LMFDB - Embedded newform 97.2.g.a.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,2,Mod(6,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.6"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	97.g (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.774548899606$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			81.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	97.81
Dual form			97.2.g.a.6.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{2} +(-0.633975 - 0.366025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-3.23205 + 0.866025i) q^{5} +(0.633975 + 1.09808i) q^{6} +(0.366025 + 1.36603i) q^{7} +1.73205i q^{8} +(-1.23205 - 2.13397i) q^{9} +(5.59808 + 1.50000i) q^{10} +(-3.00000 + 1.73205i) q^{11} -0.732051i q^{12} +(-1.86603 + 0.500000i) q^{13} +(0.633975 - 2.36603i) q^{14} +(2.36603 + 0.633975i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-0.401924 + 1.50000i) q^{17} +4.26795i q^{18} +(-3.73205 - 3.73205i) q^{19} +(-2.36603 - 2.36603i) q^{20} +(0.267949 - 1.00000i) q^{21} +6.00000 q^{22} +(2.19615 - 8.19615i) q^{23} +(0.633975 - 1.09808i) q^{24} +(5.36603 - 3.09808i) q^{25} +(3.23205 + 0.866025i) q^{26} +4.00000i q^{27} +(-1.00000 + 1.00000i) q^{28} +(0.633975 - 0.169873i) q^{29} +(-3.00000 - 3.00000i) q^{30} +(-3.63397 - 2.09808i) q^{31} +(-4.50000 + 2.59808i) q^{32} +2.53590 q^{33} +(1.90192 - 1.90192i) q^{34} +(-2.36603 - 4.09808i) q^{35} +(1.23205 - 2.13397i) q^{36} +(2.96410 + 11.0622i) q^{37} +(2.36603 + 8.83013i) q^{38} +(1.36603 + 0.366025i) q^{39} +(-1.50000 - 5.59808i) q^{40} +(-7.09808 + 1.90192i) q^{41} +(-1.26795 + 1.26795i) q^{42} +(-4.09808 + 7.09808i) q^{43} +(-3.00000 - 1.73205i) q^{44} +(5.83013 + 5.83013i) q^{45} +(-10.3923 + 10.3923i) q^{46} -0.928203 q^{47} +(-3.16987 + 1.83013i) q^{48} +(4.33013 - 2.50000i) q^{49} -10.7321 q^{50} +(0.803848 - 0.803848i) q^{51} +(-1.36603 - 1.36603i) q^{52} +(2.59808 + 1.50000i) q^{53} +(3.46410 - 6.00000i) q^{54} +(8.19615 - 8.19615i) q^{55} +(-2.36603 + 0.633975i) q^{56} +(1.00000 + 3.73205i) q^{57} +(-1.09808 - 0.294229i) q^{58} +(-1.26795 - 4.73205i) q^{59} +(0.633975 + 2.36603i) q^{60} +(0.866025 - 1.50000i) q^{61} +(3.63397 + 6.29423i) q^{62} +(2.46410 - 2.46410i) q^{63} -1.00000 q^{64} +(5.59808 - 3.23205i) q^{65} +(-3.80385 - 2.19615i) q^{66} +(-2.73205 - 2.73205i) q^{67} +(-1.50000 + 0.401924i) q^{68} +(-4.39230 + 4.39230i) q^{69} +8.19615i q^{70} +(5.36603 + 1.43782i) q^{71} +(3.69615 - 2.13397i) q^{72} +(-7.19615 + 12.4641i) q^{73} +(5.13397 - 19.1603i) q^{74} -4.53590 q^{75} +(1.36603 - 5.09808i) q^{76} +(-3.46410 - 3.46410i) q^{77} +(-1.73205 - 1.73205i) q^{78} -6.00000i q^{79} +(-4.33013 + 16.1603i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(12.2942 + 3.29423i) q^{82} +(3.63397 - 13.5622i) q^{83} +(1.00000 - 0.267949i) q^{84} -5.19615i q^{85} +(12.2942 - 7.09808i) q^{86} +(-0.464102 - 0.124356i) q^{87} +(-3.00000 - 5.19615i) q^{88} -0.464102i q^{89} +(-3.69615 - 13.7942i) q^{90} +(-1.36603 - 2.36603i) q^{91} +(8.19615 - 2.19615i) q^{92} +(1.53590 + 2.66025i) q^{93} +(1.39230 + 0.803848i) q^{94} +(15.2942 + 8.83013i) q^{95} +3.80385 q^{96} +(-9.00000 + 4.00000i) q^{97} -8.66025 q^{98} +(7.39230 + 4.26795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 6 q^{3} + 2 q^{4} - 6 q^{5} + 6 q^{6} - 2 q^{7} + 2 q^{9} + 12 q^{10} - 12 q^{11} - 4 q^{13} + 6 q^{14} + 6 q^{15} + 10 q^{16} - 12 q^{17} - 8 q^{19} - 6 q^{20} + 8 q^{21} + 24 q^{22} - 12 q^{23}+ \cdots - 12 q^{99}+O(q^{100}) $ 4 * q - 6 * q^2 - 6 * q^3 + 2 * q^4 - 6 * q^5 + 6 * q^6 - 2 * q^7 + 2 * q^9 + 12 * q^10 - 12 * q^11 - 4 * q^13 + 6 * q^14 + 6 * q^15 + 10 * q^16 - 12 * q^17 - 8 * q^19 - 6 * q^20 + 8 * q^21 + 24 * q^22 - 12 * q^23 + 6 * q^24 + 18 * q^25 + 6 * q^26 - 4 * q^28 + 6 * q^29 - 12 * q^30 - 18 * q^31 - 18 * q^32 + 24 * q^33 + 18 * q^34 - 6 * q^35 - 2 * q^36 - 2 * q^37 + 6 * q^38 + 2 * q^39 - 6 * q^40 - 18 * q^41 - 12 * q^42 - 6 * q^43 - 12 * q^44 + 6 * q^45 + 24 * q^47 - 30 * q^48 - 36 * q^50 + 24 * q^51 - 2 * q^52 + 12 * q^55 - 6 * q^56 + 4 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 + 18 * q^62 - 4 * q^63 - 4 * q^64 + 12 * q^65 - 36 * q^66 - 4 * q^67 - 6 * q^68 + 24 * q^69 + 18 * q^71 - 6 * q^72 - 8 * q^73 + 24 * q^74 - 32 * q^75 + 2 * q^76 - 2 * q^81 + 18 * q^82 + 18 * q^83 + 4 * q^84 + 18 * q^86 + 12 * q^87 - 12 * q^88 + 6 * q^90 - 2 * q^91 + 12 * q^92 + 20 * q^93 - 36 * q^94 + 30 * q^95 + 36 * q^96 - 36 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−0.633975	−	0.366025i	−0.366025	−	0.211325i	0.305695	−	0.952129i	$-0.401111\pi$
$3$	−0.633975	−	0.366025i	−0.366025	−	0.211325i	−0.671721	+	0.740805i	$0.734444\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−3.23205	+	0.866025i	−1.44542	+	0.387298i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−3.23205	+	0.866025i	−1.44542	+	0.387298i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	0.633975	+	1.09808i	0.258819	+	0.448288i
$7$	0.366025	+	1.36603i	0.138345	+	0.516309i	0.999962	+	0.00875026i	$0.00278533\pi$
$7$	0.366025	+	1.36603i	0.138345	+	0.516309i	−0.861617	+	0.507559i	$0.830548\pi$
$8$			1.73205i			0.612372i
$9$	−1.23205	−	2.13397i	−0.410684	−	0.711325i
$10$	5.59808	+	1.50000i	1.77027	+	0.474342i
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$		−	0.732051i		−	0.211325i
$13$	−1.86603	+	0.500000i	−0.517542	+	0.138675i	−0.508130	−	0.861281i	$-0.669663\pi$
$13$	−1.86603	+	0.500000i	−0.517542	+	0.138675i	−0.00941278	+	0.999956i	$0.502996\pi$
$14$	0.633975	−	2.36603i	0.169437	−	0.632347i
$15$	2.36603	+	0.633975i	0.610905	+	0.163692i
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−0.401924	+	1.50000i	−0.0974808	+	0.363803i	−0.997384	−	0.0722865i	$-0.976970\pi$
$17$	−0.401924	+	1.50000i	−0.0974808	+	0.363803i	0.899903	+	0.436090i	$0.143637\pi$
$18$			4.26795i			1.00597i
$19$	−3.73205	−	3.73205i	−0.856191	−	0.856191i	0.134696	−	0.990887i	$-0.456994\pi$
$19$	−3.73205	−	3.73205i	−0.856191	−	0.856191i	−0.990887	+	0.134696i	$0.956994\pi$
$20$	−2.36603	−	2.36603i	−0.529059	−	0.529059i
$21$	0.267949	−	1.00000i	0.0584713	−	0.218218i
$22$	6.00000			1.27920
$23$	2.19615	−	8.19615i	0.457929	−	1.70902i	−0.221401	−	0.975183i	$-0.571063\pi$
$23$	2.19615	−	8.19615i	0.457929	−	1.70902i	0.679330	−	0.733833i	$-0.262271\pi$
$24$	0.633975	−	1.09808i	0.129410	−	0.224144i
$25$	5.36603	−	3.09808i	1.07321	−	0.619615i
$26$	3.23205	+	0.866025i	0.633857	+	0.169842i
$27$			4.00000i			0.769800i
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	0.633975	−	0.169873i	0.117726	−	0.0315446i	−0.199475	−	0.979903i	$-0.563924\pi$
$29$	0.633975	−	0.169873i	0.117726	−	0.0315446i	0.317201	+	0.948358i	$0.397257\pi$
$30$	−3.00000	−	3.00000i	−0.547723	−	0.547723i
$31$	−3.63397	−	2.09808i	−0.652681	−	0.376826i	0.136802	−	0.990598i	$-0.456318\pi$
$31$	−3.63397	−	2.09808i	−0.652681	−	0.376826i	−0.789483	+	0.613773i	$0.789651\pi$
$32$	−4.50000	+	2.59808i	−0.795495	+	0.459279i
$33$	2.53590			0.441443
$34$	1.90192	−	1.90192i	0.326177	−	0.326177i
$35$	−2.36603	−	4.09808i	−0.399931	−	0.692701i
$36$	1.23205	−	2.13397i	0.205342	−	0.355662i
$37$	2.96410	+	11.0622i	0.487295	+	1.81861i	0.569495	+	0.821995i	$0.307139\pi$
$37$	2.96410	+	11.0622i	0.487295	+	1.81861i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	2.36603	+	8.83013i	0.383820	+	1.43244i
$39$	1.36603	+	0.366025i	0.218739	+	0.0586110i
$40$	−1.50000	−	5.59808i	−0.237171	−	0.885134i
$41$	−7.09808	+	1.90192i	−1.10853	+	0.297031i	−0.766235	−	0.642561i	$-0.777872\pi$
$41$	−7.09808	+	1.90192i	−1.10853	+	0.297031i	−0.342298	+	0.939591i	$0.611205\pi$
$42$	−1.26795	+	1.26795i	−0.195649	+	0.195649i
$43$	−4.09808	+	7.09808i	−0.624951	+	1.08245i	0.363600	+	0.931555i	$0.381548\pi$
$43$	−4.09808	+	7.09808i	−0.624951	+	1.08245i	−0.988550	+	0.150891i	$0.951786\pi$
$44$	−3.00000	−	1.73205i	−0.452267	−	0.261116i
$45$	5.83013	+	5.83013i	0.869104	+	0.869104i
$46$	−10.3923	+	10.3923i	−1.53226	+	1.53226i
$47$	−0.928203			−0.135392			−0.0676962	−	0.997706i	$-0.521565\pi$
$47$	−0.928203			−0.135392			−0.0676962	+	0.997706i	$0.521565\pi$
$48$	−3.16987	+	1.83013i	−0.457532	+	0.264156i
$49$	4.33013	−	2.50000i	0.618590	−	0.357143i
$50$	−10.7321			−1.51774
$51$	0.803848	−	0.803848i	0.112561	−	0.112561i
$52$	−1.36603	−	1.36603i	−0.189434	−	0.189434i
$53$	2.59808	+	1.50000i	0.356873	+	0.206041i	0.667708	−	0.744423i	$-0.267275\pi$
$53$	2.59808	+	1.50000i	0.356873	+	0.206041i	−0.310835	+	0.950464i	$0.600609\pi$
$54$	3.46410	−	6.00000i	0.471405	−	0.816497i
$55$	8.19615	−	8.19615i	1.10517	−	1.10517i
$56$	−2.36603	+	0.633975i	−0.316173	+	0.0847184i
$57$	1.00000	+	3.73205i	0.132453	+	0.494322i
$58$	−1.09808	−	0.294229i	−0.144184	−	0.0386341i
$59$	−1.26795	−	4.73205i	−0.165073	−	0.616061i	−0.998031	−	0.0627243i	$-0.980021\pi$
$59$	−1.26795	−	4.73205i	−0.165073	−	0.616061i	0.832958	−	0.553336i	$-0.186646\pi$
$60$	0.633975	+	2.36603i	0.0818458	+	0.305453i
$61$	0.866025	−	1.50000i	0.110883	−	0.192055i	−0.805243	−	0.592944i	$-0.797965\pi$
$61$	0.866025	−	1.50000i	0.110883	−	0.192055i	0.916127	+	0.400889i	$0.131299\pi$
$62$	3.63397	+	6.29423i	0.461515	+	0.799368i
$63$	2.46410	−	2.46410i	0.310448	−	0.310448i
$64$	−1.00000			−0.125000
$65$	5.59808	−	3.23205i	0.694356	−	0.400887i
$66$	−3.80385	−	2.19615i	−0.468221	−	0.270328i
$67$	−2.73205	−	2.73205i	−0.333773	−	0.333773i	0.520244	−	0.854017i	$-0.325841\pi$
$67$	−2.73205	−	2.73205i	−0.333773	−	0.333773i	−0.854017	+	0.520244i	$0.825841\pi$
$68$	−1.50000	+	0.401924i	−0.181902	+	0.0487404i
$69$	−4.39230	+	4.39230i	−0.528771	+	0.528771i
$70$			8.19615i			0.979628i
$71$	5.36603	+	1.43782i	0.636830	+	0.170638i	0.562767	−	0.826615i	$-0.309737\pi$
$71$	5.36603	+	1.43782i	0.636830	+	0.170638i	0.0740629	+	0.997254i	$0.476403\pi$
$72$	3.69615	−	2.13397i	0.435596	−	0.251491i
$73$	−7.19615	+	12.4641i	−0.842246	+	1.45881i	0.0457457	+	0.998953i	$0.485434\pi$
$73$	−7.19615	+	12.4641i	−0.842246	+	1.45881i	−0.887992	+	0.459860i	$0.847900\pi$
$74$	5.13397	−	19.1603i	0.596812	−	2.22733i
$75$	−4.53590			−0.523760
$76$	1.36603	−	5.09808i	0.156694	−	0.584789i
$77$	−3.46410	−	3.46410i	−0.394771	−	0.394771i
$78$	−1.73205	−	1.73205i	−0.196116	−	0.196116i
$79$		−	6.00000i		−	0.675053i	−0.941316	−	0.337526i	$-0.890410\pi$
$79$		−	6.00000i		−	0.675053i	0.941316	−	0.337526i	$-0.109590\pi$
$80$	−4.33013	+	16.1603i	−0.484123	+	1.80677i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	12.2942	+	3.29423i	1.35767	+	0.363787i
$83$	3.63397	−	13.5622i	0.398881	−	1.48864i	−0.416188	−	0.909278i	$-0.636634\pi$
$83$	3.63397	−	13.5622i	0.398881	−	1.48864i	0.815069	−	0.579364i	$-0.196699\pi$
$84$	1.00000	−	0.267949i	0.109109	−	0.0292357i
$85$		−	5.19615i		−	0.563602i
$86$	12.2942	−	7.09808i	1.32572	−	0.765405i
$87$	−0.464102	−	0.124356i	−0.0497569	−	0.0133323i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$		−	0.464102i		−	0.0491947i	−0.999697	−	0.0245973i	$-0.992170\pi$
$89$		−	0.464102i		−	0.0491947i	0.999697	−	0.0245973i	$-0.00783037\pi$
$90$	−3.69615	−	13.7942i	−0.389609	−	1.45404i
$91$	−1.36603	−	2.36603i	−0.143198	−	0.248027i
$92$	8.19615	−	2.19615i	0.854508	−	0.228965i
$93$	1.53590	+	2.66025i	0.159265	+	0.275855i
$94$	1.39230	+	0.803848i	0.143605	+	0.0829105i
$95$	15.2942	+	8.83013i	1.56915	+	0.905952i
$96$	3.80385			0.388229
$97$	−9.00000	+	4.00000i	−0.913812	+	0.406138i
$97$	−9.00000	+	4.00000i	−0.913812	+	0.406138i
$98$	−8.66025			−0.874818
$99$	7.39230	+	4.26795i	0.742955	+	0.428945i
$100$	5.36603	+	3.09808i	0.536603	+	0.309808i
$101$	8.42820	+	14.5981i	0.838638	+	1.45256i	0.891034	+	0.453937i	$0.149981\pi$
$101$	8.42820	+	14.5981i	0.838638	+	1.45256i	−0.0523965	+	0.998626i	$0.516686\pi$
$102$	−1.90192	+	0.509619i	−0.188319	+	0.0504598i
$103$	−3.19615	−	5.53590i	−0.314926	−	0.545468i	0.664496	−	0.747292i	$-0.268646\pi$
$103$	−3.19615	−	5.53590i	−0.314926	−	0.545468i	−0.979422	+	0.201824i	$0.935313\pi$
$104$	−0.866025	−	3.23205i	−0.0849208	−	0.316929i
$105$			3.46410i			0.338062i
$106$	−2.59808	−	4.50000i	−0.252347	−	0.437079i
$107$	−11.8301	−	3.16987i	−1.14366	−	0.306443i	−0.363239	−	0.931696i	$-0.618329\pi$
$107$	−11.8301	−	3.16987i	−1.14366	−	0.306443i	−0.780422	+	0.625253i	$0.784996\pi$
$108$	−3.46410	+	2.00000i	−0.333333	+	0.192450i
$109$		−	11.0000i		−	1.05361i	−0.849987	−	0.526804i	$-0.823390\pi$
$109$		−	11.0000i		−	1.05361i	0.849987	−	0.526804i	$-0.176610\pi$
$110$	−19.3923	+	5.19615i	−1.84898	+	0.495434i
$111$	2.16987	−	8.09808i	0.205955	−	0.768635i
$112$	6.83013	+	1.83013i	0.645386	+	0.172931i
$113$	2.19615	−	3.80385i	0.206597	−	0.357836i	−0.744044	−	0.668131i	$-0.767095\pi$
$113$	2.19615	−	3.80385i	0.206597	−	0.357836i	0.950640	+	0.310295i	$0.100428\pi$
$114$	1.73205	−	6.46410i	0.162221	−	0.605419i
$115$			28.3923i			2.64760i
$116$	0.464102	+	0.464102i	0.0430908	+	0.0430908i
$117$	3.36603	+	3.36603i	0.311189	+	0.311189i
$118$	−2.19615	+	8.19615i	−0.202172	+	0.754517i
$119$	−2.19615			−0.201321
$120$	−1.09808	+	4.09808i	−0.100240	+	0.374101i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−2.59808	+	1.50000i	−0.235219	+	0.135804i
$123$	5.19615	+	1.39230i	0.468521	+	0.125540i
$124$		−	4.19615i		−	0.376826i
$125$	−2.83013	+	2.83013i	−0.253134	+	0.253134i
$126$	−5.83013	+	1.56218i	−0.519389	+	0.139170i
$127$	−1.53590	−	1.53590i	−0.136289	−	0.136289i	0.635671	−	0.771960i	$-0.280723\pi$
$127$	−1.53590	−	1.53590i	−0.136289	−	0.136289i	−0.771960	+	0.635671i	$0.780723\pi$
$128$	10.5000	+	6.06218i	0.928078	+	0.535826i
$129$	5.19615	−	3.00000i	0.457496	−	0.264135i
$130$	−11.1962			−0.981968
$131$	−13.7321	+	13.7321i	−1.19977	+	1.19977i	−0.225541	+	0.974234i	$0.572415\pi$
$131$	−13.7321	+	13.7321i	−1.19977	+	1.19977i	−0.974234	+	0.225541i	$0.927585\pi$
$132$	1.26795	+	2.19615i	0.110361	+	0.191151i
$133$	3.73205	−	6.46410i	0.323610	−	0.560509i
$134$	1.73205	+	6.46410i	0.149626	+	0.558413i
$135$	−3.46410	−	12.9282i	−0.298142	−	1.11268i
$136$	−2.59808	−	0.696152i	−0.222783	−	0.0596946i
$137$	−1.03590	−	3.86603i	−0.0885028	−	0.330297i	0.907452	−	0.420156i	$-0.138025\pi$
$137$	−1.03590	−	3.86603i	−0.0885028	−	0.330297i	−0.995954	+	0.0898596i	$0.971358\pi$
$138$	10.3923	−	2.78461i	0.884652	−	0.237042i
$139$	−4.46410	+	4.46410i	−0.378640	+	0.378640i	−0.870611	−	0.491971i	$-0.836276\pi$
$139$	−4.46410	+	4.46410i	−0.378640	+	0.378640i	0.491971	+	0.870611i	$0.336276\pi$
$140$	2.36603	−	4.09808i	0.199966	−	0.346351i
$141$	0.588457	+	0.339746i	0.0495570	+	0.0286118i
$142$	−6.80385	−	6.80385i	−0.570966	−	0.570966i
$143$	4.73205	−	4.73205i	0.395714	−	0.395714i
$144$	−12.3205			−1.02671
$145$	−1.90192	+	1.09808i	−0.157946	+	0.0911903i
$146$	21.5885	−	12.4641i	1.78667	−	1.03154i
$147$	−3.66025			−0.301893
$148$	−8.09808	+	8.09808i	−0.665658	+	0.665658i
$149$	−14.6603	−	14.6603i	−1.20101	−	1.20101i	−0.973858	−	0.227157i	$-0.927057\pi$
$149$	−14.6603	−	14.6603i	−1.20101	−	1.20101i	−0.227157	−	0.973858i	$-0.572943\pi$
$150$	6.80385	+	3.92820i	0.555532	+	0.320736i
$151$	−1.26795	+	2.19615i	−0.103184	+	0.178720i	−0.912995	−	0.407971i	$-0.866236\pi$
$151$	−1.26795	+	2.19615i	−0.103184	+	0.178720i	0.809811	+	0.586691i	$0.199570\pi$
$152$	6.46410	−	6.46410i	0.524308	−	0.524308i
$153$	3.69615	−	0.990381i	0.298816	−	0.0800676i
$154$	2.19615	+	8.19615i	0.176971	+	0.660465i
$155$	13.5622	+	3.63397i	1.08934	+	0.291888i
$156$	0.366025	+	1.36603i	0.0293055	+	0.109370i
$157$	−4.69615	−	17.5263i	−0.374794	−	1.39875i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−4.69615	−	17.5263i	−0.374794	−	1.39875i	0.478852	−	0.877896i	$-0.341053\pi$
$158$	−5.19615	+	9.00000i	−0.413384	+	0.716002i
$159$	−1.09808	−	1.90192i	−0.0870831	−	0.150832i
$160$	12.2942	−	12.2942i	0.971944	−	0.971944i
$161$	12.0000			0.945732
$162$	6.69615	−	3.86603i	0.526099	−	0.303744i
$163$	−15.2942	−	8.83013i	−1.19794	−	0.691629i	−0.237842	−	0.971304i	$-0.576440\pi$
$163$	−15.2942	−	8.83013i	−1.19794	−	0.691629i	−0.960095	+	0.279675i	$0.909773\pi$
$164$	−5.19615	−	5.19615i	−0.405751	−	0.405751i
$165$	−8.19615	+	2.19615i	−0.638070	+	0.170970i
$166$	−17.1962	+	17.1962i	−1.33468	+	1.33468i
$167$			2.53590i			0.196234i	0.995175	+	0.0981169i	$0.0312819\pi$
$167$			2.53590i			0.196234i	−0.995175	+	0.0981169i	$0.968718\pi$
$168$	1.73205	+	0.464102i	0.133631	+	0.0358062i
$169$	−8.02628	+	4.63397i	−0.617406	+	0.356460i
$170$	−4.50000	+	7.79423i	−0.345134	+	0.597790i
$171$	−3.36603	+	12.5622i	−0.257406	+	0.960654i
$172$	−8.19615			−0.624951
$173$	−5.83013	+	21.7583i	−0.443256	+	1.65426i	0.277243	+	0.960800i	$0.410579\pi$
$173$	−5.83013	+	21.7583i	−0.443256	+	1.65426i	−0.720500	+	0.693455i	$0.756087\pi$
$174$	0.588457	+	0.588457i	0.0446108	+	0.0446108i
$175$	6.19615	+	6.19615i	0.468385	+	0.468385i
$176$			17.3205i			1.30558i
$177$	−0.928203	+	3.46410i	−0.0697680	+	0.260378i
$178$	−0.401924	+	0.696152i	−0.0301255	+	0.0521788i
$179$	21.7583	+	5.83013i	1.62629	+	0.435764i	0.952842	−	0.303467i	$-0.0981442\pi$
$179$	21.7583	+	5.83013i	1.62629	+	0.435764i	0.673452	+	0.739231i	$0.264811\pi$
$180$	−2.13397	+	7.96410i	−0.159057	+	0.593609i
$181$	3.09808	−	0.830127i	0.230278	−	0.0617029i	−0.141835	−	0.989890i	$-0.545300\pi$
$181$	3.09808	−	0.830127i	0.230278	−	0.0617029i	0.372113	+	0.928188i	$0.378633\pi$
$182$			4.73205i			0.350763i
$183$	−1.09808	+	0.633975i	−0.0811721	+	0.0468648i
$184$	14.1962	+	3.80385i	1.04655	+	0.280423i
$185$	−19.1603	−	33.1865i	−1.40869	−	2.43992i
$186$		−	5.32051i		−	0.390119i
$187$	−1.39230	−	5.19615i	−0.101815	−	0.379980i
$188$	−0.464102	−	0.803848i	−0.0338481	−	0.0586266i
$189$	−5.46410	+	1.46410i	−0.397455	+	0.106498i
$190$	−15.2942	−	26.4904i	−1.10956	−	1.92181i
$191$	6.00000	+	3.46410i	0.434145	+	0.250654i	0.701111	−	0.713052i	$-0.252688\pi$
$191$	6.00000	+	3.46410i	0.434145	+	0.250654i	−0.266966	+	0.963706i	$0.586021\pi$
$192$	0.633975	+	0.366025i	0.0457532	+	0.0264156i
$193$	19.8564			1.42930			0.714648	−	0.699485i	$-0.246587\pi$
$193$	19.8564			1.42930			0.714648	+	0.699485i	$0.246587\pi$
$194$	16.9641	+	1.79423i	1.21795	+	0.128818i
$195$	−4.73205			−0.338869
$196$	4.33013	+	2.50000i	0.309295	+	0.178571i
$197$	15.6962	+	9.06218i	1.11830	+	0.645653i	0.940968	−	0.338497i	$-0.109918\pi$
$197$	15.6962	+	9.06218i	1.11830	+	0.645653i	0.177337	+	0.984150i	$0.443252\pi$
$198$	−7.39230	−	12.8038i	−0.525348	−	0.909930i
$199$	−5.09808	+	1.36603i	−0.361393	+	0.0968350i	−0.434946	−	0.900456i	$-0.643233\pi$
$199$	−5.09808	+	1.36603i	−0.361393	+	0.0968350i	0.0735534	+	0.997291i	$0.476566\pi$
$200$	5.36603	+	9.29423i	0.379435	+	0.657201i
$201$	0.732051	+	2.73205i	0.0516349	+	0.192704i
$202$		−	29.1962i		−	2.05423i
$203$	0.464102	+	0.803848i	0.0325735	+	0.0564190i
$204$	1.09808	+	0.294229i	0.0768807	+	0.0206001i
$205$	21.2942	−	12.2942i	1.48725	−	0.858666i
$206$			11.0718i			0.771409i
$207$	−20.1962	+	5.41154i	−1.40373	+	0.376128i
$208$	−2.50000	+	9.33013i	−0.173344	+	0.646928i
$209$	17.6603	+	4.73205i	1.22159	+	0.327323i
$210$	3.00000	−	5.19615i	0.207020	−	0.358569i
$211$	−0.437822	+	1.63397i	−0.0301409	+	0.112487i	−0.979357	−	0.202136i	$-0.935212\pi$
$211$	−0.437822	+	1.63397i	−0.0301409	+	0.112487i	0.949217	+	0.314624i	$0.101878\pi$
$212$			3.00000i			0.206041i
$213$	−2.87564	−	2.87564i	−0.197036	−	0.197036i
$214$	15.0000	+	15.0000i	1.02538	+	1.02538i
$215$	7.09808	−	26.4904i	0.484085	−	1.80663i
$216$	−6.92820			−0.471405
$217$	1.53590	−	5.73205i	0.104264	−	0.389117i
$218$	−9.52628	+	16.5000i	−0.645201	+	1.11752i
$219$	9.12436	−	5.26795i	0.616567	−	0.355975i
$220$	11.1962	+	3.00000i	0.754844	+	0.202260i
$221$		−	3.00000i		−	0.201802i
$222$	−10.2679	+	10.2679i	−0.689140	+	0.689140i
$223$	−10.8301	+	2.90192i	−0.725239	+	0.194327i	−0.602508	−	0.798113i	$-0.705832\pi$
$223$	−10.8301	+	2.90192i	−0.725239	+	0.194327i	−0.122731	+	0.992440i	$0.539165\pi$
$224$	−5.19615	−	5.19615i	−0.347183	−	0.347183i
$225$	−13.2224	−	7.63397i	−0.881495	−	0.508932i
$226$	−6.58846	+	3.80385i	−0.438258	+	0.253028i
$227$	−6.58846			−0.437291			−0.218646	−	0.975804i	$-0.570164\pi$
$227$	−6.58846			−0.437291			−0.218646	+	0.975804i	$0.570164\pi$
$228$	−2.73205	+	2.73205i	−0.180934	+	0.180934i
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	24.5885	−	42.5885i	1.62131	−	2.80820i
$231$	0.928203	+	3.46410i	0.0610713	+	0.227921i
$232$	0.294229	+	1.09808i	0.0193171	+	0.0720922i
$233$	−14.0263	−	3.75833i	−0.918892	−	0.246216i	−0.231780	−	0.972768i	$-0.574455\pi$
$233$	−14.0263	−	3.75833i	−0.918892	−	0.246216i	−0.687112	+	0.726552i	$0.741122\pi$
$234$	−2.13397	−	7.96410i	−0.139502	−	0.520630i
$235$	3.00000	−	0.803848i	0.195698	−	0.0524372i
$236$	3.46410	−	3.46410i	0.225494	−	0.225494i
$237$	−2.19615	+	3.80385i	−0.142655	+	0.247086i
$238$	3.29423	+	1.90192i	0.213533	+	0.123283i
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$	8.66025	−	8.66025i	0.559017	−	0.559017i
$241$	27.9282			1.79901			0.899507	−	0.436907i	$-0.143926\pi$
$241$	27.9282			1.79901			0.899507	+	0.436907i	$0.143926\pi$
$242$	−1.50000	+	0.866025i	−0.0964237	+	0.0556702i
$243$	13.2224	−	7.63397i	0.848219	−	0.489720i
$244$	1.73205			0.110883
$245$	−11.8301	+	11.8301i	−0.755799	+	0.755799i
$246$	−6.58846	−	6.58846i	−0.420065	−	0.420065i
$247$	8.83013	+	5.09808i	0.561848	+	0.324383i
$248$	3.63397	−	6.29423i	0.230758	−	0.399684i
$249$	−7.26795	+	7.26795i	−0.460588	+	0.460588i
$250$	6.69615	−	1.79423i	0.423502	−	0.113477i
$251$	−7.43782	−	27.7583i	−0.469471	−	1.75209i	−0.641623	−	0.767020i	$-0.721739\pi$
$251$	−7.43782	−	27.7583i	−0.469471	−	1.75209i	0.172152	−	0.985070i	$-0.444928\pi$
$252$	3.36603	+	0.901924i	0.212040	+	0.0568159i
$253$	7.60770	+	28.3923i	0.478292	+	1.78501i
$254$	0.973721	+	3.63397i	0.0610967	+	0.228016i
$255$	−1.90192	+	3.29423i	−0.119103	+	0.206293i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−17.3660	+	17.3660i	−1.08326	+	1.08326i	−0.0870598	+	0.996203i	$0.527747\pi$
$257$	−17.3660	+	17.3660i	−1.08326	+	1.08326i	−0.996203	+	0.0870598i	$0.972253\pi$
$258$	−10.3923			−0.646997
$259$	−14.0263	+	8.09808i	−0.871551	+	0.503190i
$260$	5.59808	+	3.23205i	0.347178	+	0.200443i
$261$	−1.14359	−	1.14359i	−0.0707867	−	0.0707867i
$262$	32.4904	−	8.70577i	2.00726	−	0.537844i
$263$	3.00000	−	3.00000i	0.184988	−	0.184988i	−0.608537	−	0.793525i	$-0.708243\pi$
$263$	3.00000	−	3.00000i	0.184988	−	0.184988i	0.793525	+	0.608537i	$0.208243\pi$
$264$			4.39230i			0.270328i
$265$	−9.69615	−	2.59808i	−0.595630	−	0.159599i
$266$	−11.1962	+	6.46410i	−0.686480	+	0.396339i
$267$	−0.169873	+	0.294229i	−0.0103961	+	0.0180065i
$268$	1.00000	−	3.73205i	0.0610847	−	0.227971i
$269$	−16.2679			−0.991874			−0.495937	−	0.868358i	$-0.665175\pi$
$269$	−16.2679			−0.991874			−0.495937	+	0.868358i	$0.665175\pi$
$270$	−6.00000	+	22.3923i	−0.365148	+	1.36275i
$271$	8.73205	+	8.73205i	0.530434	+	0.530434i	0.920702	−	0.390267i	$-0.127617\pi$
$271$	8.73205	+	8.73205i	0.530434	+	0.530434i	−0.390267	+	0.920702i	$0.627617\pi$
$272$	5.49038	+	5.49038i	0.332903	+	0.332903i
$273$			2.00000i			0.121046i
$274$	−1.79423	+	6.69615i	−0.108393	+	0.404529i
$275$	−10.7321	+	18.5885i	−0.647167	+	1.12093i
$276$	−6.00000	−	1.60770i	−0.361158	−	0.0967719i
$277$	5.40192	−	20.1603i	0.324570	−	1.21131i	−0.590173	−	0.807277i	$-0.700941\pi$
$277$	5.40192	−	20.1603i	0.324570	−	1.21131i	0.914743	−	0.404036i	$-0.132393\pi$
$278$	10.5622	−	2.83013i	0.633477	−	0.169740i
$279$			10.3397i			0.619024i
$280$	7.09808	−	4.09808i	0.424191	−	0.244907i
$281$	−13.0981	−	3.50962i	−0.781366	−	0.209366i	−0.153979	−	0.988074i	$-0.549209\pi$
$281$	−13.0981	−	3.50962i	−0.781366	−	0.209366i	−0.627387	+	0.778708i	$0.715875\pi$
$282$	−0.588457	−	1.01924i	−0.0350421	−	0.0606947i
$283$			11.3205i			0.672934i	0.941695	+	0.336467i	$0.109232\pi$
$283$			11.3205i			0.672934i	−0.941695	+	0.336467i	$0.890768\pi$
$284$	1.43782	+	5.36603i	0.0853190	+	0.318415i
$285$	−6.46410	−	11.1962i	−0.382900	−	0.663203i
$286$	−11.1962	+	3.00000i	−0.662042	+	0.177394i
$287$	−5.19615	−	9.00000i	−0.306719	−	0.531253i
$288$	11.0885	+	6.40192i	0.653394	+	0.377237i
$289$	12.6340	+	7.29423i	0.743175	+	0.429072i
$290$	3.80385			0.223370
$291$	7.16987	+	0.758330i	0.420305	+	0.0444541i
$292$	−14.3923			−0.842246
$293$	−6.69615	−	3.86603i	−0.391193	−	0.225856i	0.291484	−	0.956576i	$-0.405851\pi$
$293$	−6.69615	−	3.86603i	−0.391193	−	0.225856i	−0.682677	+	0.730720i	$0.739184\pi$
$294$	5.49038	+	3.16987i	0.320206	+	0.184871i
$295$	8.19615	+	14.1962i	0.477198	+	0.826532i
$296$	−19.1603	+	5.13397i	−1.11367	+	0.298406i
$297$	−6.92820	−	12.0000i	−0.402015	−	0.696311i
$298$	9.29423	+	34.6865i	0.538400	+	2.00934i
$299$			16.3923i			0.947991i
$300$	−2.26795	−	3.92820i	−0.130940	−	0.226795i
$301$	−11.1962	−	3.00000i	−0.645335	−	0.172917i
$302$	3.80385	−	2.19615i	0.218887	−	0.126374i
$303$		−	12.3397i		−	0.708900i
$304$	−25.4904	+	6.83013i	−1.46197	+	0.391735i
$305$	−1.50000	+	5.59808i	−0.0858898	+	0.320545i
$306$	−6.40192	−	1.71539i	−0.365974	−	0.0980623i
$307$	−5.80385	+	10.0526i	−0.331243	+	0.573730i	−0.982756	−	0.184908i	$-0.940801\pi$
$307$	−5.80385	+	10.0526i	−0.331243	+	0.573730i	0.651513	+	0.758638i	$0.274135\pi$
$308$	1.26795	−	4.73205i	0.0722481	−	0.269634i
$309$			4.67949i			0.266207i
$310$	−17.1962	−	17.1962i	−0.976676	−	0.976676i
$311$	−7.39230	−	7.39230i	−0.419179	−	0.419179i	0.465742	−	0.884921i	$-0.345788\pi$
$311$	−7.39230	−	7.39230i	−0.419179	−	0.419179i	−0.884921	+	0.465742i	$0.845788\pi$
$312$	−0.633975	+	2.36603i	−0.0358917	+	0.133950i
$313$	1.58846			0.0897849			0.0448925	−	0.998992i	$-0.485705\pi$
$313$	1.58846			0.0897849			0.0448925	+	0.998992i	$0.485705\pi$
$314$	−8.13397	+	30.3564i	−0.459027	+	1.71311i
$315$	−5.83013	+	10.0981i	−0.328490	+	0.568962i
$316$	5.19615	−	3.00000i	0.292306	−	0.168763i
$317$	3.23205	+	0.866025i	0.181530	+	0.0486408i	0.348439	−	0.937332i	$-0.386712\pi$
$317$	3.23205	+	0.866025i	0.181530	+	0.0486408i	−0.166909	+	0.985972i	$0.553379\pi$
$318$			3.80385i			0.213309i
$319$	−1.60770	+	1.60770i	−0.0900136	+	0.0900136i
$320$	3.23205	−	0.866025i	0.180677	−	0.0484123i
$321$	6.33975	+	6.33975i	0.353850	+	0.353850i
$322$	−18.0000	−	10.3923i	−1.00310	−	0.579141i
$323$	7.09808	−	4.09808i	0.394948	−	0.228023i
$324$	−4.46410			−0.248006
$325$	−8.46410	+	8.46410i	−0.469504	+	0.469504i
$326$	15.2942	+	26.4904i	0.847069	+	1.46717i
$327$	−4.02628	+	6.97372i	−0.222654	+	0.385648i
$328$	−3.29423	−	12.2942i	−0.181893	−	0.678835i
$329$	−0.339746	−	1.26795i	−0.0187308	−	0.0699043i
$330$	14.1962	+	3.80385i	0.781472	+	0.209395i
$331$	−7.80385	−	29.1244i	−0.428938	−	1.60082i	−0.755170	−	0.655529i	$-0.772446\pi$
$331$	−7.80385	−	29.1244i	−0.428938	−	1.60082i	0.326231	−	0.945290i	$-0.394221\pi$
$332$	13.5622	−	3.63397i	0.744321	−	0.199440i
$333$	19.9545	−	19.9545i	1.09350	−	1.09350i
$334$	2.19615	−	3.80385i	0.120168	−	0.208137i
$335$	11.1962	+	6.46410i	0.611711	+	0.353172i
$336$	−3.66025	−	3.66025i	−0.199683	−	0.199683i
$337$	−1.19615	+	1.19615i	−0.0651586	+	0.0651586i	−0.738935	−	0.673777i	$-0.764671\pi$
$337$	−1.19615	+	1.19615i	−0.0651586	+	0.0651586i	0.673777	+	0.738935i	$0.264671\pi$
$338$	16.0526			0.873144
$339$	−2.78461	+	1.60770i	−0.151239	+	0.0873180i
$340$	4.50000	−	2.59808i	0.244047	−	0.140900i
$341$	14.5359			0.787163
$342$	15.9282	−	15.9282i	0.861299	−	0.861299i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−12.2942	−	7.09808i	−0.662860	−	0.382703i
$345$	10.3923	−	18.0000i	0.559503	−	0.969087i
$346$	27.5885	−	27.5885i	1.48316	−	1.48316i
$347$	15.9282	−	4.26795i	0.855071	−	0.229116i	0.195450	−	0.980714i	$-0.437383\pi$
$347$	15.9282	−	4.26795i	0.855071	−	0.229116i	0.659621	+	0.751598i	$0.270717\pi$
$348$	−0.124356	−	0.464102i	−0.00666616	−	0.0248785i
$349$	−3.09808	−	0.830127i	−0.165836	−	0.0444357i	0.174946	−	0.984578i	$-0.444025\pi$
$349$	−3.09808	−	0.830127i	−0.165836	−	0.0444357i	−0.340782	+	0.940142i	$0.610692\pi$
$350$	−3.92820	−	14.6603i	−0.209971	−	0.783624i
$351$	−2.00000	−	7.46410i	−0.106752	−	0.398404i
$352$	9.00000	−	15.5885i	0.479702	−	0.830868i
$353$	1.03590	+	1.79423i	0.0551353	+	0.0954972i	0.892276	−	0.451491i	$-0.149108\pi$
$353$	1.03590	+	1.79423i	0.0551353	+	0.0954972i	−0.837140	+	0.546988i	$0.815774\pi$
$354$	4.39230	−	4.39230i	0.233448	−	0.233448i
$355$	−18.5885			−0.986573
$356$	0.401924	−	0.232051i	0.0213019	−	0.0122987i
$357$	1.39230	+	0.803848i	0.0736886	+	0.0425441i
$358$	−27.5885	−	27.5885i	−1.45810	−	1.45810i
$359$	18.7583	−	5.02628i	0.990027	−	0.265277i	0.272765	−	0.962081i	$-0.412062\pi$
$359$	18.7583	−	5.02628i	0.990027	−	0.265277i	0.717262	+	0.696804i	$0.245395\pi$
$360$	−10.0981	+	10.0981i	−0.532215	+	0.532215i
$361$			8.85641i			0.466127i
$362$	−5.36603	−	1.43782i	−0.282032	−	0.0755703i
$363$	−0.633975	+	0.366025i	−0.0332750	+	0.0192114i
$364$	1.36603	−	2.36603i	0.0715992	−	0.124013i
$365$	12.4641	−	46.5167i	0.652401	−	2.43479i
$366$	2.19615			0.114795
$367$	0.0980762	−	0.366025i	0.00511954	−	0.0191064i	−0.963319	−	0.268360i	$-0.913518\pi$
$367$	0.0980762	−	0.366025i	0.00511954	−	0.0191064i	0.968438	+	0.249253i	$0.0801851\pi$
$368$	−30.0000	−	30.0000i	−1.56386	−	1.56386i
$369$	12.8038	+	12.8038i	0.666542	+	0.666542i
$370$			66.3731i			3.45057i
$371$	−1.09808	+	4.09808i	−0.0570093	+	0.212762i
$372$	−1.53590	+	2.66025i	−0.0796326	+	0.137928i
$373$	−13.2583	−	3.55256i	−0.686490	−	0.183945i	−0.101319	−	0.994854i	$-0.532306\pi$
$373$	−13.2583	−	3.55256i	−0.686490	−	0.183945i	−0.585172	+	0.810909i	$0.698973\pi$
$374$	−2.41154	+	9.00000i	−0.124698	+	0.465379i
$375$	2.83013	−	0.758330i	0.146147	−	0.0391600i
$376$		−	1.60770i		−	0.0829105i
$377$	−1.09808	+	0.633975i	−0.0565538	+	0.0326514i
$378$	9.46410	+	2.53590i	0.486781	+	0.130433i
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	0.994992	−	0.0999550i	$-0.0318699\pi$
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	−0.584060	+	0.811711i	$0.698537\pi$
$380$			17.6603i			0.905952i
$381$	0.411543	+	1.53590i	0.0210840	+	0.0786865i
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	24.5885	−	6.58846i	1.25641	−	0.336654i	0.431601	−	0.902064i	$-0.357949\pi$
$383$	24.5885	−	6.58846i	1.25641	−	0.336654i	0.824810	+	0.565410i	$0.191282\pi$
$384$	−4.43782	−	7.68653i	−0.226467	−	0.392252i
$385$	14.1962	+	8.19615i	0.723503	+	0.417715i
$386$	−29.7846	−	17.1962i	−1.51600	−	0.875261i
$387$	20.1962			1.02663
$388$	−7.96410	−	5.79423i	−0.404316	−	0.294157i
$389$	−8.07180			−0.409256			−0.204628	−	0.978840i	$-0.565599\pi$
$389$	−8.07180			−0.409256			−0.204628	+	0.978840i	$0.565599\pi$
$390$	7.09808	+	4.09808i	0.359425	+	0.207514i
$391$	11.4115	+	6.58846i	0.577107	+	0.333193i
$392$	4.33013	+	7.50000i	0.218704	+	0.378807i
$393$	13.7321	−	3.67949i	0.692690	−	0.185606i
$394$	−15.6962	−	27.1865i	−0.790761	−	1.36964i
$395$	5.19615	+	19.3923i	0.261447	+	0.975733i
$396$			8.53590i			0.428945i
$397$	4.73205	+	8.19615i	0.237495	+	0.411353i	0.959995	−	0.280018i	$-0.0903404\pi$
$397$	4.73205	+	8.19615i	0.237495	+	0.411353i	−0.722500	+	0.691371i	$0.757007\pi$
$398$	8.83013	+	2.36603i	0.442614	+	0.118598i
$399$	−4.73205	+	2.73205i	−0.236899	+	0.136774i
$400$		−	30.9808i		−	1.54904i
$401$	−2.76795	+	0.741670i	−0.138225	+	0.0370372i	−0.327268	−	0.944932i	$-0.606128\pi$
$401$	−2.76795	+	0.741670i	−0.138225	+	0.0370372i	0.189043	+	0.981969i	$0.439461\pi$
$402$	1.26795	−	4.73205i	0.0632396	−	0.236013i
$403$	7.83013	+	2.09808i	0.390046	+	0.104513i
$404$	−8.42820	+	14.5981i	−0.419319	+	0.726281i
$405$	3.86603	−	14.4282i	0.192104	−	0.716943i
$406$		−	1.60770i		−	0.0797886i
$407$	−28.0526	−	28.0526i	−1.39051	−	1.39051i
$408$	1.39230	+	1.39230i	0.0689294	+	0.0689294i
$409$	−1.10770	+	4.13397i	−0.0547720	+	0.204412i	−0.987889	−	0.155160i	$-0.950411\pi$
$409$	−1.10770	+	4.13397i	−0.0547720	+	0.204412i	0.933117	+	0.359572i	$0.117077\pi$
$410$	−42.5885			−2.10329
$411$	−0.758330	+	2.83013i	−0.0374057	+	0.139600i
$412$	3.19615	−	5.53590i	0.157463	−	0.272734i
$413$	6.00000	−	3.46410i	0.295241	−	0.170457i
$414$	34.9808	+	9.37307i	1.71921	+	0.460661i
$415$			46.9808i			2.30619i
$416$	7.09808	−	7.09808i	0.348012	−	0.348012i
$417$	4.46410	−	1.19615i	0.218608	−	0.0585758i
$418$	−22.3923	−	22.3923i	−1.09524	−	1.09524i
$419$	1.90192	+	1.09808i	0.0929151	+	0.0536445i	0.545738	−	0.837956i	$-0.316250\pi$
$419$	1.90192	+	1.09808i	0.0929151	+	0.0536445i	−0.452823	+	0.891601i	$0.649583\pi$
$420$	−3.00000	+	1.73205i	−0.146385	+	0.0845154i
$421$	31.6410			1.54209			0.771044	−	0.636781i	$-0.219735\pi$
$421$	31.6410			1.54209			0.771044	+	0.636781i	$0.219735\pi$
$422$	2.07180	−	2.07180i	0.100853	−	0.100853i
$423$	1.14359	+	1.98076i	0.0556034	+	0.0963079i
$424$	−2.59808	+	4.50000i	−0.126174	+	0.218539i
$425$	2.49038	+	9.29423i	0.120801	+	0.450836i
$426$	1.82309	+	6.80385i	0.0883288	+	0.329647i
$427$	2.36603	+	0.633975i	0.114500	+	0.0306802i
$428$	−3.16987	−	11.8301i	−0.153222	−	0.571831i
$429$	−4.73205	+	1.26795i	−0.228466	+	0.0612172i
$430$	−33.5885	+	33.5885i	−1.61978	+	1.61978i
$431$	4.09808	−	7.09808i	0.197397	−	0.341902i	−0.750286	−	0.661113i	$-0.770084\pi$
$431$	4.09808	−	7.09808i	0.197397	−	0.341902i	0.947684	+	0.319211i	$0.103418\pi$
$432$	17.3205	+	10.0000i	0.833333	+	0.481125i
$433$	−6.09808	−	6.09808i	−0.293055	−	0.293055i	0.545231	−	0.838286i	$-0.316442\pi$
$433$	−6.09808	−	6.09808i	−0.293055	−	0.293055i	−0.838286	+	0.545231i	$0.816442\pi$
$434$	−7.26795	+	7.26795i	−0.348873	+	0.348873i
$435$	1.60770			0.0770831
$436$	9.52628	−	5.50000i	0.456226	−	0.263402i
$437$	−38.7846	+	22.3923i	−1.85532	+	1.07117i
$438$	−18.2487			−0.871957
$439$	17.2679	−	17.2679i	0.824154	−	0.824154i	−0.162547	−	0.986701i	$-0.551971\pi$
$439$	17.2679	−	17.2679i	0.824154	−	0.824154i	0.986701	+	0.162547i	$0.0519708\pi$
$440$	14.1962	+	14.1962i	0.676775	+	0.676775i
$441$	−10.6699	−	6.16025i	−0.508089	−	0.293345i
$442$	−2.59808	+	4.50000i	−0.123578	+	0.214043i
$443$	−21.4641	+	21.4641i	−1.01979	+	1.01979i	−0.0199901	+	0.999800i	$0.506363\pi$
$443$	−21.4641	+	21.4641i	−1.01979	+	1.01979i	−0.999800	+	0.0199901i	$0.993637\pi$
$444$	8.09808	−	2.16987i	0.384318	−	0.102978i
$445$	0.401924	+	1.50000i	0.0190530	+	0.0711068i
$446$	18.7583	+	5.02628i	0.888233	+	0.238001i
$447$	3.92820	+	14.6603i	0.185798	+	0.693406i
$448$	−0.366025	−	1.36603i	−0.0172931	−	0.0645386i
$449$	9.06218	−	15.6962i	0.427671	−	0.740747i	−0.568995	−	0.822341i	$-0.692668\pi$
$449$	9.06218	−	15.6962i	0.427671	−	0.740747i	0.996666	+	0.0815937i	$0.0260010\pi$
$450$	13.2224	+	22.9019i	0.623311	+	1.07961i
$451$	18.0000	−	18.0000i	0.847587	−	0.847587i
$452$	4.39230			0.206597
$453$	1.60770	−	0.928203i	0.0755361	−	0.0436108i
$454$	9.88269	+	5.70577i	0.463817	+	0.267785i
$455$	6.46410	+	6.46410i	0.303042	+	0.303042i
$456$	−6.46410	+	1.73205i	−0.302709	+	0.0811107i
$457$	−9.73205	+	9.73205i	−0.455246	+	0.455246i	−0.897091	−	0.441845i	$-0.854324\pi$
$457$	−9.73205	+	9.73205i	−0.455246	+	0.455246i	0.441845	+	0.897091i	$0.354324\pi$
$458$			17.3205i			0.809334i
$459$	−6.00000	−	1.60770i	−0.280056	−	0.0750408i
$460$	−24.5885	+	14.1962i	−1.14644	+	0.661899i
$461$	−7.33013	+	12.6962i	−0.341398	+	0.591319i	−0.984693	−	0.174300i	$-0.944234\pi$
$461$	−7.33013	+	12.6962i	−0.341398	+	0.591319i	0.643295	+	0.765619i	$0.277567\pi$
$462$	1.60770	−	6.00000i	0.0747967	−	0.279145i
$463$	−20.1962			−0.938595			−0.469297	−	0.883040i	$-0.655493\pi$
$463$	−20.1962			−0.938595			−0.469297	+	0.883040i	$0.655493\pi$
$464$	0.849365	−	3.16987i	0.0394308	−	0.147158i
$465$	−7.26795	−	7.26795i	−0.337043	−	0.337043i
$466$	17.7846	+	17.7846i	0.823856	+	0.823856i
$467$		−	26.4449i		−	1.22372i	−0.790965	−	0.611861i	$-0.790421\pi$
$467$		−	26.4449i		−	1.22372i	0.790965	−	0.611861i	$-0.209579\pi$
$468$	−1.23205	+	4.59808i	−0.0569516	+	0.212546i
$469$	2.73205	−	4.73205i	0.126154	−	0.218506i
$470$	−5.19615	−	1.39230i	−0.239681	−	0.0642222i
$471$	−3.43782	+	12.8301i	−0.158406	+	0.591181i
$472$	8.19615	−	2.19615i	0.377258	−	0.101086i
$473$		−	28.3923i		−	1.30548i
$474$	6.58846	−	3.80385i	0.302618	−	0.174717i
$475$	−31.5885	−	8.46410i	−1.44938	−	0.388360i
$476$	−1.09808	−	1.90192i	−0.0503302	−	0.0871745i
$477$		−	7.39230i		−	0.338470i
$478$	1.90192	+	7.09808i	0.0869920	+	0.324658i
$479$	−0.803848	−	1.39230i	−0.0367287	−	0.0636160i	0.847077	−	0.531471i	$-0.178360\pi$
$479$	−0.803848	−	1.39230i	−0.0367287	−	0.0636160i	−0.883805	+	0.467855i	$0.845027\pi$
$480$	−12.2942	+	3.29423i	−0.561152	+	0.150360i
$481$	−11.0622	−	19.1603i	−0.504392	−	0.873632i
$482$	−41.8923	−	24.1865i	−1.90814	−	1.10167i
$483$	−7.60770	−	4.39230i	−0.346162	−	0.199857i
$484$	1.00000			0.0454545
$485$	25.6244	−	20.7224i	1.16354	−	0.940957i
$486$	−26.4449			−1.19956
$487$	22.3923	+	12.9282i	1.01469	+	0.585833i	0.912562	−	0.408938i	$-0.134101\pi$
$487$	22.3923	+	12.9282i	1.01469	+	0.585833i	0.102130	+	0.994771i	$0.467434\pi$
$488$	2.59808	+	1.50000i	0.117609	+	0.0679018i
$489$	6.46410	+	11.1962i	0.292317	+	0.506308i
$490$	27.9904	−	7.50000i	1.26448	−	0.338815i
$491$	−2.02628	−	3.50962i	−0.0914447	−	0.158387i	0.816675	−	0.577099i	$-0.195815\pi$
$491$	−2.02628	−	3.50962i	−0.0914447	−	0.158387i	−0.908119	+	0.418712i	$0.862482\pi$
$492$	1.39230	+	5.19615i	0.0627700	+	0.234261i
$493$			1.01924i			0.0459042i
$494$	−8.83013	−	15.2942i	−0.397286	−	0.688120i
$495$	−27.5885	−	7.39230i	−1.24001	−	0.332259i
$496$	−18.1699	+	10.4904i	−0.815851	+	0.471032i
$497$			7.85641i			0.352408i
$498$	17.1962	−	4.60770i	0.770578	−	0.206476i
$499$	−9.73205	+	36.3205i	−0.435666	+	1.62593i	0.303800	+	0.952736i	$0.401745\pi$
$499$	−9.73205	+	36.3205i	−0.435666	+	1.62593i	−0.739466	+	0.673193i	$0.764922\pi$
$500$	−3.86603	−	1.03590i	−0.172894	−	0.0463268i
$501$	0.928203	−	1.60770i	0.0414691	−	0.0718265i
$502$	−12.8827	+	48.0788i	−0.574982	+	2.14586i
$503$			24.5885i			1.09635i	0.836365	+	0.548173i	$0.184676\pi$
$503$			24.5885i			1.09635i	−0.836365	+	0.548173i	$0.815324\pi$
$504$	4.26795	+	4.26795i	0.190110	+	0.190110i
$505$	−39.8827	−	39.8827i	−1.77476	−	1.77476i
$506$	13.1769	−	49.1769i	0.585785	−	2.18618i
$507$	6.78461			0.301315
$508$	0.562178	−	2.09808i	0.0249426	−	0.0930871i
$509$	−15.1244	+	26.1962i	−0.670375	+	1.16112i	0.307422	+	0.951573i	$0.400534\pi$
$509$	−15.1244	+	26.1962i	−0.670375	+	1.16112i	−0.977798	+	0.209551i	$0.932800\pi$
$510$	5.70577	−	3.29423i	0.252656	−	0.145871i
$511$	−19.6603	−	5.26795i	−0.869718	−	0.233040i
$512$			8.66025i			0.382733i
$513$	14.9282	−	14.9282i	0.659096	−	0.659096i
$514$	41.0885	−	11.0096i	1.81233	−	0.485613i
$515$	15.1244	+	15.1244i	0.666459	+	0.666459i
$516$	5.19615	+	3.00000i	0.228748	+	0.132068i
$517$	2.78461	−	1.60770i	0.122467	−	0.0707064i
$518$	28.0526			1.23256
$519$	11.6603	−	11.6603i	0.511828	−	0.511828i
$520$	5.59808	+	9.69615i	0.245492	+	0.425204i
$521$	−4.66987	+	8.08846i	−0.204591	+	0.354362i	−0.950002	−	0.312243i	$-0.898920\pi$
$521$	−4.66987	+	8.08846i	−0.204591	+	0.354362i	0.745411	+	0.666605i	$0.232253\pi$
$522$	0.725009	+	2.70577i	0.0317328	+	0.118428i
$523$	0.830127	+	3.09808i	0.0362989	+	0.135469i	0.981697	−	0.190447i	$-0.0609938\pi$
$523$	0.830127	+	3.09808i	0.0362989	+	0.135469i	−0.945399	+	0.325917i	$0.894327\pi$
$524$	−18.7583	−	5.02628i	−0.819461	−	0.219574i
$525$	−1.66025	−	6.19615i	−0.0724594	−	0.270422i
$526$	−7.09808	+	1.90192i	−0.309491	+	0.0829278i
$527$	4.60770	−	4.60770i	0.200714	−	0.200714i
$528$	6.33975	−	10.9808i	0.275902	−	0.477876i
$529$	−42.4352	−	24.5000i	−1.84501	−	1.06522i
$530$	12.2942	+	12.2942i	0.534027	+	0.534027i
$531$	−8.53590	+	8.53590i	−0.370426	+	0.370426i
$532$	7.46410			0.323610
$533$	12.2942	−	7.09808i	0.532522	−	0.307452i
$534$	0.509619	−	0.294229i	0.0220534	−	0.0127325i
$535$	40.9808			1.77175
$536$	4.73205	−	4.73205i	0.204393	−	0.204393i
$537$	−11.6603	−	11.6603i	−0.503177	−	0.503177i
$538$	24.4019	+	14.0885i	1.05204	+	0.607397i
$539$	−8.66025	+	15.0000i	−0.373024	+	0.646096i
$540$	9.46410	−	9.46410i	0.407270	−	0.407270i
$541$	14.7942	−	3.96410i	0.636054	−	0.170430i	0.0736384	−	0.997285i	$-0.476539\pi$
$541$	14.7942	−	3.96410i	0.636054	−	0.170430i	0.562415	+	0.826855i	$0.309872\pi$
$542$	−5.53590	−	20.6603i	−0.237787	−	0.887434i
$543$	−2.26795	−	0.607695i	−0.0973270	−	0.0260787i
$544$	−2.08846	−	7.79423i	−0.0895419	−	0.334175i
$545$	9.52628	+	35.5526i	0.408061	+	1.52290i
$546$	1.73205	−	3.00000i	0.0741249	−	0.128388i
$547$	8.09808	+	14.0263i	0.346249	+	0.599720i	0.985580	−	0.169211i	$-0.0541220\pi$
$547$	8.09808	+	14.0263i	0.346249	+	0.599720i	−0.639331	+	0.768932i	$0.720789\pi$
$548$	2.83013	−	2.83013i	0.120897	−	0.120897i
$549$	−4.26795			−0.182152
$550$	32.1962	−	18.5885i	1.37285	−	0.792614i
$551$	−3.00000	−	1.73205i	−0.127804	−	0.0737878i
$552$	−7.60770	−	7.60770i	−0.323805	−	0.323805i
$553$	8.19615	−	2.19615i	0.348536	−	0.0933899i
$554$	−25.5622	+	25.5622i	−1.08603	+	1.08603i
$555$			28.0526i			1.19076i
$556$	−6.09808	−	1.63397i	−0.258616	−	0.0692960i
$557$	−1.39230	+	0.803848i	−0.0589938	+	0.0340601i	−0.529207	−	0.848493i	$-0.677510\pi$
$557$	−1.39230	+	0.803848i	−0.0589938	+	0.0340601i	0.470213	+	0.882553i	$0.344177\pi$
$558$	8.95448	−	15.5096i	0.379073	−	0.656575i
$559$	4.09808	−	15.2942i	0.173330	−	0.646877i
$560$	−23.6603			−0.999828
$561$	−1.01924	+	3.80385i	−0.0430323	+	0.160599i
$562$	16.6077	+	16.6077i	0.700553	+	0.700553i
$563$	−3.80385	−	3.80385i	−0.160313	−	0.160313i	0.622392	−	0.782705i	$-0.286161\pi$
$563$	−3.80385	−	3.80385i	−0.160313	−	0.160313i	−0.782705	+	0.622392i	$0.786161\pi$
$564$			0.679492i			0.0286118i
$565$	−3.80385	+	14.1962i	−0.160029	+	0.597237i
$566$	9.80385	−	16.9808i	0.412086	−	0.713755i
$567$	−6.09808	−	1.63397i	−0.256095	−	0.0686205i
$568$	−2.49038	+	9.29423i	−0.104494	+	0.389977i
$569$	−14.4904	+	3.88269i	−0.607468	+	0.162771i	−0.549424	−	0.835543i	$-0.685153\pi$
$569$	−14.4904	+	3.88269i	−0.607468	+	0.162771i	−0.0580439	+	0.998314i	$0.518486\pi$
$570$			22.3923i			0.937910i
$571$	0.169873	−	0.0980762i	0.00710896	−	0.00410436i	−0.496441	−	0.868070i	$-0.665360\pi$
$571$	0.169873	−	0.0980762i	0.00710896	−	0.00410436i	0.503550	+	0.863966i	$0.332027\pi$
$572$	6.46410	+	1.73205i	0.270278	+	0.0724207i
$573$	−2.53590	−	4.39230i	−0.105939	−	0.183491i
$574$			18.0000i			0.751305i
$575$	−13.6077	−	50.7846i	−0.567480	−	2.11786i
$576$	1.23205	+	2.13397i	0.0513355	+	0.0889156i
$577$	−9.96410	+	2.66987i	−0.414811	+	0.111148i	−0.460188	−	0.887822i	$-0.652218\pi$
$577$	−9.96410	+	2.66987i	−0.414811	+	0.111148i	0.0453767	+	0.998970i	$0.485551\pi$
$578$	−12.6340	−	21.8827i	−0.525504	−	0.910200i
$579$	−12.5885	−	7.26795i	−0.523158	−	0.302046i
$580$	−1.90192	−	1.09808i	−0.0789731	−	0.0455951i
$581$	19.8564			0.823783
$582$	−10.0981	−	7.34679i	−0.418579	−	0.304534i
$583$	−10.3923			−0.430405
$584$	−21.5885	−	12.4641i	−0.893337	−	0.515768i
$585$	−13.7942	−	7.96410i	−0.570321	−	0.329275i
$586$	6.69615	+	11.5981i	0.276616	+	0.479112i
$587$	−26.4904	+	7.09808i	−1.09338	+	0.292969i	−0.760064	−	0.649848i	$-0.774833\pi$
$587$	−26.4904	+	7.09808i	−1.09338	+	0.292969i	−0.333311	+	0.942817i	$0.608166\pi$
$588$	−1.83013	−	3.16987i	−0.0754732	−	0.130723i
$589$	5.73205	+	21.3923i	0.236185	+	0.881455i
$590$		−	28.3923i		−	1.16889i
$591$	−6.63397	−	11.4904i	−0.272885	−	0.472651i
$592$	55.3109	+	14.8205i	2.27326	+	0.609119i
$593$	−12.0000	+	6.92820i	−0.492781	+	0.284507i	−0.725727	−	0.687982i	$-0.758497\pi$
$593$	−12.0000	+	6.92820i	−0.492781	+	0.284507i	0.232946	+	0.972490i	$0.425163\pi$
$594$			24.0000i			0.984732i
$595$	7.09808	−	1.90192i	0.290993	−	0.0779713i
$596$	5.36603	−	20.0263i	0.219801	−	0.820308i
$597$	3.73205	+	1.00000i	0.152743	+	0.0409273i
$598$	14.1962	−	24.5885i	0.580524	−	1.00550i
$599$	−4.56218	+	17.0263i	−0.186406	+	0.695675i	0.807920	+	0.589293i	$0.200593\pi$
$599$	−4.56218	+	17.0263i	−0.186406	+	0.695675i	−0.994325	+	0.106382i	$0.966073\pi$
$600$		−	7.85641i		−	0.320736i
$601$	12.9019	+	12.9019i	0.526280	+	0.526280i	0.919461	−	0.393181i	$-0.128625\pi$
$601$	12.9019	+	12.9019i	0.526280	+	0.526280i	−0.393181	+	0.919461i	$0.628625\pi$
$602$	14.1962	+	14.1962i	0.578592	+	0.578592i
$603$	−2.46410	+	9.19615i	−0.100346	+	0.374496i
$604$	−2.53590			−0.103184
$605$	−0.866025	+	3.23205i	−0.0352089	+	0.131402i
$606$	−10.6865	+	18.5096i	−0.434111	+	0.751902i
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	−0.0607380	−	0.998154i	$-0.519345\pi$
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	0.834058	+	0.551678i	$0.186012\pi$
$608$	26.4904	+	7.09808i	1.07433	+	0.287865i
$609$		−	0.679492i		−	0.0275344i
$610$	7.09808	−	7.09808i	0.287393	−	0.287393i
$611$	1.73205	−	0.464102i	0.0700713	−	0.0187755i
$612$	2.70577	+	2.70577i	0.109374	+	0.109374i
$613$	−30.1244	−	17.3923i	−1.21671	−	0.702469i	−0.252498	−	0.967597i	$-0.581252\pi$
$613$	−30.1244	−	17.3923i	−1.21671	−	0.702469i	−0.964213	+	0.265129i	$0.914586\pi$
$614$	17.4115	−	10.0526i	0.702673	−	0.405688i
$615$	−18.0000			−0.725830
$616$	6.00000	−	6.00000i	0.241747	−	0.241747i
$617$	14.7224	+	25.5000i	0.592703	+	1.02659i	0.993867	+	0.110585i	$0.0352725\pi$
$617$	14.7224	+	25.5000i	0.592703	+	1.02659i	−0.401164	+	0.916006i	$0.631394\pi$
$618$	4.05256	−	7.01924i	0.163018	−	0.282355i
$619$	−9.70577	−	36.2224i	−0.390108	−	1.45590i	−0.829955	−	0.557830i	$-0.811634\pi$
$619$	−9.70577	−	36.2224i	−0.390108	−	1.45590i	0.439847	−	0.898073i	$-0.355033\pi$
$620$	3.63397	+	13.5622i	0.145944	+	0.544670i
$621$	32.7846	+	8.78461i	1.31560	+	0.352514i
$622$	4.68653	+	17.4904i	0.187913	+	0.701300i
$623$	0.633975	−	0.169873i	0.0253997	−	0.00680582i
$624$	5.00000	−	5.00000i	0.200160	−	0.200160i
$625$	−8.79423	+	15.2321i	−0.351769	+	0.609282i
$626$	−2.38269	−	1.37564i	−0.0952313	−	0.0549818i
$627$	−9.46410	−	9.46410i	−0.377960	−	0.377960i
$628$	12.8301	−	12.8301i	0.511978	−	0.511978i
$629$	−17.7846			−0.709119
$630$	17.4904	−	10.0981i	0.696833	−	0.402317i
$631$	25.2679	−	14.5885i	1.00590	−	0.580757i	0.0959122	−	0.995390i	$-0.469423\pi$
$631$	25.2679	−	14.5885i	1.00590	−	0.580757i	0.909989	+	0.414632i	$0.136090\pi$
$632$	10.3923			0.413384
$633$	0.875644	−	0.875644i	0.0348037	−	0.0348037i
$634$	−4.09808	−	4.09808i	−0.162755	−	0.162755i
$635$	6.29423	+	3.63397i	0.249779	+	0.144210i
$636$	1.09808	−	1.90192i	0.0435416	−	0.0754162i
$637$	−6.83013	+	6.83013i	−0.270619	+	0.270619i
$638$	3.80385	−	1.01924i	0.150596	−	0.0403520i
$639$	−3.54294	−	13.2224i	−0.140157	−	0.523071i
$640$	−39.1865	−	10.5000i	−1.54898	−	0.415049i
$641$	3.69615	+	13.7942i	0.145989	+	0.544839i	0.999709	+	0.0241072i	$0.00767429\pi$
$641$	3.69615	+	13.7942i	0.145989	+	0.544839i	−0.853720	+	0.520732i	$0.825659\pi$
$642$	−4.01924	−	15.0000i	−0.158627	−	0.592003i
$643$	5.53590	−	9.58846i	0.218315	−	0.378132i	−0.735978	−	0.677005i	$-0.763277\pi$
$643$	5.53590	−	9.58846i	0.218315	−	0.378132i	0.954293	+	0.298873i	$0.0966108\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$	−14.1962	+	14.1962i	−0.558973	+	0.558973i
$646$	−14.1962			−0.558540
$647$	−11.4904	+	6.63397i	−0.451733	+	0.260808i	−0.708562	−	0.705649i	$-0.750656\pi$
$647$	−11.4904	+	6.63397i	−0.451733	+	0.260808i	0.256829	+	0.966457i	$0.417322\pi$
$648$	−6.69615	−	3.86603i	−0.263050	−	0.151872i
$649$	12.0000	+	12.0000i	0.471041	+	0.471041i
$650$	20.0263	−	5.36603i	0.785495	−	0.210473i
$651$	−3.07180	+	3.07180i	−0.120393	+	0.120393i
$652$		−	17.6603i		−	0.691629i
$653$	−1.66987	−	0.447441i	−0.0653472	−	0.0175097i	0.225997	−	0.974128i	$-0.427436\pi$
$653$	−1.66987	−	0.447441i	−0.0653472	−	0.0175097i	−0.291345	+	0.956618i	$0.594103\pi$
$654$	12.0788	−	6.97372i	0.472320	−	0.272694i
$655$	32.4904	−	56.2750i	1.26950	−	2.19885i
$656$	−9.50962	+	35.4904i	−0.371288	+	1.38567i
$657$	35.4641			1.38359
$658$	−0.588457	+	2.19615i	−0.0229405	+	0.0856149i
$659$	−13.0526	−	13.0526i	−0.508456	−	0.508456i	0.405597	−	0.914052i	$-0.367064\pi$
$659$	−13.0526	−	13.0526i	−0.508456	−	0.508456i	−0.914052	+	0.405597i	$0.867064\pi$
$660$	−6.00000	−	6.00000i	−0.233550	−	0.233550i
$661$		−	8.07180i		−	0.313957i	−0.987602	−	0.156978i	$-0.949825\pi$
$661$		−	8.07180i		−	0.313957i	0.987602	−	0.156978i	$-0.0501753\pi$
$662$	−13.5167	+	50.4449i	−0.525340	+	1.96060i
$663$	−1.09808	+	1.90192i	−0.0426457	+	0.0738646i
$664$	23.4904	+	6.29423i	0.911604	+	0.244263i
$665$	−6.46410	+	24.1244i	−0.250667	+	0.935502i
$666$	−47.2128	+	12.6506i	−1.82946	+	0.490202i
$667$		−	5.56922i		−	0.215641i
$668$	−2.19615	+	1.26795i	−0.0849717	+	0.0490584i
$669$	7.92820	+	2.12436i	0.306522	+	0.0821323i
$670$	−11.1962	−	19.3923i	−0.432545	−	0.749190i
$671$			6.00000i			0.231627i
$672$	1.39230	+	5.19615i	0.0537093	+	0.200446i
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	0.790650	−	0.612268i	$-0.209743\pi$
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	−0.925565	+	0.378589i	$0.876409\pi$
$674$	2.83013	−	0.758330i	0.109012	−	0.0292098i
$675$	12.3923	+	21.4641i	0.476980	+	0.826154i
$676$	−8.02628	−	4.63397i	−0.308703	−	0.178230i
$677$	1.39230	+	0.803848i	0.0535106	+	0.0308944i	0.526517	−	0.850165i	$-0.323498\pi$
$677$	1.39230	+	0.803848i	0.0535106	+	0.0308944i	−0.473006	+	0.881059i	$0.656831\pi$
$678$	5.56922			0.213885
$679$	−8.75833	−	10.8301i	−0.336114	−	0.415622i
$680$	9.00000			0.345134
$681$	4.17691	+	2.41154i	0.160060	+	0.0924105i
$682$	−21.8038	−	12.5885i	−0.834912	−	0.482037i
$683$	−25.7321	−	44.5692i	−0.984610	−	1.70539i	−0.643659	−	0.765313i	$-0.722584\pi$
$683$	−25.7321	−	44.5692i	−0.984610	−	1.70539i	−0.340951	−	0.940081i	$-0.610749\pi$
$684$	−12.5622	+	3.36603i	−0.480327	+	0.128703i
$685$	6.69615	+	11.5981i	0.255847	+	0.443140i
$686$	−7.60770	−	28.3923i	−0.290463	−	1.08402i
$687$			7.32051i			0.279295i
$688$	20.4904	+	35.4904i	0.781188	+	1.35306i
$689$	−5.59808	−	1.50000i	−0.213270	−	0.0571454i
$690$	−31.1769	+	18.0000i	−1.18688	+	0.685248i
$691$		−	30.8372i		−	1.17310i	−0.809913	−	0.586551i	$-0.800486\pi$
$691$		−	30.8372i		−	1.17310i	0.809913	−	0.586551i	$-0.199514\pi$
$692$	−21.7583	+	5.83013i	−0.827128	+	0.221628i
$693$	−3.12436	+	11.6603i	−0.118684	+	0.442936i
$694$	−27.5885	−	7.39230i	−1.04724	−	0.280608i
$695$	10.5622	−	18.2942i	0.400646	−	0.693940i
$696$	0.215390	−	0.803848i	0.00816435	−	0.0304698i
$697$		−	11.4115i		−	0.432243i
$698$	3.92820	+	3.92820i	0.148685	+	0.148685i
$699$	7.51666	+	7.51666i	0.284306	+	0.284306i
$700$	−2.26795	+	8.46410i	−0.0857204	+	0.319913i
$701$	31.0526			1.17284			0.586419	−	0.810008i	$-0.300537\pi$
$701$	31.0526			1.17284			0.586419	+	0.810008i	$0.300537\pi$
$702$	−3.46410	+	12.9282i	−0.130744	+	0.487944i
$703$	30.2224	−	52.3468i	1.13986	−	1.97430i
$704$	3.00000	−	1.73205i	0.113067	−	0.0652791i
$705$	−2.19615	−	0.588457i	−0.0827119	−	0.0221626i
$706$		−	3.58846i		−	0.135053i
$707$	−16.8564	+	16.8564i	−0.633950	+	0.633950i
$708$	−3.46410	+	0.928203i	−0.130189	+	0.0348840i
$709$	−28.1506	−	28.1506i	−1.05722	−	1.05722i	−0.998260	−	0.0589589i	$-0.981222\pi$
$709$	−28.1506	−	28.1506i	−1.05722	−	1.05722i	−0.0589589	−	0.998260i	$-0.518778\pi$
$710$	27.8827	+	16.0981i	1.04642	+	0.604150i
$711$	−12.8038	+	7.39230i	−0.480182	+	0.277233i
$712$	0.803848			0.0301255
$713$	−25.1769	+	25.1769i	−0.942883	+	0.942883i
$714$	−1.39230	−	2.41154i	−0.0521057	−	0.0902497i
$715$	−11.1962	+	19.3923i	−0.418712	+	0.725231i
$716$	5.83013	+	21.7583i	0.217882	+	0.813147i
$717$	0.803848	+	3.00000i	0.0300202	+	0.112037i
$718$	−32.4904	−	8.70577i	−1.21253	−	0.324897i
$719$	7.39230	+	27.5885i	0.275686	+	1.02888i	0.955380	+	0.295380i	$0.0954461\pi$
$719$	7.39230	+	27.5885i	0.275686	+	1.02888i	−0.679694	+	0.733496i	$0.737887\pi$
$720$	39.8205	−	10.6699i	1.48402	−	0.397643i
$721$	6.39230	−	6.39230i	0.238062	−	0.238062i
$722$	7.66987	−	13.2846i	0.285443	−	0.494402i
$723$	−17.7058	−	10.2224i	−0.658485	−	0.380176i
$724$	2.26795	+	2.26795i	0.0842877	+	0.0842877i
$725$	2.87564	−	2.87564i	0.106799	−	0.106799i
$726$	1.26795			0.0470580
$727$	−16.9019	+	9.75833i	−0.626858	+	0.361916i	−0.779534	−	0.626360i	$-0.784544\pi$
$727$	−16.9019	+	9.75833i	−0.626858	+	0.361916i	0.152676	+	0.988276i	$0.451211\pi$
$728$	4.09808	−	2.36603i	0.151885	−	0.0876907i
$729$	2.21539			0.0820515
$730$	−58.9808	+	58.9808i	−2.18298	+	2.18298i
$731$	−9.00000	−	9.00000i	−0.332877	−	0.332877i
$732$	−1.09808	−	0.633975i	−0.0405861	−	0.0234324i
$733$	−12.9282	+	22.3923i	−0.477514	+	0.827079i	−0.999668	−	0.0257727i	$-0.991795\pi$
$733$	−12.9282	+	22.3923i	−0.477514	+	0.827079i	0.522154	+	0.852851i	$0.325129\pi$
$734$	−0.464102	+	0.464102i	−0.0171303	+	0.0171303i
$735$	11.8301	−	3.16987i	0.436361	−	0.116923i
$736$	11.4115	+	42.5885i	0.420635	+	1.56983i
$737$	12.9282	+	3.46410i	0.476216	+	0.127602i
$738$	−8.11731	−	30.2942i	−0.298802	−	1.11515i
$739$	4.16987	+	15.5622i	0.153391	+	0.572464i	0.999238	+	0.0390376i	$0.0124292\pi$
$739$	4.16987	+	15.5622i	0.153391	+	0.572464i	−0.845846	+	0.533426i	$0.820904\pi$
$740$	19.1603	−	33.1865i	0.704345	−	1.21996i
$741$	−3.73205	−	6.46410i	−0.137100	−	0.237465i
$742$	5.19615	−	5.19615i	0.190757	−	0.190757i
$743$	19.6077			0.719337			0.359668	−	0.933080i	$-0.382890\pi$
$743$	19.6077			0.719337			0.359668	+	0.933080i	$0.382890\pi$
$744$	−4.60770	+	2.66025i	−0.168926	+	0.0975296i
$745$	60.0788	+	34.6865i	2.20112	+	1.27082i
$746$	16.8109	+	16.8109i	0.615490	+	0.615490i
$747$	−33.4186	+	8.95448i	−1.22272	+	0.327627i
$748$	3.80385	−	3.80385i	0.139082	−	0.139082i
$749$		−	17.3205i		−	0.632878i
$750$	−4.90192	−	1.31347i	−0.178993	−	0.0479610i
$751$	−27.7128	+	16.0000i	−1.01125	+	0.583848i	−0.911559	−	0.411170i	$-0.865120\pi$
$751$	−27.7128	+	16.0000i	−1.01125	+	0.583848i	−0.0996961	+	0.995018i	$0.531787\pi$
$752$	−2.32051	+	4.01924i	−0.0846202	+	0.146567i
$753$	−5.44486	+	20.3205i	−0.198422	+	0.740520i
$754$	2.19615			0.0799792
$755$	2.19615	−	8.19615i	0.0799262	−	0.298289i
$756$	−4.00000	−	4.00000i	−0.145479	−	0.145479i
$757$	4.66025	+	4.66025i	0.169380	+	0.169380i	0.786707	−	0.617327i	$-0.211784\pi$
$757$	4.66025	+	4.66025i	0.169380	+	0.169380i	−0.617327	+	0.786707i	$0.711784\pi$
$758$		−	27.7128i		−	1.00657i
$759$	5.56922	−	20.7846i	0.202150	−	0.754434i
$760$	−15.2942	+	26.4904i	−0.554780	+	0.960907i
$761$	10.7942	+	2.89230i	0.391290	+	0.104846i	0.449100	−	0.893482i	$-0.351745\pi$
$761$	10.7942	+	2.89230i	0.391290	+	0.104846i	−0.0578092	+	0.998328i	$0.518411\pi$
$762$	0.712813	−	2.66025i	0.0258225	−	0.0963708i
$763$	15.0263	−	4.02628i	0.543988	−	0.145761i
$764$			6.92820i			0.250654i
$765$	−11.0885	+	6.40192i	−0.400904	+	0.231462i
$766$	−42.5885	−	11.4115i	−1.53878	−	0.412316i
$767$	4.73205	+	8.19615i	0.170864	+	0.295946i
$768$			13.9090i			0.501897i
$769$	−1.57180	−	5.86603i	−0.0566804	−	0.211534i	0.931777	−	0.363030i	$-0.118258\pi$
$769$	−1.57180	−	5.86603i	−0.0566804	−	0.211534i	−0.988458	+	0.151496i	$0.951591\pi$
$770$	−14.1962	−	24.5885i	−0.511594	−	0.886106i
$771$	17.3660	−	4.65321i	0.625422	−	0.167581i
$772$	9.92820	+	17.1962i	0.357324	+	0.618903i
$773$	23.3038	+	13.4545i	0.838181	+	0.483924i	0.856646	−	0.515905i	$-0.172544\pi$
$773$	23.3038	+	13.4545i	0.838181	+	0.483924i	−0.0184644	+	0.999830i	$0.505878\pi$
$774$	−30.2942	−	17.4904i	−1.08890	−	0.628679i
$775$	−26.0000			−0.933948
$776$	−6.92820	−	15.5885i	−0.248708	−	0.559593i
$777$	11.8564			0.425346
$778$	12.1077	+	6.99038i	0.434082	+	0.250617i
$779$	33.5885	+	19.3923i	1.20343	+	0.694801i
$780$	−2.36603	−	4.09808i	−0.0847173	−	0.146735i
$781$	−18.5885	+	4.98076i	−0.665147	+	0.178226i
$782$	−11.4115	−	19.7654i	−0.408076	−	0.706808i
$783$	0.679492	+	2.53590i	0.0242831	+	0.0906256i
$784$		−	25.0000i		−	0.892857i
$785$	30.3564	+	52.5788i	1.08347	+	1.87662i
$786$	−23.7846	−	6.37307i	−0.848369	−	0.227320i
$787$	25.1769	−	14.5359i	0.897460	−	0.518149i	0.0210848	−	0.999778i	$-0.493288\pi$
$787$	25.1769	−	14.5359i	0.897460	−	0.518149i	0.876375	+	0.481629i	$0.159955\pi$
$788$			18.1244i			0.645653i
$789$	−3.00000	+	0.803848i	−0.106803	+	0.0286177i
$790$	9.00000	−	33.5885i	0.320206	−	1.19502i
$791$	6.00000	+	1.60770i	0.213335	+	0.0571631i
$792$	−7.39230	+	12.8038i	−0.262674	+	0.454965i
$793$	−0.866025	+	3.23205i	−0.0307535	+	0.114773i
$794$		−	16.3923i		−	0.581741i
$795$	5.19615	+	5.19615i	0.184289	+	0.184289i
$796$	−3.73205	−	3.73205i	−0.132279	−	0.132279i
$797$	−8.84679	+	33.0167i	−0.313369	+	1.16951i	0.612129	+	0.790758i	$0.290313\pi$
$797$	−8.84679	+	33.0167i	−0.313369	+	1.16951i	−0.925498	+	0.378752i	$0.876353\pi$
$798$	9.46410			0.335026
$799$	0.373067	−	1.39230i	0.0131982	−	0.0492562i
$800$	−16.0981	+	27.8827i	−0.569153	+	0.985802i
$801$	−0.990381	+	0.571797i	−0.0349934	+	0.0202034i
$802$	4.79423	+	1.28461i	0.169290	+	0.0453611i
$803$		−	49.8564i		−	1.75939i
$804$	−2.00000	+	2.00000i	−0.0705346	+	0.0705346i
$805$	−38.7846	+	10.3923i	−1.36698	+	0.366281i
$806$	−9.92820	−	9.92820i	−0.349706	−	0.349706i
$807$	10.3135	+	5.95448i	0.363051	+	0.209608i
$808$	−25.2846	+	14.5981i	−0.889509	+	0.513559i
$809$	−32.6603			−1.14827			−0.574137	−	0.818759i	$-0.694662\pi$
$809$	−32.6603			−1.14827			−0.574137	+	0.818759i	$0.694662\pi$
$810$	−18.2942	+	18.2942i	−0.642794	+	0.642794i
$811$	−4.29423	−	7.43782i	−0.150791	−	0.261177i	0.780728	−	0.624871i	$-0.214849\pi$
$811$	−4.29423	−	7.43782i	−0.150791	−	0.261177i	−0.931518	+	0.363694i	$0.881515\pi$
$812$	−0.464102	+	0.803848i	−0.0162868	+	0.0282095i
$813$	−2.33975	−	8.73205i	−0.0820585	−	0.306246i
$814$	17.7846	+	66.3731i	0.623350	+	2.32637i
$815$	57.0788	+	15.2942i	1.99938	+	0.535733i
$816$	−1.47114	−	5.49038i	−0.0515003	−	0.192202i
$817$	41.7846	−	11.1962i	1.46186	−	0.391704i
$818$	5.24167	−	5.24167i	0.183271	−	0.183271i
$819$	−3.36603	+	5.83013i	−0.117618	+	0.203721i
$820$	21.2942	+	12.2942i	0.743627	+	0.429333i
$821$	−18.8038	−	18.8038i	−0.656259	−	0.656259i	0.298234	−	0.954493i	$-0.403602\pi$
$821$	−18.8038	−	18.8038i	−0.656259	−	0.656259i	−0.954493	+	0.298234i	$0.903602\pi$
$822$	3.58846	−	3.58846i	0.125162	−	0.125162i
$823$	−6.67949			−0.232832			−0.116416	−	0.993201i	$-0.537141\pi$
$823$	−6.67949			−0.232832			−0.116416	+	0.993201i	$0.537141\pi$
$824$	9.58846	−	5.53590i	0.334030	−	0.192852i
$825$	13.6077	−	7.85641i	0.473759	−	0.273525i
$826$	−12.0000			−0.417533
$827$	−27.5885	+	27.5885i	−0.959345	+	0.959345i	−0.999205	−	0.0398606i	$-0.987309\pi$
$827$	−27.5885	+	27.5885i	−0.959345	+	0.959345i	0.0398606	+	0.999205i	$0.487309\pi$
$828$	−14.7846	−	14.7846i	−0.513801	−	0.513801i
$829$	27.6962	+	15.9904i	0.961927	+	0.555369i	0.896766	−	0.442506i	$-0.145910\pi$
$829$	27.6962	+	15.9904i	0.961927	+	0.555369i	0.0651615	+	0.997875i	$0.479244\pi$
$830$	40.6865	−	70.4711i	1.41225	−	2.44609i
$831$	−10.8038	+	10.8038i	−0.374781	+	0.374781i
$832$	1.86603	−	0.500000i	0.0646928	−	0.0173344i
$833$	2.00962	+	7.50000i	0.0696292	+	0.259860i
$834$	−7.73205	−	2.07180i	−0.267739	−	0.0717405i
$835$	−2.19615	−	8.19615i	−0.0760010	−	0.283640i
$836$	4.73205	+	17.6603i	0.163661	+	0.610793i
$837$	8.39230	−	14.5359i	0.290080	−	0.502434i
$838$	−1.90192	−	3.29423i	−0.0657009	−	0.113797i
$839$	−8.53590	+	8.53590i	−0.294692	+	0.294692i	−0.838931	−	0.544239i	$-0.816819\pi$
$839$	−8.53590	+	8.53590i	−0.294692	+	0.294692i	0.544239	+	0.838931i	$0.316819\pi$
$840$	−6.00000			−0.207020
$841$	−24.7417	+	14.2846i	−0.853161	+	0.492573i
$842$	−47.4615	−	27.4019i	−1.63563	−	0.944333i
$843$	7.01924	+	7.01924i	0.241755	+	0.241755i
$844$	−1.63397	+	0.437822i	−0.0562437	+	0.0150705i
$845$	21.9282	−	21.9282i	0.754353	−	0.754353i
$846$		−	3.96152i		−	0.136200i
$847$	1.36603	+	0.366025i	0.0469372	+	0.0125768i
$848$	12.9904	−	7.50000i	0.446092	−	0.257551i
$849$	4.14359	−	7.17691i	0.142208	−	0.246311i
$850$	4.31347	−	16.0981i	0.147951	−	0.552159i
$851$	97.1769			3.33118
$852$	1.05256	−	3.92820i	0.0360601	−	0.134578i
$853$	−19.6147	−	19.6147i	−0.671596	−	0.671596i	0.286488	−	0.958084i	$-0.407512\pi$
$853$	−19.6147	−	19.6147i	−0.671596	−	0.671596i	−0.958084	+	0.286488i	$0.907512\pi$
$854$	−3.00000	−	3.00000i	−0.102658	−	0.102658i
$855$		−	43.5167i		−	1.48824i
$856$	5.49038	−	20.4904i	0.187657	−	0.700347i
$857$	24.9904	−	43.2846i	0.853655	−	1.47857i	−0.0242319	−	0.999706i	$-0.507714\pi$
$857$	24.9904	−	43.2846i	0.853655	−	1.47857i	0.877887	−	0.478868i	$-0.158953\pi$
$858$	8.19615	+	2.19615i	0.279812	+	0.0749754i
$859$	2.51666	−	9.39230i	0.0858673	−	0.320461i	−0.909610	−	0.415464i	$-0.863619\pi$
$859$	2.51666	−	9.39230i	0.0858673	−	0.320461i	0.995477	+	0.0950026i	$0.0302859\pi$
$860$	26.4904	−	7.09808i	0.903314	−	0.242042i
$861$			7.60770i			0.259270i
$862$	−12.2942	+	7.09808i	−0.418743	+	0.241761i
$863$	−3.92820	−	1.05256i	−0.133718	−	0.0358295i	0.191339	−	0.981524i	$-0.438717\pi$
$863$	−3.92820	−	1.05256i	−0.133718	−	0.0358295i	−0.325057	+	0.945694i	$0.605384\pi$
$864$	−10.3923	−	18.0000i	−0.353553	−	0.612372i
$865$		−	75.3731i		−	2.56276i
$866$	3.86603	+	14.4282i	0.131373	+	0.490290i
$867$	−5.33975	−	9.24871i	−0.181347	−	0.314103i
$868$	5.73205	−	1.53590i	0.194558	−	0.0521318i
$869$	10.3923	+	18.0000i	0.352535	+	0.610608i
$870$	−2.41154	−	1.39230i	−0.0817590	−	0.0472036i
$871$	6.46410	+	3.73205i	0.219028	+	0.126456i
$872$	19.0526			0.645201
$873$	19.6244	+	14.2776i	0.664184	+	0.483222i
$874$	77.5692			2.62382
$875$	−4.90192	−	2.83013i	−0.165715	−	0.0956758i
$876$	9.12436	+	5.26795i	0.308283	+	0.177988i
$877$	16.1603	+	27.9904i	0.545693	+	0.945168i	0.998563	+	0.0535914i	$0.0170669\pi$
$877$	16.1603	+	27.9904i	0.545693	+	0.945168i	−0.452870	+	0.891577i	$0.649600\pi$
$878$	−40.8564	+	10.9474i	−1.37884	+	0.369458i
$879$	2.83013	+	4.90192i	0.0954578	+	0.165338i
$880$	−15.0000	−	55.9808i	−0.505650	−	1.88711i
$881$		−	16.2679i		−	0.548081i	−0.961718	−	0.274041i	$-0.911640\pi$
$881$		−	16.2679i		−	0.548081i	0.961718	−	0.274041i	$-0.0883603\pi$
$882$	10.6699	+	18.4808i	0.359273	+	0.622280i
$883$	−50.2487	−	13.4641i	−1.69100	−	0.453103i	−0.720355	−	0.693605i	$-0.756021\pi$
$883$	−50.2487	−	13.4641i	−1.69100	−	0.453103i	−0.970649	+	0.240502i	$0.922688\pi$
$884$	2.59808	−	1.50000i	0.0873828	−	0.0504505i
$885$		−	12.0000i		−	0.403376i
$886$	50.7846	−	13.6077i	1.70614	−	0.457159i
$887$	4.73205	−	17.6603i	0.158887	−	0.592973i	−0.839854	−	0.542812i	$-0.817360\pi$
$887$	4.73205	−	17.6603i	0.158887	−	0.592973i	0.998741	−	0.0501616i	$-0.0159736\pi$
$888$	14.0263	+	3.75833i	0.470691	+	0.126121i
$889$	1.53590	−	2.66025i	0.0515124	−	0.0892221i
$890$	0.696152	−	2.59808i	0.0233351	−	0.0870877i
$891$		−	15.4641i		−	0.518067i
$892$	−7.92820	−	7.92820i	−0.265456	−	0.265456i
$893$	3.46410	+	3.46410i	0.115922	+	0.115922i
$894$	6.80385	−	25.3923i	0.227555	−	0.849246i
$895$	−75.3731			−2.51944
$896$	−4.43782	+	16.5622i	−0.148257	+	0.553304i
$897$	6.00000	−	10.3923i	0.200334	−	0.346989i
$898$	−27.1865	+	15.6962i	−0.907226	+	0.523787i
$899$	−2.66025	−	0.712813i	−0.0887244	−	0.0237736i
$900$		−	15.2679i		−	0.508932i
$901$	−3.29423	+	3.29423i	−0.109747	+	0.109747i
$902$	−42.5885	+	11.4115i	−1.41804	+	0.379963i
$903$	6.00000	+	6.00000i	0.199667	+	0.199667i
$904$	6.58846	+	3.80385i	0.219129	+	0.126514i
$905$	−9.29423	+	5.36603i	−0.308951	+	0.178373i
$906$	−3.21539			−0.106824
$907$	25.3205	−	25.3205i	0.840754	−	0.840754i	−0.148203	−	0.988957i	$-0.547349\pi$
$907$	25.3205	−	25.3205i	0.840754	−	0.840754i	0.988957	+	0.148203i	$0.0473490\pi$
$908$	−3.29423	−	5.70577i	−0.109323	−	0.189353i
$909$	20.7679	−	35.9711i	0.688829	−	1.19309i
$910$	−4.09808	−	15.2942i	−0.135850	−	0.506999i
$911$	6.16987	+	23.0263i	0.204417	+	0.762895i	0.989626	+	0.143664i	$0.0458886\pi$
$911$	6.16987	+	23.0263i	0.204417	+	0.762895i	−0.785209	+	0.619230i	$0.787445\pi$
$912$	18.6603	+	5.00000i	0.617903	+	0.165567i
$913$	12.5885	+	46.9808i	0.416617	+	1.55484i
$914$	23.0263	−	6.16987i	0.761642	−	0.204081i
$915$	3.00000	−	3.00000i	0.0991769	−	0.0991769i
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	−23.7846	−	13.7321i	−0.785437	−	0.453472i
$918$	7.60770	+	7.60770i	0.251091	+	0.251091i
$919$	−24.6603	+	24.6603i	−0.813467	+	0.813467i	−0.985152	−	0.171685i	$-0.945079\pi$
$919$	−24.6603	+	24.6603i	−0.813467	+	0.813467i	0.171685	+	0.985152i	$0.445079\pi$
$920$	−49.1769			−1.62131
$921$	7.35898	−	4.24871i	0.242487	−	0.140000i
$922$	21.9904	−	12.6962i	0.724215	−	0.418126i
$923$	−10.7321			−0.353250
$924$	−2.53590	+	2.53590i	−0.0834249	+	0.0834249i
$925$	50.1769	+	50.1769i	1.64981	+	1.64981i
$926$	30.2942	+	17.4904i	0.995530	+	0.574770i
$927$	−7.87564	+	13.6410i	−0.258670	+	0.448030i
$928$	−2.41154	+	2.41154i	−0.0791628	+	0.0791628i
$929$	−20.7224	+	5.55256i	−0.679881	+	0.182174i	−0.582202	−	0.813044i	$-0.697809\pi$
$929$	−20.7224	+	5.55256i	−0.679881	+	0.182174i	−0.0976792	+	0.995218i	$0.531142\pi$
$930$	4.60770	+	17.1962i	0.151092	+	0.563884i
$931$	−25.4904	−	6.83013i	−0.835413	−	0.223848i
$932$	−3.75833	−	14.0263i	−0.123108	−	0.459446i
$933$	1.98076	+	7.39230i	0.0648472	+	0.242013i
$934$	−22.9019	+	39.6673i	−0.749374	+	1.29795i
$935$	9.00000	+	15.5885i	0.294331	+	0.509797i
$936$	−5.83013	+	5.83013i	−0.190564	+	0.190564i
$937$	−19.1436			−0.625394			−0.312697	−	0.949853i	$-0.601232\pi$
$937$	−19.1436			−0.625394			−0.312697	+	0.949853i	$0.601232\pi$
$938$	−8.19615	+	4.73205i	−0.267614	+	0.154507i
$939$	−1.00704	−	0.581416i	−0.0328636	−	0.0189738i
$940$	2.19615	+	2.19615i	0.0716306	+	0.0716306i
$941$	14.8923	−	3.99038i	0.485475	−	0.130083i	−0.00777568	−	0.999970i	$-0.502475\pi$
$941$	14.8923	−	3.99038i	0.485475	−	0.130083i	0.493251	+	0.869887i	$0.335808\pi$
$942$	16.2679	−	16.2679i	0.530038	−	0.530038i
$943$			62.3538i			2.03052i
$944$	−23.6603	−	6.33975i	−0.770076	−	0.206341i
$945$	16.3923	−	9.46410i	0.533242	−	0.307867i
$946$	−24.5885	+	42.5885i	−0.799440	+	1.38467i
$947$	−7.90192	+	29.4904i	−0.256778	+	0.958309i	0.710315	+	0.703884i	$0.248553\pi$
$947$	−7.90192	+	29.4904i	−0.256778	+	0.958309i	−0.967093	+	0.254424i	$0.918114\pi$
$948$	−4.39230			−0.142655
$949$	7.19615	−	26.8564i	0.233597	−	0.871796i
$950$	40.0526	+	40.0526i	1.29948	+	1.29948i
$951$	−1.73205	−	1.73205i	−0.0561656	−	0.0561656i
$952$		−	3.80385i		−	0.123283i
$953$	1.66987	−	6.23205i	0.0540925	−	0.201876i	−0.933591	−	0.358340i	$-0.883343\pi$
$953$	1.66987	−	6.23205i	0.0540925	−	0.201876i	0.987684	+	0.156464i	$0.0500095\pi$
$954$	−6.40192	+	11.0885i	−0.207270	+	0.359002i
$955$	−22.3923	−	6.00000i	−0.724598	−	0.194155i
$956$	1.09808	−	4.09808i	0.0355143	−	0.132541i
$957$	1.60770	−	0.430781i	0.0519694	−	0.0139252i
$958$			2.78461i			0.0899667i
$959$	4.90192	−	2.83013i	0.158291	−	0.0913896i
$960$	−2.36603	−	0.633975i	−0.0763631	−	0.0204614i
$961$	−6.69615	−	11.5981i	−0.216005	−	0.374131i
$962$			38.3205i			1.23550i
$963$	7.81089	+	29.1506i	0.251702	+	0.939366i
$964$	13.9641	+	24.1865i	0.449753	+	0.778996i
$965$	−64.1769	+	17.1962i	−2.06593	+	0.553564i
$966$	7.60770	+	13.1769i	0.244774	+	0.423960i
$967$	−37.3923	−	21.5885i	−1.20246	−	0.694238i	−0.241355	−	0.970437i	$-0.577592\pi$
$967$	−37.3923	−	21.5885i	−1.20246	−	0.694238i	−0.961100	+	0.276199i	$0.910925\pi$
$968$	1.50000	+	0.866025i	0.0482118	+	0.0278351i
$969$	−6.00000			−0.192748
$970$	−56.3827	+	8.89230i	−1.81034	+	0.285515i
$971$	14.5359			0.466479			0.233240	−	0.972419i	$-0.425067\pi$
$971$	14.5359			0.466479			0.233240	+	0.972419i	$0.425067\pi$
$972$	13.2224	+	7.63397i	0.424110	+	0.244860i
$973$	−7.73205	−	4.46410i	−0.247878	−	0.143113i
$974$	−22.3923	−	38.7846i	−0.717496	−	1.24274i
$975$	8.46410	−	2.26795i	0.271068	−	0.0726325i
$976$	−4.33013	−	7.50000i	−0.138604	−	0.240069i
$977$	−5.25833	−	19.6244i	−0.168229	−	0.627839i	−0.997606	−	0.0691500i	$-0.977971\pi$
$977$	−5.25833	−	19.6244i	−0.168229	−	0.627839i	0.829377	−	0.558689i	$-0.188695\pi$
$978$		−	22.3923i		−	0.716027i
$979$	0.803848	+	1.39230i	0.0256911	+	0.0444983i
$980$	−16.1603	−	4.33013i	−0.516220	−	0.138321i
$981$	−23.4737	+	13.5526i	−0.749458	+	0.432700i
$982$			7.01924i			0.223993i
$983$	−19.2224	+	5.15064i	−0.613100	+	0.164280i	−0.551989	−	0.833851i	$-0.686131\pi$
$983$	−19.2224	+	5.15064i	−0.613100	+	0.164280i	−0.0611111	+	0.998131i	$0.519464\pi$
$984$	−2.41154	+	9.00000i	−0.0768772	+	0.286910i
$985$	−58.5788	−	15.6962i	−1.86648	−	0.500121i
$986$	0.882686	−	1.52886i	0.0281104	−	0.0486887i
$987$	−0.248711	+	0.928203i	−0.00791657	+	0.0295450i
$988$			10.1962i			0.324383i
$989$	49.1769	+	49.1769i	1.56373	+	1.56373i
$990$	34.9808	+	34.9808i	1.11176	+	1.11176i
$991$	−12.8756	+	48.0526i	−0.409008	+	1.52644i	0.387533	+	0.921856i	$0.373327\pi$
$991$	−12.8756	+	48.0526i	−0.409008	+	1.52644i	−0.796541	+	0.604584i	$0.793339\pi$
$992$	21.8038			0.692273
$993$	−5.71281	+	21.3205i	−0.181291	+	0.676586i
$994$	6.80385	−	11.7846i	0.215805	−	0.373785i
$995$	15.2942	−	8.83013i	0.484860	−	0.279934i
$996$	−9.92820	−	2.66025i	−0.314587	−	0.0842934i
$997$		−	33.5885i		−	1.06376i	−0.846821	−	0.531879i	$-0.821486\pi$
$997$		−	33.5885i		−	1.06376i	0.846821	−	0.531879i	$-0.178514\pi$
$998$	46.0526	−	46.0526i	1.45777	−	1.45777i
$999$	−44.2487	+	11.8564i	−1.39997	+	0.375120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.2.g.a.81.1	yes	4
3.2	odd	2		873.2.be.c.469.1		4
97.6	even	12	inner	97.2.g.a.6.1	✓	4
97.43	even	24		9409.2.a.b.1.3		4
97.54	even	24		9409.2.a.b.1.4		4
291.200	odd	12		873.2.be.c.685.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.2.g.a.6.1	✓	4	97.6	even	12	inner
97.2.g.a.81.1	yes	4	1.1	even	1	trivial
873.2.be.c.469.1		4	3.2	odd	2
873.2.be.c.685.1		4	291.200	odd	12
9409.2.a.b.1.3		4	97.43	even	24
9409.2.a.b.1.4		4	97.54	even	24

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	97.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-0.633975 - 0.366025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-3.23205 + 0.866025i) q^{5} +(0.633975 + 1.09808i) q^{6} +(0.366025 + 1.36603i) q^{7} +1.73205i q^{8} +(-1.23205 - 2.13397i) q^{9} +(5.59808 + 1.50000i) q^{10} +(-3.00000 + 1.73205i) q^{11} -0.732051i q^{12} +(-1.86603 + 0.500000i) q^{13} +(0.633975 - 2.36603i) q^{14} +(2.36603 + 0.633975i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-0.401924 + 1.50000i) q^{17} +4.26795i q^{18} +(-3.73205 - 3.73205i) q^{19} +(-2.36603 - 2.36603i) q^{20} +(0.267949 - 1.00000i) q^{21} +6.00000 q^{22} +(2.19615 - 8.19615i) q^{23} +(0.633975 - 1.09808i) q^{24} +(5.36603 - 3.09808i) q^{25} +(3.23205 + 0.866025i) q^{26} +4.00000i q^{27} +(-1.00000 + 1.00000i) q^{28} +(0.633975 - 0.169873i) q^{29} +(-3.00000 - 3.00000i) q^{30} +(-3.63397 - 2.09808i) q^{31} +(-4.50000 + 2.59808i) q^{32} +2.53590 q^{33} +(1.90192 - 1.90192i) q^{34} +(-2.36603 - 4.09808i) q^{35} +(1.23205 - 2.13397i) q^{36} +(2.96410 + 11.0622i) q^{37} +(2.36603 + 8.83013i) q^{38} +(1.36603 + 0.366025i) q^{39} +(-1.50000 - 5.59808i) q^{40} +(-7.09808 + 1.90192i) q^{41} +(-1.26795 + 1.26795i) q^{42} +(-4.09808 + 7.09808i) q^{43} +(-3.00000 - 1.73205i) q^{44} +(5.83013 + 5.83013i) q^{45} +(-10.3923 + 10.3923i) q^{46} -0.928203 q^{47} +(-3.16987 + 1.83013i) q^{48} +(4.33013 - 2.50000i) q^{49} -10.7321 q^{50} +(0.803848 - 0.803848i) q^{51} +(-1.36603 - 1.36603i) q^{52} +(2.59808 + 1.50000i) q^{53} +(3.46410 - 6.00000i) q^{54} +(8.19615 - 8.19615i) q^{55} +(-2.36603 + 0.633975i) q^{56} +(1.00000 + 3.73205i) q^{57} +(-1.09808 - 0.294229i) q^{58} +(-1.26795 - 4.73205i) q^{59} +(0.633975 + 2.36603i) q^{60} +(0.866025 - 1.50000i) q^{61} +(3.63397 + 6.29423i) q^{62} +(2.46410 - 2.46410i) q^{63} -1.00000 q^{64} +(5.59808 - 3.23205i) q^{65} +(-3.80385 - 2.19615i) q^{66} +(-2.73205 - 2.73205i) q^{67} +(-1.50000 + 0.401924i) q^{68} +(-4.39230 + 4.39230i) q^{69} +8.19615i q^{70} +(5.36603 + 1.43782i) q^{71} +(3.69615 - 2.13397i) q^{72} +(-7.19615 + 12.4641i) q^{73} +(5.13397 - 19.1603i) q^{74} -4.53590 q^{75} +(1.36603 - 5.09808i) q^{76} +(-3.46410 - 3.46410i) q^{77} +(-1.73205 - 1.73205i) q^{78} -6.00000i q^{79} +(-4.33013 + 16.1603i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(12.2942 + 3.29423i) q^{82} +(3.63397 - 13.5622i) q^{83} +(1.00000 - 0.267949i) q^{84} -5.19615i q^{85} +(12.2942 - 7.09808i) q^{86} +(-0.464102 - 0.124356i) q^{87} +(-3.00000 - 5.19615i) q^{88} -0.464102i q^{89} +(-3.69615 - 13.7942i) q^{90} +(-1.36603 - 2.36603i) q^{91} +(8.19615 - 2.19615i) q^{92} +(1.53590 + 2.66025i) q^{93} +(1.39230 + 0.803848i) q^{94} +(15.2942 + 8.83013i) q^{95} +3.80385 q^{96} +(-9.00000 + 4.00000i) q^{97} -8.66025 q^{98} +(7.39230 + 4.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 6 q^{3} + 2 q^{4} - 6 q^{5} + 6 q^{6} - 2 q^{7} + 2 q^{9} + 12 q^{10} - 12 q^{11} - 4 q^{13} + 6 q^{14} + 6 q^{15} + 10 q^{16} - 12 q^{17} - 8 q^{19} - 6 q^{20} + 8 q^{21} + 24 q^{22} - 12 q^{23}+ \cdots - 12 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 6 * q^3 + 2 * q^4 - 6 * q^5 + 6 * q^6 - 2 * q^7 + 2 * q^9 + 12 * q^10 - 12 * q^11 - 4 * q^13 + 6 * q^14 + 6 * q^15 + 10 * q^16 - 12 * q^17 - 8 * q^19 - 6 * q^20 + 8 * q^21 + 24 * q^22 - 12 * q^23 + 6 * q^24 + 18 * q^25 + 6 * q^26 - 4 * q^28 + 6 * q^29 - 12 * q^30 - 18 * q^31 - 18 * q^32 + 24 * q^33 + 18 * q^34 - 6 * q^35 - 2 * q^36 - 2 * q^37 + 6 * q^38 + 2 * q^39 - 6 * q^40 - 18 * q^41 - 12 * q^42 - 6 * q^43 - 12 * q^44 + 6 * q^45 + 24 * q^47 - 30 * q^48 - 36 * q^50 + 24 * q^51 - 2 * q^52 + 12 * q^55 - 6 * q^56 + 4 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 + 18 * q^62 - 4 * q^63 - 4 * q^64 + 12 * q^65 - 36 * q^66 - 4 * q^67 - 6 * q^68 + 24 * q^69 + 18 * q^71 - 6 * q^72 - 8 * q^73 + 24 * q^74 - 32 * q^75 + 2 * q^76 - 2 * q^81 + 18 * q^82 + 18 * q^83 + 4 * q^84 + 18 * q^86 + 12 * q^87 - 12 * q^88 + 6 * q^90 - 2 * q^91 + 12 * q^92 + 20 * q^93 - 36 * q^94 + 30 * q^95 + 36 * q^96 - 36 * q^97 - 12 * q^99

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