LMFDB - Embedded newform 1950.2.bc.f.901.3

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			901.3
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.f.751.3

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	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	−0.727376	−	0.686239i	$-0.759260\pi$
$7$	−1.31431	+	0.758819i	−0.496764	+	0.286807i	0.230612	+	0.973046i	$0.425927\pi$
$8$			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	−0.356415	−	0.934328i	$-0.616001\pi$
$11$	−4.45680	−	2.57313i	−1.34377	−	0.775829i	−0.987359	+	0.158499i	$0.949335\pi$
$12$	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	0.995296	+	0.0968774i	$0.0308855\pi$
$17$	2.39778	+	4.15307i	0.581546	+	1.00727i	−0.413750	+	0.910391i	$0.635781\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.39778	+	0.807007i	−0.320672	+	0.185140i	−0.651692	−	0.758484i	$-0.725941\pi$
$19$	−1.39778	+	0.807007i	−0.320672	+	0.185140i	0.331020	+	0.943624i	$0.392607\pi$
$20$		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	0.429407	+	0.903111i	$0.358723\pi$
$23$	−2.72122	+	4.71329i	−0.567414	+	0.982789i	−0.996821	+	0.0796783i	$0.974611\pi$
$24$	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	−0.112425	+	0.993660i	$0.535862\pi$
$29$	−4.93684	+	8.55085i	−0.916747	+	1.58785i	−0.804323	+	0.594193i	$0.797472\pi$
$30$		0			0
$31$			9.88072i			1.77463i	0.461164	+	0.887315i	$0.347432\pi$
$31$			9.88072i			1.77463i	−0.461164	+	0.887315i	$0.652568\pi$
$32$	−0.866025	+	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	0.969965	−	0.243245i	$-0.0782118\pi$
$37$	7.56873	+	4.36981i	1.24429	+	0.718392i	0.274326	+	0.961637i	$0.411545\pi$
$38$	−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	0.583738	−	0.811942i	$-0.301590\pi$
$41$	1.10418	+	0.637499i	0.172444	+	0.0995606i	−0.411294	+	0.911503i	$0.634923\pi$
$42$	−0.758819	+	1.31431i	−0.117088	+	0.202803i
$43$	−1.18336	−	2.04965i	−0.180461	−	0.312568i	0.761576	−	0.648075i	$-0.224426\pi$
$43$	−1.18336	−	2.04965i	−0.180461	−	0.312568i	−0.942038	+	0.335507i	$0.891092\pi$
$44$		−	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	$-0.833509\pi$
$47$		−	6.84909i		−	0.999043i	0.866302	−	0.499521i	$-0.166491\pi$
$48$	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	−0.921859	−	0.387526i	$-0.873330\pi$
$59$	−8.04354	+	4.64394i	−1.04718	+	0.604590i	−0.125322	+	0.992116i	$0.539996\pi$
$60$		0			0
$61$	−6.24056	−	10.8090i	−0.799022	−	1.38395i	−0.920254	−	0.391322i	$-0.872018\pi$
$61$	−6.24056	−	10.8090i	−0.799022	−	1.38395i	0.121232	−	0.992624i	$-0.461315\pi$
$62$	−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	−0.255387	−	0.966839i	$-0.582203\pi$
$67$	−9.98930	−	5.76733i	−1.22039	−	0.704591i	−0.965001	+	0.262248i	$0.915536\pi$
$68$	−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	0.642623	−	0.766182i	$-0.277846\pi$
$71$	13.7133	−	7.91737i	1.62747	−	0.939619i	0.984845	−	0.173437i	$-0.0554874\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	4.39355i		−	0.514226i	−0.966381	−	0.257113i	$-0.917229\pi$
$73$		−	4.39355i		−	0.514226i	0.966381	−	0.257113i	$-0.0827713\pi$
$74$	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	$-0.982883\pi$
$83$		−	0.979336i		−	0.107496i	0.998555	−	0.0537480i	$-0.0171168\pi$
$84$	−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	0.300418	−	0.953808i	$-0.402874\pi$
$89$	−3.54146	−	2.04466i	−0.375394	−	0.216734i	−0.675812	+	0.737074i	$0.736207\pi$
$90$		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	−0.227076	−	0.973877i	$-0.572917\pi$
$97$	4.95189	−	2.85898i	0.502789	−	0.290285i	0.729864	+	0.683592i	$0.239583\pi$
$98$	−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	−0.992547	−	0.121862i	$-0.961113\pi$
$101$	−3.92687	+	6.80153i	−0.390738	+	0.676778i	0.601809	+	0.798640i	$0.294447\pi$
$102$	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	−0.314555	−	0.949239i	$-0.601855\pi$
$107$	6.87662	−	11.9106i	0.664787	−	1.15145i	0.979343	−	0.202207i	$-0.0648112\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	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
$112$		−	1.51764i		−	0.143403i
$113$	4.82843	+	8.36308i	0.454220	+	0.786732i	0.998643	−	0.0520785i	$-0.0165846\pi$
$113$	4.82843	+	8.36308i	0.454220	+	0.786732i	−0.544423	+	0.838811i	$0.683251\pi$
$114$	−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	−0.467300	−	0.884099i	$-0.654773\pi$
$127$	5.99536	−	10.3843i	0.532002	−	0.921454i	0.999302	−	0.0373555i	$-0.0118934\pi$
$128$	−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	−0.762427	−	0.647075i	$-0.775992\pi$
$137$	−6.82684	+	3.94148i	−0.583257	+	0.336743i	0.179170	+	0.983818i	$0.442659\pi$
$138$			5.44244i			0.463291i
$139$	−2.05852	−	3.56546i	−0.174601	−	0.302419i	0.765422	−	0.643529i	$-0.222530\pi$
$139$	−2.05852	−	3.56546i	−0.174601	−	0.302419i	−0.940023	+	0.341110i	$0.889197\pi$
$140$		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	−0.790718	−	0.612180i	$-0.790293\pi$
$149$	−8.00644	+	4.62252i	−0.655913	+	0.378692i	0.134805	+	0.990872i	$0.456959\pi$
$150$		0			0
$151$			17.1479i			1.39548i	0.716351	+	0.697740i	$0.245811\pi$
$151$			17.1479i			1.39548i	−0.716351	+	0.697740i	$0.754189\pi$
$152$	−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	−0.556673	−	0.830732i	$-0.687922\pi$
$163$	−1.47555	+	0.851911i	−0.115574	+	0.0667269i	0.441098	+	0.897459i	$0.354589\pi$
$164$			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	0.667975	−	0.744184i	$-0.267161\pi$
$167$	4.61967	+	2.66717i	0.357481	+	0.206392i	−0.310494	+	0.950575i	$0.600495\pi$
$168$	−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	0.977344	+	0.211655i	$0.0678853\pi$
$173$	8.83839	+	15.3085i	0.671971	+	1.16389i	−0.305374	+	0.952233i	$0.598781\pi$
$174$			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	0.111313	+	0.993785i	$0.464494\pi$
$179$	−10.7700	+	18.6542i	−0.804987	+	1.39428i	−0.916300	+	0.400493i	$0.868839\pi$
$180$		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	0.999362	−	0.0357192i	$-0.0113722\pi$
$191$	6.47822	+	11.2206i	0.468747	+	0.811894i	−0.530615	+	0.847613i	$0.678039\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−7.49706	−	4.32843i	−0.539650	−	0.311567i	0.205287	−	0.978702i	$-0.434187\pi$
$193$	−7.49706	−	4.32843i	−0.539650	−	0.311567i	−0.744937	+	0.667135i	$0.767521\pi$
$194$	5.71795			0.410525
$195$		0			0
$196$	−4.69677			−0.335484
$197$	−3.76574	−	2.17415i	−0.268298	−	0.154902i	0.359816	−	0.933023i	$-0.382840\pi$
$197$	−3.76574	−	2.17415i	−0.268298	−	0.154902i	−0.628114	+	0.778121i	$0.716173\pi$
$198$	−2.57313	+	4.45680i	−0.182865	+	0.316731i
$199$	−3.73351	−	6.46663i	−0.264662	−	0.458407i	0.702813	−	0.711374i	$-0.251927\pi$
$199$	−3.73351	−	6.46663i	−0.264662	−	0.458407i	−0.967475	+	0.252967i	$0.918594\pi$
$200$		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	−0.999168	−	0.0407826i	$-0.987015\pi$
$211$	−6.74384	+	11.6807i	−0.464265	+	0.804131i	0.534903	+	0.844914i	$0.320348\pi$
$212$	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	0.689572	−	0.724217i	$-0.257799\pi$
$223$	6.08030	+	3.51047i	0.407167	+	0.235078i	−0.282405	+	0.959295i	$0.591132\pi$
$224$	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	−0.232200	−	0.972668i	$-0.574592\pi$
$227$	7.44370	−	4.29762i	0.494055	−	0.285243i	0.726255	+	0.687425i	$0.241259\pi$
$228$	−1.39778	+	0.807007i	−0.0925701	+	0.0534454i
$229$		−	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
$232$	−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	$-0.798320\pi$
$239$		−	18.3056i		−	1.18409i	0.805904	−	0.592046i	$-0.201680\pi$
$240$		0			0
$241$	12.4906	−	7.21147i	0.804592	−	0.464532i	−0.0404822	−	0.999180i	$-0.512889\pi$
$241$	12.4906	−	7.21147i	0.804592	−	0.464532i	0.845074	+	0.534649i	$0.179556\pi$
$242$			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	0.717100	−	0.696970i	$-0.245469\pi$
$251$	−3.88222	−	6.72420i	−0.245044	−	0.424428i	−0.962144	+	0.272542i	$0.912136\pi$
$252$			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	0.387671	+	0.921798i	$0.373280\pi$
$257$	−9.69031	+	16.7841i	−0.604465	+	1.04696i	−0.992136	+	0.125166i	$0.960054\pi$
$258$	−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	−0.893744	−	0.448578i	$-0.851931\pi$
$263$	−0.946961	+	1.64019i	−0.0583921	+	0.101138i	0.835352	+	0.549716i	$0.185264\pi$
$264$	−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	0.927608	−	0.373554i	$-0.121861\pi$
$269$	2.30104	+	3.98551i	0.140297	+	0.243001i	−0.787312	+	0.616555i	$0.788528\pi$
$270$		0			0
$271$	7.22596	+	4.17191i	0.438946	+	0.253426i	0.703150	−	0.711041i	$-0.251776\pi$
$271$	7.22596	+	4.17191i	0.438946	+	0.253426i	−0.264204	+	0.964467i	$0.585109\pi$
$272$	−4.79555			−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	−0.978444	−	0.206514i	$-0.933788\pi$
$277$	−11.1189	−	19.2585i	−0.668068	−	1.15713i	0.310375	−	0.950614i	$-0.399545\pi$
$278$		−	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	$0.204601\pi$
$281$			20.0961i			1.19883i	−0.800437	+	0.599417i	$0.795399\pi$
$282$	−3.42455	−	5.93149i	−0.203929	−	0.353215i
$283$	0.359921	−	0.623402i	0.0213951	−	0.0370574i	−0.855130	−	0.518414i	$-0.826523\pi$
$283$	0.359921	−	0.623402i	0.0213951	−	0.0370574i	0.876525	+	0.481357i	$0.159856\pi$
$284$	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	−0.795790	−	0.605573i	$-0.792944\pi$
$293$	−11.4556	+	6.61389i	−0.669243	+	0.386388i	0.126547	+	0.991961i	$0.459611\pi$
$294$			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	$-0.928068\pi$
$307$		−	7.85174i		−	0.448123i	0.974575	−	0.224061i	$-0.0719316\pi$
$308$	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	$0.266019\pi$
$317$			26.4141i			1.48357i	−0.670640	+	0.741783i	$0.733981\pi$
$318$	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	0.0723356	−	0.997380i	$-0.476955\pi$
$331$	17.6887	−	10.2126i	0.972260	−	0.561335i	0.899925	+	0.436046i	$0.143621\pi$
$332$	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	0.999644	−	0.0266782i	$-0.00849295\pi$
$347$	8.88027	+	15.3811i	0.476718	+	0.825700i	−0.522926	+	0.852378i	$0.675160\pi$
$348$	−4.93684	+	8.55085i	−0.264642	+	0.458374i
$349$	0.103747	+	0.0598981i	0.00555343	+	0.00320627i	0.502774	−	0.864418i	$-0.332313\pi$
$349$	0.103747	+	0.0598981i	0.00555343	+	0.00320627i	−0.497221	+	0.867624i	$0.665646\pi$
$350$		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	0.315737	−	0.948847i	$-0.397748\pi$
$353$	−6.54057	−	3.77620i	−0.348119	−	0.200987i	−0.663857	+	0.747860i	$0.731082\pi$
$354$	−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	$0.290366\pi$
$359$			29.9693i			1.58172i	−0.611997	+	0.790860i	$0.709634\pi$
$360$		0			0
$361$	−8.19748	+	14.1984i	−0.431446	+	0.747287i
$362$	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	0.191666	+	0.981460i	$0.438611\pi$
$367$	−14.4472	+	25.0232i	−0.754136	+	1.30620i	−0.945802	+	0.324742i	$0.894722\pi$
$368$	−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	0.991187	−	0.132471i	$-0.0422911\pi$
$373$	7.35583	+	12.7407i	0.380870	+	0.659687i	−0.610317	+	0.792158i	$0.708958\pi$
$374$	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	−0.399798	−	0.916603i	$-0.630920\pi$
$379$	−27.1285	−	15.6627i	−1.39350	−	0.804537i	−0.993701	+	0.112067i	$0.964253\pi$
$380$		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	−0.720423	−	0.693535i	$-0.756052\pi$
$383$	−9.39410	+	5.42368i	−0.480016	+	0.277137i	0.240407	+	0.970672i	$0.422719\pi$
$384$	−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	−0.493299	−	0.869860i	$-0.664209\pi$
$397$	0.266438	−	0.153828i	0.0133721	−	0.00772041i	0.506671	+	0.862139i	$0.330876\pi$
$398$		−	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	0.546512	−	0.837451i	$-0.315955\pi$
$401$	1.89266	+	1.09273i	0.0945149	+	0.0545682i	−0.451998	+	0.892019i	$0.649288\pi$
$402$	−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	0.623461	−	0.781855i	$-0.285726\pi$
$409$	32.6067	−	18.8255i	1.61230	−	0.930860i	0.988836	−	0.149006i	$-0.0476073\pi$
$410$		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	0.319328	+	0.947644i	$0.396543\pi$
$419$	−13.5307	+	23.4359i	−0.661020	+	1.14492i	−0.980348	+	0.197276i	$0.936790\pi$
$420$		0			0
$421$			11.9356i			0.581706i	0.956768	+	0.290853i	$0.0939390\pi$
$421$			11.9356i			0.581706i	−0.956768	+	0.290853i	$0.906061\pi$
$422$	−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	0.971266	−	0.237995i	$-0.0764903\pi$
$431$	25.9671	+	14.9921i	1.25079	+	0.722144i	0.279523	+	0.960139i	$0.409824\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	10.4971	+	18.1814i	0.504456	+	0.873744i	0.999987	+	0.00515336i	$0.00164037\pi$
$433$	10.4971	+	18.1814i	0.504456	+	0.873744i	−0.495530	+	0.868591i	$0.665026\pi$
$434$		−	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	−0.765467	−	0.643475i	$-0.777492\pi$
$439$	3.65685	−	6.33386i	0.174532	−	0.302299i	0.939999	+	0.341176i	$0.110825\pi$
$440$		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	−0.563104	−	0.826386i	$-0.690393\pi$
$449$	−2.73315	+	1.57798i	−0.128985	+	0.0744696i	0.434119	+	0.900855i	$0.357060\pi$
$450$		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	0.494128	−	0.869389i	$-0.335487\pi$
$457$	−0.250578	−	0.144671i	−0.0117215	−	0.00676743i	−0.505849	+	0.862622i	$0.668821\pi$
$458$	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	−0.569963	−	0.821671i	$-0.693042\pi$
$461$	−3.07799	+	1.77708i	−0.143356	+	0.0827668i	0.426606	+	0.904437i	$0.359709\pi$
$462$	6.76380	−	3.90508i	0.314681	−	0.181681i
$463$		−	12.1116i		−	0.562875i	−0.959580	−	0.281438i	$-0.909189\pi$
$463$		−	12.1116i		−	0.562875i	0.959580	−	0.281438i	$-0.0908113\pi$
$464$	−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	0.545662	−	0.838006i	$-0.316278\pi$
$479$	2.03012	+	1.17209i	0.0927584	+	0.0535541i	−0.452903	+	0.891560i	$0.649612\pi$
$480$		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	−0.424945	−	0.905219i	$-0.639706\pi$
$487$	3.23354	−	1.86689i	0.146526	−	0.0845968i	0.571471	+	0.820623i	$0.306373\pi$
$488$	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	−0.970691	−	0.240332i	$-0.922744\pi$
$491$	−6.14261	+	10.6393i	−0.277212	+	0.480145i	0.693479	+	0.720477i	$0.256077\pi$
$492$	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	$-0.869352\pi$
$499$		−	17.8267i		−	0.798033i	0.916944	−	0.399016i	$-0.130648\pi$
$500$		0			0
$501$	4.61967	−	2.66717i	0.206392	−	0.119160i
$502$		−	7.76444i		−	0.346544i
$503$	−2.78988	−	4.83222i	−0.124395	−	0.215458i	0.797101	−	0.603845i	$-0.206366\pi$
$503$	−2.78988	−	4.83222i	−0.124395	−	0.215458i	−0.921496	+	0.388387i	$0.873032\pi$
$504$	−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	0.966266	−	0.257545i	$-0.0829134\pi$
$509$	27.6679	+	15.9741i	1.22636	+	0.708039i	0.260093	+	0.965584i	$0.416247\pi$
$510$		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	0.494808	+	0.869002i	$0.335238\pi$
$523$	−11.5529	+	20.0102i	−0.505174	+	0.874986i	−0.999982	+	0.00598438i	$0.998095\pi$
$524$	−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	$-0.787431\pi$
$541$		−	28.8074i		−	1.23853i	0.785183	−	0.619264i	$-0.212569\pi$
$542$	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	0.987241	−	0.159236i	$-0.0509030\pi$
$557$	31.6950	+	18.2991i	1.34296	+	0.775358i	0.355718	+	0.934593i	$0.384236\pi$
$558$	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	0.735928	−	0.677060i	$-0.236746\pi$
$563$	−5.18180	−	8.97514i	−0.218387	−	0.378257i	−0.954315	+	0.298803i	$0.903413\pi$
$564$		−	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	−0.318187	−	0.948028i	$-0.603074\pi$
$569$	15.7893	−	27.3479i	0.661923	−	1.14648i	0.980110	−	0.198456i	$-0.0635928\pi$
$570$		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	$0.323619\pi$
$577$			40.8530i			1.70073i	−0.526193	+	0.850365i	$0.676381\pi$
$578$	−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	−0.00996119	−	0.999950i	$-0.503171\pi$
$587$	−21.3431	−	12.3224i	−0.880924	−	0.508602i	−0.870963	+	0.491349i	$0.836504\pi$
$588$	−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	$0.145453\pi$
$593$			21.4887i			0.882436i	−0.897400	+	0.441218i	$0.854547\pi$
$594$	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	−0.925748	−	0.378140i	$-0.876564\pi$
$601$	−3.31925	+	5.74910i	−0.135395	+	0.234511i	0.790353	+	0.612651i	$0.209897\pi$
$602$	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	0.524514	−	0.851402i	$-0.324247\pi$
$607$	−11.7047	−	20.2731i	−0.475078	−	0.822860i	−0.999593	+	0.0285420i	$0.990914\pi$
$608$	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	0.405252	−	0.914205i	$-0.367184\pi$
$613$	−4.55182	−	2.62799i	−0.183846	−	0.106144i	−0.589099	+	0.808061i	$0.700517\pi$
$614$	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	0.0367887	−	0.999323i	$-0.488287\pi$
$617$	22.8678	−	13.2027i	0.920622	−	0.531522i	0.883834	+	0.467802i	$0.154954\pi$
$618$	2.74919	−	1.58725i	0.110589	−	0.0638484i
$619$			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
$622$	−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	−0.378964	−	0.925411i	$-0.623720\pi$
$631$	5.85249	−	3.37894i	0.232984	−	0.134513i	0.611948	+	0.790898i	$0.290386\pi$
$632$		−	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	0.995842	+	0.0910927i	$0.0290360\pi$
$641$	14.6037	+	25.2943i	0.576810	+	0.999064i	−0.419033	+	0.907971i	$0.637631\pi$
$642$		−	13.7532i		−	0.542797i
$643$	6.98298	−	4.03163i	0.275382	−	0.158992i	−0.355949	−	0.934505i	$-0.615842\pi$
$643$	6.98298	−	4.03163i	0.275382	−	0.158992i	0.631331	+	0.775514i	$0.282509\pi$
$644$	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	−0.858859	−	0.512213i	$-0.828826\pi$
$647$	0.360179	−	0.623849i	0.0141601	−	0.0245260i	0.873019	+	0.487687i	$0.162159\pi$
$648$	−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	0.477772	+	0.878484i	$0.341445\pi$
$653$	−13.3367	+	23.0998i	−0.521904	+	0.903963i	−0.999675	+	0.0254795i	$0.991889\pi$
$654$	−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	0.986494	−	0.163796i	$-0.0523739\pi$
$659$	9.02067	+	15.6243i	0.351396	+	0.608635i	−0.635099	+	0.772431i	$0.719041\pi$
$660$		0			0
$661$	10.5904	+	6.11439i	0.411920	+	0.237822i	0.691614	−	0.722267i	$-0.256900\pi$
$661$	10.5904	+	6.11439i	0.411920	+	0.237822i	−0.279694	+	0.960089i	$0.590233\pi$
$662$	20.4252			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	−0.907419	−	0.420228i	$-0.861950\pi$
$673$	−2.32913	+	4.03417i	−0.0897814	+	0.155506i	0.817637	+	0.575734i	$0.195284\pi$
$674$	−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	−0.695081	−	0.718931i	$-0.744631\pi$
$683$	−10.9766	+	6.33735i	−0.420008	+	0.242492i	0.275072	+	0.961423i	$0.411298\pi$
$684$			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	0.722724	−	0.691137i	$-0.242890\pi$
$691$	12.7634	+	7.36897i	0.485544	+	0.280329i	−0.237180	+	0.971466i	$0.576223\pi$
$692$	−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	−0.923182	−	0.384364i	$-0.874421\pi$
$709$	−28.0091	+	16.1711i	−1.05190	+	0.607317i	−0.128722	+	0.991681i	$0.541087\pi$
$710$		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	0.709693	−	0.704511i	$-0.248834\pi$
$719$	−6.84506	−	11.8560i	−0.255278	−	0.442154i	−0.964971	+	0.262357i	$0.915500\pi$
$720$		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	$-0.688625\pi$
$733$		−	44.9158i		−	1.65900i	0.558505	−	0.829501i	$-0.311375\pi$
$734$	−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	0.738051	−	0.674745i	$-0.235746\pi$
$739$	14.2102	+	8.20427i	0.522731	+	0.301799i	−0.215320	+	0.976543i	$0.569080\pi$
$740$		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	0.601542	−	0.798841i	$-0.294553\pi$
$743$	5.73773	+	3.31268i	0.210497	+	0.121530i	−0.391045	+	0.920371i	$0.627886\pi$
$744$	−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	−0.212419	−	0.977179i	$-0.568134\pi$
$751$	20.2807	−	35.1271i	0.740052	−	1.28181i	0.952471	−	0.304629i	$-0.0985324\pi$
$752$	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	−0.997845	−	0.0656076i	$-0.979101\pi$
$757$	−12.1639	+	21.0685i	−0.442105	+	0.765748i	0.555741	+	0.831356i	$0.312435\pi$
$758$	−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	−0.506433	−	0.862279i	$-0.669036\pi$
$761$	−0.355702	+	0.205364i	−0.0128942	+	0.00744446i	0.493539	+	0.869724i	$0.335703\pi$
$762$		−	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	−0.320168	−	0.947361i	$-0.603739\pi$
$769$	−36.0692	−	20.8246i	−1.30069	−	0.750954i	−0.980522	+	0.196407i	$0.937073\pi$
$770$		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	0.622949	−	0.782262i	$-0.285934\pi$
$773$	44.8150	−	25.8739i	1.61188	−	0.930621i	0.988934	−	0.148358i	$-0.0473989\pi$
$774$	−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	−0.210209	−	0.977656i	$-0.567415\pi$
$787$	14.9066	−	8.60630i	0.531361	−	0.306782i	0.741571	+	0.670875i	$0.234081\pi$
$788$		−	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	0.559905	−	0.828557i	$-0.310838\pi$
$797$	−12.3539	−	21.3976i	−0.437599	−	0.757943i	−0.997504	+	0.0706135i	$0.977504\pi$
$798$		−	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	−0.997725	−	0.0674144i	$-0.978525\pi$
$809$	−12.5285	+	21.7001i	−0.440480	+	0.762934i	0.557245	+	0.830348i	$0.311858\pi$
$810$		0			0
$811$			35.2387i			1.23740i	0.785628	+	0.618699i	$0.212340\pi$
$811$			35.2387i			1.23740i	−0.785628	+	0.618699i	$0.787660\pi$
$812$	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	−0.0404892	−	0.999180i	$-0.512892\pi$
$821$	−26.5342	−	15.3195i	−0.926049	−	0.534655i	−0.885560	+	0.464525i	$0.846225\pi$
$822$	−3.94148	+	6.82684i	−0.137475	+	0.238113i
$823$	−17.8946	−	30.9943i	−0.623765	−	1.08039i	−0.988778	−	0.149390i	$-0.952269\pi$
$823$	−17.8946	−	30.9943i	−0.623765	−	1.08039i	0.365014	−	0.931002i	$-0.381064\pi$
$824$			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	$0.0418337\pi$
$827$			7.53716i			0.262093i	−0.991376	+	0.131046i	$0.958166\pi$
$828$	2.72122	+	4.71329i	0.0945690	+	0.163798i
$829$	−25.9628	+	44.9688i	−0.901724	+	1.56183i	−0.0764677	+	0.997072i	$0.524364\pi$
$829$	−25.9628	+	44.9688i	−0.901724	+	1.56183i	−0.825256	+	0.564759i	$0.808969\pi$
$830$		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	−0.379460	−	0.925208i	$-0.623890\pi$
$839$	6.72183	−	3.88085i	0.232063	−	0.133982i	0.611524	+	0.791226i	$0.290557\pi$
$840$		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	$0.0759596\pi$
$853$			13.8072i			0.472751i	−0.971662	+	0.236376i	$0.924040\pi$
$854$	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	$-0.848001\pi$
$863$		−	27.0018i		−	0.919153i	0.888138	−	0.459577i	$-0.151999\pi$
$864$	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	−0.852755	−	0.522311i	$-0.825070\pi$
$877$	−24.4850	+	14.1364i	−0.826799	+	0.477352i	0.0259566	+	0.999663i	$0.491737\pi$
$878$	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	−0.979596	−	0.200975i	$-0.935589\pi$
$881$	−9.37195	+	16.2327i	−0.315749	+	0.546894i	0.663847	+	0.747868i	$0.268922\pi$
$882$	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	−0.579032	−	0.815305i	$-0.696569\pi$
$887$	12.4062	−	21.4881i	0.416558	−	0.721500i	0.995591	+	0.0938043i	$0.0299028\pi$
$888$	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	−0.966645	−	0.256119i	$-0.917556\pi$
$907$	−7.87598	+	13.6416i	−0.261517	+	0.452962i	0.705128	+	0.709080i	$0.250890\pi$
$908$	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	0.801630	−	0.597821i	$-0.203967\pi$
$919$	−3.54423	−	6.13879i	−0.116913	−	0.202500i	−0.918543	+	0.395321i	$0.870633\pi$
$920$		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	−0.439043	−	0.898466i	$-0.644682\pi$
$929$	3.64324	−	2.10342i	0.119531	−	0.0690111i	0.558573	+	0.829455i	$0.311349\pi$
$930$		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	$0.241768\pi$
$941$			42.2457i			1.37717i	−0.725156	+	0.688585i	$0.758232\pi$
$942$	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	−0.210546	−	0.977584i	$-0.567524\pi$
$947$	−35.7719	−	20.6529i	−1.16243	−	0.671130i	−0.951885	+	0.306454i	$0.900857\pi$
$948$	−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	0.758912	−	0.651193i	$-0.225731\pi$
$953$	−5.69547	−	9.86484i	−0.184494	−	0.319553i	−0.943406	+	0.331640i	$0.892398\pi$
$954$		−	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	$-0.780441\pi$
$967$		−	39.5770i		−	1.27271i	0.771396	−	0.636355i	$-0.219559\pi$
$968$	−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	0.833365	−	0.552723i	$-0.186411\pi$
$971$	−1.93166	−	3.34574i	−0.0619900	−	0.107370i	−0.895355	+	0.445353i	$0.853078\pi$
$972$	−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	−0.178395	−	0.983959i	$-0.557091\pi$
$977$	−34.9993	−	20.2068i	−1.11973	−	0.646474i	−0.941331	+	0.337485i	$0.890424\pi$
$978$	−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	$0.0796259\pi$
$983$			15.5229i			0.495103i	−0.968875	+	0.247551i	$0.920374\pi$
$984$	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	−0.406829	−	0.913504i	$-0.633365\pi$
$991$	18.5010	−	32.0447i	0.587704	−	1.01793i	0.994532	−	0.104428i	$-0.0333012\pi$
$992$	−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	0.942536	+	0.334105i	$0.108434\pi$
$997$	24.0165	+	41.5979i	0.760611	+	1.31742i	−0.181925	+	0.983312i	$0.558233\pi$
$998$	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.901.3	yes	8
5.2	odd	4		1950.2.y.i.199.1		8
5.3	odd	4		1950.2.y.l.199.4		8
5.4	even	2		1950.2.bc.e.901.2	yes	8
13.10	even	6	inner	1950.2.bc.f.751.3	yes	8
65.23	odd	12		1950.2.y.i.49.1		8
65.49	even	6		1950.2.bc.e.751.2	✓	8
65.62	odd	12		1950.2.y.l.49.4		8

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

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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