LMFDB - Embedded newform 216.2.v.b.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27615 - 0.609466i) q^{2} +(1.73063 - 0.0701536i) q^{3} +(1.25710 + 1.55554i) q^{4} +(-0.426624 - 0.155279i) q^{5} +(-2.25129 - 0.965233i) q^{6} +(1.28150 + 0.225962i) q^{7} +(-0.656202 - 2.75125i) q^{8} +(2.99016 - 0.242820i) q^{9} +O(q^{10})$	\(q+(-1.27615 - 0.609466i) q^{2} +(1.73063 - 0.0701536i) q^{3} +(1.25710 + 1.55554i) q^{4} +(-0.426624 - 0.155279i) q^{5} +(-2.25129 - 0.965233i) q^{6} +(1.28150 + 0.225962i) q^{7} +(-0.656202 - 2.75125i) q^{8} +(2.99016 - 0.242820i) q^{9} +(0.449799 + 0.458171i) q^{10} +(0.00602720 + 0.0165596i) q^{11} +(2.28471 + 2.60387i) q^{12} +(1.43581 + 1.71113i) q^{13} +(-1.49766 - 1.06939i) q^{14} +(-0.749222 - 0.238801i) q^{15} +(-0.839384 + 3.91094i) q^{16} +(1.27216 - 0.734483i) q^{17} +(-3.96387 - 1.51252i) q^{18} +(0.677841 - 1.17406i) q^{19} +(-0.294769 - 0.858831i) q^{20} +(2.23365 + 0.301155i) q^{21} +(0.00240091 - 0.0248058i) q^{22} +(0.369486 + 2.09546i) q^{23} +(-1.32865 - 4.71537i) q^{24} +(-3.67233 - 3.08145i) q^{25} +(-0.789428 - 3.05873i) q^{26} +(5.15782 - 0.630001i) q^{27} +(1.25948 + 2.27747i) q^{28} +(-5.56933 - 4.67322i) q^{29} +(0.810577 + 0.761370i) q^{30} +(8.87753 - 1.56535i) q^{31} +(3.45476 - 4.47936i) q^{32} +(0.0115926 + 0.0282357i) q^{33} +(-2.07111 + 0.161969i) q^{34} +(-0.511630 - 0.295390i) q^{35} +(4.13665 + 4.34605i) q^{36} +(-4.58718 + 2.64841i) q^{37} +(-1.58057 + 1.08515i) q^{38} +(2.60490 + 2.86061i) q^{39} +(-0.147259 + 1.27565i) q^{40} +(1.56527 + 1.86542i) q^{41} +(-2.66692 - 1.74565i) q^{42} +(-10.1956 + 3.71089i) q^{43} +(-0.0181822 + 0.0301926i) q^{44} +(-1.31338 - 0.360715i) q^{45} +(0.805592 - 2.89930i) q^{46} +(-0.791397 + 4.48824i) q^{47} +(-1.17830 + 6.82727i) q^{48} +(-4.98668 - 1.81500i) q^{49} +(2.80839 + 6.17054i) q^{50} +(2.15011 - 1.36036i) q^{51} +(-0.856765 + 4.38452i) q^{52} -10.4085 q^{53} +(-6.96610 - 2.33954i) q^{54} -0.00800062i q^{55} +(-0.219241 - 3.67400i) q^{56} +(1.09073 - 2.07941i) q^{57} +(4.25911 + 9.35804i) q^{58} +(-3.75319 + 10.3118i) q^{59} +(-0.570387 - 1.46564i) q^{60} +(-8.87057 - 1.56412i) q^{61} +(-12.2831 - 3.41294i) q^{62} +(3.88674 + 0.364490i) q^{63} +(-7.13880 + 3.61076i) q^{64} +(-0.346849 - 0.952961i) q^{65} +(0.00241487 - 0.0430981i) q^{66} +(3.70041 - 3.10502i) q^{67} +(2.74175 + 1.05557i) q^{68} +(0.786447 + 3.60054i) q^{69} +(0.472885 + 0.688782i) q^{70} +(5.03714 + 8.72458i) q^{71} +(-2.63021 - 8.06734i) q^{72} +(-0.339460 + 0.587962i) q^{73} +(7.46803 - 0.584031i) q^{74} +(-6.57161 - 5.07522i) q^{75} +(2.67840 - 0.421502i) q^{76} +(0.00398198 + 0.0225829i) q^{77} +(-1.58079 - 5.23815i) q^{78} +(5.19665 - 6.19313i) q^{79} +(0.965387 - 1.53816i) q^{80} +(8.88208 - 1.45214i) q^{81} +(-0.860607 - 3.33452i) q^{82} +(1.29122 - 1.53881i) q^{83} +(2.33946 + 3.85310i) q^{84} +(-0.656785 + 0.115809i) q^{85} +(15.2727 + 1.47822i) q^{86} +(-9.96629 - 7.69691i) q^{87} +(0.0416046 - 0.0274488i) q^{88} +(-0.103744 - 0.0598964i) q^{89} +(1.45622 + 1.26078i) q^{90} +(1.45333 + 2.51724i) q^{91} +(-2.79508 + 3.20896i) q^{92} +(15.2539 - 3.33183i) q^{93} +(3.74536 - 5.24532i) q^{94} +(-0.471489 + 0.395626i) q^{95} +(5.66467 - 7.99447i) q^{96} +(-10.4801 + 3.81446i) q^{97} +(5.25755 + 5.35542i) q^{98} +(0.0220433 + 0.0480522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−1.27615	−	0.609466i	−0.902372	−	0.430957i
$2$	−1.27615	−	0.609466i	−0.902372	−	0.430957i
$3$	1.73063	−	0.0701536i	0.999179	−	0.0405032i
$3$	1.73063	−	0.0701536i	0.999179	−	0.0405032i
$4$	1.25710	+	1.55554i	0.628551	+	0.777768i
$5$	−0.426624	−	0.155279i	−0.190792	−	0.0694427i	0.244857	−	0.969559i	$-0.421259\pi$
$5$	−0.426624	−	0.155279i	−0.190792	−	0.0694427i	−0.435649	+	0.900116i	$0.643481\pi$
$6$	−2.25129	−	0.965233i	−0.919087	−	0.394055i
$7$	1.28150	+	0.225962i	0.484360	+	0.0854057i	0.410495	−	0.911863i	$-0.365356\pi$
$7$	1.28150	+	0.225962i	0.484360	+	0.0854057i	0.0738642	+	0.997268i	$0.476467\pi$
$8$	−0.656202	−	2.75125i	−0.232003	−	0.972715i
$9$	2.99016	−	0.242820i	0.996719	−	0.0809399i
$10$	0.449799	+	0.458171i	0.142239	+	0.144887i
$11$	0.00602720	+	0.0165596i	0.00181727	+	0.00499290i	0.940598	−	0.339522i	$-0.110265\pi$
$11$	0.00602720	+	0.0165596i	0.00181727	+	0.00499290i	−0.938781	+	0.344515i	$0.888043\pi$
$12$	2.28471	+	2.60387i	0.659538	+	0.751671i
$13$	1.43581	+	1.71113i	0.398222	+	0.474582i	0.927477	−	0.373881i	$-0.121973\pi$
$13$	1.43581	+	1.71113i	0.398222	+	0.474582i	−0.529255	+	0.848463i	$0.677529\pi$
$14$	−1.49766	−	1.06939i	−0.400267	−	0.285806i
$15$	−0.749222	−	0.238801i	−0.193448	−	0.0616580i
$16$	−0.839384	+	3.91094i	−0.209846	+	0.977734i
$17$	1.27216	−	0.734483i	0.308545	−	0.178138i	−0.337730	−	0.941243i	$-0.609659\pi$
$17$	1.27216	−	0.734483i	0.308545	−	0.178138i	0.646275	+	0.763105i	$0.276326\pi$
$18$	−3.96387	−	1.51252i	−0.934293	−	0.356505i
$19$	0.677841	−	1.17406i	0.155507	−	0.269347i	−0.777736	−	0.628591i	$-0.783632\pi$
$19$	0.677841	−	1.17406i	0.155507	−	0.269347i	0.933244	+	0.359244i	$0.116965\pi$
$20$	−0.294769	−	0.858831i	−0.0659124	−	0.192040i
$21$	2.23365	+	0.301155i	0.487421	+	0.0657175i
$22$	0.00240091	−	0.0248058i	0.000511876	−	0.00528862i
$23$	0.369486	+	2.09546i	0.0770432	+	0.436933i	0.998792	+	0.0491452i	$0.0156497\pi$
$23$	0.369486	+	2.09546i	0.0770432	+	0.436933i	−0.921748	+	0.387788i	$0.873239\pi$
$24$	−1.32865	−	4.71537i	−0.271210	−	0.962520i
$25$	−3.67233	−	3.08145i	−0.734465	−	0.616289i
$26$	−0.789428	−	3.05873i	−0.154820	−	0.599866i
$27$	5.15782	−	0.630001i	0.992623	−	0.121244i
$28$	1.25948	+	2.27747i	0.238019	+	0.430401i
$29$	−5.56933	−	4.67322i	−1.03420	−	0.867796i	−0.0428540	−	0.999081i	$-0.513645\pi$
$29$	−5.56933	−	4.67322i	−1.03420	−	0.867796i	−0.991345	+	0.131286i	$0.958089\pi$
$30$	0.810577	+	0.761370i	0.147990	+	0.139006i
$31$	8.87753	−	1.56535i	1.59445	−	0.281145i	0.695279	−	0.718740i	$-0.255281\pi$
$31$	8.87753	−	1.56535i	1.59445	−	0.281145i	0.899172	+	0.437595i	$0.144170\pi$
$32$	3.45476	−	4.47936i	0.610721	−	0.791846i
$33$	0.0115926	+	0.0282357i	0.00201801	+	0.00491520i
$34$	−2.07111	+	0.161969i	−0.355192	+	0.0277775i
$35$	−0.511630	−	0.295390i	−0.0864813	−	0.0499300i
$36$	4.13665	+	4.34605i	0.689442	+	0.724341i
$37$	−4.58718	+	2.64841i	−0.754128	+	0.435396i	−0.827183	−	0.561932i	$-0.810058\pi$
$37$	−4.58718	+	2.64841i	−0.754128	+	0.435396i	0.0730557	+	0.997328i	$0.476725\pi$
$38$	−1.58057	+	1.08515i	−0.256403	+	0.176034i
$39$	2.60490	+	2.86061i	0.417117	+	0.458064i
$40$	−0.147259	+	1.27565i	−0.0232837	+	0.201697i
$41$	1.56527	+	1.86542i	0.244454	+	0.291329i	0.874295	−	0.485395i	$-0.161324\pi$
$41$	1.56527	+	1.86542i	0.244454	+	0.291329i	−0.629841	+	0.776724i	$0.716880\pi$
$42$	−2.66692	−	1.74565i	−0.411514	−	0.269359i
$43$	−10.1956	+	3.71089i	−1.55481	+	0.565906i	−0.969541	−	0.244930i	$-0.921235\pi$
$43$	−10.1956	+	3.71089i	−1.55481	+	0.565906i	−0.585273	+	0.810836i	$0.699013\pi$
$44$	−0.0181822	+	0.0301926i	−0.00274107	+	0.00455171i
$45$	−1.31338	−	0.360715i	−0.195787	−	0.0537722i
$46$	0.805592	−	2.89930i	0.118778	−	0.427479i
$47$	−0.791397	+	4.48824i	−0.115437	+	0.654676i	0.871096	+	0.491113i	$0.163410\pi$
$47$	−0.791397	+	4.48824i	−0.115437	+	0.654676i	−0.986533	+	0.163563i	$0.947701\pi$
$48$	−1.17830	+	6.82727i	−0.170073	+	0.985432i
$49$	−4.98668	−	1.81500i	−0.712382	−	0.259286i
$50$	2.80839	+	6.17054i	0.397166	+	0.872646i
$51$	2.15011	−	1.36036i	0.301076	−	0.190489i
$52$	−0.856765	+	4.38452i	−0.118812	+	0.608023i
$53$	−10.4085			−1.42972			−0.714860	−	0.699267i	$-0.753510\pi$
$53$	−10.4085			−1.42972			−0.714860	+	0.699267i	$0.753510\pi$
$54$	−6.96610	−	2.33954i	−0.947966	−	0.318371i
$55$		−	0.00800062i		−	0.00107880i
$56$	−0.219241	−	3.67400i	−0.0292973	−	0.490958i
$57$	1.09073	−	2.07941i	0.144470	−	0.275424i
$58$	4.25911	+	9.35804i	0.559249	+	1.22877i
$59$	−3.75319	+	10.3118i	−0.488624	+	1.34248i	0.413302	+	0.910594i	$0.364375\pi$
$59$	−3.75319	+	10.3118i	−0.488624	+	1.34248i	−0.901926	+	0.431890i	$0.857847\pi$
$60$	−0.570387	−	1.46564i	−0.0736366	−	0.189213i
$61$	−8.87057	−	1.56412i	−1.13576	−	0.200265i	−0.426010	−	0.904718i	$-0.640081\pi$
$61$	−8.87057	−	1.56412i	−1.13576	−	0.200265i	−0.709750	+	0.704453i	$0.751192\pi$
$62$	−12.2831	−	3.41294i	−1.55995	−	0.433443i
$63$	3.88674	+	0.364490i	0.489683	+	0.0459214i
$64$	−7.13880	+	3.61076i	−0.892350	+	0.451345i
$65$	−0.346849	−	0.952961i	−0.0430214	−	0.118200i
$66$	0.00241487	−	0.0430981i	0.000297250	−	0.00530501i
$67$	3.70041	−	3.10502i	0.452078	−	0.379338i	−0.388129	−	0.921605i	$-0.626878\pi$
$67$	3.70041	−	3.10502i	0.452078	−	0.379338i	0.840206	+	0.542267i	$0.182434\pi$
$68$	2.74175	+	1.05557i	0.332486	+	0.128007i
$69$	0.786447	+	3.60054i	0.0946771	+	0.433454i
$70$	0.472885	+	0.688782i	0.0565206	+	0.0823252i
$71$	5.03714	+	8.72458i	0.597799	+	1.03542i	0.993145	+	0.116886i	$0.0372911\pi$
$71$	5.03714	+	8.72458i	0.597799	+	1.03542i	−0.395347	+	0.918532i	$0.629376\pi$
$72$	−2.63021	−	8.06734i	−0.309973	−	0.950745i
$73$	−0.339460	+	0.587962i	−0.0397308	+	0.0688158i	−0.885207	−	0.465197i	$-0.845983\pi$
$73$	−0.339460	+	0.587962i	−0.0397308	+	0.0688158i	0.845476	+	0.534013i	$0.179317\pi$
$74$	7.46803	−	0.584031i	0.868141	−	0.0678922i
$75$	−6.57161	−	5.07522i	−0.758824	−	0.586035i
$76$	2.67840	−	0.421502i	0.307234	−	0.0483496i
$77$	0.00398198	+	0.0225829i	0.000453789	+	0.00257357i
$78$	−1.58079	−	5.23815i	−0.178989	−	0.593104i
$79$	5.19665	−	6.19313i	0.584669	−	0.696782i	−0.389903	−	0.920856i	$-0.627491\pi$
$79$	5.19665	−	6.19313i	0.584669	−	0.696782i	0.974572	+	0.224074i	$0.0719358\pi$
$80$	0.965387	−	1.53816i	0.107934	−	0.171972i
$81$	8.88208	−	1.45214i	0.986897	−	0.161349i
$82$	−0.860607	−	3.33452i	−0.0950382	−	0.368237i
$83$	1.29122	−	1.53881i	0.141729	−	0.168907i	−0.690510	−	0.723323i	$-0.742614\pi$
$83$	1.29122	−	1.53881i	0.141729	−	0.168907i	0.832240	+	0.554416i	$0.187058\pi$
$84$	2.33946	+	3.85310i	0.255256	+	0.420408i
$85$	−0.656785	+	0.115809i	−0.0712383	+	0.0125612i
$86$	15.2727	+	1.47822i	1.64690	+	0.159401i
$87$	−9.96629	−	7.69691i	−1.06850	−	0.825195i
$88$	0.0416046	−	0.0274488i	0.00443506	−	0.00292605i
$89$	−0.103744	−	0.0598964i	−0.0109968	−	0.00634901i	0.494492	−	0.869182i	$-0.335354\pi$
$89$	−0.103744	−	0.0598964i	−0.0109968	−	0.00634901i	−0.505488	+	0.862833i	$0.668688\pi$
$90$	1.45622	+	1.26078i	0.153499	+	0.132898i
$91$	1.45333	+	2.51724i	0.152351	+	0.263879i
$92$	−2.79508	+	3.20896i	−0.291407	+	0.334557i
$93$	15.2539	−	3.33183i	1.58176	−	0.345495i
$94$	3.74536	−	5.24532i	0.386305	−	0.541013i
$95$	−0.471489	+	0.395626i	−0.0483738	+	0.0405904i
$96$	5.66467	−	7.99447i	0.578148	−	0.815932i
$97$	−10.4801	+	3.81446i	−1.06410	+	0.387299i	−0.813966	−	0.580913i	$-0.802696\pi$
$97$	−10.4801	+	3.81446i	−1.06410	+	0.387299i	−0.250130	+	0.968212i	$0.580474\pi$
$98$	5.25755	+	5.35542i	0.531093	+	0.540979i
$99$	0.0220433	+	0.0480522i	0.00221543	+	0.00482943i
$100$	0.176811	−	9.58613i	0.0176811	−	0.958613i
$101$	2.89743	−	16.4321i	0.288305	−	1.63506i	−0.404932	−	0.914347i	$-0.632705\pi$
$101$	2.89743	−	16.4321i	0.288305	−	1.63506i	0.693237	−	0.720710i	$-0.256184\pi$
$102$	−3.57296	+	0.425604i	−0.353776	+	0.0421411i
$103$	5.45676	−	14.9923i	0.537670	−	1.47724i	−0.312082	−	0.950055i	$-0.601026\pi$
$103$	5.45676	−	14.9923i	0.537670	−	1.47724i	0.849753	−	0.527182i	$-0.176751\pi$
$104$	3.76557	−	5.07312i	0.369245	−	0.497461i
$105$	−0.906165	−	0.475318i	−0.0884326	−	0.0463862i
$106$	13.2828	+	6.34364i	1.29014	+	0.616149i
$107$			6.73607i			0.651200i	0.945508	+	0.325600i	$0.105566\pi$
$107$			6.73607i			0.651200i	−0.945508	+	0.325600i	$0.894434\pi$
$108$	7.46390	+	7.23120i	0.718214	+	0.695822i
$109$		−	2.91699i		−	0.279397i	−0.990194	−	0.139699i	$-0.955387\pi$
$109$		−	2.91699i		−	0.279397i	0.990194	−	0.139699i	$-0.0446134\pi$
$110$	−0.00487610	+	0.0102100i	−0.000464918	+	0.000973482i
$111$	−7.75291	+	4.90522i	−0.735874	+	0.465583i
$112$	−1.95939	+	4.82218i	−0.185145	+	0.455653i
$113$	−6.67148	+	18.3297i	−0.627600	+	1.72432i	0.0599724	+	0.998200i	$0.480899\pi$
$113$	−6.67148	+	18.3297i	−0.627600	+	1.72432i	−0.687572	+	0.726116i	$0.741323\pi$
$114$	−2.65926	+	1.98887i	−0.249062	+	0.186275i
$115$	0.167748	−	0.951347i	0.0156426	−	0.0887136i
$116$	0.268145	−	14.5380i	0.0248967	−	1.34982i
$117$	4.70879	+	4.76791i	0.435328	+	0.440793i
$118$	11.0743	−	10.8719i	1.01947	−	1.00084i
$119$	1.79623	−	0.653776i	0.164661	−	0.0599315i
$120$	−0.165359	+	2.21800i	−0.0150952	+	0.202475i
$121$	8.42625	−	7.07046i	0.766023	−	0.642769i
$122$	10.3669	+	7.40236i	0.938573	+	0.670178i
$123$	2.83977	+	3.11853i	0.256053	+	0.281189i
$124$	13.5949	+	11.8415i	1.22086	+	1.06340i
$125$	2.22323	+	3.85075i	0.198852	+	0.344422i
$126$	−4.73791	−	2.83398i	−0.422086	−	0.252471i
$127$	−14.9938	−	8.65666i	−1.33048	−	0.768154i	−0.345108	−	0.938563i	$-0.612158\pi$
$127$	−14.9938	−	8.65666i	−1.33048	−	0.768154i	−0.985373	+	0.170409i	$0.945491\pi$
$128$	11.3108	−	0.257006i	0.999742	−	0.0227164i
$129$	−17.3845	+	7.13744i	−1.53062	+	0.628417i
$130$	−0.138166	+	1.42751i	−0.0121180	+	0.125201i
$131$	−3.03491	+	0.535137i	−0.265162	+	0.0467552i	−0.304648	−	0.952465i	$-0.598539\pi$
$131$	−3.03491	+	0.535137i	−0.265162	+	0.0467552i	0.0394865	+	0.999220i	$0.487428\pi$
$132$	−0.0293486	+	0.0535278i	−0.00255447	+	0.00465900i
$133$	1.13394	−	1.35138i	0.0983252	−	0.117179i
$134$	−6.61467	+	1.70718i	−0.571421	+	0.147478i
$135$	−2.29828	−	0.532125i	−0.197804	−	0.0457980i
$136$	−2.85554	−	3.01807i	−0.244861	−	0.258797i
$137$	7.57425	−	9.02665i	0.647112	−	0.771198i	−0.338363	−	0.941016i	$-0.609873\pi$
$137$	7.57425	−	9.02665i	0.647112	−	0.771198i	0.985476	+	0.169817i	$0.0543177\pi$
$138$	1.19079	−	5.07413i	0.101366	−	0.431939i
$139$	−0.930383	−	5.27646i	−0.0789140	−	0.447544i	−0.998505	−	0.0546659i	$-0.982591\pi$
$139$	−0.930383	−	5.27646i	−0.0789140	−	0.447544i	0.919591	−	0.392878i	$-0.128520\pi$
$140$	−0.183682	−	1.16719i	−0.0155240	−	0.0986459i
$141$	−1.05475	+	7.82299i	−0.0888259	+	0.658815i
$142$	−1.11080	−	14.2038i	−0.0932160	−	1.19196i
$143$	−0.0196817	+	0.0340897i	−0.00164587	+	0.00285073i
$144$	−1.56024	+	11.8981i	−0.130020	+	0.991511i
$145$	1.65036	+	2.85851i	0.137055	+	0.237386i
$146$	0.791544	−	0.543437i	0.0655086	−	0.0449752i
$147$	−8.75742	−	2.79126i	−0.722300	−	0.230219i
$148$	−9.88625	−	3.80620i	−0.812645	−	0.312868i
$149$	10.9918	−	9.22325i	0.900486	−	0.755598i	−0.0697991	−	0.997561i	$-0.522236\pi$
$149$	10.9918	−	9.22325i	0.900486	−	0.755598i	0.970285	+	0.241963i	$0.0777914\pi$
$150$	5.29317	+	10.4819i	0.432185	+	0.855843i
$151$	4.06790	+	11.1765i	0.331041	+	0.909528i	0.987842	+	0.155464i	$0.0496872\pi$
$151$	4.06790	+	11.1765i	0.331041	+	0.909528i	−0.656800	+	0.754065i	$0.728091\pi$
$152$	−3.67492	−	1.09450i	−0.298076	−	0.0887753i
$153$	3.62562	−	2.50513i	0.293114	−	0.202527i
$154$	0.00868194	−	0.0312460i	0.000699610	−	0.00251788i
$155$	−4.03044	−	0.710675i	−0.323733	−	0.0570828i
$156$	−1.17515	+	7.64808i	−0.0940876	+	0.612337i
$157$	−5.75062	+	15.7997i	−0.458950	+	1.26095i	0.467319	+	0.884089i	$0.345220\pi$
$157$	−5.75062	+	15.7997i	−0.458950	+	1.26095i	−0.926268	+	0.376865i	$0.877002\pi$
$158$	−10.4062	+	4.73616i	−0.827873	+	0.376789i
$159$	−18.0133	+	0.730195i	−1.42855	+	0.0579082i
$160$	−2.16943	+	1.37455i	−0.171509	+	0.108668i
$161$			2.76881i			0.218213i
$162$	−12.2199	−	3.56018i	−0.960083	−	0.279714i
$163$	10.1776			0.797169			0.398585	−	0.917132i	$-0.369502\pi$
$163$	10.1776			0.797169			0.398585	+	0.917132i	$0.369502\pi$
$164$	−0.934016	+	4.77985i	−0.0729344	+	0.373244i
$165$	−0.000561272	−	0.0138461i	−4.36950e−5	−	0.00107792i
$166$	−2.58564	+	1.17680i	−0.200684	+	0.0913372i
$167$	−15.0723	−	5.48587i	−1.16633	−	0.424509i	−0.314975	−	0.949100i	$-0.601996\pi$
$167$	−15.0723	−	5.48587i	−1.16633	−	0.424509i	−0.851355	+	0.524591i	$0.824218\pi$
$168$	−0.637169	−	6.34294i	−0.0491586	−	0.489369i
$169$	1.39101	−	7.88879i	0.107000	−	0.606830i
$170$	0.908736	+	0.252499i	0.0696968	+	0.0193658i
$171$	1.74177	−	3.67520i	0.133196	−	0.281050i
$172$	−18.5893	−	11.1946i	−1.41742	−	0.853584i
$173$	12.7203	−	4.62982i	0.967109	−	0.351999i	0.190293	−	0.981727i	$-0.439056\pi$
$173$	12.7203	−	4.62982i	0.967109	−	0.351999i	0.776815	+	0.629729i	$0.216834\pi$
$174$	8.02745	+	15.8965i	0.608559	+	1.20511i
$175$	−4.00978	−	4.77867i	−0.303111	−	0.361233i
$176$	−0.0698226	+	0.00967213i	−0.00526308	+	0.000729064i
$177$	−5.77198	+	18.1092i	−0.433848	+	1.36117i
$178$	0.0958874	+	0.139665i	0.00718706	+	0.0104683i
$179$	9.84897	−	5.68630i	0.736146	−	0.425014i	−0.0845201	−	0.996422i	$-0.526936\pi$
$179$	9.84897	−	5.68630i	0.736146	−	0.425014i	0.820667	+	0.571407i	$0.193602\pi$
$180$	−1.08995	−	2.49646i	−0.0812399	−	0.186075i
$181$	12.8369	+	7.41138i	0.954159	+	0.550884i	0.894370	−	0.447327i	$-0.147624\pi$
$181$	12.8369	+	7.41138i	0.954159	+	0.550884i	0.0597883	+	0.998211i	$0.480957\pi$
$182$	−0.320491	−	4.09813i	−0.0237564	−	0.303774i
$183$	−15.4614	−	2.08461i	−1.14294	−	0.154099i
$184$	5.52268	−	2.39159i	0.407138	−	0.176311i
$185$	2.36824	−	0.417585i	0.174117	−	0.0307015i
$186$	−21.4969	−	5.04483i	−1.57623	−	0.369905i
$187$	0.0198303	+	0.0166396i	0.00145014	+	0.00121681i
$188$	−7.97648	+	4.41113i	−0.581745	+	0.321715i
$189$	6.75208	+	0.358129i	0.491141	+	0.0260500i
$190$	0.842810	−	0.217521i	0.0611439	−	0.0157806i
$191$	14.4389	+	12.1157i	1.04476	+	0.876659i	0.992533	−	0.121976i	$-0.0389232\pi$
$191$	14.4389	+	12.1157i	1.04476	+	0.876659i	0.0522283	+	0.998635i	$0.483368\pi$
$192$	−12.1013	+	6.74970i	−0.873336	+	0.487117i
$193$	−0.366460	−	2.07830i	−0.0263783	−	0.149599i	0.968774	−	0.247946i	$-0.0797556\pi$
$193$	−0.366460	−	2.07830i	−0.0263783	−	0.149599i	−0.995152	+	0.0983471i	$0.968644\pi$
$194$	15.6990	+	1.51947i	1.12712	+	0.109092i
$195$	−0.667121	−	1.62489i	−0.0477735	−	0.116361i
$196$	−3.44547	−	10.0386i	−0.246105	−	0.717043i
$197$	−5.72884	+	9.92264i	−0.408163	+	0.706959i	−0.994684	−	0.102975i	$-0.967164\pi$
$197$	−5.72884	+	9.92264i	−0.408163	+	0.706959i	0.586521	+	0.809934i	$0.300497\pi$
$198$	0.00115576	−	0.0747563i	8.21360e−5	−	0.00531270i
$199$	−4.92181	+	2.84161i	−0.348898	+	0.201436i	−0.664200	−	0.747555i	$-0.731228\pi$
$199$	−4.92181	+	2.84161i	−0.348898	+	0.201436i	0.315302	+	0.948991i	$0.397894\pi$
$200$	−6.06805	+	12.1256i	−0.429076	+	0.857406i
$201$	6.18622	−	5.63323i	0.436342	−	0.397337i
$202$	−13.7124	+	19.2039i	−0.964798	+	1.35118i
$203$	−6.08110	−	7.24717i	−0.426809	−	0.508652i
$204$	4.81901	+	1.63446i	0.337398	+	0.114435i
$205$	−0.378123	−	1.03889i	−0.0264093	−	0.0725589i
$206$	−16.1009	+	15.8067i	−1.12180	+	1.10130i
$207$	1.61364	+	6.17603i	0.112156	+	0.429264i
$208$	−7.89732	+	4.17906i	−0.547581	+	0.289766i
$209$	0.0235273	+	0.00414851i	0.00162742	+	0.000286958i
$210$	0.866710	+	1.15885i	0.0598087	+	0.0799684i
$211$	15.6412	+	5.69295i	1.07679	+	0.391919i	0.818711	−	0.574206i	$-0.194689\pi$
$211$	15.6412	+	5.69295i	1.07679	+	0.391919i	0.258077	+	0.966124i	$0.416911\pi$
$212$	−13.0846	−	16.1908i	−0.898653	−	1.11199i
$213$	9.32948	+	14.7456i	0.639246	+	1.01036i
$214$	4.10540	−	8.59621i	0.280640	−	0.587625i
$215$	4.92591			0.335945
$216$	−5.11787	−	13.7771i	−0.348227	−	0.937410i
$217$	11.7302			0.796300
$218$	−1.77781	+	3.72251i	−0.120408	+	0.252120i
$219$	−0.546232	+	1.04136i	−0.0369109	+	0.0703685i
$220$	0.0124453	−	0.0100576i	0.000839059	−	0.000678083i
$221$	3.08338	+	1.12226i	0.207410	+	0.0754912i
$222$	12.8834	−	1.53465i	0.864679	−	0.102999i
$223$	2.73564	+	0.482367i	0.183192	+	0.0323017i	0.264491	−	0.964388i	$-0.414796\pi$
$223$	2.73564	+	0.482367i	0.183192	+	0.0323017i	−0.0812995	+	0.996690i	$0.525907\pi$
$224$	5.43942	−	4.95963i	0.363437	−	0.331379i
$225$	−11.7291	−	8.32230i	−0.781938	−	0.554820i
$226$	19.6851	−	19.3254i	1.30944	−	1.28551i
$227$	−8.45693	−	23.2352i	−0.561306	−	1.54218i	−0.817724	−	0.575611i	$-0.804764\pi$
$227$	−8.45693	−	23.2352i	−0.561306	−	1.54218i	0.256418	−	0.966566i	$-0.417458\pi$
$228$	4.60575	−	0.917363i	0.305023	−	0.0607539i
$229$	10.0744	+	12.0062i	0.665736	+	0.793393i	0.988197	−	0.153190i	$-0.0489546\pi$
$229$	10.0744	+	12.0062i	0.665736	+	0.793393i	−0.322461	+	0.946583i	$0.604510\pi$
$230$	−0.793885	+	1.11182i	−0.0523472	+	0.0733114i
$231$	0.00847561	+	0.0388034i	0.000557654	+	0.00255307i
$232$	−9.20261	+	18.3892i	−0.604181	+	1.20731i
$233$	17.5198	−	10.1151i	1.14776	−	0.662659i	0.199419	−	0.979914i	$-0.436094\pi$
$233$	17.5198	−	10.1151i	1.14776	−	0.662659i	0.948340	+	0.317255i	$0.102761\pi$
$234$	−3.10323	−	8.95440i	−0.202865	−	0.585367i
$235$	1.03456	−	1.79190i	0.0674870	−	0.116891i
$236$	−20.7585	+	7.12478i	−1.35127	+	0.463784i
$237$	8.55901	−	11.0826i	0.555968	−	0.719891i
$238$	−2.69071	−	0.260429i	−0.174413	−	0.0168811i
$239$	−1.48780	−	8.43773i	−0.0962378	−	0.545791i	−0.994361	−	0.106048i	$-0.966180\pi$
$239$	−1.48780	−	8.43773i	−0.0962378	−	0.545791i	0.898123	−	0.439744i	$-0.144931\pi$
$240$	1.56282	−	2.72972i	0.100880	−	0.176202i
$241$	11.0727	+	9.29110i	0.713255	+	0.598492i	0.925510	−	0.378722i	$-0.123636\pi$
$241$	11.0727	+	9.29110i	0.713255	+	0.598492i	−0.212255	+	0.977214i	$0.568081\pi$
$242$	−15.0623	+	3.88744i	−0.968244	+	0.249894i
$243$	15.2697	−	3.13622i	0.979552	−	0.201189i
$244$	−8.71818	−	15.7648i	−0.558124	−	1.00924i
$245$	1.84561	+	1.54865i	0.117912	+	0.0989395i
$246$	−1.72332	−	5.71045i	−0.109875	−	0.364085i
$247$	2.98221	−	0.525844i	0.189754	−	0.0334587i
$248$	−10.1321	−	23.3972i	−0.643391	−	1.48572i
$249$	2.12666	−	2.75370i	0.134772	−	0.174508i
$250$	−0.490270	−	6.26911i	−0.0310074	−	0.396493i
$251$	12.7128	+	7.33976i	0.802427	+	0.463281i	0.844319	−	0.535841i	$-0.180005\pi$
$251$	12.7128	+	7.33976i	0.802427	+	0.463281i	−0.0418921	+	0.999122i	$0.513339\pi$
$252$	4.31905	+	6.50417i	0.272075	+	0.409724i
$253$	−0.0324730	+	0.0187483i	−0.00204156	+	0.00117869i
$254$	13.8583	+	20.1854i	0.869548	+	1.26654i
$255$	−1.12853	+	0.246498i	−0.0706711	+	0.0154363i
$256$	−14.5909	−	6.56556i	−0.911929	−	0.410348i
$257$	−14.4703	−	17.2450i	−0.902633	−	1.07572i	−0.996782	−	0.0801575i	$-0.974458\pi$
$257$	−14.4703	−	17.2450i	−0.902633	−	1.07572i	0.0941497	−	0.995558i	$-0.469987\pi$
$258$	26.5352	+	1.48682i	1.65201	+	0.0925651i
$259$	−6.47689	+	2.35739i	−0.402454	+	0.146481i
$260$	1.04634	−	1.73751i	0.0648912	−	0.107756i
$261$	−17.7879	−	12.6213i	−1.10104	−	0.781240i
$262$	4.19914	+	1.16676i	0.259424	+	0.0720828i
$263$	−3.07511	+	17.4398i	−0.189620	+	1.07539i	0.730255	+	0.683175i	$0.239401\pi$
$263$	−3.07511	+	17.4398i	−0.189620	+	1.07539i	−0.919875	+	0.392212i	$0.871710\pi$
$264$	0.0700765	−	0.0504224i	0.00431291	−	0.00310328i
$265$	4.44053	+	1.61622i	0.272780	+	0.0992836i
$266$	−2.27070	+	1.03346i	−0.139225	+	0.0633655i
$267$	−0.183744	−	0.0963806i	−0.0112449	−	0.00589839i
$268$	9.48177	+	1.85280i	0.579191	+	0.113178i
$269$	−10.2475			−0.624803			−0.312402	−	0.949950i	$-0.601133\pi$
$269$	−10.2475			−0.624803			−0.312402	+	0.949950i	$0.601133\pi$
$270$	2.60863	+	2.07979i	0.158756	+	0.126572i
$271$			18.7315i			1.13786i	0.822386	+	0.568929i	$0.192642\pi$
$271$			18.7315i			1.13786i	−0.822386	+	0.568929i	$0.807358\pi$
$272$	1.80468	+	5.59186i	0.109425	+	0.339056i
$273$	2.69177	+	4.25446i	0.162913	+	0.257492i
$274$	−15.1673	+	6.90308i	−0.916290	+	0.417030i
$275$	0.0288937	−	0.0793847i	0.00174235	−	0.00478708i
$276$	−4.61213	+	5.74960i	−0.277618	+	0.346085i
$277$	−21.4560	−	3.78327i	−1.28917	−	0.227315i	−0.513299	−	0.858210i	$-0.671577\pi$
$277$	−21.4560	−	3.78327i	−1.28917	−	0.227315i	−0.775868	+	0.630895i	$0.782688\pi$
$278$	−2.02852	+	7.30058i	−0.121662	+	0.437860i
$279$	26.1651	−	6.83628i	1.56646	−	0.409277i
$280$	−0.476959	+	1.60146i	−0.0285038	+	0.0957055i
$281$	−3.95262	−	10.8597i	−0.235793	−	0.647837i	−0.999996	−	0.00286067i	$-0.999089\pi$
$281$	−3.95262	−	10.8597i	−0.235793	−	0.647837i	0.764203	−	0.644976i	$-0.223133\pi$
$282$	6.11386	−	9.34046i	0.364075	−	0.556216i
$283$	−3.28791	+	2.75888i	−0.195446	+	0.163998i	−0.735259	−	0.677786i	$-0.762939\pi$
$283$	−3.28791	+	2.75888i	−0.195446	+	0.163998i	0.539813	+	0.841785i	$0.318495\pi$
$284$	−7.23920	+	18.8032i	−0.429567	+	1.11576i
$285$	−0.788218	+	0.717759i	−0.0466900	+	0.0425164i
$286$	0.0458933	−	0.0315082i	0.00271373	−	0.00186312i
$287$	1.58437	+	2.74421i	0.0935226	+	0.161986i
$288$	9.24260	−	14.2329i	0.544625	−	0.838679i
$289$	−7.42107	+	12.8537i	−0.436533	+	0.756098i
$290$	−0.363940	−	4.65372i	−0.0213713	−	0.273276i
$291$	−17.8696	+	7.33663i	−1.04754	+	0.430081i
$292$	−1.34133	+	0.211087i	−0.0784956	+	0.0123529i
$293$	2.18285	+	12.3796i	0.127523	+	0.723221i	0.979777	+	0.200092i	$0.0641242\pi$
$293$	2.18285	+	12.3796i	0.127523	+	0.723221i	−0.852254	+	0.523129i	$0.824765\pi$
$294$	9.47458	+	8.89941i	0.552569	+	0.519024i
$295$	3.20241	−	3.81648i	0.186451	−	0.222204i
$296$	10.2966	+	10.8826i	0.598476	+	0.632538i
$297$	0.0415197	+	0.0816142i	0.00240922	+	0.00473574i
$298$	−19.6485	+	5.07107i	−1.13820	+	0.293759i
$299$	−3.05509	+	3.64092i	−0.176681	+	0.210560i
$300$	−0.366508	−	16.6024i	−0.0211603	−	0.958542i
$301$	−13.9041	+	2.45167i	−0.801421	+	0.141312i
$302$	1.62043	−	16.7421i	0.0932455	−	0.963398i
$303$	3.86160	−	28.6412i	0.221843	−	1.64539i
$304$	4.02269	+	3.63648i	0.230717	+	0.208566i
$305$	3.54153	+	2.04470i	0.202787	+	0.117079i
$306$	−6.15361	+	0.987219i	−0.351778	+	0.0564356i
$307$	7.46768	+	12.9344i	0.426203	+	0.738205i	0.996532	−	0.0832113i	$-0.0265176\pi$
$307$	7.46768	+	12.9344i	0.426203	+	0.738205i	−0.570329	+	0.821416i	$0.693184\pi$
$308$	−0.0301228	+	0.0345832i	−0.00171641	+	0.00197056i
$309$	8.39186	−	26.3290i	0.477396	−	1.49780i
$310$	4.71030	+	3.36334i	0.267527	+	0.191025i
$311$	−0.935160	+	0.784692i	−0.0530280	+	0.0444958i	−0.668916	−	0.743338i	$-0.733242\pi$
$311$	−0.935160	+	0.784692i	−0.0530280	+	0.0444958i	0.615888	+	0.787833i	$0.288797\pi$
$312$	6.16091	−	9.04386i	0.348793	−	0.512008i
$313$	−3.74180	+	1.36190i	−0.211499	+	0.0769794i	−0.445597	−	0.895234i	$-0.647009\pi$
$313$	−3.74180	+	1.36190i	−0.211499	+	0.0769794i	0.234098	+	0.972213i	$0.424786\pi$
$314$	16.9680	−	16.6579i	0.957561	−	0.940062i
$315$	−1.60158	−	0.759028i	−0.0902389	−	0.0427664i
$316$	16.1664	+	0.298179i	0.909429	+	0.0167739i
$317$	1.28552	−	7.29053i	0.0722018	−	0.409477i	−0.927190	−	0.374593i	$-0.877783\pi$
$317$	1.28552	−	7.29053i	0.0722018	−	0.409477i	0.999391	−	0.0348844i	$-0.0111063\pi$
$318$	23.4326	+	10.0466i	1.31404	+	0.563388i
$319$	0.0438192	−	0.120392i	0.00245340	−	0.00674067i
$320$	3.60626	−	0.431935i	0.201596	−	0.0241459i
$321$	0.472559	+	11.6576i	0.0263757	+	0.650666i
$322$	1.68750	−	3.53341i	0.0940404	−	0.196909i
$323$		−	1.99145i		−	0.110807i
$324$	13.4245	+	11.9909i	0.745808	+	0.666161i
$325$		−	10.7082i		−	0.593984i
$326$	−12.9881	−	6.20288i	−0.719343	−	0.343546i
$327$	−0.204638	−	5.04824i	−0.0113165	−	0.279168i
$328$	4.10510	−	5.53055i	0.226666	−	0.305373i
$329$	−2.02834	+	5.57283i	−0.111826	+	0.307240i
$330$	−0.00772246	+	0.0180117i	−0.000425108	+	0.000991514i
$331$	0.520452	−	2.95163i	0.0286066	−	0.162236i	−0.967158	−	0.254176i	$-0.918196\pi$
$331$	0.520452	−	2.95163i	0.0286066	−	0.162236i	0.995765	+	0.0919400i	$0.0293068\pi$
$332$	4.01687	+	0.0740888i	0.220454	+	0.00406615i
$333$	−13.0733	+	9.03302i	−0.716412	+	0.495006i
$334$	15.8910	+	16.1868i	0.869518	+	0.885704i
$335$	−2.06083	+	0.750081i	−0.112595	+	0.0409813i
$336$	−3.05269	+	8.48286i	−0.166538	+	0.462778i
$337$	−10.0788	+	8.45709i	−0.549025	+	0.460687i	−0.874611	−	0.484826i	$-0.838883\pi$
$337$	−10.0788	+	8.45709i	−0.549025	+	0.460687i	0.325586	+	0.945513i	$0.394439\pi$
$338$	−6.58307	+	9.21948i	−0.358072	+	0.501474i
$339$	−10.2600	+	32.1900i	−0.557244	+	1.74832i
$340$	−1.00579	−	0.876069i	−0.0545467	−	0.0475115i
$341$	0.0794281	+	0.137574i	0.00430127	+	0.00745003i
$342$	−4.46266	+	3.62855i	−0.241313	+	0.196210i
$343$	−13.8688	−	8.00714i	−0.748844	−	0.432345i
$344$	16.9000	+	25.6156i	0.911186	+	1.38110i
$345$	0.223570	−	1.65820i	0.0120366	−	0.0892744i
$346$	−19.0547	−	1.84427i	−1.02439	−	0.0991487i
$347$	28.8369	−	5.08472i	1.54804	−	0.272962i	0.666660	−	0.745362i	$-0.267723\pi$
$347$	28.8369	−	5.08472i	1.54804	−	0.272962i	0.881385	+	0.472400i	$0.156612\pi$
$348$	−0.555834	−	25.1787i	−0.0297958	−	1.34972i
$349$	13.4766	−	16.0608i	0.721385	−	0.859713i	−0.273380	−	0.961906i	$-0.588141\pi$
$349$	13.4766	−	16.0608i	0.721385	−	0.859713i	0.994765	+	0.102193i	$0.0325859\pi$
$350$	2.20463	+	8.54210i	0.117843	+	0.456595i
$351$	8.48366	+	7.92114i	0.452824	+	0.422799i
$352$	0.0949988	+	0.0302114i	0.00506345	+	0.00161028i
$353$	2.02760	−	2.41640i	0.107918	−	0.128612i	−0.709381	−	0.704825i	$-0.751026\pi$
$353$	2.02760	−	2.41640i	0.107918	−	0.128612i	0.817300	+	0.576213i	$0.195470\pi$
$354$	18.4028	−	19.5922i	0.978100	−	1.04131i
$355$	−0.794226	−	4.50428i	−0.0421532	−	0.239062i
$356$	−0.0372454	−	0.236673i	−0.00197400	−	0.0125436i
$357$	3.06275	−	1.25746i	0.162098	−	0.0665516i
$358$	−16.0343	+	1.25395i	−0.847441	+	0.0662734i
$359$	15.2950	−	26.4917i	0.807240	−	1.39818i	−0.107529	−	0.994202i	$-0.534294\pi$
$359$	15.2950	−	26.4917i	0.807240	−	1.39818i	0.914768	−	0.403979i	$-0.132373\pi$
$360$	−0.130575	+	3.85014i	−0.00688192	+	0.202920i
$361$	8.58106	+	14.8628i	0.451635	+	0.782255i
$362$	−11.8648	−	17.2817i	−0.623599	−	0.908304i
$363$	14.0867	−	12.8275i	0.739360	−	0.673268i
$364$	−2.08868	+	5.42514i	−0.109476	+	0.284355i
$365$	0.236120	−	0.198128i	0.0123591	−	0.0103705i
$366$	18.4605	+	12.0835i	0.964947	+	0.631613i
$367$	7.65245	+	21.0249i	0.399455	+	1.09749i	0.962551	+	0.271101i	$0.0873878\pi$
$367$	7.65245	+	21.0249i	0.399455	+	1.09749i	−0.563096	+	0.826391i	$0.690390\pi$
$368$	−8.50535	−	0.313859i	−0.443372	−	0.0163610i
$369$	5.13336	+	5.19781i	0.267232	+	0.270587i
$370$	−3.27673	−	0.910464i	−0.170349	−	0.0473327i
$371$	−13.3385	−	2.35193i	−0.692499	−	0.122106i
$372$	24.3585	+	19.5395i	1.26293	+	1.01308i
$373$	−3.91132	+	10.7463i	−0.202521	+	0.556421i	−0.998824	−	0.0484764i	$-0.984563\pi$
$373$	−3.91132	+	10.7463i	−0.202521	+	0.556421i	0.796304	+	0.604897i	$0.206786\pi$
$374$	−0.0151651	−	0.0333205i	−0.000784170	−	0.00172296i
$375$	4.11773	+	6.50825i	0.212639	+	0.336085i
$376$	12.8676	−	0.767856i	0.663595	−	0.0395992i
$377$		−	16.2397i		−	0.836387i
$378$	−8.39838	−	4.57218i	−0.431966	−	0.235168i
$379$	−21.7004			−1.11468			−0.557338	−	0.830286i	$-0.688177\pi$
$379$	−21.7004			−1.11468			−0.557338	+	0.830286i	$0.688177\pi$
$380$	−1.20812	−	0.236075i	−0.0619753	−	0.0121104i
$381$	−26.5560	−	13.9296i	−1.36050	−	0.713635i
$382$	−11.0421	−	24.2614i	−0.564961	−	1.24132i
$383$	−31.1726	−	11.3459i	−1.59285	−	0.579749i	−0.614900	−	0.788605i	$-0.710804\pi$
$383$	−31.1726	−	11.3459i	−1.59285	−	0.579749i	−0.977946	+	0.208856i	$0.933026\pi$
$384$	19.5568	−	1.23828i	0.998001	−	0.0631905i
$385$	0.00180784	−	0.0102528i	9.21359e−5	−	0.000522529i
$386$	−0.798994	+	2.87556i	−0.0406677	+	0.146362i
$387$	−29.5854	+	13.5718i	−1.50391	+	0.689896i
$388$	−19.1081	−	11.5071i	−0.970068	−	0.584182i
$389$	−6.54404	+	2.38183i	−0.331796	+	0.120764i	−0.502546	−	0.864551i	$-0.667603\pi$
$389$	−6.54404	+	2.38183i	−0.331796	+	0.120764i	0.170750	+	0.985314i	$0.445381\pi$
$390$	−0.138969	+	2.48018i	−0.00703699	+	0.125589i
$391$	2.00913	+	2.39438i	0.101606	+	0.121089i
$392$	−1.72126	+	14.9106i	−0.0869369	+	0.753100i
$393$	−5.21477	+	1.13903i	−0.263050	+	0.0574567i
$394$	13.3584	−	9.17122i	0.672984	−	0.462039i
$395$	−3.17868	+	1.83521i	−0.159937	+	0.0923395i
$396$	−0.0470363	+	0.0946957i	−0.00236366	+	0.00475864i
$397$	31.8597	+	18.3942i	1.59899	+	0.923178i	0.991682	+	0.128712i	$0.0410841\pi$
$397$	31.8597	+	18.3942i	1.59899	+	0.923178i	0.607308	+	0.794466i	$0.292249\pi$
$398$	8.01281	−	0.626635i	0.401646	−	0.0314104i
$399$	1.86763	−	2.41829i	0.0934984	−	0.121066i
$400$	15.1338	−	11.7757i	0.756692	−	0.588786i
$401$	3.00611	−	0.530059i	0.150118	−	0.0264699i	−0.0980840	−	0.995178i	$-0.531271\pi$
$401$	3.00611	−	0.530059i	0.150118	−	0.0264699i	0.248202	+	0.968708i	$0.420160\pi$
$402$	−11.3278	+	3.41854i	−0.564979	+	0.170501i
$403$	15.4250	+	12.9431i	0.768372	+	0.644740i
$404$	29.2031	−	16.1498i	1.45291	−	0.803483i
$405$	−4.01480	−	0.759679i	−0.199497	−	0.0377487i
$406$	3.34347	+	12.9547i	0.165934	+	0.642930i
$407$	−0.0715044	−	0.0599993i	−0.00354434	−	0.00297406i
$408$	−5.15362	−	5.02284i	−0.255142	−	0.248667i
$409$	−4.18256	−	23.7205i	−0.206814	−	1.17290i	−0.894559	−	0.446949i	$-0.852511\pi$
$409$	−4.18256	−	23.7205i	−0.206814	−	1.17290i	0.687745	−	0.725952i	$-0.258601\pi$
$410$	−0.150624	+	1.55622i	−0.00743879	+	0.0768564i
$411$	12.4750	−	16.1531i	0.615345	−	0.796776i
$412$	30.1808	−	10.3587i	1.48690	−	0.510337i
$413$	−7.13978	+	12.3665i	−0.351326	+	0.608514i
$414$	1.70484	−	8.86499i	0.0837883	−	0.435690i
$415$	−0.789809	+	0.455997i	−0.0387702	+	0.0223840i
$416$	12.6251	−	0.519953i	0.618998	−	0.0254928i
$417$	−1.98031	−	9.06633i	−0.0969762	−	0.443980i
$418$	−0.0274960	−	0.0196332i	−0.00134487	−	0.000960292i
$419$	−19.0854	−	22.7451i	−0.932383	−	1.11117i	−0.993590	−	0.113046i	$-0.963939\pi$
$419$	−19.0854	−	22.7451i	−0.932383	−	1.11117i	0.0612068	−	0.998125i	$-0.480505\pi$
$420$	−0.399769	−	2.00710i	−0.0195067	−	0.0979362i
$421$	−9.82045	−	26.9815i	−0.478619	−	1.31500i	−0.910666	−	0.413144i	$-0.864430\pi$
$421$	−9.82045	−	26.9815i	−0.478619	−	1.31500i	0.432046	−	0.901851i	$-0.357792\pi$
$422$	−16.4909	−	16.7978i	−0.802763	−	0.817706i
$423$	−1.27657	+	13.6127i	−0.0620689	+	0.661872i
$424$	6.83010	+	28.6365i	0.331699	+	1.39071i
$425$	−6.93506	−	1.22284i	−0.336400	−	0.0593164i
$426$	−2.91883	−	24.5036i	−0.141418	−	1.18720i
$427$	−11.0142	−	4.00883i	−0.533013	−	0.194001i
$428$	−10.4782	+	8.46793i	−0.506483	+	0.409313i
$429$	−0.0316702	+	0.0603774i	−0.00152905	+	0.00291505i
$430$	−6.28619	−	3.00218i	−0.303147	−	0.144778i
$431$	26.5585			1.27928			0.639639	−	0.768675i	$-0.279084\pi$
$431$	26.5585			1.27928			0.639639	+	0.768675i	$0.279084\pi$
$432$	−1.86550	+	20.7007i	−0.0897538	+	0.995964i
$433$	−1.55270			−0.0746180			−0.0373090	−	0.999304i	$-0.511879\pi$
$433$	−1.55270			−0.0746180			−0.0373090	+	0.999304i	$0.511879\pi$
$434$	−14.9695	−	7.14917i	−0.718559	−	0.343171i
$435$	3.05670	+	4.83124i	0.146557	+	0.231640i
$436$	4.53749	−	3.66696i	0.217306	−	0.175616i
$437$	2.71064	+	0.986591i	0.129667	+	0.0471951i
$438$	1.33175	−	0.996018i	0.0636333	−	0.0475916i
$439$	−1.13120	−	0.199460i	−0.0539891	−	0.00951973i	0.146588	−	0.989198i	$-0.453171\pi$
$439$	−1.13120	−	0.199460i	−0.0539891	−	0.00951973i	−0.200577	+	0.979678i	$0.564282\pi$
$440$	−0.0220117	+	0.00525002i	−0.00104937	+	0.000250285i
$441$	−15.3517	−	4.21628i	−0.731032	−	0.200775i
$442$	−3.25087	−	3.31138i	−0.154628	−	0.157506i
$443$	5.79518	+	15.9221i	0.275337	+	0.756483i	0.997875	+	0.0651518i	$0.0207532\pi$
$443$	5.79518	+	15.9221i	0.275337	+	0.756483i	−0.722538	+	0.691331i	$0.757025\pi$
$444$	−17.3765	−	5.89357i	−0.824650	−	0.279696i
$445$	0.0349590	+	0.0416625i	0.00165721	+	0.00197499i
$446$	−3.19709	−	2.28285i	−0.151387	−	0.108096i
$447$	18.3758	−	16.7331i	0.869143	−	0.791450i
$448$	−9.96423	+	3.01407i	−0.470766	+	0.142401i
$449$	−26.5725	+	15.3416i	−1.25403	+	0.724017i	−0.971908	−	0.235361i	$-0.924373\pi$
$449$	−26.5725	+	15.3416i	−1.25403	+	0.724017i	−0.282126	+	0.959377i	$0.591039\pi$
$450$	9.89586	+	17.7689i	0.466495	+	0.837636i
$451$	−0.0214563	+	0.0371634i	−0.00101034	+	0.00174996i
$452$	−36.8993	+	12.6646i	−1.73560	+	0.595694i
$453$	7.82410	+	19.0570i	0.367608	+	0.895374i
$454$	−3.36879	+	34.8058i	−0.158105	+	1.63352i
$455$	−0.229153	−	1.29959i	−0.0107428	−	0.0609257i
$456$	−6.43672	−	1.63636i	−0.301427	−	0.0766294i
$457$	5.48725	+	4.60435i	0.256683	+	0.215382i	0.762044	−	0.647526i	$-0.224196\pi$
$457$	5.48725	+	4.60435i	0.256683	+	0.215382i	−0.505361	+	0.862908i	$0.668641\pi$
$458$	−5.53905	−	21.4617i	−0.258823	−	1.00284i
$459$	6.09886	−	4.58979i	0.284670	−	0.214233i
$460$	1.69073	−	0.935003i	0.0788308	−	0.0435948i
$461$	−6.34887	−	5.32733i	−0.295696	−	0.248119i	0.482854	−	0.875701i	$-0.339600\pi$
$461$	−6.34887	−	5.32733i	−0.295696	−	0.248119i	−0.778550	+	0.627582i	$0.784045\pi$
$462$	0.0128332	−	0.0546844i	0.000597054	−	0.00254415i
$463$	−0.381159	+	0.0672086i	−0.0177140	+	0.00312345i	−0.182498	−	0.983206i	$-0.558418\pi$
$463$	−0.381159	+	0.0672086i	−0.0177140	+	0.00312345i	0.164784	+	0.986330i	$0.447307\pi$
$464$	22.9515	−	17.8587i	1.06550	−	0.829068i
$465$	−7.02505	−	0.947165i	−0.325779	−	0.0439237i
$466$	−28.5226	+	2.23059i	−1.32128	+	0.103330i
$467$	−5.76908	−	3.33078i	−0.266961	−	0.154130i	0.360545	−	0.932742i	$-0.382591\pi$
$467$	−5.76908	−	3.33078i	−0.266961	−	0.154130i	−0.627506	+	0.778612i	$0.715924\pi$
$468$	−1.49722	+	13.3184i	−0.0692088	+	0.615645i
$469$	5.44368	−	3.14291i	0.251366	−	0.145126i
$470$	−2.41235	+	1.65621i	−0.111273	+	0.0763951i
$471$	−8.84379	+	27.7469i	−0.407500	+	1.27851i
$472$	30.8333	+	3.55935i	1.41922	+	0.163832i
$473$	−0.122902	−	0.146469i	−0.00565103	−	0.00673463i
$474$	−17.6770	+	8.92658i	−0.811932	+	0.410011i
$475$	−6.10704	+	2.22278i	−0.280210	+	0.101988i
$476$	3.27502	+	1.97224i	0.150110	+	0.0903977i
$477$	−31.1231	+	2.52739i	−1.42503	+	0.115721i
$478$	−3.24386	+	11.6745i	−0.148371	+	0.533981i
$479$	0.196814	−	1.11619i	0.00899268	−	0.0510000i	−0.979981	−	0.199090i	$-0.936201\pi$
$479$	0.196814	−	1.11619i	0.00899268	−	0.0510000i	0.988974	+	0.148090i	$0.0473125\pi$
$480$	−3.65806	+	2.53103i	−0.166967	+	0.115525i
$481$	−11.1181	−	4.04665i	−0.506941	−	0.184511i
$482$	−8.46779	−	18.6052i	−0.385697	−	0.847446i
$483$	0.194242	+	4.79179i	0.00883832	+	0.218034i
$484$	21.5910	+	4.21904i	0.981410	+	0.191774i
$485$	5.06338			0.229916
$486$	−21.3978	−	5.30409i	−0.970625	−	0.240598i
$487$			41.9634i			1.90154i	0.309896	+	0.950771i	$0.399706\pi$
$487$			41.9634i			1.90154i	−0.309896	+	0.950771i	$0.600294\pi$
$488$	1.51760	+	25.4316i	0.0686983	+	1.15123i
$489$	17.6136	−	0.713993i	0.796515	−	0.0322879i
$490$	−1.41142	−	3.10114i	−0.0637614	−	0.140095i
$491$	−7.04382	+	19.3527i	−0.317883	+	0.873377i	0.673119	+	0.739534i	$0.264954\pi$
$491$	−7.04382	+	19.3527i	−0.317883	+	0.873377i	−0.991003	+	0.133843i	$0.957268\pi$
$492$	−1.28111	+	8.33768i	−0.0577570	+	0.375892i
$493$	−10.5175	−	1.85452i	−0.473684	−	0.0835233i
$494$	−4.12622	−	1.14650i	−0.185648	−	0.0515835i
$495$	−0.00194271	−	0.0239231i	−8.73182e−5	−	0.00107526i
$496$	−1.32968	+	36.0334i	−0.0597045	+	1.61795i
$497$	4.48365	+	12.3187i	0.201119	+	0.552570i
$498$	−4.39222	+	2.21799i	−0.196820	+	0.0993906i
$499$	7.68110	−	6.44521i	0.343853	−	0.288527i	−0.454463	−	0.890766i	$-0.650169\pi$
$499$	7.68110	−	6.44521i	0.343853	−	0.288527i	0.798316	+	0.602239i	$0.205724\pi$
$500$	−3.19515	+	8.29911i	−0.142891	+	0.371147i
$501$	−26.4694	−	8.43663i	−1.18257	−	0.376921i
$502$	−11.7501	−	17.1146i	−0.524433	−	0.763864i
$503$	−12.3849	−	21.4513i	−0.552216	−	0.956466i	−0.998114	−	0.0613824i	$-0.980449\pi$
$503$	−12.3849	−	21.4513i	−0.552216	−	0.956466i	0.445898	−	0.895084i	$-0.352884\pi$
$504$	−1.54768	−	10.9326i	−0.0689393	−	0.486976i
$505$	−3.78767	+	6.56044i	−0.168549	+	0.291936i
$506$	0.0528667	−	0.00413440i	0.00235021	−	0.000183796i
$507$	1.85389	−	13.7502i	0.0823341	−	0.610666i
$508$	−5.38297	−	34.2057i	−0.238831	−	1.51763i
$509$	5.29018	+	30.0021i	0.234483	+	1.32982i	0.843700	+	0.536816i	$0.180373\pi$
$509$	5.29018	+	30.0021i	0.234483	+	1.32982i	−0.609217	+	0.793004i	$0.708516\pi$
$510$	1.59040	+	0.373231i	0.0704240	+	0.0165269i
$511$	−0.567874	+	0.676766i	−0.0251213	+	0.0299383i
$512$	14.6186	+	17.2713i	0.646057	+	0.763289i
$513$	2.75653	−	6.48260i	0.121704	−	0.286214i
$514$	7.95597	+	30.8264i	0.350923	+	1.35969i
$515$	−4.65597	+	5.54877i	−0.205167	+	0.244508i
$516$	−32.9566	−	18.0697i	−1.45083	−	0.795473i
$517$	−0.0790932	+	0.0139463i	−0.00347852	+	0.000613356i
$518$	9.70221	+	0.939060i	0.426291	+	0.0412599i
$519$	21.6894	−	8.90488i	0.952058	−	0.390881i
$520$	−2.39423	+	1.57961i	−0.104994	+	0.0692703i
$521$	−2.67309	−	1.54331i	−0.117110	−	0.0676136i	0.440301	−	0.897850i	$-0.354872\pi$
$521$	−2.67309	−	1.54331i	−0.117110	−	0.0676136i	−0.557411	+	0.830237i	$0.688205\pi$
$522$	15.0077	+	26.9478i	0.656871	+	1.17947i
$523$	−6.24198	−	10.8114i	−0.272943	−	0.472750i	0.696671	−	0.717390i	$-0.254664\pi$
$523$	−6.24198	−	10.8114i	−0.272943	−	0.472750i	−0.969614	+	0.244640i	$0.921330\pi$
$524$	−4.64762	−	4.04820i	−0.203032	−	0.176846i
$525$	−7.27468	−	7.98880i	−0.317493	−	0.348660i
$526$	14.5533	−	20.3816i	0.634553	−	0.888681i
$527$	10.1439	−	8.51177i	0.441877	−	0.370779i
$528$	−0.120159	+	0.0216372i	−0.00522923	+	0.000941637i
$529$	17.3585	−	6.31798i	0.754717	−	0.274695i
$530$	−4.68174	−	4.76889i	−0.203362	−	0.207147i
$531$	−8.71872	+	31.7453i	−0.378360	+	1.37763i
$532$	3.52760	+	0.0650645i	0.152941	+	0.00282091i
$533$	−0.944542	+	5.35676i	−0.0409126	+	0.232027i
$534$	0.175744	+	0.234981i	0.00760517	+	0.0101686i
$535$	1.04597	−	2.87377i	0.0452211	−	0.124244i
$536$	−10.9709	−	8.14326i	−0.473871	−	0.351735i
$537$	16.6460	−	10.5318i	0.718328	−	0.454482i
$538$	13.0774	+	6.24552i	0.563805	+	0.269264i
$539$		−	0.0935167i		−	0.00402805i
$540$	−2.06143	−	4.24399i	−0.0887099	−	0.182632i
$541$		−	35.0866i		−	1.50849i	−0.656592	−	0.754246i	$-0.728003\pi$
$541$		−	35.0866i		−	1.50849i	0.656592	−	0.754246i	$-0.271997\pi$
$542$	11.4162	−	23.9042i	0.490368	−	1.02677i
$543$	22.7358	+	11.9258i	0.975688	+	0.511785i
$544$	1.10500	−	8.23593i	0.0473767	−	0.353113i
$545$	−0.452947	+	1.24446i	−0.0194021	+	0.0533069i
$546$	−0.842149	−	7.06986i	−0.0360407	−	0.302562i
$547$	−0.423952	+	2.40435i	−0.0181269	+	0.102803i	−0.992529	−	0.122010i	$-0.961066\pi$
$547$	−0.423952	+	2.40435i	−0.0181269	+	0.102803i	0.974402	+	0.224813i	$0.0721771\pi$
$548$	23.5629	+	0.434604i	1.00656	+	0.0185654i
$549$	−26.9042	−	2.52302i	−1.14824	−	0.107680i
$550$	−0.0852548	+	0.0836968i	−0.00363528	+	0.00356884i
$551$	−9.26174	+	3.37100i	−0.394563	+	0.143609i
$552$	9.38994	−	4.52640i	0.399662	−	0.192656i
$553$	8.05890	−	6.76222i	0.342699	−	0.287559i
$554$	25.0752	+	17.9047i	1.06535	+	0.760699i
$555$	4.06926	−	0.888826i	0.172730	−	0.0377286i
$556$	7.03814	−	8.08030i	0.298484	−	0.342681i
$557$	−3.41195	−	5.90968i	−0.144569	−	0.250401i	0.784643	−	0.619948i	$-0.212846\pi$
$557$	−3.41195	−	5.90968i	−0.144569	−	0.250401i	−0.929212	+	0.369547i	$0.879513\pi$
$558$	−37.5570	−	7.22265i	−1.58992	−	0.305759i
$559$	−20.9888	−	12.1179i	−0.887730	−	0.512531i
$560$	1.58471	−	1.75301i	0.0669660	−	0.0740781i
$561$	0.0354862	+	0.0274058i	0.00149823	+	0.00115707i
$562$	−1.57451	+	16.2676i	−0.0664167	+	0.686207i
$563$	20.6520	−	3.64150i	0.870377	−	0.153471i	0.279415	−	0.960170i	$-0.409859\pi$
$563$	20.6520	−	3.64150i	0.870377	−	0.153471i	0.590962	+	0.806699i	$0.298748\pi$
$564$	−13.4949	+	8.19361i	−0.568237	+	0.345013i
$565$	5.69243	−	6.78397i	0.239482	−	0.285404i
$566$	5.87730	−	1.51687i	0.247041	−	0.0637589i
$567$	11.7105	+	0.146105i	0.491793	+	0.00613585i
$568$	20.6982	−	19.5835i	0.868476	−	0.821707i
$569$	−20.8313	+	24.8258i	−0.873295	+	1.04075i	0.125521	+	0.992091i	$0.459940\pi$
$569$	−20.8313	+	24.8258i	−0.873295	+	1.04075i	−0.998815	+	0.0486610i	$0.984505\pi$
$570$	1.44333	−	0.435574i	0.0604545	−	0.0182442i
$571$	−0.396543	−	2.24891i	−0.0165948	−	0.0941139i	0.975385	−	0.220507i	$-0.0707711\pi$
$571$	−0.396543	−	2.24891i	−0.0165948	−	0.0941139i	−0.991980	+	0.126393i	$0.959660\pi$
$572$	−0.0777697	+	0.0122387i	−0.00325172	+	0.000511725i
$573$	25.8383	+	19.9548i	1.07941	+	0.833623i
$574$	−0.349388	−	4.46764i	−0.0145832	−	0.186476i
$575$	5.10017	−	8.83376i	0.212692	−	0.368393i
$576$	−20.4694	+	12.5302i	−0.852890	+	0.522091i
$577$	−10.7395	−	18.6014i	−0.447092	−	0.774387i	0.551103	−	0.834437i	$-0.314207\pi$
$577$	−10.7395	−	18.6014i	−0.447092	−	0.774387i	−0.998195	+	0.0600507i	$0.980874\pi$
$578$	17.3042	−	11.8803i	0.719762	−	0.494155i
$579$	−0.780006	−	3.57105i	−0.0324159	−	0.148408i
$580$	−2.37184	+	6.16064i	−0.0984853	+	0.255806i
$581$	2.00240	−	1.68021i	0.0830736	−	0.0697070i
$582$	27.2757	+	1.52831i	1.13061	+	0.0633504i
$583$	−0.0627342	−	0.172361i	−0.00259818	−	0.00713845i
$584$	1.84039	+	0.548119i	0.0761558	+	0.0226813i
$585$	−1.26853	−	2.76528i	−0.0524473	−	0.114330i
$586$	4.75928	−	17.1285i	0.196604	−	0.707572i
$587$	18.6609	+	3.29041i	0.770216	+	0.135810i	0.544928	−	0.838483i	$-0.316557\pi$
$587$	18.6609	+	3.29041i	0.770216	+	0.135810i	0.225287	+	0.974292i	$0.427668\pi$
$588$	−6.66707	−	17.1314i	−0.274945	−	0.706486i
$589$	4.17975	−	11.4838i	0.172224	−	0.473180i
$590$	−6.41276	+	2.91863i	−0.264009	+	0.120158i
$591$	−9.21839	+	17.5743i	−0.379194	+	0.722911i
$592$	−6.50736	−	20.1632i	−0.267451	−	0.828703i
$593$			23.6650i			0.971804i	0.874013	+	0.485902i	$0.161509\pi$
$593$			23.6650i			0.971804i	−0.874013	+	0.485902i	$0.838491\pi$
$594$	−0.00324424	−	0.129457i	−0.000133113	−	0.00531167i
$595$	−0.867835			−0.0355778
$596$	28.1650	+	5.50363i	1.15368	+	0.225437i
$597$	−8.31848	+	5.26305i	−0.340453	+	0.215402i
$598$	6.11776	−	2.78437i	0.250174	−	0.113861i
$599$	−8.37844	−	3.04950i	−0.342334	−	0.124599i	0.165131	−	0.986272i	$-0.447195\pi$
$599$	−8.37844	−	3.04950i	−0.342334	−	0.124599i	−0.507465	+	0.861672i	$0.669417\pi$
$600$	−9.65090	+	21.4105i	−0.393996	+	0.874081i
$601$	4.44934	−	25.2334i	0.181492	−	1.02929i	−0.748888	−	0.662697i	$-0.769412\pi$
$601$	4.44934	−	25.2334i	0.181492	−	1.02929i	0.930380	−	0.366597i	$-0.119477\pi$
$602$	19.2379	+	5.34540i	0.784080	+	0.217862i
$603$	10.3109	−	10.1830i	0.419891	−	0.414685i
$604$	−12.2716	+	20.3777i	−0.499326	+	0.829159i
$605$	−4.69274	+	1.70802i	−0.190787	+	0.0694407i
$606$	−22.3838	+	34.1968i	−0.909279	+	1.38915i
$607$	−8.91382	−	10.6231i	−0.361801	−	0.431177i	0.554182	−	0.832396i	$-0.313031\pi$
$607$	−8.91382	−	10.6231i	−0.361801	−	0.431177i	−0.915982	+	0.401218i	$0.868587\pi$
$608$	−2.91723	−	7.09237i	−0.118309	−	0.287634i
$609$	−11.0325	−	12.1156i	−0.447061	−	0.490947i
$610$	−3.27334	−	4.76778i	−0.132533	−	0.193042i
$611$	−8.81625	+	5.09007i	−0.356667	+	0.205922i
$612$	8.45459	+	2.49058i	0.341756	+	0.100676i
$613$	17.7329	+	10.2381i	0.716224	+	0.413512i	0.813361	−	0.581759i	$-0.197635\pi$
$613$	17.7329	+	10.2381i	0.716224	+	0.413512i	−0.0971374	+	0.995271i	$0.530969\pi$
$614$	−1.64678	−	21.0575i	−0.0664587	−	0.849811i
$615$	−0.727273	−	1.77140i	−0.0293265	−	0.0714297i
$616$	0.0595184	−	0.0257744i	0.00239807	−	0.00103848i
$617$	45.9610	−	8.10416i	1.85032	−	0.326261i	0.865644	−	0.500660i	$-0.166909\pi$
$617$	45.9610	−	8.10416i	1.85032	−	0.326261i	0.984675	+	0.174399i	$0.0557983\pi$
$618$	−26.7558	+	28.4851i	−1.07628	+	1.14584i
$619$	−20.3900	−	17.1092i	−0.819542	−	0.687678i	0.133323	−	0.991073i	$-0.457435\pi$
$619$	−20.3900	−	17.1092i	−0.819542	−	0.687678i	−0.952865	+	0.303395i	$0.901880\pi$
$620$	−3.96119	−	7.16288i	−0.159085	−	0.287668i
$621$	3.22588	+	10.5752i	0.129450	+	0.424369i
$622$	1.67164	−	0.431435i	0.0670268	−	0.0172990i
$623$	−0.119413	−	0.100199i	−0.00478417	−	0.00401439i
$624$	−13.3742	+	7.78644i	−0.535395	+	0.311707i
$625$	3.81170	+	21.6172i	0.152468	+	0.864688i
$626$	5.60513	+	0.542510i	0.224026	+	0.0216831i
$627$	0.0410081	+	0.00552900i	0.00163771	+	0.000220807i
$628$	−31.8061	+	10.9166i	−1.26920	+	0.435618i
$629$	−3.89042	+	6.73841i	−0.155121	+	0.268678i
$630$	1.58125	+	1.94474i	0.0629986	+	0.0774803i
$631$	24.6191	−	14.2138i	0.980071	−	0.565844i	0.0777793	−	0.996971i	$-0.475217\pi$
$631$	24.6191	−	14.2138i	0.980071	−	0.565844i	0.902292	+	0.431126i	$0.141884\pi$
$632$	−20.4489	−	10.2334i	−0.813415	−	0.407062i
$633$	27.4686	+	8.75510i	1.09178	+	0.347984i
$634$	−6.08384	+	8.52031i	−0.241620	+	0.338385i
$635$	5.05252	+	6.02135i	0.200503	+	0.238950i
$636$	−23.7804	−	27.1024i	−0.942955	−	1.07468i
$637$	−4.05421	−	11.1389i	−0.160634	−	0.441337i
$638$	−0.129295	+	0.126932i	−0.00511882	+	0.00502528i
$639$	17.1803	+	24.8648i	0.679644	+	0.983635i
$640$	−4.86537	−	1.64668i	−0.192321	−	0.0650907i
$641$	19.2764	+	3.39896i	0.761373	+	0.134251i	0.540836	−	0.841128i	$-0.318108\pi$
$641$	19.2764	+	3.39896i	0.761373	+	0.134251i	0.220537	+	0.975379i	$0.429219\pi$
$642$	6.50188	−	15.1649i	0.256609	−	0.598510i
$643$	−10.2317	−	3.72402i	−0.403497	−	0.146861i	0.132296	−	0.991210i	$-0.457765\pi$
$643$	−10.2317	−	3.72402i	−0.403497	−	0.146861i	−0.535793	+	0.844349i	$0.679987\pi$
$644$	−4.30698	+	3.48068i	−0.169719	+	0.137158i
$645$	8.52493	−	0.345571i	0.335669	−	0.0136068i
$646$	−1.21372	+	2.54138i	−0.0477532	+	0.0999894i
$647$	19.0202			0.747763			0.373881	−	0.927477i	$-0.378027\pi$
$647$	19.0202			0.747763			0.373881	+	0.927477i	$0.378027\pi$
$648$	−9.82364	−	23.4840i	−0.385909	−	0.922537i
$649$	−0.193381			−0.00759085
$650$	−6.52628	+	13.6652i	−0.255982	+	0.535995i
$651$	20.3007	−	0.822917i	0.795646	−	0.0322527i
$652$	12.7943	+	15.8316i	0.501062	+	0.620013i
$653$	11.7763	+	4.28623i	0.460843	+	0.167733i	0.562000	−	0.827137i	$-0.310032\pi$
$653$	11.7763	+	4.28623i	0.460843	+	0.167733i	−0.101157	+	0.994871i	$0.532254\pi$
$654$	−2.81558	+	6.56701i	−0.110098	+	0.256791i
$655$	1.37786	+	0.242955i	0.0538376	+	0.00949302i
$656$	−8.60939	+	4.55587i	−0.336140	+	0.177877i
$657$	−0.872270	+	1.84053i	−0.0340305	+	0.0718058i
$658$	5.98491	−	5.87554i	0.233316	−	0.229052i
$659$	9.65592	+	26.5294i	0.376141	+	1.03344i	0.972942	+	0.231050i	$0.0742160\pi$
$659$	9.65592	+	26.5294i	0.376141	+	1.03344i	−0.596801	+	0.802389i	$0.703562\pi$
$660$	0.0208325	−	0.0182791i	0.000810906	−	0.000711511i
$661$	−10.6735	−	12.7202i	−0.415150	−	0.494757i	0.517427	−	0.855727i	$-0.326890\pi$
$661$	−10.6735	−	12.7202i	−0.415150	−	0.494757i	−0.932577	+	0.360971i	$0.882445\pi$
$662$	−2.46309	+	3.44952i	−0.0957307	+	0.134069i
$663$	5.41491	+	1.72590i	0.210298	+	0.0670285i
$664$	−5.08096	−	2.54269i	−0.197180	−	0.0986756i
$665$	−0.693608	+	0.400455i	−0.0268970	+	0.0155290i
$666$	22.1888	−	3.55973i	0.859797	−	0.137937i
$667$	7.73476	−	13.3970i	0.299491	−	0.518734i
$668$	−10.4140	−	30.3418i	−0.402929	−	1.17396i
$669$	4.76822	+	0.642884i	0.184350	+	0.0248553i
$670$	3.08707	+	0.298792i	0.119264	+	0.0115433i
$671$	−0.0275635	−	0.156320i	−0.00106408	−	0.00603468i
$672$	9.06569	−	8.96487i	0.349717	−	0.345827i
$673$	4.64214	+	3.89522i	0.178941	+	0.150150i	0.727859	−	0.685727i	$-0.240516\pi$
$673$	4.64214	+	3.89522i	0.178941	+	0.150150i	−0.548918	+	0.835876i	$0.684960\pi$
$674$	18.0163	−	4.64982i	0.693962	−	0.179105i
$675$	−20.8825	−	13.5800i	−0.803768	−	0.522694i
$676$	14.0199	−	7.75326i	0.539228	−	0.298202i
$677$	5.34485	+	4.48486i	0.205419	+	0.172367i	0.739693	−	0.672944i	$-0.234971\pi$
$677$	5.34485	+	4.48486i	0.205419	+	0.172367i	−0.534274	+	0.845311i	$0.679415\pi$
$678$	32.7119	−	34.8261i	1.25629	−	1.33749i
$679$	−14.2922	+	2.52009i	−0.548483	+	0.0967123i
$680$	0.749603	+	1.73099i	0.0287460	+	0.0663804i
$681$	−16.2659	−	39.6183i	−0.623309	−	1.51818i
$682$	−0.0175156	−	0.223973i	−0.000670707	−	0.00857636i
$683$	25.8624	+	14.9317i	0.989597	+	0.571344i	0.905154	−	0.425084i	$-0.139756\pi$
$683$	25.8624	+	14.9317i	0.989597	+	0.571344i	0.0844432	+	0.996428i	$0.473089\pi$
$684$	7.90649	−	1.91073i	0.302312	−	0.0730584i
$685$	−4.63301	+	2.67487i	−0.177018	+	0.102201i
$686$	12.8185	+	18.6708i	0.489413	+	0.712856i
$687$	18.2773	+	20.0715i	0.697324	+	0.765777i
$688$	−5.95505	−	42.9892i	−0.227034	−	1.63895i
$689$	−14.9446	−	17.8103i	−0.569346	−	0.678520i
$690$	−1.29592	+	1.97985i	−0.0493349	+	0.0753715i
$691$	31.1175	−	11.3259i	1.18377	−	0.430856i	0.326236	−	0.945288i	$-0.394220\pi$
$691$	31.1175	−	11.3259i	1.18377	−	0.430856i	0.857531	+	0.514432i	$0.171997\pi$
$692$	23.1926	+	13.9668i	0.881651	+	0.530937i
$693$	0.0173903	+	0.0665597i	0.000660604	+	0.00252839i
$694$	−39.8991	−	11.0862i	−1.51455	−	0.420828i
$695$	−0.422398	+	2.39554i	−0.0160225	+	0.0908679i
$696$	−14.6362	+	32.4705i	−0.554786	+	1.23079i
$697$	3.36139	+	1.22345i	0.127322	+	0.0463414i
$698$	−26.9866	+	12.2824i	−1.02146	+	0.464895i
$699$	29.6107	−	18.7345i	1.11998	−	0.708603i
$700$	2.39268	−	12.2446i	0.0904350	−	0.462803i
$701$	9.68894			0.365946			0.182973	−	0.983118i	$-0.441428\pi$
$701$	9.68894			0.365946			0.182973	+	0.983118i	$0.441428\pi$
$702$	−5.99873	−	15.2790i	−0.226408	−	0.576670i
$703$			7.18080i			0.270829i
$704$	−0.102820	−	0.0964528i	−0.00387516	−	0.00363520i
$705$	1.66473	−	3.17370i	0.0626972	−	0.119528i
$706$	−4.06024	+	1.84793i	−0.152809	+	0.0695478i
$707$	7.42607	−	20.4030i	0.279286	−	0.767333i
$708$	−35.4255	+	13.7866i	−1.33137	+	0.518134i
$709$	24.6853	+	4.35269i	0.927077	+	0.163469i	0.616748	−	0.787161i	$-0.288450\pi$
$709$	24.6853	+	4.35269i	0.927077	+	0.163469i	0.310329	+	0.950629i	$0.399561\pi$
$710$	−1.73166	+	6.23218i	−0.0649879	+	0.233890i
$711$	14.0350	−	19.7803i	0.526354	−	0.741819i
$712$	−0.0967135	+	0.324729i	−0.00362449	+	0.0121697i
$713$	6.56025	+	18.0241i	0.245683	+	0.675009i
$714$	−4.67490	−	0.261943i	−0.174954	−	0.00980298i
$715$	0.0136901	−	0.0114874i	0.000511981	−	0.000429603i
$716$	21.2264	+	8.17215i	0.793268	+	0.305408i
$717$	−3.16677	−	14.4982i	−0.118265	−	0.541446i
$718$	−35.6645	+	24.4856i	−1.33099	+	0.913793i
$719$	−16.4482	−	28.4892i	−0.613415	−	1.06247i	−0.990660	−	0.136353i	$-0.956462\pi$
$719$	−16.4482	−	28.4892i	−0.613415	−	1.06247i	0.377245	−	0.926113i	$-0.376871\pi$
$720$	2.51316	−	4.83376i	0.0936600	−	0.180144i
$721$	10.3805	−	17.9796i	0.386590	−	0.669594i
$722$	−1.89231	−	24.1970i	−0.0704244	−	0.900520i
$723$	19.8145	+	15.3027i	0.736911	+	0.569112i
$724$	4.60862	+	29.2851i	0.171278	+	1.08837i
$725$	6.05210	+	34.3232i	0.224769	+	1.27473i
$726$	−25.7946	+	7.78440i	−0.957328	+	0.288906i
$727$	−20.0843	+	23.9355i	−0.744884	+	0.887719i	−0.996792	−	0.0800327i	$-0.974498\pi$
$727$	−20.0843	+	23.9355i	−0.744884	+	0.887719i	0.251908	+	0.967751i	$0.418942\pi$
$728$	5.97190	−	5.65031i	0.221333	−	0.209414i
$729$	26.2062	−	6.49886i	0.970600	−	0.240699i
$730$	−0.422076	+	0.108934i	−0.0156217	+	0.00403182i
$731$	−10.2449	+	12.2094i	−0.378920	+	0.451579i
$732$	−16.1939	−	26.6713i	−0.598543	−	0.985801i
$733$	16.2456	−	2.86454i	0.600046	−	0.105804i	0.134630	−	0.990896i	$-0.457016\pi$
$733$	16.2456	−	2.86454i	0.600046	−	0.105804i	0.465417	+	0.885092i	$0.345904\pi$
$734$	3.04832	−	31.4948i	0.112516	−	1.16249i
$735$	3.30271	+	2.55066i	0.121822	+	0.0940825i
$736$	10.6628	+	5.58425i	0.393036	+	0.205838i
$737$	0.0737209	+	0.0425628i	0.00271554	+	0.00156782i
$738$	−3.38304	−	9.76178i	−0.124531	−	0.359336i
$739$	−11.5876	−	20.0704i	−0.426258	−	0.738301i	0.570279	−	0.821451i	$-0.306835\pi$
$739$	−11.5876	−	20.0704i	−0.426258	−	0.738301i	−0.996537	+	0.0831501i	$0.973502\pi$
$740$	3.62670	+	3.15894i	0.133320	+	0.116125i
$741$	5.12421	−	1.11925i	0.188243	−	0.0411168i
$742$	15.5884	+	11.1308i	0.572269	+	0.408623i
$743$	−2.55778	+	2.14623i	−0.0938358	+	0.0787376i	−0.688499	−	0.725238i	$-0.741730\pi$
$743$	−2.55778	+	2.14623i	−0.0938358	+	0.0787376i	0.594663	+	0.803975i	$0.297286\pi$
$744$	−19.1764	−	39.7810i	−0.703039	−	1.45844i
$745$	−6.12156	+	2.22807i	−0.224277	+	0.0816300i
$746$	11.5409	−	11.3300i	0.422542	−	0.414821i
$747$	3.48729	−	4.91482i	0.127593	−	0.179824i
$748$	−0.000954765		0.0517644i	−3.49097e−5		0.00189270i
$749$	−1.52210	+	8.63224i	−0.0556162	+	0.315415i
$750$	−1.28828	−	10.8151i	−0.0470412	−	0.394912i
$751$	−0.701648	+	1.92776i	−0.0256035	+	0.0703450i	−0.951836	−	0.306608i	$-0.900806\pi$
$751$	−0.701648	+	1.92776i	−0.0256035	+	0.0703450i	0.926232	+	0.376953i	$0.123028\pi$
$752$	−16.8889	−	6.86246i	−0.615876	−	0.250248i
$753$	22.5161	+	11.8106i	0.820533	+	0.430400i
$754$	−9.89754	+	20.7243i	−0.360447	+	0.754733i
$755$		−	5.39982i		−	0.196519i
$756$	7.93097	+	10.9533i	0.288447	+	0.398368i
$757$		−	41.6394i		−	1.51341i	−0.653756	−	0.756705i	$-0.726808\pi$
$757$		−	41.6394i		−	1.51341i	0.653756	−	0.756705i	$-0.273192\pi$
$758$	27.6929	+	13.2257i	1.00585	+	0.480377i
$759$	−0.0548834	+	0.0347244i	−0.00199214	+	0.00126042i
$760$	1.39786	+	1.03758i	0.0507057	+	0.0376368i
$761$	−14.1101	+	38.7671i	−0.511490	+	1.40531i	0.368195	+	0.929749i	$0.379976\pi$
$761$	−14.1101	+	38.7671i	−0.511490	+	1.40531i	−0.879684	+	0.475558i	$0.842246\pi$
$762$	25.3997	+	33.9612i	0.920134	+	1.23028i
$763$	0.659130	−	3.73811i	0.0238621	−	0.135329i
$764$	−0.695186	+	37.6909i	−0.0251509	+	1.36361i
$765$	−1.93577	+	0.505767i	−0.0699879	+	0.0182860i
$766$	32.8659	+	33.4777i	1.18749	+	1.20960i
$767$	−23.0337	+	8.38359i	−0.831700	+	0.302714i
$768$	−25.7120	−	10.3390i	−0.927801	−	0.373075i
$769$	−33.4132	+	28.0370i	−1.20491	+	1.01104i	−0.205437	+	0.978670i	$0.565861\pi$
$769$	−33.4132	+	28.0370i	−1.20491	+	1.01104i	−0.999476	+	0.0323712i	$0.989694\pi$
$770$	−0.00855577	+	0.0119822i	−0.000308329	+	0.000431809i
$771$	−26.2525	−	28.8296i	−0.945462	−	1.03827i
$772$	2.77219	−	3.18267i	0.0997732	−	0.114547i
$773$	3.52468	+	6.10492i	0.126774	+	0.219579i	0.922425	−	0.386176i	$-0.126204\pi$
$773$	3.52468	+	6.10492i	0.126774	+	0.219579i	−0.795651	+	0.605755i	$0.792871\pi$
$774$	46.0269	+	0.711589i	1.65440	+	0.0255776i
$775$	−37.4247	−	21.6072i	−1.34434	−	0.776153i
$776$	17.3716	+	26.3305i	0.623605	+	0.945208i
$777$	−11.0437	+	4.53415i	−0.396191	+	0.162662i
$778$	9.80280	+	0.948795i	0.351447	+	0.0340160i
$779$	3.25111	−	0.573258i	0.116483	−	0.0205391i
$780$	1.68893	−	3.08038i	0.0604735	−	0.110295i
$781$	−0.114116	+	0.135998i	−0.00408338	+	0.00486638i
$782$	−1.10465	−	4.28008i	−0.0395020	−	0.153055i
$783$	−31.6697	−	20.5950i	−1.13178	−	0.736004i
$784$	11.2841	−	17.9791i	0.403004	−	0.642111i
$785$	4.90671	−	5.84759i	0.175128	−	0.208709i
$786$	7.34902	+	1.72465i	0.262131	+	0.0615162i
$787$	8.03739	+	45.5823i	0.286502	+	1.62483i	0.699871	+	0.714270i	$0.253241\pi$
$787$	8.03739	+	45.5823i	0.286502	+	1.62483i	−0.413369	+	0.910564i	$0.635648\pi$
$788$	−22.6368	+	3.56237i	−0.806402	+	0.126904i
$789$	−4.09842	+	30.3976i	−0.145907	+	1.08218i
$790$	5.17496	−	0.404704i	0.184117	−	0.0143987i
$791$	−12.6913	+	21.9820i	−0.451250	+	0.781589i
$792$	0.117739	−	0.0921786i	0.00418368	−	0.00327542i
$793$	−10.0600	−	17.4245i	−0.357242	−	0.618762i
$794$	−29.4470	−	42.8911i	−1.04503	−	1.52215i
$795$	7.79830	+	2.48556i	0.276577	+	0.0881537i
$796$	−10.6074	−	4.08386i	−0.375971	−	0.144748i
$797$	10.7323	−	9.00550i	0.380159	−	0.318991i	−0.432606	−	0.901583i	$-0.642406\pi$
$797$	10.7323	−	9.00550i	0.380159	−	0.318991i	0.812765	+	0.582592i	$0.197961\pi$
$798$	−3.85723	+	1.94783i	−0.136545	+	0.0689526i
$799$	2.28975	+	6.29103i	0.0810054	+	0.222561i
$800$	−26.4899	+	5.80399i	−0.936559	+	0.205202i
$801$	−0.324754	−	0.153909i	−0.0114746	−	0.00543810i
$802$	−4.15930	−	1.15569i	−0.146870	−	0.0408088i
$803$	−0.0117824	−	0.00207756i	−0.000415792	−	7.33153e-5i
$804$	16.5394	+	2.54133i	0.583300	+	0.0896260i
$805$	0.429937	−	1.18124i	0.0151533	−	0.0416333i
$806$	−11.7962	−	25.9182i	−0.415502	−	0.912931i
$807$	−17.7347	+	0.718901i	−0.624290	+	0.0253065i
$808$	−47.1102	+	2.81124i	−1.65733	+	0.0988991i
$809$		−	25.2574i		−	0.888002i	−0.896026	−	0.444001i	$-0.853559\pi$
$809$		−	25.2574i		−	0.888002i	0.896026	−	0.444001i	$-0.146441\pi$
$810$	4.66047	+	3.41634i	0.163752	+	0.120038i
$811$	−36.9593			−1.29782			−0.648908	−	0.760867i	$-0.724774\pi$
$811$	−36.9593			−1.29782			−0.648908	+	0.760867i	$0.724774\pi$
$812$	3.62867	−	18.5698i	0.127341	−	0.651672i
$813$	1.31408	+	32.4173i	0.0460869	+	1.13692i
$814$	0.0546826	+	0.120147i	0.00191662	+	0.00421116i
$815$	−4.34200	−	1.58036i	−0.152094	−	0.0553576i
$816$	3.51553	+	9.55083i	0.123068	+	0.334346i
$817$	−2.55420	+	14.4856i	−0.0893602	+	0.506787i
$818$	−9.11925	+	32.8199i	−0.318847	+	1.14752i
$819$	4.95693	+	7.17406i	0.173209	+	0.250682i
$820$	1.14068	−	1.89417i	0.0398344	−	0.0661473i
$821$	5.42437	−	1.97431i	0.189312	−	0.0689038i	−0.245625	−	0.969365i	$-0.578993\pi$
$821$	5.42437	−	1.97431i	0.189312	−	0.0689038i	0.434936	+	0.900461i	$0.356771\pi$
$822$	−25.7647	+	13.0107i	−0.898647	+	0.453801i
$823$	−12.2571	−	14.6074i	−0.427254	−	0.509182i	0.508874	−	0.860841i	$-0.330062\pi$
$823$	−12.2571	−	14.6074i	−0.427254	−	0.509182i	−0.936128	+	0.351659i	$0.885618\pi$
$824$	−44.8284	−	5.17493i	−1.56167	−	0.180277i
$825$	0.0444351	−	0.139412i	0.00154703	−	0.00485372i
$826$	16.6483	−	11.4300i	0.579270	−	0.397700i
$827$	−23.7503	+	13.7122i	−0.825878	+	0.476821i	−0.852439	−	0.522826i	$-0.824878\pi$
$827$	−23.7503	+	13.7122i	−0.825878	+	0.476821i	0.0265613	+	0.999647i	$0.491544\pi$
$828$	−7.57853	+	10.2740i	−0.263372	+	0.357046i
$829$	23.8710	+	13.7819i	0.829073	+	0.478666i	0.853535	−	0.521035i	$-0.174454\pi$
$829$	23.8710	+	13.7819i	0.829073	+	0.478666i	−0.0244622	+	0.999701i	$0.507787\pi$
$830$	1.28583	−	0.100557i	0.0446317	−	0.00349038i
$831$	−37.3978	−	5.04223i	−1.29732	−	0.174913i
$832$	−16.4284	−	7.03105i	−0.569553	−	0.243758i
$833$	−7.67695	+	1.35365i	−0.265991	+	0.0469013i
$834$	−2.99845	+	12.7769i	−0.103828	+	0.442428i
$835$	5.57837	+	4.68081i	0.193048	+	0.161986i
$836$	0.0231231	+	0.0418127i	0.000799731	+	0.00144612i
$837$	44.8025	−	13.6666i	1.54860	−	0.472388i
$838$	10.4934	+	40.6580i	0.362489	+	1.40451i
$839$	−22.7744	−	19.1100i	−0.786259	−	0.659750i	0.158558	−	0.987350i	$-0.449316\pi$
$839$	−22.7744	−	19.1100i	−0.786259	−	0.659750i	−0.944816	+	0.327600i	$0.893760\pi$
$840$	−0.713092	+	2.80499i	−0.0246040	+	0.0967815i
$841$	4.14263	+	23.4940i	0.142849	+	0.810138i
$842$	−3.91194	+	40.4175i	−0.134814	+	1.39288i
$843$	−7.60237	−	18.5169i	−0.261839	−	0.637755i
$844$	10.8071	+	31.4871i	0.371995	+	1.08383i
$845$	−1.81840	+	3.14956i	−0.0625548	+	0.108348i
$846$	9.92556	−	16.5938i	0.341248	−	0.570506i
$847$	12.3959	−	7.15675i	0.425927	−	0.245909i
$848$	8.73675	−	40.7071i	0.300021	−	1.39789i
$849$	−5.49660	+	5.00526i	−0.188643	+	0.171780i
$850$	8.10488	+	5.78721i	0.277995	+	0.198500i
$851$	−7.24453	−	8.63370i	−0.248339	−	0.295959i
$852$	−11.2093	+	33.0491i	−0.384023	+	1.13225i
$853$	14.9845	+	41.1697i	0.513061	+	1.40962i	0.878031	+	0.478604i	$0.158857\pi$
$853$	14.9845	+	41.1697i	0.513061	+	1.40962i	−0.364970	+	0.931019i	$0.618921\pi$
$854$	11.6124	+	11.8286i	0.397370	+	0.404767i
$855$	−1.31376	+	1.29747i	−0.0449297	+	0.0443726i
$856$	18.5326	−	4.42022i	0.633432	−	0.151080i
$857$	−12.6966	−	2.23875i	−0.433708	−	0.0764744i	−0.0474680	−	0.998873i	$-0.515115\pi$
$857$	−12.6966	−	2.23875i	−0.433708	−	0.0764744i	−0.386240	+	0.922398i	$0.626226\pi$
$858$	0.0772138	−	0.0577485i	0.00263604	−	0.00197150i
$859$	−26.7551	−	9.73806i	−0.912872	−	0.332258i	−0.157473	−	0.987523i	$-0.550335\pi$
$859$	−26.7551	−	9.73806i	−0.912872	−	0.332258i	−0.755399	+	0.655265i	$0.772557\pi$
$860$	6.19238	+	7.66244i	0.211158	+	0.261287i
$861$	2.93448	+	4.63807i	0.100007	+	0.158065i
$862$	−33.8926	−	16.1865i	−1.15439	−	0.551315i
$863$	−46.6170			−1.58686			−0.793431	−	0.608660i	$-0.791707\pi$
$863$	−46.6170			−1.58686			−0.793431	+	0.608660i	$0.791707\pi$
$864$	14.9970	−	25.2802i	0.510209	−	0.860050i
$865$	−6.14571			−0.208961
$866$	1.98147	+	0.946317i	0.0673332	+	0.0321572i
$867$	−11.9414	+	22.7656i	−0.405551	+	0.773159i
$868$	14.7461	+	18.2468i	0.500515	+	0.619336i
$869$	0.133877	+	0.0487272i	0.00454146	+	0.00165296i
$870$	−0.956320	−	8.02833i	−0.0324223	−	0.272186i
$871$	10.6262	+	1.87368i	0.360054	+	0.0634873i
$872$	−8.02539	+	1.91414i	−0.271774	+	0.0648209i
$873$	−30.4110	+	13.9506i	−1.02926	+	0.472157i
$874$	−2.85788	−	2.91108i	−0.0966692	−	0.0984686i
$875$	1.97894	+	5.43708i	0.0669003	+	0.183807i
$876$	−2.30654	+	0.459412i	−0.0779308	+	0.0155221i
$877$	3.98303	+	4.74679i	0.134497	+	0.160288i	0.829089	−	0.559116i	$-0.188859\pi$
$877$	3.98303	+	4.74679i	0.134497	+	0.160288i	−0.694592	+	0.719404i	$0.744415\pi$
$878$	1.32201	+	0.943966i	0.0446156	+	0.0318573i
$879$	4.64617	+	21.2713i	0.156712	+	0.717463i
$880$	0.0312899	+	0.00671560i	0.00105478	+	0.000226383i
$881$	−21.9173	+	12.6539i	−0.738412	+	0.426322i	−0.821492	−	0.570221i	$-0.806858\pi$
$881$	−21.9173	+	12.6539i	−0.738412	+	0.426322i	0.0830799	+	0.996543i	$0.473524\pi$
$882$	17.0213	+	14.7369i	0.573137	+	0.496217i
$883$	15.7424	−	27.2667i	0.529775	−	0.917597i	−0.469622	−	0.882868i	$-0.655610\pi$
$883$	15.7424	−	27.2667i	0.529775	−	0.917597i	0.999397	−	0.0347290i	$-0.0110568\pi$
$884$	2.13041	+	6.20710i	0.0716535	+	0.208767i
$885$	5.27444	−	6.82958i	0.177298	−	0.229574i
$886$	2.30849	−	23.8509i	0.0775552	−	0.801288i
$887$	−0.0310073	−	0.175851i	−0.00104112	−	0.00590451i	0.984283	−	0.176600i	$-0.0565098\pi$
$887$	−0.0310073	−	0.175851i	−0.00104112	−	0.00590451i	−0.985324	+	0.170695i	$0.945399\pi$
$888$	18.5830	+	18.1114i	0.623604	+	0.607779i
$889$	−17.2584	−	14.4815i	−0.578827	−	0.485694i
$890$	−0.0192209	−	0.0744737i	−0.000644287	−	0.00249636i
$891$	0.0775808	+	0.138331i	0.00259906	+	0.00463427i
$892$	2.68864	+	4.86177i	0.0900223	+	0.162784i
$893$	4.73299	+	3.97145i	0.158384	+	0.132900i
$894$	−33.6484	+	10.1546i	−1.12537	+	0.339619i
$895$	−5.08477	+	0.896582i	−0.169965	+	0.0299694i
$896$	14.5528	+	2.22646i	0.486175	+	0.0743807i
$897$	−5.03181	+	6.51541i	−0.168007	+	0.217543i
$898$	43.2606	−	3.38316i	1.44363	−	0.112898i
$899$	−56.7571	−	32.7687i	−1.89296	−	1.09290i
$900$	−1.79901	−	28.7070i	−0.0599670	−	0.956899i
$901$	−13.2413	+	7.64488i	−0.441132	+	0.254688i
$902$	0.0500313	−	0.0343491i	0.00166586	−	0.00114370i
$903$	−23.8909	+	5.21836i	−0.795040	+	0.173656i
$904$	54.8076	+	6.32691i	1.82287	+	0.210430i
$905$	−4.32570	−	5.15517i	−0.143791	−	0.171364i
$906$	1.62986	−	29.0880i	0.0541483	−	0.966384i
$907$	−18.2575	+	6.64519i	−0.606231	+	0.220650i	−0.626853	−	0.779137i	$-0.715657\pi$
$907$	−18.2575	+	6.64519i	−0.606231	+	0.220650i	0.0206225	+	0.999787i	$0.493435\pi$
$908$	25.5120	−	42.3641i	0.846646	−	1.40590i
$909$	4.67372	−	49.8382i	0.155017	−	1.65303i
$910$	−0.499623	+	1.79813i	−0.0165623	+	0.0596074i
$911$	0.423720	−	2.40304i	0.0140385	−	0.0796161i	−0.976984	−	0.213314i	$-0.931574\pi$
$911$	0.423720	−	2.40304i	0.0140385	−	0.0796161i	0.991022	+	0.133698i	$0.0426853\pi$
$912$	7.21689	+	6.01119i	0.238975	+	0.199050i
$913$	0.0332645	+	0.0121073i	0.00110089	+	0.000400693i
$914$	−4.19634	−	9.22011i	−0.138803	−	0.304974i
$915$	6.27252	+	3.29017i	0.207363	+	0.108770i
$916$	−6.01153	+	30.7641i	−0.198626	+	1.01648i
$917$	−4.01015			−0.132427
$918$	−10.5804	+	2.14021i	−0.349204	+	0.0706374i
$919$			2.20402i			0.0727038i	0.999339	+	0.0363519i	$0.0115737\pi$
$919$			2.20402i			0.0727038i	−0.999339	+	0.0363519i	$0.988426\pi$
$920$	−2.72748	+	0.162758i	−0.0899222	+	0.00536599i
$921$	13.8312	+	21.8608i	0.455753	+	0.720337i
$922$	4.85526	+	10.6679i	0.159900	+	0.351328i
$923$	−7.69653	+	21.1460i	−0.253334	+	0.696030i
$924$	−0.0497053	+	0.0619639i	−0.00163518	+	0.00203846i
$925$	25.0065	+	4.40933i	0.822210	+	0.144978i
$926$	0.527376	+	0.146535i	0.0173307	+	0.00481545i
$927$	12.6761	−	46.1544i	0.416339	−	1.51591i
$928$	−40.1737	+	8.80214i	−1.31877	+	0.288944i
$929$	3.30889	+	9.09111i	0.108561	+	0.298270i	0.982063	−	0.188551i	$-0.0603789\pi$
$929$	3.30889	+	9.09111i	0.108561	+	0.298270i	−0.873502	+	0.486820i	$0.838157\pi$
$930$	8.38773	+	5.49025i	0.275045	+	0.180032i
$931$	−5.51109	+	4.62435i	−0.180619	+	0.151557i
$932$	37.7585	+	14.5370i	1.23682	+	0.476175i
$933$	−1.56337	+	1.42362i	−0.0511823	+	0.0466071i
$934$	5.33220	+	7.76662i	0.174475	+	0.254131i
$935$	−0.00587632	−	0.0101781i	−0.000192176	−	0.000332859i
$936$	10.0278	−	16.0838i	0.327769	−	0.525715i
$937$	−22.2202	+	38.4864i	−0.725901	+	1.25730i	0.232701	+	0.972548i	$0.425243\pi$
$937$	−22.2202	+	38.4864i	−0.725901	+	1.25730i	−0.958602	+	0.284749i	$0.908090\pi$
$938$	−8.86243	+	0.693079i	−0.289369	+	0.0226298i
$939$	−6.38013	+	2.61945i	−0.208208	+	0.0854826i
$940$	4.08792	−	0.643318i	0.133333	−	0.0209827i
$941$	−7.38960	−	41.9085i	−0.240894	−	1.36618i	−0.829838	−	0.558004i	$-0.811567\pi$
$941$	−7.38960	−	41.9085i	−0.240894	−	1.36618i	0.588944	−	0.808174i	$-0.299544\pi$
$942$	28.1967	−	30.0191i	0.918699	−	0.978075i
$943$	−3.33056	+	3.96920i	−0.108458	+	0.129255i
$944$	−37.1785	−	23.3341i	−1.21006	−	0.759460i
$945$	−2.82499	−	1.20124i	−0.0918970	−	0.0390763i
$946$	0.0675731	+	0.261820i	0.00219699	+	0.00851250i
$947$	30.3650	−	36.1877i	0.986731	−	1.17594i	0.00233119	−	0.999997i	$-0.499258\pi$
$947$	30.3650	−	36.1877i	0.986731	−	1.17594i	0.984400	−	0.175943i	$-0.0562976\pi$
$948$	27.9989	−	0.618091i	0.909362	−	0.0200747i
$949$	−1.49348	+	0.263341i	−0.0484804	+	0.00854841i
$950$	9.14819	+	0.885437i	0.296807	+	0.0287274i
$951$	1.71330	−	12.7074i	0.0555575	−	0.412065i
$952$	−2.97740	−	4.51289i	−0.0964980	−	0.146264i
$953$	−23.8540	−	13.7721i	−0.772707	−	0.446123i	0.0611321	−	0.998130i	$-0.480529\pi$
$953$	−23.8540	−	13.7721i	−0.772707	−	0.446123i	−0.833840	+	0.552007i	$0.813862\pi$
$954$	41.2580	+	15.7431i	1.33578	+	0.509703i
$955$	−4.27868	−	7.41089i	−0.138455	−	0.239811i
$956$	11.2549	−	12.9214i	0.364009	−	0.417909i
$957$	0.0673888	−	0.211428i	0.00217837	−	0.00683451i
$958$	−0.931443	+	1.30447i	−0.0300936	+	0.0421455i
$959$	11.7461	−	9.85611i	0.379300	−	0.318270i
$960$	6.21080	−	1.00051i	0.200453	−	0.0322914i
$961$	47.2298	−	17.1902i	1.52354	−	0.554524i
$962$	11.7220	+	11.9402i	0.377933	+	0.384968i
$963$	1.63565	+	20.1419i	0.0527081	+	0.649064i
$964$	−0.533115	+	28.9039i	−0.0171705	+	0.930930i
$965$	−0.166374	+	0.943555i	−0.00535578	+	0.0303741i
$966$	2.67255	−	6.23341i	0.0859878	−	0.200557i
$967$	0.543982	−	1.49458i	0.0174933	−	0.0480624i	−0.930639	−	0.365939i	$-0.880748\pi$
$967$	0.543982	−	1.49458i	0.0174933	−	0.0480624i	0.948132	+	0.317877i	$0.102970\pi$
$968$	−24.9820	−	18.5431i	−0.802951	−	0.595998i
$969$	−0.139707	−	3.44646i	−0.00448805	−	0.110716i
$970$	−6.46162	−	3.08596i	−0.207470	−	0.0990842i
$971$			9.93969i			0.318980i	0.987200	+	0.159490i	$0.0509849\pi$
$971$			9.93969i			0.318980i	−0.987200	+	0.159490i	$0.949015\pi$
$972$	24.0741	+	19.8100i	0.772177	+	0.635407i
$973$		−	6.97199i		−	0.223512i
$974$	25.5752	−	53.5514i	0.819483	−	1.71590i
$975$	−0.751218	−	18.5319i	−0.0240582	−	0.593496i
$976$	13.5630	−	33.3794i	0.434141	−	1.06845i
$977$	13.5121	−	37.1242i	0.432290	−	1.18771i	−0.512113	−	0.858918i	$-0.671137\pi$
$977$	13.5121	−	37.1242i	0.432290	−	1.18771i	0.944403	−	0.328789i	$-0.106641\pi$
$978$	−22.9127	−	9.82373i	−0.732668	−	0.314128i
$979$	0.000366577	−	0.00207896i	1.17158e−5	−	6.64438e-5i
$980$	−0.0888600	+	4.81772i	−0.00283853	+	0.153896i
$981$	−0.708304	−	8.72227i	−0.0226144	−	0.278481i
$982$	20.7838	−	20.4040i	0.663237	−	0.651117i
$983$	30.2880	−	11.0239i	0.966036	−	0.351608i	0.189640	−	0.981854i	$-0.439268\pi$
$983$	30.2880	−	11.0239i	0.966036	−	0.351608i	0.776396	+	0.630245i	$0.217046\pi$
$984$	6.71642	−	9.85931i	0.214112	−	0.314303i
$985$	3.98484	−	3.34368i	0.126967	−	0.106538i
$986$	12.2916	+	8.77669i	0.391444	+	0.279507i
$987$	−3.11936	+	9.78679i	−0.0992902	+	0.311517i
$988$	4.56692	+	3.97790i	0.145293	+	0.126554i
$989$	−11.5432	−	19.9933i	−0.367051	−	0.635751i
$990$	−0.0121011	+	0.0317134i	−0.000384599	+	0.00100792i
$991$	−2.66599	−	1.53921i	−0.0846881	−	0.0488947i	0.457058	−	0.889437i	$-0.348903\pi$
$991$	−2.66599	−	1.53921i	−0.0846881	−	0.0488947i	−0.541746	+	0.840542i	$0.682237\pi$
$992$	23.6580	−	45.1735i	0.751142	−	1.43426i
$993$	0.693642	−	5.14469i	0.0220121	−	0.163262i
$994$	1.78604	−	18.4531i	0.0566499	−	0.585297i
$995$	2.54100	−	0.448048i	0.0805553	−	0.0142041i
$996$	6.95691	−	0.153578i	0.220438	−	0.00486629i
$997$	−27.9424	+	33.3004i	−0.884944	+	1.05464i	0.113190	+	0.993573i	$0.463893\pi$
$997$	−27.9424	+	33.3004i	−0.884944	+	1.05464i	−0.998134	+	0.0610619i	$0.980551\pi$
$998$	−13.7303	+	3.54367i	−0.434626	+	0.112173i
$999$	−21.9913	+	16.5499i	−0.695775	+	0.523617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.5	✓	192
3.2	odd	2		648.2.v.b.35.28		192
4.3	odd	2		864.2.bh.b.335.1		192
8.3	odd	2	inner	216.2.v.b.11.22	yes	192
8.5	even	2		864.2.bh.b.335.2		192
24.11	even	2		648.2.v.b.35.11		192
27.5	odd	18	inner	216.2.v.b.59.22	yes	192
27.22	even	9		648.2.v.b.611.11		192
108.59	even	18		864.2.bh.b.815.2		192
216.5	odd	18		864.2.bh.b.815.1		192
216.59	even	18	inner	216.2.v.b.59.5	yes	192
216.211	odd	18		648.2.v.b.611.28		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.5	✓	192	1.1	even	1	trivial
216.2.v.b.11.22	yes	192	8.3	odd	2	inner
216.2.v.b.59.5	yes	192	216.59	even	18	inner
216.2.v.b.59.22	yes	192	27.5	odd	18	inner
648.2.v.b.35.11		192	24.11	even	2
648.2.v.b.35.28		192	3.2	odd	2
648.2.v.b.611.11		192	27.22	even	9
648.2.v.b.611.28		192	216.211	odd	18
864.2.bh.b.335.1		192	4.3	odd	2
864.2.bh.b.335.2		192	8.5	even	2
864.2.bh.b.815.1		192	216.5	odd	18
864.2.bh.b.815.2		192	108.59	even	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27615 - 0.609466i) q^{2} +(1.73063 - 0.0701536i) q^{3} +(1.25710 + 1.55554i) q^{4} +(-0.426624 - 0.155279i) q^{5} +(-2.25129 - 0.965233i) q^{6} +(1.28150 + 0.225962i) q^{7} +(-0.656202 - 2.75125i) q^{8} +(2.99016 - 0.242820i) q^{9} +O(q^{10})\)	\(q+(-1.27615 - 0.609466i) q^{2} +(1.73063 - 0.0701536i) q^{3} +(1.25710 + 1.55554i) q^{4} +(-0.426624 - 0.155279i) q^{5} +(-2.25129 - 0.965233i) q^{6} +(1.28150 + 0.225962i) q^{7} +(-0.656202 - 2.75125i) q^{8} +(2.99016 - 0.242820i) q^{9} +(0.449799 + 0.458171i) q^{10} +(0.00602720 + 0.0165596i) q^{11} +(2.28471 + 2.60387i) q^{12} +(1.43581 + 1.71113i) q^{13} +(-1.49766 - 1.06939i) q^{14} +(-0.749222 - 0.238801i) q^{15} +(-0.839384 + 3.91094i) q^{16} +(1.27216 - 0.734483i) q^{17} +(-3.96387 - 1.51252i) q^{18} +(0.677841 - 1.17406i) q^{19} +(-0.294769 - 0.858831i) q^{20} +(2.23365 + 0.301155i) q^{21} +(0.00240091 - 0.0248058i) q^{22} +(0.369486 + 2.09546i) q^{23} +(-1.32865 - 4.71537i) q^{24} +(-3.67233 - 3.08145i) q^{25} +(-0.789428 - 3.05873i) q^{26} +(5.15782 - 0.630001i) q^{27} +(1.25948 + 2.27747i) q^{28} +(-5.56933 - 4.67322i) q^{29} +(0.810577 + 0.761370i) q^{30} +(8.87753 - 1.56535i) q^{31} +(3.45476 - 4.47936i) q^{32} +(0.0115926 + 0.0282357i) q^{33} +(-2.07111 + 0.161969i) q^{34} +(-0.511630 - 0.295390i) q^{35} +(4.13665 + 4.34605i) q^{36} +(-4.58718 + 2.64841i) q^{37} +(-1.58057 + 1.08515i) q^{38} +(2.60490 + 2.86061i) q^{39} +(-0.147259 + 1.27565i) q^{40} +(1.56527 + 1.86542i) q^{41} +(-2.66692 - 1.74565i) q^{42} +(-10.1956 + 3.71089i) q^{43} +(-0.0181822 + 0.0301926i) q^{44} +(-1.31338 - 0.360715i) q^{45} +(0.805592 - 2.89930i) q^{46} +(-0.791397 + 4.48824i) q^{47} +(-1.17830 + 6.82727i) q^{48} +(-4.98668 - 1.81500i) q^{49} +(2.80839 + 6.17054i) q^{50} +(2.15011 - 1.36036i) q^{51} +(-0.856765 + 4.38452i) q^{52} -10.4085 q^{53} +(-6.96610 - 2.33954i) q^{54} -0.00800062i q^{55} +(-0.219241 - 3.67400i) q^{56} +(1.09073 - 2.07941i) q^{57} +(4.25911 + 9.35804i) q^{58} +(-3.75319 + 10.3118i) q^{59} +(-0.570387 - 1.46564i) q^{60} +(-8.87057 - 1.56412i) q^{61} +(-12.2831 - 3.41294i) q^{62} +(3.88674 + 0.364490i) q^{63} +(-7.13880 + 3.61076i) q^{64} +(-0.346849 - 0.952961i) q^{65} +(0.00241487 - 0.0430981i) q^{66} +(3.70041 - 3.10502i) q^{67} +(2.74175 + 1.05557i) q^{68} +(0.786447 + 3.60054i) q^{69} +(0.472885 + 0.688782i) q^{70} +(5.03714 + 8.72458i) q^{71} +(-2.63021 - 8.06734i) q^{72} +(-0.339460 + 0.587962i) q^{73} +(7.46803 - 0.584031i) q^{74} +(-6.57161 - 5.07522i) q^{75} +(2.67840 - 0.421502i) q^{76} +(0.00398198 + 0.0225829i) q^{77} +(-1.58079 - 5.23815i) q^{78} +(5.19665 - 6.19313i) q^{79} +(0.965387 - 1.53816i) q^{80} +(8.88208 - 1.45214i) q^{81} +(-0.860607 - 3.33452i) q^{82} +(1.29122 - 1.53881i) q^{83} +(2.33946 + 3.85310i) q^{84} +(-0.656785 + 0.115809i) q^{85} +(15.2727 + 1.47822i) q^{86} +(-9.96629 - 7.69691i) q^{87} +(0.0416046 - 0.0274488i) q^{88} +(-0.103744 - 0.0598964i) q^{89} +(1.45622 + 1.26078i) q^{90} +(1.45333 + 2.51724i) q^{91} +(-2.79508 + 3.20896i) q^{92} +(15.2539 - 3.33183i) q^{93} +(3.74536 - 5.24532i) q^{94} +(-0.471489 + 0.395626i) q^{95} +(5.66467 - 7.99447i) q^{96} +(-10.4801 + 3.81446i) q^{97} +(5.25755 + 5.35542i) q^{98} +(0.0220433 + 0.0480522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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