LMFDB - Embedded newform 27.2.e.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,2,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, 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:	$0.215596085457$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.2
Root			$0.500000 - 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	27.4
Dual form			27.2.e.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.753189 + 0.274138i) q^{2} +(-1.68842 - 0.386327i) q^{3} +(-1.03995 - 0.872619i) q^{4} +(-0.477505 + 2.70806i) q^{5} +(-1.16579 - 0.753837i) q^{6} +(1.82076 - 1.52780i) q^{7} +(-1.34559 - 2.33062i) q^{8} +(2.70150 + 1.30456i) q^{9} +O(q^{10})$	\(q+(0.753189 + 0.274138i) q^{2} +(-1.68842 - 0.386327i) q^{3} +(-1.03995 - 0.872619i) q^{4} +(-0.477505 + 2.70806i) q^{5} +(-1.16579 - 0.753837i) q^{6} +(1.82076 - 1.52780i) q^{7} +(-1.34559 - 2.33062i) q^{8} +(2.70150 + 1.30456i) q^{9} +(-1.10204 + 1.90878i) q^{10} +(-0.0434396 - 0.246358i) q^{11} +(1.41875 + 1.87510i) q^{12} +(-2.45446 + 0.893351i) q^{13} +(1.79020 - 0.651581i) q^{14} +(1.85243 - 4.38787i) q^{15} +(0.0969067 + 0.549585i) q^{16} +(0.146688 - 0.254072i) q^{17} +(1.67711 + 1.72317i) q^{18} +(1.39237 + 2.41166i) q^{19} +(2.85969 - 2.39956i) q^{20} +(-3.66443 + 1.87615i) q^{21} +(0.0348180 - 0.197463i) q^{22} +(-5.12472 - 4.30015i) q^{23} +(1.37153 + 4.45490i) q^{24} +(-2.40714 - 0.876128i) q^{25} -2.09357 q^{26} +(-4.05728 - 3.24631i) q^{27} -3.22668 q^{28} +(0.333645 + 0.121437i) q^{29} +(2.59811 - 2.79707i) q^{30} +(2.11847 + 1.77761i) q^{31} +(-1.01231 + 5.74108i) q^{32} +(-0.0218307 + 0.432738i) q^{33} +(0.180135 - 0.151151i) q^{34} +(3.26796 + 5.66027i) q^{35} +(-1.67103 - 3.71406i) q^{36} +(3.49619 - 6.05558i) q^{37} +(0.387591 + 2.19814i) q^{38} +(4.48928 - 0.560124i) q^{39} +(6.95400 - 2.53105i) q^{40} +(9.13156 - 3.32362i) q^{41} +(-3.27434 + 0.408537i) q^{42} +(0.0452712 + 0.256746i) q^{43} +(-0.169802 + 0.294106i) q^{44} +(-4.82282 + 6.69291i) q^{45} +(-2.68104 - 4.64370i) q^{46} +(-8.75249 + 7.34421i) q^{47} +(0.0487006 - 0.965367i) q^{48} +(-0.234540 + 1.33014i) q^{49} +(-1.57285 - 1.31978i) q^{50} +(-0.345826 + 0.372309i) q^{51} +(3.33207 + 1.21277i) q^{52} +5.43137 q^{53} +(-2.16596 - 3.55734i) q^{54} +0.687897 q^{55} +(-6.01071 - 2.18772i) q^{56} +(-1.41922 - 4.60980i) q^{57} +(0.218007 + 0.182930i) q^{58} +(1.03788 - 5.88612i) q^{59} +(-5.75536 + 2.94669i) q^{60} +(-9.07515 + 7.61495i) q^{61} +(1.10830 + 1.91963i) q^{62} +(6.91190 - 1.75206i) q^{63} +(-1.77824 + 3.08001i) q^{64} +(-1.24723 - 7.07342i) q^{65} +(-0.135073 + 0.319949i) q^{66} +(-1.70113 + 0.619160i) q^{67} +(-0.374256 + 0.136218i) q^{68} +(6.99139 + 9.24026i) q^{69} +(0.909693 + 5.15912i) q^{70} +(0.185255 - 0.320871i) q^{71} +(-0.594663 - 8.05158i) q^{72} +(-2.51339 - 4.35333i) q^{73} +(4.29336 - 3.60255i) q^{74} +(3.72579 + 2.40921i) q^{75} +(0.656467 - 3.72301i) q^{76} +(-0.455479 - 0.382193i) q^{77} +(3.53483 + 0.808804i) q^{78} +(-0.754406 - 0.274581i) q^{79} -1.53459 q^{80} +(5.59624 + 7.04855i) q^{81} +7.78892 q^{82} +(2.58947 + 0.942488i) q^{83} +(5.44798 + 1.24655i) q^{84} +(0.617998 + 0.518562i) q^{85} +(-0.0362861 + 0.205789i) q^{86} +(-0.516417 - 0.333932i) q^{87} +(-0.515717 + 0.432738i) q^{88} +(-5.22533 - 9.05054i) q^{89} +(-5.46728 + 3.71891i) q^{90} +(-3.10412 + 5.37650i) q^{91} +(1.57704 + 8.94385i) q^{92} +(-2.89012 - 3.81976i) q^{93} +(-8.60560 + 3.13218i) q^{94} +(-7.19580 + 2.61906i) q^{95} +(3.92713 - 9.30225i) q^{96} +(-2.57600 - 14.6092i) q^{97} +(-0.541296 + 0.937552i) q^{98} +(0.204037 - 0.722208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	0.753189	+	0.274138i	0.532585	+	0.193845i	0.594292	−	0.804249i	$-0.297432\pi$
$2$	0.753189	+	0.274138i	0.532585	+	0.193845i	−0.0617072	+	0.998094i	$0.519654\pi$
$3$	−1.68842	−	0.386327i	−0.974808	−	0.223046i
$3$	−1.68842	−	0.386327i	−0.974808	−	0.223046i
$4$	−1.03995	−	0.872619i	−0.519974	−	0.436310i
$5$	−0.477505	+	2.70806i	−0.213547	+	1.21108i	0.669864	+	0.742484i	$0.266352\pi$
$5$	−0.477505	+	2.70806i	−0.213547	+	1.21108i	−0.883411	+	0.468600i	$0.844759\pi$
$6$	−1.16579	−	0.753837i	−0.475932	−	0.307753i
$7$	1.82076	−	1.52780i	0.688183	−	0.577454i	−0.230202	−	0.973143i	$-0.573939\pi$
$7$	1.82076	−	1.52780i	0.688183	−	0.577454i	0.918385	+	0.395689i	$0.129494\pi$
$8$	−1.34559	−	2.33062i	−0.475736	−	0.823999i
$9$	2.70150	+	1.30456i	0.900501	+	0.434854i
$10$	−1.10204	+	1.90878i	−0.348494	+	0.603610i
$11$	−0.0434396	−	0.246358i	−0.0130975	−	0.0742798i	0.977558	−	0.210665i	$-0.0675628\pi$
$11$	−0.0434396	−	0.246358i	−0.0130975	−	0.0742798i	−0.990656	+	0.136385i	$0.956452\pi$
$12$	1.41875	+	1.87510i	0.409557	+	0.541296i
$13$	−2.45446	+	0.893351i	−0.680745	+	0.247771i	−0.659167	−	0.751996i	$-0.729091\pi$
$13$	−2.45446	+	0.893351i	−0.680745	+	0.247771i	−0.0215777	+	0.999767i	$0.506869\pi$
$14$	1.79020	−	0.651581i	0.478452	−	0.174142i
$15$	1.85243	−	4.38787i	0.478294	−	1.13294i
$16$	0.0969067	+	0.549585i	0.0242267	+	0.137396i
$17$	0.146688	−	0.254072i	0.0355772	−	0.0616215i	−0.847689	−	0.530494i	$-0.822006\pi$
$17$	0.146688	−	0.254072i	0.0355772	−	0.0616215i	0.883266	+	0.468873i	$0.155340\pi$
$18$	1.67711	+	1.72317i	0.395299	+	0.406154i
$19$	1.39237	+	2.41166i	0.319432	+	0.553273i	0.980370	−	0.197168i	$-0.0631745\pi$
$19$	1.39237	+	2.41166i	0.319432	+	0.553273i	−0.660937	+	0.750441i	$0.729841\pi$
$20$	2.85969	−	2.39956i	0.639446	−	0.536559i
$21$	−3.66443	+	1.87615i	−0.799645	+	0.409410i
$22$	0.0348180	−	0.197463i	0.00742323	−	0.0420992i
$23$	−5.12472	−	4.30015i	−1.06858	−	0.896643i	−0.0736543	−	0.997284i	$-0.523466\pi$
$23$	−5.12472	−	4.30015i	−1.06858	−	0.896643i	−0.994923	+	0.100641i	$0.967911\pi$
$24$	1.37153	+	4.45490i	0.279962	+	0.909352i
$25$	−2.40714	−	0.876128i	−0.481428	−	0.175226i
$26$	−2.09357			−0.410584
$27$	−4.05728	−	3.24631i	−0.780823	−	0.624752i
$28$	−3.22668			−0.609786
$29$	0.333645	+	0.121437i	0.0619562	+	0.0225502i	0.372812	−	0.927907i	$-0.378394\pi$
$29$	0.333645	+	0.121437i	0.0619562	+	0.0225502i	−0.310856	+	0.950457i	$0.600616\pi$
$30$	2.59811	−	2.79707i	0.474348	−	0.510673i
$31$	2.11847	+	1.77761i	0.380488	+	0.319268i	0.812894	−	0.582411i	$-0.197891\pi$
$31$	2.11847	+	1.77761i	0.380488	+	0.319268i	−0.432406	+	0.901679i	$0.642335\pi$
$32$	−1.01231	+	5.74108i	−0.178952	+	1.01489i
$33$	−0.0218307	+	0.432738i	−0.00380023	+	0.0753299i
$34$	0.180135	−	0.151151i	0.0308929	−	0.0259222i
$35$	3.26796	+	5.66027i	0.552386	+	0.956760i
$36$	−1.67103	−	3.71406i	−0.278506	−	0.619010i
$37$	3.49619	−	6.05558i	0.574770	−	0.995531i	−0.421297	−	0.906923i	$-0.638425\pi$
$37$	3.49619	−	6.05558i	0.574770	−	0.995531i	0.996067	−	0.0886080i	$-0.0282418\pi$
$38$	0.387591	+	2.19814i	0.0628756	+	0.356585i
$39$	4.48928	−	0.560124i	0.718860	−	0.0896917i
$40$	6.95400	−	2.53105i	1.09952	−	0.400194i
$41$	9.13156	−	3.32362i	1.42611	−	0.519062i	0.490296	−	0.871556i	$-0.336888\pi$
$41$	9.13156	−	3.32362i	1.42611	−	0.519062i	0.935814	+	0.352494i	$0.114666\pi$
$42$	−3.27434	+	0.408537i	−0.505241	+	0.0630386i
$43$	0.0452712	+	0.256746i	0.00690379	+	0.0391534i	0.988065	−	0.154037i	$-0.0492276\pi$
$43$	0.0452712	+	0.256746i	0.00690379	+	0.0391534i	−0.981161	+	0.193191i	$0.938116\pi$
$44$	−0.169802	+	0.294106i	−0.0255986	+	0.0443381i
$45$	−4.82282	+	6.69291i	−0.718943	+	0.997720i
$46$	−2.68104	−	4.64370i	−0.395298	−	0.684677i
$47$	−8.75249	+	7.34421i	−1.27668	+	1.07126i	−0.282989	+	0.959123i	$0.591326\pi$
$47$	−8.75249	+	7.34421i	−1.27668	+	1.07126i	−0.993692	+	0.112140i	$0.964230\pi$
$48$	0.0487006	−	0.965367i	0.00702933	−	0.139339i
$49$	−0.234540	+	1.33014i	−0.0335057	+	0.190020i
$50$	−1.57285	−	1.31978i	−0.222435	−	0.186645i
$51$	−0.345826	+	0.372309i	−0.0484253	+	0.0521337i
$52$	3.33207	+	1.21277i	0.462074	+	0.168181i
$53$	5.43137			0.746056			0.373028	−	0.927820i	$-0.378320\pi$
$53$	5.43137			0.746056			0.373028	+	0.927820i	$0.378320\pi$
$54$	−2.16596	−	3.55734i	−0.294750	−	0.484092i
$55$	0.687897			0.0927560
$56$	−6.01071	−	2.18772i	−0.803215	−	0.292346i
$57$	−1.41922	−	4.60980i	−0.187980	−	0.610583i
$58$	0.218007	+	0.182930i	0.0286257	+	0.0240198i
$59$	1.03788	−	5.88612i	0.135121	−	0.766308i	−0.839655	−	0.543121i	$-0.817243\pi$
$59$	1.03788	−	5.88612i	0.135121	−	0.766308i	0.974776	−	0.223188i	$-0.0716462\pi$
$60$	−5.75536	+	2.94669i	−0.743014	+	0.380416i
$61$	−9.07515	+	7.61495i	−1.16195	+	0.974995i	−0.999930	−	0.0117924i	$-0.996246\pi$
$61$	−9.07515	+	7.61495i	−1.16195	+	0.974995i	−0.162023	+	0.986787i	$0.551802\pi$
$62$	1.10830	+	1.91963i	0.140754	+	0.243793i
$63$	6.91190	−	1.75206i	0.870817	−	0.220739i
$64$	−1.77824	+	3.08001i	−0.222281	+	0.385001i
$65$	−1.24723	−	7.07342i	−0.154700	−	0.877350i
$66$	−0.135073	+	0.319949i	−0.0166263	+	0.0393829i
$67$	−1.70113	+	0.619160i	−0.207826	+	0.0756424i	−0.443835	−	0.896108i	$-0.646383\pi$
$67$	−1.70113	+	0.619160i	−0.207826	+	0.0756424i	0.236010	+	0.971751i	$0.424160\pi$
$68$	−0.374256	+	0.136218i	−0.0453852	+	0.0165189i
$69$	6.99139	+	9.24026i	0.841665	+	1.11240i
$70$	0.909693	+	5.15912i	0.108729	+	0.616633i
$71$	0.185255	−	0.320871i	0.0219857	−	0.0380804i	−0.854823	−	0.518919i	$-0.826334\pi$
$71$	0.185255	−	0.320871i	0.0219857	−	0.0380804i	0.876809	+	0.480839i	$0.159668\pi$
$72$	−0.594663	−	8.05158i	−0.0700817	−	0.948888i
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	0.680621	−	0.732636i	$-0.261710\pi$
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	−0.974792	+	0.223117i	$0.928377\pi$
$74$	4.29336	−	3.60255i	0.499093	−	0.418789i
$75$	3.72579	+	2.40921i	0.430217	+	0.278192i
$76$	0.656467	−	3.72301i	0.0753019	−	0.427059i
$77$	−0.455479	−	0.382193i	−0.0519067	−	0.0435549i
$78$	3.53483	+	0.808804i	0.400240	+	0.0915790i
$79$	−0.754406	−	0.274581i	−0.0848773	−	0.0308928i	0.299233	−	0.954180i	$-0.403269\pi$
$79$	−0.754406	−	0.274581i	−0.0848773	−	0.0308928i	−0.384110	+	0.923287i	$0.625492\pi$
$80$	−1.53459			−0.171572
$81$	5.59624	+	7.04855i	0.621804	+	0.783173i
$82$	7.78892			0.860143
$83$	2.58947	+	0.942488i	0.284231	+	0.103452i	0.480201	−	0.877158i	$-0.340564\pi$
$83$	2.58947	+	0.942488i	0.284231	+	0.103452i	−0.195971	+	0.980610i	$0.562786\pi$
$84$	5.44798	+	1.24655i	0.594424	+	0.136010i
$85$	0.617998	+	0.518562i	0.0670313	+	0.0562460i
$86$	−0.0362861	+	0.205789i	−0.00391283	+	0.0221908i
$87$	−0.516417	−	0.333932i	−0.0553657	−	0.0358012i
$88$	−0.515717	+	0.432738i	−0.0549756	+	0.0461300i
$89$	−5.22533	−	9.05054i	−0.553884	−	0.959356i	−0.997989	−	0.0633809i	$-0.979812\pi$
$89$	−5.22533	−	9.05054i	−0.553884	−	0.959356i	0.444105	−	0.895975i	$-0.353522\pi$
$90$	−5.46728	+	3.71891i	−0.576302	+	0.392007i
$91$	−3.10412	+	5.37650i	−0.325401	+	0.563611i
$92$	1.57704	+	8.94385i	0.164418	+	0.932461i
$93$	−2.89012	−	3.81976i	−0.299692	−	0.396091i
$94$	−8.60560	+	3.13218i	−0.887600	+	0.323060i
$95$	−7.19580	+	2.61906i	−0.738273	+	0.268709i
$96$	3.92713	−	9.30225i	0.400811	−	0.949407i
$97$	−2.57600	−	14.6092i	−0.261553	−	1.48334i	−0.778673	−	0.627430i	$-0.784107\pi$
$97$	−2.57600	−	14.6092i	−0.261553	−	1.48334i	0.517120	−	0.855913i	$-0.327004\pi$
$98$	−0.541296	+	0.937552i	−0.0546791	+	0.0947070i
$99$	0.204037	−	0.722208i	0.0205065	−	0.0725846i
$100$	1.73877	+	3.01164i	0.173877	+	0.301164i
$101$	3.06826	−	2.57457i	0.305303	−	0.256180i	−0.477244	−	0.878771i	$-0.658364\pi$
$101$	3.06826	−	2.57457i	0.305303	−	0.256180i	0.782548	+	0.622591i	$0.213920\pi$
$102$	−0.362537	+	0.185615i	−0.0358965	+	0.0183786i
$103$	−1.02789	+	5.82943i	−0.101281	+	0.574391i	0.891360	+	0.453296i	$0.149752\pi$
$103$	−1.02789	+	5.82943i	−0.101281	+	0.574391i	−0.992641	+	0.121095i	$0.961359\pi$
$104$	5.38475	+	4.51834i	0.528018	+	0.443060i
$105$	−3.33096	−	10.8194i	−0.325069	−	1.05586i
$106$	4.09085	+	1.48895i	0.397338	+	0.144619i
$107$	−0.258978			−0.0250364			−0.0125182	−	0.999922i	$-0.503985\pi$
$107$	−0.258978			−0.0250364			−0.0125182	+	0.999922i	$0.503985\pi$
$108$	1.38656	+	6.91645i	0.133422	+	0.665535i
$109$	−8.55787			−0.819695			−0.409848	−	0.912154i	$-0.634418\pi$
$109$	−8.55787			−0.819695			−0.409848	+	0.912154i	$0.634418\pi$
$110$	0.518117	+	0.188579i	0.0494005	+	0.0179803i
$111$	−8.24246	+	8.87367i	−0.782340	+	0.842251i
$112$	1.01610	+	0.852609i	0.0960124	+	0.0805640i
$113$	−0.541640	+	3.07179i	−0.0509532	+	0.288970i	−0.999628	−	0.0272843i	$-0.991314\pi$
$113$	−0.541640	+	3.07179i	−0.0509532	+	0.288970i	0.948675	+	0.316254i	$0.102425\pi$
$114$	0.194784	−	3.86111i	0.0182432	−	0.361626i
$115$	14.0922	−	11.8247i	1.31410	−	1.10266i
$116$	−0.241005	−	0.417432i	−0.0223767	−	0.0387576i
$117$	−7.79617	−	0.788606i	−0.720756	−	0.0729066i
$118$	2.39533	−	4.14884i	0.220508	−	0.381932i
$119$	−0.121086	−	0.686714i	−0.0111000	−	0.0629510i
$120$	−12.7191	+	1.58695i	−1.16109	+	0.144868i
$121$	10.2778	−	3.74082i	0.934347	−	0.340074i
$122$	−8.92285	+	3.24765i	−0.807837	+	0.294029i
$123$	−16.7019	+	2.08388i	−1.50596	+	0.187897i
$124$	−0.651922	−	3.69724i	−0.0585444	−	0.332022i
$125$	−3.35257	+	5.80682i	−0.299863	+	0.519378i
$126$	5.68627	+	0.575183i	0.506573	+	0.0512414i
$127$	9.22726	+	15.9821i	0.818787	+	1.41818i	0.906576	+	0.422042i	$0.138686\pi$
$127$	9.22726	+	15.9821i	0.818787	+	1.41818i	−0.0877893	+	0.996139i	$0.527980\pi$
$128$	6.74783	−	5.66210i	0.596430	−	0.500464i
$129$	0.0227511	−	0.450983i	0.00200312	−	0.0397069i
$130$	0.999692	−	5.66954i	0.0876788	−	0.497251i
$131$	10.8973	+	9.14396i	0.952105	+	0.798911i	0.979651	−	0.200709i	$-0.0643246\pi$
$131$	10.8973	+	9.14396i	0.952105	+	0.798911i	−0.0275454	+	0.999621i	$0.508769\pi$
$132$	0.400318	−	0.430974i	0.0348432	−	0.0375115i
$133$	6.21971	+	2.26379i	0.539317	+	0.196295i
$134$	−1.45101			−0.125348
$135$	10.7286	−	9.43724i	0.923369	−	0.812228i
$136$	−0.789527			−0.0677014
$137$	18.4984	+	6.73287i	1.58042	+	0.575228i	0.975296	−	0.220900i	$-0.0708995\pi$
$137$	18.4984	+	6.73287i	1.58042	+	0.575228i	0.605128	+	0.796128i	$0.293122\pi$
$138$	2.73273	+	8.87627i	0.232626	+	0.755598i
$139$	−13.7206	−	11.5129i	−1.16377	−	0.976515i	−0.163815	−	0.986491i	$-0.552380\pi$
$139$	−13.7206	−	11.5129i	−1.16377	−	0.976515i	−0.999950	+	0.00997617i	$0.996824\pi$
$140$	1.54076	−	8.73806i	0.130218	−	0.738501i
$141$	17.6151	−	9.01876i	1.48346	−	0.759517i
$142$	0.227495	−	0.190891i	0.0190910	−	0.0160192i
$143$	0.326705	+	0.565870i	0.0273205	+	0.0473205i
$144$	−0.455174	+	1.61113i	−0.0379312	+	0.134261i
$145$	−0.488175	+	0.845544i	−0.0405408	+	0.0702186i
$146$	−0.699647	−	3.96789i	−0.0579032	−	0.328385i
$147$	0.909870	−	2.15522i	0.0750449	−	0.177760i
$148$	−8.92007	+	3.24664i	−0.733225	+	0.266872i
$149$	−15.3071	+	5.57132i	−1.25401	+	0.456421i	−0.881753	−	0.471711i	$-0.843637\pi$
$149$	−15.3071	+	5.57132i	−1.25401	+	0.456421i	−0.372252	+	0.928132i	$0.621414\pi$
$150$	2.14576	+	2.83597i	0.175201	+	0.231556i
$151$	2.47880	+	14.0580i	0.201722	+	1.14402i	0.902515	+	0.430659i	$0.141719\pi$
$151$	2.47880	+	14.0580i	0.201722	+	1.14402i	−0.700793	+	0.713365i	$0.747170\pi$
$152$	3.74711	−	6.49019i	0.303931	−	0.526424i
$153$	0.727731	−	0.495012i	0.0588336	−	0.0400193i
$154$	−0.238288	−	0.412728i	−0.0192018	−	0.0332585i
$155$	−5.82546	+	4.88814i	−0.467912	+	0.392625i
$156$	−5.15739	−	3.33493i	−0.412922	−	0.267008i
$157$	0.132555	−	0.751757i	0.0105790	−	0.0599968i	−0.979061	−	0.203566i	$-0.934747\pi$
$157$	0.132555	−	0.751757i	0.0105790	−	0.0599968i	0.989640	+	0.143569i	$0.0458580\pi$
$158$	−0.492937	−	0.413623i	−0.0392159	−	0.0329061i
$159$	−9.17041	−	2.09828i	−0.727261	−	0.166405i
$160$	−15.0638	−	5.48279i	−1.19090	−	0.433452i
$161$	−15.9006			−1.25315
$162$	2.28275	+	6.84304i	0.179349	+	0.537640i
$163$	5.12834			0.401682			0.200841	−	0.979624i	$-0.435632\pi$
$163$	5.12834			0.401682			0.200841	+	0.979624i	$0.435632\pi$
$164$	−12.3966	−	4.51199i	−0.968011	−	0.352327i
$165$	−1.16146	−	0.265753i	−0.0904193	−	0.0206889i
$166$	1.69198	+	1.41974i	0.131323	+	0.110193i
$167$	1.54566	−	8.76590i	0.119607	−	0.678325i	−0.864759	−	0.502188i	$-0.832529\pi$
$167$	1.54566	−	8.76590i	0.119607	−	0.678325i	0.984366	−	0.176137i	$-0.0563603\pi$
$168$	9.30341	+	6.01588i	0.717774	+	0.464135i
$169$	−4.73227	+	3.97085i	−0.364021	+	0.305450i
$170$	0.323312	+	0.559992i	0.0247969	+	0.0429495i
$171$	0.615340	+	8.33154i	0.0470562	+	0.637129i
$172$	0.176962	−	0.306507i	0.0134932	−	0.0233709i
$173$	−1.18276	−	6.70776i	−0.0899235	−	0.509982i	−0.996185	−	0.0872644i	$-0.972188\pi$
$173$	−1.18276	−	6.70776i	−0.0899235	−	0.509982i	0.906262	−	0.422717i	$-0.138924\pi$
$174$	−0.297416	−	0.393083i	−0.0225470	−	0.0297996i
$175$	−5.72137	+	2.08241i	−0.432495	+	0.157415i
$176$	0.131185	−	0.0477476i	0.00988847	−	0.00359911i
$177$	−4.02635	+	9.53727i	−0.302639	+	0.716865i
$178$	−1.45456	−	8.24923i	−0.109024	−	0.618306i
$179$	9.17382	−	15.8895i	0.685684	−	1.18764i	−0.287538	−	0.957769i	$-0.592837\pi$
$179$	9.17382	−	15.8895i	0.685684	−	1.18764i	0.973221	−	0.229870i	$-0.0738301\pi$
$180$	10.8558	−	2.75179i	0.809146	−	0.205106i
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	0.575115	−	0.818073i	$-0.304957\pi$
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	−0.996029	+	0.0890276i	$0.971624\pi$
$182$	−3.81190	+	3.19856i	−0.282557	+	0.237093i
$183$	18.2645	−	9.35124i	1.35015	−	0.691264i
$184$	−3.12628	+	17.7300i	−0.230472	+	1.30707i
$185$	14.7295	+	12.3595i	1.08293	+	0.908687i
$186$	−1.12966	−	3.66930i	−0.0828310	−	0.269046i
$187$	−0.0689648	−	0.0251011i	−0.00504321	−	0.00183558i
$188$	15.5108			1.13124
$189$	−12.3470	+	0.287957i	−0.898115	+	0.0209458i
$190$	−6.13778			−0.445281
$191$	−6.44480	−	2.34571i	−0.466329	−	0.169730i	0.0981596	−	0.995171i	$-0.468704\pi$
$191$	−6.44480	−	2.34571i	−0.466329	−	0.169730i	−0.564489	+	0.825441i	$0.690927\pi$
$192$	4.19231	−	4.51336i	0.302554	−	0.325724i
$193$	15.6371	+	13.1211i	1.12558	+	0.944477i	0.998873	−	0.0474627i	$-0.0151135\pi$
$193$	15.6371	+	13.1211i	1.12558	+	0.944477i	0.126711	+	0.991940i	$0.459558\pi$
$194$	2.06474	−	11.7097i	0.148239	−	0.840707i
$195$	−0.626800	+	12.4247i	−0.0448861	+	0.889753i
$196$	1.40462	−	1.17861i	0.100330	−	0.0841866i
$197$	−1.51786	−	2.62902i	−0.108143	−	0.187310i	0.806875	−	0.590723i	$-0.201157\pi$
$197$	−1.51786	−	2.62902i	−0.108143	−	0.187310i	−0.915018	+	0.403413i	$0.867824\pi$
$198$	0.351663	−	0.488024i	0.0249916	−	0.0346824i
$199$	1.13124	−	1.95936i	0.0801912	−	0.138895i	−0.823141	−	0.567837i	$-0.807780\pi$
$199$	1.13124	−	1.95936i	0.0801912	−	0.138895i	0.903332	+	0.428942i	$0.141114\pi$
$200$	1.19709	+	6.78904i	0.0846471	+	0.480058i
$201$	3.11141	−	0.388209i	0.219462	−	0.0273821i
$202$	3.01677	−	1.09801i	0.212259	−	0.0772560i
$203$	0.793018	−	0.288635i	0.0556589	−	0.0202582i
$204$	0.684525	−	0.0854077i	0.0479263	−	0.00597974i
$205$	4.64020	+	26.3159i	0.324086	+	1.83798i
$206$	−2.37226	+	4.10888i	−0.165283	+	0.286279i
$207$	−8.23463	−	18.3024i	−0.572346	−	1.27210i
$208$	−0.728826	−	1.26236i	−0.0505350	−	0.0875292i
$209$	0.533649	−	0.447784i	0.0369132	−	0.0309739i
$210$	0.457167	−	9.06219i	0.0315476	−	0.625351i
$211$	4.41601	−	25.0445i	0.304011	−	1.72413i	−0.324113	−	0.946018i	$-0.605066\pi$
$211$	4.41601	−	25.0445i	0.304011	−	1.72413i	0.628124	−	0.778113i	$-0.283823\pi$
$212$	−5.64834	−	4.73952i	−0.387929	−	0.325511i
$213$	−0.436749	+	0.470195i	−0.0299255	+	0.0322172i
$214$	−0.195060	−	0.0709959i	−0.0133340	−	0.00485318i
$215$	−0.716901			−0.0488923
$216$	−2.10650	+	13.8242i	−0.143329	+	0.940615i
$217$	6.57305			0.446208
$218$	−6.44569	−	2.34604i	−0.436557	−	0.158894i
$219$	2.56185	+	8.32122i	0.173114	+	0.562296i
$220$	−0.715377	−	0.600272i	−0.0482307	−	0.0404703i
$221$	−0.133066	+	0.754654i	−0.00895097	+	0.0507635i
$222$	−8.64074	+	4.42398i	−0.579929	+	0.296918i
$223$	−2.93497	+	2.46274i	−0.196540	+	0.164917i	−0.735747	−	0.677257i	$-0.763169\pi$
$223$	−2.93497	+	2.46274i	−0.196540	+	0.164917i	0.539206	+	0.842174i	$0.318724\pi$
$224$	6.92805	+	11.9997i	0.462900	+	0.801766i
$225$	−5.35994	−	5.50713i	−0.357329	−	0.367142i
$226$	−1.25005	+	2.16515i	−0.0831523	+	0.144024i
$227$	0.436897	+	2.47777i	0.0289979	+	0.164455i	0.995868	−	0.0908142i	$-0.0289469\pi$
$227$	0.436897	+	2.47777i	0.0289979	+	0.164455i	−0.966870	+	0.255269i	$0.917836\pi$
$228$	−2.54669	+	6.03238i	−0.168659	+	0.399504i
$229$	14.9783	−	5.45167i	0.989797	−	0.360257i	0.204155	−	0.978939i	$-0.434555\pi$
$229$	14.9783	−	5.45167i	0.989797	−	0.360257i	0.785642	+	0.618682i	$0.212333\pi$
$230$	13.8557	−	5.04305i	0.913615	−	0.332529i
$231$	0.621388	+	0.821264i	0.0408843	+	0.0540352i
$232$	−0.165924	−	0.941003i	−0.0108935	−	0.0617799i
$233$	−14.0641	+	24.3598i	−0.921372	+	1.59586i	−0.124077	+	0.992273i	$0.539597\pi$
$233$	−14.0641	+	24.3598i	−0.921372	+	1.59586i	−0.797295	+	0.603590i	$0.793736\pi$
$234$	−5.65580	−	2.73120i	−0.369731	−	0.178544i
$235$	−15.7092	−	27.2092i	−1.02476	−	1.77493i
$236$	−6.21569	+	5.21558i	−0.404607	+	0.339505i
$237$	1.16767	+	0.755055i	0.0758485	+	0.0490461i
$238$	0.0970539	−	0.550420i	0.00629107	−	0.0356784i
$239$	−11.2653	−	9.45270i	−0.728691	−	0.611444i	0.201083	−	0.979574i	$-0.435554\pi$
$239$	−11.2653	−	9.45270i	−0.728691	−	0.611444i	−0.929774	+	0.368130i	$0.879998\pi$
$240$	2.59102	+	0.592852i	0.167250	+	0.0382684i
$241$	−7.93378	−	2.88766i	−0.511059	−	0.186010i	0.0736022	−	0.997288i	$-0.476550\pi$
$241$	−7.93378	−	2.88766i	−0.511059	−	0.186010i	−0.584662	+	0.811277i	$0.698773\pi$
$242$	8.76664			0.563541
$243$	−6.72574	−	14.0629i	−0.431456	−	0.902134i
$244$	16.0826			1.02958
$245$	−3.49012	−	1.27030i	−0.222975	−	0.0811564i
$246$	−13.1509	−	3.00907i	−0.838474	−	0.191851i
$247$	−5.57198	−	4.67545i	−0.354537	−	0.297492i
$248$	1.29235	−	7.32927i	0.0820642	−	0.465409i
$249$	−4.00799	−	2.59169i	−0.253996	−	0.164242i
$250$	−4.11699	+	3.45457i	−0.260381	+	0.218486i
$251$	11.6102	+	20.1095i	0.732832	+	1.26930i	0.955668	+	0.294447i	$0.0951354\pi$
$251$	11.6102	+	20.1095i	0.732832	+	1.26930i	−0.222835	+	0.974856i	$0.571531\pi$
$252$	−8.71689	−	4.20940i	−0.549112	−	0.265168i
$253$	−0.836762	+	1.44931i	−0.0526067	+	0.0911176i
$254$	2.56857	+	14.5671i	0.161166	+	0.914020i
$255$	−0.843104	−	1.11430i	−0.0527972	−	0.0697801i
$256$	13.3186	−	4.84758i	0.832413	−	0.302973i
$257$	−6.45118	+	2.34804i	−0.402413	+	0.146466i	−0.535294	−	0.844666i	$-0.679799\pi$
$257$	−6.45118	+	2.34804i	−0.402413	+	0.146466i	0.132881	+	0.991132i	$0.457577\pi$
$258$	0.140768	−	0.333439i	0.00876382	−	0.0207590i
$259$	−2.88598	−	16.3672i	−0.179326	−	1.01701i
$260$	−4.87534	+	8.44434i	−0.302356	+	0.523696i
$261$	0.742920	+	0.763321i	0.0459856	+	0.0472484i
$262$	5.70105	+	9.87451i	0.352212	+	0.610049i
$263$	2.56850	−	2.15523i	0.158381	−	0.132897i	−0.560154	−	0.828389i	$-0.689258\pi$
$263$	2.56850	−	2.15523i	0.158381	−	0.132897i	0.718534	+	0.695492i	$0.244813\pi$
$264$	1.03792	−	0.531406i	0.0638797	−	0.0327058i
$265$	−2.59351	+	14.7085i	−0.159318	+	0.903536i
$266$	4.06402	+	3.41012i	0.249181	+	0.209088i
$267$	5.32607	+	17.2998i	0.325950	+	1.05873i
$268$	2.30937	+	0.840543i	0.141067	+	0.0513444i
$269$	12.7416			0.776869			0.388434	−	0.921476i	$-0.373016\pi$
$269$	12.7416			0.776869			0.388434	+	0.921476i	$0.373016\pi$
$270$	10.6678	−	4.16691i	0.649219	−	0.253590i
$271$	−23.5566			−1.43096			−0.715481	−	0.698632i	$-0.753792\pi$
$271$	−23.5566			−1.43096			−0.715481	+	0.698632i	$0.753792\pi$
$272$	0.153849	+	0.0559965i	0.00932848	+	0.00339529i
$273$	7.31814	−	7.87857i	0.442914	−	0.476833i
$274$	12.0871	+	10.1422i	0.730206	+	0.612715i
$275$	−0.111276	+	0.631078i	−0.00671020	+	0.0380554i
$276$	0.792545	−	15.7102i	0.0477056	−	0.945643i
$277$	3.20300	−	2.68763i	0.192450	−	0.161484i	−0.541472	−	0.840719i	$-0.682133\pi$
$277$	3.20300	−	2.68763i	0.192450	−	0.161484i	0.733921	+	0.679235i	$0.237688\pi$
$278$	−7.17806	−	12.4328i	−0.430511	−	0.745667i
$279$	3.40406	+	7.56589i	0.203795	+	0.452958i
$280$	8.79463	−	15.2327i	0.525580	−	0.910331i
$281$	−3.75705	−	21.3073i	−0.224127	−	1.27109i	−0.864347	−	0.502896i	$-0.832268\pi$
$281$	−3.75705	−	21.3073i	−0.224127	−	1.27109i	0.640220	−	0.768192i	$-0.278843\pi$
$282$	15.7399	−	1.96386i	0.937297	−	0.116946i
$283$	−4.91209	+	1.78785i	−0.291993	+	0.106277i	−0.483864	−	0.875143i	$-0.660767\pi$
$283$	−4.91209	+	1.78785i	−0.291993	+	0.106277i	0.191870	+	0.981420i	$0.438545\pi$
$284$	−0.472654	+	0.172032i	−0.0280468	+	0.0102082i
$285$	13.1613	−	1.64213i	0.779609	−	0.0972713i
$286$	0.0909441	+	0.515770i	0.00537764	+	0.0304981i
$287$	11.5486	−	20.0027i	0.681690	−	1.18072i
$288$	−10.2243	+	14.1889i	−0.602475	+	0.836090i
$289$	8.45697	+	14.6479i	0.497469	+	0.861641i
$290$	−0.599484	+	0.503027i	−0.0352029	+	0.0295388i
$291$	−1.29457	+	25.6617i	−0.0758893	+	1.50431i
$292$	−1.18500	+	6.72047i	−0.0693468	+	0.393285i
$293$	−4.70517	−	3.94811i	−0.274879	−	0.230651i	0.494918	−	0.868940i	$-0.335198\pi$
$293$	−4.70517	−	3.94811i	−0.274879	−	0.230651i	−0.769797	+	0.638289i	$0.779643\pi$
$294$	1.27613	−	1.37386i	0.0744257	−	0.0801252i
$295$	15.4444	+	5.62131i	0.899208	+	0.327285i
$296$	−18.8177			−1.09376
$297$	−0.623508	+	1.14056i	−0.0361796	+	0.0661821i
$298$	−13.0564			−0.756339
$299$	16.4200	+	5.97638i	0.949591	+	0.345623i
$300$	−1.77230	−	5.75665i	−0.102324	−	0.332360i
$301$	0.474684	+	0.398307i	0.0273603	+	0.0229580i
$302$	−1.98683	+	11.2679i	−0.114329	+	0.648393i
$303$	−6.17513	+	3.16160i	−0.354752	+	0.181629i
$304$	−1.19048	+	0.998934i	−0.0682789	+	0.0572928i
$305$	−16.2884	−	28.2123i	−0.932669	−	1.61543i
$306$	0.683821	−	0.173338i	0.0390914	−	0.00990909i
$307$	−9.50194	+	16.4578i	−0.542304	+	0.939298i	0.456467	+	0.889740i	$0.349115\pi$
$307$	−9.50194	+	16.4578i	−0.542304	+	0.939298i	−0.998771	+	0.0495580i	$0.984219\pi$
$308$	0.140166	+	0.794920i	0.00798669	+	0.0452948i
$309$	3.98757	−	9.44541i	0.226845	−	0.537331i
$310$	−5.72769	+	2.08471i	−0.325311	+	0.118404i
$311$	20.2475	−	7.36948i	1.14813	−	0.417885i	0.303286	−	0.952900i	$-0.401916\pi$
$311$	20.2475	−	7.36948i	1.14813	−	0.417885i	0.844843	+	0.535015i	$0.179694\pi$
$312$	−7.34615	−	9.70912i	−0.415894	−	0.549671i
$313$	−0.662228	−	3.75568i	−0.0374313	−	0.212284i	0.960355	−	0.278778i	$-0.0899295\pi$
$313$	−0.662228	−	3.75568i	−0.0374313	−	0.212284i	−0.997787	+	0.0664949i	$0.978818\pi$
$314$	0.305925	−	0.529877i	0.0172643	−	0.0299027i
$315$	1.44423	+	19.5545i	0.0813731	+	1.10177i
$316$	0.544937	+	0.943859i	0.0306551	+	0.0530962i
$317$	3.25913	−	2.73473i	0.183051	−	0.153598i	−0.546658	−	0.837356i	$-0.684100\pi$
$317$	3.25913	−	2.73473i	0.183051	−	0.153598i	0.729709	+	0.683758i	$0.239656\pi$
$318$	−6.33183	−	4.09437i	−0.355072	−	0.229601i
$319$	0.0154235	−	0.0874713i	0.000863553	−	0.00489745i
$320$	−7.49175	−	6.28632i	−0.418801	−	0.351416i
$321$	0.437264	+	0.100050i	0.0244057	+	0.00558426i
$322$	−11.9762	−	4.35898i	−0.667407	−	0.242916i
$323$	0.816980			0.0454580
$324$	0.330912	−	12.2135i	0.0183840	−	0.678528i
$325$	6.69092			0.371146
$326$	3.86261	+	1.40587i	0.213930	+	0.0778642i
$327$	14.4493	+	3.30614i	0.799046	+	0.182830i
$328$	−20.0334	−	16.8100i	−1.10616	−	0.928178i
$329$	−4.71570	+	26.7441i	−0.259985	+	1.47445i
$330$	−0.801944	−	0.518562i	−0.0441455	−	0.0285459i
$331$	−10.9497	+	9.18787i	−0.601849	+	0.505011i	−0.892039	−	0.451958i	$-0.850726\pi$
$331$	−10.9497	+	9.18787i	−0.601849	+	0.505011i	0.290191	+	0.956969i	$0.406281\pi$
$332$	−1.87047	−	3.23976i	−0.102656	−	0.177805i
$333$	17.3448	−	11.7982i	0.950491	−	0.646536i
$334$	3.56725	−	6.17865i	0.195191	−	0.338081i
$335$	−0.864428	−	4.90242i	−0.0472288	−	0.267848i
$336$	−1.38621	−	1.83211i	−0.0756242	−	0.0999496i
$337$	−33.5644	+	12.2164i	−1.82837	+	0.665472i	−0.835037	+	0.550194i	$0.814554\pi$
$337$	−33.5644	+	12.2164i	−1.82837	+	0.665472i	−0.993333	+	0.115278i	$0.963224\pi$
$338$	−4.65286	+	1.69350i	−0.253082	+	0.0921143i
$339$	2.10123	−	4.97721i	0.114123	−	0.270325i
$340$	−0.190178	−	1.07855i	−0.0103139	−	0.0584928i
$341$	0.345903	−	0.599121i	0.0187317	−	0.0324442i
$342$	−1.82053	+	6.44391i	−0.0984429	+	0.348447i
$343$	9.92407	+	17.1890i	0.535849	+	0.928118i
$344$	0.537461	−	0.450983i	0.0289780	−	0.0243154i
$345$	−28.3616	+	14.5209i	−1.52694	+	0.781778i
$346$	0.948013	−	5.37645i	0.0509655	−	0.289040i
$347$	−14.8931	−	12.4968i	−0.799502	−	0.670862i	0.148575	−	0.988901i	$-0.452531\pi$
$347$	−14.8931	−	12.4968i	−0.799502	−	0.670862i	−0.948078	+	0.318039i	$0.896976\pi$
$348$	0.245651	+	0.797906i	0.0131683	+	0.0427723i
$349$	7.53700	+	2.74324i	0.403446	+	0.146842i	0.535770	−	0.844364i	$-0.320022\pi$
$349$	7.53700	+	2.74324i	0.403446	+	0.146842i	−0.132323	+	0.991207i	$0.542244\pi$
$350$	−4.88014			−0.260855
$351$	12.8585	+	4.34336i	0.686337	+	0.231832i
$352$	1.45834			0.0777296
$353$	−8.22589	−	2.99398i	−0.437820	−	0.159354i	0.113700	−	0.993515i	$-0.463730\pi$
$353$	−8.22589	−	2.99398i	−0.437820	−	0.159354i	−0.551520	+	0.834162i	$0.685952\pi$
$354$	−5.64713	+	6.07959i	−0.300142	+	0.323127i
$355$	0.780479	+	0.654900i	0.0414235	+	0.0347585i
$356$	−2.46361	+	13.9718i	−0.130571	+	0.740505i
$357$	−0.0608521	+	1.20624i	−0.00322063	+	0.0638409i
$358$	11.2656	−	9.45292i	0.595403	−	0.499602i
$359$	4.13896	+	7.16888i	0.218446	+	0.378359i	0.954333	−	0.298745i	$-0.0965680\pi$
$359$	4.13896	+	7.16888i	0.218446	+	0.378359i	−0.735887	+	0.677104i	$0.763235\pi$
$360$	22.0882	+	2.23428i	1.16415	+	0.117757i
$361$	5.62260	−	9.73862i	0.295926	−	0.512559i
$362$	−1.57635	−	8.93990i	−0.0828509	−	0.469871i
$363$	−18.7984	+	2.34547i	−0.986661	+	0.123105i
$364$	7.91977	−	2.88256i	0.415108	−	0.151087i
$365$	12.9892	−	4.72770i	0.679888	−	0.247459i
$366$	16.3201	−	2.03625i	0.853068	−	0.106437i
$367$	−2.56997	−	14.5750i	−0.134151	−	0.760809i	−0.975447	−	0.220234i	$-0.929318\pi$
$367$	−2.56997	−	14.5750i	−0.134151	−	0.760809i	0.841296	−	0.540575i	$-0.181793\pi$
$368$	1.86668	−	3.23318i	0.0973074	−	0.168541i
$369$	29.0048	+	2.93392i	1.50993	+	0.152734i
$370$	7.70585	+	13.3469i	0.400608	+	0.693874i
$371$	9.88922	−	8.29804i	0.513423	−	0.430813i
$372$	−0.327625	+	6.49433i	−0.0169865	+	0.336715i
$373$	4.43383	−	25.1455i	0.229575	−	1.30198i	−0.624168	−	0.781290i	$-0.714562\pi$
$373$	4.43383	−	25.1455i	0.229575	−	1.30198i	0.853743	−	0.520694i	$-0.174327\pi$
$374$	−0.0450623	−	0.0378118i	−0.00233012	−	0.00195520i
$375$	7.90387	−	8.50915i	0.408154	−	0.439411i
$376$	28.8938	+	10.5165i	1.49008	+	0.542346i
$377$	−0.927403			−0.0477637
$378$	−9.37859	−	3.16791i	−0.482383	−	0.162940i
$379$	20.1244			1.03372			0.516861	−	0.856070i	$-0.327101\pi$
$379$	20.1244			1.03372			0.516861	+	0.856070i	$0.327101\pi$
$380$	9.76869	+	3.55551i	0.501123	+	0.182394i
$381$	−9.40516	−	30.5492i	−0.481841	−	1.56508i
$382$	−4.21110	−	3.53353i	−0.215459	−	0.180791i
$383$	−4.14346	+	23.4987i	−0.211721	+	1.20073i	0.674785	+	0.738014i	$0.264236\pi$
$383$	−4.14346	+	23.4987i	−0.211721	+	1.20073i	−0.886507	+	0.462716i	$0.846875\pi$
$384$	−13.5806	+	6.95312i	−0.693031	+	0.354825i
$385$	1.25250	−	1.05097i	0.0638331	−	0.0535623i
$386$	8.18070	+	14.1694i	0.416387	+	0.721203i
$387$	−0.212640	+	0.752659i	−0.0108091	+	0.0382598i
$388$	−10.0694	+	17.4407i	−0.511196	+	0.885418i
$389$	6.59400	+	37.3964i	0.334329	+	1.89607i	0.433760	+	0.901029i	$0.357187\pi$
$389$	6.59400	+	37.3964i	0.334329	+	1.89607i	−0.0994307	+	0.995044i	$0.531702\pi$
$390$	−3.87819	+	9.18633i	−0.196380	+	0.465168i
$391$	−1.84428	+	0.671264i	−0.0932694	+	0.0339473i
$392$	3.41565	−	1.24320i	0.172516	−	0.0627908i
$393$	−14.8667	−	19.6487i	−0.749926	−	0.991148i
$394$	−0.422524	−	2.39625i	−0.0212864	−	0.120721i
$395$	1.10382	−	1.91187i	0.0555390	−	0.0961964i
$396$	−0.842400	+	0.573011i	−0.0423322	+	0.0287949i
$397$	−10.1747	−	17.6230i	−0.510651	−	0.884474i	−0.999924	−	0.0123433i	$-0.996071\pi$
$397$	−10.1747	−	17.6230i	−0.510651	−	0.884474i	0.489272	−	0.872131i	$-0.337262\pi$
$398$	1.38917	−	1.16565i	0.0696328	−	0.0584289i
$399$	−9.62690	−	6.22506i	−0.481948	−	0.311643i
$400$	0.248239	−	1.40783i	0.0124119	−	0.0703916i
$401$	5.32015	+	4.46414i	0.265676	+	0.222928i	0.765887	−	0.642975i	$-0.222300\pi$
$401$	5.32015	+	4.46414i	0.265676	+	0.222928i	−0.500212	+	0.865903i	$0.666744\pi$
$402$	2.44990	+	0.560563i	0.122190	+	0.0279583i
$403$	−6.78773	−	2.47053i	−0.338121	−	0.123066i
$404$	−5.43745			−0.270523
$405$	−21.7602	+	11.7893i	−1.08127	+	0.585813i
$406$	0.676418			0.0335701
$407$	−1.64372	−	0.598264i	−0.0814760	−	0.0296548i
$408$	1.33305	+	0.305015i	0.0659958	+	0.0151005i
$409$	−8.35444	−	7.01021i	−0.413101	−	0.346633i	0.412431	−	0.910989i	$-0.364680\pi$
$409$	−8.35444	−	7.01021i	−0.413101	−	0.346633i	−0.825531	+	0.564356i	$0.809124\pi$
$410$	−3.71925	+	21.0929i	−0.183681	+	1.04170i
$411$	−28.6319	−	18.5143i	−1.41231	−	0.913244i
$412$	6.15582	−	5.16535i	0.303276	−	0.254478i
$413$	−7.10308	−	12.3029i	−0.349520	−	0.605386i
$414$	−1.18485	−	16.0426i	−0.0582322	−	0.788449i
$415$	−3.78880	+	6.56240i	−0.185985	+	0.322135i
$416$	−2.64413	−	14.9956i	−0.129639	−	0.735220i
$417$	18.7183	+	24.7393i	0.916640	+	1.21149i
$418$	0.524693	−	0.190973i	0.0256636	−	0.00934078i
$419$	9.46194	−	3.44386i	0.462246	−	0.168244i	−0.100391	−	0.994948i	$-0.532009\pi$
$419$	9.46194	−	3.44386i	0.462246	−	0.168244i	0.562637	+	0.826704i	$0.309787\pi$
$420$	−5.97719	+	14.1583i	−0.291657	+	0.690852i
$421$	−0.539623	−	3.06035i	−0.0262996	−	0.149152i	0.968830	−	0.247726i	$-0.0796832\pi$
$421$	−0.539623	−	3.06035i	−0.0262996	−	0.149152i	−0.995130	+	0.0985733i	$0.968572\pi$
$422$	10.1917	−	17.6526i	0.496126	−	0.859315i
$423$	−33.2258	+	8.42224i	−1.61550	+	0.409504i
$424$	−7.30837	−	12.6585i	−0.354926	−	0.614750i
$425$	−0.575699	+	0.483069i	−0.0279255	+	0.0234323i
$426$	−0.457853	+	0.234416i	−0.0221830	+	0.0113575i
$427$	−4.88955	+	27.7300i	−0.236622	+	1.34195i
$428$	0.269324	+	0.225990i	0.0130183	+	0.0109236i
$429$	−0.333004	−	1.08164i	−0.0160776	−	0.0522221i
$430$	−0.539962	−	0.196530i	−0.0260393	−	0.00947753i
$431$	−28.0701			−1.35209			−0.676044	−	0.736862i	$-0.736307\pi$
$431$	−28.0701			−1.35209			−0.676044	+	0.736862i	$0.736307\pi$
$432$	1.39095	−	2.54441i	0.0669219	−	0.122418i
$433$	19.5251			0.938317			0.469158	−	0.883114i	$-0.344557\pi$
$433$	19.5251			0.938317			0.469158	+	0.883114i	$0.344557\pi$
$434$	4.95075	+	1.80193i	0.237644	+	0.0864952i
$435$	1.15090	−	1.23904i	0.0551814	−	0.0594072i
$436$	8.89973	+	7.46776i	0.426220	+	0.357641i
$437$	3.23498	−	18.3465i	0.154750	−	0.877631i
$438$	−0.351609	+	6.96975i	−0.0168005	+	0.333028i
$439$	11.2069	−	9.40371i	0.534876	−	0.448815i	−0.334905	−	0.942252i	$-0.608704\pi$
$439$	11.2069	−	9.40371i	0.534876	−	0.448815i	0.869781	+	0.493437i	$0.164260\pi$
$440$	−0.925624	−	1.60323i	−0.0441274	−	0.0764309i
$441$	−2.36886	+	3.28741i	−0.112803	+	0.156543i
$442$	−0.307103	+	0.531918i	−0.0146074	+	0.0253008i
$443$	3.18748	+	18.0771i	0.151442	+	0.858868i	0.961967	+	0.273165i	$0.0880704\pi$
$443$	3.18748	+	18.0771i	0.151442	+	0.858868i	−0.810526	+	0.585703i	$0.800818\pi$
$444$	16.3151	−	2.03562i	0.774278	−	0.0966062i
$445$	27.0046	−	9.82886i	1.28014	−	0.465933i
$446$	−2.88572	+	1.05032i	−0.136643	+	0.0497339i
$447$	27.9971	−	3.49318i	1.32422	−	0.165222i
$448$	1.46788	+	8.32476i	0.0693508	+	0.393308i
$449$	−6.92969	+	12.0026i	−0.327032	+	0.566437i	−0.981922	−	0.189288i	$-0.939382\pi$
$449$	−6.92969	+	12.0026i	−0.327032	+	0.566437i	0.654889	+	0.755725i	$0.272715\pi$
$450$	−2.52733	−	5.61727i	−0.119140	−	0.264801i
$451$	−1.21547	−	2.10526i	−0.0572344	−	0.0991328i
$452$	3.24378	−	2.72185i	0.152575	−	0.128025i
$453$	1.24573	−	24.6934i	0.0585294	−	1.16020i
$454$	−0.350185	+	1.98600i	−0.0164350	+	0.0932075i
$455$	−13.0777	−	10.9735i	−0.613091	−	0.514445i
$456$	−8.83402	+	9.51053i	−0.413691	+	0.445372i
$457$	−16.5838	−	6.03602i	−0.775758	−	0.282353i	−0.0763555	−	0.997081i	$-0.524328\pi$
$457$	−16.5838	−	6.03602i	−0.775758	−	0.282353i	−0.699403	+	0.714728i	$0.746551\pi$
$458$	12.7760			0.596985
$459$	−1.41995	+	0.554644i	−0.0662776	+	0.0258886i
$460$	−24.9736			−1.16440
$461$	−24.0919	−	8.76872i	−1.12207	−	0.408400i	−0.286663	−	0.958032i	$-0.592546\pi$
$461$	−24.0919	−	8.76872i	−1.12207	−	0.408400i	−0.835407	+	0.549631i	$0.814768\pi$
$462$	0.242882	+	0.788913i	0.0112999	+	0.0367036i
$463$	14.0549	+	11.7935i	0.653189	+	0.548090i	0.908037	−	0.418891i	$-0.137581\pi$
$463$	14.0549	+	11.7935i	0.653189	+	0.548090i	−0.254848	+	0.966981i	$0.582025\pi$
$464$	−0.0344074	+	0.195134i	−0.00159732	+	0.00905888i
$465$	11.7242	−	6.00268i	0.543698	−	0.278368i
$466$	−17.2709	+	14.4920i	−0.800059	+	0.671329i
$467$	8.13092	+	14.0832i	0.376254	+	0.651692i	0.990514	−	0.137412i	$-0.0438786\pi$
$467$	8.13092	+	14.0832i	0.376254	+	0.651692i	−0.614260	+	0.789104i	$0.710545\pi$
$468$	7.41945	+	7.62319i	0.342964	+	0.352382i
$469$	−2.15139	+	3.72632i	−0.0993421	+	0.172066i
$470$	−4.37294	−	24.8002i	−0.201709	−	1.14395i
$471$	−0.514232	+	1.21807i	−0.0236946	+	0.0561257i
$472$	−15.1149	+	5.50137i	−0.695719	+	0.253221i
$473$	0.0612849	−	0.0223059i	0.00281788	−	0.00102563i
$474$	0.672489	+	0.888803i	0.0308884	+	0.0408241i
$475$	−1.23872	−	7.02510i	−0.0568362	−	0.322334i
$476$	−0.473317	+	0.819809i	−0.0216944	+	0.0375759i
$477$	14.6729	+	7.08555i	0.671824	+	0.324425i
$478$	−5.89354	−	10.2079i	−0.269564	−	0.466899i
$479$	−7.25575	+	6.08830i	−0.331524	+	0.278181i	−0.793320	−	0.608804i	$-0.791649\pi$
$479$	−7.25575	+	6.08830i	−0.331524	+	0.278181i	0.461797	+	0.886986i	$0.347205\pi$
$480$	23.3159	+	15.0768i	1.06422	+	0.688158i
$481$	−3.17151	+	17.9865i	−0.144608	+	0.820114i
$482$	−5.18401	−	4.34990i	−0.236125	−	0.198133i
$483$	26.8469	+	6.14284i	1.22158	+	0.279509i
$484$	−13.9527	−	5.07836i	−0.634213	−	0.230835i
$485$	40.7928			1.85231
$486$	−1.21058	−	12.4358i	−0.0549129	−	0.564099i
$487$	−0.467564			−0.0211874			−0.0105937	−	0.999944i	$-0.503372\pi$
$487$	−0.467564			−0.0211874			−0.0105937	+	0.999944i	$0.503372\pi$
$488$	29.9590	+	10.9042i	1.35618	+	0.493608i
$489$	−8.65877	−	1.98121i	−0.391563	−	0.0895936i
$490$	−2.28048	−	1.91355i	−0.103022	−	0.0864453i
$491$	4.34936	−	24.6665i	0.196284	−	1.11318i	−0.714294	−	0.699846i	$-0.753252\pi$
$491$	4.34936	−	24.6665i	0.196284	−	1.11318i	0.910578	−	0.413337i	$-0.135637\pi$
$492$	19.1875	+	12.4073i	0.865040	+	0.559363i
$493$	0.0797954	−	0.0669563i	0.00359380	−	0.00301556i
$494$	−2.91504	−	5.04899i	−0.131154	−	0.227165i
$495$	1.85836	+	0.897404i	0.0835269	+	0.0403353i
$496$	−0.771653	+	1.33654i	−0.0346482	+	0.0600125i
$497$	−0.152922	−	0.867261i	−0.00685947	−	0.0389020i
$498$	−2.30829	−	3.05078i	−0.103437	−	0.136709i
$499$	13.1878	−	4.79996i	0.590367	−	0.214876i	−0.0295240	−	0.999564i	$-0.509399\pi$
$499$	13.1878	−	4.79996i	0.590367	−	0.214876i	0.619891	+	0.784688i	$0.287177\pi$
$500$	8.55364	−	3.11327i	0.382530	−	0.139230i
$501$	−5.99623	+	14.2034i	−0.267892	+	0.634559i
$502$	3.23191	+	18.3291i	0.144247	+	0.818068i
$503$	−14.1558	+	24.5186i	−0.631176	+	1.09323i	0.356136	+	0.934434i	$0.384094\pi$
$503$	−14.1558	+	24.5186i	−0.631176	+	1.09323i	−0.987312	+	0.158794i	$0.949239\pi$
$504$	−13.3839	−	13.7515i	−0.596168	−	0.612539i
$505$	5.50701	+	9.53842i	0.245059	+	0.424454i
$506$	−1.02755	+	0.862218i	−0.0456803	+	0.0383303i
$507$	9.52410	−	4.87624i	0.422980	−	0.216562i
$508$	4.35041	−	24.6724i	0.193018	−	1.09466i
$509$	−21.9759	−	18.4399i	−0.974063	−	0.817336i	0.00912008	−	0.999958i	$-0.497097\pi$
$509$	−21.9759	−	18.4399i	−0.974063	−	0.817336i	−0.983183	+	0.182622i	$0.941541\pi$
$510$	−0.329545	−	1.07040i	−0.0145925	−	0.0473983i
$511$	−11.2273	−	4.08640i	−0.496666	−	0.180772i
$512$	−6.25700			−0.276523
$513$	2.17975	−	14.3048i	0.0962382	−	0.631574i
$514$	−5.50264			−0.242711
$515$	−15.2957	−	5.56716i	−0.674007	−	0.245319i
$516$	−0.417197	+	0.449146i	−0.0183661	+	0.0197725i
$517$	2.18951	+	1.83722i	0.0962946	+	0.0808008i
$518$	2.31319	−	13.1188i	0.101636	−	0.576406i
$519$	−0.594397	+	11.7824i	−0.0260911	+	0.517191i
$520$	−14.8072	+	12.4247i	−0.649339	+	0.544860i
$521$	12.4548	+	21.5724i	0.545655	+	0.945102i	0.998565	+	0.0535462i	$0.0170525\pi$
$521$	12.4548	+	21.5724i	0.545655	+	0.945102i	−0.452910	+	0.891556i	$0.649614\pi$
$522$	0.350304	+	0.778588i	0.0153324	+	0.0340779i
$523$	12.9324	−	22.3995i	0.565494	−	0.979464i	−0.431510	−	0.902108i	$-0.642019\pi$
$523$	12.9324	−	22.3995i	0.565494	−	0.979464i	0.997004	−	0.0773554i	$-0.0246476\pi$
$524$	−3.35347	−	19.0185i	−0.146497	−	0.830826i
$525$	10.4646	−	1.30566i	0.456711	−	0.0569835i
$526$	2.52540	−	0.919169i	0.110113	−	0.0400777i
$527$	0.762395	−	0.277489i	0.0332104	−	0.0120876i
$528$	−0.239942	+	0.0299374i	−0.0104421	+	0.00130286i
$529$	3.77754	+	21.4235i	0.164241	+	0.931456i
$530$	−5.98556	+	10.3673i	−0.259996	+	0.450327i
$531$	10.4827	−	14.5474i	0.454908	−	0.631303i
$532$	−4.49274	−	7.78166i	−0.194785	−	0.337378i
$533$	−19.4439	+	16.3154i	−0.842209	+	0.706698i
$534$	−0.730992	+	14.4901i	−0.0316331	+	0.627047i
$535$	0.123663	−	0.701330i	0.00534644	−	0.0303212i
$536$	3.73204	+	3.13155i	0.161200	+	0.135262i
$537$	−21.6278	+	23.2841i	−0.933308	+	1.00478i
$538$	9.59683	+	3.49296i	0.413749	+	0.150592i
$539$	0.337880			0.0145535
$540$	−19.3923	+	0.452267i	−0.834511	+	0.0194625i
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$	−17.7426	−	6.45777i	−0.762109	−	0.277385i
$543$	5.77200	+	18.7482i	0.247700	+	0.804562i
$544$	1.31015	+	1.09935i	0.0561723	+	0.0471342i
$545$	4.08643	−	23.1753i	0.175043	−	0.992720i
$546$	7.67176	−	3.92787i	0.328321	−	0.168097i
$547$	−7.64210	+	6.41248i	−0.326752	+	0.274178i	−0.791375	−	0.611331i	$-0.790634\pi$
$547$	−7.64210	+	6.41248i	−0.326752	+	0.274178i	0.464623	+	0.885509i	$0.346190\pi$
$548$	−13.3621	−	23.1439i	−0.570802	−	0.988658i
$549$	−34.4507	+	8.73273i	−1.47032	+	0.372704i
$550$	−0.256815	+	0.444816i	−0.0109506	+	0.0189670i
$551$	0.171694	+	0.973722i	0.00731439	+	0.0414820i
$552$	12.1280	−	28.7278i	0.516203	−	1.22274i
$553$	−1.79310	+	0.652634i	−0.0762502	+	0.0277528i
$554$	3.14925	−	1.14623i	0.133799	−	0.0486987i
$555$	−20.0947	−	26.5583i	−0.852971	−	1.12734i
$556$	4.22227	+	23.9457i	0.179064	+	1.01552i
$557$	9.26650	−	16.0500i	0.392634	−	0.680062i	−0.600162	−	0.799879i	$-0.704897\pi$
$557$	9.26650	−	16.0500i	0.392634	−	0.680062i	0.992796	+	0.119816i	$0.0382305\pi$
$558$	0.489797	+	6.63172i	0.0207348	+	0.280743i
$559$	−0.340480	−	0.589729i	−0.0144008	−	0.0249429i
$560$	−2.79411	+	2.34454i	−0.118073	+	0.0990749i
$561$	0.106744	+	0.0690241i	0.00450674	+	0.00291420i
$562$	3.01138	−	17.0784i	0.127027	−	0.720408i
$563$	33.4632	+	28.0789i	1.41031	+	1.18339i	0.956300	+	0.292388i	$0.0944498\pi$
$563$	33.4632	+	28.0789i	1.41031	+	1.18339i	0.454005	+	0.890999i	$0.349995\pi$
$564$	−26.1887	−	5.99225i	−1.10274	−	0.252319i
$565$	−8.05997	−	2.93359i	−0.339086	−	0.123417i
$566$	−4.18985			−0.176113
$567$	20.9582	+	4.28380i	0.880161	+	0.179903i
$568$	−0.997105			−0.0418376
$569$	−12.7485	−	4.64008i	−0.534446	−	0.194522i	0.0606766	−	0.998157i	$-0.480674\pi$
$569$	−12.7485	−	4.64008i	−0.534446	−	0.194522i	−0.595122	+	0.803635i	$0.702896\pi$
$570$	10.3631	+	2.37119i	0.434064	+	0.0993182i
$571$	18.1926	+	15.2654i	0.761335	+	0.638836i	0.938474	−	0.345350i	$-0.112240\pi$
$571$	18.1926	+	15.2654i	0.761335	+	0.638836i	−0.177139	+	0.984186i	$0.556684\pi$
$572$	0.154033	−	0.873565i	0.00644044	−	0.0365256i
$573$	9.97529	+	6.45034i	0.416724	+	0.269467i
$574$	14.1818	−	11.8999i	0.591935	−	0.496693i
$575$	8.56844	+	14.8410i	0.357329	+	0.618911i
$576$	−8.82200	+	6.00083i	−0.367583	+	0.250034i
$577$	4.05951	−	7.03128i	0.169000	−	0.292716i	−0.769069	−	0.639166i	$-0.779280\pi$
$577$	4.05951	−	7.03128i	0.169000	−	0.292716i	0.938068	+	0.346450i	$0.112613\pi$
$578$	2.35414	+	13.3510i	0.0979194	+	0.555329i
$579$	−21.3329	−	28.1949i	−0.886566	−	1.17174i
$580$	1.24551	−	0.453330i	0.0517172	−	0.0188235i
$581$	6.15473	−	2.24014i	0.255341	−	0.0929366i
$582$	−8.00990	+	18.9732i	−0.332021	+	0.786464i
$583$	−0.235937	−	1.33806i	−0.00977150	−	0.0554169i
$584$	−6.76397	+	11.7155i	−0.279895	+	0.484793i
$585$	5.85830	−	20.7360i	0.242211	−	0.857326i
$586$	−2.46156	−	4.26354i	−0.101686	−	0.176125i
$587$	−2.82823	+	2.37317i	−0.116734	+	0.0979511i	−0.699286	−	0.714842i	$-0.746499\pi$
$587$	−2.82823	+	2.37317i	−0.116734	+	0.0979511i	0.582552	+	0.812793i	$0.302054\pi$
$588$	−2.82691	+	1.44735i	−0.116580	+	0.0596877i
$589$	−1.33729	+	7.58412i	−0.0551019	+	0.312498i
$590$	10.0915	+	8.46781i	0.415462	+	0.348614i
$591$	1.54713	+	5.02527i	0.0636403	+	0.206712i
$592$	3.66686	+	1.33463i	0.150707	+	0.0548529i
$593$	29.4590			1.20974			0.604869	−	0.796325i	$-0.293226\pi$
$593$	29.4590			1.20974			0.604869	+	0.796325i	$0.293226\pi$
$594$	−0.782291	+	0.688131i	−0.0320978	+	0.0282344i
$595$	1.91749			0.0786093
$596$	20.7802	+	7.56338i	0.851190	+	0.309808i
$597$	−2.66695	+	2.87119i	−0.109151	+	0.117510i
$598$	10.7290	+	9.00268i	0.438740	+	0.368147i
$599$	−3.79862	+	21.5431i	−0.155207	+	0.880225i	0.803388	+	0.595455i	$0.203028\pi$
$599$	−3.79862	+	21.5431i	−0.155207	+	0.880225i	−0.958596	+	0.284770i	$0.908083\pi$
$600$	0.601600	−	11.9252i	0.0245602	−	0.486844i
$601$	27.9764	−	23.4750i	1.14118	−	0.957566i	0.141706	−	0.989909i	$-0.454741\pi$
$601$	27.9764	−	23.4750i	1.14118	−	0.957566i	0.999477	+	0.0323424i	$0.0102967\pi$
$602$	0.248335	+	0.430130i	0.0101214	+	0.0175308i
$603$	−5.40333	−	0.546563i	−0.220041	−	0.0222578i
$604$	9.68946	−	16.7826i	0.394258	−	0.682876i
$605$	5.22267	+	29.6192i	0.212332	+	1.20419i
$606$	−5.51775	+	0.688447i	−0.224143	+	0.0279662i
$607$	6.18395	−	2.25077i	0.250999	−	0.0913561i	−0.213457	−	0.976953i	$-0.568472\pi$
$607$	6.18395	−	2.25077i	0.250999	−	0.0913561i	0.464456	+	0.885596i	$0.346250\pi$
$608$	−15.2550	+	5.55238i	−0.618674	+	0.225179i
$609$	−1.45045	+	0.180972i	−0.0587753	+	0.00733335i
$610$	−4.53415	−	25.7144i	−0.183582	−	1.04115i
$611$	14.9217	−	25.8451i	0.603667	−	1.04558i
$612$	−1.18876	−	0.120247i	−0.0480527	−	0.00486068i
$613$	3.57434	+	6.19093i	0.144366	+	0.250049i	0.929136	−	0.369737i	$-0.120552\pi$
$613$	3.57434	+	6.19093i	0.144366	+	0.250049i	−0.784770	+	0.619787i	$0.787219\pi$
$614$	−11.6685	+	9.79101i	−0.470901	+	0.395133i
$615$	2.33194	−	46.2249i	0.0940330	−	1.86397i
$616$	−0.277860	+	1.57582i	−0.0111953	+	0.0634917i
$617$	12.6684	+	10.6301i	0.510012	+	0.427951i	0.861133	−	0.508379i	$-0.169755\pi$
$617$	12.6684	+	10.6301i	0.510012	+	0.427951i	−0.351121	+	0.936330i	$0.614200\pi$
$618$	5.59274	−	6.02103i	0.224973	−	0.242202i
$619$	1.40893	+	0.512808i	0.0566296	+	0.0206115i	0.370180	−	0.928960i	$-0.379296\pi$
$619$	1.40893	+	0.512808i	0.0566296	+	0.0206115i	−0.313550	+	0.949572i	$0.601518\pi$
$620$	10.3236			0.414608
$621$	6.83279	+	34.0833i	0.274190	+	1.36772i
$622$	17.2704			0.692481
$623$	−23.3415	−	8.49561i	−0.935157	−	0.340369i
$624$	0.742878	+	2.41296i	0.0297389	+	0.0965958i
$625$	−23.9360	−	20.0847i	−0.957439	−	0.803387i
$626$	0.530793	−	3.01028i	0.0212148	−	0.120315i
$627$	−1.07401	+	0.549884i	−0.0428919	+	0.0219602i
$628$	−0.793848	+	0.666118i	−0.0316780	+	0.0265810i
$629$	−1.02570	−	1.77657i	−0.0408974	−	0.0708363i
$630$	−4.27286	+	15.1241i	−0.170235	+	0.602560i
$631$	17.9456	−	31.0827i	0.714404	−	1.23738i	−0.248785	−	0.968559i	$-0.580031\pi$
$631$	17.9456	−	31.0827i	0.714404	−	1.23738i	0.963189	−	0.268826i	$-0.0866356\pi$
$632$	0.375172	+	2.12771i	0.0149235	+	0.0846356i
$633$	−17.1314	+	40.5795i	−0.680913	+	1.61289i
$634$	3.20443	−	1.16632i	0.127264	−	0.0463204i
$635$	−47.6866	+	17.3565i	−1.89238	+	0.688772i
$636$	7.70574	+	10.1844i	0.305553	+	0.403837i
$637$	−0.612614	−	3.47431i	−0.0242727	−	0.137657i
$638$	0.0355961	−	0.0616542i	0.00140926	−	0.00244091i
$639$	0.919063	−	0.625157i	0.0363576	−	0.0247308i
$640$	12.1112	+	20.9772i	0.478738	+	0.829198i
$641$	30.0504	−	25.2152i	1.18692	−	0.995942i	0.187010	−	0.982358i	$-0.440120\pi$
$641$	30.0504	−	25.2152i	1.18692	−	0.995942i	0.999908	−	0.0135840i	$-0.00432406\pi$
$642$	0.301914	+	0.195227i	0.0119156	+	0.00770501i
$643$	−1.80915	+	10.2602i	−0.0713461	+	0.404624i	0.928130	+	0.372256i	$0.121416\pi$
$643$	−1.80915	+	10.2602i	−0.0713461	+	0.404624i	−0.999476	+	0.0323674i	$0.989695\pi$
$644$	16.5358	+	13.8752i	0.651603	+	0.546760i
$645$	1.21043	+	0.276958i	0.0476606	+	0.0109052i
$646$	0.615340	+	0.223965i	0.0242102	+	0.00881180i
$647$	−39.1517			−1.53921			−0.769606	−	0.638519i	$-0.779547\pi$
$647$	−39.1517			−1.53921			−0.769606	+	0.638519i	$0.779547\pi$
$648$	8.89730	−	22.5271i	0.349519	−	0.884950i
$649$	−1.49518			−0.0586910
$650$	5.03953	+	1.83424i	0.197667	+	0.0719448i
$651$	−11.0981	−	2.53935i	−0.434967	−	0.0995248i
$652$	−5.33320	−	4.47509i	−0.208864	−	0.175258i
$653$	5.71474	−	32.4099i	0.223635	−	1.26830i	−0.641642	−	0.767004i	$-0.721747\pi$
$653$	5.71474	−	32.4099i	0.223635	−	1.26830i	0.865277	−	0.501294i	$-0.167142\pi$
$654$	9.97668	+	6.45124i	0.390119	+	0.252263i
$655$	−29.9660	+	25.1444i	−1.17087	+	0.982474i
$656$	2.71152	+	4.69649i	0.105867	+	0.183367i
$657$	−1.11076	−	15.0394i	−0.0433349	−	0.586743i
$658$	−10.8834	+	18.8506i	−0.424279	+	0.734873i
$659$	−3.74532	−	21.2407i	−0.145897	−	0.827422i	−0.966643	−	0.256128i	$-0.917553\pi$
$659$	−3.74532	−	21.2407i	−0.145897	−	0.827422i	0.820746	−	0.571293i	$-0.193558\pi$
$660$	0.975953	+	1.28988i	0.0379889	+	0.0502085i
$661$	−24.7105	+	8.99389i	−0.961127	+	0.349822i	−0.774475	−	0.632604i	$-0.781986\pi$
$661$	−24.7105	+	8.99389i	−0.961127	+	0.349822i	−0.186652	+	0.982426i	$0.559764\pi$
$662$	−10.7659	+	3.91848i	−0.418430	+	0.152296i
$663$	0.516213	−	1.22276i	0.0200481	−	0.0474882i
$664$	−1.28776	−	7.30326i	−0.0499749	−	0.283422i
$665$	−9.10043	+	15.7624i	−0.352900	+	0.611240i
$666$	16.2983	−	4.13136i	0.631545	−	0.160087i
$667$	−1.18764	−	2.05705i	−0.0459855	−	0.0796493i
$668$	−9.25670	+	7.76729i	−0.358152	+	0.300526i
$669$	5.90688	−	3.02427i	0.228373	−	0.116925i
$670$	0.692862	−	3.92942i	0.0267676	−	0.151807i
$671$	2.27023	+	1.90495i	0.0876412	+	0.0735397i
$672$	−7.06161	−	22.9370i	−0.272408	−	0.884815i
$673$	−10.8272	−	3.94080i	−0.417360	−	0.151907i	0.124800	−	0.992182i	$-0.460171\pi$
$673$	−10.8272	−	3.94080i	−0.417360	−	0.151907i	−0.542160	+	0.840275i	$0.682393\pi$
$674$	−28.6293			−1.10276
$675$	6.92226	+	11.3690i	0.266438	+	0.437593i
$676$	8.38635			0.322552
$677$	31.8791	+	11.6030i	1.22521	+	0.445941i	0.871955	−	0.489585i	$-0.162852\pi$
$677$	31.8791	+	11.6030i	1.22521	+	0.445941i	0.353257	+	0.935526i	$0.385074\pi$
$678$	2.94707	−	3.17275i	0.113181	−	0.121849i
$679$	−27.0103	−	22.6643i	−1.03656	−	0.869776i
$680$	0.377003	−	2.13809i	0.0144574	−	0.0819920i
$681$	0.219563	−	4.35229i	0.00841369	−	0.166780i
$682$	0.424772	−	0.356426i	0.0162654	−	0.0136483i
$683$	−18.3777	−	31.8310i	−0.703201	−	1.21798i	−0.967337	−	0.253495i	$-0.918420\pi$
$683$	−18.3777	−	31.8310i	−0.703201	−	1.21798i	0.264135	−	0.964486i	$-0.414913\pi$
$684$	6.63034	−	9.20132i	0.253518	−	0.351821i
$685$	−27.0661	+	46.8799i	−1.03414	+	1.79119i
$686$	2.76254	+	15.6671i	0.105474	+	0.598174i
$687$	−27.3958	+	3.41816i	−1.04522	+	0.130411i
$688$	−0.136717	+	0.0497608i	−0.00521227	+	0.00189711i
$689$	−13.3311	+	4.85212i	−0.507874	+	0.184851i
$690$	−25.3424	+	3.16195i	−0.964769	+	0.120374i
$691$	2.32309	+	13.1749i	0.0883744	+	0.501196i	0.996577	+	0.0826660i	$0.0263435\pi$
$691$	2.32309	+	13.1749i	0.0883744	+	0.501196i	−0.908203	+	0.418530i	$0.862545\pi$
$692$	−4.62331	+	8.00781i	−0.175752	+	0.304411i
$693$	−0.731885	−	1.62670i	−0.0278020	−	0.0617930i
$694$	−7.79146	−	13.4952i	−0.295760	−	0.512271i
$695$	37.7294	−	31.6588i	1.43116	−	1.20089i
$696$	−0.0833854	+	1.65291i	−0.00316072	+	0.0626532i
$697$	0.495057	−	2.80761i	0.0187516	−	0.106346i
$698$	4.92475	+	4.13236i	0.186405	+	0.156412i
$699$	33.1570	−	35.6961i	1.25411	−	1.35015i
$700$	7.76708	+	2.82699i	0.293568	+	0.106850i
$701$	5.00452			0.189018			0.0945091	−	0.995524i	$-0.469872\pi$
$701$	5.00452			0.189018			0.0945091	+	0.995524i	$0.469872\pi$
$702$	8.49421	+	6.79639i	0.320593	+	0.256513i
$703$	19.4720			0.734400
$704$	0.836033	+	0.304291i	0.0315092	+	0.0114684i
$705$	16.0121	+	52.0094i	0.603050	+	1.95879i
$706$	−5.37489	−	4.51007i	−0.202287	−	0.169739i
$707$	1.65313	−	9.37537i	0.0621724	−	0.352597i
$708$	12.5096	−	6.40479i	0.470139	−	0.240707i
$709$	13.1330	−	11.0199i	0.493218	−	0.413859i	−0.361960	−	0.932194i	$-0.617892\pi$
$709$	13.1330	−	11.0199i	0.493218	−	0.413859i	0.855178	+	0.518334i	$0.173448\pi$
$710$	0.408315	+	0.707223i	0.0153238	+	0.0265416i
$711$	−1.67982	−	1.72595i	−0.0629982	−	0.0647282i
$712$	−14.0623	+	24.3566i	−0.527006	+	0.912800i
$713$	−3.21258	−	18.2195i	−0.120312	−	0.682324i
$714$	−0.376509	+	0.891844i	−0.0140905	+	0.0333764i
$715$	−1.68842	+	0.614533i	−0.0631432	+	0.0229822i
$716$	−23.4058	+	8.51902i	−0.874716	+	0.318371i
$717$	15.3687	+	20.3122i	0.573954	+	0.758572i
$718$	1.15215	+	6.53417i	0.0429979	+	0.243853i
$719$	21.6760	−	37.5439i	0.808377	−	1.40015i	−0.105610	−	0.994408i	$-0.533680\pi$
$719$	21.6760	−	37.5439i	0.808377	−	1.40015i	0.913987	−	0.405742i	$-0.132987\pi$
$720$	−4.14569	−	2.00196i	−0.154501	−	0.0746087i
$721$	7.03467	+	12.1844i	0.261985	+	0.453771i
$722$	6.90461	−	5.79365i	0.256963	−	0.215617i
$723$	12.2799	+	7.94060i	0.456696	+	0.295314i
$724$	−2.66987	+	15.1416i	−0.0992251	+	0.562733i
$725$	−0.696735	−	0.584630i	−0.0258761	−	0.0217126i
$726$	−14.8017	−	3.38679i	−0.549344	−	0.125695i
$727$	34.1521	+	12.4303i	1.26663	+	0.461016i	0.885989	−	0.463706i	$-0.153481\pi$
$727$	34.1521	+	12.4303i	1.26663	+	0.461016i	0.380642	+	0.924722i	$0.375703\pi$
$728$	16.7075			0.619220
$729$	5.92298	+	26.3423i	0.219370	+	0.975642i
$730$	11.0794			0.410067
$731$	0.0718726	+	0.0261595i	0.00265830	+	0.000967544i
$732$	−27.1542	−	6.21315i	−1.00365	−	0.229645i
$733$	2.96889	+	2.49119i	0.109658	+	0.0920143i	0.695968	−	0.718073i	$-0.254975\pi$
$733$	2.96889	+	2.49119i	0.109658	+	0.0920143i	−0.586310	+	0.810087i	$0.699420\pi$
$734$	2.05990	−	11.6823i	0.0760322	−	0.431200i
$735$	5.40202	+	3.49312i	0.199257	+	0.128846i
$736$	29.8753	−	25.0683i	1.10122	−	0.924031i
$737$	0.226432	+	0.392191i	0.00834071	+	0.0144465i
$738$	21.0418	+	10.1611i	0.774559	+	0.374036i
$739$	−13.2241	+	22.9048i	−0.486456	+	0.842567i	−0.999879	−	0.0155689i	$-0.995044\pi$
$739$	−13.2241	+	22.9048i	−0.486456	+	0.842567i	0.513422	+	0.858136i	$0.328377\pi$
$740$	−4.53273	−	25.7064i	−0.166627	−	0.944986i
$741$	7.60158	+	10.0467i	0.279251	+	0.369075i
$742$	9.72326	−	3.53898i	0.356952	−	0.129920i
$743$	12.6514	−	4.60474i	0.464136	−	0.168932i	−0.0993584	−	0.995052i	$-0.531679\pi$
$743$	12.6514	−	4.60474i	0.464136	−	0.168932i	0.563494	+	0.826120i	$0.309457\pi$
$744$	−5.01352	+	11.8756i	−0.183805	+	0.435381i
$745$	−7.77830	−	44.1129i	−0.284975	−	1.61617i
$746$	10.2329	−	17.7238i	0.374651	−	0.648915i
$747$	5.76591	+	5.92425i	0.210964	+	0.216757i
$748$	0.0498160	+	0.0862839i	0.00182145	+	0.00315485i
$749$	−0.471538	+	0.395667i	−0.0172296	+	0.0144574i
$750$	8.28579	−	4.24224i	0.302554	−	0.154905i
$751$	0.654359	−	3.71106i	0.0238779	−	0.135418i	−0.970538	−	0.240946i	$-0.922542\pi$
$751$	0.654359	−	3.71106i	0.0238779	−	0.135418i	0.994416	+	0.105528i	$0.0336533\pi$
$752$	−4.88444	−	4.09854i	−0.178117	−	0.149458i
$753$	−11.8341	−	38.4386i	−0.431258	−	1.40078i
$754$	−0.698510	−	0.254237i	−0.0254382	−	0.00925876i
$755$	−39.2536			−1.42859
$756$	13.0915	+	10.4748i	0.476135	+	0.380965i
$757$	−33.7073			−1.22511			−0.612556	−	0.790427i	$-0.709859\pi$
$757$	−33.7073			−1.22511			−0.612556	+	0.790427i	$0.709859\pi$
$758$	15.1575	+	5.51687i	0.550544	+	0.200382i
$759$	1.97271	−	2.12378i	0.0716049	−	0.0770884i
$760$	15.7866	+	13.2465i	0.572640	+	0.480502i
$761$	−1.67665	+	9.50874i	−0.0607784	+	0.344692i	0.939221	+	0.343314i	$0.111550\pi$
$761$	−1.67665	+	9.50874i	−0.0607784	+	0.344692i	−0.999999	+	0.00137744i	$0.999562\pi$
$762$	1.29084	−	25.5876i	0.0467621	−	0.926941i
$763$	−15.5818	+	13.0747i	−0.564100	+	0.473336i
$764$	4.65533	+	8.06327i	0.168424	+	0.291719i
$765$	0.993028	+	2.20711i	0.0359030	+	0.0797984i
$766$	−9.56272	+	16.5631i	−0.345515	+	0.598450i
$767$	2.71093	+	15.3745i	0.0978861	+	0.555139i
$768$	−24.3601	+	3.03939i	−0.879019	+	0.109675i
$769$	−36.3764	+	13.2399i	−1.31177	+	0.477445i	−0.900812	−	0.434210i	$-0.857027\pi$
$769$	−36.3764	+	13.2399i	−1.31177	+	0.477445i	−0.410957	+	0.911655i	$0.634805\pi$
$770$	1.23148	−	0.448221i	0.0443793	−	0.0161528i
$771$	11.7994	−	1.47220i	0.424944	−	0.0530200i
$772$	−4.81205	−	27.2905i	−0.173189	−	0.982206i
$773$	−12.1519	+	21.0478i	−0.437075	+	0.757036i	−0.997462	−	0.0711944i	$-0.977319\pi$
$773$	−12.1519	+	21.0478i	−0.437075	+	0.757036i	0.560387	+	0.828231i	$0.310652\pi$
$774$	−0.366491	+	0.508601i	−0.0131732	+	0.0182813i
$775$	−3.54205	−	6.13500i	−0.127234	−	0.220376i
$776$	−30.5824	+	25.6617i	−1.09784	+	0.921200i
$777$	−1.45036	+	28.7496i	−0.0520312	+	1.03139i
$778$	−5.28527	+	29.9742i	−0.189486	+	1.07463i
$779$	20.7300	+	17.3945i	0.742728	+	0.623223i
$780$	11.4939	−	12.3741i	0.411547	−	0.443064i
$781$	−0.0870967	−	0.0317006i	−0.00311656	−	0.00113434i
$782$	−1.57311			−0.0562544
$783$	−0.959467	−	1.57581i	−0.0342886	−	0.0563150i
$784$	−0.753755			−0.0269198
$785$	1.97251	+	0.717936i	0.0704020	+	0.0256242i
$786$	−5.81096	−	18.8748i	−0.207270	−	0.673240i
$787$	16.0414	+	13.4604i	0.571816	+	0.479810i	0.882248	−	0.470785i	$-0.156029\pi$
$787$	16.0414	+	13.4604i	0.571816	+	0.479810i	−0.310432	+	0.950596i	$0.600474\pi$
$788$	−0.715633	+	4.05856i	−0.0254934	+	0.144580i
$789$	−5.16932	+	2.64664i	−0.184033	+	0.0942229i
$790$	1.35550	−	1.13740i	0.0482264	−	0.0404668i
$791$	3.70688	+	6.42051i	0.131802	+	0.228287i
$792$	−1.95774	+	0.496258i	−0.0695654	+	0.0176338i
$793$	15.4718	−	26.7979i	0.549419	−	0.951621i
$794$	−2.83229	−	16.0627i	−0.100514	−	0.570045i
$795$	10.0612	−	23.8321i	0.356834	−	0.845239i
$796$	−2.88620	+	1.05049i	−0.102299	+	0.0372337i
$797$	−11.2169	+	4.08261i	−0.397322	+	0.144614i	−0.532951	−	0.846146i	$-0.678917\pi$
$797$	−11.2169	+	4.08261i	−0.397322	+	0.144614i	0.135628	+	0.990760i	$0.456695\pi$
$798$	−5.54435	−	7.32775i	−0.196268	−	0.259400i
$799$	0.582068	+	3.30107i	0.0205921	+	0.116783i
$800$	7.46668	−	12.9327i	0.263987	−	0.457239i
$801$	−2.30926	−	31.2668i	−0.0815939	−	1.10476i
$802$	2.78329	+	4.82080i	0.0982814	+	0.170228i
$803$	−0.963297	+	0.808303i	−0.0339940	+	0.0285244i
$804$	−3.57446	−	2.31136i	−0.126062	−	0.0815154i
$805$	7.59263	−	43.0600i	0.267605	−	1.51766i
$806$	−4.43518	−	3.72155i	−0.156222	−	0.131086i
$807$	−21.5131	−	4.92242i	−0.757298	−	0.173277i
$808$	−10.1290	−	3.68664i	−0.356336	−	0.129696i
$809$	8.60808			0.302644			0.151322	−	0.988485i	$-0.451647\pi$
$809$	8.60808			0.302644			0.151322	+	0.988485i	$0.451647\pi$
$810$	−19.6214	+	2.91424i	−0.689426	+	0.102396i
$811$	1.53770			0.0539958			0.0269979	−	0.999635i	$-0.491405\pi$
$811$	1.53770			0.0539958			0.0269979	+	0.999635i	$0.491405\pi$
$812$	−1.07656	−	0.391837i	−0.0377800	−	0.0137508i
$813$	39.7734	+	9.10055i	1.39491	+	0.319170i
$814$	−1.07402	−	0.901211i	−0.0376444	−	0.0315874i
$815$	−2.44881	+	13.8879i	−0.0857779	+	0.486471i
$816$	−0.238129	−	0.153982i	−0.00833617	−	0.00539043i
$817$	−0.556149	+	0.466665i	−0.0194572	+	0.0163265i
$818$	−4.37071	−	7.57029i	−0.152818	−	0.264689i
$819$	−15.3998	+	10.4751i	−0.538112	+	0.366030i
$820$	18.1382	−	31.4163i	0.633413	−	1.09710i
$821$	5.03168	+	28.5361i	0.175607	+	0.995915i	0.937441	+	0.348144i	$0.113188\pi$
$821$	5.03168	+	28.5361i	0.175607	+	0.995915i	−0.761835	+	0.647772i	$0.775701\pi$
$822$	−16.4898	−	21.7939i	−0.575147	−	0.760149i
$823$	10.5779	−	3.85004i	0.368722	−	0.134204i	−0.151012	−	0.988532i	$-0.548253\pi$
$823$	10.5779	−	3.85004i	0.368722	−	0.134204i	0.519734	+	0.854328i	$0.326031\pi$
$824$	14.9693	−	5.44838i	0.521481	−	0.189803i
$825$	0.431683	−	1.02253i	0.0150293	−	0.0356001i
$826$	−1.97727	−	11.2136i	−0.0687979	−	0.390172i
$827$	−15.4640	+	26.7844i	−0.537734	+	0.931383i	0.461291	+	0.887249i	$0.347386\pi$
$827$	−15.4640	+	26.7844i	−0.537734	+	0.931383i	−0.999026	+	0.0441346i	$0.985947\pi$
$828$	−7.40742	+	26.2192i	−0.257426	+	0.911180i
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	0.938698	−	0.344739i	$-0.112033\pi$
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	−0.767902	+	0.640567i	$0.778699\pi$
$830$	−4.65269	+	3.90407i	−0.161497	+	0.135512i
$831$	−6.44630	+	3.30044i	−0.223620	+	0.114491i
$832$	1.61310	−	9.14836i	0.0559243	−	0.317162i
$833$	0.303547	+	0.254706i	0.0105173	+	0.00882505i
$834$	7.31644	+	23.7648i	0.253348	+	0.822906i
$835$	23.0006	+	8.37152i	0.795967	+	0.289708i
$836$	−0.945711			−0.0327081
$837$	−2.82456	−	14.0894i	−0.0976310	−	0.487003i
$838$	8.07072			0.278798
$839$	12.3506	+	4.49524i	0.426389	+	0.155193i	0.546296	−	0.837592i	$-0.316037\pi$
$839$	12.3506	+	4.49524i	0.426389	+	0.155193i	−0.119907	+	0.992785i	$0.538260\pi$
$840$	−20.7338	+	22.3216i	−0.715385	+	0.770169i
$841$	−22.1187	−	18.5598i	−0.762714	−	0.639993i
$842$	0.432522	−	2.45296i	0.0149057	−	0.0845344i
$843$	−1.88811	+	37.4271i	−0.0650301	+	1.28906i
$844$	−26.4467	+	22.1914i	−0.910333	+	0.763860i
$845$	−8.49363	−	14.7114i	−0.292190	−	0.506088i
$846$	−27.3342	−	2.76494i	−0.939769	−	0.0950604i
$847$	12.9982	−	22.5136i	0.446624	−	0.773575i
$848$	0.526336	+	2.98500i	0.0180745	+	0.102505i
$849$	8.98435	−	1.12097i	0.308342	−	0.0384717i
$850$	−0.566038	+	0.206021i	−0.0194149	+	0.00706646i
$851$	−43.9569	+	15.9990i	−1.50682	+	0.548438i
$852$	0.864497	−	0.107863i	0.0296172	−	0.00369531i
$853$	2.68153	+	15.2077i	0.0918139	+	0.520703i	0.995677	+	0.0928812i	$0.0296077\pi$
$853$	2.68153	+	15.2077i	0.0918139	+	0.520703i	−0.903863	+	0.427821i	$0.859281\pi$
$854$	−11.2846	+	19.5455i	−0.386151	+	0.668834i
$855$	−22.8562	−	2.31197i	−0.781665	−	0.0790678i
$856$	0.348478	+	0.603581i	0.0119107	+	0.0206300i
$857$	16.8398	−	14.1302i	0.575235	−	0.482680i	−0.308143	−	0.951340i	$-0.599708\pi$
$857$	16.8398	−	14.1302i	0.575235	−	0.482680i	0.883378	+	0.468660i	$0.155263\pi$
$858$	0.0457041	−	0.905968i	0.00156031	−	0.0309293i
$859$	3.39772	−	19.2694i	0.115929	−	0.657464i	−0.870358	−	0.492420i	$-0.836112\pi$
$859$	3.39772	−	19.2694i	0.115929	−	0.657464i	0.986286	−	0.165044i	$-0.0527765\pi$
$860$	0.745540	+	0.625582i	0.0254227	+	0.0213322i
$861$	−27.2264	+	29.3114i	−0.927873	+	0.998929i
$862$	−21.1421	−	7.69508i	−0.720101	−	0.262095i
$863$	21.8676			0.744383			0.372191	−	0.928156i	$-0.378607\pi$
$863$	21.8676			0.744383			0.372191	+	0.928156i	$0.378607\pi$
$864$	22.7445	−	20.0069i	0.773784	−	0.680648i
$865$	18.7298			0.636833
$866$	14.7061	+	5.35258i	0.499733	+	0.181888i
$867$	−8.62001	−	27.9989i	−0.292751	−	0.950893i
$868$	−6.83563	−	5.73577i	−0.232016	−	0.194685i
$869$	−0.0348743	+	0.197782i	−0.00118303	+	0.00670929i
$870$	1.20651	−	0.617723i	0.0409046	−	0.0209428i
$871$	3.62223	−	3.03941i	0.122734	−	0.102986i
$872$	11.5153	+	19.9452i	0.389959	+	0.675428i
$873$	12.0996	−	42.8275i	0.409508	−	1.44949i
$874$	7.46602	−	12.9315i	0.252542	−	0.437416i
$875$	2.76743	+	15.6949i	0.0935563	+	0.530584i
$876$	4.59707	−	10.8891i	0.155321	−	0.367910i
$877$	36.7419	−	13.3729i	1.24068	−	0.451572i	0.363441	−	0.931617i	$-0.381602\pi$
$877$	36.7419	−	13.3729i	1.24068	−	0.451572i	0.877244	+	0.480045i	$0.159380\pi$
$878$	11.0188	−	4.01053i	0.371868	−	0.135349i
$879$	6.41903	+	8.48379i	0.216509	+	0.286151i
$880$	0.0666619	+	0.378058i	0.00224717	+	0.0127443i
$881$	3.65254	−	6.32639i	0.123057	−	0.213141i	−0.797915	−	0.602771i	$-0.794063\pi$
$881$	3.65254	−	6.32639i	0.123057	−	0.213141i	0.920972	+	0.389629i	$0.127397\pi$
$882$	−2.68541	+	1.82665i	−0.0904223	+	0.0615063i
$883$	1.74646	+	3.02496i	0.0587732	+	0.101798i	0.893915	−	0.448237i	$-0.147948\pi$
$883$	1.74646	+	3.02496i	0.0587732	+	0.101798i	−0.835142	+	0.550035i	$0.814614\pi$
$884$	0.796907	−	0.668684i	0.0268029	−	0.0224903i
$885$	−23.9049	−	15.4577i	−0.803556	−	0.519605i
$886$	−2.55485	+	14.4893i	−0.0858318	+	0.486776i
$887$	21.7720	+	18.2688i	0.731031	+	0.613408i	0.930413	−	0.366514i	$-0.119449\pi$
$887$	21.7720	+	18.2688i	0.731031	+	0.613408i	−0.199381	+	0.979922i	$0.563893\pi$
$888$	31.7721	+	7.26978i	1.06620	+	0.243958i
$889$	41.2181	+	15.0021i	1.38241	+	0.503156i
$890$	23.0340			0.772102
$891$	1.49337	−	1.68487i	0.0500298	−	0.0564452i
$892$	5.20125			0.174151
$893$	−29.8985	−	10.8821i	−1.00051	−	0.364157i
$894$	22.0447	+	5.04405i	0.737286	+	0.168698i
$895$	38.6493	+	32.4306i	1.29190	+	1.08404i
$896$	3.63563	−	20.6187i	0.121458	−	0.688821i
$897$	−25.4149	−	16.4341i	−0.848579	−	0.548718i
$898$	−8.50974	+	7.14052i	−0.283974	+	0.238282i
$899$	0.490949	+	0.850349i	0.0163741	+	0.0283607i
$900$	0.768427	+	10.4043i	0.0256142	+	0.346810i
$901$	0.796719	−	1.37996i	0.0265426	−	0.0459731i
$902$	−0.338348	−	1.91887i	−0.0112658	−	0.0638913i
$903$	−0.647588	−	0.855892i	−0.0215504	−	0.0284823i
$904$	7.88800	−	2.87100i	0.262351	−	0.0954880i
$905$	29.2655	−	10.6518i	0.972819	−	0.354077i
$906$	7.70767	−	18.2573i	0.256070	−	0.606558i
$907$	9.22362	+	52.3097i	0.306265	+	1.73692i	0.617489	+	0.786579i	$0.288150\pi$
$907$	9.22362	+	52.3097i	0.306265	+	1.73692i	−0.311224	+	0.950337i	$0.600739\pi$
$908$	1.70780	−	2.95799i	0.0566753	−	0.0981644i
$909$	11.6476	−	2.95249i	0.386327	−	0.0979279i
$910$	−6.84171	−	11.8502i	−0.226801	−	0.392830i
$911$	−6.18649	+	5.19108i	−0.204968	+	0.171988i	−0.739493	−	0.673164i	$-0.764935\pi$
$911$	−6.18649	+	5.19108i	−0.204968	+	0.171988i	0.534526	+	0.845152i	$0.320490\pi$
$912$	2.39595	−	1.22670i	0.0793377	−	0.0406201i
$913$	0.119704	−	0.678878i	0.00396164	−	0.0224676i
$914$	−10.8360	−	9.09252i	−0.358424	−	0.300754i
$915$	16.6024	+	53.9267i	0.548858	+	1.78276i
$916$	−20.3339	−	7.40094i	−0.671852	−	0.244534i
$917$	33.8116			1.11656
$918$	−1.22154	+	0.0284888i	−0.0403168	+	0.000940269i
$919$	−47.9961			−1.58325			−0.791623	−	0.611009i	$-0.790764\pi$
$919$	−47.9961			−1.58325			−0.791623	+	0.611009i	$0.790764\pi$
$920$	−46.5212	−	16.9323i	−1.53376	−	0.558242i
$921$	22.4013	−	24.1168i	0.738149	−	0.794677i
$922$	−15.7419	−	13.2090i	−0.518431	−	0.435016i
$923$	−0.168051	+	0.953063i	−0.00553146	+	0.0313705i
$924$	0.0704406	−	1.39631i	0.00231732	−	0.0459351i
$925$	−13.7213	+	11.5135i	−0.451153	+	0.378562i
$926$	7.35298	+	12.7357i	0.241634	+	0.418522i
$927$	−10.3817	+	14.4073i	−0.340979	+	0.473197i
$928$	−1.03493	+	1.79255i	−0.0339732	+	0.0588433i
$929$	−5.03474	−	28.5534i	−0.165185	−	0.936808i	−0.948874	−	0.315655i	$-0.897776\pi$
$929$	−5.03474	−	28.5534i	−0.165185	−	0.936808i	0.783689	−	0.621153i	$-0.213335\pi$
$930$	10.4761	−	1.30710i	0.343525	−	0.0428614i
$931$	−3.53442	+	1.28642i	−0.115836	+	0.0421608i
$932$	35.8828	−	13.0603i	1.17538	−	0.427803i
$933$	−37.0332	+	4.62061i	−1.21241	+	0.151272i
$934$	2.26338	+	12.8363i	0.0740602	+	0.420016i
$935$	0.100907	−	0.174775i	0.00330000	−	0.00571576i
$936$	8.65246	+	19.2311i	0.282815	+	0.628587i
$937$	−2.51425	−	4.35481i	−0.0821369	−	0.142265i	0.822031	−	0.569443i	$-0.192841\pi$
$937$	−2.51425	−	4.35481i	−0.0821369	−	0.142265i	−0.904168	+	0.427178i	$0.859508\pi$
$938$	−2.64193	+	2.21685i	−0.0862622	+	0.0723826i
$939$	−0.332803	+	6.59699i	−0.0108606	+	0.215285i
$940$	−7.40649	+	42.0043i	−0.241573	+	1.37003i
$941$	−42.7767	−	35.8939i	−1.39448	−	1.17011i	−0.963487	−	0.267755i	$-0.913718\pi$
$941$	−42.7767	−	35.8939i	−1.39448	−	1.17011i	−0.430995	−	0.902354i	$-0.641837\pi$
$942$	−0.721234	+	0.776466i	−0.0234991	+	0.0252986i
$943$	−61.0887	−	22.2345i	−1.98932	−	0.724054i
$944$	3.33551			0.108561
$945$	5.11596	−	33.5741i	0.166422	−	1.09216i
$946$	0.0522740			0.00169957
$947$	−39.9645	−	14.5459i	−1.29867	−	0.472678i	−0.402109	−	0.915592i	$-0.631723\pi$
$947$	−39.9645	−	14.5459i	−1.29867	−	0.472678i	−0.896564	+	0.442914i	$0.853945\pi$
$948$	−0.555443	−	1.80415i	−0.0180400	−	0.0585961i
$949$	10.0581	+	8.43973i	0.326499	+	0.273965i
$950$	0.992864	−	5.63081i	0.0322127	−	0.182688i
$951$	−6.55926	+	3.35828i	−0.212699	+	0.108900i
$952$	−1.43754	+	1.20624i	−0.0465909	+	0.0390944i
$953$	−10.9074	−	18.8922i	−0.353325	−	0.611977i	0.633505	−	0.773739i	$-0.281616\pi$
$953$	−10.9074	−	18.8922i	−0.353325	−	0.611977i	−0.986830	+	0.161762i	$0.948282\pi$
$954$	9.10901	+	9.35916i	0.294915	+	0.303014i
$955$	9.42977	−	16.3328i	0.305140	−	0.528518i
$956$	3.46670	+	19.6606i	0.112121	+	0.635870i
$957$	−0.0598339	+	0.141729i	−0.00193415	+	0.00458146i
$958$	−7.13399	+	2.59656i	−0.230489	+	0.0838910i
$959$	43.9676	−	16.0029i	1.41979	−	0.516761i
$960$	10.2206	+	13.5082i	0.329869	+	0.435975i
$961$	−4.05507	−	22.9974i	−0.130809	−	0.741852i
$962$	−7.31954	+	12.6778i	−0.235991	+	0.408749i
$963$	−0.699631	−	0.337853i	−0.0225453	−	0.0108872i
$964$	5.73088	+	9.92618i	0.184579	+	0.319701i
$965$	−42.9996	+	36.0809i	−1.38421	+	1.16149i
$966$	18.5368	+	11.9865i	0.596412	+	0.385659i
$967$	0.803746	−	4.55827i	0.0258467	−	0.146584i	−0.969153	−	0.246459i	$-0.920733\pi$
$967$	0.803746	−	4.55827i	0.0258467	−	0.146584i	0.995000	+	0.0998746i	$0.0318442\pi$
$968$	−22.5481	−	18.9201i	−0.724724	−	0.608115i
$969$	−1.37940	−	0.315621i	−0.0443128	−	0.0101392i
$970$	30.7247	+	11.1829i	0.986511	+	0.359060i
$971$	−21.6509			−0.694809			−0.347405	−	0.937715i	$-0.612937\pi$
$971$	−21.6509			−0.694809			−0.347405	+	0.937715i	$0.612937\pi$
$972$	−5.27712	+	20.4937i	−0.169264	+	0.657334i
$973$	−42.5714			−1.36478
$974$	−0.352164	−	0.128177i	−0.0112841	−	0.00410707i
$975$	−11.2971	−	2.58488i	−0.361796	−	0.0827825i
$976$	−5.06451	−	4.24963i	−0.162111	−	0.136027i
$977$	−3.83499	+	21.7493i	−0.122692	+	0.695822i	0.859960	+	0.510362i	$0.170489\pi$
$977$	−3.83499	+	21.7493i	−0.122692	+	0.695822i	−0.982652	+	0.185460i	$0.940623\pi$
$978$	−5.97856	−	3.86593i	−0.191173	−	0.123619i
$979$	−2.00269	+	1.68046i	−0.0640063	+	0.0537076i
$980$	2.52105	+	4.36659i	0.0805320	+	0.139485i
$981$	−23.1191	−	11.1643i	−0.738137	−	0.356448i
$982$	10.0379	−	17.3862i	0.320323	−	0.554815i
$983$	−2.40729	−	13.6524i	−0.0767807	−	0.435445i	−0.998829	−	0.0483713i	$-0.984597\pi$
$983$	−2.40729	−	13.6524i	−0.0767807	−	0.435445i	0.922049	−	0.387074i	$-0.126514\pi$
$984$	27.3306	+	36.1217i	0.871266	+	1.15152i
$985$	7.84434	−	2.85511i	0.249941	−	0.0909712i
$986$	0.0784563	−	0.0285558i	0.00249856	−	0.000909401i
$987$	18.2940	−	43.3334i	0.582305	−	1.37932i
$988$	1.71468	+	9.72444i	0.0545513	+	0.309376i
$989$	0.872042	−	1.51042i	0.0277293	−	0.0480286i
$990$	1.15368	+	1.18536i	0.0366664	+	0.0376733i
$991$	−17.4112	−	30.1570i	−0.553084	−	0.957970i	−0.998050	−	0.0624224i	$-0.980117\pi$
$991$	−17.4112	−	30.1570i	−0.553084	−	0.957970i	0.444966	−	0.895548i	$-0.353216\pi$
$992$	−12.3499	+	10.3628i	−0.392111	+	0.329020i
$993$	22.0371	−	11.2828i	0.699328	−	0.358049i
$994$	0.122571	−	0.695133i	0.00388771	−	0.0220483i
$995$	4.76590	+	3.99906i	0.151089	+	0.126779i
$996$	1.90653	+	6.19267i	0.0604109	+	0.196222i
$997$	23.2572	+	8.46492i	0.736562	+	0.268087i	0.682940	−	0.730475i	$-0.260701\pi$
$997$	23.2572	+	8.46492i	0.736562	+	0.268087i	0.0536221	+	0.998561i	$0.482923\pi$
$998$	11.2488			0.356073
$999$	−33.8433	+	13.2195i	−1.07075	+	0.418245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.2.e.a.4.2	✓	12
3.2	odd	2		81.2.e.a.64.1		12
4.3	odd	2		432.2.u.c.193.2		12
5.2	odd	4		675.2.u.b.274.2		24
5.3	odd	4		675.2.u.b.274.3		24
5.4	even	2		675.2.l.c.301.1		12
9.2	odd	6		243.2.e.b.28.2		12
9.4	even	3		243.2.e.d.109.1		12
9.5	odd	6		243.2.e.a.109.2		12
9.7	even	3		243.2.e.c.28.1		12
27.2	odd	18		243.2.e.a.136.2		12
27.4	even	9		729.2.c.e.244.4		12
27.5	odd	18		729.2.c.b.487.3		12
27.7	even	9	inner	27.2.e.a.7.2	yes	12
27.11	odd	18		243.2.e.b.217.2		12
27.13	even	9		729.2.a.a.1.3		6
27.14	odd	18		729.2.a.d.1.4		6
27.16	even	9		243.2.e.c.217.1		12
27.20	odd	18		81.2.e.a.19.1		12
27.22	even	9		729.2.c.e.487.4		12
27.23	odd	18		729.2.c.b.244.3		12
27.25	even	9		243.2.e.d.136.1		12
108.7	odd	18		432.2.u.c.385.2		12
135.7	odd	36		675.2.u.b.574.3		24
135.34	even	18		675.2.l.c.601.1		12
135.88	odd	36		675.2.u.b.574.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	1.1	even	1	trivial
27.2.e.a.7.2	yes	12	27.7	even	9	inner
81.2.e.a.19.1		12	27.20	odd	18
81.2.e.a.64.1		12	3.2	odd	2
243.2.e.a.109.2		12	9.5	odd	6
243.2.e.a.136.2		12	27.2	odd	18
243.2.e.b.28.2		12	9.2	odd	6
243.2.e.b.217.2		12	27.11	odd	18
243.2.e.c.28.1		12	9.7	even	3
243.2.e.c.217.1		12	27.16	even	9
243.2.e.d.109.1		12	9.4	even	3
243.2.e.d.136.1		12	27.25	even	9
432.2.u.c.193.2		12	4.3	odd	2
432.2.u.c.385.2		12	108.7	odd	18
675.2.l.c.301.1		12	5.4	even	2
675.2.l.c.601.1		12	135.34	even	18
675.2.u.b.274.2		24	5.2	odd	4
675.2.u.b.274.3		24	5.3	odd	4
675.2.u.b.574.2		24	135.88	odd	36
675.2.u.b.574.3		24	135.7	odd	36
729.2.a.a.1.3		6	27.13	even	9
729.2.a.d.1.4		6	27.14	odd	18
729.2.c.b.244.3		12	27.23	odd	18
729.2.c.b.487.3		12	27.5	odd	18
729.2.c.e.244.4		12	27.4	even	9
729.2.c.e.487.4		12	27.22	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.753189 + 0.274138i) q^{2} +(-1.68842 - 0.386327i) q^{3} +(-1.03995 - 0.872619i) q^{4} +(-0.477505 + 2.70806i) q^{5} +(-1.16579 - 0.753837i) q^{6} +(1.82076 - 1.52780i) q^{7} +(-1.34559 - 2.33062i) q^{8} +(2.70150 + 1.30456i) q^{9} +O(q^{10})\)	\(q+(0.753189 + 0.274138i) q^{2} +(-1.68842 - 0.386327i) q^{3} +(-1.03995 - 0.872619i) q^{4} +(-0.477505 + 2.70806i) q^{5} +(-1.16579 - 0.753837i) q^{6} +(1.82076 - 1.52780i) q^{7} +(-1.34559 - 2.33062i) q^{8} +(2.70150 + 1.30456i) q^{9} +(-1.10204 + 1.90878i) q^{10} +(-0.0434396 - 0.246358i) q^{11} +(1.41875 + 1.87510i) q^{12} +(-2.45446 + 0.893351i) q^{13} +(1.79020 - 0.651581i) q^{14} +(1.85243 - 4.38787i) q^{15} +(0.0969067 + 0.549585i) q^{16} +(0.146688 - 0.254072i) q^{17} +(1.67711 + 1.72317i) q^{18} +(1.39237 + 2.41166i) q^{19} +(2.85969 - 2.39956i) q^{20} +(-3.66443 + 1.87615i) q^{21} +(0.0348180 - 0.197463i) q^{22} +(-5.12472 - 4.30015i) q^{23} +(1.37153 + 4.45490i) q^{24} +(-2.40714 - 0.876128i) q^{25} -2.09357 q^{26} +(-4.05728 - 3.24631i) q^{27} -3.22668 q^{28} +(0.333645 + 0.121437i) q^{29} +(2.59811 - 2.79707i) q^{30} +(2.11847 + 1.77761i) q^{31} +(-1.01231 + 5.74108i) q^{32} +(-0.0218307 + 0.432738i) q^{33} +(0.180135 - 0.151151i) q^{34} +(3.26796 + 5.66027i) q^{35} +(-1.67103 - 3.71406i) q^{36} +(3.49619 - 6.05558i) q^{37} +(0.387591 + 2.19814i) q^{38} +(4.48928 - 0.560124i) q^{39} +(6.95400 - 2.53105i) q^{40} +(9.13156 - 3.32362i) q^{41} +(-3.27434 + 0.408537i) q^{42} +(0.0452712 + 0.256746i) q^{43} +(-0.169802 + 0.294106i) q^{44} +(-4.82282 + 6.69291i) q^{45} +(-2.68104 - 4.64370i) q^{46} +(-8.75249 + 7.34421i) q^{47} +(0.0487006 - 0.965367i) q^{48} +(-0.234540 + 1.33014i) q^{49} +(-1.57285 - 1.31978i) q^{50} +(-0.345826 + 0.372309i) q^{51} +(3.33207 + 1.21277i) q^{52} +5.43137 q^{53} +(-2.16596 - 3.55734i) q^{54} +0.687897 q^{55} +(-6.01071 - 2.18772i) q^{56} +(-1.41922 - 4.60980i) q^{57} +(0.218007 + 0.182930i) q^{58} +(1.03788 - 5.88612i) q^{59} +(-5.75536 + 2.94669i) q^{60} +(-9.07515 + 7.61495i) q^{61} +(1.10830 + 1.91963i) q^{62} +(6.91190 - 1.75206i) q^{63} +(-1.77824 + 3.08001i) q^{64} +(-1.24723 - 7.07342i) q^{65} +(-0.135073 + 0.319949i) q^{66} +(-1.70113 + 0.619160i) q^{67} +(-0.374256 + 0.136218i) q^{68} +(6.99139 + 9.24026i) q^{69} +(0.909693 + 5.15912i) q^{70} +(0.185255 - 0.320871i) q^{71} +(-0.594663 - 8.05158i) q^{72} +(-2.51339 - 4.35333i) q^{73} +(4.29336 - 3.60255i) q^{74} +(3.72579 + 2.40921i) q^{75} +(0.656467 - 3.72301i) q^{76} +(-0.455479 - 0.382193i) q^{77} +(3.53483 + 0.808804i) q^{78} +(-0.754406 - 0.274581i) q^{79} -1.53459 q^{80} +(5.59624 + 7.04855i) q^{81} +7.78892 q^{82} +(2.58947 + 0.942488i) q^{83} +(5.44798 + 1.24655i) q^{84} +(0.617998 + 0.518562i) q^{85} +(-0.0362861 + 0.205789i) q^{86} +(-0.516417 - 0.333932i) q^{87} +(-0.515717 + 0.432738i) q^{88} +(-5.22533 - 9.05054i) q^{89} +(-5.46728 + 3.71891i) q^{90} +(-3.10412 + 5.37650i) q^{91} +(1.57704 + 8.94385i) q^{92} +(-2.89012 - 3.81976i) q^{93} +(-8.60560 + 3.13218i) q^{94} +(-7.19580 + 2.61906i) q^{95} +(3.92713 - 9.30225i) q^{96} +(-2.57600 - 14.6092i) q^{97} +(-0.541296 + 0.937552i) q^{98} +(0.204037 - 0.722208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

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