LMFDB - Embedded newform 418.2.q.b.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	418.109
Dual form			418.2.q.b.395.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.00614027 + 0.00108270i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.03422 - 2.54601i) q^{5} +(-0.00614027 + 0.00108270i) q^{6} +(2.10812 - 1.21712i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.81904 - 1.02605i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.00614027 + 0.00108270i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.03422 - 2.54601i) q^{5} +(-0.00614027 + 0.00108270i) q^{6} +(2.10812 - 1.21712i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.81904 - 1.02605i) q^{9} +(3.72202 + 1.35470i) q^{10} +(-2.72629 + 1.88874i) q^{11} +(0.00539966 - 0.00311750i) q^{12} +(0.855119 + 4.84962i) q^{13} +(-1.56470 + 1.86474i) q^{14} +(-0.0158744 - 0.0189183i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.83317 + 5.03660i) q^{17} +2.99996 q^{18} +(-4.31425 - 0.622263i) q^{19} -3.96089 q^{20} +(0.0142622 - 0.00519102i) q^{21} +(1.91589 - 2.70728i) q^{22} +(-2.96119 + 2.48473i) q^{23} +(-0.00400778 + 0.00477628i) q^{24} +(1.85607 + 10.5263i) q^{25} +(-2.46222 - 4.26469i) q^{26} +(-0.0323978 - 0.0187049i) q^{27} +(0.832561 - 2.28744i) q^{28} +(-3.57425 - 1.30092i) q^{29} +(0.0213875 + 0.0123481i) q^{30} +(2.37203 - 1.36949i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.0187851 + 0.00864562i) q^{33} +(-3.44523 - 4.10587i) q^{34} +(-9.49531 - 1.67428i) q^{35} +(-2.81904 + 1.02605i) q^{36} -11.7703i q^{37} +(4.26690 - 0.890826i) q^{38} +0.0307038i q^{39} +(3.72202 - 1.35470i) q^{40} +(-0.821313 + 4.65790i) q^{41} +(-0.0116267 + 0.00975592i) q^{42} +(-1.69576 + 2.02092i) q^{43} +(-0.874404 + 3.19928i) q^{44} +(5.94126 + 10.2906i) q^{45} +(1.93278 - 3.34767i) q^{46} +(-5.95285 - 2.16666i) q^{47} +(0.00213249 - 0.00585898i) q^{48} +(-0.537221 + 0.930494i) q^{49} +(-5.34433 - 9.25666i) q^{50} +(0.00580307 + 0.0329108i) q^{51} +(3.77234 + 3.16537i) q^{52} +(-1.30391 - 1.55394i) q^{53} +(0.0368414 + 0.00649613i) q^{54} +(13.0809 + 1.21033i) q^{55} +2.43425i q^{56} +(-0.0258170 - 0.00849189i) q^{57} +3.80364 q^{58} +(-1.84090 - 5.05784i) q^{59} +(-0.0243210 - 0.00428844i) q^{60} +(-2.89701 - 3.45252i) q^{61} +(-1.76059 + 2.09818i) q^{62} +(-7.19170 + 1.26809i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(9.75258 - 16.8920i) q^{65} +(0.0146952 - 0.0145491i) q^{66} +(-2.58140 + 7.09233i) q^{67} +(4.64175 + 2.67992i) q^{68} +(-0.0208727 + 0.0120509i) q^{69} +(9.49531 - 1.67428i) q^{70} +(-1.81041 + 2.15756i) q^{71} +(2.29810 - 1.92834i) q^{72} +(-13.1670 - 2.32169i) q^{73} +(4.02566 + 11.0604i) q^{74} +0.0666438i q^{75} +(-3.70489 + 2.29647i) q^{76} +(-3.44852 + 7.29992i) q^{77} +(-0.0105013 - 0.0288522i) q^{78} +(-2.01344 + 11.4188i) q^{79} +(-3.03422 + 2.54601i) q^{80} +(6.89413 + 5.78486i) q^{81} +(-0.821313 - 4.65790i) q^{82} +(10.0333 - 5.79273i) q^{83} +(0.00758876 - 0.0131441i) q^{84} +(7.26099 - 19.9494i) q^{85} +(0.902294 - 2.47903i) q^{86} +(-0.0205384 - 0.0118578i) q^{87} +(-0.272549 - 3.30541i) q^{88} +(-1.68775 + 0.297596i) q^{89} +(-9.10254 - 7.63794i) q^{90} +(7.70528 + 9.18280i) q^{91} +(-0.671247 + 3.80683i) q^{92} +(0.0160477 - 0.00584087i) q^{93} +6.33489 q^{94} +(11.5061 + 12.8722i) q^{95} +0.00623500i q^{96} +(-2.34621 - 6.44617i) q^{97} +(0.186575 - 1.05812i) q^{98} +(9.62346 - 2.52713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.00614027	+	0.00108270i	0.00354509	+	0.000625095i	0.175420	−	0.984494i	$-0.443872\pi$
$3$	0.00614027	+	0.00108270i	0.00354509	+	0.000625095i	−0.171875	+	0.985119i	$0.554983\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−3.03422	−	2.54601i	−1.35694	−	1.13861i	−0.976913	−	0.213638i	$-0.931469\pi$
$5$	−3.03422	−	2.54601i	−1.35694	−	1.13861i	−0.380031	−	0.924974i	$-0.624087\pi$
$6$	−0.00614027	+	0.00108270i	−0.00250676	+	0.000442009i
$7$	2.10812	−	1.21712i	0.796794	−	0.460029i	−0.0455547	−	0.998962i	$-0.514506\pi$
$7$	2.10812	−	1.21712i	0.796794	−	0.460029i	0.842349	+	0.538932i	$0.181172\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.81904	−	1.02605i	−0.939680	−	0.342016i
$10$	3.72202	+	1.35470i	1.17701	+	0.428395i
$11$	−2.72629	+	1.88874i	−0.822008	+	0.569476i
$11$	−2.72629	+	1.88874i	−0.822008	+	0.569476i
$12$	0.00539966	−	0.00311750i	0.00155875	−	0.000899944i
$13$	0.855119	+	4.84962i	0.237167	+	1.34504i	0.838001	+	0.545669i	$0.183724\pi$
$13$	0.855119	+	4.84962i	0.237167	+	1.34504i	−0.600833	+	0.799374i	$0.705164\pi$
$14$	−1.56470	+	1.86474i	−0.418185	+	0.498373i
$15$	−0.0158744	−	0.0189183i	−0.00409875	−	0.00488470i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	1.83317	+	5.03660i	0.444609	+	1.22155i	0.936429	+	0.350857i	$0.114110\pi$
$17$	1.83317	+	5.03660i	0.444609	+	1.22155i	−0.491820	+	0.870697i	$0.663668\pi$
$18$	2.99996			0.707098
$19$	−4.31425	−	0.622263i	−0.989758	−	0.142757i
$19$	−4.31425	−	0.622263i	−0.989758	−	0.142757i
$20$	−3.96089			−0.885682
$21$	0.0142622	−	0.00519102i	0.00311227	−	0.00113277i
$22$	1.91589	−	2.70728i	0.408469	−	0.577194i
$23$	−2.96119	+	2.48473i	−0.617450	+	0.518102i	−0.897001	−	0.442029i	$-0.854259\pi$
$23$	−2.96119	+	2.48473i	−0.617450	+	0.518102i	0.279551	+	0.960131i	$0.409814\pi$
$24$	−0.00400778	+	0.00477628i	−0.000818084	+	0.000974955i
$25$	1.85607	+	10.5263i	0.371213	+	2.10526i
$26$	−2.46222	−	4.26469i	−0.482881	−	0.836374i
$27$	−0.0323978	−	0.0187049i	−0.00623496	−	0.00359975i
$28$	0.832561	−	2.28744i	0.157339	−	0.432286i
$29$	−3.57425	−	1.30092i	−0.663722	−	0.241575i	−0.0118796	−	0.999929i	$-0.503781\pi$
$29$	−3.57425	−	1.30092i	−0.663722	−	0.241575i	−0.651843	+	0.758354i	$0.726004\pi$
$30$	0.0213875	+	0.0123481i	0.00390480	+	0.00225444i
$31$	2.37203	−	1.36949i	0.426029	−	0.245968i	−0.271624	−	0.962403i	$-0.587561\pi$
$31$	2.37203	−	1.36949i	0.426029	−	0.245968i	0.697654	+	0.716435i	$0.254227\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.0187851	+	0.00864562i	−0.00327007	+	0.00150501i
$34$	−3.44523	−	4.10587i	−0.590853	−	0.704151i
$35$	−9.49531	−	1.67428i	−1.60500	−	0.283005i
$36$	−2.81904	+	1.02605i	−0.469840	+	0.171008i
$37$		−	11.7703i		−	1.93502i	−0.252836	−	0.967509i	$-0.581363\pi$
$37$		−	11.7703i		−	1.93502i	0.252836	−	0.967509i	$-0.418637\pi$
$38$	4.26690	−	0.890826i	0.692182	−	0.144511i
$39$			0.0307038i			0.00491655i
$40$	3.72202	−	1.35470i	0.588503	−	0.214198i
$41$	−0.821313	+	4.65790i	−0.128267	+	0.727441i	0.851046	+	0.525091i	$0.175969\pi$
$41$	−0.821313	+	4.65790i	−0.128267	+	0.727441i	−0.979313	+	0.202350i	$0.935142\pi$
$42$	−0.0116267	+	0.00975592i	−0.00179403	+	0.00150537i
$43$	−1.69576	+	2.02092i	−0.258601	+	0.308188i	−0.879686	−	0.475555i	$-0.842247\pi$
$43$	−1.69576	+	2.02092i	−0.258601	+	0.308188i	0.621086	+	0.783743i	$0.286692\pi$
$44$	−0.874404	+	3.19928i	−0.131821	+	0.482310i
$45$	5.94126	+	10.2906i	0.885671	+	1.53403i
$46$	1.93278	−	3.34767i	0.284972	−	0.493587i
$47$	−5.95285	−	2.16666i	−0.868313	−	0.316040i	−0.130829	−	0.991405i	$-0.541764\pi$
$47$	−5.95285	−	2.16666i	−0.868313	−	0.316040i	−0.737484	+	0.675365i	$0.763986\pi$
$48$	0.00213249	−	0.00585898i	0.000307799	−	0.000845671i
$49$	−0.537221	+	0.930494i	−0.0767458	+	0.132928i
$50$	−5.34433	−	9.25666i	−0.755803	−	1.30909i
$51$	0.00580307	+	0.0329108i	0.000812592	+	0.00460844i
$52$	3.77234	+	3.16537i	0.523129	+	0.438957i
$53$	−1.30391	−	1.55394i	−0.179106	−	0.213451i	0.669020	−	0.743244i	$-0.266714\pi$
$53$	−1.30391	−	1.55394i	−0.179106	−	0.213451i	−0.848127	+	0.529794i	$0.822269\pi$
$54$	0.0368414	+	0.00649613i	0.00501348	+	0.000884012i
$55$	13.0809	+	1.21033i	1.76383	+	0.163201i
$56$			2.43425i			0.325290i
$57$	−0.0258170	−	0.00849189i	−0.00341954	−	0.00112478i
$58$	3.80364			0.499443
$59$	−1.84090	−	5.05784i	−0.239665	−	0.658474i	−0.999960	−	0.00889684i	$-0.997168\pi$
$59$	−1.84090	−	5.05784i	−0.239665	−	0.658474i	0.760295	−	0.649578i	$-0.225054\pi$
$60$	−0.0243210	−	0.00428844i	−0.00313982	−	0.000553635i
$61$	−2.89701	−	3.45252i	−0.370924	−	0.442050i	0.548004	−	0.836476i	$-0.315388\pi$
$61$	−2.89701	−	3.45252i	−0.370924	−	0.442050i	−0.918928	+	0.394426i	$0.870944\pi$
$62$	−1.76059	+	2.09818i	−0.223595	+	0.266470i
$63$	−7.19170	+	1.26809i	−0.906069	+	0.159764i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	9.75258	−	16.8920i	1.20966	−	2.09519i
$66$	0.0146952	−	0.0145491i	0.00180886	−	0.00179087i
$67$	−2.58140	+	7.09233i	−0.315368	+	0.866466i	0.676181	+	0.736735i	$0.263634\pi$
$67$	−2.58140	+	7.09233i	−0.315368	+	0.866466i	−0.991549	+	0.129731i	$0.958589\pi$
$68$	4.64175	+	2.67992i	0.562895	+	0.324988i
$69$	−0.0208727	+	0.0120509i	−0.00251278	+	0.00145075i
$70$	9.49531	−	1.67428i	1.13491	−	0.200115i
$71$	−1.81041	+	2.15756i	−0.214856	+	0.256055i	−0.862698	−	0.505719i	$-0.831227\pi$
$71$	−1.81041	+	2.15756i	−0.214856	+	0.256055i	0.647842	+	0.761774i	$0.275672\pi$
$72$	2.29810	−	1.92834i	0.270834	−	0.227257i
$73$	−13.1670	−	2.32169i	−1.54108	−	0.271734i	−0.662401	−	0.749150i	$-0.730462\pi$
$73$	−13.1670	−	2.32169i	−1.54108	−	0.271734i	−0.878677	+	0.477416i	$0.841574\pi$
$74$	4.02566	+	11.0604i	0.467974	+	1.28575i
$75$			0.0666438i			0.00769536i
$76$	−3.70489	+	2.29647i	−0.424980	+	0.263423i
$77$	−3.44852	+	7.29992i	−0.392996	+	0.831903i
$78$	−0.0105013	−	0.0288522i	−0.00118904	−	0.00326686i
$79$	−2.01344	+	11.4188i	−0.226530	+	1.28472i	0.633209	+	0.773981i	$0.281738\pi$
$79$	−2.01344	+	11.4188i	−0.226530	+	1.28472i	−0.859739	+	0.510734i	$0.829374\pi$
$80$	−3.03422	+	2.54601i	−0.339236	+	0.284653i
$81$	6.89413	+	5.78486i	0.766015	+	0.642763i
$82$	−0.821313	−	4.65790i	−0.0906988	−	0.514379i
$83$	10.0333	−	5.79273i	1.10130	−	0.635835i	0.164737	−	0.986338i	$-0.447323\pi$
$83$	10.0333	−	5.79273i	1.10130	−	0.635835i	0.936562	+	0.350503i	$0.113989\pi$
$84$	0.00758876	−	0.0131441i	0.000828002	−	0.00143414i
$85$	7.26099	−	19.9494i	0.787565	−	2.16382i
$86$	0.902294	−	2.47903i	0.0972968	−	0.267321i
$87$	−0.0205384	−	0.0118578i	−0.00220195	−	0.00127129i
$88$	−0.272549	−	3.30541i	−0.0290538	−	0.352358i
$89$	−1.68775	+	0.297596i	−0.178901	+	0.0315452i	−0.262381	−	0.964964i	$-0.584508\pi$
$89$	−1.68775	+	0.297596i	−0.178901	+	0.0315452i	0.0834796	+	0.996509i	$0.473397\pi$
$90$	−9.10254	−	7.63794i	−0.959492	−	0.805109i
$91$	7.70528	+	9.18280i	0.807733	+	0.962619i
$92$	−0.671247	+	3.80683i	−0.0699823	+	0.396889i
$93$	0.0160477	−	0.00584087i	0.00166407	−	0.000605670i
$94$	6.33489			0.653394
$95$	11.5061	+	12.8722i	1.18050	+	1.32066i
$96$			0.00623500i			0.000636357i
$97$	−2.34621	−	6.44617i	−0.238222	−	0.654509i	−0.999978	−	0.00664539i	$-0.997885\pi$
$97$	−2.34621	−	6.44617i	−0.238222	−	0.654509i	0.761756	−	0.647864i	$-0.224338\pi$
$98$	0.186575	−	1.05812i	0.0188469	−	0.106886i
$99$	9.62346	−	2.52713i	0.967195	−	0.253986i
$100$	8.18799	+	6.87054i	0.818799	+	0.687054i
$101$	9.47270	−	1.67029i	0.942569	−	0.166200i	0.318811	−	0.947818i	$-0.396716\pi$
$101$	9.47270	−	1.67029i	0.942569	−	0.166200i	0.623757	+	0.781618i	$0.285605\pi$
$102$	−0.0167093	−	0.0289413i	−0.00165446	−	0.00286562i
$103$	3.46093	+	1.99817i	0.341015	+	0.196885i	0.660721	−	0.750632i	$-0.270251\pi$
$103$	3.46093	+	1.99817i	0.341015	+	0.196885i	−0.319706	+	0.947517i	$0.603584\pi$
$104$	−4.62746	−	1.68426i	−0.453759	−	0.165155i
$105$	−0.0564910	−	0.0205611i	−0.00551296	−	0.00200655i
$106$	1.75676	+	1.01426i	0.170631	+	0.0985141i
$107$	−4.49809	−	7.79093i	−0.434847	−	0.753177i	0.562436	−	0.826841i	$-0.309864\pi$
$107$	−4.49809	−	7.79093i	−0.434847	−	0.753177i	−0.997283	+	0.0736634i	$0.976531\pi$
$108$	−0.0368414	+	0.00649613i	−0.00354506	+	0.000625091i
$109$	−6.21157	−	5.21213i	−0.594961	−	0.499231i	0.294861	−	0.955540i	$-0.404727\pi$
$109$	−6.21157	−	5.21213i	−0.594961	−	0.499231i	−0.889821	+	0.456309i	$0.849171\pi$
$110$	−12.7060	+	3.33660i	−1.21147	+	0.318132i
$111$	0.0127436	−	0.0722726i	0.00120957	−	0.00685981i
$112$	−0.832561	−	2.28744i	−0.0786697	−	0.216143i
$113$		−	11.7945i		−	1.10953i	−0.832006	−	0.554766i	$-0.812808\pi$
$113$		−	11.7945i		−	1.10953i	0.832006	−	0.554766i	$-0.187192\pi$
$114$	0.0271644		0.000850160i	0.00254418		7.96248e-5i
$115$	15.3110			1.42776
$116$	−3.57425	+	1.30092i	−0.331861	+	0.120788i
$117$	2.56532	−	14.5487i	0.237164	−	1.34503i
$118$	3.45976	+	4.12319i	0.318497	+	0.379570i
$119$	9.99470	+	8.38655i	0.916213	+	0.768794i
$120$	0.0243210	−	0.00428844i	0.00222019	−	0.000391479i
$121$	3.86534	−	10.2985i	0.351395	−	0.936227i
$122$	3.90313	+	2.25347i	0.353373	+	0.204020i
$123$	−0.0100862	+	0.0277115i	−0.000909439	+	0.00249866i
$124$	0.936788	−	2.57380i	0.0841261	−	0.231134i
$125$	11.2661	−	19.5134i	1.00767	−	1.74534i
$126$	6.32428	−	3.65132i	0.563411	−	0.325286i
$127$	2.20366	+	12.4976i	0.195543	+	1.10898i	0.911644	+	0.410982i	$0.134814\pi$
$127$	2.20366	+	12.4976i	0.195543	+	1.10898i	−0.716101	+	0.697997i	$0.754075\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−0.0126005	+	0.0105730i	−0.00110941	+	0.000930904i
$130$	−3.38704	+	19.2088i	−0.297063	+	1.68473i
$131$	−0.0869464	−	0.238883i	−0.00759655	−	0.0208713i	0.935836	−	0.352435i	$-0.114646\pi$
$131$	−0.0869464	−	0.238883i	−0.00759655	−	0.0208713i	−0.943433	+	0.331563i	$0.892424\pi$
$132$	−0.00883293	+	0.0186978i	−0.000768808	+	0.00162743i
$133$	−9.85234	+	3.93918i	−0.854306	+	0.341570i
$134$		−	7.54750i		−	0.652005i
$135$	0.0506791	+	0.139240i	0.00436177	+	0.0119839i
$136$	−5.27841	−	0.930725i	−0.452620	−	0.0798090i
$137$	3.87156	−	3.24862i	0.330769	−	0.277548i	−0.462244	−	0.886753i	$-0.652956\pi$
$137$	3.87156	−	3.24862i	0.330769	−	0.277548i	0.793013	+	0.609204i	$0.208511\pi$
$138$	0.0154923	−	0.0184630i	0.00131879	−	0.00157167i
$139$	−9.74979	+	1.71915i	−0.826966	+	0.145816i	−0.571084	−	0.820892i	$-0.693477\pi$
$139$	−9.74979	+	1.71915i	−0.826966	+	0.145816i	−0.255882	+	0.966708i	$0.582366\pi$
$140$	−8.35003	+	4.82089i	−0.705707	+	0.407440i
$141$	−0.0342063	−	0.0197490i	−0.00288069	−	0.00166317i
$142$	0.963297	−	2.64664i	0.0808381	−	0.222101i
$143$	−11.4910	−	11.6064i	−0.960923	−	0.970575i
$144$	−1.49998	+	2.59804i	−0.124998	+	0.216504i
$145$	7.53291	+	13.0474i	0.625574	+	1.08353i
$146$	13.1670	−	2.32169i	1.08971	−	0.192145i
$147$	−0.00430612	+	0.00513184i	−0.000355163	+	0.000423267i
$148$	−7.56577	−	9.01654i	−0.621903	−	0.741155i
$149$	10.2190	+	1.80189i	0.837174	+	0.147616i	0.575769	−	0.817613i	$-0.304703\pi$
$149$	10.2190	+	1.80189i	0.837174	+	0.147616i	0.261406	+	0.965229i	$0.415814\pi$
$150$	−0.0227935	−	0.0626247i	−0.00186108	−	0.00511328i
$151$	10.5401			0.857737			0.428869	−	0.903367i	$-0.358912\pi$
$151$	10.5401			0.857737			0.428869	+	0.903367i	$0.358912\pi$
$152$	2.69602	−	3.42512i	0.218676	−	0.277814i
$153$		−	16.0793i		−	1.29993i
$154$	0.743833	−	8.03915i	0.0599397	−	0.647813i
$155$	−10.6840	−	1.88388i	−0.858160	−	0.151317i
$156$	0.0197360	+	0.0235205i	0.00158015	+	0.00188315i
$157$	−5.24621	−	4.40209i	−0.418693	−	0.351325i	0.408972	−	0.912547i	$-0.365887\pi$
$157$	−5.24621	−	4.40209i	−0.418693	−	0.351325i	−0.827666	+	0.561221i	$0.810332\pi$
$158$	−2.01344	−	11.4188i	−0.160181	−	0.908431i
$159$	−0.00632393	−	0.0109534i	−0.000501521	−	0.000868659i
$160$	1.98045	−	3.43023i	0.156568	−	0.271184i
$161$	−3.21831	+	8.84224i	−0.253639	+	0.696866i
$162$	−8.45690	−	3.07806i	−0.664437	−	0.241835i
$163$	−10.3317	+	17.8950i	−0.809238	+	1.40164i	0.104155	+	0.994561i	$0.466786\pi$
$163$	−10.3317	+	17.8950i	−0.809238	+	1.40164i	−0.913393	+	0.407080i	$0.866547\pi$
$164$	2.36488	+	4.09608i	0.184666	+	0.319850i
$165$	0.0790100	+	0.0215944i	0.00615092	+	0.00168112i
$166$	−7.44699	+	8.87498i	−0.577999	+	0.688832i
$167$	−11.8988	+	9.98424i	−0.920753	+	0.772604i	−0.974134	−	0.225970i	$-0.927445\pi$
$167$	−11.8988	+	9.98424i	−0.920753	+	0.772604i	0.0533808	+	0.998574i	$0.483000\pi$
$168$	−0.00263555	+	0.0149469i	−0.000203337	+	0.00115318i
$169$	−10.5716	+	3.84775i	−0.813201	+	0.295981i
$170$			21.2297i			1.62825i
$171$	11.5236	+	6.18081i	0.881231	+	0.472659i
$172$			2.63813i			0.201156i
$173$	−6.79310	+	2.47249i	−0.516470	+	0.187980i	−0.587087	−	0.809524i	$-0.699725\pi$
$173$	−6.79310	+	2.47249i	−0.516470	+	0.187980i	0.0706172	+	0.997503i	$0.477503\pi$
$174$	0.0233554	+	0.00411819i	0.00177057	+	0.000312199i
$175$	16.7246	+	19.9316i	1.26426	+	1.50669i
$176$	1.38663	+	3.01285i	0.104521	+	0.227102i
$177$	−0.00582754	−	0.0330496i	−0.000438025	−	0.00248416i
$178$	1.48419	−	0.856895i	0.111244	−	0.0642270i
$179$	−18.5205	−	10.6928i	−1.38429	−	0.799218i	−0.391623	−	0.920126i	$-0.628086\pi$
$179$	−18.5205	−	10.6928i	−1.38429	−	0.799218i	−0.992664	+	0.120907i	$0.961420\pi$
$180$	11.1659	+	4.06406i	0.832258	+	0.302917i
$181$	−3.68788	+	10.1324i	−0.274118	+	0.753133i	0.723882	+	0.689923i	$0.242356\pi$
$181$	−3.68788	+	10.1324i	−0.274118	+	0.753133i	−0.998000	+	0.0632094i	$0.979866\pi$
$182$	−10.3813	−	5.99365i	−0.769513	−	0.444279i
$183$	−0.0140504	−	0.0243360i	−0.00103864	−	0.00179897i
$184$	−0.671247	−	3.80683i	−0.0494850	−	0.280643i
$185$	−29.9672	+	35.7135i	−2.20323	+	2.62571i
$186$	−0.0130822	+	0.0109772i	−0.000959232	+	0.000804891i
$187$	−14.5106	−	10.2689i	−1.06112	−	0.750933i
$188$	−5.95285	+	2.16666i	−0.434156	+	0.158020i
$189$	−0.0910645			−0.00662397
$190$	−15.2148	−	8.16062i	−1.10379	−	0.592033i
$191$	5.47610			0.396237			0.198118	−	0.980178i	$-0.436517\pi$
$191$	5.47610			0.396237			0.198118	+	0.980178i	$0.436517\pi$
$192$	−0.00213249	−	0.00585898i	−0.000153900	−	0.000422835i
$193$	2.98682	−	16.9391i	0.214996	−	1.21930i	−0.665918	−	0.746025i	$-0.731960\pi$
$193$	2.98682	−	16.9391i	0.214996	−	1.21930i	0.880914	−	0.473277i	$-0.156929\pi$
$194$	4.40944	+	5.25497i	0.316579	+	0.377285i
$195$	0.0781723	−	0.0931622i	0.00559804	−	0.00667148i
$196$	0.186575	+	1.05812i	0.0133268	+	0.0755799i
$197$	−20.4611	+	11.8132i	−1.45779	+	0.841655i	−0.998902	−	0.0468394i	$-0.985085\pi$
$197$	−20.4611	+	11.8132i	−1.45779	+	0.841655i	−0.458887	+	0.888495i	$0.651752\pi$
$198$	−8.17877	+	5.66614i	−0.581240	+	0.402675i
$199$	−8.36281	−	3.04381i	−0.592824	−	0.215770i	0.0281472	−	0.999604i	$-0.491039\pi$
$199$	−8.36281	−	3.04381i	−0.592824	−	0.215770i	−0.620971	+	0.783834i	$0.713262\pi$
$200$	−10.0441	−	3.65574i	−0.710222	−	0.258500i
$201$	−0.0235293	+	0.0407540i	−0.00165963	+	0.00287456i
$202$	−8.33015	+	4.80942i	−0.586107	+	0.338389i
$203$	−9.11834	+	1.60781i	−0.639982	+	0.112846i
$204$	0.0256001	+	0.0214810i	0.00179236	+	0.00150397i
$205$	14.3511	−	12.0420i	1.00232	−	0.841050i
$206$	−3.93562	−	0.693956i	−0.274208	−	0.0483502i
$207$	10.8972	−	3.96624i	0.757405	−	0.275673i
$208$	4.92444			0.341448
$209$	12.9372	−	6.45202i	0.894886	−	0.446296i
$210$	0.0601165			0.00414843
$211$	−14.5473	+	5.29478i	−1.00148	+	0.364508i	−0.790154	−	0.612909i	$-0.789999\pi$
$211$	−14.5473	+	5.29478i	−1.00148	+	0.364508i	−0.211323	+	0.977416i	$0.567777\pi$
$212$	−1.99771	−	0.352250i	−0.137203	−	0.0241927i
$213$	−0.0134524	+	0.0112879i	−0.000921741	+	0.000773432i
$214$	6.89148	+	5.78264i	0.471092	+	0.395293i
$215$	10.2906	−	1.81451i	0.701813	−	0.123749i
$216$	0.0323978	−	0.0187049i	0.00220439	−	0.00127270i
$217$	3.33368	−	5.77411i	0.226305	−	0.391972i
$218$	7.61962	+	2.77332i	0.516066	+	0.187833i
$219$	−0.0783351	−	0.0285117i	−0.00529340	−	0.00192664i
$220$	10.7985	−	7.48109i	0.728038	−	0.504375i
$221$	−22.8580	+	13.1971i	−1.53760	+	0.887732i
$222$	0.0127436	+	0.0722726i	0.000855295	+	0.00485062i
$223$	15.8580	−	18.8988i	1.06193	−	1.26556i	0.0992046	−	0.995067i	$-0.468370\pi$
$223$	15.8580	−	18.8988i	1.06193	−	1.26556i	0.962723	−	0.270489i	$-0.0871854\pi$
$224$	1.56470	+	1.86474i	0.104546	+	0.124593i
$225$	5.56813	−	31.5784i	0.371209	−	2.10523i
$226$	4.03395	+	11.0832i	0.268335	+	0.737243i
$227$	−6.82371			−0.452905			−0.226453	−	0.974022i	$-0.572713\pi$
$227$	−6.82371			−0.452905			−0.226453	+	0.974022i	$0.572713\pi$
$228$	−0.0252354	+	0.0100897i	−0.00167126	+	0.000668204i
$229$	7.06767			0.467045			0.233522	−	0.972351i	$-0.424975\pi$
$229$	7.06767			0.467045			0.233522	+	0.972351i	$0.424975\pi$
$230$	−14.3877	+	5.23669i	−0.948695	+	0.345297i
$231$	−0.0290785	+	0.0410898i	−0.00191322	+	0.00270351i
$232$	2.91376	−	2.44493i	0.191298	−	0.160518i
$233$	2.67711	−	3.19046i	0.175383	−	0.209014i	−0.671191	−	0.741285i	$-0.734217\pi$
$233$	2.67711	−	3.19046i	0.175383	−	0.209014i	0.846574	+	0.532271i	$0.178661\pi$
$234$	2.56532	+	14.5487i	0.167701	+	0.951077i
$235$	12.5459	+	21.7302i	0.818405	+	1.41752i
$236$	−4.66133	−	2.69122i	−0.303427	−	0.175183i
$237$	−0.0247262	+	0.0679346i	−0.00160614	+	0.00441283i
$238$	−12.2603	−	4.46239i	−0.794718	−	0.289254i
$239$	14.5373	+	8.39309i	0.940337	+	0.542904i	0.890066	−	0.455832i	$-0.150658\pi$
$239$	14.5373	+	8.39309i	0.940337	+	0.542904i	0.0502708	+	0.998736i	$0.483992\pi$
$240$	−0.0213875	+	0.0123481i	−0.00138056	+	0.000797065i
$241$	1.41761	+	8.03968i	0.0913165	+	0.517882i	0.995814	+	0.0914027i	$0.0291350\pi$
$241$	1.41761	+	8.03968i	0.0913165	+	0.517882i	−0.904498	+	0.426479i	$0.859754\pi$
$242$	−0.109936	+	10.9995i	−0.00706697	+	0.707071i
$243$	0.108208	+	0.128957i	0.00694156	+	0.00827262i
$244$	−4.43848	−	0.782624i	−0.284145	−	0.0501023i
$245$	3.99909	−	1.45555i	0.255493	−	0.0929918i
$246$		−	0.0294900i		−	0.00188021i
$247$	−0.671461	−	21.4546i	−0.0427241	−	1.36512i
$248$			2.73899i			0.173926i
$249$	0.0678790	−	0.0247059i	0.00430166	−	0.00156567i
$250$	−3.91267	+	22.1899i	−0.247459	+	1.40341i
$251$	−12.0925	+	10.1468i	−0.763272	+	0.640461i	−0.938976	−	0.343982i	$-0.888224\pi$
$251$	−12.0925	+	10.1468i	−0.763272	+	0.640461i	0.175705	+	0.984443i	$0.443780\pi$
$252$	−4.69405	+	5.59415i	−0.295697	+	0.352398i
$253$	3.38006	−	12.3670i	0.212502	−	0.777507i
$254$	−6.34517	−	10.9902i	−0.398132	−	0.689584i
$255$	0.0661836	−	0.114633i	0.00414458	−	0.00717862i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	10.2127	−	28.0592i	0.637051	−	1.75028i	−0.0237449	−	0.999718i	$-0.507559\pi$
$257$	10.2127	−	28.0592i	0.637051	−	1.75028i	0.660796	−	0.750566i	$-0.270219\pi$
$258$	0.00822436	−	0.0142450i	0.000512027	−	0.000886856i
$259$	−14.3259	−	24.8131i	−0.890165	−	1.54181i
$260$	−3.38704	−	19.2088i	−0.210055	−	1.19128i
$261$	8.74116	+	7.33471i	0.541064	+	0.454007i
$262$	0.163406	+	0.194740i	0.0100952	+	0.0120310i
$263$	26.5764	+	4.68614i	1.63877	+	0.288960i	0.915715	−	0.401827i	$-0.131625\pi$
$263$	26.5764	+	4.68614i	1.63877	+	0.288960i	0.723058	+	0.690787i	$0.242736\pi$
$264$	0.00190523	−	0.0205912i	0.000117259	−	0.00126730i
$265$			8.03478i			0.493573i
$266$	7.91089	−	7.07131i	0.485048	−	0.433570i
$267$	−0.0106855			−0.000653940
$268$	2.58140	+	7.09233i	0.157684	+	0.433233i
$269$	11.3536	+	2.00195i	0.692244	+	0.122061i	0.508692	−	0.860949i	$-0.330129\pi$
$269$	11.3536	+	2.00195i	0.692244	+	0.122061i	0.183552	+	0.983010i	$0.441240\pi$
$270$	−0.0952456	−	0.113509i	−0.00579646	−	0.00690796i
$271$	−12.4702	+	14.8614i	−0.757513	+	0.902768i	−0.997688	−	0.0679612i	$-0.978351\pi$
$271$	−12.4702	+	14.8614i	−0.757513	+	0.902768i	0.240175	+	0.970729i	$0.422795\pi$
$272$	5.27841	−	0.930725i	0.320050	−	0.0564335i
$273$	0.0373704	+	0.0647274i	0.00226176	+	0.00391748i
$274$	−2.52698	+	4.37686i	−0.152660	+	0.264416i
$275$	−24.9416	−	25.1921i	−1.50403	−	1.51914i
$276$	−0.00824327	+	0.0226482i	−0.000496187	+	0.00136326i
$277$	14.8786	+	8.59014i	0.893966	+	0.516131i	0.875238	−	0.483693i	$-0.160705\pi$
$277$	14.8786	+	8.59014i	0.893966	+	0.516131i	0.0187281	+	0.999825i	$0.494038\pi$
$278$	8.57382	−	4.95010i	0.514223	−	0.296887i
$279$	−8.09202	+	1.42684i	−0.484456	+	0.0854228i
$280$	6.19762	−	7.38604i	0.370379	−	0.441400i
$281$	−1.40891	+	1.18221i	−0.0840482	+	0.0705248i	−0.683844	−	0.729628i	$-0.739693\pi$
$281$	−1.40891	+	1.18221i	−0.0840482	+	0.0705248i	0.599796	+	0.800153i	$0.295249\pi$
$282$	0.0388980	+	0.00685876i	0.00231634	+	0.000408433i
$283$	−10.9623	−	30.1188i	−0.651643	−	1.79038i	−0.611586	−	0.791178i	$-0.709468\pi$
$283$	−10.9623	−	30.1188i	−0.651643	−	1.79038i	−0.0400568	−	0.999197i	$-0.512754\pi$
$284$			2.81649i			0.167128i
$285$	0.0567139	+	0.0914966i	0.00335944	+	0.00541979i
$286$	14.7676	+	6.97630i	0.873227	+	0.412517i
$287$	3.93781	+	10.8190i	0.232442	+	0.638628i
$288$	0.520938	−	2.95438i	0.0306966	−	0.174089i
$289$	−8.98403	+	7.53850i	−0.528472	+	0.443441i
$290$	−11.5411	−	9.68412i	−0.677716	−	0.568671i
$291$	−0.00742715	−	0.0421215i	−0.000435387	−	0.00246920i
$292$	−11.5788	+	6.68505i	−0.677601	+	0.391213i
$293$	3.79057	−	6.56547i	0.221448	−	0.383559i	−0.733800	−	0.679365i	$-0.762255\pi$
$293$	3.79057	−	6.56547i	0.221448	−	0.383559i	0.955248	+	0.295807i	$0.0955884\pi$
$294$	0.00229124	−	0.00629513i	0.000133628	−	0.000367140i
$295$	−7.29162	+	20.0335i	−0.424534	+	1.16640i
$296$	10.1933	+	5.88513i	0.592476	+	0.342066i
$297$	0.123654	−	0.0101960i	0.00717516	−	0.000591630i
$298$	−10.2190	+	1.80189i	−0.591972	+	0.104381i
$299$	−14.5822	−	12.2359i	−0.843309	−	0.707620i
$300$	0.0428378	+	0.0510521i	0.00247324	+	0.00294749i
$301$	−1.11514	+	6.32430i	−0.0642758	+	0.364526i
$302$	−9.90441	+	3.60491i	−0.569935	+	0.207439i
$303$	0.0599734			0.00344538
$304$	−1.36197	+	4.14066i	−0.0781144	+	0.237483i
$305$			17.8515i			1.02218i
$306$	5.49944	+	15.1096i	0.314382	+	0.863758i
$307$	1.54307	−	8.75119i	0.0880677	−	0.499457i	−0.908585	−	0.417701i	$-0.862836\pi$
$307$	1.54307	−	8.75119i	0.0880677	−	0.499457i	0.996652	−	0.0817562i	$-0.0260529\pi$
$308$	2.05058	+	7.80873i	0.116842	+	0.444944i
$309$	0.0190876	+	0.0160164i	0.00108586	+	0.000911142i
$310$	10.6840	−	1.88388i	0.606811	−	0.106997i
$311$	4.40362	+	7.62729i	0.249706	+	0.432504i	0.963444	−	0.267909i	$-0.0863326\pi$
$311$	4.40362	+	7.62729i	0.249706	+	0.432504i	−0.713738	+	0.700413i	$0.752999\pi$
$312$	−0.0265903	−	0.0153519i	−0.00150538	−	0.000869131i
$313$	−15.7278	−	5.72447i	−0.888990	−	0.323566i	−0.143158	−	0.989700i	$-0.545726\pi$
$313$	−15.7278	−	5.72447i	−0.888990	−	0.323566i	−0.745832	+	0.666134i	$0.767948\pi$
$314$	6.43543	+	2.34231i	0.363172	+	0.132184i
$315$	25.0498	+	14.4625i	1.41140	+	0.814869i
$316$	5.79748	+	10.0415i	0.326134	+	0.564880i
$317$	11.5424	−	2.03523i	0.648284	−	0.114310i	0.160169	−	0.987090i	$-0.448796\pi$
$317$	11.5424	−	2.03523i	0.648284	−	0.114310i	0.488114	+	0.872780i	$0.337685\pi$
$318$	0.00968883	+	0.00812989i	0.000543323	+	0.000455902i
$319$	12.2016	−	3.20413i	0.683156	−	0.179397i
$320$	−0.687802	+	3.90072i	−0.0384493	+	0.218057i
$321$	−0.0191843	−	0.0527085i	−0.00107076	−	0.00294190i
$322$		−	9.40972i		−	0.524383i
$323$	−4.77468	−	22.8699i	−0.265670	−	1.27251i
$324$	8.99965			0.499981
$325$	−49.4613	+	18.0025i	−2.74362	+	0.998596i
$326$	3.58815	−	20.3494i	0.198729	−	1.12705i
$327$	−0.0324976	−	0.0387291i	−0.00179712	−	0.00214173i
$328$	−3.62320	−	3.04023i	−0.200058	−	0.167868i
$329$	−15.1864	+	2.67778i	−0.837254	+	0.147631i
$330$	−0.0816308	+	0.00673090i	−0.00449363	+	0.000370524i
$331$	22.2367	+	12.8384i	1.22224	+	0.705661i	0.965395	−	0.260791i	$-0.0839835\pi$
$331$	22.2367	+	12.8384i	1.22224	+	0.705661i	0.256846	+	0.966452i	$0.417317\pi$
$332$	3.96246	−	10.8868i	0.217468	−	0.597489i
$333$	−12.0768	+	33.1808i	−0.661807	+	1.81830i
$334$	7.76636	−	13.4517i	0.424956	−	0.736046i
$335$	25.8897	−	14.9474i	1.41451	−	0.816665i
$336$	−0.00263555	−	0.0149469i	−0.000143781	−	0.000815422i
$337$	18.7051	+	15.6954i	1.01893	+	0.854985i	0.989493	−	0.144581i	$-0.0461835\pi$
$337$	18.7051	+	15.6954i	1.01893	+	0.854985i	0.0294389	+	0.999567i	$0.490628\pi$
$338$	8.61805	−	7.23140i	0.468760	−	0.393337i
$339$	0.0127698	−	0.0724214i	0.000693563	−	0.00393339i
$340$	−7.26099	−	19.9494i	−0.393783	−	1.08191i
$341$	−3.88024	+	8.21378i	−0.210127	+	0.444801i
$342$	−12.9426	−	1.86676i	−0.699855	−	0.100943i
$343$			19.6552i			1.06128i
$344$	−0.902294	−	2.47903i	−0.0486484	−	0.133660i
$345$	0.0940140	+	0.0165772i	0.00506154	+	0.000892487i
$346$	5.53778	−	4.64675i	0.297713	−	0.249811i
$347$	−23.5305	+	28.0426i	−1.26318	+	1.50540i	−0.489243	+	0.872147i	$0.662727\pi$
$347$	−23.5305	+	28.0426i	−1.26318	+	1.50540i	−0.773941	+	0.633257i	$0.781718\pi$
$348$	−0.0233554	+	0.00411819i	−0.00125198	+	0.000220758i
$349$	1.44957	−	0.836907i	0.0775934	−	0.0447986i	−0.460701	−	0.887555i	$-0.652402\pi$
$349$	1.44957	−	0.836907i	0.0775934	−	0.0447986i	0.538295	+	0.842757i	$0.319069\pi$
$350$	−22.5330	−	13.0094i	−1.20444	−	0.695383i
$351$	0.0630076	−	0.173112i	0.00336310	−	0.00924003i
$352$	−2.33346	−	2.35690i	−0.124374	−	0.125623i
$353$	10.6215	−	18.3969i	0.565324	−	0.979170i	−0.431695	−	0.902019i	$-0.642084\pi$
$353$	10.6215	−	18.3969i	0.565324	−	0.979170i	0.997019	−	0.0771507i	$-0.0245822\pi$
$354$	0.0167797	+	0.0290634i	0.000891833	+	0.00154470i
$355$	10.9863	−	1.93719i	0.583094	−	0.102815i
$356$	−1.10160	+	1.31284i	−0.0583848	+	0.0695803i
$357$	0.0522901	+	0.0623169i	0.00276749	+	0.00329816i
$358$	21.0607	+	3.71358i	1.11309	+	0.196269i
$359$	0.317775	+	0.873078i	0.0167715	+	0.0460793i	0.947796	−	0.318878i	$-0.103306\pi$
$359$	0.317775	+	0.873078i	0.0167715	+	0.0460793i	−0.931024	+	0.364957i	$0.881084\pi$
$360$	−11.8825			−0.626264
$361$	18.2256	+	5.36920i	0.959241	+	0.282590i
$362$		−	10.7826i		−	0.566723i
$363$	0.0348844	−	0.0590506i	0.00183096	−	0.00309935i
$364$	11.8052	+	2.08157i	0.618760	+	0.109104i
$365$	34.0404	+	40.5678i	1.78176	+	2.12342i
$366$	0.0215265	+	0.0180629i	0.00112521	+	0.000944161i
$367$	0.819895	+	4.64986i	0.0427982	+	0.242720i	0.998700	−	0.0509644i	$-0.0162295\pi$
$367$	0.819895	+	4.64986i	0.0427982	+	0.242720i	−0.955902	+	0.293685i	$0.905118\pi$
$368$	1.93278	+	3.34767i	0.100753	+	0.174509i
$369$	7.09454	−	12.2881i	0.369327	−	0.639693i
$370$	15.9452	−	43.8091i	0.828953	−	2.27753i
$371$	−4.64015	−	1.68887i	−0.240904	−	0.0876820i
$372$	0.00853878	−	0.0147896i	0.000442715	−	0.000766805i
$373$	−17.1417	−	29.6902i	−0.887562	−	1.53730i	−0.842749	−	0.538307i	$-0.819064\pi$
$373$	−17.1417	−	29.6902i	−0.887562	−	1.53730i	−0.0448128	−	0.998995i	$-0.514269\pi$
$374$	17.1476	+	4.68666i	0.886683	+	0.242341i
$375$	0.0903040	−	0.107620i	0.00466328	−	0.00555748i
$376$	4.85281	−	4.07199i	0.250265	−	0.209997i
$377$	3.25257	−	18.4462i	0.167516	−	0.950029i
$378$	0.0855727	−	0.0311459i	0.00440138	−	0.00160197i
$379$		−	13.5865i		−	0.697894i	−0.937142	−	0.348947i	$-0.886539\pi$
$379$		−	13.5865i		−	0.697894i	0.937142	−	0.348947i	$-0.113461\pi$
$380$	17.0883	+	2.46472i	0.876611	+	0.126437i
$381$			0.0791243i			0.00405366i
$382$	−5.14585	+	1.87294i	−0.263285	+	0.0958278i
$383$	−5.26717	−	0.928745i	−0.269140	−	0.0474566i	0.0374493	−	0.999299i	$-0.488077\pi$
$383$	−5.26717	−	0.928745i	−0.269140	−	0.0474566i	−0.306589	+	0.951842i	$0.599188\pi$
$384$	0.00400778	+	0.00477628i	0.000204521	+	0.000243739i
$385$	29.0493	−	13.3696i	1.48049	−	0.681377i
$386$	2.98682	+	16.9391i	0.152025	+	0.862177i
$387$	6.85397	−	3.95714i	0.348407	−	0.201153i
$388$	−5.94082	−	3.42994i	−0.301600	−	0.174129i
$389$	8.13328	+	2.96027i	0.412374	+	0.150092i	0.539872	−	0.841747i	$-0.318473\pi$
$389$	8.13328	+	2.96027i	0.412374	+	0.150092i	−0.127499	+	0.991839i	$0.540695\pi$
$390$	−0.0415946	+	0.114280i	−0.00210623	+	0.00578681i
$391$	−17.9429	−	10.3594i	−0.907414	−	0.523896i
$392$	−0.537221	−	0.930494i	−0.0271338	−	0.0469970i
$393$	−0.000275237	−	0.00156095i	−1.38839e−5	−	7.87393e-5i
$394$	15.1867	−	18.0989i	0.765097	−	0.911808i
$395$	35.1816	−	29.5209i	1.77018	−	1.48536i
$396$	5.74760	−	8.12173i	0.288828	−	0.408132i
$397$	3.91664	−	1.42554i	0.196570	−	0.0715458i	−0.241859	−	0.970311i	$-0.577757\pi$
$397$	3.91664	−	1.42554i	0.196570	−	0.0715458i	0.438429	+	0.898766i	$0.355535\pi$
$398$	8.89952			0.446092
$399$	−0.0647609	+	0.0135205i	−0.00324210	+	0.000676873i
$400$	10.6887			0.534433
$401$	12.0245	+	33.0370i	0.600475	+	1.64979i	0.750315	+	0.661081i	$0.229902\pi$
$401$	12.0245	+	33.0370i	0.600475	+	1.64979i	−0.149840	+	0.988710i	$0.547876\pi$
$402$	0.00817165	−	0.0463437i	0.000407565	−	0.00231141i
$403$	8.66989	+	10.3324i	0.431878	+	0.514692i
$404$	6.18286	−	7.36845i	0.307609	−	0.366594i
$405$	−6.18997	−	35.1051i	−0.307582	−	1.74439i
$406$	8.01853	−	4.62950i	0.397953	−	0.229758i
$407$	22.2309	+	32.0892i	1.10195	+	1.59060i
$408$	−0.0314032	−	0.0114298i	−0.00155469	−	0.000565860i
$409$	−36.6741	−	13.3483i	−1.81342	−	0.660029i	−0.996530	−	0.0832292i	$-0.973477\pi$
$409$	−36.6741	−	13.3483i	−1.81342	−	0.660029i	−0.816885	−	0.576800i	$-0.804301\pi$
$410$	−9.36702	+	16.2242i	−0.462604	+	0.801254i
$411$	0.0272897	−	0.0157557i	0.00134610	−	0.000777172i
$412$	3.93562	−	0.693956i	0.193894	−	0.0341888i
$413$	−10.0369	−	8.42192i	−0.493881	−	0.414416i
$414$	−8.88345	+	7.45410i	−0.436598	+	0.366349i
$415$	−45.1916	−	7.96850i	−2.21837	−	0.391158i
$416$	−4.62746	+	1.68426i	−0.226880	+	0.0825775i
$417$	−0.0617277			−0.00302282
$418$	−9.95028	+	10.4877i	−0.486684	+	0.512970i
$419$	−17.7667			−0.867962			−0.433981	−	0.900922i	$-0.642892\pi$
$419$	−17.7667			−0.867962			−0.433981	+	0.900922i	$0.642892\pi$
$420$	−0.0564910	+	0.0205611i	−0.00275648	+	0.00100328i
$421$	35.6435	+	6.28491i	1.73716	+	0.306308i	0.950418	−	0.310977i	$-0.100656\pi$
$421$	35.6435	+	6.28491i	1.73716	+	0.306308i	0.786740	+	0.617284i	$0.211767\pi$
$422$	11.8591	−	9.95093i	0.577290	−	0.484404i
$423$	14.5582	+	12.2158i	0.707846	+	0.593953i
$424$	1.99771	−	0.352250i	0.0970174	−	0.0171068i
$425$	−49.6141	+	28.6447i	−2.40664	+	1.38947i
$426$	0.00878041	−	0.0152081i	0.000425412	−	0.000736835i
$427$	−10.3094	−	3.75231i	−0.498907	−	0.181587i
$428$	−8.45365	−	3.07688i	−0.408623	−	0.148727i
$429$	−0.0579915	−	0.0837076i	−0.00279986	−	0.00404144i
$430$	−9.04940	+	5.22467i	−0.436401	+	0.251956i
$431$	−3.88789	−	22.0493i	−0.187273	−	1.06208i	−0.923000	−	0.384800i	$-0.874270\pi$
$431$	−3.88789	−	22.0493i	−0.187273	−	1.06208i	0.735727	−	0.677278i	$-0.236841\pi$
$432$	−0.0240465	+	0.0286575i	−0.00115694	+	0.00137879i
$433$	−9.82627	−	11.7105i	−0.472220	−	0.562770i	0.476383	−	0.879238i	$-0.341948\pi$
$433$	−9.82627	−	11.7105i	−0.472220	−	0.562770i	−0.948603	+	0.316468i	$0.897503\pi$
$434$	−1.15778	+	6.56608i	−0.0555750	+	0.315182i
$435$	0.0321278	+	0.0882703i	0.00154041	+	0.00423224i
$436$	−8.10863			−0.388333
$437$	14.3215	−	8.87712i	0.685089	−	0.424650i
$438$	0.0833625			0.00398322
$439$	−24.9622	+	9.08550i	−1.19138	+	0.433627i	−0.860208	−	0.509943i	$-0.829666\pi$
$439$	−24.9622	+	9.08550i	−1.19138	+	0.433627i	−0.331173	+	0.943570i	$0.607444\pi$
$440$	−7.58864	+	10.7232i	−0.361774	+	0.511211i
$441$	2.46918	−	2.07189i	0.117580	−	0.0986613i
$442$	16.9658	−	20.2191i	0.806983	−	0.961724i
$443$	5.34684	+	30.3234i	0.254036	+	1.44071i	0.798535	+	0.601949i	$0.205609\pi$
$443$	5.34684	+	30.3234i	0.254036	+	1.44071i	−0.544499	+	0.838762i	$0.683280\pi$
$444$	−0.0366937	−	0.0635554i	−0.00174141	−	0.00301621i
$445$	5.87870	+	3.39407i	0.278677	+	0.160894i
$446$	−8.43785	+	23.1828i	−0.399544	+	1.09774i
$447$	0.0607966	+	0.0221282i	0.00287558	+	0.00104663i
$448$	−2.10812	−	1.21712i	−0.0995993	−	0.0575037i
$449$	13.6295	−	7.86900i	0.643216	−	0.371361i	−0.142636	−	0.989775i	$-0.545558\pi$
$449$	13.6295	−	7.86900i	0.643216	−	0.371361i	0.785852	+	0.618414i	$0.212225\pi$
$450$	5.56813	+	31.5784i	0.262484	+	1.48862i
$451$	−6.55840	−	14.2500i	−0.308823	−	0.671008i
$452$	−7.58135	−	9.03511i	−0.356597	−	0.424976i
$453$	0.0647188	+	0.0114117i	0.00304075	+	0.000536167i
$454$	6.41219	−	2.33385i	0.300939	−	0.109533i
$455$		−	47.4804i		−	2.22591i
$456$	0.0202627	−	0.0181122i	0.000948887	−	0.000848182i
$457$			8.71652i			0.407742i	0.978998	+	0.203871i	$0.0653523\pi$
$457$			8.71652i			0.407742i	−0.978998	+	0.203871i	$0.934648\pi$
$458$	−6.64144	+	2.41729i	−0.310334	+	0.112952i
$459$	0.0348182	−	0.197464i	0.00162517	−	0.00921682i
$460$	11.7289	−	9.84175i	0.546865	−	0.458874i
$461$	−7.57092	+	9.02267i	−0.352613	+	0.420228i	−0.912972	−	0.408022i	$-0.866219\pi$
$461$	−7.57092	+	9.02267i	−0.352613	+	0.420228i	0.560359	+	0.828250i	$0.310663\pi$
$462$	0.0132713	−	0.0485572i	0.000617436	−	0.00225909i
$463$	16.5088	+	28.5942i	0.767231	+	1.32888i	0.939059	+	0.343756i	$0.111699\pi$
$463$	16.5088	+	28.5942i	0.767231	+	1.32888i	−0.171828	+	0.985127i	$0.554967\pi$
$464$	−1.90182	+	3.29405i	−0.0882898	+	0.152922i
$465$	−0.0635631	−	0.0231351i	−0.00294767	−	0.00107286i
$466$	−1.42446	+	3.91367i	−0.0659869	+	0.181297i
$467$	−14.4212	+	24.9782i	−0.667333	+	1.15585i	0.311315	+	0.950307i	$0.399231\pi$
$467$	−14.4212	+	24.9782i	−0.667333	+	1.15585i	−0.978647	+	0.205547i	$0.934103\pi$
$468$	−7.38656	−	12.7939i	−0.341444	−	0.591398i
$469$	3.19035	+	18.0934i	0.147317	+	0.835474i
$470$	−19.2215	−	16.1287i	−0.886619	−	0.743962i
$471$	−0.0274470	−	0.0327101i	−0.00126469	−	0.00150720i
$472$	5.30067	+	0.934651i	0.243983	+	0.0430208i
$473$	0.806133	−	8.71247i	0.0370660	−	0.400600i
$474$		−	0.0722945i		−	0.00332060i
$475$	−1.45743	−	46.5680i	−0.0668715	−	2.13669i
$476$	13.0472			0.598016
$477$	2.08137	+	5.71851i	0.0952992	+	0.261832i
$478$	−16.5312	−	2.91489i	−0.756117	−	0.133324i
$479$	0.917930	+	1.09395i	0.0419413	+	0.0499837i	0.786607	−	0.617454i	$-0.211836\pi$
$479$	0.917930	+	1.09395i	0.0419413	+	0.0499837i	−0.744666	+	0.667437i	$0.767391\pi$
$480$	0.0158744	−	0.0189183i	0.000724563	−	0.000863500i
$481$	57.0813	−	10.0650i	2.60268	−	0.458923i
$482$	−4.08185	−	7.06998i	−0.185923	−	0.322029i
$483$	−0.0293348	+	0.0508093i	−0.00133478	+	0.00231190i
$484$	−3.65873	−	10.3737i	−0.166306	−	0.471532i
$485$	−9.29310	+	25.5326i	−0.421978	+	1.15937i
$486$	−0.145788	−	0.0841710i	−0.00661310	−	0.00381807i
$487$	−27.5122	+	15.8842i	−1.24670	+	0.719780i	−0.970449	−	0.241306i	$-0.922424\pi$
$487$	−27.5122	+	15.8842i	−1.24670	+	0.719780i	−0.276247	+	0.961087i	$0.589091\pi$
$488$	4.43848	−	0.782624i	0.200921	−	0.0354277i
$489$	−0.0828140	+	0.0986938i	−0.00374498	+	0.00446309i
$490$	−3.26009	+	2.73554i	−0.147276	+	0.123579i
$491$	12.8748	+	2.27017i	0.581030	+	0.102451i	0.456436	−	0.889756i	$-0.349126\pi$
$491$	12.8748	+	2.27017i	0.581030	+	0.102451i	0.124595	+	0.992208i	$0.460237\pi$
$492$	0.0100862	+	0.0277115i	0.000454720	+	0.00124933i
$493$		−	20.3869i		−	0.918179i
$494$	7.96888	+	19.9311i	0.358537	+	0.896742i
$495$	−35.6338	−	16.8336i	−1.60162	−	0.756614i
$496$	−0.936788	−	2.57380i	−0.0420630	−	0.115567i
$497$	−1.19054	+	6.75188i	−0.0534029	+	0.302863i
$498$	−0.0553355	+	0.0464320i	−0.00247964	+	0.00208067i
$499$	−7.55098	−	6.33602i	−0.338028	−	0.283639i	0.457933	−	0.888987i	$-0.348590\pi$
$499$	−7.55098	−	6.33602i	−0.338028	−	0.283639i	−0.795962	+	0.605347i	$0.793034\pi$
$500$	−3.91267	−	22.1899i	−0.174980	−	0.992361i
$501$	−0.0838715	+	0.0484232i	−0.00374710	+	0.00216339i
$502$	7.89282	−	13.6708i	0.352274	−	0.610156i
$503$	4.52517	−	12.4328i	0.201767	−	0.554351i	−0.797001	−	0.603979i	$-0.793581\pi$
$503$	4.52517	−	12.4328i	0.201767	−	0.554351i	0.998768	+	0.0496277i	$0.0158035\pi$
$504$	2.49765	−	6.86224i	0.111254	−	0.305669i
$505$	−32.9948	−	19.0496i	−1.46825	−	0.847695i
$506$	1.05355	+	12.7772i	0.0468361	+	0.568017i
$507$	−0.0690785	+	0.0121804i	−0.00306788	+	0.000540951i
$508$	9.72137	+	8.15720i	0.431316	+	0.361917i
$509$	−9.97564	−	11.8885i	−0.442162	−	0.526948i	0.498228	−	0.867046i	$-0.333984\pi$
$509$	−9.97564	−	11.8885i	−0.442162	−	0.526948i	−0.940390	+	0.340098i	$0.889540\pi$
$510$	−0.0229853	+	0.130356i	−0.00101781	+	0.00577227i
$511$	−30.5834	+	11.1314i	−1.35293	+	0.492425i
$512$	1.00000			0.0441942
$513$	0.128133	+	0.100857i	0.00565721	+	0.00445297i
$514$			29.8600i			1.31707i
$515$	−5.41385	−	14.8744i	−0.238563	−	0.655446i
$516$	−0.00285629	+	0.0161988i	−0.000125741	+	0.000713114i
$517$	20.3215	−	5.33642i	0.893737	−	0.234696i
$518$	21.9485	+	18.4170i	0.964361	+	0.809195i
$519$	−0.0443884	+	0.00782688i	−0.00194844	+	0.000343562i
$520$	9.75258	+	16.8920i	0.427679	+	0.740762i
$521$	11.3055	+	6.52722i	0.495302	+	0.285963i	0.726771	−	0.686880i	$-0.241020\pi$
$521$	11.3055	+	6.52722i	0.495302	+	0.285963i	−0.231470	+	0.972842i	$0.574353\pi$
$522$	−10.7226	−	3.90272i	−0.469316	−	0.170817i
$523$	31.5302	+	11.4760i	1.37872	+	0.501813i	0.921790	−	0.387690i	$-0.126727\pi$
$523$	31.5302	+	11.4760i	1.37872	+	0.501813i	0.456929	+	0.889503i	$0.348949\pi$
$524$	−0.220156	−	0.127107i	−0.00961757	−	0.00555270i
$525$	0.0811137	+	0.140493i	0.00354009	+	0.00613162i
$526$	−26.5764	+	4.68614i	−1.15879	+	0.204326i
$527$	11.2459	+	9.43645i	0.489880	+	0.411058i
$528$	0.00525227	+	0.0200010i	0.000228576	+	0.000870432i
$529$	−1.39917	+	7.93507i	−0.0608334	+	0.345003i
$530$	−2.74806	−	7.55023i	−0.119368	−	0.327961i
$531$			16.1471i			0.700725i
$532$	−5.01527	+	9.35054i	−0.217440	+	0.405397i
$533$	−23.2914			−1.00886
$534$	0.0100411	−	0.00365465i	0.000434519	−	0.000158152i
$535$	−6.18759	+	35.0916i	−0.267513	+	1.51714i
$536$	−4.85144	−	5.78172i	−0.209550	−	0.249732i
$537$	−0.102144	−	0.0857088i	−0.00440783	−	0.00369861i
$538$	−11.3536	+	2.00195i	−0.489490	+	0.0863104i
$539$	−0.292838	−	3.55147i	−0.0126134	−	0.152973i
$540$	0.128324	+	0.0740880i	0.00552219	+	0.00318824i
$541$	11.0418	−	30.3372i	0.474726	−	1.30430i	−0.439190	−	0.898394i	$-0.644734\pi$
$541$	11.0418	−	30.3372i	0.474726	−	1.30430i	0.913916	−	0.405904i	$-0.133043\pi$
$542$	6.63527	−	18.2303i	0.285009	−	0.783057i
$543$	−0.0336149	+	0.0582226i	−0.00144255	+	0.00249857i
$544$	−4.64175	+	2.67992i	−0.199013	+	0.114900i
$545$	5.57713	+	31.6295i	0.238898	+	1.35486i
$546$	−0.0572547	−	0.0480424i	−0.00245028	−	0.00205603i
$547$	−2.85070	+	2.39202i	−0.121887	+	0.102275i	−0.701694	−	0.712479i	$-0.747573\pi$
$547$	−2.85070	+	2.39202i	−0.121887	+	0.102275i	0.579807	+	0.814754i	$0.303128\pi$
$548$	0.877611	−	4.97718i	0.0374897	−	0.212614i
$549$	4.62434	+	12.7053i	0.197362	+	0.542248i
$550$	32.0536	+	15.1423i	1.36677	+	0.645670i
$551$	14.6107	+	7.83663i	0.622438	+	0.333852i
$552$		−	0.0241017i		−	0.00102584i
$553$	9.65351	+	26.5228i	0.410509	+	1.12786i
$554$	−16.9193	−	2.98332i	−0.718831	−	0.126749i
$555$	−0.222674	+	0.186845i	−0.00945197	+	0.00793115i
$556$	−6.36372	+	7.58399i	−0.269882	+	0.321633i
$557$	−16.0020	+	2.82158i	−0.678026	+	0.119554i	−0.502048	−	0.864840i	$-0.667420\pi$
$557$	−16.0020	+	2.82158i	−0.678026	+	0.119554i	−0.175978	+	0.984394i	$0.556309\pi$
$558$	7.11600	−	4.10843i	0.301244	−	0.173924i
$559$	−11.2508	−	6.49565i	−0.475858	−	0.274737i
$560$	−3.29769	+	9.06032i	−0.139353	+	0.382868i
$561$	−0.0779808	−	0.0787641i	−0.00329235	−	0.00332542i
$562$	0.919598	−	1.59279i	0.0387909	−	0.0671878i
$563$	8.52282	+	14.7620i	0.359194	+	0.622142i	0.987826	−	0.155560i	$-0.0497183\pi$
$563$	8.52282	+	14.7620i	0.359194	+	0.622142i	−0.628632	+	0.777703i	$0.716385\pi$
$564$	−0.0388980	+	0.00685876i	−0.00163790	+	0.000288806i
$565$	−30.0289	+	35.7871i	−1.26333	+	1.50557i
$566$	20.6025	+	24.5530i	0.865986	+	1.03204i
$567$	21.5745	+	3.80418i	0.906046	+	0.159760i
$568$	−0.963297	−	2.64664i	−0.0404190	−	0.111050i
$569$	−7.42468			−0.311259			−0.155629	−	0.987816i	$-0.549741\pi$
$569$	−7.42468			−0.311259			−0.155629	+	0.987816i	$0.549741\pi$
$570$	−0.0845873	−	0.0665814i	−0.00354297	−	0.00278879i
$571$			42.2838i			1.76952i	0.466047	+	0.884760i	$0.345678\pi$
$571$			42.2838i			1.76952i	−0.466047	+	0.884760i	$0.654322\pi$
$572$	−16.2630	−	1.50476i	−0.679992	−	0.0629172i
$573$	0.0336247	+	0.00592895i	0.00140469	+	0.000247685i
$574$	−7.40066	−	8.81976i	−0.308898	−	0.368130i
$575$	−31.6511	−	26.5585i	−1.31994	−	1.10756i
$576$	0.520938	+	2.95438i	0.0217057	+	0.123099i
$577$	−23.0994	−	40.0093i	−0.961641	−	1.66561i	−0.718381	−	0.695650i	$-0.755117\pi$
$577$	−23.0994	−	40.0093i	−0.961641	−	1.66561i	−0.243260	−	0.969961i	$-0.578217\pi$
$578$	5.86391	−	10.1566i	0.243906	−	0.422458i
$579$	0.0366798	−	0.100777i	0.00152436	−	0.00418814i
$580$	14.1572	+	5.15281i	0.587847	+	0.213959i
$581$	14.1009	−	24.4235i	0.585006	−	1.01326i
$582$	0.0213856	+	0.0370410i	0.000886463	+	0.00153540i
$583$	6.48984	+	1.77375i	0.268782	+	0.0734614i
$584$	8.59413	−	10.2421i	0.355628	−	0.423821i
$585$	−44.8249	+	37.6125i	−1.85328	+	1.55509i
$586$	−1.31645	+	7.46598i	−0.0543822	+	0.308417i
$587$	30.3633	−	11.0513i	1.25323	−	0.456138i	0.371737	−	0.928338i	$-0.378762\pi$
$587$	30.3633	−	11.0513i	1.25323	−	0.456138i	0.881491	+	0.472201i	$0.156540\pi$
$588$			0.00669914i			0.000276268i
$589$	−11.0857	+	4.43231i	−0.456780	+	0.182630i
$590$		−	21.3193i		−	0.877700i
$591$	−0.138427	+	0.0503831i	−0.00569411	+	0.00207249i
$592$	−11.5914	−	2.04388i	−0.476405	−	0.0840031i
$593$	−0.644126	−	0.767639i	−0.0264511	−	0.0315232i	0.752657	−	0.658413i	$-0.228772\pi$
$593$	−0.644126	−	0.767639i	−0.0264511	−	0.0315232i	−0.779108	+	0.626890i	$0.784328\pi$
$594$	−0.112710	+	0.0518734i	−0.00462454	+	0.00212839i
$595$	−8.97386	−	50.8933i	−0.367892	−	2.08642i
$596$	8.98645	−	5.18833i	0.368099	−	0.212522i
$597$	−0.0480544	−	0.0277442i	−0.00196674	−	0.00113550i
$598$	17.8877	+	6.51058i	0.731482	+	0.266238i
$599$	−0.648620	+	1.78207i	−0.0265019	+	0.0728133i	−0.952238	−	0.305357i	$-0.901224\pi$
$599$	−0.648620	+	1.78207i	−0.0265019	+	0.0728133i	0.925736	+	0.378170i	$0.123447\pi$
$600$	−0.0577152	−	0.0333219i	−0.00235621	−	0.00136036i
$601$	−3.03921	−	5.26406i	−0.123972	−	0.214725i	0.797359	−	0.603506i	$-0.206230\pi$
$601$	−3.03921	−	5.26406i	−0.123972	−	0.214725i	−0.921331	+	0.388780i	$0.872897\pi$
$602$	−1.11514	−	6.32430i	−0.0454499	−	0.257759i
$603$	14.5541	−	17.3449i	0.592690	−	0.706341i
$604$	8.07415	−	6.77501i	0.328532	−	0.275671i
$605$	−37.9484	+	21.4067i	−1.54282	+	0.870307i
$606$	−0.0563565	+	0.0205121i	−0.00228933	+	0.000833247i
$607$	−9.96298			−0.404385			−0.202192	−	0.979346i	$-0.564807\pi$
$607$	−9.96298			−0.404385			−0.202192	+	0.979346i	$0.564807\pi$
$608$	−0.136353	−	4.35677i	−0.00552984	−	0.176690i
$609$	−0.0577298			−0.00233933
$610$	−6.10559	−	16.7750i	−0.247208	−	0.679198i
$611$	5.41709	−	30.7218i	0.219152	−	1.24287i
$612$	−10.3356	−	12.3175i	−0.417791	−	0.497904i
$613$	−17.0241	+	20.2885i	−0.687597	+	0.819446i	−0.991063	−	0.133396i	$-0.957412\pi$
$613$	−17.0241	+	20.2885i	−0.687597	+	0.819446i	0.303466	+	0.952842i	$0.401856\pi$
$614$	1.54307	+	8.75119i	0.0622733	+	0.353169i
$615$	0.101158	−	0.0584033i	0.00407906	−	0.00235505i
$616$	−4.59765	−	6.63647i	−0.185245	−	0.267391i
$617$	16.8727	+	6.14115i	0.679268	+	0.247234i	0.658533	−	0.752552i	$-0.271177\pi$
$617$	16.8727	+	6.14115i	0.679268	+	0.247234i	0.0207351	+	0.999785i	$0.493399\pi$
$618$	−0.0234144	−	0.00852216i	−0.000941867	−	0.000342811i
$619$	16.3653	−	28.3456i	0.657777	−	1.13930i	−0.323412	−	0.946258i	$-0.604830\pi$
$619$	16.3653	−	28.3456i	0.657777	−	1.13930i	0.981190	−	0.193046i	$-0.0618366\pi$
$620$	−9.39536	+	5.42441i	−0.377327	+	0.217850i
$621$	0.142412	−	0.0251112i	0.00571481	−	0.00100768i
$622$	−6.74674	−	5.66118i	−0.270519	−	0.226993i
$623$	−3.19577	+	2.68157i	−0.128036	+	0.107435i
$624$	0.0302374	+	0.00533167i	0.00121046	+	0.000213437i
$625$	−33.6450	+	12.2458i	−1.34580	+	0.489831i
$626$	16.7372			0.668954
$627$	0.0864236	−	0.0256101i	0.00345142	−	0.00102277i
$628$	−6.84844			−0.273283
$629$	59.2820	−	21.5769i	2.36373	−	0.860327i
$630$	−28.4856	−	5.02277i	−1.13489	−	0.200112i
$631$	−9.34658	+	7.84271i	−0.372082	+	0.312214i	−0.809584	−	0.587004i	$-0.800307\pi$
$631$	−9.34658	+	7.84271i	−0.372082	+	0.312214i	0.437503	+	0.899217i	$0.355863\pi$
$632$	−8.88225	−	7.45309i	−0.353317	−	0.296468i
$633$	−0.0950569	+	0.0167611i	−0.00377817	+	0.000666194i
$634$	−10.1502	+	5.86021i	−0.403115	+	0.232739i
$635$	25.1325	−	43.5308i	0.997355	−	1.72747i
$636$	−0.0118851	−	0.00432583i	−0.000471275	−	0.000171530i
$637$	−4.97193	−	1.80964i	−0.196995	−	0.0717004i
$638$	−10.3698	+	7.18408i	−0.410546	+	0.284420i
$639$	7.31736	−	4.22468i	0.289470	−	0.167126i
$640$	−0.687802	−	3.90072i	−0.0271877	−	0.154189i
$641$	−17.0509	+	20.3205i	−0.673470	+	0.802610i	−0.989252	−	0.146222i	$-0.953289\pi$
$641$	−17.0509	+	20.3205i	−0.673470	+	0.802610i	0.315782	+	0.948832i	$0.397733\pi$
$642$	0.0360547	+	0.0429684i	0.00142297	+	0.00169583i
$643$	−3.14512	+	17.8369i	−0.124032	+	0.703418i	0.857847	+	0.513905i	$0.171802\pi$
$643$	−3.14512	+	17.8369i	−0.124032	+	0.703418i	−0.981878	+	0.189512i	$0.939309\pi$
$644$	3.21831	+	8.84224i	0.126819	+	0.348433i
$645$	0.0651516			0.00256534
$646$	12.3087	+	19.8576i	0.484279	+	0.781287i
$647$	1.89817			0.0746247			0.0373124	−	0.999304i	$-0.488120\pi$
$647$	1.89817			0.0746247			0.0373124	+	0.999304i	$0.488120\pi$
$648$	−8.45690	+	3.07806i	−0.332219	+	0.120918i
$649$	14.5718	+	10.3122i	0.571992	+	0.404788i
$650$	40.3212	−	33.8335i	1.58153	−	1.32706i
$651$	0.0267213	−	0.0318452i	0.00104729	−	0.00124811i
$652$	3.58815	+	20.3494i	0.140523	+	0.796944i
$653$	0.845662	+	1.46473i	0.0330933	+	0.0573193i	0.882098	−	0.471066i	$-0.156131\pi$
$653$	0.845662	+	1.46473i	0.0330933	+	0.0573193i	−0.849004	+	0.528386i	$0.822797\pi$
$654$	0.0437839	+	0.0252786i	0.00171209	+	0.000988473i
$655$	−0.344385	+	0.946191i	−0.0134563	+	0.0369708i
$656$	4.44451	+	1.61767i	0.173529	+	0.0631594i
$657$	34.7361	+	20.0549i	1.35518	+	0.782416i
$658$	13.3547	−	7.71035i	0.520621	−	0.300581i
$659$	−3.02974	−	17.1825i	−0.118022	−	0.669335i	−0.985210	−	0.171354i	$-0.945186\pi$
$659$	−3.02974	−	17.1825i	−0.118022	−	0.669335i	0.867188	−	0.497981i	$-0.165925\pi$
$660$	0.0744058	−	0.0342444i	0.00289624	−	0.00133296i
$661$	−23.7318	−	28.2824i	−0.923059	−	1.10006i	−0.994720	−	0.102630i	$-0.967274\pi$
$661$	−23.7318	−	28.2824i	−0.923059	−	1.10006i	0.0716608	−	0.997429i	$-0.477170\pi$
$662$	−25.2867	−	4.45872i	−0.982794	−	0.173293i
$663$	−0.154643	+	0.0562854i	−0.00600583	+	0.00218594i
$664$			11.5855i			0.449603i
$665$	39.9233	+	13.1318i	1.54816	+	0.509231i
$666$		−	35.3103i		−	1.36825i
$667$	13.8165	−	5.02878i	0.534976	−	0.194715i
$668$	−2.69723	+	15.2967i	−0.104359	+	0.591849i
$669$	0.117834	−	0.0988743i	0.00455572	−	0.00382270i
$670$	−19.2160	+	22.9008i	−0.742380	+	0.884734i
$671$	14.4190	+	3.94089i	0.556640	+	0.152137i
$672$	0.00758876	+	0.0131441i	0.000292743	+	0.000507045i
$673$	−13.8839	+	24.0477i	−0.535186	+	0.926970i	0.463968	+	0.885852i	$0.346425\pi$
$673$	−13.8839	+	24.0477i	−0.535186	+	0.926970i	−0.999154	+	0.0411178i	$0.986908\pi$
$674$	−22.9452	−	8.35137i	−0.883816	−	0.321683i
$675$	0.136760	−	0.375746i	0.00526390	−	0.0144625i
$676$	−5.62503	+	9.74285i	−0.216347	+	0.374725i
$677$	−3.23239	−	5.59866i	−0.124231	−	0.215174i	0.797201	−	0.603714i	$-0.206313\pi$
$677$	−3.23239	−	5.59866i	−0.124231	−	0.215174i	−0.921432	+	0.388540i	$0.872980\pi$
$678$	0.0127698	+	0.0724214i	0.000490423	+	0.00278133i
$679$	−12.7919	−	10.7337i	−0.490908	−	0.411920i
$680$	13.6462	+	16.2629i	0.523308	+	0.623654i
$681$	−0.0418994	−	0.00738800i	−0.00160559	−	0.000283109i
$682$	0.836952	−	9.04555i	0.0320485	−	0.346372i
$683$		−	6.40122i		−	0.244936i	−0.992472	−	0.122468i	$-0.960919\pi$
$683$		−	6.40122i		−	0.244936i	0.992472	−	0.122468i	$-0.0390809\pi$
$684$	12.8005	−	2.67244i	0.489441	−	0.102183i
$685$	−20.0182			−0.764855
$686$	−6.72247	−	18.4698i	−0.256665	−	0.705181i
$687$	0.0433974	+	0.00765214i	0.00165571	+	0.000291947i
$688$	1.69576	+	2.02092i	0.0646501	+	0.0770470i
$689$	6.42104	−	7.65229i	0.244622	−	0.291529i
$690$	−0.0940140	+	0.0165772i	−0.00357905	+	0.000631083i
$691$	14.2460	+	24.6749i	0.541945	+	0.938676i	0.998792	+	0.0491309i	$0.0156451\pi$
$691$	14.2460	+	24.6749i	0.541945	+	0.938676i	−0.456848	+	0.889545i	$0.651022\pi$
$692$	−3.61453	+	6.26055i	−0.137404	+	0.237991i
$693$	17.2116	−	17.0404i	0.653814	−	0.647312i
$694$	12.5203	−	34.3993i	0.475265	−	1.30578i
$695$	33.9600	+	19.6068i	1.28817	+	0.743728i
$696$	0.0205384	−	0.0118578i	0.000778506	−	0.000449470i
$697$	−24.9655	+	4.40210i	−0.945638	+	0.166741i
$698$	−1.07591	+	1.28222i	−0.0407237	+	0.0485326i
$699$	0.0198925	−	0.0166918i	0.000752403	−	0.000631341i
$700$	25.6236	+	4.51813i	0.968480	+	0.170769i
$701$	9.04598	+	24.8536i	0.341662	+	0.938709i	0.984913	+	0.173053i	$0.0553632\pi$
$701$	9.04598	+	24.8536i	0.341662	+	0.938709i	−0.643250	+	0.765656i	$0.722415\pi$
$702$			0.184222i			0.00695300i
$703$	−7.32420	+	50.7799i	−0.276237	+	1.91520i
$704$	2.99884	+	1.41667i	0.113023	+	0.0533927i
$705$	0.0535082	+	0.147012i	0.00201523	+	0.00553681i
$706$	−3.68880	+	20.9202i	−0.138830	+	0.787343i
$707$	17.9366	−	15.0506i	0.674576	−	0.566037i
$708$	−0.0257081	−	0.0215716i	−0.000966168	−	0.000810711i
$709$	3.61241	+	20.4870i	0.135667	+	0.769406i	0.974393	+	0.224852i	$0.0721899\pi$
$709$	3.61241	+	20.4870i	0.135667	+	0.769406i	−0.838726	+	0.544554i	$0.816699\pi$
$710$	−9.66122	+	5.57791i	−0.362579	+	0.209335i
$711$	17.3922	−	30.1242i	0.652259	−	1.12975i
$712$	0.586151	−	1.61044i	0.0219669	−	0.0603536i
$713$	−3.62121	+	9.94918i	−0.135615	+	0.372600i
$714$	−0.0704503	−	0.0406745i	−0.00263654	−	0.00152220i
$715$	5.31610	+	64.4725i	0.198811	+	2.41113i
$716$	−21.0607	+	3.71358i	−0.787076	+	0.138783i
$717$	0.0801755	+	0.0672752i	0.00299421	+	0.00251244i
$718$	−0.597221	−	0.711740i	−0.0222881	−	0.0265619i
$719$	−7.43998	+	42.1942i	−0.277465	+	1.57358i	0.453558	+	0.891227i	$0.350154\pi$
$719$	−7.43998	+	42.1942i	−0.277465	+	1.57358i	−0.731023	+	0.682353i	$0.760957\pi$
$720$	11.1659	−	4.06406i	0.416129	−	0.151459i
$721$	9.72806			0.362292
$722$	−18.9628	+	1.18812i	−0.705723	+	0.0442171i
$723$			0.0509007i			0.00189302i
$724$	3.68788	+	10.1324i	0.137059	+	0.376566i
$725$	7.05981	−	40.0382i	0.262195	−	1.48698i
$726$	−0.0125841	+	0.0674206i	−0.000467040	+	0.00250221i
$727$	−33.4142	−	28.0378i	−1.23926	−	1.03987i	−0.997581	−	0.0695101i	$-0.977856\pi$
$727$	−33.4142	−	28.0378i	−1.23926	−	1.03987i	−0.241682	−	0.970355i	$-0.577699\pi$
$728$	−11.8052	+	2.08157i	−0.437529	+	0.0771482i
$729$	−13.4990	−	23.3809i	−0.499961	−	0.865958i
$730$	−45.8626	−	26.4788i	−1.69745	−	0.980023i
$731$	−13.2872	−	4.83614i	−0.491445	−	0.178871i
$732$	−0.0264061	−	0.00961104i	−0.000975999	−	0.000355234i
$733$	3.20000	+	1.84752i	0.118195	+	0.0682398i	0.557932	−	0.829887i	$-0.311595\pi$
$733$	3.20000	+	1.84752i	0.118195	+	0.0682398i	−0.439737	+	0.898127i	$0.644928\pi$
$734$	−2.36079	−	4.08901i	−0.0871385	−	0.150928i
$735$	0.0261314	−	0.00460768i	0.000963873	−	0.000169957i
$736$	−2.96119	−	2.48473i	−0.109151	−	0.0915884i
$737$	−6.35791	−	24.2114i	−0.234197	−	0.891837i
$738$	−2.46391	+	13.9735i	−0.0906976	+	0.514372i
$739$	17.2165	+	47.3019i	0.633319	+	1.74003i	0.671760	+	0.740769i	$0.265539\pi$
$739$	17.2165	+	47.3019i	0.633319	+	1.74003i	−0.0384407	+	0.999261i	$0.512239\pi$
$740$			46.6207i			1.71381i
$741$	0.0191059	−	0.132464i	0.000701871	−	0.00486619i
$742$	4.93794			0.181277
$743$	−8.15228	+	2.96719i	−0.299078	+	0.108856i	−0.487201	−	0.873290i	$-0.661982\pi$
$743$	−8.15228	+	2.96719i	−0.299078	+	0.108856i	0.188123	+	0.982146i	$0.439760\pi$
$744$	−0.00296549	+	0.0168181i	−0.000108720	+	0.000616582i
$745$	−26.4191	−	31.4851i	−0.967921	−	1.15352i
$746$	26.2626	+	22.0369i	0.961540	+	0.806828i
$747$	−34.2279	+	6.03531i	−1.25233	+	0.220820i
$748$	−17.7164	+	1.46082i	−0.647777	+	0.0534127i
$749$	−18.9650	−	10.9495i	−0.692968	−	0.400085i
$750$	−0.0480498	+	0.132016i	−0.00175453	+	0.00482053i
$751$	10.1139	−	27.7876i	0.369060	−	1.01398i	−0.606660	−	0.794962i	$-0.707491\pi$
$751$	10.1139	−	27.7876i	0.369060	−	1.01398i	0.975720	−	0.219023i	$-0.0702868\pi$
$752$	−3.16745	+	5.48618i	−0.115505	+	0.200060i
$753$	−0.0852371	+	0.0492117i	−0.00310621	+	0.00179337i
$754$	3.25257	+	18.4462i	0.118452	+	0.671772i
$755$	−31.9808	−	26.8351i	−1.16390	−	0.976629i
$756$	−0.0697595	+	0.0585352i	−0.00253713	+	0.00212890i
$757$	−2.30427	+	13.0681i	−0.0837500	+	0.474970i	0.913869	+	0.406008i	$0.133080\pi$
$757$	−2.30427	+	13.0681i	−0.0837500	+	0.474970i	−0.997619	+	0.0689614i	$0.978031\pi$
$758$	4.64687	+	12.7672i	0.168782	+	0.463725i
$759$	0.0341442	−	0.0722772i	0.00123935	−	0.00262350i
$760$	−16.9007	+	3.52846i	−0.613054	+	0.127991i
$761$			13.2371i			0.479844i	0.970792	+	0.239922i	$0.0771218\pi$
$761$			13.2371i			0.479844i	−0.970792	+	0.239922i	$0.922878\pi$
$762$	−0.0270621	−	0.0743525i	−0.000980356	−	0.00269351i
$763$	−19.4385	−	3.42754i	−0.703722	−	0.124085i
$764$	4.19494	−	3.51997i	0.151767	−	0.127348i
$765$	−40.9381	+	48.7881i	−1.48012	+	1.76394i
$766$	5.26717	−	0.928745i	0.190311	−	0.0335569i
$767$	22.9544	−	13.2527i	0.828836	−	0.478529i
$768$	−0.00539966	−	0.00311750i	−0.000194844	−	0.000112493i
$769$	−0.913697	+	2.51036i	−0.0329488	+	0.0905260i	−0.955076	−	0.296360i	$-0.904227\pi$
$769$	−0.913697	+	2.51036i	−0.0329488	+	0.0905260i	0.922127	+	0.386886i	$0.126449\pi$
$770$	−22.7247	+	22.4987i	−0.818942	+	0.810798i
$771$	0.0930883	−	0.161234i	0.00335250	−	0.00580669i
$772$	−8.60020	−	14.8960i	−0.309528	−	0.536118i
$773$	−0.334798	+	0.0590340i	−0.0120419	+	0.00212330i	−0.179666	−	0.983728i	$-0.557502\pi$
$773$	−0.334798	+	0.0590340i	−0.0120419	+	0.00212330i	0.167624	+	0.985851i	$0.446391\pi$
$774$	−5.08721	+	6.06270i	−0.182856	+	0.217919i
$775$	18.8183	+	22.4268i	0.675974	+	0.805594i
$776$	6.75565	+	1.19120i	0.242514	+	0.0427617i
$777$	−0.0610996	−	0.167870i	−0.00219194	−	0.00602230i
$778$	−8.65525			−0.310306
$779$	6.44179	−	19.5843i	0.230801	−	0.701679i
$780$		−	0.121615i		−	0.00435450i
$781$	0.860635	−	9.30151i	0.0307959	−	0.332834i
$782$	20.4040	+	3.59777i	0.729644	+	0.128656i
$783$	0.0914643	+	0.109003i	0.00326867	+	0.00389545i
$784$	0.823070	+	0.690638i	0.0293954	+	0.0246656i
$785$	4.71037	+	26.7138i	0.168120	+	0.953458i
$786$	0.000792513		0.00137267i	2.82680e−5		4.89616e-5i
$787$	10.0426	−	17.3943i	0.357980	−	0.620039i	−0.629643	−	0.776884i	$-0.716799\pi$
$787$	10.0426	−	17.3943i	0.357980	−	0.620039i	0.987623	+	0.156845i	$0.0501323\pi$
$788$	−8.08070	+	22.2015i	−0.287863	+	0.790897i
$789$	0.158113	+	0.0575484i	0.00562897	+	0.00204878i
$790$	−22.9632	+	39.7734i	−0.816993	+	1.41507i
$791$	−14.3554	−	24.8642i	−0.510418	−	0.884069i
$792$	−2.62318	+	9.59773i	−0.0932106	+	0.341040i
$793$	14.2661	−	17.0017i	0.506606	−	0.603749i
$794$	−3.19287	+	2.67914i	−0.113311	+	0.0950791i
$795$	−0.00869922	+	0.0493358i	−0.000308530	+	0.00174976i
$796$	−8.36281	+	3.04381i	−0.296412	+	0.107885i
$797$			6.25404i			0.221529i	0.993847	+	0.110765i	$0.0353300\pi$
$797$			6.25404i			0.221529i	−0.993847	+	0.110765i	$0.964670\pi$
$798$	0.0562311	−	0.0348547i	0.00199056	−	0.00123384i
$799$		−	33.9540i		−	1.20121i
$800$	−10.0441	+	3.65574i	−0.355111	+	0.129250i
$801$	5.06319	+	0.892778i	0.178899	+	0.0315447i
$802$	−22.5987	−	26.9320i	−0.797987	−	0.951003i
$803$	40.2821	−	18.5394i	1.42152	−	0.654240i
$804$	0.00817165	+	0.0463437i	0.000288192	+	0.00163442i
$805$	32.2775	−	18.6354i	1.13763	−	0.656813i
$806$	−11.6809	−	6.74398i	−0.411443	−	0.237547i
$807$	0.0675470	+	0.0245851i	0.00237777	+	0.000865436i
$808$	−3.28983	+	9.03874i	−0.115736	+	0.317982i
$809$	−34.8443	−	20.1173i	−1.22506	−	0.707288i	−0.259067	−	0.965859i	$-0.583415\pi$
$809$	−34.8443	−	20.1173i	−1.22506	−	0.707288i	−0.965992	+	0.258571i	$0.916748\pi$
$810$	17.8233	+	30.8709i	0.626248	+	1.08469i
$811$	−3.67736	−	20.8553i	−0.129130	−	0.732330i	−0.978769	−	0.204966i	$-0.934292\pi$
$811$	−3.67736	−	20.8553i	−0.129130	−	0.732330i	0.849639	−	0.527364i	$-0.176820\pi$
$812$	−5.95157	+	7.09281i	−0.208859	+	0.248909i
$813$	−0.0926610	+	0.0777518i	−0.00324976	+	0.00272688i
$814$	−31.8654	−	22.5505i	−1.11688	−	0.790395i
$815$	76.9093	−	27.9927i	2.69401	−	0.980541i
$816$	0.0334185			0.00116988
$817$	8.57347	−	7.66358i	0.299948	−	0.268115i
$818$	39.0277			1.36457
$819$	−12.2995	−	33.7927i	−0.429780	−	1.18081i
$820$	3.25313	−	18.4494i	0.113604	−	0.644282i
$821$	1.15099	+	1.37170i	0.0401698	+	0.0478725i	0.785755	−	0.618537i	$-0.212275\pi$
$821$	1.15099	+	1.37170i	0.0401698	+	0.0478725i	−0.745585	+	0.666410i	$0.767830\pi$
$822$	−0.0202551	+	0.0241391i	−0.000706479	+	0.000841949i
$823$	−3.76979	−	21.3795i	−0.131407	−	0.745244i	−0.977295	−	0.211884i	$-0.932040\pi$
$823$	−3.76979	−	21.3795i	−0.131407	−	0.745244i	0.845888	−	0.533360i	$-0.179071\pi$
$824$	−3.46093	+	1.99817i	−0.120567	+	0.0696094i
$825$	−0.125873	−	0.181690i	−0.00438232	−	0.00632565i
$826$	12.3120	+	4.48121i	0.428390	+	0.155921i
$827$	−30.9026	−	11.2476i	−1.07459	−	0.391118i	−0.256698	−	0.966492i	$-0.582635\pi$
$827$	−30.9026	−	11.2476i	−1.07459	−	0.391118i	−0.817891	+	0.575373i	$0.804857\pi$
$828$	5.79826	−	10.0429i	0.201503	−	0.349014i
$829$	6.07178	−	3.50554i	0.210882	−	0.121753i	−0.390839	−	0.920459i	$-0.627815\pi$
$829$	6.07178	−	3.50554i	0.210882	−	0.121753i	0.601721	+	0.798706i	$0.294482\pi$
$830$	45.1916	−	7.96850i	1.56862	−	0.276591i
$831$	0.0820579	+	0.0688547i	0.00284656	+	0.00238854i
$832$	3.77234	−	3.16537i	0.130782	−	0.109739i
$833$	−5.67134	−	1.00001i	−0.196500	−	0.0346483i
$834$	0.0580050	−	0.0211121i	0.00200855	−	0.000731052i
$835$	61.5234			2.12911
$836$	5.76320	−	13.2584i	0.199324	−	0.458552i
$837$	−0.102465			−0.00354170
$838$	16.6953	−	6.07659i	0.576729	−	0.209912i
$839$	−13.9425	−	2.45844i	−0.481348	−	0.0848747i	−0.0722914	−	0.997384i	$-0.523031\pi$
$839$	−13.9425	−	2.45844i	−0.481348	−	0.0848747i	−0.409057	+	0.912509i	$0.634142\pi$
$840$	0.0460519	−	0.0386422i	0.00158894	−	0.00133328i
$841$	−11.1324	−	9.34119i	−0.383876	−	0.322110i
$842$	−35.6435	+	6.28491i	−1.22836	+	0.216592i
$843$	−0.00993104	+	0.00573369i	−0.000342043	+	0.000197479i
$844$	−7.74045	+	13.4069i	−0.266437	+	0.461483i
$845$	41.8730	+	15.2405i	1.44047	+	0.524290i
$846$	−17.8583	−	6.49990i	−0.613982	−	0.223471i
$847$	−4.38595	−	26.4151i	−0.150703	−	0.907633i
$848$	−1.75676	+	1.01426i	−0.0603273	+	0.0348300i
$849$	−0.0347023	−	0.196806i	−0.00119098	−	0.00675438i
$850$	36.8250	−	43.8863i	1.26309	−	1.50529i
$851$	29.2459	+	34.8539i	1.00254	+	1.19478i
$852$	−0.00304940	+	0.0172940i	−0.000104471	+	0.000592483i
$853$	7.19001	+	19.7544i	0.246181	+	0.676377i	0.999818	+	0.0190859i	$0.00607559\pi$
$853$	7.19001	+	19.7544i	0.246181	+	0.676377i	−0.753637	+	0.657291i	$0.771702\pi$
$854$	10.9710			0.375421
$855$	−19.2287	−	48.0931i	−0.657607	−	1.64475i
$856$	8.99619			0.307483
$857$	51.0939	−	18.5966i	1.74533	−	0.635249i	0.745811	−	0.666158i	$-0.232062\pi$
$857$	51.0939	−	18.5966i	1.74533	−	0.635249i	0.999522	+	0.0309087i	$0.00984011\pi$
$858$	0.0831239	+	0.0588252i	0.00283780	+	0.00200826i
$859$	−30.4880	+	25.5825i	−1.04024	+	0.872863i	−0.992034	−	0.125974i	$-0.959794\pi$
$859$	−30.4880	+	25.5825i	−1.04024	+	0.872863i	−0.0482044	+	0.998837i	$0.515350\pi$
$860$	6.71671	−	8.00466i	0.229038	−	0.272957i
$861$	0.0124655	+	0.0706953i	0.000424823	+	0.00240929i
$862$	11.1947	+	19.3898i	0.381294	+	0.660421i
$863$	−38.4923	−	22.2235i	−1.31029	−	0.756498i	−0.328148	−	0.944626i	$-0.606425\pi$
$863$	−38.4923	−	22.2235i	−1.31029	−	0.756498i	−0.982144	+	0.188129i	$0.939758\pi$
$864$	0.0127949	−	0.0351536i	0.000435291	−	0.00119595i
$865$	26.9067	+	9.79325i	0.914856	+	0.332980i
$866$	13.2389	+	7.64348i	0.449876	+	0.259736i
$867$	−0.0633263	+	0.0365614i	−0.00215067	+	0.00124169i
$868$	−1.15778	−	6.56608i	−0.0392975	−	0.222867i
$869$	−16.0779	−	34.9339i	−0.545405	−	1.18505i
$870$	−0.0603804	−	0.0719586i	−0.00204709	−	0.00243962i
$871$	−36.6025	−	6.45402i	−1.24023	−	0.218686i
$872$	7.61962	−	2.77332i	0.258033	−	0.0939163i
$873$			20.5793i			0.696505i
$874$	−10.4216	+	13.2400i	−0.352517	+	0.447850i
$875$		−	54.8489i		−	1.85423i
$876$	−0.0783351	+	0.0285117i	−0.00264670	+	0.000963320i
$877$	−5.88625	+	33.3826i	−0.198765	+	1.12725i	0.708190	+	0.706022i	$0.249512\pi$
$877$	−5.88625	+	33.3826i	−0.198765	+	1.12725i	−0.906955	+	0.421229i	$0.861599\pi$
$878$	20.3494	−	17.0752i	0.686758	−	0.576258i
$879$	0.0303836	−	0.0362097i	0.00102481	−	0.00122132i
$880$	3.46342	−	12.6720i	0.116752	−	0.427174i
$881$	−19.8634	−	34.4045i	−0.669216	−	1.15912i	−0.978124	−	0.208024i	$-0.933297\pi$
$881$	−19.8634	−	34.4045i	−0.669216	−	1.15912i	0.308908	−	0.951092i	$-0.400037\pi$
$882$	−1.61164	+	2.79145i	−0.0542668	+	0.0939929i
$883$	11.8703	+	4.32043i	0.399467	+	0.145394i	0.533938	−	0.845523i	$-0.320711\pi$
$883$	11.8703	+	4.32043i	0.399467	+	0.145394i	−0.134471	+	0.990917i	$0.542934\pi$
$884$	−9.02733	+	24.8024i	−0.303622	+	0.834195i
$885$	−0.0664627	+	0.115117i	−0.00223412	+	0.00386961i
$886$	−15.3956	−	26.6660i	−0.517226	−	0.895862i
$887$	5.51965	+	31.3035i	0.185332	+	1.05107i	0.925529	+	0.378678i	$0.123621\pi$
$887$	5.51965	+	31.3035i	0.185332	+	1.05107i	−0.740197	+	0.672390i	$0.765268\pi$
$888$	0.0562181	+	0.0471726i	0.00188656	+	0.00158301i
$889$	19.8566	+	23.6642i	0.665970	+	0.793672i
$890$	−6.68501	−	1.17875i	−0.224082	−	0.0395117i
$891$	−29.7215	−	2.75002i	−0.995708	−	0.0921292i
$892$		−	24.6706i		−	0.826033i
$893$	24.3339	+	13.0518i	0.814302	+	0.436761i
$894$	−0.0646984			−0.00216384
$895$	28.9712	+	79.5977i	0.968401	+	2.66066i
$896$	2.39727	+	0.422703i	0.0800870	+	0.0141215i
$897$	−0.0762908	−	0.0909198i	−0.00254727	−	0.00303572i
$898$	−10.1162	+	12.0560i	−0.337582	+	0.402314i
$899$	−10.2598	+	1.80909i	−0.342185	+	0.0603364i
$900$	−16.0328	−	27.7696i	−0.534426	−	0.925654i
$901$	5.43629	−	9.41593i	0.181109	−	0.313690i
$902$	11.0367	+	11.1475i	0.367481	+	0.371173i
$903$	−0.0136946	+	0.0376255i	−0.000455727	+	0.00125210i
$904$	10.2143	+	5.89725i	0.339724	+	0.196140i
$905$	36.9870	−	21.3544i	1.22949	−	0.709845i
$906$	−0.0647188	+	0.0114117i	−0.00215014	+	0.000379127i
$907$	−8.34934	+	9.95036i	−0.277235	+	0.330396i	−0.886637	−	0.462465i	$-0.846965\pi$
$907$	−8.34934	+	9.95036i	−0.277235	+	0.330396i	0.609402	+	0.792861i	$0.291410\pi$
$908$	−5.22726	+	4.38619i	−0.173473	+	0.145561i
$909$	−28.4177	−	5.01081i	−0.942557	−	0.166198i
$910$	16.2392	+	44.6170i	0.538326	+	1.47904i
$911$			3.18360i			0.105477i	0.998608	+	0.0527387i	$0.0167950\pi$
$911$			3.18360i			0.105477i	−0.998608	+	0.0527387i	$0.983205\pi$
$912$	−0.0128459	+	0.0239502i	−0.000425372	+	0.000793069i
$913$	−16.4128	+	34.7430i	−0.543184	+	1.14982i
$914$	−2.98123	−	8.19085i	−0.0986102	−	0.270929i
$915$	−0.0193278	+	0.109613i	−0.000638957	+	0.00362370i
$916$	5.41415	−	4.54301i	0.178889	−	0.150105i
$917$	−0.474044	−	0.397770i	−0.0156543	−	0.0131355i
$918$	0.0348182	+	0.197464i	0.00114917	+	0.00651727i
$919$	19.4464	−	11.2274i	0.641477	−	0.370357i	−0.143706	−	0.989620i	$-0.545902\pi$
$919$	19.4464	−	11.2274i	0.641477	−	0.370357i	0.785183	+	0.619264i	$0.212569\pi$
$920$	−7.65552	+	13.2598i	−0.252395	+	0.437161i
$921$	0.0189498	−	0.0520640i	0.000624416	−	0.00171557i
$922$	4.02840	−	11.0679i	0.132668	−	0.364503i
$923$	−12.0115	−	6.93482i	−0.395362	−	0.228262i
$924$	0.00413661	+	0.0501679i	0.000136085	+	0.00165040i
$925$	123.897	−	21.8464i	4.07371	−	0.718305i
$926$	−25.2930	−	21.2234i	−0.831180	−	0.697443i
$927$	−7.70628	−	9.18399i	−0.253107	−	0.301642i
$928$	0.660495	−	3.74586i	0.0216818	−	0.122964i
$929$	9.79572	−	3.56535i	0.321387	−	0.116975i	−0.176289	−	0.984339i	$-0.556409\pi$
$929$	9.79572	−	3.56535i	0.321387	−	0.116975i	0.497676	+	0.867363i	$0.334187\pi$
$930$	0.0676424			0.00221808
$931$	2.89672	−	3.68009i	0.0949361	−	0.120610i
$932$		−	4.16484i		−	0.136424i
$933$	0.0187814	+	0.0516014i	0.000614875	+	0.00168935i
$934$	5.00842	−	28.4042i	0.163881	−	0.929413i
$935$	17.8836	+	68.1020i	0.584857	+	2.22718i
$936$	11.3169	+	9.49598i	0.369903	+	0.310386i
$937$	−48.2073	+	8.50026i	−1.57487	+	0.277691i	−0.891719	−	0.452590i	$-0.850500\pi$
$937$	−48.2073	+	8.50026i	−1.57487	+	0.277691i	−0.683147	+	0.730281i	$0.739389\pi$
$938$	−9.18624	−	15.9110i	−0.299941	−	0.519514i
$939$	−0.0903754	−	0.0521782i	−0.00294929	−	0.00170277i
$940$	23.5786	+	8.58191i	0.769049	+	0.279911i
$941$	29.9181	+	10.8893i	0.975303	+	0.354981i	0.780012	−	0.625764i	$-0.215213\pi$
$941$	29.9181	+	10.8893i	0.975303	+	0.354981i	0.195291	+	0.980745i	$0.437435\pi$
$942$	0.0369793	+	0.0213500i	0.00120485	+	0.000695621i
$943$	−9.14156	−	15.8336i	−0.297690	−	0.515614i
$944$	−5.30067	+	0.934651i	−0.172522	+	0.0304203i
$945$	0.276310	+	0.231851i	0.00898836	+	0.00754213i
$946$	2.22232	+	8.46276i	0.0722540	+	0.275148i
$947$	6.93357	−	39.3222i	0.225311	−	1.27780i	−0.636780	−	0.771046i	$-0.719734\pi$
$947$	6.93357	−	39.3222i	0.225311	−	1.27780i	0.862090	−	0.506754i	$-0.169155\pi$
$948$	0.0247262	+	0.0679346i	0.000803069	+	0.00220641i
$949$		−	65.8402i		−	2.13726i
$950$	17.2967	+	43.2611i	0.561180	+	1.40358i
$951$	0.0730768			0.00236968
$952$	−12.2603	+	4.46239i	−0.397359	+	0.144627i
$953$	6.16561	−	34.9669i	0.199724	−	1.13269i	−0.705806	−	0.708406i	$-0.749415\pi$
$953$	6.16561	−	34.9669i	0.199724	−	1.13269i	0.905529	−	0.424284i	$-0.139474\pi$
$954$	−3.91169	−	4.66177i	−0.126646	−	0.150930i
$955$	−16.6157	−	13.9422i	−0.537671	−	0.451160i
$956$	16.5312	−	2.91489i	0.534656	−	0.0942742i
$957$	0.0783900	−	0.00646368i	0.00253399	−	0.000208941i
$958$	−1.23672	−	0.714023i	−0.0399567	−	0.0230690i
$959$	4.20773	−	11.5606i	0.135875	−	0.373313i
$960$	−0.00844658	+	0.0232068i	−0.000272612	+	0.000748996i
$961$	−11.7490	+	20.3498i	−0.378999	+	0.656446i
$962$	−50.1965	+	28.9809i	−1.61840	+	0.934383i
$963$	4.68645	+	26.5782i	0.151019	+	0.856471i
$964$	6.25376	+	5.24753i	0.201420	+	0.169012i
$965$	−52.1898	+	43.7924i	−1.68005	+	1.40973i
$966$	0.0101879	−	0.0577782i	0.000327789	−	0.00185898i
$967$	−4.18261	−	11.4916i	−0.134504	−	0.369546i	0.854096	−	0.520116i	$-0.174111\pi$
$967$	−4.18261	−	11.4916i	−0.134504	−	0.369546i	−0.988599	+	0.150570i	$0.951889\pi$
$968$	6.98609	+	8.49673i	0.224542	+	0.273095i
$969$	−0.00455672	−	0.145597i	−0.000146383	−	0.00467724i
$970$		−	27.1712i		−	0.872415i
$971$	13.6546	+	37.5157i	0.438197	+	1.20394i	0.940664	+	0.339341i	$0.110204\pi$
$971$	13.6546	+	37.5157i	0.438197	+	1.20394i	−0.502466	+	0.864597i	$0.667574\pi$
$972$	0.165784	+	0.0292323i	0.00531754	+	0.000937626i
$973$	−18.4613	+	15.4909i	−0.591842	+	0.496614i
$974$	20.4203	−	24.3360i	0.654308	−	0.779774i
$975$	−0.323197	+	0.0569884i	−0.0103506	+	0.00182509i
$976$	−3.90313	+	2.25347i	−0.124936	+	0.0721320i
$977$	15.6575	+	9.03988i	0.500929	+	0.289211i	0.729097	−	0.684410i	$-0.239940\pi$
$977$	15.6575	+	9.03988i	0.500929	+	0.289211i	−0.228168	+	0.973622i	$0.573274\pi$
$978$	0.0440644	−	0.121066i	0.00140902	−	0.00387126i
$979$	4.03923	−	3.99906i	0.129094	−	0.127810i
$980$	2.12787	−	3.68559i	0.0679724	−	0.117732i
$981$	12.1628	+	21.0666i	0.388328	+	0.672604i
$982$	−12.8748	+	2.27017i	−0.410850	+	0.0724440i
$983$	30.1036	−	35.8761i	0.960156	−	1.14427i	−0.0293191	−	0.999570i	$-0.509334\pi$
$983$	30.1036	−	35.8761i	0.960156	−	1.14427i	0.989476	−	0.144700i	$-0.0462216\pi$
$984$	−0.0189558	−	0.0225906i	−0.000604289	−	0.000720163i
$985$	92.1599	+	16.2503i	2.93646	+	0.517777i
$986$	6.97273	+	19.1574i	0.222057	+	0.610096i
$987$	−0.0961480			−0.00306042
$988$	−14.3051	−	16.0036i	−0.455107	−	0.509142i
$989$		−	10.1978i		−	0.324272i
$990$	39.2422	+	3.63094i	1.24720	+	0.115399i
$991$	−36.8949	−	6.50557i	−1.17201	−	0.206656i	−0.446443	−	0.894812i	$-0.647309\pi$
$991$	−36.8949	−	6.50557i	−1.17201	−	0.206656i	−0.725563	+	0.688156i	$0.758420\pi$
$992$	1.76059	+	2.09818i	0.0558987	+	0.0666174i
$993$	0.122639	+	0.102907i	0.00389185	+	0.00326565i
$994$	−1.19054	−	6.75188i	−0.0377616	−	0.214157i
$995$	17.6250	+	30.5274i	0.558750	+	0.967784i
$996$	0.0361177	−	0.0625576i	0.00114443	−	0.00198221i
$997$	8.44039	−	23.1898i	0.267310	−	0.734427i	−0.731317	−	0.682038i	$-0.761094\pi$
$997$	8.44039	−	23.1898i	0.267310	−	0.734427i	0.998627	−	0.0523897i	$-0.0166838\pi$
$998$	9.26264	+	3.37133i	0.293204	+	0.106717i
$999$	−0.220161	+	0.381330i	−0.00696559	+	0.0120648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.b.109.6	yes	60
11.10	odd	2		418.2.q.a.109.6	✓	60
19.15	odd	18		418.2.q.a.395.6	yes	60
209.186	even	18	inner	418.2.q.b.395.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.109.6	✓	60	11.10	odd	2
418.2.q.a.395.6	yes	60	19.15	odd	18
418.2.q.b.109.6	yes	60	1.1	even	1	trivial
418.2.q.b.395.6	yes	60	209.186	even	18	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.00614027 + 0.00108270i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.03422 - 2.54601i) q^{5} +(-0.00614027 + 0.00108270i) q^{6} +(2.10812 - 1.21712i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.81904 - 1.02605i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.00614027 + 0.00108270i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.03422 - 2.54601i) q^{5} +(-0.00614027 + 0.00108270i) q^{6} +(2.10812 - 1.21712i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.81904 - 1.02605i) q^{9} +(3.72202 + 1.35470i) q^{10} +(-2.72629 + 1.88874i) q^{11} +(0.00539966 - 0.00311750i) q^{12} +(0.855119 + 4.84962i) q^{13} +(-1.56470 + 1.86474i) q^{14} +(-0.0158744 - 0.0189183i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.83317 + 5.03660i) q^{17} +2.99996 q^{18} +(-4.31425 - 0.622263i) q^{19} -3.96089 q^{20} +(0.0142622 - 0.00519102i) q^{21} +(1.91589 - 2.70728i) q^{22} +(-2.96119 + 2.48473i) q^{23} +(-0.00400778 + 0.00477628i) q^{24} +(1.85607 + 10.5263i) q^{25} +(-2.46222 - 4.26469i) q^{26} +(-0.0323978 - 0.0187049i) q^{27} +(0.832561 - 2.28744i) q^{28} +(-3.57425 - 1.30092i) q^{29} +(0.0213875 + 0.0123481i) q^{30} +(2.37203 - 1.36949i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.0187851 + 0.00864562i) q^{33} +(-3.44523 - 4.10587i) q^{34} +(-9.49531 - 1.67428i) q^{35} +(-2.81904 + 1.02605i) q^{36} -11.7703i q^{37} +(4.26690 - 0.890826i) q^{38} +0.0307038i q^{39} +(3.72202 - 1.35470i) q^{40} +(-0.821313 + 4.65790i) q^{41} +(-0.0116267 + 0.00975592i) q^{42} +(-1.69576 + 2.02092i) q^{43} +(-0.874404 + 3.19928i) q^{44} +(5.94126 + 10.2906i) q^{45} +(1.93278 - 3.34767i) q^{46} +(-5.95285 - 2.16666i) q^{47} +(0.00213249 - 0.00585898i) q^{48} +(-0.537221 + 0.930494i) q^{49} +(-5.34433 - 9.25666i) q^{50} +(0.00580307 + 0.0329108i) q^{51} +(3.77234 + 3.16537i) q^{52} +(-1.30391 - 1.55394i) q^{53} +(0.0368414 + 0.00649613i) q^{54} +(13.0809 + 1.21033i) q^{55} +2.43425i q^{56} +(-0.0258170 - 0.00849189i) q^{57} +3.80364 q^{58} +(-1.84090 - 5.05784i) q^{59} +(-0.0243210 - 0.00428844i) q^{60} +(-2.89701 - 3.45252i) q^{61} +(-1.76059 + 2.09818i) q^{62} +(-7.19170 + 1.26809i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(9.75258 - 16.8920i) q^{65} +(0.0146952 - 0.0145491i) q^{66} +(-2.58140 + 7.09233i) q^{67} +(4.64175 + 2.67992i) q^{68} +(-0.0208727 + 0.0120509i) q^{69} +(9.49531 - 1.67428i) q^{70} +(-1.81041 + 2.15756i) q^{71} +(2.29810 - 1.92834i) q^{72} +(-13.1670 - 2.32169i) q^{73} +(4.02566 + 11.0604i) q^{74} +0.0666438i q^{75} +(-3.70489 + 2.29647i) q^{76} +(-3.44852 + 7.29992i) q^{77} +(-0.0105013 - 0.0288522i) q^{78} +(-2.01344 + 11.4188i) q^{79} +(-3.03422 + 2.54601i) q^{80} +(6.89413 + 5.78486i) q^{81} +(-0.821313 - 4.65790i) q^{82} +(10.0333 - 5.79273i) q^{83} +(0.00758876 - 0.0131441i) q^{84} +(7.26099 - 19.9494i) q^{85} +(0.902294 - 2.47903i) q^{86} +(-0.0205384 - 0.0118578i) q^{87} +(-0.272549 - 3.30541i) q^{88} +(-1.68775 + 0.297596i) q^{89} +(-9.10254 - 7.63794i) q^{90} +(7.70528 + 9.18280i) q^{91} +(-0.671247 + 3.80683i) q^{92} +(0.0160477 - 0.00584087i) q^{93} +6.33489 q^{94} +(11.5061 + 12.8722i) q^{95} +0.00623500i q^{96} +(-2.34621 - 6.44617i) q^{97} +(0.186575 - 1.05812i) q^{98} +(9.62346 - 2.52713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Introduction

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