LMFDB - Embedded newform 1050.2.bc.a.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			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.a.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-4.05317 - 4.05317i) q^{13} +(-2.59808 + 0.500000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-7.20977 - 1.93185i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-1.13397 + 1.96410i) q^{19} +(0.866025 - 2.50000i) q^{21} +(0.707107 + 0.707107i) q^{22} +(-1.53433 - 5.72620i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 2.86603i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.38014 - 1.15539i) q^{28} +6.92820i q^{29} +(6.46410 - 3.73205i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.965926 + 0.258819i) q^{33} +7.46410 q^{34} -1.00000 q^{36} +(-3.79435 + 1.01669i) q^{37} +(0.586988 - 2.19067i) q^{38} +(-4.96410 + 2.86603i) q^{39} -2.26795i q^{41} +(-0.189469 + 2.63896i) q^{42} +(6.31319 - 6.31319i) q^{43} +(-0.866025 - 0.500000i) q^{44} +(2.96410 + 5.13397i) q^{46} +(-0.309587 - 1.15539i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(6.92820 + 1.00000i) q^{49} +(-3.73205 + 6.46410i) q^{51} +(-5.53674 - 1.48356i) q^{52} +(-0.965926 - 0.258819i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} +(1.60368 + 1.60368i) q^{57} +(-1.79315 - 6.69213i) q^{58} +(-5.73205 - 9.92820i) q^{59} +(-9.92820 - 5.73205i) q^{61} +(-5.27792 + 5.27792i) q^{62} +(-2.19067 - 1.48356i) q^{63} -1.00000i q^{64} +(0.866025 - 0.500000i) q^{66} +(-0.517638 + 1.93185i) q^{67} +(-7.20977 + 1.93185i) q^{68} -5.92820 q^{69} -8.92820 q^{71} +(0.965926 - 0.258819i) q^{72} +(1.03528 - 3.86370i) q^{73} +(3.40192 - 1.96410i) q^{74} +2.26795i q^{76} +(-1.15539 - 2.38014i) q^{77} +(4.05317 - 4.05317i) q^{78} +(2.66025 + 1.53590i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.586988 + 2.19067i) q^{82} +(7.34847 + 7.34847i) q^{83} +(-0.500000 - 2.59808i) q^{84} +(-4.46410 + 7.73205i) q^{86} +(6.69213 + 1.79315i) q^{87} +(0.965926 + 0.258819i) q^{88} +(-3.46410 + 6.00000i) q^{89} +(-9.92820 - 11.4641i) q^{91} +(-4.19187 - 4.19187i) q^{92} +(-1.93185 - 7.20977i) q^{93} +(0.598076 + 1.03590i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-2.07055 + 2.07055i) q^{97} +(-6.95095 + 0.827225i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} + 4 q^{16} - 16 q^{19} + 4 q^{24} + 12 q^{26} + 24 q^{31} + 32 q^{34} - 8 q^{36} - 12 q^{39} - 4 q^{46} - 16 q^{51} + 4 q^{54} - 16 q^{56} - 32 q^{59} - 24 q^{61} + 8 q^{69} - 16 q^{71} + 48 q^{74} - 48 q^{79} + 4 q^{81} - 4 q^{84} - 8 q^{86} - 24 q^{91} - 16 q^{94}+O(q^{100}) $ 8 * q - 4 * q^11 + 4 * q^16 - 16 * q^19 + 4 * q^24 + 12 * q^26 + 24 * q^31 + 32 * q^34 - 8 * q^36 - 12 * q^39 - 4 * q^46 - 16 * q^51 + 4 * q^54 - 16 * q^56 - 32 * q^59 - 24 * q^61 + 8 * q^69 - 16 * q^71 + 48 * q^74 - 48 * q^79 + 4 * q^81 - 4 * q^84 - 8 * q^86 - 24 * q^91 - 16 * 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
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	−4.05317	−	4.05317i	−1.12415	−	1.12415i	−0.991111	−	0.133037i	$-0.957527\pi$
$13$	−4.05317	−	4.05317i	−1.12415	−	1.12415i	−0.133037	−	0.991111i	$-0.542473\pi$
$14$	−2.59808	+	0.500000i	−0.694365	+	0.133631i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−7.20977	−	1.93185i	−1.74863	−	0.468543i	−0.764294	−	0.644868i	$-0.776912\pi$
$17$	−7.20977	−	1.93185i	−1.74863	−	0.468543i	−0.984332	+	0.176325i	$0.943579\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	−1.13397	+	1.96410i	−0.260152	+	0.450596i	−0.966282	−	0.257486i	$-0.917106\pi$
$19$	−1.13397	+	1.96410i	−0.260152	+	0.450596i	0.706130	+	0.708082i	$0.250439\pi$
$20$		0			0
$21$	0.866025	−	2.50000i	0.188982	−	0.545545i
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	−1.53433	−	5.72620i	−0.319930	−	1.19400i	−0.919311	−	0.393532i	$-0.871253\pi$
$23$	−1.53433	−	5.72620i	−0.319930	−	1.19400i	0.599381	−	0.800464i	$-0.295414\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	4.96410	+	2.86603i	0.973540	+	0.562074i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	2.38014	−	1.15539i	0.449804	−	0.218349i
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$		0			0
$31$	6.46410	−	3.73205i	1.16099	−	0.670296i	0.209447	−	0.977820i	$-0.432834\pi$
$31$	6.46410	−	3.73205i	1.16099	−	0.670296i	0.951540	+	0.307524i	$0.0995004\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.965926	+	0.258819i	−0.168146	+	0.0450546i
$34$	7.46410			1.28008
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−3.79435	+	1.01669i	−0.623788	+	0.167143i	−0.556849	−	0.830614i	$-0.687990\pi$
$37$	−3.79435	+	1.01669i	−0.623788	+	0.167143i	−0.0669387	+	0.997757i	$0.521323\pi$
$38$	0.586988	−	2.19067i	0.0952221	−	0.355374i
$39$	−4.96410	+	2.86603i	−0.794892	+	0.458931i
$40$		0			0
$41$		−	2.26795i		−	0.354194i	−0.984193	−	0.177097i	$-0.943329\pi$
$41$		−	2.26795i		−	0.354194i	0.984193	−	0.177097i	$-0.0566707\pi$
$42$	−0.189469	+	2.63896i	−0.0292357	+	0.407200i
$43$	6.31319	−	6.31319i	0.962753	−	0.962753i	−0.0365779	−	0.999331i	$-0.511646\pi$
$43$	6.31319	−	6.31319i	0.962753	−	0.962753i	0.999331	+	0.0365779i	$0.0116457\pi$
$44$	−0.866025	−	0.500000i	−0.130558	−	0.0753778i
$45$		0			0
$46$	2.96410	+	5.13397i	0.437033	+	0.756963i
$47$	−0.309587	−	1.15539i	−0.0451579	−	0.168532i	0.939664	−	0.342098i	$-0.111138\pi$
$47$	−0.309587	−	1.15539i	−0.0451579	−	0.168532i	−0.984822	+	0.173566i	$0.944471\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	6.92820	+	1.00000i	0.989743	+	0.142857i
$50$		0			0
$51$	−3.73205	+	6.46410i	−0.522592	+	0.905155i
$52$	−5.53674	−	1.48356i	−0.767807	−	0.205733i
$53$	−0.965926	−	0.258819i	−0.132680	−	0.0355515i	0.191868	−	0.981421i	$-0.438546\pi$
$53$	−0.965926	−	0.258819i	−0.132680	−	0.0355515i	−0.324548	+	0.945869i	$0.605212\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$	1.60368	+	1.60368i	0.212413	+	0.212413i
$58$	−1.79315	−	6.69213i	−0.235452	−	0.878720i
$59$	−5.73205	−	9.92820i	−0.746249	−	1.29254i	−0.949609	−	0.313438i	$-0.898519\pi$
$59$	−5.73205	−	9.92820i	−0.746249	−	1.29254i	0.203359	−	0.979104i	$-0.434814\pi$
$60$		0			0
$61$	−9.92820	−	5.73205i	−1.27118	−	0.733914i	−0.295967	−	0.955198i	$-0.595642\pi$
$61$	−9.92820	−	5.73205i	−1.27118	−	0.733914i	−0.975209	+	0.221284i	$0.928975\pi$
$62$	−5.27792	+	5.27792i	−0.670296	+	0.670296i
$63$	−2.19067	−	1.48356i	−0.275999	−	0.186911i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	0.866025	−	0.500000i	0.106600	−	0.0615457i
$67$	−0.517638	+	1.93185i	−0.0632396	+	0.236013i	−0.990310	−	0.138874i	$-0.955652\pi$
$67$	−0.517638	+	1.93185i	−0.0632396	+	0.236013i	0.927071	+	0.374887i	$0.122318\pi$
$68$	−7.20977	+	1.93185i	−0.874313	+	0.234271i
$69$	−5.92820			−0.713672
$70$		0			0
$71$	−8.92820			−1.05958			−0.529791	−	0.848128i	$-0.677730\pi$
$71$	−8.92820			−1.05958			−0.529791	+	0.848128i	$0.677730\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	1.03528	−	3.86370i	0.121170	−	0.452212i	−0.878504	−	0.477734i	$-0.841458\pi$
$73$	1.03528	−	3.86370i	0.121170	−	0.452212i	0.999674	+	0.0255221i	$0.00812481\pi$
$74$	3.40192	−	1.96410i	0.395466	−	0.228322i
$75$		0			0
$76$			2.26795i			0.260152i
$77$	−1.15539	−	2.38014i	−0.131669	−	0.271242i
$78$	4.05317	−	4.05317i	0.458931	−	0.458931i
$79$	2.66025	+	1.53590i	0.299302	+	0.172802i	0.642129	−	0.766596i	$-0.278051\pi$
$79$	2.66025	+	1.53590i	0.299302	+	0.172802i	−0.342827	+	0.939398i	$0.611385\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	0.586988	+	2.19067i	0.0648220	+	0.241919i
$83$	7.34847	+	7.34847i	0.806599	+	0.806599i	0.984118	−	0.177518i	$-0.0568069\pi$
$83$	7.34847	+	7.34847i	0.806599	+	0.806599i	−0.177518	+	0.984118i	$0.556807\pi$
$84$	−0.500000	−	2.59808i	−0.0545545	−	0.283473i
$85$		0			0
$86$	−4.46410	+	7.73205i	−0.481376	+	0.833768i
$87$	6.69213	+	1.79315i	0.717472	+	0.192246i
$88$	0.965926	+	0.258819i	0.102968	+	0.0275902i
$89$	−3.46410	+	6.00000i	−0.367194	+	0.635999i	−0.989126	−	0.147073i	$-0.953015\pi$
$89$	−3.46410	+	6.00000i	−0.367194	+	0.635999i	0.621932	+	0.783072i	$0.286348\pi$
$90$		0			0
$91$	−9.92820	−	11.4641i	−1.04076	−	1.20176i
$92$	−4.19187	−	4.19187i	−0.437033	−	0.437033i
$93$	−1.93185	−	7.20977i	−0.200324	−	0.747618i
$94$	0.598076	+	1.03590i	0.0616869	+	0.106845i
$95$		0			0
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−2.07055	+	2.07055i	−0.210233	+	0.210233i	−0.804366	−	0.594134i	$-0.797495\pi$
$97$	−2.07055	+	2.07055i	−0.210233	+	0.210233i	0.594134	+	0.804366i	$0.297495\pi$
$98$	−6.95095	+	0.827225i	−0.702152	+	0.0835624i
$99$			1.00000i			0.100504i
$100$		0			0
$101$	0.928203	−	0.535898i	0.0923597	−	0.0533239i	−0.453109	−	0.891455i	$-0.649685\pi$
$101$	0.928203	−	0.535898i	0.0923597	−	0.0533239i	0.545468	+	0.838131i	$0.316352\pi$
$102$	1.93185	−	7.20977i	0.191282	−	0.713873i
$103$	−17.7656	+	4.76028i	−1.75050	+	0.469044i	−0.984732	−	0.174077i	$-0.944306\pi$
$103$	−17.7656	+	4.76028i	−1.75050	+	0.469044i	−0.765765	+	0.643121i	$0.777639\pi$
$104$	5.73205			0.562074
$105$		0			0
$106$	1.00000			0.0971286
$107$	−14.4195	+	3.86370i	−1.39399	+	0.373518i	−0.876183	−	0.481979i	$-0.839918\pi$
$107$	−14.4195	+	3.86370i	−1.39399	+	0.373518i	−0.517807	+	0.855498i	$0.673251\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	14.6603	−	8.46410i	1.40420	−	0.810714i	0.409378	−	0.912365i	$-0.365746\pi$
$109$	14.6603	−	8.46410i	1.40420	−	0.810714i	0.994820	+	0.101651i	$0.0324126\pi$
$110$		0			0
$111$			3.92820i			0.372849i
$112$	1.48356	−	2.19067i	0.140184	−	0.206999i
$113$	9.14162	−	9.14162i	0.859971	−	0.859971i	−0.131363	−	0.991334i	$-0.541935\pi$
$113$	9.14162	−	9.14162i	0.859971	−	0.859971i	0.991334	+	0.131363i	$0.0419354\pi$
$114$	−1.96410	−	1.13397i	−0.183955	−	0.106206i
$115$		0			0
$116$	3.46410	+	6.00000i	0.321634	+	0.557086i
$117$	1.48356	+	5.53674i	0.137156	+	0.511871i
$118$	8.10634	+	8.10634i	0.746249	+	0.746249i
$119$	−18.6603	−	6.46410i	−1.71058	−	0.592563i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	11.0735	+	2.96713i	1.00255	+	0.268631i
$123$	−2.19067	−	0.586988i	−0.197526	−	0.0529270i
$124$	3.73205	−	6.46410i	0.335148	−	0.580493i
$125$		0			0
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$	3.53553	+	3.53553i	0.313728	+	0.313728i	0.846352	−	0.532624i	$-0.178794\pi$
$127$	3.53553	+	3.53553i	0.313728	+	0.313728i	−0.532624	+	0.846352i	$0.678794\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−4.46410	−	7.73205i	−0.393042	−	0.680769i
$130$		0			0
$131$	3.57180	+	2.06218i	0.312069	+	0.180173i	0.647852	−	0.761766i	$-0.275667\pi$
$131$	3.57180	+	2.06218i	0.312069	+	0.180173i	−0.335783	+	0.941939i	$0.609001\pi$
$132$	−0.707107	+	0.707107i	−0.0615457	+	0.0615457i
$133$	−3.36465	+	4.96833i	−0.291752	+	0.430809i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$	6.46410	−	3.73205i	0.554292	−	0.320021i
$137$	4.89898	−	18.2832i	0.418548	−	1.56204i	−0.359073	−	0.933309i	$-0.616907\pi$
$137$	4.89898	−	18.2832i	0.418548	−	1.56204i	0.777621	−	0.628733i	$-0.216426\pi$
$138$	5.72620	−	1.53433i	0.487447	−	0.130611i
$139$	10.3923			0.881464			0.440732	−	0.897639i	$-0.354719\pi$
$139$	10.3923			0.881464			0.440732	+	0.897639i	$0.354719\pi$
$140$		0			0
$141$	−1.19615			−0.100734
$142$	8.62398	−	2.31079i	0.723708	−	0.193917i
$143$	−1.48356	+	5.53674i	−0.124062	+	0.463005i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$		0			0
$146$			4.00000i			0.331042i
$147$	2.75908	−	6.43331i	0.227565	−	0.530611i
$148$	−2.77766	+	2.77766i	−0.228322	+	0.228322i
$149$	0.803848	+	0.464102i	0.0658538	+	0.0380207i	0.532565	−	0.846389i	$-0.321228\pi$
$149$	0.803848	+	0.464102i	0.0658538	+	0.0380207i	−0.466712	+	0.884410i	$0.654561\pi$
$150$		0			0
$151$	1.92820	+	3.33975i	0.156915	+	0.271785i	0.933755	−	0.357914i	$-0.116512\pi$
$151$	1.92820	+	3.33975i	0.156915	+	0.271785i	−0.776840	+	0.629698i	$0.783178\pi$
$152$	−0.586988	−	2.19067i	−0.0476110	−	0.177687i
$153$	5.27792	+	5.27792i	0.426694	+	0.426694i
$154$	1.73205	+	2.00000i	0.139573	+	0.161165i
$155$		0			0
$156$	−2.86603	+	4.96410i	−0.229466	+	0.397446i
$157$	−4.50146	−	1.20616i	−0.359256	−	0.0962622i	0.0746765	−	0.997208i	$-0.476208\pi$
$157$	−4.50146	−	1.20616i	−0.359256	−	0.0962622i	−0.433932	+	0.900946i	$0.642874\pi$
$158$	−2.96713	−	0.795040i	−0.236052	−	0.0632499i
$159$	−0.500000	+	0.866025i	−0.0396526	+	0.0686803i
$160$		0			0
$161$	−2.96410	−	15.4019i	−0.233604	−	1.21384i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	3.10583	+	11.5911i	0.243267	+	0.907886i	0.974246	+	0.225486i	$0.0723970\pi$
$163$	3.10583	+	11.5911i	0.243267	+	0.907886i	−0.730979	+	0.682400i	$0.760936\pi$
$164$	−1.13397	−	1.96410i	−0.0885485	−	0.153371i
$165$		0			0
$166$	−9.00000	−	5.19615i	−0.698535	−	0.403300i
$167$	4.81105	−	4.81105i	0.372290	−	0.372290i	−0.496021	−	0.868311i	$-0.665206\pi$
$167$	4.81105	−	4.81105i	0.372290	−	0.372290i	0.868311	+	0.496021i	$0.165206\pi$
$168$	1.15539	+	2.38014i	0.0891406	+	0.183632i
$169$			19.8564i			1.52742i
$170$		0			0
$171$	1.96410	−	1.13397i	0.150199	−	0.0867172i
$172$	2.31079	−	8.62398i	0.176196	−	0.657572i
$173$	7.32989	−	1.96404i	0.557281	−	0.149323i	0.0308241	−	0.999525i	$-0.490187\pi$
$173$	7.32989	−	1.96404i	0.557281	−	0.149323i	0.526457	+	0.850202i	$0.323520\pi$
$174$	−6.92820			−0.525226
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−11.0735	+	2.96713i	−0.832333	+	0.223023i
$178$	1.79315	−	6.69213i	0.134402	−	0.501596i
$179$	−7.79423	+	4.50000i	−0.582568	+	0.336346i	−0.762153	−	0.647397i	$-0.775858\pi$
$179$	−7.79423	+	4.50000i	−0.582568	+	0.336346i	0.179585	+	0.983742i	$0.442524\pi$
$180$		0			0
$181$		−	14.3923i		−	1.06977i	−0.844924	−	0.534886i	$-0.820355\pi$
$181$		−	14.3923i		−	1.06977i	0.844924	−	0.534886i	$-0.179645\pi$
$182$	12.5570	+	8.50386i	0.930789	+	0.630348i
$183$	−8.10634	+	8.10634i	−0.599238	+	0.599238i
$184$	5.13397	+	2.96410i	0.378482	+	0.218516i
$185$		0			0
$186$	3.73205	+	6.46410i	0.273647	+	0.473971i
$187$	1.93185	+	7.20977i	0.141271	+	0.527230i
$188$	−0.845807	−	0.845807i	−0.0616869	−	0.0616869i
$189$	−2.00000	+	1.73205i	−0.145479	+	0.125988i
$190$		0			0
$191$	−1.46410	+	2.53590i	−0.105939	+	0.183491i	−0.914121	−	0.405441i	$-0.867118\pi$
$191$	−1.46410	+	2.53590i	−0.105939	+	0.183491i	0.808183	+	0.588932i	$0.200451\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	22.0082	+	5.89709i	1.58419	+	0.424482i	0.940219	−	0.340570i	$-0.110620\pi$
$193$	22.0082	+	5.89709i	1.58419	+	0.424482i	0.643969	+	0.765052i	$0.277287\pi$
$194$	1.46410	−	2.53590i	0.105116	−	0.182067i
$195$		0			0
$196$	6.50000	−	2.59808i	0.464286	−	0.185577i
$197$	11.9193	+	11.9193i	0.849213	+	0.849213i	0.990035	−	0.140822i	$-0.0449744\pi$
$197$	11.9193	+	11.9193i	0.849213	+	0.849213i	−0.140822	+	0.990035i	$0.544974\pi$
$198$	−0.258819	−	0.965926i	−0.0183935	−	0.0686454i
$199$	−6.26795	−	10.8564i	−0.444323	−	0.769590i	0.553682	−	0.832728i	$-0.313222\pi$
$199$	−6.26795	−	10.8564i	−0.444323	−	0.769590i	−0.998005	+	0.0631382i	$0.979889\pi$
$200$		0			0
$201$	1.73205	+	1.00000i	0.122169	+	0.0705346i
$202$	−0.757875	+	0.757875i	−0.0533239	+	0.0533239i
$203$	−1.31268	+	18.2832i	−0.0921319	+	1.28323i
$204$			7.46410i			0.522592i
$205$		0			0
$206$	15.9282	−	9.19615i	1.10977	−	0.640726i
$207$	−1.53433	+	5.72620i	−0.106643	+	0.397999i
$208$	−5.53674	+	1.48356i	−0.383904	+	0.102867i
$209$	2.26795			0.156877
$210$		0			0
$211$	−19.7846			−1.36203			−0.681014	−	0.732270i	$-0.738461\pi$
$211$	−19.7846			−1.36203			−0.681014	+	0.732270i	$0.738461\pi$
$212$	−0.965926	+	0.258819i	−0.0663401	+	0.0177758i
$213$	−2.31079	+	8.62398i	−0.158333	+	0.590906i
$214$	12.9282	−	7.46410i	0.883754	−	0.510235i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	17.7656	−	8.62398i	1.20601	−	0.585434i
$218$	−11.9700	+	11.9700i	−0.810714	+	0.810714i
$219$	−3.46410	−	2.00000i	−0.234082	−	0.135147i
$220$		0			0
$221$	21.3923	+	37.0526i	1.43900	+	2.49242i
$222$	−1.01669	−	3.79435i	−0.0682360	−	0.254660i
$223$	−6.59059	−	6.59059i	−0.441339	−	0.441339i	0.451123	−	0.892462i	$-0.351024\pi$
$223$	−6.59059	−	6.59059i	−0.441339	−	0.441339i	−0.892462	+	0.451123i	$0.851024\pi$
$224$	−0.866025	+	2.50000i	−0.0578638	+	0.167038i
$225$		0			0
$226$	−6.46410	+	11.1962i	−0.429986	+	0.744757i
$227$	3.34607	+	0.896575i	0.222086	+	0.0595078i	0.368146	−	0.929768i	$-0.379993\pi$
$227$	3.34607	+	0.896575i	0.222086	+	0.0595078i	−0.146060	+	0.989276i	$0.546659\pi$
$228$	2.19067	+	0.586988i	0.145081	+	0.0388743i
$229$	1.46410	−	2.53590i	0.0967506	−	0.167577i	−0.813587	−	0.581443i	$-0.802488\pi$
$229$	1.46410	−	2.53590i	0.0967506	−	0.167577i	0.910338	+	0.413866i	$0.135822\pi$
$230$		0			0
$231$	−2.59808	+	0.500000i	−0.170941	+	0.0328976i
$232$	−4.89898	−	4.89898i	−0.321634	−	0.321634i
$233$	0.480473	+	1.79315i	0.0314769	+	0.117473i	0.979877	−	0.199603i	$-0.0639654\pi$
$233$	0.480473	+	1.79315i	0.0314769	+	0.117473i	−0.948400	+	0.317077i	$0.897299\pi$
$234$	−2.86603	−	4.96410i	−0.187358	−	0.324513i
$235$		0			0
$236$	−9.92820	−	5.73205i	−0.646271	−	0.373125i
$237$	2.17209	−	2.17209i	0.141092	−	0.141092i
$238$	19.6975	+	1.41421i	1.27680	+	0.0916698i
$239$		−	24.0000i		−	1.55243i	−0.630468	−	0.776215i	$-0.717137\pi$
$239$		−	24.0000i		−	1.55243i	0.630468	−	0.776215i	$-0.282863\pi$
$240$		0			0
$241$	19.2846	−	11.1340i	1.24223	−	0.717202i	0.272683	−	0.962104i	$-0.412089\pi$
$241$	19.2846	−	11.1340i	1.24223	−	0.717202i	0.969548	+	0.244902i	$0.0787557\pi$
$242$	−2.58819	+	9.65926i	−0.166375	+	0.620921i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−11.4641			−0.733914
$245$		0			0
$246$	2.26795			0.144599
$247$	12.5570	−	3.36465i	0.798985	−	0.214087i
$248$	−1.93185	+	7.20977i	−0.122673	+	0.457821i
$249$	9.00000	−	5.19615i	0.570352	−	0.329293i
$250$		0			0
$251$			7.33975i			0.463281i	0.972801	+	0.231640i	$0.0744092\pi$
$251$			7.33975i			0.463281i	−0.972801	+	0.231640i	$0.925591\pi$
$252$	−2.63896	−	0.189469i	−0.166239	−	0.0119354i
$253$	−4.19187	+	4.19187i	−0.263541	+	0.263541i
$254$	−4.33013	−	2.50000i	−0.271696	−	0.156864i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.619174	−	2.31079i	−0.0386230	−	0.144143i	0.943922	−	0.330169i	$-0.107106\pi$
$257$	−0.619174	−	2.31079i	−0.0386230	−	0.144143i	−0.982545	+	0.186026i	$0.940439\pi$
$258$	6.31319	+	6.31319i	0.393042	+	0.393042i
$259$	−10.2058	+	1.96410i	−0.634156	+	0.122043i
$260$		0			0
$261$	3.46410	−	6.00000i	0.214423	−	0.371391i
$262$	−3.98382	−	1.06746i	−0.246121	−	0.0659480i
$263$	28.8391	+	7.72741i	1.77829	+	0.476492i	0.990271	−	0.139154i	$-0.0444383\pi$
$263$	28.8391	+	7.72741i	1.77829	+	0.476492i	0.788023	+	0.615646i	$0.211105\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$		0			0
$266$	1.96410	−	5.66987i	0.120427	−	0.347642i
$267$	4.89898	+	4.89898i	0.299813	+	0.299813i
$268$	0.517638	+	1.93185i	0.0316198	+	0.118007i
$269$	12.6603	+	21.9282i	0.771909	+	1.33699i	0.936515	+	0.350627i	$0.114031\pi$
$269$	12.6603	+	21.9282i	0.771909	+	1.33699i	−0.164606	+	0.986359i	$0.552635\pi$
$270$		0			0
$271$	6.92820	+	4.00000i	0.420858	+	0.242983i	0.695444	−	0.718580i	$-0.255208\pi$
$271$	6.92820	+	4.00000i	0.420858	+	0.242983i	−0.274586	+	0.961563i	$0.588541\pi$
$272$	−5.27792	+	5.27792i	−0.320021	+	0.320021i
$273$	−13.6431	+	6.62278i	−0.825717	+	0.400829i
$274$			18.9282i			1.14349i
$275$		0			0
$276$	−5.13397	+	2.96410i	−0.309029	+	0.178418i
$277$	−5.69402	+	21.2504i	−0.342120	+	1.27681i	0.553820	+	0.832636i	$0.313170\pi$
$277$	−5.69402	+	21.2504i	−0.342120	+	1.27681i	−0.895940	+	0.444174i	$0.853497\pi$
$278$	−10.0382	+	2.68973i	−0.602051	+	0.161319i
$279$	−7.46410			−0.446864
$280$		0			0
$281$	−27.9282			−1.66606			−0.833028	−	0.553230i	$-0.813395\pi$
$281$	−27.9282			−1.66606			−0.833028	+	0.553230i	$0.813395\pi$
$282$	1.15539	−	0.309587i	0.0688027	−	0.0184356i
$283$	−3.24453	+	12.1087i	−0.192867	+	0.719790i	0.799941	+	0.600078i	$0.204864\pi$
$283$	−3.24453	+	12.1087i	−0.192867	+	0.719790i	−0.992809	+	0.119712i	$0.961803\pi$
$284$	−7.73205	+	4.46410i	−0.458813	+	0.264896i
$285$		0			0
$286$		−	5.73205i		−	0.338943i
$287$	0.429705	−	5.98502i	0.0253647	−	0.353285i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	33.5263	+	19.3564i	1.97213	+	1.13861i
$290$		0			0
$291$	1.46410	+	2.53590i	0.0858272	+	0.148657i
$292$	−1.03528	−	3.86370i	−0.0605850	−	0.226106i
$293$	1.22474	+	1.22474i	0.0715504	+	0.0715504i	0.741976	−	0.670426i	$-0.233889\pi$
$293$	1.22474	+	1.22474i	0.0715504	+	0.0715504i	−0.670426	+	0.741976i	$0.733889\pi$
$294$	−1.00000	+	6.92820i	−0.0583212	+	0.404061i
$295$		0			0
$296$	1.96410	−	3.40192i	0.114161	−	0.197733i
$297$	0.965926	+	0.258819i	0.0560487	+	0.0150182i
$298$	−0.896575	−	0.240237i	−0.0519372	−	0.0139165i
$299$	−16.9904	+	29.4282i	−0.982579	+	1.70188i
$300$		0			0
$301$	17.8564	−	15.4641i	1.02923	−	0.891336i
$302$	−2.72689	−	2.72689i	−0.156915	−	0.156915i
$303$	−0.277401	−	1.03528i	−0.0159363	−	0.0594751i
$304$	1.13397	+	1.96410i	0.0650379	+	0.112649i
$305$		0			0
$306$	−6.46410	−	3.73205i	−0.369528	−	0.213347i
$307$	15.8338	−	15.8338i	0.903680	−	0.903680i	−0.0920724	−	0.995752i	$-0.529349\pi$
$307$	15.8338	−	15.8338i	0.903680	−	0.903680i	0.995752	+	0.0920724i	$0.0293491\pi$
$308$	−2.19067	−	1.48356i	−0.124825	−	0.0845339i
$309$			18.3923i			1.04630i
$310$		0			0
$311$	17.7846	−	10.2679i	1.00847	−	0.582242i	0.0977286	−	0.995213i	$-0.468842\pi$
$311$	17.7846	−	10.2679i	1.00847	−	0.582242i	0.910744	+	0.412971i	$0.135509\pi$
$312$	1.48356	−	5.53674i	0.0839903	−	0.313456i
$313$	−30.1146	+	8.06918i	−1.70218	+	0.456097i	−0.973486	−	0.228746i	$-0.926538\pi$
$313$	−30.1146	+	8.06918i	−1.70218	+	0.456097i	−0.728691	+	0.684843i	$0.759871\pi$
$314$	4.66025			0.262993
$315$		0			0
$316$	3.07180			0.172802
$317$	13.5230	−	3.62347i	0.759525	−	0.203514i	0.141786	−	0.989897i	$-0.454715\pi$
$317$	13.5230	−	3.62347i	0.759525	−	0.203514i	0.617739	+	0.786383i	$0.288049\pi$
$318$	0.258819	−	0.965926i	0.0145139	−	0.0541664i
$319$	6.00000	−	3.46410i	0.335936	−	0.193952i
$320$		0			0
$321$			14.9282i			0.833211i
$322$	6.84941	+	14.1100i	0.381703	+	0.786317i
$323$	11.9700	−	11.9700i	0.666031	−	0.666031i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$		0			0
$326$	−6.00000	−	10.3923i	−0.332309	−	0.575577i
$327$	−4.38134	−	16.3514i	−0.242289	−	0.904234i
$328$	1.60368	+	1.60368i	0.0885485	+	0.0885485i
$329$	−0.598076	−	3.10770i	−0.0329730	−	0.171333i
$330$		0			0
$331$	−12.8923	+	22.3301i	−0.708625	+	1.22737i	0.256742	+	0.966480i	$0.417351\pi$
$331$	−12.8923	+	22.3301i	−0.708625	+	1.22737i	−0.965367	+	0.260895i	$0.915982\pi$
$332$	10.0382	+	2.68973i	0.550918	+	0.147618i
$333$	3.79435	+	1.01669i	0.207929	+	0.0557145i
$334$	−3.40192	+	5.89230i	−0.186145	+	0.322413i
$335$		0			0
$336$	−1.73205	−	2.00000i	−0.0944911	−	0.109109i
$337$	−7.82894	−	7.82894i	−0.426470	−	0.426470i	0.460954	−	0.887424i	$-0.347507\pi$
$337$	−7.82894	−	7.82894i	−0.426470	−	0.426470i	−0.887424	+	0.460954i	$0.847507\pi$
$338$	−5.13922	−	19.1798i	−0.279537	−	1.04324i
$339$	−6.46410	−	11.1962i	−0.351082	−	0.608092i
$340$		0			0
$341$	−6.46410	−	3.73205i	−0.350051	−	0.202102i
$342$	−1.60368	+	1.60368i	−0.0867172	+	0.0867172i
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$			8.92820i			0.481376i
$345$		0			0
$346$	−6.57180	+	3.79423i	−0.353302	+	0.203979i
$347$	−0.757875	+	2.82843i	−0.0406848	+	0.151838i	−0.983280	−	0.182099i	$-0.941711\pi$
$347$	−0.757875	+	2.82843i	−0.0406848	+	0.151838i	0.942595	+	0.333937i	$0.108377\pi$
$348$	6.69213	−	1.79315i	0.358736	−	0.0961230i
$349$	−1.85641			−0.0993712			−0.0496856	−	0.998765i	$-0.515822\pi$
$349$	−1.85641			−0.0993712			−0.0496856	+	0.998765i	$0.515822\pi$
$350$		0			0
$351$	5.73205			0.305954
$352$	0.965926	−	0.258819i	0.0514840	−	0.0137951i
$353$	1.79315	−	6.69213i	0.0954398	−	0.356186i	−0.901646	−	0.432475i	$-0.857640\pi$
$353$	1.79315	−	6.69213i	0.0954398	−	0.356186i	0.997086	+	0.0762887i	$0.0243071\pi$
$354$	9.92820	−	5.73205i	0.527678	−	0.304655i
$355$		0			0
$356$			6.92820i			0.367194i
$357$	−11.0735	+	16.3514i	−0.586070	+	0.865407i
$358$	6.36396	−	6.36396i	0.336346	−	0.336346i
$359$	4.39230	+	2.53590i	0.231817	+	0.133840i	0.611410	−	0.791314i	$-0.290603\pi$
$359$	4.39230	+	2.53590i	0.231817	+	0.133840i	−0.379593	+	0.925154i	$0.623936\pi$
$360$		0			0
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$	3.72500	+	13.9019i	0.195782	+	0.730668i
$363$	−7.07107	−	7.07107i	−0.371135	−	0.371135i
$364$	−14.3301	−	4.96410i	−0.751103	−	0.260190i
$365$		0			0
$366$	5.73205	−	9.92820i	0.299619	−	0.518955i
$367$	−29.4768	−	7.89829i	−1.53868	−	0.412288i	−0.612840	−	0.790207i	$-0.709973\pi$
$367$	−29.4768	−	7.89829i	−1.53868	−	0.412288i	−0.925838	+	0.377920i	$0.876640\pi$
$368$	−5.72620	−	1.53433i	−0.298499	−	0.0799826i
$369$	−1.13397	+	1.96410i	−0.0590324	+	0.102247i
$370$		0			0
$371$	−2.50000	−	0.866025i	−0.129794	−	0.0449618i
$372$	−5.27792	−	5.27792i	−0.273647	−	0.273647i
$373$	6.72930	+	25.1141i	0.348430	+	1.30036i	0.888554	+	0.458772i	$0.151711\pi$
$373$	6.72930	+	25.1141i	0.348430	+	1.30036i	−0.540124	+	0.841585i	$0.681623\pi$
$374$	−3.73205	−	6.46410i	−0.192980	−	0.334251i
$375$		0			0
$376$	1.03590	+	0.598076i	0.0534224	+	0.0308434i
$377$	28.0812	−	28.0812i	1.44626	−	1.44626i
$378$	1.48356	−	2.19067i	0.0763063	−	0.112676i
$379$		−	3.92820i		−	0.201778i	−0.994898	−	0.100889i	$-0.967831\pi$
$379$		−	3.92820i		−	0.201778i	0.994898	−	0.100889i	$-0.0321687\pi$
$380$		0			0
$381$	4.33013	−	2.50000i	0.221839	−	0.128079i
$382$	0.757875	−	2.82843i	0.0387762	−	0.144715i
$383$	21.2318	−	5.68904i	1.08489	−	0.290696i	0.328294	−	0.944575i	$-0.393526\pi$
$383$	21.2318	−	5.68904i	1.08489	−	0.290696i	0.756599	+	0.653879i	$0.226859\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−22.7846			−1.15971
$387$	−8.62398	+	2.31079i	−0.438382	+	0.117464i
$388$	−0.757875	+	2.82843i	−0.0384753	+	0.143592i
$389$	31.7321	−	18.3205i	1.60888	−	0.928887i	0.619257	−	0.785188i	$-0.287434\pi$
$389$	31.7321	−	18.3205i	1.60888	−	0.928887i	0.989622	−	0.143699i	$-0.0458996\pi$
$390$		0			0
$391$			44.2487i			2.23775i
$392$	−5.60609	+	4.19187i	−0.283150	+	0.211722i
$393$	2.91636	−	2.91636i	0.147111	−	0.147111i
$394$	−14.5981	−	8.42820i	−0.735440	−	0.424607i
$395$		0			0
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	7.45001	+	27.8038i	0.373905	+	1.39543i	0.854938	+	0.518730i	$0.173595\pi$
$397$	7.45001	+	27.8038i	0.373905	+	1.39543i	−0.481033	+	0.876702i	$0.659738\pi$
$398$	8.86422	+	8.86422i	0.444323	+	0.444323i
$399$	3.92820	+	4.53590i	0.196656	+	0.227079i
$400$		0			0
$401$	−0.964102	+	1.66987i	−0.0481449	+	0.0833895i	−0.889094	−	0.457725i	$-0.848664\pi$
$401$	−0.964102	+	1.66987i	−0.0481449	+	0.0833895i	0.840949	+	0.541115i	$0.181998\pi$
$402$	−1.93185	−	0.517638i	−0.0963520	−	0.0258174i
$403$	−41.3268	−	11.0735i	−2.05863	−	0.551609i
$404$	0.535898	−	0.928203i	0.0266619	−	0.0461798i
$405$		0			0
$406$	−3.46410	−	18.0000i	−0.171920	−	0.893325i
$407$	2.77766	+	2.77766i	0.137683	+	0.137683i
$408$	−1.93185	−	7.20977i	−0.0956409	−	0.356937i
$409$	−14.3923	−	24.9282i	−0.711654	−	1.23262i	−0.964236	−	0.265045i	$-0.914613\pi$
$409$	−14.3923	−	24.9282i	−0.711654	−	1.23262i	0.252582	−	0.967575i	$-0.418720\pi$
$410$		0			0
$411$	−16.3923	−	9.46410i	−0.808573	−	0.466830i
$412$	−13.0053	+	13.0053i	−0.640726	+	0.640726i
$413$	−13.2456	−	27.2862i	−0.651771	−	1.34266i
$414$		−	5.92820i		−	0.291355i
$415$		0			0
$416$	4.96410	−	2.86603i	0.243385	−	0.140518i
$417$	2.68973	−	10.0382i	0.131716	−	0.491573i
$418$	−2.19067	+	0.586988i	−0.107149	+	0.0287105i
$419$	11.0526			0.539953			0.269976	−	0.962867i	$-0.412984\pi$
$419$	11.0526			0.539953			0.269976	+	0.962867i	$0.412984\pi$
$420$		0			0
$421$	−13.8564			−0.675320			−0.337660	−	0.941268i	$-0.609635\pi$
$421$	−13.8564			−0.675320			−0.337660	+	0.941268i	$0.609635\pi$
$422$	19.1105	−	5.12063i	0.930283	−	0.249269i
$423$	−0.309587	+	1.15539i	−0.0150526	+	0.0561772i
$424$	0.866025	−	0.500000i	0.0420579	−	0.0242821i
$425$		0			0
$426$		−	8.92820i		−	0.432573i
$427$	−25.1141	−	17.0077i	−1.21536	−	0.823062i
$428$	−10.5558	+	10.5558i	−0.510235	+	0.510235i
$429$	4.96410	+	2.86603i	0.239669	+	0.138373i
$430$		0			0
$431$	16.8564	+	29.1962i	0.811945	+	1.40633i	0.911501	+	0.411297i	$0.134924\pi$
$431$	16.8564	+	29.1962i	0.811945	+	1.40633i	−0.0995567	+	0.995032i	$0.531742\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	−11.3137	−	11.3137i	−0.543702	−	0.543702i	0.380910	−	0.924612i	$-0.375611\pi$
$433$	−11.3137	−	11.3137i	−0.543702	−	0.543702i	−0.924612	+	0.380910i	$0.875611\pi$
$434$	−14.9282	+	12.9282i	−0.716577	+	0.620574i
$435$		0			0
$436$	8.46410	−	14.6603i	0.405357	−	0.702099i
$437$	12.9867	+	3.47979i	0.621240	+	0.166461i
$438$	3.86370	+	1.03528i	0.184615	+	0.0494674i
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	−0.522387	−	0.852709i	$-0.674958\pi$
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	0.999661	+	0.0260459i	$0.00829161\pi$
$440$		0			0
$441$	−5.50000	−	4.33013i	−0.261905	−	0.206197i
$442$	−30.2533	−	30.2533i	−1.43900	−	1.43900i
$443$	−7.20977	−	26.9072i	−0.342546	−	1.27840i	−0.895452	−	0.445157i	$-0.853148\pi$
$443$	−7.20977	−	26.9072i	−0.342546	−	1.27840i	0.552906	−	0.833244i	$-0.313519\pi$
$444$	1.96410	+	3.40192i	0.0932121	+	0.161448i
$445$		0			0
$446$	8.07180	+	4.66025i	0.382211	+	0.220669i
$447$	0.656339	−	0.656339i	0.0310438	−	0.0310438i
$448$	0.189469	−	2.63896i	0.00895155	−	0.124679i
$449$		−	13.9282i		−	0.657313i	−0.944450	−	0.328656i	$-0.893404\pi$
$449$		−	13.9282i		−	0.657313i	0.944450	−	0.328656i	$-0.106596\pi$
$450$		0			0
$451$	−1.96410	+	1.13397i	−0.0924859	+	0.0533968i
$452$	3.34607	−	12.4877i	0.157386	−	0.587371i
$453$	3.72500	−	0.998111i	0.175016	−	0.0468954i
$454$	−3.46410			−0.162578
$455$		0			0
$456$	−2.26795			−0.106206
$457$	−15.3161	+	4.10394i	−0.716458	+	0.191974i	−0.598591	−	0.801055i	$-0.704272\pi$
$457$	−15.3161	+	4.10394i	−0.716458	+	0.191974i	−0.117867	+	0.993029i	$0.537606\pi$
$458$	−0.757875	+	2.82843i	−0.0354132	+	0.132164i
$459$	6.46410	−	3.73205i	0.301718	−	0.174197i
$460$		0			0
$461$		−	38.6410i		−	1.79969i	−0.436208	−	0.899846i	$-0.643679\pi$
$461$		−	38.6410i		−	1.79969i	0.436208	−	0.899846i	$-0.356321\pi$
$462$	2.38014	−	1.15539i	0.110734	−	0.0537538i
$463$	16.0604	−	16.0604i	0.746389	−	0.746389i	−0.227410	−	0.973799i	$-0.573026\pi$
$463$	16.0604	−	16.0604i	0.746389	−	0.746389i	0.973799	+	0.227410i	$0.0730257\pi$
$464$	6.00000	+	3.46410i	0.278543	+	0.160817i
$465$		0			0
$466$	−0.928203	−	1.60770i	−0.0429982	−	0.0744750i
$467$	1.65445	+	6.17449i	0.0765588	+	0.285721i	0.993582	−	0.113112i	$-0.0360819\pi$
$467$	1.65445	+	6.17449i	0.0765588	+	0.285721i	−0.917023	+	0.398833i	$0.869415\pi$
$468$	4.05317	+	4.05317i	0.187358	+	0.187358i
$469$	−1.73205	+	5.00000i	−0.0799787	+	0.230879i
$470$		0			0
$471$	−2.33013	+	4.03590i	−0.107367	+	0.185964i
$472$	11.0735	+	2.96713i	0.509698	+	0.136573i
$473$	−8.62398	−	2.31079i	−0.396531	−	0.106250i
$474$	−1.53590	+	2.66025i	−0.0705461	+	0.122190i
$475$		0			0
$476$	−19.3923	+	3.73205i	−0.888845	+	0.171058i
$477$	0.707107	+	0.707107i	0.0323762	+	0.0323762i
$478$	6.21166	+	23.1822i	0.284115	+	1.06033i
$479$	−14.5359	−	25.1769i	−0.664162	−	1.15036i	−0.979512	−	0.201387i	$-0.935455\pi$
$479$	−14.5359	−	25.1769i	−0.664162	−	1.15036i	0.315350	−	0.948976i	$-0.397878\pi$
$480$		0			0
$481$	19.5000	+	11.2583i	0.889123	+	0.513336i
$482$	−15.7458	+	15.7458i	−0.717202	+	0.717202i
$483$	−15.6443	−	1.12321i	−0.711839	−	0.0511078i
$484$		−	10.0000i		−	0.454545i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−1.51575	+	5.65685i	−0.0686852	+	0.256337i	−0.991727	−	0.128362i	$-0.959028\pi$
$487$	−1.51575	+	5.65685i	−0.0686852	+	0.256337i	0.923042	+	0.384699i	$0.125695\pi$
$488$	11.0735	−	2.96713i	0.501273	−	0.134316i
$489$	12.0000			0.542659
$490$		0			0
$491$	−11.7128			−0.528592			−0.264296	−	0.964442i	$-0.585140\pi$
$491$	−11.7128			−0.528592			−0.264296	+	0.964442i	$0.585140\pi$
$492$	−2.19067	+	0.586988i	−0.0987631	+	0.0264635i
$493$	13.3843	−	49.9507i	0.602797	−	2.24967i
$494$	−11.2583	+	6.50000i	−0.506536	+	0.292449i
$495$		0			0
$496$		−	7.46410i		−	0.335148i
$497$	−23.5612	−	1.69161i	−1.05686	−	0.0758793i
$498$	−7.34847	+	7.34847i	−0.329293	+	0.329293i
$499$	−24.2487	−	14.0000i	−1.08552	−	0.626726i	−0.153141	−	0.988204i	$-0.548939\pi$
$499$	−24.2487	−	14.0000i	−1.08552	−	0.626726i	−0.932381	+	0.361478i	$0.882272\pi$
$500$		0			0
$501$	−3.40192	−	5.89230i	−0.151987	−	0.263249i
$502$	−1.89967	−	7.08965i	−0.0847862	−	0.316427i
$503$	−9.62209	−	9.62209i	−0.429028	−	0.429028i	0.459269	−	0.888297i	$-0.348111\pi$
$503$	−9.62209	−	9.62209i	−0.429028	−	0.429028i	−0.888297	+	0.459269i	$0.848111\pi$
$504$	2.59808	−	0.500000i	0.115728	−	0.0222718i
$505$		0			0
$506$	2.96410	−	5.13397i	0.131770	−	0.228233i
$507$	19.1798	+	5.13922i	0.851806	+	0.228241i
$508$	4.82963	+	1.29410i	0.214280	+	0.0574162i
$509$	5.19615	−	9.00000i	0.230315	−	0.398918i	−0.727586	−	0.686017i	$-0.759358\pi$
$509$	5.19615	−	9.00000i	0.230315	−	0.398918i	0.957901	+	0.287099i	$0.0926909\pi$
$510$		0			0
$511$	3.46410	−	10.0000i	0.153243	−	0.442374i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.586988	−	2.19067i	−0.0259162	−	0.0967205i
$514$	1.19615	+	2.07180i	0.0527600	+	0.0913830i
$515$		0			0
$516$	−7.73205	−	4.46410i	−0.340385	−	0.196521i
$517$	−0.845807	+	0.845807i	−0.0371986	+	0.0371986i
$518$	9.34967	−	4.53862i	0.410801	−	0.199416i
$519$		−	7.58846i		−	0.333096i
$520$		0			0
$521$	27.8205	−	16.0622i	1.21884	−	0.703697i	0.254169	−	0.967160i	$-0.418198\pi$
$521$	27.8205	−	16.0622i	1.21884	−	0.703697i	0.964669	+	0.263463i	$0.0848647\pi$
$522$	−1.79315	+	6.69213i	−0.0784841	+	0.292907i
$523$	5.93426	−	1.59008i	0.259487	−	0.0695293i	−0.126730	−	0.991937i	$-0.540448\pi$
$523$	5.93426	−	1.59008i	0.259487	−	0.0695293i	0.386217	+	0.922408i	$0.373782\pi$
$524$	4.12436			0.180173
$525$		0			0
$526$	−29.8564			−1.30180
$527$	−53.8144	+	14.4195i	−2.34419	+	0.628125i
$528$	−0.258819	+	0.965926i	−0.0112637	+	0.0420365i
$529$	−10.5167	+	6.07180i	−0.457246	+	0.263991i
$530$		0			0
$531$			11.4641i			0.497500i
$532$	−0.429705	+	5.98502i	−0.0186301	+	0.259484i
$533$	−9.19239	+	9.19239i	−0.398167	+	0.398167i
$534$	−6.00000	−	3.46410i	−0.259645	−	0.149906i
$535$		0			0
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$	2.32937	+	8.69333i	0.100520	+	0.375145i
$538$	−17.9043	−	17.9043i	−0.771909	−	0.771909i
$539$	−2.59808	−	6.50000i	−0.111907	−	0.279975i
$540$		0			0
$541$	−15.4641	+	26.7846i	−0.664854	+	1.15156i	0.314471	+	0.949267i	$0.398173\pi$
$541$	−15.4641	+	26.7846i	−0.664854	+	1.15156i	−0.979325	+	0.202293i	$0.935161\pi$
$542$	−7.72741	−	2.07055i	−0.331921	−	0.0889378i
$543$	−13.9019	−	3.72500i	−0.596588	−	0.159855i
$544$	3.73205	−	6.46410i	0.160010	−	0.277146i
$545$		0			0
$546$	11.4641	−	9.92820i	0.490618	−	0.424888i
$547$	18.1817	+	18.1817i	0.777394	+	0.777394i	0.979387	−	0.201993i	$-0.0647419\pi$
$547$	18.1817	+	18.1817i	0.777394	+	0.777394i	−0.201993	+	0.979387i	$0.564742\pi$
$548$	−4.89898	−	18.2832i	−0.209274	−	0.781021i
$549$	5.73205	+	9.92820i	0.244638	+	0.423725i
$550$		0			0
$551$	−13.6077	−	7.85641i	−0.579707	−	0.334694i
$552$	4.19187	−	4.19187i	0.178418	−	0.178418i
$553$	6.72930	+	4.55721i	0.286159	+	0.193792i
$554$		−	22.0000i		−	0.934690i
$555$		0			0
$556$	9.00000	−	5.19615i	0.381685	−	0.220366i
$557$	−1.25693	+	4.69093i	−0.0532579	+	0.198761i	−0.987429	−	0.158065i	$-0.949474\pi$
$557$	−1.25693	+	4.69093i	−0.0532579	+	0.198761i	0.934171	+	0.356826i	$0.116141\pi$
$558$	7.20977	−	1.93185i	0.305214	−	0.0817818i
$559$	−51.1769			−2.16455
$560$		0			0
$561$	7.46410			0.315135
$562$	26.9766	−	7.22835i	1.13794	−	0.304910i
$563$	−0.619174	+	2.31079i	−0.0260951	+	0.0973881i	−0.977745	−	0.209796i	$-0.932720\pi$
$563$	−0.619174	+	2.31079i	−0.0260951	+	0.0973881i	0.951650	+	0.307184i	$0.0993867\pi$
$564$	−1.03590	+	0.598076i	−0.0436192	+	0.0251836i
$565$		0			0
$566$		−	12.5359i		−	0.526923i
$567$	1.15539	+	2.38014i	0.0485220	+	0.0999565i
$568$	6.31319	−	6.31319i	0.264896	−	0.264896i
$569$	27.5263	+	15.8923i	1.15396	+	0.666240i	0.949849	−	0.312707i	$-0.101236\pi$
$569$	27.5263	+	15.8923i	1.15396	+	0.666240i	0.204112	+	0.978948i	$0.434569\pi$
$570$		0			0
$571$	6.92820	+	12.0000i	0.289936	+	0.502184i	0.973794	−	0.227431i	$-0.0730325\pi$
$571$	6.92820	+	12.0000i	0.289936	+	0.502184i	−0.683858	+	0.729615i	$0.739699\pi$
$572$	1.48356	+	5.53674i	0.0620309	+	0.231503i
$573$	2.07055	+	2.07055i	0.0864986	+	0.0864986i
$574$	1.13397	+	5.89230i	0.0473312	+	0.245940i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−20.3538	−	5.45378i	−0.847339	−	0.227044i	−0.191076	−	0.981575i	$-0.561198\pi$
$577$	−20.3538	−	5.45378i	−0.847339	−	0.227044i	−0.656264	+	0.754531i	$0.727864\pi$
$578$	−37.3937	−	10.0196i	−1.55537	−	0.416761i
$579$	11.3923	−	19.7321i	0.473448	−	0.820036i
$580$		0			0
$581$	18.0000	+	20.7846i	0.746766	+	0.862291i
$582$	−2.07055	−	2.07055i	−0.0858272	−	0.0858272i
$583$	0.258819	+	0.965926i	0.0107192	+	0.0400046i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$		0			0
$586$	−1.50000	−	0.866025i	−0.0619644	−	0.0357752i
$587$	−15.0759	+	15.0759i	−0.622248	+	0.622248i	−0.946106	−	0.323858i	$-0.895020\pi$
$587$	−15.0759	+	15.0759i	−0.622248	+	0.622248i	0.323858	+	0.946106i	$0.395020\pi$
$588$	−0.827225	−	6.95095i	−0.0341142	−	0.286652i
$589$			16.9282i			0.697514i
$590$		0			0
$591$	14.5981	−	8.42820i	0.600485	−	0.346690i
$592$	−1.01669	+	3.79435i	−0.0417859	+	0.155947i
$593$	40.9478	−	10.9719i	1.68153	−	0.450563i	0.713344	−	0.700814i	$-0.247180\pi$
$593$	40.9478	−	10.9719i	1.68153	−	0.450563i	0.968181	+	0.250250i	$0.0805129\pi$
$594$	−1.00000			−0.0410305
$595$		0			0
$596$	0.928203			0.0380207
$597$	−12.1087	+	3.24453i	−0.495578	+	0.132790i
$598$	8.79487	−	32.8229i	0.359649	−	1.34223i
$599$	36.2487	−	20.9282i	1.48108	−	0.855103i	0.481312	−	0.876549i	$-0.340160\pi$
$599$	36.2487	−	20.9282i	1.48108	−	0.855103i	0.999770	+	0.0214460i	$0.00682701\pi$
$600$		0			0
$601$			28.7846i			1.17415i	0.809533	+	0.587074i	$0.199720\pi$
$601$			28.7846i			1.17415i	−0.809533	+	0.587074i	$0.800280\pi$
$602$	−13.2456	+	19.5588i	−0.539849	+	0.797155i
$603$	1.41421	−	1.41421i	0.0575912	−	0.0575912i
$604$	3.33975	+	1.92820i	0.135892	+	0.0784575i
$605$		0			0
$606$	0.535898	+	0.928203i	0.0217694	+	0.0377057i
$607$	4.93117	+	18.4034i	0.200150	+	0.746969i	0.990873	+	0.134796i	$0.0430379\pi$
$607$	4.93117	+	18.4034i	0.200150	+	0.746969i	−0.790724	+	0.612173i	$0.790295\pi$
$608$	−1.60368	−	1.60368i	−0.0650379	−	0.0650379i
$609$	17.3205	+	6.00000i	0.701862	+	0.243132i
$610$		0			0
$611$	−3.42820	+	5.93782i	−0.138690	+	0.240219i
$612$	7.20977	+	1.93185i	0.291438	+	0.0780905i
$613$	17.3173	+	4.64016i	0.699440	+	0.187414i	0.590980	−	0.806686i	$-0.298741\pi$
$613$	17.3173	+	4.64016i	0.699440	+	0.187414i	0.108460	+	0.994101i	$0.465408\pi$
$614$	−11.1962	+	19.3923i	−0.451840	+	0.782610i
$615$		0			0
$616$	2.50000	+	0.866025i	0.100728	+	0.0348932i
$617$	−2.17209	−	2.17209i	−0.0874450	−	0.0874450i	0.662031	−	0.749476i	$-0.269695\pi$
$617$	−2.17209	−	2.17209i	−0.0874450	−	0.0874450i	−0.749476	+	0.662031i	$0.769695\pi$
$618$	−4.76028	−	17.7656i	−0.191486	−	0.714637i
$619$	−5.79423	−	10.0359i	−0.232890	−	0.403377i	0.725768	−	0.687940i	$-0.241485\pi$
$619$	−5.79423	−	10.0359i	−0.232890	−	0.403377i	−0.958657	+	0.284563i	$0.908151\pi$
$620$		0			0
$621$	5.13397	+	2.96410i	0.206019	+	0.118945i
$622$	−14.5211	+	14.5211i	−0.582242	+	0.582242i
$623$	−10.2784	+	15.1774i	−0.411797	+	0.608070i
$624$			5.73205i			0.229466i
$625$		0			0
$626$	27.0000	−	15.5885i	1.07914	−	0.623040i
$627$	0.586988	−	2.19067i	0.0234421	−	0.0874870i
$628$	−4.50146	+	1.20616i	−0.179628	+	0.0481311i
$629$	29.3205			1.16909
$630$		0			0
$631$	42.7846			1.70323			0.851614	−	0.524169i	$-0.175624\pi$
$631$	42.7846			1.70323			0.851614	+	0.524169i	$0.175624\pi$
$632$	−2.96713	+	0.795040i	−0.118026	+	0.0316250i
$633$	−5.12063	+	19.1105i	−0.203527	+	0.759573i
$634$	−12.1244	+	7.00000i	−0.481520	+	0.278006i
$635$		0			0
$636$			1.00000i			0.0396526i
$637$	−24.0280	−	32.1344i	−0.952025	−	1.27321i
$638$	−4.89898	+	4.89898i	−0.193952	+	0.193952i
$639$	7.73205	+	4.46410i	0.305875	+	0.176597i
$640$		0			0
$641$	−15.9641	−	27.6506i	−0.630544	−	1.09213i	−0.987441	−	0.157991i	$-0.949498\pi$
$641$	−15.9641	−	27.6506i	−0.630544	−	1.09213i	0.356897	−	0.934144i	$-0.383835\pi$
$642$	−3.86370	−	14.4195i	−0.152488	−	0.569094i
$643$	−29.2180	−	29.2180i	−1.15225	−	1.15225i	−0.986101	−	0.166144i	$-0.946868\pi$
$643$	−29.2180	−	29.2180i	−1.15225	−	1.15225i	−0.166144	−	0.986101i	$-0.553132\pi$
$644$	−10.2679	−	11.8564i	−0.404614	−	0.467208i
$645$		0			0
$646$	−8.46410	+	14.6603i	−0.333016	+	0.576800i
$647$	4.26122	+	1.14179i	0.167526	+	0.0448884i	0.341607	−	0.939843i	$-0.389029\pi$
$647$	4.26122	+	1.14179i	0.167526	+	0.0448884i	−0.174081	+	0.984731i	$0.555695\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−5.73205	+	9.92820i	−0.225003	+	0.389716i
$650$		0			0
$651$	−3.73205	−	19.3923i	−0.146271	−	0.760044i
$652$	8.48528	+	8.48528i	0.332309	+	0.332309i
$653$	6.39615	+	23.8707i	0.250301	+	0.934134i	0.970645	+	0.240518i	$0.0773172\pi$
$653$	6.39615	+	23.8707i	0.250301	+	0.934134i	−0.720344	+	0.693617i	$0.756016\pi$
$654$	8.46410	+	14.6603i	0.330973	+	0.573261i
$655$		0			0
$656$	−1.96410	−	1.13397i	−0.0766853	−	0.0442743i
$657$	−2.82843	+	2.82843i	−0.110347	+	0.110347i
$658$	1.38203	+	2.84701i	0.0538771	+	0.110988i
$659$			39.7128i			1.54699i	0.633801	+	0.773496i	$0.281494\pi$
$659$			39.7128i			1.54699i	−0.633801	+	0.773496i	$0.718506\pi$
$660$		0			0
$661$	7.85641	−	4.53590i	0.305579	−	0.176426i	−0.339368	−	0.940654i	$-0.610213\pi$
$661$	7.85641	−	4.53590i	0.305579	−	0.176426i	0.644946	+	0.764228i	$0.276880\pi$
$662$	6.67355	−	24.9060i	0.259375	−	0.968000i
$663$	41.3268	−	11.0735i	1.60500	−	0.430058i
$664$	−10.3923			−0.403300
$665$		0			0
$666$	−3.92820			−0.152215
$667$	39.6723	−	10.6302i	1.53612	−	0.411602i
$668$	1.76097	−	6.57201i	0.0681338	−	0.254279i
$669$	−8.07180	+	4.66025i	−0.312074	+	0.180176i
$670$		0			0
$671$			11.4641i			0.442567i
$672$	2.19067	+	1.48356i	0.0845070	+	0.0572297i
$673$	−17.5254	+	17.5254i	−0.675553	+	0.675553i	−0.958991	−	0.283438i	$-0.908525\pi$
$673$	−17.5254	+	17.5254i	−0.675553	+	0.675553i	0.283438	+	0.958991i	$0.408525\pi$
$674$	9.58846	+	5.53590i	0.369334	+	0.213235i
$675$		0			0
$676$	9.92820	+	17.1962i	0.381854	+	0.661390i
$677$	−12.9360	−	48.2777i	−0.497170	−	1.85546i	−0.517522	−	0.855670i	$-0.673145\pi$
$677$	−12.9360	−	48.2777i	−0.497170	−	1.85546i	0.0203517	−	0.999793i	$-0.493521\pi$
$678$	9.14162	+	9.14162i	0.351082	+	0.351082i
$679$	−5.85641	+	5.07180i	−0.224748	+	0.194638i
$680$		0			0
$681$	1.73205	−	3.00000i	0.0663723	−	0.114960i
$682$	7.20977	+	1.93185i	0.276076	+	0.0739744i
$683$	13.6617	+	3.66063i	0.522749	+	0.140070i	0.510538	−	0.859855i	$-0.329446\pi$
$683$	13.6617	+	3.66063i	0.522749	+	0.140070i	0.0122111	+	0.999925i	$0.496113\pi$
$684$	1.13397	−	1.96410i	0.0433586	−	0.0750993i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$	−2.07055	−	2.07055i	−0.0789965	−	0.0789965i
$688$	−2.31079	−	8.62398i	−0.0880980	−	0.328786i
$689$	2.86603	+	4.96410i	0.109187	+	0.189117i
$690$		0			0
$691$	−34.8564	−	20.1244i	−1.32600	−	0.765567i	−0.341322	−	0.939947i	$-0.610875\pi$
$691$	−34.8564	−	20.1244i	−1.32600	−	0.765567i	−0.984678	+	0.174380i	$0.944208\pi$
$692$	5.36585	−	5.36585i	0.203979	−	0.203979i
$693$	−0.189469	+	2.63896i	−0.00719732	+	0.100246i
$694$		−	2.92820i		−	0.111153i
$695$		0			0
$696$	−6.00000	+	3.46410i	−0.227429	+	0.131306i
$697$	−4.38134	+	16.3514i	−0.165955	+	0.619353i
$698$	1.79315	−	0.480473i	0.0678718	−	0.0181862i
$699$	1.85641			0.0702157
$700$		0			0
$701$	−4.14359			−0.156501			−0.0782507	−	0.996934i	$-0.524933\pi$
$701$	−4.14359			−0.156501			−0.0782507	+	0.996934i	$0.524933\pi$
$702$	−5.53674	+	1.48356i	−0.208971	+	0.0559935i
$703$	2.30581	−	8.60540i	0.0869653	−	0.324559i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$		0			0
$706$			6.92820i			0.260746i
$707$	2.55103	−	1.23835i	0.0959412	−	0.0465729i
$708$	−8.10634	+	8.10634i	−0.304655	+	0.304655i
$709$	−23.3205	−	13.4641i	−0.875820	−	0.505655i	−0.00654213	−	0.999979i	$-0.502082\pi$
$709$	−23.3205	−	13.4641i	−0.875820	−	0.505655i	−0.869278	+	0.494324i	$0.835416\pi$
$710$		0			0
$711$	−1.53590	−	2.66025i	−0.0576007	−	0.0997673i
$712$	−1.79315	−	6.69213i	−0.0672012	−	0.250798i
$713$	−31.2886	−	31.2886i	−1.17177	−	1.17177i
$714$	6.46410	−	18.6603i	0.241913	−	0.698342i
$715$		0			0
$716$	−4.50000	+	7.79423i	−0.168173	+	0.291284i
$717$	−23.1822	−	6.21166i	−0.865756	−	0.231979i
$718$	−4.89898	−	1.31268i	−0.182828	−	0.0489887i
$719$	−3.19615	+	5.53590i	−0.119196	+	0.206454i	−0.919449	−	0.393208i	$-0.871365\pi$
$719$	−3.19615	+	5.53590i	−0.119196	+	0.206454i	0.800253	+	0.599662i	$0.204698\pi$
$720$		0			0
$721$	−47.7846	+	9.19615i	−1.77959	+	0.342483i
$722$	−9.79796	−	9.79796i	−0.364642	−	0.364642i
$723$	−5.76337	−	21.5092i	−0.214342	−	0.799935i
$724$	−7.19615	−	12.4641i	−0.267443	−	0.463225i
$725$		0			0
$726$	8.66025	+	5.00000i	0.321412	+	0.185567i
$727$	10.8468	−	10.8468i	0.402287	−	0.402287i	−0.476751	−	0.879038i	$-0.658186\pi$
$727$	10.8468	−	10.8468i	0.402287	−	0.402287i	0.879038	+	0.476751i	$0.158186\pi$
$728$	15.1266	+	1.08604i	0.560631	+	0.0402515i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−57.7128	+	33.3205i	−2.13459	+	1.23240i
$732$	−2.96713	+	11.0735i	−0.109668	+	0.409287i
$733$	−14.5397	+	3.89589i	−0.537034	+	0.143898i	−0.517135	−	0.855904i	$-0.673001\pi$
$733$	−14.5397	+	3.89589i	−0.537034	+	0.143898i	−0.0198997	+	0.999802i	$0.506335\pi$
$734$	30.5167			1.12639
$735$		0			0
$736$	5.92820			0.218516
$737$	1.93185	−	0.517638i	0.0711607	−	0.0190674i
$738$	0.586988	−	2.19067i	0.0216073	−	0.0806397i
$739$	−17.2583	+	9.96410i	−0.634858	+	0.366535i	−0.782631	−	0.622486i	$-0.786123\pi$
$739$	−17.2583	+	9.96410i	−0.634858	+	0.366535i	0.147773	+	0.989021i	$0.452789\pi$
$740$		0			0
$741$		−	13.0000i		−	0.477567i
$742$	2.63896	+	0.189469i	0.0968792	+	0.00695561i
$743$	5.50455	−	5.50455i	0.201942	−	0.201942i	−0.598889	−	0.800832i	$-0.704391\pi$
$743$	5.50455	−	5.50455i	0.201942	−	0.201942i	0.800832	+	0.598889i	$0.204391\pi$
$744$	6.46410	+	3.73205i	0.236985	+	0.136824i
$745$		0			0
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	−2.68973	−	10.0382i	−0.0984119	−	0.367278i
$748$	5.27792	+	5.27792i	0.192980	+	0.192980i
$749$	−38.7846	+	7.46410i	−1.41716	+	0.272732i
$750$		0			0
$751$	6.92820	−	12.0000i	0.252814	−	0.437886i	−0.711486	−	0.702701i	$-0.751977\pi$
$751$	6.92820	−	12.0000i	0.252814	−	0.437886i	0.964299	+	0.264814i	$0.0853107\pi$
$752$	−1.15539	−	0.309587i	−0.0421329	−	0.0112895i
$753$	7.08965	+	1.89967i	0.258361	+	0.0692277i
$754$	−19.8564	+	34.3923i	−0.723128	+	1.25249i
$755$		0			0
$756$	−0.866025	+	2.50000i	−0.0314970	+	0.0909241i
$757$	26.6670	+	26.6670i	0.969228	+	0.969228i	0.999540	−	0.0303124i	$-0.00965021\pi$
$757$	26.6670	+	26.6670i	0.969228	+	0.969228i	−0.0303124	+	0.999540i	$0.509650\pi$
$758$	1.01669	+	3.79435i	0.0369280	+	0.137817i
$759$	2.96410	+	5.13397i	0.107590	+	0.186351i
$760$		0			0
$761$	41.8923	+	24.1865i	1.51859	+	0.876761i	0.999760	+	0.0218864i	$0.00696721\pi$
$761$	41.8923	+	24.1865i	1.51859	+	0.876761i	0.518834	+	0.854875i	$0.326366\pi$
$762$	−3.53553	+	3.53553i	−0.128079	+	0.128079i
$763$	40.2915	−	19.5588i	1.45865	−	0.708074i
$764$			2.92820i			0.105939i
$765$		0			0
$766$	−19.0359	+	10.9904i	−0.687795	+	0.397099i
$767$	−17.0077	+	63.4737i	−0.614113	+	2.29190i
$768$	−0.965926	+	0.258819i	−0.0348548	+	0.00933933i
$769$	10.8038			0.389597			0.194798	−	0.980843i	$-0.437595\pi$
$769$	10.8038			0.389597			0.194798	+	0.980843i	$0.437595\pi$
$770$		0			0
$771$	−2.39230			−0.0861568
$772$	22.0082	−	5.89709i	0.792094	−	0.212241i
$773$	−9.41404	+	35.1337i	−0.338600	+	1.26367i	0.561314	+	0.827603i	$0.310296\pi$
$773$	−9.41404	+	35.1337i	−0.338600	+	1.26367i	−0.899914	+	0.436068i	$0.856371\pi$
$774$	7.73205	−	4.46410i	0.277923	−	0.160459i
$775$		0			0
$776$		−	2.92820i		−	0.105116i
$777$	−0.744272	+	10.3664i	−0.0267006	+	0.371891i
$778$	−25.9091	+	25.9091i	−0.928887	+	0.928887i
$779$	4.45448	+	2.57180i	0.159598	+	0.0921442i
$780$		0			0
$781$	4.46410	+	7.73205i	0.159738	+	0.276675i
$782$	−11.4524	−	42.7410i	−0.409537	−	1.52841i
$783$	−4.89898	−	4.89898i	−0.175075	−	0.175075i
$784$	4.33013	−	5.50000i	0.154647	−	0.196429i
$785$		0			0
$786$	−2.06218	+	3.57180i	−0.0735554	+	0.127402i
$787$	−2.31079	−	0.619174i	−0.0823707	−	0.0220712i	0.217398	−	0.976083i	$-0.430243\pi$
$787$	−2.31079	−	0.619174i	−0.0823707	−	0.0220712i	−0.299769	+	0.954012i	$0.596910\pi$
$788$	16.2820	+	4.36276i	0.580024	+	0.155417i
$789$	14.9282	−	25.8564i	0.531458	−	0.920512i
$790$		0			0
$791$	25.8564	−	22.3923i	0.919348	−	0.796179i
$792$	−0.707107	−	0.707107i	−0.0251259	−	0.0251259i
$793$	17.0077	+	63.4737i	0.603962	+	2.25402i
$794$	−14.3923	−	24.9282i	−0.510764	−	0.884669i
$795$		0			0
$796$	−10.8564	−	6.26795i	−0.384795	−	0.222162i
$797$	21.1117	−	21.1117i	0.747814	−	0.747814i	−0.226255	−	0.974068i	$-0.572648\pi$
$797$	21.1117	−	21.1117i	0.747814	−	0.747814i	0.974068	+	0.226255i	$0.0726481\pi$
$798$	−4.96833	−	3.36465i	−0.175877	−	0.119107i
$799$			8.92820i			0.315857i
$800$		0			0
$801$	6.00000	−	3.46410i	0.212000	−	0.122398i
$802$	0.499056	−	1.86250i	0.0176223	−	0.0657672i
$803$	−3.86370	+	1.03528i	−0.136347	+	0.0365341i
$804$	2.00000			0.0705346
$805$		0			0
$806$	42.7846			1.50702
$807$	24.4577	−	6.55343i	0.860953	−	0.230692i
$808$	−0.277401	+	1.03528i	−0.00975895	+	0.0364209i
$809$	−22.2058	+	12.8205i	−0.780713	+	0.450745i	−0.836683	−	0.547687i	$-0.815508\pi$
$809$	−22.2058	+	12.8205i	−0.780713	+	0.450745i	0.0559697	+	0.998432i	$0.482175\pi$
$810$		0			0
$811$			2.51666i			0.0883719i	0.999023	+	0.0441860i	$0.0140694\pi$
$811$			2.51666i			0.0883719i	−0.999023	+	0.0441860i	$0.985931\pi$
$812$	8.00481	+	16.4901i	0.280914	+	0.578689i
$813$	5.65685	−	5.65685i	0.198395	−	0.198395i
$814$	−3.40192	−	1.96410i	−0.119237	−	0.0688417i
$815$		0			0
$816$	3.73205	+	6.46410i	0.130648	+	0.226289i
$817$	5.24075	+	19.5588i	0.183351	+	0.684274i
$818$	20.3538	+	20.3538i	0.711654	+	0.711654i
$819$	2.86603	+	14.8923i	0.100147	+	0.520379i
$820$		0			0
$821$	11.9282	−	20.6603i	0.416297	−	0.721048i	−0.579266	−	0.815138i	$-0.696661\pi$
$821$	11.9282	−	20.6603i	0.416297	−	0.721048i	0.995564	+	0.0940904i	$0.0299943\pi$
$822$	18.2832	+	4.89898i	0.637701	+	0.170872i
$823$	−34.4959	−	9.24316i	−1.20245	−	0.322196i	−0.398656	−	0.917101i	$-0.630523\pi$
$823$	−34.4959	−	9.24316i	−1.20245	−	0.322196i	−0.803796	+	0.594904i	$0.797190\pi$
$824$	9.19615	−	15.9282i	0.320363	−	0.554885i
$825$		0			0
$826$	19.8564	+	22.9282i	0.690893	+	0.797774i
$827$	−31.0112	−	31.0112i	−1.07836	−	1.07836i	−0.996656	−	0.0817074i	$-0.973963\pi$
$827$	−31.0112	−	31.0112i	−1.07836	−	1.07836i	−0.0817074	−	0.996656i	$-0.526037\pi$
$828$	1.53433	+	5.72620i	0.0533217	+	0.198999i
$829$	8.26795	+	14.3205i	0.287158	+	0.497372i	0.973130	−	0.230256i	$-0.0739563\pi$
$829$	8.26795	+	14.3205i	0.287158	+	0.497372i	−0.685972	+	0.727628i	$0.740623\pi$
$830$		0			0
$831$	19.0526	+	11.0000i	0.660926	+	0.381586i
$832$	−4.05317	+	4.05317i	−0.140518	+	0.140518i
$833$	−48.0189	−	20.5940i	−1.66376	−	0.713541i
$834$			10.3923i			0.359856i
$835$		0			0
$836$	1.96410	−	1.13397i	0.0679299	−	0.0392193i
$837$	−1.93185	+	7.20977i	−0.0667746	+	0.249206i
$838$	−10.6760	+	2.86061i	−0.368795	+	0.0988182i
$839$	8.53590			0.294692			0.147346	−	0.989085i	$-0.452927\pi$
$839$	8.53590			0.294692			0.147346	+	0.989085i	$0.452927\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	13.3843	−	3.58630i	0.461252	−	0.123592i
$843$	−7.22835	+	26.9766i	−0.248958	+	0.929123i
$844$	−17.1340	+	9.89230i	−0.589776	+	0.340507i
$845$		0			0
$846$		−	1.19615i		−	0.0411246i
$847$	14.8356	−	21.9067i	0.509759	−	0.752723i
$848$	−0.707107	+	0.707107i	−0.0242821	+	0.0242821i
$849$	10.8564	+	6.26795i	0.372591	+	0.215115i
$850$		0			0
$851$	11.6436	+	20.1673i	0.399137	+	0.691326i
$852$	2.31079	+	8.62398i	0.0791663	+	0.295453i
$853$	5.56892	+	5.56892i	0.190676	+	0.190676i	0.795988	−	0.605312i	$-0.206952\pi$
$853$	5.56892	+	5.56892i	0.190676	+	0.190676i	−0.605312	+	0.795988i	$0.706952\pi$
$854$	28.6603	+	9.92820i	0.980734	+	0.339736i
$855$		0			0
$856$	7.46410	−	12.9282i	0.255118	−	0.441877i
$857$	15.4548	+	4.14110i	0.527926	+	0.141457i	0.512931	−	0.858430i	$-0.328560\pi$
$857$	15.4548	+	4.14110i	0.527926	+	0.141457i	0.0149958	+	0.999888i	$0.495227\pi$
$858$	−5.53674	−	1.48356i	−0.189021	−	0.0506480i
$859$	−6.80385	+	11.7846i	−0.232144	+	0.402086i	−0.958439	−	0.285298i	$-0.907907\pi$
$859$	−6.80385	+	11.7846i	−0.232144	+	0.402086i	0.726295	+	0.687384i	$0.241241\pi$
$860$		0			0
$861$	−5.66987	−	1.96410i	−0.193229	−	0.0669364i
$862$	−23.8386	−	23.8386i	−0.811945	−	0.811945i
$863$	10.2598	+	38.2903i	0.349249	+	1.30342i	0.887569	+	0.460675i	$0.152393\pi$
$863$	10.2598	+	38.2903i	0.349249	+	1.30342i	−0.538319	+	0.842741i	$0.680941\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	13.8564	+	8.00000i	0.470860	+	0.271851i
$867$	27.3741	−	27.3741i	0.929673	−	0.929673i
$868$	11.0735	−	16.3514i	0.375858	−	0.555002i
$869$		−	3.07180i		−	0.104204i
$870$		0			0
$871$	9.92820	−	5.73205i	0.336404	−	0.194223i
$872$	−4.38134	+	16.3514i	−0.148371	+	0.553728i
$873$	2.82843	−	0.757875i	0.0957278	−	0.0256502i
$874$	−13.4449			−0.454779
$875$		0			0
$876$	−4.00000			−0.135147
$877$	3.79435	−	1.01669i	0.128126	−	0.0343313i	−0.194186	−	0.980965i	$-0.562207\pi$
$877$	3.79435	−	1.01669i	0.128126	−	0.0343313i	0.322312	+	0.946633i	$0.395540\pi$
$878$	−5.17638	+	19.3185i	−0.174694	+	0.651968i
$879$	1.50000	−	0.866025i	0.0505937	−	0.0292103i
$880$		0			0
$881$		−	36.9090i		−	1.24349i	−0.783218	−	0.621747i	$-0.786423\pi$
$881$		−	36.9090i		−	1.24349i	0.783218	−	0.621747i	$-0.213577\pi$
$882$	6.43331	+	2.75908i	0.216621	+	0.0929029i
$883$	24.6980	−	24.6980i	0.831153	−	0.831153i	−0.156522	−	0.987675i	$-0.550028\pi$
$883$	24.6980	−	24.6980i	0.831153	−	0.831153i	0.987675	+	0.156522i	$0.0500281\pi$
$884$	37.0526	+	21.3923i	1.24621	+	0.719501i
$885$		0			0
$886$	13.9282	+	24.1244i	0.467927	+	0.810474i
$887$	0.896575	+	3.34607i	0.0301041	+	0.112350i	0.979343	−	0.202206i	$-0.0648111\pi$
$887$	0.896575	+	3.34607i	0.0301041	+	0.112350i	−0.949239	+	0.314556i	$0.898144\pi$
$888$	−2.77766	−	2.77766i	−0.0932121	−	0.0932121i
$889$	8.66025	+	10.0000i	0.290456	+	0.335389i
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−9.00292	−	2.41233i	−0.301440	−	0.0807706i
$893$	2.62038	+	0.702128i	0.0876875	+	0.0234958i
$894$	−0.464102	+	0.803848i	−0.0155219	+	0.0268847i
$895$		0			0
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$	24.0280	+	24.0280i	0.802272	+	0.802272i
$898$	3.60488	+	13.4536i	0.120297	+	0.448953i
$899$	25.8564	+	44.7846i	0.862359	+	1.49365i
$900$		0			0
$901$	6.46410	+	3.73205i	0.215350	+	0.124333i
$902$	1.60368	−	1.60368i	0.0533968	−	0.0533968i
$903$	−10.3156	−	21.2504i	−0.343282	−	0.707168i
$904$			12.9282i			0.429986i
$905$		0			0
$906$	−3.33975	+	1.92820i	−0.110956	+	0.0640603i
$907$	0.554803	−	2.07055i	0.0184219	−	0.0687516i	−0.956103	−	0.293031i	$-0.905336\pi$
$907$	0.554803	−	2.07055i	0.0184219	−	0.0687516i	0.974525	+	0.224279i	$0.0720028\pi$
$908$	3.34607	−	0.896575i	0.111043	−	0.0297539i
$909$	−1.07180			−0.0355493
$910$		0			0
$911$	−2.28719			−0.0757779			−0.0378889	−	0.999282i	$-0.512063\pi$
$911$	−2.28719			−0.0757779			−0.0378889	+	0.999282i	$0.512063\pi$
$912$	2.19067	−	0.586988i	0.0725404	−	0.0194371i
$913$	2.68973	−	10.0382i	0.0890170	−	0.332216i
$914$	13.7321	−	7.92820i	0.454216	−	0.262242i
$915$		0			0
$916$		−	2.92820i		−	0.0967506i
$917$	9.03511	+	6.11875i	0.298365	+	0.202059i
$918$	−5.27792	+	5.27792i	−0.174197	+	0.174197i
$919$	−38.7846	−	22.3923i	−1.27939	−	0.738654i	−0.302651	−	0.953102i	$-0.597872\pi$
$919$	−38.7846	−	22.3923i	−1.27939	−	0.738654i	−0.976736	+	0.214448i	$0.931205\pi$
$920$		0			0
$921$	−11.1962	−	19.3923i	−0.368926	−	0.638998i
$922$	10.0010	+	37.3244i	0.329366	+	1.22921i
$923$	36.1875	+	36.1875i	1.19113	+	1.19113i
$924$	−2.00000	+	1.73205i	−0.0657952	+	0.0569803i
$925$		0			0
$926$	−11.3564	+	19.6699i	−0.373195	+	0.646392i
$927$	17.7656	+	4.76028i	0.583499	+	0.156348i
$928$	−6.69213	−	1.79315i	−0.219680	−	0.0588631i
$929$	−8.06218	+	13.9641i	−0.264511	+	0.458147i	−0.967436	−	0.253118i	$-0.918544\pi$
$929$	−8.06218	+	13.9641i	−0.264511	+	0.458147i	0.702924	+	0.711265i	$0.251877\pi$
$930$		0			0
$931$	−9.82051	+	12.4737i	−0.321854	+	0.408810i
$932$	1.31268	+	1.31268i	0.0429982	+	0.0429982i
$933$	−5.31508	−	19.8362i	−0.174008	−	0.649407i
$934$	−3.19615	−	5.53590i	−0.104581	−	0.181140i
$935$		0			0
$936$	−4.96410	−	2.86603i	−0.162257	−	0.0936790i
$937$	6.79367	−	6.79367i	0.221939	−	0.221939i	−0.587375	−	0.809315i	$-0.699839\pi$
$937$	6.79367	−	6.79367i	0.221939	−	0.221939i	0.809315	+	0.587375i	$0.199839\pi$
$938$	0.378937	−	5.27792i	0.0123727	−	0.172330i
$939$			31.1769i			1.01742i
$940$		0			0
$941$	6.67949	−	3.85641i	0.217745	−	0.125715i	−0.387161	−	0.922012i	$-0.626544\pi$
$941$	6.67949	−	3.85641i	0.217745	−	0.125715i	0.604906	+	0.796297i	$0.293211\pi$
$942$	1.20616	−	4.50146i	0.0392989	−	0.146665i
$943$	−12.9867	+	3.47979i	−0.422906	+	0.113317i
$944$	−11.4641			−0.373125
$945$		0			0
$946$	8.92820			0.290281
$947$	−17.5254	+	4.69591i	−0.569498	+	0.152596i	−0.532066	−	0.846703i	$-0.678584\pi$
$947$	−17.5254	+	4.69591i	−0.569498	+	0.152596i	−0.0374316	+	0.999299i	$0.511918\pi$
$948$	0.795040	−	2.96713i	0.0258217	−	0.0963678i
$949$	−19.8564	+	11.4641i	−0.644566	+	0.372140i
$950$		0			0
$951$		−	14.0000i		−	0.453981i
$952$	17.7656	−	8.62398i	0.575786	−	0.279505i
$953$	−32.2223	+	32.2223i	−1.04378	+	1.04378i	−0.0447862	+	0.998997i	$0.514261\pi$
$953$	−32.2223	+	32.2223i	−1.04378	+	1.04378i	−0.998997	+	0.0447862i	$0.985739\pi$
$954$	−0.866025	−	0.500000i	−0.0280386	−	0.0161881i
$955$		0			0
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$	−1.79315	−	6.69213i	−0.0579643	−	0.216326i
$958$	20.5569	+	20.5569i	0.664162	+	0.664162i
$959$	16.3923	−	47.3205i	0.529335	−	1.52806i
$960$		0			0
$961$	12.3564	−	21.4019i	0.398594	−	0.690385i
$962$	−21.7494	−	5.82774i	−0.701230	−	0.187894i
$963$	14.4195	+	3.86370i	0.464663	+	0.124506i
$964$	11.1340	−	19.2846i	0.358601	−	0.621115i
$965$		0			0
$966$	15.4019	−	2.96410i	0.495549	−	0.0953684i
$967$	−21.1117	−	21.1117i	−0.678905	−	0.678905i	0.280847	−	0.959753i	$-0.409385\pi$
$967$	−21.1117	−	21.1117i	−0.678905	−	0.678905i	−0.959753	+	0.280847i	$0.909385\pi$
$968$	2.58819	+	9.65926i	0.0831876	+	0.310460i
$969$	−8.46410	−	14.6603i	−0.271906	−	0.470955i
$970$		0			0
$971$	−38.2128	−	22.0622i	−1.22631	−	0.708009i	−0.260052	−	0.965595i	$-0.583740\pi$
$971$	−38.2128	−	22.0622i	−1.22631	−	0.708009i	−0.966255	+	0.257586i	$0.917073\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	27.4249	+	1.96902i	0.879201	+	0.0631238i
$974$		−	5.85641i		−	0.187651i
$975$		0			0
$976$	−9.92820	+	5.73205i	−0.317794	+	0.183478i
$977$	7.76457	−	28.9778i	0.248411	−	0.927081i	−0.723228	−	0.690610i	$-0.757342\pi$
$977$	7.76457	−	28.9778i	0.248411	−	0.927081i	0.971638	−	0.236472i	$-0.0759910\pi$
$978$	−11.5911	+	3.10583i	−0.370643	+	0.0993134i
$979$	6.92820			0.221426
$980$		0			0
$981$	−16.9282			−0.540476
$982$	11.3137	−	3.03150i	0.361035	−	0.0967390i
$983$	−14.5261	+	54.2120i	−0.463309	+	1.72909i	0.199126	+	0.979974i	$0.436190\pi$
$983$	−14.5261	+	54.2120i	−0.463309	+	1.72909i	−0.662435	+	0.749119i	$0.730477\pi$
$984$	1.96410	−	1.13397i	0.0626133	−	0.0361498i
$985$		0			0
$986$			51.7128i			1.64687i
$987$	−3.15660	−	0.226633i	−0.100476	−	0.00721382i
$988$	9.19239	−	9.19239i	0.292449	−	0.292449i
$989$	−45.8372	−	26.4641i	−1.45754	−	0.841509i
$990$		0			0
$991$	−12.3923	−	21.4641i	−0.393655	−	0.681830i	0.599274	−	0.800544i	$-0.295456\pi$
$991$	−12.3923	−	21.4641i	−0.393655	−	0.681830i	−0.992928	+	0.118714i	$0.962123\pi$
$992$	1.93185	+	7.20977i	0.0613364	+	0.228910i
$993$	18.2325	+	18.2325i	0.578590	+	0.578590i
$994$	23.1962	−	4.46410i	0.735737	−	0.141593i
$995$		0			0
$996$	5.19615	−	9.00000i	0.164646	−	0.285176i
$997$	−3.58630	−	0.960947i	−0.113579	−	0.0304335i	0.201582	−	0.979472i	$-0.435392\pi$
$997$	−3.58630	−	0.960947i	−0.113579	−	0.0304335i	−0.315161	+	0.949038i	$0.602059\pi$
$998$	27.0459	+	7.24693i	0.856124	+	0.229398i
$999$	1.96410	−	3.40192i	0.0621414	−	0.107632i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63896 + 0.189469i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-4.05317 - 4.05317i) q^{13} +(-2.59808 + 0.500000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-7.20977 - 1.93185i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-1.13397 + 1.96410i) q^{19} +(0.866025 - 2.50000i) q^{21} +(0.707107 + 0.707107i) q^{22} +(-1.53433 - 5.72620i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 2.86603i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.38014 - 1.15539i) q^{28} +6.92820i q^{29} +(6.46410 - 3.73205i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.965926 + 0.258819i) q^{33} +7.46410 q^{34} -1.00000 q^{36} +(-3.79435 + 1.01669i) q^{37} +(0.586988 - 2.19067i) q^{38} +(-4.96410 + 2.86603i) q^{39} -2.26795i q^{41} +(-0.189469 + 2.63896i) q^{42} +(6.31319 - 6.31319i) q^{43} +(-0.866025 - 0.500000i) q^{44} +(2.96410 + 5.13397i) q^{46} +(-0.309587 - 1.15539i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(6.92820 + 1.00000i) q^{49} +(-3.73205 + 6.46410i) q^{51} +(-5.53674 - 1.48356i) q^{52} +(-0.965926 - 0.258819i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} +(1.60368 + 1.60368i) q^{57} +(-1.79315 - 6.69213i) q^{58} +(-5.73205 - 9.92820i) q^{59} +(-9.92820 - 5.73205i) q^{61} +(-5.27792 + 5.27792i) q^{62} +(-2.19067 - 1.48356i) q^{63} -1.00000i q^{64} +(0.866025 - 0.500000i) q^{66} +(-0.517638 + 1.93185i) q^{67} +(-7.20977 + 1.93185i) q^{68} -5.92820 q^{69} -8.92820 q^{71} +(0.965926 - 0.258819i) q^{72} +(1.03528 - 3.86370i) q^{73} +(3.40192 - 1.96410i) q^{74} +2.26795i q^{76} +(-1.15539 - 2.38014i) q^{77} +(4.05317 - 4.05317i) q^{78} +(2.66025 + 1.53590i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.586988 + 2.19067i) q^{82} +(7.34847 + 7.34847i) q^{83} +(-0.500000 - 2.59808i) q^{84} +(-4.46410 + 7.73205i) q^{86} +(6.69213 + 1.79315i) q^{87} +(0.965926 + 0.258819i) q^{88} +(-3.46410 + 6.00000i) q^{89} +(-9.92820 - 11.4641i) q^{91} +(-4.19187 - 4.19187i) q^{92} +(-1.93185 - 7.20977i) q^{93} +(0.598076 + 1.03590i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-2.07055 + 2.07055i) q^{97} +(-6.95095 + 0.827225i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} + 4 q^{16} - 16 q^{19} + 4 q^{24} + 12 q^{26} + 24 q^{31} + 32 q^{34} - 8 q^{36} - 12 q^{39} - 4 q^{46} - 16 q^{51} + 4 q^{54} - 16 q^{56} - 32 q^{59} - 24 q^{61} + 8 q^{69} - 16 q^{71} + 48 q^{74} - 48 q^{79} + 4 q^{81} - 4 q^{84} - 8 q^{86} - 24 q^{91} - 16 q^{94}+O(q^{100}) \) 8 * q - 4 * q^11 + 4 * q^16 - 16 * q^19 + 4 * q^24 + 12 * q^26 + 24 * q^31 + 32 * q^34 - 8 * q^36 - 12 * q^39 - 4 * q^46 - 16 * q^51 + 4 * q^54 - 16 * q^56 - 32 * q^59 - 24 * q^61 + 8 * q^69 - 16 * q^71 + 48 * q^74 - 48 * q^79 + 4 * q^81 - 4 * q^84 - 8 * q^86 - 24 * q^91 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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