LMFDB - Embedded newform 37.2.h.a.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(3,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("37.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.h (of order $18$, degree $6$, 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:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 30x^{16} + 333x^{14} + 1826x^{12} + 5490x^{10} + 9432x^{8} + 9385x^{6} + 5316x^{4} + 1584x^{2} + 192 $ x^18 + 30x^16 + 333x^14 + 1826x^12 + 5490x^10 + 9432x^8 + 9385x^6 + 5316x^4 + 1584x^2 + 192
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			28.2
Root			$0.834738i$ of defining polynomial
Character	$\chi$	$=$	37.28
Dual form			37.2.h.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11764 + 0.197069i) q^{2} +(-0.522172 + 2.96139i) q^{3} +(-0.669111 + 0.243536i) q^{4} +(1.89897 - 2.26310i) q^{5} -3.41266i q^{6} +(1.25550 + 1.05349i) q^{7} +(2.66549 - 1.53892i) q^{8} +(-5.67807 - 2.06665i) q^{9} +O(q^{10})$	\(q+(-1.11764 + 0.197069i) q^{2} +(-0.522172 + 2.96139i) q^{3} +(-0.669111 + 0.243536i) q^{4} +(1.89897 - 2.26310i) q^{5} -3.41266i q^{6} +(1.25550 + 1.05349i) q^{7} +(2.66549 - 1.53892i) q^{8} +(-5.67807 - 2.06665i) q^{9} +(-1.67637 + 2.90355i) q^{10} +(-0.588101 - 1.01862i) q^{11} +(-0.371814 - 2.10866i) q^{12} +(0.543140 + 1.49227i) q^{13} +(-1.61080 - 0.929995i) q^{14} +(5.71033 + 6.80531i) q^{15} +(-1.58485 + 1.32985i) q^{16} +(1.29620 - 3.56127i) q^{17} +(6.75329 + 1.19079i) q^{18} +(-1.80842 - 0.318873i) q^{19} +(-0.719472 + 1.97673i) q^{20} +(-3.77537 + 3.16791i) q^{21} +(0.858022 + 1.02255i) q^{22} +(-2.76838 - 1.59832i) q^{23} +(3.16550 + 8.69714i) q^{24} +(-0.647311 - 3.67108i) q^{25} +(-0.901113 - 1.56077i) q^{26} +(4.57447 - 7.92321i) q^{27} +(-1.09663 - 0.399140i) q^{28} +(-3.99823 + 2.30838i) q^{29} +(-7.72319 - 6.48053i) q^{30} -7.07583i q^{31} +(-2.44759 + 2.91693i) q^{32} +(3.32362 - 1.20970i) q^{33} +(-0.746859 + 4.23565i) q^{34} +(4.76830 - 0.840779i) q^{35} +4.30256 q^{36} +(3.80039 + 4.74942i) q^{37} +2.08399 q^{38} +(-4.70279 + 0.829228i) q^{39} +(1.57895 - 8.95466i) q^{40} +(-0.914644 + 0.332903i) q^{41} +(3.59519 - 4.28458i) q^{42} -0.234622i q^{43} +(0.641576 + 0.538346i) q^{44} +(-15.4595 + 8.92555i) q^{45} +(3.40902 + 1.24078i) q^{46} +(-4.78138 + 8.28159i) q^{47} +(-3.11063 - 5.38777i) q^{48} +(-0.749100 - 4.24836i) q^{49} +(1.44692 + 3.97537i) q^{50} +(9.86947 + 5.69814i) q^{51} +(-0.726842 - 0.866216i) q^{52} +(4.70480 - 3.94780i) q^{53} +(-3.55117 + 9.75676i) q^{54} +(-3.42203 - 0.603396i) q^{55} +(4.96776 + 0.875949i) q^{56} +(1.88861 - 5.18891i) q^{57} +(4.01365 - 3.36785i) q^{58} +(0.638035 + 0.760380i) q^{59} +(-5.47818 - 3.16283i) q^{60} +(1.95677 + 5.37617i) q^{61} +(1.39443 + 7.90820i) q^{62} +(-4.95161 - 8.57644i) q^{63} +(4.22956 - 7.32580i) q^{64} +(4.40856 + 1.60458i) q^{65} +(-3.47620 + 2.00699i) q^{66} +(12.0781 + 10.1347i) q^{67} +2.69856i q^{68} +(6.17882 - 7.36363i) q^{69} +(-5.16353 + 1.87937i) q^{70} +(1.34232 - 7.61269i) q^{71} +(-18.3153 + 3.22948i) q^{72} -15.9089 q^{73} +(-5.18342 - 4.55919i) q^{74} +11.2095 q^{75} +(1.28769 - 0.227054i) q^{76} +(0.334745 - 1.89843i) q^{77} +(5.09259 - 1.85355i) q^{78} +(-7.34295 + 8.75099i) q^{79} +6.11202i q^{80} +(7.18862 + 6.03197i) q^{81} +(0.956634 - 0.552313i) q^{82} +(-6.50611 - 2.36803i) q^{83} +(1.75464 - 3.03912i) q^{84} +(-5.59809 - 9.69617i) q^{85} +(0.0462369 + 0.262222i) q^{86} +(-4.74823 - 13.0457i) q^{87} +(-3.13516 - 1.81008i) q^{88} +(-4.87316 - 5.80761i) q^{89} +(15.5192 - 13.0221i) q^{90} +(-0.890171 + 2.44573i) q^{91} +(2.24160 + 0.395255i) q^{92} +(20.9543 + 3.69480i) q^{93} +(3.71179 - 10.1981i) q^{94} +(-4.15577 + 3.48710i) q^{95} +(-7.36008 - 8.77140i) q^{96} +(11.3862 + 6.57381i) q^{97} +(1.67444 + 4.60049i) q^{98} +(1.23415 + 6.99919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−1.11764	+	0.197069i	−0.790288	+	0.139349i	−0.554201	−	0.832383i	$-0.686976\pi$
$2$	−1.11764	+	0.197069i	−0.790288	+	0.139349i	−0.236087	+	0.971732i	$0.575865\pi$
$3$	−0.522172	+	2.96139i	−0.301476	+	1.70976i	0.338167	+	0.941086i	$0.390193\pi$
$3$	−0.522172	+	2.96139i	−0.301476	+	1.70976i	−0.639644	+	0.768671i	$0.720918\pi$
$4$	−0.669111	+	0.243536i	−0.334555	+	0.121768i
$5$	1.89897	−	2.26310i	0.849245	−	1.01209i	−0.150480	−	0.988613i	$-0.548082\pi$
$5$	1.89897	−	2.26310i	0.849245	−	1.01209i	0.999724	−	0.0234772i	$-0.00747370\pi$
$6$		−	3.41266i		−	1.39321i
$7$	1.25550	+	1.05349i	0.474533	+	0.398181i	0.848445	−	0.529284i	$-0.177539\pi$
$7$	1.25550	+	1.05349i	0.474533	+	0.398181i	−0.373912	+	0.927464i	$0.621984\pi$
$8$	2.66549	−	1.53892i	0.942395	−	0.544092i
$9$	−5.67807	−	2.06665i	−1.89269	−	0.688883i
$10$	−1.67637	+	2.90355i	−0.530114	+	0.918184i
$11$	−0.588101	−	1.01862i	−0.177319	−	0.307126i	0.763642	−	0.645640i	$-0.223409\pi$
$11$	−0.588101	−	1.01862i	−0.177319	−	0.307126i	−0.940961	+	0.338514i	$0.890076\pi$
$12$	−0.371814	−	2.10866i	−0.107334	−	0.608719i
$13$	0.543140	+	1.49227i	0.150640	+	0.413880i	0.991943	−	0.126684i	$-0.0404333\pi$
$13$	0.543140	+	1.49227i	0.150640	+	0.413880i	−0.841303	+	0.540564i	$0.818211\pi$
$14$	−1.61080	−	0.929995i	−0.430504	−	0.248552i
$15$	5.71033	+	6.80531i	1.47440	+	1.75712i
$16$	−1.58485	+	1.32985i	−0.396213	+	0.332462i
$17$	1.29620	−	3.56127i	0.314374	−	0.863736i	−0.677386	−	0.735628i	$-0.736887\pi$
$17$	1.29620	−	3.56127i	0.314374	−	0.863736i	0.991760	−	0.128108i	$-0.0408904\pi$
$18$	6.75329	+	1.19079i	1.59177	+	0.280671i
$19$	−1.80842	−	0.318873i	−0.414879	−	0.0731544i	−0.0376874	−	0.999290i	$-0.511999\pi$
$19$	−1.80842	−	0.318873i	−0.414879	−	0.0731544i	−0.377192	+	0.926135i	$0.623110\pi$
$20$	−0.719472	+	1.97673i	−0.160879	+	0.442011i
$21$	−3.77537	+	3.16791i	−0.823853	+	0.691294i
$22$	0.858022	+	1.02255i	0.182931	+	0.218008i
$23$	−2.76838	−	1.59832i	−0.577246	−	0.333273i	0.182792	−	0.983152i	$-0.441487\pi$
$23$	−2.76838	−	1.59832i	−0.577246	−	0.333273i	−0.760038	+	0.649878i	$0.774820\pi$
$24$	3.16550	+	8.69714i	0.646155	+	1.77530i
$25$	−0.647311	−	3.67108i	−0.129462	−	0.734216i
$26$	−0.901113	−	1.56077i	−0.176723	−	0.306093i
$27$	4.57447	−	7.92321i	0.880357	−	1.52482i
$28$	−1.09663	−	0.399140i	−0.207243	−	0.0754304i
$29$	−3.99823	+	2.30838i	−0.742452	+	0.428655i	−0.822960	−	0.568099i	$-0.807679\pi$
$29$	−3.99823	+	2.30838i	−0.742452	+	0.428655i	0.0805082	+	0.996754i	$0.474346\pi$
$30$	−7.72319	−	6.48053i	−1.41006	−	1.18318i
$31$		−	7.07583i		−	1.27086i	−0.772160	−	0.635428i	$-0.780824\pi$
$31$		−	7.07583i		−	1.27086i	0.772160	−	0.635428i	$-0.219176\pi$
$32$	−2.44759	+	2.91693i	−0.432677	+	0.515644i
$33$	3.32362	−	1.20970i	0.578568	−	0.210581i
$34$	−0.746859	+	4.23565i	−0.128085	+	0.726408i
$35$	4.76830	−	0.840779i	0.805989	−	0.142118i
$36$	4.30256			0.717093
$37$	3.80039	+	4.74942i	0.624781	+	0.780800i
$37$	3.80039	+	4.74942i	0.624781	+	0.780800i
$38$	2.08399			0.338068
$39$	−4.70279	+	0.829228i	−0.753049	+	0.132783i
$40$	1.57895	−	8.95466i	0.249654	−	1.41586i
$41$	−0.914644	+	0.332903i	−0.142843	+	0.0519907i	−0.412453	−	0.910979i	$-0.635328\pi$
$41$	−0.914644	+	0.332903i	−0.142843	+	0.0519907i	0.269609	+	0.962970i	$0.413106\pi$
$42$	3.59519	−	4.28458i	0.554750	−	0.661125i
$43$		−	0.234622i		−	0.0357796i	−0.999840	−	0.0178898i	$-0.994305\pi$
$43$		−	0.234622i		−	0.0357796i	0.999840	−	0.0178898i	$-0.00569480\pi$
$44$	0.641576	+	0.538346i	0.0967212	+	0.0811587i
$45$	−15.4595	+	8.92555i	−2.30457	+	1.33054i
$46$	3.40902	+	1.24078i	0.502632	+	0.182943i
$47$	−4.78138	+	8.28159i	−0.697436	+	1.20799i	0.271917	+	0.962321i	$0.412342\pi$
$47$	−4.78138	+	8.28159i	−0.697436	+	1.20799i	−0.969353	+	0.245673i	$0.920991\pi$
$48$	−3.11063	−	5.38777i	−0.448980	−	0.777657i
$49$	−0.749100	−	4.24836i	−0.107014	−	0.606908i
$50$	1.44692	+	3.97537i	0.204625	+	0.562202i
$51$	9.86947	+	5.69814i	1.38200	+	0.797899i
$52$	−0.726842	−	0.866216i	−0.100795	−	0.120123i
$53$	4.70480	−	3.94780i	0.646255	−	0.542272i	−0.259677	−	0.965695i	$-0.583616\pi$
$53$	4.70480	−	3.94780i	0.646255	−	0.542272i	0.905932	+	0.423423i	$0.139172\pi$
$54$	−3.55117	+	9.75676i	−0.483253	+	1.32773i
$55$	−3.42203	−	0.603396i	−0.461426	−	0.0813619i
$56$	4.96776	+	0.875949i	0.663844	+	0.117054i
$57$	1.88861	−	5.18891i	0.250153	−	0.687288i
$58$	4.01365	−	3.36785i	0.527018	−	0.442221i
$59$	0.638035	+	0.760380i	0.0830651	+	0.0989931i	0.805976	−	0.591948i	$-0.201641\pi$
$59$	0.638035	+	0.760380i	0.0830651	+	0.0989931i	−0.722911	+	0.690941i	$0.757196\pi$
$60$	−5.47818	−	3.16283i	−0.707231	−	0.408320i
$61$	1.95677	+	5.37617i	0.250538	+	0.688349i	0.999664	+	0.0259206i	$0.00825172\pi$
$61$	1.95677	+	5.37617i	0.250538	+	0.688349i	−0.749126	+	0.662428i	$0.769526\pi$
$62$	1.39443	+	7.90820i	0.177093	+	1.00434i
$63$	−4.95161	−	8.57644i	−0.623844	−	1.08053i
$64$	4.22956	−	7.32580i	0.528694	−	0.915726i
$65$	4.40856	+	1.60458i	0.546814	+	0.199024i
$66$	−3.47620	+	2.00699i	−0.427891	+	0.247043i
$67$	12.0781	+	10.1347i	1.47558	+	1.23816i	0.910758	+	0.412940i	$0.135498\pi$
$67$	12.0781	+	10.1347i	1.47558	+	1.23816i	0.564818	+	0.825216i	$0.308946\pi$
$68$			2.69856i			0.327248i
$69$	6.17882	−	7.36363i	0.743843	−	0.886477i
$70$	−5.16353	+	1.87937i	−0.617160	+	0.224628i
$71$	1.34232	−	7.61269i	0.159304	−	0.903460i	−0.795440	−	0.606032i	$-0.792760\pi$
$71$	1.34232	−	7.61269i	0.159304	−	0.903460i	0.954744	−	0.297427i	$-0.0961286\pi$
$72$	−18.3153	+	3.22948i	−2.15848	+	0.380598i
$73$	−15.9089			−1.86200			−0.930999	−	0.365022i	$-0.881062\pi$
$73$	−15.9089			−1.86200			−0.930999	+	0.365022i	$0.881062\pi$
$74$	−5.18342	−	4.55919i	−0.602561	−	0.529995i
$75$	11.2095			1.29436
$76$	1.28769	−	0.227054i	0.147708	−	0.0260449i
$77$	0.334745	−	1.89843i	0.0381477	−	0.216346i
$78$	5.09259	−	1.85355i	0.576622	−	0.209873i
$79$	−7.34295	+	8.75099i	−0.826146	+	0.984563i	−1.00000		0.000208541i	$-0.999934\pi$
$79$	−7.34295	+	8.75099i	−0.826146	+	0.984563i	0.173854	+	0.984772i	$0.444378\pi$
$80$			6.11202i			0.683344i
$81$	7.18862	+	6.03197i	0.798736	+	0.670219i
$82$	0.956634	−	0.552313i	0.105643	−	0.0609928i
$83$	−6.50611	−	2.36803i	−0.714138	−	0.259925i	−0.0407031	−	0.999171i	$-0.512960\pi$
$83$	−6.50611	−	2.36803i	−0.714138	−	0.259925i	−0.673435	+	0.739246i	$0.735182\pi$
$84$	1.75464	−	3.03912i	0.191447	−	0.331595i
$85$	−5.59809	−	9.69617i	−0.607198	−	1.05170i
$86$	0.0462369	+	0.262222i	0.00498585	+	0.0282762i
$87$	−4.74823	−	13.0457i	−0.509064	−	1.39864i
$88$	−3.13516	−	1.81008i	−0.334209	−	0.192956i
$89$	−4.87316	−	5.80761i	−0.516554	−	0.615605i	0.443208	−	0.896419i	$-0.353840\pi$
$89$	−4.87316	−	5.80761i	−0.516554	−	0.615605i	−0.959762	+	0.280813i	$0.909396\pi$
$90$	15.5192	−	13.0221i	1.63586	−	1.37265i
$91$	−0.890171	+	2.44573i	−0.0933153	+	0.256382i
$92$	2.24160	+	0.395255i	0.233703	+	0.0412081i
$93$	20.9543	+	3.69480i	2.17286	+	0.383133i
$94$	3.71179	−	10.1981i	0.382842	−	1.05185i
$95$	−4.15577	+	3.48710i	−0.426373	+	0.357769i
$96$	−7.36008	−	8.77140i	−0.751185	−	0.895227i
$97$	11.3862	+	6.57381i	1.15609	+	0.667469i	0.950364	−	0.311141i	$-0.100711\pi$
$97$	11.3862	+	6.57381i	1.15609	+	0.667469i	0.205726	+	0.978610i	$0.434044\pi$
$98$	1.67444	+	4.60049i	0.169144	+	0.464720i
$99$	1.23415	+	6.99919i	0.124036	+	0.703445i
$100$	1.32716	+	2.29872i	0.132716	+	0.229872i
$101$	−6.73565	+	11.6665i	−0.670222	+	1.16086i	0.307619	+	0.951510i	$0.400468\pi$
$101$	−6.73565	+	11.6665i	−0.670222	+	1.16086i	−0.977841	+	0.209349i	$0.932865\pi$
$102$	−12.1534	−	4.42348i	−1.20337	−	0.437990i
$103$	−0.964968	+	0.557125i	−0.0950812	+	0.0548951i	−0.546787	−	0.837272i	$-0.684149\pi$
$103$	−0.964968	+	0.557125i	−0.0950812	+	0.0548951i	0.451705	+	0.892167i	$0.350816\pi$
$104$	3.74422	+	3.14177i	0.367151	+	0.308076i
$105$			14.5598i			1.42089i
$106$	−4.48027	+	5.33938i	−0.435162	+	0.518606i
$107$	−13.8841	+	5.05341i	−1.34223	+	0.488531i	−0.910514	−	0.413479i	$-0.864314\pi$
$107$	−13.8841	+	5.05341i	−1.34223	+	0.488531i	−0.431715	+	0.902010i	$0.642091\pi$
$108$	−1.13124	+	6.41556i	−0.108853	+	0.617337i
$109$	9.49542	−	1.67430i	0.909496	−	0.160369i	0.300722	−	0.953712i	$-0.402772\pi$
$109$	9.49542	−	1.67430i	0.909496	−	0.160369i	0.608775	+	0.793343i	$0.291661\pi$
$110$	3.94349			0.375997
$111$	−16.0493	+	8.77441i	−1.52334	+	0.832830i
$112$	−3.39075			−0.320396
$113$	9.57993	−	1.68920i	0.901204	−	0.158907i	0.296197	−	0.955127i	$-0.404282\pi$
$113$	9.57993	−	1.68920i	0.901204	−	0.158907i	0.605007	+	0.796220i	$0.293170\pi$
$114$	−1.08820	+	6.17151i	−0.101920	+	0.578014i
$115$	−8.87423	+	3.22996i	−0.827526	+	0.301195i
$116$	2.11308	−	2.51827i	0.196195	−	0.233816i
$117$		−	9.59567i		−	0.887120i
$118$	−0.862939	−	0.724092i	−0.0794400	−	0.0666580i
$119$	5.37913	−	3.10564i	0.493104	−	0.284694i
$120$	25.6937	+	9.35175i	2.34550	+	0.853694i
$121$	4.80828	−	8.32818i	0.437116	−	0.757107i
$122$	−3.24643	−	5.62299i	−0.293918	−	0.509082i
$123$	−0.508253	−	2.88245i	−0.0458276	−	0.259901i
$124$	1.72322	+	4.73451i	0.154750	+	0.425172i
$125$	3.25511	+	1.87934i	0.291146	+	0.168093i
$126$	7.22425	+	8.60953i	0.643588	+	0.766998i
$127$	3.49282	−	2.93083i	0.309938	−	0.260069i	−0.474529	−	0.880240i	$-0.657381\pi$
$127$	3.49282	−	2.93083i	0.309938	−	0.260069i	0.784466	+	0.620171i	$0.212937\pi$
$128$	−0.678741	+	1.86482i	−0.0599928	+	0.164829i
$129$	0.694807	+	0.122513i	0.0611744	+	0.0107867i
$130$	−5.24338	−	0.924549i	−0.459875	−	0.0810883i
$131$	3.50193	−	9.62147i	0.305965	−	0.840631i	−0.687468	−	0.726215i	$-0.741278\pi$
$131$	3.50193	−	9.62147i	0.305965	−	0.840631i	0.993433	−	0.114417i	$-0.0364999\pi$
$132$	−1.92926	+	1.61884i	−0.167921	+	0.140902i
$133$	−1.93453	−	2.30549i	−0.167745	−	0.199911i
$134$	−15.4962	−	8.94673i	−1.33867	−	0.772879i
$135$	−9.24427	−	25.3984i	−0.795620	−	2.18595i
$136$	−2.02552	−	11.4873i	−0.173687	−	0.985028i
$137$	2.10698	+	3.64940i	0.180012	+	0.311789i	0.941884	−	0.335938i	$-0.109053\pi$
$137$	2.10698	+	3.64940i	0.180012	+	0.311789i	−0.761873	+	0.647727i	$0.775720\pi$
$138$	−5.45453	+	9.44752i	−0.464320	+	0.804227i
$139$	4.86737	+	1.77158i	0.412845	+	0.150263i	0.540089	−	0.841608i	$-0.318391\pi$
$139$	4.86737	+	1.77158i	0.412845	+	0.150263i	−0.127243	+	0.991872i	$0.540613\pi$
$140$	−2.98576	+	1.72383i	−0.252343	+	0.145690i
$141$	−22.0283	−	18.4839i	−1.85512	−	1.55663i
$142$			8.77274i			0.736192i
$143$	1.20063	−	1.43086i	0.100402	−	0.119654i
$144$	11.7472	−	4.27564i	0.978935	−	0.356303i
$145$	−2.36841	+	13.4319i	−0.196686	+	1.11546i
$146$	17.7804	−	3.13516i	1.47152	−	0.259468i
$147$	12.9722			1.06993
$148$	−3.69954	−	2.25236i	−0.304100	−	0.185143i
$149$	9.18328			0.752323			0.376162	−	0.926554i	$-0.377244\pi$
$149$	9.18328			0.752323			0.376162	+	0.926554i	$0.377244\pi$
$150$	−12.5281	+	2.20905i	−1.02292	+	0.180368i
$151$	1.55484	−	8.81794i	0.126531	−	0.717594i	−0.853855	−	0.520510i	$-0.825742\pi$
$151$	1.55484	−	8.81794i	0.126531	−	0.717594i	0.980387	−	0.197084i	$-0.0631471\pi$
$152$	−5.31104	+	1.93306i	−0.430783	+	0.156792i
$153$	−14.7198	+	17.5424i	−1.19003	+	1.41822i
$154$			2.18772i			0.176292i
$155$	−16.0133	−	13.4368i	−1.28622	−	1.07927i
$156$	2.94474	−	1.70015i	0.235768	−	0.136121i
$157$	−8.68888	−	3.16249i	−0.693448	−	0.252394i	−0.0288372	−	0.999584i	$-0.509180\pi$
$157$	−8.68888	−	3.16249i	−0.693448	−	0.252394i	−0.664611	+	0.747190i	$0.731403\pi$
$158$	6.48220	−	11.2275i	0.515696	−	0.893211i
$159$	9.23424	+	15.9942i	0.732323	+	1.26842i
$160$	1.95340	+	11.0783i	0.154430	+	0.875816i
$161$	−1.79188	−	4.92314i	−0.141220	−	0.387998i
$162$	−9.22298	−	5.32489i	−0.724626	−	0.418363i
$163$	4.81293	+	5.73583i	0.376978	+	0.449265i	0.920858	−	0.389898i	$-0.127490\pi$
$163$	4.81293	+	5.73583i	0.376978	+	0.449265i	−0.543880	+	0.839163i	$0.683045\pi$
$164$	0.530924	−	0.445498i	0.0414582	−	0.0347876i
$165$	3.57378	−	9.81887i	0.278218	−	0.764398i
$166$	7.73813	+	1.36444i	0.600596	+	0.105901i
$167$	−3.19436	−	0.563251i	−0.247187	−	0.0435857i	0.0486818	−	0.998814i	$-0.484498\pi$
$167$	−3.19436	−	0.563251i	−0.247187	−	0.0435857i	−0.295869	+	0.955229i	$0.595609\pi$
$168$	−5.18805	+	14.2540i	−0.400267	+	1.09972i
$169$	8.02672	−	6.73522i	0.617440	−	0.518094i
$170$	8.16745	+	9.73358i	0.626415	+	0.746532i
$171$	9.60932	+	5.54794i	0.734843	+	0.424262i
$172$	0.0571390	+	0.156988i	0.00435681	+	0.0119702i
$173$	2.19302	+	12.4373i	0.166733	+	0.945587i	0.947260	+	0.320466i	$0.103839\pi$
$173$	2.19302	+	12.4373i	0.166733	+	0.945587i	−0.780528	+	0.625121i	$0.785049\pi$
$174$	7.87770	+	13.6446i	0.597207	+	1.03439i
$175$	3.05474	−	5.29096i	0.230917	−	0.399959i
$176$	2.28666	+	0.832277i	0.172364	+	0.0627352i
$177$	−2.58494	+	1.49242i	−0.194296	+	0.112177i
$178$	6.59093	+	5.53044i	0.494011	+	0.414524i
$179$		−	9.86627i		−	0.737440i	−0.929541	−	0.368720i	$-0.879796\pi$
$179$		−	9.86627i		−	0.737440i	0.929541	−	0.368720i	$-0.120204\pi$
$180$	8.17043	−	9.73714i	0.608988	−	0.725763i
$181$	−5.54467	+	2.01810i	−0.412132	+	0.150004i	−0.539761	−	0.841818i	$-0.681486\pi$
$181$	−5.54467	+	2.01810i	−0.412132	+	0.150004i	0.127629	+	0.991822i	$0.459263\pi$
$182$	0.512910	−	2.90886i	0.0380194	−	0.215619i
$183$	−16.9427	+	2.98746i	−1.25244	+	0.220839i
$184$	−9.83879			−0.725325
$185$	17.9653	+	0.418328i	1.32083	+	0.0307561i
$186$	−24.1474			−1.77057
$187$	−4.38988	+	0.774054i	−0.321020	+	0.0566045i
$188$	1.18240	−	6.70574i	0.0862356	−	0.489066i
$189$	14.0902	−	5.12842i	1.02491	−	0.373038i
$190$	3.95743	−	4.71629i	0.287102	−	0.342155i
$191$		−	0.594347i		−	0.0430055i	−0.999769	−	0.0215027i	$-0.993155\pi$
$191$		−	0.594347i		−	0.0430055i	0.999769	−	0.0215027i	$-0.00684506\pi$
$192$	19.4860	+	16.3507i	1.40628	+	1.18001i
$193$	3.72931	−	2.15312i	0.268442	−	0.154985i	−0.359737	−	0.933054i	$-0.617134\pi$
$193$	3.72931	−	2.15312i	0.268442	−	0.154985i	0.628179	+	0.778069i	$0.283800\pi$
$194$	−14.0211	−	5.10326i	−1.00666	−	0.366393i
$195$	−7.05382	+	12.2176i	−0.505134	+	0.874918i
$196$	1.53586	+	2.66019i	0.109704	+	0.190013i
$197$	0.881689	+	5.00030i	0.0628177	+	0.356257i	0.999973	+	0.00734447i	$0.00233784\pi$
$197$	0.881689	+	5.00030i	0.0628177	+	0.356257i	−0.937155	+	0.348912i	$0.886551\pi$
$198$	−2.75865	−	7.57934i	−0.196049	−	0.538640i
$199$	−1.72135	−	0.993824i	−0.122023	−	0.0704503i	0.437746	−	0.899099i	$-0.355777\pi$
$199$	−1.72135	−	0.993824i	−0.122023	−	0.0704503i	−0.559769	+	0.828648i	$0.689110\pi$
$200$	−7.37492	−	8.78909i	−0.521486	−	0.621482i
$201$	−36.3197	+	30.4759i	−2.56180	+	2.14960i
$202$	5.22890	−	14.3663i	0.367904	−	1.01081i
$203$	−7.45160	−	1.31392i	−0.523000	−	0.0922190i
$204$	−7.99147	−	1.40911i	−0.559515	−	0.0986576i
$205$	−0.983486	+	2.70211i	−0.0686896	+	0.188723i
$206$	0.968691	−	0.812829i	0.0674919	−	0.0566325i
$207$	12.4159	+	14.7967i	0.862962	+	1.02844i
$208$	−2.84528	−	1.64272i	−0.197285	−	0.113902i
$209$	0.738721	+	2.02962i	0.0510984	+	0.140392i
$210$	−2.86929	−	16.2726i	−0.198000	−	1.12291i
$211$	9.78853	+	16.9542i	0.673870	+	1.16718i	0.976798	+	0.214164i	$0.0687025\pi$
$211$	9.78853	+	16.9542i	0.673870	+	1.16718i	−0.302928	+	0.953013i	$0.597964\pi$
$212$	−2.18660	+	3.78731i	−0.150176	+	0.260113i
$213$	21.8432	+	7.95027i	1.49667	+	0.544743i
$214$	14.5215	−	8.38401i	0.992671	−	0.573119i
$215$	−0.530974	−	0.445540i	−0.0362121	−	0.0303856i
$216$		−	28.1590i		−	1.91598i
$217$	7.45429	−	8.88368i	0.506030	−	0.603063i
$218$	−10.2825	+	3.74251i	−0.696417	+	0.253475i
$219$	8.30720	−	47.1125i	0.561348	−	3.18357i
$220$	2.43666	−	0.429650i	0.164280	−	0.0289670i
$221$	6.01838			0.404840
$222$	16.2082	−	12.9694i	1.08782	−	0.870452i
$223$	−13.4568			−0.901136			−0.450568	−	0.892742i	$-0.648779\pi$
$223$	−13.4568			−0.901136			−0.450568	+	0.892742i	$0.648779\pi$
$224$	−6.14588	+	1.08369i	−0.410639	+	0.0724068i
$225$	−3.91136	+	22.1824i	−0.260757	+	1.47883i
$226$	−10.3740	+	3.77582i	−0.690067	+	0.251164i
$227$	16.8351	−	20.0633i	1.11739	−	1.33165i	0.179876	−	0.983689i	$-0.442430\pi$
$227$	16.8351	−	20.0633i	1.11739	−	1.33165i	0.937510	−	0.347959i	$-0.113125\pi$
$228$			3.93190i			0.260397i
$229$	−4.05007	−	3.39841i	−0.267636	−	0.224573i	0.499086	−	0.866552i	$-0.333669\pi$
$229$	−4.05007	−	3.39841i	−0.267636	−	0.224573i	−0.766722	+	0.641979i	$0.778114\pi$
$230$	9.28164	−	5.35876i	0.612013	−	0.353346i
$231$	5.44719	+	1.98262i	0.358399	+	0.130447i
$232$	−7.10483	+	12.3059i	−0.466455	+	0.807924i
$233$	6.94943	+	12.0368i	0.455272	+	0.788555i	0.998704	−	0.0508988i	$-0.0162086\pi$
$233$	6.94943	+	12.0368i	0.455272	+	0.788555i	−0.543432	+	0.839453i	$0.682875\pi$
$234$	1.89101	+	10.7245i	0.123619	+	0.701080i
$235$	9.66240	+	26.5472i	0.630305	+	1.73175i
$236$	−0.612096	−	0.353394i	−0.0398441	−	0.0230040i
$237$	−22.0808	−	26.3148i	−1.43430	−	1.70933i
$238$	−5.39988	+	4.53104i	−0.350022	+	0.293704i
$239$	−6.03514	+	16.5814i	−0.390380	+	1.07256i	0.576448	+	0.817134i	$0.304438\pi$
$239$	−6.03514	+	16.5814i	−0.390380	+	1.07256i	−0.966828	+	0.255427i	$0.917784\pi$
$240$	−18.1000	−	3.19153i	−1.16835	−	0.206012i
$241$	−20.4582	−	3.60734i	−1.31783	−	0.232369i	−0.529862	−	0.848084i	$-0.677756\pi$
$241$	−20.4582	−	3.60734i	−1.31783	−	0.232369i	−0.787969	+	0.615715i	$0.788867\pi$
$242$	−3.73267	+	10.2554i	−0.239945	+	0.659244i
$243$	−0.591217	+	0.496090i	−0.0379266	+	0.0318242i
$244$	−2.61859	−	3.12071i	−0.167638	−	0.199783i
$245$	−11.0370	−	6.37221i	−0.705127	−	0.407105i
$246$	1.13608	+	3.12137i	0.0724341	+	0.199011i
$247$	−0.506381	−	2.87183i	−0.0322203	−	0.182730i
$248$	−10.8892	−	18.8606i	−0.691462	−	1.19765i
$249$	10.4100	−	18.0306i	0.659705	−	1.14264i
$250$	−4.00839	−	1.45893i	−0.253513	−	0.0922711i
$251$	−0.868227	+	0.501271i	−0.0548020	+	0.0316400i	−0.527151	−	0.849772i	$-0.676740\pi$
$251$	−0.868227	+	0.501271i	−0.0548020	+	0.0316400i	0.472349	+	0.881412i	$0.343406\pi$
$252$	5.40185	+	4.53269i	0.340285	+	0.285533i
$253$			3.75990i			0.236383i
$254$	−3.32613	+	3.96393i	−0.208700	+	0.248719i
$255$	31.6373	−	11.5150i	1.98120	−	0.721099i
$256$	−2.54673	+	14.4432i	−0.159171	+	0.902703i
$257$	−6.65311	+	1.17312i	−0.415009	+	0.0731773i	−0.377254	−	0.926110i	$-0.623132\pi$
$257$	−6.65311	+	1.17312i	−0.415009	+	0.0731773i	−0.0377550	+	0.999287i	$0.512021\pi$
$258$	−0.800685			−0.0498485
$259$	−0.232075	+	9.96655i	−0.0144204	+	0.619291i
$260$	−3.34059			−0.207174
$261$	27.4728	−	4.84420i	1.70052	−	0.299848i
$262$	−2.01778	+	11.4434i	−0.124659	+	0.706977i
$263$	0.636940	−	0.231827i	0.0392754	−	0.0142951i	−0.322308	−	0.946635i	$-0.604459\pi$
$263$	0.636940	−	0.231827i	0.0392754	−	0.0142951i	0.361583	+	0.932340i	$0.382236\pi$
$264$	6.99745	−	8.33924i	0.430664	−	0.513245i
$265$		−	18.1442i		−	1.11459i
$266$	2.61644	+	2.19546i	0.160425	+	0.134612i
$267$	19.7432	−	11.3987i	1.20826	−	0.697592i
$268$	−10.5498	−	3.83980i	−0.644430	−	0.234553i
$269$	2.72818	−	4.72534i	0.166340	−	0.288109i	−0.770790	−	0.637089i	$-0.780138\pi$
$269$	2.72818	−	4.72534i	0.166340	−	0.288109i	0.937130	+	0.348980i	$0.113472\pi$
$270$	15.3370	+	26.5644i	0.933379	+	1.61666i
$271$	0.587917	+	3.33424i	0.0357134	+	0.202541i	0.997444	−	0.0714572i	$-0.0227649\pi$
$271$	0.587917	+	3.33424i	0.0357134	+	0.202541i	−0.961730	+	0.273998i	$0.911654\pi$
$272$	2.68167	+	7.36783i	0.162600	+	0.446740i
$273$	−6.77792	−	3.91323i	−0.410218	−	0.236840i
$274$	−3.07403	−	3.66348i	−0.185709	−	0.221319i
$275$	−3.35876	+	2.81833i	−0.202541	+	0.169952i
$276$	−2.34100	+	6.43185i	−0.140912	+	0.387152i
$277$	−14.9351	−	2.63346i	−0.897364	−	0.158230i	−0.294103	−	0.955774i	$-0.595021\pi$
$277$	−14.9351	−	2.63346i	−0.897364	−	0.158230i	−0.603261	+	0.797544i	$0.706132\pi$
$278$	−5.78908	−	1.02077i	−0.347206	−	0.0612218i
$279$	−14.6232	+	40.1770i	−0.875471	+	2.40534i
$280$	11.4160	−	9.57914i	0.682235	−	0.572463i
$281$	9.12276	+	10.8721i	0.544218	+	0.648574i	0.966128	−	0.258064i	$-0.0830844\pi$
$281$	9.12276	+	10.8721i	0.544218	+	0.648574i	−0.421909	+	0.906638i	$0.638640\pi$
$282$	28.2622	+	16.3172i	1.68299	+	0.971675i
$283$	−2.16360	−	5.94444i	−0.128613	−	0.353360i	0.858627	−	0.512600i	$-0.171318\pi$
$283$	−2.16360	−	5.94444i	−0.128613	−	0.353360i	−0.987240	+	0.159240i	$0.949096\pi$
$284$	0.955804	+	5.42063i	0.0567165	+	0.321655i
$285$	−8.15663	−	14.1277i	−0.483157	−	0.836853i
$286$	−1.05989	+	1.83578i	−0.0626727	+	0.108552i
$287$	−1.49904	−	0.545606i	−0.0884856	−	0.0322061i
$288$	19.9258	−	11.5042i	1.17414	−	0.677891i
$289$	2.02021	+	1.69516i	0.118836	+	0.0997154i
$290$		−	15.4788i		−	0.908944i
$291$	−25.4131	+	30.2862i	−1.48974	+	1.77541i
$292$	10.6448	−	3.87440i	0.622941	−	0.226732i
$293$	−4.38105	+	24.8462i	−0.255944	+	1.45153i	0.537696	+	0.843139i	$0.319295\pi$
$293$	−4.38105	+	24.8462i	−0.255944	+	1.45153i	−0.793639	+	0.608389i	$0.791816\pi$
$294$	−14.4982	+	2.55642i	−0.845551	+	0.149094i
$295$	2.93243			0.170733
$296$	17.4389	+	6.81105i	1.01362	+	0.395884i
$297$	−10.7610			−0.624416
$298$	−10.2636	+	1.80974i	−0.594552	+	0.104836i
$299$	0.881506	−	4.99927i	0.0509788	−	0.289115i
$300$	−7.50040	+	2.72992i	−0.433036	+	0.157612i
$301$	0.247171	−	0.294567i	0.0142467	−	0.0169786i
$302$			10.1617i			0.584738i
$303$	−31.0318	−	26.0388i	−1.78273	−	1.49589i
$304$	3.29012	−	1.89955i	0.188701	−	0.108947i
$305$	15.8827	+	5.78082i	0.909439	+	0.331009i
$306$	12.9943	−	22.5068i	0.742836	−	1.28663i
$307$	−10.4560	−	18.1102i	−0.596753	−	1.03361i	−0.993297	−	0.115590i	$-0.963124\pi$
$307$	−10.4560	−	18.1102i	−0.596753	−	1.03361i	0.396544	−	0.918016i	$-0.370209\pi$
$308$	0.238356	+	1.35178i	0.0135816	+	0.0770250i
$309$	−1.14598	−	3.14856i	−0.0651926	−	0.179115i
$310$	20.5450	+	11.8617i	1.16688	+	0.673699i
$311$	16.2362	+	19.3495i	0.920668	+	1.09721i	0.994990	+	0.0999751i	$0.0318763\pi$
$311$	16.2362	+	19.3495i	0.920668	+	1.09721i	−0.0743219	+	0.997234i	$0.523679\pi$
$312$	−11.2591	+	9.44754i	−0.637423	+	0.534862i
$313$	9.88917	−	27.1703i	0.558969	−	1.53575i	−0.262167	−	0.965022i	$-0.584437\pi$
$313$	9.88917	−	27.1703i	0.558969	−	1.53575i	0.821136	−	0.570732i	$-0.193341\pi$
$314$	10.3342	+	1.82221i	0.583195	+	0.102833i
$315$	−28.8123	−	5.08039i	−1.62339	−	0.286247i
$316$	2.78206	−	7.64365i	0.156503	−	0.429989i
$317$	−21.1772	+	17.7698i	−1.18943	+	0.998052i	−0.189563	+	0.981868i	$0.560707\pi$
$317$	−21.1772	+	17.7698i	−1.18943	+	0.998052i	−0.999869	+	0.0161838i	$0.994848\pi$
$318$	−13.4725	−	16.0559i	−0.755500	−	0.900369i
$319$	4.70272	+	2.71512i	0.263302	+	0.152017i
$320$	−8.54725	−	23.4834i	−0.477806	−	1.31276i
$321$	−7.71519	−	43.7550i	−0.430620	−	2.44217i
$322$	2.97287	+	5.14915i	0.165671	+	0.286951i
$323$	−3.47966	+	6.02694i	−0.193613	+	0.335348i
$324$	−6.27899	−	2.28536i	−0.348833	−	0.126965i
$325$	5.12665	−	2.95987i	0.284375	−	0.164184i
$326$	−6.50946	−	5.46209i	−0.360526	−	0.302517i
$327$			28.9939i			1.60337i
$328$	−1.92567	+	2.29492i	−0.106327	+	0.126716i
$329$	−14.7275	+	5.36039i	−0.811956	+	0.295528i
$330$	−2.05918	+	11.6782i	−0.113354	+	0.642864i
$331$	24.3628	−	4.29582i	1.33910	−	0.236120i	0.542211	−	0.840243i	$-0.317587\pi$
$331$	24.3628	−	4.29582i	1.33910	−	0.236120i	0.796891	+	0.604123i	$0.206476\pi$
$332$	4.93001			0.270569
$333$	−11.7635	−	34.8216i	−0.644636	−	1.90821i
$334$	3.68113			0.201422
$335$	45.8719	−	8.08845i	2.50625	−	0.441919i
$336$	1.77056	−	10.0413i	0.0965918	−	0.547799i
$337$	30.0379	−	10.9329i	1.63627	−	0.595554i	0.649889	−	0.760029i	$-0.274815\pi$
$337$	30.0379	−	10.9329i	1.63627	−	0.595554i	0.986381	+	0.164475i	$0.0525930\pi$
$338$	−7.64365	+	9.10935i	−0.415760	+	0.495483i
$339$			29.2519i			1.58875i
$340$	6.10711	+	5.12448i	0.331205	+	0.277914i
$341$	−7.20758	+	4.16130i	−0.390312	+	0.225347i
$342$	−11.8330	−	4.30688i	−0.639858	−	0.232889i
$343$	9.27137	−	16.0585i	0.500607	−	0.867076i
$344$	−0.361066	−	0.625384i	−0.0194674	−	0.0337185i
$345$	−4.93127	−	27.9666i	−0.265491	−	1.50567i
$346$	−4.90201	−	13.4682i	−0.263534	−	0.724052i
$347$	−23.9920	−	13.8518i	−1.28796	−	0.743603i	−0.309669	−	0.950844i	$-0.600218\pi$
$347$	−23.9920	−	13.8518i	−1.28796	−	0.743603i	−0.978290	+	0.207241i	$0.933552\pi$
$348$	6.35419	+	7.57263i	0.340620	+	0.405935i
$349$	−2.35715	+	1.97788i	−0.126175	+	0.105874i	−0.703692	−	0.710505i	$-0.748466\pi$
$349$	−2.35715	+	1.97788i	−0.126175	+	0.105874i	0.577516	+	0.816379i	$0.304022\pi$
$350$	−2.37140	+	6.51537i	−0.126757	+	0.348261i
$351$	14.3081	+	2.52291i	0.763711	+	0.134663i
$352$	4.41067	+	0.777720i	0.235089	+	0.0414526i
$353$	5.61858	−	15.4369i	0.299047	−	0.821624i	−0.695613	−	0.718417i	$-0.744867\pi$
$353$	5.61858	−	15.4369i	0.299047	−	0.821624i	0.994660	−	0.103208i	$-0.0329106\pi$
$354$	2.59492	−	2.17739i	0.137918	−	0.115727i
$355$	−14.6793	−	17.4941i	−0.779094	−	0.928488i
$356$	4.67505	+	2.69914i	0.247777	+	0.143054i
$357$	6.38817	+	17.5514i	0.338098	+	0.928916i
$358$	1.94434	+	11.0269i	0.102762	+	0.582790i
$359$	3.46694	+	6.00492i	0.182978	+	0.316928i	0.942893	−	0.333095i	$-0.108093\pi$
$359$	3.46694	+	6.00492i	0.182978	+	0.316928i	−0.759915	+	0.650022i	$0.774760\pi$
$360$	−27.4715	+	47.5820i	−1.44787	+	2.50779i
$361$	−14.6855	−	5.34507i	−0.772919	−	0.281320i
$362$	5.79922	−	3.34818i	0.304800	−	0.175977i
$363$	22.1522	+	18.5879i	1.16269	+	0.975612i
$364$		−	1.85325i		−	0.0971367i
$365$	−30.2105	+	36.0035i	−1.58129	+	1.88451i
$366$	18.3470	−	6.67778i	0.959015	−	0.349053i
$367$	4.08368	−	23.1597i	0.213166	−	1.20893i	−0.670894	−	0.741554i	$-0.734089\pi$
$367$	4.08368	−	23.1597i	0.213166	−	1.20893i	0.884060	−	0.467373i	$-0.154800\pi$
$368$	6.51299	−	1.14842i	0.339513	−	0.0598653i
$369$	5.88140			0.306174
$370$	−20.1611	+	3.07286i	−1.04812	+	0.159751i
$371$	10.0658			0.522591
$372$	−14.9205	+	2.63089i	−0.773594	+	0.136405i
$373$	−3.67322	+	20.8319i	−0.190192	+	1.07863i	0.728909	+	0.684611i	$0.240028\pi$
$373$	−3.67322	+	20.8319i	−0.190192	+	1.07863i	−0.919101	+	0.394023i	$0.871083\pi$
$374$	4.75375	−	1.73022i	0.245810	−	0.0894677i
$375$	−7.26517	+	8.65830i	−0.375172	+	0.447112i
$376$			29.4327i			1.51788i
$377$	−5.61631	−	4.71264i	−0.289255	−	0.242713i
$378$	−14.7371	+	8.50847i	−0.757994	+	0.437628i
$379$	4.63012	+	1.68523i	0.237833	+	0.0865642i	0.458187	−	0.888856i	$-0.348499\pi$
$379$	4.63012	+	1.68523i	0.237833	+	0.0865642i	−0.220354	+	0.975420i	$0.570721\pi$
$380$	1.93143	−	3.34534i	0.0990804	−	0.171612i
$381$	6.85545	+	11.8740i	0.351215	+	0.608323i
$382$	0.117128	+	0.664264i	0.00599277	+	0.0339867i
$383$	−0.425682	−	1.16955i	−0.0217513	−	0.0597613i	0.928342	−	0.371728i	$-0.121235\pi$
$383$	−0.425682	−	1.16955i	−0.0217513	−	0.0597613i	−0.950093	+	0.311967i	$0.899012\pi$
$384$	−5.16805	−	2.98377i	−0.263731	−	0.152265i
$385$	−3.66067	−	4.36262i	−0.186565	−	0.222340i
$386$	−3.74370	+	3.14134i	−0.190549	+	0.159890i
$387$	−0.484882	+	1.33220i	−0.0246479	+	0.0677196i
$388$	−9.21957	−	1.62566i	−0.468053	−	0.0825303i
$389$	21.4798	+	3.78748i	1.08907	+	0.192033i	0.689223	−	0.724549i	$-0.257952\pi$
$389$	21.4798	+	3.78748i	1.08907	+	0.192033i	0.399848	+	0.916582i	$0.369063\pi$
$390$	5.47589	−	15.0449i	0.277283	−	0.761828i
$391$	−9.28043	+	7.78720i	−0.469331	+	0.393816i
$392$	−8.53462	−	10.1712i	−0.431063	−	0.513721i
$393$	26.6643	+	15.3946i	1.34503	+	0.776556i
$394$	−1.97081	−	5.41477i	−0.0992882	−	0.272792i
$395$	5.86035	+	33.2357i	0.294866	+	1.67227i
$396$	−2.53034	−	4.38268i	−0.127154	−	0.220238i
$397$	−3.28166	+	5.68400i	−0.164702	+	0.285272i	−0.936549	−	0.350536i	$-0.886000\pi$
$397$	−3.28166	+	5.68400i	−0.164702	+	0.285272i	0.771848	+	0.635808i	$0.219333\pi$
$398$	2.11970	+	0.771507i	0.106251	+	0.0386722i
$399$	7.83759	−	4.52504i	0.392371	−	0.226535i
$400$	5.90787	+	4.95729i	0.295394	+	0.247865i
$401$			0.723640i			0.0361368i	0.999837	+	0.0180684i	$0.00575167\pi$
$401$			0.723640i			0.0361368i	−0.999837	+	0.0180684i	$0.994248\pi$
$402$	34.5864	−	41.2185i	1.72501	−	2.05579i
$403$	10.5590	−	3.84317i	0.525982	−	0.191442i
$404$	1.66568	−	9.44655i	0.0828707	−	0.469983i
$405$	27.3019	−	4.81407i	1.35664	−	0.239213i
$406$	8.58712			0.426171
$407$	2.60285	−	6.66430i	0.129018	−	0.330337i
$408$	35.0760			1.73652
$409$	−36.3613	+	6.41147i	−1.79795	+	0.317027i	−0.969877	−	0.243594i	$-0.921673\pi$
$409$	−36.3613	+	6.41147i	−1.79795	+	0.317027i	−0.828072	+	0.560621i	$0.810562\pi$
$410$	0.566677	−	3.21379i	0.0279862	−	0.158718i
$411$	−11.9075	+	4.33397i	−0.587353	+	0.213779i
$412$	0.509991	−	0.607783i	0.0251254	−	0.0299433i
$413$			1.62682i			0.0800504i
$414$	−16.7924	−	14.0905i	−0.825301	−	0.692510i
$415$	−17.7140	+	10.2272i	−0.869546	+	0.502033i
$416$	−5.68221	−	2.06816i	−0.278593	−	0.101400i
$417$	−7.78794	+	13.4891i	−0.381377	+	0.660565i
$418$	−1.22560	−	2.12280i	−0.0599459	−	0.103829i
$419$	−2.50447	−	14.2036i	−0.122352	−	0.693890i	−0.982846	−	0.184430i	$-0.940956\pi$
$419$	−2.50447	−	14.2036i	−0.122352	−	0.693890i	0.860494	−	0.509460i	$-0.170155\pi$
$420$	−3.54584	−	9.74212i	−0.173019	−	0.475367i
$421$	−10.1949	−	5.88605i	−0.496871	−	0.286869i	0.230549	−	0.973061i	$-0.425948\pi$
$421$	−10.1949	−	5.88605i	−0.496871	−	0.286869i	−0.727421	+	0.686192i	$0.759281\pi$
$422$	−14.2812	−	17.0196i	−0.695197	−	0.828503i
$423$	44.2641	−	37.1420i	2.15220	−	1.80591i
$424$	6.46527	−	17.7632i	0.313981	−	0.862656i
$425$	−13.9128	−	2.45320i	−0.674869	−	0.118998i
$426$	−25.9795	−	4.58088i	−1.25871	−	0.221945i
$427$	−3.20701	+	8.81120i	−0.155198	+	0.426404i
$428$	8.05933	−	6.76258i	0.389562	−	0.326882i
$429$	3.61038	+	4.30269i	0.174311	+	0.207736i
$430$	0.681238	+	0.393313i	0.0328522	+	0.0189672i
$431$	−7.60115	−	20.8840i	−0.366134	−	1.00595i	−0.976818	−	0.214071i	$-0.931328\pi$
$431$	−7.60115	−	20.8840i	−0.366134	−	1.00595i	0.610684	−	0.791875i	$-0.290895\pi$
$432$	3.28682	+	18.6405i	0.158137	+	0.896839i
$433$	2.75623	+	4.77392i	0.132456	+	0.229420i	0.924623	−	0.380884i	$-0.124380\pi$
$433$	2.75623	+	4.77392i	0.132456	+	0.229420i	−0.792167	+	0.610305i	$0.791047\pi$
$434$	−6.58048	+	11.3977i	−0.315873	+	0.547109i
$435$	−38.5404	−	14.0276i	−1.84787	−	0.672570i
$436$	−5.94573	+	3.43277i	−0.284749	+	0.164400i
$437$	4.49672	+	3.77319i	0.215107	+	0.180496i
$438$			54.2917i			2.59416i
$439$	17.6124	−	20.9897i	0.840595	−	1.00178i	−0.159299	−	0.987230i	$-0.550923\pi$
$439$	17.6124	−	20.9897i	0.840595	−	1.00178i	0.999894	−	0.0145518i	$-0.00463215\pi$
$440$	−10.0500	+	3.65789i	−0.479114	+	0.174383i
$441$	−4.52642	+	25.6706i	−0.215544	+	1.22241i
$442$	−6.72636	+	1.18604i	−0.319940	+	0.0564141i
$443$	−7.19623			−0.341903			−0.170952	−	0.985279i	$-0.554684\pi$
$443$	−7.19623			−0.341903			−0.170952	+	0.985279i	$0.554684\pi$
$444$	8.60189	−	9.77965i	0.408228	−	0.464122i
$445$	−22.3972			−1.06173
$446$	15.0398	−	2.65193i	0.712157	−	0.125573i
$447$	−4.79525	+	27.1952i	−0.226808	+	1.28629i
$448$	13.0278	−	4.74174i	0.615507	−	0.224026i
$449$	−9.26776	+	11.0449i	−0.437373	+	0.521240i	−0.939034	−	0.343824i	$-0.888278\pi$
$449$	−9.26776	+	11.0449i	−0.437373	+	0.521240i	0.501662	+	0.865064i	$0.332722\pi$
$450$		−	25.5627i		−	1.20504i
$451$	0.877005	+	0.735894i	0.0412965	+	0.0346519i
$452$	−5.99865	+	3.46332i	−0.282153	+	0.162901i
$453$	25.3014	+	9.20897i	1.18877	+	0.432675i
$454$	−14.8617	+	25.7412i	−0.697493	+	1.20809i
$455$	3.84452	+	6.65890i	0.180234	+	0.312174i
$456$	−2.95126	−	16.7374i	−0.138206	−	0.783803i
$457$	4.38593	+	12.0502i	0.205165	+	0.563687i	0.999012	−	0.0444304i	$-0.0141473\pi$
$457$	4.38593	+	12.0502i	0.205165	+	0.563687i	−0.793847	+	0.608117i	$0.791925\pi$
$458$	5.19622	+	3.00004i	0.242804	+	0.140183i
$459$	−22.2873	−	26.5610i	−1.04028	−	1.23976i
$460$	5.15123	−	4.32240i	0.240177	−	0.201533i
$461$	2.53841	−	6.97424i	0.118226	−	0.324823i	−0.866438	−	0.499284i	$-0.833596\pi$
$461$	2.53841	−	6.97424i	0.118226	−	0.324823i	0.984664	+	0.174462i	$0.0558185\pi$
$462$	−6.47869	−	1.14237i	−0.301416	−	0.0531478i
$463$	27.7816	+	4.89865i	1.29112	+	0.227660i	0.776696	−	0.629875i	$-0.216894\pi$
$463$	27.7816	+	4.89865i	1.29112	+	0.227660i	0.514426	+	0.857535i	$0.328005\pi$
$464$	3.26680	−	8.97546i	0.151657	−	0.416675i
$465$	48.1532	−	40.4053i	2.23305	−	1.87375i
$466$	−10.1390	−	12.0832i	−0.469681	−	0.559744i
$467$	−35.3542	−	20.4118i	−1.63600	−	0.944543i	−0.982192	−	0.187880i	$-0.939838\pi$
$467$	−35.3542	−	20.4118i	−1.63600	−	0.944543i	−0.653805	−	0.756663i	$-0.726828\pi$
$468$	2.33689	+	6.42056i	0.108023	+	0.296791i
$469$	4.48721	+	25.4483i	0.207200	+	1.17509i
$470$	−16.0307	−	27.7660i	−0.739441	−	1.28075i
$471$	13.9025	−	24.0798i	0.640592	−	1.10954i
$472$	2.87085	+	1.04490i	0.132141	+	0.0480955i
$473$	−0.238991	+	0.137982i	−0.0109888	+	0.00634440i
$474$	29.8641	+	25.0590i	1.37170	+	1.15100i
$475$			6.84525i			0.314082i
$476$	−2.84289	+	3.38803i	−0.130304	+	0.155290i
$477$	−34.8729	+	12.6927i	−1.59672	+	0.581159i
$478$	3.47740	−	19.7213i	0.159053	−	0.902032i
$479$	−11.7111	+	2.06497i	−0.535092	+	0.0943511i	−0.434663	−	0.900593i	$-0.643133\pi$
$479$	−11.7111	+	2.06497i	−0.535092	+	0.0943511i	−0.100429	+	0.994944i	$0.532021\pi$
$480$	−33.8271			−1.54399
$481$	−5.02326	+	8.25080i	−0.229041	+	0.376204i
$482$	23.5758			1.07385
$483$	15.5150	−	2.73571i	0.705956	−	0.124479i
$484$	−1.18905	+	6.74346i	−0.0540479	+	0.306521i
$485$	36.4992	−	13.2846i	1.65734	−	0.603223i
$486$	0.563001	−	0.670959i	0.0255382	−	0.0304353i
$487$		−	8.77782i		−	0.397761i	−0.980024	−	0.198880i	$-0.936269\pi$
$487$		−	8.77782i		−	0.397761i	0.980024	−	0.198880i	$-0.0637306\pi$
$488$	13.4893	+	11.3188i	0.610631	+	0.512380i
$489$	−19.4992	+	11.2579i	−0.881783	+	0.509098i
$490$	13.5911	+	4.94676i	0.613983	+	0.223472i
$491$	9.74824	−	16.8844i	0.439932	−	0.761984i	−0.557752	−	0.830008i	$-0.688336\pi$
$491$	9.74824	−	16.8844i	0.439932	−	0.761984i	0.997684	+	0.0680234i	$0.0216693\pi$
$492$	1.04206	+	1.80490i	0.0469796	+	0.0813711i
$493$	3.03827	+	17.2309i	0.136837	+	0.776040i
$494$	1.13190	+	3.10987i	0.0509266	+	0.139920i
$495$	18.1835	+	10.4982i	0.817288	+	0.471861i
$496$	9.40977	+	11.2141i	0.422511	+	0.503529i
$497$	9.70514	−	8.14358i	0.435335	−	0.365290i
$498$	−8.08128	+	22.2031i	−0.362131	+	0.994946i
$499$	−12.7816	−	2.25373i	−0.572181	−	0.100891i	−0.119931	−	0.992782i	$-0.538267\pi$
$499$	−12.7816	−	2.25373i	−0.572181	−	0.100891i	−0.452250	+	0.891891i	$0.649379\pi$
$500$	−2.63571	−	0.464748i	−0.117873	−	0.0207841i
$501$	3.33601	−	9.16561i	0.149042	−	0.409489i
$502$	0.871577	−	0.731340i	0.0389004	−	0.0326413i
$503$	−1.45684	−	1.73620i	−0.0649574	−	0.0774132i	0.732587	−	0.680673i	$-0.238313\pi$
$503$	−1.45684	−	1.73620i	−0.0649574	−	0.0774132i	−0.797545	+	0.603260i	$0.793868\pi$
$504$	−26.3970	−	15.2403i	−1.17581	−	0.678857i
$505$	13.6117	+	37.3978i	0.605711	+	1.66418i
$506$	−0.740961	−	4.20220i	−0.0329398	−	0.186811i
$507$	15.7543	+	27.2872i	0.699671	+	1.21187i
$508$	−1.62332	+	2.81168i	−0.0720233	+	0.124748i
$509$	1.01906	+	0.370907i	0.0451690	+	0.0164402i	0.364506	−	0.931201i	$-0.381238\pi$
$509$	1.01906	+	0.370907i	0.0451690	+	0.0164402i	−0.319337	+	0.947641i	$0.603460\pi$
$510$	−33.0897	+	19.1044i	−1.46524	+	0.845955i
$511$	−19.9736	−	16.7598i	−0.883580	−	0.741411i
$512$		−	20.6132i		−	0.910983i
$513$	−10.7990	+	12.8698i	−0.476789	+	0.568215i
$514$	7.20457	−	2.62225i	0.317780	−	0.115662i
$515$	−0.571614	+	3.24178i	−0.0251883	+	0.142850i
$516$	−0.494739	+	0.0872359i	−0.0217797	+	0.00384035i
$517$	11.2477			0.494674
$518$	−1.70473	−	11.1847i	−0.0749014	−	0.491428i
$519$	−37.9767			−1.66699
$520$	14.2203	−	2.50743i	0.623602	−	0.109958i
$521$	6.02346	−	34.1608i	0.263893	−	1.49661i	−0.508277	−	0.861194i	$-0.669717\pi$
$521$	6.02346	−	34.1608i	0.263893	−	1.49661i	0.772170	−	0.635416i	$-0.219171\pi$
$522$	−29.7500	+	10.8281i	−1.30212	+	0.473933i
$523$	−6.35179	+	7.56976i	−0.277744	+	0.331003i	−0.886825	−	0.462106i	$-0.847094\pi$
$523$	−6.35179	+	7.56976i	−0.277744	+	0.331003i	0.609081	+	0.793108i	$0.291539\pi$
$524$			7.29067i			0.318495i
$525$	14.0735	+	11.8091i	0.614218	+	0.515390i
$526$	−0.666181	+	0.384620i	−0.0290469	+	0.0167702i
$527$	−25.1990	−	9.17167i	−1.09768	−	0.399524i
$528$	−3.65872	+	6.33710i	−0.159226	+	0.275787i
$529$	−6.39073	−	11.0691i	−0.277858	−	0.481264i
$530$	3.57567	+	20.2786i	0.155317	+	0.880847i
$531$	−2.05137	−	5.63609i	−0.0890218	−	0.244585i
$532$	1.85589	+	1.07150i	0.0804629	+	0.0464553i
$533$	−0.993560	−	1.18408i	−0.0430359	−	0.0512881i
$534$	−19.8194	+	16.6304i	−0.857669	+	0.719669i
$535$	−14.9291	+	41.0175i	−0.645443	+	1.77334i
$536$	47.7907	+	8.42680i	2.06425	+	0.363982i
$537$	29.2179	+	5.15190i	1.26084	+	0.222321i
$538$	−2.11789	+	5.81885i	−0.0913087	+	0.250869i
$539$	−3.88692	+	3.26151i	−0.167421	+	0.140483i
$540$	12.3709	+	14.7430i	0.532358	+	0.634439i
$541$	16.6461	+	9.61063i	0.715672	+	0.413193i	0.813157	−	0.582044i	$-0.197747\pi$
$541$	16.6461	+	9.61063i	0.715672	+	0.413193i	−0.0974860	+	0.995237i	$0.531080\pi$
$542$	−1.31415	−	3.61061i	−0.0564478	−	0.155089i
$543$	−3.08109	−	17.4737i	−0.132222	−	0.749869i
$544$	7.21541	+	12.4975i	0.309358	+	0.535824i
$545$	14.2424	−	24.6685i	0.610077	−	1.05668i
$546$	8.34642	+	3.03785i	0.357194	+	0.130008i
$547$	33.0546	−	19.0841i	1.41331	−	0.815978i	0.417616	−	0.908624i	$-0.362866\pi$
$547$	33.0546	−	19.0841i	1.41331	−	0.815978i	0.995699	+	0.0926461i	$0.0295325\pi$
$548$	−2.29857	−	1.92873i	−0.0981899	−	0.0823911i
$549$		−	34.5702i		−	1.47542i
$550$	3.19846	−	3.81178i	0.136383	−	0.162535i
$551$	7.96653	−	2.89958i	0.339386	−	0.123526i
$552$	5.13755	−	29.1365i	0.218668	−	1.24013i
$553$	−18.4381	+	3.25113i	−0.784068	+	0.138252i
$554$	17.2110			0.731225
$555$	−10.6198	+	52.9836i	−0.450785	+	2.24903i
$556$	−3.68826			−0.156417
$557$	−19.9385	+	3.51570i	−0.844822	+	0.148965i	−0.579274	−	0.815133i	$-0.696664\pi$
$557$	−19.9385	+	3.51570i	−0.844822	+	0.148965i	−0.265548	+	0.964098i	$0.585553\pi$
$558$	8.42580	−	47.7851i	0.356693	−	2.02291i
$559$	0.350119	−	0.127433i	0.0148084	−	0.00538983i
$560$	−6.43893	+	7.67362i	−0.272094	+	0.324270i
$561$		−	13.4043i		−	0.565931i
$562$	−12.3385	−	10.3532i	−0.520468	−	0.436724i
$563$	15.0044	−	8.66277i	0.632358	−	0.365092i	−0.149307	−	0.988791i	$-0.547704\pi$
$563$	15.0044	−	8.66277i	0.632358	−	0.365092i	0.781665	+	0.623699i	$0.214371\pi$
$564$	19.2409	+	7.00310i	0.810187	+	0.294884i
$565$	14.3691	−	24.8881i	0.604515	−	1.04705i
$566$	3.58958	+	6.21734i	0.150881	+	0.261334i
$567$	2.67069	+	15.1462i	0.112158	+	0.636082i
$568$	−8.13739	−	22.3573i	−0.341437	−	0.938092i
$569$	−7.57443	−	4.37310i	−0.317536	−	0.183330i	0.332757	−	0.943012i	$-0.392021\pi$
$569$	−7.57443	−	4.37310i	−0.317536	−	0.183330i	−0.650294	+	0.759683i	$0.725354\pi$
$570$	11.9003	+	14.1822i	0.498448	+	0.594027i
$571$	−14.1820	+	11.9001i	−0.593499	+	0.498005i	−0.889349	−	0.457230i	$-0.848842\pi$
$571$	−14.1820	+	11.9001i	−0.593499	+	0.498005i	0.295850	+	0.955235i	$0.404397\pi$
$572$	−0.454889	+	1.24980i	−0.0190199	+	0.0522567i
$573$	1.76009	+	0.310352i	0.0735289	+	0.0129651i
$574$	1.78291	+	0.314374i	0.0744170	+	0.0131217i
$575$	−4.07558	+	11.1976i	−0.169963	+	0.466970i
$576$	−39.1556	+	32.8554i	−1.63148	+	1.36898i
$577$	−0.438579	−	0.522678i	−0.0182583	−	0.0217594i	0.756838	−	0.653602i	$-0.226743\pi$
$577$	−0.438579	−	0.522678i	−0.0182583	−	0.0217594i	−0.775096	+	0.631843i	$0.782299\pi$
$578$	−2.59193	−	1.49645i	−0.107810	−	0.0622442i
$579$	4.42888	+	12.1682i	0.184058	+	0.505695i
$580$	−1.68643	−	9.56424i	−0.0700254	−	0.397134i
$581$	−5.67371	−	9.82716i	−0.235385	−	0.407699i
$582$	22.4342	−	38.8571i	0.929926	−	1.61068i
$583$	−6.78821	−	2.47071i	−0.281139	−	0.102326i
$584$	−42.4051	+	24.4826i	−1.75474	+	1.01310i
$585$	−21.7160	−	18.2219i	−0.897845	−	0.753382i
$586$		−	28.6323i		−	1.18279i
$587$	−7.84190	+	9.34562i	−0.323670	+	0.385735i	−0.903203	−	0.429214i	$-0.858791\pi$
$587$	−7.84190	+	9.34562i	−0.323670	+	0.385735i	0.579533	+	0.814949i	$0.303235\pi$
$588$	−8.67983	+	3.15920i	−0.357950	+	0.130283i
$589$	−2.25629	+	12.7960i	−0.0929687	+	0.527252i
$590$	−3.27739	+	0.577892i	−0.134928	+	0.0237914i
$591$	−15.2682			−0.628051
$592$	−12.3391	−	2.47318i	−0.507132	−	0.101647i
$593$	−1.01320			−0.0416070			−0.0208035	−	0.999784i	$-0.506622\pi$
$593$	−1.01320			−0.0416070			−0.0208035	+	0.999784i	$0.506622\pi$
$594$	12.0269	−	2.12066i	0.493469	−	0.0870119i
$595$	3.18641	−	18.0710i	0.130630	−	0.740840i
$596$	−6.14463	+	2.23646i	−0.251694	+	0.0916091i
$597$	3.84194	−	4.57864i	0.157240	−	0.187391i
$598$			5.76108i			0.235588i
$599$	34.1074	+	28.6195i	1.39359	+	1.16936i	0.963861	+	0.266406i	$0.0858363\pi$
$599$	34.1074	+	28.6195i	1.39359	+	1.16936i	0.429732	+	0.902957i	$0.358608\pi$
$600$	29.8789	−	17.2506i	1.21980	−	0.704252i
$601$	9.73534	+	3.54337i	0.397113	+	0.144537i	0.532854	−	0.846207i	$-0.321119\pi$
$601$	9.73534	+	3.54337i	0.397113	+	0.144537i	−0.135741	+	0.990744i	$0.543342\pi$
$602$	−0.218197	+	0.377929i	−0.00889307	+	0.0154032i
$603$	−47.6354	−	82.5070i	−1.93986	−	3.35994i
$604$	1.10713	+	6.27884i	0.0450484	+	0.255482i
$605$	−9.71675	−	26.6966i	−0.395042	−	1.08537i
$606$	39.8137	+	22.9865i	1.61732	+	0.933761i
$607$	13.5317	+	16.1265i	0.549235	+	0.654553i	0.967232	−	0.253896i	$-0.0817120\pi$
$607$	13.5317	+	16.1265i	0.549235	+	0.654553i	−0.417996	+	0.908449i	$0.637268\pi$
$608$	5.35639	−	4.49455i	0.217230	−	0.182278i
$609$	7.78204	−	21.3810i	0.315344	−	0.866401i
$610$	−18.8903	−	3.33087i	−0.764845	−	0.134863i
$611$	−14.9553	−	2.63702i	−0.605026	−	0.106682i
$612$	5.57697	−	15.3226i	0.225436	−	0.619379i
$613$	−20.1944	+	16.9451i	−0.815645	+	0.684407i	−0.951948	−	0.306260i	$-0.900922\pi$
$613$	−20.1944	+	16.9451i	−0.815645	+	0.684407i	0.136303	+	0.990667i	$0.456478\pi$
$614$	15.2549	+	18.1801i	0.615639	+	0.733690i
$615$	−7.48843	−	4.32345i	−0.301963	−	0.174338i
$616$	−2.02928	−	5.57540i	−0.0817621	−	0.224639i
$617$	−1.32031	−	7.48787i	−0.0531538	−	0.301450i	0.946628	−	0.322328i	$-0.104465\pi$
$617$	−1.32031	−	7.48787i	−0.0531538	−	0.301450i	−0.999782	+	0.0208771i	$0.993354\pi$
$618$	1.90128	+	3.29311i	0.0764805	+	0.132468i
$619$	−6.24522	+	10.8170i	−0.251017	+	0.434774i	−0.963806	−	0.266605i	$-0.914098\pi$
$619$	−6.24522	+	10.8170i	−0.251017	+	0.434774i	0.712789	+	0.701378i	$0.247432\pi$
$620$	13.9870	+	5.09086i	0.561733	+	0.204454i
$621$	−25.3277	+	14.6230i	−1.01637	+	0.586799i
$622$	−21.9593	−	18.4261i	−0.880488	−	0.738817i
$623$		−	12.4252i		−	0.497807i
$624$	6.35047	−	7.56820i	0.254222	−	0.302970i
$625$	27.9490	−	10.1726i	1.11796	−	0.406904i
$626$	−5.69807	+	32.3153i	−0.227741	+	1.29158i
$627$	−6.39623	+	1.12783i	−0.255441	+	0.0450411i
$628$	6.58400			0.262730
$629$	21.8401	−	7.37804i	0.870820	−	0.294182i
$630$	33.2029			1.32283
$631$	−15.2426	+	2.68768i	−0.606798	+	0.106995i	−0.468601	−	0.883410i	$-0.655242\pi$
$631$	−15.2426	+	2.68768i	−0.606798	+	0.106995i	−0.138197	+	0.990405i	$0.544131\pi$
$632$	−6.10549	+	34.6260i	−0.242863	+	1.37735i
$633$	−55.3193	+	20.1346i	−2.19875	+	0.800278i
$634$	20.1666	−	24.0336i	0.800917	−	0.954495i
$635$		−	13.4702i		−	0.534547i
$636$	−10.0739	−	8.45300i	−0.399456	−	0.335183i
$637$	5.93281	−	3.42531i	0.235066	−	0.135716i
$638$	−5.79100	−	2.10775i	−0.229268	−	0.0834466i
$639$	−23.3545	+	40.4512i	−0.923891	+	1.60023i
$640$	2.93138	+	5.07730i	0.115873	+	0.200698i
$641$	5.19527	+	29.4638i	0.205201	+	1.16375i	0.897123	+	0.441780i	$0.145653\pi$
$641$	5.19527	+	29.4638i	0.205201	+	1.16375i	−0.691923	+	0.721972i	$0.743236\pi$
$642$	17.2456	+	47.3818i	0.680628	+	1.87001i
$643$	23.1565	+	13.3694i	0.913202	+	0.527238i	0.881460	−	0.472258i	$-0.156561\pi$
$643$	23.1565	+	13.3694i	0.913202	+	0.527238i	0.0317423	+	0.999496i	$0.489894\pi$
$644$	2.39793	+	2.85774i	0.0944915	+	0.112611i
$645$	1.59668	−	1.33977i	0.0628691	−	0.0527534i
$646$	2.70126	−	7.42166i	0.106280	−	0.292001i
$647$	31.0124	+	5.46831i	1.21922	+	0.214982i	0.745990	−	0.665957i	$-0.231976\pi$
$647$	31.0124	+	5.46831i	1.21922	+	0.214982i	0.473231	+	0.880938i	$0.343088\pi$
$648$	28.4440	+	5.01544i	1.11738	+	0.197025i
$649$	0.399310	−	1.09710i	0.0156743	−	0.0430648i
$650$	−5.14643	+	4.31837i	−0.201860	+	0.169380i
$651$	22.4156	+	26.7138i	0.878536	+	1.04700i
$652$	−4.61726	−	2.66578i	−0.180826	−	0.104400i
$653$	−13.6877	−	37.6067i	−0.535641	−	1.47166i	−0.852264	−	0.523111i	$-0.824771\pi$
$653$	−13.6877	−	37.6067i	−0.535641	−	1.47166i	0.316623	−	0.948551i	$-0.397451\pi$
$654$	−5.71381	−	32.4046i	−0.223428	−	1.26712i
$655$	−15.1243	−	26.1961i	−0.590956	−	1.02357i
$656$	1.00686	−	1.74394i	0.0393114	−	0.0680894i
$657$	90.3319	+	32.8781i	3.52418	+	1.28270i
$658$	15.4037	−	8.89331i	0.600498	−	0.346698i
$659$	−24.1350	−	20.2517i	−0.940167	−	0.788894i	0.0374470	−	0.999299i	$-0.488077\pi$
$659$	−24.1350	−	20.2517i	−0.940167	−	0.788894i	−0.977614	+	0.210405i	$0.932522\pi$
$660$			7.44025i			0.289612i
$661$	7.12275	−	8.48856i	0.277043	−	0.330167i	−0.609524	−	0.792768i	$-0.708639\pi$
$661$	7.12275	−	8.48856i	0.277043	−	0.330167i	0.886567	+	0.462601i	$0.153084\pi$
$662$	−26.3822	+	9.60234i	−1.02537	+	0.373205i
$663$	−3.14263	+	17.8228i	−0.122050	+	0.692179i
$664$	−20.9862	+	3.70044i	−0.814423	+	0.143605i
$665$	−8.89117			−0.344785
$666$	20.0096	+	36.5997i	0.775356	+	1.41821i
$667$	14.7581			0.571437
$668$	2.27455	−	0.401065i	0.0880050	−	0.0155177i
$669$	7.02679	−	39.8509i	0.271671	−	1.54072i
$670$	−49.6741	+	18.0799i	−1.91908	+	0.698488i
$671$	4.32550	−	5.15494i	0.166984	−	0.199004i
$672$		−	18.7662i		−	0.723922i
$673$	7.48506	+	6.28071i	0.288528	+	0.242104i	0.775550	−	0.631286i	$-0.217473\pi$
$673$	7.48506	+	6.28071i	0.288528	+	0.242104i	−0.487022	+	0.873389i	$0.661917\pi$
$674$	−31.4169	+	18.1386i	−1.21014	+	0.698672i
$675$	−32.0479	−	11.6645i	−1.23352	−	0.448966i
$676$	−3.73049	+	6.46141i	−0.143481	+	0.248516i
$677$	21.4857	+	37.2142i	0.825761	+	1.43026i	0.901336	+	0.433120i	$0.142587\pi$
$677$	21.4857	+	37.2142i	0.825761	+	1.43026i	−0.0755755	+	0.997140i	$0.524079\pi$
$678$	−5.76466	−	32.6930i	−0.221390	−	1.25557i
$679$	7.36988	+	20.2486i	0.282830	+	0.777069i
$680$	−29.8434	−	17.2301i	−1.14444	−	0.660743i
$681$	50.6244	+	60.3318i	1.93993	+	2.31192i
$682$	7.23539	−	6.07121i	0.277057	−	0.232479i
$683$	−12.1063	+	33.2617i	−0.463234	+	1.27272i	0.459806	+	0.888019i	$0.347919\pi$
$683$	−12.1063	+	33.2617i	−0.463234	+	1.27272i	−0.923040	+	0.384705i	$0.874303\pi$
$684$	−7.78082	−	1.37197i	−0.297507	−	0.0524585i
$685$	12.2601	+	2.16178i	0.468433	+	0.0825974i
$686$	−7.19738	+	19.7746i	−0.274797	+	0.754999i
$687$	12.1788	−	10.2193i	0.464652	−	0.389889i
$688$	0.312012	+	0.371841i	0.0118953	+	0.0141763i
$689$	8.44653	+	4.87661i	0.321787	+	0.185784i
$690$	11.0227	+	30.2847i	0.419628	+	1.15292i
$691$	−8.23986	−	46.7306i	−0.313459	−	1.77771i	−0.580733	−	0.814094i	$-0.697234\pi$
$691$	−8.23986	−	46.7306i	−0.313459	−	1.77771i	0.267274	−	0.963621i	$-0.413877\pi$
$692$	−4.49630	−	7.78782i	−0.170924	−	0.296049i
$693$	−5.82409	+	10.0876i	−0.221239	+	0.383197i
$694$	29.5441	+	10.7532i	1.12148	+	0.408185i
$695$	13.2523	−	7.65119i	0.502687	−	0.290226i
$696$	−32.7327	−	27.4660i	−1.24073	−	1.04110i
$697$			3.68880i			0.139723i
$698$	2.24466	−	2.67508i	0.0849615	−	0.101253i
$699$	−39.2743	+	14.2947i	−1.48549	+	0.540674i
$700$	−0.755417	+	4.28418i	−0.0285521	+	0.161927i
$701$	18.4793	−	3.25840i	0.697954	−	0.123068i	0.186597	−	0.982437i	$-0.440254\pi$
$701$	18.4793	−	3.25840i	0.697954	−	0.123068i	0.511357	+	0.859369i	$0.329143\pi$
$702$	−16.4885			−0.622317
$703$	−5.35823	−	9.80077i	−0.202089	−	0.369643i
$704$	−9.94962			−0.374990
$705$	−83.6620	+	14.7519i	−3.15089	+	0.555588i
$706$	−3.23738	+	18.3601i	−0.121841	+	0.690992i
$707$	−20.7471	+	7.55132i	−0.780274	+	0.283997i
$708$	1.36616	−	1.62812i	0.0513433	−	0.0611885i
$709$		−	47.0548i		−	1.76718i	−0.468261	−	0.883590i	$-0.655119\pi$
$709$		−	47.0548i		−	1.76718i	0.468261	−	0.883590i	$-0.344881\pi$
$710$	19.8536	+	16.6592i	0.745093	+	0.625207i
$711$	59.7790	−	34.5134i	2.24189	−	1.29435i
$712$	−21.9269	−	7.98073i	−0.821744	−	0.299090i
$713$	−11.3095	+	19.5886i	−0.423543	+	0.733597i
$714$	−10.5985	−	18.3571i	−0.396638	−	0.686998i
$715$	−0.958214	−	5.43430i	−0.0358352	−	0.203231i
$716$	2.40280	+	6.60163i	0.0897967	+	0.246714i
$717$	−45.9525	−	26.5307i	−1.71613	−	0.990808i
$718$	−5.05817	−	6.02809i	−0.188769	−	0.224966i
$719$	25.6104	−	21.4897i	0.955108	−	0.801431i	−0.0250422	−	0.999686i	$-0.507972\pi$
$719$	25.6104	−	21.4897i	0.955108	−	0.801431i	0.980150	+	0.198255i	$0.0635276\pi$
$720$	12.6314	−	34.7045i	0.470744	−	1.29336i
$721$	−1.79844	−	0.317113i	−0.0669773	−	0.0118099i
$722$	17.4664	+	3.07979i	0.650031	+	0.114618i
$723$	21.3655	−	58.7011i	0.794590	−	2.18312i
$724$	3.21852	−	2.70066i	0.119615	−	0.100369i
$725$	11.0623	+	13.1836i	0.410845	+	0.489626i
$726$	−28.4212	−	16.4090i	−1.05481	−	0.608995i
$727$	1.85076	+	5.08492i	0.0686408	+	0.188589i	0.969270	−	0.245999i	$-0.0791161\pi$
$727$	1.85076	+	5.08492i	0.0686408	+	0.188589i	−0.900629	+	0.434588i	$0.856894\pi$
$728$	1.39104	+	7.88897i	0.0515553	+	0.292385i
$729$	12.9157	+	22.3707i	0.478360	+	0.828544i
$730$	26.6692	−	46.1924i	0.987071	−	1.70966i
$731$	−0.835554	−	0.304117i	−0.0309041	−	0.0112482i
$732$	10.6090	−	6.12510i	0.392120	−	0.226390i
$733$	15.2919	+	12.8315i	0.564821	+	0.473941i	0.879923	−	0.475117i	$-0.157594\pi$
$733$	15.2919	+	12.8315i	0.564821	+	0.473941i	−0.315102	+	0.949058i	$0.602039\pi$
$734$			26.6889i			0.985105i
$735$	24.6338	−	29.3574i	0.908630	−	1.08286i
$736$	11.4380	−	4.16311i	0.421612	−	0.153454i
$737$	3.22031	−	18.2633i	0.118621	−	0.672736i
$738$	−6.57327	+	1.15905i	−0.241965	+	0.0426650i
$739$	1.23647			0.0454843			0.0227421	−	0.999741i	$-0.492760\pi$
$739$	1.23647			0.0454843			0.0227421	+	0.999741i	$0.492760\pi$
$740$	−12.1226	+	4.09529i	−0.445636	+	0.150546i
$741$	8.76902			0.322138
$742$	−11.2499	+	1.98367i	−0.412998	+	0.0728227i
$743$	−7.84009	+	44.4634i	−0.287625	+	1.63120i	0.408130	+	0.912924i	$0.366181\pi$
$743$	−7.84009	+	44.4634i	−0.287625	+	1.63120i	−0.695755	+	0.718279i	$0.744930\pi$
$744$	61.5395	−	22.3985i	2.25615	−	0.821170i
$745$	17.4388	−	20.7827i	0.638907	−	0.761419i
$746$		−	24.0063i		−	0.878935i
$747$	32.0483	+	26.8917i	1.17258	+	0.983915i
$748$	2.74881	−	1.58702i	0.100506	−	0.0580273i
$749$	−22.7552	−	8.28220i	−0.831456	−	0.302625i
$750$	6.41354	−	11.1086i	0.234189	−	0.405628i
$751$	−4.85572	−	8.41035i	−0.177188	−	0.306898i	0.763729	−	0.645538i	$-0.223367\pi$
$751$	−4.85572	−	8.41035i	−0.177188	−	0.306898i	−0.940916	+	0.338640i	$0.890033\pi$
$752$	−3.43548	−	19.4836i	−0.125279	−	0.710493i
$753$	−1.03109	−	2.83291i	−0.0375751	−	0.103237i
$754$	7.20571	+	4.16022i	0.262416	+	0.151506i
$755$	−17.0033	−	20.2638i	−0.618814	−	0.737474i
$756$	−8.17897	+	6.86297i	−0.297466	+	0.249604i
$757$	−6.63132	+	18.2194i	−0.241019	+	0.662195i	0.758920	+	0.651184i	$0.225727\pi$
$757$	−6.63132	+	18.2194i	−0.241019	+	0.662195i	−0.999939	+	0.0110115i	$0.996495\pi$
$758$	−5.50690	−	0.971014i	−0.200019	−	0.0352688i
$759$	−11.1345	−	1.96332i	−0.404157	−	0.0712639i
$760$	−5.71079	+	15.6903i	−0.207152	+	0.569146i
$761$	−26.0596	+	21.8666i	−0.944659	+	0.792663i	−0.978390	−	0.206768i	$-0.933705\pi$
$761$	−26.0596	+	21.8666i	−0.944659	+	0.792663i	0.0337313	+	0.999431i	$0.489261\pi$
$762$	−10.0019	−	11.9198i	−0.362331	−	0.431809i
$763$	13.6853	+	7.90122i	0.495442	+	0.286043i
$764$	0.144745	+	0.397684i	0.00523670	+	0.0143877i
$765$	11.7478	+	66.6248i	0.424741	+	2.40883i
$766$	0.706240	+	1.22324i	0.0255175	+	0.0441976i
$767$	−0.788147	+	1.36511i	−0.0284583	+	0.0492913i
$768$	−41.4422	−	15.0837i	−1.49542	−	0.544287i
$769$	−43.0489	+	24.8543i	−1.55238	+	0.896270i	−0.554438	+	0.832225i	$0.687067\pi$
$769$	−43.0489	+	24.8543i	−1.55238	+	0.896270i	−0.997947	+	0.0640446i	$0.979600\pi$
$770$	4.95104	+	4.15442i	0.178423	+	0.149715i
$771$		−	20.3150i		−	0.731627i
$772$	−1.97096	+	2.34890i	−0.0709364	+	0.0845387i
$773$	−12.1644	+	4.42746i	−0.437521	+	0.159245i	−0.551384	−	0.834252i	$-0.685900\pi$
$773$	−12.1644	+	4.42746i	−0.437521	+	0.159245i	0.113862	+	0.993497i	$0.463678\pi$
$774$	0.279385	−	1.58447i	0.0100423	−	0.0569527i
$775$	−25.9759	+	4.58026i	−0.933083	+	0.164528i
$776$	40.4664			1.45266
$777$	−29.3936	−	5.89152i	−1.05449	−	0.211357i
$778$	−24.7530			−0.887440
$779$	1.76021	−	0.310373i	0.0630661	−	0.0111203i
$780$	1.74436	−	9.89277i	0.0624582	−	0.354218i
$781$	−8.54386	+	3.10971i	−0.305723	+	0.111274i
$782$	8.83752	−	10.5322i	0.316029	−	0.376629i
$783$			42.2384i			1.50948i
$784$	6.83688	+	5.73682i	0.244174	+	0.204886i
$785$	−23.6570	+	13.6584i	−0.844353	+	0.487487i
$786$	−32.8348	−	11.9509i	−1.17118	−	0.426274i
$787$	−5.90504	+	10.2278i	−0.210492	+	0.364583i	−0.951869	−	0.306506i	$-0.900840\pi$
$787$	−5.90504	+	10.2278i	−0.210492	+	0.364583i	0.741377	+	0.671089i	$0.234173\pi$
$788$	−1.80770	−	3.13103i	−0.0643968	−	0.111538i
$789$	0.353937	+	2.00728i	0.0126005	+	0.0714610i
$790$	−13.0995	−	35.9905i	−0.466059	−	1.28049i
$791$	13.8071	+	7.97154i	0.490925	+	0.283435i
$792$	14.0608	+	16.7571i	0.499630	+	0.595436i
$793$	−6.95988	+	5.84003i	−0.247153	+	0.207386i
$794$	2.54756	−	6.99936i	0.0904095	−	0.248398i
$795$	53.7320	+	9.47440i	1.90568	+	0.336022i
$796$	1.39381	+	0.245766i	0.0494022	+	0.00871094i
$797$	4.71468	−	12.9535i	0.167002	−	0.458836i	−0.827756	−	0.561088i	$-0.810383\pi$
$797$	4.71468	−	12.9535i	0.167002	−	0.458836i	0.994758	+	0.102253i	$0.0326050\pi$
$798$	−7.86783	+	6.60190i	−0.278518	+	0.233705i
$799$	23.2954	+	27.7624i	0.824132	+	0.982162i
$800$	12.2926	+	7.09715i	0.434610	+	0.250922i
$801$	15.6679	+	43.0471i	0.553597	+	1.52100i
$802$	−0.142607	−	0.808766i	−0.00503564	−	0.0285585i
$803$	9.35605	+	16.2051i	0.330168	+	0.571867i
$804$	16.8799	−	29.2369i	0.595310	−	1.03111i
$805$	−14.5443	−	5.29369i	−0.512619	−	0.186578i
$806$	−11.0438	+	6.37612i	−0.389000	+	0.224589i
$807$	12.5690	+	10.5466i	0.442449	+	0.371259i
$808$			41.4626i			1.45865i
$809$	32.3311	−	38.5307i	1.13670	−	1.35467i	0.210518	−	0.977590i	$-0.432485\pi$
$809$	32.3311	−	38.5307i	1.13670	−	1.35467i	0.926182	−	0.377077i	$-0.123071\pi$
$810$	−29.5649	+	10.7608i	−1.03881	+	0.378094i
$811$	4.11795	−	23.3541i	0.144601	−	0.820072i	−0.823086	−	0.567917i	$-0.807750\pi$
$811$	4.11795	−	23.3541i	0.144601	−	0.820072i	0.967687	−	0.252155i	$-0.0811394\pi$
$812$	5.30593	−	0.935579i	0.186202	−	0.0328324i
$813$	−10.1810			−0.357062
$814$	−1.59571	+	7.96120i	−0.0559295	+	0.279040i
$815$	22.1204			0.774843
$816$	−23.2193	+	4.09419i	−0.812838	+	0.143325i
$817$	−0.0748146	+	0.424295i	−0.00261743	+	0.0148442i
$818$	39.3752	−	14.3314i	1.37672	−	0.501085i
$819$	10.1089	−	12.0473i	0.353234	−	0.420968i
$820$		−	2.04752i		−	0.0715026i
$821$	−15.1134	−	12.6816i	−0.527460	−	0.442591i	0.339763	−	0.940511i	$-0.389653\pi$
$821$	−15.1134	−	12.6816i	−0.527460	−	0.442591i	−0.867223	+	0.497920i	$0.834097\pi$
$822$	12.4542	−	7.19041i	0.434389	−	0.250794i
$823$	34.3407	+	12.4990i	1.19704	+	0.435687i	0.862190	−	0.506584i	$-0.169092\pi$
$823$	34.3407	+	12.4990i	1.19704	+	0.435687i	0.334850	+	0.942271i	$0.391314\pi$
$824$	−1.71475	+	2.97003i	−0.0597360	+	0.103466i
$825$	−6.59232	−	11.4182i	−0.229515	−	0.397532i
$826$	−0.320596	−	1.81819i	−0.0111550	−	0.0632629i
$827$	4.88153	+	13.4119i	0.169747	+	0.466377i	0.995173	−	0.0981333i	$-0.0312872\pi$
$827$	4.88153	+	13.4119i	0.169747	+	0.466377i	−0.825426	+	0.564511i	$0.809065\pi$
$828$	−11.9111	−	6.87688i	−0.413940	−	0.238988i
$829$	0.162972	+	0.194223i	0.00566027	+	0.00674565i	0.768867	−	0.639409i	$-0.220821\pi$
$829$	0.162972	+	0.194223i	0.00566027	+	0.00674565i	−0.763207	+	0.646154i	$0.776376\pi$
$830$	17.7823	−	14.9212i	0.617234	−	0.517921i
$831$	15.5974	−	42.8535i	0.541068	−	1.48657i
$832$	13.2293	+	2.33268i	0.458643	+	0.0808711i
$833$	−16.1005	−	2.83896i	−0.557851	−	0.0983641i
$834$	6.04579	−	16.6107i	0.209349	−	0.575181i
$835$	−7.34068	+	6.15956i	−0.254035	+	0.213160i
$836$	−0.988572	−	1.17813i	−0.0341905	−	0.0407466i
$837$	−56.0633	−	32.3682i	−1.93783	−	1.11881i
$838$	5.59818	+	15.3809i	0.193386	+	0.531324i
$839$	2.03707	+	11.5528i	0.0703275	+	0.398847i	0.999569	+	0.0293730i	$0.00935107\pi$
$839$	2.03707	+	11.5528i	0.0703275	+	0.398847i	−0.929241	+	0.369474i	$0.879538\pi$
$840$	22.4064	+	38.8091i	0.773095	+	1.33904i
$841$	−3.84279	+	6.65591i	−0.132510	+	0.229514i
$842$	12.5542	+	4.56936i	0.432646	+	0.157470i
$843$	−36.9601	+	21.3389i	−1.27297	+	0.734952i
$844$	−10.6786	−	8.96039i	−0.367572	−	0.308429i
$845$		−	30.9553i		−	1.06489i
$846$	−42.1516	+	50.2344i	−1.44920	+	1.72709i
$847$	14.8104	−	5.39054i	0.508891	−	0.185221i
$848$	−2.20644	+	12.5133i	−0.0757695	+	0.429710i
$849$	18.7335	−	3.30323i	0.642934	−	0.113367i
$850$	16.0329			0.549923
$851$	−2.92980	−	19.2224i	−0.100432	−	0.658937i
$852$	−16.5517			−0.567051
$853$	39.1664	−	6.90609i	1.34103	−	0.236460i	0.543333	−	0.839517i	$-0.317162\pi$
$853$	39.1664	−	6.90609i	1.34103	−	0.236460i	0.797698	+	0.603057i	$0.206051\pi$
$854$	1.84786	−	10.4797i	0.0632324	−	0.358609i
$855$	30.8033	−	11.2115i	1.05345	−	0.383425i
$856$	−29.2312	+	34.8364i	−0.999104	+	1.19069i
$857$			5.52768i			0.188822i	0.995533	+	0.0944109i	$0.0300968\pi$
$857$			5.52768i			0.188822i	−0.995533	+	0.0944109i	$0.969903\pi$
$858$	−4.88302	−	4.09734i	−0.166704	−	0.139881i
$859$	−20.7384	+	11.9733i	−0.707586	+	0.408525i	−0.810167	−	0.586200i	$-0.800623\pi$
$859$	−20.7384	+	11.9733i	−0.707586	+	0.408525i	0.102581	+	0.994725i	$0.467290\pi$
$860$	0.463786	+	0.168804i	0.0158150	+	0.00575618i
$861$	2.39851	−	4.15434i	0.0817410	−	0.141580i
$862$	12.6109	+	21.8427i	0.429529	+	0.743967i
$863$	−2.09160	−	11.8621i	−0.0711991	−	0.403790i	−0.999490	−	0.0319351i	$-0.989833\pi$
$863$	−2.09160	−	11.8621i	−0.0711991	−	0.403790i	0.928291	−	0.371855i	$-0.121278\pi$
$864$	11.9150	+	32.7362i	0.405356	+	1.11371i
$865$	32.3113	+	18.6549i	1.09862	+	0.634286i
$866$	−4.02125	−	4.79234i	−0.136648	−	0.162850i
$867$	−6.07493	+	5.09747i	−0.206315	+	0.173119i
$868$	−2.82425	+	7.75955i	−0.0958612	+	0.263376i
$869$	13.2323	+	2.33322i	0.448876	+	0.0791489i
$870$	45.8386	+	8.08258i	1.55407	+	0.274025i
$871$	−8.56361	+	23.5283i	−0.290167	+	0.797227i
$872$	22.7334	−	19.0756i	0.769849	−	0.645980i
$873$	−51.0657	−	60.8577i	−1.72831	−	2.05972i
$874$	−5.76927	−	3.33089i	−0.195149	−	0.112669i
$875$	2.10692	+	5.78872i	0.0712269	+	0.195694i
$876$	5.91516	+	33.5466i	0.199855	+	1.13343i
$877$	−12.9745	−	22.4725i	−0.438118	−	0.758843i	0.559426	−	0.828880i	$-0.311021\pi$
$877$	−12.9745	−	22.4725i	−0.438118	−	0.758843i	−0.997544	+	0.0700374i	$0.977688\pi$
$878$	−15.5479	+	26.9297i	−0.524715	+	0.908833i
$879$	−71.2914	−	25.9480i	−2.40460	−	0.875203i
$880$	6.22583	−	3.59448i	0.209873	−	0.121170i
$881$	−17.6091	−	14.7758i	−0.593267	−	0.497810i	0.296006	−	0.955186i	$-0.404345\pi$
$881$	−17.6091	−	14.7758i	−0.593267	−	0.497810i	−0.889274	+	0.457376i	$0.848790\pi$
$882$		−	29.5824i		−	0.996091i
$883$	6.91218	−	8.23762i	0.232613	−	0.277218i	−0.637093	−	0.770787i	$-0.719863\pi$
$883$	6.91218	−	8.23762i	0.232613	−	0.277218i	0.869707	+	0.493569i	$0.164308\pi$
$884$	−4.02696	+	1.46570i	−0.135441	+	0.0492967i
$885$	−1.53123	+	8.68405i	−0.0514718	+	0.291911i
$886$	8.04277	−	1.41816i	0.270202	−	0.0476439i
$887$	−52.8009			−1.77288			−0.886441	−	0.462842i	$-0.846830\pi$
$887$	−52.8009			−1.77288			−0.886441	+	0.462842i	$0.846830\pi$
$888$	−29.2763	+	48.0869i	−0.982447	+	1.61369i
$889$	7.47281			0.250630
$890$	25.0319	−	4.41380i	0.839072	−	0.147951i
$891$	1.91665	−	10.8699i	0.0642103	−	0.364155i
$892$	9.00411	−	3.27723i	0.301480	−	0.109730i
$893$	11.2875	−	13.4519i	0.377722	−	0.450151i
$894$		−	31.3394i		−	1.04815i
$895$	−22.3284	−	18.7357i	−0.746356	−	0.626267i
$896$	−2.81672	+	1.62624i	−0.0941002	+	0.0543287i
$897$	14.3445	+	5.22096i	0.478948	+	0.174323i
$898$	8.18137	−	14.1706i	0.273016	−	0.472878i
$899$	16.3337	+	28.2908i	0.544759	+	0.943550i
$900$	−2.78509	−	15.7951i	−0.0928365	−	0.526502i
$901$	−7.96084	−	21.8722i	−0.265214	−	0.728669i
$902$	−1.12519	−	0.649631i	−0.0374649	−	0.0216304i
$903$	0.743262	+	0.885785i	0.0247342	+	0.0294771i
$904$	22.9357	−	19.2453i	0.762830	−	0.640090i
$905$	−5.96200	+	16.3805i	−0.198184	+	0.544505i
$906$	−30.0926	−	5.30614i	−0.999760	−	0.176285i
$907$	−21.2360	−	3.74448i	−0.705130	−	0.124333i	−0.190426	−	0.981701i	$-0.560987\pi$
$907$	−21.2360	−	3.74448i	−0.705130	−	0.124333i	−0.514704	+	0.857368i	$0.672098\pi$
$908$	−6.37841	+	17.5245i	−0.211675	+	0.581572i
$909$	62.3560	−	52.3229i	2.06822	−	1.73544i
$910$	−5.60904	−	6.68460i	−0.185938	−	0.221592i
$911$	−10.6720	−	6.16151i	−0.353581	−	0.204140i	0.312681	−	0.949858i	$-0.398773\pi$
$911$	−10.6720	−	6.16151i	−0.353581	−	0.204140i	−0.666261	+	0.745719i	$0.732106\pi$
$912$	3.90730	+	10.7352i	0.129384	+	0.355479i
$913$	1.41412	+	8.01990i	0.0468007	+	0.265420i
$914$	−7.27661	−	12.6035i	−0.240689	−	0.416885i
$915$	−25.4127	+	44.0162i	−0.840119	+	1.45513i
$916$	3.53758	+	1.28757i	0.116885	+	0.0425426i
$917$	14.5327	−	8.39048i	0.479914	−	0.277078i
$918$	30.1435	+	25.2934i	0.994883	+	0.834806i
$919$			11.9251i			0.393373i	0.980466	+	0.196687i	$0.0630181\pi$
$919$			11.9251i			0.393373i	−0.980466	+	0.196687i	$0.936982\pi$
$920$	−18.6836	+	22.2662i	−0.615979	+	0.734095i
$921$	59.0912	−	21.5075i	1.94712	−	0.708695i
$922$	−1.46262	+	8.29490i	−0.0481687	+	0.273178i
$923$	12.0892	−	2.13166i	0.397921	−	0.0701643i
$924$	−4.12761			−0.135789
$925$	14.9755	−	17.0259i	0.492391	−	0.559808i
$926$	−32.0151			−1.05208
$927$	6.63054	−	1.16914i	0.217775	−	0.0383997i
$928$	3.05266	−	17.3125i	0.100208	−	0.568310i
$929$	−10.7124	+	3.89898i	−0.351462	+	0.127922i	−0.511717	−	0.859154i	$-0.670990\pi$
$929$	−10.7124	+	3.89898i	−0.351462	+	0.127922i	0.160256	+	0.987076i	$0.448768\pi$
$930$	−45.8551	+	54.6480i	−1.50365	+	1.79198i
$931$			7.92166i			0.259622i
$932$	−7.58133	−	6.36149i	−0.248335	−	0.208377i
$933$	−65.7794	+	37.9778i	−2.15352	+	1.24334i
$934$	43.5357	+	15.8457i	1.42453	+	0.518487i
$935$	−6.58448	+	11.4047i	−0.215336	+	0.372972i
$936$	−14.7670	−	25.5772i	−0.482675	−	0.836017i
$937$	−7.30368	−	41.4212i	−0.238601	−	1.35317i	−0.834896	−	0.550408i	$-0.814472\pi$
$937$	−7.30368	−	41.4212i	−0.238601	−	1.35317i	0.596295	−	0.802765i	$-0.296639\pi$
$938$	−10.0301	−	27.5576i	−0.327496	−	0.899788i
$939$	75.2978	+	43.4732i	2.45725	+	1.41870i
$940$	−12.9304	−	15.4099i	−0.421744	−	0.502615i
$941$	22.7117	−	19.0574i	0.740381	−	0.621254i	−0.192559	−	0.981285i	$-0.561679\pi$
$941$	22.7117	−	19.0574i	0.740381	−	0.621254i	0.932940	+	0.360032i	$0.117234\pi$
$942$	−10.7925	+	29.6522i	−0.351639	+	0.966120i
$943$	3.06417	+	0.540295i	0.0997830	+	0.0175944i
$944$	−2.02238	−	0.356600i	−0.0658229	−	0.0116063i
$945$	15.1508	−	41.6264i	0.492854	−	1.35411i
$946$	0.239913	−	0.201311i	0.00780025	−	0.00654518i
$947$	−5.71568	−	6.81168i	−0.185735	−	0.221350i	0.665140	−	0.746719i	$-0.268372\pi$
$947$	−5.71568	−	6.81168i	−0.185735	−	0.221350i	−0.850875	+	0.525369i	$0.823927\pi$
$948$	21.1831	+	12.2301i	0.687995	+	0.397214i
$949$	−8.64077	−	23.7403i	−0.280491	−	0.770644i
$950$	−1.34899	−	7.65050i	−0.0437670	−	0.248215i
$951$	−41.5651	−	71.9929i	−1.34784	−	2.33453i
$952$	9.55869	−	16.5561i	0.309799	−	0.536587i
$953$	−30.6845	−	11.1682i	−0.993968	−	0.361775i	−0.206712	−	0.978402i	$-0.566276\pi$
$953$	−30.6845	−	11.1682i	−0.993968	−	0.361775i	−0.787255	+	0.616627i	$0.788499\pi$
$954$	36.4739	−	21.0582i	1.18089	−	0.681785i
$955$	−1.34507	−	1.12865i	−0.0435254	−	0.0365222i
$956$		−	12.5646i		−	0.406367i
$957$	−10.4961	+	12.5088i	−0.339292	+	0.404352i
$958$	12.6818	−	4.61578i	0.409729	−	0.149129i
$959$	−1.19929	+	6.80149i	−0.0387270	+	0.219632i
$960$	74.0065	−	13.0493i	2.38855	−	0.421166i
$961$	−19.0673			−0.615075
$962$	3.98819	−	10.2113i	0.128584	−	0.329226i
$963$	89.2786			2.87696
$964$	14.5673	−	2.56862i	0.469183	−	0.0827296i
$965$	2.20912	−	12.5285i	0.0711140	−	0.403308i
$966$	−16.8010	+	6.11506i	−0.540563	+	0.196749i
$967$	−29.9880	+	35.7383i	−0.964349	+	1.14927i	0.0244032	+	0.999702i	$0.492231\pi$
$967$	−29.9880	+	35.7383i	−0.964349	+	1.14927i	−0.988752	+	0.149564i	$0.952213\pi$
$968$		−	29.5983i		−	0.951325i
$969$	−16.0311	−	13.4517i	−0.514994	−	0.432131i
$970$	−38.1748	+	22.0402i	−1.22572	+	0.707669i
$971$	11.7900	+	4.29121i	0.378359	+	0.137711i	0.524197	−	0.851597i	$-0.324366\pi$
$971$	11.7900	+	4.29121i	0.378359	+	0.137711i	−0.145838	+	0.989308i	$0.546588\pi$
$972$	0.274773	−	0.475922i	0.00881336	−	0.0152652i
$973$	4.24464	+	7.35193i	0.136077	+	0.235692i
$974$	1.72984	+	9.81041i	0.0554276	+	0.314346i
$975$	6.08833	+	16.7276i	0.194983	+	0.535710i
$976$	−10.2507	−	5.91823i	−0.328116	−	0.189438i
$977$	10.6527	+	12.6954i	0.340810	+	0.406161i	0.909040	−	0.416708i	$-0.136816\pi$
$977$	10.6527	+	12.6954i	0.340810	+	0.406161i	−0.568231	+	0.822869i	$0.692372\pi$
$978$	19.5744	−	16.4249i	0.625921	−	0.525210i
$979$	−3.04984	+	8.37936i	−0.0974733	+	0.267806i
$980$	8.93683	+	1.57580i	0.285476	+	0.0503372i
$981$	−57.3758	−	10.1169i	−1.83187	−	0.323008i
$982$	−7.56758	+	20.7917i	−0.241491	+	0.663491i
$983$	−22.8673	+	19.1879i	−0.729354	+	0.612001i	−0.929955	−	0.367672i	$-0.880155\pi$
$983$	−22.8673	+	19.1879i	−0.729354	+	0.612001i	0.200602	+	0.979673i	$0.435710\pi$
$984$	−5.79061	−	6.90098i	−0.184598	−	0.219995i
$985$	12.9905	+	7.50007i	0.413912	+	0.238972i
$986$	−6.79136	−	18.6591i	−0.216281	−	0.594227i
$987$	−8.18387	−	46.4130i	−0.260495	−	1.47734i
$988$	1.03822	+	1.79825i	0.0330302	+	0.0572099i
$989$	−0.375002	+	0.649523i	−0.0119244	+	0.0206536i
$990$	−22.3914	−	8.14981i	−0.711646	−	0.259018i
$991$	−22.3726	+	12.9168i	−0.710689	+	0.410316i	−0.811316	−	0.584608i	$-0.801248\pi$
$991$	−22.3726	+	12.9168i	−0.710689	+	0.410316i	0.100627	+	0.994924i	$0.467915\pi$
$992$	20.6397	+	17.3187i	0.655310	+	0.549870i
$993$			74.3909i			2.36072i
$994$	−9.24197	+	11.0142i	−0.293137	+	0.349348i
$995$	−5.51792	+	2.00836i	−0.174930	+	0.0636692i
$996$	−2.57431	+	14.5997i	−0.0815703	+	0.462608i
$997$	−39.0502	+	6.88561i	−1.23673	+	0.218069i	−0.753515	−	0.657431i	$-0.771643\pi$
$997$	−39.0502	+	6.88561i	−1.23673	+	0.218069i	−0.483218	+	0.875500i	$0.660532\pi$
$998$	14.7293			0.466247
$999$	55.0155	−	8.38522i	1.74061	−	0.265297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.h.a.28.2	yes	18
3.2	odd	2		333.2.bl.d.28.2		18
4.3	odd	2		592.2.bq.d.65.3		18
5.2	odd	4		925.2.ba.a.324.2		36
5.3	odd	4		925.2.ba.a.324.5		36
5.4	even	2		925.2.bb.a.176.2		18
37.2	odd	36		1369.2.a.m.1.7		18
37.4	even	18	inner	37.2.h.a.4.2	✓	18
37.12	even	9		1369.2.b.g.1368.12		18
37.25	even	18		1369.2.b.g.1368.7		18
37.35	odd	36		1369.2.a.m.1.12		18
111.41	odd	18		333.2.bl.d.226.2		18
148.115	odd	18		592.2.bq.d.337.3		18
185.4	even	18		925.2.bb.a.226.2		18
185.78	odd	36		925.2.ba.a.374.2		36
185.152	odd	36		925.2.ba.a.374.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.4.2	✓	18	37.4	even	18	inner
37.2.h.a.28.2	yes	18	1.1	even	1	trivial
333.2.bl.d.28.2		18	3.2	odd	2
333.2.bl.d.226.2		18	111.41	odd	18
592.2.bq.d.65.3		18	4.3	odd	2
592.2.bq.d.337.3		18	148.115	odd	18
925.2.ba.a.324.2		36	5.2	odd	4
925.2.ba.a.324.5		36	5.3	odd	4
925.2.ba.a.374.2		36	185.78	odd	36
925.2.ba.a.374.5		36	185.152	odd	36
925.2.bb.a.176.2		18	5.4	even	2
925.2.bb.a.226.2		18	185.4	even	18
1369.2.a.m.1.7		18	37.2	odd	36
1369.2.a.m.1.12		18	37.35	odd	36
1369.2.b.g.1368.7		18	37.25	even	18
1369.2.b.g.1368.12		18	37.12	even	9

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11764 + 0.197069i) q^{2} +(-0.522172 + 2.96139i) q^{3} +(-0.669111 + 0.243536i) q^{4} +(1.89897 - 2.26310i) q^{5} -3.41266i q^{6} +(1.25550 + 1.05349i) q^{7} +(2.66549 - 1.53892i) q^{8} +(-5.67807 - 2.06665i) q^{9} +O(q^{10})\)	\(q+(-1.11764 + 0.197069i) q^{2} +(-0.522172 + 2.96139i) q^{3} +(-0.669111 + 0.243536i) q^{4} +(1.89897 - 2.26310i) q^{5} -3.41266i q^{6} +(1.25550 + 1.05349i) q^{7} +(2.66549 - 1.53892i) q^{8} +(-5.67807 - 2.06665i) q^{9} +(-1.67637 + 2.90355i) q^{10} +(-0.588101 - 1.01862i) q^{11} +(-0.371814 - 2.10866i) q^{12} +(0.543140 + 1.49227i) q^{13} +(-1.61080 - 0.929995i) q^{14} +(5.71033 + 6.80531i) q^{15} +(-1.58485 + 1.32985i) q^{16} +(1.29620 - 3.56127i) q^{17} +(6.75329 + 1.19079i) q^{18} +(-1.80842 - 0.318873i) q^{19} +(-0.719472 + 1.97673i) q^{20} +(-3.77537 + 3.16791i) q^{21} +(0.858022 + 1.02255i) q^{22} +(-2.76838 - 1.59832i) q^{23} +(3.16550 + 8.69714i) q^{24} +(-0.647311 - 3.67108i) q^{25} +(-0.901113 - 1.56077i) q^{26} +(4.57447 - 7.92321i) q^{27} +(-1.09663 - 0.399140i) q^{28} +(-3.99823 + 2.30838i) q^{29} +(-7.72319 - 6.48053i) q^{30} -7.07583i q^{31} +(-2.44759 + 2.91693i) q^{32} +(3.32362 - 1.20970i) q^{33} +(-0.746859 + 4.23565i) q^{34} +(4.76830 - 0.840779i) q^{35} +4.30256 q^{36} +(3.80039 + 4.74942i) q^{37} +2.08399 q^{38} +(-4.70279 + 0.829228i) q^{39} +(1.57895 - 8.95466i) q^{40} +(-0.914644 + 0.332903i) q^{41} +(3.59519 - 4.28458i) q^{42} -0.234622i q^{43} +(0.641576 + 0.538346i) q^{44} +(-15.4595 + 8.92555i) q^{45} +(3.40902 + 1.24078i) q^{46} +(-4.78138 + 8.28159i) q^{47} +(-3.11063 - 5.38777i) q^{48} +(-0.749100 - 4.24836i) q^{49} +(1.44692 + 3.97537i) q^{50} +(9.86947 + 5.69814i) q^{51} +(-0.726842 - 0.866216i) q^{52} +(4.70480 - 3.94780i) q^{53} +(-3.55117 + 9.75676i) q^{54} +(-3.42203 - 0.603396i) q^{55} +(4.96776 + 0.875949i) q^{56} +(1.88861 - 5.18891i) q^{57} +(4.01365 - 3.36785i) q^{58} +(0.638035 + 0.760380i) q^{59} +(-5.47818 - 3.16283i) q^{60} +(1.95677 + 5.37617i) q^{61} +(1.39443 + 7.90820i) q^{62} +(-4.95161 - 8.57644i) q^{63} +(4.22956 - 7.32580i) q^{64} +(4.40856 + 1.60458i) q^{65} +(-3.47620 + 2.00699i) q^{66} +(12.0781 + 10.1347i) q^{67} +2.69856i q^{68} +(6.17882 - 7.36363i) q^{69} +(-5.16353 + 1.87937i) q^{70} +(1.34232 - 7.61269i) q^{71} +(-18.3153 + 3.22948i) q^{72} -15.9089 q^{73} +(-5.18342 - 4.55919i) q^{74} +11.2095 q^{75} +(1.28769 - 0.227054i) q^{76} +(0.334745 - 1.89843i) q^{77} +(5.09259 - 1.85355i) q^{78} +(-7.34295 + 8.75099i) q^{79} +6.11202i q^{80} +(7.18862 + 6.03197i) q^{81} +(0.956634 - 0.552313i) q^{82} +(-6.50611 - 2.36803i) q^{83} +(1.75464 - 3.03912i) q^{84} +(-5.59809 - 9.69617i) q^{85} +(0.0462369 + 0.262222i) q^{86} +(-4.74823 - 13.0457i) q^{87} +(-3.13516 - 1.81008i) q^{88} +(-4.87316 - 5.80761i) q^{89} +(15.5192 - 13.0221i) q^{90} +(-0.890171 + 2.44573i) q^{91} +(2.24160 + 0.395255i) q^{92} +(20.9543 + 3.69480i) q^{93} +(3.71179 - 10.1981i) q^{94} +(-4.15577 + 3.48710i) q^{95} +(-7.36008 - 8.77140i) q^{96} +(11.3862 + 6.57381i) q^{97} +(1.67444 + 4.60049i) q^{98} +(1.23415 + 6.99919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more