LMFDB - Embedded newform 1950.2.bc.f.751.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, degree $2$, 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			751.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.f.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.31431 - 0.758819i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.31431 - 0.758819i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.45680 + 2.57313i) q^{11} +1.00000 q^{12} +(-3.08725 + 1.86250i) q^{13} -1.51764 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.39778 - 4.15307i) q^{17} +1.00000i q^{18} +(-1.39778 - 0.807007i) q^{19} -1.51764i q^{21} +(-2.57313 + 4.45680i) q^{22} +(-2.72122 - 4.71329i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.74238 + 3.15660i) q^{26} -1.00000 q^{27} +(-1.31431 + 0.758819i) q^{28} +(-4.93684 - 8.55085i) q^{29} -9.88072i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.45680 - 2.57313i) q^{33} -4.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.56873 - 4.36981i) q^{37} -1.61401 q^{38} +(-3.15660 - 1.74238i) q^{39} +(1.10418 - 0.637499i) q^{41} +(-0.758819 - 1.31431i) q^{42} +(-1.18336 + 2.04965i) q^{43} +5.14626i q^{44} +(-4.71329 - 2.72122i) q^{46} +6.84909i q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.34839 - 4.06753i) q^{49} +4.79555 q^{51} +(0.0693504 + 3.60488i) q^{52} +0.881964 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.758819 + 1.31431i) q^{56} -1.61401i q^{57} +(-8.55085 - 4.93684i) q^{58} +(-8.04354 - 4.64394i) q^{59} +(-6.24056 + 10.8090i) q^{61} +(-4.94036 - 8.55695i) q^{62} +(1.31431 - 0.758819i) q^{63} -1.00000 q^{64} -5.14626 q^{66} +(-9.98930 + 5.76733i) q^{67} +(-2.39778 - 4.15307i) q^{68} +(2.72122 - 4.71329i) q^{69} +(13.7133 + 7.91737i) q^{71} +(0.866025 + 0.500000i) q^{72} +4.39355i q^{73} +(4.36981 - 7.56873i) q^{74} +(-1.39778 + 0.807007i) q^{76} +7.81017 q^{77} +(-3.60488 + 0.0693504i) q^{78} -11.0382 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.637499 - 1.10418i) q^{82} +0.979336i q^{83} +(-1.31431 - 0.758819i) q^{84} +2.36673i q^{86} +(4.93684 - 8.55085i) q^{87} +(2.57313 + 4.45680i) q^{88} +(-3.54146 + 2.04466i) q^{89} +(5.47091 - 0.105249i) q^{91} -5.44244 q^{92} +(8.55695 - 4.94036i) q^{93} +(3.42455 + 5.93149i) q^{94} -1.00000i q^{96} +(4.95189 + 2.85898i) q^{97} +(-4.06753 - 2.34839i) q^{98} -5.14626i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} + 8 q^{12} - 8 q^{14} - 4 q^{16} - 4 q^{17} + 12 q^{19} - 8 q^{22} - 4 q^{23} - 8 q^{27} + 4 q^{29} - 12 q^{33} + 4 q^{36} + 24 q^{37} - 4 q^{42} + 4 q^{43} + 12 q^{46} + 4 q^{48} - 16 q^{49} - 8 q^{51} + 8 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 16 q^{66} - 24 q^{67} + 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} + 8 q^{77} - 8 q^{79} - 4 q^{81} + 20 q^{82} - 4 q^{87} + 8 q^{88} + 24 q^{89} + 8 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} - 12 q^{97} - 12 q^{98}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 + 8 * q^12 - 8 * q^14 - 4 * q^16 - 4 * q^17 + 12 * q^19 - 8 * q^22 - 4 * q^23 - 8 * q^27 + 4 * q^29 - 12 * q^33 + 4 * q^36 + 24 * q^37 - 4 * q^42 + 4 * q^43 + 12 * q^46 + 4 * q^48 - 16 * q^49 - 8 * q^51 + 8 * q^53 - 4 * q^56 - 12 * q^58 - 12 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 16 * q^66 - 24 * q^67 + 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 + 8 * q^77 - 8 * q^79 - 4 * q^81 + 20 * q^82 - 4 * q^87 + 8 * q^88 + 24 * q^89 + 8 * q^91 - 8 * q^92 + 24 * q^93 + 16 * q^94 - 12 * q^97 - 12 * 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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−1.31431	−	0.758819i	−0.496764	−	0.286807i	0.230612	−	0.973046i	$-0.425927\pi$
$7$	−1.31431	−	0.758819i	−0.496764	−	0.286807i	−0.727376	+	0.686239i	$0.759260\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−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	$0.616001\pi$
$12$	1.00000			0.288675
$13$	−3.08725	+	1.86250i	−0.856248	+	0.516565i
$13$	−3.08725	+	1.86250i	−0.856248	+	0.516565i
$14$	−1.51764			−0.405606
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.39778	−	4.15307i	0.581546	−	1.00727i	−0.413750	−	0.910391i	$-0.635781\pi$
$17$	2.39778	−	4.15307i	0.581546	−	1.00727i	0.995296	−	0.0968774i	$-0.0308855\pi$
$18$			1.00000i			0.235702i
$19$	−1.39778	−	0.807007i	−0.320672	−	0.185140i	0.331020	−	0.943624i	$-0.392607\pi$
$19$	−1.39778	−	0.807007i	−0.320672	−	0.185140i	−0.651692	+	0.758484i	$0.725941\pi$
$20$		0			0
$21$		−	1.51764i		−	0.331176i
$22$	−2.57313	+	4.45680i	−0.548594	+	0.950192i
$23$	−2.72122	−	4.71329i	−0.567414	−	0.982789i	−0.996821	−	0.0796783i	$-0.974611\pi$
$23$	−2.72122	−	4.71329i	−0.567414	−	0.982789i	0.429407	−	0.903111i	$-0.358723\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	−1.74238	+	3.15660i	−0.341709	+	0.619060i
$27$	−1.00000			−0.192450
$28$	−1.31431	+	0.758819i	−0.248382	+	0.143403i
$29$	−4.93684	−	8.55085i	−0.916747	−	1.58785i	−0.804323	−	0.594193i	$-0.797472\pi$
$29$	−4.93684	−	8.55085i	−0.916747	−	1.58785i	−0.112425	−	0.993660i	$-0.535862\pi$
$30$		0			0
$31$		−	9.88072i		−	1.77463i	−0.461164	−	0.887315i	$-0.652568\pi$
$31$		−	9.88072i		−	1.77463i	0.461164	−	0.887315i	$-0.347432\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.45680	−	2.57313i	−0.775829	−	0.447925i
$34$		−	4.79555i		−	0.822431i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	7.56873	−	4.36981i	1.24429	−	0.718392i	0.274326	−	0.961637i	$-0.411545\pi$
$37$	7.56873	−	4.36981i	1.24429	−	0.718392i	0.969965	+	0.243245i	$0.0782118\pi$
$38$	−1.61401			−0.261828
$39$	−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	$0.301590\pi$
$42$	−0.758819	−	1.31431i	−0.117088	−	0.202803i
$43$	−1.18336	+	2.04965i	−0.180461	+	0.312568i	−0.942038	−	0.335507i	$-0.891092\pi$
$43$	−1.18336	+	2.04965i	−0.180461	+	0.312568i	0.761576	+	0.648075i	$0.224426\pi$
$44$			5.14626i			0.775829i
$45$		0			0
$46$	−4.71329	−	2.72122i	−0.694937	−	0.401222i
$47$			6.84909i			0.999043i	0.866302	+	0.499521i	$0.166491\pi$
$47$			6.84909i			0.999043i	−0.866302	+	0.499521i	$0.833509\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−2.34839	−	4.06753i	−0.335484	−	0.581075i
$50$		0			0
$51$	4.79555			0.671512
$52$	0.0693504	+	3.60488i	0.00961716	+	0.499908i
$53$	0.881964			0.121147			0.0605735	−	0.998164i	$-0.480707\pi$
$53$	0.881964			0.121147			0.0605735	+	0.998164i	$0.480707\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−0.758819	+	1.31431i	−0.101401	+	0.175632i
$57$		−	1.61401i		−	0.213781i
$58$	−8.55085	−	4.93684i	−1.12278	−	0.648238i
$59$	−8.04354	−	4.64394i	−1.04718	−	0.604590i	−0.125322	−	0.992116i	$-0.539996\pi$
$59$	−8.04354	−	4.64394i	−1.04718	−	0.604590i	−0.921859	+	0.387526i	$0.873330\pi$
$60$		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	$0.872018\pi$
$62$	−4.94036	−	8.55695i	−0.627426	−	1.08673i
$63$	1.31431	−	0.758819i	0.165588	−	0.0956022i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.14626			−0.633461
$67$	−9.98930	+	5.76733i	−1.22039	+	0.704591i	−0.965001	−	0.262248i	$-0.915536\pi$
$67$	−9.98930	+	5.76733i	−1.22039	+	0.704591i	−0.255387	+	0.966839i	$0.582203\pi$
$68$	−2.39778	−	4.15307i	−0.290773	−	0.503634i
$69$	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	$0.277846\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			4.39355i			0.514226i	0.966381	+	0.257113i	$0.0827713\pi$
$73$			4.39355i			0.514226i	−0.966381	+	0.257113i	$0.917229\pi$
$74$	4.36981	−	7.56873i	0.507980	−	0.879847i
$75$		0			0
$76$	−1.39778	+	0.807007i	−0.160336	+	0.0925701i
$77$	7.81017			0.890051
$78$	−3.60488	+	0.0693504i	−0.408173	+	0.00785238i
$79$	−11.0382			−1.24189			−0.620947	−	0.783853i	$-0.713252\pi$
$79$	−11.0382			−1.24189			−0.620947	+	0.783853i	$0.713252\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.637499	−	1.10418i	0.0704000	−	0.121936i
$83$			0.979336i			0.107496i	0.998555	+	0.0537480i	$0.0171168\pi$
$83$			0.979336i			0.107496i	−0.998555	+	0.0537480i	$0.982883\pi$
$84$	−1.31431	−	0.758819i	−0.143403	−	0.0827939i
$85$		0			0
$86$			2.36673i			0.255211i
$87$	4.93684	−	8.55085i	0.529284	−	0.916747i
$88$	2.57313	+	4.45680i	0.274297	+	0.475096i
$89$	−3.54146	+	2.04466i	−0.375394	+	0.216734i	−0.675812	−	0.737074i	$-0.736207\pi$
$89$	−3.54146	+	2.04466i	−0.375394	+	0.216734i	0.300418	+	0.953808i	$0.402874\pi$
$90$		0			0
$91$	5.47091	−	0.105249i	0.573507	−	0.0110331i
$92$	−5.44244			−0.567414
$93$	8.55695	−	4.94036i	0.887315	−	0.512291i
$94$	3.42455	+	5.93149i	0.353215	+	0.611786i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	4.95189	+	2.85898i	0.502789	+	0.290285i	0.729864	−	0.683592i	$-0.239583\pi$
$97$	4.95189	+	2.85898i	0.502789	+	0.290285i	−0.227076	+	0.973877i	$0.572917\pi$
$98$	−4.06753	−	2.34839i	−0.410882	−	0.237223i
$99$		−	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	$0.961113\pi$
$102$	4.15307	−	2.39778i	0.411215	−	0.237415i
$103$	3.17449			0.312792			0.156396	−	0.987694i	$-0.450012\pi$
$103$	3.17449			0.312792			0.156396	+	0.987694i	$0.450012\pi$
$104$	1.86250	+	3.08725i	0.182633	+	0.302729i
$105$		0			0
$106$	0.763803	−	0.440982i	0.0741871	−	0.0428319i
$107$	6.87662	+	11.9106i	0.664787	+	1.15145i	0.979343	+	0.202207i	$0.0648112\pi$
$107$	6.87662	+	11.9106i	0.664787	+	1.15145i	−0.314555	+	0.949239i	$0.601855\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			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
$112$			1.51764i			0.143403i
$113$	4.82843	−	8.36308i	0.454220	−	0.786732i	−0.544423	−	0.838811i	$-0.683251\pi$
$113$	4.82843	−	8.36308i	0.454220	−	0.786732i	0.998643	+	0.0520785i	$0.0165846\pi$
$114$	−0.807007	−	1.39778i	−0.0755831	−	0.130914i
$115$		0			0
$116$	−9.87367			−0.916747
$117$	−0.0693504	−	3.60488i	−0.00641144	−	0.333272i
$118$	−9.28788			−0.855019
$119$	−6.30286	+	3.63896i	−0.577782	+	0.333583i
$120$		0			0
$121$	7.74202	−	13.4096i	0.703820	−	1.21905i
$122$			12.4811i			1.12999i
$123$	1.10418	+	0.637499i	0.0995606	+	0.0574813i
$124$	−8.55695	−	4.94036i	−0.768437	−	0.443657i
$125$		0			0
$126$	0.758819	−	1.31431i	0.0676010	−	0.117088i
$127$	5.99536	+	10.3843i	0.532002	+	0.921454i	0.999302	+	0.0373555i	$0.0118934\pi$
$127$	5.99536	+	10.3843i	0.532002	+	0.921454i	−0.467300	+	0.884099i	$0.654773\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−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	$0.848667\pi$
$132$	−4.45680	+	2.57313i	−0.387914	+	0.223962i
$133$	1.22474	+	2.12132i	0.106199	+	0.183942i
$134$	−5.76733	+	9.98930i	−0.498221	+	0.862944i
$135$		0			0
$136$	−4.15307	−	2.39778i	−0.356123	−	0.205608i
$137$	−6.82684	−	3.94148i	−0.583257	−	0.336743i	0.179170	−	0.983818i	$-0.442659\pi$
$137$	−6.82684	−	3.94148i	−0.583257	−	0.336743i	−0.762427	+	0.647075i	$0.775992\pi$
$138$		−	5.44244i		−	0.463291i
$139$	−2.05852	+	3.56546i	−0.174601	+	0.302419i	−0.940023	−	0.341110i	$-0.889197\pi$
$139$	−2.05852	+	3.56546i	−0.174601	+	0.302419i	0.765422	+	0.643529i	$0.222530\pi$
$140$		0			0
$141$	−5.93149	+	3.42455i	−0.499521	+	0.288399i
$142$	15.8347			1.32882
$143$	8.96676	−	16.2447i	0.749838	−	1.35845i
$144$	1.00000			0.0833333
$145$		0			0
$146$	2.19677	+	3.80493i	0.181806	+	0.314898i
$147$	2.34839	−	4.06753i	0.193692	−	0.335484i
$148$		−	8.73961i		−	0.718392i
$149$	−8.00644	−	4.62252i	−0.655913	−	0.378692i	0.134805	−	0.990872i	$-0.456959\pi$
$149$	−8.00644	−	4.62252i	−0.655913	−	0.378692i	−0.790718	+	0.612180i	$0.790293\pi$
$150$		0			0
$151$		−	17.1479i		−	1.39548i	−0.716351	−	0.697740i	$-0.754189\pi$
$151$		−	17.1479i		−	1.39548i	0.716351	−	0.697740i	$-0.245811\pi$
$152$	−0.807007	+	1.39778i	−0.0654569	+	0.113375i
$153$	2.39778	+	4.15307i	0.193849	+	0.335756i
$154$	6.76380	−	3.90508i	0.545043	−	0.314681i
$155$		0			0
$156$	−3.08725	+	1.86250i	−0.247178	+	0.149119i
$157$	18.2791			1.45883			0.729415	−	0.684072i	$-0.239793\pi$
$157$	18.2791			1.45883			0.729415	+	0.684072i	$0.239793\pi$
$158$	−9.55936	+	5.51910i	−0.760502	+	0.439076i
$159$	0.440982	+	0.763803i	0.0349721	+	0.0605735i
$160$		0			0
$161$			8.25966i			0.650952i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−1.47555	−	0.851911i	−0.115574	−	0.0667269i	0.441098	−	0.897459i	$-0.354589\pi$
$163$	−1.47555	−	0.851911i	−0.115574	−	0.0667269i	−0.556673	+	0.830732i	$0.687922\pi$
$164$		−	1.27500i		−	0.0995606i
$165$		0			0
$166$	0.489668	+	0.848130i	0.0380056	+	0.0658276i
$167$	4.61967	−	2.66717i	0.357481	−	0.206392i	−0.310494	−	0.950575i	$-0.600495\pi$
$167$	4.61967	−	2.66717i	0.357481	−	0.206392i	0.667975	+	0.744184i	$0.267161\pi$
$168$	−1.51764			−0.117088
$169$	6.06218	−	11.5000i	0.466321	−	0.884615i
$170$		0			0
$171$	1.39778	−	0.807007i	0.106891	−	0.0617134i
$172$	1.18336	+	2.04965i	0.0902307	+	0.156284i
$173$	8.83839	−	15.3085i	0.671971	−	1.16389i	−0.305374	−	0.952233i	$-0.598781\pi$
$173$	8.83839	−	15.3085i	0.671971	−	1.16389i	0.977344	−	0.211655i	$-0.0678853\pi$
$174$		−	9.87367i		−	0.748521i
$175$		0			0
$176$	4.45680	+	2.57313i	0.335944	+	0.193957i
$177$		−	9.28788i		−	0.698120i
$178$	−2.04466	+	3.54146i	−0.153254	+	0.265444i
$179$	−10.7700	−	18.6542i	−0.804987	−	1.39428i	−0.916300	−	0.400493i	$-0.868839\pi$
$179$	−10.7700	−	18.6542i	−0.804987	−	1.39428i	0.111313	−	0.993785i	$-0.464494\pi$
$180$		0			0
$181$	4.08328			0.303507			0.151754	−	0.988418i	$-0.451508\pi$
$181$	4.08328			0.303507			0.151754	+	0.988418i	$0.451508\pi$
$182$	4.68532	−	2.82660i	0.347299	−	0.209522i
$183$	−12.4811			−0.922631
$184$	−4.71329	+	2.72122i	−0.347469	+	0.200611i
$185$		0			0
$186$	4.94036	−	8.55695i	0.362245	−	0.627426i
$187$			24.6792i			1.80472i
$188$	5.93149	+	3.42455i	0.432598	+	0.249761i
$189$	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	$0.0113722\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−7.49706	+	4.32843i	−0.539650	+	0.311567i	−0.744937	−	0.667135i	$-0.767521\pi$
$193$	−7.49706	+	4.32843i	−0.539650	+	0.311567i	0.205287	+	0.978702i	$0.434187\pi$
$194$	5.71795			0.410525
$195$		0			0
$196$	−4.69677			−0.335484
$197$	−3.76574	+	2.17415i	−0.268298	+	0.154902i	−0.628114	−	0.778121i	$-0.716173\pi$
$197$	−3.76574	+	2.17415i	−0.268298	+	0.154902i	0.359816	+	0.933023i	$0.382840\pi$
$198$	−2.57313	−	4.45680i	−0.182865	−	0.316731i
$199$	−3.73351	+	6.46663i	−0.264662	+	0.458407i	−0.967475	−	0.252967i	$-0.918594\pi$
$199$	−3.73351	+	6.46663i	−0.264662	+	0.458407i	0.702813	+	0.711374i	$0.251927\pi$
$200$		0			0
$201$	−9.98930	−	5.76733i	−0.704591	−	0.406796i
$202$	−6.80153	−	3.92687i	−0.478554	−	0.276293i
$203$			14.9847i			1.05172i
$204$	2.39778	−	4.15307i	0.167878	−	0.290773i
$205$		0			0
$206$	2.74919	−	1.58725i	0.191545	−	0.110589i
$207$	5.44244			0.378276
$208$	3.15660	+	1.74238i	0.218871	+	0.120813i
$209$	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	$0.987015\pi$
$212$	0.440982	−	0.763803i	0.0302868	−	0.0524582i
$213$			15.8347i			1.08498i
$214$	11.9106	+	6.87662i	0.814195	+	0.470076i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−7.49768	+	12.9864i	−0.508976	+	0.881571i
$218$	8.39475	+	14.5401i	0.568564	+	0.984782i
$219$	−3.80493	+	2.19677i	−0.257113	+	0.148444i
$220$		0			0
$221$	0.332573	+	17.2874i	0.0223713	+	1.16288i
$222$	8.73961			0.586565
$223$	6.08030	−	3.51047i	0.407167	−	0.235078i	−0.282405	−	0.959295i	$-0.591132\pi$
$223$	6.08030	−	3.51047i	0.407167	−	0.235078i	0.689572	+	0.724217i	$0.257799\pi$
$224$	0.758819	+	1.31431i	0.0507007	+	0.0878162i
$225$		0			0
$226$		−	9.65685i		−	0.642364i
$227$	7.44370	+	4.29762i	0.494055	+	0.285243i	0.726255	−	0.687425i	$-0.241259\pi$
$227$	7.44370	+	4.29762i	0.494055	+	0.285243i	−0.232200	+	0.972668i	$0.574592\pi$
$228$	−1.39778	−	0.807007i	−0.0925701	−	0.0534454i
$229$			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
$232$	−8.55085	+	4.93684i	−0.561391	+	0.324119i
$233$	6.94230			0.454805			0.227403	−	0.973801i	$-0.426977\pi$
$233$	6.94230			0.454805			0.227403	+	0.973801i	$0.426977\pi$
$234$	−1.86250	−	3.08725i	−0.121756	−	0.201820i
$235$		0			0
$236$	−8.04354	+	4.64394i	−0.523590	+	0.302295i
$237$	−5.51910	−	9.55936i	−0.358504	−	0.620947i
$238$	−3.63896	+	6.30286i	−0.235879	+	0.408554i
$239$			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	0.845074	−	0.534649i	$-0.179556\pi$
$241$	12.4906	+	7.21147i	0.804592	+	0.464532i	−0.0404822	+	0.999180i	$0.512889\pi$
$242$		−	15.4840i		−	0.995352i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	6.24056	+	10.8090i	0.399511	+	0.691973i
$245$		0			0
$246$	1.27500			0.0812909
$247$	5.81834	−	0.111932i	0.370212	−	0.00712209i
$248$	−9.88072			−0.627426
$249$	−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	$0.245469\pi$
$252$		−	1.51764i		−	0.0956022i
$253$	24.2558	+	14.0041i	1.52495	+	0.880432i
$254$	10.3843	+	5.99536i	0.651566	+	0.376182i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.69031	−	16.7841i	−0.604465	−	1.04696i	−0.992136	−	0.125166i	$-0.960054\pi$
$257$	−9.69031	−	16.7841i	−0.604465	−	1.04696i	0.387671	−	0.921798i	$-0.373280\pi$
$258$	−2.04965	+	1.18336i	−0.127606	+	0.0736731i
$259$	−13.2636			−0.824158
$260$		0			0
$261$	9.87367			0.611165
$262$	−17.6257	+	10.1762i	−1.08892	+	0.628687i
$263$	−0.946961	−	1.64019i	−0.0583921	−	0.101138i	0.835352	−	0.549716i	$-0.185264\pi$
$263$	−0.946961	−	1.64019i	−0.0583921	−	0.101138i	−0.893744	+	0.448578i	$0.851931\pi$
$264$	−2.57313	+	4.45680i	−0.158365	+	0.274297i
$265$		0			0
$266$	2.12132	+	1.22474i	0.130066	+	0.0750939i
$267$	−3.54146	−	2.04466i	−0.216734	−	0.125131i
$268$			11.5347i			0.704591i
$269$	2.30104	−	3.98551i	0.140297	−	0.243001i	−0.787312	−	0.616555i	$-0.788528\pi$
$269$	2.30104	−	3.98551i	0.140297	−	0.243001i	0.927608	+	0.373554i	$0.121861\pi$
$270$		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	$0.251776\pi$
$272$	−4.79555			−0.290773
$273$	2.82660	+	4.68532i	0.171074	+	0.283569i
$274$	−7.88296			−0.476227
$275$		0			0
$276$	−2.72122	−	4.71329i	−0.163798	−	0.283707i
$277$	−11.1189	+	19.2585i	−0.668068	+	1.15713i	0.310375	+	0.950614i	$0.399545\pi$
$277$	−11.1189	+	19.2585i	−0.668068	+	1.15713i	−0.978444	+	0.206514i	$0.933788\pi$
$278$			4.11704i			0.246924i
$279$	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	$-0.204601\pi$
$282$	−3.42455	+	5.93149i	−0.203929	+	0.353215i
$283$	0.359921	+	0.623402i	0.0213951	+	0.0370574i	0.876525	−	0.481357i	$-0.159856\pi$
$283$	0.359921	+	0.623402i	0.0213951	+	0.0370574i	−0.855130	+	0.518414i	$0.826523\pi$
$284$	13.7133	−	7.91737i	0.813734	−	0.469810i
$285$		0			0
$286$	−0.356895	−	18.5517i	−0.0211037	−	1.09698i
$287$	−1.93498			−0.114219
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−2.99867	−	5.19386i	−0.176393	−	0.305521i
$290$		0			0
$291$			5.71795i			0.335192i
$292$	3.80493	+	2.19677i	0.222666	+	0.128557i
$293$	−11.4556	−	6.61389i	−0.669243	−	0.386388i	0.126547	−	0.991961i	$-0.459611\pi$
$293$	−11.4556	−	6.61389i	−0.669243	−	0.386388i	−0.795790	+	0.605573i	$0.792944\pi$
$294$		−	4.69677i		−	0.273921i
$295$		0			0
$296$	−4.36981	−	7.56873i	−0.253990	−	0.439923i
$297$	4.45680	−	2.57313i	0.258610	−	0.149308i
$298$	−9.24504			−0.535551
$299$	17.1796	+	9.48282i	0.993521	+	0.548405i
$300$		0			0
$301$	3.11062	−	1.79592i	0.179293	−	0.103515i
$302$	−8.57397	−	14.8506i	−0.493377	−	0.854553i
$303$	3.92687	−	6.80153i	0.225593	−	0.390738i
$304$			1.61401i			0.0925701i
$305$		0			0
$306$	4.15307	+	2.39778i	0.237415	+	0.137072i
$307$			7.85174i			0.448123i	0.974575	+	0.224061i	$0.0719316\pi$
$307$			7.85174i			0.448123i	−0.974575	+	0.224061i	$0.928068\pi$
$308$	3.90508	−	6.76380i	0.222513	−	0.385403i
$309$	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	$0.647557\pi$
$312$	−1.74238	+	3.15660i	−0.0986430	+	0.178707i
$313$	21.0613			1.19045			0.595227	−	0.803558i	$-0.297062\pi$
$313$	21.0613			1.19045			0.595227	+	0.803558i	$0.297062\pi$
$314$	15.8301	−	9.13954i	0.893347	−	0.515774i
$315$		0			0
$316$	−5.51910	+	9.55936i	−0.310474	+	0.537756i
$317$		−	26.4141i		−	1.48357i	−0.670640	−	0.741783i	$-0.733981\pi$
$317$		−	26.4141i		−	1.48357i	0.670640	−	0.741783i	$-0.266019\pi$
$318$	0.763803	+	0.440982i	0.0428319	+	0.0247290i
$319$	44.0049	+	25.4063i	2.46380	+	1.42248i
$320$		0			0
$321$	−6.87662	+	11.9106i	−0.383815	+	0.664787i
$322$	4.12983	+	7.15307i	0.230146	+	0.398625i
$323$	−6.70312	+	3.87005i	−0.372972	+	0.215335i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−1.70382			−0.0943660
$327$	−14.5401	+	8.39475i	−0.804071	+	0.464231i
$328$	−0.637499	−	1.10418i	−0.0352000	−	0.0609681i
$329$	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	$0.476955\pi$
$332$	0.848130	+	0.489668i	0.0465472	+	0.0268740i
$333$			8.73961i			0.478928i
$334$	2.66717	−	4.61967i	0.145941	−	0.252777i
$335$		0			0
$336$	−1.31431	+	0.758819i	−0.0717017	+	0.0413970i
$337$	−13.1035			−0.713791			−0.356895	−	0.934144i	$-0.616165\pi$
$337$	−13.1035			−0.713791			−0.356895	+	0.934144i	$0.616165\pi$
$338$	−0.500000	−	12.9904i	−0.0271964	−	0.706584i
$339$	9.65685			0.524488
$340$		0			0
$341$	25.4244	+	44.0363i	1.37681	+	2.38470i
$342$	0.807007	−	1.39778i	0.0436380	−	0.0755831i
$343$			17.7515i			0.958489i
$344$	2.04965	+	1.18336i	0.110510	+	0.0638028i
$345$		0			0
$346$		−	17.6768i		−	0.950310i
$347$	8.88027	−	15.3811i	0.476718	−	0.825700i	−0.522926	−	0.852378i	$-0.675160\pi$
$347$	8.88027	−	15.3811i	0.476718	−	0.825700i	0.999644	+	0.0266782i	$0.00849295\pi$
$348$	−4.93684	−	8.55085i	−0.264642	−	0.458374i
$349$	0.103747	−	0.0598981i	0.00555343	−	0.00320627i	−0.497221	−	0.867624i	$-0.665646\pi$
$349$	0.103747	−	0.0598981i	0.00555343	−	0.00320627i	0.502774	+	0.864418i	$0.332313\pi$
$350$		0			0
$351$	3.08725	−	1.86250i	0.164785	−	0.0994130i
$352$	5.14626			0.274297
$353$	−6.54057	+	3.77620i	−0.348119	+	0.200987i	−0.663857	−	0.747860i	$-0.731082\pi$
$353$	−6.54057	+	3.77620i	−0.348119	+	0.200987i	0.315737	+	0.948847i	$0.397748\pi$
$354$	−4.64394	−	8.04354i	−0.246823	−	0.427510i
$355$		0			0
$356$			4.08933i			0.216734i
$357$	−6.30286	−	3.63896i	−0.333583	−	0.192594i
$358$	−18.6542	−	10.7700i	−0.985903	−	0.569212i
$359$		−	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
$362$	3.53622	−	2.04164i	0.185860	−	0.107306i
$363$	15.4840			0.812701
$364$	2.64431	−	4.79057i	0.138599	−	0.251094i
$365$		0			0
$366$	−10.8090	+	6.24056i	−0.564994	+	0.326199i
$367$	−14.4472	−	25.0232i	−0.754136	−	1.30620i	−0.945802	−	0.324742i	$-0.894722\pi$
$367$	−14.4472	−	25.0232i	−0.754136	−	1.30620i	0.191666	−	0.981460i	$-0.438611\pi$
$368$	−2.72122	+	4.71329i	−0.141853	+	0.245697i
$369$			1.27500i			0.0663737i
$370$		0			0
$371$	−1.15918	−	0.669251i	−0.0601814	−	0.0347458i
$372$		−	9.88072i		−	0.512291i
$373$	7.35583	−	12.7407i	0.380870	−	0.659687i	−0.610317	−	0.792158i	$-0.708958\pi$
$373$	7.35583	−	12.7407i	0.380870	−	0.659687i	0.991187	+	0.132471i	$0.0422911\pi$
$374$	12.3396	+	21.3728i	0.638065	+	1.10516i
$375$		0			0
$376$	6.84909			0.353215
$377$	31.1672	+	17.2037i	1.60519	+	0.886036i
$378$	1.51764			0.0780589
$379$	−27.1285	+	15.6627i	−1.39350	+	0.804537i	−0.993701	−	0.112067i	$-0.964253\pi$
$379$	−27.1285	+	15.6627i	−1.39350	+	0.804537i	−0.399798	+	0.916603i	$0.630920\pi$
$380$		0			0
$381$	−5.99536	+	10.3843i	−0.307151	+	0.532002i
$382$		−	12.9564i		−	0.662909i
$383$	−9.39410	−	5.42368i	−0.480016	−	0.277137i	0.240407	−	0.970672i	$-0.422719\pi$
$383$	−9.39410	−	5.42368i	−0.480016	−	0.277137i	−0.720423	+	0.693535i	$0.756052\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	−4.32843	+	7.49706i	−0.220311	+	0.381590i
$387$	−1.18336	−	2.04965i	−0.0601538	−	0.104189i
$388$	4.95189	−	2.85898i	0.251394	−	0.145143i
$389$	−18.2977			−0.927730			−0.463865	−	0.885906i	$-0.653538\pi$
$389$	−18.2977			−0.927730			−0.463865	+	0.885906i	$0.653538\pi$
$390$		0			0
$391$	−26.0995			−1.31991
$392$	−4.06753	+	2.34839i	−0.205441	+	0.118611i
$393$	−10.1762	−	17.6257i	−0.513321	−	0.889098i
$394$	−2.17415	+	3.76574i	−0.109532	+	0.189715i
$395$		0			0
$396$	−4.45680	−	2.57313i	−0.223962	−	0.129305i
$397$	0.266438	+	0.153828i	0.0133721	+	0.00772041i	0.506671	−	0.862139i	$-0.330876\pi$
$397$	0.266438	+	0.153828i	0.0133721	+	0.00772041i	−0.493299	+	0.869860i	$0.664209\pi$
$398$			7.46702i			0.374288i
$399$	−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	$0.315955\pi$
$402$	−11.5347			−0.575296
$403$	18.4029	+	30.5042i	0.916711	+	1.51952i
$404$	−7.85374			−0.390738
$405$		0			0
$406$	7.49233	+	12.9771i	0.371838	+	0.644042i
$407$	−22.4882	+	38.9507i	−1.11470	+	1.93071i
$408$		−	4.79555i		−	0.237415i
$409$	32.6067	+	18.8255i	1.61230	+	0.930860i	0.988836	+	0.149006i	$0.0476073\pi$
$409$	32.6067	+	18.8255i	1.61230	+	0.930860i	0.623461	+	0.781855i	$0.285726\pi$
$410$		0			0
$411$		−	7.88296i		−	0.388838i
$412$	1.58725	−	2.74919i	0.0781980	−	0.135443i
$413$	7.04782	+	12.2072i	0.346801	+	0.600676i
$414$	4.71329	−	2.72122i	0.231646	−	0.133741i
$415$		0			0
$416$	3.60488	−	0.0693504i	0.176744	−	0.00340018i
$417$	−4.11704			−0.201612
$418$	7.19333	−	4.15307i	0.351837	−	0.203133i
$419$	−13.5307	−	23.4359i	−0.661020	−	1.14492i	−0.980348	−	0.197276i	$-0.936790\pi$
$419$	−13.5307	−	23.4359i	−0.661020	−	1.14492i	0.319328	−	0.947644i	$-0.396543\pi$
$420$		0			0
$421$		−	11.9356i		−	0.581706i	−0.956768	−	0.290853i	$-0.906061\pi$
$421$		−	11.9356i		−	0.581706i	0.956768	−	0.290853i	$-0.0939390\pi$
$422$	−11.6807	−	6.74384i	−0.568607	−	0.328285i
$423$	−5.93149	−	3.42455i	−0.288399	−	0.166507i
$424$		−	0.881964i		−	0.0428319i
$425$		0			0
$426$	7.91737	+	13.7133i	0.383598	+	0.664411i
$427$	16.4041	−	9.47091i	0.793850	−	0.458329i
$428$	13.7532			0.664787
$429$	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	$0.0764903\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	10.4971	−	18.1814i	0.504456	−	0.873744i	−0.495530	−	0.868591i	$-0.665026\pi$
$433$	10.4971	−	18.1814i	0.504456	−	0.873744i	0.999987	−	0.00515336i	$-0.00164037\pi$
$434$			14.9954i			0.719800i
$435$		0			0
$436$	14.5401	+	8.39475i	0.696346	+	0.402036i
$437$			8.78418i			0.420204i
$438$	−2.19677	+	3.80493i	−0.104966	+	0.181806i
$439$	3.65685	+	6.33386i	0.174532	+	0.302299i	0.939999	−	0.341176i	$-0.110825\pi$
$439$	3.65685	+	6.33386i	0.174532	+	0.302299i	−0.765467	+	0.643475i	$0.777492\pi$
$440$		0			0
$441$	4.69677			0.223656
$442$	8.93173	+	14.8051i	0.424839	+	0.704205i
$443$	12.8231			0.609244			0.304622	−	0.952473i	$-0.401470\pi$
$443$	12.8231			0.609244			0.304622	+	0.952473i	$0.401470\pi$
$444$	7.56873	−	4.36981i	0.359196	−	0.207382i
$445$		0			0
$446$	3.51047	−	6.08030i	0.166225	−	0.287911i
$447$		−	9.24504i		−	0.437276i
$448$	1.31431	+	0.758819i	0.0620955	+	0.0358508i
$449$	−2.73315	−	1.57798i	−0.128985	−	0.0744696i	0.434119	−	0.900855i	$-0.357060\pi$
$449$	−2.73315	−	1.57798i	−0.128985	−	0.0744696i	−0.563104	+	0.826386i	$0.690393\pi$
$450$		0			0
$451$	−3.28074	+	5.68240i	−0.154484	+	0.267574i
$452$	−4.82843	−	8.36308i	−0.227110	−	0.393366i
$453$	14.8506	−	8.57397i	0.697740	−	0.402840i
$454$	8.59524			0.403395
$455$		0			0
$456$	−1.61401			−0.0755831
$457$	−0.250578	+	0.144671i	−0.0117215	+	0.00676743i	−0.505849	−	0.862622i	$-0.668821\pi$
$457$	−0.250578	+	0.144671i	−0.0117215	+	0.00676743i	0.494128	+	0.869389i	$0.335487\pi$
$458$	8.20429	+	14.2102i	0.383361	+	0.664001i
$459$	−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	$0.693042\pi$
$462$	6.76380	+	3.90508i	0.314681	+	0.181681i
$463$			12.1116i			0.562875i	0.959580	+	0.281438i	$0.0908113\pi$
$463$			12.1116i			0.562875i	−0.959580	+	0.281438i	$0.909189\pi$
$464$	−4.93684	+	8.55085i	−0.229187	+	0.396963i
$465$		0			0
$466$	6.01221	−	3.47115i	0.278510	−	0.160798i
$467$	−29.9323			−1.38510			−0.692550	−	0.721369i	$-0.743513\pi$
$467$	−29.9323			−1.38510			−0.692550	+	0.721369i	$0.743513\pi$
$468$	−3.15660	−	1.74238i	−0.145914	−	0.0805417i
$469$	17.5054			0.808326
$470$		0			0
$471$	9.13954	+	15.8301i	0.421128	+	0.729415i
$472$	−4.64394	+	8.04354i	−0.213755	+	0.370234i
$473$		−	12.1798i		−	0.560029i
$474$	−9.55936	−	5.51910i	−0.439076	−	0.253501i
$475$		0			0
$476$			7.27792i			0.333583i
$477$	−0.440982	+	0.763803i	−0.0201912	+	0.0349721i
$478$	9.15281	+	15.8531i	0.418640	+	0.725106i
$479$	2.03012	−	1.17209i	0.0927584	−	0.0535541i	−0.452903	−	0.891560i	$-0.649612\pi$
$479$	2.03012	−	1.17209i	0.0927584	−	0.0535541i	0.545662	+	0.838006i	$0.316278\pi$
$480$		0			0
$481$	−15.2278	+	27.5874i	−0.694326	+	1.25788i
$482$	14.4229			0.656947
$483$	−7.15307	+	4.12983i	−0.325476	+	0.187914i
$484$	−7.74202	−	13.4096i	−0.351910	−	0.609526i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	3.23354	+	1.86689i	0.146526	+	0.0845968i	0.571471	−	0.820623i	$-0.306373\pi$
$487$	3.23354	+	1.86689i	0.146526	+	0.0845968i	−0.424945	+	0.905219i	$0.639706\pi$
$488$	10.8090	+	6.24056i	0.489299	+	0.282497i
$489$		−	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	$0.922744\pi$
$492$	1.10418	−	0.637499i	0.0497803	−	0.0287407i
$493$	−47.3497			−2.13252
$494$	4.98286	−	3.00610i	0.224189	−	0.135251i
$495$		0			0
$496$	−8.55695	+	4.94036i	−0.384219	+	0.221829i
$497$	−12.0157	−	20.8118i	−0.538978	−	0.933537i
$498$	−0.489668	+	0.848130i	−0.0219425	+	0.0380056i
$499$			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
$502$			7.76444i			0.346544i
$503$	−2.78988	+	4.83222i	−0.124395	+	0.215458i	−0.921496	−	0.388387i	$-0.873032\pi$
$503$	−2.78988	+	4.83222i	−0.124395	+	0.215458i	0.797101	+	0.603845i	$0.206366\pi$
$504$	−0.758819	−	1.31431i	−0.0338005	−	0.0585442i
$505$		0			0
$506$	28.0082			1.24512
$507$	12.9904	−	0.500000i	0.576923	−	0.0222058i
$508$	11.9907			0.532002
$509$	27.6679	−	15.9741i	1.22636	−	0.708039i	0.260093	−	0.965584i	$-0.416247\pi$
$509$	27.6679	−	15.9741i	1.22636	−	0.708039i	0.966266	+	0.257545i	$0.0829134\pi$
$510$		0			0
$511$	3.33391	−	5.77450i	0.147483	−	0.255449i
$512$			1.00000i			0.0441942i
$513$	1.39778	+	0.807007i	0.0617134	+	0.0356302i
$514$	−16.7841	−	9.69031i	−0.740315	−	0.427421i
$515$		0			0
$516$	−1.18336	+	2.04965i	−0.0520947	+	0.0902307i
$517$	−17.6236	−	30.5250i	−0.775086	−	1.34249i
$518$	−11.4866	+	6.63179i	−0.504692	+	0.291384i
$519$	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	$0.502359\pi$
$522$	8.55085	−	4.93684i	0.374261	−	0.216079i
$523$	−11.5529	−	20.0102i	−0.505174	−	0.874986i	−0.999982	−	0.00598438i	$-0.998095\pi$
$523$	−11.5529	−	20.0102i	−0.505174	−	0.874986i	0.494808	−	0.869002i	$-0.335238\pi$
$524$	−10.1762	+	17.6257i	−0.444549	+	0.769981i
$525$		0			0
$526$	−1.64019	−	0.946961i	−0.0715155	−	0.0412895i
$527$	−41.0353	−	23.6918i	−1.78753	−	1.03203i
$528$			5.14626i			0.223962i
$529$	−3.31008	+	5.73324i	−0.143917	+	0.249271i
$530$		0			0
$531$	8.04354	−	4.64394i	0.349060	−	0.201530i
$532$	2.44949			0.106199
$533$	−2.22153	+	4.02465i	−0.0962253	+	0.174327i
$534$	−4.08933			−0.176963
$535$		0			0
$536$	5.76733	+	9.98930i	0.249111	+	0.431472i
$537$	10.7700	−	18.6542i	0.464759	−	0.804987i
$538$		−	4.60207i		−	0.198409i
$539$	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	$0.787431\pi$
$542$	4.17191	−	7.22596i	0.179199	−	0.310382i
$543$	2.04164	+	3.53622i	0.0876151	+	0.151754i
$544$	−4.15307	+	2.39778i	−0.178062	+	0.102804i
$545$		0			0
$546$	4.79057	+	2.64431i	0.205018	+	0.113166i
$547$	−33.4957			−1.43217			−0.716086	−	0.698013i	$-0.754068\pi$
$547$	−33.4957			−1.43217			−0.716086	+	0.698013i	$0.754068\pi$
$548$	−6.82684	+	3.94148i	−0.291628	+	0.168372i
$549$	−6.24056	−	10.8090i	−0.266341	−	0.461315i
$550$		0			0
$551$			15.9362i			0.678907i
$552$	−4.71329	−	2.72122i	−0.200611	−	0.115823i
$553$	14.5076	+	8.37599i	0.616928	+	0.356183i
$554$			22.2377i			0.944791i
$555$		0			0
$556$	2.05852	+	3.56546i	0.0873007	+	0.151209i
$557$	31.6950	−	18.2991i	1.34296	−	0.775358i	0.355718	−	0.934593i	$-0.384236\pi$
$557$	31.6950	−	18.2991i	1.34296	−	0.775358i	0.987241	+	0.159236i	$0.0509030\pi$
$558$	9.88072			0.418284
$559$	−0.164134	−	8.53179i	−0.00694211	−	0.360856i
$560$		0			0
$561$	−21.3728	+	12.3396i	−0.902361	+	0.520978i
$562$	−10.0481	−	17.4038i	−0.423852	−	0.734133i
$563$	−5.18180	+	8.97514i	−0.218387	+	0.378257i	−0.954315	−	0.298803i	$-0.903413\pi$
$563$	−5.18180	+	8.97514i	−0.218387	+	0.378257i	0.735928	+	0.677060i	$0.236746\pi$
$564$			6.84909i			0.288399i
$565$		0			0
$566$	0.623402	+	0.359921i	0.0262036	+	0.0151286i
$567$			1.51764i			0.0637348i
$568$	7.91737	−	13.7133i	0.332206	−	0.575397i
$569$	15.7893	+	27.3479i	0.661923	+	1.14648i	0.980110	+	0.198456i	$0.0635928\pi$
$569$	15.7893	+	27.3479i	0.661923	+	1.14648i	−0.318187	+	0.948028i	$0.603074\pi$
$570$		0			0
$571$	33.7160			1.41097			0.705485	−	0.708725i	$-0.250729\pi$
$571$	33.7160			1.41097			0.705485	+	0.708725i	$0.250729\pi$
$572$	−9.58492	−	15.8878i	−0.400766	−	0.664302i
$573$	12.9564			0.541263
$574$	−1.67575	+	0.967492i	−0.0699443	+	0.0403823i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	40.8530i		−	1.70073i	−0.526193	−	0.850365i	$-0.676381\pi$
$577$		−	40.8530i		−	1.70073i	0.526193	−	0.850365i	$-0.323619\pi$
$578$	−5.19386	−	2.99867i	−0.216036	−	0.124728i
$579$	−7.49706	−	4.32843i	−0.311567	−	0.179883i
$580$		0			0
$581$	0.743139	−	1.28715i	0.0308306	−	0.0534001i
$582$	2.85898	+	4.95189i	0.118508	+	0.205263i
$583$	−3.93073	+	2.26941i	−0.162794	+	0.0939893i
$584$	4.39355			0.181806
$585$		0			0
$586$	−13.2278			−0.546435
$587$	−21.3431	+	12.3224i	−0.880924	+	0.508602i	−0.870963	−	0.491349i	$-0.836504\pi$
$587$	−21.3431	+	12.3224i	−0.880924	+	0.508602i	−0.00996119	+	0.999950i	$0.503171\pi$
$588$	−2.34839	−	4.06753i	−0.0968459	−	0.167742i
$589$	−7.97381	+	13.8110i	−0.328555	+	0.569074i
$590$		0			0
$591$	−3.76574	−	2.17415i	−0.154902	−	0.0894327i
$592$	−7.56873	−	4.36981i	−0.311073	−	0.179598i
$593$		−	21.4887i		−	0.882436i	−0.897400	−	0.441218i	$-0.854547\pi$
$593$		−	21.4887i		−	0.882436i	0.897400	−	0.441218i	$-0.145453\pi$
$594$	2.57313	−	4.45680i	0.105577	−	0.182865i
$595$		0			0
$596$	−8.00644	+	4.62252i	−0.327957	+	0.189346i
$597$	−7.46702			−0.305605
$598$	19.6194	−	0.377435i	0.802296	−	0.0154345i
$599$	−29.1850			−1.19247			−0.596233	−	0.802812i	$-0.703337\pi$
$599$	−29.1850			−1.19247			−0.596233	+	0.802812i	$0.703337\pi$
$600$		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	$0.876564\pi$
$602$	1.79592	−	3.11062i	0.0731962	−	0.126780i
$603$		−	11.5347i		−	0.469727i
$604$	−14.8506	−	8.57397i	−0.604260	−	0.348870i
$605$		0			0
$606$		−	7.85374i		−	0.319036i
$607$	−11.7047	+	20.2731i	−0.475078	+	0.822860i	−0.999593	−	0.0285420i	$-0.990914\pi$
$607$	−11.7047	+	20.2731i	−0.475078	+	0.822860i	0.524514	+	0.851402i	$0.324247\pi$
$608$	0.807007	+	1.39778i	0.0327285	+	0.0566874i
$609$	−12.9771	+	7.49233i	−0.525858	+	0.303605i
$610$		0			0
$611$	−12.7564	−	21.1448i	−0.516070	−	0.855428i
$612$	4.79555			0.193849
$613$	−4.55182	+	2.62799i	−0.183846	+	0.106144i	−0.589099	−	0.808061i	$-0.700517\pi$
$613$	−4.55182	+	2.62799i	−0.183846	+	0.106144i	0.405252	+	0.914205i	$0.367184\pi$
$614$	3.92587	+	6.79981i	0.158435	+	0.274418i
$615$		0			0
$616$		−	7.81017i		−	0.314681i
$617$	22.8678	+	13.2027i	0.920622	+	0.531522i	0.883834	−	0.467802i	$-0.154954\pi$
$617$	22.8678	+	13.2027i	0.920622	+	0.531522i	0.0367887	+	0.999323i	$0.488287\pi$
$618$	2.74919	+	1.58725i	0.110589	+	0.0638484i
$619$		−	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
$622$	−13.6579	+	7.88538i	−0.547631	+	0.316175i
$623$	6.20612			0.248643
$624$	0.0693504	+	3.60488i	0.00277624	+	0.144311i
$625$		0			0
$626$	18.2396	−	10.5306i	0.729001	−	0.420889i
$627$	4.15307	+	7.19333i	0.165858	+	0.287274i
$628$	9.13954	−	15.8301i	0.364707	−	0.631692i
$629$		−	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	$0.623720\pi$
$632$			11.0382i			0.439076i
$633$	6.74384	−	11.6807i	0.268044	−	0.464265i
$634$	−13.2071	−	22.8753i	−0.524520	−	0.908494i
$635$		0			0
$636$	0.881964			0.0349721
$637$	14.8258	+	8.18358i	0.587420	+	0.324245i
$638$	50.8125			2.01169
$639$	−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	$-0.0290360\pi$
$642$			13.7532i			0.542797i
$643$	6.98298	+	4.03163i	0.275382	+	0.158992i	0.631331	−	0.775514i	$-0.282509\pi$
$643$	6.98298	+	4.03163i	0.275382	+	0.158992i	−0.355949	+	0.934505i	$0.615842\pi$
$644$	7.15307	+	4.12983i	0.281871	+	0.162738i
$645$		0			0
$646$	−3.87005	+	6.70312i	−0.152265	+	0.263731i
$647$	0.360179	+	0.623849i	0.0141601	+	0.0245260i	0.873019	−	0.487687i	$-0.162159\pi$
$647$	0.360179	+	0.623849i	0.0141601	+	0.0245260i	−0.858859	+	0.512213i	$0.828826\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	47.7979			1.87623
$650$		0			0
$651$	−14.9954			−0.587714
$652$	−1.47555	+	0.851911i	−0.0577871	+	0.0333634i
$653$	−13.3367	−	23.0998i	−0.521904	−	0.903963i	−0.999675	−	0.0254795i	$-0.991889\pi$
$653$	−13.3367	−	23.0998i	−0.521904	−	0.903963i	0.477772	−	0.878484i	$-0.341445\pi$
$654$	−8.39475	+	14.5401i	−0.328261	+	0.568564i
$655$		0			0
$656$	−1.10418	−	0.637499i	−0.0431110	−	0.0248901i
$657$	−3.80493	−	2.19677i	−0.148444	−	0.0857043i
$658$		−	10.3944i		−	0.405218i
$659$	9.02067	−	15.6243i	0.351396	−	0.608635i	−0.635099	−	0.772431i	$-0.719041\pi$
$659$	9.02067	−	15.6243i	0.351396	−	0.608635i	0.986494	+	0.163796i	$0.0523739\pi$
$660$		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	$0.256900\pi$
$662$	20.4252			0.793847
$663$	−14.8051	+	8.93173i	−0.574981	+	0.346880i
$664$	0.979336			0.0380056
$665$		0			0
$666$	4.36981	+	7.56873i	0.169327	+	0.293282i
$667$	−26.8684	+	46.5375i	−1.04035	+	1.80194i
$668$		−	5.33434i		−	0.206392i
$669$	6.08030	+	3.51047i	0.235078	+	0.135722i
$670$		0			0
$671$		−	64.2311i		−	2.47962i
$672$	−0.758819	+	1.31431i	−0.0292721	+	0.0507007i
$673$	−2.32913	−	4.03417i	−0.0897814	−	0.155506i	0.817637	−	0.575734i	$-0.195284\pi$
$673$	−2.32913	−	4.03417i	−0.0897814	−	0.155506i	−0.907419	+	0.420228i	$0.861950\pi$
$674$	−11.3479	+	6.55173i	−0.437106	+	0.252363i
$675$		0			0
$676$	−6.92820	−	11.0000i	−0.266469	−	0.423077i
$677$	22.1830			0.852561			0.426280	−	0.904591i	$-0.359824\pi$
$677$	22.1830			0.852561			0.426280	+	0.904591i	$0.359824\pi$
$678$	8.36308	−	4.82843i	0.321182	−	0.185435i
$679$	−4.33889	−	7.51518i	−0.166511	−	0.288406i
$680$		0			0
$681$			8.59524i			0.329370i
$682$	44.0363	+	25.4244i	1.68624	+	0.973550i
$683$	−10.9766	−	6.33735i	−0.420008	−	0.242492i	0.275072	−	0.961423i	$-0.411298\pi$
$683$	−10.9766	−	6.33735i	−0.420008	−	0.242492i	−0.695081	+	0.718931i	$0.744631\pi$
$684$		−	1.61401i		−	0.0617134i
$685$		0			0
$686$	8.87574	+	15.3732i	0.338877	+	0.586952i
$687$	−14.2102	+	8.20429i	−0.542155	+	0.313013i
$688$	2.36673			0.0902307
$689$	−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	$0.242890\pi$
$692$	−8.83839	−	15.3085i	−0.335985	−	0.581944i
$693$	−3.90508	+	6.76380i	−0.148342	+	0.256936i
$694$		−	17.7605i		−	0.674181i
$695$		0			0
$696$	−8.55085	−	4.93684i	−0.324119	−	0.187130i
$697$		−	6.11432i		−	0.231596i
$698$	0.0598981	−	0.103747i	0.00226718	−	0.00392687i
$699$	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	$0.337146\pi$
$702$	1.74238	−	3.15660i	0.0657620	−	0.119138i
$703$	−14.1059			−0.532013
$704$	4.45680	−	2.57313i	0.167972	−	0.0969786i
$705$		0			0
$706$	−3.77620	+	6.54057i	−0.142119	+	0.246158i
$707$			11.9191i			0.448265i
$708$	−8.04354	−	4.64394i	−0.302295	−	0.174530i
$709$	−28.0091	−	16.1711i	−1.05190	−	0.607317i	−0.128722	−	0.991681i	$-0.541087\pi$
$709$	−28.0091	−	16.1711i	−1.05190	−	0.607317i	−0.923182	+	0.384364i	$0.874421\pi$
$710$		0			0
$711$	5.51910	−	9.55936i	0.206982	−	0.358504i
$712$	2.04466	+	3.54146i	0.0766270	+	0.132722i
$713$	−46.5707	+	26.8876i	−1.74409	+	1.00695i
$714$	−7.27792			−0.272369
$715$		0			0
$716$	−21.5400			−0.804987
$717$	−15.8531	+	9.15281i	−0.592046	+	0.341818i
$718$	−14.9847	−	25.9542i	−0.559223	−	0.968602i
$719$	−6.84506	+	11.8560i	−0.255278	+	0.442154i	−0.964971	−	0.262357i	$-0.915500\pi$
$719$	−6.84506	+	11.8560i	−0.255278	+	0.442154i	0.709693	+	0.704511i	$0.248834\pi$
$720$		0			0
$721$	−4.17228	−	2.40887i	−0.155384	−	0.0897108i
$722$	−14.1984	−	8.19748i	−0.528412	−	0.305079i
$723$			14.4229i			0.536395i
$724$	2.04164	−	3.53622i	0.0758769	−	0.131423i
$725$		0			0
$726$	13.4096	−	7.74202i	0.497676	−	0.287333i
$727$	49.1587			1.82319			0.911597	−	0.411084i	$-0.134850\pi$
$727$	49.1587			1.82319			0.911597	+	0.411084i	$0.134850\pi$
$728$	−0.105249	−	5.47091i	−0.00390078	−	0.202765i
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.67489	+	9.82920i	0.209893	+	0.363546i
$732$	−6.24056	+	10.8090i	−0.230658	+	0.399511i
$733$			44.9158i			1.65900i	0.558505	+	0.829501i	$0.311375\pi$
$733$			44.9158i			1.65900i	−0.558505	+	0.829501i	$0.688625\pi$
$734$	−25.0232	−	14.4472i	−0.923625	−	0.533255i
$735$		0			0
$736$			5.44244i			0.200611i
$737$	29.6802	−	51.4076i	1.09328	−	1.89362i
$738$	0.637499	+	1.10418i	0.0234667	+	0.0406454i
$739$	14.2102	−	8.20427i	0.522731	−	0.301799i	−0.215320	−	0.976543i	$-0.569080\pi$
$739$	14.2102	−	8.20427i	0.522731	−	0.301799i	0.738051	+	0.674745i	$0.235746\pi$
$740$		0			0
$741$	3.00610	+	4.98286i	0.110432	+	0.183050i
$742$	−1.33850			−0.0491379
$743$	5.73773	−	3.31268i	0.210497	−	0.121530i	−0.391045	−	0.920371i	$-0.627886\pi$
$743$	5.73773	−	3.31268i	0.210497	−	0.121530i	0.601542	+	0.798841i	$0.294553\pi$
$744$	−4.94036	−	8.55695i	−0.181122	−	0.313713i
$745$		0			0
$746$		−	14.7117i		−	0.538632i
$747$	−0.848130	−	0.489668i	−0.0310314	−	0.0179160i
$748$	21.3728	+	12.3396i	0.781467	+	0.451180i
$749$		−	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	$0.568134\pi$
$752$	5.93149	−	3.42455i	0.216299	−	0.124880i
$753$	−7.76444			−0.282952
$754$	35.5934	−	0.684743i	1.29624	−	0.0249369i
$755$		0			0
$756$	1.31431	−	0.758819i	0.0478011	−	0.0275980i
$757$	−12.1639	−	21.0685i	−0.442105	−	0.765748i	0.555741	−	0.831356i	$-0.312435\pi$
$757$	−12.1639	−	21.0685i	−0.442105	−	0.765748i	−0.997845	+	0.0656076i	$0.979101\pi$
$758$	−15.6627	+	27.1285i	−0.568893	+	0.985352i
$759$			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	$0.669036\pi$
$762$			11.9907i			0.434378i
$763$	12.7402	−	22.0667i	0.461226	−	0.798867i
$764$	−6.47822	−	11.2206i	−0.234374	−	0.405947i
$765$		0			0
$766$	−10.8474			−0.391931
$767$	33.4817	−	0.644118i	1.20896	−	0.0232578i
$768$	−1.00000			−0.0360844
$769$	−36.0692	+	20.8246i	−1.30069	+	0.750954i	−0.980522	−	0.196407i	$-0.937073\pi$
$769$	−36.0692	+	20.8246i	−1.30069	+	0.750954i	−0.320168	+	0.947361i	$0.603739\pi$
$770$		0			0
$771$	9.69031	−	16.7841i	0.348988	−	0.604465i
$772$			8.65685i			0.311567i
$773$	44.8150	+	25.8739i	1.61188	+	0.930621i	0.988934	+	0.148358i	$0.0473989\pi$
$773$	44.8150	+	25.8739i	1.61188	+	0.930621i	0.622949	+	0.782262i	$0.285934\pi$
$774$	−2.04965	−	1.18336i	−0.0736731	−	0.0425352i
$775$		0			0
$776$	2.85898	−	4.95189i	0.102631	−	0.177763i
$777$	−6.63179	−	11.4866i	−0.237914	−	0.412079i
$778$	−15.8463	+	9.14884i	−0.568116	+	0.328002i
$779$	−2.05786			−0.0737306
$780$		0			0
$781$	−81.4898			−2.91593
$782$	−22.6029	+	13.0498i	−0.808276	+	0.466659i
$783$	4.93684	+	8.55085i	0.176428	+	0.305582i
$784$	−2.34839	+	4.06753i	−0.0838710	+	0.145269i
$785$		0			0
$786$	−17.6257	−	10.1762i	−0.628687	−	0.362973i
$787$	14.9066	+	8.60630i	0.531361	+	0.306782i	0.741571	−	0.670875i	$-0.234081\pi$
$787$	14.9066	+	8.60630i	0.531361	+	0.306782i	−0.210209	+	0.977656i	$0.567415\pi$
$788$			4.34831i			0.154902i
$789$	0.946961	−	1.64019i	0.0337127	−	0.0583921i
$790$		0			0
$791$	−12.6921	+	7.32780i	−0.451280	+	0.260547i
$792$	−5.14626			−0.182865
$793$	−0.865570	−	44.9930i	−0.0307373	−	1.59775i
$794$	0.307656			0.0109183
$795$		0			0
$796$	3.73351	+	6.46663i	0.132331	+	0.229204i
$797$	−12.3539	+	21.3976i	−0.437599	+	0.757943i	−0.997504	−	0.0706135i	$-0.977504\pi$
$797$	−12.3539	+	21.3976i	−0.437599	+	0.757943i	0.559905	+	0.828557i	$0.310838\pi$
$798$			2.44949i			0.0867110i
$799$	28.4448	+	16.4226i	1.00630	+	0.580990i
$800$		0			0
$801$		−	4.08933i		−	0.144489i
$802$	1.09273	−	1.89266i	0.0385856	−	0.0668322i
$803$	−11.3052	−	19.5812i	−0.398951	−	0.691004i
$804$	−9.98930	+	5.76733i	−0.352296	+	0.203398i
$805$		0			0
$806$	31.1894	+	17.2160i	1.09860	+	0.606408i
$807$	4.60207			0.162001
$808$	−6.80153	+	3.92687i	−0.239277	+	0.138147i
$809$	−12.5285	−	21.7001i	−0.440480	−	0.762934i	0.557245	−	0.830348i	$-0.311858\pi$
$809$	−12.5285	−	21.7001i	−0.440480	−	0.762934i	−0.997725	+	0.0674144i	$0.978525\pi$
$810$		0			0
$811$		−	35.2387i		−	1.23740i	−0.785628	−	0.618699i	$-0.787660\pi$
$811$		−	35.2387i		−	1.23740i	0.785628	−	0.618699i	$-0.212340\pi$
$812$	12.9771	+	7.49233i	0.455407	+	0.262929i
$813$	7.22596	+	4.17191i	0.253426	+	0.146315i
$814$			44.9764i			1.57642i
$815$		0			0
$816$	−2.39778	−	4.15307i	−0.0839390	−	0.145387i
$817$	3.30816	−	1.90997i	0.115738	−	0.0668213i
$818$	37.6510			1.31644
$819$	−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	$0.512892\pi$
$822$	−3.94148	−	6.82684i	−0.137475	−	0.238113i
$823$	−17.8946	+	30.9943i	−0.623765	+	1.08039i	0.365014	+	0.931002i	$0.381064\pi$
$823$	−17.8946	+	30.9943i	−0.623765	+	1.08039i	−0.988778	+	0.149390i	$0.952269\pi$
$824$		−	3.17449i		−	0.110589i
$825$		0			0
$826$	12.2072	+	7.04782i	0.424742	+	0.245225i
$827$		−	7.53716i		−	0.262093i	−0.991376	−	0.131046i	$-0.958166\pi$
$827$		−	7.53716i		−	0.262093i	0.991376	−	0.131046i	$-0.0418337\pi$
$828$	2.72122	−	4.71329i	0.0945690	−	0.163798i
$829$	−25.9628	−	44.9688i	−0.901724	−	1.56183i	−0.825256	−	0.564759i	$-0.808969\pi$
$829$	−25.9628	−	44.9688i	−0.901724	−	1.56183i	−0.0764677	−	0.997072i	$-0.524364\pi$
$830$		0			0
$831$	−22.2377			−0.771419
$832$	3.08725	−	1.86250i	0.107031	−	0.0645706i
$833$	−22.5236			−0.780398
$834$	−3.56546	+	2.05852i	−0.123462	+	0.0712807i
$835$		0			0
$836$	4.15307	−	7.19333i	0.143637	−	0.248787i
$837$			9.88072i			0.341528i
$838$	−23.4359	−	13.5307i	−0.809581	−	0.467412i
$839$	6.72183	+	3.88085i	0.232063	+	0.133982i	0.611524	−	0.791226i	$-0.290557\pi$
$839$	6.72183	+	3.88085i	0.232063	+	0.133982i	−0.379460	+	0.925208i	$0.623890\pi$
$840$		0			0
$841$	−34.2447	+	59.3135i	−1.18085	+	2.04529i
$842$	−5.96780	−	10.3365i	−0.205664	−	0.356221i
$843$	17.4038	−	10.0481i	0.599417	−	0.346074i
$844$	−13.4877			−0.464265
$845$		0			0
$846$	−6.84909			−0.235477
$847$	−20.3509	+	11.7496i	−0.699264	+	0.403720i
$848$	−0.440982	−	0.763803i	−0.0151434	−	0.0262291i
$849$	−0.359921	+	0.623402i	−0.0123525	+	0.0213951i
$850$		0			0
$851$	−41.1924	−	23.7824i	−1.41206	−	0.815251i
$852$	13.7133	+	7.91737i	0.469810	+	0.271245i
$853$		−	13.8072i		−	0.472751i	−0.971662	−	0.236376i	$-0.924040\pi$
$853$		−	13.8072i		−	0.472751i	0.971662	−	0.236376i	$-0.0759596\pi$
$854$	9.47091	−	16.4041i	0.324088	−	0.561337i
$855$		0			0
$856$	11.9106	−	6.87662i	0.407098	−	0.235038i
$857$	40.8095			1.39403			0.697013	−	0.717059i	$-0.254512\pi$
$857$	40.8095			1.39403			0.697013	+	0.717059i	$0.254512\pi$
$858$	15.8878	−	9.58492i	0.542400	−	0.327224i
$859$	24.7784			0.845427			0.422713	−	0.906263i	$-0.361078\pi$
$859$	24.7784			0.845427			0.422713	+	0.906263i	$0.361078\pi$
$860$		0			0
$861$	−0.967492	−	1.67575i	−0.0329720	−	0.0571093i
$862$	14.9921	−	25.9671i	0.510633	−	0.884442i
$863$			27.0018i			0.919153i	0.888138	+	0.459577i	$0.151999\pi$
$863$			27.0018i			0.919153i	−0.888138	+	0.459577i	$0.848001\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$		−	20.9941i		−	0.713409i
$867$	2.99867	−	5.19386i	0.101840	−	0.176393i
$868$	7.49768	+	12.9864i	0.254488	+	0.440786i
$869$	49.1950	−	28.4027i	1.66883	−	0.963497i
$870$		0			0
$871$	20.0978	−	36.4102i	0.680987	−	1.23371i
$872$	16.7895			0.568564
$873$	−4.95189	+	2.85898i	−0.167596	+	0.0967617i
$874$	4.39209	+	7.60732i	0.148565	+	0.257322i
$875$		0			0
$876$			4.39355i			0.148444i
$877$	−24.4850	−	14.1364i	−0.826799	−	0.477352i	0.0259566	−	0.999663i	$-0.491737\pi$
$877$	−24.4850	−	14.1364i	−0.826799	−	0.477352i	−0.852755	+	0.522311i	$0.825070\pi$
$878$	6.33386	+	3.65685i	0.213757	+	0.123413i
$879$		−	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	$0.935589\pi$
$882$	4.06753	−	2.34839i	0.136961	−	0.0790743i
$883$	−54.1400			−1.82196			−0.910978	−	0.412456i	$-0.864671\pi$
$883$	−54.1400			−1.82196			−0.910978	+	0.412456i	$0.864671\pi$
$884$	15.1376	+	8.35569i	0.509134	+	0.281032i
$885$		0			0
$886$	11.1051	−	6.41155i	0.373084	−	0.215400i
$887$	12.4062	+	21.4881i	0.416558	+	0.721500i	0.995591	−	0.0938043i	$-0.0299028\pi$
$887$	12.4062	+	21.4881i	0.416558	+	0.721500i	−0.579032	+	0.815305i	$0.696569\pi$
$888$	4.36981	−	7.56873i	0.146641	−	0.253990i
$889$		−	18.1976i		−	0.610327i
$890$		0			0
$891$	4.45680	+	2.57313i	0.149308	+	0.0862032i
$892$		−	7.02093i		−	0.235078i
$893$	5.52727	−	9.57351i	0.184963	−	0.320365i
$894$	−4.62252	−	8.00644i	−0.154600	−	0.267776i
$895$		0			0
$896$	1.51764			0.0507007
$897$	0.377435	+	19.6194i	0.0126022	+	0.655072i
$898$	−3.15597			−0.105316
$899$	−84.4885	+	48.7795i	−2.81785	+	1.62689i
$900$		0			0
$901$	2.11475	−	3.66286i	0.0704526	−	0.122028i
$902$			6.56147i			0.218473i
$903$	3.11062	+	1.79592i	0.103515	+	0.0597645i
$904$	−8.36308	−	4.82843i	−0.278152	−	0.160591i
$905$		0			0
$906$	8.57397	−	14.8506i	0.284851	−	0.493377i
$907$	−7.87598	−	13.6416i	−0.261517	−	0.452962i	0.705128	−	0.709080i	$-0.250890\pi$
$907$	−7.87598	−	13.6416i	−0.261517	−	0.452962i	−0.966645	+	0.256119i	$0.917556\pi$
$908$	7.44370	−	4.29762i	0.247028	−	0.142622i
$909$	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	$0.529490\pi$
$912$	−1.39778	+	0.807007i	−0.0462850	+	0.0267227i
$913$	−2.51996	−	4.36470i	−0.0833985	−	0.144450i
$914$	−0.144671	+	0.250578i	−0.00478530	+	0.00828838i
$915$		0			0
$916$	14.2102	+	8.20429i	0.469520	+	0.271077i
$917$	26.7494	+	15.4438i	0.883343	+	0.509998i
$918$			4.79555i			0.158277i
$919$	−3.54423	+	6.13879i	−0.116913	+	0.202500i	−0.918543	−	0.395321i	$-0.870633\pi$
$919$	−3.54423	+	6.13879i	−0.116913	+	0.202500i	0.801630	+	0.597821i	$0.203967\pi$
$920$		0			0
$921$	−6.79981	+	3.92587i	−0.224061	+	0.129362i
$922$	−3.55416			−0.117050
$923$	−57.0824	+	1.09815i	−1.87889	+	0.0361459i
$924$	7.81017			0.256936
$925$		0			0
$926$	6.05582	+	10.4890i	0.199006	+	0.344689i
$927$	−1.58725	+	2.74919i	−0.0521320	+	0.0902953i
$928$			9.87367i			0.324119i
$929$	3.64324	+	2.10342i	0.119531	+	0.0690111i	0.558573	−	0.829455i	$-0.311349\pi$
$929$	3.64324	+	2.10342i	0.119531	+	0.0690111i	−0.439043	+	0.898466i	$0.644682\pi$
$930$		0			0
$931$			7.58066i			0.248446i
$932$	3.47115	−	6.01221i	0.113701	−	0.196936i
$933$	−7.88538	−	13.6579i	−0.258156	−	0.447139i
$934$	−25.9221	+	14.9661i	−0.848198	+	0.489707i
$935$		0			0
$936$	−3.60488	+	0.0693504i	−0.117829	+	0.00226679i
$937$	25.2818			0.825920			0.412960	−	0.910749i	$-0.364495\pi$
$937$	25.2818			0.825920			0.412960	+	0.910749i	$0.364495\pi$
$938$	15.1601	−	8.75272i	0.494996	−	0.285786i
$939$	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	$-0.241768\pi$
$942$	15.8301	+	9.13954i	0.515774	+	0.297782i
$943$	−6.00944	−	3.46955i	−0.195694	−	0.112984i
$944$			9.28788i			0.302295i
$945$		0			0
$946$	−6.08991	−	10.5480i	−0.198000	−	0.342946i
$947$	−35.7719	+	20.6529i	−1.16243	+	0.671130i	−0.951885	−	0.306454i	$-0.900857\pi$
$947$	−35.7719	+	20.6529i	−1.16243	+	0.671130i	−0.210546	+	0.977584i	$0.567524\pi$
$948$	−11.0382			−0.358504
$949$	−8.18299	−	13.5640i	−0.265631	−	0.440305i
$950$		0			0
$951$	22.8753	−	13.2071i	0.741783	−	0.428268i
$952$	3.63896	+	6.30286i	0.117939	+	0.204277i
$953$	−5.69547	+	9.86484i	−0.184494	+	0.319553i	−0.943406	−	0.331640i	$-0.892398\pi$
$953$	−5.69547	+	9.86484i	−0.184494	+	0.319553i	0.758912	+	0.651193i	$0.225731\pi$
$954$			0.881964i			0.0285546i
$955$		0			0
$956$	15.8531	+	9.15281i	0.512727	+	0.296023i
$957$			50.8125i			1.64254i
$958$	1.17209	−	2.03012i	0.0378685	−	0.0655901i
$959$	5.98174	+	10.3607i	0.193160	+	0.334564i
$960$		0			0
$961$	−66.6286			−2.14931
$962$	0.606095	+	31.5053i	0.0195413	+	1.01577i
$963$	−13.7532			−0.443192
$964$	12.4906	−	7.21147i	0.402296	−	0.232266i
$965$		0			0
$966$	−4.12983	+	7.15307i	−0.132875	+	0.230146i
$967$			39.5770i			1.27271i	0.771396	+	0.636355i	$0.219559\pi$
$967$			39.5770i			1.27271i	−0.771396	+	0.636355i	$0.780441\pi$
$968$	−13.4096	−	7.74202i	−0.431000	−	0.248838i
$969$	−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	$0.186411\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	5.41108	−	3.12409i	0.173471	−	0.100154i
$974$	3.73378			0.119638
$975$		0			0
$976$	12.4811			0.399511
$977$	−34.9993	+	20.2068i	−1.11973	+	0.646474i	−0.941331	−	0.337485i	$-0.890424\pi$
$977$	−34.9993	+	20.2068i	−1.11973	+	0.646474i	−0.178395	+	0.983959i	$0.557091\pi$
$978$	−0.851911	−	1.47555i	−0.0272411	−	0.0471830i
$979$	10.5224	−	18.2253i	0.336297	−	0.582483i
$980$		0			0
$981$	−14.5401	−	8.39475i	−0.464231	−	0.268024i
$982$	−10.6393	−	6.14261i	−0.339514	−	0.196018i
$983$		−	15.5229i		−	0.495103i	−0.968875	−	0.247551i	$-0.920374\pi$
$983$		−	15.5229i		−	0.495103i	0.968875	−	0.247551i	$-0.0796259\pi$
$984$	0.637499	−	1.10418i	0.0203227	−	0.0352000i
$985$		0			0
$986$	−41.0061	+	23.6749i	−1.30590	+	0.753961i
$987$	10.3944			0.330859
$988$	2.81223	−	5.09479i	0.0894690	−	0.162087i
$989$	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	$0.633365\pi$
$992$	−4.94036	+	8.55695i	−0.156857	+	0.271684i
$993$			20.4252i			0.648173i
$994$	−20.8118	−	12.0157i	−0.660111	−	0.381115i
$995$		0			0
$996$			0.979336i			0.0310314i
$997$	24.0165	−	41.5979i	0.760611	−	1.31742i	−0.181925	−	0.983312i	$-0.558233\pi$
$997$	24.0165	−	41.5979i	0.760611	−	1.31742i	0.942536	−	0.334105i	$-0.108434\pi$
$998$	8.91335	+	15.4384i	0.282147	+	0.488693i
$999$	−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.bc.f.751.3	yes	8
5.2	odd	4		1950.2.y.l.49.4		8
5.3	odd	4		1950.2.y.i.49.1		8
5.4	even	2		1950.2.bc.e.751.2	✓	8
13.4	even	6	inner	1950.2.bc.f.901.3	yes	8
65.4	even	6		1950.2.bc.e.901.2	yes	8
65.17	odd	12		1950.2.y.i.199.1		8
65.43	odd	12		1950.2.y.l.199.4		8

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

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.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.31431 - 0.758819i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.31431 - 0.758819i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.45680 + 2.57313i) q^{11} +1.00000 q^{12} +(-3.08725 + 1.86250i) q^{13} -1.51764 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.39778 - 4.15307i) q^{17} +1.00000i q^{18} +(-1.39778 - 0.807007i) q^{19} -1.51764i q^{21} +(-2.57313 + 4.45680i) q^{22} +(-2.72122 - 4.71329i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.74238 + 3.15660i) q^{26} -1.00000 q^{27} +(-1.31431 + 0.758819i) q^{28} +(-4.93684 - 8.55085i) q^{29} -9.88072i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.45680 - 2.57313i) q^{33} -4.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.56873 - 4.36981i) q^{37} -1.61401 q^{38} +(-3.15660 - 1.74238i) q^{39} +(1.10418 - 0.637499i) q^{41} +(-0.758819 - 1.31431i) q^{42} +(-1.18336 + 2.04965i) q^{43} +5.14626i q^{44} +(-4.71329 - 2.72122i) q^{46} +6.84909i q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.34839 - 4.06753i) q^{49} +4.79555 q^{51} +(0.0693504 + 3.60488i) q^{52} +0.881964 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.758819 + 1.31431i) q^{56} -1.61401i q^{57} +(-8.55085 - 4.93684i) q^{58} +(-8.04354 - 4.64394i) q^{59} +(-6.24056 + 10.8090i) q^{61} +(-4.94036 - 8.55695i) q^{62} +(1.31431 - 0.758819i) q^{63} -1.00000 q^{64} -5.14626 q^{66} +(-9.98930 + 5.76733i) q^{67} +(-2.39778 - 4.15307i) q^{68} +(2.72122 - 4.71329i) q^{69} +(13.7133 + 7.91737i) q^{71} +(0.866025 + 0.500000i) q^{72} +4.39355i q^{73} +(4.36981 - 7.56873i) q^{74} +(-1.39778 + 0.807007i) q^{76} +7.81017 q^{77} +(-3.60488 + 0.0693504i) q^{78} -11.0382 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.637499 - 1.10418i) q^{82} +0.979336i q^{83} +(-1.31431 - 0.758819i) q^{84} +2.36673i q^{86} +(4.93684 - 8.55085i) q^{87} +(2.57313 + 4.45680i) q^{88} +(-3.54146 + 2.04466i) q^{89} +(5.47091 - 0.105249i) q^{91} -5.44244 q^{92} +(8.55695 - 4.94036i) q^{93} +(3.42455 + 5.93149i) q^{94} -1.00000i q^{96} +(4.95189 + 2.85898i) q^{97} +(-4.06753 - 2.34839i) q^{98} -5.14626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} + 8 q^{12} - 8 q^{14} - 4 q^{16} - 4 q^{17} + 12 q^{19} - 8 q^{22} - 4 q^{23} - 8 q^{27} + 4 q^{29} - 12 q^{33} + 4 q^{36} + 24 q^{37} - 4 q^{42} + 4 q^{43} + 12 q^{46} + 4 q^{48} - 16 q^{49} - 8 q^{51} + 8 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 16 q^{66} - 24 q^{67} + 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} + 8 q^{77} - 8 q^{79} - 4 q^{81} + 20 q^{82} - 4 q^{87} + 8 q^{88} + 24 q^{89} + 8 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} - 12 q^{97} - 12 q^{98}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 + 8 * q^12 - 8 * q^14 - 4 * q^16 - 4 * q^17 + 12 * q^19 - 8 * q^22 - 4 * q^23 - 8 * q^27 + 4 * q^29 - 12 * q^33 + 4 * q^36 + 24 * q^37 - 4 * q^42 + 4 * q^43 + 12 * q^46 + 4 * q^48 - 16 * q^49 - 8 * q^51 + 8 * q^53 - 4 * q^56 - 12 * q^58 - 12 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 16 * q^66 - 24 * q^67 + 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 + 8 * q^77 - 8 * q^79 - 4 * q^81 + 20 * q^82 - 4 * q^87 + 8 * q^88 + 24 * q^89 + 8 * q^91 - 8 * q^92 + 24 * q^93 + 16 * q^94 - 12 * q^97 - 12 * q^98

Introduction

L-functions

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