LMFDB - Embedded newform 216.2.v.b.11.24

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			11.24
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.860856 - 1.12202i) q^{2} +(1.59734 + 0.669704i) q^{3} +(-0.517853 - 1.93179i) q^{4} +(3.00936 + 1.09532i) q^{5} +(2.12650 - 1.21573i) q^{6} +(-4.58614 - 0.808660i) q^{7} +(-2.61331 - 1.08196i) q^{8} +(2.10299 + 2.13949i) q^{9} +O(q^{10})$	\(q+(0.860856 - 1.12202i) q^{2} +(1.59734 + 0.669704i) q^{3} +(-0.517853 - 1.93179i) q^{4} +(3.00936 + 1.09532i) q^{5} +(2.12650 - 1.21573i) q^{6} +(-4.58614 - 0.808660i) q^{7} +(-2.61331 - 1.08196i) q^{8} +(2.10299 + 2.13949i) q^{9} +(3.81960 - 2.43365i) q^{10} +(-0.303411 - 0.833616i) q^{11} +(0.466542 - 3.43254i) q^{12} +(1.22056 + 1.45461i) q^{13} +(-4.85534 + 4.44959i) q^{14} +(4.07344 + 3.76498i) q^{15} +(-3.46366 + 2.00077i) q^{16} +(-4.03247 + 2.32815i) q^{17} +(4.21092 - 0.517807i) q^{18} +(-0.171350 + 0.296787i) q^{19} +(0.557523 - 6.38069i) q^{20} +(-6.78406 - 4.36306i) q^{21} +(-1.19653 - 0.377190i) q^{22} +(-1.00156 - 5.68012i) q^{23} +(-3.44975 - 3.47839i) q^{24} +(4.02633 + 3.37849i) q^{25} +(2.68283 - 0.117284i) q^{26} +(1.92637 + 4.82588i) q^{27} +(0.812780 + 9.27824i) q^{28} +(-4.16935 - 3.49850i) q^{29} +(7.73102 - 1.32937i) q^{30} +(7.80815 - 1.37679i) q^{31} +(-0.736809 + 5.60866i) q^{32} +(0.0736241 - 1.53476i) q^{33} +(-0.859151 + 6.52870i) q^{34} +(-12.9156 - 7.45683i) q^{35} +(3.04401 - 5.17049i) q^{36} +(-2.31812 + 1.33837i) q^{37} +(0.185493 + 0.447749i) q^{38} +(0.975496 + 3.14092i) q^{39} +(-6.67930 - 6.11841i) q^{40} +(0.0346849 + 0.0413359i) q^{41} +(-10.7355 + 3.85588i) q^{42} +(-2.85915 + 1.04064i) q^{43} +(-1.45325 + 1.01782i) q^{44} +(3.98525 + 8.74195i) q^{45} +(-7.23540 - 3.76600i) q^{46} +(-1.90179 + 10.7856i) q^{47} +(-6.87256 + 0.876288i) q^{48} +(13.8009 + 5.02311i) q^{49} +(7.25682 - 1.60922i) q^{50} +(-8.00039 + 1.01828i) q^{51} +(2.17793 - 3.11115i) q^{52} +1.27415 q^{53} +(7.07306 + 1.99296i) q^{54} -2.84099i q^{55} +(11.1100 + 7.07528i) q^{56} +(-0.472464 + 0.359316i) q^{57} +(-7.51460 + 1.66638i) q^{58} +(2.43399 - 6.68734i) q^{59} +(5.16372 - 9.81875i) q^{60} +(8.19039 + 1.44419i) q^{61} +(5.17691 - 9.94610i) q^{62} +(-7.91450 - 11.5126i) q^{63} +(5.65874 + 5.65497i) q^{64} +(2.07985 + 5.71435i) q^{65} +(-1.65865 - 1.40382i) q^{66} +(-6.31205 + 5.29644i) q^{67} +(6.58572 + 6.58426i) q^{68} +(2.20417 - 9.74384i) q^{69} +(-19.4852 + 8.07230i) q^{70} +(-0.186788 - 0.323526i) q^{71} +(-3.18093 - 7.86649i) q^{72} +(6.29550 - 10.9041i) q^{73} +(-0.493895 + 3.75312i) q^{74} +(4.16883 + 8.09304i) q^{75} +(0.662065 + 0.177321i) q^{76} +(0.717374 + 4.06843i) q^{77} +(4.36393 + 1.60936i) q^{78} +(-2.54509 + 3.03312i) q^{79} +(-12.6149 + 2.22724i) q^{80} +(-0.154829 + 8.99867i) q^{81} +(0.0762384 - 0.00333288i) q^{82} +(8.90996 - 10.6185i) q^{83} +(-4.91538 + 15.3648i) q^{84} +(-14.6852 + 2.58940i) q^{85} +(-1.29369 + 4.10386i) q^{86} +(-4.31692 - 8.38053i) q^{87} +(-0.109029 + 2.50677i) q^{88} +(-6.35012 - 3.66624i) q^{89} +(13.2394 + 3.05404i) q^{90} +(-4.42138 - 7.65805i) q^{91} +(-10.4542 + 4.87627i) q^{92} +(13.3943 + 3.02994i) q^{93} +(10.4645 + 11.4187i) q^{94} +(-0.840731 + 0.705457i) q^{95} +(-4.93308 + 8.46550i) q^{96} +(-0.833364 + 0.303320i) q^{97} +(17.5166 - 11.1607i) q^{98} +(1.14544 - 2.40223i) 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 $

$2$	0.860856	−	1.12202i	0.608717	−	0.793387i
$2$	0.860856	−	1.12202i	0.608717	−	0.793387i
$3$	1.59734	+	0.669704i	0.922225	+	0.386654i
$3$	1.59734	+	0.669704i	0.922225	+	0.386654i
$4$	−0.517853	−	1.93179i	−0.258926	−	0.965897i
$5$	3.00936	+	1.09532i	1.34583	+	0.489842i	0.911643	−	0.410982i	$-0.134814\pi$
$5$	3.00936	+	1.09532i	1.34583	+	0.489842i	0.434185	+	0.900824i	$0.357036\pi$
$6$	2.12650	−	1.21573i	0.868140	−	0.496319i
$7$	−4.58614	−	0.808660i	−1.73340	−	0.305645i	−0.784242	−	0.620455i	$-0.786948\pi$
$7$	−4.58614	−	0.808660i	−1.73340	−	0.305645i	−0.949155	+	0.314810i	$0.898059\pi$
$8$	−2.61331	−	1.08196i	−0.923943	−	0.382529i
$9$	2.10299	+	2.13949i	0.700998	+	0.713163i
$10$	3.81960	−	2.43365i	1.20786	−	0.769588i
$11$	−0.303411	−	0.833616i	−0.0914819	−	0.251345i	0.885510	−	0.464620i	$-0.153809\pi$
$11$	−0.303411	−	0.833616i	−0.0914819	−	0.251345i	−0.976992	+	0.213275i	$0.931587\pi$
$12$	0.466542	−	3.43254i	0.134679	−	0.990889i
$13$	1.22056	+	1.45461i	0.338523	+	0.403436i	0.908270	−	0.418384i	$-0.137403\pi$
$13$	1.22056	+	1.45461i	0.338523	+	0.403436i	−0.569747	+	0.821820i	$0.692959\pi$
$14$	−4.85534	+	4.44959i	−1.29764	+	1.18920i
$15$	4.07344	+	3.76498i	1.05176	+	0.972113i
$16$	−3.46366	+	2.00077i	−0.865914	+	0.500192i
$17$	−4.03247	+	2.32815i	−0.978017	+	0.564658i	−0.901671	−	0.432423i	$-0.857659\pi$
$17$	−4.03247	+	2.32815i	−0.978017	+	0.564658i	−0.0763460	+	0.997081i	$0.524325\pi$
$18$	4.21092	−	0.517807i	0.992524	−	0.122048i
$19$	−0.171350	+	0.296787i	−0.0393104	+	0.0680876i	−0.885011	−	0.465570i	$-0.845849\pi$
$19$	−0.171350	+	0.296787i	−0.0393104	+	0.0680876i	0.845701	+	0.533657i	$0.179183\pi$
$20$	0.557523	−	6.38069i	0.124666	−	1.42676i
$21$	−6.78406	−	4.36306i	−1.48040	−	0.952097i
$22$	−1.19653	−	0.377190i	−0.255100	−	0.0804172i
$23$	−1.00156	−	5.68012i	−0.208839	−	1.18439i	−0.891282	−	0.453449i	$-0.850194\pi$
$23$	−1.00156	−	5.68012i	−0.208839	−	1.18439i	0.682443	−	0.730939i	$-0.260918\pi$
$24$	−3.44975	−	3.47839i	−0.704177	−	0.710024i
$25$	4.02633	+	3.37849i	0.805265	+	0.675698i
$26$	2.68283	−	0.117284i	0.526146	−	0.0230013i
$27$	1.92637	+	4.82588i	0.370731	+	0.928740i
$28$	0.812780	+	9.27824i	0.153601	+	1.75342i
$29$	−4.16935	−	3.49850i	−0.774229	−	0.649655i	0.167559	−	0.985862i	$-0.446411\pi$
$29$	−4.16935	−	3.49850i	−0.774229	−	0.649655i	−0.941788	+	0.336207i	$0.890856\pi$
$30$	7.73102	−	1.32937i	1.41149	−	0.242709i
$31$	7.80815	−	1.37679i	1.40238	−	0.247278i	0.579262	−	0.815142i	$-0.303341\pi$
$31$	7.80815	−	1.37679i	1.40238	−	0.247278i	0.823123	+	0.567864i	$0.192230\pi$
$32$	−0.736809	+	5.60866i	−0.130251	+	0.991481i
$33$	0.0736241	−	1.53476i	0.0128163	−	0.267168i
$34$	−0.859151	+	6.52870i	−0.147343	+	1.11966i
$35$	−12.9156	−	7.45683i	−2.18314	−	1.26044i
$36$	3.04401	−	5.17049i	0.507335	−	0.861749i
$37$	−2.31812	+	1.33837i	−0.381097	+	0.220026i	−0.678295	−	0.734789i	$-0.737281\pi$
$37$	−2.31812	+	1.33837i	−0.381097	+	0.220026i	0.297199	+	0.954816i	$0.403948\pi$
$38$	0.185493	+	0.447749i	0.0300909	+	0.0726344i
$39$	0.975496	+	3.14092i	0.156204	+	0.502950i
$40$	−6.67930	−	6.11841i	−1.05609	−	0.967405i
$41$	0.0346849	+	0.0413359i	0.00541687	+	0.00645558i	0.768746	−	0.639554i	$-0.220881\pi$
$41$	0.0346849	+	0.0413359i	0.00541687	+	0.00645558i	−0.763329	+	0.646010i	$0.776437\pi$
$42$	−10.7355	+	3.85588i	−1.65653	+	0.594975i
$43$	−2.85915	+	1.04064i	−0.436016	+	0.158697i	−0.550696	−	0.834706i	$-0.685638\pi$
$43$	−2.85915	+	1.04064i	−0.436016	+	0.158697i	0.114681	+	0.993402i	$0.463416\pi$
$44$	−1.45325	+	1.01782i	−0.219086	+	0.153442i
$45$	3.98525	+	8.74195i	0.594086	+	1.30317i
$46$	−7.23540	−	3.76600i	−1.06680	−	0.555267i
$47$	−1.90179	+	10.7856i	−0.277404	+	1.57324i	0.453814	+	0.891096i	$0.350063\pi$
$47$	−1.90179	+	10.7856i	−0.277404	+	1.57324i	−0.731219	+	0.682143i	$0.761048\pi$
$48$	−6.87256	+	0.876288i	−0.991969	+	0.126481i
$49$	13.8009	+	5.02311i	1.97155	+	0.717587i
$50$	7.25682	−	1.60922i	1.02627	−	0.227578i
$51$	−8.00039	+	1.01828i	−1.12028	+	0.142588i
$52$	2.17793	−	3.11115i	0.302025	−	0.431438i
$53$	1.27415			0.175018			0.0875092	−	0.996164i	$-0.472109\pi$
$53$	1.27415			0.175018			0.0875092	+	0.996164i	$0.472109\pi$
$54$	7.07306	+	1.99296i	0.962521	+	0.271207i
$55$		−	2.84099i		−	0.383078i
$56$	11.1100	+	7.07528i	1.48464	+	0.945474i
$57$	−0.472464	+	0.359316i	−0.0625793	+	0.0475926i
$58$	−7.51460	+	1.66638i	−0.986715	+	0.218807i
$59$	2.43399	−	6.68734i	0.316879	−	0.870618i	−0.674344	−	0.738417i	$-0.735573\pi$
$59$	2.43399	−	6.68734i	0.316879	−	0.870618i	0.991223	−	0.132201i	$-0.0422043\pi$
$60$	5.16372	−	9.81875i	0.666634	−	1.26760i
$61$	8.19039	+	1.44419i	1.04867	+	0.184909i	0.671326	−	0.741163i	$-0.265725\pi$
$61$	8.19039	+	1.44419i	1.04867	+	0.184909i	0.377347	+	0.926072i	$0.376836\pi$
$62$	5.17691	−	9.94610i	0.657468	−	1.26316i
$63$	−7.91450	−	11.5126i	−0.997134	−	1.45045i
$64$	5.65874	+	5.65497i	0.707343	+	0.706871i
$65$	2.07985	+	5.71435i	0.257974	+	0.708778i
$66$	−1.65865	−	1.40382i	−0.204166	−	0.172798i
$67$	−6.31205	+	5.29644i	−0.771139	+	0.647063i	−0.941000	−	0.338405i	$-0.890113\pi$
$67$	−6.31205	+	5.29644i	−0.771139	+	0.647063i	0.169861	+	0.985468i	$0.445668\pi$
$68$	6.58572	+	6.58426i	0.798636	+	0.798459i
$69$	2.20417	−	9.74384i	0.265351	−	1.17302i
$70$	−19.4852	+	8.07230i	−2.32893	+	0.964825i
$71$	−0.186788	−	0.323526i	−0.0221676	−	0.0383955i	0.854729	−	0.519075i	$-0.173723\pi$
$71$	−0.186788	−	0.323526i	−0.0221676	−	0.0383955i	−0.876896	+	0.480679i	$0.840390\pi$
$72$	−3.18093	−	7.86649i	−0.374877	−	0.927075i
$73$	6.29550	−	10.9041i	0.736832	−	1.27623i	−0.217083	−	0.976153i	$-0.569654\pi$
$73$	6.29550	−	10.9041i	0.736832	−	1.27623i	0.953915	−	0.300077i	$-0.0970125\pi$
$74$	−0.493895	+	3.75312i	−0.0574141	+	0.436291i
$75$	4.16883	+	8.09304i	0.481375	+	0.934504i
$76$	0.662065	+	0.177321i	0.0759441	+	0.0203401i
$77$	0.717374	+	4.06843i	0.0817524	+	0.463641i
$78$	4.36393	+	1.60936i	0.494118	+	0.182224i
$79$	−2.54509	+	3.03312i	−0.286345	+	0.341252i	−0.889973	−	0.456014i	$-0.849277\pi$
$79$	−2.54509	+	3.03312i	−0.286345	+	0.341252i	0.603628	+	0.797266i	$0.293721\pi$
$80$	−12.6149	+	2.22724i	−1.41039	+	0.249013i
$81$	−0.154829	+	8.99867i	−0.0172032	+	0.999852i
$82$	0.0762384	−	0.00333288i	0.00841912	−	0.000368055i
$83$	8.90996	−	10.6185i	0.977996	−	1.16553i	−0.00820363	−	0.999966i	$-0.502611\pi$
$83$	8.90996	−	10.6185i	0.977996	−	1.16553i	0.986199	−	0.165563i	$-0.0529442\pi$
$84$	−4.91538	+	15.3648i	−0.536312	+	1.67644i
$85$	−14.6852	+	2.58940i	−1.59284	+	0.280860i
$86$	−1.29369	+	4.10386i	−0.139502	+	0.442531i
$87$	−4.31692	−	8.38053i	−0.462822	−	0.898487i
$88$	−0.109029	+	2.50677i	−0.0116226	+	0.267223i
$89$	−6.35012	−	3.66624i	−0.673111	−	0.388621i	0.124143	−	0.992264i	$-0.460382\pi$
$89$	−6.35012	−	3.66624i	−0.673111	−	0.388621i	−0.797254	+	0.603644i	$0.793715\pi$
$90$	13.2394	+	3.05404i	1.39555	+	0.321924i
$91$	−4.42138	−	7.65805i	−0.463487	−	0.802782i
$92$	−10.4542	+	4.87627i	−1.08992	+	0.508387i
$93$	13.3943	+	3.02994i	1.38892	+	0.314191i
$94$	10.4645	+	11.4187i	1.07933	+	1.17775i
$95$	−0.840731	+	0.705457i	−0.0862572	+	0.0723783i
$96$	−4.93308	+	8.46550i	−0.503480	+	0.864007i
$97$	−0.833364	+	0.303320i	−0.0846153	+	0.0307975i	−0.383981	−	0.923341i	$-0.625447\pi$
$97$	−0.833364	+	0.303320i	−0.0846153	+	0.0307975i	0.299366	+	0.954138i	$0.403225\pi$
$98$	17.5166	−	11.1607i	1.76944	−	1.12740i
$99$	1.14544	−	2.40223i	0.115121	−	0.241434i
$100$	4.44150	−	9.52759i	0.444150	−	0.952759i
$101$	1.09507	−	6.21046i	0.108964	−	0.617964i	−0.880599	−	0.473862i	$-0.842860\pi$
$101$	1.09507	−	6.21046i	0.108964	−	0.617964i	0.989563	−	0.144102i	$-0.0460294\pi$
$102$	−5.74465	+	9.85319i	−0.568805	+	0.975611i
$103$	−2.99018	+	8.21544i	−0.294631	+	0.809492i	0.700743	+	0.713414i	$0.252852\pi$
$103$	−2.99018	+	8.21544i	−0.294631	+	0.809492i	−0.995374	+	0.0960778i	$0.969370\pi$
$104$	−1.61588	−	5.12193i	−0.158450	−	0.502247i
$105$	−15.6368	−	20.5607i	−1.52599	−	2.00652i
$106$	1.09686	−	1.42962i	0.106537	−	0.138857i
$107$		−	3.23101i		−	0.312354i	−0.987729	−	0.156177i	$-0.950083\pi$
$107$		−	3.23101i		−	0.312354i	0.987729	−	0.156177i	$-0.0499170\pi$
$108$	8.32502	−	6.22045i	0.801075	−	0.598563i
$109$		−	10.8688i		−	1.04104i	−0.853849	−	0.520521i	$-0.825738\pi$
$109$		−	10.8688i		−	1.04104i	0.853849	−	0.520521i	$-0.174262\pi$
$110$	−3.18764	−	2.44568i	−0.303929	−	0.233186i
$111$	−4.59914	+	0.585375i	−0.436531	+	0.0555614i
$112$	17.5027	−	6.37489i	1.65385	−	0.602370i
$113$	3.71933	−	10.2188i	0.349885	−	0.961301i	−0.632521	−	0.774543i	$-0.717980\pi$
$113$	3.71933	−	10.2188i	0.349885	−	0.961301i	0.982406	−	0.186758i	$-0.0597979\pi$
$114$	−0.00356379	+	0.839432i	−0.000333779	+	0.0786201i
$115$	3.20749	−	18.1906i	0.299100	−	1.69628i
$116$	−4.59927	+	9.86604i	−0.427032	+	0.916038i
$117$	−0.545285	+	5.67041i	−0.0504117	+	0.524230i
$118$	−5.40801	−	8.48783i	−0.497847	−	0.781368i
$119$	20.3761	−	7.41630i	1.86788	−	0.679851i
$120$	−6.57160	−	14.2463i	−0.599903	−	1.30051i
$121$	7.82363	−	6.56481i	0.711239	−	0.596801i
$122$	8.67116	−	7.94654i	0.785050	−	0.719446i
$123$	0.0277209	+	0.0892561i	0.00249950	+	0.00804795i
$124$	−6.70314	−	14.3708i	−0.601960	−	1.29053i
$125$	0.409913	+	0.709991i	0.0366638	+	0.0635035i
$126$	−19.7306	−	1.03047i	−1.75774	−	0.0918018i
$127$	12.2372	+	7.06513i	1.08587	+	0.626929i	0.932475	−	0.361235i	$-0.117645\pi$
$127$	12.2372	+	7.06513i	1.08587	+	0.626929i	0.153399	+	0.988164i	$0.450978\pi$
$128$	11.2163	−	1.48110i	0.991394	−	0.130912i
$129$	−5.26395	−	0.252517i	−0.463465	−	0.0222329i
$130$	8.20207	+	2.58560i	0.719369	+	0.226772i
$131$	−3.55599	+	0.627016i	−0.310688	+	0.0547827i	−0.326818	−	0.945087i	$-0.605976\pi$
$131$	−3.55599	+	0.627016i	−0.310688	+	0.0547827i	0.0161302	+	0.999870i	$0.494865\pi$
$132$	−3.00297	+	0.652555i	−0.261375	+	0.0567976i
$133$	1.02583	−	1.22254i	0.0889511	−	0.106008i
$134$	0.508936	+	11.6417i	0.0439654	+	1.00569i
$135$	0.511290	+	16.6328i	0.0440049	+	1.43152i
$136$	13.0570	−	1.72120i	1.11963	−	0.147592i
$137$	−8.46244	+	10.0851i	−0.722995	+	0.861632i	−0.994918	−	0.100687i	$-0.967896\pi$
$137$	−8.46244	+	10.0851i	−0.722995	+	0.861632i	0.271923	+	0.962319i	$0.412340\pi$
$138$	−9.03530	−	10.8612i	−0.769136	−	0.924563i
$139$	2.08259	+	11.8109i	0.176643	+	1.00179i	0.936230	+	0.351387i	$0.114290\pi$
$139$	2.08259	+	11.8109i	0.176643	+	1.00179i	−0.759588	+	0.650405i	$0.774599\pi$
$140$	−7.71668	+	28.8119i	−0.652179	+	2.43505i
$141$	−10.2609	+	15.9546i	−0.864128	+	1.34362i
$142$	−0.523800	−	0.0689300i	−0.0439563	−	0.00578447i
$143$	0.842252	−	1.45882i	0.0704327	−	0.121993i
$144$	−11.5647	−	3.20285i	−0.963723	−	0.266904i
$145$	−8.71512	−	15.0950i	−0.723751	−	1.25357i
$146$	−6.81511	−	16.4505i	−0.564022	−	1.36146i
$147$	18.6807	+	17.2661i	1.54076	+	1.42408i
$148$	3.78590	+	3.78505i	0.311199	+	0.311129i
$149$	−6.78333	+	5.69189i	−0.555712	+	0.466298i	−0.876870	−	0.480728i	$-0.840372\pi$
$149$	−6.78333	+	5.69189i	−0.555712	+	0.466298i	0.321158	+	0.947026i	$0.395928\pi$
$150$	12.6693	+	2.28944i	1.03444	+	0.186932i
$151$	−1.00187	−	2.75261i	−0.0815308	−	0.224004i	0.892229	−	0.451584i	$-0.149141\pi$
$151$	−1.00187	−	2.75261i	−0.0815308	−	0.224004i	−0.973759	+	0.227580i	$0.926919\pi$
$152$	0.768900	−	0.590202i	0.0623661	−	0.0478717i
$153$	−13.4613	−	3.73134i	−1.08828	−	0.301661i
$154$	5.18241	+	2.69743i	0.417611	+	0.217365i
$155$	25.0056	+	4.40916i	2.00850	+	0.354152i
$156$	5.56245	−	3.51099i	0.445352	−	0.281104i
$157$	3.73399	−	10.2591i	0.298005	−	0.818762i	−0.696828	−	0.717238i	$-0.745406\pi$
$157$	3.73399	−	10.2591i	0.298005	−	0.818762i	0.994833	−	0.101524i	$-0.0323717\pi$
$158$	1.21226	+	5.46671i	0.0964422	+	0.434908i
$159$	2.03526	+	0.853305i	0.161406	+	0.0676715i
$160$	−8.36060	+	16.0715i	−0.660964	+	1.27056i
$161$			26.8597i			2.11684i
$162$	9.96339	+	7.92028i	0.782798	+	0.622276i
$163$	−0.983434			−0.0770285			−0.0385143	−	0.999258i	$-0.512263\pi$
$163$	−0.983434			−0.0770285			−0.0385143	+	0.999258i	$0.512263\pi$
$164$	0.0618907	−	0.0884100i	0.00483285	−	0.00690366i
$165$	1.90262	−	4.53802i	0.148119	−	0.353284i
$166$	−4.24394	−	19.1381i	−0.329393	−	1.48541i
$167$	−1.50427	−	0.547510i	−0.116404	−	0.0423676i	0.283161	−	0.959072i	$-0.408617\pi$
$167$	−1.50427	−	0.547510i	−0.116404	−	0.0423676i	−0.399565	+	0.916705i	$0.630839\pi$
$168$	13.0082	+	18.7421i	1.00360	+	1.44598i
$169$	1.63131	−	9.25162i	0.125485	−	0.711663i
$170$	−9.73651	+	18.7062i	−0.746756	+	1.43470i
$171$	−0.995320	+	0.257540i	−0.0761141	+	0.0196946i
$172$	3.49093	+	4.98438i	0.266181	+	0.380056i
$173$	−13.3229	+	4.84914i	−1.01292	+	0.368673i	−0.794554	−	0.607193i	$-0.792295\pi$
$173$	−13.3229	+	4.84914i	−1.01292	+	0.368673i	−0.218367	+	0.975867i	$0.570073\pi$
$174$	−13.1194	−	2.37077i	−0.994576	−	0.179727i
$175$	−15.7332	−	18.7501i	−1.18932	−	1.41738i
$176$	2.71879	+	2.28030i	0.204936	+	0.171884i
$177$	8.36646	−	9.05191i	0.628861	−	0.680383i
$178$	−9.58013	+	3.96884i	−0.718061	+	0.297477i
$179$	−5.27151	+	3.04351i	−0.394011	+	0.227483i	−0.683897	−	0.729579i	$-0.739716\pi$
$179$	−5.27151	+	3.04351i	−0.394011	+	0.227483i	0.289885	+	0.957061i	$0.406383\pi$
$180$	14.8239	−	12.2257i	1.10491	−	0.911252i
$181$	11.4059	+	6.58520i	0.847795	+	0.489474i	0.859906	−	0.510452i	$-0.170522\pi$
$181$	11.4059	+	6.58520i	0.847795	+	0.489474i	−0.0121116	+	0.999927i	$0.503855\pi$
$182$	−12.3987	−	1.63161i	−0.919049	−	0.120943i
$183$	12.1157	+	7.79200i	0.895616	+	0.576001i
$184$	−3.52827	+	15.9275i	−0.260107	+	1.17419i
$185$	−8.44201	+	1.48855i	−0.620669	+	0.109441i
$186$	14.9302	−	12.4203i	1.09474	−	0.910702i
$187$	3.16427	+	2.65514i	0.231395	+	0.194163i
$188$	21.8204	−	1.91148i	1.59141	−	0.139409i
$189$	−4.93213	−	23.6899i	−0.358760	−	1.72319i
$190$	0.0677875	+	1.55061i	0.00491783	+	0.112493i
$191$	−16.3786	−	13.7433i	−1.18512	−	0.994431i	−0.999931	−	0.0117270i	$-0.996267\pi$
$191$	−16.3786	−	13.7433i	−1.18512	−	0.994431i	−0.185185	−	0.982704i	$-0.559288\pi$
$192$	5.25178	+	12.8226i	0.379015	+	0.925391i
$193$	3.64547	+	20.6745i	0.262407	+	1.48818i	0.776319	+	0.630341i	$0.217085\pi$
$193$	3.64547	+	20.6745i	0.262407	+	1.48818i	−0.513912	+	0.857843i	$0.671804\pi$
$194$	−0.377076	+	1.19616i	−0.0270725	+	0.0858796i
$195$	−0.504686	+	10.5207i	−0.0361413	+	0.753399i
$196$	2.55679	−	29.2617i	0.182628	−	2.09012i
$197$	5.23281	−	9.06349i	0.372822	−	0.645747i	−0.617176	−	0.786825i	$-0.711723\pi$
$197$	5.23281	−	9.06349i	0.372822	−	0.645747i	0.989999	+	0.141078i	$0.0450568\pi$
$198$	−1.70929	−	3.35318i	−0.121474	−	0.238300i
$199$	−14.3685	+	8.29565i	−1.01855	+	0.588063i	−0.913685	−	0.406423i	$-0.866776\pi$
$199$	−14.3685	+	8.29565i	−1.01855	+	0.588063i	−0.104870	+	0.994486i	$0.533443\pi$
$200$	−6.86665	−	13.1853i	−0.485545	−	0.932344i
$201$	−13.6295	+	4.23301i	−0.961353	+	0.298574i
$202$	−6.02556	−	6.57501i	−0.423957	−	0.462616i
$203$	16.2921	+	19.4162i	1.14348	+	1.36275i
$204$	6.11014	+	14.9278i	0.427795	+	1.04515i
$205$	0.0591036	+	0.162386i	0.00412797	+	0.0113415i
$206$	6.64377	+	10.4273i	0.462893	+	0.726508i
$207$	10.0463	−	14.0881i	0.698265	−	0.979190i
$208$	−7.13794	−	2.59620i	−0.494927	−	0.180014i
$209$	0.299396	+	0.0527915i	0.0207096	+	0.00365167i
$210$	−36.5306	−	0.155090i	−2.52085	−	0.0107022i
$211$	−8.76523	−	3.19028i	−0.603423	−	0.219628i	0.0222000	−	0.999754i	$-0.492933\pi$
$211$	−8.76523	−	3.19028i	−0.603423	−	0.219628i	−0.625623	+	0.780126i	$0.715155\pi$
$212$	−0.659824	−	2.46140i	−0.0453169	−	0.169050i
$213$	−0.0816973	−	0.641874i	−0.00559781	−	0.0439805i
$214$	−3.62526	−	2.78144i	−0.247817	−	0.190135i
$215$	−9.74405			−0.664539
$216$	0.187180	−	14.6957i	0.0127360	−	0.999919i
$217$	−36.9226			−2.50647
$218$	−12.1950	−	9.35647i	−0.825949	−	0.633700i
$219$	17.3586	−	13.2015i	1.17298	−	0.892073i
$220$	−5.48820	+	1.47121i	−0.370014	+	0.0991891i
$221$	−8.30841	−	3.02402i	−0.558884	−	0.203417i
$222$	−3.30239	+	5.66424i	−0.221642	+	0.380159i
$223$	18.4672	+	3.25626i	1.23665	+	0.218055i	0.753481	−	0.657470i	$-0.228373\pi$
$223$	18.4672	+	3.25626i	1.23665	+	0.218055i	0.483172	+	0.875525i	$0.339485\pi$
$224$	7.91461	−	25.1263i	0.528817	−	1.67882i
$225$	1.23910	+	15.7192i	0.0826067	+	1.04795i
$226$	−8.26384	−	12.9700i	−0.549703	−	0.862755i
$227$	1.73323	+	4.76200i	0.115038	+	0.316065i	0.983828	−	0.179116i	$-0.0573238\pi$
$227$	1.73323	+	4.76200i	0.115038	+	0.316065i	−0.868790	+	0.495181i	$0.835102\pi$
$228$	0.938791	+	0.726629i	0.0621730	+	0.0481222i
$229$	14.4905	+	17.2691i	0.957559	+	1.14117i	0.989910	+	0.141698i	$0.0452562\pi$
$229$	14.4905	+	17.2691i	0.957559	+	1.14117i	−0.0323508	+	0.999477i	$0.510299\pi$
$230$	−17.6490	−	19.2583i	−1.16374	−	1.26986i
$231$	−1.57875	+	6.97910i	−0.103874	+	0.459191i
$232$	7.11056	+	13.6537i	0.466831	+	0.896410i
$233$	4.93700	−	2.85038i	0.323434	−	0.186735i	−0.329488	−	0.944160i	$-0.606876\pi$
$233$	4.93700	−	2.85038i	0.323434	−	0.186735i	0.652922	+	0.757425i	$0.273543\pi$
$234$	5.89290	+	5.49323i	0.385231	+	0.359104i
$235$	−17.5368	+	30.3747i	−1.14398	+	1.98143i
$236$	−14.1790	−	1.23892i	−0.922976	−	0.0806466i
$237$	−6.09666	+	3.14047i	−0.396020	+	0.203995i
$238$	9.21968	−	29.2468i	0.597623	−	1.89579i
$239$	3.99952	+	22.6824i	0.258707	+	1.46720i	0.786374	+	0.617750i	$0.211956\pi$
$239$	3.99952	+	22.6824i	0.258707	+	1.46720i	−0.527667	+	0.849451i	$0.676933\pi$
$240$	−21.6419	−	4.89058i	−1.39698	−	0.315686i
$241$	16.6164	+	13.9428i	1.07036	+	0.898137i	0.995085	−	0.0990259i	$-0.0315727\pi$
$241$	16.6164	+	13.9428i	1.07036	+	0.898137i	0.0752732	+	0.997163i	$0.476017\pi$
$242$	−0.630814	−	14.4296i	−0.0405503	−	0.927571i
$243$	−6.27375	+	14.2702i	−0.402462	+	0.915437i
$244$	−1.45155	−	16.5700i	−0.0929257	−	1.06079i
$245$	36.0300	+	30.2327i	2.30187	+	1.93150i
$246$	0.124011	+	0.0457334i	0.00790663	+	0.00291585i
$247$	−0.640852	+	0.112999i	−0.0407764	+	0.00718999i
$248$	−21.8947	−	4.85011i	−1.39031	−	0.307982i
$249$	21.3435	−	10.9943i	1.35259	−	0.696735i
$250$	1.14950	+	0.151269i	0.0727007	+	0.00956712i
$251$	−6.86745	−	3.96493i	−0.433470	−	0.250264i	0.267354	−	0.963598i	$-0.413851\pi$
$251$	−6.86745	−	3.96493i	−0.433470	−	0.250264i	−0.700824	+	0.713334i	$0.747184\pi$
$252$	−18.1414	+	21.2510i	−1.14280	+	1.33869i
$253$	−4.43115	+	2.55833i	−0.278584	+	0.160841i
$254$	18.4617	−	7.64827i	1.15839	−	0.479895i
$255$	−25.1914	−	5.69859i	−1.57755	−	0.356860i
$256$	7.99384	−	13.8600i	0.499615	−	0.866248i
$257$	0.0798480	+	0.0951592i	0.00498078	+	0.00593587i	0.768529	−	0.639815i	$-0.220989\pi$
$257$	0.0798480	+	0.0951592i	0.00498078	+	0.00593587i	−0.763548	+	0.645751i	$0.776545\pi$
$258$	−4.81484	+	5.68888i	−0.299759	+	0.354174i
$259$	11.7135	−	4.26337i	0.727842	−	0.264913i
$260$	9.96189	−	6.97704i	0.617810	−	0.432698i
$261$	−1.28312	−	16.2776i	−0.0794229	−	1.00756i
$262$	−2.35767	+	4.52965i	−0.145657	+	0.279843i
$263$	−0.961362	+	5.45215i	−0.0592801	+	0.336194i	−0.999995	−	0.00300271i	$-0.999044\pi$
$263$	−0.961362	+	5.45215i	−0.0592801	+	0.336194i	0.940715	+	0.339197i	$0.110155\pi$
$264$	−1.85295	+	3.93115i	−0.114041	+	0.241946i
$265$	3.83439	+	1.39560i	0.235545	+	0.0857313i
$266$	−0.488619	−	2.20344i	−0.0299591	−	0.135101i
$267$	−7.68800	−	10.1089i	−0.470498	−	0.618657i
$268$	13.5003	+	9.45080i	0.824664	+	0.577300i
$269$	−5.59805			−0.341319			−0.170659	−	0.985330i	$-0.554590\pi$
$269$	−5.59805			−0.341319			−0.170659	+	0.985330i	$0.554590\pi$
$270$	19.1025	+	13.7448i	1.16254	+	0.836481i
$271$		−	1.56554i		−	0.0951000i	−0.998869	−	0.0475500i	$-0.984859\pi$
$271$		−	1.56554i		−	0.0951000i	0.998869	−	0.0475500i	$-0.0151413\pi$
$272$	9.30900	−	16.1319i	0.564441	−	0.978142i
$273$	−1.93382	−	15.1935i	−0.117040	−	0.919555i
$274$	4.03078	+	18.1769i	0.243508	+	1.09811i
$275$	1.59473	−	4.38148i	0.0961657	−	0.264213i
$276$	−19.9645	+	0.787876i	−1.20172	+	0.0474246i
$277$	−27.6100	−	4.86839i	−1.65893	−	0.292513i	−0.735854	−	0.677140i	$-0.763219\pi$
$277$	−27.6100	−	4.86839i	−1.65893	−	0.292513i	−0.923072	+	0.384627i	$0.874330\pi$
$278$	15.0449	+	7.83083i	0.902334	+	0.469662i
$279$	19.3661	+	13.8101i	1.15942	+	0.826787i
$280$	25.6845	+	33.4611i	1.53494	+	1.99968i
$281$	3.07719	+	8.45452i	0.183570	+	0.504354i	0.997008	−	0.0772972i	$-0.0246290\pi$
$281$	3.07719	+	8.45452i	0.183570	+	0.504354i	−0.813438	+	0.581651i	$0.802407\pi$
$282$	9.06818	+	25.2476i	0.540002	+	1.50347i
$283$	−22.1256	+	18.5656i	−1.31523	+	1.10361i	−0.327936	+	0.944700i	$0.606353\pi$
$283$	−22.1256	+	18.5656i	−1.31523	+	1.10361i	−0.987293	+	0.158909i	$0.949202\pi$
$284$	−0.528257	+	0.528375i	−0.0313463	+	0.0313533i
$285$	−1.81538	+	0.563815i	−0.107534	+	0.0333975i
$286$	−0.911770	−	2.20086i	−0.0539141	−	0.130140i
$287$	−0.125643	−	0.217620i	−0.00741648	−	0.0128457i
$288$	−13.5492	+	10.2186i	−0.798393	+	0.602136i
$289$	2.34052	−	4.05391i	0.137678	−	0.238465i
$290$	−24.4394	−	3.21612i	−1.43513	−	0.188857i
$291$	−1.53430	−	0.0736019i	−0.0899423	−	0.00431462i
$292$	−24.3247	−	6.51487i	−1.42349	−	0.381254i
$293$	−3.10437	−	17.6058i	−0.181359	−	1.02854i	−0.930545	−	0.366179i	$-0.880666\pi$
$293$	−3.10437	−	17.6058i	−0.181359	−	1.02854i	0.749185	−	0.662360i	$-0.230445\pi$
$294$	35.4543	−	6.09647i	2.06774	−	0.355553i
$295$	14.6495	−	17.4587i	0.852930	−	1.01648i
$296$	7.50601	−	0.989458i	0.436278	−	0.0575111i
$297$	3.43844	−	3.07008i	0.199519	−	0.178144i
$298$	0.546935	+	12.5109i	0.0316831	+	0.724738i
$299$	7.03989	−	8.38981i	0.407127	−	0.485196i
$300$	13.4753	−	12.2443i	0.777994	−	0.706926i
$301$	13.9540	−	2.46046i	0.804293	−	0.141819i
$302$	−3.95094	−	1.24549i	−0.227351	−	0.0716697i
$303$	5.90837	−	9.18685i	0.339427	−	0.527771i
$304$	−0.000304701	−	1.37080i	−1.74758e−5	−	0.0786208i
$305$	23.0660	+	13.3172i	1.32076	+	0.762540i
$306$	−15.7749	+	11.8917i	−0.901790	+	0.679802i
$307$	2.66885	+	4.62258i	0.152319	+	0.263825i	0.932080	−	0.362253i	$-0.117992\pi$
$307$	2.66885	+	4.62258i	0.152319	+	0.263825i	−0.779760	+	0.626078i	$0.784659\pi$
$308$	7.48788	−	3.49267i	0.426662	−	0.199013i
$309$	−10.2782	+	11.1203i	−0.584709	+	0.632613i
$310$	26.4734	−	24.2611i	1.50359	−	1.37794i
$311$	7.48203	−	6.27817i	0.424267	−	0.356002i	−0.405517	−	0.914088i	$-0.632908\pi$
$311$	7.48203	−	6.27817i	0.424267	−	0.356002i	0.829783	+	0.558086i	$0.188464\pi$
$312$	0.849069	−	9.26363i	0.0480690	−	0.524450i
$313$	−20.9377	+	7.62069i	−1.18347	+	0.430747i	−0.857425	−	0.514608i	$-0.827937\pi$
$313$	−20.9377	+	7.62069i	−1.18347	+	0.430747i	−0.326042	+	0.945355i	$0.605715\pi$
$314$	−8.29642	−	13.0212i	−0.468194	−	0.734828i
$315$	−11.2077	−	43.3145i	−0.631480	−	2.44050i
$316$	7.17733	+	3.34587i	0.403757	+	0.188220i
$317$	2.75422	−	15.6200i	0.154692	−	0.877304i	−0.804374	−	0.594123i	$-0.797499\pi$
$317$	2.75422	−	15.6200i	0.154692	−	0.877304i	0.959067	−	0.283181i	$-0.0913897\pi$
$318$	2.70949	−	1.54902i	0.151941	−	0.0868650i
$319$	−1.65138	+	4.53712i	−0.0924593	+	0.254030i
$320$	10.8352	+	23.2160i	0.605707	+	1.29781i
$321$	2.16382	−	5.16103i	0.120773	−	0.288060i
$322$	30.1371	+	23.1224i	1.67948	+	1.28856i
$323$		−	1.59571i		−	0.0887877i
$324$	17.4638	−	4.36089i	0.970208	−	0.242272i
$325$			9.98038i			0.553612i
$326$	−0.846596	+	1.10343i	−0.0468886	+	0.0611134i
$327$	7.27887	−	17.3612i	0.402522	−	0.960075i
$328$	−0.0459187	−	0.145551i	−0.00253544	−	0.00803670i
$329$	17.4437	−	47.9263i	0.961704	−	2.64226i
$330$	−3.45386	−	6.04136i	−0.190129	−	0.332566i
$331$	4.91331	−	27.8648i	0.270060	−	1.53159i	−0.484169	−	0.874974i	$-0.660878\pi$
$331$	4.91331	−	27.8648i	0.270060	−	1.53159i	0.754229	−	0.656611i	$-0.228011\pi$
$332$	−25.1268	−	11.7134i	−1.37901	−	0.642857i
$333$	−7.73842	−	2.14501i	−0.424063	−	0.117546i
$334$	−1.90928	+	1.21649i	−0.104471	+	0.0665636i
$335$	−24.7965	+	9.02520i	−1.35478	+	0.493099i
$336$	32.2271	+	1.53879i	1.75813	+	0.0839478i
$337$	−2.65131	+	2.22472i	−0.144426	+	0.121188i	−0.712138	−	0.702039i	$-0.752273\pi$
$337$	−2.65131	+	2.22472i	−0.144426	+	0.121188i	0.567712	+	0.823227i	$0.307829\pi$
$338$	−8.97617	−	9.79468i	−0.488239	−	0.532760i
$339$	12.7846	−	13.8320i	0.694363	−	0.751251i
$340$	12.6070	+	27.0279i	0.683709	+	1.46579i
$341$	−3.51679	−	6.09126i	−0.190445	−	0.329860i
$342$	−0.567863	+	1.33847i	−0.0307065	+	0.0723763i
$343$	−30.9999	−	17.8978i	−1.67383	−	0.966389i
$344$	8.59776	+	0.373950i	0.463560	+	0.0201620i
$345$	17.3058	−	26.9085i	0.931710	−	1.44870i
$346$	−6.02828	+	19.1230i	−0.324082	+	1.02806i
$347$	−21.3082	+	3.75721i	−1.14388	+	0.201698i	−0.713304	−	0.700854i	$-0.752802\pi$
$347$	−21.3082	+	3.75721i	−1.14388	+	0.201698i	−0.430581	+	0.902552i	$0.641691\pi$
$348$	−13.9539	+	12.6793i	−0.748009	+	0.679680i
$349$	−13.6098	+	16.2195i	−0.728514	+	0.868209i	−0.995428	−	0.0955113i	$-0.969551\pi$
$349$	−13.6098	+	16.2195i	−0.728514	+	0.868209i	0.266915	+	0.963720i	$0.413996\pi$
$350$	−34.5821	+	1.51181i	−1.84849	+	0.0808097i
$351$	−4.66850	+	8.69240i	−0.249186	+	0.463966i
$352$	4.89903	−	1.08752i	0.261119	−	0.0579648i
$353$	−10.0326	+	11.9564i	−0.533980	+	0.636373i	−0.963827	−	0.266529i	$-0.914123\pi$
$353$	−10.0326	+	11.9564i	−0.533980	+	0.636373i	0.429847	+	0.902902i	$0.358568\pi$
$354$	−2.95410	−	17.1797i	−0.157009	−	0.913092i
$355$	−0.207748	−	1.17820i	−0.0110261	−	0.0625324i
$356$	−3.79400	+	14.1657i	−0.201081	+	0.750780i
$357$	37.5143	+	1.79960i	1.98547	+	0.0952449i
$358$	−1.12314	+	8.53476i	−0.0593598	+	0.451076i
$359$	−2.44114	+	4.22817i	−0.128838	+	0.223154i	−0.923227	−	0.384256i	$-0.874458\pi$
$359$	−2.44114	+	4.22817i	−0.128838	+	0.223154i	0.794389	+	0.607410i	$0.207791\pi$
$360$	−0.956274	−	27.1573i	−0.0504001	−	1.43131i
$361$	9.44128	+	16.3528i	0.496909	+	0.860672i
$362$	17.2076	−	7.12873i	0.904410	−	0.374678i
$363$	16.8935	−	5.24672i	0.886678	−	0.275381i
$364$	−12.5042	+	12.5069i	−0.655396	+	0.655542i
$365$	30.8889	−	25.9189i	1.61680	−	1.35666i
$366$	19.1726	−	6.88623i	1.00217	−	0.359949i
$367$	3.44230	+	9.45764i	0.179687	+	0.493685i	0.996536	−	0.0831666i	$-0.0265033\pi$
$367$	3.44230	+	9.45764i	0.179687	+	0.493685i	−0.816849	+	0.576852i	$0.804281\pi$
$368$	14.8337	+	17.6701i	0.773259	+	0.921118i
$369$	−0.0154955	+	0.161137i	−0.000806662	+	0.00838846i
$370$	−5.59717	+	10.7535i	−0.290983	+	0.559049i
$371$	−5.84344	−	1.03036i	−0.303376	−	0.0534935i
$372$	−1.08305	−	27.4441i	−0.0561535	−	1.42291i
$373$	0.511543	−	1.40545i	0.0264867	−	0.0727717i	−0.925745	−	0.378149i	$-0.876561\pi$
$373$	0.511543	−	1.40545i	0.0264867	−	0.0727717i	0.952231	+	0.305378i	$0.0987828\pi$
$374$	5.70310	−	1.26468i	0.294901	−	0.0653951i
$375$	0.179288	+	1.40862i	0.00925839	+	0.0727407i
$376$	16.6395	−	26.1284i	0.858116	−	1.34747i
$377$		−	10.3349i		−	0.532275i
$378$	−30.8264	−	14.8597i	−1.58554	−	0.764299i
$379$	26.4034			1.35625			0.678126	−	0.734945i	$-0.262792\pi$
$379$	26.4034			1.35625			0.678126	+	0.734945i	$0.262792\pi$
$380$	1.79817	+	1.25880i	0.0922443	+	0.0645749i
$381$	14.8154	+	19.4807i	0.759015	+	0.998027i
$382$	−29.5199	+	6.54612i	−1.51037	+	0.334929i
$383$	14.7665	+	5.37456i	0.754532	+	0.274627i	0.690511	−	0.723321i	$-0.257386\pi$
$383$	14.7665	+	5.37456i	0.754532	+	0.274627i	0.0640204	+	0.997949i	$0.479608\pi$
$384$	18.9082	+	5.14581i	0.964906	+	0.262596i
$385$	−2.29739	+	13.0291i	−0.117086	+	0.664027i
$386$	26.3354	+	13.7075i	1.34044	+	0.697693i
$387$	−8.23922	−	3.92864i	−0.418823	−	0.199704i
$388$	1.01751	+	1.45281i	0.0516563	+	0.0737554i
$389$	−19.0208	+	6.92300i	−0.964393	+	0.351010i	−0.775753	−	0.631036i	$-0.782630\pi$
$389$	−19.0208	+	6.92300i	−0.964393	+	0.351010i	−0.188639	+	0.982046i	$0.560408\pi$
$390$	11.3699	+	9.62304i	0.575738	+	0.487281i
$391$	17.2629	+	20.5731i	0.873023	+	1.04043i
$392$	−30.6311	−	28.0589i	−1.54711	−	1.41719i
$393$	−6.10004	−	1.37990i	−0.307706	−	0.0696066i
$394$	−5.66471	−	13.6737i	−0.285384	−	0.688870i
$395$	−10.9813	+	6.34007i	−0.552530	+	0.319003i
$396$	−5.23379	−	0.968750i	−0.263008	−	0.0486815i
$397$	−23.8679	−	13.7801i	−1.19789	−	0.691604i	−0.237808	−	0.971312i	$-0.576429\pi$
$397$	−23.8679	−	13.7801i	−1.19789	−	0.691604i	−0.960085	+	0.279708i	$0.909762\pi$
$398$	−3.06133	+	23.2631i	−0.153450	+	1.16607i
$399$	2.45735	−	1.26581i	0.123021	−	0.0633698i
$400$	−20.7054	−	3.64617i	−1.03527	−	0.182309i
$401$	−6.68368	+	1.17851i	−0.333767	+	0.0588521i	−0.338020	−	0.941139i	$-0.609757\pi$
$401$	−6.68368	+	1.17851i	−0.333767	+	0.0588521i	0.00425323	+	0.999991i	$0.498646\pi$
$402$	−6.98355	+	18.9366i	−0.348308	+	0.944472i
$403$	11.5330	+	9.67734i	0.574500	+	0.482063i
$404$	−12.5644	+	1.10065i	−0.625103	+	0.0547595i
$405$	−10.3223	+	26.9107i	−0.512922	+	1.33720i
$406$	35.8105	−	1.56551i	1.77725	−	0.0776952i
$407$	1.81903	+	1.52635i	0.0901659	+	0.0756581i
$408$	22.0092	+	5.99498i	1.08962	+	0.296796i
$409$	−2.97274	−	16.8592i	−0.146992	−	0.833636i	−0.965746	−	0.259490i	$-0.916445\pi$
$409$	−2.97274	−	16.8592i	−0.146992	−	0.833636i	0.818753	−	0.574145i	$-0.194666\pi$
$410$	0.233080	+	0.0734755i	0.0115110	+	0.00362869i
$411$	−20.2715	+	10.4421i	−0.999917	+	0.515070i
$412$	17.4190	+	1.52202i	0.858173	+	0.0749843i
$413$	−16.5704	+	28.7008i	−0.815377	+	1.41227i
$414$	−7.15869	−	23.3999i	−0.351831	−	1.15004i
$415$	38.4439	−	22.1956i	1.88714	−	1.08954i
$416$	−9.05773	+	5.77395i	−0.444092	+	0.283091i
$417$	−4.58323	+	20.2608i	−0.224442	+	0.992177i
$418$	0.316970	−	0.290482i	0.0155035	−	0.0142079i
$419$	0.999049	+	1.19062i	0.0488067	+	0.0581656i	0.789896	−	0.613241i	$-0.210135\pi$
$419$	0.999049	+	1.19062i	0.0488067	+	0.0581656i	−0.741089	+	0.671407i	$0.765690\pi$
$420$	−31.6216	+	40.8545i	−1.54297	+	1.99349i
$421$	−4.61578	−	12.6818i	−0.224959	−	0.618071i	0.774943	−	0.632031i	$-0.217778\pi$
$421$	−4.61578	−	12.6818i	−0.224959	−	0.618071i	−0.999903	+	0.0139601i	$0.995556\pi$
$422$	−11.1252	+	7.08837i	−0.541564	+	0.345057i
$423$	−27.0751	+	18.6132i	−1.31644	+	0.905003i
$424$	−3.32975	−	1.37858i	−0.161707	−	0.0669497i
$425$	−24.1016	−	4.24977i	−1.16910	−	0.206144i
$426$	−0.790524	−	0.460895i	−0.0383010	−	0.0223304i
$427$	−36.3944	−	13.2465i	−1.76125	−	0.641042i
$428$	−6.24165	+	1.67319i	−0.301702	+	0.0808766i
$429$	2.32234	−	1.76618i	0.112124	−	0.0852719i
$430$	−8.38823	+	10.9330i	−0.404516	+	0.527237i
$431$	32.6219			1.57134			0.785671	−	0.618644i	$-0.212318\pi$
$431$	32.6219			1.57134			0.785671	+	0.618644i	$0.212318\pi$
$432$	−16.3278	−	12.8609i	−0.785570	−	0.618773i
$433$	−20.4173			−0.981192			−0.490596	−	0.871387i	$-0.663221\pi$
$433$	−20.4173			−0.981192			−0.490596	+	0.871387i	$0.663221\pi$
$434$	−31.7850	+	41.4278i	−1.52573	+	1.98860i
$435$	−3.81182	−	29.9485i	−0.182763	−	1.43592i
$436$	−20.9963	+	5.62843i	−1.00554	+	0.269553i
$437$	1.85740	+	0.676039i	0.0888516	+	0.0323393i
$438$	0.130936	−	30.8412i	0.00625635	−	1.47365i
$439$	−5.01912	−	0.885007i	−0.239550	−	0.0422391i	0.0525843	−	0.998616i	$-0.483254\pi$
$439$	−5.01912	−	0.885007i	−0.239550	−	0.0422391i	−0.292134	+	0.956377i	$0.594365\pi$
$440$	−3.07382	+	7.42436i	−0.146539	+	0.353943i
$441$	18.2763	+	40.0904i	0.870299	+	1.90907i
$442$	−10.5454	+	6.71896i	−0.501591	+	0.319588i
$443$	6.33577	+	17.4074i	0.301022	+	0.827050i	0.994323	+	0.106403i	$0.0339332\pi$
$443$	6.33577	+	17.4074i	0.301022	+	0.827050i	−0.693301	+	0.720648i	$0.743845\pi$
$444$	3.51250	+	8.58145i	0.166696	+	0.407257i
$445$	−15.0941	−	17.9885i	−0.715529	−	0.852735i
$446$	19.5512	−	17.9173i	0.925774	−	0.848410i
$447$	−14.6472	+	4.54907i	−0.692787	+	0.215163i
$448$	−21.3788	−	30.5105i	−1.01005	−	1.44148i
$449$	16.4019	−	9.46962i	0.774052	−	0.446899i	−0.0602665	−	0.998182i	$-0.519195\pi$
$449$	16.4019	−	9.46962i	0.774052	−	0.446899i	0.834318	+	0.551283i	$0.185862\pi$
$450$	18.7040	+	12.1417i	0.881713	+	0.572365i
$451$	0.0239344	−	0.0414557i	0.00112703	−	0.00195207i
$452$	−21.6666	−	1.89316i	−1.01911	−	0.0890466i
$453$	0.243108	−	5.06781i	0.0114222	−	0.238106i
$454$	6.83512	+	2.15469i	0.320788	+	0.101124i
$455$	−4.91753	−	27.8887i	−0.230537	−	1.30744i
$456$	1.62346	−	0.427818i	0.0760253	−	0.0200344i
$457$	−8.02025	−	6.72979i	−0.375172	−	0.314806i	0.435632	−	0.900125i	$-0.356525\pi$
$457$	−8.02025	−	6.72979i	−0.375172	−	0.314806i	−0.810803	+	0.585319i	$0.800969\pi$
$458$	31.8505	−	1.39240i	1.48828	−	0.0650624i
$459$	−19.0034	−	14.9753i	−0.887002	−	0.698987i
$460$	−36.8015	+	3.22383i	−1.71588	+	0.150312i
$461$	−18.6832	−	15.6771i	−0.870163	−	0.730153i	0.0939698	−	0.995575i	$-0.470044\pi$
$461$	−18.6832	−	15.6771i	−0.870163	−	0.730153i	−0.964132	+	0.265422i	$0.914489\pi$
$462$	6.47160	+	7.77939i	0.301086	+	0.361930i
$463$	−15.5149	+	2.73570i	−0.721039	+	0.127139i	−0.522113	−	0.852876i	$-0.674856\pi$
$463$	−15.5149	+	2.73570i	−0.721039	+	0.127139i	−0.198925	+	0.980015i	$0.563745\pi$
$464$	21.4409	+	3.77569i	0.995369	+	0.175282i
$465$	36.9896	+	23.7892i	1.71535	+	1.10320i
$466$	1.05187	−	7.99318i	0.0487269	−	0.370277i
$467$	−6.64718	−	3.83775i	−0.307595	−	0.177590i	0.338255	−	0.941055i	$-0.390163\pi$
$467$	−6.64718	−	3.83775i	−0.307595	−	0.177590i	−0.645850	+	0.763465i	$0.723497\pi$
$468$	11.2364	−	1.88306i	0.519405	−	0.0870445i
$469$	33.2309	−	19.1859i	1.53446	−	0.885922i
$470$	18.9843	+	45.8249i	0.875679	+	2.11374i
$471$	12.8350	−	13.8865i	0.591405	−	0.639858i
$472$	−13.5962	+	14.8426i	−0.625815	+	0.683186i
$473$	1.73499	+	2.06769i	0.0797751	+	0.0950723i
$474$	−1.72468	+	9.54405i	−0.0792174	+	0.438373i
$475$	−1.69260	+	0.616057i	−0.0776619	+	0.0282666i
$476$	−24.8786	−	35.5219i	−1.14031	−	1.62814i
$477$	2.67954	+	2.72604i	0.122688	+	0.124817i
$478$	28.8931	+	15.0387i	1.32154	+	0.687856i
$479$	5.41592	−	30.7152i	0.247460	−	1.40341i	−0.567250	−	0.823545i	$-0.691993\pi$
$479$	5.41592	−	30.7152i	0.247460	−	1.40341i	0.814710	−	0.579869i	$-0.196896\pi$
$480$	−24.1179	+	20.0725i	−1.10082	+	0.916180i
$481$	−4.77621	−	1.73840i	−0.217776	−	0.0792641i
$482$	29.9485	−	6.64116i	1.36412	−	0.302497i
$483$	−17.9881	+	42.9042i	−0.818485	+	1.95221i
$484$	−16.7333	−	11.7140i	−0.760607	−	0.532457i
$485$	−2.84013			−0.128964
$486$	10.6107	+	19.3239i	0.481311	+	0.876550i
$487$			14.2176i			0.644263i	0.946695	+	0.322131i	$0.104399\pi$
$487$			14.2176i			0.644263i	−0.946695	+	0.322131i	$0.895601\pi$
$488$	−19.8415	−	12.6358i	−0.898181	−	0.571994i
$489$	−1.57088	−	0.658609i	−0.0710376	−	0.0297833i
$490$	64.9383	−	14.4003i	2.93361	−	0.650537i
$491$	0.483056	−	1.32718i	0.0218000	−	0.0598950i	−0.928315	−	0.371794i	$-0.878743\pi$
$491$	0.483056	−	1.32718i	0.0218000	−	0.0598950i	0.950115	+	0.311899i	$0.100965\pi$
$492$	0.158069	−	0.0997725i	0.00712630	−	0.00449809i
$493$	24.9578	+	4.40073i	1.12404	+	0.198199i
$494$	−0.424894	+	0.816324i	−0.0191169	+	0.0367282i
$495$	6.07826	−	5.97458i	0.273197	−	0.268537i
$496$	−24.2901	+	20.3910i	−1.09066	+	0.915584i
$497$	0.595012	+	1.63478i	0.0266899	+	0.0733300i
$498$	6.03786	−	33.4123i	0.270563	−	1.49724i
$499$	22.9472	−	19.2550i	1.02726	−	0.861971i	0.0367345	−	0.999325i	$-0.488304\pi$
$499$	22.9472	−	19.2550i	1.02726	−	0.861971i	0.990522	+	0.137355i	$0.0438600\pi$
$500$	1.15928	−	1.15954i	0.0518446	−	0.0518561i
$501$	−2.03616	−	1.88198i	−0.0909691	−	0.0840805i
$502$	−10.3606	+	4.29218i	−0.462417	+	0.191569i
$503$	4.40212	+	7.62469i	0.196281	+	0.339968i	0.947320	−	0.320290i	$-0.103780\pi$
$503$	4.40212	+	7.62469i	0.196281	+	0.339968i	−0.751039	+	0.660258i	$0.770447\pi$
$504$	8.22689	+	38.6491i	0.366455	+	1.72157i
$505$	10.0979	−	17.4901i	0.449351	−	0.778299i
$506$	−0.944095	+	7.17419i	−0.0419701	+	0.318932i
$507$	8.80160	−	13.6855i	0.390893	−	0.607794i
$508$	7.31133	−	27.2984i	0.324388	−	1.21117i
$509$	3.62638	+	20.5662i	0.160737	+	0.911582i	0.953352	+	0.301860i	$0.0976077\pi$
$509$	3.62638	+	20.5662i	0.160737	+	0.911582i	−0.792616	+	0.609722i	$0.791281\pi$
$510$	−28.0801	+	23.3596i	−1.24341	+	1.03438i
$511$	−37.6897	+	44.9169i	−1.66730	+	1.98701i
$512$	−8.66959	−	20.9007i	−0.383145	−	0.923688i
$513$	−1.76234	−	0.255191i	−0.0778093	−	0.0112670i
$514$	0.175508	−	0.00767262i	0.00774133	−	0.000338425i
$515$	−17.9971	+	21.4481i	−0.793045	+	0.945114i
$516$	2.23814	+	10.2996i	0.0985287	+	0.453416i
$517$	9.56806	−	1.68711i	0.420803	−	0.0741988i
$518$	5.30006	−	16.8129i	0.232871	−	0.738717i
$519$	−24.5287	−	1.17667i	−1.07669	−	0.0516499i
$520$	0.747385	−	17.1837i	0.0327750	−	0.753553i
$521$	18.8404	+	10.8775i	0.825413	+	0.476552i	0.852280	−	0.523087i	$-0.175220\pi$
$521$	18.8404	+	10.8775i	0.825413	+	0.476552i	−0.0268665	+	0.999639i	$0.508553\pi$
$522$	−19.3684	−	12.5730i	−0.847730	−	0.550305i
$523$	2.21522	+	3.83687i	0.0968647	+	0.167775i	0.910385	−	0.413761i	$-0.135785\pi$
$523$	2.21522	+	3.83687i	0.0968647	+	0.167775i	−0.813521	+	0.581536i	$0.802452\pi$
$524$	3.05274	+	6.54473i	0.133360	+	0.285908i
$525$	−12.5743	−	40.4870i	−0.548788	−	1.76700i
$526$	5.28983	+	5.77219i	0.230647	+	0.251679i
$527$	−28.2807	+	23.7303i	−1.23193	+	1.03371i
$528$	2.81570	+	5.46320i	0.122538	+	0.237755i
$529$	−9.64774	+	3.51149i	−0.419467	+	0.152673i
$530$	4.86676	−	3.10085i	0.211398	−	0.134692i
$531$	19.4262	−	8.85594i	0.843024	−	0.384315i
$532$	−2.89293	−	1.34860i	−0.125424	−	0.0584694i
$533$	−0.0177924	+	0.100906i	−0.000770676	+	0.00437072i
$534$	−17.9607	−	0.0762516i	−0.777235	−	0.00329973i
$535$	3.53899	−	9.72329i	0.153004	−	0.420375i
$536$	22.2258	−	7.01185i	0.960009	−	0.302866i
$537$	−10.4586	+	1.33117i	−0.451324	+	0.0574442i
$538$	−4.81911	+	6.28112i	−0.207767	+	0.270798i
$539$		−	13.0287i		−	0.561186i
$540$	31.8664	−	9.60106i	1.37131	−	0.413164i
$541$			37.3027i			1.60377i	0.597479	+	0.801884i	$0.296169\pi$
$541$			37.3027i			1.60377i	−0.597479	+	0.801884i	$0.703831\pi$
$542$	−1.75657	−	1.34771i	−0.0754511	−	0.0578890i
$543$	13.8090	+	18.1574i	0.592600	+	0.779208i
$544$	−10.0866	−	24.3321i	−0.432461	−	1.04323i
$545$	11.9048	−	32.7082i	0.509945	−	1.40106i
$546$	−18.7122	−	10.9097i	−0.800807	−	0.466890i
$547$	3.56925	−	20.2422i	0.152610	−	0.865496i	−0.808328	−	0.588733i	$-0.799627\pi$
$547$	3.56925	−	20.2422i	0.152610	−	0.865496i	0.960938	−	0.276763i	$-0.0892618\pi$
$548$	23.8647	+	11.1251i	1.01945	+	0.475239i
$549$	14.1345	+	20.5604i	0.603247	+	0.877496i
$550$	−3.54327	−	5.56114i	−0.151086	−	0.237128i
$551$	1.75273	−	0.637941i	0.0746687	−	0.0271772i
$552$	−16.3026	+	23.0788i	−0.693884	+	0.982300i
$553$	14.1249	−	11.8522i	0.600651	−	0.504006i
$554$	−29.2307	+	26.7880i	−1.24189	+	1.13811i
$555$	−14.4816	−	3.27591i	−0.614712	−	0.139055i
$556$	21.7378	−	10.1395i	0.921890	−	0.430009i
$557$	13.7564	+	23.8268i	0.582877	+	1.00957i	0.995136	+	0.0985064i	$0.0314065\pi$
$557$	13.7564	+	23.8268i	0.582877	+	1.00957i	−0.412259	+	0.911067i	$0.635260\pi$
$558$	32.1666	−	9.84065i	1.36172	−	0.416588i
$559$	−5.00349	−	2.88877i	−0.211625	−	0.122182i
$560$	59.6547	−	0.0132600i	2.52087	−	0.000560338i
$561$	3.27627	+	6.36029i	0.138324	+	0.268532i
$562$	12.1351	+	3.82546i	0.511890	+	0.161367i
$563$	−28.2129	+	4.97470i	−1.18903	+	0.209658i	−0.732952	−	0.680280i	$-0.761858\pi$
$563$	−28.2129	+	4.97470i	−1.18903	+	0.209658i	−0.456080	+	0.889939i	$0.650747\pi$
$564$	36.1347	+	11.5599i	1.52155	+	0.486759i
$565$	22.3856	−	26.6781i	0.941770	−	1.12236i
$566$	1.78397	+	40.8076i	0.0749859	+	1.71527i
$567$	7.98693	−	41.1439i	0.335419	−	1.72788i
$568$	0.138093	+	1.04757i	0.00579424	+	0.0439550i
$569$	−4.16772	+	4.96689i	−0.174720	+	0.208223i	−0.846297	−	0.532712i	$-0.821173\pi$
$569$	−4.16772	+	4.96689i	−0.174720	+	0.208223i	0.671577	+	0.740935i	$0.265617\pi$
$570$	−0.930171	+	2.52225i	−0.0389606	+	0.105646i
$571$	−4.13866	−	23.4715i	−0.173197	−	0.982252i	−0.940204	−	0.340612i	$-0.889366\pi$
$571$	−4.13866	−	23.4715i	−0.173197	−	0.982252i	0.767006	−	0.641639i	$-0.221745\pi$
$572$	−3.25431	−	0.871602i	−0.136070	−	0.0364435i
$573$	−16.9583	−	32.9216i	−0.708444	−	1.37532i
$574$	−0.352335	−	0.0463658i	−0.0147062	−	0.00193527i
$575$	15.1576	−	26.2538i	0.632117	−	1.09486i
$576$	−0.198445	+	23.9992i	−0.00826852	+	0.999966i
$577$	9.82303	+	17.0140i	0.408938	+	0.708302i	0.994771	−	0.102130i	$-0.0325658\pi$
$577$	9.82303	+	17.0140i	0.408938	+	0.708302i	−0.585833	+	0.810432i	$0.699232\pi$
$578$	−2.53371	−	6.11595i	−0.105388	−	0.254390i
$579$	−8.02273	+	35.4656i	−0.333413	+	1.47390i
$580$	−24.6473	+	24.6528i	−1.02343	+	1.02365i
$581$	−49.4491	+	41.4927i	−2.05149	+	1.72141i
$582$	−1.40340	+	1.65815i	−0.0581726	+	0.0687327i
$583$	−0.386593	−	1.06215i	−0.0160110	−	0.0439899i
$584$	−28.2498	+	21.6843i	−1.16899	+	0.897305i
$585$	−7.85187	+	16.4671i	−0.324635	+	0.680830i
$586$	−22.4264	−	11.6729i	−0.926426	−	0.482202i
$587$	−0.851961	−	0.150224i	−0.0351642	−	0.00620040i	0.156038	−	0.987751i	$-0.450128\pi$
$587$	−0.851961	−	0.150224i	−0.0351642	−	0.00620040i	−0.191203	+	0.981551i	$0.561239\pi$
$588$	23.6807	−	45.0286i	0.976576	−	1.85695i
$589$	−0.929313	+	2.55327i	−0.0382917	+	0.105206i
$590$	−6.97778	−	31.4665i	−0.287271	−	1.29545i
$591$	14.4284	−	10.9731i	0.593507	−	0.451371i
$592$	5.35141	−	9.27367i	0.219942	−	0.381145i
$593$		−	14.5405i		−	0.597108i	−0.954393	−	0.298554i	$-0.903496\pi$
$593$		−	14.5405i		−	0.597108i	0.954393	−	0.298554i	$-0.0965044\pi$
$594$	−0.484685	−	6.50090i	−0.0198869	−	0.266735i
$595$	69.4424			2.84686
$596$	14.5083	+	10.1564i	0.594284	+	0.416024i
$597$	−28.5070	+	3.62835i	−1.16671	+	0.148499i
$598$	−3.35320	−	15.1213i	−0.137122	−	0.618357i
$599$	−19.6014	−	7.13433i	−0.800892	−	0.291501i	−0.0910360	−	0.995848i	$-0.529018\pi$
$599$	−19.6014	−	7.13433i	−0.800892	−	0.291501i	−0.709856	+	0.704347i	$0.751240\pi$
$600$	−2.13811	−	25.6601i	−0.0872878	−	1.04757i
$601$	−3.10434	+	17.6056i	−0.126629	+	0.718147i	0.853699	+	0.520768i	$0.174354\pi$
$601$	−3.10434	+	17.6056i	−0.126629	+	0.718147i	−0.980327	+	0.197379i	$0.936757\pi$
$602$	9.25168	−	17.7747i	0.377070	−	0.724443i
$603$	−24.6059	−	2.36618i	−1.00203	−	0.0963583i
$604$	−4.79865	+	3.36085i	−0.195254	+	0.136751i
$605$	30.7347	−	11.1865i	1.24954	−	0.454797i
$606$	−5.22156	−	14.5379i	−0.212111	−	0.590560i
$607$	11.4075	+	13.5950i	0.463017	+	0.551803i	0.946143	−	0.323748i	$-0.104943\pi$
$607$	11.4075	+	13.5950i	0.463017	+	0.551803i	−0.483126	+	0.875551i	$0.660499\pi$
$608$	−1.53833	−	1.17972i	−0.0623873	−	0.0478440i
$609$	13.0210	+	41.9252i	0.527636	+	1.69889i
$610$	34.7987	−	14.4163i	1.40896	−	0.583701i
$611$	−18.0101	+	10.3981i	−0.728609	+	0.420662i
$612$	−0.237214	+	27.9367i	−0.00958880	+	1.12928i
$613$	6.61359	+	3.81836i	0.267120	+	0.154222i	0.627578	−	0.778554i	$-0.284046\pi$
$613$	6.61359	+	3.81836i	0.267120	+	0.154222i	−0.360458	+	0.932775i	$0.617380\pi$
$614$	7.48412	+	0.984880i	0.302035	+	0.0397465i
$615$	−0.0143418	+	0.298967i	−0.000578315	+	0.0120555i
$616$	2.52715	−	11.4082i	0.101822	−	0.459651i
$617$	1.20638	−	0.212717i	0.0485669	−	0.00856365i	−0.149312	−	0.988790i	$-0.547706\pi$
$617$	1.20638	−	0.212717i	0.0485669	−	0.00856365i	0.197879	+	0.980226i	$0.436595\pi$
$618$	3.62913	+	21.1054i	0.145985	+	0.848983i
$619$	−4.70712	−	3.94975i	−0.189195	−	0.158754i	0.543270	−	0.839558i	$-0.317186\pi$
$619$	−4.70712	−	3.94975i	−0.189195	−	0.158754i	−0.732465	+	0.680804i	$0.761630\pi$
$620$	−4.43162	−	50.5889i	−0.177978	−	2.03170i
$621$	25.4822	−	15.7754i	1.02256	−	0.633047i
$622$	−0.603271	−	13.7996i	−0.0241890	−	0.553313i
$623$	26.1578	+	21.9490i	1.04799	+	0.879367i
$624$	−9.66304	−	8.92733i	−0.386831	−	0.357379i
$625$	−4.10756	−	23.2951i	−0.164302	−	0.931805i
$626$	−9.47377	+	30.0528i	−0.378648	+	1.20115i
$627$	0.442882	+	0.284832i	0.0176870	+	0.0113751i
$628$	−21.7520	−	1.90062i	−0.868001	−	0.0758430i
$629$	6.23183	−	10.7938i	0.248479	−	0.430379i
$630$	−58.2479	−	24.7124i	−2.32065	−	0.984564i
$631$	−4.14675	+	2.39413i	−0.165080	+	0.0953088i	−0.580264	−	0.814429i	$-0.697051\pi$
$631$	−4.14675	+	2.39413i	−0.165080	+	0.0953088i	0.415184	+	0.909737i	$0.363717\pi$
$632$	9.93279	−	5.17279i	0.395105	−	0.205762i
$633$	−11.8645	−	10.9661i	−0.471572	−	0.435862i
$634$	−15.1549	−	16.5368i	−0.601878	−	0.656761i
$635$	29.0875	+	34.6652i	1.15430	+	1.37565i
$636$	0.594446	−	4.37359i	0.0235713	−	0.173424i
$637$	9.53816	+	26.2059i	0.377916	+	1.03832i
$638$	3.66914	+	5.75868i	0.145263	+	0.227989i
$639$	0.299367	−	1.08000i	0.0118428	−	0.0427243i
$640$	35.3763	+	7.82831i	1.39837	+	0.309441i
$641$	7.66053	+	1.35076i	0.302573	+	0.0533517i	0.322873	−	0.946442i	$-0.395351\pi$
$641$	7.66053	+	1.35076i	0.302573	+	0.0533517i	−0.0203006	+	0.999794i	$0.506462\pi$
$642$	−3.92803	−	6.87075i	−0.155027	−	0.271167i
$643$	22.0412	+	8.02234i	0.869220	+	0.316370i	0.737851	−	0.674964i	$-0.235841\pi$
$643$	22.0412	+	8.02234i	0.869220	+	0.316370i	0.131369	+	0.991334i	$0.458063\pi$
$644$	51.8875	−	13.9094i	2.04465	−	0.548107i
$645$	−15.5646	−	6.52563i	−0.612854	−	0.256946i
$646$	−1.79042	−	1.37368i	−0.0704430	−	0.0540466i
$647$	−11.2669			−0.442948			−0.221474	−	0.975166i	$-0.571087\pi$
$647$	−11.2669			−0.442948			−0.221474	+	0.975166i	$0.571087\pi$
$648$	10.1408	−	23.3488i	0.398368	−	0.917226i
$649$	−6.31318			−0.247814
$650$	11.1982	+	8.59168i	0.439229	+	0.336993i
$651$	−58.9779	−	24.7272i	−2.31153	−	0.969135i
$652$	0.509274	+	1.89979i	0.0199447	+	0.0744016i
$653$	36.3675	+	13.2367i	1.42317	+	0.517991i	0.934965	−	0.354739i	$-0.115430\pi$
$653$	36.3675	+	13.2367i	1.42317	+	0.517991i	0.488203	+	0.872730i	$0.337653\pi$
$654$	−13.2135	−	23.1125i	−0.516689	−	0.903770i
$655$	−11.3880	−	2.00802i	−0.444968	−	0.0784598i
$656$	−0.202840	−	0.0737768i	−0.00791958	−	0.00288050i
$657$	36.5686	−	9.46215i	1.42668	−	0.369154i
$658$	−38.7576	−	60.8298i	−1.51093	−	2.37139i
$659$	−11.6740	−	32.0740i	−0.454753	−	1.24942i	−0.929343	−	0.369217i	$-0.879626\pi$
$659$	−11.6740	−	32.0740i	−0.454753	−	1.24942i	0.474590	−	0.880207i	$-0.342596\pi$
$660$	−9.75180	−	1.32544i	−0.379588	−	0.0515926i
$661$	−32.5831	−	38.8310i	−1.26734	−	1.51035i	−0.762252	−	0.647281i	$-0.775906\pi$
$661$	−32.5831	−	38.8310i	−1.26734	−	1.51035i	−0.505083	−	0.863071i	$-0.668538\pi$
$662$	−27.0351	−	29.5004i	−1.05075	−	1.14656i
$663$	−11.2462	−	10.3946i	−0.436765	−	0.403691i
$664$	−34.7732	+	18.1091i	−1.34946	+	0.702771i
$665$	4.42618	−	2.55546i	0.171640	−	0.0990964i
$666$	−9.06841	+	6.83610i	−0.351394	+	0.264893i
$667$	−15.6961	+	27.1864i	−0.607754	+	1.05266i
$668$	−0.278686	+	3.18947i	−0.0107827	+	0.123404i
$669$	27.3176	+	17.5689i	1.05616	+	0.679252i
$670$	−11.2198	+	35.5916i	−0.433459	+	1.37502i
$671$	−1.28116	−	7.26582i	−0.0494587	−	0.280494i
$672$	29.4695	−	34.8348i	1.13681	−	1.34378i
$673$	17.6716	+	14.8283i	0.681191	+	0.571587i	0.916354	−	0.400369i	$-0.131118\pi$
$673$	17.6716	+	14.8283i	0.681191	+	0.571587i	−0.235163	+	0.971956i	$0.575562\pi$
$674$	0.213774	+	4.88999i	0.00823426	+	0.188355i
$675$	−8.54795	+	25.9388i	−0.329011	+	0.998384i
$676$	−18.7170	+	1.63962i	−0.719885	+	0.0630624i
$677$	−32.2459	−	27.0575i	−1.23931	−	1.03991i	−0.997578	−	0.0695623i	$-0.977840\pi$
$677$	−32.2459	−	27.0575i	−1.23931	−	1.03991i	−0.241733	−	0.970343i	$-0.577716\pi$
$678$	−4.51409	−	26.2519i	−0.173363	−	1.00820i
$679$	4.06720	−	0.717158i	0.156085	−	0.0275220i
$680$	41.1786	+	9.12187i	1.57913	+	0.349808i
$681$	−0.420576	+	8.76729i	−0.0161165	+	0.335963i
$682$	−9.86196	−	1.29779i	−0.377634	−	0.0496951i
$683$	34.0757	+	19.6736i	1.30387	+	0.752789i	0.981065	−	0.193676i	$-0.0620412\pi$
$683$	34.0757	+	19.6736i	1.30387	+	0.752789i	0.322804	+	0.946466i	$0.395375\pi$
$684$	1.01294	+	1.78939i	0.0387308	+	0.0684189i
$685$	−36.5130	+	21.0808i	−1.39509	+	0.805456i
$686$	−46.7681	+	19.3750i	−1.78561	+	0.739741i
$687$	11.5811	+	37.2890i	0.441846	+	1.42266i
$688$	7.82101	−	9.32493i	0.298173	−	0.355510i
$689$	1.55518	+	1.85340i	0.0592478	+	0.0706087i
$690$	−15.2941	−	42.5817i	−0.582235	−	1.62106i
$691$	34.6497	−	12.6115i	1.31814	−	0.479762i	0.415276	−	0.909696i	$-0.363685\pi$
$691$	34.6497	−	12.6115i	1.31814	−	0.479762i	0.902861	+	0.429933i	$0.141463\pi$
$692$	16.2668	+	23.2260i	0.618372	+	0.882919i
$693$	−7.19573	+	10.0907i	−0.273343	+	0.383314i
$694$	−14.1276	+	27.1426i	−0.536278	+	1.03032i
$695$	−6.66949	+	37.8245i	−0.252988	+	1.43477i
$696$	2.21406	+	26.5716i	0.0839236	+	1.00719i
$697$	−0.236102	−	0.0859340i	−0.00894299	−	0.00325498i
$698$	6.48252	+	29.2331i	0.245367	+	1.10649i
$699$	9.79498	−	1.24670i	0.370480	−	0.0471545i
$700$	−28.0739	+	40.1032i	−1.06109	+	1.51576i
$701$	6.58502			0.248713			0.124356	−	0.992238i	$-0.460313\pi$
$701$	6.58502			0.248713			0.124356	+	0.992238i	$0.460313\pi$
$702$	5.73413	+	12.7211i	0.216421	+	0.480125i
$703$		−	0.917317i		−	0.0345973i
$704$	2.99714	−	6.43300i	0.112959	−	0.242453i
$705$	−48.3543	+	36.7742i	−1.82113	+	1.38500i
$706$	4.77866	+	21.5495i	0.179847	+	0.811024i
$707$	−10.0443	+	27.5965i	−0.377755	+	1.03787i
$708$	−21.8190	−	11.4747i	−0.820009	−	0.431246i
$709$	11.2866	+	1.99013i	0.423876	+	0.0747408i	0.381517	−	0.924362i	$-0.375402\pi$
$709$	11.2866	+	1.99013i	0.423876	+	0.0747408i	0.0423588	+	0.999102i	$0.486513\pi$
$710$	−1.50080	−	0.781163i	−0.0563242	−	0.0293165i
$711$	−11.8416	+	0.933440i	−0.444095	+	0.0350067i
$712$	12.6281	+	16.4516i	0.473257	+	0.616548i
$713$	−15.6406	−	42.9723i	−0.585746	−	1.60932i
$714$	34.3136	−	40.5426i	1.28416	−	1.51727i
$715$	4.13252	−	3.46760i	0.154548	−	0.129681i
$716$	8.60930	+	8.60739i	0.321745	+	0.321673i
$717$	−8.80188	+	38.9100i	−0.328712	+	1.45312i
$718$	2.64262	+	6.37885i	0.0986217	+	0.238057i
$719$	−14.6250	−	25.3313i	−0.545421	−	0.944697i	−0.998580	−	0.0532673i	$-0.983036\pi$
$719$	−14.6250	−	25.3313i	−0.545421	−	0.944697i	0.453159	−	0.891430i	$-0.350297\pi$
$720$	−31.2942	−	22.3055i	−1.16627	−	0.831279i
$721$	20.3569	−	35.2591i	0.758129	−	1.31312i
$722$	26.4757	+	3.48410i	0.985324	+	0.129665i
$723$	17.2045	+	33.3995i	0.639843	+	1.24214i
$724$	6.81468	−	25.4440i	0.253266	−	0.945620i
$725$	−4.96752	−	28.1722i	−0.184489	−	1.04629i
$726$	8.65594	−	23.4715i	0.321252	−	0.871108i
$727$	32.7533	−	39.0339i	1.21475	−	1.44769i	0.356628	−	0.934246i	$-0.383926\pi$
$727$	32.7533	−	39.0339i	1.21475	−	1.44769i	0.858125	−	0.513440i	$-0.171629\pi$
$728$	3.26874	+	24.7966i	0.121147	+	0.919022i
$729$	−19.5782	+	18.5929i	−0.725117	+	0.688626i
$730$	−2.49055	−	56.9704i	−0.0921795	−	2.10857i
$731$	9.10664	−	10.8529i	0.336821	−	0.401408i
$732$	8.77840	−	27.4401i	0.324459	−	1.01422i
$733$	−2.54100	+	0.448046i	−0.0938538	+	0.0165490i	−0.220378	−	0.975415i	$-0.570729\pi$
$733$	−2.54100	+	0.448046i	−0.0938538	+	0.0165490i	0.126524	+	0.991964i	$0.459618\pi$
$734$	13.5750	+	4.27935i	0.501062	+	0.157954i
$735$	37.3052	+	72.4213i	1.37602	+	2.67130i
$736$	32.5959	−	1.43224i	1.20150	−	0.0527931i
$737$	6.33034	+	3.65482i	0.233181	+	0.134627i
$738$	0.167460	+	0.156102i	0.00616427	+	0.00574620i
$739$	3.86165	+	6.68857i	0.142053	+	0.246043i	0.928270	−	0.371908i	$-0.121296\pi$
$739$	3.86165	+	6.68857i	0.142053	+	0.246043i	−0.786217	+	0.617951i	$0.787963\pi$
$740$	7.24730	+	15.5374i	0.266416	+	0.571165i
$741$	−1.09934	−	0.248682i	−0.0403851	−	0.00913557i
$742$	−6.18645	+	5.66947i	−0.227112	+	0.208133i
$743$	9.80501	−	8.22738i	0.359711	−	0.301833i	−0.444965	−	0.895548i	$-0.646784\pi$
$743$	9.80501	−	8.22738i	0.359711	−	0.301833i	0.804676	+	0.593715i	$0.202339\pi$
$744$	−31.7252	−	22.4102i	−1.16310	−	0.821599i
$745$	−26.6479	+	9.69906i	−0.976305	+	0.355346i
$746$	−1.13658	−	1.78386i	−0.0416132	−	0.0653116i
$747$	41.4557	−	3.26783i	1.51679	−	0.119564i
$748$	3.49056	−	7.48770i	0.127627	−	0.273777i
$749$	−2.61279	+	14.8179i	−0.0954693	+	0.541433i
$750$	1.73484	+	1.01145i	0.0633473	+	0.0369330i
$751$	15.0834	−	41.4413i	0.550401	−	1.51221i	−0.282763	−	0.959190i	$-0.591251\pi$
$751$	15.0834	−	41.4413i	0.550401	−	1.51221i	0.833165	−	0.553025i	$-0.186527\pi$
$752$	−14.9923	−	41.1626i	−0.546714	−	1.50105i
$753$	−8.31434	−	10.9325i	−0.302991	−	0.398402i
$754$	−11.5960	−	8.89687i	−0.422300	−	0.324005i
$755$		−	9.38096i		−	0.341408i
$756$	−43.2099	+	21.7957i	−1.57153	+	0.792704i
$757$		−	27.9094i		−	1.01438i	−0.861833	−	0.507192i	$-0.830684\pi$
$757$		−	27.9094i		−	1.01438i	0.861833	−	0.507192i	$-0.169316\pi$
$758$	22.7295	−	29.6251i	0.825574	−	1.07603i
$759$	−8.79138	+	1.11896i	−0.319107	+	0.0406157i
$760$	2.96036	−	0.933941i	0.107384	−	0.0338776i
$761$	−7.20399	+	19.7928i	−0.261145	+	0.717489i	0.737946	+	0.674859i	$0.235796\pi$
$761$	−7.20399	+	19.7928i	−0.261145	+	0.717489i	−0.999091	+	0.0426294i	$0.986427\pi$
$762$	34.6116	+	0.146943i	1.25385	+	0.00532318i
$763$	−8.78916	+	49.8458i	−0.318189	+	1.80454i
$764$	−18.0675	+	38.7572i	−0.653660	+	1.40218i
$765$	−36.4229	−	25.9734i	−1.31687	−	0.939070i
$766$	18.7422	−	11.9415i	0.677182	−	0.431466i
$767$	12.6983	−	4.62181i	0.458509	−	0.166884i
$768$	22.0509	−	16.7856i	0.795695	−	0.605697i
$769$	−9.76794	+	8.19627i	−0.352241	+	0.295565i	−0.801689	−	0.597741i	$-0.796065\pi$
$769$	−9.76794	+	8.19627i	−0.352241	+	0.295565i	0.449448	+	0.893306i	$0.351621\pi$
$770$	12.6412	+	13.7939i	0.455558	+	0.497099i
$771$	0.0638161	+	0.205476i	0.00229828	+	0.00740004i
$772$	38.0511	−	17.7487i	1.36949	−	0.638788i
$773$	−24.3894	−	42.2437i	−0.877226	−	1.51940i	−0.854372	−	0.519661i	$-0.826058\pi$
$773$	−24.3894	−	42.2437i	−0.877226	−	1.51940i	−0.0228536	−	0.999739i	$-0.507275\pi$
$774$	−11.5008	+	5.86256i	−0.413388	+	0.210725i
$775$	36.0896	+	20.8363i	1.29638	+	0.748463i
$776$	2.50601	+	0.108996i	0.0899607	+	0.00391274i
$777$	21.5656	+	1.03453i	0.773663	+	0.0371134i
$778$	−8.60643	+	27.3014i	−0.308556	+	0.978803i
$779$	−0.0182112	+	0.00321113i	−0.000652484	+	0.000115051i
$780$	20.5851	−	4.47320i	0.737064	−	0.160166i
$781$	−0.213023	+	0.253871i	−0.00762256	+	0.00908421i
$782$	37.9443	−	1.65880i	1.35689	−	0.0593185i
$783$	8.85160	−	26.8602i	0.316330	−	0.959905i
$784$	−57.8516	+	10.2141i	−2.06613	+	0.364788i
$785$	22.4739	−	26.7833i	0.802127	−	0.955938i
$786$	−6.79953	+	5.65646i	−0.242531	+	0.201759i
$787$	−4.56672	−	25.8991i	−0.162786	−	0.923205i	−0.951318	−	0.308211i	$-0.900270\pi$
$787$	−4.56672	−	25.8991i	−0.162786	−	0.923205i	0.788532	−	0.614994i	$-0.210841\pi$
$788$	−20.2186	−	5.41516i	−0.720259	−	0.192907i
$789$	−5.18695	+	8.06512i	−0.184660	+	0.287126i
$790$	−2.33966	+	17.7791i	−0.0832414	+	0.632553i
$791$	−25.3209	+	43.8570i	−0.900306	+	1.55938i
$792$	−5.59250	+	5.03846i	−0.198721	+	0.179034i
$793$	7.89615	+	13.6765i	0.280401	+	0.485668i
$794$	−36.0084	+	14.9175i	−1.27789	+	0.529402i
$795$	5.19019	+	4.79716i	0.184077	+	0.170138i
$796$	23.4662	+	23.4610i	0.831739	+	0.831554i
$797$	27.3124	−	22.9179i	0.967456	−	0.811792i	−0.0146935	−	0.999892i	$-0.504677\pi$
$797$	27.3124	−	22.9179i	0.967456	−	0.811792i	0.982150	+	0.188100i	$0.0602328\pi$
$798$	0.695159	−	3.84687i	0.0246084	−	0.136178i
$799$	−17.4415	−	47.9201i	−0.617036	−	1.69529i
$800$	−21.9154	+	20.0930i	−0.774828	+	0.710395i
$801$	−5.51037	−	21.2961i	−0.194700	−	0.752460i
$802$	−4.43137	+	8.51375i	−0.156477	+	0.300631i
$803$	−11.0000	−	1.93959i	−0.388180	−	0.0684467i
$804$	15.2354	+	24.1374i	0.537311	+	0.851259i
$805$	−29.4200	+	80.8307i	−1.03692	+	2.84891i
$806$	20.7864	−	4.60945i	0.732171	−	0.162361i
$807$	−8.94199	−	3.74903i	−0.314773	−	0.131972i
$808$	−9.58121	+	15.0450i	−0.337066	+	0.529282i
$809$		−	41.4917i		−	1.45877i	−0.684103	−	0.729385i	$-0.739806\pi$
$809$		−	41.4917i		−	1.45877i	0.684103	−	0.729385i	$-0.260194\pi$
$810$	21.3082	+	34.7481i	0.748695	+	1.22092i
$811$	29.0442			1.01988			0.509940	−	0.860210i	$-0.329667\pi$
$811$	29.0442			1.01988			0.509940	+	0.860210i	$0.329667\pi$
$812$	29.0712	−	41.5277i	1.02020	−	1.45734i
$813$	1.04845	−	2.50071i	0.0367708	−	0.0877036i
$814$	3.27851	−	0.727019i	0.114912	−	0.0254820i
$815$	−2.95951	−	1.07717i	−0.103667	−	0.0377318i
$816$	25.6733	−	19.5339i	0.898744	−	0.683824i
$817$	0.181065	−	1.02687i	0.00633467	−	0.0359257i
$818$	−21.4755	−	11.1779i	−0.750873	−	0.390827i
$819$	7.08619	−	25.5643i	0.247611	−	0.893290i
$820$	0.283089	−	0.198268i	0.00988589	−	0.00692381i
$821$	47.7187	−	17.3682i	1.66539	−	0.606153i	0.674196	−	0.738552i	$-0.264490\pi$
$821$	47.7187	−	17.3682i	1.66539	−	0.606153i	0.991197	+	0.132399i	$0.0422679\pi$
$822$	−5.73459	+	31.7341i	−0.200017	+	1.10685i
$823$	10.2372	+	12.2002i	0.356847	+	0.425274i	0.914365	−	0.404891i	$-0.132691\pi$
$823$	10.2372	+	12.2002i	0.356847	+	0.425274i	−0.557518	+	0.830165i	$0.688246\pi$
$824$	16.7030	−	18.2342i	0.581877	−	0.635219i
$825$	5.48162	−	5.93072i	0.190845	−	0.206481i
$826$	17.9381	+	43.2996i	0.624146	+	1.50659i
$827$	26.8166	−	15.4826i	0.932504	−	0.538381i	0.0449012	−	0.998991i	$-0.485703\pi$
$827$	26.8166	−	15.4826i	0.932504	−	0.538381i	0.887603	+	0.460610i	$0.152369\pi$
$828$	−32.4178	−	12.1118i	−1.12660	−	0.420914i
$829$	5.02207	+	2.89949i	0.174424	+	0.100704i	0.584670	−	0.811271i	$-0.301224\pi$
$829$	5.02207	+	2.89949i	0.174424	+	0.100704i	−0.410246	+	0.911975i	$0.634557\pi$
$830$	8.19081	−	62.2421i	0.284307	−	2.16045i
$831$	−40.8422	−	26.2670i	−1.41680	−	0.911193i
$832$	−1.31892	+	15.1335i	−0.0457255	+	0.524659i
$833$	−67.3461	+	11.8749i	−2.33340	+	0.411442i
$834$	18.7875	+	22.5841i	0.650559	+	0.782025i
$835$	−3.92720	−	3.29531i	−0.135906	−	0.114039i
$836$	−0.0530605	−	0.605709i	−0.00183514	−	0.0209489i
$837$	21.6856	+	35.0289i	0.749565	+	1.21078i
$838$	2.19594	−	0.0959989i	0.0758573	−	0.00331623i
$839$	11.9037	+	9.98841i	0.410962	+	0.344838i	0.824712	−	0.565552i	$-0.191337\pi$
$839$	11.9037	+	9.98841i	0.410962	+	0.344838i	−0.413750	+	0.910390i	$0.635781\pi$
$840$	18.6178	+	70.6498i	0.642377	+	2.43765i
$841$	0.108181	+	0.613526i	0.00373038	+	0.0211561i
$842$	−18.2027	−	5.73817i	−0.627306	−	0.197751i
$843$	−0.746695	+	15.5655i	−0.0257175	+	0.536106i
$844$	−1.62387	+	18.5847i	−0.0558959	+	0.639712i
$845$	15.0427	−	26.0547i	0.517484	−	0.896309i
$846$	−2.42344	+	46.4020i	−0.0833197	+	1.59533i
$847$	−41.1889	+	23.7804i	−1.41527	+	0.817106i
$848$	−4.41323	+	2.54929i	−0.151551	+	0.0875429i
$849$	−47.7755	+	14.8380i	−1.63965	+	0.509237i
$850$	−25.5164	+	23.3841i	−0.875204	+	0.802067i
$851$	9.92382	+	11.8268i	0.340184	+	0.405416i
$852$	−1.19766	+	0.490219i	−0.0410312	+	0.0167946i
$853$	−5.27000	−	14.4792i	−0.180441	−	0.495758i	0.816189	−	0.577785i	$-0.196083\pi$
$853$	−5.27000	−	14.4792i	−0.180441	−	0.495758i	−0.996630	+	0.0820269i	$0.973861\pi$
$854$	−46.1932	+	29.4319i	−1.58070	+	1.00714i
$855$	−3.27737	−	0.315163i	−0.112084	−	0.0107783i
$856$	−3.49582	+	8.44363i	−0.119485	+	0.288597i
$857$	−43.4090	−	7.65418i	−1.48282	−	0.261462i	−0.627118	−	0.778924i	$-0.715766\pi$
$857$	−43.4090	−	7.65418i	−1.48282	−	0.261462i	−0.855706	+	0.517463i	$0.826877\pi$
$858$	0.0175174	−	4.12614i	0.000598035	−	0.140864i
$859$	49.6251	+	18.0621i	1.69319	+	0.616270i	0.995021	−	0.0996665i	$-0.0317776\pi$
$859$	49.6251	+	18.0621i	1.69319	+	0.616270i	0.698166	+	0.715936i	$0.254000\pi$
$860$	5.04598	+	18.8235i	0.172067	+	0.641876i
$861$	−0.0549538	−	0.431757i	−0.00187282	−	0.0147143i
$862$	28.0828	−	36.6024i	0.956504	−	1.24668i
$863$	−51.1622			−1.74158			−0.870791	−	0.491653i	$-0.836393\pi$
$863$	−51.1622			−1.74158			−0.870791	+	0.491653i	$0.836393\pi$
$864$	−28.4861	+	7.24864i	−0.969116	+	0.246604i
$865$	−45.4048			−1.54381
$866$	−17.5764	+	22.9086i	−0.597269	+	0.778465i
$867$	6.45353	−	4.90801i	0.219173	−	0.166685i
$868$	19.1205	+	71.3268i	0.648991	+	2.42099i
$869$	3.30066	+	1.20134i	0.111967	+	0.0407527i
$870$	−36.8842	−	21.5044i	−1.25049	−	0.729067i
$871$	−15.4085	−	2.71693i	−0.522097	−	0.0920597i
$872$	−11.7596	+	28.4035i	−0.398229	+	0.961863i
$873$	−2.40151	−	1.14509i	−0.0812788	−	0.0387556i
$874$	2.35749	−	1.50207i	0.0797431	−	0.0508082i
$875$	−1.30578	−	3.58759i	−0.0441433	−	0.121283i
$876$	−34.4917	−	26.6968i	−1.16537	−	0.902000i
$877$	21.3535	+	25.4481i	0.721055	+	0.859320i	0.994733	−	0.102501i	$-0.0326845\pi$
$877$	21.3535	+	25.4481i	0.721055	+	0.859320i	−0.273678	+	0.961822i	$0.588240\pi$
$878$	−5.31374	+	4.86969i	−0.179330	+	0.164344i
$879$	6.83190	−	30.2014i	0.230434	−	1.01867i
$880$	5.68416	+	9.84020i	0.191613	+	0.331713i
$881$	−24.0135	+	13.8642i	−0.809034	+	0.467096i	−0.846620	−	0.532197i	$-0.821366\pi$
$881$	−24.0135	+	13.8642i	−0.809034	+	0.467096i	0.0375862	+	0.999293i	$0.488033\pi$
$882$	60.7154	+	14.0057i	2.04439	+	0.471598i
$883$	7.38127	−	12.7847i	0.248400	−	0.430241i	−0.714682	−	0.699449i	$-0.753429\pi$
$883$	7.38127	−	12.7847i	0.248400	−	0.430241i	0.963082	+	0.269208i	$0.0867621\pi$
$884$	−1.53924	+	17.6161i	−0.0517702	+	0.592495i
$885$	35.0924	−	18.0766i	1.17962	−	0.607637i
$886$	24.9856	+	7.87641i	0.839408	+	0.264613i
$887$	3.08832	+	17.5147i	0.103695	+	0.588086i	0.991733	+	0.128316i	$0.0409572\pi$
$887$	3.08832	+	17.5147i	0.103695	+	0.588086i	−0.888038	+	0.459770i	$0.847932\pi$
$888$	12.6523	+	3.44630i	0.424584	+	0.115650i
$889$	−50.4081	−	42.2974i	−1.69063	−	1.41861i
$890$	−33.1772	+	1.45040i	−1.11210	+	0.0486174i
$891$	7.54841	−	2.60123i	0.252881	−	0.0871445i
$892$	−3.27285	−	37.3610i	−0.109583	−	1.25094i
$893$	−2.87515	−	2.41254i	−0.0962132	−	0.0807324i
$894$	−7.50497	+	20.3505i	−0.251004	+	0.680622i
$895$	−19.1975	+	3.38504i	−0.641702	+	0.113149i
$896$	−52.6374	−	2.27768i	−1.75849	−	0.0760921i
$897$	16.8638	−	8.68675i	0.563066	−	0.290042i
$898$	3.49455	−	26.5552i	0.116615	−	0.886158i
$899$	−37.3716	−	21.5765i	−1.24641	−	0.719616i
$900$	29.7246	−	10.5339i	0.990821	−	0.351131i
$901$	−5.13798	+	2.96642i	−0.171171	+	0.0988256i
$902$	−0.0259099	−	0.0625423i	−0.000862706	−	0.00208243i
$903$	23.9370	+	5.41483i	0.796574	+	0.180194i
$904$	−20.7760	+	22.6806i	−0.691000	+	0.754346i
$905$	27.1116	+	32.3104i	0.901221	+	1.07403i
$906$	−5.47689	−	4.63543i	−0.181958	−	0.154002i
$907$	−33.8368	+	12.3156i	−1.12353	+	0.408932i	−0.835940	−	0.548821i	$-0.815077\pi$
$907$	−33.8368	+	12.3156i	−1.12353	+	0.408932i	−0.287591	+	0.957753i	$0.592854\pi$
$908$	8.30165	−	5.81426i	0.275500	−	0.192953i
$909$	15.5901	−	10.7177i	0.517093	−	0.355483i
$910$	−35.5249	−	18.4906i	−1.17764	−	0.612957i
$911$	−0.0484884	+	0.274992i	−0.00160649	+	0.00911088i	−0.985600	−	0.169091i	$-0.945917\pi$
$911$	−0.0484884	+	0.274992i	−0.00160649	+	0.00911088i	0.983994	+	0.178202i	$0.0570280\pi$
$912$	0.917543	−	2.18984i	0.0303829	−	0.0725128i
$913$	−11.5551	−	4.20572i	−0.382418	−	0.139189i
$914$	−14.4552	+	3.20549i	−0.478137	+	0.106028i
$915$	27.9258	+	36.7195i	0.923197	+	1.21391i
$916$	25.8564	−	36.9355i	0.854320	−	1.22038i
$917$	16.8153			0.555290
$918$	−33.1618	+	8.43057i	−1.09450	+	0.278250i
$919$			19.5234i			0.644017i	0.946737	+	0.322008i	$0.104358\pi$
$919$			19.5234i			0.644017i	−0.946737	+	0.322008i	$0.895642\pi$
$920$	−28.0636	+	44.0672i	−0.925229	+	1.45285i
$921$	1.16730	+	9.17118i	0.0384639	+	0.302201i
$922$	−33.6735	+	7.46719i	−1.10898	+	0.245919i
$923$	0.242618	−	0.666587i	0.00798586	−	0.0219410i
$924$	14.2997	−	0.564323i	0.470427	−	0.0185649i
$925$	−13.8552	−	2.44304i	−0.455555	−	0.0803267i
$926$	−10.2866	+	19.7631i	−0.338039	+	0.649454i
$927$	−23.8652	+	10.8796i	−0.783835	+	0.357332i
$928$	22.6939	−	20.8068i	0.744965	−	0.683015i
$929$	−12.7507	−	35.0323i	−0.418338	−	1.14937i	−0.952645	−	0.304083i	$-0.901650\pi$
$929$	−12.7507	−	35.0323i	−0.418338	−	1.14937i	0.534308	−	0.845290i	$-0.320572\pi$
$930$	58.5347	−	21.0239i	1.91943	−	0.689401i
$931$	−3.85557	+	3.23521i	−0.126361	+	0.106030i
$932$	−8.06299	−	8.06120i	−0.264112	−	0.264053i
$933$	16.1559	−	5.01763i	0.528919	−	0.164270i
$934$	−10.0283	+	4.15451i	−0.328136	+	0.135940i
$935$	6.61423	+	11.4562i	0.216308	+	0.374657i
$936$	7.56014	−	14.2285i	0.247111	−	0.465075i
$937$	−1.65449	+	2.86566i	−0.0540499	+	0.0936171i	−0.891784	−	0.452461i	$-0.850546\pi$
$937$	−1.65449	+	2.86566i	−0.0540499	+	0.0936171i	0.837735	+	0.546078i	$0.183880\pi$
$938$	7.08013	−	53.8020i	0.231174	−	1.75670i
$939$	−38.5482	−	1.84920i	−1.25797	−	0.0603462i
$940$	67.7591	+	18.1479i	2.21006	+	0.591920i
$941$	8.25196	+	46.7992i	0.269006	+	1.52561i	0.757379	+	0.652975i	$0.226479\pi$
$941$	8.25196	+	46.7992i	0.269006	+	1.52561i	−0.488373	+	0.872635i	$0.662409\pi$
$942$	−4.53188	−	26.3554i	−0.147657	−	0.858705i
$943$	0.200054	−	0.238415i	0.00651465	−	0.00776386i
$944$	4.94932	+	28.0325i	0.161087	+	0.912381i
$945$	11.1054	−	76.6938i	0.361260	−	2.49485i
$946$	3.81356	−	0.166716i	0.123990	−	0.00542041i
$947$	15.7887	−	18.8162i	0.513063	−	0.611444i	−0.445863	−	0.895101i	$-0.647103\pi$
$947$	15.7887	−	18.8162i	0.513063	−	0.611444i	0.958926	+	0.283657i	$0.0915477\pi$
$948$	9.22390	+	10.1512i	0.299578	+	0.329695i
$949$	23.5453	−	4.15167i	0.764312	−	0.134769i
$950$	−0.765860	+	2.42947i	−0.0248478	+	0.0788224i
$951$	14.8602	−	23.1059i	0.481874	−	0.749259i
$952$	−61.2732	−	2.66501i	−1.98587	−	0.0863735i
$953$	−5.53399	−	3.19505i	−0.179264	−	0.103498i	0.407683	−	0.913124i	$-0.366337\pi$
$953$	−5.53399	−	3.19505i	−0.179264	−	0.103498i	−0.586947	+	0.809626i	$0.699670\pi$
$954$	5.36536	−	0.659765i	0.173710	−	0.0213607i
$955$	−34.2360	−	59.2984i	−1.10785	−	1.91885i
$956$	41.7465	−	19.4724i	1.35018	−	0.629782i
$957$	−5.67634	+	6.14139i	−0.183490	+	0.198523i
$958$	−29.8007	−	32.5182i	−0.962818	−	1.05061i
$959$	46.9654	−	39.4086i	1.51659	−	1.27257i
$960$	1.75971	+	44.3402i	0.0567943	+	1.43107i
$961$	29.9411	−	10.8977i	0.965843	−	0.351538i
$962$	−6.06214	+	3.86249i	−0.195451	+	0.124532i
$963$	6.91272	−	6.79480i	0.222759	−	0.218959i
$964$	18.3298	−	39.3199i	0.590364	−	1.26641i
$965$	−11.6746	+	66.2101i	−0.375819	+	2.13138i
$966$	32.6541	+	57.1173i	1.05063	+	1.83772i
$967$	7.29798	−	20.0510i	0.234687	−	0.644798i	−0.765312	−	0.643659i	$-0.777415\pi$
$967$	7.29798	−	20.0510i	0.234687	−	0.644798i	0.999999	−	0.00113855i	$-0.000362411\pi$
$968$	−27.5484	+	8.69102i	−0.885439	+	0.279340i
$969$	1.06865	−	2.54889i	0.0343301	−	0.0818823i
$970$	−2.44494	+	3.18668i	−0.0785024	+	0.102318i
$971$			18.8858i			0.606074i	0.952979	+	0.303037i	$0.0980006\pi$
$971$			18.8858i			0.606074i	−0.952979	+	0.303037i	$0.901999\pi$
$972$	30.8161	+	4.72971i	0.988426	+	0.151706i
$973$		−	55.8507i		−	1.79049i
$974$	15.9525	+	12.2393i	0.511150	+	0.392174i
$975$	−6.68390	+	15.9421i	−0.214056	+	0.510555i
$976$	−31.2582	+	11.3849i	−1.00055	+	0.364423i
$977$	−12.8528	+	35.3129i	−0.411199	+	1.12976i	0.545355	+	0.838205i	$0.316395\pi$
$977$	−12.8528	+	35.3129i	−0.411199	+	1.12976i	−0.956554	+	0.291555i	$0.905827\pi$
$978$	−2.09127	+	1.19559i	−0.0668716	+	0.0382307i
$979$	−1.12954	+	6.40593i	−0.0361002	+	0.204735i
$980$	39.7452	−	85.2586i	1.26961	−	2.72348i
$981$	23.2537	−	22.8570i	0.742432	−	0.729768i
$982$	−1.07328	−	1.68451i	−0.0342499	−	0.0537549i
$983$	0.0615360	−	0.0223973i	0.00196269	−	0.000714362i	−0.341039	−	0.940049i	$-0.610779\pi$
$983$	0.0615360	−	0.0223973i	0.00196269	−	0.000714362i	0.343001	+	0.939335i	$0.388556\pi$
$984$	0.0241281	−	0.263246i	0.000769177	−	0.00839198i
$985$	25.6749	−	21.5438i	0.818069	−	0.686441i
$986$	26.4228	−	24.2147i	0.841472	−	0.771153i
$987$	59.9600	−	64.8724i	1.90855	−	2.06491i
$988$	0.550159	+	1.17948i	0.0175029	+	0.0375242i
$989$	8.77459	+	15.1980i	0.279016	+	0.483269i
$990$	−1.47108	−	11.9632i	−0.0467540	−	0.380215i
$991$	−2.32285	−	1.34110i	−0.0737876	−	0.0426013i	0.462652	−	0.886540i	$-0.346898\pi$
$991$	−2.32285	−	1.34110i	−0.0737876	−	0.0426013i	−0.536440	+	0.843939i	$0.680231\pi$
$992$	1.96882	+	44.8077i	0.0625101	+	1.42265i
$993$	26.5094	−	41.2191i	0.841249	−	1.30805i
$994$	2.34648	+	0.739698i	0.0744257	+	0.0234618i
$995$	−52.3264	+	9.22655i	−1.65886	+	0.292501i
$996$	−32.2915	−	35.5378i	−1.02320	−	1.12606i
$997$	−6.81445	+	8.12114i	−0.215816	+	0.257199i	−0.863081	−	0.505066i	$-0.831468\pi$
$997$	−6.81445	+	8.12114i	−0.215816	+	0.257199i	0.647265	+	0.762265i	$0.275913\pi$
$998$	−1.85021	−	42.3229i	−0.0585675	−	1.33971i
$999$	−10.9244	−	8.60876i	−0.345632	−	0.272369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.24	✓	192
3.2	odd	2		648.2.v.b.35.9		192
4.3	odd	2		864.2.bh.b.335.4		192
8.3	odd	2	inner	216.2.v.b.11.25	yes	192
8.5	even	2		864.2.bh.b.335.3		192
24.11	even	2		648.2.v.b.35.8		192
27.5	odd	18	inner	216.2.v.b.59.25	yes	192
27.22	even	9		648.2.v.b.611.8		192
108.59	even	18		864.2.bh.b.815.3		192
216.5	odd	18		864.2.bh.b.815.4		192
216.59	even	18	inner	216.2.v.b.59.24	yes	192
216.211	odd	18		648.2.v.b.611.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.24	✓	192	1.1	even	1	trivial
216.2.v.b.11.25	yes	192	8.3	odd	2	inner
216.2.v.b.59.24	yes	192	216.59	even	18	inner
216.2.v.b.59.25	yes	192	27.5	odd	18	inner
648.2.v.b.35.8		192	24.11	even	2
648.2.v.b.35.9		192	3.2	odd	2
648.2.v.b.611.8		192	27.22	even	9
648.2.v.b.611.9		192	216.211	odd	18
864.2.bh.b.335.3		192	8.5	even	2
864.2.bh.b.335.4		192	4.3	odd	2
864.2.bh.b.815.3		192	108.59	even	18
864.2.bh.b.815.4		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)

\(f(q)\)	\(=\)	\(q+(0.860856 - 1.12202i) q^{2} +(1.59734 + 0.669704i) q^{3} +(-0.517853 - 1.93179i) q^{4} +(3.00936 + 1.09532i) q^{5} +(2.12650 - 1.21573i) q^{6} +(-4.58614 - 0.808660i) q^{7} +(-2.61331 - 1.08196i) q^{8} +(2.10299 + 2.13949i) q^{9} +O(q^{10})\)	\(q+(0.860856 - 1.12202i) q^{2} +(1.59734 + 0.669704i) q^{3} +(-0.517853 - 1.93179i) q^{4} +(3.00936 + 1.09532i) q^{5} +(2.12650 - 1.21573i) q^{6} +(-4.58614 - 0.808660i) q^{7} +(-2.61331 - 1.08196i) q^{8} +(2.10299 + 2.13949i) q^{9} +(3.81960 - 2.43365i) q^{10} +(-0.303411 - 0.833616i) q^{11} +(0.466542 - 3.43254i) q^{12} +(1.22056 + 1.45461i) q^{13} +(-4.85534 + 4.44959i) q^{14} +(4.07344 + 3.76498i) q^{15} +(-3.46366 + 2.00077i) q^{16} +(-4.03247 + 2.32815i) q^{17} +(4.21092 - 0.517807i) q^{18} +(-0.171350 + 0.296787i) q^{19} +(0.557523 - 6.38069i) q^{20} +(-6.78406 - 4.36306i) q^{21} +(-1.19653 - 0.377190i) q^{22} +(-1.00156 - 5.68012i) q^{23} +(-3.44975 - 3.47839i) q^{24} +(4.02633 + 3.37849i) q^{25} +(2.68283 - 0.117284i) q^{26} +(1.92637 + 4.82588i) q^{27} +(0.812780 + 9.27824i) q^{28} +(-4.16935 - 3.49850i) q^{29} +(7.73102 - 1.32937i) q^{30} +(7.80815 - 1.37679i) q^{31} +(-0.736809 + 5.60866i) q^{32} +(0.0736241 - 1.53476i) q^{33} +(-0.859151 + 6.52870i) q^{34} +(-12.9156 - 7.45683i) q^{35} +(3.04401 - 5.17049i) q^{36} +(-2.31812 + 1.33837i) q^{37} +(0.185493 + 0.447749i) q^{38} +(0.975496 + 3.14092i) q^{39} +(-6.67930 - 6.11841i) q^{40} +(0.0346849 + 0.0413359i) q^{41} +(-10.7355 + 3.85588i) q^{42} +(-2.85915 + 1.04064i) q^{43} +(-1.45325 + 1.01782i) q^{44} +(3.98525 + 8.74195i) q^{45} +(-7.23540 - 3.76600i) q^{46} +(-1.90179 + 10.7856i) q^{47} +(-6.87256 + 0.876288i) q^{48} +(13.8009 + 5.02311i) q^{49} +(7.25682 - 1.60922i) q^{50} +(-8.00039 + 1.01828i) q^{51} +(2.17793 - 3.11115i) q^{52} +1.27415 q^{53} +(7.07306 + 1.99296i) q^{54} -2.84099i q^{55} +(11.1100 + 7.07528i) q^{56} +(-0.472464 + 0.359316i) q^{57} +(-7.51460 + 1.66638i) q^{58} +(2.43399 - 6.68734i) q^{59} +(5.16372 - 9.81875i) q^{60} +(8.19039 + 1.44419i) q^{61} +(5.17691 - 9.94610i) q^{62} +(-7.91450 - 11.5126i) q^{63} +(5.65874 + 5.65497i) q^{64} +(2.07985 + 5.71435i) q^{65} +(-1.65865 - 1.40382i) q^{66} +(-6.31205 + 5.29644i) q^{67} +(6.58572 + 6.58426i) q^{68} +(2.20417 - 9.74384i) q^{69} +(-19.4852 + 8.07230i) q^{70} +(-0.186788 - 0.323526i) q^{71} +(-3.18093 - 7.86649i) q^{72} +(6.29550 - 10.9041i) q^{73} +(-0.493895 + 3.75312i) q^{74} +(4.16883 + 8.09304i) q^{75} +(0.662065 + 0.177321i) q^{76} +(0.717374 + 4.06843i) q^{77} +(4.36393 + 1.60936i) q^{78} +(-2.54509 + 3.03312i) q^{79} +(-12.6149 + 2.22724i) q^{80} +(-0.154829 + 8.99867i) q^{81} +(0.0762384 - 0.00333288i) q^{82} +(8.90996 - 10.6185i) q^{83} +(-4.91538 + 15.3648i) q^{84} +(-14.6852 + 2.58940i) q^{85} +(-1.29369 + 4.10386i) q^{86} +(-4.31692 - 8.38053i) q^{87} +(-0.109029 + 2.50677i) q^{88} +(-6.35012 - 3.66624i) q^{89} +(13.2394 + 3.05404i) q^{90} +(-4.42138 - 7.65805i) q^{91} +(-10.4542 + 4.87627i) q^{92} +(13.3943 + 3.02994i) q^{93} +(10.4645 + 11.4187i) q^{94} +(-0.840731 + 0.705457i) q^{95} +(-4.93308 + 8.46550i) q^{96} +(-0.833364 + 0.303320i) q^{97} +(17.5166 - 11.1607i) q^{98} +(1.14544 - 2.40223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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