LMFDB - Embedded newform 216.2.v.b.11.21

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			11.21
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580483 - 1.28959i) q^{2} +(-1.63375 + 0.575207i) q^{3} +(-1.32608 - 1.49717i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-0.206584 + 2.44076i) q^{6} +(2.85909 + 0.504135i) q^{7} +(-2.70050 + 0.841014i) q^{8} +(2.33827 - 1.87949i) q^{9} +O(q^{10})$	\(q+(0.580483 - 1.28959i) q^{2} +(-1.63375 + 0.575207i) q^{3} +(-1.32608 - 1.49717i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-0.206584 + 2.44076i) q^{6} +(2.85909 + 0.504135i) q^{7} +(-2.70050 + 0.841014i) q^{8} +(2.33827 - 1.87949i) q^{9} +(3.37559 - 3.46708i) q^{10} +(-0.927560 - 2.54845i) q^{11} +(3.02766 + 1.68323i) q^{12} +(-1.60411 - 1.91170i) q^{13} +(2.30978 - 3.39441i) q^{14} +(-5.92612 - 0.0624707i) q^{15} +(-0.483033 + 3.97073i) q^{16} +(4.30856 - 2.48755i) q^{17} +(-1.06644 - 4.10642i) q^{18} +(-1.31569 + 2.27884i) q^{19} +(-2.51163 - 6.36570i) q^{20} +(-4.96102 + 0.820939i) q^{21} +(-3.82488 - 0.283162i) q^{22} +(-0.157970 - 0.895893i) q^{23} +(3.92818 - 2.92735i) q^{24} +(5.13833 + 4.31157i) q^{25} +(-3.39646 + 0.958928i) q^{26} +(-2.73906 + 4.41560i) q^{27} +(-3.03660 - 4.94907i) q^{28} +(7.00248 + 5.87578i) q^{29} +(-3.52058 + 7.60600i) q^{30} +(-2.90502 + 0.512234i) q^{31} +(4.84021 + 2.92786i) q^{32} +(2.98129 + 3.62999i) q^{33} +(-0.706867 - 7.00026i) q^{34} +(8.60284 + 4.96685i) q^{35} +(-5.91465 - 1.00844i) q^{36} +(-9.78021 + 5.64661i) q^{37} +(2.17503 + 3.01952i) q^{38} +(3.72033 + 2.20055i) q^{39} +(-9.66710 - 0.456210i) q^{40} +(-3.04161 - 3.62485i) q^{41} +(-1.82112 + 6.87422i) q^{42} +(-6.12779 + 2.23033i) q^{43} +(-2.58544 + 4.76816i) q^{44} +(9.71774 - 3.30669i) q^{45} +(-1.24703 - 0.316335i) q^{46} +(0.225833 - 1.28076i) q^{47} +(-1.49483 - 6.76502i) q^{48} +(1.34241 + 0.488598i) q^{49} +(8.54287 - 4.12354i) q^{50} +(-5.60826 + 6.54235i) q^{51} +(-0.734968 + 4.93668i) q^{52} -10.3399 q^{53} +(4.10433 + 6.09544i) q^{54} -9.27950i q^{55} +(-8.14496 + 1.04312i) q^{56} +(0.838700 - 4.47984i) q^{57} +(11.6422 - 5.61953i) q^{58} +(2.96267 - 8.13988i) q^{59} +(7.76498 + 8.95525i) q^{60} +(-0.720351 - 0.127017i) q^{61} +(-1.02575 + 4.04363i) q^{62} +(7.63286 - 4.19482i) q^{63} +(6.58539 - 4.54231i) q^{64} +(-2.92046 - 8.02391i) q^{65} +(6.41178 - 1.73748i) q^{66} +(5.00144 - 4.19671i) q^{67} +(-9.43778 - 3.15196i) q^{68} +(0.773408 + 1.37280i) q^{69} +(11.3990 - 8.21095i) q^{70} +(5.18176 + 8.97507i) q^{71} +(-4.73383 + 7.04208i) q^{72} +(-7.34034 + 12.7138i) q^{73} +(1.60455 + 15.8902i) q^{74} +(-10.8748 - 4.08843i) q^{75} +(5.15651 - 1.05211i) q^{76} +(-1.36722 - 7.75387i) q^{77} +(4.99739 - 3.52032i) q^{78} +(-5.64811 + 6.73115i) q^{79} +(-6.19991 + 12.2018i) q^{80} +(1.93505 - 8.78952i) q^{81} +(-6.44017 + 1.81826i) q^{82} +(3.15228 - 3.75674i) q^{83} +(7.80779 + 6.33886i) q^{84} +(16.7644 - 2.95601i) q^{85} +(-0.680867 + 9.19700i) q^{86} +(-14.8201 - 5.57168i) q^{87} +(4.64815 + 6.10199i) q^{88} +(-4.90094 - 2.82956i) q^{89} +(1.37672 - 14.4514i) q^{90} +(-3.62253 - 6.27441i) q^{91} +(-1.13182 + 1.42453i) q^{92} +(4.45144 - 2.50785i) q^{93} +(-1.52056 - 1.03469i) q^{94} +(-6.89717 + 5.78741i) q^{95} +(-9.59182 - 1.99926i) q^{96} +(-0.126739 + 0.0461291i) q^{97} +(1.40934 - 1.44754i) q^{98} +(-6.95867 - 4.21564i) 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 $

$2$	0.580483	−	1.28959i	0.410464	−	0.911877i
$2$	0.580483	−	1.28959i	0.410464	−	0.911877i
$3$	−1.63375	+	0.575207i	−0.943246	+	0.332096i
$3$	−1.63375	+	0.575207i	−0.943246	+	0.332096i
$4$	−1.32608	−	1.49717i	−0.663039	−	0.748585i
$5$	3.21529	+	1.17027i	1.43792	+	0.523361i	0.939191	−	0.343396i	$-0.111577\pi$
$5$	3.21529	+	1.17027i	1.43792	+	0.523361i	0.498731	+	0.866757i	$0.333800\pi$
$6$	−0.206584	+	2.44076i	−0.0843375	+	0.996437i
$7$	2.85909	+	0.504135i	1.08064	+	0.190545i	0.685496	−	0.728076i	$-0.259585\pi$
$7$	2.85909	+	0.504135i	1.08064	+	0.190545i	0.395139	+	0.918621i	$0.370696\pi$
$8$	−2.70050	+	0.841014i	−0.954771	+	0.297343i
$9$	2.33827	−	1.87949i	0.779425	−	0.626496i
$10$	3.37559	−	3.46708i	1.06745	−	1.09639i
$11$	−0.927560	−	2.54845i	−0.279670	−	0.768386i	−0.997400	−	0.0720650i	$-0.977041\pi$
$11$	−0.927560	−	2.54845i	−0.279670	−	0.768386i	0.717730	−	0.696321i	$-0.245181\pi$
$12$	3.02766	+	1.68323i	0.874011	+	0.485907i
$13$	−1.60411	−	1.91170i	−0.444899	−	0.530210i	0.496260	−	0.868174i	$-0.334706\pi$
$13$	−1.60411	−	1.91170i	−0.444899	−	0.530210i	−0.941159	+	0.337964i	$0.890262\pi$
$14$	2.30978	−	3.39441i	0.617315	−	0.907195i
$15$	−5.92612	−	0.0624707i	−1.53012	−	0.0161299i
$16$	−0.483033	+	3.97073i	−0.120758	+	0.992682i
$17$	4.30856	−	2.48755i	1.04498	−	0.603319i	0.123740	−	0.992315i	$-0.460511\pi$
$17$	4.30856	−	2.48755i	1.04498	−	0.603319i	0.921240	+	0.388995i	$0.127178\pi$
$18$	−1.06644	−	4.10642i	−0.251362	−	0.967893i
$19$	−1.31569	+	2.27884i	−0.301839	+	0.522801i	−0.976553	−	0.215279i	$-0.930934\pi$
$19$	−1.31569	+	2.27884i	−0.301839	+	0.522801i	0.674713	+	0.738080i	$0.264267\pi$
$20$	−2.51163	−	6.36570i	−0.561618	−	1.42341i
$21$	−4.96102	+	0.820939i	−1.08258	+	0.179144i
$22$	−3.82488	−	0.283162i	−0.815468	−	0.0603703i
$23$	−0.157970	−	0.895893i	−0.0329391	−	0.186807i	0.963899	−	0.266269i	$-0.0857909\pi$
$23$	−0.157970	−	0.895893i	−0.0329391	−	0.186807i	−0.996838	+	0.0794621i	$0.974680\pi$
$24$	3.92818	−	2.92735i	0.801837	−	0.597543i
$25$	5.13833	+	4.31157i	1.02767	+	0.862315i
$26$	−3.39646	+	0.958928i	−0.666101	+	0.188061i
$27$	−2.73906	+	4.41560i	−0.527132	+	0.849783i
$28$	−3.03660	−	4.94907i	−0.573864	−	0.935286i
$29$	7.00248	+	5.87578i	1.30033	+	1.09111i	0.990088	+	0.140447i	$0.0448540\pi$
$29$	7.00248	+	5.87578i	1.30033	+	1.09111i	0.310241	+	0.950658i	$0.399590\pi$
$30$	−3.52058	+	7.60600i	−0.642767	+	1.38866i
$31$	−2.90502	+	0.512234i	−0.521758	+	0.0920000i	−0.428324	−	0.903625i	$-0.640896\pi$
$31$	−2.90502	+	0.512234i	−0.521758	+	0.0920000i	−0.0934343	+	0.995625i	$0.529785\pi$
$32$	4.84021	+	2.92786i	0.855637	+	0.517577i
$33$	2.98129	+	3.62999i	0.518975	+	0.631900i
$34$	−0.706867	−	7.00026i	−0.121227	−	1.20053i
$35$	8.60284	+	4.96685i	1.45414	+	0.839551i
$36$	−5.91465	−	1.00844i	−0.985774	−	0.168074i
$37$	−9.78021	+	5.64661i	−1.60786	+	0.928296i	−0.618008	+	0.786172i	$0.712060\pi$
$37$	−9.78021	+	5.64661i	−1.60786	+	0.928296i	−0.989849	+	0.142124i	$0.954607\pi$
$38$	2.17503	+	3.01952i	0.352836	+	0.489831i
$39$	3.72033	+	2.20055i	0.595730	+	0.352369i
$40$	−9.66710	−	0.456210i	−1.52850	−	0.0721332i
$41$	−3.04161	−	3.62485i	−0.475020	−	0.566106i	0.474322	−	0.880351i	$-0.342693\pi$
$41$	−3.04161	−	3.62485i	−0.475020	−	0.566106i	−0.949342	+	0.314245i	$0.898249\pi$
$42$	−1.82112	+	6.87422i	−0.281004	+	1.06072i
$43$	−6.12779	+	2.23033i	−0.934479	+	0.340123i	−0.763983	−	0.645236i	$-0.776759\pi$
$43$	−6.12779	+	2.23033i	−0.934479	+	0.340123i	−0.170496	+	0.985358i	$0.554537\pi$
$44$	−2.58544	+	4.76816i	−0.389770	+	0.718827i
$45$	9.71774	−	3.30669i	1.44863	−	0.492932i
$46$	−1.24703	−	0.316335i	−0.183865	−	0.0466410i
$47$	0.225833	−	1.28076i	0.0329411	−	0.186818i	−0.963897	−	0.266275i	$-0.914207\pi$
$47$	0.225833	−	1.28076i	0.0329411	−	0.186818i	0.996838	+	0.0794561i	$0.0253183\pi$
$48$	−1.49483	−	6.76502i	−0.215761	−	0.976446i
$49$	1.34241	+	0.488598i	0.191773	+	0.0697997i
$50$	8.54287	−	4.12354i	1.20814	−	0.583157i
$51$	−5.60826	+	6.54235i	−0.785313	+	0.916112i
$52$	−0.734968	+	4.93668i	−0.101922	+	0.684595i
$53$	−10.3399			−1.42029			−0.710146	−	0.704054i	$-0.751371\pi$
$53$	−10.3399			−1.42029			−0.710146	+	0.704054i	$0.751371\pi$
$54$	4.10433	+	6.09544i	0.558529	+	0.829485i
$55$		−	9.27950i		−	1.25125i
$56$	−8.14496	+	1.04312i	−1.08842	+	0.139393i
$57$	0.838700	−	4.47984i	0.111089	−	0.593369i
$58$	11.6422	−	5.61953i	1.52869	−	0.737881i
$59$	2.96267	−	8.13988i	0.385707	−	1.05972i	−0.583207	−	0.812324i	$-0.698202\pi$
$59$	2.96267	−	8.13988i	0.385707	−	1.05972i	0.968914	−	0.247398i	$-0.0795755\pi$
$60$	7.76498	+	8.95525i	1.00245	+	1.15612i
$61$	−0.720351	−	0.127017i	−0.0922315	−	0.0162629i	0.127342	−	0.991859i	$-0.459355\pi$
$61$	−0.720351	−	0.127017i	−0.0922315	−	0.0162629i	−0.219573	+	0.975596i	$0.570467\pi$
$62$	−1.02575	+	4.04363i	−0.130270	+	0.513542i
$63$	7.63286	−	4.19482i	0.961650	−	0.528498i
$64$	6.58539	−	4.54231i	0.823174	−	0.567789i
$65$	−2.92046	−	8.02391i	−0.362239	−	0.995243i
$66$	6.41178	−	1.73748i	0.789235	−	0.213870i
$67$	5.00144	−	4.19671i	0.611023	−	0.512709i	−0.283944	−	0.958841i	$-0.591643\pi$
$67$	5.00144	−	4.19671i	0.611023	−	0.512709i	0.894968	+	0.446131i	$0.147199\pi$
$68$	−9.43778	−	3.15196i	−1.14450	−	0.382232i
$69$	0.773408	+	1.37280i	0.0931073	+	0.165266i
$70$	11.3990	−	8.21095i	1.36244	−	0.981396i
$71$	5.18176	+	8.97507i	0.614961	+	1.06514i	0.990391	+	0.138294i	$0.0441618\pi$
$71$	5.18176	+	8.97507i	0.614961	+	1.06514i	−0.375430	+	0.926851i	$0.622505\pi$
$72$	−4.73383	+	7.04208i	−0.557888	+	0.829917i
$73$	−7.34034	+	12.7138i	−0.859122	+	1.48804i	0.0136452	+	0.999907i	$0.495656\pi$
$73$	−7.34034	+	12.7138i	−0.859122	+	1.48804i	−0.872767	+	0.488136i	$0.837677\pi$
$74$	1.60455	+	15.8902i	0.186525	+	1.84720i
$75$	−10.8748	−	4.08843i	−1.25571	−	0.472091i
$76$	5.15651	−	1.05211i	0.591492	−	0.120685i
$77$	−1.36722	−	7.75387i	−0.155809	−	0.883635i
$78$	4.99739	−	3.52032i	0.565843	−	0.398597i
$79$	−5.64811	+	6.73115i	−0.635462	+	0.757314i	−0.983646	−	0.180112i	$-0.942354\pi$
$79$	−5.64811	+	6.73115i	−0.635462	+	0.757314i	0.348184	+	0.937426i	$0.386798\pi$
$80$	−6.19991	+	12.2018i	−0.693171	+	1.36420i
$81$	1.93505	−	8.78952i	0.215006	−	0.976613i
$82$	−6.44017	+	1.81826i	−0.711197	+	0.200793i
$83$	3.15228	−	3.75674i	0.346007	−	0.412356i	−0.564773	−	0.825246i	$-0.691036\pi$
$83$	3.15228	−	3.75674i	0.346007	−	0.412356i	0.910781	+	0.412891i	$0.135481\pi$
$84$	7.80779	+	6.33886i	0.851900	+	0.691627i
$85$	16.7644	−	2.95601i	1.81835	−	0.320625i
$86$	−0.680867	+	9.19700i	−0.0734198	+	0.991738i
$87$	−14.8201	−	5.57168i	−1.58888	−	0.597347i
$88$	4.64815	+	6.10199i	0.495495	+	0.650475i
$89$	−4.90094	−	2.82956i	−0.519499	−	0.299933i	0.217231	−	0.976120i	$-0.430298\pi$
$89$	−4.90094	−	2.82956i	−0.519499	−	0.299933i	−0.736730	+	0.676187i	$0.763631\pi$
$90$	1.37672	−	14.4514i	0.145119	−	1.52331i
$91$	−3.62253	−	6.27441i	−0.379745	−	0.657737i
$92$	−1.13182	+	1.42453i	−0.118001	+	0.148518i
$93$	4.45144	−	2.50785i	0.461593	−	0.260052i
$94$	−1.52056	−	1.03469i	−0.156834	−	0.106720i
$95$	−6.89717	+	5.78741i	−0.707635	+	0.593776i
$96$	−9.59182	−	1.99926i	−0.978961	−	0.204048i
$97$	−0.126739	+	0.0461291i	−0.0128684	+	0.00468370i	−0.348446	−	0.937329i	$-0.613291\pi$
$97$	−0.126739	+	0.0461291i	−0.0128684	+	0.00468370i	0.335578	+	0.942012i	$0.391068\pi$
$98$	1.40934	−	1.44754i	0.142365	−	0.146223i
$99$	−6.95867	−	4.21564i	−0.699372	−	0.423687i
$100$	−0.358675	−	13.4104i	−0.0358675	−	1.34104i
$101$	2.26461	−	12.8432i	0.225337	−	1.27795i	−0.636704	−	0.771109i	$-0.719702\pi$
$101$	2.26461	−	12.8432i	0.225337	−	1.27795i	0.862040	−	0.506840i	$-0.169186\pi$
$102$	5.18144	+	11.0301i	0.513039	+	1.09214i
$103$	−0.422665	+	1.16126i	−0.0416464	+	0.114423i	−0.958773	−	0.284174i	$-0.908281\pi$
$103$	−0.422665	+	1.16126i	−0.0416464	+	0.114423i	0.917126	+	0.398597i	$0.130503\pi$
$104$	5.93965	+	3.81347i	0.582431	+	0.373941i
$105$	−16.9118	−	3.16618i	−1.65043	−	0.308987i
$106$	−6.00213	+	13.3342i	−0.582979	+	1.29513i
$107$			15.9792i			1.54476i	0.635159	+	0.772382i	$0.280935\pi$
$107$			15.9792i			1.54476i	−0.635159	+	0.772382i	$0.719065\pi$
$108$	10.2431	−	1.75460i	0.985644	−	0.168836i
$109$		−	2.38211i		−	0.228165i	−0.993471	−	0.114082i	$-0.963607\pi$
$109$		−	2.38211i		−	0.228165i	0.993471	−	0.114082i	$-0.0363927\pi$
$110$	−11.9667	−	5.38659i	−1.14098	−	0.513591i
$111$	12.7304	−	14.8508i	1.20832	−	1.40957i
$112$	−3.38282	+	11.1092i	−0.319646	+	1.04972i
$113$	−3.24570	+	8.91748i	−0.305330	+	0.838886i	0.688221	+	0.725501i	$0.258392\pi$
$113$	−3.24570	+	8.91748i	−0.305330	+	0.838886i	−0.993551	+	0.113386i	$0.963830\pi$
$114$	−5.29030	−	3.68205i	−0.495482	−	0.344856i
$115$	0.540517	−	3.06542i	0.0504035	−	0.285852i
$116$	−0.488800	−	18.2757i	−0.0453840	−	1.69685i
$117$	−7.34386	−	1.45518i	−0.678940	−	0.134531i
$118$	−8.77731	−	8.54569i	−0.808017	−	0.786695i
$119$	13.5726	−	4.94004i	1.24420	−	0.452853i
$120$	16.0560	−	4.81525i	1.46571	−	0.439570i
$121$	2.79226	−	2.34299i	0.253842	−	0.212999i
$122$	−0.581952	+	0.855225i	−0.0526874	+	0.0774284i
$123$	7.05426	+	4.17254i	0.636062	+	0.376225i
$124$	4.61919	+	3.67005i	0.414816	+	0.329580i
$125$	2.92143	+	5.06006i	0.261300	+	0.452586i
$126$	−0.978850	−	12.2783i	−0.0872029	−	1.09384i
$127$	3.94090	+	2.27528i	0.349698	+	0.201898i	0.664552	−	0.747242i	$-0.268622\pi$
$127$	3.94090	+	2.27528i	0.349698	+	0.201898i	−0.314854	+	0.949140i	$0.601956\pi$
$128$	−2.03501	−	11.1292i	−0.179871	−	0.983690i
$129$	8.72837	−	7.16855i	0.768490	−	0.631156i
$130$	−12.0428	−	0.891548i	−1.05623	−	0.0781939i
$131$	1.53208	−	0.270147i	0.133858	−	0.0236028i	−0.106318	−	0.994332i	$-0.533906\pi$
$131$	1.53208	−	0.270147i	0.133858	−	0.0236028i	0.240176	+	0.970729i	$0.422795\pi$
$132$	1.48129	−	9.27714i	0.128930	−	0.807471i
$133$	−4.91051	+	5.85212i	−0.425796	+	0.507443i
$134$	−2.50877	−	8.88592i	−0.216725	−	0.767627i
$135$	−13.9743	+	10.9920i	−1.20272	+	0.946041i
$136$	−9.54321	+	10.3412i	−0.818323	+	0.886749i
$137$	−0.557261	+	0.664118i	−0.0476101	+	0.0567394i	−0.789324	−	0.613977i	$-0.789569\pi$
$137$	−0.557261	+	0.664118i	−0.0476101	+	0.0567394i	0.741714	+	0.670716i	$0.234013\pi$
$138$	2.21930	−	0.200491i	0.188919	−	0.0170669i
$139$	−2.63752	−	14.9581i	−0.223711	−	1.26873i	−0.865133	−	0.501542i	$-0.832766\pi$
$139$	−2.63752	−	14.9581i	−0.223711	−	1.26873i	0.641422	−	0.767188i	$-0.278345\pi$
$140$	−3.97182	−	19.4663i	−0.335680	−	1.64521i
$141$	0.367749	+	2.22235i	0.0309700	+	0.187155i
$142$	14.5821	−	1.47246i	1.22370	−	0.123566i
$143$	−3.38397	+	5.86120i	−0.282981	+	0.490138i
$144$	6.33347	+	10.1925i	0.527789	+	0.849375i
$145$	15.6388	+	27.0871i	1.29873	+	2.24946i
$146$	12.1347	+	16.8462i	1.00427	+	1.39420i
$147$	−2.47421	−	0.0260821i	−0.204069	−	0.00215121i
$148$	21.4232	+	7.15479i	1.76098	+	0.588120i
$149$	6.54605	−	5.49279i	0.536273	−	0.449987i	−0.333988	−	0.942577i	$-0.608394\pi$
$149$	6.54605	−	5.49279i	0.536273	−	0.449987i	0.870261	+	0.492591i	$0.163950\pi$
$150$	−11.5850	+	11.6508i	−0.945914	+	0.951280i
$151$	−3.59322	−	9.87229i	−0.292412	−	0.803396i	−0.995712	−	0.0925028i	$-0.970513\pi$
$151$	−3.59322	−	9.87229i	−0.292412	−	0.803396i	0.703300	−	0.710893i	$-0.251709\pi$
$152$	1.63648	−	7.26051i	0.132736	−	0.588905i
$153$	5.39928	−	13.9145i	0.436506	−	1.12492i
$154$	−10.7929	−	2.73784i	−0.869720	−	0.220622i
$155$	−9.93995	−	1.75268i	−0.798396	−	0.140779i
$156$	−1.63886	−	8.48806i	−0.131214	−	0.679589i
$157$	−3.29479	+	9.05237i	−0.262953	+	0.722458i	0.736012	+	0.676969i	$0.236707\pi$
$157$	−3.29479	+	9.05237i	−0.262953	+	0.722458i	−0.998965	+	0.0454891i	$0.985515\pi$
$158$	5.40179	+	11.1911i	0.429743	+	0.890313i
$159$	16.8928	−	5.94757i	1.33968	−	0.471673i
$160$	12.1363	+	15.0783i	0.959459	+	1.19204i
$161$		−	2.64108i		−	0.208146i
$162$	−10.2116	−	7.59759i	−0.802299	−	0.596923i
$163$	19.6202			1.53678			0.768388	−	0.639984i	$-0.221059\pi$
$163$	19.6202			1.53678			0.768388	+	0.639984i	$0.221059\pi$
$164$	−1.39360	+	9.36064i	−0.108822	+	0.730943i
$165$	5.33763	+	15.1604i	0.415534	+	1.18023i
$166$	−3.01480	−	6.24587i	−0.233994	−	0.484773i
$167$	10.7043	+	3.89606i	0.828327	+	0.301486i	0.721172	−	0.692756i	$-0.243604\pi$
$167$	10.7043	+	3.89606i	0.828327	+	0.301486i	0.107155	+	0.994242i	$0.465826\pi$
$168$	12.7068	−	6.38923i	0.980352	−	0.492940i
$169$	1.17599	−	6.66936i	0.0904606	−	0.513028i
$170$	5.91940	−	23.3351i	0.453998	−	1.78972i
$171$	1.20661	+	7.80136i	0.0922717	+	0.596585i
$172$	11.4651	+	6.21674i	0.874207	+	0.474022i
$173$	−14.8832	+	5.41704i	−1.13155	+	0.411850i	−0.838854	−	0.544356i	$-0.816774\pi$
$173$	−14.8832	+	5.41704i	−1.13155	+	0.411850i	−0.292694	+	0.956206i	$0.594552\pi$
$174$	−15.7880	+	15.8776i	−1.19688	+	1.20367i
$175$	12.5174	+	14.9176i	0.946223	+	1.12767i
$176$	10.5672	−	2.45210i	0.796536	−	0.184834i
$177$	−0.158152	+	15.0027i	−0.0118874	+	1.12767i
$178$	−6.49389	+	4.67769i	−0.486737	+	0.350608i
$179$	13.6572	−	7.88498i	1.02079	−	0.589351i	0.106454	−	0.994318i	$-0.466050\pi$
$179$	13.6572	−	7.88498i	1.02079	−	0.589351i	0.914331	+	0.404967i	$0.132717\pi$
$180$	−17.8371	−	10.1642i	−1.32950	−	0.757593i
$181$	−4.39147	−	2.53542i	−0.326416	−	0.188456i	0.327833	−	0.944736i	$-0.393682\pi$
$181$	−4.39147	−	2.53542i	−0.326416	−	0.188456i	−0.654249	+	0.756280i	$0.727015\pi$
$182$	−10.1942	+	1.02939i	−0.755647	+	0.0763033i
$183$	1.24993	−	0.206836i	0.0923978	−	0.0152898i
$184$	1.18006	+	2.28650i	0.0869949	+	0.168563i
$185$	−38.0543	+	6.70999i	−2.79780	+	0.493328i
$186$	−0.650111	−	7.19630i	−0.0476684	−	0.527658i
$187$	−10.3358	−	8.67280i	−0.755832	−	0.634218i
$188$	−2.21699	+	1.36028i	−0.161691	+	0.0992087i
$189$	−10.0573	+	11.2438i	−0.731560	+	0.817863i
$190$	3.45969	+	12.2540i	0.250992	+	0.888999i
$191$	−19.1259	−	16.0486i	−1.38390	−	1.16123i	−0.967742	−	0.251944i	$-0.918930\pi$
$191$	−19.1259	−	16.0486i	−1.38390	−	1.16123i	−0.416163	−	0.909290i	$-0.636625\pi$
$192$	−8.14611	+	11.2090i	−0.587895	+	0.808937i
$193$	−1.63585	−	9.27734i	−0.117751	−	0.667798i	−0.985351	−	0.170536i	$-0.945450\pi$
$193$	−1.63585	−	9.27734i	−0.117751	−	0.667798i	0.867601	−	0.497262i	$-0.165661\pi$
$194$	−0.0140821	+	0.190218i	−0.00101104	+	0.0136569i
$195$	9.38671	+	11.4292i	0.672196	+	0.818461i
$196$	−1.04863	−	2.65774i	−0.0749021	−	0.189838i
$197$	−0.195281	+	0.338236i	−0.0139132	+	0.0240983i	−0.872898	−	0.487902i	$-0.837762\pi$
$197$	−0.195281	+	0.338236i	−0.0139132	+	0.0240983i	0.858985	+	0.512001i	$0.171096\pi$
$198$	−9.47583	+	6.52671i	−0.673418	+	0.463833i
$199$	−6.27422	+	3.62242i	−0.444768	+	0.256787i	−0.705618	−	0.708592i	$-0.749330\pi$
$199$	−6.27422	+	3.62242i	−0.444768	+	0.256787i	0.260850	+	0.965379i	$0.415997\pi$
$200$	−17.5022	−	7.32199i	−1.23759	−	0.517743i
$201$	−5.75713	+	9.73323i	−0.406076	+	0.686529i
$202$	−15.2479	−	10.3757i	−1.07284	−	0.730031i
$203$	17.0586	+	20.3296i	1.19728	+	1.42686i
$204$	17.2320	−	0.279155i	1.20648	−	0.0195448i
$205$	−5.53760	−	15.2144i	−0.386763	−	1.06262i
$206$	1.25220	+	1.21916i	0.0872450	+	0.0849427i
$207$	−2.05320	−	1.79794i	−0.142707	−	0.124966i
$208$	8.36568	−	5.44606i	0.580055	−	0.377616i
$209$	7.02788	+	1.23920i	0.486128	+	0.0857176i
$210$	−13.9001	+	19.9714i	−0.959199	+	1.37816i
$211$	20.9809	+	7.63642i	1.44438	+	0.525713i	0.941017	−	0.338359i	$-0.109872\pi$
$211$	20.9809	+	7.63642i	1.44438	+	0.525713i	0.503368	+	0.864072i	$0.332094\pi$
$212$	13.7115	+	15.4806i	0.941710	+	1.06321i
$213$	−13.6282	−	11.6824i	−0.933790	−	0.800467i
$214$	20.6065	+	9.27563i	1.40863	+	0.634069i
$215$	−22.3127			−1.52171
$216$	3.68325	−	14.2279i	0.250613	−	0.968087i
$217$	−8.56397			−0.581360
$218$	−3.07194	−	1.38277i	−0.208058	−	0.0936532i
$219$	4.67919	−	24.9935i	0.316190	−	1.68890i
$220$	−13.8930	+	12.3053i	−0.936664	+	0.829626i
$221$	−11.6668	−	4.24638i	−0.784797	−	0.285643i
$222$	−11.7616	−	25.0377i	−0.789386	−	1.68042i
$223$	7.83765	+	1.38199i	0.524848	+	0.0925448i	0.429793	−	0.902927i	$-0.358586\pi$
$223$	7.83765	+	1.38199i	0.524848	+	0.0925448i	0.0950544	+	0.995472i	$0.469697\pi$
$224$	12.3626	+	10.8111i	0.826010	+	0.722349i
$225$	20.1184	+	0.424206i	1.34123	+	0.0282804i
$226$	9.61581	+	9.36207i	0.639634	+	0.622755i
$227$	−2.95471	−	8.11801i	−0.196111	−	0.538811i	0.802190	−	0.597068i	$-0.203668\pi$
$227$	−2.95471	−	8.11801i	−0.196111	−	0.538811i	−0.998302	+	0.0582571i	$0.981446\pi$
$228$	−7.81926	+	4.68494i	−0.517843	+	0.310268i
$229$	4.90565	+	5.84633i	0.324175	+	0.386336i	0.903377	−	0.428848i	$-0.141080\pi$
$229$	4.90565	+	5.84633i	0.324175	+	0.386336i	−0.579202	+	0.815184i	$0.696636\pi$
$230$	−3.63938	−	2.47647i	−0.239973	−	0.163294i
$231$	6.69377	+	11.8814i	0.440417	+	0.781742i
$232$	−23.8518	−	9.97836i	−1.56595	−	0.655111i
$233$	−6.15633	+	3.55436i	−0.403315	+	0.232854i	−0.687913	−	0.725793i	$-0.741473\pi$
$233$	−6.15633	+	3.55436i	−0.403315	+	0.232854i	0.284599	+	0.958647i	$0.408140\pi$
$234$	−6.13957	+	8.62585i	−0.401356	+	0.563889i
$235$	2.22496	−	3.85374i	0.145140	−	0.251390i
$236$	−16.1155	+	6.35849i	−1.04903	+	0.413902i
$237$	5.35579	−	14.2459i	0.347896	−	0.925367i
$238$	1.50808	−	20.3707i	0.0977540	−	1.32044i
$239$	−0.386367	−	2.19120i	−0.0249920	−	0.141737i	0.969759	−	0.244066i	$-0.0784815\pi$
$239$	−0.386367	−	2.19120i	−0.0249920	−	0.141737i	−0.994751	+	0.102330i	$0.967370\pi$
$240$	3.11057	−	23.5009i	0.200786	−	1.51697i
$241$	0.156407	+	0.131241i	0.0100750	+	0.00845397i	0.647811	−	0.761801i	$-0.275685\pi$
$241$	0.156407	+	0.131241i	0.0100750	+	0.00845397i	−0.637736	+	0.770255i	$0.720129\pi$
$242$	−1.40063	−	4.96094i	−0.0900358	−	0.318901i
$243$	1.89440	+	15.4729i	0.121526	+	0.992588i
$244$	0.765075	+	1.24692i	0.0489789	+	0.0798260i
$245$	3.74445	+	3.14197i	0.239224	+	0.200733i
$246$	9.47574	−	6.67501i	0.604151	−	0.425583i
$247$	6.46696	−	1.14030i	0.411483	−	0.0725555i
$248$	7.41422	−	3.82645i	0.470804	−	0.242980i
$249$	−2.98913	+	7.95078i	−0.189428	+	0.503860i
$250$	8.22124	−	0.830159i	0.519957	−	0.0525039i
$251$	11.4836	+	6.63004i	0.724837	+	0.418485i	0.816530	−	0.577303i	$-0.195895\pi$
$251$	11.4836	+	6.63004i	0.724837	+	0.418485i	−0.0916936	+	0.995787i	$0.529228\pi$
$252$	−16.4021	−	5.86502i	−1.03324	−	0.369461i
$253$	−2.13661	+	1.23357i	−0.134328	+	0.0775541i
$254$	5.22180	−	3.76138i	0.327645	−	0.236010i
$255$	−25.6885	+	14.4724i	−1.60868	+	0.906295i
$256$	−15.5334	−	3.83599i	−0.970835	−	0.239749i
$257$	14.5879	+	17.3851i	0.909966	+	1.08446i	0.996105	+	0.0881721i	$0.0281025\pi$
$257$	14.5879	+	17.3851i	0.909966	+	1.08446i	−0.0861393	+	0.996283i	$0.527453\pi$
$258$	−4.17781	−	15.4172i	−0.260099	−	0.959835i
$259$	−30.8092	+	11.2136i	−1.91439	+	0.696781i
$260$	−8.14039	+	15.0128i	−0.504845	+	0.931052i
$261$	27.4172	+	0.578105i	1.69708	+	0.0357838i
$262$	0.540968	−	2.13257i	0.0334211	−	0.131750i
$263$	−3.05022	+	17.2987i	−0.188085	+	1.06668i	0.733843	+	0.679319i	$0.237725\pi$
$263$	−3.05022	+	17.2987i	−0.188085	+	1.06668i	−0.921927	+	0.387363i	$0.873386\pi$
$264$	−11.1038	−	7.29548i	−0.683393	−	0.449006i
$265$	−33.2457	−	12.1005i	−2.04227	−	0.743325i
$266$	4.69636	+	9.72960i	0.287952	+	0.596560i
$267$	9.63450	+	1.80374i	0.589622	+	0.110387i
$268$	−12.9155	−	1.92284i	−0.788939	−	0.117456i
$269$	25.2404			1.53894			0.769468	−	0.638686i	$-0.220522\pi$
$269$	25.2404			1.53894			0.769468	+	0.638686i	$0.220522\pi$
$270$	6.06331	+	24.4018i	0.369001	+	1.48505i
$271$			28.2779i			1.71776i	0.512175	+	0.858881i	$0.328840\pi$
$271$			28.2779i			1.71776i	−0.512175	+	0.858881i	$0.671160\pi$
$272$	7.79621	+	18.3097i	0.472714	+	1.11019i
$273$	9.52740	+	8.16711i	0.576625	+	0.494296i
$274$	0.532958	+	1.10415i	0.0321972	+	0.0667040i
$275$	6.22172	−	17.0940i	0.375184	−	1.03081i
$276$	1.02971	−	2.97836i	0.0619815	−	0.179276i
$277$	10.7115	+	1.88873i	0.643592	+	0.113483i	0.485912	−	0.874008i	$-0.338488\pi$
$277$	10.7115	+	1.88873i	0.643592	+	0.113483i	0.157680	+	0.987490i	$0.449599\pi$
$278$	−20.8208	−	5.28162i	−1.24875	−	0.316770i
$279$	−5.83001	+	6.65770i	−0.349033	+	0.398586i
$280$	−27.4091	−	6.17787i	−1.63801	−	0.369199i
$281$	1.98862	+	5.46370i	0.118631	+	0.325937i	0.984769	−	0.173869i	$-0.0556269\pi$
$281$	1.98862	+	5.46370i	0.118631	+	0.325937i	−0.866137	+	0.499806i	$0.833405\pi$
$282$	3.07938	+	0.815790i	0.183375	+	0.0485796i
$283$	6.97262	−	5.85072i	0.414479	−	0.347789i	−0.411579	−	0.911374i	$-0.635023\pi$
$283$	6.97262	−	5.85072i	0.414479	−	0.347789i	0.826058	+	0.563585i	$0.190578\pi$
$284$	6.56578	−	19.6596i	0.389607	−	1.16658i
$285$	7.93929	−	13.4225i	0.470283	−	0.795079i
$286$	5.59420	+	7.76625i	0.330792	+	0.459228i
$287$	−6.86883	−	11.8972i	−0.405454	−	0.702267i
$288$	16.8206	−	2.25099i	0.991164	−	0.132641i
$289$	3.87581	−	6.71310i	0.227989	−	0.394888i
$290$	44.0093	−	4.44394i	2.58432	−	0.260957i
$291$	0.180526	−	0.148264i	0.0105826	−	0.00869141i
$292$	28.7687	−	5.86982i	1.68356	−	0.343505i
$293$	−0.704403	−	3.99487i	−0.0411517	−	0.233383i	0.957294	−	0.289116i	$-0.0933614\pi$
$293$	−0.704403	−	3.99487i	−0.0411517	−	0.233383i	−0.998446	+	0.0557335i	$0.982250\pi$
$294$	−1.46987	+	3.17557i	−0.0857247	+	0.185203i
$295$	19.0517	−	22.7049i	1.10923	−	1.32193i
$296$	21.6626	−	23.4739i	1.25911	−	1.36440i
$297$	13.7936	+	2.88462i	0.800385	+	0.167383i
$298$	−3.28357	−	11.6302i	−0.190212	−	0.673719i
$299$	−1.45928	+	1.73910i	−0.0843922	+	0.100575i
$300$	8.29976	+	21.7030i	0.479187	+	1.25302i
$301$	−18.6443	+	3.28749i	−1.07464	+	0.189488i
$302$	−14.8170	−	1.09692i	−0.852623	−	0.0631209i
$303$	3.68771	+	22.2852i	0.211853	+	1.28025i
$304$	−8.41312	−	6.32499i	−0.482526	−	0.362763i
$305$	−2.16749	−	1.25140i	−0.124110	−	0.0716551i
$306$	−14.8097	−	15.0400i	−0.846617	−	0.859778i
$307$	−16.8379	−	29.1641i	−0.960989	−	1.66448i	−0.720025	−	0.693948i	$-0.755870\pi$
$307$	−16.8379	−	29.1641i	−0.960989	−	1.66448i	−0.240964	−	0.970534i	$-0.577464\pi$
$308$	−9.79582	+	12.3292i	−0.558169	+	0.702521i
$309$	0.0225625	−	2.14033i	0.00128353	−	0.121759i
$310$	−8.03021	+	11.8010i	−0.456085	+	0.670254i
$311$	9.39589	−	7.88409i	0.532792	−	0.447066i	−0.336272	−	0.941765i	$-0.609166\pi$
$311$	9.39589	−	7.88409i	0.532792	−	0.447066i	0.869064	+	0.494699i	$0.164722\pi$
$312$	−11.8974	−	2.81372i	−0.673560	−	0.159296i
$313$	−5.01611	+	1.82572i	−0.283528	+	0.103196i	−0.479869	−	0.877340i	$-0.659316\pi$
$313$	−5.01611	+	1.82572i	−0.283528	+	0.103196i	0.196342	+	0.980535i	$0.437094\pi$
$314$	9.76126	+	9.50368i	0.550860	+	0.536324i
$315$	29.4509	−	4.55507i	1.65937	−	0.256649i
$316$	17.5675	−	0.469860i	0.988250	−	0.0264317i
$317$	−0.00253246	+	0.0143623i	−0.000142237	+	0.000806666i	−0.984879	−	0.173245i	$-0.944575\pi$
$317$	−0.00253246	+	0.0143623i	−0.000142237	+	0.000806666i	0.984737	+	0.174051i	$0.0556859\pi$
$318$	2.13605	−	25.2372i	0.119784	−	1.41523i
$319$	8.47891	−	23.2956i	0.474728	−	1.30430i
$320$	26.4897	−	6.89817i	1.48082	−	0.385619i
$321$	−9.19132	−	26.1059i	−0.513010	−	1.45709i
$322$	−3.40591	−	1.53310i	−0.189804	−	0.0854365i
$323$			13.0914i			0.728422i
$324$	−15.7254	+	8.75848i	−0.873635	+	0.486582i
$325$		−	16.7392i		−	0.928523i
$326$	11.3892	−	25.3021i	0.630791	−	1.40135i
$327$	1.37020	+	3.89177i	0.0757725	+	0.215215i
$328$	11.2624	+	7.23087i	0.621863	+	0.399258i
$329$	1.29136	−	3.54797i	0.0711947	−	0.195606i
$330$	22.6490	+	1.91700i	1.24679	+	0.105527i
$331$	0.663118	−	3.76073i	0.0364482	−	0.206708i	−0.961145	−	0.276043i	$-0.910977\pi$
$331$	0.663118	−	3.76073i	0.0364482	−	0.206708i	0.997593	+	0.0693351i	$0.0220878\pi$
$332$	−9.80464	+	0.262235i	−0.538100	+	0.0143920i
$333$	−12.2561	+	31.5851i	−0.671629	+	1.73085i
$334$	11.2380	−	11.5426i	0.614917	−	0.631583i
$335$	20.9924	−	7.64060i	1.14694	−	0.417450i
$336$	−0.863388	−	20.0954i	−0.0471017	−	1.09629i
$337$	6.62429	−	5.55844i	0.360848	−	0.302787i	−0.444281	−	0.895888i	$-0.646541\pi$
$337$	6.62429	−	5.55844i	0.360848	−	0.302787i	0.805129	+	0.593100i	$0.202096\pi$
$338$	−7.91809	−	5.38799i	−0.430687	−	0.293068i
$339$	0.173260	−	16.4359i	0.00941020	−	0.892674i
$340$	−26.6565	−	21.1792i	−1.44565	−	1.14860i
$341$	3.99999	+	6.92818i	0.216611	+	0.375182i
$342$	10.7610	+	2.97253i	0.581886	+	0.160736i
$343$	−14.0079	−	8.08749i	−0.756358	−	0.436684i
$344$	14.6723	−	11.1766i	0.791080	−	0.602600i
$345$	0.880184	+	5.31904i	0.0473875	+	0.286368i
$346$	−1.65369	+	22.3377i	−0.0889031	+	1.20088i
$347$	−24.1858	+	4.26461i	−1.29836	+	0.228936i	−0.779759	−	0.626079i	$-0.784659\pi$
$347$	−24.1858	+	4.26461i	−1.29836	+	0.228936i	−0.518602	+	0.855016i	$0.673547\pi$
$348$	11.3109	+	29.5767i	0.606326	+	1.58548i
$349$	4.36508	−	5.20210i	0.233658	−	0.278462i	−0.636457	−	0.771313i	$-0.719601\pi$
$349$	4.36508	−	5.20210i	0.233658	−	0.278462i	0.870114	+	0.492850i	$0.164045\pi$
$350$	26.5037	−	7.48282i	1.41668	−	0.399974i
$351$	12.8351	−	1.84684i	0.685084	−	0.0985770i
$352$	2.97190	−	15.0508i	0.158403	−	0.802210i
$353$	9.32471	−	11.1128i	0.496304	−	0.591472i	−0.458505	−	0.888692i	$-0.651615\pi$
$353$	9.32471	−	11.1128i	0.496304	−	0.591472i	0.954809	+	0.297220i	$0.0960594\pi$
$354$	19.2555	+	8.91275i	1.02342	+	0.473707i
$355$	6.15760	+	34.9215i	0.326812	+	1.85344i
$356$	2.26270	+	11.0898i	0.119923	+	0.587756i
$357$	−19.3328	+	15.8779i	−1.02320	+	0.840346i
$358$	−2.24061	−	22.1893i	−0.118420	−	1.17274i
$359$	1.61294	−	2.79370i	0.0851279	−	0.147446i	−0.820318	−	0.571908i	$-0.806203\pi$
$359$	1.61294	−	2.79370i	0.0851279	−	0.147446i	0.905446	+	0.424462i	$0.139537\pi$
$360$	−23.4618	+	17.1025i	−1.23654	+	0.901378i
$361$	6.03793	+	10.4580i	0.317786	+	0.550422i
$362$	−5.81882	+	4.19142i	−0.305830	+	0.220296i
$363$	−3.21416	+	5.43398i	−0.168699	+	0.285210i
$364$	−4.59010	+	13.7439i	−0.240586	+	0.720377i
$365$	−38.4800	+	32.2885i	−2.01413	+	1.69006i
$366$	0.458832	−	1.73197i	0.0239835	−	0.0905313i
$367$	−10.2734	−	28.2260i	−0.536268	−	1.47338i	−0.851492	−	0.524367i	$-0.824302\pi$
$367$	−10.2734	−	28.2260i	−0.536268	−	1.47338i	0.315224	−	0.949017i	$-0.397920\pi$
$368$	3.63365	−	0.194510i	0.189417	−	0.0101396i
$369$	−13.9250	−	2.75922i	−0.724905	−	0.143639i
$370$	−13.4367	+	52.9694i	−0.698542	+	2.75375i
$371$	−29.5627	−	5.21270i	−1.53482	−	0.270630i
$372$	−9.65764	−	3.33895i	−0.500725	−	0.173117i
$373$	5.31103	−	14.5919i	0.274995	−	0.755542i	−0.722916	−	0.690936i	$-0.757199\pi$
$373$	5.31103	−	14.5919i	0.274995	−	0.755542i	0.997911	−	0.0646062i	$-0.0205791\pi$
$374$	−17.1841	+	8.29457i	−0.888570	+	0.428902i
$375$	−7.68346	−	6.58645i	−0.396772	−	0.340123i
$376$	0.467277	+	3.64863i	0.0240980	+	0.188164i
$377$		−	22.8120i		−	1.17488i
$378$	8.66174	+	19.4966i	0.445512	+	1.00280i
$379$	−6.68763			−0.343521			−0.171760	−	0.985139i	$-0.554945\pi$
$379$	−6.68763			−0.343521			−0.171760	+	0.985139i	$0.554945\pi$
$380$	17.8109	+	2.65167i	0.913681	+	0.136028i
$381$	−7.74719	−	1.45040i	−0.396901	−	0.0743064i
$382$	−31.7983	+	15.3487i	−1.62694	+	0.785306i
$383$	−6.52420	−	2.37461i	−0.333371	−	0.121337i	0.169911	−	0.985459i	$-0.445652\pi$
$383$	−6.52420	−	2.37461i	−0.333371	−	0.121337i	−0.503282	+	0.864122i	$0.667874\pi$
$384$	9.72627	+	17.0117i	0.496342	+	0.868127i
$385$	4.67812	−	26.5309i	0.238419	−	1.35214i
$386$	−12.9135	−	3.27577i	−0.657282	−	0.166732i
$387$	−10.1366	+	16.7322i	−0.515271	+	0.850547i
$388$	0.237129	+	0.128579i	0.0120384	+	0.00652759i
$389$	1.33770	−	0.486883i	0.0678241	−	0.0246860i	−0.307885	−	0.951423i	$-0.599621\pi$
$389$	1.33770	−	0.486883i	0.0678241	−	0.0246860i	0.375709	+	0.926738i	$0.377399\pi$
$390$	20.1878	−	5.47055i	1.02225	−	0.277012i
$391$	−2.90920	−	3.46705i	−0.147125	−	0.175336i
$392$	−4.03610	−	0.190472i	−0.203854	−	0.00962028i
$393$	−2.34764	+	1.32261i	−0.118423	+	0.0667171i
$394$	0.322828	+	0.448172i	0.0162639	+	0.0225786i
$395$	−26.0376	+	15.0328i	−1.31009	+	0.756382i
$396$	2.91622	+	16.0086i	0.146545	+	0.804461i
$397$	16.5544	+	9.55769i	0.830842	+	0.479687i	0.854141	−	0.520042i	$-0.174084\pi$
$397$	16.5544	+	9.55769i	0.830842	+	0.479687i	−0.0232990	+	0.999729i	$0.507417\pi$
$398$	1.02936	+	10.1939i	0.0515969	+	0.510975i
$399$	4.65637	−	12.3855i	0.233110	−	0.620049i
$400$	−19.6021	+	18.3203i	−0.980104	+	0.916015i
$401$	−18.4212	+	3.24815i	−0.919909	+	0.162205i	−0.613500	−	0.789695i	$-0.710239\pi$
$401$	−18.4212	+	3.24815i	−0.919909	+	0.162205i	−0.306409	+	0.951900i	$0.599128\pi$
$402$	9.20995	+	13.0743i	0.459351	+	0.652087i
$403$	5.63921	+	4.73186i	0.280909	+	0.235711i
$404$	−22.2315	+	13.6406i	−1.10606	+	0.678646i
$405$	16.5079	−	25.9963i	0.820282	−	1.29177i
$406$	36.1190	−	10.1975i	1.79256	−	0.506095i
$407$	23.4618	+	19.6868i	1.16296	+	0.975838i
$408$	9.64289	−	22.3842i	0.477394	−	1.10818i
$409$	−3.21877	−	18.2546i	−0.159158	−	0.902630i	−0.954885	−	0.296975i	$-0.904022\pi$
$409$	−3.21877	−	18.2546i	−0.159158	−	0.902630i	0.795727	−	0.605655i	$-0.207089\pi$
$410$	−22.8349	−	1.69050i	−1.12773	−	0.0834877i
$411$	0.528420	−	1.40554i	0.0260650	−	0.0693303i
$412$	2.29909	−	0.907124i	0.113268	−	0.0446908i
$413$	12.5742	−	21.7791i	0.618734	−	1.07168i
$414$	−3.51045	+	1.60411i	−0.172529	+	0.0788375i
$415$	14.5319	−	8.38999i	0.713342	−	0.411848i
$416$	−2.16704	−	13.9496i	−0.106248	−	0.683937i
$417$	12.9130	+	22.9207i	0.632355	+	1.12243i
$418$	5.67763	−	8.34373i	0.277702	−	0.408105i
$419$	−14.4375	−	17.2059i	−0.705317	−	0.840564i	0.287800	−	0.957691i	$-0.407076\pi$
$419$	−14.4375	−	17.2059i	−0.705317	−	0.840564i	−0.993117	+	0.117126i	$0.962632\pi$
$420$	17.6861	+	29.5185i	0.862995	+	1.44036i
$421$	5.98056	+	16.4314i	0.291475	+	0.800820i	0.995851	+	0.0909935i	$0.0290043\pi$
$421$	5.98056	+	16.4314i	0.291475	+	0.800820i	−0.704377	+	0.709826i	$0.748774\pi$
$422$	22.0269	−	22.6239i	1.07225	−	1.10131i
$423$	−1.87912	−	3.41922i	−0.0913659	−	0.166248i
$424$	27.9229	−	8.69599i	1.35605	−	0.422314i
$425$	32.8641	+	5.79483i	1.59414	+	0.281090i
$426$	−22.9765	+	10.7933i	−1.11321	+	0.522939i
$427$	−1.99552	−	0.726309i	−0.0965698	−	0.0351485i
$428$	23.9235	−	21.1896i	1.15639	−	1.02424i
$429$	2.15715	−	11.5222i	0.104148	−	0.556298i
$430$	−12.9522	+	28.7742i	−0.624608	+	1.38762i
$431$	13.1374			0.632807			0.316403	−	0.948625i	$-0.397525\pi$
$431$	13.1374			0.632807			0.316403	+	0.948625i	$0.397525\pi$
$432$	−16.2101	−	13.0089i	−0.779909	−	0.625893i
$433$	−22.6607			−1.08900			−0.544502	−	0.838759i	$-0.683281\pi$
$433$	−22.6607			−1.08900			−0.544502	+	0.838759i	$0.683281\pi$
$434$	−4.97124	+	11.0440i	−0.238627	+	0.530129i
$435$	−41.1305	−	35.2581i	−1.97206	−	1.69049i
$436$	−3.56642	+	3.15886i	−0.170800	+	0.151282i
$437$	2.24943	+	0.818727i	0.107605	+	0.0391650i
$438$	−29.5151	−	20.5425i	−1.41029	−	0.981559i
$439$	−14.8982	−	2.62696i	−0.711053	−	0.125378i	−0.193589	−	0.981083i	$-0.562013\pi$
$439$	−14.8982	−	2.62696i	−0.711053	−	0.125378i	−0.517464	+	0.855705i	$0.673124\pi$
$440$	7.80418	+	25.0593i	0.372050	+	1.19465i
$441$	4.05724	−	1.38057i	0.193202	−	0.0657414i
$442$	−12.2485	+	12.5805i	−0.582602	+	0.598392i
$443$	1.36146	+	3.74057i	0.0646848	+	0.177720i	0.967824	−	0.251628i	$-0.0809658\pi$
$443$	1.36146	+	3.74057i	0.0646848	+	0.177720i	−0.903139	+	0.429347i	$0.858744\pi$
$444$	−39.1157	+	0.633668i	−1.85635	+	0.0300725i
$445$	−12.4466	−	14.8333i	−0.590026	−	0.703165i
$446$	6.33182	−	9.30512i	0.299821	−	0.440610i
$447$	−7.53512	+	12.7392i	−0.356399	+	0.602542i
$448$	21.1182	−	9.66697i	0.997741	−	0.456721i
$449$	22.3682	−	12.9143i	1.05562	−	0.609464i	0.131404	−	0.991329i	$-0.458052\pi$
$449$	22.3682	−	12.9143i	1.05562	−	0.609464i	0.924218	+	0.381865i	$0.124718\pi$
$450$	12.2254	−	25.6982i	0.576313	−	1.21142i
$451$	−6.41647	+	11.1136i	−0.302140	+	0.523321i
$452$	17.6550	−	6.96592i	0.830423	−	0.327649i
$453$	11.5490	+	14.0620i	0.542621	+	0.660691i
$454$	−12.1841	−	0.902004i	−0.571826	−	0.0423331i
$455$	−4.30474	−	24.4134i	−0.201809	−	1.14452i
$456$	1.50270	+	12.8032i	0.0703703	+	0.599563i
$457$	2.14884	+	1.80309i	0.100518	+	0.0843449i	0.691662	−	0.722221i	$-0.256879\pi$
$457$	2.14884	+	1.80309i	0.100518	+	0.0843449i	−0.591143	+	0.806566i	$0.701323\pi$
$458$	10.3870	−	2.93258i	0.485353	−	0.137030i
$459$	−0.817376	+	25.8385i	−0.0381519	+	1.20604i
$460$	−5.30623	+	3.25575i	−0.247404	+	0.151800i
$461$	11.5119	+	9.65964i	0.536163	+	0.449894i	0.870223	−	0.492657i	$-0.163974\pi$
$461$	11.5119	+	9.65964i	0.536163	+	0.449894i	−0.334060	+	0.942552i	$0.608419\pi$
$462$	19.2078	−	1.73523i	0.893628	−	0.0807300i
$463$	−21.5380	+	3.79772i	−1.00095	+	0.176495i	−0.650030	−	0.759909i	$-0.725244\pi$
$463$	−21.5380	+	3.79772i	−1.00095	+	0.176495i	−0.350924	+	0.936404i	$0.614132\pi$
$464$	−26.7136	+	24.9668i	−1.24015	+	1.15905i
$465$	17.2475	−	2.85409i	0.799835	−	0.132355i
$466$	1.01001	+	10.0024i	0.0467880	+	0.463351i
$467$	−16.2109	−	9.35938i	−0.750152	−	0.433100i	0.0755968	−	0.997138i	$-0.475914\pi$
$467$	−16.2109	−	9.35938i	−0.750152	−	0.433100i	−0.825749	+	0.564038i	$0.809247\pi$
$468$	7.55988	+	12.9247i	0.349456	+	0.597444i
$469$	16.4153	−	9.47738i	0.757988	−	0.437625i
$470$	−3.67819	−	5.10631i	−0.169662	−	0.235536i
$471$	0.175881	−	16.6845i	0.00810416	−	0.768781i
$472$	−1.15495	+	24.4734i	−0.0531608	+	1.12648i
$473$	11.3678	+	13.5476i	0.522691	+	0.622919i
$474$	−15.2623	−	15.1762i	−0.701023	−	0.697068i
$475$	−16.5858	+	6.03674i	−0.761009	+	0.276985i
$476$	−25.3945	−	13.7697i	−1.16395	−	0.631132i
$477$	−24.1775	+	19.4337i	−1.10701	+	0.889808i
$478$	−3.05002	−	0.773698i	−0.139505	−	0.0353881i
$479$	−3.48398	+	19.7587i	−0.159187	+	0.902796i	0.795670	+	0.605731i	$0.207119\pi$
$479$	−3.48398	+	19.7587i	−0.159187	+	0.902796i	−0.954857	+	0.297065i	$0.903992\pi$
$480$	−28.5008	−	17.6532i	−1.30088	−	0.805755i
$481$	26.4831	+	9.63907i	1.20753	+	0.439504i
$482$	0.260038	−	0.125517i	0.0118444	−	0.00571716i
$483$	1.51917	+	4.31486i	0.0691245	+	0.196333i
$484$	−7.21061	−	1.07351i	−0.327755	−	0.0487958i
$485$	−0.461485			−0.0209550
$486$	21.0534	+	6.53877i	0.955000	+	0.296605i
$487$			14.0996i			0.638916i	0.947600	+	0.319458i	$0.103501\pi$
$487$			14.0996i			0.638916i	−0.947600	+	0.319458i	$0.896499\pi$
$488$	2.05213	−	0.262815i	0.0928956	−	0.0118971i
$489$	−32.0546	+	11.2857i	−1.44956	+	0.510357i
$490$	6.22544	−	3.00494i	0.281237	−	0.135749i
$491$	0.766879	−	2.10698i	0.0346088	−	0.0950868i	−0.921185	−	0.389125i	$-0.872777\pi$
$491$	0.766879	−	2.10698i	0.0346088	−	0.0950868i	0.955794	+	0.294039i	$0.0949995\pi$
$492$	−3.10751	−	16.0945i	−0.140097	−	0.725598i
$493$	44.7869	+	7.89715i	2.01710	+	0.355670i
$494$	2.28344	−	9.00164i	0.102737	−	0.405003i
$495$	−17.4407	−	21.6980i	−0.783901	−	0.975253i
$496$	−0.630720	−	11.7825i	−0.0283201	−	0.529049i
$497$	10.2905	+	28.2729i	0.461591	+	1.26821i
$498$	8.51810	+	8.47004i	0.381705	+	0.379552i
$499$	−7.09602	+	5.95427i	−0.317661	+	0.266550i	−0.787650	−	0.616123i	$-0.788702\pi$
$499$	−7.09602	+	5.95427i	−0.317661	+	0.266550i	0.469989	+	0.882672i	$0.344258\pi$
$500$	3.70173	−	11.0839i	0.165546	−	0.495688i
$501$	−19.7293	−	0.207977i	−0.881438	−	0.00929175i
$502$	15.2161	−	10.9605i	0.679126	−	0.489189i
$503$	−7.08381	−	12.2695i	−0.315852	−	0.547071i	0.663767	−	0.747940i	$-0.268957\pi$
$503$	−7.08381	−	12.2695i	−0.315852	−	0.547071i	−0.979618	+	0.200869i	$0.935624\pi$
$504$	−17.0846	+	17.7475i	−0.761010	+	0.790535i
$505$	22.3114	−	38.6445i	0.992844	−	1.71966i
$506$	0.350535	+	3.47142i	0.0155832	+	0.154323i
$507$	1.91499	+	11.5725i	0.0850478	+	0.513953i
$508$	−1.81946	−	8.91739i	−0.0807255	−	0.395645i
$509$	−7.28735	−	41.3286i	−0.323006	−	1.83186i	−0.523333	−	0.852129i	$-0.675311\pi$
$509$	−7.28735	−	41.3286i	−0.323006	−	1.83186i	0.200327	−	0.979729i	$-0.435800\pi$
$510$	3.75167	+	41.5285i	0.166127	+	1.83891i
$511$	−27.3962	+	32.6495i	−1.21194	+	1.44433i
$512$	−13.9637	+	17.8049i	−0.617114	+	0.786874i
$513$	−6.45869	−	12.0514i	−0.285158	−	0.532083i
$514$	30.8877	−	8.72056i	1.36240	−	0.384647i
$515$	−2.71798	+	3.23916i	−0.119769	+	0.142735i
$516$	−22.3070	−	3.56179i	−0.982013	−	0.156799i
$517$	−3.47343	+	0.612460i	−0.152761	+	0.0269359i
$518$	−3.42325	+	46.2405i	−0.150409	+	2.03169i
$519$	21.1995	−	17.4110i	0.930555	−	0.764258i
$520$	14.6349	+	19.2124i	0.641784	+	0.842520i
$521$	4.99532	+	2.88405i	0.218849	+	0.126353i	0.605417	−	0.795908i	$-0.293006\pi$
$521$	4.99532	+	2.88405i	0.218849	+	0.126353i	−0.386568	+	0.922261i	$0.626340\pi$
$522$	16.6607	−	35.0213i	0.729221	−	1.53284i
$523$	−3.83688	−	6.64566i	−0.167775	−	0.290595i	0.769862	−	0.638210i	$-0.220325\pi$
$523$	−3.83688	−	6.64566i	−0.167775	−	0.290595i	−0.937637	+	0.347615i	$0.886991\pi$
$524$	−2.43611	−	1.93555i	−0.106422	−	0.0845547i
$525$	−29.0309	−	17.1716i	−1.26701	−	0.749428i
$526$	20.5376	+	13.9751i	0.895481	+	0.609344i
$527$	−11.2423	+	9.43339i	−0.489721	+	0.410925i
$528$	−15.8538	+	10.0845i	−0.689946	+	0.438870i
$529$	20.8353	−	7.58341i	0.905881	−	0.329714i
$530$	−34.9032	+	35.8492i	−1.51610	+	1.55719i
$531$	−8.37126	−	24.6016i	−0.363282	−	1.06762i
$532$	15.2733	−	0.408501i	0.662183	−	0.0177107i
$533$	−2.05056	+	11.6293i	−0.0888195	+	0.503720i
$534$	7.91874	−	11.3775i	0.342678	−	0.492352i
$535$	−18.6999	+	51.3776i	−0.808468	+	2.22125i
$536$	−9.97690	+	15.5395i	−0.430937	+	0.671204i
$537$	−17.7769	+	20.7378i	−0.767131	+	0.894902i
$538$	14.6516	−	32.5498i	0.631677	−	1.40332i
$539$		−	3.87427i		−	0.166877i
$540$	34.9879	+	6.34566i	1.50564	+	0.273074i
$541$			34.8844i			1.49980i	0.661552	+	0.749899i	$0.269898\pi$
$541$			34.8844i			1.49980i	−0.661552	+	0.749899i	$0.730102\pi$
$542$	36.4669	+	16.4149i	1.56639	+	0.705079i
$543$	8.63295	+	1.61623i	0.370475	+	0.0693591i
$544$	28.1375	+	0.574577i	1.20639	+	0.0246348i
$545$	2.78771	−	7.65917i	0.119412	−	0.328083i
$546$	16.0627	−	7.54556i	0.687421	−	0.322920i
$547$	−5.15974	+	29.2623i	−0.220614	+	1.25117i	0.650279	+	0.759695i	$0.274652\pi$
$547$	−5.15974	+	29.2623i	−0.220614	+	1.25117i	−0.870894	+	0.491471i	$0.836459\pi$
$548$	1.73327	−	0.0463580i	0.0740416	−	0.00198032i
$549$	−1.92311	+	1.05689i	−0.0820761	+	0.0451069i
$550$	−18.4327	−	17.9463i	−0.785971	−	0.765231i
$551$	−22.6030	+	8.22683i	−0.962921	+	0.350475i
$552$	−3.24313	−	3.05680i	−0.138037	−	0.130106i
$553$	−19.5419	+	16.3976i	−0.831005	+	0.697296i
$554$	8.65353	−	12.7171i	0.367653	−	0.540296i
$555$	58.3115	−	32.8515i	2.47518	−	1.39447i
$556$	−18.8973	+	23.7844i	−0.801422	+	1.00868i
$557$	−8.65814	−	14.9963i	−0.366857	−	0.635415i	0.622215	−	0.782846i	$-0.286233\pi$
$557$	−8.65814	−	14.9963i	−0.366857	−	0.635415i	−0.989072	+	0.147431i	$0.952900\pi$
$558$	5.20148	+	11.3830i	0.220196	+	0.481881i
$559$	14.0934	+	8.13680i	0.596085	+	0.344150i
$560$	−23.8775	+	31.7604i	−1.00901	+	1.34212i
$561$	21.8748	+	8.22394i	0.923556	+	0.347215i
$562$	8.20029	+	0.607080i	0.345908	+	0.0256081i
$563$	19.0265	−	3.35488i	0.801870	−	0.141391i	0.242329	−	0.970194i	$-0.422089\pi$
$563$	19.0265	−	3.35488i	0.801870	−	0.141391i	0.559541	+	0.828803i	$0.310978\pi$
$564$	2.83956	−	3.49759i	0.119567	−	0.147275i
$565$	−20.8717	+	24.8739i	−0.878080	+	1.04645i
$566$	−3.49753	−	12.3881i	−0.147012	−	0.520709i
$567$	9.96360	−	24.1545i	0.418432	−	1.01439i
$568$	−21.5415	−	19.8792i	−0.903861	−	0.834114i
$569$	14.3568	−	17.1097i	0.601867	−	0.717277i	−0.375973	−	0.926631i	$-0.622691\pi$
$569$	14.3568	−	17.1097i	0.601867	−	0.717277i	0.977840	+	0.209353i	$0.0671359\pi$
$570$	−12.7009	−	18.0299i	−0.531980	−	0.755191i
$571$	6.51955	+	36.9742i	0.272835	+	1.54732i	0.745757	+	0.666218i	$0.232088\pi$
$571$	6.51955	+	36.9742i	0.272835	+	1.54732i	−0.472922	+	0.881104i	$0.656801\pi$
$572$	13.2626	−	2.70604i	0.554538	−	0.113145i
$573$	40.4782	+	15.2180i	1.69100	+	0.635740i
$574$	−19.3297	+	1.95186i	−0.806805	+	0.0814691i
$575$	3.05101	−	5.28450i	0.127236	−	0.220379i
$576$	6.86123	−	22.9983i	0.285885	−	0.958264i
$577$	11.0922	+	19.2123i	0.461775	+	0.799817i	0.999050	−	0.0435901i	$-0.0138796\pi$
$577$	11.0922	+	19.2123i	0.461775	+	0.799817i	−0.537275	+	0.843407i	$0.680546\pi$
$578$	−6.40729	−	8.89504i	−0.266508	−	0.369985i
$579$	8.00895	+	14.2159i	0.332841	+	0.590793i
$580$	19.8158	−	59.3335i	0.822807	−	2.46369i
$581$	10.9066	−	9.15169i	0.452480	−	0.379676i
$582$	−0.0864081	−	0.318869i	−0.00358173	−	0.0132175i
$583$	9.59086	+	26.3507i	0.397213	+	1.09133i
$584$	9.13007	−	40.5071i	0.377805	−	1.67619i
$585$	−21.9097	−	13.2731i	−0.905854	−	0.548776i
$586$	−5.56063	−	1.41056i	−0.229708	−	0.0582699i
$587$	−8.52654	−	1.50346i	−0.351928	−	0.0620544i	−0.00511024	−	0.999987i	$-0.501627\pi$
$587$	−8.52654	−	1.50346i	−0.351928	−	0.0620544i	−0.346818	+	0.937933i	$0.612738\pi$
$588$	3.24194	+	3.73890i	0.133696	+	0.154190i
$589$	2.65481	−	7.29402i	0.109389	−	0.300545i
$590$	−18.2208	−	37.7487i	−0.750140	−	1.55409i
$591$	0.124484	−	0.664920i	0.00512059	−	0.0273511i
$592$	−17.6970	−	41.5620i	−0.727341	−	1.70819i
$593$		−	19.4361i		−	0.798144i	−0.916920	−	0.399072i	$-0.869332\pi$
$593$		−	19.4361i		−	0.798144i	0.916920	−	0.399072i	$-0.130668\pi$
$594$	11.7269	−	16.1136i	0.481161	−	0.661148i
$595$	49.4212			2.02607
$596$	−16.9042	−	2.51668i	−0.692424	−	0.103087i
$597$	8.16686	−	9.52711i	0.334248	−	0.389919i
$598$	1.39564	+	2.89139i	0.0570719	+	0.118238i
$599$	6.17877	+	2.24889i	0.252458	+	0.0918871i	0.465149	−	0.885232i	$-0.346001\pi$
$599$	6.17877	+	2.24889i	0.252458	+	0.0918871i	−0.212691	+	0.977119i	$0.568223\pi$
$600$	32.8058	+	1.89494i	1.33929	+	0.0773606i
$601$	−0.821185	+	4.65717i	−0.0334968	+	0.189970i	−0.996965	−	0.0778536i	$-0.975193\pi$
$601$	−0.821185	+	4.65717i	−0.0334968	+	0.189970i	0.963468	+	0.267824i	$0.0863044\pi$
$602$	−6.58319	+	25.9518i	−0.268311	+	1.05772i
$603$	3.80708	−	19.2132i	0.155036	−	0.782422i
$604$	−10.0156	+	18.4711i	−0.407529	+	0.751578i
$605$	11.7199	−	4.26568i	0.476480	−	0.173425i
$606$	30.8794	+	8.18057i	1.25439	+	0.332313i
$607$	−22.8132	−	27.1877i	−0.925960	−	1.10352i	−0.994381	−	0.105859i	$-0.966241\pi$
$607$	−22.8132	−	27.1877i	−0.925960	−	1.10352i	0.0684212	−	0.997657i	$-0.478204\pi$
$608$	−13.0403	+	7.17791i	−0.528854	+	0.291103i
$609$	−39.5631	−	23.4013i	−1.60318	−	0.948268i
$610$	−2.87199	+	2.06876i	−0.116283	+	0.0837615i
$611$	−2.81069	+	1.62275i	−0.113709	+	0.0656496i
$612$	−27.9922	+	10.3680i	−1.13152	+	0.419103i
$613$	−35.0635	−	20.2439i	−1.41620	−	0.817644i	−0.420238	−	0.907414i	$-0.638053\pi$
$613$	−35.0635	−	20.2439i	−1.41620	−	0.817644i	−0.995963	+	0.0897701i	$0.971387\pi$
$614$	−47.3838	+	4.78469i	−1.91225	+	0.193094i
$615$	17.7985	+	21.6713i	0.717705	+	0.873872i
$616$	10.2133	+	19.7895i	0.411505	+	0.797340i
$617$	10.1725	−	1.79368i	0.409528	−	0.0722109i	0.0349111	−	0.999390i	$-0.488885\pi$
$617$	10.1725	−	1.79368i	0.409528	−	0.0722109i	0.374617	+	0.927179i	$0.377774\pi$
$618$	−2.74705	−	1.27152i	−0.110503	−	0.0511482i
$619$	10.0980	+	8.47326i	0.405874	+	0.340569i	0.822759	−	0.568390i	$-0.192434\pi$
$619$	10.0980	+	8.47326i	0.405874	+	0.340569i	−0.416885	+	0.908959i	$0.636878\pi$
$620$	10.5571	+	17.2060i	0.423983	+	0.691009i
$621$	4.38860	+	1.75637i	0.176108	+	0.0704808i
$622$	−4.71307	−	16.6934i	−0.188977	−	0.669345i
$623$	−12.5858	−	10.5607i	−0.504238	−	0.423106i
$624$	−10.5348	+	13.7095i	−0.421730	+	0.548819i
$625$	−2.35223	−	13.3402i	−0.0940891	−	0.533606i
$626$	−0.557347	+	7.52852i	−0.0222761	+	0.300900i
$627$	−12.1946	+	2.01793i	−0.487005	+	0.0805885i
$628$	17.9221	−	7.07129i	0.715169	−	0.282175i
$629$	−28.0924	+	48.6575i	−1.12012	+	1.94010i
$630$	11.2216	−	40.6237i	0.447079	−	1.61849i
$631$	30.9490	−	17.8684i	1.23206	−	0.711329i	0.264600	−	0.964358i	$-0.414760\pi$
$631$	30.9490	−	17.8684i	1.23206	−	0.711329i	0.967459	+	0.253029i	$0.0814267\pi$
$632$	9.59172	−	22.9276i	0.381538	−	0.912012i
$633$	−38.6701	−	0.407643i	−1.53700	−	0.0162024i
$634$	0.0170514	+	0.0116029i	0.000677197	+	0.000460810i
$635$	10.0084	+	11.9276i	0.397173	+	0.473332i
$636$	−31.3057	−	17.4044i	−1.24135	−	0.690130i
$637$	−1.21932	−	3.35005i	−0.0483112	−	0.132734i
$638$	−25.1199	−	24.4570i	−0.994506	−	0.968263i
$639$	28.9849	+	11.2471i	1.14662	+	0.444929i
$640$	6.48102	−	38.1651i	0.256185	−	1.50861i
$641$	23.8743	+	4.20968i	0.942977	+	0.166272i	0.623942	−	0.781471i	$-0.285530\pi$
$641$	23.8743	+	4.20968i	0.942977	+	0.166272i	0.319035	+	0.947743i	$0.396641\pi$
$642$	−39.0013	−	3.30104i	−1.53926	−	0.130282i
$643$	24.2825	+	8.83811i	0.957609	+	0.348541i	0.773096	−	0.634289i	$-0.218707\pi$
$643$	24.2825	+	8.83811i	0.957609	+	0.348541i	0.184513	+	0.982830i	$0.440929\pi$
$644$	−3.95415	+	3.50228i	−0.155815	+	0.138009i
$645$	36.4534	−	12.8344i	1.43535	−	0.505355i
$646$	16.8825	+	7.59931i	0.664231	+	0.298991i
$647$	19.0593			0.749298			0.374649	−	0.927167i	$-0.377763\pi$
$647$	19.0593			0.749298			0.374649	+	0.927167i	$0.377763\pi$
$648$	2.16650	+	25.3635i	0.0851080	+	0.996372i
$649$	−23.4921			−0.922146
$650$	−21.5867	−	9.71681i	−0.846698	−	0.381125i
$651$	13.9914	−	4.92606i	0.548366	−	0.193067i
$652$	−26.0180	−	29.3748i	−1.01894	−	1.15041i
$653$	37.3455	+	13.5927i	1.46144	+	0.531922i	0.945762	−	0.324860i	$-0.105317\pi$
$653$	37.3455	+	13.5927i	1.46144	+	0.531922i	0.515680	+	0.856781i	$0.327539\pi$
$654$	5.81416	+	0.492105i	0.227352	+	0.0192428i
$655$	5.24222	+	0.924345i	0.204831	+	0.0361172i
$656$	15.8625	−	10.3265i	0.619326	−	0.403181i
$657$	6.73179	+	43.5245i	0.262632	+	1.69805i
$658$	−3.82581	−	3.72485i	−0.149146	−	0.145210i
$659$	−8.73494	−	23.9990i	−0.340265	−	0.934870i	−0.985318	−	0.170732i	$-0.945387\pi$
$659$	−8.73494	−	23.9990i	−0.340265	−	0.934870i	0.645053	−	0.764138i	$-0.276835\pi$
$660$	15.6195	−	28.0952i	0.607989	−	1.09360i
$661$	4.94246	+	5.89019i	0.192239	+	0.229102i	0.853551	−	0.521009i	$-0.174444\pi$
$661$	4.94246	+	5.89019i	0.192239	+	0.229102i	−0.661312	+	0.750111i	$0.730000\pi$
$662$	−4.46486	−	3.03819i	−0.173532	−	0.118083i
$663$	21.5032	+	0.226678i	0.835117	+	0.00880345i
$664$	−5.35326	+	12.7962i	−0.207747	+	0.496588i
$665$	−22.6373	+	13.0696i	−0.877836	+	0.506819i
$666$	33.6173	+	34.1399i	1.30265	+	1.32290i
$667$	4.15789	−	7.20168i	0.160994	−	0.278850i
$668$	−8.36173	−	21.1927i	−0.323525	−	0.819970i
$669$	−13.5997	+	2.25045i	−0.525794	+	0.0870073i
$670$	2.33249	−	31.5068i	0.0901120	−	1.21721i
$671$	0.344471	+	1.95359i	0.0132982	+	0.0754176i
$672$	−26.4160	−	10.5516i	−1.01902	−	0.407038i
$673$	8.06476	+	6.76714i	0.310874	+	0.260854i	0.784853	−	0.619682i	$-0.212738\pi$
$673$	8.06476	+	6.76714i	0.310874	+	0.260854i	−0.473979	+	0.880536i	$0.657183\pi$
$674$	−3.32281	−	11.7692i	−0.127990	−	0.453332i
$675$	−33.1124	+	10.8792i	−1.27450	+	0.418740i
$676$	−11.5446	+	7.08344i	−0.444024	+	0.272440i
$677$	−27.3660	−	22.9628i	−1.05176	−	0.882533i	−0.0584838	−	0.998288i	$-0.518627\pi$
$677$	−27.3660	−	22.9628i	−1.05176	−	0.882533i	−0.993278	+	0.115756i	$0.963071\pi$
$678$	−21.0950	−	9.76419i	−0.810147	−	0.374991i
$679$	−0.385613	+	0.0679940i	−0.0147985	+	0.00260937i
$680$	−42.7862	+	22.0818i	−1.64077	+	0.846798i
$681$	9.49680	+	11.5632i	0.363918	+	0.443104i
$682$	11.2564	−	1.13664i	0.431031	−	0.0435244i
$683$	11.6024	+	6.69864i	0.443953	+	0.256316i	0.705273	−	0.708936i	$-0.250824\pi$
$683$	11.6024	+	6.69864i	0.443953	+	0.256316i	−0.261320	+	0.965252i	$0.584158\pi$
$684$	10.0799	−	12.1517i	0.385415	−	0.464632i
$685$	−2.56895	+	1.48319i	−0.0981547	+	0.0566696i
$686$	−18.5609	+	13.3698i	−0.708659	+	0.510463i
$687$	−11.3775	−	6.72967i	−0.434077	−	0.256753i
$688$	−5.89612	−	25.4091i	−0.224787	−	0.968713i
$689$	16.5863	+	19.7668i	0.631887	+	0.753054i
$690$	7.37031	+	1.95254i	0.280583	+	0.0743320i
$691$	32.2794	−	11.7487i	1.22797	−	0.446943i	0.355066	−	0.934841i	$-0.384458\pi$
$691$	32.2794	−	11.7487i	1.22797	−	0.446943i	0.872901	+	0.487898i	$0.162236\pi$
$692$	27.8465	+	15.0992i	1.05857	+	0.573987i
$693$	−17.7702	−	15.5610i	−0.675035	−	0.591114i
$694$	−8.53986	+	33.6653i	−0.324169	+	1.27792i
$695$	9.02463	−	51.1812i	0.342324	−	1.94142i
$696$	44.7075	+	2.58241i	1.69463	+	0.0978860i
$697$	−22.1220	−	8.05173i	−0.837929	−	0.304981i
$698$	−4.17472	−	8.64890i	−0.158015	−	0.327366i
$699$	8.01341	−	9.34810i	0.303095	−	0.353577i
$700$	5.73519	−	38.5225i	0.216770	−	1.45601i
$701$	−5.81942			−0.219796			−0.109898	−	0.993943i	$-0.535052\pi$
$701$	−5.81942			−0.219796			−0.109898	+	0.993943i	$0.535052\pi$
$702$	5.06887	−	17.6240i	0.191312	−	0.665175i
$703$		−	29.7167i		−	1.12079i
$704$	−17.6842	−	12.5693i	−0.666498	−	0.473722i
$705$	−1.41832	+	7.57585i	−0.0534172	+	0.285323i
$706$	−8.91804	−	18.4758i	−0.335635	−	0.695346i
$707$	12.9494	−	35.5783i	0.487014	−	1.33806i
$708$	22.6713	−	19.6579i	0.852038	−	0.738790i
$709$	−43.2874	−	7.63273i	−1.62569	−	0.286653i	−0.714809	−	0.699320i	$-0.753486\pi$
$709$	−43.2874	−	7.63273i	−1.62569	−	0.286653i	−0.910882	+	0.412666i	$0.864598\pi$
$710$	48.6087	+	12.3306i	1.82425	+	0.462758i
$711$	−0.555705	+	26.3548i	−0.0208406	+	0.988384i
$712$	15.6147	+	3.51947i	0.585185	+	0.131898i
$713$	0.917815	+	2.52167i	0.0343724	+	0.0944375i
$714$	9.25357	+	34.1481i	0.346306	+	1.27796i
$715$	−17.7396	+	14.8853i	−0.663424	+	0.556679i
$716$	−29.9156	−	9.99102i	−1.11800	−	0.373382i
$717$	1.89162	+	3.35762i	0.0706438	+	0.125393i
$718$	−2.66644	−	3.70173i	−0.0995106	−	0.138147i
$719$	13.4590	+	23.3117i	0.501938	+	0.869381i	0.999997	+	0.00223877i	$0.000712623\pi$
$719$	13.4590	+	23.3117i	0.501938	+	0.869381i	−0.498060	+	0.867143i	$0.665954\pi$
$720$	8.43596	+	40.1837i	0.314390	+	1.49756i
$721$	−1.79387	+	3.10708i	−0.0668073	+	0.115714i
$722$	16.9915	−	1.71575i	0.632356	−	0.0638537i
$723$	−0.331020	−	0.124448i	−0.0123108	−	0.00462829i
$724$	2.02749	+	9.93694i	0.0753509	+	0.369303i
$725$	10.6472	+	60.3835i	0.395428	+	2.24259i
$726$	5.14184	+	7.29928i	0.190832	+	0.270902i
$727$	7.10391	−	8.46611i	0.263470	−	0.313991i	−0.618050	−	0.786139i	$-0.712077\pi$
$727$	7.10391	−	8.46611i	0.263470	−	0.313991i	0.881519	+	0.472148i	$0.156521\pi$
$728$	15.0595	+	13.8975i	0.558143	+	0.515074i
$729$	−11.9951	−	24.1892i	−0.444263	−	0.895896i
$730$	19.3019	+	68.3663i	0.714397	+	2.53035i
$731$	−20.8539	+	24.8527i	−0.771309	+	0.919211i
$732$	−1.96718	−	1.59708i	−0.0727090	−	0.0590299i
$733$	−5.25607	+	0.926787i	−0.194137	+	0.0342316i	−0.269871	−	0.962896i	$-0.586981\pi$
$733$	−5.25607	+	0.926787i	−0.194137	+	0.0342316i	0.0757339	+	0.997128i	$0.475870\pi$
$734$	−42.3635	−	3.13623i	−1.56366	−	0.115760i
$735$	−7.92477	−	2.97935i	−0.292310	−	0.109895i
$736$	1.85844	−	4.79883i	0.0685029	−	0.176887i
$737$	−15.3342	−	8.85322i	−0.564844	−	0.326113i
$738$	−11.6415	+	16.3558i	−0.428529	+	0.602066i
$739$	7.72474	+	13.3796i	0.284159	+	0.492178i	0.972405	−	0.233299i	$-0.0749522\pi$
$739$	7.72474	+	13.3796i	0.284159	+	0.492178i	−0.688246	+	0.725478i	$0.741619\pi$
$740$	60.5089	+	48.0757i	2.22435	+	1.76730i
$741$	−9.90948	+	5.58280i	−0.364034	+	0.205089i
$742$	−23.8829	+	35.0978i	−0.876769	+	1.28848i
$743$	−21.9616	+	18.4280i	−0.805692	+	0.676056i	−0.949575	−	0.313539i	$-0.898485\pi$
$743$	−21.9616	+	18.4280i	−0.805692	+	0.676056i	0.143883	+	0.989595i	$0.454041\pi$
$744$	−9.91198	+	10.5162i	−0.363391	+	0.385542i
$745$	27.4755	−	10.0003i	1.00662	−	0.366381i
$746$	−15.7346	−	15.3194i	−0.576086	−	0.560884i
$747$	0.310146	−	14.7090i	0.0113476	−	0.538172i
$748$	0.721481	+	26.9753i	0.0263800	+	0.986315i
$749$	−8.05566	+	45.6859i	−0.294347	+	1.66933i
$750$	−12.9539	+	6.08519i	−0.473011	+	0.222200i
$751$	−8.91474	+	24.4930i	−0.325303	+	0.893764i	0.663979	+	0.747751i	$0.268866\pi$
$751$	−8.91474	+	24.4930i	−0.325303	+	0.893764i	−0.989283	+	0.146013i	$0.953356\pi$
$752$	4.97647	+	1.51537i	0.181473	+	0.0552599i
$753$	−22.5749	−	4.22640i	−0.822676	−	0.154019i
$754$	−29.4181	−	13.2420i	−1.07135	−	0.482245i
$755$		−	35.9473i		−	1.30826i
$756$	30.1706	+	0.147353i	1.09729	+	0.00535917i
$757$		−	6.07158i		−	0.220675i	−0.993894	−	0.110338i	$-0.964807\pi$
$757$		−	6.07158i		−	0.220675i	0.993894	−	0.110338i	$-0.0351932\pi$
$758$	−3.88206	+	8.62430i	−0.141003	+	0.313249i
$759$	2.78113	−	3.24434i	0.100949	−	0.117762i
$760$	13.7585	−	21.4295i	0.499074	−	0.777330i
$761$	7.74422	−	21.2771i	0.280728	−	0.771293i	−0.716549	−	0.697537i	$-0.754279\pi$
$761$	7.74422	−	21.2771i	0.280728	−	0.771293i	0.997276	−	0.0737560i	$-0.0234986\pi$
$762$	−6.36754	+	9.14876i	−0.230672	+	0.331425i
$763$	1.20090	−	6.81067i	0.0434757	−	0.246563i
$764$	1.33506	+	49.9164i	0.0483009	+	1.80591i
$765$	33.6439	−	38.4204i	1.21640	−	1.38909i
$766$	−6.84946	+	7.03511i	−0.247481	+	0.254189i
$767$	−20.3134	+	7.39349i	−0.733476	+	0.266963i
$768$	27.5841	−	2.66785i	0.995355	−	0.0962679i
$769$	−11.2565	+	9.44536i	−0.405921	+	0.340608i	−0.822777	−	0.568364i	$-0.807576\pi$
$769$	−11.2565	+	9.44536i	−0.405921	+	0.340608i	0.416856	+	0.908973i	$0.363132\pi$
$770$	−31.4984	−	21.4336i	−1.13512	−	0.772414i
$771$	−33.8330	−	20.0119i	−1.21846	−	0.720712i
$772$	−11.7205	+	14.7516i	−0.421830	+	0.530922i
$773$	−9.84699	−	17.0555i	−0.354172	−	0.613443i	0.632804	−	0.774312i	$-0.281904\pi$
$773$	−9.84699	−	17.0555i	−0.354172	−	0.613443i	−0.986976	+	0.160869i	$0.948570\pi$
$774$	15.6936	+	22.7848i	0.564095	+	0.818982i
$775$	−17.1355	−	9.89320i	−0.615526	−	0.355374i
$776$	0.303463	−	0.231161i	0.0108937	−	0.00829818i
$777$	43.8843	−	36.0419i	1.57434	−	1.29300i
$778$	0.148634	−	2.00771i	0.00532878	−	0.0719799i
$779$	12.2622	−	2.16216i	0.439341	−	0.0774676i
$780$	4.66391	−	29.2095i	0.166995	−	1.04587i
$781$	18.0661	−	21.5304i	0.646456	−	0.770417i
$782$	−6.15982	+	1.73911i	−0.220275	+	0.0621904i
$783$	−45.1253	+	14.8261i	−1.61265	+	0.529841i
$784$	−2.58852	+	5.09434i	−0.0924471	+	0.181941i
$785$	−21.1874	+	25.2502i	−0.756212	+	0.901218i
$786$	0.342861	+	3.79525i	0.0122295	+	0.135372i
$787$	−2.49296	−	14.1383i	−0.0888646	−	0.503976i	−0.996456	−	0.0841207i	$-0.973192\pi$
$787$	−2.49296	−	14.1383i	−0.0888646	−	0.503976i	0.907591	−	0.419855i	$-0.137919\pi$
$788$	0.765354	−	0.156159i	0.0272646	−	0.00556294i
$789$	−4.96702	−	30.0162i	−0.176830	−	1.06861i
$790$	4.27175	+	42.3041i	0.151982	+	1.50511i
$791$	−13.7754	+	23.8596i	−0.489796	+	0.848351i
$792$	22.3373	+	5.53199i	0.793721	+	0.196571i
$793$	0.912701	+	1.58084i	0.0324110	+	0.0561374i
$794$	21.9350	−	15.8003i	0.778446	−	0.560732i
$795$	61.2755	+	0.645940i	2.17322	+	0.0229091i
$796$	13.7435	+	4.58996i	0.487125	+	0.162687i
$797$	16.5677	−	13.9019i	0.586857	−	0.492431i	−0.300334	−	0.953834i	$-0.597098\pi$
$797$	16.5677	−	13.9019i	0.586857	−	0.492431i	0.887191	+	0.461403i	$0.152654\pi$
$798$	−13.2692	−	13.1944i	−0.469725	−	0.467075i
$799$	−2.21295	−	6.08002i	−0.0782884	−	0.215096i
$800$	12.2470	+	35.9132i	0.432996	+	1.26972i
$801$	−16.7779	+	2.59497i	−0.592817	+	0.0916889i
$802$	−6.50440	+	25.6412i	−0.229678	+	0.905423i
$803$	39.2092	+	6.91364i	1.38366	+	0.243977i
$804$	22.2067	−	4.28763i	0.783170	−	0.151213i
$805$	3.09078	−	8.49184i	0.108936	−	0.299298i
$806$	9.37562	−	4.52550i	0.330242	−	0.159404i
$807$	−41.2365	+	14.5185i	−1.45159	+	0.511074i
$808$	4.68576	+	36.5877i	0.164844	+	1.28715i
$809$			27.7706i			0.976363i	0.872742	+	0.488182i	$0.162340\pi$
$809$			27.7706i			0.976363i	−0.872742	+	0.488182i	$0.837660\pi$
$810$	−23.9420	−	36.3788i	−0.841236	−	1.27822i
$811$	−6.91746			−0.242905			−0.121452	−	0.992597i	$-0.538755\pi$
$811$	−6.91746			−0.242905			−0.121452	+	0.992597i	$0.538755\pi$
$812$	7.81587	−	52.4982i	0.274283	−	1.84233i
$813$	−16.2657	−	46.1990i	−0.570462	−	1.62027i
$814$	39.0071	−	18.8282i	1.36720	−	0.659929i
$815$	63.0848	+	22.9610i	2.20976	+	0.804288i
$816$	−23.2689	−	25.4290i	−0.814575	−	0.890194i
$817$	2.97969	−	16.8987i	0.104246	−	0.591209i
$818$	−25.4093	−	6.44558i	−0.888416	−	0.225364i
$819$	−20.2632	−	7.86279i	−0.708052	−	0.274748i
$820$	−15.4353	+	28.4663i	−0.539024	+	0.994085i
$821$	−6.71754	+	2.44498i	−0.234444	+	0.0853305i	−0.456570	−	0.889687i	$-0.650922\pi$
$821$	−6.71754	+	2.44498i	−0.234444	+	0.0853305i	0.222127	+	0.975018i	$0.428700\pi$
$822$	−1.50583	−	1.49734i	−0.0525220	−	0.0522257i
$823$	−1.29022	−	1.53762i	−0.0449742	−	0.0535981i	0.743088	−	0.669193i	$-0.233360\pi$
$823$	−1.29022	−	1.53762i	−0.0449742	−	0.0535981i	−0.788063	+	0.615595i	$0.788916\pi$
$824$	0.164769	−	3.49146i	0.00574000	−	0.121631i
$825$	−0.332124	+	31.5061i	−0.0115631	+	1.09690i
$826$	−20.7870	−	28.8579i	−0.723271	−	1.00409i
$827$	−22.7464	+	13.1326i	−0.790969	+	0.456666i	−0.840303	−	0.542116i	$-0.817623\pi$
$827$	−22.7464	+	13.1326i	−0.790969	+	0.456666i	0.0493347	+	0.998782i	$0.484290\pi$
$828$	0.0308786	+	5.45820i	0.00107311	+	0.189685i
$829$	36.0689	+	20.8244i	1.25272	+	0.723260i	0.971649	−	0.236426i	$-0.0759761\pi$
$829$	36.0689	+	20.8244i	1.25272	+	0.723260i	0.281074	+	0.959686i	$0.409309\pi$
$830$	−2.38412	−	23.6104i	−0.0827539	−	0.819529i
$831$	−18.5863	+	3.07562i	−0.644752	+	0.106692i
$832$	−19.2472	−	5.30294i	−0.667277	−	0.183846i
$833$	6.99928	−	1.23416i	0.242511	−	0.0427611i
$834$	37.0541	−	3.34745i	1.28308	−	0.115913i
$835$	29.8581	+	25.0539i	1.03328	+	0.867027i
$836$	−7.46422	−	12.1652i	−0.258155	−	0.420742i
$837$	5.69521	−	14.2305i	0.196855	−	0.491877i
$838$	−30.5693	+	8.63066i	−1.05600	+	0.298141i
$839$	−17.8040	−	14.9393i	−0.614662	−	0.515762i	0.281459	−	0.959573i	$-0.409182\pi$
$839$	−17.8040	−	14.9393i	−0.614662	−	0.515762i	−0.896120	+	0.443811i	$0.853626\pi$
$840$	48.3332	−	5.67283i	1.66765	−	0.195731i
$841$	9.47417	+	53.7307i	0.326696	+	1.85278i
$842$	24.6614	+	1.82572i	0.849889	+	0.0629185i
$843$	−6.39167	−	7.78245i	−0.220141	−	0.268042i
$844$	−16.3893	−	41.5385i	−0.564143	−	1.42981i
$845$	11.5861	−	20.0677i	0.398574	−	0.690350i
$846$	−5.50019	+	0.438487i	−0.189100	+	0.0150755i
$847$	9.16452	−	5.29114i	0.314897	−	0.181806i
$848$	4.99451	−	41.0569i	0.171512	−	1.40990i
$849$	−8.02613	+	13.5693i	−0.275456	+	0.465697i
$850$	26.5500	−	39.0174i	0.910658	−	1.33828i
$851$	6.60374	+	7.87003i	0.226373	+	0.269781i
$852$	0.581502	+	35.8956i	0.0199219	+	1.22976i
$853$	−0.546744	−	1.50217i	−0.0187202	−	0.0514332i	0.929981	−	0.367609i	$-0.119823\pi$
$853$	−0.546744	−	1.50217i	−0.0187202	−	0.0514332i	−0.948701	+	0.316175i	$0.897601\pi$
$854$	−2.09500	+	2.15179i	−0.0716895	+	0.0736326i
$855$	−5.25010	+	26.4957i	−0.179550	+	0.906134i
$856$	−13.4387	−	43.1517i	−0.459325	−	1.47489i
$857$	−21.3303	−	3.76110i	−0.728629	−	0.128477i	−0.202985	−	0.979182i	$-0.565064\pi$
$857$	−21.3303	−	3.76110i	−0.728629	−	0.128477i	−0.525644	+	0.850705i	$0.676175\pi$
$858$	−13.6067	−	9.47029i	−0.464526	−	0.323310i
$859$	−13.9293	−	5.06987i	−0.475263	−	0.172982i	0.0932719	−	0.995641i	$-0.470267\pi$
$859$	−13.9293	−	5.06987i	−0.475263	−	0.172982i	−0.568535	+	0.822659i	$0.692490\pi$
$860$	29.5884	+	33.4059i	1.00896	+	1.13913i
$861$	18.0653	+	15.4860i	0.615663	+	0.527761i
$862$	7.62605	−	16.9419i	0.259744	−	0.577042i
$863$	37.5749			1.27907			0.639533	−	0.768764i	$-0.279128\pi$
$863$	37.5749			1.27907			0.639533	+	0.768764i	$0.279128\pi$
$864$	−26.1859	+	13.3529i	−0.890862	+	0.454275i
$865$	−54.1932			−1.84262
$866$	−13.1542	+	29.2230i	−0.446997	+	0.993038i
$867$	−2.47068	+	13.1969i	−0.0839087	+	0.448191i
$868$	11.3565	+	12.8217i	0.385465	+	0.435197i
$869$	22.3930	+	8.15037i	0.759629	+	0.276482i
$870$	−69.3440	+	32.5747i	−2.35098	+	1.10439i
$871$	−16.0457	−	2.82929i	−0.543688	−	0.0958668i
$872$	2.00338	+	6.43288i	0.0678432	+	0.217845i
$873$	−0.209651	+	0.346066i	−0.00709560	+	0.0117126i
$874$	2.36158	−	2.42559i	0.0798816	−	0.0820467i
$875$	5.80168	+	15.9400i	0.196133	+	0.538870i
$876$	−43.6244	+	26.1377i	−1.47393	+	0.883112i
$877$	25.3049	+	30.1572i	0.854484	+	1.01833i	0.999582	+	0.0289176i	$0.00920603\pi$
$877$	25.3049	+	30.1572i	0.854484	+	1.01833i	−0.145097	+	0.989417i	$0.546350\pi$
$878$	−12.0359	+	17.6877i	−0.406191	+	0.596930i
$879$	3.44869	+	6.12144i	0.116322	+	0.206471i
$880$	36.8464	+	4.48230i	1.24209	+	0.151098i
$881$	22.6325	−	13.0669i	0.762509	−	0.440235i	−0.0676867	−	0.997707i	$-0.521562\pi$
$881$	22.6325	−	13.0669i	0.762509	−	0.440235i	0.830196	+	0.557472i	$0.188228\pi$
$882$	0.574792	−	6.03357i	0.0193543	−	0.203161i
$883$	−24.4508	+	42.3501i	−0.822837	+	1.42519i	0.0807251	+	0.996736i	$0.474276\pi$
$883$	−24.4508	+	42.3501i	−0.822837	+	1.42519i	−0.903562	+	0.428458i	$0.859057\pi$
$884$	9.11359	+	23.0983i	0.306523	+	0.776879i
$885$	−18.0657	+	48.0528i	−0.607271	+	1.61528i
$886$	5.61410	+	0.415620i	0.188609	+	0.0139630i
$887$	2.89846	+	16.4380i	0.0973207	+	0.551933i	0.994011	+	0.109276i	$0.0348531\pi$
$887$	2.89846	+	16.4380i	0.0973207	+	0.551933i	−0.896691	+	0.442658i	$0.854036\pi$
$888$	−21.8888	+	50.8110i	−0.734541	+	1.70511i
$889$	10.1203	+	8.49198i	0.339425	+	0.284812i
$890$	−26.3539	+	7.44052i	−0.883384	+	0.249407i
$891$	−24.1945	+	3.22142i	−0.810546	+	0.107922i
$892$	−8.32427	−	13.5669i	−0.278717	−	0.454254i
$893$	2.62152	+	2.19972i	0.0877259	+	0.0736108i
$894$	12.0543	+	17.1121i	0.403156	+	0.572314i
$895$	53.1394	−	9.36990i	1.77625	−	0.313201i
$896$	−0.207655	−	32.8453i	−0.00693728	−	1.09728i
$897$	1.38375	−	3.68064i	0.0462022	−	0.122893i
$898$	−3.66976	−	36.3423i	−0.122461	−	1.21276i
$899$	−23.3522	−	13.4824i	−0.778838	−	0.449663i
$900$	−26.0434	−	30.6832i	−0.868115	−	1.02277i
$901$	−44.5501	+	25.7210i	−1.48418	+	0.856890i
$902$	10.6074	+	14.7259i	0.353187	+	0.490319i
$903$	28.5691	−	16.0953i	0.950721	−	0.535617i
$904$	1.26528	−	26.8113i	0.0420826	−	0.891732i
$905$	−11.1527	−	13.2913i	−0.370729	−	0.441818i
$906$	24.8382	−	6.73074i	0.825195	−	0.223614i
$907$	9.94085	−	3.61817i	0.330081	−	0.120140i	−0.171663	−	0.985156i	$-0.554914\pi$
$907$	9.94085	−	3.61817i	0.330081	−	0.120140i	0.501744	+	0.865016i	$0.332692\pi$
$908$	−8.23586	+	15.1888i	−0.273316	+	0.504059i
$909$	−18.8434	−	34.2873i	−0.624996	−	1.13724i
$910$	−33.9821	−	8.62023i	−1.12649	−	0.285758i
$911$	10.2298	−	58.0158i	0.338927	−	1.92215i	−0.0454332	−	0.998967i	$-0.514467\pi$
$911$	10.2298	−	58.0158i	0.338927	−	1.92215i	0.384360	−	0.923183i	$-0.374422\pi$
$912$	17.3831	+	5.49416i	0.575612	+	0.181930i
$913$	−12.4978	−	4.54882i	−0.413616	−	0.150544i
$914$	3.57261	−	1.72445i	0.118171	−	0.0570399i
$915$	4.26095	+	0.797721i	0.140863	+	0.0263719i
$916$	2.24767	−	15.0973i	0.0742650	−	0.498828i
$917$	4.51655			0.149150
$918$	32.8465	+	16.0529i	1.08410	+	0.529824i
$919$			25.4259i			0.838724i	0.907819	+	0.419362i	$0.137746\pi$
$919$			25.4259i			0.838724i	−0.907819	+	0.419362i	$0.862254\pi$
$920$	1.11840	+	8.73276i	0.0368725	+	0.287911i
$921$	44.2843	+	37.9615i	1.45922	+	1.25087i
$922$	19.1394	−	9.23837i	0.630324	−	0.304250i
$923$	8.84554	−	24.3029i	0.291155	−	0.799941i
$924$	8.91208	−	25.7774i	0.293186	−	0.848015i
$925$	−74.5997	−	13.1539i	−2.45282	−	0.432499i
$926$	−7.60492	+	29.9796i	−0.249913	+	0.985191i
$927$	1.19427	+	3.50974i	0.0392250	+	0.115275i
$928$	16.6901	+	48.9423i	0.547879	+	1.60661i
$929$	−1.65289	−	4.54128i	−0.0542296	−	0.148995i	0.909620	−	0.415441i	$-0.136373\pi$
$929$	−1.65289	−	4.54128i	−0.0542296	−	0.148995i	−0.963850	+	0.266446i	$0.914151\pi$
$930$	6.33131	−	23.8990i	0.207612	−	0.783678i
$931$	−2.87963	+	2.41630i	−0.0943760	+	0.0791909i
$932$	13.4853	+	4.50371i	0.441724	+	0.147524i
$933$	−10.8156	+	18.2852i	−0.354085	+	0.598631i
$934$	−21.4799	+	15.4725i	−0.702845	+	0.506274i
$935$	−23.0832	−	39.9813i	−0.754902	−	1.30753i
$936$	21.0559	−	2.24657i	0.688234	−	0.0734315i
$937$	25.7048	−	44.5220i	0.839738	−	1.45447i	−0.0503753	−	0.998730i	$-0.516042\pi$
$937$	25.7048	−	44.5220i	0.839738	−	1.45447i	0.890114	−	0.455739i	$-0.150625\pi$
$938$	−2.69311	−	26.6704i	−0.0879332	−	0.870821i
$939$	7.14491	−	5.86807i	0.233165	−	0.191497i
$940$	−8.72016	+	1.77922i	−0.284420	+	0.0580318i
$941$	−6.83831	−	38.7820i	−0.222922	−	1.26426i	−0.866617	−	0.498973i	$-0.833711\pi$
$941$	−6.83831	−	38.7820i	−0.222922	−	1.26426i	0.643695	−	0.765282i	$-0.277401\pi$
$942$	−21.4140	−	9.91189i	−0.697707	−	0.322947i
$943$	−2.76699	+	3.29758i	−0.0901057	+	0.107384i
$944$	30.8902	+	15.6958i	1.00539	+	0.510855i
$945$	−45.4953	+	24.3822i	−1.47996	+	0.793154i
$946$	24.0696	−	6.79561i	0.782571	−	0.220944i
$947$	18.2848	−	21.7910i	0.594178	−	0.708113i	−0.382226	−	0.924069i	$-0.624842\pi$
$947$	18.2848	−	21.7910i	0.594178	−	0.708113i	0.976403	+	0.215956i	$0.0692867\pi$
$948$	−28.4306	+	10.8726i	−0.923385	+	0.353125i
$949$	36.0798	−	6.36183i	1.17120	−	0.206514i
$950$	−1.84287	+	24.8931i	−0.0597907	+	0.807639i
$951$	−0.00412388	−	0.0249211i	−0.000133726	−	0.000808121i
$952$	−32.4983	+	24.7553i	−1.05328	+	0.802325i
$953$	−24.5811	−	14.1919i	−0.796261	−	0.459722i	0.0459008	−	0.998946i	$-0.485384\pi$
$953$	−24.5811	−	14.1919i	−0.796261	−	0.459722i	−0.842162	+	0.539224i	$0.818718\pi$
$954$	11.0268	+	42.4600i	0.357007	+	1.37469i
$955$	−42.7143	−	73.9833i	−1.38220	−	2.39404i
$956$	−2.76824	+	3.48415i	−0.0895312	+	0.112686i
$957$	−0.452616	+	42.9363i	−0.0146310	+	1.38793i
$958$	23.4581	+	15.9625i	0.757898	+	0.515724i
$959$	−1.92807	+	1.61784i	−0.0622605	+	0.0522428i
$960$	−39.3096	+	26.5069i	−1.26871	+	0.855507i
$961$	−20.9537	+	7.62652i	−0.675925	+	0.246017i
$962$	27.8034	−	28.5570i	0.896419	−	0.920715i
$963$	30.0326	+	37.3636i	0.967788	+	1.20403i
$964$	−0.0109178	−	0.408203i	−0.000351638	−	0.0131473i
$965$	5.59727	−	31.7437i	0.180183	−	1.02187i
$966$	6.44625	+	0.545605i	0.207405	+	0.0175546i
$967$	14.1101	−	38.7671i	0.453749	−	1.24667i	−0.476317	−	0.879274i	$-0.658028\pi$
$967$	14.1101	−	38.7671i	0.453749	−	1.24667i	0.930066	−	0.367392i	$-0.119749\pi$
$968$	−5.57002	+	8.67557i	−0.179027	+	0.278843i
$969$	−7.53023	−	21.3880i	−0.241906	−	0.687081i
$970$	−0.267884	+	0.595126i	−0.00860125	+	0.0191083i
$971$			5.59715i			0.179621i	0.995959	+	0.0898105i	$0.0286261\pi$
$971$			5.59715i			0.179621i	−0.995959	+	0.0898105i	$0.971374\pi$
$972$	20.6535	−	23.3545i	0.662460	−	0.749097i
$973$		−	44.0963i		−	1.41366i
$974$	18.1827	+	8.18461i	0.582613	+	0.262252i
$975$	9.62849	+	27.3476i	0.308358	+	0.875825i
$976$	0.852305	−	2.79896i	0.0272816	−	0.0895927i
$977$	7.61083	−	20.9106i	0.243492	−	0.668989i	−0.756397	−	0.654112i	$-0.773042\pi$
$977$	7.61083	−	20.9106i	0.243492	−	0.668989i	0.999889	−	0.0148763i	$-0.00473544\pi$
$978$	−4.05323	+	47.8884i	−0.129608	+	1.53130i
$979$	−2.66507	+	15.1144i	−0.0851762	+	0.483058i
$980$	−0.261377	−	9.77257i	−0.00834938	−	0.312173i
$981$	−4.47714	−	5.57002i	−0.142944	−	0.177837i
$982$	−2.27198	−	2.21203i	−0.0725018	−	0.0705886i
$983$	−43.7402	+	15.9201i	−1.39510	+	0.507774i	−0.926719	−	0.375755i	$-0.877383\pi$
$983$	−43.7402	+	15.9201i	−1.39510	+	0.507774i	−0.468378	+	0.883528i	$0.655161\pi$
$984$	−22.5592	−	5.33521i	−0.719161	−	0.170080i
$985$	−1.02371	+	0.858996i	−0.0326182	+	0.0273699i
$986$	36.1821	−	53.1726i	1.15227	−	1.69336i
$987$	−0.0689344	+	6.53929i	−0.00219421	+	0.208148i
$988$	−10.2829	−	8.17000i	−0.327143	−	0.259922i
$989$	2.96615	+	5.13752i	0.0943180	+	0.163364i
$990$	−38.1055	+	9.89600i	−1.21107	+	0.314516i
$991$	−38.1847	−	22.0460i	−1.21298	−	0.700313i	−0.249571	−	0.968357i	$-0.580289\pi$
$991$	−38.1847	−	22.0460i	−1.21298	−	0.700313i	−0.963407	+	0.268044i	$0.913623\pi$
$992$	−15.5607	−	6.02617i	−0.494052	−	0.191331i
$993$	1.07983	+	6.52552i	0.0342673	+	0.207081i
$994$	42.4338	+	3.14144i	1.34592	+	0.0996403i
$995$	−24.4127	+	4.30461i	−0.773933	+	0.136465i
$996$	15.8675	−	6.06812i	0.502781	−	0.192276i
$997$	13.4946	−	16.0822i	0.427378	−	0.509330i	−0.508786	−	0.860893i	$-0.669905\pi$
$997$	13.4946	−	16.0822i	0.427378	−	0.509330i	0.936164	+	0.351563i	$0.114350\pi$
$998$	3.55943	+	12.6073i	0.112672	+	0.399077i
$999$	1.85540	−	58.6519i	0.0587023	−	1.85566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.21	✓	192
3.2	odd	2		648.2.v.b.35.12		192
4.3	odd	2		864.2.bh.b.335.28		192
8.3	odd	2	inner	216.2.v.b.11.27	yes	192
8.5	even	2		864.2.bh.b.335.27		192
24.11	even	2		648.2.v.b.35.6		192
27.5	odd	18	inner	216.2.v.b.59.27	yes	192
27.22	even	9		648.2.v.b.611.6		192
108.59	even	18		864.2.bh.b.815.27		192
216.5	odd	18		864.2.bh.b.815.28		192
216.59	even	18	inner	216.2.v.b.59.21	yes	192
216.211	odd	18		648.2.v.b.611.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.21	✓	192	1.1	even	1	trivial
216.2.v.b.11.27	yes	192	8.3	odd	2	inner
216.2.v.b.59.21	yes	192	216.59	even	18	inner
216.2.v.b.59.27	yes	192	27.5	odd	18	inner
648.2.v.b.35.6		192	24.11	even	2
648.2.v.b.35.12		192	3.2	odd	2
648.2.v.b.611.6		192	27.22	even	9
648.2.v.b.611.12		192	216.211	odd	18
864.2.bh.b.335.27		192	8.5	even	2
864.2.bh.b.335.28		192	4.3	odd	2
864.2.bh.b.815.27		192	108.59	even	18
864.2.bh.b.815.28		192	216.5	odd	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)

\(f(q)\)	\(=\)	\(q+(0.580483 - 1.28959i) q^{2} +(-1.63375 + 0.575207i) q^{3} +(-1.32608 - 1.49717i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-0.206584 + 2.44076i) q^{6} +(2.85909 + 0.504135i) q^{7} +(-2.70050 + 0.841014i) q^{8} +(2.33827 - 1.87949i) q^{9} +O(q^{10})\)	\(q+(0.580483 - 1.28959i) q^{2} +(-1.63375 + 0.575207i) q^{3} +(-1.32608 - 1.49717i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-0.206584 + 2.44076i) q^{6} +(2.85909 + 0.504135i) q^{7} +(-2.70050 + 0.841014i) q^{8} +(2.33827 - 1.87949i) q^{9} +(3.37559 - 3.46708i) q^{10} +(-0.927560 - 2.54845i) q^{11} +(3.02766 + 1.68323i) q^{12} +(-1.60411 - 1.91170i) q^{13} +(2.30978 - 3.39441i) q^{14} +(-5.92612 - 0.0624707i) q^{15} +(-0.483033 + 3.97073i) q^{16} +(4.30856 - 2.48755i) q^{17} +(-1.06644 - 4.10642i) q^{18} +(-1.31569 + 2.27884i) q^{19} +(-2.51163 - 6.36570i) q^{20} +(-4.96102 + 0.820939i) q^{21} +(-3.82488 - 0.283162i) q^{22} +(-0.157970 - 0.895893i) q^{23} +(3.92818 - 2.92735i) q^{24} +(5.13833 + 4.31157i) q^{25} +(-3.39646 + 0.958928i) q^{26} +(-2.73906 + 4.41560i) q^{27} +(-3.03660 - 4.94907i) q^{28} +(7.00248 + 5.87578i) q^{29} +(-3.52058 + 7.60600i) q^{30} +(-2.90502 + 0.512234i) q^{31} +(4.84021 + 2.92786i) q^{32} +(2.98129 + 3.62999i) q^{33} +(-0.706867 - 7.00026i) q^{34} +(8.60284 + 4.96685i) q^{35} +(-5.91465 - 1.00844i) q^{36} +(-9.78021 + 5.64661i) q^{37} +(2.17503 + 3.01952i) q^{38} +(3.72033 + 2.20055i) q^{39} +(-9.66710 - 0.456210i) q^{40} +(-3.04161 - 3.62485i) q^{41} +(-1.82112 + 6.87422i) q^{42} +(-6.12779 + 2.23033i) q^{43} +(-2.58544 + 4.76816i) q^{44} +(9.71774 - 3.30669i) q^{45} +(-1.24703 - 0.316335i) q^{46} +(0.225833 - 1.28076i) q^{47} +(-1.49483 - 6.76502i) q^{48} +(1.34241 + 0.488598i) q^{49} +(8.54287 - 4.12354i) q^{50} +(-5.60826 + 6.54235i) q^{51} +(-0.734968 + 4.93668i) q^{52} -10.3399 q^{53} +(4.10433 + 6.09544i) q^{54} -9.27950i q^{55} +(-8.14496 + 1.04312i) q^{56} +(0.838700 - 4.47984i) q^{57} +(11.6422 - 5.61953i) q^{58} +(2.96267 - 8.13988i) q^{59} +(7.76498 + 8.95525i) q^{60} +(-0.720351 - 0.127017i) q^{61} +(-1.02575 + 4.04363i) q^{62} +(7.63286 - 4.19482i) q^{63} +(6.58539 - 4.54231i) q^{64} +(-2.92046 - 8.02391i) q^{65} +(6.41178 - 1.73748i) q^{66} +(5.00144 - 4.19671i) q^{67} +(-9.43778 - 3.15196i) q^{68} +(0.773408 + 1.37280i) q^{69} +(11.3990 - 8.21095i) q^{70} +(5.18176 + 8.97507i) q^{71} +(-4.73383 + 7.04208i) q^{72} +(-7.34034 + 12.7138i) q^{73} +(1.60455 + 15.8902i) q^{74} +(-10.8748 - 4.08843i) q^{75} +(5.15651 - 1.05211i) q^{76} +(-1.36722 - 7.75387i) q^{77} +(4.99739 - 3.52032i) q^{78} +(-5.64811 + 6.73115i) q^{79} +(-6.19991 + 12.2018i) q^{80} +(1.93505 - 8.78952i) q^{81} +(-6.44017 + 1.81826i) q^{82} +(3.15228 - 3.75674i) q^{83} +(7.80779 + 6.33886i) q^{84} +(16.7644 - 2.95601i) q^{85} +(-0.680867 + 9.19700i) q^{86} +(-14.8201 - 5.57168i) q^{87} +(4.64815 + 6.10199i) q^{88} +(-4.90094 - 2.82956i) q^{89} +(1.37672 - 14.4514i) q^{90} +(-3.62253 - 6.27441i) q^{91} +(-1.13182 + 1.42453i) q^{92} +(4.45144 - 2.50785i) q^{93} +(-1.52056 - 1.03469i) q^{94} +(-6.89717 + 5.78741i) q^{95} +(-9.59182 - 1.99926i) q^{96} +(-0.126739 + 0.0461291i) q^{97} +(1.40934 - 1.44754i) q^{98} +(-6.95867 - 4.21564i) 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

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Database

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