LMFDB - Embedded newform 546.2.s.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(43,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("546.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.43
Dual form			546.2.s.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(4.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(2.36603 + 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} +1.00000i q^{18} +(-5.59808 + 3.23205i) q^{19} +(2.36603 - 1.36603i) q^{20} -1.00000i q^{21} +(-2.59808 - 4.50000i) q^{22} +(-0.267949 + 0.464102i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(5.23205 - 9.06218i) q^{29} +(-1.36603 - 2.36603i) q^{30} -6.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.50000 + 2.59808i) q^{33} +5.73205i q^{34} +(1.36603 + 2.36603i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.83013 - 1.63397i) q^{37} +6.46410 q^{38} +(3.46410 + 1.00000i) q^{39} -2.73205 q^{40} +(1.33013 + 0.767949i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-2.63397 - 4.56218i) q^{43} +5.19615i q^{44} +(-2.36603 + 1.36603i) q^{45} +(0.464102 - 0.267949i) q^{46} -9.92820i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(2.13397 + 1.23205i) q^{50} +5.73205 q^{51} +(2.59808 - 2.50000i) q^{52} +3.92820 q^{53} +(-0.866025 - 0.500000i) q^{54} +(7.09808 - 12.2942i) q^{55} +(0.500000 + 0.866025i) q^{56} -6.46410i q^{57} +(-9.06218 + 5.23205i) q^{58} +(4.26795 - 2.46410i) q^{59} +2.73205i q^{60} +(-0.133975 - 0.232051i) q^{61} +(-3.36603 + 5.83013i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-9.56218 + 2.36603i) q^{65} +5.19615 q^{66} +(-8.66025 - 5.00000i) q^{67} +(2.86603 - 4.96410i) q^{68} +(-0.267949 - 0.464102i) q^{69} -2.73205i q^{70} +(-9.29423 + 5.36603i) q^{71} +(-0.866025 + 0.500000i) q^{72} +5.46410i q^{73} +(1.63397 + 2.83013i) q^{74} +(1.23205 - 2.13397i) q^{75} +(-5.59808 - 3.23205i) q^{76} -5.19615 q^{77} +(-2.50000 - 2.59808i) q^{78} +9.00000 q^{79} +(2.36603 + 1.36603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.767949 - 1.33013i) q^{82} +12.7321i q^{83} +(0.866025 - 0.500000i) q^{84} +(-13.5622 + 7.83013i) q^{85} +5.26795i q^{86} +(5.23205 + 9.06218i) q^{87} +(2.59808 - 4.50000i) q^{88} +(-9.40192 - 5.42820i) q^{89} +2.73205 q^{90} +(2.50000 + 2.59808i) q^{91} -0.535898 q^{92} +(5.83013 + 3.36603i) q^{93} +(-4.96410 + 8.59808i) q^{94} +(8.83013 + 15.2942i) q^{95} +1.00000i q^{96} +(3.29423 - 1.90192i) q^{97} +(-0.866025 + 0.500000i) q^{98} -5.19615i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} + 18 q^{11} - 4 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{20} - 8 q^{23} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 14 q^{29} - 2 q^{30} - 18 q^{33} + 2 q^{35} + 2 q^{36} + 6 q^{37} + 12 q^{38} - 4 q^{40} - 12 q^{41} - 2 q^{42} - 14 q^{43} - 6 q^{45} - 12 q^{46} - 2 q^{48} + 2 q^{49} + 12 q^{50} + 16 q^{51} - 12 q^{53} + 18 q^{55} + 2 q^{56} - 12 q^{58} + 24 q^{59} - 4 q^{61} - 10 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{68} - 8 q^{69} - 6 q^{71} + 10 q^{74} - 2 q^{75} - 12 q^{76} - 10 q^{78} + 36 q^{79} + 6 q^{80} - 2 q^{81} - 10 q^{82} - 30 q^{85} + 14 q^{87} - 48 q^{89} + 4 q^{90} + 10 q^{91} - 16 q^{92} + 6 q^{93} - 6 q^{94} + 18 q^{95} - 18 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 18 * q^11 - 4 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^20 - 8 * q^23 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 14 * q^29 - 2 * q^30 - 18 * q^33 + 2 * q^35 + 2 * q^36 + 6 * q^37 + 12 * q^38 - 4 * q^40 - 12 * q^41 - 2 * q^42 - 14 * q^43 - 6 * q^45 - 12 * q^46 - 2 * q^48 + 2 * q^49 + 12 * q^50 + 16 * q^51 - 12 * q^53 + 18 * q^55 + 2 * q^56 - 12 * q^58 + 24 * q^59 - 4 * q^61 - 10 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^68 - 8 * q^69 - 6 * q^71 + 10 * q^74 - 2 * q^75 - 12 * q^76 - 10 * q^78 + 36 * q^79 + 6 * q^80 - 2 * q^81 - 10 * q^82 - 30 * q^85 + 14 * q^87 - 48 * q^89 + 4 * q^90 + 10 * q^91 - 16 * q^92 + 6 * q^93 - 6 * q^94 + 18 * q^95 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	2.73205i		−	1.22181i	−0.791704	−	0.610905i	$-0.790806\pi$
$5$		−	2.73205i		−	1.22181i	0.791704	−	0.610905i	$-0.209194\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.36603	+	2.36603i	−0.431975	+	0.748203i
$11$	4.50000	+	2.59808i	1.35680	+	0.783349i	0.989191	−	0.146631i	$-0.0468429\pi$
$11$	4.50000	+	2.59808i	1.35680	+	0.783349i	0.367610	+	0.929980i	$0.380176\pi$
$12$	−1.00000			−0.288675
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$14$	1.00000			0.267261
$15$	2.36603	+	1.36603i	0.610905	+	0.352706i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.86603	−	4.96410i	−0.695113	−	1.20397i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−2.86603	−	4.96410i	−0.695113	−	1.20397i	0.275029	−	0.961436i	$-0.411312\pi$
$18$			1.00000i			0.235702i
$19$	−5.59808	+	3.23205i	−1.28429	+	0.741483i	−0.977629	−	0.210337i	$-0.932544\pi$
$19$	−5.59808	+	3.23205i	−1.28429	+	0.741483i	−0.306658	+	0.951820i	$0.599211\pi$
$20$	2.36603	−	1.36603i	0.529059	−	0.305453i
$21$		−	1.00000i		−	0.218218i
$22$	−2.59808	−	4.50000i	−0.553912	−	0.959403i
$23$	−0.267949	+	0.464102i	−0.0558713	+	0.0967719i	−0.892608	−	0.450833i	$-0.851127\pi$
$23$	−0.267949	+	0.464102i	−0.0558713	+	0.0967719i	0.836737	+	0.547605i	$0.184460\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−2.46410			−0.492820
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	1.00000			0.192450
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	5.23205	−	9.06218i	0.971567	−	1.68280i	0.280741	−	0.959784i	$-0.409420\pi$
$29$	5.23205	−	9.06218i	0.971567	−	1.68280i	0.690826	−	0.723021i	$-0.257247\pi$
$30$	−1.36603	−	2.36603i	−0.249401	−	0.431975i
$31$		−	6.73205i		−	1.20911i	−0.796563	−	0.604556i	$-0.793351\pi$
$31$		−	6.73205i		−	1.20911i	0.796563	−	0.604556i	$-0.206649\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$			5.73205i			0.983039i
$35$	1.36603	+	2.36603i	0.230900	+	0.399931i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.83013	−	1.63397i	−0.465270	−	0.268624i	0.248988	−	0.968507i	$-0.419902\pi$
$37$	−2.83013	−	1.63397i	−0.465270	−	0.268624i	−0.714258	+	0.699883i	$0.753235\pi$
$38$	6.46410			1.04862
$39$	3.46410	+	1.00000i	0.554700	+	0.160128i
$40$	−2.73205			−0.431975
$41$	1.33013	+	0.767949i	0.207731	+	0.119934i	0.600256	−	0.799808i	$-0.295065\pi$
$41$	1.33013	+	0.767949i	0.207731	+	0.119934i	−0.392525	+	0.919741i	$0.628399\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−2.63397	−	4.56218i	−0.401677	−	0.695726i	0.592251	−	0.805753i	$-0.298239\pi$
$43$	−2.63397	−	4.56218i	−0.401677	−	0.695726i	−0.993929	+	0.110028i	$0.964906\pi$
$44$			5.19615i			0.783349i
$45$	−2.36603	+	1.36603i	−0.352706	+	0.203635i
$46$	0.464102	−	0.267949i	0.0684280	−	0.0395070i
$47$		−	9.92820i		−	1.44818i	−0.689707	−	0.724089i	$-0.742261\pi$
$47$		−	9.92820i		−	1.44818i	0.689707	−	0.724089i	$-0.257739\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	2.13397	+	1.23205i	0.301790	+	0.174238i
$51$	5.73205			0.802648
$52$	2.59808	−	2.50000i	0.360288	−	0.346688i
$53$	3.92820			0.539580			0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820			0.539580			0.269790	+	0.962919i	$0.413046\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	7.09808	−	12.2942i	0.957104	−	1.65775i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		−	6.46410i		−	0.856191i
$58$	−9.06218	+	5.23205i	−1.18992	+	0.687002i
$59$	4.26795	−	2.46410i	0.555640	−	0.320799i	−0.195754	−	0.980653i	$-0.562715\pi$
$59$	4.26795	−	2.46410i	0.555640	−	0.320799i	0.751394	+	0.659854i	$0.229382\pi$
$60$			2.73205i			0.352706i
$61$	−0.133975	−	0.232051i	−0.0171537	−	0.0297111i	0.857321	−	0.514782i	$-0.172127\pi$
$61$	−0.133975	−	0.232051i	−0.0171537	−	0.0297111i	−0.874475	+	0.485071i	$0.838794\pi$
$62$	−3.36603	+	5.83013i	−0.427486	+	0.740427i
$63$	0.866025	+	0.500000i	0.109109	+	0.0629941i
$64$	−1.00000			−0.125000
$65$	−9.56218	+	2.36603i	−1.18604	+	0.293469i
$66$	5.19615			0.639602
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.133135	−	0.991098i	$-0.542504\pi$
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.924883	+	0.380251i	$0.875838\pi$
$68$	2.86603	−	4.96410i	0.347557	−	0.601986i
$69$	−0.267949	−	0.464102i	−0.0322573	−	0.0558713i
$70$		−	2.73205i		−	0.326543i
$71$	−9.29423	+	5.36603i	−1.10302	+	0.636830i	−0.937013	−	0.349294i	$-0.886421\pi$
$71$	−9.29423	+	5.36603i	−1.10302	+	0.636830i	−0.166009	+	0.986124i	$0.553088\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			5.46410i			0.639525i	0.947498	+	0.319762i	$0.103603\pi$
$73$			5.46410i			0.639525i	−0.947498	+	0.319762i	$0.896397\pi$
$74$	1.63397	+	2.83013i	0.189946	+	0.328996i
$75$	1.23205	−	2.13397i	0.142265	−	0.246410i
$76$	−5.59808	−	3.23205i	−0.642143	−	0.370742i
$77$	−5.19615			−0.592157
$78$	−2.50000	−	2.59808i	−0.283069	−	0.294174i
$79$	9.00000			1.01258			0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000			1.01258			0.506290	+	0.862364i	$0.331017\pi$
$80$	2.36603	+	1.36603i	0.264530	+	0.152726i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.767949	−	1.33013i	−0.0848058	−	0.146888i
$83$			12.7321i			1.39752i	0.715354	+	0.698762i	$0.246265\pi$
$83$			12.7321i			1.39752i	−0.715354	+	0.698762i	$0.753735\pi$
$84$	0.866025	−	0.500000i	0.0944911	−	0.0545545i
$85$	−13.5622	+	7.83013i	−1.47102	+	0.849297i
$86$			5.26795i			0.568058i
$87$	5.23205	+	9.06218i	0.560935	+	0.971567i
$88$	2.59808	−	4.50000i	0.276956	−	0.479702i
$89$	−9.40192	−	5.42820i	−0.996602	−	0.575388i	−0.0893608	−	0.995999i	$-0.528482\pi$
$89$	−9.40192	−	5.42820i	−0.996602	−	0.575388i	−0.907241	+	0.420611i	$0.861816\pi$
$90$	2.73205			0.287983
$91$	2.50000	+	2.59808i	0.262071	+	0.272352i
$92$	−0.535898			−0.0558713
$93$	5.83013	+	3.36603i	0.604556	+	0.349041i
$94$	−4.96410	+	8.59808i	−0.512008	+	0.886824i
$95$	8.83013	+	15.2942i	0.905952	+	1.56915i
$96$			1.00000i			0.102062i
$97$	3.29423	−	1.90192i	0.334478	−	0.193111i	−0.323349	−	0.946280i	$-0.604809\pi$
$97$	3.29423	−	1.90192i	0.334478	−	0.193111i	0.657828	+	0.753169i	$0.271476\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		−	5.19615i		−	0.522233i
$100$	−1.23205	−	2.13397i	−0.123205	−	0.213397i
$101$	−4.46410	+	7.73205i	−0.444195	+	0.769368i	−0.997996	−	0.0632812i	$-0.979843\pi$
$101$	−4.46410	+	7.73205i	−0.444195	+	0.769368i	0.553801	+	0.832649i	$0.313177\pi$
$102$	−4.96410	−	2.86603i	−0.491519	−	0.283779i
$103$	5.80385			0.571870			0.285935	−	0.958249i	$-0.407696\pi$
$103$	5.80385			0.571870			0.285935	+	0.958249i	$0.407696\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$	−2.73205			−0.266621
$106$	−3.40192	−	1.96410i	−0.330424	−	0.190770i
$107$	9.96410	−	17.2583i	0.963266	−	1.66843i	0.249063	−	0.968487i	$-0.419877\pi$
$107$	9.96410	−	17.2583i	0.963266	−	1.66843i	0.714203	−	0.699938i	$-0.246789\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			14.7321i			1.41107i	0.708673	+	0.705537i	$0.249294\pi$
$109$			14.7321i			1.41107i	−0.708673	+	0.705537i	$0.750706\pi$
$110$	−12.2942	+	7.09808i	−1.17221	+	0.676775i
$111$	2.83013	−	1.63397i	0.268624	−	0.155090i
$112$		−	1.00000i		−	0.0944911i
$113$	4.83013	+	8.36603i	0.454380	+	0.787009i	0.998652	−	0.0518992i	$-0.0165275\pi$
$113$	4.83013	+	8.36603i	0.454380	+	0.787009i	−0.544272	+	0.838909i	$0.683194\pi$
$114$	−3.23205	+	5.59808i	−0.302709	+	0.524308i
$115$	1.26795	+	0.732051i	0.118237	+	0.0682641i
$116$	10.4641			0.971567
$117$	−2.59808	+	2.50000i	−0.240192	+	0.231125i
$118$	−4.92820			−0.453678
$119$	4.96410	+	2.86603i	0.455058	+	0.262728i
$120$	1.36603	−	2.36603i	0.124700	−	0.215988i
$121$	8.00000	+	13.8564i	0.727273	+	1.25967i
$122$			0.267949i			0.0242590i
$123$	−1.33013	+	0.767949i	−0.119934	+	0.0692436i
$124$	5.83013	−	3.36603i	0.523561	−	0.302278i
$125$		−	6.92820i		−	0.619677i
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	−3.19615	+	5.53590i	−0.283613	+	0.491232i	−0.972272	−	0.233854i	$-0.924866\pi$
$127$	−3.19615	+	5.53590i	−0.283613	+	0.491232i	0.688659	+	0.725085i	$0.258200\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	5.26795			0.463817
$130$	9.46410	+	2.73205i	0.830057	+	0.239617i
$131$	−1.07180			−0.0936433			−0.0468217	−	0.998903i	$-0.514909\pi$
$131$	−1.07180			−0.0936433			−0.0468217	+	0.998903i	$0.514909\pi$
$132$	−4.50000	−	2.59808i	−0.391675	−	0.226134i
$133$	3.23205	−	5.59808i	0.280254	−	0.485415i
$134$	5.00000	+	8.66025i	0.431934	+	0.748132i
$135$		−	2.73205i		−	0.235137i
$136$	−4.96410	+	2.86603i	−0.425668	+	0.245760i
$137$	10.8564	−	6.26795i	0.927525	−	0.535507i	0.0414973	−	0.999139i	$-0.486787\pi$
$137$	10.8564	−	6.26795i	0.927525	−	0.535507i	0.886028	+	0.463632i	$0.153454\pi$
$138$			0.535898i			0.0456187i
$139$	10.5263	+	18.2321i	0.892827	+	1.54642i	0.836471	+	0.548012i	$0.184615\pi$
$139$	10.5263	+	18.2321i	0.892827	+	1.54642i	0.0563567	+	0.998411i	$0.482052\pi$
$140$	−1.36603	+	2.36603i	−0.115450	+	0.199966i
$141$	8.59808	+	4.96410i	0.724089	+	0.418053i
$142$	10.7321			0.900614
$143$	5.19615	−	18.0000i	0.434524	−	1.50524i
$144$	1.00000			0.0833333
$145$	−24.7583	−	14.2942i	−2.05607	−	1.18707i
$146$	2.73205	−	4.73205i	0.226106	−	0.391627i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$		−	3.26795i		−	0.268624i
$149$	6.92820	−	4.00000i	0.567581	−	0.327693i	−0.188602	−	0.982054i	$-0.560396\pi$
$149$	6.92820	−	4.00000i	0.567581	−	0.327693i	0.756182	+	0.654361i	$0.227062\pi$
$150$	−2.13397	+	1.23205i	−0.174238	+	0.100597i
$151$			9.19615i			0.748372i	0.927354	+	0.374186i	$0.122078\pi$
$151$			9.19615i			0.748372i	−0.927354	+	0.374186i	$0.877922\pi$
$152$	3.23205	+	5.59808i	0.262154	+	0.454064i
$153$	−2.86603	+	4.96410i	−0.231704	+	0.401324i
$154$	4.50000	+	2.59808i	0.362620	+	0.209359i
$155$	−18.3923			−1.47731
$156$	0.866025	+	3.50000i	0.0693375	+	0.280224i
$157$	−4.53590			−0.362004			−0.181002	−	0.983483i	$-0.557934\pi$
$157$	−4.53590			−0.362004			−0.181002	+	0.983483i	$0.557934\pi$
$158$	−7.79423	−	4.50000i	−0.620076	−	0.358001i
$159$	−1.96410	+	3.40192i	−0.155763	+	0.269790i
$160$	−1.36603	−	2.36603i	−0.107994	−	0.187051i
$161$		−	0.535898i		−	0.0422347i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−14.8301	+	8.56218i	−1.16159	+	0.670642i	−0.951683	−	0.307081i	$-0.900648\pi$
$163$	−14.8301	+	8.56218i	−1.16159	+	0.670642i	−0.209902	+	0.977722i	$0.567314\pi$
$164$			1.53590i			0.119934i
$165$	7.09808	+	12.2942i	0.552584	+	0.957104i
$166$	6.36603	−	11.0263i	0.494099	−	0.855805i
$167$	16.3923	+	9.46410i	1.26847	+	0.732354i	0.974699	−	0.223520i	$-0.0717549\pi$
$167$	16.3923	+	9.46410i	1.26847	+	0.732354i	0.293775	+	0.955874i	$0.405088\pi$
$168$	−1.00000			−0.0771517
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$	15.6603			1.20109
$171$	5.59808	+	3.23205i	0.428096	+	0.247161i
$172$	2.63397	−	4.56218i	0.200839	−	0.347863i
$173$	−4.09808	−	7.09808i	−0.311571	−	0.539657i	0.667132	−	0.744940i	$-0.267522\pi$
$173$	−4.09808	−	7.09808i	−0.311571	−	0.539657i	−0.978703	+	0.205283i	$0.934188\pi$
$174$		−	10.4641i		−	0.793281i
$175$	2.13397	−	1.23205i	0.161313	−	0.0931343i
$176$	−4.50000	+	2.59808i	−0.339200	+	0.195837i
$177$			4.92820i			0.370426i
$178$	5.42820	+	9.40192i	0.406861	+	0.704704i
$179$	1.73205	−	3.00000i	0.129460	−	0.224231i	−0.794008	−	0.607908i	$-0.792009\pi$
$179$	1.73205	−	3.00000i	0.129460	−	0.224231i	0.923467	+	0.383677i	$0.125342\pi$
$180$	−2.36603	−	1.36603i	−0.176353	−	0.101818i
$181$	17.7321			1.31801			0.659006	−	0.752137i	$-0.270977\pi$
$181$	17.7321			1.31801			0.659006	+	0.752137i	$0.270977\pi$
$182$	−0.866025	−	3.50000i	−0.0641941	−	0.259437i
$183$	0.267949			0.0198074
$184$	0.464102	+	0.267949i	0.0342140	+	0.0197535i
$185$	−4.46410	+	7.73205i	−0.328207	+	0.568472i
$186$	−3.36603	−	5.83013i	−0.246809	−	0.427486i
$187$		−	29.7846i		−	2.17807i
$188$	8.59808	−	4.96410i	0.627079	−	0.362044i
$189$	−0.866025	+	0.500000i	−0.0629941	+	0.0363696i
$190$		−	17.6603i		−	1.28121i
$191$	−1.09808	−	1.90192i	−0.0794540	−	0.137618i	0.823560	−	0.567228i	$-0.191984\pi$
$191$	−1.09808	−	1.90192i	−0.0794540	−	0.137618i	−0.903014	+	0.429610i	$0.858651\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	20.4282	+	11.7942i	1.47045	+	0.848967i	0.999450	−	0.0331638i	$-0.0105583\pi$
$193$	20.4282	+	11.7942i	1.47045	+	0.848967i	0.471004	+	0.882131i	$0.343892\pi$
$194$	−3.80385			−0.273100
$195$	2.73205	−	9.46410i	0.195646	−	0.677738i
$196$	1.00000			0.0714286
$197$	−3.23205	−	1.86603i	−0.230274	−	0.132949i	0.380424	−	0.924812i	$-0.375778\pi$
$197$	−3.23205	−	1.86603i	−0.230274	−	0.132949i	−0.610698	+	0.791863i	$0.709111\pi$
$198$	−2.59808	+	4.50000i	−0.184637	+	0.319801i
$199$	−3.29423	−	5.70577i	−0.233522	−	0.404471i	0.725320	−	0.688412i	$-0.241692\pi$
$199$	−3.29423	−	5.70577i	−0.233522	−	0.404471i	−0.958842	+	0.283940i	$0.908358\pi$
$200$			2.46410i			0.174238i
$201$	8.66025	−	5.00000i	0.610847	−	0.352673i
$202$	7.73205	−	4.46410i	0.544025	−	0.314093i
$203$			10.4641i			0.734436i
$204$	2.86603	+	4.96410i	0.200662	+	0.347557i
$205$	2.09808	−	3.63397i	0.146536	−	0.253808i
$206$	−5.02628	−	2.90192i	−0.350197	−	0.202187i
$207$	0.535898			0.0372475
$208$	3.46410	+	1.00000i	0.240192	+	0.0693375i
$209$	−33.5885			−2.32336
$210$	2.36603	+	1.36603i	0.163271	+	0.0942647i
$211$	−5.53590	+	9.58846i	−0.381107	+	0.660097i	−0.991221	−	0.132217i	$-0.957790\pi$
$211$	−5.53590	+	9.58846i	−0.381107	+	0.660097i	0.610114	+	0.792314i	$0.291124\pi$
$212$	1.96410	+	3.40192i	0.134895	+	0.233645i
$213$		−	10.7321i		−	0.735348i
$214$	−17.2583	+	9.96410i	−1.17976	+	0.681132i
$215$	−12.4641	+	7.19615i	−0.850045	+	0.490774i
$216$		−	1.00000i		−	0.0680414i
$217$	3.36603	+	5.83013i	0.228501	+	0.395775i
$218$	7.36603	−	12.7583i	0.498890	−	0.864103i
$219$	−4.73205	−	2.73205i	−0.319762	−	0.184615i
$220$	14.1962			0.957104
$221$	−14.8923	+	14.3301i	−1.00176	+	0.963949i
$222$	−3.26795			−0.219330
$223$	−1.26795	−	0.732051i	−0.0849082	−	0.0490217i	0.456945	−	0.889495i	$-0.348944\pi$
$223$	−1.26795	−	0.732051i	−0.0849082	−	0.0490217i	−0.541853	+	0.840473i	$0.682277\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	1.23205	+	2.13397i	0.0821367	+	0.142265i
$226$		−	9.66025i		−	0.642591i
$227$	−18.4641	+	10.6603i	−1.22551	+	0.707546i	−0.966086	−	0.258219i	$-0.916864\pi$
$227$	−18.4641	+	10.6603i	−1.22551	+	0.707546i	−0.259419	+	0.965765i	$0.583531\pi$
$228$	5.59808	−	3.23205i	0.370742	−	0.214048i
$229$		−	3.39230i		−	0.224170i	−0.993699	−	0.112085i	$-0.964247\pi$
$229$		−	3.39230i		−	0.224170i	0.993699	−	0.112085i	$-0.0357529\pi$
$230$	−0.732051	−	1.26795i	−0.0482700	−	0.0836061i
$231$	2.59808	−	4.50000i	0.170941	−	0.296078i
$232$	−9.06218	−	5.23205i	−0.594961	−	0.343501i
$233$	−12.5885			−0.824697			−0.412349	−	0.911026i	$-0.635291\pi$
$233$	−12.5885			−0.824697			−0.412349	+	0.911026i	$0.635291\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$	−27.1244			−1.76940
$236$	4.26795	+	2.46410i	0.277820	+	0.160399i
$237$	−4.50000	+	7.79423i	−0.292306	+	0.506290i
$238$	−2.86603	−	4.96410i	−0.185777	−	0.321775i
$239$		−	4.58846i		−	0.296803i	−0.988927	−	0.148401i	$-0.952587\pi$
$239$		−	4.58846i		−	0.296803i	0.988927	−	0.148401i	$-0.0474127\pi$
$240$	−2.36603	+	1.36603i	−0.152726	+	0.0881766i
$241$	2.53590	−	1.46410i	0.163352	−	0.0943111i	−0.416096	−	0.909321i	$-0.636602\pi$
$241$	2.53590	−	1.46410i	0.163352	−	0.0943111i	0.579447	+	0.815010i	$0.303269\pi$
$242$		−	16.0000i		−	1.02852i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.133975	−	0.232051i	0.00857684	−	0.0148555i
$245$	−2.36603	−	1.36603i	−0.151160	−	0.0872722i
$246$	1.53590			0.0979253
$247$	16.1603	+	16.7942i	1.02825	+	1.06859i
$248$	−6.73205			−0.427486
$249$	−11.0263	−	6.36603i	−0.698762	−	0.403430i
$250$	−3.46410	+	6.00000i	−0.219089	+	0.379473i
$251$	−13.7583	−	23.8301i	−0.868418	−	1.50414i	−0.863613	−	0.504156i	$-0.831804\pi$
$251$	−13.7583	−	23.8301i	−0.868418	−	1.50414i	−0.00480540	−	0.999988i	$-0.501530\pi$
$252$			1.00000i			0.0629941i
$253$	−2.41154	+	1.39230i	−0.151612	+	0.0875335i
$254$	5.53590	−	3.19615i	0.347353	−	0.200544i
$255$		−	15.6603i		−	0.980683i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.52628	−	11.3038i	0.407098	−	0.705115i	−0.587465	−	0.809250i	$-0.699874\pi$
$257$	6.52628	−	11.3038i	0.407098	−	0.705115i	0.994563	+	0.104135i	$0.0332074\pi$
$258$	−4.56218	−	2.63397i	−0.284029	−	0.163984i
$259$	3.26795			0.203060
$260$	−6.83013	−	7.09808i	−0.423586	−	0.440204i
$261$	−10.4641			−0.647712
$262$	0.928203	+	0.535898i	0.0573446	+	0.0331079i
$263$	10.5622	−	18.2942i	0.651292	−	1.12807i	−0.331518	−	0.943449i	$-0.607561\pi$
$263$	10.5622	−	18.2942i	0.651292	−	1.12807i	0.982810	−	0.184622i	$-0.0591059\pi$
$264$	2.59808	+	4.50000i	0.159901	+	0.276956i
$265$		−	10.7321i		−	0.659265i
$266$	−5.59808	+	3.23205i	−0.343240	+	0.198170i
$267$	9.40192	−	5.42820i	0.575388	−	0.332201i
$268$		−	10.0000i		−	0.610847i
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	0.920534	−	0.390664i	$-0.127754\pi$
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	−0.798591	+	0.601874i	$0.794421\pi$
$270$	−1.36603	+	2.36603i	−0.0831337	+	0.143992i
$271$	8.36603	+	4.83013i	0.508200	+	0.293409i	0.732093	−	0.681204i	$-0.238543\pi$
$271$	8.36603	+	4.83013i	0.508200	+	0.293409i	−0.223894	+	0.974614i	$0.571877\pi$
$272$	5.73205			0.347557
$273$	−3.50000	+	0.866025i	−0.211830	+	0.0524142i
$274$	−12.5359			−0.757321
$275$	−11.0885	−	6.40192i	−0.668659	−	0.386051i
$276$	0.267949	−	0.464102i	0.0161286	−	0.0279356i
$277$	3.19615	+	5.53590i	0.192038	+	0.332620i	0.945926	−	0.324384i	$-0.105157\pi$
$277$	3.19615	+	5.53590i	0.192038	+	0.332620i	−0.753887	+	0.657004i	$0.771824\pi$
$278$		−	21.0526i		−	1.26265i
$279$	−5.83013	+	3.36603i	−0.349041	+	0.201519i
$280$	2.36603	−	1.36603i	0.141397	−	0.0816356i
$281$			9.26795i			0.552879i	0.961031	+	0.276440i	$0.0891546\pi$
$281$			9.26795i			0.552879i	−0.961031	+	0.276440i	$0.910845\pi$
$282$	−4.96410	−	8.59808i	−0.295608	−	0.512008i
$283$	4.92820	−	8.53590i	0.292951	−	0.507406i	−0.681555	−	0.731767i	$-0.738696\pi$
$283$	4.92820	−	8.53590i	0.292951	−	0.507406i	0.974506	+	0.224360i	$0.0720293\pi$
$284$	−9.29423	−	5.36603i	−0.551511	−	0.318415i
$285$	−17.6603			−1.04610
$286$	−13.5000	+	12.9904i	−0.798272	+	0.768137i
$287$	−1.53590			−0.0906612
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−7.92820	+	13.7321i	−0.466365	+	0.807768i
$290$	14.2942	+	24.7583i	0.839386	+	1.45386i
$291$			3.80385i			0.222985i
$292$	−4.73205	+	2.73205i	−0.276922	+	0.159881i
$293$	−12.9282	+	7.46410i	−0.755274	+	0.436057i	−0.827596	−	0.561324i	$-0.810292\pi$
$293$	−12.9282	+	7.46410i	−0.755274	+	0.436057i	0.0723226	+	0.997381i	$0.476959\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	−6.73205	−	11.6603i	−0.391955	−	0.678886i
$296$	−1.63397	+	2.83013i	−0.0949728	+	0.164498i
$297$	4.50000	+	2.59808i	0.261116	+	0.150756i
$298$	−8.00000			−0.463428
$299$	1.85641	+	0.535898i	0.107359	+	0.0309918i
$300$	2.46410			0.142265
$301$	4.56218	+	2.63397i	0.262960	+	0.151820i
$302$	4.59808	−	7.96410i	0.264590	−	0.458283i
$303$	−4.46410	−	7.73205i	−0.256456	−	0.444195i
$304$		−	6.46410i		−	0.370742i
$305$	−0.633975	+	0.366025i	−0.0363013	+	0.0209586i
$306$	4.96410	−	2.86603i	0.283779	−	0.163840i
$307$		−	5.00000i		−	0.285365i	−0.989769	−	0.142683i	$-0.954427\pi$
$307$		−	5.00000i		−	0.285365i	0.989769	−	0.142683i	$-0.0455728\pi$
$308$	−2.59808	−	4.50000i	−0.148039	−	0.256411i
$309$	−2.90192	+	5.02628i	−0.165085	+	0.285935i
$310$	15.9282	+	9.19615i	0.904661	+	0.522306i
$311$	25.1962			1.42874			0.714371	−	0.699767i	$-0.246713\pi$
$311$	25.1962			1.42874			0.714371	+	0.699767i	$0.246713\pi$
$312$	1.00000	−	3.46410i	0.0566139	−	0.196116i
$313$	31.1244			1.75925			0.879626	−	0.475665i	$-0.157793\pi$
$313$	31.1244			1.75925			0.879626	+	0.475665i	$0.157793\pi$
$314$	3.92820	+	2.26795i	0.221681	+	0.127988i
$315$	1.36603	−	2.36603i	0.0769668	−	0.133310i
$316$	4.50000	+	7.79423i	0.253145	+	0.438460i
$317$		−	26.7846i		−	1.50437i	−0.658950	−	0.752187i	$-0.728999\pi$
$317$		−	26.7846i		−	1.50437i	0.658950	−	0.752187i	$-0.271001\pi$
$318$	3.40192	−	1.96410i	0.190770	−	0.110141i
$319$	47.0885	−	27.1865i	2.63645	−	1.52215i
$320$			2.73205i			0.152726i
$321$	9.96410	+	17.2583i	0.556142	+	0.963266i
$322$	−0.267949	+	0.464102i	−0.0149322	+	0.0258634i
$323$	32.0885	+	18.5263i	1.78545	+	1.03083i
$324$	−1.00000			−0.0555556
$325$	2.13397	+	8.62436i	0.118372	+	0.478393i
$326$	17.1244			0.948430
$327$	−12.7583	−	7.36603i	−0.705537	−	0.407342i
$328$	0.767949	−	1.33013i	0.0424029	−	0.0734440i
$329$	4.96410	+	8.59808i	0.273680	+	0.474027i
$330$		−	14.1962i		−	0.781472i
$331$	30.1244	−	17.3923i	1.65578	−	0.955968i	0.681156	−	0.732138i	$-0.261478\pi$
$331$	30.1244	−	17.3923i	1.65578	−	0.955968i	0.974628	−	0.223829i	$-0.0718558\pi$
$332$	−11.0263	+	6.36603i	−0.605146	+	0.349381i
$333$			3.26795i			0.179083i
$334$	−9.46410	−	16.3923i	−0.517853	−	0.896947i
$335$	−13.6603	+	23.6603i	−0.746339	+	1.29270i
$336$	0.866025	+	0.500000i	0.0472456	+	0.0272772i
$337$	−11.0000			−0.599208			−0.299604	−	0.954064i	$-0.596855\pi$
$337$	−11.0000			−0.599208			−0.299604	+	0.954064i	$0.596855\pi$
$338$	12.9904	+	0.500000i	0.706584	+	0.0271964i
$339$	−9.66025			−0.524673
$340$	−13.5622	−	7.83013i	−0.735512	−	0.424648i
$341$	17.4904	−	30.2942i	0.947157	−	1.64052i
$342$	−3.23205	−	5.59808i	−0.174769	−	0.302709i
$343$			1.00000i			0.0539949i
$344$	−4.56218	+	2.63397i	−0.245976	+	0.142014i
$345$	−1.26795	+	0.732051i	−0.0682641	+	0.0394123i
$346$			8.19615i			0.440628i
$347$	−0.232051	−	0.401924i	−0.0124571	−	0.0215764i	0.859730	−	0.510749i	$-0.170632\pi$
$347$	−0.232051	−	0.401924i	−0.0124571	−	0.0215764i	−0.872187	+	0.489173i	$0.837299\pi$
$348$	−5.23205	+	9.06218i	−0.280467	+	0.485784i
$349$	−29.3205	−	16.9282i	−1.56949	−	0.906146i	−0.996228	−	0.0867744i	$-0.972344\pi$
$349$	−29.3205	−	16.9282i	−1.56949	−	0.906146i	−0.573263	−	0.819372i	$-0.694323\pi$
$350$	−2.46410			−0.131712
$351$	−0.866025	−	3.50000i	−0.0462250	−	0.186816i
$352$	5.19615			0.276956
$353$	2.87564	+	1.66025i	0.153055	+	0.0883664i	0.574572	−	0.818454i	$-0.305169\pi$
$353$	2.87564	+	1.66025i	0.153055	+	0.0883664i	−0.421516	+	0.906821i	$0.638502\pi$
$354$	2.46410	−	4.26795i	0.130966	−	0.226839i
$355$	14.6603	+	25.3923i	0.778085	+	1.34768i
$356$		−	10.8564i		−	0.575388i
$357$	−4.96410	+	2.86603i	−0.262728	+	0.151686i
$358$	−3.00000	+	1.73205i	−0.158555	+	0.0915417i
$359$			24.4449i			1.29015i	0.764119	+	0.645075i	$0.223174\pi$
$359$			24.4449i			1.29015i	−0.764119	+	0.645075i	$0.776826\pi$
$360$	1.36603	+	2.36603i	0.0719959	+	0.124700i
$361$	11.3923	−	19.7321i	0.599595	−	1.03853i
$362$	−15.3564	−	8.86603i	−0.807115	−	0.465988i
$363$	−16.0000			−0.839782
$364$	−1.00000	+	3.46410i	−0.0524142	+	0.181568i
$365$	14.9282			0.781378
$366$	−0.232051	−	0.133975i	−0.0121295	−	0.00700296i
$367$	10.6603	−	18.4641i	0.556461	−	0.963818i	−0.441328	−	0.897346i	$-0.645492\pi$
$367$	10.6603	−	18.4641i	0.556461	−	0.963818i	0.997788	−	0.0664722i	$-0.0211744\pi$
$368$	−0.267949	−	0.464102i	−0.0139678	−	0.0241930i
$369$		−	1.53590i		−	0.0799557i
$370$	7.73205	−	4.46410i	0.401970	−	0.232078i
$371$	−3.40192	+	1.96410i	−0.176619	+	0.101971i
$372$			6.73205i			0.349041i
$373$	−4.56218	−	7.90192i	−0.236221	−	0.409146i	0.723406	−	0.690423i	$-0.242575\pi$
$373$	−4.56218	−	7.90192i	−0.236221	−	0.409146i	−0.959627	+	0.281277i	$0.909242\pi$
$374$	−14.8923	+	25.7942i	−0.770063	+	1.33379i
$375$	6.00000	+	3.46410i	0.309839	+	0.178885i
$376$	−9.92820			−0.512008
$377$	−36.2487	−	10.4641i	−1.86690	−	0.538929i
$378$	1.00000			0.0514344
$379$	−1.77757	−	1.02628i	−0.0913075	−	0.0527164i	0.453651	−	0.891179i	$-0.350121\pi$
$379$	−1.77757	−	1.02628i	−0.0913075	−	0.0527164i	−0.544959	+	0.838463i	$0.683455\pi$
$380$	−8.83013	+	15.2942i	−0.452976	+	0.784577i
$381$	−3.19615	−	5.53590i	−0.163744	−	0.283613i
$382$			2.19615i			0.112365i
$383$	−26.8468	+	15.5000i	−1.37181	+	0.792013i	−0.991155	−	0.132706i	$-0.957633\pi$
$383$	−26.8468	+	15.5000i	−1.37181	+	0.792013i	−0.380651	+	0.924719i	$0.624300\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$			14.1962i			0.723503i
$386$	−11.7942	−	20.4282i	−0.600310	−	1.03977i
$387$	−2.63397	+	4.56218i	−0.133892	+	0.231909i
$388$	3.29423	+	1.90192i	0.167239	+	0.0965556i
$389$	14.5359			0.736999			0.368500	−	0.929628i	$-0.379872\pi$
$389$	14.5359			0.736999			0.368500	+	0.929628i	$0.379872\pi$
$390$	−7.09808	+	6.83013i	−0.359425	+	0.345857i
$391$	3.07180			0.155347
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$	0.535898	−	0.928203i	0.0270325	−	0.0468217i
$394$	1.86603	+	3.23205i	0.0940090	+	0.162828i
$395$		−	24.5885i		−	1.23718i
$396$	4.50000	−	2.59808i	0.226134	−	0.130558i
$397$	0.526279	−	0.303848i	0.0264132	−	0.0152497i	−0.486735	−	0.873550i	$-0.661812\pi$
$397$	0.526279	−	0.303848i	0.0264132	−	0.0152497i	0.513148	+	0.858300i	$0.328479\pi$
$398$			6.58846i			0.330250i
$399$	3.23205	+	5.59808i	0.161805	+	0.280254i
$400$	1.23205	−	2.13397i	0.0616025	−	0.106699i
$401$	21.5885	+	12.4641i	1.07808	+	0.622428i	0.930377	−	0.366605i	$-0.119480\pi$
$401$	21.5885	+	12.4641i	1.07808	+	0.622428i	0.147699	+	0.989032i	$0.452813\pi$
$402$	−10.0000			−0.498755
$403$	−23.5622	+	5.83013i	−1.17372	+	0.290419i
$404$	−8.92820			−0.444195
$405$	2.36603	+	1.36603i	0.117569	+	0.0678783i
$406$	5.23205	−	9.06218i	0.259662	−	0.449748i
$407$	−8.49038	−	14.7058i	−0.420853	−	0.728938i
$408$		−	5.73205i		−	0.283779i
$409$	−12.6340	+	7.29423i	−0.624710	+	0.360676i	−0.778700	−	0.627396i	$-0.784121\pi$
$409$	−12.6340	+	7.29423i	−0.624710	+	0.360676i	0.153991	+	0.988072i	$0.450787\pi$
$410$	−3.63397	+	2.09808i	−0.179469	+	0.103617i
$411$			12.5359i			0.618350i
$412$	2.90192	+	5.02628i	0.142968	+	0.247627i
$413$	−2.46410	+	4.26795i	−0.121251	+	0.210012i
$414$	−0.464102	−	0.267949i	−0.0228093	−	0.0131690i
$415$	34.7846			1.70751
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	−21.0526			−1.03095
$418$	29.0885	+	16.7942i	1.42276	+	0.821433i
$419$	−8.29423	+	14.3660i	−0.405200	+	0.701826i	−0.994345	−	0.106201i	$-0.966131\pi$
$419$	−8.29423	+	14.3660i	−0.405200	+	0.701826i	0.589145	+	0.808027i	$0.299465\pi$
$420$	−1.36603	−	2.36603i	−0.0666552	−	0.115450i
$421$		−	9.32051i		−	0.454254i	−0.973865	−	0.227127i	$-0.927067\pi$
$421$		−	9.32051i		−	0.454254i	0.973865	−	0.227127i	$-0.0729332\pi$
$422$	9.58846	−	5.53590i	0.466759	−	0.269483i
$423$	−8.59808	+	4.96410i	−0.418053	+	0.241363i
$424$		−	3.92820i		−	0.190770i
$425$	7.06218	+	12.2321i	0.342566	+	0.593342i
$426$	−5.36603	+	9.29423i	−0.259985	+	0.450307i
$427$	0.232051	+	0.133975i	0.0112297	+	0.00648349i
$428$	19.9282			0.963266
$429$	12.9904	+	13.5000i	0.627182	+	0.651786i
$430$	14.3923			0.694059
$431$	9.63397	+	5.56218i	0.464052	+	0.267921i	0.713747	−	0.700404i	$-0.246997\pi$
$431$	9.63397	+	5.56218i	0.464052	+	0.267921i	−0.249694	+	0.968325i	$0.580330\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	19.9282	+	34.5167i	0.957688	+	1.65876i	0.728093	+	0.685479i	$0.240407\pi$
$433$	19.9282	+	34.5167i	0.957688	+	1.65876i	0.229596	+	0.973286i	$0.426260\pi$
$434$		−	6.73205i		−	0.323149i
$435$	24.7583	−	14.2942i	1.18707	−	0.685356i
$436$	−12.7583	+	7.36603i	−0.611013	+	0.352769i
$437$		−	3.46410i		−	0.165710i
$438$	2.73205	+	4.73205i	0.130542	+	0.226106i
$439$	−5.66025	+	9.80385i	−0.270149	+	0.467912i	−0.968900	−	0.247453i	$-0.920406\pi$
$439$	−5.66025	+	9.80385i	−0.270149	+	0.467912i	0.698751	+	0.715365i	$0.253740\pi$
$440$	−12.2942	−	7.09808i	−0.586104	−	0.338388i
$441$	−1.00000			−0.0476190
$442$	20.0622	−	4.96410i	0.954260	−	0.236118i
$443$	−25.0000			−1.18779			−0.593893	−	0.804544i	$-0.702410\pi$
$443$	−25.0000			−1.18779			−0.593893	+	0.804544i	$0.702410\pi$
$444$	2.83013	+	1.63397i	0.134312	+	0.0775450i
$445$	−14.8301	+	25.6865i	−0.703015	+	1.21766i
$446$	0.732051	+	1.26795i	0.0346636	+	0.0600391i
$447$			8.00000i			0.378387i
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	19.9019	−	11.4904i	0.939230	−	0.542265i	0.0495110	−	0.998774i	$-0.484234\pi$
$449$	19.9019	−	11.4904i	0.939230	−	0.542265i	0.889719	+	0.456509i	$0.150900\pi$
$450$		−	2.46410i		−	0.116159i
$451$	3.99038	+	6.91154i	0.187900	+	0.325452i
$452$	−4.83013	+	8.36603i	−0.227190	+	0.393505i
$453$	−7.96410	−	4.59808i	−0.374186	−	0.216036i
$454$	21.3205			1.00062
$455$	7.09808	−	6.83013i	0.332763	−	0.320201i
$456$	−6.46410			−0.302709
$457$	−22.2679	−	12.8564i	−1.04165	−	0.601397i	−0.121350	−	0.992610i	$-0.538722\pi$
$457$	−22.2679	−	12.8564i	−1.04165	−	0.601397i	−0.920300	+	0.391212i	$0.872056\pi$
$458$	−1.69615	+	2.93782i	−0.0792560	+	0.137275i
$459$	−2.86603	−	4.96410i	−0.133775	−	0.231704i
$460$			1.46410i			0.0682641i
$461$	6.00000	−	3.46410i	0.279448	−	0.161339i	−0.353726	−	0.935349i	$-0.615085\pi$
$461$	6.00000	−	3.46410i	0.279448	−	0.161339i	0.633173	+	0.774010i	$0.281752\pi$
$462$	−4.50000	+	2.59808i	−0.209359	+	0.120873i
$463$			32.6603i			1.51785i	0.651178	+	0.758925i	$0.274275\pi$
$463$			32.6603i			1.51785i	−0.651178	+	0.758925i	$0.725725\pi$
$464$	5.23205	+	9.06218i	0.242892	+	0.420701i
$465$	9.19615	−	15.9282i	0.426461	−	0.738653i
$466$	10.9019	+	6.29423i	0.505022	+	0.291575i
$467$	5.07180			0.234695			0.117347	−	0.993091i	$-0.462561\pi$
$467$	5.07180			0.234695			0.117347	+	0.993091i	$0.462561\pi$
$468$	−3.46410	−	1.00000i	−0.160128	−	0.0462250i
$469$	10.0000			0.461757
$470$	23.4904	+	13.5622i	1.08353	+	0.625577i
$471$	2.26795	−	3.92820i	0.104502	−	0.181002i
$472$	−2.46410	−	4.26795i	−0.113419	−	0.196448i
$473$		−	27.3731i		−	1.25861i
$474$	7.79423	−	4.50000i	0.358001	−	0.206692i
$475$	13.7942	−	7.96410i	0.632923	−	0.365418i
$476$			5.73205i			0.262728i
$477$	−1.96410	−	3.40192i	−0.0899300	−	0.155763i
$478$	−2.29423	+	3.97372i	−0.104936	+	0.181754i
$479$	19.7942	+	11.4282i	0.904421	+	0.522168i	0.878632	−	0.477499i	$-0.158457\pi$
$479$	19.7942	+	11.4282i	0.904421	+	0.522168i	0.0257894	+	0.999667i	$0.491790\pi$
$480$	2.73205			0.124700
$481$	−3.26795	+	11.3205i	−0.149006	+	0.516171i
$482$	−2.92820			−0.133376
$483$	0.464102	+	0.267949i	0.0211174	+	0.0121921i
$484$	−8.00000	+	13.8564i	−0.363636	+	0.629837i
$485$	−5.19615	−	9.00000i	−0.235945	−	0.408669i
$486$			1.00000i			0.0453609i
$487$	−25.5000	+	14.7224i	−1.15552	+	0.667137i	−0.950225	−	0.311564i	$-0.899147\pi$
$487$	−25.5000	+	14.7224i	−1.15552	+	0.667137i	−0.205290	+	0.978701i	$0.565814\pi$
$488$	−0.232051	+	0.133975i	−0.0105044	+	0.00606475i
$489$		−	17.1244i		−	0.774390i
$490$	1.36603	+	2.36603i	0.0617107	+	0.106886i
$491$	7.19615	−	12.4641i	0.324758	−	0.562497i	−0.656706	−	0.754147i	$-0.728051\pi$
$491$	7.19615	−	12.4641i	0.324758	−	0.562497i	0.981463	+	0.191650i	$0.0613839\pi$
$492$	−1.33013	−	0.767949i	−0.0599668	−	0.0346218i
$493$	−59.9808			−2.70140
$494$	−5.59808	−	22.6244i	−0.251869	−	1.01792i
$495$	−14.1962			−0.638070
$496$	5.83013	+	3.36603i	0.261780	+	0.151139i
$497$	5.36603	−	9.29423i	0.240699	−	0.416903i
$498$	6.36603	+	11.0263i	0.285268	+	0.494099i
$499$		−	10.5885i		−	0.474004i	−0.971509	−	0.237002i	$-0.923835\pi$
$499$		−	10.5885i		−	0.474004i	0.971509	−	0.237002i	$-0.0761649\pi$
$500$	6.00000	−	3.46410i	0.268328	−	0.154919i
$501$	−16.3923	+	9.46410i	−0.732354	+	0.422825i
$502$			27.5167i			1.22813i
$503$	8.53590	+	14.7846i	0.380597	+	0.659213i	0.991148	−	0.132764i	$-0.0423852\pi$
$503$	8.53590	+	14.7846i	0.380597	+	0.659213i	−0.610551	+	0.791977i	$0.709052\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	21.1244	+	12.1962i	0.940021	+	0.542722i
$506$	2.78461			0.123791
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$	−6.39230			−0.283613
$509$	10.6865	+	6.16987i	0.473672	+	0.273475i	0.717776	−	0.696274i	$-0.245160\pi$
$509$	10.6865	+	6.16987i	0.473672	+	0.273475i	−0.244103	+	0.969749i	$0.578494\pi$
$510$	−7.83013	+	13.5622i	−0.346724	+	0.600543i
$511$	−2.73205	−	4.73205i	−0.120859	−	0.209334i
$512$			1.00000i			0.0441942i
$513$	−5.59808	+	3.23205i	−0.247161	+	0.142699i
$514$	−11.3038	+	6.52628i	−0.498591	+	0.287862i
$515$		−	15.8564i		−	0.698717i
$516$	2.63397	+	4.56218i	0.115954	+	0.200839i
$517$	25.7942	−	44.6769i	1.13443	−	1.96489i
$518$	−2.83013	−	1.63397i	−0.124349	−	0.0717927i
$519$	8.19615			0.359771
$520$	2.36603	+	9.56218i	0.103757	+	0.419329i
$521$	9.58846			0.420078			0.210039	−	0.977693i	$-0.432641\pi$
$521$	9.58846			0.420078			0.210039	+	0.977693i	$0.432641\pi$
$522$	9.06218	+	5.23205i	0.396641	+	0.229001i
$523$	7.40192	−	12.8205i	0.323664	−	0.560602i	−0.657577	−	0.753387i	$-0.728419\pi$
$523$	7.40192	−	12.8205i	0.323664	−	0.560602i	0.981241	+	0.192785i	$0.0617521\pi$
$524$	−0.535898	−	0.928203i	−0.0234108	−	0.0405487i
$525$			2.46410i			0.107542i
$526$	−18.2942	+	10.5622i	−0.797666	+	0.460533i
$527$	−33.4186	+	19.2942i	−1.45574	+	0.840470i
$528$		−	5.19615i		−	0.226134i
$529$	11.3564	+	19.6699i	0.493757	+	0.855212i
$530$	−5.36603	+	9.29423i	−0.233085	+	0.403715i
$531$	−4.26795	−	2.46410i	−0.185213	−	0.106933i
$532$	6.46410			0.280254
$533$	1.53590	−	5.32051i	0.0665271	−	0.230457i
$534$	−10.8564			−0.469803
$535$	−47.1506	−	27.2224i	−2.03850	−	1.17693i
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	1.73205	+	3.00000i	0.0747435	+	0.129460i
$538$		−	4.00000i		−	0.172452i
$539$	4.50000	−	2.59808i	0.193829	−	0.111907i
$540$	2.36603	−	1.36603i	0.101818	−	0.0587844i
$541$		−	30.0526i		−	1.29206i	−0.763312	−	0.646030i	$-0.776428\pi$
$541$		−	30.0526i		−	1.29206i	0.763312	−	0.646030i	$-0.223572\pi$
$542$	−4.83013	−	8.36603i	−0.207472	−	0.359352i
$543$	−8.86603	+	15.3564i	−0.380478	+	0.659006i
$544$	−4.96410	−	2.86603i	−0.212834	−	0.122880i
$545$	40.2487			1.72407
$546$	3.46410	+	1.00000i	0.148250	+	0.0427960i
$547$	6.19615			0.264928			0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615			0.264928			0.132464	+	0.991188i	$0.457711\pi$
$548$	10.8564	+	6.26795i	0.463763	+	0.267754i
$549$	−0.133975	+	0.232051i	−0.00571790	+	0.00990369i
$550$	6.40192	+	11.0885i	0.272979	+	0.472813i
$551$			67.6410i			2.88160i
$552$	−0.464102	+	0.267949i	−0.0197535	+	0.0114047i
$553$	−7.79423	+	4.50000i	−0.331444	+	0.191359i
$554$		−	6.39230i		−	0.271583i
$555$	−4.46410	−	7.73205i	−0.189491	−	0.328207i
$556$	−10.5263	+	18.2321i	−0.446414	+	0.773211i
$557$	−14.0885	−	8.13397i	−0.596947	−	0.344648i	0.170893	−	0.985290i	$-0.445335\pi$
$557$	−14.0885	−	8.13397i	−0.596947	−	0.344648i	−0.767840	+	0.640642i	$0.778668\pi$
$558$	6.73205			0.284990
$559$	−13.6865	+	13.1699i	−0.578879	+	0.557026i
$560$	−2.73205			−0.115450
$561$	25.7942	+	14.8923i	1.08903	+	0.628754i
$562$	4.63397	−	8.02628i	0.195472	−	0.338568i
$563$	1.83013	+	3.16987i	0.0771307	+	0.133594i	0.902011	−	0.431713i	$-0.142091\pi$
$563$	1.83013	+	3.16987i	0.0771307	+	0.133594i	−0.824880	+	0.565308i	$0.808757\pi$
$564$			9.92820i			0.418053i
$565$	22.8564	−	13.1962i	0.961576	−	0.555166i
$566$	−8.53590	+	4.92820i	−0.358791	+	0.207148i
$567$		−	1.00000i		−	0.0419961i
$568$	5.36603	+	9.29423i	0.225153	+	0.389977i
$569$	−7.83013	+	13.5622i	−0.328256	+	0.568556i	−0.982166	−	0.188016i	$-0.939794\pi$
$569$	−7.83013	+	13.5622i	−0.328256	+	0.568556i	0.653910	+	0.756572i	$0.273128\pi$
$570$	15.2942	+	8.83013i	0.640605	+	0.369853i
$571$	−5.51666			−0.230865			−0.115433	−	0.993315i	$-0.536825\pi$
$571$	−5.51666			−0.230865			−0.115433	+	0.993315i	$0.536825\pi$
$572$	18.1865	−	4.50000i	0.760417	−	0.188154i
$573$	2.19615			0.0917456
$574$	1.33013	+	0.767949i	0.0555184	+	0.0320536i
$575$	0.660254	−	1.14359i	0.0275345	−	0.0476911i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			2.58846i			0.107759i	0.998547	+	0.0538794i	$0.0171587\pi$
$577$			2.58846i			0.107759i	−0.998547	+	0.0538794i	$0.982841\pi$
$578$	13.7321	−	7.92820i	0.571178	−	0.329770i
$579$	−20.4282	+	11.7942i	−0.848967	+	0.490151i
$580$		−	28.5885i		−	1.18707i
$581$	−6.36603	−	11.0263i	−0.264107	−	0.457447i
$582$	1.90192	−	3.29423i	0.0788373	−	0.136550i
$583$	17.6769	+	10.2058i	0.732103	+	0.422680i
$584$	5.46410			0.226106
$585$	6.83013	+	7.09808i	0.282391	+	0.293469i
$586$	14.9282			0.616678
$587$	−16.5622	−	9.56218i	−0.683594	−	0.394673i	0.117614	−	0.993059i	$-0.462476\pi$
$587$	−16.5622	−	9.56218i	−0.683594	−	0.394673i	−0.801208	+	0.598386i	$0.795809\pi$
$588$	−0.500000	+	0.866025i	−0.0206197	+	0.0357143i
$589$	21.7583	+	37.6865i	0.896536	+	1.55285i
$590$			13.4641i			0.554308i
$591$	3.23205	−	1.86603i	0.132949	−	0.0767580i
$592$	2.83013	−	1.63397i	0.116318	−	0.0671559i
$593$		−	37.0000i		−	1.51941i	−0.650269	−	0.759704i	$-0.725344\pi$
$593$		−	37.0000i		−	1.51941i	0.650269	−	0.759704i	$-0.274656\pi$
$594$	−2.59808	−	4.50000i	−0.106600	−	0.184637i
$595$	7.83013	−	13.5622i	0.321004	−	0.555995i
$596$	6.92820	+	4.00000i	0.283790	+	0.163846i
$597$	6.58846			0.269648
$598$	−1.33975	−	1.39230i	−0.0547863	−	0.0569356i
$599$	35.5692			1.45332			0.726659	−	0.686998i	$-0.241072\pi$
$599$	35.5692			1.45332			0.726659	+	0.686998i	$0.241072\pi$
$600$	−2.13397	−	1.23205i	−0.0871191	−	0.0502983i
$601$	−19.1506	+	33.1699i	−0.781171	+	1.35303i	0.150089	+	0.988672i	$0.452044\pi$
$601$	−19.1506	+	33.1699i	−0.781171	+	1.35303i	−0.931260	+	0.364355i	$0.881290\pi$
$602$	−2.63397	−	4.56218i	−0.107353	−	0.185940i
$603$			10.0000i			0.407231i
$604$	−7.96410	+	4.59808i	−0.324055	+	0.187093i
$605$	37.8564	−	21.8564i	1.53908	−	0.888589i
$606$			8.92820i			0.362683i
$607$	4.16987	+	7.22243i	0.169250	+	0.293149i	0.938156	−	0.346212i	$-0.112532\pi$
$607$	4.16987	+	7.22243i	0.169250	+	0.293149i	−0.768906	+	0.639361i	$0.779199\pi$
$608$	−3.23205	+	5.59808i	−0.131077	+	0.227032i
$609$	−9.06218	−	5.23205i	−0.367218	−	0.212013i
$610$	0.732051			0.0296399
$611$	−34.7487	+	8.59808i	−1.40578	+	0.347841i
$612$	−5.73205			−0.231704
$613$	−6.67949	−	3.85641i	−0.269782	−	0.155759i	0.359006	−	0.933335i	$-0.383116\pi$
$613$	−6.67949	−	3.85641i	−0.269782	−	0.155759i	−0.628789	+	0.777576i	$0.716449\pi$
$614$	−2.50000	+	4.33013i	−0.100892	+	0.174750i
$615$	2.09808	+	3.63397i	0.0846026	+	0.146536i
$616$			5.19615i			0.209359i
$617$	−20.9545	+	12.0981i	−0.843596	+	0.487050i	−0.858485	−	0.512839i	$-0.828594\pi$
$617$	−20.9545	+	12.0981i	−0.843596	+	0.487050i	0.0148891	+	0.999889i	$0.495260\pi$
$618$	5.02628	−	2.90192i	0.202187	−	0.116732i
$619$		−	9.39230i		−	0.377509i	−0.982024	−	0.188754i	$-0.939555\pi$
$619$		−	9.39230i		−	0.377509i	0.982024	−	0.188754i	$-0.0604450\pi$
$620$	−9.19615	−	15.9282i	−0.369326	−	0.639692i
$621$	−0.267949	+	0.464102i	−0.0107524	+	0.0186238i
$622$	−21.8205	−	12.5981i	−0.874923	−	0.505137i
$623$	10.8564			0.434953
$624$	−2.59808	+	2.50000i	−0.104006	+	0.100080i
$625$	−31.2487			−1.24995
$626$	−26.9545	−	15.5622i	−1.07732	−	0.621990i
$627$	16.7942	−	29.0885i	0.670697	−	1.16168i
$628$	−2.26795	−	3.92820i	−0.0905010	−	0.156752i
$629$			18.7321i			0.746896i
$630$	−2.36603	+	1.36603i	−0.0942647	+	0.0544238i
$631$	−22.6244	+	13.0622i	−0.900661	+	0.519997i	−0.877415	−	0.479733i	$-0.840734\pi$
$631$	−22.6244	+	13.0622i	−0.900661	+	0.519997i	−0.0232467	+	0.999730i	$0.507400\pi$
$632$		−	9.00000i		−	0.358001i
$633$	−5.53590	−	9.58846i	−0.220032	−	0.381107i
$634$	−13.3923	+	23.1962i	−0.531876	+	0.921237i
$635$	15.1244	+	8.73205i	0.600192	+	0.346521i
$636$	−3.92820			−0.155763
$637$	−3.46410	−	1.00000i	−0.137253	−	0.0396214i
$638$	−54.3731			−2.15265
$639$	9.29423	+	5.36603i	0.367674	+	0.212277i
$640$	1.36603	−	2.36603i	0.0539969	−	0.0935254i
$641$	8.66025	+	15.0000i	0.342059	+	0.592464i	0.984815	−	0.173607i	$-0.0555422\pi$
$641$	8.66025	+	15.0000i	0.342059	+	0.592464i	−0.642756	+	0.766071i	$0.722209\pi$
$642$		−	19.9282i		−	0.786503i
$643$	27.9904	−	16.1603i	1.10383	−	0.637298i	0.166608	−	0.986023i	$-0.446719\pi$
$643$	27.9904	−	16.1603i	1.10383	−	0.637298i	0.937225	+	0.348725i	$0.113385\pi$
$644$	0.464102	−	0.267949i	0.0182882	−	0.0105587i
$645$		−	14.3923i		−	0.566696i
$646$	−18.5263	−	32.0885i	−0.728907	−	1.26250i
$647$	−10.1340	+	17.5526i	−0.398408	+	0.690062i	−0.993530	−	0.113573i	$-0.963770\pi$
$647$	−10.1340	+	17.5526i	−0.398408	+	0.690062i	0.595122	+	0.803635i	$0.297104\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	25.6077			1.00519
$650$	2.46410	−	8.53590i	0.0966500	−	0.334805i
$651$	−6.73205			−0.263850
$652$	−14.8301	−	8.56218i	−0.580793	−	0.335321i
$653$	−20.3564	+	35.2583i	−0.796608	+	1.37977i	0.125206	+	0.992131i	$0.460041\pi$
$653$	−20.3564	+	35.2583i	−0.796608	+	1.37977i	−0.921813	+	0.387634i	$0.873292\pi$
$654$	7.36603	+	12.7583i	0.288034	+	0.498890i
$655$			2.92820i			0.114414i
$656$	−1.33013	+	0.767949i	−0.0519327	+	0.0299834i
$657$	4.73205	−	2.73205i	0.184615	−	0.106587i
$658$		−	9.92820i		−	0.387042i
$659$	−17.6244	−	30.5263i	−0.686547	−	1.18914i	−0.972948	−	0.231025i	$-0.925792\pi$
$659$	−17.6244	−	30.5263i	−0.686547	−	1.18914i	0.286400	−	0.958110i	$-0.407541\pi$
$660$	−7.09808	+	12.2942i	−0.276292	+	0.478552i
$661$	−25.5167	−	14.7321i	−0.992483	−	0.573010i	−0.0864675	−	0.996255i	$-0.527558\pi$
$661$	−25.5167	−	14.7321i	−0.992483	−	0.573010i	−0.906016	+	0.423244i	$0.860891\pi$
$662$	−34.7846			−1.35194
$663$	−4.96410	−	20.0622i	−0.192790	−	0.779150i
$664$	12.7321			0.494099
$665$	−15.2942	−	8.83013i	−0.593085	−	0.342418i
$666$	1.63397	−	2.83013i	0.0633152	−	0.109665i
$667$	2.80385	+	4.85641i	0.108565	+	0.188041i
$668$			18.9282i			0.732354i
$669$	1.26795	−	0.732051i	0.0490217	−	0.0283027i
$670$	23.6603	−	13.6603i	0.914075	−	0.527742i
$671$		−	1.39230i		−	0.0537493i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	12.8205	−	22.2058i	0.494194	−	0.855970i	−0.505783	−	0.862661i	$-0.668796\pi$
$673$	12.8205	−	22.2058i	0.494194	−	0.855970i	0.999978	+	0.00669096i	$0.00212981\pi$
$674$	9.52628	+	5.50000i	0.366939	+	0.211852i
$675$	−2.46410			−0.0948433
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	46.7321			1.79606			0.898029	−	0.439936i	$-0.144999\pi$
$677$	46.7321			1.79606			0.898029	+	0.439936i	$0.144999\pi$
$678$	8.36603	+	4.83013i	0.321295	+	0.185500i
$679$	−1.90192	+	3.29423i	−0.0729891	+	0.126421i
$680$	7.83013	+	13.5622i	0.300272	+	0.520086i
$681$		−	21.3205i		−	0.817004i
$682$	−30.2942	+	17.4904i	−1.16003	+	0.669741i
$683$	−15.0000	+	8.66025i	−0.573959	+	0.331375i	−0.758729	−	0.651406i	$-0.774179\pi$
$683$	−15.0000	+	8.66025i	−0.573959	+	0.331375i	0.184770	+	0.982782i	$0.440846\pi$
$684$			6.46410i			0.247161i
$685$	−17.1244	−	29.6603i	−0.654288	−	1.13326i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	2.93782	+	1.69615i	0.112085	+	0.0647123i
$688$	5.26795			0.200839
$689$	−3.40192	−	13.7487i	−0.129603	−	0.523784i
$690$	1.46410			0.0557374
$691$	−44.1051	−	25.4641i	−1.67784	−	0.968700i	−0.963036	−	0.269373i	$-0.913184\pi$
$691$	−44.1051	−	25.4641i	−1.67784	−	0.968700i	−0.714802	−	0.699327i	$-0.753483\pi$
$692$	4.09808	−	7.09808i	0.155785	−	0.269828i
$693$	2.59808	+	4.50000i	0.0986928	+	0.170941i
$694$			0.464102i			0.0176171i
$695$	49.8109	−	28.7583i	1.88943	−	1.09087i
$696$	9.06218	−	5.23205i	0.343501	−	0.198320i
$697$		−	8.80385i		−	0.333470i
$698$	16.9282	+	29.3205i	0.640742	+	1.10980i
$699$	6.29423	−	10.9019i	0.238070	−	0.412349i
$700$	2.13397	+	1.23205i	0.0806567	+	0.0465671i
$701$	15.7846			0.596176			0.298088	−	0.954538i	$-0.403651\pi$
$701$	15.7846			0.596176			0.298088	+	0.954538i	$0.403651\pi$
$702$	−1.00000	+	3.46410i	−0.0377426	+	0.130744i
$703$	21.1244			0.796720
$704$	−4.50000	−	2.59808i	−0.169600	−	0.0979187i
$705$	13.5622	−	23.4904i	0.510781	−	0.884699i
$706$	−1.66025	−	2.87564i	−0.0624845	−	0.108226i
$707$		−	8.92820i		−	0.335780i
$708$	−4.26795	+	2.46410i	−0.160399	+	0.0926066i
$709$	18.5096	−	10.6865i	0.695143	−	0.401341i	−0.110393	−	0.993888i	$-0.535211\pi$
$709$	18.5096	−	10.6865i	0.695143	−	0.401341i	0.805536	+	0.592547i	$0.201878\pi$
$710$		−	29.3205i		−	1.10038i
$711$	−4.50000	−	7.79423i	−0.168763	−	0.292306i
$712$	−5.42820	+	9.40192i	−0.203431	+	0.352352i
$713$	3.12436	+	1.80385i	0.117008	+	0.0675546i
$714$	5.73205			0.214517
$715$	−49.1769	−	14.1962i	−1.83911	−	0.530906i
$716$	3.46410			0.129460
$717$	3.97372	+	2.29423i	0.148401	+	0.0856795i
$718$	12.2224	−	21.1699i	0.456137	−	0.790053i
$719$	−9.72243	−	16.8397i	−0.362586	−	0.628017i	0.625800	−	0.779984i	$-0.284773\pi$
$719$	−9.72243	−	16.8397i	−0.362586	−	0.628017i	−0.988386	+	0.151967i	$0.951439\pi$
$720$		−	2.73205i		−	0.101818i
$721$	−5.02628	+	2.90192i	−0.187188	+	0.108073i
$722$	−19.7321	+	11.3923i	−0.734351	+	0.423978i
$723$			2.92820i			0.108901i
$724$	8.86603	+	15.3564i	0.329503	+	0.570716i
$725$	−12.8923	+	22.3301i	−0.478808	+	0.829320i
$726$	13.8564	+	8.00000i	0.514259	+	0.296908i
$727$	24.3923			0.904661			0.452330	−	0.891851i	$-0.350593\pi$
$727$	24.3923			0.904661			0.452330	+	0.891851i	$0.350593\pi$
$728$	2.59808	−	2.50000i	0.0962911	−	0.0926562i
$729$	1.00000			0.0370370
$730$	−12.9282	−	7.46410i	−0.478494	−	0.276259i
$731$	−15.0981	+	26.1506i	−0.558423	+	0.967216i
$732$	0.133975	+	0.232051i	0.00495184	+	0.00857684i
$733$			15.7846i			0.583018i	0.956568	+	0.291509i	$0.0941573\pi$
$733$			15.7846i			0.583018i	−0.956568	+	0.291509i	$0.905843\pi$
$734$	−18.4641	+	10.6603i	−0.681522	+	0.393477i
$735$	2.36603	−	1.36603i	0.0872722	−	0.0503866i
$736$			0.535898i			0.0197535i
$737$	−25.9808	−	45.0000i	−0.957014	−	1.65760i
$738$	−0.767949	+	1.33013i	−0.0282686	+	0.0489627i
$739$	−20.0718	−	11.5885i	−0.738353	−	0.426288i	0.0831172	−	0.996540i	$-0.473512\pi$
$739$	−20.0718	−	11.5885i	−0.738353	−	0.426288i	−0.821470	+	0.570251i	$0.806846\pi$
$740$	−8.92820			−0.328207
$741$	−22.6244	+	5.59808i	−0.831126	+	0.205650i
$742$	3.92820			0.144209
$743$	20.8301	+	12.0263i	0.764183	+	0.441201i	0.830796	−	0.556578i	$-0.187886\pi$
$743$	20.8301	+	12.0263i	0.764183	+	0.441201i	−0.0666124	+	0.997779i	$0.521219\pi$
$744$	3.36603	−	5.83013i	0.123404	−	0.213743i
$745$	−10.9282	−	18.9282i	−0.400378	−	0.693476i
$746$			9.12436i			0.334066i
$747$	11.0263	−	6.36603i	0.403430	−	0.232921i
$748$	25.7942	−	14.8923i	0.943130	−	0.544517i
$749$			19.9282i			0.728161i
$750$	−3.46410	−	6.00000i	−0.126491	−	0.219089i
$751$	16.4282	−	28.4545i	0.599474	−	1.03832i	−0.393425	−	0.919357i	$-0.628710\pi$
$751$	16.4282	−	28.4545i	0.599474	−	1.03832i	0.992899	−	0.118962i	$-0.0379567\pi$
$752$	8.59808	+	4.96410i	0.313540	+	0.181022i
$753$	27.5167			1.00276
$754$	26.1603	+	27.1865i	0.952700	+	0.990075i
$755$	25.1244			0.914369
$756$	−0.866025	−	0.500000i	−0.0314970	−	0.0181848i
$757$	−2.90192	+	5.02628i	−0.105472	+	0.182683i	−0.913931	−	0.405870i	$-0.866969\pi$
$757$	−2.90192	+	5.02628i	−0.105472	+	0.182683i	0.808459	+	0.588553i	$0.200302\pi$
$758$	1.02628	+	1.77757i	0.0372761	+	0.0645642i
$759$		−	2.78461i		−	0.101075i
$760$	15.2942	−	8.83013i	0.554780	−	0.320302i
$761$	−26.1962	+	15.1244i	−0.949610	+	0.548257i	−0.892960	−	0.450137i	$-0.851375\pi$
$761$	−26.1962	+	15.1244i	−0.949610	+	0.548257i	−0.0566501	+	0.998394i	$0.518042\pi$
$762$			6.39230i			0.231569i
$763$	−7.36603	−	12.7583i	−0.266668	−	0.461883i
$764$	1.09808	−	1.90192i	0.0397270	−	0.0688092i
$765$	13.5622	+	7.83013i	0.490342	+	0.283099i
$766$	31.0000			1.12008
$767$	−12.3205	−	12.8038i	−0.444868	−	0.462320i
$768$	1.00000			0.0360844
$769$	40.4711	+	23.3660i	1.45943	+	0.842600i	0.998983	−	0.0450885i	$-0.0143570\pi$
$769$	40.4711	+	23.3660i	1.45943	+	0.842600i	0.460444	+	0.887689i	$0.347690\pi$
$770$	7.09808	−	12.2942i	0.255797	−	0.443053i
$771$	6.52628	+	11.3038i	0.235038	+	0.407098i
$772$			23.5885i			0.848967i
$773$	37.3923	−	21.5885i	1.34491	−	0.776483i	0.357385	−	0.933957i	$-0.383669\pi$
$773$	37.3923	−	21.5885i	1.34491	−	0.776483i	0.987523	+	0.157474i	$0.0503352\pi$
$774$	4.56218	−	2.63397i	0.163984	−	0.0946763i
$775$			16.5885i			0.595875i
$776$	−1.90192	−	3.29423i	−0.0682751	−	0.118256i
$777$	−1.63397	+	2.83013i	−0.0586185	+	0.101530i
$778$	−12.5885	−	7.26795i	−0.451318	−	0.260569i
$779$	−9.92820			−0.355715
$780$	9.56218	−	2.36603i	0.342381	−	0.0847173i
$781$	−55.7654			−1.99544
$782$	−2.66025	−	1.53590i	−0.0951305	−	0.0549236i
$783$	5.23205	−	9.06218i	0.186978	−	0.323856i
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$			12.3923i			0.442300i
$786$	−0.928203	+	0.535898i	−0.0331079	+	0.0191149i
$787$	16.3301	−	9.42820i	0.582106	−	0.336079i	−0.179864	−	0.983692i	$-0.557566\pi$
$787$	16.3301	−	9.42820i	0.582106	−	0.336079i	0.761970	+	0.647612i	$0.224232\pi$
$788$		−	3.73205i		−	0.132949i
$789$	10.5622	+	18.2942i	0.376023	+	0.651292i
$790$	−12.2942	+	21.2942i	−0.437409	+	0.757615i
$791$	−8.36603	−	4.83013i	−0.297462	−	0.171740i
$792$	−5.19615			−0.184637
$793$	−0.696152	+	0.669873i	−0.0247211	+	0.0237879i
$794$	−0.607695			−0.0215663
$795$	9.29423	+	5.36603i	0.329632	+	0.190313i
$796$	3.29423	−	5.70577i	0.116761	−	0.202236i
$797$	−18.6865	−	32.3660i	−0.661911	−	1.14646i	−0.980113	−	0.198440i	$-0.936412\pi$
$797$	−18.6865	−	32.3660i	−0.661911	−	1.14646i	0.318202	−	0.948023i	$-0.396921\pi$
$798$		−	6.46410i		−	0.228827i
$799$	−49.2846	+	28.4545i	−1.74356	+	1.00665i
$800$	−2.13397	+	1.23205i	−0.0754474	+	0.0435596i
$801$			10.8564i			0.383592i
$802$	−12.4641	−	21.5885i	−0.440123	−	0.762315i
$803$	−14.1962	+	24.5885i	−0.500971	+	0.867708i
$804$	8.66025	+	5.00000i	0.305424	+	0.176336i
$805$	−1.46410			−0.0516028
$806$	23.3205	+	6.73205i	0.821430	+	0.237126i
$807$	−4.00000			−0.140807
$808$	7.73205	+	4.46410i	0.272013	+	0.157047i
$809$	6.36603	−	11.0263i	0.223818	−	0.387663i	−0.732146	−	0.681147i	$-0.761481\pi$
$809$	6.36603	−	11.0263i	0.223818	−	0.387663i	0.955964	+	0.293484i	$0.0948147\pi$
$810$	−1.36603	−	2.36603i	−0.0479972	−	0.0831337i
$811$			54.1051i			1.89989i	0.312421	+	0.949944i	$0.398860\pi$
$811$			54.1051i			1.89989i	−0.312421	+	0.949944i	$0.601140\pi$
$812$	−9.06218	+	5.23205i	−0.318020	+	0.183609i
$813$	−8.36603	+	4.83013i	−0.293409	+	0.169400i
$814$			16.9808i			0.595175i
$815$	23.3923	+	40.5167i	0.819397	+	1.41924i
$816$	−2.86603	+	4.96410i	−0.100331	+	0.173778i
$817$	29.4904	+	17.0263i	1.03174	+	0.595674i
$818$	14.5885			0.510073
$819$	1.00000	−	3.46410i	0.0349428	−	0.121046i
$820$	4.19615			0.146536
$821$	25.2846	+	14.5981i	0.882439	+	0.509476i	0.871462	−	0.490463i	$-0.163172\pi$
$821$	25.2846	+	14.5981i	0.882439	+	0.509476i	0.0109772	+	0.999940i	$0.496506\pi$
$822$	6.26795	−	10.8564i	0.218620	−	0.378661i
$823$	−16.8564	−	29.1962i	−0.587577	−	1.01771i	−0.994549	−	0.104273i	$-0.966748\pi$
$823$	−16.8564	−	29.1962i	−0.587577	−	1.01771i	0.406971	−	0.913441i	$-0.366585\pi$
$824$		−	5.80385i		−	0.202187i
$825$	11.0885	−	6.40192i	0.386051	−	0.222886i
$826$	4.26795	−	2.46410i	0.148501	−	0.0857371i
$827$			16.3923i			0.570016i	0.958525	+	0.285008i	$0.0919963\pi$
$827$			16.3923i			0.570016i	−0.958525	+	0.285008i	$0.908004\pi$
$828$	0.267949	+	0.464102i	0.00931188	+	0.0161286i
$829$	23.2583	−	40.2846i	0.807795	−	1.39914i	−0.106593	−	0.994303i	$-0.533994\pi$
$829$	23.2583	−	40.2846i	0.807795	−	1.39914i	0.914388	−	0.404840i	$-0.132673\pi$
$830$	−30.1244	−	17.3923i	−1.04563	−	0.603696i
$831$	−6.39230			−0.221747
$832$	0.866025	+	3.50000i	0.0300240	+	0.121341i
$833$	−5.73205			−0.198604
$834$	18.2321	+	10.5263i	0.631324	+	0.364495i
$835$	25.8564	−	44.7846i	0.894798	−	1.54984i
$836$	−16.7942	−	29.0885i	−0.580841	−	1.00605i
$837$		−	6.73205i		−	0.232694i
$838$	14.3660	−	8.29423i	0.496266	−	0.286519i
$839$	2.32051	−	1.33975i	0.0801128	−	0.0462532i	−0.459408	−	0.888225i	$-0.651939\pi$
$839$	2.32051	−	1.33975i	0.0801128	−	0.0462532i	0.539521	+	0.841972i	$0.318605\pi$
$840$			2.73205i			0.0942647i
$841$	−40.2487	−	69.7128i	−1.38789	−	2.40389i
$842$	−4.66025	+	8.07180i	−0.160603	+	0.278172i
$843$	−8.02628	−	4.63397i	−0.276440	−	0.159603i
$844$	−11.0718			−0.381107
$845$	16.5622	+	31.4186i	0.569756	+	1.08083i
$846$	9.92820			0.341339
$847$	−13.8564	−	8.00000i	−0.476112	−	0.274883i
$848$	−1.96410	+	3.40192i	−0.0674475	+	0.116823i
$849$	4.92820	+	8.53590i	0.169135	+	0.292951i
$850$		−	14.1244i		−	0.484461i
$851$	1.51666	−	0.875644i	0.0519905	−	0.0300167i
$852$	9.29423	−	5.36603i	0.318415	−	0.183837i
$853$			23.2487i			0.796021i	0.917381	+	0.398010i	$0.130299\pi$
$853$			23.2487i			0.796021i	−0.917381	+	0.398010i	$0.869701\pi$
$854$	−0.133975	−	0.232051i	−0.00458452	−	0.00794062i
$855$	8.83013	−	15.2942i	0.301984	−	0.523052i
$856$	−17.2583	−	9.96410i	−0.589878	−	0.340566i
$857$	−12.5359			−0.428218			−0.214109	−	0.976810i	$-0.568685\pi$
$857$	−12.5359			−0.428218			−0.214109	+	0.976810i	$0.568685\pi$
$858$	−4.50000	−	18.1865i	−0.153627	−	0.620878i
$859$	27.1962			0.927921			0.463960	−	0.885856i	$-0.346428\pi$
$859$	27.1962			0.927921			0.463960	+	0.885856i	$0.346428\pi$
$860$	−12.4641	−	7.19615i	−0.425022	−	0.245387i
$861$	0.767949	−	1.33013i	0.0261716	−	0.0453306i
$862$	−5.56218	−	9.63397i	−0.189449	−	0.328134i
$863$			11.8564i			0.403597i	0.979427	+	0.201798i	$0.0646786\pi$
$863$			11.8564i			0.403597i	−0.979427	+	0.201798i	$0.935321\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−19.3923	+	11.1962i	−0.659358	+	0.380681i
$866$		−	39.8564i		−	1.35438i
$867$	−7.92820	−	13.7321i	−0.269256	−	0.466365i
$868$	−3.36603	+	5.83013i	−0.114250	+	0.197887i
$869$	40.5000	+	23.3827i	1.37387	+	0.793203i
$870$	−28.5885			−0.969239
$871$	−10.0000	+	34.6410i	−0.338837	+	1.17377i
$872$	14.7321			0.498890
$873$	−3.29423	−	1.90192i	−0.111493	−	0.0643704i
$874$	−1.73205	+	3.00000i	−0.0585875	+	0.101477i
$875$	3.46410	+	6.00000i	0.117108	+	0.202837i
$876$		−	5.46410i		−	0.184615i
$877$	16.8109	−	9.70577i	0.567663	−	0.327741i	−0.188552	−	0.982063i	$-0.560379\pi$
$877$	16.8109	−	9.70577i	0.567663	−	0.327741i	0.756216	+	0.654323i	$0.227046\pi$
$878$	9.80385	−	5.66025i	0.330864	−	0.191024i
$879$		−	14.9282i		−	0.503516i
$880$	7.09808	+	12.2942i	0.239276	+	0.414438i
$881$	7.85641	−	13.6077i	0.264689	−	0.458455i	−0.702793	−	0.711394i	$-0.748064\pi$
$881$	7.85641	−	13.6077i	0.264689	−	0.458455i	0.967482	+	0.252939i	$0.0813973\pi$
$882$	0.866025	+	0.500000i	0.0291606	+	0.0168359i
$883$	19.5167			0.656788			0.328394	−	0.944541i	$-0.393493\pi$
$883$	19.5167			0.656788			0.328394	+	0.944541i	$0.393493\pi$
$884$	−19.8564	−	5.73205i	−0.667843	−	0.192790i
$885$	13.4641			0.452591
$886$	21.6506	+	12.5000i	0.727367	+	0.419946i
$887$	1.66987	−	2.89230i	0.0560688	−	0.0971141i	−0.836629	−	0.547770i	$-0.815477\pi$
$887$	1.66987	−	2.89230i	0.0560688	−	0.0971141i	0.892697	+	0.450656i	$0.148810\pi$
$888$	−1.63397	−	2.83013i	−0.0548326	−	0.0949728i
$889$		−	6.39230i		−	0.214391i
$890$	25.6865	−	14.8301i	0.861015	−	0.497107i
$891$	−4.50000	+	2.59808i	−0.150756	+	0.0870388i
$892$		−	1.46410i		−	0.0490217i
$893$	32.0885	+	55.5788i	1.07380	+	1.85987i
$894$	4.00000	−	6.92820i	0.133780	−	0.231714i
$895$	−8.19615	−	4.73205i	−0.273967	−	0.158175i
$896$	−1.00000			−0.0334077
$897$	−1.39230	+	1.33975i	−0.0464877	+	0.0447328i
$898$	−22.9808			−0.766878
$899$	−61.0070	−	35.2224i	−2.03470	−	1.17473i
$900$	−1.23205	+	2.13397i	−0.0410684	+	0.0711325i
$901$	−11.2583	−	19.5000i	−0.375069	−	0.649639i
$902$		−	7.98076i		−	0.265730i
$903$	−4.56218	+	2.63397i	−0.151820	+	0.0876532i
$904$	8.36603	−	4.83013i	0.278250	−	0.160648i
$905$		−	48.4449i		−	1.61036i
$906$	4.59808	+	7.96410i	0.152761	+	0.264590i
$907$	4.80385	−	8.32051i	0.159509	−	0.276278i	−0.775183	−	0.631737i	$-0.782342\pi$
$907$	4.80385	−	8.32051i	0.159509	−	0.276278i	0.934692	+	0.355459i	$0.115676\pi$
$908$	−18.4641	−	10.6603i	−0.612753	−	0.353773i
$909$	8.92820			0.296130
$910$	−9.56218	+	2.36603i	−0.316983	+	0.0784330i
$911$	14.8756			0.492852			0.246426	−	0.969162i	$-0.420744\pi$
$911$	14.8756			0.492852			0.246426	+	0.969162i	$0.420744\pi$
$912$	5.59808	+	3.23205i	0.185371	+	0.107024i
$913$	−33.0788	+	57.2942i	−1.09475	+	1.89616i
$914$	12.8564	+	22.2679i	0.425252	+	0.736558i
$915$		−	0.732051i		−	0.0242009i
$916$	2.93782	−	1.69615i	0.0970684	−	0.0560425i
$917$	0.928203	−	0.535898i	0.0306520	−	0.0176969i
$918$			5.73205i			0.189186i
$919$	−21.3564	−	36.9904i	−0.704483	−	1.22020i	−0.966878	−	0.255240i	$-0.917846\pi$
$919$	−21.3564	−	36.9904i	−0.704483	−	1.22020i	0.262395	−	0.964961i	$-0.415488\pi$
$920$	0.732051	−	1.26795i	0.0241350	−	0.0418030i
$921$	4.33013	+	2.50000i	0.142683	+	0.0823778i
$922$	−6.92820			−0.228168
$923$	26.8301	+	27.8827i	0.883124	+	0.917770i
$924$	5.19615			0.170941
$925$	6.97372	+	4.02628i	0.229295	+	0.132383i
$926$	16.3301	−	28.2846i	0.536641	−	0.929490i
$927$	−2.90192	−	5.02628i	−0.0953117	−	0.165085i
$928$		−	10.4641i		−	0.343501i
$929$	8.59808	−	4.96410i	0.282094	−	0.162867i	−0.352277	−	0.935896i	$-0.614593\pi$
$929$	8.59808	−	4.96410i	0.282094	−	0.162867i	0.634371	+	0.773029i	$0.281259\pi$
$930$	−15.9282	+	9.19615i	−0.522306	+	0.301554i
$931$			6.46410i			0.211852i
$932$	−6.29423	−	10.9019i	−0.206174	−	0.357104i
$933$	−12.5981	+	21.8205i	−0.412442	+	0.714371i
$934$	−4.39230	−	2.53590i	−0.143721	−	0.0829771i
$935$	−81.3731			−2.66118
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$	−11.7128			−0.382641			−0.191320	−	0.981528i	$-0.561277\pi$
$937$	−11.7128			−0.382641			−0.191320	+	0.981528i	$0.561277\pi$
$938$	−8.66025	−	5.00000i	−0.282767	−	0.163256i
$939$	−15.5622	+	26.9545i	−0.507852	+	0.879626i
$940$	−13.5622	−	23.4904i	−0.442349	−	0.766172i
$941$			7.32051i			0.238642i	0.992856	+	0.119321i	$0.0380717\pi$
$941$			7.32051i			0.238642i	−0.992856	+	0.119321i	$0.961928\pi$
$942$	−3.92820	+	2.26795i	−0.127988	+	0.0738938i
$943$	−0.712813	+	0.411543i	−0.0232124	+	0.0134017i
$944$			4.92820i			0.160399i
$945$	1.36603	+	2.36603i	0.0444368	+	0.0769668i
$946$	−13.6865	+	23.7058i	−0.444988	+	0.770741i
$947$	−19.8397	−	11.4545i	−0.644705	−	0.372221i	0.141720	−	0.989907i	$-0.454737\pi$
$947$	−19.8397	−	11.4545i	−0.644705	−	0.372221i	−0.786425	+	0.617686i	$0.788070\pi$
$948$	−9.00000			−0.292306
$949$	19.1244	−	4.73205i	0.620803	−	0.153609i
$950$	−15.9282			−0.516779
$951$	23.1962	+	13.3923i	0.752187	+	0.434275i
$952$	2.86603	−	4.96410i	0.0928884	−	0.160887i
$953$	−8.83013	−	15.2942i	−0.286036	−	0.495429i	0.686824	−	0.726824i	$-0.259004\pi$
$953$	−8.83013	−	15.2942i	−0.286036	−	0.495429i	−0.972860	+	0.231395i	$0.925671\pi$
$954$			3.92820i			0.127180i
$955$	−5.19615	+	3.00000i	−0.168144	+	0.0970777i
$956$	3.97372	−	2.29423i	0.128519	−	0.0742007i
$957$			54.3731i			1.75763i
$958$	−11.4282	−	19.7942i	−0.369228	−	0.639522i
$959$	−6.26795	+	10.8564i	−0.202403	+	0.350572i
$960$	−2.36603	−	1.36603i	−0.0763631	−	0.0440883i
$961$	−14.3205			−0.461952
$962$	8.49038	−	8.16987i	0.273741	−	0.263407i
$963$	−19.9282			−0.642177
$964$	2.53590	+	1.46410i	0.0816758	+	0.0471555i
$965$	32.2224	−	55.8109i	1.03728	−	1.79662i
$966$	−0.267949	−	0.464102i	−0.00862112	−	0.0149322i
$967$			28.7846i			0.925651i	0.886450	+	0.462825i	$0.153164\pi$
$967$			28.7846i			0.925651i	−0.886450	+	0.462825i	$0.846836\pi$
$968$	13.8564	−	8.00000i	0.445362	−	0.257130i
$969$	−32.0885	+	18.5263i	−1.03083	+	0.595150i
$970$			10.3923i			0.333677i
$971$	19.0526	+	33.0000i	0.611426	+	1.05902i	0.991000	+	0.133859i	$0.0427370\pi$
$971$	19.0526	+	33.0000i	0.611426	+	1.05902i	−0.379575	+	0.925161i	$0.623930\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−18.2321	−	10.5263i	−0.584493	−	0.337457i
$974$	29.4449			0.943474
$975$	−8.53590	−	2.46410i	−0.273368	−	0.0789144i
$976$	0.267949			0.00857684
$977$	16.9808	+	9.80385i	0.543263	+	0.313653i	0.746400	−	0.665497i	$-0.231781\pi$
$977$	16.9808	+	9.80385i	0.543263	+	0.313653i	−0.203138	+	0.979150i	$0.565114\pi$
$978$	−8.56218	+	14.8301i	−0.273788	+	0.474215i
$979$	−28.2058	−	48.8538i	−0.901460	−	1.56138i
$980$		−	2.73205i		−	0.0872722i
$981$	12.7583	−	7.36603i	0.407342	−	0.235179i
$982$	−12.4641	+	7.19615i	−0.397745	+	0.229638i
$983$			18.0000i			0.574111i	0.957914	+	0.287055i	$0.0926764\pi$
$983$			18.0000i			0.574111i	−0.957914	+	0.287055i	$0.907324\pi$
$984$	0.767949	+	1.33013i	0.0244813	+	0.0424029i
$985$	−5.09808	+	8.83013i	−0.162438	+	0.281351i
$986$	51.9449	+	29.9904i	1.65426	+	0.955088i
$987$	−9.92820			−0.316018
$988$	−6.46410	+	22.3923i	−0.205650	+	0.712394i
$989$	2.82309			0.0897689
$990$	12.2942	+	7.09808i	0.390736	+	0.225592i
$991$	5.62436	−	9.74167i	0.178664	−	0.309454i	−0.762759	−	0.646682i	$-0.776156\pi$
$991$	5.62436	−	9.74167i	0.178664	−	0.309454i	0.941423	+	0.337228i	$0.109489\pi$
$992$	−3.36603	−	5.83013i	−0.106871	−	0.185107i
$993$			34.7846i			1.10386i
$994$	−9.29423	+	5.36603i	−0.294795	+	0.170200i
$995$	−15.5885	+	9.00000i	−0.494187	+	0.285319i
$996$		−	12.7321i		−	0.403430i
$997$	4.45448	+	7.71539i	0.141075	+	0.244349i	0.927902	−	0.372825i	$-0.121611\pi$
$997$	4.45448	+	7.71539i	0.141075	+	0.244349i	−0.786827	+	0.617174i	$0.788278\pi$
$998$	−5.29423	+	9.16987i	−0.167586	+	0.290267i
$999$	−2.83013	−	1.63397i	−0.0895413	−	0.0516967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.s.b.43.1	✓	4
3.2	odd	2		1638.2.bj.a.1135.2		4
13.6	odd	12		7098.2.a.by.1.1		2
13.7	odd	12		7098.2.a.bo.1.2		2
13.10	even	6	inner	546.2.s.b.127.1	yes	4
39.23	odd	6		1638.2.bj.a.127.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.b.43.1	✓	4	1.1	even	1	trivial
546.2.s.b.127.1	yes	4	13.10	even	6	inner
1638.2.bj.a.127.2		4	39.23	odd	6
1638.2.bj.a.1135.2		4	3.2	odd	2
7098.2.a.bo.1.2		2	13.7	odd	12
7098.2.a.by.1.1		2	13.6	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(4.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(2.36603 + 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} +1.00000i q^{18} +(-5.59808 + 3.23205i) q^{19} +(2.36603 - 1.36603i) q^{20} -1.00000i q^{21} +(-2.59808 - 4.50000i) q^{22} +(-0.267949 + 0.464102i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(5.23205 - 9.06218i) q^{29} +(-1.36603 - 2.36603i) q^{30} -6.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.50000 + 2.59808i) q^{33} +5.73205i q^{34} +(1.36603 + 2.36603i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.83013 - 1.63397i) q^{37} +6.46410 q^{38} +(3.46410 + 1.00000i) q^{39} -2.73205 q^{40} +(1.33013 + 0.767949i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-2.63397 - 4.56218i) q^{43} +5.19615i q^{44} +(-2.36603 + 1.36603i) q^{45} +(0.464102 - 0.267949i) q^{46} -9.92820i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(2.13397 + 1.23205i) q^{50} +5.73205 q^{51} +(2.59808 - 2.50000i) q^{52} +3.92820 q^{53} +(-0.866025 - 0.500000i) q^{54} +(7.09808 - 12.2942i) q^{55} +(0.500000 + 0.866025i) q^{56} -6.46410i q^{57} +(-9.06218 + 5.23205i) q^{58} +(4.26795 - 2.46410i) q^{59} +2.73205i q^{60} +(-0.133975 - 0.232051i) q^{61} +(-3.36603 + 5.83013i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-9.56218 + 2.36603i) q^{65} +5.19615 q^{66} +(-8.66025 - 5.00000i) q^{67} +(2.86603 - 4.96410i) q^{68} +(-0.267949 - 0.464102i) q^{69} -2.73205i q^{70} +(-9.29423 + 5.36603i) q^{71} +(-0.866025 + 0.500000i) q^{72} +5.46410i q^{73} +(1.63397 + 2.83013i) q^{74} +(1.23205 - 2.13397i) q^{75} +(-5.59808 - 3.23205i) q^{76} -5.19615 q^{77} +(-2.50000 - 2.59808i) q^{78} +9.00000 q^{79} +(2.36603 + 1.36603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.767949 - 1.33013i) q^{82} +12.7321i q^{83} +(0.866025 - 0.500000i) q^{84} +(-13.5622 + 7.83013i) q^{85} +5.26795i q^{86} +(5.23205 + 9.06218i) q^{87} +(2.59808 - 4.50000i) q^{88} +(-9.40192 - 5.42820i) q^{89} +2.73205 q^{90} +(2.50000 + 2.59808i) q^{91} -0.535898 q^{92} +(5.83013 + 3.36603i) q^{93} +(-4.96410 + 8.59808i) q^{94} +(8.83013 + 15.2942i) q^{95} +1.00000i q^{96} +(3.29423 - 1.90192i) q^{97} +(-0.866025 + 0.500000i) q^{98} -5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} + 18 q^{11} - 4 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{20} - 8 q^{23} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 14 q^{29} - 2 q^{30} - 18 q^{33} + 2 q^{35} + 2 q^{36} + 6 q^{37} + 12 q^{38} - 4 q^{40} - 12 q^{41} - 2 q^{42} - 14 q^{43} - 6 q^{45} - 12 q^{46} - 2 q^{48} + 2 q^{49} + 12 q^{50} + 16 q^{51} - 12 q^{53} + 18 q^{55} + 2 q^{56} - 12 q^{58} + 24 q^{59} - 4 q^{61} - 10 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{68} - 8 q^{69} - 6 q^{71} + 10 q^{74} - 2 q^{75} - 12 q^{76} - 10 q^{78} + 36 q^{79} + 6 q^{80} - 2 q^{81} - 10 q^{82} - 30 q^{85} + 14 q^{87} - 48 q^{89} + 4 q^{90} + 10 q^{91} - 16 q^{92} + 6 q^{93} - 6 q^{94} + 18 q^{95} - 18 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 18 * q^11 - 4 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^20 - 8 * q^23 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 14 * q^29 - 2 * q^30 - 18 * q^33 + 2 * q^35 + 2 * q^36 + 6 * q^37 + 12 * q^38 - 4 * q^40 - 12 * q^41 - 2 * q^42 - 14 * q^43 - 6 * q^45 - 12 * q^46 - 2 * q^48 + 2 * q^49 + 12 * q^50 + 16 * q^51 - 12 * q^53 + 18 * q^55 + 2 * q^56 - 12 * q^58 + 24 * q^59 - 4 * q^61 - 10 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^68 - 8 * q^69 - 6 * q^71 + 10 * q^74 - 2 * q^75 - 12 * q^76 - 10 * q^78 + 36 * q^79 + 6 * q^80 - 2 * q^81 - 10 * q^82 - 30 * q^85 + 14 * q^87 - 48 * q^89 + 4 * q^90 + 10 * q^91 - 16 * q^92 + 6 * q^93 - 6 * q^94 + 18 * q^95 - 18 * q^97

Introduction

L-functions

Modular forms

Varieties

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