LMFDB - Embedded newform 1050.2.bc.b.607.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			607.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.b.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.48356 + 2.19067i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.48356 + 2.19067i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.366025 + 0.633975i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-1.03528 - 1.03528i) q^{13} +(0.866025 - 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.19067 - 0.586988i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.09808 - 3.63397i) q^{19} +(1.73205 + 2.00000i) q^{21} +(-0.517638 - 0.517638i) q^{22} +(-0.965926 - 3.60488i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.26795 + 0.732051i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.189469 + 2.63896i) q^{28} -8.19615i q^{29} +(6.86603 - 3.96410i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.707107 - 0.189469i) q^{33} +2.26795 q^{34} -1.00000 q^{36} +(4.57081 - 1.22474i) q^{37} +(-1.08604 + 4.05317i) q^{38} +(-1.26795 + 0.732051i) q^{39} +2.46410i q^{41} +(-2.19067 - 1.48356i) q^{42} +(-0.138701 + 0.138701i) q^{43} +(0.633975 + 0.366025i) q^{44} +(1.86603 + 3.23205i) q^{46} +(-2.84701 - 10.6252i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-2.59808 - 6.50000i) q^{49} +(-1.13397 + 1.96410i) q^{51} +(-1.41421 - 0.378937i) q^{52} +(-5.08845 - 1.36345i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(-2.96713 - 2.96713i) q^{57} +(2.12132 + 7.91688i) q^{58} +(0.267949 + 0.464102i) q^{59} +(10.5622 + 6.09808i) q^{61} +(-5.60609 + 5.60609i) q^{62} +(2.38014 - 1.15539i) q^{63} -1.00000i q^{64} +(-0.633975 + 0.366025i) q^{66} +(1.03528 - 3.86370i) q^{67} +(-2.19067 + 0.586988i) q^{68} -3.73205 q^{69} -12.8564 q^{71} +(0.965926 - 0.258819i) q^{72} +(-2.07055 + 7.72741i) q^{73} +(-4.09808 + 2.36603i) q^{74} -4.19615i q^{76} +(-1.93185 - 0.138701i) q^{77} +(1.03528 - 1.03528i) q^{78} +(-7.03590 - 4.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.637756 - 2.38014i) q^{82} +(-8.24504 - 8.24504i) q^{83} +(2.50000 + 0.866025i) q^{84} +(0.0980762 - 0.169873i) q^{86} +(-7.91688 - 2.12132i) q^{87} +(-0.707107 - 0.189469i) q^{88} +(3.23205 - 5.59808i) q^{89} +(3.80385 - 0.732051i) q^{91} +(-2.63896 - 2.63896i) q^{92} +(-2.05197 - 7.65806i) q^{93} +(5.50000 + 9.52628i) q^{94} +(0.866025 + 0.500000i) q^{96} +(4.94975 - 4.94975i) q^{97} +(4.19187 + 5.60609i) q^{98} -0.732051i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} + 4 q^{16} - 4 q^{19} + 4 q^{24} + 24 q^{26} + 48 q^{31} + 32 q^{34} - 8 q^{36} - 24 q^{39} + 12 q^{44} + 8 q^{46} - 16 q^{51} + 4 q^{54} - 4 q^{56} + 16 q^{59} + 36 q^{61} - 12 q^{66} - 16 q^{69} + 8 q^{71} - 12 q^{74} - 84 q^{79} + 4 q^{81} + 20 q^{84} - 20 q^{86} + 12 q^{89} + 72 q^{91} + 44 q^{94}+O(q^{100}) $ 8 * q - 4 * q^11 + 4 * q^16 - 4 * q^19 + 4 * q^24 + 24 * q^26 + 48 * q^31 + 32 * q^34 - 8 * q^36 - 24 * q^39 + 12 * q^44 + 8 * q^46 - 16 * q^51 + 4 * q^54 - 4 * q^56 + 16 * q^59 + 36 * q^61 - 12 * q^66 - 16 * q^69 + 8 * q^71 - 12 * q^74 - 84 * q^79 + 4 * q^81 + 20 * q^84 - 20 * q^86 + 12 * q^89 + 72 * q^91 + 44 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−1.48356	+	2.19067i	−0.560734	+	0.827996i
$7$	−1.48356	+	2.19067i	−0.560734	+	0.827996i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	0.915916	−	0.401371i	$-0.131466\pi$
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	−0.805555	+	0.592521i	$0.798133\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	−1.03528	−	1.03528i	−0.287134	−	0.287134i	0.548812	−	0.835946i	$-0.315080\pi$
$13$	−1.03528	−	1.03528i	−0.287134	−	0.287134i	−0.835946	+	0.548812i	$0.815080\pi$
$14$	0.866025	−	2.50000i	0.231455	−	0.668153i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.19067	−	0.586988i	−0.531316	−	0.142366i	−0.0168199	−	0.999859i	$-0.505354\pi$
$17$	−2.19067	−	0.586988i	−0.531316	−	0.142366i	−0.514496	+	0.857493i	$0.672021\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	2.09808	−	3.63397i	0.481332	−	0.833691i	−0.518439	−	0.855115i	$-0.673487\pi$
$19$	2.09808	−	3.63397i	0.481332	−	0.833691i	0.999770	+	0.0214238i	$0.00681993\pi$
$20$		0			0
$21$	1.73205	+	2.00000i	0.377964	+	0.436436i
$22$	−0.517638	−	0.517638i	−0.110361	−	0.110361i
$23$	−0.965926	−	3.60488i	−0.201409	−	0.751670i	−0.990514	−	0.137411i	$-0.956122\pi$
$23$	−0.965926	−	3.60488i	−0.201409	−	0.751670i	0.789105	−	0.614259i	$-0.210545\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	1.26795	+	0.732051i	0.248665	+	0.143567i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.189469	+	2.63896i	−0.0358062	+	0.498716i
$29$		−	8.19615i		−	1.52199i	−0.648759	−	0.760994i	$-0.724712\pi$
$29$		−	8.19615i		−	1.52199i	0.648759	−	0.760994i	$-0.275288\pi$
$30$		0			0
$31$	6.86603	−	3.96410i	1.23317	−	0.711974i	0.265484	−	0.964115i	$-0.414468\pi$
$31$	6.86603	−	3.96410i	1.23317	−	0.711974i	0.967690	+	0.252142i	$0.0811349\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.707107	−	0.189469i	0.123091	−	0.0329823i
$34$	2.26795			0.388950
$35$		0			0
$36$	−1.00000			−0.166667
$37$	4.57081	−	1.22474i	0.751437	−	0.201347i	0.137281	−	0.990532i	$-0.456164\pi$
$37$	4.57081	−	1.22474i	0.751437	−	0.201347i	0.614155	+	0.789185i	$0.289497\pi$
$38$	−1.08604	+	4.05317i	−0.176180	+	0.657511i
$39$	−1.26795	+	0.732051i	−0.203034	+	0.117222i
$40$		0			0
$41$			2.46410i			0.384828i	0.981314	+	0.192414i	$0.0616316\pi$
$41$			2.46410i			0.384828i	−0.981314	+	0.192414i	$0.938368\pi$
$42$	−2.19067	−	1.48356i	−0.338028	−	0.228919i
$43$	−0.138701	+	0.138701i	−0.0211517	+	0.0211517i	−0.717604	−	0.696452i	$-0.754761\pi$
$43$	−0.138701	+	0.138701i	−0.0211517	+	0.0211517i	0.696452	+	0.717604i	$0.254761\pi$
$44$	0.633975	+	0.366025i	0.0955753	+	0.0551804i
$45$		0			0
$46$	1.86603	+	3.23205i	0.275130	+	0.476540i
$47$	−2.84701	−	10.6252i	−0.415279	−	1.54984i	−0.784276	−	0.620412i	$-0.786965\pi$
$47$	−2.84701	−	10.6252i	−0.415279	−	1.54984i	0.368997	−	0.929431i	$-0.379701\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−2.59808	−	6.50000i	−0.371154	−	0.928571i
$50$		0			0
$51$	−1.13397	+	1.96410i	−0.158788	+	0.275029i
$52$	−1.41421	−	0.378937i	−0.196116	−	0.0525492i
$53$	−5.08845	−	1.36345i	−0.698952	−	0.187284i	−0.108191	−	0.994130i	$-0.534506\pi$
$53$	−5.08845	−	1.36345i	−0.698952	−	0.187284i	−0.590761	+	0.806846i	$0.701172\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$	−2.96713	−	2.96713i	−0.393006	−	0.393006i
$58$	2.12132	+	7.91688i	0.278543	+	1.03954i
$59$	0.267949	+	0.464102i	0.0348840	+	0.0604209i	0.882940	−	0.469485i	$-0.155560\pi$
$59$	0.267949	+	0.464102i	0.0348840	+	0.0604209i	−0.848056	+	0.529906i	$0.822227\pi$
$60$		0			0
$61$	10.5622	+	6.09808i	1.35235	+	0.780779i	0.988578	−	0.150710i	$-0.0481560\pi$
$61$	10.5622	+	6.09808i	1.35235	+	0.780779i	0.363770	+	0.931489i	$0.381489\pi$
$62$	−5.60609	+	5.60609i	−0.711974	+	0.711974i
$63$	2.38014	−	1.15539i	0.299869	−	0.145566i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−0.633975	+	0.366025i	−0.0780369	+	0.0450546i
$67$	1.03528	−	3.86370i	0.126479	−	0.472026i	−0.873409	−	0.486987i	$-0.838096\pi$
$67$	1.03528	−	3.86370i	0.126479	−	0.472026i	0.999888	+	0.0149610i	$0.00476240\pi$
$68$	−2.19067	+	0.586988i	−0.265658	+	0.0711828i
$69$	−3.73205			−0.449286
$70$		0			0
$71$	−12.8564			−1.52577			−0.762887	−	0.646531i	$-0.776219\pi$
$71$	−12.8564			−1.52577			−0.762887	+	0.646531i	$0.776219\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−2.07055	+	7.72741i	−0.242340	+	0.904425i	0.732362	+	0.680915i	$0.238418\pi$
$73$	−2.07055	+	7.72741i	−0.242340	+	0.904425i	−0.974702	+	0.223509i	$0.928249\pi$
$74$	−4.09808	+	2.36603i	−0.476392	+	0.275045i
$75$		0			0
$76$		−	4.19615i		−	0.481332i
$77$	−1.93185	−	0.138701i	−0.220155	−	0.0158064i
$78$	1.03528	−	1.03528i	0.117222	−	0.117222i
$79$	−7.03590	−	4.06218i	−0.791600	−	0.457031i	0.0489252	−	0.998802i	$-0.484420\pi$
$79$	−7.03590	−	4.06218i	−0.791600	−	0.457031i	−0.840526	+	0.541772i	$0.817754\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.637756	−	2.38014i	−0.0704284	−	0.262842i
$83$	−8.24504	−	8.24504i	−0.905011	−	0.905011i	0.0908531	−	0.995864i	$-0.471041\pi$
$83$	−8.24504	−	8.24504i	−0.905011	−	0.905011i	−0.995864	+	0.0908531i	$0.971041\pi$
$84$	2.50000	+	0.866025i	0.272772	+	0.0944911i
$85$		0			0
$86$	0.0980762	−	0.169873i	0.0105758	−	0.0183179i
$87$	−7.91688	−	2.12132i	−0.848778	−	0.227429i
$88$	−0.707107	−	0.189469i	−0.0753778	−	0.0201974i
$89$	3.23205	−	5.59808i	0.342597	−	0.593395i	−0.642317	−	0.766439i	$-0.722027\pi$
$89$	3.23205	−	5.59808i	0.342597	−	0.593395i	0.984914	+	0.173044i	$0.0553602\pi$
$90$		0			0
$91$	3.80385	−	0.732051i	0.398752	−	0.0767398i
$92$	−2.63896	−	2.63896i	−0.275130	−	0.275130i
$93$	−2.05197	−	7.65806i	−0.212779	−	0.794103i
$94$	5.50000	+	9.52628i	0.567282	+	0.982561i
$95$		0			0
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	4.94975	−	4.94975i	0.502571	−	0.502571i	−0.409665	−	0.912236i	$-0.634354\pi$
$97$	4.94975	−	4.94975i	0.502571	−	0.502571i	0.912236	+	0.409665i	$0.134354\pi$
$98$	4.19187	+	5.60609i	0.423443	+	0.566300i
$99$		−	0.732051i		−	0.0735739i
$100$		0			0
$101$	−0.169873	+	0.0980762i	−0.0169030	+	0.00975895i	−0.508428	−	0.861105i	$-0.669773\pi$
$101$	−0.169873	+	0.0980762i	−0.0169030	+	0.00975895i	0.491525	+	0.870864i	$0.336440\pi$
$102$	0.586988	−	2.19067i	0.0581205	−	0.216909i
$103$	6.43331	−	1.72380i	0.633893	−	0.169851i	0.0724573	−	0.997372i	$-0.476916\pi$
$103$	6.43331	−	1.72380i	0.633893	−	0.169851i	0.561436	+	0.827520i	$0.310249\pi$
$104$	1.46410			0.143567
$105$		0			0
$106$	5.26795			0.511668
$107$	9.65926	−	2.58819i	0.933796	−	0.250210i	0.240323	−	0.970693i	$-0.422747\pi$
$107$	9.65926	−	2.58819i	0.933796	−	0.250210i	0.693472	+	0.720483i	$0.256080\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−11.8301	+	6.83013i	−1.13312	+	0.654208i	−0.944718	−	0.327884i	$-0.893664\pi$
$109$	−11.8301	+	6.83013i	−1.13312	+	0.654208i	−0.188403	+	0.982092i	$0.560331\pi$
$110$		0			0
$111$		−	4.73205i		−	0.449146i
$112$	1.15539	+	2.38014i	0.109175	+	0.224902i
$113$	2.12132	−	2.12132i	0.199557	−	0.199557i	−0.600253	−	0.799810i	$-0.704933\pi$
$113$	2.12132	−	2.12132i	0.199557	−	0.199557i	0.799810	+	0.600253i	$0.204933\pi$
$114$	3.63397	+	2.09808i	0.340353	+	0.196503i
$115$		0			0
$116$	−4.09808	−	7.09808i	−0.380497	−	0.659040i
$117$	0.378937	+	1.41421i	0.0350328	+	0.130744i
$118$	−0.378937	−	0.378937i	−0.0348840	−	0.0348840i
$119$	4.53590	−	3.92820i	0.415805	−	0.360098i
$120$		0			0
$121$	5.23205	−	9.06218i	0.475641	−	0.823834i
$122$	−11.7806	−	3.15660i	−1.06656	−	0.285785i
$123$	2.38014	+	0.637756i	0.214610	+	0.0575046i
$124$	3.96410	−	6.86603i	0.355987	−	0.616587i
$125$		0			0
$126$	−2.00000	+	1.73205i	−0.178174	+	0.154303i
$127$	11.2122	+	11.2122i	0.994919	+	0.994919i	0.999987	−	0.00506773i	$-0.00161312\pi$
$127$	11.2122	+	11.2122i	0.994919	+	0.994919i	−0.00506773	+	0.999987i	$0.501613\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	0.0980762	+	0.169873i	0.00863513	+	0.0149565i
$130$		0			0
$131$	−11.8301	−	6.83013i	−1.03360	−	0.596751i	−0.115588	−	0.993297i	$-0.536875\pi$
$131$	−11.8301	−	6.83013i	−1.03360	−	0.596751i	−0.918015	+	0.396546i	$0.870209\pi$
$132$	0.517638	−	0.517638i	0.0450546	−	0.0450546i
$133$	4.84821	+	9.98743i	0.420393	+	0.866020i
$134$			4.00000i			0.345547i
$135$		0			0
$136$	1.96410	−	1.13397i	0.168420	−	0.0972375i
$137$	2.08913	−	7.79676i	0.178487	−	0.666122i	−0.817445	−	0.576007i	$-0.804610\pi$
$137$	2.08913	−	7.79676i	0.178487	−	0.666122i	0.995931	−	0.0901146i	$-0.0287233\pi$
$138$	3.60488	−	0.965926i	0.306868	−	0.0822251i
$139$	−12.9282			−1.09656			−0.548278	−	0.836296i	$-0.684716\pi$
$139$	−12.9282			−1.09656			−0.548278	+	0.836296i	$0.684716\pi$
$140$		0			0
$141$	−11.0000			−0.926367
$142$	12.4183	−	3.32748i	1.04212	−	0.279236i
$143$	0.277401	−	1.03528i	0.0231975	−	0.0865741i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$		0			0
$146$		−	8.00000i		−	0.662085i
$147$	−6.95095	+	0.827225i	−0.573305	+	0.0682284i
$148$	3.34607	−	3.34607i	0.275045	−	0.275045i
$149$	15.5885	+	9.00000i	1.27706	+	0.737309i	0.976306	−	0.216394i	$-0.0694297\pi$
$149$	15.5885	+	9.00000i	1.27706	+	0.737309i	0.300750	+	0.953703i	$0.402763\pi$
$150$		0			0
$151$	−5.46410	−	9.46410i	−0.444662	−	0.770178i	0.553366	−	0.832938i	$-0.313343\pi$
$151$	−5.46410	−	9.46410i	−0.444662	−	0.770178i	−0.998029	+	0.0627603i	$0.980010\pi$
$152$	1.08604	+	4.05317i	0.0880898	+	0.328756i
$153$	1.60368	+	1.60368i	0.129650	+	0.129650i
$154$	1.90192	−	0.366025i	0.153261	−	0.0294952i
$155$		0			0
$156$	−0.732051	+	1.26795i	−0.0586110	+	0.101517i
$157$	20.0256	+	5.36585i	1.59822	+	0.428241i	0.944504	−	0.328500i	$-0.106543\pi$
$157$	20.0256	+	5.36585i	1.59822	+	0.428241i	0.653715	+	0.756741i	$0.273210\pi$
$158$	7.84752	+	2.10274i	0.624316	+	0.167285i
$159$	−2.63397	+	4.56218i	−0.208888	+	0.361804i
$160$		0			0
$161$	9.33013	+	3.23205i	0.735317	+	0.254721i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−3.10583	−	11.5911i	−0.243267	−	0.907886i	−0.974246	−	0.225486i	$-0.927603\pi$
$163$	−3.10583	−	11.5911i	−0.243267	−	0.907886i	0.730979	−	0.682400i	$-0.239064\pi$
$164$	1.23205	+	2.13397i	0.0962070	+	0.166635i
$165$		0			0
$166$	10.0981	+	5.83013i	0.783763	+	0.452506i
$167$	−3.58630	+	3.58630i	−0.277516	+	0.277516i	−0.832117	−	0.554600i	$-0.812871\pi$
$167$	−3.58630	+	3.58630i	−0.277516	+	0.277516i	0.554600	+	0.832117i	$0.312871\pi$
$168$	−2.63896	−	0.189469i	−0.203600	−	0.0146178i
$169$		−	10.8564i		−	0.835108i
$170$		0			0
$171$	−3.63397	+	2.09808i	−0.277897	+	0.160444i
$172$	−0.0507680	+	0.189469i	−0.00387102	+	0.0144469i
$173$	7.20977	−	1.93185i	0.548149	−	0.146876i	0.0258926	−	0.999665i	$-0.491757\pi$
$173$	7.20977	−	1.93185i	0.548149	−	0.146876i	0.522256	+	0.852789i	$0.325091\pi$
$174$	8.19615			0.621349
$175$		0			0
$176$	0.732051			0.0551804
$177$	0.517638	−	0.138701i	0.0389081	−	0.0104254i
$178$	−1.67303	+	6.24384i	−0.125399	+	0.467996i
$179$	−17.1962	+	9.92820i	−1.28530	+	0.742069i	−0.977812	−	0.209483i	$-0.932822\pi$
$179$	−17.1962	+	9.92820i	−1.28530	+	0.742069i	−0.307488	+	0.951552i	$0.599489\pi$
$180$		0			0
$181$		−	0.196152i		−	0.0145799i	−0.999973	−	0.00728995i	$-0.997680\pi$
$181$		−	0.196152i		−	0.0145799i	0.999973	−	0.00728995i	$-0.00232048\pi$
$182$	−3.48477	+	1.69161i	−0.258308	+	0.125391i
$183$	8.62398	−	8.62398i	0.637503	−	0.637503i
$184$	3.23205	+	1.86603i	0.238270	+	0.137565i
$185$		0			0
$186$	3.96410	+	6.86603i	0.290662	+	0.503441i
$187$	−0.429705	−	1.60368i	−0.0314232	−	0.117273i
$188$	−7.77817	−	7.77817i	−0.567282	−	0.567282i
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$		0			0
$191$	−12.4282	+	21.5263i	−0.899273	+	1.55759i	−0.0708481	+	0.997487i	$0.522571\pi$
$191$	−12.4282	+	21.5263i	−0.899273	+	1.55759i	−0.828425	+	0.560100i	$0.810763\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−22.9234	−	6.14231i	−1.65006	−	0.442133i	−0.690432	−	0.723397i	$-0.742580\pi$
$193$	−22.9234	−	6.14231i	−1.65006	−	0.442133i	−0.959630	+	0.281264i	$0.909246\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$	18.2832	+	18.2832i	1.30263	+	1.30263i	0.926615	+	0.376012i	$0.122705\pi$
$197$	18.2832	+	18.2832i	1.30263	+	1.30263i	0.376012	+	0.926615i	$0.377295\pi$
$198$	0.189469	+	0.707107i	0.0134650	+	0.0502519i
$199$	13.2321	+	22.9186i	0.937995	+	1.62466i	0.769204	+	0.639004i	$0.220653\pi$
$199$	13.2321	+	22.9186i	0.937995	+	1.62466i	0.168791	+	0.985652i	$0.446014\pi$
$200$		0			0
$201$	−3.46410	−	2.00000i	−0.244339	−	0.141069i
$202$	0.138701	−	0.138701i	0.00975895	−	0.00975895i
$203$	17.9551	+	12.1595i	1.26020	+	0.853431i
$204$			2.26795i			0.158788i
$205$		0			0
$206$	−5.76795	+	3.33013i	−0.401872	+	0.232021i
$207$	−0.965926	+	3.60488i	−0.0671365	+	0.250557i
$208$	−1.41421	+	0.378937i	−0.0980581	+	0.0262746i
$209$	3.07180			0.212481
$210$		0			0
$211$	−19.6603			−1.35347			−0.676734	−	0.736228i	$-0.736605\pi$
$211$	−19.6603			−1.35347			−0.676734	+	0.736228i	$0.736605\pi$
$212$	−5.08845	+	1.36345i	−0.349476	+	0.0936418i
$213$	−3.32748	+	12.4183i	−0.227995	+	0.850890i
$214$	−8.66025	+	5.00000i	−0.592003	+	0.341793i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−1.50215	+	20.9222i	−0.101972	+	1.42029i
$218$	9.65926	−	9.65926i	0.654208	−	0.654208i
$219$	6.92820	+	4.00000i	0.468165	+	0.270295i
$220$		0			0
$221$	1.66025	+	2.87564i	0.111681	+	0.193437i
$222$	1.22474	+	4.57081i	0.0821995	+	0.306773i
$223$	8.67475	+	8.67475i	0.580904	+	0.580904i	0.935152	−	0.354247i	$-0.115263\pi$
$223$	8.67475	+	8.67475i	0.580904	+	0.580904i	−0.354247	+	0.935152i	$0.615263\pi$
$224$	−1.73205	−	2.00000i	−0.115728	−	0.133631i
$225$		0			0
$226$	−1.50000	+	2.59808i	−0.0997785	+	0.172821i
$227$	−5.13922	−	1.37705i	−0.341102	−	0.0913979i	0.0842018	−	0.996449i	$-0.473166\pi$
$227$	−5.13922	−	1.37705i	−0.341102	−	0.0913979i	−0.425304	+	0.905051i	$0.639833\pi$
$228$	−4.05317	−	1.08604i	−0.268428	−	0.0719250i
$229$	5.90192	−	10.2224i	0.390010	−	0.675517i	−0.602440	−	0.798164i	$-0.705805\pi$
$229$	5.90192	−	10.2224i	0.390010	−	0.675517i	0.992450	+	0.122647i	$0.0391382\pi$
$230$		0			0
$231$	−0.633975	+	1.83013i	−0.0417125	+	0.120414i
$232$	5.79555	+	5.79555i	0.380497	+	0.380497i
$233$	−4.89898	−	18.2832i	−0.320943	−	1.19777i	−0.918328	−	0.395820i	$-0.870460\pi$
$233$	−4.89898	−	18.2832i	−0.320943	−	1.19777i	0.597385	−	0.801954i	$-0.296206\pi$
$234$	−0.732051	−	1.26795i	−0.0478557	−	0.0828884i
$235$		0			0
$236$	0.464102	+	0.267949i	0.0302104	+	0.0174420i
$237$	−5.74479	+	5.74479i	−0.373164	+	0.373164i
$238$	−3.36465	+	4.96833i	−0.218098	+	0.322049i
$239$		−	4.85641i		−	0.314135i	−0.987588	−	0.157067i	$-0.949796\pi$
$239$		−	4.85641i		−	0.314135i	0.987588	−	0.157067i	$-0.0502040\pi$
$240$		0			0
$241$	11.1962	−	6.46410i	0.721208	−	0.416389i	−0.0939894	−	0.995573i	$-0.529962\pi$
$241$	11.1962	−	6.46410i	0.721208	−	0.416389i	0.815197	+	0.579184i	$0.196629\pi$
$242$	−2.70831	+	10.1075i	−0.174097	+	0.649738i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	12.1962			0.780779
$245$		0			0
$246$	−2.46410			−0.157105
$247$	−5.93426	+	1.59008i	−0.377588	+	0.101174i
$248$	−2.05197	+	7.65806i	−0.130300	+	0.486287i
$249$	−10.0981	+	5.83013i	−0.639940	+	0.369469i
$250$		0			0
$251$			17.8564i			1.12709i	0.826087	+	0.563543i	$0.190562\pi$
$251$			17.8564i			1.12709i	−0.826087	+	0.563543i	$0.809438\pi$
$252$	1.48356	−	2.19067i	0.0934557	−	0.137999i
$253$	1.93185	−	1.93185i	0.121454	−	0.121454i
$254$	−13.7321	−	7.92820i	−0.861625	−	0.497460i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.998111	+	3.72500i	0.0622605	+	0.232359i	0.990044	−	0.140760i	$-0.0449547\pi$
$257$	0.998111	+	3.72500i	0.0622605	+	0.232359i	−0.927783	+	0.373120i	$0.878288\pi$
$258$	−0.138701	−	0.138701i	−0.00863513	−	0.00863513i
$259$	−4.09808	+	11.8301i	−0.254642	+	0.735088i
$260$		0			0
$261$	−4.09808	+	7.09808i	−0.253665	+	0.439360i
$262$	13.1948	+	3.53553i	0.815177	+	0.218426i
$263$	−17.8857	−	4.79246i	−1.10288	−	0.295516i	−0.338944	−	0.940807i	$-0.610070\pi$
$263$	−17.8857	−	4.79246i	−1.10288	−	0.295516i	−0.763937	+	0.645291i	$0.776736\pi$
$264$	−0.366025	+	0.633975i	−0.0225273	+	0.0390184i
$265$		0			0
$266$	−7.26795	−	8.39230i	−0.445627	−	0.514565i
$267$	−4.57081	−	4.57081i	−0.279729	−	0.279729i
$268$	−1.03528	−	3.86370i	−0.0632396	−	0.236013i
$269$	12.8301	+	22.2224i	0.782267	+	1.35493i	0.930618	+	0.365991i	$0.119270\pi$
$269$	12.8301	+	22.2224i	0.782267	+	1.35493i	−0.148352	+	0.988935i	$0.547397\pi$
$270$		0			0
$271$	2.13397	+	1.23205i	0.129630	+	0.0748418i	0.563413	−	0.826176i	$-0.309488\pi$
$271$	2.13397	+	1.23205i	0.129630	+	0.0748418i	−0.433783	+	0.901017i	$0.642821\pi$
$272$	−1.60368	+	1.60368i	−0.0972375	+	0.0972375i
$273$	0.277401	−	3.86370i	0.0167891	−	0.233842i
$274$			8.07180i			0.487635i
$275$		0			0
$276$	−3.23205	+	1.86603i	−0.194547	+	0.112322i
$277$	−4.29341	+	16.0232i	−0.257966	+	0.962742i	0.708450	+	0.705761i	$0.249395\pi$
$277$	−4.29341	+	16.0232i	−0.257966	+	0.962742i	−0.966416	+	0.256981i	$0.917272\pi$
$278$	12.4877	−	3.34607i	0.748962	−	0.200684i
$279$	−7.92820			−0.474649
$280$		0			0
$281$	19.9808			1.19195			0.595976	−	0.803002i	$-0.296765\pi$
$281$	19.9808			1.19195			0.595976	+	0.803002i	$0.296765\pi$
$282$	10.6252	−	2.84701i	0.632721	−	0.169537i
$283$	−1.84392	+	6.88160i	−0.109610	+	0.409069i	−0.998827	−	0.0484158i	$-0.984583\pi$
$283$	−1.84392	+	6.88160i	−0.109610	+	0.409069i	0.889218	+	0.457484i	$0.151249\pi$
$284$	−11.1340	+	6.42820i	−0.660680	+	0.381444i
$285$		0			0
$286$			1.07180i			0.0633767i
$287$	−5.39804	−	3.65565i	−0.318636	−	0.215786i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	−10.2679	−	5.92820i	−0.603997	−	0.348718i
$290$		0			0
$291$	−3.50000	−	6.06218i	−0.205174	−	0.355371i
$292$	2.07055	+	7.72741i	0.121170	+	0.452212i
$293$	9.38186	+	9.38186i	0.548094	+	0.548094i	0.925889	−	0.377795i	$-0.123318\pi$
$293$	9.38186	+	9.38186i	0.548094	+	0.548094i	−0.377795	+	0.925889i	$0.623318\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$		0			0
$296$	−2.36603	+	4.09808i	−0.137522	+	0.238196i
$297$	−0.707107	−	0.189469i	−0.0410305	−	0.0109941i
$298$	−17.3867	−	4.65874i	−1.00718	−	0.269874i
$299$	−2.73205	+	4.73205i	−0.157999	+	0.273662i
$300$		0			0
$301$	−0.0980762	−	0.509619i	−0.00565302	−	0.0293739i
$302$	7.72741	+	7.72741i	0.444662	+	0.444662i
$303$	0.0507680	+	0.189469i	0.00291654	+	0.0108847i
$304$	−2.09808	−	3.63397i	−0.120333	−	0.208423i
$305$		0			0
$306$	−1.96410	−	1.13397i	−0.112280	−	0.0648250i
$307$	13.3843	−	13.3843i	0.763880	−	0.763880i	−0.213141	−	0.977021i	$-0.568369\pi$
$307$	13.3843	−	13.3843i	0.763880	−	0.763880i	0.977021	+	0.213141i	$0.0683695\pi$
$308$	−1.74238	+	0.845807i	−0.0992815	+	0.0481944i
$309$		−	6.66025i		−	0.378889i
$310$		0			0
$311$	−11.8923	+	6.86603i	−0.674351	+	0.389337i	−0.797723	−	0.603024i	$-0.793962\pi$
$311$	−11.8923	+	6.86603i	−0.674351	+	0.389337i	0.123372	+	0.992360i	$0.460629\pi$
$312$	0.378937	−	1.41421i	0.0214531	−	0.0800641i
$313$	−17.8350	+	4.77886i	−1.00809	+	0.270117i	−0.724832	−	0.688926i	$-0.758082\pi$
$313$	−17.8350	+	4.77886i	−1.00809	+	0.270117i	−0.283260	+	0.959043i	$0.591416\pi$
$314$	−20.7321			−1.16998
$315$		0			0
$316$	−8.12436			−0.457031
$317$	11.4016	−	3.05506i	0.640380	−	0.171589i	0.0760044	−	0.997107i	$-0.475784\pi$
$317$	11.4016	−	3.05506i	0.640380	−	0.171589i	0.564376	+	0.825518i	$0.309117\pi$
$318$	1.36345	−	5.08845i	0.0764582	−	0.285346i
$319$	5.19615	−	3.00000i	0.290929	−	0.167968i
$320$		0			0
$321$		−	10.0000i		−	0.558146i
$322$	−9.84873	−	0.707107i	−0.548848	−	0.0394055i
$323$	−6.72930	+	6.72930i	−0.374428	+	0.374428i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$		0			0
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	3.53553	+	13.1948i	0.195515	+	0.729674i
$328$	−1.74238	−	1.74238i	−0.0962070	−	0.0962070i
$329$	27.5000	+	9.52628i	1.51612	+	0.525201i
$330$		0			0
$331$	5.92820	−	10.2679i	0.325844	−	0.564378i	−0.655839	−	0.754901i	$-0.727685\pi$
$331$	5.92820	−	10.2679i	0.325844	−	0.564378i	0.981683	+	0.190523i	$0.0610184\pi$
$332$	−11.2629	−	3.01790i	−0.618134	−	0.165629i
$333$	−4.57081	−	1.22474i	−0.250479	−	0.0671156i
$334$	2.53590	−	4.39230i	0.138758	−	0.240336i
$335$		0			0
$336$	2.59808	−	0.500000i	0.141737	−	0.0272772i
$337$	13.2963	+	13.2963i	0.724297	+	0.724297i	0.969477	−	0.245180i	$-0.0788472\pi$
$337$	13.2963	+	13.2963i	0.724297	+	0.724297i	−0.245180	+	0.969477i	$0.578847\pi$
$338$	2.80984	+	10.4865i	0.152835	+	0.570390i
$339$	−1.50000	−	2.59808i	−0.0814688	−	0.141108i
$340$		0			0
$341$	5.02628	+	2.90192i	0.272188	+	0.157148i
$342$	2.96713	−	2.96713i	0.160444	−	0.160444i
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$		−	0.196152i		−	0.0105758i
$345$		0			0
$346$	−6.46410	+	3.73205i	−0.347512	+	0.200636i
$347$	7.39924	−	27.6143i	0.397212	−	1.48241i	−0.420768	−	0.907168i	$-0.638239\pi$
$347$	7.39924	−	27.6143i	0.397212	−	1.48241i	0.817980	−	0.575247i	$-0.195094\pi$
$348$	−7.91688	+	2.12132i	−0.424389	+	0.113715i
$349$	−7.26795			−0.389044			−0.194522	−	0.980898i	$-0.562316\pi$
$349$	−7.26795			−0.389044			−0.194522	+	0.980898i	$0.562316\pi$
$350$		0			0
$351$	1.46410			0.0781480
$352$	−0.707107	+	0.189469i	−0.0376889	+	0.0100987i
$353$	−0.928761	+	3.46618i	−0.0494330	+	0.184486i	−0.986228	−	0.165393i	$-0.947111\pi$
$353$	−0.928761	+	3.46618i	−0.0494330	+	0.184486i	0.936795	+	0.349879i	$0.113777\pi$
$354$	−0.464102	+	0.267949i	−0.0246667	+	0.0142413i
$355$		0			0
$356$		−	6.46410i		−	0.342597i
$357$	−2.62038	−	5.39804i	−0.138685	−	0.285694i
$358$	14.0406	−	14.0406i	0.742069	−	0.742069i
$359$	18.0000	+	10.3923i	0.950004	+	0.548485i	0.893082	−	0.449894i	$-0.148538\pi$
$359$	18.0000	+	10.3923i	0.950004	+	0.548485i	0.0569216	+	0.998379i	$0.481871\pi$
$360$		0			0
$361$	0.696152	+	1.20577i	0.0366396	+	0.0634617i
$362$	0.0507680	+	0.189469i	0.00266831	+	0.00995825i
$363$	−7.39924	−	7.39924i	−0.388359	−	0.388359i
$364$	2.92820	−	2.53590i	0.153480	−	0.132917i
$365$		0			0
$366$	−6.09808	+	10.5622i	−0.318752	+	0.552094i
$367$	−30.2533	−	8.10634i	−1.57921	−	0.423148i	−0.640528	−	0.767935i	$-0.721284\pi$
$367$	−30.2533	−	8.10634i	−1.57921	−	0.423148i	−0.938681	+	0.344787i	$0.887951\pi$
$368$	−3.60488	−	0.965926i	−0.187918	−	0.0503524i
$369$	1.23205	−	2.13397i	0.0641380	−	0.111090i
$370$		0			0
$371$	10.5359	−	9.12436i	0.546997	−	0.473713i
$372$	−5.60609	−	5.60609i	−0.290662	−	0.290662i
$373$	1.59008	+	5.93426i	0.0823312	+	0.307264i	0.994795	−	0.101892i	$-0.0324897\pi$
$373$	1.59008	+	5.93426i	0.0823312	+	0.307264i	−0.912464	+	0.409156i	$0.865823\pi$
$374$	0.830127	+	1.43782i	0.0429248	+	0.0743480i
$375$		0			0
$376$	9.52628	+	5.50000i	0.491280	+	0.283641i
$377$	−8.48528	+	8.48528i	−0.437014	+	0.437014i
$378$	1.15539	+	2.38014i	0.0594271	+	0.122421i
$379$			10.0526i			0.516365i	0.966096	+	0.258183i	$0.0831236\pi$
$379$			10.0526i			0.516365i	−0.966096	+	0.258183i	$0.916876\pi$
$380$		0			0
$381$	13.7321	−	7.92820i	0.703514	−	0.406174i
$382$	6.43331	−	24.0094i	0.329157	−	1.22843i
$383$	25.5624	−	6.84941i	1.30618	−	0.349989i	0.462394	−	0.886675i	$-0.346991\pi$
$383$	25.5624	−	6.84941i	1.30618	−	0.349989i	0.843782	+	0.536686i	$0.180324\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	23.7321			1.20793
$387$	0.189469	−	0.0507680i	0.00963123	−	0.00258068i
$388$	1.81173	−	6.76148i	0.0919768	−	0.343262i
$389$	−23.9545	+	13.8301i	−1.21454	+	0.701215i	−0.963745	−	0.266825i	$-0.914025\pi$
$389$	−23.9545	+	13.8301i	−1.21454	+	0.701215i	−0.250795	+	0.968040i	$0.580692\pi$
$390$		0			0
$391$			8.46410i			0.428048i
$392$	6.43331	+	2.75908i	0.324931	+	0.139354i
$393$	−9.65926	+	9.65926i	−0.487245	+	0.487245i
$394$	−22.3923	−	12.9282i	−1.12811	−	0.651313i
$395$		0			0
$396$	−0.366025	−	0.633975i	−0.0183935	−	0.0318584i
$397$	−5.03768	−	18.8009i	−0.252834	−	0.943589i	−0.969283	−	0.245949i	$-0.920900\pi$
$397$	−5.03768	−	18.8009i	−0.252834	−	0.943589i	0.716449	−	0.697640i	$-0.245766\pi$
$398$	−18.7129	−	18.7129i	−0.937995	−	0.937995i
$399$	10.9019	−	2.09808i	0.545779	−	0.105035i
$400$		0			0
$401$	10.4641	−	18.1244i	0.522552	−	0.905087i	−0.477103	−	0.878847i	$-0.658313\pi$
$401$	10.4641	−	18.1244i	0.522552	−	0.905087i	0.999656	−	0.0262399i	$-0.00835339\pi$
$402$	3.86370	+	1.03528i	0.192704	+	0.0516349i
$403$	−11.2122	−	3.00429i	−0.558518	−	0.149654i
$404$	−0.0980762	+	0.169873i	−0.00487947	+	0.00845150i
$405$		0			0
$406$	−20.4904	−	7.09808i	−1.01692	−	0.352272i
$407$	2.44949	+	2.44949i	0.121417	+	0.121417i
$408$	−0.586988	−	2.19067i	−0.0290603	−	0.108454i
$409$	16.5981	+	28.7487i	0.820722	+	1.42153i	0.905145	+	0.425102i	$0.139762\pi$
$409$	16.5981	+	28.7487i	0.820722	+	1.42153i	−0.0844233	+	0.996430i	$0.526905\pi$
$410$		0			0
$411$	−6.99038	−	4.03590i	−0.344810	−	0.199076i
$412$	4.70951	−	4.70951i	0.232021	−	0.232021i
$413$	−1.41421	−	0.101536i	−0.0695889	−	0.00499626i
$414$		−	3.73205i		−	0.183420i
$415$		0			0
$416$	1.26795	−	0.732051i	0.0621663	−	0.0358917i
$417$	−3.34607	+	12.4877i	−0.163858	+	0.611525i
$418$	−2.96713	+	0.795040i	−0.145127	+	0.0388867i
$419$	10.5885			0.517280			0.258640	−	0.965974i	$-0.416726\pi$
$419$	10.5885			0.517280			0.258640	+	0.965974i	$0.416726\pi$
$420$		0			0
$421$	−2.53590			−0.123592			−0.0617961	−	0.998089i	$-0.519683\pi$
$421$	−2.53590			−0.123592			−0.0617961	+	0.998089i	$0.519683\pi$
$422$	18.9903	−	5.08845i	0.924436	−	0.247702i
$423$	−2.84701	+	10.6252i	−0.138426	+	0.516614i
$424$	4.56218	−	2.63397i	0.221559	−	0.127917i
$425$		0			0
$426$		−	12.8564i		−	0.622895i
$427$	−29.0285	+	14.0914i	−1.40479	+	0.681929i
$428$	7.07107	−	7.07107i	0.341793	−	0.341793i
$429$	−0.928203	−	0.535898i	−0.0448141	−	0.0258734i
$430$		0			0
$431$	−0.232051	−	0.401924i	−0.0111775	−	0.0193600i	0.860383	−	0.509649i	$-0.170225\pi$
$431$	−0.232051	−	0.401924i	−0.0111775	−	0.0193600i	−0.871560	+	0.490289i	$0.836891\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	20.0256	+	20.0256i	0.962370	+	0.962370i	0.999317	−	0.0369472i	$-0.0117633\pi$
$433$	20.0256	+	20.0256i	0.962370	+	0.962370i	−0.0369472	+	0.999317i	$0.511763\pi$
$434$	−3.96410	−	20.5981i	−0.190283	−	0.988739i
$435$		0			0
$436$	−6.83013	+	11.8301i	−0.327104	+	0.566560i
$437$	−15.1266	−	4.05317i	−0.723606	−	0.193890i
$438$	−7.72741	−	2.07055i	−0.369230	−	0.0989348i
$439$	19.6962	−	34.1147i	0.940046	−	1.62821i	0.174667	−	0.984628i	$-0.444115\pi$
$439$	19.6962	−	34.1147i	0.940046	−	1.62821i	0.765379	−	0.643580i	$-0.222552\pi$
$440$		0			0
$441$	−1.00000	+	6.92820i	−0.0476190	+	0.329914i
$442$	−2.34795	−	2.34795i	−0.111681	−	0.111681i
$443$	−5.56892	−	20.7835i	−0.264587	−	0.987454i	−0.962502	−	0.271273i	$-0.912555\pi$
$443$	−5.56892	−	20.7835i	−0.264587	−	0.987454i	0.697915	−	0.716181i	$-0.254111\pi$
$444$	−2.36603	−	4.09808i	−0.112287	−	0.194486i
$445$		0			0
$446$	−10.6244	−	6.13397i	−0.503078	−	0.290452i
$447$	12.7279	−	12.7279i	0.602010	−	0.602010i
$448$	2.19067	+	1.48356i	0.103499	+	0.0700918i
$449$		−	29.7321i		−	1.40314i	−0.712599	−	0.701571i	$-0.752482\pi$
$449$		−	29.7321i		−	1.40314i	0.712599	−	0.701571i	$-0.247518\pi$
$450$		0			0
$451$	−1.56218	+	0.901924i	−0.0735601	+	0.0424699i
$452$	0.776457	−	2.89778i	0.0365215	−	0.136300i
$453$	−10.5558	+	2.82843i	−0.495956	+	0.132891i
$454$	5.32051			0.249704
$455$		0			0
$456$	4.19615			0.196503
$457$	−32.7028	+	8.76268i	−1.52977	+	0.409901i	−0.922945	−	0.384933i	$-0.874225\pi$
$457$	−32.7028	+	8.76268i	−1.52977	+	0.409901i	−0.606827	+	0.794834i	$0.707558\pi$
$458$	−3.05506	+	11.4016i	−0.142754	+	0.532764i
$459$	1.96410	−	1.13397i	0.0916764	−	0.0529294i
$460$		0			0
$461$			19.3205i			0.899846i	0.893067	+	0.449923i	$0.148549\pi$
$461$			19.3205i			0.899846i	−0.893067	+	0.449923i	$0.851451\pi$
$462$	0.138701	−	1.93185i	0.00645294	−	0.0898779i
$463$	10.3292	−	10.3292i	0.480039	−	0.480039i	−0.425105	−	0.905144i	$-0.639763\pi$
$463$	10.3292	−	10.3292i	0.480039	−	0.480039i	0.905144	+	0.425105i	$0.139763\pi$
$464$	−7.09808	−	4.09808i	−0.329520	−	0.190248i
$465$		0			0
$466$	9.46410	+	16.3923i	0.438416	+	0.759359i
$467$	−2.08416	−	7.77817i	−0.0964432	−	0.359931i	0.900791	−	0.434253i	$-0.142988\pi$
$467$	−2.08416	−	7.77817i	−0.0964432	−	0.359931i	−0.997234	+	0.0743217i	$0.976321\pi$
$468$	1.03528	+	1.03528i	0.0478557	+	0.0478557i
$469$	6.92820	+	8.00000i	0.319915	+	0.369406i
$470$		0			0
$471$	10.3660	−	17.9545i	0.477641	−	0.827299i
$472$	−0.517638	−	0.138701i	−0.0238262	−	0.00638422i
$473$	−0.138701	−	0.0371647i	−0.00637747	−	0.00170884i
$474$	4.06218	−	7.03590i	0.186582	−	0.323170i
$475$		0			0
$476$	1.96410	−	5.66987i	0.0900244	−	0.259878i
$477$	3.72500	+	3.72500i	0.170556	+	0.170556i
$478$	1.25693	+	4.69093i	0.0574907	+	0.214558i
$479$	−9.99038	−	17.3038i	−0.456472	−	0.790633i	0.542299	−	0.840185i	$-0.317554\pi$
$479$	−9.99038	−	17.3038i	−0.456472	−	0.790633i	−0.998772	+	0.0495524i	$0.984221\pi$
$480$		0			0
$481$	−6.00000	−	3.46410i	−0.273576	−	0.157949i
$482$	−9.14162	+	9.14162i	−0.416389	+	0.416389i
$483$	5.53674	−	8.17569i	0.251930	−	0.372007i
$484$		−	10.4641i		−	0.475641i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	3.50335	−	13.0747i	0.158752	−	0.592470i	−0.840003	−	0.542582i	$-0.817447\pi$
$487$	3.50335	−	13.0747i	0.158752	−	0.592470i	0.998755	−	0.0498882i	$-0.0158865\pi$
$488$	−11.7806	+	3.15660i	−0.533282	+	0.142892i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	−1.66025			−0.0749262			−0.0374631	−	0.999298i	$-0.511928\pi$
$491$	−1.66025			−0.0749262			−0.0374631	+	0.999298i	$0.511928\pi$
$492$	2.38014	−	0.637756i	0.107305	−	0.0287523i
$493$	−4.81105	+	17.9551i	−0.216679	+	0.808656i
$494$	5.32051	−	3.07180i	0.239381	−	0.138207i
$495$		0			0
$496$		−	7.92820i		−	0.355987i
$497$	19.0733	−	28.1642i	0.855554	−	1.26333i
$498$	8.24504	−	8.24504i	0.369469	−	0.369469i
$499$	−18.1699	−	10.4904i	−0.813395	−	0.469614i	0.0347383	−	0.999396i	$-0.488940\pi$
$499$	−18.1699	−	10.4904i	−0.813395	−	0.469614i	−0.848134	+	0.529782i	$0.822274\pi$
$500$		0			0
$501$	2.53590	+	4.39230i	0.113296	+	0.196234i
$502$	−4.62158	−	17.2480i	−0.206271	−	0.769814i
$503$	30.5307	+	30.5307i	1.36130	+	1.36130i	0.872268	+	0.489028i	$0.162648\pi$
$503$	30.5307	+	30.5307i	1.36130	+	1.36130i	0.489028	+	0.872268i	$0.337352\pi$
$504$	−0.866025	+	2.50000i	−0.0385758	+	0.111359i
$505$		0			0
$506$	−1.36603	+	2.36603i	−0.0607272	+	0.105183i
$507$	−10.4865	−	2.80984i	−0.465721	−	0.124790i
$508$	15.3161	+	4.10394i	0.679543	+	0.182083i
$509$	2.02628	−	3.50962i	0.0898133	−	0.155561i	−0.817619	−	0.575760i	$-0.804706\pi$
$509$	2.02628	−	3.50962i	0.0898133	−	0.155561i	0.907432	+	0.420199i	$0.138040\pi$
$510$		0			0
$511$	−13.8564	−	16.0000i	−0.612971	−	0.707798i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.08604	+	4.05317i	0.0479500	+	0.178952i
$514$	−1.92820	−	3.33975i	−0.0850494	−	0.147310i
$515$		0			0
$516$	0.169873	+	0.0980762i	0.00747824	+	0.00431756i
$517$	5.69402	−	5.69402i	0.250423	−	0.250423i
$518$	0.896575	−	12.4877i	0.0393933	−	0.548677i
$519$		−	7.46410i		−	0.327638i
$520$		0			0
$521$	27.3109	−	15.7679i	1.19651	−	0.690806i	0.236736	−	0.971574i	$-0.423922\pi$
$521$	27.3109	−	15.7679i	1.19651	−	0.690806i	0.959776	+	0.280768i	$0.0905890\pi$
$522$	2.12132	−	7.91688i	0.0928477	−	0.346512i
$523$	6.50266	−	1.74238i	0.284342	−	0.0761891i	−0.113829	−	0.993500i	$-0.536312\pi$
$523$	6.50266	−	1.74238i	0.284342	−	0.0761891i	0.398171	+	0.917311i	$0.369645\pi$
$524$	−13.6603			−0.596751
$525$		0			0
$526$	18.5167			0.807365
$527$	−17.3681	+	4.65376i	−0.756566	+	0.202721i
$528$	0.189469	−	0.707107i	0.00824557	−	0.0307729i
$529$	7.85641	−	4.53590i	0.341583	−	0.197213i
$530$		0			0
$531$		−	0.535898i		−	0.0232560i
$532$	9.19239	+	6.22526i	0.398541	+	0.269899i
$533$	2.55103	−	2.55103i	0.110497	−	0.110497i
$534$	5.59808	+	3.23205i	0.242252	+	0.139865i
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	5.13922	+	19.1798i	0.221774	+	0.827670i
$538$	−18.1445	−	18.1445i	−0.782267	−	0.782267i
$539$	3.16987	−	4.02628i	0.136536	−	0.173424i
$540$		0			0
$541$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$541$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$542$	−2.38014	−	0.637756i	−0.102236	−	0.0273940i
$543$	−0.189469	−	0.0507680i	−0.00813088	−	0.00217866i
$544$	1.13397	−	1.96410i	0.0486188	−	0.0842102i
$545$		0			0
$546$	0.732051	+	3.80385i	0.0313289	+	0.162790i
$547$	−31.0483	−	31.0483i	−1.32753	−	1.32753i	−0.907519	−	0.420012i	$-0.862026\pi$
$547$	−31.0483	−	31.0483i	−1.32753	−	1.32753i	−0.420012	−	0.907519i	$-0.637974\pi$
$548$	−2.08913	−	7.79676i	−0.0892434	−	0.333061i
$549$	−6.09808	−	10.5622i	−0.260260	−	0.450783i
$550$		0			0
$551$	−29.7846	−	17.1962i	−1.26887	−	0.732581i
$552$	2.63896	−	2.63896i	0.112322	−	0.112322i
$553$	19.3371	−	9.38684i	0.822297	−	0.399169i
$554$		−	16.5885i		−	0.704776i
$555$		0			0
$556$	−11.1962	+	6.46410i	−0.474823	+	0.274139i
$557$	3.17020	−	11.8313i	0.134326	−	0.501310i	−0.865674	−	0.500608i	$-0.833110\pi$
$557$	3.17020	−	11.8313i	0.134326	−	0.501310i	1.00000		0.000702224i	$-0.000223525\pi$
$558$	7.65806	−	2.05197i	0.324191	−	0.0868668i
$559$	0.287187			0.0121467
$560$		0			0
$561$	−1.66025			−0.0700960
$562$	−19.2999	+	5.17140i	−0.814119	+	0.218142i
$563$	−10.3292	+	38.5491i	−0.435324	+	1.62465i	0.304966	+	0.952363i	$0.401355\pi$
$563$	−10.3292	+	38.5491i	−0.435324	+	1.62465i	−0.740290	+	0.672288i	$0.765312\pi$
$564$	−9.52628	+	5.50000i	−0.401129	+	0.231592i
$565$		0			0
$566$		−	7.12436i		−	0.299459i
$567$	−2.63896	−	0.189469i	−0.110826	−	0.00795694i
$568$	9.09085	−	9.09085i	0.381444	−	0.381444i
$569$	−5.55256	−	3.20577i	−0.232775	−	0.134393i	0.379076	−	0.925365i	$-0.376242\pi$
$569$	−5.55256	−	3.20577i	−0.232775	−	0.134393i	−0.611852	+	0.790972i	$0.709575\pi$
$570$		0			0
$571$	3.80385	+	6.58846i	0.159186	+	0.275718i	0.934575	−	0.355765i	$-0.115780\pi$
$571$	3.80385	+	6.58846i	0.159186	+	0.275718i	−0.775389	+	0.631483i	$0.782446\pi$
$572$	−0.277401	−	1.03528i	−0.0115987	−	0.0432871i
$573$	17.5761	+	17.5761i	0.734254	+	0.734254i
$574$	6.16025	+	2.13397i	0.257124	+	0.0890704i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.17209	+	0.582009i	0.0904252	+	0.0242294i	0.303748	−	0.952752i	$-0.401762\pi$
$577$	2.17209	+	0.582009i	0.0904252	+	0.0242294i	−0.213323	+	0.976982i	$0.568429\pi$
$578$	11.4524	+	3.06866i	0.476357	+	0.127640i
$579$	−11.8660	+	20.5526i	−0.493135	+	0.854135i
$580$		0			0
$581$	30.2942	−	5.83013i	1.25682	−	0.241874i
$582$	4.94975	+	4.94975i	0.205174	+	0.205174i
$583$	−0.998111	−	3.72500i	−0.0413376	−	0.154274i
$584$	−4.00000	−	6.92820i	−0.165521	−	0.286691i
$585$		0			0
$586$	−11.4904	−	6.63397i	−0.474663	−	0.274047i
$587$	13.0053	−	13.0053i	0.536787	−	0.536787i	−0.385797	−	0.922584i	$-0.626073\pi$
$587$	13.0053	−	13.0053i	0.536787	−	0.536787i	0.922584	+	0.385797i	$0.126073\pi$
$588$	−5.60609	+	4.19187i	−0.231191	+	0.172870i
$589$		−	33.2679i		−	1.37078i
$590$		0			0
$591$	22.3923	−	12.9282i	0.921096	−	0.531795i
$592$	1.22474	−	4.57081i	0.0503367	−	0.187859i
$593$	−16.2313	+	4.34916i	−0.666538	+	0.178598i	−0.576195	−	0.817312i	$-0.695463\pi$
$593$	−16.2313	+	4.34916i	−0.666538	+	0.178598i	−0.0903434	+	0.995911i	$0.528796\pi$
$594$	0.732051			0.0300364
$595$		0			0
$596$	18.0000			0.737309
$597$	25.5624	−	6.84941i	1.04620	−	0.280328i
$598$	1.41421	−	5.27792i	0.0578315	−	0.215830i
$599$	38.0429	−	21.9641i	1.55439	−	0.897429i	0.556617	−	0.830770i	$-0.312099\pi$
$599$	38.0429	−	21.9641i	1.55439	−	0.897429i	0.997776	−	0.0666594i	$-0.0212341\pi$
$600$		0			0
$601$			20.2487i			0.825962i	0.910740	+	0.412981i	$0.135512\pi$
$601$			20.2487i			0.825962i	−0.910740	+	0.412981i	$0.864488\pi$
$602$	0.226633	+	0.466870i	0.00923689	+	0.0190282i
$603$	−2.82843	+	2.82843i	−0.115182	+	0.115182i
$604$	−9.46410	−	5.46410i	−0.385089	−	0.222331i
$605$		0			0
$606$	−0.0980762	−	0.169873i	−0.00398407	−	0.00690062i
$607$	−6.24384	−	23.3023i	−0.253430	−	0.945813i	−0.968957	−	0.247228i	$-0.920480\pi$
$607$	−6.24384	−	23.3023i	−0.253430	−	0.945813i	0.715528	−	0.698585i	$-0.246186\pi$
$608$	2.96713	+	2.96713i	0.120333	+	0.120333i
$609$	16.3923	−	14.1962i	0.664250	−	0.575257i
$610$		0			0
$611$	−8.05256	+	13.9474i	−0.325772	+	0.564253i
$612$	2.19067	+	0.586988i	0.0885526	+	0.0237276i
$613$	−4.43211	−	1.18758i	−0.179011	−	0.0479659i	0.168200	−	0.985753i	$-0.446205\pi$
$613$	−4.43211	−	1.18758i	−0.179011	−	0.0479659i	−0.347211	+	0.937787i	$0.612871\pi$
$614$	−9.46410	+	16.3923i	−0.381940	+	0.661540i
$615$		0			0
$616$	1.46410	−	1.26795i	0.0589903	−	0.0510871i
$617$	3.05506	+	3.05506i	0.122992	+	0.122992i	0.765924	−	0.642932i	$-0.222282\pi$
$617$	3.05506	+	3.05506i	0.122992	+	0.122992i	−0.642932	+	0.765924i	$0.722282\pi$
$618$	1.72380	+	6.43331i	0.0693414	+	0.258786i
$619$	6.90192	+	11.9545i	0.277412	+	0.480491i	0.970741	−	0.240130i	$-0.0771901\pi$
$619$	6.90192	+	11.9545i	0.277412	+	0.480491i	−0.693329	+	0.720621i	$0.743857\pi$
$620$		0			0
$621$	3.23205	+	1.86603i	0.129698	+	0.0748810i
$622$	9.71003	−	9.71003i	0.389337	−	0.389337i
$623$	7.46859	+	15.3855i	0.299223	+	0.616406i
$624$			1.46410i			0.0586110i
$625$		0			0
$626$	15.9904	−	9.23205i	0.639104	−	0.368987i
$627$	0.795040	−	2.96713i	0.0317508	−	0.118496i
$628$	20.0256	−	5.36585i	0.799109	−	0.214121i
$629$	−10.7321			−0.427915
$630$		0			0
$631$	−16.4115			−0.653333			−0.326667	−	0.945140i	$-0.605925\pi$
$631$	−16.4115			−0.653333			−0.326667	+	0.945140i	$0.605925\pi$
$632$	7.84752	−	2.10274i	0.312158	−	0.0836424i
$633$	−5.08845	+	18.9903i	−0.202248	+	0.754799i
$634$	−10.2224	+	5.90192i	−0.405985	+	0.234395i
$635$		0			0
$636$			5.26795i			0.208888i
$637$	−4.03957	+	9.41902i	−0.160054	+	0.373195i
$638$	−4.24264	+	4.24264i	−0.167968	+	0.167968i
$639$	11.1340	+	6.42820i	0.440453	+	0.254296i
$640$		0			0
$641$	−0.330127	−	0.571797i	−0.0130392	−	0.0225846i	0.859432	−	0.511250i	$-0.170817\pi$
$641$	−0.330127	−	0.571797i	−0.0130392	−	0.0225846i	−0.872471	+	0.488665i	$0.837484\pi$
$642$	2.58819	+	9.65926i	0.102148	+	0.381221i
$643$	−24.3190	−	24.3190i	−0.959049	−	0.959049i	0.0401449	−	0.999194i	$-0.487218\pi$
$643$	−24.3190	−	24.3190i	−0.959049	−	0.959049i	−0.999194	+	0.0401449i	$0.987218\pi$
$644$	9.69615	−	1.86603i	0.382082	−	0.0735317i
$645$		0			0
$646$	4.75833	−	8.24167i	0.187214	−	0.324264i
$647$	−18.8009	−	5.03768i	−0.739139	−	0.198052i	−0.130444	−	0.991456i	$-0.541640\pi$
$647$	−18.8009	−	5.03768i	−0.739139	−	0.198052i	−0.608695	+	0.793404i	$0.708307\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−0.196152	+	0.339746i	−0.00769966	+	0.0133362i
$650$		0			0
$651$	19.8205	+	6.86603i	0.776827	+	0.269101i
$652$	−8.48528	−	8.48528i	−0.332309	−	0.332309i
$653$	5.85993	+	21.8695i	0.229317	+	0.855821i	0.980629	+	0.195875i	$0.0627545\pi$
$653$	5.85993	+	21.8695i	0.229317	+	0.855821i	−0.751312	+	0.659947i	$0.770579\pi$
$654$	−6.83013	−	11.8301i	−0.267079	−	0.462595i
$655$		0			0
$656$	2.13397	+	1.23205i	0.0833177	+	0.0481035i
$657$	5.65685	−	5.65685i	0.220695	−	0.220695i
$658$	−29.0285	−	2.08416i	−1.13165	−	0.0812488i
$659$		−	14.1962i		−	0.553004i	−0.961013	−	0.276502i	$-0.910825\pi$
$659$		−	14.1962i		−	0.553004i	0.961013	−	0.276502i	$-0.0891752\pi$
$660$		0			0
$661$	−34.5167	+	19.9282i	−1.34254	+	0.775117i	−0.987180	−	0.159611i	$-0.948976\pi$
$661$	−34.5167	+	19.9282i	−1.34254	+	0.775117i	−0.355363	+	0.934729i	$0.615643\pi$
$662$	−3.06866	+	11.4524i	−0.119267	+	0.445111i
$663$	3.20736	−	0.859411i	0.124564	−	0.0333767i
$664$	11.6603			0.452506
$665$		0			0
$666$	4.73205			0.183363
$667$	−29.5462	+	7.91688i	−1.14403	+	0.306543i
$668$	−1.31268	+	4.89898i	−0.0507890	+	0.189547i
$669$	10.6244	−	6.13397i	0.410761	−	0.237153i
$670$		0			0
$671$			8.92820i			0.344669i
$672$	−2.38014	+	1.15539i	−0.0918159	+	0.0445703i
$673$	−1.60368	+	1.60368i	−0.0618174	+	0.0618174i	−0.737340	−	0.675522i	$-0.763918\pi$
$673$	−1.60368	+	1.60368i	−0.0618174	+	0.0618174i	0.675522	+	0.737340i	$0.263918\pi$
$674$	−16.2846	−	9.40192i	−0.627260	−	0.362149i
$675$		0			0
$676$	−5.42820	−	9.40192i	−0.208777	−	0.361612i
$677$	11.0871	+	41.3775i	0.426111	+	1.59027i	0.761485	+	0.648183i	$0.224471\pi$
$677$	11.0871	+	41.3775i	0.426111	+	1.59027i	−0.335374	+	0.942085i	$0.608863\pi$
$678$	2.12132	+	2.12132i	0.0814688	+	0.0814688i
$679$	3.50000	+	18.1865i	0.134318	+	0.697935i
$680$		0			0
$681$	−2.66025	+	4.60770i	−0.101941	+	0.176567i
$682$	−5.60609	−	1.50215i	−0.214668	−	0.0575202i
$683$	−36.7052	−	9.83512i	−1.40448	−	0.376331i	−0.524532	−	0.851391i	$-0.675760\pi$
$683$	−36.7052	−	9.83512i	−1.40448	−	0.376331i	−0.879953	+	0.475060i	$0.842426\pi$
$684$	−2.09808	+	3.63397i	−0.0802219	+	0.138948i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$	−8.34658	−	8.34658i	−0.318442	−	0.318442i
$688$	0.0507680	+	0.189469i	0.00193551	+	0.00722343i
$689$	3.85641	+	6.67949i	0.146917	+	0.254468i
$690$		0			0
$691$	17.6147	+	10.1699i	0.670096	+	0.386880i	0.796113	−	0.605148i	$-0.206886\pi$
$691$	17.6147	+	10.1699i	0.670096	+	0.386880i	−0.126017	+	0.992028i	$0.540219\pi$
$692$	5.27792	−	5.27792i	0.200636	−	0.200636i
$693$	1.60368	+	1.08604i	0.0609189	+	0.0412554i
$694$			28.5885i			1.08520i
$695$		0			0
$696$	7.09808	−	4.09808i	0.269052	−	0.155337i
$697$	1.44640	−	5.39804i	0.0547863	−	0.204465i
$698$	7.02030	−	1.88108i	0.265722	−	0.0712001i
$699$	−18.9282			−0.715930
$700$		0			0
$701$	21.4641			0.810688			0.405344	−	0.914164i	$-0.367152\pi$
$701$	21.4641			0.810688			0.405344	+	0.914164i	$0.367152\pi$
$702$	−1.41421	+	0.378937i	−0.0533761	+	0.0143021i
$703$	5.13922	−	19.1798i	0.193829	−	0.723380i
$704$	0.633975	−	0.366025i	0.0238938	−	0.0137951i
$705$		0			0
$706$		−	3.58846i		−	0.135053i
$707$	0.0371647	−	0.517638i	0.00139772	−	0.0194678i
$708$	0.378937	−	0.378937i	0.0142413	−	0.0142413i
$709$	−33.9282	−	19.5885i	−1.27420	−	0.735660i	−0.298425	−	0.954433i	$-0.596461\pi$
$709$	−33.9282	−	19.5885i	−1.27420	−	0.735660i	−0.975776	+	0.218773i	$0.929795\pi$
$710$		0			0
$711$	4.06218	+	7.03590i	0.152344	+	0.263867i
$712$	1.67303	+	6.24384i	0.0626995	+	0.233998i
$713$	−20.9222	−	20.9222i	−0.783543	−	0.783543i
$714$	3.92820	+	4.53590i	0.147009	+	0.169752i
$715$		0			0
$716$	−9.92820	+	17.1962i	−0.371034	+	0.642650i
$717$	−4.69093	−	1.25693i	−0.175186	−	0.0469409i
$718$	−20.0764	−	5.37945i	−0.749244	−	0.200759i
$719$	6.66987	−	11.5526i	0.248744	−	0.430838i	−0.714433	−	0.699703i	$-0.753315\pi$
$719$	6.66987	−	11.5526i	0.248744	−	0.430838i	0.963178	+	0.268866i	$0.0866488\pi$
$720$		0			0
$721$	−5.76795	+	16.6506i	−0.214810	+	0.620102i
$722$	−0.984508	−	0.984508i	−0.0366396	−	0.0366396i
$723$	−3.34607	−	12.4877i	−0.124442	−	0.464422i
$724$	−0.0980762	−	0.169873i	−0.00364497	−	0.00631328i
$725$		0			0
$726$	9.06218	+	5.23205i	0.336329	+	0.194180i
$727$	−0.0879327	+	0.0879327i	−0.00326124	+	0.00326124i	−0.708736	−	0.705474i	$-0.750734\pi$
$727$	−0.0879327	+	0.0879327i	−0.00326124	+	0.00326124i	0.705474	+	0.708736i	$0.250734\pi$
$728$	−2.17209	+	3.20736i	−0.0805029	+	0.118873i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	0.385263	−	0.222432i	0.0142495	−	0.00822694i
$732$	3.15660	−	11.7806i	0.116671	−	0.435423i
$733$	−26.2509	+	7.03390i	−0.969599	+	0.259803i	−0.708658	−	0.705552i	$-0.750699\pi$
$733$	−26.2509	+	7.03390i	−0.969599	+	0.259803i	−0.260940	+	0.965355i	$0.584033\pi$
$734$	31.3205			1.15606
$735$		0			0
$736$	3.73205			0.137565
$737$	2.82843	−	0.757875i	0.104186	−	0.0279167i
$738$	−0.637756	+	2.38014i	−0.0234761	+	0.0876141i
$739$	11.6147	−	6.70577i	0.427255	−	0.246676i	−0.270922	−	0.962601i	$-0.587328\pi$
$739$	11.6147	−	6.70577i	0.427255	−	0.246676i	0.698177	+	0.715926i	$0.253995\pi$
$740$		0			0
$741$			6.14359i			0.225691i
$742$	−7.81534	+	11.5403i	−0.286910	+	0.423659i
$743$	−27.2354	+	27.2354i	−0.999170	+	0.999170i	−1.00000		0.000830035i	$-0.999736\pi$
$743$	−27.2354	+	27.2354i	−0.999170	+	0.999170i	0.000830035		1.00000i	$0.499736\pi$
$744$	6.86603	+	3.96410i	0.251721	+	0.145331i
$745$		0			0
$746$	−3.07180	−	5.32051i	−0.112466	−	0.194798i
$747$	3.01790	+	11.2629i	0.110419	+	0.412089i
$748$	−1.17398	−	1.17398i	−0.0429248	−	0.0429248i
$749$	−8.66025	+	25.0000i	−0.316439	+	0.913480i
$750$		0			0
$751$	12.9282	−	22.3923i	0.471757	−	0.817107i	−0.527721	−	0.849418i	$-0.676953\pi$
$751$	12.9282	−	22.3923i	0.471757	−	0.817107i	0.999478	+	0.0323109i	$0.0102867\pi$
$752$	−10.6252	−	2.84701i	−0.387461	−	0.103820i
$753$	17.2480	+	4.62158i	0.628551	+	0.168420i
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$		0			0
$756$	−1.73205	−	2.00000i	−0.0629941	−	0.0727393i
$757$	−14.9743	−	14.9743i	−0.544252	−	0.544252i	0.380521	−	0.924772i	$-0.375745\pi$
$757$	−14.9743	−	14.9743i	−0.544252	−	0.544252i	−0.924772	+	0.380521i	$0.875745\pi$
$758$	−2.60179	−	9.71003i	−0.0945014	−	0.352684i
$759$	−1.36603	−	2.36603i	−0.0495836	−	0.0858813i
$760$		0			0
$761$	−10.7942	−	6.23205i	−0.391290	−	0.225912i	0.291429	−	0.956593i	$-0.405869\pi$
$761$	−10.7942	−	6.23205i	−0.391290	−	0.225912i	−0.682719	+	0.730681i	$0.739203\pi$
$762$	−11.2122	+	11.2122i	−0.406174	+	0.406174i
$763$	2.58819	−	36.0488i	0.0936988	−	1.30506i
$764$			24.8564i			0.899273i
$765$		0			0
$766$	−22.9186	+	13.2321i	−0.828082	+	0.478093i
$767$	0.203072	−	0.757875i	0.00733250	−	0.0273653i
$768$	−0.965926	+	0.258819i	−0.0348548	+	0.00933933i
$769$	9.07180			0.327137			0.163569	−	0.986532i	$-0.447699\pi$
$769$	9.07180			0.327137			0.163569	+	0.986532i	$0.447699\pi$
$770$		0			0
$771$	3.85641			0.138885
$772$	−22.9234	+	6.14231i	−0.825031	+	0.221066i
$773$	9.88589	−	36.8947i	0.355571	−	1.32701i	−0.524194	−	0.851599i	$-0.675633\pi$
$773$	9.88589	−	36.8947i	0.355571	−	1.32701i	0.879765	−	0.475409i	$-0.157700\pi$
$774$	−0.169873	+	0.0980762i	−0.00610596	+	0.00352528i
$775$		0			0
$776$			7.00000i			0.251285i
$777$	10.3664	+	7.02030i	0.371891	+	0.251852i
$778$	19.5588	−	19.5588i	0.701215	−	0.701215i
$779$	8.95448	+	5.16987i	0.320828	+	0.185230i
$780$		0			0
$781$	−4.70577	−	8.15064i	−0.168386	−	0.291653i
$782$	−2.19067	−	8.17569i	−0.0783382	−	0.292362i
$783$	5.79555	+	5.79555i	0.207116	+	0.207116i
$784$	−6.92820	−	1.00000i	−0.247436	−	0.0357143i
$785$		0			0
$786$	6.83013	−	11.8301i	0.243623	−	0.421967i
$787$	6.74290	+	1.80675i	0.240358	+	0.0644038i	0.376987	−	0.926218i	$-0.376960\pi$
$787$	6.74290	+	1.80675i	0.240358	+	0.0644038i	−0.136629	+	0.990622i	$0.543627\pi$
$788$	24.9754	+	6.69213i	0.889711	+	0.238397i
$789$	−9.25833	+	16.0359i	−0.329605	+	0.570893i
$790$		0			0
$791$	1.50000	+	7.79423i	0.0533339	+	0.277131i
$792$	0.517638	+	0.517638i	0.0183935	+	0.0183935i
$793$	−4.62158	−	17.2480i	−0.164117	−	0.612493i
$794$	9.73205	+	16.8564i	0.345378	+	0.598211i
$795$		0			0
$796$	22.9186	+	13.2321i	0.812328	+	0.468998i
$797$	−29.7356	+	29.7356i	−1.05329	+	1.05329i	−0.0547930	+	0.998498i	$0.517450\pi$
$797$	−29.7356	+	29.7356i	−1.05329	+	1.05329i	−0.998498	+	0.0547930i	$0.982550\pi$
$798$	−9.98743	+	4.84821i	−0.353551	+	0.171625i
$799$			24.9474i			0.882577i
$800$		0			0
$801$	−5.59808	+	3.23205i	−0.197798	+	0.114199i
$802$	−5.41662	+	20.2151i	−0.191267	+	0.713820i
$803$	−5.65685	+	1.51575i	−0.199626	+	0.0534896i
$804$	−4.00000			−0.141069
$805$		0			0
$806$	11.6077			0.408864
$807$	24.7859	−	6.64136i	0.872505	−	0.233787i
$808$	0.0507680	−	0.189469i	0.00178601	−	0.00666549i
$809$	−2.78461	+	1.60770i	−0.0979017	+	0.0565236i	−0.548151	−	0.836379i	$-0.684668\pi$
$809$	−2.78461	+	1.60770i	−0.0979017	+	0.0565236i	0.450250	+	0.892903i	$0.351335\pi$
$810$		0			0
$811$			36.7846i			1.29168i	0.763472	+	0.645841i	$0.223493\pi$
$811$			36.7846i			1.29168i	−0.763472	+	0.645841i	$0.776507\pi$
$812$	21.6293	+	1.55291i	0.759040	+	0.0544966i
$813$	1.74238	−	1.74238i	0.0611080	−	0.0611080i
$814$	−3.00000	−	1.73205i	−0.105150	−	0.0607083i
$815$		0			0
$816$	1.13397	+	1.96410i	0.0396971	+	0.0687573i
$817$	0.213030	+	0.795040i	0.00745298	+	0.0278149i
$818$	−23.4732	−	23.4732i	−0.820722	−	0.820722i
$819$	−3.66025	−	1.26795i	−0.127900	−	0.0443057i
$820$		0			0
$821$	18.2224	−	31.5622i	0.635967	−	1.10153i	−0.350342	−	0.936622i	$-0.613935\pi$
$821$	18.2224	−	31.5622i	0.635967	−	1.10153i	0.986309	−	0.164906i	$-0.0527320\pi$
$822$	7.79676	+	2.08913i	0.271943	+	0.0728669i
$823$	17.0077	+	4.55721i	0.592852	+	0.158854i	0.542756	−	0.839890i	$-0.317381\pi$
$823$	17.0077	+	4.55721i	0.592852	+	0.158854i	0.0500957	+	0.998744i	$0.484047\pi$
$824$	−3.33013	+	5.76795i	−0.116010	+	0.200936i
$825$		0			0
$826$	1.39230	−	0.267949i	0.0484445	−	0.00932314i
$827$	23.5983	+	23.5983i	0.820594	+	0.820594i	0.986193	−	0.165599i	$-0.0529558\pi$
$827$	23.5983	+	23.5983i	0.820594	+	0.820594i	−0.165599	+	0.986193i	$0.552956\pi$
$828$	0.965926	+	3.60488i	0.0335682	+	0.125278i
$829$	20.8564	+	36.1244i	0.724373	+	1.25465i	0.959232	+	0.282621i	$0.0912039\pi$
$829$	20.8564	+	36.1244i	0.724373	+	1.25465i	−0.234859	+	0.972030i	$0.575463\pi$
$830$		0			0
$831$	14.3660	+	8.29423i	0.498352	+	0.287724i
$832$	−1.03528	+	1.03528i	−0.0358917	+	0.0358917i
$833$	1.87610	+	15.7644i	0.0650032	+	0.546204i
$834$		−	12.9282i		−	0.447667i
$835$		0			0
$836$	2.66025	−	1.53590i	0.0920068	−	0.0531202i
$837$	−2.05197	+	7.65806i	−0.0709265	+	0.264701i
$838$	−10.2277	+	2.74049i	−0.353309	+	0.0946688i
$839$	−24.1244			−0.832865			−0.416433	−	0.909167i	$-0.636720\pi$
$839$	−24.1244			−0.832865			−0.416433	+	0.909167i	$0.636720\pi$
$840$		0			0
$841$	−38.1769			−1.31645
$842$	2.44949	−	0.656339i	0.0844150	−	0.0226189i
$843$	5.17140	−	19.2999i	0.178113	−	0.664725i
$844$	−17.0263	+	9.83013i	−0.586069	+	0.338367i
$845$		0			0
$846$		−	11.0000i		−	0.378188i
$847$	12.0902	+	24.9060i	0.415423	+	0.855781i
$848$	−3.72500	+	3.72500i	−0.127917	+	0.127917i
$849$	6.16987	+	3.56218i	0.211749	+	0.122254i
$850$		0			0
$851$	−8.83013	−	15.2942i	−0.302693	−	0.524279i
$852$	3.32748	+	12.4183i	0.113998	+	0.425445i
$853$	10.1397	+	10.1397i	0.347178	+	0.347178i	0.859057	−	0.511879i	$-0.171051\pi$
$853$	10.1397	+	10.1397i	0.347178	+	0.347178i	−0.511879	+	0.859057i	$0.671051\pi$
$854$	24.3923	−	21.1244i	0.834687	−	0.722861i
$855$		0			0
$856$	−5.00000	+	8.66025i	−0.170896	+	0.296001i
$857$	26.1493	+	7.00670i	0.893245	+	0.239344i	0.676113	−	0.736798i	$-0.263663\pi$
$857$	26.1493	+	7.00670i	0.893245	+	0.239344i	0.217132	+	0.976142i	$0.430330\pi$
$858$	1.03528	+	0.277401i	0.0353437	+	0.00947033i
$859$	−14.9545	+	25.9019i	−0.510240	+	0.883762i	0.489689	+	0.871897i	$0.337110\pi$
$859$	−14.9545	+	25.9019i	−0.510240	+	0.883762i	−0.999930	+	0.0118652i	$0.996223\pi$
$860$		0			0
$861$	−4.92820	+	4.26795i	−0.167953	+	0.145451i
$862$	0.328169	+	0.328169i	0.0111775	+	0.0111775i
$863$	2.93494	+	10.9534i	0.0999066	+	0.372856i	0.997718	−	0.0675244i	$-0.0215101\pi$
$863$	2.93494	+	10.9534i	0.0999066	+	0.372856i	−0.897811	+	0.440381i	$0.854843\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−24.5263	−	14.1603i	−0.833437	−	0.481185i
$867$	−8.38375	+	8.38375i	−0.284727	+	0.284727i
$868$	9.16020	+	18.8702i	0.310918	+	0.640497i
$869$		−	5.94744i		−	0.201753i
$870$		0			0
$871$	−5.07180	+	2.92820i	−0.171851	+	0.0992184i
$872$	3.53553	−	13.1948i	0.119728	−	0.446832i
$873$	−6.76148	+	1.81173i	−0.228841	+	0.0613179i
$874$	15.6603			0.529716
$875$		0			0
$876$	8.00000			0.270295
$877$	−39.2562	+	10.5187i	−1.32559	+	0.355190i	−0.851068	−	0.525055i	$-0.824045\pi$
$877$	−39.2562	+	10.5187i	−1.32559	+	0.355190i	−0.474519	+	0.880245i	$0.657378\pi$
$878$	−10.1955	+	38.0500i	−0.344081	+	1.28413i
$879$	11.4904	−	6.63397i	0.387561	−	0.223758i
$880$		0			0
$881$			4.32051i			0.145562i	0.997348	+	0.0727808i	$0.0231874\pi$
$881$			4.32051i			0.145562i	−0.997348	+	0.0727808i	$0.976813\pi$
$882$	−0.827225	−	6.95095i	−0.0278541	−	0.234051i
$883$	11.9700	−	11.9700i	0.402824	−	0.402824i	−0.476403	−	0.879227i	$-0.658060\pi$
$883$	11.9700	−	11.9700i	0.402824	−	0.402824i	0.879227	+	0.476403i	$0.158060\pi$
$884$	2.87564	+	1.66025i	0.0967184	+	0.0558404i
$885$		0			0
$886$	10.7583	+	18.6340i	0.361433	+	0.626021i
$887$	14.6969	+	54.8497i	0.493475	+	1.84167i	0.538409	+	0.842683i	$0.319025\pi$
$887$	14.6969	+	54.8497i	0.493475	+	1.84167i	−0.0449344	+	0.998990i	$0.514308\pi$
$888$	3.34607	+	3.34607i	0.112287	+	0.112287i
$889$	−41.1962	+	7.92820i	−1.38167	+	0.265903i
$890$		0			0
$891$	−0.366025	+	0.633975i	−0.0122623	+	0.0212389i
$892$	11.8499	+	3.17518i	0.396765	+	0.106313i
$893$	−44.5849	−	11.9465i	−1.49198	−	0.399774i
$894$	−9.00000	+	15.5885i	−0.301005	+	0.521356i
$895$		0			0
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$	3.86370	+	3.86370i	0.129005	+	0.129005i
$898$	7.69522	+	28.7190i	0.256793	+	0.958364i
$899$	−32.4904	−	56.2750i	−1.08361	−	1.87688i
$900$		0			0
$901$	10.3468	+	5.97372i	0.344701	+	0.199013i
$902$	1.27551	−	1.27551i	0.0424699	−	0.0424699i
$903$	−0.517638	−	0.0371647i	−0.0172259	−	0.00123677i
$904$			3.00000i			0.0997785i
$905$		0			0
$906$	9.46410	−	5.46410i	0.314424	−	0.181533i
$907$	12.0580	−	45.0010i	0.400379	−	1.49423i	−0.412044	−	0.911164i	$-0.635185\pi$
$907$	12.0580	−	45.0010i	0.400379	−	1.49423i	0.812422	−	0.583069i	$-0.198148\pi$
$908$	−5.13922	+	1.37705i	−0.170551	+	0.0456990i
$909$	0.196152			0.00650597
$910$		0			0
$911$	−35.7846			−1.18560			−0.592799	−	0.805351i	$-0.701977\pi$
$911$	−35.7846			−1.18560			−0.592799	+	0.805351i	$0.701977\pi$
$912$	−4.05317	+	1.08604i	−0.134214	+	0.0359625i
$913$	2.20925	−	8.24504i	0.0731156	−	0.272871i
$914$	29.3205	−	16.9282i	0.969836	−	0.559935i
$915$		0			0
$916$		−	11.8038i		−	0.390010i
$917$	32.5133	−	15.7830i	1.07368	−	0.521200i
$918$	−1.60368	+	1.60368i	−0.0529294	+	0.0529294i
$919$	0.696152	+	0.401924i	0.0229639	+	0.0132582i	0.511438	−	0.859320i	$-0.329113\pi$
$919$	0.696152	+	0.401924i	0.0229639	+	0.0132582i	−0.488474	+	0.872578i	$0.662446\pi$
$920$		0			0
$921$	−9.46410	−	16.3923i	−0.311853	−	0.540145i
$922$	−5.00052	−	18.6622i	−0.164683	−	0.614606i
$923$	13.3099	+	13.3099i	0.438102	+	0.438102i
$924$	0.366025	+	1.90192i	0.0120414	+	0.0625687i
$925$		0			0
$926$	−7.30385	+	12.6506i	−0.240019	+	0.415726i
$927$	−6.43331	−	1.72380i	−0.211298	−	0.0566170i
$928$	7.91688	+	2.12132i	0.259884	+	0.0696358i
$929$	−29.1244	+	50.4449i	−0.955539	+	1.65504i	−0.222410	+	0.974953i	$0.571392\pi$
$929$	−29.1244	+	50.4449i	−0.955539	+	1.65504i	−0.733130	+	0.680089i	$0.761941\pi$
$930$		0			0
$931$	−29.0718	−	4.19615i	−0.952790	−	0.137523i
$932$	−13.3843	−	13.3843i	−0.438416	−	0.438416i
$933$	3.55412	+	13.2641i	0.116357	+	0.434249i
$934$	4.02628	+	6.97372i	0.131744	+	0.228187i
$935$		0			0
$936$	−1.26795	−	0.732051i	−0.0414442	−	0.0239278i
$937$	8.76268	−	8.76268i	0.286264	−	0.286264i	−0.549337	−	0.835601i	$-0.685120\pi$
$937$	8.76268	−	8.76268i	0.286264	−	0.286264i	0.835601	+	0.549337i	$0.185120\pi$
$938$	−8.76268	−	5.93426i	−0.286112	−	0.193760i
$939$			18.4641i			0.602553i
$940$		0			0
$941$	−7.43782	+	4.29423i	−0.242466	+	0.139988i	−0.616310	−	0.787504i	$-0.711373\pi$
$941$	−7.43782	+	4.29423i	−0.242466	+	0.139988i	0.373844	+	0.927492i	$0.378040\pi$
$942$	−5.36585	+	20.0256i	−0.174829	+	0.652470i
$943$	8.88280	−	2.38014i	0.289264	−	0.0775080i
$944$	0.535898			0.0174420
$945$		0			0
$946$	0.143594			0.00466863
$947$	44.6728	−	11.9700i	1.45167	−	0.388974i	0.555067	−	0.831806i	$-0.312693\pi$
$947$	44.6728	−	11.9700i	1.45167	−	0.388974i	0.896605	+	0.442831i	$0.146026\pi$
$948$	−2.10274	+	7.84752i	−0.0682938	+	0.254876i
$949$	10.1436	−	5.85641i	0.329275	−	0.190107i
$950$		0			0
$951$		−	11.8038i		−	0.382766i
$952$	−0.429705	+	5.98502i	−0.0139268	+	0.193976i
$953$	17.2480	−	17.2480i	0.558716	−	0.558716i	−0.370226	−	0.928942i	$-0.620720\pi$
$953$	17.2480	−	17.2480i	0.558716	−	0.558716i	0.928942	+	0.370226i	$0.120720\pi$
$954$	−4.56218	−	2.63397i	−0.147706	−	0.0852781i
$955$		0			0
$956$	−2.42820	−	4.20577i	−0.0785337	−	0.136024i
$957$	−1.55291	−	5.79555i	−0.0501986	−	0.187344i
$958$	14.1285	+	14.1285i	0.456472	+	0.456472i
$959$	13.9808	+	16.1436i	0.451462	+	0.521304i
$960$		0			0
$961$	15.9282	−	27.5885i	0.513813	−	0.889950i
$962$	6.69213	+	1.79315i	0.215763	+	0.0578135i
$963$	−9.65926	−	2.58819i	−0.311265	−	0.0834033i
$964$	6.46410	−	11.1962i	0.208195	−	0.360604i
$965$		0			0
$966$	−3.23205	+	9.33013i	−0.103990	+	0.300192i
$967$	23.6119	+	23.6119i	0.759308	+	0.759308i	0.976196	−	0.216888i	$-0.0695907\pi$
$967$	23.6119	+	23.6119i	0.759308	+	0.759308i	−0.216888	+	0.976196i	$0.569591\pi$
$968$	2.70831	+	10.1075i	0.0870483	+	0.324869i
$969$	4.75833	+	8.24167i	0.152860	+	0.264761i
$970$		0			0
$971$	−26.0263	−	15.0263i	−0.835223	−	0.482216i	0.0204146	−	0.999792i	$-0.493501\pi$
$971$	−26.0263	−	15.0263i	−0.835223	−	0.482216i	−0.855638	+	0.517575i	$0.826835\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	19.1798	−	28.3214i	0.614877	−	0.907944i
$974$			13.5359i			0.433718i
$975$		0			0
$976$	10.5622	−	6.09808i	0.338087	−	0.195195i
$977$	−11.1193	+	41.4976i	−0.355737	+	1.32763i	0.523818	+	0.851830i	$0.324507\pi$
$977$	−11.1193	+	41.4976i	−0.355737	+	1.32763i	−0.879555	+	0.475797i	$0.842160\pi$
$978$	11.5911	−	3.10583i	0.370643	−	0.0993134i
$979$	4.73205			0.151237
$980$		0			0
$981$	13.6603			0.436138
$982$	1.60368	−	0.429705i	0.0511756	−	0.0137124i
$983$	10.4171	−	38.8773i	0.332255	−	1.23999i	−0.574560	−	0.818463i	$-0.694827\pi$
$983$	10.4171	−	38.8773i	0.332255	−	1.23999i	0.906815	−	0.421530i	$-0.138507\pi$
$984$	−2.13397	+	1.23205i	−0.0680286	+	0.0392763i
$985$		0			0
$986$		−	18.5885i		−	0.591977i
$987$	16.3192	−	24.0974i	0.519446	−	0.767028i
$988$	−4.34418	+	4.34418i	−0.138207	+	0.138207i
$989$	0.633975	+	0.366025i	0.0201592	+	0.0116389i
$990$		0			0
$991$	24.2583	+	42.0167i	0.770591	+	1.33470i	0.937239	+	0.348687i	$0.113372\pi$
$991$	24.2583	+	42.0167i	0.770591	+	1.33470i	−0.166648	+	0.986016i	$0.553294\pi$
$992$	2.05197	+	7.65806i	0.0651501	+	0.243144i
$993$	−8.38375	−	8.38375i	−0.266050	−	0.266050i
$994$	−11.1340	+	32.1410i	−0.353148	+	1.01945i
$995$		0			0
$996$	−5.83013	+	10.0981i	−0.184735	+	0.319970i
$997$	36.5665	+	9.79796i	1.15807	+	0.310304i	0.786196	−	0.617978i	$-0.212048\pi$
$997$	36.5665	+	9.79796i	1.15807	+	0.310304i	0.371876	+	0.928282i	$0.378714\pi$
$998$	20.2659	+	5.43022i	0.641505	+	0.171891i
$999$	−2.36603	+	4.09808i	−0.0748577	+	0.129657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.b.607.1	yes	8
5.2	odd	4		1050.2.bc.c.943.1	yes	8
5.3	odd	4		1050.2.bc.c.943.2	yes	8
5.4	even	2	inner	1050.2.bc.b.607.2	yes	8
7.3	odd	6		1050.2.bc.c.157.2	yes	8
35.3	even	12	inner	1050.2.bc.b.493.1	✓	8
35.17	even	12	inner	1050.2.bc.b.493.2	yes	8
35.24	odd	6		1050.2.bc.c.157.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.b.493.1	✓	8	35.3	even	12	inner
1050.2.bc.b.493.2	yes	8	35.17	even	12	inner
1050.2.bc.b.607.1	yes	8	1.1	even	1	trivial
1050.2.bc.b.607.2	yes	8	5.4	even	2	inner
1050.2.bc.c.157.1	yes	8	35.24	odd	6
1050.2.bc.c.157.2	yes	8	7.3	odd	6
1050.2.bc.c.943.1	yes	8	5.2	odd	4
1050.2.bc.c.943.2	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.48356 + 2.19067i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.48356 + 2.19067i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.366025 + 0.633975i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-1.03528 - 1.03528i) q^{13} +(0.866025 - 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.19067 - 0.586988i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.09808 - 3.63397i) q^{19} +(1.73205 + 2.00000i) q^{21} +(-0.517638 - 0.517638i) q^{22} +(-0.965926 - 3.60488i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.26795 + 0.732051i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.189469 + 2.63896i) q^{28} -8.19615i q^{29} +(6.86603 - 3.96410i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.707107 - 0.189469i) q^{33} +2.26795 q^{34} -1.00000 q^{36} +(4.57081 - 1.22474i) q^{37} +(-1.08604 + 4.05317i) q^{38} +(-1.26795 + 0.732051i) q^{39} +2.46410i q^{41} +(-2.19067 - 1.48356i) q^{42} +(-0.138701 + 0.138701i) q^{43} +(0.633975 + 0.366025i) q^{44} +(1.86603 + 3.23205i) q^{46} +(-2.84701 - 10.6252i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-2.59808 - 6.50000i) q^{49} +(-1.13397 + 1.96410i) q^{51} +(-1.41421 - 0.378937i) q^{52} +(-5.08845 - 1.36345i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(-2.96713 - 2.96713i) q^{57} +(2.12132 + 7.91688i) q^{58} +(0.267949 + 0.464102i) q^{59} +(10.5622 + 6.09808i) q^{61} +(-5.60609 + 5.60609i) q^{62} +(2.38014 - 1.15539i) q^{63} -1.00000i q^{64} +(-0.633975 + 0.366025i) q^{66} +(1.03528 - 3.86370i) q^{67} +(-2.19067 + 0.586988i) q^{68} -3.73205 q^{69} -12.8564 q^{71} +(0.965926 - 0.258819i) q^{72} +(-2.07055 + 7.72741i) q^{73} +(-4.09808 + 2.36603i) q^{74} -4.19615i q^{76} +(-1.93185 - 0.138701i) q^{77} +(1.03528 - 1.03528i) q^{78} +(-7.03590 - 4.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.637756 - 2.38014i) q^{82} +(-8.24504 - 8.24504i) q^{83} +(2.50000 + 0.866025i) q^{84} +(0.0980762 - 0.169873i) q^{86} +(-7.91688 - 2.12132i) q^{87} +(-0.707107 - 0.189469i) q^{88} +(3.23205 - 5.59808i) q^{89} +(3.80385 - 0.732051i) q^{91} +(-2.63896 - 2.63896i) q^{92} +(-2.05197 - 7.65806i) q^{93} +(5.50000 + 9.52628i) q^{94} +(0.866025 + 0.500000i) q^{96} +(4.94975 - 4.94975i) q^{97} +(4.19187 + 5.60609i) q^{98} -0.732051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} + 4 q^{16} - 4 q^{19} + 4 q^{24} + 24 q^{26} + 48 q^{31} + 32 q^{34} - 8 q^{36} - 24 q^{39} + 12 q^{44} + 8 q^{46} - 16 q^{51} + 4 q^{54} - 4 q^{56} + 16 q^{59} + 36 q^{61} - 12 q^{66} - 16 q^{69} + 8 q^{71} - 12 q^{74} - 84 q^{79} + 4 q^{81} + 20 q^{84} - 20 q^{86} + 12 q^{89} + 72 q^{91} + 44 q^{94}+O(q^{100}) \) 8 * q - 4 * q^11 + 4 * q^16 - 4 * q^19 + 4 * q^24 + 24 * q^26 + 48 * q^31 + 32 * q^34 - 8 * q^36 - 24 * q^39 + 12 * q^44 + 8 * q^46 - 16 * q^51 + 4 * q^54 - 4 * q^56 + 16 * q^59 + 36 * q^61 - 12 * q^66 - 16 * q^69 + 8 * q^71 - 12 * q^74 - 84 * q^79 + 4 * q^81 + 20 * q^84 - 20 * q^86 + 12 * q^89 + 72 * q^91 + 44 * q^94

Introduction

L-functions

Modular forms

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