LMFDB - Embedded newform 546.2.s.e.127.3

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			127.3
Root			$1.72124 - 0.193255i$ of defining polynomial
Character	$\chi$	$=$	546.127
Dual form			546.2.s.e.43.4

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	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	$-0.869075\pi$
$5$		−	1.78801i		−	0.799624i	0.916597	−	0.399812i	$-0.130925\pi$
$6$	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	−0.0245627	−	0.999698i	$-0.507819\pi$
$11$	2.74922	−	1.58726i	0.828920	−	0.478577i	0.853483	+	0.521121i	$0.174486\pi$
$12$	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	−0.302277	−	0.953220i	$-0.597747\pi$
$17$	2.78052	−	4.81599i	0.674374	−	1.16805i	0.976651	−	0.214830i	$-0.0689198\pi$
$18$			1.00000i			0.235702i
$19$	−5.36028	−	3.09476i	−1.22973	−	0.709986i	−0.262758	−	0.964862i	$-0.584632\pi$
$19$	−5.36028	−	3.09476i	−1.22973	−	0.709986i	−0.966974	+	0.254875i	$0.917966\pi$
$20$	−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	0.985550	+	0.169386i	$0.0541784\pi$
$23$	3.06678	+	5.31181i	0.639467	+	1.10759i	−0.346083	+	0.938204i	$0.612488\pi$
$24$	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	0.753310	−	0.657665i	$-0.228456\pi$
$29$	−1.03880	−	1.79925i	−0.192900	−	0.334112i	−0.946210	+	0.323553i	$0.895123\pi$
$30$	0.894007	−	1.54846i	0.163223	−	0.282710i
$31$		−	5.63862i		−	1.01273i	−0.862320	−	0.506363i	$-0.830989\pi$
$31$		−	5.63862i		−	1.01273i	0.862320	−	0.506363i	$-0.169011\pi$
$32$	−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	−0.703988	−	0.710211i	$-0.748599\pi$
$37$	−2.68202	+	1.54846i	−0.440921	+	0.254566i	0.263067	+	0.964778i	$0.415266\pi$
$38$	−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	−0.597897	−	0.801573i	$-0.703997\pi$
$41$	−1.29768	+	0.749217i	−0.202664	+	0.117008i	0.395234	+	0.918581i	$0.370664\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	−4.81931	+	8.34729i	−0.734938	+	1.27295i	0.219812	+	0.975542i	$0.429456\pi$
$43$	−4.81931	+	8.34729i	−0.734938	+	1.27295i	−0.954750	+	0.297408i	$0.903878\pi$
$44$		−	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	$0.277962\pi$
$47$			10.5086i			1.53283i	−0.642344	+	0.766416i	$0.722038\pi$
$48$	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	0.334941	−	0.942239i	$-0.391284\pi$
$59$	−2.40874	−	1.39069i	−0.313592	−	0.181052i	−0.648533	+	0.761187i	$0.724617\pi$
$60$		−	1.78801i		−	0.230832i
$61$	−0.844395	+	1.46254i	−0.108114	+	0.187259i	−0.915006	−	0.403440i	$-0.867814\pi$
$61$	−0.844395	+	1.46254i	−0.108114	+	0.187259i	0.806892	+	0.590699i	$0.201148\pi$
$62$	−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	−0.965445	−	0.260606i	$-0.916078\pi$
$67$	−10.0064	+	5.77720i	−1.22248	+	0.705797i	−0.257031	+	0.966403i	$0.582744\pi$
$68$	−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	0.468928	−	0.883236i	$-0.344640\pi$
$71$	−0.518313	−	0.299248i	−0.0615124	−	0.0355142i	−0.530441	+	0.847722i	$0.677974\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	0.423973i		−	0.0496223i	−0.999692	−	0.0248112i	$-0.992102\pi$
$73$		−	0.423973i		−	0.0496223i	0.999692	−	0.0248112i	$-0.00789845\pi$
$74$	−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	$0.0758753\pi$
$83$			4.30228i			0.472237i	−0.971724	+	0.236118i	$0.924125\pi$
$84$	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	−0.999988	−	0.00496618i	$-0.998419\pi$
$89$	−14.1102	+	8.14654i	−1.49568	+	0.863532i	−0.495693	+	0.868498i	$0.665086\pi$
$90$	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	−0.998964	−	0.0455062i	$-0.985510\pi$
$97$	−15.1461	−	8.74462i	−1.53786	−	0.887881i	−0.538892	−	0.842375i	$-0.681157\pi$
$98$	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	0.746885	−	0.664953i	$-0.231548\pi$
$101$	−2.03433	−	3.52357i	−0.202424	−	0.350608i	−0.949309	+	0.314345i	$0.898215\pi$
$102$	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	0.900878	−	0.434073i	$-0.142924\pi$
$107$	0.770847	+	1.33515i	0.0745206	+	0.129073i	−0.826357	+	0.563146i	$0.809591\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		−	7.37731i		−	0.706618i	−0.935507	−	0.353309i	$-0.885056\pi$
$109$		−	7.37731i		−	0.706618i	0.935507	−	0.353309i	$-0.114944\pi$
$110$	−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	−0.532980	−	0.846128i	$-0.678928\pi$
$113$	4.95660	−	8.58509i	0.466278	−	0.807617i	0.999258	+	0.0385104i	$0.0122613\pi$
$114$	−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	0.909967	+	0.414680i	$0.136107\pi$
$127$	9.17452	+	15.8907i	0.814107	+	1.41008i	−0.0958600	+	0.995395i	$0.530560\pi$
$128$	−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	0.788966	−	0.614437i	$-0.210617\pi$
$137$	7.62363	+	4.40150i	0.651331	+	0.376046i	−0.137635	+	0.990483i	$0.543950\pi$
$138$			6.13356i			0.522123i
$139$	−9.48720	+	16.4323i	−0.804694	+	1.39377i	0.111804	+	0.993730i	$0.464337\pi$
$139$	−9.48720	+	16.4323i	−0.804694	+	1.39377i	−0.916498	+	0.400040i	$0.868996\pi$
$140$	−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	0.905456	−	0.424440i	$-0.139529\pi$
$149$	12.0919	+	6.98127i	0.990608	+	0.571928i	0.0851520	+	0.996368i	$0.472862\pi$
$150$	1.56145	+	0.901504i	0.127492	+	0.0736075i
$151$		−	17.8426i		−	1.45201i	−0.687688	−	0.726006i	$-0.741374\pi$
$151$		−	17.8426i		−	1.45201i	0.687688	−	0.726006i	$-0.258626\pi$
$152$	−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	0.854655	−	0.519197i	$-0.173769\pi$
$163$	10.6267	+	6.13531i	0.832344	+	0.480554i	−0.0223103	+	0.999751i	$0.507102\pi$
$164$			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	0.177872	−	0.984054i	$-0.443079\pi$
$167$	14.4610	−	8.34904i	1.11902	−	0.646068i	0.941151	+	0.337985i	$0.109745\pi$
$168$	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	−0.691051	−	0.722806i	$-0.742852\pi$
$173$	3.68865	−	6.38894i	0.280443	−	0.485742i	0.971494	+	0.237064i	$0.0761852\pi$
$174$		−	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	0.952171	+	0.305567i	$0.0988459\pi$
$179$	9.91008	+	17.1648i	0.740714	+	1.28295i	−0.211457	+	0.977387i	$0.567821\pi$
$180$	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	−0.454903	−	0.890541i	$-0.650326\pi$
$191$	7.51518	−	13.0167i	0.543779	−	0.941854i	0.998683	−	0.0513127i	$-0.0163405\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−4.72408	+	2.72745i	−0.340047	+	0.196326i	−0.660293	−	0.751008i	$-0.729568\pi$
$193$	−4.72408	+	2.72745i	−0.340047	+	0.196326i	0.320246	+	0.947334i	$0.396234\pi$
$194$	−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	−0.716560	−	0.697525i	$-0.754284\pi$
$197$	−6.60751	+	3.81485i	−0.470766	+	0.271797i	0.245795	+	0.969322i	$0.420951\pi$
$198$	1.58726	+	2.74922i	0.112802	+	0.195378i
$199$	2.99512	−	5.18769i	0.212318	−	0.367746i	−0.740121	−	0.672473i	$-0.765232\pi$
$199$	2.99512	−	5.18769i	0.212318	−	0.367746i	0.952440	+	0.304727i	$0.0985653\pi$
$200$		−	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	0.909797	−	0.415054i	$-0.136237\pi$
$211$	1.38651	+	2.40150i	0.0954512	+	0.165326i	−0.814346	+	0.580380i	$0.802904\pi$
$212$	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	0.325327	−	0.945602i	$-0.394526\pi$
$223$	19.5163	−	11.2677i	1.30691	−	0.754542i	0.981578	+	0.191060i	$0.0611924\pi$
$224$	−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	0.446437	−	0.894815i	$-0.352693\pi$
$227$	−1.58616	−	0.915773i	−0.105277	−	0.0607820i	−0.551714	+	0.834033i	$0.686026\pi$
$228$	−5.36028	−	3.09476i	−0.354993	−	0.204955i
$229$		−	22.6060i		−	1.49385i	−0.664910	−	0.746924i	$-0.731530\pi$
$229$		−	22.6060i		−	1.49385i	0.664910	−	0.746924i	$-0.268470\pi$
$230$	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	$-0.828364\pi$
$239$		−	15.8757i		−	1.02692i	0.858115	−	0.513458i	$-0.171636\pi$
$240$	−1.54846	−	0.894007i	−0.0999530	−	0.0577079i
$241$	20.7197	+	11.9625i	1.33467	+	0.770575i	0.986012	−	0.166674i	$-0.0533027\pi$
$241$	20.7197	+	11.9625i	1.33467	+	0.770575i	0.348662	+	0.937248i	$0.386636\pi$
$242$			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	0.335949	+	0.941880i	$0.390943\pi$
$251$	−10.2618	+	17.7739i	−0.647718	+	1.12188i	−0.983667	+	0.180000i	$0.942390\pi$
$252$			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	0.852846	−	0.522163i	$-0.174875\pi$
$257$	−0.413344	−	0.715933i	−0.0257837	−	0.0446587i	−0.878629	+	0.477504i	$0.841541\pi$
$258$	−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	−0.988001	−	0.154445i	$-0.950641\pi$
$263$	−10.1805	−	17.6331i	−0.627754	−	1.08730i	0.360248	−	0.932857i	$-0.382692\pi$
$264$	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	−0.362959	−	0.931805i	$-0.618234\pi$
$269$	10.2587	−	17.7687i	0.625487	−	1.08338i	0.988446	−	0.151570i	$-0.0484330\pi$
$270$	0.894007	+	1.54846i	0.0544075	+	0.0942366i
$271$	−10.5495	+	6.09076i	−0.640837	+	0.369988i	−0.784937	−	0.619576i	$-0.787305\pi$
$271$	−10.5495	+	6.09076i	−0.640837	+	0.369988i	0.144100	+	0.989563i	$0.453971\pi$
$272$	−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	−0.706895	−	0.707318i	$-0.749905\pi$
$277$	4.31242	−	7.46933i	0.259108	−	0.448789i	0.966003	+	0.258530i	$0.0832380\pi$
$278$			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	$-0.742035\pi$
$281$		−	24.2922i		−	1.44915i	0.689194	−	0.724577i	$-0.257965\pi$
$282$	−5.25429	+	9.10069i	−0.312888	+	0.541938i
$283$	5.36054	+	9.28472i	0.318651	+	0.551919i	0.980207	−	0.197976i	$-0.0634369\pi$
$283$	5.36054	+	9.28472i	0.318651	+	0.551919i	−0.661556	+	0.749896i	$0.730104\pi$
$284$	−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	−0.152112	−	0.988363i	$-0.548607\pi$
$293$	−18.5571	−	10.7139i	−1.08412	−	0.625914i	−0.932004	+	0.362449i	$0.881941\pi$
$294$			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	$0.0695280\pi$
$307$			7.59364i			0.433392i	−0.976239	+	0.216696i	$0.930472\pi$
$308$	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	$-0.617513\pi$
$317$		−	33.2098i		−	1.86525i	0.360850	−	0.932624i	$-0.382487\pi$
$318$	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	0.613381	−	0.789787i	$-0.289809\pi$
$331$	4.29537	+	2.47994i	0.236095	+	0.136310i	−0.377286	+	0.926097i	$0.623142\pi$
$332$	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	−0.753616	−	0.657315i	$-0.771692\pi$
$347$	3.58483	−	6.20911i	0.192444	−	0.333323i	0.946060	+	0.323993i	$0.105025\pi$
$348$	−1.03880	−	1.79925i	−0.0556853	−	0.0964498i
$349$	10.7155	−	6.18662i	0.573590	−	0.331162i	−0.184992	−	0.982740i	$-0.559226\pi$
$349$	10.7155	−	6.18662i	0.573590	−	0.331162i	0.758582	+	0.651578i	$0.225893\pi$
$350$	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	0.245909	−	0.969293i	$-0.420913\pi$
$353$	22.7018	−	13.1069i	1.20830	−	0.697610i	0.962387	+	0.271683i	$0.0875801\pi$
$354$	−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	$0.0304503\pi$
$359$			3.61956i			0.191033i	−0.995428	+	0.0955165i	$0.969550\pi$
$360$	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	0.951869	−	0.306506i	$-0.0991601\pi$
$367$	4.03245	+	6.98440i	0.210492	+	0.364583i	−0.741377	+	0.671089i	$0.765827\pi$
$368$	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	0.190094	+	0.981766i	$0.439121\pi$
$373$	−14.5851	+	25.2621i	−0.755187	+	1.30802i	−0.945281	+	0.326257i	$0.894213\pi$
$374$	−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	−0.960763	−	0.277369i	$-0.910538\pi$
$379$	−23.3797	+	13.4983i	−1.20094	+	0.693361i	−0.240173	+	0.970730i	$0.577204\pi$
$380$	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	0.950250	−	0.311488i	$-0.100827\pi$
$383$	22.6159	+	13.0573i	1.15562	+	0.667197i	0.205368	+	0.978685i	$0.434161\pi$
$384$	−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	0.486772	−	0.873529i	$-0.338174\pi$
$397$	−0.524826	−	0.303008i	−0.0263403	−	0.0152076i	−0.513112	+	0.858321i	$0.671508\pi$
$398$		−	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	−0.262774	−	0.964857i	$-0.584637\pi$
$401$	8.83963	−	5.10356i	0.441430	−	0.254860i	0.704204	+	0.709998i	$0.251304\pi$
$402$	−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	0.684971	−	0.728570i	$-0.259815\pi$
$409$	8.01863	+	4.62956i	0.396496	+	0.228917i	−0.288475	+	0.957487i	$0.593148\pi$
$410$	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	0.665339	−	0.746542i	$-0.268287\pi$
$419$	−6.42444	−	11.1275i	−0.313855	−	0.543612i	−0.979193	+	0.202930i	$0.934954\pi$
$420$	0.894007	−	1.54846i	0.0436231	−	0.0755574i
$421$			7.21371i			0.351575i	0.984428	+	0.175787i	$0.0562471\pi$
$421$			7.21371i			0.351575i	−0.984428	+	0.175787i	$0.943753\pi$
$422$	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	−0.619528	−	0.784975i	$-0.712676\pi$
$431$	−5.17941	+	2.99033i	−0.249483	+	0.144039i	0.370044	+	0.929014i	$0.379342\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	6.30144	−	10.9144i	0.302828	−	0.524513i	−0.673947	−	0.738779i	$-0.735403\pi$
$433$	6.30144	−	10.9144i	0.302828	−	0.524513i	0.976775	+	0.214266i	$0.0687359\pi$
$434$		−	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	0.999279	−	0.0379690i	$-0.0120888\pi$
$439$	9.77965	+	16.9389i	0.466757	+	0.808447i	−0.532522	+	0.846416i	$0.678755\pi$
$440$	−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	−0.215967	−	0.976401i	$-0.569290\pi$
$449$	−24.7821	−	14.3079i	−1.16954	−	0.675234i	−0.953571	+	0.301167i	$0.902624\pi$
$450$			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	−0.365824	−	0.930684i	$-0.619213\pi$
$457$	5.49961	−	3.17520i	0.257261	−	0.148530i	0.623084	+	0.782155i	$0.285879\pi$
$458$	−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	0.901383	−	0.433023i	$-0.142553\pi$
$461$	20.9785	+	12.1119i	0.977065	+	0.564109i	0.0756821	+	0.997132i	$0.475887\pi$
$462$	2.74922	+	1.58726i	0.127905	+	0.0738461i
$463$			17.3851i			0.807954i	0.914769	+	0.403977i	$0.132372\pi$
$463$			17.3851i			0.807954i	−0.914769	+	0.403977i	$0.867628\pi$
$464$	−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	−0.531387	+	0.847129i	$0.678329\pi$
$479$	−33.5014	+	19.3420i	−1.53072	+	0.883759i	−0.999329	+	0.0366302i	$0.988338\pi$
$480$	−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	0.911049	−	0.412298i	$-0.135274\pi$
$487$	22.2780	+	12.8622i	1.00951	+	0.582843i	0.0984640	+	0.995141i	$0.468607\pi$
$488$	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	0.581287	−	0.813699i	$-0.302549\pi$
$491$	−9.17452	−	15.8907i	−0.414040	−	0.717139i	−0.995327	+	0.0965597i	$0.969216\pi$
$492$	−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	$-0.869484\pi$
$499$		−	17.8096i		−	0.797269i	0.917110	−	0.398635i	$-0.130516\pi$
$500$	−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	0.282072	+	0.959393i	$0.408978\pi$
$503$	−15.4711	+	26.7967i	−0.689823	+	1.19481i	−0.971895	+	0.235415i	$0.924355\pi$
$504$	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	−0.210991	−	0.977488i	$-0.567669\pi$
$509$	11.9583	−	6.90414i	0.530044	−	0.306021i	0.741034	+	0.671467i	$0.234336\pi$
$510$	−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	0.855675	−	0.517513i	$-0.173142\pi$
$523$	−0.465198	−	0.805747i	−0.0203417	−	0.0352329i	−0.876017	+	0.482280i	$0.839809\pi$
$524$	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	$-0.836979\pi$
$541$		−	22.7965i		−	0.980097i	0.871695	−	0.490048i	$-0.163021\pi$
$542$	−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	−0.685494	−	0.728078i	$-0.740414\pi$
$557$	−9.38623	+	5.41914i	−0.397707	+	0.229616i	0.287787	+	0.957694i	$0.407080\pi$
$558$	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	−0.655679	−	0.755040i	$-0.727617\pi$
$563$	7.73626	−	13.3996i	0.326044	−	0.564725i	0.981723	+	0.190315i	$0.0609508\pi$
$564$			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	0.965933	+	0.258793i	$0.0833249\pi$
$569$	16.8667	+	29.2139i	0.707088	+	1.22471i	−0.258845	+	0.965919i	$0.583342\pi$
$570$	−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	$0.0724249\pi$
$577$			10.8368i			0.451143i	−0.974227	+	0.225571i	$0.927575\pi$
$578$	−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	0.0440666	−	0.999029i	$-0.485969\pi$
$587$	22.5632	−	13.0269i	0.931284	−	0.537677i	0.887217	+	0.461352i	$0.152635\pi$
$588$	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	$-0.988992\pi$
$593$		−	1.68393i		−	0.0691509i	0.999402	−	0.0345754i	$-0.0110079\pi$
$594$	−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	−0.929140	−	0.369727i	$-0.879451\pi$
$601$	−19.2387	−	33.3224i	−0.784763	−	1.35925i	0.144377	−	0.989523i	$-0.453882\pi$
$602$	−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	−0.754250	−	0.656587i	$-0.771999\pi$
$607$	4.71797	−	8.17176i	0.191496	−	0.331682i	0.945746	+	0.324906i	$0.105333\pi$
$608$	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	−0.873727	−	0.486416i	$-0.838304\pi$
$613$	−22.0191	+	12.7127i	−0.889342	+	0.513462i	−0.0156146	+	0.999878i	$0.504970\pi$
$614$	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	0.908427	−	0.418044i	$-0.137284\pi$
$617$	24.8545	+	14.3497i	1.00060	+	0.577699i	0.0921772	+	0.995743i	$0.470617\pi$
$618$	−15.6549	−	9.03838i	−0.629734	−	0.363577i
$619$		−	9.61494i		−	0.386457i	−0.981154	−	0.193229i	$-0.938104\pi$
$619$		−	9.61494i		−	0.386457i	0.981154	−	0.193229i	$-0.0618959\pi$
$620$	−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	0.958776	−	0.284162i	$-0.0917153\pi$
$631$	29.9445	+	17.2885i	1.19207	+	0.688244i	0.233297	+	0.972406i	$0.425049\pi$
$632$		−	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	−0.794521	−	0.607237i	$-0.792278\pi$
$641$	3.25646	−	5.64035i	0.128622	−	0.222780i	0.923143	+	0.384457i	$0.125611\pi$
$642$			1.54169i			0.0608458i
$643$	−21.8991	−	12.6435i	−0.863617	−	0.498609i	0.00160504	−	0.999999i	$-0.499489\pi$
$643$	−21.8991	−	12.6435i	−0.863617	−	0.498609i	−0.865222	+	0.501389i	$0.832822\pi$
$644$	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	0.959049	−	0.283241i	$-0.0914096\pi$
$647$	5.95794	+	10.3194i	0.234231	+	0.405699i	−0.724818	+	0.688940i	$0.758076\pi$
$648$	−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	−0.911432	−	0.411451i	$-0.865022\pi$
$653$	−20.7508	−	35.9415i	−0.812043	−	1.40650i	0.0993891	−	0.995049i	$-0.468311\pi$
$654$	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	−0.977591	−	0.210514i	$-0.932486\pi$
$659$	−7.86778	+	13.6274i	−0.306485	+	0.530848i	0.671106	+	0.741362i	$0.265820\pi$
$660$	−2.83804	−	4.91564i	−0.110471	−	0.191341i
$661$	−22.6071	+	13.0522i	−0.879315	+	0.507673i	−0.870432	−	0.492288i	$-0.836161\pi$
$661$	−22.6071	+	13.0522i	−0.879315	+	0.507673i	−0.00888248	+	0.999961i	$0.502827\pi$
$662$	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	0.877743	−	0.479131i	$-0.159048\pi$
$673$	0.620853	+	1.07535i	0.0239321	+	0.0414516i	−0.853811	+	0.520583i	$0.825715\pi$
$674$	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	−0.421535	−	0.906812i	$-0.638509\pi$
$683$	−37.0486	−	21.3900i	−1.41762	−	0.818466i	−0.996090	+	0.0883461i	$0.971842\pi$
$684$		−	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	−0.777861	−	0.628437i	$-0.783695\pi$
$691$	−16.3649	+	9.44827i	−0.622549	+	0.359429i	0.155312	+	0.987866i	$0.450362\pi$
$692$	−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	0.959668	−	0.281136i	$-0.0907113\pi$
$709$	31.8468	+	18.3867i	1.19603	+	0.690529i	0.236363	+	0.971665i	$0.424045\pi$
$710$			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	−0.674965	−	0.737850i	$-0.735841\pi$
$719$	8.08486	−	14.0034i	0.301514	−	0.522238i	0.976479	+	0.215612i	$0.0691746\pi$
$720$		−	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	$-0.738267\pi$
$733$		−	39.6734i		−	1.46537i	0.680567	−	0.732686i	$-0.261733\pi$
$734$	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	−0.846866	−	0.531806i	$-0.821514\pi$
$739$	−22.0125	+	12.7089i	−0.809742	+	0.467505i	0.0371244	+	0.999311i	$0.488180\pi$
$740$	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	−0.839711	−	0.543034i	$-0.817275\pi$
$743$	−21.5143	+	12.4213i	−0.789285	+	0.455694i	0.0504260	+	0.998728i	$0.483942\pi$
$744$	−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	−0.898743	−	0.438476i	$-0.855518\pi$
$751$	−22.7211	−	39.3540i	−0.829103	−	1.43605i	0.0696398	−	0.997572i	$-0.477815\pi$
$752$	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	0.801855	−	0.597519i	$-0.203847\pi$
$757$	−3.20643	−	5.55369i	−0.116540	−	0.201852i	−0.918394	+	0.395667i	$0.870514\pi$
$758$	−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	0.910864	−	0.412706i	$-0.135416\pi$
$761$	27.8313	+	16.0684i	1.00888	+	0.582479i	0.0980185	+	0.995185i	$0.468750\pi$
$762$			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	−0.964327	−	0.264714i	$-0.914722\pi$
$769$	−33.7551	+	19.4885i	−1.21724	+	0.702774i	−0.252914	+	0.967489i	$0.581389\pi$
$770$	−2.83804	−	4.91564i	−0.102276	−	0.177147i
$771$	0.413344	−	0.715933i	0.0148862	−	0.0257837i
$772$			5.45490i			0.196326i
$773$	2.09922	+	1.21199i	0.0755038	+	0.0435921i	0.537277	−	0.843406i	$-0.319453\pi$
$773$	2.09922	+	1.21199i	0.0755038	+	0.0435921i	−0.461773	+	0.886998i	$0.652786\pi$
$774$	−8.34729	−	4.81931i	−0.300037	−	0.173227i
$775$		−	10.1665i		−	0.365191i
$776$	−8.74462	+	15.1461i	−0.313913	+	0.543714i
$777$	−1.54846	−	2.68202i	−0.0555509	−	0.0962169i
$778$	−28.3286	+	16.3555i	−1.01563	+	0.586374i
$779$	9.27458			0.332296
$780$	5.87901	−	2.64539i	0.210502	−	0.0947203i
$781$	−1.89994			−0.0679851
$782$	29.5392	−	17.0544i	1.05632	−	0.609866i
$783$	1.03880	+	1.79925i	0.0371235	+	0.0642999i
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	8.18760i		−	0.292228i
$786$	5.12624	+	2.95964i	0.182847	+	0.105567i
$787$	−43.9662	−	25.3839i	−1.56722	−	0.904837i	−0.996491	−	0.0837017i	$-0.973326\pi$
$787$	−43.9662	−	25.3839i	−1.56722	−	0.904837i	−0.570733	−	0.821136i	$-0.693341\pi$
$788$			7.62970i			0.271797i
$789$	10.1805	−	17.6331i	0.362434	−	0.627754i
$790$	−6.22455	−	10.7812i	−0.221460	−	0.383579i
$791$	8.58509	−	4.95660i	0.305251	−	0.176237i
$792$	3.17452			0.112802
$793$	−6.05813	−	0.612538i	−0.215131	−	0.0217519i
$794$	−0.606017			−0.0215067
$795$	5.57757	−	3.22021i	0.197816	−	0.114209i
$796$	−2.99512	−	5.18769i	−0.106159	−	0.183873i
$797$	13.6044	−	23.5636i	0.481894	−	0.834664i	−0.517890	−	0.855447i	$-0.673283\pi$
$797$	13.6044	−	23.5636i	0.481894	−	0.834664i	0.999784	+	0.0207828i	$0.00661586\pi$
$798$		−	6.18952i		−	0.219107i
$799$	50.6092	+	29.2193i	1.79043	+	1.03370i
$800$	−1.56145	−	0.901504i	−0.0552056	−	0.0318730i
$801$		−	16.2931i		−	0.575688i
$802$	5.10356	−	8.83963i	0.180213	−	0.312138i
$803$	−0.672957	−	1.16559i	−0.0237481	−	0.0411329i
$804$	−10.0064	+	5.77720i	−0.352899	+	0.203746i
$805$	10.9669			0.386532
$806$	11.8848	−	16.4947i	0.418624	−	0.581001i
$807$	20.5175			0.722250
$808$	−3.52357	+	2.03433i	−0.123959	+	0.0715676i
$809$	21.7049	+	37.5939i	0.763102	+	1.32173i	0.941244	+	0.337727i	$0.109658\pi$
$809$	21.7049	+	37.5939i	0.763102	+	1.32173i	−0.178142	+	0.984005i	$0.557009\pi$
$810$	−0.894007	+	1.54846i	−0.0314122	+	0.0544075i
$811$		−	38.1252i		−	1.33876i	−0.742922	−	0.669378i	$-0.766561\pi$
$811$		−	38.1252i		−	1.33876i	0.742922	−	0.669378i	$-0.233439\pi$
$812$	−1.79925	−	1.03880i	−0.0631412	−	0.0364546i
$813$	−10.5495	−	6.09076i	−0.369988	−	0.213612i
$814$			9.83127i			0.344586i
$815$	10.9700	−	19.0006i	0.384263	−	0.665562i
$816$	−2.78052	−	4.81599i	−0.0973375	−	0.168594i
$817$	51.6657	−	29.8292i	1.80755	−	1.04359i
$818$	9.25912			0.323738
$819$	−2.92531	−	2.10774i	−0.102218	−	0.0736506i
$820$	2.67922			0.0935624
$821$	21.2937	−	12.2939i	0.743157	−	0.429062i	−0.0800593	−	0.996790i	$-0.525511\pi$
$821$	21.2937	−	12.2939i	0.743157	−	0.429062i	0.823216	+	0.567728i	$0.192178\pi$
$822$	4.40150	+	7.62363i	0.153520	+	0.265905i
$823$	−15.6465	+	27.1005i	−0.545402	+	0.944663i	0.453180	+	0.891419i	$0.350290\pi$
$823$	−15.6465	+	27.1005i	−0.545402	+	0.944663i	−0.998582	+	0.0532443i	$0.983044\pi$
$824$			18.0768i			0.629734i
$825$	4.95686	+	2.86185i	0.172576	+	0.0996367i
$826$	−2.40874	−	1.39069i	−0.0838109	−	0.0483883i
$827$			10.9236i			0.379851i	0.981798	+	0.189926i	$0.0608247\pi$
$827$			10.9236i			0.379851i	−0.981798	+	0.189926i	$0.939175\pi$
$828$	−3.06678	+	5.31181i	−0.106578	+	0.184598i
$829$	21.8838	+	37.9039i	0.760057	+	1.31646i	0.942820	+	0.333301i	$0.108163\pi$
$829$	21.8838	+	37.9039i	0.760057	+	1.31646i	−0.182763	+	0.983157i	$0.558504\pi$
$830$	6.66193	−	3.84627i	0.231239	−	0.133506i
$831$	8.62484			0.299192
$832$	−1.47952	−	3.28801i	−0.0512930	−	0.113991i
$833$	5.56103			0.192678
$834$	−16.4323	+	9.48720i	−0.569004	+	0.328515i
$835$	−14.9282	−	25.8564i	−0.516612	−	0.894798i
$836$	−9.82438	+	17.0163i	−0.339783	+	0.588522i
$837$			5.63862i			0.194899i
$838$	−11.1275	−	6.42444i	−0.384392	−	0.221929i
$839$	−16.7145	−	9.65012i	−0.577048	−	0.333159i	0.182911	−	0.983129i	$-0.441448\pi$
$839$	−16.7145	−	9.65012i	−0.577048	−	0.333159i	−0.759959	+	0.649970i	$0.774781\pi$
$840$		−	1.78801i		−	0.0616923i
$841$	12.3418	−	21.3766i	0.425579	−	0.737125i
$842$	3.60686	+	6.24726i	0.124300	+	0.215295i
$843$	21.0377	−	12.1461i	0.724577	−	0.418335i
$844$	2.77302			0.0954512
$845$	17.3962	+	15.4164i	0.598447	+	0.530339i
$846$	−10.5086			−0.361292
$847$	−0.798828	+	0.461204i	−0.0274481	+	0.0158471i
$848$	−1.80100	−	3.11942i	−0.0618466	−	0.107121i
$849$	−5.36054	+	9.28472i	−0.183973	+	0.318651i
$850$		−	10.0266i		−	0.343909i
$851$	−16.4503	−	9.49759i	−0.563910	−	0.325573i
$852$	−0.518313	−	0.299248i	−0.0177571	−	0.0102521i
$853$			28.9164i			0.990078i	0.868871	+	0.495039i	$0.164846\pi$
$853$			28.9164i			0.990078i	−0.868871	+	0.495039i	$0.835154\pi$
$854$	−0.844395	+	1.46254i	−0.0288946	+	0.0500469i
$855$	−5.53347	−	9.58425i	−0.189241	−	0.327774i
$856$	1.33515	−	0.770847i	0.0456344	−	0.0263470i
$857$	−16.6946			−0.570278			−0.285139	−	0.958486i	$-0.592040\pi$
$857$	−16.6946			−0.570278			−0.285139	+	0.958486i	$0.592040\pi$
$858$	4.69676	+	10.4379i	0.160345	+	0.356343i
$859$	27.5825			0.941103			0.470552	−	0.882372i	$-0.344055\pi$
$859$	27.5825			0.941103			0.470552	+	0.882372i	$0.344055\pi$
$860$	14.9251	−	8.61699i	0.508941	−	0.293837i
$861$	−0.749217	−	1.29768i	−0.0255332	−	0.0442249i
$862$	−2.99033	+	5.17941i	−0.101851	+	0.176411i
$863$		−	31.9313i		−	1.08696i	−0.839424	−	0.543478i	$-0.817107\pi$
$863$		−	31.9313i		−	1.08696i	0.839424	−	0.543478i	$-0.182893\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−11.4235	−	6.59536i	−0.388411	−	0.224249i
$866$		−	12.6029i		−	0.428263i
$867$	6.96254	−	12.0595i	0.236460	−	0.409561i
$868$	−2.81931	−	4.88319i	−0.0956937	−	0.165746i
$869$	19.1415	−	11.0514i	0.649332	−	0.374892i
$870$	−3.71476			−0.125942
$871$	−33.8001	−	24.3537i	−1.14527	−	0.825194i
$872$	−7.37731			−0.249827
$873$	15.1461	−	8.74462i	0.512619	−	0.295960i
$874$	−18.9819	−	32.8776i	−0.642071	−	1.11210i
$875$	6.08193	−	10.5342i	0.205607	−	0.356122i
$876$		−	0.423973i		−	0.0143247i
$877$	25.6513	+	14.8098i	0.866183	+	0.500091i	0.866078	−	0.499909i	$-0.166633\pi$
$877$	25.6513	+	14.8098i	0.866183	+	0.500091i	0.000104747		1.00000i	$0.499967\pi$
$878$	16.9389	+	9.77965i	0.571659	+	0.330047i
$879$		−	21.4278i		−	0.722743i
$880$	−2.83804	+	4.91564i	−0.0956704	+	0.165706i
$881$	−5.04872	−	8.74464i	−0.170096	−	0.294615i	0.768357	−	0.640021i	$-0.221074\pi$
$881$	−5.04872	−	8.74464i	−0.170096	−	0.294615i	−0.938453	+	0.345407i	$0.887741\pi$
$882$	−0.866025	+	0.500000i	−0.0291606	+	0.0168359i
$883$	46.5103			1.56520			0.782598	−	0.622527i	$-0.213894\pi$
$883$	46.5103			1.56520			0.782598	+	0.622527i	$0.213894\pi$
$884$	11.7212	−	16.2677i	0.394228	−	0.547142i
$885$	−4.97314			−0.167170
$886$	−34.8662	+	20.1300i	−1.17135	+	0.676282i
$887$	13.2691	+	22.9828i	0.445534	+	0.771688i	0.998089	−	0.0617884i	$-0.0196804\pi$
$887$	13.2691	+	22.9828i	0.445534	+	0.771688i	−0.552555	+	0.833476i	$0.686347\pi$
$888$	−1.54846	+	2.68202i	−0.0519631	+	0.0900027i
$889$			18.3490i			0.615407i
$890$	25.2293	+	14.5661i	0.845687	+	0.488258i
$891$	−2.74922	−	1.58726i	−0.0921022	−	0.0531753i
$892$		−	22.5354i		−	0.754542i
$893$	32.5215	−	56.3289i	1.08829	−	1.88497i
$894$	6.98127	+	12.0919i	0.233489	+	0.404414i
$895$	30.6908	−	17.7193i	1.02588	−	0.592292i
$896$	−1.00000			−0.0334077
$897$	−22.0027	−	2.22469i	−0.734648	−	0.0742802i
$898$	−28.6159			−0.954924
$899$	−10.1453	+	5.85738i	−0.338364	+	0.195355i
$900$	0.901504	+	1.56145i	0.0300501	+	0.0520484i
$901$	10.0154	−	17.3472i	0.333662	−	0.577919i
$902$			4.75681i			0.158385i
$903$	−8.34729	−	4.81931i	−0.277781	−	0.160377i
$904$	−8.58509	−	4.95660i	−0.285536	−	0.164854i
$905$			32.7682i			1.08925i
$906$	8.92131	−	15.4522i	0.296391	−	0.513364i
$907$	−11.8195	−	20.4721i	−0.392462	−	0.679763i	0.600312	−	0.799766i	$-0.295043\pi$
$907$	−11.8195	−	20.4721i	−0.392462	−	0.679763i	−0.992774	+	0.120002i	$0.961710\pi$
$908$	−1.58616	+	0.915773i	−0.0526387	+	0.0303910i
$909$	4.06866			0.134949
$910$	5.87901	−	2.64539i	0.194887	−	0.0876940i
$911$	−1.46896			−0.0486688			−0.0243344	−	0.999704i	$-0.507747\pi$
$911$	−1.46896			−0.0486688			−0.0243344	+	0.999704i	$0.507747\pi$
$912$	−5.36028	+	3.09476i	−0.177497	+	0.102478i
$913$	6.82884	+	11.8279i	0.226002	+	0.391447i
$914$	3.17520	−	5.49961i	0.105026	−	0.181911i
$915$			3.01958i			0.0998242i
$916$	−19.5774	−	11.3030i	−0.646855	−	0.373462i
$917$	5.12624	+	2.95964i	0.169283	+	0.0977359i
$918$			5.56103i			0.183541i
$919$	−21.5188	+	37.2717i	−0.709841	+	1.22948i	0.255075	+	0.966921i	$0.417900\pi$
$919$	−21.5188	+	37.2717i	−0.709841	+	1.22948i	−0.964916	+	0.262559i	$0.915434\pi$
$920$	−5.48344	−	9.49759i	−0.180784	−	0.313126i
$921$	−6.57628	+	3.79682i	−0.216696	+	0.125109i
$922$	24.2238			0.797770
$923$	0.217079	−	2.14696i	0.00714525	−	0.0706681i
$924$	3.17452			0.104434
$925$	−4.83570	+	2.79190i	−0.158997	+	0.0917970i
$926$	8.69255	+	15.0559i	0.285655	+	0.494769i
$927$	9.03838	−	15.6549i	0.296859	−	0.514175i
$928$			2.07759i			0.0682003i
$929$	−1.48827	−	0.859255i	−0.0488286	−	0.0281912i	0.475387	−	0.879777i	$-0.342308\pi$
$929$	−1.48827	−	0.859255i	−0.0488286	−	0.0281912i	−0.524216	+	0.851586i	$0.675641\pi$
$930$	−8.73121	−	5.04097i	−0.286308	−	0.165300i
$931$		−	6.18952i		−	0.202853i
$932$	−4.71948	+	8.17439i	−0.154592	+	0.267761i
$933$	12.8177	+	22.2010i	0.419634	+	0.726828i
$934$	−12.8637	+	7.42687i	−0.420914	+	0.243015i
$935$	−31.5649			−1.03228
$936$	−0.362708	+	3.58726i	−0.0118555	+	0.117253i
$937$	−20.0024			−0.653451			−0.326725	−	0.945119i	$-0.605945\pi$
$937$	−20.0024			−0.653451			−0.326725	+	0.945119i	$0.605945\pi$
$938$	−10.0064	+	5.77720i	−0.326721	+	0.188632i
$939$	−0.856542	−	1.48357i	−0.0279522	−	0.0484146i
$940$	9.39473	−	16.2722i	0.306422	−	0.530739i
$941$			11.8846i			0.387428i	0.981058	+	0.193714i	$0.0620533\pi$
$941$			11.8846i			0.387428i	−0.981058	+	0.193714i	$0.937947\pi$
$942$	3.96567	+	2.28958i	0.129208	+	0.0745985i
$943$	−7.95940	−	4.59536i	−0.259194	−	0.149646i
$944$			2.78138i			0.0905262i
$945$	−0.894007	+	1.54846i	−0.0290820	+	0.0503716i
$946$	15.2990	+	26.4987i	0.497414	+	0.861546i
$947$	5.34394	−	3.08532i	0.173655	−	0.100260i	−0.410653	−	0.911792i	$-0.634699\pi$
$947$	5.34394	−	3.08532i	0.173655	−	0.100260i	0.584308	+	0.811532i	$0.301366\pi$
$948$	6.96254			0.226133
$949$	1.39403	−	0.627276i	0.0452521	−	0.0203622i
$950$	−11.1598			−0.362070
$951$	28.7605	−	16.6049i	0.932624	−	0.538451i
$952$	−2.78052	−	4.81599i	−0.0901170	−	0.156087i
$953$	20.5361	−	35.5696i	0.665231	−	1.15221i	−0.313992	−	0.949426i	$-0.601667\pi$
$953$	20.5361	−	35.5696i	0.665231	−	1.15221i	0.979223	−	0.202788i	$-0.0650001\pi$
$954$			3.60200i			0.116619i
$955$	−23.2740	−	13.4372i	−0.753129	−	0.434819i
$956$	−13.7488	−	7.93787i	−0.444668	−	0.256729i
$957$		−	6.59536i		−	0.213198i
$958$	−19.3420	+	33.5014i	−0.624912	+	1.08238i
$959$	4.40150	+	7.62363i	0.142132	+	0.246180i
$960$	−1.54846	+	0.894007i	−0.0499765	+	0.0288539i
$961$	−0.794081			−0.0256155
$962$	−11.1095	−	1.12328i	−0.358185	−	0.0362160i
$963$	−1.54169			−0.0496804
$964$	20.7197	−	11.9625i	0.667337	−	0.385287i
$965$	4.87672	+	8.44672i	0.156987	+	0.271910i
$966$	−3.06678	+	5.31181i	−0.0986719	+	0.170905i
$967$		−	34.4847i		−	1.10895i	−0.832199	−	0.554477i	$-0.812919\pi$
$967$		−	34.4847i		−	1.10895i	0.832199	−	0.554477i	$-0.187081\pi$
$968$	0.798828	+	0.461204i	0.0256753	+	0.0148236i
$969$	−29.8087	−	17.2101i	−0.957593	−	0.552866i
$970$			31.2710i			1.00405i
$971$	−1.94777	+	3.37364i	−0.0625071	+	0.108265i	−0.895585	−	0.444890i	$-0.853243\pi$
$971$	−1.94777	+	3.37364i	−0.0625071	+	0.108265i	0.833078	+	0.553155i	$0.186576\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−16.4323	+	9.48720i	−0.526796	+	0.304146i
$974$	25.7244			0.824264
$975$	−3.80028	+	5.27435i	−0.121706	+	0.168914i
$976$	1.68879			0.0540569
$977$	45.7455	−	26.4112i	1.46353	−	0.844968i	0.464356	−	0.885649i	$-0.346286\pi$
$977$	45.7455	−	26.4112i	1.46353	−	0.844968i	0.999172	+	0.0406804i	$0.0129525\pi$
$978$	6.13531	+	10.6267i	0.196185	+	0.339803i
$979$	−25.8614	+	44.7932i	−0.826533	+	1.43160i
$980$		−	1.78801i		−	0.0571160i
$981$	6.38894	+	3.68865i	0.203983	+	0.117770i
$982$	−15.8907	−	9.17452i	−0.507094	−	0.292771i
$983$		−	40.2176i		−	1.28274i	−0.767231	−	0.641371i	$-0.778366\pi$
$983$		−	40.2176i		−	1.28274i	0.767231	−	0.641371i	$-0.221634\pi$
$984$	−0.749217	+	1.29768i	−0.0238842	+	0.0413686i
$985$	6.82100	+	11.8143i	0.217335	+	0.376435i
$986$	−10.0057	+	5.77678i	−0.318646	+	0.183970i
$987$	−10.5086			−0.334492
$988$	−18.1062	−	13.0459i	−0.576036	−	0.415046i
$989$	−59.1190			−1.87988
$990$	4.91564	−	2.83804i	0.156229	−	0.0901990i
$991$	−18.5909	−	32.2004i	−0.590559	−	1.02288i	−0.994157	−	0.107942i	$-0.965574\pi$
$991$	−18.5909	−	32.2004i	−0.590559	−	1.02288i	0.403598	−	0.914937i	$-0.367760\pi$
$992$	−2.81931	+	4.88319i	−0.0895132	+	0.155041i
$993$			4.95987i			0.157397i
$994$	−0.518313	−	0.299248i	−0.0164399	−	0.00949157i
$995$	−9.27567	−	5.35531i	−0.294058	−	0.169775i
$996$			4.30228i			0.136323i
$997$	0.0370447	−	0.0641633i	0.00117322	−	0.00203207i	−0.865438	−	0.501016i	$-0.832960\pi$
$997$	0.0370447	−	0.0641633i	0.00117322	−	0.00203207i	0.866611	+	0.498984i	$0.166293\pi$
$998$	−8.90482	−	15.4236i	−0.281877	−	0.488226i
$999$	2.68202	−	1.54846i	0.0848554	−	0.0489913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.s.e.127.3	yes	8
3.2	odd	2		1638.2.bj.f.127.2		8
13.2	odd	12		7098.2.a.co.1.1		4
13.4	even	6	inner	546.2.s.e.43.4	✓	8
13.11	odd	12		7098.2.a.cn.1.4		4
39.17	odd	6		1638.2.bj.f.1135.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.e.43.4	✓	8	13.4	even	6	inner
546.2.s.e.127.3	yes	8	1.1	even	1	trivial
1638.2.bj.f.127.2		8	3.2	odd	2
1638.2.bj.f.1135.1		8	39.17	odd	6
7098.2.a.cn.1.4		4	13.11	odd	12
7098.2.a.co.1.1		4	13.2	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.78801i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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

Introduction

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