LMFDB - Embedded newform 441.2.bb.e.46.3

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			46.3
Character	$\chi$	$=$	441.46
Dual form			441.2.bb.e.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.317978 + 0.810194i) q^{2} +(0.910799 + 0.845098i) q^{4} +(-2.75602 - 1.87902i) q^{5} +(-2.42550 + 1.05686i) q^{7} +(-2.54264 + 1.22447i) q^{8} +O(q^{10})$	\(q+(-0.317978 + 0.810194i) q^{2} +(0.910799 + 0.845098i) q^{4} +(-2.75602 - 1.87902i) q^{5} +(-2.42550 + 1.05686i) q^{7} +(-2.54264 + 1.22447i) q^{8} +(2.39873 - 1.63543i) q^{10} +(2.72022 - 0.410007i) q^{11} +(-3.23053 - 4.05096i) q^{13} +(-0.0850052 - 2.30118i) q^{14} +(0.00214464 + 0.0286182i) q^{16} +(-0.283495 - 0.0874465i) q^{17} +(-3.95735 - 6.85433i) q^{19} +(-0.922223 - 4.04053i) q^{20} +(-0.532783 + 2.33428i) q^{22} +(-2.30016 + 0.709505i) q^{23} +(2.23822 + 5.70290i) q^{25} +(4.30930 - 1.32924i) q^{26} +(-3.10229 - 1.08720i) q^{28} +(-1.10335 - 4.83411i) q^{29} +(-4.11589 + 7.12894i) q^{31} +(-5.41734 - 1.67103i) q^{32} +(0.160994 - 0.201880i) q^{34} +(8.67060 + 1.64485i) q^{35} +(0.350549 - 0.325262i) q^{37} +(6.81169 - 1.02670i) q^{38} +(9.30838 + 1.40301i) q^{40} +(-2.72215 + 1.31092i) q^{41} +(2.46338 + 1.18630i) q^{43} +(2.82407 + 1.92542i) q^{44} +(0.156563 - 2.08918i) q^{46} +(-3.79989 + 9.68195i) q^{47} +(4.76610 - 5.12682i) q^{49} -5.33216 q^{50} +(0.481092 - 6.41972i) q^{52} +(-5.85144 - 5.42935i) q^{53} +(-8.26739 - 3.98137i) q^{55} +(4.87308 - 5.65716i) q^{56} +(4.26741 + 0.643208i) q^{58} +(9.14824 - 6.23716i) q^{59} +(0.386554 - 0.358670i) q^{61} +(-4.46706 - 5.60152i) q^{62} +(3.04067 - 3.81287i) q^{64} +(1.29157 + 17.2348i) q^{65} +(-2.75569 + 4.77300i) q^{67} +(-0.184306 - 0.319227i) q^{68} +(-4.08970 + 6.50184i) q^{70} +(0.595203 - 2.60776i) q^{71} +(1.35415 + 3.45031i) q^{73} +(0.152059 + 0.387439i) q^{74} +(2.18823 - 9.58727i) q^{76} +(-6.16457 + 3.86935i) q^{77} +(2.80156 + 4.85245i) q^{79} +(0.0478636 - 0.0829023i) q^{80} +(-0.196515 - 2.62231i) q^{82} +(-8.64321 + 10.8382i) q^{83} +(0.617004 + 0.773698i) q^{85} +(-1.74444 + 1.61860i) q^{86} +(-6.41449 + 4.37332i) q^{88} +(1.81136 + 0.273019i) q^{89} +(12.1169 + 6.41138i) q^{91} +(-2.69459 - 1.29764i) q^{92} +(-6.63598 - 6.15729i) q^{94} +(-1.97291 + 26.3267i) q^{95} -6.73950 q^{97} +(2.63820 + 5.49168i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

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 $

$2$	−0.317978	+	0.810194i	−0.224844	+	0.572894i	−0.998128	−	0.0611670i	$-0.980518\pi$
$2$	−0.317978	+	0.810194i	−0.224844	+	0.572894i	0.773283	+	0.634061i	$0.218613\pi$
$3$		0			0
$3$		0			0
$4$	0.910799	+	0.845098i	0.455400	+	0.422549i
$5$	−2.75602	−	1.87902i	−1.23253	−	0.840325i	−0.241042	−	0.970515i	$-0.577489\pi$
$5$	−2.75602	−	1.87902i	−1.23253	−	0.840325i	−0.991489	+	0.130189i	$0.958442\pi$
$6$		0			0
$7$	−2.42550	+	1.05686i	−0.916753	+	0.399455i
$7$	−2.42550	+	1.05686i	−0.916753	+	0.399455i
$8$	−2.54264	+	1.22447i	−0.898959	+	0.432916i
$9$		0			0
$10$	2.39873	−	1.63543i	0.758545	−	0.517167i
$11$	2.72022	−	0.410007i	0.820176	−	0.123622i	0.274467	−	0.961596i	$-0.411499\pi$
$11$	2.72022	−	0.410007i	0.820176	−	0.123622i	0.545709	+	0.837975i	$0.316260\pi$
$12$		0			0
$13$	−3.23053	−	4.05096i	−0.895988	−	1.12353i	−0.991757	−	0.128130i	$-0.959103\pi$
$13$	−3.23053	−	4.05096i	−0.895988	−	1.12353i	0.0957695	−	0.995404i	$-0.469469\pi$
$14$	−0.0850052	−	2.30118i	−0.0227186	−	0.615017i
$15$		0			0
$16$	0.00214464	+	0.0286182i	0.000536160	+	0.00715455i
$17$	−0.283495	−	0.0874465i	−0.0687576	−	0.0212089i	0.260186	−	0.965559i	$-0.416216\pi$
$17$	−0.283495	−	0.0874465i	−0.0687576	−	0.0212089i	−0.328943	+	0.944350i	$0.606692\pi$
$18$		0			0
$19$	−3.95735	−	6.85433i	−0.907879	−	1.57249i	−0.817006	−	0.576629i	$-0.804368\pi$
$19$	−3.95735	−	6.85433i	−0.907879	−	1.57249i	−0.0908725	−	0.995863i	$-0.528966\pi$
$20$	−0.922223	−	4.04053i	−0.206215	−	0.903489i
$21$		0			0
$22$	−0.532783	+	2.33428i	−0.113590	+	0.497669i
$23$	−2.30016	+	0.709505i	−0.479617	+	0.147942i	−0.525131	−	0.851022i	$-0.675984\pi$
$23$	−2.30016	+	0.709505i	−0.479617	+	0.147942i	0.0455142	+	0.998964i	$0.485507\pi$
$24$		0			0
$25$	2.23822	+	5.70290i	0.447645	+	1.14058i
$26$	4.30930	−	1.32924i	0.845123	−	0.260686i
$27$		0			0
$28$	−3.10229	−	1.08720i	−0.586278	−	0.205462i
$29$	−1.10335	−	4.83411i	−0.204888	−	0.897671i	−0.967910	−	0.251299i	$-0.919142\pi$
$29$	−1.10335	−	4.83411i	−0.204888	−	0.897671i	0.763022	−	0.646373i	$-0.223715\pi$
$30$		0			0
$31$	−4.11589	+	7.12894i	−0.739237	+	1.28040i	0.213603	+	0.976921i	$0.431480\pi$
$31$	−4.11589	+	7.12894i	−0.739237	+	1.28040i	−0.952840	+	0.303475i	$0.901853\pi$
$32$	−5.41734	−	1.67103i	−0.957660	−	0.295399i
$33$		0			0
$34$	0.160994	−	0.201880i	0.0276102	−	0.0346221i
$35$	8.67060	+	1.64485i	1.46560	+	0.278030i
$36$		0			0
$37$	0.350549	−	0.325262i	0.0576299	−	0.0534727i	−0.650832	−	0.759222i	$-0.725580\pi$
$37$	0.350549	−	0.325262i	0.0576299	−	0.0534727i	0.708462	+	0.705749i	$0.249389\pi$
$38$	6.81169	−	1.02670i	1.10500	−	0.166552i
$39$		0			0
$40$	9.30838	+	1.40301i	1.47178	+	0.221836i
$41$	−2.72215	+	1.31092i	−0.425129	+	0.204731i	−0.634200	−	0.773169i	$-0.718670\pi$
$41$	−2.72215	+	1.31092i	−0.425129	+	0.204731i	0.209071	+	0.977900i	$0.432956\pi$
$42$		0			0
$43$	2.46338	+	1.18630i	0.375662	+	0.180909i	0.612181	−	0.790717i	$-0.290292\pi$
$43$	2.46338	+	1.18630i	0.375662	+	0.180909i	−0.236519	+	0.971627i	$0.576007\pi$
$44$	2.82407	+	1.92542i	0.425744	+	0.290267i
$45$		0			0
$46$	0.156563	−	2.08918i	0.0230839	−	0.308033i
$47$	−3.79989	+	9.68195i	−0.554270	+	1.41226i	0.329419	+	0.944184i	$0.393147\pi$
$47$	−3.79989	+	9.68195i	−0.554270	+	1.41226i	−0.883689	+	0.468074i	$0.844948\pi$
$48$		0			0
$49$	4.76610	−	5.12682i	0.680872	−	0.732403i
$50$	−5.33216			−0.754082
$51$		0			0
$52$	0.481092	−	6.41972i	0.0667154	−	0.890256i
$53$	−5.85144	−	5.42935i	−0.803757	−	0.745778i	0.166970	−	0.985962i	$-0.446602\pi$
$53$	−5.85144	−	5.42935i	−0.803757	−	0.745778i	−0.970727	+	0.240184i	$0.922792\pi$
$54$		0			0
$55$	−8.26739	−	3.98137i	−1.11477	−	0.536847i
$56$	4.87308	−	5.65716i	0.651193	−	0.755970i
$57$		0			0
$58$	4.26741	+	0.643208i	0.560338	+	0.0844573i
$59$	9.14824	−	6.23716i	1.19100	−	0.812009i	0.205000	−	0.978762i	$-0.434280\pi$
$59$	9.14824	−	6.23716i	1.19100	−	0.812009i	0.985999	+	0.166753i	$0.0533281\pi$
$60$		0			0
$61$	0.386554	−	0.358670i	0.0494932	−	0.0459230i	−0.655038	−	0.755596i	$-0.727348\pi$
$61$	0.386554	−	0.358670i	0.0494932	−	0.0459230i	0.704532	+	0.709673i	$0.251157\pi$
$62$	−4.46706	−	5.60152i	−0.567317	−	0.711393i
$63$		0			0
$64$	3.04067	−	3.81287i	0.380083	−	0.476609i
$65$	1.29157	+	17.2348i	0.160199	+	2.13771i
$66$		0			0
$67$	−2.75569	+	4.77300i	−0.336662	+	0.583115i	−0.983803	−	0.179255i	$-0.942631\pi$
$67$	−2.75569	+	4.77300i	−0.336662	+	0.583115i	0.647141	+	0.762370i	$0.275965\pi$
$68$	−0.184306	−	0.319227i	−0.0223504	−	0.0387120i
$69$		0			0
$70$	−4.08970	+	6.50184i	−0.488813	+	0.777119i
$71$	0.595203	−	2.60776i	0.0706376	−	0.309484i	−0.927250	−	0.374442i	$-0.877834\pi$
$71$	0.595203	−	2.60776i	0.0706376	−	0.309484i	0.997888	+	0.0649583i	$0.0206914\pi$
$72$		0			0
$73$	1.35415	+	3.45031i	0.158491	+	0.403828i	0.987957	−	0.154729i	$-0.0494504\pi$
$73$	1.35415	+	3.45031i	0.158491	+	0.403828i	−0.829466	+	0.558557i	$0.811355\pi$
$74$	0.152059	+	0.387439i	0.0176764	+	0.0450388i
$75$		0			0
$76$	2.18823	−	9.58727i	0.251007	−	1.09974i
$77$	−6.16457	+	3.86935i	−0.702518	+	0.440954i
$78$		0			0
$79$	2.80156	+	4.85245i	0.315201	+	0.545943i	0.979480	−	0.201541i	$-0.0645949\pi$
$79$	2.80156	+	4.85245i	0.315201	+	0.545943i	−0.664280	+	0.747484i	$0.731262\pi$
$80$	0.0478636	−	0.0829023i	0.00535132	−	0.00926876i
$81$		0			0
$82$	−0.196515	−	2.62231i	−0.0217015	−	0.289586i
$83$	−8.64321	+	10.8382i	−0.948716	+	1.18965i	0.0330302	+	0.999454i	$0.489484\pi$
$83$	−8.64321	+	10.8382i	−0.948716	+	1.18965i	−0.981746	+	0.190197i	$0.939087\pi$
$84$		0			0
$85$	0.617004	+	0.773698i	0.0669235	+	0.0839194i
$86$	−1.74444	+	1.61860i	−0.188107	+	0.174538i
$87$		0			0
$88$	−6.41449	+	4.37332i	−0.683787	+	0.466198i
$89$	1.81136	+	0.273019i	0.192004	+	0.0289400i	0.244340	−	0.969690i	$-0.421429\pi$
$89$	1.81136	+	0.273019i	0.192004	+	0.0289400i	−0.0523362	+	0.998630i	$0.516667\pi$
$90$		0			0
$91$	12.1169	+	6.41138i	1.27020	+	0.672096i
$92$	−2.69459	−	1.29764i	−0.280930	−	0.135289i
$93$		0			0
$94$	−6.63598	−	6.15729i	−0.684449	−	0.635076i
$95$	−1.97291	+	26.3267i	−0.202416	+	2.70106i
$96$		0			0
$97$	−6.73950			−0.684292			−0.342146	−	0.939647i	$-0.611154\pi$
$97$	−6.73950			−0.684292			−0.342146	+	0.939647i	$0.611154\pi$
$98$	2.63820	+	5.49168i	0.266499	+	0.554744i
$99$		0			0
$100$	−2.78094	+	7.08572i	−0.278094	+	0.708572i
$101$	0.101154	−	1.34980i	0.0100652	−	0.134310i	−0.989907	−	0.141715i	$-0.954738\pi$
$101$	0.101154	−	1.34980i	0.0100652	−	0.134310i	0.999973	+	0.00740540i	$0.00235723\pi$
$102$		0			0
$103$	12.5455	+	8.55337i	1.23614	+	0.842789i	0.991912	−	0.126928i	$-0.0405117\pi$
$103$	12.5455	+	8.55337i	1.23614	+	0.842789i	0.244232	+	0.969717i	$0.421464\pi$
$104$	13.1744	+	6.34443i	1.29185	+	0.622123i
$105$		0			0
$106$	6.25945	−	3.01439i	0.607972	−	0.292784i
$107$	7.85861	+	1.18449i	0.759720	+	0.114509i	0.517466	−	0.855704i	$-0.326875\pi$
$107$	7.85861	+	1.18449i	0.759720	+	0.114509i	0.242254	+	0.970213i	$0.422113\pi$
$108$		0			0
$109$	−6.39699	+	0.964191i	−0.612721	+	0.0923528i	−0.448069	−	0.893999i	$-0.647888\pi$
$109$	−6.39699	+	0.964191i	−0.612721	+	0.0923528i	−0.164652	+	0.986352i	$0.552650\pi$
$110$	5.85453	−	5.43221i	0.558207	−	0.517940i
$111$		0			0
$112$	−0.0354472	−	0.0671469i	−0.00334945	−	0.00634478i
$113$	5.82558	−	7.30504i	0.548024	−	0.687201i	−0.428269	−	0.903651i	$-0.640877\pi$
$113$	5.82558	−	7.30504i	0.548024	−	0.687201i	0.976294	+	0.216450i	$0.0694479\pi$
$114$		0			0
$115$	7.67247	+	2.36664i	0.715462	+	0.220691i
$116$	3.08036	−	5.33534i	0.286004	−	0.495374i
$117$		0			0
$118$	2.14438	+	9.39512i	0.197406	+	0.864891i
$119$	0.780035	−	0.0875121i	0.0715057	−	0.00802222i
$120$		0			0
$121$	−3.27983	+	1.01169i	−0.298166	+	0.0919721i
$122$	0.167677	+	0.427233i	0.0151807	+	0.0386799i
$123$		0			0
$124$	−9.77341	+	3.01470i	−0.877678	+	0.270728i
$125$	0.836066	−	3.66304i	0.0747800	−	0.327633i
$126$		0			0
$127$	−4.52149	−	19.8099i	−0.401217	−	1.75785i	−0.622481	−	0.782635i	$-0.713875\pi$
$127$	−4.52149	−	19.8099i	−0.401217	−	1.75785i	0.221264	−	0.975214i	$-0.428982\pi$
$128$	−3.54691	−	6.14342i	−0.313505	−	0.543007i
$129$		0			0
$130$	−14.3742	−	4.43385i	−1.26070	−	0.388875i
$131$	−1.02824	−	13.7209i	−0.0898375	−	1.19880i	−0.841873	−	0.539675i	$-0.818547\pi$
$131$	−1.02824	−	13.7209i	−0.0898375	−	1.19880i	0.752036	−	0.659122i	$-0.229072\pi$
$132$		0			0
$133$	16.8426	+	12.4428i	1.46044	+	1.07893i
$134$	−2.99081	−	3.75036i	−0.258367	−	0.323981i
$135$		0			0
$136$	0.827901	−	0.124786i	0.0709919	−	0.0107003i
$137$	−13.8021	+	9.41011i	−1.17919	+	0.803960i	−0.984237	−	0.176852i	$-0.943408\pi$
$137$	−13.8021	+	9.41011i	−1.17919	+	0.803960i	−0.194955	+	0.980812i	$0.562456\pi$
$138$		0			0
$139$	−4.73129	+	2.27847i	−0.401303	+	0.193257i	−0.623638	−	0.781713i	$-0.714346\pi$
$139$	−4.73129	+	2.27847i	−0.401303	+	0.193257i	0.222336	+	0.974970i	$0.428632\pi$
$140$	6.50712	+	8.82563i	0.549952	+	0.745902i
$141$		0			0
$142$	1.92353	+	1.31144i	0.161419	+	0.110053i
$143$	−10.4487	−	9.69494i	−0.873761	−	0.810732i
$144$		0			0
$145$	−6.04254	+	15.3961i	−0.501806	+	1.27858i
$146$	−3.22601			−0.266986
$147$		0			0
$148$	0.594158			0.0488395
$149$	−4.39760	+	11.2049i	−0.360265	+	0.917941i	0.629726	+	0.776817i	$0.283167\pi$
$149$	−4.39760	+	11.2049i	−0.360265	+	0.917941i	−0.989992	+	0.141124i	$0.954928\pi$
$150$		0			0
$151$	2.82921	+	2.62513i	0.230238	+	0.213630i	0.786852	−	0.617141i	$-0.211709\pi$
$151$	2.82921	+	2.62513i	0.230238	+	0.213630i	−0.556614	+	0.830771i	$0.687900\pi$
$152$	18.4550	+	12.5824i	1.49690	+	1.02057i
$153$		0			0
$154$	−1.17473	−	6.22486i	−0.0946627	−	0.501614i
$155$	24.7390	−	11.9137i	1.98708	−	0.956928i
$156$		0			0
$157$	−2.73766	+	1.86651i	−0.218489	+	0.148963i	−0.667619	−	0.744503i	$-0.732686\pi$
$157$	−2.73766	+	1.86651i	−0.218489	+	0.148963i	0.449130	+	0.893466i	$0.351734\pi$
$158$	−4.82226	+	0.726839i	−0.383638	+	0.0578242i
$159$		0			0
$160$	11.7904	+	14.7847i	0.932115	+	1.16883i
$161$	4.82919	−	4.15185i	0.380594	−	0.327212i
$162$		0			0
$163$	−1.65130	−	22.0351i	−0.129340	−	1.72592i	−0.564382	−	0.825514i	$-0.690886\pi$
$163$	−1.65130	−	22.0351i	−0.129340	−	1.72592i	0.435042	−	0.900410i	$-0.356733\pi$
$164$	−3.58719	−	1.10650i	−0.280113	−	0.0864033i
$165$		0			0
$166$	−6.03273	−	10.4490i	−0.468231	−	0.810999i
$167$	−2.09538	−	9.18045i	−0.162145	−	0.710405i	−0.988991	−	0.147976i	$-0.952724\pi$
$167$	−2.09538	−	9.18045i	−0.162145	−	0.710405i	0.826846	−	0.562429i	$-0.190133\pi$
$168$		0			0
$169$	−3.08115	+	13.4994i	−0.237012	+	1.03842i
$170$	−0.823039	+	0.253874i	−0.0631242	+	0.0194712i
$171$		0			0
$172$	1.24111	+	3.16228i	0.0946334	+	0.241122i
$173$	3.63633	−	1.12166i	0.276465	−	0.0852782i	−0.153422	−	0.988161i	$-0.549029\pi$
$173$	3.63633	−	1.12166i	0.276465	−	0.0852782i	0.429887	+	0.902882i	$0.358553\pi$
$174$		0			0
$175$	−11.4560	−	11.4669i	−0.865990	−	0.866817i
$176$	0.0175675	+	0.0769684i	0.00132420	+	0.00580171i
$177$		0			0
$178$	−0.797171	+	1.38074i	−0.0597505	+	0.103491i
$179$	8.28964	+	2.55701i	0.619596	+	0.191120i	0.588633	−	0.808400i	$-0.299666\pi$
$179$	8.28964	+	2.55701i	0.619596	+	0.191120i	0.0309634	+	0.999521i	$0.490142\pi$
$180$		0			0
$181$	−1.23302	+	1.54616i	−0.0916497	+	0.114925i	−0.825542	−	0.564341i	$-0.809130\pi$
$181$	−1.23302	+	1.54616i	−0.0916497	+	0.114925i	0.733892	+	0.679266i	$0.237702\pi$
$182$	−9.04738	+	7.77839i	−0.670636	+	0.576573i
$183$		0			0
$184$	4.97971	−	4.62049i	0.367109	−	0.340627i
$185$	−1.57730	+	0.237739i	−0.115965	+	0.0174789i
$186$		0			0
$187$	−0.807021	−	0.121639i	−0.0590152	−	0.00889511i
$188$	−11.6431	+	5.60704i	−0.849163	+	0.408935i
$189$		0			0
$190$	−20.7024	−	9.96973i	−1.50191	−	0.723280i
$191$	−11.7714	−	8.02557i	−0.851745	−	0.580710i	0.0568523	−	0.998383i	$-0.481894\pi$
$191$	−11.7714	−	8.02557i	−0.851745	−	0.580710i	−0.908598	+	0.417672i	$0.862846\pi$
$192$		0			0
$193$	0.532753	−	7.10909i	0.0383484	−	0.511724i	−0.944646	−	0.328090i	$-0.893595\pi$
$193$	0.532753	−	7.10909i	0.0383484	−	0.511724i	0.982995	−	0.183633i	$-0.0587860\pi$
$194$	2.14301	−	5.46030i	0.153859	−	0.392027i
$195$		0			0
$196$	8.67363	−	0.641680i	0.619545	−	0.0458343i
$197$	−21.5278			−1.53379			−0.766895	−	0.641772i	$-0.778200\pi$
$197$	−21.5278			−1.53379			−0.766895	+	0.641772i	$0.778200\pi$
$198$		0			0
$199$	0.994073	−	13.2650i	0.0704680	−	0.940330i	−0.844175	−	0.536068i	$-0.819909\pi$
$199$	0.994073	−	13.2650i	0.0704680	−	0.940330i	0.914643	−	0.404262i	$-0.132472\pi$
$200$	−12.6740	−	11.7598i	−0.896190	−	0.831543i
$201$		0			0
$202$	1.06144	+	0.511160i	0.0746823	+	0.0359651i
$203$	7.78515	+	10.5590i	0.546410	+	0.741099i
$204$		0			0
$205$	9.96557	+	1.50207i	0.696025	+	0.104909i
$206$	−10.9191	+	7.44450i	−0.760768	+	0.518683i
$207$		0			0
$208$	0.109003	−	0.101140i	0.00755798	−	0.00701278i
$209$	−13.5752	−	17.0227i	−0.939014	−	1.17749i
$210$		0			0
$211$	6.72505	−	8.43295i	0.462972	−	0.580548i	−0.494463	−	0.869199i	$-0.664635\pi$
$211$	6.72505	−	8.43295i	0.462972	−	0.580548i	0.957434	+	0.288651i	$0.0932066\pi$
$212$	−0.741160	−	9.89009i	−0.0509031	−	0.679254i
$213$		0			0
$214$	−3.45853	+	5.99035i	−0.236420	+	0.409492i
$215$	−4.56005	−	7.89824i	−0.310993	−	0.538655i
$216$		0			0
$217$	2.44883	−	21.6412i	0.166237	−	1.46910i
$218$	1.25292	−	5.48940i	0.0848584	−	0.371789i
$219$		0			0
$220$	−4.16529	−	10.6130i	−0.280824	−	0.715527i
$221$	0.561596	+	1.43092i	0.0377770	+	0.0962543i
$222$		0			0
$223$	2.12553	−	9.31257i	0.142336	−	0.623616i	−0.852553	−	0.522641i	$-0.824947\pi$
$223$	2.12553	−	9.31257i	0.142336	−	0.623616i	0.994889	−	0.100975i	$-0.0321961\pi$
$224$	14.9058	−	1.67228i	0.995936	−	0.111734i
$225$		0			0
$226$	4.06610	+	7.04269i	0.270473	+	0.468473i
$227$	2.10412	−	3.64445i	0.139656	−	0.241891i	−0.787711	−	0.616045i	$-0.788734\pi$
$227$	2.10412	−	3.64445i	0.139656	−	0.241891i	0.927366	+	0.374155i	$0.122067\pi$
$228$		0			0
$229$	−1.25832	−	16.7910i	−0.0831518	−	1.10958i	−0.870202	−	0.492695i	$-0.836012\pi$
$229$	−1.25832	−	16.7910i	−0.0831518	−	1.10958i	0.787050	−	0.616889i	$-0.211607\pi$
$230$	−4.35712	+	5.46365i	−0.287300	+	0.360262i
$231$		0			0
$232$	8.72465	+	10.9404i	0.572801	+	0.718270i
$233$	14.3764	−	13.3393i	0.941827	−	0.873888i	−0.0503490	−	0.998732i	$-0.516033\pi$
$233$	14.3764	−	13.3393i	0.941827	−	0.873888i	0.992176	+	0.124844i	$0.0398429\pi$
$234$		0			0
$235$	28.6652	−	19.5436i	1.86991	−	1.27488i
$236$	13.6032	+	2.05036i	0.885494	+	0.133467i
$237$		0			0
$238$	−0.177132	+	0.659807i	−0.0114818	+	0.0427689i
$239$	5.26661	+	2.53627i	0.340669	+	0.164057i	0.596394	−	0.802692i	$-0.296600\pi$
$239$	5.26661	+	2.53627i	0.340669	+	0.164057i	−0.255725	+	0.966750i	$0.582314\pi$
$240$		0			0
$241$	11.7378	+	10.8911i	0.756100	+	0.701558i	0.960793	−	0.277268i	$-0.0894291\pi$
$241$	11.7378	+	10.8911i	0.756100	+	0.701558i	−0.204693	+	0.978826i	$0.565620\pi$
$242$	0.223245	−	2.97899i	0.0143507	−	0.191497i
$243$		0			0
$244$	0.655185			0.0419439
$245$	−22.7689	+	5.17401i	−1.45465	+	0.330555i
$246$		0			0
$247$	−14.9823	+	38.1742i	−0.953299	+	2.42897i
$248$	1.73606	−	23.1661i	0.110240	−	1.47105i
$249$		0			0
$250$	2.70192	+	1.84214i	0.170885	+	0.116507i
$251$	−17.6419	−	8.49589i	−1.11355	−	0.536256i	−0.215654	−	0.976470i	$-0.569188\pi$
$251$	−17.6419	−	8.49589i	−1.11355	−	0.536256i	−0.897893	+	0.440214i	$0.854903\pi$
$252$		0			0
$253$	−5.96603	+	2.87309i	−0.375081	+	0.180630i
$254$	17.4876	+	2.63584i	1.09727	+	0.165387i
$255$		0			0
$256$	15.7500	−	2.37392i	0.984373	−	0.148370i
$257$	12.5896	−	11.6814i	0.785316	−	0.728667i	−0.181708	−	0.983353i	$-0.558162\pi$
$257$	12.5896	−	11.6814i	0.785316	−	0.728667i	0.967024	+	0.254686i	$0.0819720\pi$
$258$		0			0
$259$	−0.506501	+	1.15940i	−0.0314724	+	0.0720418i
$260$	−13.3887	+	16.7889i	−0.830333	+	1.04121i
$261$		0			0
$262$	11.4435	+	3.52986i	0.706983	+	0.218075i
$263$	3.43834	−	5.95538i	0.212017	−	0.367224i	−0.740329	−	0.672245i	$-0.765330\pi$
$263$	3.43834	−	5.95538i	0.212017	−	0.367224i	0.952346	+	0.305021i	$0.0986635\pi$
$264$		0			0
$265$	5.92484	+	25.9584i	0.363960	+	1.59461i
$266$	−15.4367	+	9.68924i	−0.946483	+	0.594086i
$267$		0			0
$268$	−6.54354	+	2.01842i	−0.399710	+	0.123294i
$269$	10.2422	+	26.0967i	0.624478	+	1.59115i	0.795551	+	0.605887i	$0.207182\pi$
$269$	10.2422	+	26.0967i	0.624478	+	1.59115i	−0.171072	+	0.985258i	$0.554723\pi$
$270$		0			0
$271$	14.5602	−	4.49121i	0.884467	−	0.272822i	0.180943	−	0.983494i	$-0.442085\pi$
$271$	14.5602	−	4.49121i	0.884467	−	0.272822i	0.703524	+	0.710672i	$0.251609\pi$
$272$	0.00189457	−	0.00830065i	0.000114875	−	0.000503301i
$273$		0			0
$274$	−3.23525	−	14.1746i	−0.195449	−	0.856317i
$275$	8.42668	+	14.5954i	0.508148	+	0.880138i
$276$		0			0
$277$	−23.2741	−	7.17910i	−1.39840	−	0.431350i	−0.498292	−	0.867009i	$-0.666039\pi$
$277$	−23.2741	−	7.17910i	−1.39840	−	0.431350i	−0.900112	+	0.435659i	$0.856515\pi$
$278$	−0.341557	−	4.55777i	−0.0204852	−	0.273357i
$279$		0			0
$280$	−24.0603	+	6.43463i	−1.43788	+	0.384543i
$281$	2.84601	+	3.56878i	0.169779	+	0.212896i	0.859440	−	0.511236i	$-0.170812\pi$
$281$	2.84601	+	3.56878i	0.169779	+	0.212896i	−0.689662	+	0.724132i	$0.742241\pi$
$282$		0			0
$283$	2.17867	−	0.328382i	0.129509	−	0.0195203i	−0.0839681	−	0.996468i	$-0.526759\pi$
$283$	2.17867	−	0.328382i	0.129509	−	0.0195203i	0.213477	+	0.976948i	$0.431521\pi$
$284$	2.74592	−	1.87214i	0.162940	−	0.111091i
$285$		0			0
$286$	11.1772	−	5.38267i	0.660923	−	0.318284i
$287$	5.21713	−	6.05656i	0.307957	−	0.357508i
$288$		0			0
$289$	−13.9733	−	9.52686i	−0.821961	−	0.560404i
$290$	−10.5525	−	9.79126i	−0.619662	−	0.574963i
$291$		0			0
$292$	−1.68250	+	4.28693i	−0.0984606	+	0.250874i
$293$	15.2581			0.891389			0.445694	−	0.895185i	$-0.352957\pi$
$293$	15.2581			0.891389			0.445694	+	0.895185i	$0.352957\pi$
$294$		0			0
$295$	−36.9325			−2.15030
$296$	−0.493046	+	1.25626i	−0.0286577	+	0.0730187i
$297$		0			0
$298$	−7.67981	−	7.12582i	−0.444879	−	0.412788i
$299$	10.3049	+	7.02577i	0.595949	+	0.406311i
$300$		0			0
$301$	−7.22869	−	0.273931i	−0.416655	−	0.0157891i
$302$	−3.02649	+	1.45748i	−0.174155	+	0.0838685i
$303$		0			0
$304$	0.187672	−	0.127952i	0.0107637	−	0.00733857i
$305$	−1.73930	+	0.262158i	−0.0995922	+	0.0150111i
$306$		0			0
$307$	−8.61323	−	10.8007i	−0.491583	−	0.616426i	0.472724	−	0.881210i	$-0.343271\pi$
$307$	−8.61323	−	10.8007i	−0.491583	−	0.616426i	−0.964308	+	0.264785i	$0.914699\pi$
$308$	−8.88467	−	1.68546i	−0.506251	−	0.0960379i
$309$		0			0
$310$	1.78593	+	23.8316i	0.101434	+	1.35355i
$311$	4.80024	+	1.48068i	0.272197	+	0.0839616i	0.427849	−	0.903850i	$-0.359272\pi$
$311$	4.80024	+	1.48068i	0.272197	+	0.0839616i	−0.155652	+	0.987812i	$0.549748\pi$
$312$		0			0
$313$	7.30131	+	12.6462i	0.412694	+	0.714807i	0.995183	−	0.0980311i	$-0.0312545\pi$
$313$	7.30131	+	12.6462i	0.412694	+	0.714807i	−0.582489	+	0.812838i	$0.697921\pi$
$314$	−0.641716	−	2.81154i	−0.0362141	−	0.158665i
$315$		0			0
$316$	−1.54914	+	6.78720i	−0.0871457	+	0.381810i
$317$	−6.44563	+	1.98821i	−0.362023	+	0.111669i	−0.470430	−	0.882437i	$-0.655901\pi$
$317$	−6.44563	+	1.98821i	−0.362023	+	0.111669i	0.108407	+	0.994107i	$0.465425\pi$
$318$		0			0
$319$	−4.98338	−	12.6974i	−0.279016	−	0.710920i
$320$	−15.5446	+	4.79488i	−0.868971	+	0.268042i
$321$		0			0
$322$	1.82823	+	5.23278i	0.101883	+	0.291611i
$323$	0.522500	+	2.28922i	0.0290727	+	0.127376i
$324$		0			0
$325$	15.8716	−	27.4904i	0.880396	−	1.52489i
$326$	18.3778	+	5.66880i	1.01785	+	0.313966i
$327$		0			0
$328$	5.31627	−	6.66639i	0.293542	−	0.368090i
$329$	−1.01583	−	27.4995i	−0.0560043	−	1.51610i
$330$		0			0
$331$	−10.2405	+	9.50182i	−0.562870	+	0.522267i	−0.909483	−	0.415741i	$-0.863522\pi$
$331$	−10.2405	+	9.50182i	−0.562870	+	0.522267i	0.346613	+	0.938008i	$0.387332\pi$
$332$	−17.0316	+	2.56710i	−0.934731	+	0.140888i
$333$		0			0
$334$	8.10423	+	1.22152i	0.443444	+	0.0668384i
$335$	16.5633	−	7.97649i	0.904952	−	0.435802i
$336$		0			0
$337$	13.5172	+	6.50954i	0.736328	+	0.354597i	0.764170	−	0.645015i	$-0.223149\pi$
$337$	13.5172	+	6.50954i	0.736328	+	0.354597i	−0.0278413	+	0.999612i	$0.508863\pi$
$338$	−9.95741	−	6.78885i	−0.541612	−	0.369265i
$339$		0			0
$340$	−0.0918845	+	1.22611i	−0.00498313	+	0.0664953i
$341$	−8.27321	+	21.0798i	−0.448020	+	1.14154i
$342$		0			0
$343$	−6.14186	+	17.4722i	−0.331629	+	0.943410i
$344$	−7.71609			−0.416024
$345$		0			0
$346$	−0.247510	+	3.30280i	−0.0133062	+	0.177559i
$347$	6.06110	+	5.62388i	0.325377	+	0.301906i	0.825899	−	0.563818i	$-0.190668\pi$
$347$	6.06110	+	5.62388i	0.325377	+	0.301906i	−0.500522	+	0.865724i	$0.666859\pi$
$348$		0			0
$349$	−24.1161	−	11.6137i	−1.29090	−	0.621667i	−0.342735	−	0.939432i	$-0.611353\pi$
$349$	−24.1161	−	11.6137i	−1.29090	−	0.621667i	−0.948169	+	0.317765i	$0.897068\pi$
$350$	12.9332	−	5.63534i	0.691307	−	0.301222i
$351$		0			0
$352$	−15.4215	−	2.32441i	−0.821968	−	0.123892i
$353$	21.2902	−	14.5154i	1.13316	−	0.772577i	0.156569	−	0.987667i	$-0.449957\pi$
$353$	21.2902	−	14.5154i	1.13316	−	0.772577i	0.976594	+	0.215090i	$0.0690044\pi$
$354$		0			0
$355$	−6.54043	+	6.06863i	−0.347130	+	0.322090i
$356$	1.41906	+	1.77944i	0.0752100	+	0.0943104i
$357$		0			0
$358$	−4.70760	+	5.90314i	−0.248804	+	0.311991i
$359$	−1.41020	−	18.8178i	−0.0744275	−	0.993166i	−0.901980	−	0.431778i	$-0.857886\pi$
$359$	−1.41020	−	18.8178i	−0.0744275	−	0.993166i	0.827553	−	0.561388i	$-0.189733\pi$
$360$		0			0
$361$	−21.8212	+	37.7955i	−1.14849	+	1.98924i
$362$	−0.860615	−	1.49063i	−0.0452329	−	0.0783458i
$363$		0			0
$364$	5.61785	+	16.0795i	0.294455	+	0.842794i
$365$	2.75116	−	12.0536i	0.144002	−	0.630915i
$366$		0			0
$367$	4.04572	+	10.3083i	0.211185	+	0.538090i	0.996738	−	0.0807041i	$-0.0257169\pi$
$367$	4.04572	+	10.3083i	0.211185	+	0.538090i	−0.785553	+	0.618794i	$0.787622\pi$
$368$	−0.0252378	−	0.0643048i	−0.00131561	−	0.00335212i
$369$		0			0
$370$	0.308930	−	1.35351i	0.0160605	−	0.0703657i
$371$	19.9307	+	6.98473i	1.03475	+	0.362629i
$372$		0			0
$373$	−5.19359	−	8.99556i	−0.268914	−	0.465772i	0.699668	−	0.714468i	$-0.253331\pi$
$373$	−5.19359	−	8.99556i	−0.268914	−	0.465772i	−0.968582	+	0.248696i	$0.919998\pi$
$374$	0.355166	−	0.615165i	0.0183652	−	0.0318094i
$375$		0			0
$376$	−2.19352	−	29.2706i	−0.113122	−	1.50951i
$377$	−16.0183	+	20.0864i	−0.824987	+	1.03450i
$378$		0			0
$379$	18.9635	+	23.7795i	0.974092	+	1.22147i	0.975167	+	0.221473i	$0.0710864\pi$
$379$	18.9635	+	23.7795i	0.974092	+	1.22147i	−0.00107485	+	0.999999i	$0.500342\pi$
$380$	−24.0455	+	22.3110i	−1.23351	+	1.14453i
$381$		0			0
$382$	10.2453	−	6.98513i	0.524195	−	0.357390i
$383$	−12.9662	−	1.95435i	−0.662544	−	0.0998624i	−0.190842	−	0.981621i	$-0.561122\pi$
$383$	−12.9662	−	1.95435i	−0.662544	−	0.0998624i	−0.471701	+	0.881758i	$0.656360\pi$
$384$		0			0
$385$	24.2603	+	0.919343i	1.23642	+	0.0468540i
$386$	5.59034	+	2.69217i	0.284541	+	0.137028i
$387$		0			0
$388$	−6.13833	−	5.69554i	−0.311627	−	0.289147i
$389$	−2.16511	+	28.8914i	−0.109776	+	1.46485i	0.621844	+	0.783141i	$0.286384\pi$
$389$	−2.16511	+	28.8914i	−0.109776	+	1.46485i	−0.731620	+	0.681713i	$0.761235\pi$
$390$		0			0
$391$	0.714127			0.0361150
$392$	−5.84084	+	18.8716i	−0.295007	+	0.953160i
$393$		0			0
$394$	6.84535	−	17.4417i	0.344864	−	0.878699i
$395$	1.39670	−	18.6377i	0.0702756	−	0.937763i
$396$		0			0
$397$	−12.2597	−	8.35850i	−0.615295	−	0.419501i	0.215166	−	0.976577i	$-0.430971\pi$
$397$	−12.2597	−	8.35850i	−0.615295	−	0.419501i	−0.830461	+	0.557076i	$0.811923\pi$
$398$	10.4311	+	5.02336i	0.522865	+	0.251798i
$399$		0			0
$400$	−0.158407	+	0.0762846i	−0.00792033	+	0.00381423i
$401$	−14.6444	−	2.20728i	−0.731305	−	0.110227i	−0.227175	−	0.973854i	$-0.572949\pi$
$401$	−14.6444	−	2.20728i	−0.731305	−	0.110227i	−0.504131	+	0.863627i	$0.668187\pi$
$402$		0			0
$403$	42.1755	−	6.35694i	2.10091	−	0.316662i
$404$	1.23284	−	1.14391i	0.0613363	−	0.0569118i
$405$		0			0
$406$	−11.0304	+	2.94994i	−0.547428	+	0.146403i
$407$	0.820210	−	1.02851i	0.0406563	−	0.0509814i
$408$		0			0
$409$	−15.1637	−	4.67737i	−0.749794	−	0.231281i	−0.103774	−	0.994601i	$-0.533092\pi$
$409$	−15.1637	−	4.67737i	−0.749794	−	0.231281i	−0.646021	+	0.763320i	$0.723568\pi$
$410$	−4.38579	+	7.59642i	−0.216599	+	0.375160i
$411$		0			0
$412$	4.19799	+	18.3926i	0.206820	+	0.906137i
$413$	−15.5973	+	24.7966i	−0.767491	+	1.22016i
$414$		0			0
$415$	44.1862	−	13.6296i	2.16902	−	0.669053i
$416$	10.7316	+	27.3437i	0.526161	+	1.34064i
$417$		0			0
$418$	18.1083	−	5.58567i	0.885707	−	0.273204i
$419$	1.32847	−	5.82040i	0.0649000	−	0.284345i	−0.932056	−	0.362315i	$-0.881987\pi$
$419$	1.32847	−	5.82040i	0.0649000	−	0.284345i	0.996956	+	0.0779695i	$0.0248437\pi$
$420$		0			0
$421$	0.687361	+	3.01153i	0.0334999	+	0.146773i	0.988912	−	0.148503i	$-0.0474455\pi$
$421$	0.687361	+	3.01153i	0.0334999	+	0.146773i	−0.955412	+	0.295276i	$0.904588\pi$
$422$	4.69391	+	8.13009i	0.228496	+	0.395766i
$423$		0			0
$424$	21.5262	+	6.63995i	1.04540	+	0.322464i
$425$	−0.135826	−	1.81247i	−0.00658851	−	0.0879176i
$426$		0			0
$427$	−0.558524	+	1.27849i	−0.0270289	+	0.0618703i
$428$	6.15660	+	7.72013i	0.297590	+	0.373167i
$429$		0			0
$430$	7.84910	−	1.18306i	0.378517	−	0.0570523i
$431$	26.6524	−	18.1713i	1.28380	−	0.875282i	0.287219	−	0.957865i	$-0.407269\pi$
$431$	26.6524	−	18.1713i	1.28380	−	0.875282i	0.996584	+	0.0825831i	$0.0263170\pi$
$432$		0			0
$433$	−2.58507	+	1.24490i	−0.124230	+	0.0598262i	−0.494967	−	0.868912i	$-0.664820\pi$
$433$	−2.58507	+	1.24490i	−0.124230	+	0.0598262i	0.370736	+	0.928738i	$0.379105\pi$
$434$	16.7549	+	8.86543i	0.804259	+	0.425554i
$435$		0			0
$436$	−6.64121	−	4.52790i	−0.318056	−	0.216847i
$437$	13.9657	+	12.9583i	0.668071	+	0.619880i
$438$		0			0
$439$	−6.58025	+	16.7662i	−0.314058	+	0.800207i	0.683473	+	0.729976i	$0.260469\pi$
$439$	−6.58025	+	16.7662i	−0.314058	+	0.800207i	−0.997531	+	0.0702307i	$0.977626\pi$
$440$	25.8961			1.23455
$441$		0			0
$442$	−1.33790			−0.0636374
$443$	−1.60719	+	4.09505i	−0.0763598	+	0.194562i	−0.963957	−	0.266060i	$-0.914278\pi$
$443$	−1.60719	+	4.09505i	−0.0763598	+	0.194562i	0.887597	+	0.460621i	$0.152373\pi$
$444$		0			0
$445$	−4.47915	−	4.15604i	−0.212332	−	0.197015i
$446$	6.86912	+	4.68329i	0.325262	+	0.221760i
$447$		0			0
$448$	−3.34547	+	12.4617i	−0.158059	+	0.588759i
$449$	−14.0851	+	6.78301i	−0.664716	+	0.320110i	−0.735641	−	0.677371i	$-0.763119\pi$
$449$	−14.0851	+	6.78301i	−0.664716	+	0.320110i	0.0709256	+	0.997482i	$0.477405\pi$
$450$		0			0
$451$	−6.86736	+	4.68209i	−0.323371	+	0.220471i
$452$	11.4794	−	1.73024i	0.539946	−	0.0813838i
$453$		0			0
$454$	2.28365	+	2.86360i	0.107177	+	0.134395i
$455$	−21.3474	−	40.4380i	−1.00078	−	1.89576i
$456$		0			0
$457$	−1.07356	−	14.3257i	−0.0502190	−	0.670127i	−0.964337	−	0.264678i	$-0.914734\pi$
$457$	−1.07356	−	14.3257i	−0.0502190	−	0.670127i	0.914118	−	0.405449i	$-0.132885\pi$
$458$	14.0041	+	4.31970i	0.654370	+	0.201846i
$459$		0			0
$460$	4.98804	+	8.63953i	0.232568	+	0.402820i
$461$	−0.413022	−	1.80957i	−0.0192364	−	0.0842800i	0.964399	−	0.264453i	$-0.0851914\pi$
$461$	−0.413022	−	1.80957i	−0.0192364	−	0.0842800i	−0.983635	+	0.180173i	$0.942334\pi$
$462$		0			0
$463$	2.00586	−	8.78826i	0.0932203	−	0.408425i	−0.906690	−	0.421797i	$-0.861399\pi$
$463$	2.00586	−	8.78826i	0.0932203	−	0.408425i	0.999911	+	0.0133722i	$0.00425662\pi$
$464$	0.135977	−	0.0419434i	0.00631258	−	0.00194717i
$465$		0			0
$466$	6.23607	+	15.8893i	0.288881	+	0.736056i
$467$	−8.85032	+	2.72996i	−0.409544	+	0.126328i	−0.492680	−	0.870211i	$-0.663983\pi$
$467$	−8.85032	+	2.72996i	−0.409544	+	0.126328i	0.0831358	+	0.996538i	$0.473506\pi$
$468$		0			0
$469$	1.63955	−	14.4893i	0.0757074	−	0.669054i
$470$	6.71921	+	29.4388i	0.309934	+	1.35791i
$471$		0			0
$472$	−15.6234	+	27.0606i	−0.719127	+	1.24557i
$473$	7.18733	+	2.21700i	0.330474	+	0.101938i
$474$		0			0
$475$	30.2322	−	37.9099i	1.38715	−	1.73943i
$476$	0.784412	+	0.579500i	0.0359535	+	0.0265614i
$477$		0			0
$478$	−3.72953	+	3.46050i	−0.170585	+	0.158280i
$479$	−9.01221	+	1.35837i	−0.411779	+	0.0620656i	−0.351665	−	0.936126i	$-0.614384\pi$
$479$	−9.01221	+	1.35837i	−0.411779	+	0.0620656i	−0.0601135	+	0.998192i	$0.519146\pi$
$480$		0			0
$481$	−2.45008	−	0.369290i	−0.111714	−	0.0168382i
$482$	−12.5563	+	6.04678i	−0.571923	+	0.275423i
$483$		0			0
$484$	−3.84225	−	1.85033i	−0.174648	−	0.0841058i
$485$	18.5742	+	12.6637i	0.843412	+	0.575028i
$486$		0			0
$487$	−0.251574	+	3.35702i	−0.0113999	+	0.152121i	0.988599	+	0.150573i	$0.0481118\pi$
$487$	−0.251574	+	3.35702i	−0.0113999	+	0.152121i	−0.999999	+	0.00154808i	$0.999507\pi$
$488$	−0.543687	+	1.38529i	−0.0246116	+	0.0627093i
$489$		0			0
$490$	3.04805	−	20.0925i	0.137697	−	0.907684i
$491$	−4.91287			−0.221715			−0.110857	−	0.993836i	$-0.535360\pi$
$491$	−4.91287			−0.221715			−0.110857	+	0.993836i	$0.535360\pi$
$492$		0			0
$493$	−0.109931	+	1.46693i	−0.00495105	+	0.0660671i
$494$	−26.1645	−	24.2771i	−1.17720	−	1.09228i
$495$		0			0
$496$	−0.212845	−	0.102501i	−0.00955700	−	0.00460241i
$497$	1.31236	+	6.95416i	0.0588675	+	0.311937i
$498$		0			0
$499$	21.1856	+	3.19321i	0.948396	+	0.142948i	0.604984	−	0.796237i	$-0.293179\pi$
$499$	21.1856	+	3.19321i	0.948396	+	0.142948i	0.343411	+	0.939185i	$0.388418\pi$
$500$	3.85712	−	2.62974i	0.172496	−	0.117606i
$501$		0			0
$502$	12.4931	−	11.5919i	0.557592	−	0.517370i
$503$	12.5492	+	15.7362i	0.559543	+	0.701645i	0.978473	−	0.206374i	$-0.0661663\pi$
$503$	12.5492	+	15.7362i	0.559543	+	0.701645i	−0.418930	+	0.908018i	$0.637595\pi$
$504$		0			0
$505$	−2.81509	+	3.53001i	−0.125270	+	0.157083i
$506$	−0.430695	−	5.74722i	−0.0191467	−	0.255495i
$507$		0			0
$508$	12.6232	−	21.8640i	0.560063	−	0.970058i
$509$	−6.27506	−	10.8687i	−0.278137	−	0.481748i	0.692785	−	0.721145i	$-0.256384\pi$
$509$	−6.27506	−	10.8687i	−0.278137	−	0.481748i	−0.970922	+	0.239397i	$0.923050\pi$
$510$		0			0
$511$	−6.93097	−	6.93759i	−0.306608	−	0.306901i
$512$	0.0722477	−	0.316538i	0.00319293	−	0.0139891i
$513$		0			0
$514$	5.46101	+	13.9144i	0.240875	+	0.613739i
$515$	−18.5037	−	47.1466i	−0.815369	−	2.07753i
$516$		0			0
$517$	−6.36685	+	27.8950i	−0.280014	+	1.22682i
$518$	−0.778286	−	0.779029i	−0.0341959	−	0.0342285i
$519$		0			0
$520$	−24.3875	−	42.2403i	−1.06946	−	1.85236i
$521$	−13.2783	+	22.9988i	−0.581734	+	1.00759i	0.413539	+	0.910486i	$0.364292\pi$
$521$	−13.2783	+	22.9988i	−0.581734	+	1.00759i	−0.995274	+	0.0971075i	$0.969041\pi$
$522$		0			0
$523$	1.56712	+	20.9118i	0.0685255	+	0.914409i	0.920479	+	0.390792i	$0.127799\pi$
$523$	1.56712	+	20.9118i	0.0685255	+	0.914409i	−0.851954	+	0.523617i	$0.824582\pi$
$524$	10.6590	−	13.3659i	0.465639	−	0.583893i
$525$		0			0
$526$	3.73169	+	4.67940i	0.162710	+	0.204031i
$527$	1.79024	−	1.66110i	0.0779839	−	0.0723585i
$528$		0			0
$529$	−14.2162	+	9.69241i	−0.618094	+	0.421409i
$530$	−22.9153	−	3.45393i	−0.995377	−	0.150029i
$531$		0			0
$532$	4.82483	+	25.5666i	0.209183	+	1.10845i
$533$	14.1045	+	6.79236i	0.610933	+	0.294210i
$534$		0			0
$535$	−19.4328	−	18.0310i	−0.840153	−	0.779548i
$536$	1.16234	−	15.5103i	0.0502053	−	0.669943i
$537$		0			0
$538$	−24.4002			−1.05197
$539$	10.8628	−	15.9002i	0.467894	−	0.684870i
$540$		0			0
$541$	11.1375	−	28.3778i	0.478837	−	1.22006i	−0.463711	−	0.885986i	$-0.653483\pi$
$541$	11.1375	−	28.3778i	0.478837	−	1.22006i	0.942548	−	0.334070i	$-0.108422\pi$
$542$	−0.991051	+	13.2247i	−0.0425693	+	0.568048i
$543$		0			0
$544$	1.38966	+	0.947456i	0.0595813	+	0.0406218i
$545$	19.4420	+	9.36277i	0.832804	+	0.401057i
$546$		0			0
$547$	−5.38658	+	2.59404i	−0.230313	+	0.110913i	−0.545482	−	0.838123i	$-0.683653\pi$
$547$	−5.38658	+	2.59404i	−0.230313	+	0.110913i	0.315168	+	0.949036i	$0.397939\pi$
$548$	−20.5234	−	3.09341i	−0.876716	−	0.132144i
$549$		0			0
$550$	−14.5046	+	2.18622i	−0.618480	+	0.0932208i
$551$	−28.7682	+	26.6930i	−1.22557	+	1.13716i
$552$		0			0
$553$	−11.9235	−	8.80876i	−0.507041	−	0.374587i
$554$	13.2171	−	16.5737i	0.561541	−	0.704150i
$555$		0			0
$556$	−6.23479	−	1.92318i	−0.264414	−	0.0815609i
$557$	−14.5723	+	25.2400i	−0.617448	+	1.06945i	0.372501	+	0.928032i	$0.378500\pi$
$557$	−14.5723	+	25.2400i	−0.617448	+	1.06945i	−0.989950	+	0.141420i	$0.954833\pi$
$558$		0			0
$559$	−3.15237	−	13.8114i	−0.133331	−	0.584162i
$560$	−0.0284773	+	0.251665i	−0.00120339	+	0.0106348i
$561$		0			0
$562$	−3.79637	+	1.17103i	−0.160140	+	0.0493967i
$563$	−14.1102	−	35.9521i	−0.594672	−	1.51520i	−0.838232	−	0.545314i	$-0.816411\pi$
$563$	−14.1102	−	35.9521i	−0.594672	−	1.51520i	0.243560	−	0.969886i	$-0.421685\pi$
$564$		0			0
$565$	−29.7818	+	9.18647i	−1.25293	+	0.386478i
$566$	−0.426716	+	1.86956i	−0.0179362	+	0.0785836i
$567$		0			0
$568$	1.67973	+	7.35939i	0.0704800	+	0.308793i
$569$	−20.8729	−	36.1528i	−0.875036	−	1.51561i	−0.856725	−	0.515774i	$-0.827505\pi$
$569$	−20.8729	−	36.1528i	−0.875036	−	1.51561i	−0.0183107	−	0.999832i	$-0.505829\pi$
$570$		0			0
$571$	−4.92240	−	1.51836i	−0.205996	−	0.0635413i	0.190040	−	0.981776i	$-0.439138\pi$
$571$	−4.92240	−	1.51836i	−0.205996	−	0.0635413i	−0.396036	+	0.918235i	$0.629614\pi$
$572$	−1.32346	−	17.6603i	−0.0553365	−	0.738414i
$573$		0			0
$574$	3.24806	+	6.15274i	0.135572	+	0.256810i
$575$	−9.19452	−	11.5296i	−0.383438	−	0.480816i
$576$		0			0
$577$	−39.8177	+	6.00156i	−1.65763	+	0.249848i	−0.910104	−	0.414381i	$-0.863998\pi$
$577$	−39.8177	+	6.00156i	−1.65763	+	0.249848i	−0.747530	+	0.664229i	$0.768760\pi$
$578$	12.1618	−	8.29178i	0.505865	−	0.344893i
$579$		0			0
$580$	−18.5148	+	8.91625i	−0.768785	+	0.370227i
$581$	9.50962	−	35.4228i	0.394526	−	1.46959i
$582$		0			0
$583$	−18.1433	−	12.3699i	−0.751417	−	0.512307i
$584$	−7.66791	−	7.11478i	−0.317300	−	0.294412i
$585$		0			0
$586$	−4.85174	+	12.3620i	−0.200424	+	0.510671i
$587$	20.3219			0.838776			0.419388	−	0.907807i	$-0.362245\pi$
$587$	20.3219			0.838776			0.419388	+	0.907807i	$0.362245\pi$
$588$		0			0
$589$	65.1522			2.68455
$590$	11.7437	−	29.9225i	0.483481	−	1.23189i
$591$		0			0
$592$	0.0100602	+	0.00933452i	0.000413472	+	0.000383646i
$593$	−15.8001	−	10.7723i	−0.648833	−	0.442367i	0.193664	−	0.981068i	$-0.437963\pi$
$593$	−15.8001	−	10.7723i	−0.648833	−	0.442367i	−0.842497	+	0.538701i	$0.818915\pi$
$594$		0			0
$595$	−2.31423	−	1.22452i	−0.0948743	−	0.0502004i
$596$	−13.4746	+	6.48901i	−0.551940	+	0.265800i
$597$		0			0
$598$	−8.96897	+	6.11494i	−0.366768	+	0.250058i
$599$	22.2744	−	3.35733i	0.910108	−	0.137177i	0.322732	−	0.946491i	$-0.395399\pi$
$599$	22.2744	−	3.35733i	0.910108	−	0.137177i	0.587376	+	0.809314i	$0.300161\pi$
$600$		0			0
$601$	18.0310	+	22.6101i	0.735498	+	0.922286i	0.999103	−	0.0423451i	$-0.0134829\pi$
$601$	18.0310	+	22.6101i	0.735498	+	0.922286i	−0.263605	+	0.964631i	$0.584911\pi$
$602$	2.52050	−	5.76954i	0.102728	−	0.235149i
$603$		0			0
$604$	0.358356	+	4.78193i	0.0145813	+	0.194574i
$605$	10.9403	+	3.37463i	0.444786	+	0.137198i
$606$		0			0
$607$	11.0117	+	19.0729i	0.446952	+	0.774144i	0.998186	−	0.0602072i	$-0.0191761\pi$
$607$	11.0117	+	19.0729i	0.446952	+	0.774144i	−0.551234	+	0.834351i	$0.685843\pi$
$608$	9.98454	+	43.7451i	0.404927	+	1.77410i
$609$		0			0
$610$	0.340661	−	1.49253i	0.0137930	−	0.0604309i
$611$	51.4968	−	15.8847i	2.08334	−	0.642625i
$612$		0			0
$613$	−4.58724	−	11.6881i	−0.185277	−	0.472077i	0.807812	−	0.589440i	$-0.200651\pi$
$613$	−4.58724	−	11.6881i	−0.185277	−	0.472077i	−0.993089	+	0.117362i	$0.962556\pi$
$614$	11.4894	−	3.54402i	0.463676	−	0.143025i
$615$		0			0
$616$	10.9364	−	17.3867i	0.440638	−	0.700530i
$617$	6.78871	+	29.7433i	0.273303	+	1.19742i	0.906087	+	0.423091i	$0.139055\pi$
$617$	6.78871	+	29.7433i	0.273303	+	1.19742i	−0.632784	+	0.774328i	$0.718088\pi$
$618$		0			0
$619$	−0.0762256	+	0.132027i	−0.00306376	+	0.00530660i	−0.867553	−	0.497344i	$-0.834309\pi$
$619$	−0.0762256	+	0.132027i	−0.00306376	+	0.00530660i	0.864489	+	0.502651i	$0.167642\pi$
$620$	32.6004	+	10.0559i	1.30926	+	0.403855i
$621$		0			0
$622$	−2.72601	+	3.41830i	−0.109303	+	0.137062i
$623$	−4.68200	+	1.25215i	−0.187580	+	0.0501662i
$624$		0			0
$625$	13.2677	−	12.3106i	0.530707	−	0.492424i
$626$	−12.5676	+	1.89425i	−0.502300	+	0.0757096i
$627$		0			0
$628$	−4.07084	−	0.613580i	−0.162444	−	0.0244845i
$629$	−0.127822	+	0.0615558i	−0.00509659	+	0.00245439i
$630$		0			0
$631$	14.4690	+	6.96792i	0.576003	+	0.277388i	0.699121	−	0.715004i	$-0.253575\pi$
$631$	14.4690	+	6.96792i	0.576003	+	0.277388i	−0.123118	+	0.992392i	$0.539289\pi$
$632$	−13.0650	−	8.90760i	−0.519700	−	0.354325i
$633$		0			0
$634$	0.438728	−	5.85442i	0.0174241	−	0.232509i
$635$	−24.7620	+	63.0927i	−0.982652	+	2.50376i
$636$		0			0
$637$	−36.1656	−	2.74493i	−1.43293	−	0.108758i
$638$	11.8720			0.470017
$639$		0			0
$640$	−1.76829	+	23.5961i	−0.0698977	+	0.932720i
$641$	−29.4640	−	27.3386i	−1.16376	−	1.07981i	−0.995567	−	0.0940562i	$-0.970017\pi$
$641$	−29.4640	−	27.3386i	−1.16376	−	1.07981i	−0.168192	−	0.985754i	$-0.553793\pi$
$642$		0			0
$643$	−12.5702	−	6.05350i	−0.495722	−	0.238727i	0.169281	−	0.985568i	$-0.445855\pi$
$643$	−12.5702	−	6.05350i	−0.495722	−	0.238727i	−0.665003	+	0.746841i	$0.731570\pi$
$644$	7.90715	+	0.299641i	0.311585	+	0.0118075i
$645$		0			0
$646$	−2.02086	−	0.304595i	−0.0795096	−	0.0119841i
$647$	−31.6903	+	21.6061i	−1.24588	+	0.849424i	−0.993005	−	0.118076i	$-0.962327\pi$
$647$	−31.6903	+	21.6061i	−1.24588	+	0.849424i	−0.252871	+	0.967500i	$0.581375\pi$
$648$		0			0
$649$	22.3279	−	20.7173i	0.876447	−	0.813224i
$650$	17.2257	+	21.6004i	0.675648	+	0.847236i
$651$		0			0
$652$	17.1178	−	21.4651i	0.670386	−	0.840638i
$653$	1.34437	+	17.9393i	0.0526091	+	0.702020i	0.959689	+	0.281062i	$0.0906868\pi$
$653$	1.34437	+	17.9393i	0.0526091	+	0.702020i	−0.907080	+	0.420957i	$0.861694\pi$
$654$		0			0
$655$	−22.9480	+	39.7471i	−0.896653	+	1.55305i
$656$	−0.0433542	−	0.0750917i	−0.00169270	−	0.00293184i
$657$		0			0
$658$	22.6029	+	7.92121i	0.881155	+	0.308801i
$659$	3.97996	−	17.4373i	0.155037	−	0.679262i	−0.836339	−	0.548213i	$-0.815308\pi$
$659$	3.97996	−	17.4373i	0.155037	−	0.679262i	0.991376	−	0.131049i	$-0.0418345\pi$
$660$		0			0
$661$	2.14253	+	5.45908i	0.0833348	+	0.212334i	0.966467	−	0.256790i	$-0.0826650\pi$
$661$	2.14253	+	5.45908i	0.0833348	+	0.212334i	−0.883132	+	0.469124i	$0.844570\pi$
$662$	−4.44206	−	11.3182i	−0.172645	−	0.439893i
$663$		0			0
$664$	8.70546	−	38.1411i	0.337837	−	1.48016i
$665$	−23.0383	−	65.9404i	−0.893385	−	2.55706i
$666$		0			0
$667$	5.96772	+	10.3364i	0.231071	+	0.400226i
$668$	5.84992	−	10.1324i	0.226340	−	0.392032i
$669$		0			0
$670$	1.19573	+	15.9559i	0.0461950	+	0.616429i
$671$	0.904454	−	1.13415i	0.0349161	−	0.0437834i
$672$		0			0
$673$	−28.4575	−	35.6846i	−1.09696	−	1.37554i	−0.920274	−	0.391273i	$-0.872035\pi$
$673$	−28.4575	−	35.6846i	−1.09696	−	1.37554i	−0.176683	−	0.984268i	$-0.556537\pi$
$674$	−9.57215	+	8.88166i	−0.368706	+	0.342109i
$675$		0			0
$676$	−14.2146	+	9.69138i	−0.546717	+	0.372745i
$677$	−43.3233	−	6.52994i	−1.66505	−	0.250966i	−0.752103	−	0.659045i	$-0.770961\pi$
$677$	−43.3233	−	6.52994i	−1.66505	−	0.250966i	−0.912946	+	0.408079i	$0.866199\pi$
$678$		0			0
$679$	16.3467	−	7.12269i	0.627327	−	0.273344i
$680$	−2.51619	−	1.21173i	−0.0964914	−	0.0464678i
$681$		0			0
$682$	−14.4480	−	13.4058i	−0.553244	−	0.513335i
$683$	−2.51971	+	33.6232i	−0.0964142	+	1.28656i	0.713769	+	0.700381i	$0.246987\pi$
$683$	−2.51971	+	33.6232i	−0.0964142	+	1.28656i	−0.810183	+	0.586177i	$0.800632\pi$
$684$		0			0
$685$	55.7207			2.12898
$686$	−12.2029	−	10.5319i	−0.465909	−	0.402108i
$687$		0			0
$688$	−0.0286668	+	0.0730418i	−0.00109291	+	0.00278469i
$689$	−3.09078	+	41.2436i	−0.117749	+	1.57126i
$690$		0			0
$691$	−32.8960	−	22.4281i	−1.25142	−	0.853205i	−0.257826	−	0.966191i	$-0.583006\pi$
$691$	−32.8960	−	22.4281i	−1.25142	−	0.853205i	−0.993597	+	0.112986i	$0.963958\pi$
$692$	4.25988	+	2.05145i	0.161936	+	0.0779845i
$693$		0			0
$694$	−6.48373	+	3.12240i	−0.246119	+	0.118525i
$695$	17.3208	+	2.61070i	0.657017	+	0.0990294i
$696$		0			0
$697$	0.886351	−	0.133596i	0.0335729	−	0.00506031i
$698$	17.0777	−	15.8458i	0.646401	−	0.599773i
$699$		0			0
$700$	−0.743431	−	20.1255i	−0.0280990	−	0.760672i
$701$	−12.2622	+	15.3763i	−0.463138	+	0.580757i	−0.957476	−	0.288513i	$-0.906839\pi$
$701$	−12.2622	+	15.3763i	−0.463138	+	0.580757i	0.494338	+	0.869270i	$0.335411\pi$
$702$		0			0
$703$	−3.61670	−	1.11560i	−0.136406	−	0.0420758i
$704$	6.70797	−	11.6185i	0.252816	−	0.437890i
$705$		0			0
$706$	4.99049	+	21.8648i	0.187820	+	0.822891i
$707$	1.18120	+	3.38084i	0.0444236	+	0.127150i
$708$		0			0
$709$	8.03074	−	2.47715i	0.301601	−	0.0930315i	−0.140261	−	0.990115i	$-0.544794\pi$
$709$	8.03074	−	2.47715i	0.301601	−	0.0930315i	0.441862	+	0.897083i	$0.354318\pi$
$710$	−2.83706	−	7.22871i	−0.106473	−	0.271289i
$711$		0			0
$712$	−4.93994	+	1.52377i	−0.185132	+	0.0571057i
$713$	4.40920	−	19.3180i	0.165126	−	0.723463i
$714$		0			0
$715$	10.5797	+	46.3528i	0.395659	+	1.73350i
$716$	5.38927	+	9.33448i	0.201406	+	0.348846i
$717$		0			0
$718$	15.6945	+	4.84111i	0.585713	+	0.180669i
$719$	0.242531	+	3.23635i	0.00904488	+	0.120696i	0.999899	−	0.0142454i	$-0.00453459\pi$
$719$	0.242531	+	3.23635i	0.00904488	+	0.120696i	−0.990854	+	0.134941i	$0.956916\pi$
$720$		0			0
$721$	−39.4688	−	7.48740i	−1.46989	−	0.278845i
$722$	−23.6830	−	29.6976i	−0.881391	−	1.10523i
$723$		0			0
$724$	−2.42969	+	0.366217i	−0.0902987	+	0.0136103i
$725$	25.0989	−	17.1121i	0.932150	−	0.635529i
$726$		0			0
$727$	27.9970	−	13.4826i	1.03835	−	0.500043i	0.164570	−	0.986365i	$-0.447376\pi$
$727$	27.9970	−	13.4826i	1.03835	−	0.500043i	0.873779	+	0.486322i	$0.161662\pi$
$728$	−38.6596	−	1.46500i	−1.43282	−	0.0542966i
$729$		0			0
$730$	8.89096	+	6.06175i	0.329069	+	0.224356i
$731$	−0.594618	−	0.551725i	−0.0219927	−	0.0204063i
$732$		0			0
$733$	2.99391	−	7.62837i	0.110583	−	0.281760i	−0.864860	−	0.502013i	$-0.832593\pi$
$733$	2.99391	−	7.62837i	0.110583	−	0.281760i	0.975443	+	0.220253i	$0.0706882\pi$
$734$	−9.63818			−0.355752
$735$		0			0
$736$	13.6464			0.503012
$737$	−5.53912	+	14.1135i	−0.204036	+	0.519876i
$738$		0			0
$739$	30.4769	+	28.2784i	1.12111	+	1.04024i	0.998860	+	0.0477380i	$0.0152013\pi$
$739$	30.4769	+	28.2784i	1.12111	+	1.04024i	0.122249	+	0.992499i	$0.460989\pi$
$740$	−1.63751	−	1.11644i	−0.0601962	−	0.0410411i
$741$		0			0
$742$	−11.9965	+	13.9268i	−0.440406	+	0.511267i
$743$	21.5904	−	10.3974i	0.792074	−	0.381443i	0.00631879	−	0.999980i	$-0.497989\pi$
$743$	21.5904	−	10.3974i	0.792074	−	0.381443i	0.785756	+	0.618537i	$0.212274\pi$
$744$		0			0
$745$	33.1742	−	22.6178i	1.21541	−	0.828651i
$746$	8.93959	−	1.34743i	0.327302	−	0.0493328i
$747$		0			0
$748$	−0.632237	−	0.792800i	−0.0231169	−	0.0289877i
$749$	−20.3129	+	5.43244i	−0.742217	+	0.198497i
$750$		0			0
$751$	2.78963	+	37.2250i	0.101795	+	1.35836i	0.781056	+	0.624461i	$0.214681\pi$
$751$	2.78963	+	37.2250i	0.101795	+	1.35836i	−0.679261	+	0.733897i	$0.737700\pi$
$752$	−0.285229	−	0.0879816i	−0.0104012	−	0.00320836i
$753$		0			0
$754$	−11.1804	−	19.3650i	−0.407165	−	0.705231i
$755$	−2.86470	−	12.5511i	−0.104257	−	0.456780i
$756$		0			0
$757$	3.26401	−	14.3006i	0.118633	−	0.519763i	−0.880336	−	0.474351i	$-0.842683\pi$
$757$	3.26401	−	14.3006i	0.118633	−	0.519763i	0.998968	−	0.0454121i	$-0.0144601\pi$
$758$	−25.2960	+	7.80279i	−0.918793	+	0.283410i
$759$		0			0
$760$	−27.2198	−	69.3550i	−0.987367	−	2.51577i
$761$	29.1472	−	8.99071i	1.05658	−	0.325913i	0.282679	−	0.959215i	$-0.408777\pi$
$761$	29.1472	−	8.99071i	1.05658	−	0.325913i	0.773905	+	0.633301i	$0.218301\pi$
$762$		0			0
$763$	14.4969	−	9.09936i	0.524823	−	0.329419i
$764$	−3.93894	−	17.2576i	−0.142506	−	0.624360i
$765$		0			0
$766$	5.70637	−	9.88373i	0.206180	−	0.357114i
$767$	−54.8201	−	16.9098i	−1.97944	−	0.610577i
$768$		0			0
$769$	−28.9202	+	36.2648i	−1.04289	+	1.30774i	−0.0928259	+	0.995682i	$0.529590\pi$
$769$	−28.9202	+	36.2648i	−1.04289	+	1.30774i	−0.950063	+	0.312059i	$0.898981\pi$
$770$	−8.45908	+	19.3632i	−0.304844	+	0.697802i
$771$		0			0
$772$	6.49311	−	6.02473i	0.233692	−	0.216835i
$773$	26.4570	−	3.98775i	0.951593	−	0.143430i	0.345142	−	0.938551i	$-0.387831\pi$
$773$	26.4570	−	3.98775i	0.951593	−	0.143430i	0.606451	+	0.795121i	$0.292593\pi$
$774$		0			0
$775$	−49.8680	−	7.51638i	−1.79131	−	0.269996i
$776$	17.1361	−	8.25232i	0.615151	−	0.296241i
$777$		0			0
$778$	−22.7192	−	10.9410i	−0.814523	−	0.392254i
$779$	19.7580	+	13.4708i	0.707903	+	0.482640i
$780$		0			0
$781$	0.549884	−	7.33770i	0.0196764	−	0.262563i
$782$	−0.227076	+	0.578581i	−0.00812024	+	0.0206900i
$783$		0			0
$784$	0.156942	+	0.125402i	0.00560507	+	0.00447865i
$785$	11.0523			0.394472
$786$		0			0
$787$	−0.680630	+	9.08238i	−0.0242618	+	0.323752i	0.971847	+	0.235615i	$0.0757104\pi$
$787$	−0.680630	+	9.08238i	−0.0242618	+	0.323752i	−0.996108	+	0.0881370i	$0.971909\pi$
$788$	−19.6075	−	18.1931i	−0.698488	−	0.648102i
$789$		0			0
$790$	14.6560	+	7.05796i	0.521437	+	0.251111i
$791$	−6.40955	+	23.8752i	−0.227897	+	0.848904i
$792$		0			0
$793$	−2.70173	−	0.407221i	−0.0959413	−	0.0144608i
$794$	10.6703	−	7.27489i	0.378675	−	0.258176i
$795$		0			0
$796$	12.1156	−	11.2417i	0.429427	−	0.398450i
$797$	−25.4860	−	31.9584i	−0.902759	−	1.13202i	−0.990723	−	0.135900i	$-0.956607\pi$
$797$	−25.4860	−	31.9584i	−0.902759	−	1.13202i	0.0879636	−	0.996124i	$-0.471964\pi$
$798$		0			0
$799$	1.92390	−	2.41249i	0.0680627	−	0.0853479i
$800$	−2.59551	−	34.6347i	−0.0917653	−	1.22452i
$801$		0			0
$802$	6.44491	−	11.1629i	0.227578	−	0.394176i
$803$	5.09822	+	8.83038i	0.179912	+	0.311617i
$804$		0			0
$805$	−21.1108	+	2.36842i	−0.744058	+	0.0834758i
$806$	−8.26053	+	36.1917i	−0.290965	+	1.27480i
$807$		0			0
$808$	1.39559	+	3.55591i	0.0490968	+	0.125097i
$809$	12.2918	+	31.3189i	0.432155	+	1.10111i	0.966686	+	0.255965i	$0.0823931\pi$
$809$	12.2918	+	31.3189i	0.432155	+	1.10111i	−0.534531	+	0.845149i	$0.679512\pi$
$810$		0			0
$811$	1.48085	−	6.48804i	0.0519998	−	0.227826i	−0.942250	−	0.334910i	$-0.891294\pi$
$811$	1.48085	−	6.48804i	0.0519998	−	0.227826i	0.994250	+	0.107084i	$0.0341513\pi$
$812$	−1.83272	+	16.1964i	−0.0643157	+	0.568382i
$813$		0			0
$814$	0.572485	+	0.991572i	0.0200656	+	0.0347546i
$815$	−36.8535	+	63.8321i	−1.29092	+	2.23594i
$816$		0			0
$817$	−1.61716	−	21.5795i	−0.0565772	−	0.754970i
$818$	8.61128	−	10.7982i	0.301086	−	0.377550i
$819$		0			0
$820$	7.80724	+	9.78996i	0.272641	+	0.341880i
$821$	36.5409	−	33.9050i	1.27528	−	1.18329i	0.302097	−	0.953277i	$-0.402313\pi$
$821$	36.5409	−	33.9050i	1.27528	−	1.18329i	0.973187	−	0.230014i	$-0.0738773\pi$
$822$		0			0
$823$	8.29521	−	5.65558i	0.289153	−	0.197141i	−0.410053	−	0.912062i	$-0.634490\pi$
$823$	8.29521	−	5.65558i	0.289153	−	0.197141i	0.699205	+	0.714921i	$0.253537\pi$
$824$	−42.3720	−	6.38655i	−1.47610	−	0.222486i
$825$		0			0
$826$	−15.1305	−	20.5216i	−0.526457	−	0.714037i
$827$	28.6418	+	13.7931i	0.995972	+	0.479635i	0.859570	−	0.511019i	$-0.170732\pi$
$827$	28.6418	+	13.7931i	0.995972	+	0.479635i	0.136402	+	0.990654i	$0.456446\pi$
$828$		0			0
$829$	35.3677	+	32.8165i	1.22837	+	1.13976i	0.985495	+	0.169706i	$0.0542818\pi$
$829$	35.3677	+	32.8165i	1.22837	+	1.13976i	0.242878	+	0.970057i	$0.421909\pi$
$830$	−3.00758	+	40.1333i	−0.104395	+	1.39305i
$831$		0			0
$832$	−25.2688			−0.876037
$833$	−1.79949	+	1.03665i	−0.0623485	+	0.0359177i
$834$		0			0
$835$	−11.4754	+	29.2388i	−0.397122	+	1.01185i
$836$	2.02162	−	26.9766i	0.0699192	−	0.933007i
$837$		0			0
$838$	4.29323	+	2.92708i	0.148307	+	0.101114i
$839$	−37.5183	−	18.0679i	−1.29528	−	0.623772i	−0.346005	−	0.938233i	$-0.612462\pi$
$839$	−37.5183	−	18.0679i	−1.29528	−	0.623772i	−0.949270	+	0.314461i	$0.898176\pi$
$840$		0			0
$841$	3.97689	−	1.91517i	0.137134	−	0.0660404i
$842$	−2.65849	−	0.400702i	−0.0916175	−	0.0138091i
$843$		0			0
$844$	13.2518	−	1.99739i	0.456147	−	0.0687531i
$845$	33.8575	−	31.4151i	1.16473	−	1.08071i
$846$		0			0
$847$	6.88601	−	5.92018i	0.236606	−	0.203420i
$848$	0.142829	−	0.179102i	0.00490476	−	0.00615038i
$849$		0			0
$850$	1.51164	+	0.466279i	0.0518488	+	0.0159932i
$851$	−0.575544	+	0.996871i	−0.0197294	+	0.0341723i
$852$		0			0
$853$	−6.91045	−	30.2767i	−0.236609	−	1.03665i	−0.944030	−	0.329860i	$-0.892998\pi$
$853$	−6.91045	−	30.2767i	−0.236609	−	1.03665i	0.707420	−	0.706793i	$-0.249859\pi$
$854$	−0.858224	−	0.859043i	−0.0293678	−	0.0293959i
$855$		0			0
$856$	−21.4320	+	6.61089i	−0.732530	+	0.225956i
$857$	18.7442	+	47.7595i	0.640290	+	1.63143i	0.768623	+	0.639702i	$0.220942\pi$
$857$	18.7442	+	47.7595i	0.640290	+	1.63143i	−0.128332	+	0.991731i	$0.540962\pi$
$858$		0			0
$859$	−27.9382	+	8.61780i	−0.953240	+	0.294036i	−0.732093	−	0.681205i	$-0.761456\pi$
$859$	−27.9382	+	8.61780i	−0.953240	+	0.294036i	−0.221147	+	0.975240i	$0.570980\pi$
$860$	2.52150	−	11.0474i	0.0859823	−	0.376713i
$861$		0			0
$862$	6.24742	+	27.3717i	0.212788	+	0.932284i
$863$	−19.3127	−	33.4506i	−0.657412	−	1.13867i	−0.981283	−	0.192570i	$-0.938318\pi$
$863$	−19.3127	−	33.4506i	−0.657412	−	1.13867i	0.323871	−	0.946101i	$-0.395015\pi$
$864$		0			0
$865$	−12.1294	−	3.74144i	−0.412413	−	0.127213i
$866$	−0.186619	−	2.49026i	−0.00634157	−	0.0846223i
$867$		0			0
$868$	20.5193	−	17.6413i	0.696470	−	0.598783i
$869$	9.61040	+	12.0511i	0.326010	+	0.408804i
$870$		0			0
$871$	28.2376	−	4.25613i	0.956794	−	0.144213i
$872$	15.0846	−	10.2845i	0.510830	−	0.348278i
$873$		0			0
$874$	−14.9395	+	7.19450i	−0.505337	+	0.243357i
$875$	1.84344	+	9.76831i	0.0623196	+	0.330229i
$876$		0			0
$877$	25.4201	+	17.3311i	0.858376	+	0.585231i	0.910546	−	0.413407i	$-0.135661\pi$
$877$	25.4201	+	17.3311i	0.858376	+	0.585231i	−0.0521700	+	0.998638i	$0.516614\pi$
$878$	−11.4915	−	10.6626i	−0.387819	−	0.359844i
$879$		0			0
$880$	0.0962090	−	0.245137i	0.00324320	−	0.00826355i
$881$	2.51427			0.0847078			0.0423539	−	0.999103i	$-0.486514\pi$
$881$	2.51427			0.0847078			0.0423539	+	0.999103i	$0.486514\pi$
$882$		0			0
$883$	−20.2465			−0.681350			−0.340675	−	0.940181i	$-0.610656\pi$
$883$	−20.2465			−0.681350			−0.340675	+	0.940181i	$0.610656\pi$
$884$	−0.697770	+	1.77789i	−0.0234685	+	0.0597969i
$885$		0			0
$886$	−2.80673	−	2.60427i	−0.0942940	−	0.0874921i
$887$	40.8856	+	27.8753i	1.37280	+	0.935962i	0.999967	+	0.00806424i	$0.00256695\pi$
$887$	40.8856	+	27.8753i	1.37280	+	0.935962i	0.372836	+	0.927897i	$0.378385\pi$
$888$		0			0
$889$	31.9032	+	43.2705i	1.07000	+	1.45124i
$890$	4.79147	−	2.30745i	0.160610	−	0.0773459i
$891$		0			0
$892$	9.80598	−	6.68560i	0.328328	−	0.223850i
$893$	81.4008	−	12.2692i	2.72397	−	0.410573i
$894$		0			0
$895$	−18.0417	−	22.6236i	−0.603069	−	0.756224i
$896$	15.0958	+	11.1523i	0.504314	+	0.372572i
$897$		0			0
$898$	−1.01682	−	13.5685i	−0.0339316	−	0.452786i
$899$	39.0033	+	12.0309i	1.30083	+	0.401254i
$900$		0			0
$901$	1.18408	+	2.05088i	0.0394473	+	0.0683247i
$902$	−1.60973	−	7.05269i	−0.0535982	−	0.234829i
$903$		0			0
$904$	−5.86753	+	25.7073i	−0.195151	+	0.855014i
$905$	6.30350	−	1.94437i	0.209536	−	0.0646332i
$906$		0			0
$907$	9.56598	+	24.3737i	0.317633	+	0.809316i	0.997135	+	0.0756422i	$0.0241007\pi$
$907$	9.56598	+	24.3737i	0.317633	+	0.809316i	−0.679502	+	0.733674i	$0.737804\pi$
$908$	4.99635	−	1.54117i	0.165810	−	0.0511455i
$909$		0			0
$910$	39.5506	−	4.43718i	1.31109	−	0.147091i
$911$	0.872296	+	3.82178i	0.0289005	+	0.126621i	0.987320	−	0.158741i	$-0.0507434\pi$
$911$	0.872296	+	3.82178i	0.0289005	+	0.126621i	−0.958420	+	0.285362i	$0.907886\pi$
$912$		0			0
$913$	−19.0677	+	33.0261i	−0.631047	+	1.09301i
$914$	11.9479	+	3.68545i	0.395203	+	0.121904i
$915$		0			0
$916$	13.0440	−	16.3567i	0.430986	−	0.540440i
$917$	16.9950	+	32.1933i	0.561224	+	1.06312i
$918$		0			0
$919$	−25.1562	+	23.3416i	−0.829827	+	0.769967i	−0.975648	−	0.219344i	$-0.929608\pi$
$919$	−25.1562	+	23.3416i	−0.829827	+	0.769967i	0.145820	+	0.989311i	$0.453418\pi$
$920$	−22.4062	+	3.37719i	−0.738711	+	0.111343i
$921$		0			0
$922$	1.59743	+	0.240774i	0.0526087	+	0.00792948i
$923$	−12.4867	+	6.01329i	−0.411006	+	0.197930i
$924$		0			0
$925$	2.63955	+	1.27114i	0.0867877	+	0.0417948i
$926$	6.48237	+	4.41961i	0.213024	+	0.145237i
$927$		0			0
$928$	−2.10069	+	28.0318i	−0.0689585	+	0.920188i
$929$	7.33783	−	18.6965i	0.240747	−	0.613412i	−0.758522	−	0.651647i	$-0.774078\pi$
$929$	7.33783	−	18.6965i	0.240747	−	0.613412i	0.999269	+	0.0382350i	$0.0121735\pi$
$930$		0			0
$931$	−54.0021	−	12.3798i	−1.76985	−	0.405732i
$932$	24.3670			0.798169
$933$		0			0
$934$	0.602406	−	8.03855i	0.0197113	−	0.263029i
$935$	1.99561	+	1.85165i	0.0652633	+	0.0605555i
$936$		0			0
$937$	15.9366	+	7.67467i	0.520626	+	0.250720i	0.675692	−	0.737184i	$-0.263845\pi$
$937$	15.9366	+	7.67467i	0.520626	+	0.250720i	−0.155066	+	0.987904i	$0.549559\pi$
$938$	11.2178	+	5.93563i	0.366274	+	0.193805i
$939$		0			0
$940$	42.6245	+	6.42461i	1.39026	+	0.209548i
$941$	−19.5212	+	13.3093i	−0.636374	+	0.433872i	−0.838060	−	0.545578i	$-0.816310\pi$
$941$	−19.5212	+	13.3093i	−0.636374	+	0.433872i	0.201686	+	0.979450i	$0.435358\pi$
$942$		0			0
$943$	5.33128	−	4.94671i	0.173610	−	0.161087i
$944$	0.198116	+	0.248430i	0.00644813	+	0.00808570i
$945$		0			0
$946$	−4.08161	+	5.11817i	−0.132704	+	0.166406i
$947$	2.03688	+	27.1803i	0.0661897	+	0.883240i	0.927179	+	0.374617i	$0.122226\pi$
$947$	2.03688	+	27.1803i	0.0661897	+	0.883240i	−0.860990	+	0.508622i	$0.830155\pi$
$948$		0			0
$949$	9.60245	−	16.6319i	0.311709	−	0.539895i
$950$	21.1012	+	36.5484i	0.684615	+	1.18579i
$951$		0			0
$952$	−1.87619	+	1.17764i	−0.0608077	+	0.0381676i
$953$	−2.67165	+	11.7053i	−0.0865433	+	0.379171i	−0.999588	−	0.0286875i	$-0.990867\pi$
$953$	−2.67165	+	11.7053i	−0.0865433	+	0.379171i	0.913045	+	0.407859i	$0.133724\pi$
$954$		0			0
$955$	17.3619	+	44.2373i	0.561817	+	1.43149i
$956$	2.65343	+	6.76083i	0.0858181	+	0.218661i
$957$		0			0
$958$	1.76514	−	7.73357i	0.0570290	−	0.249860i
$959$	23.5318	−	37.4111i	0.759882	−	1.20807i
$960$		0			0
$961$	−18.3812	−	31.8371i	−0.592941	−	1.02700i
$962$	1.07827	−	1.86762i	0.0347648	−	0.0602143i
$963$		0			0
$964$	1.48674	+	19.8392i	0.0478848	+	0.638979i
$965$	−14.8264	+	18.5918i	−0.477280	+	0.598490i
$966$		0			0
$967$	−31.1323	−	39.0386i	−1.00115	−	1.25540i	−0.966679	−	0.255992i	$-0.917598\pi$
$967$	−31.1323	−	39.0386i	−1.00115	−	1.25540i	−0.0344672	−	0.999406i	$-0.510973\pi$
$968$	7.10063	−	6.58842i	0.228223	−	0.211760i
$969$		0			0
$970$	−16.1662	+	11.0219i	−0.519066	+	0.353893i
$971$	−38.8850	−	5.86097i	−1.24788	−	0.188088i	−0.508314	−	0.861172i	$-0.669731\pi$
$971$	−38.8850	−	5.86097i	−1.24788	−	0.188088i	−0.739566	+	0.673084i	$0.764969\pi$
$972$		0			0
$973$	9.06773	−	10.5267i	0.290698	−	0.337471i
$974$	−2.63984	−	1.27128i	−0.0845859	−	0.0407344i
$975$		0			0
$976$	0.0110935	+	0.0102933i	0.000355095	+	0.000329480i
$977$	1.28472	−	17.1434i	0.0411019	−	0.548467i	−0.938204	−	0.346082i	$-0.887512\pi$
$977$	1.28472	−	17.1434i	0.0411019	−	0.548467i	0.979306	−	0.202385i	$-0.0648692\pi$
$978$		0			0
$979$	5.03924			0.161055
$980$	−25.1105	−	14.5295i	−0.802124	−	0.464127i
$981$		0			0
$982$	1.56218	−	3.98038i	0.0498513	−	0.127019i
$983$	−0.859964	+	11.4754i	−0.0274286	+	0.366009i	0.966553	+	0.256465i	$0.0825580\pi$
$983$	−0.859964	+	11.4754i	−0.0274286	+	0.366009i	−0.993982	+	0.109544i	$0.965061\pi$
$984$		0			0
$985$	59.3311	+	40.4512i	1.89044	+	1.28888i
$986$	−1.15354	−	0.555516i	−0.0367362	−	0.0176912i
$987$		0			0
$988$	−45.9068	+	22.1075i	−1.46049	+	0.703334i
$989$	−6.50786	−	0.980903i	−0.206938	−	0.0311909i
$990$		0			0
$991$	26.6458	−	4.01621i	0.846432	−	0.127579i	0.288514	−	0.957476i	$-0.406839\pi$
$991$	26.6458	−	4.01621i	0.846432	−	0.127579i	0.557917	+	0.829896i	$0.311601\pi$
$992$	34.2099	−	31.7421i	1.08616	−	1.00781i
$993$		0			0
$994$	−6.05152	−	1.14800i	−0.191943	−	0.0364123i
$995$	−27.6649	+	34.6907i	−0.877037	+	1.09977i
$996$		0			0
$997$	28.6604	+	8.84055i	0.907683	+	0.279983i	0.713231	−	0.700929i	$-0.247231\pi$
$997$	28.6604	+	8.84055i	0.907683	+	0.279983i	0.194452	+	0.980912i	$0.437707\pi$
$998$	−9.32365	+	16.1490i	−0.295135	+	0.511189i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.46.3		60
3.2	odd	2		147.2.m.b.46.3	yes	60
49.16	even	21	inner	441.2.bb.e.163.3		60
147.53	odd	42		7203.2.a.n.1.18		30
147.65	odd	42		147.2.m.b.16.3	✓	60
147.143	even	42		7203.2.a.m.1.18		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.16.3	✓	60	147.65	odd	42
147.2.m.b.46.3	yes	60	3.2	odd	2
441.2.bb.e.46.3		60	1.1	even	1	trivial
441.2.bb.e.163.3		60	49.16	even	21	inner
7203.2.a.m.1.18		30	147.143	even	42
7203.2.a.n.1.18		30	147.53	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)

\(f(q)\)	\(=\)	\(q+(-0.317978 + 0.810194i) q^{2} +(0.910799 + 0.845098i) q^{4} +(-2.75602 - 1.87902i) q^{5} +(-2.42550 + 1.05686i) q^{7} +(-2.54264 + 1.22447i) q^{8} +O(q^{10})\)	\(q+(-0.317978 + 0.810194i) q^{2} +(0.910799 + 0.845098i) q^{4} +(-2.75602 - 1.87902i) q^{5} +(-2.42550 + 1.05686i) q^{7} +(-2.54264 + 1.22447i) q^{8} +(2.39873 - 1.63543i) q^{10} +(2.72022 - 0.410007i) q^{11} +(-3.23053 - 4.05096i) q^{13} +(-0.0850052 - 2.30118i) q^{14} +(0.00214464 + 0.0286182i) q^{16} +(-0.283495 - 0.0874465i) q^{17} +(-3.95735 - 6.85433i) q^{19} +(-0.922223 - 4.04053i) q^{20} +(-0.532783 + 2.33428i) q^{22} +(-2.30016 + 0.709505i) q^{23} +(2.23822 + 5.70290i) q^{25} +(4.30930 - 1.32924i) q^{26} +(-3.10229 - 1.08720i) q^{28} +(-1.10335 - 4.83411i) q^{29} +(-4.11589 + 7.12894i) q^{31} +(-5.41734 - 1.67103i) q^{32} +(0.160994 - 0.201880i) q^{34} +(8.67060 + 1.64485i) q^{35} +(0.350549 - 0.325262i) q^{37} +(6.81169 - 1.02670i) q^{38} +(9.30838 + 1.40301i) q^{40} +(-2.72215 + 1.31092i) q^{41} +(2.46338 + 1.18630i) q^{43} +(2.82407 + 1.92542i) q^{44} +(0.156563 - 2.08918i) q^{46} +(-3.79989 + 9.68195i) q^{47} +(4.76610 - 5.12682i) q^{49} -5.33216 q^{50} +(0.481092 - 6.41972i) q^{52} +(-5.85144 - 5.42935i) q^{53} +(-8.26739 - 3.98137i) q^{55} +(4.87308 - 5.65716i) q^{56} +(4.26741 + 0.643208i) q^{58} +(9.14824 - 6.23716i) q^{59} +(0.386554 - 0.358670i) q^{61} +(-4.46706 - 5.60152i) q^{62} +(3.04067 - 3.81287i) q^{64} +(1.29157 + 17.2348i) q^{65} +(-2.75569 + 4.77300i) q^{67} +(-0.184306 - 0.319227i) q^{68} +(-4.08970 + 6.50184i) q^{70} +(0.595203 - 2.60776i) q^{71} +(1.35415 + 3.45031i) q^{73} +(0.152059 + 0.387439i) q^{74} +(2.18823 - 9.58727i) q^{76} +(-6.16457 + 3.86935i) q^{77} +(2.80156 + 4.85245i) q^{79} +(0.0478636 - 0.0829023i) q^{80} +(-0.196515 - 2.62231i) q^{82} +(-8.64321 + 10.8382i) q^{83} +(0.617004 + 0.773698i) q^{85} +(-1.74444 + 1.61860i) q^{86} +(-6.41449 + 4.37332i) q^{88} +(1.81136 + 0.273019i) q^{89} +(12.1169 + 6.41138i) q^{91} +(-2.69459 - 1.29764i) q^{92} +(-6.63598 - 6.15729i) q^{94} +(-1.97291 + 26.3267i) q^{95} -6.73950 q^{97} +(2.63820 + 5.49168i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 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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