LMFDB - Embedded newform 546.2.s.e.43.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.4
Root			$1.72124 + 0.193255i$ of defining polynomial
Character	$\chi$	$=$	546.43
Dual form			546.2.s.e.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.894007 + 1.54846i) q^{10} +(2.74922 + 1.58726i) q^{11} +1.00000 q^{12} +(1.47952 - 3.28801i) q^{13} +1.00000 q^{14} +(1.54846 + 0.894007i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.78052 + 4.81599i) q^{17} -1.00000i q^{18} +(-5.36028 + 3.09476i) q^{19} +(-1.54846 + 0.894007i) q^{20} -1.00000i q^{21} +(1.58726 + 2.74922i) q^{22} +(3.06678 - 5.31181i) q^{23} +(0.866025 + 0.500000i) q^{24} +1.80301 q^{25} +(2.92531 - 2.10774i) q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(-1.03880 + 1.79925i) q^{29} +(0.894007 + 1.54846i) q^{30} +5.63862i q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.74922 - 1.58726i) q^{33} +5.56103i q^{34} +(0.894007 + 1.54846i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.68202 - 1.54846i) q^{37} -6.18952 q^{38} +(-2.10774 - 2.92531i) q^{39} -1.78801 q^{40} +(-1.29768 - 0.749217i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-4.81931 - 8.34729i) q^{43} +3.17452i q^{44} +(1.54846 - 0.894007i) q^{45} +(5.31181 - 3.06678i) q^{46} -10.5086i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(1.56145 + 0.901504i) q^{50} +5.56103 q^{51} +(3.58726 - 0.362708i) q^{52} +3.60200 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.83804 + 4.91564i) q^{55} +(0.500000 + 0.866025i) q^{56} +6.18952i q^{57} +(-1.79925 + 1.03880i) q^{58} +(-2.40874 + 1.39069i) q^{59} +1.78801i q^{60} +(-0.844395 - 1.46254i) q^{61} +(-2.81931 + 4.88319i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(5.87901 + 2.64539i) q^{65} +3.17452 q^{66} +(-10.0064 - 5.77720i) q^{67} +(-2.78052 + 4.81599i) q^{68} +(-3.06678 - 5.31181i) q^{69} +1.78801i q^{70} +(-0.518313 + 0.299248i) q^{71} +(0.866025 - 0.500000i) q^{72} +0.423973i q^{73} +(-1.54846 - 2.68202i) q^{74} +(0.901504 - 1.56145i) q^{75} +(-5.36028 - 3.09476i) q^{76} +3.17452 q^{77} +(-0.362708 - 3.58726i) q^{78} +6.96254 q^{79} +(-1.54846 - 0.894007i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.749217 - 1.29768i) q^{82} -4.30228i q^{83} +(0.866025 - 0.500000i) q^{84} +(-8.61106 + 4.97160i) q^{85} -9.63862i q^{86} +(1.03880 + 1.79925i) q^{87} +(-1.58726 + 2.74922i) q^{88} +(-14.1102 - 8.14654i) q^{89} +1.78801 q^{90} +(-0.362708 - 3.58726i) q^{91} +6.13356 q^{92} +(4.88319 + 2.81931i) q^{93} +(5.25429 - 9.10069i) q^{94} +(-5.53347 - 9.58425i) q^{95} +1.00000i q^{96} +(-15.1461 + 8.74462i) q^{97} +(0.866025 - 0.500000i) q^{98} -3.17452i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{10} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 8 q^{14} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 12 q^{19} - 6 q^{20} - 4 q^{22} + 8 q^{23} - 24 q^{25} + 6 q^{26} - 8 q^{27} + 2 q^{29} - 6 q^{30} + 6 q^{33} - 6 q^{35} + 4 q^{36} + 18 q^{37} - 4 q^{38} + 12 q^{40} + 12 q^{41} + 4 q^{42} - 8 q^{43} + 6 q^{45} + 18 q^{46} + 4 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} + 12 q^{52} - 12 q^{53} - 22 q^{55} + 4 q^{56} - 24 q^{58} + 18 q^{59} - 8 q^{61} + 8 q^{62} - 8 q^{64} + 46 q^{65} - 8 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} + 6 q^{71} - 6 q^{74} - 12 q^{75} - 12 q^{76} - 8 q^{77} + 6 q^{78} - 4 q^{79} - 6 q^{80} - 4 q^{81} + 10 q^{82} - 54 q^{85} - 2 q^{87} + 4 q^{88} - 18 q^{89} - 12 q^{90} + 6 q^{91} + 16 q^{92} + 30 q^{93} - 2 q^{94} - 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^10 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 8 * q^14 + 6 * q^15 - 4 * q^16 + 2 * q^17 - 12 * q^19 - 6 * q^20 - 4 * q^22 + 8 * q^23 - 24 * q^25 + 6 * q^26 - 8 * q^27 + 2 * q^29 - 6 * q^30 + 6 * q^33 - 6 * q^35 + 4 * q^36 + 18 * q^37 - 4 * q^38 + 12 * q^40 + 12 * q^41 + 4 * q^42 - 8 * q^43 + 6 * q^45 + 18 * q^46 + 4 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 + 12 * q^52 - 12 * q^53 - 22 * q^55 + 4 * q^56 - 24 * q^58 + 18 * q^59 - 8 * q^61 + 8 * q^62 - 8 * q^64 + 46 * q^65 - 8 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 + 6 * q^71 - 6 * q^74 - 12 * q^75 - 12 * q^76 - 8 * q^77 + 6 * q^78 - 4 * q^79 - 6 * q^80 - 4 * q^81 + 10 * q^82 - 54 * q^85 - 2 * q^87 + 4 * q^88 - 18 * q^89 - 12 * q^90 + 6 * q^91 + 16 * q^92 + 30 * q^93 - 2 * q^94 - 50 * q^95 - 54 * 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
$5$			1.78801i			0.799624i	0.916597	+	0.399812i	$0.130925\pi$
$5$			1.78801i			0.799624i	−0.916597	+	0.399812i	$0.869075\pi$
$6$	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
$10$	−0.894007	+	1.54846i	−0.282710	+	0.489668i
$11$	2.74922	+	1.58726i	0.828920	+	0.478577i	0.853483	−	0.521121i	$-0.174486\pi$
$11$	2.74922	+	1.58726i	0.828920	+	0.478577i	−0.0245627	+	0.999698i	$0.507819\pi$
$12$	1.00000			0.288675
$13$	1.47952	−	3.28801i	0.410344	−	0.911931i
$13$	1.47952	−	3.28801i	0.410344	−	0.911931i
$14$	1.00000			0.267261
$15$	1.54846	+	0.894007i	0.399812	+	0.230832i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.78052	+	4.81599i	0.674374	+	1.16805i	0.976651	+	0.214830i	$0.0689198\pi$
$17$	2.78052	+	4.81599i	0.674374	+	1.16805i	−0.302277	+	0.953220i	$0.597747\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−5.36028	+	3.09476i	−1.22973	+	0.709986i	−0.966974	−	0.254875i	$-0.917966\pi$
$19$	−5.36028	+	3.09476i	−1.22973	+	0.709986i	−0.262758	+	0.964862i	$0.584632\pi$
$20$	−1.54846	+	0.894007i	−0.346247	+	0.199906i
$21$		−	1.00000i		−	0.218218i
$22$	1.58726	+	2.74922i	0.338405	+	0.586135i
$23$	3.06678	−	5.31181i	0.639467	−	1.10759i	−0.346083	−	0.938204i	$-0.612488\pi$
$23$	3.06678	−	5.31181i	0.639467	−	1.10759i	0.985550	−	0.169386i	$-0.0541784\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	1.80301			0.360602
$26$	2.92531	−	2.10774i	0.573700	−	0.413363i
$27$	−1.00000			−0.192450
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	−1.03880	+	1.79925i	−0.192900	+	0.334112i	−0.946210	−	0.323553i	$-0.895123\pi$
$29$	−1.03880	+	1.79925i	−0.192900	+	0.334112i	0.753310	+	0.657665i	$0.228456\pi$
$30$	0.894007	+	1.54846i	0.163223	+	0.282710i
$31$			5.63862i			1.01273i	0.862320	+	0.506363i	$0.169011\pi$
$31$			5.63862i			1.01273i	−0.862320	+	0.506363i	$0.830989\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.74922	−	1.58726i	0.478577	−	0.276307i
$34$			5.56103i			0.953709i
$35$	0.894007	+	1.54846i	0.151115	+	0.261738i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.68202	−	1.54846i	−0.440921	−	0.254566i	0.263067	−	0.964778i	$-0.415266\pi$
$37$	−2.68202	−	1.54846i	−0.440921	−	0.254566i	−0.703988	+	0.710211i	$0.748599\pi$
$38$	−6.18952			−1.00407
$39$	−2.10774	−	2.92531i	−0.337509	−	0.468424i
$40$	−1.78801			−0.282710
$41$	−1.29768	−	0.749217i	−0.202664	−	0.117008i	0.395234	−	0.918581i	$-0.370664\pi$
$41$	−1.29768	−	0.749217i	−0.202664	−	0.117008i	−0.597897	+	0.801573i	$0.703997\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	−4.81931	−	8.34729i	−0.734938	−	1.27295i	−0.954750	−	0.297408i	$-0.903878\pi$
$43$	−4.81931	−	8.34729i	−0.734938	−	1.27295i	0.219812	−	0.975542i	$-0.429456\pi$
$44$			3.17452i			0.478577i
$45$	1.54846	−	0.894007i	0.230832	−	0.133271i
$46$	5.31181	−	3.06678i	0.783184	−	0.452172i
$47$		−	10.5086i		−	1.53283i	−0.642344	−	0.766416i	$-0.722038\pi$
$47$		−	10.5086i		−	1.53283i	0.642344	−	0.766416i	$-0.277962\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	1.56145	+	0.901504i	0.220823	+	0.127492i
$51$	5.56103			0.778700
$52$	3.58726	−	0.362708i	0.497464	−	0.0502985i
$53$	3.60200			0.494773			0.247386	−	0.968917i	$-0.420428\pi$
$53$	3.60200			0.494773			0.247386	+	0.968917i	$0.420428\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−2.83804	+	4.91564i	−0.382682	+	0.662824i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$			6.18952i			0.819822i
$58$	−1.79925	+	1.03880i	−0.236253	+	0.136401i
$59$	−2.40874	+	1.39069i	−0.313592	+	0.181052i	−0.648533	−	0.761187i	$-0.724617\pi$
$59$	−2.40874	+	1.39069i	−0.313592	+	0.181052i	0.334941	+	0.942239i	$0.391284\pi$
$60$			1.78801i			0.230832i
$61$	−0.844395	−	1.46254i	−0.108114	−	0.187259i	0.806892	−	0.590699i	$-0.201148\pi$
$61$	−0.844395	−	1.46254i	−0.108114	−	0.187259i	−0.915006	+	0.403440i	$0.867814\pi$
$62$	−2.81931	+	4.88319i	−0.358053	+	0.620166i
$63$	−0.866025	−	0.500000i	−0.109109	−	0.0629941i
$64$	−1.00000			−0.125000
$65$	5.87901	+	2.64539i	0.729202	+	0.328121i
$66$	3.17452			0.390757
$67$	−10.0064	−	5.77720i	−1.22248	−	0.705797i	−0.257031	−	0.966403i	$-0.582744\pi$
$67$	−10.0064	−	5.77720i	−1.22248	−	0.705797i	−0.965445	+	0.260606i	$0.916078\pi$
$68$	−2.78052	+	4.81599i	−0.337187	+	0.584025i
$69$	−3.06678	−	5.31181i	−0.369197	−	0.639467i
$70$			1.78801i			0.213708i
$71$	−0.518313	+	0.299248i	−0.0615124	+	0.0355142i	−0.530441	−	0.847722i	$-0.677974\pi$
$71$	−0.518313	+	0.299248i	−0.0615124	+	0.0355142i	0.468928	+	0.883236i	$0.344640\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			0.423973i			0.0496223i	0.999692	+	0.0248112i	$0.00789845\pi$
$73$			0.423973i			0.0496223i	−0.999692	+	0.0248112i	$0.992102\pi$
$74$	−1.54846	−	2.68202i	−0.180005	−	0.311778i
$75$	0.901504	−	1.56145i	0.104097	−	0.180301i
$76$	−5.36028	−	3.09476i	−0.614866	−	0.354993i
$77$	3.17452			0.361770
$78$	−0.362708	−	3.58726i	−0.0410686	−	0.406177i
$79$	6.96254			0.783346			0.391673	−	0.920104i	$-0.371896\pi$
$79$	6.96254			0.783346			0.391673	+	0.920104i	$0.371896\pi$
$80$	−1.54846	−	0.894007i	−0.173124	−	0.0999530i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.749217	−	1.29768i	−0.0827372	−	0.143305i
$83$		−	4.30228i		−	0.472237i	−0.971724	−	0.236118i	$-0.924125\pi$
$83$		−	4.30228i		−	0.472237i	0.971724	−	0.236118i	$-0.0758753\pi$
$84$	0.866025	−	0.500000i	0.0944911	−	0.0545545i
$85$	−8.61106	+	4.97160i	−0.934001	+	0.539246i
$86$		−	9.63862i		−	1.03936i
$87$	1.03880	+	1.79925i	0.111371	+	0.192900i
$88$	−1.58726	+	2.74922i	−0.169203	+	0.293068i
$89$	−14.1102	−	8.14654i	−1.49568	−	0.863532i	−0.495693	−	0.868498i	$-0.665086\pi$
$89$	−14.1102	−	8.14654i	−1.49568	−	0.863532i	−0.999988	+	0.00496618i	$0.998419\pi$
$90$	1.78801			0.188473
$91$	−0.362708	−	3.58726i	−0.0380221	−	0.376047i
$92$	6.13356			0.639467
$93$	4.88319	+	2.81931i	0.506363	+	0.292349i
$94$	5.25429	−	9.10069i	0.541938	−	0.938665i
$95$	−5.53347	−	9.58425i	−0.567722	−	0.983323i
$96$			1.00000i			0.102062i
$97$	−15.1461	+	8.74462i	−1.53786	+	0.887881i	−0.538892	+	0.842375i	$0.681157\pi$
$97$	−15.1461	+	8.74462i	−1.53786	+	0.887881i	−0.998964	+	0.0455062i	$0.985510\pi$
$98$	0.866025	−	0.500000i	0.0874818	−	0.0505076i
$99$		−	3.17452i		−	0.319052i
$100$	0.901504	+	1.56145i	0.0901504	+	0.156145i
$101$	−2.03433	+	3.52357i	−0.202424	+	0.350608i	−0.949309	−	0.314345i	$-0.898215\pi$
$101$	−2.03433	+	3.52357i	−0.202424	+	0.350608i	0.746885	+	0.664953i	$0.231548\pi$
$102$	4.81599	+	2.78052i	0.476855	+	0.275312i
$103$	−18.0768			−1.78116			−0.890578	−	0.454831i	$-0.849700\pi$
$103$	−18.0768			−1.78116			−0.890578	+	0.454831i	$0.849700\pi$
$104$	3.28801	+	1.47952i	0.322416	+	0.145079i
$105$	1.78801			0.174492
$106$	3.11942	+	1.80100i	0.302985	+	0.174929i
$107$	0.770847	−	1.33515i	0.0745206	−	0.129073i	−0.826357	−	0.563146i	$-0.809591\pi$
$107$	0.770847	−	1.33515i	0.0745206	−	0.129073i	0.900878	+	0.434073i	$0.142924\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			7.37731i			0.706618i	0.935507	+	0.353309i	$0.114944\pi$
$109$			7.37731i			0.706618i	−0.935507	+	0.353309i	$0.885056\pi$
$110$	−4.91564	+	2.83804i	−0.468688	+	0.270597i
$111$	−2.68202	+	1.54846i	−0.254566	+	0.146974i
$112$			1.00000i			0.0944911i
$113$	4.95660	+	8.58509i	0.466278	+	0.807617i	0.999258	−	0.0385104i	$-0.0122613\pi$
$113$	4.95660	+	8.58509i	0.466278	+	0.807617i	−0.532980	+	0.846128i	$0.678928\pi$
$114$	−3.09476	+	5.36028i	−0.289851	+	0.502036i
$115$	9.49759	+	5.48344i	0.885655	+	0.511333i
$116$	−2.07759			−0.192900
$117$	−3.58726	+	0.362708i	−0.331642	+	0.0335324i
$118$	−2.78138			−0.256047
$119$	4.81599	+	2.78052i	0.441481	+	0.254889i
$120$	−0.894007	+	1.54846i	−0.0816113	+	0.141355i
$121$	−0.461204	−	0.798828i	−0.0419276	−	0.0726208i
$122$		−	1.68879i		−	0.152896i
$123$	−1.29768	+	0.749217i	−0.117008	+	0.0675546i
$124$	−4.88319	+	2.81931i	−0.438524	+	0.253182i
$125$			12.1639i			1.08797i
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	9.17452	−	15.8907i	0.814107	−	1.41008i	−0.0958600	−	0.995395i	$-0.530560\pi$
$127$	9.17452	−	15.8907i	0.814107	−	1.41008i	0.909967	−	0.414680i	$-0.136107\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−9.63862			−0.848634
$130$	3.76868	+	5.23048i	0.330535	+	0.458744i
$131$	5.91928			0.517170			0.258585	−	0.965989i	$-0.416744\pi$
$131$	5.91928			0.517170			0.258585	+	0.965989i	$0.416744\pi$
$132$	2.74922	+	1.58726i	0.239289	+	0.138153i
$133$	−3.09476	+	5.36028i	−0.268350	+	0.464795i
$134$	−5.77720	−	10.0064i	−0.499074	−	0.864421i
$135$		−	1.78801i		−	0.153888i
$136$	−4.81599	+	2.78052i	−0.412968	+	0.238427i
$137$	7.62363	−	4.40150i	0.651331	−	0.376046i	−0.137635	−	0.990483i	$-0.543950\pi$
$137$	7.62363	−	4.40150i	0.651331	−	0.376046i	0.788966	+	0.614437i	$0.210617\pi$
$138$		−	6.13356i		−	0.522123i
$139$	−9.48720	−	16.4323i	−0.804694	−	1.39377i	−0.916498	−	0.400040i	$-0.868996\pi$
$139$	−9.48720	−	16.4323i	−0.804694	−	1.39377i	0.111804	−	0.993730i	$-0.464337\pi$
$140$	−0.894007	+	1.54846i	−0.0755574	+	0.130869i
$141$	−9.10069	−	5.25429i	−0.766416	−	0.442491i
$142$	−0.598496			−0.0502247
$143$	9.28645	−	6.69108i	0.776572	−	0.559537i
$144$	1.00000			0.0833333
$145$	−3.21708	−	1.85738i	−0.267164	−	0.154247i
$146$	−0.211987	+	0.367172i	−0.0175441	+	0.0303873i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$		−	3.09693i		−	0.254566i
$149$	12.0919	−	6.98127i	0.990608	−	0.571928i	0.0851520	−	0.996368i	$-0.472862\pi$
$149$	12.0919	−	6.98127i	0.990608	−	0.571928i	0.905456	+	0.424440i	$0.139529\pi$
$150$	1.56145	−	0.901504i	0.127492	−	0.0736075i
$151$			17.8426i			1.45201i	0.687688	+	0.726006i	$0.258626\pi$
$151$			17.8426i			1.45201i	−0.687688	+	0.726006i	$0.741374\pi$
$152$	−3.09476	−	5.36028i	−0.251018	−	0.434776i
$153$	2.78052	−	4.81599i	0.224791	−	0.389350i
$154$	2.74922	+	1.58726i	0.221538	+	0.127905i
$155$	−10.0819			−0.809800
$156$	1.47952	−	3.28801i	0.118456	−	0.263252i
$157$	4.57916			0.365457			0.182728	−	0.983163i	$-0.441507\pi$
$157$	4.57916			0.365457			0.182728	+	0.983163i	$0.441507\pi$
$158$	6.02973	+	3.48127i	0.479700	+	0.276955i
$159$	1.80100	−	3.11942i	0.142829	−	0.247386i
$160$	−0.894007	−	1.54846i	−0.0706774	−	0.122417i
$161$		−	6.13356i		−	0.483392i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	10.6267	−	6.13531i	0.832344	−	0.480554i	−0.0223103	−	0.999751i	$-0.507102\pi$
$163$	10.6267	−	6.13531i	0.832344	−	0.480554i	0.854655	+	0.519197i	$0.173769\pi$
$164$		−	1.49843i		−	0.117008i
$165$	2.83804	+	4.91564i	0.220941	+	0.382682i
$166$	2.15114	−	3.72589i	0.166961	−	0.289185i
$167$	14.4610	+	8.34904i	1.11902	+	0.646068i	0.941151	−	0.337985i	$-0.109745\pi$
$167$	14.4610	+	8.34904i	1.11902	+	0.646068i	0.177872	+	0.984054i	$0.443079\pi$
$168$	1.00000			0.0771517
$169$	−8.62206	−	9.72934i	−0.663236	−	0.748411i
$170$	−9.94320			−0.762609
$171$	5.36028	+	3.09476i	0.409911	+	0.236662i
$172$	4.81931	−	8.34729i	0.367469	−	0.636475i
$173$	3.68865	+	6.38894i	0.280443	+	0.485742i	0.971494	−	0.237064i	$-0.0761852\pi$
$173$	3.68865	+	6.38894i	0.280443	+	0.485742i	−0.691051	+	0.722806i	$0.742852\pi$
$174$			2.07759i			0.157502i
$175$	1.56145	−	0.901504i	0.118035	−	0.0681473i
$176$	−2.74922	+	1.58726i	−0.207230	+	0.119644i
$177$			2.78138i			0.209061i
$178$	−8.14654	−	14.1102i	−0.610609	−	1.05761i
$179$	9.91008	−	17.1648i	0.740714	−	1.28295i	−0.211457	−	0.977387i	$-0.567821\pi$
$179$	9.91008	−	17.1648i	0.740714	−	1.28295i	0.952171	−	0.305567i	$-0.0988459\pi$
$180$	1.54846	+	0.894007i	0.115416	+	0.0666353i
$181$	−18.3266			−1.36220			−0.681102	−	0.732189i	$-0.738499\pi$
$181$	−18.3266			−1.36220			−0.681102	+	0.732189i	$0.738499\pi$
$182$	1.47952	−	3.28801i	0.109669	−	0.243724i
$183$	−1.68879			−0.124839
$184$	5.31181	+	3.06678i	0.391592	+	0.226086i
$185$	2.76868	−	4.79549i	0.203557	−	0.352571i
$186$	2.81931	+	4.88319i	0.206722	+	0.358053i
$187$			17.6536i			1.29096i
$188$	9.10069	−	5.25429i	0.663736	−	0.383208i
$189$	−0.866025	+	0.500000i	−0.0629941	+	0.0363696i
$190$		−	11.0669i		−	0.802880i
$191$	7.51518	+	13.0167i	0.543779	+	0.941854i	0.998683	+	0.0513127i	$0.0163405\pi$
$191$	7.51518	+	13.0167i	0.543779	+	0.941854i	−0.454903	+	0.890541i	$0.650326\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−4.72408	−	2.72745i	−0.340047	−	0.196326i	0.320246	−	0.947334i	$-0.396234\pi$
$193$	−4.72408	−	2.72745i	−0.340047	−	0.196326i	−0.660293	+	0.751008i	$0.729568\pi$
$194$	−17.4892			−1.25565
$195$	5.23048	−	3.76868i	0.374563	−	0.269880i
$196$	1.00000			0.0714286
$197$	−6.60751	−	3.81485i	−0.470766	−	0.271797i	0.245795	−	0.969322i	$-0.420951\pi$
$197$	−6.60751	−	3.81485i	−0.470766	−	0.271797i	−0.716560	+	0.697525i	$0.754284\pi$
$198$	1.58726	−	2.74922i	0.112802	−	0.195378i
$199$	2.99512	+	5.18769i	0.212318	+	0.367746i	0.952440	−	0.304727i	$-0.0985653\pi$
$199$	2.99512	+	5.18769i	0.212318	+	0.367746i	−0.740121	+	0.672473i	$0.765232\pi$
$200$			1.80301i			0.127492i
$201$	−10.0064	+	5.77720i	−0.705797	+	0.407492i
$202$	−3.52357	+	2.03433i	−0.247917	+	0.143135i
$203$			2.07759i			0.145818i
$204$	2.78052	+	4.81599i	0.194675	+	0.337187i
$205$	1.33961	−	2.32027i	0.0935624	−	0.162055i
$206$	−15.6549	−	9.03838i	−1.09073	−	0.629734i
$207$	−6.13356			−0.426312
$208$	2.10774	+	2.92531i	0.146146	+	0.202833i
$209$	−19.6488			−1.35913
$210$	1.54846	+	0.894007i	0.106854	+	0.0616923i
$211$	1.38651	−	2.40150i	0.0954512	−	0.165326i	−0.814346	−	0.580380i	$-0.802904\pi$
$211$	1.38651	−	2.40150i	0.0954512	−	0.165326i	0.909797	+	0.415054i	$0.136237\pi$
$212$	1.80100	+	3.11942i	0.123693	+	0.214243i
$213$			0.598496i			0.0410083i
$214$	1.33515	−	0.770847i	0.0912687	−	0.0526940i
$215$	14.9251	−	8.61699i	1.01788	−	0.587674i
$216$		−	1.00000i		−	0.0680414i
$217$	2.81931	+	4.88319i	0.191387	+	0.331493i
$218$	−3.68865	+	6.38894i	−0.249827	+	0.432713i
$219$	0.367172	+	0.211987i	0.0248112	+	0.0143247i
$220$	−5.67609			−0.382682
$221$	19.9489	−	2.01703i	1.34191	−	0.135680i
$222$	−3.09693			−0.207852
$223$	19.5163	+	11.2677i	1.30691	+	0.754542i	0.981578	−	0.191060i	$-0.0611924\pi$
$223$	19.5163	+	11.2677i	1.30691	+	0.754542i	0.325327	+	0.945602i	$0.394526\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−0.901504	−	1.56145i	−0.0601003	−	0.104097i
$226$			9.91321i			0.659417i
$227$	−1.58616	+	0.915773i	−0.105277	+	0.0607820i	−0.551714	−	0.834033i	$-0.686026\pi$
$227$	−1.58616	+	0.915773i	−0.105277	+	0.0607820i	0.446437	+	0.894815i	$0.352693\pi$
$228$	−5.36028	+	3.09476i	−0.354993	+	0.204955i
$229$			22.6060i			1.49385i	0.664910	+	0.746924i	$0.268470\pi$
$229$			22.6060i			1.49385i	−0.664910	+	0.746924i	$0.731530\pi$
$230$	5.48344	+	9.49759i	0.361567	+	0.626253i
$231$	1.58726	−	2.74922i	0.104434	−	0.180885i
$232$	−1.79925	−	1.03880i	−0.118126	−	0.0682003i
$233$	−9.43897			−0.618367			−0.309184	−	0.951002i	$-0.600056\pi$
$233$	−9.43897			−0.618367			−0.309184	+	0.951002i	$0.600056\pi$
$234$	−3.28801	−	1.47952i	−0.214944	−	0.0967190i
$235$	18.7895			1.22569
$236$	−2.40874	−	1.39069i	−0.156796	−	0.0905262i
$237$	3.48127	−	6.02973i	0.226133	−	0.391673i
$238$	2.78052	+	4.81599i	0.180234	+	0.312175i
$239$			15.8757i			1.02692i	0.858115	+	0.513458i	$0.171636\pi$
$239$			15.8757i			1.02692i	−0.858115	+	0.513458i	$0.828364\pi$
$240$	−1.54846	+	0.894007i	−0.0999530	+	0.0577079i
$241$	20.7197	−	11.9625i	1.33467	−	0.770575i	0.348662	−	0.937248i	$-0.386636\pi$
$241$	20.7197	−	11.9625i	1.33467	−	0.770575i	0.986012	+	0.166674i	$0.0533027\pi$
$242$		−	0.922407i		−	0.0592946i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.844395	−	1.46254i	0.0540569	−	0.0936293i
$245$	1.54846	+	0.894007i	0.0989278	+	0.0571160i
$246$	−1.49843			−0.0955367
$247$	2.24499	+	22.2034i	0.142845	+	1.41277i
$248$	−5.63862			−0.358053
$249$	−3.72589	−	2.15114i	−0.236118	−	0.136323i
$250$	−6.08193	+	10.5342i	−0.384655	+	0.666243i
$251$	−10.2618	−	17.7739i	−0.647718	−	1.12188i	−0.983667	−	0.180000i	$-0.942390\pi$
$251$	−10.2618	−	17.7739i	−0.647718	−	1.12188i	0.335949	−	0.941880i	$-0.390943\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	16.8625	−	9.73555i	1.06013	−	0.612069i
$254$	15.8907	−	9.17452i	0.997074	−	0.575661i
$255$			9.94320i			0.622667i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.413344	+	0.715933i	−0.0257837	+	0.0446587i	−0.878629	−	0.477504i	$-0.841541\pi$
$257$	−0.413344	+	0.715933i	−0.0257837	+	0.0446587i	0.852846	+	0.522163i	$0.174875\pi$
$258$	−8.34729	−	4.81931i	−0.519680	−	0.300037i
$259$	−3.09693			−0.192434
$260$	0.648527	+	6.41407i	0.0402199	+	0.397784i
$261$	2.07759			0.128600
$262$	5.12624	+	2.95964i	0.316700	+	0.182847i
$263$	−10.1805	+	17.6331i	−0.627754	+	1.08730i	0.360248	+	0.932857i	$0.382692\pi$
$263$	−10.1805	+	17.6331i	−0.627754	+	1.08730i	−0.988001	+	0.154445i	$0.950641\pi$
$264$	1.58726	+	2.74922i	0.0976892	+	0.169203i
$265$			6.44042i			0.395632i
$266$	−5.36028	+	3.09476i	−0.328660	+	0.189752i
$267$	−14.1102	+	8.14654i	−0.863532	+	0.498560i
$268$		−	11.5544i		−	0.705797i
$269$	10.2587	+	17.7687i	0.625487	+	1.08338i	0.988446	+	0.151570i	$0.0484330\pi$
$269$	10.2587	+	17.7687i	0.625487	+	1.08338i	−0.362959	+	0.931805i	$0.618234\pi$
$270$	0.894007	−	1.54846i	0.0544075	−	0.0942366i
$271$	−10.5495	−	6.09076i	−0.640837	−	0.369988i	0.144100	−	0.989563i	$-0.453971\pi$
$271$	−10.5495	−	6.09076i	−0.640837	−	0.369988i	−0.784937	+	0.619576i	$0.787305\pi$
$272$	−5.56103			−0.337187
$273$	−3.28801	−	1.47952i	−0.199000	−	0.0895444i
$274$	8.80301			0.531809
$275$	4.95686	+	2.86185i	0.298910	+	0.172576i
$276$	3.06678	−	5.31181i	0.184598	−	0.319734i
$277$	4.31242	+	7.46933i	0.259108	+	0.448789i	0.966003	−	0.258530i	$-0.0832380\pi$
$277$	4.31242	+	7.46933i	0.259108	+	0.448789i	−0.706895	+	0.707318i	$0.749905\pi$
$278$		−	18.9744i		−	1.13801i
$279$	4.88319	−	2.81931i	0.292349	−	0.168788i
$280$	−1.54846	+	0.894007i	−0.0925385	+	0.0534271i
$281$			24.2922i			1.44915i	0.689194	+	0.724577i	$0.257965\pi$
$281$			24.2922i			1.44915i	−0.689194	+	0.724577i	$0.742035\pi$
$282$	−5.25429	−	9.10069i	−0.312888	−	0.541938i
$283$	5.36054	−	9.28472i	0.318651	−	0.551919i	−0.661556	−	0.749896i	$-0.730104\pi$
$283$	5.36054	−	9.28472i	0.318651	−	0.551919i	0.980207	+	0.197976i	$0.0634369\pi$
$284$	−0.518313	−	0.299248i	−0.0307562	−	0.0177571i
$285$	−11.0669			−0.655549
$286$	11.3878	−	1.15142i	0.673377	−	0.0680852i
$287$	−1.49843			−0.0884498
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−6.96254	+	12.0595i	−0.409561	+	0.709380i
$290$	−1.85738	−	3.21708i	−0.109069	−	0.188913i
$291$			17.4892i			1.02524i
$292$	−0.367172	+	0.211987i	−0.0214871	+	0.0124056i
$293$	−18.5571	+	10.7139i	−1.08412	+	0.625914i	−0.932004	−	0.362449i	$-0.881941\pi$
$293$	−18.5571	+	10.7139i	−1.08412	+	0.625914i	−0.152112	+	0.988363i	$0.548607\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	−2.48657	−	4.30687i	−0.144774	−	0.250755i
$296$	1.54846	−	2.68202i	0.0900027	−	0.155889i
$297$	−2.74922	−	1.58726i	−0.159526	−	0.0921022i
$298$	13.9625			0.808828
$299$	−12.9280	−	17.9425i	−0.747644	−	1.03764i
$300$	1.80301			0.104097
$301$	−8.34729	−	4.81931i	−0.481130	−	0.277781i
$302$	−8.92131	+	15.4522i	−0.513364	+	0.889172i
$303$	2.03433	+	3.52357i	0.116869	+	0.202424i
$304$		−	6.18952i		−	0.354993i
$305$	2.61503	−	1.50979i	0.149736	−	0.0864503i
$306$	4.81599	−	2.78052i	0.275312	−	0.158952i
$307$		−	7.59364i		−	0.433392i	−0.976239	−	0.216696i	$-0.930472\pi$
$307$		−	7.59364i		−	0.433392i	0.976239	−	0.216696i	$-0.0695280\pi$
$308$	1.58726	+	2.74922i	0.0904426	+	0.156651i
$309$	−9.03838	+	15.6549i	−0.514175	+	0.890578i
$310$	−8.73121	−	5.04097i	−0.495899	−	0.286308i
$311$	25.6355			1.45366			0.726828	−	0.686820i	$-0.240994\pi$
$311$	25.6355			1.45366			0.726828	+	0.686820i	$0.240994\pi$
$312$	2.92531	−	2.10774i	0.165613	−	0.119328i
$313$	−1.71308			−0.0968293			−0.0484146	−	0.998827i	$-0.515417\pi$
$313$	−1.71308			−0.0968293			−0.0484146	+	0.998827i	$0.515417\pi$
$314$	3.96567	+	2.28958i	0.223796	+	0.129208i
$315$	0.894007	−	1.54846i	0.0503716	−	0.0872461i
$316$	3.48127	+	6.02973i	0.195837	+	0.339199i
$317$			33.2098i			1.86525i	0.360850	+	0.932624i	$0.382487\pi$
$317$			33.2098i			1.86525i	−0.360850	+	0.932624i	$0.617513\pi$
$318$	3.11942	−	1.80100i	0.174929	−	0.100995i
$319$	−5.71175	+	3.29768i	−0.319797	+	0.184635i
$320$		−	1.78801i		−	0.0999530i
$321$	−0.770847	−	1.33515i	−0.0430245	−	0.0745206i
$322$	3.06678	−	5.31181i	0.170905	−	0.296016i
$323$	−29.8087	−	17.2101i	−1.65860	−	0.957593i
$324$	−1.00000			−0.0555556
$325$	2.66758	−	5.92832i	0.147971	−	0.328844i
$326$	12.2706			0.679606
$327$	6.38894	+	3.68865i	0.353309	+	0.203983i
$328$	0.749217	−	1.29768i	0.0413686	−	0.0716525i
$329$	−5.25429	−	9.10069i	−0.289678	−	0.501737i
$330$			5.67609i			0.312458i
$331$	4.29537	−	2.47994i	0.236095	−	0.136310i	−0.377286	−	0.926097i	$-0.623142\pi$
$331$	4.29537	−	2.47994i	0.236095	−	0.136310i	0.613381	+	0.789787i	$0.289809\pi$
$332$	3.72589	−	2.15114i	0.204485	−	0.118059i
$333$			3.09693i			0.169711i
$334$	8.34904	+	14.4610i	0.456839	+	0.791269i
$335$	10.3297	−	17.8916i	0.564372	−	0.977521i
$336$	0.866025	+	0.500000i	0.0472456	+	0.0272772i
$337$	23.6174			1.28652			0.643260	−	0.765648i	$-0.277581\pi$
$337$	23.6174			1.28652			0.643260	+	0.765648i	$0.277581\pi$
$338$	−2.60226	−	12.7369i	−0.141544	−	0.692795i
$339$	9.91321			0.538412
$340$	−8.61106	−	4.97160i	−0.467000	−	0.269623i
$341$	−8.94997	+	15.5018i	−0.484668	+	0.839470i
$342$	3.09476	+	5.36028i	0.167345	+	0.289851i
$343$		−	1.00000i		−	0.0539949i
$344$	8.34729	−	4.81931i	0.450056	−	0.259840i
$345$	9.49759	−	5.48344i	0.511333	−	0.295218i
$346$			7.37731i			0.396607i
$347$	3.58483	+	6.20911i	0.192444	+	0.333323i	0.946060	−	0.323993i	$-0.105025\pi$
$347$	3.58483	+	6.20911i	0.192444	+	0.333323i	−0.753616	+	0.657315i	$0.771692\pi$
$348$	−1.03880	+	1.79925i	−0.0556853	+	0.0964498i
$349$	10.7155	+	6.18662i	0.573590	+	0.331162i	0.758582	−	0.651578i	$-0.225893\pi$
$349$	10.7155	+	6.18662i	0.573590	+	0.331162i	−0.184992	+	0.982740i	$0.559226\pi$
$350$	1.80301			0.0963749
$351$	−1.47952	+	3.28801i	−0.0789707	+	0.175501i
$352$	−3.17452			−0.169203
$353$	22.7018	+	13.1069i	1.20830	+	0.697610i	0.962387	−	0.271683i	$-0.0875801\pi$
$353$	22.7018	+	13.1069i	1.20830	+	0.697610i	0.245909	+	0.969293i	$0.420913\pi$
$354$	−1.39069	+	2.40874i	−0.0739143	+	0.128023i
$355$	−0.535059	−	0.926750i	−0.0283980	−	0.0491868i
$356$		−	16.2931i		−	0.863532i
$357$	4.81599	−	2.78052i	0.254889	−	0.147160i
$358$	17.1648	−	9.91008i	0.907186	−	0.523764i
$359$		−	3.61956i		−	0.191033i	−0.995428	−	0.0955165i	$-0.969550\pi$
$359$		−	3.61956i		−	0.191033i	0.995428	−	0.0955165i	$-0.0304503\pi$
$360$	0.894007	+	1.54846i	0.0471183	+	0.0816113i
$361$	9.65506	−	16.7231i	0.508161	−	0.880161i
$362$	−15.8713	−	9.16329i	−0.834176	−	0.481612i
$363$	−0.922407			−0.0484138
$364$	2.92531	−	2.10774i	0.153328	−	0.110476i
$365$	−0.758070			−0.0396792
$366$	−1.46254	−	0.844395i	−0.0764480	−	0.0441373i
$367$	4.03245	−	6.98440i	0.210492	−	0.364583i	−0.741377	−	0.671089i	$-0.765827\pi$
$367$	4.03245	−	6.98440i	0.210492	−	0.364583i	0.951869	+	0.306506i	$0.0991601\pi$
$368$	3.06678	+	5.31181i	0.159867	+	0.276897i
$369$			1.49843i			0.0780054i
$370$	4.79549	−	2.76868i	0.249306	−	0.143937i
$371$	3.11942	−	1.80100i	0.161952	−	0.0935032i
$372$			5.63862i			0.292349i
$373$	−14.5851	−	25.2621i	−0.755187	−	1.30802i	−0.945281	−	0.326257i	$-0.894213\pi$
$373$	−14.5851	−	25.2621i	−0.755187	−	1.30802i	0.190094	−	0.981766i	$-0.439121\pi$
$374$	−8.82681	+	15.2885i	−0.456423	+	0.790549i
$375$	10.5342	+	6.08193i	0.543985	+	0.314070i
$376$	10.5086			0.541938
$377$	4.37904	+	6.07759i	0.225532	+	0.313012i
$378$	−1.00000			−0.0514344
$379$	−23.3797	−	13.4983i	−1.20094	−	0.693361i	−0.240173	−	0.970730i	$-0.577204\pi$
$379$	−23.3797	−	13.4983i	−1.20094	−	0.693361i	−0.960763	+	0.277369i	$0.910538\pi$
$380$	5.53347	−	9.58425i	0.283861	−	0.491662i
$381$	−9.17452	−	15.8907i	−0.470025	−	0.814107i
$382$			15.0304i			0.769020i
$383$	22.6159	−	13.0573i	1.15562	−	0.667197i	0.205368	−	0.978685i	$-0.434161\pi$
$383$	22.6159	−	13.0573i	1.15562	−	0.667197i	0.950250	+	0.311488i	$0.100827\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$			5.67609i			0.289280i
$386$	−2.72745	−	4.72408i	−0.138824	−	0.240450i
$387$	−4.81931	+	8.34729i	−0.244979	+	0.424317i
$388$	−15.1461	−	8.74462i	−0.768928	−	0.443941i
$389$	−32.7110			−1.65852			−0.829258	−	0.558866i	$-0.811236\pi$
$389$	−32.7110			−1.65852			−0.829258	+	0.558866i	$0.811236\pi$
$390$	6.41407	−	0.648527i	0.324789	−	0.0328394i
$391$	34.1089			1.72496
$392$	0.866025	+	0.500000i	0.0437409	+	0.0252538i
$393$	2.95964	−	5.12624i	0.149294	−	0.258585i
$394$	−3.81485	−	6.60751i	−0.192189	−	0.332882i
$395$			12.4491i			0.626383i
$396$	2.74922	−	1.58726i	0.138153	−	0.0797629i
$397$	−0.524826	+	0.303008i	−0.0263403	+	0.0152076i	−0.513112	−	0.858321i	$-0.671508\pi$
$397$	−0.524826	+	0.303008i	−0.0263403	+	0.0152076i	0.486772	+	0.873529i	$0.338174\pi$
$398$			5.99023i			0.300263i
$399$	3.09476	+	5.36028i	0.154932	+	0.268350i
$400$	−0.901504	+	1.56145i	−0.0450752	+	0.0780726i
$401$	8.83963	+	5.10356i	0.441430	+	0.254860i	0.704204	−	0.709998i	$-0.251304\pi$
$401$	8.83963	+	5.10356i	0.441430	+	0.254860i	−0.262774	+	0.964857i	$0.584637\pi$
$402$	−11.5544			−0.576281
$403$	18.5399	+	8.34244i	0.923537	+	0.415566i
$404$	−4.06866			−0.202424
$405$	−1.54846	−	0.894007i	−0.0769438	−	0.0444235i
$406$	−1.03880	+	1.79925i	−0.0515546	+	0.0892952i
$407$	−4.91564	−	8.51413i	−0.243659	−	0.422030i
$408$			5.56103i			0.275312i
$409$	8.01863	−	4.62956i	0.396496	−	0.228917i	−0.288475	−	0.957487i	$-0.593148\pi$
$409$	8.01863	−	4.62956i	0.396496	−	0.228917i	0.684971	+	0.728570i	$0.259815\pi$
$410$	2.32027	−	1.33961i	0.114590	−	0.0661586i
$411$		−	8.80301i		−	0.434220i
$412$	−9.03838	−	15.6549i	−0.445289	−	0.771263i
$413$	−1.39069	+	2.40874i	−0.0684313	+	0.118527i
$414$	−5.31181	−	3.06678i	−0.261061	−	0.150724i
$415$	7.69254			0.377612
$416$	0.362708	+	3.58726i	0.0177832	+	0.175880i
$417$	−18.9744			−0.929180
$418$	−17.0163	−	9.82438i	−0.832296	−	0.480526i
$419$	−6.42444	+	11.1275i	−0.313855	+	0.543612i	−0.979193	−	0.202930i	$-0.934954\pi$
$419$	−6.42444	+	11.1275i	−0.313855	+	0.543612i	0.665339	+	0.746542i	$0.268287\pi$
$420$	0.894007	+	1.54846i	0.0436231	+	0.0755574i
$421$		−	7.21371i		−	0.351575i	−0.984428	−	0.175787i	$-0.943753\pi$
$421$		−	7.21371i		−	0.351575i	0.984428	−	0.175787i	$-0.0562471\pi$
$422$	2.40150	−	1.38651i	0.116903	−	0.0674942i
$423$	−9.10069	+	5.25429i	−0.442491	+	0.255472i
$424$			3.60200i			0.174929i
$425$	5.01329	+	8.68328i	0.243180	+	0.421201i
$426$	−0.299248	+	0.518313i	−0.0144986	+	0.0251123i
$427$	−1.46254	−	0.844395i	−0.0707771	−	0.0408632i
$428$	1.54169			0.0745206
$429$	−1.15142	−	11.3878i	−0.0555913	−	0.549810i
$430$	17.2340			0.831097
$431$	−5.17941	−	2.99033i	−0.249483	−	0.144039i	0.370044	−	0.929014i	$-0.379342\pi$
$431$	−5.17941	−	2.99033i	−0.249483	−	0.144039i	−0.619528	+	0.784975i	$0.712676\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	6.30144	+	10.9144i	0.302828	+	0.524513i	0.976775	−	0.214266i	$-0.0687359\pi$
$433$	6.30144	+	10.9144i	0.302828	+	0.524513i	−0.673947	+	0.738779i	$0.735403\pi$
$434$			5.63862i			0.270663i
$435$	−3.21708	+	1.85738i	−0.154247	+	0.0890546i
$436$	−6.38894	+	3.68865i	−0.305975	+	0.176655i
$437$			37.9637i			1.81605i
$438$	0.211987	+	0.367172i	0.0101291	+	0.0175441i
$439$	9.77965	−	16.9389i	0.466757	−	0.808447i	−0.532522	−	0.846416i	$-0.678755\pi$
$439$	9.77965	−	16.9389i	0.466757	−	0.808447i	0.999279	+	0.0379690i	$0.0120888\pi$
$440$	−4.91564	−	2.83804i	−0.234344	−	0.135298i
$441$	−1.00000			−0.0476190
$442$	18.2847	+	8.22764i	0.869717	+	0.391349i
$443$	−40.2601			−1.91281			−0.956407	−	0.292038i	$-0.905666\pi$
$443$	−40.2601			−1.91281			−0.956407	+	0.292038i	$0.905666\pi$
$444$	−2.68202	−	1.54846i	−0.127283	−	0.0734869i
$445$	14.5661	−	25.2293i	0.690500	−	1.19598i
$446$	11.2677	+	19.5163i	0.533542	+	0.924121i
$447$		−	13.9625i		−	0.660405i
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	−24.7821	+	14.3079i	−1.16954	+	0.675234i	−0.953571	−	0.301167i	$-0.902624\pi$
$449$	−24.7821	+	14.3079i	−1.16954	+	0.675234i	−0.215967	+	0.976401i	$0.569290\pi$
$450$		−	1.80301i		−	0.0849946i
$451$	−2.37841	−	4.11952i	−0.111995	−	0.193981i
$452$	−4.95660	+	8.58509i	−0.233139	+	0.403809i
$453$	15.4522	+	8.92131i	0.726006	+	0.419160i
$454$	−1.83155			−0.0859587
$455$	6.41407	−	0.648527i	0.300696	−	0.0304034i
$456$	−6.18952			−0.289851
$457$	5.49961	+	3.17520i	0.257261	+	0.148530i	0.623084	−	0.782155i	$-0.285879\pi$
$457$	5.49961	+	3.17520i	0.257261	+	0.148530i	−0.365824	+	0.930684i	$0.619213\pi$
$458$	−11.3030	+	19.5774i	−0.528155	+	0.914791i
$459$	−2.78052	−	4.81599i	−0.129783	−	0.224791i
$460$			10.9669i			0.511333i
$461$	20.9785	−	12.1119i	0.977065	−	0.564109i	0.0756821	−	0.997132i	$-0.475887\pi$
$461$	20.9785	−	12.1119i	0.977065	−	0.564109i	0.901383	+	0.433023i	$0.142553\pi$
$462$	2.74922	−	1.58726i	0.127905	−	0.0738461i
$463$		−	17.3851i		−	0.807954i	−0.914769	−	0.403977i	$-0.867628\pi$
$463$		−	17.3851i		−	0.807954i	0.914769	−	0.403977i	$-0.132372\pi$
$464$	−1.03880	−	1.79925i	−0.0482249	−	0.0835280i
$465$	−5.04097	+	8.73121i	−0.233769	+	0.404900i
$466$	−8.17439	−	4.71948i	−0.378671	−	0.218626i
$467$	−14.8537			−0.687349			−0.343675	−	0.939089i	$-0.611672\pi$
$467$	−14.8537			−0.687349			−0.343675	+	0.939089i	$0.611672\pi$
$468$	−2.10774	−	2.92531i	−0.0974305	−	0.135222i
$469$	−11.5544			−0.533532
$470$	16.2722	+	9.39473i	0.750579	+	0.433347i
$471$	2.28958	−	3.96567i	0.105498	−	0.182728i
$472$	−1.39069	−	2.40874i	−0.0640117	−	0.110871i
$473$		−	30.5980i		−	1.40690i
$474$	6.02973	−	3.48127i	0.276955	−	0.159900i
$475$	−9.66463	+	5.57988i	−0.443444	+	0.256022i
$476$			5.56103i			0.254889i
$477$	−1.80100	−	3.11942i	−0.0824621	−	0.142829i
$478$	−7.93787	+	13.7488i	−0.363070	+	0.628855i
$479$	−33.5014	−	19.3420i	−1.53072	−	0.883759i	−0.999329	−	0.0366302i	$-0.988338\pi$
$479$	−33.5014	−	19.3420i	−1.53072	−	0.883759i	−0.531387	−	0.847129i	$-0.678329\pi$
$480$	−1.78801			−0.0816113
$481$	−9.05947	+	6.52754i	−0.413076	+	0.297630i
$482$	23.9251			1.08976
$483$	−5.31181	−	3.06678i	−0.241696	−	0.139543i
$484$	0.461204	−	0.798828i	0.0209638	−	0.0363104i
$485$	−15.6355	−	27.0815i	−0.709971	−	1.22971i
$486$			1.00000i			0.0453609i
$487$	22.2780	−	12.8622i	1.00951	−	0.582843i	0.0984640	−	0.995141i	$-0.468607\pi$
$487$	22.2780	−	12.8622i	1.00951	−	0.582843i	0.911049	+	0.412298i	$0.135274\pi$
$488$	1.46254	−	0.844395i	0.0662059	−	0.0382240i
$489$		−	12.2706i		−	0.554896i
$490$	0.894007	+	1.54846i	0.0403871	+	0.0699525i
$491$	−9.17452	+	15.8907i	−0.414040	+	0.717139i	−0.995327	−	0.0965597i	$-0.969216\pi$
$491$	−9.17452	+	15.8907i	−0.414040	+	0.717139i	0.581287	+	0.813699i	$0.302549\pi$
$492$	−1.29768	−	0.749217i	−0.0585040	−	0.0337773i
$493$	−11.5536			−0.520346
$494$	−9.15749	+	20.3512i	−0.412015	+	0.915644i
$495$	5.67609			0.255121
$496$	−4.88319	−	2.81931i	−0.219262	−	0.126591i
$497$	−0.299248	+	0.518313i	−0.0134231	+	0.0232495i
$498$	−2.15114	−	3.72589i	−0.0963949	−	0.166961i
$499$			17.8096i			0.797269i	0.917110	+	0.398635i	$0.130516\pi$
$499$			17.8096i			0.797269i	−0.917110	+	0.398635i	$0.869484\pi$
$500$	−10.5342	+	6.08193i	−0.471105	+	0.271992i
$501$	14.4610	−	8.34904i	0.646068	−	0.373008i
$502$		−	20.5236i		−	0.916012i
$503$	−15.4711	−	26.7967i	−0.689823	−	1.19481i	−0.971895	−	0.235415i	$-0.924355\pi$
$503$	−15.4711	−	26.7967i	−0.689823	−	1.19481i	0.282072	−	0.959393i	$-0.408978\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	−6.30019	−	3.63741i	−0.280355	−	0.161863i
$506$	19.4711			0.865596
$507$	−12.7369	+	2.60226i	−0.565665	+	0.115570i
$508$	18.3490			0.814107
$509$	11.9583	+	6.90414i	0.530044	+	0.306021i	0.741034	−	0.671467i	$-0.234336\pi$
$509$	11.9583	+	6.90414i	0.530044	+	0.306021i	−0.210991	+	0.977488i	$0.567669\pi$
$510$	−4.97160	+	8.61106i	−0.220146	+	0.381304i
$511$	0.211987	+	0.367172i	0.00937774	+	0.0162427i
$512$		−	1.00000i		−	0.0441942i
$513$	5.36028	−	3.09476i	0.236662	−	0.136637i
$514$	−0.715933	+	0.413344i	−0.0315784	+	0.0182318i
$515$		−	32.3215i		−	1.42425i
$516$	−4.81931	−	8.34729i	−0.212158	−	0.367469i
$517$	16.6798	−	28.8903i	0.733579	−	1.27060i
$518$	−2.68202	−	1.54846i	−0.117841	−	0.0680356i
$519$	7.37731			0.323828
$520$	−2.64539	+	5.87901i	−0.116008	+	0.257812i
$521$	−11.4549			−0.501848			−0.250924	−	0.968007i	$-0.580734\pi$
$521$	−11.4549			−0.501848			−0.250924	+	0.968007i	$0.580734\pi$
$522$	1.79925	+	1.03880i	0.0787509	+	0.0454669i
$523$	−0.465198	+	0.805747i	−0.0203417	+	0.0352329i	−0.876017	−	0.482280i	$-0.839809\pi$
$523$	−0.465198	+	0.805747i	−0.0203417	+	0.0352329i	0.855675	+	0.517513i	$0.173142\pi$
$524$	2.95964	+	5.12624i	0.129292	+	0.223941i
$525$		−	1.80301i		−	0.0786897i
$526$	−17.6331	+	10.1805i	−0.768838	+	0.443889i
$527$	−27.1556	+	15.6783i	−1.18292	+	0.682957i
$528$			3.17452i			0.138153i
$529$	−7.31025	−	12.6617i	−0.317837	−	0.550510i
$530$	−3.22021	+	5.57757i	−0.139877	+	0.242274i
$531$	2.40874	+	1.39069i	0.104531	+	0.0603508i
$532$	−6.18952			−0.268350
$533$	−4.38338	+	3.15832i	−0.189865	+	0.136802i
$534$	−16.2931			−0.705071
$535$	2.38726	+	1.37828i	0.103210	+	0.0595884i
$536$	5.77720	−	10.0064i	0.249537	−	0.432211i
$537$	−9.91008	−	17.1648i	−0.427651	−	0.740714i
$538$			20.5175i			0.884572i
$539$	2.74922	−	1.58726i	0.118417	−	0.0683682i
$540$	1.54846	−	0.894007i	0.0666353	−	0.0384719i
$541$			22.7965i			0.980097i	0.871695	+	0.490048i	$0.163021\pi$
$541$			22.7965i			0.980097i	−0.871695	+	0.490048i	$0.836979\pi$
$542$	−6.09076	−	10.5495i	−0.261621	−	0.453140i
$543$	−9.16329	+	15.8713i	−0.393234	+	0.681102i
$544$	−4.81599	−	2.78052i	−0.206484	−	0.119214i
$545$	−13.1907			−0.565029
$546$	−2.10774	−	2.92531i	−0.0902032	−	0.125192i
$547$	31.6698			1.35410			0.677052	−	0.735935i	$-0.263257\pi$
$547$	31.6698			1.35410			0.677052	+	0.735935i	$0.263257\pi$
$548$	7.62363	+	4.40150i	0.325665	+	0.188023i
$549$	−0.844395	+	1.46254i	−0.0360379	+	0.0624195i
$550$	2.86185	+	4.95686i	0.122029	+	0.211361i
$551$		−	12.8593i		−	0.547824i
$552$	5.31181	−	3.06678i	0.226086	−	0.130531i
$553$	6.02973	−	3.48127i	0.256410	−	0.148039i
$554$			8.62484i			0.366434i
$555$	−2.76868	−	4.79549i	−0.117524	−	0.203557i
$556$	9.48720	−	16.4323i	0.402347	−	0.696885i
$557$	−9.38623	−	5.41914i	−0.397707	−	0.229616i	0.287787	−	0.957694i	$-0.407080\pi$
$557$	−9.38623	−	5.41914i	−0.397707	−	0.229616i	−0.685494	+	0.728078i	$0.740414\pi$
$558$	5.63862			0.238702
$559$	−34.5763	+	3.49601i	−1.46242	+	0.147865i
$560$	−1.78801			−0.0755574
$561$	15.2885	+	8.82681i	0.645480	+	0.372668i
$562$	−12.1461	+	21.0377i	−0.512353	+	0.887422i
$563$	7.73626	+	13.3996i	0.326044	+	0.564725i	0.981723	−	0.190315i	$-0.0609508\pi$
$563$	7.73626	+	13.3996i	0.326044	+	0.564725i	−0.655679	+	0.755040i	$0.727617\pi$
$564$		−	10.5086i		−	0.442491i
$565$	−15.3503	+	8.86247i	−0.645790	+	0.372847i
$566$	9.28472	−	5.36054i	0.390266	−	0.225320i
$567$			1.00000i			0.0419961i
$568$	−0.299248	−	0.518313i	−0.0125562	−	0.0217479i
$569$	16.8667	−	29.2139i	0.707088	−	1.22471i	−0.258845	−	0.965919i	$-0.583342\pi$
$569$	16.8667	−	29.2139i	0.707088	−	1.22471i	0.965933	−	0.258793i	$-0.0833249\pi$
$570$	−9.58425	−	5.53347i	−0.401440	−	0.231772i
$571$	−43.6140			−1.82519			−0.912594	−	0.408868i	$-0.865924\pi$
$571$	−43.6140			−1.82519			−0.912594	+	0.408868i	$0.865924\pi$
$572$	10.4379	+	4.69676i	0.436429	+	0.196381i
$573$	15.0304			0.627902
$574$	−1.29768	−	0.749217i	−0.0541642	−	0.0312717i
$575$	5.52943	−	9.57725i	0.230593	−	0.399399i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	10.8368i		−	0.451143i	−0.974227	−	0.225571i	$-0.927575\pi$
$577$		−	10.8368i		−	0.451143i	0.974227	−	0.225571i	$-0.0724249\pi$
$578$	−12.0595	+	6.96254i	−0.501608	+	0.289603i
$579$	−4.72408	+	2.72745i	−0.196326	+	0.113349i
$580$		−	3.71476i		−	0.154247i
$581$	−2.15114	−	3.72589i	−0.0892444	−	0.154576i
$582$	−8.74462	+	15.1461i	−0.362476	+	0.627827i
$583$	9.90268	+	5.71731i	0.410127	+	0.236787i
$584$	−0.423973			−0.0175441
$585$	−0.648527	−	6.41407i	−0.0268133	−	0.265189i
$586$	−21.4278			−0.885176
$587$	22.5632	+	13.0269i	0.931284	+	0.537677i	0.887217	−	0.461352i	$-0.152635\pi$
$587$	22.5632	+	13.0269i	0.931284	+	0.537677i	0.0440666	+	0.999029i	$0.485969\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$	−17.4502	−	30.2246i	−0.719022	−	1.24538i
$590$		−	4.97314i		−	0.204741i
$591$	−6.60751	+	3.81485i	−0.271797	+	0.156922i
$592$	2.68202	−	1.54846i	0.110230	−	0.0636415i
$593$			1.68393i			0.0691509i	0.999402	+	0.0345754i	$0.0110079\pi$
$593$			1.68393i			0.0691509i	−0.999402	+	0.0345754i	$0.988992\pi$
$594$	−1.58726	−	2.74922i	−0.0651261	−	0.112802i
$595$	−4.97160	+	8.61106i	−0.203816	+	0.353019i
$596$	12.0919	+	6.98127i	0.495304	+	0.285964i
$597$	5.99023			0.245164
$598$	−2.22469	−	22.0027i	−0.0909743	−	0.899756i
$599$	−6.54081			−0.267250			−0.133625	−	0.991032i	$-0.542662\pi$
$599$	−6.54081			−0.267250			−0.133625	+	0.991032i	$0.542662\pi$
$600$	1.56145	+	0.901504i	0.0637460	+	0.0368038i
$601$	−19.2387	+	33.3224i	−0.784763	+	1.35925i	0.144377	+	0.989523i	$0.453882\pi$
$601$	−19.2387	+	33.3224i	−0.784763	+	1.35925i	−0.929140	+	0.369727i	$0.879451\pi$
$602$	−4.81931	−	8.34729i	−0.196420	−	0.340210i
$603$			11.5544i			0.470531i
$604$	−15.4522	+	8.92131i	−0.628740	+	0.363003i
$605$	1.42832	−	0.824638i	0.0580693	−	0.0335263i
$606$			4.06866i			0.165278i
$607$	4.71797	+	8.17176i	0.191496	+	0.331682i	0.945746	−	0.324906i	$-0.105333\pi$
$607$	4.71797	+	8.17176i	0.191496	+	0.331682i	−0.754250	+	0.656587i	$0.771999\pi$
$608$	3.09476	−	5.36028i	0.125509	−	0.217388i
$609$	1.79925	+	1.03880i	0.0729092	+	0.0420941i
$610$	3.01958			0.122259
$611$	−34.5523	−	15.5476i	−1.39784	−	0.628989i
$612$	5.56103			0.224791
$613$	−22.0191	−	12.7127i	−0.889342	−	0.513462i	−0.0156146	−	0.999878i	$-0.504970\pi$
$613$	−22.0191	−	12.7127i	−0.889342	−	0.513462i	−0.873727	+	0.486416i	$0.838304\pi$
$614$	3.79682	−	6.57628i	0.153227	−	0.265397i
$615$	−1.33961	−	2.32027i	−0.0540183	−	0.0935624i
$616$			3.17452i			0.127905i
$617$	24.8545	−	14.3497i	1.00060	−	0.577699i	0.0921772	−	0.995743i	$-0.470617\pi$
$617$	24.8545	−	14.3497i	1.00060	−	0.577699i	0.908427	+	0.418044i	$0.137284\pi$
$618$	−15.6549	+	9.03838i	−0.629734	+	0.363577i
$619$			9.61494i			0.386457i	0.981154	+	0.193229i	$0.0618959\pi$
$619$			9.61494i			0.386457i	−0.981154	+	0.193229i	$0.938104\pi$
$620$	−5.04097	−	8.73121i	−0.202450	−	0.350654i
$621$	−3.06678	+	5.31181i	−0.123066	+	0.213156i
$622$	22.2010	+	12.8177i	0.890178	+	0.513945i
$623$	−16.2931			−0.652769
$624$	3.58726	−	0.362708i	0.143605	−	0.0145199i
$625$	−12.7341			−0.509365
$626$	−1.48357	−	0.856542i	−0.0592956	−	0.0342343i
$627$	−9.82438	+	17.0163i	−0.392348	+	0.679567i
$628$	2.28958	+	3.96567i	0.0913642	+	0.158247i
$629$		−	17.2221i		−	0.686691i
$630$	1.54846	−	0.894007i	0.0616923	−	0.0356181i
$631$	29.9445	−	17.2885i	1.19207	−	0.688244i	0.233297	−	0.972406i	$-0.425049\pi$
$631$	29.9445	−	17.2885i	1.19207	−	0.688244i	0.958776	+	0.284162i	$0.0917153\pi$
$632$			6.96254i			0.276955i
$633$	−1.38651	−	2.40150i	−0.0551088	−	0.0954512i
$634$	−16.6049	+	28.7605i	−0.659465	+	1.14223i
$635$	28.4129	+	16.4042i	1.12753	+	0.650980i
$636$	3.60200			0.142829
$637$	−2.10774	−	2.92531i	−0.0835119	−	0.115905i
$638$	−6.59536			−0.261113
$639$	0.518313	+	0.299248i	0.0205041	+	0.0118381i
$640$	0.894007	−	1.54846i	0.0353387	−	0.0612085i
$641$	3.25646	+	5.64035i	0.128622	+	0.222780i	0.923143	−	0.384457i	$-0.125611\pi$
$641$	3.25646	+	5.64035i	0.128622	+	0.222780i	−0.794521	+	0.607237i	$0.792278\pi$
$642$		−	1.54169i		−	0.0608458i
$643$	−21.8991	+	12.6435i	−0.863617	+	0.498609i	−0.865222	−	0.501389i	$-0.832822\pi$
$643$	−21.8991	+	12.6435i	−0.863617	+	0.498609i	0.00160504	+	0.999999i	$0.499489\pi$
$644$	5.31181	−	3.06678i	0.209315	−	0.120848i
$645$		−	17.2340i		−	0.678588i
$646$	−17.2101	−	29.8087i	−0.677120	−	1.17281i
$647$	5.95794	−	10.3194i	0.234231	−	0.405699i	−0.724818	−	0.688940i	$-0.758076\pi$
$647$	5.95794	−	10.3194i	0.234231	−	0.405699i	0.959049	+	0.283241i	$0.0914096\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−8.82955			−0.346590
$650$	5.27435	−	3.80028i	0.206877	−	0.149059i
$651$	5.63862			0.220995
$652$	10.6267	+	6.13531i	0.416172	+	0.240277i
$653$	−20.7508	+	35.9415i	−0.812043	+	1.40650i	0.0993891	+	0.995049i	$0.468311\pi$
$653$	−20.7508	+	35.9415i	−0.812043	+	1.40650i	−0.911432	+	0.411451i	$0.865022\pi$
$654$	3.68865	+	6.38894i	0.144238	+	0.249827i
$655$			10.5837i			0.413541i
$656$	1.29768	−	0.749217i	0.0506660	−	0.0292520i
$657$	0.367172	−	0.211987i	0.0143247	−	0.00827039i
$658$		−	10.5086i		−	0.409667i
$659$	−7.86778	−	13.6274i	−0.306485	−	0.530848i	0.671106	−	0.741362i	$-0.265820\pi$
$659$	−7.86778	−	13.6274i	−0.306485	−	0.530848i	−0.977591	+	0.210514i	$0.932486\pi$
$660$	−2.83804	+	4.91564i	−0.110471	+	0.191341i
$661$	−22.6071	−	13.0522i	−0.879315	−	0.507673i	−0.00888248	−	0.999961i	$-0.502827\pi$
$661$	−22.6071	−	13.0522i	−0.879315	−	0.507673i	−0.870432	+	0.492288i	$0.836161\pi$
$662$	4.95987			0.192771
$663$	8.22764	−	18.2847i	0.319535	−	0.710121i
$664$	4.30228			0.166961
$665$	−9.58425	−	5.53347i	−0.371661	−	0.214579i
$666$	−1.54846	+	2.68202i	−0.0600018	+	0.103926i
$667$	6.37151	+	11.0358i	0.246706	+	0.427307i
$668$			16.6981i			0.646068i
$669$	19.5163	−	11.2677i	0.754542	−	0.435635i
$670$	17.8916	−	10.3297i	0.691212	−	0.399071i
$671$		−	5.36110i		−	0.206963i
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	0.620853	−	1.07535i	0.0239321	−	0.0414516i	−0.853811	−	0.520583i	$-0.825715\pi$
$673$	0.620853	−	1.07535i	0.0239321	−	0.0414516i	0.877743	+	0.479131i	$0.159048\pi$
$674$	20.4532	+	11.8087i	0.787829	+	0.454853i
$675$	−1.80301			−0.0693978
$676$	4.11482	−	12.3316i	0.158262	−	0.474292i
$677$	29.2845			1.12550			0.562748	−	0.826629i	$-0.309744\pi$
$677$	29.2845			1.12550			0.562748	+	0.826629i	$0.309744\pi$
$678$	8.58509	+	4.95660i	0.329708	+	0.190357i
$679$	−8.74462	+	15.1461i	−0.335588	+	0.581255i
$680$	−4.97160	−	8.61106i	−0.190652	−	0.330219i
$681$			1.83155i			0.0701850i
$682$	−15.5018	+	8.94997i	−0.593595	+	0.342712i
$683$	−37.0486	+	21.3900i	−1.41762	+	0.818466i	−0.996090	−	0.0883461i	$-0.971842\pi$
$683$	−37.0486	+	21.3900i	−1.41762	+	0.818466i	−0.421535	+	0.906812i	$0.638509\pi$
$684$			6.18952i			0.236662i
$685$	7.86995	+	13.6311i	0.300695	+	0.520819i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	19.5774	+	11.3030i	0.746924	+	0.431237i
$688$	9.63862			0.367469
$689$	5.32922	−	11.8434i	0.203027	−	0.451198i
$690$	10.9669			0.417502
$691$	−16.3649	−	9.44827i	−0.622549	−	0.359429i	0.155312	−	0.987866i	$-0.450362\pi$
$691$	−16.3649	−	9.44827i	−0.622549	−	0.359429i	−0.777861	+	0.628437i	$0.783695\pi$
$692$	−3.68865	+	6.38894i	−0.140222	+	0.242871i
$693$	−1.58726	−	2.74922i	−0.0602951	−	0.104434i
$694$			7.16967i			0.272157i
$695$	29.3812	−	16.9632i	1.11449	−	0.643452i
$696$	−1.79925	+	1.03880i	−0.0682003	+	0.0393755i
$697$		−	8.33284i		−	0.315629i
$698$	6.18662	+	10.7155i	0.234167	+	0.405589i
$699$	−4.71948	+	8.17439i	−0.178507	+	0.309184i
$700$	1.56145	+	0.901504i	0.0590173	+	0.0340737i
$701$	−3.35161			−0.126589			−0.0632943	−	0.997995i	$-0.520161\pi$
$701$	−3.35161			−0.126589			−0.0632943	+	0.997995i	$0.520161\pi$
$702$	−2.92531	+	2.10774i	−0.110409	+	0.0795517i
$703$	19.1685			0.722954
$704$	−2.74922	−	1.58726i	−0.103615	−	0.0598222i
$705$	9.39473	−	16.2722i	0.353826	−	0.612845i
$706$	13.1069	+	22.7018i	0.493285	+	0.854395i
$707$			4.06866i			0.153018i
$708$	−2.40874	+	1.39069i	−0.0905262	+	0.0522653i
$709$	31.8468	−	18.3867i	1.19603	−	0.690529i	0.236363	−	0.971665i	$-0.424045\pi$
$709$	31.8468	−	18.3867i	1.19603	−	0.690529i	0.959668	+	0.281136i	$0.0907113\pi$
$710$		−	1.07012i		−	0.0401608i
$711$	−3.48127	−	6.02973i	−0.130558	−	0.226133i
$712$	8.14654	−	14.1102i	0.305305	−	0.528803i
$713$	29.9513	+	17.2924i	1.12169	+	0.647606i
$714$	5.56103			0.208116
$715$	11.9637	+	16.6043i	0.447419	+	0.620965i
$716$	19.8202			0.740714
$717$	13.7488	+	7.93787i	0.513458	+	0.296445i
$718$	1.80978	−	3.13463i	0.0675404	−	0.116983i
$719$	8.08486	+	14.0034i	0.301514	+	0.522238i	0.976479	−	0.215612i	$-0.0691746\pi$
$719$	8.08486	+	14.0034i	0.301514	+	0.522238i	−0.674965	+	0.737850i	$0.735841\pi$
$720$			1.78801i			0.0666353i
$721$	−15.6549	+	9.03838i	−0.583020	+	0.336607i
$722$	16.7231	−	9.65506i	0.622368	−	0.359324i
$723$		−	23.9251i		−	0.889783i
$724$	−9.16329	−	15.8713i	−0.340551	−	0.589851i
$725$	−1.87296	+	3.24406i	−0.0695599	+	0.120481i
$726$	−0.798828	−	0.461204i	−0.0296473	−	0.0171169i
$727$	27.2522			1.01073			0.505363	−	0.862907i	$-0.331358\pi$
$727$	27.2522			1.01073			0.505363	+	0.862907i	$0.331358\pi$
$728$	3.58726	−	0.362708i	0.132953	−	0.0134429i
$729$	1.00000			0.0370370
$730$	−0.656508	−	0.379035i	−0.0242984	−	0.0140287i
$731$	26.8003	−	46.4196i	0.991247	−	1.71689i
$732$	−0.844395	−	1.46254i	−0.0312098	−	0.0540569i
$733$			39.6734i			1.46537i	0.680567	+	0.732686i	$0.261733\pi$
$733$			39.6734i			1.46537i	−0.680567	+	0.732686i	$0.738267\pi$
$734$	6.98440	−	4.03245i	0.257799	−	0.148840i
$735$	1.54846	−	0.894007i	0.0571160	−	0.0329759i
$736$			6.13356i			0.226086i
$737$	−18.3398	−	31.7655i	−0.675557	−	1.17010i
$738$	−0.749217	+	1.29768i	−0.0275791	+	0.0477683i
$739$	−22.0125	−	12.7089i	−0.809742	−	0.467505i	0.0371244	−	0.999311i	$-0.488180\pi$
$739$	−22.0125	−	12.7089i	−0.809742	−	0.467505i	−0.846866	+	0.531806i	$0.821514\pi$
$740$	5.53735			0.203557
$741$	20.3512	+	9.15749i	0.747621	+	0.336409i
$742$	3.60200			0.132234
$743$	−21.5143	−	12.4213i	−0.789285	−	0.455694i	0.0504260	−	0.998728i	$-0.483942\pi$
$743$	−21.5143	−	12.4213i	−0.789285	−	0.455694i	−0.839711	+	0.543034i	$0.817275\pi$
$744$	−2.81931	+	4.88319i	−0.103361	+	0.179026i
$745$	12.4826	+	21.6205i	0.457327	+	0.792114i
$746$		−	29.1702i		−	1.06800i
$747$	−3.72589	+	2.15114i	−0.136323	+	0.0787061i
$748$	−15.2885	+	8.82681i	−0.559002	+	0.322740i
$749$		−	1.54169i		−	0.0563323i
$750$	6.08193	+	10.5342i	0.222081	+	0.384655i
$751$	−22.7211	+	39.3540i	−0.829103	+	1.43605i	0.0696398	+	0.997572i	$0.477815\pi$
$751$	−22.7211	+	39.3540i	−0.829103	+	1.43605i	−0.898743	+	0.438476i	$0.855518\pi$
$752$	9.10069	+	5.25429i	0.331868	+	0.191604i
$753$	−20.5236			−0.747920
$754$	0.753559	+	7.45287i	0.0274430	+	0.271417i
$755$	−31.9028			−1.16106
$756$	−0.866025	−	0.500000i	−0.0314970	−	0.0181848i
$757$	−3.20643	+	5.55369i	−0.116540	+	0.201852i	−0.918394	−	0.395667i	$-0.870514\pi$
$757$	−3.20643	+	5.55369i	−0.116540	+	0.201852i	0.801855	+	0.597519i	$0.203847\pi$
$758$	−13.4983	−	23.3797i	−0.490280	−	0.849190i
$759$		−	19.4711i		−	0.706756i
$760$	9.58425	−	5.53347i	0.347657	−	0.200720i
$761$	27.8313	−	16.0684i	1.00888	−	0.582479i	0.0980185	−	0.995185i	$-0.468750\pi$
$761$	27.8313	−	16.0684i	1.00888	−	0.582479i	0.910864	+	0.412706i	$0.135416\pi$
$762$		−	18.3490i		−	0.664716i
$763$	3.68865	+	6.38894i	0.133538	+	0.231295i
$764$	−7.51518	+	13.0167i	−0.271890	+	0.470927i
$765$	8.61106	+	4.97160i	0.311334	+	0.179749i
$766$	26.1146			0.943558
$767$	1.00883	+	9.97753i	0.0364267	+	0.360268i
$768$	−1.00000			−0.0360844
$769$	−33.7551	−	19.4885i	−1.21724	−	0.702774i	−0.252914	−	0.967489i	$-0.581389\pi$
$769$	−33.7551	−	19.4885i	−1.21724	−	0.702774i	−0.964327	+	0.264714i	$0.914722\pi$
$770$	−2.83804	+	4.91564i	−0.102276	+	0.177147i
$771$	0.413344	+	0.715933i	0.0148862	+

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.894007 + 1.54846i) q^{10} +(2.74922 + 1.58726i) q^{11} +1.00000 q^{12} +(1.47952 - 3.28801i) q^{13} +1.00000 q^{14} +(1.54846 + 0.894007i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.78052 + 4.81599i) q^{17} -1.00000i q^{18} +(-5.36028 + 3.09476i) q^{19} +(-1.54846 + 0.894007i) q^{20} -1.00000i q^{21} +(1.58726 + 2.74922i) q^{22} +(3.06678 - 5.31181i) q^{23} +(0.866025 + 0.500000i) q^{24} +1.80301 q^{25} +(2.92531 - 2.10774i) q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(-1.03880 + 1.79925i) q^{29} +(0.894007 + 1.54846i) q^{30} +5.63862i q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.74922 - 1.58726i) q^{33} +5.56103i q^{34} +(0.894007 + 1.54846i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.68202 - 1.54846i) q^{37} -6.18952 q^{38} +(-2.10774 - 2.92531i) q^{39} -1.78801 q^{40} +(-1.29768 - 0.749217i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-4.81931 - 8.34729i) q^{43} +3.17452i q^{44} +(1.54846 - 0.894007i) q^{45} +(5.31181 - 3.06678i) q^{46} -10.5086i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(1.56145 + 0.901504i) q^{50} +5.56103 q^{51} +(3.58726 - 0.362708i) q^{52} +3.60200 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.83804 + 4.91564i) q^{55} +(0.500000 + 0.866025i) q^{56} +6.18952i q^{57} +(-1.79925 + 1.03880i) q^{58} +(-2.40874 + 1.39069i) q^{59} +1.78801i q^{60} +(-0.844395 - 1.46254i) q^{61} +(-2.81931 + 4.88319i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(5.87901 + 2.64539i) q^{65} +3.17452 q^{66} +(-10.0064 - 5.77720i) q^{67} +(-2.78052 + 4.81599i) q^{68} +(-3.06678 - 5.31181i) q^{69} +1.78801i q^{70} +(-0.518313 + 0.299248i) q^{71} +(0.866025 - 0.500000i) q^{72} +0.423973i q^{73} +(-1.54846 - 2.68202i) q^{74} +(0.901504 - 1.56145i) q^{75} +(-5.36028 - 3.09476i) q^{76} +3.17452 q^{77} +(-0.362708 - 3.58726i) q^{78} +6.96254 q^{79} +(-1.54846 - 0.894007i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.749217 - 1.29768i) q^{82} -4.30228i q^{83} +(0.866025 - 0.500000i) q^{84} +(-8.61106 + 4.97160i) q^{85} -9.63862i q^{86} +(1.03880 + 1.79925i) q^{87} +(-1.58726 + 2.74922i) q^{88} +(-14.1102 - 8.14654i) q^{89} +1.78801 q^{90} +(-0.362708 - 3.58726i) q^{91} +6.13356 q^{92} +(4.88319 + 2.81931i) q^{93} +(5.25429 - 9.10069i) q^{94} +(-5.53347 - 9.58425i) q^{95} +1.00000i q^{96} +(-15.1461 + 8.74462i) q^{97} +(0.866025 - 0.500000i) q^{98} -3.17452i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{10} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 8 q^{14} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 12 q^{19} - 6 q^{20} - 4 q^{22} + 8 q^{23} - 24 q^{25} + 6 q^{26} - 8 q^{27} + 2 q^{29} - 6 q^{30} + 6 q^{33} - 6 q^{35} + 4 q^{36} + 18 q^{37} - 4 q^{38} + 12 q^{40} + 12 q^{41} + 4 q^{42} - 8 q^{43} + 6 q^{45} + 18 q^{46} + 4 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} + 12 q^{52} - 12 q^{53} - 22 q^{55} + 4 q^{56} - 24 q^{58} + 18 q^{59} - 8 q^{61} + 8 q^{62} - 8 q^{64} + 46 q^{65} - 8 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} + 6 q^{71} - 6 q^{74} - 12 q^{75} - 12 q^{76} - 8 q^{77} + 6 q^{78} - 4 q^{79} - 6 q^{80} - 4 q^{81} + 10 q^{82} - 54 q^{85} - 2 q^{87} + 4 q^{88} - 18 q^{89} - 12 q^{90} + 6 q^{91} + 16 q^{92} + 30 q^{93} - 2 q^{94} - 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^10 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 8 * q^14 + 6 * q^15 - 4 * q^16 + 2 * q^17 - 12 * q^19 - 6 * q^20 - 4 * q^22 + 8 * q^23 - 24 * q^25 + 6 * q^26 - 8 * q^27 + 2 * q^29 - 6 * q^30 + 6 * q^33 - 6 * q^35 + 4 * q^36 + 18 * q^37 - 4 * q^38 + 12 * q^40 + 12 * q^41 + 4 * q^42 - 8 * q^43 + 6 * q^45 + 18 * q^46 + 4 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 + 12 * q^52 - 12 * q^53 - 22 * q^55 + 4 * q^56 - 24 * q^58 + 18 * q^59 - 8 * q^61 + 8 * q^62 - 8 * q^64 + 46 * q^65 - 8 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 + 6 * q^71 - 6 * q^74 - 12 * q^75 - 12 * q^76 - 8 * q^77 + 6 * q^78 - 4 * q^79 - 6 * q^80 - 4 * q^81 + 10 * q^82 - 54 * q^85 - 2 * q^87 + 4 * q^88 - 18 * q^89 - 12 * q^90 + 6 * q^91 + 16 * q^92 + 30 * q^93 - 2 * q^94 - 50 * q^95 - 54 * q^97

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