LMFDB - Embedded newform 441.2.bb.e.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.e.352.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.227517 + 0.211105i) q^{2} +(-0.142261 + 1.89835i) q^{4} +(-1.53122 + 3.90148i) q^{5} +(2.06200 + 1.65775i) q^{7} +(-0.755410 - 0.947254i) q^{8} +O(q^{10})$	\(q+(-0.227517 + 0.211105i) q^{2} +(-0.142261 + 1.89835i) q^{4} +(-1.53122 + 3.90148i) q^{5} +(2.06200 + 1.65775i) q^{7} +(-0.755410 - 0.947254i) q^{8} +(-0.475244 - 1.21090i) q^{10} +(-3.87883 - 1.19646i) q^{11} +(-0.440498 - 1.92995i) q^{13} +(-0.819102 + 0.0581320i) q^{14} +(-3.39298 - 0.511409i) q^{16} +(3.47723 - 2.37073i) q^{17} +(-0.0899481 - 0.155795i) q^{19} +(-7.18853 - 3.46181i) q^{20} +(1.13508 - 0.546626i) q^{22} +(3.84140 + 2.61902i) q^{23} +(-9.21165 - 8.54716i) q^{25} +(0.507644 + 0.346106i) q^{26} +(-3.44033 + 3.67856i) q^{28} +(1.17149 + 0.564159i) q^{29} +(0.715134 - 1.23865i) q^{31} +(2.88204 - 1.96494i) q^{32} +(-0.290655 + 1.27344i) q^{34} +(-9.62506 + 5.50648i) q^{35} +(0.839018 + 11.1959i) q^{37} +(0.0533538 + 0.0164575i) q^{38} +(4.85239 - 1.49676i) q^{40} +(1.93867 + 2.43101i) q^{41} +(-4.67037 + 5.85646i) q^{43} +(2.82311 - 7.19316i) q^{44} +(-1.42687 + 0.215067i) q^{46} +(1.34706 - 1.24989i) q^{47} +(1.50371 + 6.83658i) q^{49} +3.90016 q^{50} +(3.72638 - 0.561661i) q^{52} +(-1.00425 + 13.4008i) q^{53} +(10.6073 - 13.3011i) q^{55} +(0.0126562 - 3.20552i) q^{56} +(-0.385631 + 0.118951i) q^{58} +(-0.840831 - 2.14240i) q^{59} +(0.367550 + 4.90462i) q^{61} +(0.0987799 + 0.432783i) q^{62} +(1.28617 - 5.63507i) q^{64} +(8.20415 + 1.23658i) q^{65} +(2.37968 - 4.12173i) q^{67} +(4.00580 + 6.93825i) q^{68} +(1.02742 - 3.28472i) q^{70} +(-4.62389 + 2.22675i) q^{71} +(-6.73633 - 6.25040i) q^{73} +(-2.55441 - 2.37015i) q^{74} +(0.308548 - 0.148589i) q^{76} +(-6.01472 - 8.89725i) q^{77} +(-0.946091 - 1.63868i) q^{79} +(7.19064 - 12.4545i) q^{80} +(-0.954280 - 0.143835i) q^{82} +(1.24416 - 5.45103i) q^{83} +(3.92497 + 17.1964i) q^{85} +(-0.173739 - 2.31839i) q^{86} +(1.79675 + 4.57805i) q^{88} +(-1.87875 + 0.579517i) q^{89} +(2.29107 - 4.70980i) q^{91} +(-5.51829 + 6.91972i) q^{92} +(-0.0426215 + 0.568745i) q^{94} +(0.745559 - 0.112375i) q^{95} -10.4804 q^{97} +(-1.78536 - 1.23800i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

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 $

$2$	−0.227517	+	0.211105i	−0.160879	+	0.149274i	−0.756505	−	0.653988i	$-0.773095\pi$
$2$	−0.227517	+	0.211105i	−0.160879	+	0.149274i	0.595626	+	0.803262i	$0.296904\pi$
$3$		0			0
$3$		0			0
$4$	−0.142261	+	1.89835i	−0.0711307	+	0.949174i
$5$	−1.53122	+	3.90148i	−0.684781	+	1.74479i	−0.0176610	+	0.999844i	$0.505622\pi$
$5$	−1.53122	+	3.90148i	−0.684781	+	1.74479i	−0.667120	+	0.744950i	$0.732473\pi$
$6$		0			0
$7$	2.06200	+	1.65775i	0.779364	+	0.626572i
$7$	2.06200	+	1.65775i	0.779364	+	0.626572i
$8$	−0.755410	−	0.947254i	−0.267078	−	0.334905i
$9$		0			0
$10$	−0.475244	−	1.21090i	−0.150285	−	0.382921i
$11$	−3.87883	−	1.19646i	−1.16951	−	0.360746i	−0.351633	−	0.936138i	$-0.614374\pi$
$11$	−3.87883	−	1.19646i	−1.16951	−	0.360746i	−0.817878	+	0.575391i	$0.804850\pi$
$12$		0			0
$13$	−0.440498	−	1.92995i	−0.122172	−	0.535272i	−0.998559	−	0.0536638i	$-0.982910\pi$
$13$	−0.440498	−	1.92995i	−0.122172	−	0.535272i	0.876387	−	0.481608i	$-0.159947\pi$
$14$	−0.819102	+	0.0581320i	−0.218914	+	0.0155364i
$15$		0			0
$16$	−3.39298	−	0.511409i	−0.848244	−	0.127852i
$17$	3.47723	−	2.37073i	0.843351	−	0.574987i	−0.0627592	−	0.998029i	$-0.519990\pi$
$17$	3.47723	−	2.37073i	0.843351	−	0.574987i	0.906110	+	0.423042i	$0.139038\pi$
$18$		0			0
$19$	−0.0899481	−	0.155795i	−0.0206355	−	0.0357417i	0.855523	−	0.517764i	$-0.173236\pi$
$19$	−0.0899481	−	0.155795i	−0.0206355	−	0.0357417i	−0.876159	+	0.482023i	$0.839902\pi$
$20$	−7.18853	−	3.46181i	−1.60740	−	0.774085i
$21$		0			0
$22$	1.13508	−	0.546626i	0.242000	−	0.116541i
$23$	3.84140	+	2.61902i	0.800987	+	0.546103i	0.893213	−	0.449635i	$-0.148446\pi$
$23$	3.84140	+	2.61902i	0.800987	+	0.546103i	−0.0922259	+	0.995738i	$0.529398\pi$
$24$		0			0
$25$	−9.21165	−	8.54716i	−1.84233	−	1.70943i
$26$	0.507644	+	0.346106i	0.0995571	+	0.0678769i
$27$		0			0
$28$	−3.44033	+	3.67856i	−0.650162	+	0.695183i
$29$	1.17149	+	0.564159i	0.217540	+	0.104762i	0.539480	−	0.841998i	$-0.318621\pi$
$29$	1.17149	+	0.564159i	0.217540	+	0.104762i	−0.321940	+	0.946760i	$0.604335\pi$
$30$		0			0
$31$	0.715134	−	1.23865i	0.128442	−	0.222468i	−0.794631	−	0.607092i	$-0.792336\pi$
$31$	0.715134	−	1.23865i	0.128442	−	0.222468i	0.923073	+	0.384625i	$0.125669\pi$
$32$	2.88204	−	1.96494i	0.509477	−	0.347355i
$33$		0			0
$34$	−0.290655	+	1.27344i	−0.0498470	+	0.218394i
$35$	−9.62506	+	5.50648i	−1.62693	+	0.930765i
$36$		0			0
$37$	0.839018	+	11.1959i	0.137934	+	1.84060i	0.452978	+	0.891522i	$0.350362\pi$
$37$	0.839018	+	11.1959i	0.137934	+	1.84060i	−0.315044	+	0.949077i	$0.602019\pi$
$38$	0.0533538	+	0.0164575i	0.00865513	+	0.00266976i
$39$		0			0
$40$	4.85239	−	1.49676i	0.767230	−	0.236659i
$41$	1.93867	+	2.43101i	0.302769	+	0.379660i	0.909820	−	0.415002i	$-0.136219\pi$
$41$	1.93867	+	2.43101i	0.302769	+	0.379660i	−0.607051	+	0.794663i	$0.707648\pi$
$42$		0			0
$43$	−4.67037	+	5.85646i	−0.712225	+	0.893102i	−0.997870	−	0.0652333i	$-0.979221\pi$
$43$	−4.67037	+	5.85646i	−0.712225	+	0.893102i	0.285645	+	0.958336i	$0.407792\pi$
$44$	2.82311	−	7.19316i	0.425599	−	1.08441i
$45$		0			0
$46$	−1.42687	+	0.215067i	−0.210381	+	0.0317098i
$47$	1.34706	−	1.24989i	0.196489	−	0.182316i	−0.575792	−	0.817596i	$-0.695306\pi$
$47$	1.34706	−	1.24989i	0.196489	−	0.182316i	0.772281	+	0.635281i	$0.219116\pi$
$48$		0			0
$49$	1.50371	+	6.83658i	0.214816	+	0.976655i
$50$	3.90016			0.551566
$51$		0			0
$52$	3.72638	−	0.561661i	0.516756	−	0.0778884i
$53$	−1.00425	+	13.4008i	−0.137944	+	1.84074i	0.314871	+	0.949134i	$0.398039\pi$
$53$	−1.00425	+	13.4008i	−0.137944	+	1.84074i	−0.452816	+	0.891604i	$0.649580\pi$
$54$		0			0
$55$	10.6073	−	13.3011i	1.43029	−	1.79352i
$56$	0.0126562	−	3.20552i	0.00169126	−	0.428356i
$57$		0			0
$58$	−0.385631	+	0.118951i	−0.0506358	+	0.0156191i
$59$	−0.840831	−	2.14240i	−0.109467	−	0.278917i	0.865635	−	0.500676i	$-0.166915\pi$
$59$	−0.840831	−	2.14240i	−0.109467	−	0.278917i	−0.975101	+	0.221759i	$0.928820\pi$
$60$		0			0
$61$	0.367550	+	4.90462i	0.0470600	+	0.627972i	0.970012	+	0.243057i	$0.0781501\pi$
$61$	0.367550	+	4.90462i	0.0470600	+	0.627972i	−0.922952	+	0.384915i	$0.874231\pi$
$62$	0.0987799	+	0.432783i	0.0125451	+	0.0549635i
$63$		0			0
$64$	1.28617	−	5.63507i	0.160771	−	0.704384i
$65$	8.20415	+	1.23658i	1.01760	+	0.153379i
$66$		0			0
$67$	2.37968	−	4.12173i	0.290724	−	0.503549i	−0.683257	−	0.730178i	$-0.739437\pi$
$67$	2.37968	−	4.12173i	0.290724	−	0.503549i	0.973981	+	0.226629i	$0.0727705\pi$
$68$	4.00580	+	6.93825i	0.485774	+	0.841386i
$69$		0			0
$70$	1.02742	−	3.28472i	0.122800	−	0.392599i
$71$	−4.62389	+	2.22675i	−0.548754	+	0.264266i	−0.687652	−	0.726041i	$-0.741358\pi$
$71$	−4.62389	+	2.22675i	−0.548754	+	0.264266i	0.138897	+	0.990307i	$0.455644\pi$
$72$		0			0
$73$	−6.73633	−	6.25040i	−0.788427	−	0.731554i	0.179234	−	0.983806i	$-0.442638\pi$
$73$	−6.73633	−	6.25040i	−0.788427	−	0.731554i	−0.967661	+	0.252253i	$0.918829\pi$
$74$	−2.55441	−	2.37015i	−0.296944	−	0.275524i
$75$		0			0
$76$	0.308548	−	0.148589i	0.0353929	−	0.0170443i
$77$	−6.01472	−	8.89725i	−0.685441	−	1.01394i
$78$		0			0
$79$	−0.946091	−	1.63868i	−0.106444	−	0.184366i	0.807883	−	0.589342i	$-0.200613\pi$
$79$	−0.946091	−	1.63868i	−0.106444	−	0.184366i	−0.914327	+	0.404977i	$0.867280\pi$
$80$	7.19064	−	12.4545i	0.803938	−	1.39246i
$81$		0			0
$82$	−0.954280	−	0.143835i	−0.105383	−	0.0158839i
$83$	1.24416	−	5.45103i	0.136565	−	0.598329i	−0.859611	−	0.510950i	$-0.829294\pi$
$83$	1.24416	−	5.45103i	0.136565	−	0.598329i	0.996175	−	0.0873788i	$-0.0278491\pi$
$84$		0			0
$85$	3.92497	+	17.1964i	0.425723	+	1.86521i
$86$	−0.173739	−	2.31839i	−0.0187348	−	0.249998i
$87$		0			0
$88$	1.79675	+	4.57805i	0.191535	+	0.488022i
$89$	−1.87875	+	0.579517i	−0.199147	+	0.0614287i	−0.392724	−	0.919656i	$-0.628467\pi$
$89$	−1.87875	+	0.579517i	−0.199147	+	0.0614287i	0.193577	+	0.981085i	$0.437991\pi$
$90$		0			0
$91$	2.29107	−	4.70980i	0.240169	−	0.493721i
$92$	−5.51829	+	6.91972i	−0.575322	+	0.721431i
$93$		0			0
$94$	−0.0426215	+	0.568745i	−0.00439607	+	0.0586615i
$95$	0.745559	−	0.112375i	0.0764928	−	0.0115294i
$96$		0			0
$97$	−10.4804			−1.06413			−0.532063	−	0.846705i	$-0.678583\pi$
$97$	−10.4804			−1.06413			−0.532063	+	0.846705i	$0.678583\pi$
$98$	−1.78536	−	1.23800i	−0.180349	−	0.125057i
$99$		0			0
$100$	17.5359	−	16.2710i	1.75359	−	1.62710i
$101$	−2.48300	+	0.374252i	−0.247068	+	0.0372394i	−0.271408	−	0.962464i	$-0.587489\pi$
$101$	−2.48300	+	0.374252i	−0.247068	+	0.0372394i	0.0243408	+	0.999704i	$0.492251\pi$
$102$		0			0
$103$	2.60952	−	6.64895i	0.257124	−	0.655140i	−0.742773	−	0.669544i	$-0.766490\pi$
$103$	2.60952	−	6.64895i	0.257124	−	0.655140i	0.999896	+	0.0144033i	$0.00458487\pi$
$104$	−1.49540	+	1.87517i	−0.146636	+	0.183875i
$105$		0			0
$106$	−2.60049	−	3.26091i	−0.252582	−	0.316728i
$107$	10.5844	−	3.26487i	1.02324	−	0.315627i	0.262669	−	0.964886i	$-0.415397\pi$
$107$	10.5844	−	3.26487i	1.02324	−	0.315627i	0.760567	+	0.649259i	$0.224921\pi$
$108$		0			0
$109$	15.9339	+	4.91496i	1.52619	+	0.470768i	0.940508	−	0.339772i	$-0.110350\pi$
$109$	15.9339	+	4.91496i	1.52619	+	0.470768i	0.585684	+	0.810540i	$0.300826\pi$
$110$	0.394594	+	5.26550i	0.0376231	+	0.502045i
$111$		0			0
$112$	−6.14854	−	6.67924i	−0.580982	−	0.631129i
$113$	−0.528095	+	2.31374i	−0.0496790	+	0.217658i	−0.993674	−	0.112301i	$-0.964178\pi$
$113$	−0.528095	+	2.31374i	−0.0496790	+	0.217658i	0.943995	+	0.329959i	$0.107035\pi$
$114$		0			0
$115$	−16.1001	+	10.9768i	−1.50134	+	1.02360i
$116$	−1.23763	+	2.14363i	−0.114911	+	0.199031i
$117$		0			0
$118$	0.643576	+	0.309930i	0.0592460	+	0.0285314i
$119$	11.1001	+	0.875925i	1.01755	+	0.0802960i
$120$		0			0
$121$	4.52518	+	3.08521i	0.411380	+	0.280474i
$122$	−1.11901	−	1.03829i	−0.101311	−	0.0940027i
$123$		0			0
$124$	2.24965	+	1.53378i	0.202024	+	0.137738i
$125$	28.5709	−	13.7590i	2.55546	−	1.23064i
$126$		0			0
$127$	5.86406	+	2.82398i	0.520351	+	0.250588i	0.675575	−	0.737292i	$-0.263896\pi$
$127$	5.86406	+	2.82398i	0.520351	+	0.250588i	−0.155224	+	0.987879i	$0.549610\pi$
$128$	4.38511	+	7.59523i	0.387592	+	0.671330i
$129$		0			0
$130$	−2.12764	+	1.45060i	−0.186606	+	0.127226i
$131$	7.22551	+	1.08907i	0.631296	+	0.0951525i	0.456893	−	0.889522i	$-0.348962\pi$
$131$	7.22551	+	1.08907i	0.631296	+	0.0951525i	0.174403	+	0.984674i	$0.444200\pi$
$132$		0			0
$133$	0.0727959	−	0.470361i	0.00631220	−	0.0407854i
$134$	0.328700	+	1.44013i	0.0283953	+	0.124408i
$135$		0			0
$136$	−4.87241	−	1.50294i	−0.417806	−	0.128876i
$137$	−2.21412	−	5.64150i	−0.189165	−	0.481986i	0.804555	−	0.593878i	$-0.202404\pi$
$137$	−2.21412	−	5.64150i	−0.189165	−	0.481986i	−0.993720	+	0.111893i	$0.964309\pi$
$138$		0			0
$139$	11.4261	+	14.3278i	0.969147	+	1.21527i	0.976548	+	0.215299i	$0.0690726\pi$
$139$	11.4261	+	14.3278i	0.969147	+	1.21527i	−0.00740138	+	0.999973i	$0.502356\pi$
$140$	−9.08393	−	19.0551i	−0.767732	−	1.61045i
$141$		0			0
$142$	0.581937	−	1.48275i	0.0488351	−	0.124430i
$143$	−0.600490	+	8.01298i	−0.0502155	+	0.670079i
$144$		0			0
$145$	−3.99485	+	3.70668i	−0.331755	+	0.307823i
$146$	2.85212			0.236043
$147$		0			0
$148$	−21.3731			−1.75686
$149$	−2.87593	+	2.66847i	−0.235605	+	0.218610i	−0.789135	−	0.614220i	$-0.789471\pi$
$149$	−2.87593	+	2.66847i	−0.235605	+	0.218610i	0.553530	+	0.832829i	$0.313280\pi$
$150$		0			0
$151$	−1.41123	+	18.8315i	−0.114844	+	1.53249i	0.580768	+	0.814069i	$0.302752\pi$
$151$	−1.41123	+	18.8315i	−0.114844	+	1.53249i	−0.695612	+	0.718417i	$0.744867\pi$
$152$	−0.0796294	+	0.202892i	−0.00645880	+	0.0164567i
$153$		0			0
$154$	3.24671	+	0.754539i	0.261627	+	0.0608025i
$155$	3.73753	+	4.68672i	0.300206	+	0.376446i
$156$		0			0
$157$	−6.08252	−	15.4980i	−0.485438	−	1.23688i	−0.938464	−	0.345378i	$-0.887751\pi$
$157$	−6.08252	−	15.4980i	−0.485438	−	1.23688i	0.453026	−	0.891497i	$-0.350345\pi$
$158$	0.561186	+	0.173103i	0.0446456	+	0.0137713i
$159$		0			0
$160$	3.25314	+	14.2529i	0.257184	+	1.12679i
$161$	3.57928	+	11.7685i	0.282087	+	0.927489i
$162$		0			0
$163$	5.30503	+	0.799604i	0.415522	+	0.0626298i	0.353476	−	0.935444i	$-0.385000\pi$
$163$	5.30503	+	0.799604i	0.415522	+	0.0626298i	0.0620454	+	0.998073i	$0.480238\pi$
$164$	−4.89070	+	3.33442i	−0.381900	+	0.260375i
$165$		0			0
$166$	0.867673	+	1.50285i	0.0673445	+	0.116644i
$167$	−3.10920	−	1.49731i	−0.240597	−	0.115865i	0.309700	−	0.950834i	$-0.399771\pi$
$167$	−3.10920	−	1.49731i	−0.240597	−	0.115865i	−0.550297	+	0.834969i	$0.685486\pi$
$168$		0			0
$169$	8.18193	−	3.94021i	0.629379	−	0.303093i
$170$	−4.52326	−	3.08390i	−0.346918	−	0.236525i
$171$		0			0
$172$	−10.4532	−	9.69914i	−0.797048	−	0.739552i
$173$	16.3049	+	11.1165i	1.23964	+	0.845171i	0.992312	−	0.123761i	$-0.0394957\pi$
$173$	16.3049	+	11.1165i	1.23964	+	0.845171i	0.247326	+	0.968932i	$0.420448\pi$
$174$		0			0
$175$	−4.82536	−	32.8949i	−0.364763	−	2.48662i
$176$	12.5489	+	6.04323i	0.945909	+	0.455526i
$177$		0			0
$178$	0.305109	−	0.528464i	0.0228689	−	0.0396100i
$179$	−16.2081	+	11.0505i	−1.21145	+	0.825951i	−0.988844	−	0.148957i	$-0.952408\pi$
$179$	−16.2081	+	11.0505i	−1.21145	+	0.825951i	−0.222605	+	0.974909i	$0.571456\pi$
$180$		0			0
$181$	0.837732	−	3.67034i	0.0622681	−	0.272815i	−0.934204	−	0.356739i	$-0.883888\pi$
$181$	0.837732	−	3.67034i	0.0622681	−	0.272815i	0.996472	+	0.0839248i	$0.0267456\pi$
$182$	0.473005	+	1.55522i	0.0350615	+	0.115280i
$183$		0			0
$184$	−0.420952	−	5.61721i	−0.0310330	−	0.414106i
$185$	−44.9654	−	13.8700i	−3.30592	−	1.01974i
$186$		0			0
$187$	−16.3241	+	5.03530i	−1.19373	+	0.368218i
$188$	2.18109	+	2.73501i	0.159073	+	0.199471i
$189$		0			0
$190$	−0.145905	+	0.182959i	−0.0105850	+	0.0132732i
$191$	3.42501	−	8.72678i	0.247825	−	0.631448i	−0.751784	−	0.659409i	$-0.770806\pi$
$191$	3.42501	−	8.72678i	0.247825	−	0.631448i	0.999609	+	0.0279618i	$0.00890166\pi$
$192$		0			0
$193$	−3.95604	+	0.596278i	−0.284762	+	0.0429210i	−0.289870	−	0.957066i	$-0.593612\pi$
$193$	−3.95604	+	0.596278i	−0.284762	+	0.0429210i	0.00510803	+	0.999987i	$0.498374\pi$
$194$	2.38448	−	2.21247i	0.171196	−	0.158846i
$195$		0			0
$196$	−13.1921	+	1.88198i	−0.942295	+	0.134427i
$197$	−22.5071			−1.60356			−0.801782	−	0.597616i	$-0.796115\pi$
$197$	−22.5071			−1.60356			−0.801782	+	0.597616i	$0.796115\pi$
$198$		0			0
$199$	16.9133	−	2.54927i	1.19895	−	0.180713i	0.480947	−	0.876750i	$-0.340293\pi$
$199$	16.9133	−	2.54927i	1.19895	−	0.180713i	0.718006	+	0.696037i	$0.245055\pi$
$200$	−1.13776	+	15.1824i	−0.0804519	+	1.07356i
$201$		0			0
$202$	0.485919	−	0.609323i	0.0341891	−	0.0428718i
$203$	1.48037	+	3.10533i	0.103902	+	0.217952i
$204$		0			0
$205$	−12.4531	+	3.84126i	−0.869759	+	0.268285i
$206$	0.809917	+	2.06364i	0.0564296	+	0.143780i
$207$		0			0
$208$	0.507607	+	6.77355i	0.0351962	+	0.469661i
$209$	0.162491	+	0.711920i	0.0112397	+	0.0492445i
$210$		0			0
$211$	0.357330	−	1.56557i	0.0245996	−	0.107778i	−0.961138	−	0.276070i	$-0.910968\pi$
$211$	0.357330	−	1.56557i	0.0245996	−	0.107778i	0.985737	+	0.168292i	$0.0538251\pi$
$212$	−25.2965	−	3.81283i	−1.73737	−	0.261866i
$213$		0			0
$214$	−1.71891	+	2.97725i	−0.117503	+	0.203520i
$215$	−15.6975	−	27.1889i	−1.07056	−	1.85427i
$216$		0			0
$217$	3.52798	−	1.36858i	0.239495	−	0.0929053i
$218$	−4.66282	+	2.24549i	−0.315806	+	0.152084i
$219$		0			0
$220$	23.7412	+	22.0286i	1.60063	+	1.48517i
$221$	−6.10711	−	5.66657i	−0.410808	−	0.381174i
$222$		0			0
$223$	18.8970	−	9.10033i	1.26544	−	0.609403i	0.323831	−	0.946115i	$-0.395029\pi$
$223$	18.8970	−	9.10033i	1.26544	−	0.609403i	0.941608	+	0.336712i	$0.109315\pi$
$224$	9.20015	+	0.725995i	0.614711	+	0.0485076i
$225$		0			0
$226$	−0.368291	−	0.637899i	−0.0244984	−	0.0424324i
$227$	3.46255	−	5.99732i	0.229818	−	0.398056i	−0.727936	−	0.685645i	$-0.759520\pi$
$227$	3.46255	−	5.99732i	0.229818	−	0.398056i	0.957754	+	0.287589i	$0.0928536\pi$
$228$		0			0
$229$	3.42591	+	0.516373i	0.226391	+	0.0341229i	0.261258	−	0.965269i	$-0.415863\pi$
$229$	3.42591	+	0.516373i	0.226391	+	0.0341229i	−0.0348672	+	0.999392i	$0.511101\pi$
$230$	1.34578	−	5.89623i	0.0887379	−	0.388786i
$231$		0			0
$232$	−0.350552	−	1.53587i	−0.0230148	−	0.100835i
$233$	0.719821	+	9.60534i	0.0471570	+	0.629267i	0.969846	+	0.243720i	$0.0783679\pi$
$233$	0.719821	+	9.60534i	0.0471570	+	0.629267i	−0.922688	+	0.385546i	$0.874013\pi$
$234$		0			0
$235$	2.81378	+	7.16939i	0.183551	+	0.467680i
$236$	4.18664	−	1.29141i	0.272527	−	0.0840635i
$237$		0			0
$238$	−2.71039	+	2.14401i	−0.175688	+	0.138976i
$239$	−0.491532	+	0.616362i	−0.0317946	+	0.0398691i	−0.797475	−	0.603353i	$-0.793831\pi$
$239$	−0.491532	+	0.616362i	−0.0317946	+	0.0398691i	0.765680	+	0.643222i	$0.222403\pi$
$240$		0			0
$241$	1.62931	−	21.7416i	0.104953	−	1.40050i	−0.657499	−	0.753455i	$-0.728386\pi$
$241$	1.62931	−	21.7416i	0.104953	−	1.40050i	0.762452	−	0.647045i	$-0.223995\pi$
$242$	−1.68086	+	0.253349i	−0.108050	+	0.0162859i
$243$		0			0
$244$	−9.36295			−0.599402
$245$	−28.9753	−	4.60160i	−1.85116	−	0.293986i
$246$		0			0
$247$	−0.261054	+	0.242222i	−0.0166105	+	0.0154122i
$248$	−1.71353	+	0.258274i	−0.108809	+	0.0164004i
$249$		0			0
$250$	−3.59577	+	9.16188i	−0.227417	+	0.579448i
$251$	12.8679	−	16.1358i	0.812215	−	1.01849i	−0.187132	−	0.982335i	$-0.559919\pi$
$251$	12.8679	−	16.1358i	0.812215	−	1.01849i	0.999346	−	0.0361503i	$-0.0115095\pi$
$252$		0			0
$253$	−11.7666	−	14.7548i	−0.739758	−	0.927627i
$254$	−1.93033	+	0.595429i	−0.121120	+	0.0373605i
$255$		0			0
$256$	8.44532	+	2.60504i	0.527832	+	0.162815i
$257$	1.12506	+	15.0128i	0.0701791	+	0.936475i	0.915526	+	0.402258i	$0.131775\pi$
$257$	1.12506	+	15.0128i	0.0701791	+	0.936475i	−0.845347	+	0.534217i	$0.820606\pi$
$258$		0			0
$259$	−16.8300	+	24.4769i	−1.04577	+	1.52092i
$260$	−3.51459	+	15.3984i	−0.217966	+	0.954969i
$261$		0			0
$262$	−1.87384	+	1.27756i	−0.115766	+	0.0789280i
$263$	11.8085	−	20.4529i	0.728143	−	1.26118i	−0.229524	−	0.973303i	$-0.573717\pi$
$263$	11.8085	−	20.4529i	0.728143	−	1.26118i	0.957667	−	0.287878i	$-0.0929498\pi$
$264$		0			0
$265$	−50.7451	−	24.4376i	−3.11725	−	1.50119i
$266$	0.0827333	+	0.122383i	0.00507270	+	0.00750377i
$267$		0			0
$268$	7.48593	+	5.10382i	0.457276	+	0.311766i
$269$	10.7679	+	9.99113i	0.656529	+	0.609170i	0.936428	−	0.350860i	$-0.114111\pi$
$269$	10.7679	+	9.99113i	0.656529	+	0.609170i	−0.279899	+	0.960029i	$0.590301\pi$
$270$		0			0
$271$	15.9609	+	10.8819i	0.969553	+	0.661030i	0.940945	−	0.338561i	$-0.109940\pi$
$271$	15.9609	+	10.8819i	0.969553	+	0.661030i	0.0286083	+	0.999591i	$0.490892\pi$
$272$	−13.0106	+	6.26555i	−0.788881	+	0.379905i
$273$		0			0
$274$	1.69470	+	0.816125i	0.102381	+	0.0493039i
$275$	25.5041	+	44.1743i	1.53795	+	2.66381i
$276$		0			0
$277$	−1.67357	+	1.14102i	−0.100555	+	0.0685572i	−0.612554	−	0.790429i	$-0.709858\pi$
$277$	−1.67357	+	1.14102i	−0.100555	+	0.0685572i	0.511999	+	0.858986i	$0.328905\pi$
$278$	−5.62431	−	0.847729i	−0.337324	−	0.0508434i
$279$		0			0
$280$	12.4869	+	4.95773i	0.746235	+	0.296281i
$281$	2.58571	+	11.3287i	0.154250	+	0.675814i	0.991621	+	0.129179i	$0.0412343\pi$
$281$	2.58571	+	11.3287i	0.154250	+	0.675814i	−0.837371	+	0.546635i	$0.815909\pi$
$282$		0			0
$283$	27.3594	+	8.43927i	1.62635	+	0.501663i	0.967979	−	0.251031i	$-0.0807695\pi$
$283$	27.3594	+	8.43927i	1.62635	+	0.501663i	0.658371	+	0.752693i	$0.271246\pi$
$284$	−3.56934	−	9.09452i	−0.211801	−	0.539661i
$285$		0			0
$286$	−1.55496	−	1.94986i	−0.0919468	−	0.115298i
$287$	−0.0324806	+	8.22658i	−0.00191727	+	0.485600i
$288$		0			0
$289$	0.259928	−	0.662286i	0.0152899	−	0.0389580i
$290$	0.126398	−	1.68667i	0.00742237	−	0.0990447i
$291$		0			0
$292$	12.8237	−	11.8987i	0.750453	−	0.696319i
$293$	−13.9307			−0.813841			−0.406921	−	0.913463i	$-0.633397\pi$
$293$	−13.9307			−0.813841			−0.406921	+	0.913463i	$0.633397\pi$
$294$		0			0
$295$	9.64603			0.561614
$296$	9.97158	−	9.25227i	0.579586	−	0.537777i
$297$		0			0
$298$	0.0909953	−	1.21425i	0.00527122	−	0.0703395i
$299$	3.36245	−	8.56738i	0.194455	−	0.495464i
$300$		0			0
$301$	−19.3389	+	4.33372i	−1.11468	+	0.249791i
$302$	−3.65435	−	4.58241i	−0.210284	−	0.263688i
$303$		0			0
$304$	0.225517	+	0.574608i	0.0129343	+	0.0329560i
$305$	−19.6980	−	6.07604i	−1.12791	−	0.347913i
$306$		0			0
$307$	−0.509864	−	2.23386i	−0.0290995	−	0.127493i	0.958292	−	0.285791i	$-0.0922564\pi$
$307$	−0.509864	−	2.23386i	−0.0290995	−	0.127493i	−0.987391	+	0.158298i	$0.949399\pi$
$308$	17.7457	−	10.1523i	1.01116	−	0.578481i
$309$		0			0
$310$	−1.83975	−	0.277297i	−0.104491	−	0.0157494i
$311$	22.5349	−	15.3640i	1.27784	−	0.871213i	0.281739	−	0.959491i	$-0.409089\pi$
$311$	22.5349	−	15.3640i	1.27784	−	0.871213i	0.996096	+	0.0882778i	$0.0281363\pi$
$312$		0			0
$313$	6.36027	+	11.0163i	0.359504	+	0.622679i	0.987878	−	0.155233i	$-0.0496127\pi$
$313$	6.36027	+	11.0163i	0.359504	+	0.622679i	−0.628374	+	0.777911i	$0.716279\pi$
$314$	4.65559	+	2.24201i	0.262730	+	0.126524i
$315$		0			0
$316$	3.24537	−	1.56289i	0.182566	−	0.0879194i
$317$	−24.1416	−	16.4595i	−1.35593	−	0.924456i	−0.355979	−	0.934494i	$-0.615853\pi$
$317$	−24.1416	−	16.4595i	−1.35593	−	0.924456i	−0.999950	+	0.0100376i	$0.996805\pi$
$318$		0			0
$319$	−3.86901	−	3.58991i	−0.216623	−	0.200997i
$320$	20.0157	+	13.6465i	1.11891	+	0.762861i
$321$		0			0
$322$	−3.29875	−	1.92194i	−0.183832	−	0.107105i
$323$	−0.682117	−	0.328490i	−0.0379540	−	0.0182777i
$324$		0			0
$325$	−12.4379	+	21.5430i	−0.689929	+	1.19499i
$326$	−1.37579	+	0.937995i	−0.0761978	+	0.0519508i
$327$		0			0
$328$	0.838297	−	3.67282i	0.0462872	−	0.202797i
$329$	4.84966	−	0.344182i	0.267370	−	0.0189754i
$330$		0			0
$331$	−0.803345	−	10.7199i	−0.0441558	−	0.589219i	−0.974769	−	0.223215i	$-0.928345\pi$
$331$	−0.803345	−	10.7199i	−0.0441558	−	0.589219i	0.930613	−	0.366004i	$-0.119274\pi$
$332$	10.1710	+	3.13732i	0.558204	+	0.172183i
$333$		0			0
$334$	1.02349	−	0.315704i	0.0560027	−	0.0172746i
$335$	12.4370	+	15.5955i	0.679507	+	0.852075i
$336$		0			0
$337$	6.15955	−	7.72383i	0.335532	−	0.420744i	−0.585231	−	0.810867i	$-0.698996\pi$
$337$	6.15955	−	7.72383i	0.335532	−	0.420744i	0.920763	+	0.390123i	$0.127568\pi$
$338$	−1.02973	+	2.62372i	−0.0560101	+	0.142711i
$339$		0			0
$340$	−33.2032	+	5.00457i	−1.80069	+	0.271411i
$341$	−4.25588	+	3.94888i	−0.230469	+	0.213844i
$342$		0			0
$343$	−8.23271	+	16.5898i	−0.444525	+	0.895767i
$344$	9.07560			0.489324
$345$		0			0
$346$	−6.05640	+	0.912855i	−0.325594	+	0.0490754i
$347$	−0.805537	+	10.7491i	−0.0432435	+	0.577044i	0.932931	+	0.360056i	$0.117242\pi$
$347$	−0.805537	+	10.7491i	−0.0432435	+	0.577044i	−0.976174	+	0.216988i	$0.930377\pi$
$348$		0			0
$349$	−13.1758	+	16.5219i	−0.705284	+	0.884399i	−0.997406	−	0.0719827i	$-0.977067\pi$
$349$	−13.1758	+	16.5219i	−0.705284	+	0.884399i	0.292122	+	0.956381i	$0.405639\pi$
$350$	8.04214	+	6.46550i	0.429871	+	0.345596i
$351$		0			0
$352$	−13.5299	+	4.17342i	−0.721146	+	0.222444i
$353$	−1.81332	−	4.62027i	−0.0965135	−	0.245912i	0.874461	−	0.485096i	$-0.161215\pi$
$353$	−1.81332	−	4.62027i	−0.0965135	−	0.245912i	−0.970974	+	0.239184i	$0.923120\pi$
$354$		0			0
$355$	−1.60743	−	21.4496i	−0.0853134	−	1.13843i
$356$	−0.832851	−	3.64896i	−0.0441410	−	0.193394i
$357$		0			0
$358$	1.35480	−	5.93579i	0.0716037	−	0.313716i
$359$	−17.5145	−	2.63989i	−0.924381	−	0.139328i	−0.330431	−	0.943830i	$-0.607194\pi$
$359$	−17.5145	−	2.63989i	−0.924381	−	0.139328i	−0.593950	+	0.804502i	$0.702432\pi$
$360$		0			0
$361$	9.48382	−	16.4265i	0.499148	−	0.864550i
$362$	0.584231	+	1.01192i	0.0307065	+	0.0531852i
$363$		0			0
$364$	8.61490	+	5.01927i	0.451544	+	0.263081i
$365$	34.7006	−	16.7109i	1.81631	−	0.874689i
$366$		0			0
$367$	−18.2018	−	16.8888i	−0.950127	−	0.881589i	0.0429477	−	0.999077i	$-0.486325\pi$
$367$	−18.2018	−	16.8888i	−0.950127	−	0.881589i	−0.993074	+	0.117489i	$0.962516\pi$
$368$	−11.6944	−	10.8508i	−0.609612	−	0.565637i
$369$		0			0
$370$	13.1584	−	6.33677i	0.684074	−	0.329433i
$371$	−24.2859	+	25.9676i	−1.26086	+	1.34817i
$372$		0			0
$373$	−4.42697	−	7.66774i	−0.229220	−	0.397021i	0.728357	−	0.685198i	$-0.240284\pi$
$373$	−4.42697	−	7.66774i	−0.229220	−	0.397021i	−0.957577	+	0.288177i	$0.906951\pi$
$374$	2.65103	−	4.59171i	0.137081	−	0.237432i
$375$		0			0
$376$	−2.20155	−	0.331830i	−0.113536	−	0.0171128i
$377$	0.572759	−	2.50942i	0.0294986	−	0.129242i
$378$		0			0
$379$	−3.49469	−	15.3112i	−0.179510	−	0.786485i	−0.981856	−	0.189626i	$-0.939272\pi$
$379$	−3.49469	−	15.3112i	−0.179510	−	0.786485i	0.802346	−	0.596859i	$-0.203585\pi$
$380$	0.107262	+	1.43132i	0.00550244	+	0.0734250i
$381$		0			0
$382$	1.06302	+	2.70853i	0.0543889	+	0.138581i
$383$	19.1917	−	5.91986i	0.980651	−	0.302491i	0.237333	−	0.971428i	$-0.423727\pi$
$383$	19.1917	−	5.91986i	0.980651	−	0.302491i	0.743319	+	0.668938i	$0.233251\pi$
$384$		0			0
$385$	43.9223	−	9.84268i	2.23849	−	0.501630i
$386$	0.774191	−	0.970805i	0.0394053	−	0.0494127i
$387$		0			0
$388$	1.49096	−	19.8955i	0.0756921	−	1.01004i
$389$	22.8016	−	3.43679i	1.15609	−	0.174252i	0.457119	−	0.889406i	$-0.348881\pi$
$389$	22.8016	−	3.43679i	1.15609	−	0.174252i	0.698967	+	0.715154i	$0.253643\pi$
$390$		0			0
$391$	19.5664			0.989515
$392$	5.34006	−	6.58881i	0.269714	−	0.332785i
$393$		0			0
$394$	5.12076	−	4.75137i	0.257980	−	0.239370i
$395$	7.84194	−	1.18198i	0.394571	−	0.0594720i
$396$		0			0
$397$	−6.11196	+	15.5730i	−0.306750	+	0.781587i	0.691495	+	0.722381i	$0.256952\pi$
$397$	−6.11196	+	15.5730i	−0.306750	+	0.781587i	−0.998246	+	0.0592063i	$0.981143\pi$
$398$	−3.30991	+	4.15049i	−0.165911	+	0.208045i
$399$		0			0
$400$	26.8838	+	33.7112i	1.34419	+	1.68556i
$401$	16.0827	−	4.96085i	0.803131	−	0.247733i	0.134100	−	0.990968i	$-0.457186\pi$
$401$	16.0827	−	4.96085i	0.803131	−	0.247733i	0.669031	+	0.743235i	$0.266709\pi$
$402$		0			0
$403$	−2.70554	−	0.834550i	−0.134773	−	0.0415719i
$404$	−0.357225	−	4.76683i	−0.0177726	−	0.237159i
$405$		0			0
$406$	−0.992364	−	0.394003i	−0.0492502	−	0.0195540i
$407$	10.1411	−	44.4309i	0.502674	−	2.20236i
$408$		0			0
$409$	14.3405	−	9.77716i	0.709090	−	0.483449i	−0.154276	−	0.988028i	$-0.549304\pi$
$409$	14.3405	−	9.77716i	0.709090	−	0.483449i	0.863366	+	0.504579i	$0.168352\pi$
$410$	2.02238	−	3.50286i	0.0998781	−	0.172994i
$411$		0			0
$412$	12.2508	+	5.89967i	0.603553	+	0.290656i
$413$	1.81778	−	5.81153i	0.0894470	−	0.285967i
$414$		0			0
$415$	19.3620	+	13.2008i	0.950443	+	0.648001i
$416$	−5.06177	−	4.69663i	−0.248173	−	0.230271i
$417$		0			0
$418$	−0.187260	−	0.127671i	−0.00915917	−	0.00624462i
$419$	−2.24494	+	1.08111i	−0.109673	+	0.0528155i	−0.487916	−	0.872891i	$-0.662243\pi$
$419$	−2.24494	+	1.08111i	−0.109673	+	0.0528155i	0.378243	+	0.925706i	$0.376528\pi$
$420$		0			0
$421$	7.73923	+	3.72702i	0.377187	+	0.181644i	0.612865	−	0.790187i	$-0.290017\pi$
$421$	7.73923	+	3.72702i	0.377187	+	0.181644i	−0.235678	+	0.971831i	$0.575731\pi$
$422$	0.249200	+	0.431628i	0.0121309	+	0.0210113i
$423$		0			0
$424$	13.4526	−	9.17180i	0.653314	−	0.445422i
$425$	−52.2940	−	7.88205i	−2.53663	−	0.382336i
$426$		0			0
$427$	−7.37275	+	10.7226i	−0.356792	+	0.518905i
$428$	4.69209	+	20.5574i	0.226801	+	0.993680i
$429$		0			0
$430$	9.31117	+	2.87212i	0.449025	+	0.138506i
$431$	10.7173	+	27.3073i	0.516235	+	1.31535i	0.916899	+	0.399120i	$0.130684\pi$
$431$	10.7173	+	27.3073i	0.516235	+	1.31535i	−0.400663	+	0.916225i	$0.631220\pi$
$432$		0			0
$433$	10.1853	+	12.7720i	0.489474	+	0.613782i	0.963819	−	0.266558i	$-0.0858863\pi$
$433$	10.1853	+	12.7720i	0.489474	+	0.613782i	−0.474345	+	0.880339i	$0.657315\pi$
$434$	−0.513763	+	1.05615i	−0.0246614	+	0.0506969i
$435$		0			0
$436$	−11.5971	+	29.5489i	−0.555399	+	1.41513i
$437$	0.0625030	−	0.834045i	0.00298992	−	0.0398978i
$438$		0			0
$439$	0.926092	−	0.859287i	0.0441999	−	0.0410115i	−0.657764	−	0.753224i	$-0.728497\pi$
$439$	0.926092	−	0.859287i	0.0441999	−	0.0410115i	0.701964	+	0.712213i	$0.252307\pi$
$440$	−20.6124			−0.982657
$441$		0			0
$442$	2.58572			0.122990
$443$	−1.09754	+	1.01836i	−0.0521455	+	0.0483840i	−0.705815	−	0.708396i	$-0.749419\pi$
$443$	−1.09754	+	1.01836i	−0.0521455	+	0.0483840i	0.653670	+	0.756780i	$0.273229\pi$
$444$		0			0
$445$	0.615798	−	8.21726i	0.0291916	−	0.389535i
$446$	−2.37828	+	6.05975i	−0.112615	+	0.286937i
$447$		0			0
$448$	11.9936	−	9.48738i	0.566646	−	0.448237i
$449$	5.28443	+	6.62646i	0.249388	+	0.312722i	0.890730	−	0.454533i	$-0.150194\pi$
$449$	5.28443	+	6.62646i	0.249388	+	0.312722i	−0.641343	+	0.767255i	$0.721622\pi$
$450$		0			0
$451$	−4.61115	−	11.7490i	−0.217131	−	0.553240i
$452$	−4.31715	−	1.33166i	−0.203062	−	0.0626362i
$453$		0			0
$454$	0.478275	+	2.09546i	0.0224466	+	0.0983448i
$455$	14.8670	+	16.1503i	0.696978	+	0.757137i
$456$		0			0
$457$	−6.80611	−	1.02586i	−0.318376	−	0.0479875i	−0.0120899	−	0.999927i	$-0.503848\pi$
$457$	−6.80611	−	1.02586i	−0.318376	−	0.0479875i	−0.306286	+	0.951939i	$0.599087\pi$
$458$	−0.888464	+	0.605745i	−0.0415152	+	0.0283046i
$459$		0			0
$460$	−18.5474	−	32.1251i	−0.864778	−	1.49784i
$461$	−22.1786	−	10.6806i	−1.03296	−	0.497446i	−0.160963	−	0.986960i	$-0.551460\pi$
$461$	−22.1786	−	10.6806i	−1.03296	−	0.497446i	−0.871995	+	0.489514i	$0.837174\pi$
$462$		0			0
$463$	−26.8701	+	12.9399i	−1.24876	+	0.601370i	−0.937179	−	0.348849i	$-0.886572\pi$
$463$	−26.8701	+	12.9399i	−1.24876	+	0.601370i	−0.311580	+	0.950220i	$0.600858\pi$
$464$	−3.68631	−	2.51329i	−0.171133	−	0.116676i
$465$		0			0
$466$	−2.19151	−	2.03342i	−0.101520	−	0.0941966i
$467$	−7.60586	−	5.18559i	−0.351957	−	0.239960i	0.374416	−	0.927261i	$-0.377843\pi$
$467$	−7.60586	−	5.18559i	−0.351957	−	0.239960i	−0.726373	+	0.687300i	$0.758796\pi$
$468$		0			0
$469$	11.7397	−	4.55409i	0.542089	−	0.210288i
$470$	−2.15368	−	1.03716i	−0.0993419	−	0.0478405i
$471$		0			0
$472$	−1.39423	+	2.41487i	−0.0641745	+	0.111153i
$473$	25.1226	−	17.1283i	1.15514	−	0.787560i
$474$		0			0
$475$	−0.503032	+	2.20393i	−0.0230807	+	0.101123i
$476$	−3.24193	+	20.9473i	−0.148594	+	0.960118i
$477$		0			0
$478$	−0.0182851	−	0.243998i	−0.000836343	−	0.0111602i
$479$	22.6694	+	6.99258i	1.03579	+	0.319499i	0.765607	−	0.643309i	$-0.222439\pi$
$479$	22.6694	+	6.99258i	1.03579	+	0.319499i	0.270185	+	0.962808i	$0.412915\pi$
$480$		0			0
$481$	21.2380	−	6.55105i	0.968369	−	0.298702i
$482$	4.21907	+	5.29055i	0.192174	+	0.240978i
$483$		0			0
$484$	−6.50056	+	8.15145i	−0.295480	+	0.370520i
$485$	16.0478	−	40.8892i	0.728693	−	1.85668i
$486$		0			0
$487$	5.83460	−	0.879424i	0.264391	−	0.0398505i	−0.0155089	−	0.999880i	$-0.504937\pi$
$487$	5.83460	−	0.879424i	0.264391	−	0.0398505i	0.279900	+	0.960029i	$0.409699\pi$
$488$	4.36826	−	4.05316i	0.197742	−	0.183478i
$489$		0			0
$490$	7.56381	−	5.06989i	0.341698	−	0.229034i
$491$	−13.2329			−0.597192			−0.298596	−	0.954380i	$-0.596518\pi$
$491$	−13.2329			−0.597192			−0.298596	+	0.954380i	$0.596518\pi$
$492$		0			0
$493$	5.41100	−	0.815576i	0.243699	−	0.0367317i
$494$	0.00825982	−	0.110220i	0.000371627	−	0.00495902i
$495$		0			0
$496$	−3.05989	+	3.83698i	−0.137393	+	0.172285i
$497$	−13.2259	−	3.07371i	−0.593261	−	0.137875i
$498$		0			0
$499$	−11.6043	+	3.57946i	−0.519481	+	0.160239i	−0.543398	−	0.839475i	$-0.682863\pi$
$499$	−11.6043	+	3.57946i	−0.519481	+	0.160239i	0.0239168	+	0.999714i	$0.492386\pi$
$500$	22.0548	+	56.1948i	0.986323	+	2.51311i
$501$		0			0
$502$	0.478690	+	6.38767i	0.0213650	+	0.285096i
$503$	−2.67697	−	11.7286i	−0.119360	−	0.522951i	−0.998890	−	0.0471071i	$-0.985000\pi$
$503$	−2.67697	−	11.7286i	−0.119360	−	0.522951i	0.879530	−	0.475844i	$-0.157857\pi$
$504$		0			0
$505$	2.34187	−	10.2604i	0.104212	−	0.456583i
$506$	5.79192	+	0.872991i	0.257482	+	0.0388092i
$507$		0			0
$508$	−6.19512	+	10.7303i	−0.274864	+	0.476079i
$509$	−14.3126	−	24.7902i	−0.634395	−	1.09881i	−0.986643	−	0.162898i	$-0.947916\pi$
$509$	−14.3126	−	24.7902i	−0.634395	−	1.09881i	0.352247	−	0.935907i	$-0.385418\pi$
$510$		0			0
$511$	−3.52871	−	24.0555i	−0.156101	−	1.06415i
$512$	−18.2748	+	8.80067i	−0.807639	+	0.388938i
$513$		0			0
$514$	−3.42526	−	3.17818i	−0.151082	−	0.140183i
$515$	21.9450	+	20.3620i	0.967012	+	0.897256i
$516$		0			0
$517$	−6.72048	+	3.23641i	−0.295566	+	0.142337i
$518$	−1.33808	−	9.12183i	−0.0587920	−	0.400790i
$519$		0			0
$520$	−5.02614	−	8.70554i	−0.220411	−	0.381763i
$521$	−3.01540	+	5.22282i	−0.132107	+	0.228816i	−0.924489	−	0.381210i	$-0.875508\pi$
$521$	−3.01540	+	5.22282i	−0.132107	+	0.228816i	0.792382	+	0.610026i	$0.208841\pi$
$522$		0			0
$523$	−37.4254	−	5.64097i	−1.63650	−	0.246662i	−0.734565	−	0.678538i	$-0.762614\pi$
$523$	−37.4254	−	5.64097i	−1.63650	−	0.246662i	−0.901933	+	0.431875i	$0.857852\pi$
$524$	−3.09534	+	13.5616i	−0.135221	+	0.592441i
$525$		0			0
$526$	1.63108	+	7.14623i	0.0711185	+	0.311591i
$527$	−0.449822	−	6.00245i	−0.0195945	−	0.261471i
$528$		0			0
$529$	−0.505779	−	1.28870i	−0.0219904	−	0.0560306i
$530$	16.7043	−	5.15259i	0.725588	−	0.223814i
$531$		0			0
$532$	0.882552	+	0.205106i	0.0382635	+	0.00889247i
$533$	3.83775	−	4.81239i	0.166231	−	0.208448i
$534$		0			0
$535$	−3.46927	+	46.2942i	−0.149990	+	2.00147i
$536$	−5.70195	+	0.859431i	−0.246287	+	0.0371218i
$537$		0			0
$538$	−4.55906			−0.196555
$539$	2.34707	−	28.3171i	0.101095	−	1.21970i
$540$		0			0
$541$	−3.12661	+	2.90107i	−0.134423	+	0.124727i	−0.744519	−	0.667601i	$-0.767321\pi$
$541$	−3.12661	+	2.90107i	−0.134423	+	0.124727i	0.610096	+	0.792327i	$0.291131\pi$
$542$	−5.92861	+	0.893593i	−0.254655	+	0.0383831i
$543$		0			0
$544$	5.36315	−	13.6651i	0.229943	−	0.585885i
$545$	−43.5739	+	54.6399i	−1.86650	+	2.34052i
$546$		0			0
$547$	0.545248	+	0.683720i	0.0233131	+	0.0292338i	0.793351	−	0.608764i	$-0.208334\pi$
$547$	0.545248	+	0.683720i	0.0233131	+	0.0292338i	−0.770038	+	0.637998i	$0.779763\pi$
$548$	11.0245	−	3.40061i	0.470943	−	0.145267i
$549$		0			0
$550$	−15.1281	−	4.66639i	−0.645063	−	0.198975i
$551$	−0.0174802	−	0.233256i	−0.000744680	−	0.00993706i
$552$		0			0
$553$	0.765681	−	4.94734i	0.0325601	−	0.210382i
$554$	0.139891	−	0.612901i	0.00594338	−	0.0260396i
$555$		0			0
$556$	−28.8247	+	19.6524i	−1.22244	+	0.833445i
$557$	14.6289	−	25.3380i	0.619846	−	1.07360i	−0.369668	−	0.929164i	$-0.620528\pi$
$557$	14.6289	−	25.3380i	0.619846	−	1.07360i	0.989514	−	0.144440i	$-0.0461382\pi$
$558$		0			0
$559$	13.3600	+	6.43382i	0.565067	+	0.272122i
$560$	35.4737	−	13.7610i	1.49904	−	0.581509i
$561$		0			0
$562$	−2.97985	−	2.03162i	−0.125697	−	0.0856989i
$563$	−14.7954	−	13.7282i	−0.623553	−	0.578573i	0.303811	−	0.952732i	$-0.401741\pi$
$563$	−14.7954	−	13.7282i	−0.623553	−	0.578573i	−0.927364	+	0.374159i	$0.877931\pi$
$564$		0			0
$565$	−8.21836	−	5.60319i	−0.345749	−	0.235728i
$566$	−8.00633	+	3.85564i	−0.336531	+	0.162065i
$567$		0			0
$568$	5.60222	+	2.69789i	0.235064	+	0.113201i
$569$	13.3743	+	23.1650i	0.560680	+	0.971127i	0.997437	+	0.0715471i	$0.0227936\pi$
$569$	13.3743	+	23.1650i	0.560680	+	0.971127i	−0.436757	+	0.899580i	$0.643873\pi$
$570$		0			0
$571$	34.6938	−	23.6538i	1.45189	−	0.989881i	0.456941	−	0.889497i	$-0.348945\pi$
$571$	34.6938	−	23.6538i	1.45189	−	0.989881i	0.994949	−	0.100384i	$-0.0320072\pi$
$572$	−15.1260	−	2.27988i	−0.632450	−	0.0953265i
$573$		0			0
$574$	−1.72929	−	1.87855i	−0.0721790	−	0.0784091i
$575$	−13.0004	−	56.9585i	−0.542155	−	2.37533i
$576$		0			0
$577$	−16.5612	−	5.10846i	−0.689453	−	0.212668i	−0.0698197	−	0.997560i	$-0.522242\pi$
$577$	−16.5612	−	5.10846i	−0.689453	−	0.212668i	−0.619633	+	0.784892i	$0.712719\pi$
$578$	0.0806740	+	0.205554i	0.00335559	+	0.00854992i
$579$		0			0
$580$	−6.46826	−	8.11094i	−0.268580	−	0.336788i
$581$	11.6019	−	9.17753i	0.481329	−	0.380748i
$582$		0			0
$583$	19.9288	−	50.7778i	0.825367	−	2.10300i
$584$	−0.832026	+	11.1026i	−0.0344295	+	0.459430i
$585$		0			0
$586$	3.16948	−	2.94085i	0.130930	−	0.121485i
$587$	35.3362			1.45848			0.729241	−	0.684256i	$-0.239873\pi$
$587$	35.3362			1.45848			0.729241	+	0.684256i	$0.239873\pi$
$588$		0			0
$589$	−0.257300			−0.0106019
$590$	−2.19464	+	2.03633i	−0.0903519	+	0.0838343i
$591$		0			0
$592$	2.87893	−	38.4166i	0.118323	−	1.57891i
$593$	−14.6542	+	37.3384i	−0.601778	+	1.53330i	0.227098	+	0.973872i	$0.427076\pi$
$593$	−14.6542	+	37.3384i	−0.601778	+	1.53330i	−0.828876	+	0.559433i	$0.811019\pi$
$594$		0			0
$595$	−20.4141	+	41.9657i	−0.836898	+	1.72043i
$596$	−4.65655	−	5.83913i	−0.190740	−	0.239180i
$597$		0			0
$598$	1.04360	+	2.65906i	0.0426761	+	0.108737i
$599$	27.7351	+	8.55514i	1.13322	+	0.349553i	0.803959	−	0.594684i	$-0.202723\pi$
$599$	27.7351	+	8.55514i	1.13322	+	0.349553i	0.329265	+	0.944238i	$0.393199\pi$
$600$		0			0
$601$	2.90245	+	12.7164i	0.118393	+	0.518715i	0.998994	+	0.0448547i	$0.0142825\pi$
$601$	2.90245	+	12.7164i	0.118393	+	0.518715i	−0.880600	+	0.473860i	$0.842860\pi$
$602$	3.48506	−	5.06854i	0.142041	−	0.206578i
$603$		0			0
$604$	−35.5480	−	5.35799i	−1.44643	−	0.218014i
$605$	−18.9659	+	12.9307i	−0.771074	+	0.525709i
$606$		0			0
$607$	−19.5646	−	33.8869i	−0.794102	−	1.37543i	−0.923408	−	0.383821i	$-0.874608\pi$
$607$	−19.5646	−	33.8869i	−0.794102	−	1.37543i	0.129305	−	0.991605i	$-0.458725\pi$
$608$	−0.565360	−	0.272263i	−0.0229284	−	0.0110417i
$609$		0			0
$610$	5.76433	−	2.77596i	0.233391	−	0.112395i
$611$	−3.00561	−	2.04919i	−0.121594	−	0.0829013i
$612$		0			0
$613$	26.5961	+	24.6776i	1.07421	+	0.996719i	1.00000		0.000523958i	$-0.000166781\pi$
$613$	26.5961	+	24.6776i	1.07421	+	0.996719i	0.0742076	+	0.997243i	$0.476357\pi$
$614$	0.587582	+	0.400607i	0.0237129	+	0.0161672i
$615$		0			0
$616$	−3.88437	+	12.4185i	−0.156506	+	0.500357i
$617$	−34.4213	−	16.5764i	−1.38575	−	0.667341i	−0.415532	−	0.909579i	$-0.636404\pi$
$617$	−34.4213	−	16.5764i	−1.38575	−	0.667341i	−0.970217	+	0.242237i	$0.922119\pi$
$618$		0			0
$619$	−6.87765	+	11.9124i	−0.276436	+	0.478801i	−0.970496	−	0.241115i	$-0.922487\pi$
$619$	−6.87765	+	11.9124i	−0.276436	+	0.478801i	0.694060	+	0.719917i	$0.255820\pi$
$620$	−9.42873	+	6.42840i	−0.378667	+	0.258171i
$621$		0			0
$622$	−1.88365	+	8.25281i	−0.0755275	+	0.330908i
$623$	−4.83468	−	1.91953i	−0.193697	−	0.0769045i
$624$		0			0
$625$	5.23690	+	69.8816i	0.209476	+	2.79526i
$626$	−3.77267	−	1.16372i	−0.150786	−	0.0465114i
$627$		0			0
$628$	30.2859	−	9.34196i	1.20854	−	0.372785i
$629$	29.4600	+	36.9417i	1.17465	+	1.47296i
$630$		0			0
$631$	−11.0800	+	13.8938i	−0.441087	+	0.553105i	−0.951829	−	0.306628i	$-0.900799\pi$
$631$	−11.0800	+	13.8938i	−0.441087	+	0.553105i	0.510743	+	0.859734i	$0.329371\pi$
$632$	−0.837557	+	2.13406i	−0.0333162	+	0.0848884i
$633$		0			0
$634$	8.96732	−	1.35161i	0.356138	−	0.0536792i
$635$	−19.9968	+	18.5544i	−0.793550	+	0.736307i
$636$		0			0
$637$	12.5319	−	5.91359i	0.496531	−	0.234305i
$638$	1.63812			0.0648537
$639$		0			0
$640$	−36.3472	+	5.47845i	−1.43675	+	0.216555i
$641$	−0.153334	+	2.04610i	−0.00605634	+	0.0808162i	−0.999413	−	0.0342606i	$-0.989092\pi$
$641$	−0.153334	+	2.04610i	−0.00605634	+	0.0808162i	0.993357	+	0.115077i	$0.0367114\pi$
$642$		0			0
$643$	−5.75764	+	7.21986i	−0.227059	+	0.284723i	−0.882291	−	0.470705i	$-0.844000\pi$
$643$	−5.75764	+	7.21986i	−0.227059	+	0.284723i	0.655231	+	0.755428i	$0.272571\pi$
$644$	−22.8499	+	5.12051i	−0.900413	+	0.201777i
$645$		0			0
$646$	0.224540	−	0.0692613i	0.00883439	−	0.00272505i
$647$	2.90657	+	7.40581i	0.114269	+	0.291152i	0.976555	−	0.215270i	$-0.0690630\pi$
$647$	2.90657	+	7.40581i	0.114269	+	0.291152i	−0.862286	+	0.506422i	$0.830968\pi$
$648$		0			0
$649$	0.698140	+	9.31603i	0.0274044	+	0.365686i
$650$	−1.71801	−	7.52711i	−0.0673861	−	0.295238i
$651$		0			0
$652$	−2.27263	+	9.95703i	−0.0890029	+	0.389947i
$653$	−26.1114	−	3.93566i	−1.02182	−	0.154014i	−0.383302	−	0.923623i	$-0.625213\pi$
$653$	−26.1114	−	3.93566i	−1.02182	−	0.154014i	−0.638515	+	0.769609i	$0.720451\pi$
$654$		0			0
$655$	−15.3128	+	26.5226i	−0.598321	+	1.03632i
$656$	−5.33461	−	9.23982i	−0.208282	−	0.360754i
$657$		0			0
$658$	−1.03072	+	1.10210i	−0.0401818	+	0.0429642i
$659$	−9.99668	+	4.81415i	−0.389415	+	0.187533i	−0.618338	−	0.785912i	$-0.712194\pi$
$659$	−9.99668	+	4.81415i	−0.389415	+	0.187533i	0.228923	+	0.973445i	$0.426480\pi$
$660$		0			0
$661$	2.19937	+	2.04072i	0.0855458	+	0.0793749i	0.721787	−	0.692115i	$-0.243321\pi$
$661$	2.19937	+	2.04072i	0.0855458	+	0.0793749i	−0.636241	+	0.771490i	$0.719512\pi$
$662$	2.44580	+	2.26937i	0.0950588	+	0.0882017i
$663$		0			0
$664$	−6.10336	+	2.93922i	−0.236856	+	0.114064i
$665$	1.72364	+	1.00424i	0.0668397	+	0.0389426i
$666$		0			0
$667$	3.02261	+	5.23531i	0.117036	+	0.202712i
$668$	3.28474	−	5.68933i	0.127090	−	0.220127i
$669$		0			0
$670$	−6.12194	−	0.922734i	−0.236511	−	0.0356483i
$671$	4.44251	−	19.4639i	0.171501	−	0.751397i
$672$		0			0
$673$	−3.21059	−	14.0665i	−0.123759	−	0.542225i	−0.998353	−	0.0573685i	$-0.981729\pi$
$673$	−3.21059	−	14.0665i	−0.123759	−	0.542225i	0.874594	−	0.484856i	$-0.161128\pi$
$674$	0.229137	+	3.05762i	0.00882602	+	0.117775i
$675$		0			0
$676$	6.31591	+	16.0927i	0.242920	+	0.618949i
$677$	−36.3288	+	11.2060i	−1.39623	+	0.430680i	−0.899384	−	0.437159i	$-0.855985\pi$
$677$	−36.3288	+	11.2060i	−1.39623	+	0.430680i	−0.496845	+	0.867839i	$0.665508\pi$
$678$		0			0
$679$	−21.6107	−	17.3740i	−0.829341	−	0.666751i
$680$	13.3244	−	16.7083i	0.510968	−	0.640734i
$681$		0			0
$682$	0.134657	−	1.79688i	0.00515630	−	0.0688060i
$683$	23.6764	−	3.56864i	0.905951	−	0.136550i	0.320491	−	0.947251i	$-0.396152\pi$
$683$	23.6764	−	3.56864i	0.905951	−	0.136550i	0.585460	+	0.810701i	$0.300914\pi$
$684$		0			0
$685$	25.4005			0.970502
$686$	−1.62912	−	5.51245i	−0.0621999	−	0.210466i
$687$		0			0
$688$	18.8415	−	17.4824i	0.718326	−	0.666509i
$689$	26.3052	−	3.96487i	1.00215	−	0.151050i
$690$		0			0
$691$	5.45567	−	13.9008i	0.207544	−	0.528812i	−0.788761	−	0.614700i	$-0.789277\pi$
$691$	5.45567	−	13.9008i	0.207544	−	0.528812i	0.996305	+	0.0858873i	$0.0273725\pi$
$692$	−23.4225	+	29.3709i	−0.890390	+	1.11651i
$693$		0			0
$694$	−2.08593	−	2.61567i	−0.0791808	−	0.0992895i
$695$	−73.3956	+	22.6395i	−2.78405	+	0.858766i
$696$		0			0
$697$	12.5045	+	3.85711i	0.473640	+	0.146099i
$698$	−0.490143	−	6.54051i	−0.0185522	−	0.247562i
$699$		0			0
$700$	63.1324	−	4.48053i	2.38618	−	0.169348i
$701$	−6.15827	+	26.9811i	−0.232595	+	1.01906i	0.714884	+	0.699243i	$0.246480\pi$
$701$	−6.15827	+	26.9811i	−0.232595	+	1.01906i	−0.947478	+	0.319820i	$0.896378\pi$
$702$		0			0
$703$	1.66880	−	1.13777i	0.0629399	−	0.0429117i
$704$	−11.7310	+	20.3186i	−0.442128	+	0.765787i
$705$		0			0
$706$	1.38793	+	0.668391i	0.0522353	+	0.0251552i
$707$	−5.74037	−	3.34449i	−0.215889	−	0.125782i
$708$		0			0
$709$	−24.2578	−	16.5387i	−0.911020	−	0.621123i	0.0144702	−	0.999895i	$-0.495394\pi$
$709$	−24.2578	−	16.5387i	−0.911020	−	0.621123i	−0.925490	+	0.378773i	$0.876346\pi$
$710$	4.89385	+	4.54083i	0.183663	+	0.170414i
$711$		0			0
$712$	1.96817	+	1.34188i	0.0737604	+	0.0502890i
$713$	5.99116	−	2.88519i	0.224371	−	0.108051i
$714$		0			0
$715$	−30.3430	−	14.6124i	−1.13476	−	0.546474i
$716$	−18.6719	−	32.3406i	−0.697800	−	1.20863i
$717$		0			0
$718$	4.54215	−	3.09679i	0.169512	−	0.115571i
$719$	48.7169	+	7.34290i	1.81683	+	0.273844i	0.967290	−	0.253673i	$-0.0816386\pi$
$719$	48.7169	+	7.34290i	1.81683	+	0.273844i	0.849545	+	0.527517i	$0.176877\pi$
$720$		0			0
$721$	16.4032	−	9.38421i	0.610885	−	0.349486i
$722$	1.30998	+	5.73939i	0.0487523	+	0.213598i
$723$		0			0
$724$	6.84841	+	2.11246i	0.254519	+	0.0785088i
$725$	−5.96938	−	15.2097i	−0.221697	−	0.564875i
$726$		0			0
$727$	6.08426	+	7.62942i	0.225653	+	0.282960i	0.881750	−	0.471717i	$-0.156365\pi$
$727$	6.08426	+	7.62942i	0.225653	+	0.282960i	−0.656097	+	0.754676i	$0.727794\pi$
$728$	−6.19207	+	1.38760i	−0.229493	+	0.0514279i
$729$		0			0
$730$	−4.36722	+	11.1275i	−0.161638	+	0.411847i
$731$	−2.35584	+	31.4364i	−0.0871337	+	1.16272i
$732$		0			0
$733$	−19.0251	+	17.6527i	−0.702708	+	0.652018i	−0.948307	−	0.317353i	$-0.897206\pi$
$733$	−19.0251	+	17.6527i	−0.702708	+	0.652018i	0.245599	+	0.969372i	$0.421015\pi$
$734$	7.70655			0.284454
$735$		0			0
$736$	16.2173			0.597776
$737$	−14.1619	+	13.1403i	−0.521659	+	0.484029i
$738$		0			0
$739$	1.58623	−	21.1668i	0.0583504	−	0.778632i	−0.888893	−	0.458116i	$-0.848524\pi$
$739$	1.58623	−	21.1668i	0.0583504	−	0.778632i	0.947243	−	0.320516i	$-0.103856\pi$
$740$	32.7269	−	83.3867i	1.20306	−	3.06536i
$741$		0			0
$742$	0.0435689	−	11.0350i	0.00159946	−	0.405107i
$743$	−14.8026	−	18.5619i	−0.543054	−	0.680968i	0.432270	−	0.901744i	$-0.357713\pi$
$743$	−14.8026	−	18.5619i	−0.543054	−	0.680968i	−0.975325	+	0.220776i	$0.929141\pi$
$744$		0			0
$745$	−6.00731	−	15.3064i	−0.220091	−	0.560782i
$746$	2.62592	+	0.809988i	0.0961416	+	0.0296558i
$747$		0			0
$748$	−7.23647	−	31.7051i	−0.264592	−	1.15925i
$749$	27.2375	+	10.8142i	0.995236	+	0.395143i
$750$		0			0
$751$	−7.39844	−	1.11513i	−0.269973	−	0.0406918i	0.0126606	−	0.999920i	$-0.495970\pi$
$751$	−7.39844	−	1.11513i	−0.269973	−	0.0406918i	−0.282633	+	0.959228i	$0.591208\pi$
$752$	−5.20976	+	3.55195i	−0.189980	+	0.129526i
$753$		0			0
$754$	0.399440	+	0.691850i	0.0145467	+	0.0251957i
$755$	−71.3098	−	34.3410i	−2.59523	−	1.24980i
$756$		0			0
$757$	−13.1642	+	6.33954i	−0.478460	+	0.230414i	−0.657539	−	0.753420i	$-0.728403\pi$
$757$	−13.1642	+	6.33954i	−0.478460	+	0.230414i	0.179079	+	0.983835i	$0.442688\pi$
$758$	4.02738	+	2.74582i	0.146281	+	0.0997328i
$759$		0			0
$760$	−0.669650	−	0.621345i	−0.0242908	−	0.0225385i
$761$	−25.8872	−	17.6496i	−0.938410	−	0.639797i	−0.00553043	−	0.999985i	$-0.501760\pi$
$761$	−25.8872	−	17.6496i	−0.938410	−	0.639797i	−0.932880	+	0.360187i	$0.882713\pi$
$762$		0			0
$763$	24.7080	+	36.5491i	0.894489	+	1.32317i
$764$	16.0792	+	7.74334i	0.581725	+	0.280144i
$765$		0			0
$766$	−3.11674	+	5.39835i	−0.112612	+	0.195050i
$767$	−3.76434	+	2.56649i	−0.135923	+	0.0926704i
$768$		0			0
$769$	2.96080	−	12.9721i	0.106769	−	0.467787i	−0.893071	−	0.449916i	$-0.851454\pi$
$769$	2.96080	−	12.9721i	0.106769	−	0.467787i	0.999840	−	0.0178709i	$-0.00568880\pi$
$770$	−7.91524	+	11.5116i	−0.285245	+	0.414849i
$771$		0			0
$772$	−0.569149	−	7.59477i	−0.0204841	−	0.273342i
$773$	−37.7087	−	11.6316i	−1.35629	−	0.418359i	−0.470478	−	0.882412i	$-0.655919\pi$
$773$	−37.7087	−	11.6316i	−1.35629	−	0.418359i	−0.885808	+	0.464053i	$0.846395\pi$
$774$		0			0
$775$	−17.1745	+	5.29763i	−0.616926	+	0.190296i
$776$	7.91701	+	9.92762i	0.284204	+	0.356381i
$777$		0			0
$778$	−4.46224	+	5.59547i	−0.159979	+	0.200607i
$779$	0.204359	−	0.520699i	0.00732193	−	0.0186560i
$780$		0			0
$781$	20.5995	−	3.10487i	0.737107	−	0.111101i
$782$	−4.45170	+	4.13057i	−0.159192	+	0.147709i
$783$		0			0
$784$	−1.60576	−	23.9654i	−0.0573486	−	0.855906i
$785$	69.7788			2.49051
$786$		0			0
$787$	50.9123	−	7.67380i	1.81483	−	0.273541i	0.848191	−	0.529690i	$-0.177692\pi$
$787$	50.9123	−	7.67380i	1.81483	−	0.273541i	0.966637	+	0.256149i	$0.0824538\pi$
$788$	3.20189	−	42.7263i	0.114063	−	1.52206i
$789$		0			0
$790$	−1.53466	+	1.92440i	−0.0546006	+	0.0684670i
$791$	−4.92454	+	3.89548i	−0.175096	+	0.138507i
$792$		0			0
$793$	9.30375	−	2.86983i	0.330386	−	0.101911i
$794$	−1.89697	−	4.83340i	−0.0673209	−	0.171531i
$795$		0			0
$796$	2.43329	+	32.4700i	0.0862457	+	1.15087i
$797$	−4.24488	−	18.5980i	−0.150361	−	0.658776i	−0.992780	−	0.119952i	$-0.961726\pi$
$797$	−4.24488	−	18.5980i	−0.150361	−	0.658776i	0.842418	−	0.538824i	$-0.181131\pi$
$798$		0			0
$799$	1.72088	−	7.53968i	0.0608805	−	0.266735i
$800$	−43.3429	−	6.53290i	−1.53240	−	0.230973i
$801$		0			0
$802$	−2.61183	+	4.52382i	−0.0922269	+	0.159742i
$803$	18.6507	+	32.3040i	0.658169	+	1.13998i
$804$		0			0
$805$	−51.3953	−	4.05566i	−1.81144	−	0.142943i
$806$	0.791737	−	0.381280i	0.0278877	−	0.0134300i
$807$		0			0
$808$	2.23019	+	2.06932i	0.0784579	+	0.0727983i
$809$	29.4882	+	27.3611i	1.03675	+	0.961965i	0.999303	−	0.0373338i	$-0.0118865\pi$
$809$	29.4882	+	27.3611i	1.03675	+	0.961965i	0.0374486	+	0.999299i	$0.488077\pi$
$810$		0			0
$811$	−41.2734	+	19.8762i	−1.44930	+	0.697948i	−0.982474	−	0.186400i	$-0.940318\pi$
$811$	−41.2734	+	19.8762i	−1.44930	+	0.697948i	−0.466830	+	0.884347i	$0.654604\pi$
$812$	−6.10560	+	2.36850i	−0.214265	+	0.0831179i
$813$		0			0
$814$	7.07234	+	12.2496i	0.247885	+	0.429350i
$815$	−11.2428	+	19.4731i	−0.393818	+	0.682112i
$816$		0			0
$817$	1.33250	+	0.200842i	0.0466181	+	0.00702656i
$818$	−1.19869	+	5.25182i	−0.0419113	+	0.183626i
$819$		0			0
$820$	−5.52045	−	24.1867i	−0.192783	−	0.844636i
$821$	−0.514740	−	6.86873i	−0.0179646	−	0.239720i	−0.998956	−	0.0456718i	$-0.985457\pi$
$821$	−0.514740	−	6.86873i	−0.0179646	−	0.239720i	0.980992	−	0.194048i	$-0.0621619\pi$
$822$		0			0
$823$	−9.76900	−	24.8910i	−0.340526	−	0.867646i	−0.993867	−	0.110582i	$-0.964728\pi$
$823$	−9.76900	−	24.8910i	−0.340526	−	0.867646i	0.653341	−	0.757064i	$-0.273367\pi$
$824$	−8.26950	+	2.55080i	−0.288082	+	0.0888614i
$825$		0			0
$826$	0.813268	+	1.70597i	0.0282972	+	0.0593582i
$827$	7.93634	−	9.95185i	0.275973	−	0.346060i	−0.624457	−	0.781059i	$-0.714680\pi$
$827$	7.93634	−	9.95185i	0.275973	−	0.346060i	0.900431	+	0.434999i	$0.143251\pi$
$828$		0			0
$829$	1.14756	−	15.3131i	0.0398564	−	0.531847i	−0.941165	−	0.337947i	$-0.890267\pi$
$829$	1.14756	−	15.3131i	0.0398564	−	0.531847i	0.981021	−	0.193899i	$-0.0621135\pi$
$830$	−7.19195	+	1.08401i	−0.249636	+	0.0376266i
$831$		0			0
$832$	−11.4420			−0.396679
$833$	21.4364	+	20.2074i	0.742729	+	0.700147i
$834$		0			0
$835$	10.6026	−	9.83776i	0.366918	−	0.340450i
$836$	−1.37459	+	0.207186i	−0.0475411	+	0.00716567i
$837$		0			0
$838$	0.282536	−	0.719890i	0.00976004	−	0.0248682i
$839$	−12.1068	+	15.1815i	−0.417974	+	0.524122i	−0.945590	−	0.325360i	$-0.894514\pi$
$839$	−12.1068	+	15.1815i	−0.417974	+	0.524122i	0.527616	+	0.849483i	$0.323086\pi$
$840$		0			0
$841$	−17.0271	−	21.3513i	−0.587141	−	0.736252i
$842$	−2.54760	+	0.785832i	−0.0877962	+	0.0270816i
$843$		0			0
$844$	2.92115	+	0.901056i	0.100550	+	0.0310156i
$845$	2.84433	+	37.9549i	0.0978479	+	1.30569i
$846$		0			0
$847$	4.21640	+	13.8633i	0.144877	+	0.476350i
$848$	10.2607	−	44.9549i	0.352353	−	1.54376i
$849$		0			0
$850$	13.5617	−	9.24624i	0.465164	−	0.317143i
$851$	−26.0993	+	45.2054i	−0.894674	+	1.54962i
$852$		0			0
$853$	50.4495	+	24.2952i	1.72736	+	0.831851i	0.987214	+	0.159403i	$0.0509569\pi$
$853$	50.4495	+	24.2952i	1.72736	+	0.831851i	0.740144	+	0.672449i	$0.234757\pi$
$854$	−0.586176	−	3.99601i	−0.0200585	−	0.136741i
$855$		0			0
$856$	−11.0882	−	7.55984i	−0.378988	−	0.258390i
$857$	8.34886	+	7.74661i	0.285192	+	0.264619i	0.809776	−	0.586739i	$-0.199589\pi$
$857$	8.34886	+	7.74661i	0.285192	+	0.264619i	−0.524584	+	0.851359i	$0.675779\pi$
$858$		0			0
$859$	9.60243	+	6.54683i	0.327631	+	0.223375i	0.715953	−	0.698149i	$-0.245993\pi$
$859$	9.60243	+	6.54683i	0.327631	+	0.223375i	−0.388322	+	0.921524i	$0.626945\pi$
$860$	53.8471	−	25.9314i	1.83617	−	0.884253i
$861$		0			0
$862$	−8.20309	−	3.95040i	−0.279398	−	0.134551i
$863$	23.5114	+	40.7230i	0.800339	+	1.38623i	0.919393	+	0.393340i	$0.128680\pi$
$863$	23.5114	+	40.7230i	0.800339	+	1.38623i	−0.119054	+	0.992888i	$0.537986\pi$
$864$		0			0
$865$	−68.3371	+	46.5914i	−2.32353	+	1.58416i
$866$	−5.01356	−	0.755673i	−0.170368	−	0.0256788i
$867$		0			0
$868$	2.09615	+	6.89203i	0.0711478	+	0.233931i
$869$	1.70911	+	7.48811i	0.0579777	+	0.254017i
$870$		0			0
$871$	−9.00297	−	2.77705i	−0.305054	−	0.0940967i
$872$	−7.38091	−	18.8063i	−0.249949	−	0.636860i
$873$		0			0
$874$	0.161851	+	0.202954i	0.00547468	+	0.00686504i
$875$	81.7223	+	18.9924i	2.76272	+	0.642059i
$876$		0			0
$877$	3.47878	−	8.86379i	0.117470	−	0.299309i	−0.860030	−	0.510243i	$-0.829555\pi$
$877$	3.47878	−	8.86379i	0.117470	−	0.299309i	0.977500	+	0.210934i	$0.0676506\pi$
$878$	−0.0293018	+	0.391006i	−0.000988889	+	0.0131958i
$879$		0			0
$880$	−42.7926	+	39.7058i	−1.44254	+	1.33848i
$881$	40.5865			1.36739			0.683697	−	0.729766i	$-0.260371\pi$
$881$	40.5865			1.36739			0.683697	+	0.729766i	$0.260371\pi$
$882$		0			0
$883$	10.3699			0.348977			0.174488	−	0.984659i	$-0.444173\pi$
$883$	10.3699			0.348977			0.174488	+	0.984659i	$0.444173\pi$
$884$	11.6259	−	10.7873i	0.391022	−	0.362815i
$885$		0			0
$886$	0.0347264	−	0.463391i	0.00116666	−	0.0155679i
$887$	18.9609	−	48.3115i	0.636644	−	1.62214i	−0.138503	−	0.990362i	$-0.544229\pi$
$887$	18.9609	−	48.3115i	0.636644	−	1.62214i	0.775147	−	0.631780i	$-0.217676\pi$
$888$		0			0
$889$	7.41024	+	15.5442i	0.248531	+	0.521336i
$890$	1.59460	+	1.99957i	0.0534512	+	0.0670257i
$891$		0			0
$892$	14.5873	+	37.1678i	0.488418	+	1.24447i
$893$	−0.315892	−	0.0974398i	−0.0105709	−	0.00326070i
$894$		0			0
$895$	−18.2951	−	80.1561i	−0.611538	−	2.67932i
$896$	−3.54891	+	22.9308i	−0.118561	+	0.766065i
$897$		0			0
$898$	−2.60118	−	0.392065i	−0.0868026	−	0.0130834i
$899$	1.53657	−	1.04761i	0.0512473	−	0.0349398i
$900$		0			0
$901$	28.2777	+	48.9783i	0.942065	+	1.63170i
$902$	3.52940	+	1.69967i	0.117516	+	0.0565928i
$903$		0			0
$904$	2.59062	−	1.24758i	0.0861629	−	0.0414938i
$905$	13.0370	+	8.88849i	0.433365	+	0.295463i
$906$		0			0
$907$	4.52832	+	4.20167i	0.150360	+	0.139514i	0.751766	−	0.659429i	$-0.229202\pi$
$907$	4.52832	+	4.20167i	0.150360	+	0.139514i	−0.601406	+	0.798944i	$0.705393\pi$
$908$	10.8924	+	7.42632i	0.361477	+	0.246451i
$909$		0			0
$910$	−6.79192	−	0.535959i	−0.225150	−	0.0177669i
$911$	−32.8859	−	15.8370i	−1.08956	−	0.524703i	−0.199197	−	0.979959i	$-0.563833\pi$
$911$	−32.8859	−	15.8370i	−1.08956	−	0.524703i	−0.890360	+	0.455256i	$0.849548\pi$
$912$		0			0
$913$	−11.3478	+	19.6550i	−0.375559	+	0.650487i
$914$	1.76507	−	1.20341i	0.0583834	−	0.0398051i
$915$		0			0
$916$	−1.46763	+	6.43011i	−0.0484919	+	0.212457i
$917$	13.0936	+	14.2238i	0.432389	+	0.469710i
$918$		0			0
$919$	−1.06114	−	14.1599i	−0.0350036	−	0.467091i	−0.986972	−	0.160894i	$-0.948562\pi$
$919$	−1.06114	−	14.1599i	−0.0350036	−	0.467091i	0.951968	−	0.306197i	$-0.0990567\pi$
$920$	22.5600	+	6.95884i	0.743781	+	0.229426i
$921$		0			0
$922$	7.30075	−	2.25198i	0.240437	−	0.0741651i
$923$	6.33432	+	7.94299i	0.208497	+	0.261447i
$924$		0			0
$925$	87.9646	−	110.304i	2.89226	−	3.62678i
$926$	3.38172	−	8.61648i	0.111130	−	0.283155i
$927$		0			0
$928$	4.48481	−	0.675976i	0.147221	−	0.0221900i
$929$	1.65138	−	1.53226i	0.0541800	−	0.0502717i	−0.652618	−	0.757687i	$-0.726329\pi$
$929$	1.65138	−	1.53226i	0.0541800	−	0.0502717i	0.706798	+	0.707415i	$0.250139\pi$
$930$		0			0
$931$	0.929847	−	0.849207i	0.0304745	−	0.0278316i
$932$	−18.3367			−0.600638
$933$		0			0
$934$	2.82517	−	0.425826i	0.0924424	−	0.0139335i
$935$	5.35055	−	71.3981i	0.174982	−	2.33497i
$936$		0			0
$937$	−34.5788	+	43.3604i	−1.12964	+	1.41652i	−0.233721	+	0.972304i	$0.575090\pi$
$937$	−34.5788	+	43.3604i	−1.12964	+	1.41652i	−0.895918	+	0.444219i	$0.853481\pi$
$938$	−1.70960	+	3.51445i	−0.0558203	+	0.114751i
$939$		0			0
$940$	−14.0103	+	4.32160i	−0.456965	+	0.140955i
$941$	−8.97125	−	22.8584i	−0.292454	−	0.745161i	−0.999286	−	0.0377797i	$-0.987971\pi$
$941$	−8.97125	−	22.8584i	−0.292454	−	0.745161i	0.706832	−	0.707382i	$-0.250124\pi$
$942$		0			0
$943$	1.08032	+	14.4159i	0.0351801	+	0.469446i
$944$	1.75728	+	7.69913i	0.0571945	+	0.250585i
$945$		0			0
$946$	−2.09996	+	9.20051i	−0.0682754	+	0.299134i
$947$	6.35081	+	0.957231i	0.206374	+	0.0311058i	0.251415	−	0.967879i	$-0.419104\pi$
$947$	6.35081	+	0.957231i	0.206374	+	0.0311058i	−0.0450417	+	0.998985i	$0.514342\pi$
$948$		0			0
$949$	−9.09561	+	15.7541i	−0.295256	+	0.511398i
$950$	−0.350812	−	0.607624i	−0.0113818	−	0.0197139i
$951$		0			0
$952$	−7.55543	−	11.1763i	−0.244873	−	0.362227i
$953$	43.0415	−	20.7277i	1.39425	−	0.671435i	0.422263	−	0.906473i	$-0.361236\pi$
$953$	43.0415	−	20.7277i	1.39425	−	0.671435i	0.971986	+	0.235038i	$0.0755215\pi$
$954$		0			0
$955$	28.8029	+	26.7252i	0.932040	+	0.864807i
$956$	−1.10014	−	1.02078i	−0.0355812	−	0.0330145i
$957$		0			0
$958$	−6.63386	+	3.19470i	−0.214330	+	0.103216i
$959$	4.78668	−	15.3032i	0.154570	−	0.494168i
$960$		0			0
$961$	14.4772	+	25.0752i	0.467005	+	0.808877i
$962$	−3.44905	+	5.97393i	−0.111202	+	0.192607i
$963$		0			0
$964$	41.0413	+	6.18599i	1.32185	+	0.199237i
$965$	3.73120	−	16.3474i	0.120112	−	0.526243i
$966$		0			0
$967$	−3.71504	−	16.2767i	−0.119468	−	0.523422i	−0.998878	−	0.0473575i	$-0.984920\pi$
$967$	−3.71504	−	16.2767i	−0.119468	−	0.523422i	0.879410	−	0.476065i	$-0.157937\pi$
$968$	−0.495882	−	6.61709i	−0.0159383	−	0.212681i
$969$		0			0
$970$	4.98076	+	12.6908i	0.159923	+	0.407476i
$971$	34.2291	−	10.5583i	1.09846	−	0.338831i	0.308029	−	0.951377i	$-0.400331\pi$
$971$	34.2291	−	10.5583i	1.09846	−	0.338831i	0.790435	+	0.612545i	$0.209854\pi$
$972$		0			0
$973$	−0.191433	+	48.4857i	−0.00613707	+	1.55438i
$974$	−1.14182	+	1.43180i	−0.0365863	+	0.0458778i
$975$		0			0
$976$	1.26118	−	16.8292i	0.0403692	−	0.538690i
$977$	−8.88989	+	1.33993i	−0.284413	+	0.0428683i	−0.289699	−	0.957118i	$-0.593555\pi$
$977$	−8.88989	+	1.33993i	−0.284413	+	0.0428683i	0.00528662	+	0.999986i	$0.498317\pi$
$978$		0			0
$979$	7.98071			0.255065
$980$	12.8575	−	54.3505i	0.410718	−	1.73616i
$981$		0			0
$982$	3.01072	−	2.79354i	0.0960758	−	0.0891453i
$983$	−41.0425	+	6.18615i	−1.30905	+	0.197308i	−0.766244	−	0.642550i	$-0.777877\pi$
$983$	−41.0425	+	6.18615i	−1.30905	+	0.197308i	−0.542807	+	0.839857i	$0.682638\pi$
$984$		0			0
$985$	34.4633	−	87.8109i	1.09809	−	2.79789i
$986$	−1.05892	+	1.32785i	−0.0337230	+	0.0422873i
$987$		0			0
$988$	−0.422685	−	0.530030i	−0.0134474	−	0.0168625i
$989$	−33.2790	+	10.2652i	−1.05821	+	0.326414i
$990$		0			0
$991$	−41.6698	−	12.8534i	−1.32369	−	0.408303i	−0.449233	−	0.893415i	$-0.648303\pi$
$991$	−41.6698	−	12.8534i	−1.32369	−	0.408303i	−0.874452	+	0.485112i	$0.838779\pi$
$992$	−0.372827	−	4.97503i	−0.0118373	−	0.157957i
$993$		0			0
$994$	3.65799	−	2.09273i	0.116024	−	0.0663773i
$995$	−15.9520	+	69.8904i	−0.505713	+	2.21567i
$996$		0			0
$997$	12.7922	−	8.72157i	0.405133	−	0.276215i	−0.343562	−	0.939130i	$-0.611633\pi$
$997$	12.7922	−	8.72157i	0.405133	−	0.276215i	0.748694	+	0.662915i	$0.230681\pi$
$998$	1.88454	−	3.26413i	0.0596542	−	0.103324i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.109.3		60
3.2	odd	2		147.2.m.b.109.3	yes	60
49.9	even	21	inner	441.2.bb.e.352.3		60
147.95	odd	42		7203.2.a.n.1.13		30
147.101	even	42		7203.2.a.m.1.13		30
147.107	odd	42		147.2.m.b.58.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.58.3	✓	60	147.107	odd	42
147.2.m.b.109.3	yes	60	3.2	odd	2
441.2.bb.e.109.3		60	1.1	even	1	trivial
441.2.bb.e.352.3		60	49.9	even	21	inner
7203.2.a.m.1.13		30	147.101	even	42
7203.2.a.n.1.13		30	147.95	odd	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.227517 + 0.211105i) q^{2} +(-0.142261 + 1.89835i) q^{4} +(-1.53122 + 3.90148i) q^{5} +(2.06200 + 1.65775i) q^{7} +(-0.755410 - 0.947254i) q^{8} +O(q^{10})\)	\(q+(-0.227517 + 0.211105i) q^{2} +(-0.142261 + 1.89835i) q^{4} +(-1.53122 + 3.90148i) q^{5} +(2.06200 + 1.65775i) q^{7} +(-0.755410 - 0.947254i) q^{8} +(-0.475244 - 1.21090i) q^{10} +(-3.87883 - 1.19646i) q^{11} +(-0.440498 - 1.92995i) q^{13} +(-0.819102 + 0.0581320i) q^{14} +(-3.39298 - 0.511409i) q^{16} +(3.47723 - 2.37073i) q^{17} +(-0.0899481 - 0.155795i) q^{19} +(-7.18853 - 3.46181i) q^{20} +(1.13508 - 0.546626i) q^{22} +(3.84140 + 2.61902i) q^{23} +(-9.21165 - 8.54716i) q^{25} +(0.507644 + 0.346106i) q^{26} +(-3.44033 + 3.67856i) q^{28} +(1.17149 + 0.564159i) q^{29} +(0.715134 - 1.23865i) q^{31} +(2.88204 - 1.96494i) q^{32} +(-0.290655 + 1.27344i) q^{34} +(-9.62506 + 5.50648i) q^{35} +(0.839018 + 11.1959i) q^{37} +(0.0533538 + 0.0164575i) q^{38} +(4.85239 - 1.49676i) q^{40} +(1.93867 + 2.43101i) q^{41} +(-4.67037 + 5.85646i) q^{43} +(2.82311 - 7.19316i) q^{44} +(-1.42687 + 0.215067i) q^{46} +(1.34706 - 1.24989i) q^{47} +(1.50371 + 6.83658i) q^{49} +3.90016 q^{50} +(3.72638 - 0.561661i) q^{52} +(-1.00425 + 13.4008i) q^{53} +(10.6073 - 13.3011i) q^{55} +(0.0126562 - 3.20552i) q^{56} +(-0.385631 + 0.118951i) q^{58} +(-0.840831 - 2.14240i) q^{59} +(0.367550 + 4.90462i) q^{61} +(0.0987799 + 0.432783i) q^{62} +(1.28617 - 5.63507i) q^{64} +(8.20415 + 1.23658i) q^{65} +(2.37968 - 4.12173i) q^{67} +(4.00580 + 6.93825i) q^{68} +(1.02742 - 3.28472i) q^{70} +(-4.62389 + 2.22675i) q^{71} +(-6.73633 - 6.25040i) q^{73} +(-2.55441 - 2.37015i) q^{74} +(0.308548 - 0.148589i) q^{76} +(-6.01472 - 8.89725i) q^{77} +(-0.946091 - 1.63868i) q^{79} +(7.19064 - 12.4545i) q^{80} +(-0.954280 - 0.143835i) q^{82} +(1.24416 - 5.45103i) q^{83} +(3.92497 + 17.1964i) q^{85} +(-0.173739 - 2.31839i) q^{86} +(1.79675 + 4.57805i) q^{88} +(-1.87875 + 0.579517i) q^{89} +(2.29107 - 4.70980i) q^{91} +(-5.51829 + 6.91972i) q^{92} +(-0.0426215 + 0.568745i) q^{94} +(0.745559 - 0.112375i) q^{95} -10.4804 q^{97} +(-1.78536 - 1.23800i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

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