LMFDB - Embedded newform 378.2.u.e.85.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.4
Character	$\chi$	$=$	378.85
Dual form			378.2.u.e.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.927705 + 1.46266i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.587615 - 3.33253i) q^{5} +(0.371500 + 1.69174i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.27873 + 2.71383i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.927705 + 1.46266i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.587615 - 3.33253i) q^{5} +(0.371500 + 1.69174i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.27873 + 2.71383i) q^{9} +(1.69197 - 2.93058i) q^{10} +(0.344024 + 1.95106i) q^{11} +(-0.229514 + 1.71678i) q^{12} +(4.04527 - 1.47236i) q^{13} +(0.939693 - 0.342020i) q^{14} +(5.41948 - 2.23213i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.73027 + 4.72896i) q^{17} +(-2.12979 + 2.11281i) q^{18} +(-3.16278 - 5.47810i) q^{19} +(2.59225 - 2.17515i) q^{20} +(1.65084 + 0.524143i) q^{21} +(-0.344024 + 1.95106i) q^{22} +(1.24289 + 1.04291i) q^{23} +(-0.802845 + 1.53474i) q^{24} +(-6.06200 - 2.20639i) q^{25} +4.30489 q^{26} +(-5.15568 + 0.647292i) q^{27} +1.00000 q^{28} +(-8.55655 - 3.11433i) q^{29} +(5.85608 - 0.243941i) q^{30} +(5.08858 + 4.26982i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-2.53457 + 2.31319i) q^{33} +(-4.18301 + 3.50996i) q^{34} +(-1.69197 - 2.93058i) q^{35} +(-2.72398 + 1.25696i) q^{36} +(-1.38210 + 2.39388i) q^{37} +(-1.09842 - 6.22947i) q^{38} +(5.90638 + 4.55093i) q^{39} +(3.17986 - 1.15738i) q^{40} +(-7.31356 + 2.66192i) q^{41} +(1.37202 + 1.05715i) q^{42} +(-0.0470198 - 0.266663i) q^{43} +(-0.990577 + 1.71573i) q^{44} +(8.29251 + 5.85608i) q^{45} +(0.811242 + 1.40511i) q^{46} +(4.41372 - 3.70355i) q^{47} +(-1.27934 + 1.16760i) q^{48} +(0.173648 - 0.984808i) q^{49} +(-4.94179 - 4.14665i) q^{50} +(-9.44972 + 0.393638i) q^{51} +(4.04527 + 1.47236i) q^{52} -12.3528 q^{53} +(-5.06614 - 1.15509i) q^{54} +6.70411 q^{55} +(0.939693 + 0.342020i) q^{56} +(5.07845 - 9.70812i) q^{57} +(-6.97536 - 5.85302i) q^{58} +(1.81517 - 10.2943i) q^{59} +(5.58635 + 1.77367i) q^{60} +(1.50232 - 1.26059i) q^{61} +(3.32133 + 5.75272i) q^{62} +(0.764853 + 2.90086i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.52962 - 14.3462i) q^{65} +(-3.17288 + 1.30682i) q^{66} +(0.410141 - 0.149279i) q^{67} +(-5.13122 + 1.86761i) q^{68} +(-0.372383 + 2.78544i) q^{69} +(-0.587615 - 3.33253i) q^{70} +(5.21797 - 9.03779i) q^{71} +(-2.98961 + 0.249503i) q^{72} +(2.40066 + 4.15807i) q^{73} +(-2.11751 + 1.77680i) q^{74} +(-2.39656 - 10.9135i) q^{75} +(1.09842 - 6.22947i) q^{76} +(1.51765 + 1.27346i) q^{77} +(3.99367 + 6.29658i) q^{78} +(-3.80215 - 1.38387i) q^{79} +3.38394 q^{80} +(-5.72971 - 6.94049i) q^{81} -7.78293 q^{82} +(12.2510 + 4.45900i) q^{83} +(0.927705 + 1.46266i) q^{84} +(14.1551 + 11.8775i) q^{85} +(0.0470198 - 0.266663i) q^{86} +(-3.38276 - 15.4045i) q^{87} +(-1.51765 + 1.27346i) q^{88} +(3.08069 + 5.33591i) q^{89} +(5.78951 + 8.33912i) q^{90} +(2.15245 - 3.72814i) q^{91} +(0.281741 + 1.59783i) q^{92} +(-1.52459 + 11.4040i) q^{93} +(5.41423 - 1.97062i) q^{94} +(-20.1144 + 7.32105i) q^{95} +(-1.60153 + 0.659623i) q^{96} +(-1.77416 - 10.0618i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-5.73474 - 1.56125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.927705	+	1.46266i	0.535611	+	0.844465i
$3$	0.927705	+	1.46266i	0.535611	+	0.844465i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.587615	−	3.33253i	0.262789	−	1.49035i	−0.512467	−	0.858707i	$-0.671268\pi$
$5$	0.587615	−	3.33253i	0.262789	−	1.49035i	0.775257	−	0.631646i	$-0.217620\pi$
$6$	0.371500	+	1.69174i	0.151664	+	0.690650i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.27873	+	2.71383i	−0.426242	+	0.904609i
$10$	1.69197	−	2.93058i	0.535048	−	0.926730i
$11$	0.344024	+	1.95106i	0.103727	+	0.588266i	0.991721	+	0.128411i	$0.0409875\pi$
$11$	0.344024	+	1.95106i	0.103727	+	0.588266i	−0.887994	+	0.459855i	$0.847901\pi$
$12$	−0.229514	+	1.71678i	−0.0662550	+	0.495591i
$13$	4.04527	−	1.47236i	1.12196	−	0.408359i	0.286591	−	0.958053i	$-0.407478\pi$
$13$	4.04527	−	1.47236i	1.12196	−	0.408359i	0.835366	+	0.549694i	$0.185256\pi$
$14$	0.939693	−	0.342020i	0.251143	−	0.0914087i
$15$	5.41948	−	2.23213i	1.39930	−	0.576332i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.73027	+	4.72896i	−0.662187	+	1.14694i	0.317853	+	0.948140i	$0.397038\pi$
$17$	−2.73027	+	4.72896i	−0.662187	+	1.14694i	−0.980040	+	0.198801i	$0.936295\pi$
$18$	−2.12979	+	2.11281i	−0.501997	+	0.497995i
$19$	−3.16278	−	5.47810i	−0.725592	−	1.25676i	−0.958730	−	0.284319i	$-0.908233\pi$
$19$	−3.16278	−	5.47810i	−0.725592	−	1.25676i	0.233138	−	0.972444i	$-0.425101\pi$
$20$	2.59225	−	2.17515i	0.579644	−	0.486379i
$21$	1.65084	+	0.524143i	0.360243	+	0.114377i
$22$	−0.344024	+	1.95106i	−0.0733461	+	0.415967i
$23$	1.24289	+	1.04291i	0.259161	+	0.217462i	0.763105	−	0.646274i	$-0.223674\pi$
$23$	1.24289	+	1.04291i	0.259161	+	0.217462i	−0.503944	+	0.863736i	$0.668118\pi$
$24$	−0.802845	+	1.53474i	−0.163880	+	0.313278i
$25$	−6.06200	−	2.20639i	−1.21240	−	0.441278i
$26$	4.30489			0.844258
$27$	−5.15568	+	0.647292i	−0.992211	+	0.124571i
$28$	1.00000			0.188982
$29$	−8.55655	−	3.11433i	−1.58891	−	0.578316i	−0.611794	−	0.791017i	$-0.709552\pi$
$29$	−8.55655	−	3.11433i	−1.58891	−	0.578316i	−0.977117	+	0.212701i	$0.931774\pi$
$30$	5.85608	−	0.243941i	1.06917	−	0.0445373i
$31$	5.08858	+	4.26982i	0.913935	+	0.766883i	0.972864	−	0.231379i	$-0.0743239\pi$
$31$	5.08858	+	4.26982i	0.913935	+	0.766883i	−0.0589283	+	0.998262i	$0.518768\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−2.53457	+	2.31319i	−0.441212	+	0.402675i
$34$	−4.18301	+	3.50996i	−0.717380	+	0.601953i
$35$	−1.69197	−	2.93058i	−0.285995	−	0.495358i
$36$	−2.72398	+	1.25696i	−0.453996	+	0.209494i
$37$	−1.38210	+	2.39388i	−0.227217	+	0.393551i	−0.956982	−	0.290147i	$-0.906296\pi$
$37$	−1.38210	+	2.39388i	−0.227217	+	0.393551i	0.729766	+	0.683697i	$0.239629\pi$
$38$	−1.09842	−	6.22947i	−0.178188	−	1.01055i
$39$	5.90638	+	4.55093i	0.945777	+	0.728732i
$40$	3.17986	−	1.15738i	0.502781	−	0.182997i
$41$	−7.31356	+	2.66192i	−1.14219	+	0.415722i	−0.842702	−	0.538380i	$-0.819037\pi$
$41$	−7.31356	+	2.66192i	−1.14219	+	0.415722i	−0.299484	+	0.954101i	$0.596814\pi$
$42$	1.37202	+	1.05715i	0.211707	+	0.163122i
$43$	−0.0470198	−	0.266663i	−0.00717046	−	0.0406657i	0.981013	−	0.193944i	$-0.0621280\pi$
$43$	−0.0470198	−	0.266663i	−0.00717046	−	0.0406657i	−0.988183	+	0.153278i	$0.951017\pi$
$44$	−0.990577	+	1.71573i	−0.149335	+	0.258656i
$45$	8.29251	+	5.85608i	1.23617	+	0.872973i
$46$	0.811242	+	1.40511i	0.119611	+	0.207172i
$47$	4.41372	−	3.70355i	0.643807	−	0.540218i	−0.261378	−	0.965237i	$-0.584177\pi$
$47$	4.41372	−	3.70355i	0.643807	−	0.540218i	0.905185	+	0.425018i	$0.139732\pi$
$48$	−1.27934	+	1.16760i	−0.184657	+	0.168528i
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$	−4.94179	−	4.14665i	−0.698875	−	0.586425i
$51$	−9.44972	+	0.393638i	−1.32323	+	0.0551203i
$52$	4.04527	+	1.47236i	0.560979	+	0.204179i
$53$	−12.3528			−1.69679			−0.848394	−	0.529365i	$-0.822430\pi$
$53$	−12.3528			−1.69679			−0.848394	+	0.529365i	$0.822430\pi$
$54$	−5.06614	−	1.15509i	−0.689414	−	0.157188i
$55$	6.70411			0.903982
$56$	0.939693	+	0.342020i	0.125572	+	0.0457044i
$57$	5.07845	−	9.70812i	0.672657	−	1.28587i
$58$	−6.97536	−	5.85302i	−0.915910	−	0.768540i
$59$	1.81517	−	10.2943i	0.236315	−	1.34021i	−0.603512	−	0.797354i	$-0.706233\pi$
$59$	1.81517	−	10.2943i	0.236315	−	1.34021i	0.839827	−	0.542854i	$-0.182656\pi$
$60$	5.58635	+	1.77367i	0.721194	+	0.228979i
$61$	1.50232	−	1.26059i	0.192352	−	0.161402i	−0.541526	−	0.840684i	$-0.682153\pi$
$61$	1.50232	−	1.26059i	0.192352	−	0.161402i	0.733878	+	0.679282i	$0.237709\pi$
$62$	3.32133	+	5.75272i	0.421810	+	0.730596i
$63$	0.764853	+	2.90086i	0.0963624	+	0.365474i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.52962	−	14.3462i	−0.313761	−	1.77942i
$66$	−3.17288	+	1.30682i	−0.390554	+	0.160858i
$67$	0.410141	−	0.149279i	0.0501067	−	0.0182373i	−0.316845	−	0.948477i	$-0.602624\pi$
$67$	0.410141	−	0.149279i	0.0501067	−	0.0182373i	0.366952	+	0.930240i	$0.380401\pi$
$68$	−5.13122	+	1.86761i	−0.622252	+	0.226481i
$69$	−0.372383	+	2.78544i	−0.0448296	+	0.335328i
$70$	−0.587615	−	3.33253i	−0.0702334	−	0.398314i
$71$	5.21797	−	9.03779i	0.619259	−	1.07259i	−0.370362	−	0.928888i	$-0.620766\pi$
$71$	5.21797	−	9.03779i	0.619259	−	1.07259i	0.989621	−	0.143701i	$-0.0459004\pi$
$72$	−2.98961	+	0.249503i	−0.352329	+	0.0294042i
$73$	2.40066	+	4.15807i	0.280976	+	0.486665i	0.971625	−	0.236525i	$-0.0760085\pi$
$73$	2.40066	+	4.15807i	0.280976	+	0.486665i	−0.690649	+	0.723190i	$0.742675\pi$
$74$	−2.11751	+	1.77680i	−0.246155	+	0.206549i
$75$	−2.39656	−	10.9135i	−0.276731	−	1.26018i
$76$	1.09842	−	6.22947i	0.125998	−	0.714569i
$77$	1.51765	+	1.27346i	0.172953	+	0.145124i
$78$	3.99367	+	6.29658i	0.452194	+	0.712947i
$79$	−3.80215	−	1.38387i	−0.427775	−	0.155698i	0.119155	−	0.992876i	$-0.461982\pi$
$79$	−3.80215	−	1.38387i	−0.427775	−	0.155698i	−0.546930	+	0.837178i	$0.684204\pi$
$80$	3.38394			0.378336
$81$	−5.72971	−	6.94049i	−0.636635	−	0.771165i
$82$	−7.78293			−0.859481
$83$	12.2510	+	4.45900i	1.34472	+	0.489439i	0.911297	−	0.411750i	$-0.135082\pi$
$83$	12.2510	+	4.45900i	1.34472	+	0.489439i	0.433426	+	0.901189i	$0.357304\pi$
$84$	0.927705	+	1.46266i	0.101221	+	0.159589i
$85$	14.1551	+	11.8775i	1.53533	+	1.28830i
$86$	0.0470198	−	0.266663i	0.00507028	−	0.0287550i
$87$	−3.38276	−	15.4045i	−0.362670	−	1.65153i
$88$	−1.51765	+	1.27346i	−0.161782	+	0.135751i
$89$	3.08069	+	5.33591i	0.326553	+	0.565606i	0.981825	−	0.189787i	$-0.0607796\pi$
$89$	3.08069	+	5.33591i	0.326553	+	0.565606i	−0.655273	+	0.755392i	$0.727446\pi$
$90$	5.78951	+	8.33912i	0.610268	+	0.879021i
$91$	2.15245	−	3.72814i	0.225638	−	0.390816i
$92$	0.281741	+	1.59783i	0.0293736	+	0.166586i
$93$	−1.52459	+	11.4040i	−0.158092	+	1.18254i
$94$	5.41423	−	1.97062i	0.558435	−	0.203254i
$95$	−20.1144	+	7.32105i	−2.06370	+	0.751124i
$96$	−1.60153	+	0.659623i	−0.163455	+	0.0673225i
$97$	−1.77416	−	10.0618i	−0.180139	−	1.02162i	−0.932043	−	0.362347i	$-0.881976\pi$
$97$	−1.77416	−	10.0618i	−0.180139	−	1.02162i	0.751904	−	0.659272i	$-0.229136\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−5.73474	−	1.56125i	−0.576363	−	0.156911i
$100$	−3.22552	−	5.58677i	−0.322552	−	0.558677i
$101$	−2.92259	+	2.45235i	−0.290809	+	0.244018i	−0.776506	−	0.630109i	$-0.783010\pi$
$101$	−2.92259	+	2.45235i	−0.290809	+	0.244018i	0.485698	+	0.874127i	$0.338566\pi$
$102$	−9.01446	−	2.86210i	−0.892565	−	0.283390i
$103$	−1.21033	+	6.86413i	−0.119257	+	0.676342i	0.865296	+	0.501260i	$0.167130\pi$
$103$	−1.21033	+	6.86413i	−0.119257	+	0.676342i	−0.984554	+	0.175082i	$0.943981\pi$
$104$	3.29774	+	2.76713i	0.323370	+	0.271339i
$105$	2.71678	−	5.19348i	0.265131	−	0.506832i
$106$	−11.6078	−	4.22491i	−1.12745	−	0.410359i
$107$	−18.3385			−1.77285			−0.886423	−	0.462876i	$-0.846817\pi$
$107$	−18.3385			−1.77285			−0.886423	+	0.462876i	$0.846817\pi$
$108$	−4.36555	−	2.81815i	−0.420075	−	0.271177i
$109$	6.65667			0.637594			0.318797	−	0.947823i	$-0.396721\pi$
$109$	6.65667			0.637594			0.318797	+	0.947823i	$0.396721\pi$
$110$	6.29980	+	2.29294i	0.600662	+	0.218623i
$111$	−4.78360	+	0.199266i	−0.454039	+	0.0189135i
$112$	0.766044	+	0.642788i	0.0723844	+	0.0607377i
$113$	−3.01768	+	17.1141i	−0.283879	+	1.60996i	0.425382	+	0.905014i	$0.360140\pi$
$113$	−3.01768	+	17.1141i	−0.283879	+	1.60996i	−0.709261	+	0.704946i	$0.750971\pi$
$114$	8.09255	−	7.38572i	0.757937	−	0.691736i
$115$	4.20588	−	3.52915i	0.392200	−	0.329095i
$116$	−4.55284	−	7.88576i	−0.422721	−	0.732174i
$117$	−1.17707	+	12.8609i	−0.108820	+	1.18899i
$118$	5.22657	−	9.05268i	0.481145	−	0.833367i
$119$	0.948211	+	5.37757i	0.0869224	+	0.492961i
$120$	4.64282	+	3.57734i	0.423829	+	0.326565i
$121$	6.64835	−	2.41980i	0.604395	−	0.219982i
$122$	1.84286	−	0.670748i	0.166845	−	0.0607267i
$123$	−10.6783	−	8.22775i	−0.962830	−	0.741871i
$124$	1.15349	+	6.54175i	0.103586	+	0.587466i
$125$	−2.45513	+	4.25241i	−0.219594	+	0.380347i
$126$	−0.273427	+	2.98751i	−0.0243588	+	0.266149i
$127$	8.11901	+	14.0625i	0.720445	+	1.24785i	0.960821	+	0.277168i	$0.0893959\pi$
$127$	8.11901	+	14.0625i	0.720445	+	1.24785i	−0.240376	+	0.970680i	$0.577271\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	0.346415	−	0.316158i	0.0305002	−	0.0278362i
$130$	2.52962	−	14.3462i	0.221862	−	1.25824i
$131$	6.08371	+	5.10484i	0.531537	+	0.446012i	0.868632	−	0.495458i	$-0.165000\pi$
$131$	6.08371	+	5.10484i	0.531537	+	0.446012i	−0.337095	+	0.941471i	$0.609444\pi$
$132$	−3.42849	+	0.142817i	−0.298412	+	0.0124306i
$133$	−5.94409	−	2.16347i	−0.515418	−	0.187597i
$134$	0.436463			0.0377046
$135$	−0.872433	+	17.5618i	−0.0750870	+	1.51148i
$136$	−5.46053			−0.468237
$137$	8.79167	+	3.19991i	0.751123	+	0.273387i	0.689078	−	0.724687i	$-0.258016\pi$
$137$	8.79167	+	3.19991i	0.751123	+	0.273387i	0.0620450	+	0.998073i	$0.480238\pi$
$138$	−1.30260	+	2.49010i	−0.110885	+	0.211971i
$139$	−3.07463	−	2.57992i	−0.260787	−	0.218826i	0.503014	−	0.864278i	$-0.332224\pi$
$139$	−3.07463	−	2.57992i	−0.260787	−	0.218826i	−0.763801	+	0.645452i	$0.776669\pi$
$140$	0.587615	−	3.33253i	0.0496625	−	0.281650i
$141$	9.51165	+	3.01995i	0.801025	+	0.254326i
$142$	7.99440	−	6.70810i	0.670875	−	0.562931i
$143$	4.26433	+	7.38603i	0.356601	+	0.617651i
$144$	−2.89465	−	0.788049i	−0.241221	−	0.0656708i
$145$	−15.4065	+	26.6849i	−1.27944	+	2.21606i
$146$	0.833741	+	4.72838i	0.0690009	+	0.391324i
$147$	1.60153	−	0.659623i	0.132092	−	0.0544048i
$148$	−2.59751	+	0.945415i	−0.213514	+	0.0777127i
$149$	−8.51986	+	3.10097i	−0.697974	+	0.254042i	−0.666546	−	0.745464i	$-0.732228\pi$
$149$	−8.51986	+	3.10097i	−0.697974	+	0.254042i	−0.0314282	+	0.999506i	$0.510006\pi$
$150$	1.48061	−	11.0750i	0.120891	−	0.904271i
$151$	−1.49949	−	8.50403i	−0.122027	−	0.692048i	−0.983029	−	0.183448i	$-0.941274\pi$
$151$	−1.49949	−	8.50403i	−0.122027	−	0.692048i	0.861003	−	0.508601i	$-0.169837\pi$
$152$	3.16278	−	5.47810i	0.256536	−	0.444333i
$153$	−9.34231	−	13.4565i	−0.755281	−	1.08789i
$154$	0.990577	+	1.71573i	0.0798230	+	0.138257i
$155$	17.2194	−	14.4488i	1.38310	−	1.16056i
$156$	1.59926	+	7.28276i	0.128044	+	0.583087i
$157$	4.21615	−	23.9109i	0.336485	−	1.90830i	−0.0755663	−	0.997141i	$-0.524076\pi$
$157$	4.21615	−	23.9109i	0.336485	−	1.90830i	0.412051	−	0.911161i	$-0.364812\pi$
$158$	−3.09954	−	2.60082i	−0.246586	−	0.206911i
$159$	−11.4598	−	18.0679i	−0.908818	−	1.43288i
$160$	3.17986	+	1.15738i	0.251390	+	0.0914986i
$161$	1.62248			0.127870
$162$	−3.01038	−	8.48160i	−0.236518	−	0.666378i
$163$	3.37355			0.264237			0.132118	−	0.991234i	$-0.457822\pi$
$163$	3.37355			0.264237			0.132118	+	0.991234i	$0.457822\pi$
$164$	−7.31356	−	2.66192i	−0.571093	−	0.207861i
$165$	6.21943	+	9.80581i	0.484182	+	0.763381i
$166$	9.98712	+	8.38019i	0.775151	+	0.650429i
$167$	0.968264	−	5.49130i	0.0749265	−	0.424929i	−0.924153	−	0.382023i	$-0.875227\pi$
$167$	0.968264	−	5.49130i	0.0749265	−	0.424929i	0.999079	−	0.0429058i	$-0.0136615\pi$
$168$	0.371500	+	1.69174i	0.0286618	+	0.130521i
$169$	4.23782	−	3.55595i	0.325986	−	0.273535i
$170$	9.23905	+	16.0025i	0.708603	+	1.22734i
$171$	18.9110	−	1.57825i	1.44616	−	0.120692i
$172$	0.135388	−	0.234499i	0.0103233	−	0.0178804i
$173$	−1.72619	−	9.78968i	−0.131239	−	0.744296i	−0.977405	−	0.211376i	$-0.932206\pi$
$173$	−1.72619	−	9.78968i	−0.131239	−	0.744296i	0.846165	−	0.532920i	$-0.178905\pi$
$174$	2.08988	−	15.6324i	0.158434	−	1.18509i
$175$	−6.06200	+	2.20639i	−0.458244	+	0.166787i
$176$	−1.86168	+	0.677595i	−0.140329	+	0.0510756i
$177$	16.7410	−	6.89513i	1.25833	−	0.518270i
$178$	1.06991	+	6.06778i	0.0801934	+	0.454799i
$179$	−2.65986	+	4.60702i	−0.198807	+	0.344345i	−0.948142	−	0.317847i	$-0.897040\pi$
$179$	−2.65986	+	4.60702i	−0.198807	+	0.344345i	0.749335	+	0.662192i	$0.230374\pi$
$180$	2.58821	+	9.81634i	0.192914	+	0.731667i
$181$	9.89022	+	17.1304i	0.735134	+	1.27329i	0.954665	+	0.297684i	$0.0962141\pi$
$181$	9.89022	+	17.1304i	0.735134	+	1.27329i	−0.219531	+	0.975606i	$0.570453\pi$
$182$	3.29774	−	2.76713i	0.244445	−	0.205113i
$183$	3.23752	+	1.02791i	0.239325	+	0.0759856i
$184$	−0.281741	+	1.59783i	−0.0207702	+	0.117794i
$185$	7.16552	+	6.01258i	0.526819	+	0.442054i
$186$	−5.33303	+	10.1948i	−0.391037	+	0.747518i
$187$	−10.1657	−	3.70003i	−0.743393	−	0.270573i
$188$	5.76170			0.420215
$189$	−3.53341	+	3.80986i	−0.257018	+	0.277127i
$190$	−21.4053			−1.55291
$191$	−0.579723	−	0.211002i	−0.0419473	−	0.0152676i	0.320961	−	0.947092i	$-0.395994\pi$
$191$	−0.579723	−	0.211002i	−0.0419473	−	0.0152676i	−0.362909	+	0.931825i	$0.618216\pi$
$192$	−1.73055	+	0.0720879i	−0.124892	+	0.00520249i
$193$	11.1934	+	9.39241i	0.805721	+	0.676080i	0.949582	−	0.313518i	$-0.101507\pi$
$193$	11.1934	+	9.39241i	0.805721	+	0.676080i	−0.143861	+	0.989598i	$0.545952\pi$
$194$	1.77416	−	10.0618i	0.127378	−	0.722394i
$195$	18.6368	−	17.0090i	1.33461	−	1.21804i
$196$	0.766044	−	0.642788i	0.0547175	−	0.0459134i
$197$	3.55506	+	6.15754i	0.253287	+	0.438707i	0.964429	−	0.264342i	$-0.0851548\pi$
$197$	3.55506	+	6.15754i	0.253287	+	0.438707i	−0.711141	+	0.703049i	$0.751821\pi$
$198$	−4.85492	−	3.42849i	−0.345024	−	0.243652i
$199$	−9.98547	+	17.2953i	−0.707851	+	1.22603i	0.257801	+	0.966198i	$0.417002\pi$
$199$	−9.98547	+	17.2953i	−0.707851	+	1.22603i	−0.965653	+	0.259836i	$0.916331\pi$
$200$	−1.12021	−	6.35304i	−0.0792110	−	0.449228i
$201$	0.598833	+	0.461408i	0.0422384	+	0.0325452i
$202$	−3.58509	+	1.30487i	−0.252246	+	0.0918101i
$203$	−8.55655	+	3.11433i	−0.600552	+	0.218583i
$204$	−7.49193	−	5.77262i	−0.524540	−	0.404164i
$205$	4.57337	+	25.9368i	0.319418	+	1.81151i
$206$	−3.48501	+	6.03621i	−0.242812	+	0.420563i
$207$	−4.41961	+	2.03940i	−0.307184	+	0.141748i
$208$	2.15245	+	3.72814i	0.149245	+	0.258500i
$209$	9.60001	−	8.05537i	0.664047	−	0.557201i
$210$	4.32921	−	3.95108i	0.298744	−	0.272651i
$211$	−1.02502	+	5.81318i	−0.0705653	+	0.400196i	0.928982	+	0.370124i	$0.120685\pi$
$211$	−1.02502	+	5.81318i	−0.0705653	+	0.400196i	−0.999548	+	0.0300719i	$0.990426\pi$
$212$	−9.46280	−	7.94023i	−0.649908	−	0.545337i
$213$	18.0599	−	0.752305i	1.23745	−	0.0515471i
$214$	−17.2325	−	6.27212i	−1.17799	−	0.428753i
$215$	−0.916291			−0.0624905
$216$	−3.13841	−	4.14130i	−0.213542	−	0.281780i
$217$	6.64266			0.450933
$218$	6.25523	+	2.27672i	0.423657	+	0.154199i
$219$	−3.85472	+	7.36880i	−0.260478	+	0.497938i
$220$	5.13565	+	4.30932i	0.346245	+	0.290534i
$221$	−4.08194	+	23.1499i	−0.274581	+	1.55723i
$222$	−4.56327	−	1.44884i	−0.306267	−	0.0972397i
$223$	17.5470	−	14.7237i	1.17504	−	0.985972i	0.175036	−	0.984562i	$-0.443996\pi$
$223$	17.5470	−	14.7237i	1.17504	−	0.985972i	0.999999	−	0.00140971i	$-0.000448724\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	13.7394	−	13.6299i	0.915960	−	0.908657i
$226$	−8.68906	+	15.0499i	−0.577988	+	1.00110i
$227$	−0.681543	−	3.86522i	−0.0452356	−	0.256544i	0.953800	−	0.300441i	$-0.0971338\pi$
$227$	−0.681543	−	3.86522i	−0.0452356	−	0.256544i	−0.999036	+	0.0438969i	$0.986023\pi$
$228$	10.1306	−	4.17249i	0.670914	−	0.276330i
$229$	−17.5617	+	6.39194i	−1.16051	+	0.422391i	−0.849279	−	0.527944i	$-0.822963\pi$
$229$	−17.5617	+	6.39194i	−1.16051	+	0.422391i	−0.311230	+	0.950335i	$0.600741\pi$
$230$	5.15927	−	1.87782i	0.340193	−	0.123820i
$231$	−0.454703	+	3.40120i	−0.0299173	+	0.223783i
$232$	−1.58119	−	8.96735i	−0.103810	−	0.588736i
$233$	7.66093	−	13.2691i	0.501884	−	0.869289i	−0.498113	−	0.867112i	$-0.665974\pi$
$233$	7.66093	−	13.2691i	0.501884	−	0.869289i	0.999998	−	0.00217730i	$-0.000693057\pi$
$234$	−5.50478	+	11.6827i	−0.359859	+	0.763724i
$235$	−9.74863	−	16.8851i	−0.635930	−	1.10146i
$236$	8.00757	−	6.71915i	0.521248	−	0.437379i
$237$	−1.50315	−	6.84506i	−0.0976400	−	0.444635i
$238$	−0.948211	+	5.37757i	−0.0614634	+	0.348576i
$239$	5.30830	+	4.45419i	0.343365	+	0.288118i	0.798119	−	0.602499i	$-0.205828\pi$
$239$	5.30830	+	4.45419i	0.343365	+	0.288118i	−0.454754	+	0.890617i	$0.650273\pi$
$240$	3.13930	+	4.94954i	0.202641	+	0.319491i
$241$	−16.4977	−	6.00468i	−1.06271	−	0.386796i	−0.249265	−	0.968435i	$-0.580189\pi$
$241$	−16.4977	−	6.00468i	−1.06271	−	0.386796i	−0.813447	+	0.581640i	$0.802411\pi$
$242$	7.07503			0.454800
$243$	4.83607	−	14.8193i	0.310234	−	0.950660i
$244$	1.96114			0.125549
$245$	−3.17986	−	1.15738i	−0.203154	−	0.0739420i
$246$	−7.22026	−	11.3838i	−0.460347	−	0.725801i
$247$	−20.8601	−	17.5037i	−1.32729	−	1.11373i
$248$	−1.15349	+	6.54175i	−0.0732465	+	0.415401i
$249$	4.84333	+	22.0557i	0.306934	+	1.39772i
$250$	−3.76148	+	3.15625i	−0.237897	+	0.199619i
$251$	13.3992	+	23.2081i	0.845751	+	1.46488i	0.884968	+	0.465652i	$0.154180\pi$
$251$	13.3992	+	23.2081i	0.845751	+	1.46488i	−0.0392171	+	0.999231i	$0.512486\pi$
$252$	−1.27873	+	2.71383i	−0.0805522	+	0.170955i
$253$	−1.60720	+	2.78374i	−0.101044	+	0.175012i
$254$	2.81970	+	15.9913i	0.176924	+	1.00338i
$255$	−4.24099	+	31.7228i	−0.265581	+	1.98656i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	4.05775	−	1.47690i	0.253115	−	0.0921264i	−0.212346	−	0.977194i	$-0.568111\pi$
$257$	4.05775	−	1.47690i	0.253115	−	0.0921264i	0.465462	+	0.885068i	$0.345888\pi$
$258$	0.433656	−	0.178610i	0.0269983	−	0.0111198i
$259$	0.480000	+	2.72221i	0.0298257	+	0.169150i
$260$	7.28374	−	12.6158i	0.451719	−	0.782400i
$261$	19.3932	−	19.2386i	1.20041	−	1.19084i
$262$	3.97086	+	6.87774i	0.245321	+	0.424908i
$263$	−2.05459	+	1.72401i	−0.126692	+	0.106307i	−0.703932	−	0.710267i	$-0.748574\pi$
$263$	−2.05459	+	1.72401i	−0.126692	+	0.106307i	0.577240	+	0.816574i	$0.304130\pi$
$264$	−3.27057	−	1.03841i	−0.201290	−	0.0639096i
$265$	−7.25869	+	41.1661i	−0.445898	+	2.52881i
$266$	−4.84566	−	4.06599i	−0.297107	−	0.249302i
$267$	−4.94664	+	9.45615i	−0.302729	+	0.578707i
$268$	0.410141	+	0.149279i	0.0250533	+	0.00911867i
$269$	19.3294			1.17853			0.589267	−	0.807938i	$-0.299417\pi$
$269$	19.3294			1.17853			0.589267	+	0.807938i	$0.299417\pi$
$270$	−6.82631	+	16.2043i	−0.415436	+	0.986163i
$271$	2.06153			0.125229			0.0626146	−	0.998038i	$-0.480056\pi$
$271$	2.06153			0.125229			0.0626146	+	0.998038i	$0.480056\pi$
$272$	−5.13122	−	1.86761i	−0.311126	−	0.113241i
$273$	7.44983	−	0.310330i	0.450884	−	0.0187820i
$274$	7.16704	+	6.01386i	0.432977	+	0.363310i
$275$	2.21931	−	12.5864i	0.133830	−	0.758986i
$276$	−2.07571	+	1.89441i	−0.124943	+	0.114030i
$277$	12.9176	−	10.8391i	0.776143	−	0.651261i	−0.166131	−	0.986104i	$-0.553128\pi$
$277$	12.9176	−	10.8391i	0.776143	−	0.651261i	0.942274	+	0.334842i	$0.108683\pi$
$278$	−2.00682	−	3.47592i	−0.120361	−	0.208472i
$279$	−18.0945	+	8.34958i	−1.08329	+	0.499876i
$280$	1.69197	−	2.93058i	0.101115	−	0.175136i
$281$	0.278502	+	1.57947i	0.0166141	+	0.0942230i	0.991987	−	0.126338i	$-0.0403223\pi$
$281$	0.278502	+	1.57947i	0.0166141	+	0.0942230i	−0.975373	+	0.220561i	$0.929211\pi$
$282$	7.90514	+	6.09100i	0.470744	+	0.362714i
$283$	18.0013	−	6.55195i	1.07007	−	0.389473i	0.253867	−	0.967239i	$-0.418298\pi$
$283$	18.0013	−	6.55195i	1.07007	−	0.389473i	0.816202	+	0.577766i	$0.196075\pi$
$284$	9.80658	−	3.56930i	0.581914	−	0.211799i
$285$	−29.3684	−	22.6287i	−1.73964	−	1.34041i
$286$	1.48099	+	8.39908i	0.0875725	+	0.496648i
$287$	−3.89146	+	6.74021i	−0.229706	+	0.397862i
$288$	−2.45055	−	1.73055i	−0.144400	−	0.101974i
$289$	−6.40870	−	11.1002i	−0.376982	−	0.652952i
$290$	−23.6042	+	19.8063i	−1.38609	+	1.16306i
$291$	13.0710	−	11.9294i	0.766237	−	0.699311i
$292$	−0.833741	+	4.72838i	−0.0487910	+	0.276708i
$293$	−9.63613	−	8.08567i	−0.562949	−	0.472370i	0.316349	−	0.948643i	$-0.397543\pi$
$293$	−9.63613	−	8.08567i	−0.562949	−	0.472370i	−0.879297	+	0.476273i	$0.841987\pi$
$294$	1.73055	−	0.0720879i	0.100928	−	0.00420425i
$295$	−33.2395	−	12.0982i	−1.93528	−	0.704385i
$296$	−2.76421			−0.160666
$297$	−3.03658	−	9.83634i	−0.176200	−	0.570762i
$298$	−9.06664			−0.525216
$299$	6.56339	+	2.38888i	0.379571	+	0.138152i
$300$	5.17919	−	9.90071i	0.299021	−	0.571618i
$301$	−0.207427	−	0.174052i	−0.0119559	−	0.0100322i
$302$	1.49949	−	8.50403i	0.0862860	−	0.489352i
$303$	−6.29824	−	1.99969i	−0.361825	−	0.114879i
$304$	4.84566	−	4.06599i	0.277918	−	0.233201i
$305$	−3.31818	−	5.74726i	−0.189999	−	0.329087i
$306$	−4.17650	−	15.8402i	−0.238755	−	0.905527i
$307$	13.3754	−	23.1669i	0.763375	−	1.32220i	−0.177726	−	0.984080i	$-0.556874\pi$
$307$	13.3754	−	23.1669i	0.763375	−	1.32220i	0.941101	−	0.338124i	$-0.109792\pi$
$308$	0.344024	+	1.95106i	0.0196026	+	0.111172i
$309$	−11.1627	+	4.59759i	−0.635023	+	0.261548i
$310$	21.1228	−	7.68806i	1.19969	−	0.436652i
$311$	23.3655	−	8.50435i	1.32494	−	0.482238i	0.419900	−	0.907571i	$-0.362065\pi$
$311$	23.3655	−	8.50435i	1.32494	−	0.482238i	0.905037	+	0.425333i	$0.139843\pi$
$312$	−0.988033	+	7.39054i	−0.0559364	+	0.418407i
$313$	5.86999	+	33.2903i	0.331791	+	1.88168i	0.456868	+	0.889535i	$0.348971\pi$
$313$	5.86999	+	33.2903i	0.331791	+	1.88168i	−0.125076	+	0.992147i	$0.539918\pi$
$314$	12.1399	−	21.0269i	0.685095	−	1.18662i
$315$	10.1166	−	0.844304i	0.570009	−	0.0475711i
$316$	−2.02308	−	3.50408i	−0.113807	−	0.197120i
$317$	8.38530	−	7.03610i	0.470965	−	0.395187i	−0.376181	−	0.926546i	$-0.622763\pi$
$317$	8.38530	−	7.03610i	0.470965	−	0.395187i	0.847147	+	0.531359i	$0.178319\pi$
$318$	−4.58906	−	20.8978i	−0.257342	−	1.17189i
$319$	3.13257	−	17.7657i	0.175390	−	0.994689i
$320$	2.59225	+	2.17515i	0.144911	+	0.121595i
$321$	−17.0127	−	26.8229i	−0.949555	−	1.49711i
$322$	1.52464	+	0.554922i	0.0849646	+	0.0309246i
$323$	34.5409			1.92191
$324$	0.0720447	−	8.99971i	0.00400248	−	0.499984i
$325$	−27.7711			−1.54046
$326$	3.17010	+	1.15382i	0.175575	+	0.0639042i
$327$	6.17543	+	9.73643i	0.341502	+	0.538426i
$328$	−5.96207	−	5.00277i	−0.329200	−	0.276232i
$329$	1.00051	−	5.67417i	0.0551598	−	0.312827i
$330$	2.49057	+	11.3416i	0.137102	+	0.624335i
$331$	−7.48986	+	6.28474i	−0.411680	+	0.345440i	−0.824987	−	0.565151i	$-0.808818\pi$
$331$	−7.48986	+	6.28474i	−0.411680	+	0.345440i	0.413308	+	0.910591i	$0.364373\pi$
$332$	6.51863	+	11.2906i	0.357756	+	0.619652i
$333$	−4.72923	−	6.81191i	−0.259160	−	0.373290i
$334$	2.78800	−	4.82897i	0.152553	−	0.264229i
$335$	−0.256472	−	1.45452i	−0.0140126	−	0.0794692i
$336$	−0.229514	+	1.71678i	−0.0125210	+	0.0936579i
$337$	−23.3251	+	8.48965i	−1.27060	+	0.462461i	−0.887313	−	0.461168i	$-0.847430\pi$
$337$	−23.3251	+	8.48965i	−1.27060	+	0.462461i	−0.383288	+	0.923629i	$0.625208\pi$
$338$	5.19846	−	1.89208i	0.282759	−	0.102916i
$339$	−27.8316	+	11.4630i	−1.51160	+	0.622585i
$340$	3.20869	+	18.1974i	0.174016	+	0.986892i
$341$	−6.58007	+	11.3970i	−0.356331	+	0.617183i
$342$	18.3103	+	4.98486i	0.990106	+	0.269550i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	0.207427	−	0.174052i	0.0111837	−	0.00938424i
$345$	9.06375	+	2.87774i	0.487976	+	0.154933i
$346$	1.72619	−	9.78968i	0.0928003	−	0.526297i
$347$	−7.20623	−	6.04674i	−0.386851	−	0.324606i	0.428534	−	0.903526i	$-0.359030\pi$
$347$	−7.20623	−	6.04674i	−0.386851	−	0.324606i	−0.815385	+	0.578919i	$0.803475\pi$
$348$	7.31046	−	13.9749i	0.391882	−	0.749133i
$349$	−19.3943	−	7.05893i	−1.03815	−	0.377856i	−0.233972	−	0.972243i	$-0.575172\pi$
$349$	−19.3943	−	7.05893i	−1.03815	−	0.377856i	−0.804179	+	0.594388i	$0.797395\pi$
$350$	−6.45105			−0.344823
$351$	−19.9031	+	10.2095i	−1.06235	+	0.544942i
$352$	−1.98115			−0.105596
$353$	−32.7719	−	11.9280i	−1.74427	−	0.634863i	−0.744798	−	0.667290i	$-0.767454\pi$
$353$	−32.7719	−	11.9280i	−1.74427	−	0.634863i	−0.999474	+	0.0324266i	$0.989676\pi$
$354$	18.0897	−	0.753544i	0.961455	−	0.0400504i
$355$	−27.0526	−	22.6998i	−1.43580	−	1.20478i
$356$	−1.06991	+	6.06778i	−0.0567053	+	0.321592i
$357$	−6.98588	+	6.37571i	−0.369732	+	0.337438i
$358$	−4.07515	+	3.41945i	−0.215378	+	0.180724i
$359$	13.3701	+	23.1577i	0.705646	+	1.22221i	0.966458	+	0.256825i	$0.0826764\pi$
$359$	13.3701	+	23.1577i	0.705646	+	1.22221i	−0.260812	+	0.965390i	$0.583990\pi$
$360$	−0.925260	+	10.1096i	−0.0487655	+	0.532821i
$361$	−10.5064	+	18.1976i	−0.552968	+	0.957768i
$362$	3.43484	+	19.4799i	0.180531	+	1.02384i
$363$	9.70704	+	7.47939i	0.509488	+	0.392566i
$364$	4.04527	−	1.47236i	0.212030	−	0.0771726i
$365$	15.2676	−	5.55693i	0.799140	−	0.290863i
$366$	2.69071	+	2.07322i	0.140646	+	0.108369i
$367$	−3.98417	−	22.5954i	−0.207972	−	1.17947i	−0.892694	−	0.450664i	$-0.851187\pi$
$367$	−3.98417	−	22.5954i	−0.207972	−	1.17947i	0.684722	−	0.728804i	$-0.259924\pi$
$368$	−0.811242	+	1.40511i	−0.0422889	+	0.0732465i
$369$	2.12806	−	23.2516i	0.110783	−	1.21043i
$370$	4.67696	+	8.10073i	0.243144	+	0.421137i
$371$	−9.46280	+	7.94023i	−0.491284	+	0.412236i
$372$	−8.49823	+	7.75597i	−0.440613	+	0.402128i
$373$	2.36691	−	13.4234i	0.122554	−	0.695038i	−0.860177	−	0.509996i	$-0.829647\pi$
$373$	2.36691	−	13.4234i	0.122554	−	0.695038i	0.982731	−	0.185042i	$-0.0592421\pi$
$374$	−8.28719	−	6.95378i	−0.428520	−	0.359571i
$375$	−8.49745	+	0.353970i	−0.438807	+	0.0182789i
$376$	5.41423	+	1.97062i	0.279217	+	0.101627i
$377$	−39.1990			−2.01885
$378$	−4.62337	+	2.37160i	−0.237800	+	0.121982i
$379$	36.9410			1.89753			0.948767	−	0.315977i	$-0.102332\pi$
$379$	36.9410			1.89753			0.948767	+	0.315977i	$0.102332\pi$
$380$	−20.1144	−	7.32105i	−1.03185	−	0.375562i
$381$	−13.0366	+	24.9212i	−0.667886	+	1.27675i
$382$	−0.472595	−	0.396554i	−0.0241801	−	0.0202895i
$383$	2.31489	−	13.1284i	0.118285	−	0.670830i	−0.866786	−	0.498681i	$-0.833818\pi$
$383$	2.31489	−	13.1284i	0.118285	−	0.670830i	0.985071	−	0.172149i	$-0.0550710\pi$
$384$	−1.65084	−	0.524143i	−0.0842441	−	0.0267475i
$385$	5.13565	−	4.30932i	0.261737	−	0.219623i
$386$	7.30600	+	12.6544i	0.371865	+	0.644090i
$387$	0.783802	+	0.213385i	0.0398429	+	0.0108470i
$388$	5.10850	−	8.84818i	0.259345	−	0.449198i
$389$	−0.269050	−	1.52586i	−0.0136414	−	0.0773641i	0.977227	−	0.212196i	$-0.0680616\pi$
$389$	−0.269050	−	1.52586i	−0.0136414	−	0.0773641i	−0.990868	+	0.134832i	$0.956950\pi$
$390$	23.3303	−	9.60906i	1.18137	−	0.486574i
$391$	−8.32532	+	3.03017i	−0.421029	+	0.153242i
$392$	0.939693	−	0.342020i	0.0474616	−	0.0172746i
$393$	−1.82274	+	13.6342i	−0.0919450	+	0.687753i
$394$	1.23466	+	7.00210i	0.0622012	+	0.352761i
$395$	−6.84599	+	11.8576i	−0.344459	+	0.596621i
$396$	−3.38952	−	4.88221i	−0.170330	−	0.245340i
$397$	8.85671	+	15.3403i	0.444506	+	0.769906i	0.998018	−	0.0629350i	$-0.0200461\pi$
$397$	8.85671	+	15.3403i	0.444506	+	0.769906i	−0.553512	+	0.832841i	$0.686713\pi$
$398$	−15.2986	+	12.8371i	−0.766851	+	0.643464i
$399$	−2.34994	−	10.7012i	−0.117644	−	0.535731i
$400$	1.12021	−	6.35304i	0.0560106	−	0.317652i
$401$	0.816316	+	0.684971i	0.0407649	+	0.0342058i	0.662942	−	0.748670i	$-0.269307\pi$
$401$	0.816316	+	0.684971i	0.0407649	+	0.0342058i	−0.622178	+	0.782876i	$0.713752\pi$
$402$	0.404908	+	0.638395i	0.0201950	+	0.0318402i
$403$	26.8714	+	9.78039i	1.33856	+	0.487196i
$404$	−3.81517			−0.189812
$405$	−26.4963	+	15.0161i	−1.31661	+	0.746156i
$406$	−9.10569			−0.451908
$407$	−5.14606	−	1.87301i	−0.255081	−	0.0928419i
$408$	−5.06576	−	7.98688i	−0.250793	−	0.395409i
$409$	−22.3753	−	18.7751i	−1.10639	−	0.928369i	−0.108549	−	0.994091i	$-0.534620\pi$
$409$	−22.3753	−	18.7751i	−1.10639	−	0.928369i	−0.997838	+	0.0657223i	$0.979065\pi$
$410$	−4.57337	+	25.9368i	−0.225862	+	1.28093i
$411$	3.47571	+	15.8278i	0.171444	+	0.780726i
$412$	−5.33934	+	4.48024i	−0.263051	+	0.220726i
$413$	−5.22657	−	9.05268i	−0.257183	−	0.445453i
$414$	−4.85059	+	0.404815i	−0.238393	+	0.0198956i
$415$	22.0586	−	38.2067i	1.08282	−	1.87549i
$416$	0.747536	+	4.23949i	0.0366510	+	0.207858i
$417$	0.921189	−	6.89054i	0.0451108	−	0.337431i
$418$	11.7762	−	4.28617i	0.575991	−	0.209643i
$419$	6.94002	−	2.52596i	0.339042	−	0.123401i	−0.166888	−	0.985976i	$-0.553372\pi$
$419$	6.94002	−	2.52596i	0.339042	−	0.123401i	0.505930	+	0.862575i	$0.331149\pi$
$420$	5.41948	−	2.23213i	0.264444	−	0.108917i
$421$	−2.19564	−	12.4521i	−0.107009	−	0.606879i	−0.990399	−	0.138240i	$-0.955856\pi$
$421$	−2.19564	−	12.4521i	−0.107009	−	0.606879i	0.883390	−	0.468639i	$-0.155256\pi$
$422$	−2.95143	+	5.11202i	−0.143673	+	0.248849i
$423$	4.40685	+	16.7139i	0.214268	+	0.812658i
$424$	−6.17640	−	10.6978i	−0.299953	−	0.519533i
$425$	26.9848	−	22.6429i	1.30895	−	1.09834i
$426$	17.2281	+	5.46992i	0.834703	+	0.265019i
$427$	0.340548	−	1.93134i	0.0164803	−	0.0934642i
$428$	−14.0481	−	11.7877i	−0.679039	−	0.569782i
$429$	−6.84719	+	13.0893i	−0.330585	+	0.631957i
$430$	−0.861032	−	0.313390i	−0.0415227	−	0.0151130i
$431$	2.88270			0.138855			0.0694273	−	0.997587i	$-0.477883\pi$
$431$	2.88270			0.138855			0.0694273	+	0.997587i	$0.477883\pi$
$432$	−1.53273	−	4.96495i	−0.0737436	−	0.238876i
$433$	−18.2648			−0.877752			−0.438876	−	0.898548i	$-0.644623\pi$
$433$	−18.2648			−0.877752			−0.438876	+	0.898548i	$0.644623\pi$
$434$	6.24206	+	2.27193i	0.299629	+	0.109056i
$435$	−53.3236	+	2.22125i	−2.55667	+	0.106501i
$436$	5.09931	+	4.27883i	0.244213	+	0.204919i
$437$	1.78217	−	10.1072i	0.0852529	−	0.483493i
$438$	−6.14253	+	5.60602i	−0.293501	+	0.267866i
$439$	−21.0807	+	17.6888i	−1.00613	+	0.844240i	−0.987821	−	0.155593i	$-0.950271\pi$
$439$	−21.0807	+	17.6888i	−1.00613	+	0.844240i	−0.0183042	+	0.999832i	$0.505827\pi$
$440$	3.35205	+	5.80593i	0.159803	+	0.276787i
$441$	2.45055	+	1.73055i	0.116693	+	0.0824072i
$442$	−11.7535	+	20.3576i	−0.559057	+	0.968314i
$443$	−1.75024	−	9.92609i	−0.0831563	−	0.471603i	−0.997739	−	0.0672045i	$-0.978592\pi$
$443$	−1.75024	−	9.92609i	−0.0831563	−	0.471603i	0.914583	−	0.404398i	$-0.132519\pi$
$444$	−3.79254	−	2.92219i	−0.179986	−	0.138681i
$445$	19.5924	−	7.13103i	0.928767	−	0.338043i
$446$	21.5246	−	7.83432i	1.01922	−	0.370966i
$447$	−12.4396	−	9.58483i	−0.588371	−	0.453347i
$448$	0.173648	+	0.984808i	0.00820411	+	0.0465278i
$449$	12.0738	−	20.9124i	0.569798	−	0.986919i	−0.426787	−	0.904352i	$-0.640355\pi$
$449$	12.0738	−	20.9124i	0.569798	−	0.986919i	0.996586	−	0.0825672i	$-0.0263119\pi$
$450$	17.5725	−	8.10872i	0.828376	−	0.382249i
$451$	−7.70959	−	13.3534i	−0.363031	−	0.628787i
$452$	−13.3124	+	11.1704i	−0.626163	+	0.525413i
$453$	11.0474	−	10.0825i	0.519052	−	0.473716i
$454$	0.681543	−	3.86522i	0.0319864	−	0.181404i
$455$	−11.1593	−	9.36380i	−0.523158	−	0.438982i
$456$	10.9467	−	0.455996i	0.512626	−	0.0213540i
$457$	−2.00381	−	0.729327i	−0.0937343	−	0.0341165i	0.294727	−	0.955581i	$-0.404771\pi$
$457$	−2.00381	−	0.729327i	−0.0937343	−	0.0341165i	−0.388462	+	0.921465i	$0.626993\pi$
$458$	−18.6888			−0.873269
$459$	11.0153	−	26.1483i	0.514152	−	1.22050i
$460$	5.49039			0.255991
$461$	11.1663	+	4.06420i	0.520066	+	0.189289i	0.588697	−	0.808354i	$-0.299641\pi$
$461$	11.1663	+	4.06420i	0.520066	+	0.189289i	−0.0686313	+	0.997642i	$0.521863\pi$
$462$	−1.59056	+	3.04057i	−0.0739996	+	0.141460i
$463$	14.4351	+	12.1125i	0.670856	+	0.562915i	0.913319	−	0.407246i	$-0.133511\pi$
$463$	14.4351	+	12.1125i	0.670856	+	0.562915i	−0.242463	+	0.970161i	$0.577955\pi$
$464$	1.58119	−	8.96735i	0.0734047	−	0.416299i
$465$	37.1082	+	11.7819i	1.72085	+	0.546371i
$466$	11.7372	−	9.84871i	0.543717	−	0.456232i
$467$	−17.1460	−	29.6977i	−0.793422	−	1.37425i	−0.923837	−	0.382787i	$-0.874964\pi$
$467$	−17.1460	−	29.6977i	−0.793422	−	1.37425i	0.130415	−	0.991459i	$-0.458369\pi$
$468$	−9.16853	+	9.09543i	−0.423815	+	0.420436i
$469$	0.218231	−	0.377988i	0.0100770	−	0.0174538i
$470$	−3.38566	−	19.2010i	−0.156169	−	0.885678i
$471$	38.8848	−	16.0155i	1.79172	−	0.737957i
$472$	9.82273	−	3.57518i	0.452128	−	0.164561i
$473$	0.504098	−	0.183477i	0.0231785	−	0.00843627i
$474$	0.928652	−	6.94636i	0.0426544	−	0.319057i
$475$	7.08598	+	40.1866i	0.325127	+	1.84389i
$476$	−2.73027	+	4.72896i	−0.125141	+	0.216751i
$477$	15.7959	−	33.5234i	0.723243	−	1.53493i
$478$	3.46475	+	6.00112i	0.158474	+	0.274485i
$479$	−6.86328	+	5.75897i	−0.313591	+	0.263134i	−0.785974	−	0.618259i	$-0.787838\pi$
$479$	−6.86328	+	5.75897i	−0.313591	+	0.263134i	0.472383	+	0.881393i	$0.343394\pi$
$480$	1.25713	+	5.72475i	0.0573800	+	0.261298i
$481$	−2.06635	+	11.7188i	−0.0942173	+	0.534333i
$482$	−13.4491	−	11.2851i	−0.612588	−	0.514023i
$483$	1.50519	+	2.37314i	0.0684883	+	0.107981i
$484$	6.64835	+	2.41980i	0.302198	+	0.109991i
$485$	−34.5737			−1.56991
$486$	9.61292	−	12.2716i	0.436051	−	0.556650i
$487$	−9.14881			−0.414572			−0.207286	−	0.978280i	$-0.566463\pi$
$487$	−9.14881			−0.414572			−0.207286	+	0.978280i	$0.566463\pi$
$488$	1.84286	+	0.670748i	0.0834226	+	0.0303633i
$489$	3.12966	+	4.93434i	0.141528	+	0.223139i
$490$	−2.59225	−	2.17515i	−0.117106	−	0.0982635i
$491$	−4.57960	+	25.9722i	−0.206674	+	1.17211i	0.688109	+	0.725607i	$0.258441\pi$
$491$	−4.57960	+	25.9722i	−0.206674	+	1.17211i	−0.894783	+	0.446501i	$0.852670\pi$
$492$	−2.89135	−	13.1667i	−0.130352	−	0.593601i
$493$	38.0892	−	31.9606i	1.71545	−	1.43943i
$494$	−13.6154	−	23.5826i	−0.612587	−	1.06103i
$495$	−8.57273	+	18.1938i	−0.385315	+	0.817750i
$496$	−3.32133	+	5.75272i	−0.149132	+	0.258305i
$497$	−1.81218	−	10.2774i	−0.0812875	−	0.461004i
$498$	−2.99224	+	22.3821i	−0.134085	+	1.00296i
$499$	−9.87857	+	3.59551i	−0.442226	+	0.160957i	−0.553530	−	0.832829i	$-0.686719\pi$
$499$	−9.87857	+	3.59551i	−0.442226	+	0.160957i	0.111304	+	0.993786i	$0.464497\pi$
$500$	−4.61414	+	1.67941i	−0.206350	+	0.0751054i
$501$	8.93014	−	3.67807i	0.398969	−	0.164324i
$502$	4.65350	+	26.3913i	0.207696	+	1.17790i
$503$	−5.24672	+	9.08758i	−0.233939	+	0.405195i	−0.958964	−	0.283528i	$-0.908495\pi$
$503$	−5.24672	+	9.08758i	−0.233939	+	0.405195i	0.725024	+	0.688723i	$0.241828\pi$
$504$	−2.12979	+	2.11281i	−0.0948686	+	0.0941122i
$505$	6.45516	+	11.1807i	0.287251	+	0.497533i
$506$	−2.46237	+	2.06617i	−0.109466	+	0.0918525i
$507$	9.13258	+	2.89960i	0.405592	+	0.128776i
$508$	−2.81970	+	15.9913i	−0.125104	+	0.709500i
$509$	3.53055	+	2.96248i	0.156489	+	0.131310i	0.717670	−	0.696383i	$-0.245209\pi$
$509$	3.53055	+	2.96248i	0.156489	+	0.131310i	−0.561181	+	0.827693i	$0.689653\pi$
$510$	−14.8351	+	28.3592i	−0.656907	+	1.25576i
$511$	4.51177	+	1.64215i	0.199589	+	0.0726444i
$512$	−1.00000			−0.0441942
$513$	19.8522	+	26.1961i	0.876497	+	1.15658i
$514$	4.31816			0.190466
$515$	22.1637	+	8.06693i	0.976649	+	0.355471i
$516$	0.468592	−	0.0195197i	0.0206286	−	0.000859307i
$517$	8.74426	+	7.33731i	0.384572	+	0.322694i
$518$	−0.480000	+	2.72221i	−0.0210900	+	0.119607i
$519$	12.7176	−	11.6068i	0.558239	−	0.509480i
$520$	11.1593	−	9.36380i	0.489370	−	0.410630i
$521$	−10.0361	−	17.3831i	−0.439691	−	0.761567i	0.557974	−	0.829858i	$-0.311579\pi$
$521$	−10.0361	−	17.3831i	−0.439691	−	0.761567i	−0.997665	+	0.0682910i	$0.978245\pi$
$522$	24.8037	−	11.4455i	1.08563	−	0.500956i
$523$	7.28693	−	12.6213i	0.318635	−	0.551892i	−0.661568	−	0.749885i	$-0.730109\pi$
$523$	7.28693	−	12.6213i	0.318635	−	0.551892i	0.980203	+	0.197993i	$0.0634422\pi$
$524$	1.37907	+	7.82107i	0.0602448	+	0.341665i
$525$	−8.85094	−	6.81975i	−0.386287	−	0.297638i
$526$	−2.52033	+	0.917325i	−0.109892	+	0.0399973i
$527$	−34.0850	+	12.4059i	−1.48476	+	0.540410i
$528$	−2.71817	−	2.09438i	−0.118293	−	0.0911464i
$529$	−3.53679	−	20.0581i	−0.153773	−	0.872092i
$530$	−20.9006	+	36.2009i	−0.907863	+	1.57247i
$531$	25.6159	+	18.0897i	1.11164	+	0.785026i
$532$	−3.16278	−	5.47810i	−0.137124	−	0.237506i
$533$	−25.6661	+	21.5364i	−1.11172	+	0.932844i
$534$	−7.88251	+	7.19402i	−0.341110	+	0.311316i
$535$	−10.7760	+	61.1135i	−0.465885	+	2.64217i
$536$	0.334350	+	0.280553i	0.0144417	+	0.0121180i
$537$	−9.20605	+	0.383488i	−0.397270	+	0.0165487i
$538$	18.1637	+	6.61105i	0.783093	+	0.285022i
$539$	1.98115			0.0853344
$540$	−11.9568	+	12.8923i	−0.514540	+	0.554798i
$541$	17.9461			0.771564			0.385782	−	0.922590i	$-0.373932\pi$
$541$	17.9461			0.771564			0.385782	+	0.922590i	$0.373932\pi$
$542$	1.93721	+	0.705086i	0.0832102	+	0.0302860i
$543$	−15.8806	+	30.3579i	−0.681503	+	1.30278i
$544$	−4.18301	−	3.50996i	−0.179345	−	0.150488i
$545$	3.91156	−	22.1836i	0.167553	−	0.950240i
$546$	7.10669	+	2.25638i	0.304138	+	0.0965640i
$547$	12.4347	−	10.4340i	0.531670	−	0.446124i	−0.337007	−	0.941502i	$-0.609415\pi$
$547$	12.4347	−	10.4340i	0.531670	−	0.446124i	0.868678	+	0.495378i	$0.164970\pi$
$548$	4.67795	+	8.10245i	0.199832	+	0.346120i
$549$	1.49998	+	5.68898i	0.0640176	+	0.242800i
$550$	6.39026	−	11.0683i	0.272482	−	0.471952i
$551$	10.0019	+	56.7236i	0.426095	+	2.41651i
$552$	−2.59845	+	1.07023i	−0.110598	+	0.0455519i
$553$	−3.80215	+	1.38387i	−0.161684	+	0.0588481i
$554$	15.8458	−	5.76739i	0.673222	−	0.245033i
$555$	−2.14686	+	16.0586i	−0.0911290	+	0.681649i
$556$	−0.696962	−	3.95267i	−0.0295578	−	0.167631i
$557$	8.99833	−	15.5856i	0.381272	−	0.660382i	−0.609973	−	0.792422i	$-0.708820\pi$
$557$	8.99833	−	15.5856i	0.381272	−	0.660382i	0.991244	+	0.132041i	$0.0421529\pi$
$558$	−19.8590	+	1.65737i	−0.840697	+	0.0701619i
$559$	−0.582831	−	1.00949i	−0.0246511	−	0.0426970i
$560$	2.59225	−	2.17515i	0.109542	−	0.0919171i
$561$	−4.01894	−	18.3015i	−0.169680	−	0.772691i
$562$	−0.278502	+	1.57947i	−0.0117479	+	0.0666257i
$563$	8.71844	+	7.31564i	0.367439	+	0.308318i	0.807747	−	0.589529i	$-0.200687\pi$
$563$	8.71844	+	7.31564i	0.367439	+	0.308318i	−0.440309	+	0.897846i	$0.645131\pi$
$564$	5.34516	+	8.42739i	0.225072	+	0.354857i
$565$	55.2600	+	20.1130i	2.32481	+	0.846161i
$566$	19.1566			0.805213
$567$	−8.85048	−	1.63373i	−0.371685	−	0.0686104i
$568$	10.4359			0.437883
$569$	15.3559	+	5.58907i	0.643751	+	0.234306i	0.643205	−	0.765694i	$-0.277604\pi$
$569$	15.3559	+	5.58907i	0.643751	+	0.234306i	0.000545484		1.00000i	$0.499826\pi$
$570$	−19.8578	−	31.3086i	−0.831753	−	1.31137i
$571$	13.1392	+	11.0251i	0.549857	+	0.461385i	0.874893	−	0.484317i	$-0.160932\pi$
$571$	13.1392	+	11.0251i	0.549857	+	0.461385i	−0.325036	+	0.945702i	$0.605376\pi$
$572$	−1.48099	+	8.39908i	−0.0619231	+	0.351183i
$573$	−0.229189	−	1.04368i	−0.00957450	−	0.0436005i
$574$	−5.96207	+	5.00277i	−0.248852	+	0.208812i
$575$	−5.23336	−	9.06444i	−0.218246	−	0.378013i
$576$	−1.71088	−	2.46432i	−0.0712866	−	0.102680i
$577$	0.751000	−	1.30077i	0.0312645	−	0.0541518i	−0.849970	−	0.526831i	$-0.823380\pi$
$577$	0.751000	−	1.30077i	0.0312645	−	0.0541518i	0.881234	+	0.472680i	$0.156713\pi$
$578$	−2.22572	−	12.6227i	−0.0925776	−	0.525034i
$579$	−3.35366	+	25.0855i	−0.139373	+	1.04252i
$580$	−28.9548	+	10.5387i	−1.20228	+	0.437596i
$581$	12.2510	−	4.45900i	0.508258	−	0.184991i
$582$	16.3628	−	6.73937i	0.678261	−	0.279356i
$583$	−4.24966	−	24.1010i	−0.176003	−	0.998163i
$584$	−2.40066	+	4.15807i	−0.0993401	+	0.172062i
$585$	42.1677	+	11.4799i	1.74342	+	0.474635i
$586$	−6.28954	−	10.8938i	−0.259818	−	0.450019i
$587$	−25.5351	+	21.4265i	−1.05395	+	0.884365i	−0.993503	−	0.113807i	$-0.963696\pi$
$587$	−25.5351	+	21.4265i	−1.05395	+	0.884365i	−0.0604422	+	0.998172i	$0.519251\pi$
$588$	1.65084	+	0.524143i	0.0680795	+	0.0216153i
$589$	7.29645	−	41.3802i	0.300645	−	1.70504i
$590$	−27.0971	−	22.7372i	−1.11557	−	0.936075i
$591$	−5.70832	+	10.9122i	−0.234809	+	0.448868i
$592$	−2.59751	−	0.945415i	−0.106757	−	0.0388563i
$593$	20.3968			0.837597			0.418798	−	0.908079i	$-0.362451\pi$
$593$	20.3968			0.837597			0.418798	+	0.908079i	$0.362451\pi$
$594$	0.510773	−	10.2817i	0.0209573	−	0.421863i
$595$	18.4781			0.757528
$596$	−8.51986	−	3.10097i	−0.348987	−	0.127021i
$597$	−34.5607	+	1.43966i	−1.41448	+	0.0589215i
$598$	5.35052	+	4.48962i	0.218799	+	0.183594i
$599$	1.30092	−	7.37788i	0.0531541	−	0.301452i	−0.946628	−	0.322328i	$-0.895535\pi$
$599$	1.30092	−	7.37788i	0.0531541	−	0.301452i	0.999782	+	0.0208764i	$0.00664563\pi$
$600$	8.25309	−	7.53224i	0.336931	−	0.307502i
$601$	4.37109	−	3.66778i	0.178300	−	0.149612i	−0.549270	−	0.835645i	$-0.685094\pi$
$601$	4.37109	−	3.66778i	0.178300	−	0.149612i	0.727570	+	0.686033i	$0.240650\pi$
$602$	−0.135388	−	0.234499i	−0.00551801	−	0.00955748i
$603$	−0.119341	+	1.30394i	−0.00485993	+	0.0531005i
$604$	4.31761	−	7.47832i	0.175681	−	0.304289i
$605$	−4.15739	−	23.5777i	−0.169022	−	0.958571i
$606$	−5.23448	−	4.03322i	−0.212636	−	0.163839i
$607$	13.1397	−	4.78246i	0.533324	−	0.194114i	−0.0612981	−	0.998120i	$-0.519524\pi$
$607$	13.1397	−	4.78246i	0.533324	−	0.194114i	0.594622	+	0.804006i	$0.297302\pi$
$608$	5.94409	−	2.16347i	0.241065	−	0.0877403i
$609$	−12.4931	−	9.62611i	−0.506248	−	0.390070i
$610$	−1.15239	−	6.53554i	−0.0466590	−	0.264616i
$611$	12.4017	−	21.4805i	0.501721	−	0.869006i
$612$	1.49306	−	16.3134i	0.0603532	−	0.659430i
$613$	6.17259	+	10.6912i	0.249309	+	0.431815i	0.963334	−	0.268304i	$-0.0864633\pi$
$613$	6.17259	+	10.6912i	0.249309	+	0.431815i	−0.714026	+	0.700120i	$0.753130\pi$
$614$	20.4923	−	17.1951i	0.827003	−	0.693938i
$615$	−33.6940	+	30.7510i	−1.35867	+	1.24000i
$616$	−0.344024	+	1.95106i	−0.0138611	+	0.0786103i
$617$	28.9401	+	24.2836i	1.16508	+	0.977622i	0.999963	−	0.00865107i	$-0.00275376\pi$
$617$	28.9401	+	24.2836i	1.16508	+	0.977622i	0.165122	+	0.986273i	$0.447198\pi$
$618$	−12.0620	+	0.502454i	−0.485203	+	0.0202116i
$619$	−19.2801	−	7.01738i	−0.774933	−	0.282052i	−0.0758747	−	0.997117i	$-0.524175\pi$
$619$	−19.2801	−	7.01738i	−0.774933	−	0.282052i	−0.699058	+	0.715065i	$0.746397\pi$
$620$	22.4784			0.902753
$621$	−7.08303	−	4.57240i	−0.284232	−	0.183484i
$622$	24.8651			0.996998
$623$	5.78981	+	2.10732i	0.231964	+	0.0844279i
$624$	−3.45616	+	6.60691i	−0.138357	+	0.264488i
$625$	−11.9803	−	10.0527i	−0.479213	−	0.402108i
$626$	−5.86999	+	33.2903i	−0.234612	+	1.33055i
$627$	20.6882	+	6.56851i	0.826207	+	0.262321i
$628$	18.5994	−	15.6068i	0.742197	−	0.622778i
$629$	−7.54702	−	13.0718i	−0.300920	−	0.521208i
$630$	9.79531	+	2.66671i	0.390254	+	0.106244i
$631$	−16.8037	+	29.1049i	−0.668945	+	1.15865i	0.309255	+	0.950979i	$0.399920\pi$
$631$	−16.8037	+	29.1049i	−0.668945	+	1.15865i	−0.978199	+	0.207667i	$0.933413\pi$
$632$	−0.702609	−	3.98469i	−0.0279483	−	0.158503i
$633$	−9.45360	+	3.89366i	−0.375747	+	0.154759i
$634$	10.2861	−	3.74383i	0.408513	−	0.148687i
$635$	51.6347	−	18.7935i	2.04906	−	0.745797i
$636$	2.83514	−	21.2070i	0.112421	−	0.840913i
$637$	−0.747536	−	4.23949i	−0.0296185	−	0.167975i
$638$	9.01989	−	15.6229i	0.357101	−	0.618517i
$639$	17.8546	+	25.7175i	0.706319	+	1.01737i
$640$	1.69197	+	2.93058i	0.0668810	+	0.115841i
$641$	2.07384	−	1.74016i	0.0819118	−	0.0687321i	−0.600912	−	0.799315i	$-0.705196\pi$
$641$	2.07384	−	1.74016i	0.0819118	−	0.0687321i	0.682824	+	0.730583i	$0.260752\pi$
$642$	−6.81273	−	31.0239i	−0.268877	−	1.22442i
$643$	3.24928	−	18.4276i	0.128139	−	0.726713i	−0.851255	−	0.524753i	$-0.824158\pi$
$643$	3.24928	−	18.4276i	0.128139	−	0.726713i	0.979394	−	0.201960i	$-0.0647312\pi$
$644$	1.24289	+	1.04291i	0.0489769	+	0.0410965i
$645$	−0.850048	−	1.34022i	−0.0334706	−	0.0527711i
$646$	32.4579	+	11.8137i	1.27704	+	0.464804i
$647$	31.7286			1.24738			0.623690	−	0.781672i	$-0.285633\pi$
$647$	31.7286			1.24738			0.623690	+	0.781672i	$0.285633\pi$
$648$	3.14578	−	8.43232i	0.123578	−	0.331253i
$649$	20.7093			0.812910
$650$	−26.0963	−	9.49826i	−1.02358	−	0.372552i
$651$	6.16243	+	9.71594i	0.241525	+	0.380798i
$652$	2.58429	+	2.16847i	0.101208	+	0.0849240i
$653$	−5.56093	+	31.5376i	−0.217616	+	1.23416i	0.658693	+	0.752412i	$0.271110\pi$
$653$	−5.56093	+	31.5376i	−0.217616	+	1.23416i	−0.876309	+	0.481750i	$0.840001\pi$
$654$	2.47295	+	11.2614i	0.0967000	+	0.440354i
$655$	20.5869	−	17.2745i	0.804398	−	0.674970i
$656$	−3.89146	−	6.74021i	−0.151936	−	0.263161i
$657$	−14.3541	+	1.19795i	−0.560006	+	0.0467363i
$658$	2.88085	−	4.98978i	0.112307	−	0.194522i
$659$	1.74751	+	9.91061i	0.0680732	+	0.386063i	0.999741	+	0.0227515i	$0.00724265\pi$
$659$	1.74751	+	9.91061i	0.0680732	+	0.386063i	−0.931668	+	0.363311i	$0.881646\pi$
$660$	−1.53869	+	11.5095i	−0.0598933	+	0.448005i
$661$	−28.8004	+	10.4825i	−1.12021	+	0.407722i	−0.834728	−	0.550663i	$-0.814375\pi$
$661$	−28.8004	+	10.4825i	−1.12021	+	0.407722i	−0.285479	+	0.958385i	$0.592153\pi$
$662$	−9.18767	+	3.34404i	−0.357089	+	0.129970i
$663$	−37.6471	+	15.5058i	−1.46209	+	0.602194i
$664$	2.26390	+	12.8392i	0.0878562	+	0.498257i
$665$	−10.7027	+	18.5376i	−0.415032	+	0.718856i
$666$	−2.11421	−	8.01859i	−0.0819241	−	0.310714i
$667$	−7.38691	−	12.7945i	−0.286022	−	0.495405i
$668$	4.27147	−	3.58419i	0.165268	−	0.138676i
$669$	37.8142	+	12.0060i	1.46198	+	0.464179i
$670$	0.256472	−	1.45452i	0.00990838	−	0.0561932i
$671$	2.97632	+	2.49743i	0.114900	+	0.0964123i
$672$	−0.802845	+	1.53474i	−0.0309704	+	0.0592040i
$673$	−6.82105	−	2.48266i	−0.262932	−	0.0956994i	0.207190	−	0.978301i	$-0.433568\pi$
$673$	−6.82105	−	2.48266i	−0.262932	−	0.0956994i	−0.470122	+	0.882601i	$0.655790\pi$
$674$	−24.8221			−0.956111
$675$	32.6819	+	7.45154i	1.25793	+	0.286810i
$676$	5.53208			0.212772
$677$	12.7863	+	4.65382i	0.491416	+	0.178861i	0.575829	−	0.817570i	$-0.304679\pi$
$677$	12.7863	+	4.65382i	0.491416	+	0.178861i	−0.0844131	+	0.996431i	$0.526902\pi$
$678$	−30.0737	+	1.25275i	−1.15497	+	0.0481116i
$679$	−7.82668	−	6.56736i	−0.300360	−	0.252032i
$680$	−3.20869	+	18.1974i	−0.123048	+	0.697838i
$681$	5.02122	−	4.58265i	0.192414	−	0.175608i
$682$	−10.0813	+	8.45918i	−0.386031	+	0.323919i
$683$	−15.3290	−	26.5507i	−0.586549	−	1.01593i	−0.994680	−	0.103010i	$-0.967153\pi$
$683$	−15.3290	−	26.5507i	−0.586549	−	1.01593i	0.408131	−	0.912923i	$-0.366181\pi$
$684$	15.5011	+	10.9467i	0.592700	+	0.418558i
$685$	15.8299	−	27.4182i	0.604830	−	1.04760i
$686$	−0.173648	−	0.984808i	−0.00662992	−	0.0376001i
$687$	−25.6413	−	19.7569i	−0.978276	−	0.753773i
$688$	0.254447	−	0.0926110i	0.00970069	−	0.00353076i
$689$	−49.9705	+	18.1878i	−1.90372	+	0.692899i
$690$	7.53289	+	5.80418i	0.286772	+	0.220961i
$691$	0.665449	+	3.77395i	0.0253149	+	0.143568i	0.994845	−	0.101402i	$-0.0323329\pi$
$691$	0.665449	+	3.77395i	0.0253149	+	0.143568i	−0.969531	+	0.244970i	$0.921222\pi$
$692$	4.97035	−	8.60890i	0.188944	−	0.327261i
$693$	−5.39662	+	2.49024i	−0.205001	+	0.0945963i
$694$	−4.70353	−	8.14676i	−0.178544	−	0.309247i
$695$	−10.4044	+	8.73030i	−0.394660	+	0.331159i
$696$	11.6493	−	10.6318i	0.441565	−	0.402997i
$697$	7.37986	−	41.8533i	0.279532	−	1.58531i
$698$	−15.8103	−	13.2664i	−0.598430	−	0.502143i
$699$	26.5153	−	1.10452i	1.00290	−	0.0417768i
$700$	−6.06200	−	2.20639i	−0.229122	−	0.0833936i
$701$	−33.2070			−1.25421			−0.627105	−	0.778935i	$-0.715760\pi$
$701$	−33.2070			−1.25421			−0.627105	+	0.778935i	$0.715760\pi$
$702$	−22.1946	+	2.78652i	−0.837682	+	0.105171i
$703$	17.4852			0.659466
$704$	−1.86168	−	0.677595i	−0.0701646	−	0.0255378i
$705$	15.6533	−	29.9233i	0.589536	−	1.12698i
$706$	−26.7159	−	22.4173i	−1.00547	−	0.843686i
$707$	−0.662498	+	3.75721i	−0.0249158	+	0.141305i
$708$	17.2565	+	5.47893i	0.648537	+	0.205911i
$709$	0.293392	−	0.246185i	0.0110186	−	0.00924569i	−0.637262	−	0.770647i	$-0.719933\pi$
$709$	0.293392	−	0.246185i	0.0110186	−	0.00924569i	0.648280	+	0.761402i	$0.275489\pi$
$710$	−17.6573	−	30.5834i	−0.662667	−	1.14777i
$711$	8.61750	−	8.54879i	0.323181	−	0.320605i
$712$	−3.08069	+	5.33591i	−0.115454	+	0.199972i
$713$	1.87151	+	10.6139i	0.0700887	+	0.397493i
$714$	−8.74520	+	3.60189i	−0.327281	+	0.134797i
$715$	27.1200	−	9.87086i	1.01423	−	0.369149i
$716$	−4.99891	+	1.81945i	−0.186818	+	0.0679962i
$717$	−1.59042	+	11.8964i	−0.0593952	+	0.444279i
$718$	4.64338	+	26.3339i	0.173289	+	0.982773i
$719$	10.7683	−	18.6512i	0.401589	−	0.695573i	−0.592329	−	0.805696i	$-0.701791\pi$
$719$	10.7683	−	18.6512i	0.401589	−	0.695573i	0.993918	+	0.110123i	$0.0351246\pi$
$720$	−4.32714	+	9.18343i	−0.161263	+	0.342246i
$721$	3.48501	+	6.03621i	0.129788	+	0.224800i
$722$	−16.0967	+	13.5067i	−0.599058	+	0.502669i
$723$	−6.52224	−	29.7011i	−0.242565	−	1.10459i
$724$	−3.43484	+	19.4799i	−0.127655	+	0.723966i
$725$	44.9984	+	37.7581i	1.67120	+	1.40230i
$726$	6.56354	+	10.3483i	0.243596	+	0.384063i
$727$	−47.2924	−	17.2130i	−1.75398	−	0.638395i	−0.754144	−	0.656709i	$-0.771948\pi$
$727$	−47.2924	−	17.2130i	−1.75398	−	0.638395i	−0.999832	+	0.0183140i	$0.994170\pi$
$728$	4.30489			0.159550
$729$	26.1620	−	6.67446i	0.968964	−	0.247202i
$730$	16.2474			0.601343
$731$	1.38941	+	0.505705i	0.0513893	+	0.0187042i
$732$	1.81936	+	2.86847i	0.0672453	+	0.106022i
$733$	−23.0633	−	19.3524i	−0.851863	−	0.714798i	0.108336	−	0.994114i	$-0.465448\pi$
$733$	−23.0633	−	19.3524i	−0.851863	−	0.714798i	−0.960199	+	0.279316i	$0.909892\pi$
$734$	3.98417	−	22.5954i	0.147058	−	0.834010i
$735$	−1.25713	−	5.72475i	−0.0463700	−	0.211161i
$736$	−1.24289	+	1.04291i	−0.0458137	+	0.0384423i
$737$	0.432350	+	0.748852i	0.0159258	+	0.0275843i
$738$	9.95224	−	21.1215i	0.366347	−	0.777494i
$739$	6.72475	−	11.6476i	0.247374	−	0.428464i	−0.715423	−	0.698692i	$-0.753766\pi$
$739$	6.72475	−	11.6476i	0.247374	−	0.428464i	0.962796	+	0.270228i	$0.0870991\pi$
$740$	1.62429	+	9.21181i	0.0597101	+	0.338633i
$741$	6.24987	−	46.7493i	0.229595	−	1.71738i
$742$	−11.6078	+	4.22491i	−0.426137	+	0.155101i
$743$	−39.9822	+	14.5523i	−1.46681	+	0.533874i	−0.947231	−	0.320551i	$-0.896132\pi$
$743$	−39.9822	+	14.5523i	−1.46681	+	0.533874i	−0.519575	+	0.854425i	$0.673910\pi$
$744$	−10.6384	+	4.38166i	−0.390024	+	0.160639i
$745$	5.32769	+	30.2149i	0.195192	+	1.10699i
$746$	6.81525	−	11.8044i	0.249524	−	0.432188i
$747$	−27.7667	+	27.5453i	−1.01593	+	1.00783i
$748$	−5.40908	−	9.36880i	−0.197775	−	0.342557i
$749$	−14.0481	+	11.7877i	−0.513305	+	0.430714i
$750$	−8.10606	−	2.57368i	−0.295991	−	0.0939774i
$751$	−7.42689	+	42.1200i	−0.271011	+	1.53698i	0.480343	+	0.877081i	$0.340512\pi$
$751$	−7.42689	+	42.1200i	−0.271011	+	1.53698i	−0.751354	+	0.659900i	$0.770599\pi$
$752$	4.41372	+	3.70355i	0.160952	+	0.135055i
$753$	−21.5150	+	41.1287i	−0.784049	+	1.49881i
$754$	−36.8350	−	13.4068i	−1.34145	−	0.488248i
$755$	−29.2211			−1.06346
$756$	−5.15568	+	0.647292i	−0.187510	+	0.0235418i
$757$	−48.7823			−1.77302			−0.886511	−	0.462708i	$-0.846878\pi$
$757$	−48.7823			−1.77302			−0.886511	+	0.462708i	$0.846878\pi$
$758$	34.7132	+	12.6346i	1.26084	+	0.458909i
$759$	−5.56266	+	0.231719i	−0.201912	+	0.00841085i
$760$	−16.3974	−	13.7591i	−0.594797	−	0.499094i
$761$	5.31072	−	30.1186i	0.192513	−	1.09180i	−0.723402	−	0.690427i	$-0.757423\pi$
$761$	5.31072	−	30.1186i	0.192513	−	1.09180i	0.915916	−	0.401371i	$-0.131466\pi$
$762$	−20.7740	+	18.9595i	−0.752561	+	0.686830i
$763$	5.09931	−	4.27883i	0.184607	−	0.154904i
$764$	−0.308464	−	0.534276i	−0.0111598	−	0.0193294i
$765$	−50.3339	+	23.2263i	−1.81983	+	0.839748i
$766$	6.66546	−	11.5449i	0.240833	−	0.417135i
$767$	−7.81410	−	44.3160i	−0.282151	−	1.60016i
$768$	−1.37202	−	1.05715i	−0.0495083	−	0.0381467i
$769$	−39.4223	+	14.3485i	−1.42160	+	0.517421i	−0.934512	−	0.355930i	$-0.884164\pi$
$769$	−39.4223	+	14.3485i	−1.42160	+	0.517421i	−0.487090	+	0.873352i	$0.661942\pi$
$770$	6.29980	−	2.29294i	0.227029	−	0.0826318i
$771$	5.92459	+	4.56496i	0.213369	+	0.164403i
$772$	2.53735	+	14.3900i	0.0913211	+	0.517908i
$773$	9.30505	−	16.1168i	0.334679	−	0.579682i	−0.648744	−	0.761007i	$-0.724705\pi$
$773$	9.30505	−	16.1168i	0.334679	−	0.579682i	0.983423	+	0.181325i	$0.0580387\pi$
$774$	0.663551	+	0.468593i	0.0238508	+	0.0168432i
$775$	−21.4261	−	37.1111i	−0.769647	−	1.33307i
$776$	7.82668	−	6.56736i	0.280961	−	0.235755i
$777$	−3.53637	+	3.22749i	−0.126866	+	0.115785i
$778$	0.269050	−	1.52586i	0.00964591	−	0.0547047i
$779$	37.7135	+	31.6453i	1.35122	+	1.13381i
$780$	25.2098	−	1.05014i	0.902655	−	0.0376010i
$781$	19.4284	+	7.07134i	0.695201	+	0.253033i
$782$	−8.85962			−0.316819
$783$	46.1307	+	10.5179i	1.64858	+	0.375879i
$784$	1.00000			0.0357143
$785$	−77.2065	−	28.1009i	−2.75562	−	1.00296i
$786$	−6.37597	+	12.1885i	−0.227423	+	0.434750i
$787$	−11.0285	−	9.25402i	−0.393124	−	0.329870i	0.424705	−	0.905332i	$-0.360378\pi$
$787$	−11.0285	−	9.25402i	−0.393124	−	0.329870i	−0.817829	+	0.575462i	$0.804822\pi$
$788$	−1.23466	+	7.00210i	−0.0439829	+	0.249439i
$789$	−4.42768	−	1.40579i	−0.157630	−	0.0500475i
$790$	−10.4887	+	8.80103i	−0.373170	+	0.313127i
$791$	8.68906	+	15.0499i	0.308947	+	0.535113i
$792$	−1.51529	−	5.74706i	−0.0538435	−	0.204213i
$793$	4.22124	−	7.31140i	0.149901	−	0.259635i
$794$	3.07590	+	17.4443i	0.109160	+	0.619075i
$795$	−66.9458	+	27.5730i	−2.37432	+	0.977914i
$796$	−18.7665	+	6.83046i	−0.665163	+	0.242099i
$797$	20.2336	−	7.36443i	0.716711	−	0.260862i	0.0421824	−	0.999110i	$-0.486569\pi$
$797$	20.2336	−	7.36443i	0.716711	−	0.260862i	0.674529	+	0.738248i	$0.264347\pi$
$798$	1.45181	−	10.8596i	0.0513934	−	0.384425i
$799$	5.46331	+	30.9840i	0.193278	+	1.09613i
$800$	3.22552	−	5.58677i	0.114040	−	0.197522i
$801$	−18.4201	+	1.53729i	−0.650843	+	0.0543173i
$802$	0.532813	+	0.922858i	0.0188143	+	0.0325873i
$803$	−7.28674	+	6.11430i	−0.257143	+	0.215769i
$804$	0.162146	+	0.738382i	0.00571844	+	0.0260407i
$805$	0.953395	−	5.40697i	0.0336028	−	0.190571i
$806$	21.9058	+	18.3811i	0.771598	+	0.647447i
$807$	17.9320	+	28.2723i	0.631236	+	0.995231i
$808$	−3.58509	−	1.30487i	−0.126123	−	0.0459050i
$809$	−40.6584			−1.42947			−0.714736	−	0.699394i	$-0.753453\pi$
$809$	−40.6584			−1.42947			−0.714736	+	0.699394i	$0.753453\pi$
$810$	−30.0341	+	5.04827i	−1.05529	+	0.177378i
$811$	−25.8485			−0.907664			−0.453832	−	0.891087i	$-0.649943\pi$
$811$	−25.8485			−0.907664			−0.453832	+	0.891087i	$0.649943\pi$
$812$	−8.55655	−	3.11433i	−0.300276	−	0.109292i
$813$	1.91250	+	3.01532i	0.0670741	+	0.105752i
$814$	−4.19511	−	3.52011i	−0.147039	−	0.123380i
$815$	1.98235	−	11.2424i	0.0694386	−	0.393806i
$816$	−2.02858	−	9.23780i	−0.0710147	−	0.323388i
$817$	−1.31209	+	1.10098i	−0.0459043	+	0.0385183i
$818$	−14.6044	−	25.2956i	−0.510632	−	0.884441i
$819$	7.36515	+	10.6086i	0.257359	+	0.370696i
$820$	−13.1685	+	22.8085i	−0.459863	+	0.796507i
$821$	3.47313	+	19.6971i	0.121213	+	0.687433i	0.983485	+	0.180988i	$0.0579296\pi$
$821$	3.47313	+	19.6971i	0.121213	+	0.687433i	−0.862272	+	0.506445i	$0.830959\pi$
$822$	−2.14731	+	16.0620i	−0.0748961	+	0.560227i
$823$	7.56620	−	2.75387i	0.263741	−	0.0959940i	−0.206765	−	0.978391i	$-0.566294\pi$
$823$	7.56620	−	2.75387i	0.263741	−	0.0959940i	0.470506	+	0.882397i	$0.344071\pi$
$824$	−6.54967	+	2.38389i	−0.228169	+	0.0830466i
$825$	20.4684	−	8.43033i	0.712618	−	0.293507i
$826$	−1.81517	−	10.2943i	−0.0631578	−	0.358185i
$827$	9.48981	−	16.4368i	0.329993	−	0.571565i	−0.652517	−	0.757774i	$-0.726287\pi$
$827$	9.48981	−	16.4368i	0.329993	−	0.571565i	0.982510	+	0.186209i	$0.0596203\pi$
$828$	−4.69652	−	1.27860i	−0.163215	−	0.0444343i
$829$	10.7785	+	18.6689i	0.374353	+	0.648399i	0.990230	−	0.139444i	$-0.0445314\pi$
$829$	10.7785	+	18.6689i	0.374353	+	0.648399i	−0.615877	+	0.787843i	$0.711198\pi$
$830$	33.7958	−	28.3580i	1.17307	−	0.984322i
$831$	27.8377	+	8.83847i	0.965678	+	0.306603i
$832$	−0.747536	+	4.23949i	−0.0259162	+	0.146978i
$833$	4.18301	+	3.50996i	0.144933	+	0.121613i
$834$	3.22234	−	6.15992i	0.111580	−	0.213301i
$835$	−17.7309	−	6.45354i	−0.613605	−	0.223334i
$836$	12.5319			0.433426
$837$	−28.9989	−	18.7200i	−1.00235	−	0.647059i
$838$	7.38542			0.255125
$839$	36.4415	+	13.2636i	1.25810	+	0.457911i	0.883131	−	0.469126i	$-0.155431\pi$
$839$	36.4415	+	13.2636i	1.25810	+	0.457911i	0.374969	+	0.927037i	$0.377653\pi$
$840$	5.85608	−	0.243941i	0.202054	−	0.00841676i
$841$	41.3002	+	34.6550i	1.42414	+	1.19500i
$842$	2.19564	−	12.4521i	0.0756669	−	0.429128i
$843$	−2.05185	+	1.87263i	−0.0706694	+	0.0644968i
$844$	−4.52185	+	3.79428i	−0.155649	+	0.130605i
$845$	−9.36011	−	16.2122i	−0.321998	−	0.557716i
$846$	−1.57540	+	17.2132i	−0.0541635	+	0.591801i
$847$	3.53751	−	6.12715i	0.121550	−	0.210531i
$848$	−2.14504	−	12.1651i	−0.0736611	−	0.417753i
$849$	26.2832	+	20.2515i	0.902037	+	0.695030i
$850$	33.1017	−	12.0481i	1.13538	−	0.413245i
$851$	−4.21441	+	1.53392i	−0.144468	+	0.0525821i
$852$	14.3183	+	11.0324i	0.490536	+	0.377964i
$853$	3.04371	+	17.2618i	0.104215	+	0.591032i	0.991531	+	0.129870i	$0.0414560\pi$
$853$	3.04371	+	17.2618i	0.104215	+	0.591032i	−0.887316	+	0.461162i	$0.847433\pi$
$854$	0.980568	−	1.69839i	0.0335543	−	0.0581178i
$855$	5.85280	−	63.9487i	0.200161	−	2.18700i
$856$	−9.16923	−	15.8816i	−0.313398	−	0.542821i
$857$	14.6190	−	12.2668i	0.499375	−	0.419026i	−0.357997	−	0.933723i	$-0.616540\pi$
$857$	14.6190	−	12.2668i	0.499375	−	0.419026i	0.857372	+	0.514697i	$0.172096\pi$
$858$	−10.9111	+	9.95804i	−0.372497	+	0.339962i
$859$	−1.76711	+	10.0218i	−0.0602929	+	0.341938i	−1.00000		4.24196e-5i	$-0.999986\pi$
$859$	−1.76711	+	10.0218i	−0.0602929	+	0.341938i	0.939707	+	0.341980i	$0.111098\pi$
$860$	−0.701920	−	0.588981i	−0.0239353	−	0.0200841i
$861$	−13.4687	+	0.561055i	−0.459014	+	0.0191207i
$862$	2.70885	+	0.985941i	0.0922638	+	0.0335813i
$863$	−24.3087			−0.827478			−0.413739	−	0.910396i	$-0.635777\pi$
$863$	−24.3087			−0.827478			−0.413739	+	0.910396i	$0.635777\pi$
$864$	0.257816	−	5.18975i	0.00877107	−	0.176559i
$865$	−33.6387			−1.14375
$866$	−17.1633	−	6.24694i	−0.583234	−	0.212280i
$867$	10.2904	−	19.6714i	0.349480	−	0.668076i
$868$	5.08858	+	4.26982i	0.172718	+	0.144927i
$869$	1.39198	−	7.89430i	0.0472196	−	0.267796i
$870$	−50.8675	−	16.1505i	−1.72457	−	0.547552i
$871$	1.43934	−	1.20775i	0.0487701	−	0.0409230i
$872$	3.32834	+	5.76485i	0.112712	+	0.195222i
$873$	29.5746	+	8.05150i	1.00095	+	0.272502i
$874$	5.13156	−	8.88813i	0.173578	−	0.300645i
$875$	0.852658	+	4.83566i	0.0288251	+	0.163475i
$876$	−7.68946	+	3.16706i	−0.259803	+	0.107005i
$877$	−42.5556	+	15.4890i	−1.43700	+	0.523025i	−0.938929	−	0.344111i	$-0.888180\pi$
$877$	−42.5556	+	15.4890i	−1.43700	+	0.523025i	−0.498071	+	0.867136i	$0.665958\pi$
$878$	−25.8593	+	9.41200i	−0.872708	+	0.317640i
$879$	2.88708	−	21.5955i	0.0973786	−	0.728397i
$880$	1.16416	+	6.60226i	0.0392437	+	0.222562i
$881$	−4.49174	+	7.77993i	−0.151331	+	0.262113i	−0.931717	−	0.363185i	$-0.881689\pi$
$881$	−4.49174	+	7.77993i	−0.151331	+	0.262113i	0.780386	+	0.625298i	$0.215023\pi$
$882$	1.71088	+	2.46432i	0.0576083	+	0.0829781i
$883$	0.795711	+	1.37821i	0.0267778	+	0.0463805i	0.879104	−	0.476630i	$-0.158142\pi$
$883$	0.795711	+	1.37821i	0.0267778	+	0.0463805i	−0.852326	+	0.523011i	$0.824809\pi$
$884$	−18.0074	+	15.1100i	−0.605654	+	0.508204i
$885$	−13.1410	−	59.8416i	−0.441729	−	2.01155i
$886$	1.75024	−	9.92609i	0.0588004	−	0.333474i
$887$	−16.0445	−	13.4629i	−0.538722	−	0.452041i	0.332379	−	0.943146i	$-0.392149\pi$
$887$	−16.0445	−	13.4629i	−0.538722	−	0.452041i	−0.871101	+	0.491105i	$0.836593\pi$
$888$	−2.56437	−	4.04309i	−0.0860546	−	0.135677i
$889$	15.2587	+	5.55373i	0.511762	+	0.186266i
$890$	20.8497			0.698885
$891$	11.5701	−	13.5667i	0.387614	−	0.454501i
$892$	22.9060			0.766950
$893$	−34.2481	−	12.4653i	−1.14607	−	0.417134i
$894$	−8.41117	−	13.2614i	−0.281312	−	0.443527i
$895$	13.7901	+	11.5712i	0.460951	+	0.386783i
$896$	−0.173648	+	0.984808i	−0.00580118	+	0.0329001i
$897$	2.59478	+	11.8162i	0.0866372	+	0.394530i
$898$	18.4981	−	15.5218i	0.617291	−	0.517969i
$899$	−30.2430	−	52.3824i	−1.00866	−	1.74705i
$900$	19.2861	−	1.60956i	0.642870	−	0.0536519i
$901$	33.7264	−	58.4159i	1.12359	−	1.94612i
$902$	−2.67751	−	15.1849i	−0.0891515	−	0.505603i
$903$	0.0621470	−	0.464863i	0.00206812	−	0.0154697i
$904$	−16.3301	+	5.94367i	−0.543131	+	0.197683i
$905$	62.8991	−	22.8934i	2.09084	−	0.761002i
$906$	13.8296	−	5.69599i	0.459456	−	0.189237i
$907$	7.75520	+	43.9819i	0.257507	+	1.46039i	0.789555	+	0.613680i	$0.210312\pi$
$907$	7.75520	+	43.9819i	0.257507	+	1.46039i	−0.532047	+	0.846715i	$0.678577\pi$
$908$	1.96243	−	3.39902i	0.0651254	−	0.112800i
$909$	−2.91805	−	11.0673i	−0.0967854	−	0.367079i
$910$	−7.28374	−	12.6158i	−0.241454	−	0.418210i
$911$	−18.1414	+	15.2224i	−0.601050	+	0.504341i	−0.891783	−	0.452463i	$-0.850545\pi$
$911$	−18.1414	+	15.2224i	−0.601050	+	0.504341i	0.290733	+	0.956804i	$0.406101\pi$
$912$	10.4425	+	3.31550i	0.345786	+	0.109787i
$913$	−4.48513	+	25.4364i	−0.148436	+	0.841823i
$914$	−1.63352	−	1.37069i	−0.0540321	−	0.0453383i
$915$	5.32797	−	10.1851i	0.176137	−	0.336710i
$916$	−17.5617	−	6.39194i	−0.580255	−	0.211196i
$917$	7.94172			0.262259
$918$	19.2943	−	20.8039i	0.636806	−	0.686630i
$919$	−14.6079			−0.481872			−0.240936	−	0.970541i	$-0.577454\pi$
$919$	−14.6079			−0.481872			−0.240936	+	0.970541i	$0.577454\pi$
$920$	5.15927	+	1.87782i	0.170096	+	0.0619100i
$921$	46.2936	−	1.92841i	1.52543	−	0.0635433i
$922$	9.10284	+	7.63819i	0.299786	+	0.251550i
$923$	7.80125	−	44.2431i	0.256781	−	1.45628i
$924$	−2.53457	+	2.31319i	−0.0833813	+	0.0760985i
$925$	13.6601	−	11.4622i	0.449143	−	0.376875i
$926$	9.42184	+	16.3191i	0.309621	+	0.536279i
$927$	−17.0804	−	12.0620i	−0.560993	−	0.396167i
$928$	4.55284	−	7.88576i	0.149454	−	0.258863i
$929$	1.47564	+	8.36879i	0.0484143	+	0.274571i	0.999399	−	0.0346671i	$-0.0110371\pi$
$929$	1.47564	+	8.36879i	0.0484143	+	0.274571i	−0.950985	+	0.309238i	$0.899926\pi$
$930$	30.8407	+	23.7631i	1.01131	+	0.779223i
$931$	−5.94409	+	2.16347i	−0.194810	+	0.0709049i
$932$	14.3978	−	5.24039i	0.471617	−	0.171655i
$933$	34.1152	+	26.2862i	1.11688	+	0.860571i
$934$	−5.95474	−	33.7710i	−0.194845	−	1.10502i
$935$	−18.3040	+	31.7034i	−0.598605	+	1.03681i
$936$	−11.7264	+	5.41108i	−0.383290	+	0.176867i
$937$	−15.1913	−	26.3121i	−0.496278	−	0.859578i	0.503713	−	0.863871i	$-0.331967\pi$
$937$	−15.1913	−	26.3121i	−0.496278	−	0.859578i	−0.999991	+	0.00429280i	$0.998634\pi$
$938$	0.334350	−	0.280553i	0.0109169	−	0.00916037i
$939$	−43.2467	+	39.4694i	−1.41130	+	1.28804i
$940$	3.38566	−	19.2010i	0.110428	−	0.626269i
$941$	−13.9536	−	11.7085i	−0.454875	−	0.381685i	0.386366	−	0.922345i	$-0.373730\pi$
$941$	−13.9536	−	11.7085i	−0.454875	−	0.381685i	−0.841241	+	0.540660i	$0.818174\pi$
$942$	42.0174	−	1.75028i	1.36900	−	0.0570272i
$943$	−11.8661	−	4.31892i	−0.386414	−	0.140643i
$944$	10.4531			0.340221
$945$	10.6202	+	14.0139i	0.345475	+	0.455873i
$946$	0.536450			0.0174415
$947$	27.0393	+	9.84149i	0.878658	+	0.319805i	0.741668	−	0.670767i	$-0.234035\pi$
$947$	27.0393	+	9.84149i	0.878658	+	0.319805i	0.136990	+	0.990572i	$0.456257\pi$
$948$	3.24844	−	6.20983i	0.105505	−	0.201686i
$949$	15.8335	+	13.2859i	0.513977	+	0.431278i
$950$	−7.08598	+	40.1866i	−0.229900	+	1.30382i
$951$	18.0705	+	5.73739i	0.585976	+	0.186047i
$952$	−4.18301	+	3.50996i	−0.135572	+	0.113758i
$953$	−7.37456	−	12.7731i	−0.238885	−	0.413762i	0.721509	−	0.692405i	$-0.243449\pi$
$953$	−7.37456	−	12.7731i	−0.238885	−	0.413762i	−0.960395	+	0.278643i	$0.910115\pi$
$954$	26.3089	−	26.0992i	0.851783	−	0.844992i
$955$	−1.04382	+	1.80796i	−0.0337774	+	0.0585041i
$956$	1.20329	+	6.82422i	0.0389173	+	0.220711i
$957$	28.8912	−	11.8995i	0.933921	−	0.384655i
$958$	−8.41906	+	3.06429i	−0.272007	+	0.0990026i
$959$	8.79167	−	3.19991i	0.283898	−	0.103330i
$960$	−0.776662	+	5.80947i	−0.0250667	+	0.187500i
$961$	2.27913	+	12.9256i	0.0735204	+	0.416955i
$962$	−5.94981	+	10.3054i	−0.191830	+	0.332258i
$963$	23.4499	−	49.7674i	0.755662	−	1.60373i
$964$	−8.77826	−	15.2044i	−0.282729	−	0.489700i
$965$	37.8779	−	31.7833i	1.21933	−	1.02314i
$966$	0.602752	+	2.74482i	0.0193932	+	0.0883132i
$967$	−7.11012	+	40.3235i	−0.228646	+	1.29672i	0.626945	+	0.779064i	$0.284305\pi$
$967$	−7.11012	+	40.3235i	−0.228646	+	1.29672i	−0.855591	+	0.517653i	$0.826806\pi$
$968$	5.41978	+	4.54774i	0.174198	+	0.146170i
$969$	32.0438	+	50.5215i	1.02940	+	1.62299i
$970$	−32.4887	−	11.8249i	−1.04315	−	0.379675i
$971$	43.1536			1.38486			0.692432	−	0.721483i	$-0.256539\pi$
$971$	43.1536			1.38486			0.692432	+	0.721483i	$0.256539\pi$
$972$	13.2303	−	8.24370i	0.424363	−	0.264417i
$973$	−4.01365			−0.128672
$974$	−8.59707	−	3.12908i	−0.275468	−	0.100262i
$975$	−25.7633	−	40.6195i	−0.825087	−	1.30087i
$976$	1.50232	+	1.26059i	0.0480880	+	0.0403506i
$977$	2.31105	−	13.1066i	0.0739371	−	0.419318i	−0.925263	−	0.379326i	$-0.876156\pi$
$977$	2.31105	−	13.1066i	0.0739371	−	0.419318i	0.999200	−	0.0399916i	$-0.0127331\pi$
$978$	1.25327	+	5.70717i	0.0400752	+	0.182495i
$979$	−9.35084	+	7.84629i	−0.298854	+	0.250768i
$980$	−1.69197	−	2.93058i	−0.0540480	−	0.0936139i
$981$	−8.51207	+	18.0651i	−0.271769	+	0.576773i
$982$	−13.1864	+	22.8395i	−0.420796	+	0.728839i
$983$	0.561573	+	3.18484i	0.0179114	+	0.101581i	0.992453	−	0.122627i	$-0.0391318\pi$
$983$	0.561573	+	3.18484i	0.0179114	+	0.101581i	−0.974541	+	0.224207i	$0.928021\pi$
$984$	1.78629	−	13.3616i	0.0569449	−	0.425951i
$985$	22.6092	−	8.22908i	0.720389	−	0.262200i
$986$	46.7233	−	17.0059i	1.48797	−	0.541578i
$987$	9.22754	−	3.80055i	0.293716	−	0.120973i
$988$	−4.72859	−	26.8172i	−0.150436	−	0.853168i
$989$	0.219665	−	0.380471i	0.00698494	−	0.0120983i
$990$	−14.2784	+	14.1645i	−0.453796	+	0.450178i
$991$	19.1585	+	33.1835i	0.608589	+	1.05411i	0.991473	+	0.130311i	$0.0415977\pi$
$991$	19.1585	+	33.1835i	0.608589	+	1.05411i	−0.382884	+	0.923797i	$0.625069\pi$
$992$	−5.08858	+	4.26982i	−0.161562	+	0.135567i
$993$	−16.1408	−	5.12471i	−0.512213	−	0.162628i
$994$	1.81218	−	10.2774i	0.0574790	−	0.325979i
$995$	51.7696	+	43.4399i	1.64121	+	1.37714i
$996$	−10.4669	+	20.0089i	−0.331656	+	0.634005i
$997$	−53.8752	−	19.6090i	−1.70625	−	0.621023i	−0.709733	−	0.704470i	$-0.751185\pi$
$997$	−53.8752	−	19.6090i	−1.70625	−	0.621023i	−0.996512	+	0.0834479i	$0.973407\pi$
$998$	−10.5126			−0.332769
$999$	5.57615	−	13.2367i	0.176422	−	0.418790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.85.4	✓	36
27.7	even	9	inner	378.2.u.e.169.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.85.4	✓	36	1.1	even	1	trivial
378.2.u.e.169.4	yes	36	27.7	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.927705 + 1.46266i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.587615 - 3.33253i) q^{5} +(0.371500 + 1.69174i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.27873 + 2.71383i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.927705 + 1.46266i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.587615 - 3.33253i) q^{5} +(0.371500 + 1.69174i) q^{6} +(0.766044 - 0.642788i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.27873 + 2.71383i) q^{9} +(1.69197 - 2.93058i) q^{10} +(0.344024 + 1.95106i) q^{11} +(-0.229514 + 1.71678i) q^{12} +(4.04527 - 1.47236i) q^{13} +(0.939693 - 0.342020i) q^{14} +(5.41948 - 2.23213i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.73027 + 4.72896i) q^{17} +(-2.12979 + 2.11281i) q^{18} +(-3.16278 - 5.47810i) q^{19} +(2.59225 - 2.17515i) q^{20} +(1.65084 + 0.524143i) q^{21} +(-0.344024 + 1.95106i) q^{22} +(1.24289 + 1.04291i) q^{23} +(-0.802845 + 1.53474i) q^{24} +(-6.06200 - 2.20639i) q^{25} +4.30489 q^{26} +(-5.15568 + 0.647292i) q^{27} +1.00000 q^{28} +(-8.55655 - 3.11433i) q^{29} +(5.85608 - 0.243941i) q^{30} +(5.08858 + 4.26982i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-2.53457 + 2.31319i) q^{33} +(-4.18301 + 3.50996i) q^{34} +(-1.69197 - 2.93058i) q^{35} +(-2.72398 + 1.25696i) q^{36} +(-1.38210 + 2.39388i) q^{37} +(-1.09842 - 6.22947i) q^{38} +(5.90638 + 4.55093i) q^{39} +(3.17986 - 1.15738i) q^{40} +(-7.31356 + 2.66192i) q^{41} +(1.37202 + 1.05715i) q^{42} +(-0.0470198 - 0.266663i) q^{43} +(-0.990577 + 1.71573i) q^{44} +(8.29251 + 5.85608i) q^{45} +(0.811242 + 1.40511i) q^{46} +(4.41372 - 3.70355i) q^{47} +(-1.27934 + 1.16760i) q^{48} +(0.173648 - 0.984808i) q^{49} +(-4.94179 - 4.14665i) q^{50} +(-9.44972 + 0.393638i) q^{51} +(4.04527 + 1.47236i) q^{52} -12.3528 q^{53} +(-5.06614 - 1.15509i) q^{54} +6.70411 q^{55} +(0.939693 + 0.342020i) q^{56} +(5.07845 - 9.70812i) q^{57} +(-6.97536 - 5.85302i) q^{58} +(1.81517 - 10.2943i) q^{59} +(5.58635 + 1.77367i) q^{60} +(1.50232 - 1.26059i) q^{61} +(3.32133 + 5.75272i) q^{62} +(0.764853 + 2.90086i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.52962 - 14.3462i) q^{65} +(-3.17288 + 1.30682i) q^{66} +(0.410141 - 0.149279i) q^{67} +(-5.13122 + 1.86761i) q^{68} +(-0.372383 + 2.78544i) q^{69} +(-0.587615 - 3.33253i) q^{70} +(5.21797 - 9.03779i) q^{71} +(-2.98961 + 0.249503i) q^{72} +(2.40066 + 4.15807i) q^{73} +(-2.11751 + 1.77680i) q^{74} +(-2.39656 - 10.9135i) q^{75} +(1.09842 - 6.22947i) q^{76} +(1.51765 + 1.27346i) q^{77} +(3.99367 + 6.29658i) q^{78} +(-3.80215 - 1.38387i) q^{79} +3.38394 q^{80} +(-5.72971 - 6.94049i) q^{81} -7.78293 q^{82} +(12.2510 + 4.45900i) q^{83} +(0.927705 + 1.46266i) q^{84} +(14.1551 + 11.8775i) q^{85} +(0.0470198 - 0.266663i) q^{86} +(-3.38276 - 15.4045i) q^{87} +(-1.51765 + 1.27346i) q^{88} +(3.08069 + 5.33591i) q^{89} +(5.78951 + 8.33912i) q^{90} +(2.15245 - 3.72814i) q^{91} +(0.281741 + 1.59783i) q^{92} +(-1.52459 + 11.4040i) q^{93} +(5.41423 - 1.97062i) q^{94} +(-20.1144 + 7.32105i) q^{95} +(-1.60153 + 0.659623i) q^{96} +(-1.77416 - 10.0618i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-5.73474 - 1.56125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

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