LMFDB - Embedded newform 731.2.d.c.560.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.d (of order $2$, degree $1$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 29 x^{18} + 358 x^{16} + 2458 x^{14} + 10298 x^{12} + 27188 x^{10} + 45053 x^{8} + 44980 x^{6} + \cdots + 36 $ x^20 + 29x^18 + 358x^16 + 2458x^14 + 10298x^12 + 27188x^10 + 45053x^8 + 44980x^6 + 24400x^4 + 5448*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.14
Root			$-2.00110i$ of defining polynomial
Character	$\chi$	$=$	731.560
Dual form			731.2.d.c.560.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73078 q^{2} +2.30609i q^{3} +0.995588 q^{4} +0.771574i q^{5} +3.99132i q^{6} +3.40847i q^{7} -1.73841 q^{8} -2.31803 q^{9} +O(q^{10})$	\(q+1.73078 q^{2} +2.30609i q^{3} +0.995588 q^{4} +0.771574i q^{5} +3.99132i q^{6} +3.40847i q^{7} -1.73841 q^{8} -2.31803 q^{9} +1.33542i q^{10} -1.19477i q^{11} +2.29591i q^{12} +3.11604 q^{13} +5.89931i q^{14} -1.77932 q^{15} -4.99998 q^{16} +(-2.74372 - 3.07766i) q^{17} -4.01200 q^{18} -1.18363 q^{19} +0.768170i q^{20} -7.86024 q^{21} -2.06789i q^{22} +1.80070i q^{23} -4.00893i q^{24} +4.40467 q^{25} +5.39317 q^{26} +1.57267i q^{27} +3.39344i q^{28} +3.79894i q^{29} -3.07960 q^{30} -4.18322i q^{31} -5.17702 q^{32} +2.75525 q^{33} +(-4.74877 - 5.32674i) q^{34} -2.62989 q^{35} -2.30780 q^{36} +0.0262173i q^{37} -2.04859 q^{38} +7.18586i q^{39} -1.34131i q^{40} +10.8029i q^{41} -13.6043 q^{42} +1.00000 q^{43} -1.18950i q^{44} -1.78853i q^{45} +3.11661i q^{46} +10.0978 q^{47} -11.5304i q^{48} -4.61770 q^{49} +7.62351 q^{50} +(7.09735 - 6.32726i) q^{51} +3.10229 q^{52} -4.81035 q^{53} +2.72195i q^{54} +0.921856 q^{55} -5.92534i q^{56} -2.72954i q^{57} +6.57512i q^{58} +12.4443 q^{59} -1.77147 q^{60} -8.94454i q^{61} -7.24022i q^{62} -7.90096i q^{63} +1.03969 q^{64} +2.40426i q^{65} +4.76872 q^{66} +9.61957 q^{67} +(-2.73161 - 3.06408i) q^{68} -4.15257 q^{69} -4.55175 q^{70} +14.8067i q^{71} +4.02970 q^{72} -5.92245i q^{73} +0.0453762i q^{74} +10.1576i q^{75} -1.17840 q^{76} +4.07235 q^{77} +12.4371i q^{78} -7.15629i q^{79} -3.85786i q^{80} -10.5808 q^{81} +18.6974i q^{82} +4.12635 q^{83} -7.82555 q^{84} +(2.37464 - 2.11698i) q^{85} +1.73078 q^{86} -8.76069 q^{87} +2.07701i q^{88} -2.65204 q^{89} -3.09555i q^{90} +10.6209i q^{91} +1.79275i q^{92} +9.64687 q^{93} +17.4770 q^{94} -0.913255i q^{95} -11.9387i q^{96} -8.58923i q^{97} -7.99221 q^{98} +2.76952i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9	$ 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9} - 4 q^{13} + 26 q^{15} + 6 q^{16} + 16 q^{17} - 22 q^{18} - 4 q^{19} + 20 q^{21} - 2 q^{25} + 22 q^{26} - 72 q^{30} + 38 q^{32} - 12 q^{33} + 12 q^{34} - 30 q^{35} - 104 q^{36} - 22 q^{38} + 26 q^{42} + 20 q^{43} - 34 q^{47} + 22 q^{49} + 42 q^{50} + 52 q^{51} - 110 q^{52} + 14 q^{53} + 12 q^{55} + 20 q^{59} + 42 q^{60} - 22 q^{64} + 50 q^{66} - 12 q^{67} + 50 q^{68} - 82 q^{69} - 30 q^{70} - 50 q^{72} + 2 q^{76} + 78 q^{77} + 44 q^{81} + 20 q^{83} + 62 q^{84} + 76 q^{85} + 2 q^{86} + 12 q^{87} - 46 q^{89} + 58 q^{93} - 18 q^{94} - 62 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9 - 4 * q^13 + 26 * q^15 + 6 * q^16 + 16 * q^17 - 22 * q^18 - 4 * q^19 + 20 * q^21 - 2 * q^25 + 22 * q^26 - 72 * q^30 + 38 * q^32 - 12 * q^33 + 12 * q^34 - 30 * q^35 - 104 * q^36 - 22 * q^38 + 26 * q^42 + 20 * q^43 - 34 * q^47 + 22 * q^49 + 42 * q^50 + 52 * q^51 - 110 * q^52 + 14 * q^53 + 12 * q^55 + 20 * q^59 + 42 * q^60 - 22 * q^64 + 50 * q^66 - 12 * q^67 + 50 * q^68 - 82 * q^69 - 30 * q^70 - 50 * q^72 + 2 * q^76 + 78 * q^77 + 44 * q^81 + 20 * q^83 + 62 * q^84 + 76 * q^85 + 2 * q^86 + 12 * q^87 - 46 * q^89 + 58 * q^93 - 18 * q^94 - 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.73078			1.22384			0.611922	−	0.790918i	$-0.290397\pi$
$2$	1.73078			1.22384			0.611922	+	0.790918i	$0.290397\pi$
$3$			2.30609i			1.33142i	0.746211	+	0.665710i	$0.231871\pi$
$3$			2.30609i			1.33142i	−0.746211	+	0.665710i	$0.768129\pi$
$4$	0.995588			0.497794
$5$			0.771574i			0.345058i	0.985004	+	0.172529i	$0.0551939\pi$
$5$			0.771574i			0.345058i	−0.985004	+	0.172529i	$0.944806\pi$
$6$			3.99132i			1.62945i
$7$			3.40847i			1.28828i	0.764907	+	0.644141i	$0.222785\pi$
$7$			3.40847i			1.28828i	−0.764907	+	0.644141i	$0.777215\pi$
$8$	−1.73841			−0.614622
$9$	−2.31803			−0.772678
$10$			1.33542i			0.422298i
$11$		−	1.19477i		−	0.360238i	−0.983645	−	0.180119i	$-0.942352\pi$
$11$		−	1.19477i		−	0.360238i	0.983645	−	0.180119i	$-0.0576482\pi$
$12$			2.29591i			0.662772i
$13$	3.11604			0.864234			0.432117	−	0.901817i	$-0.357767\pi$
$13$	3.11604			0.864234			0.432117	+	0.901817i	$0.357767\pi$
$14$			5.89931i			1.57666i
$15$	−1.77932			−0.459417
$16$	−4.99998			−1.25000
$17$	−2.74372	−	3.07766i	−0.665450	−	0.746442i
$17$	−2.74372	−	3.07766i	−0.665450	−	0.746442i
$18$	−4.01200			−0.945637
$19$	−1.18363			−0.271542			−0.135771	−	0.990740i	$-0.543351\pi$
$19$	−1.18363			−0.271542			−0.135771	+	0.990740i	$0.543351\pi$
$20$			0.768170i			0.171768i
$21$	−7.86024			−1.71524
$22$		−	2.06789i		−	0.440875i
$23$			1.80070i			0.375472i	0.982220	+	0.187736i	$0.0601149\pi$
$23$			1.80070i			0.375472i	−0.982220	+	0.187736i	$0.939885\pi$
$24$		−	4.00893i		−	0.818320i
$25$	4.40467			0.880935
$26$	5.39317			1.05769
$27$			1.57267i			0.302661i
$28$			3.39344i			0.641299i
$29$			3.79894i			0.705446i	0.935728	+	0.352723i	$0.114744\pi$
$29$			3.79894i			0.705446i	−0.935728	+	0.352723i	$0.885256\pi$
$30$	−3.07960			−0.562255
$31$		−	4.18322i		−	0.751329i	−0.926756	−	0.375664i	$-0.877415\pi$
$31$		−	4.18322i		−	0.751329i	0.926756	−	0.375664i	$-0.122585\pi$
$32$	−5.17702			−0.915177
$33$	2.75525			0.479627
$34$	−4.74877	−	5.32674i	−0.814407	−	0.913529i
$35$	−2.62989			−0.444533
$36$	−2.30780			−0.384634
$37$			0.0262173i			0.00431009i	0.999998	+	0.00215505i	$0.000685973\pi$
$37$			0.0262173i			0.00431009i	−0.999998	+	0.00215505i	$0.999314\pi$
$38$	−2.04859			−0.332326
$39$			7.18586i			1.15066i
$40$		−	1.34131i		−	0.212081i
$41$			10.8029i			1.68713i	0.537030	+	0.843563i	$0.319546\pi$
$41$			10.8029i			1.68713i	−0.537030	+	0.843563i	$0.680454\pi$
$42$	−13.6043			−2.09919
$43$	1.00000			0.152499
$43$	1.00000			0.152499
$44$		−	1.18950i		−	0.179324i
$45$		−	1.78853i		−	0.266619i
$46$			3.11661i			0.459519i
$47$	10.0978			1.47292			0.736458	−	0.676483i	$-0.236497\pi$
$47$	10.0978			1.47292			0.736458	+	0.676483i	$0.236497\pi$
$48$		−	11.5304i		−	1.66427i
$49$	−4.61770			−0.659672
$50$	7.62351			1.07813
$51$	7.09735	−	6.32726i	0.993828	−	0.885993i
$52$	3.10229			0.430211
$53$	−4.81035			−0.660753			−0.330376	−	0.943849i	$-0.607176\pi$
$53$	−4.81035			−0.660753			−0.330376	+	0.943849i	$0.607176\pi$
$54$			2.72195i			0.370410i
$55$	0.921856			0.124303
$56$		−	5.92534i		−	0.791807i
$57$		−	2.72954i		−	0.361537i
$58$			6.57512i			0.863356i
$59$	12.4443			1.62011			0.810057	−	0.586351i	$-0.199436\pi$
$59$	12.4443			1.62011			0.810057	+	0.586351i	$0.199436\pi$
$60$	−1.77147			−0.228695
$61$		−	8.94454i		−	1.14523i	−0.819824	−	0.572615i	$-0.805929\pi$
$61$		−	8.94454i		−	1.14523i	0.819824	−	0.572615i	$-0.194071\pi$
$62$		−	7.24022i		−	0.919509i
$63$		−	7.90096i		−	0.995427i
$64$	1.03969			0.129962
$65$			2.40426i			0.298211i
$66$	4.76872			0.586989
$67$	9.61957			1.17522			0.587608	−	0.809145i	$-0.300070\pi$
$67$	9.61957			1.17522			0.587608	+	0.809145i	$0.300070\pi$
$68$	−2.73161	−	3.06408i	−0.331257	−	0.371574i
$69$	−4.15257			−0.499910
$70$	−4.55175			−0.544039
$71$			14.8067i			1.75723i	0.477531	+	0.878615i	$0.341532\pi$
$71$			14.8067i			1.75723i	−0.477531	+	0.878615i	$0.658468\pi$
$72$	4.02970			0.474905
$73$		−	5.92245i		−	0.693170i	−0.938019	−	0.346585i	$-0.887341\pi$
$73$		−	5.92245i		−	0.693170i	0.938019	−	0.346585i	$-0.112659\pi$
$74$			0.0453762i			0.00527488i
$75$			10.1576i			1.17289i
$76$	−1.17840			−0.135172
$77$	4.07235			0.464088
$78$			12.4371i			1.40823i
$79$		−	7.15629i		−	0.805146i	−0.915388	−	0.402573i	$-0.868116\pi$
$79$		−	7.15629i		−	0.805146i	0.915388	−	0.402573i	$-0.131884\pi$
$80$		−	3.85786i		−	0.431321i
$81$	−10.5808			−1.17565
$82$			18.6974i			2.06478i
$83$	4.12635			0.452926			0.226463	−	0.974020i	$-0.427284\pi$
$83$	4.12635			0.452926			0.226463	+	0.974020i	$0.427284\pi$
$84$	−7.82555			−0.853838
$85$	2.37464	−	2.11698i	0.257566	−	0.229619i
$86$	1.73078			0.186634
$87$	−8.76069			−0.939245
$88$			2.07701i			0.221410i
$89$	−2.65204			−0.281116			−0.140558	−	0.990072i	$-0.544890\pi$
$89$	−2.65204			−0.281116			−0.140558	+	0.990072i	$0.544890\pi$
$90$		−	3.09555i		−	0.326300i
$91$			10.6209i			1.11338i
$92$			1.79275i			0.186908i
$93$	9.64687			1.00033
$94$	17.4770			1.80262
$95$		−	0.913255i		−	0.0936980i
$96$		−	11.9387i		−	1.21848i
$97$		−	8.58923i		−	0.872104i	−0.899922	−	0.436052i	$-0.856376\pi$
$97$		−	8.58923i		−	0.872104i	0.899922	−	0.436052i	$-0.143624\pi$
$98$	−7.99221			−0.807335
$99$			2.76952i			0.278348i
$100$	4.38524			0.438524
$101$	−4.09352			−0.407321			−0.203660	−	0.979042i	$-0.565284\pi$
$101$	−4.09352			−0.407321			−0.203660	+	0.979042i	$0.565284\pi$
$102$	12.2839	−	10.9511i	1.21629	−	1.08432i
$103$	−16.9822			−1.67331			−0.836654	−	0.547732i	$-0.815491\pi$
$103$	−16.9822			−1.67331			−0.836654	+	0.547732i	$0.815491\pi$
$104$	−5.41697			−0.531178
$105$		−	6.06475i		−	0.591859i
$106$	−8.32565			−0.808658
$107$		−	1.90465i		−	0.184129i	−0.995753	−	0.0920645i	$-0.970653\pi$
$107$		−	1.90465i		−	0.184129i	0.995753	−	0.0920645i	$-0.0293466\pi$
$108$			1.56574i			0.150663i
$109$			1.72929i			0.165636i	0.996565	+	0.0828181i	$0.0263921\pi$
$109$			1.72929i			0.165636i	−0.996565	+	0.0828181i	$0.973608\pi$
$110$	1.59553			0.152128
$111$	−0.0604593			−0.00573854
$112$		−	17.0423i		−	1.61035i
$113$		−	14.2132i		−	1.33706i	−0.743683	−	0.668532i	$-0.766923\pi$
$113$		−	14.2132i		−	1.33706i	0.743683	−	0.668532i	$-0.233077\pi$
$114$		−	4.72423i		−	0.442465i
$115$	−1.38937			−0.129560
$116$			3.78218i			0.351167i
$117$	−7.22309			−0.667775
$118$	21.5384			1.98277
$119$	10.4901	−	9.35191i	0.961628	−	0.857288i
$120$	3.09319			0.282368
$121$	9.57252			0.870229
$122$		−	15.4810i		−	1.40158i
$123$	−24.9124			−2.24627
$124$		−	4.16476i		−	0.374007i
$125$			7.25640i			0.649032i
$126$		−	13.6748i		−	1.21825i
$127$	17.1741			1.52396			0.761980	−	0.647601i	$-0.224228\pi$
$127$	17.1741			1.52396			0.761980	+	0.647601i	$0.224228\pi$
$128$	12.1535			1.07423
$129$			2.30609i			0.203040i
$130$			4.16123i			0.364964i
$131$			18.7230i			1.63584i	0.575333	+	0.817919i	$0.304872\pi$
$131$			18.7230i			1.63584i	−0.575333	+	0.817919i	$0.695128\pi$
$132$	2.74309			0.238756
$133$		−	4.03436i		−	0.349823i
$134$	16.6493			1.43828
$135$	−1.21343			−0.104436
$136$	4.76972	+	5.35025i	0.409000	+	0.458780i
$137$	6.00130			0.512726			0.256363	−	0.966581i	$-0.417476\pi$
$137$	6.00130			0.512726			0.256363	+	0.966581i	$0.417476\pi$
$138$	−7.18717			−0.611812
$139$		−	16.7705i		−	1.42245i	−0.702963	−	0.711227i	$-0.748140\pi$
$139$		−	16.7705i		−	1.42245i	0.702963	−	0.711227i	$-0.251860\pi$
$140$	−2.61829			−0.221286
$141$			23.2864i			1.96107i
$142$			25.6271i			2.15057i
$143$		−	3.72296i		−	0.311330i
$144$	11.5901			0.965843
$145$	−2.93117			−0.243420
$146$		−	10.2504i		−	0.848332i
$147$		−	10.6488i		−	0.878299i
$148$			0.0261016i			0.00214554i
$149$	−15.0084			−1.22953			−0.614766	−	0.788710i	$-0.710750\pi$
$149$	−15.0084			−1.22953			−0.614766	+	0.788710i	$0.710750\pi$
$150$			17.5805i			1.43544i
$151$	4.72046			0.384146			0.192073	−	0.981381i	$-0.438479\pi$
$151$	4.72046			0.384146			0.192073	+	0.981381i	$0.438479\pi$
$152$	2.05763			0.166896
$153$	6.36004	+	7.13412i	0.514179	+	0.576759i
$154$	7.04834			0.567971
$155$	3.22766			0.259252
$156$			7.15415i			0.572791i
$157$	−8.65804			−0.690987			−0.345493	−	0.938421i	$-0.612288\pi$
$157$	−8.65804			−0.690987			−0.345493	+	0.938421i	$0.612288\pi$
$158$		−	12.3859i		−	0.985373i
$159$		−	11.0931i		−	0.879739i
$160$		−	3.99446i		−	0.315789i
$161$	−6.13764			−0.483714
$162$	−18.3130			−1.43881
$163$			8.62387i			0.675474i	0.941241	+	0.337737i	$0.109661\pi$
$163$			8.62387i			0.675474i	−0.941241	+	0.337737i	$0.890339\pi$
$164$			10.7552i			0.839841i
$165$			2.12588i			0.165500i
$166$	7.14180			0.554311
$167$		−	1.40671i		−	0.108855i	−0.998518	−	0.0544274i	$-0.982667\pi$
$167$		−	1.40671i		−	0.108855i	0.998518	−	0.0544274i	$-0.0173334\pi$
$168$	13.6643			1.05423
$169$	−3.29028			−0.253099
$170$	4.10998	−	3.66403i	0.315221	−	0.281018i
$171$	2.74368			0.209815
$172$	0.995588			0.0759128
$173$		−	15.0664i		−	1.14547i	−0.819739	−	0.572737i	$-0.805882\pi$
$173$		−	15.0664i		−	1.14547i	0.819739	−	0.572737i	$-0.194118\pi$
$174$	−15.1628			−1.14949
$175$			15.0132i			1.13489i
$176$			5.97384i			0.450295i
$177$			28.6977i			2.15705i
$178$	−4.59010			−0.344042
$179$	21.4565			1.60373			0.801867	−	0.597502i	$-0.203840\pi$
$179$	21.4565			1.60373			0.801867	+	0.597502i	$0.203840\pi$
$180$		−	1.78064i		−	0.132721i
$181$		−	12.4739i		−	0.927176i	−0.886051	−	0.463588i	$-0.846562\pi$
$181$		−	12.4739i		−	0.927176i	0.886051	−	0.463588i	$-0.153438\pi$
$182$			18.3825i			1.36260i
$183$	20.6269			1.52478
$184$		−	3.13036i		−	0.230773i
$185$	−0.0202286			−0.00148723
$186$	16.6966			1.22425
$187$	−3.67711	+	3.27813i	−0.268897	+	0.239720i
$188$	10.0532			0.733208
$189$	−5.36042			−0.389913
$190$		−	1.58064i		−	0.114672i
$191$	7.52219			0.544287			0.272143	−	0.962257i	$-0.412267\pi$
$191$	7.52219			0.544287			0.272143	+	0.962257i	$0.412267\pi$
$192$			2.39762i			0.173033i
$193$			6.40533i			0.461066i	0.973065	+	0.230533i	$0.0740469\pi$
$193$			6.40533i			0.461066i	−0.973065	+	0.230533i	$0.925953\pi$
$194$		−	14.8660i		−	1.06732i
$195$	−5.54442			−0.397044
$196$	−4.59733			−0.328380
$197$		−	6.13495i		−	0.437097i	−0.975826	−	0.218549i	$-0.929868\pi$
$197$		−	6.13495i		−	0.437097i	0.975826	−	0.218549i	$-0.0701322\pi$
$198$			4.79343i			0.340654i
$199$		−	14.8882i		−	1.05539i	−0.849433	−	0.527697i	$-0.823056\pi$
$199$		−	14.8882i		−	1.05539i	0.849433	−	0.527697i	$-0.176944\pi$
$200$	−7.65714			−0.541442
$201$			22.1835i			1.56471i
$202$	−7.08497			−0.498497
$203$	−12.9486			−0.908814
$204$	7.06603	−	6.29934i	0.494721	−	0.441042i
$205$	−8.33522			−0.582157
$206$	−29.3924			−2.04787
$207$		−	4.17408i		−	0.290119i
$208$	−15.5801			−1.08029
$209$			1.41416i			0.0978198i
$210$		−	10.4967i		−	0.724344i
$211$			8.15082i			0.561125i	0.959836	+	0.280563i	$0.0905211\pi$
$211$			8.15082i			0.561125i	−0.959836	+	0.280563i	$0.909479\pi$
$212$	−4.78913			−0.328919
$213$	−34.1455			−2.33961
$214$		−	3.29652i		−	0.225345i
$215$			0.771574i			0.0526209i
$216$		−	2.73396i		−	0.186022i
$217$	14.2584			0.967923
$218$			2.99302i			0.202713i
$219$	13.6577			0.922900
$220$	0.917788			0.0618773
$221$	−8.54955	−	9.59012i	−0.575105	−	0.645101i
$222$	−0.104642			−0.00702308
$223$	−14.7750			−0.989404			−0.494702	−	0.869063i	$-0.664723\pi$
$223$	−14.7750			−0.989404			−0.494702	+	0.869063i	$0.664723\pi$
$224$		−	17.6457i		−	1.17901i
$225$	−10.2102			−0.680679
$226$		−	24.5998i		−	1.63636i
$227$		−	15.6946i		−	1.04169i	−0.853652	−	0.520844i	$-0.825617\pi$
$227$		−	15.6946i		−	1.04169i	0.853652	−	0.520844i	$-0.174383\pi$
$228$		−	2.71750i		−	0.179971i
$229$	−1.24728			−0.0824228			−0.0412114	−	0.999150i	$-0.513122\pi$
$229$	−1.24728			−0.0824228			−0.0412114	+	0.999150i	$0.513122\pi$
$230$	−2.40469			−0.158561
$231$			9.39120i			0.617896i
$232$		−	6.60414i		−	0.433583i
$233$		−	2.64345i		−	0.173178i	−0.996244	−	0.0865892i	$-0.972403\pi$
$233$		−	2.64345i		−	0.173178i	0.996244	−	0.0865892i	$-0.0275968\pi$
$234$	−12.5016			−0.817252
$235$			7.79120i			0.508242i
$236$	12.3894			0.806483
$237$	16.5030			1.07199
$238$	18.1561	−	16.1861i	1.17688	−	1.04919i
$239$	1.14450			0.0740316			0.0370158	−	0.999315i	$-0.488215\pi$
$239$	1.14450			0.0740316			0.0370158	+	0.999315i	$0.488215\pi$
$240$	8.89655			0.574270
$241$		−	4.74714i		−	0.305790i	−0.988242	−	0.152895i	$-0.951140\pi$
$241$		−	4.74714i		−	0.305790i	0.988242	−	0.152895i	$-0.0488596\pi$
$242$	16.5679			1.06502
$243$		−	19.6823i		−	1.26262i
$244$		−	8.90507i		−	0.570089i
$245$		−	3.56290i		−	0.227625i
$246$	−43.1178			−2.74909
$247$	−3.68823			−0.234676
$248$			7.27217i			0.461783i
$249$			9.51573i			0.603035i
$250$			12.5592i			0.794314i
$251$	−20.9830			−1.32444			−0.662218	−	0.749311i	$-0.730385\pi$
$251$	−20.9830			−1.32444			−0.662218	+	0.749311i	$0.730385\pi$
$252$		−	7.86609i		−	0.495517i
$253$	2.15143			0.135259
$254$	29.7246			1.86509
$255$	4.88195	+	5.47613i	0.305719	+	0.342929i
$256$	18.9556			1.18473
$257$	−30.7435			−1.91773			−0.958865	−	0.283864i	$-0.908384\pi$
$257$	−30.7435			−1.91773			−0.958865	+	0.283864i	$0.908384\pi$
$258$			3.99132i			0.248489i
$259$	−0.0893609			−0.00555262
$260$			2.39365i			0.148448i
$261$		−	8.80608i		−	0.545082i
$262$			32.4054i			2.00201i
$263$	−11.3342			−0.698897			−0.349448	−	0.936956i	$-0.613631\pi$
$263$	−11.3342			−0.698897			−0.349448	+	0.936956i	$0.613631\pi$
$264$	−4.78976			−0.294790
$265$		−	3.71154i		−	0.227998i
$266$		−	6.98257i		−	0.428129i
$267$		−	6.11584i		−	0.374284i
$268$	9.57712			0.585016
$269$			7.12126i			0.434191i	0.976150	+	0.217095i	$0.0696583\pi$
$269$			7.12126i			0.434191i	−0.976150	+	0.217095i	$0.930342\pi$
$270$	−2.10018			−0.127813
$271$	4.12058			0.250307			0.125154	−	0.992137i	$-0.460058\pi$
$271$	4.12058			0.250307			0.125154	+	0.992137i	$0.460058\pi$
$272$	13.7186	+	15.3882i	0.831810	+	0.933049i
$273$	−24.4928			−1.48237
$274$	10.3869			0.627497
$275$		−	5.26259i		−	0.317346i
$276$	−4.13424			−0.248852
$277$		−	5.05816i		−	0.303916i	−0.988387	−	0.151958i	$-0.951442\pi$
$277$		−	5.05816i		−	0.303916i	0.988387	−	0.151958i	$-0.0485578\pi$
$278$		−	29.0260i		−	1.74086i
$279$			9.69684i			0.580535i
$280$	4.57184			0.273220
$281$	−4.16921			−0.248714			−0.124357	−	0.992238i	$-0.539687\pi$
$281$	−4.16921			−0.248714			−0.124357	+	0.992238i	$0.539687\pi$
$282$			40.3036i			2.40004i
$283$		−	2.33436i		−	0.138763i	−0.997590	−	0.0693815i	$-0.977897\pi$
$283$		−	2.33436i		−	0.138763i	0.997590	−	0.0693815i	$-0.0221026\pi$
$284$			14.7413i			0.874738i
$285$	2.10604			0.124751
$286$		−	6.44362i		−	0.381019i
$287$	−36.8214			−2.17350
$288$	12.0005			0.707137
$289$	−1.94398	+	16.8885i	−0.114352	+	0.993440i
$290$	−5.07319			−0.297908
$291$	19.8075			1.16114
$292$		−	5.89632i		−	0.345056i
$293$	−14.6914			−0.858282			−0.429141	−	0.903238i	$-0.641184\pi$
$293$	−14.6914			−0.858282			−0.429141	+	0.903238i	$0.641184\pi$
$294$		−	18.4307i		−	1.07490i
$295$			9.60173i			0.559034i
$296$		−	0.0455765i		−	0.00264908i
$297$	1.87899			0.109030
$298$	−25.9761			−1.50476
$299$			5.61105i			0.324496i
$300$			10.1127i			0.583859i
$301$			3.40847i			0.196461i
$302$	8.17006			0.470134
$303$		−	9.44002i		−	0.542315i
$304$	5.91811			0.339427
$305$	6.90137			0.395171
$306$	11.0078	+	12.3476i	0.629274	+	0.705863i
$307$	−7.26952			−0.414893			−0.207447	−	0.978246i	$-0.566515\pi$
$307$	−7.26952			−0.414893			−0.207447	+	0.978246i	$0.566515\pi$
$308$	4.05439			0.231020
$309$		−	39.1625i		−	2.22787i
$310$	5.58637			0.317284
$311$			31.5515i			1.78912i	0.446948	+	0.894560i	$0.352511\pi$
$311$			31.5515i			1.78912i	−0.446948	+	0.894560i	$0.647489\pi$
$312$		−	12.4920i		−	0.707220i
$313$		−	1.25733i		−	0.0710687i	−0.999368	−	0.0355343i	$-0.988687\pi$
$313$		−	1.25733i		−	0.0710687i	0.999368	−	0.0355343i	$-0.0113133\pi$
$314$	−14.9851			−0.845660
$315$	6.09617			0.343480
$316$		−	7.12471i		−	0.400796i
$317$			4.17902i			0.234717i	0.993090	+	0.117359i	$0.0374427\pi$
$317$			4.17902i			0.234717i	−0.993090	+	0.117359i	$0.962557\pi$
$318$		−	19.1997i		−	1.07666i
$319$	4.53888			0.254128
$320$			0.802200i			0.0448443i
$321$	4.39228			0.245153
$322$	−10.6229			−0.591990
$323$	3.24754	+	3.64280i	0.180698	+	0.202691i
$324$	−10.5341			−0.585230
$325$	13.7251			0.761334
$326$			14.9260i			0.826674i
$327$	−3.98790			−0.220531
$328$		−	18.7799i		−	1.03695i
$329$			34.4181i			1.89753i
$330$			3.67942i			0.202546i
$331$	−15.0034			−0.824661			−0.412330	−	0.911034i	$-0.635285\pi$
$331$	−15.0034			−0.824661			−0.412330	+	0.911034i	$0.635285\pi$
$332$	4.10815			0.225464
$333$		−	0.0607725i		−	0.00333031i
$334$		−	2.43471i		−	0.133221i
$335$			7.42221i			0.405519i
$336$	39.3010			2.14405
$337$		−	12.2556i		−	0.667604i	−0.942643	−	0.333802i	$-0.891668\pi$
$337$		−	12.2556i		−	0.667604i	0.942643	−	0.333802i	$-0.108332\pi$
$338$	−5.69475			−0.309753
$339$	32.7768			1.78019
$340$	2.36416	−	2.10764i	0.128215	−	0.114303i
$341$	−4.99800			−0.270657
$342$	4.74870			0.256781
$343$			8.12001i			0.438439i
$344$	−1.73841			−0.0937290
$345$		−	3.20401i		−	0.172498i
$346$		−	26.0765i		−	1.40188i
$347$		−	29.1310i		−	1.56383i	−0.623382	−	0.781917i	$-0.714242\pi$
$347$		−	29.1310i		−	1.56383i	0.623382	−	0.781917i	$-0.285758\pi$
$348$	−8.72204			−0.467550
$349$	3.66258			0.196053			0.0980266	−	0.995184i	$-0.468747\pi$
$349$	3.66258			0.196053			0.0980266	+	0.995184i	$0.468747\pi$
$350$			25.9845i			1.38893i
$351$			4.90052i			0.261570i
$352$			6.18537i			0.329681i
$353$	5.28885			0.281497			0.140748	−	0.990045i	$-0.455049\pi$
$353$	5.28885			0.281497			0.140748	+	0.990045i	$0.455049\pi$
$354$			49.6693i			2.63990i
$355$	−11.4244			−0.606347
$356$	−2.64034			−0.139938
$357$	21.5663	+	24.1911i	1.14141	+	1.28033i
$358$	37.1364			1.96272
$359$	25.0572			1.32247			0.661235	−	0.750179i	$-0.270033\pi$
$359$	25.0572			1.32247			0.661235	+	0.750179i	$0.270033\pi$
$360$			3.10921i			0.163870i
$361$	−17.5990			−0.926265
$362$		−	21.5895i		−	1.13472i
$363$			22.0750i			1.15864i
$364$			10.5741i			0.554233i
$365$	4.56961			0.239184
$366$	35.7005			1.86610
$367$		−	0.883060i		−	0.0460954i	−0.999734	−	0.0230477i	$-0.992663\pi$
$367$		−	0.883060i		−	0.0460954i	0.999734	−	0.0230477i	$-0.00733695\pi$
$368$		−	9.00346i		−	0.469338i
$369$		−	25.0414i		−	1.30361i
$370$	−0.0350111			−0.00182014
$371$		−	16.3960i		−	0.851236i
$372$	9.60430			0.497960
$373$	−2.98147			−0.154375			−0.0771873	−	0.997017i	$-0.524594\pi$
$373$	−2.98147			−0.154375			−0.0771873	+	0.997017i	$0.524594\pi$
$374$	−6.36425	+	5.67370i	−0.329087	+	0.293380i
$375$	−16.7339			−0.864134
$376$	−17.5542			−0.905287
$377$			11.8377i			0.609671i
$378$	−9.27769			−0.477193
$379$		−	18.5449i		−	0.952587i	−0.879286	−	0.476293i	$-0.841980\pi$
$379$		−	18.5449i		−	0.952587i	0.879286	−	0.476293i	$-0.158020\pi$
$380$		−	0.909225i		−	0.0466423i
$381$			39.6051i			2.02903i
$382$	13.0192			0.666122
$383$	29.0357			1.48365			0.741827	−	0.670591i	$-0.233960\pi$
$383$	29.0357			1.48365			0.741827	+	0.670591i	$0.233960\pi$
$384$			28.0271i			1.43025i
$385$			3.14212i			0.160137i
$386$			11.0862i			0.564273i
$387$	−2.31803			−0.117832
$388$		−	8.55133i		−	0.434128i
$389$	33.9321			1.72043			0.860213	−	0.509935i	$-0.170330\pi$
$389$	33.9321			1.72043			0.860213	+	0.509935i	$0.170330\pi$
$390$	−9.59616			−0.485920
$391$	5.54194	−	4.94062i	0.280268	−	0.249858i
$392$	8.02747			0.405449
$393$	−43.1769			−2.17799
$394$		−	10.6182i		−	0.534939i
$395$	5.52161			0.277822
$396$			2.75730i			0.138560i
$397$		−	3.55711i		−	0.178526i	−0.996008	−	0.0892631i	$-0.971549\pi$
$397$		−	3.55711i		−	0.178526i	0.996008	−	0.0892631i	$-0.0284512\pi$
$398$		−	25.7681i		−	1.29164i
$399$	9.30358			0.465762
$400$	−22.0233			−1.10116
$401$		−	5.61697i		−	0.280498i	−0.990116	−	0.140249i	$-0.955210\pi$
$401$		−	5.61697i		−	0.280498i	0.990116	−	0.140249i	$-0.0447903\pi$
$402$			38.3948i			1.91496i
$403$		−	13.0351i		−	0.649324i
$404$	−4.07546			−0.202762
$405$		−	8.16389i		−	0.405667i
$406$	−22.4111			−1.11225
$407$	0.0313237			0.00155266
$408$	−12.3381	+	10.9994i	−0.610828	+	0.544551i
$409$	26.9939			1.33476			0.667382	−	0.744715i	$-0.267415\pi$
$409$	26.9939			1.33476			0.667382	+	0.744715i	$0.267415\pi$
$410$	−14.4264			−0.712470
$411$			13.8395i			0.682653i
$412$	−16.9073			−0.832962
$413$			42.4162i			2.08717i
$414$		−	7.22440i		−	0.355060i
$415$			3.18379i			0.156286i
$416$	−16.1318			−0.790927
$417$	38.6742			1.89388
$418$			2.44760i			0.119716i
$419$			19.3645i			0.946017i	0.881058	+	0.473008i	$0.156832\pi$
$419$			19.3645i			0.946017i	−0.881058	+	0.473008i	$0.843168\pi$
$420$		−	6.03799i		−	0.294624i
$421$	−0.0122804			−0.000598512			−0.000299256	−	1.00000i	$-0.500095\pi$
$421$	−0.0122804			−0.000598512			−0.000299256		1.00000i	$0.500095\pi$
$422$			14.1072i			0.686730i
$423$	−23.4070			−1.13809
$424$	8.36238			0.406113
$425$	−12.0852	−	13.5561i	−0.586218	−	0.657567i
$426$	−59.0982			−2.86332
$427$	30.4872			1.47538
$428$		−	1.89624i		−	0.0916583i
$429$	8.58547			0.414511
$430$			1.33542i			0.0643998i
$431$		−	12.9038i		−	0.621555i	−0.950483	−	0.310777i	$-0.899411\pi$
$431$		−	12.9038i		−	0.621555i	0.950483	−	0.310777i	$-0.100589\pi$
$432$		−	7.86334i		−	0.378325i
$433$	−36.7931			−1.76816			−0.884081	−	0.467334i	$-0.845214\pi$
$433$	−36.7931			−1.76816			−0.884081	+	0.467334i	$0.845214\pi$
$434$	24.6781			1.18459
$435$		−	6.75952i		−	0.324094i
$436$			1.72166i			0.0824527i
$437$		−	2.13135i		−	0.101957i
$438$	23.6384			1.12949
$439$		−	30.8608i		−	1.47290i	−0.676489	−	0.736452i	$-0.736499\pi$
$439$		−	30.8608i		−	1.47290i	0.676489	−	0.736452i	$-0.263501\pi$
$440$	−1.60257			−0.0763994
$441$	10.7040			0.509713
$442$	−14.7974	−	16.5984i	−0.703839	−	0.789503i
$443$	−8.09059			−0.384396			−0.192198	−	0.981356i	$-0.561562\pi$
$443$	−8.09059			−0.384396			−0.192198	+	0.981356i	$0.561562\pi$
$444$	−0.0601925			−0.00285661
$445$		−	2.04625i		−	0.0970015i
$446$	−25.5722			−1.21088
$447$		−	34.6106i		−	1.63702i
$448$			3.54377i			0.167427i
$449$			1.01343i			0.0478268i	0.999714	+	0.0239134i	$0.00761260\pi$
$449$			1.01343i			0.0478268i	−0.999714	+	0.0239134i	$0.992387\pi$
$450$	−17.6715			−0.833044
$451$	12.9070			0.607767
$452$		−	14.1505i		−	0.665582i
$453$			10.8858i			0.511459i
$454$		−	27.1639i		−	1.27486i
$455$	−8.19485			−0.384180
$456$			4.74508i			0.222208i
$457$	13.2933			0.621834			0.310917	−	0.950437i	$-0.399364\pi$
$457$	13.2933			0.621834			0.310917	+	0.950437i	$0.399364\pi$
$458$	−2.15877			−0.100873
$459$	4.84016	−	4.31498i	0.225919	−	0.201406i
$460$	−1.38324			−0.0644940
$461$	−39.9136			−1.85896			−0.929480	−	0.368872i	$-0.879744\pi$
$461$	−39.9136			−1.85896			−0.929480	+	0.368872i	$0.879744\pi$
$462$			16.2541i			0.756208i
$463$	−6.34364			−0.294814			−0.147407	−	0.989076i	$-0.547093\pi$
$463$	−6.34364			−0.294814			−0.147407	+	0.989076i	$0.547093\pi$
$464$		−	18.9946i		−	0.881804i
$465$			7.44327i			0.345173i
$466$		−	4.57523i		−	0.211943i
$467$	16.5127			0.764115			0.382058	−	0.924139i	$-0.375216\pi$
$467$	16.5127			0.764115			0.382058	+	0.924139i	$0.375216\pi$
$468$	−7.19122			−0.332414
$469$			32.7880i			1.51401i
$470$			13.4848i			0.622009i
$471$		−	19.9662i		−	0.919993i
$472$	−21.6334			−0.995758
$473$		−	1.19477i		−	0.0549357i
$474$	28.5630			1.31194
$475$	−5.21349			−0.239211
$476$	10.4438	−	9.31064i	0.478693	−	0.426753i
$477$	11.1506			0.510549
$478$	1.98088			0.0906031
$479$		−	1.25278i		−	0.0572410i	−0.999590	−	0.0286205i	$-0.990889\pi$
$479$		−	1.25278i		−	0.0572410i	0.999590	−	0.0286205i	$-0.00911143\pi$
$480$	9.21156			0.420448
$481$			0.0816941i			0.00372493i
$482$		−	8.21624i		−	0.374239i
$483$		−	14.1539i		−	0.644026i
$484$	9.53028			0.433194
$485$	6.62722			0.300927
$486$		−	34.0656i		−	1.54525i
$487$			7.03061i			0.318588i	0.987231	+	0.159294i	$0.0509217\pi$
$487$			7.03061i			0.318588i	−0.987231	+	0.159294i	$0.949078\pi$
$488$			15.5493i			0.703884i
$489$	−19.8874			−0.899339
$490$		−	6.16658i		−	0.278578i
$491$	−13.1613			−0.593963			−0.296982	−	0.954883i	$-0.595980\pi$
$491$	−13.1613			−0.593963			−0.296982	+	0.954883i	$0.595980\pi$
$492$	−24.8025			−1.11818
$493$	11.6919	−	10.4232i	0.526575	−	0.469439i
$494$	−6.38350			−0.287207
$495$	−2.13689			−0.0960462
$496$			20.9160i			0.939157i
$497$	−50.4682			−2.26381
$498$			16.4696i			0.738020i
$499$			19.6281i			0.878675i	0.898322	+	0.439337i	$0.144787\pi$
$499$			19.6281i			0.878675i	−0.898322	+	0.439337i	$0.855213\pi$
$500$			7.22438i			0.323084i
$501$	3.24401			0.144931
$502$	−36.3169			−1.62090
$503$			26.9487i			1.20158i	0.799405	+	0.600792i	$0.205148\pi$
$503$			26.9487i			1.20158i	−0.799405	+	0.600792i	$0.794852\pi$
$504$			13.7351i			0.611811i
$505$		−	3.15846i		−	0.140549i
$506$	3.72364			0.165536
$507$		−	7.58768i		−	0.336981i
$508$	17.0984			0.758617
$509$	−15.3674			−0.681149			−0.340575	−	0.940217i	$-0.610622\pi$
$509$	−15.3674			−0.681149			−0.340575	+	0.940217i	$0.610622\pi$
$510$	8.44956	+	9.47796i	0.374153	+	0.419691i
$511$	20.1865			0.892999
$512$	8.50094			0.375692
$513$		−	1.86146i		−	0.0821854i
$514$	−53.2102			−2.34700
$515$		−	13.1030i		−	0.577389i
$516$			2.29591i			0.101072i
$517$		−	12.0646i		−	0.530600i
$518$	−0.154664			−0.00679554
$519$	34.7443			1.52511
$520$		−	4.17959i		−	0.183287i
$521$			14.3749i			0.629774i	0.949129	+	0.314887i	$0.101967\pi$
$521$			14.3749i			0.629774i	−0.949129	+	0.314887i	$0.898033\pi$
$522$		−	15.2414i		−	0.667096i
$523$	22.6000			0.988228			0.494114	−	0.869397i	$-0.335493\pi$
$523$	22.6000			0.988228			0.494114	+	0.869397i	$0.335493\pi$
$524$			18.6404i			0.814310i
$525$	−34.6218			−1.51102
$526$	−19.6170			−0.855340
$527$	−12.8745	+	11.4776i	−0.560823	+	0.499972i
$528$	−13.7762			−0.599532
$529$	19.7575			0.859021
$530$		−	6.42385i		−	0.279034i
$531$	−28.8464			−1.25183
$532$		−	4.01656i		−	0.174140i
$533$			33.6622i			1.45807i
$534$		−	10.5852i		−	0.458065i
$535$	1.46958			0.0635353
$536$	−16.7228			−0.722314
$537$			49.4806i			2.13524i
$538$			12.3253i			0.531382i
$539$			5.51711i			0.237639i
$540$	−1.20808			−0.0519875
$541$		−	17.3615i		−	0.746427i	−0.927745	−	0.373214i	$-0.878256\pi$
$541$		−	17.3615i		−	0.746427i	0.927745	−	0.373214i	$-0.121744\pi$
$542$	7.13180			0.306337
$543$	28.7658			1.23446
$544$	14.2043	+	15.9331i	0.609005	+	0.683127i
$545$	−1.33428			−0.0571542
$546$	−42.3916			−1.81419
$547$		−	6.66694i		−	0.285058i	−0.989791	−	0.142529i	$-0.954477\pi$
$547$		−	6.66694i		−	0.285058i	0.989791	−	0.142529i	$-0.0455234\pi$
$548$	5.97482			0.255232
$549$			20.7337i			0.884894i
$550$		−	9.10836i		−	0.388382i
$551$		−	4.49653i		−	0.191559i
$552$	7.21888			0.307256
$553$	24.3920			1.03725
$554$		−	8.75455i		−	0.371945i
$555$		−	0.0466488i		−	0.00198013i
$556$		−	16.6965i		−	0.708088i
$557$	−30.5966			−1.29642			−0.648210	−	0.761462i	$-0.724482\pi$
$557$	−30.5966			−1.29642			−0.648210	+	0.761462i	$0.724482\pi$
$558$			16.7831i			0.710484i
$559$	3.11604			0.131795
$560$	13.1494			0.555664
$561$	−7.55964	−	8.47972i	−0.319168	−	0.358014i
$562$	−7.21597			−0.304388
$563$	4.09082			0.172407			0.0862037	−	0.996278i	$-0.472526\pi$
$563$	4.09082			0.172407			0.0862037	+	0.996278i	$0.472526\pi$
$564$			23.1837i			0.976208i
$565$	10.9665			0.461365
$566$		−	4.04025i		−	0.169824i
$567$		−	36.0645i		−	1.51457i
$568$		−	25.7401i		−	1.08003i
$569$	35.2961			1.47969			0.739844	−	0.672778i	$-0.234899\pi$
$569$	35.2961			1.47969			0.739844	+	0.672778i	$0.234899\pi$
$570$	3.64509			0.152676
$571$		−	19.3620i		−	0.810276i	−0.914255	−	0.405138i	$-0.867223\pi$
$571$		−	19.3620i		−	0.810276i	0.914255	−	0.405138i	$-0.132777\pi$
$572$		−	3.70654i		−	0.154978i
$573$			17.3468i			0.724674i
$574$	−63.7295			−2.66002
$575$			7.93149i			0.330766i
$576$	−2.41004			−0.100418
$577$	47.4597			1.97577			0.987886	−	0.155182i	$-0.0495965\pi$
$577$	47.4597			1.97577			0.987886	+	0.155182i	$0.0495965\pi$
$578$	−3.36460	+	29.2302i	−0.139949	+	1.21582i
$579$	−14.7712			−0.613872
$580$	−2.91823			−0.121173
$581$			14.0646i			0.583497i
$582$	34.2824			1.42105
$583$			5.74728i			0.238028i
$584$			10.2957i			0.426038i
$585$		−	5.57315i		−	0.230421i
$586$	−25.4276			−1.05040
$587$	−41.8053			−1.72549			−0.862745	−	0.505640i	$-0.831257\pi$
$587$	−41.8053			−1.72549			−0.862745	+	0.505640i	$0.831257\pi$
$588$		−	10.6018i		−	0.437212i
$589$			4.95137i			0.204018i
$590$			16.6184i			0.684171i
$591$	14.1477			0.581960
$592$		−	0.131086i		−	0.00538760i
$593$	21.0383			0.863939			0.431969	−	0.901888i	$-0.357819\pi$
$593$	21.0383			0.863939			0.431969	+	0.901888i	$0.357819\pi$
$594$	3.25211			0.133436
$595$	7.21569	+	8.09391i	0.295814	+	0.331818i
$596$	−14.9421			−0.612053
$597$	34.3334			1.40517
$598$			9.71148i			0.397132i
$599$	23.5695			0.963023			0.481511	−	0.876440i	$-0.340088\pi$
$599$	23.5695			0.963023			0.481511	+	0.876440i	$0.340088\pi$
$600$		−	17.6580i		−	0.720886i
$601$			31.9345i			1.30263i	0.758805	+	0.651317i	$0.225783\pi$
$601$			31.9345i			1.30263i	−0.758805	+	0.651317i	$0.774217\pi$
$602$			5.89931i			0.240438i
$603$	−22.2985			−0.908064
$604$	4.69963			0.191225
$605$			7.38591i			0.300280i
$606$		−	16.3386i		−	0.663709i
$607$		−	40.8163i		−	1.65668i	−0.560224	−	0.828341i	$-0.689285\pi$
$607$		−	40.8163i		−	1.65668i	0.560224	−	0.828341i	$-0.310715\pi$
$608$	6.12766			0.248509
$609$		−	29.8606i		−	1.21001i
$610$	11.9447			0.483628
$611$	31.4652			1.27294
$612$	6.33197	+	7.10264i	0.255955	+	0.287107i
$613$	−23.5549			−0.951372			−0.475686	−	0.879615i	$-0.657800\pi$
$613$	−23.5549			−0.951372			−0.475686	+	0.879615i	$0.657800\pi$
$614$	−12.5819			−0.507765
$615$		−	19.2217i		−	0.775096i
$616$	−7.07944			−0.285239
$617$		−	29.8401i		−	1.20132i	−0.799505	−	0.600659i	$-0.794905\pi$
$617$		−	29.8401i		−	1.20132i	0.799505	−	0.600659i	$-0.205095\pi$
$618$		−	67.7815i		−	2.72657i
$619$			10.1293i			0.407131i	0.979061	+	0.203566i	$0.0652530\pi$
$619$			10.1293i			0.407131i	−0.979061	+	0.203566i	$0.934747\pi$
$620$	3.21342			0.129054
$621$	−2.83191			−0.113641
$622$			54.6086i			2.18960i
$623$		−	9.03943i		−	0.362157i
$624$		−	35.9292i		−	1.43832i
$625$	16.4245			0.656981
$626$		−	2.17616i		−	0.0869769i
$627$	−3.26119			−0.130239
$628$	−8.61984			−0.343969
$629$	0.0806879	−	0.0719329i	0.00321724	−	0.00286815i
$630$	10.5511			0.420366
$631$	21.0577			0.838294			0.419147	−	0.907918i	$-0.362329\pi$
$631$	21.0577			0.838294			0.419147	+	0.907918i	$0.362329\pi$
$632$			12.4406i			0.494860i
$633$	−18.7965			−0.747093
$634$			7.23295i			0.287257i
$635$			13.2511i			0.525855i
$636$		−	11.0441i		−	0.437929i
$637$	−14.3889			−0.570111
$638$	7.85578			0.311013
$639$		−	34.3224i		−	1.35777i
$640$			9.37734i			0.370672i
$641$			20.4177i			0.806450i	0.915101	+	0.403225i	$0.132111\pi$
$641$			20.4177i			0.806450i	−0.915101	+	0.403225i	$0.867889\pi$
$642$	7.60205			0.300029
$643$		−	26.9847i		−	1.06417i	−0.846690	−	0.532087i	$-0.821408\pi$
$643$		−	26.9847i		−	1.06417i	0.846690	−	0.532087i	$-0.178592\pi$
$644$	−6.11056			−0.240790
$645$	−1.77932			−0.0700605
$646$	5.62077	+	6.30487i	0.221146	+	0.248062i
$647$	−23.7154			−0.932347			−0.466174	−	0.884693i	$-0.654368\pi$
$647$	−23.7154			−0.932347			−0.466174	+	0.884693i	$0.654368\pi$
$648$	18.3938			0.722578
$649$		−	14.8682i		−	0.583626i
$650$	23.7552			0.931754
$651$			32.8811i			1.28871i
$652$			8.58582i			0.336247i
$653$		−	12.8967i		−	0.504686i	−0.967638	−	0.252343i	$-0.918799\pi$
$653$		−	12.8967i		−	0.504686i	0.967638	−	0.252343i	$-0.0812011\pi$
$654$	−6.90216			−0.269896
$655$	−14.4462			−0.564460
$656$		−	54.0142i		−	2.10890i
$657$			13.7284i			0.535597i
$658$			59.5701i			2.32228i
$659$	−16.1132			−0.627682			−0.313841	−	0.949475i	$-0.601616\pi$
$659$	−16.1132			−0.627682			−0.313841	+	0.949475i	$0.601616\pi$
$660$			2.11650i			0.0823846i
$661$	36.6732			1.42642			0.713211	−	0.700950i	$-0.247240\pi$
$661$	36.6732			1.42642			0.713211	+	0.700950i	$0.247240\pi$
$662$	−25.9675			−1.00926
$663$	22.1156	−	19.7160i	0.858900	−	0.765706i
$664$	−7.17331			−0.278378
$665$	3.11281			0.120709
$666$		−	0.105184i		−	0.00407578i
$667$	−6.84076			−0.264875
$668$		−	1.40051i		−	0.0541873i
$669$		−	34.0723i		−	1.31731i
$670$			12.8462i			0.496291i
$671$	−10.6867			−0.412555
$672$	40.6926			1.56975
$673$		−	14.4542i		−	0.557168i	−0.960412	−	0.278584i	$-0.910135\pi$
$673$		−	14.4542i		−	0.557168i	0.960412	−	0.278584i	$-0.0898650\pi$
$674$		−	21.2117i		−	0.817043i
$675$			6.92712i			0.266625i
$676$	−3.27577			−0.125991
$677$		−	3.00794i		−	0.115605i	−0.998328	−	0.0578023i	$-0.981591\pi$
$677$		−	3.00794i		−	0.115605i	0.998328	−	0.0578023i	$-0.0184093\pi$
$678$	56.7294			2.17868
$679$	29.2762			1.12352
$680$	−4.12811	+	3.68019i	−0.158306	+	0.141129i
$681$	36.1932			1.38692
$682$	−8.65042			−0.331242
$683$		−	38.8281i		−	1.48571i	−0.669450	−	0.742857i	$-0.733470\pi$
$683$		−	38.8281i		−	1.48571i	0.669450	−	0.742857i	$-0.266530\pi$
$684$	2.73158			0.104444
$685$			4.63045i			0.176920i
$686$			14.0539i			0.536581i
$687$		−	2.87634i		−	0.109739i
$688$	−4.99998			−0.190622
$689$	−14.9893			−0.571045
$690$		−	5.54543i		−	0.211111i
$691$		−	16.5970i		−	0.631381i	−0.948862	−	0.315690i	$-0.897764\pi$
$691$		−	16.5970i		−	0.631381i	0.948862	−	0.315690i	$-0.102236\pi$
$692$		−	14.9999i		−	0.570210i
$693$	−9.43985			−0.358590
$694$		−	50.4193i		−	1.91389i
$695$	12.9397			0.490830
$696$	15.2297			0.577280
$697$	33.2476	−	29.6401i	1.25934	−	1.12270i
$698$	6.33910			0.239939
$699$	6.09603			0.230573
$700$			14.9470i			0.564942i
$701$	−21.2251			−0.801660			−0.400830	−	0.916153i	$-0.631278\pi$
$701$	−21.2251			−0.801660			−0.400830	+	0.916153i	$0.631278\pi$
$702$			8.48170i			0.320121i
$703$		−	0.0310314i		−	0.00117037i
$704$		−	1.24220i		−	0.0468171i
$705$	−17.9672			−0.676683
$706$	9.15381			0.344508
$707$		−	13.9527i		−	0.524744i
$708$			28.5711i			1.07377i
$709$			42.6721i			1.60258i	0.598274	+	0.801291i	$0.295853\pi$
$709$			42.6721i			1.60258i	−0.598274	+	0.801291i	$0.704147\pi$
$710$	−19.7732			−0.742074
$711$			16.5885i			0.622118i
$712$	4.61035			0.172780
$713$	7.53272			0.282103
$714$	37.3264	+	41.8695i	1.39691	+	1.56692i
$715$	2.87254			0.107427
$716$	21.3618			0.798329
$717$			2.63932i			0.0985671i
$718$	43.3685			1.61850
$719$			35.1170i			1.30964i	0.755784	+	0.654821i	$0.227256\pi$
$719$			35.1170i			1.30964i	−0.755784	+	0.654821i	$0.772744\pi$
$720$			8.94264i			0.333272i
$721$		−	57.8835i		−	2.15569i
$722$	−30.4600			−1.13360
$723$	10.9473			0.407135
$724$		−	12.4188i		−	0.461542i
$725$			16.7331i			0.621452i
$726$			38.2070i			1.41799i
$727$	−2.97904			−0.110486			−0.0552432	−	0.998473i	$-0.517593\pi$
$727$	−2.97904			−0.110486			−0.0552432	+	0.998473i	$0.517593\pi$
$728$		−	18.4636i		−	0.684307i
$729$	13.6465			0.505427
$730$	7.90897			0.292724
$731$	−2.74372	−	3.07766i	−0.101480	−	0.113831i
$732$	20.5359			0.759027
$733$	36.3091			1.34111			0.670554	−	0.741861i	$-0.266057\pi$
$733$	36.3091			1.34111			0.670554	+	0.741861i	$0.266057\pi$
$734$		−	1.52838i		−	0.0564135i
$735$	8.21635			0.303065
$736$		−	9.32226i		−	0.343623i
$737$		−	11.4932i		−	0.423357i
$738$		−	43.3411i		−	1.59541i
$739$	−30.0007			−1.10359			−0.551796	−	0.833979i	$-0.686057\pi$
$739$	−30.0007			−1.10359			−0.551796	+	0.833979i	$0.686057\pi$
$740$	−0.0201393			−0.000740336
$741$		−	8.50537i		−	0.312453i
$742$		−	28.3778i		−	1.04178i
$743$			33.2196i			1.21871i	0.792898	+	0.609355i	$0.208572\pi$
$743$			33.2196i			1.21871i	−0.792898	+	0.609355i	$0.791428\pi$
$744$	−16.7702			−0.614827
$745$		−	11.5801i		−	0.424260i
$746$	−5.16026			−0.188930
$747$	−9.56502			−0.349966
$748$	−3.66088	+	3.26366i	−0.133855	+	0.119331i
$749$	6.49194			0.237210
$750$	−28.9626			−1.05757
$751$			51.0887i			1.86425i	0.362133	+	0.932126i	$0.382049\pi$
$751$			51.0887i			1.86425i	−0.362133	+	0.932126i	$0.617951\pi$
$752$	−50.4888			−1.84114
$753$		−	48.3887i		−	1.76338i
$754$			20.4884i			0.746142i
$755$			3.64219i			0.132553i
$756$	−5.33677			−0.194096
$757$	15.8817			0.577229			0.288614	−	0.957445i	$-0.406805\pi$
$757$	15.8817			0.577229			0.288614	+	0.957445i	$0.406805\pi$
$758$		−	32.0971i		−	1.16582i
$759$			4.96138i			0.180087i
$760$			1.58762i			0.0575888i
$761$	−0.137362			−0.00497938			−0.00248969	−	0.999997i	$-0.500792\pi$
$761$	−0.137362			−0.00497938			−0.00248969	+	0.999997i	$0.500792\pi$
$762$			68.5475i			2.48321i
$763$	−5.89425			−0.213386
$764$	7.48900			0.270943
$765$	−5.50450	+	4.90724i	−0.199016	+	0.177422i
$766$	50.2543			1.81576
$767$	38.7771			1.40016
$768$			43.7133i			1.57737i
$769$	−12.4953			−0.450592			−0.225296	−	0.974290i	$-0.572335\pi$
$769$	−12.4953			−0.450592			−0.225296	+	0.974290i	$0.572335\pi$
$770$			5.43831i			0.195983i
$771$		−	70.8972i		−	2.55330i
$772$			6.37707i			0.229516i
$773$	44.9963			1.61841			0.809203	−	0.587529i	$-0.199899\pi$
$773$	44.9963			1.61841			0.809203	+	0.587529i	$0.199899\pi$
$774$	−4.01200			−0.144208
$775$		−	18.4257i		−	0.661871i
$776$			14.9316i			0.536014i
$777$		−	0.206074i		−	0.00739286i
$778$	58.7289			2.10553
$779$		−	12.7866i		−	0.458127i
$780$	−5.51996			−0.197646
$781$	17.6906			0.633020
$782$	9.59186	−	8.55111i	0.343004	−	0.305787i
$783$	−5.97450			−0.213511
$784$	23.0884			0.824586
$785$		−	6.68032i		−	0.238431i
$786$	−74.7296			−2.66552
$787$		−	27.9578i		−	0.996589i	−0.867008	−	0.498295i	$-0.833960\pi$
$787$		−	27.9578i		−	0.996589i	0.867008	−	0.498295i	$-0.166040\pi$
$788$		−	6.10788i		−	0.217584i
$789$		−	26.1376i		−	0.930524i
$790$	9.55667			0.340011
$791$	48.4453			1.72252
$792$		−	4.81458i		−	0.171079i
$793$		−	27.8715i		−	0.989748i
$794$		−	6.15656i		−	0.218488i
$795$	8.55914			0.303561
$796$		−	14.8225i		−	0.525369i
$797$	−33.9435			−1.20234			−0.601170	−	0.799121i	$-0.705299\pi$
$797$	−33.9435			−1.20234			−0.601170	+	0.799121i	$0.705299\pi$
$798$	16.1024			0.570019
$799$	−27.7056	−	31.0776i	−0.980152	−	1.09945i
$800$	−22.8031			−0.806211
$801$	6.14753			0.217212
$802$		−	9.72171i		−	0.343286i
$803$	−7.07598			−0.249706
$804$			22.0857i			0.778901i
$805$		−	4.73564i		−	0.166909i
$806$		−	22.5608i		−	0.794671i
$807$	−16.4222			−0.578090
$808$	7.11624			0.250348
$809$		−	36.2481i		−	1.27442i	−0.770691	−	0.637209i	$-0.780089\pi$
$809$		−	36.2481i		−	1.27442i	0.770691	−	0.637209i	$-0.219911\pi$
$810$		−	14.1299i		−	0.496473i
$811$		−	33.5500i		−	1.17810i	−0.808097	−	0.589049i	$-0.799502\pi$
$811$		−	33.5500i		−	1.17810i	0.808097	−	0.589049i	$-0.200498\pi$
$812$	−12.8915			−0.452402
$813$			9.50241i			0.333264i
$814$	0.0542143			0.00190021
$815$	−6.65396			−0.233078
$816$	−35.4866	+	31.6362i	−1.24228	+	1.10749i
$817$	−1.18363			−0.0414098
$818$	46.7205			1.63354
$819$		−	24.6197i		−	0.860282i
$820$	−8.29845			−0.289794
$821$			12.7174i			0.443842i	0.975065	+	0.221921i	$0.0712327\pi$
$821$			12.7174i			0.443842i	−0.975065	+	0.221921i	$0.928767\pi$
$822$			23.9531i			0.835461i
$823$		−	1.93404i		−	0.0674165i	−0.999432	−	0.0337082i	$-0.989268\pi$
$823$		−	1.93404i		−	0.0674165i	0.999432	−	0.0337082i	$-0.0107317\pi$
$824$	29.5221			1.02845
$825$	12.1360			0.422520
$826$			73.4130i			2.55436i
$827$			24.1262i			0.838950i	0.907767	+	0.419475i	$0.137786\pi$
$827$			24.1262i			0.838950i	−0.907767	+	0.419475i	$0.862214\pi$
$828$		−	4.15566i		−	0.144419i
$829$	−44.9441			−1.56097			−0.780487	−	0.625172i	$-0.785029\pi$
$829$	−44.9441			−1.56097			−0.780487	+	0.625172i	$0.785029\pi$
$830$			5.51042i			0.191270i
$831$	11.6646			0.404639
$832$	3.23973			0.112317
$833$	12.6697	+	14.2117i	0.438979	+	0.492407i
$834$	66.9363			2.31782
$835$	1.08538			0.0375613
$836$			1.40792i			0.0486941i
$837$	6.57884			0.227398
$838$			33.5156i			1.15778i
$839$			43.3382i			1.49620i	0.663586	+	0.748100i	$0.269034\pi$
$839$			43.3382i			1.49620i	−0.663586	+	0.748100i	$0.730966\pi$
$840$			10.5431i			0.363770i
$841$	14.5680			0.502346
$842$	−0.0212547			−0.000732486
$843$		−	9.61456i		−	0.331143i
$844$			8.11485i			0.279325i
$845$		−	2.53870i		−	0.0873339i
$846$	−40.5124			−1.39284
$847$			32.6277i			1.12110i
$848$	24.0517			0.825938
$849$	5.38323			0.184752
$850$	−20.9168	−	23.4626i	−0.717440	−	0.804759i
$851$	−0.0472094			−0.00161832
$852$	−33.9948			−1.16464
$853$			16.7390i			0.573132i	0.958060	+	0.286566i	$0.0925138\pi$
$853$			16.7390i			0.573132i	−0.958060	+	0.286566i	$0.907486\pi$
$854$	52.7666			1.80563
$855$			2.11696i			0.0723983i
$856$			3.31106i			0.113170i
$857$			34.8843i			1.19163i	0.803123	+	0.595813i	$0.203170\pi$
$857$			34.8843i			1.19163i	−0.803123	+	0.595813i	$0.796830\pi$
$858$	14.8595			0.507296
$859$	23.3157			0.795520			0.397760	−	0.917490i	$-0.369788\pi$
$859$	23.3157			0.795520			0.397760	+	0.917490i	$0.369788\pi$
$860$			0.768170i			0.0261944i
$861$		−	84.9132i		−	2.89383i
$862$		−	22.3336i		−	0.760686i
$863$	−40.7022			−1.38552			−0.692759	−	0.721169i	$-0.743605\pi$
$863$	−40.7022			−1.38552			−0.692759	+	0.721169i	$0.743605\pi$
$864$		−	8.14177i		−	0.276989i
$865$	11.6248			0.395255
$866$	−63.6806			−2.16395
$867$	−38.9463	−	4.48300i	−1.32269	−	0.152250i
$868$	14.1955			0.481826
$869$	−8.55015			−0.290044
$870$		−	11.6992i		−	0.396641i
$871$	29.9750			1.01566
$872$		−	3.00623i		−	0.101804i
$873$			19.9101i			0.673855i
$874$		−	3.68890i		−	0.124779i
$875$	−24.7333			−0.836137
$876$	13.5974			0.459414
$877$		−	28.3948i		−	0.958823i	−0.877590	−	0.479412i	$-0.840850\pi$
$877$		−	28.3948i		−	0.958823i	0.877590	−	0.479412i	$-0.159150\pi$
$878$		−	53.4131i		−	1.80261i
$879$		−	33.8797i		−	1.14273i
$880$	−4.60926			−0.155378
$881$		−	35.1842i		−	1.18539i	−0.805428	−	0.592694i	$-0.798065\pi$
$881$		−	35.1842i		−	1.18539i	0.805428	−	0.592694i	$-0.201935\pi$
$882$	18.5262			0.623810
$883$	17.2900			0.581855			0.290928	−	0.956745i	$-0.406036\pi$
$883$	17.2900			0.581855			0.290928	+	0.956745i	$0.406036\pi$
$884$	−8.51183	−	9.54780i	−0.286284	−	0.321127i
$885$	−22.1424			−0.744309
$886$	−14.0030			−0.470440
$887$		−	11.7077i		−	0.393105i	−0.980493	−	0.196553i	$-0.937025\pi$
$887$		−	11.7077i		−	0.393105i	0.980493	−	0.196553i	$-0.0629747\pi$
$888$	0.105103			0.00352703
$889$			58.5376i			1.96329i
$890$		−	3.54160i		−	0.118715i
$891$			12.6417i			0.423512i
$892$	−14.7098			−0.492519
$893$	−11.9520			−0.399959
$894$		−	59.9031i		−	2.00346i
$895$			16.5553i			0.553382i
$896$			41.4250i			1.38391i
$897$	−12.9396			−0.432040
$898$			1.75403i			0.0585326i
$899$	15.8918			0.530022
$900$	−10.1651			−0.338838
$901$	13.1983	+	14.8046i	0.439698	+	0.493214i
$902$	22.3391			0.743812
$903$	−7.86024			−0.261572
$904$			24.7084i			0.821789i
$905$	9.62452			0.319930
$906$			18.8409i			0.625946i
$907$		−	32.4487i		−	1.07744i	−0.842484	−	0.538721i	$-0.818908\pi$
$907$		−	32.4487i		−	1.07744i	0.842484	−	0.538721i	$-0.181092\pi$
$908$		−	15.6254i		−	0.518546i
$909$	9.48892			0.314728
$910$	−14.1835			−0.470177
$911$		−	31.4271i		−	1.04123i	−0.853793	−	0.520613i	$-0.825704\pi$
$911$		−	31.4271i		−	1.04123i	0.853793	−	0.520613i	$-0.174296\pi$
$912$			13.6477i			0.451919i
$913$		−	4.93006i		−	0.163161i
$914$	23.0077			0.761028
$915$			15.9152i			0.526139i
$916$	−1.24178			−0.0410295
$917$	−63.8170			−2.10742
$918$	8.37723	−	7.46827i	0.276490	−	0.246490i
$919$	48.0686			1.58564			0.792819	−	0.609458i	$-0.208613\pi$
$919$	48.0686			1.58564			0.792819	+	0.609458i	$0.208613\pi$
$920$	2.41530			0.0796302
$921$		−	16.7641i		−	0.552397i
$922$	−69.0815			−2.27508
$923$			46.1382i			1.51866i
$924$			9.34976i			0.307585i
$925$			0.115479i			0.00379691i
$926$	−10.9794			−0.360806
$927$	39.3653			1.29293
$928$		−	19.6672i		−	0.645608i
$929$		−	45.4179i		−	1.49011i	−0.667001	−	0.745057i	$-0.732422\pi$
$929$		−	45.4179i		−	1.49011i	0.667001	−	0.745057i	$-0.267578\pi$
$930$			12.8826i			0.422438i
$931$	5.46563			0.179129
$932$		−	2.63179i		−	0.0862072i
$933$	−72.7604			−2.38207
$934$	28.5797			0.935158
$935$	−2.52932	−	2.83716i	−0.0827175	−	0.0927851i
$936$	12.5567			0.410429
$937$	−6.32713			−0.206698			−0.103349	−	0.994645i	$-0.532956\pi$
$937$	−6.32713			−0.206698			−0.103349	+	0.994645i	$0.532956\pi$
$938$			56.7488i			1.85291i
$939$	2.89952			0.0946222
$940$			7.75682i			0.253000i
$941$			56.6305i			1.84610i	0.384679	+	0.923050i	$0.374312\pi$
$941$			56.6305i			1.84610i	−0.384679	+	0.923050i	$0.625688\pi$
$942$		−	34.5570i		−	1.12593i
$943$	−19.4527			−0.633469
$944$	−62.2214			−2.02514
$945$		−	4.13596i		−	0.134543i
$946$		−	2.06789i		−	0.0672328i
$947$		−	11.1112i		−	0.361064i	−0.983569	−	0.180532i	$-0.942218\pi$
$947$		−	11.1112i		−	0.361064i	0.983569	−	0.180532i	$-0.0577819\pi$
$948$	16.4302			0.533628
$949$		−	18.4546i		−	0.599062i
$950$	−9.02338			−0.292757
$951$	−9.63718			−0.312507
$952$	−18.2362	+	16.2575i	−0.591038	+	0.526908i
$953$	−0.547952			−0.0177499			−0.00887495	−	0.999961i	$-0.502825\pi$
$953$	−0.547952			−0.0177499			−0.00887495	+	0.999961i	$0.502825\pi$
$954$	19.2991			0.624832
$955$			5.80393i			0.187811i
$956$	1.13945			0.0368525
$957$			10.4670i			0.338351i
$958$		−	2.16828i		−	0.0700541i
$959$			20.4553i			0.660536i
$960$	−1.84994			−0.0597066
$961$	13.5007			0.435505
$962$			0.141394i			0.00455873i
$963$			4.41503i			0.142272i
$964$		−	4.72619i		−	0.152220i
$965$	−4.94219			−0.159095
$966$		−	24.4973i		−	0.788187i
$967$	−50.2092			−1.61462			−0.807309	−	0.590129i	$-0.799077\pi$
$967$	−50.2092			−1.61462			−0.807309	+	0.590129i	$0.799077\pi$
$968$	−16.6410			−0.534862
$969$	−8.40061	+	7.48911i	−0.269866	+	0.240585i
$970$	11.4702			0.368287
$971$	−27.1547			−0.871436			−0.435718	−	0.900083i	$-0.643505\pi$
$971$	−27.1547			−0.871436			−0.435718	+	0.900083i	$0.643505\pi$
$972$		−	19.5954i		−	0.628523i
$973$	57.1618			1.83252
$974$			12.1684i			0.389901i
$975$			31.6514i			1.01366i
$976$			44.7225i			1.43153i
$977$	−17.2944			−0.553297			−0.276648	−	0.960971i	$-0.589224\pi$
$977$	−17.2944			−0.553297			−0.276648	+	0.960971i	$0.589224\pi$
$978$	−34.4206			−1.10065
$979$			3.16859i			0.101269i
$980$		−	3.54718i		−	0.113310i
$981$		−	4.00856i		−	0.127983i
$982$	−22.7794			−0.726918
$983$		−	10.8569i		−	0.346280i	−0.984897	−	0.173140i	$-0.944609\pi$
$983$		−	10.8569i		−	0.346280i	0.984897	−	0.173140i	$-0.0553914\pi$
$984$	43.3080			1.38061
$985$	4.73357			0.150824
$986$	20.2360	−	18.0403i	0.644445	−	0.574520i
$987$	−79.3711			−2.52641
$988$	−3.67195			−0.116820
$989$			1.80070i			0.0572589i
$990$	−3.69848			−0.117546
$991$		−	12.1470i		−	0.385862i	−0.981212	−	0.192931i	$-0.938201\pi$
$991$		−	12.1470i		−	0.385862i	0.981212	−	0.192931i	$-0.0617994\pi$
$992$			21.6566i			0.687599i
$993$		−	34.5991i		−	1.09797i
$994$	−87.3492			−2.77055
$995$	11.4873			0.364173
$996$			9.47374i			0.300187i
$997$			21.5489i			0.682461i	0.939980	+	0.341230i	$0.110844\pi$
$997$			21.5489i			0.682461i	−0.939980	+	0.341230i	$0.889156\pi$
$998$			33.9719i			1.07536i
$999$	−0.0412312			−0.00130450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.c.560.14	yes	20
17.16	even	2	inner	731.2.d.c.560.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.c.560.13	✓	20	17.16	even	2	inner
731.2.d.c.560.14	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.73078 q^{2} +2.30609i q^{3} +0.995588 q^{4} +0.771574i q^{5} +3.99132i q^{6} +3.40847i q^{7} -1.73841 q^{8} -2.31803 q^{9} +O(q^{10})\)	\(q+1.73078 q^{2} +2.30609i q^{3} +0.995588 q^{4} +0.771574i q^{5} +3.99132i q^{6} +3.40847i q^{7} -1.73841 q^{8} -2.31803 q^{9} +1.33542i q^{10} -1.19477i q^{11} +2.29591i q^{12} +3.11604 q^{13} +5.89931i q^{14} -1.77932 q^{15} -4.99998 q^{16} +(-2.74372 - 3.07766i) q^{17} -4.01200 q^{18} -1.18363 q^{19} +0.768170i q^{20} -7.86024 q^{21} -2.06789i q^{22} +1.80070i q^{23} -4.00893i q^{24} +4.40467 q^{25} +5.39317 q^{26} +1.57267i q^{27} +3.39344i q^{28} +3.79894i q^{29} -3.07960 q^{30} -4.18322i q^{31} -5.17702 q^{32} +2.75525 q^{33} +(-4.74877 - 5.32674i) q^{34} -2.62989 q^{35} -2.30780 q^{36} +0.0262173i q^{37} -2.04859 q^{38} +7.18586i q^{39} -1.34131i q^{40} +10.8029i q^{41} -13.6043 q^{42} +1.00000 q^{43} -1.18950i q^{44} -1.78853i q^{45} +3.11661i q^{46} +10.0978 q^{47} -11.5304i q^{48} -4.61770 q^{49} +7.62351 q^{50} +(7.09735 - 6.32726i) q^{51} +3.10229 q^{52} -4.81035 q^{53} +2.72195i q^{54} +0.921856 q^{55} -5.92534i q^{56} -2.72954i q^{57} +6.57512i q^{58} +12.4443 q^{59} -1.77147 q^{60} -8.94454i q^{61} -7.24022i q^{62} -7.90096i q^{63} +1.03969 q^{64} +2.40426i q^{65} +4.76872 q^{66} +9.61957 q^{67} +(-2.73161 - 3.06408i) q^{68} -4.15257 q^{69} -4.55175 q^{70} +14.8067i q^{71} +4.02970 q^{72} -5.92245i q^{73} +0.0453762i q^{74} +10.1576i q^{75} -1.17840 q^{76} +4.07235 q^{77} +12.4371i q^{78} -7.15629i q^{79} -3.85786i q^{80} -10.5808 q^{81} +18.6974i q^{82} +4.12635 q^{83} -7.82555 q^{84} +(2.37464 - 2.11698i) q^{85} +1.73078 q^{86} -8.76069 q^{87} +2.07701i q^{88} -2.65204 q^{89} -3.09555i q^{90} +10.6209i q^{91} +1.79275i q^{92} +9.64687 q^{93} +17.4770 q^{94} -0.913255i q^{95} -11.9387i q^{96} -8.58923i q^{97} -7.99221 q^{98} +2.76952i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9	\( 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9} - 4 q^{13} + 26 q^{15} + 6 q^{16} + 16 q^{17} - 22 q^{18} - 4 q^{19} + 20 q^{21} - 2 q^{25} + 22 q^{26} - 72 q^{30} + 38 q^{32} - 12 q^{33} + 12 q^{34} - 30 q^{35} - 104 q^{36} - 22 q^{38} + 26 q^{42} + 20 q^{43} - 34 q^{47} + 22 q^{49} + 42 q^{50} + 52 q^{51} - 110 q^{52} + 14 q^{53} + 12 q^{55} + 20 q^{59} + 42 q^{60} - 22 q^{64} + 50 q^{66} - 12 q^{67} + 50 q^{68} - 82 q^{69} - 30 q^{70} - 50 q^{72} + 2 q^{76} + 78 q^{77} + 44 q^{81} + 20 q^{83} + 62 q^{84} + 76 q^{85} + 2 q^{86} + 12 q^{87} - 46 q^{89} + 58 q^{93} - 18 q^{94} - 62 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9 - 4 * q^13 + 26 * q^15 + 6 * q^16 + 16 * q^17 - 22 * q^18 - 4 * q^19 + 20 * q^21 - 2 * q^25 + 22 * q^26 - 72 * q^30 + 38 * q^32 - 12 * q^33 + 12 * q^34 - 30 * q^35 - 104 * q^36 - 22 * q^38 + 26 * q^42 + 20 * q^43 - 34 * q^47 + 22 * q^49 + 42 * q^50 + 52 * q^51 - 110 * q^52 + 14 * q^53 + 12 * q^55 + 20 * q^59 + 42 * q^60 - 22 * q^64 + 50 * q^66 - 12 * q^67 + 50 * q^68 - 82 * q^69 - 30 * q^70 - 50 * q^72 + 2 * q^76 + 78 * q^77 + 44 * q^81 + 20 * q^83 + 62 * q^84 + 76 * q^85 + 2 * q^86 + 12 * q^87 - 46 * q^89 + 58 * q^93 - 18 * q^94 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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