LMFDB - Embedded newform 567.2.bd.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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([11, 3]))

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

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

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, 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 $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87320 + 0.330296i) q^{2} +(1.52040 - 0.553380i) q^{4} +(0.848304 - 0.308757i) q^{5} +(2.48993 + 0.894564i) q^{7} +(0.629295 - 0.363324i) q^{8} +O(q^{10})$	\(q+(-1.87320 + 0.330296i) q^{2} +(1.52040 - 0.553380i) q^{4} +(0.848304 - 0.308757i) q^{5} +(2.48993 + 0.894564i) q^{7} +(0.629295 - 0.363324i) q^{8} +(-1.48706 + 0.858555i) q^{10} +(1.19563 - 3.28497i) q^{11} +(-1.35464 - 3.72184i) q^{13} +(-4.95961 - 0.853285i) q^{14} +(-3.53767 + 2.96846i) q^{16} +(0.233932 + 0.405183i) q^{17} +(3.14258 + 1.81437i) q^{19} +(1.11890 - 0.938869i) q^{20} +(-1.15465 + 6.54832i) q^{22} +(-3.44344 - 0.607171i) q^{23} +(-3.20593 + 2.69010i) q^{25} +(3.76682 + 6.52432i) q^{26} +(4.28072 - 0.0177830i) q^{28} +(1.79273 - 4.92550i) q^{29} +(-2.38270 - 6.54641i) q^{31} +(4.71214 - 5.61571i) q^{32} +(-0.572032 - 0.681722i) q^{34} +(2.38842 - 0.00992201i) q^{35} +9.85377 q^{37} +(-6.48596 - 2.36070i) q^{38} +(0.421655 - 0.502508i) q^{40} +(-2.71326 + 0.987547i) q^{41} +(-1.54504 - 8.76238i) q^{43} -5.65611i q^{44} +6.65080 q^{46} +(3.13508 + 1.14108i) q^{47} +(5.39951 + 4.45481i) q^{49} +(5.11683 - 6.09800i) q^{50} +(-4.11919 - 4.90906i) q^{52} +(8.75304 + 5.05357i) q^{53} -3.15581i q^{55} +(1.89192 - 0.341706i) q^{56} +(-1.73128 + 9.81858i) q^{58} +(2.48304 + 2.08352i) q^{59} +(0.0209011 - 0.0574254i) q^{61} +(6.62553 + 11.4757i) q^{62} +(-2.35384 + 4.07697i) q^{64} +(-2.29829 - 2.73900i) q^{65} +(1.78024 - 10.0962i) q^{67} +(0.579891 + 0.486586i) q^{68} +(-4.47071 + 0.807471i) q^{70} +(2.19935 + 1.26979i) q^{71} -8.37008i q^{73} +(-18.4581 + 3.25466i) q^{74} +(5.78202 + 1.01953i) q^{76} +(5.91566 - 7.10978i) q^{77} +(1.64089 + 9.30597i) q^{79} +(-2.08449 + 3.61044i) q^{80} +(4.75630 - 2.74605i) q^{82} +(10.6153 + 3.86367i) q^{83} +(0.323549 + 0.271490i) q^{85} +(5.78836 + 15.9034i) q^{86} +(-0.441103 - 2.50162i) q^{88} +(1.51868 - 2.63043i) q^{89} +(-0.0435318 - 10.4789i) q^{91} +(-5.57140 + 0.982388i) q^{92} +(-6.24952 - 1.10196i) q^{94} +(3.22606 + 0.568842i) q^{95} +(5.02929 - 0.886800i) q^{97} +(-11.5858 - 6.56131i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.87320	+	0.330296i	−1.32455	+	0.233554i	−0.790794	−	0.612082i	$-0.790332\pi$
$2$	−1.87320	+	0.330296i	−1.32455	+	0.233554i	−0.533759	+	0.845637i	$0.679221\pi$
$3$		0			0
$3$		0			0
$4$	1.52040	−	0.553380i	0.760200	−	0.276690i
$5$	0.848304	−	0.308757i	0.379373	−	0.138080i	−0.145293	−	0.989389i	$-0.546412\pi$
$5$	0.848304	−	0.308757i	0.379373	−	0.138080i	0.524666	+	0.851308i	$0.324190\pi$
$6$		0			0
$7$	2.48993	+	0.894564i	0.941105	+	0.338114i
$7$	2.48993	+	0.894564i	0.941105	+	0.338114i
$8$	0.629295	−	0.363324i	0.222489	−	0.128454i
$9$		0			0
$10$	−1.48706	+	0.858555i	−0.470250	+	0.271499i
$11$	1.19563	−	3.28497i	0.360497	−	0.990456i	−0.618358	−	0.785897i	$-0.712202\pi$
$11$	1.19563	−	3.28497i	0.360497	−	0.990456i	0.978854	−	0.204559i	$-0.0655761\pi$
$12$		0			0
$13$	−1.35464	−	3.72184i	−0.375709	−	1.03225i	−0.973116	−	0.230315i	$-0.926024\pi$
$13$	−1.35464	−	3.72184i	−0.375709	−	1.03225i	0.597407	−	0.801938i	$-0.296198\pi$
$14$	−4.95961	−	0.853285i	−1.32551	−	0.228050i
$15$		0			0
$16$	−3.53767	+	2.96846i	−0.884419	+	0.742115i
$17$	0.233932	+	0.405183i	0.0567369	+	0.0982712i	0.892999	−	0.450059i	$-0.148597\pi$
$17$	0.233932	+	0.405183i	0.0567369	+	0.0982712i	−0.836262	+	0.548330i	$0.815264\pi$
$18$		0			0
$19$	3.14258	+	1.81437i	0.720958	+	0.416245i	0.815105	−	0.579313i	$-0.196679\pi$
$19$	3.14258	+	1.81437i	0.720958	+	0.416245i	−0.0941474	+	0.995558i	$0.530013\pi$
$20$	1.11890	−	0.938869i	0.250194	−	0.209938i
$21$		0			0
$22$	−1.15465	+	6.54832i	−0.246171	+	1.39611i
$23$	−3.44344	−	0.607171i	−0.718006	−	0.126604i	−0.197304	−	0.980342i	$-0.563219\pi$
$23$	−3.44344	−	0.607171i	−0.718006	−	0.126604i	−0.520702	+	0.853738i	$0.674330\pi$
$24$		0			0
$25$	−3.20593	+	2.69010i	−0.641187	+	0.538020i
$26$	3.76682	+	6.52432i	0.738734	+	1.27953i
$27$		0			0
$28$	4.28072	−	0.0177830i	0.808981	−	0.00336068i
$29$	1.79273	−	4.92550i	0.332902	−	0.914642i	−0.654451	−	0.756105i	$-0.727100\pi$
$29$	1.79273	−	4.92550i	0.332902	−	0.914642i	0.987353	−	0.158537i	$-0.0506777\pi$
$30$		0			0
$31$	−2.38270	−	6.54641i	−0.427945	−	1.17577i	−0.947057	−	0.321064i	$-0.895959\pi$
$31$	−2.38270	−	6.54641i	−0.427945	−	1.17577i	0.519112	−	0.854706i	$-0.326263\pi$
$32$	4.71214	−	5.61571i	0.832997	−	0.992727i
$33$		0			0
$34$	−0.572032	−	0.681722i	−0.0981027	−	0.116914i
$35$	2.38842	−	0.00992201i	0.403717	−	0.00167713i
$36$		0			0
$37$	9.85377			1.61995			0.809975	−	0.586464i	$-0.199481\pi$
$37$	9.85377			1.61995			0.809975	+	0.586464i	$0.199481\pi$
$38$	−6.48596	−	2.36070i	−1.05216	−	0.382956i
$39$		0			0
$40$	0.421655	−	0.502508i	0.0666695	−	0.0794536i
$41$	−2.71326	+	0.987547i	−0.423741	+	0.154229i	−0.545084	−	0.838382i	$-0.683502\pi$
$41$	−2.71326	+	0.987547i	−0.423741	+	0.154229i	0.121343	+	0.992611i	$0.461280\pi$
$42$		0			0
$43$	−1.54504	−	8.76238i	−0.235617	−	1.33625i	−0.841310	−	0.540553i	$-0.818215\pi$
$43$	−1.54504	−	8.76238i	−0.235617	−	1.33625i	0.605693	−	0.795698i	$-0.292896\pi$
$44$		−	5.65611i		−	0.852690i
$45$		0			0
$46$	6.65080			0.980606
$47$	3.13508	+	1.14108i	0.457298	+	0.166443i	0.560390	−	0.828229i	$-0.310651\pi$
$47$	3.13508	+	1.14108i	0.457298	+	0.166443i	−0.103092	+	0.994672i	$0.532874\pi$
$48$		0			0
$49$	5.39951	+	4.45481i	0.771358	+	0.636401i
$50$	5.11683	−	6.09800i	0.723629	−	0.862387i
$51$		0			0
$52$	−4.11919	−	4.90906i	−0.571228	−	0.680764i
$53$	8.75304	+	5.05357i	1.20232	+	0.694161i	0.961071	−	0.276302i	$-0.0891090\pi$
$53$	8.75304	+	5.05357i	1.20232	+	0.694161i	0.241251	+	0.970463i	$0.422442\pi$
$54$		0			0
$55$		−	3.15581i		−	0.425530i
$56$	1.89192	−	0.341706i	0.252818	−	0.0456624i
$57$		0			0
$58$	−1.73128	+	9.81858i	−0.227328	+	1.28924i
$59$	2.48304	+	2.08352i	0.323265	+	0.271251i	0.789949	−	0.613173i	$-0.210107\pi$
$59$	2.48304	+	2.08352i	0.323265	+	0.271251i	−0.466684	+	0.884424i	$0.654551\pi$
$60$		0			0
$61$	0.0209011	−	0.0574254i	0.00267611	−	0.00735257i	−0.938347	−	0.345694i	$-0.887644\pi$
$61$	0.0209011	−	0.0574254i	0.00267611	−	0.00735257i	0.941023	+	0.338341i	$0.109866\pi$
$62$	6.62553	+	11.4757i	0.841443	+	1.45742i
$63$		0			0
$64$	−2.35384	+	4.07697i	−0.294230	+	0.509621i
$65$	−2.29829	−	2.73900i	−0.285068	−	0.339731i
$66$		0			0
$67$	1.78024	−	10.0962i	0.217491	−	1.23345i	−0.659041	−	0.752107i	$-0.729038\pi$
$67$	1.78024	−	10.0962i	0.217491	−	1.23345i	0.876532	−	0.481344i	$-0.159851\pi$
$68$	0.579891	+	0.486586i	0.0703221	+	0.0590072i
$69$		0			0
$70$	−4.47071	+	0.807471i	−0.534352	+	0.0965113i
$71$	2.19935	+	1.26979i	0.261014	+	0.150697i	0.624797	−	0.780787i	$-0.285182\pi$
$71$	2.19935	+	1.26979i	0.261014	+	0.150697i	−0.363783	+	0.931484i	$0.618515\pi$
$72$		0			0
$73$		−	8.37008i		−	0.979643i	−0.871823	−	0.489822i	$-0.837062\pi$
$73$		−	8.37008i		−	0.979643i	0.871823	−	0.489822i	$-0.162938\pi$
$74$	−18.4581	+	3.25466i	−2.14571	+	0.378346i
$75$		0			0
$76$	5.78202	+	1.01953i	0.663243	+	0.116948i
$77$	5.91566	−	7.10978i	0.674152	−	0.810235i
$78$		0			0
$79$	1.64089	+	9.30597i	0.184615	+	1.04700i	0.926449	+	0.376420i	$0.122845\pi$
$79$	1.64089	+	9.30597i	0.184615	+	1.04700i	−0.741834	+	0.670583i	$0.766044\pi$
$80$	−2.08449	+	3.61044i	−0.233053	+	0.403659i
$81$		0			0
$82$	4.75630	−	2.74605i	0.525246	−	0.303251i
$83$	10.6153	+	3.86367i	1.16518	+	0.424092i	0.850947	−	0.525252i	$-0.176029\pi$
$83$	10.6153	+	3.86367i	1.16518	+	0.424092i	0.314237	+	0.949344i	$0.398251\pi$
$84$		0			0
$85$	0.323549	+	0.271490i	0.0350938	+	0.0294472i
$86$	5.78836	+	15.9034i	0.624175	+	1.71491i
$87$		0			0
$88$	−0.441103	−	2.50162i	−0.0470217	−	0.266673i
$89$	1.51868	−	2.63043i	0.160980	−	0.278825i	−0.774241	−	0.632891i	$-0.781868\pi$
$89$	1.51868	−	2.63043i	0.160980	−	0.278825i	0.935220	+	0.354066i	$0.115201\pi$
$90$		0			0
$91$	−0.0435318	−	10.4789i	−0.00456337	−	1.09849i
$92$	−5.57140	+	0.982388i	−0.580858	+	0.102421i
$93$		0			0
$94$	−6.24952	−	1.10196i	−0.644589	−	0.113658i
$95$	3.22606	+	0.568842i	0.330987	+	0.0583620i
$96$		0			0
$97$	5.02929	−	0.886800i	0.510647	−	0.0900409i	0.0876131	−	0.996155i	$-0.472076\pi$
$97$	5.02929	−	0.886800i	0.510647	−	0.0900409i	0.423034	+	0.906114i	$0.360965\pi$
$98$	−11.5858	−	6.56131i	−1.17034	−	0.662792i
$99$		0			0
$100$	−3.38565	+	5.86413i	−0.338565	+	0.586413i
$101$	−2.32953	−	13.2114i	−0.231797	−	1.31459i	−0.849255	−	0.527983i	$-0.822948\pi$
$101$	−2.32953	−	13.2114i	−0.231797	−	1.31459i	0.617457	−	0.786604i	$-0.288163\pi$
$102$		0			0
$103$	5.15600	+	14.1660i	0.508036	+	1.39582i	0.883260	+	0.468883i	$0.155343\pi$
$103$	5.15600	+	14.1660i	0.508036	+	1.39582i	−0.375225	+	0.926934i	$0.622434\pi$
$104$	−2.20470	−	1.84996i	−0.216189	−	0.181404i
$105$		0			0
$106$	−18.0654	−	6.57525i	−1.75466	−	0.638645i
$107$	−12.8332	+	7.40924i	−1.24063	+	0.716278i	−0.969222	−	0.246187i	$-0.920822\pi$
$107$	−12.8332	+	7.40924i	−1.24063	+	0.716278i	−0.271407	+	0.962465i	$0.587489\pi$
$108$		0			0
$109$	−1.48332	+	2.56918i	−0.142076	+	0.246083i	−0.928278	−	0.371886i	$-0.878711\pi$
$109$	−1.48332	+	2.56918i	−0.142076	+	0.246083i	0.786202	+	0.617969i	$0.212044\pi$
$110$	1.04235	+	5.91147i	0.0993844	+	0.563637i
$111$		0			0
$112$	−11.4640	+	4.22659i	−1.08325	+	0.399375i
$113$	−12.0005	−	2.11601i	−1.12891	−	0.199058i	−0.422162	−	0.906520i	$-0.638729\pi$
$113$	−12.0005	−	2.11601i	−1.12891	−	0.199058i	−0.706751	+	0.707463i	$0.749840\pi$
$114$		0			0
$115$	−3.10855	+	0.548121i	−0.289874	+	0.0511126i
$116$		−	8.48079i		−	0.787421i
$117$		0			0
$118$	−5.33942	−	3.08271i	−0.491533	−	0.283787i
$119$	0.220013	+	1.21814i	0.0201686	+	0.111667i
$120$		0			0
$121$	−0.935012	−	0.784569i	−0.0850011	−	0.0713244i
$122$	−0.0201846	+	0.114473i	−0.00182743	+	0.0103639i
$123$		0			0
$124$	−7.24531	−	8.63463i	−0.650648	−	0.775412i
$125$	−4.14588	+	7.18088i	−0.370819	+	0.642277i
$126$		0			0
$127$	−4.12812	−	7.15011i	−0.366311	−	0.634469i	0.622675	−	0.782481i	$-0.286046\pi$
$127$	−4.12812	−	7.15011i	−0.366311	−	0.634469i	−0.988986	+	0.148012i	$0.952713\pi$
$128$	−1.95195	+	5.36295i	−0.172530	+	0.474022i
$129$		0			0
$130$	5.20984	+	4.37157i	0.456933	+	0.383412i
$131$	−3.60230	+	20.4297i	−0.314734	+	1.78495i	0.258970	+	0.965885i	$0.416617\pi$
$131$	−3.60230	+	20.4297i	−0.314734	+	1.78495i	−0.573704	+	0.819062i	$0.694494\pi$
$132$		0			0
$133$	6.20174	+	7.32890i	0.537759	+	0.635496i
$134$			19.5003i			1.68457i
$135$		0			0
$136$	0.294425	+	0.169986i	0.0252467	+	0.0145762i
$137$	−7.84338	−	9.34738i	−0.670105	−	0.798600i	0.318693	−	0.947858i	$-0.396756\pi$
$137$	−7.84338	−	9.34738i	−0.670105	−	0.798600i	−0.988798	+	0.149258i	$0.952312\pi$
$138$		0			0
$139$	−11.5620	+	13.7791i	−0.980677	+	1.16873i	0.00498385	+	0.999988i	$0.498414\pi$
$139$	−11.5620	+	13.7791i	−0.980677	+	1.16873i	−0.985661	+	0.168738i	$0.946031\pi$
$140$	3.62586	−	1.33679i	0.306441	−	0.112979i
$141$		0			0
$142$	−4.53923	−	1.65214i	−0.380923	−	0.138645i
$143$	−13.8458			−1.15784
$144$		0			0
$145$		−	4.73184i		−	0.392958i
$146$	2.76460	+	15.6788i	0.228800	+	1.29759i
$147$		0			0
$148$	14.9817	−	5.45288i	1.23149	−	0.448224i
$149$	7.23973	−	8.62797i	0.593102	−	0.706831i	−0.383097	−	0.923708i	$-0.625143\pi$
$149$	7.23973	−	8.62797i	0.593102	−	0.706831i	0.976199	+	0.216877i	$0.0695870\pi$
$150$		0			0
$151$	5.72173	+	2.08254i	0.465628	+	0.169475i	0.564171	−	0.825658i	$-0.309196\pi$
$151$	5.72173	+	2.08254i	0.465628	+	0.169475i	−0.0985428	+	0.995133i	$0.531418\pi$
$152$	2.63682			0.213874
$153$		0			0
$154$	−8.73288	+	15.2720i	−0.703716	+	1.23065i
$155$	−4.04251	−	4.81767i	−0.324702	−	0.386965i
$156$		0			0
$157$	3.07275	−	3.66196i	0.245232	−	0.292256i	−0.629362	−	0.777112i	$-0.716684\pi$
$157$	3.07275	−	3.66196i	0.245232	−	0.292256i	0.874594	+	0.484856i	$0.161128\pi$
$158$	−6.14744	−	16.8900i	−0.489064	−	1.34369i
$159$		0			0
$160$	2.26344	−	6.21874i	0.178940	−	0.491635i
$161$	−8.03077	−	4.59219i	−0.632913	−	0.361915i
$162$		0			0
$163$	3.98040	+	6.89426i	0.311769	+	0.540000i	0.978745	−	0.205079i	$-0.0657451\pi$
$163$	3.98040	+	6.89426i	0.311769	+	0.540000i	−0.666976	+	0.745079i	$0.732412\pi$
$164$	−3.57876	+	3.00293i	−0.279454	+	0.234490i
$165$		0			0
$166$	−21.1608	−	3.73122i	−1.64240	−	0.289599i
$167$	3.90196	−	22.1291i	0.301943	−	1.71240i	−0.335613	−	0.942000i	$-0.608943\pi$
$167$	3.90196	−	22.1291i	0.301943	−	1.71240i	0.637556	−	0.770404i	$-0.279945\pi$
$168$		0			0
$169$	−2.05848	+	1.72727i	−0.158344	+	0.132867i
$170$	−0.695744	−	0.401688i	−0.0533611	−	0.0308080i
$171$		0			0
$172$	−7.19802	−	12.4673i	−0.548844	−	0.950625i
$173$	−5.93288	+	4.97828i	−0.451069	+	0.378491i	−0.839832	−	0.542846i	$-0.817347\pi$
$173$	−5.93288	+	4.97828i	−0.451069	+	0.378491i	0.388764	+	0.921338i	$0.372902\pi$
$174$		0			0
$175$	−10.3890	+	3.83024i	−0.785336	+	0.289539i
$176$	5.52155	+	15.1703i	0.416203	+	1.14351i
$177$		0			0
$178$	−1.97597	+	5.42893i	−0.148105	+	0.406916i
$179$	−1.62040	+	0.935541i	−0.121115	+	0.0699256i	−0.559333	−	0.828943i	$-0.688943\pi$
$179$	−1.62040	+	0.935541i	−0.121115	+	0.0699256i	0.438219	+	0.898868i	$0.355610\pi$
$180$		0			0
$181$	−18.1786	+	10.4954i	−1.35121	+	0.780121i	−0.988419	−	0.151751i	$-0.951509\pi$
$181$	−18.1786	+	10.4954i	−1.35121	+	0.780121i	−0.362790	+	0.931871i	$0.618176\pi$
$182$	3.54269	+	19.6148i	0.262602	+	1.45394i
$183$		0			0
$184$	−2.38754	+	0.868993i	−0.176012	+	0.0640630i
$185$	8.35899	−	3.04242i	0.614565	−	0.223683i
$186$		0			0
$187$	1.61071	−	0.284012i	0.117787	−	0.0207690i
$188$	5.39802			0.393691
$189$		0			0
$190$	−6.23095			−0.452041
$191$	−10.0948	+	1.77999i	−0.730436	+	0.128796i	−0.526484	−	0.850185i	$-0.676490\pi$
$191$	−10.0948	+	1.77999i	−0.730436	+	0.128796i	−0.203952	+	0.978981i	$0.565379\pi$
$192$		0			0
$193$	9.47459	−	3.44847i	0.681996	−	0.248226i	0.0222917	−	0.999752i	$-0.492904\pi$
$193$	9.47459	−	3.44847i	0.681996	−	0.248226i	0.659704	+	0.751525i	$0.270682\pi$
$194$	−9.12797	+	3.32231i	−0.655350	+	0.238528i
$195$		0			0
$196$	10.6746	+	3.78510i	0.762472	+	0.270365i
$197$	23.0223	−	13.2919i	1.64027	−	0.947010i	0.659533	−	0.751676i	$-0.270754\pi$
$197$	23.0223	−	13.2919i	1.64027	−	0.947010i	0.980737	−	0.195334i	$-0.0625791\pi$
$198$		0			0
$199$	−16.8725	+	9.74135i	−1.19606	+	0.690546i	−0.959675	−	0.281113i	$-0.909297\pi$
$199$	−16.8725	+	9.74135i	−1.19606	+	0.690546i	−0.236387	+	0.971659i	$0.575963\pi$
$200$	−1.04010	+	2.85766i	−0.0735464	+	0.202067i
$201$		0			0
$202$	8.72737	+	23.9782i	0.614055	+	1.68710i
$203$	8.86996	−	10.6604i	0.622549	−	0.748215i
$204$		0			0
$205$	−1.99676	+	1.67548i	−0.139460	+	0.117021i
$206$	−14.3372	−	24.8327i	−0.998919	−	1.73018i
$207$		0			0
$208$	15.8404	+	9.14547i	1.09834	+	0.634124i
$209$	9.71752	−	8.15397i	0.672175	−	0.564022i
$210$		0			0
$211$	−0.926175	+	5.25260i	−0.0637605	+	0.361604i	0.936188	+	0.351499i	$0.114328\pi$
$211$	−0.926175	+	5.25260i	−0.0637605	+	0.361604i	−0.999949	+	0.0101053i	$0.996783\pi$
$212$	16.1047	+	2.83969i	1.10607	+	0.195030i
$213$		0			0
$214$	21.5919	−	18.1177i	1.47599	−	1.23850i
$215$	−4.01612	−	6.95612i	−0.273897	−	0.474403i
$216$		0			0
$217$	−0.0765688	−	18.4316i	−0.00519783	−	1.25122i
$218$	1.92996	−	5.30253i	0.130713	−	0.359132i
$219$		0			0
$220$	−1.74636	−	4.79810i	−0.117740	−	0.323488i
$221$	1.19113	−	1.41954i	0.0801242	−	0.0954883i
$222$		0			0
$223$	5.44697	+	6.49144i	0.364756	+	0.434699i	0.916941	−	0.399022i	$-0.130650\pi$
$223$	5.44697	+	6.49144i	0.364756	+	0.434699i	−0.552185	+	0.833721i	$0.686206\pi$
$224$	16.7565	−	9.76742i	1.11959	−	0.652613i
$225$		0			0
$226$	23.1783			1.54180
$227$	21.1352	+	7.69258i	1.40279	+	0.510575i	0.929006	−	0.370065i	$-0.120665\pi$
$227$	21.1352	+	7.69258i	1.40279	+	0.510575i	0.473787	+	0.880640i	$0.342887\pi$
$228$		0			0
$229$	0.509720	−	0.607461i	0.0336833	−	0.0401421i	−0.748940	−	0.662638i	$-0.769437\pi$
$229$	0.509720	−	0.607461i	0.0336833	−	0.0401421i	0.782623	+	0.622496i	$0.213881\pi$
$230$	5.64189	−	2.05348i	0.372015	−	0.135403i
$231$		0			0
$232$	−0.661391	−	3.75093i	−0.0434224	−	0.246261i
$233$		−	8.67731i		−	0.568470i	−0.958755	−	0.284235i	$-0.908260\pi$
$233$		−	8.67731i		−	0.568470i	0.958755	−	0.284235i	$-0.0917395\pi$
$234$		0			0
$235$	3.01181			0.196469
$236$	4.92820	+	1.79372i	0.320798	+	0.116761i
$237$		0			0
$238$	−0.814477	−	2.20916i	−0.0527947	−	0.143199i
$239$	−14.4054	+	17.1677i	−0.931810	+	1.11049i	0.0618527	+	0.998085i	$0.480299\pi$
$239$	−14.4054	+	17.1677i	−0.931810	+	1.11049i	−0.993663	+	0.112403i	$0.964145\pi$
$240$		0			0
$241$	6.75864	+	8.05464i	0.435362	+	0.518845i	0.938461	−	0.345384i	$-0.112251\pi$
$241$	6.75864	+	8.05464i	0.435362	+	0.518845i	−0.503099	+	0.864229i	$0.667807\pi$
$242$	2.01061	+	1.16082i	0.129247	+	0.0746206i
$243$		0			0
$244$		−	0.0988758i		−	0.00632987i
$245$	5.95588	+	2.11189i	0.380507	+	0.134924i
$246$		0			0
$247$	2.49573	−	14.1540i	0.158800	−	0.900598i
$248$	−3.87789	−	3.25394i	−0.246246	−	0.206625i
$249$		0			0
$250$	5.39426	−	14.8206i	0.341163	−	0.937337i
$251$	4.71175	+	8.16098i	0.297403	+	0.515117i	0.975541	−	0.219818i	$-0.0705463\pi$
$251$	4.71175	+	8.16098i	0.297403	+	0.515117i	−0.678138	+	0.734934i	$0.737213\pi$
$252$		0			0
$253$	−6.11162	+	10.5856i	−0.384234	+	0.665514i
$254$	10.0944	+	12.0301i	0.633381	+	0.754835i
$255$		0			0
$256$	3.52000	−	19.9629i	0.220000	−	1.24768i
$257$	−9.03217	−	7.57889i	−0.563411	−	0.472758i	0.316041	−	0.948746i	$-0.397646\pi$
$257$	−9.03217	−	7.57889i	−0.563411	−	0.472758i	−0.879452	+	0.475987i	$0.842091\pi$
$258$		0			0
$259$	24.5352	+	8.81483i	1.52454	+	0.547727i
$260$	−5.01003	−	2.89254i	−0.310709	−	0.179388i
$261$		0			0
$262$		−	39.4587i		−	2.43777i
$263$	4.57306	−	0.806354i	0.281987	−	0.0497219i	−0.0308658	−	0.999524i	$-0.509826\pi$
$263$	4.57306	−	0.806354i	0.281987	−	0.0497219i	0.312853	+	0.949802i	$0.398715\pi$
$264$		0			0
$265$	8.98556	+	1.58440i	0.551978	+	0.0973287i
$266$	−14.0378	−	11.6801i	−0.860713	−	0.716152i
$267$		0			0
$268$	−2.88038	−	16.3355i	−0.175947	−	0.997847i
$269$	−13.5452	+	23.4609i	−0.825864	+	1.43044i	0.0753937	+	0.997154i	$0.475979\pi$
$269$	−13.5452	+	23.4609i	−0.825864	+	1.43044i	−0.901257	+	0.433284i	$0.857355\pi$
$270$		0			0
$271$	−3.93162	+	2.26992i	−0.238829	+	0.137888i	−0.614638	−	0.788809i	$-0.710698\pi$
$271$	−3.93162	+	2.26992i	−0.238829	+	0.137888i	0.375810	+	0.926697i	$0.377365\pi$
$272$	−2.03035	−	0.738985i	−0.123108	−	0.0448076i
$273$		0			0
$274$	17.7796	+	14.9189i	1.07411	+	0.901282i
$275$	5.00378	+	13.7478i	0.301739	+	0.829022i
$276$		0			0
$277$	1.38431	+	7.85082i	0.0831752	+	0.471710i	0.997735	+	0.0672603i	$0.0214258\pi$
$277$	1.38431	+	7.85082i	0.0831752	+	0.471710i	−0.914560	+	0.404450i	$0.867463\pi$
$278$	17.1068	−	29.6298i	1.02600	−	1.77708i
$279$		0			0
$280$	1.49942	−	0.874014i	0.0896073	−	0.0522323i
$281$	−6.05459	+	1.06759i	−0.361187	+	0.0636870i	−0.351297	−	0.936264i	$-0.614259\pi$
$281$	−6.05459	+	1.06759i	−0.361187	+	0.0636870i	−0.00988990	+	0.999951i	$0.503148\pi$
$282$		0			0
$283$	−11.2989	−	1.99229i	−0.671647	−	0.118430i	−0.172584	−	0.984995i	$-0.555212\pi$
$283$	−11.2989	−	1.99229i	−0.671647	−	0.118430i	−0.499064	+	0.866565i	$0.666323\pi$
$284$	4.04657	+	0.713519i	0.240119	+	0.0423395i
$285$		0			0
$286$	25.9359	−	4.57321i	1.53362	−	0.270419i
$287$	−7.63926	+	0.0317351i	−0.450931	+	0.00187327i
$288$		0			0
$289$	8.39055	−	14.5329i	0.493562	−	0.854874i
$290$	1.56291	+	8.86368i	0.0917770	+	0.520493i
$291$		0			0
$292$	−4.63183	−	12.7259i	−0.271058	−	0.744725i
$293$	0.840836	+	0.705545i	0.0491222	+	0.0412184i	0.667018	−	0.745041i	$-0.267570\pi$
$293$	0.840836	+	0.705545i	0.0491222	+	0.0412184i	−0.617896	+	0.786260i	$0.712015\pi$
$294$		0			0
$295$	2.74968	+	1.00080i	0.160092	+	0.0582689i
$296$	6.20093	−	3.58011i	0.360422	−	0.208090i
$297$		0			0
$298$	−10.7117	+	18.5532i	−0.620511	+	1.07476i
$299$	2.40482	+	13.6384i	0.139074	+	0.788730i
$300$		0			0
$301$	3.99146	−	23.1999i	0.230064	−	1.33722i
$302$	−11.4058	−	2.01115i	−0.656331	−	0.115729i
$303$		0			0
$304$	−16.5033	+	2.90998i	−0.946530	+	0.166899i
$305$		−	0.0551675i		−	0.00315888i
$306$		0			0
$307$	−5.93612	−	3.42722i	−0.338792	−	0.195602i	0.320945	−	0.947098i	$-0.395999\pi$
$307$	−5.93612	−	3.42722i	−0.338792	−	0.195602i	−0.659738	+	0.751496i	$0.729333\pi$
$308$	5.05975	−	14.0833i	0.288306	−	0.802472i
$309$		0			0
$310$	9.16368	+	7.68924i	0.520462	+	0.436720i
$311$	−3.87680	+	21.9864i	−0.219833	+	1.24674i	0.652487	+	0.757800i	$0.273726\pi$
$311$	−3.87680	+	21.9864i	−0.219833	+	1.24674i	−0.872320	+	0.488935i	$0.837385\pi$
$312$		0			0
$313$	0.650065	+	0.774717i	0.0367439	+	0.0437896i	0.784103	−	0.620630i	$-0.213123\pi$
$313$	0.650065	+	0.774717i	0.0367439	+	0.0437896i	−0.747360	+	0.664420i	$0.768679\pi$
$314$	−4.54635	+	7.87450i	−0.256565	+	0.444384i
$315$		0			0
$316$	7.64455	+	13.2408i	0.430040	+	0.744850i
$317$	8.50091	−	23.3561i	0.477459	−	1.31181i	−0.434184	−	0.900824i	$-0.642963\pi$
$317$	8.50091	−	23.3561i	0.477459	−	1.31181i	0.911643	−	0.410983i	$-0.134814\pi$
$318$		0			0
$319$	−14.0367	−	11.7782i	−0.785902	−	0.659450i
$320$	−0.737976	+	4.18527i	−0.0412541	+	0.233964i
$321$		0			0
$322$	16.5600	+	5.94956i	0.922854	+	0.331556i
$323$			1.69776i			0.0944659i
$324$		0			0
$325$	14.3550	+	8.28786i	0.796272	+	0.459728i
$326$	−9.73324	−	11.5996i	−0.539074	−	0.642444i
$327$		0			0
$328$	−1.34864	+	1.60725i	−0.0744664	+	0.0887457i
$329$	6.78536	+	5.64573i	0.374089	+	0.311259i
$330$		0			0
$331$	−24.9441	−	9.07889i	−1.37105	−	0.499021i	−0.451597	−	0.892222i	$-0.649145\pi$
$331$	−24.9441	−	9.07889i	−1.37105	−	0.499021i	−0.919453	+	0.393201i	$0.871368\pi$
$332$	18.2776			1.00312
$333$		0			0
$334$			42.7411i			2.33869i
$335$	−1.60710	−	9.11434i	−0.0878054	−	0.497969i
$336$		0			0
$337$	23.2967	−	8.47930i	1.26905	−	0.461897i	0.382254	−	0.924057i	$-0.375148\pi$
$337$	23.2967	−	8.47930i	1.26905	−	0.461897i	0.886796	+	0.462161i	$0.152926\pi$
$338$	3.28543	−	3.91542i	0.178704	−	0.212971i
$339$		0			0
$340$	0.642160	+	0.233727i	0.0348260	+	0.0126756i
$341$	−24.3536			−1.31882
$342$		0			0
$343$	9.45929	+	15.9224i	0.510754	+	0.859727i
$344$	−4.15587	−	4.95278i	−0.224070	−	0.267036i
$345$		0			0
$346$	9.46917	−	11.2849i	0.509066	−	0.606681i
$347$	6.40998	+	17.6113i	0.344106	+	0.945423i	0.984190	+	0.177118i	$0.0566774\pi$
$347$	6.40998	+	17.6113i	0.344106	+	0.945423i	−0.640084	+	0.768305i	$0.721100\pi$
$348$		0			0
$349$	−8.31455	+	22.8440i	−0.445067	+	1.22281i	0.491052	+	0.871130i	$0.336613\pi$
$349$	−8.31455	+	22.8440i	−0.445067	+	1.22281i	−0.936119	+	0.351682i	$0.885610\pi$
$350$	18.1956	−	10.6063i	0.972596	−	0.566929i
$351$		0			0
$352$	−12.8135	−	22.1936i	−0.682960	−	1.18292i
$353$	−17.5265	+	14.7065i	−0.932841	+	0.782747i	−0.976325	−	0.216307i	$-0.930599\pi$
$353$	−17.5265	+	14.7065i	−0.932841	+	0.782747i	0.0434839	+	0.999054i	$0.486154\pi$
$354$		0			0
$355$	2.25777	+	0.398106i	0.119830	+	0.0211293i
$356$	0.853371	−	4.83971i	0.0452286	−	0.256504i
$357$		0			0
$358$	2.72634	−	2.28767i	0.144091	−	0.120907i
$359$	−7.23348	−	4.17625i	−0.381768	−	0.220414i	0.296819	−	0.954934i	$-0.404074\pi$
$359$	−7.23348	−	4.17625i	−0.381768	−	0.220414i	−0.678587	+	0.734520i	$0.737408\pi$
$360$		0			0
$361$	−2.91612	−	5.05087i	−0.153480	−	0.265835i
$362$	30.5857	−	25.6644i	1.60755	−	1.34889i
$363$		0			0
$364$	−5.86502	−	15.9081i	−0.307411	−	0.833810i
$365$	−2.58432	−	7.10037i	−0.135270	−	0.371650i
$366$		0			0
$367$	3.33853	−	9.17253i	0.174270	−	0.478802i	−0.821551	−	0.570136i	$-0.806891\pi$
$367$	3.33853	−	9.17253i	0.174270	−	0.478802i	0.995820	+	0.0913333i	$0.0291129\pi$
$368$	13.9841	−	8.07374i	0.728973	−	0.420873i
$369$		0			0
$370$	−14.6532	+	8.46001i	−0.761782	+	0.439815i
$371$	17.2737	+	20.4132i	0.896806	+	1.05980i
$372$		0			0
$373$	−9.95905	+	3.62480i	−0.515660	+	0.187685i	−0.586724	−	0.809787i	$-0.699583\pi$
$373$	−9.95905	+	3.62480i	−0.515660	+	0.187685i	0.0710640	+	0.997472i	$0.477361\pi$
$374$	−2.92338	+	1.06402i	−0.151164	+	0.0550193i
$375$		0			0
$376$	2.38747	−	0.420975i	0.123124	−	0.0217102i
$377$	−20.7604			−1.06922
$378$		0			0
$379$	−6.26462			−0.321792			−0.160896	−	0.986971i	$-0.551438\pi$
$379$	−6.26462			−0.321792			−0.160896	+	0.986971i	$0.551438\pi$
$380$	5.21969	−	0.920373i	0.267765	−	0.0472141i
$381$		0			0
$382$	18.3217	−	6.66856i	0.937420	−	0.341193i
$383$	−7.86054	+	2.86100i	−0.401655	+	0.146190i	−0.534945	−	0.844887i	$-0.679668\pi$
$383$	−7.86054	+	2.86100i	−0.401655	+	0.146190i	0.133291	+	0.991077i	$0.457446\pi$
$384$		0			0
$385$	2.82308	−	7.85776i	0.143877	−	0.400468i
$386$	−16.6088	+	9.58909i	−0.845365	+	0.488072i
$387$		0			0
$388$	7.15580	−	4.13140i	0.363281	−	0.209740i
$389$	6.64622	−	18.2603i	0.336977	−	0.925835i	−0.649270	−	0.760558i	$-0.724926\pi$
$389$	6.64622	−	18.2603i	0.336977	−	0.925835i	0.986247	−	0.165278i	$-0.0528521\pi$
$390$		0			0
$391$	−0.559516	−	1.53726i	−0.0282960	−	0.0777425i
$392$	5.01642	+	0.841618i	0.253368	+	0.0425081i
$393$		0			0
$394$	−38.7351	+	32.5026i	−1.95145	+	1.63746i
$395$	4.26526	+	7.38765i	0.214609	+	0.371713i
$396$		0			0
$397$	−24.5677	−	14.1842i	−1.23302	−	0.711882i	−0.265359	−	0.964150i	$-0.585490\pi$
$397$	−24.5677	−	14.1842i	−1.23302	−	0.711882i	−0.967658	+	0.252267i	$0.918824\pi$
$398$	28.3881	−	23.8204i	1.42297	−	1.19401i
$399$		0			0
$400$	3.35610	−	19.0334i	0.167805	−	0.951669i
$401$	19.2271	+	3.39026i	0.960157	+	0.169302i	0.631696	−	0.775216i	$-0.282359\pi$
$401$	19.2271	+	3.39026i	0.960157	+	0.169302i	0.328461	+	0.944518i	$0.393470\pi$
$402$		0			0
$403$	−21.1370	+	17.7361i	−1.05291	+	0.883496i
$404$	−10.8528	−	18.7976i	−0.539946	−	0.935213i
$405$		0			0
$406$	−13.0941	+	22.8988i	−0.649850	+	1.13645i
$407$	11.7815	−	32.3694i	0.583986	−	1.60449i
$408$		0			0
$409$	11.9596	+	32.8586i	0.591362	+	1.62475i	0.767980	+	0.640474i	$0.221262\pi$
$409$	11.9596	+	32.8586i	0.591362	+	1.62475i	−0.176618	+	0.984279i	$0.556516\pi$
$410$	3.18693	−	3.79803i	0.157391	−	0.187571i
$411$		0			0
$412$	15.6784	+	18.6847i	0.772418	+	0.920531i
$413$	4.31876	+	7.40907i	0.212512	+	0.364576i
$414$		0			0
$415$	10.1980			0.500598
$416$	−27.2840	−	9.93058i	−1.33771	−	0.486887i
$417$		0			0
$418$	−15.5096	+	18.4837i	−0.758602	+	0.904066i
$419$	−38.1160	+	13.8731i	−1.86209	+	0.677745i	−0.884748	+	0.466070i	$0.845669\pi$
$419$	−38.1160	+	13.8731i	−1.86209	+	0.677745i	−0.977340	+	0.211674i	$0.932108\pi$
$420$		0			0
$421$	2.74861	+	15.5881i	0.133959	+	0.759718i	0.975579	+	0.219649i	$0.0704911\pi$
$421$	2.74861	+	15.5881i	0.133959	+	0.759718i	−0.841620	+	0.540070i	$0.818398\pi$
$422$		−	10.1451i		−	0.493855i
$423$		0			0
$424$	7.34433			0.356672
$425$	−1.83995	−	0.669688i	−0.0892508	−	0.0324846i
$426$		0			0
$427$	0.103413	−	0.124288i	0.00500451	−	0.00601471i
$428$	−15.4114	+	18.3666i	−0.744939	+	0.887784i
$429$		0			0
$430$	9.82057	+	11.7037i	0.473590	+	0.564403i
$431$	6.88208	+	3.97337i	0.331498	+	0.191391i	0.656506	−	0.754321i	$-0.272034\pi$
$431$	6.88208	+	3.97337i	0.331498	+	0.191391i	−0.325008	+	0.945711i	$0.605367\pi$
$432$		0			0
$433$		−	16.4757i		−	0.791770i	−0.918300	−	0.395885i	$-0.870438\pi$
$433$		−	16.4757i		−	0.791770i	0.918300	−	0.395885i	$-0.129562\pi$
$434$	6.23131	+	34.5008i	0.299112	+	1.65609i
$435$		0			0
$436$	−0.833501	+	4.72702i	−0.0399175	+	0.226383i
$437$	−9.71965	−	8.15575i	−0.464954	−	0.390143i
$438$		0			0
$439$	2.08683	−	5.73351i	0.0995988	−	0.273646i	−0.879879	−	0.475198i	$-0.842376\pi$
$439$	2.08683	−	5.73351i	0.0995988	−	0.273646i	0.979478	+	0.201552i	$0.0645986\pi$
$440$	−1.14658	−	1.98594i	−0.0546612	−	0.0946759i
$441$		0			0
$442$	−1.76236	+	3.05250i	−0.0838270	+	0.145193i
$443$	−12.7961	−	15.2497i	−0.607959	−	0.724537i	0.370991	−	0.928636i	$-0.379018\pi$
$443$	−12.7961	−	15.2497i	−0.607959	−	0.724537i	−0.978950	+	0.204099i	$0.934574\pi$
$444$		0			0
$445$	0.476137	−	2.70031i	0.0225710	−	0.128007i
$446$	−12.3474	−	10.3607i	−0.584664	−	0.490592i
$447$		0			0
$448$	−9.50800	+	8.04570i	−0.449211	+	0.380124i
$449$	0.412263	+	0.238020i	0.0194559	+	0.0112329i	0.509696	−	0.860354i	$-0.329758\pi$
$449$	0.412263	+	0.238020i	0.0194559	+	0.0112329i	−0.490241	+	0.871587i	$0.663091\pi$
$450$		0			0
$451$			10.0937i			0.475295i
$452$	−19.4165	+	3.42366i	−0.913277	+	0.161035i
$453$		0			0
$454$	−42.1313	−	7.42888i	−1.97732	−	0.348655i
$455$	−3.27238	−	8.87588i	−0.153411	−	0.416108i
$456$		0			0
$457$	2.00670	+	11.3806i	0.0938695	+	0.532360i	0.995088	+	0.0989952i	$0.0315628\pi$
$457$	2.00670	+	11.3806i	0.0938695	+	0.532360i	−0.901218	+	0.433365i	$0.857326\pi$
$458$	−0.754166	+	1.30625i	−0.0352399	+	0.0610373i
$459$		0			0
$460$	−4.42292	+	2.55357i	−0.206220	+	0.119061i
$461$	−19.0273	−	6.92536i	−0.886189	−	0.322546i	−0.141484	−	0.989941i	$-0.545187\pi$
$461$	−19.0273	−	6.92536i	−0.886189	−	0.322546i	−0.744705	+	0.667394i	$0.767410\pi$
$462$		0			0
$463$	−4.74389	−	3.98059i	−0.220467	−	0.184994i	0.525864	−	0.850569i	$-0.323742\pi$
$463$	−4.74389	−	3.98059i	−0.220467	−	0.184994i	−0.746331	+	0.665575i	$0.768186\pi$
$464$	8.27904	+	22.7465i	0.384345	+	1.05598i
$465$		0			0
$466$	2.86608	+	16.2543i	0.132769	+	0.752968i
$467$	−1.90348	+	3.29692i	−0.0880826	+	0.152563i	−0.906701	−	0.421775i	$-0.861407\pi$
$467$	−1.90348	+	3.29692i	−0.0880826	+	0.152563i	0.818618	+	0.574338i	$0.194741\pi$
$468$		0			0
$469$	13.4644	−	23.5464i	0.621728	−	1.08727i
$470$	−5.64173	+	0.994790i	−0.260234	+	0.0458862i
$471$		0			0
$472$	2.31956	+	0.409001i	0.106766	+	0.0188258i
$473$	−30.6315	−	5.40116i	−1.40844	−	0.248346i
$474$		0			0
$475$	−14.9557	+	2.63710i	−0.686217	+	0.120998i
$476$	1.00861	+	1.73032i	0.0462293	+	0.0793089i
$477$		0			0
$478$	21.3138	−	36.9166i	0.974872	−	1.68853i
$479$	5.21941	+	29.6008i	0.238481	+	1.35249i	0.835157	+	0.550011i	$0.185377\pi$
$479$	5.21941	+	29.6008i	0.238481	+	1.35249i	−0.596676	+	0.802482i	$0.703512\pi$
$480$		0			0
$481$	−13.3483	−	36.6742i	−0.608630	−	1.67220i
$482$	−15.3207	−	12.8556i	−0.697839	−	0.585556i
$483$		0			0
$484$	−1.85576	−	0.675440i	−0.0843526	−	0.0307018i
$485$	3.99256	−	2.30511i	0.181293	−	0.104670i
$486$		0			0
$487$	−18.9944	+	32.8993i	−0.860720	+	1.49081i	0.0105150	+	0.999945i	$0.496653\pi$
$487$	−18.9944	+	32.8993i	−0.860720	+	1.49081i	−0.871235	+	0.490866i	$0.836680\pi$
$488$	−0.00771102	−	0.0437314i	−0.000349062	−	0.00197963i
$489$		0			0
$490$	−11.8541	−	1.98879i	−0.535514	−	0.0898445i
$491$	31.0131	+	5.46844i	1.39960	+	0.246787i	0.821979	−	0.569517i	$-0.192870\pi$
$491$	31.0131	+	5.46844i	1.39960	+	0.246787i	0.577622	+	0.816305i	$0.303981\pi$
$492$		0			0
$493$	2.41510	−	0.425848i	0.108771	−	0.0191792i
$494$			27.3376i			1.22998i
$495$		0			0
$496$	27.8620	+	16.0861i	1.25104	+	0.722288i
$497$	4.34031	+	5.12916i	0.194689	+	0.230074i
$498$		0			0
$499$	−14.4091	−	12.0907i	−0.645039	−	0.541252i	0.260522	−	0.965468i	$-0.416105\pi$
$499$	−14.4091	−	12.0907i	−0.645039	−	0.541252i	−0.905561	+	0.424216i	$0.860550\pi$
$500$	−2.32964	+	13.2121i	−0.104185	+	0.590861i
$501$		0			0
$502$	−11.5216	−	13.7309i	−0.514233	−	0.612839i
$503$	−3.04934	+	5.28161i	−0.135963	+	0.235495i	−0.925965	−	0.377609i	$-0.876746\pi$
$503$	−3.04934	+	5.28161i	−0.135963	+	0.235495i	0.790002	+	0.613105i	$0.210080\pi$
$504$		0			0
$505$	−6.05528	−	10.4881i	−0.269456	−	0.466712i
$506$	7.95190	−	21.8477i	0.353505	−	0.971247i
$507$		0			0
$508$	−10.2331	−	8.58660i	−0.454021	−	0.380969i
$509$	−7.51248	+	42.6054i	−0.332985	+	1.88845i	0.113303	+	0.993560i	$0.463857\pi$
$509$	−7.51248	+	42.6054i	−0.332985	+	1.88845i	−0.446288	+	0.894889i	$0.647254\pi$
$510$		0			0
$511$	7.48757	−	20.8409i	0.331231	−	0.921947i
$512$			27.1429i			1.19956i
$513$		0			0
$514$	19.4223	+	11.2135i	0.856683	+	0.494606i
$515$	8.74771	+	10.4251i	0.385470	+	0.459385i
$516$		0			0
$517$	7.49680	−	8.93434i	0.329709	−	0.392932i
$518$	−48.8709	−	8.40807i	−2.14726	−	0.369430i
$519$		0			0
$520$	−2.44145	−	0.888614i	−0.107065	−	0.0389683i
$521$	20.0431			0.878105			0.439053	−	0.898461i	$-0.355314\pi$
$521$	20.0431			0.878105			0.439053	+	0.898461i	$0.355314\pi$
$522$		0			0
$523$			26.6736i			1.16635i	0.812345	+	0.583177i	$0.198191\pi$
$523$			26.6736i			1.16635i	−0.812345	+	0.583177i	$0.801809\pi$
$524$	5.82843	+	33.0547i	0.254616	+	1.44400i
$525$		0			0
$526$	−8.29992	+	3.02093i	−0.361894	+	0.131719i
$527$	2.09510	−	2.49685i	0.0912641	−	0.108764i
$528$		0			0
$529$	−10.1243	−	3.68495i	−0.440188	−	0.160215i
$530$	−17.3551			−0.753856
$531$		0			0
$532$	13.4848	+	7.71093i	0.584640	+	0.334311i
$533$	7.35099	+	8.76057i	0.318407	+	0.379462i
$534$		0			0
$535$	−8.59877	+	10.2476i	−0.371757	+	0.443043i
$536$	−2.54791	−	7.00032i	−0.110053	−	0.302368i
$537$		0			0
$538$	17.6238	−	48.4209i	0.759815	−	2.08757i
$539$	21.0897	−	12.4109i	0.908399	−	0.534576i
$540$		0			0
$541$	−5.16825	−	8.95167i	−0.222200	−	0.384862i	0.733275	−	0.679932i	$-0.237991\pi$
$541$	−5.16825	−	8.95167i	−0.222200	−	0.384862i	−0.955476	+	0.295069i	$0.904657\pi$
$542$	6.61497	−	5.55061i	0.284137	−	0.238419i
$543$		0			0
$544$	3.37771	+	0.595582i	0.144818	+	0.0255354i
$545$	−0.465050	+	2.63743i	−0.0199206	+	0.112975i
$546$		0			0
$547$	2.39360	−	2.00847i	0.102343	−	0.0858758i	−0.590181	−	0.807271i	$-0.700943\pi$
$547$	2.39360	−	2.00847i	0.102343	−	0.0858758i	0.692523	+	0.721396i	$0.256499\pi$
$548$	−17.0977	−	9.87138i	−0.730379	−	0.421684i
$549$		0			0
$550$	−13.9139	−	24.0996i	−0.593291	−	1.02761i
$551$	14.5705	−	12.2261i	0.620724	−	0.520849i
$552$		0			0
$553$	−4.23908	+	24.6391i	−0.180264	+	1.04776i
$554$	−5.18618	−	14.2489i	−0.220340	−	0.605379i
$555$		0			0
$556$	−9.95382	+	27.3479i	−0.422136	+	1.15981i
$557$	−12.2609	+	7.07881i	−0.519509	+	0.299939i	−0.736734	−	0.676183i	$-0.763633\pi$
$557$	−12.2609	+	7.07881i	−0.519509	+	0.299939i	0.217225	+	0.976122i	$0.430300\pi$
$558$		0			0
$559$	−30.5192	+	17.6203i	−1.29083	+	0.745259i
$560$	−8.42000	+	7.12504i	−0.355810	+	0.301088i
$561$		0			0
$562$	10.9888	−	3.99961i	0.463537	−	0.168714i
$563$	21.1089	−	7.68303i	0.889636	−	0.323801i	0.143544	−	0.989644i	$-0.454150\pi$
$563$	21.1089	−	7.68303i	0.889636	−	0.323801i	0.746092	+	0.665843i	$0.231928\pi$
$564$		0			0
$565$	−10.8334	+	1.91022i	−0.455765	+	0.0803637i
$566$	21.8231			0.917292
$567$		0			0
$568$	1.84539			0.0774306
$569$	18.4001	−	3.24444i	0.771373	−	0.136014i	0.225909	−	0.974148i	$-0.427465\pi$
$569$	18.4001	−	3.24444i	0.771373	−	0.136014i	0.545464	+	0.838135i	$0.316354\pi$
$570$		0			0
$571$	34.2455	−	12.4643i	1.43313	−	0.521616i	0.495303	−	0.868720i	$-0.335057\pi$
$571$	34.2455	−	12.4643i	1.43313	−	0.521616i	0.937827	+	0.347104i	$0.112835\pi$
$572$	−21.0511	+	7.66199i	−0.880192	+	0.320364i
$573$		0			0
$574$	14.2994	−	2.58266i	0.596845	−	0.107798i
$575$	12.6728	−	7.31663i	0.528492	−	0.305125i
$576$		0			0
$577$	−25.0637	+	14.4705i	−1.04341	+	0.602416i	−0.920799	−	0.390039i	$-0.872462\pi$
$577$	−25.0637	+	14.4705i	−1.04341	+	0.602416i	−0.122616	+	0.992454i	$0.539128\pi$
$578$	−10.9170	+	29.9943i	−0.454089	+	1.24760i
$579$		0			0
$580$	−2.61850	−	7.19428i	−0.108728	−	0.298726i
$581$	22.9751	+	19.1164i	0.953170	+	0.793080i
$582$		0			0
$583$	27.0662	−	22.7113i	1.12097	−	0.940605i
$584$	−3.04105	−	5.26725i	−0.125839	−	0.217960i
$585$		0			0
$586$	−1.80809	−	1.04390i	−0.0746916	−	0.0431232i
$587$	−24.4251	+	20.4951i	−1.00813	+	0.845924i	−0.988090	−	0.153875i	$-0.950825\pi$
$587$	−24.4251	+	20.4951i	−1.00813	+	0.845924i	−0.0200431	+	0.999799i	$0.506380\pi$
$588$		0			0
$589$	4.38979	−	24.8957i	0.180878	−	1.02581i
$590$	−5.48126	−	0.966494i	−0.225660	−	0.0397899i
$591$		0			0
$592$	−34.8594	+	29.2505i	−1.43271	+	1.20219i
$593$	−2.99491	−	5.18734i	−0.122986	−	0.213018i	0.797958	−	0.602713i	$-0.205914\pi$
$593$	−2.99491	−	5.18734i	−0.122986	−	0.213018i	−0.920944	+	0.389695i	$0.872580\pi$
$594$		0			0
$595$	0.562749	+	0.965426i	0.0230705	+	0.0395786i
$596$	6.23273	−	17.1243i	0.255303	−	0.701438i
$597$		0			0
$598$	−9.00943	−	24.7532i	−0.368423	−	1.01223i
$599$	−5.26383	+	6.27319i	−0.215074	+	0.256316i	−0.862785	−	0.505570i	$-0.831282\pi$
$599$	−5.26383	+	6.27319i	−0.215074	+	0.256316i	0.647711	+	0.761886i	$0.275726\pi$
$600$		0			0
$601$	−11.1245	−	13.2576i	−0.453777	−	0.540791i	0.489847	−	0.871808i	$-0.337052\pi$
$601$	−11.1245	−	13.2576i	−0.453777	−	0.540791i	−0.943625	+	0.331018i	$0.892608\pi$
$602$	0.186011	+	44.7764i	0.00758123	+	1.82495i
$603$		0			0
$604$	9.85176			0.400862
$605$	−1.03542	−	0.376860i	−0.0420956	−	0.0153216i
$606$		0			0
$607$	−12.6088	+	15.0266i	−0.511776	+	0.609911i	−0.958616	−	0.284703i	$-0.908105\pi$
$607$	−12.6088	+	15.0266i	−0.511776	+	0.609911i	0.446839	+	0.894614i	$0.352550\pi$
$608$	24.9973	−	9.09826i	1.01377	−	0.368983i
$609$		0			0
$610$	0.0182216	+	0.103340i	0.000737771	+	0.00418411i
$611$		−	13.2140i		−	0.534582i
$612$		0			0
$613$	27.8234			1.12378			0.561889	−	0.827213i	$-0.310075\pi$
$613$	27.8234			1.12378			0.561889	+	0.827213i	$0.310075\pi$
$614$	12.2515	+	4.45920i	0.494432	+	0.179959i
$615$		0			0
$616$	1.13954	−	6.62345i	0.0459135	−	0.266866i
$617$	18.1901	−	21.6782i	0.732308	−	0.872730i	−0.263457	−	0.964671i	$-0.584863\pi$
$617$	18.1901	−	21.6782i	0.732308	−	0.872730i	0.995764	+	0.0919408i	$0.0293071\pi$
$618$		0			0
$619$	−18.7035	−	22.2899i	−0.751755	−	0.895907i	0.245542	−	0.969386i	$-0.421034\pi$
$619$	−18.7035	−	22.2899i	−0.751755	−	0.895907i	−0.997297	+	0.0734791i	$0.976590\pi$
$620$	−8.81223	−	5.08774i	−0.353908	−	0.204329i
$621$		0			0
$622$		−	42.4655i		−	1.70271i
$623$	6.13449	−	5.19103i	0.245773	−	0.207974i
$624$		0			0
$625$	2.33381	−	13.2357i	0.0933525	−	0.529428i
$626$	−1.47359	−	1.23649i	−0.0588964	−	0.0494200i
$627$		0			0
$628$	2.64535	−	7.26804i	0.105561	−	0.290026i
$629$	2.30512	+	3.99258i	0.0919110	+	0.159194i
$630$		0			0
$631$	3.11061	−	5.38773i	0.123831	−	0.214482i	−0.797444	−	0.603393i	$-0.793815\pi$
$631$	3.11061	−	5.38773i	0.123831	−	0.214482i	0.921275	+	0.388911i	$0.127149\pi$
$632$	4.41368	+	5.26002i	0.175567	+	0.209233i
$633$		0			0
$634$	−8.20950	+	46.5584i	−0.326041	+	1.84907i
$635$	−5.70954	−	4.79088i	−0.226576	−	0.190120i
$636$		0			0
$637$	9.26569	−	26.1308i	0.367120	−	1.03534i
$638$	30.1838	+	17.4266i	1.19499	+	0.689926i
$639$		0			0
$640$			5.15209i			0.203654i
$641$	−6.29675	+	1.11029i	−0.248707	+	0.0438537i	−0.296612	−	0.954998i	$-0.595857\pi$
$641$	−6.29675	+	1.11029i	−0.248707	+	0.0438537i	0.0479049	+	0.998852i	$0.484746\pi$
$642$		0			0
$643$	2.20568	+	0.388920i	0.0869834	+	0.0153375i	0.216970	−	0.976178i	$-0.430382\pi$
$643$	2.20568	+	0.388920i	0.0869834	+	0.0153375i	−0.129987	+	0.991516i	$0.541494\pi$
$644$	−14.7512	−	2.53790i	−0.581279	−	0.100007i
$645$		0			0
$646$	−0.560763	−	3.18024i	−0.0220629	−	0.125125i
$647$	13.4891	−	23.3638i	0.530311	−	0.918525i	−0.469064	−	0.883164i	$-0.655409\pi$
$647$	13.4891	−	23.3638i	0.530311	−	0.918525i	0.999375	−	0.0353609i	$-0.0112581\pi$
$648$		0			0
$649$	9.81311	−	5.66560i	0.385198	−	0.222394i
$650$	−29.6272	−	10.7834i	−1.16208	−	0.422961i
$651$		0			0
$652$	9.86695	+	8.27936i	0.386420	+	0.324245i
$653$	7.80301	+	21.4386i	0.305355	+	0.838957i	0.993546	+	0.113427i	$0.0361828\pi$
$653$	7.80301	+	21.4386i	0.305355	+	0.838957i	−0.688191	+	0.725529i	$0.741595\pi$
$654$		0			0
$655$	3.25196	+	18.4428i	0.127065	+	0.720620i
$656$	6.66715	−	11.5478i	0.260308	−	0.450867i
$657$		0			0
$658$	−14.5751	−	8.33441i	−0.568197	−	0.324909i
$659$	−21.2918	+	3.75431i	−0.829409	+	0.146247i	−0.572206	−	0.820110i	$-0.693912\pi$
$659$	−21.2918	+	3.75431i	−0.829409	+	0.146247i	−0.257203	+	0.966357i	$0.582801\pi$
$660$		0			0
$661$	28.7597	+	5.07112i	1.11862	+	0.197244i	0.702237	−	0.711944i	$-0.252185\pi$
$661$	28.7597	+	5.07112i	1.11862	+	0.197244i	0.416387	+	0.909187i	$0.363296\pi$
$662$	49.7239	+	8.76767i	1.93258	+	0.340765i
$663$		0			0
$664$	8.08394	−	1.42542i	0.313718	−	0.0553169i
$665$	7.52381	+	4.30230i	0.291761	+	0.166836i
$666$		0			0
$667$	−9.16379	+	15.8721i	−0.354823	+	0.614572i
$668$	−6.31328	−	35.8044i	−0.244268	−	1.38531i
$669$		0			0
$670$	6.02085	+	16.5422i	0.232606	+	0.639079i
$671$	−0.163651	−	0.137319i	−0.00631766	−	0.00530115i
$672$		0			0
$673$	22.4647	+	8.17648i	0.865950	+	0.315180i	0.736526	−	0.676409i	$-0.236465\pi$
$673$	22.4647	+	8.17648i	0.865950	+	0.315180i	0.129424	+	0.991589i	$0.458687\pi$
$674$	−40.8387	+	23.5782i	−1.57305	+	0.908199i
$675$		0			0
$676$	−2.17387	+	3.76525i	−0.0836104	+	0.144817i
$677$	5.37818	+	30.5012i	0.206700	+	1.17225i	0.894742	+	0.446584i	$0.147359\pi$
$677$	5.37818	+	30.5012i	0.206700	+	1.17225i	−0.688042	+	0.725671i	$0.741529\pi$
$678$		0			0
$679$	13.3159	+	2.29096i	0.511017	+	0.0879188i
$680$	0.302246	+	0.0532942i	0.0115906	+	0.00204374i
$681$		0			0
$682$	45.6192	−	8.04390i	1.74685	−	0.308017i
$683$		−	3.83140i		−	0.146604i	−0.997310	−	0.0733022i	$-0.976646\pi$
$683$		−	3.83140i		−	0.146604i	0.997310	−	0.0733022i	$-0.0233538\pi$
$684$		0			0
$685$	−9.53964	−	5.50771i	−0.364491	−	0.210439i
$686$	−22.9782	−	26.7014i	−0.877313	−	1.01947i
$687$		0			0
$688$	31.4767	+	26.4121i	1.20004	+	1.00695i
$689$	6.95137	−	39.4232i	0.264826	−	1.50190i
$690$		0			0
$691$	−5.31576	−	6.33507i	−0.202221	−	0.240998i	0.655397	−	0.755284i	$-0.272501\pi$
$691$	−5.31576	−	6.33507i	−0.202221	−	0.240998i	−0.857618	+	0.514287i	$0.828057\pi$
$692$	−6.26547	+	10.8521i	−0.238177	+	0.412535i
$693$		0			0
$694$	−17.8241	−	30.8723i	−0.676594	−	1.17190i
$695$	−5.55371	+	15.2587i	−0.210664	+	0.578795i
$696$		0			0
$697$	−1.03486	−	0.868348i	−0.0391980	−	0.0328910i
$698$	8.02953	−	45.5377i	0.303922	−	1.72363i
$699$		0			0
$700$	−13.6759	+	11.5726i	−0.516900	+	0.437402i
$701$		−	19.8898i		−	0.751226i	−0.926777	−	0.375613i	$-0.877432\pi$
$701$		−	19.8898i		−	0.751226i	0.926777	−	0.375613i	$-0.122568\pi$
$702$		0			0
$703$	30.9663	+	17.8784i	1.16792	+	0.674296i
$704$	10.5784	+	12.6068i	0.398688	+	0.475138i
$705$		0			0
$706$	27.9732	−	33.3371i	1.05278	−	1.25466i
$707$	6.01811	−	34.9795i	0.226334	−	1.31554i
$708$		0			0
$709$	−13.1341	−	4.78042i	−0.493262	−	0.179533i	0.0833991	−	0.996516i	$-0.473422\pi$
$709$	−13.1341	−	4.78042i	−0.493262	−	0.179533i	−0.576661	+	0.816984i	$0.695645\pi$
$710$	−4.36075			−0.163656
$711$		0			0
$712$		−	2.20709i		−	0.0827141i
$713$	4.22989	+	23.9889i	0.158410	+	0.898390i
$714$		0			0
$715$	−11.7454	+	4.27499i	−0.439254	+	0.159876i
$716$	−1.94595	+	2.31910i	−0.0727237	+	0.0866687i
$717$		0			0
$718$	14.9292	+	5.43377i	0.557151	+	0.202786i
$719$	31.4331			1.17226			0.586128	−	0.810218i	$-0.300652\pi$
$719$	31.4331			1.17226			0.586128	+	0.810218i	$0.300652\pi$
$720$		0			0
$721$	0.165690	+	39.8847i	0.00617061	+	1.48538i
$722$	7.13076	+	8.49811i	0.265380	+	0.316267i
$723$		0			0
$724$	−21.8308	+	26.0170i	−0.811337	+	0.966914i
$725$	7.50268	+	20.6134i	0.278643	+	0.765564i
$726$		0			0
$727$	−9.57818	+	26.3158i	−0.355235	+	0.976000i	0.625426	+	0.780284i	$0.284925\pi$
$727$	−9.57818	+	26.3158i	−0.355235	+	0.976000i	−0.980661	+	0.195716i	$0.937297\pi$
$728$	−3.83464	−	6.57853i	−0.142121	−	0.243817i
$729$		0			0
$730$	7.18617	+	12.4468i	0.265972	+	0.460677i
$731$	3.18893	−	2.67583i	0.117947	−	0.0989692i
$732$		0			0
$733$	−24.5292	−	4.32516i	−0.906006	−	0.159753i	−0.298817	−	0.954311i	$-0.596592\pi$
$733$	−24.5292	−	4.32516i	−0.906006	−	0.159753i	−0.607189	+	0.794557i	$0.707703\pi$
$734$	−3.22409	+	18.2847i	−0.119003	+	0.674900i
$735$		0			0
$736$	−19.6357	+	16.4763i	−0.723780	+	0.607324i
$737$	−31.0373	−	17.9194i	−1.14327	−	0.660070i
$738$		0			0
$739$	−23.2659	−	40.2978i	−0.855851	−	1.48238i	−0.875853	−	0.482578i	$-0.839701\pi$
$739$	−23.2659	−	40.2978i	−0.855851	−	1.48238i	0.0200017	−	0.999800i	$-0.493633\pi$
$740$	11.0254	−	9.25140i	0.405301	−	0.340088i
$741$		0			0
$742$	−39.0995	−	32.5326i	−1.43539	−	1.19431i
$743$	11.9890	+	32.9395i	0.439834	+	1.20843i	0.939600	+	0.342273i	$0.111197\pi$
$743$	11.9890	+	32.9395i	0.439834	+	1.20843i	−0.499767	+	0.866160i	$0.666581\pi$
$744$		0			0
$745$	3.47754	−	9.55446i	0.127407	−	0.350048i
$746$	17.4580	−	10.0794i	0.639185	−	0.369033i
$747$		0			0
$748$	2.29176	−	1.32315i	0.0837949	−	0.0483790i
$749$	−38.5817	+	6.96838i	−1.40975	+	0.254619i
$750$		0			0
$751$	−3.85948	+	1.40474i	−0.140834	+	0.0512595i	−0.411476	−	0.911421i	$-0.634986\pi$
$751$	−3.85948	+	1.40474i	−0.140834	+	0.0512595i	0.270641	+	0.962680i	$0.412764\pi$
$752$	−14.4781	+	5.26961i	−0.527963	+	0.192163i
$753$		0			0
$754$	38.8884	−	6.85708i	1.41623	−	0.249720i
$755$	5.49677			0.200048
$756$		0			0
$757$	−15.6872			−0.570161			−0.285081	−	0.958504i	$-0.592020\pi$
$757$	−15.6872			−0.570161			−0.285081	+	0.958504i	$0.592020\pi$
$758$	11.7349	−	2.06918i	0.426231	−	0.0751560i
$759$		0			0
$760$	2.23682	−	0.814136i	0.0811380	−	0.0295318i
$761$	26.4207	−	9.61636i	0.957751	−	0.348593i	0.184599	−	0.982814i	$-0.440901\pi$
$761$	26.4207	−	9.61636i	0.957751	−	0.348593i	0.773152	+	0.634221i	$0.218679\pi$
$762$		0			0
$763$	−5.99166	+	5.07016i	−0.216912	+	0.183552i
$764$	−14.3632	+	8.29258i	−0.519641	+	0.300015i
$765$		0			0
$766$	13.7794	−	7.95553i	0.497869	−	0.287445i
$767$	4.39091	−	12.0639i	0.158546	−	0.435603i
$768$		0			0
$769$	9.49574	+	26.0893i	0.342425	+	0.940806i	0.984689	+	0.174322i	$0.0557733\pi$
$769$	9.49574	+	26.0893i	0.342425	+	0.940806i	−0.642263	+	0.766484i	$0.722004\pi$
$770$	−2.69281	+	15.6516i	−0.0970420	+	0.564045i
$771$		0			0
$772$	12.4969	−	10.4861i	0.449772	−	0.377403i
$773$	6.54808	+	11.3416i	0.235518	+	0.407929i	0.959423	−	0.281970i	$-0.0909880\pi$
$773$	6.54808	+	11.3416i	0.235518	+	0.407929i	−0.723905	+	0.689900i	$0.757655\pi$
$774$		0			0
$775$	25.2493	+	14.5777i	0.906981	+	0.523646i
$776$	2.84272	−	2.38532i	0.102048	−	0.0856280i
$777$		0			0
$778$	−6.41839	+	36.4005i	−0.230110	+	1.30502i
$779$	−10.3184	−	1.81942i	−0.369696	−	0.0651874i
$780$		0			0
$781$	6.80084	−	5.70659i	0.243353	−	0.204198i
$782$	1.55584	+	2.69479i	0.0556366	+	0.0963654i
$783$		0			0
$784$	−32.3256	+	0.268580i	−1.15449	+	0.00959214i
$785$	1.47597	−	4.05519i	0.0526796	−	0.144736i
$786$		0			0
$787$	16.1148	+	44.2749i	0.574429	+	1.57823i	0.797430	+	0.603412i	$0.206193\pi$
$787$	16.1148	+	44.2749i	0.574429	+	1.57823i	−0.223001	+	0.974818i	$0.571585\pi$
$788$	27.6476	−	32.9491i	0.984904	−	1.17376i
$789$		0			0
$790$	−10.4298	−	12.4297i	−0.371076	−	0.442231i
$791$	−27.9875	−	16.0040i	−0.995122	−	0.569035i
$792$		0			0
$793$	−0.242042			−0.00859515
$794$	50.7052	+	18.4552i	1.79946	+	0.654949i
$795$		0			0
$796$	−20.2623	+	24.1477i	−0.718178	+	0.855892i
$797$	35.7462	−	13.0105i	1.26619	−	0.460857i	0.380352	−	0.924842i	$-0.375803\pi$
$797$	35.7462	−	13.0105i	1.26619	−	0.460857i	0.885843	+	0.463985i	$0.153581\pi$
$798$		0			0
$799$	0.271052	+	1.53721i	0.00958914	+	0.0543827i
$800$			30.6797i			1.08469i
$801$		0			0
$802$	−37.1361			−1.31132
$803$	−27.4955	−	10.0075i	−0.970294	−	0.353158i
$804$		0			0
$805$	−8.23040	−	1.41601i	−0.290084	−	0.0499079i
$806$	33.7357	−	40.2047i	1.18829	−	1.41615i
$807$		0			0
$808$	−6.26600	−	7.46752i	−0.220437	−	0.262707i
$809$	7.26934	+	4.19695i	0.255576	+	0.147557i	0.622315	−	0.782767i	$-0.286192\pi$
$809$	7.26934	+	4.19695i	0.255576	+	0.147557i	−0.366739	+	0.930324i	$0.619526\pi$
$810$		0			0
$811$		−	36.2880i		−	1.27425i	−0.770762	−	0.637123i	$-0.780124\pi$
$811$		−	36.2880i		−	1.27425i	0.770762	−	0.637123i	$-0.219876\pi$
$812$	7.58661	−	21.1166i	0.266238	−	0.741046i
$813$		0			0
$814$	−11.3776	+	64.5257i	−0.398785	+	2.26162i
$815$	5.50524	+	4.61945i	0.192840	+	0.161812i
$816$		0			0
$817$	11.0428	−	30.3398i	0.386338	−	1.06145i
$818$	−33.2557	−	57.6006i	−1.16276	−	2.01396i
$819$		0			0
$820$	−2.10869	+	3.65237i	−0.0736388	+	0.127546i
$821$	−32.8795	−	39.1842i	−1.14750	−	1.36754i	−0.919125	−	0.393967i	$-0.871103\pi$
$821$	−32.8795	−	39.1842i	−1.14750	−	1.36754i	−0.228377	−	0.973573i	$-0.573342\pi$
$822$		0			0
$823$	0.738462	−	4.18802i	0.0257412	−	0.145985i	−0.969228	−	0.246163i	$-0.920830\pi$
$823$	0.738462	−	4.18802i	0.0257412	−	0.145985i	0.994970	+	0.100178i	$0.0319412\pi$
$824$	8.39149	+	7.04130i	0.292331	+	0.245295i
$825$		0			0
$826$	−10.5371	−	12.4522i	−0.366632	−	0.433267i
$827$	−15.9647	−	9.21722i	−0.555147	−	0.320514i	0.196048	−	0.980594i	$-0.437189\pi$
$827$	−15.9647	−	9.21722i	−0.555147	−	0.320514i	−0.751195	+	0.660080i	$0.770522\pi$
$828$		0			0
$829$			2.47231i			0.0858670i	0.999078	+	0.0429335i	$0.0136704\pi$
$829$			2.47231i			0.0858670i	−0.999078	+	0.0429335i	$0.986330\pi$
$830$	−19.1028	+	3.36834i	−0.663069	+	0.116917i
$831$		0			0
$832$	18.3624	+	3.23779i	0.636602	+	0.112250i
$833$	−0.541891	+	3.22991i	−0.0187754	+	0.111910i
$834$		0			0
$835$	−3.52248	−	19.9770i	−0.121901	−	0.691332i
$836$	10.2623	−	17.7748i	0.354928	−	0.614754i
$837$		0			0
$838$	66.8167	−	38.5766i	2.30814	−	1.33261i
$839$	−11.0811	−	4.03321i	−0.382563	−	0.139242i	0.143578	−	0.989639i	$-0.454139\pi$
$839$	−11.0811	−	4.03321i	−0.382563	−	0.139242i	−0.526141	+	0.850397i	$0.676362\pi$
$840$		0			0
$841$	1.16867	+	0.980630i	0.0402989	+	0.0338148i
$842$	−10.2974	−	28.2918i	−0.354871	−	0.975001i
$843$		0			0
$844$	1.49853	+	8.49858i	0.0515815	+	0.292533i
$845$	−1.21291	+	2.10082i	−0.0417252	+	0.0722702i
$846$		0			0
$847$	−1.62627	−	2.78995i	−0.0558793	−	0.0958638i
$848$	−45.9667	+	8.10517i	−1.57850	+	0.278333i
$849$		0			0
$850$	3.66780	+	0.646731i	0.125804	+	0.0221827i
$851$	−33.9308	−	5.98292i	−1.16313	−	0.205092i
$852$		0			0
$853$	14.3072	−	2.52275i	0.489869	−	0.0863772i	0.0767431	−	0.997051i	$-0.475548\pi$
$853$	14.3072	−	2.52275i	0.489869	−	0.0863772i	0.413126	+	0.910674i	$0.364437\pi$
$854$	−0.152662	+	0.266973i	−0.00522397	+	0.00913562i
$855$		0			0
$856$	−5.38390	+	9.32519i	−0.184018	+	0.318729i
$857$	−2.88185	−	16.3438i	−0.0984422	−	0.558293i	−0.993638	−	0.112621i	$-0.964076\pi$
$857$	−2.88185	−	16.3438i	−0.0984422	−	0.558293i	0.895196	−	0.445673i	$-0.147036\pi$
$858$		0			0
$859$	7.49548	+	20.5937i	0.255742	+	0.702647i	0.999418	+	0.0341061i	$0.0108584\pi$
$859$	7.49548	+	20.5937i	0.255742	+	0.702647i	−0.743676	+	0.668540i	$0.766919\pi$
$860$	−9.95548	−	8.35364i	−0.339479	−	0.284857i
$861$		0			0
$862$	−14.2039	−	5.16980i	−0.483787	−	0.176084i
$863$	−6.94716	+	4.01095i	−0.236484	+	0.136534i	−0.613560	−	0.789648i	$-0.710263\pi$
$863$	−6.94716	+	4.01095i	−0.236484	+	0.136534i	0.377076	+	0.926182i	$0.376930\pi$
$864$		0			0
$865$	−3.49580	+	6.05491i	−0.118861	+	0.205873i
$866$	5.44185	+	30.8622i	0.184921	+	1.04874i
$867$		0			0
$868$	−10.3161	−	27.9810i	−0.350151	−	0.949738i
$869$	32.5317	+	5.73622i	1.10356	+	0.194588i
$870$		0			0
$871$	−39.9882	+	7.05099i	−1.35495	+	0.238914i
$872$			2.15570i			0.0730012i
$873$		0			0
$874$	20.9007	+	12.0670i	0.706976	+	0.408173i
$875$	−16.7467	+	14.1711i	−0.566142	+	0.479072i
$876$		0			0
$877$	27.6050	+	23.1634i	0.932155	+	0.782171i	0.976203	−	0.216858i	$-0.0695810\pi$
$877$	27.6050	+	23.1634i	0.932155	+	0.782171i	−0.0440478	+	0.999029i	$0.514025\pi$
$878$	−2.01529	+	11.4293i	−0.0680128	+	0.385720i
$879$		0			0
$880$	9.36791	+	11.1642i	0.315792	+	0.376346i
$881$	21.1819	−	36.6881i	0.713636	−	1.23605i	−0.249847	−	0.968285i	$-0.580380\pi$
$881$	21.1819	−	36.6881i	0.713636	−	1.23605i	0.963483	−	0.267769i	$-0.0862865\pi$
$882$		0			0
$883$	−3.68137	−	6.37633i	−0.123888	−	0.214580i	0.797410	−	0.603438i	$-0.206203\pi$
$883$	−3.68137	−	6.37633i	−0.123888	−	0.214580i	−0.921298	+	0.388858i	$0.872870\pi$
$884$	1.02545	−	2.81741i	0.0344897	−	0.0947598i
$885$		0			0
$886$	29.0065	+	24.3393i	0.974493	+	0.817696i
$887$	−0.0845808	+	0.479682i	−0.00283995	+	0.0161061i	−0.986195	−	0.165589i	$-0.947047\pi$
$887$	−0.0845808	+	0.479682i	−0.00283995	+	0.0161061i	0.983355	+	0.181695i	$0.0581585\pi$
$888$		0			0
$889$	−3.88249	−	21.4961i	−0.130215	−	0.720957i
$890$			5.21548i			0.174823i
$891$		0			0
$892$	11.8738	+	6.85534i	0.397564	+	0.229534i
$893$	7.78191	+	9.27412i	0.260412	+	0.310346i
$894$		0			0
$895$	−1.08574	+	1.29393i	−0.0362923	+	0.0432515i
$896$	−9.65773	+	11.6072i	−0.322642	+	0.387770i
$897$		0			0
$898$	−0.850867	−	0.309690i	−0.0283938	−	0.0103345i
$899$	−36.5159			−1.21787
$900$		0			0
$901$			4.72877i			0.157538i
$902$	−3.33392	−	18.9076i	−0.111007	−	0.629554i
$903$		0			0
$904$	−8.32066	+	3.02847i	−0.276741	+	0.100726i
$905$	−12.1805	+	14.5161i	−0.404892	+	0.482532i
$906$		0			0
$907$	2.19110	+	0.797495i	0.0727542	+	0.0264804i	0.378141	−	0.925748i	$-0.376563\pi$
$907$	2.19110	+	0.797495i	0.0727542	+	0.0264804i	−0.305387	+	0.952228i	$0.598786\pi$
$908$	36.3909			1.20767
$909$		0			0
$910$	9.06148	+	15.5455i	0.300385	+	0.515327i
$911$	17.0700	+	20.3432i	0.565553	+	0.674000i	0.970712	−	0.240246i	$-0.0772281\pi$
$911$	17.0700	+	20.3432i	0.565553	+	0.674000i	−0.405159	+	0.914246i	$0.632784\pi$
$912$		0			0
$913$	25.3841	−	30.2515i	0.840090	−	1.00118i
$914$	−7.51791	−	20.6553i	−0.248670	−	0.683216i
$915$		0			0
$916$	0.438822	−	1.20565i	0.0144991	−	0.0398359i
$917$	−27.2451	+	47.6460i	−0.899713	+	1.57341i
$918$		0			0
$919$	−4.06315	−	7.03758i	−0.134031	−	0.232148i	0.791196	−	0.611563i	$-0.209459\pi$
$919$	−4.06315	−	7.03758i	−0.134031	−	0.232148i	−0.925227	+	0.379414i	$0.876125\pi$
$920$	−1.75705	+	1.47434i	−0.0579282	+	0.0486075i
$921$		0			0
$922$	37.9293	+	6.68796i	1.24914	+	0.220256i
$923$	1.74665	−	9.90573i	0.0574916	−	0.326051i
$924$		0			0
$925$	−31.5905	+	26.5076i	−1.03869	+	0.871565i
$926$	10.2010	+	5.88956i	0.335226	+	0.193543i
$927$		0			0
$928$	−19.2126	−	33.2771i	−0.630683	−	1.09238i
$929$	−15.6525	+	13.1340i	−0.513541	+	0.430912i	−0.862373	−	0.506273i	$-0.831023\pi$
$929$	−15.6525	+	13.1340i	−0.513541	+	0.430912i	0.348832	+	0.937185i	$0.386578\pi$
$930$		0			0
$931$	8.88573	+	23.7963i	0.291218	+	0.779892i
$932$	−4.80185	−	13.1930i	−0.157290	−	0.432150i
$933$		0			0
$934$	2.47664	−	6.80451i	0.0810381	−	0.222650i
$935$	1.27868	−	0.738247i	0.0418173	−	0.0241433i
$936$		0			0
$937$	29.2827	−	16.9064i	0.956625	−	0.552308i	0.0614921	−	0.998108i	$-0.480414\pi$
$937$	29.2827	−	16.9064i	0.956625	−	0.552308i	0.895133	+	0.445800i	$0.147081\pi$
$938$	−17.4443	+	48.5543i	−0.569575	+	1.58536i
$939$		0			0
$940$	4.57916	−	1.66668i	0.149356	−	0.0543611i
$941$	42.3099	−	15.3995i	1.37926	−	0.502011i	0.457309	−	0.889308i	$-0.348814\pi$
$941$	42.3099	−	15.3995i	1.37926	−	0.502011i	0.921955	+	0.387297i	$0.126591\pi$
$942$		0			0
$943$	9.94256	−	1.75314i	0.323774	−	0.0570902i
$944$	−14.9691			−0.487201
$945$		0			0
$946$	59.1629			1.92355
$947$	1.23405	−	0.217597i	0.0401014	−	0.00707095i	−0.153562	−	0.988139i	$-0.549074\pi$
$947$	1.23405	−	0.217597i	0.0401014	−	0.00707095i	0.193663	+	0.981068i	$0.437963\pi$
$948$		0			0
$949$	−31.1521	+	11.3384i	−1.01124	+	0.368061i
$950$	27.1441	−	9.87964i	0.880670	−	0.320538i
$951$		0			0
$952$	0.581034	+	0.686636i	0.0188314	+	0.0222540i
$953$	−41.3947	+	23.8992i	−1.34091	+	0.774172i	−0.986940	−	0.161086i	$-0.948500\pi$
$953$	−41.3947	+	23.8992i	−1.34091	+	0.774172i	−0.353965	+	0.935259i	$0.615167\pi$
$954$		0			0
$955$	−8.01390	+	4.62682i	−0.259324	+	0.149721i
$956$	−12.4017	+	34.0735i	−0.401101	+	1.10202i
$957$		0			0
$958$	−19.5540	−	53.7242i	−0.631762	−	1.73575i
$959$	−11.1676	−	30.2907i	−0.360622	−	0.978139i
$960$		0			0
$961$	−13.4309	+	11.2699i	−0.433255	+	0.363544i
$962$	37.1174	+	64.2892i	1.19671	+	2.07277i
$963$		0			0
$964$	14.7331	+	8.50617i	0.474522	+	0.273965i
$965$	6.97259	−	5.85070i	0.224456	−	0.188341i
$966$		0			0
$967$	−3.01993	+	17.1269i	−0.0971143	+	0.550763i	0.896965	+	0.442102i	$0.145767\pi$
$967$	−3.01993	+	17.1269i	−0.0971143	+	0.550763i	−0.994079	+	0.108660i	$0.965344\pi$
$968$	−0.873451	−	0.154013i	−0.0280738	−	0.00495017i
$969$		0			0
$970$	−6.71750	+	5.63665i	−0.215686	+	0.180982i
$971$	−13.6117	−	23.5762i	−0.436821	−	0.756596i	0.560622	−	0.828072i	$-0.310562\pi$
$971$	−13.6117	−	23.5762i	−0.436821	−	0.756596i	−0.997442	+	0.0714765i	$0.977229\pi$
$972$		0			0
$973$	−41.1149	+	23.9660i	−1.31808	+	0.768314i
$974$	24.7139	−	67.9008i	0.791884	−	2.17568i
$975$		0			0
$976$	0.0965236	+	0.265196i	0.00308965	+	0.00848873i
$977$	14.5399	−	17.3280i	0.465173	−	0.554372i	−0.481550	−	0.876418i	$-0.659926\pi$
$977$	14.5399	−	17.3280i	0.465173	−	0.554372i	0.946724	+	0.322046i	$0.104371\pi$
$978$		0			0
$979$	−6.82510	−	8.13384i	−0.218131	−	0.259959i
$980$	10.2240	−	0.0849468i	0.326593	−	0.00271353i
$981$		0			0
$982$	−59.8999			−1.91148
$983$	20.7495	+	7.55220i	0.661806	+	0.240878i	0.651016	−	0.759064i	$-0.274343\pi$
$983$	20.7495	+	7.55220i	0.661806	+	0.240878i	0.0107901	+	0.999942i	$0.496565\pi$
$984$		0			0
$985$	15.4259	−	18.3839i	0.491510	−	0.585759i
$986$	−4.38332	+	1.59540i	−0.139593	+	0.0508078i
$987$		0			0
$988$	−4.03804	−	22.9008i	−0.128467	−	0.728573i
$989$			31.1108i			0.989267i
$990$		0			0
$991$	10.8816			0.345665			0.172832	−	0.984951i	$-0.444708\pi$
$991$	10.8816			0.345665			0.172832	+	0.984951i	$0.444708\pi$
$992$	−47.9904	−	17.4671i	−1.52370	−	0.554580i
$993$		0			0
$994$	−9.82441	−	8.17435i	−0.311611	−	0.259275i
$995$	−11.3053	+	13.4731i	−0.358402	+	0.427127i
$996$		0			0
$997$	3.84409	+	4.58120i	0.121743	+	0.145088i	0.823473	−	0.567355i	$-0.192033\pi$
$997$	3.84409	+	4.58120i	0.121743	+	0.145088i	−0.701730	+	0.712443i	$0.747589\pi$
$998$	30.9846	+	17.8890i	0.980801	+	0.566266i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.4		132
3.2	odd	2		189.2.bd.a.185.19	yes	132
7.5	odd	6		567.2.ba.a.341.19		132
21.5	even	6		189.2.ba.a.131.4	yes	132
27.7	even	9		189.2.ba.a.101.4	✓	132
27.20	odd	18		567.2.ba.a.143.19		132
189.47	even	18	inner	567.2.bd.a.467.4		132
189.61	odd	18		189.2.bd.a.47.19	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.4	✓	132	27.7	even	9
189.2.ba.a.131.4	yes	132	21.5	even	6
189.2.bd.a.47.19	yes	132	189.61	odd	18
189.2.bd.a.185.19	yes	132	3.2	odd	2
567.2.ba.a.143.19		132	27.20	odd	18
567.2.ba.a.341.19		132	7.5	odd	6
567.2.bd.a.17.4		132	1.1	even	1	trivial
567.2.bd.a.467.4		132	189.47	even	18	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.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.87320 + 0.330296i) q^{2} +(1.52040 - 0.553380i) q^{4} +(0.848304 - 0.308757i) q^{5} +(2.48993 + 0.894564i) q^{7} +(0.629295 - 0.363324i) q^{8} +O(q^{10})\)	\(q+(-1.87320 + 0.330296i) q^{2} +(1.52040 - 0.553380i) q^{4} +(0.848304 - 0.308757i) q^{5} +(2.48993 + 0.894564i) q^{7} +(0.629295 - 0.363324i) q^{8} +(-1.48706 + 0.858555i) q^{10} +(1.19563 - 3.28497i) q^{11} +(-1.35464 - 3.72184i) q^{13} +(-4.95961 - 0.853285i) q^{14} +(-3.53767 + 2.96846i) q^{16} +(0.233932 + 0.405183i) q^{17} +(3.14258 + 1.81437i) q^{19} +(1.11890 - 0.938869i) q^{20} +(-1.15465 + 6.54832i) q^{22} +(-3.44344 - 0.607171i) q^{23} +(-3.20593 + 2.69010i) q^{25} +(3.76682 + 6.52432i) q^{26} +(4.28072 - 0.0177830i) q^{28} +(1.79273 - 4.92550i) q^{29} +(-2.38270 - 6.54641i) q^{31} +(4.71214 - 5.61571i) q^{32} +(-0.572032 - 0.681722i) q^{34} +(2.38842 - 0.00992201i) q^{35} +9.85377 q^{37} +(-6.48596 - 2.36070i) q^{38} +(0.421655 - 0.502508i) q^{40} +(-2.71326 + 0.987547i) q^{41} +(-1.54504 - 8.76238i) q^{43} -5.65611i q^{44} +6.65080 q^{46} +(3.13508 + 1.14108i) q^{47} +(5.39951 + 4.45481i) q^{49} +(5.11683 - 6.09800i) q^{50} +(-4.11919 - 4.90906i) q^{52} +(8.75304 + 5.05357i) q^{53} -3.15581i q^{55} +(1.89192 - 0.341706i) q^{56} +(-1.73128 + 9.81858i) q^{58} +(2.48304 + 2.08352i) q^{59} +(0.0209011 - 0.0574254i) q^{61} +(6.62553 + 11.4757i) q^{62} +(-2.35384 + 4.07697i) q^{64} +(-2.29829 - 2.73900i) q^{65} +(1.78024 - 10.0962i) q^{67} +(0.579891 + 0.486586i) q^{68} +(-4.47071 + 0.807471i) q^{70} +(2.19935 + 1.26979i) q^{71} -8.37008i q^{73} +(-18.4581 + 3.25466i) q^{74} +(5.78202 + 1.01953i) q^{76} +(5.91566 - 7.10978i) q^{77} +(1.64089 + 9.30597i) q^{79} +(-2.08449 + 3.61044i) q^{80} +(4.75630 - 2.74605i) q^{82} +(10.6153 + 3.86367i) q^{83} +(0.323549 + 0.271490i) q^{85} +(5.78836 + 15.9034i) q^{86} +(-0.441103 - 2.50162i) q^{88} +(1.51868 - 2.63043i) q^{89} +(-0.0435318 - 10.4789i) q^{91} +(-5.57140 + 0.982388i) q^{92} +(-6.24952 - 1.10196i) q^{94} +(3.22606 + 0.568842i) q^{95} +(5.02929 - 0.886800i) q^{97} +(-11.5858 - 6.56131i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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