LMFDB - Embedded newform 1950.2.y.i.199.1

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			199.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.i.49.1

$q$-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 $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

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

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	0.686239	−	0.727376i	$-0.259260\pi$
$7$	−0.758819	−	1.31431i	−0.286807	−	0.496764i	−0.973046	+	0.230612i	$0.925927\pi$
$8$	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	−0.356415	−	0.934328i	$-0.616001\pi$
$11$	−4.45680	−	2.57313i	−1.34377	−	0.775829i	−0.987359	+	0.158499i	$0.949335\pi$
$12$			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	−0.910391	−	0.413750i	$-0.864219\pi$
$17$	−4.15307	+	2.39778i	−1.00727	+	0.581546i	−0.0968774	+	0.995296i	$0.530885\pi$
$18$	−1.00000			−0.235702
$19$	1.39778	−	0.807007i	0.320672	−	0.185140i	−0.331020	−	0.943624i	$-0.607393\pi$
$19$	1.39778	−	0.807007i	0.320672	−	0.185140i	0.651692	+	0.758484i	$0.274059\pi$
$20$		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	0.903111	−	0.429407i	$-0.141277\pi$
$23$	4.71329	+	2.72122i	0.982789	+	0.567414i	0.0796783	+	0.996821i	$0.474611\pi$
$24$	−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	0.112425	−	0.993660i	$-0.464138\pi$
$29$	4.93684	−	8.55085i	0.916747	−	1.58785i	0.804323	−	0.594193i	$-0.202528\pi$
$30$		0			0
$31$			9.88072i			1.77463i	0.461164	+	0.887315i	$0.347432\pi$
$31$			9.88072i			1.77463i	−0.461164	+	0.887315i	$0.652568\pi$
$32$	−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	0.243245	+	0.969965i	$0.421788\pi$
$37$	−4.36981	+	7.56873i	−0.718392	+	1.24429i	−0.961637	+	0.274326i	$0.911545\pi$
$38$			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	0.583738	−	0.811942i	$-0.301590\pi$
$41$	1.10418	+	0.637499i	0.172444	+	0.0995606i	−0.411294	+	0.911503i	$0.634923\pi$
$42$	−1.31431	−	0.758819i	−0.202803	−	0.117088i
$43$	−2.04965	+	1.18336i	−0.312568	+	0.180461i	−0.648075	−	0.761576i	$-0.724426\pi$
$43$	−2.04965	+	1.18336i	−0.312568	+	0.180461i	0.335507	+	0.942038i	$0.391092\pi$
$44$			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	$-0.980707\pi$
$53$		−	0.881964i		−	0.121147i	0.998164	−	0.0605735i	$-0.0192930\pi$
$54$	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	0.125322	−	0.992116i	$-0.460004\pi$
$59$	8.04354	−	4.64394i	1.04718	−	0.604590i	0.921859	+	0.387526i	$0.126670\pi$
$60$		0			0
$61$	−6.24056	−	10.8090i	−0.799022	−	1.38395i	−0.920254	−	0.391322i	$-0.872018\pi$
$61$	−6.24056	−	10.8090i	−0.799022	−	1.38395i	0.121232	−	0.992624i	$-0.461315\pi$
$62$	−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	−0.262248	−	0.965001i	$-0.584464\pi$
$67$	5.76733	−	9.98930i	0.704591	−	1.22039i	0.966839	−	0.255387i	$-0.0822029\pi$
$68$	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	0.642623	−	0.766182i	$-0.277846\pi$
$71$	13.7133	−	7.91737i	1.62747	−	0.939619i	0.984845	−	0.173437i	$-0.0554874\pi$
$72$	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	0.675812	−	0.737074i	$-0.263793\pi$
$89$	3.54146	+	2.04466i	0.375394	+	0.216734i	−0.300418	+	0.953808i	$0.597126\pi$
$90$		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	0.973877	−	0.227076i	$-0.0729165\pi$
$97$	2.85898	+	4.95189i	0.290285	+	0.502789i	−0.683592	+	0.729864i	$0.739583\pi$
$98$	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	−0.992547	−	0.121862i	$-0.961113\pi$
$101$	−3.92687	+	6.80153i	−0.390738	+	0.676778i	0.601809	+	0.798640i	$0.294447\pi$
$102$	−2.39778	+	4.15307i	−0.237415	+	0.411215i
$103$		−	3.17449i		−	0.312792i	−0.987694	−	0.156396i	$-0.950012\pi$
$103$		−	3.17449i		−	0.312792i	0.987694	−	0.156396i	$-0.0499876\pi$
$104$	−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	0.949239	−	0.314555i	$-0.101855\pi$
$107$	11.9106	+	6.87662i	1.15145	+	0.664787i	0.202207	+	0.979343i	$0.435189\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$			16.7895i			1.60814i	0.594533	+	0.804071i	$0.297337\pi$
$109$			16.7895i			1.60814i	−0.594533	+	0.804071i	$0.702663\pi$
$110$		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	−0.0520785	−	0.998643i	$-0.516585\pi$
$113$	8.36308	−	4.82843i	0.786732	−	0.454220i	0.838811	+	0.544423i	$0.183251\pi$
$114$	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	0.884099	−	0.467300i	$-0.154773\pi$
$127$	10.3843	+	5.99536i	0.921454	+	0.532002i	0.0373555	+	0.999302i	$0.488107\pi$
$128$	−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	0.647075	−	0.762427i	$-0.275992\pi$
$137$	−3.94148	−	6.82684i	−0.336743	−	0.583257i	−0.983818	+	0.179170i	$0.942659\pi$
$138$	5.44244			0.463291
$139$	2.05852	+	3.56546i	0.174601	+	0.302419i	0.940023	−	0.341110i	$-0.110803\pi$
$139$	2.05852	+	3.56546i	0.174601	+	0.302419i	−0.765422	+	0.643529i	$0.777470\pi$
$140$		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	−0.134805	−	0.990872i	$-0.543041\pi$
$149$	8.00644	−	4.62252i	0.655913	−	0.378692i	0.790718	+	0.612180i	$0.209707\pi$
$150$		0			0
$151$			17.1479i			1.39548i	0.716351	+	0.697740i	$0.245811\pi$
$151$			17.1479i			1.39548i	−0.716351	+	0.697740i	$0.754189\pi$
$152$	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	$0.260207\pi$
$157$			18.2791i			1.45883i	−0.684072	+	0.729415i	$0.739793\pi$
$158$	−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	0.897459	−	0.441098i	$-0.145411\pi$
$163$	0.851911	+	1.47555i	0.0667269	+	0.115574i	−0.830732	+	0.556673i	$0.812078\pi$
$164$		−	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	−0.950575	−	0.310494i	$-0.899505\pi$
$167$	−2.66717	+	4.61967i	−0.206392	+	0.357481i	0.744184	+	0.667975i	$0.232839\pi$
$168$			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	0.211655	−	0.977344i	$-0.432115\pi$
$173$	15.3085	−	8.83839i	1.16389	−	0.671971i	0.952233	+	0.305374i	$0.0987814\pi$
$174$		−	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	−0.111313	−	0.993785i	$-0.535506\pi$
$179$	10.7700	−	18.6542i	0.804987	−	1.39428i	0.916300	−	0.400493i	$-0.131161\pi$
$180$		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	0.999362	−	0.0357192i	$-0.0113722\pi$
$191$	6.47822	+	11.2206i	0.468747	+	0.811894i	−0.530615	+	0.847613i	$0.678039\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−4.32843	+	7.49706i	−0.311567	+	0.539650i	−0.978702	−	0.205287i	$-0.934187\pi$
$193$	−4.32843	+	7.49706i	−0.311567	+	0.539650i	0.667135	+	0.744937i	$0.267521\pi$
$194$	−5.71795			−0.410525
$195$		0			0
$196$	−4.69677			−0.335484
$197$	2.17415	−	3.76574i	0.154902	−	0.268298i	−0.778121	−	0.628114i	$-0.783827\pi$
$197$	2.17415	−	3.76574i	0.154902	−	0.268298i	0.933023	+	0.359816i	$0.117160\pi$
$198$	4.45680	+	2.57313i	0.316731	+	0.182865i
$199$	3.73351	+	6.46663i	0.264662	+	0.458407i	0.967475	−	0.252967i	$-0.0814064\pi$
$199$	3.73351	+	6.46663i	0.264662	+	0.458407i	−0.702813	+	0.711374i	$0.748073\pi$
$200$		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	−0.999168	−	0.0407826i	$-0.987015\pi$
$211$	−6.74384	+	11.6807i	−0.464265	+	0.804131i	0.534903	+	0.844914i	$0.320348\pi$
$212$	−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	−0.724217	−	0.689572i	$-0.757799\pi$
$223$	3.51047	−	6.08030i	0.235078	−	0.407167i	0.959295	+	0.282405i	$0.0911321\pi$
$224$	−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	0.972668	−	0.232200i	$-0.0745924\pi$
$227$	4.29762	+	7.44370i	0.285243	+	0.494055i	−0.687425	+	0.726255i	$0.741259\pi$
$228$	0.807007	+	1.39778i	0.0534454	+	0.0925701i
$229$			16.4086i			1.08431i	0.840279	+	0.542155i	$0.182391\pi$
$229$			16.4086i			1.08431i	−0.840279	+	0.542155i	$0.817609\pi$
$230$		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	$-0.926977\pi$
$233$		−	6.94230i		−	0.454805i	0.973801	−	0.227403i	$-0.0730233\pi$
$234$	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	$0.201680\pi$
$239$			18.3056i			1.18409i	−0.805904	+	0.592046i	$0.798320\pi$
$240$		0			0
$241$	12.4906	−	7.21147i	0.804592	−	0.464532i	−0.0404822	−	0.999180i	$-0.512889\pi$
$241$	12.4906	−	7.21147i	0.804592	−	0.464532i	0.845074	+	0.534649i	$0.179556\pi$
$242$	−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	0.717100	−	0.696970i	$-0.245469\pi$
$251$	−3.88222	−	6.72420i	−0.245044	−	0.424428i	−0.962144	+	0.272542i	$0.912136\pi$
$252$	−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	−0.125166	−	0.992136i	$-0.539946\pi$
$257$	−16.7841	−	9.69031i	−1.04696	−	0.604465i	−0.921798	+	0.387671i	$0.873280\pi$
$258$	−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	0.549716	−	0.835352i	$-0.314736\pi$
$263$	1.64019	+	0.946961i	0.101138	+	0.0583921i	−0.448578	+	0.893744i	$0.648069\pi$
$264$	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	0.787312	−	0.616555i	$-0.211472\pi$
$269$	−2.30104	−	3.98551i	−0.140297	−	0.243001i	−0.927608	+	0.373554i	$0.878139\pi$
$270$		0			0
$271$	7.22596	+	4.17191i	0.438946	+	0.253426i	0.703150	−	0.711041i	$-0.251776\pi$
$271$	7.22596	+	4.17191i	0.438946	+	0.253426i	−0.264204	+	0.964467i	$0.585109\pi$
$272$		−	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	0.206514	−	0.978444i	$-0.433788\pi$
$277$	19.2585	−	11.1189i	1.15713	−	0.668068i	0.950614	+	0.310375i	$0.100455\pi$
$278$	−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	$0.204601\pi$
$281$			20.0961i			1.19883i	−0.800437	+	0.599417i	$0.795399\pi$
$282$	5.93149	−	3.42455i	0.353215	−	0.203929i
$283$	−0.623402	−	0.359921i	−0.0370574	−	0.0213951i	0.481357	−	0.876525i	$-0.340144\pi$
$283$	−0.623402	−	0.359921i	−0.0370574	−	0.0213951i	−0.518414	+	0.855130i	$0.673477\pi$
$284$	−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	0.991961	−	0.126547i	$-0.0403894\pi$
$293$	6.61389	+	11.4556i	0.386388	+	0.669243i	−0.605573	+	0.795790i	$0.707056\pi$
$294$		−	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	$-0.797062\pi$
$313$		−	21.0613i		−	1.19045i	0.803558	−	0.595227i	$-0.202938\pi$
$314$	−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	0.0723356	−	0.997380i	$-0.476955\pi$
$331$	17.6887	−	10.2126i	0.972260	−	0.561335i	0.899925	+	0.436046i	$0.143621\pi$
$332$	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	$-0.883835\pi$
$337$		−	13.1035i		−	0.713791i	0.934144	−	0.356895i	$-0.116165\pi$
$338$	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	−0.852378	−	0.522926i	$-0.824840\pi$
$347$	−15.3811	+	8.88027i	−0.825700	+	0.476718i	0.0266782	+	0.999644i	$0.491507\pi$
$348$	8.55085	+	4.93684i	0.458374	+	0.264642i
$349$	−0.103747	−	0.0598981i	−0.00555343	−	0.00320627i	0.497221	−	0.867624i	$-0.334354\pi$
$349$	−0.103747	−	0.0598981i	−0.00555343	−	0.00320627i	−0.502774	+	0.864418i	$0.667687\pi$
$350$		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	−0.948847	−	0.315737i	$-0.897748\pi$
$353$	−3.77620	+	6.54057i	−0.200987	+	0.348119i	0.747860	+	0.663857i	$0.231082\pi$
$354$	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	$-0.709634\pi$
$359$		−	29.9693i		−	1.58172i	0.611997	−	0.790860i	$-0.290366\pi$
$360$		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	−0.324742	−	0.945802i	$-0.605278\pi$
$367$	−25.0232	−	14.4472i	−1.30620	−	0.754136i	−0.981460	+	0.191666i	$0.938611\pi$
$368$	−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	−0.132471	−	0.991187i	$-0.542291\pi$
$373$	12.7407	−	7.35583i	0.659687	−	0.380870i	0.792158	+	0.610317i	$0.208958\pi$
$374$	−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	0.993701	−	0.112067i	$-0.0357470\pi$
$379$	27.1285	+	15.6627i	1.39350	+	0.804537i	0.399798	+	0.916603i	$0.369080\pi$
$380$		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	0.970672	−	0.240407i	$-0.0772810\pi$
$383$	5.42368	+	9.39410i	0.277137	+	0.480016i	−0.693535	+	0.720423i	$0.743948\pi$
$384$	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	0.869860	−	0.493299i	$-0.164209\pi$
$397$	0.153828	+	0.266438i	0.00772041	+	0.0133721i	−0.862139	+	0.506671i	$0.830876\pi$
$398$	−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	0.546512	−	0.837451i	$-0.315955\pi$
$401$	1.89266	+	1.09273i	0.0945149	+	0.0545682i	−0.451998	+	0.892019i	$0.649288\pi$
$402$		−	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	−0.623461	+	0.781855i	$0.714274\pi$
$409$	−32.6067	+	18.8255i	−1.61230	+	0.930860i	−0.988836	+	0.149006i	$0.952393\pi$
$410$		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	−0.319328	−	0.947644i	$-0.603457\pi$
$419$	13.5307	−	23.4359i	0.661020	−	1.14492i	0.980348	−	0.197276i	$-0.0632096\pi$
$420$		0			0
$421$			11.9356i			0.581706i	0.956768	+	0.290853i	$0.0939390\pi$
$421$			11.9356i			0.581706i	−0.956768	+	0.290853i	$0.906061\pi$
$422$	−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	0.971266	−	0.237995i	$-0.0764903\pi$
$431$	25.9671	+	14.9921i	1.25079	+	0.722144i	0.279523	+	0.960139i	$0.409824\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	18.1814	−	10.4971i	0.873744	−	0.504456i	0.00515336	−	0.999987i	$-0.498360\pi$
$433$	18.1814	−	10.4971i	0.873744	−	0.504456i	0.868591	+	0.495530i	$0.165026\pi$
$434$			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	−0.939999	−	0.341176i	$-0.889175\pi$
$439$	−3.65685	+	6.33386i	−0.174532	+	0.302299i	0.765467	+	0.643475i	$0.222508\pi$
$440$		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	$-0.901470\pi$
$443$		−	12.8231i		−	0.609244i	0.952473	−	0.304622i	$-0.0985301\pi$
$444$	−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	−0.434119	−	0.900855i	$-0.642940\pi$
$449$	2.73315	−	1.57798i	0.128985	−	0.0744696i	0.563104	+	0.826386i	$0.309607\pi$
$450$		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	−0.862622	−	0.505849i	$-0.831179\pi$
$457$	0.144671	−	0.250578i	0.00676743	−	0.0117215i	0.869389	+	0.494128i	$0.164513\pi$
$458$	−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	−0.569963	−	0.821671i	$-0.693042\pi$
$461$	−3.07799	+	1.77708i	−0.143356	+	0.0827668i	0.426606	+	0.904437i	$0.359709\pi$
$462$	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	$-0.756487\pi$
$467$		−	29.9323i		−	1.38510i	0.721369	−	0.692550i	$-0.243513\pi$
$468$	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	0.452903	−	0.891560i	$-0.350388\pi$
$479$	−2.03012	−	1.17209i	−0.0927584	−	0.0535541i	−0.545662	+	0.838006i	$0.683722\pi$
$480$		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	0.905219	−	0.424945i	$-0.139706\pi$
$487$	1.86689	+	3.23354i	0.0845968	+	0.146526i	−0.820623	+	0.571471i	$0.806373\pi$
$488$	−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	−0.970691	−	0.240332i	$-0.922744\pi$
$491$	−6.14261	+	10.6393i	−0.277212	+	0.480145i	0.693479	+	0.720477i	$0.256077\pi$
$492$	−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	$0.130648\pi$
$499$			17.8267i			0.798033i	−0.916944	+	0.399016i	$0.869352\pi$
$500$		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	−0.603845	−	0.797101i	$-0.706366\pi$
$503$	−4.83222	+	2.78988i	−0.215458	+	0.124395i	0.388387	+	0.921496i	$0.373032\pi$
$504$	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	−0.260093	−	0.965584i	$-0.583753\pi$
$509$	−27.6679	−	15.9741i	−1.22636	−	0.708039i	−0.966266	+	0.257545i	$0.917087\pi$
$510$		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	0.869002	−	0.494808i	$-0.164762\pi$
$523$	20.0102	+	11.5529i	0.874986	+	0.505174i	0.00598438	+	0.999982i	$0.498095\pi$
$524$	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	$-0.787431\pi$
$541$		−	28.8074i		−	1.23853i	0.785183	−	0.619264i	$-0.212569\pi$
$542$	−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	$-0.745932\pi$
$547$		−	33.4957i		−	1.43217i	0.698013	−	0.716086i	$-0.254068\pi$
$548$	−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	0.159236	+	0.987241i	$0.449097\pi$
$557$	−18.2991	+	31.6950i	−0.775358	+	1.34296i	−0.934593	+	0.355718i	$0.884236\pi$
$558$		−	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	−0.677060	−	0.735928i	$-0.736746\pi$
$563$	−8.97514	+	5.18180i	−0.378257	+	0.218387i	0.298803	+	0.954315i	$0.403413\pi$
$564$			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	0.318187	+	0.948028i	$0.396926\pi$
$569$	−15.7893	+	27.3479i	−0.661923	+	1.14648i	−0.980110	+	0.198456i	$0.936407\pi$
$570$		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	−0.491349	−	0.870963i	$-0.663496\pi$
$587$	12.3224	−	21.3431i	0.508602	−	0.880924i	0.999950	−	0.00996119i	$-0.00317080\pi$
$588$	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	−0.925748	−	0.378140i	$-0.876564\pi$
$601$	−3.31925	+	5.74910i	−0.135395	+	0.234511i	0.790353	+	0.612651i	$0.209897\pi$
$602$	−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	−0.0285420	−	0.999593i	$-0.509086\pi$
$607$	20.2731	−	11.7047i	0.822860	−	0.475078i	0.851402	+	0.524514i	$0.175753\pi$
$608$	−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	−0.914205	−	0.405252i	$-0.867184\pi$
$613$	−2.62799	+	4.55182i	−0.106144	+	0.183846i	0.808061	+	0.589099i	$0.200517\pi$
$614$	−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	0.999323	+	0.0367887i	$0.0117129\pi$
$617$	13.2027	+	22.8678i	0.531522	+	0.920622i	−0.467802	+	0.883834i	$0.654954\pi$
$618$	−1.58725	−	2.74919i	−0.0638484	−	0.110589i
$619$		−	4.68483i		−	0.188299i	−0.995558	−	0.0941497i	$-0.969987\pi$
$619$		−	4.68483i		−	0.188299i	0.995558	−	0.0941497i	$-0.0300132\pi$
$620$		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	−0.378964	−	0.925411i	$-0.623720\pi$
$631$	5.85249	−	3.37894i	0.232984	−	0.134513i	0.611948	+	0.790898i	$0.290386\pi$
$632$	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	0.995842	+	0.0910927i	$0.0290360\pi$
$641$	14.6037	+	25.2943i	0.576810	+	0.999064i	−0.419033	+	0.907971i	$0.637631\pi$
$642$	13.7532			0.542797
$643$	−4.03163	−	6.98298i	−0.158992	−	0.275382i	0.775514	−	0.631331i	$-0.217491\pi$
$643$	−4.03163	−	6.98298i	−0.158992	−	0.275382i	−0.934505	+	0.355949i	$0.884158\pi$
$644$	−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	0.512213	−	0.858859i	$-0.328826\pi$
$647$	0.623849	+	0.360179i	0.0245260	+	0.0141601i	−0.487687	+	0.873019i	$0.662159\pi$
$648$	−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	0.878484	−	0.477772i	$-0.158555\pi$
$653$	23.0998	+	13.3367i	0.903963	+	0.521904i	0.0254795	+	0.999675i	$0.491889\pi$
$654$	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	0.635099	−	0.772431i	$-0.280959\pi$
$659$	−9.02067	−	15.6243i	−0.351396	−	0.608635i	−0.986494	+	0.163796i	$0.947626\pi$
$660$		0			0
$661$	10.5904	+	6.11439i	0.411920	+	0.237822i	0.691614	−	0.722267i	$-0.256900\pi$
$661$	10.5904	+	6.11439i	0.411920	+	0.237822i	−0.279694	+	0.960089i	$0.590233\pi$
$662$			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	0.575734	−	0.817637i	$-0.304716\pi$
$673$	4.03417	+	2.32913i	0.155506	+	0.0897814i	−0.420228	+	0.907419i	$0.638050\pi$
$674$	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	$0.140176\pi$
$677$			22.1830i			0.852561i	−0.904591	+	0.426280i	$0.859824\pi$
$678$	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	0.961423	−	0.275072i	$-0.0887019\pi$
$683$	6.33735	+	10.9766i	0.242492	+	0.420008i	−0.718931	+	0.695081i	$0.755369\pi$
$684$		−	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	0.722724	−	0.691137i	$-0.242890\pi$
$691$	12.7634	+	7.36897i	0.485544	+	0.280329i	−0.237180	+	0.971466i	$0.576223\pi$
$692$	−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	0.128722	−	0.991681i	$-0.458913\pi$
$709$	28.0091	−	16.1711i	1.05190	−	0.607317i	0.923182	+	0.384364i	$0.125579\pi$
$710$		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	0.964971	−	0.262357i	$-0.0844998\pi$
$719$	6.84506	+	11.8560i	0.255278	+	0.442154i	−0.709693	+	0.704511i	$0.751166\pi$
$720$		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	$0.365150\pi$
$727$			49.1587i			1.82319i	−0.411084	+	0.911597i	$0.634850\pi$
$728$	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	0.215320	−	0.976543i	$-0.430920\pi$
$739$	−14.2102	−	8.20427i	−0.522731	−	0.301799i	−0.738051	+	0.674745i	$0.764254\pi$
$740$		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	−0.798841	−	0.601542i	$-0.794553\pi$
$743$	3.31268	−	5.73773i	0.121530	−	0.210497i	0.920371	+	0.391045i	$0.127886\pi$
$744$	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	−0.212419	−	0.977179i	$-0.568134\pi$
$751$	20.2807	−	35.1271i	0.740052	−	1.28181i	0.952471	−	0.304629i	$-0.0985324\pi$
$752$	−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	0.0656076	−	0.997845i	$-0.479101\pi$
$757$	−21.0685	−	12.1639i	−0.765748	−	0.442105i	−0.831356	+	0.555741i	$0.812435\pi$
$758$	−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	−0.506433	−	0.862279i	$-0.669036\pi$
$761$	−0.355702	+	0.205364i	−0.0128942	+	0.00744446i	0.493539	+	0.869724i	$0.335703\pi$
$762$	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	0.980522	−	0.196407i	$-0.0629273\pi$
$769$	36.0692	+	20.8246i	1.30069	+	0.750954i	0.320168	+	0.947361i	$0.396261\pi$
$770$		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	−0.782262	−	0.622949i	$-0.785934\pi$
$773$	−25.8739	−	44.8150i	−0.930621	−	1.61188i	−0.148358	−	0.988934i	$-0.547399\pi$
$774$	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	0.977656	−	0.210209i	$-0.0674146\pi$
$787$	8.60630	+	14.9066i	0.306782	+	0.531361i	−0.670875	+	0.741571i	$0.734081\pi$
$788$	−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	−0.0706135	−	0.997504i	$-0.522496\pi$
$797$	21.3976	−	12.3539i	0.757943	−	0.437599i	0.828557	+	0.559905i	$0.189162\pi$
$798$	−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	−0.557245	−	0.830348i	$-0.688142\pi$
$809$	12.5285	−	21.7001i	0.440480	−	0.762934i	0.997725	+	0.0674144i	$0.0214750\pi$
$810$		0			0
$811$			35.2387i			1.23740i	0.785628	+	0.618699i	$0.212340\pi$
$811$			35.2387i			1.23740i	−0.785628	+	0.618699i	$0.787660\pi$
$812$	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	−0.0404892	−	0.999180i	$-0.512892\pi$
$821$	−26.5342	−	15.3195i	−0.926049	−	0.534655i	−0.885560	+	0.464525i	$0.846225\pi$
$822$	−6.82684	−	3.94148i	−0.238113	−	0.137475i
$823$	−30.9943	+	17.8946i	−1.08039	+	0.623765i	−0.931002	−	0.365014i	$-0.881064\pi$
$823$	−30.9943	+	17.8946i	−1.08039	+	0.623765i	−0.149390	+	0.988778i	$0.547731\pi$
$824$		−	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	0.0764677	−	0.997072i	$-0.475636\pi$
$829$	25.9628	−	44.9688i	0.901724	−	1.56183i	0.825256	−	0.564759i	$-0.191031\pi$
$830$		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	−0.611524	−	0.791226i	$-0.709443\pi$
$839$	−6.72183	+	3.88085i	−0.232063	+	0.133982i	0.379460	+	0.925208i	$0.376110\pi$
$840$		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	$0.245488\pi$
$857$			40.8095i			1.39403i	−0.717059	+	0.697013i	$0.754512\pi$
$858$	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	0.522311	−	0.852755i	$-0.325070\pi$
$877$	−14.1364	−	24.4850i	−0.477352	−	0.826799i	−0.999663	+	0.0259566i	$0.991737\pi$
$878$	−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	−0.979596	−	0.200975i	$-0.935589\pi$
$881$	−9.37195	+	16.2327i	−0.315749	+	0.546894i	0.663847	+	0.747868i	$0.268922\pi$
$882$	−2.34839	+	4.06753i	−0.0790743	+	0.136961i
$883$			54.1400i			1.82196i	0.412456	+	0.910978i	$0.364671\pi$
$883$			54.1400i			1.82196i	−0.412456	+	0.910978i	$0.635329\pi$
$884$	−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	0.815305	−	0.579032i	$-0.196569\pi$
$887$	21.4881	+	12.4062i	0.721500	+	0.416558i	−0.0938043	+	0.995591i	$0.529903\pi$
$888$	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	0.256119	−	0.966645i	$-0.417556\pi$
$907$	−13.6416	−	7.87598i	−0.452962	−	0.261517i	−0.709080	+	0.705128i	$0.750890\pi$
$908$	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	0.918543	−	0.395321i	$-0.129367\pi$
$919$	3.54423	+	6.13879i	0.116913	+	0.202500i	−0.801630	+	0.597821i	$0.796033\pi$
$920$		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	−0.558573	−	0.829455i	$-0.688651\pi$
$929$	−3.64324	+	2.10342i	−0.119531	+	0.0690111i	0.439043	+	0.898466i	$0.355318\pi$
$930$		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	$0.135505\pi$
$937$			25.2818i			0.825920i	−0.910749	+	0.412960i	$0.864495\pi$
$938$	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	$0.241768\pi$
$941$			42.2457i			1.37717i	−0.725156	+	0.688585i	$0.758232\pi$
$942$	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	−0.306454	−	0.951885i	$-0.599143\pi$
$947$	20.6529	−	35.7719i	0.671130	−	1.16243i	0.977584	−	0.210546i	$-0.0675240\pi$
$948$			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	−0.651193	−	0.758912i	$-0.725731\pi$
$953$	−9.86484	+	5.69547i	−0.319553	+	0.184494i	0.331640	+	0.943406i	$0.392398\pi$
$954$			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	0.833365	−	0.552723i	$-0.186411\pi$
$971$	−1.93166	−	3.34574i	−0.0619900	−	0.107370i	−0.895355	+	0.445353i	$0.853078\pi$
$972$	−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	−0.337485	−	0.941331i	$-0.609576\pi$
$977$	20.2068	−	34.9993i	0.646474	−	1.11973i	0.983959	−	0.178395i	$-0.0570906\pi$
$978$	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	−0.406829	−	0.913504i	$-0.633365\pi$
$991$	18.5010	−	32.0447i	0.587704	−	1.01793i	0.994532	−	0.104428i	$-0.0333012\pi$
$992$	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	−0.983312	−	0.181925i	$-0.941767\pi$
$997$	−41.5979	+	24.0165i	−1.31742	+	0.760611i	−0.334105	+	0.942536i	$0.608434\pi$
$998$	−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.199.1		8
5.2	odd	4		1950.2.bc.e.901.2	yes	8
5.3	odd	4		1950.2.bc.f.901.3	yes	8
5.4	even	2		1950.2.y.l.199.4		8
13.10	even	6		1950.2.y.l.49.4		8
65.23	odd	12		1950.2.bc.f.751.3	yes	8
65.49	even	6	inner	1950.2.y.i.49.1		8
65.62	odd	12		1950.2.bc.e.751.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.i.49.1		8	65.49	even	6	inner
1950.2.y.i.199.1		8	1.1	even	1	trivial
1950.2.y.l.49.4		8	13.10	even	6
1950.2.y.l.199.4		8	5.4	even	2
1950.2.bc.e.751.2	✓	8	65.62	odd	12
1950.2.bc.e.901.2	yes	8	5.2	odd	4
1950.2.bc.f.751.3	yes	8	65.23	odd	12
1950.2.bc.f.901.3	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
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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