LMFDB - Embedded newform 81.2.g.a.40.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

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("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			40.1
Character	$\chi$	$=$	81.40
Dual form			81.2.g.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.122925 - 2.11055i) q^{2} +(-0.328212 - 1.70067i) q^{3} +(-2.45283 + 0.286694i) q^{4} +(2.90939 + 0.689539i) q^{5} +(-3.54900 + 0.901762i) q^{6} +(-2.09765 + 2.81764i) q^{7} +(0.172370 + 0.977557i) q^{8} +(-2.78455 + 1.11636i) q^{9} +O(q^{10})$	\(q+(-0.122925 - 2.11055i) q^{2} +(-0.328212 - 1.70067i) q^{3} +(-2.45283 + 0.286694i) q^{4} +(2.90939 + 0.689539i) q^{5} +(-3.54900 + 0.901762i) q^{6} +(-2.09765 + 2.81764i) q^{7} +(0.172370 + 0.977557i) q^{8} +(-2.78455 + 1.11636i) q^{9} +(1.09767 - 6.22518i) q^{10} +(1.34549 + 1.42613i) q^{11} +(1.29262 + 4.07735i) q^{12} +(1.48971 - 0.748159i) q^{13} +(6.20462 + 4.08084i) q^{14} +(0.217782 - 5.17423i) q^{15} +(-2.76393 + 0.655063i) q^{16} +(3.65626 - 1.33077i) q^{17} +(2.69842 + 5.73971i) q^{18} +(-0.0155726 - 0.00566795i) q^{19} +(-7.33393 - 0.857214i) q^{20} +(5.48035 + 2.64264i) q^{21} +(2.84453 - 3.01503i) q^{22} +(-4.61293 - 6.19624i) q^{23} +(1.60593 - 0.613989i) q^{24} +(3.52095 + 1.76829i) q^{25} +(-1.76215 - 3.05213i) q^{26} +(2.81248 + 4.36921i) q^{27} +(4.33738 - 7.51257i) q^{28} +(-3.86125 + 2.53958i) q^{29} +(-10.9472 + 0.176407i) q^{30} +(-4.06577 + 9.42551i) q^{31} +(2.29168 + 7.65475i) q^{32} +(1.98378 - 2.75630i) q^{33} +(-3.25810 - 7.55312i) q^{34} +(-8.04578 + 6.75121i) q^{35} +(6.50998 - 3.53655i) q^{36} +(5.48325 + 4.60100i) q^{37} +(-0.0100482 + 0.0335634i) q^{38} +(-1.76131 - 2.28794i) q^{39} +(-0.172572 + 2.96295i) q^{40} +(0.328910 - 5.64716i) q^{41} +(4.90374 - 11.8914i) q^{42} +(1.30885 - 4.37185i) q^{43} +(-3.70912 - 3.11232i) q^{44} +(-8.87114 + 1.32787i) q^{45} +(-12.5104 + 10.4975i) q^{46} +(-1.13936 - 2.64134i) q^{47} +(2.02120 + 4.48553i) q^{48} +(-1.53131 - 5.11494i) q^{49} +(3.29924 - 7.64851i) q^{50} +(-3.46322 - 5.78131i) q^{51} +(-3.43950 + 2.26220i) q^{52} +(-1.40413 + 2.43202i) q^{53} +(8.87569 - 6.47296i) q^{54} +(2.93118 + 5.07695i) q^{55} +(-3.11597 - 1.56490i) q^{56} +(-0.00452821 + 0.0283441i) q^{57} +(5.83456 + 7.83717i) q^{58} +(3.40162 - 3.60551i) q^{59} +(0.949244 + 12.7539i) q^{60} +(-9.31935 - 1.08928i) q^{61} +(20.3928 + 7.42236i) q^{62} +(2.69554 - 10.1876i) q^{63} +(10.5356 - 3.83466i) q^{64} +(4.85003 - 1.14948i) q^{65} +(-6.06117 - 3.84804i) q^{66} +(3.74567 + 2.46356i) q^{67} +(-8.58664 + 4.31237i) q^{68} +(-9.02374 + 9.87875i) q^{69} +(15.2378 + 16.1511i) q^{70} +(-1.33743 + 7.58494i) q^{71} +(-1.57128 - 2.52963i) q^{72} +(-0.696188 - 3.94828i) q^{73} +(9.03659 - 12.1383i) q^{74} +(1.85166 - 6.56835i) q^{75} +(0.0398218 + 0.00943793i) q^{76} +(-6.84070 + 0.799563i) q^{77} +(-4.61231 + 3.99858i) q^{78} +(-0.473972 - 8.13778i) q^{79} -8.49305 q^{80} +(6.50749 - 6.21712i) q^{81} -11.9590 q^{82} +(-0.299799 - 5.14735i) q^{83} +(-14.2000 - 4.91075i) q^{84} +(11.5551 - 1.35060i) q^{85} +(-9.38790 - 2.22497i) q^{86} +(5.58630 + 5.73319i) q^{87} +(-1.16221 + 1.56111i) q^{88} +(0.829745 + 4.70572i) q^{89} +(3.89302 + 18.5597i) q^{90} +(-1.01685 + 5.76683i) q^{91} +(13.0912 + 13.8758i) q^{92} +(17.3641 + 3.82097i) q^{93} +(-5.43461 + 2.72936i) q^{94} +(-0.0413984 - 0.0272282i) q^{95} +(12.2660 - 6.40977i) q^{96} +(-11.3173 + 2.68224i) q^{97} +(-10.6071 + 3.86067i) q^{98} +(-5.33866 - 2.46910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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 $

$2$	−0.122925	−	2.11055i	−0.0869214	−	1.49238i	−0.706648	−	0.707565i	$-0.749793\pi$
$2$	−0.122925	−	2.11055i	−0.0869214	−	1.49238i	0.619726	−	0.784818i	$-0.287244\pi$
$3$	−0.328212	−	1.70067i	−0.189493	−	0.981882i
$3$	−0.328212	−	1.70067i	−0.189493	−	0.981882i
$4$	−2.45283	+	0.286694i	−1.22641	+	0.143347i
$5$	2.90939	+	0.689539i	1.30112	+	0.308371i	0.822055	−	0.569408i	$-0.192827\pi$
$5$	2.90939	+	0.689539i	1.30112	+	0.308371i	0.479066	+	0.877779i	$0.340976\pi$
$6$	−3.54900	+	0.901762i	−1.44887	+	0.368143i
$7$	−2.09765	+	2.81764i	−0.792839	+	1.06497i	0.203466	+	0.979082i	$0.434779\pi$
$7$	−2.09765	+	2.81764i	−0.792839	+	1.06497i	−0.996305	+	0.0858856i	$0.972628\pi$
$8$	0.172370	+	0.977557i	0.0609419	+	0.345618i
$9$	−2.78455	+	1.11636i	−0.928185	+	0.372120i
$10$	1.09767	−	6.22518i	0.347113	−	1.96858i
$11$	1.34549	+	1.42613i	0.405680	+	0.429996i	0.897713	−	0.440581i	$-0.145228\pi$
$11$	1.34549	+	1.42613i	0.405680	+	0.429996i	−0.492033	+	0.870577i	$0.663746\pi$
$12$	1.29262	+	4.07735i	0.373147	+	1.17703i
$13$	1.48971	−	0.748159i	0.413170	−	0.207502i	−0.230057	−	0.973177i	$-0.573891\pi$
$13$	1.48971	−	0.748159i	0.413170	−	0.207502i	0.643227	+	0.765675i	$0.277595\pi$
$14$	6.20462	+	4.08084i	1.65825	+	1.09065i
$15$	0.217782	−	5.17423i	0.0562309	−	1.33598i
$16$	−2.76393	+	0.655063i	−0.690982	+	0.163766i
$17$	3.65626	−	1.33077i	0.886772	−	0.322759i	0.141833	−	0.989891i	$-0.454700\pi$
$17$	3.65626	−	1.33077i	0.886772	−	0.322759i	0.744940	+	0.667132i	$0.232478\pi$
$18$	2.69842	+	5.73971i	0.636024	+	1.35286i
$19$	−0.0155726	−	0.00566795i	−0.00357259	−	0.00130032i	0.340233	−	0.940341i	$-0.389494\pi$
$19$	−0.0155726	−	0.00566795i	−0.00357259	−	0.00130032i	−0.343806	+	0.939041i	$0.611716\pi$
$20$	−7.33393	−	0.857214i	−1.63992	−	0.191679i
$21$	5.48035	+	2.64264i	1.19591	+	0.576670i
$22$	2.84453	−	3.01503i	0.606456	−	0.642806i
$23$	−4.61293	−	6.19624i	−0.961863	−	1.29201i	−0.956412	−	0.292021i	$-0.905672\pi$
$23$	−4.61293	−	6.19624i	−0.961863	−	1.29201i	−0.00545056	−	0.999985i	$-0.501735\pi$
$24$	1.60593	−	0.613989i	0.327809	−	0.125330i
$25$	3.52095	+	1.76829i	0.704190	+	0.353658i
$26$	−1.76215	−	3.05213i	−0.345586	−	0.598572i
$27$	2.81248	+	4.36921i	0.541262	+	0.840854i
$28$	4.33738	−	7.51257i	0.819689	−	1.41974i
$29$	−3.86125	+	2.53958i	−0.717016	+	0.471589i	−0.854856	−	0.518866i	$-0.826354\pi$
$29$	−3.86125	+	2.53958i	−0.717016	+	0.471589i	0.137840	+	0.990455i	$0.455984\pi$
$30$	−10.9472	+	0.176407i	−1.99868	+	0.0322073i
$31$	−4.06577	+	9.42551i	−0.730233	+	1.69287i	−0.00921275	+	0.999958i	$0.502933\pi$
$31$	−4.06577	+	9.42551i	−0.730233	+	1.69287i	−0.721021	+	0.692914i	$0.756327\pi$
$32$	2.29168	+	7.65475i	0.405116	+	1.35318i
$33$	1.98378	−	2.75630i	0.345331	−	0.479811i
$34$	−3.25810	−	7.55312i	−0.558759	−	1.29535i
$35$	−8.04578	+	6.75121i	−1.35998	+	1.14116i
$36$	6.50998	−	3.53655i	1.08500	−	0.589425i
$37$	5.48325	+	4.60100i	0.901441	+	0.756399i	0.970472	−	0.241215i	$-0.0775460\pi$
$37$	5.48325	+	4.60100i	0.901441	+	0.756399i	−0.0690302	+	0.997615i	$0.521990\pi$
$38$	−0.0100482	+	0.0335634i	−0.00163004	+	0.00544470i
$39$	−1.76131	−	2.28794i	−0.282035	−	0.366364i
$40$	−0.172572	+	2.96295i	−0.0272861	+	0.468484i
$41$	0.328910	−	5.64716i	0.0513671	−	0.881938i	−0.869953	−	0.493134i	$-0.835851\pi$
$41$	0.328910	−	5.64716i	0.0513671	−	0.881938i	0.921320	−	0.388804i	$-0.127112\pi$
$42$	4.90374	−	11.8914i	0.756663	−	1.83488i
$43$	1.30885	−	4.37185i	0.199597	−	0.666701i	−0.798322	−	0.602230i	$-0.794279\pi$
$43$	1.30885	−	4.37185i	0.199597	−	0.666701i	0.997920	−	0.0644708i	$-0.0205359\pi$
$44$	−3.70912	−	3.11232i	−0.559170	−	0.469199i
$45$	−8.87114	+	1.32787i	−1.32243	+	0.197947i
$46$	−12.5104	+	10.4975i	−1.84456	+	1.54777i
$47$	−1.13936	−	2.64134i	−0.166193	−	0.385278i	0.814685	−	0.579904i	$-0.196910\pi$
$47$	−1.13936	−	2.64134i	−0.166193	−	0.385278i	−0.980878	+	0.194626i	$0.937651\pi$
$48$	2.02120	+	4.48553i	0.291735	+	0.647430i
$49$	−1.53131	−	5.11494i	−0.218759	−	0.730706i
$50$	3.29924	−	7.64851i	0.466583	−	1.08166i
$51$	−3.46322	−	5.78131i	−0.484948	−	0.809545i
$52$	−3.43950	+	2.26220i	−0.476973	+	0.313710i
$53$	−1.40413	+	2.43202i	−0.192872	+	0.334063i	−0.946201	−	0.323580i	$-0.895113\pi$
$53$	−1.40413	+	2.43202i	−0.192872	+	0.334063i	0.753329	+	0.657644i	$0.228447\pi$
$54$	8.87569	−	6.47296i	1.20783	−	0.880859i
$55$	2.93118	+	5.07695i	0.395240	+	0.684576i
$56$	−3.11597	−	1.56490i	−0.416390	−	0.209119i
$57$	−0.00452821	+	0.0283441i	−0.000599776	+	0.00375426i
$58$	5.83456	+	7.83717i	0.766115	+	1.02907i
$59$	3.40162	−	3.60551i	0.442853	−	0.469397i	−0.467042	−	0.884235i	$-0.654680\pi$
$59$	3.40162	−	3.60551i	0.442853	−	0.469397i	0.909895	+	0.414838i	$0.136162\pi$
$60$	0.949244	+	12.7539i	0.122547	+	1.64653i
$61$	−9.31935	−	1.08928i	−1.19322	−	0.139467i	−0.503794	−	0.863824i	$-0.668063\pi$
$61$	−9.31935	−	1.08928i	−1.19322	−	0.139467i	−0.689426	+	0.724356i	$0.742137\pi$
$62$	20.3928	+	7.42236i	2.58989	+	0.942641i
$63$	2.69554	−	10.1876i	0.339606	−	1.28352i
$64$	10.5356	−	3.83466i	1.31695	−	0.479332i
$65$	4.85003	−	1.14948i	0.601572	−	0.142575i
$66$	−6.06117	−	3.84804i	−0.746079	−	0.473661i
$67$	3.74567	+	2.46356i	0.457606	+	0.300972i	0.757305	−	0.653062i	$-0.226516\pi$
$67$	3.74567	+	2.46356i	0.457606	+	0.300972i	−0.299699	+	0.954034i	$0.596886\pi$
$68$	−8.58664	+	4.31237i	−1.04128	+	0.522952i
$69$	−9.02374	+	9.87875i	−1.08633	+	1.18926i
$70$	15.2378	+	16.1511i	1.82126	+	1.93043i
$71$	−1.33743	+	7.58494i	−0.158724	+	0.900166i	0.796578	+	0.604535i	$0.206641\pi$
$71$	−1.33743	+	7.58494i	−0.158724	+	0.900166i	−0.955302	+	0.295631i	$0.904470\pi$
$72$	−1.57128	−	2.52963i	−0.185177	−	0.298120i
$73$	−0.696188	−	3.94828i	−0.0814827	−	0.462111i	−0.998060	−	0.0622545i	$-0.980171\pi$
$73$	−0.696188	−	3.94828i	−0.0814827	−	0.462111i	0.916578	−	0.399857i	$-0.130940\pi$
$74$	9.03659	−	12.1383i	1.05048	−	1.41104i
$75$	1.85166	−	6.56835i	0.213811	−	0.758447i
$76$	0.0398218	+	0.00943793i	0.00456787	+	0.00108261i
$77$	−6.84070	+	0.799563i	−0.779570	+	0.0911187i
$78$	−4.61231	+	3.99858i	−0.522241	+	0.452750i
$79$	−0.473972	−	8.13778i	−0.0533260	−	0.915572i	−0.913822	−	0.406115i	$-0.866883\pi$
$79$	−0.473972	−	8.13778i	−0.0533260	−	0.915572i	0.860496	−	0.509457i	$-0.170154\pi$
$80$	−8.49305			−0.949552
$81$	6.50749	−	6.21712i	0.723054	−	0.690791i
$82$	−11.9590			−1.32065
$83$	−0.299799	−	5.14735i	−0.0329072	−	0.564995i	−0.973958	−	0.226729i	$-0.927197\pi$
$83$	−0.299799	−	5.14735i	−0.0329072	−	0.564995i	0.941051	−	0.338266i	$-0.109840\pi$
$84$	−14.2000	−	4.91075i	−1.54934	−	0.535806i
$85$	11.5551	−	1.35060i	1.25333	−	0.146493i
$86$	−9.38790	−	2.22497i	−1.01232	−	0.239925i
$87$	5.58630	+	5.73319i	0.598914	+	0.614662i
$88$	−1.16221	+	1.56111i	−0.123892	+	0.166415i
$89$	0.829745	+	4.70572i	0.0879528	+	0.498805i	0.996680	+	0.0814153i	$0.0259440\pi$
$89$	0.829745	+	4.70572i	0.0879528	+	0.498805i	−0.908727	+	0.417390i	$0.862945\pi$
$90$	3.89302	+	18.5597i	0.410360	+	1.95637i
$91$	−1.01685	+	5.76683i	−0.106595	+	0.604528i
$92$	13.0912	+	13.8758i	1.36485	+	1.44665i
$93$	17.3641	+	3.82097i	1.80057	+	0.396216i
$94$	−5.43461	+	2.72936i	−0.560537	+	0.281512i
$95$	−0.0413984	−	0.0272282i	−0.00424739	−	0.00279355i
$96$	12.2660	−	6.40977i	1.25190	−	0.654195i
$97$	−11.3173	+	2.68224i	−1.14909	+	0.272340i	−0.760669	−	0.649140i	$-0.775129\pi$
$97$	−11.3173	+	2.68224i	−1.14909	+	0.272340i	−0.388425	+	0.921481i	$0.626981\pi$
$98$	−10.6071	+	3.86067i	−1.07148	+	0.389986i
$99$	−5.33866	−	2.46910i	−0.536556	−	0.248154i
$100$	−9.14325	−	3.32787i	−0.914325	−	0.332787i
$101$	−2.83994	−	0.331942i	−0.282585	−	0.0330294i	−0.0263802	−	0.999652i	$-0.508398\pi$
$101$	−2.83994	−	0.331942i	−0.282585	−	0.0330294i	−0.256205	+	0.966623i	$0.582472\pi$
$102$	−11.7760	+	8.01997i	−1.16600	+	0.794095i
$103$	1.96327	−	2.08095i	0.193447	−	0.205042i	−0.623389	−	0.781912i	$-0.714245\pi$
$103$	1.96327	−	2.08095i	0.193447	−	0.205042i	0.816836	+	0.576870i	$0.195726\pi$
$104$	0.988148	+	1.32731i	0.0968958	+	0.130154i
$105$	14.1223	+	11.4674i	1.37819	+	1.11910i
$106$	5.30549	+	2.66452i	0.515315	+	0.258801i
$107$	−7.89300	−	13.6711i	−0.763045	−	1.32163i	−0.941274	−	0.337644i	$-0.890370\pi$
$107$	−7.89300	−	13.6711i	−0.763045	−	1.32163i	0.178229	−	0.983989i	$-0.442963\pi$
$108$	−8.15116	−	9.91059i	−0.784346	−	0.953647i
$109$	0.145393	−	0.251828i	0.0139261	−	0.0241207i	−0.858978	−	0.512012i	$-0.828900\pi$
$109$	0.145393	−	0.251828i	0.0139261	−	0.0241207i	0.872904	+	0.487891i	$0.162234\pi$
$110$	10.3548	−	6.81049i	0.987295	−	0.649354i
$111$	6.02511	−	10.8353i	0.571878	−	1.02844i
$112$	3.95203	−	9.16185i	0.373432	−	0.865713i
$113$	0.927413	+	3.09777i	0.0872436	+	0.291414i	0.990466	−	0.137759i	$-0.0439901\pi$
$113$	0.927413	+	3.09777i	0.0872436	+	0.291414i	−0.903222	+	0.429173i	$0.858805\pi$
$114$	0.0603781	+	0.00607281i	0.00565493	+	0.000568770i
$115$	−9.14829	−	21.2081i	−0.853082	−	1.97767i
$116$	8.74289	−	7.33616i	0.811757	−	0.681145i
$117$	−3.31295	+	3.74634i	−0.306283	+	0.346349i
$118$	−8.02774	−	6.73608i	−0.739014	−	0.620106i
$119$	−3.91994	+	13.0935i	−0.359340	+	1.20028i
$120$	5.09565	−	0.678987i	0.465167	−	0.0619828i
$121$	0.416073	−	7.14370i	0.0378248	−	0.649427i
$122$	−1.15338	+	19.8028i	−0.104422	+	1.79286i
$123$	−9.71191	+	1.29410i	−0.875693	+	0.116685i
$124$	7.27039	−	24.2848i	0.652900	−	2.18084i
$125$	−2.42779	−	2.03716i	−0.217149	−	0.182209i
$126$	−21.8328	−	4.43675i	−1.94502	−	0.395257i
$127$	10.0576	−	8.43933i	0.892468	−	0.748870i	−0.0762356	−	0.997090i	$-0.524290\pi$
$127$	10.0576	−	8.43933i	0.892468	−	0.748870i	0.968704	+	0.248220i	$0.0798457\pi$
$128$	−3.05863	−	7.09071i	−0.270348	−	0.626736i
$129$	−7.86465	−	0.791023i	−0.692444	−	0.0696457i
$130$	−3.02222	−	10.0949i	−0.265066	−	0.885383i
$131$	−0.000127832	0	0.000296348i	−1.11687e−5	0	2.58921e-5i	−0.918222	−	0.396067i	$-0.870375\pi$
$131$	−0.000127832	0	0.000296348i	−1.11687e−5	0	2.58921e-5i	0.918211	+	0.396093i	$0.129634\pi$
$132$	−4.07565	+	7.32948i	−0.354740	+	0.637949i
$133$	0.0486361	−	0.0319885i	0.00421728	−	0.00277375i
$134$	4.73903	−	8.20825i	0.409390	−	0.709085i
$135$	5.16988	+	14.6511i	0.444952	+	1.26096i
$136$	1.93113	+	3.34481i	0.165593	+	0.286815i
$137$	11.5229	+	5.78704i	0.984471	+	0.494420i	0.866813	−	0.498634i	$-0.166165\pi$
$137$	11.5229	+	5.78704i	0.984471	+	0.494420i	0.117659	+	0.993054i	$0.462461\pi$
$138$	21.9588	+	17.8307i	1.86926	+	1.51785i
$139$	0.382991	+	0.514447i	0.0324849	+	0.0436348i	0.818069	−	0.575120i	$-0.195045\pi$
$139$	0.382991	+	0.514447i	0.0324849	+	0.0436348i	−0.785584	+	0.618755i	$0.787637\pi$
$140$	17.7994	−	18.8662i	1.50432	−	1.59449i
$141$	−4.11809	+	2.80459i	−0.346806	+	0.236189i
$142$	16.1728	+	1.89033i	1.35719	+	0.158633i
$143$	3.07136	+	1.11788i	0.256840	+	0.0934820i
$144$	6.96502	−	4.90959i	0.580418	−	0.409133i
$145$	−12.9850	+	4.72617i	−1.07835	+	0.392487i
$146$	−8.24746	+	1.95468i	−0.682565	+	0.161771i
$147$	−8.19623	+	4.28304i	−0.676014	+	0.353259i
$148$	−14.7686	−	9.71343i	−1.21397	−	0.798439i
$149$	11.5482	−	5.79972i	0.946064	−	0.475131i	0.0922656	−	0.995734i	$-0.470589\pi$
$149$	11.5482	−	5.79972i	0.946064	−	0.475131i	0.853799	+	0.520603i	$0.174293\pi$
$150$	−14.0904	−	3.10060i	−1.15048	−	0.253163i
$151$	11.5173	+	12.2076i	0.937265	+	0.993443i	0.999989	−	0.00458769i	$-0.00146031\pi$
$151$	11.5173	+	12.2076i	0.937265	+	0.993443i	−0.0627241	+	0.998031i	$0.519979\pi$
$152$	0.00285650	−	0.0162000i	0.000231693	−	0.00131400i
$153$	−8.69543	+	7.78729i	−0.702984	+	0.629565i
$154$	2.52841	+	14.3393i	0.203745	+	1.15550i
$155$	−18.3282	+	24.6190i	−1.47215	+	1.97745i
$156$	4.97613	+	5.10698i	0.398409	+	0.408885i
$157$	−8.36915	−	1.98352i	−0.667931	−	0.158303i	−0.117358	−	0.993090i	$-0.537443\pi$
$157$	−8.36915	−	1.98352i	−0.667931	−	0.158303i	−0.550573	+	0.834787i	$0.685591\pi$
$158$	−17.1169	+	2.00068i	−1.36175	+	0.159166i
$159$	4.59691	+	1.58974i	0.364559	+	0.126074i
$160$	1.38916	+	23.8509i	0.109822	+	1.88558i
$161$	27.1351			2.13855
$162$	−13.9215	−	12.9701i	−1.09377	−	1.01903i
$163$	0.674482			0.0528295			0.0264148	−	0.999651i	$-0.491591\pi$
$163$	0.674482			0.0528295			0.0264148	+	0.999651i	$0.491591\pi$
$164$	0.812251	+	13.9458i	0.0634261	+	1.08898i
$165$	7.67217	−	6.65128i	0.597278	−	0.517802i
$166$	−10.8269	+	1.26548i	−0.840329	+	0.0982204i
$167$	−15.6852	−	3.71746i	−1.21376	−	0.287666i	−0.426613	−	0.904434i	$-0.640293\pi$
$167$	−15.6852	−	3.71746i	−1.21376	−	0.287666i	−0.787145	+	0.616769i	$0.788441\pi$
$168$	−1.63868	+	5.81286i	−0.126427	+	0.448472i
$169$	−6.10358	+	8.19853i	−0.469506	+	0.630656i
$170$	−4.27092	−	24.2216i	−0.327565	−	1.85771i
$171$	0.0496901	−	0.00160185i	0.00379990	−	0.000122497i
$172$	−1.95699	+	11.0986i	−0.149219	+	0.846263i
$173$	−11.0692	−	11.7327i	−0.841575	−	0.892018i	0.153798	−	0.988102i	$-0.450850\pi$
$173$	−11.0692	−	11.7327i	−0.841575	−	0.892018i	−0.995373	+	0.0960847i	$0.969368\pi$
$174$	11.4135	−	12.4949i	0.865253	−	0.947236i
$175$	−12.3681	+	6.21151i	−0.934943	+	0.469546i
$176$	−4.65304	−	3.06035i	−0.350736	−	0.230683i
$177$	−7.24823	−	4.60166i	−0.544810	−	0.345882i
$178$	9.82965	−	2.32967i	0.736764	−	0.174616i
$179$	7.45990	−	2.71518i	0.557579	−	0.202942i	−0.0478318	−	0.998855i	$-0.515231\pi$
$179$	7.45990	−	2.71518i	0.557579	−	0.202942i	0.605411	+	0.795913i	$0.293009\pi$
$180$	21.3787	−	5.80034i	1.59347	−	0.432332i
$181$	13.0001	+	4.73166i	0.966292	+	0.351702i	0.776496	−	0.630122i	$-0.216995\pi$
$181$	13.0001	+	4.73166i	0.966292	+	0.351702i	0.189796	+	0.981824i	$0.439217\pi$
$182$	12.2962	+	1.43722i	0.911453	+	0.106534i
$183$	1.20622	+	16.2066i	0.0891663	+	1.19803i
$184$	5.26205	−	5.57745i	0.387923	−	0.411175i
$185$	12.7804	+	17.1670i	0.939632	+	1.26215i
$186$	5.92984	−	37.1175i	0.434797	−	2.72159i
$187$	6.81730	+	3.42378i	0.498531	+	0.250371i
$188$	3.55191	+	6.15209i	0.259050	+	0.448687i
$189$	−18.2105	−	1.24053i	−1.32462	−	0.0902352i
$190$	−0.0523775	+	0.0907205i	−0.00379986	+	0.00658155i
$191$	12.0095	−	7.89878i	0.868978	−	0.571536i	−0.0348691	−	0.999392i	$-0.511101\pi$
$191$	12.0095	−	7.89878i	0.868978	−	0.571536i	0.903847	+	0.427856i	$0.140731\pi$
$192$	−9.97940	−	16.6591i	−0.720201	−	1.20226i
$193$	−1.65716	+	3.84172i	−0.119285	+	0.276533i	−0.967389	−	0.253297i	$-0.918485\pi$
$193$	−1.65716	+	3.84172i	−0.119285	+	0.276533i	0.848104	+	0.529830i	$0.177744\pi$
$194$	7.05217	+	23.5559i	0.506317	+	1.69122i
$195$	−3.54672	−	7.87102i	−0.253986	−	0.563656i
$196$	5.22247	+	12.1071i	0.373034	+	0.864790i
$197$	−0.181162	+	0.152013i	−0.0129073	+	0.0108305i	−0.649218	−	0.760602i	$-0.724904\pi$
$197$	−0.181162	+	0.152013i	−0.0129073	+	0.0108305i	0.636311	+	0.771432i	$0.280459\pi$
$198$	−4.55490	+	11.5710i	−0.323703	+	0.822317i
$199$	19.9860	+	16.7702i	1.41677	+	1.18881i	0.953044	+	0.302832i	$0.0979322\pi$
$199$	19.9860	+	16.7702i	1.41677	+	1.18881i	0.463726	+	0.885979i	$0.346512\pi$
$200$	−1.12170	+	3.74673i	−0.0793159	+	0.264934i
$201$	2.96034	−	7.17871i	0.208806	−	0.506347i
$202$	−0.351478	+	6.03464i	−0.0247299	+	0.424596i
$203$	0.943937	−	16.2068i	0.0662514	−	1.13749i
$204$	10.1522	+	13.1877i	0.710793	+	0.923322i
$205$	4.85087	−	16.2030i	0.338799	−	1.13167i
$206$	−4.63328	−	3.88778i	−0.322816	−	0.270874i
$207$	19.7622	+	12.1041i	1.37357	+	0.841292i
$208$	−3.62735	+	3.04371i	−0.251511	+	0.211043i
$209$	−0.0128694	−	0.0298347i	−0.000890197	−	0.00206371i
$210$	22.4665	−	31.2154i	1.55034	−	2.15407i
$211$	3.38403	+	11.3034i	0.232966	+	0.778161i	0.991903	+	0.126997i	$0.0405338\pi$
$211$	3.38403	+	11.3034i	0.232966	+	0.778161i	−0.758937	+	0.651164i	$0.774281\pi$
$212$	2.74683	−	6.36788i	0.188653	−	0.437348i
$213$	13.3384	−	0.214939i	0.913934	−	0.0147274i
$214$	−27.8832	+	18.3391i	−1.90606	+	1.25363i
$215$	6.82251	−	11.8169i	0.465292	−	0.805909i
$216$	−3.78636	+	3.50248i	−0.257629	+	0.238313i
$217$	−18.0291	−	31.2273i	−1.22390	−	2.11985i
$218$	−0.549367	−	0.275903i	−0.0372078	−	0.0186865i
$219$	−6.48622	+	2.47986i	−0.438298	+	0.167573i
$220$	−8.64522	−	11.6125i	−0.582860	−	0.782917i
$221$	4.45112	−	4.71791i	0.299415	−	0.317361i
$222$	−23.6091	−	11.3843i	−1.58454	−	0.764067i
$223$	26.1580	+	3.05743i	1.75167	+	0.204741i	0.930587	−	0.366071i	$-0.119297\pi$
$223$	26.1580	+	3.05743i	1.75167	+	0.204741i	0.821081	+	0.570811i	$0.193371\pi$
$224$	−26.3755	−	9.59989i	−1.76229	−	0.641420i
$225$	−11.7783	−	0.993250i	−0.785222	−	0.0662166i
$226$	6.42400	−	2.33814i	0.427318	−	0.155531i
$227$	−0.992030	+	0.235115i	−0.0658433	+	0.0156052i	−0.263405	−	0.964685i	$-0.584846\pi$
$227$	−0.992030	+	0.235115i	−0.0658433	+	0.0156052i	0.197562	+	0.980290i	$0.436698\pi$
$228$	0.00298084	−	0.0708213i	0.000197411	−	0.00469026i
$229$	−21.7908	−	14.3320i	−1.43998	−	0.947087i	−0.998765	−	0.0496840i	$-0.984179\pi$
$229$	−21.7908	−	14.3320i	−1.43998	−	0.947087i	−0.441211	−	0.897403i	$-0.645451\pi$
$230$	−43.6362	+	21.9149i	−2.87729	+	1.44503i
$231$	3.60499	+	11.3713i	0.237191	+	0.748180i
$232$	−3.14815	−	3.33684i	−0.206686	−	0.219074i
$233$	0.779551	−	4.42105i	0.0510701	−	0.289633i	−0.948567	−	0.316577i	$-0.897467\pi$
$233$	0.779551	−	4.42105i	0.0510701	−	0.289633i	0.999637	+	0.0269441i	$0.00857761\pi$
$234$	8.31407	+	6.53163i	0.543508	+	0.426986i
$235$	−1.49355	−	8.47032i	−0.0974282	−	0.552543i
$236$	−7.30991	+	9.81891i	−0.475835	+	0.639157i
$237$	−13.6841	+	3.47698i	−0.888879	+	0.225854i
$238$	28.1163	+	6.66369i	1.82251	+	0.431943i
$239$	1.51467	−	0.177040i	0.0979761	−	0.0114518i	−0.0669635	−	0.997755i	$-0.521331\pi$
$239$	1.51467	−	0.177040i	0.0979761	−	0.0114518i	0.164940	+	0.986304i	$0.447257\pi$
$240$	2.78752	+	14.4439i	0.179933	+	0.932348i
$241$	−0.0489678	−	0.840744i	−0.00315429	−	0.0541571i	0.996364	−	0.0852020i	$-0.0271536\pi$
$241$	−0.0489678	−	0.840744i	−0.00315429	−	0.0541571i	−0.999518	+	0.0310449i	$0.990117\pi$
$242$	−15.1283			−0.972482
$243$	−12.7091	−	9.02655i	−0.815289	−	0.579054i
$244$	23.1711			1.48337
$245$	−0.928241	−	15.9373i	−0.0593032	−	1.01820i
$246$	3.92509	+	20.3384i	0.250255	+	1.29673i
$247$	−0.0274391	+	0.00320717i	−0.00174591	+	0.000204067i
$248$	−9.91478	−	2.34985i	−0.629589	−	0.149215i
$249$	−8.65554	+	2.19928i	−0.548523	+	0.139374i
$250$	−4.00109	+	5.37440i	−0.253051	+	0.339907i
$251$	2.59126	+	14.6958i	0.163559	+	0.927590i	0.950538	+	0.310609i	$0.100533\pi$
$251$	2.59126	+	14.6958i	0.163559	+	0.927590i	−0.786978	+	0.616980i	$0.788356\pi$
$252$	−3.69096	+	25.7612i	−0.232509	+	1.62281i
$253$	2.63003	−	14.9156i	0.165348	−	0.937737i
$254$	−19.0480	−	20.1897i	−1.19518	−	1.26681i
$255$	−6.08944	−	19.2081i	−0.381336	−	1.20286i
$256$	5.44914	−	2.73666i	0.340571	−	0.171041i
$257$	7.70656	+	5.06869i	0.480722	+	0.316176i	0.766639	−	0.642079i	$-0.221928\pi$
$257$	7.70656	+	5.06869i	0.480722	+	0.316176i	−0.285917	+	0.958254i	$0.592298\pi$
$258$	−0.702727	+	16.6960i	−0.0437499	+	1.03945i
$259$	−24.4659	+	5.79853i	−1.52024	+	0.360303i
$260$	−11.5667	+	4.20995i	−0.717339	+	0.261090i
$261$	7.91677	−	11.3821i	0.490036	−	0.704537i
$262$	0.000641171	0	0.000233367i	3.96117e−5	0	1.44175e-5i
$263$	−0.236423	−	0.0276339i	−0.0145785	−	0.00170398i	0.108801	−	0.994064i	$-0.465299\pi$
$263$	−0.236423	−	0.0276339i	−0.0145785	−	0.00170398i	−0.123379	+	0.992360i	$0.539373\pi$
$264$	3.03639	+	1.46415i	0.186877	+	0.0901123i
$265$	−5.76213	+	6.10750i	−0.353965	+	0.375181i
$266$	−0.0734918	−	0.0987166i	−0.00450607	−	0.00605270i
$267$	7.73054	−	2.95559i	0.473102	−	0.180879i
$268$	−9.89377	−	4.96884i	−0.604358	−	0.303520i
$269$	7.21026	+	12.4885i	0.439617	+	0.761439i	0.997660	−	0.0683731i	$-0.0217808\pi$
$269$	7.21026	+	12.4885i	0.439617	+	0.761439i	−0.558043	+	0.829812i	$0.688447\pi$
$270$	30.2863	−	12.7123i	1.84316	−	0.773644i
$271$	−8.33200	+	14.4314i	−0.506133	+	0.876648i	0.493842	+	0.869552i	$0.335592\pi$
$271$	−8.33200	+	14.4314i	−0.506133	+	0.876648i	−0.999975	+	0.00709598i	$0.997741\pi$
$272$	−9.23389	+	6.07322i	−0.559887	+	0.368243i
$273$	10.1412	−	0.163418i	0.613775	−	0.00989052i
$274$	10.7974	−	25.0311i	0.652293	−	1.51218i
$275$	2.21558	+	7.40056i	0.133605	+	0.446270i
$276$	19.3015	−	26.8179i	1.16181	−	1.61425i
$277$	9.82960	+	22.7876i	0.590603	+	1.36917i	0.907235	+	0.420624i	$0.138189\pi$
$277$	9.82960	+	22.7876i	0.590603	+	1.36917i	−0.316632	+	0.948548i	$0.602552\pi$
$278$	1.03869	−	0.871561i	0.0622962	−	0.0522727i
$279$	0.799101	−	30.7847i	0.0478410	−	1.84303i
$280$	−7.98654	−	6.70150i	−0.477287	−	0.400491i
$281$	5.54249	−	18.5132i	0.330637	−	1.10441i	−0.617507	−	0.786565i	$-0.711857\pi$
$281$	5.54249	−	18.5132i	0.330637	−	1.10441i	0.948144	−	0.317840i	$-0.102958\pi$
$282$	6.42545	+	8.34667i	0.382630	+	0.497037i
$283$	−0.0649046	+	1.11437i	−0.00385818	+	0.0662424i	−0.999688	−	0.0249916i	$-0.992044\pi$
$283$	−0.0649046	+	1.11437i	−0.00385818	+	0.0662424i	0.995829	+	0.0912340i	$0.0290811\pi$
$284$	1.10592	−	18.9880i	0.0656245	−	1.12673i
$285$	−0.0327187	+	0.0793417i	−0.00193809	+	0.00469980i
$286$	1.98180	−	6.61966i	0.117186	−	0.391429i
$287$	15.2217	+	12.7725i	0.898510	+	0.753939i
$288$	−14.9268	−	18.7567i	−0.879568	−	1.10525i
$289$	−1.42549	+	1.19613i	−0.0838523	+	0.0703605i
$290$	11.5710	+	26.8246i	0.679472	+	1.57519i
$291$	8.27605	+	18.3666i	0.485151	+	1.07667i
$292$	2.83958	+	9.48486i	0.166174	+	0.555059i
$293$	−3.18356	+	7.38032i	−0.185985	+	0.431163i	−0.985543	−	0.169427i	$-0.945808\pi$
$293$	−3.18356	+	7.38032i	−0.185985	+	0.431163i	0.799557	+	0.600590i	$0.205068\pi$
$294$	10.0471	+	16.7721i	0.585958	+	0.978166i
$295$	12.3828	−	8.14429i	0.720954	−	0.474179i
$296$	−3.55259	+	6.15326i	−0.206490	+	0.357651i
$297$	−2.44691	+	9.88969i	−0.141984	+	0.573858i
$298$	−13.6602	−	23.6601i	−0.791311	−	1.37059i
$299$	−11.5077	−	5.77938i	−0.665507	−	0.334230i
$300$	−2.65869	+	16.6419i	−0.153499	+	0.960820i
$301$	9.57279	+	12.8585i	0.551767	+	0.741151i
$302$	24.3490	−	25.8085i	1.40113	−	1.48511i
$303$	0.367579	+	4.93875i	0.0211169	+	0.283724i
$304$	0.0467543	+	0.00546479i	0.00268154	+	0.000313427i
$305$	−26.3626	−	9.59519i	−1.50952	−	0.549419i
$306$	17.5043	+	17.3949i	1.00066	+	0.994399i
$307$	−15.7796	+	5.74331i	−0.900590	+	0.327788i	−0.750489	−	0.660883i	$-0.770182\pi$
$307$	−15.7796	+	5.74331i	−0.900590	+	0.327788i	−0.150101	+	0.988671i	$0.547960\pi$
$308$	16.5498	−	3.92238i	0.943014	−	0.223498i
$309$	−4.18337	−	2.65589i	−0.237984	−	0.151088i
$310$	54.2126	+	35.6562i	3.07907	+	2.02514i
$311$	−4.60665	+	2.31355i	−0.261219	+	0.131189i	−0.574589	−	0.818442i	$-0.694838\pi$
$311$	−4.60665	+	2.31355i	−0.261219	+	0.131189i	0.313370	+	0.949631i	$0.398542\pi$
$312$	1.93300	−	2.11615i	0.109435	−	0.119804i
$313$	−19.1736	−	20.3229i	−1.08376	−	1.14872i	−0.988181	−	0.153293i	$-0.951012\pi$
$313$	−19.1736	−	20.3229i	−1.08376	−	1.14872i	−0.0955764	−	0.995422i	$-0.530469\pi$
$314$	−3.15754	+	17.9073i	−0.178191	+	1.01057i
$315$	14.8671	−	27.7811i	0.837668	−	1.56529i
$316$	3.49563	+	19.8247i	0.196644	+	1.11523i
$317$	−5.49046	+	7.37497i	−0.308375	+	0.414220i	−0.929111	−	0.369800i	$-0.879426\pi$
$317$	−5.49046	+	7.37497i	−0.308375	+	0.414220i	0.620736	+	0.784019i	$0.286834\pi$
$318$	2.79014	−	9.89742i	0.156463	−	0.555020i
$319$	−8.81705	−	2.08968i	−0.493660	−	0.117000i
$320$	33.2965	−	3.89180i	1.86133	−	0.217558i
$321$	−20.6594	+	17.9104i	−1.15310	+	0.999660i
$322$	−3.33560	−	57.2700i	−0.185886	−	3.19153i
$323$	−0.0644800			−0.00358776
$324$	−14.1793	+	17.1152i	−0.787741	+	0.950844i
$325$	6.56814			0.364335
$326$	−0.0829110	−	1.42353i	−0.00459202	−	0.0788419i
$327$	−0.475995	−	0.164612i	−0.0263226	−	0.00910308i
$328$	5.57711	−	0.651871i	0.307945	−	0.0359936i
$329$	9.83232	+	2.33030i	0.542073	+	0.128474i
$330$	−14.9810	−	15.3749i	−0.824675	−	0.846359i
$331$	10.1224	−	13.5968i	0.556379	−	0.747347i	−0.431578	−	0.902076i	$-0.642043\pi$
$331$	10.1224	−	13.5968i	0.556379	−	0.747347i	0.987957	+	0.154729i	$0.0494504\pi$
$332$	2.21107	+	12.5396i	0.121348	+	0.688201i
$333$	−20.4048	−	6.69045i	−1.11818	−	0.366634i
$334$	−5.91777	+	33.5613i	−0.323806	+	1.83640i
$335$	9.19890	+	9.75027i	0.502590	+	0.532714i
$336$	−16.8784	−	3.71408i	−0.920791	−	0.202620i
$337$	11.6581	−	5.85489i	0.635055	−	0.318936i	−0.101985	−	0.994786i	$-0.532519\pi$
$337$	11.6581	−	5.85489i	0.635055	−	0.318936i	0.737040	+	0.675850i	$0.236223\pi$
$338$	18.0537	+	11.8741i	0.981991	+	0.645865i
$339$	4.96390	−	2.59395i	0.269602	−	0.140884i
$340$	−27.9555	+	6.62557i	−1.51610	+	0.359322i
$341$	−18.9125	+	6.88358i	−1.02417	+	0.372767i
$342$	−0.00948897	−	0.104676i	−0.000513105	−	0.00566025i
$343$	−5.48195	−	1.99527i	−0.295997	−	0.107734i
$344$	4.49934	+	0.525897i	0.242588	+	0.0283545i
$345$	−33.0654	+	22.5190i	−1.78018	+	1.21238i
$346$	−23.4017	+	24.8043i	−1.25808	+	1.33349i
$347$	−8.59518	−	11.5453i	−0.461414	−	0.619786i	0.509136	−	0.860686i	$-0.329965\pi$
$347$	−8.59518	−	11.5453i	−0.461414	−	0.619786i	−0.970550	+	0.240900i	$0.922557\pi$
$348$	−15.3459	−	12.4610i	−0.822627	−	0.667978i
$349$	7.26816	+	3.65021i	0.389056	+	0.195391i	0.632565	−	0.774508i	$-0.282002\pi$
$349$	7.26816	+	3.65021i	0.389056	+	0.195391i	−0.243509	+	0.969899i	$0.578299\pi$
$350$	14.6301	+	25.3400i	0.782010	+	1.35448i
$351$	7.45863	+	4.40465i	0.398112	+	0.235103i
$352$	−7.83327	+	13.5676i	−0.417515	+	0.723157i
$353$	22.6466	−	14.8949i	1.20536	−	0.792775i	0.222103	−	0.975023i	$-0.428708\pi$
$353$	22.6466	−	14.8949i	1.20536	−	0.792775i	0.983253	+	0.182248i	$0.0583374\pi$
$354$	−8.82104	+	15.8634i	−0.468833	+	0.843130i
$355$	−9.12122	+	21.1454i	−0.484104	+	1.12228i
$356$	−3.38433	−	11.3044i	−0.179369	−	0.599134i
$357$	23.5543	+	2.36908i	1.24663	+	0.125385i
$358$	−6.64753	−	15.4107i	−0.351333	−	0.814481i
$359$	19.0992	−	16.0261i	1.00802	−	0.845828i	0.0199431	−	0.999801i	$-0.493651\pi$
$359$	19.0992	−	16.0261i	1.00802	−	0.845828i	0.988075	+	0.153974i	$0.0492071\pi$
$360$	−2.82718	−	8.44316i	−0.149006	−	0.444994i
$361$	−14.5546	−	12.2128i	−0.766033	−	0.642778i
$362$	8.38836	−	28.0191i	0.440882	−	1.47265i
$363$	−12.2856	+	1.63704i	−0.644828	+	0.0859224i
$364$	0.840835	−	14.4366i	0.0440717	−	0.756682i
$365$	0.697007	−	11.9672i	0.0364830	−	0.626390i
$366$	34.0566	−	4.53800i	1.78017	−	0.237205i
$367$	−3.75486	+	12.5421i	−0.196002	+	0.654693i	0.802326	+	0.596887i	$0.203596\pi$
$367$	−3.75486	+	12.5421i	−0.196002	+	0.654693i	−0.998328	+	0.0578064i	$0.981589\pi$
$368$	16.8087	+	14.1042i	0.876216	+	0.735232i
$369$	5.38839	+	16.0920i	0.280508	+	0.837716i
$370$	34.6608	−	29.0839i	1.80193	−	1.51200i
$371$	−3.90718	−	9.05785i	−0.202851	−	0.470260i
$372$	−43.6866	−	4.39398i	−2.26505	−	0.227817i
$373$	8.25291	+	27.5666i	0.427319	+	1.42735i	0.852733	+	0.522347i	$0.174943\pi$
$373$	8.25291	+	27.5666i	0.427319	+	1.42735i	−0.425414	+	0.904999i	$0.639871\pi$
$374$	6.38803	−	14.8091i	0.330317	−	0.765761i
$375$	−2.66771	+	4.79750i	−0.137760	+	0.247742i
$376$	2.38566	−	1.56908i	0.123031	−	0.0809189i
$377$	−3.85211	+	6.67206i	−0.198394	+	0.343628i
$378$	−0.379668	+	38.5865i	−0.0195280	+	1.98468i
$379$	10.4915	+	18.1718i	0.538912	+	0.933422i	0.998963	+	0.0455300i	$0.0144977\pi$
$379$	10.4915	+	18.1718i	0.538912	+	0.933422i	−0.460051	+	0.887892i	$0.652169\pi$
$380$	0.109349	+	0.0549174i	0.00560951	+	0.00281720i
$381$	−17.6535	−	14.3348i	−0.904418	−	0.734393i
$382$	−18.1470	−	24.3757i	−0.928483	−	1.24717i
$383$	−16.8095	+	17.8171i	−0.858927	+	0.910410i	−0.996792	−	0.0800414i	$-0.974495\pi$
$383$	−16.8095	+	17.8171i	−0.858927	+	0.910410i	0.137864	+	0.990451i	$0.455976\pi$
$384$	−11.0551	+	7.52898i	−0.564152	+	0.384211i
$385$	−20.4536	−	2.39069i	−1.04241	−	0.121841i
$386$	8.31185	+	3.02526i	0.423062	+	0.153982i
$387$	1.23600	+	13.6348i	0.0628295	+	0.693096i
$388$	26.9903	−	9.82366i	1.37022	−	0.498721i
$389$	−15.3418	+	3.63608i	−0.777862	+	0.184357i	−0.600324	−	0.799757i	$-0.704962\pi$
$389$	−15.3418	+	3.63608i	−0.777862	+	0.184357i	−0.177539	+	0.984114i	$0.556813\pi$
$390$	−16.1762	+	8.45307i	−0.819114	+	0.428038i
$391$	−25.1118	−	16.5163i	−1.26996	−	0.835265i
$392$	4.73620	−	2.37861i	0.239214	−	0.120138i
$393$	0.000545946	0	0.000120135i	2.75394e−5	0	6.06003e-6i
$394$	0.343100	+	0.363665i	0.0172851	+	0.0183212i
$395$	4.23235	−	24.0028i	0.212953	−	1.20771i
$396$	13.8027	+	4.52571i	0.693612	+	0.227426i
$397$	−4.48471	−	25.4340i	−0.225081	−	1.27650i	−0.862530	−	0.506005i	$-0.831122\pi$
$397$	−4.48471	−	25.4340i	−0.225081	−	1.27650i	0.637449	−	0.770492i	$-0.279989\pi$
$398$	32.9376	−	44.2429i	1.65101	−	2.21770i
$399$	−0.0703647	−	0.0722149i	−0.00352264	−	0.00361527i
$400$	−10.8900	−	2.58098i	−0.544500	−	0.129049i
$401$	−16.2679	+	1.90144i	−0.812378	+	0.0949534i	−0.512130	−	0.858908i	$-0.671144\pi$
$401$	−16.2679	+	1.90144i	−0.812378	+	0.0949534i	−0.300248	+	0.953861i	$0.597069\pi$
$402$	−15.5149	−	5.36549i	−0.773814	−	0.267606i
$403$	0.994976	+	17.0831i	0.0495633	+	0.850969i
$404$	7.06106			0.351301
$405$	23.2198	−	13.6009i	1.15380	−	0.675834i
$406$	−34.3212			−1.70333
$407$	0.816015	+	14.0104i	0.0404484	+	0.694472i
$408$	5.05460	−	4.38202i	0.250240	−	0.216942i
$409$	25.1846	−	2.94366i	1.24530	−	0.145555i	0.532200	−	0.846618i	$-0.321365\pi$
$409$	25.1846	−	2.94366i	1.24530	−	0.145555i	0.713099	+	0.701064i	$0.247291\pi$
$410$	−34.7936	−	8.24623i	−1.71833	−	0.407252i
$411$	6.05988	−	21.4961i	0.298912	−	1.06032i
$412$	−4.21897	+	5.66706i	−0.207854	+	0.279196i
$413$	3.02359	+	17.1476i	0.148781	+	0.843781i
$414$	23.1170	−	43.1970i	1.13614	−	2.12301i
$415$	2.67707	−	15.1824i	0.131412	−	0.745275i
$416$	9.14090	+	9.68879i	0.448170	+	0.475032i
$417$	0.749202	−	0.820189i	0.0366886	−	0.0401648i
$418$	−0.0613856	+	0.0308290i	−0.00300247	+	0.00150790i
$419$	5.31350	+	3.49475i	0.259582	+	0.170730i	0.672629	−	0.739980i	$-0.265165\pi$
$419$	5.31350	+	3.49475i	0.259582	+	0.170730i	−0.413047	+	0.910710i	$0.635536\pi$
$420$	−37.9272	−	24.0787i	−1.85066	−	1.17492i
$421$	25.5568	−	6.05707i	1.24556	−	0.295203i	0.445588	−	0.895238i	$-0.352995\pi$
$421$	25.5568	−	6.05707i	1.24556	−	0.295203i	0.799974	+	0.600035i	$0.204847\pi$
$422$	23.4405	−	8.53163i	1.14106	−	0.415313i
$423$	6.12129	+	6.08301i	0.297627	+	0.295766i
$424$	−2.61946	−	0.953407i	−0.127212	−	0.0463015i
$425$	15.2267	+	1.77974i	0.738603	+	0.0863303i
$426$	−2.09327	−	28.1250i	−0.101419	−	1.36266i
$427$	22.6180	−	23.9736i	1.09456	−	1.16017i
$428$	23.2796	+	31.2699i	1.12526	+	1.51149i
$429$	0.893094	−	5.59026i	0.0431190	−	0.269901i
$430$	−25.7789	−	12.9466i	−1.24317	−	0.624343i
$431$	6.16440	+	10.6771i	0.296929	+	0.514296i	0.975432	−	0.220302i	$-0.0707042\pi$
$431$	6.16440	+	10.6771i	0.296929	+	0.514296i	−0.678503	+	0.734598i	$0.737371\pi$
$432$	−10.6356	−	10.2338i	−0.511705	−	0.492375i
$433$	3.37556	−	5.84664i	0.162219	−	0.280972i	−0.773445	−	0.633863i	$-0.781468\pi$
$433$	3.37556	−	5.84664i	0.162219	−	0.280972i	0.935664	+	0.352891i	$0.114802\pi$
$434$	−63.6906	+	41.8899i	−3.05724	+	2.01078i
$435$	12.2995	+	20.5321i	0.589715	+	0.984438i
$436$	−0.284426	+	0.659373i	−0.0136215	+	0.0315783i
$437$	0.0367152	+	0.122637i	0.00175632	+	0.00586653i
$438$	6.03118	+	13.3847i	0.288181	+	0.639543i
$439$	−1.76906	−	4.10115i	−0.0844327	−	0.195737i	0.870769	−	0.491692i	$-0.163621\pi$
$439$	−1.76906	−	4.10115i	−0.0844327	−	0.195737i	−0.955202	+	0.295955i	$0.904362\pi$
$440$	−4.45776	+	3.74051i	−0.212516	+	0.178322i
$441$	9.97414	+	12.5333i	0.474959	+	0.596826i
$442$	−10.5045	−	8.81436i	−0.499650	−	0.419256i
$443$	−8.09109	+	27.0261i	−0.384419	+	1.28405i	0.518810	+	0.854890i	$0.326375\pi$
$443$	−8.09109	+	27.0261i	−0.384419	+	1.28405i	−0.903229	+	0.429160i	$0.858810\pi$
$444$	−11.6721	+	28.3045i	−0.553935	+	1.34327i
$445$	−0.830722	+	14.2629i	−0.0393800	+	0.676128i
$446$	3.23737	−	55.5835i	0.153294	−	2.63196i
$447$	−13.6537	−	17.7361i	−0.645796	−	0.838890i
$448$	−11.2954	+	37.7294i	−0.533660	+	1.78255i
$449$	−20.0933	−	16.8603i	−0.948260	−	0.795685i	0.0307434	−	0.999527i	$-0.490213\pi$
$449$	−20.0933	−	16.8603i	−0.948260	−	0.795685i	−0.979004	+	0.203842i	$0.934657\pi$
$450$	−0.648446	+	24.9808i	−0.0305680	+	1.17761i
$451$	8.49615	−	7.12912i	0.400068	−	0.335697i
$452$	−3.16290	−	7.33242i	−0.148770	−	0.344888i
$453$	16.9810	−	23.5938i	0.797839	−	1.10853i
$454$	0.618168	+	2.06483i	0.0290121	+	0.0969070i
$455$	−6.93487	+	16.0768i	−0.325112	+	0.753694i
$456$	−0.0284885		0.000459070i	−0.00133409		2.14979e-5i
$457$	20.1644	−	13.2624i	0.943253	−	0.620387i	0.0180404	−	0.999837i	$-0.494257\pi$
$457$	20.1644	−	13.2624i	0.943253	−	0.620387i	0.925212	+	0.379450i	$0.123887\pi$
$458$	−27.5698	+	47.7523i	−1.28825	+	2.23132i
$459$	16.0975	+	12.2322i	0.751369	+	0.570949i
$460$	28.5194	+	49.3971i	1.32972	+	2.30315i
$461$	−16.8956	−	8.48530i	−0.786908	−	0.395200i	0.00950395	−	0.999955i	$-0.496975\pi$
$461$	−16.8956	−	8.48530i	−0.786908	−	0.395200i	−0.796412	+	0.604755i	$0.793271\pi$
$462$	23.5566	−	9.00633i	1.09595	−	0.419013i
$463$	1.01456	+	1.36279i	0.0471505	+	0.0633341i	0.825073	−	0.565026i	$-0.191134\pi$
$463$	1.01456	+	1.36279i	0.0471505	+	0.0633341i	−0.777923	+	0.628360i	$0.783726\pi$
$464$	9.00862	−	9.54858i	0.418215	−	0.443282i
$465$	47.8843	+	23.0899i	2.22058	+	1.07077i
$466$	−9.42667	−	1.10182i	−0.436682	−	0.0510408i
$467$	−1.44533	−	0.526058i	−0.0668820	−	0.0243431i	0.308362	−	0.951269i	$-0.400219\pi$
$467$	−1.44533	−	0.526058i	−0.0668820	−	0.0243431i	−0.375245	+	0.926926i	$0.622441\pi$
$468$	7.05206	−	10.1389i	0.325981	−	0.468672i
$469$	−14.7986	+	5.38623i	−0.683334	+	0.248713i
$470$	−17.6934	+	4.19342i	−0.816137	+	0.193428i
$471$	−0.626469	+	14.8842i	−0.0288662	+	0.685827i
$472$	4.11092	+	2.70380i	0.189221	+	0.124452i
$473$	7.99588	−	4.01568i	0.367651	−	0.184641i
$474$	9.02047	+	28.4536i	0.414324	+	1.30692i
$475$	−0.0448076	−	0.0474933i	−0.00205592	−	0.00217914i
$476$	5.86110	−	33.2399i	0.268643	−	1.52355i
$477$	1.19486	−	8.33959i	0.0547089	−	0.381844i
$478$	−0.559844	−	3.17503i	−0.0256067	−	0.145223i
$479$	9.48910	−	12.7461i	0.433568	−	0.582383i	−0.530618	−	0.847611i	$-0.678040\pi$
$479$	9.48910	−	12.7461i	0.433568	−	0.582383i	0.964186	+	0.265228i	$0.0854474\pi$
$480$	40.1066	−	10.1906i	1.83061	−	0.465137i
$481$	11.6107	+	2.75179i	0.529403	+	0.125471i
$482$	−1.76841	+	0.206698i	−0.0805489	+	0.00941482i
$483$	−8.90606	−	46.1479i	−0.405240	−	2.09980i
$484$	1.02750	+	17.6415i	0.0467047	+	0.801889i
$485$	−34.7759			−1.57909
$486$	−17.4887	+	27.9328i	−0.793304	+	1.26706i
$487$	39.0750			1.77066			0.885330	−	0.464964i	$-0.153933\pi$
$487$	39.0750			1.77066			0.885330	+	0.464964i	$0.153933\pi$
$488$	−0.541544	−	9.29795i	−0.0245145	−	0.420898i
$489$	−0.221373	−	1.14707i	−0.0100108	−	0.0518724i
$490$	−33.5223	+	3.91820i	−1.51438	+	0.177006i
$491$	−37.5440	−	8.89810i	−1.69434	−	0.401566i	−0.733724	−	0.679448i	$-0.762219\pi$
$491$	−37.5440	−	8.89810i	−1.69434	−	0.401566i	−0.960615	+	0.277882i	$0.910368\pi$
$492$	23.4506	−	5.95855i	1.05724	−	0.268632i
$493$	−10.7381	+	14.4238i	−0.483620	+	0.649615i
$494$	0.0101418	+	0.0575172i	0.000456303	+	0.00258782i
$495$	−13.8297	−	10.8648i	−0.621600	−	0.488337i
$496$	5.06319	−	28.7147i	0.227344	−	1.28933i
$497$	−18.5662	−	19.6790i	−0.832806	−	0.882723i
$498$	5.70567	+	17.9976i	0.255677	+	0.806492i
$499$	4.76243	−	2.39178i	0.213195	−	0.107071i	−0.338997	−	0.940787i	$-0.610088\pi$
$499$	4.76243	−	2.39178i	0.213195	−	0.107071i	0.552192	+	0.833717i	$0.313791\pi$
$500$	6.53901	+	4.30077i	0.292433	+	0.192336i
$501$	−1.17411	+	27.8955i	−0.0524553	+	1.24628i
$502$	30.6976	−	7.27547i	1.37010	−	0.324720i
$503$	21.2859	−	7.74742i	0.949090	−	0.345440i	0.179341	−	0.983787i	$-0.442604\pi$
$503$	21.2859	−	7.74742i	0.949090	−	0.345440i	0.769749	+	0.638347i	$0.220381\pi$
$504$	10.4236	+	0.879007i	0.464304	+	0.0391541i
$505$	−8.03363	−	2.92400i	−0.357492	−	0.130116i
$506$	−31.8035	−	3.71729i	−1.41384	−	0.165254i
$507$	15.9463	+	7.68932i	0.708198	+	0.341495i
$508$	−22.2501	+	23.5837i	−0.987187	+	1.04636i
$509$	18.6809	+	25.0927i	0.828014	+	1.11222i	0.992060	+	0.125764i	$0.0401381\pi$
$509$	18.6809	+	25.0927i	0.828014	+	1.11222i	−0.164046	+	0.986453i	$0.552455\pi$
$510$	−39.7912	+	15.2132i	−1.76198	+	0.673653i
$511$	12.5852	+	6.32052i	0.556736	+	0.279603i
$512$	−14.1680	−	24.5396i	−0.626141	−	1.08451i
$513$	−0.0190331	−	0.0839807i	−0.000840331	−	0.00370784i
$514$	9.75038	−	16.8881i	0.430071	−	0.744904i
$515$	7.14683	−	4.70054i	0.314927	−	0.207131i
$516$	19.5174	−	0.314509i	0.859207	−	0.0138455i
$517$	2.23390	−	5.17877i	0.0982469	−	0.227762i
$518$	15.2456	+	50.9237i	0.669852	+	2.23746i
$519$	−16.3203	+	22.6758i	−0.716383	+	0.995359i
$520$	1.95968	+	4.54304i	0.0859375	+	0.199226i
$521$	−22.0317	+	18.4868i	−0.965226	+	0.809921i	−0.981795	−	0.189942i	$-0.939170\pi$
$521$	−22.0317	+	18.4868i	−0.965226	+	0.809921i	0.0165695	+	0.999863i	$0.494726\pi$
$522$	−24.9957	−	15.3096i	−1.09403	−	0.670082i
$523$	−5.64380	−	4.73571i	−0.246786	−	0.207078i	0.511001	−	0.859580i	$-0.329275\pi$
$523$	−5.64380	−	4.73571i	−0.246786	−	0.207078i	−0.757787	+	0.652502i	$0.773719\pi$
$524$	0.000228589	0	0.000763540i	9.98595e−6	0	3.33554e-5i
$525$	14.6231	+	18.9954i	0.638204	+	0.829028i
$526$	−0.0292603	+	0.502380i	−0.00127581	+	0.0219048i
$527$	−2.32232	+	39.8727i	−0.101162	+	1.73688i
$528$	−3.67747	+	8.91772i	−0.160041	+	0.388094i
$529$	−10.5178	+	35.1319i	−0.457296	+	1.52747i
$530$	13.5985	+	11.4105i	0.590680	+	0.495640i
$531$	−5.44696	+	13.8372i	−0.236378	+	0.600481i
$532$	−0.110125	+	0.0924059i	−0.00477453	+	0.00400630i
$533$	−3.73499	−	8.65869i	−0.161781	−	0.375049i
$534$	−7.18821	−	15.9524i	−0.311064	−	0.690327i
$535$	−13.5371	−	45.2171i	−0.585260	−	1.95491i
$536$	−1.76263	+	4.08625i	−0.0761342	+	0.176499i
$537$	−7.06605	−	11.7957i	−0.304923	−	0.509021i
$538$	25.4713	−	16.7528i	1.09815	−	0.722263i
$539$	5.23423	−	9.06595i	0.225454	−	0.390498i
$540$	−16.8812	−	34.4544i	−0.726451	−	1.48268i
$541$	12.6202	+	21.8588i	0.542583	+	0.939782i	0.998755	+	0.0498899i	$0.0158870\pi$
$541$	12.6202	+	21.8588i	0.542583	+	0.939782i	−0.456171	+	0.889892i	$0.650780\pi$
$542$	31.4825	+	15.8111i	1.35229	+	0.679145i
$543$	3.78020	−	23.6619i	0.162224	−	1.01543i
$544$	18.5657	+	24.9380i	0.795997	+	1.06921i
$545$	0.596650	−	0.632412i	0.0255577	−	0.0270896i
$546$	−1.59152	−	21.3835i	−0.0681106	−	0.915127i
$547$	−17.9882	−	2.10252i	−0.769119	−	0.0898971i	−0.277521	−	0.960719i	$-0.589513\pi$
$547$	−17.9882	−	2.10252i	−0.769119	−	0.0898971i	−0.491598	+	0.870822i	$0.663587\pi$
$548$	−29.9229	−	10.8910i	−1.27824	−	0.465242i
$549$	27.1663	−	7.37059i	1.15943	−	0.314569i
$550$	15.3469	−	5.58581i	0.654393	−	0.238180i
$551$	0.0745237	−	0.0176624i	0.00317482	−	0.000752445i
$552$	−11.2125	−	7.11842i	−0.477234	−	0.302980i
$553$	23.9236	+	15.7348i	1.01733	+	0.669111i
$554$	46.8860	−	23.5470i	1.99199	−	1.00042i
$555$	25.0008	−	27.3696i	1.06122	−	1.16178i
$556$	−1.08690	−	1.15205i	−0.0460949	−	0.0488577i
$557$	1.58101	−	8.96634i	0.0669894	−	0.379916i	−0.932819	−	0.360345i	$-0.882659\pi$
$557$	1.58101	−	8.96634i	0.0669894	−	0.379916i	0.999808	−	0.0195708i	$-0.00622998\pi$
$558$	−65.0708	+	2.09768i	−2.75467	+	0.0888019i
$559$	−1.32104	−	7.49200i	−0.0558741	−	0.316878i
$560$	17.8155	−	23.9303i	0.752841	−	1.01124i
$561$	3.58520	−	12.7177i	0.151367	−	0.536942i
$562$	−39.7543	−	9.42195i	−1.67694	−	0.397441i
$563$	17.5699	−	2.05362i	0.740481	−	0.0865498i	0.262515	−	0.964928i	$-0.415448\pi$
$563$	17.5699	−	2.05362i	0.740481	−	0.0865498i	0.477966	+	0.878378i	$0.341374\pi$
$564$	9.29690	−	8.05982i	0.391470	−	0.339380i
$565$	0.562173	+	9.65214i	0.0236508	+	0.406068i
$566$	2.35991			0.0991944
$567$	3.86715	+	31.3771i	0.162405	+	1.31772i
$568$	−7.64524			−0.320787
$569$	2.42906	+	41.7053i	0.101831	+	1.74838i	0.533008	+	0.846110i	$0.321062\pi$
$569$	2.42906	+	41.7053i	0.101831	+	1.74838i	−0.431177	+	0.902267i	$0.641901\pi$
$570$	0.171476	+	0.0593013i	0.00718236	+	0.00248386i
$571$	−19.5741	+	2.28788i	−0.819149	+	0.0957448i	−0.515337	−	0.856987i	$-0.672333\pi$
$571$	−19.5741	+	2.28788i	−0.819149	+	0.0957448i	−0.303812	+	0.952732i	$0.598259\pi$
$572$	−7.85400	−	1.86143i	−0.328392	−	0.0778304i
$573$	−17.3749	−	17.8317i	−0.725846	−	0.744932i
$574$	25.0859	−	33.6963i	1.04707	−	1.40645i
$575$	−5.28516	−	29.9737i	−0.220407	−	1.24999i
$576$	−25.0562	+	22.4394i	−1.04401	+	0.934974i
$577$	−1.35567	+	7.68841i	−0.0564374	+	0.320073i	−0.999936	−	0.0113037i	$-0.996402\pi$
$577$	−1.35567	+	7.68841i	−0.0564374	+	0.320073i	0.943499	+	0.331376i	$0.107513\pi$
$578$	2.69972	+	2.86153i	0.112293	+	0.119024i
$579$	7.07740	+	1.55738i	0.294127	+	0.0647225i
$580$	30.4951	−	15.3152i	1.26624	−	0.635930i
$581$	15.1323	+	9.95264i	0.627792	+	0.412905i
$582$	37.7462	−	19.7247i	1.56463	−	0.817617i
$583$	−5.35762	+	1.26978i	−0.221890	+	0.0525889i
$584$	3.73967	−	1.36113i	0.154748	−	0.0563238i
$585$	−12.2219	+	8.61516i	−0.505315	+	0.356193i
$586$	15.9679	+	5.81183i	0.659626	+	0.240084i
$587$	−20.8296	−	2.43463i	−0.859729	−	0.100488i	−0.325207	−	0.945643i	$-0.605434\pi$
$587$	−20.8296	−	2.43463i	−0.859729	−	0.100488i	−0.534522	+	0.845155i	$0.679508\pi$
$588$	18.8760	−	12.8554i	0.778434	−	0.530147i
$589$	0.116738	−	0.123735i	0.00481009	−	0.00509840i
$590$	−18.7111	−	25.1333i	−0.770323	−	1.03472i
$591$	0.317983	+	0.258204i	0.0130801	+	0.0106211i
$592$	−18.1693	−	9.12494i	−0.746752	−	0.375033i
$593$	−11.8196	−	20.4722i	−0.485373	−	0.840691i	0.514485	−	0.857499i	$-0.327983\pi$
$593$	−11.8196	−	20.4722i	−0.485373	−	0.840691i	−0.999859	+	0.0168078i	$0.994650\pi$
$594$	21.1735	+	3.94864i	0.868757	+	0.162014i
$595$	−20.4331	+	35.3912i	−0.837677	+	1.45090i
$596$	−26.6630	+	17.5365i	−1.09216	+	0.718324i
$597$	21.9610	−	39.4938i	0.898804	−	1.61637i
$598$	−10.7831	+	24.9980i	−0.440952	+	1.02224i
$599$	0.458208	+	1.53052i	0.0187219	+	0.0625354i	0.966840	−	0.255383i	$-0.0822015\pi$
$599$	0.458208	+	1.53052i	0.0187219	+	0.0625354i	−0.948118	+	0.317918i	$0.897016\pi$
$600$	6.74010	+	0.677916i	0.275163	+	0.0276758i
$601$	12.5634	+	29.1253i	0.512473	+	1.18805i	0.956421	+	0.291993i	$0.0943183\pi$
$601$	12.5634	+	29.1253i	0.512473	+	1.18805i	−0.443948	+	0.896053i	$0.646422\pi$
$602$	25.9617	−	21.7845i	1.05812	−	0.887869i
$603$	−13.1802	−	2.67842i	−0.536741	−	0.109074i
$604$	−31.7498	−	26.6413i	−1.29188	−	1.08402i
$605$	6.13638	−	20.4969i	0.249479	−	0.833319i
$606$	10.3783	−	1.38289i	0.421589	−	0.0561761i
$607$	−0.618504	+	10.6193i	−0.0251043	+	0.431024i	0.962216	+	0.272286i	$0.0877796\pi$
$607$	−0.618504	+	10.6193i	−0.0251043	+	0.431024i	−0.987321	+	0.158738i	$0.949257\pi$
$608$	0.00769938	−	0.132193i	0.000312251	−	0.00536114i
$609$	−27.8722	+	3.71392i	−1.12944	+	0.150496i
$610$	−17.0105	+	56.8190i	−0.688734	+	2.30053i
$611$	−3.67345	−	3.08239i	−0.148612	−	0.124700i
$612$	19.0958	−	21.5938i	0.771903	−	0.872878i
$613$	−34.7629	+	29.1695i	−1.40406	+	1.17815i	−0.444796	+	0.895632i	$0.646724\pi$
$613$	−34.7629	+	29.1695i	−1.40406	+	1.17815i	−0.959263	+	0.282513i	$0.908832\pi$
$614$	14.0613	+	32.5976i	0.567466	+	1.31553i
$615$	−29.1481	−	2.93170i	−1.17536	−	0.118218i
$616$	−1.96075	−	6.54935i	−0.0790008	−	0.263881i
$617$	9.14677	−	21.2046i	0.368235	−	0.853665i	−0.628862	−	0.777517i	$-0.716479\pi$
$617$	9.14677	−	21.2046i	0.368235	−	0.853665i	0.997097	−	0.0761474i	$-0.0242620\pi$
$618$	−5.09113	+	9.15568i	−0.204795	+	0.368296i
$619$	−1.64285	+	1.08052i	−0.0660317	+	0.0434297i	−0.582096	−	0.813120i	$-0.697767\pi$
$619$	−1.64285	+	1.08052i	−0.0660317	+	0.0434297i	0.516064	+	0.856550i	$0.327397\pi$
$620$	37.8977	−	65.6408i	1.52201	−	2.63620i
$621$	14.0989	−	37.5817i	0.565768	−	1.50810i
$622$	5.44913	+	9.43817i	0.218490	+	0.378436i
$623$	−14.9995	−	7.53305i	−0.600944	−	0.301805i
$624$	6.36688	+	5.16994i	0.254879	+	0.206963i
$625$	−17.4229	−	23.4030i	−0.696915	−	0.936119i
$626$	−40.5354	+	42.9651i	−1.62012	+	1.71723i
$627$	−0.0465151	+	0.0316788i	−0.00185763	+	0.00126513i
$628$	21.0968	+	2.46586i	0.841852	+	0.0983984i
$629$	26.1710	+	9.52548i	1.04351	+	0.379806i
$630$	−60.4609	−	27.9628i	−2.40882	−	1.11407i
$631$	−45.7709	+	16.6593i	−1.82211	+	0.663195i	−0.827265	+	0.561812i	$0.810104\pi$
$631$	−45.7709	+	16.6593i	−1.82211	+	0.663195i	−0.994848	+	0.101382i	$0.967673\pi$
$632$	7.87344	−	1.86604i	0.313189	−	0.0742271i
$633$	18.1127	−	9.46503i	0.719917	−	0.376201i
$634$	16.2401	+	10.6813i	0.644979	+	0.424209i
$635$	35.0808	−	17.6182i	1.39214	−	0.699158i
$636$	−11.7312	−	2.58145i	−0.465172	−	0.102361i
$637$	−6.10800	−	6.47410i	−0.242008	−	0.256513i
$638$	−3.32653	+	18.8657i	−0.131699	+	0.746899i
$639$	−4.74337	−	22.6137i	−0.187645	−	0.894585i
$640$	−4.00945	−	22.7387i	−0.158487	−	0.898827i
$641$	−14.7307	+	19.7867i	−0.581827	+	0.781529i	−0.991417	−	0.130741i	$-0.958264\pi$
$641$	−14.7307	+	19.7867i	−0.581827	+	0.781529i	0.409590	+	0.912270i	$0.365672\pi$
$642$	40.3403	+	41.4010i	1.59211	+	1.63397i
$643$	−10.3060	−	2.44256i	−0.406428	−	0.0963251i	0.0223168	−	0.999751i	$-0.492896\pi$
$643$	−10.3060	−	2.44256i	−0.406428	−	0.0963251i	−0.428744	+	0.903426i	$0.641044\pi$
$644$	−66.5578	+	7.77949i	−2.62274	+	0.306555i
$645$	−22.3359	−	7.72439i	−0.879477	−	0.304147i
$646$	0.00792623	+	0.136088i	0.000311853	+	0.00535432i
$647$	−12.2785			−0.482716			−0.241358	−	0.970436i	$-0.577593\pi$
$647$	−12.2785			−0.482716			−0.241358	+	0.970436i	$0.577593\pi$
$648$	7.19928	+	5.28979i	0.282815	+	0.207803i
$649$	9.71877			0.381495
$650$	−0.807392	−	13.8624i	−0.0316685	−	0.543727i
$651$	−47.1900	+	40.9107i	−1.84952	+	1.60342i
$652$	−1.65439	+	0.193370i	−0.0647909	+	0.00757297i
$653$	−2.78606	−	0.660308i	−0.109027	−	0.0258398i	0.175740	−	0.984437i	$-0.443768\pi$
$653$	−2.78606	−	0.660308i	−0.109027	−	0.0258398i	−0.284767	+	0.958597i	$0.591916\pi$
$654$	−0.288910	+	1.02485i	−0.0112973	+	0.0400747i
$655$	−0.000576258	0	0.000774049i	−2.25163e−5	0	3.02446e-5i
$656$	2.79016	+	15.8238i	0.108938	+	0.617815i
$657$	6.34627	+	10.2170i	0.247592	+	0.398603i
$658$	3.70957	−	21.0380i	0.144614	−	0.820148i
$659$	32.0561	+	33.9775i	1.24873	+	1.32357i	0.926209	+	0.377011i	$0.123048\pi$
$659$	32.0561	+	33.9775i	1.24873	+	1.32357i	0.322519	+	0.946563i	$0.395470\pi$
$660$	−16.9116	+	18.5140i	−0.658285	+	0.720658i
$661$	21.3064	−	10.7005i	0.828724	−	0.416201i	0.0167255	−	0.999860i	$-0.494676\pi$
$661$	21.3064	−	10.7005i	0.828724	−	0.416201i	0.811999	+	0.583659i	$0.198380\pi$
$662$	−29.9410	−	19.6925i	−1.16369	−	0.765370i
$663$	−9.48452	−	6.02141i	−0.368348	−	0.233852i
$664$	4.98015	−	1.18032i	0.193267	−	0.0458052i
$665$	0.163559	−	0.0595306i	0.00634254	−	0.00230850i
$666$	−11.6122	+	43.8877i	−0.449965	+	1.70061i
$667$	33.5475	+	12.2103i	1.29897	+	0.472785i
$668$	39.5389	+	4.62143i	1.52981	+	0.178809i
$669$	−3.38567	−	45.4896i	−0.130898	−	1.75873i
$670$	19.4476	−	20.6133i	0.751328	−	0.796361i
$671$	−10.9856	−	14.7562i	−0.424095	−	0.569659i
$672$	−7.66951	+	48.0068i	−0.295858	+	1.85190i
$673$	4.03318	+	2.02554i	0.155468	+	0.0780789i	0.524832	−	0.851206i	$-0.324128\pi$
$673$	4.03318	+	2.02554i	0.155468	+	0.0780789i	−0.369364	+	0.929285i	$0.620424\pi$
$674$	−13.7901	−	23.8852i	−0.531175	−	0.920023i
$675$	2.17659	+	20.3570i	0.0837771	+	0.783543i
$676$	12.6206	−	21.8594i	0.485406	−	0.840748i
$677$	−10.5372	+	6.93043i	−0.404978	+	0.266358i	−0.735615	−	0.677400i	$-0.763107\pi$
$677$	−10.5372	+	6.93043i	−0.404978	+	0.266358i	0.330637	+	0.943758i	$0.392736\pi$
$678$	−6.08484	−	10.1577i	−0.233687	−	0.390104i
$679$	16.1821	−	37.5144i	0.621012	−	1.43967i
$680$	3.31204	+	11.0630i	0.127011	+	0.424246i
$681$	0.725449	+	1.60995i	0.0277993	+	0.0616933i
$682$	16.8530	+	39.0695i	0.645333	+	1.49605i
$683$	−13.8210	+	11.5972i	−0.528845	+	0.443754i	−0.867702	−	0.497084i	$-0.834404\pi$
$683$	−13.8210	+	11.5972i	−0.528845	+	0.443754i	0.338857	+	0.940838i	$0.389960\pi$
$684$	−0.121422	+	0.0181749i	−0.00464269	+	0.000694936i
$685$	29.5344	+	24.7823i	1.12845	+	0.946883i
$686$	−3.53724	+	11.8152i	−0.135052	+	0.451106i
$687$	−17.2221	+	41.7629i	−0.657063	+	1.59335i
$688$	−0.753719	+	12.9409i	−0.0287353	+	0.493366i
$689$	−0.272200	+	4.67350i	−0.0103700	+	0.178046i
$690$	51.5919	+	67.0180i	1.96407	+	2.55133i
$691$	9.54290	−	31.8755i	0.363029	−	1.21260i	−0.560202	−	0.828356i	$-0.689277\pi$
$691$	9.54290	−	31.8755i	0.363029	−	1.21260i	0.923231	−	0.384245i	$-0.125538\pi$
$692$	30.5145	+	25.6047i	1.15999	+	0.973345i
$693$	18.1557	−	9.86310i	0.689678	−	0.374668i
$694$	−23.3104	+	19.5598i	−0.884852	+	0.742479i
$695$	0.759542	+	1.76082i	0.0288111	+	0.0667916i
$696$	−4.64161	+	6.44915i	−0.175940	+	0.244454i
$697$	−6.31249	−	21.0852i	−0.239102	−	0.798658i
$698$	6.81050	−	15.7885i	0.257781	−	0.597604i
$699$	−7.77461	+	0.125282i	−0.294063	+	0.00473860i
$700$	28.5561	−	18.7816i	1.07932	−	0.709880i
$701$	−9.13385	+	15.8203i	−0.344981	+	0.597524i	−0.985350	−	0.170543i	$-0.945448\pi$
$701$	−9.13385	+	15.8203i	−0.344981	+	0.597524i	0.640370	+	0.768067i	$0.278781\pi$
$702$	8.37938	−	16.2832i	0.316259	−	0.614571i
$703$	−0.0593101	−	0.102728i	−0.00223692	−	0.00387446i
$704$	19.6443	+	9.86574i	0.740373	+	0.371829i
$705$	−13.9150	+	5.32009i	−0.524070	+	0.200366i
$706$	−34.2202	−	45.9657i	−1.28790	−	1.72994i
$707$	6.89251	−	7.30564i	0.259220	−	0.274757i
$708$	19.0979	+	9.20906i	0.717744	+	0.346098i
$709$	−1.96503	−	0.229679i	−0.0737982	−	0.00862577i	0.0791137	−	0.996866i	$-0.474791\pi$
$709$	−1.96503	−	0.229679i	−0.0737982	−	0.00862577i	−0.152912	+	0.988240i	$0.548865\pi$
$710$	45.7496	+	16.6515i	1.71695	+	0.624919i
$711$	10.4045	+	22.1310i	0.390199	+	0.829976i
$712$	−4.45709	+	1.62225i	−0.167036	+	0.0607963i
$713$	77.1578	−	18.2867i	2.88958	−	0.684844i
$714$	2.10464	−	50.0037i	0.0787640	−	1.87134i
$715$	8.16496	+	5.37018i	0.305352	+	0.200833i
$716$	−17.5194	+	8.79858i	−0.654731	+	0.328818i
$717$	−0.798220	−	2.51785i	−0.0298101	−	0.0940310i
$718$	−36.1717	−	38.3398i	−1.34992	−	1.43083i
$719$	2.42853	−	13.7729i	0.0905690	−	0.513642i	−0.905446	−	0.424461i	$-0.860464\pi$
$719$	2.42853	−	13.7729i	0.0905690	−	0.513642i	0.996015	−	0.0891816i	$-0.0284252\pi$
$720$	23.6494	−	9.48129i	0.881359	−	0.353347i
$721$	1.74509	+	9.89690i	0.0649906	+	0.368580i
$722$	−23.9865	+	32.2195i	−0.892687	+	1.19909i
$723$	−1.41376	+	0.359220i	−0.0525781	+	0.0133595i
$724$	−33.2436	−	7.87889i	−1.23549	−	0.292817i
$725$	−18.0860	+	2.11395i	−0.671696	+	0.0785100i
$726$	4.96527	+	25.7282i	0.184279	+	0.954863i
$727$	−2.17347	−	37.3171i	−0.0806097	−	1.38401i	−0.759850	−	0.650099i	$-0.774728\pi$
$727$	−2.17347	−	37.3171i	−0.0806097	−	1.38401i	0.679240	−	0.733916i	$-0.262310\pi$
$728$	−5.81268			−0.215432
$729$	−11.1799	+	24.5766i	−0.414071	+	0.910245i
$730$	−25.3429			−0.937984
$731$	−1.03244	−	17.7264i	−0.0381863	−	0.655634i
$732$	−7.60501	−	39.4063i	−0.281089	−	1.45650i
$733$	−26.4282	+	3.08901i	−0.976148	+	0.114095i	−0.589183	−	0.807999i	$-0.700550\pi$
$733$	−26.4282	+	3.08901i	−0.976148	+	0.114095i	−0.386965	+	0.922095i	$0.626476\pi$
$734$	26.9323	+	6.38308i	0.994090	+	0.235604i
$735$	−26.7994	+	6.80943i	−0.988511	+	0.251170i
$736$	36.8593	−	49.5107i	1.35865	−	1.82499i
$737$	1.52638	+	8.65652i	0.0562249	+	0.318867i
$738$	33.3006	−	13.3506i	1.22581	−	0.491442i
$739$	7.56956	−	42.9291i	0.278451	−	1.57917i	−0.449332	−	0.893365i	$-0.648338\pi$
$739$	7.56956	−	42.9291i	0.278451	−	1.57917i	0.727782	−	0.685808i	$-0.240551\pi$
$740$	−36.2698	−	38.4437i	−1.33330	−	1.41322i
$741$	0.0144601	+	0.0456121i	0.000531207	+	0.00167560i
$742$	−18.6367	+	9.35973i	−0.684177	+	0.343606i
$743$	−42.4988	−	27.9519i	−1.55913	−	1.02545i	−0.977227	−	0.212195i	$-0.931939\pi$
$743$	−42.4988	−	27.9519i	−1.55913	−	1.02545i	−0.581901	−	0.813260i	$-0.697691\pi$
$744$	−0.742167	+	17.6330i	−0.0272092	+	0.646458i
$745$	37.5974	−	8.91074i	1.37746	−	0.326464i
$746$	57.1662	−	20.8068i	2.09300	−	0.761791i
$747$	6.58110	+	13.9984i	0.240790	+	0.512174i
$748$	−17.7033	−	6.44346i	−0.647295	−	0.235596i
$749$	55.0769	+	6.43757i	2.01247	+	0.235224i
$750$	10.4533	+	5.04059i	0.381700	+	0.184056i
$751$	−8.69620	+	9.21743i	−0.317329	+	0.336349i	−0.866329	−	0.499473i	$-0.833527\pi$
$751$	−8.69620	+	9.21743i	−0.317329	+	0.336349i	0.549001	+	0.835822i	$0.315008\pi$
$752$	4.87935	+	6.55411i	0.177932	+	0.239004i
$753$	24.1422	−	9.23021i	0.879791	−	0.336368i
$754$	14.5552	+	7.30991i	0.530070	+	0.266211i
$755$	25.0908	+	43.4585i	0.913146	+	1.58162i
$756$	45.0228	−	2.17803i	1.63746	−	0.0792143i
$757$	7.49384	−	12.9797i	0.272368	−	0.471756i	−0.697100	−	0.716974i	$-0.745526\pi$
$757$	7.49384	−	12.9797i	0.272368	−	0.471756i	0.969468	+	0.245219i	$0.0788598\pi$
$758$	37.0628	−	24.3766i	1.34618	−	0.885397i
$759$	−26.2298	+	0.422673i	−0.952080	+	0.0153421i
$760$	0.0194813	−	0.0451626i	0.000706660	−	0.00163822i
$761$	−3.02594	−	10.1074i	−0.109690	−	0.366391i	0.885465	−	0.464706i	$-0.153840\pi$
$761$	−3.02594	−	10.1074i	−0.109690	−	0.366391i	−0.995155	+	0.0983148i	$0.968655\pi$
$762$	−28.0842	+	39.0208i	−1.01738	+	1.41357i
$763$	0.404576	+	0.937912i	0.0146466	+	0.0339547i
$764$	−27.1927	+	22.8174i	−0.983798	+	0.825505i
$765$	−30.6681	+	16.6605i	−1.10881	+	0.602360i
$766$	39.6701	+	33.2872i	1.43334	+	1.20271i
$767$	2.36992	−	7.91610i	0.0855730	−	0.285834i
$768$

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.122925 - 2.11055i) q^{2} +(-0.328212 - 1.70067i) q^{3} +(-2.45283 + 0.286694i) q^{4} +(2.90939 + 0.689539i) q^{5} +(-3.54900 + 0.901762i) q^{6} +(-2.09765 + 2.81764i) q^{7} +(0.172370 + 0.977557i) q^{8} +(-2.78455 + 1.11636i) q^{9} +O(q^{10})\)	\(q+(-0.122925 - 2.11055i) q^{2} +(-0.328212 - 1.70067i) q^{3} +(-2.45283 + 0.286694i) q^{4} +(2.90939 + 0.689539i) q^{5} +(-3.54900 + 0.901762i) q^{6} +(-2.09765 + 2.81764i) q^{7} +(0.172370 + 0.977557i) q^{8} +(-2.78455 + 1.11636i) q^{9} +(1.09767 - 6.22518i) q^{10} +(1.34549 + 1.42613i) q^{11} +(1.29262 + 4.07735i) q^{12} +(1.48971 - 0.748159i) q^{13} +(6.20462 + 4.08084i) q^{14} +(0.217782 - 5.17423i) q^{15} +(-2.76393 + 0.655063i) q^{16} +(3.65626 - 1.33077i) q^{17} +(2.69842 + 5.73971i) q^{18} +(-0.0155726 - 0.00566795i) q^{19} +(-7.33393 - 0.857214i) q^{20} +(5.48035 + 2.64264i) q^{21} +(2.84453 - 3.01503i) q^{22} +(-4.61293 - 6.19624i) q^{23} +(1.60593 - 0.613989i) q^{24} +(3.52095 + 1.76829i) q^{25} +(-1.76215 - 3.05213i) q^{26} +(2.81248 + 4.36921i) q^{27} +(4.33738 - 7.51257i) q^{28} +(-3.86125 + 2.53958i) q^{29} +(-10.9472 + 0.176407i) q^{30} +(-4.06577 + 9.42551i) q^{31} +(2.29168 + 7.65475i) q^{32} +(1.98378 - 2.75630i) q^{33} +(-3.25810 - 7.55312i) q^{34} +(-8.04578 + 6.75121i) q^{35} +(6.50998 - 3.53655i) q^{36} +(5.48325 + 4.60100i) q^{37} +(-0.0100482 + 0.0335634i) q^{38} +(-1.76131 - 2.28794i) q^{39} +(-0.172572 + 2.96295i) q^{40} +(0.328910 - 5.64716i) q^{41} +(4.90374 - 11.8914i) q^{42} +(1.30885 - 4.37185i) q^{43} +(-3.70912 - 3.11232i) q^{44} +(-8.87114 + 1.32787i) q^{45} +(-12.5104 + 10.4975i) q^{46} +(-1.13936 - 2.64134i) q^{47} +(2.02120 + 4.48553i) q^{48} +(-1.53131 - 5.11494i) q^{49} +(3.29924 - 7.64851i) q^{50} +(-3.46322 - 5.78131i) q^{51} +(-3.43950 + 2.26220i) q^{52} +(-1.40413 + 2.43202i) q^{53} +(8.87569 - 6.47296i) q^{54} +(2.93118 + 5.07695i) q^{55} +(-3.11597 - 1.56490i) q^{56} +(-0.00452821 + 0.0283441i) q^{57} +(5.83456 + 7.83717i) q^{58} +(3.40162 - 3.60551i) q^{59} +(0.949244 + 12.7539i) q^{60} +(-9.31935 - 1.08928i) q^{61} +(20.3928 + 7.42236i) q^{62} +(2.69554 - 10.1876i) q^{63} +(10.5356 - 3.83466i) q^{64} +(4.85003 - 1.14948i) q^{65} +(-6.06117 - 3.84804i) q^{66} +(3.74567 + 2.46356i) q^{67} +(-8.58664 + 4.31237i) q^{68} +(-9.02374 + 9.87875i) q^{69} +(15.2378 + 16.1511i) q^{70} +(-1.33743 + 7.58494i) q^{71} +(-1.57128 - 2.52963i) q^{72} +(-0.696188 - 3.94828i) q^{73} +(9.03659 - 12.1383i) q^{74} +(1.85166 - 6.56835i) q^{75} +(0.0398218 + 0.00943793i) q^{76} +(-6.84070 + 0.799563i) q^{77} +(-4.61231 + 3.99858i) q^{78} +(-0.473972 - 8.13778i) q^{79} -8.49305 q^{80} +(6.50749 - 6.21712i) q^{81} -11.9590 q^{82} +(-0.299799 - 5.14735i) q^{83} +(-14.2000 - 4.91075i) q^{84} +(11.5551 - 1.35060i) q^{85} +(-9.38790 - 2.22497i) q^{86} +(5.58630 + 5.73319i) q^{87} +(-1.16221 + 1.56111i) q^{88} +(0.829745 + 4.70572i) q^{89} +(3.89302 + 18.5597i) q^{90} +(-1.01685 + 5.76683i) q^{91} +(13.0912 + 13.8758i) q^{92} +(17.3641 + 3.82097i) q^{93} +(-5.43461 + 2.72936i) q^{94} +(-0.0413984 - 0.0272282i) q^{95} +(12.2660 - 6.40977i) q^{96} +(-11.3173 + 2.68224i) q^{97} +(-10.6071 + 3.86067i) q^{98} +(-5.33866 - 2.46910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

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