LMFDB - Embedded newform 1950.2.y.l.49.4

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			49.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.l.199.4

$q$-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	−0.686239	−	0.727376i	$-0.740740\pi$
$7$	0.758819	−	1.31431i	0.286807	−	0.496764i	0.973046	+	0.230612i	$0.0740729\pi$
$8$	−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	0.910391	−	0.413750i	$-0.135781\pi$
$17$	4.15307	+	2.39778i	1.00727	+	0.581546i	0.0968774	+	0.995296i	$0.469115\pi$
$18$	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	−0.903111	−	0.429407i	$-0.858723\pi$
$23$	−4.71329	+	2.72122i	−0.982789	+	0.567414i	−0.0796783	+	0.996821i	$0.525389\pi$
$24$	−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	$0.0884548\pi$
$37$	4.36981	+	7.56873i	0.718392	+	1.24429i	−0.243245	+	0.969965i	$0.578212\pi$
$38$			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	0.648075	−	0.761576i	$-0.275574\pi$
$43$	2.04965	+	1.18336i	0.312568	+	0.180461i	−0.335507	+	0.942038i	$0.608908\pi$
$44$		−	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	$-0.666491\pi$
$47$	−6.84909			−0.999043			−0.499521	+	0.866302i	$0.666491\pi$
$48$	−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	0.921859	−	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	$-0.917797\pi$
$67$	−5.76733	−	9.98930i	−0.704591	−	1.22039i	0.262248	−	0.965001i	$-0.415536\pi$
$68$	−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	$-0.417229\pi$
$73$	4.39355			0.514226			0.257113	+	0.966381i	$0.417229\pi$
$74$	−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	$-0.482883\pi$
$83$	0.979336			0.107496			0.0537480	+	0.998555i	$0.482883\pi$
$84$	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	−0.973877	−	0.227076i	$-0.927083\pi$
$97$	−2.85898	+	4.95189i	−0.290285	+	0.502789i	0.683592	+	0.729864i	$0.260417\pi$
$98$	−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	$-0.950012\pi$
$103$		−	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	$-0.898145\pi$
$107$	−11.9106	+	6.87662i	−1.15145	+	0.664787i	−0.202207	+	0.979343i	$0.564811\pi$
$108$	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	0.0520785	−	0.998643i	$-0.483415\pi$
$113$	−8.36308	−	4.82843i	−0.786732	−	0.454220i	−0.838811	+	0.544423i	$0.816749\pi$
$114$	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	$-0.845227\pi$
$127$	−10.3843	+	5.99536i	−0.921454	+	0.532002i	−0.0373555	+	0.999302i	$0.511893\pi$
$128$	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	$-0.724008\pi$
$137$	3.94148	−	6.82684i	0.336743	−	0.583257i	0.983818	+	0.179170i	$0.0573412\pi$
$138$	−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	$0.260207\pi$
$157$			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	$-0.854589\pi$
$163$	−0.851911	+	1.47555i	−0.0667269	+	0.115574i	0.830732	+	0.556673i	$0.187922\pi$
$164$			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	$-0.100495\pi$
$167$	2.66717	+	4.61967i	0.206392	+	0.357481i	−0.744184	+	0.667975i	$0.767161\pi$
$168$			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	$-0.567885\pi$
$173$	−15.3085	−	8.83839i	−1.16389	−	0.671971i	−0.952233	+	0.305374i	$0.901219\pi$
$174$			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	0.978702	−	0.205287i	$-0.0658128\pi$
$193$	4.32843	+	7.49706i	0.311567	+	0.539650i	−0.667135	+	0.744937i	$0.732479\pi$
$194$	−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	$-0.216173\pi$
$197$	−2.17415	−	3.76574i	−0.154902	−	0.268298i	−0.933023	+	0.359816i	$0.882840\pi$
$198$	−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	0.724217	−	0.689572i	$-0.242201\pi$
$223$	−3.51047	−	6.08030i	−0.235078	−	0.407167i	−0.959295	+	0.282405i	$0.908868\pi$
$224$	−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	$-0.925408\pi$
$227$	−4.29762	+	7.44370i	−0.285243	+	0.494055i	0.687425	+	0.726255i	$0.258741\pi$
$228$	−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	$-0.926977\pi$
$233$		−	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	$-0.798320\pi$
$239$		−	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	0.125166	−	0.992136i	$-0.460054\pi$
$257$	16.7841	−	9.69031i	1.04696	−	0.604465i	0.921798	+	0.387671i	$0.126720\pi$
$258$	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	$-0.685264\pi$
$263$	−1.64019	+	0.946961i	−0.101138	+	0.0583921i	0.448578	+	0.893744i	$0.351931\pi$
$264$	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	−0.206514	−	0.978444i	$-0.566212\pi$
$277$	−19.2585	−	11.1189i	−1.15713	−	0.668068i	−0.950614	+	0.310375i	$0.899545\pi$
$278$	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	−0.481357	−	0.876525i	$-0.659856\pi$
$283$	0.623402	−	0.359921i	0.0370574	−	0.0213951i	0.518414	+	0.855130i	$0.326523\pi$
$284$	−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	$-0.959611\pi$
$293$	−6.61389	+	11.4556i	−0.386388	+	0.669243i	0.605573	+	0.795790i	$0.292944\pi$
$294$			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	$-0.571932\pi$
$307$	−7.85174			−0.448123			−0.224061	+	0.974575i	$0.571932\pi$
$308$	−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	$-0.233981\pi$
$317$	26.4141			1.48357			0.741783	+	0.670640i	$0.233981\pi$
$318$	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	$-0.883835\pi$
$337$		−	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	$-0.175160\pi$
$347$	15.3811	+	8.88027i	0.825700	+	0.476718i	−0.0266782	+	0.999644i	$0.508493\pi$
$348$	−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	0.948847	−	0.315737i	$-0.102252\pi$
$353$	3.77620	+	6.54057i	0.200987	+	0.348119i	−0.747860	+	0.663857i	$0.768918\pi$
$354$	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	0.324742	−	0.945802i	$-0.394722\pi$
$367$	25.0232	−	14.4472i	1.30620	−	0.754136i	0.981460	+	0.191666i	$0.0613890\pi$
$368$	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	$-0.457709\pi$
$373$	−12.7407	−	7.35583i	−0.659687	−	0.380870i	−0.792158	+	0.610317i	$0.791042\pi$
$374$	−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	−0.970672	−	0.240407i	$-0.922719\pi$
$383$	−5.42368	+	9.39410i	−0.277137	+	0.480016i	0.693535	+	0.720423i	$0.256052\pi$
$384$	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	$-0.835791\pi$
$397$	−0.153828	+	0.266438i	−0.00772041	+	0.0133721i	0.862139	+	0.506671i	$0.169124\pi$
$398$	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	−0.00515336	−	0.999987i	$-0.501640\pi$
$433$	−18.1814	−	10.4971i	−0.873744	−	0.504456i	−0.868591	+	0.495530i	$0.834974\pi$
$434$		−	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	$-0.901470\pi$
$443$		−	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	0.563104	−	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	0.862622	−	0.505849i	$-0.168821\pi$
$457$	−0.144671	−	0.250578i	−0.00676743	−	0.0117215i	−0.869389	+	0.494128i	$0.835487\pi$
$458$	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	$-0.409189\pi$
$463$	12.1116			0.562875			0.281438	+	0.959580i	$0.409189\pi$
$464$	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	−0.545662	−	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	−0.905219	−	0.424945i	$-0.860294\pi$
$487$	−1.86689	+	3.23354i	−0.0845968	+	0.146526i	0.820623	+	0.571471i	$0.193627\pi$
$488$	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	0.603845	−	0.797101i	$-0.293634\pi$
$503$	4.83222	+	2.78988i	0.215458	+	0.124395i	−0.388387	+	0.921496i	$0.626968\pi$
$504$	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	−0.869002	−	0.494808i	$-0.835238\pi$
$523$	−20.0102	+	11.5529i	−0.874986	+	0.505174i	−0.00598438	+	0.999982i	$0.501905\pi$
$524$	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	$-0.745932\pi$
$547$		−	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	0.934593	+	0.355718i	$0.115764\pi$
$557$	18.2991	+	31.6950i	0.775358	+	1.34296i	−0.159236	+	0.987241i	$0.550903\pi$
$558$		−	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	$-0.263254\pi$
$563$	8.97514	+	5.18180i	0.378257	+	0.218387i	−0.298803	+	0.954315i	$0.596587\pi$
$564$		−	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	$-0.176381\pi$
$577$	40.8530			1.70073			0.850365	+	0.526193i	$0.176381\pi$
$578$	−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	$-0.996829\pi$
$587$	−12.3224	−	21.3431i	−0.508602	−	0.880924i	0.491349	−	0.870963i	$-0.336504\pi$
$588$	−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	$-0.645453\pi$
$593$	−21.4887			−0.882436			−0.441218	+	0.897400i	$0.645453\pi$
$594$	−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	0.0285420	−	0.999593i	$-0.490914\pi$
$607$	−20.2731	−	11.7047i	−0.822860	−	0.475078i	−0.851402	+	0.524514i	$0.824247\pi$
$608$	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	$-0.132816\pi$
$613$	2.62799	+	4.55182i	0.106144	+	0.183846i	−0.808061	+	0.589099i	$0.799483\pi$
$614$	−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	$0.345046\pi$
$617$	−13.2027	+	22.8678i	−0.531522	+	0.920622i	−0.999323	+	0.0367887i	$0.988287\pi$
$618$	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	−0.775514	−	0.631331i	$-0.782509\pi$
$643$	4.03163	−	6.98298i	0.158992	−	0.275382i	0.934505	+	0.355949i	$0.115842\pi$
$644$	−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	$-0.671174\pi$
$647$	−0.623849	+	0.360179i	−0.0245260	+	0.0141601i	0.487687	+	0.873019i	$0.337841\pi$
$648$	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	$-0.841445\pi$
$653$	−23.0998	+	13.3367i	−0.903963	+	0.521904i	−0.0254795	+	0.999675i	$0.508111\pi$
$654$	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	−0.575734	−	0.817637i	$-0.695284\pi$
$673$	−4.03417	+	2.32913i	−0.155506	+	0.0897814i	0.420228	+	0.907419i	$0.361950\pi$
$674$	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	$-0.911298\pi$
$683$	−6.33735	+	10.9766i	−0.242492	+	0.420008i	0.718931	+	0.695081i	$0.244631\pi$
$684$			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	$0.365150\pi$
$727$			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	$-0.188625\pi$
$733$	44.9158			1.65900			0.829501	+	0.558505i	$0.188625\pi$
$734$	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	0.798841	−	0.601542i	$-0.205447\pi$
$743$	−3.31268	−	5.73773i	−0.121530	−	0.210497i	−0.920371	+	0.391045i	$0.872114\pi$
$744$	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	−0.0656076	−	0.997845i	$-0.520899\pi$
$757$	21.0685	−	12.1639i	0.765748	−	0.442105i	0.831356	+	0.555741i	$0.187565\pi$
$758$	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	$-0.452601\pi$
$773$	25.8739	−	44.8150i	0.930621	−	1.61188i	0.782262	−	0.622949i	$-0.214066\pi$
$774$	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	$-0.932585\pi$
$787$	−8.60630	+	14.9066i	−0.306782	+	0.531361i	0.670875	+	0.741571i	$0.265919\pi$
$788$	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	$-0.477504\pi$
$797$	−21.3976	−	12.3539i	−0.757943	−	0.437599i	−0.828557	+	0.559905i	$0.810838\pi$
$798$	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	0.931002	−	0.365014i	$-0.118936\pi$
$823$	30.9943	+	17.8946i	1.08039	+	0.623765i	0.149390	+	0.988778i	$0.452269\pi$
$824$			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	$-0.458166\pi$
$827$	7.53716			0.262093			0.131046	+	0.991376i	$0.458166\pi$
$828$	−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	$-0.575960\pi$
$853$	−13.8072			−0.472751			−0.236376	+	0.971662i	$0.575960\pi$
$854$	−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	$-0.348001\pi$
$863$	27.0018			0.919153			0.459577	+	0.888138i	$0.348001\pi$
$864$	−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	$-0.674930\pi$
$877$	14.1364	−	24.4850i	0.477352	−	0.826799i	0.999663	+	0.0259566i	$0.00826316\pi$
$878$	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	$0.364671\pi$
$883$			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	$-0.803431\pi$
$887$	−21.4881	+	12.4062i	−0.721500	+	0.416558i	0.0938043	+	0.995591i	$0.470097\pi$
$888$	−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	$-0.582444\pi$
$907$	13.6416	−	7.87598i	0.452962	−	0.261517i	0.709080	+	0.705128i	$0.249110\pi$
$908$	−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	$0.135505\pi$
$937$			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	$-0.758232\pi$
$941$		−	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	$-0.932476\pi$
$947$	−20.6529	−	35.7719i	−0.671130	−	1.16243i	0.306454	−	0.951885i	$-0.400857\pi$
$948$			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	$-0.274269\pi$
$953$	9.86484	+	5.69547i	0.319553	+	0.184494i	−0.331640	+	0.943406i	$0.607602\pi$
$954$		−	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	$-0.719559\pi$
$967$	−39.5770			−1.27271			−0.636355	+	0.771396i	$0.719559\pi$
$968$	−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	$-0.942909\pi$
$977$	−20.2068	−	34.9993i	−0.646474	−	1.11973i	0.337485	−	0.941331i	$-0.390424\pi$
$978$	−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	$-0.579626\pi$
$983$	−15.5229			−0.495103			−0.247551	+	0.968875i	$0.579626\pi$
$984$	−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	0.983312	−	0.181925i	$-0.0582327\pi$
$997$	41.5979	+	24.0165i	1.31742	+	0.760611i	0.334105	+	0.942536i	$0.391566\pi$
$998$	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.l.49.4		8
5.2	odd	4		1950.2.bc.e.751.2	✓	8
5.3	odd	4		1950.2.bc.f.751.3	yes	8
5.4	even	2		1950.2.y.i.49.1		8
13.4	even	6		1950.2.y.i.199.1		8
65.4	even	6	inner	1950.2.y.l.199.4		8
65.17	odd	12		1950.2.bc.e.901.2	yes	8
65.43	odd	12		1950.2.bc.f.901.3	yes	8

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