LMFDB - Embedded newform 414.2.i.b.397.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			397.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	414.397
Dual form			414.2.i.b.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.43450 + 1.56456i) q^{5} +(0.394306 - 2.74246i) q^{7} +(-0.959493 + 0.281733i) q^{8} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.43450 + 1.56456i) q^{5} +(0.394306 - 2.74246i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.411844 + 2.86444i) q^{10} +(-2.26413 - 4.95774i) q^{11} +(-0.0520365 - 0.361922i) q^{13} +(-2.33083 - 1.49793i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-4.12405 + 4.75941i) q^{17} +(-4.01801 - 4.63704i) q^{19} +(2.77667 + 0.815304i) q^{20} -5.45027 q^{22} +(0.965501 - 4.69764i) q^{23} +(1.40187 - 3.06967i) q^{25} +(-0.350833 - 0.103014i) q^{26} +(-2.33083 + 1.49793i) q^{28} +(2.23325 - 2.57731i) q^{29} +(-7.37071 + 2.16423i) q^{31} +(0.841254 + 0.540641i) q^{32} +(2.61612 + 5.72850i) q^{34} +(3.33080 + 7.29343i) q^{35} +(4.06209 + 2.61055i) q^{37} +(-5.88714 + 1.72862i) q^{38} +(1.89510 - 2.18706i) q^{40} +(3.56427 - 2.29062i) q^{41} +(6.75145 + 1.98241i) q^{43} +(-2.26413 + 4.95774i) q^{44} +(-3.87204 - 2.82972i) q^{46} +6.68409 q^{47} +(-0.649167 - 0.190613i) q^{49} +(-2.20991 - 2.55037i) q^{50} +(-0.239446 + 0.276335i) q^{52} +(1.01536 - 7.06200i) q^{53} +(13.2687 + 8.52726i) q^{55} +(0.394306 + 2.74246i) q^{56} +(-1.41668 - 3.10209i) q^{58} +(0.0626320 + 0.435615i) q^{59} +(-7.80450 + 2.29161i) q^{61} +(-1.09325 + 7.60369i) q^{62} +(0.841254 - 0.540641i) q^{64} +(0.692931 + 0.799685i) q^{65} +(1.84829 - 4.04720i) q^{67} +6.29760 q^{68} +8.01801 q^{70} +(0.586952 - 1.28525i) q^{71} +(2.58092 + 2.97855i) q^{73} +(4.06209 - 2.61055i) q^{74} +(-0.873198 + 6.07322i) q^{76} +(-14.4892 + 4.25441i) q^{77} +(0.565652 + 3.93420i) q^{79} +(-1.20217 - 2.63238i) q^{80} +(-0.602967 - 4.19373i) q^{82} +(-13.5461 - 8.70557i) q^{83} +(2.59363 - 18.0391i) q^{85} +(4.60791 - 5.31782i) q^{86} +(3.56917 + 4.11904i) q^{88} +(13.2033 + 3.87683i) q^{89} -1.01308 q^{91} +(-4.18251 + 2.34662i) q^{92} +(2.77667 - 6.08006i) q^{94} +(17.0368 + 5.00244i) q^{95} +(-3.64397 + 2.34184i) q^{97} +(-0.443061 + 0.511320i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$		0			0
$3$		0			0
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−2.43450	+	1.56456i	−1.08874	+	0.699691i	−0.956560	−	0.291534i	$-0.905834\pi$
$5$	−2.43450	+	1.56456i	−1.08874	+	0.699691i	−0.132181	+	0.991226i	$0.542198\pi$
$6$		0			0
$7$	0.394306	−	2.74246i	0.149034	−	1.03655i	−0.768772	−	0.639523i	$-0.779132\pi$
$7$	0.394306	−	2.74246i	0.149034	−	1.03655i	0.917806	−	0.397030i	$-0.129959\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$		0			0
$10$	0.411844	+	2.86444i	0.130237	+	0.905815i
$11$	−2.26413	−	4.95774i	−0.682659	−	1.49482i	−0.859800	−	0.510630i	$-0.829412\pi$
$11$	−2.26413	−	4.95774i	−0.682659	−	1.49482i	0.177141	−	0.984185i	$-0.443315\pi$
$12$		0			0
$13$	−0.0520365	−	0.361922i	−0.0144323	−	0.100379i	0.981332	−	0.192321i	$-0.0616016\pi$
$13$	−0.0520365	−	0.361922i	−0.0144323	−	0.100379i	−0.995764	+	0.0919422i	$0.970692\pi$
$14$	−2.33083	−	1.49793i	−0.622941	−	0.400340i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−4.12405	+	4.75941i	−1.00023	+	1.15433i	−0.0122207	+	0.999925i	$0.503890\pi$
$17$	−4.12405	+	4.75941i	−1.00023	+	1.15433i	−0.988008	+	0.154401i	$0.950655\pi$
$18$		0			0
$19$	−4.01801	−	4.63704i	−0.921796	−	1.06381i	−0.997773	−	0.0666993i	$-0.978753\pi$
$19$	−4.01801	−	4.63704i	−0.921796	−	1.06381i	0.0759775	−	0.997110i	$-0.475792\pi$
$20$	2.77667	+	0.815304i	0.620883	+	0.182308i
$21$		0			0
$22$	−5.45027			−1.16200
$23$	0.965501	−	4.69764i	0.201321	−	0.979525i
$23$	0.965501	−	4.69764i	0.201321	−	0.979525i
$24$		0			0
$25$	1.40187	−	3.06967i	0.280374	−	0.613933i
$26$	−0.350833	−	0.103014i	−0.0688039	−	0.0202027i
$27$		0			0
$28$	−2.33083	+	1.49793i	−0.440485	+	0.283083i
$29$	2.23325	−	2.57731i	0.414704	−	0.478594i	−0.509512	−	0.860463i	$-0.670174\pi$
$29$	2.23325	−	2.57731i	0.414704	−	0.478594i	0.924216	+	0.381869i	$0.124720\pi$
$30$		0			0
$31$	−7.37071	+	2.16423i	−1.32382	+	0.388708i	−0.865869	−	0.500270i	$-0.833234\pi$
$31$	−7.37071	+	2.16423i	−1.32382	+	0.388708i	−0.457949	+	0.888979i	$0.651416\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$		0			0
$34$	2.61612	+	5.72850i	0.448660	+	0.982429i
$35$	3.33080	+	7.29343i	0.563008	+	1.23282i
$36$		0			0
$37$	4.06209	+	2.61055i	0.667804	+	0.429171i	0.830133	−	0.557565i	$-0.188264\pi$
$37$	4.06209	+	2.61055i	0.667804	+	0.429171i	−0.162329	+	0.986737i	$0.551901\pi$
$38$	−5.88714	+	1.72862i	−0.955020	+	0.280419i
$39$		0			0
$40$	1.89510	−	2.18706i	0.299641	−	0.345804i
$41$	3.56427	−	2.29062i	0.556645	−	0.357734i	−0.231873	−	0.972746i	$-0.574485\pi$
$41$	3.56427	−	2.29062i	0.556645	−	0.357734i	0.788518	+	0.615012i	$0.210849\pi$
$42$		0			0
$43$	6.75145	+	1.98241i	1.02959	+	0.302314i	0.752543	−	0.658543i	$-0.228827\pi$
$43$	6.75145	+	1.98241i	1.02959	+	0.302314i	0.277044	+	0.960857i	$0.410645\pi$
$44$	−2.26413	+	4.95774i	−0.341330	+	0.747408i
$45$		0			0
$46$	−3.87204	−	2.82972i	−0.570901	−	0.417219i
$47$	6.68409			0.974975			0.487487	−	0.873130i	$-0.337914\pi$
$47$	6.68409			0.974975			0.487487	+	0.873130i	$0.337914\pi$
$48$		0			0
$49$	−0.649167	−	0.190613i	−0.0927382	−	0.0272304i
$50$	−2.20991	−	2.55037i	−0.312528	−	0.360677i
$51$		0			0
$52$	−0.239446	+	0.276335i	−0.0332051	+	0.0383208i
$53$	1.01536	−	7.06200i	0.139471	−	0.970040i	−0.793110	−	0.609078i	$-0.791539\pi$
$53$	1.01536	−	7.06200i	0.139471	−	0.970040i	0.932581	−	0.360962i	$-0.117551\pi$
$54$		0			0
$55$	13.2687	+	8.52726i	1.78915	+	1.14982i
$56$	0.394306	+	2.74246i	0.0526914	+	0.366477i
$57$		0			0
$58$	−1.41668	−	3.10209i	−0.186019	−	0.407324i
$59$	0.0626320	+	0.435615i	0.00815399	+	0.0567122i	0.993492	−	0.113900i	$-0.0363344\pi$
$59$	0.0626320	+	0.435615i	0.00815399	+	0.0567122i	−0.985338	+	0.170613i	$0.945425\pi$
$60$		0			0
$61$	−7.80450	+	2.29161i	−0.999264	+	0.293411i	−0.740154	−	0.672437i	$-0.765247\pi$
$61$	−7.80450	+	2.29161i	−0.999264	+	0.293411i	−0.259110	+	0.965848i	$0.583429\pi$
$62$	−1.09325	+	7.60369i	−0.138842	+	0.965669i
$63$		0			0
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	0.692931	+	0.799685i	0.0859475	+	0.0991887i
$66$		0			0
$67$	1.84829	−	4.04720i	0.225805	−	0.494444i	−0.762490	−	0.647000i	$-0.776023\pi$
$67$	1.84829	−	4.04720i	0.225805	−	0.494444i	0.988295	+	0.152556i	$0.0487505\pi$
$68$	6.29760			0.763696
$69$		0			0
$70$	8.01801			0.958335
$71$	0.586952	−	1.28525i	0.0696584	−	0.152531i	−0.871600	−	0.490218i	$-0.836917\pi$
$71$	0.586952	−	1.28525i	0.0696584	−	0.152531i	0.941258	+	0.337687i	$0.109645\pi$
$72$		0			0
$73$	2.58092	+	2.97855i	0.302074	+	0.348612i	0.886411	−	0.462899i	$-0.153191\pi$
$73$	2.58092	+	2.97855i	0.302074	+	0.348612i	−0.584337	+	0.811511i	$0.698645\pi$
$74$	4.06209	−	2.61055i	0.472209	−	0.303470i
$75$		0			0
$76$	−0.873198	+	6.07322i	−0.100163	+	0.696647i
$77$	−14.4892	+	4.25441i	−1.65120	+	0.484835i
$78$		0			0
$79$	0.565652	+	3.93420i	0.0636408	+	0.442632i	0.996582	+	0.0826040i	$0.0263237\pi$
$79$	0.565652	+	3.93420i	0.0636408	+	0.442632i	−0.932942	+	0.360028i	$0.882767\pi$
$80$	−1.20217	−	2.63238i	−0.134406	−	0.294309i
$81$		0			0
$82$	−0.602967	−	4.19373i	−0.0665866	−	0.463120i
$83$	−13.5461	−	8.70557i	−1.48688	−	0.955561i	−0.996459	−	0.0840759i	$-0.973206\pi$
$83$	−13.5461	−	8.70557i	−1.48688	−	0.955561i	−0.490422	−	0.871485i	$-0.663157\pi$
$84$		0			0
$85$	2.59363	−	18.0391i	0.281319	−	1.95661i
$86$	4.60791	−	5.31782i	0.496884	−	0.573435i
$87$		0			0
$88$	3.56917	+	4.11904i	0.380475	+	0.439091i
$89$	13.2033	+	3.87683i	1.39954	+	0.410943i	0.892528	−	0.450993i	$-0.148930\pi$
$89$	13.2033	+	3.87683i	1.39954	+	0.410943i	0.507017	+	0.861936i	$0.330748\pi$
$90$		0			0
$91$	−1.01308			−0.106199
$92$	−4.18251	+	2.34662i	−0.436057	+	0.244652i
$93$		0			0
$94$	2.77667	−	6.08006i	0.286392	−	0.627110i
$95$	17.0368	+	5.00244i	1.74793	+	0.513240i
$96$		0			0
$97$	−3.64397	+	2.34184i	−0.369989	+	0.237778i	−0.712401	−	0.701772i	$-0.752392\pi$
$97$	−3.64397	+	2.34184i	−0.369989	+	0.237778i	0.342412	+	0.939550i	$0.388756\pi$
$98$	−0.443061	+	0.511320i	−0.0447560	+	0.0516511i
$99$		0			0
$100$	−3.23793	+	0.950741i	−0.323793	+	0.0950741i
$101$	−5.40610	−	3.47429i	−0.537927	−	0.345705i	0.243301	−	0.969951i	$-0.421770\pi$
$101$	−5.40610	−	3.47429i	−0.537927	−	0.345705i	−0.781228	+	0.624246i	$0.785406\pi$
$102$		0			0
$103$	−5.10326	−	11.1746i	−0.502839	−	1.10106i	−0.975536	−	0.219839i	$-0.929447\pi$
$103$	−5.10326	−	11.1746i	−0.502839	−	1.10106i	0.472697	−	0.881225i	$-0.343280\pi$
$104$	0.151894	+	0.332601i	0.0148944	+	0.0326142i
$105$		0			0
$106$	−6.00202	−	3.85727i	−0.582968	−	0.374651i
$107$	9.53368	−	2.79934i	0.921656	−	0.270623i	0.213716	−	0.976896i	$-0.431443\pi$
$107$	9.53368	−	2.79934i	0.921656	−	0.270623i	0.707939	+	0.706273i	$0.249625\pi$
$108$		0			0
$109$	6.81481	−	7.86470i	0.652740	−	0.753302i	−0.328833	−	0.944388i	$-0.606655\pi$
$109$	6.81481	−	7.86470i	0.652740	−	0.753302i	0.981573	+	0.191086i	$0.0612009\pi$
$110$	13.2687	−	8.52726i	1.26512	−	0.813043i
$111$		0			0
$112$	2.65843	+	0.780586i	0.251198	+	0.0737584i
$113$	−4.46613	+	9.77947i	−0.420138	+	0.919975i	0.574687	+	0.818373i	$0.305124\pi$
$113$	−4.46613	+	9.77947i	−0.420138	+	0.919975i	−0.994825	+	0.101601i	$0.967603\pi$
$114$		0			0
$115$	4.99921	+	12.9470i	0.466179	+	1.20731i
$116$	−3.41027			−0.316635
$117$		0			0
$118$	0.422268	+	0.123989i	0.0388729	+	0.0114141i
$119$	11.4264	+	13.1867i	1.04745	+	1.20882i
$120$		0			0
$121$	−12.2495	+	14.1367i	−1.11359	+	1.28515i
$122$	−1.15759	+	8.05120i	−0.104803	+	0.728921i
$123$		0			0
$124$	6.46241	+	4.15314i	0.580341	+	0.372963i
$125$	−0.669402	−	4.65579i	−0.0598731	−	0.416427i
$126$		0			0
$127$	−4.03228	−	8.82946i	−0.357807	−	0.783488i	−0.999858	−	0.0168262i	$-0.994644\pi$
$127$	−4.03228	−	8.82946i	−0.357807	−	0.783488i	0.642052	−	0.766661i	$-0.278083\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$		0			0
$130$	1.01527	−	0.298111i	0.0890453	−	0.0261461i
$131$	−1.86823	+	12.9938i	−0.163228	+	1.13527i	0.729271	+	0.684225i	$0.239859\pi$
$131$	−1.86823	+	12.9938i	−0.163228	+	1.13527i	−0.892499	+	0.451049i	$0.851050\pi$
$132$		0			0
$133$	−14.3012	+	9.19084i	−1.24007	+	0.796947i
$134$	−2.91365	−	3.36253i	−0.251701	−	0.290479i
$135$		0			0
$136$	2.61612	−	5.72850i	0.224330	−	0.491215i
$137$	3.83057			0.327268			0.163634	−	0.986521i	$-0.447678\pi$
$137$	3.83057			0.327268			0.163634	+	0.986521i	$0.447678\pi$
$138$		0			0
$139$	17.3000			1.46736			0.733682	−	0.679494i	$-0.237800\pi$
$139$	17.3000			1.46736			0.733682	+	0.679494i	$0.237800\pi$
$140$	3.33080	−	7.29343i	0.281504	−	0.616408i
$141$		0			0
$142$	−0.925273	−	1.06782i	−0.0776471	−	0.0896096i
$143$	−1.67650	+	1.07742i	−0.140196	+	0.0900984i
$144$		0			0
$145$	−1.40450	+	9.76850i	−0.116637	+	0.811230i
$146$	3.78154	−	1.11036i	0.312962	−	0.0918940i
$147$		0			0
$148$	−0.687184	−	4.77947i	−0.0564862	−	0.392870i
$149$	−6.04641	−	13.2398i	−0.495341	−	1.08465i	−0.977956	−	0.208813i	$-0.933040\pi$
$149$	−6.04641	−	13.2398i	−0.495341	−	1.08465i	0.482615	−	0.875833i	$-0.339687\pi$
$150$		0			0
$151$	1.35418	+	9.41856i	0.110202	+	0.766471i	0.967722	+	0.252021i	$0.0810951\pi$
$151$	1.35418	+	9.41856i	0.110202	+	0.766471i	−0.857520	+	0.514451i	$0.827996\pi$
$152$	5.16166	+	3.31720i	0.418666	+	0.269060i
$153$		0			0
$154$	−2.14908	+	14.9472i	−0.173178	+	1.20448i
$155$	14.5579	−	16.8007i	1.16932	−	1.34947i
$156$		0			0
$157$	−15.6273	−	18.0349i	−1.24720	−	1.43934i	−0.854318	−	0.519750i	$-0.826025\pi$
$157$	−15.6273	−	18.0349i	−1.24720	−	1.43934i	−0.392878	−	0.919591i	$-0.628521\pi$
$158$	3.81365	+	1.11979i	0.303398	+	0.0890856i
$159$		0			0
$160$	−2.89389			−0.228782
$161$	−12.5024	−	4.50016i	−0.985326	−	0.354662i
$162$		0			0
$163$	3.39382	−	7.43143i	0.265824	−	0.582074i	−0.728904	−	0.684616i	$-0.759970\pi$
$163$	3.39382	−	7.43143i	0.265824	−	0.582074i	0.994729	+	0.102541i	$0.0326974\pi$
$164$	−4.06523	−	1.19366i	−0.317441	−	0.0932091i
$165$		0			0
$166$	−13.5461	+	8.70557i	−1.05138	+	0.675684i
$167$	−6.70343	+	7.73618i	−0.518727	+	0.598643i	−0.953312	−	0.301988i	$-0.902350\pi$
$167$	−6.70343	+	7.73618i	−0.518727	+	0.598643i	0.434584	+	0.900631i	$0.356895\pi$
$168$		0			0
$169$	12.3451	−	3.62486i	0.949625	−	0.278835i
$170$	−15.3315	−	9.85295i	−1.17587	−	0.755687i
$171$		0			0
$172$	−2.92306	−	6.40061i	−0.222881	−	0.488042i
$173$	1.40929	+	3.08592i	0.107147	+	0.234618i	0.955609	−	0.294637i	$-0.0951987\pi$
$173$	1.40929	+	3.08592i	0.107147	+	0.234618i	−0.848463	+	0.529255i	$0.822471\pi$
$174$		0			0
$175$	−7.86567	−	5.05496i	−0.594589	−	0.382119i
$176$	5.22950	−	1.53552i	0.394188	−	0.115744i
$177$		0			0
$178$	9.01133	−	10.3996i	0.675428	−	0.779485i
$179$	−5.74526	+	3.69226i	−0.429421	+	0.275972i	−0.737446	−	0.675406i	$-0.763968\pi$
$179$	−5.74526	+	3.69226i	−0.429421	+	0.275972i	0.308025	+	0.951378i	$0.400332\pi$
$180$		0			0
$181$	−0.902420	−	0.264975i	−0.0670764	−	0.0196954i	0.248022	−	0.968754i	$-0.420219\pi$
$181$	−0.902420	−	0.264975i	−0.0670764	−	0.0196954i	−0.315099	+	0.949059i	$0.602038\pi$
$182$	−0.420847	+	0.921526i	−0.0311952	+	0.0683080i
$183$		0			0
$184$	0.397086	+	4.77936i	0.0292736	+	0.352339i
$185$	−13.9735			−1.02735
$186$		0			0
$187$	32.9333	+	9.67008i	2.40832	+	0.707147i
$188$	−4.37715	−	5.05150i	−0.319236	−	0.368418i
$189$		0			0
$190$	11.6277	−	13.4191i	0.843563	−	0.973523i
$191$	−0.290991	+	2.02388i	−0.0210553	+	0.146443i	−0.997637	−	0.0687033i	$-0.978114\pi$
$191$	−0.290991	+	2.02388i	−0.0210553	+	0.146443i	0.976582	+	0.215146i	$0.0690229\pi$
$192$		0			0
$193$	−19.8456	−	12.7540i	−1.42852	−	0.918054i	−0.999894	−	0.0145713i	$-0.995362\pi$
$193$	−19.8456	−	12.7540i	−1.42852	−	0.918054i	−0.428625	−	0.903482i	$-0.641002\pi$
$194$	0.616451	+	4.28751i	0.0442586	+	0.307825i
$195$		0			0
$196$	0.281059	+	0.615433i	0.0200756	+	0.0439595i
$197$	−0.479933	−	3.33801i	−0.0341938	−	0.237823i	0.965556	−	0.260196i	$-0.0837871\pi$
$197$	−0.479933	−	3.33801i	−0.0341938	−	0.237823i	−0.999750	+	0.0223725i	$0.992878\pi$
$198$		0			0
$199$	−20.7972	+	6.10661i	−1.47427	+	0.432886i	−0.917486	−	0.397768i	$-0.869785\pi$
$199$	−20.7972	+	6.10661i	−1.47427	+	0.432886i	−0.556789	+	0.830654i	$0.687967\pi$
$200$	−0.480259	+	3.34027i	−0.0339594	+	0.236193i
$201$		0			0
$202$	−5.40610	+	3.47429i	−0.380372	+	0.244450i
$203$	−6.18758	−	7.14085i	−0.434283	−	0.501190i
$204$		0			0
$205$	−5.09341	+	11.1530i	−0.355739	+	0.778959i
$206$	−12.2847			−0.855917
$207$		0			0
$208$	0.365644			0.0253528
$209$	−13.8919	+	30.4191i	−0.960926	+	2.10413i
$210$		0			0
$211$	15.0163	+	17.3298i	1.03377	+	1.19303i	0.980917	+	0.194429i	$0.0622854\pi$
$211$	15.0163	+	17.3298i	1.03377	+	1.19303i	0.0528511	+	0.998602i	$0.483169\pi$
$212$	−6.00202	+	3.85727i	−0.412221	+	0.264918i
$213$		0			0
$214$	1.41406	−	9.83503i	0.0966634	−	0.672309i
$215$	−19.5380	+	5.73687i	−1.33248	+	0.391251i
$216$		0			0
$217$	3.02901	+	21.0673i	0.205623	+	1.43014i
$218$	−4.32301	−	9.46608i	−0.292791	−	0.641124i
$219$		0			0
$220$	−2.24466	−	15.6120i	−0.151335	−	1.05256i
$221$	1.93714	+	1.24492i	0.130306	+	0.0837425i
$222$		0			0
$223$	2.82161	−	19.6247i	0.188949	−	1.31417i	−0.645787	−	0.763518i	$-0.723470\pi$
$223$	2.82161	−	19.6247i	0.188949	−	1.31417i	0.834736	−	0.550651i	$-0.185620\pi$
$224$	1.81440	−	2.09393i	0.121230	−	0.139906i
$225$		0			0
$226$	7.04042	+	8.12507i	0.468322	+	0.540472i
$227$	−19.1242	−	5.61537i	−1.26932	−	0.372705i	−0.423362	−	0.905960i	$-0.639150\pi$
$227$	−19.1242	−	5.61537i	−1.26932	−	0.372705i	−0.845954	+	0.533255i	$0.820968\pi$
$228$		0			0
$229$	−16.2991			−1.07708			−0.538539	−	0.842601i	$-0.681023\pi$
$229$	−16.2991			−1.07708			−0.538539	+	0.842601i	$0.681023\pi$
$230$	13.8537	+	0.830924i	0.913488	+	0.0547895i
$231$		0			0
$232$	−1.41668	+	3.10209i	−0.0930094	+	0.203662i
$233$	17.8818	+	5.25056i	1.17147	+	0.343976i	0.808881	−	0.587972i	$-0.200073\pi$
$233$	17.8818	+	5.25056i	1.17147	+	0.343976i	0.362593	+	0.931948i	$0.381892\pi$
$234$		0			0
$235$	−16.2724	+	10.4576i	−1.06149	+	0.682181i
$236$	0.288201	−	0.332601i	0.0187603	−	0.0216505i
$237$		0			0
$238$	16.7417	−	4.91582i	1.08521	−	0.318645i
$239$	−3.70719	−	2.38247i	−0.239798	−	0.154109i	0.415222	−	0.909720i	$-0.363704\pi$
$239$	−3.70719	−	2.38247i	−0.239798	−	0.154109i	−0.655021	+	0.755611i	$0.727340\pi$
$240$		0			0
$241$	5.44932	+	11.9323i	0.351022	+	0.768630i	0.999970	+	0.00779736i	$0.00248200\pi$
$241$	5.44932	+	11.9323i	0.351022	+	0.768630i	−0.648948	+	0.760833i	$0.724791\pi$
$242$	7.77054	+	17.0151i	0.499509	+	1.09377i
$243$		0			0
$244$	6.84275	+	4.39757i	0.438062	+	0.281525i
$245$	1.87862	−	0.551613i	0.120021	−	0.0352413i
$246$		0			0
$247$	−1.46916	+	1.69550i	−0.0934805	+	0.107882i
$248$	6.46241	−	4.15314i	0.410363	−	0.263724i
$249$		0			0
$250$	−4.51314	−	1.32518i	−0.285436	−	0.0838115i
$251$	3.82791	−	8.38196i	0.241616	−	0.529065i	−0.749510	−	0.661993i	$-0.769711\pi$
$251$	3.82791	−	8.38196i	0.241616	−	0.529065i	0.991126	+	0.132928i	$0.0424380\pi$
$252$		0			0
$253$	−25.4757	+	5.84934i	−1.60164	+	0.367745i
$254$	−9.70663			−0.609048
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	1.59428	+	1.83990i	0.0994485	+	0.114770i	0.803292	−	0.595585i	$-0.203080\pi$
$257$	1.59428	+	1.83990i	0.0994485	+	0.114770i	−0.703844	+	0.710355i	$0.748534\pi$
$258$		0			0
$259$	8.76104	−	10.1108i	0.544384	−	0.628253i
$260$	0.150588	−	1.04736i	0.00933908	−	0.0649548i
$261$		0			0
$262$	11.0435	+	7.09722i	0.682269	+	0.438468i
$263$	−0.513250	−	3.56974i	−0.0316484	−	0.220119i	0.967859	−	0.251492i	$-0.0809212\pi$
$263$	−0.513250	−	3.56974i	−0.0316484	−	0.220119i	−0.999508	+	0.0313727i	$0.990012\pi$
$264$		0			0
$265$	8.57700	+	18.7810i	0.526881	+	1.15371i
$266$	2.41934	+	16.8269i	0.148339	+	1.03172i
$267$		0			0
$268$	−4.26904	+	1.25350i	−0.260773	+	0.0765699i
$269$	3.21946	−	22.3918i	0.196294	−	1.36525i	−0.618628	−	0.785684i	$-0.712311\pi$
$269$	3.21946	−	22.3918i	0.196294	−	1.36525i	0.814922	−	0.579570i	$-0.196780\pi$
$270$		0			0
$271$	11.5214	−	7.40434i	0.699874	−	0.449782i	−0.141710	−	0.989908i	$-0.545260\pi$
$271$	11.5214	−	7.40434i	0.699874	−	0.449782i	0.841584	+	0.540127i	$0.181624\pi$
$272$	−4.12405	−	4.75941i	−0.250057	−	0.288581i
$273$		0			0
$274$	1.59128	−	3.48441i	0.0961326	−	0.210501i
$275$	−18.3926			−1.10912
$276$		0			0
$277$	−10.2577			−0.616324			−0.308162	−	0.951334i	$-0.599714\pi$
$277$	−10.2577			−0.616324			−0.308162	+	0.951334i	$0.599714\pi$
$278$	7.18666	−	15.7366i	0.431027	−	0.943818i
$279$		0			0
$280$	−5.25068	−	6.05960i	−0.313788	−	0.362131i
$281$	2.62009	−	1.68383i	0.156302	−	0.100449i	−0.460152	−	0.887840i	$-0.652205\pi$
$281$	2.62009	−	1.68383i	0.156302	−	0.100449i	0.616454	+	0.787391i	$0.288569\pi$
$282$		0			0
$283$	1.35249	−	9.40677i	0.0803972	−	0.559174i	−0.909316	−	0.416107i	$-0.863394\pi$
$283$	1.35249	−	9.40677i	0.0803972	−	0.559174i	0.989713	−	0.143068i	$-0.0456967\pi$
$284$	−1.35570	+	0.398068i	−0.0804458	+	0.0236210i
$285$		0			0
$286$	0.283613	+	1.97257i	0.0167704	+	0.116641i
$287$	−4.87651	−	10.6781i	−0.287851	−	0.630307i
$288$		0			0
$289$	−3.22482	−	22.4291i	−0.189695	−	1.31936i
$290$	8.30229	+	5.33556i	0.487527	+	0.313315i
$291$		0			0
$292$	0.560888	−	3.90107i	0.0328235	−	0.228293i
$293$	16.4960	−	19.0374i	0.963704	−	1.11217i	−0.0299335	−	0.999552i	$-0.509530\pi$
$293$	16.4960	−	19.0374i	0.963704	−	1.11217i	0.993638	−	0.112622i	$-0.0359250\pi$
$294$		0			0
$295$	−0.834022	−	0.962513i	−0.0485586	−	0.0560397i
$296$	−4.63303	−	1.36038i	−0.269289	−	0.0790704i
$297$		0			0
$298$	−14.5551			−0.843155
$299$	−1.75042	−	0.104987i	−0.101229	−	0.00607157i
$300$		0			0
$301$	8.09881	−	17.7339i	0.466808	−	1.02217i
$302$	9.12997	+	2.68080i	0.525371	+	0.154263i
$303$		0			0
$304$	5.16166	−	3.31720i	0.296042	−	0.190254i
$305$	15.4147	−	17.7895i	0.882643	−	1.01862i
$306$		0			0
$307$	−1.27637	+	0.374777i	−0.0728464	+	0.0213896i	−0.317953	−	0.948107i	$-0.602995\pi$
$307$	−1.27637	+	0.374777i	−0.0728464	+	0.0213896i	0.245106	+	0.969496i	$0.421177\pi$
$308$	12.7037	+	8.16415i	0.723858	+	0.465195i
$309$		0			0
$310$	−9.23490	−	20.2216i	−0.524507	−	1.14851i
$311$	3.61737	+	7.92093i	0.205122	+	0.449155i	0.984034	−	0.177978i	$-0.0569556\pi$
$311$	3.61737	+	7.92093i	0.205122	+	0.449155i	−0.778912	+	0.627133i	$0.784228\pi$
$312$		0			0
$313$	10.7667	+	6.91932i	0.608568	+	0.391103i	0.808320	−	0.588744i	$-0.200377\pi$
$313$	10.7667	+	6.91932i	0.608568	+	0.391103i	−0.199752	+	0.979847i	$0.564014\pi$
$314$	−22.8969	+	6.72315i	−1.29215	+	0.379409i
$315$		0			0
$316$	2.60284	−	3.00384i	0.146421	−	0.168979i
$317$	−11.0873	+	7.12540i	−0.622727	+	0.400202i	−0.813610	−	0.581410i	$-0.802501\pi$
$317$	−11.0873	+	7.12540i	−0.622727	+	0.400202i	0.190884	+	0.981613i	$0.438865\pi$
$318$		0			0
$319$	−17.8340	−	5.23653i	−0.998512	−	0.293190i
$320$	−1.20217	+	2.63238i	−0.0672032	+	0.147154i
$321$		0			0
$322$	−9.28717	+	9.50314i	−0.517554	+	0.529589i
$323$	38.6400			2.14999
$324$		0			0
$325$	−1.18393	−	0.347633i	−0.0656725	−	0.0192832i
$326$	−5.35002	−	6.17425i	−0.296310	−	0.341960i
$327$		0			0
$328$	−2.77455	+	3.20200i	−0.153199	+	0.176801i
$329$	2.63558	−	18.3309i	0.145304	−	1.01061i
$330$		0			0
$331$	−26.6439	−	17.1230i	−1.46448	−	0.941166i	−0.998407	−	0.0564208i	$-0.982031\pi$
$331$	−26.6439	−	17.1230i	−1.46448	−	0.941166i	−0.466075	−	0.884745i	$-0.654332\pi$
$332$	2.29160	+	15.9384i	0.125768	+	0.874735i
$333$		0			0
$334$	4.25237	+	9.31138i	0.232679	+	0.509496i
$335$	1.83241	+	12.7447i	0.100115	+	0.696315i
$336$		0			0
$337$	−8.77072	+	2.57532i	−0.477772	+	0.140286i	−0.511747	−	0.859136i	$-0.671001\pi$
$337$	−8.77072	+	2.57532i	−0.477772	+	0.140286i	0.0339752	+	0.999423i	$0.489183\pi$
$338$	1.83107	−	12.7353i	0.0995969	−	0.692711i
$339$		0			0
$340$	−15.3315	+	9.85295i	−0.831467	+	0.534351i
$341$	27.4179	+	31.6420i	1.48476	+	1.71351i
$342$		0			0
$343$	7.27811	−	15.9368i	0.392981	−	0.860508i
$344$	−7.03648			−0.379381
$345$		0			0
$346$	3.39250			0.182382
$347$	−7.40034	+	16.2045i	−0.397271	+	0.869903i	0.600268	+	0.799799i	$0.295060\pi$
$347$	−7.40034	+	16.2045i	−0.397271	+	0.869903i	−0.997540	+	0.0701041i	$0.977667\pi$
$348$		0			0
$349$	13.6513	+	15.7545i	0.730739	+	0.843318i	0.992555	−	0.121800i	$-0.0388666\pi$
$349$	13.6513	+	15.7545i	0.730739	+	0.843318i	−0.261815	+	0.965118i	$0.584321\pi$
$350$	−7.86567	+	5.05496i	−0.420438	+	0.270199i
$351$		0			0
$352$	0.775655	−	5.39480i	0.0413425	−	0.287544i
$353$	21.2394	−	6.23645i	1.13046	−	0.331933i	0.337571	−	0.941300i	$-0.390395\pi$
$353$	21.2394	−	6.23645i	1.13046	−	0.331933i	0.792888	+	0.609367i	$0.208576\pi$
$354$		0			0
$355$	0.581907	+	4.04725i	0.0308844	+	0.214806i
$356$	−5.71639	−	12.5172i	−0.302968	−	0.663408i
$357$		0			0
$358$	0.971926	+	6.75990i	0.0513679	+	0.357272i
$359$	23.4475	+	15.0688i	1.23751	+	0.795302i	0.985044	−	0.172303i	$-0.0551208\pi$
$359$	23.4475	+	15.0688i	1.23751	+	0.795302i	0.252470	+	0.967605i	$0.418757\pi$
$360$		0			0
$361$	−2.65368	+	18.4567i	−0.139667	+	0.971407i
$362$	−0.615908	+	0.710796i	−0.0323714	+	0.0373586i
$363$		0			0
$364$	0.663423	+	0.765631i	0.0347728	+	0.0401300i
$365$	−10.9434	−	3.21326i	−0.572802	−	0.168190i
$366$		0			0
$367$	17.5832			0.917835			0.458917	−	0.888479i	$-0.348237\pi$
$367$	17.5832			0.917835			0.458917	+	0.888479i	$0.348237\pi$
$368$	4.51242	+	1.62422i	0.235226	+	0.0846682i
$369$		0			0
$370$	−5.80481	+	12.7108i	−0.301777	+	0.660800i
$371$	−18.9669	−	5.56918i	−0.984712	−	0.289138i
$372$		0			0
$373$	22.2145	−	14.2764i	1.15022	−	0.739205i	0.180541	−	0.983567i	$-0.442215\pi$
$373$	22.2145	−	14.2764i	1.15022	−	0.739205i	0.969684	+	0.244363i	$0.0785788\pi$
$374$	22.4772	−	25.9401i	1.16227	−	1.34133i
$375$		0			0
$376$	−6.41334	+	1.88313i	−0.330743	+	0.0971148i
$377$	−1.04900	−	0.674148i	−0.0540260	−	0.0347204i
$378$		0			0
$379$	1.05257	+	2.30481i	0.0540671	+	0.118390i	0.934737	−	0.355339i	$-0.115635\pi$
$379$	1.05257	+	2.30481i	0.0540671	+	0.118390i	−0.880670	+	0.473730i	$0.842907\pi$
$380$	−7.37611	−	16.1514i	−0.378386	−	0.828551i
$381$		0			0
$382$	1.72011	+	1.10545i	0.0880084	+	0.0565596i
$383$	3.40668	−	1.00029i	0.174073	−	0.0511124i	−0.193535	−	0.981093i	$-0.561995\pi$
$383$	3.40668	−	1.00029i	0.174073	−	0.0511124i	0.367608	+	0.929981i	$0.380177\pi$
$384$		0			0
$385$	28.6176	−	33.0265i	1.45849	−	1.68319i
$386$	−19.8456	+	12.7540i	−1.01012	+	0.649162i
$387$		0			0
$388$	4.15614	+	1.22035i	0.210996	+	0.0619540i
$389$	−11.5072	+	25.1973i	−0.583439	+	1.27755i	0.355887	+	0.934529i	$0.384179\pi$
$389$	−11.5072	+	25.1973i	−0.583439	+	1.27755i	−0.939326	+	0.343025i	$0.888548\pi$
$390$		0			0
$391$	18.3762	+	23.9685i	0.929324	+	1.21214i
$392$	0.676573			0.0341721
$393$		0			0
$394$	−3.23573	−	0.950097i	−0.163014	−	0.0478652i
$395$	−7.53236	−	8.69280i	−0.378994	−	0.437382i
$396$		0			0
$397$	13.9539	−	16.1037i	0.700329	−	0.808222i	−0.288468	−	0.957489i	$-0.593146\pi$
$397$	13.9539	−	16.1037i	0.700329	−	0.808222i	0.988797	+	0.149267i	$0.0476915\pi$
$398$	−3.08470	+	21.4546i	−0.154622	+	1.07542i
$399$		0			0
$400$	2.83891	+	1.82446i	0.141946	+	0.0912230i
$401$	1.55920	+	10.8445i	0.0778629	+	0.541549i	0.990996	+	0.133888i	$0.0427462\pi$
$401$	1.55920	+	10.8445i	0.0778629	+	0.541549i	−0.913134	+	0.407661i	$0.866345\pi$
$402$		0			0
$403$	1.16683	+	2.55500i	0.0581240	+	0.127274i
$404$	0.914549	+	6.36083i	0.0455005	+	0.316463i
$405$		0			0
$406$	−9.06596	+	2.66201i	−0.449936	+	0.132113i
$407$	3.74534	−	26.0494i	0.185650	−	1.29122i
$408$		0			0
$409$	24.3974	−	15.6793i	1.20638	−	0.775290i	0.226327	−	0.974051i	$-0.427328\pi$
$409$	24.3974	−	15.6793i	1.20638	−	0.775290i	0.980048	+	0.198761i	$0.0636918\pi$
$410$	8.02925	+	9.26625i	0.396536	+	0.457627i
$411$		0			0
$412$	−5.10326	+	11.1746i	−0.251419	+	0.550532i
$413$	1.21935			0.0600005
$414$		0			0
$415$	46.5984			2.28743
$416$	0.151894	−	0.332601i	0.00744721	−	0.0163071i
$417$		0			0
$418$	21.8993	+	25.2731i	1.07113	+	1.23615i
$419$	7.03546	−	4.52142i	0.343705	−	0.220886i	−0.357387	−	0.933956i	$-0.616332\pi$
$419$	7.03546	−	4.52142i	0.343705	−	0.220886i	0.701092	+	0.713071i	$0.252696\pi$
$420$		0			0
$421$	1.50874	−	10.4935i	0.0735315	−	0.511423i	−0.919455	−	0.393195i	$-0.871370\pi$
$421$	1.50874	−	10.4935i	0.0735315	−	0.511423i	0.992987	−	0.118228i	$-0.0377213\pi$
$422$	22.0017	−	6.46029i	1.07103	−	0.314482i
$423$		0			0
$424$	1.01536	+	7.06200i	0.0493103	+	0.342961i
$425$	8.82841	+	19.3315i	0.428241	+	0.937717i
$426$		0			0
$427$	3.20728	+	22.3072i	0.155211	+	1.07952i
$428$	−8.35884	−	5.37190i	−0.404040	−	0.259660i
$429$		0			0
$430$	−2.89793	+	20.1556i	−0.139751	+	0.971987i
$431$	0.308153	−	0.355628i	0.0148432	−	0.0171300i	−0.748279	−	0.663384i	$-0.769120\pi$
$431$	0.308153	−	0.355628i	0.0148432	−	0.0171300i	0.763123	+	0.646254i	$0.223665\pi$
$432$		0			0
$433$	18.9929	+	21.9190i	0.912743	+	1.05336i	0.998372	+	0.0570343i	$0.0181644\pi$
$433$	18.9929	+	21.9190i	0.912743	+	1.05336i	−0.0856295	+	0.996327i	$0.527290\pi$
$434$	20.4217	+	5.99637i	0.980275	+	0.287835i
$435$		0			0
$436$	−10.4065			−0.498381
$437$	−25.6625	+	14.3981i	−1.22760	+	0.688755i
$438$		0			0
$439$	−6.26627	+	13.7212i	−0.299073	+	0.654878i	−0.998191	−	0.0601285i	$-0.980849\pi$
$439$	−6.26627	+	13.7212i	−0.299073	+	0.654878i	0.699118	+	0.715006i	$0.253576\pi$
$440$	−15.1336	−	4.44363i	−0.721467	−	0.211842i
$441$		0			0
$442$	1.93714	−	1.24492i	0.0921401	−	0.0592149i
$443$	−17.4014	+	20.0823i	−0.826765	+	0.954137i	−0.999525	−	0.0308265i	$-0.990186\pi$
$443$	−17.4014	+	20.0823i	−0.826765	+	0.954137i	0.172760	+	0.984964i	$0.444732\pi$
$444$		0			0
$445$	−38.2089	+	11.2191i	−1.81127	+	0.531838i
$446$	−16.6791	−	10.7190i	−0.789780	−	0.507561i
$447$		0			0
$448$	−1.15098	−	2.52028i	−0.0543785	−	0.119072i
$449$	−1.61015	−	3.52574i	−0.0759878	−	0.166390i	0.867826	−	0.496869i	$-0.165517\pi$
$449$	−1.61015	−	3.52574i	−0.0759878	−	0.166390i	−0.943813	+	0.330479i	$0.892790\pi$
$450$		0			0
$451$	−19.4262	−	12.4845i	−0.914746	−	0.587871i
$452$	10.3155	−	3.02891i	0.485201	−	0.142468i
$453$		0			0
$454$	−13.0524	+	15.0633i	−0.612579	+	0.706954i
$455$	2.46633	−	1.58501i	0.115623	−	0.0743066i
$456$		0			0
$457$	−3.09150	−	0.907746i	−0.144614	−	0.0424626i	0.208624	−	0.977996i	$-0.433101\pi$
$457$	−3.09150	−	0.907746i	−0.144614	−	0.0424626i	−0.353239	+	0.935533i	$0.614920\pi$
$458$	−6.77091	+	14.8262i	−0.316384	+	0.692784i
$459$		0			0
$460$	6.51088	−	12.2566i	0.303572	−	0.571468i
$461$	25.7463			1.19912			0.599562	−	0.800329i	$-0.295342\pi$
$461$	25.7463			1.19912			0.599562	+	0.800329i	$0.295342\pi$
$462$		0			0
$463$	−17.8150	−	5.23097i	−0.827936	−	0.243104i	−0.159806	−	0.987148i	$-0.551087\pi$
$463$	−17.8150	−	5.23097i	−0.827936	−	0.243104i	−0.668130	+	0.744045i	$0.732905\pi$
$464$	2.23325	+	2.57731i	0.103676	+	0.119649i
$465$		0			0
$466$	12.2044	−	14.0847i	0.565360	−	0.652460i
$467$	0.885467	−	6.15856i	0.0409745	−	0.284984i	−0.959024	−	0.283325i	$-0.908563\pi$
$467$	0.885467	−	6.15856i	0.0409745	−	0.284984i	0.999999	−	0.00165959i	$-0.000528263\pi$
$468$		0			0
$469$	−10.3705	−	6.66471i	−0.478865	−	0.307748i
$470$	2.75280	+	19.1462i	0.126977	+	0.883147i
$471$		0			0
$472$	−0.182822	−	0.400324i	−0.00841506	−	0.0184264i
$473$	−5.45788	−	37.9604i	−0.250953	−	1.74542i
$474$		0			0
$475$	−19.8669	+	5.83344i	−0.911555	+	0.267657i
$476$	2.48318	−	17.2709i	0.113817	−	0.791611i
$477$		0			0
$478$	−3.70719	+	2.38247i	−0.169563	+	0.108972i
$479$	−6.76132	−	7.80298i	−0.308933	−	0.356527i	0.579958	−	0.814646i	$-0.303069\pi$
$479$	−6.76132	−	7.80298i	−0.308933	−	0.356527i	−0.888891	+	0.458119i	$0.848523\pi$
$480$		0			0
$481$	0.733438	−	1.60600i	0.0334419	−	0.0732275i
$482$	13.1178			0.597498
$483$		0			0
$484$	18.7055			0.850249
$485$	5.20730	−	11.4024i	0.236451	−	0.517757i
$486$		0			0
$487$	−16.4493	−	18.9835i	−0.745387	−	0.860223i	0.248726	−	0.968574i	$-0.419988\pi$
$487$	−16.4493	−	18.9835i	−0.745387	−	0.860223i	−0.994113	+	0.108351i	$0.965443\pi$
$488$	6.84275	−	4.39757i	0.309757	−	0.199068i
$489$		0			0
$490$	0.278643	−	1.93800i	0.0125878	−	0.0875500i
$491$	1.47060	−	0.431806i	0.0663671	−	0.0194871i	−0.248380	−	0.968663i	$-0.579898\pi$
$491$	1.47060	−	0.431806i	0.0663671	−	0.0194871i	0.314748	+	0.949175i	$0.398080\pi$
$492$		0			0
$493$	3.05642	+	21.2579i	0.137654	+	0.957408i
$494$	0.931972	+	2.04073i	0.0419314	+	0.0918170i
$495$		0			0
$496$	−1.09325	−	7.60369i	−0.0490882	−	0.341416i
$497$	−3.29330	−	2.11648i	−0.147725	−	0.0949369i
$498$		0			0
$499$	3.33474	−	23.1936i	0.149283	−	1.03829i	−0.768113	−	0.640314i	$-0.778804\pi$
$499$	3.33474	−	23.1936i	0.149283	−	1.03829i	0.917397	−	0.397974i	$-0.130287\pi$
$500$	−3.08025	+	3.55480i	−0.137753	+	0.158975i
$501$		0			0
$502$	−6.03433	−	6.96399i	−0.269325	−	0.310818i
$503$	9.03611	+	2.65324i	0.402900	+	0.118302i	0.476903	−	0.878956i	$-0.341759\pi$
$503$	9.03611	+	2.65324i	0.402900	+	0.118302i	−0.0740030	+	0.997258i	$0.523577\pi$
$504$		0			0
$505$	18.5969			0.827549
$506$	−5.26224	+	25.6034i	−0.233935	+	1.13821i
$507$		0			0
$508$	−4.03228	+	8.82946i	−0.178903	+	0.391744i
$509$	9.58906	+	2.81560i	0.425027	+	0.124799i	0.487249	−	0.873263i	$-0.338000\pi$
$509$	9.58906	+	2.81560i	0.425027	+	0.124799i	−0.0622217	+	0.998062i	$0.519819\pi$
$510$		0			0
$511$	9.18622	−	5.90363i	0.406375	−	0.261161i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$		0			0
$514$	2.33592	−	0.685888i	0.103033	−	0.0302532i
$515$	29.9071	+	19.2201i	1.31787	+	0.846941i
$516$		0			0
$517$	−15.1336	−	33.1380i	−0.665576	−	1.45741i
$518$	−5.55762	−	12.1695i	−0.244188	−	0.534697i
$519$		0			0
$520$	−0.890159	−	0.572071i	−0.0390361	−	0.0250870i
$521$	−37.0292	+	10.8728i	−1.62228	+	0.476345i	−0.961630	−	0.274349i	$-0.911538\pi$
$521$	−37.0292	+	10.8728i	−1.62228	+	0.476345i	−0.660650	+	0.750694i	$0.729719\pi$
$522$		0			0
$523$	6.29792	−	7.26819i	0.275389	−	0.317816i	−0.601160	−	0.799129i	$-0.705295\pi$
$523$	6.29792	−	7.26819i	0.275389	−	0.317816i	0.876549	+	0.481313i	$0.159840\pi$
$524$	11.0435	−	7.09722i	0.482437	−	0.310044i
$525$		0			0
$526$	−3.46036	−	1.01605i	−0.150879	−	0.0443020i
$527$	20.0967	−	44.0056i	0.875426	−	1.91691i
$528$		0			0
$529$	−21.1356	−	9.07115i	−0.918940	−	0.394398i
$530$	20.6468			0.896841
$531$		0			0
$532$	16.3113	+	4.78942i	0.707184	+	0.207648i
$533$	−1.01450	−	1.17079i	−0.0439427	−	0.0507126i
$534$		0			0
$535$	−18.8300	+	21.7310i	−0.814092	+	0.939512i
$536$	−0.633197	+	4.40398i	−0.0273499	+	0.190223i
$537$		0			0
$538$	−19.0309	−	12.2304i	−0.820481	−	0.527291i
$539$	0.524787	+	3.64998i	0.0226042	+	0.157216i
$540$		0			0
$541$	5.98880	+	13.1137i	0.257479	+	0.563800i	0.993588	−	0.113063i	$-0.0360662\pi$
$541$	5.98880	+	13.1137i	0.257479	+	0.563800i	−0.736109	+	0.676863i	$0.763339\pi$
$542$	−1.94907	−	13.5561i	−0.0837198	−	0.582284i
$543$		0			0
$544$	−6.04250	+	1.77424i	−0.259070	+	0.0760699i
$545$	−4.28585	+	29.8088i	−0.183586	+	1.27687i
$546$		0			0
$547$	−11.8995	+	7.64737i	−0.508788	+	0.326978i	−0.769723	−	0.638378i	$-0.779605\pi$
$547$	−11.8995	+	7.64737i	−0.508788	+	0.326978i	0.260935	+	0.965356i	$0.415969\pi$
$548$	−2.50849	−	2.89496i	−0.107158	−	0.123666i
$549$		0			0
$550$	−7.64057	+	16.7305i	−0.325795	+	0.713392i
$551$	−20.9243			−0.891405
$552$		0			0
$553$	11.0124			0.468296
$554$	−4.26119	+	9.33071i	−0.181041	+	0.396424i
$555$		0			0
$556$	−11.3291	−	13.0744i	−0.480459	−	0.554479i
$557$	−8.83021	+	5.67483i	−0.374148	+	0.240450i	−0.714178	−	0.699964i	$-0.753199\pi$
$557$	−8.83021	+	5.67483i	−0.374148	+	0.240450i	0.340030	+	0.940415i	$0.389563\pi$
$558$		0			0
$559$	0.366154	−	2.54666i	0.0154867	−	0.107712i
$560$	−7.69322	+	2.25893i	−0.325098	+	0.0954573i
$561$		0			0
$562$	−0.443241	−	3.08281i	−0.0186970	−	0.130040i
$563$	9.84751	+	21.5630i	0.415023	+	0.908774i	0.995524	+	0.0945139i	$0.0301297\pi$
$563$	9.84751	+	21.5630i	0.415023	+	0.908774i	−0.580500	+	0.814260i	$0.697143\pi$
$564$		0			0
$565$	−4.42774	−	30.7956i	−0.186276	−	1.29558i
$566$	−7.99486	−	5.13798i	−0.336049	−	0.215965i
$567$		0			0
$568$	−0.201081	+	1.39855i	−0.00843717	+	0.0586818i
$569$	6.40005	−	7.38606i	0.268304	−	0.309640i	−0.605570	−	0.795792i	$-0.707055\pi$
$569$	6.40005	−	7.38606i	0.268304	−	0.309640i	0.873874	+	0.486153i	$0.161600\pi$
$570$		0			0
$571$	16.1753	+	18.6673i	0.676916	+	0.781203i	0.985442	−	0.170013i	$-0.0543810\pi$
$571$	16.1753	+	18.6673i	0.676916	+	0.781203i	−0.308526	+	0.951216i	$0.599836\pi$
$572$	1.91213	+	0.561453i	0.0799503	+	0.0234755i
$573$		0			0
$574$	−11.7389			−0.489972
$575$	−13.0667	−	9.54924i	−0.544918	−	0.398231i
$576$		0			0
$577$	−0.394559	+	0.863965i	−0.0164257	+	0.0359673i	−0.917667	−	0.397350i	$-0.869930\pi$
$577$	−0.394559	+	0.863965i	−0.0164257	+	0.0359673i	0.901241	+	0.433317i	$0.142657\pi$
$578$	−21.7419	−	6.38399i	−0.904343	−	0.265539i
$579$		0			0
$580$	8.30229	−	5.33556i	0.344734	−	0.221547i
$581$	−29.2160	+	33.7171i	−1.21209	+	1.39882i
$582$		0			0
$583$	−37.3105	+	10.9553i	−1.54524	+	0.453724i
$584$	−3.31553	−	2.13076i	−0.137198	−	0.0881716i
$585$		0			0
$586$	−10.4643	−	22.9137i	−0.432277	−	0.946554i
$587$	−1.71897	−	3.76402i	−0.0709494	−	0.155358i	0.870834	−	0.491576i	$-0.163579\pi$
$587$	−1.71897	−	3.76402i	−0.0709494	−	0.155358i	−0.941784	+	0.336219i	$0.890852\pi$
$588$		0			0
$589$	39.6512	+	25.4823i	1.63380	+	1.04998i
$590$	−1.22200	+	0.358811i	−0.0503088	+	0.0147720i
$591$		0			0
$592$	−3.16207	+	3.64923i	−0.129960	+	0.149982i
$593$	31.0039	−	19.9250i	1.27318	−	0.818221i	0.283147	−	0.959077i	$-0.408622\pi$
$593$	31.0039	−	19.9250i	1.27318	−	0.818221i	0.990030	+	0.140855i	$0.0449853\pi$
$594$		0			0
$595$	−48.4488	−	14.2259i	−1.98621	−	0.583203i
$596$	−6.04641	+	13.2398i	−0.247671	+	0.542323i
$597$		0			0
$598$	−0.822651	+	1.54862i	−0.0336407	+	0.0633280i
$599$	−1.06163			−0.0433771			−0.0216885	−	0.999765i	$-0.506904\pi$
$599$	−1.06163			−0.0433771			−0.0216885	+	0.999765i	$0.506904\pi$
$600$		0			0
$601$	7.52005	+	2.20809i	0.306749	+	0.0900697i	0.431484	−	0.902120i	$-0.357990\pi$
$601$	7.52005	+	2.20809i	0.306749	+	0.0900697i	−0.124735	+	0.992190i	$0.539808\pi$
$602$	−12.7670	−	14.7339i	−0.520343	−	0.600508i
$603$		0			0
$604$	6.23127	−	7.19127i	0.253547	−	0.292608i
$605$	7.70374	−	53.5807i	0.313202	−	2.17836i
$606$		0			0
$607$	−1.37597	−	0.884282i	−0.0558489	−	0.0358919i	0.512418	−	0.858736i	$-0.328750\pi$
$607$	−1.37597	−	0.884282i	−0.0558489	−	0.0358919i	−0.568267	+	0.822844i	$0.692386\pi$
$608$	−0.873198	−	6.07322i	−0.0354129	−	0.246302i
$609$		0			0
$610$	−9.77841	−	21.4117i	−0.395916	−	0.866936i
$611$	−0.347817	−	2.41912i	−0.0140712	−	0.0978671i
$612$		0			0
$613$	26.5787	−	7.80421i	1.07350	−	0.315209i	0.303226	−	0.952919i	$-0.401936\pi$
$613$	26.5787	−	7.80421i	1.07350	−	0.315209i	0.770277	+	0.637710i	$0.220118\pi$
$614$	−0.189315	+	1.31672i	−0.00764015	+	0.0531384i
$615$		0			0
$616$	12.7037	−	8.16415i	0.511845	−	0.328943i
$617$	−7.51758	−	8.67575i	−0.302646	−	0.349273i	0.583972	−	0.811774i	$-0.301498\pi$
$617$	−7.51758	−	8.67575i	−0.302646	−	0.349273i	−0.886619	+	0.462501i	$0.846952\pi$
$618$		0			0
$619$	−17.4123	+	38.1276i	−0.699858	+	1.53248i	0.140285	+	0.990111i	$0.455198\pi$
$619$	−17.4123	+	38.1276i	−0.699858	+	1.53248i	−0.840143	+	0.542365i	$0.817529\pi$
$620$	−22.2305			−0.892800
$621$		0			0
$622$	8.70784			0.349152
$623$	15.8382	−	34.6808i	0.634544	−	1.38946i
$624$		0			0
$625$	19.9635	+	23.0391i	0.798538	+	0.921562i
$626$	10.7667	−	6.91932i	0.430323	−	0.276552i
$627$		0			0
$628$	−3.39614	+	23.6207i	−0.135521	+	0.942568i
$629$	−29.1769	+	8.56712i	−1.16336	+	0.341593i
$630$		0			0
$631$	3.46844	+	24.1235i	0.138076	+	0.960343i	0.934591	+	0.355724i	$0.115766\pi$
$631$	3.46844	+	24.1235i	0.138076	+	0.960343i	−0.796515	+	0.604619i	$0.793325\pi$
$632$	−1.65113	−	3.61547i	−0.0656784	−	0.143816i
$633$		0			0
$634$	1.87564	+	13.0454i	0.0744913	+	0.518099i
$635$	23.6308	+	15.1866i	0.937758	+	0.602661i
$636$		0			0
$637$	−0.0352065	+	0.244867i	−0.00139493	+	0.00970198i
$638$	−12.1718	+	14.0470i	−0.481887	+	0.556127i
$639$		0			0
$640$	1.89510	+	2.18706i	0.0749103	+	0.0864511i
$641$	−36.3068	−	10.6606i	−1.43403	−	0.421070i	−0.529805	−	0.848119i	$-0.677735\pi$
$641$	−36.3068	−	10.6606i	−1.43403	−	0.421070i	−0.904228	+	0.427049i	$0.859553\pi$
$642$		0			0
$643$	−5.62757			−0.221930			−0.110965	−	0.993824i	$-0.535394\pi$
$643$	−5.62757			−0.221930			−0.110965	+	0.993824i	$0.535394\pi$
$644$	4.78633	+	12.3957i	0.188608	+	0.488457i
$645$		0			0
$646$	16.0516	−	35.1482i	0.631544	−	1.38289i
$647$	−23.6526	−	6.94504i	−0.929881	−	0.273038i	−0.218494	−	0.975838i	$-0.570114\pi$
$647$	−23.6526	−	6.94504i	−0.929881	−	0.273038i	−0.711387	+	0.702801i	$0.751933\pi$
$648$		0			0
$649$	2.01786	−	1.29680i	0.0792079	−	0.0509039i
$650$	−0.808039	+	0.932527i	−0.0316939	+	0.0365767i
$651$		0			0
$652$	−7.83878	+	2.30167i	−0.306990	+	0.0901405i
$653$	−34.8323	−	22.3853i	−1.36309	−	0.876006i	−0.364614	−	0.931159i	$-0.618799\pi$
$653$	−34.8323	−	22.3853i	−1.36309	−	0.876006i	−0.998478	+	0.0551529i	$0.982435\pi$
$654$		0			0
$655$	−15.7814	−	34.5564i	−0.616629	−	1.35023i
$656$	1.76005	+	3.85398i	0.0687185	+	0.150473i
$657$		0			0
$658$	−15.5795	−	10.0123i	−0.607351	−	0.390321i
$659$	−14.6710	+	4.30780i	−0.571502	+	0.167808i	−0.554699	−	0.832051i	$-0.687167\pi$
$659$	−14.6710	+	4.30780i	−0.571502	+	0.167808i	−0.0168022	+	0.999859i	$0.505349\pi$
$660$		0			0
$661$	10.7039	−	12.3530i	0.416333	−	0.480474i	−0.508383	−	0.861131i	$-0.669757\pi$
$661$	10.7039	−	12.3530i	0.416333	−	0.480474i	0.924716	+	0.380657i	$0.124302\pi$
$662$	−26.6439	+	17.1230i	−1.03555	+	0.665505i
$663$		0			0
$664$	15.4501	+	4.53655i	0.599579	+	0.176052i
$665$	20.4367	−	44.7502i	0.792502	−	1.73534i
$666$		0			0
$667$	−9.95106	−	12.9794i	−0.385306	−	0.502564i
$668$	10.2364			0.396059
$669$		0			0
$670$	12.3542	+	3.62751i	0.477283	+	0.140143i
$671$	29.0316	+	33.5042i	1.12075	+	1.29342i
$672$		0			0
$673$	26.4324	−	30.5046i	1.01890	−	1.17587i	0.0345886	−	0.999402i	$-0.488988\pi$
$673$	26.4324	−	30.5046i	1.01890	−	1.17587i	0.984307	−	0.176466i	$-0.0564666\pi$
$674$	−1.30090	+	9.04796i	−0.0501088	+	0.348514i
$675$		0			0
$676$	−10.8238	−	6.95605i	−0.416301	−	0.267540i
$677$	0.668686	+	4.65081i	0.0256997	+	0.178745i	0.998628	−	0.0523609i	$-0.0166746\pi$
$677$	0.668686	+	4.65081i	0.0256997	+	0.178745i	−0.972929	+	0.231106i	$0.925766\pi$
$678$		0			0
$679$	4.98556	+	10.9169i	0.191328	+	0.418950i
$680$	2.59363	+	18.0391i	0.0994611	+	0.691767i
$681$		0			0
$682$	40.1724	−	11.7957i	1.53828	−	0.451680i
$683$	4.09817	−	28.5034i	0.156812	−	1.09065i	−0.747648	−	0.664095i	$-0.768817\pi$
$683$	4.09817	−	28.5034i	0.156812	−	1.09065i	0.904460	−	0.426558i	$-0.140274\pi$
$684$		0			0
$685$	−9.32553	+	5.99315i	−0.356310	+	0.228987i
$686$	−11.4732	−	13.2408i	−0.438049	−	0.505536i
$687$		0			0
$688$	−2.92306	+	6.40061i	−0.111441	+	0.244021i
$689$	−2.60873			−0.0993846
$690$		0			0
$691$	−27.0579			−1.02933			−0.514666	−	0.857391i	$-0.672084\pi$
$691$	−27.0579			−1.02933			−0.514666	+	0.857391i	$0.672084\pi$
$692$	1.40929	−	3.08592i	0.0535733	−	0.117309i
$693$		0			0
$694$	11.6659	+	13.4632i	0.442832	+	0.511055i
$695$	−42.1167	+	27.0668i	−1.59758	+	1.02670i
$696$		0			0
$697$	−3.79724	+	26.4104i	−0.143831	+	1.00037i
$698$	20.0018	−	5.87305i	0.757078	−	0.222298i
$699$		0			0
$700$	1.33064	+	9.25478i	0.0502933	+	0.349798i
$701$	13.5565	+	29.6846i	0.512023	+	1.12117i	0.972372	+	0.233436i	$0.0749968\pi$
$701$	13.5565	+	29.6846i	0.512023	+	1.12117i	−0.460350	+	0.887738i	$0.652276\pi$
$702$		0			0
$703$	−4.21634	−	29.3253i	−0.159022	−	1.10602i
$704$	−4.58506	−	2.94664i	−0.172806	−	0.111056i
$705$		0			0
$706$	3.15029	−	21.9108i	0.118563	−	0.824622i
$707$	−11.6598	+	13.4561i	−0.438510	+	0.506068i
$708$		0			0
$709$	−27.8915	−	32.1885i	−1.04749	−	1.20886i	−0.977417	−	0.211322i	$-0.932223\pi$
$709$	−27.8915	−	32.1885i	−1.04749	−	1.20886i	−0.0700701	−	0.997542i	$-0.522322\pi$
$710$	3.92324	+	1.15197i	0.147237	+	0.0432326i
$711$		0			0
$712$	−13.7607			−0.515703
$713$	3.05037	+	36.7145i	0.114237	+	1.37497i
$714$		0			0
$715$	2.39575	−	5.24596i	0.0895959	−	0.196188i
$716$	6.55277	+	1.92407i	0.244889	+	0.0719058i
$717$		0			0
$718$	23.4475	−	15.0688i	0.875054	−	0.562363i
$719$	11.9137	−	13.7491i	0.444305	−	0.512756i	−0.488782	−	0.872406i	$-0.662559\pi$
$719$	11.9137	−	13.7491i	0.444305	−	0.512756i	0.933087	+	0.359650i	$0.117104\pi$
$720$		0			0
$721$	−32.6581	+	9.58928i	−1.21625	+	0.357123i
$722$	15.6865	+	10.0811i	0.583790	+	0.375179i
$723$		0			0
$724$	0.390705	+	0.855525i	0.0145204	+	0.0317953i
$725$	−4.78075	−	10.4684i	−0.177553	−	0.388786i
$726$		0			0
$727$	1.52173	+	0.977954i	0.0564377	+	0.0362703i	0.568555	−	0.822645i	$-0.307502\pi$
$727$	1.52173	+	0.977954i	0.0564377	+	0.0362703i	−0.512118	+	0.858915i	$0.671139\pi$
$728$	0.972039	−	0.285416i	0.0360262	−	0.0105782i
$729$		0			0
$730$	−7.46892	+	8.61960i	−0.276437	+	0.319026i
$731$	−37.2784	+	23.9574i	−1.37879	+	0.886095i
$732$		0			0
$733$	16.3902	+	4.81260i	0.605386	+	0.177757i	0.570039	−	0.821618i	$-0.306928\pi$
$733$	16.3902	+	4.81260i	0.605386	+	0.177757i	0.0353471	+	0.999375i	$0.488746\pi$
$734$	7.30432	−	15.9942i	0.269607	−	0.590358i
$735$		0			0
$736$	3.35197	−	3.42992i	0.123555	−	0.126428i
$737$	−24.2497			−0.893250
$738$		0			0
$739$	39.2196	+	11.5159i	1.44272	+	0.423620i	0.907127	−	0.420857i	$-0.138271\pi$
$739$	39.2196	+	11.5159i	1.44272	+	0.423620i	0.535591	+	0.844477i	$0.320089\pi$
$740$	9.15070	+	10.5605i	0.336387	+	0.388211i
$741$		0			0
$742$	−12.9450	+	14.9394i	−0.475227	+	0.548442i
$743$	−5.24294	+	36.4654i	−0.192345	+	1.33779i	0.633436	+	0.773795i	$0.281644\pi$
$743$	−5.24294	+	36.4654i	−0.192345	+	1.33779i	−0.825780	+	0.563992i	$0.809265\pi$
$744$		0			0
$745$	35.4344	+	22.7723i	1.29822	+	0.834312i
$746$	−3.75803	−	26.1377i	−0.137591	−	0.956969i
$747$		0			0
$748$	−14.2586	−	31.2219i	−0.521344	−	1.14158i
$749$	−3.91789	−	27.2496i	−0.143157	−	0.995677i
$750$		0			0
$751$	−1.84969	+	0.543119i	−0.0674963	+	0.0198187i	−0.315306	−	0.948990i	$-0.602107\pi$
$751$	−1.84969	+	0.543119i	−0.0674963	+	0.0198187i	0.247810	+	0.968809i	$0.420289\pi$
$752$	−0.951245	+	6.61606i	−0.0346883	+	0.241263i
$753$		0			0
$754$	−1.04900	+	0.674148i	−0.0382022	+	0.0245510i
$755$	−18.0326	−	20.8108i	−0.656275	−	0.757381i
$756$		0			0
$757$	−9.77413	+	21.4024i	−0.355247	+	0.777882i	0.644663	+	0.764467i	$0.276998\pi$
$757$	−9.77413	+	21.4024i	−0.355247	+	0.777882i	−0.999910	+	0.0134152i	$0.995730\pi$
$758$	2.53379			0.0920313
$759$		0			0
$760$	−17.7560			−0.644078
$761$	−7.99143	+	17.4988i	−0.289689	+	0.634331i	−0.997392	−	0.0721799i	$-0.977004\pi$
$761$	−7.99143	+	17.4988i	−0.289689	+	0.634331i	0.707703	+	0.706511i	$0.249732\pi$
$762$		0			0
$763$	−18.8815	−	21.7904i	−0.683557	−	0.788867i
$764$	1.72011	−	1.10545i	0.0622313	−	0.0399937i
$765$		0			0
$766$	0.505288	−	3.51436i	0.0182568	−	0.126979i
$767$	0.154399	−	0.0453358i	0.00557504	−	0.00163698i
$768$		0			0
$769$	2.94235	+	20.4645i	0.106104	+	0.737967i	0.971527	+	0.236927i	$0.0761402\pi$
$769$	2.94235	+	20.4645i	0.106104	+	0.737967i	−0.865424	+	0.501041i	$0.832951\pi$
$770$	−18.1538	−	39.7512i	−0.654216	−	1.43253i
$771$		0			0
$772$	3.35728	+	23.3504i	0.120831	+	0.840400i
$773$	9.50279	+	6.10708i	0.341792	+	0.219656i	0.700264	−	0.713884i	$-0.253066\pi$
$773$	9.50279	+	6.10708i	0.341792	+	0.219656i	−0.358472	+	0.933541i	$0.616702\pi$
$774$		0			0
$775$	−3.68929	+	25.6596i	−0.132523	+	0.921719i
$776$	2.83659	−	3.27360i	0.101828	−	0.117515i
$777$		0			0
$778$	18.1400	+	20.9347i	0.650350	+	0.750544i
$779$	−24.9429	−	7.32391i	−0.893674	−	0.262406i
$780$		0			0
$781$	−7.70086			−0.275558
$782$	29.4363	−	6.75870i	1.05264	−	0.241691i
$783$		0			0
$784$	0.281059	−	0.615433i	0.0100378	−	0.0219797i
$785$	66.2613	+	19.4561i	2.36497	+	0.694417i
$786$		0			0
$787$	−24.6527	+	15.8433i	−0.878774	+	0.564754i	−0.900425	−	0.435012i	$-0.856744\pi$
$787$	−24.6527	+	15.8433i	−0.878774	+	0.564754i	0.0216507	+	0.999766i	$0.493108\pi$
$788$	−2.20841	+	2.54864i	−0.0786713	+	0.0907916i
$789$		0			0
$790$	−11.0363	+	3.24055i	−0.392654	+	0.115294i
$791$	25.0588	+	16.1043i	0.890988	+	0.572603i
$792$		0			0
$793$	1.23550	+	2.70537i	0.0438740	+	0.0960707i
$794$	−8.85177	−	19.3827i	−0.314138	−	0.687866i
$795$		0			0
$796$	18.2343	+	11.7185i	0.646299	+	0.415351i
$797$	31.8929	−	9.36459i	1.12970	−	0.331711i	0.337112	−	0.941464i	$-0.390550\pi$
$797$	31.8929	−	9.36459i	1.12970	−	0.331711i	0.792591	+	0.609754i	$0.208732\pi$
$798$		0			0
$799$	−27.5655	+	31.8123i	−0.975198	+	1.12544i
$800$	2.83891	−	1.82446i	0.100371	−	0.0645044i
$801$		0			0
$802$	10.5122	+	3.08667i	0.371199	+	0.108994i
$803$	8.92333	−	19.5394i	0.314897	−	0.689529i
$804$		0			0
$805$	37.4778	−	8.60507i	1.32092	−	0.303289i
$806$	2.80883			0.0989368
$807$		0			0
$808$	6.16593	+	1.81048i	0.216917	+	0.0636925i
$809$	24.3450	+	28.0956i	0.855924	+	0.987789i	0.999998	−	0.00177791i	$-0.000565927\pi$
$809$	24.3450	+	28.0956i	0.855924	+	0.987789i	−0.144074	+	0.989567i	$0.546020\pi$
$810$		0			0
$811$	1.19838	−	1.38300i	0.0420808	−	0.0485638i	−0.734319	−	0.678805i	$-0.762498\pi$
$811$	1.19838	−	1.38300i	0.0420808	−	0.0485638i	0.776400	+	0.630241i	$0.217044\pi$
$812$	−1.34469	+	9.35253i	−0.0471894	+	0.328209i
$813$		0			0
$814$	−22.1395	−	14.2282i	−0.775989	−	0.498698i
$815$	3.36465	+	23.4016i	0.117858	+	0.819723i
$816$		0			0
$817$	−17.9349	−	39.2721i	−0.627464	−	1.37396i
$818$	−4.12731	−	28.7061i	−0.144308	−	1.00368i
$819$		0			0
$820$	11.7643	−	3.45432i	0.410829	−	0.120630i
$821$	−4.33882	+	30.1772i	−0.151426	+	1.05319i	0.762407	+	0.647098i	$0.224018\pi$
$821$	−4.33882	+	30.1772i	−0.151426	+	1.05319i	−0.913832	+	0.406092i	$0.866891\pi$
$822$		0			0
$823$	42.2413	−	27.1468i	1.47244	−	0.946280i	0.474626	−	0.880187i	$-0.342583\pi$
$823$	42.2413	−	27.1468i	1.47244	−	0.946280i	0.997814	−	0.0660922i	$-0.0210531\pi$
$824$	8.04478	+	9.28417i	0.280253	+	0.323429i
$825$		0			0
$826$	0.506538	−	1.10916i	0.0176247	−	0.0385927i
$827$	47.7273			1.65964			0.829821	−	0.558030i	$-0.188443\pi$
$827$	47.7273			1.65964			0.829821	+	0.558030i	$0.188443\pi$
$828$		0			0
$829$	−53.8283			−1.86953			−0.934767	−	0.355262i	$-0.884392\pi$
$829$	−53.8283			−1.86953			−0.934767	+	0.355262i	$0.884392\pi$
$830$	19.3577	−	42.3874i	0.671915	−	1.47129i
$831$		0			0
$832$	−0.239446	−	0.276335i	−0.00830129	−	0.00958020i
$833$	3.58440	−	2.30356i	0.124192	−	0.0798135i
$834$		0			0
$835$	4.21581	−	29.3216i	0.145894	−	1.01472i
$836$	32.0865	−	9.42145i	1.10974	−	0.325848i
$837$		0			0
$838$	−1.19019	−	8.27795i	−0.0411144	−	0.285957i
$839$	2.95446	+	6.46937i	0.101999	+	0.223347i	0.953751	−	0.300599i	$-0.0971865\pi$
$839$	2.95446	+	6.46937i	0.101999	+	0.223347i	−0.851751	+	0.523946i	$0.824459\pi$
$840$		0			0
$841$	2.47202	+	17.1933i	0.0852420	+	0.592871i
$842$	−8.91849	−	5.73157i	−0.307352	−	0.197523i
$843$		0			0
$844$	3.26336	−	22.6972i	0.112330	−	0.781269i
$845$	−24.3829	+	28.1394i	−0.838797	+	0.968024i
$846$		0			0
$847$	33.9392	+	39.1679i	1.16616	+	1.34583i
$848$	6.84562	+	2.01005i	0.235079	+	0.0690255i
$849$		0			0
$850$	21.2520			0.728938
$851$	16.1854	−	16.5618i	0.554827	−	0.567730i
$852$		0			0
$853$	−5.38730	+	11.7965i	−0.184458	+	0.403906i	−0.979159	−	0.203094i	$-0.934900\pi$
$853$	−5.38730	+	11.7965i	−0.184458	+	0.403906i	0.794701	+	0.607001i	$0.207627\pi$
$854$	21.6237	+	6.34928i	0.739946	+	0.217268i
$855$		0			0
$856$	−8.35884	+	5.37190i	−0.285699	+	0.183608i
$857$	16.3004	−	18.8117i	0.556812	−	0.642595i	−0.405645	−	0.914031i	$-0.632953\pi$
$857$	16.3004	−	18.8117i	0.556812	−	0.642595i	0.962457	+	0.271436i	$0.0874985\pi$
$858$		0			0
$859$	19.5842	−	5.75043i	0.668204	−	0.196202i	0.0700007	−	0.997547i	$-0.477700\pi$
$859$	19.5842	−	5.75043i	0.668204	−	0.196202i	0.598203	+	0.801345i	$0.295882\pi$
$860$	17.1303	+	11.0090i	0.584138	+	0.375403i
$861$		0			0
$862$	−0.195479	−	0.428039i	−0.00665804	−	0.0145791i
$863$	−14.8781	−	32.5785i	−0.506457	−	1.10899i	−0.974316	−	0.225183i	$-0.927702\pi$
$863$	−14.8781	−	32.5785i	−0.506457	−	1.10899i	0.467860	−	0.883803i	$-0.345025\pi$
$864$		0			0
$865$	−8.25903	−	5.30776i	−0.280815	−	0.180469i
$866$	27.8282	−	8.17110i	0.945641	−	0.277665i
$867$		0			0
$868$	13.9380	−	16.0853i	0.473086	−	0.545970i
$869$	18.2240	−	11.7119i	0.618208	−	0.397298i
$870$		0			0
$871$	−1.56095	−	0.458336i	−0.0528907	−	0.0155301i
$872$	−4.32301	+	9.46608i	−0.146396	+	0.320562i
$873$		0			0
$874$	2.43639	+	29.3246i	0.0824122	+	0.991921i
$875$	−13.0323			−0.440571
$876$		0			0
$877$	−4.24819	−	1.24738i	−0.143451	−	0.0421211i	0.209219	−	0.977869i	$-0.432908\pi$
$877$	−4.24819	−	1.24738i	−0.143451	−	0.0421211i	−0.352670	+	0.935748i	$0.614726\pi$
$878$	9.87815	+	11.4000i	0.333372	+	0.384731i
$879$		0			0
$880$	−10.3288	+	11.9201i	−0.348184	+	0.401825i
$881$	−4.17060	+	29.0071i	−0.140511	+	0.977276i	0.790546	+	0.612402i	$0.209797\pi$
$881$	−4.17060	+	29.0071i	−0.140511	+	0.977276i	−0.931057	+	0.364873i	$0.881112\pi$
$882$		0			0
$883$	9.76420	+	6.27507i	0.328591	+	0.211173i	0.694526	−	0.719468i	$-0.255614\pi$
$883$	9.76420	+	6.27507i	0.328591	+	0.211173i	−0.365934	+	0.930641i	$0.619251\pi$
$884$	−0.327705	−	2.27924i	−0.0110219	−	0.0766591i
$885$		0			0
$886$	11.0387	+	24.1713i	0.370852	+	0.812052i
$887$	−1.44706	−	10.0646i	−0.0485877	−	0.337935i	−0.999587	−	0.0287413i	$-0.990850\pi$
$887$	−1.44706	−	10.0646i	−0.0485877	−	0.337935i	0.950999	−	0.309193i	$-0.100059\pi$
$888$		0			0
$889$	−25.8044	+	7.57686i	−0.865452	+	0.254120i
$890$	−5.66725	+	39.4166i	−0.189967	+	1.32125i
$891$		0			0
$892$	−16.6791	+	10.7190i	−0.558459	+	0.358900i
$893$	−26.8568	−	30.9944i	−0.898727	−	1.03719i
$894$		0			0
$895$	8.21009	−	17.9776i	0.274433	−	0.600925i
$896$	−2.77066			−0.0925614
$897$		0			0
$898$	−3.87601			−0.129344
$899$	−10.8827	+	23.8299i	−0.362960	+	0.794771i
$900$		0			0
$901$	29.4235	+	33.9566i	0.980240	+	1.13126i
$902$	−19.4262	+	12.4845i	−0.646823	+	0.415688i
$903$		0			0
$904$	1.53003	−	10.6416i	0.0508880	−	0.353934i
$905$	2.61151	−	0.766808i	0.0868095	−	0.0254896i
$906$		0			0
$907$	4.32726	+	30.0968i	0.143684	+	0.999347i	0.926285	+	0.376823i	$0.122984\pi$
$907$	4.32726	+	30.0968i	0.143684	+	0.999347i	−0.782601	+	0.622524i	$0.786107\pi$
$908$	8.27987	+	18.1304i	0.274777	+	0.601678i
$909$		0			0
$910$	−0.417229	−	2.90189i	−0.0138310	−	0.0961968i
$911$	−11.2501	−	7.23002i	−0.372734	−	0.239541i	0.340841	−	0.940121i	$-0.389288\pi$
$911$	−11.2501	−	7.23002i	−0.372734	−	0.239541i	−0.713574	+	0.700580i	$0.752925\pi$
$912$		0			0
$913$	−12.4898	+	86.8688i	−0.413353	+	2.87494i
$914$	−2.10997	+	2.43503i	−0.0697916	+	0.0805438i
$915$		0			0
$916$	10.6737	+	12.3181i	0.352668	+	0.407000i
$917$	34.8984	+	10.2471i	1.15245	+	0.338389i
$918$		0			0
$919$	−28.5942			−0.943237			−0.471618	−	0.881803i	$-0.656330\pi$
$919$	−28.5942			−0.943237			−0.471618	+	0.881803i	$0.656330\pi$
$920$	−8.44430	−	11.0141i	−0.278400	−	0.363124i
$921$		0			0
$922$	10.6954	−	23.4196i	0.352234	−	0.771284i
$923$	−0.495702	−	0.145551i	−0.0163162	−	0.00479088i
$924$		0			0
$925$	13.7080	−	8.80962i	0.450717	−	0.289658i
$926$	−12.1589	+	14.0321i	−0.399566	+	0.461124i
$927$		0			0
$928$	3.27213	−	0.960783i	0.107413	−	0.0315393i
$929$	44.8992	+	28.8549i	1.47309	+	0.946700i	0.997760	+	0.0668947i	$0.0213091\pi$
$929$	44.8992	+	28.8549i	1.47309	+	0.946700i	0.475334	+	0.879805i	$0.342327\pi$
$930$		0			0
$931$	1.72449	+	3.77610i	0.0565177	+	0.123757i
$932$	−7.74196	−	16.9525i	−0.253596	−	0.555299i
$933$		0			0
$934$	−5.23419	−	3.36381i	−0.171268	−	0.110067i
$935$	−95.3054	+	27.9842i	−3.11682	+	0.915181i
$936$		0			0
$937$	27.4714	−	31.7036i	0.897450	−	1.03571i	−0.101713	−	0.994814i	$-0.532432\pi$
$937$	27.4714	−	31.7036i	0.897450	−	1.03571i	0.999163	−	0.0408993i	$-0.0130223\pi$
$938$	−10.3705	+	6.66471i	−0.338609	+	0.217610i
$939$		0			0
$940$	18.5595	+	5.44957i	0.605345	+	0.177745i
$941$	−8.63855	+	18.9158i	−0.281609	+	0.616637i	−0.996591	−	0.0825060i	$-0.973708\pi$
$941$	−8.63855	+	18.9158i	−0.281609	+	0.616637i	0.714982	+	0.699143i	$0.246435\pi$
$942$		0			0
$943$	−7.31918	−	18.9552i	−0.238345	−	0.617267i
$944$	−0.440095			−0.0143239
$945$		0			0
$946$	−36.7973	−	10.8046i	−1.19638	−	0.351289i
$947$	25.7079	+	29.6685i	0.835395	+	0.964097i	0.999751	−	0.0223042i	$-0.00710025\pi$
$947$	25.7079	+	29.6685i	0.835395	+	0.964097i	−0.164357	+	0.986401i	$0.552555\pi$
$948$		0			0
$949$	0.943699	−	1.08909i	0.0306338	−	0.0353532i
$950$	−2.94671	+	20.4948i	−0.0956040	+	0.664941i
$951$		0			0
$952$	−14.6786	−	9.43338i	−0.475737	−	0.305738i
$953$	2.93480	+	20.4120i	0.0950675	+	0.661209i	0.980511	+	0.196462i	$0.0629454\pi$
$953$	2.93480	+	20.4120i	0.0950675	+	0.661209i	−0.885444	+	0.464746i	$0.846146\pi$
$954$		0			0
$955$	−2.45807	−	5.38242i	−0.0795412	−	0.174171i
$956$	0.627146	+	4.36190i	0.0202834	+	0.141074i
$957$		0			0
$958$	−9.90660	+	2.90884i	−0.320068	+	0.0939803i
$959$	1.51042	−	10.5052i	0.0487740	−	0.339231i
$960$		0			0
$961$	23.5646	−	15.1440i	0.760147	−	0.488517i
$962$	−1.15619	−	1.33432i	−0.0372771	−	0.0430201i
$963$		0			0
$964$	5.44932	−	11.9323i	0.175511	−	0.384315i
$965$	68.2685			2.19764
$966$		0			0
$967$	−12.2331			−0.393391			−0.196696	−	0.980465i	$-0.563021\pi$
$967$	−12.2331			−0.393391			−0.196696	+	0.980465i	$0.563021\pi$
$968$	7.77054	−	17.0151i	0.249754	−	0.546886i
$969$		0			0
$970$	−8.20880	−	9.47346i	−0.263569	−	0.304174i
$971$	12.2126	−	7.84857i	0.391922	−	0.251873i	−0.329808	−	0.944048i	$-0.606984\pi$
$971$	12.2126	−	7.84857i	0.391922	−	0.251873i	0.721729	+	0.692175i	$0.243348\pi$
$972$		0			0
$973$	6.82148	−	47.4445i	0.218687	−	1.52100i
$974$	−24.1012	+	7.07676i	−0.772253	+	0.226754i
$975$		0			0
$976$	−1.15759	−	8.05120i	−0.0370535	−	0.257713i
$977$	−1.95709	−	4.28543i	−0.0626129	−	0.137103i	0.875739	−	0.482785i	$-0.160375\pi$
$977$	−1.95709	−	4.28543i	−0.0626129	−	0.137103i	−0.938352	+	0.345682i	$0.887648\pi$
$978$		0			0
$979$	−10.6735	−	74.2361i	−0.341128	−	2.37260i
$980$	−1.64712	−	1.05854i	−0.0526152	−	0.0338138i
$981$		0			0
$982$	0.218123	−	1.51708i	0.00696059	−	0.0484120i
$983$	19.0233	−	21.9541i	0.606750	−	0.700227i	−0.366384	−	0.930464i	$-0.619405\pi$
$983$	19.0233	−	21.9541i	0.606750	−	0.700227i	0.973135	+	0.230236i	$0.0739500\pi$
$984$		0			0
$985$	6.39090	+	7.37550i	0.203631	+	0.235003i
$986$	20.6065	+	6.05063i	0.656246	+	0.192691i
$987$		0			0
$988$	2.24347			0.0713743
$989$	15.8312	−	29.8019i	0.503401	−	0.947644i
$990$		0			0
$991$	−7.58329	+	16.6051i	−0.240891	+	0.527478i	−0.991004	−	0.133832i	$-0.957272\pi$
$991$	−7.58329	+	16.6051i	−0.240891	+	0.527478i	0.750113	+	0.661310i	$0.229999\pi$
$992$	−7.37071	−	2.16423i	−0.234020	−	0.0687145i
$993$		0			0
$994$	−3.29330	+	2.11648i	−0.104457	+	0.0671305i
$995$	41.0766	−	47.4049i	1.30222	−	1.50284i
$996$		0			0
$997$	−18.5836	+	5.45665i	−0.588549	+	0.172814i	−0.562430	−	0.826845i	$-0.690133\pi$
$997$	−18.5836	+	5.45665i	−0.588549	+	0.172814i	−0.0261198	+	0.999659i	$0.508315\pi$
$998$	−19.7123	−	12.6684i	−0.623983	−	0.401010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.b.397.1		10
3.2	odd	2		138.2.e.c.121.1	yes	10
23.2	even	11		9522.2.a.bv.1.3		5
23.4	even	11	inner	414.2.i.b.73.1		10
23.21	odd	22		9522.2.a.ca.1.3		5
69.2	odd	22		3174.2.a.z.1.3		5
69.44	even	22		3174.2.a.y.1.3		5
69.50	odd	22		138.2.e.c.73.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.73.1	✓	10	69.50	odd	22
138.2.e.c.121.1	yes	10	3.2	odd	2
414.2.i.b.73.1		10	23.4	even	11	inner
414.2.i.b.397.1		10	1.1	even	1	trivial
3174.2.a.y.1.3		5	69.44	even	22
3174.2.a.z.1.3		5	69.2	odd	22
9522.2.a.bv.1.3		5	23.2	even	11
9522.2.a.ca.1.3		5	23.21	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.43450 + 1.56456i) q^{5} +(0.394306 - 2.74246i) q^{7} +(-0.959493 + 0.281733i) q^{8} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.43450 + 1.56456i) q^{5} +(0.394306 - 2.74246i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.411844 + 2.86444i) q^{10} +(-2.26413 - 4.95774i) q^{11} +(-0.0520365 - 0.361922i) q^{13} +(-2.33083 - 1.49793i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-4.12405 + 4.75941i) q^{17} +(-4.01801 - 4.63704i) q^{19} +(2.77667 + 0.815304i) q^{20} -5.45027 q^{22} +(0.965501 - 4.69764i) q^{23} +(1.40187 - 3.06967i) q^{25} +(-0.350833 - 0.103014i) q^{26} +(-2.33083 + 1.49793i) q^{28} +(2.23325 - 2.57731i) q^{29} +(-7.37071 + 2.16423i) q^{31} +(0.841254 + 0.540641i) q^{32} +(2.61612 + 5.72850i) q^{34} +(3.33080 + 7.29343i) q^{35} +(4.06209 + 2.61055i) q^{37} +(-5.88714 + 1.72862i) q^{38} +(1.89510 - 2.18706i) q^{40} +(3.56427 - 2.29062i) q^{41} +(6.75145 + 1.98241i) q^{43} +(-2.26413 + 4.95774i) q^{44} +(-3.87204 - 2.82972i) q^{46} +6.68409 q^{47} +(-0.649167 - 0.190613i) q^{49} +(-2.20991 - 2.55037i) q^{50} +(-0.239446 + 0.276335i) q^{52} +(1.01536 - 7.06200i) q^{53} +(13.2687 + 8.52726i) q^{55} +(0.394306 + 2.74246i) q^{56} +(-1.41668 - 3.10209i) q^{58} +(0.0626320 + 0.435615i) q^{59} +(-7.80450 + 2.29161i) q^{61} +(-1.09325 + 7.60369i) q^{62} +(0.841254 - 0.540641i) q^{64} +(0.692931 + 0.799685i) q^{65} +(1.84829 - 4.04720i) q^{67} +6.29760 q^{68} +8.01801 q^{70} +(0.586952 - 1.28525i) q^{71} +(2.58092 + 2.97855i) q^{73} +(4.06209 - 2.61055i) q^{74} +(-0.873198 + 6.07322i) q^{76} +(-14.4892 + 4.25441i) q^{77} +(0.565652 + 3.93420i) q^{79} +(-1.20217 - 2.63238i) q^{80} +(-0.602967 - 4.19373i) q^{82} +(-13.5461 - 8.70557i) q^{83} +(2.59363 - 18.0391i) q^{85} +(4.60791 - 5.31782i) q^{86} +(3.56917 + 4.11904i) q^{88} +(13.2033 + 3.87683i) q^{89} -1.01308 q^{91} +(-4.18251 + 2.34662i) q^{92} +(2.77667 - 6.08006i) q^{94} +(17.0368 + 5.00244i) q^{95} +(-3.64397 + 2.34184i) q^{97} +(-0.443061 + 0.511320i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

Introduction

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