LMFDB - Embedded newform 441.2.bb.e.37.1

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			37.1
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.e.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23975 + 1.52704i) q^{2} +(1.95397 - 4.97862i) q^{4} +(2.15929 + 0.666054i) q^{5} +(1.59254 + 2.11277i) q^{7} +(2.01973 + 8.84903i) q^{8} +O(q^{10})$	\(q+(-2.23975 + 1.52704i) q^{2} +(1.95397 - 4.97862i) q^{4} +(2.15929 + 0.666054i) q^{5} +(1.59254 + 2.11277i) q^{7} +(2.01973 + 8.84903i) q^{8} +(-5.85337 + 1.80553i) q^{10} +(-0.416983 - 5.56426i) q^{11} +(1.70561 + 0.821378i) q^{13} +(-6.79318 - 2.30022i) q^{14} +(-10.1953 - 9.45985i) q^{16} +(2.16419 + 0.326199i) q^{17} +(1.13739 - 1.97003i) q^{19} +(7.53522 - 9.44886i) q^{20} +(9.43077 + 11.8258i) q^{22} +(4.03119 - 0.607604i) q^{23} +(0.0877252 + 0.0598100i) q^{25} +(-5.07442 + 0.764845i) q^{26} +(13.6305 - 3.80037i) q^{28} +(1.96938 - 2.46952i) q^{29} +(-0.209425 - 0.362735i) q^{31} +(19.3300 + 2.91354i) q^{32} +(-5.34537 + 2.57419i) q^{34} +(2.03154 + 5.62282i) q^{35} +(-0.661712 - 1.68601i) q^{37} +(0.460820 + 6.14921i) q^{38} +(-1.53273 + 20.4529i) q^{40} +(1.79602 + 7.86890i) q^{41} +(0.851216 - 3.72942i) q^{43} +(-28.5171 - 8.79637i) q^{44} +(-8.10103 + 7.51666i) q^{46} +(-8.77398 + 5.98200i) q^{47} +(-1.92763 + 6.72936i) q^{49} -0.287815 q^{50} +(7.42203 - 6.88664i) q^{52} +(-0.294313 + 0.749898i) q^{53} +(2.80570 - 12.2926i) q^{55} +(-15.4795 + 18.3597i) q^{56} +(-0.639867 + 8.53844i) q^{58} +(7.29598 - 2.25051i) q^{59} +(4.32929 + 11.0309i) q^{61} +(1.02297 + 0.492636i) q^{62} +(-22.6822 + 10.9232i) q^{64} +(3.13583 + 2.90962i) q^{65} +(2.19891 + 3.80862i) q^{67} +(5.85278 - 10.1373i) q^{68} +(-13.1364 - 9.49148i) q^{70} +(2.51070 + 3.14832i) q^{71} +(0.979999 + 0.668152i) q^{73} +(4.05668 + 2.76580i) q^{74} +(-7.58559 - 9.51202i) q^{76} +(11.0920 - 9.74229i) q^{77} +(4.29123 - 7.43262i) q^{79} +(-15.7139 - 27.2172i) q^{80} +(-16.0388 - 14.8818i) q^{82} +(-1.73859 + 0.837263i) q^{83} +(4.45585 + 2.14583i) q^{85} +(3.78845 + 9.65282i) q^{86} +(48.3961 - 14.9282i) q^{88} +(-0.414115 + 5.52598i) q^{89} +(0.980863 + 4.91164i) q^{91} +(4.85177 - 21.2570i) q^{92} +(10.5168 - 26.7964i) q^{94} +(3.76811 - 3.49630i) q^{95} -17.9375 q^{97} +(-5.95855 - 18.0157i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

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 $

$2$	−2.23975	+	1.52704i	−1.58374	+	1.07978i	−0.631096	+	0.775705i	$0.717394\pi$
$2$	−2.23975	+	1.52704i	−1.58374	+	1.07978i	−0.952649	+	0.304074i	$0.901653\pi$
$3$		0			0
$3$		0			0
$4$	1.95397	−	4.97862i	0.976983	−	2.48931i
$5$	2.15929	+	0.666054i	0.965665	+	0.297868i	0.737193	−	0.675682i	$-0.236151\pi$
$5$	2.15929	+	0.666054i	0.965665	+	0.297868i	0.228472	+	0.973550i	$0.426627\pi$
$6$		0			0
$7$	1.59254	+	2.11277i	0.601923	+	0.798554i
$7$	1.59254	+	2.11277i	0.601923	+	0.798554i
$8$	2.01973	+	8.84903i	0.714084	+	3.12861i
$9$		0			0
$10$	−5.85337	+	1.80553i	−1.85100	+	0.570957i
$11$	−0.416983	−	5.56426i	−0.125725	−	1.67769i	−0.602082	−	0.798434i	$-0.705662\pi$
$11$	−0.416983	−	5.56426i	−0.125725	−	1.67769i	0.476357	−	0.879252i	$-0.341957\pi$
$12$		0			0
$13$	1.70561	+	0.821378i	0.473051	+	0.227809i	0.655191	−	0.755463i	$-0.272588\pi$
$13$	1.70561	+	0.821378i	0.473051	+	0.227809i	−0.182140	+	0.983273i	$0.558302\pi$
$14$	−6.79318	−	2.30022i	−1.81555	−	0.614761i
$15$		0			0
$16$	−10.1953	−	9.45985i	−2.54882	−	2.36496i
$17$	2.16419	+	0.326199i	0.524893	+	0.0791149i	0.406143	−	0.913809i	$-0.366873\pi$
$17$	2.16419	+	0.326199i	0.524893	+	0.0791149i	0.118750	+	0.992924i	$0.462111\pi$
$18$		0			0
$19$	1.13739	−	1.97003i	0.260936	−	0.451955i	−0.705555	−	0.708655i	$-0.749302\pi$
$19$	1.13739	−	1.97003i	0.260936	−	0.451955i	0.966491	+	0.256701i	$0.0826354\pi$
$20$	7.53522	−	9.44886i	1.68493	−	2.11283i
$21$		0			0
$22$	9.43077	+	11.8258i	2.01065	+	2.52127i
$23$	4.03119	−	0.607604i	0.840561	−	0.126694i	0.285370	−	0.958417i	$-0.407883\pi$
$23$	4.03119	−	0.607604i	0.840561	−	0.126694i	0.555190	+	0.831723i	$0.312645\pi$
$24$		0			0
$25$	0.0877252	+	0.0598100i	0.0175450	+	0.0119620i
$26$	−5.07442	+	0.764845i	−0.995175	+	0.149998i
$27$		0			0
$28$	13.6305	−	3.80037i	2.57592	−	0.718202i
$29$	1.96938	−	2.46952i	0.365705	−	0.458579i	−0.564601	−	0.825364i	$-0.690970\pi$
$29$	1.96938	−	2.46952i	0.365705	−	0.458579i	0.930306	+	0.366785i	$0.119541\pi$
$30$		0			0
$31$	−0.209425	−	0.362735i	−0.0376138	−	0.0651491i	0.846606	−	0.532221i	$-0.178642\pi$
$31$	−0.209425	−	0.362735i	−0.0376138	−	0.0651491i	−0.884219	+	0.467072i	$0.845309\pi$
$32$	19.3300	+	2.91354i	3.41710	+	0.515045i
$33$		0			0
$34$	−5.34537	+	2.57419i	−0.916723	+	0.441470i
$35$	2.03154	+	5.62282i	0.343393	+	0.950430i
$36$		0			0
$37$	−0.661712	−	1.68601i	−0.108785	−	0.277179i	0.866107	−	0.499859i	$-0.166615\pi$
$37$	−0.661712	−	1.68601i	−0.108785	−	0.277179i	−0.974892	+	0.222680i	$0.928520\pi$
$38$	0.460820	+	6.14921i	0.0747548	+	0.997534i
$39$		0			0
$40$	−1.53273	+	20.4529i	−0.242346	+	3.23389i
$41$	1.79602	+	7.86890i	0.280492	+	1.22892i	0.897165	+	0.441696i	$0.145623\pi$
$41$	1.79602	+	7.86890i	0.280492	+	1.22892i	−0.616673	+	0.787219i	$0.711520\pi$
$42$		0			0
$43$	0.851216	−	3.72942i	0.129809	−	0.568731i	−0.867630	−	0.497211i	$-0.834358\pi$
$43$	0.851216	−	3.72942i	0.129809	−	0.568731i	0.997439	−	0.0715208i	$-0.0227852\pi$
$44$	−28.5171	−	8.79637i	−4.29912	−	1.32610i
$45$		0			0
$46$	−8.10103	+	7.51666i	−1.19443	+	1.10827i
$47$	−8.77398	+	5.98200i	−1.27982	+	0.872564i	−0.996261	−	0.0863921i	$-0.972466\pi$
$47$	−8.77398	+	5.98200i	−1.27982	+	0.872564i	−0.283555	+	0.958956i	$0.591514\pi$
$48$		0			0
$49$	−1.92763	+	6.72936i	−0.275376	+	0.961337i
$50$	−0.287815			−0.0407032
$51$		0			0
$52$	7.42203	−	6.88664i	1.02925	−	0.955005i
$53$	−0.294313	+	0.749898i	−0.0404270	+	0.103006i	−0.949661	−	0.313278i	$-0.898573\pi$
$53$	−0.294313	+	0.749898i	−0.0404270	+	0.103006i	0.909234	+	0.416285i	$0.136668\pi$
$54$		0			0
$55$	2.80570	−	12.2926i	0.378321	−	1.65753i
$56$	−15.4795	+	18.3597i	−2.06854	+	2.45342i
$57$		0			0
$58$	−0.639867	+	8.53844i	−0.0840187	+	1.12115i
$59$	7.29598	−	2.25051i	0.949856	−	0.292992i	0.219155	−	0.975690i	$-0.429670\pi$
$59$	7.29598	−	2.25051i	0.949856	−	0.292992i	0.730700	+	0.682698i	$0.239194\pi$
$60$		0			0
$61$	4.32929	+	11.0309i	0.554309	+	1.41236i	0.883651	+	0.468146i	$0.155078\pi$
$61$	4.32929	+	11.0309i	0.554309	+	1.41236i	−0.329342	+	0.944211i	$0.606827\pi$
$62$	1.02297	+	0.492636i	0.129917	+	0.0625649i
$63$		0			0
$64$	−22.6822	+	10.9232i	−2.83528	+	1.36540i
$65$	3.13583	+	2.90962i	0.388952	+	0.360894i
$66$		0			0
$67$	2.19891	+	3.80862i	0.268640	+	0.465297i	0.968511	−	0.248972i	$-0.0800926\pi$
$67$	2.19891	+	3.80862i	0.268640	+	0.465297i	−0.699871	+	0.714269i	$0.746759\pi$
$68$	5.85278	−	10.1373i	0.709753	−	1.22933i
$69$		0			0
$70$	−13.1364	−	9.49148i	−1.57010	−	1.13445i
$71$	2.51070	+	3.14832i	0.297965	+	0.373637i	0.908166	−	0.418610i	$-0.137483\pi$
$71$	2.51070	+	3.14832i	0.297965	+	0.373637i	−0.610201	+	0.792247i	$0.708911\pi$
$72$		0			0
$73$	0.979999	+	0.668152i	0.114700	+	0.0782013i	0.619312	−	0.785145i	$-0.287412\pi$
$73$	0.979999	+	0.668152i	0.114700	+	0.0782013i	−0.504611	+	0.863347i	$0.668364\pi$
$74$	4.05668	+	2.76580i	0.471579	+	0.321517i
$75$		0			0
$76$	−7.58559	−	9.51202i	−0.870126	−	1.09110i
$77$	11.0920	−	9.74229i	1.26405	−	1.11024i
$78$		0			0
$79$	4.29123	−	7.43262i	0.482801	−	0.836235i	−0.517004	−	0.855983i	$-0.672953\pi$
$79$	4.29123	−	7.43262i	0.482801	−	0.836235i	0.999805	+	0.0197474i	$0.00628619\pi$
$80$	−15.7139	−	27.2172i	−1.75686	−	3.04298i
$81$		0			0
$82$	−16.0388	−	14.8818i	−1.77118	−	1.64342i
$83$	−1.73859	+	0.837263i	−0.190836	+	0.0919016i	−0.526861	−	0.849951i	$-0.676631\pi$
$83$	−1.73859	+	0.837263i	−0.190836	+	0.0919016i	0.336026	+	0.941853i	$0.390917\pi$
$84$		0			0
$85$	4.45585	+	2.14583i	0.483305	+	0.232747i
$86$	3.78845	+	9.65282i	0.408519	+	1.04089i
$87$		0			0
$88$	48.3961	−	14.9282i	5.15904	−	1.59135i
$89$	−0.414115	+	5.52598i	−0.0438961	+	0.585753i	0.931277	+	0.364311i	$0.118695\pi$
$89$	−0.414115	+	5.52598i	−0.0438961	+	0.585753i	−0.975174	+	0.221442i	$0.928924\pi$
$90$		0			0
$91$	0.980863	+	4.91164i	0.102822	+	0.514880i
$92$	4.85177	−	21.2570i	0.505832	−	2.21620i
$93$		0			0
$94$	10.5168	−	26.7964i	1.08473	−	2.76384i
$95$	3.76811	−	3.49630i	0.386600	−	0.358712i
$96$		0			0
$97$	−17.9375			−1.82128			−0.910639	−	0.413204i	$-0.864410\pi$
$97$	−17.9375			−1.82128			−0.910639	+	0.413204i	$0.864410\pi$
$98$	−5.95855	−	18.0157i	−0.601905	−	1.81986i
$99$		0			0
$100$	0.469184	−	0.319884i	0.0469184	−	0.0319884i
$101$	6.46638	−	5.99993i	0.643429	−	0.597015i	−0.289455	−	0.957192i	$-0.593474\pi$
$101$	6.46638	−	5.99993i	0.643429	−	0.597015i	0.932884	+	0.360177i	$0.117284\pi$
$102$		0			0
$103$	12.4532	+	3.84131i	1.22705	+	0.378496i	0.839504	−	0.543353i	$-0.182846\pi$
$103$	12.4532	+	3.84131i	1.22705	+	0.378496i	0.387549	+	0.921849i	$0.373322\pi$
$104$	−3.82352	+	16.7520i	−0.374927	+	1.64266i
$105$		0			0
$106$	−0.485933	−	2.12901i	−0.0471980	−	0.206788i
$107$	−0.0706065	+	0.942178i	−0.00682579	+	0.0910838i	−0.999576	−	0.0291102i	$-0.990733\pi$
$107$	−0.0706065	+	0.942178i	−0.00682579	+	0.0910838i	0.992750	+	0.120194i	$0.0383517\pi$
$108$		0			0
$109$	0.335921	+	4.48255i	0.0321754	+	0.429351i	0.989910	+	0.141697i	$0.0452560\pi$
$109$	0.335921	+	4.48255i	0.0321754	+	0.429351i	−0.957735	+	0.287653i	$0.907125\pi$
$110$	12.4872	+	31.8168i	1.19060	+	3.03361i
$111$		0			0
$112$	3.75012	−	36.6056i	0.354353	−	3.45890i
$113$	−6.52186	+	3.14076i	−0.613525	+	0.295458i	−0.714722	−	0.699408i	$-0.753447\pi$
$113$	−6.52186	+	3.14076i	−0.613525	+	0.295458i	0.101197	+	0.994866i	$0.467733\pi$
$114$		0			0
$115$	9.10921	+	1.37299i	0.849438	+	0.128032i
$116$	−8.44673	−	14.6302i	−0.784259	−	1.35838i
$117$		0			0
$118$	−12.9046	+	16.1818i	−1.18796	+	1.48966i
$119$	2.75737	+	5.09193i	0.252768	+	0.466776i
$120$		0			0
$121$	−19.9099	+	3.00094i	−1.80999	+	0.272813i
$122$	−26.5411	−	18.0954i	−2.40292	−	1.63828i
$123$		0			0
$124$	−2.21513	+	0.333877i	−0.198925	+	0.0299830i
$125$	−6.89486	−	8.64589i	−0.616695	−	0.773311i
$126$		0			0
$127$	4.81837	−	6.04205i	0.427561	−	0.536145i	−0.520656	−	0.853766i	$-0.674313\pi$
$127$	4.81837	−	6.04205i	0.427561	−	0.536145i	0.948218	+	0.317621i	$0.102884\pi$
$128$	14.5741	−	25.2430i	1.28818	−	2.23119i
$129$		0			0
$130$	−11.4666	−	1.72831i	−1.00569	−	0.151583i
$131$	−14.9455	−	13.8674i	−1.30579	−	1.21160i	−0.962158	−	0.272493i	$-0.912152\pi$
$131$	−14.9455	−	13.8674i	−1.30579	−	1.21160i	−0.343634	−	0.939104i	$-0.611658\pi$
$132$		0			0
$133$	5.97357	−	0.734285i	0.517974	−	0.0636706i
$134$	−10.7409	−	5.17256i	−0.927875	−	0.446841i
$135$		0			0
$136$	1.48454	+	19.8098i	0.127298	+	1.69868i
$137$	−13.5835	+	4.18995i	−1.16052	+	0.357972i	−0.814447	−	0.580237i	$-0.802960\pi$
$137$	−13.5835	+	4.18995i	−1.16052	+	0.357972i	−0.346069	+	0.938209i	$0.612484\pi$
$138$		0			0
$139$	−2.84046	−	12.4449i	−0.240925	−	1.05556i	−0.940177	−	0.340686i	$-0.889341\pi$
$139$	−2.84046	−	12.4449i	−0.240925	−	1.05556i	0.699252	−	0.714875i	$-0.253516\pi$
$140$	31.9635	+	0.872525i	2.70140	+	0.0737418i
$141$		0			0
$142$	−10.4310	−	3.21752i	−0.875346	−	0.270008i
$143$	3.85915	−	9.83295i	0.322718	−	0.822272i
$144$		0			0
$145$	5.89730	−	4.02071i	0.489744	−	0.333902i
$146$	−3.21525			−0.266096
$147$		0			0
$148$	−9.68699			−0.796266
$149$	4.90526	−	3.34435i	0.401855	−	0.273980i	−0.345482	−	0.938425i	$-0.612285\pi$
$149$	4.90526	−	3.34435i	0.401855	−	0.273980i	0.747337	+	0.664445i	$0.231332\pi$
$150$		0			0
$151$	−5.13017	+	13.0714i	−0.417487	+	1.06374i	0.555220	+	0.831703i	$0.312634\pi$
$151$	−5.13017	+	13.0714i	−0.417487	+	1.06374i	−0.972707	+	0.232036i	$0.925461\pi$
$152$	19.7301	+	6.08592i	1.60032	+	0.493633i
$153$		0			0
$154$	−9.96640	+	38.7582i	−0.803115	+	3.12322i
$155$	−0.210609	−	0.922739i	−0.0169165	−	0.0741162i
$156$		0			0
$157$	−7.88268	+	2.43149i	−0.629106	+	0.194054i	−0.592881	−	0.805290i	$-0.702010\pi$
$157$	−7.88268	+	2.43149i	−0.629106	+	0.194054i	−0.0362253	+	0.999344i	$0.511533\pi$
$158$	1.73861	+	23.2001i	0.138316	+	1.84570i
$159$		0			0
$160$	39.7987	+	19.1660i	3.14636	+	1.51521i
$161$	7.70356	+	7.54936i	0.607125	+	0.594973i
$162$		0			0
$163$	2.77939	+	2.57890i	0.217699	+	0.201995i	0.781482	−	0.623928i	$-0.214464\pi$
$163$	2.77939	+	2.57890i	0.217699	+	0.201995i	−0.563783	+	0.825923i	$0.690655\pi$
$164$	42.6857	+	6.43383i	3.33319	+	0.502398i
$165$		0			0
$166$	2.61549	−	4.53016i	0.203001	−	0.351609i
$167$	8.30334	−	10.4121i	0.642532	−	0.805709i	−0.348786	−	0.937203i	$-0.613406\pi$
$167$	8.30334	−	10.4121i	0.642532	−	0.805709i	0.991317	+	0.131494i	$0.0419773\pi$
$168$		0			0
$169$	−5.87093	−	7.36191i	−0.451610	−	0.566301i
$170$	−13.2568	+	1.99814i	−1.01675	+	0.153250i
$171$		0			0
$172$	−16.9041	−	11.5250i	−1.28893	−	0.878777i
$173$	−0.640671	+	0.0965655i	−0.0487093	+	0.00734174i	−0.173352	−	0.984860i	$-0.555460\pi$
$173$	−0.640671	+	0.0965655i	−0.0487093	+	0.00734174i	0.124642	+	0.992202i	$0.460222\pi$
$174$		0			0
$175$	0.0133408	+	0.280594i	0.00100847	+	0.0212109i
$176$	−48.3858	+	60.6739i	−3.64722	+	4.57346i
$177$		0			0
$178$	−7.51087	−	13.0092i	−0.562963	−	0.975081i
$179$	−18.6334	−	2.80853i	−1.39273	−	0.209920i	−0.590547	−	0.807003i	$-0.701088\pi$
$179$	−18.6334	−	2.80853i	−1.39273	−	0.209920i	−0.802179	+	0.597084i	$0.796326\pi$
$180$		0			0
$181$	12.0589	−	5.80727i	0.896332	−	0.431651i	0.0717694	−	0.997421i	$-0.477135\pi$
$181$	12.0589	−	5.80727i	0.896332	−	0.431651i	0.824563	+	0.565770i	$0.191421\pi$
$182$	−9.69716	−	9.50305i	−0.718801	−	0.704413i
$183$		0			0
$184$	13.5186	+	34.4449i	0.996607	+	2.53931i
$185$	−0.305854	−	4.08133i	−0.0224868	−	0.300066i
$186$		0			0
$187$	0.912624	−	12.1781i	0.0667377	−	0.890553i
$188$	12.6381	+	55.3710i	0.921725	+	4.03834i
$189$		0			0
$190$	−3.10066	+	13.5849i	−0.224946	+	0.985551i
$191$	−18.4994	−	5.70631i	−1.33857	−	0.412894i	−0.458904	−	0.888486i	$-0.651758\pi$
$191$	−18.4994	−	5.70631i	−1.33857	−	0.412894i	−0.879666	+	0.475591i	$0.842234\pi$
$192$		0			0
$193$	11.5051	−	10.6751i	0.828153	−	0.768414i	−0.147190	−	0.989108i	$-0.547023\pi$
$193$	11.5051	−	10.6751i	0.828153	−	0.768414i	0.975343	+	0.220694i	$0.0708324\pi$
$194$	40.1756	−	27.3912i	2.88444	−	1.96658i
$195$		0			0
$196$	29.7364	+	22.7459i	2.12403	+	1.62471i
$197$	−10.4369			−0.743595			−0.371798	−	0.928314i	$-0.621259\pi$
$197$	−10.4369			−0.743595			−0.371798	+	0.928314i	$0.621259\pi$
$198$		0			0
$199$	3.89547	−	3.61447i	0.276143	−	0.256223i	−0.529927	−	0.848043i	$-0.677781\pi$
$199$	3.89547	−	3.61447i	0.276143	−	0.256223i	0.806070	+	0.591820i	$0.201590\pi$
$200$	−0.352080	+	0.897084i	−0.0248958	+	0.0634334i
$201$		0			0
$202$	−5.32098	+	23.3128i	−0.374383	+	1.64028i
$203$	8.35386	+	0.228040i	0.586326	+	0.0160053i
$204$		0			0
$205$	−1.36297	+	18.1875i	−0.0951936	+	1.27027i
$206$	−33.7580	+	10.4130i	−2.35203	+	0.725505i
$207$		0			0
$208$	−9.61908	−	24.5090i	−0.666963	−	1.69939i
$209$	−11.4360	−	5.50729i	−0.791045	−	0.380947i
$210$		0			0
$211$	−21.9684	+	10.5794i	−1.51237	+	0.728318i	−0.992072	−	0.125668i	$-0.959893\pi$
$211$	−21.9684	+	10.5794i	−1.51237	+	0.728318i	−0.520296	+	0.853986i	$0.674178\pi$
$212$	3.15838	+	2.93055i	0.216918	+	0.201271i
$213$		0			0
$214$	−1.28060	−	2.21807i	−0.0875401	−	0.151624i
$215$	4.32202	−	7.48596i	0.294759	−	0.510538i
$216$		0			0
$217$	0.432859	−	1.02014i	0.0293844	−	0.0692514i
$218$	−7.59741	−	9.52685i	−0.514561	−	0.645240i
$219$		0			0
$220$	−55.7180	−	37.9879i	−3.75650	−	2.56114i
$221$	3.42333	+	2.33399i	0.230278	+	0.157001i
$222$		0			0
$223$	−13.2601	−	16.6276i	−0.887962	−	1.11347i	−0.992895	−	0.118990i	$-0.962034\pi$
$223$	−13.2601	−	16.6276i	−0.887962	−	1.11347i	0.104933	−	0.994479i	$-0.466537\pi$
$224$	24.6282	+	45.4800i	1.64554	+	3.03876i
$225$		0			0
$226$	9.81129	−	16.9937i	0.652637	−	1.13040i
$227$	14.2002	+	24.5955i	0.942502	+	1.63246i	0.760677	+	0.649131i	$0.224867\pi$
$227$	14.2002	+	24.5955i	0.942502	+	1.63246i	0.181826	+	0.983331i	$0.441799\pi$
$228$		0			0
$229$	7.90991	+	7.33933i	0.522702	+	0.484996i	0.896827	−	0.442382i	$-0.145866\pi$
$229$	7.90991	+	7.33933i	0.522702	+	0.484996i	−0.374125	+	0.927378i	$0.622057\pi$
$230$	−22.4990	+	10.8349i	−1.48354	+	0.714435i
$231$		0			0
$232$	25.8305	+	12.4393i	1.69586	+	0.816682i
$233$	10.3733	+	26.4307i	0.679576	+	1.73153i	0.681805	+	0.731534i	$0.261195\pi$
$233$	10.3733	+	26.4307i	0.679576	+	1.73153i	−0.00222916	+	0.999998i	$0.500710\pi$
$234$		0			0
$235$	−22.9299	+	7.07294i	−1.49578	+	0.461388i
$236$	3.05165	−	40.7214i	0.198645	−	2.65074i
$237$		0			0
$238$	−13.9514	−	7.19405i	−0.904335	−	0.466321i
$239$	3.37096	−	14.7691i	0.218049	−	0.955336i	−0.740868	−	0.671651i	$-0.765586\pi$
$239$	3.37096	−	14.7691i	0.218049	−	0.955336i	0.958917	−	0.283686i	$-0.0915573\pi$
$240$		0			0
$241$	−9.00219	+	22.9372i	−0.579882	+	1.47752i	0.276418	+	0.961037i	$0.410852\pi$
$241$	−9.00219	+	22.9372i	−0.579882	+	1.47752i	−0.856300	+	0.516478i	$0.827243\pi$
$242$	40.0108	−	37.1246i	2.57199	−	2.38646i
$243$		0			0
$244$	63.3778			4.05735
$245$	−8.64444	+	13.2467i	−0.552273	+	0.846303i
$246$		0			0
$247$	3.55809	−	2.42586i	0.226396	−	0.154354i
$248$	2.78687	−	2.58584i	0.176966	−	0.164201i
$249$		0			0
$250$	28.6454	+	8.83593i	1.81169	+	0.558833i
$251$	4.53807	−	19.8826i	0.286440	−	1.25498i	−0.602932	−	0.797793i	$-0.706001\pi$
$251$	4.53807	−	19.8826i	0.286440	−	1.25498i	0.889372	−	0.457184i	$-0.151142\pi$
$252$		0			0
$253$	−5.06180	−	22.1772i	−0.318233	−	1.39427i
$254$	−1.56553	+	20.8905i	−0.0982300	+	1.31079i
$255$		0			0
$256$	2.14203	+	28.5833i	0.133877	+	1.78646i
$257$	3.03137	+	7.72380i	0.189092	+	0.481797i	0.993709	−	0.111997i	$-0.0357246\pi$
$257$	3.03137	+	7.72380i	0.189092	+	0.481797i	−0.804617	+	0.593794i	$0.797629\pi$
$258$		0			0
$259$	2.50837	−	4.08309i	0.155862	−	0.253711i
$260$	20.6132	−	9.92680i	1.27838	−	0.615634i
$261$		0			0
$262$	54.6501	+	8.23718i	3.37630	+	0.508895i
$263$	−0.304323	−	0.527103i	−0.0187654	−	0.0325026i	0.856490	−	0.516163i	$-0.172640\pi$
$263$	−0.304323	−	0.527103i	−0.0187654	−	0.0325026i	−0.875256	+	0.483661i	$0.839307\pi$
$264$		0			0
$265$	−1.13498	+	1.42322i	−0.0697213	+	0.0874277i
$266$	−12.2580	+	10.7665i	−0.751588	+	0.660135i
$267$		0			0
$268$	23.2583	−	3.50563i	1.42073	−	0.214140i
$269$	1.64686	+	1.12281i	0.100411	+	0.0684590i	0.612485	−	0.790483i	$-0.290170\pi$
$269$	1.64686	+	1.12281i	0.100411	+	0.0684590i	−0.512074	+	0.858942i	$0.671123\pi$
$270$		0			0
$271$	−11.7856	+	1.77640i	−0.715926	+	0.107909i	−0.496897	−	0.867810i	$-0.665527\pi$
$271$	−11.7856	+	1.77640i	−0.715926	+	0.107909i	−0.219030	+	0.975718i	$0.570289\pi$
$272$	−18.9788	−	23.7986i	−1.15076	−	1.44300i
$273$		0			0
$274$	24.0255	−	30.1270i	1.45143	−	1.82004i
$275$	0.296218	−	0.513065i	0.0178626	−	0.0309390i
$276$		0			0
$277$	−24.2143	−	3.64972i	−1.45490	−	0.219290i	−0.626495	−	0.779425i	$-0.715511\pi$
$277$	−24.2143	−	3.64972i	−1.45490	−	0.219290i	−0.828402	+	0.560135i	$0.810749\pi$
$278$	25.3657	+	23.5360i	1.52133	+	1.41159i
$279$		0			0
$280$	−45.6533	+	29.3338i	−2.72831	+	1.75303i
$281$	8.76577	+	4.22137i	0.522922	+	0.251826i	0.676673	−	0.736284i	$-0.263421\pi$
$281$	8.76577	+	4.22137i	0.522922	+	0.251826i	−0.153751	+	0.988110i	$0.549135\pi$
$282$		0			0
$283$	−1.68583	−	22.4958i	−0.100212	−	1.33724i	−0.789947	−	0.613175i	$-0.789892\pi$
$283$	−1.68583	−	22.4958i	−0.100212	−	1.33724i	0.689735	−	0.724062i	$-0.257727\pi$
$284$	20.5801	−	6.34813i	1.22121	−	0.376692i
$285$		0			0
$286$	6.37174	+	27.9164i	0.376769	+	1.65073i
$287$	−13.7650	+	16.3261i	−0.812520	+	0.963701i
$288$		0			0
$289$	−11.6674	−	3.59893i	−0.686319	−	0.211701i
$290$	−7.06872	+	18.0108i	−0.415089	+	1.05763i
$291$		0			0
$292$	5.24137	−	3.57350i	0.306728	−	0.209123i
$293$	−4.87482			−0.284790			−0.142395	−	0.989810i	$-0.545480\pi$
$293$	−4.87482			−0.284790			−0.142395	+	0.989810i	$0.545480\pi$
$294$		0			0
$295$	17.2531			1.00452
$296$	13.5831	−	9.26081i	0.789502	−	0.538274i
$297$		0			0
$298$	−5.87963	+	14.9810i	−0.340598	+	0.867829i
$299$	7.37470	+	2.27479i	0.426490	+	0.131555i
$300$		0			0
$301$	9.23502	−	4.14082i	0.532298	−	0.238673i
$302$	−8.47029	−	37.1108i	−0.487410	−	2.13548i
$303$		0			0
$304$	−30.2322	+	9.32541i	−1.73394	+	0.534849i
$305$	2.00107	+	26.7024i	0.114581	+	1.52897i
$306$		0			0
$307$	6.29601	+	3.03200i	0.359332	+	0.173045i	0.604835	−	0.796350i	$-0.293239\pi$
$307$	6.29601	+	3.03200i	0.359332	+	0.173045i	−0.245503	+	0.969396i	$0.578953\pi$
$308$	−26.8299	−	74.2588i	−1.52878	−	4.23129i
$309$		0			0
$310$	1.88077	+	1.74510i	0.106821	+	0.0991150i
$311$	−9.20841	−	1.38794i	−0.522161	−	0.0787031i	−0.117327	−	0.993093i	$-0.537433\pi$
$311$	−9.20841	−	1.38794i	−0.522161	−	0.0787031i	−0.404834	+	0.914390i	$0.632671\pi$
$312$		0			0
$313$	0.713017	−	1.23498i	0.0403021	−	0.0698053i	−0.845171	−	0.534496i	$-0.820501\pi$
$313$	0.713017	−	1.23498i	0.0403021	−	0.0698053i	0.885473	+	0.464691i	$0.153835\pi$
$314$	13.9423	−	17.4831i	0.786809	−	0.986627i
$315$		0			0
$316$	−28.6193	−	35.8875i	−1.60996	−	2.01883i
$317$	10.0180	−	1.50996i	0.562664	−	0.0848080i	0.138449	−	0.990370i	$-0.455788\pi$
$317$	10.0180	−	1.50996i	0.562664	−	0.0848080i	0.424215	+	0.905562i	$0.360550\pi$
$318$		0			0
$319$	−14.5623	−	9.92838i	−0.815330	−	0.555883i
$320$	−56.2530	+	8.47877i	−3.14464	+	0.473978i
$321$		0			0
$322$	−28.7822	−	5.14507i	−1.60397	−	0.286724i
$323$	3.10416	−	3.89249i	0.172720	−	0.216584i
$324$		0			0
$325$	0.100498	+	0.174068i	0.00557464	+	0.00965556i
$326$	−10.1632	−	1.53186i	−0.562890	−	0.0848419i
$327$		0			0
$328$	−66.0047	+	31.7862i	−3.64450	+	1.75510i
$329$	−26.6115	−	9.01087i	−1.46714	−	0.496785i
$330$		0			0
$331$	3.78058	+	9.63276i	0.207799	+	0.529464i	0.996336	−	0.0855234i	$-0.0272562\pi$
$331$	3.78058	+	9.63276i	0.207799	+	0.529464i	−0.788537	+	0.614988i	$0.789161\pi$
$332$	0.771263	+	10.2918i	0.0423286	+	0.564836i
$333$		0			0
$334$	−2.69782	+	35.9999i	−0.147618	+	1.96983i
$335$	2.21134	+	9.68853i	0.120819	+	0.529341i
$336$		0			0
$337$	4.96231	−	21.7413i	0.270314	−	1.18432i	−0.639329	−	0.768933i	$-0.720788\pi$
$337$	4.96231	−	21.7413i	0.270314	−	1.18432i	0.909643	−	0.415390i	$-0.136355\pi$
$338$	24.3913	+	7.52373i	1.32671	+	0.409237i
$339$		0			0
$340$	19.3898	−	17.9911i	1.05156	−	0.975707i
$341$	−1.93102	+	1.31655i	−0.104571	+	0.0712951i
$342$		0			0
$343$	−17.2874	+	6.64411i	−0.933434	+	0.358748i
$344$	34.7210			1.87203
$345$		0			0
$346$	1.28748	−	1.19461i	0.0692156	−	0.0642227i
$347$	3.47521	−	8.85469i	0.186559	−	0.475345i	−0.806741	−	0.590905i	$-0.798771\pi$
$347$	3.47521	−	8.85469i	0.186559	−	0.475345i	0.993301	+	0.115560i	$0.0368662\pi$
$348$		0			0
$349$	2.95052	−	12.9271i	0.157938	−	0.691969i	−0.832502	−	0.554022i	$-0.813092\pi$
$349$	2.95052	−	12.9271i	0.157938	−	0.691969i	0.990440	−	0.137947i	$-0.0440505\pi$
$350$	−0.458357	−	0.608088i	−0.0245002	−	0.0325037i
$351$		0			0
$352$	8.15135	−	108.772i	0.434469	−	5.79758i
$353$	−4.91123	+	1.51491i	−0.261399	+	0.0806308i	−0.422684	−	0.906277i	$-0.638912\pi$
$353$	−4.91123	+	1.51491i	−0.261399	+	0.0806308i	0.161286	+	0.986908i	$0.448436\pi$
$354$		0			0
$355$	3.32439	+	8.47041i	0.176440	+	0.449563i
$356$	26.7026	+	12.8593i	1.41524	+	0.681542i
$357$		0			0
$358$	46.0229	−	22.1635i	2.43239	−	1.17138i
$359$	−21.5051	−	19.9538i	−1.13500	−	1.05312i	−0.998042	−	0.0625440i	$-0.980079\pi$
$359$	−21.5051	−	19.9538i	−1.13500	−	1.05312i	−0.136953	−	0.990578i	$-0.543731\pi$
$360$		0			0
$361$	6.91267	+	11.9731i	0.363825	+	0.630163i
$362$	−18.1411	+	31.4213i	−0.953474	+	1.65146i
$363$		0			0
$364$	26.3698	+	4.71384i	1.38215	+	0.247072i
$365$	1.67108	+	2.09547i	0.0874684	+	0.109682i
$366$		0			0
$367$	29.6732	+	20.2308i	1.54893	+	1.05604i	0.970739	+	0.240137i	$0.0771923\pi$
$367$	29.6732	+	20.2308i	1.54893	+	1.05604i	0.578188	+	0.815904i	$0.303760\pi$
$368$	−46.8470	−	31.9397i	−2.44207	−	1.66497i
$369$		0			0
$370$	6.91739	+	8.67413i	0.359618	+	0.450946i
$371$	−2.05307	+	0.572424i	−0.106590	+	0.0297188i
$372$		0			0
$373$	−11.8872	+	20.5892i	−0.615496	+	1.06607i	0.374802	+	0.927105i	$0.377711\pi$
$373$	−11.8872	+	20.5892i	−0.615496	+	1.06607i	−0.990297	+	0.138965i	$0.955623\pi$
$374$	16.5524	+	28.6696i	0.855904	+	1.48247i
$375$		0			0
$376$	−70.6560	−	65.5592i	−3.64381	−	3.38096i
$377$	5.38740	−	2.59444i	0.277465	−	0.133620i
$378$		0			0
$379$	−29.6054	−	14.2572i	−1.52073	−	0.732344i	−0.527614	−	0.849484i	$-0.676913\pi$
$379$	−29.6054	−	14.2572i	−1.52073	−	0.732344i	−0.993115	+	0.117140i	$0.962627\pi$
$380$	−10.0440	−	25.5917i	−0.515245	−	1.31282i
$381$		0			0
$382$	50.1479	−	15.4686i	2.56579	−	0.791441i
$383$	0.489724	−	6.53491i	0.0250237	−	0.333918i	−0.970616	−	0.240634i	$-0.922645\pi$
$383$	0.489724	−	6.53491i	0.0250237	−	0.333918i	0.995640	−	0.0932840i	$-0.0297364\pi$
$384$		0			0
$385$	30.4397	−	13.6486i	1.55135	−	0.695598i
$386$	−9.46716	+	41.4784i	−0.481866	+	2.11119i
$387$		0			0
$388$	−35.0493	+	89.3041i	−1.77936	+	4.53373i
$389$	−17.3485	+	16.0970i	−0.879602	+	0.816151i	−0.983960	−	0.178388i	$-0.942912\pi$
$389$	−17.3485	+	16.0970i	−0.879602	+	0.816151i	0.104358	+	0.994540i	$0.466721\pi$
$390$		0			0
$391$	8.92245			0.451228
$392$	−63.4416	−	3.46619i	−3.20429	−	0.175069i
$393$		0			0
$394$	23.3760	−	15.9375i	1.17767	−	0.802918i
$395$	14.2165	−	13.1910i	0.715312	−	0.663712i
$396$		0			0
$397$	4.81397	+	1.48491i	0.241606	+	0.0745256i	0.413193	−	0.910643i	$-0.364413\pi$
$397$	4.81397	+	1.48491i	0.241606	+	0.0745256i	−0.171587	+	0.985169i	$0.554890\pi$
$398$	−3.20546	+	14.0440i	−0.160675	+	0.703965i
$399$		0			0
$400$	−0.328591	−	1.43965i	−0.0164295	−	0.0719825i
$401$	1.54955	−	20.6774i	0.0773811	−	1.03258i	−0.814457	−	0.580224i	$-0.802965\pi$
$401$	1.54955	−	20.6774i	0.0773811	−	1.03258i	0.891838	−	0.452355i	$-0.149416\pi$
$402$		0			0
$403$	−0.0592548	−	0.790701i	−0.00295169	−	0.0393876i
$404$	−17.2363	−	43.9173i	−0.857537	−	2.18497i
$405$		0			0
$406$	−19.0588	+	12.2459i	−0.945873	+	0.607754i
$407$	−9.10549	+	4.38497i	−0.451342	+	0.217355i
$408$		0			0
$409$	19.7060	+	2.97020i	0.974398	+	0.146867i	0.616895	−	0.787045i	$-0.288390\pi$
$409$	19.7060	+	2.97020i	0.974398	+	0.146867i	0.357503	+	0.933912i	$0.383628\pi$
$410$	−24.7203	−	42.8168i	−1.22085	−	2.11457i
$411$		0			0
$412$	43.4577	−	54.4942i	2.14101	−	2.68474i
$413$	16.3740	+	11.8307i	0.805710	+	0.582152i
$414$		0			0
$415$	−4.31180	+	0.649899i	−0.211658	+	0.0319023i
$416$	30.5764	+	20.8466i	1.49913	+	1.02209i
$417$		0			0
$418$	34.0236	−	5.12824i	1.66415	−	0.250830i
$419$	5.74132	+	7.19939i	0.280482	+	0.351713i	0.902038	−	0.431656i	$-0.142071\pi$
$419$	5.74132	+	7.19939i	0.280482	+	0.351713i	−0.621556	+	0.783370i	$0.713499\pi$
$420$		0			0
$421$	−14.0503	+	17.6185i	−0.684770	+	0.858674i	−0.995784	−	0.0917314i	$-0.970760\pi$
$421$	−14.0503	+	17.6185i	−0.684770	+	0.858674i	0.311014	+	0.950405i	$0.399331\pi$
$422$	33.0486	−	57.2419i	1.60878	−	2.78649i
$423$		0			0
$424$	−7.23030	−	1.08979i	−0.351135	−	0.0529250i
$425$	0.170344	+	0.158056i	0.00826290	+	0.00766685i
$426$		0			0
$427$	−16.4111	+	26.7139i	−0.794191	+	1.29278i
$428$	4.55279	+	2.19251i	0.220067	+	0.105979i
$429$		0			0
$430$	1.75108	+	23.3666i	0.0844447	+	1.12684i
$431$	24.9405	−	7.69312i	1.20134	−	0.370565i	0.371430	−	0.928461i	$-0.378868\pi$
$431$	24.9405	−	7.69312i	1.20134	−	0.370565i	0.829911	+	0.557896i	$0.188391\pi$
$432$		0			0
$433$	2.13881	+	9.37074i	0.102785	+	0.450329i	0.999963	+	0.00865949i	$0.00275644\pi$
$433$	2.13881	+	9.37074i	0.102785	+	0.450329i	−0.897178	+	0.441669i	$0.854386\pi$
$434$	0.588291	+	2.94585i	0.0282389	+	0.141405i
$435$		0			0
$436$	22.9733	+	7.08633i	1.10022	+	0.339374i
$437$	3.38806	−	8.63263i	0.162073	−	0.412954i
$438$		0			0
$439$	−9.05079	+	6.17072i	−0.431970	+	0.294512i	−0.759718	−	0.650253i	$-0.774663\pi$
$439$	−9.05079	+	6.17072i	−0.431970	+	0.294512i	0.327747	+	0.944765i	$0.393711\pi$
$440$	114.444			5.45592
$441$		0			0
$442$	−11.2315			−0.534227
$443$	4.13413	−	2.81860i	0.196418	−	0.133916i	−0.461117	−	0.887339i	$-0.652551\pi$
$443$	4.13413	−	2.81860i	0.196418	−	0.133916i	0.657536	+	0.753423i	$0.271599\pi$
$444$		0			0
$445$	−4.57480	+	11.6564i	−0.216866	+	0.552566i
$446$	55.0904	+	16.9931i	2.60861	+	0.804648i
$447$		0			0
$448$	−59.2006	−	30.5268i	−2.79696	−	1.44226i
$449$	3.22051	+	14.1100i	0.151985	+	0.665891i	0.992307	+	0.123803i	$0.0395090\pi$
$449$	3.22051	+	14.1100i	0.151985	+	0.665891i	−0.840322	+	0.542088i	$0.817634\pi$
$450$		0			0
$451$	43.0357	−	13.2747i	2.02647	−	0.625083i
$452$	2.89318	+	38.6068i	0.136084	+	1.81591i
$453$		0			0
$454$	−69.3633	−	33.4036i	−3.25538	−	1.56771i
$455$	−1.15345	+	11.2590i	−0.0540744	+	0.527829i
$456$		0			0
$457$	−14.9328	−	13.8556i	−0.698526	−	0.648137i	0.248746	−	0.968569i	$-0.419982\pi$
$457$	−14.9328	−	13.8556i	−0.698526	−	0.648137i	−0.947272	+	0.320432i	$0.896172\pi$
$458$	−28.9237	−	4.35954i	−1.35151	−	0.203708i
$459$		0			0
$460$	24.6347	−	42.6686i	1.14860	−	1.98943i
$461$	8.57042	−	10.7470i	0.399164	−	0.500536i	−0.541111	−	0.840951i	$-0.681996\pi$
$461$	8.57042	−	10.7470i	0.399164	−	0.500536i	0.940275	+	0.340415i	$0.110568\pi$
$462$		0			0
$463$	17.4173	+	21.8405i	0.809448	+	1.01502i	0.999448	+	0.0332320i	$0.0105800\pi$
$463$	17.4173	+	21.8405i	0.809448	+	1.01502i	−0.189999	+	0.981784i	$0.560849\pi$
$464$	−43.4397	+	6.54749i	−2.01664	+	0.303959i
$465$		0			0
$466$	−63.5942	−	43.3578i	−2.94594	−	2.00851i
$467$	−10.2418	+	1.54370i	−0.473933	+	0.0714339i	−0.381666	−	0.924300i	$-0.624649\pi$
$467$	−10.2418	+	1.54370i	−0.473933	+	0.0714339i	−0.0922672	+	0.995734i	$0.529411\pi$
$468$		0			0
$469$	−4.54491	+	10.7112i	−0.209865	+	0.494597i
$470$	40.5567	−	50.8565i	1.87074	−	2.34584i
$471$		0			0
$472$	34.6508	+	60.0169i	1.59493	+	2.76250i
$473$	−21.1064	−	3.18128i	−0.970473	−	0.146275i
$474$		0			0
$475$	0.217605	−	0.104793i	0.00998442	−	0.00480825i
$476$	30.7386	−	3.77846i	1.40890	−	0.173186i
$477$		0			0
$478$	15.0029	+	38.2268i	0.686217	+	1.74845i
$479$	0.581663	+	7.76176i	0.0265769	+	0.354644i	0.994600	+	0.103783i	$0.0330947\pi$
$479$	0.581663	+	7.76176i	0.0265769	+	0.354644i	−0.968023	+	0.250861i	$0.919286\pi$
$480$		0			0
$481$	0.256233	−	3.41920i	0.0116832	−	0.155902i
$482$	−14.8633	−	65.1204i	−0.677005	−	2.96615i
$483$		0			0
$484$	−23.9628	+	104.988i	−1.08922	+	4.77218i
$485$	−38.7323	−	11.9473i	−1.75874	−	0.542501i
$486$		0			0
$487$	9.20774	−	8.54353i	0.417242	−	0.387144i	−0.443425	−	0.896311i	$-0.646237\pi$
$487$	9.20774	−	8.54353i	0.417242	−	0.387144i	0.860668	+	0.509167i	$0.170046\pi$
$488$	−88.8684	+	60.5894i	−4.02288	+	2.74276i
$489$		0			0
$490$	−0.866869	−	42.8698i	−0.0391611	−	1.93666i
$491$	13.5669			0.612264			0.306132	−	0.951989i	$-0.400965\pi$
$491$	13.5669			0.612264			0.306132	+	0.951989i	$0.400965\pi$
$492$		0			0
$493$	5.06766	−	4.70211i	0.228236	−	0.211772i
$494$	−4.26485	+	10.8667i	−0.191885	+	0.488914i
$495$		0			0
$496$	−1.29627	+	5.67932i	−0.0582041	+	0.255009i
$497$	−2.65330	+	10.3184i	−0.119017	+	0.462842i
$498$		0			0
$499$	−1.83268	+	24.4554i	−0.0820419	+	1.09477i	0.792516	+	0.609852i	$0.208771\pi$
$499$	−1.83268	+	24.4554i	−0.0820419	+	1.09477i	−0.874557	+	0.484922i	$0.838848\pi$
$500$	−56.5169	+	17.4332i	−2.52751	+	0.779635i
$501$		0			0
$502$	20.1973	+	51.4618i	0.901449	+	2.29685i
$503$	−35.5819	−	17.1353i	−1.58652	−	0.764026i	−0.587538	−	0.809197i	$-0.699903\pi$
$503$	−35.5819	−	17.1353i	−1.58652	−	0.764026i	−0.998979	+	0.0451703i	$0.985617\pi$
$504$		0			0
$505$	17.9591	−	8.64864i	0.799169	−	0.384859i
$506$	45.2026	+	41.9419i	2.00950	+	1.86454i
$507$		0			0
$508$	−20.6661	−	35.7948i	−0.916912	−	1.58814i
$509$	−1.78200	+	3.08652i	−0.0789859	+	0.136808i	−0.902813	−	0.430034i	$-0.858502\pi$
$509$	−1.78200	+	3.08652i	−0.0789859	+	0.136808i	0.823827	+	0.566842i	$0.191835\pi$
$510$		0			0
$511$	0.149033	+	3.13458i	0.00659282	+	0.138666i
$512$	−12.0983	−	15.1708i	−0.534675	−	0.670461i
$513$		0			0
$514$	−18.5840	−	12.6704i	−0.819707	−	0.558867i
$515$	24.3317	+	16.5890i	1.07218	+	0.731001i
$516$		0			0
$517$	36.9440	+	46.3263i	1.62479	+	2.03743i
$518$	0.616917	+	12.9755i	0.0271058	+	0.570110i
$519$		0			0
$520$	−19.4138	+	33.6257i	−0.851352	+	1.47458i
$521$	−4.18499	−	7.24861i	−0.183348	−	0.317567i	0.759671	−	0.650308i	$-0.225360\pi$
$521$	−4.18499	−	7.24861i	−0.183348	−	0.317567i	−0.943018	+	0.332740i	$0.892027\pi$
$522$		0			0
$523$	−7.69326	−	7.13830i	−0.336403	−	0.312136i	0.493824	−	0.869562i	$-0.335599\pi$
$523$	−7.69326	−	7.13830i	−0.336403	−	0.312136i	−0.830227	+	0.557426i	$0.811789\pi$
$524$	−98.2433	+	47.3115i	−4.29178	+	2.06681i
$525$		0			0
$526$	1.48651	+	0.715868i	0.0648151	+	0.0312133i
$527$	−0.334912	−	0.853341i	−0.0145890	−	0.0371721i
$528$		0			0
$529$	−6.09689	+	1.88064i	−0.265082	+	0.0817670i
$530$	0.368764	−	4.92082i	0.0160181	−	0.213747i
$531$		0			0
$532$	8.01642	−	31.1749i	0.347556	−	1.35160i
$533$	−3.40002	+	14.8965i	−0.147271	+	0.645238i
$534$		0			0
$535$	−0.780002	+	1.98741i	−0.0337224	+	0.0859233i
$536$	−29.2614	+	27.1506i	−1.26390	+	1.17273i
$537$		0			0
$538$	−5.40314			−0.232946
$539$	38.2477	+	7.91982i	1.64744	+	0.341131i
$540$		0			0
$541$	10.7367	−	7.32014i	0.461606	−	0.314718i	−0.310092	−	0.950706i	$-0.600360\pi$
$541$	10.7367	−	7.32014i	0.461606	−	0.314718i	0.771698	+	0.635989i	$0.219408\pi$
$542$	23.6843	−	21.9758i	1.01733	−	0.943942i
$543$		0			0
$544$	40.8835	+	12.6109i	1.75287	+	0.540687i
$545$	−2.26027	+	9.90289i	−0.0968193	+	0.424193i
$546$		0			0
$547$	0.584454	+	2.56066i	0.0249894	+	0.109486i	0.985884	−	0.167427i	$-0.0535458\pi$
$547$	0.584454	+	2.56066i	0.0249894	+	0.109486i	−0.960895	+	0.276913i	$0.910689\pi$
$548$	−5.68149	+	75.8142i	−0.242701	+	3.23862i
$549$		0			0
$550$	0.120014	+	1.60148i	0.00511742	+	0.0682872i
$551$	−2.62506	−	6.68855i	−0.111831	−	0.284942i
$552$		0			0
$553$	22.5374	−	2.77035i	0.958388	−	0.117807i
$554$	59.8073	−	28.8017i	2.54097	−	1.22367i
$555$		0			0
$556$	−67.5085	−	10.1753i	−2.86300	−	0.431528i
$557$	7.93787	+	13.7488i	0.336338	+	0.582555i	0.983741	−	0.179593i	$-0.0574781\pi$
$557$	7.93787	+	13.7488i	0.336338	+	0.582555i	−0.647403	+	0.762148i	$0.724145\pi$
$558$		0			0
$559$	4.51511	−	5.66176i	0.190969	−	0.239467i
$560$	32.4789	−	76.5444i	1.37248	−	3.23459i
$561$		0			0
$562$	−26.0793	+	3.93083i	−1.10009	+	0.165812i
$563$	15.1707	+	10.3432i	0.639368	+	0.435914i	0.839130	−	0.543931i	$-0.183065\pi$
$563$	15.1707	+	10.3432i	0.639368	+	0.435914i	−0.199762	+	0.979844i	$0.564017\pi$
$564$		0			0
$565$	−16.1745	+	2.43792i	−0.680467	+	0.102564i
$566$	38.1278	+	47.8107i	1.60263	+	2.00964i
$567$		0			0
$568$	−22.7886	+	28.5761i	−0.956190	+	1.19902i
$569$	7.22104	−	12.5072i	0.302722	−	0.524329i	−0.674030	−	0.738704i	$-0.735438\pi$
$569$	7.22104	−	12.5072i	0.302722	−	0.524329i	0.976751	+	0.214375i	$0.0687714\pi$
$570$		0			0
$571$	33.4285	+	5.03854i	1.39894	+	0.210856i	0.804819	−	0.593520i	$-0.202262\pi$
$571$	33.4285	+	5.03854i	1.39894	+	0.210856i	0.594120	+	0.804376i	$0.297500\pi$
$572$	−41.4139	−	38.4265i	−1.73160	−	1.60669i
$573$		0			0
$574$	5.89951	−	57.5861i	0.246241	−	2.40360i
$575$	0.389978	+	0.187803i	0.0162632	+	0.00783194i
$576$		0			0
$577$	−3.39909	−	45.3577i	−0.141506	−	1.88827i	−0.391734	−	0.920079i	$-0.628125\pi$
$577$	−3.39909	−	45.3577i	−0.141506	−	1.88827i	0.250228	−	0.968187i	$-0.419494\pi$
$578$	31.6278	−	9.75590i	1.31555	−	0.405792i
$579$		0			0
$580$	−8.49449	−	37.2168i	−0.352714	−	1.54534i
$581$	−4.53773	−	2.33988i	−0.188257	−	0.0970747i
$582$		0			0
$583$	4.29535	+	1.32494i	0.177895	+	0.0548734i
$584$	−3.93316	+	10.0215i	−0.162755	+	0.414694i
$585$		0			0
$586$	10.9184	−	7.44404i	0.451035	−	0.307510i
$587$	−23.6490			−0.976099			−0.488050	−	0.872816i	$-0.662292\pi$
$587$	−23.6490			−0.976099			−0.488050	+	0.872816i	$0.662292\pi$
$588$		0			0
$589$	−0.952795			−0.0392593
$590$	−38.6427	+	26.3462i	−1.59090	+	1.08465i
$591$		0			0
$592$	−9.20310	+	23.4491i	−0.378245	+	0.963753i
$593$	15.4454	+	4.76427i	0.634265	+	0.195645i	0.595182	−	0.803591i	$-0.297080\pi$
$593$	15.4454	+	4.76427i	0.634265	+	0.195645i	0.0390834	+	0.999236i	$0.487556\pi$
$594$		0			0
$595$	2.56248	+	12.8315i	0.105051	+	0.526041i
$596$	−7.06556	−	30.9562i	−0.289416	−	1.26802i
$597$		0			0
$598$	−19.9912	+	6.16647i	−0.817501	+	0.252166i
$599$	−2.51557	−	33.5679i	−0.102783	−	1.37155i	−0.775360	−	0.631520i	$-0.782431\pi$
$599$	−2.51557	−	33.5679i	−0.102783	−	1.37155i	0.672577	−	0.740028i	$-0.265188\pi$
$600$		0			0
$601$	−4.91190	−	2.36545i	−0.200361	−	0.0964886i	0.331013	−	0.943626i	$-0.392610\pi$
$601$	−4.91190	−	2.36545i	−0.200361	−	0.0964886i	−0.531374	+	0.847138i	$0.678324\pi$
$602$	−14.3610	+	23.3766i	−0.585310	+	0.952761i
$603$		0			0
$604$	55.0537	+	51.0823i	2.24010	+	2.07851i
$605$	−44.9902	−	6.78118i	−1.82911	−	0.275694i
$606$		0			0
$607$	−11.5811	+	20.0590i	−0.470060	+	0.814168i	−0.999414	−	0.0342329i	$-0.989101\pi$
$607$	−11.5811	+	20.0590i	−0.470060	+	0.814168i	0.529354	+	0.848401i	$0.322435\pi$
$608$	27.7256	−	34.7668i	1.12442	−	1.40998i
$609$		0			0
$610$	−45.2574	−	56.7510i	−1.83242	−	2.29778i
$611$	−19.8785	+	2.99619i	−0.804196	+	0.121213i
$612$		0			0
$613$	8.21571	+	5.60137i	0.331829	+	0.226237i	0.717760	−	0.696290i	$-0.245167\pi$
$613$	8.21571	+	5.60137i	0.331829	+	0.226237i	−0.385931	+	0.922528i	$0.626120\pi$
$614$	−18.7315	+	2.82332i	−0.755941	+	0.113940i
$615$		0			0
$616$	108.613	+	78.4763i	4.37613	+	3.16190i
$617$	−2.88260	+	3.61467i	−0.116049	+	0.145521i	−0.836463	−	0.548023i	$-0.815380\pi$
$617$	−2.88260	+	3.61467i	−0.116049	+	0.145521i	0.720414	+	0.693544i	$0.243952\pi$
$618$		0			0
$619$	−18.6593	−	32.3189i	−0.749982	−	1.29901i	−0.947831	−	0.318774i	$-0.896729\pi$
$619$	−18.6593	−	32.3189i	−0.749982	−	1.29901i	0.197849	−	0.980233i	$-0.436604\pi$
$620$	−5.00549	−	0.754457i	−0.201025	−	0.0302997i
$621$		0			0
$622$	22.7440	−	10.9529i	0.911951	−	0.439173i
$623$	−12.3346	+	7.92541i	−0.494177	+	0.317525i
$624$		0			0
$625$	−9.32336	−	23.7555i	−0.372934	−	0.950221i
$626$	0.288882	+	3.85486i	0.0115460	+	0.154071i
$627$		0			0
$628$	−3.29704	+	43.9960i	−0.131566	+	1.75563i
$629$	−0.882093	−	3.86470i	−0.0351714	−	0.154096i
$630$		0			0
$631$	−5.57078	+	24.4072i	−0.221769	+	0.971635i	0.734376	+	0.678743i	$0.237475\pi$
$631$	−5.57078	+	24.4072i	−0.221769	+	0.971635i	−0.956145	+	0.292892i	$0.905382\pi$
$632$	74.4387	+	22.9613i	2.96101	+	0.913351i
$633$		0			0
$634$	−20.1320	+	18.6797i	−0.799543	+	0.741867i
$635$	14.4286	−	9.83726i	0.572582	−	0.390380i
$636$		0			0
$637$	−8.81513	+	9.89433i	−0.349268	+	0.392028i
$638$	47.7769			1.89150
$639$		0			0
$640$	48.2829	−	44.8000i	1.90855	−	1.77087i
$641$	−11.3295	+	28.8671i	−0.447488	+	1.14018i	0.512138	+	0.858903i	$0.328854\pi$
$641$	−11.3295	+	28.8671i	−0.447488	+	1.14018i	−0.959626	+	0.281279i	$0.909241\pi$
$642$		0			0
$643$	1.23093	−	5.39305i	0.0485431	−	0.212681i	−0.944839	−	0.327534i	$-0.893782\pi$
$643$	1.23093	−	5.39305i	0.0485431	−	0.212681i	0.993383	+	0.114853i	$0.0366396\pi$
$644$	52.6379	−	23.6019i	2.07422	−	0.930046i
$645$		0			0
$646$	−1.00857	+	13.4584i	−0.0396815	+	0.529513i
$647$	33.7212	−	10.4016i	1.32572	−	0.408930i	0.450550	−	0.892751i	$-0.351228\pi$
$647$	33.7212	−	10.4016i	1.32572	−	0.408930i	0.875167	+	0.483821i	$0.160752\pi$
$648$		0			0
$649$	−15.5647	−	39.6583i	−0.610969	−	1.55672i
$650$	−0.490900	−	0.236405i	−0.0192547	−	0.00927256i
$651$		0			0
$652$	18.2702	−	8.79848i	0.715517	−	0.344575i
$653$	−3.25151	−	3.01696i	−0.127241	−	0.118063i	0.613986	−	0.789317i	$-0.289565\pi$
$653$	−3.25151	−	3.01696i	−0.127241	−	0.118063i	−0.741227	+	0.671255i	$0.765756\pi$
$654$		0			0
$655$	−23.0352	−	39.8982i	−0.900061	−	1.55895i
$656$	56.1276	−	97.2159i	2.19142	−	3.79564i
$657$		0			0
$658$	73.3632	−	20.4547i	2.85999	−	0.797406i
$659$	−6.95646	−	8.72313i	−0.270985	−	0.339805i	0.627655	−	0.778492i	$-0.284015\pi$
$659$	−6.95646	−	8.72313i	−0.270985	−	0.339805i	−0.898640	+	0.438687i	$0.855444\pi$
$660$		0			0
$661$	9.46755	+	6.45487i	0.368245	+	0.251065i	0.733277	−	0.679930i	$-0.237990\pi$
$661$	9.46755	+	6.45487i	0.368245	+	0.251065i	−0.365032	+	0.930995i	$0.618942\pi$
$662$	−23.1771	−	15.8019i	−0.900805	−	0.614159i
$663$		0			0
$664$	−10.9205	−	13.6938i	−0.423796	−	0.531424i
$665$	13.3878	+	2.39318i	0.519155	+	0.0928035i
$666$		0			0
$667$	6.43844	−	11.1517i	0.249298	−	0.431796i
$668$	−35.6133	−	61.6840i	−1.37792	−	2.38663i
$669$		0			0
$670$	−19.7476	−	18.3231i	−0.762917	−	0.707883i
$671$	59.5733	−	28.6890i	2.29980	−	1.10753i
$672$		0			0
$673$	−9.00925	−	4.33863i	−0.347281	−	0.167242i	0.252109	−	0.967699i	$-0.418876\pi$
$673$	−9.00925	−	4.33863i	−0.347281	−	0.167242i	−0.599390	+	0.800457i	$0.704590\pi$
$674$	22.0854	+	56.2727i	0.850698	+	2.16754i
$675$		0			0
$676$	−48.1238	+	14.8442i	−1.85091	+	0.570932i
$677$	0.193223	−	2.57838i	0.00742616	−	0.0990952i	−0.992259	−	0.124185i	$-0.960368\pi$
$677$	0.193223	−	2.57838i	0.00742616	−	0.0990952i	0.999685	+	0.0250902i	$0.00798730\pi$
$678$		0			0
$679$	−28.5662	−	37.8979i	−1.09627	−	1.45439i
$680$	−9.98885	+	43.7640i	−0.383055	+	1.67827i
$681$		0			0
$682$	2.31459	−	5.89749i	0.0886304	−	0.225826i
$683$	−28.1089	+	26.0812i	−1.07556	+	0.997970i	−0.0755567	+	0.997142i	$0.524073\pi$
$683$	−28.1089	+	26.0812i	−1.07556	+	0.997970i	−1.00000		0.000828970i	$0.999736\pi$
$684$		0			0
$685$	−32.1215			−1.22730
$686$	28.5738	−	41.2797i	1.09095	−	1.57607i
$687$		0			0
$688$	−43.9582	+	29.9702i	−1.67589	+	1.14260i
$689$	−1.11793	+	1.03729i	−0.0425898	+	0.0395176i
$690$		0			0
$691$	41.7306	+	12.8722i	1.58751	+	0.489681i	0.957868	−	0.287208i	$-0.0927270\pi$
$691$	41.7306	+	12.8722i	1.58751	+	0.489681i	0.629638	+	0.776889i	$0.283203\pi$
$692$	−0.771085	+	3.37834i	−0.0293123	+	0.128425i
$693$		0			0
$694$	5.73783	+	25.1391i	0.217805	+	0.954267i
$695$	2.15557	−	28.7640i	0.0817653	−	1.09108i
$696$		0			0
$697$	1.32011	+	17.6156i	0.0500027	+	0.667240i
$698$	13.1317	+	33.4590i	0.497041	+	1.26644i
$699$		0			0
$700$	1.42304	+	0.481852i	0.0537857	+	0.0182123i
$701$	−23.7730	+	11.4485i	−0.897892	+	0.432402i	−0.825127	−	0.564947i	$-0.808897\pi$
$701$	−23.7730	+	11.4485i	−0.897892	+	0.432402i	−0.0727649	+	0.997349i	$0.523182\pi$
$702$		0			0
$703$	−4.07412	−	0.614074i	−0.153658	−	0.0231603i
$704$	70.2375	+	121.655i	2.64718	+	4.58504i
$705$		0			0
$706$	8.68661	−	10.8927i	0.326925	−	0.409951i
$707$	22.9745	+	4.10689i	0.864044	+	0.154455i
$708$		0			0
$709$	−3.32729	+	0.501509i	−0.124959	+	0.0188346i	−0.211224	−	0.977438i	$-0.567745\pi$
$709$	−3.32729	+	0.501509i	−0.124959	+	0.0188346i	0.0862649	+	0.996272i	$0.472507\pi$
$710$	−20.3804	−	13.8951i	−0.764864	−	0.521476i
$711$		0			0
$712$	−49.7360	+	7.49650i	−1.86394	+	0.280943i
$713$	−1.06463	−	1.33500i	−0.0398707	−	0.0499963i
$714$		0			0
$715$	14.8823	−	18.6618i	0.556566	−	0.697912i
$716$	−50.3917	+	87.2809i	−1.88323	+	3.26184i
$717$		0			0
$718$	78.6363	+	11.8525i	2.93468	+	0.442332i
$719$	−10.0611	−	9.33533i	−0.375215	−	0.348149i	0.469913	−	0.882713i	$-0.344285\pi$
$719$	−10.0611	−	9.33533i	−0.375215	−	0.348149i	−0.845128	+	0.534564i	$0.820476\pi$
$720$		0			0
$721$	11.7164	+	32.4283i	0.436343	+	1.20769i
$722$	−33.7660	−	16.2609i	−1.25664	−	0.605167i
$723$		0			0
$724$	−5.34949	−	71.3840i	−0.198812	−	2.65297i
$725$	0.320467	−	0.0988508i	0.0119018	−	0.00367123i
$726$		0			0
$727$	−1.16226	−	5.09218i	−0.0431057	−	0.188858i	0.948791	−	0.315904i	$-0.102308\pi$
$727$	−1.16226	−	5.09218i	−0.0431057	−	0.188858i	−0.991897	+	0.127045i	$0.959451\pi$
$728$	−41.4822	+	18.5999i	−1.53743	+	0.689359i
$729$		0			0
$730$	−6.94267	−	2.14153i	−0.256960	−	0.0792615i
$731$	3.05873	−	7.79351i	0.113131	−	0.288253i
$732$		0			0
$733$	−4.96670	+	3.38624i	−0.183449	+	0.125074i	−0.651563	−	0.758595i	$-0.725886\pi$
$733$	−4.96670	+	3.38624i	−0.183449	+	0.125074i	0.468113	+	0.883668i	$0.344934\pi$
$734$	−97.3538			−3.59339
$735$		0			0
$736$	79.6933			2.93753
$737$	20.2753	−	13.8234i	0.746849	−	0.509193i
$738$		0			0
$739$	−0.456831	+	1.16399i	−0.0168048	+	0.0428180i	−0.939030	−	0.343835i	$-0.888274\pi$
$739$	−0.456831	+	1.16399i	−0.0168048	+	0.0428180i	0.922225	+	0.386653i	$0.126369\pi$
$740$	−20.9171	−	6.45206i	−0.768926	−	0.237182i
$741$		0			0
$742$	3.72426	−	4.41720i	0.136722	−	0.162161i
$743$	−2.45105	−	10.7387i	−0.0899202	−	0.393966i	0.909860	−	0.414915i	$-0.136189\pi$
$743$	−2.45105	−	10.7387i	−0.0899202	−	0.393966i	−0.999781	+	0.0209484i	$0.993331\pi$
$744$		0			0
$745$	12.8194	−	3.95427i	0.469667	−	0.144873i
$746$	−4.81614	−	64.2670i	−0.176332	−	2.35298i
$747$		0			0
$748$	−58.8471	−	28.3393i	−2.15166	−	1.03619i
$749$	−2.10305	+	1.35128i	−0.0768439	+	0.0493747i
$750$		0			0
$751$	−30.4012	−	28.2082i	−1.10936	−	1.02933i	−0.999373	−	0.0353996i	$-0.988730\pi$
$751$	−30.4012	−	28.2082i	−1.10936	−	1.02933i	−0.109984	−	0.993933i	$-0.535080\pi$
$752$	146.042	+	22.0123i	5.32561	+	0.802706i
$753$		0			0
$754$	−8.10465	+	14.0377i	−0.295154	+	0.511221i
$755$	−19.7838	+	24.8081i	−0.720007	+	0.902860i
$756$		0			0
$757$	−13.6959	−	17.1741i	−0.497786	−	0.624203i	0.467943	−	0.883759i	$-0.344995\pi$
$757$	−13.6959	−	17.1741i	−0.497786	−	0.624203i	−0.965728	+	0.259555i	$0.916424\pi$
$758$	88.0802	−	13.2759i	3.19922	−	0.482204i
$759$		0			0
$760$	38.5494	+	26.2826i	1.39833	+	0.953368i
$761$	−20.2723	+	3.05556i	−0.734872	+	0.110764i	−0.505806	−	0.862647i	$-0.668805\pi$
$761$	−20.2723	+	3.05556i	−0.734872	+	0.110764i	−0.229065	+	0.973411i	$0.573567\pi$
$762$		0			0
$763$	−8.93566	+	7.84837i	−0.323493	+	0.284130i
$764$	−64.5568	+	80.9517i	−2.33558	+	2.92873i
$765$		0			0
$766$	8.88220	+	15.3844i	0.320927	+	0.555861i
$767$	14.2926	+	2.15426i	0.516076	+	0.0777860i
$768$		0			0
$769$	−13.1195	+	6.31803i	−0.473102	+	0.227834i	−0.655213	−	0.755444i	$-0.727421\pi$
$769$	−13.1195	+	6.31803i	−0.473102	+	0.227834i	0.182111	+	0.983278i	$0.441707\pi$
$770$	−47.3354	+	77.0521i	−1.70585	+	2.77676i
$771$		0			0
$772$	−30.6670	−	78.1383i	−1.10373	−	2.81226i
$773$	−2.26137	−	30.1759i	−0.0813359	−	1.08535i	−0.877279	−	0.479980i	$-0.840644\pi$
$773$	−2.26137	−	30.1759i	−0.0813359	−	1.08535i	0.795943	−	0.605371i	$-0.206975\pi$
$774$		0			0
$775$	0.00332333	−	0.0443467i	0.000119377	−	0.00159298i
$776$	−36.2290	−	158.730i	−1.30054	−	5.69806i
$777$		0			0
$778$	14.2755	−	62.5451i	0.511802	−	2.24235i
$779$	17.5447	+	5.41183i	0.628605	+	0.193899i
$780$		0			0
$781$	16.4711	−	15.2830i	0.589384	−	0.546868i
$782$	−19.9841	+	13.6249i	−0.714629	+	0.487226i
$783$		0			0
$784$	83.3115	−	50.3727i	2.97541	−	1.79902i
$785$	−18.6405			−0.665309
$786$		0			0
$787$	−22.0730	+	20.4808i	−0.786819	+	0.730061i	−0.967332	−	0.253511i	$-0.918415\pi$
$787$	−22.0730	+	20.4808i	−0.786819	+	0.730061i	0.180513	+	0.983573i	$0.442224\pi$
$788$	−20.3933	+	51.9612i	−0.726480	+	1.85104i
$789$		0			0
$790$	−11.6984	+	51.2538i	−0.416209	+	1.82353i
$791$	−17.0220	−	8.77743i	−0.605234	−	0.312089i
$792$		0			0
$793$	−1.67642	+	22.3703i	−0.0595315	+	0.794393i
$794$	−13.0496	+	4.02527i	−0.463114	+	0.142852i
$795$		0			0
$796$	−10.3835	−	26.4566i	−0.368032	−	0.937731i
$797$	25.8769	+	12.4616i	0.916605	+	0.441414i	0.831858	−	0.554989i	$-0.187277\pi$
$797$	25.8769	+	12.4616i	0.916605	+	0.441414i	0.0847474	+	0.996402i	$0.472992\pi$
$798$		0			0
$799$	−20.9399	+	10.0841i	−0.740799	+	0.356750i
$800$	1.52147	+	1.41172i	0.0537922	+	0.0499119i
$801$		0			0
$802$	28.1045	+	48.6784i	0.992404	+	1.71889i
$803$	3.30913	−	5.73158i	0.116777	−	0.202263i
$804$		0			0
$805$	11.6060	+	21.4323i	0.409056	+	0.755388i
$806$	1.34015	+	1.68049i	0.0472046	+	0.0591927i
$807$		0			0
$808$	66.1539	+	45.1030i	2.32729	+	1.58672i
$809$	14.6778	+	10.0072i	0.516044	+	0.351833i	0.793170	−	0.609001i	$-0.208429\pi$
$809$	14.6778	+	10.0072i	0.516044	+	0.351833i	−0.277126	+	0.960834i	$0.589382\pi$
$810$		0			0
$811$	9.64248	+	12.0913i	0.338593	+	0.424583i	0.921755	−	0.387774i	$-0.126756\pi$
$811$	9.64248	+	12.0913i	0.338593	+	0.424583i	−0.583161	+	0.812356i	$0.698184\pi$
$812$	17.4585	−	41.1452i	0.612673	−	1.44391i
$813$		0			0
$814$	13.6980	−	23.7257i	0.480116	−	0.831585i
$815$	4.28384	+	7.41983i	0.150056	+	0.259905i
$816$		0			0
$817$	−6.37889	−	5.91874i	−0.223169	−	0.207071i
$818$	−48.6721	+	23.4393i	−1.70178	+	0.819534i
$819$		0			0
$820$	87.8856	+	42.3235i	3.06910	+	1.47800i
$821$	13.9171	+	35.4603i	0.485711	+	1.23757i	0.938291	+	0.345848i	$0.112409\pi$
$821$	13.9171	+	35.4603i	0.485711	+	1.23757i	−0.452579	+	0.891724i	$0.649496\pi$
$822$		0			0
$823$	−33.9068	+	10.4589i	−1.18192	+	0.364573i	−0.822588	−	0.568638i	$-0.807471\pi$
$823$	−33.9068	+	10.4589i	−1.18192	+	0.364573i	−0.359329	+	0.933211i	$0.616994\pi$
$824$	−8.83969	+	117.958i	−0.307945	+	4.10925i
$825$		0			0
$826$	−54.7396	−	1.49426i	−1.90463	−	0.0519919i
$827$	−1.55778	+	6.82509i	−0.0541694	+	0.237332i	−0.994764	−	0.102201i	$-0.967412\pi$
$827$	−1.55778	+	6.82509i	−0.0541694	+	0.237332i	0.940594	+	0.339532i	$0.110269\pi$
$828$		0			0
$829$	2.45137	−	6.24598i	0.0851395	−	0.216932i	−0.881963	−	0.471318i	$-0.843778\pi$
$829$	2.45137	−	6.24598i	0.0851395	−	0.216932i	0.967103	+	0.254386i	$0.0818735\pi$
$830$	8.66494	−	8.03989i	0.300764	−	0.279069i
$831$		0			0
$832$	−47.6591			−1.65228
$833$	−6.36687	+	13.9348i	−0.220599	+	0.482812i
$834$		0			0
$835$	24.8643	−	16.9522i	0.860466	−	0.586655i
$836$	−49.7643	+	46.1745i	−1.72113	+	1.59698i
$837$		0			0
$838$	−23.8529	−	7.35764i	−0.823984	−	0.254165i
$839$	−3.78148	+	16.5678i	−0.130551	+	0.571983i	0.866762	+	0.498723i	$0.166197\pi$
$839$	−3.78148	+	16.5678i	−0.130551	+	0.571983i	−0.997313	+	0.0732599i	$0.976660\pi$
$840$		0			0
$841$	4.23302	+	18.5461i	0.145966	+	0.639519i
$842$	4.56506	−	60.9164i	0.157322	−	2.09932i
$843$		0			0
$844$	9.74548	+	130.044i	0.335453	+	4.47631i
$845$	−7.77363	−	19.8069i	−0.267421	−	0.681377i
$846$		0			0
$847$	−38.0477	−	37.2861i	−1.30733	−	1.28117i
$848$	10.0945	−	4.86127i	0.346648	−	0.166937i
$849$		0			0
$850$	−0.622886	−	0.0938850i	−0.0213648	−	0.00322023i
$851$	−3.69191	−	6.39458i	−0.126557	−	0.219203i
$852$		0			0
$853$	−32.5884	+	40.8646i	−1.11581	+	1.39918i	−0.208853	+	0.977947i	$0.566973\pi$
$853$	−32.5884	+	40.8646i	−1.11581	+	1.39918i	−0.906954	+	0.421230i	$0.861598\pi$
$854$	−4.03622	−	84.8929i	−0.138116	−	2.90498i
$855$		0			0
$856$	−8.47998	+	1.27815i	−0.289840	+	0.0436863i
$857$	17.5620	+	11.9736i	0.599907	+	0.409010i	0.824841	−	0.565364i	$-0.191264\pi$
$857$	17.5620	+	11.9736i	0.599907	+	0.409010i	−0.224934	+	0.974374i	$0.572217\pi$
$858$		0			0
$859$	−29.7161	+	4.47898i	−1.01390	+	0.152821i	−0.634915	−	0.772582i	$-0.718965\pi$
$859$	−29.7161	+	4.47898i	−1.01390	+	0.152821i	−0.378985	+	0.925403i	$0.623727\pi$
$860$	−28.8247	−	36.1450i	−0.982914	−	1.23254i
$861$		0			0
$862$	−44.1128	+	55.3157i	−1.50249	+	1.88406i
$863$	−24.2812	+	42.0563i	−0.826541	+	1.43161i	0.0741941	+	0.997244i	$0.476362\pi$
$863$	−24.2812	+	42.0563i	−0.826541	+	1.43161i	−0.900736	+	0.434368i	$0.856972\pi$
$864$		0			0
$865$	−1.44771	−	0.218208i	−0.0492237	−	0.00741928i
$866$	−19.0999	−	17.7221i	−0.649040	−	0.602221i
$867$		0			0
$868$	−4.23309	−	4.14836i	−0.143680	−	0.140804i
$869$	−43.1464	−	20.7782i	−1.46364	−	0.704852i
$870$		0			0
$871$	0.622161	+	8.30216i	0.0210811	+	0.281308i
$872$	−38.9878	+	12.0261i	−1.32029	+	0.407257i
$873$		0			0
$874$	5.59394	+	24.5086i	0.189218	+	0.829017i
$875$	7.28646	−	28.3362i	0.246327	−	0.957939i
$876$		0			0
$877$	45.4881	+	14.0312i	1.53602	+	0.473800i	0.943394	−	0.331675i	$-0.107614\pi$
$877$	45.4881	+	14.0312i	1.53602	+	0.473800i	0.592629	+	0.805475i	$0.298090\pi$
$878$	10.8486	−	27.6418i	0.366122	−	0.932865i
$879$		0			0
$880$	−144.891	+	98.7851i	−4.88428	+	3.33005i
$881$	49.0250			1.65170			0.825848	−	0.563893i	$-0.190697\pi$
$881$	49.0250			1.65170			0.825848	+	0.563893i	$0.190697\pi$
$882$		0			0
$883$	23.9404			0.805660			0.402830	−	0.915275i	$-0.368027\pi$
$883$	23.9404			0.805660			0.402830	+	0.915275i	$0.368027\pi$
$884$	18.3091	−	12.4829i	0.615802	−	0.419847i
$885$		0			0
$886$	−4.95532	+	12.6259i	−0.166477	+	0.424177i
$887$	−7.40241	−	2.28334i	−0.248549	−	0.0766671i	0.167978	−	0.985791i	$-0.446276\pi$
$887$	−7.40241	−	2.28334i	−0.248549	−	0.0766671i	−0.416526	+	0.909124i	$0.636753\pi$
$888$		0			0
$889$	20.4389	+	0.557934i	0.685500	+	0.0187125i
$890$	−7.55333	−	33.0933i	−0.253188	−	1.10929i
$891$		0			0
$892$	−108.693	+	33.5272i	−3.63930	+	1.12257i
$893$	1.80521	+	24.0888i	0.0604090	+	0.806103i
$894$		0			0
$895$	−38.3643	−	18.4753i	−1.28238	−	0.617561i
$896$	76.5426	−	9.40880i	2.55711	−	0.314326i
$897$		0			0
$898$	−28.7596	−	26.6850i	−0.959721	−	0.890490i
$899$	−1.30822	−	0.197182i	−0.0436315	−	0.00657640i
$900$		0			0
$901$	−0.881565	+	1.52692i	−0.0293692	+	0.0508689i
$902$	−76.1182	+	95.4492i	−2.53446	+	3.17811i
$903$		0			0
$904$	−40.9651	−	51.3687i	−1.36248	−	1.70850i
$905$	29.9067	−	4.50771i	0.994132	−	0.149841i
$906$		0			0
$907$	10.1951	+	6.95091i	0.338523	+	0.230801i	0.720635	−	0.693315i	$-0.243851\pi$
$907$	10.1951	+	6.95091i	0.338523	+	0.230801i	−0.382111	+	0.924116i	$0.624803\pi$
$908$	150.199	−	22.6388i	4.98452	−	0.751295i
$909$		0			0
$910$	−14.6095	−	26.9787i	−0.484299	−	0.894335i
$911$	1.90169	−	2.38465i	0.0630058	−	0.0790068i	−0.749330	−	0.662197i	$-0.769624\pi$
$911$	1.90169	−	2.38465i	0.0630058	−	0.0790068i	0.812336	+	0.583190i	$0.198196\pi$
$912$		0			0
$913$	5.38371	+	9.32486i	0.178175	+	0.308608i
$914$	54.6037	+	8.23019i	1.80613	+	0.272230i
$915$		0			0
$916$	51.9955	−	25.0397i	1.71798	−	0.827335i
$917$	5.49737	−	53.6607i	0.181539	−	1.77203i
$918$		0			0
$919$	−3.76430	−	9.59129i	−0.124173	−	0.316387i	0.855247	−	0.518221i	$-0.173405\pi$
$919$	−3.76430	−	9.59129i	−0.124173	−	0.316387i	−0.979420	+	0.201833i	$0.935310\pi$
$920$	6.24853	+	83.3808i	0.206008	+	2.74898i
$921$		0			0
$922$	−2.78460	+	37.1579i	−0.0917059	+	1.22373i
$923$	1.69631	+	7.43204i	0.0558348	+	0.244628i
$924$		0			0
$925$	0.0427918	−	0.187483i	0.00140698	−	0.00616440i
$926$	−72.3617	−	22.3206i	−2.37795	−	0.733501i
$927$		0			0
$928$	45.2632	−	41.9981i	1.48584	−	1.37866i
$929$	31.4952	−	21.4730i	1.03332	−	0.704508i	0.0770633	−	0.997026i	$-0.475446\pi$
$929$	31.4952	−	21.4730i	1.03332	−	0.704508i	0.956260	+	0.292518i	$0.0944933\pi$
$930$		0			0
$931$	11.0645	+	11.4514i	0.362625	+	0.375305i
$932$	151.857			4.97426
$933$		0			0
$934$	20.5818	−	19.0971i	0.673456	−	0.624876i
$935$	10.0819	−	25.6883i	0.329714	−	0.840097i
$936$		0			0
$937$	7.95836	−	34.8679i	0.259988	−	1.13908i	−0.661275	−	0.750144i	$-0.729984\pi$
$937$	7.95836	−	34.8679i	0.259988	−	1.13908i	0.921263	−	0.388940i	$-0.127158\pi$
$938$	−6.17690	−	30.9307i	−0.201683	−	1.00992i
$939$		0			0
$940$	−9.59076	+	127.980i	−0.312816	+	4.17424i
$941$	18.6891	−	5.76483i	0.609247	−	0.187928i	0.0252470	−	0.999681i	$-0.491963\pi$
$941$	18.6891	−	5.76483i	0.609247	−	0.187928i	0.584001	+	0.811753i	$0.301487\pi$
$942$		0			0
$943$	12.0213	+	30.6297i	0.391467	+	0.997441i
$944$	−95.6742	−	46.0743i	−3.11393	−	1.49959i
$945$		0			0
$946$	52.1310	−	25.1050i	1.69493	−	0.816234i
$947$	−10.9011	−	10.1147i	−0.354237	−	0.328684i	0.482902	−	0.875674i	$-0.339583\pi$
$947$	−10.9011	−	10.1147i	−0.354237	−	0.328684i	−0.837139	+	0.546991i	$0.815773\pi$
$948$		0			0
$949$	1.12269	+	1.94456i	0.0364441	+	0.0631230i
$950$	−0.327359	+	0.567003i	−0.0106209	+	0.0183960i
$951$		0			0
$952$	−39.4895	+	34.6844i	−1.27986	+	1.12413i
$953$	−9.19465	−	11.5297i	−0.297844	−	0.373485i	0.610280	−	0.792186i	$-0.291057\pi$
$953$	−9.19465	−	11.5297i	−0.297844	−	0.373485i	−0.908124	+	0.418701i	$0.862485\pi$
$954$		0			0
$955$	−36.1449	−	24.6432i	−1.16962	−	0.797435i
$956$	−66.9433	−	45.6412i	−2.16510	−	1.47614i
$957$		0			0
$958$	−13.1553	−	16.4962i	−0.425028	−	0.532968i
$959$	−30.4847	−	22.0262i	−0.984402	−	0.711263i
$960$		0			0
$961$	15.4123	−	26.6949i	0.497170	−	0.861124i
$962$	4.64734	+	8.04943i	0.149836	+	0.259524i
$963$		0			0
$964$	96.6058	+	89.6371i	3.11146	+	2.88702i
$965$	31.9530	−	15.3878i	1.02860	−	0.495350i
$966$		0			0
$967$	40.1192	+	19.3204i	1.29015	+	0.621302i	0.947978	−	0.318336i	$-0.103124\pi$
$967$	40.1192	+	19.3204i	1.29015	+	0.621302i	0.342169	+	0.939638i	$0.388838\pi$
$968$	−66.7682	−	170.123i	−2.14601	−	5.46795i
$969$		0			0
$970$	104.995	−	32.3866i	3.37118	−	1.03987i
$971$	−2.10743	+	28.1217i	−0.0676307	+	0.902468i	0.855456	+	0.517876i	$0.173277\pi$
$971$	−2.10743	+	28.1217i	−0.0676307	+	0.902468i	−0.923086	+	0.384593i	$0.874342\pi$
$972$		0			0
$973$	21.7697	−	25.8202i	0.697904	−	0.827758i
$974$	−7.57676	+	33.1960i	−0.242775	+	1.06367i
$975$		0			0
$976$	60.2119	−	153.417i	1.92733	−	4.91077i
$977$	8.64066	−	8.01736i	0.276439	−	0.256498i	−0.529753	−	0.848152i	$-0.677715\pi$
$977$	8.64066	−	8.01736i	0.276439	−	0.256498i	0.806192	+	0.591654i	$0.201525\pi$
$978$		0			0
$979$	30.9207			0.988229
$980$	49.0596	+	68.9211i	1.56715	+	2.20160i
$981$		0			0
$982$	−30.3864	+	20.7171i	−0.969669	+	0.661109i
$983$	−13.0899	+	12.1457i	−0.417504	+	0.387387i	−0.860763	−	0.509007i	$-0.830013\pi$
$983$	−13.0899	+	12.1457i	−0.417504	+	0.387387i	0.443259	+	0.896394i	$0.353822\pi$
$984$		0			0
$985$	−22.5362	−	6.95151i	−0.718064	−	0.221493i
$986$	−4.17002	+	18.2701i	−0.132801	+	0.581837i
$987$		0			0
$988$	−5.12508	−	22.4544i	−0.163050	−	0.714370i
$989$	1.16540	−	15.5512i	0.0370576	−	0.494499i
$990$		0			0
$991$	−3.68526	−	49.1764i	−0.117066	−	1.56214i	−0.678489	−	0.734611i	$-0.737365\pi$
$991$	−3.68526	−	49.1764i	−0.117066	−	1.56214i	0.561422	−	0.827529i	$-0.310254\pi$
$992$	−2.99135	−	7.62185i	−0.0949756	−	0.241994i
$993$		0			0
$994$	−9.81381	−	27.1623i	−0.311275	−	0.861535i
$995$	10.8189	−	5.21011i	0.342982	−	0.165171i
$996$		0			0
$997$	−8.99162	−	1.35527i	−0.284767	−	0.0429218i	0.00510542	−	0.999987i	$-0.498375\pi$
$997$	−8.99162	−	1.35527i	−0.284767	−	0.0429218i	−0.289873	+	0.957065i	$0.593613\pi$
$998$	−33.2395	−	57.5726i	−1.05218	−	1.82243i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.37.1		60
3.2	odd	2		147.2.m.b.37.5	yes	60
49.4	even	21	inner	441.2.bb.e.298.1		60
147.2	odd	42		7203.2.a.n.1.28		30
147.47	even	42		7203.2.a.m.1.28		30
147.53	odd	42		147.2.m.b.4.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.4.5	✓	60	147.53	odd	42
147.2.m.b.37.5	yes	60	3.2	odd	2
441.2.bb.e.37.1		60	1.1	even	1	trivial
441.2.bb.e.298.1		60	49.4	even	21	inner
7203.2.a.m.1.28		30	147.47	even	42
7203.2.a.n.1.28		30	147.2	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)

\(f(q)\)	\(=\)	\(q+(-2.23975 + 1.52704i) q^{2} +(1.95397 - 4.97862i) q^{4} +(2.15929 + 0.666054i) q^{5} +(1.59254 + 2.11277i) q^{7} +(2.01973 + 8.84903i) q^{8} +O(q^{10})\)	\(q+(-2.23975 + 1.52704i) q^{2} +(1.95397 - 4.97862i) q^{4} +(2.15929 + 0.666054i) q^{5} +(1.59254 + 2.11277i) q^{7} +(2.01973 + 8.84903i) q^{8} +(-5.85337 + 1.80553i) q^{10} +(-0.416983 - 5.56426i) q^{11} +(1.70561 + 0.821378i) q^{13} +(-6.79318 - 2.30022i) q^{14} +(-10.1953 - 9.45985i) q^{16} +(2.16419 + 0.326199i) q^{17} +(1.13739 - 1.97003i) q^{19} +(7.53522 - 9.44886i) q^{20} +(9.43077 + 11.8258i) q^{22} +(4.03119 - 0.607604i) q^{23} +(0.0877252 + 0.0598100i) q^{25} +(-5.07442 + 0.764845i) q^{26} +(13.6305 - 3.80037i) q^{28} +(1.96938 - 2.46952i) q^{29} +(-0.209425 - 0.362735i) q^{31} +(19.3300 + 2.91354i) q^{32} +(-5.34537 + 2.57419i) q^{34} +(2.03154 + 5.62282i) q^{35} +(-0.661712 - 1.68601i) q^{37} +(0.460820 + 6.14921i) q^{38} +(-1.53273 + 20.4529i) q^{40} +(1.79602 + 7.86890i) q^{41} +(0.851216 - 3.72942i) q^{43} +(-28.5171 - 8.79637i) q^{44} +(-8.10103 + 7.51666i) q^{46} +(-8.77398 + 5.98200i) q^{47} +(-1.92763 + 6.72936i) q^{49} -0.287815 q^{50} +(7.42203 - 6.88664i) q^{52} +(-0.294313 + 0.749898i) q^{53} +(2.80570 - 12.2926i) q^{55} +(-15.4795 + 18.3597i) q^{56} +(-0.639867 + 8.53844i) q^{58} +(7.29598 - 2.25051i) q^{59} +(4.32929 + 11.0309i) q^{61} +(1.02297 + 0.492636i) q^{62} +(-22.6822 + 10.9232i) q^{64} +(3.13583 + 2.90962i) q^{65} +(2.19891 + 3.80862i) q^{67} +(5.85278 - 10.1373i) q^{68} +(-13.1364 - 9.49148i) q^{70} +(2.51070 + 3.14832i) q^{71} +(0.979999 + 0.668152i) q^{73} +(4.05668 + 2.76580i) q^{74} +(-7.58559 - 9.51202i) q^{76} +(11.0920 - 9.74229i) q^{77} +(4.29123 - 7.43262i) q^{79} +(-15.7139 - 27.2172i) q^{80} +(-16.0388 - 14.8818i) q^{82} +(-1.73859 + 0.837263i) q^{83} +(4.45585 + 2.14583i) q^{85} +(3.78845 + 9.65282i) q^{86} +(48.3961 - 14.9282i) q^{88} +(-0.414115 + 5.52598i) q^{89} +(0.980863 + 4.91164i) q^{91} +(4.85177 - 21.2570i) q^{92} +(10.5168 - 26.7964i) q^{94} +(3.76811 - 3.49630i) q^{95} -17.9375 q^{97} +(-5.95855 - 18.0157i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 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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