LMFDB - Embedded newform 804.2.bd.a.35.9

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			35.9
Character	$\chi$	$=$	804.35
Dual form			804.2.bd.a.23.9

$q$-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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{19}{33}\right)$	$-1$

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	0.673404	−	0.739275i	$-0.264832\pi$
$5$	1.24254	+	0.567451i	0.555682	+	0.253772i	−0.117721	+	0.993047i	$0.537559\pi$
$6$	−2.19289	+	1.09144i	−0.895243	+	0.445579i
$7$	2.47543	−	2.59615i	0.935623	−	0.981253i	−0.0642376	−	0.997935i	$-0.520462\pi$
$7$	2.47543	−	2.59615i	0.935623	−	0.981253i	0.999861	+	0.0166812i	$0.00531003\pi$
$8$	−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	0.618640	−	0.785674i	$-0.287684\pi$
$11$	4.55967	−	0.435395i	1.37479	−	0.131277i	0.756151	+	0.654398i	$0.227078\pi$
$12$	2.79890	−	2.04111i	0.807974	−	0.589218i
$13$	−3.40571	+	0.656397i	−0.944574	+	0.182052i	−0.638210	−	0.769863i	$-0.720325\pi$
$13$	−3.40571	+	0.656397i	−0.944574	+	0.182052i	−0.306364	+	0.951914i	$0.599113\pi$
$14$	−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	0.943622	−	0.331024i	$-0.107394\pi$
$17$	0.522081	+	1.01270i	0.126623	+	0.245615i	−0.816999	+	0.576639i	$0.804364\pi$
$18$	−3.08871	+	2.90859i	−0.728016	+	0.685560i
$19$	1.53989	+	1.61499i	0.353275	+	0.370504i	0.876261	−	0.481837i	$-0.160030\pi$
$19$	1.53989	+	1.61499i	0.353275	+	0.370504i	−0.522986	+	0.852341i	$0.675182\pi$
$20$	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	−0.519558	−	0.854435i	$-0.673903\pi$
$23$	−7.12280	−	2.85154i	−1.48521	−	0.594587i	−0.965649	+	0.259848i	$0.916327\pi$
$24$	−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	0.133364	−	0.991067i	$-0.457422\pi$
$29$	5.69931	−	3.29050i	1.05834	−	0.611030i	0.924971	+	0.380037i	$0.124089\pi$
$30$	−3.34410	+	0.111809i	−0.610546	+	0.0204134i
$31$	−1.80721	+	9.37669i	−0.324584	+	1.68410i	0.342814	+	0.939403i	$0.388620\pi$
$31$	−1.80721	+	9.37669i	−0.324584	+	1.68410i	−0.667399	+	0.744701i	$0.732592\pi$
$32$	−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	−0.998589	−	0.0531037i	$-0.983089\pi$
$37$	−2.75735	+	4.77587i	−0.453305	+	0.785148i	0.545284	+	0.838252i	$0.316422\pi$
$38$	−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	−0.172784	−	0.984960i	$-0.555276\pi$
$41$	−2.80721	−	0.133724i	−0.438412	−	0.0208841i	−0.265628	+	0.964076i	$0.585579\pi$
$42$	−2.59478	+	8.39485i	−0.400384	+	1.29535i
$43$	−1.26514	+	1.96860i	−0.192932	+	0.300209i	−0.924220	−	0.381861i	$-0.875283\pi$
$43$	−1.26514	+	1.96860i	−0.192932	+	0.300209i	0.731287	+	0.682069i	$0.238920\pi$
$44$	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	−0.933472	−	0.358649i	$-0.883237\pi$
$47$	−5.51885	+	4.34007i	−0.805007	+	0.633065i	0.128465	+	0.991714i	$0.458995\pi$
$48$	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	−0.983316	−	0.181908i	$-0.941773\pi$
$53$	−5.38947	−	8.38618i	−0.740301	−	1.15193i	0.243015	−	0.970023i	$-0.421864\pi$
$54$	−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	−0.901950	−	0.431839i	$-0.857865\pi$
$59$	−2.65879	+	3.06841i	−0.346146	+	0.399473i	0.555805	+	0.831313i	$0.312410\pi$
$60$	4.63599	−	0.947929i	0.598504	−	0.122377i
$61$	−6.02926	−	0.575724i	−0.771968	−	0.0737140i	−0.298364	−	0.954452i	$-0.596441\pi$
$61$	−6.02926	−	0.575724i	−0.771968	−	0.0737140i	−0.473603	+	0.880738i	$0.657047\pi$
$62$	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	0.999714	−	0.0239170i	$-0.00761374\pi$
$71$	13.1458	+	6.77715i	1.56012	+	0.804299i	0.560409	+	0.828216i	$0.310644\pi$
$72$	−3.90993	+	7.53077i	−0.460790	+	0.887509i
$73$	10.5533	+	1.00772i	1.23517	+	0.117945i	0.692138	−	0.721765i	$-0.256669\pi$
$73$	10.5533	+	1.00772i	1.23517	+	0.117945i	0.543035	+	0.839710i	$0.317275\pi$
$74$	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	0.826257	−	0.563294i	$-0.190466\pi$
$79$	10.0217	+	3.46856i	1.12753	+	0.390243i	0.301277	+	0.953537i	$0.402587\pi$
$80$	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	0.850586	−	0.525835i	$-0.176247\pi$
$83$	0.687583	+	0.965575i	0.0754720	+	0.105986i	−0.775114	+	0.631821i	$0.782308\pi$
$84$	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	0.0405465	−	0.999178i	$-0.487090\pi$
$89$	−1.90614	−	0.274061i	−0.202050	−	0.0290504i	−0.242597	+	0.970127i	$0.577999\pi$
$90$	−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	−0.923535	−	0.383514i	$-0.874714\pi$
$97$	−1.27676	+	2.21141i	−0.129635	+	0.224535i	0.793900	+	0.608048i	$0.208047\pi$
$98$	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	0.370065	−	0.929006i	$-0.379335\pi$
$101$	11.3030	−	2.74207i	1.12469	−	0.272846i	0.754622	+	0.656159i	$0.227820\pi$
$102$	−2.25016	−	1.65091i	−0.222799	−	0.163464i
$103$	−2.40294	+	12.4676i	−0.236768	+	1.22847i	0.647709	+	0.761888i	$0.275727\pi$
$103$	−2.40294	+	12.4676i	−0.236768	+	1.22847i	−0.884477	+	0.466583i	$0.845485\pi$
$104$	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	0.957250	+	0.289263i	$0.0934102\pi$
$107$	5.67885	+	12.4349i	0.548995	+	1.20213i	−0.408255	+	0.912868i	$0.633863\pi$
$108$	3.59864	−	9.74935i	0.346279	−	0.938131i
$109$	−10.0541	−	11.6030i	−0.963007	−	1.11137i	−0.993726	−	0.111841i	$-0.964325\pi$
$109$	−10.0541	−	11.6030i	−0.963007	−	1.11137i	0.0307194	−	0.999528i	$-0.490220\pi$
$110$	−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	0.702757	−	0.711430i	$-0.251952\pi$
$113$	2.76708	+	1.97043i	0.260305	+	0.185363i	−0.442452	+	0.896792i	$0.645891\pi$
$114$	−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	−0.519539	−	0.854447i	$-0.673896\pi$
$127$	4.04190	−	4.23902i	0.358661	−	0.376152i	0.878200	+	0.478294i	$0.158745\pi$
$128$	−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	−0.989168	−	0.146788i	$-0.953106\pi$
$131$	−0.931932	−	6.48173i	−0.0814232	−	0.566311i	0.907745	−	0.419523i	$-0.137803\pi$
$132$	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	0.343275	−	0.939235i	$-0.388464\pi$
$137$	10.9703	−	1.57730i	0.937259	−	0.134757i	0.593983	+	0.804477i	$0.297554\pi$
$138$	18.7318	−	1.52102i	1.59456	−	0.129478i
$139$	5.94066	+	2.71301i	0.503881	+	0.230115i	0.651104	−	0.758989i	$-0.274306\pi$
$139$	5.94066	+	2.71301i	0.503881	+	0.230115i	−0.147223	+	0.989103i	$0.547034\pi$
$140$	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	−0.905498	−	0.424350i	$-0.860502\pi$
$149$	1.04582	−	3.56172i	0.0856766	−	0.291788i	0.991175	+	0.132563i	$0.0423206\pi$
$150$	7.08583	+	2.95397i	0.578556	+	0.241191i
$151$	−7.71494	−	14.9649i	−0.627833	−	1.21783i	−0.961414	−	0.275105i	$-0.911288\pi$
$151$	−7.71494	−	14.9649i	−0.627833	−	1.21783i	0.333581	−	0.942721i	$-0.391743\pi$
$152$	−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	0.128060	−	0.991766i	$-0.459125\pi$
$157$	−5.80960	−	2.32581i	−0.463656	−	0.185620i	−0.591716	+	0.806146i	$0.701549\pi$
$158$	−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	−0.300784	−	0.953692i	$-0.597248\pi$
$163$	4.78444	−	2.76230i	0.374747	−	0.216360i	0.675530	+	0.737332i	$0.263915\pi$
$164$	−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	0.996698	−	0.0811999i	$-0.0258752\pi$
$167$	0.950986	+	3.92002i	0.0735895	+	0.303340i	−0.923108	+	0.384540i	$0.874360\pi$
$168$	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	−0.562891	−	0.826531i	$-0.690311\pi$
$173$	−6.50314	+	2.25076i	−0.494425	+	0.171122i	0.0684660	+	0.997653i	$0.478190\pi$
$174$	−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	0.755294	+	0.655386i	$0.227494\pi$
$179$	−2.06103	+	14.3348i	−0.154049	+	1.07143i	−0.909343	+	0.416048i	$0.863415\pi$
$180$	7.21120	−	3.89507i	0.537491	−	0.290321i
$181$	−18.1606	+	14.2817i	−1.34987	+	1.06155i	−0.358075	+	0.933693i	$0.616567\pi$
$181$	−18.1606	+	14.2817i	−1.34987	+	1.06155i	−0.991793	+	0.127855i	$0.959191\pi$
$182$	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	0.574283	−	0.818657i	$-0.305281\pi$
$191$	−1.18722	−	0.933642i	−0.0859044	−	0.0675560i	−0.660188	+	0.751101i	$0.729523\pi$
$192$	3.66426	−	13.3631i	0.264445	−	0.964401i
$193$	−13.3173	+	15.3690i	−0.958601	+	1.10628i	0.0356668	+	0.999364i	$0.488645\pi$
$193$	−13.3173	+	15.3690i	−0.958601	+	1.10628i	−0.994268	+	0.106921i	$0.965901\pi$
$194$	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	−0.987591	−	0.157050i	$-0.949801\pi$
$197$	−4.02546	+	7.80831i	−0.286802	+	0.556319i	0.700788	+	0.713369i	$0.252832\pi$
$198$	−12.8171	+	14.6070i	−0.910872	+	1.03807i
$199$	−24.9309	−	6.04817i	−1.76730	−	0.428743i	−0.785535	−	0.618817i	$-0.787612\pi$
$199$	−24.9309	−	6.04817i	−1.76730	−	0.428743i	−0.981770	+	0.190074i	$0.939127\pi$
$200$	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	−0.790481	−	0.612487i	$-0.790169\pi$
$211$	−0.129225	+	0.164323i	−0.00889621	+	0.0113124i	0.781585	+	0.623799i	$0.214412\pi$
$212$	−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	0.140313	−	0.990107i	$-0.455189\pi$
$223$	−0.0597759	−	0.00859447i	−0.00400289	−	0.000575529i	−0.144316	+	0.989532i	$0.546098\pi$
$224$	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	0.908003	+	0.418963i	$0.137606\pi$
$227$	−0.538078	+	11.2956i	−0.0357135	+	0.749718i	−0.943717	+	0.330755i	$0.892697\pi$
$228$	7.60637	+	1.37712i	0.503744	+	0.0912018i
$229$	6.59311	+	19.0495i	0.435685	+	1.25883i	0.922728	+	0.385451i	$0.125954\pi$
$229$	6.59311	+	19.0495i	0.435685	+	1.25883i	−0.487044	+	0.873378i	$0.661925\pi$
$230$	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	0.876502	−	0.481398i	$-0.159871\pi$
$233$	−1.37462	−	3.43364i	−0.0900546	−	0.224945i	−0.966557	+	0.256452i	$0.917446\pi$
$234$	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	1.00000		0.000371818i	$-0.000118353\pi$
$239$	7.72483	+	13.3798i	0.499678	+	0.865468i	−0.500322	+	0.865839i	$0.666785\pi$
$240$	8.12580	−	4.85132i	0.524518	−	0.313151i
$241$	−8.98290	−	19.6698i	−0.578639	−	1.26704i	−0.942068	−	0.335422i	$-0.891121\pi$
$241$	−8.98290	−	19.6698i	−0.578639	−	1.26704i	0.363429	−	0.931622i	$-0.381606\pi$
$242$	−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	−0.999566	−	0.0294645i	$-0.990620\pi$
$251$	−24.6417	+	12.7037i	−1.55537	+	0.801849i	−0.555804	+	0.831313i	$0.687589\pi$
$252$	−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	−0.989331	−	0.145686i	$-0.953461\pi$
$257$	−0.728614	−	7.63039i	−0.0454497	−	0.475971i	0.943881	−	0.330285i	$-0.107145\pi$
$258$	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	−0.607331	−	0.794449i	$-0.707760\pi$
$263$	6.33756	−	13.8773i	0.390791	−	0.855712i	0.998122	−	0.0612634i	$-0.0195130\pi$
$264$	−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	$0.263994\pi$
$269$			24.1918i			1.47500i	−0.675347	+	0.737500i	$0.736006\pi$
$270$	−8.16656	+	5.83667i	−0.497001	+	0.355208i
$271$	5.05073	−	0.726186i	0.306810	−	0.0441126i	0.0128098	−	0.999918i	$-0.495922\pi$
$271$	5.05073	−	0.726186i	0.306810	−	0.0441126i	0.294000	+	0.955805i	$0.405013\pi$
$272$	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	0.144308	−	0.989533i	$-0.453904\pi$
$277$	13.3261	−	3.91290i	0.800689	−	0.235103i	0.656381	+	0.754429i	$0.272086\pi$
$278$	−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	−0.979186	−	0.202963i	$-0.934943\pi$
$281$	−2.44028	−	12.6614i	−0.145575	−	0.755314i	0.833612	−	0.552351i	$-0.186269\pi$
$282$	7.36528	−	15.5408i	0.438596	−	0.925441i
$283$	2.38353	−	8.11756i	0.141686	−	0.482539i	−0.857820	−	0.513950i	$-0.828182\pi$
$283$	2.38353	−	8.11756i	0.141686	−	0.482539i	0.999507	+	0.0314107i	$0.00999999\pi$
$284$	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	−0.303011	+	0.952987i	$0.597992\pi$
$293$	−22.0713	+	19.1249i	−1.28942	+	1.11729i	−0.986410	+	0.164303i	$0.947463\pi$
$294$	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	0.575806	−	0.817586i	$-0.304688\pi$
$307$	26.8747	−	9.30142i	1.53382	−	0.530860i	0.958013	+	0.286726i	$0.0925670\pi$
$308$	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	0.0223819	−	0.999749i	$-0.492875\pi$
$311$	−15.4788	−	9.94765i	−0.877724	−	0.564079i	−0.900106	+	0.435670i	$0.856511\pi$
$312$	9.34071	−	14.1938i	0.528814	−	0.803566i
$313$	−2.45737	+	17.0914i	−0.138899	+	0.966063i	0.794511	+	0.607250i	$0.207727\pi$
$313$	−2.45737	+	17.0914i	−0.138899	+	0.966063i	−0.933410	+	0.358813i	$0.883182\pi$
$314$	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	−0.872815	−	0.488051i	$-0.837708\pi$
$317$	−30.1837	+	1.43783i	−1.69529	+	0.0807564i	−0.822471	+	0.568808i	$0.807405\pi$
$318$	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	−0.986236	−	0.165342i	$-0.947127\pi$
$331$	−5.08468	+	9.86290i	−0.279479	+	0.542114i	0.706757	+	0.707456i	$0.250157\pi$
$332$	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	−0.756579	−	0.653902i	$-0.773131\pi$
$337$	3.95662	−	16.3094i	0.215531	−	0.888430i	0.972110	−	0.234527i	$-0.0753542\pi$
$338$	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	−0.670167	−	0.742210i	$-0.733778\pi$
$347$	5.87569	−	16.9767i	0.315424	−	0.911357i	0.985591	−	0.169147i	$-0.0541012\pi$
$348$	9.23556	−	20.8427i	0.495078	−	1.11729i
$349$	−4.98437	+	3.20326i	−0.266807	+	0.171466i	−0.667203	−	0.744876i	$-0.732509\pi$
$349$	−4.98437	+	3.20326i	−0.266807	+	0.171466i	0.400396	+	0.916342i	$0.368872\pi$
$350$	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	0.00978880	−	0.999952i	$-0.496884\pi$
$353$	2.15285	−	0.102553i	0.114585	−	0.00545834i	0.104796	+	0.994494i	$0.466581\pi$
$354$	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	0.999944	+	0.0105960i	$0.00337289\pi$
$359$	26.9994	+	17.3515i	1.42497	+	0.915775i	0.425030	+	0.905179i	$0.360263\pi$
$360$	−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	0.890545	+	0.454895i	$0.150323\pi$
$367$	10.7269	+	26.7945i	0.559941	+	1.39866i	−0.330605	+	0.943769i	$0.607253\pi$
$368$	−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	−0.997127	−	0.0757428i	$-0.975867\pi$
$373$	−10.8957	−	18.8719i	−0.564159	−	0.977152i	0.432969	−	0.901409i	$-0.357466\pi$
$374$	−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	−0.603297	−	0.797516i	$-0.706147\pi$
$379$	7.46943	−	18.6577i	0.383679	−	0.958383i	0.986976	−	0.160867i	$-0.0514289\pi$
$380$	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	−0.557013	−	0.830504i	$-0.688053\pi$
$383$	4.81521	−	4.59130i	0.246046	−	0.234604i	0.803059	+	0.595899i	$0.203204\pi$
$384$	−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	−0.971381	−	0.237529i	$-0.923663\pi$
$389$	−3.11354	−	16.1546i	−0.157863	−	0.819068i	0.813518	−	0.581540i	$-0.197550\pi$
$390$	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	−0.892593	−	0.450863i	$-0.851116\pi$
$397$	0.650954	−	1.42539i	0.0326704	−	0.0715383i	0.925264	+	0.379325i	$0.123844\pi$
$398$	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	$0.0410925\pi$
$401$			5.15593i			0.257475i	−0.991679	+	0.128738i	$0.958908\pi$
$402$	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	0.988386	+	0.151964i	$0.0485599\pi$
$409$	24.0098	+	22.8933i	1.18721	+	1.13200i	0.198822	+	0.980036i	$0.436289\pi$
$410$	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	−0.0931858	−	0.995649i	$-0.529705\pi$
$419$	13.5875	−	7.00484i	0.663793	−	0.342209i	0.756978	+	0.653440i	$0.226675\pi$
$420$	9.01509	−	14.3823i	0.439891	−	0.701783i
$421$	2.58838	−	2.46801i	0.126150	−	0.120284i	−0.624378	−	0.781122i	$-0.714648\pi$
$421$	2.58838	−	2.46801i	0.126150	−	0.120284i	0.750528	+	0.660838i	$0.229799\pi$
$422$	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	0.565696	−	0.824614i	$-0.308608\pi$
$431$	−8.95379	−	15.5084i	−0.431289	−	0.747015i	−0.996985	+	0.0775996i	$0.975274\pi$
$432$	0.354641	−	20.7816i	0.0170627	−	0.999854i
$433$	−11.2419	−	2.16669i	−0.540250	−	0.104125i	−0.0881758	−	0.996105i	$-0.528104\pi$
$433$	−11.2419	−	2.16669i	−0.540250	−	0.104125i	−0.452074	+	0.891980i	$0.649316\pi$
$434$	−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	0.240378	−	0.970679i	$-0.422729\pi$
$439$	−10.0585	−	5.80727i	−0.480065	−	0.277166i	−0.720444	+	0.693513i	$0.756062\pi$
$440$	−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	−0.999861	−	0.0166742i	$-0.994692\pi$
$443$	−0.0619317	+	1.30011i	−0.00294246	+	0.0617699i	0.996919	+	0.0784441i	$0.0249952\pi$
$444$	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	0.573345	−	0.819314i	$-0.305646\pi$
$449$	−7.58685	−	9.64747i	−0.358046	−	0.455292i	−0.931390	+	0.364022i	$0.881403\pi$
$450$	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	−0.119501	−	0.992834i	$-0.538129\pi$
$457$	12.5735	−	36.3287i	0.588162	−	1.69938i	0.707663	−	0.706550i	$-0.249749\pi$
$458$	−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	0.471306	−	0.881970i	$-0.343783\pi$
$461$	−7.18444	−	6.22535i	−0.334613	−	0.289944i	−0.805919	+	0.592026i	$0.798328\pi$
$462$	−8.17626	+	39.4075i	−0.380394	+	1.83340i
$463$	0.172224	−	1.80361i	0.00800394	−	0.0838211i	−0.990587	−	0.136882i	$-0.956292\pi$
$463$	0.172224	−	1.80361i	0.00800394	−	0.0838211i	0.998591	+	0.0530612i	$0.0168979\pi$
$464$	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	0.583557	+	0.812072i	$0.301661\pi$
$467$	−6.63956	+	27.3686i	−0.307242	+	1.26647i	−0.890799	+	0.454398i	$0.849855\pi$
$468$	−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	0.867713	−	0.497066i	$-0.165589\pi$
$479$	12.8959	+	10.1415i	0.589229	+	0.463375i	−0.278483	+	0.960441i	$0.589832\pi$
$480$	−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	−0.294342	−	0.955700i	$-0.595101\pi$
$487$	−10.9569	+	0.521943i	−0.496506	+	0.0236515i	−0.202164	+	0.979352i	$0.564797\pi$
$488$	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	0.744716	+	0.667381i	$0.232585\pi$
$491$	−3.49787	+	24.3282i	−0.157857	+	1.09792i	−0.902573	+	0.430537i	$0.858324\pi$
$492$	−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	0.674042	−	0.738693i	$-0.264557\pi$
$499$	8.29500	+	4.78912i	0.371335	+	0.214390i	−0.302707	+	0.953084i	$0.597890\pi$
$500$	−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	−0.832829	−	0.553531i	$-0.813280\pi$
$503$	−7.76499	−	32.0077i	−0.346224	−	1.42715i	0.486605	−	0.873622i	$-0.338235\pi$
$504$	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	0.499220	−	0.866475i	$-0.333620\pi$
$509$	33.4124	−	15.2589i	1.48098	−	0.676340i	0.981758	+	0.190136i	$0.0608928\pi$
$510$	−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	−0.538217	−	0.842807i	$-0.680902\pi$
$521$	8.45033	−	28.7792i	0.370216	−	1.26084i	0.908432	−	0.418032i	$-0.137280\pi$
$522$	−8.03282	+	26.7403i	−0.351587	+	1.17039i
$523$	−0.171216	−	0.888352i	−0.00748674	−	0.0388449i	0.977993	−	0.208637i	$-0.0669026\pi$
$523$	−0.171216	−	0.888352i	−0.00748674	−	0.0388449i	−0.985480	+	0.169792i	$0.945690\pi$
$524$	−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	−0.977701	−	0.210001i	$-0.932653\pi$
$541$	−4.15727	+	9.10315i	−0.178735	+	0.391375i	0.798966	+	0.601376i	$0.205381\pi$
$542$	−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	0.968878	+	0.247540i	$0.0796220\pi$
$547$	1.50516	+	15.7628i	0.0643561	+	0.673967i	−0.904522	+	0.426428i	$0.859772\pi$
$548$	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	0.00625147	−	0.999980i	$-0.498010\pi$
$557$	−22.1066	−	15.7420i	−0.936686	−	0.667011i	−0.942938	+	0.332969i	$0.891949\pi$
$558$	−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	0.785539	−	0.618813i	$-0.212386\pi$
$563$	−4.66360	−	10.2119i	−0.196547	−	0.430379i	−0.982086	+	0.188434i	$0.939659\pi$
$564$	−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	0.529007	−	0.848618i	$-0.322565\pi$
$569$	33.1105	−	8.03253i	1.38807	−	0.336741i	0.859059	+	0.511877i	$0.171049\pi$
$570$	−5.33011	−	5.22851i	−0.223254	−	0.218998i
$571$	9.86655	+	24.6454i	0.412902	+	1.03138i	0.978417	+	0.206641i	$0.0662533\pi$
$571$	9.86655	+	24.6454i	0.412902	+	1.03138i	−0.565515	+	0.824738i	$0.691322\pi$
$572$	−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	−0.840267	−	0.542173i	$-0.817602\pi$
$577$	1.14656	−	24.0693i	0.0477320	−	1.00202i	0.887999	−	0.459845i	$-0.152095\pi$
$578$	−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	0.490264	−	0.871574i	$-0.336900\pi$
$587$	−11.9620	−	16.7982i	−0.493723	−	0.693338i	−0.983988	+	0.178236i	$0.942961\pi$
$588$	−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	0.178274	+	0.983981i	$0.442949\pi$
$593$	−19.9683	+	25.3918i	−0.820000	+	1.04271i	−0.998274	+	0.0587340i	$0.981294\pi$
$594$	−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	0.0295136	−	0.999564i	$-0.490604\pi$
$599$	−18.7863	−	9.68502i	−0.767588	−	0.395719i	−0.797102	+	0.603845i	$0.793634\pi$
$600$	15.3276	+	0.896738i	0.625747	+	0.0366092i
$601$	−2.16453	+	8.92233i	−0.0882932	+	0.363949i	−0.998768	−	0.0496141i	$-0.984201\pi$
$601$	−2.16453	+	8.92233i	−0.0882932	+	0.363949i	0.910475	+	0.413563i	$0.135716\pi$
$602$	−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	−0.890873	−	0.454252i	$-0.849907\pi$
$607$	−0.100853	+	0.195627i	−0.00409348	+	0.00794024i	0.886780	+	0.462192i	$0.152937\pi$
$608$	−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	0.300145	−	0.953893i	$-0.402965\pi$
$613$	−13.7683	−	10.8275i	−0.556097	−	0.437320i	−0.856243	+	0.516574i	$0.827207\pi$
$614$	−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	0.858515	+	0.512789i	$0.171388\pi$
$617$	24.0527	+	37.4267i	0.968324	+	1.50674i	0.109809	+	0.993953i	$0.464976\pi$
$618$	−8.33831	−	29.9627i	−0.335416	−	1.20528i
$619$	10.3542	−	7.37320i	0.416171	−	0.296354i	−0.352726	−	0.935727i	$-0.614745\pi$
$619$	10.3542	−	7.37320i	0.416171	−	0.296354i	0.768897	+	0.639373i	$0.220806\pi$
$620$	−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	−0.319630	−	0.947543i	$-0.603559\pi$
$631$	0.373183	−	0.129160i	0.0148562	−	0.00514178i	0.334486	+	0.942401i	$0.391437\pi$
$632$	−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	−0.636803	+	0.771027i	$0.719744\pi$
$641$	−41.0894	+	23.7230i	−1.62293	+	0.937001i	−0.986130	+	0.165974i	$0.946923\pi$
$642$	−26.0251	−	21.0703i	−1.02713	−	0.831578i
$643$	9.47337	−	4.32634i	0.373593	−	0.170614i	−0.219765	−	0.975553i	$-0.570529\pi$
$643$	9.47337	−	4.32634i	0.373593	−	0.170614i	0.593358	+	0.804939i	$0.297802\pi$
$644$	−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	−0.345006	−	0.938600i	$-0.612123\pi$
$647$	−31.6021	−	12.6516i	−1.24241	−	0.497385i	−0.897401	+	0.441216i	$0.854547\pi$
$648$	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	0.771503	−	0.636225i	$-0.219505\pi$
$653$	−4.96425	−	9.62930i	−0.194266	−	0.376824i	−0.965770	+	0.259401i	$0.916475\pi$
$654$	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	0.460795	−	0.887507i	$-0.347564\pi$
$659$	27.7561	−	2.65039i	1.08122	−	0.103244i	0.620429	+	0.784262i	$0.286958\pi$
$660$	20.7258	−	6.34073i	0.806752	−	0.246812i
$661$	2.71889	−	0.798338i	0.105753	−	0.0310518i	−0.228428	−	0.973561i	$-0.573359\pi$
$661$	2.71889	−	0.798338i	0.105753	−	0.0310518i	0.334181	+	0.942509i	$0.391540\pi$
$662$	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	0.971888	−	0.235443i	$-0.0756540\pi$
$673$	−0.699495	−	4.86509i	−0.0269635	−	0.187536i	−0.998852	+	0.0479070i	$0.984745\pi$
$674$	−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	−0.848867	−	0.528607i	$-0.822714\pi$
$677$	−7.29755	+	7.65345i	−0.280468	+	0.294146i	0.568399	+	0.822753i	$0.307563\pi$
$678$	−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	0.134605	−	0.990899i	$-0.457023\pi$
$683$	16.4084	−	3.16245i	0.627848	−	0.121008i	0.493243	+	0.869891i	$0.335811\pi$
$684$	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	−0.0254352	−	0.999676i	$-0.508097\pi$
$691$	−25.7204	−	18.3154i	−0.978449	−	0.696751i	−0.953014	+	0.302926i	$0.902037\pi$
$692$	−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	0.782781	+	0.622297i	$0.213800\pi$
$701$	−4.63899	+	24.0694i	−0.175212	+	0.909087i	−0.957993	+	0.286790i	$0.907412\pi$
$702$	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	0.897279	−	0.441464i	$-0.145541\pi$
$709$	−2.15479	−	6.22586i	−0.0809248	−	0.233817i	−0.978204	+	0.207647i	$0.933419\pi$
$710$	−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	0.833025	+	0.553236i	$0.186607\pi$
$719$	1.51126	+	31.7252i	0.0563604	+	1.18315i	−0.776664	+	0.629915i	$0.783090\pi$
$720$	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	−0.225200	−	0.974313i	$-0.572303\pi$
$727$	20.8893	−	26.5629i	0.774742	−	0.985164i	0.999941	−	0.0108514i	$-0.00345417\pi$
$728$	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	0.336078	−	0.941834i	$-0.390899\pi$
$733$	−6.39414	−	3.29641i	−0.236173	−	0.121756i	−0.572251	+	0.820078i	$0.693930\pi$
$734$	−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	0.590241	−	0.807227i	$-0.299033\pi$
$739$	20.2518	+	4.91303i	0.744974	+	0.180729i	0.154734	+	0.987956i	$0.450548\pi$
$740$	−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	0.723560	−	0.690262i	$-0.242505\pi$
$743$	35.5284	+	3.39255i	1.30341	+	0.124461i	0.579851	+	0.814723i	$0.303111\pi$
$744$	−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	0.989981	+	0.141198i	$0.0450954\pi$
$751$	19.3795	+	30.1550i	0.707166	+	1.10037i	−0.282815	+	0.959174i	$0.591268\pi$
$752$	−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	−0.941753	−	0.336306i	$-0.890822\pi$
$757$	−23.0276	+	18.1091i	−0.836953	+	0.658187i	0.104800	+	0.994493i	$0.466580\pi$
$758$	−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	−0.413583	−	0.910467i	$-0.635723\pi$
$761$	16.1770	−	25.1719i	0.586415	−	0.912480i	0.999998	−	0.00201361i	$-0.000640952\pi$
$762$	−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	−0.662046	−	0.749463i	$-0.730312\pi$
$769$	−17.3041	+	6.92753i	−0.624003	+	0.249813i	0.0380433	+	0.999276i	$0.487888\pi$
$770$	−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	−0.616661	−	0.787229i	$-0.711515\pi$
$773$	6.90653	−	35.8345i	0.248411	−	1.28888i	0.865072	−	0.501648i	$-0.167273\pi$
$774$	−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	0.972399	−	0.233324i	$-0.0749604\pi$
$787$	6.12385	+	11.8786i	0.218292	+	0.423427i	−0.754107	+	0.656751i	$0.771930\pi$
$788$	−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	−0.0866752	−	0.996237i	$-0.527624\pi$
$797$	25.7626	−	27.0190i	0.912557	−	0.957062i	0.999232	+	0.0391742i	$0.0124727\pi$
$798$	−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	0.876426	−	0.481537i	$-0.159921\pi$
$809$	30.9016	+	14.1123i	1.08644	+	0.496161i	0.210016	+	0.977698i	$0.432648\pi$
$810$	−10.6146	+	13.7698i	−0.372960	+	0.483822i
$811$	−9.59282	+	10.0607i	−0.336849	+	0.353277i	−0.870272	−	0.492571i	$-0.836057\pi$
$811$	−9.59282	+	10.0607i	−0.336849	+	0.353277i	0.533423	+	0.845849i	$0.320906\pi$
$812$	−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	−0.979298	−	0.202424i	$-0.935118\pi$
$821$	−16.5082	−	32.0214i	−0.576139	−	1.11755i	0.403159	−	0.915130i	$-0.367912\pi$
$822$	−22.3352	+	15.4323i	−0.779029	+	0.538264i
$823$	2.55036	+	2.67474i	0.0889000	+	0.0932356i	0.766681	−	0.642028i	$-0.221907\pi$
$823$	2.55036	+	2.67474i	0.0889000	+	0.0932356i	−0.677781	+	0.735264i	$0.737058\pi$
$824$	−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	0.890899	−	0.454202i	$-0.150076\pi$
$827$	35.1486	+	14.0714i	1.22224	+	0.489310i	0.331338	+	0.943512i	$0.392500\pi$
$828$	−39.4166	+	23.7801i	−1.36982	+	0.826415i
$829$	12.2345	+	14.1193i	0.424921	+	0.490385i	0.927330	−	0.374245i	$-0.122098\pi$
$829$	12.2345	+	14.1193i	0.424921	+	0.490385i	−0.502409	+	0.864630i	$0.667553\pi$
$830$	−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	−0.127463	−	0.991843i	$-0.540683\pi$
$839$	13.4614	−	5.38912i	0.464738	−	0.186053i	0.592201	+	0.805790i	$0.298259\pi$
$840$	−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	0.859501	+	0.511134i	$0.170774\pi$
$853$	1.53269	+	32.1751i	0.0524782	+	1.10165i	−0.807023	+	0.590520i	$0.798923\pi$
$854$	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	0.758034	−	0.652215i	$-0.226160\pi$
$857$	−4.39530	−	6.83923i	−0.150141	−	0.233624i	−0.908175	+	0.418592i	$0.862524\pi$
$858$	28.5414	−	26.4518i	0.974386	−	0.903051i
$859$	−23.6389	−	8.18150i	−0.806549	−	0.279149i	−0.107483	−	0.994207i	$-0.534279\pi$
$859$	−23.6389	−	8.18150i	−0.806549	−	0.279149i	−0.699066	+	0.715058i	$0.746400\pi$
$860$	−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	−0.566778	−	0.823871i	$-0.691810\pi$
$863$	9.67581	−	11.1665i	0.329368	−	0.380111i	0.896146	+	0.443760i	$0.146356\pi$
$864$	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	0.253460	−	0.967346i	$-0.418431\pi$
$877$	9.45489	+	0.902832i	0.319269	+	0.0304865i	0.0658085	+	0.997832i	$0.479037\pi$
$878$	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	−0.617232	−	0.786781i	$-0.711746\pi$
$881$	8.69342	−	11.0546i	0.292889	−	0.372438i	0.910121	+	0.414343i	$0.135989\pi$
$882$	17.9099	+	17.2912i	0.603057	+	0.582224i
$883$	−13.6360	−	4.71946i	−0.458887	−	0.158822i	0.0878375	−	0.996135i	$-0.472004\pi$
$883$	−13.6360	−	4.71946i	−0.458887	−	0.158822i	−0.546725	+	0.837312i	$0.684126\pi$
$884$	−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	−0.992419	−	0.122898i	$-0.960781\pi$
$887$	−23.3486	−	32.7885i	−0.783969	−	1.10093i	0.208450	−	0.978033i	$-0.433158\pi$
$888$	−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	0.786854	+	0.617139i	$0.211708\pi$
$907$	−5.21024	+	27.0333i	−0.173003	+	0.897626i	−0.959858	+	0.280487i	$0.909504\pi$
$908$	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	0.997540	+	0.0701027i	$0.0223327\pi$
$911$	11.9907	+	26.2560i	0.397270	+	0.869900i	−0.600270	+	0.799798i	$0.704940\pi$
$912$	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	0.446643	−	0.894712i	$-0.352620\pi$
$919$	−14.1968	−	14.8892i	−0.468309	−	0.491148i	−0.914951	+	0.403564i	$0.867771\pi$
$920$	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	0.874509	−	0.485009i	$-0.161184\pi$
$929$	−3.76089	−	12.8084i	−0.123391	−	0.420230i	−0.997900	+	0.0647793i	$0.979366\pi$
$930$	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	−0.469027	−	0.883184i	$-0.655395\pi$
$941$	−20.5599	+	2.95606i	−0.670233	+	0.0963649i	−0.201206	+	0.979549i	$0.564486\pi$
$942$	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	−0.405134	−	0.914257i	$-0.632775\pi$
$947$	−7.74470	+	2.27405i	−0.251669	+	0.0738967i	0.153465	+	0.988154i	$0.450957\pi$
$948$	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	−0.975494	−	0.220025i	$-0.929386\pi$
$953$	−1.10830	+	3.77454i	−0.0359015	+	0.122269i	0.939593	+	0.342295i	$0.111204\pi$
$954$	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	0.223887	−	0.974615i	$-0.428126\pi$
$967$	36.6900	−	21.1830i	1.17987	−	0.681199i	0.955985	+	0.293416i	$0.0947922\pi$
$968$	−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	−0.996955	−	0.0779774i	$-0.975154\pi$
$971$	−4.56686	−	18.8248i	−0.146557	−	0.604118i	0.850398	−	0.526140i	$-0.176361\pi$
$972$	−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	0.139237	−	0.990259i	$-0.455535\pi$
$977$	26.9067	−	9.31251i	0.860823	−	0.297934i	0.721585	+	0.692325i	$0.243414\pi$
$978$	−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	0.807291	+	0.590154i	$0.200933\pi$
$983$	−4.18763	+	29.1256i	−0.133565	+	0.928962i	−0.940855	+	0.338808i	$0.889976\pi$
$984$	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	0.989452	+	0.144860i	$0.0462733\pi$
$991$	22.3568	+	34.7879i	0.710189	+	1.10507i	−0.279264	+	0.960214i	$0.590090\pi$
$992$	−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	−0.127503	−	0.991838i	$-0.540696\pi$
$997$	27.5458	−	31.7896i	0.872385	−	1.00679i	0.999888	−	0.0149478i	$-0.00475821\pi$
$998$	−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.35.9	yes	2640
3.2	odd	2	inner	804.2.bd.a.35.124	yes	2640
4.3	odd	2	inner	804.2.bd.a.35.27	yes	2640
12.11	even	2	inner	804.2.bd.a.35.106	yes	2640
67.23	even	33	inner	804.2.bd.a.23.106	yes	2640
201.23	odd	66	inner	804.2.bd.a.23.27	yes	2640
268.23	odd	66	inner	804.2.bd.a.23.124	yes	2640
804.23	even	66	inner	804.2.bd.a.23.9	✓	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.9	✓	2640	804.23	even	66	inner
804.2.bd.a.23.27	yes	2640	201.23	odd	66	inner
804.2.bd.a.23.106	yes	2640	67.23	even	33	inner
804.2.bd.a.23.124	yes	2640	268.23	odd	66	inner
804.2.bd.a.35.9	yes	2640	1.1	even	1	trivial
804.2.bd.a.35.27	yes	2640	4.3	odd	2	inner
804.2.bd.a.35.106	yes	2640	12.11	even	2	inner
804.2.bd.a.35.124	yes	2640	3.2	odd	2	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

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