LMFDB - Embedded newform 216.2.v.b.11.23

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			11.23
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.844953 + 1.13404i) q^{2} +(0.0447181 + 1.73147i) q^{3} +(-0.572109 + 1.91643i) q^{4} +(-4.00434 - 1.45746i) q^{5} +(-1.92578 + 1.51373i) q^{6} +(1.46723 + 0.258712i) q^{7} +(-2.65672 + 0.970494i) q^{8} +(-2.99600 + 0.154856i) q^{9} +O(q^{10})$	\(q+(0.844953 + 1.13404i) q^{2} +(0.0447181 + 1.73147i) q^{3} +(-0.572109 + 1.91643i) q^{4} +(-4.00434 - 1.45746i) q^{5} +(-1.92578 + 1.51373i) q^{6} +(1.46723 + 0.258712i) q^{7} +(-2.65672 + 0.970494i) q^{8} +(-2.99600 + 0.154856i) q^{9} +(-1.73065 - 5.77258i) q^{10} +(1.57835 + 4.33649i) q^{11} +(-3.34383 - 0.904892i) q^{12} +(2.82693 + 3.36900i) q^{13} +(0.946349 + 1.88250i) q^{14} +(2.34449 - 6.99858i) q^{15} +(-3.34538 - 2.19281i) q^{16} +(2.43381 - 1.40516i) q^{17} +(-2.70709 - 3.26675i) q^{18} +(0.516826 - 0.895168i) q^{19} +(5.08403 - 6.84019i) q^{20} +(-0.382341 + 2.55204i) q^{21} +(-3.58413 + 5.45405i) q^{22} +(-0.345539 - 1.95965i) q^{23} +(-1.79919 - 4.55663i) q^{24} +(10.0803 + 8.45837i) q^{25} +(-1.43197 + 6.05250i) q^{26} +(-0.402105 - 5.18057i) q^{27} +(-1.33522 + 2.66383i) q^{28} +(0.783266 + 0.657238i) q^{29} +(9.91767 - 3.25472i) q^{30} +(6.04883 - 1.06657i) q^{31} +(-0.339950 - 5.64663i) q^{32} +(-7.43793 + 2.92679i) q^{33} +(3.64997 + 1.57275i) q^{34} +(-5.49822 - 3.17440i) q^{35} +(1.41727 - 5.83021i) q^{36} +(-5.15589 + 2.97676i) q^{37} +(1.45185 - 0.170272i) q^{38} +(-5.70692 + 5.04540i) q^{39} +(12.0528 - 0.0141293i) q^{40} +(2.77589 + 3.30817i) q^{41} +(-3.21718 + 1.72276i) q^{42} +(-2.28164 + 0.830449i) q^{43} +(-9.21355 + 0.543853i) q^{44} +(12.2227 + 3.74645i) q^{45} +(1.93036 - 2.04767i) q^{46} +(-0.806279 + 4.57264i) q^{47} +(3.64719 - 5.89050i) q^{48} +(-4.49202 - 1.63496i) q^{49} +(-1.07479 + 18.5784i) q^{50} +(2.54184 + 4.15125i) q^{51} +(-8.07375 + 3.49016i) q^{52} -3.14544 q^{53} +(5.53523 - 4.83334i) q^{54} -19.6651i q^{55} +(-4.14909 + 0.736613i) q^{56} +(1.57307 + 0.854840i) q^{57} +(-0.0835137 + 1.44359i) q^{58} +(2.77458 - 7.62310i) q^{59} +(12.0710 + 8.49698i) q^{60} +(2.25575 + 0.397750i) q^{61} +(6.32052 + 5.95844i) q^{62} +(-4.43588 - 0.547892i) q^{63} +(6.11628 - 5.15666i) q^{64} +(-6.40978 - 17.6107i) q^{65} +(-9.60381 - 5.96193i) q^{66} +(7.24112 - 6.07602i) q^{67} +(1.30049 + 5.46813i) q^{68} +(3.37763 - 0.685923i) q^{69} +(-1.04583 - 8.91743i) q^{70} +(2.21770 + 3.84117i) q^{71} +(7.80924 - 3.31901i) q^{72} +(6.12067 - 10.6013i) q^{73} +(-7.73226 - 3.33179i) q^{74} +(-14.1947 + 17.8320i) q^{75} +(1.41984 + 1.50259i) q^{76} +(1.19390 + 6.77096i) q^{77} +(-10.5438 - 2.20876i) q^{78} +(-2.19872 + 2.62033i) q^{79} +(10.2001 + 13.6565i) q^{80} +(8.95204 - 0.927899i) q^{81} +(-1.40612 + 5.94322i) q^{82} +(3.23224 - 3.85203i) q^{83} +(-4.67205 - 2.19277i) q^{84} +(-11.7938 + 2.07956i) q^{85} +(-2.86965 - 1.88579i) q^{86} +(-1.10296 + 1.38559i) q^{87} +(-8.40177 - 9.98903i) q^{88} +(-3.14150 - 1.81374i) q^{89} +(6.07896 + 17.0266i) q^{90} +(3.27615 + 5.67445i) q^{91} +(3.95321 + 0.458932i) q^{92} +(2.11723 + 10.4257i) q^{93} +(-5.86684 + 2.94931i) q^{94} +(-3.37421 + 2.83130i) q^{95} +(9.76179 - 0.841121i) q^{96} +(-5.20281 + 1.89367i) q^{97} +(-1.94143 - 6.47561i) q^{98} +(-5.40028 - 12.7477i) 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 $

$2$	0.844953	+	1.13404i	0.597472	+	0.801890i
$2$	0.844953	+	1.13404i	0.597472	+	0.801890i
$3$	0.0447181	+	1.73147i	0.0258180	+	0.999667i
$3$	0.0447181	+	1.73147i	0.0258180	+	0.999667i
$4$	−0.572109	+	1.91643i	−0.286054	+	0.958213i
$5$	−4.00434	−	1.45746i	−1.79079	−	0.651796i	−0.999168	−	0.0407891i	$-0.987013\pi$
$5$	−4.00434	−	1.45746i	−1.79079	−	0.651796i	−0.791626	−	0.611006i	$-0.790765\pi$
$6$	−1.92578	+	1.51373i	−0.786197	+	0.617976i
$7$	1.46723	+	0.258712i	0.554561	+	0.0977840i	0.443903	−	0.896075i	$-0.353593\pi$
$7$	1.46723	+	0.258712i	0.554561	+	0.0977840i	0.110657	+	0.993859i	$0.464704\pi$
$8$	−2.65672	+	0.970494i	−0.939291	+	0.343121i
$9$	−2.99600	+	0.154856i	−0.998667	+	0.0516188i
$10$	−1.73065	−	5.77258i	−0.547281	−	1.82545i
$11$	1.57835	+	4.33649i	0.475891	+	1.30750i	0.912952	+	0.408068i	$0.133797\pi$
$11$	1.57835	+	4.33649i	0.475891	+	1.30750i	−0.437060	+	0.899432i	$0.643980\pi$
$12$	−3.34383	−	0.904892i	−0.965279	−	0.261220i
$13$	2.82693	+	3.36900i	0.784048	+	0.934392i	0.999109	−	0.0422087i	$-0.0134394\pi$
$13$	2.82693	+	3.36900i	0.784048	+	0.934392i	−0.215061	+	0.976601i	$0.568995\pi$
$14$	0.946349	+	1.88250i	0.252922	+	0.503120i
$15$	2.34449	−	6.99858i	0.605344	−	1.80702i
$16$	−3.34538	−	2.19281i	−0.836346	−	0.548202i
$17$	2.43381	−	1.40516i	0.590286	−	0.340802i	−0.174924	−	0.984582i	$-0.555968\pi$
$17$	2.43381	−	1.40516i	0.590286	−	0.340802i	0.765211	+	0.643780i	$0.222635\pi$
$18$	−2.70709	−	3.26675i	−0.638068	−	0.769980i
$19$	0.516826	−	0.895168i	0.118568	−	0.205366i	−0.800632	−	0.599156i	$-0.795503\pi$
$19$	0.516826	−	0.895168i	0.118568	−	0.205366i	0.919200	+	0.393790i	$0.128836\pi$
$20$	5.08403	−	6.84019i	1.13682	−	1.52951i
$21$	−0.382341	+	2.55204i	−0.0834337	+	0.556900i
$22$	−3.58413	+	5.45405i	−0.764139	+	1.16281i
$23$	−0.345539	−	1.95965i	−0.0720498	−	0.408615i	−0.999407	−	0.0344371i	$-0.989036\pi$
$23$	−0.345539	−	1.95965i	−0.0720498	−	0.408615i	0.927357	−	0.374178i	$-0.122075\pi$
$24$	−1.79919	−	4.55663i	−0.367258	−	0.930119i
$25$	10.0803	+	8.45837i	2.01606	+	1.69167i
$26$	−1.43197	+	6.05250i	−0.280833	+	1.18699i
$27$	−0.402105	−	5.18057i	−0.0773851	−	0.997001i
$28$	−1.33522	+	2.66383i	−0.252332	+	0.503416i
$29$	0.783266	+	0.657238i	0.145449	+	0.122046i	0.712609	−	0.701562i	$-0.247513\pi$
$29$	0.783266	+	0.657238i	0.145449	+	0.122046i	−0.567160	+	0.823608i	$0.691958\pi$
$30$	9.91767	−	3.25472i	1.81071	−	0.594228i
$31$	6.04883	−	1.06657i	1.08640	−	0.191562i	0.398358	−	0.917230i	$-0.369580\pi$
$31$	6.04883	−	1.06657i	1.08640	−	0.191562i	0.688045	+	0.725668i	$0.258469\pi$
$32$	−0.339950	−	5.64663i	−0.0600952	−	0.998193i
$33$	−7.43793	+	2.92679i	−1.29478	+	0.509490i
$34$	3.64997	+	1.57275i	0.625965	+	0.269725i
$35$	−5.49822	−	3.17440i	−0.929368	−	0.536571i
$36$	1.41727	−	5.83021i	0.236211	−	0.971702i
$37$	−5.15589	+	2.97676i	−0.847624	+	0.489376i	−0.859848	−	0.510549i	$-0.829442\pi$
$37$	−5.15589	+	2.97676i	−0.847624	+	0.489376i	0.0122246	+	0.999925i	$0.496109\pi$
$38$	1.45185	−	0.170272i	0.235522	−	0.0276218i
$39$	−5.70692	+	5.04540i	−0.913838	+	0.807911i
$40$	12.0528	−	0.0141293i	1.90572	−	0.00223404i
$41$	2.77589	+	3.30817i	0.433520	+	0.516650i	0.937935	−	0.346812i	$-0.112736\pi$
$41$	2.77589	+	3.30817i	0.433520	+	0.516650i	−0.504414	+	0.863462i	$0.668291\pi$
$42$	−3.21718	+	1.72276i	−0.496422	+	0.265828i
$43$	−2.28164	+	0.830449i	−0.347947	+	0.126642i	−0.510081	−	0.860126i	$-0.670385\pi$
$43$	−2.28164	+	0.830449i	−0.347947	+	0.126642i	0.162134	+	0.986769i	$0.448162\pi$
$44$	−9.21355	+	0.543853i	−1.38899	+	0.0819890i
$45$	12.2227	+	3.74645i	1.82205	+	0.558488i
$46$	1.93036	−	2.04767i	0.284616	−	0.301912i
$47$	−0.806279	+	4.57264i	−0.117608	+	0.666987i	0.867818	+	0.496882i	$0.165522\pi$
$47$	−0.806279	+	4.57264i	−0.117608	+	0.666987i	−0.985426	+	0.170105i	$0.945589\pi$
$48$	3.64719	−	5.89050i	0.526427	−	0.850220i
$49$	−4.49202	−	1.63496i	−0.641717	−	0.233566i
$50$	−1.07479	+	18.5784i	−0.151998	+	2.62739i
$51$	2.54184	+	4.15125i	0.355928	+	0.581291i
$52$	−8.07375	+	3.49016i	−1.11963	+	0.483998i
$53$	−3.14544			−0.432059			−0.216030	−	0.976387i	$-0.569311\pi$
$53$	−3.14544			−0.432059			−0.216030	+	0.976387i	$0.569311\pi$
$54$	5.53523	−	4.83334i	0.753250	−	0.657735i
$55$		−	19.6651i		−	2.65165i
$56$	−4.14909	+	0.736613i	−0.554445	+	0.0984340i
$57$	1.57307	+	0.854840i	0.208358	+	0.113226i
$58$	−0.0835137	+	1.44359i	−0.0109659	+	0.189553i
$59$	2.77458	−	7.62310i	0.361220	−	0.992443i	−0.617379	−	0.786666i	$-0.711805\pi$
$59$	2.77458	−	7.62310i	0.361220	−	0.992443i	0.978599	−	0.205777i	$-0.0659723\pi$
$60$	12.0710	+	8.49698i	1.55835	+	1.09696i
$61$	2.25575	+	0.397750i	0.288820	+	0.0509267i	0.316181	−	0.948699i	$-0.397599\pi$
$61$	2.25575	+	0.397750i	0.288820	+	0.0509267i	−0.0273613	+	0.999626i	$0.508710\pi$
$62$	6.32052	+	5.95844i	0.802707	+	0.756722i
$63$	−4.43588	−	0.547892i	−0.558869	−	0.0690279i
$64$	6.11628	−	5.15666i	0.764535	−	0.644582i
$65$	−6.40978	−	17.6107i	−0.795035	−	2.18434i
$66$	−9.60381	−	5.96193i	−1.18215	−	0.733863i
$67$	7.24112	−	6.07602i	0.884643	−	0.742304i	−0.0824851	−	0.996592i	$-0.526286\pi$
$67$	7.24112	−	6.07602i	0.884643	−	0.742304i	0.967128	+	0.254288i	$0.0818413\pi$
$68$	1.30049	+	5.46813i	0.157707	+	0.663108i
$69$	3.37763	−	0.685923i	0.406618	−	0.0825754i
$70$	−1.04583	−	8.91743i	−0.125001	−	1.06584i
$71$	2.21770	+	3.84117i	0.263193	+	0.455863i	0.967089	−	0.254440i	$-0.0818912\pi$
$71$	2.21770	+	3.84117i	0.263193	+	0.455863i	−0.703896	+	0.710303i	$0.748558\pi$
$72$	7.80924	−	3.31901i	0.920327	−	0.391149i
$73$	6.12067	−	10.6013i	0.716370	−	1.24079i	−0.246059	−	0.969255i	$-0.579136\pi$
$73$	6.12067	−	10.6013i	0.716370	−	1.24079i	0.962429	−	0.271534i	$-0.0875309\pi$
$74$	−7.73226	−	3.33179i	−0.898857	−	0.387313i
$75$	−14.1947	+	17.8320i	−1.63906	+	2.05906i
$76$	1.41984	+	1.50259i	0.162867	+	0.172359i
$77$	1.19390	+	6.77096i	0.136058	+	0.771622i
$78$	−10.5438	−	2.20876i	−1.19385	−	0.250093i
$79$	−2.19872	+	2.62033i	−0.247375	+	0.294811i	−0.875416	−	0.483370i	$-0.839413\pi$
$79$	−2.19872	+	2.62033i	−0.247375	+	0.294811i	0.628041	+	0.778180i	$0.283857\pi$
$80$	10.2001	+	13.6565i	1.14041	+	1.52684i
$81$	8.95204	−	0.927899i	0.994671	−	0.103100i
$82$	−1.40612	+	5.94322i	−0.155280	+	0.656319i
$83$	3.23224	−	3.85203i	0.354784	−	0.422816i	−0.558903	−	0.829233i	$-0.688778\pi$
$83$	3.23224	−	3.85203i	0.354784	−	0.422816i	0.913688	+	0.406417i	$0.133222\pi$
$84$	−4.67205	−	2.19277i	−0.509763	−	0.239251i
$85$	−11.7938	+	2.07956i	−1.27921	+	0.225560i
$86$	−2.86965	−	1.88579i	−0.309442	−	0.203350i
$87$	−1.10296	+	1.38559i	−0.118250	+	0.148551i
$88$	−8.40177	−	9.98903i	−0.895632	−	1.06483i
$89$	−3.14150	−	1.81374i	−0.332998	−	0.192257i	0.324173	−	0.945998i	$-0.394914\pi$
$89$	−3.14150	−	1.81374i	−0.332998	−	0.192257i	−0.657171	+	0.753741i	$0.728247\pi$
$90$	6.07896	+	17.0266i	0.640779	+	1.79476i
$91$	3.27615	+	5.67445i	0.343433	+	0.594844i
$92$	3.95321	+	0.458932i	0.412150	+	0.0478470i
$93$	2.11723	+	10.4257i	0.219547	+	1.08109i
$94$	−5.86684	+	2.94931i	−0.605118	+	0.304198i
$95$	−3.37421	+	2.83130i	−0.346187	+	0.290485i
$96$	9.76179	−	0.841121i	0.996308	−	0.0858465i
$97$	−5.20281	+	1.89367i	−0.528265	+	0.192273i	−0.592364	−	0.805671i	$-0.701805\pi$
$97$	−5.20281	+	1.89367i	−0.528265	+	0.192273i	0.0640983	+	0.997944i	$0.479583\pi$
$98$	−1.94143	−	6.47561i	−0.196114	−	0.654135i
$99$	−5.40028	−	12.7477i	−0.542748	−	1.28119i
$100$	−21.9769	+	14.4790i	−2.19769	+	1.44790i
$101$	1.04151	−	5.90670i	0.103634	−	0.587738i	−0.888123	−	0.459606i	$-0.847991\pi$
$101$	1.04151	−	5.90670i	0.103634	−	0.587738i	0.991757	−	0.128132i	$-0.0408982\pi$
$102$	−2.55996	+	6.39016i	−0.253474	+	0.632720i
$103$	0.518867	−	1.42558i	0.0511255	−	0.140466i	−0.911502	−	0.411297i	$-0.865076\pi$
$103$	0.518867	−	1.42558i	0.0511255	−	0.140466i	0.962627	+	0.270830i	$0.0872983\pi$
$104$	−10.7799	−	6.20696i	−1.05706	−	0.608642i
$105$	5.25051	−	9.66197i	0.512398	−	0.942912i
$106$	−2.65775	−	3.56707i	−0.258143	−	0.346464i
$107$		−	3.84196i		−	0.371416i	−0.982605	−	0.185708i	$-0.940542\pi$
$107$		−	3.84196i		−	0.371416i	0.982605	−	0.185708i	$-0.0594579\pi$
$108$	10.1582	+	2.19325i	0.977476	+	0.211045i
$109$		−	0.0790719i		−	0.00757371i	−0.999993	−	0.00378686i	$-0.998795\pi$
$109$		−	0.0790719i		−	0.00757371i	0.999993	−	0.00378686i	$-0.00120540\pi$
$110$	22.3011	−	16.6161i	2.12633	−	1.58428i
$111$	−5.38474	−	8.79418i	−0.511097	−	0.834707i
$112$	−4.34114	−	4.08285i	−0.410199	−	0.385793i
$113$	−4.70897	+	12.9378i	−0.442983	+	1.21708i	0.494538	+	0.869156i	$0.335337\pi$
$113$	−4.70897	+	12.9378i	−0.442983	+	1.21708i	−0.937521	+	0.347929i	$0.886885\pi$
$114$	0.359746	+	2.50623i	0.0336933	+	0.234730i
$115$	−1.47245	+	8.35070i	−0.137307	+	0.778706i
$116$	−1.70766	+	1.12506i	−0.158552	+	0.104459i
$117$	−8.99118	−	9.65575i	−0.831235	−	0.892675i
$118$	10.9893	−	3.29467i	1.01165	−	0.303299i
$119$	3.93449	−	1.43204i	0.360675	−	0.131275i
$120$	0.563444	+	20.8685i	0.0514352	+	1.90503i
$121$	−7.88744	+	6.61835i	−0.717040	+	0.601668i
$122$	1.45494	+	2.89420i	0.131724	+	0.262029i
$123$	−5.60388	+	4.95431i	−0.505285	+	0.446715i
$124$	−1.41658	+	12.2023i	−0.127213	+	1.09580i
$125$	−17.3838	−	30.1097i	−1.55486	−	2.69309i
$126$	−3.12678	−	5.49343i	−0.278556	−	0.489393i
$127$	8.10161	+	4.67747i	0.718901	+	0.415058i	0.814348	−	0.580377i	$-0.197095\pi$
$127$	8.10161	+	4.67747i	0.718901	+	0.415058i	−0.0954468	+	0.995435i	$0.530428\pi$
$128$	11.0158	+	2.57900i	0.973672	+	0.227953i
$129$	−1.53993	−	3.91346i	−0.135583	−	0.344561i
$130$	14.5554	−	22.1492i	1.27659	−	1.94261i
$131$	18.8914	−	3.33107i	1.65055	−	0.291037i	0.730522	−	0.682889i	$-0.239277\pi$
$131$	18.8914	−	3.33107i	1.65055	−	0.291037i	0.920028	+	0.391852i	$0.128166\pi$
$132$	−1.35368	−	15.9287i	−0.117823	−	1.38642i
$133$	0.989892	−	1.17971i	0.0858346	−	0.102294i
$134$	13.0089	+	3.07779i	1.12380	+	0.265881i
$135$	−5.94031	+	21.3308i	−0.511260	+	1.83586i
$136$	−5.10225	+	6.09512i	−0.437514	+	0.522652i
$137$	−13.3756	+	15.9404i	−1.14275	+	1.36188i	−0.220454	+	0.975397i	$0.570754\pi$
$137$	−13.3756	+	15.9404i	−1.14275	+	1.36188i	−0.922297	+	0.386481i	$0.873690\pi$
$138$	3.63180	+	3.25080i	0.309159	+	0.276727i
$139$	−0.182725	−	1.03628i	−0.0154985	−	0.0878964i	0.976077	−	0.217423i	$-0.0697652\pi$
$139$	−0.182725	−	1.03628i	−0.0154985	−	0.0878964i	−0.991576	+	0.129527i	$0.958654\pi$
$140$	9.22908	−	8.72083i	0.779999	−	0.737044i
$141$	−7.95345	−	1.19157i	−0.669802	−	0.100348i
$142$	−2.48220	+	5.76058i	−0.208302	+	0.483417i
$143$	−10.1477	+	17.5764i	−0.848596	+	1.46981i
$144$	10.3623	+	6.05161i	0.863528	+	0.504300i
$145$	−2.17856	−	3.77338i	−0.180920	−	0.313362i
$146$	17.1940	−	2.01650i	1.42299	−	0.166887i
$147$	2.63002	−	7.85092i	0.216920	−	0.647533i
$148$	−2.75500	−	11.5839i	−0.226460	−	0.952193i
$149$	0.754433	−	0.633045i	0.0618056	−	0.0518610i	−0.611362	−	0.791351i	$-0.709378\pi$
$149$	0.754433	−	0.633045i	0.0618056	−	0.0518610i	0.673167	+	0.739490i	$0.264933\pi$
$150$	−32.2161	−	1.03017i	−2.63043	−	0.0841132i
$151$	−4.23102	−	11.6246i	−0.344315	−	0.945999i	−0.984127	−	0.177467i	$-0.943210\pi$
$151$	−4.23102	−	11.6246i	−0.344315	−	0.945999i	0.639811	−	0.768532i	$-0.279012\pi$
$152$	−0.504304	+	2.87978i	−0.0409044	+	0.233581i
$153$	−7.07411	+	4.58676i	−0.571908	+	0.370818i
$154$	−6.66977	+	7.07508i	−0.537465	+	0.570126i
$155$	−25.7760	−	4.54501i	−2.07038	−	0.365064i
$156$	−6.40416	−	13.8234i	−0.512743	−	1.10676i
$157$	−6.41069	+	17.6132i	−0.511629	+	1.40569i	0.367910	+	0.929861i	$0.380073\pi$
$157$	−6.41069	+	17.6132i	−0.511629	+	1.40569i	−0.879539	+	0.475827i	$0.842149\pi$
$158$	−4.82939	−	0.279386i	−0.384206	−	0.0222268i
$159$	−0.140658	−	5.44625i	−0.0111549	−	0.431915i
$160$	−6.86846	+	23.1065i	−0.542999	+	1.82673i
$161$		−	2.96465i		−	0.233647i
$162$	8.61633	+	9.36797i	0.676963	+	0.736017i
$163$	−9.89370			−0.774934			−0.387467	−	0.921883i	$-0.626650\pi$
$163$	−9.89370			−0.774934			−0.387467	+	0.921883i	$0.626650\pi$
$164$	−7.92798	+	3.42715i	−0.619071	+	0.267615i
$165$	34.0497	−	0.879387i	2.65076	−	0.0684602i
$166$	7.09946	+	0.410713i	0.551025	+	0.0318775i
$167$	22.3929	+	8.15035i	1.73281	+	0.630693i	0.998825	−	0.0484679i	$-0.0154339\pi$
$167$	22.3929	+	8.15035i	1.73281	+	0.630693i	0.733990	+	0.679161i	$0.237656\pi$
$168$	−1.46096	−	7.15110i	−0.112716	−	0.551719i
$169$	−1.10122	+	6.24531i	−0.0847090	+	0.480408i
$170$	−12.3235	−	11.6175i	−0.945169	−	0.891023i
$171$	−1.40979	+	2.76196i	−0.107809	+	0.211212i
$172$	−0.286148	−	4.84771i	−0.0218186	−	0.369634i
$173$	16.0204	−	5.83093i	1.21801	−	0.443318i	0.348532	−	0.937297i	$-0.386680\pi$
$173$	16.0204	−	5.83093i	1.21801	−	0.443318i	0.869474	+	0.493979i	$0.164458\pi$
$174$	−2.50328	−	0.0800471i	−0.189773	−	0.00606836i
$175$	12.6018	+	15.0183i	0.952608	+	1.13527i
$176$	4.22890	−	17.9682i	0.318765	−	1.35441i
$177$	13.3233	+	4.46322i	1.00144	+	0.335477i
$178$	−0.597553	−	5.09512i	−0.0447885	−	0.381896i
$179$	9.77705	−	5.64478i	0.730771	−	0.421911i	−0.0879331	−	0.996126i	$-0.528026\pi$
$179$	9.77705	−	5.64478i	0.730771	−	0.421911i	0.818704	+	0.574215i	$0.194693\pi$
$180$	−14.1725	+	21.2805i	−1.05636	+	1.58616i
$181$	4.81082	+	2.77753i	0.357586	+	0.206452i	0.668021	−	0.744142i	$-0.267142\pi$
$181$	4.81082	+	2.77753i	0.357586	+	0.206452i	−0.310436	+	0.950594i	$0.600475\pi$
$182$	−3.66689	+	8.50994i	−0.271808	+	0.630799i
$183$	−0.587821	+	3.92356i	−0.0434530	+	0.290038i
$184$	2.81982	+	4.87088i	0.207880	+	0.359086i
$185$	24.9844	−	4.40543i	1.83689	−	0.323894i
$186$	−10.0342	+	11.2103i	−0.735746	+	0.821976i
$187$	9.93489	+	8.33636i	0.726511	+	0.609615i
$188$	−8.30184	−	4.16122i	−0.605474	−	0.303488i
$189$	0.750296	−	7.70511i	0.0545760	−	0.560465i
$190$	−6.06187	−	1.43419i	−0.439774	−	0.104047i
$191$	−1.68403	−	1.41307i	−0.121852	−	0.102246i	0.579825	−	0.814741i	$-0.303121\pi$
$191$	−1.68403	−	1.41307i	−0.121852	−	0.102246i	−0.701677	+	0.712495i	$0.747565\pi$
$192$	9.20212	+	10.3596i	0.664106	+	0.747639i
$193$	−0.352543	−	1.99937i	−0.0253766	−	0.143918i	0.969487	−	0.245143i	$-0.0788349\pi$
$193$	−0.352543	−	1.99937i	−0.0253766	−	0.143918i	−0.994864	+	0.101225i	$0.967724\pi$
$194$	−6.54363	−	4.30015i	−0.469805	−	0.308733i
$195$	30.2059	−	11.8859i	2.16309	−	0.851166i
$196$	5.70321	−	7.67325i	0.407372	−	0.548089i
$197$	1.87110	−	3.24084i	0.133310	−	0.230900i	−0.791640	−	0.610987i	$-0.790773\pi$
$197$	1.87110	−	3.24084i	0.133310	−	0.230900i	0.924951	+	0.380087i	$0.124106\pi$
$198$	9.89347	−	16.8954i	0.703098	−	1.20070i
$199$	−4.64777	+	2.68339i	−0.329472	+	0.190220i	−0.655606	−	0.755103i	$-0.727587\pi$
$199$	−4.64777	+	2.68339i	−0.329472	+	0.190220i	0.326135	+	0.945323i	$0.394254\pi$
$200$	−34.9893	−	12.6886i	−2.47412	−	0.897222i
$201$	10.8443	+	12.2661i	0.764896	+	0.865184i
$202$	7.57848	−	3.80976i	0.533220	−	0.268054i
$203$	0.979195	+	1.16696i	0.0687260	+	0.0819045i
$204$	−9.40977	+	2.49628i	−0.658816	+	0.174775i
$205$	−6.29405	−	17.2928i	−0.439596	−	1.20778i
$206$	2.05508	−	0.616126i	0.143184	−	0.0429276i
$207$	1.33870	+	5.81760i	0.0930459	+	0.404351i
$208$	−2.06957	−	17.4695i	−0.143499	−	1.21129i
$209$	4.69762	+	0.828317i	0.324941	+	0.0572959i
$210$	15.3935	−	2.20960i	1.06225	−	0.152477i
$211$	−19.5453	−	7.11390i	−1.34555	−	0.489741i	−0.433995	−	0.900915i	$-0.642897\pi$
$211$	−19.5453	−	7.11390i	−1.34555	−	0.489741i	−0.911557	+	0.411174i	$0.865119\pi$
$212$	1.79953	−	6.02801i	0.123593	−	0.414005i
$213$	−6.55171	+	4.01166i	−0.448916	+	0.274874i
$214$	4.35695	−	3.24627i	0.297835	−	0.221911i
$215$	10.3468			0.705646
$216$	6.09599	+	13.3731i	0.414780	+	0.909922i
$217$	9.15096			0.621208
$218$	0.0896709	−	0.0668120i	0.00607328	−	0.00452508i
$219$	18.6296	+	10.1237i	1.25887	+	0.684096i
$220$	37.6868	+	11.2506i	2.54084	+	0.758515i
$221$	11.6142	+	4.22722i	0.781256	+	0.284354i
$222$	5.42313	−	13.5372i	0.363977	−	0.908557i
$223$	0.670958	+	0.118308i	0.0449307	+	0.00792249i	0.196068	−	0.980590i	$-0.437183\pi$
$223$	0.670958	+	0.118308i	0.0449307	+	0.00792249i	−0.151138	+	0.988513i	$0.548294\pi$
$224$	0.962067	−	8.37285i	0.0642808	−	0.559435i
$225$	−31.5104	−	23.7803i	−2.10069	−	1.58535i
$226$	−18.6509	+	5.59165i	−1.24064	+	0.371951i
$227$	7.91255	+	21.7395i	0.525174	+	1.44290i	0.864691	+	0.502304i	$0.167514\pi$
$227$	7.91255	+	21.7395i	0.525174	+	1.44290i	−0.339517	+	0.940600i	$0.610264\pi$
$228$	−2.53821	+	2.52561i	−0.168097	+	0.167263i
$229$	−18.0468	−	21.5073i	−1.19256	−	1.42124i	−0.882362	−	0.470572i	$-0.844048\pi$
$229$	−18.0468	−	21.5073i	−1.19256	−	1.42124i	−0.310202	−	0.950671i	$-0.600397\pi$
$230$	−10.7142	+	5.38612i	−0.706474	+	0.355150i
$231$	−11.6703	+	2.37000i	−0.767852	+	0.155934i
$232$	−2.71876	−	0.985940i	−0.178495	−	0.0647302i
$233$	1.33665	−	0.771717i	0.0875670	−	0.0505568i	−0.455577	−	0.890196i	$-0.650567\pi$
$233$	1.33665	−	0.771717i	0.0875670	−	0.0505568i	0.543144	+	0.839639i	$0.317234\pi$
$234$	3.35292	−	18.3550i	0.219187	−	1.19991i
$235$	9.89304	−	17.1353i	0.645351	−	1.11778i
$236$	13.0218	+	9.67853i	0.847644	+	0.630018i
$237$	−4.63536	−	3.68985i	−0.301099	−	0.239682i
$238$	4.94846	+	3.25188i	0.320761	+	0.210788i
$239$	−3.40625	−	19.3178i	−0.220332	−	1.24957i	−0.871410	−	0.490555i	$-0.836794\pi$
$239$	−3.40625	−	19.3178i	−0.220332	−	1.24957i	0.651078	−	0.759011i	$-0.274317\pi$
$240$	−23.1897	+	18.2719i	−1.49689	+	1.17945i
$241$	−9.13377	−	7.66414i	−0.588358	−	0.493691i	0.299322	−	0.954152i	$-0.403240\pi$
$241$	−9.13377	−	7.66414i	−0.588358	−	0.493691i	−0.887680	+	0.460461i	$0.847684\pi$
$242$	−14.1700	−	3.35251i	−0.910882	−	0.215507i
$243$	2.00695	+	15.4587i	0.128746	+	0.991678i
$244$	−2.05280	+	4.09543i	−0.131417	+	0.262183i
$245$	15.6047	+	13.0939i	0.996945	+	0.836536i
$246$	−10.3534	−	2.16889i	−0.660110	−	0.138283i
$247$	4.47685	−	0.789389i	0.284855	−	0.0502276i
$248$	−15.0349	+	8.70394i	−0.954719	+	0.552701i
$249$	6.81423	+	5.42428i	0.431834	+	0.343750i
$250$	19.4572	−	45.1553i	1.23058	−	2.85587i
$251$	7.11140	+	4.10577i	0.448868	+	0.259154i	0.707352	−	0.706862i	$-0.249890\pi$
$251$	7.11140	+	4.10577i	0.448868	+	0.259154i	−0.258484	+	0.966016i	$0.583223\pi$
$252$	3.58780	−	8.18759i	0.226010	−	0.515770i
$253$	7.95260	−	4.59144i	0.499976	−	0.288661i
$254$	1.54103	+	13.1398i	0.0966927	+	0.824465i
$255$	−4.12810	−	20.3276i	−0.258512	−	1.27296i
$256$	6.38317	+	14.6716i	0.398948	+	0.916973i
$257$	−7.92624	−	9.44612i	−0.494425	−	0.589233i	0.459912	−	0.887964i	$-0.347881\pi$
$257$	−7.92624	−	9.44612i	−0.494425	−	0.589233i	−0.954337	+	0.298732i	$0.903436\pi$
$258$	3.13687	−	5.05304i	0.195293	−	0.314589i
$259$	−8.33500	+	3.03369i	−0.517912	+	0.188504i
$260$	37.4168	−	2.20862i	2.32049	−	0.136973i
$261$	−2.44844	−	1.84779i	−0.151555	−	0.114375i
$262$	19.7399	+	18.6091i	1.21954	+	1.14967i
$263$	−4.03911	+	22.9069i	−0.249062	+	1.41250i	0.561804	+	0.827270i	$0.310107\pi$
$263$	−4.03911	+	22.9069i	−0.249062	+	1.41250i	−0.810866	+	0.585231i	$0.801004\pi$
$264$	16.9200	−	14.9941i	1.04136	−	0.922825i
$265$	12.5954	+	4.58435i	0.773729	+	0.281614i
$266$	2.17425	+	0.125783i	0.133312	+	0.00771227i
$267$	2.99997	−	5.52053i	0.183595	−	0.337851i
$268$	7.50154	+	17.3532i	0.458229	+	1.06002i
$269$	−16.2085			−0.988253			−0.494126	−	0.869390i	$-0.664512\pi$
$269$	−16.2085			−0.988253			−0.494126	+	0.869390i	$0.664512\pi$
$270$	−29.2093	+	11.2870i	−1.77762	+	0.686902i
$271$		−	19.1260i		−	1.16182i	−0.813968	−	0.580909i	$-0.802697\pi$
$271$		−	19.1260i		−	1.16182i	0.813968	−	0.580909i	$-0.197303\pi$
$272$	−11.2233	−	0.636082i	−0.680512	−	0.0385681i
$273$	−9.67866	+	5.92631i	−0.585779	+	0.358677i
$274$	−29.3788	−	1.69960i	−1.77484	−	0.102677i
$275$	−20.7694	+	57.0634i	−1.25244	+	3.44105i
$276$	−0.617849	+	6.86539i	−0.0371901	+	0.413248i
$277$	31.5288	+	5.55937i	1.89438	+	0.334030i	0.994726	−	0.102571i	$-0.0327069\pi$
$277$	31.5288	+	5.55937i	1.89438	+	0.334030i	0.899655	+	0.436602i	$0.143818\pi$
$278$	1.02080	−	1.08283i	0.0612233	−	0.0649437i
$279$	−17.9571	+	4.13215i	−1.07507	+	0.247385i
$280$	17.6879	+	3.09748i	1.05706	+	0.185110i
$281$	2.24857	+	6.17789i	0.134138	+	0.368542i	0.988517	−	0.151109i	$-0.0482843\pi$
$281$	2.24857	+	6.17789i	0.134138	+	0.368542i	−0.854379	+	0.519651i	$0.826062\pi$
$282$	−5.36900	−	10.0264i	−0.319719	−	0.597062i
$283$	−13.4541	+	11.2893i	−0.799762	+	0.671080i	−0.948141	−	0.317851i	$-0.897039\pi$
$283$	−13.4541	+	11.2893i	−0.799762	+	0.671080i	0.148379	+	0.988931i	$0.452594\pi$
$284$	−8.63009	+	2.05249i	−0.512101	+	0.121793i
$285$	−5.05321	−	5.71575i	−0.299326	−	0.338572i
$286$	−28.5067	+	3.34325i	−1.68564	+	0.197691i
$287$	3.21700	+	5.57200i	0.189893	+	0.328905i
$288$	1.89291	+	16.8647i	0.111541	+	0.993760i
$289$	−4.55104	+	7.88262i	−0.267708	+	0.463684i
$290$	2.43839	−	5.65891i	0.143187	−	0.332303i
$291$	−3.51150	−	8.92385i	−0.205847	−	0.523125i
$292$	16.8149	+	17.7949i	0.984020	+	1.04137i
$293$	−3.90627	−	22.1536i	−0.228207	−	1.29423i	−0.856459	−	0.516215i	$-0.827340\pi$
$293$	−3.90627	−	22.1536i	−0.228207	−	1.29423i	0.628252	−	0.778010i	$-0.283771\pi$
$294$	11.1255	−	3.65111i	0.648854	−	0.212937i
$295$	−22.2207	+	26.4816i	−1.29374	+	1.54182i
$296$	10.8088	−	12.9122i	0.628250	−	0.750504i
$297$	21.8308	−	9.92049i	1.26675	−	0.575645i
$298$	1.35536	+	0.320667i	0.0785139	+	0.0185757i
$299$	5.62524	−	6.70390i	0.325316	−	0.387696i
$300$	−26.0528	−	37.4049i	−1.50416	−	2.15957i
$301$	−3.56254	+	0.628171i	−0.205341	+	0.0362072i
$302$	9.60782	−	14.6204i	0.552868	−	0.841311i
$303$	10.2739	+	1.53921i	0.590218	+	0.0884253i
$304$	−3.69191	+	1.86138i	−0.211746	+	0.106757i
$305$	−8.45309	−	4.88039i	−0.484022	−	0.279450i
$306$	−11.1789	−	4.14675i	−0.639054	−	0.237054i
$307$	−12.6479	−	21.9068i	−0.721854	−	1.25029i	−0.960256	−	0.279122i	$-0.909957\pi$
$307$	−12.6479	−	21.9068i	−0.721854	−	1.25029i	0.238401	−	0.971167i	$-0.423377\pi$
$308$	−13.6591	−	1.58570i	−0.778299	−	0.0903536i
$309$	2.49155	+	0.834655i	0.141739	+	0.0474819i
$310$	−16.6253	−	33.0715i	−0.944254	−	1.87833i
$311$	21.8726	−	18.3533i	1.24028	−	1.04072i	0.242782	−	0.970081i	$-0.421940\pi$
$311$	21.8726	−	18.3533i	1.24028	−	1.04072i	0.997502	−	0.0706412i	$-0.0225045\pi$
$312$	10.2651	−	18.9427i	0.581148	−	1.07242i
$313$	−13.8017	+	5.02339i	−0.780116	+	0.283939i	−0.701221	−	0.712944i	$-0.747361\pi$
$313$	−13.8017	+	5.02339i	−0.780116	+	0.283939i	−0.0788947	+	0.996883i	$0.525139\pi$
$314$	−25.3909	+	7.61235i	−1.43289	+	0.429590i
$315$	16.9642	+	8.65906i	0.955826	+	0.487883i
$316$	−3.76377	−	5.71280i	−0.211729	−	0.321370i
$317$	1.05728	−	5.99616i	0.0593830	−	0.336778i	−0.940613	−	0.339480i	$-0.889749\pi$
$317$	1.05728	−	5.99616i	0.0593830	−	0.336778i	0.999996	+	0.00270208i	$0.000860098\pi$
$318$	6.05743	−	4.76133i	0.339684	−	0.267002i
$319$	−1.61384	+	4.43398i	−0.0903574	+	0.248255i
$320$	−32.0073	+	11.7347i	−1.78926	+	0.655992i
$321$	6.65225	−	0.171805i	0.371292	−	0.00958922i
$322$	3.36204	−	2.50499i	0.187359	−	0.139597i
$323$		−	2.90490i		−	0.161633i
$324$	−3.34329	+	17.6868i	−0.185738	+	0.982599i
$325$			57.8717i			3.21014i
$326$	−8.35971	−	11.2199i	−0.463002	−	0.621412i
$327$	0.136911	−	0.00353594i	0.00757119	−	0.000195538i
$328$	−10.5853	−	6.09489i	−0.584475	−	0.336534i
$329$	−2.36599	+	6.50051i	−0.130441	+	0.358385i
$330$	29.7676	+	37.8708i	1.63865	+	2.08472i
$331$	2.68280	−	15.2149i	0.147460	−	0.836286i	−0.817899	−	0.575361i	$-0.804861\pi$
$331$	2.68280	−	15.2149i	0.147460	−	0.836286i	0.965359	−	0.260925i	$-0.0840275\pi$
$332$	5.53295	+	8.39813i	0.303660	+	0.460907i
$333$	14.9861	−	9.71679i	0.821233	−	0.532477i
$334$	9.67810	+	32.2812i	0.529562	+	1.76635i
$335$	−37.8514	+	13.7768i	−2.06804	+	0.752706i
$336$	6.87521	−	7.69914i	0.375073	−	0.420023i
$337$	1.94751	−	1.63416i	0.106088	−	0.0890183i	−0.588201	−	0.808715i	$-0.700164\pi$
$337$	1.94751	−	1.63416i	0.106088	−	0.0890183i	0.694289	+	0.719697i	$0.255719\pi$
$338$	−8.01293	+	4.02817i	−0.435846	+	0.219103i
$339$	−22.6120	−	7.57490i	−1.22812	−	0.411412i
$340$	2.76200	−	23.7916i	0.149790	−	1.29028i
$341$	14.1724	+	24.5473i	0.767477	+	1.32931i
$342$	−4.32338	+	0.734965i	−0.233782	+	0.0397423i
$343$	−15.1997	−	8.77552i	−0.820704	−	0.473834i
$344$	5.25573	−	4.42059i	0.283370	−	0.238342i
$345$	−14.5249	−	2.17609i	−0.781992	−	0.117157i
$346$	20.1490	+	13.2409i	1.08322	+	0.711836i
$347$	−9.54409	+	1.68288i	−0.512354	+	0.0903418i	−0.423847	−	0.905734i	$-0.639321\pi$
$347$	−9.54409	+	1.68288i	−0.512354	+	0.0903418i	−0.0885067	+	0.996076i	$0.528209\pi$
$348$	−2.02438	−	2.90646i	−0.108518	−	0.155803i
$349$	−2.08774	+	2.48808i	−0.111754	+	0.133184i	−0.819022	−	0.573762i	$-0.805483\pi$
$349$	−2.08774	+	2.48808i	−0.111754	+	0.133184i	0.707267	+	0.706946i	$0.249928\pi$
$350$	−6.38342	+	26.9807i	−0.341208	+	1.44218i
$351$	16.3166	−	15.9998i	0.870916	−	0.854005i
$352$	23.9500	−	10.3866i	1.27654	−	0.553606i
$353$	−13.0109	+	15.5058i	−0.692500	+	0.825289i	−0.991656	−	0.128915i	$-0.958850\pi$
$353$	−13.0109	+	15.5058i	−0.692500	+	0.825289i	0.299156	+	0.954204i	$0.403295\pi$
$354$	6.19605	+	18.8804i	0.329316	+	1.00348i
$355$	−3.28207	−	18.6135i	−0.174194	−	0.987904i
$356$	5.27319	−	4.98279i	0.279478	−	0.264087i
$357$	2.65548	+	6.74843i	0.140543	+	0.357165i
$358$	14.6626	+	6.31802i	0.774941	+	0.333918i
$359$	4.72922	−	8.19125i	0.249599	−	0.432318i	−0.713816	−	0.700333i	$-0.753035\pi$
$359$	4.72922	−	8.19125i	0.249599	−	0.432318i	0.963414	+	0.268016i	$0.0863680\pi$
$360$	−36.1081	+	1.90879i	−1.90307	+	0.100602i
$361$	8.96578	+	15.5292i	0.471883	+	0.817326i
$362$	0.915080	+	7.80256i	0.0480955	+	0.410094i
$363$	−11.8122	−	13.3609i	−0.619980	−	0.701267i
$364$	−12.7490	+	3.03209i	−0.668228	+	0.158925i
$365$	−39.9602	+	33.5306i	−2.09161	+	1.75507i
$366$	−4.94617	+	2.64861i	−0.258541	+	0.138445i
$367$	8.44113	+	23.1918i	0.440623	+	1.21060i	0.939083	+	0.343690i	$0.111677\pi$
$367$	8.44113	+	23.1918i	0.440623	+	1.21060i	−0.498460	+	0.866913i	$0.666101\pi$
$368$	−3.14117	+	7.31347i	−0.163745	+	0.381241i
$369$	−8.82885	−	9.48142i	−0.459611	−	0.493583i
$370$	26.1066	+	24.6111i	1.35722	+	1.27947i
$371$	−4.61508	−	0.813763i	−0.239603	−	0.0422485i
$372$	−21.1914	−	1.90711i	−1.09872	−	0.0988791i
$373$	10.2604	−	28.1901i	0.531262	−	1.45963i	−0.326308	−	0.945263i	$-0.605805\pi$
$373$	10.2604	−	28.1901i	0.531262	−	1.45963i	0.857570	−	0.514367i	$-0.171973\pi$
$374$	−1.05928	+	18.3104i	−0.0547741	+	0.946809i
$375$	51.3568	−	31.4461i	2.65205	−	1.62387i
$376$	−2.29566	−	12.9307i	−0.118390	−	0.666849i
$377$			4.49679i			0.231596i
$378$	9.37190	−	5.65959i	0.482038	−	0.291098i
$379$	20.4012			1.04794			0.523968	−	0.851738i	$-0.324451\pi$
$379$	20.4012			1.04794			0.523968	+	0.851738i	$0.324451\pi$
$380$	−3.49556	−	8.08625i	−0.179319	−	0.414816i
$381$	−7.73662	+	14.2369i	−0.396359	+	0.729378i
$382$	0.179555	−	3.10374i	0.00918685	−	0.158801i
$383$	−11.0572	−	4.02450i	−0.564998	−	0.205642i	0.0436999	−	0.999045i	$-0.486085\pi$
$383$	−11.0572	−	4.02450i	−0.564998	−	0.205642i	−0.608697	+	0.793402i	$0.708308\pi$
$384$	−3.97286	+	19.1890i	−0.202739	+	0.979233i
$385$	5.08761	−	28.8533i	0.259289	−	1.47050i
$386$	1.96949	−	2.08917i	0.100244	−	0.106336i
$387$	6.70720	−	2.84135i	0.340946	−	0.144434i
$388$	−0.652502	−	11.0542i	−0.0331258	−	0.561191i
$389$	−18.5353	+	6.74631i	−0.939779	+	0.342052i	−0.766079	−	0.642747i	$-0.777795\pi$
$389$	−18.5353	+	6.74631i	−0.939779	+	0.342052i	−0.173701	+	0.984799i	$0.555573\pi$
$390$	39.0017	+	24.2118i	1.97493	+	1.22601i
$391$	−3.59460	−	4.28388i	−0.181787	−	0.216645i
$392$	13.5207	−	0.0158501i	0.682900	−	0.000800552i
$393$	6.61244	+	32.5610i	0.333553	+	1.64249i
$394$	5.25625	−	0.616449i	0.264806	−	0.0310563i
$395$	12.6234	−	7.28815i	0.635155	−	0.366707i
$396$	27.5196	−	3.05616i	1.38291	−	0.153578i
$397$	−22.2665	−	12.8556i	−1.11752	−	0.645202i	−0.176755	−	0.984255i	$-0.556560\pi$
$397$	−22.2665	−	12.8556i	−1.11752	−	0.645202i	−0.940767	+	0.339053i	$0.889893\pi$
$398$	−6.97023	−	3.00343i	−0.349386	−	0.150548i
$399$	2.08690	+	1.66122i	0.104476	+	0.0831649i
$400$	−15.1748	−	50.4007i	−0.758742	−	2.52003i
$401$	9.57894	−	1.68903i	0.478350	−	0.0843459i	0.0707256	−	0.997496i	$-0.477469\pi$
$401$	9.57894	−	1.68903i	0.478350	−	0.0843459i	0.407624	+	0.913150i	$0.366357\pi$
$402$	−4.74738	+	22.6622i	−0.236778	+	1.13029i
$403$	20.6929	+	17.3634i	1.03079	+	0.864932i
$404$	10.7239	+	5.37525i	0.533534	+	0.267429i
$405$	−37.1993	−	9.33161i	−1.84845	−	0.463691i
$406$	−0.496009	+	2.09648i	−0.0246165	+	0.104046i
$407$	−21.0465	−	17.6601i	−1.04324	−	0.875379i
$408$	−10.7817	−	8.56185i	−0.533774	−	0.423875i
$409$	−4.65112	−	26.3778i	−0.229983	−	1.30430i	−0.852927	−	0.522031i	$-0.825175\pi$
$409$	−4.65112	−	26.3778i	−0.229983	−	1.30430i	0.622944	−	0.782267i	$-0.285937\pi$
$410$	14.2926	−	21.7493i	0.705860	−	1.07412i
$411$	−28.1985	−	22.4466i	−1.39093	−	1.10721i
$412$	2.43516	+	1.80995i	0.119972	+	0.0891701i
$413$	6.04314	−	10.4670i	0.297363	−	0.515048i
$414$	−5.46627	+	6.43374i	−0.268652	+	0.316201i
$415$	−18.5572	+	10.7140i	−0.910935	+	0.525929i
$416$	18.0625	−	17.1079i	0.885586	−	0.838783i
$417$	1.78613	−	0.362724i	0.0874670	−	0.0177627i
$418$	3.02992	+	6.02719i	0.148198	+	0.294800i
$419$	−19.9068	−	23.7240i	−0.972513	−	1.15900i	−0.987262	−	0.159104i	$-0.949139\pi$
$419$	−19.9068	−	23.7240i	−0.972513	−	1.15900i	0.0147490	−	0.999891i	$-0.495305\pi$
$420$	15.5126	+	15.5899i	0.756937	+	0.760710i
$421$	2.69119	+	7.39397i	0.131160	+	0.360360i	0.987837	−	0.155494i	$-0.0496969\pi$
$421$	2.69119	+	7.39397i	0.131160	+	0.360360i	−0.856676	+	0.515854i	$0.827475\pi$
$422$	−8.44737	−	28.1761i	−0.411212	−	1.37159i
$423$	1.70751	−	13.8245i	0.0830220	−	0.672169i
$424$	8.35654	−	3.05263i	0.405830	−	0.148249i
$425$	36.4190	+	6.42164i	1.76658	+	0.311495i
$426$	−10.0853	−	4.04026i	−0.488634	−	0.195751i
$427$	3.20680	+	1.16718i	0.155188	+	0.0564838i
$428$	7.36283	+	2.19802i	0.355896	+	0.106245i
$429$	−30.8868	−	16.7845i	−1.49123	−	0.810366i
$430$	8.74256	+	11.7337i	0.421604	+	0.565850i
$431$	14.2911			0.688376			0.344188	−	0.938901i	$-0.388154\pi$
$431$	14.2911			0.688376			0.344188	+	0.938901i	$0.388154\pi$
$432$	−10.0148	+	18.2127i	−0.481838	+	0.876260i
$433$	7.63072			0.366709			0.183354	−	0.983047i	$-0.441304\pi$
$433$	7.63072			0.366709			0.183354	+	0.983047i	$0.441304\pi$
$434$	7.73213	+	10.3776i	0.371154	+	0.498140i
$435$	6.43609	−	3.94086i	0.308587	−	0.188950i
$436$	0.151535	+	0.0452377i	0.00725723	+	0.00216649i
$437$	−1.93280	−	0.703481i	−0.0924582	−	0.0336520i
$438$	4.26040	+	29.6808i	0.203570	+	1.41820i
$439$	23.4363	+	4.13245i	1.11855	+	0.197231i	0.702206	−	0.711974i	$-0.252199\pi$
$439$	23.4363	+	4.13245i	1.11855	+	0.197231i	0.416348	+	0.909205i	$0.363310\pi$
$440$	19.0849	+	52.2447i	0.909837	+	2.49067i
$441$	13.7113	+	4.20273i	0.652918	+	0.200130i
$442$	5.01960	+	16.7428i	0.238758	+	0.796374i
$443$	−3.05225	−	8.38600i	−0.145017	−	0.398431i	0.845824	−	0.533461i	$-0.179109\pi$
$443$	−3.05225	−	8.38600i	−0.145017	−	0.398431i	−0.990841	+	0.135030i	$0.956887\pi$
$444$	19.9341	−	5.28823i	0.946028	−	0.250968i
$445$	9.93615	+	11.8414i	0.471019	+	0.561338i
$446$	0.432762	+	0.860860i	0.0204919	+	0.0407629i
$447$	1.12984	+	1.27797i	0.0534394	+	0.0604460i
$448$	10.3081	−	5.98364i	0.487011	−	0.282700i
$449$	−14.0779	+	8.12787i	−0.664377	+	0.383578i	−0.793943	−	0.607993i	$-0.791975\pi$
$449$	−14.0779	+	8.12787i	−0.664377	+	0.383578i	0.129566	+	0.991571i	$0.458642\pi$
$450$	0.343073	−	55.8274i	0.0161726	−	2.63173i
$451$	−9.96452	+	17.2591i	−0.469211	+	0.812697i
$452$	−22.1003	−	16.4262i	−1.03951	−	0.772624i
$453$	19.9385	−	7.84573i	0.936794	−	0.368624i
$454$	−17.9679	+	27.3421i	−0.843273	+	1.28323i
$455$	−4.84851	−	27.4973i	−0.227302	−	1.28909i
$456$	−5.00882	−	0.744410i	−0.234560	−	0.0348602i
$457$	−14.7151	−	12.3474i	−0.688344	−	0.577589i	0.230087	−	0.973170i	$-0.426099\pi$
$457$	−14.7151	−	12.3474i	−0.688344	−	0.577589i	−0.918431	+	0.395581i	$0.870543\pi$
$458$	9.14154	−	38.6385i	0.427156	−	1.80546i
$459$	−8.25819	−	12.0435i	−0.385459	−	0.562143i
$460$	−15.1611	−	7.59936i	−0.706890	−	0.354322i
$461$	20.6273	+	17.3084i	0.960710	+	0.806132i	0.981068	−	0.193661i	$-0.0620362\pi$
$461$	20.6273	+	17.3084i	0.960710	+	0.806132i	−0.0203582	+	0.999793i	$0.506481\pi$
$462$	−12.5486	−	11.2321i	−0.583812	−	0.522567i
$463$	21.4454	−	3.78140i	0.996652	−	0.175737i	0.348550	−	0.937290i	$-0.386674\pi$
$463$	21.4454	−	3.78140i	0.996652	−	0.175737i	0.648102	+	0.761554i	$0.275563\pi$
$464$	−1.17913	−	3.91627i	−0.0547396	−	0.181808i
$465$	6.71691	−	44.8338i	0.311489	−	2.07912i
$466$	2.00457	+	0.863758i	0.0928599	+	0.0400128i
$467$	12.1934	+	7.03986i	0.564243	+	0.325766i	0.754847	−	0.655901i	$-0.227711\pi$
$467$	12.1934	+	7.03986i	0.564243	+	0.325766i	−0.190604	+	0.981667i	$0.561044\pi$
$468$	23.6485	−	11.7068i	1.09315	−	0.541147i
$469$	12.1963	−	7.04155i	0.563174	−	0.325148i
$470$	27.7913	−	3.25934i	1.28192	−	0.150342i
$471$	−30.7835	−	10.3123i	−1.41843	−	0.475166i
$472$	0.0268982	+	22.9451i	0.00123809	+	1.05614i
$473$	−7.20247	−	8.58357i	−0.331170	−	0.394673i
$474$	0.267789	−	8.37445i	0.0123000	−	0.384651i
$475$	12.7814	−	4.65206i	0.586452	−	0.213451i
$476$	0.493438	+	8.35945i	0.0226167	+	0.383155i
$477$	9.42374	−	0.487091i	0.431483	−	0.0223024i
$478$	19.0291	−	20.1855i	0.870372	−	0.923263i
$479$	6.31561	−	35.8176i	0.288567	−	1.63655i	−0.403690	−	0.914896i	$-0.632272\pi$
$479$	6.31561	−	35.8176i	0.288567	−	1.63655i	0.692257	−	0.721651i	$-0.256616\pi$
$480$	−40.3154	−	10.8593i	−1.84014	−	0.495656i
$481$	−24.6040	−	8.95513i	−1.12185	−	0.408319i
$482$	0.973865	−	16.8339i	0.0443583	−	0.766765i
$483$	5.13321	−	0.132573i	0.233569	−	0.00603229i
$484$	−8.17110	−	18.9021i	−0.371414	−	0.859187i
$485$	23.5937			1.07134
$486$	−15.8351	+	15.3379i	−0.718294	+	0.695740i
$487$		−	9.85092i		−	0.446388i	−0.974774	−	0.223194i	$-0.928352\pi$
$487$		−	9.85092i		−	0.446388i	0.974774	−	0.223194i	$-0.0716483\pi$
$488$	−6.37891	+	1.13249i	−0.288760	+	0.0512652i
$489$	−0.442427	−	17.1307i	−0.0200072	−	0.774676i
$490$	−1.66381	+	28.7601i	−0.0751631	+	1.29925i
$491$	10.0967	−	27.7405i	0.455659	−	1.25191i	−0.473027	−	0.881048i	$-0.656839\pi$
$491$	10.0967	−	27.7405i	0.455659	−	1.25191i	0.928687	−	0.370865i	$-0.120939\pi$
$492$	−6.28854	−	13.5738i	−0.283509	−	0.611955i
$493$	2.82985	+	0.498979i	0.127450	+	0.0224729i
$494$	4.67793	+	4.40994i	0.210470	+	0.198413i
$495$	3.04527	+	58.9168i	0.136875	+	2.64811i
$496$	−22.5745	−	9.69585i	−1.01362	−	0.435356i
$497$	2.26012	+	6.20962i	0.101380	+	0.278540i
$498$	−0.393665	+	12.3109i	−0.0176405	+	0.551665i
$499$	−22.3305	+	18.7375i	−0.999652	+	0.838808i	−0.986936	−	0.161112i	$-0.948492\pi$
$499$	−22.3305	+	18.7375i	−0.999652	+	0.838808i	−0.0127158	+	0.999919i	$0.504048\pi$
$500$	67.6485	−	16.0888i	3.02533	−	0.719515i
$501$	−13.1107	+	39.1372i	−0.585745	+	1.74852i
$502$	1.35268	+	11.5338i	0.0603730	+	0.514780i
$503$	10.0189	+	17.3533i	0.446721	+	0.773743i	0.998170	−	0.0604650i	$-0.0192584\pi$
$503$	10.0189	+	17.3533i	0.446721	+	0.773743i	−0.551449	+	0.834208i	$0.685925\pi$
$504$	12.3166	−	2.84940i	0.548625	−	0.126923i
$505$	−12.7793	+	22.1344i	−0.568672	+	0.984969i
$506$	11.9265	+	5.13905i	0.530196	+	0.228459i
$507$	−10.8628	−	1.62745i	−0.482435	−	0.0722776i
$508$	−13.5990	+	12.8501i	−0.603359	+	0.570132i
$509$	3.92993	+	22.2877i	0.174191	+	0.987886i	0.939074	+	0.343716i	$0.111686\pi$
$509$	3.92993	+	22.2877i	0.174191	+	0.987886i	−0.764883	+	0.644170i	$0.777203\pi$
$510$	19.5643	−	21.8573i	0.866324	−	0.967858i
$511$	11.7231	−	13.9711i	0.518600	−	0.618043i
$512$	−11.2447	+	19.6356i	−0.496951	+	0.867778i
$513$	−4.84530	−	2.31750i	−0.213925	−	0.102320i
$514$	4.01501	−	16.9702i	0.177095	−	0.748525i
$515$	−4.15544	+	4.95226i	−0.183110	+	0.218222i
$516$	8.38088	−	0.712238i	0.368948	−	0.0313545i
$517$	−21.1018	+	3.72081i	−0.928055	+	0.163641i
$518$	−10.4830	−	6.88893i	−0.460598	−	0.302682i
$519$	10.8125	+	27.4781i	0.474616	+	1.20615i
$520$	34.1201	+	40.5661i	1.49626	+	1.77894i
$521$	−0.870834	−	0.502776i	−0.0381519	−	0.0220270i	0.480803	−	0.876829i	$-0.340345\pi$
$521$	−0.870834	−	0.502776i	−0.0381519	−	0.0220270i	−0.518955	+	0.854802i	$0.673679\pi$
$522$	0.0266577	−	4.33794i	0.00116678	−	0.189866i
$523$	14.5895	+	25.2698i	0.637955	+	1.10497i	0.985881	+	0.167448i	$0.0535528\pi$
$523$	14.5895	+	25.2698i	0.637955	+	1.10497i	−0.347926	+	0.937522i	$0.613114\pi$
$524$	−4.42420	+	38.1097i	−0.193272	+	1.66483i
$525$	−25.4402	+	22.4913i	−1.11030	+	0.981601i
$526$	−29.3903	+	14.7747i	−1.28148	+	0.644210i
$527$	13.2230	−	11.0954i	0.576004	−	0.483325i
$528$	31.3006	+	6.51872i	1.36219	+	0.283691i
$529$	17.8921	−	6.51220i	0.777918	−	0.283139i
$530$	5.44367	+	18.1573i	0.236458	+	0.788702i
$531$	−7.13216	+	23.2685i	−0.309510	+	1.00977i
$532$	1.69450	+	2.57198i	0.0734658	+	0.111509i
$533$	−3.29800	+	18.7039i	−0.142852	+	0.810156i
$534$	8.79535	−	1.26249i	0.380612	−	0.0546333i
$535$	−5.59950	+	15.3845i	−0.242087	+	0.665130i
$536$	−13.3409	+	23.1697i	−0.576237	+	1.00078i
$537$	10.2110	+	16.6763i	0.440637	+	0.719635i
$538$	−13.6955	−	18.3812i	−0.590453	−	0.792470i
$539$		−	22.0601i		−	0.950197i
$540$	−37.4804	−	23.5877i	−1.61290	−	1.01505i
$541$			16.9478i			0.728644i	0.931273	+	0.364322i	$0.118699\pi$
$541$			16.9478i			0.728644i	−0.931273	+	0.364322i	$0.881301\pi$
$542$	21.6897	−	16.1605i	0.931651	−	0.694154i
$543$	−4.59409	+	8.45402i	−0.197151	+	0.362797i
$544$	−8.76181	−	13.2652i	−0.375659	−	0.568739i
$545$	−0.115244	+	0.316630i	−0.00493651	+	0.0135630i
$546$	−14.8987	−	5.96857i	−0.637606	−	0.255431i
$547$	1.00315	−	5.68915i	0.0428916	−	0.243250i	−0.955823	−	0.293944i	$-0.905032\pi$
$547$	1.00315	−	5.68915i	0.0428916	−	0.243250i	0.998714	+	0.0506936i	$0.0161432\pi$
$548$	−22.8963	−	34.7529i	−0.978081	−	1.48457i
$549$	−6.81983	−	0.842342i	−0.291063	−	0.0359503i
$550$	−82.2615	+	24.6625i	−3.50764	+	1.05161i
$551$	0.993151	−	0.361477i	0.0423096	−	0.0153995i
$552$	−8.30771	+	5.10027i	−0.353600	+	0.217082i
$553$	−3.90394	+	3.27579i	−0.166012	+	0.139301i
$554$	20.3358	+	40.4524i	0.863984	+	1.71866i
$555$	8.74514	+	43.0629i	0.371211	+	1.82792i
$556$	2.09050	+	0.242688i	0.0886569	+	0.0102923i
$557$	6.09737	+	10.5610i	0.258354	+	0.447482i	0.965801	−	0.259284i	$-0.0834866\pi$
$557$	6.09737	+	10.5610i	0.258354	+	0.447482i	−0.707447	+	0.706766i	$0.750153\pi$
$558$	−19.8590	−	16.8727i	−0.840698	−	0.714279i
$559$	−9.24781	−	5.33923i	−0.391141	−	0.225825i
$560$	11.4328	+	22.6761i	0.483124	+	0.958241i
$561$	−13.9899	+	17.5748i	−0.590655	+	0.742008i
$562$	−5.10606	+	7.77000i	−0.215386	+	0.327758i
$563$	10.5639	−	1.86270i	0.445214	−	0.0785033i	0.0534534	−	0.998570i	$-0.482977\pi$
$563$	10.5639	−	1.86270i	0.445214	−	0.0785033i	0.391761	+	0.920067i	$0.371866\pi$
$564$	6.83380	−	14.5605i	0.287755	−	0.613108i
$565$	37.7126	−	44.9441i	1.58658	−	1.89081i
$566$	−24.1706	−	5.71857i	−1.01597	−	0.240369i
$567$	13.3748	+	0.954560i	0.561687	+	0.0400878i
$568$	−9.61963	−	8.05263i	−0.403631	−	0.337881i
$569$	23.2358	−	27.6913i	0.974094	−	1.16088i	−0.0128670	−	0.999917i	$-0.504096\pi$
$569$	23.2358	−	27.6913i	0.974094	−	1.16088i	0.986961	−	0.160962i	$-0.0514597\pi$
$570$	2.21218	−	10.5601i	0.0926582	−	0.442314i
$571$	4.57114	+	25.9242i	0.191296	+	1.08490i	0.917595	+	0.397516i	$0.130128\pi$
$571$	4.57114	+	25.9242i	0.191296	+	1.08490i	−0.726299	+	0.687379i	$0.758761\pi$
$572$	−27.8783	−	29.5030i	−1.16565	−	1.23358i
$573$	2.37138	−	2.97904i	0.0990660	−	0.124451i
$574$	−3.60068	+	8.35629i	−0.150289	+	0.348785i
$575$	13.0923	−	22.6765i	0.545987	−	0.945676i
$576$	−17.5258	+	16.3965i	−0.730244	+	0.683187i
$577$	−21.6322	−	37.4681i	−0.900562	−	1.55982i	−0.826766	−	0.562546i	$-0.809822\pi$
$577$	−21.6322	−	37.4681i	−0.900562	−	1.55982i	−0.0737957	−	0.997273i	$-0.523511\pi$
$578$	−12.7846	+	1.49938i	−0.531771	+	0.0623658i
$579$	3.44609	−	0.699827i	0.143215	−	0.0290838i
$580$	8.47778	−	2.01627i	0.352021	−	0.0837211i
$581$	5.73900	−	4.81560i	0.238094	−	0.199785i
$582$	7.15298	−	11.5224i	0.296501	−	0.477620i
$583$	−4.96461	−	13.6402i	−0.205613	−	0.564918i
$584$	−5.97237	+	34.1047i	−0.247138	+	1.41126i
$585$	21.9308	+	51.7692i	0.906729	+	2.14039i
$586$	21.8225	−	23.1486i	0.901479	−	0.956260i
$587$	12.1230	+	2.13761i	0.500370	+	0.0882287i	0.418136	−	0.908384i	$-0.362684\pi$
$587$	12.1230	+	2.13761i	0.500370	+	0.0882287i	0.0822336	+	0.996613i	$0.473795\pi$
$588$	13.5411	+	9.53182i	0.558424	+	0.393086i
$589$	2.17143	−	5.96596i	0.0894722	−	0.245823i
$590$	−48.8068	−	2.82353i	−2.00934	−	0.116243i
$591$	5.69510	+	3.09484i	0.234265	+	0.127305i
$592$	23.7759	+	1.34750i	0.977183	+	0.0553820i
$593$		−	15.7162i		−	0.645387i	−0.946504	−	0.322693i	$-0.895412\pi$
$593$		−	15.7162i		−	0.645387i	0.946504	−	0.322693i	$-0.104588\pi$
$594$	29.6963	+	16.3747i	1.21845	+	0.671864i
$595$	−17.8422			−0.731458
$596$	0.781566	+	1.80799i	0.0320142	+	0.0740580i
$597$	−4.85406	−	7.92749i	−0.198663	−	0.324451i
$598$	12.3556	+	0.714786i	0.505257	+	0.0292298i
$599$	−36.3559	−	13.2324i	−1.48546	−	0.540663i	−0.533210	−	0.845983i	$-0.679014\pi$
$599$	−36.3559	−	13.2324i	−1.48546	−	0.540663i	−0.952250	+	0.305320i	$0.901237\pi$
$600$	20.4054	−	61.1504i	0.833046	−	2.49646i
$601$	−1.65205	+	9.36926i	−0.0673887	+	0.382180i	0.932396	+	0.361438i	$0.117714\pi$
$601$	−1.65205	+	9.36926i	−0.0673887	+	0.382180i	−0.999785	+	0.0207422i	$0.993397\pi$
$602$	−3.72255	−	3.50930i	−0.151720	−	0.143028i
$603$	−20.7535	+	19.3251i	−0.845147	+	0.786978i
$604$	24.6983	−	1.45788i	1.00496	−	0.0593204i
$605$	41.2299	−	15.0065i	1.67623	−	0.610099i
$606$	6.93540	+	12.9516i	0.281731	+	0.526121i
$607$	−3.82679	−	4.56060i	−0.155325	−	0.185109i	0.682770	−	0.730633i	$-0.260775\pi$
$607$	−3.82679	−	4.56060i	−0.155325	−	0.185109i	−0.838095	+	0.545524i	$0.816331\pi$
$608$	−5.23038	−	2.61401i	−0.212120	−	0.106012i
$609$	−1.97677	+	1.74763i	−0.0801028	+	0.0708177i
$610$	−1.60788	−	13.7099i	−0.0651013	−	0.555096i
$611$	−17.6845	+	10.2101i	−0.715438	+	0.413058i
$612$	−4.74303	−	16.1811i	−0.191726	−	0.654084i
$613$	−26.9850	−	15.5798i	−1.08991	−	0.629261i	−0.156359	−	0.987700i	$-0.549976\pi$
$613$	−26.9850	−	15.5798i	−1.08991	−	0.629261i	−0.933553	+	0.358439i	$0.883309\pi$
$614$	14.1564	−	32.8535i	0.571306	−	1.32586i
$615$	29.6605	−	11.6713i	1.19603	−	0.470632i
$616$	−9.74304	−	16.8298i	−0.392558	−	0.678094i
$617$	−3.66800	+	0.646768i	−0.147668	+	0.0260379i	−0.246994	−	0.969017i	$-0.579443\pi$
$617$	−3.66800	+	0.646768i	−0.147668	+	0.0260379i	0.0993254	+	0.995055i	$0.468332\pi$
$618$	1.15871	+	3.53077i	0.0466100	+	0.142028i
$619$	3.75932	+	3.15444i	0.151100	+	0.126788i	0.715204	−	0.698916i	$-0.246334\pi$
$619$	3.75932	+	3.15444i	0.151100	+	0.126788i	−0.564104	+	0.825704i	$0.690778\pi$
$620$	23.4569	−	46.7977i	0.942051	−	1.87944i
$621$	−10.0131	+	2.57807i	−0.401814	+	0.103454i
$622$	39.2948	+	9.29683i	1.57558	+	0.372769i
$623$	−4.14006	−	3.47392i	−0.165868	−	0.139180i
$624$	30.1554	−	4.36462i	1.20718	−	0.174724i
$625$	14.3020	+	81.1107i	0.572080	+	3.24443i
$626$	−17.3585	−	11.4071i	−0.693785	−	0.455921i
$627$	−1.22414	+	8.17084i	−0.0488875	+	0.326312i
$628$	−30.0868	−	22.3623i	−1.20060	−	0.892353i
$629$	−8.36566	+	14.4897i	−0.333561	+	0.577744i
$630$	4.51423	+	26.5547i	0.179851	+	1.05796i
$631$	−6.82322	+	3.93939i	−0.271628	+	0.156825i	−0.629627	−	0.776897i	$-0.716792\pi$
$631$	−6.82322	+	3.93939i	−0.271628	+	0.156825i	0.357999	+	0.933722i	$0.383459\pi$
$632$	3.29836	−	9.09533i	0.131202	−	0.361793i
$633$	11.4435	−	34.1602i	0.454838	−	1.35775i
$634$	7.69326	−	3.86746i	0.305538	−	0.153597i
$635$	−25.6243	−	30.5379i	−1.01687	−	1.21186i
$636$	10.5178	+	2.84629i	0.417058	+	0.112863i
$637$	−7.19042	−	19.7555i	−0.284895	−	0.782742i
$638$	−6.39194	+	1.91634i	−0.253059	+	0.0758687i
$639$	−7.23906	−	11.1647i	−0.286373	−	0.441670i
$640$	−40.3523	−	26.3823i	−1.59507	−	1.04285i
$641$	−31.6909	−	5.58797i	−1.25172	−	0.220711i	−0.491786	−	0.870716i	$-0.663656\pi$
$641$	−31.6909	−	5.58797i	−1.25172	−	0.220711i	−0.759930	+	0.650005i	$0.774767\pi$
$642$	5.81567	+	7.39877i	0.229526	+	0.292006i
$643$	30.3155	+	11.0340i	1.19553	+	0.435137i	0.861661	−	0.507483i	$-0.169424\pi$
$643$	30.3155	+	11.0340i	1.19553	+	0.435137i	0.333867	+	0.942620i	$0.391646\pi$
$644$	5.68153	+	1.69610i	0.223884	+	0.0668357i
$645$	0.462689	+	17.9152i	0.0182184	+	0.705411i
$646$	3.29428	−	2.45450i	0.129612	−	0.0965710i
$647$	−27.3194			−1.07404			−0.537018	−	0.843571i	$-0.680449\pi$
$647$	−27.3194			−1.07404			−0.537018	+	0.843571i	$0.680449\pi$
$648$	−22.8825	+	11.1531i	−0.898910	+	0.438134i
$649$	37.4368			1.46952
$650$	−65.6290	+	48.8989i	−2.57418	+	1.91797i
$651$	0.409213	+	15.8446i	0.0160383	+	0.621001i
$652$	5.66027	−	18.9606i	0.221673	−	0.742552i
$653$	36.1219	+	13.1473i	1.41356	+	0.514494i	0.932172	−	0.362015i	$-0.117911\pi$
$653$	36.1219	+	13.1473i	1.41356	+	0.514494i	0.481387	+	0.876508i	$0.340133\pi$
$654$	0.119693	+	0.152275i	0.00468037	+	0.00595443i
$655$	−80.5025	−	14.1948i	−3.14549	−	0.554635i
$656$	−2.03221	−	17.1541i	−0.0793444	−	0.669755i
$657$	−16.6958	+	32.7093i	−0.651367	+	1.27611i
$658$	−9.37101	+	2.80949i	−0.365320	+	0.109525i
$659$	3.90831	+	10.7380i	0.152246	+	0.418293i	0.992245	−	0.124295i	$-0.0396668\pi$
$659$	3.90831	+	10.7380i	0.152246	+	0.418293i	−0.839999	+	0.542588i	$0.817445\pi$
$660$	−17.7948	+	65.7568i	−0.692663	+	2.55958i
$661$	−24.6764	−	29.4082i	−0.959801	−	1.14385i	−0.989536	−	0.144288i	$-0.953911\pi$
$661$	−24.6764	−	29.4082i	−0.959801	−	1.14385i	0.0297350	−	0.999558i	$-0.490534\pi$
$662$	19.5212	−	9.81346i	0.758712	−	0.381411i
$663$	−6.79996	+	20.2987i	−0.264089	+	0.788337i
$664$	−4.84877	+	13.3706i	−0.188169	+	0.518881i
$665$	−5.68324	+	3.28122i	−0.220387	+	0.127240i
$666$	23.6818	+	8.78465i	0.917651	+	0.340398i
$667$	1.01731	−	1.76203i	0.0393903	−	0.0682259i
$668$	−28.4307	+	38.2515i	−1.10002	+	1.47999i
$669$	−0.174843	+	1.16704i	−0.00675983	+	0.0451202i
$670$	−47.6061	−	31.2844i	−1.83919	−	1.20862i
$671$	1.83553	+	10.4098i	0.0708600	+	0.401867i
$672$	14.5404	+	1.29138i	0.560908	+	0.0498159i
$673$	20.4768	+	17.1821i	0.789324	+	0.662322i	0.945578	−	0.325395i	$-0.105497\pi$
$673$	20.4768	+	17.1821i	0.789324	+	0.662322i	−0.156254	+	0.987717i	$0.549942\pi$
$674$	3.49876	+	0.827779i	0.134767	+	0.0318848i
$675$	39.7659	−	55.6228i	1.53059	−	2.14092i
$676$	−11.3387	−	5.68340i	−0.436102	−	0.218592i
$677$	−32.6497	−	27.3963i	−1.25483	−	1.05293i	−0.996213	−	0.0869471i	$-0.972289\pi$
$677$	−32.6497	−	27.3963i	−1.25483	−	1.05293i	−0.258617	−	0.965980i	$-0.583267\pi$
$678$	−10.5158	−	32.0434i	−0.403858	−	1.23062i
$679$	−8.12363	+	1.43241i	−0.311756	+	0.0549710i
$680$	29.3145	−	16.9706i	1.12416	−	0.650792i
$681$	−37.2876	+	14.6725i	−1.42886	+	0.562252i
$682$	−15.8627	+	36.8134i	−0.607413	+	1.40966i
$683$	−15.4409	−	8.91481i	−0.590829	−	0.341116i	0.174596	−	0.984640i	$-0.444138\pi$
$683$	−15.4409	−	8.91481i	−0.590829	−	0.341116i	−0.765425	+	0.643525i	$0.777471\pi$
$684$	−4.48654	−	4.28190i	−0.171547	−	0.163722i
$685$	76.7927	−	44.3363i	2.93410	−	1.69400i
$686$	−2.89117	−	24.6520i	−0.110385	−	0.941217i
$687$	36.4323	−	32.2093i	1.38998	−	1.22886i
$688$	9.45398	+	2.22503i	0.360430	+	0.0848286i
$689$	−8.89192	−	10.5970i	−0.338755	−	0.403713i
$690$	−9.80504	−	18.3105i	−0.373272	−	0.697069i
$691$	−31.4339	+	11.4410i	−1.19580	+	0.435236i	−0.861757	−	0.507321i	$-0.830636\pi$
$691$	−31.4339	+	11.4410i	−1.19580	+	0.435236i	−0.334045	+	0.942557i	$0.608414\pi$
$692$	2.00917	+	34.0378i	0.0763771	+	1.29392i
$693$	−4.62546	−	20.1009i	−0.175707	−	0.763571i
$694$	−9.97277	−	9.40146i	−0.378561	−	0.356875i
$695$	−0.778650	+	4.41594i	−0.0295359	+	0.167506i
$696$	1.58555	−	4.75155i	0.0601002	−	0.180107i
$697$	11.4045	+	4.15090i	0.431976	+	0.157227i
$698$	−4.58563	−	0.265285i	−0.173569	−	0.0100412i
$699$	1.39598	+	2.27987i	0.0528008	+	0.0862326i
$700$	−35.9910	+	15.5584i	−1.36033	+	0.588052i
$701$	−39.7889			−1.50281			−0.751403	−	0.659844i	$-0.770622\pi$
$701$	−39.7889			−1.50281			−0.751403	+	0.659844i	$0.770622\pi$
$702$	31.9312	+	4.98469i	1.20517	+	0.188135i
$703$			6.15386i			0.232097i
$704$	32.0154	+	18.3842i	1.20663	+	0.692879i
$705$	30.1116	+	16.3633i	1.13407	+	0.616277i
$706$	−28.5778	−	1.65326i	−1.07554	−	0.0622214i
$707$	3.05627	−	8.39703i	0.114943	−	0.315803i
$708$	−16.1758	+	22.9796i	−0.607924	+	0.863627i
$709$	16.3390	+	2.88100i	0.613623	+	0.108198i	0.471818	−	0.881696i	$-0.343598\pi$
$709$	16.3390	+	2.88100i	0.613623	+	0.108198i	0.141806	+	0.989895i	$0.454709\pi$
$710$	18.3354	−	19.4496i	0.688114	−	0.729930i
$711$	6.18159	−	8.19101i	0.231828	−	0.307187i
$712$	10.1063	+	1.76980i	0.378749	+	0.0663260i
$713$	−4.18021	−	11.4850i	−0.156550	−	0.430118i
$714$	−5.40926	+	8.71354i	−0.202437	+	0.326096i
$715$	66.2518	−	55.5919i	2.47768	−	2.07902i
$716$	5.22428	+	21.9664i	0.195240	+	0.820924i
$717$	33.2960	−	6.76169i	1.24346	−	0.252520i
$718$	13.2852	−	1.55808i	0.495799	−	0.0581470i
$719$	14.9664	+	25.9226i	0.558153	+	0.966749i	0.997651	+	0.0685052i	$0.0218230\pi$
$719$	14.9664	+	25.9226i	0.558153	+	0.966749i	−0.439498	+	0.898244i	$0.644844\pi$
$720$	−32.6743	−	39.3353i	−1.21770	−	1.46594i
$721$	1.13011	−	1.95741i	0.0420875	−	0.0728977i
$722$	−10.0351	+	23.2890i	−0.373468	+	0.866728i
$723$	12.8618	−	16.1576i	0.478336	−	0.600908i
$724$	−8.07525	+	7.63054i	−0.300114	+	0.283587i
$725$	2.33639	+	13.2503i	0.0867713	+	0.492104i
$726$	5.17112	−	24.6849i	0.191918	−	0.916143i
$727$	−26.9841	+	32.1584i	−1.00078	+	1.19269i	−0.0195611	+	0.999809i	$0.506227\pi$
$727$	−26.9841	+	32.1584i	−1.00078	+	1.19269i	−0.981223	+	0.192879i	$0.938218\pi$
$728$	−14.2108	−	11.8959i	−0.526688	−	0.440892i
$729$	−26.6766	+	4.16627i	−0.988023	+	0.154306i
$730$	−71.7896	−	16.9848i	−2.65705	−	0.628636i
$731$	−4.38617	+	5.22724i	−0.162228	+	0.193336i
$732$	−7.18292	−	3.37122i	−0.265488	−	0.124604i
$733$	14.2918	−	2.52003i	0.527879	−	0.0930793i	0.0966442	−	0.995319i	$-0.469189\pi$
$733$	14.2918	−	2.52003i	0.527879	−	0.0930793i	0.431235	+	0.902240i	$0.358078\pi$
$734$	−19.1682	+	29.1686i	−0.707510	+	1.07663i
$735$	−21.9739	+	27.6046i	−0.810519	+	1.01821i
$736$	−10.9479	+	2.61731i	−0.403546	+	0.0964754i
$737$	37.7776	+	21.8109i	1.39156	+	0.803415i
$738$	3.29238	−	18.0236i	0.121194	−	0.663460i
$739$	6.49029	+	11.2415i	0.238749	+	0.413525i	0.960356	−	0.278778i	$-0.0899293\pi$
$739$	6.49029	+	11.2415i	0.238749	+	0.413525i	−0.721607	+	0.692303i	$0.756596\pi$
$740$	−5.85113	+	50.4012i	−0.215092	+	1.85279i
$741$	1.56700	+	7.71624i	0.0575653	+	0.283463i
$742$	−2.97668	−	5.92130i	−0.109278	−	0.217378i
$743$	−26.7968	+	22.4852i	−0.983080	+	0.824902i	−0.984551	−	0.175097i	$-0.943976\pi$
$743$	−26.7968	+	22.4852i	−0.983080	+	0.824902i	0.00147128	+	0.999999i	$0.499532\pi$
$744$	−15.7430	−	25.6434i	−0.577165	−	0.940131i
$745$	−3.94364	+	1.43537i	−0.144484	+	0.0525878i
$746$	40.6384	−	12.1836i	1.48788	−	0.446075i
$747$	−9.08728	+	12.0412i	−0.332486	+	0.440565i
$748$	−21.6599	+	14.2702i	−0.791963	+	0.521769i
$749$	0.993961	−	5.63703i	0.0363186	−	0.205973i
$750$	79.0553	+	31.6703i	2.88669	+	1.15644i
$751$	8.56526	−	23.5329i	0.312551	−	0.858726i	−0.679589	−	0.733593i	$-0.737842\pi$
$751$	8.56526	−	23.5329i	0.312551	−	0.858726i	0.992140	−	0.125133i	$-0.0399358\pi$
$752$	12.7242	−	13.5292i	0.464005	−	0.493359i
$753$	−6.79103	+	12.4968i	−0.247479	+	0.455409i
$754$	−5.09955	+	3.79957i	−0.185715	+	0.138372i
$755$			52.7154i			1.91851i
$756$	14.3370	+	5.84605i	0.521433	+	0.212619i
$757$			22.7174i			0.825679i	0.910804	+	0.412840i	$0.135463\pi$
$757$			22.7174i			0.825679i	−0.910804	+	0.412840i	$0.864537\pi$
$758$	17.2380	+	23.1358i	0.626113	+	0.840330i
$759$	8.30558	+	13.5644i	0.301473	+	0.492357i
$760$	6.21657	−	10.7966i	0.225499	−	0.391635i
$761$	0.0127475	−	0.0350234i	0.000462095	−	0.00126960i	−0.939461	−	0.342655i	$-0.888674\pi$
$761$	0.0127475	−	0.0350234i	0.000462095	−	0.00126960i	0.939923	+	0.341385i	$0.110896\pi$
$762$	−22.6823	+	3.25584i	−0.821694	+	0.117947i
$763$	0.0204568	−	0.116017i	0.000740588	−	0.00420008i
$764$	3.67149	−	2.41889i	0.132830	−	0.0875124i
$765$	35.0121	−	8.05670i	1.26587	−	0.291291i
$766$	−4.77887	−	15.9399i	−0.172668	−	0.575931i
$767$	33.5258	−	12.2024i	1.21054	−	0.440602i
$768$	−25.1180	+	11.7084i	−0.906368	+	0.422490i
$769$	24.5418	−	20.5930i	0.884999	−	0.742602i	−0.0822020	−	0.996616i	$-0.526195\pi$
$769$	24.5418	−	20.5930i	0.884999	−	0.742602i	0.967201	+	0.254014i	$0.0817508\pi$
$770$	37.0196	−	18.6101i	1.33410	−	0.670661i
$771$	16.0013	−	14.1465i	0.576271	−	0.509473i
$772$	4.03334	+	0.468235i	0.145163	+	0.0168521i
$773$	−19.2134	−	33.2786i	−0.691057	−	1.19695i	−0.971492	−	0.237073i	$-0.923812\pi$
$773$	−19.2134	−	33.2786i	−0.691057	−	1.19695i	0.280435	−	0.959873i	$-0.409521\pi$
$774$	8.88948	+	5.20544i	0.319526	+	0.187106i
$775$	69.9955	+	40.4119i	2.51431	+	1.45164i
$776$	11.9846	−	10.0802i	0.430222	−	0.361859i
$777$	−5.62548	−	14.2962i	−0.201813	−	0.512872i
$778$	−23.3121	−	15.3196i	−0.835780	−	0.549233i
$779$	4.39602	−	0.775137i	0.157504	−	0.0277722i
$780$	5.49737	+	64.6874i	0.196838	+	2.31618i
$781$	−13.1569	+	15.6797i	−0.470790	+	0.561065i
$782$	1.82084	−	7.69611i	0.0651129	−	0.275212i
$783$	3.08991	−	4.32204i	0.110425	−	0.154457i
$784$	11.4424	+	15.3197i	0.408656	+	0.547133i
$785$	51.3411	−	61.1860i	1.83244	−	2.18382i
$786$	−31.3384	+	35.0113i	−1.11780	+	1.24881i
$787$	0.888555	+	5.03924i	0.0316736	+	0.179630i	0.996540	−	0.0831097i	$-0.0264852\pi$
$787$	0.888555	+	5.03924i	0.0316736	+	0.179630i	−0.964867	+	0.262739i	$0.915374\pi$
$788$	5.14036	+	5.43994i	0.183118	+	0.193790i
$789$	−39.8433	−	5.96926i	−1.41846	−	0.212511i
$790$	18.9313	+	8.15739i	0.673545	+	0.290227i
$791$	−10.2563	+	17.7644i	−0.364672	+	0.631630i
$792$	26.7186	+	28.6261i	0.949403	+	1.01718i
$793$	5.03682	+	8.72404i	0.178863	+	0.309800i
$794$	−4.23537	−	36.1135i	−0.150308	−	1.28162i
$795$	−7.37444	+	22.0136i	−0.261544	+	0.780742i
$796$	−2.48349	−	10.4423i	−0.0880250	−	0.370117i
$797$	−17.4986	+	14.6831i	−0.619833	+	0.520102i	−0.897751	−	0.440503i	$-0.854800\pi$
$797$	−17.4986	+	14.6831i	−0.619833	+	0.520102i	0.277918	+	0.960605i	$0.410356\pi$
$798$	−0.120562	+	3.77029i	−0.00426785	+	0.133467i
$799$	4.46296	+	12.2619i	0.157888	+	0.433795i
$800$	44.3345	−	59.7951i	1.56746	−	2.11408i
$801$	9.69280	+	4.94750i	0.342478	+	0.174811i
$802$	10.0092	+	9.43579i	0.353437	+	0.333189i
$803$	55.6330	+	9.80960i	1.96325	+	0.346173i
$804$	−29.7112	+	13.7647i	−1.04783	+	0.485444i
$805$	−4.32085	+	11.8714i	−0.152290	+	0.418413i
$806$	−2.20633	+	38.1379i	−0.0777145	+	1.34335i
$807$	−0.724815	−	28.0647i	−0.0255147	−	0.987923i
$808$	2.96542	+	16.7032i	0.104323	+	0.587616i
$809$			7.98095i			0.280595i	0.990109	+	0.140298i	$0.0448059\pi$
$809$			7.98095i			0.280595i	−0.990109	+	0.140298i	$0.955194\pi$
$810$	−20.8492	−	50.0704i	−0.732568	−	1.75930i
$811$	−15.3983			−0.540709			−0.270354	−	0.962761i	$-0.587141\pi$
$811$	−15.3983			−0.540709			−0.270354	+	0.962761i	$0.587141\pi$
$812$	−2.79660	+	1.20893i	−0.0981414	+	0.0424251i
$813$	33.1161	−	0.855276i	1.16143	−	0.0299958i
$814$	2.24403	−	38.7896i	0.0786531	−	1.35957i
$815$	39.6177	+	14.4197i	1.38775	+	0.505099i
$816$	0.599475	−	19.4613i	0.0209858	−	0.681281i
$817$	−0.435819	+	2.47165i	−0.0152474	+	0.0864721i
$818$	25.9836	−	27.5626i	0.908495	−	0.963702i
$819$	−10.6941	−	16.4933i	−0.373681	−	0.576324i
$820$	36.7412	−	2.16874i	1.28306	−	0.0757358i
$821$	−20.0433	+	7.29516i	−0.699515	+	0.254603i	−0.667204	−	0.744875i	$-0.732509\pi$
$821$	−20.0433	+	7.29516i	−0.699515	+	0.254603i	−0.0323115	+	0.999478i	$0.510287\pi$
$822$	1.62905	−	50.9446i	0.0568197	−	1.77690i
$823$	27.7027	+	33.0148i	0.965657	+	1.15083i	0.988521	+	0.151086i	$0.0482772\pi$
$823$	27.7027	+	33.0148i	0.965657	+	1.15083i	−0.0228636	+	0.999739i	$0.507278\pi$
$824$	0.00503015	+	4.29091i	0.000175234	+	0.149481i
$825$	−99.7325	−	33.4098i	−3.47224	−	1.16318i
$826$	16.9762	−	1.99096i	0.590678	−	0.0692744i
$827$	−38.2037	+	22.0569i	−1.32847	+	0.766995i	−0.985064	−	0.172191i	$-0.944916\pi$
$827$	−38.2037	+	22.0569i	−1.32847	+	0.766995i	−0.343410	+	0.939185i	$0.611582\pi$
$828$	−11.9149	−	0.762782i	−0.414071	−	0.0265085i
$829$	11.0164	+	6.36030i	0.382614	+	0.220902i	0.678955	−	0.734180i	$-0.262433\pi$
$829$	11.0164	+	6.36030i	0.382614	+	0.220902i	−0.296341	+	0.955082i	$0.595766\pi$
$830$	−27.8300	−	11.9918i	−0.965995	−	0.416242i
$831$	−8.21600	+	54.8398i	−0.285010	+	1.90237i
$832$	34.6630	+	6.02827i	1.20172	+	0.208993i
$833$	−13.2301	+	2.33283i	−0.458397	+	0.0808277i
$834$	1.92054	+	1.71906i	0.0665028	+	0.0595262i
$835$	−77.7899	−	65.2735i	−2.69203	−	2.25888i
$836$	−4.27496	+	8.52875i	−0.147853	+	0.294973i
$837$	−7.95772	−	30.9075i	−0.275059	−	1.06832i
$838$	10.0838	−	42.6209i	0.348338	−	1.47232i
$839$	−23.1960	−	19.4638i	−0.800816	−	0.671964i	0.147581	−	0.989050i	$-0.452851\pi$
$839$	−23.1960	−	19.4638i	−0.800816	−	0.671964i	−0.948397	+	0.317086i	$0.897296\pi$
$840$	−4.57224	+	30.7647i	−0.157757	+	1.06148i
$841$	−4.85425	−	27.5298i	−0.167388	−	0.949305i
$842$	−6.11116	+	9.29948i	−0.210604	+	0.320481i
$843$	−10.5963	+	4.16960i	−0.364956	+	0.143609i
$844$	24.8153	−	33.3872i	0.854178	−	1.14923i
$845$	13.5119	−	23.4033i	0.464824	−	0.805099i
$846$	17.1203	−	9.74464i	0.588609	−	0.335028i
$847$	−13.2849	+	7.67005i	−0.456475	+	0.263546i
$848$	10.5227	+	6.89735i	0.361351	+	0.236856i
$849$	−20.1488	−	22.7905i	−0.691504	−	0.782169i
$850$	23.4899	+	46.7267i	0.805696	+	1.60271i
$851$	7.61496	+	9.07515i	0.261037	+	0.311092i
$852$	−3.93976	−	14.8510i	−0.134974	−	0.508786i
$853$	−5.79837	−	15.9309i	−0.198532	−	0.545463i	0.799978	−	0.600030i	$-0.204845\pi$
$853$	−5.79837	−	15.9309i	−0.198532	−	0.545463i	−0.998510	+	0.0545663i	$0.982622\pi$
$854$	1.38596	+	4.62287i	0.0474267	+	0.158191i
$855$	9.67070	−	9.00510i	0.330731	−	0.307968i
$856$	3.72860	+	10.2070i	0.127441	+	0.348868i
$857$	−47.6315	−	8.39871i	−1.62706	−	0.286895i	−0.715670	−	0.698438i	$-0.753879\pi$
$857$	−47.6315	−	8.39871i	−1.62706	−	0.286895i	−0.911390	+	0.411544i	$0.864990\pi$
$858$	−7.06352	−	49.2092i	−0.241145	−	1.67997i
$859$	46.3857	+	16.8830i	1.58266	+	0.576041i	0.975780	−	0.218754i	$-0.0701991\pi$
$859$	46.3857	+	16.8830i	1.58266	+	0.576041i	0.606879	+	0.794794i	$0.292421\pi$
$860$	−5.91950	+	19.8289i	−0.201853	+	0.676160i
$861$	−9.50391	+	5.81931i	−0.323893	+	0.198322i
$862$	12.0753	+	16.2067i	0.411286	+	0.552002i
$863$	−14.4959			−0.493447			−0.246724	−	0.969086i	$-0.579354\pi$
$863$	−14.4959			−0.493447			−0.246724	+	0.969086i	$0.579354\pi$
$864$	−29.1161	+	4.03167i	−0.990549	+	0.137160i
$865$	−72.6492			−2.47015
$866$	6.44760	+	8.65356i	0.219098	+	0.294060i
$867$	−13.8521	−	7.52750i	−0.470441	−	0.255647i
$868$	−5.23535	+	17.5371i	−0.177699	+	0.595249i
$869$	−14.8334	−	5.39892i	−0.503189	−	0.183146i
$870$	9.90730	+	3.96896i	0.335889	+	0.134560i
$871$	40.9402	+	7.21886i	1.38721	+	0.244602i
$872$	0.0767388	+	0.210072i	0.00259870	+	0.00711392i
$873$	15.2944	−	6.47912i	0.517636	−	0.219285i
$874$	−0.835345	−	2.78628i	−0.0282560	−	0.0942475i
$875$	−17.7163	−	48.6753i	−0.598922	−	1.64552i
$876$	−30.0595	+	29.9104i	−1.01562	+	1.01058i
$877$	3.01975	+	3.59880i	0.101970	+	0.121523i	0.814616	−	0.580001i	$-0.196948\pi$
$877$	3.01975	+	3.59880i	0.101970	+	0.121523i	−0.712646	+	0.701524i	$0.752503\pi$
$878$	15.1162	+	30.0695i	0.510147	+	1.01480i
$879$	38.1836	−	7.75427i	1.28790	−	0.261545i
$880$	−43.1219	+	65.7874i	−1.45364	+	2.21769i
$881$	31.4940	−	18.1830i	1.06106	−	0.612602i	0.135334	−	0.990800i	$-0.456789\pi$
$881$	31.4940	−	18.1830i	1.06106	−	0.612602i	0.925725	+	0.378198i	$0.123456\pi$
$882$	6.81931	+	19.1003i	0.229618	+	0.643140i
$883$	−14.0669	+	24.3645i	−0.473387	+	0.819931i	−0.999536	−	0.0304617i	$-0.990302\pi$
$883$	−14.0669	+	24.3645i	−0.473387	+	0.819931i	0.526149	+	0.850393i	$0.323636\pi$
$884$	−14.7457	+	19.8393i	−0.495953	+	0.667269i
$885$	−46.8459	−	37.2904i	−1.57471	−	1.25350i
$886$	6.93108	−	10.5472i	0.232854	−	0.354339i
$887$	3.68942	+	20.9238i	0.123879	+	0.702551i	0.981968	+	0.189050i	$0.0605407\pi$
$887$	3.68942	+	20.9238i	0.123879	+	0.702551i	−0.858089	+	0.513501i	$0.828348\pi$
$888$	22.8404	+	18.1378i	0.766474	+	0.608664i
$889$	10.6768	+	8.95890i	0.358088	+	0.300472i
$890$	−5.03313	+	21.2735i	−0.168711	+	0.713089i
$891$	18.1533	+	37.3559i	0.608158	+	1.25147i
$892$	−0.610590	+	1.21816i	−0.0204441	+	0.0407869i
$893$	3.67657	+	3.08501i	0.123032	+	0.103236i
$894$	−0.494617	+	2.36111i	−0.0165425	+	0.0789673i
$895$	−47.3776	+	8.35396i	−1.58366	+	0.279242i
$896$	15.4955	+	6.63391i	0.517670	+	0.221623i
$897$	11.8592	+	9.44016i	0.395966	+	0.315198i
$898$	−21.1125	−	9.09727i	−0.704534	−	0.303580i
$899$	5.43884	+	3.14011i	0.181395	+	0.104729i
$900$	63.6006	−	46.7825i	2.12002	−	1.55942i
$901$	−7.65541	+	4.41986i	−0.255039	+	0.147247i
$902$	−27.9921	+	3.28289i	−0.932034	+	0.109308i
$903$	−1.24697	−	6.14035i	−0.0414966	−	0.204338i
$904$	−0.0456511	−	38.9421i	−0.00151833	−	1.29519i
$905$	−15.2160	−	18.1337i	−0.505797	−	0.602786i
$906$	25.7445	+	15.9819i	0.855304	+	0.530963i
$907$	30.0902	−	10.9519i	0.999129	−	0.363653i	0.209880	−	0.977727i	$-0.432693\pi$
$907$	30.0902	−	10.9519i	0.999129	−	0.363653i	0.789248	+	0.614074i	$0.210470\pi$
$908$	−46.1891	+	2.72643i	−1.53284	+	0.0904797i
$909$	−2.20568	+	17.8577i	−0.0731576	+	0.592304i
$910$	27.0863	−	28.7323i	0.897903	−	0.952467i
$911$	2.84421	−	16.1303i	0.0942328	−	0.534421i	−0.900747	−	0.434344i	$-0.856980\pi$
$911$	2.84421	−	16.1303i	0.0942328	−	0.534421i	0.994980	−	0.100077i	$-0.0319088\pi$
$912$	−3.38803	−	6.30921i	−0.112189	−	0.208919i
$913$	21.8059	+	7.93670i	0.721670	+	0.262666i
$914$	1.56896	−	27.1206i	0.0518966	−	0.897069i
$915$	8.07226	−	14.8545i	0.266861	−	0.491076i
$916$	51.5419	−	22.2808i	1.70299	−	0.736178i
$917$	28.5798			0.943789
$918$	6.68009	−	19.5414i	0.220476	−	0.644961i
$919$		−	18.7009i		−	0.616887i	−0.951243	−	0.308444i	$-0.900192\pi$
$919$		−	18.7009i		−	0.616887i	0.951243	−	0.308444i	$-0.0998081\pi$
$920$	−4.19241	−	23.6144i	−0.138220	−	0.778545i
$921$	37.3655	−	22.8792i	1.23123	−	0.753894i
$922$	−2.19934	+	38.0171i	−0.0724313	+	1.25202i
$923$	−6.67162	+	18.3301i	−0.219599	+	0.603343i
$924$	2.13479	−	23.7213i	0.0702294	−	0.780372i
$925$	−77.1515	−	13.6039i	−2.53672	−	0.447293i
$926$	22.4086	+	21.1249i	0.736393	+	0.694207i
$927$	−1.33377	+	4.35137i	−0.0438066	+	0.142918i
$928$	3.44491	−	4.64624i	0.113085	−	0.152520i
$929$	−8.77648	−	24.1132i	−0.287947	−	0.791128i	−0.996353	−	0.0853232i	$-0.972808\pi$
$929$	−8.77648	−	24.1132i	−0.287947	−	0.791128i	0.708406	−	0.705805i	$-0.249415\pi$
$930$	56.5189	−	30.2652i	1.85333	−	0.992434i
$931$	−3.78516	+	3.17612i	−0.124053	+	0.104093i
$932$	0.714228	+	3.00310i	0.0233953	+	0.0983699i
$933$	32.7564	+	37.0512i	1.07240	+	1.21300i
$934$	2.31934	+	19.7762i	0.0758911	+	0.647097i
$935$	−27.6327	−	47.8613i	−0.903686	−	1.56523i
$936$	33.2579	+	16.9267i	1.08707	+	0.553267i
$937$	11.0095	−	19.0691i	0.359666	−	0.622960i	−0.628239	−	0.778020i	$-0.716224\pi$
$937$	11.0095	−	19.0691i	0.359666	−	0.622960i	0.987905	+	0.155061i	$0.0495573\pi$
$938$	18.2907	+	7.88138i	0.597214	+	0.257336i
$939$	−9.31505	−	23.6726i	−0.303985	−	0.772525i
$940$	27.1786	+	28.7625i	0.886467	+	0.938130i
$941$	0.337804	+	1.91578i	0.0110121	+	0.0624527i	0.989819	−	0.142335i	$-0.0454609\pi$
$941$	0.337804	+	1.91578i	0.0110121	+	0.0624527i	−0.978807	+	0.204787i	$0.934350\pi$
$942$	−14.3160	−	43.6232i	−0.466441	−	1.42132i
$943$	5.52367	−	6.58286i	0.179876	−	0.214367i
$944$	−25.9980	+	19.4181i	−0.846164	+	0.632004i
$945$	−14.2343	+	29.7603i	−0.463043	+	0.968104i
$946$	3.64839	−	15.4206i	0.118619	−	0.501368i
$947$	−23.1314	+	27.5669i	−0.751668	+	0.895803i	−0.997291	−	0.0735625i	$-0.976563\pi$
$947$	−23.1314	+	27.5669i	−0.751668	+	0.895803i	0.245623	+	0.969366i	$0.421008\pi$
$948$	9.72326	−	6.77233i	0.315797	−	0.219955i
$949$	53.0184	−	9.34858i	1.72105	−	0.303468i
$950$	16.0753	+	10.5639i	0.521553	+	0.342739i
$951$	10.4295	+	1.56252i	0.338199	+	0.0506683i
$952$	−9.06305	+	7.62292i	−0.293735	+	0.247060i
$953$	−1.81538	−	1.04811i	−0.0588061	−	0.0339517i	0.470309	−	0.882502i	$-0.344143\pi$
$953$	−1.81538	−	1.04811i	−0.0588061	−	0.0339517i	−0.529115	+	0.848550i	$0.677476\pi$
$954$	8.51500	+	10.2754i	0.275683	+	0.332677i
$955$	4.68393	+	8.11281i	0.151568	+	0.262524i
$956$	38.9700	+	4.52406i	1.26038	+	0.146319i
$957$	−7.74948	−	2.59603i	−0.250505	−	0.0839179i
$958$	45.9551	−	23.1020i	1.48474	−	0.746392i
$959$	−23.7490	+	19.9278i	−0.766895	+	0.643501i
$960$	−21.7497	−	54.8950i	−0.701969	−	1.77173i
$961$	6.32034	−	2.30042i	0.203882	−	0.0742069i
$962$	−10.6337	−	35.4687i	−0.342845	−	1.14356i
$963$	0.594952	+	11.5105i	0.0191720	+	0.370921i
$964$	19.9133	−	13.1195i	0.641364	−	0.422550i
$965$	−1.50230	+	8.51997i	−0.0483608	+	0.274268i
$966$	4.48766	+	5.70926i	0.144388	+	0.183692i
$967$	8.96560	−	24.6328i	0.288314	−	0.792137i	−0.707988	−	0.706224i	$-0.750397\pi$
$967$	8.96560	−	24.6328i	0.288314	−	0.792137i	0.996303	−	0.0859130i	$-0.0273807\pi$
$968$	14.5316	−	25.2378i	0.467064	−	0.811173i
$969$	5.02975	−	0.129901i	0.161579	−	0.00417303i
$970$	19.9356	+	26.7563i	0.640094	+	0.859094i
$971$		−	35.5567i		−	1.14107i	−0.821274	−	0.570534i	$-0.806736\pi$
$971$		−	35.5567i		−	1.14107i	0.821274	−	0.570534i	$-0.193264\pi$
$972$	−30.7737	−	4.99790i	−0.987067	−	0.160308i
$973$		−	1.56774i		−	0.0502594i
$974$	11.1714	−	8.32356i	0.357954	−	0.266704i
$975$	−100.203	+	2.58791i	−3.20907	+	0.0828795i
$976$	−6.67417	−	6.27706i	−0.213635	−	0.200924i
$977$	−18.2608	+	50.1711i	−0.584215	+	1.60512i	0.196689	+	0.980466i	$0.436981\pi$
$977$	−18.2608	+	50.1711i	−0.584215	+	1.60512i	−0.780904	+	0.624651i	$0.785241\pi$
$978$	19.0531	−	14.9763i	0.609251	−	0.478891i
$979$	2.90689	−	16.4858i	0.0929046	−	0.526888i
$980$	−34.0210	+	22.4141i	−1.08676	+	0.715991i
$981$	0.0122448	+	0.236899i	0.000390946	+	0.00756361i
$982$	39.9902	−	11.9893i	1.27614	−	0.382595i
$983$	−30.4366	+	11.0780i	−0.970776	+	0.353334i	−0.778247	−	0.627958i	$-0.783891\pi$
$983$	−30.4366	+	11.0780i	−0.970776	+	0.353334i	−0.192529	+	0.981291i	$0.561669\pi$
$984$	10.0798	−	18.6007i	0.321332	−	0.592969i
$985$	−12.2159	+	10.2504i	−0.389231	+	0.326604i
$986$	1.82523	+	3.63079i	0.0581271	+	0.115628i
$987$	−11.3613	−	3.80596i	−0.361633	−	0.121145i
$988$	−1.04844	+	9.03117i	−0.0333553	+	0.287320i
$989$	2.41578	+	4.18426i	0.0768174	+	0.133052i
$990$	−64.2411	+	53.2354i	−2.04171	+	1.69193i
$991$	36.6096	+	21.1366i	1.16294	+	0.671426i	0.952008	−	0.306074i	$-0.0990156\pi$
$991$	36.6096	+	21.1366i	1.16294	+	0.671426i	0.210936	+	0.977500i	$0.432349\pi$
$992$	−8.07884	−	33.7929i	−0.256503	−	1.07293i
$993$	26.4642	+	3.96481i	0.839815	+	0.125819i
$994$	−5.13229	+	7.80991i	−0.162786	+	0.247715i
$995$	22.5222	−	3.97126i	0.714000	−	0.125898i
$996$	−14.2937	+	9.95570i	−0.452914	+	0.315458i
$997$	−14.6554	+	17.4657i	−0.464142	+	0.553143i	−0.946447	−	0.322861i	$-0.895355\pi$
$997$	−14.6554	+	17.4657i	−0.464142	+	0.553143i	0.482304	+	0.876004i	$0.339800\pi$
$998$	−40.1174	−	9.49145i	−1.26990	−	0.300447i
$999$	17.4945	+	25.5135i	0.553502	+	0.807212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.23	yes	192
3.2	odd	2		648.2.v.b.35.10		192
4.3	odd	2		864.2.bh.b.335.15		192
8.3	odd	2	inner	216.2.v.b.11.6	✓	192
8.5	even	2		864.2.bh.b.335.16		192
24.11	even	2		648.2.v.b.35.27		192
27.5	odd	18	inner	216.2.v.b.59.6	yes	192
27.22	even	9		648.2.v.b.611.27		192
108.59	even	18		864.2.bh.b.815.16		192
216.5	odd	18		864.2.bh.b.815.15		192
216.59	even	18	inner	216.2.v.b.59.23	yes	192
216.211	odd	18		648.2.v.b.611.10		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.6	✓	192	8.3	odd	2	inner
216.2.v.b.11.23	yes	192	1.1	even	1	trivial
216.2.v.b.59.6	yes	192	27.5	odd	18	inner
216.2.v.b.59.23	yes	192	216.59	even	18	inner
648.2.v.b.35.10		192	3.2	odd	2
648.2.v.b.35.27		192	24.11	even	2
648.2.v.b.611.10		192	216.211	odd	18
648.2.v.b.611.27		192	27.22	even	9
864.2.bh.b.335.15		192	4.3	odd	2
864.2.bh.b.335.16		192	8.5	even	2
864.2.bh.b.815.15		192	216.5	odd	18
864.2.bh.b.815.16		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)

\(f(q)\)	\(=\)	\(q+(0.844953 + 1.13404i) q^{2} +(0.0447181 + 1.73147i) q^{3} +(-0.572109 + 1.91643i) q^{4} +(-4.00434 - 1.45746i) q^{5} +(-1.92578 + 1.51373i) q^{6} +(1.46723 + 0.258712i) q^{7} +(-2.65672 + 0.970494i) q^{8} +(-2.99600 + 0.154856i) q^{9} +O(q^{10})\)	\(q+(0.844953 + 1.13404i) q^{2} +(0.0447181 + 1.73147i) q^{3} +(-0.572109 + 1.91643i) q^{4} +(-4.00434 - 1.45746i) q^{5} +(-1.92578 + 1.51373i) q^{6} +(1.46723 + 0.258712i) q^{7} +(-2.65672 + 0.970494i) q^{8} +(-2.99600 + 0.154856i) q^{9} +(-1.73065 - 5.77258i) q^{10} +(1.57835 + 4.33649i) q^{11} +(-3.34383 - 0.904892i) q^{12} +(2.82693 + 3.36900i) q^{13} +(0.946349 + 1.88250i) q^{14} +(2.34449 - 6.99858i) q^{15} +(-3.34538 - 2.19281i) q^{16} +(2.43381 - 1.40516i) q^{17} +(-2.70709 - 3.26675i) q^{18} +(0.516826 - 0.895168i) q^{19} +(5.08403 - 6.84019i) q^{20} +(-0.382341 + 2.55204i) q^{21} +(-3.58413 + 5.45405i) q^{22} +(-0.345539 - 1.95965i) q^{23} +(-1.79919 - 4.55663i) q^{24} +(10.0803 + 8.45837i) q^{25} +(-1.43197 + 6.05250i) q^{26} +(-0.402105 - 5.18057i) q^{27} +(-1.33522 + 2.66383i) q^{28} +(0.783266 + 0.657238i) q^{29} +(9.91767 - 3.25472i) q^{30} +(6.04883 - 1.06657i) q^{31} +(-0.339950 - 5.64663i) q^{32} +(-7.43793 + 2.92679i) q^{33} +(3.64997 + 1.57275i) q^{34} +(-5.49822 - 3.17440i) q^{35} +(1.41727 - 5.83021i) q^{36} +(-5.15589 + 2.97676i) q^{37} +(1.45185 - 0.170272i) q^{38} +(-5.70692 + 5.04540i) q^{39} +(12.0528 - 0.0141293i) q^{40} +(2.77589 + 3.30817i) q^{41} +(-3.21718 + 1.72276i) q^{42} +(-2.28164 + 0.830449i) q^{43} +(-9.21355 + 0.543853i) q^{44} +(12.2227 + 3.74645i) q^{45} +(1.93036 - 2.04767i) q^{46} +(-0.806279 + 4.57264i) q^{47} +(3.64719 - 5.89050i) q^{48} +(-4.49202 - 1.63496i) q^{49} +(-1.07479 + 18.5784i) q^{50} +(2.54184 + 4.15125i) q^{51} +(-8.07375 + 3.49016i) q^{52} -3.14544 q^{53} +(5.53523 - 4.83334i) q^{54} -19.6651i q^{55} +(-4.14909 + 0.736613i) q^{56} +(1.57307 + 0.854840i) q^{57} +(-0.0835137 + 1.44359i) q^{58} +(2.77458 - 7.62310i) q^{59} +(12.0710 + 8.49698i) q^{60} +(2.25575 + 0.397750i) q^{61} +(6.32052 + 5.95844i) q^{62} +(-4.43588 - 0.547892i) q^{63} +(6.11628 - 5.15666i) q^{64} +(-6.40978 - 17.6107i) q^{65} +(-9.60381 - 5.96193i) q^{66} +(7.24112 - 6.07602i) q^{67} +(1.30049 + 5.46813i) q^{68} +(3.37763 - 0.685923i) q^{69} +(-1.04583 - 8.91743i) q^{70} +(2.21770 + 3.84117i) q^{71} +(7.80924 - 3.31901i) q^{72} +(6.12067 - 10.6013i) q^{73} +(-7.73226 - 3.33179i) q^{74} +(-14.1947 + 17.8320i) q^{75} +(1.41984 + 1.50259i) q^{76} +(1.19390 + 6.77096i) q^{77} +(-10.5438 - 2.20876i) q^{78} +(-2.19872 + 2.62033i) q^{79} +(10.2001 + 13.6565i) q^{80} +(8.95204 - 0.927899i) q^{81} +(-1.40612 + 5.94322i) q^{82} +(3.23224 - 3.85203i) q^{83} +(-4.67205 - 2.19277i) q^{84} +(-11.7938 + 2.07956i) q^{85} +(-2.86965 - 1.88579i) q^{86} +(-1.10296 + 1.38559i) q^{87} +(-8.40177 - 9.98903i) q^{88} +(-3.14150 - 1.81374i) q^{89} +(6.07896 + 17.0266i) q^{90} +(3.27615 + 5.67445i) q^{91} +(3.95321 + 0.458932i) q^{92} +(2.11723 + 10.4257i) q^{93} +(-5.86684 + 2.94931i) q^{94} +(-3.37421 + 2.83130i) q^{95} +(9.76179 - 0.841121i) q^{96} +(-5.20281 + 1.89367i) q^{97} +(-1.94143 - 6.47561i) q^{98} +(-5.40028 - 12.7477i) 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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