140297	+	0.243001i	0.787312	+	0.616555i	$0.211472\pi$
$270$		0			0
$271$	7.22596	−	4.17191i	0.438946	−	0.253426i	−0.264204	−	0.964467i	$-0.585109\pi$
$271$	7.22596	−	4.17191i	0.438946	−	0.253426i	0.703150	+	0.711041i	$0.251776\pi$
$272$			4.79555i			0.290773i
$273$	−4.68532	+	2.82660i	−0.283569	+	0.171074i
$274$	7.88296			0.476227
$275$		0			0
$276$	−2.72122	−	4.71329i	−0.163798	−	0.283707i
$277$	19.2585	+	11.1189i	1.15713	+	0.668068i	0.950614	−	0.310375i	$-0.100455\pi$
$277$	19.2585	+	11.1189i	1.15713	+	0.668068i	0.206514	+	0.978444i	$0.433788\pi$
$278$	−4.11704			−0.246924
$279$	−8.55695	−	4.94036i	−0.512291	−	0.295772i
$280$		0			0
$281$		−	20.0961i		−	1.19883i	−0.800437	−	0.599417i	$-0.795399\pi$
$281$		−	20.0961i		−	1.19883i	0.800437	−	0.599417i	$-0.204601\pi$
$282$	5.93149	+	3.42455i	0.353215	+	0.203929i
$283$	−0.623402	+	0.359921i	−0.0370574	+	0.0213951i	−0.518414	−	0.855130i	$-0.673477\pi$
$283$	−0.623402	+	0.359921i	−0.0370574	+	0.0213951i	0.481357	+	0.876525i	$0.340144\pi$
$284$	−13.7133	+	7.91737i	−0.813734	+	0.469810i
$285$		0			0
$286$	−0.356895	−	18.5517i	−0.0211037	−	1.09698i
$287$			1.93498i			0.114219i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	2.99867	+	5.19386i	0.176393	+	0.305521i
$290$		0			0
$291$			5.71795i			0.335192i
$292$	2.19677	−	3.80493i	0.128557	−	0.222666i
$293$	6.61389	−	11.4556i	0.386388	−	0.669243i	−0.605573	−	0.795790i	$-0.707056\pi$
$293$	6.61389	−	11.4556i	0.386388	−	0.669243i	0.991961	+	0.126547i	$0.0403894\pi$
$294$			4.69677i			0.273921i
$295$		0			0
$296$	−4.36981	−	7.56873i	−0.253990	−	0.439923i
$297$	−2.57313	−	4.45680i	−0.149308	−	0.258610i
$298$		−	9.24504i		−	0.535551i
$299$	−17.1796	−	9.48282i	−0.993521	−	0.548405i
$300$		0			0
$301$	3.11062	−	1.79592i	0.179293	−	0.103515i
$302$	−14.8506	+	8.57397i	−0.854553	+	0.493377i
$303$	6.80153	+	3.92687i	0.390738	+	0.225593i
$304$		−	1.61401i		−	0.0925701i
$305$		0			0
$306$	4.15307	+	2.39778i	0.237415	+	0.137072i
$307$	7.85174			0.448123			0.224061	−	0.974575i	$-0.428068\pi$
$307$	7.85174			0.448123			0.224061	+	0.974575i	$0.428068\pi$
$308$	6.76380	+	3.90508i	0.385403	+	0.222513i
$309$	−1.58725	−	2.74919i	−0.0902953	−	0.156396i
$310$		0			0
$311$	−15.7708			−0.894278			−0.447139	−	0.894465i	$-0.647557\pi$
$311$	−15.7708			−0.894278			−0.447139	+	0.894465i	$0.647557\pi$
$312$	3.15660	+	1.74238i	0.178707	+	0.0986430i
$313$			21.0613i			1.19045i	0.803558	+	0.595227i	$0.202938\pi$
$313$			21.0613i			1.19045i	−0.803558	+	0.595227i	$0.797062\pi$
$314$	−15.8301	+	9.13954i	−0.893347	+	0.515774i
$315$		0			0
$316$	−5.51910	+	9.55936i	−0.310474	+	0.537756i
$317$	−26.4141			−1.48357			−0.741783	−	0.670640i	$-0.766019\pi$
$317$	−26.4141			−1.48357			−0.741783	+	0.670640i	$0.766019\pi$
$318$	−0.440982	+	0.763803i	−0.0247290	+	0.0428319i
$319$	−44.0049	−	25.4063i	−2.46380	−	1.42248i
$320$		0			0
$321$	−6.87662	+	11.9106i	−0.383815	+	0.664787i
$322$	7.15307	−	4.12983i	0.398625	−	0.230146i
$323$	−3.87005	−	6.70312i	−0.215335	−	0.372972i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−1.70382			−0.0943660
$327$	8.39475	+	14.5401i	0.464231	+	0.804071i
$328$	1.10418	−	0.637499i	0.0609681	−	0.0352000i
$329$	−5.19722	+	9.00185i	−0.286532	+	0.496288i
$330$		0			0
$331$	17.6887	+	10.2126i	0.972260	+	0.561335i	0.899925	−	0.436046i	$-0.143621\pi$
$331$	17.6887	+	10.2126i	0.972260	+	0.561335i	0.0723356	+	0.997380i	$0.476955\pi$
$332$	0.489668	−	0.848130i	0.0268740	−	0.0465472i
$333$	−8.73961			−0.478928
$334$	−2.66717	+	4.61967i	−0.145941	+	0.252777i
$335$		0			0
$336$	−1.31431	+	0.758819i	−0.0717017	+	0.0413970i
$337$			13.1035i			0.713791i	0.934144	+	0.356895i	$0.116165\pi$
$337$			13.1035i			0.713791i	−0.934144	+	0.356895i	$0.883835\pi$
$338$	12.9904	−	0.500000i	0.706584	−	0.0271964i
$339$	−9.65685			−0.524488
$340$		0			0
$341$	25.4244	+	44.0363i	1.37681	+	2.38470i
$342$	−1.39778	−	0.807007i	−0.0755831	−	0.0436380i
$343$	−17.7515			−0.958489
$344$	−2.04965	−	1.18336i	−0.110510	−	0.0638028i
$345$		0			0
$346$		−	17.6768i		−	0.950310i
$347$	−15.3811	−	8.88027i	−0.825700	−	0.476718i	0.0266782	−	0.999644i	$-0.491507\pi$
$347$	−15.3811	−	8.88027i	−0.825700	−	0.476718i	−0.852378	+	0.522926i	$0.824840\pi$
$348$	8.55085	−	4.93684i	0.458374	−	0.264642i
$349$	−0.103747	+	0.0598981i	−0.00555343	+	0.00320627i	−0.502774	−	0.864418i	$-0.667687\pi$
$349$	−0.103747	+	0.0598981i	−0.00555343	+	0.00320627i	0.497221	+	0.867624i	$0.334354\pi$
$350$		0			0
$351$	3.08725	−	1.86250i	0.164785	−	0.0994130i
$352$		−	5.14626i		−	0.274297i
$353$	−3.77620	−	6.54057i	−0.200987	−	0.348119i	0.747860	−	0.663857i	$-0.231082\pi$
$353$	−3.77620	−	6.54057i	−0.200987	−	0.348119i	−0.948847	+	0.315737i	$0.897748\pi$
$354$	4.64394	+	8.04354i	0.246823	+	0.427510i
$355$		0			0
$356$			4.08933i			0.216734i
$357$	−3.63896	+	6.30286i	−0.192594	+	0.333583i
$358$	10.7700	−	18.6542i	0.569212	−	0.985903i
$359$			29.9693i			1.58172i	0.611997	+	0.790860i	$0.290366\pi$
$359$			29.9693i			1.58172i	−0.611997	+	0.790860i	$0.709634\pi$
$360$		0			0
$361$	−8.19748	−	14.1984i	−0.431446	−	0.747287i
$362$	−2.04164	−	3.53622i	−0.107306	−	0.185860i
$363$			15.4840i			0.812701i
$364$	−2.64431	+	4.79057i	−0.138599	+	0.251094i
$365$		0			0
$366$	−10.8090	+	6.24056i	−0.564994	+	0.326199i
$367$	−25.0232	+	14.4472i	−1.30620	+	0.754136i	−0.981460	−	0.191666i	$-0.938611\pi$
$367$	−25.0232	+	14.4472i	−1.30620	+	0.754136i	−0.324742	+	0.945802i	$0.605278\pi$
$368$	−4.71329	−	2.72122i	−0.245697	−	0.141853i
$369$		−	1.27500i		−	0.0663737i
$370$		0			0
$371$	−1.15918	−	0.669251i	−0.0601814	−	0.0347458i
$372$	−9.88072			−0.512291
$373$	12.7407	+	7.35583i	0.659687	+	0.380870i	0.792158	−	0.610317i	$-0.208958\pi$
$373$	12.7407	+	7.35583i	0.659687	+	0.380870i	−0.132471	+	0.991187i	$0.542291\pi$
$374$	−12.3396	−	21.3728i	−0.638065	−	1.10516i
$375$		0			0
$376$	6.84909			0.353215
$377$	17.2037	−	31.1672i	0.886036	−	1.60519i
$378$			1.51764i			0.0780589i
$379$	27.1285	−	15.6627i	1.39350	−	0.804537i	0.399798	−	0.916603i	$-0.369080\pi$
$379$	27.1285	−	15.6627i	1.39350	−	0.804537i	0.993701	+	0.112067i	$0.0357470\pi$
$380$		0			0
$381$	−5.99536	+	10.3843i	−0.307151	+	0.532002i
$382$	−12.9564			−0.662909
$383$	5.42368	−	9.39410i	0.277137	−	0.480016i	−0.693535	−	0.720423i	$-0.743948\pi$
$383$	5.42368	−	9.39410i	0.277137	−	0.480016i	0.970672	+	0.240407i	$0.0772810\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	−4.32843	+	7.49706i	−0.220311	+	0.381590i
$387$	−2.04965	+	1.18336i	−0.104189	+	0.0601538i
$388$	2.85898	+	4.95189i	0.145143	+	0.251394i
$389$	18.2977			0.927730			0.463865	−	0.885906i	$-0.346462\pi$
$389$	18.2977			0.927730			0.463865	+	0.885906i	$0.346462\pi$
$390$		0			0
$391$	−26.0995			−1.31991
$392$	2.34839	+	4.06753i	0.118611	+	0.205441i
$393$	17.6257	−	10.1762i	0.889098	−	0.513321i
$394$	2.17415	−	3.76574i	0.109532	−	0.189715i
$395$		0			0
$396$	−4.45680	−	2.57313i	−0.223962	−	0.129305i
$397$	0.153828	−	0.266438i	0.00772041	−	0.0133721i	−0.862139	−	0.506671i	$-0.830876\pi$
$397$	0.153828	−	0.266438i	0.00772041	−	0.0133721i	0.869860	+	0.493299i	$0.164209\pi$
$398$	−7.46702			−0.374288
$399$	1.22474	−	2.12132i	0.0613139	−	0.106199i
$400$		0			0
$401$	1.89266	−	1.09273i	0.0945149	−	0.0545682i	−0.451998	−	0.892019i	$-0.649288\pi$
$401$	1.89266	−	1.09273i	0.0945149	−	0.0545682i	0.546512	+	0.837451i	$0.315955\pi$
$402$			11.5347i			0.575296i
$403$	−30.5042	+	18.4029i	−1.51952	+	0.916711i
$404$	7.85374			0.390738
$405$		0			0
$406$	7.49233	+	12.9771i	0.371838	+	0.644042i
$407$	38.9507	+	22.4882i	1.93071	+	1.11470i
$408$	4.79555			0.237415
$409$	−32.6067	−	18.8255i	−1.61230	−	0.930860i	−0.988836	−	0.149006i	$-0.952393\pi$
$409$	−32.6067	−	18.8255i	−1.61230	−	0.930860i	−0.623461	−	0.781855i	$-0.714274\pi$
$410$		0			0
$411$		−	7.88296i		−	0.388838i
$412$	−2.74919	−	1.58725i	−0.135443	−	0.0781980i
$413$	−12.2072	+	7.04782i	−0.600676	+	0.346801i
$414$	−4.71329	+	2.72122i	−0.231646	+	0.133741i
$415$		0			0
$416$	3.60488	−	0.0693504i	0.176744	−	0.00340018i
$417$			4.11704i			0.201612i
$418$	4.15307	+	7.19333i	0.203133	+	0.351837i
$419$	13.5307	+	23.4359i	0.661020	+	1.14492i	0.980348	+	0.197276i	$0.0632096\pi$
$419$	13.5307	+	23.4359i	0.661020	+	1.14492i	−0.319328	+	0.947644i	$0.603457\pi$
$420$		0			0
$421$		−	11.9356i		−	0.581706i	−0.956768	−	0.290853i	$-0.906061\pi$
$421$		−	11.9356i		−	0.581706i	0.956768	−	0.290853i	$-0.0939390\pi$
$422$	−6.74384	+	11.6807i	−0.328285	+	0.568607i
$423$	3.42455	−	5.93149i	0.166507	−	0.288399i
$424$			0.881964i			0.0428319i
$425$		0			0
$426$	7.91737	+	13.7133i	0.383598	+	0.664411i
$427$	−9.47091	−	16.4041i	−0.458329	−	0.793850i
$428$			13.7532i			0.664787i
$429$	−18.5517	+	0.356895i	−0.895684	+	0.0172311i
$430$		0			0
$431$	25.9671	−	14.9921i	1.25079	−	0.722144i	0.279523	−	0.960139i	$-0.409824\pi$
$431$	25.9671	−	14.9921i	1.25079	−	0.722144i	0.971266	+	0.237995i	$0.0764903\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	18.1814	+	10.4971i	0.873744	+	0.504456i	0.868591	−	0.495530i	$-0.165026\pi$
$433$	18.1814	+	10.4971i	0.873744	+	0.504456i	0.00515336	+	0.999987i	$0.498360\pi$
$434$		−	14.9954i		−	0.719800i
$435$		0			0
$436$	14.5401	+	8.39475i	0.696346	+	0.402036i
$437$	8.78418			0.420204
$438$	−3.80493	−	2.19677i	−0.181806	−	0.104966i
$439$	−3.65685	−	6.33386i	−0.174532	−	0.302299i	0.765467	−	0.643475i	$-0.222508\pi$
$439$	−3.65685	−	6.33386i	−0.174532	−	0.302299i	−0.939999	+	0.341176i	$0.889175\pi$
$440$		0			0
$441$	4.69677			0.223656
$442$	14.8051	−	8.93173i	0.704205	−	0.424839i
$443$			12.8231i			0.609244i	0.952473	+	0.304622i	$0.0985301\pi$
$443$			12.8231i			0.609244i	−0.952473	+	0.304622i	$0.901470\pi$
$444$	−7.56873	+	4.36981i	−0.359196	+	0.207382i
$445$		0			0
$446$	3.51047	−	6.08030i	0.166225	−	0.287911i
$447$	−9.24504			−0.437276
$448$	−0.758819	+	1.31431i	−0.0358508	+	0.0620955i
$449$	2.73315	+	1.57798i	0.128985	+	0.0744696i	0.563104	−	0.826386i	$-0.309607\pi$
$449$	2.73315	+	1.57798i	0.128985	+	0.0744696i	−0.434119	+	0.900855i	$0.642940\pi$
$450$		0			0
$451$	−3.28074	+	5.68240i	−0.154484	+	0.267574i
$452$	−8.36308	+	4.82843i	−0.393366	+	0.227110i
$453$	8.57397	+	14.8506i	0.402840	+	0.697740i
$454$	−8.59524			−0.403395
$455$		0			0
$456$	−1.61401			−0.0755831
$457$	0.144671	+	0.250578i	0.00676743	+	0.0117215i	0.869389	−	0.494128i	$-0.164513\pi$
$457$	0.144671	+	0.250578i	0.00676743	+	0.0117215i	−0.862622	+	0.505849i	$0.831179\pi$
$458$	−14.2102	+	8.20429i	−0.664001	+	0.383361i
$459$	2.39778	−	4.15307i	0.111919	−	0.193849i
$460$		0			0
$461$	−3.07799	−	1.77708i	−0.143356	−	0.0827668i	0.426606	−	0.904437i	$-0.359709\pi$
$461$	−3.07799	−	1.77708i	−0.143356	−	0.0827668i	−0.569963	+	0.821671i	$0.693042\pi$
$462$	3.90508	−	6.76380i	0.181681	−	0.314681i
$463$	−12.1116			−0.562875			−0.281438	−	0.959580i	$-0.590811\pi$
$463$	−12.1116			−0.562875			−0.281438	+	0.959580i	$0.590811\pi$
$464$	4.93684	−	8.55085i	0.229187	−	0.396963i
$465$		0			0
$466$	6.01221	−	3.47115i	0.278510	−	0.160798i
$467$			29.9323i			1.38510i	0.721369	+	0.692550i	$0.243513\pi$
$467$			29.9323i			1.38510i	−0.721369	+	0.692550i	$0.756487\pi$
$468$	1.74238	−	3.15660i	0.0805417	−	0.145914i
$469$	−17.5054			−0.808326
$470$		0			0
$471$	9.13954	+	15.8301i	0.421128	+	0.729415i
$472$	8.04354	+	4.64394i	0.370234	+	0.213755i
$473$	12.1798			0.560029
$474$	9.55936	+	5.51910i	0.439076	+	0.253501i
$475$		0			0
$476$			7.27792i			0.333583i
$477$	0.763803	+	0.440982i	0.0349721	+	0.0201912i
$478$	−15.8531	+	9.15281i	−0.725106	+	0.418640i
$479$	−2.03012	+	1.17209i	−0.0927584	+	0.0535541i	−0.545662	−	0.838006i	$-0.683722\pi$
$479$	−2.03012	+	1.17209i	−0.0927584	+	0.0535541i	0.452903	+	0.891560i	$0.350388\pi$
$480$		0			0
$481$	−15.2278	+	27.5874i	−0.694326	+	1.25788i
$482$		−	14.4229i		−	0.656947i
$483$	−4.12983	−	7.15307i	−0.187914	−	0.325476i
$484$	7.74202	+	13.4096i	0.351910	+	0.609526i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	1.86689	−	3.23354i	0.0845968	−	0.146526i	−0.820623	−	0.571471i	$-0.806373\pi$
$487$	1.86689	−	3.23354i	0.0845968	−	0.146526i	0.905219	+	0.424945i	$0.139706\pi$
$488$	−6.24056	+	10.8090i	−0.282497	+	0.489299i
$489$			1.70382i			0.0770495i
$490$		0			0
$491$	−6.14261	−	10.6393i	−0.277212	−	0.480145i	0.693479	−	0.720477i	$-0.256077\pi$
$491$	−6.14261	−	10.6393i	−0.277212	−	0.480145i	−0.970691	+	0.240332i	$0.922744\pi$
$492$	−0.637499	−	1.10418i	−0.0287407	−	0.0497803i
$493$		−	47.3497i		−	2.13252i
$494$	−4.98286	+	3.00610i	−0.224189	+	0.135251i
$495$		0			0
$496$	−8.55695	+	4.94036i	−0.384219	+	0.221829i
$497$	−20.8118	+	12.0157i	−0.933537	+	0.538978i
$498$	−0.848130	−	0.489668i	−0.0380056	−	0.0219425i
$499$		−	17.8267i		−	0.798033i	−0.916944	−	0.399016i	$-0.869352\pi$
$499$		−	17.8267i		−	0.798033i	0.916944	−	0.399016i	$-0.130648\pi$
$500$		0			0
$501$	4.61967	+	2.66717i	0.206392	+	0.119160i
$502$	7.76444			0.346544
$503$	−4.83222	−	2.78988i	−0.215458	−	0.124395i	0.388387	−	0.921496i	$-0.373032\pi$
$503$	−4.83222	−	2.78988i	−0.215458	−	0.124395i	−0.603845	+	0.797101i	$0.706366\pi$
$504$	0.758819	+	1.31431i	0.0338005	+	0.0585442i
$505$		0			0
$506$	28.0082			1.24512
$507$	−0.500000	−	12.9904i	−0.0222058	−	0.576923i
$508$			11.9907i			0.532002i
$509$	−27.6679	+	15.9741i	−1.22636	+	0.708039i	−0.966266	−	0.257545i	$-0.917087\pi$
$509$	−27.6679	+	15.9741i	−1.22636	+	0.708039i	−0.260093	+	0.965584i	$0.583753\pi$
$510$		0			0
$511$	3.33391	−	5.77450i	0.147483	−	0.255449i
$512$	1.00000			0.0441942
$513$	−0.807007	+	1.39778i	−0.0356302	+	0.0617134i
$514$	16.7841	+	9.69031i	0.740315	+	0.427421i
$515$		0			0
$516$	−1.18336	+	2.04965i	−0.0520947	+	0.0902307i
$517$	−30.5250	+	17.6236i	−1.34249	+	0.775086i
$518$	−6.63179	−	11.4866i	−0.291384	−	0.504692i
$519$	−17.6768			−0.775925
$520$		0			0
$521$	−0.338338			−0.0148228			−0.00741142	−	0.999973i	$-0.502359\pi$
$521$	−0.338338			−0.0148228			−0.00741142	+	0.999973i	$0.502359\pi$
$522$	−4.93684	−	8.55085i	−0.216079	−	0.374261i
$523$	20.0102	−	11.5529i	0.874986	−	0.505174i	0.00598438	−	0.999982i	$-0.498095\pi$
$523$	20.0102	−	11.5529i	0.874986	−	0.505174i	0.869002	+	0.494808i	$0.164762\pi$
$524$	10.1762	−	17.6257i	0.444549	−	0.769981i
$525$		0			0
$526$	−1.64019	−	0.946961i	−0.0715155	−	0.0412895i
$527$	−23.6918	+	41.0353i	−1.03203	+	1.78753i
$528$	−5.14626			−0.223962
$529$	3.31008	−	5.73324i	0.143917	−	0.249271i
$530$		0			0
$531$	8.04354	−	4.64394i	0.349060	−	0.201530i
$532$		−	2.44949i		−	0.106199i
$533$	−4.02465	−	2.22153i	−0.174327	−	0.0962253i
$534$	4.08933			0.176963
$535$		0			0
$536$	5.76733	+	9.98930i	0.249111	+	0.431472i
$537$	−18.6542	−	10.7700i	−0.804987	−	0.464759i
$538$	4.60207			0.198409
$539$	−20.9326	−	12.0854i	−0.901629	−	0.520556i
$540$		0			0
$541$			28.8074i			1.23853i	0.785183	+	0.619264i	$0.212569\pi$
$541$			28.8074i			1.23853i	−0.785183	+	0.619264i	$0.787431\pi$
$542$	−7.22596	−	4.17191i	−0.310382	−	0.179199i
$543$	−3.53622	+	2.04164i	−0.151754	+	0.0876151i
$544$	4.15307	−	2.39778i	0.178062	−	0.102804i
$545$		0			0
$546$	4.79057	+	2.64431i	0.205018	+	0.113166i
$547$			33.4957i			1.43217i	0.698013	+	0.716086i	$0.254068\pi$
$547$			33.4957i			1.43217i	−0.698013	+	0.716086i	$0.745932\pi$
$548$	−3.94148	−	6.82684i	−0.168372	−	0.291628i
$549$	6.24056	+	10.8090i	0.266341	+	0.461315i
$550$		0			0
$551$			15.9362i			0.678907i
$552$	−2.72122	+	4.71329i	−0.115823	+	0.200611i
$553$	−8.37599	+	14.5076i	−0.356183	+	0.616928i
$554$		−	22.2377i		−	0.944791i
$555$		0			0
$556$	2.05852	+	3.56546i	0.0873007	+	0.151209i
$557$	−18.2991	−	31.6950i	−0.775358	−	1.34296i	−0.934593	−	0.355718i	$-0.884236\pi$
$557$	−18.2991	−	31.6950i	−0.775358	−	1.34296i	0.159236	−	0.987241i	$-0.449097\pi$
$558$			9.88072i			0.418284i
$559$	0.164134	+	8.53179i	0.00694211	+	0.360856i
$560$		0			0
$561$	−21.3728	+	12.3396i	−0.902361	+	0.520978i
$562$	−17.4038	+	10.0481i	−0.734133	+	0.423852i
$563$	−8.97514	−	5.18180i	−0.378257	−	0.218387i	0.298803	−	0.954315i	$-0.403413\pi$
$563$	−8.97514	−	5.18180i	−0.378257	−	0.218387i	−0.677060	+	0.735928i	$0.736746\pi$
$564$		−	6.84909i		−	0.288399i
$565$		0			0
$566$	0.623402	+	0.359921i	0.0262036	+	0.0151286i
$567$	1.51764			0.0637348
$568$	13.7133	+	7.91737i	0.575397	+	0.332206i
$569$	−15.7893	−	27.3479i	−0.661923	−	1.14648i	−0.980110	−	0.198456i	$-0.936407\pi$
$569$	−15.7893	−	27.3479i	−0.661923	−	1.14648i	0.318187	−	0.948028i	$-0.396926\pi$
$570$		0			0
$571$	33.7160			1.41097			0.705485	−	0.708725i	$-0.250729\pi$
$571$	33.7160			1.41097			0.705485	+	0.708725i	$0.250729\pi$
$572$	−15.8878	+	9.58492i	−0.664302	+	0.400766i
$573$			12.9564i			0.541263i
$574$	1.67575	−	0.967492i	0.0699443	−	0.0403823i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−40.8530			−1.70073			−0.850365	−	0.526193i	$-0.823619\pi$
$577$	−40.8530			−1.70073			−0.850365	+	0.526193i	$0.823619\pi$
$578$	2.99867	−	5.19386i	0.124728	−	0.216036i
$579$	7.49706	+	4.32843i	0.311567	+	0.179883i
$580$		0			0
$581$	0.743139	−	1.28715i	0.0308306	−	0.0534001i
$582$	4.95189	−	2.85898i	0.205263	−	0.118508i
$583$	−2.26941	−	3.93073i	−0.0939893	−	0.162794i
$584$	−4.39355			−0.181806
$585$		0			0
$586$	−13.2278			−0.546435
$587$	12.3224	+	21.3431i	0.508602	+	0.880924i	0.999950	+	0.00996119i	$0.00317080\pi$
$587$	12.3224	+	21.3431i	0.508602	+	0.880924i	−0.491349	+	0.870963i	$0.663496\pi$
$588$	4.06753	−	2.34839i	0.167742	−	0.0968459i
$589$	7.97381	−	13.8110i	0.328555	−	0.569074i
$590$		0			0
$591$	−3.76574	−	2.17415i	−0.154902	−	0.0894327i
$592$	−4.36981	+	7.56873i	−0.179598	+	0.311073i
$593$	21.4887			0.882436			0.441218	−	0.897400i	$-0.354547\pi$
$593$	21.4887			0.882436			0.441218	+	0.897400i	$0.354547\pi$
$594$	−2.57313	+	4.45680i	−0.105577	+	0.182865i
$595$		0			0
$596$	−8.00644	+	4.62252i	−0.327957	+	0.189346i
$597$			7.46702i			0.305605i
$598$	0.377435	+	19.6194i	0.0154345	+	0.802296i
$599$	29.1850			1.19247			0.596233	−	0.802812i	$-0.296663\pi$
$599$	29.1850			1.19247			0.596233	+	0.802812i	$0.296663\pi$
$600$		0			0
$601$	−3.31925	−	5.74910i	−0.135395	−	0.234511i	0.790353	−	0.612651i	$-0.209897\pi$
$601$	−3.31925	−	5.74910i	−0.135395	−	0.234511i	−0.925748	+	0.378140i	$0.876564\pi$
$602$	−3.11062	−	1.79592i	−0.126780	−	0.0731962i
$603$	11.5347			0.469727
$604$	14.8506	+	8.57397i	0.604260	+	0.348870i
$605$		0			0
$606$		−	7.85374i		−	0.319036i
$607$	20.2731	+	11.7047i	0.822860	+	0.475078i	0.851402	−	0.524514i	$-0.175753\pi$
$607$	20.2731	+	11.7047i	0.822860	+	0.475078i	−0.0285420	+	0.999593i	$0.509086\pi$
$608$	−1.39778	+	0.807007i	−0.0566874	+	0.0327285i
$609$	12.9771	−	7.49233i	0.525858	−	0.303605i
$610$		0			0
$611$	−12.7564	−	21.1448i	−0.516070	−	0.855428i
$612$		−	4.79555i		−	0.193849i
$613$	−2.62799	−	4.55182i	−0.106144	−	0.183846i	0.808061	−	0.589099i	$-0.200517\pi$
$613$	−2.62799	−	4.55182i	−0.106144	−	0.183846i	−0.914205	+	0.405252i	$0.867184\pi$
$614$	−3.92587	−	6.79981i	−0.158435	−	0.274418i
$615$		0			0
$616$		−	7.81017i		−	0.314681i
$617$	13.2027	−	22.8678i	0.531522	−	0.920622i	−0.467802	−	0.883834i	$-0.654954\pi$
$617$	13.2027	−	22.8678i	0.531522	−	0.920622i	0.999323	−	0.0367887i	$-0.0117129\pi$
$618$	−1.58725	+	2.74919i	−0.0638484	+	0.110589i
$619$			4.68483i			0.188299i	0.995558	+	0.0941497i	$0.0300132\pi$
$619$			4.68483i			0.188299i	−0.995558	+	0.0941497i	$0.969987\pi$
$620$		0			0
$621$	2.72122	+	4.71329i	0.109199	+	0.189138i
$622$	7.88538	+	13.6579i	0.316175	+	0.547631i
$623$			6.20612i			0.248643i
$624$	−0.0693504	−	3.60488i	−0.00277624	−	0.144311i
$625$		0			0
$626$	18.2396	−	10.5306i	0.729001	−	0.420889i
$627$	7.19333	−	4.15307i	0.287274	−	0.165858i
$628$	15.8301	+	9.13954i	0.631692	+	0.364707i
$629$			41.9113i			1.67111i
$630$		0			0
$631$	5.85249	+	3.37894i	0.232984	+	0.134513i	0.611948	−	0.790898i	$-0.290386\pi$
$631$	5.85249	+	3.37894i	0.232984	+	0.134513i	−0.378964	+	0.925411i	$0.623720\pi$
$632$	11.0382			0.439076
$633$	11.6807	+	6.74384i	0.464265	+	0.268044i
$634$	13.2071	+	22.8753i	0.524520	+	0.908494i
$635$		0			0
$636$	0.881964			0.0349721
$637$	8.18358	−	14.8258i	0.324245	−	0.587420i
$638$			50.8125i			2.01169i
$639$	13.7133	−	7.91737i	0.542489	−	0.313206i
$640$		0			0
$641$	14.6037	−	25.2943i	0.576810	−	0.999064i	−0.419033	−	0.907971i	$-0.637631\pi$
$641$	14.6037	−	25.2943i	0.576810	−	0.999064i	0.995842	−	0.0910927i	$-0.0290360\pi$
$642$	13.7532			0.542797
$643$	−4.03163	+	6.98298i	−0.158992	+	0.275382i	−0.934505	−	0.355949i	$-0.884158\pi$
$643$	−4.03163	+	6.98298i	−0.158992	+	0.275382i	0.775514	+	0.631331i	$0.217491\pi$
$644$	−7.15307	−	4.12983i	−0.281871	−	0.162738i
$645$		0			0
$646$	−3.87005	+	6.70312i	−0.152265	+	0.263731i
$647$	0.623849	−	0.360179i	0.0245260	−	0.0141601i	−0.487687	−	0.873019i	$-0.662159\pi$
$647$	0.623849	−	0.360179i	0.0245260	−	0.0141601i	0.512213	+	0.858859i	$0.328826\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−47.7979			−1.87623
$650$		0			0
$651$	−14.9954			−0.587714
$652$	0.851911	+	1.47555i	0.0333634	+	0.0577871i
$653$	23.0998	−	13.3367i	0.903963	−	0.521904i	0.0254795	−	0.999675i	$-0.491889\pi$
$653$	23.0998	−	13.3367i	0.903963	−	0.521904i	0.878484	+	0.477772i	$0.158555\pi$
$654$	8.39475	−	14.5401i	0.328261	−	0.568564i
$655$		0			0
$656$	−1.10418	−	0.637499i	−0.0431110	−	0.0248901i
$657$	−2.19677	+	3.80493i	−0.0857043	+	0.148444i
$658$	10.3944			0.405218
$659$	−9.02067	+	15.6243i	−0.351396	+	0.608635i	−0.986494	−	0.163796i	$-0.947626\pi$
$659$	−9.02067	+	15.6243i	−0.351396	+	0.608635i	0.635099	+	0.772431i	$0.280959\pi$
$660$		0			0
$661$	10.5904	−	6.11439i	0.411920	−	0.237822i	−0.279694	−	0.960089i	$-0.590233\pi$
$661$	10.5904	−	6.11439i	0.411920	−	0.237822i	0.691614	+	0.722267i	$0.256900\pi$
$662$		−	20.4252i		−	0.793847i
$663$	−8.93173	−	14.8051i	−0.346880	−	0.574981i
$664$	−0.979336			−0.0380056
$665$		0			0
$666$	4.36981	+	7.56873i	0.169327	+	0.293282i
$667$	46.5375	+	26.8684i	1.80194	+	1.04035i
$668$	5.33434			0.206392
$669$	−6.08030	−	3.51047i	−0.235078	−	0.135722i
$670$		0			0
$671$		−	64.2311i		−	2.47962i
$672$	1.31431	+	0.758819i	0.0507007	+	0.0292721i
$673$	4.03417	−	2.32913i	0.155506	−	0.0897814i	−0.420228	−	0.907419i	$-0.638050\pi$
$673$	4.03417	−	2.32913i	0.155506	−	0.0897814i	0.575734	+	0.817637i	$0.304716\pi$
$674$	11.3479	−	6.55173i	0.437106	−	0.252363i
$675$		0			0
$676$	−6.92820	−	11.0000i	−0.266469	−	0.423077i
$677$		−	22.1830i		−	0.852561i	−0.904591	−	0.426280i	$-0.859824\pi$
$677$		−	22.1830i		−	0.852561i	0.904591	−	0.426280i	$-0.140176\pi$
$678$	4.82843	+	8.36308i	0.185435	+	0.321182i
$679$	4.33889	+	7.51518i	0.166511	+	0.288406i
$680$		0			0
$681$			8.59524i			0.329370i
$682$	25.4244	−	44.0363i	0.973550	−	1.68624i
$683$	6.33735	−	10.9766i	0.242492	−	0.420008i	−0.718931	−	0.695081i	$-0.755369\pi$
$683$	6.33735	−	10.9766i	0.242492	−	0.420008i	0.961423	+	0.275072i	$0.0887019\pi$
$684$			1.61401i			0.0617134i
$685$		0			0
$686$	8.87574	+	15.3732i	0.338877	+	0.586952i
$687$	8.20429	+	14.2102i	0.313013	+	0.542155i
$688$			2.36673i			0.0902307i
$689$	2.72284	−	1.64266i	0.103732	−	0.0625803i
$690$		0			0
$691$	12.7634	−	7.36897i	0.485544	−	0.280329i	−0.237180	−	0.971466i	$-0.576223\pi$
$691$	12.7634	−	7.36897i	0.485544	−	0.280329i	0.722724	+	0.691137i	$0.242890\pi$
$692$	−15.3085	+	8.83839i	−0.581944	+	0.335985i
$693$	−6.76380	−	3.90508i	−0.256936	−	0.148342i
$694$			17.7605i			0.674181i
$695$		0			0
$696$	−8.55085	−	4.93684i	−0.324119	−	0.187130i
$697$	−6.11432			−0.231596
$698$	0.103747	+	0.0598981i	0.00392687	+	0.00226718i
$699$	−3.47115	−	6.01221i	−0.131291	−	0.227403i
$700$		0			0
$701$	25.9252			0.979182			0.489591	−	0.871952i	$-0.337146\pi$
$701$	25.9252			0.979182			0.489591	+	0.871952i	$0.337146\pi$
$702$	−3.15660	−	1.74238i	−0.119138	−	0.0657620i
$703$		−	14.1059i		−	0.532013i
$704$	−4.45680	+	2.57313i	−0.167972	+	0.0969786i
$705$		0			0
$706$	−3.77620	+	6.54057i	−0.142119	+	0.246158i
$707$	11.9191			0.448265
$708$	4.64394	−	8.04354i	0.174530	−	0.302295i
$709$	28.0091	+	16.1711i	1.05190	+	0.607317i	0.923182	−	0.384364i	$-0.125579\pi$
$709$	28.0091	+	16.1711i	1.05190	+	0.607317i	0.128722	+	0.991681i	$0.458913\pi$
$710$		0			0
$711$	5.51910	−	9.55936i	0.206982	−	0.358504i
$712$	3.54146	−	2.04466i	0.132722	−	0.0766270i
$713$	−26.8876	−	46.5707i	−1.00695	−	1.74409i
$714$	7.27792			0.272369
$715$		0			0
$716$	−21.5400			−0.804987
$717$	9.15281	+	15.8531i	0.341818	+	0.592046i
$718$	25.9542	−	14.9847i	0.968602	−	0.559223i
$719$	6.84506	−	11.8560i	0.255278	−	0.442154i	−0.709693	−	0.704511i	$-0.751166\pi$
$719$	6.84506	−	11.8560i	0.255278	−	0.442154i	0.964971	+	0.262357i	$0.0844998\pi$
$720$		0			0
$721$	−4.17228	−	2.40887i	−0.155384	−	0.0897108i
$722$	−8.19748	+	14.1984i	−0.305079	+	0.528412i
$723$	−14.4229			−0.536395
$724$	−2.04164	+	3.53622i	−0.0758769	+	0.131423i
$725$		0			0
$726$	13.4096	−	7.74202i	0.497676	−	0.287333i
$727$		−	49.1587i		−	1.82319i	−0.411084	−	0.911597i	$-0.634850\pi$
$727$		−	49.1587i		−	1.82319i	0.411084	−	0.911597i	$-0.365150\pi$
$728$	5.47091	−	0.105249i	0.202765	−	0.00390078i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	5.67489	+	9.82920i	0.209893	+	0.363546i
$732$	10.8090	+	6.24056i	0.399511	+	0.230658i
$733$	−44.9158			−1.65900			−0.829501	−	0.558505i	$-0.811375\pi$
$733$	−44.9158			−1.65900			−0.829501	+	0.558505i	$0.811375\pi$
$734$	25.0232	+	14.4472i	0.923625	+	0.533255i
$735$		0			0
$736$			5.44244i			0.200611i
$737$	−51.4076	−	29.6802i	−1.89362	−	1.09328i
$738$	−1.10418	+	0.637499i	−0.0406454	+	0.0234667i
$739$	−14.2102	+	8.20427i	−0.522731	+	0.301799i	−0.738051	−	0.674745i	$-0.764254\pi$
$739$	−14.2102	+	8.20427i	−0.522731	+	0.301799i	0.215320	+	0.976543i	$0.430920\pi$
$740$		0			0
$741$	3.00610	+	4.98286i	0.110432	+	0.183050i
$742$			1.33850i			0.0491379i
$743$	3.31268	+	5.73773i	0.121530	+	0.210497i	0.920371	−	0.391045i	$-0.127886\pi$
$743$	3.31268	+	5.73773i	0.121530	+	0.210497i	−0.798841	+	0.601542i	$0.794553\pi$
$744$	4.94036	+	8.55695i	0.181122	+	0.313713i
$745$		0			0
$746$		−	14.7117i		−	0.538632i
$747$	−0.489668	+	0.848130i	−0.0179160	+	0.0310314i
$748$	−12.3396	+	21.3728i	−0.451180	+	0.781467i
$749$			20.8724i			0.762662i
$750$		0			0
$751$	20.2807	+	35.1271i	0.740052	+	1.28181i	0.952471	+	0.304629i	$0.0985324\pi$
$751$	20.2807	+	35.1271i	0.740052	+	1.28181i	−0.212419	+	0.977179i	$0.568134\pi$
$752$	−3.42455	−	5.93149i	−0.124880	−	0.216299i
$753$		−	7.76444i		−	0.282952i
$754$	−35.5934	+	0.684743i	−1.29624	+	0.0249369i
$755$		0			0
$756$	1.31431	−	0.758819i	0.0478011	−	0.0275980i
$757$	−21.0685	+	12.1639i	−0.765748	+	0.442105i	−0.831356	−	0.555741i	$-0.812435\pi$
$757$	−21.0685	+	12.1639i	−0.765748	+	0.442105i	0.0656076	+	0.997845i	$0.479101\pi$
$758$	−27.1285	−	15.6627i	−0.985352	−	0.568893i
$759$		−	28.0082i		−	1.01663i
$760$		0			0
$761$	−0.355702	−	0.205364i	−0.0128942	−	0.00744446i	0.493539	−	0.869724i	$-0.335703\pi$
$761$	−0.355702	−	0.205364i	−0.0128942	−	0.00744446i	−0.506433	+	0.862279i	$0.669036\pi$
$762$	11.9907			0.434378
$763$	22.0667	+	12.7402i	0.798867	+	0.461226i
$764$	6.47822	+	11.2206i	0.234374	+	0.405947i
$765$		0			0
$766$	−10.8474			−0.391931
$767$	−0.644118	−	33.4817i	−0.0232578	−	1.20896i
$768$		−	1.00000i		−	0.0360844i
$769$	36.0692	−	20.8246i	1.30069	−	0.750954i	0.320168	−	0.947361i	$-0.396261\pi$
$769$	36.0692	−	20.8246i	1.30069	−	0.750954i	0.980522	+	0.196407i	$0.0629273\pi$
$770$		0			0
$771$	9.69031	−	16.7841i	0.348988	−	0.604465i
$772$	8.65685			0.311567
$773$	−25.8739	+	44.8150i	−0.930621	+	1.61188i	−0.148358	+	0.988934i	$0.547399\pi$
$773$	−25.8739	+	44.8150i	−0.930621	+	1.61188i	−0.782262	+	0.622949i	$0.785934\pi$
$774$	2.04965	+	1.18336i	0.0736731	+	0.0425352i
$775$		0			0
$776$	2.85898	−	4.95189i	0.102631	−	0.177763i
$777$	−11.4866	+	6.63179i	−0.412079	+	0.237914i
$778$	−9.14884	−	15.8463i	−0.328002	−	0.568116i
$779$	2.05786			0.0737306
$780$		0			0
$781$	−81.4898			−2.91593
$782$	13.0498	+	22.6029i	0.466659	+	0.808276i
$783$	−8.55085	+	4.93684i	−0.305582	+	0.176428i
$784$	2.34839	−	4.06753i	0.0838710	−	0.145269i
$785$		0			0
$786$	−17.6257	−	10.1762i	−0.628687	−	0.362973i
$787$	8.60630	−	14.9066i	0.306782	−	0.531361i	−0.670875	−	0.741571i	$-0.734081\pi$
$787$	8.60630	−	14.9066i	0.306782	−	0.531361i	0.977656	+	0.210209i	$0.0674146\pi$
$788$	−4.34831			−0.154902
$789$	−0.946961	+	1.64019i	−0.0337127	+	0.0583921i
$790$		0			0
$791$	−12.6921	+	7.32780i	−0.451280	+	0.260547i
$792$			5.14626i			0.182865i
$793$	44.9930	−	0.865570i	1.59775	−	0.0307373i
$794$	−0.307656			−0.0109183
$795$		0			0
$796$	3.73351	+	6.46663i	0.132331	+	0.229204i
$797$	21.3976	+	12.3539i	0.757943	+	0.437599i	0.828557	−	0.559905i	$-0.189162\pi$
$797$	21.3976	+	12.3539i	0.757943	+	0.437599i	−0.0706135	+	0.997504i	$0.522496\pi$
$798$	−2.44949			−0.0867110
$799$	−28.4448	−	16.4226i	−1.00630	−	0.580990i
$800$		0			0
$801$		−	4.08933i		−	0.144489i
$802$	−1.89266	−	1.09273i	−0.0668322	−	0.0385856i
$803$	19.5812	−	11.3052i	0.691004	−	0.398951i
$804$	9.98930	−	5.76733i	0.352296	−	0.203398i
$805$		0			0
$806$	31.1894	+	17.2160i	1.09860	+	0.606408i
$807$		−	4.60207i		−	0.162001i
$808$	−3.92687	−	6.80153i	−0.138147	−	0.239277i
$809$	12.5285	+	21.7001i	0.440480	+	0.762934i	0.997725	−	0.0674144i	$-0.0214750\pi$
$809$	12.5285	+	21.7001i	0.440480	+	0.762934i	−0.557245	+	0.830348i	$0.688142\pi$
$810$		0			0
$811$		−	35.2387i		−	1.23740i	−0.785628	−	0.618699i	$-0.787660\pi$
$811$		−	35.2387i		−	1.23740i	0.785628	−	0.618699i	$-0.212340\pi$
$812$	7.49233	−	12.9771i	0.262929	−	0.455407i
$813$	−4.17191	+	7.22596i	−0.146315	+	0.253426i
$814$		−	44.9764i		−	1.57642i
$815$		0			0
$816$	−2.39778	−	4.15307i	−0.0839390	−	0.145387i
$817$	−1.90997	−	3.30816i	−0.0668213	−	0.115738i
$818$			37.6510i			1.31644i
$819$	2.64431	−	4.79057i	0.0923996	−	0.167396i
$820$		0			0
$821$	−26.5342	+	15.3195i	−0.926049	+	0.534655i	−0.885560	−	0.464525i	$-0.846225\pi$
$821$	−26.5342	+	15.3195i	−0.926049	+	0.534655i	−0.0404892	+	0.999180i	$0.512892\pi$
$822$	−6.82684	+	3.94148i	−0.238113	+	0.137475i
$823$	−30.9943	−	17.8946i	−1.08039	−	0.623765i	−0.149390	−	0.988778i	$-0.547731\pi$
$823$	−30.9943	−	17.8946i	−1.08039	−	0.623765i	−0.931002	+	0.365014i	$0.881064\pi$
$824$			3.17449i			0.110589i
$825$		0			0
$826$	12.2072	+	7.04782i	0.424742	+	0.245225i
$827$	−7.53716			−0.262093			−0.131046	−	0.991376i	$-0.541834\pi$
$827$	−7.53716			−0.262093			−0.131046	+	0.991376i	$0.541834\pi$
$828$	4.71329	+	2.72122i	0.163798	+	0.0945690i
$829$	25.9628	+	44.9688i	0.901724	+	1.56183i	0.825256	+	0.564759i	$0.191031\pi$
$829$	25.9628	+	44.9688i	0.901724	+	1.56183i	0.0764677	+	0.997072i	$0.475636\pi$
$830$		0			0
$831$	−22.2377			−0.771419
$832$	−1.86250	−	3.08725i	−0.0645706	−	0.107031i
$833$		−	22.5236i		−	0.780398i
$834$	3.56546	−	2.05852i	0.123462	−	0.0712807i
$835$		0			0
$836$	4.15307	−	7.19333i	0.143637	−	0.248787i
$837$	9.88072			0.341528
$838$	13.5307	−	23.4359i	0.467412	−	0.809581i
$839$	−6.72183	−	3.88085i	−0.232063	−	0.133982i	0.379460	−	0.925208i	$-0.376110\pi$
$839$	−6.72183	−	3.88085i	−0.232063	−	0.133982i	−0.611524	+	0.791226i	$0.709443\pi$
$840$		0			0
$841$	−34.2447	+	59.3135i	−1.18085	+	2.04529i
$842$	−10.3365	+	5.96780i	−0.356221	+	0.205664i
$843$	10.0481	+	17.4038i	0.346074	+	0.599417i
$844$	13.4877			0.464265
$845$		0			0
$846$	−6.84909			−0.235477
$847$	11.7496	+	20.3509i	0.403720	+	0.699264i
$848$	0.763803	−	0.440982i	0.0262291	−	0.0151434i
$849$	0.359921	−	0.623402i	0.0123525	−	0.0213951i
$850$		0			0
$851$	−41.1924	−	23.7824i	−1.41206	−	0.815251i
$852$	7.91737	−	13.7133i	0.271245	−	0.469810i
$853$	13.8072			0.472751			0.236376	−	0.971662i	$-0.424040\pi$
$853$	13.8072			0.472751			0.236376	+	0.971662i	$0.424040\pi$
$854$	−9.47091	+	16.4041i	−0.324088	+	0.561337i
$855$		0			0
$856$	11.9106	−	6.87662i	0.407098	−	0.235038i
$857$		−	40.8095i		−	1.39403i	−0.717059	−	0.697013i	$-0.754512\pi$
$857$		−	40.8095i		−	1.39403i	0.717059	−	0.697013i	$-0.245488\pi$
$858$	9.58492	+	15.8878i	0.327224	+	0.542400i
$859$	−24.7784			−0.845427			−0.422713	−	0.906263i	$-0.638922\pi$
$859$	−24.7784			−0.845427			−0.422713	+	0.906263i	$0.638922\pi$
$860$		0			0
$861$	−0.967492	−	1.67575i	−0.0329720	−	0.0571093i
$862$	−25.9671	−	14.9921i	−0.884442	−	0.510633i
$863$	−27.0018			−0.919153			−0.459577	−	0.888138i	$-0.651999\pi$
$863$	−27.0018			−0.919153			−0.459577	+	0.888138i	$0.651999\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$		−	20.9941i		−	0.713409i
$867$	−5.19386	−	2.99867i	−0.176393	−	0.101840i
$868$	−12.9864	+	7.49768i	−0.440786	+	0.254488i
$869$	−49.1950	+	28.4027i	−1.66883	+	0.963497i
$870$		0			0
$871$	20.0978	−	36.4102i	0.680987	−	1.23371i
$872$		−	16.7895i		−	0.568564i
$873$	−2.85898	−	4.95189i	−0.0967617	−	0.167596i
$874$	−4.39209	−	7.60732i	−0.148565	−	0.257322i
$875$		0			0
$876$			4.39355i			0.148444i
$877$	−14.1364	+	24.4850i	−0.477352	+	0.826799i	−0.999663	−	0.0259566i	$-0.991737\pi$
$877$	−14.1364	+	24.4850i	−0.477352	+	0.826799i	0.522311	+	0.852755i	$0.325070\pi$
$878$	−3.65685	+	6.33386i	−0.123413	+	0.213757i
$879$			13.2278i			0.446162i
$880$		0			0
$881$	−9.37195	−	16.2327i	−0.315749	−	0.546894i	0.663847	−	0.747868i	$-0.268922\pi$
$881$	−9.37195	−	16.2327i	−0.315749	−	0.546894i	−0.979596	+	0.200975i	$0.935589\pi$
$882$	−2.34839	−	4.06753i	−0.0790743	−	0.136961i
$883$		−	54.1400i		−	1.82196i	−0.412456	−	0.910978i	$-0.635329\pi$
$883$		−	54.1400i		−	1.82196i	0.412456	−	0.910978i	$-0.364671\pi$
$884$	−15.1376	−	8.35569i	−0.509134	−	0.281032i
$885$		0			0
$886$	11.1051	−	6.41155i	0.373084	−	0.215400i
$887$	21.4881	−	12.4062i	0.721500	−	0.416558i	−0.0938043	−	0.995591i	$-0.529903\pi$
$887$	21.4881	−	12.4062i	0.721500	−	0.416558i	0.815305	+	0.579032i	$0.196569\pi$
$888$	7.56873	+	4.36981i	0.253990	+	0.146641i
$889$			18.1976i			0.610327i
$890$		0			0
$891$	4.45680	+	2.57313i	0.149308	+	0.0862032i
$892$	−7.02093			−0.235078
$893$	9.57351	+	5.52727i	0.320365	+	0.184963i
$894$	4.62252	+	8.00644i	0.154600	+	0.267776i
$895$		0			0
$896$	1.51764			0.0507007
$897$	19.6194	−	0.377435i	0.655072	−	0.0126022i
$898$		−	3.15597i		−	0.105316i
$899$	84.4885	−	48.7795i	2.81785	−	1.62689i
$900$		0			0
$901$	2.11475	−	3.66286i	0.0704526	−	0.122028i
$902$	6.56147			0.218473
$903$	−1.79592	+	3.11062i	−0.0597645	+	0.103515i
$904$	8.36308	+	4.82843i	0.278152	+	0.160591i
$905$		0			0
$906$	8.57397	−	14.8506i	0.284851	−	0.493377i
$907$	−13.6416	+	7.87598i	−0.452962	+	0.261517i	−0.709080	−	0.705128i	$-0.750890\pi$
$907$	−13.6416	+	7.87598i	−0.452962	+	0.261517i	0.256119	+	0.966645i	$0.417556\pi$
$908$	4.29762	+	7.44370i	0.142622	+	0.247028i
$909$	−7.85374			−0.260492
$910$		0			0
$911$	−5.58458			−0.185025			−0.0925126	−	0.995712i	$-0.529490\pi$
$911$	−5.58458			−0.185025			−0.0925126	+	0.995712i	$0.529490\pi$
$912$	0.807007	+	1.39778i	0.0267227	+	0.0462850i
$913$	4.36470	−	2.51996i	0.144450	−	0.0833985i
$914$	0.144671	−	0.250578i	0.00478530	−	0.00828838i
$915$		0			0
$916$	14.2102	+	8.20429i	0.469520	+	0.271077i
$917$	15.4438	−	26.7494i	0.509998	−	0.883343i
$918$	−4.79555			−0.158277
$919$	3.54423	−	6.13879i	0.116913	−	0.202500i	−0.801630	−	0.597821i	$-0.796033\pi$
$919$	3.54423	−	6.13879i	0.116913	−	0.202500i	0.918543	+	0.395321i	$0.129367\pi$
$920$		0			0
$921$	−6.79981	+	3.92587i	−0.224061	+	0.129362i
$922$			3.55416i			0.117050i
$923$	−1.09815	−	57.0824i	−0.0361459	−	1.87889i
$924$	−7.81017			−0.256936
$925$		0			0
$926$	6.05582	+	10.4890i	0.199006	+	0.344689i
$927$	2.74919	+	1.58725i	0.0902953	+	0.0521320i
$928$	−9.87367			−0.324119
$929$	−3.64324	−	2.10342i	−0.119531	−	0.0690111i	0.439043	−	0.898466i	$-0.355318\pi$
$929$	−3.64324	−	2.10342i	−0.119531	−	0.0690111i	−0.558573	+	0.829455i	$0.688651\pi$
$930$		0			0
$931$			7.58066i			0.248446i
$932$	−6.01221	−	3.47115i	−0.196936	−	0.113701i
$933$	13.6579	−	7.88538i	0.447139	−	0.258156i
$934$	25.9221	−	14.9661i	0.848198	−	0.489707i
$935$		0			0
$936$	−3.60488	+	0.0693504i	−0.117829	+	0.00226679i
$937$		−	25.2818i		−	0.825920i	−0.910749	−	0.412960i	$-0.864495\pi$
$937$		−	25.2818i		−	0.825920i	0.910749	−	0.412960i	$-0.135505\pi$
$938$	8.75272	+	15.1601i	0.285786	+	0.494996i
$939$	−10.5306	−	18.2396i	−0.343654	−	0.595227i
$940$		0			0
$941$		−	42.2457i		−	1.37717i	−0.725156	−	0.688585i	$-0.758232\pi$
$941$		−	42.2457i		−	1.37717i	0.725156	−	0.688585i	$-0.241768\pi$
$942$	9.13954	−	15.8301i	0.297782	−	0.515774i
$943$	3.46955	−	6.00944i	0.112984	−	0.195694i
$944$		−	9.28788i		−	0.302295i
$945$		0			0
$946$	−6.08991	−	10.5480i	−0.198000	−	0.342946i
$947$	20.6529	+	35.7719i	0.671130	+	1.16243i	0.977584	+	0.210546i	$0.0675240\pi$
$947$	20.6529	+	35.7719i	0.671130	+	1.16243i	−0.306454	+	0.951885i	$0.599143\pi$
$948$		−	11.0382i		−	0.358504i
$949$	8.18299	+	13.5640i	0.265631	+	0.440305i
$950$		0			0
$951$	22.8753	−	13.2071i	0.741783	−	0.428268i
$952$	6.30286	−	3.63896i	0.204277	−	0.117939i
$953$	−9.86484	−	5.69547i	−0.319553	−	0.184494i	0.331640	−	0.943406i	$-0.392398\pi$
$953$	−9.86484	−	5.69547i	−0.319553	−	0.184494i	−0.651193	+	0.758912i	$0.725731\pi$
$954$		−	0.881964i		−	0.0285546i
$955$		0			0
$956$	15.8531	+	9.15281i	0.512727	+	0.296023i
$957$	50.8125			1.64254
$958$	2.03012	+	1.17209i	0.0655901	+	0.0378685i
$959$	−5.98174	−	10.3607i	−0.193160	−	0.334564i
$960$		0			0
$961$	−66.6286			−2.14931
$962$	31.5053	−	0.606095i	1.01577	−	0.0195413i
$963$		−	13.7532i		−	0.443192i
$964$	−12.4906	+	7.21147i	−0.402296	+	0.232266i
$965$		0			0
$966$	−4.12983	+	7.15307i	−0.132875	+	0.230146i
$967$	39.5770			1.27271			0.636355	−	0.771396i	$-0.280441\pi$
$967$	39.5770			1.27271			0.636355	+	0.771396i	$0.280441\pi$
$968$	7.74202	−	13.4096i	0.248838	−	0.431000i
$969$	6.70312	+	3.87005i	0.215335	+	0.124324i
$970$		0			0
$971$	−1.93166	+	3.34574i	−0.0619900	+	0.107370i	−0.895355	−	0.445353i	$-0.853078\pi$
$971$	−1.93166	+	3.34574i	−0.0619900	+	0.107370i	0.833365	+	0.552723i	$0.186411\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	3.12409	+	5.41108i	0.100154	+	0.173471i
$974$	−3.73378			−0.119638
$975$		0			0
$976$	12.4811			0.399511
$977$	20.2068	+	34.9993i	0.646474	+	1.11973i	0.983959	+	0.178395i	$0.0570906\pi$
$977$	20.2068	+	34.9993i	0.646474	+	1.11973i	−0.337485	+	0.941331i	$0.609576\pi$
$978$	1.47555	−	0.851911i	0.0471830	−	0.0272411i
$979$	−10.5224	+	18.2253i	−0.336297	+	0.582483i
$980$		0			0
$981$	−14.5401	−	8.39475i	−0.464231	−	0.268024i
$982$	−6.14261	+	10.6393i	−0.196018	+	0.339514i
$983$	15.5229			0.495103			0.247551	−	0.968875i	$-0.420374\pi$
$983$	15.5229			0.495103			0.247551	+	0.968875i	$0.420374\pi$
$984$	−0.637499	+	1.10418i	−0.0203227	+	0.0352000i
$985$		0			0
$986$	−41.0061	+	23.6749i	−1.30590	+	0.753961i
$987$		−	10.3944i		−	0.330859i
$988$	5.09479	+	2.81223i	0.162087	+	0.0894690i
$989$	−12.8808			−0.409585
$990$		0			0
$991$	18.5010	+	32.0447i	0.587704	+	1.01793i	0.994532	+	0.104428i	$0.0333012\pi$
$991$	18.5010	+	32.0447i	0.587704	+	1.01793i	−0.406829	+	0.913504i	$0.633365\pi$
$992$	8.55695	+	4.94036i	0.271684	+	0.156857i
$993$	−20.4252			−0.648173
$994$	20.8118	+	12.0157i	0.660111	+	0.381115i
$995$		0			0
$996$			0.979336i			0.0310314i
$997$	−41.5979	−	24.0165i	−1.31742	−	0.760611i	−0.334105	−	0.942536i	$-0.608434\pi$
$997$	−41.5979	−	24.0165i	−1.31742	−	0.760611i	−0.983312	+	0.181925i	$0.941767\pi$
$998$	−15.4384	+	8.91335i	−0.488693	+	0.282147i
$999$	7.56873	−	4.36981i	0.239464	−	0.138255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.i.49.1		8
5.2	odd	4		1950.2.bc.f.751.3	yes	8
5.3	odd	4		1950.2.bc.e.751.2	✓	8
5.4	even	2		1950.2.y.l.49.4		8
13.4	even	6		1950.2.y.l.199.4		8
65.4	even	6	inner	1950.2.y.i.199.1		8
65.17	odd	12		1950.2.bc.f.901.3	yes	8
65.43	odd	12		1950.2.bc.e.901.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.i.49.1		8	1.1	even	1	trivial
1950.2.y.i.199.1		8	65.4	even	6	inner
1950.2.y.l.49.4		8	5.4	even	2
1950.2.y.l.199.4		8	13.4	even	6
1950.2.bc.e.751.2	✓	8	5.3	odd	4
1950.2.bc.e.901.2	yes	8	65.43	odd	12
1950.2.bc.f.751.3	yes	8	5.2	odd	4
1950.2.bc.f.901.3	yes	8	65.17	odd	12

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.758819 + 1.31431i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.758819 + 1.31431i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.45680 + 2.57313i) q^{11} -1.00000i q^{12} +(-1.86250 - 3.08725i) q^{13} +1.51764 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.15307 - 2.39778i) q^{17} -1.00000 q^{18} +(1.39778 + 0.807007i) q^{19} -1.51764i q^{21} +(4.45680 + 2.57313i) q^{22} +(4.71329 - 2.72122i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.74238 + 3.15660i) q^{26} +1.00000i q^{27} +(-0.758819 - 1.31431i) q^{28} +(4.93684 + 8.55085i) q^{29} -9.88072i q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.57313 - 4.45680i) q^{33} +4.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(-4.36981 - 7.56873i) q^{37} -1.61401i q^{38} +(3.15660 + 1.74238i) q^{39} +(1.10418 - 0.637499i) q^{41} +(-1.31431 + 0.758819i) q^{42} +(-2.04965 - 1.18336i) q^{43} -5.14626i q^{44} +(-4.71329 - 2.72122i) q^{46} +6.84909 q^{47} +(0.866025 + 0.500000i) q^{48} +(2.34839 + 4.06753i) q^{49} +4.79555 q^{51} +(3.60488 - 0.0693504i) q^{52} +0.881964i q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.758819 + 1.31431i) q^{56} -1.61401 q^{57} +(4.93684 - 8.55085i) q^{58} +(8.04354 + 4.64394i) q^{59} +(-6.24056 + 10.8090i) q^{61} +(-8.55695 + 4.94036i) q^{62} +(0.758819 + 1.31431i) q^{63} +1.00000 q^{64} -5.14626 q^{66} +(5.76733 + 9.98930i) q^{67} +(4.15307 - 2.39778i) q^{68} +(-2.72122 + 4.71329i) q^{69} +(13.7133 + 7.91737i) q^{71} +(0.500000 - 0.866025i) q^{72} -4.39355 q^{73} +(-4.36981 + 7.56873i) q^{74} +(-1.39778 + 0.807007i) q^{76} -7.81017i q^{77} +(-0.0693504 - 3.60488i) q^{78} +11.0382 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.10418 - 0.637499i) q^{82} -0.979336 q^{83} +(1.31431 + 0.758819i) q^{84} +2.36673i q^{86} +(-8.55085 - 4.93684i) q^{87} +(-4.45680 + 2.57313i) q^{88} +(3.54146 - 2.04466i) q^{89} +(5.47091 - 0.105249i) q^{91} +5.44244i q^{92} +(4.94036 + 8.55695i) q^{93} +(-3.42455 - 5.93149i) q^{94} -1.00000i q^{96} +(2.85898 - 4.95189i) q^{97} +(2.34839 - 4.06753i) q^{98} +5.14626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9} - 12 q^{11} + 8 q^{14} - 4 q^{16} - 8 q^{18} - 12 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{28} - 4 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{36} - 16 q^{37} + 24 q^{43} + 12 q^{46} + 32 q^{47} + 16 q^{49} - 8 q^{51} - 4 q^{56} - 4 q^{58} + 12 q^{59} - 16 q^{61} - 24 q^{62} + 4 q^{63} + 8 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{69} + 60 q^{71} + 4 q^{72} - 24 q^{73} - 16 q^{74} + 12 q^{76} + 8 q^{79} - 4 q^{81} - 8 q^{83} - 12 q^{87} - 12 q^{88} - 24 q^{89} + 8 q^{91} + 4 q^{93} - 16 q^{94} + 16 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9 - 12 * q^11 + 8 * q^14 - 4 * q^16 - 8 * q^18 - 12 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^28 - 4 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^36 - 16 * q^37 + 24 * q^43 + 12 * q^46 + 32 * q^47 + 16 * q^49 - 8 * q^51 - 4 * q^56 - 4 * q^58 + 12 * q^59 - 16 * q^61 - 24 * q^62 + 4 * q^63 + 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^69 + 60 * q^71 + 4 * q^72 - 24 * q^73 - 16 * q^74 + 12 * q^76 + 8 * q^79 - 4 * q^81 - 8 * q^83 - 12 * q^87 - 12 * q^88 - 24 * q^89 + 8 * q^91 + 4 * q^93 - 16 * q^94 + 16 * q^98

Introduction

L-functions

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