LMFDB - Embedded newform 804.2.bd.a.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	804.23
Dual form			804.2.bd.a.35.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39424 - 0.236847i) q^{2} +(1.65796 + 0.501176i) q^{3} +(1.88781 + 0.660444i) q^{4} +(1.24254 - 0.567451i) q^{5} +(-2.19289 - 1.09144i) q^{6} +(2.47543 + 2.59615i) q^{7} +(-2.47563 - 1.36794i) q^{8} +(2.49765 + 1.66186i) q^{9} +O(q^{10})$	\(q+(-1.39424 - 0.236847i) q^{2} +(1.65796 + 0.501176i) q^{3} +(1.88781 + 0.660444i) q^{4} +(1.24254 - 0.567451i) q^{5} +(-2.19289 - 1.09144i) q^{6} +(2.47543 + 2.59615i) q^{7} +(-2.47563 - 1.36794i) q^{8} +(2.49765 + 1.66186i) q^{9} +(-1.86680 + 0.496869i) q^{10} +(4.55967 + 0.435395i) q^{11} +(2.79890 + 2.04111i) q^{12} +(-3.40571 - 0.656397i) q^{13} +(-2.83645 - 4.20596i) q^{14} +(2.34448 - 0.318076i) q^{15} +(3.12763 + 2.49358i) q^{16} +(0.522081 - 1.01270i) q^{17} +(-3.08871 - 2.90859i) q^{18} +(1.53989 - 1.61499i) q^{19} +(2.72045 - 0.250607i) q^{20} +(2.80302 + 5.54493i) q^{21} +(-6.25414 - 1.68699i) q^{22} +(-7.12280 + 2.85154i) q^{23} +(-3.41891 - 3.50871i) q^{24} +(-2.05239 + 2.36858i) q^{25} +(4.59291 + 1.72181i) q^{26} +(3.30811 + 4.00705i) q^{27} +(2.95851 + 6.53591i) q^{28} +(5.69931 + 3.29050i) q^{29} +(-3.34410 - 0.111809i) q^{30} +(-1.80721 - 9.37669i) q^{31} +(-3.77006 - 4.21742i) q^{32} +(7.34152 + 3.00706i) q^{33} +(-0.967759 + 1.28829i) q^{34} +(4.54901 + 1.82115i) q^{35} +(3.61751 + 4.78682i) q^{36} +(-2.75735 - 4.77587i) q^{37} +(-2.52948 + 1.88696i) q^{38} +(-5.31755 - 2.79514i) q^{39} +(-3.85232 - 0.294926i) q^{40} +(-2.80721 + 0.133724i) q^{41} +(-2.59478 - 8.39485i) q^{42} +(-1.26514 - 1.96860i) q^{43} +(8.32021 + 3.83335i) q^{44} +(4.04646 + 0.647638i) q^{45} +(10.6063 - 2.28871i) q^{46} +(-5.51885 - 4.34007i) q^{47} +(3.93575 + 5.70174i) q^{48} +(-0.279199 + 5.86110i) q^{49} +(3.42251 - 2.81627i) q^{50} +(1.37313 - 1.41735i) q^{51} +(-5.99581 - 3.48843i) q^{52} +(-5.38947 + 8.38618i) q^{53} +(-3.66324 - 6.37030i) q^{54} +(5.91265 - 2.04639i) q^{55} +(-2.57686 - 9.81335i) q^{56} +(3.36246 - 1.90583i) q^{57} +(-7.16686 - 5.93761i) q^{58} +(-2.65879 - 3.06841i) q^{59} +(4.63599 + 0.947929i) q^{60} +(-6.02926 + 0.575724i) q^{61} +(0.298837 + 13.5014i) q^{62} +(1.86831 + 10.5981i) q^{63} +(4.25749 + 6.77302i) q^{64} +(-4.60421 + 1.11697i) q^{65} +(-9.52363 - 5.93138i) q^{66} +(-2.62262 + 7.75383i) q^{67} +(1.65442 - 1.56697i) q^{68} +(-13.2384 + 1.15796i) q^{69} +(-5.91108 - 3.61654i) q^{70} +(13.1458 - 6.77715i) q^{71} +(-3.90993 - 7.53077i) q^{72} +(10.5533 - 1.00772i) q^{73} +(2.71325 + 7.31177i) q^{74} +(-4.58985 + 2.89840i) q^{75} +(3.97362 - 2.03178i) q^{76} +(10.1568 + 12.9154i) q^{77} +(6.75192 + 5.15654i) q^{78} +(10.0217 - 3.46856i) q^{79} +(5.30120 + 1.32361i) q^{80} +(3.47647 + 8.30146i) q^{81} +(3.94559 + 0.478437i) q^{82} +(0.687583 - 0.965575i) q^{83} +(1.62945 + 12.3190i) q^{84} +(0.0740534 - 1.55457i) q^{85} +(1.29765 + 3.04435i) q^{86} +(7.80010 + 8.31186i) q^{87} +(-10.6925 - 7.31522i) q^{88} +(-1.90614 + 0.274061i) q^{89} +(-5.48834 - 1.86135i) q^{90} +(-6.72648 - 10.4666i) q^{91} +(-15.3298 + 0.678945i) q^{92} +(1.70309 - 16.4519i) q^{93} +(6.66666 + 7.35822i) q^{94} +(0.996953 - 2.88051i) q^{95} +(-4.13694 - 8.88177i) q^{96} +(-1.27676 - 2.21141i) q^{97} +(1.77746 - 8.10565i) q^{98} +(10.6649 + 8.66497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{14}{33}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.39424	−	0.236847i	−0.985876	−	0.167476i
$2$	−1.39424	−	0.236847i	−0.985876	−	0.167476i
$3$	1.65796	+	0.501176i	0.957222	+	0.289354i
$3$	1.65796	+	0.501176i	0.957222	+	0.289354i
$4$	1.88781	+	0.660444i	0.943903	+	0.330222i
$5$	1.24254	−	0.567451i	0.555682	−	0.253772i	−0.117721	−	0.993047i	$-0.537559\pi$
$5$	1.24254	−	0.567451i	0.555682	−	0.253772i	0.673404	+	0.739275i	$0.264832\pi$
$6$	−2.19289	−	1.09144i	−0.895243	−	0.445579i
$7$	2.47543	+	2.59615i	0.935623	+	0.981253i	0.999861	−	0.0166812i	$-0.00531003\pi$
$7$	2.47543	+	2.59615i	0.935623	+	0.981253i	−0.0642376	+	0.997935i	$0.520462\pi$
$8$	−2.47563	−	1.36794i	−0.875267	−	0.483639i
$9$	2.49765	+	1.66186i	0.832549	+	0.553952i
$10$	−1.86680	+	0.496869i	−0.590335	+	0.157124i
$11$	4.55967	+	0.435395i	1.37479	+	0.131277i	0.756151	−	0.654398i	$-0.227078\pi$
$11$	4.55967	+	0.435395i	1.37479	+	0.131277i	0.618640	+	0.785674i	$0.287684\pi$
$12$	2.79890	+	2.04111i	0.807974	+	0.589218i
$13$	−3.40571	−	0.656397i	−0.944574	−	0.182052i	−0.306364	−	0.951914i	$-0.599113\pi$
$13$	−3.40571	−	0.656397i	−0.944574	−	0.182052i	−0.638210	+	0.769863i	$0.720325\pi$
$14$	−2.83645	−	4.20596i	−0.758072	−	1.12409i
$15$	2.34448	−	0.318076i	0.605341	−	0.0821270i
$16$	3.12763	+	2.49358i	0.781907	+	0.623395i
$17$	0.522081	−	1.01270i	0.126623	−	0.245615i	−0.816999	−	0.576639i	$-0.804364\pi$
$17$	0.522081	−	1.01270i	0.126623	−	0.245615i	0.943622	+	0.331024i	$0.107394\pi$
$18$	−3.08871	−	2.90859i	−0.728016	−	0.685560i
$19$	1.53989	−	1.61499i	0.353275	−	0.370504i	−0.522986	−	0.852341i	$-0.675182\pi$
$19$	1.53989	−	1.61499i	0.353275	−	0.370504i	0.876261	+	0.481837i	$0.160030\pi$
$20$	2.72045	−	0.250607i	0.608311	−	0.0560374i
$21$	2.80302	+	5.54493i	0.611670	+	1.21000i
$22$	−6.25414	−	1.68699i	−1.33339	−	0.359668i
$23$	−7.12280	+	2.85154i	−1.48521	+	0.594587i	−0.965649	−	0.259848i	$-0.916327\pi$
$23$	−7.12280	+	2.85154i	−1.48521	+	0.594587i	−0.519558	+	0.854435i	$0.673903\pi$
$24$	−3.41891	−	3.50871i	−0.697882	−	0.716212i
$25$	−2.05239	+	2.36858i	−0.410478	+	0.473717i
$26$	4.59291	+	1.72181i	0.900743	+	0.337674i
$27$	3.30811	+	4.00705i	0.636646	+	0.771156i
$28$	2.95851	+	6.53591i	0.559106	+	1.23517i
$29$	5.69931	+	3.29050i	1.05834	+	0.611030i	0.924971	−	0.380037i	$-0.124089\pi$
$29$	5.69931	+	3.29050i	1.05834	+	0.611030i	0.133364	+	0.991067i	$0.457422\pi$
$30$	−3.34410	−	0.111809i	−0.610546	−	0.0204134i
$31$	−1.80721	−	9.37669i	−0.324584	−	1.68410i	−0.667399	−	0.744701i	$-0.732592\pi$
$31$	−1.80721	−	9.37669i	−0.324584	−	1.68410i	0.342814	−	0.939403i	$-0.388620\pi$
$32$	−3.77006	−	4.21742i	−0.666459	−	0.745541i
$33$	7.34152	+	3.00706i	1.27800	+	0.523462i
$34$	−0.967759	+	1.28829i	−0.165969	+	0.220939i
$35$	4.54901	+	1.82115i	0.768924	+	0.307831i
$36$	3.61751	+	4.78682i	0.602918	+	0.797803i
$37$	−2.75735	−	4.77587i	−0.453305	−	0.785148i	0.545284	−	0.838252i	$-0.316422\pi$
$37$	−2.75735	−	4.77587i	−0.453305	−	0.785148i	−0.998589	+	0.0531037i	$0.983089\pi$
$38$	−2.52948	+	1.88696i	−0.410336	+	0.306106i
$39$	−5.31755	−	2.79514i	−0.851490	−	0.447580i
$40$	−3.85232	−	0.294926i	−0.609105	−	0.0466319i
$41$	−2.80721	+	0.133724i	−0.438412	+	0.0208841i	−0.265628	−	0.964076i	$-0.585579\pi$
$41$	−2.80721	+	0.133724i	−0.438412	+	0.0208841i	−0.172784	+	0.984960i	$0.555276\pi$
$42$	−2.59478	−	8.39485i	−0.400384	−	1.29535i
$43$	−1.26514	−	1.96860i	−0.192932	−	0.300209i	0.731287	−	0.682069i	$-0.238920\pi$
$43$	−1.26514	−	1.96860i	−0.192932	−	0.300209i	−0.924220	+	0.381861i	$0.875283\pi$
$44$	8.32021	+	3.83335i	1.25432	+	0.577899i
$45$	4.04646	+	0.647638i	0.603210	+	0.0965441i
$46$	10.6063	−	2.28871i	1.56381	−	0.337452i
$47$	−5.51885	−	4.34007i	−0.805007	−	0.633065i	0.128465	−	0.991714i	$-0.458995\pi$
$47$	−5.51885	−	4.34007i	−0.805007	−	0.633065i	−0.933472	+	0.358649i	$0.883237\pi$
$48$	3.93575	+	5.70174i	0.568077	+	0.822976i
$49$	−0.279199	+	5.86110i	−0.0398855	+	0.837300i
$50$	3.42251	−	2.81627i	0.484017	−	0.398281i
$51$	1.37313	−	1.41735i	0.192276	−	0.198469i
$52$	−5.99581	−	3.48843i	−0.831469	−	0.483758i
$53$	−5.38947	+	8.38618i	−0.740301	+	1.15193i	0.243015	+	0.970023i	$0.421864\pi$
$53$	−5.38947	+	8.38618i	−0.740301	+	1.15193i	−0.983316	+	0.181908i	$0.941773\pi$
$54$	−3.66324	−	6.37030i	−0.498503	−	0.866888i
$55$	5.91265	−	2.04639i	0.797261	−	0.275935i
$56$	−2.57686	−	9.81335i	−0.344348	−	1.31136i
$57$	3.36246	−	1.90583i	0.445369	−	0.252433i
$58$	−7.16686	−	5.93761i	−0.941055	−	0.779646i
$59$	−2.65879	−	3.06841i	−0.346146	−	0.399473i	0.555805	−	0.831313i	$-0.312410\pi$
$59$	−2.65879	−	3.06841i	−0.346146	−	0.399473i	−0.901950	+	0.431839i	$0.857865\pi$
$60$	4.63599	+	0.947929i	0.598504	+	0.122377i
$61$	−6.02926	+	0.575724i	−0.771968	+	0.0737140i	−0.473603	−	0.880738i	$-0.657047\pi$
$61$	−6.02926	+	0.575724i	−0.771968	+	0.0737140i	−0.298364	+	0.954452i	$0.596441\pi$
$62$	0.298837	+	13.5014i	0.0379524	+	1.71468i
$63$	1.86831	+	10.5981i	0.235385	+	1.33523i
$64$	4.25749	+	6.77302i	0.532186	+	0.846628i
$65$	−4.60421	+	1.11697i	−0.571083	+	0.138543i
$66$	−9.52363	−	5.93138i	−1.17228	−	0.730103i
$67$	−2.62262	+	7.75383i	−0.320404	+	0.947281i
$67$	−2.62262	+	7.75383i	−0.320404	+	0.947281i
$68$	1.65442	−	1.56697i	0.200627	−	0.190023i
$69$	−13.2384	+	1.15796i	−1.59372	+	0.139402i
$70$	−5.91108	−	3.61654i	−0.706509	−	0.432259i
$71$	13.1458	−	6.77715i	1.56012	−	0.804299i	0.560409	−	0.828216i	$-0.310644\pi$
$71$	13.1458	−	6.77715i	1.56012	−	0.804299i	0.999714	+	0.0239170i	$0.00761374\pi$
$72$	−3.90993	−	7.53077i	−0.460790	−	0.887509i
$73$	10.5533	−	1.00772i	1.23517	−	0.117945i	0.543035	−	0.839710i	$-0.317275\pi$
$73$	10.5533	−	1.00772i	1.23517	−	0.117945i	0.692138	+	0.721765i	$0.256669\pi$
$74$	2.71325	+	7.31177i	0.315409	+	0.849976i
$75$	−4.58985	+	2.89840i	−0.529990	+	0.334679i
$76$	3.97362	−	2.03178i	0.455806	−	0.233061i
$77$	10.1568	+	12.9154i	1.15747	+	1.47184i
$78$	6.75192	+	5.15654i	0.764504	+	0.583863i
$79$	10.0217	−	3.46856i	1.12753	−	0.390243i	0.301277	−	0.953537i	$-0.402587\pi$
$79$	10.0217	−	3.46856i	1.12753	−	0.390243i	0.826257	+	0.563294i	$0.190466\pi$
$80$	5.30120	+	1.32361i	0.592692	+	0.147984i
$81$	3.47647	+	8.30146i	0.386274	+	0.922384i
$82$	3.94559	+	0.478437i	0.435718	+	0.0528345i
$83$	0.687583	−	0.965575i	0.0754720	−	0.105986i	−0.775114	−	0.631821i	$-0.782308\pi$
$83$	0.687583	−	0.965575i	0.0754720	−	0.105986i	0.850586	+	0.525835i	$0.176247\pi$
$84$	1.62945	+	12.3190i	0.177787	+	1.34411i
$85$	0.0740534	−	1.55457i	0.00803222	−	0.168617i
$86$	1.29765	+	3.04435i	0.139930	+	0.328280i
$87$	7.80010	+	8.31186i	0.836258	+	0.891125i
$88$	−10.6925	−	7.31522i	−1.13982	−	0.779805i
$89$	−1.90614	+	0.274061i	−0.202050	+	0.0290504i	−0.242597	−	0.970127i	$-0.577999\pi$
$89$	−1.90614	+	0.274061i	−0.202050	+	0.0290504i	0.0405465	+	0.999178i	$0.487090\pi$
$90$	−5.48834	−	1.86135i	−0.578521	−	0.196204i
$91$	−6.72648	−	10.4666i	−0.705126	−	1.09720i
$92$	−15.3298	+	0.678945i	−1.59824	+	0.0707849i
$93$	1.70309	−	16.4519i	0.176603	−	1.70598i
$94$	6.66666	+	7.35822i	0.687614	+	0.758943i
$95$	0.996953	−	2.88051i	0.102285	−	0.295534i
$96$	−4.13694	−	8.88177i	−0.422224	−	0.906491i
$97$	−1.27676	−	2.21141i	−0.129635	−	0.224535i	0.793900	−	0.608048i	$-0.208047\pi$
$97$	−1.27676	−	2.21141i	−0.129635	−	0.224535i	−0.923535	+	0.383514i	$0.874714\pi$
$98$	1.77746	−	8.10565i	0.179550	−	0.818794i
$99$	10.6649	+	8.66497i	1.07186	+	0.870862i
$100$	−5.43883	+	3.11594i	−0.543883	+	0.311594i
$101$	11.3030	+	2.74207i	1.12469	+	0.272846i	0.754622	−	0.656159i	$-0.227820\pi$
$101$	11.3030	+	2.74207i	1.12469	+	0.272846i	0.370065	+	0.929006i	$0.379335\pi$
$102$	−2.25016	+	1.65091i	−0.222799	+	0.163464i
$103$	−2.40294	−	12.4676i	−0.236768	−	1.22847i	−0.884477	−	0.466583i	$-0.845485\pi$
$103$	−2.40294	−	12.4676i	−0.236768	−	1.22847i	0.647709	−	0.761888i	$-0.275727\pi$
$104$	7.53336	+	6.28380i	0.738707	+	0.616177i
$105$	6.62936	+	5.29925i	0.646959	+	0.517153i
$106$	9.50046	−	10.4159i	0.922766	−	1.01168i
$107$	5.67885	−	12.4349i	0.548995	−	1.20213i	−0.408255	−	0.912868i	$-0.633863\pi$
$107$	5.67885	−	12.4349i	0.548995	−	1.20213i	0.957250	−	0.289263i	$-0.0934102\pi$
$108$	3.59864	+	9.74935i	0.346279	+	0.938131i
$109$	−10.0541	+	11.6030i	−0.963007	+	1.11137i	0.0307194	+	0.999528i	$0.490220\pi$
$109$	−10.0541	+	11.6030i	−0.963007	+	1.11137i	−0.993726	+	0.111841i	$0.964325\pi$
$110$	−8.72833	+	1.45276i	−0.832214	+	0.138515i
$111$	−2.17802	−	9.30010i	−0.206728	−	0.882727i
$112$	1.26850	+	14.2925i	0.119862	+	1.35051i
$113$	2.76708	−	1.97043i	0.260305	−	0.185363i	−0.442452	−	0.896792i	$-0.645891\pi$
$113$	2.76708	−	1.97043i	0.260305	−	0.185363i	0.702757	+	0.711430i	$0.251952\pi$
$114$	−5.13947	+	1.86079i	−0.481355	+	0.174279i
$115$	−7.23228	+	7.58500i	−0.674414	+	0.707305i
$116$	8.58601	+	9.97590i	0.797191	+	0.926239i
$117$	−7.41542	−	7.29924i	−0.685556	−	0.674815i
$118$	2.98025	+	4.90783i	0.274354	+	0.451802i
$119$	3.92148	−	1.15145i	0.359482	−	0.105553i
$120$	−6.23917	−	2.41966i	−0.569555	−	0.220884i
$121$	9.79977	+	1.88875i	0.890888	+	0.171705i
$122$	8.54259	+	0.625317i	0.773410	+	0.0566135i
$123$	−4.72125	−	1.18520i	−0.425701	−	0.106865i
$124$	2.78112	−	18.8949i	0.249752	−	1.69682i
$125$	−3.13034	+	10.6610i	−0.279986	+	0.953546i
$126$	−0.0947420	−	15.2188i	−0.00844029	−	1.35579i
$127$	4.04190	+	4.23902i	0.358661	+	0.376152i	0.878200	−	0.478294i	$-0.158745\pi$
$127$	4.04190	+	4.23902i	0.358661	+	0.376152i	−0.519539	+	0.854447i	$0.673896\pi$
$128$	−4.33178	−	10.4516i	−0.382879	−	0.923798i
$129$	−1.11094	−	3.89791i	−0.0978126	−	0.343192i
$130$	6.68393	−	0.466828i	0.586219	−	0.0409435i
$131$	−0.931932	+	6.48173i	−0.0814232	+	0.566311i	0.907745	+	0.419523i	$0.137803\pi$
$131$	−0.931932	+	6.48173i	−0.0814232	+	0.566311i	−0.989168	+	0.146788i	$0.953106\pi$
$132$	11.8734	+	10.5254i	1.03345	+	0.916120i
$133$	8.00464			0.694090
$134$	5.49304	−	10.1895i	0.474526	−	0.880241i
$135$	6.38427	+	3.10174i	0.549471	+	0.266955i
$136$	−2.67778	+	1.79288i	−0.229618	+	0.153739i
$137$	10.9703	+	1.57730i	0.937259	+	0.134757i	0.593983	−	0.804477i	$-0.297554\pi$
$137$	10.9703	+	1.57730i	0.937259	+	0.134757i	0.343275	+	0.939235i	$0.388464\pi$
$138$	18.7318	+	1.52102i	1.59456	+	0.129478i
$139$	5.94066	−	2.71301i	0.503881	−	0.230115i	−0.147223	−	0.989103i	$-0.547034\pi$
$139$	5.94066	−	2.71301i	0.503881	−	0.230115i	0.651104	+	0.758989i	$0.274306\pi$
$140$	7.38489	+	6.44235i	0.624137	+	0.544478i
$141$	−6.97488	−	9.96157i	−0.587391	−	0.838915i
$142$	−19.9336	+	6.33541i	−1.67279	+	0.531656i
$143$	−15.2431	−	4.47578i	−1.27469	−	0.374283i
$144$	3.66773	+	11.4257i	0.305645	+	0.952146i
$145$	8.94884	+	0.854511i	0.743161	+	0.0709632i
$146$	−14.9525	−	1.09452i	−1.23748	−	0.0905835i
$147$	−3.40034	+	9.57752i	−0.280455	+	0.789941i
$148$	−2.05115	−	10.8370i	−0.168603	−	0.890795i
$149$	1.04582	+	3.56172i	0.0856766	+	0.291788i	0.991175	−	0.132563i	$-0.0423206\pi$
$149$	1.04582	+	3.56172i	0.0856766	+	0.291788i	−0.905498	+	0.424350i	$0.860502\pi$
$150$	7.08583	−	2.95397i	0.578556	−	0.241191i
$151$	−7.71494	+	14.9649i	−0.627833	+	1.21783i	0.333581	+	0.942721i	$0.391743\pi$
$151$	−7.71494	+	14.9649i	−0.627833	+	1.21783i	−0.961414	+	0.275105i	$0.911288\pi$
$152$	−6.02140	+	1.89164i	−0.488400	+	0.153432i
$153$	2.98693	−	1.66173i	0.241479	−	0.134343i
$154$	−11.1020	−	20.4127i	−0.894624	−	1.64490i
$155$	−7.56635	−	10.6254i	−0.607744	−	0.853457i
$156$	−8.19248	−	8.78862i	−0.655923	−	0.703653i
$157$	−5.80960	+	2.32581i	−0.463656	+	0.185620i	−0.591716	−	0.806146i	$-0.701549\pi$
$157$	−5.80960	+	2.32581i	−0.463656	+	0.185620i	0.128060	+	0.991766i	$0.459125\pi$
$158$	−14.7942	+	2.46238i	−1.17696	+	0.195896i
$159$	−13.1385	+	11.2029i	−1.04195	+	0.888444i
$160$	−7.07765	−	3.10100i	−0.559537	−	0.245156i
$161$	−25.0350	−	11.4331i	−1.97303	−	0.901055i
$162$	−2.88085	−	12.3976i	−0.226341	−	0.974048i
$163$	4.78444	+	2.76230i	0.374747	+	0.216360i	0.675530	−	0.737332i	$-0.263915\pi$
$163$	4.78444	+	2.76230i	0.374747	+	0.216360i	−0.300784	+	0.953692i	$0.597248\pi$
$164$	−5.38778	−	1.60156i	−0.420715	−	0.125061i
$165$	10.8285	−	0.429548i	0.842999	−	0.0334403i
$166$	−1.18735	+	1.18339i	−0.0921561	+	0.0918489i
$167$	0.950986	−	3.92002i	0.0735895	−	0.303340i	−0.923108	−	0.384540i	$-0.874360\pi$
$167$	0.950986	−	3.92002i	0.0735895	−	0.303340i	0.996698	+	0.0811999i	$0.0258752\pi$
$168$	0.645883	−	17.5616i	0.0498310	−	1.35490i
$169$	−0.900785	−	0.360620i	−0.0692912	−	0.0277400i
$170$	−0.471445	+	2.14991i	−0.0361582	+	0.164890i
$171$	6.52998	−	1.47460i	0.499360	−	0.112765i
$172$	−1.08819	−	4.55189i	−0.0829740	−	0.347079i
$173$	−6.50314	−	2.25076i	−0.494425	−	0.171122i	0.0684660	−	0.997653i	$-0.478190\pi$
$173$	−6.50314	−	2.25076i	−0.494425	−	0.171122i	−0.562891	+	0.826531i	$0.690311\pi$
$174$	−8.90656	−	13.4362i	−0.675205	−	1.01859i
$175$	−11.2297	+	0.534939i	−0.848889	+	0.0404376i
$176$	13.1752	+	12.7316i	0.993121	+	0.959684i
$177$	−2.87035	−	6.41982i	−0.215749	−	0.482543i
$178$	2.72252	+	0.0693568i	0.204062	+	0.00519851i
$179$	−2.06103	−	14.3348i	−0.154049	−	1.07143i	−0.909343	−	0.416048i	$-0.863415\pi$
$179$	−2.06103	−	14.3348i	−0.154049	−	1.07143i	0.755294	−	0.655386i	$-0.227494\pi$
$180$	7.21120	+	3.89507i	0.537491	+	0.290321i
$181$	−18.1606	−	14.2817i	−1.34987	−	1.06155i	−0.991793	−	0.127855i	$-0.959191\pi$
$181$	−18.1606	−	14.2817i	−1.34987	−	1.06155i	−0.358075	−	0.933693i	$-0.616567\pi$
$182$	6.89933	+	16.1861i	0.511412	+	1.19979i
$183$	−10.2848	−	2.06719i	−0.760274	−	0.152811i
$184$	21.5342	+	2.68420i	1.58752	+	0.197882i
$185$	−6.13620	−	4.36957i	−0.451142	−	0.321257i
$186$	−6.27111	+	22.5345i	−0.459820	+	1.65231i
$187$	2.82144	−	4.39024i	0.206324	−	0.321046i
$188$	−7.55215	−	11.8381i	−0.550797	−	0.863383i
$189$	−2.21392	+	18.5075i	−0.161039	+	1.34622i
$190$	−2.07223	+	3.77999i	−0.150335	+	0.274229i
$191$	−1.18722	+	0.933642i	−0.0859044	+	0.0675560i	−0.660188	−	0.751101i	$-0.729523\pi$
$191$	−1.18722	+	0.933642i	−0.0859044	+	0.0675560i	0.574283	+	0.818657i	$0.305281\pi$
$192$	3.66426	+	13.3631i	0.264445	+	0.964401i
$193$	−13.3173	−	15.3690i	−0.958601	−	1.10628i	−0.994268	−	0.106921i	$-0.965901\pi$
$193$	−13.3173	−	15.3690i	−0.958601	−	1.10628i	0.0356668	−	0.999364i	$-0.488645\pi$
$194$	1.25634	+	3.38563i	0.0901999	+	0.243074i
$195$	−8.19339	−	0.455631i	−0.586741	−	0.0326284i
$196$	−4.39800	+	10.8802i	−0.314143	+	0.777159i
$197$	−4.02546	−	7.80831i	−0.286802	−	0.556319i	0.700788	−	0.713369i	$-0.252832\pi$
$197$	−4.02546	−	7.80831i	−0.286802	−	0.556319i	−0.987591	+	0.157050i	$0.949801\pi$
$198$	−12.8171	−	14.6070i	−0.910872	−	1.03807i
$199$	−24.9309	+	6.04817i	−1.76730	+	0.428743i	−0.981770	−	0.190074i	$-0.939127\pi$
$199$	−24.9309	+	6.04817i	−1.76730	+	0.428743i	−0.785535	+	0.618817i	$0.787612\pi$
$200$	8.32103	−	3.05619i	0.588386	−	0.216105i
$201$	−8.23423	+	11.5411i	−0.580798	+	0.814048i
$202$	−15.1096	−	6.50018i	−1.06311	−	0.457351i
$203$	5.56559	+	22.9417i	0.390628	+	1.61019i
$204$	3.52828	−	1.76881i	0.247029	−	0.123842i
$205$	−3.41220	+	1.75911i	−0.238318	+	0.122862i
$206$	0.397346	+	17.9520i	0.0276844	+	1.25077i
$207$	−22.5291	−	4.71493i	−1.56588	−	0.327711i
$208$	−9.01501	−	10.5454i	−0.625079	−	0.731190i
$209$	7.72454	−	6.69335i	0.534317	−	0.462989i
$210$	−7.98780	−	8.95856i	−0.551210	−	0.618199i
$211$	−0.129225	−	0.164323i	−0.00889621	−	0.0113124i	0.781585	−	0.623799i	$-0.214412\pi$
$211$	−0.129225	−	0.164323i	−0.00889621	−	0.0113124i	−0.790481	+	0.612487i	$0.790169\pi$
$212$	−15.7129	+	12.2720i	−1.07916	+	0.842847i
$213$	25.1918	−	4.64785i	1.72611	−	0.318465i
$214$	−10.8629	+	15.9923i	−0.742569	+	1.09321i
$215$	−2.68908	−	1.72817i	−0.183394	−	0.117860i
$216$	−2.70826	−	14.4453i	−0.184274	−	0.982875i
$217$	19.8697	−	27.9031i	1.34884	−	1.89419i
$218$	16.7659	−	13.7961i	1.13553	−	0.934391i
$219$	18.0020	+	3.61831i	1.21646	+	0.244503i
$220$	12.5135	+	0.0417886i	0.843658	+	0.00281739i
$221$	−2.44278	+	3.10625i	−0.164319	+	0.208949i
$222$	0.833974	+	13.4824i	0.0559726	+	0.904881i
$223$	−0.0597759	+	0.00859447i	−0.00400289	+	0.000575529i	−0.144316	−	0.989532i	$-0.546098\pi$
$223$	−0.0597759	+	0.00859447i	−0.00400289	+	0.000575529i	0.140313	+	0.990107i	$0.455189\pi$
$224$	1.61655	−	20.2276i	0.108010	−	1.35151i
$225$	−9.06239	+	2.50511i	−0.604159	+	0.167007i
$226$	−4.32467	+	2.09188i	−0.287673	+	0.139149i
$227$	−0.538078	−	11.2956i	−0.0357135	−	0.749718i	−0.943717	−	0.330755i	$-0.892697\pi$
$227$	−0.538078	−	11.2956i	−0.0357135	−	0.749718i	0.908003	−	0.418963i	$-0.137606\pi$
$228$	7.60637	−	1.37712i	0.503744	−	0.0912018i
$229$	6.59311	−	19.0495i	0.435685	−	1.25883i	−0.487044	−	0.873378i	$-0.661925\pi$
$229$	6.59311	−	19.0495i	0.435685	−	1.25883i	0.922728	−	0.385451i	$-0.125954\pi$
$230$	11.8800	−	8.86236i	0.783346	−	0.584367i
$231$	10.3666	+	26.5035i	0.682073	+	1.74380i
$232$	−9.60818	−	15.9424i	−0.630808	−	1.04667i
$233$	−1.37462	+	3.43364i	−0.0900546	+	0.224945i	−0.966557	−	0.256452i	$-0.917446\pi$
$233$	−1.37462	+	3.43364i	−0.0900546	+	0.224945i	0.876502	+	0.481398i	$0.159871\pi$
$234$	8.61006	+	11.9332i	0.562857	+	0.780099i
$235$	−9.32019	−	2.26105i	−0.607982	−	0.147495i
$236$	−2.99278	−	7.54855i	−0.194813	−	0.491369i
$237$	18.3540	−	0.728069i	1.19222	−	0.0472932i
$238$	−5.74020	+	0.676606i	−0.372082	+	0.0438578i
$239$	7.72483	−	13.3798i	0.499678	−	0.865468i	−0.500322	−	0.865839i	$-0.666785\pi$
$239$	7.72483	−	13.3798i	0.499678	−	0.865468i	1.00000		0.000371818i	$0.000118353\pi$
$240$	8.12580	+	4.85132i	0.524518	+	0.313151i
$241$	−8.98290	+	19.6698i	−0.578639	+	1.26704i	0.363429	+	0.931622i	$0.381606\pi$
$241$	−8.98290	+	19.6698i	−0.578639	+	1.26704i	−0.942068	+	0.335422i	$0.891121\pi$
$242$	−13.2159	−	4.95442i	−0.849549	−	0.318482i
$243$	1.60335	+	15.5058i	0.102855	+	0.994696i
$244$	−11.7623	−	2.89513i	−0.753005	−	0.185342i
$245$	2.97897	+	7.44110i	0.190319	+	0.475395i
$246$	6.30184	+	2.77066i	0.401791	+	0.176651i
$247$	−6.30449	+	4.48940i	−0.401145	+	0.285654i
$248$	−8.35276	+	25.6854i	−0.530401	+	1.63102i
$249$	1.62391	−	1.25628i	0.102911	−	0.0796137i
$250$	6.88947	−	14.1225i	0.435728	−	0.893187i
$251$	−24.6417	−	12.7037i	−1.55537	−	0.801849i	−0.555804	−	0.831313i	$-0.687589\pi$
$251$	−24.6417	−	12.7037i	−1.55537	−	0.801849i	−0.999566	+	0.0294645i	$0.990620\pi$
$252$	−3.47243	+	21.2410i	−0.218742	+	1.33806i
$253$	−33.7191	+	9.90084i	−2.11990	+	0.622460i
$254$	−4.63137	−	6.86753i	−0.290598	−	0.430907i
$255$	0.901891	−	2.54030i	0.0564786	−	0.159080i
$256$	3.56411	+	15.5980i	0.222757	+	0.974874i
$257$	−0.728614	+	7.63039i	−0.0454497	+	0.475971i	0.943881	+	0.330285i	$0.107145\pi$
$257$	−0.728614	+	7.63039i	−0.0454497	+	0.475971i	−0.989331	+	0.145686i	$0.953461\pi$
$258$	0.625703	+	5.69775i	0.0389545	+	0.354726i
$259$	5.57327	−	18.9808i	0.346306	−	1.17941i
$260$	−9.42956	−	0.932201i	−0.584797	−	0.0578127i
$261$	8.76653	+	17.6899i	0.542634	+	1.09498i
$262$	2.83452	−	8.81635i	0.175117	−	0.544676i
$263$	6.33756	+	13.8773i	0.390791	+	0.855712i	0.998122	+	0.0612634i	$0.0195130\pi$
$263$	6.33756	+	13.8773i	0.390791	+	0.855712i	−0.607331	+	0.794449i	$0.707760\pi$
$264$	−14.0614	−	17.4871i	−0.865420	−	1.07626i
$265$	−1.93791	+	13.4785i	−0.119045	+	0.827975i
$266$	−11.1604	−	1.89588i	−0.684287	−	0.116244i
$267$	−3.29765	−	0.500928i	−0.201813	−	0.0306563i
$268$	−10.0720	+	12.9056i	−0.615244	+	0.788337i
$269$		−	24.1918i		−	1.47500i	−0.675347	−	0.737500i	$-0.736006\pi$
$269$		−	24.1918i		−	1.47500i	0.675347	−	0.737500i	$-0.263994\pi$
$270$	−8.16656	−	5.83667i	−0.497001	−	0.355208i
$271$	5.05073	+	0.726186i	0.306810	+	0.0441126i	0.294000	−	0.955805i	$-0.405013\pi$
$271$	5.05073	+	0.726186i	0.306810	+	0.0441126i	0.0128098	+	0.999918i	$0.495922\pi$
$272$	4.15811	−	1.86548i	0.252122	−	0.113112i
$273$	−5.90661	−	20.7243i	−0.357484	−	1.25429i
$274$	−14.9217	−	4.79742i	−0.901452	−	0.289823i
$275$	−10.3895	+	9.90635i	−0.626509	+	0.597375i
$276$	−25.7564	−	6.55724i	−1.55035	−	0.394699i
$277$	13.3261	+	3.91290i	0.800689	+	0.235103i	0.656381	−	0.754429i	$-0.272086\pi$
$277$	13.3261	+	3.91290i	0.800689	+	0.235103i	0.144308	+	0.989533i	$0.453904\pi$
$278$	−8.92528	+	2.37556i	−0.535303	+	0.142476i
$279$	11.0689	−	26.4230i	0.662680	−	1.58190i
$280$	−8.77045	−	10.7313i	−0.524135	−	0.641316i
$281$	−2.44028	+	12.6614i	−0.145575	+	0.755314i	0.833612	+	0.552351i	$0.186269\pi$
$281$	−2.44028	+	12.6614i	−0.145575	+	0.755314i	−0.979186	+	0.202963i	$0.934943\pi$
$282$	7.36528	+	15.5408i	0.438596	+	0.925441i
$283$	2.38353	+	8.11756i	0.141686	+	0.482539i	0.999507	−	0.0314107i	$-0.00999999\pi$
$283$	2.38353	+	8.11756i	0.141686	+	0.482539i	−0.857820	+	0.513950i	$0.828182\pi$
$284$	29.2927	−	4.11186i	1.73820	−	0.243994i
$285$	3.09654	−	4.27611i	0.183423	−	0.253295i
$286$	20.1925	+	9.85060i	1.19401	+	0.582478i
$287$	−7.29620	−	6.95692i	−0.430681	−	0.410654i
$288$	−2.40754	−	16.7989i	−0.141866	−	0.989886i
$289$	9.10798	+	12.7904i	0.535764	+	0.752375i
$290$	−12.2744	−	3.31090i	−0.720780	−	0.194423i
$291$	−1.00851	−	4.30630i	−0.0591197	−	0.252440i
$292$	20.5882	+	5.06750i	1.20483	+	0.296553i
$293$	−22.0713	−	19.1249i	−1.28942	−	1.11729i	−0.986410	−	0.164303i	$-0.947463\pi$
$293$	−22.0713	−	19.1249i	−1.28942	−	1.11729i	−0.303011	−	0.952987i	$-0.597992\pi$
$294$	7.00930	−	12.5480i	0.408791	−	0.731814i
$295$	−5.04484	−	2.30390i	−0.293722	−	0.134138i
$296$	0.293079	+	15.5952i	0.0170349	+	0.906451i
$297$	13.3392	+	19.7111i	0.774020	+	1.14376i
$298$	−0.614533	−	5.21359i	−0.0355989	−	0.302015i
$299$	26.1299	−	5.03613i	1.51113	−	0.291247i
$300$	−10.5790	+	2.44029i	−0.610778	+	0.140890i
$301$	1.97902	−	8.15763i	0.114069	−	0.470198i
$302$	14.3009	−	19.0374i	0.822922	−	1.09548i
$303$	17.3656	+	10.2110i	0.997627	+	0.586607i
$304$	8.84330	−	1.21125i	0.507198	−	0.0694698i
$305$	−7.16492	+	4.13667i	−0.410262	+	0.236865i
$306$	−4.55807	+	1.60941i	−0.260567	+	0.0920036i
$307$	26.8747	+	9.30142i	1.53382	+	0.530860i	0.958013	−	0.286726i	$-0.0925670\pi$
$307$	26.8747	+	9.30142i	1.53382	+	0.530860i	0.575806	+	0.817586i	$0.304688\pi$
$308$	10.6441	+	31.0897i	0.606505	+	1.77150i
$309$	2.26450	−	21.8751i	0.128823	−	1.24443i
$310$	8.03269	+	16.6065i	0.456226	+	0.943185i
$311$	−15.4788	+	9.94765i	−0.877724	+	0.564079i	−0.900106	−	0.435670i	$-0.856511\pi$
$311$	−15.4788	+	9.94765i	−0.877724	+	0.564079i	0.0223819	+	0.999749i	$0.492875\pi$
$312$	9.34071	+	14.1938i	0.528814	+	0.803566i
$313$	−2.45737	−	17.0914i	−0.138899	−	0.966063i	−0.933410	−	0.358813i	$-0.883182\pi$
$313$	−2.45737	−	17.0914i	−0.138899	−	0.966063i	0.794511	−	0.607250i	$-0.207727\pi$
$314$	8.65083	−	1.86675i	0.488195	−	0.105347i
$315$	8.33534	+	12.1084i	0.469643	+	0.682231i
$316$	21.2099	+	0.0708303i	1.19315	+	0.00398452i
$317$	−30.1837	−	1.43783i	−1.69529	−	0.0807564i	−0.822471	−	0.568808i	$-0.807405\pi$
$317$	−30.1837	−	1.43783i	−1.69529	−	0.0807564i	−0.872815	+	0.488051i	$0.837708\pi$
$318$	20.9715	−	12.5077i	1.17602	−	0.701394i
$319$	24.5543	+	17.4850i	1.37478	+	0.978974i
$320$	9.13347	+	5.99986i	0.510576	+	0.335402i
$321$	15.6474	−	17.7705i	0.873351	−	0.991853i
$322$	32.1969	+	21.8700i	1.79426	+	1.21877i
$323$	−0.831545	−	2.40259i	−0.0462684	−	0.133684i
$324$	1.08026	+	17.9676i	0.0600143	+	0.998198i
$325$	8.54457	−	6.71952i	0.473967	−	0.372732i
$326$	−6.01642	−	4.98449i	−0.333218	−	0.276065i
$327$	−22.4844	+	14.1985i	−1.24339	+	0.785177i
$328$	7.13253	+	3.50904i	0.393828	+	0.193754i
$329$	−2.39402	−	25.0713i	−0.131987	−	1.38223i
$330$	−15.1993	−	1.96581i	−0.836693	−	0.108215i
$331$	−5.08468	−	9.86290i	−0.279479	−	0.542114i	0.706757	−	0.707456i	$-0.250157\pi$
$331$	−5.08468	−	9.86290i	−0.279479	−	0.542114i	−0.986236	+	0.165342i	$0.947127\pi$
$332$	1.93573	−	1.36871i	0.106237	−	0.0751177i
$333$	1.04992	−	16.5107i	0.0575355	−	0.904783i
$334$	−2.25435	+	5.24021i	−0.123352	+	0.286731i
$335$	1.14119	+	11.1227i	0.0623500	+	0.607697i
$336$	−5.05993	+	24.3321i	−0.276042	+	1.32742i
$337$	3.95662	+	16.3094i	0.215531	+	0.888430i	0.972110	+	0.234527i	$0.0753542\pi$
$337$	3.95662	+	16.3094i	0.215531	+	0.888430i	−0.756579	+	0.653902i	$0.773131\pi$
$338$	1.17050	+	0.716139i	0.0636667	+	0.0389528i
$339$	5.57524	−	1.88010i	0.302805	−	0.102113i
$340$	1.16651	−	2.88582i	0.0632627	−	0.156506i
$341$	−4.15770	−	43.5414i	−0.225152	−	2.35790i
$342$	−9.45360	+	0.509334i	−0.511192	+	0.0275416i
$343$	3.06954	−	2.65977i	0.165740	−	0.143614i
$344$	0.439100	+	6.60416i	0.0236747	+	0.356073i
$345$	−15.7922	+	8.95097i	−0.850226	+	0.481904i
$346$	8.53385	+	4.67835i	0.458782	+	0.251510i
$347$	5.87569	+	16.9767i	0.315424	+	0.911357i	0.985591	+	0.169147i	$0.0541012\pi$
$347$	5.87569	+	16.9767i	0.315424	+	0.911357i	−0.670167	+	0.742210i	$0.733778\pi$
$348$	9.23556	+	20.8427i	0.495078	+	1.11729i
$349$	−4.98437	−	3.20326i	−0.266807	−	0.171466i	0.400396	−	0.916342i	$-0.368872\pi$
$349$	−4.98437	−	3.20326i	−0.266807	−	0.171466i	−0.667203	+	0.744876i	$0.732509\pi$
$350$	15.7836	+	1.91390i	0.843671	+	0.102302i
$351$	−8.63625	−	15.8183i	−0.460969	−	0.844316i
$352$	−15.3540	−	20.8715i	−0.818370	−	1.11245i
$353$	2.15285	+	0.102553i	0.114585	+	0.00545834i	0.104796	−	0.994494i	$-0.466581\pi$
$353$	2.15285	+	0.102553i	0.114585	+	0.00545834i	0.00978880	+	0.999952i	$0.496884\pi$
$354$	2.48144	+	9.63060i	0.131887	+	0.511861i
$355$	12.4886	−	15.8805i	0.662824	−	0.842850i
$356$	−3.77942	−	0.741523i	−0.200309	−	0.0393006i
$357$	7.07873	+	0.0562946i	0.374646	+	0.00297942i
$358$	−0.521587	+	20.4743i	−0.0275667	+	1.08210i
$359$	26.9994	−	17.3515i	1.42497	−	0.915775i	0.425030	−	0.905179i	$-0.360263\pi$
$359$	26.9994	−	17.3515i	1.42497	−	0.915775i	0.999944	−	0.0105960i	$-0.00337289\pi$
$360$	−9.13160	−	7.13861i	−0.481277	−	0.376238i
$361$	0.667125	+	14.0047i	0.0351118	+	0.737088i
$362$	21.9377	+	24.2134i	1.15302	+	1.27263i
$363$	15.3010	+	8.04287i	0.803094	+	0.422141i
$364$	−5.78568	−	24.2014i	−0.303252	−	1.26850i
$365$	12.5411	−	7.24063i	0.656433	−	0.378992i
$366$	13.8499	+	5.31809i	0.723944	+	0.277981i
$367$	10.7269	−	26.7945i	0.559941	−	1.39866i	−0.330605	−	0.943769i	$-0.607253\pi$
$367$	10.7269	−	26.7945i	0.559941	−	1.39866i	0.890545	−	0.454895i	$-0.150323\pi$
$368$	−29.3880	−	8.84273i	−1.53196	−	0.460959i
$369$	−7.23364	−	4.33118i	−0.376568	−	0.225472i
$370$	7.52041	+	7.54556i	0.390967	+	0.392275i
$371$	−35.1130	+	6.76748i	−1.82298	+	0.351350i
$372$	14.0807	−	29.9332i	0.730048	−	1.55196i
$373$	−10.8957	+	18.8719i	−0.564159	+	0.977152i	0.432969	+	0.901409i	$0.357466\pi$
$373$	−10.8957	+	18.8719i	−0.564159	+	0.977152i	−0.997127	+	0.0757428i	$0.975867\pi$
$374$	−4.97357	+	5.45279i	−0.257177	+	0.281957i
$375$	−10.5330	+	16.1066i	−0.543921	+	0.831740i
$376$	7.72568	+	18.2939i	0.398421	+	0.943434i
$377$	−17.2503	−	14.9475i	−0.888437	−	0.769835i
$378$	7.47019	−	25.2795i	0.384225	−	1.30024i
$379$	7.46943	+	18.6577i	0.383679	+	0.958383i	0.986976	+	0.160867i	$0.0514289\pi$
$379$	7.46943	+	18.6577i	0.383679	+	0.958383i	−0.603297	+	0.797516i	$0.706147\pi$
$380$	3.78447	−	4.77941i	0.194139	−	0.245178i
$381$	4.57680	+	9.05382i	0.234477	+	0.463841i
$382$	1.87640	−	1.02053i	0.0960052	−	0.0522149i
$383$	4.81521	+	4.59130i	0.246046	+	0.234604i	0.803059	−	0.595899i	$-0.203204\pi$
$383$	4.81521	+	4.59130i	0.246046	+	0.234604i	−0.557013	+	0.830504i	$0.688053\pi$
$384$	−1.94383	−	19.4993i	−0.0991957	−	0.995068i
$385$	19.9491	+	10.2845i	1.01670	+	0.524144i
$386$	14.9274	+	24.5822i	0.759785	+	1.25120i
$387$	0.111652	−	7.01935i	0.00567558	−	0.356814i
$388$	−0.949760	−	5.01794i	−0.0482168	−	0.254747i
$389$	−3.11354	+	16.1546i	−0.157863	+	0.819068i	0.813518	+	0.581540i	$0.197550\pi$
$389$	−3.11354	+	16.1546i	−0.157863	+	0.819068i	−0.971381	+	0.237529i	$0.923663\pi$
$390$	11.3156	+	2.57584i	0.572989	+	0.130433i
$391$	−0.830936	+	8.70196i	−0.0420223	+	0.440077i
$392$	8.70882	−	14.1280i	0.439862	−	0.713571i
$393$	−4.79359	+	10.2794i	−0.241804	+	0.518525i
$394$	3.76308	+	11.8401i	0.189581	+	0.596494i
$395$	10.4842	−	9.99668i	0.527518	−	0.502987i
$396$	14.4105	+	23.4013i	0.724154	+	1.17596i
$397$	0.650954	+	1.42539i	0.0326704	+	0.0715383i	0.925264	−	0.379325i	$-0.123844\pi$
$397$	0.650954	+	1.42539i	0.0326704	+	0.0715383i	−0.892593	+	0.450863i	$0.851116\pi$
$398$	36.1921	−	2.52778i	1.81415	−	0.126706i
$399$	13.2714	+	4.01173i	0.664399	+	0.200838i
$400$	−12.3254	+	2.29025i	−0.616268	+	0.114512i
$401$		−	5.15593i		−	0.257475i	−0.991679	−	0.128738i	$-0.958908\pi$
$401$		−	5.15593i		−	0.257475i	0.991679	−	0.128738i	$-0.0410925\pi$
$402$	14.2140	−	14.1408i	0.708928	−	0.705281i
$403$			33.1205i			1.64985i
$404$	19.5268	+	12.6415i	0.971497	+	0.628937i
$405$	9.03033	+	8.34220i	0.448721	+	0.414527i
$406$	−2.32609	−	33.3044i	−0.115442	−	1.65287i
$407$	−10.4932	−	22.9769i	−0.520129	−	1.13892i
$408$	−5.33820	+	1.63049i	−0.264280	+	0.0807210i
$409$	24.0098	−	22.8933i	1.18721	−	1.13200i	0.198822	−	0.980036i	$-0.436289\pi$
$409$	24.0098	−	22.8933i	1.18721	−	1.13200i	0.988386	−	0.151964i	$-0.0485599\pi$
$410$	5.17406	−	1.64445i	0.255529	−	0.0812136i
$411$	17.3978	+	8.11315i	0.858172	+	0.400192i
$412$	3.69788	−	25.1235i	0.182182	−	1.23774i
$413$	1.38442	−	14.4983i	0.0681227	−	0.713413i
$414$	30.2942	+	11.9097i	1.48888	+	0.585330i
$415$	0.306436	−	1.58994i	0.0150423	−	0.0780470i
$416$	10.0714	+	16.8380i	0.493793	+	0.825549i
$417$	11.2091	−	1.52074i	0.548910	−	0.0744709i
$418$	−12.3552	+	7.50260i	−0.604310	+	0.366964i
$419$	13.5875	+	7.00484i	0.663793	+	0.342209i	0.756978	−	0.653440i	$-0.226675\pi$
$419$	13.5875	+	7.00484i	0.663793	+	0.342209i	−0.0931858	+	0.995649i	$0.529705\pi$
$420$	9.01509	+	14.3823i	0.439891	+	0.701783i
$421$	2.58838	+	2.46801i	0.126150	+	0.120284i	0.750528	−	0.660838i	$-0.229799\pi$
$421$	2.58838	+	2.46801i	0.126150	+	0.120284i	−0.624378	+	0.781122i	$0.714648\pi$
$422$	0.141251	+	0.259712i	0.00687599	+	0.0126426i
$423$	−6.57156	−	20.0115i	−0.319520	−	0.972992i
$424$	24.8141	−	13.3886i	1.20508	−	0.650208i
$425$	1.32714	+	3.31504i	0.0643757	+	0.160803i
$426$	−36.2242	+	0.513611i	−1.75507	+	0.0248845i
$427$	−16.4197	−	14.2277i	−0.794603	−	0.688527i
$428$	18.9331	−	19.7242i	0.915168	−	0.953405i
$429$	−23.0293	−	15.0601i	−1.11186	−	0.727110i
$430$	3.33991	+	3.04638i	0.161065	+	0.146909i
$431$	−8.95379	+	15.5084i	−0.431289	+	0.747015i	−0.996985	−	0.0775996i	$-0.975274\pi$
$431$	−8.95379	+	15.5084i	−0.431289	+	0.747015i	0.565696	+	0.824614i	$0.308608\pi$
$432$	0.354641	+	20.7816i	0.0170627	+	0.999854i
$433$	−11.2419	+	2.16669i	−0.540250	+	0.104125i	−0.452074	−	0.891980i	$-0.649316\pi$
$433$	−11.2419	+	2.16669i	−0.540250	+	0.104125i	−0.0881758	+	0.996105i	$0.528104\pi$
$434$	−34.3119	+	34.1975i	−1.64702	+	1.64153i
$435$	14.4085	+	5.90168i	0.690836	+	0.282964i
$436$	−26.6433	+	15.2641i	−1.27598	+	0.731019i
$437$	−6.36312	+	15.8943i	−0.304389	+	0.760328i
$438$	−24.2421	−	9.30852i	−1.15833	−	0.444778i
$439$	−10.0585	+	5.80727i	−0.480065	+	0.277166i	−0.720444	−	0.693513i	$-0.756062\pi$
$439$	−10.0585	+	5.80727i	−0.480065	+	0.277166i	0.240378	+	0.970679i	$0.422729\pi$
$440$	−17.4369	−	3.02204i	−0.831270	−	0.144070i
$441$	−10.4376	+	14.1750i	−0.497030	+	0.674998i
$442$	4.14153	−	3.75229i	0.196993	−	0.178478i
$443$	−0.0619317	−	1.30011i	−0.00294246	−	0.0617699i	0.996919	−	0.0784441i	$-0.0249952\pi$
$443$	−0.0619317	−	1.30011i	−0.00294246	−	0.0617699i	−0.999861	+	0.0166742i	$0.994692\pi$
$444$	2.03052	−	18.9953i	0.0963642	−	0.901475i
$445$	−2.21294	+	1.42217i	−0.104904	+	0.0674174i
$446$	0.0853775	+	0.00217501i	0.00404274	+	0.000102990i
$447$	−0.0511300	+	6.42932i	−0.00241837	+	0.304096i
$448$	−7.04470	+	27.8192i	−0.332831	+	1.31433i
$449$	−7.58685	+	9.64747i	−0.358046	+	0.455292i	−0.931390	−	0.364022i	$-0.881403\pi$
$449$	−7.58685	+	9.64747i	−0.358046	+	0.455292i	0.573345	+	0.819314i	$0.305646\pi$
$450$	13.2285	−	1.34632i	0.623596	−	0.0634660i
$451$	−12.8582	−	0.612509i	−0.605467	−	0.0288419i
$452$	6.52508	−	1.89229i	0.306914	−	0.0890058i
$453$	−20.2911	+	20.9446i	−0.953358	+	0.984064i
$454$	−1.92513	+	15.8763i	−0.0903510	+	0.745110i
$455$	−14.2972	−	9.18827i	−0.670264	−	0.430753i
$456$	−10.9313	+	0.118481i	−0.511904	+	0.00554836i
$457$	12.5735	+	36.3287i	0.588162	+	1.69938i	0.707663	+	0.706550i	$0.249749\pi$
$457$	12.5735	+	36.3287i	0.588162	+	1.69938i	−0.119501	+	0.992834i	$0.538129\pi$
$458$	−13.7042	+	24.9980i	−0.640355	+	1.16808i
$459$	5.78501	−	1.25810i	0.270021	−	0.0587233i
$460$	−18.6626	+	9.54250i	−0.870149	+	0.444921i
$461$	−7.18444	+	6.22535i	−0.334613	+	0.289944i	−0.805919	−	0.592026i	$-0.798328\pi$
$461$	−7.18444	+	6.22535i	−0.334613	+	0.289944i	0.471306	+	0.881970i	$0.343783\pi$
$462$	−8.17626	−	39.4075i	−0.380394	−	1.83340i
$463$	0.172224	+	1.80361i	0.00800394	+	0.0838211i	0.998591	−	0.0530612i	$-0.0168979\pi$
$463$	0.172224	+	1.80361i	0.00800394	+	0.0838211i	−0.990587	+	0.136882i	$0.956292\pi$
$464$	9.62020	+	24.5031i	0.446607	+	1.13753i
$465$	−7.21947	−	21.4086i	−0.334795	−	0.992801i
$466$	2.72980	−	4.46175i	0.126456	−	0.206686i
$467$	−6.63956	−	27.3686i	−0.307242	−	1.26647i	−0.890799	−	0.454398i	$-0.849855\pi$
$467$	−6.63956	−	27.3686i	−0.307242	−	1.26647i	0.583557	−	0.812072i	$-0.301661\pi$
$468$	−9.17814	−	18.6770i	−0.424259	−	0.863346i
$469$	−26.6222	+	12.3853i	−1.22930	+	0.571900i
$470$	12.4591	+	5.35991i	0.574693	+	0.247234i
$471$	−10.7977	+	0.944468i	−0.497532	+	0.0435188i
$472$	2.38479	+	11.2333i	0.109769	+	0.517056i
$473$	−4.91151	−	9.52700i	−0.225831	−	0.438052i
$474$	−25.7623	−	3.33199i	−1.18330	−	0.153043i
$475$	0.664785	+	6.96194i	0.0305024	+	0.319436i
$476$	8.16347	+	0.416202i	0.374172	+	0.0190766i
$477$	−27.3976	+	11.9892i	−1.25445	+	0.548947i
$478$	−13.9392	+	16.8250i	−0.637566	+	0.769560i
$479$	12.8959	−	10.1415i	0.589229	−	0.463375i	−0.278483	−	0.960441i	$-0.589832\pi$
$479$	12.8959	−	10.1415i	0.589229	−	0.463375i	0.867713	+	0.497066i	$0.165589\pi$
$480$	−10.1803	−	8.68847i	−0.464664	−	0.396573i
$481$	6.25586	+	18.0751i	0.285243	+	0.824155i
$482$	17.1831	−	25.2968i	0.782667	−	1.15224i
$483$	−35.7770	−	31.5025i	−1.62791	−	1.43342i
$484$	17.2527	+	10.0378i	0.784212	+	0.456263i
$485$	−2.84129	−	2.02328i	−0.129017	−	0.0918722i
$486$	1.43705	−	21.9985i	0.0651858	−	0.997873i
$487$	−10.9569	−	0.521943i	−0.496506	−	0.0236515i	−0.202164	−	0.979352i	$-0.564797\pi$
$487$	−10.9569	−	0.521943i	−0.496506	−	0.0236515i	−0.294342	+	0.955700i	$0.595101\pi$
$488$	15.7138	+	6.82238i	0.711329	+	0.308835i
$489$	6.54801	+	6.97762i	0.296111	+	0.315539i
$490$	−2.39099	−	11.0802i	−0.108014	−	0.500554i
$491$	−3.49787	−	24.3282i	−0.157857	−	1.09792i	−0.902573	−	0.430537i	$-0.858324\pi$
$491$	−3.49787	−	24.3282i	−0.157857	−	1.09792i	0.744716	−	0.667381i	$-0.232585\pi$
$492$	−8.13005	−	5.35554i	−0.366531	−	0.241446i
$493$	6.30777	−	4.05376i	0.284088	−	0.182572i
$494$	9.85327	−	4.76610i	0.443319	−	0.214437i
$495$	18.1685	+	4.71482i	0.816614	+	0.211915i
$496$	17.7293	−	33.8332i	0.796067	−	1.51916i
$497$	50.1360	+	17.3522i	2.24891	+	0.778355i
$498$	−2.56166	+	1.36694i	−0.114791	+	0.0612541i
$499$	8.29500	−	4.78912i	0.371335	−	0.214390i	−0.302707	−	0.953084i	$-0.597890\pi$
$499$	8.29500	−	4.78912i	0.371335	−	0.214390i	0.674042	+	0.738693i	$0.264557\pi$
$500$	−12.9504	+	18.0584i	−0.579162	+	0.807597i
$501$	3.54131	−	6.02261i	0.158214	−	0.269070i
$502$	31.3476	+	23.5483i	1.39911	+	1.05101i
$503$	−7.76499	+	32.0077i	−0.346224	+	1.42715i	0.486605	+	0.873622i	$0.338235\pi$
$503$	−7.76499	+	32.0077i	−0.346224	+	1.42715i	−0.832829	+	0.553531i	$0.813280\pi$
$504$	9.87228	−	28.7926i	0.439746	−	1.28253i
$505$	15.6004	−	3.00674i	0.694210	−	0.133798i
$506$	49.3575	−	5.81784i	2.19421	−	0.258635i
$507$	−1.31273	−	1.04934i	−0.0583004	−	0.0466030i
$508$	4.83069	+	10.6719i	0.214327	+	0.473489i
$509$	33.4124	+	15.2589i	1.48098	+	0.676340i	0.981758	−	0.190136i	$-0.0608928\pi$
$509$	33.4124	+	15.2589i	1.48098	+	0.676340i	0.499220	+	0.866475i	$0.333620\pi$
$510$	−1.85912	+	3.32818i	−0.0823231	+	0.147374i
$511$	28.7402	+	24.9035i	1.27139	+	1.10167i
$512$	−1.27488	−	22.5915i	−0.0563423	−	0.998412i
$513$	11.5655	+	0.827846i	0.510627	+	0.0365503i
$514$	2.82310	−	10.4660i	0.124522	−	0.461636i
$515$	−10.0605	−	14.1280i	−0.443319	−	0.622554i
$516$	0.477117	−	8.09222i	0.0210039	−	0.356240i
$517$	−23.2745	−	22.1922i	−1.02361	−	0.976010i
$518$	−12.2660	+	25.1438i	−0.538938	+	1.10475i
$519$	−9.65390	−	6.99088i	−0.423759	−	0.306865i
$520$	12.9263	+	3.53308i	0.566855	+	0.154936i
$521$	8.45033	+	28.7792i	0.370216	+	1.26084i	0.908432	+	0.418032i	$0.137280\pi$
$521$	8.45033	+	28.7792i	0.370216	+	1.26084i	−0.538217	+	0.842807i	$0.680902\pi$
$522$	−8.03282	−	26.7403i	−0.351587	−	1.17039i
$523$	−0.171216	+	0.888352i	−0.00748674	+	0.0388449i	−0.985480	−	0.169792i	$-0.945690\pi$
$523$	−0.171216	+	0.888352i	−0.00748674	+	0.0388449i	0.977993	+	0.208637i	$0.0669026\pi$
$524$	−6.04012	+	11.6208i	−0.263864	+	0.507655i
$525$	−18.8865	−	4.74117i	−0.824276	−	0.206922i
$526$	−5.54927	−	20.8493i	−0.241960	−	0.909075i
$527$	−10.4392	−	3.06524i	−0.454740	−	0.133524i
$528$	15.4632	+	27.7116i	0.672949	+	1.20599i
$529$	25.9572	−	24.7501i	1.12857	−	1.07609i
$530$	5.89425	−	18.3332i	0.256030	−	0.796343i
$531$	−1.54147	−	12.0823i	−0.0668940	−	0.524329i
$532$	15.1112	+	5.28662i	0.655154	+	0.229204i
$533$	9.64831	+	1.38722i	0.417915	+	0.0600870i
$534$	4.47907	+	1.47945i	0.193828	+	0.0640222i
$535$		−	18.6734i		−	0.807322i
$536$	17.0994	−	15.6080i	0.738582	−	0.674164i
$537$	3.76715	−	24.7994i	0.162565	−	1.07018i
$538$	−5.72977	+	33.7292i	−0.247028	+	1.45417i
$539$	−3.82495	+	26.6031i	−0.164752	+	1.14588i
$540$	10.0037	+	10.0719i	0.430493	+	0.433427i
$541$	−4.15727	−	9.10315i	−0.178735	−	0.391375i	0.798966	−	0.601376i	$-0.205381\pi$
$541$	−4.15727	−	9.10315i	−0.178735	−	0.391375i	−0.977701	+	0.210001i	$0.932653\pi$
$542$	−6.86994	−	2.20873i	−0.295089	−	0.0948731i
$543$	−22.9519	−	32.7800i	−0.984960	−	1.40673i
$544$	−6.23924	+	1.61609i	−0.267505	+	0.0692894i
$545$	−5.90849	+	20.1225i	−0.253092	+	0.861952i
$546$	3.32672	+	30.2936i	0.142370	+	1.29645i
$547$	1.50516	−	15.7628i	0.0643561	−	0.673967i	−0.904522	−	0.426428i	$-0.859772\pi$
$547$	1.50516	−	15.7628i	0.0643561	−	0.673967i	0.968878	−	0.247540i	$-0.0796220\pi$
$548$	19.6682	+	10.2229i	0.840182	+	0.436701i
$549$	−16.0157	−	8.58180i	−0.683535	−	0.366262i
$550$	16.8317	−	11.3511i	0.717707	−	0.484013i
$551$	14.0904	−	4.13732i	0.600272	−	0.176256i
$552$	34.3575	+	15.2427i	1.46235	+	0.648772i
$553$	33.8130	+	17.4318i	1.43787	+	0.741276i
$554$	−17.6530	−	8.61178i	−0.750006	−	0.365879i
$555$	−7.98363	−	10.3199i	−0.338886	−	0.438054i
$556$	13.0066	−	1.19816i	0.551603	−	0.0508135i
$557$	−22.1066	+	15.7420i	−0.936686	+	0.667011i	−0.942938	−	0.332969i	$-0.891949\pi$
$557$	−22.1066	+	15.7420i	−0.936686	+	0.667011i	0.00625147	+	0.999980i	$0.498010\pi$
$558$	−21.6910	+	34.2183i	−0.918252	+	1.44858i
$559$	3.01652	+	7.53491i	0.127585	+	0.318693i
$560$	9.68644	+	17.0392i	0.409327	+	0.720038i
$561$	6.87810	−	5.86480i	0.290394	−	0.247612i
$562$	6.40115	−	17.0750i	0.270016	−	0.720266i
$563$	−4.66360	+	10.2119i	−0.196547	+	0.430379i	−0.982086	−	0.188434i	$-0.939659\pi$
$563$	−4.66360	+	10.2119i	−0.196547	+	0.430379i	0.785539	+	0.618813i	$0.212386\pi$
$564$	−6.58817	−	23.4120i	−0.277412	−	0.985824i
$565$	2.32010	−	4.01853i	0.0976073	−	0.169061i
$566$	−1.40059	−	11.8824i	−0.0588712	−	0.499453i
$567$	−12.9461	+	29.5751i	−0.543685	+	1.24204i
$568$	−41.8149	−	1.20499i	−1.75452	−	0.0505601i
$569$	33.1105	+	8.03253i	1.38807	+	0.336741i	0.859059	−	0.511877i	$-0.171049\pi$
$569$	33.1105	+	8.03253i	1.38807	+	0.336741i	0.529007	+	0.848618i	$0.322565\pi$
$570$	−5.33011	+	5.22851i	−0.223254	+	0.218998i
$571$	9.86655	−	24.6454i	0.412902	−	1.03138i	−0.565515	−	0.824738i	$-0.691322\pi$
$571$	9.86655	−	24.6454i	0.412902	−	1.03138i	0.978417	−	0.206641i	$-0.0662533\pi$
$572$	−25.8200	−	18.5166i	−1.07959	−	0.774219i
$573$	−2.43628	+	0.952932i	−0.101777	+	0.0398093i
$574$	8.52493	+	11.4277i	0.355824	+	0.476983i
$575$	7.86465	−	22.7234i	0.327979	−	0.947632i
$576$	−0.622091	+	23.9919i	−0.0259205	+	0.999664i
$577$	1.14656	+	24.0693i	0.0477320	+	1.00202i	0.887999	+	0.459845i	$0.152095\pi$
$577$	1.14656	+	24.0693i	0.0477320	+	1.00202i	−0.840267	+	0.542173i	$0.817602\pi$
$578$	−9.66934	−	19.9900i	−0.402192	−	0.831476i
$579$	−14.3770	−	32.1554i	−0.597486	−	1.33633i
$580$	16.3293	+	7.52336i	0.678038	+	0.312390i
$581$	4.20884	−	0.605140i	0.174612	−	0.0251054i
$582$	0.386162	+	6.24288i	0.0160069	+	0.258776i
$583$	−28.2255	+	35.8916i	−1.16898	+	1.48648i
$584$	−27.5046	−	11.9416i	−1.13815	−	0.494145i
$585$	−13.3559	−	4.86174i	−0.552200	−	0.201008i
$586$	26.2430	+	31.8923i	1.08409	+	1.31746i
$587$	−11.9620	+	16.7982i	−0.493723	+	0.693338i	−0.983988	−	0.178236i	$-0.942961\pi$
$587$	−11.9620	+	16.7982i	−0.493723	+	0.693338i	0.490264	+	0.871574i	$0.336900\pi$
$588$	−12.7446	+	15.8348i	−0.525578	+	0.653015i
$589$	−17.9262	−	11.5204i	−0.738635	−	0.474692i
$590$	6.48804	+	4.40705i	0.267109	+	0.181435i
$591$	−2.76071	−	14.9633i	−0.113561	−	0.615508i
$592$	3.28505	−	21.8128i	0.135015	−	0.896501i
$593$	−19.9683	−	25.3918i	−0.820000	−	1.04271i	−0.998274	−	0.0587340i	$-0.981294\pi$
$593$	−19.9683	−	25.3918i	−0.820000	−	1.04271i	0.178274	−	0.983981i	$-0.442949\pi$
$594$	−13.9295	−	30.6414i	−0.571536	−	1.25723i
$595$	4.21922	−	3.65598i	0.172971	−	0.149880i
$596$	−0.378019	+	7.41454i	−0.0154843	+	0.303712i
$597$	−44.3656	−	2.46715i	−1.81576	−	0.100974i
$598$	−37.6242	+	0.832767i	−1.53857	+	0.0340544i
$599$	−18.7863	+	9.68502i	−0.767588	+	0.395719i	−0.797102	−	0.603845i	$-0.793634\pi$
$599$	−18.7863	+	9.68502i	−0.767588	+	0.395719i	0.0295136	+	0.999564i	$0.490604\pi$
$600$	15.3276	−	0.896738i	0.625747	−	0.0366092i
$601$	−2.16453	−	8.92233i	−0.0882932	−	0.363949i	0.910475	−	0.413563i	$-0.135716\pi$
$601$	−2.16453	−	8.92233i	−0.0882932	−	0.363949i	−0.998768	+	0.0496141i	$0.984201\pi$
$602$	−4.69134	+	10.9050i	−0.191205	+	0.444453i
$603$	−19.4361	+	15.0079i	−0.791500	+	0.611169i
$604$	−24.4478	+	23.1555i	−0.994766	+	0.942186i
$605$	13.2484	−	3.21403i	0.538625	−	0.130669i
$606$	−21.7933	−	18.3496i	−0.885294	−	0.745401i
$607$	−0.100853	−	0.195627i	−0.00409348	−	0.00794024i	0.886780	−	0.462192i	$-0.152937\pi$
$607$	−0.100853	−	0.195627i	−0.00409348	−	0.00794024i	−0.890873	+	0.454252i	$0.849907\pi$
$608$	−12.6166	−	0.405745i	−0.511669	−	0.0164551i
$609$	−2.27030	+	40.8256i	−0.0919971	+	1.65434i
$610$	10.9694	−	4.07051i	0.444137	−	0.164810i
$611$	15.9468	+	18.4036i	0.645138	+	0.744529i
$612$	6.73622	−	1.16433i	0.272295	−	0.0470652i
$613$	−13.7683	+	10.8275i	−0.556097	+	0.437320i	−0.856243	−	0.516574i	$-0.827207\pi$
$613$	−13.7683	+	10.8275i	−0.556097	+	0.437320i	0.300145	+	0.953893i	$0.402965\pi$
$614$	−35.2667	−	19.3336i	−1.42325	−	0.780241i
$615$	−6.53890	+	1.20642i	−0.263674	+	0.0486475i
$616$	−7.47694	−	45.8675i	−0.301255	−	1.84806i
$617$	24.0527	−	37.4267i	0.968324	−	1.50674i	0.109809	−	0.993953i	$-0.464976\pi$
$617$	24.0527	−	37.4267i	0.968324	−	1.50674i	0.858515	−	0.512789i	$-0.171388\pi$
$618$	−8.33831	+	29.9627i	−0.335416	+	1.20528i
$619$	10.3542	+	7.37320i	0.416171	+	0.296354i	0.768897	−	0.639373i	$-0.220806\pi$
$619$	10.3542	+	7.37320i	0.416171	+	0.296354i	−0.352726	+	0.935727i	$0.614745\pi$
$620$	−7.26629	−	25.0559i	−0.291821	−	1.00627i
$621$	−34.9893	−	19.1082i	−1.40407	−	0.766785i
$622$	23.9373	−	10.2033i	0.959797	−	0.409114i
$623$	−5.43001	−	4.27021i	−0.217549	−	0.171082i
$624$	−9.66142	−	22.0019i	−0.386766	−	0.880780i
$625$	−0.0701488	−	0.487896i	−0.00280595	−	0.0195158i
$626$	−0.621888	+	24.4115i	−0.0248557	+	0.975681i
$627$	16.1615	−	7.22594i	0.645428	−	0.288576i
$628$	−12.5035	+	0.553770i	−0.498942	+	0.0220978i
$629$	−6.27606	+	0.298965i	−0.250243	+	0.0119205i
$630$	−8.75361	−	18.8562i	−0.348752	−	0.751249i
$631$	0.373183	+	0.129160i	0.0148562	+	0.00514178i	0.334486	−	0.942401i	$-0.391437\pi$
$631$	0.373183	+	0.129160i	0.0148562	+	0.00514178i	−0.319630	+	0.947543i	$0.603559\pi$
$632$	−29.5549	−	5.12226i	−1.17563	−	0.203753i
$633$	−0.131895	−	0.337205i	−0.00524235	−	0.0134027i
$634$	41.7428	+	9.15361i	1.65782	+	0.363536i
$635$	7.42767	+	2.97359i	0.294758	+	0.118003i
$636$	−32.2017	+	12.4716i	−1.27688	+	0.494532i
$637$	4.79807	−	19.7779i	0.190107	−	0.783630i
$638$	−30.0933	−	30.1939i	−1.19140	−	1.19539i
$639$	44.0963	+	4.91956i	1.74442	+	0.194615i
$640$	−11.3132	−	10.5285i	−0.447193	−	0.416175i
$641$	−41.0894	−	23.7230i	−1.62293	−	0.937001i	−0.986130	−	0.165974i	$-0.946923\pi$
$641$	−41.0894	−	23.7230i	−1.62293	−	0.937001i	−0.636803	−	0.771027i	$-0.719744\pi$
$642$	−26.0251	+	21.0703i	−1.02713	+	0.831578i
$643$	9.47337	+	4.32634i	0.373593	+	0.170614i	0.593358	−	0.804939i	$-0.297802\pi$
$643$	9.47337	+	4.32634i	0.373593	+	0.170614i	−0.219765	+	0.975553i	$0.570529\pi$
$644$	−39.7103	−	38.1177i	−1.56481	−	1.50205i
$645$	−3.59226	−	4.21293i	−0.141445	−	0.165884i
$646$	0.590325	+	3.54674i	0.0232260	+	0.139545i
$647$	−31.6021	+	12.6516i	−1.24241	+	0.497385i	−0.897401	−	0.441216i	$-0.854547\pi$
$647$	−31.6021	+	12.6516i	−1.24241	+	0.497385i	−0.345006	+	0.938600i	$0.612123\pi$
$648$	2.74943	−	25.3069i	0.108008	−	0.994150i
$649$	−10.7872	−	15.1486i	−0.423436	−	0.594633i
$650$	−13.5047	+	7.34487i	−0.529697	+	0.288089i
$651$	46.9275	−	36.3039i	1.83923	−	1.42286i
$652$	7.20776	+	8.37455i	0.282278	+	0.327973i
$653$	−4.96425	+	9.62930i	−0.194266	+	0.376824i	−0.965770	−	0.259401i	$-0.916475\pi$
$653$	−4.96425	+	9.62930i	−0.194266	+	0.376824i	0.771503	+	0.636225i	$0.219505\pi$
$654$	34.7115	−	14.4707i	1.35733	−	0.565849i
$655$	2.52009	+	8.58265i	0.0984682	+	0.335352i
$656$	−9.11335	−	6.58176i	−0.355817	−	0.256975i
$657$	28.0332	+	15.0212i	1.09368	+	0.586032i
$658$	−2.60024	+	35.5224i	−0.101368	+	1.38481i
$659$	27.7561	+	2.65039i	1.08122	+	0.103244i	0.620429	−	0.784262i	$-0.286958\pi$
$659$	27.7561	+	2.65039i	1.08122	+	0.103244i	0.460795	+	0.887507i	$0.347564\pi$
$660$	20.7258	+	6.34073i	0.806752	+	0.246812i
$661$	2.71889	+	0.798338i	0.105753	+	0.0310518i	0.334181	−	0.942509i	$-0.391540\pi$
$661$	2.71889	+	0.798338i	0.105753	+	0.0310518i	−0.228428	+	0.973561i	$0.573359\pi$
$662$	4.75326	+	14.9555i	0.184741	+	0.581263i
$663$	−5.60681	+	3.92577i	−0.217750	+	0.152464i
$664$	−3.02305	+	1.44983i	−0.117317	+	0.0562645i
$665$	9.94611	−	4.54224i	0.385694	−	0.176140i
$666$	−5.37437	+	22.7713i	−0.208253	+	0.882368i
$667$	−49.9781	−	7.18576i	−1.93516	−	0.278234i
$668$	4.38423	−	6.77216i	0.169631	−	0.262023i
$669$	−0.103413	−	0.0157089i	−0.00399819	−	0.000607343i
$670$	1.04328	−	15.7780i	0.0403055	−	0.609556i
$671$	−27.7421			−1.07097
$672$	12.8177	−	32.7263i	0.494455	−	1.26244i
$673$	−0.699495	+	4.86509i	−0.0269635	+	0.187536i	−0.998852	−	0.0479070i	$-0.984745\pi$
$673$	−0.699495	+	4.86509i	−0.0269635	+	0.187536i	0.971888	+	0.235443i	$0.0756540\pi$
$674$	−1.65363	−	23.6763i	−0.0636956	−	0.911978i
$675$	−16.2805	−	0.388485i	−0.626639	−	0.0149528i
$676$	−1.46234	−	1.27570i	−0.0562438	−	0.0490653i
$677$	−7.29755	−	7.65345i	−0.280468	−	0.294146i	0.568399	−	0.822753i	$-0.307563\pi$
$677$	−7.29755	−	7.65345i	−0.280468	−	0.294146i	−0.848867	+	0.528607i	$0.822714\pi$
$678$	−8.21851	+	1.30082i	−0.315630	+	0.0499578i
$679$	2.58064	−	8.78884i	0.0990358	−	0.337285i
$680$	−2.30989	+	3.74725i	−0.0885802	+	0.143700i
$681$	4.76899	−	18.9974i	0.182748	−	0.727981i
$682$	−4.51584	+	61.6919i	−0.172921	+	2.36231i
$683$	16.4084	+	3.16245i	0.627848	+	0.121008i	0.493243	−	0.869891i	$-0.335811\pi$
$683$	16.4084	+	3.16245i	0.627848	+	0.121008i	0.134605	+	0.990899i	$0.457023\pi$
$684$	13.3012	+	1.52893i	0.508585	+	0.0584600i
$685$	14.5262	−	4.26526i	0.555016	−	0.162967i
$686$	−4.90964	+	2.98135i	−0.187451	+	0.113828i
$687$	20.4783	−	28.2790i	0.781294	−	1.07891i
$688$	0.951969	−	9.31178i	0.0362935	−	0.355008i
$689$	23.8596	−	25.0233i	0.908979	−	0.953310i
$690$	24.1382	−	8.73944i	0.918925	−	0.332705i
$691$	−25.7204	+	18.3154i	−0.978449	+	0.696751i	−0.953014	−	0.302926i	$-0.902037\pi$
$691$	−25.7204	+	18.3154i	−0.978449	+	0.696751i	−0.0254352	+	0.999676i	$0.508097\pi$
$692$	−10.7902	−	8.54396i	−0.410181	−	0.324792i
$693$	3.90451	+	49.1371i	0.148320	+	1.86656i
$694$	−4.17123	−	25.0612i	−0.158338	−	0.951311i
$695$	5.84204	−	6.74207i	0.221601	−	0.255741i
$696$	−7.94003	−	31.2472i	−0.300966	−	1.18442i
$697$	−1.33017	+	2.91266i	−0.0503837	+	0.110325i
$698$	6.19072	+	5.64664i	0.234322	+	0.213729i
$699$	−3.99993	+	5.00391i	−0.151291	+	0.189265i
$700$	−21.5529	−	6.40675i	−0.814622	−	0.242153i
$701$	−4.63899	−	24.0694i	−0.175212	−	0.909087i	−0.957993	−	0.286790i	$-0.907412\pi$
$701$	−4.63899	−	24.0694i	−0.175212	−	0.909087i	0.782781	−	0.622297i	$-0.213800\pi$
$702$	8.29448	+	24.0999i	0.313055	+	0.909593i
$703$	−11.9590	−	2.90122i	−0.451042	−	0.109422i
$704$	16.4638	+	32.7364i	0.620502	+	1.23380i
$705$	−14.3193	−	8.41978i	−0.539296	−	0.317107i
$706$	−2.97730	−	0.652881i	−0.112052	−	0.0245715i
$707$	20.8608	+	36.1320i	0.784553	+	1.35889i
$708$	−1.17874	−	14.0151i	−0.0442999	−	0.526719i
$709$	−2.15479	+	6.22586i	−0.0809248	+	0.233817i	−0.978204	−	0.207647i	$-0.933419\pi$
$709$	−2.15479	+	6.22586i	−0.0809248	+	0.233817i	0.897279	+	0.441464i	$0.145541\pi$
$710$	−21.1733	+	19.1833i	−0.794620	+	0.719938i
$711$	30.7950	+	7.99146i	1.15490	+	0.299703i
$712$	5.09379	+	1.92901i	0.190898	+	0.0722926i
$713$	39.6104	+	61.6350i	1.48342	+	2.30825i
$714$	−9.85611	−	1.75507i	−0.368856	−	0.0656817i
$715$	−21.4800	+	3.08836i	−0.803307	+	0.115498i
$716$	5.57650	−	28.4225i	0.208404	−	1.06220i
$717$	19.5131	−	18.3116i	0.728729	−	0.683861i
$718$	−41.7533	+	17.7974i	−1.55822	+	0.664191i
$719$	1.51126	−	31.7252i	0.0563604	−	1.18315i	−0.776664	−	0.629915i	$-0.783090\pi$
$719$	1.51126	−	31.7252i	0.0563604	−	1.18315i	0.833025	−	0.553236i	$-0.186607\pi$
$720$	11.0409	+	12.1157i	0.411469	+	0.451527i
$721$	26.4195	−	37.1011i	0.983915	−	1.38172i
$722$	2.38684	−	19.6839i	0.0888289	−	0.732558i
$723$	−24.7513	+	28.1097i	−0.920511	+	1.04541i
$724$	−24.8515	−	38.9551i	−0.923598	−	1.44775i
$725$	−19.4910	+	6.74591i	−0.723879	+	0.250537i
$726$	−19.4283	−	14.8377i	−0.721053	−	0.550678i
$727$	20.8893	+	26.5629i	0.774742	+	0.985164i	0.999941	+	0.0108514i	$0.00345417\pi$
$727$	20.8893	+	26.5629i	0.774742	+	0.985164i	−0.225200	+	0.974313i	$0.572303\pi$
$728$	2.33459	+	35.1128i	0.0865258	+	1.30137i
$729$	−5.11283	+	26.5115i	−0.189364	+	0.981907i
$730$	−19.2003	+	7.12483i	−0.710634	+	0.263702i
$731$	−2.65410	+	0.253436i	−0.0981654	+	0.00937365i
$732$	−18.0504	−	10.6950i	−0.667163	−	0.395298i
$733$	−6.39414	+	3.29641i	−0.236173	+	0.121756i	−0.572251	−	0.820078i	$-0.693930\pi$
$733$	−6.39414	+	3.29641i	−0.236173	+	0.121756i	0.336078	+	0.941834i	$0.390899\pi$
$734$	−21.3021	+	34.8174i	−0.786275	+	1.28513i
$735$	1.20970	+	13.8300i	0.0446206	+	0.510128i
$736$	38.8796	+	19.2894i	1.43312	+	0.711015i
$737$	−15.3343	+	34.2130i	−0.564845	+	1.26025i
$738$	9.05960	+	7.75197i	0.333488	+	0.285354i
$739$	20.2518	−	4.91303i	0.744974	−	0.180729i	0.154734	−	0.987956i	$-0.450548\pi$
$739$	20.2518	−	4.91303i	0.744974	−	0.180729i	0.590241	+	0.807227i	$0.299033\pi$
$740$	−8.69810	−	12.3015i	−0.319748	−	0.452212i
$741$	−12.7026	+	4.28359i	−0.466640	+	0.157361i
$742$	50.5588	−	1.11906i	1.85607	−	0.0410820i
$743$	35.5284	−	3.39255i	1.30341	−	0.124461i	0.579851	−	0.814723i	$-0.303111\pi$
$743$	35.5284	−	3.39255i	1.30341	−	0.124461i	0.723560	+	0.690262i	$0.242505\pi$
$744$	−26.7214	+	38.3991i	−0.979654	+	1.40778i
$745$	3.32057	+	3.83215i	0.121656	+	0.140399i
$746$	19.6610	−	23.7314i	0.719841	−	0.868867i
$747$	3.32198	−	1.26900i	0.121545	−	0.0464303i
$748$	8.22583	−	6.42452i	0.300766	−	0.234904i
$749$	46.3406	−	16.0386i	1.69325	−	0.586039i
$750$	18.5003	−	19.9617i	0.675536	−	0.728898i
$751$	19.3795	−	30.1550i	0.707166	−	1.10037i	−0.282815	−	0.959174i	$-0.591268\pi$
$751$	19.3795	−	30.1550i	0.707166	−	1.10037i	0.989981	−	0.141198i	$-0.0450954\pi$
$752$	−6.43859	−	27.3358i	−0.234791	−	0.996835i
$753$	−34.4881	−	33.4120i	−1.25682	−	1.21760i
$754$	20.5108	+	24.9261i	0.746959	+	0.907754i
$755$	−1.09431	+	22.9724i	−0.0398260	+	0.836051i
$756$	−16.4026	+	33.4764i	−0.596558	+	1.21753i
$757$	−23.0276	−	18.1091i	−0.836953	−	0.658187i	0.104800	−	0.994493i	$-0.466580\pi$
$757$	−23.0276	−	18.1091i	−0.836953	−	0.658187i	−0.941753	+	0.336306i	$0.890822\pi$
$758$	−5.99513	−	27.7824i	−0.217753	−	1.00910i
$759$	−60.8670	−	0.484053i	−2.20933	−	0.0175700i
$760$	−6.40844	+	5.76729i	−0.232459	+	0.209202i
$761$	16.1770	+	25.1719i	0.586415	+	0.912480i	0.999998	+	0.00201361i	$0.000640952\pi$
$761$	16.1770	+	25.1719i	0.586415	+	0.912480i	−0.413583	+	0.910467i	$0.635723\pi$
$762$	−4.23679	−	13.7072i	−0.153483	−	0.496559i
$763$	−55.0114	+	2.62052i	−1.99155	+	0.0948690i
$764$	−2.85787	+	0.978442i	−0.103394	+	0.0353988i
$765$	2.76844	−	3.75971i	0.100093	−	0.135932i
$766$	−5.62612	−	7.54184i	−0.203280	−	0.272498i
$767$	7.04099	+	12.1953i	0.254235	+	0.440348i
$768$	−1.90819	+	27.6470i	−0.0688558	+	0.997627i
$769$	−17.3041	−	6.92753i	−0.624003	−	0.249813i	0.0380433	−	0.999276i	$-0.487888\pi$
$769$	−17.3041	−	6.92753i	−0.624003	−	0.249813i	−0.662046	+	0.749463i	$0.730312\pi$
$770$	−25.3779	−	19.0639i	−0.914557	−	0.687015i
$771$	−5.03218	+	12.2857i	−0.181229	+	0.442459i
$772$	−14.9901	−	37.8090i	−0.539507	−	1.36078i
$773$	6.90653	+	35.8345i	0.248411	+	1.28888i	0.865072	+	0.501648i	$0.167273\pi$
$773$	6.90653	+	35.8345i	0.248411	+	1.28888i	−0.616661	+	0.787229i	$0.711515\pi$
$774$	−1.81818	+	9.76021i	−0.0653533	+	0.350823i
$775$	25.9186	+	14.9641i	0.931023	+	0.537526i
$776$	0.135707	+	7.22116i	0.00487159	+	0.259225i
$777$	18.7530	−	28.6762i	0.672759	−	1.02875i
$778$	8.16718	−	21.7859i	0.292808	−	0.781062i
$779$	−4.10683	+	4.73953i	−0.147142	+	0.169811i
$780$	−15.1666	−	6.27142i	−0.543052	−	0.224553i
$781$	62.8913	−	25.1779i	2.25043	−	0.900936i
$782$	3.21956	−	11.9358i	0.115131	−	0.426824i
$783$	5.66876	+	33.7227i	0.202585	+	1.20515i
$784$	−15.4884	+	17.6351i	−0.553155	+	0.629826i
$785$	−5.89889	+	6.18658i	−0.210541	+	0.220809i
$786$	9.11805	−	13.1965i	0.325230	−	0.470705i
$787$	6.12385	−	11.8786i	0.218292	−	0.423427i	−0.754107	−	0.656751i	$-0.771930\pi$
$787$	6.12385	−	11.8786i	0.218292	−	0.423427i	0.972399	+	0.233324i	$0.0749604\pi$
$788$	−2.44235	−	17.3992i	−0.0870050	−	0.619820i
$789$	3.55243	+	26.1842i	0.126470	+	0.932184i
$790$	−16.9852	+	11.4546i	−0.604306	+	0.407536i
$791$	11.9652	+	2.30611i	0.425435	+	0.0819959i
$792$	−14.5491	−	36.0401i	−0.516980	−	1.28063i
$793$	20.9118	+	1.99684i	0.742600	+	0.0709097i
$794$	−0.569986	−	2.14151i	−0.0202280	−	0.0759994i
$795$	−9.96804	+	21.3755i	−0.353530	+	0.758110i
$796$	−51.0592	−	5.04768i	−1.80975	−	0.178910i
$797$	25.7626	+	27.0190i	0.912557	+	0.957062i	0.999232	−	0.0391742i	$-0.0124727\pi$
$797$	25.7626	+	27.0190i	0.912557	+	0.957062i	−0.0866752	+	0.996237i	$0.527624\pi$
$798$	−17.5533	−	8.73660i	−0.621379	−	0.309272i
$799$	−7.27645	+	3.32305i	−0.257422	+	0.117561i
$800$	17.7269	−	0.273925i	0.626742	−	0.00968471i
$801$	−5.21631	−	2.48322i	−0.184309	−	0.0877402i
$802$	−1.22117	+	7.18861i	−0.0431210	+	0.253838i
$803$	48.5584			1.71359
$804$	−23.1669	+	16.3492i	−0.817033	+	0.576591i
$805$	−37.5948			−1.32504
$806$	7.84451	−	46.1780i	0.276311	−	1.62655i
$807$	12.1243	−	40.1090i	0.426797	−	1.41190i
$808$	−24.2310	−	22.2501i	−0.852443	−	0.782757i
$809$	30.9016	−	14.1123i	1.08644	−	0.496161i	0.210016	−	0.977698i	$-0.432648\pi$
$809$	30.9016	−	14.1123i	1.08644	−	0.496161i	0.876426	+	0.481537i	$0.159921\pi$
$810$	−10.6146	−	13.7698i	−0.372960	−	0.483822i
$811$	−9.59282	−	10.0607i	−0.336849	−	0.353277i	0.533423	−	0.845849i	$-0.320906\pi$
$811$	−9.59282	−	10.0607i	−0.336849	−	0.353277i	−0.870272	+	0.492571i	$0.836057\pi$
$812$	−4.64493	+	46.9852i	−0.163005	+	1.64886i
$813$	8.00995	+	3.73529i	0.280921	+	0.131002i
$814$	9.18801	+	34.5206i	0.322040	+	1.20995i
$815$	7.51235	+	0.717342i	0.263146	+	0.0251274i
$816$	7.82890	−	1.00895i	0.274066	−	0.0353202i
$817$	−5.12745	−	0.988234i	−0.179387	−	0.0345739i
$818$	−38.8976	+	26.2321i	−1.36002	+	0.917183i
$819$	0.593627	−	37.3203i	0.0207430	−	1.30408i
$820$	−7.60336	+	1.06729i	−0.265521	+	0.0372715i
$821$	−16.5082	+	32.0214i	−0.576139	+	1.11755i	0.403159	+	0.915130i	$0.367912\pi$
$821$	−16.5082	+	32.0214i	−0.576139	+	1.11755i	−0.979298	+	0.202424i	$0.935118\pi$
$822$	−22.3352	−	15.4323i	−0.779029	−	0.538264i
$823$	2.55036	−	2.67474i	0.0889000	−	0.0932356i	−0.677781	−	0.735264i	$-0.737058\pi$
$823$	2.55036	−	2.67474i	0.0889000	−	0.0932356i	0.766681	+	0.642028i	$0.221907\pi$
$824$	−11.1062	+	34.1523i	−0.386901	+	1.18975i
$825$	−22.1901	+	11.2174i	−0.772561	+	0.390538i
$826$	−5.36408	+	19.8862i	−0.186640	+	0.691928i
$827$	35.1486	−	14.0714i	1.22224	−	0.489310i	0.331338	−	0.943512i	$-0.392500\pi$
$827$	35.1486	−	14.0714i	1.22224	−	0.489310i	0.890899	+	0.454202i	$0.150076\pi$
$828$	−39.4166	−	23.7801i	−1.36982	−	0.826415i
$829$	12.2345	−	14.1193i	0.424921	−	0.490385i	−0.502409	−	0.864630i	$-0.667553\pi$
$829$	12.2345	−	14.1193i	0.424921	−	0.490385i	0.927330	+	0.374245i	$0.122098\pi$
$830$	−0.803817	+	2.14418i	−0.0279009	+	0.0744254i
$831$	20.1331	+	13.1662i	0.698409	+	0.456729i
$832$	−10.0540	−	25.8615i	−0.348559	−	0.896588i
$833$	5.78974	+	3.34271i	0.200603	+	0.115818i
$834$	−15.9883	−	0.534562i	−0.553630	−	0.0185104i
$835$	−1.04278	−	5.41043i	−0.0360867	−	0.187236i
$836$	19.0030	−	7.53413i	0.657233	−	0.260573i
$837$	31.5944	−	38.2607i	1.09206	−	1.32248i
$838$	−17.2851	−	12.9846i	−0.597105	−	0.448545i
$839$	13.4614	+	5.38912i	0.464738	+	0.186053i	0.592201	−	0.805790i	$-0.298259\pi$
$839$	13.4614	+	5.38912i	0.464738	+	0.186053i	−0.127463	+	0.991843i	$0.540683\pi$
$840$	−9.16279	−	22.1875i	−0.316146	−	0.765542i
$841$	7.15477	+	12.3924i	0.246716	+	0.427325i
$842$	−3.02428	−	4.05405i	−0.104223	−	0.139712i
$843$	−10.3915	+	19.7690i	−0.357901	+	0.680881i
$844$	−0.135426	−	0.395555i	−0.00466154	−	0.0136156i
$845$	−1.32390	+	0.0630651i	−0.0455435	+	0.00216951i
$846$	4.42266	+	29.4573i	0.152054	+	1.01276i
$847$	19.3551	+	30.1172i	0.665050	+	1.03484i
$848$	−37.7679	+	12.7898i	−1.29695	+	0.439202i
$849$	−0.116531	+	14.6531i	−0.00399934	+	0.502894i
$850$	−1.06519	−	4.93628i	−0.0365358	−	0.169313i
$851$	33.2586	+	26.1549i	1.14009	+	0.896578i
$852$	50.6268	+	7.86351i	1.73445	+	0.269399i
$853$	1.53269	−	32.1751i	0.0524782	−	1.10165i	−0.807023	−	0.590520i	$-0.798923\pi$
$853$	1.53269	−	32.1751i	0.0524782	−	1.10165i	0.859501	−	0.511134i	$-0.170774\pi$
$854$	19.5231	+	23.7258i	0.668068	+	0.811880i
$855$	7.27702	−	5.53769i	0.248869	−	0.189385i
$856$	−31.0690	+	23.0160i	−1.06192	+	0.786670i
$857$	−4.39530	+	6.83923i	−0.150141	+	0.233624i	−0.908175	−	0.418592i	$-0.862524\pi$
$857$	−4.39530	+	6.83923i	−0.150141	+	0.233624i	0.758034	+	0.652215i	$0.226160\pi$
$858$	28.5414	+	26.4518i	0.974386	+	0.903051i
$859$	−23.6389	+	8.18150i	−0.806549	+	0.279149i	−0.699066	−	0.715058i	$-0.746400\pi$
$859$	−23.6389	+	8.18150i	−0.806549	+	0.279149i	−0.107483	+	0.994207i	$0.534279\pi$
$860$	−3.93510	−	5.03843i	−0.134186	−	0.171809i
$861$	−8.61016	−	15.1909i	−0.293433	−	0.517706i
$862$	16.1569	−	19.5018i	0.550305	−	0.664233i
$863$	9.67581	+	11.1665i	0.329368	+	0.380111i	0.896146	−	0.443760i	$-0.146356\pi$
$863$	9.67581	+	11.1665i	0.329368	+	0.380111i	−0.566778	+	0.823871i	$0.691810\pi$
$864$	4.42761	−	29.0585i	0.150630	−	0.988590i
$865$	−9.35763	+	0.893545i	−0.318169	+	0.0303815i
$866$	16.1870	−	0.358281i	0.550058	−	0.0121749i
$867$	8.69043	+	25.7706i	0.295142	+	0.875215i
$868$	55.9386	−	39.5528i	1.89868	−	1.34251i
$869$	47.2060	−	11.4520i	1.60135	−	0.388484i
$870$	−18.6911	−	11.6410i	−0.633689	−	0.394666i
$871$	14.0215	−	24.6858i	0.475100	−	0.836446i
$872$	40.7624	−	14.9714i	1.38039	−	0.506997i
$873$	0.486155	−	7.64511i	0.0164539	−	0.258748i
$874$	12.6362	−	20.6534i	0.427427	−	0.698611i
$875$	−35.4264	+	18.2636i	−1.19763	+	0.617422i
$876$	31.5946	+	18.7200i	1.06748	+	0.632490i
$877$	9.45489	−	0.902832i	0.319269	−	0.0304865i	0.0658085	−	0.997832i	$-0.479037\pi$
$877$	9.45489	−	0.902832i	0.319269	−	0.0304865i	0.253460	+	0.967346i	$0.418431\pi$
$878$	15.3994	−	5.71440i	0.519704	−	0.192852i
$879$	−27.0084	−	42.7699i	−0.910970	−	1.44259i
$880$	23.5954	+	8.34333i	0.795401	+	0.281254i
$881$	8.69342	+	11.0546i	0.292889	+	0.372438i	0.910121	−	0.414343i	$-0.135989\pi$
$881$	8.69342	+	11.0546i	0.292889	+	0.372438i	−0.617232	+	0.786781i	$0.711746\pi$
$882$	17.9099	−	17.2912i	0.603057	−	0.582224i
$883$	−13.6360	+	4.71946i	−0.458887	+	0.158822i	−0.546725	−	0.837312i	$-0.684126\pi$
$883$	−13.6360	+	4.71946i	−0.458887	+	0.158822i	0.0878375	+	0.996135i	$0.472004\pi$
$884$	−6.66301	+	4.25068i	−0.224101	+	0.142966i
$885$	−7.20947	−	6.34812i	−0.242344	−	0.213390i
$886$	−0.221579	+	1.82733i	−0.00744409	+	0.0613902i
$887$	−23.3486	+	32.7885i	−0.783969	+	1.10093i	0.208450	+	0.978033i	$0.433158\pi$
$887$	−23.3486	+	32.7885i	−0.783969	+	1.10093i	−0.992419	+	0.122898i	$0.960781\pi$
$888$	−7.33001	+	26.0030i	−0.245979	+	0.872604i
$889$	−0.999723	+	20.9868i	−0.0335296	+	0.703874i
$890$	3.42221	−	1.45872i	0.114713	−	0.0488964i
$891$	12.2371	+	39.3655i	0.409959	+	1.31879i
$892$	−0.118521	−	0.0232539i	−0.00396839	−	0.000778598i
$893$	−15.5076	+	2.22965i	−0.518942	+	0.0746125i
$894$	1.59406	−	8.95190i	0.0533132	−	0.299396i
$895$	−10.6952	−	16.6421i	−0.357502	−	0.556284i
$896$	16.4109	−	37.1181i	0.548250	−	1.24003i
$897$	45.8463	+	4.74599i	1.53076	+	0.158464i
$898$	12.8629	−	11.6540i	0.429239	−	0.388897i
$899$	20.5542	−	59.3873i	0.685519	−	1.98068i
$900$	−18.7625	−	1.25604i	−0.625417	−	0.0418680i
$901$	5.67890	+	9.83615i	0.189192	+	0.327690i
$902$	17.7823	+	3.89940i	0.592085	+	0.129836i
$903$	7.36953	−	12.5332i	0.245243	−	0.417078i
$904$	−9.54570	+	1.09286i	−0.317485	+	0.0363479i
$905$	−30.6695	−	7.44034i	−1.01949	−	0.247325i
$906$	33.2513	−	24.3959i	1.10470	−	0.810500i
$907$	−5.21024	−	27.0333i	−0.173003	−	0.897626i	−0.959858	−	0.280487i	$-0.909504\pi$
$907$	−5.21024	−	27.0333i	−0.173003	−	0.897626i	0.786854	−	0.617139i	$-0.211708\pi$
$908$	6.44435	−	21.6794i	0.213863	−	0.719455i
$909$	23.6739	+	25.6326i	0.785214	+	0.850181i
$910$	17.7575	+	16.1969i	0.588656	+	0.536922i
$911$	11.9907	−	26.2560i	0.397270	−	0.869900i	−0.600270	−	0.799798i	$-0.704940\pi$
$911$	11.9907	−	26.2560i	0.397270	−	0.869900i	0.997540	−	0.0701027i	$-0.0223327\pi$
$912$	15.2689	+	2.42385i	0.505603	+	0.0802618i
$913$	3.55555	−	4.10333i	0.117672	−	0.135800i
$914$	−8.92608	−	53.6289i	−0.295249	−	1.77389i
$915$	−13.9523	+	3.26754i	−0.461250	+	0.108021i
$916$	25.0277	−	31.6075i	0.826937	−	1.04434i
$917$	−19.1345	+	13.6256i	−0.631876	+	0.449957i
$918$	−8.36367	+	0.383934i	−0.276042	+	0.0126717i
$919$	−14.1968	+	14.8892i	−0.468309	+	0.491148i	−0.914951	−	0.403564i	$-0.867771\pi$
$919$	−14.1968	+	14.8892i	−0.468309	+	0.491148i	0.446643	+	0.894712i	$0.352620\pi$
$920$	28.2803	−	8.88433i	0.932373	−	0.292908i
$921$	39.8954	+	28.8903i	1.31460	+	0.951967i
$922$	11.4913	−	6.97801i	0.378445	−	0.229809i
$923$	−49.2194	+	14.4521i	−1.62007	+	0.475697i
$924$	2.06610	+	56.8800i	0.0679698	+	1.87121i
$925$	16.9712	+	3.27093i	0.558009	+	0.107548i
$926$	0.187059	−	2.55546i	0.00614716	−	0.0839777i
$927$	14.7177	−	35.1330i	0.483393	−	1.15392i
$928$	−7.60935	−	36.4418i	−0.249789	−	1.19626i
$929$	−3.76089	+	12.8084i	−0.123391	+	0.420230i	−0.997900	−	0.0647793i	$-0.979366\pi$
$929$	−3.76089	+	12.8084i	−0.123391	+	0.420230i	0.874509	+	0.485009i	$0.161184\pi$
$930$	4.99509	+	31.5586i	0.163795	+	1.03485i
$931$	9.03567	+	9.47634i	0.296132	+	0.310575i
$932$	−4.86275	+	5.57419i	−0.159285	+	0.182589i
$933$	−30.6488	+	8.73516i	−1.00340	+	0.285976i
$934$	2.77495	+	39.7310i	0.0907990	+	1.30004i
$935$	1.01451	−	7.05609i	0.0331781	−	0.230759i
$936$	8.37291	+	28.2141i	0.273677	+	0.922206i
$937$	−13.8096			−0.451139			−0.225569	−	0.974227i	$-0.572424\pi$
$937$	−13.8096			−0.451139			−0.225569	+	0.974227i	$0.572424\pi$
$938$	40.0512	−	10.9627i	1.30772	−	0.357944i
$939$	4.49157	−	29.5684i	0.146577	−	0.964928i
$940$	−16.1014	−	10.4239i	−0.525170	−	0.339990i
$941$	−20.5599	−	2.95606i	−0.670233	−	0.0963649i	−0.201206	−	0.979549i	$-0.564486\pi$
$941$	−20.5599	−	2.95606i	−0.670233	−	0.0963649i	−0.469027	+	0.883184i	$0.655395\pi$
$942$	15.2783	+	1.24059i	0.497793	+	0.0404207i
$943$	19.6139	−	8.95735i	0.638715	−	0.291692i
$944$	−0.664385	−	16.2268i	−0.0216239	−	0.528136i
$945$	7.75120	+	24.2527i	0.252147	+	0.788939i
$946$	4.59137	+	14.4462i	0.149278	+	0.469686i
$947$	−7.74470	−	2.27405i	−0.251669	−	0.0738967i	0.153465	−	0.988154i	$-0.450957\pi$
$947$	−7.74470	−	2.27405i	−0.251669	−	0.0738967i	−0.405134	+	0.914257i	$0.632775\pi$
$948$	35.1296	+	10.7473i	1.14096	+	0.349057i
$949$	−36.6030	−	3.49517i	−1.18818	−	0.113458i
$950$	0.722049	−	9.86406i	0.0234263	−	0.320033i
$951$	−49.3227	−	17.5112i	−1.59940	−	0.567839i
$952$	−11.2833	−	2.51378i	−0.365692	−	0.0814721i
$953$	−1.10830	−	3.77454i	−0.0359015	−	0.122269i	0.939593	−	0.342295i	$-0.111204\pi$
$953$	−1.10830	−	3.77454i	−0.0359015	−	0.122269i	−0.975494	+	0.220025i	$0.929386\pi$
$954$	41.0384	−	10.2267i	1.32867	−	0.331103i
$955$	−0.945380	+	1.83378i	−0.0305918	+	0.0593398i
$956$	23.4196	−	20.1567i	0.757444	−	0.651913i
$957$	31.9469	+	41.2954i	1.03270	+	1.33489i
$958$	−20.3820	+	11.0853i	−0.658512	+	0.358148i
$959$	23.0614	+	32.3851i	0.744690	+	1.04577i
$960$	12.1359	+	14.5250i	0.391685	+	0.468792i
$961$	−55.8770	+	22.3698i	−1.80248	+	0.721605i
$962$	−4.44112	−	26.6827i	−0.143188	−	0.860286i
$963$	34.8488	−	21.6206i	1.12299	−	0.696716i
$964$	−29.9488	+	31.2001i	−0.964585	+	1.00489i
$965$	−25.2685	−	11.5397i	−0.813421	−	0.371477i
$966$	42.4204	+	52.3958i	1.36485	+	1.68581i
$967$	36.6900	+	21.1830i	1.17987	+	0.681199i	0.955985	−	0.293416i	$-0.0947922\pi$
$967$	36.6900	+	21.1830i	1.17987	+	0.681199i	0.223887	+	0.974615i	$0.428126\pi$
$968$	−21.6769	−	18.0813i	−0.696722	−	0.581156i
$969$	−0.174546	−	4.40015i	−0.00560722	−	0.141353i
$970$	3.48224	+	3.49388i	0.111808	+	0.112182i
$971$	−4.56686	+	18.8248i	−0.146557	+	0.604118i	0.850398	+	0.526140i	$0.176361\pi$
$971$	−4.56686	+	18.8248i	−0.146557	+	0.604118i	−0.996955	+	0.0779774i	$0.975154\pi$
$972$	−7.21388	+	30.3308i	−0.231385	+	0.972862i
$973$	21.7491	+	8.70701i	0.697243	+	0.279134i
$974$	15.1530	+	3.32284i	0.485533	+	0.106471i
$975$	17.5342	−	6.85836i	0.561544	−	0.219643i
$976$	−20.2929	−	13.2338i	−0.649560	−	0.423603i
$977$	26.9067	+	9.31251i	0.860823	+	0.297934i	0.721585	−	0.692325i	$-0.243414\pi$
$977$	26.9067	+	9.31251i	0.860823	+	0.297934i	0.139237	+	0.990259i	$0.455535\pi$
$978$	−7.47686	−	11.2794i	−0.239084	−	0.360674i
$979$	−8.81068	+	0.419704i	−0.281590	+	0.0134138i
$980$	0.709285	+	16.0148i	0.0226573	+	0.511574i
$981$	−44.3941	+	12.2718i	−1.41739	+	0.391809i
$982$	−0.885208	+	34.7478i	−0.0282481	+	1.10885i
$983$	−4.18763	−	29.1256i	−0.133565	−	0.928962i	−0.940855	−	0.338808i	$-0.889976\pi$
$983$	−4.18763	−	29.1256i	−0.133565	−	0.928962i	0.807291	−	0.590154i	$-0.200933\pi$
$984$	10.0668	+	9.39249i	0.320918	+	0.299422i
$985$	−9.43264	−	7.41791i	−0.300549	−	0.236354i
$986$	−9.75466	+	4.15793i	−0.310652	+	0.132415i
$987$	8.59595	−	42.7670i	0.273612	−	1.36129i
$988$	−14.8667	+	4.31137i	−0.472971	+	0.137163i
$989$	14.6249	+	10.4143i	0.465045	+	0.331157i
$990$	−24.2146	−	10.8767i	−0.769589	−	0.345686i
$991$	22.3568	−	34.7879i	0.710189	−	1.10507i	−0.279264	−	0.960214i	$-0.590090\pi$
$991$	22.3568	−	34.7879i	0.710189	−	1.10507i	0.989452	−	0.144860i	$-0.0462733\pi$
$992$	−32.7321	+	42.9725i	−1.03925	+	1.36438i
$993$	−3.48713	−	18.9006i	−0.110661	−	0.599792i
$994$	−65.7918	−	36.0678i	−2.08679	−	1.14400i
$995$	−27.5457	+	21.6622i	−0.873257	+	0.686737i
$996$	3.89532	−	1.29912i	0.123428	−	0.0411642i
$997$	27.5458	+	31.7896i	0.872385	+	1.00679i	0.999888	+	0.0149478i	$0.00475821\pi$
$997$	27.5458	+	31.7896i	0.872385	+	1.00679i	−0.127503	+	0.991838i	$0.540696\pi$
$998$	−12.6995	+	4.71253i	−0.401996	+	0.149172i
$999$	10.0155	−	26.8479i	0.316877	−	0.849430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.23.9	✓	2640
3.2	odd	2	inner	804.2.bd.a.23.124	yes	2640
4.3	odd	2	inner	804.2.bd.a.23.27	yes	2640
12.11	even	2	inner	804.2.bd.a.23.106	yes	2640
67.35	even	33	inner	804.2.bd.a.35.106	yes	2640
201.35	odd	66	inner	804.2.bd.a.35.27	yes	2640
268.35	odd	66	inner	804.2.bd.a.35.124	yes	2640
804.35	even	66	inner	804.2.bd.a.35.9	yes	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.9	✓	2640	1.1	even	1	trivial
804.2.bd.a.23.27	yes	2640	4.3	odd	2	inner
804.2.bd.a.23.106	yes	2640	12.11	even	2	inner
804.2.bd.a.23.124	yes	2640	3.2	odd	2	inner
804.2.bd.a.35.9	yes	2640	804.35	even	66	inner
804.2.bd.a.35.27	yes	2640	201.35	odd	66	inner
804.2.bd.a.35.106	yes	2640	67.35	even	33	inner
804.2.bd.a.35.124	yes	2640	268.35	odd	66	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39424 - 0.236847i) q^{2} +(1.65796 + 0.501176i) q^{3} +(1.88781 + 0.660444i) q^{4} +(1.24254 - 0.567451i) q^{5} +(-2.19289 - 1.09144i) q^{6} +(2.47543 + 2.59615i) q^{7} +(-2.47563 - 1.36794i) q^{8} +(2.49765 + 1.66186i) q^{9} +O(q^{10})\)	\(q+(-1.39424 - 0.236847i) q^{2} +(1.65796 + 0.501176i) q^{3} +(1.88781 + 0.660444i) q^{4} +(1.24254 - 0.567451i) q^{5} +(-2.19289 - 1.09144i) q^{6} +(2.47543 + 2.59615i) q^{7} +(-2.47563 - 1.36794i) q^{8} +(2.49765 + 1.66186i) q^{9} +(-1.86680 + 0.496869i) q^{10} +(4.55967 + 0.435395i) q^{11} +(2.79890 + 2.04111i) q^{12} +(-3.40571 - 0.656397i) q^{13} +(-2.83645 - 4.20596i) q^{14} +(2.34448 - 0.318076i) q^{15} +(3.12763 + 2.49358i) q^{16} +(0.522081 - 1.01270i) q^{17} +(-3.08871 - 2.90859i) q^{18} +(1.53989 - 1.61499i) q^{19} +(2.72045 - 0.250607i) q^{20} +(2.80302 + 5.54493i) q^{21} +(-6.25414 - 1.68699i) q^{22} +(-7.12280 + 2.85154i) q^{23} +(-3.41891 - 3.50871i) q^{24} +(-2.05239 + 2.36858i) q^{25} +(4.59291 + 1.72181i) q^{26} +(3.30811 + 4.00705i) q^{27} +(2.95851 + 6.53591i) q^{28} +(5.69931 + 3.29050i) q^{29} +(-3.34410 - 0.111809i) q^{30} +(-1.80721 - 9.37669i) q^{31} +(-3.77006 - 4.21742i) q^{32} +(7.34152 + 3.00706i) q^{33} +(-0.967759 + 1.28829i) q^{34} +(4.54901 + 1.82115i) q^{35} +(3.61751 + 4.78682i) q^{36} +(-2.75735 - 4.77587i) q^{37} +(-2.52948 + 1.88696i) q^{38} +(-5.31755 - 2.79514i) q^{39} +(-3.85232 - 0.294926i) q^{40} +(-2.80721 + 0.133724i) q^{41} +(-2.59478 - 8.39485i) q^{42} +(-1.26514 - 1.96860i) q^{43} +(8.32021 + 3.83335i) q^{44} +(4.04646 + 0.647638i) q^{45} +(10.6063 - 2.28871i) q^{46} +(-5.51885 - 4.34007i) q^{47} +(3.93575 + 5.70174i) q^{48} +(-0.279199 + 5.86110i) q^{49} +(3.42251 - 2.81627i) q^{50} +(1.37313 - 1.41735i) q^{51} +(-5.99581 - 3.48843i) q^{52} +(-5.38947 + 8.38618i) q^{53} +(-3.66324 - 6.37030i) q^{54} +(5.91265 - 2.04639i) q^{55} +(-2.57686 - 9.81335i) q^{56} +(3.36246 - 1.90583i) q^{57} +(-7.16686 - 5.93761i) q^{58} +(-2.65879 - 3.06841i) q^{59} +(4.63599 + 0.947929i) q^{60} +(-6.02926 + 0.575724i) q^{61} +(0.298837 + 13.5014i) q^{62} +(1.86831 + 10.5981i) q^{63} +(4.25749 + 6.77302i) q^{64} +(-4.60421 + 1.11697i) q^{65} +(-9.52363 - 5.93138i) q^{66} +(-2.62262 + 7.75383i) q^{67} +(1.65442 - 1.56697i) q^{68} +(-13.2384 + 1.15796i) q^{69} +(-5.91108 - 3.61654i) q^{70} +(13.1458 - 6.77715i) q^{71} +(-3.90993 - 7.53077i) q^{72} +(10.5533 - 1.00772i) q^{73} +(2.71325 + 7.31177i) q^{74} +(-4.58985 + 2.89840i) q^{75} +(3.97362 - 2.03178i) q^{76} +(10.1568 + 12.9154i) q^{77} +(6.75192 + 5.15654i) q^{78} +(10.0217 - 3.46856i) q^{79} +(5.30120 + 1.32361i) q^{80} +(3.47647 + 8.30146i) q^{81} +(3.94559 + 0.478437i) q^{82} +(0.687583 - 0.965575i) q^{83} +(1.62945 + 12.3190i) q^{84} +(0.0740534 - 1.55457i) q^{85} +(1.29765 + 3.04435i) q^{86} +(7.80010 + 8.31186i) q^{87} +(-10.6925 - 7.31522i) q^{88} +(-1.90614 + 0.274061i) q^{89} +(-5.48834 - 1.86135i) q^{90} +(-6.72648 - 10.4666i) q^{91} +(-15.3298 + 0.678945i) q^{92} +(1.70309 - 16.4519i) q^{93} +(6.66666 + 7.35822i) q^{94} +(0.996953 - 2.88051i) q^{95} +(-4.13694 - 8.88177i) q^{96} +(-1.27676 - 2.21141i) q^{97} +(1.77746 - 8.10565i) q^{98} +(10.6649 + 8.66497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more