LMFDB - Embedded newform 74.2.e.b.11.2

Newspace parameters

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.e (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	74.11
Dual form			74.2.e.b.27.2

$q$-expansion

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +1.73205 q^{10} -4.73205 q^{11} +(1.36603 + 2.36603i) q^{12} +(-3.00000 - 1.73205i) q^{13} -2.00000i q^{14} +(-4.09808 + 2.36603i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.69615 - 3.86603i) q^{17} +(-3.86603 - 2.23205i) q^{18} +(1.09808 + 0.633975i) q^{19} +(1.50000 - 0.866025i) q^{20} +(2.73205 + 4.73205i) q^{21} +(-4.09808 + 2.36603i) q^{22} +4.73205i q^{23} +(2.36603 + 1.36603i) q^{24} +(-1.00000 - 1.73205i) q^{25} -3.46410 q^{26} +4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +8.66025i q^{29} +(-2.36603 + 4.09808i) q^{30} -1.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(6.46410 - 11.1962i) q^{33} +(3.86603 - 6.69615i) q^{34} +(3.00000 - 1.73205i) q^{35} -4.46410 q^{36} +(-5.69615 - 2.13397i) q^{37} +1.26795 q^{38} +(8.19615 - 4.73205i) q^{39} +(0.866025 - 1.50000i) q^{40} +(-4.96410 + 8.59808i) q^{41} +(4.73205 + 2.73205i) q^{42} -0.928203i q^{43} +(-2.36603 + 4.09808i) q^{44} -7.73205i q^{45} +(2.36603 + 4.09808i) q^{46} +4.73205 q^{47} +2.73205 q^{48} +(1.50000 + 2.59808i) q^{49} +(-1.73205 - 1.00000i) q^{50} +21.1244i q^{51} +(-3.00000 + 1.73205i) q^{52} +(-1.26795 - 2.19615i) q^{53} +(3.46410 - 2.00000i) q^{54} +(-7.09808 - 4.09808i) q^{55} +(-1.73205 - 1.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(4.33013 + 7.50000i) q^{58} +(2.19615 - 1.26795i) q^{59} +4.73205i q^{60} +(1.50000 + 0.866025i) q^{61} +(-0.633975 - 1.09808i) q^{62} -8.92820 q^{63} -1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -12.9282i q^{66} +(5.09808 - 8.83013i) q^{67} -7.73205i q^{68} +(-11.1962 - 6.46410i) q^{69} +(1.73205 - 3.00000i) q^{70} +(-1.73205 + 3.00000i) q^{71} +(-3.86603 + 2.23205i) q^{72} +4.00000 q^{73} +(-6.00000 + 1.00000i) q^{74} +5.46410 q^{75} +(1.09808 - 0.633975i) q^{76} +(-4.73205 + 8.19615i) q^{77} +(4.73205 - 8.19615i) q^{78} +(-11.4904 - 6.63397i) q^{79} -1.73205i q^{80} +(1.23205 - 2.13397i) q^{81} +9.92820i q^{82} +(2.83013 + 4.90192i) q^{83} +5.46410 q^{84} +13.3923 q^{85} +(-0.464102 - 0.803848i) q^{86} +(-20.4904 - 11.8301i) q^{87} +4.73205i q^{88} +(-5.89230 + 3.40192i) q^{89} +(-3.86603 - 6.69615i) q^{90} +(-6.00000 + 3.46410i) q^{91} +(4.09808 + 2.36603i) q^{92} +(3.00000 + 1.73205i) q^{93} +(4.09808 - 2.36603i) q^{94} +(1.09808 + 1.90192i) q^{95} +(2.36603 - 1.36603i) q^{96} +7.73205i q^{97} +(2.59808 + 1.50000i) q^{98} +(10.5622 + 18.2942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9} - 12 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} - 6 q^{22} + 6 q^{24} - 4 q^{25} + 16 q^{27} - 4 q^{28} - 6 q^{30} + 12 q^{33} + 12 q^{34} + 12 q^{35} - 4 q^{36} - 2 q^{37} + 12 q^{38} + 12 q^{39} - 6 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} + 6 q^{49} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 12 q^{57} - 12 q^{59} + 6 q^{61} - 6 q^{62} - 8 q^{63} - 4 q^{64} - 12 q^{65} + 10 q^{67} - 24 q^{69} - 12 q^{72} + 16 q^{73} - 24 q^{74} + 8 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 6 q^{79} - 2 q^{81} - 6 q^{83} + 8 q^{84} + 12 q^{85} + 12 q^{86} - 30 q^{87} + 18 q^{89} - 12 q^{90} - 24 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} + 6 q^{96} + 18 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9 - 12 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^18 - 6 * q^19 + 6 * q^20 + 4 * q^21 - 6 * q^22 + 6 * q^24 - 4 * q^25 + 16 * q^27 - 4 * q^28 - 6 * q^30 + 12 * q^33 + 12 * q^34 + 12 * q^35 - 4 * q^36 - 2 * q^37 + 12 * q^38 + 12 * q^39 - 6 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 + 6 * q^49 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 12 * q^57 - 12 * q^59 + 6 * q^61 - 6 * q^62 - 8 * q^63 - 4 * q^64 - 12 * q^65 + 10 * q^67 - 24 * q^69 - 12 * q^72 + 16 * q^73 - 24 * q^74 + 8 * q^75 - 6 * q^76 - 12 * q^77 + 12 * q^78 + 6 * q^79 - 2 * q^81 - 6 * q^83 + 8 * q^84 + 12 * q^85 + 12 * q^86 - 30 * q^87 + 18 * q^89 - 12 * q^90 - 24 * q^91 + 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 + 6 * q^96 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	0.138104	+	0.990418i	$0.455899\pi$
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	−0.926779	+	0.375608i	$0.877434\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$			2.73205i			1.11536i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$	1.73205			0.547723
$11$	−4.73205			−1.42677			−0.713384	−	0.700774i	$-0.752838\pi$
$11$	−4.73205			−1.42677			−0.713384	+	0.700774i	$0.752838\pi$
$12$	1.36603	+	2.36603i	0.394338	+	0.683013i
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$		−	2.00000i		−	0.534522i
$15$	−4.09808	+	2.36603i	−1.05812	+	0.610905i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.69615	−	3.86603i	1.62406	−	0.937649i	0.638236	−	0.769841i	$-0.279664\pi$
$17$	6.69615	−	3.86603i	1.62406	−	0.937649i	0.985820	−	0.167808i	$-0.0536689\pi$
$18$	−3.86603	−	2.23205i	−0.911231	−	0.526099i
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	0.620641	−	0.784095i	$-0.286872\pi$
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	−0.368725	+	0.929538i	$0.620206\pi$
$20$	1.50000	−	0.866025i	0.335410	−	0.193649i
$21$	2.73205	+	4.73205i	0.596182	+	1.03262i
$22$	−4.09808	+	2.36603i	−0.873713	+	0.504438i
$23$			4.73205i			0.986701i	0.869831	+	0.493350i	$0.164228\pi$
$23$			4.73205i			0.986701i	−0.869831	+	0.493350i	$0.835772\pi$
$24$	2.36603	+	1.36603i	0.482963	+	0.278839i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−3.46410			−0.679366
$27$	4.00000			0.769800
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$			8.66025i			1.60817i	0.594515	+	0.804084i	$0.297344\pi$
$29$			8.66025i			1.60817i	−0.594515	+	0.804084i	$0.702656\pi$
$30$	−2.36603	+	4.09808i	−0.431975	+	0.748203i
$31$		−	1.26795i		−	0.227730i	−0.993496	−	0.113865i	$-0.963677\pi$
$31$		−	1.26795i		−	0.227730i	0.993496	−	0.113865i	$-0.0363232\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	6.46410	−	11.1962i	1.12526	−	1.94900i
$34$	3.86603	−	6.69615i	0.663018	−	1.14838i
$35$	3.00000	−	1.73205i	0.507093	−	0.292770i
$36$	−4.46410			−0.744017
$37$	−5.69615	−	2.13397i	−0.936442	−	0.350823i
$37$	−5.69615	−	2.13397i	−0.936442	−	0.350823i
$38$	1.26795			0.205689
$39$	8.19615	−	4.73205i	1.31243	−	0.757735i
$40$	0.866025	−	1.50000i	0.136931	−	0.237171i
$41$	−4.96410	+	8.59808i	−0.775262	+	1.34279i	0.159384	+	0.987217i	$0.449049\pi$
$41$	−4.96410	+	8.59808i	−0.775262	+	1.34279i	−0.934647	+	0.355577i	$0.884284\pi$
$42$	4.73205	+	2.73205i	0.730171	+	0.421565i
$43$		−	0.928203i		−	0.141550i	−0.997492	−	0.0707748i	$-0.977453\pi$
$43$		−	0.928203i		−	0.141550i	0.997492	−	0.0707748i	$-0.0225472\pi$
$44$	−2.36603	+	4.09808i	−0.356692	+	0.617808i
$45$		−	7.73205i		−	1.15263i
$46$	2.36603	+	4.09808i	0.348851	+	0.604228i
$47$	4.73205			0.690241			0.345120	−	0.938558i	$-0.387838\pi$
$47$	4.73205			0.690241			0.345120	+	0.938558i	$0.387838\pi$
$48$	2.73205			0.394338
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−1.73205	−	1.00000i	−0.244949	−	0.141421i
$51$			21.1244i			2.95800i
$52$	−3.00000	+	1.73205i	−0.416025	+	0.240192i
$53$	−1.26795	−	2.19615i	−0.174166	−	0.301665i	0.765706	−	0.643191i	$-0.222390\pi$
$53$	−1.26795	−	2.19615i	−0.174166	−	0.301665i	−0.939872	+	0.341526i	$0.889056\pi$
$54$	3.46410	−	2.00000i	0.471405	−	0.272166i
$55$	−7.09808	−	4.09808i	−0.957104	−	0.552584i
$56$	−1.73205	−	1.00000i	−0.231455	−	0.133631i
$57$	−3.00000	+	1.73205i	−0.397360	+	0.229416i
$58$	4.33013	+	7.50000i	0.568574	+	0.984798i
$59$	2.19615	−	1.26795i	0.285915	−	0.165073i	−0.350183	−	0.936681i	$-0.613881\pi$
$59$	2.19615	−	1.26795i	0.285915	−	0.165073i	0.636098	+	0.771608i	$0.280547\pi$
$60$			4.73205i			0.610905i
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	0.592944	−	0.805243i	$-0.297965\pi$
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	−0.400889	+	0.916127i	$0.631299\pi$
$62$	−0.633975	−	1.09808i	−0.0805149	−	0.139456i
$63$	−8.92820			−1.12485
$64$	−1.00000			−0.125000
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$		−	12.9282i		−	1.59135i
$67$	5.09808	−	8.83013i	0.622829	−	1.07877i	−0.366127	−	0.930565i	$-0.619317\pi$
$67$	5.09808	−	8.83013i	0.622829	−	1.07877i	0.988956	−	0.148207i	$-0.0473502\pi$
$68$		−	7.73205i		−	0.937649i
$69$	−11.1962	−	6.46410i	−1.34786	−	0.778186i
$70$	1.73205	−	3.00000i	0.207020	−	0.358569i
$71$	−1.73205	+	3.00000i	−0.205557	+	0.356034i	−0.950310	−	0.311305i	$-0.899234\pi$
$71$	−1.73205	+	3.00000i	−0.205557	+	0.356034i	0.744753	+	0.667340i	$0.232567\pi$
$72$	−3.86603	+	2.23205i	−0.455615	+	0.263050i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	−6.00000	+	1.00000i	−0.697486	+	0.116248i
$75$	5.46410			0.630940
$76$	1.09808	−	0.633975i	0.125958	−	0.0727219i
$77$	−4.73205	+	8.19615i	−0.539267	+	0.934038i
$78$	4.73205	−	8.19615i	0.535799	−	0.928032i
$79$	−11.4904	−	6.63397i	−1.29277	−	0.746380i	−0.313625	−	0.949547i	$-0.601543\pi$
$79$	−11.4904	−	6.63397i	−1.29277	−	0.746380i	−0.979144	+	0.203167i	$0.934877\pi$
$80$		−	1.73205i		−	0.193649i
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$			9.92820i			1.09639i
$83$	2.83013	+	4.90192i	0.310647	+	0.538056i	0.978503	−	0.206235i	$-0.0661210\pi$
$83$	2.83013	+	4.90192i	0.310647	+	0.538056i	−0.667856	+	0.744291i	$0.732788\pi$
$84$	5.46410			0.596182
$85$	13.3923			1.45260
$86$	−0.464102	−	0.803848i	−0.0500454	−	0.0866811i
$87$	−20.4904	−	11.8301i	−2.19680	−	1.26832i
$88$			4.73205i			0.504438i
$89$	−5.89230	+	3.40192i	−0.624583	+	0.360603i	−0.778651	−	0.627457i	$-0.784096\pi$
$89$	−5.89230	+	3.40192i	−0.624583	+	0.360603i	0.154068	+	0.988060i	$0.450762\pi$
$90$	−3.86603	−	6.69615i	−0.407515	−	0.705836i
$91$	−6.00000	+	3.46410i	−0.628971	+	0.363137i
$92$	4.09808	+	2.36603i	0.427254	+	0.246675i
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	4.09808	−	2.36603i	0.422684	−	0.244037i
$95$	1.09808	+	1.90192i	0.112660	+	0.195133i
$96$	2.36603	−	1.36603i	0.241481	−	0.139419i
$97$			7.73205i			0.785071i	0.919737	+	0.392535i	$0.128402\pi$
$97$			7.73205i			0.785071i	−0.919737	+	0.392535i	$0.871598\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	10.5622	+	18.2942i	1.06154	+	1.83864i
$100$	−2.00000			−0.200000
$101$	12.4641			1.24022			0.620112	−	0.784513i	$-0.287087\pi$
$101$	12.4641			1.24022			0.620112	+	0.784513i	$0.287087\pi$
$102$	10.5622	+	18.2942i	1.04581	+	1.81140i
$103$		−	8.53590i		−	0.841067i	−0.907277	−	0.420534i	$-0.861843\pi$
$103$		−	8.53590i		−	0.841067i	0.907277	−	0.420534i	$-0.138157\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$			9.46410i			0.923602i
$106$	−2.19615	−	1.26795i	−0.213309	−	0.123154i
$107$	5.19615	−	9.00000i	0.502331	−	0.870063i	−0.497665	−	0.867369i	$-0.665809\pi$
$107$	5.19615	−	9.00000i	0.502331	−	0.870063i	0.999996	−	0.00269372i	$-0.000857438\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	2.30385	−	1.33013i	0.220669	−	0.127403i	−0.385591	−	0.922670i	$-0.626002\pi$
$109$	2.30385	−	1.33013i	0.220669	−	0.127403i	0.606260	+	0.795267i	$0.292669\pi$
$110$	−8.19615			−0.781472
$111$	12.8301	−	10.5622i	1.21778	−	1.00252i
$112$	−2.00000			−0.188982
$113$	−3.00000	+	1.73205i	−0.282216	+	0.162938i	−0.634426	−	0.772983i	$-0.718764\pi$
$113$	−3.00000	+	1.73205i	−0.282216	+	0.162938i	0.352210	+	0.935921i	$0.385430\pi$
$114$	−1.73205	+	3.00000i	−0.162221	+	0.280976i
$115$	−4.09808	+	7.09808i	−0.382148	+	0.661899i
$116$	7.50000	+	4.33013i	0.696358	+	0.402042i
$117$			15.4641i			1.42966i
$118$	1.26795	−	2.19615i	0.116724	−	0.202172i
$119$		−	15.4641i		−	1.41759i
$120$	2.36603	+	4.09808i	0.215988	+	0.374101i
$121$	11.3923			1.03566
$122$	1.73205			0.156813
$123$	−13.5622	−	23.4904i	−1.22286	−	2.11806i
$124$	−1.09808	−	0.633975i	−0.0986102	−	0.0569326i
$125$		−	12.1244i		−	1.08444i
$126$	−7.73205	+	4.46410i	−0.688826	+	0.397694i
$127$	3.90192	+	6.75833i	0.346240	+	0.599705i	0.985578	−	0.169221i	$-0.0541250\pi$
$127$	3.90192	+	6.75833i	0.346240	+	0.599705i	−0.639338	+	0.768925i	$0.720792\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.19615	+	1.26795i	0.193360	+	0.111637i
$130$	−5.19615	−	3.00000i	−0.455733	−	0.263117i
$131$	8.49038	−	4.90192i	0.741808	−	0.428283i	−0.0809183	−	0.996721i	$-0.525785\pi$
$131$	8.49038	−	4.90192i	0.741808	−	0.428283i	0.822726	+	0.568438i	$0.192452\pi$
$132$	−6.46410	−	11.1962i	−0.562628	−	0.974500i
$133$	2.19615	−	1.26795i	0.190431	−	0.109945i
$134$		−	10.1962i		−	0.880813i
$135$	6.00000	+	3.46410i	0.516398	+	0.298142i
$136$	−3.86603	−	6.69615i	−0.331509	−	0.574190i
$137$	−1.39230			−0.118953			−0.0594763	−	0.998230i	$-0.518943\pi$
$137$	−1.39230			−0.118953			−0.0594763	+	0.998230i	$0.518943\pi$
$138$	−12.9282			−1.10052
$139$	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	$0.495410\pi$
$140$		−	3.46410i		−	0.292770i
$141$	−6.46410	+	11.1962i	−0.544376	+	0.942886i
$142$			3.46410i			0.290701i
$143$	14.1962	+	8.19615i	1.18714	+	0.685397i
$144$	−2.23205	+	3.86603i	−0.186004	+	0.322169i
$145$	−7.50000	+	12.9904i	−0.622841	+	1.07879i
$146$	3.46410	−	2.00000i	0.286691	−	0.165521i
$147$	−8.19615			−0.676007
$148$	−4.69615	+	3.86603i	−0.386021	+	0.317785i
$149$	−15.9282			−1.30489			−0.652445	−	0.757836i	$-0.726257\pi$
$149$	−15.9282			−1.30489			−0.652445	+	0.757836i	$0.726257\pi$
$150$	4.73205	−	2.73205i	0.386370	−	0.223071i
$151$	−2.09808	+	3.63397i	−0.170739	+	0.295729i	−0.938678	−	0.344794i	$-0.887949\pi$
$151$	−2.09808	+	3.63397i	−0.170739	+	0.295729i	0.767939	+	0.640522i	$0.221282\pi$
$152$	0.633975	−	1.09808i	0.0514221	−	0.0890657i
$153$	−29.8923	−	17.2583i	−2.41665	−	1.39525i
$154$			9.46410i			0.762639i
$155$	1.09808	−	1.90192i	0.0881996	−	0.152766i
$156$		−	9.46410i		−	0.757735i
$157$	−0.500000	−	0.866025i	−0.0399043	−	0.0691164i	0.845383	−	0.534160i	$-0.179372\pi$
$157$	−0.500000	−	0.866025i	−0.0399043	−	0.0691164i	−0.885288	+	0.465044i	$0.846039\pi$
$158$	−13.2679			−1.05554
$159$	6.92820			0.549442
$160$	−0.866025	−	1.50000i	−0.0684653	−	0.118585i
$161$	8.19615	+	4.73205i	0.645947	+	0.372938i
$162$		−	2.46410i		−	0.193598i
$163$	11.1962	−	6.46410i	0.876950	−	0.506308i	0.00729867	−	0.999973i	$-0.497677\pi$
$163$	11.1962	−	6.46410i	0.876950	−	0.506308i	0.869652	+	0.493666i	$0.164343\pi$
$164$	4.96410	+	8.59808i	0.387631	+	0.671397i
$165$	19.3923	−	11.1962i	1.50969	−	0.871619i
$166$	4.90192	+	2.83013i	0.380463	+	0.219660i
$167$	−12.0000	−	6.92820i	−0.928588	−	0.536120i	−0.0422232	−	0.999108i	$-0.513444\pi$
$167$	−12.0000	−	6.92820i	−0.928588	−	0.536120i	−0.886365	+	0.462988i	$0.846777\pi$
$168$	4.73205	−	2.73205i	0.365086	−	0.210782i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	11.5981	−	6.69615i	0.889532	−	0.513571i
$171$		−	5.66025i		−	0.432850i
$172$	−0.803848	−	0.464102i	−0.0612928	−	0.0353874i
$173$	−2.76795	−	4.79423i	−0.210443	−	0.364498i	0.741410	−	0.671052i	$-0.234157\pi$
$173$	−2.76795	−	4.79423i	−0.210443	−	0.364498i	−0.951853	+	0.306554i	$0.900824\pi$
$174$	−23.6603			−1.79368
$175$	−4.00000			−0.302372
$176$	2.36603	+	4.09808i	0.178346	+	0.308904i
$177$			6.92820i			0.520756i
$178$	−3.40192	+	5.89230i	−0.254985	+	0.441647i
$179$		−	9.46410i		−	0.707380i	−0.935363	−	0.353690i	$-0.884927\pi$
$179$		−	9.46410i		−	0.707380i	0.935363	−	0.353690i	$-0.115073\pi$
$180$	−6.69615	−	3.86603i	−0.499102	−	0.288157i
$181$	4.69615	−	8.13397i	0.349062	−	0.604594i	−0.637021	−	0.770847i	$-0.719834\pi$
$181$	4.69615	−	8.13397i	0.349062	−	0.604594i	0.986083	+	0.166253i	$0.0531668\pi$
$182$	−3.46410	+	6.00000i	−0.256776	+	0.444750i
$183$	−4.09808	+	2.36603i	−0.302939	+	0.174902i
$184$	4.73205			0.348851
$185$	−6.69615	−	8.13397i	−0.492311	−	0.598022i
$186$	3.46410			0.254000
$187$	−31.6865	+	18.2942i	−2.31715	+	1.33781i
$188$	2.36603	−	4.09808i	0.172560	−	0.298883i
$189$	4.00000	−	6.92820i	0.290957	−	0.503953i
$190$	1.90192	+	1.09808i	0.137980	+	0.0796628i
$191$			2.19615i			0.158908i	0.996839	+	0.0794540i	$0.0253177\pi$
$191$			2.19615i			0.158908i	−0.996839	+	0.0794540i	$0.974682\pi$
$192$	1.36603	−	2.36603i	0.0985844	−	0.170753i
$193$			11.1962i			0.805917i	0.915218	+	0.402958i	$0.132018\pi$
$193$			11.1962i			0.805917i	−0.915218	+	0.402958i	$0.867982\pi$
$194$	3.86603	+	6.69615i	0.277564	+	0.480756i
$195$	16.3923			1.17388
$196$	3.00000			0.214286
$197$	−3.23205	−	5.59808i	−0.230274	−	0.398846i	0.727615	−	0.685986i	$-0.240629\pi$
$197$	−3.23205	−	5.59808i	−0.230274	−	0.398846i	−0.957889	+	0.287140i	$0.907296\pi$
$198$	18.2942	+	10.5622i	1.30011	+	0.750621i
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$	−1.73205	+	1.00000i	−0.122474	+	0.0707107i
$201$	13.9282	+	24.1244i	0.982420	+	1.70160i
$202$	10.7942	−	6.23205i	0.759479	−	0.438486i
$203$	15.0000	+	8.66025i	1.05279	+	0.607831i
$204$	18.2942	+	10.5622i	1.28085	+	0.739500i
$205$	−14.8923	+	8.59808i	−1.04012	+	0.600516i
$206$	−4.26795	−	7.39230i	−0.297362	−	0.515046i
$207$	18.2942	−	10.5622i	1.27154	−	0.734122i
$208$			3.46410i			0.240192i
$209$	−5.19615	−	3.00000i	−0.359425	−	0.207514i
$210$	4.73205	+	8.19615i	0.326543	+	0.565588i
$211$	−2.39230			−0.164693			−0.0823465	−	0.996604i	$-0.526241\pi$
$211$	−2.39230			−0.164693			−0.0823465	+	0.996604i	$0.526241\pi$
$212$	−2.53590			−0.174166
$213$	−4.73205	−	8.19615i	−0.324235	−	0.561591i
$214$		−	10.3923i		−	0.710403i
$215$	0.803848	−	1.39230i	0.0548219	−	0.0949544i
$216$		−	4.00000i		−	0.272166i
$217$	−2.19615	−	1.26795i	−0.149085	−	0.0860740i
$218$	1.33013	−	2.30385i	0.0900876	−	0.156036i
$219$	−5.46410	+	9.46410i	−0.369230	+	0.639525i
$220$	−7.09808	+	4.09808i	−0.478552	+	0.276292i
$221$	−26.7846			−1.80173
$222$	5.83013	−	15.5622i	0.391293	−	1.04446i
$223$	16.1962			1.08457			0.542287	−	0.840193i	$-0.317558\pi$
$223$	16.1962			1.08457			0.542287	+	0.840193i	$0.317558\pi$
$224$	−1.73205	+	1.00000i	−0.115728	+	0.0668153i
$225$	−4.46410	+	7.73205i	−0.297607	+	0.515470i
$226$	−1.73205	+	3.00000i	−0.115214	+	0.199557i
$227$	1.09808	+	0.633975i	0.0728819	+	0.0420784i	0.535998	−	0.844219i	$-0.319935\pi$
$227$	1.09808	+	0.633975i	0.0728819	+	0.0420784i	−0.463116	+	0.886298i	$0.653269\pi$
$228$			3.46410i			0.229416i
$229$	−13.6962	+	23.7224i	−0.905067	+	1.56762i	−0.0842403	+	0.996445i	$0.526846\pi$
$229$	−13.6962	+	23.7224i	−0.905067	+	1.56762i	−0.820827	+	0.571177i	$0.806487\pi$
$230$			8.19615i			0.540438i
$231$	−12.9282	−	22.3923i	−0.850613	−	1.47331i
$232$	8.66025			0.568574
$233$	15.0000			0.982683			0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000			0.982683			0.491341	+	0.870967i	$0.336507\pi$
$234$	7.73205	+	13.3923i	0.505460	+	0.875482i
$235$	7.09808	+	4.09808i	0.463027	+	0.267329i
$236$		−	2.53590i		−	0.165073i
$237$	31.3923	−	18.1244i	2.03915	−	1.17730i
$238$	−7.73205	−	13.3923i	−0.501194	−	0.868094i
$239$	−15.0000	+	8.66025i	−0.970269	+	0.560185i	−0.899318	−	0.437295i	$-0.855937\pi$
$239$	−15.0000	+	8.66025i	−0.970269	+	0.560185i	−0.0709510	+	0.997480i	$0.522603\pi$
$240$	4.09808	+	2.36603i	0.264530	+	0.152726i
$241$	13.3923	+	7.73205i	0.862674	+	0.498065i	0.864907	−	0.501932i	$-0.167377\pi$
$241$	13.3923	+	7.73205i	0.862674	+	0.498065i	−0.00223270	+	0.999998i	$0.500711\pi$
$242$	9.86603	−	5.69615i	0.634212	−	0.366163i
$243$	9.36603	+	16.2224i	0.600831	+	1.04067i
$244$	1.50000	−	0.866025i	0.0960277	−	0.0554416i
$245$			5.19615i			0.331970i
$246$	−23.4904	−	13.5622i	−1.49769	−	0.864693i
$247$	−2.19615	−	3.80385i	−0.139738	−	0.242033i
$248$	−1.26795			−0.0805149
$249$	−15.4641			−0.979998
$250$	−6.06218	−	10.5000i	−0.383406	−	0.664078i
$251$		−	17.3205i		−	1.09326i	−0.837374	−	0.546630i	$-0.815910\pi$
$251$		−	17.3205i		−	1.09326i	0.837374	−	0.546630i	$-0.184090\pi$
$252$	−4.46410	+	7.73205i	−0.281212	+	0.487073i
$253$		−	22.3923i		−	1.40779i
$254$	6.75833	+	3.90192i	0.424055	+	0.244828i
$255$	−18.2942	+	31.6865i	−1.14563	+	1.98429i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.89230	−	3.40192i	0.367552	−	0.212206i	−0.304837	−	0.952405i	$-0.598602\pi$
$257$	5.89230	−	3.40192i	0.367552	−	0.212206i	0.672388	+	0.740199i	$0.265268\pi$
$258$	2.53590			0.157878
$259$	−9.39230	+	7.73205i	−0.583609	+	0.480446i
$260$	−6.00000			−0.372104
$261$	33.4808	−	19.3301i	2.07241	−	1.19650i
$262$	4.90192	−	8.49038i	0.302842	−	0.524537i
$263$	−10.7321	+	18.5885i	−0.661767	+	1.14621i	0.318385	+	0.947962i	$0.396860\pi$
$263$	−10.7321	+	18.5885i	−0.661767	+	1.14621i	−0.980151	+	0.198252i	$0.936474\pi$
$264$	−11.1962	−	6.46410i	−0.689076	−	0.397838i
$265$		−	4.39230i		−	0.269817i
$266$	1.26795	−	2.19615i	0.0777430	−	0.134655i
$267$		−	18.5885i		−	1.13760i
$268$	−5.09808	−	8.83013i	−0.311415	−	0.539386i
$269$	−4.39230			−0.267804			−0.133902	−	0.990995i	$-0.542751\pi$
$269$	−4.39230			−0.267804			−0.133902	+	0.990995i	$0.542751\pi$
$270$	6.92820			0.421637
$271$	1.29423	+	2.24167i	0.0786188	+	0.136172i	0.902654	−	0.430367i	$-0.141616\pi$
$271$	1.29423	+	2.24167i	0.0786188	+	0.136172i	−0.824035	+	0.566538i	$0.808282\pi$
$272$	−6.69615	−	3.86603i	−0.406014	−	0.234412i
$273$		−	18.9282i		−	1.14559i
$274$	−1.20577	+	0.696152i	−0.0728433	+	0.0420561i
$275$	4.73205	+	8.19615i	0.285353	+	0.494247i
$276$	−11.1962	+	6.46410i	−0.673929	+	0.389093i
$277$	9.69615	+	5.59808i	0.582585	+	0.336356i	0.762160	−	0.647389i	$-0.224139\pi$
$277$	9.69615	+	5.59808i	0.582585	+	0.336356i	−0.179575	+	0.983744i	$0.557472\pi$
$278$	17.8301	+	10.2942i	1.06938	+	0.617407i
$279$	−4.90192	+	2.83013i	−0.293471	+	0.169435i
$280$	−1.73205	−	3.00000i	−0.103510	−	0.179284i
$281$	−23.8923	+	13.7942i	−1.42530	+	0.822895i	−0.996745	−	0.0806230i	$-0.974309\pi$
$281$	−23.8923	+	13.7942i	−1.42530	+	0.822895i	−0.428551	+	0.903518i	$0.640976\pi$
$282$			12.9282i			0.769863i
$283$	−6.80385	−	3.92820i	−0.404447	−	0.233507i	0.283954	−	0.958838i	$-0.408354\pi$
$283$	−6.80385	−	3.92820i	−0.404447	−	0.233507i	−0.688401	+	0.725330i	$0.741687\pi$
$284$	1.73205	+	3.00000i	0.102778	+	0.178017i
$285$	−6.00000			−0.355409
$286$	16.3923			0.969297
$287$	9.92820	+	17.1962i	0.586043	+	1.01506i
$288$			4.46410i			0.263050i
$289$	21.3923	−	37.0526i	1.25837	−	2.17956i
$290$			15.0000i			0.880830i
$291$	−18.2942	−	10.5622i	−1.07243	−	0.619166i
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	0.696152	−	1.20577i	0.0406697	−	0.0704419i	−0.844974	−	0.534807i	$-0.820384\pi$
$293$	0.696152	−	1.20577i	0.0406697	−	0.0704419i	0.885644	+	0.464365i	$0.153718\pi$
$294$	−7.09808	+	4.09808i	−0.413968	+	0.239005i
$295$	4.39230			0.255730
$296$	−2.13397	+	5.69615i	−0.124035	+	0.331082i
$297$	−18.9282			−1.09833
$298$	−13.7942	+	7.96410i	−0.799078	+	0.461348i
$299$	8.19615	−	14.1962i	0.473996	−	0.820985i
$300$	2.73205	−	4.73205i	0.157735	−	0.273205i
$301$	−1.60770	−	0.928203i	−0.0926660	−	0.0535007i
$302$			4.19615i			0.241461i
$303$	−17.0263	+	29.4904i	−0.978134	+	1.69418i
$304$		−	1.26795i		−	0.0727219i
$305$	1.50000	+	2.59808i	0.0858898	+	0.148765i
$306$	−34.5167			−1.97319
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$	4.73205	+	8.19615i	0.269634	+	0.467019i
$309$	20.1962	+	11.6603i	1.14892	+	0.663329i
$310$		−	2.19615i		−	0.124733i
$311$	−15.5885	+	9.00000i	−0.883940	+	0.510343i	−0.871956	−	0.489585i	$-0.837148\pi$
$311$	−15.5885	+	9.00000i	−0.883940	+	0.510343i	−0.0119847	+	0.999928i	$0.503815\pi$
$312$	−4.73205	−	8.19615i	−0.267900	−	0.464016i
$313$	20.8923	−	12.0622i	1.18090	−	0.681795i	0.224680	−	0.974433i	$-0.427866\pi$
$313$	20.8923	−	12.0622i	1.18090	−	0.681795i	0.956223	+	0.292638i	$0.0945331\pi$
$314$	−0.866025	−	0.500000i	−0.0488726	−	0.0282166i
$315$	−13.3923	−	7.73205i	−0.754571	−	0.435652i
$316$	−11.4904	+	6.63397i	−0.646384	+	0.373190i
$317$	−3.69615	−	6.40192i	−0.207597	−	0.359568i	0.743360	−	0.668891i	$-0.233231\pi$
$317$	−3.69615	−	6.40192i	−0.207597	−	0.359568i	−0.950957	+	0.309323i	$0.899897\pi$
$318$	6.00000	−	3.46410i	0.336463	−	0.194257i
$319$		−	40.9808i		−	2.29448i
$320$	−1.50000	−	0.866025i	−0.0838525	−	0.0484123i
$321$	14.1962	+	24.5885i	0.792352	+	1.37239i
$322$	9.46410			0.527414
$323$	9.80385			0.545501
$324$	−1.23205	−	2.13397i	−0.0684473	−	0.118554i
$325$			6.92820i			0.384308i
$326$	6.46410	−	11.1962i	0.358013	−	0.620098i
$327$			7.26795i			0.401919i
$328$	8.59808	+	4.96410i	0.474749	+	0.274097i
$329$	4.73205	−	8.19615i	0.260886	−	0.451869i
$330$	11.1962	−	19.3923i	0.616328	−	1.06751i
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	5.66025			0.310647
$333$	4.46410	+	26.7846i	0.244631	+	1.46779i
$334$	−13.8564			−0.758189
$335$	15.2942	−	8.83013i	0.835613	−	0.482441i
$336$	2.73205	−	4.73205i	0.149046	−	0.258155i
$337$	16.0885	−	27.8660i	0.876394	−	1.51796i	0.0211239	−	0.999777i	$-0.493276\pi$
$337$	16.0885	−	27.8660i	0.876394	−	1.51796i	0.855270	−	0.518182i	$-0.173391\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$		−	9.46410i		−	0.514019i
$340$	6.69615	−	11.5981i	0.363150	−	0.628994i
$341$			6.00000i			0.324918i
$342$	−2.83013	−	4.90192i	−0.153036	−	0.265066i
$343$	20.0000			1.07990
$344$	−0.928203			−0.0500454
$345$	−11.1962	−	19.3923i	−0.602781	−	1.04405i
$346$	−4.79423	−	2.76795i	−0.257739	−	0.148806i
$347$			9.12436i			0.489821i	0.969546	+	0.244911i	$0.0787586\pi$
$347$			9.12436i			0.489821i	−0.969546	+	0.244911i	$0.921241\pi$
$348$	−20.4904	+	11.8301i	−1.09840	+	0.634161i
$349$	−5.69615	−	9.86603i	−0.304908	−	0.528116i	0.672333	−	0.740249i	$-0.265292\pi$
$349$	−5.69615	−	9.86603i	−0.304908	−	0.528116i	−0.977241	+	0.212133i	$0.931959\pi$
$350$	−3.46410	+	2.00000i	−0.185164	+	0.106904i
$351$	−12.0000	−	6.92820i	−0.640513	−	0.369800i
$352$	4.09808	+	2.36603i	0.218428	+	0.126110i
$353$	−17.0885	+	9.86603i	−0.909527	+	0.525116i	−0.880279	−	0.474457i	$-0.842645\pi$
$353$	−17.0885	+	9.86603i	−0.909527	+	0.525116i	−0.0292479	+	0.999572i	$0.509311\pi$
$354$	3.46410	+	6.00000i	0.184115	+	0.318896i
$355$	−5.19615	+	3.00000i	−0.275783	+	0.159223i
$356$			6.80385i			0.360603i
$357$	36.5885	+	21.1244i	1.93647	+	1.11802i
$358$	−4.73205	−	8.19615i	−0.250097	−	0.433180i
$359$	35.3205			1.86415			0.932073	−	0.362272i	$-0.117999\pi$
$359$	35.3205			1.86415			0.932073	+	0.362272i	$0.117999\pi$
$360$	−7.73205			−0.407515
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$		−	9.39230i		−	0.493649i
$363$	−15.5622	+	26.9545i	−0.816803	+	1.41474i
$364$			6.92820i			0.363137i
$365$	6.00000	+	3.46410i	0.314054	+	0.181319i
$366$	−2.36603	+	4.09808i	−0.123674	+	0.214210i
$367$	−6.19615	+	10.7321i	−0.323437	+	0.560208i	−0.981195	−	0.193021i	$-0.938172\pi$
$367$	−6.19615	+	10.7321i	−0.323437	+	0.560208i	0.657758	+	0.753229i	$0.271505\pi$
$368$	4.09808	−	2.36603i	0.213627	−	0.123338i
$369$	44.3205			2.30723
$370$	−9.86603	−	3.69615i	−0.512910	−	0.192154i
$371$	−5.07180			−0.263315
$372$	3.00000	−	1.73205i	0.155543	−	0.0898027i
$373$	−3.50000	+	6.06218i	−0.181223	+	0.313888i	−0.942297	−	0.334777i	$-0.891339\pi$
$373$	−3.50000	+	6.06218i	−0.181223	+	0.313888i	0.761074	+	0.648665i	$0.224672\pi$
$374$	−18.2942	+	31.6865i	−0.945972	+	1.63847i
$375$	28.6865	+	16.5622i	1.48137	+	0.855267i
$376$		−	4.73205i		−	0.244037i
$377$	15.0000	−	25.9808i	0.772539	−	1.33808i
$378$		−	8.00000i		−	0.411476i
$379$	17.3923	+	30.1244i	0.893383	+	1.54738i	0.835794	+	0.549044i	$0.185008\pi$
$379$	17.3923	+	30.1244i	0.893383	+	1.54738i	0.0575891	+	0.998340i	$0.481659\pi$
$380$	2.19615			0.112660
$381$	−21.3205			−1.09228
$382$	1.09808	+	1.90192i	0.0561825	+	0.0973109i
$383$	−3.00000	−	1.73205i	−0.153293	−	0.0885037i	0.421392	−	0.906879i	$-0.361542\pi$
$383$	−3.00000	−	1.73205i	−0.153293	−	0.0885037i	−0.574684	+	0.818375i	$0.694875\pi$
$384$		−	2.73205i		−	0.139419i
$385$	−14.1962	+	8.19615i	−0.723503	+	0.417715i
$386$	5.59808	+	9.69615i	0.284935	+	0.493521i
$387$	−3.58846	+	2.07180i	−0.182412	+	0.105315i
$388$	6.69615	+	3.86603i	0.339946	+	0.196268i
$389$	−22.5000	−	12.9904i	−1.14080	−	0.658638i	−0.194168	−	0.980968i	$-0.562201\pi$
$389$	−22.5000	−	12.9904i	−1.14080	−	0.658638i	−0.946627	+	0.322330i	$0.895534\pi$
$390$	14.1962	−	8.19615i	0.718850	−	0.415028i
$391$	18.2942	+	31.6865i	0.925179	+	1.60246i
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$			26.7846i			1.35110i
$394$	−5.59808	−	3.23205i	−0.282027	−	0.162828i
$395$	−11.4904	−	19.9019i	−0.578144	−	1.00137i
$396$	21.1244			1.06154
$397$	−23.0000			−1.15434			−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000			−1.15434			−0.577168	+	0.816625i	$0.695842\pi$
$398$	−5.19615	−	9.00000i	−0.260460	−	0.451129i
$399$			6.92820i			0.346844i
$400$	−1.00000	+	1.73205i	−0.0500000	+	0.0866025i
$401$		−	10.3923i		−	0.518967i	−0.965748	−	0.259483i	$-0.916448\pi$
$401$		−	10.3923i		−	0.518967i	0.965748	−	0.259483i	$-0.0835523\pi$
$402$	24.1244	+	13.9282i	1.20321	+	0.694676i
$403$	−2.19615	+	3.80385i	−0.109398	+	0.189483i
$404$	6.23205	−	10.7942i	0.310056	−	0.537033i
$405$	3.69615	−	2.13397i	0.183663	−	0.106038i
$406$	17.3205			0.859602
$407$	26.9545	+	10.0981i	1.33608	+	0.500543i
$408$	21.1244			1.04581
$409$	9.10770	−	5.25833i	0.450347	−	0.260008i	−0.257630	−	0.966244i	$-0.582942\pi$
$409$	9.10770	−	5.25833i	0.450347	−	0.260008i	0.707977	+	0.706236i	$0.249608\pi$
$410$	−8.59808	+	14.8923i	−0.424629	+	0.735479i
$411$	1.90192	−	3.29423i	0.0938150	−	0.162492i
$412$	−7.39230	−	4.26795i	−0.364193	−	0.210267i
$413$		−	5.07180i		−	0.249567i
$414$	10.5622	−	18.2942i	0.519103	−	0.899112i
$415$			9.80385i			0.481252i
$416$	1.73205	+	3.00000i	0.0849208	+	0.147087i
$417$	−56.2487			−2.75451
$418$	−6.00000			−0.293470
$419$	2.07180	+	3.58846i	0.101214	+	0.175308i	0.912185	−	0.409779i	$-0.134394\pi$
$419$	2.07180	+	3.58846i	0.101214	+	0.175308i	−0.810971	+	0.585086i	$0.801061\pi$
$420$	8.19615	+	4.73205i	0.399931	+	0.230900i
$421$		−	12.1244i		−	0.590905i	−0.955357	−	0.295452i	$-0.904530\pi$
$421$		−	12.1244i		−	0.590905i	0.955357	−	0.295452i	$-0.0954704\pi$
$422$	−2.07180	+	1.19615i	−0.100853	+	0.0582278i
$423$	−10.5622	−	18.2942i	−0.513551	−	0.889496i
$424$	−2.19615	+	1.26795i	−0.106655	+	0.0615771i
$425$	−13.3923	−	7.73205i	−0.649622	−	0.375060i
$426$	−8.19615	−	4.73205i	−0.397105	−	0.229269i
$427$	3.00000	−	1.73205i	0.145180	−	0.0838198i
$428$	−5.19615	−	9.00000i	−0.251166	−	0.435031i
$429$	−38.7846	+	22.3923i	−1.87254	+	1.08111i
$430$		−	1.60770i		−	0.0775299i
$431$	−15.2942	−	8.83013i	−0.736697	−	0.425332i	0.0841701	−	0.996451i	$-0.473176\pi$
$431$	−15.2942	−	8.83013i	−0.736697	−	0.425332i	−0.820867	+	0.571119i	$0.806509\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	15.7846			0.758560			0.379280	−	0.925282i	$-0.376172\pi$
$433$	15.7846			0.758560			0.379280	+	0.925282i	$0.376172\pi$
$434$	−2.53590			−0.121727
$435$	−20.4904	−	35.4904i	−0.982439	−	1.70163i
$436$		−	2.66025i		−	0.127403i
$437$	−3.00000	+	5.19615i	−0.143509	+	0.248566i
$438$			10.9282i			0.522170i
$439$	−15.8038	−	9.12436i	−0.754276	−	0.435482i	0.0729605	−	0.997335i	$-0.476755\pi$
$439$	−15.8038	−	9.12436i	−0.754276	−	0.435482i	−0.827237	+	0.561853i	$0.810089\pi$
$440$	−4.09808	+	7.09808i	−0.195368	+	0.338388i
$441$	6.69615	−	11.5981i	0.318864	−	0.552289i
$442$	−23.1962	+	13.3923i	−1.10333	+	0.637007i
$443$	−14.5359			−0.690621			−0.345311	−	0.938488i	$-0.612226\pi$
$443$	−14.5359			−0.690621			−0.345311	+	0.938488i	$0.612226\pi$
$444$	−2.73205	−	16.3923i	−0.129657	−	0.777944i
$445$	−11.7846			−0.558644
$446$	14.0263	−	8.09808i	0.664164	−	0.383455i
$447$	21.7583	−	37.6865i	1.02913	−	1.78251i
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	17.7846	+	10.2679i	0.839308	+	0.484574i	0.857029	−	0.515268i	$-0.172308\pi$
$449$	17.7846	+	10.2679i	0.839308	+	0.484574i	−0.0177212	+	0.999843i	$0.505641\pi$
$450$			8.92820i			0.420880i
$451$	23.4904	−	40.6865i	1.10612	−	1.91585i
$452$			3.46410i			0.162938i
$453$	−5.73205	−	9.92820i	−0.269315	−	0.466468i
$454$	1.26795			0.0595078
$455$	−12.0000			−0.562569
$456$	1.73205	+	3.00000i	0.0811107	+	0.140488i
$457$	−32.8923	−	18.9904i	−1.53864	−	0.888333i	−0.998919	−	0.0464868i	$-0.985197\pi$
$457$	−32.8923	−	18.9904i	−1.53864	−	0.888333i	−0.539718	−	0.841846i	$-0.681469\pi$
$458$			27.3923i			1.27996i
$459$	26.7846	−	15.4641i	1.25020	−	0.721802i
$460$	4.09808	+	7.09808i	0.191074	+	0.330950i
$461$	−34.1769	+	19.7321i	−1.59178	+	0.919013i	−0.598775	+	0.800917i	$0.704346\pi$
$461$	−34.1769	+	19.7321i	−1.59178	+	0.919013i	−0.993002	+	0.118096i	$0.962321\pi$
$462$	−22.3923	−	12.9282i	−1.04178	−	0.601474i
$463$	−25.9808	−	15.0000i	−1.20743	−	0.697109i	−0.245232	−	0.969465i	$-0.578864\pi$
$463$	−25.9808	−	15.0000i	−1.20743	−	0.697109i	−0.962197	+	0.272355i	$0.912197\pi$
$464$	7.50000	−	4.33013i	0.348179	−	0.201021i
$465$	3.00000	+	5.19615i	0.139122	+	0.240966i
$466$	12.9904	−	7.50000i	0.601768	−	0.347431i
$467$		−	2.53590i		−	0.117347i	−0.998277	−	0.0586737i	$-0.981313\pi$
$467$		−	2.53590i		−	0.117347i	0.998277	−	0.0586737i	$-0.0186871\pi$
$468$	13.3923	+	7.73205i	0.619060	+	0.357414i
$469$	−10.1962	−	17.6603i	−0.470815	−	0.815475i
$470$	8.19615			0.378060
$471$	2.73205			0.125886
$472$	−1.26795	−	2.19615i	−0.0583621	−	0.101086i
$473$			4.39230i			0.201958i
$474$	18.1244	−	31.3923i	0.832479	−	1.44190i
$475$		−	2.53590i		−	0.116355i
$476$	−13.3923	−	7.73205i	−0.613835	−	0.354398i
$477$	−5.66025	+	9.80385i	−0.259165	+	0.448887i
$478$	−8.66025	+	15.0000i	−0.396111	+	0.686084i
$479$	8.19615	−	4.73205i	0.374492	−	0.216213i	−0.300927	−	0.953647i	$-0.597296\pi$
$479$	8.19615	−	4.73205i	0.374492	−	0.216213i	0.675419	+	0.737434i	$0.263963\pi$
$480$	4.73205			0.215988
$481$	13.3923	+	16.2679i	0.610637	+	0.741755i
$482$	15.4641			0.704371
$483$	−22.3923	+	12.9282i	−1.01889	+	0.588254i
$484$	5.69615	−	9.86603i	0.258916	−	0.448456i
$485$	−6.69615	+	11.5981i	−0.304057	+	0.526642i
$486$	16.2224	+	9.36603i	0.735864	+	0.424852i
$487$			16.0526i			0.727411i	0.931514	+	0.363705i	$0.118489\pi$
$487$			16.0526i			0.727411i	−0.931514	+	0.363705i	$0.881511\pi$
$488$	0.866025	−	1.50000i	0.0392031	−	0.0679018i
$489$			35.3205i			1.59725i
$490$	2.59808	+	4.50000i	0.117369	+	0.203289i
$491$	26.1962			1.18222			0.591108	−	0.806592i	$-0.298691\pi$
$491$	26.1962			1.18222			0.591108	+	0.806592i	$0.298691\pi$
$492$	−27.1244			−1.22286
$493$	33.4808	+	57.9904i	1.50790	+	2.61176i
$494$	−3.80385	−	2.19615i	−0.171143	−	0.0988096i
$495$			36.5885i			1.64453i
$496$	−1.09808	+	0.633975i	−0.0493051	+	0.0284663i
$497$	3.46410	+	6.00000i	0.155386	+	0.269137i
$498$	−13.3923	+	7.73205i	−0.600124	+	0.346481i
$499$	−17.4904	−	10.0981i	−0.782977	−	0.452052i	0.0545073	−	0.998513i	$-0.482641\pi$
$499$	−17.4904	−	10.0981i	−0.782977	−	0.452052i	−0.837484	+	0.546461i	$0.815975\pi$
$500$	−10.5000	−	6.06218i	−0.469574	−	0.271109i
$501$	32.7846	−	18.9282i	1.46471	−	0.845650i
$502$	−8.66025	−	15.0000i	−0.386526	−	0.669483i
$503$	−17.4904	+	10.0981i	−0.779858	+	0.450251i	−0.836380	−	0.548150i	$-0.815332\pi$
$503$	−17.4904	+	10.0981i	−0.779858	+	0.450251i	0.0565223	+	0.998401i	$0.481999\pi$
$504$			8.92820i			0.397694i
$505$	18.6962	+	10.7942i	0.831968	+	0.480337i
$506$	−11.1962	−	19.3923i	−0.497730	−	0.862093i
$507$	2.73205			0.121335
$508$	7.80385			0.346240
$509$	3.23205	+	5.59808i	0.143258	+	0.248130i	0.928722	−	0.370777i	$-0.120909\pi$
$509$	3.23205	+	5.59808i	0.143258	+	0.248130i	−0.785464	+	0.618908i	$0.787575\pi$
$510$			36.5885i			1.62016i
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$			1.00000i			0.0441942i
$513$	4.39230	+	2.53590i	0.193925	+	0.111963i
$514$	3.40192	−	5.89230i	0.150052	−	0.259898i
$515$	7.39230	−	12.8038i	0.325744	−	0.564205i
$516$	2.19615	−	1.26795i	0.0966802	−	0.0558184i
$517$	−22.3923			−0.984812
$518$	−4.26795	+	11.3923i	−0.187523	+	0.500549i
$519$	15.1244			0.663886
$520$	−5.19615	+	3.00000i	−0.227866	+	0.131559i
$521$	−2.53590	+	4.39230i	−0.111100	+	0.192430i	−0.916214	−	0.400689i	$-0.868771\pi$
$521$	−2.53590	+	4.39230i	−0.111100	+	0.192430i	0.805114	+	0.593120i	$0.202104\pi$
$522$	19.3301	−	33.4808i	0.846057	−	1.46541i
$523$	17.7058	+	10.2224i	0.774219	+	0.446996i	0.834378	−	0.551193i	$-0.185827\pi$
$523$	17.7058	+	10.2224i	0.774219	+	0.446996i	−0.0601584	+	0.998189i	$0.519161\pi$
$524$		−	9.80385i		−	0.428283i
$525$	5.46410	−	9.46410i	0.238473	−	0.413047i
$526$			21.4641i			0.935879i
$527$	−4.90192	−	8.49038i	−0.213531	−	0.369847i
$528$	−12.9282			−0.562628
$529$	0.607695			0.0264215
$530$	−2.19615	−	3.80385i	−0.0953948	−	0.165229i
$531$	−9.80385	−	5.66025i	−0.425451	−	0.245634i
$532$		−	2.53590i		−	0.109945i
$533$	29.7846	−	17.1962i	1.29011	−	0.744848i
$534$	−9.29423	−	16.0981i	−0.402201	−	0.696632i
$535$	15.5885	−	9.00000i	0.673948	−	0.389104i
$536$	−8.83013	−	5.09808i	−0.381403	−	0.220203i
$537$	22.3923	+	12.9282i	0.966299	+	0.557893i
$538$	−3.80385	+	2.19615i	−0.163996	+	0.0946829i
$539$	−7.09808	−	12.2942i	−0.305736	−	0.529550i
$540$	6.00000	−	3.46410i	0.258199	−	0.149071i
$541$			19.0526i			0.819133i	0.912280	+	0.409567i	$0.134320\pi$
$541$			19.0526i			0.819133i	−0.912280	+	0.409567i	$0.865680\pi$
$542$	2.24167	+	1.29423i	0.0962880	+	0.0555919i
$543$	12.8301	+	22.2224i	0.550593	+	0.953656i
$544$	−7.73205			−0.331509
$545$	4.60770			0.197372
$546$	−9.46410	−	16.3923i	−0.405026	−	0.701526i
$547$			41.6603i			1.78126i	0.454725	+	0.890632i	$0.349738\pi$
$547$			41.6603i			1.78126i	−0.454725	+	0.890632i	$0.650262\pi$
$548$	−0.696152	+	1.20577i	−0.0297382	+	0.0515080i
$549$		−	7.73205i		−	0.329996i
$550$	8.19615	+	4.73205i	0.349485	+	0.201775i
$551$	−5.49038	+	9.50962i	−0.233898	+	0.405123i
$552$	−6.46410	+	11.1962i	−0.275130	+	0.476540i
$553$	−22.9808	+	13.2679i	−0.977241	+	0.564211i
$554$	11.1962			0.475679
$555$	28.3923	−	4.73205i	1.20519	−	0.200864i
$556$	20.5885			0.873145
$557$	20.3038	−	11.7224i	0.860302	−	0.496695i	−0.00381165	−	0.999993i	$-0.501213\pi$
$557$	20.3038	−	11.7224i	0.860302	−	0.496695i	0.864113	+	0.503297i	$0.167880\pi$
$558$	−2.83013	+	4.90192i	−0.119809	+	0.207515i
$559$	−1.60770	+	2.78461i	−0.0679983	+	0.117776i
$560$	−3.00000	−	1.73205i	−0.126773	−	0.0731925i
$561$		−	99.9615i		−	4.22038i
$562$	−13.7942	+	23.8923i	−0.581874	+	1.00784i
$563$		−	18.5885i		−	0.783410i	−0.920091	−	0.391705i	$-0.871885\pi$
$563$		−	18.5885i		−	0.783410i	0.920091	−	0.391705i	$-0.128115\pi$
$564$	6.46410	+	11.1962i	0.272188	+	0.471443i
$565$	−6.00000			−0.252422
$566$	−7.85641			−0.330229
$567$	−2.46410	−	4.26795i	−0.103483	−	0.179237i
$568$	3.00000	+	1.73205i	0.125877	+	0.0726752i
$569$		−	5.87564i		−	0.246320i	−0.992387	−	0.123160i	$-0.960697\pi$
$569$		−	5.87564i		−	0.246320i	0.992387	−	0.123160i	$-0.0393028\pi$
$570$	−5.19615	+	3.00000i	−0.217643	+	0.125656i
$571$	−18.6865	−	32.3660i	−0.782007	−	1.35448i	−0.930771	−	0.365603i	$-0.880863\pi$
$571$	−18.6865	−	32.3660i	−0.782007	−	1.35448i	0.148764	−	0.988873i	$-0.452471\pi$
$572$	14.1962	−	8.19615i	0.593571	−	0.342698i
$573$	−5.19615	−	3.00000i	−0.217072	−	0.125327i
$574$	17.1962	+	9.92820i	0.717754	+	0.414395i
$575$	8.19615	−	4.73205i	0.341803	−	0.197340i
$576$	2.23205	+	3.86603i	0.0930021	+	0.161084i
$577$	−0.803848	+	0.464102i	−0.0334646	+	0.0193208i	−0.516639	−	0.856203i	$-0.672817\pi$
$577$	−0.803848	+	0.464102i	−0.0334646	+	0.0193208i	0.483174	+	0.875524i	$0.339484\pi$
$578$		−	42.7846i		−	1.77961i
$579$	−26.4904	−	15.2942i	−1.10090	−	0.635606i
$580$	7.50000	+	12.9904i	0.311421	+	0.539396i
$581$	11.3205			0.469654
$582$	−21.1244			−0.875633
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$		−	4.00000i		−	0.165521i
$585$	−13.3923	+	23.1962i	−0.553704	+	0.959043i
$586$		−	1.39230i		−	0.0575156i
$587$	28.6865	+	16.5622i	1.18402	+	0.683594i	0.956941	−	0.290282i	$-0.0937492\pi$
$587$	28.6865	+	16.5622i	1.18402	+	0.683594i	0.227079	+	0.973876i	$0.427082\pi$
$588$	−4.09808	+	7.09808i	−0.169002	+	0.292720i
$589$	0.803848	−	1.39230i	0.0331220	−	0.0573689i
$590$	3.80385	−	2.19615i	0.156602	−	0.0904142i
$591$	17.6603			0.726446
$592$	1.00000	+	6.00000i	0.0410997	+	0.246598i
$593$	43.6410			1.79212			0.896061	−	0.443931i	$-0.146417\pi$
$593$	43.6410			1.79212			0.896061	+	0.443931i	$0.146417\pi$
$594$	−16.3923	+	9.46410i	−0.672584	+	0.388317i
$595$	13.3923	−	23.1962i	0.549031	−	0.950950i
$596$	−7.96410	+	13.7942i	−0.326222	+	0.565034i
$597$	24.5885	+	14.1962i	1.00634	+	0.581010i
$598$		−	16.3923i		−	0.670331i
$599$	−23.8301	+	41.2750i	−0.973673	+	1.68645i	−0.289425	+	0.957201i	$0.593464\pi$
$599$	−23.8301	+	41.2750i	−0.973673	+	1.68645i	−0.684248	+	0.729250i	$0.739869\pi$
$600$		−	5.46410i		−	0.223071i
$601$	6.30385	+	10.9186i	0.257139	+	0.445378i	0.965474	−	0.260498i	$-0.0838867\pi$
$601$	6.30385	+	10.9186i	0.257139	+	0.445378i	−0.708335	+	0.705876i	$0.750553\pi$
$602$	−1.85641			−0.0756615
$603$	−45.5167			−1.85358
$604$	2.09808	+	3.63397i	0.0853695	+	0.147864i
$605$	17.0885	+	9.86603i	0.694745	+	0.401111i
$606$			34.0526i			1.38329i
$607$	−20.7058	+	11.9545i	−0.840421	+	0.485217i	−0.857407	−	0.514638i	$-0.827926\pi$
$607$	−20.7058	+	11.9545i	−0.840421	+	0.485217i	0.0169861	+	0.999856i	$0.494593\pi$
$608$	−0.633975	−	1.09808i	−0.0257111	−	0.0445329i
$609$	−40.9808	+	23.6603i	−1.66062	+	0.958762i
$610$	2.59808	+	1.50000i	0.105193	+	0.0607332i
$611$	−14.1962	−	8.19615i	−0.574315	−	0.331581i
$612$	−29.8923	+	17.2583i	−1.20832	+	0.697627i
$613$	−3.89230	−	6.74167i	−0.157209	−	0.272293i	0.776652	−	0.629929i	$-0.216916\pi$
$613$	−3.89230	−	6.74167i	−0.157209	−	0.272293i	−0.933861	+	0.357636i	$0.883583\pi$
$614$	−19.0526	+	11.0000i	−0.768899	+	0.443924i
$615$		−	46.9808i		−	1.89445i
$616$	8.19615	+	4.73205i	0.330232	+	0.190660i
$617$	−6.33975	−	10.9808i	−0.255229	−	0.442069i	0.709729	−	0.704475i	$-0.248817\pi$
$617$	−6.33975	−	10.9808i	−0.255229	−	0.442069i	−0.964958	+	0.262406i	$0.915484\pi$
$618$	23.3205			0.938088
$619$	30.3923			1.22157			0.610785	−	0.791797i	$-0.290854\pi$
$619$	30.3923			1.22157			0.610785	+	0.791797i	$0.290854\pi$
$620$	−1.09808	−	1.90192i	−0.0440998	−	0.0763831i
$621$			18.9282i			0.759563i
$622$	−9.00000	+	15.5885i	−0.360867	+	0.625040i
$623$			13.6077i			0.545181i
$624$	−8.19615	−	4.73205i	−0.328109	−	0.189434i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	12.0622	−	20.8923i	0.482102	−	0.835024i
$627$	14.1962	−	8.19615i	0.566940	−	0.327323i
$628$	−1.00000			−0.0399043
$629$	−46.3923	+	7.73205i	−1.84978	+	0.308297i
$630$	−15.4641			−0.616105
$631$	−30.2942	+	17.4904i	−1.20599	+	0.696281i	−0.961882	−	0.273466i	$-0.911830\pi$
$631$	−30.2942	+	17.4904i	−1.20599	+	0.696281i	−0.244112	+	0.969747i	$0.578497\pi$
$632$	−6.63397	+	11.4904i	−0.263885	+	0.457063i
$633$	3.26795	−	5.66025i	0.129889	−	0.224975i
$634$	−6.40192	−	3.69615i	−0.254253	−	0.146793i
$635$			13.5167i			0.536392i
$636$	3.46410	−	6.00000i	0.137361	−	0.237915i
$637$		−	10.3923i		−	0.411758i
$638$	−20.4904	−	35.4904i	−0.811222	−	1.40508i
$639$	15.4641			0.611750
$640$	−1.73205			−0.0684653
$641$	−0.571797	−	0.990381i	−0.0225846	−	0.0391177i	0.854512	−	0.519431i	$-0.173856\pi$
$641$	−0.571797	−	0.990381i	−0.0225846	−	0.0391177i	−0.877097	+	0.480314i	$0.840523\pi$
$642$	24.5885	+	14.1962i	0.970429	+	0.560277i
$643$		−	13.2679i		−	0.523237i	−0.965171	−	0.261618i	$-0.915744\pi$
$643$		−	13.2679i		−	0.523237i	0.965171	−	0.261618i	$-0.0842562\pi$
$644$	8.19615	−	4.73205i	0.322974	−	0.186469i
$645$	2.19615	+	3.80385i	0.0864734	+	0.149776i
$646$	8.49038	−	4.90192i	0.334050	−	0.192864i
$647$	19.9808	+	11.5359i	0.785525	+	0.453523i	0.838385	−	0.545079i	$-0.183500\pi$
$647$	19.9808	+	11.5359i	0.785525	+	0.453523i	−0.0528599	+	0.998602i	$0.516834\pi$
$648$	−2.13397	−	1.23205i	−0.0838304	−	0.0483995i
$649$	−10.3923	+	6.00000i	−0.407934	+	0.235521i
$650$	3.46410	+	6.00000i	0.135873	+	0.235339i
$651$	6.00000	−	3.46410i	0.235159	−	0.135769i
$652$		−	12.9282i		−	0.506308i
$653$	−38.0885	−	21.9904i	−1.49052	−	0.860550i	−0.490575	−	0.871399i	$-0.663213\pi$
$653$	−38.0885	−	21.9904i	−1.49052	−	0.860550i	−0.999941	+	0.0108487i	$0.996547\pi$
$654$	3.63397	+	6.29423i	0.142100	+	0.246124i
$655$	16.9808			0.663493
$656$	9.92820			0.387631
$657$	−8.92820	−	15.4641i	−0.348322	−	0.603312i
$658$		−	9.46410i		−	0.368949i
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	−0.759018	−	0.651070i	$-0.774320\pi$
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	0.943352	+	0.331793i	$0.107654\pi$
$660$		−	22.3923i		−	0.871619i
$661$	1.50000	+	0.866025i	0.0583432	+	0.0336845i	0.528888	−	0.848692i	$-0.322609\pi$
$661$	1.50000	+	0.866025i	0.0583432	+	0.0336845i	−0.470545	+	0.882376i	$0.655943\pi$
$662$		0			0
$663$	36.5885	−	63.3731i	1.42098	−	2.46121i
$664$	4.90192	−	2.83013i	0.190232	−	0.109830i
$665$	4.39230			0.170326
$666$	17.2583	+	20.9641i	0.668747	+	0.812342i
$667$	−40.9808			−1.58678
$668$	−12.0000	+	6.92820i	−0.464294	+	0.268060i
$669$	−22.1244	+	38.3205i	−0.855377	+	1.48156i
$670$	8.83013	−	15.2942i	0.341138	−	0.590868i
$671$	−7.09808	−	4.09808i	−0.274018	−	0.158204i
$672$		−	5.46410i		−	0.210782i
$673$	−8.00000	+	13.8564i	−0.308377	+	0.534125i	−0.978008	−	0.208569i	$-0.933119\pi$
$673$	−8.00000	+	13.8564i	−0.308377	+	0.534125i	0.669630	+	0.742695i	$0.266453\pi$
$674$		−	32.1769i		−	1.23941i
$675$	−4.00000	−	6.92820i	−0.153960	−	0.266667i
$676$	−1.00000			−0.0384615
$677$	33.9282			1.30397			0.651983	−	0.758233i	$-0.273937\pi$
$677$	33.9282			1.30397			0.651983	+	0.758233i	$0.273937\pi$
$678$	−4.73205	−	8.19615i	−0.181733	−	0.314771i
$679$	13.3923	+	7.73205i	0.513949	+	0.296729i
$680$		−	13.3923i		−	0.513571i
$681$	−3.00000	+	1.73205i	−0.114960	+	0.0663723i
$682$	3.00000	+	5.19615i	0.114876	+	0.198971i
$683$	−17.7846	+	10.2679i	−0.680509	+	0.392892i	−0.800047	−	0.599938i	$-0.795192\pi$
$683$	−17.7846	+	10.2679i	−0.680509	+	0.392892i	0.119538	+	0.992830i	$0.461859\pi$
$684$	−4.90192	−	2.83013i	−0.187430	−	0.108213i
$685$	−2.08846	−	1.20577i	−0.0797959	−	0.0460702i
$686$	17.3205	−	10.0000i	0.661300	−	0.381802i
$687$	−37.4186	−	64.8109i	−1.42761	−	2.47269i
$688$	−0.803848	+	0.464102i	−0.0306464	+	0.0176937i
$689$			8.78461i			0.334667i
$690$	−19.3923	−	11.1962i	−0.738252	−	0.426230i
$691$	−13.4904	−	23.3660i	−0.513198	−	0.888885i	−0.999883	−	0.0153077i	$-0.995127\pi$
$691$	−13.4904	−	23.3660i	−0.513198	−	0.888885i	0.486685	−	0.873578i	$-0.338206\pi$
$692$	−5.53590			−0.210443
$693$	42.2487			1.60490
$694$	4.56218	+	7.90192i	0.173178	+	0.299953i
$695$			35.6603i			1.35267i
$696$	−11.8301	+	20.4904i	−0.448420	+	0.776686i
$697$			76.7654i			2.90770i
$698$	−9.86603	−	5.69615i	−0.373435	−	0.215603i
$699$	−20.4904	+	35.4904i	−0.775017	+	1.34237i
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	16.3923	−	9.46410i	0.619129	−	0.357454i	−0.157401	−	0.987535i	$-0.550311\pi$
$701$	16.3923	−	9.46410i	0.619129	−	0.357454i	0.776530	+	0.630081i	$0.216978\pi$
$702$	−13.8564			−0.522976
$703$	−4.90192	−	5.95448i	−0.184880	−	0.224578i
$704$	4.73205			0.178346
$705$	−19.3923	+	11.1962i	−0.730356	+	0.421671i
$706$	−9.86603	+	17.0885i	−0.371313	+	0.643133i
$707$	12.4641	−	21.5885i	0.468761	−	0.811917i
$708$	6.00000	+	3.46410i	0.225494	+	0.130189i
$709$		−	9.71281i		−	0.364772i	−0.983227	−	0.182386i	$-0.941618\pi$
$709$		−	9.71281i		−	0.364772i	0.983227	−	0.182386i	$-0.0583821\pi$
$710$	−3.00000	+	5.19615i	−0.112588	+	0.195008i
$711$			59.2295i			2.22128i
$712$	3.40192	+	5.89230i	0.127492	+	0.220823i
$713$	6.00000			0.224702
$714$	42.2487			1.58112
$715$	14.1962	+	24.5885i	0.530906	+	0.919556i
$716$	−8.19615	−	4.73205i	−0.306305	−	0.176845i
$717$		−	47.3205i		−	1.76722i
$718$	30.5885	−	17.6603i	1.14155	−	0.659075i
$719$	−18.6340	−	32.2750i	−0.694930	−	1.20365i	−0.970204	−	0.242288i	$-0.922102\pi$
$719$	−18.6340	−	32.2750i	−0.694930	−	1.20365i	0.275274	−	0.961366i	$-0.411231\pi$
$720$	−6.69615	+	3.86603i	−0.249551	+	0.144078i
$721$	−14.7846	−	8.53590i	−0.550608	−	0.317893i
$722$	−15.0622	−	8.69615i	−0.560556	−	0.323637i
$723$	−36.5885	+	21.1244i	−1.36074	+	0.785623i
$724$	−4.69615	−	8.13397i	−0.174531	−	0.302297i
$725$	15.0000	−	8.66025i	0.557086	−	0.321634i
$726$			31.1244i			1.15513i
$727$	34.3923	+	19.8564i	1.27554	+	0.736433i	0.976025	−	0.217658i	$-0.0698418\pi$
$727$	34.3923	+	19.8564i	1.27554	+	0.736433i	0.299515	+	0.954092i	$0.403175\pi$
$728$	3.46410	+	6.00000i	0.128388	+	0.222375i
$729$	−43.7846			−1.62165
$730$	6.92820			0.256424
$731$	−3.58846	−	6.21539i	−0.132724	−	0.229885i
$732$			4.73205i			0.174902i
$733$	16.7846	−	29.0718i	0.619954	−	1.07379i	−0.369540	−	0.929215i	$-0.620485\pi$
$733$	16.7846	−	29.0718i	0.619954	−	1.07379i	0.989494	−	0.144576i	$-0.0461820\pi$
$734$			12.3923i			0.457408i
$735$	−12.2942	−	7.09808i	−0.453479	−	0.261816i
$736$	2.36603	−	4.09808i	0.0872129	−	0.151057i
$737$	−24.1244	+	41.7846i	−0.888632	+	1.53916i
$738$	38.3827	−	22.1603i	1.41289	−	0.815730i
$739$	32.5885			1.19879			0.599393	−	0.800455i	$-0.295409\pi$
$739$	32.5885			1.19879			0.599393	+	0.800455i	$0.295409\pi$
$740$	−10.3923	+	1.73205i	−0.382029	+	0.0636715i
$741$	12.0000			0.440831
$742$	−4.39230	+	2.53590i	−0.161247	+	0.0930958i
$743$	−0.758330	+	1.31347i	−0.0278204	+	0.0481864i	−0.879600	−	0.475713i	$-0.842190\pi$
$743$	−0.758330	+	1.31347i	−0.0278204	+	0.0481864i	0.851780	+	0.523900i	$0.175523\pi$
$744$	1.73205	−	3.00000i	0.0635001	−	0.109985i
$745$	−23.8923	−	13.7942i	−0.875346	−	0.505381i
$746$			7.00000i			0.256288i
$747$	12.6340	−	21.8827i	0.462253	−	0.800646i
$748$			36.5885i			1.33781i
$749$	−10.3923	−	18.0000i	−0.379727	−	0.657706i
$750$	33.1244			1.20953
$751$	29.6077			1.08040			0.540200	−	0.841537i	$-0.318349\pi$
$751$	29.6077			1.08040			0.540200	+	0.841537i	$0.318349\pi$
$752$	−2.36603	−	4.09808i	−0.0862801	−	0.149441i
$753$	40.9808	+	23.6603i	1.49342	+	0.862228i
$754$		−	30.0000i		−	1.09254i
$755$	−6.29423	+	3.63397i	−0.229070	+	0.132254i
$756$	−4.00000	−	6.92820i	−0.145479	−	0.251976i
$757$	14.8923	−	8.59808i	0.541270	−	0.312502i	−0.204323	−	0.978903i	$-0.565499\pi$
$757$	14.8923	−	8.59808i	0.541270	−	0.312502i	0.745593	+	0.666401i	$0.232166\pi$
$758$	30.1244	+	17.3923i	1.09417	+	0.631717i
$759$	52.9808	+	30.5885i	1.92308	+	1.11029i
$760$	1.90192	−	1.09808i	0.0689900	−	0.0398314i
$761$	1.16025	+	2.00962i	0.0420592	+	0.0728486i	0.886289	−	0.463133i	$-0.153275\pi$
$761$	1.16025	+	2.00962i	0.0420592	+	0.0728486i	−0.844229	+	0.535982i	$0.819942\pi$
$762$	−18.4641	+	10.6603i	−0.668884	+	0.386180i
$763$		−	5.32051i		−	0.192615i
$764$	1.90192	+	1.09808i	0.0688092	+	0.0397270i
$765$	−29.8923	−	51.7750i	−1.08076	−	1.87193i
$766$	−3.46410			−0.125163
$767$	−8.78461			−0.317194
$768$	−1.36603	−	2.36603i	−0.0492922	−	0.0853766i
$769$			13.6077i			0.490706i	0.969434	+	0.245353i	$0.0789039\pi$
$769$			13.6077i			0.490706i	−0.969434	+	0.245353i	$0.921096\pi$
$770$	−8.19615	+	14.1962i	−0.295369	+	0.511594i
$771$			18.5885i			0.669447i
$772$	9.69615	+	5.59808i	0.348972	+	0.201479i
$773$	−16.9641	+	29.3827i	−0.610156	+	1.05682i	0.381057	+	0.924551i	$0.375560\pi$
$773$	−16.9641	+	29.3827i	−0.610156	+	1.05682i	−0.991214

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +1.73205 q^{10} -4.73205 q^{11} +(1.36603 + 2.36603i) q^{12} +(-3.00000 - 1.73205i) q^{13} -2.00000i q^{14} +(-4.09808 + 2.36603i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.69615 - 3.86603i) q^{17} +(-3.86603 - 2.23205i) q^{18} +(1.09808 + 0.633975i) q^{19} +(1.50000 - 0.866025i) q^{20} +(2.73205 + 4.73205i) q^{21} +(-4.09808 + 2.36603i) q^{22} +4.73205i q^{23} +(2.36603 + 1.36603i) q^{24} +(-1.00000 - 1.73205i) q^{25} -3.46410 q^{26} +4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +8.66025i q^{29} +(-2.36603 + 4.09808i) q^{30} -1.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(6.46410 - 11.1962i) q^{33} +(3.86603 - 6.69615i) q^{34} +(3.00000 - 1.73205i) q^{35} -4.46410 q^{36} +(-5.69615 - 2.13397i) q^{37} +1.26795 q^{38} +(8.19615 - 4.73205i) q^{39} +(0.866025 - 1.50000i) q^{40} +(-4.96410 + 8.59808i) q^{41} +(4.73205 + 2.73205i) q^{42} -0.928203i q^{43} +(-2.36603 + 4.09808i) q^{44} -7.73205i q^{45} +(2.36603 + 4.09808i) q^{46} +4.73205 q^{47} +2.73205 q^{48} +(1.50000 + 2.59808i) q^{49} +(-1.73205 - 1.00000i) q^{50} +21.1244i q^{51} +(-3.00000 + 1.73205i) q^{52} +(-1.26795 - 2.19615i) q^{53} +(3.46410 - 2.00000i) q^{54} +(-7.09808 - 4.09808i) q^{55} +(-1.73205 - 1.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(4.33013 + 7.50000i) q^{58} +(2.19615 - 1.26795i) q^{59} +4.73205i q^{60} +(1.50000 + 0.866025i) q^{61} +(-0.633975 - 1.09808i) q^{62} -8.92820 q^{63} -1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -12.9282i q^{66} +(5.09808 - 8.83013i) q^{67} -7.73205i q^{68} +(-11.1962 - 6.46410i) q^{69} +(1.73205 - 3.00000i) q^{70} +(-1.73205 + 3.00000i) q^{71} +(-3.86603 + 2.23205i) q^{72} +4.00000 q^{73} +(-6.00000 + 1.00000i) q^{74} +5.46410 q^{75} +(1.09808 - 0.633975i) q^{76} +(-4.73205 + 8.19615i) q^{77} +(4.73205 - 8.19615i) q^{78} +(-11.4904 - 6.63397i) q^{79} -1.73205i q^{80} +(1.23205 - 2.13397i) q^{81} +9.92820i q^{82} +(2.83013 + 4.90192i) q^{83} +5.46410 q^{84} +13.3923 q^{85} +(-0.464102 - 0.803848i) q^{86} +(-20.4904 - 11.8301i) q^{87} +4.73205i q^{88} +(-5.89230 + 3.40192i) q^{89} +(-3.86603 - 6.69615i) q^{90} +(-6.00000 + 3.46410i) q^{91} +(4.09808 + 2.36603i) q^{92} +(3.00000 + 1.73205i) q^{93} +(4.09808 - 2.36603i) q^{94} +(1.09808 + 1.90192i) q^{95} +(2.36603 - 1.36603i) q^{96} +7.73205i q^{97} +(2.59808 + 1.50000i) q^{98} +(10.5622 + 18.2942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9} - 12 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} - 6 q^{22} + 6 q^{24} - 4 q^{25} + 16 q^{27} - 4 q^{28} - 6 q^{30} + 12 q^{33} + 12 q^{34} + 12 q^{35} - 4 q^{36} - 2 q^{37} + 12 q^{38} + 12 q^{39} - 6 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} + 6 q^{49} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 12 q^{57} - 12 q^{59} + 6 q^{61} - 6 q^{62} - 8 q^{63} - 4 q^{64} - 12 q^{65} + 10 q^{67} - 24 q^{69} - 12 q^{72} + 16 q^{73} - 24 q^{74} + 8 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 6 q^{79} - 2 q^{81} - 6 q^{83} + 8 q^{84} + 12 q^{85} + 12 q^{86} - 30 q^{87} + 18 q^{89} - 12 q^{90} - 24 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} + 6 q^{96} + 18 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^5 + 4 * q^7 - 2 * q^9 - 12 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 12 * q^18 - 6 * q^19 + 6 * q^20 + 4 * q^21 - 6 * q^22 + 6 * q^24 - 4 * q^25 + 16 * q^27 - 4 * q^28 - 6 * q^30 + 12 * q^33 + 12 * q^34 + 12 * q^35 - 4 * q^36 - 2 * q^37 + 12 * q^38 + 12 * q^39 - 6 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 + 6 * q^49 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 12 * q^57 - 12 * q^59 + 6 * q^61 - 6 * q^62 - 8 * q^63 - 4 * q^64 - 12 * q^65 + 10 * q^67 - 24 * q^69 - 12 * q^72 + 16 * q^73 - 24 * q^74 + 8 * q^75 - 6 * q^76 - 12 * q^77 + 12 * q^78 + 6 * q^79 - 2 * q^81 - 6 * q^83 + 8 * q^84 + 12 * q^85 + 12 * q^86 - 30 * q^87 + 18 * q^89 - 12 * q^90 - 24 * q^91 + 6 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 + 6 * q^96 + 18 * q^99

Introduction

L-functions

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