LMFDB - Embedded newform 567.2.w.a.37.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 6]))

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

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

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.w (of order $9$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.16
Character	$\chi$	$=$	567.37
Dual form			567.2.w.a.46.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.199381 + 1.13075i) q^{2} +(0.640547 - 0.233140i) q^{4} +(0.0295570 - 0.167626i) q^{5} +(-1.82867 - 1.91206i) q^{7} +(1.53953 + 2.66654i) q^{8} +O(q^{10})$	\(q+(0.199381 + 1.13075i) q^{2} +(0.640547 - 0.233140i) q^{4} +(0.0295570 - 0.167626i) q^{5} +(-1.82867 - 1.91206i) q^{7} +(1.53953 + 2.66654i) q^{8} +0.195436 q^{10} +(0.0250224 + 0.141909i) q^{11} +(4.82298 + 4.04696i) q^{13} +(1.79745 - 2.44900i) q^{14} +(-1.66387 + 1.39616i) q^{16} +3.38088 q^{17} -1.68694 q^{19} +(-0.0201477 - 0.114263i) q^{20} +(-0.155475 + 0.0565881i) q^{22} +(3.64166 + 3.05571i) q^{23} +(4.67124 + 1.70019i) q^{25} +(-3.61448 + 6.26046i) q^{26} +(-1.61713 - 0.798425i) q^{28} +(7.64234 - 6.41269i) q^{29} +(-2.01924 + 0.734943i) q^{31} +(2.80694 + 2.35530i) q^{32} +(0.674084 + 3.82292i) q^{34} +(-0.374561 + 0.250018i) q^{35} +(-2.27659 - 3.94317i) q^{37} +(-0.336344 - 1.90750i) q^{38} +(0.492485 - 0.179250i) q^{40} +(-4.05191 - 3.39995i) q^{41} +(-4.02809 - 1.46610i) q^{43} +(0.0491128 + 0.0850658i) q^{44} +(-2.72916 + 4.72705i) q^{46} +(-9.05842 - 3.29700i) q^{47} +(-0.311918 + 6.99305i) q^{49} +(-0.991130 + 5.62098i) q^{50} +(4.03285 + 1.46784i) q^{52} +(1.26185 + 2.18560i) q^{53} +0.0245273 q^{55} +(2.28328 - 7.81989i) q^{56} +(8.77488 + 7.36299i) q^{58} +(-1.23304 - 1.03464i) q^{59} +(-11.8170 - 4.30105i) q^{61} +(-1.23363 - 2.13672i) q^{62} +(-4.27563 + 7.40562i) q^{64} +(0.820929 - 0.688841i) q^{65} +(-0.674721 + 3.82653i) q^{67} +(2.16561 - 0.788218i) q^{68} +(-0.357388 - 0.373685i) q^{70} +(-4.00049 + 6.92905i) q^{71} +(4.47237 - 7.74637i) q^{73} +(4.00482 - 3.36045i) q^{74} +(-1.08056 + 0.393292i) q^{76} +(0.225581 - 0.307350i) q^{77} +(0.903043 + 5.12141i) q^{79} +(0.184853 + 0.320175i) q^{80} +(3.03661 - 5.25957i) q^{82} +(-6.82581 + 5.72754i) q^{83} +(0.0999286 - 0.566723i) q^{85} +(0.854669 - 4.84707i) q^{86} +(-0.339884 + 0.285197i) q^{88} -9.26283 q^{89} +(-1.08163 - 16.6224i) q^{91} +(3.04506 + 1.10831i) q^{92} +(1.92199 - 10.9001i) q^{94} +(-0.0498608 + 0.282774i) q^{95} +(-4.89392 - 1.78124i) q^{97} +(-7.96956 + 1.04158i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.199381	+	1.13075i	0.140984	+	0.799560i	0.970504	+	0.241083i	$0.0775027\pi$
$2$	0.199381	+	1.13075i	0.140984	+	0.799560i	−0.829520	+	0.558476i	$0.811386\pi$
$3$		0			0
$3$		0			0
$4$	0.640547	−	0.233140i	0.320274	−	0.116570i
$5$	0.0295570	−	0.167626i	0.0132183	−	0.0749647i	−0.977485	−	0.211005i	$-0.932326\pi$
$5$	0.0295570	−	0.167626i	0.0132183	−	0.0749647i	0.990703	+	0.136040i	$0.0434376\pi$
$6$		0			0
$7$	−1.82867	−	1.91206i	−0.691173	−	0.722689i
$7$	−1.82867	−	1.91206i	−0.691173	−	0.722689i
$8$	1.53953	+	2.66654i	0.544305	+	0.942764i
$9$		0			0
$10$	0.195436			0.0618023
$11$	0.0250224	+	0.141909i	0.00754455	+	0.0427873i	0.988348	−	0.152214i	$-0.0486402\pi$
$11$	0.0250224	+	0.141909i	0.00754455	+	0.0427873i	−0.980803	+	0.195001i	$0.937529\pi$
$12$		0			0
$13$	4.82298	+	4.04696i	1.33765	+	1.12242i	0.982222	+	0.187723i	$0.0601106\pi$
$13$	4.82298	+	4.04696i	1.33765	+	1.12242i	0.355432	+	0.934702i	$0.384334\pi$
$14$	1.79745	−	2.44900i	0.480389	−	0.654522i
$15$		0			0
$16$	−1.66387	+	1.39616i	−0.415968	+	0.349039i
$17$	3.38088			0.819983			0.409992	−	0.912089i	$-0.365532\pi$
$17$	3.38088			0.819983			0.409992	+	0.912089i	$0.365532\pi$
$18$		0			0
$19$	−1.68694			−0.387010			−0.193505	−	0.981099i	$-0.561986\pi$
$19$	−1.68694			−0.387010			−0.193505	+	0.981099i	$0.561986\pi$
$20$	−0.0201477	−	0.114263i	−0.00450516	−	0.0255501i
$21$		0			0
$22$	−0.155475	+	0.0565881i	−0.0331473	+	0.0120646i
$23$	3.64166	+	3.05571i	0.759338	+	0.637160i	0.937954	−	0.346758i	$-0.112718\pi$
$23$	3.64166	+	3.05571i	0.759338	+	0.637160i	−0.178616	+	0.983919i	$0.557162\pi$
$24$		0			0
$25$	4.67124	+	1.70019i	0.934248	+	0.340038i
$26$	−3.61448	+	6.26046i	−0.708858	+	1.22778i
$27$		0			0
$28$	−1.61713	−	0.798425i	−0.305608	−	0.150888i
$29$	7.64234	−	6.41269i	1.41915	−	1.19081i	0.467353	−	0.884071i	$-0.345208\pi$
$29$	7.64234	−	6.41269i	1.41915	−	1.19081i	0.951795	−	0.306735i	$-0.0992366\pi$
$30$		0			0
$31$	−2.01924	+	0.734943i	−0.362666	+	0.132000i	−0.516925	−	0.856031i	$-0.672923\pi$
$31$	−2.01924	+	0.734943i	−0.362666	+	0.132000i	0.154259	+	0.988030i	$0.450701\pi$
$32$	2.80694	+	2.35530i	0.496202	+	0.416363i
$33$		0			0
$34$	0.674084	+	3.82292i	0.115604	+	0.655625i
$35$	−0.374561	+	0.250018i	−0.0633123	+	0.0422608i
$36$		0			0
$37$	−2.27659	−	3.94317i	−0.374269	−	0.648254i	0.615948	−	0.787787i	$-0.288773\pi$
$37$	−2.27659	−	3.94317i	−0.374269	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$38$	−0.336344	−	1.90750i	−0.0545621	−	0.309437i
$39$		0			0
$40$	0.492485	−	0.179250i	0.0778688	−	0.0283419i
$41$	−4.05191	−	3.39995i	−0.632801	−	0.530983i	0.268997	−	0.963141i	$-0.413308\pi$
$41$	−4.05191	−	3.39995i	−0.632801	−	0.530983i	−0.901798	+	0.432158i	$0.857752\pi$
$42$		0			0
$43$	−4.02809	−	1.46610i	−0.614278	−	0.223579i	0.0160961	−	0.999870i	$-0.494876\pi$
$43$	−4.02809	−	1.46610i	−0.614278	−	0.223579i	−0.630374	+	0.776292i	$0.717098\pi$
$44$	0.0491128	+	0.0850658i	0.00740403	+	0.0128242i
$45$		0			0
$46$	−2.72916	+	4.72705i	−0.402393	+	0.696965i
$47$	−9.05842	−	3.29700i	−1.32131	−	0.480916i	−0.417430	−	0.908709i	$-0.637069\pi$
$47$	−9.05842	−	3.29700i	−1.32131	−	0.480916i	−0.903877	+	0.427793i	$0.859291\pi$
$48$		0			0
$49$	−0.311918	+	6.99305i	−0.0445597	+	0.999007i
$50$	−0.991130	+	5.62098i	−0.140167	+	0.794927i
$51$		0			0
$52$	4.03285	+	1.46784i	0.559256	+	0.203553i
$53$	1.26185	+	2.18560i	0.173329	+	0.300215i	0.939582	−	0.342325i	$-0.111214\pi$
$53$	1.26185	+	2.18560i	0.173329	+	0.300215i	−0.766253	+	0.642539i	$0.777881\pi$
$54$		0			0
$55$	0.0245273			0.00330726
$56$	2.28328	−	7.81989i	0.305117	−	1.04498i
$57$		0			0
$58$	8.77488	+	7.36299i	1.15220	+	0.966809i
$59$	−1.23304	−	1.03464i	−0.160528	−	0.134699i	0.558986	−	0.829177i	$-0.311191\pi$
$59$	−1.23304	−	1.03464i	−0.160528	−	0.134699i	−0.719513	+	0.694479i	$0.755635\pi$
$60$		0			0
$61$	−11.8170	−	4.30105i	−1.51302	−	0.550693i	−0.553624	−	0.832767i	$-0.686756\pi$
$61$	−11.8170	−	4.30105i	−1.51302	−	0.550693i	−0.959393	+	0.282073i	$0.908978\pi$
$62$	−1.23363	−	2.13672i	−0.156672	−	0.271363i
$63$		0			0
$64$	−4.27563	+	7.40562i	−0.534454	+	0.925702i
$65$	0.820929	−	0.688841i	0.101824	−	0.0854402i
$66$		0			0
$67$	−0.674721	+	3.82653i	−0.0824302	+	0.467485i	0.915451	+	0.402429i	$0.131834\pi$
$67$	−0.674721	+	3.82653i	−0.0824302	+	0.467485i	−0.997882	+	0.0650565i	$0.979277\pi$
$68$	2.16561	−	0.788218i	0.262619	−	0.0955855i
$69$		0			0
$70$	−0.357388	−	0.373685i	−0.0427161	−	0.0446638i
$71$	−4.00049	+	6.92905i	−0.474770	+	0.822326i	−0.999583	−	0.0288917i	$-0.990802\pi$
$71$	−4.00049	+	6.92905i	−0.474770	+	0.822326i	0.524812	+	0.851218i	$0.324136\pi$
$72$		0			0
$73$	4.47237	−	7.74637i	0.523451	−	0.906644i	−0.476176	−	0.879350i	$-0.657978\pi$
$73$	4.47237	−	7.74637i	0.523451	−	0.906644i	0.999627	−	0.0272943i	$-0.00868914\pi$
$74$	4.00482	−	3.36045i	0.465551	−	0.390644i
$75$		0			0
$76$	−1.08056	+	0.393292i	−0.123949	+	0.0451137i
$77$	0.225581	−	0.307350i	0.0257073	−	0.0350258i
$78$		0			0
$79$	0.903043	+	5.12141i	0.101600	+	0.576204i	0.992524	+	0.122051i	$0.0389471\pi$
$79$	0.903043	+	5.12141i	0.101600	+	0.576204i	−0.890924	+	0.454153i	$0.849942\pi$
$80$	0.184853	+	0.320175i	0.0206672	+	0.0357966i
$81$		0			0
$82$	3.03661	−	5.25957i	0.335338	−	0.580822i
$83$	−6.82581	+	5.72754i	−0.749230	+	0.628679i	−0.935299	−	0.353858i	$-0.884870\pi$
$83$	−6.82581	+	5.72754i	−0.749230	+	0.628679i	0.186069	+	0.982537i	$0.440425\pi$
$84$		0			0
$85$	0.0999286	−	0.566723i	0.0108388	−	0.0614698i
$86$	0.854669	−	4.84707i	0.0921613	−	0.522673i
$87$		0			0
$88$	−0.339884	+	0.285197i	−0.0362318	+	0.0304021i
$89$	−9.26283			−0.981858			−0.490929	−	0.871200i	$-0.663342\pi$
$89$	−9.26283			−0.981858			−0.490929	+	0.871200i	$0.663342\pi$
$90$		0			0
$91$	−1.08163	−	16.6224i	−0.113386	−	1.74250i
$92$	3.04506	+	1.10831i	0.317470	+	0.115550i
$93$		0			0
$94$	1.92199	−	10.9001i	0.198238	−	1.12426i
$95$	−0.0498608	+	0.282774i	−0.00511561	+	0.0290120i
$96$		0			0
$97$	−4.89392	−	1.78124i	−0.496903	−	0.180858i	0.0813978	−	0.996682i	$-0.474062\pi$
$97$	−4.89392	−	1.78124i	−0.496903	−	0.180858i	−0.578300	+	0.815824i	$0.696284\pi$
$98$	−7.96956	+	1.04158i	−0.805048	+	0.105216i
$99$		0			0
$100$	3.38853			0.338853
$101$	−5.03195	+	4.22231i	−0.500698	+	0.420136i	−0.857842	−	0.513914i	$-0.828195\pi$
$101$	−5.03195	+	4.22231i	−0.500698	+	0.420136i	0.357144	+	0.934049i	$0.383751\pi$
$102$		0			0
$103$	2.81219	−	15.9487i	0.277093	−	1.57147i	−0.455141	−	0.890419i	$-0.650411\pi$
$103$	2.81219	−	15.9487i	0.277093	−	1.57147i	0.732234	−	0.681053i	$-0.238478\pi$
$104$	−3.36627	+	19.0911i	−0.330090	+	1.87203i
$105$		0			0
$106$	−2.21977	+	1.86261i	−0.215603	+	0.180912i
$107$	−2.29216	+	3.97014i	−0.221591	+	0.383808i	−0.955291	−	0.295666i	$-0.904458\pi$
$107$	−2.29216	+	3.97014i	−0.221591	+	0.383808i	0.733700	+	0.679474i	$0.237792\pi$
$108$		0			0
$109$	−3.28698	−	5.69321i	−0.314835	−	0.545311i	0.664567	−	0.747229i	$-0.268616\pi$
$109$	−3.28698	−	5.69321i	−0.314835	−	0.545311i	−0.979403	+	0.201918i	$0.935283\pi$
$110$	0.00489028	+	0.0277342i	0.000466270	+	0.00264435i
$111$		0			0
$112$	5.71221	+	0.628309i	0.539753	+	0.0593696i
$113$	14.6216	−	5.32182i	1.37548	−	0.500635i	0.454677	−	0.890656i	$-0.349755\pi$
$113$	14.6216	−	5.32182i	1.37548	−	0.500635i	0.920806	+	0.390022i	$0.127532\pi$
$114$		0			0
$115$	0.619854	−	0.520119i	0.0578017	−	0.0485014i
$116$	3.40023	−	5.88937i	0.315703	−	0.546814i
$117$		0			0
$118$	0.924074	−	1.60054i	0.0850679	−	0.147342i
$119$	−6.18252	−	6.46443i	−0.566750	−	0.592593i
$120$		0			0
$121$	10.3171	−	3.75512i	0.937919	−	0.341375i
$122$	2.50731	−	14.2196i	0.227001	−	1.28739i
$123$		0			0
$124$	−1.12207	+	0.941531i	−0.100765	+	0.0845520i
$125$	0.848594	−	1.46981i	0.0759006	−	0.131464i
$126$		0			0
$127$	−3.63522	−	6.29639i	−0.322574	−	0.558714i	0.658445	−	0.752629i	$-0.271215\pi$
$127$	−3.63522	−	6.29639i	−0.322574	−	0.558714i	−0.981018	+	0.193915i	$0.937881\pi$
$128$	−2.33993	−	0.851663i	−0.206822	−	0.0752771i
$129$		0			0
$130$	0.942584	+	0.790922i	0.0826701	+	0.0693684i
$131$	0.200888	+	0.168565i	0.0175517	+	0.0147276i	0.651521	−	0.758630i	$-0.274131\pi$
$131$	0.200888	+	0.168565i	0.0175517	+	0.0147276i	−0.633970	+	0.773358i	$0.718576\pi$
$132$		0			0
$133$	3.08485	+	3.22552i	0.267491	+	0.279688i
$134$	−4.46137			−0.385404
$135$		0			0
$136$	5.20495	+	9.01524i	0.446321	+	0.773051i
$137$	−19.6986	−	7.16970i	−1.68296	−	0.612549i	−0.689252	−	0.724521i	$-0.742061\pi$
$137$	−19.6986	−	7.16970i	−1.68296	−	0.612549i	−0.993711	+	0.111973i	$0.964283\pi$
$138$		0			0
$139$	−1.75432	+	9.94926i	−0.148800	+	0.843885i	0.815438	+	0.578845i	$0.196496\pi$
$139$	−1.75432	+	9.94926i	−0.148800	+	0.843885i	−0.964237	+	0.265040i	$0.914615\pi$
$140$	−0.181634	+	0.247474i	−0.0153509	+	0.0209153i
$141$		0			0
$142$	−8.63263	−	3.14202i	−0.724434	−	0.263672i
$143$	−0.453619	+	0.785690i	−0.0379335	+	0.0657027i
$144$		0			0
$145$	−0.849049	−	1.47060i	−0.0705097	−	0.122126i
$146$	9.65090	+	3.51264i	0.798714	+	0.290708i
$147$		0			0
$148$	−2.37758	−	1.99502i	−0.195436	−	0.163990i
$149$	3.01891	−	1.09879i	0.247318	−	0.0900166i	−0.215387	−	0.976529i	$-0.569101\pi$
$149$	3.01891	−	1.09879i	0.247318	−	0.0900166i	0.462705	+	0.886512i	$0.346879\pi$
$150$		0			0
$151$	−2.63217	−	14.9278i	−0.214203	−	1.21480i	−0.882285	−	0.470716i	$-0.843996\pi$
$151$	−2.63217	−	14.9278i	−0.214203	−	1.21480i	0.668082	−	0.744088i	$-0.267116\pi$
$152$	−2.59708	−	4.49828i	−0.210651	−	0.364859i
$153$		0			0
$154$	0.392512	+	0.193795i	0.0316295	+	0.0156165i
$155$	0.0635129	+	0.360200i	0.00510148	+	0.0289319i
$156$		0			0
$157$	1.76394	+	1.48012i	0.140778	+	0.118126i	0.710457	−	0.703741i	$-0.248488\pi$
$157$	1.76394	+	1.48012i	0.140778	+	0.118126i	−0.569680	+	0.821867i	$0.692933\pi$
$158$	−5.61098	+	2.04223i	−0.446385	+	0.162471i
$159$		0			0
$160$	0.477775	−	0.400901i	0.0377714	−	0.0316940i
$161$	−0.816701	−	12.5510i	−0.0643651	−	0.989154i
$162$		0			0
$163$	9.50735	−	16.4672i	0.744673	−	1.28981i	−0.205675	−	0.978620i	$-0.565939\pi$
$163$	9.50735	−	16.4672i	0.744673	−	1.28981i	0.950348	−	0.311191i	$-0.100728\pi$
$164$	−3.38810	−	1.23317i	−0.264566	−	0.0962942i
$165$		0			0
$166$	−7.83734	−	6.57631i	−0.608296	−	0.510421i
$167$	14.0837	−	5.12605i	1.08983	−	0.396665i	0.266272	−	0.963898i	$-0.414208\pi$
$167$	14.0837	−	5.12605i	1.08983	−	0.396665i	0.823558	+	0.567233i	$0.191986\pi$
$168$		0			0
$169$	4.62582	+	26.2343i	0.355832	+	2.01802i
$170$	0.660745			0.0506768
$171$		0			0
$172$	−2.92199			−0.222800
$173$	−4.30632	+	3.61343i	−0.327404	+	0.274724i	−0.791641	−	0.610987i	$-0.790773\pi$
$173$	−4.30632	+	3.61343i	−0.327404	+	0.274724i	0.464237	+	0.885711i	$0.346328\pi$
$174$		0			0
$175$	−5.29130	−	12.0408i	−0.399985	−	0.910196i
$176$	−0.239762	−	0.201184i	−0.0180727	−	0.0151648i
$177$		0			0
$178$	−1.84684	−	10.4739i	−0.138426	−	0.785054i
$179$	11.1863			0.836101			0.418051	−	0.908424i	$-0.362713\pi$
$179$	11.1863			0.836101			0.418051	+	0.908424i	$0.362713\pi$
$180$		0			0
$181$	8.26924	+	14.3227i	0.614648	+	1.06460i	0.990446	+	0.137900i	$0.0440351\pi$
$181$	8.26924	+	14.3227i	0.614648	+	1.06460i	−0.375799	+	0.926701i	$0.622632\pi$
$182$	18.5801	−	4.53724i	1.37725	−	0.336323i
$183$		0			0
$184$	−2.54175	+	14.4150i	−0.187380	+	1.06269i
$185$	−0.728268	+	0.265068i	−0.0535433	+	0.0194882i
$186$		0			0
$187$	0.0845978	+	0.479778i	0.00618640	+	0.0350848i
$188$	−6.57101			−0.479240
$189$		0			0
$190$	−0.329688			−0.0239181
$191$	1.39660	+	7.92052i	0.101055	+	0.573109i	0.992723	+	0.120420i	$0.0384241\pi$
$191$	1.39660	+	7.92052i	0.101055	+	0.573109i	−0.891668	+	0.452689i	$0.850465\pi$
$192$		0			0
$193$	−1.38108	+	0.502671i	−0.0994121	+	0.0361830i	−0.391247	−	0.920286i	$-0.627956\pi$
$193$	−1.38108	+	0.502671i	−0.0994121	+	0.0361830i	0.291835	+	0.956469i	$0.405734\pi$
$194$	1.03838	−	5.88894i	0.0745513	−	0.422801i
$195$		0			0
$196$	1.43056	+	4.55210i	0.102183	+	0.325150i
$197$	7.69876	+	13.3346i	0.548514	+	0.950054i	0.998377	+	0.0569560i	$0.0181395\pi$
$197$	7.69876	+	13.3346i	0.548514	+	0.950054i	−0.449863	+	0.893098i	$0.648527\pi$
$198$		0			0
$199$	12.4103			0.879745			0.439873	−	0.898060i	$-0.355024\pi$
$199$	12.4103			0.879745			0.439873	+	0.898060i	$0.355024\pi$
$200$	2.65787	+	15.0735i	0.187940	+	1.06586i
$201$		0			0
$202$	−5.77765	−	4.84802i	−0.406514	−	0.341106i
$203$	−26.2368	−	2.88589i	−1.84146	−	0.202550i
$204$		0			0
$205$	−0.689683	+	0.578713i	−0.0481695	+	0.0404190i
$206$	18.5947			1.29555
$207$		0			0
$208$	−13.6750			−0.948192
$209$	−0.0422112	−	0.239392i	−0.00291981	−	0.0165591i
$210$		0			0
$211$	−9.70321	+	3.53168i	−0.667996	+	0.243131i	−0.653685	−	0.756767i	$-0.726778\pi$
$211$	−9.70321	+	3.53168i	−0.667996	+	0.243131i	−0.0143113	+	0.999898i	$0.504556\pi$
$212$	1.31783	+	1.10579i	0.0905087	+	0.0759458i
$213$		0			0
$214$	−4.94624	−	1.80028i	−0.338118	−	0.123065i
$215$	−0.364816	+	0.631879i	−0.0248802	+	0.0430938i
$216$		0			0
$217$	5.09778	+	2.51693i	0.346060	+	0.170860i
$218$	5.78223	−	4.85187i	0.391622	−	0.328610i
$219$		0			0
$220$	0.0157109	−	0.00571829i	0.00105923	−	0.000385527i
$221$	16.3059	+	13.6823i	1.09685	+	0.920370i
$222$		0			0
$223$	−1.67098	−	9.47662i	−0.111897	−	0.634602i	−0.988240	−	0.152913i	$-0.951135\pi$
$223$	−1.67098	−	9.47662i	−0.111897	−	0.634602i	0.876342	−	0.481689i	$-0.159976\pi$
$224$	−0.629502	−	9.67410i	−0.0420604	−	0.646378i
$225$		0			0
$226$	8.93291	+	15.4723i	0.594208	+	1.02920i
$227$	−0.561288	−	3.18322i	−0.0372540	−	0.211278i	0.960498	−	0.278285i	$-0.0897660\pi$
$227$	−0.561288	−	3.18322i	−0.0372540	−	0.211278i	−0.997752	+	0.0670073i	$0.978655\pi$
$228$		0			0
$229$	−16.7042	+	6.07983i	−1.10384	+	0.401766i	−0.828732	−	0.559646i	$-0.810937\pi$
$229$	−16.7042	+	6.07983i	−1.10384	+	0.401766i	−0.275112	+	0.961412i	$0.588715\pi$
$230$	0.711711	+	0.597196i	0.0469288	+	0.0393780i
$231$		0			0
$232$	28.8653	+	10.5061i	1.89510	+	0.689760i
$233$	−8.80418	−	15.2493i	−0.576781	−	0.999014i	−0.995846	−	0.0910579i	$-0.970975\pi$
$233$	−8.80418	−	15.2493i	−0.576781	−	0.999014i	0.419064	−	0.907957i	$-0.362358\pi$
$234$		0			0
$235$	−0.820402	+	1.42098i	−0.0535171	+	0.0926944i
$236$	−1.03103	−	0.375266i	−0.0671147	−	0.0244277i
$237$		0			0
$238$	6.07696	−	8.27975i	0.393911	−	0.536697i
$239$	−3.30378	+	18.7366i	−0.213704	+	1.21197i	0.669439	+	0.742867i	$0.266535\pi$
$239$	−3.30378	+	18.7366i	−0.213704	+	1.21197i	−0.883142	+	0.469105i	$0.844576\pi$
$240$		0			0
$241$	1.16633	+	0.424509i	0.0751298	+	0.0273450i	0.379312	−	0.925269i	$-0.376161\pi$
$241$	1.16633	+	0.424509i	0.0751298	+	0.0273450i	−0.304182	+	0.952614i	$0.598383\pi$
$242$	6.30313	+	10.9173i	0.405181	+	0.701794i
$243$		0			0
$244$	−8.57212			−0.548774
$245$	1.16300	+	0.258979i	0.0743012	+	0.0165456i
$246$		0			0
$247$	−8.13606	−	6.82696i	−0.517685	−	0.434389i
$248$	−5.06843	−	4.25292i	−0.321845	−	0.270060i
$249$		0			0
$250$	1.83118	+	0.666494i	0.115814	+	0.0421528i
$251$	−5.68476	−	9.84629i	−0.358819	−	0.621492i	0.628945	−	0.777450i	$-0.283487\pi$
$251$	−5.68476	−	9.84629i	−0.358819	−	0.621492i	−0.987764	+	0.155958i	$0.950154\pi$
$252$		0			0
$253$	−0.342511	+	0.593246i	−0.0215335	+	0.0372971i
$254$	6.39483	−	5.36590i	0.401247	−	0.336687i
$255$		0			0
$256$	−2.47335	+	14.0270i	−0.154584	+	0.876690i
$257$	−6.00030	+	2.18393i	−0.374289	+	0.136230i	−0.522313	−	0.852754i	$-0.674931\pi$
$257$	−6.00030	+	2.18393i	−0.374289	+	0.136230i	0.148025	+	0.988984i	$0.452709\pi$
$258$		0			0
$259$	−3.37643	+	11.5637i	−0.209801	+	0.718536i
$260$	0.365247	−	0.632627i	0.0226517	−	0.0392338i
$261$		0			0
$262$	−0.150551	+	0.260762i	−0.00930108	+	0.0161099i
$263$	−20.5043	+	17.2052i	−1.26435	+	1.06092i	−0.269146	+	0.963099i	$0.586741\pi$
$263$	−20.5043	+	17.2052i	−1.26435	+	1.06092i	−0.995204	+	0.0978163i	$0.968814\pi$
$264$		0			0
$265$	0.403659	−	0.146920i	0.0247966	−	0.00902522i
$266$	−3.03218	+	4.13130i	−0.185915	+	0.253306i
$267$		0			0
$268$	0.459927	+	2.60838i	0.0280945	+	0.159332i
$269$	−2.65842	−	4.60452i	−0.162087	−	0.280743i	0.773530	−	0.633760i	$-0.218489\pi$
$269$	−2.65842	−	4.60452i	−0.162087	−	0.280743i	−0.935617	+	0.353017i	$0.885156\pi$
$270$		0			0
$271$	−15.2433	+	26.4022i	−0.925966	+	1.60382i	−0.135965	+	0.990714i	$0.543413\pi$
$271$	−15.2433	+	26.4022i	−0.925966	+	1.60382i	−0.790001	+	0.613106i	$0.789920\pi$
$272$	−5.62535	+	4.72023i	−0.341087	+	0.286206i
$273$		0			0
$274$	4.17959	−	23.7036i	0.252498	−	1.43199i
$275$	−0.124387	+	0.705435i	−0.00750083	+	0.0425393i
$276$		0			0
$277$	7.36221	−	6.17763i	0.442353	−	0.371178i	−0.394236	−	0.919009i	$-0.628991\pi$
$277$	7.36221	−	6.17763i	0.442353	−	0.371178i	0.836589	+	0.547831i	$0.184546\pi$
$278$	−11.5999			−0.695715
$279$		0			0
$280$	−1.24333	−	0.613870i	−0.0743032	−	0.0366858i
$281$	−13.3568	−	4.86148i	−0.796800	−	0.290012i	−0.0886405	−	0.996064i	$-0.528252\pi$
$281$	−13.3568	−	4.86148i	−0.796800	−	0.290012i	−0.708160	+	0.706052i	$0.750474\pi$
$282$		0			0
$283$	−3.41132	+	19.3466i	−0.202782	+	1.15003i	0.698110	+	0.715991i	$0.254025\pi$
$283$	−3.41132	+	19.3466i	−0.202782	+	1.15003i	−0.900892	+	0.434043i	$0.857086\pi$
$284$	−0.947062	+	5.37105i	−0.0561978	+	0.318713i
$285$		0			0
$286$	−0.978861	−	0.356276i	−0.0578813	−	0.0210671i
$287$	0.908706	+	13.9649i	0.0536392	+	0.824320i
$288$		0			0
$289$	−5.56967			−0.327628
$290$	1.49359	−	1.25327i	0.0877066	−	0.0735945i
$291$		0			0
$292$	1.05877	−	6.00460i	0.0619601	−	0.351393i
$293$	2.82867	−	16.0422i	0.165253	−	0.937194i	−0.783551	−	0.621327i	$-0.786594\pi$
$293$	2.82867	−	16.0422i	0.165253	−	0.937194i	0.948804	−	0.315866i	$-0.102295\pi$
$294$		0			0
$295$	−0.209878	+	0.176108i	−0.0122196	+	0.0102534i
$296$	7.00975	−	12.1412i	0.407434	−	0.705696i
$297$		0			0
$298$	1.84437	+	3.19454i	0.106842	+	0.185055i
$299$	5.19729	+	29.4753i	0.300567	+	1.70460i
$300$		0			0
$301$	4.56278	+	10.3830i	0.262994	+	0.598464i
$302$	16.3547	−	5.95263i	0.941109	−	0.342536i
$303$		0			0
$304$	2.80685	−	2.35523i	0.160984	−	0.135081i
$305$	−1.07024	+	1.85372i	−0.0612820	+	0.106144i
$306$		0			0
$307$	0.900231	−	1.55925i	0.0513789	−	0.0889909i	−0.839192	−	0.543835i	$-0.816972\pi$
$307$	0.900231	−	1.55925i	0.0513789	−	0.0889909i	0.890571	+	0.454844i	$0.150305\pi$
$308$	0.0728395	−	0.249464i	0.00415042	−	0.0142145i
$309$		0			0
$310$	−0.394632	+	0.143634i	−0.0224136	+	0.00815788i
$311$	5.54458	−	31.4449i	0.314404	−	1.78307i	−0.261138	−	0.965302i	$-0.584098\pi$
$311$	5.54458	−	31.4449i	0.314404	−	1.78307i	0.575542	−	0.817772i	$-0.304791\pi$
$312$		0			0
$313$	−0.362407	+	0.304095i	−0.0204844	+	0.0171885i	−0.652972	−	0.757382i	$-0.726478\pi$
$313$	−0.362407	+	0.304095i	−0.0204844	+	0.0171885i	0.632488	+	0.774570i	$0.282034\pi$
$314$	−1.32195	+	2.28968i	−0.0746017	+	0.129214i
$315$		0			0
$316$	1.77245	+	3.06997i	0.0997080	+	0.172699i
$317$	25.8577	+	9.41144i	1.45231	+	0.528599i	0.943236	−	0.332122i	$-0.107765\pi$
$317$	25.8577	+	9.41144i	1.45231	+	0.528599i	0.509077	+	0.860721i	$0.329987\pi$
$318$		0			0
$319$	1.10125	+	0.924058i	0.0616582	+	0.0517373i
$320$	1.11500	+	0.935596i	0.0623304	+	0.0523014i
$321$		0			0
$322$	14.0291	−	3.42591i	0.781813	−	0.190918i
$323$	−5.70332			−0.317341
$324$		0			0
$325$	15.6487	+	27.1043i	0.868032	+	1.50348i
$326$	20.5158	+	7.46716i	1.13627	+	0.413568i
$327$		0			0
$328$	2.82809	−	16.0389i	0.156155	−	0.885599i
$329$	10.2608	+	23.3493i	0.565698	+	1.28729i
$330$		0			0
$331$	−6.43669	−	2.34276i	−0.353792	−	0.128770i	0.159009	−	0.987277i	$-0.449170\pi$
$331$	−6.43669	−	2.34276i	−0.353792	−	0.128770i	−0.512801	+	0.858507i	$0.671392\pi$
$332$	−3.03694	+	5.26013i	−0.166674	+	0.288687i
$333$		0			0
$334$	8.60430	+	14.9031i	0.470806	+	0.815460i
$335$	0.621484	+	0.226202i	0.0339553	+	0.0123587i
$336$		0			0
$337$	12.1130	+	10.1640i	0.659838	+	0.553670i	0.910038	−	0.414524i	$-0.136052\pi$
$337$	12.1130	+	10.1640i	0.659838	+	0.553670i	−0.250200	+	0.968194i	$0.580496\pi$
$338$	−28.7421	+	10.4613i	−1.56336	+	0.569018i
$339$		0			0
$340$	−0.0681169	−	0.386310i	−0.00369416	−	0.0209506i
$341$	−0.154821	−	0.268159i	−0.00838405	−	0.0145216i
$342$		0			0
$343$	13.9415	−	12.1916i	0.752770	−	0.658284i
$344$	−2.29193	−	12.9982i	−0.123572	−	0.700814i
$345$		0			0
$346$	−4.94448	−	4.14892i	−0.265817	−	0.223047i
$347$	−13.5036	+	4.91489i	−0.724909	+	0.263845i	−0.678008	−	0.735054i	$-0.737157\pi$
$347$	−13.5036	+	4.91489i	−0.724909	+	0.263845i	−0.0469006	+	0.998900i	$0.514934\pi$
$348$		0			0
$349$	−3.00207	+	2.51903i	−0.160697	+	0.134841i	−0.719590	−	0.694399i	$-0.755670\pi$
$349$	−3.00207	+	2.51903i	−0.160697	+	0.134841i	0.558894	+	0.829239i	$0.311226\pi$
$350$	12.5601	−	8.38383i	0.671365	−	0.448135i
$351$		0			0
$352$	−0.264003	+	0.457266i	−0.0140714	+	0.0243724i
$353$	17.7900	+	6.47501i	0.946864	+	0.344630i	0.768873	−	0.639402i	$-0.220818\pi$
$353$	17.7900	+	6.47501i	0.946864	+	0.344630i	0.177991	+	0.984032i	$0.443040\pi$
$354$		0			0
$355$	1.04325	+	0.875388i	0.0553698	+	0.0464607i
$356$	−5.93328	+	2.15954i	−0.314463	+	0.114455i
$357$		0			0
$358$	2.23033	+	12.6489i	0.117877	+	0.668513i
$359$	31.3361			1.65386			0.826929	−	0.562307i	$-0.190086\pi$
$359$	31.3361			1.65386			0.826929	+	0.562307i	$0.190086\pi$
$360$		0			0
$361$	−16.1542			−0.850224
$362$	−14.5467	+	12.2061i	−0.764556	+	0.641539i
$363$		0			0
$364$	−4.56818	−	10.3952i	−0.239438	−	0.544859i
$365$	−1.16630	−	0.978645i	−0.0610471	−	0.0512246i
$366$		0			0
$367$	−2.66822	−	15.1322i	−0.139280	−	0.789895i	−0.971783	−	0.235875i	$-0.924204\pi$
$367$	−2.66822	−	15.1322i	−0.139280	−	0.789895i	0.832503	−	0.554020i	$-0.186907\pi$
$368$	−10.3255			−0.538255
$369$		0			0
$370$	−0.444928	−	0.770638i	−0.0231307	−	0.0400635i
$371$	1.87146	−	6.40947i	0.0971616	−	0.332763i
$372$		0			0
$373$	0.591390	−	3.35394i	0.0306210	−	0.173660i	−0.965662	−	0.259802i	$-0.916343\pi$
$373$	0.591390	−	3.35394i	0.0306210	−	0.173660i	0.996283	+	0.0861417i	$0.0274538\pi$
$374$	−0.525641	+	0.191318i	−0.0271802	+	0.00989279i
$375$		0			0
$376$	−5.15412	−	29.2305i	−0.265803	−	1.50745i
$377$	62.8108			3.23492
$378$		0			0
$379$	−24.3746			−1.25204			−0.626020	−	0.779807i	$-0.715317\pi$
$379$	−24.3746			−1.25204			−0.626020	+	0.779807i	$0.715317\pi$
$380$	0.0339879	+	0.192755i	0.00174354	+	0.00988812i
$381$		0			0
$382$	−8.67766	+	3.15841i	−0.443988	+	0.161598i
$383$	4.27865	−	24.2655i	0.218629	−	1.23991i	−0.655868	−	0.754876i	$-0.727697\pi$
$383$	4.27865	−	24.2655i	0.218629	−	1.23991i	0.874497	−	0.485031i	$-0.161192\pi$
$384$		0			0
$385$	−0.0448524	−	0.0468975i	−0.00228589	−	0.00239012i
$386$	−0.843755	−	1.46143i	−0.0429460	−	0.0743847i
$387$		0			0
$388$	−3.55007			−0.180227
$389$	−5.99424	−	33.9950i	−0.303920	−	1.72362i	−0.628544	−	0.777774i	$-0.716349\pi$
$389$	−5.99424	−	33.9950i	−0.303920	−	1.72362i	0.324624	−	0.945843i	$-0.394762\pi$
$390$		0			0
$391$	12.3120	+	10.3310i	0.622645	+	0.522461i
$392$	−19.1274	+	9.93425i	−0.966082	+	0.501755i
$393$		0			0
$394$	−13.5431	+	11.3640i	−0.682293	+	0.572512i
$395$	0.885174			0.0445379
$396$		0			0
$397$	16.7173			0.839016			0.419508	−	0.907752i	$-0.362203\pi$
$397$	16.7173			0.839016			0.419508	+	0.907752i	$0.362203\pi$
$398$	2.47439	+	14.0330i	0.124030	+	0.703409i
$399$		0			0
$400$	−10.1461	+	3.69287i	−0.507304	+	0.184644i
$401$	−12.3699	−	10.3795i	−0.617721	−	0.518330i	0.279365	−	0.960185i	$-0.409876\pi$
$401$	−12.3699	−	10.3795i	−0.617721	−	0.518330i	−0.897086	+	0.441855i	$0.854321\pi$
$402$		0			0
$403$	−12.7130	−	4.62717i	−0.633281	−	0.230496i
$404$	−2.23881	+	3.87774i	−0.111385	+	0.192925i
$405$		0			0
$406$	−1.96791	−	30.2426i	−0.0976657	−	1.50091i
$407$	0.502607	−	0.421737i	0.0249133	−	0.0209047i
$408$		0			0
$409$	−26.4285	+	9.61920i	−1.30681	+	0.475639i	−0.899208	−	0.437522i	$-0.855856\pi$
$409$	−26.4285	+	9.61920i	−1.30681	+	0.475639i	−0.407599	+	0.913161i	$0.633634\pi$
$410$	−0.791888	−	0.664473i	−0.0391086	−	0.0328160i
$411$		0			0
$412$	−1.91694	−	10.8715i	−0.0944410	−	0.535602i
$413$	0.276529	+	4.24966i	0.0136071	+	0.209112i
$414$		0			0
$415$	0.758334	+	1.31347i	0.0372252	+	0.0644759i
$416$	4.00600	+	22.7191i	0.196410	+	1.11390i
$417$		0			0
$418$	0.262276	−	0.0954605i	0.0128283	−	0.00466913i
$419$	−19.3269	−	16.2172i	−0.944179	−	0.792260i	0.0341285	−	0.999417i	$-0.489134\pi$
$419$	−19.3269	−	16.2172i	−0.944179	−	0.792260i	−0.978308	+	0.207157i	$0.933579\pi$
$420$		0			0
$421$	27.7584	+	10.1032i	1.35286	+	0.492401i	0.913840	−	0.406075i	$-0.133103\pi$
$421$	27.7584	+	10.1032i	1.35286	+	0.492401i	0.439022	+	0.898476i	$0.355325\pi$
$422$	−5.92808	−	10.2677i	−0.288574	−	0.499825i
$423$		0			0
$424$	−3.88532	+	6.72957i	−0.188688	+	0.326817i
$425$	15.7929	+	5.74814i	0.766067	+	0.278826i
$426$		0			0
$427$	13.3856	+	30.4601i	0.647777	+	1.47407i
$428$	−0.542638	+	3.07745i	−0.0262294	+	0.148754i
$429$		0			0
$430$	−0.787234	−	0.286530i	−0.0379638	−	0.0138177i
$431$	−7.92346	−	13.7238i	−0.381659	−	0.661054i	0.609640	−	0.792678i	$-0.291314\pi$
$431$	−7.92346	−	13.7238i	−0.381659	−	0.661054i	−0.991300	+	0.131625i	$0.957981\pi$
$432$		0			0
$433$	−11.1256			−0.534664			−0.267332	−	0.963604i	$-0.586142\pi$
$433$	−11.1256			−0.534664			−0.267332	+	0.963604i	$0.586142\pi$
$434$	−1.82961	+	6.26613i	−0.0878241	+	0.300784i
$435$		0			0
$436$	−3.43278	−	2.88044i	−0.164400	−	0.137948i
$437$	−6.14324	−	5.15479i	−0.293871	−	0.246587i
$438$		0			0
$439$	21.7138	+	7.90316i	1.03634	+	0.377197i	0.803492	−	0.595315i	$-0.202973\pi$
$439$	21.7138	+	7.90316i	1.03634	+	0.377197i	0.232849	+	0.972513i	$0.425195\pi$
$440$	0.0377604	+	0.0654030i	0.00180016	+	0.00311796i
$441$		0			0
$442$	−12.2201	+	21.1659i	−0.581252	+	1.00676i
$443$	9.54788	−	8.01163i	0.453634	−	0.380644i	−0.387149	−	0.922017i	$-0.626540\pi$
$443$	9.54788	−	8.01163i	0.453634	−	0.380644i	0.840782	+	0.541374i	$0.182096\pi$
$444$		0			0
$445$	−0.273781	+	1.55269i	−0.0129785	+	0.0736046i
$446$	10.3825	−	3.77892i	0.491626	−	0.178937i
$447$		0			0
$448$	21.9787	−	5.36719i	1.03840	−	0.253576i
$449$	−13.3099	+	23.0533i	−0.628131	+	1.08795i	0.359796	+	0.933031i	$0.382846\pi$
$449$	−13.3099	+	23.0533i	−0.628131	+	1.08795i	−0.987926	+	0.154924i	$0.950487\pi$
$450$		0			0
$451$	0.381096	−	0.660078i	0.0179451	−	0.0310819i
$452$	8.12508	−	6.81775i	0.382172	−	0.320680i
$453$		0			0
$454$	3.48751	−	1.26935i	0.163677	−	0.0595736i
$455$	−2.81831	−	0.309998i	−0.132125	−	0.0145329i
$456$		0			0
$457$	−1.43187	−	8.12052i	−0.0669799	−	0.379862i	−0.999809	−	0.0195428i	$-0.993779\pi$
$457$	−1.43187	−	8.12052i	−0.0669799	−	0.379862i	0.932829	−	0.360319i	$-0.117332\pi$
$458$	−10.2053	−	17.6760i	−0.476860	−	0.825946i
$459$		0			0
$460$	0.275785	−	0.477674i	0.0128585	−	0.0222716i
$461$	9.76859	−	8.19682i	0.454968	−	0.381764i	−0.386307	−	0.922370i	$-0.626250\pi$
$461$	9.76859	−	8.19682i	0.454968	−	0.381764i	0.841276	+	0.540606i	$0.181805\pi$
$462$		0			0
$463$	2.80583	−	15.9126i	0.130398	−	0.739523i	−0.847557	−	0.530705i	$-0.821927\pi$
$463$	2.80583	−	15.9126i	0.130398	−	0.739523i	0.977954	−	0.208818i	$-0.0669617\pi$
$464$	−3.76278	+	21.3398i	−0.174683	+	0.990676i
$465$		0			0
$466$	15.4877	−	12.9957i	0.717455	−	0.602016i
$467$	23.6225			1.09312			0.546559	−	0.837421i	$-0.315938\pi$
$467$	23.6225			1.09312			0.546559	+	0.837421i	$0.315938\pi$
$468$		0			0
$469$	8.55038	−	5.70737i	0.394820	−	0.263542i
$470$	−1.77034	−	0.644351i	−0.0816597	−	0.0297217i
$471$		0			0
$472$	0.860617	−	4.88080i	0.0396131	−	0.224657i
$473$	0.107261	−	0.608309i	0.00493188	−	0.0279701i
$474$		0			0
$475$	−7.88008	−	2.86811i	−0.361563	−	0.131598i
$476$	−5.46731	−	2.69938i	−0.250594	−	0.123726i
$477$		0			0
$478$	−21.8451			−0.999173
$479$	−18.1348	+	15.2169i	−0.828602	+	0.695280i	−0.954970	−	0.296704i	$-0.904113\pi$
$479$	−18.1348	+	15.2169i	−0.828602	+	0.695280i	0.126367	+	0.991983i	$0.459668\pi$
$480$		0			0
$481$	4.97791	−	28.2311i	0.226973	−	1.28723i
$482$	−0.247468	+	1.40346i	−0.0112719	+	0.0639260i
$483$		0			0
$484$	5.73312	−	4.81066i	0.260597	−	0.218666i
$485$	−0.443232	+	0.767701i	−0.0201261	+	0.0348595i
$486$		0			0
$487$	−1.88121	−	3.25835i	−0.0852456	−	0.147650i	0.820250	−	0.572005i	$-0.193834\pi$
$487$	−1.88121	−	3.25835i	−0.0852456	−	0.147650i	−0.905496	+	0.424355i	$0.860501\pi$
$488$	−6.72374	−	38.1322i	−0.304369	−	1.72616i
$489$		0			0
$490$	−0.0609600	+	1.36669i	−0.00275389	+	0.0617409i
$491$	−7.52536	+	2.73901i	−0.339615	+	0.123610i	−0.506197	−	0.862418i	$-0.668949\pi$
$491$	−7.52536	+	2.73901i	−0.339615	+	0.123610i	0.166582	+	0.986028i	$0.446727\pi$
$492$		0			0
$493$	25.8378	−	21.6805i	1.16368	−	0.976441i
$494$	6.09740	−	10.5610i	0.274335	−	0.475162i
$495$		0			0
$496$	2.33366	−	4.04202i	0.104785	−	0.181492i
$497$	20.5643	−	5.02180i	0.922435	−	0.225258i
$498$		0			0
$499$	5.14058	−	1.87102i	0.230124	−	0.0837582i	−0.224385	−	0.974501i	$-0.572037\pi$
$499$	5.14058	−	1.87102i	0.230124	−	0.0837582i	0.454508	+	0.890742i	$0.349815\pi$
$500$	0.200893	−	1.13932i	0.00898422	−	0.0509521i
$501$		0			0
$502$	10.0002	−	8.39119i	0.446332	−	0.374517i
$503$	5.10072	−	8.83470i	0.227430	−	0.393920i	−0.729616	−	0.683857i	$-0.760301\pi$
$503$	5.10072	−	8.83470i	0.227430	−	0.393920i	0.957046	+	0.289937i	$0.0936345\pi$
$504$		0			0
$505$	0.559040	+	0.968286i	0.0248769	+	0.0430881i
$506$	−0.739103	−	0.269011i	−0.0328571	−	0.0119590i
$507$		0			0
$508$	−3.79647	−	3.18562i	−0.168441	−	0.141339i
$509$	16.0751	+	13.4886i	0.712515	+	0.597871i	0.925303	−	0.379228i	$-0.123810\pi$
$509$	16.0751	+	13.4886i	0.712515	+	0.597871i	−0.212789	+	0.977098i	$0.568255\pi$
$510$		0			0
$511$	−22.9900	+	5.61415i	−1.01702	+	0.248355i
$512$	−21.3344			−0.942855
$513$		0			0
$514$	−3.66582	−	6.34939i	−0.161693	−	0.280060i
$515$	−2.59030	−	0.942792i	−0.114142	−	0.0415444i
$516$		0			0
$517$	0.241210	−	1.36797i	0.0106084	−	0.0601634i
$518$	−13.7489	−	1.51229i	−0.604091	−	0.0664464i
$519$		0			0
$520$	3.10066	+	1.12855i	0.135973	+	0.0494902i
$521$	−17.6162	+	30.5121i	−0.771779	+	1.33676i	0.164808	+	0.986326i	$0.447299\pi$
$521$	−17.6162	+	30.5121i	−0.771779	+	1.33676i	−0.936587	+	0.350435i	$0.886034\pi$
$522$		0			0
$523$	13.8870	+	24.0530i	0.607237	+	1.05177i	0.991694	+	0.128622i	$0.0410555\pi$
$523$	13.8870	+	24.0530i	0.607237	+	1.05177i	−0.384457	+	0.923143i	$0.625611\pi$
$524$	0.167977	+	0.0611388i	0.00733813	+	0.00267086i
$525$		0			0
$526$	−23.5429	−	19.7548i	−1.02652	−	0.861351i
$527$	−6.82680	+	2.48475i	−0.297380	+	0.108237i
$528$		0			0
$529$	−0.0696228	−	0.394851i	−0.00302708	−	0.0171674i
$530$	0.246612	+	0.427144i	0.0107121	+	0.0185539i
$531$		0			0
$532$	2.72799	+	1.34689i	0.118273	+	0.0583952i
$533$	−5.78278	−	32.7958i	−0.250480	−	1.42054i
$534$		0			0
$535$	0.597749	+	0.501571i	0.0258429	+	0.0216848i
$536$	−11.2423	+	4.09188i	−0.485595	+	0.176742i
$537$		0			0
$538$	4.67651	−	3.92406i	0.201619	−	0.169178i
$539$	−1.00018	+	0.130719i	−0.0430809	+	0.00563047i
$540$		0			0
$541$	0.621748	−	1.07690i	0.0267311	−	0.0462995i	−0.852350	−	0.522971i	$-0.824824\pi$
$541$	0.621748	−	1.07690i	0.0267311	−	0.0462995i	0.879081	+	0.476672i	$0.158157\pi$
$542$	−32.8935	−	11.9722i	−1.41290	−	0.514252i
$543$		0			0
$544$	9.48992	+	7.96299i	0.406877	+	0.341410i
$545$	−1.05148	+	0.382709i	−0.0450406	+	0.0163935i
$546$		0			0
$547$	−2.80105	−	15.8856i	−0.119764	−	0.679218i	−0.984280	−	0.176612i	$-0.943486\pi$
$547$	−2.80105	−	15.8856i	−0.119764	−	0.679218i	0.864516	−	0.502605i	$-0.167625\pi$
$548$	−14.2894			−0.610414
$549$		0			0
$550$	−0.822470			−0.0350702
$551$	−12.8921	+	10.8178i	−0.549224	+	0.460853i
$552$		0			0
$553$	8.14106	−	11.0921i	0.346193	−	0.471682i
$554$	8.45323	+	7.09310i	0.359143	+	0.301357i
$555$		0			0
$556$	1.19584	+	6.78197i	0.0507151	+	0.287620i
$557$	−3.13294			−0.132747			−0.0663734	−	0.997795i	$-0.521143\pi$
$557$	−3.13294			−0.132747			−0.0663734	+	0.997795i	$0.521143\pi$
$558$		0			0
$559$	−13.4941	−	23.3725i	−0.570741	−	0.988552i
$560$	0.274157	−	0.938944i	0.0115852	−	0.0396776i
$561$		0			0
$562$	2.83401	−	16.0725i	0.119546	−	0.677976i
$563$	−16.8513	+	6.13337i	−0.710198	+	0.258491i	−0.671759	−	0.740770i	$-0.734461\pi$
$563$	−16.8513	+	6.13337i	−0.710198	+	0.258491i	−0.0384390	+	0.999261i	$0.512239\pi$
$564$		0			0
$565$	−0.459906	−	2.60826i	−0.0193484	−	0.109730i
$566$	−22.5562			−0.948110
$567$		0			0
$568$	−24.6354			−1.03368
$569$	4.33817	+	24.6030i	0.181866	+	1.03141i	0.929917	+	0.367770i	$0.119879\pi$
$569$	4.33817	+	24.6030i	0.181866	+	1.03141i	−0.748051	+	0.663641i	$0.769010\pi$
$570$		0			0
$571$	16.7730	−	6.10486i	0.701926	−	0.255480i	0.0336931	−	0.999432i	$-0.489273\pi$
$571$	16.7730	−	6.10486i	0.701926	−	0.255480i	0.668233	+	0.743952i	$0.267051\pi$
$572$	−0.107388	+	0.609028i	−0.00449012	+	0.0254648i
$573$		0			0
$574$	−15.6096	+	3.81185i	−0.651531	+	0.159104i
$575$	11.8158	+	20.4655i	0.492751	+	0.853470i
$576$		0			0
$577$	2.97264			0.123753			0.0618763	−	0.998084i	$-0.480292\pi$
$577$	2.97264			0.123753			0.0618763	+	0.998084i	$0.480292\pi$
$578$	−1.11049	−	6.29789i	−0.0461902	−	0.261958i
$579$		0			0
$580$	−0.886711	−	0.744039i	−0.0368187	−	0.0308945i
$581$	23.4335	+	2.57755i	0.972187	+	0.106935i
$582$		0			0
$583$	−0.278582	+	0.233758i	−0.0115377	+	0.00968125i
$584$	27.5413			1.13967
$585$		0			0
$586$	18.7036			0.772640
$587$	0.386555	+	2.19226i	0.0159548	+	0.0904843i	0.991745	−	0.128223i	$-0.0409272\pi$
$587$	0.386555	+	2.19226i	0.0159548	+	0.0904843i	−0.975791	+	0.218707i	$0.929816\pi$
$588$		0			0
$589$	3.40633	−	1.23980i	0.140355	−	0.0510851i
$590$	−0.240980	−	0.202206i	−0.00992098	−	0.00832469i
$591$		0			0
$592$	9.29325	+	3.38246i	0.381950	+	0.139018i
$593$	−6.77093	+	11.7276i	−0.278049	+	0.481595i	−0.970900	−	0.239486i	$-0.923021\pi$
$593$	−6.77093	+	11.7276i	−0.278049	+	0.481595i	0.692851	+	0.721081i	$0.256354\pi$
$594$		0			0
$595$	−1.26634	+	0.845282i	−0.0519150	+	0.0346532i
$596$	1.67758	−	1.40766i	0.0687163	−	0.0576598i
$597$		0			0
$598$	−32.2929	+	11.7536i	−1.32055	+	0.480642i
$599$	−29.3842	−	24.6563i	−1.20061	−	1.00743i	−0.999613	−	0.0278348i	$-0.991139\pi$
$599$	−29.3842	−	24.6563i	−1.20061	−	1.00743i	−0.200993	−	0.979593i	$-0.564417\pi$
$600$		0			0
$601$	−1.21460	−	6.88834i	−0.0495446	−	0.280981i	0.949963	−	0.312363i	$-0.101120\pi$
$601$	−1.21460	−	6.88834i	−0.0495446	−	0.280981i	−0.999507	+	0.0313815i	$0.990009\pi$
$602$	−10.8308	+	7.22952i	−0.441430	+	0.294653i
$603$		0			0
$604$	−5.16629	−	8.94827i	−0.210213	−	0.364100i
$605$	−0.324513	−	1.84041i	−0.0131933	−	0.0748232i
$606$		0			0
$607$	−25.5923	+	9.31485i	−1.03876	+	0.378078i	−0.804410	−	0.594074i	$-0.797519\pi$
$607$	−25.5923	+	9.31485i	−1.03876	+	0.378078i	−0.234350	+	0.972152i	$0.575296\pi$
$608$	−4.73513	−	3.97324i	−0.192035	−	0.161136i
$609$		0			0
$610$	−2.30947	−	0.840580i	−0.0935079	−	0.0340341i
$611$	−30.3458	−	52.5604i	−1.22766	−	2.12637i
$612$		0			0
$613$	−4.52791	+	7.84256i	−0.182880	+	0.316758i	−0.942860	−	0.333189i	$-0.891875\pi$
$613$	−4.52791	+	7.84256i	−0.182880	+	0.316758i	0.759980	+	0.649947i	$0.225209\pi$
$614$	1.94260	+	0.707050i	0.0783971	+	0.0285342i
$615$		0			0
$616$	1.16685	+	0.128346i	0.0470137	+	0.00517122i
$617$	4.13673	−	23.4606i	0.166538	−	0.944486i	−0.780926	−	0.624624i	$-0.785252\pi$
$617$	4.13673	−	23.4606i	0.166538	−	0.944486i	0.947464	−	0.319862i	$-0.103637\pi$
$618$		0			0
$619$	−30.0609	−	10.9413i	−1.20825	−	0.439767i	−0.342154	−	0.939644i	$-0.611156\pi$
$619$	−30.0609	−	10.9413i	−1.20825	−	0.439767i	−0.866096	+	0.499877i	$0.833379\pi$
$620$	0.124660	+	0.215918i	0.00500647	+	0.00867146i
$621$		0			0
$622$	36.6617			1.47000
$623$	16.9387	+	17.7110i	0.678634	+	0.709578i
$624$		0			0
$625$	18.8188	+	15.7909i	0.752754	+	0.631635i
$626$	−0.416112	−	0.349160i	−0.0166312	−	0.0139552i
$627$		0			0
$628$	1.47496	+	0.536842i	0.0588573	+	0.0214223i
$629$	−7.69688	−	13.3314i	−0.306895	−	0.531557i
$630$		0			0
$631$	11.0446	−	19.1298i	0.439679	−	0.761547i	−0.557985	−	0.829851i	$-0.688425\pi$
$631$	11.0446	−	19.1298i	0.439679	−	0.761547i	0.997665	+	0.0683041i	$0.0217588\pi$
$632$	−12.2662	+	10.2926i	−0.487923	+	0.409416i
$633$		0			0
$634$	−5.48642	+	31.1150i	−0.217893	+	1.23574i
$635$	−1.16288	+	0.423255i	−0.0461477	+	0.0167964i
$636$		0			0
$637$	−29.8050	+	32.4650i	−1.18092	+	1.28631i
$638$	−0.825308	+	1.42948i	−0.0326743	+	0.0565935i
$639$		0			0
$640$	−0.211922	+	0.367060i	−0.00837696	+	0.0145093i
$641$	−27.4876	+	23.0648i	−1.08569	+	0.911005i	−0.996381	−	0.0849982i	$-0.972912\pi$
$641$	−27.4876	+	23.0648i	−1.08569	+	0.911005i	−0.0893129	+	0.996004i	$0.528467\pi$
$642$		0			0
$643$	1.07085	−	0.389759i	0.0422303	−	0.0153706i	−0.320819	−	0.947141i	$-0.603958\pi$
$643$	1.07085	−	0.389759i	0.0422303	−	0.0153706i	0.363049	+	0.931770i	$0.381736\pi$
$644$	−3.44927	−	7.84907i	−0.135920	−	0.309297i
$645$		0			0
$646$	−1.13714	−	6.44902i	−0.0447400	−	0.253733i
$647$	11.4892	+	19.8998i	0.451686	+	0.782344i	0.998491	−	0.0549166i	$-0.0174893\pi$
$647$	11.4892	+	19.8998i	0.451686	+	0.782344i	−0.546805	+	0.837260i	$0.684156\pi$
$648$		0			0
$649$	0.115972	−	0.200869i	0.00455228	−	0.00788479i
$650$	−27.5281	+	23.0988i	−1.07974	+	0.906010i
$651$		0			0
$652$	2.25074	−	12.7646i	0.0881457	−	0.499899i
$653$	1.52399	−	8.64300i	0.0596385	−	0.338227i	−0.940360	−	0.340182i	$-0.889511\pi$
$653$	1.52399	−	8.64300i	0.0596385	−	0.338227i	0.999998	+	0.00195535i	$0.000622409\pi$
$654$		0			0
$655$	0.0341935	−	0.0286918i	0.00133605	−	0.00112108i
$656$	11.4887			0.448559
$657$		0			0
$658$	−24.3564	+	16.2578i	−0.949511	+	0.633797i
$659$	10.1921	+	3.70964i	0.397030	+	0.144507i	0.532816	−	0.846231i	$-0.321134\pi$
$659$	10.1921	+	3.70964i	0.397030	+	0.144507i	−0.135786	+	0.990738i	$0.543356\pi$
$660$		0			0
$661$	7.90818	−	44.8495i	0.307592	−	1.74444i	−0.303452	−	0.952847i	$-0.598139\pi$
$661$	7.90818	−	44.8495i	0.307592	−	1.74444i	0.611044	−	0.791596i	$-0.290750\pi$
$662$	1.36572	−	7.74538i	0.0530802	−	0.301033i
$663$		0			0
$664$	−25.7812	−	9.38360i	−1.00051	−	0.364154i
$665$	0.631860	−	0.421765i	0.0245025	−	0.0163553i
$666$		0			0
$667$	47.4261			1.83635
$668$	7.82619	−	6.56695i	0.302804	−	0.254083i
$669$		0			0
$670$	−0.131865	+	0.747842i	−0.00509438	+	0.0288916i
$671$	0.314668	−	1.78457i	0.0121476	−	0.0688926i
$672$		0			0
$673$	−7.07457	+	5.93627i	−0.272704	+	0.228826i	−0.768875	−	0.639399i	$-0.779183\pi$
$673$	−7.07457	+	5.93627i	−0.272704	+	0.228826i	0.496171	+	0.868225i	$0.334739\pi$
$674$	−9.07784	+	15.7233i	−0.349665	+	0.605638i
$675$		0			0
$676$	9.07932	+	15.7259i	0.349205	+	0.604840i
$677$	−3.43872	−	19.5019i	−0.132161	−	0.749520i	−0.976795	−	0.214176i	$-0.931293\pi$
$677$	−3.43872	−	19.5019i	−0.132161	−	0.749520i	0.844634	−	0.535344i	$-0.179818\pi$
$678$		0			0
$679$	5.54354	+	12.6148i	0.212742	+	0.484110i
$680$	1.66503	−	0.606022i	0.0638511	−	0.0232399i
$681$		0			0
$682$	0.272351	−	0.228530i	0.0104289	−	0.00875086i
$683$	14.7646	−	25.5731i	0.564953	−	0.978528i	−0.432101	−	0.901825i	$-0.642227\pi$
$683$	14.7646	−	25.5731i	0.564953	−	0.978528i	0.997054	−	0.0767027i	$-0.0244392\pi$
$684$		0			0
$685$	−1.78406	+	3.09008i	−0.0681654	+	0.118066i
$686$	16.5653	+	13.3335i	0.632465	+	0.509077i
$687$		0			0
$688$	8.74914	−	3.18443i	0.333558	−	0.121405i
$689$	−2.75912	+	15.6478i	−0.105114	+	0.596132i
$690$		0			0
$691$	−0.0177436	+	0.0148886i	−0.000674998	+	0.000566391i	−0.643125	−	0.765761i	$-0.722362\pi$
$691$	−0.0177436	+	0.0148886i	−0.000674998	+	0.000566391i	0.642450	+	0.766328i	$0.277918\pi$
$692$	−1.91597	+	3.31855i	−0.0728341	+	0.126152i
$693$		0			0
$694$	−8.24986	−	14.2892i	−0.313160	−	0.542410i
$695$	1.61590	+	0.588141i	0.0612947	+	0.0223094i
$696$		0			0
$697$	−13.6990	−	11.4948i	−0.518886	−	0.435397i
$698$	−3.44695	−	2.89233i	−0.130469	−	0.109476i
$699$		0			0
$700$	−6.19651	−	6.47906i	−0.234206	−	0.244886i
$701$	−39.4674			−1.49066			−0.745332	−	0.666693i	$-0.767709\pi$
$701$	−39.4674			−1.49066			−0.745332	+	0.666693i	$0.767709\pi$
$702$		0			0
$703$	3.84046	+	6.65188i	0.144846	+	0.250880i
$704$	−1.15791	−	0.421446i	−0.0436405	−	0.0158838i
$705$		0			0
$706$	−3.77462	+	21.4070i	−0.142060	+	0.805661i
$707$	17.2751	+	1.90016i	0.649697	+	0.0714628i
$708$		0			0
$709$	5.73210	+	2.08631i	0.215274	+	0.0783532i	0.447406	−	0.894331i	$-0.352348\pi$
$709$	5.73210	+	2.08631i	0.215274	+	0.0783532i	−0.232132	+	0.972684i	$0.574570\pi$
$710$	−0.781839	+	1.35418i	−0.0293419	+	0.0508216i
$711$		0			0
$712$	−14.2604	−	24.6997i	−0.534430	−	0.925660i
$713$	−9.59915	−	3.49381i	−0.359491	−	0.130844i
$714$		0			0
$715$	0.118295	+	0.0992609i	0.00442397	+	0.00371215i
$716$	7.16533	−	2.60797i	0.267781	−	0.0974644i
$717$		0			0
$718$	6.24784	+	35.4333i	0.233167	+	1.32236i
$719$	12.5915	+	21.8092i	0.469585	+	0.813345i	0.999395	−	0.0347714i	$-0.0110703\pi$
$719$	12.5915	+	21.8092i	0.469585	+	0.813345i	−0.529811	+	0.848116i	$0.677737\pi$
$720$		0			0
$721$	−35.6374	+	23.7879i	−1.32721	+	0.885907i
$722$	−3.22086	−	18.2664i	−0.119868	−	0.679804i
$723$		0			0
$724$	8.63604	+	7.24650i	0.320956	+	0.269314i
$725$	46.6020	−	16.9617i	1.73076	−	0.629943i
$726$		0			0
$727$	3.05828	−	2.56620i	0.113425	−	0.0951750i	−0.584311	−	0.811530i	$-0.698635\pi$
$727$	3.05828	−	2.56620i	0.113425	−	0.0951750i	0.697736	+	0.716355i	$0.254191\pi$
$728$	42.6590	−	28.4748i	1.58105	−	1.05535i
$729$		0			0
$730$	0.874062	−	1.51392i	0.0323505	−	0.0560327i
$731$	−13.6185	−	4.95672i	−0.503698	−	0.183331i
$732$		0			0
$733$	30.8858	+	25.9163i	1.14079	+	0.957240i	0.999464	−	0.0327220i	$-0.0104176\pi$
$733$	30.8858	+	25.9163i	1.14079	+	0.957240i	0.141330	+	0.989962i	$0.454862\pi$
$734$	16.5787	−	6.03417i	0.611932	−	0.222725i
$735$		0			0
$736$	3.02479	+	17.1544i	0.111495	+	0.632320i
$737$	−0.559903			−0.0206243
$738$		0			0
$739$	27.1966			1.00044			0.500221	−	0.865898i	$-0.333252\pi$
$739$	27.1966			1.00044			0.500221	+	0.865898i	$0.333252\pi$
$740$	−0.404692	+	0.339577i	−0.0148768	+	0.0124831i
$741$		0			0
$742$	7.62063	+	0.838225i	0.279762	+	0.0307722i
$743$	38.5421	+	32.3406i	1.41397	+	1.18646i	0.954478	+	0.298281i	$0.0964132\pi$
$743$	38.5421	+	32.3406i	1.41397	+	1.18646i	0.459493	+	0.888181i	$0.348031\pi$
$744$		0			0
$745$	−0.0949564	−	0.538524i	−0.00347893	−	0.0197300i
$746$	3.91037			0.143169
$747$		0			0
$748$	0.166044	+	0.287597i	0.00607118	+	0.0105156i
$749$	11.7827	−	2.87734i	0.430532	−	0.105136i
$750$		0			0
$751$	−8.31549	+	47.1595i	−0.303436	+	1.72087i	0.327338	+	0.944907i	$0.393848\pi$
$751$	−8.31549	+	47.1595i	−0.303436	+	1.72087i	−0.630774	+	0.775966i	$0.717263\pi$
$752$	19.6752	−	7.16118i	0.717480	−	0.261141i
$753$		0			0
$754$	12.5233	+	71.0231i	0.456072	+	2.58651i
$755$	−2.58008			−0.0938988
$756$		0			0
$757$	7.71059			0.280246			0.140123	−	0.990134i	$-0.455250\pi$
$757$	7.71059			0.280246			0.140123	+	0.990134i	$0.455250\pi$
$758$	−4.85985	−	27.5616i	−0.176518	−	1.00108i
$759$		0			0
$760$	−0.830791	+	0.302383i	−0.0301360	+	0.0109686i
$761$	−3.43253	+	19.4668i	−0.124429	+	0.705672i	0.857216	+	0.514957i	$0.172192\pi$
$761$	−3.43253	+	19.4668i	−0.124429	+	0.705672i	−0.981645	+	0.190716i	$0.938919\pi$
$762$		0			0
$763$	−4.87494	+	16.6959i	−0.176485	+	0.604432i
$764$	2.74118	+	4.74786i	0.0991724	+	0.171772i
$765$		0			0
$766$	28.2912			1.02220
$767$	−1.75976	−	9.98011i	−0.0635413	−	0.360361i
$768$		0			0
$769$	13.3451	+	11.1979i	0.481237	+	0.403806i	0.850873	−	0.525371i	$-0.176073\pi$
$769$	13.3451	+	11.1979i	0.481237	+	0.403806i	−0.369637	+	0.929176i	$0.620518\pi$
$770$	0.0440866	−	0.0600672i	0.00158877	−	0.00216467i
$771$		0			0
$772$	−0.767452	+	0.643969i	−0.0276212	+	0.0231769i
$773$	46.5170			1.67310			0.836550	−	0.547890i	$-0.184569\pi$
$773$	46.5170			1.67310			0.836550	+	0.547890i	$0.184569\pi$
$774$		0			0
$775$	−10.6819			−0.383705
$776$	−2.78458	−	15.7921i	−0.0999604	−	0.566904i
$777$		0			0
$778$	37.2447	−	13.5560i	1.33529	−	0.486005i
$779$	6.83530	+	5.73550i	0.244900	+	0.205496i
$780$		0			0
$781$	−1.08340	−	0.394325i	−0.0387670	−	0.0141100i
$782$	−9.22697	+	15.9816i	−0.329956	+	0.571500i
$783$		0			0
$784$	−9.24439	−	12.0710i	−0.330157	−	0.431108i
$785$	0.300243	−	0.251934i	0.0107161	−	0.00899191i
$786$		0			0
$787$	−39.1878	+	14.2632i	−1.39689	+	0.508427i	−0.927255	−	0.374431i	$-0.877838\pi$
$787$	−39.1878	+	14.2632i	−1.39689	+	0.508427i	−0.469638	+	0.882859i	$0.655616\pi$
$788$	8.04025	+	6.74657i	0.286422	+	0.240337i
$789$		0			0
$790$	0.176487	+	1.00091i	0.00627913	+	0.0356107i
$791$	−36.9137	−	18.2254i	−1.31250	−	0.648021i
$792$		0			0
$793$	−39.5872	−	68.5670i	−1.40578	−	2.43488i
$794$	3.33311	+	18.9030i	0.118288	+	0.670844i
$795$		0			0
$796$	7.94941	−	2.89335i	0.281759	−	0.102552i
$797$	26.8243	+	22.5083i	0.950165	+	0.797283i	0.979325	−	0.202292i	$-0.0648389\pi$
$797$	26.8243	+	22.5083i	0.950165	+	0.797283i	−0.0291602	+	0.999575i	$0.509283\pi$
$798$		0			0
$799$	−30.6254	−	11.1467i	−1.08345	−	0.394343i
$800$	9.10742	+	15.7745i	0.321996	+	0.557713i
$801$		0			0
$802$	9.27033	−	16.0567i	0.327347	−	0.566981i
$803$	1.21119	+	0.440838i	0.0427420	+	0.0155568i
$804$		0			0
$805$	−2.12801	−	0.234068i	−0.0750024	−	0.00824982i
$806$	2.69742	−	15.2978i	0.0950124	−	0.538842i
$807$		0			0
$808$	−19.0058	−	6.91754i	−0.668621	−	0.243358i
$809$	18.6727	+	32.3421i	0.656498	+	1.13709i	0.981516	+	0.191380i	$0.0612962\pi$
$809$	18.6727	+	32.3421i	0.656498	+	1.13709i	−0.325018	+	0.945708i	$0.605370\pi$
$810$		0			0
$811$	44.3920			1.55881			0.779407	−	0.626518i	$-0.215520\pi$
$811$	44.3920			1.55881			0.779407	+	0.626518i	$0.215520\pi$
$812$	−17.4787	+	4.26829i	−0.613382	+	0.149788i
$813$		0			0
$814$	0.577089	+	0.484235i	0.0202270	+	0.0169724i
$815$	−2.47932	−	2.08040i	−0.0868469	−	0.0728732i
$816$		0			0
$817$	6.79513	+	2.47322i	0.237731	+	0.0865272i
$818$	−16.1462	−	27.9661i	−0.564540	−	0.977813i
$819$		0			0
$820$	−0.306853	+	0.531485i	−0.0107158	+	0.0185603i
$821$	7.12649	−	5.97983i	0.248716	−	0.208698i	−0.509903	−	0.860232i	$-0.670319\pi$
$821$	7.12649	−	5.97983i	0.248716	−	0.208698i	0.758619	+	0.651534i	$0.225874\pi$
$822$		0			0
$823$	4.36892	−	24.7774i	0.152291	−	0.863685i	−0.808930	−	0.587905i	$-0.799953\pi$
$823$	4.36892	−	24.7774i	0.152291	−	0.863685i	0.961221	−	0.275780i	$-0.0889361\pi$
$824$	46.8573	−	17.0547i	1.63235	−	0.594127i
$825$		0			0
$826$	−4.75016	+	1.15999i	−0.165279	+	0.0403611i
$827$	6.97147	−	12.0749i	0.242422	−	0.419887i	−0.718982	−	0.695029i	$-0.755392\pi$
$827$	6.97147	−	12.0749i	0.242422	−	0.419887i	0.961404	+	0.275142i	$0.0887249\pi$
$828$		0			0
$829$	−13.0177	+	22.5473i	−0.452122	+	0.783099i	−0.998518	−	0.0544286i	$-0.982666\pi$
$829$	−13.0177	+	22.5473i	−0.452122	+	0.783099i	0.546395	+	0.837527i	$0.316000\pi$
$830$	−1.33401	+	1.11937i	−0.0463041	+	0.0388538i
$831$		0			0
$832$	−50.5915	+	18.4138i	−1.75395	+	0.638384i
$833$	−1.05456	+	23.6426i	−0.0365382	+	0.819169i
$834$		0			0
$835$	−0.442987	−	2.51231i	−0.0153302	−	0.0869419i
$836$	−0.0828501	−	0.143501i	−0.00286543	−	0.00496307i
$837$		0			0
$838$	14.4841	−	25.0872i	0.500345	−	0.866624i
$839$	30.3032	−	25.4274i	1.04618	−	0.877851i	0.0534949	−	0.998568i	$-0.482964\pi$
$839$	30.3032	−	25.4274i	1.04618	−	0.877851i	0.992687	+	0.120717i	$0.0385195\pi$
$840$		0			0
$841$	12.2471	−	69.4565i	0.422312	−	2.39505i
$842$	−5.88970	+	33.4022i	−0.202972	+	1.15111i
$843$		0			0
$844$	−5.39198	+	4.52441i	−0.185600	+	0.155737i
$845$	4.53428			0.155984
$846$		0			0
$847$	−26.0466	−	12.8600i	−0.894972	−	0.441875i
$848$	−5.15100	−	1.87481i	−0.176886	−	0.0643812i
$849$		0			0
$850$	−3.35089	+	19.0038i	−0.114935	+	0.651826i
$851$	3.75864	−	21.3163i	0.128844	−	0.730713i
$852$		0			0
$853$	51.7193	+	18.8243i	1.77084	+	0.644532i	0.999972	+	0.00753249i	$0.00239769\pi$
$853$	51.7193	+	18.8243i	1.77084	+	0.644532i	0.770864	+	0.636999i	$0.219825\pi$
$854$	−31.7738	+	21.2090i	−1.08728	+	0.725755i
$855$		0			0
$856$	−14.1154			−0.482453
$857$	−17.8156	+	14.9491i	−0.608569	+	0.510650i	−0.894187	−	0.447693i	$-0.852246\pi$
$857$	−17.8156	+	14.9491i	−0.608569	+	0.510650i	0.285618	+	0.958344i	$0.407801\pi$
$858$		0			0
$859$	2.34655	−	13.3080i	0.0800634	−	0.454062i	−0.918250	−	0.396002i	$-0.870397\pi$
$859$	2.34655	−	13.3080i	0.0800634	−	0.454062i	0.998313	−	0.0580601i	$-0.0184915\pi$
$860$	−0.0863652	+	0.489802i	−0.00294503	+	0.0167021i
$861$		0			0
$862$	13.9384	−	11.6957i	0.474744	−	0.398357i
$863$	−24.3552	+	42.1844i	−0.829059	+	1.43597i	0.0697177	+	0.997567i	$0.477790\pi$
$863$	−24.3552	+	42.1844i	−0.829059	+	1.43597i	−0.898777	+	0.438406i	$0.855543\pi$
$864$		0			0
$865$	0.478424	+	0.828654i	0.0162669	+	0.0281751i
$866$	−2.21825	−	12.5803i	−0.0753790	−	0.427496i
$867$		0			0
$868$	3.85216	+	0.423715i	0.130751	+	0.0143818i
$869$	−0.704180	+	0.256300i	−0.0238877	+	0.00869440i
$870$		0			0
$871$	−18.7400	+	15.7247i	−0.634980	+	0.532812i
$872$	10.1208	−	17.5297i	0.342733	−	0.593631i
$873$		0			0
$874$	4.60392	−	7.97423i	0.155730	−	0.269732i
$875$	−4.36216	+	1.06524i	−0.147468	+	0.0360116i
$876$		0			0
$877$	−6.44297	+	2.34505i	−0.217564	+	0.0791867i	−0.448503	−	0.893782i	$-0.648043\pi$
$877$	−6.44297	+	2.34505i	−0.217564	+	0.0791867i	0.230939	+	0.972968i	$0.425820\pi$
$878$	−4.60717	+	26.1285i	−0.155484	+	0.881795i
$879$		0			0
$880$	−0.0408103	+	0.0342439i	−0.00137572	+	0.00115436i
$881$	−28.9915	+	50.2148i	−0.976749	+	1.69178i	−0.302709	+	0.953083i	$0.597891\pi$
$881$	−28.9915	+	50.2148i	−0.976749	+	1.69178i	−0.674040	+	0.738695i	$0.735442\pi$
$882$		0			0
$883$	7.00145	+	12.1269i	0.235617	+	0.408101i	0.959452	−	0.281872i	$-0.0909554\pi$
$883$	7.00145	+	12.1269i	0.235617	+	0.408101i	−0.723835	+	0.689974i	$0.757622\pi$
$884$	13.6346	+	4.96258i	0.458581	+	0.166910i
$885$		0			0
$886$	10.9628	+	9.19888i	0.368302	+	0.309042i
$887$	−15.1487	−	12.7113i	−0.508644	−	0.426803i	0.352008	−	0.935997i	$-0.385499\pi$
$887$	−15.1487	−	12.7113i	−0.508644	−	0.426803i	−0.860652	+	0.509194i	$0.829943\pi$
$888$		0			0
$889$	−5.39142	+	18.4648i	−0.180822	+	0.619288i
$890$	−1.81029			−0.0606810
$891$		0			0
$892$	−3.27972	−	5.68065i	−0.109813	−	0.190202i
$893$	15.2810	+	5.56182i	0.511358	+	0.186119i
$894$		0			0
$895$	0.330633	−	1.87511i	0.0110518	−	0.0626781i
$896$	2.65053	+	6.03148i	0.0885479	+	0.201498i
$897$		0			0
$898$	−28.7213	−	10.4537i	−0.958441	−	0.348844i
$899$	−10.7188	+	18.5654i	−0.357491	+	0.619192i
$900$		0			0
$901$	4.26617	+	7.38923i	0.142127	+	0.246171i
$902$	0.822365	+	0.299317i	0.0273818	+	0.00996615i
$903$		0			0
$904$	36.7012	+	30.7959i	1.22066	+	1.02426i
$905$	2.64528	−	0.962803i	0.0879320	−	0.0320046i
$906$		0			0
$907$	1.63499	+	9.27248i	0.0542889	+	0.307888i	0.999846	−	0.0175697i	$-0.00559289\pi$
$907$	1.63499	+	9.27248i	0.0542889	+	0.307888i	−0.945557	+	0.325457i	$0.894482\pi$
$908$	−1.10167	−	1.90815i	−0.0365601	−	0.0633240i
$909$		0			0
$910$	−0.211390	−	3.24861i	−0.00700750	−	0.107690i
$911$	−1.41448	−	8.02194i	−0.0468639	−	0.265779i	0.952369	−	0.304949i	$-0.0986395\pi$
$911$	−1.41448	−	8.02194i	−0.0468639	−	0.265779i	−0.999233	+	0.0391707i	$0.987528\pi$
$912$		0			0
$913$	−0.983589	−	0.825329i	−0.0325520	−	0.0273144i
$914$	8.89677	−	3.23816i	0.294279	−	0.107109i
$915$		0			0
$916$	−9.28237	+	7.78883i	−0.306698	+	0.257350i
$917$	−0.0450524	−	0.692359i	−0.00148776	−	0.0228637i
$918$		0			0
$919$	−5.23459	+	9.06658i	−0.172673	+	0.299079i	−0.939354	−	0.342950i	$-0.888574\pi$
$919$	−5.23459	+	9.06658i	−0.172673	+	0.299079i	0.766680	+	0.642029i	$0.221907\pi$
$920$	2.34120	+	0.852127i	0.0771871	+	0.0280938i
$921$		0			0
$922$	11.2162	+	9.41152i	0.369386	+	0.309952i
$923$	−47.3358	+	17.2288i	−1.55808	+	0.567094i
$924$		0			0
$925$	−3.93035	−	22.2901i	−0.129229	−	0.732895i
$926$	18.5526			0.609677
$927$		0			0
$928$	36.5554			1.19999
$929$	32.6961	−	27.4353i	1.07273	−	0.900124i	0.0774290	−	0.996998i	$-0.475329\pi$
$929$	32.6961	−	27.4353i	1.07273	−	0.900124i	0.995297	+	0.0968742i	$0.0308844\pi$
$930$		0			0
$931$	0.526186	−	11.7968i	0.0172450	−	0.386625i
$932$	−9.19472	−	7.71528i	−0.301183	−	0.252722i
$933$		0			0
$934$	4.70988	+	26.7111i	0.154112	+	0.874012i
$935$	0.0829237			0.00271190
$936$		0			0
$937$	12.3773	+	21.4382i	0.404350	+	0.700355i	0.994246	−	0.107125i	$-0.0341645\pi$
$937$	12.3773	+	21.4382i	0.404350	+	0.700355i	−0.589896	+	0.807479i	$0.700831\pi$
$938$	8.15838	+	8.53039i	0.266381	+	0.278527i
$939$		0			0
$940$	−0.194219	+	1.10147i	−0.00633473	+	0.0359261i
$941$	34.1809	−	12.4408i	1.11426	−	0.405559i	0.281708	−	0.959500i	$-0.409099\pi$
$941$	34.1809	−	12.4408i	1.11426	−	0.405559i	0.832556	+	0.553941i	$0.186877\pi$
$942$		0			0
$943$	−4.36637	−	24.7629i	−0.142189	−	0.806392i
$944$	3.49614			0.113790
$945$		0			0
$946$	0.709230			0.0230591
$947$	1.99686	+	11.3248i	0.0648892	+	0.368005i	0.999910	+	0.0134123i	$0.00426941\pi$
$947$	1.99686	+	11.3248i	0.0648892	+	0.368005i	−0.935021	+	0.354593i	$0.884619\pi$
$948$		0			0
$949$	52.9194	−	19.2611i	1.71784	−	0.625241i
$950$	1.67197	−	9.48223i	0.0542460	−	0.307644i
$951$		0			0
$952$	7.71950	−	26.4381i	0.250190	−	0.856863i
$953$	−20.4267	−	35.3801i	−0.661686	−	1.14607i	−0.980172	−	0.198147i	$-0.936508\pi$
$953$	−20.4267	−	35.3801i	−0.661686	−	1.14607i	0.318486	−	0.947927i	$-0.396826\pi$
$954$		0			0
$955$	1.36897			0.0442987
$956$	2.25204	+	12.7719i	0.0728361	+	0.413074i
$957$		0			0
$958$	−20.8223	−	17.4720i	−0.672737	−	0.564493i
$959$	22.3134	+	50.7758i	0.720537	+	1.63964i
$960$		0			0
$961$	−20.2102	+	16.9584i	−0.651942	+	0.547044i
$962$	32.9148			1.06122
$963$		0			0
$964$	0.846058			0.0272497
$965$	0.0434403	+	0.246362i	0.00139839	+	0.00793067i
$966$		0			0
$967$	−31.8205	+	11.5817i	−1.02328	+	0.372443i	−0.798518	−	0.601971i	$-0.794382\pi$
$967$	−31.8205	+	11.5817i	−1.02328	+	0.372443i	−0.224761	+	0.974414i	$0.572160\pi$
$968$	25.8966	+	21.7299i	0.832350	+	0.698424i
$969$		0			0
$970$	−0.956449	−	0.348119i	−0.0307097	−	0.0111774i
$971$	12.6853	−	21.9715i	0.407090	−	0.705100i	−0.587472	−	0.809244i	$-0.699877\pi$
$971$	12.6853	−	21.9715i	0.407090	−	0.705100i	0.994562	+	0.104144i	$0.0332103\pi$
$972$		0			0
$973$	22.2316	−	14.8396i	0.712713	−	0.475735i
$974$	3.30929	−	2.77682i	0.106036	−	0.0889752i
$975$		0			0
$976$	25.6670	−	9.34203i	0.821581	−	0.299031i
$977$	−28.7995	−	24.1656i	−0.921377	−	0.773127i	0.0528718	−	0.998601i	$-0.483163\pi$
$977$	−28.7995	−	24.1656i	−0.921377	−	0.773127i	−0.974249	+	0.225474i	$0.927607\pi$
$978$		0			0
$979$	−0.231778	−	1.31448i	−0.00740767	−	0.0420110i
$980$	0.805333	−	0.105253i	0.0257254	−	0.00336219i
$981$		0			0
$982$	−4.59754	−	7.96318i	−0.146713	−	0.254115i
$983$	0.385671	+	2.18725i	0.0123010	+	0.0697625i	0.990340	−	0.138658i	$-0.0442789\pi$
$983$	0.385671	+	2.18725i	0.0123010	+	0.0697625i	−0.978039	+	0.208420i	$0.933168\pi$
$984$		0			0
$985$	2.46279	−	0.896380i	0.0784709	−	0.0285611i
$986$	29.6668	+	24.8934i	0.944783	+	0.792767i
$987$		0			0
$988$	−6.80317	−	2.47615i	−0.216438	−	0.0787768i
$989$	−10.1889	−	17.6477i	−0.323989	−	0.561166i
$990$		0			0
$991$	20.3854	−	35.3086i	0.647565	−	1.12161i	−0.336138	−	0.941813i	$-0.609121\pi$
$991$	20.3854	−	35.3086i	0.647565	−	1.12161i	0.983703	−	0.179802i	$-0.0575458\pi$
$992$	−7.39889	−	2.69298i	−0.234915	−	0.0855021i
$993$		0			0
$994$	9.77852	+	22.2518i	0.310156	+	0.705784i
$995$	0.366812	−	2.08030i	0.0116287	−	0.0659498i
$996$		0			0
$997$	56.6621	+	20.6233i	1.79451	+	0.653147i	0.998878	+	0.0473602i	$0.0150809\pi$
$997$	56.6621	+	20.6233i	1.79451	+	0.653147i	0.795627	+	0.605786i	$0.207141\pi$
$998$	3.14058	+	5.43965i	0.0994135	+	0.172189i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.w.a.37.16		132
3.2	odd	2		189.2.w.a.184.7	yes	132
7.4	even	3		567.2.u.a.361.7		132
21.11	odd	6		189.2.u.a.130.16	yes	132
27.11	odd	18		189.2.u.a.16.16	✓	132
27.16	even	9		567.2.u.a.289.7		132
189.11	odd	18		189.2.w.a.151.7	yes	132
189.151	even	9	inner	567.2.w.a.46.16		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.16	✓	132	27.11	odd	18
189.2.u.a.130.16	yes	132	21.11	odd	6
189.2.w.a.151.7	yes	132	189.11	odd	18
189.2.w.a.184.7	yes	132	3.2	odd	2
567.2.u.a.289.7		132	27.16	even	9
567.2.u.a.361.7		132	7.4	even	3
567.2.w.a.37.16		132	1.1	even	1	trivial
567.2.w.a.46.16		132	189.151	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.w (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.199381 + 1.13075i) q^{2} +(0.640547 - 0.233140i) q^{4} +(0.0295570 - 0.167626i) q^{5} +(-1.82867 - 1.91206i) q^{7} +(1.53953 + 2.66654i) q^{8} +O(q^{10})\)	\(q+(0.199381 + 1.13075i) q^{2} +(0.640547 - 0.233140i) q^{4} +(0.0295570 - 0.167626i) q^{5} +(-1.82867 - 1.91206i) q^{7} +(1.53953 + 2.66654i) q^{8} +0.195436 q^{10} +(0.0250224 + 0.141909i) q^{11} +(4.82298 + 4.04696i) q^{13} +(1.79745 - 2.44900i) q^{14} +(-1.66387 + 1.39616i) q^{16} +3.38088 q^{17} -1.68694 q^{19} +(-0.0201477 - 0.114263i) q^{20} +(-0.155475 + 0.0565881i) q^{22} +(3.64166 + 3.05571i) q^{23} +(4.67124 + 1.70019i) q^{25} +(-3.61448 + 6.26046i) q^{26} +(-1.61713 - 0.798425i) q^{28} +(7.64234 - 6.41269i) q^{29} +(-2.01924 + 0.734943i) q^{31} +(2.80694 + 2.35530i) q^{32} +(0.674084 + 3.82292i) q^{34} +(-0.374561 + 0.250018i) q^{35} +(-2.27659 - 3.94317i) q^{37} +(-0.336344 - 1.90750i) q^{38} +(0.492485 - 0.179250i) q^{40} +(-4.05191 - 3.39995i) q^{41} +(-4.02809 - 1.46610i) q^{43} +(0.0491128 + 0.0850658i) q^{44} +(-2.72916 + 4.72705i) q^{46} +(-9.05842 - 3.29700i) q^{47} +(-0.311918 + 6.99305i) q^{49} +(-0.991130 + 5.62098i) q^{50} +(4.03285 + 1.46784i) q^{52} +(1.26185 + 2.18560i) q^{53} +0.0245273 q^{55} +(2.28328 - 7.81989i) q^{56} +(8.77488 + 7.36299i) q^{58} +(-1.23304 - 1.03464i) q^{59} +(-11.8170 - 4.30105i) q^{61} +(-1.23363 - 2.13672i) q^{62} +(-4.27563 + 7.40562i) q^{64} +(0.820929 - 0.688841i) q^{65} +(-0.674721 + 3.82653i) q^{67} +(2.16561 - 0.788218i) q^{68} +(-0.357388 - 0.373685i) q^{70} +(-4.00049 + 6.92905i) q^{71} +(4.47237 - 7.74637i) q^{73} +(4.00482 - 3.36045i) q^{74} +(-1.08056 + 0.393292i) q^{76} +(0.225581 - 0.307350i) q^{77} +(0.903043 + 5.12141i) q^{79} +(0.184853 + 0.320175i) q^{80} +(3.03661 - 5.25957i) q^{82} +(-6.82581 + 5.72754i) q^{83} +(0.0999286 - 0.566723i) q^{85} +(0.854669 - 4.84707i) q^{86} +(-0.339884 + 0.285197i) q^{88} -9.26283 q^{89} +(-1.08163 - 16.6224i) q^{91} +(3.04506 + 1.10831i) q^{92} +(1.92199 - 10.9001i) q^{94} +(-0.0498608 + 0.282774i) q^{95} +(-4.89392 - 1.78124i) q^{97} +(-7.96956 + 1.04158i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

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