LMFDB - Embedded newform 637.2.g.d.373.2

Newspace parameters

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.d.263.2

$q$-expansion

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 + 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 + 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205 q^{11} +(-0.366025 + 0.633975i) q^{12} +(1.59808 + 3.23205i) q^{13} +(-0.633975 + 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-2.13397 + 3.69615i) q^{17} +(-2.13397 - 3.69615i) q^{18} -2.00000 q^{19} +(-0.866025 - 1.50000i) q^{20} +(4.09808 + 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +1.26795 q^{24} +(1.00000 + 1.73205i) q^{25} +(-3.46410 + 5.19615i) q^{26} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{29} -2.19615 q^{30} +(-3.09808 - 5.36603i) q^{31} +(-2.59808 + 4.50000i) q^{32} +3.46410 q^{33} -7.39230 q^{34} +(1.23205 - 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} +(-1.73205 - 3.00000i) q^{38} +(1.16987 + 2.36603i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(2.59808 - 4.50000i) q^{41} +(-5.09808 - 8.83013i) q^{43} +(-2.36603 + 4.09808i) q^{44} +(2.13397 - 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} +(-0.464102 + 0.803848i) q^{47} +(1.83013 + 3.16987i) q^{48} +(-1.73205 + 3.00000i) q^{50} +(-1.56218 + 2.70577i) q^{51} +(-3.59808 - 0.232051i) q^{52} +(-1.96410 - 3.40192i) q^{53} +(-3.46410 - 6.00000i) q^{54} +(-4.09808 + 7.09808i) q^{55} -1.46410 q^{57} +5.19615 q^{58} +(5.36603 - 9.29423i) q^{59} +(-0.633975 - 1.09808i) q^{60} +15.1962 q^{61} +(5.36603 - 9.29423i) q^{62} +1.00000 q^{64} +(-6.23205 - 0.401924i) q^{65} +(3.00000 + 5.19615i) q^{66} +4.19615 q^{67} +(-2.13397 - 3.69615i) q^{68} +(-0.464102 - 0.803848i) q^{69} +(-3.00000 - 5.19615i) q^{71} -4.26795 q^{72} +(3.59808 + 6.23205i) q^{73} +(-6.06218 + 10.5000i) q^{74} +(0.732051 + 1.26795i) q^{75} +(1.00000 - 1.73205i) q^{76} +(-2.53590 + 3.80385i) q^{78} +(-2.90192 + 5.02628i) q^{79} -8.66025 q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615 q^{83} +(-3.69615 - 6.40192i) q^{85} +(8.83013 - 15.2942i) q^{86} +(1.09808 - 1.90192i) q^{87} +8.19615 q^{88} +(-0.464102 - 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} -1.60770 q^{94} +(1.73205 - 3.00000i) q^{95} +(-1.90192 + 3.29423i) q^{96} +(-7.19615 - 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9	$ 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{19} + 6 q^{22} - 6 q^{23} + 12 q^{24} + 4 q^{25} - 16 q^{27} + 6 q^{29} + 12 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} - 6 q^{60} + 40 q^{61} + 18 q^{62} + 4 q^{64} - 18 q^{65} + 12 q^{66} - 4 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} - 24 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} - 6 q^{87} + 12 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} - 48 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 8 * q^19 + 6 * q^22 - 6 * q^23 + 12 * q^24 + 4 * q^25 - 16 * q^27 + 6 * q^29 + 12 * q^30 - 2 * q^31 + 12 * q^34 - 2 * q^36 + 14 * q^37 + 22 * q^39 - 6 * q^40 - 10 * q^43 - 6 * q^44 + 12 * q^45 - 6 * q^46 + 12 * q^47 - 10 * q^48 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 - 6 * q^60 + 40 * q^61 + 18 * q^62 + 4 * q^64 - 18 * q^65 + 12 * q^66 - 4 * q^67 - 12 * q^68 + 12 * q^69 - 12 * q^71 - 24 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 - 24 * q^78 - 22 * q^79 + 4 * q^81 + 36 * q^82 - 12 * q^83 + 6 * q^85 + 18 * q^86 - 6 * q^87 + 12 * q^88 + 12 * q^89 - 12 * q^90 + 12 * q^92 - 16 * q^93 - 48 * q^94 - 18 * q^96 - 8 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$	0.732051			0.422650			0.211325	−	0.977416i	$-0.432222\pi$
$3$	0.732051			0.422650			0.211325	+	0.977416i	$0.432222\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	−0.992085	−	0.125567i	$-0.959925\pi$
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	0.604787	+	0.796387i	$0.293258\pi$
$6$	0.633975	+	1.09808i	0.258819	+	0.448288i
$7$		0			0
$7$		0			0
$8$	1.73205			0.612372
$9$	−2.46410			−0.821367
$10$	−3.00000			−0.948683
$11$	4.73205			1.42677			0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205			1.42677			0.713384	+	0.700774i	$0.247162\pi$
$12$	−0.366025	+	0.633975i	−0.105662	+	0.183013i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$14$		0			0
$15$	−0.633975	+	1.09808i	−0.163692	+	0.283522i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−2.13397	+	3.69615i	−0.517565	+	0.896449i	0.482227	+	0.876046i	$0.339828\pi$
$17$	−2.13397	+	3.69615i	−0.517565	+	0.896449i	−0.999792	+	0.0204023i	$0.993505\pi$
$18$	−2.13397	−	3.69615i	−0.502983	−	0.871191i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	−0.866025	−	1.50000i	−0.193649	−	0.335410i
$21$		0			0
$22$	4.09808	+	7.09808i	0.873713	+	1.51331i
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$	1.26795			0.258819
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	−3.46410	+	5.19615i	−0.679366	+	1.01905i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	−2.19615			−0.400961
$31$	−3.09808	−	5.36603i	−0.556431	−	0.963767i	−0.997791	−	0.0664364i	$-0.978837\pi$
$31$	−3.09808	−	5.36603i	−0.556431	−	0.963767i	0.441360	−	0.897330i	$-0.354496\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$	3.46410			0.603023
$34$	−7.39230			−1.26777
$35$		0			0
$36$	1.23205	−	2.13397i	0.205342	−	0.355662i
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−1.73205	−	3.00000i	−0.280976	−	0.486664i
$39$	1.16987	+	2.36603i	0.187330	+	0.378867i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	2.59808	−	4.50000i	0.405751	−	0.702782i	−0.588657	−	0.808383i	$-0.700343\pi$
$41$	2.59808	−	4.50000i	0.405751	−	0.702782i	0.994409	+	0.105601i	$0.0336766\pi$
$42$		0			0
$43$	−5.09808	−	8.83013i	−0.777449	−	1.34658i	−0.933408	−	0.358818i	$-0.883180\pi$
$43$	−5.09808	−	8.83013i	−0.777449	−	1.34658i	0.155958	−	0.987764i	$-0.450153\pi$
$44$	−2.36603	+	4.09808i	−0.356692	+	0.617808i
$45$	2.13397	−	3.69615i	0.318114	−	0.550990i
$46$	1.09808	−	1.90192i	0.161903	−	0.280423i
$47$	−0.464102	+	0.803848i	−0.0676962	+	0.117253i	−0.897887	−	0.440226i	$-0.854898\pi$
$47$	−0.464102	+	0.803848i	−0.0676962	+	0.117253i	0.830191	+	0.557480i	$0.188232\pi$
$48$	1.83013	+	3.16987i	0.264156	+	0.457532i
$49$		0			0
$50$	−1.73205	+	3.00000i	−0.244949	+	0.424264i
$51$	−1.56218	+	2.70577i	−0.218749	+	0.378884i
$52$	−3.59808	−	0.232051i	−0.498963	−	0.0321797i
$53$	−1.96410	−	3.40192i	−0.269790	−	0.467290i	0.699017	−	0.715105i	$-0.253621\pi$
$53$	−1.96410	−	3.40192i	−0.269790	−	0.467290i	−0.968808	+	0.247814i	$0.920288\pi$
$54$	−3.46410	−	6.00000i	−0.471405	−	0.816497i
$55$	−4.09808	+	7.09808i	−0.552584	+	0.957104i
$56$		0			0
$57$	−1.46410			−0.193925
$58$	5.19615			0.682288
$59$	5.36603	−	9.29423i	0.698597	−	1.21001i	−0.270356	−	0.962760i	$-0.587141\pi$
$59$	5.36603	−	9.29423i	0.698597	−	1.21001i	0.968953	−	0.247245i	$-0.0795253\pi$
$60$	−0.633975	−	1.09808i	−0.0818458	−	0.141761i
$61$	15.1962			1.94567			0.972834	−	0.231504i	$-0.0743646\pi$
$61$	15.1962			1.94567			0.972834	+	0.231504i	$0.0743646\pi$
$62$	5.36603	−	9.29423i	0.681486	−	1.18037i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.23205	−	0.401924i	−0.772991	−	0.0498525i
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	4.19615			0.512642			0.256321	−	0.966592i	$-0.417490\pi$
$67$	4.19615			0.512642			0.256321	+	0.966592i	$0.417490\pi$
$68$	−2.13397	−	3.69615i	−0.258782	−	0.448224i
$69$	−0.464102	−	0.803848i	−0.0558713	−	0.0967719i
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−4.26795			−0.502983
$73$	3.59808	+	6.23205i	0.421123	+	0.729406i	0.996050	−	0.0887986i	$-0.0283027\pi$
$73$	3.59808	+	6.23205i	0.421123	+	0.729406i	−0.574927	+	0.818205i	$0.694969\pi$
$74$	−6.06218	+	10.5000i	−0.704714	+	1.22060i
$75$	0.732051	+	1.26795i	0.0845299	+	0.146410i
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$		0			0
$78$	−2.53590	+	3.80385i	−0.287134	+	0.430701i
$79$	−2.90192	+	5.02628i	−0.326492	+	0.565501i	−0.981813	−	0.189850i	$-0.939200\pi$
$79$	−2.90192	+	5.02628i	−0.326492	+	0.565501i	0.655321	+	0.755350i	$0.272533\pi$
$80$	−8.66025			−0.968246
$81$	4.46410			0.496011
$82$	9.00000			0.993884
$83$	−8.19615			−0.899645			−0.449822	−	0.893118i	$-0.648513\pi$
$83$	−8.19615			−0.899645			−0.449822	+	0.893118i	$0.648513\pi$
$84$		0			0
$85$	−3.69615	−	6.40192i	−0.400904	−	0.694386i
$86$	8.83013	−	15.2942i	0.952177	−	1.64922i
$87$	1.09808	−	1.90192i	0.117726	−	0.203908i
$88$	8.19615			0.873713
$89$	−0.464102	−	0.803848i	−0.0491947	−	0.0852077i	0.840379	−	0.541998i	$-0.182332\pi$
$89$	−0.464102	−	0.803848i	−0.0491947	−	0.0852077i	−0.889574	+	0.456791i	$0.848999\pi$
$90$	7.39230			0.779217
$91$		0			0
$92$	1.26795			0.132193
$93$	−2.26795	−	3.92820i	−0.235175	−	0.407336i
$94$	−1.60770			−0.165821
$95$	1.73205	−	3.00000i	0.177705	−	0.307794i
$96$	−1.90192	+	3.29423i	−0.194114	+	0.336216i
$97$	−7.19615	−	12.4641i	−0.730659	−	1.26554i	−0.956602	−	0.291397i	$-0.905880\pi$
$97$	−7.19615	−	12.4641i	−0.730659	−	1.26554i	0.225944	−	0.974140i	$-0.427454\pi$
$98$		0			0
$99$	−11.6603			−1.17190
$100$	−2.00000			−0.200000
$101$	4.26795			0.424677			0.212338	−	0.977196i	$-0.431892\pi$
$101$	4.26795			0.424677			0.212338	+	0.977196i	$0.431892\pi$
$102$	−5.41154			−0.535823
$103$	3.19615	−	5.53590i	0.314926	−	0.545468i	−0.664496	−	0.747292i	$-0.731354\pi$
$103$	3.19615	−	5.53590i	0.314926	−	0.545468i	0.979422	+	0.201824i	$0.0646869\pi$
$104$	2.76795	+	5.59808i	0.271420	+	0.548937i
$105$		0			0
$106$	3.40192	−	5.89230i	0.330424	−	0.572311i
$107$	−9.92820	−	17.1962i	−0.959796	−	1.66241i	−0.722991	−	0.690858i	$-0.757233\pi$
$107$	−9.92820	−	17.1962i	−0.959796	−	1.66241i	−0.236805	−	0.971557i	$-0.576100\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	−6.19615	−	10.7321i	−0.593484	−	1.02794i	−0.993759	−	0.111549i	$-0.964419\pi$
$109$	−6.19615	−	10.7321i	−0.593484	−	1.02794i	0.400275	−	0.916395i	$-0.368915\pi$
$110$	−14.1962			−1.35355
$111$	2.56218	+	4.43782i	0.243191	+	0.421219i
$112$		0			0
$113$	3.69615	+	6.40192i	0.347705	+	0.602242i	0.985841	−	0.167681i	$-0.0536278\pi$
$113$	3.69615	+	6.40192i	0.347705	+	0.602242i	−0.638137	+	0.769923i	$0.720294\pi$
$114$	−1.26795	−	2.19615i	−0.118754	−	0.205689i
$115$	2.19615			0.204792
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	−3.93782	−	7.96410i	−0.364052	−	0.736281i
$118$	18.5885			1.71121
$119$		0			0
$120$	−1.09808	+	1.90192i	−0.100240	+	0.173621i
$121$	11.3923			1.03566
$122$	13.1603	+	22.7942i	1.19147	+	2.06369i
$123$	1.90192	−	3.29423i	0.171491	−	0.297031i
$124$	6.19615			0.556431
$125$	−12.1244			−1.08444
$126$		0			0
$127$	1.19615	−	2.07180i	0.106141	−	0.183842i	−0.808063	−	0.589097i	$-0.799484\pi$
$127$	1.19615	−	2.07180i	0.106141	−	0.183842i	0.914204	+	0.405254i	$0.132817\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$	−3.73205	−	6.46410i	−0.328589	−	0.569132i
$130$	−4.79423	−	9.69615i	−0.420482	−	0.850409i
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	−0.780387	−	0.625297i	$-0.784978\pi$
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	0.931717	+	0.363186i	$0.118311\pi$
$132$	−1.73205	+	3.00000i	−0.150756	+	0.261116i
$133$		0			0
$134$	3.63397	+	6.29423i	0.313928	+	0.543739i
$135$	3.46410	−	6.00000i	0.298142	−	0.516398i
$136$	−3.69615	+	6.40192i	−0.316942	+	0.548960i
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.165200	+	0.986260i	$0.552827\pi$
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.771526	+	0.636198i	$0.780506\pi$
$138$	0.803848	−	1.39230i	0.0684280	−	0.118521i
$139$	10.2942	+	17.8301i	0.873145	+	1.51233i	0.858726	+	0.512436i	$0.171257\pi$
$139$	10.2942	+	17.8301i	0.873145	+	1.51233i	0.0144194	+	0.999896i	$0.495410\pi$
$140$		0			0
$141$	−0.339746	+	0.588457i	−0.0286118	+	0.0495570i
$142$	5.19615	−	9.00000i	0.436051	−	0.755263i
$143$	7.56218	+	15.2942i	0.632381	+	1.27897i
$144$	−6.16025	−	10.6699i	−0.513355	−	0.889156i
$145$	2.59808	+	4.50000i	0.215758	+	0.373705i
$146$	−6.23205	+	10.7942i	−0.515768	+	0.893337i
$147$		0			0
$148$	−7.00000			−0.575396
$149$	0.464102			0.0380207			0.0190103	−	0.999819i	$-0.493948\pi$
$149$	0.464102			0.0380207			0.0190103	+	0.999819i	$0.493948\pi$
$150$	−1.26795	+	2.19615i	−0.103528	+	0.179315i
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$	−3.46410			−0.280976
$153$	5.25833	−	9.10770i	0.425111	−	0.736314i
$154$		0			0
$155$	10.7321			0.862019
$156$	−2.63397	−	0.169873i	−0.210887	−	0.0136007i
$157$	−4.59808	−	7.96410i	−0.366966	−	0.635605i	0.622123	−	0.782919i	$-0.286270\pi$
$157$	−4.59808	−	7.96410i	−0.366966	−	0.635605i	−0.989090	+	0.147315i	$0.952937\pi$
$158$	−10.0526			−0.799739
$159$	−1.43782	−	2.49038i	−0.114027	−	0.197500i
$160$	−4.50000	−	7.79423i	−0.355756	−	0.616188i
$161$		0			0
$162$	3.86603	+	6.69615i	0.303744	+	0.526099i
$163$	5.80385			0.454592			0.227296	−	0.973826i	$-0.427011\pi$
$163$	5.80385			0.454592			0.227296	+	0.973826i	$0.427011\pi$
$164$	2.59808	+	4.50000i	0.202876	+	0.351391i
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−7.09808	−	12.2942i	−0.550918	−	0.954217i
$167$	12.2942	−	21.2942i	0.951356	−	1.64780i	0.208861	−	0.977945i	$-0.433024\pi$
$167$	12.2942	−	21.2942i	0.951356	−	1.64780i	0.742495	−	0.669852i	$-0.233642\pi$
$168$		0			0
$169$	−7.89230	+	10.3301i	−0.607100	+	0.794625i
$170$	6.40192	−	11.0885i	0.491005	−	0.850446i
$171$	4.92820			0.376869
$172$	10.1962			0.777449
$173$	−15.4641			−1.17571			−0.587857	−	0.808965i	$-0.700028\pi$
$173$	−15.4641			−1.17571			−0.587857	+	0.808965i	$0.700028\pi$
$174$	3.80385			0.288369
$175$		0			0
$176$	11.8301	+	20.4904i	0.891729	+	1.54452i
$177$	3.92820	−	6.80385i	0.295262	−	0.511409i
$178$	0.803848	−	1.39230i	0.0602509	−	0.104358i
$179$	6.92820			0.517838			0.258919	−	0.965899i	$-0.416634\pi$
$179$	6.92820			0.517838			0.258919	+	0.965899i	$0.416634\pi$
$180$	2.13397	+	3.69615i	0.159057	+	0.275495i
$181$	25.5885			1.90198			0.950988	−	0.309229i	$-0.100071\pi$
$181$	25.5885			1.90198			0.950988	+	0.309229i	$0.100071\pi$
$182$		0			0
$183$	11.1244			0.822336
$184$	−1.09808	−	1.90192i	−0.0809513	−	0.140212i
$185$	−12.1244			−0.891400
$186$	3.92820	−	6.80385i	0.288030	−	0.498882i
$187$	−10.0981	+	17.4904i	−0.738444	+	1.27902i
$188$	−0.464102	−	0.803848i	−0.0338481	−	0.0586266i
$189$		0			0
$190$	6.00000			0.435286
$191$	1.26795			0.0917456			0.0458728	−	0.998947i	$-0.485393\pi$
$191$	1.26795			0.0917456			0.0458728	+	0.998947i	$0.485393\pi$
$192$	0.732051			0.0528312
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	12.4641	−	21.5885i	0.894870	−	1.54996i
$195$	−4.56218	−	0.294229i	−0.326704	−	0.0210702i
$196$		0			0
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$	−10.0981	−	17.4904i	−0.717639	−	1.24299i
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$	1.73205	+	3.00000i	0.122474	+	0.212132i
$201$	3.07180			0.216668
$202$	3.69615	+	6.40192i	0.260060	+	0.450438i
$203$		0			0
$204$	−1.56218	−	2.70577i	−0.109374	−	0.189442i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	11.0718			0.771409
$207$	1.56218	+	2.70577i	0.108579	+	0.188064i
$208$	−10.0000	+	15.0000i	−0.693375	+	1.04006i
$209$	−9.46410			−0.654646
$210$		0			0
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	−0.576111	−	0.817371i	$-0.695430\pi$
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	0.995920	+	0.0902411i	$0.0287638\pi$
$212$	3.92820			0.269790
$213$	−2.19615	−	3.80385i	−0.150478	−	0.260635i
$214$	17.1962	−	29.7846i	1.17550	−	2.03603i
$215$	17.6603			1.20442
$216$	−6.92820			−0.471405
$217$		0			0
$218$	10.7321	−	18.5885i	0.726866	−	1.25897i
$219$	2.63397	+	4.56218i	0.177988	+	0.308283i
$220$	−4.09808	−	7.09808i	−0.276292	−	0.478552i
$221$	−15.3564	−	0.990381i	−1.03298	−	0.0666202i
$222$	−4.43782	+	7.68653i	−0.297847	+	0.515886i
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$		0			0
$225$	−2.46410	−	4.26795i	−0.164273	−	0.284530i
$226$	−6.40192	+	11.0885i	−0.425850	+	0.737593i
$227$	−5.83013	+	10.0981i	−0.386959	+	0.670233i	−0.992039	−	0.125932i	$-0.959808\pi$
$227$	−5.83013	+	10.0981i	−0.386959	+	0.670233i	0.605080	+	0.796165i	$0.293141\pi$
$228$	0.732051	−	1.26795i	0.0484812	−	0.0839720i
$229$	3.19615	−	5.53590i	0.211208	−	0.365822i	−0.740885	−	0.671632i	$-0.765594\pi$
$229$	3.19615	−	5.53590i	0.211208	−	0.365822i	0.952093	+	0.305809i	$0.0989270\pi$
$230$	1.90192	+	3.29423i	0.125409	+	0.217215i
$231$		0			0
$232$	2.59808	−	4.50000i	0.170572	−	0.295439i
$233$	−12.9282	+	22.3923i	−0.846955	+	1.46697i	0.0369580	+	0.999317i	$0.488233\pi$
$233$	−12.9282	+	22.3923i	−0.846955	+	1.46697i	−0.883913	+	0.467652i	$0.845100\pi$
$234$	8.53590	−	12.8038i	0.558009	−	0.837014i
$235$	−0.803848	−	1.39230i	−0.0524372	−	0.0908240i
$236$	5.36603	+	9.29423i	0.349299	+	0.605003i
$237$	−2.12436	+	3.67949i	−0.137992	+	0.239009i
$238$		0			0
$239$	−26.1962			−1.69449			−0.847244	−	0.531204i	$-0.821740\pi$
$239$	−26.1962			−1.69449			−0.847244	+	0.531204i	$0.821740\pi$
$240$	−6.33975			−0.409229
$241$	−5.40192	+	9.35641i	−0.347969	+	0.602699i	−0.985888	−	0.167404i	$-0.946462\pi$
$241$	−5.40192	+	9.35641i	−0.347969	+	0.602699i	0.637920	+	0.770103i	$0.279795\pi$
$242$	9.86603	+	17.0885i	0.634212	+	1.09849i
$243$	15.2679			0.979439
$244$	−7.59808	+	13.1603i	−0.486417	+	0.842499i
$245$		0			0
$246$	6.58846			0.420065
$247$	−3.19615	−	6.46410i	−0.203366	−	0.411301i
$248$	−5.36603	−	9.29423i	−0.340743	−	0.590184i
$249$	−6.00000			−0.380235
$250$	−10.5000	−	18.1865i	−0.664078	−	1.15022i
$251$	−11.1962	−	19.3923i	−0.706695	−	1.22403i	−0.966076	−	0.258256i	$-0.916852\pi$
$251$	−11.1962	−	19.3923i	−0.706695	−	1.22403i	0.259382	−	0.965775i	$-0.416481\pi$
$252$		0			0
$253$	−3.00000	−	5.19615i	−0.188608	−	0.326679i
$254$	4.14359			0.259992
$255$	−2.70577	−	4.68653i	−0.169442	−	0.293482i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−9.06218	−	15.6962i	−0.565283	−	0.979099i	−0.997023	−	0.0771011i	$-0.975434\pi$
$257$	−9.06218	−	15.6962i	−0.565283	−	0.979099i	0.431740	−	0.901998i	$-0.357900\pi$
$258$	6.46410	−	11.1962i	0.402437	−	0.697042i
$259$		0			0
$260$	3.46410	−	5.19615i	0.214834	−	0.322252i
$261$	−3.69615	+	6.40192i	−0.228786	+	0.396269i
$262$	6.00000			0.370681
$263$	4.73205			0.291791			0.145895	−	0.989300i	$-0.453394\pi$
$263$	4.73205			0.291791			0.145895	+	0.989300i	$0.453394\pi$
$264$	6.00000			0.369274
$265$	6.80385			0.417957
$266$		0			0
$267$	−0.339746	−	0.588457i	−0.0207921	−	0.0360130i
$268$	−2.09808	+	3.63397i	−0.128160	+	0.221980i
$269$	9.46410	−	16.3923i	0.577036	−	0.999456i	−0.418781	−	0.908087i	$-0.637542\pi$
$269$	9.46410	−	16.3923i	0.577036	−	0.999456i	0.995817	−	0.0913690i	$-0.0291243\pi$
$270$	12.0000			0.730297
$271$	8.09808	+	14.0263i	0.491923	+	0.852036i	0.999957	−	0.00930143i	$-0.00296078\pi$
$271$	8.09808	+	14.0263i	0.491923	+	0.852036i	−0.508034	+	0.861337i	$0.669627\pi$
$272$	−21.3397			−1.29391
$273$		0			0
$274$	−37.9808			−2.29450
$275$	4.73205	+	8.19615i	0.285353	+	0.494247i
$276$	0.928203			0.0558713
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$	−17.8301	+	30.8827i	−1.06938	+	1.85222i
$279$	7.63397	+	13.2224i	0.457034	+	0.791606i
$280$		0			0
$281$	−7.39230			−0.440988			−0.220494	−	0.975388i	$-0.570767\pi$
$281$	−7.39230			−0.440988			−0.220494	+	0.975388i	$0.570767\pi$
$282$	−1.17691			−0.0700842
$283$	0.196152			0.0116601			0.00583003	−	0.999983i	$-0.498144\pi$
$283$	0.196152			0.0116601			0.00583003	+	0.999983i	$0.498144\pi$
$284$	6.00000			0.356034
$285$	1.26795	−	2.19615i	0.0751068	−	0.130089i
$286$	−16.3923	+	24.5885i	−0.969297	+	1.45395i
$287$		0			0
$288$	6.40192	−	11.0885i	0.377237	−	0.653394i
$289$	−0.607695	−	1.05256i	−0.0357468	−	0.0619152i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	−5.26795	−	9.12436i	−0.308813	−	0.534879i
$292$	−7.19615			−0.421123
$293$	−5.59808	−	9.69615i	−0.327043	−	0.566455i	0.654881	−	0.755732i	$-0.272719\pi$
$293$	−5.59808	−	9.69615i	−0.327043	−	0.566455i	−0.981924	+	0.189277i	$0.939386\pi$
$294$		0			0
$295$	9.29423	+	16.0981i	0.541131	+	0.937266i
$296$	6.06218	+	10.5000i	0.352357	+	0.610300i
$297$	−18.9282			−1.09833
$298$	0.401924	+	0.696152i	0.0232828	+	0.0403270i
$299$	2.53590	−	3.80385i	0.146655	−	0.219982i
$300$	−1.46410			−0.0845299
$301$		0			0
$302$	1.73205	−	3.00000i	0.0996683	−	0.172631i
$303$	3.12436			0.179490
$304$	−5.00000	−	8.66025i	−0.286770	−	0.496700i
$305$	−13.1603	+	22.7942i	−0.753554	+	1.30519i
$306$	18.2154			1.04130
$307$	−26.5885			−1.51748			−0.758742	−	0.651392i	$-0.774186\pi$
$307$	−26.5885			−1.51748			−0.758742	+	0.651392i	$0.774186\pi$
$308$		0			0
$309$	2.33975	−	4.05256i	0.133103	−	0.230542i
$310$	9.29423	+	16.0981i	0.527877	+	0.914309i
$311$	2.36603	+	4.09808i	0.134165	+	0.232381i	0.925278	−	0.379289i	$-0.123831\pi$
$311$	2.36603	+	4.09808i	0.134165	+	0.232381i	−0.791113	+	0.611670i	$0.790498\pi$
$312$	2.02628	+	4.09808i	0.114715	+	0.232008i
$313$	−6.39230	+	11.0718i	−0.361314	+	0.625815i	−0.988177	−	0.153315i	$-0.951005\pi$
$313$	−6.39230	+	11.0718i	−0.361314	+	0.625815i	0.626863	+	0.779129i	$0.284339\pi$
$314$	7.96410	−	13.7942i	0.449440	−	0.778453i
$315$		0			0
$316$	−2.90192	−	5.02628i	−0.163246	−	0.282750i
$317$	−0.232051	+	0.401924i	−0.0130333	+	0.0225743i	−0.872468	−	0.488670i	$-0.837482\pi$
$317$	−0.232051	+	0.401924i	−0.0130333	+	0.0225743i	0.859435	+	0.511245i	$0.170815\pi$
$318$	2.49038	−	4.31347i	0.139654	−	0.241887i
$319$	7.09808	−	12.2942i	0.397416	−	0.688345i
$320$	−0.866025	+	1.50000i	−0.0484123	+	0.0838525i
$321$	−7.26795	−	12.5885i	−0.405657	−	0.702619i
$322$		0			0
$323$	4.26795	−	7.39230i	0.237475	−	0.411319i
$324$	−2.23205	+	3.86603i	−0.124003	+	0.214779i
$325$	−4.00000	+	6.00000i	−0.221880	+	0.332820i
$326$	5.02628	+	8.70577i	0.278380	+	0.482168i
$327$	−4.53590	−	7.85641i	−0.250836	−	0.434460i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$	−10.3923			−0.572078
$331$	−26.9808			−1.48300			−0.741498	−	0.670955i	$-0.765885\pi$
$331$	−26.9808			−1.48300			−0.741498	+	0.670955i	$0.765885\pi$
$332$	4.09808	−	7.09808i	0.224911	−	0.389558i
$333$	−8.62436	−	14.9378i	−0.472612	−	0.818588i
$334$	42.5885			2.33034
$335$	−3.63397	+	6.29423i	−0.198545	+	0.343890i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	−22.3301	−	2.89230i	−1.21460	−	0.157321i
$339$	2.70577	+	4.68653i	0.146957	+	0.254538i
$340$	7.39230			0.400904
$341$	−14.6603	−	25.3923i	−0.793897	−	1.37507i
$342$	4.26795	+	7.39230i	0.230784	+	0.399730i
$343$		0			0
$344$	−8.83013	−	15.2942i	−0.476089	−	0.824610i
$345$	1.60770			0.0865554
$346$	−13.3923	−	23.1962i	−0.719975	−	1.24703i
$347$	−5.36603	+	9.29423i	−0.288063	+	0.498940i	−0.973347	−	0.229336i	$-0.926345\pi$
$347$	−5.36603	+	9.29423i	−0.288063	+	0.498940i	0.685284	+	0.728276i	$0.259678\pi$
$348$	1.09808	+	1.90192i	0.0588631	+	0.101954i
$349$	8.39230	−	14.5359i	0.449230	−	0.778089i	−0.549106	−	0.835753i	$-0.685032\pi$
$349$	8.39230	−	14.5359i	0.449230	−	0.778089i	0.998336	+	0.0576637i	$0.0183651\pi$
$350$		0			0
$351$	−6.39230	−	12.9282i	−0.341196	−	0.690056i
$352$	−12.2942	+	21.2942i	−0.655285	+	1.13499i
$353$	−3.33975			−0.177757			−0.0888784	−	0.996042i	$-0.528328\pi$
$353$	−3.33975			−0.177757			−0.0888784	+	0.996042i	$0.528328\pi$
$354$	13.6077			0.723241
$355$	10.3923			0.551566
$356$	0.928203			0.0491947
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−2.53590	+	4.39230i	−0.133840	+	0.231817i	−0.925154	−	0.379593i	$-0.876064\pi$
$359$	−2.53590	+	4.39230i	−0.133840	+	0.231817i	0.791314	+	0.611410i	$0.209397\pi$
$360$	3.69615	−	6.40192i	0.194804	−	0.337411i
$361$	−15.0000			−0.789474
$362$	22.1603	+	38.3827i	1.16472	+	2.01735i
$363$	8.33975			0.437723
$364$		0			0
$365$	−12.4641			−0.652401
$366$	9.63397	+	16.6865i	0.503576	+	0.872219i
$367$	6.19615			0.323437			0.161718	−	0.986837i	$-0.448296\pi$
$367$	6.19615			0.323437			0.161718	+	0.986837i	$0.448296\pi$
$368$	3.16987	−	5.49038i	0.165241	−	0.286206i
$369$	−6.40192	+	11.0885i	−0.333271	+	0.577242i
$370$	−10.5000	−	18.1865i	−0.545869	−	0.945473i
$371$		0			0
$372$	4.53590			0.235175
$373$	9.39230			0.486315			0.243158	−	0.969987i	$-0.421817\pi$
$373$	9.39230			0.486315			0.243158	+	0.969987i	$0.421817\pi$
$374$	−34.9808			−1.80881
$375$	−8.87564			−0.458336
$376$	−0.803848	+	1.39230i	−0.0414553	+	0.0718026i
$377$	10.7942	+	0.696152i	0.555931	+	0.0358537i
$378$		0			0
$379$	2.29423	−	3.97372i	0.117847	−	0.204116i	−0.801067	−	0.598574i	$-0.795734\pi$
$379$	2.29423	−	3.97372i	0.117847	−	0.204116i	0.918914	+	0.394458i	$0.129068\pi$
$380$	1.73205	+	3.00000i	0.0888523	+	0.153897i
$381$	0.875644	−	1.51666i	0.0448606	−	0.0777009i
$382$	1.09808	+	1.90192i	0.0561825	+	0.0973109i
$383$	−5.66025			−0.289225			−0.144613	−	0.989488i	$-0.546194\pi$
$383$	−5.66025			−0.289225			−0.144613	+	0.989488i	$0.546194\pi$
$384$	4.43782	+	7.68653i	0.226467	+	0.392252i
$385$		0			0
$386$	4.33013	+	7.50000i	0.220398	+	0.381740i
$387$	12.5622	+	21.7583i	0.638571	+	1.10604i
$388$	14.3923			0.730659
$389$	15.2321	+	26.3827i	0.772296	+	1.33766i	0.936302	+	0.351196i	$0.114225\pi$
$389$	15.2321	+	26.3827i	0.772296	+	1.33766i	−0.164006	+	0.986459i	$0.552442\pi$
$390$	−3.50962	−	7.09808i	−0.177716	−	0.359425i
$391$	5.41154			0.273673
$392$		0			0
$393$	1.26795	−	2.19615i	0.0639596	−	0.110781i
$394$	−20.7846			−1.04711
$395$	−5.02628	−	8.70577i	−0.252900	−	0.438035i
$396$	5.83013	−	10.0981i	0.292975	−	0.507447i
$397$	−22.7846			−1.14353			−0.571763	−	0.820419i	$-0.693740\pi$
$397$	−22.7846			−1.14353			−0.571763	+	0.820419i	$0.693740\pi$
$398$	3.46410			0.173640
$399$		0			0
$400$	−5.00000	+	8.66025i	−0.250000	+	0.433013i
$401$	−8.42820	−	14.5981i	−0.420884	−	0.728993i	0.575142	−	0.818054i	$-0.304947\pi$
$401$	−8.42820	−	14.5981i	−0.420884	−	0.728993i	−0.996026	+	0.0890606i	$0.971614\pi$
$402$	2.66025	+	4.60770i	0.132681	+	0.229811i
$403$	12.3923	−	18.5885i	0.617305	−	0.925957i
$404$	−2.13397	+	3.69615i	−0.106169	+	0.183890i
$405$	−3.86603	+	6.69615i	−0.192104	+	0.332734i
$406$		0			0
$407$	16.5622	+	28.6865i	0.820957	+	1.42194i
$408$	−2.70577	+	4.68653i	−0.133956	+	0.232018i
$409$	−13.5981	+	23.5526i	−0.672382	+	1.16460i	0.304845	+	0.952402i	$0.401395\pi$
$409$	−13.5981	+	23.5526i	−0.672382	+	1.16460i	−0.977227	+	0.212197i	$0.931938\pi$
$410$	−7.79423	+	13.5000i	−0.384930	+	0.666717i
$411$	−8.02628	+	13.9019i	−0.395907	+	0.685731i
$412$	3.19615	+	5.53590i	0.157463	+	0.272734i
$413$		0			0
$414$	−2.70577	+	4.68653i	−0.132981	+	0.230331i
$415$	7.09808	−	12.2942i	0.348431	−	0.603500i
$416$	−18.6962	−	1.20577i	−0.916654	−	0.0591178i
$417$	7.53590	+	13.0526i	0.369035	+	0.639187i
$418$	−8.19615	−	14.1962i	−0.400887	−	0.694357i
$419$	−10.9019	+	18.8827i	−0.532594	+	0.922480i	0.466682	+	0.884425i	$0.345449\pi$
$419$	−10.9019	+	18.8827i	−0.532594	+	0.922480i	−0.999276	+	0.0380543i	$0.987884\pi$
$420$		0			0
$421$	30.1769			1.47073			0.735366	−	0.677670i	$-0.237010\pi$
$421$	30.1769			1.47073			0.735366	+	0.677670i	$0.237010\pi$
$422$	21.1244			1.02832
$423$	1.14359	−	1.98076i	0.0556034	−	0.0963079i
$424$	−3.40192	−	5.89230i	−0.165212	−	0.286156i
$425$	−8.53590			−0.414052
$426$	3.80385	−	6.58846i	0.184297	−	0.319212i
$427$		0			0
$428$	19.8564			0.959796
$429$	5.53590	+	11.1962i	0.267276	+	0.540555i
$430$	15.2942	+	26.4904i	0.737553	+	1.27748i
$431$	35.3205			1.70133			0.850665	−	0.525709i	$-0.176200\pi$
$431$	35.3205			1.70133			0.850665	+	0.525709i	$0.176200\pi$
$432$	−10.0000	−	17.3205i	−0.481125	−	0.833333i
$433$	8.79423	+	15.2321i	0.422624	+	0.732006i	0.996195	−	0.0871498i	$-0.0277759\pi$
$433$	8.79423	+	15.2321i	0.422624	+	0.732006i	−0.573572	+	0.819155i	$0.694443\pi$
$434$		0			0
$435$	1.90192	+	3.29423i	0.0911903	+	0.157946i
$436$	12.3923			0.593484
$437$	1.26795	+	2.19615i	0.0606542	+	0.105056i
$438$	−4.56218	+	7.90192i	−0.217989	+	0.377569i
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	0.597349	−	0.801982i	$-0.296221\pi$
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	−0.993211	+	0.116329i	$0.962887\pi$
$440$	−7.09808	+	12.2942i	−0.338388	+	0.586104i
$441$		0			0
$442$	−11.8135	−	23.8923i	−0.561909	−	1.13644i
$443$	5.66025	−	9.80385i	0.268927	−	0.465795i	−0.699658	−	0.714478i	$-0.746664\pi$
$443$	5.66025	−	9.80385i	0.268927	−	0.465795i	0.968585	+	0.248683i	$0.0799977\pi$
$444$	−5.12436			−0.243191
$445$	1.60770			0.0762121
$446$	−17.3205			−0.820150
$447$	0.339746			0.0160694
$448$		0			0
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	0.972161	−	0.234315i	$-0.0752847\pi$
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	−0.689003	+	0.724758i	$0.741951\pi$
$450$	4.26795	−	7.39230i	0.201193	−	0.348477i
$451$	12.2942	−	21.2942i	0.578913	−	1.00271i
$452$	−7.39230			−0.347705
$453$	−0.732051	−	1.26795i	−0.0343947	−	0.0595734i
$454$	−20.1962			−0.947852
$455$		0			0
$456$	−2.53590			−0.118754
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$	11.0718			0.517351
$459$	8.53590	−	14.7846i	0.398422	−	0.690086i
$460$	−1.09808	+	1.90192i	−0.0511981	+	0.0886777i
$461$	7.79423	+	13.5000i	0.363013	+	0.628758i	0.988455	−	0.151513i	$-0.0484146\pi$
$461$	7.79423	+	13.5000i	0.363013	+	0.628758i	−0.625442	+	0.780271i	$0.715081\pi$
$462$		0			0
$463$	26.5885			1.23567			0.617835	−	0.786308i	$-0.288010\pi$
$463$	26.5885			1.23567			0.617835	+	0.786308i	$0.288010\pi$
$464$	15.0000			0.696358
$465$	7.85641			0.364332
$466$	−44.7846			−2.07461
$467$	−9.75833	+	16.9019i	−0.451562	+	0.782128i	−0.998483	−	0.0550561i	$-0.982466\pi$
$467$	−9.75833	+	16.9019i	−0.451562	+	0.782128i	0.546922	+	0.837184i	$0.315800\pi$
$468$	8.86603	+	0.571797i	0.409832	+	0.0264313i
$469$		0			0
$470$	1.39230	−	2.41154i	0.0642222	−	0.111236i
$471$	−3.36603	−	5.83013i	−0.155098	−	0.268638i
$472$	9.29423	−	16.0981i	0.427802	−	0.740974i
$473$	−24.1244	−	41.7846i	−1.10924	−	1.92126i
$474$	−7.35898			−0.338009
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$	4.83975	+	8.38269i	0.221597	+	0.383817i
$478$	−22.6865	−	39.2942i	−1.03766	−	1.79728i
$479$	−4.73205			−0.216213			−0.108106	−	0.994139i	$-0.534479\pi$
$479$	−4.73205			−0.216213			−0.108106	+	0.994139i	$0.534479\pi$
$480$	−3.29423	−	5.70577i	−0.150360	−	0.260432i
$481$	−14.0000	+	21.0000i	−0.638345	+	0.957518i
$482$	−18.7128			−0.852345
$483$		0			0
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$	24.9282			1.13193
$486$	13.2224	+	22.9019i	0.599782	+	1.03885i
$487$	0.392305	−	0.679492i	0.0177770	−	0.0307907i	−0.857000	−	0.515316i	$-0.827674\pi$
$487$	0.392305	−	0.679492i	0.0177770	−	0.0307907i	0.874777	+	0.484526i	$0.161008\pi$
$488$	26.3205			1.19147
$489$	4.24871			0.192133
$490$		0			0
$491$	−14.1962	+	24.5885i	−0.640663	+	1.10966i	0.344622	+	0.938742i	$0.388007\pi$
$491$	−14.1962	+	24.5885i	−0.640663	+	1.10966i	−0.985285	+	0.170920i	$0.945326\pi$
$492$	1.90192	+	3.29423i	0.0857453	+	0.148515i
$493$	6.40192	+	11.0885i	0.288328	+	0.499399i
$494$	6.92820	−	10.3923i	0.311715	−	0.467572i
$495$	10.0981	−	17.4904i	0.453875	−	0.786134i
$496$	15.4904	−	26.8301i	0.695539	−	1.20471i
$497$		0			0
$498$	−5.19615	−	9.00000i	−0.232845	−	0.403300i
$499$	−6.49038	+	11.2417i	−0.290549	+	0.503246i	−0.973940	−	0.226807i	$-0.927171\pi$
$499$	−6.49038	+	11.2417i	−0.290549	+	0.503246i	0.683390	+	0.730053i	$0.260505\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	19.3923	−	33.5885i	0.865521	−	1.49913i
$503$	6.29423	+	10.9019i	0.280646	+	0.486093i	0.971544	−	0.236859i	$-0.0761181\pi$
$503$	6.29423	+	10.9019i	0.280646	+	0.486093i	−0.690898	+	0.722952i	$0.742785\pi$
$504$		0			0
$505$	−3.69615	+	6.40192i	−0.164477	+	0.284882i
$506$	5.19615	−	9.00000i	0.230997	−	0.400099i
$507$	−5.77757	+	7.56218i	−0.256591	+	0.335848i
$508$	1.19615	+	2.07180i	0.0530707	+	0.0919211i
$509$	5.13397	+	8.89230i	0.227559	+	0.394144i	0.957084	−	0.289810i	$-0.0935921\pi$
$509$	5.13397	+	8.89230i	0.227559	+	0.394144i	−0.729525	+	0.683954i	$0.760259\pi$
$510$	4.68653	−	8.11731i	0.207523	−	0.359441i
$511$		0			0
$512$	−8.66025			−0.382733
$513$	8.00000			0.353209
$514$	15.6962	−	27.1865i	0.692328	−	1.19915i
$515$	5.53590	+	9.58846i	0.243941	+	0.422518i
$516$	7.46410			0.328589
$517$	−2.19615	+	3.80385i	−0.0965867	+	0.167293i
$518$		0			0
$519$	−11.3205			−0.496915
$520$	−10.7942	−	0.696152i	−0.473358	−	0.0305283i
$521$	0.0621778	+	0.107695i	0.00272406	+	0.00471821i	0.867384	−	0.497639i	$-0.165800\pi$
$521$	0.0621778	+	0.107695i	0.00272406	+	0.00471821i	−0.864660	+	0.502357i	$0.832466\pi$
$522$	−12.8038			−0.560409
$523$	16.5885	+	28.7321i	0.725363	+	1.25636i	0.958825	+	0.283999i	$0.0916612\pi$
$523$	16.5885	+	28.7321i	0.725363	+	1.25636i	−0.233462	+	0.972366i	$0.575005\pi$
$524$	1.73205	+	3.00000i	0.0756650	+	0.131056i
$525$		0			0
$526$	4.09808	+	7.09808i	0.178685	+	0.309491i
$527$	26.4449			1.15196
$528$	8.66025	+	15.0000i	0.376889	+	0.652791i
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	5.89230	+	10.2058i	0.255945	+	0.443310i
$531$	−13.2224	+	22.9019i	−0.573805	+	0.993859i
$532$		0			0
$533$	18.6962	+	1.20577i	0.809820	+	0.0522278i
$534$	0.588457	−	1.01924i	0.0254650	−	0.0441067i
$535$	34.3923			1.48691
$536$	7.26795			0.313928
$537$	5.07180			0.218864
$538$	32.7846			1.41344
$539$		0			0
$540$	3.46410	+	6.00000i	0.149071	+	0.258199i
$541$	17.6962	−	30.6506i	0.760817	−	1.31777i	−0.181613	−	0.983370i	$-0.558132\pi$
$541$	17.6962	−	30.6506i	0.760817	−	1.31777i	0.942430	−	0.334404i	$-0.108535\pi$
$542$	−14.0263	+	24.2942i	−0.602480	+	1.04353i
$543$	18.7321			0.803869
$544$	−11.0885	−	19.2058i	−0.475414	−	0.823441i
$545$	21.4641			0.919421
$546$		0			0
$547$	28.1962			1.20558			0.602790	−	0.797900i	$-0.294056\pi$
$547$	28.1962			1.20558			0.602790	+	0.797900i	$0.294056\pi$
$548$	−10.9641	−	18.9904i	−0.468363	−	0.811229i
$549$	−37.4449			−1.59811
$550$	−8.19615	+	14.1962i	−0.349485	+	0.605326i
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$	−0.803848	−	1.39230i	−0.0342140	−	0.0592604i
$553$		0			0
$554$	−29.4449			−1.25099
$555$	−8.87564			−0.376750
$556$	−20.5885			−0.873145
$557$	−25.6410			−1.08644			−0.543222	−	0.839589i	$-0.682796\pi$
$557$	−25.6410			−1.08644			−0.543222	+	0.839589i	$0.682796\pi$
$558$	−13.2224	+	22.9019i	−0.559750	+	0.969516i
$559$	20.3923	−	30.5885i	0.862503	−	1.29375i
$560$		0			0
$561$	−7.39230	+	12.8038i	−0.312103	+	0.540579i
$562$	−6.40192	−	11.0885i	−0.270049	−	0.467738i
$563$	−5.02628	+	8.70577i	−0.211832	+	0.366905i	−0.952288	−	0.305201i	$-0.901276\pi$
$563$	−5.02628	+	8.70577i	−0.211832	+	0.366905i	0.740456	+	0.672105i	$0.234610\pi$
$564$	−0.339746	−	0.588457i	−0.0143059	−	0.0247785i
$565$	−12.8038			−0.538662
$566$	0.169873	+	0.294229i	0.00714029	+	0.0123674i
$567$		0			0
$568$	−5.19615	−	9.00000i	−0.218026	−	0.377632i
$569$	−14.5359	−	25.1769i	−0.609377	−	1.05547i	−0.991343	−	0.131295i	$-0.958086\pi$
$569$	−14.5359	−	25.1769i	−0.609377	−	1.05547i	0.381967	−	0.924176i	$-0.375247\pi$
$570$	4.39230			0.183973
$571$	12.3923	+	21.4641i	0.518602	+	0.898245i	0.999766	+	0.0216144i	$0.00688062\pi$
$571$	12.3923	+	21.4641i	0.518602	+	0.898245i	−0.481165	+	0.876630i	$0.659786\pi$
$572$	−17.0263	−	1.09808i	−0.711905	−	0.0459129i
$573$	0.928203			0.0387762
$574$		0			0
$575$	1.26795	−	2.19615i	0.0528771	−	0.0915859i
$576$	−2.46410			−0.102671
$577$	16.4019	+	28.4090i	0.682821	+	1.18268i	0.974116	+	0.226048i	$0.0725805\pi$
$577$	16.4019	+	28.4090i	0.682821	+	1.18268i	−0.291295	+	0.956633i	$0.594086\pi$
$578$	1.05256	−	1.82309i	0.0437807	−	0.0758304i
$579$	3.66025			0.152115
$580$	−5.19615			−0.215758
$581$		0			0
$582$	9.12436	−	15.8038i	0.378217	−	0.655091i
$583$	−9.29423	−	16.0981i	−0.384928	−	0.666714i
$584$	6.23205	+	10.7942i	0.257884	+	0.446668i
$585$	15.3564	+	0.990381i	0.634909	+	0.0409472i
$586$	9.69615	−	16.7942i	0.400544	−	0.693763i
$587$	−2.19615	+	3.80385i	−0.0906449	+	0.157002i	−0.907783	−	0.419441i	$-0.862226\pi$
$587$	−2.19615	+	3.80385i	−0.0906449	+	0.157002i	0.817138	+	0.576442i	$0.195559\pi$
$588$		0			0
$589$	6.19615	+	10.7321i	0.255308	+	0.442206i
$590$	−16.0981	+	27.8827i	−0.662747	+	1.14791i
$591$	−4.39230	+	7.60770i	−0.180675	+	0.312939i
$592$	−17.5000	+	30.3109i	−0.719246	+	1.24577i
$593$	20.7224	−	35.8923i	0.850968	−	1.47392i	−0.0293672	−	0.999569i	$-0.509349\pi$
$593$	20.7224	−	35.8923i	0.850968	−	1.47392i	0.880335	−	0.474352i	$-0.157317\pi$
$594$	−16.3923	−	28.3923i	−0.672584	−	1.16495i
$595$		0			0
$596$	−0.232051	+	0.401924i	−0.00950517	+	0.0164634i
$597$	0.732051	−	1.26795i	0.0299608	−	0.0518937i
$598$	7.90192	+	0.509619i	0.323134	+	0.0208399i
$599$	−8.07180	−	13.9808i	−0.329805	−	0.571238i	0.652668	−	0.757644i	$-0.273650\pi$
$599$	−8.07180	−	13.9808i	−0.329805	−	0.571238i	−0.982473	+	0.186405i	$0.940316\pi$
$600$	1.26795	+	2.19615i	0.0517638	+	0.0896575i
$601$	10.9904	−	19.0359i	0.448307	−	0.776490i	−0.549969	−	0.835185i	$-0.685360\pi$
$601$	10.9904	−	19.0359i	0.448307	−	0.776490i	0.998276	+	0.0586946i	$0.0186938\pi$
$602$		0			0
$603$	−10.3397			−0.421067
$604$	2.00000			0.0813788
$605$	−9.86603	+	17.0885i	−0.401111	+	0.694745i
$606$	2.70577	+	4.68653i	0.109914	+	0.190377i
$607$	−6.39230			−0.259456			−0.129728	−	0.991550i	$-0.541410\pi$
$607$	−6.39230			−0.259456			−0.129728	+	0.991550i	$0.541410\pi$
$608$	5.19615	−	9.00000i	0.210732	−	0.364998i
$609$		0			0
$610$	−45.5885			−1.84582
$611$	−3.33975	−	0.215390i	−0.135112	−	0.00871376i
$612$	5.25833	+	9.10770i	0.212555	+	0.368157i
$613$	−17.3923			−0.702469			−0.351234	−	0.936288i	$-0.614238\pi$
$613$	−17.3923			−0.702469			−0.351234	+	0.936288i	$0.614238\pi$
$614$	−23.0263	−	39.8827i	−0.929265	−	1.60953i
$615$	3.29423	+	5.70577i	0.132836	+	0.230079i
$616$		0			0
$617$	−14.3038	−	24.7750i	−0.575851	−	0.997404i	−0.995949	−	0.0899245i	$-0.971337\pi$
$617$	−14.3038	−	24.7750i	−0.575851	−	0.997404i	0.420097	−	0.907479i	$-0.361996\pi$
$618$	8.10512			0.326036
$619$	−18.6865	−	32.3660i	−0.751075	−	1.30090i	−0.947302	−	0.320342i	$-0.896202\pi$
$619$	−18.6865	−	32.3660i	−0.751075	−	1.30090i	0.196227	−	0.980559i	$-0.437131\pi$
$620$	−5.36603	+	9.29423i	−0.215505	+	0.373265i
$621$	2.53590	+	4.39230i	0.101762	+	0.176257i
$622$	−4.09808	+	7.09808i	−0.164318	+	0.284607i
$623$		0			0
$624$	−7.32051	+	10.9808i	−0.293055	+	0.439582i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	−22.1436			−0.885036
$627$	−6.92820			−0.276686
$628$	9.19615			0.366966
$629$	−29.8756			−1.19122
$630$		0			0
$631$	−14.3923	−	24.9282i	−0.572949	−	0.992376i	−0.996261	−	0.0863924i	$-0.972466\pi$
$631$	−14.3923	−	24.9282i	−0.572949	−	0.992376i	0.423313	−	0.905984i	$-0.360867\pi$
$632$	−5.02628	+	8.70577i	−0.199935	+	0.346297i
$633$	4.46410	−	7.73205i	0.177432	−	0.307321i
$634$	−0.803848			−0.0319249
$635$	2.07180	+	3.58846i	0.0822167	+	0.142404i
$636$	2.87564			0.114027
$637$		0			0
$638$	24.5885			0.973466
$639$	7.39230	+	12.8038i	0.292435	+	0.506512i
$640$	−21.0000			−0.830098
$641$	−0.571797	+	0.990381i	−0.0225846	+	0.0391177i	−0.877097	−	0.480314i	$-0.840523\pi$
$641$	−0.571797	+	0.990381i	−0.0225846	+	0.0391177i	0.854512	+	0.519431i	$0.173856\pi$
$642$	12.5885	−	21.8038i	0.496827	−	0.860529i
$643$	20.3923	+	35.3205i	0.804194	+	1.39290i	0.916834	+	0.399269i	$0.130736\pi$
$643$	20.3923	+	35.3205i	0.804194	+	1.39290i	−0.112640	+	0.993636i	$0.535931\pi$
$644$		0			0
$645$	12.9282			0.509048
$646$	14.7846			0.581693
$647$	45.0333			1.77044			0.885221	−	0.465170i	$-0.154007\pi$
$647$	45.0333			1.77044			0.885221	+	0.465170i	$0.154007\pi$
$648$	7.73205			0.303744
$649$	25.3923	−	43.9808i	0.996735	−	1.72640i
$650$	−12.4641	−	0.803848i	−0.488882	−	0.0315295i
$651$		0			0
$652$	−2.90192	+	5.02628i	−0.113648	+	0.196844i
$653$	5.07180	+	8.78461i	0.198475	+	0.343768i	0.948034	−	0.318169i	$-0.103068\pi$
$653$	5.07180	+	8.78461i	0.198475	+	0.343768i	−0.749559	+	0.661937i	$0.769735\pi$
$654$	7.85641	−	13.6077i	0.307210	−	0.532103i
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$	25.9808			1.01438
$657$	−8.86603	−	15.3564i	−0.345897	−	0.599110i
$658$		0			0
$659$	−3.80385	−	6.58846i	−0.148177	−	0.256650i	0.782377	−	0.622805i	$-0.214007\pi$
$659$	−3.80385	−	6.58846i	−0.148177	−	0.256650i	−0.930554	+	0.366156i	$0.880674\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	22.8038			0.886967			0.443483	−	0.896283i	$-0.353742\pi$
$661$	22.8038			0.886967			0.443483	+	0.896283i	$0.353742\pi$
$662$	−23.3660	−	40.4711i	−0.908146	−	1.57296i
$663$	−11.2417	−	0.725009i	−0.436590	−	0.0281570i
$664$	−14.1962			−0.550918
$665$		0			0
$666$	14.9378	−	25.8731i	0.578829	−	1.00256i
$667$	−3.80385			−0.147286
$668$	12.2942	+	21.2942i	0.475678	+	0.823898i
$669$	−3.66025	+	6.33975i	−0.141514	+	0.245109i
$670$	−12.5885			−0.486335
$671$	71.9090			2.77601
$672$		0			0
$673$	−9.08846	+	15.7417i	−0.350334	+	0.606797i	−0.986308	−	0.164914i	$-0.947265\pi$
$673$	−9.08846	+	15.7417i	−0.350334	+	0.606797i	0.635974	+	0.771711i	$0.280599\pi$
$674$	9.52628	+	16.5000i	0.366939	+	0.635556i
$675$	−4.00000	−	6.92820i	−0.153960	−	0.266667i
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	−18.4641	+	31.9808i	−0.709633	+	1.22912i	0.255360	+	0.966846i	$0.417806\pi$
$677$	−18.4641	+	31.9808i	−0.709633	+	1.22912i	−0.964993	+	0.262275i	$0.915527\pi$
$678$	−4.68653	+	8.11731i	−0.179985	+	0.311744i
$679$		0			0
$680$	−6.40192	−	11.0885i	−0.245503	−	0.425223i
$681$	−4.26795	+	7.39230i	−0.163548	+	0.283274i
$682$	25.3923	−	43.9808i	0.972322	−	1.68411i
$683$	−4.26795	+	7.39230i	−0.163309	+	0.282859i	−0.936053	−	0.351858i	$-0.885550\pi$
$683$	−4.26795	+	7.39230i	−0.163309	+	0.282859i	0.772745	+	0.634717i	$0.218883\pi$
$684$	−2.46410	+	4.26795i	−0.0942173	+	0.163189i
$685$	−18.9904	−	32.8923i	−0.725585	−	1.25675i
$686$		0			0
$687$	2.33975	−	4.05256i	0.0892669	−	0.154615i
$688$	25.4904	−	44.1506i	0.971812	−	1.68323i
$689$	7.85641	−	11.7846i	0.299305	−	0.448958i
$690$	1.39230	+	2.41154i	0.0530041	+	0.0918059i
$691$	−10.1962	−	17.6603i	−0.387880	−	0.671828i	0.604284	−	0.796769i	$-0.293459\pi$
$691$	−10.1962	−	17.6603i	−0.387880	−	0.671828i	−0.992164	+	0.124941i	$0.960126\pi$
$692$	7.73205	−	13.3923i	0.293928	−	0.509099i
$693$		0			0
$694$	−18.5885			−0.705608
$695$	−35.6603			−1.35267
$696$	1.90192	−	3.29423i	0.0720922	−	0.124867i
$697$	11.0885	+	19.2058i	0.420005	+	0.727470i
$698$	29.0718			1.10038
$699$	−9.46410	+	16.3923i	−0.357965	+	0.620014i
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	13.8564	−	20.7846i	0.522976	−	0.784465i
$703$	−7.00000	−	12.1244i	−0.264010	−	0.457279i
$704$	4.73205			0.178346
$705$	−0.588457	−	1.01924i	−0.0221626	−	0.0383867i
$706$	−2.89230	−	5.00962i	−0.108853	−	0.188539i
$707$		0			0
$708$	3.92820	+	6.80385i	0.147631	+	0.255704i
$709$	−32.1769			−1.20843			−0.604215	−	0.796822i	$-0.706513\pi$
$709$	−32.1769			−1.20843			−0.604215	+	0.796822i	$0.706513\pi$
$710$	9.00000	+	15.5885i	0.337764	+	0.585024i
$711$	7.15064	−	12.3853i	0.268170	−	0.464484i
$712$	−0.803848	−	1.39230i	−0.0301255	−	0.0521788i
$713$	−3.92820	+	6.80385i	−0.147112	+	0.254806i
$714$		0			0
$715$	−29.4904	−	1.90192i	−1.10288	−	0.0711279i
$716$	−3.46410	+	6.00000i	−0.129460	+	0.224231i
$717$	−19.1769			−0.716175
$718$	−8.78461			−0.327839
$719$	10.7321			0.400238			0.200119	−	0.979772i	$-0.435867\pi$
$719$	10.7321			0.400238			0.200119	+	0.979772i	$0.435867\pi$
$720$	21.3397			0.795285
$721$		0			0
$722$	−12.9904	−	22.5000i	−0.483452	−	0.837363i
$723$	−3.95448	+	6.84936i	−0.147069	+	0.254731i
$724$	−12.7942	+	22.1603i	−0.475494	+	0.823579i
$725$	6.00000			0.222834
$726$	7.22243	+	12.5096i	0.268050	+	0.464276i
$727$	−21.1769			−0.785408			−0.392704	−	0.919665i	$-0.628460\pi$
$727$	−21.1769			−0.785408			−0.392704	+	0.919665i	$0.628460\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	−10.7942	−	18.6962i	−0.399512	−	0.691976i
$731$	43.5167			1.60952
$732$	−5.56218	+	9.63397i	−0.205584	+	0.356082i
$733$	−3.79423	+	6.57180i	−0.140143	+	0.242735i	−0.927550	−	0.373698i	$-0.878090\pi$
$733$	−3.79423	+	6.57180i	−0.140143	+	0.242735i	0.787407	+	0.616433i	$0.211423\pi$
$734$	5.36603	+	9.29423i	0.198064	+	0.343056i
$735$		0			0
$736$	6.58846			0.242854
$737$	19.8564			0.731420
$738$	−22.1769			−0.816344
$739$	−0.784610			−0.0288623			−0.0144312	−	0.999896i	$-0.504594\pi$
$739$	−0.784610			−0.0288623			−0.0144312	+	0.999896i	$0.504594\pi$
$740$	6.06218	−	10.5000i	0.222850	−	0.385988i
$741$	−2.33975	−	4.73205i	−0.0859527	−	0.173836i
$742$		0			0
$743$	14.1962	−	24.5885i	0.520806	−	0.902063i	−0.478901	−	0.877869i	$-0.658965\pi$
$743$	14.1962	−	24.5885i	0.520806	−	0.902063i	0.999707	−	0.0241941i	$-0.00770196\pi$
$744$	−3.92820	−	6.80385i	−0.144015	−	0.249441i
$745$	−0.401924	+	0.696152i	−0.0147253	+	0.0255051i
$746$	8.13397	+	14.0885i	0.297806	+	0.515815i
$747$	20.1962			0.738939
$748$	−10.0981	−	17.4904i	−0.369222	−	0.639512i
$749$		0			0
$750$	−7.68653	−	13.3135i	−0.280673	−	0.486139i
$751$	−23.0981	−	40.0070i	−0.842861	−	1.45988i	−0.887466	−	0.460873i	$-0.847536\pi$
$751$	−23.0981	−	40.0070i	−0.842861	−	1.45988i	0.0446053	−	0.999005i	$-0.485797\pi$
$752$	−4.64102			−0.169240
$753$	−8.19615	−	14.1962i	−0.298684	−	0.517337i
$754$	8.30385	+	16.7942i	0.302408	+	0.611610i
$755$	3.46410			0.126072
$756$		0			0
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	−0.683226	−	0.730207i	$-0.739424\pi$
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	0.973991	+	0.226587i	$0.0727569\pi$
$758$	7.94744			0.288664
$759$	−2.19615	−	3.80385i	−0.0797153	−	0.138071i
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	−6.67949			−0.242131			−0.121066	−	0.992644i	$-0.538631\pi$
$761$	−6.67949			−0.242131			−0.121066	+	0.992644i	$0.538631\pi$
$762$	3.03332			0.109886
$763$		0			0
$764$	−0.633975	+	1.09808i	−0.0229364	+	0.0397270i
$765$	9.10770	+	15.7750i	0.329289	+	0.570346i
$766$	−4.90192	−	8.49038i	−0.177114	−	0.306770i
$767$	38.6147	+	2.49038i	1.39430	+	0.0899224i
$768$	−6.95448	+	12.0455i	−0.250948	+	0.434655i
$769$	−23.5885	+	40.8564i	−0.850622	+	1.47332i	0.0300268	+	0.999549i	$0.490441\pi$
$769$	−23.5885	+	40.8564i	−0.850622	+	1.47332i	−0.880648	+	0.473771i	$0.842893\pi$
$770$		0			0
$771$	−6.63397	−	11.4904i	−0.238917	−	0.413816i
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	0.464102	−	0.803848i	0.0166926	−	0.0289124i	−0.857558	−	0.514387i	$-0.828020\pi$
$773$	0.464102	−	0.803848i	0.0166926	−	0.0289124i	0.874251	+	0.485474i	$0.161353\pi$
$774$	−21.7583	+	37.6865i	−0.782087	+	1.35461i
$775$	6.19615	−	10.7321i	0.222572	−	0.385507i
$776$	−12.4641	−	21.5885i	−0.447435	−	0.774980i
$777$		0			0
$778$	−26.3827	+	45.6962i	−0.945865	+	1.63829i
$779$	−5.19615	+	9.00000i	−0.186171	+	0.322458i
$780$

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 + 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 + 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205 q^{11} +(-0.366025 + 0.633975i) q^{12} +(1.59808 + 3.23205i) q^{13} +(-0.633975 + 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-2.13397 + 3.69615i) q^{17} +(-2.13397 - 3.69615i) q^{18} -2.00000 q^{19} +(-0.866025 - 1.50000i) q^{20} +(4.09808 + 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +1.26795 q^{24} +(1.00000 + 1.73205i) q^{25} +(-3.46410 + 5.19615i) q^{26} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{29} -2.19615 q^{30} +(-3.09808 - 5.36603i) q^{31} +(-2.59808 + 4.50000i) q^{32} +3.46410 q^{33} -7.39230 q^{34} +(1.23205 - 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} +(-1.73205 - 3.00000i) q^{38} +(1.16987 + 2.36603i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(2.59808 - 4.50000i) q^{41} +(-5.09808 - 8.83013i) q^{43} +(-2.36603 + 4.09808i) q^{44} +(2.13397 - 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} +(-0.464102 + 0.803848i) q^{47} +(1.83013 + 3.16987i) q^{48} +(-1.73205 + 3.00000i) q^{50} +(-1.56218 + 2.70577i) q^{51} +(-3.59808 - 0.232051i) q^{52} +(-1.96410 - 3.40192i) q^{53} +(-3.46410 - 6.00000i) q^{54} +(-4.09808 + 7.09808i) q^{55} -1.46410 q^{57} +5.19615 q^{58} +(5.36603 - 9.29423i) q^{59} +(-0.633975 - 1.09808i) q^{60} +15.1962 q^{61} +(5.36603 - 9.29423i) q^{62} +1.00000 q^{64} +(-6.23205 - 0.401924i) q^{65} +(3.00000 + 5.19615i) q^{66} +4.19615 q^{67} +(-2.13397 - 3.69615i) q^{68} +(-0.464102 - 0.803848i) q^{69} +(-3.00000 - 5.19615i) q^{71} -4.26795 q^{72} +(3.59808 + 6.23205i) q^{73} +(-6.06218 + 10.5000i) q^{74} +(0.732051 + 1.26795i) q^{75} +(1.00000 - 1.73205i) q^{76} +(-2.53590 + 3.80385i) q^{78} +(-2.90192 + 5.02628i) q^{79} -8.66025 q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615 q^{83} +(-3.69615 - 6.40192i) q^{85} +(8.83013 - 15.2942i) q^{86} +(1.09808 - 1.90192i) q^{87} +8.19615 q^{88} +(-0.464102 - 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} -1.60770 q^{94} +(1.73205 - 3.00000i) q^{95} +(-1.90192 + 3.29423i) q^{96} +(-7.19615 - 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9	\( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{19} + 6 q^{22} - 6 q^{23} + 12 q^{24} + 4 q^{25} - 16 q^{27} + 6 q^{29} + 12 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} - 6 q^{60} + 40 q^{61} + 18 q^{62} + 4 q^{64} - 18 q^{65} + 12 q^{66} - 4 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} - 24 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} - 6 q^{87} + 12 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} - 48 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 8 * q^19 + 6 * q^22 - 6 * q^23 + 12 * q^24 + 4 * q^25 - 16 * q^27 + 6 * q^29 + 12 * q^30 - 2 * q^31 + 12 * q^34 - 2 * q^36 + 14 * q^37 + 22 * q^39 - 6 * q^40 - 10 * q^43 - 6 * q^44 + 12 * q^45 - 6 * q^46 + 12 * q^47 - 10 * q^48 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 - 6 * q^60 + 40 * q^61 + 18 * q^62 + 4 * q^64 - 18 * q^65 + 12 * q^66 - 4 * q^67 - 12 * q^68 + 12 * q^69 - 12 * q^71 - 24 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 - 24 * q^78 - 22 * q^79 + 4 * q^81 + 36 * q^82 - 12 * q^83 + 6 * q^85 + 18 * q^86 - 6 * q^87 + 12 * q^88 + 12 * q^89 - 12 * q^90 + 12 * q^92 - 16 * q^93 - 48 * q^94 - 18 * q^96 - 8 * q^97 - 12 * q^99

Introduction

L-functions

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