LMFDB - Embedded newform 567.2.ba.a.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (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			143.1
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75048 + 2.08614i) q^{2} +(-0.940509 - 5.33389i) q^{4} +(-2.08375 + 1.74847i) q^{5} +(-0.122613 + 2.64291i) q^{7} +(8.05677 + 4.65158i) q^{8} +O(q^{10})$	\(q+(-1.75048 + 2.08614i) q^{2} +(-0.940509 - 5.33389i) q^{4} +(-2.08375 + 1.74847i) q^{5} +(-0.122613 + 2.64291i) q^{7} +(8.05677 + 4.65158i) q^{8} -7.40767i q^{10} +(-0.0911635 + 0.108644i) q^{11} +(-0.695830 + 1.91178i) q^{13} +(-5.29885 - 4.88215i) q^{14} +(-13.6280 + 4.96018i) q^{16} -4.00161 q^{17} +3.04328i q^{19} +(11.2860 + 9.47004i) q^{20} +(-0.0670678 - 0.380360i) q^{22} +(0.449297 - 1.23443i) q^{23} +(0.416612 - 2.36273i) q^{25} +(-2.77020 - 4.79813i) q^{26} +(14.2123 - 1.83168i) q^{28} +(-2.12744 - 5.84511i) q^{29} +(-4.18959 + 0.738737i) q^{31} +(7.14417 - 19.6284i) q^{32} +(7.00474 - 8.34792i) q^{34} +(-4.36556 - 5.72155i) q^{35} +(4.69031 - 8.12386i) q^{37} +(-6.34871 - 5.32720i) q^{38} +(-24.9215 + 4.39432i) q^{40} +(-0.303455 - 0.110449i) q^{41} +(0.643705 - 3.65063i) q^{43} +(0.665238 + 0.384075i) q^{44} +(1.78872 + 3.09815i) q^{46} +(1.15909 - 6.57353i) q^{47} +(-6.96993 - 0.648108i) q^{49} +(4.19971 + 5.00502i) q^{50} +(10.8516 + 1.91344i) q^{52} +(6.59926 + 3.81008i) q^{53} -0.385785i q^{55} +(-13.2816 + 20.7230i) q^{56} +(15.9178 + 5.79360i) q^{58} +(6.06369 + 2.20700i) q^{59} +(-11.1600 - 1.96782i) q^{61} +(5.79268 - 10.0332i) q^{62} +(13.9394 + 24.1437i) q^{64} +(-1.89276 - 5.20030i) q^{65} +(-1.37385 + 1.15280i) q^{67} +(3.76355 + 21.3441i) q^{68} +(19.5778 + 0.908274i) q^{70} +(-6.03534 + 3.48450i) q^{71} +(3.67285 - 2.12052i) q^{73} +(8.73722 + 24.0053i) q^{74} +(16.2325 - 2.86223i) q^{76} +(-0.275960 - 0.254258i) q^{77} +(-11.4740 - 9.62781i) q^{79} +(19.7246 - 34.1640i) q^{80} +(0.761604 - 0.439712i) q^{82} +(0.966634 - 0.351826i) q^{83} +(8.33835 - 6.99670i) q^{85} +(6.48894 + 7.73322i) q^{86} +(-1.23985 + 0.451269i) q^{88} +5.17217 q^{89} +(-4.96733 - 2.07342i) q^{91} +(-7.00690 - 1.23551i) q^{92} +(11.6843 + 13.9249i) q^{94} +(-5.32109 - 6.34143i) q^{95} +(-7.25860 - 1.27989i) q^{97} +(13.5528 - 13.4058i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−1.75048	+	2.08614i	−1.23778	+	1.47513i	−0.411946	+	0.911208i	$0.635151\pi$
$2$	−1.75048	+	2.08614i	−1.23778	+	1.47513i	−0.825831	+	0.563917i	$0.809294\pi$
$3$		0			0
$3$		0			0
$4$	−0.940509	−	5.33389i	−0.470255	−	2.66695i
$5$	−2.08375	+	1.74847i	−0.931881	+	0.781941i	−0.976154	−	0.217078i	$-0.930347\pi$
$5$	−2.08375	+	1.74847i	−0.931881	+	0.781941i	0.0442728	+	0.999019i	$0.485903\pi$
$6$		0			0
$7$	−0.122613	+	2.64291i	−0.0463432	+	0.998926i
$7$	−0.122613	+	2.64291i	−0.0463432	+	0.998926i
$8$	8.05677	+	4.65158i	2.84850	+	1.64458i
$9$		0			0
$10$		−	7.40767i		−	2.34251i
$11$	−0.0911635	+	0.108644i	−0.0274868	+	0.0327575i	−0.779613	−	0.626262i	$-0.784584\pi$
$11$	−0.0911635	+	0.108644i	−0.0274868	+	0.0327575i	0.752126	+	0.659019i	$0.229029\pi$
$12$		0			0
$13$	−0.695830	+	1.91178i	−0.192988	+	0.530231i	−0.998013	−	0.0630103i	$-0.979930\pi$
$13$	−0.695830	+	1.91178i	−0.192988	+	0.530231i	0.805024	+	0.593242i	$0.202152\pi$
$14$	−5.29885	−	4.88215i	−1.41618	−	1.30481i
$15$		0			0
$16$	−13.6280	+	4.96018i	−3.40700	+	1.24005i
$17$	−4.00161			−0.970532			−0.485266	−	0.874367i	$-0.661277\pi$
$17$	−4.00161			−0.970532			−0.485266	+	0.874367i	$0.661277\pi$
$18$		0			0
$19$			3.04328i			0.698176i	0.937090	+	0.349088i	$0.113509\pi$
$19$			3.04328i			0.698176i	−0.937090	+	0.349088i	$0.886491\pi$
$20$	11.2860	+	9.47004i	2.52362	+	2.11757i
$21$		0			0
$22$	−0.0670678	−	0.380360i	−0.0142989	−	0.0810931i
$23$	0.449297	−	1.23443i	0.0936849	−	0.257397i	−0.883995	−	0.467496i	$-0.845156\pi$
$23$	0.449297	−	1.23443i	0.0936849	−	0.257397i	0.977680	+	0.210099i	$0.0673785\pi$
$24$		0			0
$25$	0.416612	−	2.36273i	0.0833225	−	0.472545i
$26$	−2.77020	−	4.79813i	−0.543281	−	0.940990i
$27$		0			0
$28$	14.2123	−	1.83168i	2.68587	−	0.346154i
$29$	−2.12744	−	5.84511i	−0.395056	−	1.08541i	−0.964662	−	0.263491i	$-0.915126\pi$
$29$	−2.12744	−	5.84511i	−0.395056	−	1.08541i	0.569605	−	0.821918i	$-0.307096\pi$
$30$		0			0
$31$	−4.18959	+	0.738737i	−0.752472	+	0.132681i	−0.536712	−	0.843765i	$-0.680334\pi$
$31$	−4.18959	+	0.738737i	−0.752472	+	0.132681i	−0.215760	+	0.976446i	$0.569223\pi$
$32$	7.14417	−	19.6284i	1.26292	−	3.46985i
$33$		0			0
$34$	7.00474	−	8.34792i	1.20130	−	1.43166i
$35$	−4.36556	−	5.72155i	−0.737915	−	0.967118i
$36$		0			0
$37$	4.69031	−	8.12386i	0.771083	−	1.33555i	−0.165888	−	0.986145i	$-0.553049\pi$
$37$	4.69031	−	8.12386i	0.771083	−	1.33555i	0.936970	−	0.349409i	$-0.113618\pi$
$38$	−6.34871	−	5.32720i	−1.02990	−	0.864186i
$39$		0			0
$40$	−24.9215	+	4.39432i	−3.94043	+	0.694804i
$41$	−0.303455	−	0.110449i	−0.0473917	−	0.0172492i	0.318216	−	0.948018i	$-0.396916\pi$
$41$	−0.303455	−	0.110449i	−0.0473917	−	0.0172492i	−0.365607	+	0.930769i	$0.619139\pi$
$42$		0			0
$43$	0.643705	−	3.65063i	0.0981640	−	0.556716i	−0.895568	−	0.444925i	$-0.853230\pi$
$43$	0.643705	−	3.65063i	0.0981640	−	0.556716i	0.993732	−	0.111791i	$-0.0356586\pi$
$44$	0.665238	+	0.384075i	0.100288	+	0.0579015i
$45$		0			0
$46$	1.78872	+	3.09815i	0.263732	+	0.456797i
$47$	1.15909	−	6.57353i	0.169071	−	0.958847i	−0.775697	−	0.631106i	$-0.782601\pi$
$47$	1.15909	−	6.57353i	0.169071	−	0.958847i	0.944767	−	0.327741i	$-0.106287\pi$
$48$		0			0
$49$	−6.96993	−	0.648108i	−0.995705	−	0.0925868i
$50$	4.19971	+	5.00502i	0.593929	+	0.707817i
$51$		0			0
$52$	10.8516	+	1.91344i	1.50485	+	0.265346i
$53$	6.59926	+	3.81008i	0.906477	+	0.523355i	0.879296	−	0.476276i	$-0.158014\pi$
$53$	6.59926	+	3.81008i	0.906477	+	0.523355i	0.0271813	+	0.999631i	$0.491347\pi$
$54$		0			0
$55$		−	0.385785i		−	0.0520192i
$56$	−13.2816	+	20.7230i	−1.77482	+	2.76922i
$57$		0			0
$58$	15.9178	+	5.79360i	2.09011	+	0.760736i
$59$	6.06369	+	2.20700i	0.789425	+	0.287327i	0.705097	−	0.709111i	$-0.250904\pi$
$59$	6.06369	+	2.20700i	0.789425	+	0.287327i	0.0843278	+	0.996438i	$0.473126\pi$
$60$		0			0
$61$	−11.1600	−	1.96782i	−1.42890	−	0.251953i	−0.594935	−	0.803774i	$-0.702822\pi$
$61$	−11.1600	−	1.96782i	−1.42890	−	0.251953i	−0.833963	+	0.551821i	$0.813933\pi$
$62$	5.79268	−	10.0332i	0.735671	−	1.27422i
$63$		0			0
$64$	13.9394	+	24.1437i	1.74242	+	3.01796i
$65$	−1.89276	−	5.20030i	−0.234767	−	0.645018i
$66$		0			0
$67$	−1.37385	+	1.15280i	−0.167843	+	0.140837i	−0.722840	−	0.691015i	$-0.757164\pi$
$67$	−1.37385	+	1.15280i	−0.167843	+	0.140837i	0.554997	+	0.831852i	$0.312719\pi$
$68$	3.76355	+	21.3441i	0.456397	+	2.58836i
$69$		0			0
$70$	19.5778	+	0.908274i	2.33999	+	0.108560i
$71$	−6.03534	+	3.48450i	−0.716263	+	0.413534i	−0.813376	−	0.581739i	$-0.802373\pi$
$71$	−6.03534	+	3.48450i	−0.716263	+	0.413534i	0.0971130	+	0.995273i	$0.469039\pi$
$72$		0			0
$73$	3.67285	−	2.12052i	0.429875	−	0.248188i	−0.269418	−	0.963023i	$-0.586831\pi$
$73$	3.67285	−	2.12052i	0.429875	−	0.248188i	0.699293	+	0.714835i	$0.253498\pi$
$74$	8.73722	+	24.0053i	1.01568	+	2.79056i
$75$		0			0
$76$	16.2325	−	2.86223i	1.86200	−	0.328320i
$77$	−0.275960	−	0.254258i	−0.0314485	−	0.0289754i
$78$		0			0
$79$	−11.4740	−	9.62781i	−1.29092	−	1.08321i	−0.991638	−	0.129049i	$-0.958808\pi$
$79$	−11.4740	−	9.62781i	−1.29092	−	1.08321i	−0.299284	−	0.954164i	$-0.596748\pi$
$80$	19.7246	−	34.1640i	2.20528	−	3.81965i
$81$		0			0
$82$	0.761604	−	0.439712i	0.0841050	−	0.0485581i
$83$	0.966634	−	0.351826i	0.106102	−	0.0386179i	−0.288424	−	0.957503i	$-0.593131\pi$
$83$	0.966634	−	0.351826i	0.106102	−	0.0386179i	0.394526	+	0.918885i	$0.370909\pi$
$84$		0			0
$85$	8.33835	−	6.99670i	0.904421	−	0.758899i
$86$	6.48894	+	7.73322i	0.699721	+	0.833895i
$87$		0			0
$88$	−1.23985	+	0.451269i	−0.132169	+	0.0481054i
$89$	5.17217			0.548249			0.274124	−	0.961694i	$-0.411612\pi$
$89$	5.17217			0.548249			0.274124	+	0.961694i	$0.411612\pi$
$90$		0			0
$91$	−4.96733	−	2.07342i	−0.520718	−	0.217354i
$92$	−7.00690	−	1.23551i	−0.730520	−	0.128810i
$93$		0			0
$94$	11.6843	+	13.9249i	1.20515	+	1.43624i
$95$	−5.32109	−	6.34143i	−0.545932	−	0.650617i
$96$		0			0
$97$	−7.25860	−	1.27989i	−0.736999	−	0.129953i	−0.207466	−	0.978242i	$-0.566522\pi$
$97$	−7.25860	−	1.27989i	−0.736999	−	0.129953i	−0.529533	+	0.848289i	$0.677633\pi$
$98$	13.5528	−	13.4058i	1.36904	−	1.35419i
$99$		0			0
$100$	−12.9944			−1.29944
$101$	−6.33569	+	2.30600i	−0.630425	+	0.229456i	−0.637416	−	0.770520i	$-0.719997\pi$
$101$	−6.33569	+	2.30600i	−0.630425	+	0.229456i	0.00699121	+	0.999976i	$0.497775\pi$
$102$		0			0
$103$	7.37734	+	8.79197i	0.726911	+	0.866299i	0.995283	−	0.0970166i	$-0.0309300\pi$
$103$	7.37734	+	8.79197i	0.726911	+	0.866299i	−0.268372	+	0.963315i	$0.586486\pi$
$104$	−14.4989	+	12.1660i	−1.42174	+	1.19298i
$105$		0			0
$106$	−19.5002	+	7.09751i	−1.89403	+	0.689371i
$107$	−15.4754	+	8.93470i	−1.49606	+	0.863750i	−0.999990	−	0.00453289i	$-0.998557\pi$
$107$	−15.4754	+	8.93470i	−1.49606	+	0.863750i	−0.496069	+	0.868283i	$0.665224\pi$
$108$		0			0
$109$	−4.74241	+	8.21409i	−0.454240	+	0.786768i	−0.998644	−	0.0520558i	$-0.983423\pi$
$109$	−4.74241	+	8.21409i	−0.454240	+	0.786768i	0.544404	+	0.838823i	$0.316756\pi$
$110$	0.804802	+	0.675309i	0.0767349	+	0.0643882i
$111$		0			0
$112$	−11.4383	−	36.6257i	−1.08082	−	3.46081i
$113$	1.54842	−	0.273029i	0.145663	−	0.0256844i	−0.100341	−	0.994953i	$-0.531993\pi$
$113$	1.54842	−	0.273029i	0.145663	−	0.0256844i	0.246004	+	0.969269i	$0.420882\pi$
$114$		0			0
$115$	1.22215	+	3.35783i	0.113966	+	0.313120i
$116$	−29.1763	+	16.8449i	−2.70895	+	1.56401i
$117$		0			0
$118$	−15.2185	+	8.78640i	−1.40098	+	0.808853i
$119$	0.490647	−	10.5759i	0.0449776	−	0.969489i
$120$		0			0
$121$	1.90664	+	10.8131i	0.173331	+	0.983007i
$122$	23.6406	−	19.8368i	2.14032	−	1.79594i
$123$		0			0
$124$	7.88069	+	21.6520i	0.707707	+	1.94441i
$125$	−3.53731	−	6.12679i	−0.316386	−	0.547997i
$126$		0			0
$127$	9.03739	−	15.6532i	0.801938	−	1.38900i	−0.116400	−	0.993202i	$-0.537136\pi$
$127$	9.03739	−	15.6532i	0.801938	−	1.38900i	0.918339	−	0.395795i	$-0.129531\pi$
$128$	−33.6262	−	5.92921i	−2.97217	−	0.524073i
$129$		0			0
$130$	14.1618	+	5.15448i	1.24207	+	0.452077i
$131$	−5.15318	−	1.87560i	−0.450235	−	0.163872i	0.106943	−	0.994265i	$-0.465894\pi$
$131$	−5.15318	−	1.87560i	−0.450235	−	0.163872i	−0.557178	+	0.830393i	$0.688116\pi$
$132$		0			0
$133$	−8.04310	−	0.373144i	−0.697425	−	0.0323557i
$134$		−	4.88401i		−	0.421914i
$135$		0			0
$136$	−32.2400	−	18.6138i	−2.76456	−	1.59612i
$137$	4.12294	+	0.726986i	0.352247	+	0.0621106i	0.346972	−	0.937875i	$-0.387210\pi$
$137$	4.12294	+	0.726986i	0.352247	+	0.0621106i	0.00527469	+	0.999986i	$0.498321\pi$
$138$		0			0
$139$	−7.34520	−	8.75367i	−0.623012	−	0.742477i	0.358573	−	0.933502i	$-0.383263\pi$
$139$	−7.34520	−	8.75367i	−0.623012	−	0.742477i	−0.981585	+	0.191025i	$0.938819\pi$
$140$	−26.4123	+	28.6666i	−2.23224	+	2.42277i
$141$		0			0
$142$	3.29557	−	18.6901i	0.276558	−	1.56844i
$143$	−0.144270	−	0.249882i	−0.0120644	−	0.0208962i
$144$		0			0
$145$	14.6531	+	8.45996i	1.21687	+	0.702561i
$146$	−2.00555	+	11.3740i	−0.165980	+	0.941322i
$147$		0			0
$148$	−47.7431	−	17.3771i	−3.92446	−	1.42839i
$149$	−22.8439	+	4.02799i	−1.87144	+	0.329986i	−0.989860	−	0.142044i	$-0.954633\pi$
$149$	−22.8439	+	4.02799i	−1.87144	+	0.329986i	−0.881583	+	0.472030i	$0.843522\pi$
$150$		0			0
$151$	0.176411	+	0.148026i	0.0143561	+	0.0120462i	0.649937	−	0.759988i	$-0.274795\pi$
$151$	0.176411	+	0.148026i	0.0143561	+	0.0120462i	−0.635581	+	0.772034i	$0.719240\pi$
$152$	−14.1560	+	24.5190i	−1.14821	+	1.98875i
$153$		0			0
$154$	1.01348	−	0.130617i	0.0816686	−	0.0105254i
$155$	7.43839	−	8.86472i	0.597466	−	0.712032i
$156$		0			0
$157$	−3.36532	+	9.24614i	−0.268582	+	0.737922i	0.729937	+	0.683514i	$0.239549\pi$
$157$	−3.36532	+	9.24614i	−0.268582	+	0.737922i	−0.998519	+	0.0544079i	$0.982673\pi$
$158$	40.1699	−	7.08305i	3.19575	−	0.563497i
$159$		0			0
$160$	19.4332	+	53.3921i	1.53633	+	4.22102i
$161$	3.20740	+	1.33881i	0.252779	+	0.105513i
$162$		0			0
$163$	−0.272626	−	0.472203i	−0.0213537	−	0.0369858i	0.855151	−	0.518379i	$-0.173464\pi$
$163$	−0.272626	−	0.472203i	−0.0213537	−	0.0369858i	−0.876505	+	0.481393i	$0.840131\pi$
$164$	−0.303719	+	1.72247i	−0.0237164	+	0.134503i
$165$		0			0
$166$	−0.958116	+	2.63240i	−0.0743642	+	0.204314i
$167$	2.22249	+	12.6044i	0.171981	+	0.975354i	0.941571	+	0.336815i	$0.109350\pi$
$167$	2.22249	+	12.6044i	0.171981	+	0.975354i	−0.769590	+	0.638539i	$0.779539\pi$
$168$		0			0
$169$	6.78787	+	5.69570i	0.522144	+	0.438131i
$170$			29.6426i			2.27348i
$171$		0			0
$172$	−20.0775			−1.53089
$173$	−3.16024	+	1.15023i	−0.240269	+	0.0874506i	−0.459348	−	0.888256i	$-0.651917\pi$
$173$	−3.16024	+	1.15023i	−0.240269	+	0.0874506i	0.219079	+	0.975707i	$0.429695\pi$
$174$		0			0
$175$	6.19339	+	1.39077i	0.468176	+	0.105132i
$176$	0.703479	−	1.93279i	0.0530268	−	0.145690i
$177$		0			0
$178$	−9.05378	+	10.7899i	−0.678610	+	0.808736i
$179$		−	1.33384i		−	0.0996962i	−0.998757	−	0.0498481i	$-0.984126\pi$
$179$		−	1.33384i		−	0.0996962i	0.998757	−	0.0498481i	$-0.0158737\pi$
$180$		0			0
$181$	2.64678	+	1.52812i	0.196733	+	0.113584i	0.595131	−	0.803629i	$-0.297100\pi$
$181$	2.64678	+	1.52812i	0.196733	+	0.113584i	−0.398398	+	0.917213i	$0.630434\pi$
$182$	13.0207	−	6.73308i	0.965157	−	0.499089i
$183$		0			0
$184$	9.36194	−	7.85560i	0.690171	−	0.579123i
$185$	4.43092	+	25.1290i	0.325768	+	1.84752i
$186$		0			0
$187$	0.364800	−	0.434752i	0.0266769	−	0.0317922i
$188$	−36.1526			−2.63670
$189$		0			0
$190$	22.5436			1.63548
$191$	9.72666	−	11.5918i	0.703797	−	0.838752i	−0.289154	−	0.957283i	$-0.593374\pi$
$191$	9.72666	−	11.5918i	0.703797	−	0.838752i	0.992950	+	0.118530i	$0.0378183\pi$
$192$		0			0
$193$	0.829438	+	4.70398i	0.0597042	+	0.338600i	0.999998	−	0.00176318i	$-0.000561238\pi$
$193$	0.829438	+	4.70398i	0.0597042	+	0.338600i	−0.940294	+	0.340363i	$0.889450\pi$
$194$	15.3761	−	12.9021i	1.10394	−	0.926314i
$195$		0			0
$196$	3.09835	+	37.7864i	0.221310	+	2.69903i
$197$	−7.02585	−	4.05638i	−0.500571	−	0.289005i	0.228378	−	0.973572i	$-0.426658\pi$
$197$	−7.02585	−	4.05638i	−0.500571	−	0.289005i	−0.728949	+	0.684568i	$0.759991\pi$
$198$		0			0
$199$			5.04150i			0.357382i	0.983905	+	0.178691i	$0.0571863\pi$
$199$			5.04150i			0.357382i	−0.983905	+	0.178691i	$0.942814\pi$
$200$	14.3470	−	17.0980i	1.01448	−	1.20901i
$201$		0			0
$202$	6.27986	−	17.2538i	0.441850	−	1.21397i
$203$	15.7089	−	4.90596i	1.10255	−	0.344331i
$204$		0			0
$205$	0.825441	−	0.300436i	0.0576513	−	0.0209833i
$206$	−31.2552			−2.17765
$207$		0			0
$208$		−	29.5051i		−	2.04581i
$209$	−0.330635	−	0.277436i	−0.0228705	−	0.0191906i
$210$		0			0
$211$	−0.533965	−	3.02827i	−0.0367597	−	0.208474i	0.960896	−	0.276910i	$-0.0893104\pi$
$211$	−0.533965	−	3.02827i	−0.0367597	−	0.208474i	−0.997656	+	0.0684355i	$0.978199\pi$
$212$	14.1159	−	38.7831i	0.969484	−	2.66364i
$213$		0			0
$214$	8.45026	−	47.9238i	0.577648	−	3.27600i
$215$	5.04171	+	8.73250i	0.343842	+	0.595552i
$216$		0			0
$217$	−1.43872	−	11.1633i	−0.0976666	−	0.757812i
$218$	−8.83427	−	24.2720i	−0.598332	−	1.64390i
$219$		0			0
$220$	−2.05774	+	0.362834i	−0.138732	+	0.0244623i
$221$	2.78444	−	7.65017i	0.187301	−	0.514606i
$222$		0			0
$223$	−11.4325	+	13.6247i	−0.765576	+	0.912378i	−0.998187	−	0.0601917i	$-0.980829\pi$
$223$	−11.4325	+	13.6247i	−0.765576	+	0.912378i	0.232611	+	0.972570i	$0.425273\pi$
$224$	51.0002	+	21.2881i	3.40759	+	1.42237i
$225$		0			0
$226$	−2.14091	+	3.70816i	−0.142411	+	0.246663i
$227$	5.54136	+	4.64975i	0.367793	+	0.308615i	0.807888	−	0.589336i	$-0.200611\pi$
$227$	5.54136	+	4.64975i	0.367793	+	0.308615i	−0.440095	+	0.897951i	$0.645055\pi$
$228$		0			0
$229$	14.9612	−	2.63807i	0.988665	−	0.174328i	0.344146	−	0.938916i	$-0.388169\pi$
$229$	14.9612	−	2.63807i	0.988665	−	0.174328i	0.644519	+	0.764588i	$0.277057\pi$
$230$	−9.14427	−	3.32824i	−0.602956	−	0.219458i
$231$		0			0
$232$	10.0486	−	56.9886i	0.659725	−	3.74149i
$233$	10.7311	+	6.19561i	0.703019	+	0.405888i	0.808471	−	0.588536i	$-0.200296\pi$
$233$	10.7311	+	6.19561i	0.703019	+	0.405888i	−0.105452	+	0.994424i	$0.533629\pi$
$234$		0			0
$235$	9.07838	+	15.7242i	0.592208	+	1.02574i
$236$	6.06895	−	34.4187i	0.395055	−	2.24047i
$237$		0			0
$238$	21.2039	+	19.5364i	1.37445	+	1.26636i
$239$	−5.11974	−	6.10146i	−0.331168	−	0.394671i	0.574607	−	0.818430i	$-0.305155\pi$
$239$	−5.11974	−	6.10146i	−0.331168	−	0.394671i	−0.905775	+	0.423759i	$0.860710\pi$
$240$		0			0
$241$	0.540011	+	0.0952186i	0.0347852	+	0.00613357i	0.191014	−	0.981587i	$-0.438823\pi$
$241$	0.540011	+	0.0952186i	0.0347852	+	0.00613357i	−0.156229	+	0.987721i	$0.549934\pi$
$242$	−25.8952	−	14.9506i	−1.66460	−	0.961059i
$243$		0			0
$244$			61.3772i			3.92927i
$245$	15.6568	−	10.8363i	1.00028	−	0.692303i
$246$		0			0
$247$	−5.81806	−	2.11760i	−0.370195	−	0.134740i
$248$	−37.1908	−	13.5363i	−2.36162	−	0.859559i
$249$		0			0
$250$	18.9734	+	3.34551i	1.19998	+	0.211589i
$251$	−8.86627	+	15.3568i	−0.559634	+	0.969314i	0.437893	+	0.899027i	$0.355725\pi$
$251$	−8.86627	+	15.3568i	−0.559634	+	0.969314i	−0.997527	+	0.0702870i	$0.977608\pi$
$252$		0			0
$253$	0.0931548	+	0.161349i	0.00585659	+	0.0101439i
$254$	16.8351	+	46.2539i	1.05633	+	2.90223i
$255$		0			0
$256$	28.5185	−	23.9299i	1.78241	−	1.49562i
$257$	4.85836	+	27.5531i	0.303056	+	1.71872i	0.632516	+	0.774547i	$0.282022\pi$
$257$	4.85836	+	27.5531i	0.303056	+	1.71872i	−0.329460	+	0.944169i	$0.606867\pi$
$258$		0			0
$259$	20.8955	+	13.3922i	1.29838	+	0.832148i
$260$	−25.9577	+	14.9867i	−1.60983	+	0.929435i
$261$		0			0
$262$	12.9333	−	7.46705i	0.799023	−	0.461316i
$263$	−3.81588	−	10.4841i	−0.235297	−	0.646475i	−0.999998	−	0.00208847i	$-0.999335\pi$
$263$	−3.81588	−	10.4841i	−0.235297	−	0.646475i	0.764700	−	0.644386i	$-0.222887\pi$
$264$		0			0
$265$	−20.4130	+	3.59937i	−1.25396	+	0.221107i
$266$	14.8577	−	16.1259i	0.910986	−	0.988741i
$267$		0			0
$268$	7.44103	+	6.24377i	0.454533	+	0.381399i
$269$	−2.38895	+	4.13779i	−0.145657	+	0.252286i	−0.929618	−	0.368525i	$-0.879863\pi$
$269$	−2.38895	+	4.13779i	−0.145657	+	0.252286i	0.783961	+	0.620810i	$0.213196\pi$
$270$		0			0
$271$	−18.5269	+	10.6965i	−1.12543	+	0.649766i	−0.942781	−	0.333412i	$-0.891800\pi$
$271$	−18.5269	+	10.6965i	−1.12543	+	0.649766i	−0.182647	+	0.983179i	$0.558467\pi$
$272$	54.5339	−	19.8487i	3.30660	−	1.20350i
$273$		0			0
$274$	−8.73373	+	7.32847i	−0.527624	+	0.442729i
$275$	0.218717	+	0.260657i	0.0131892	+	0.0157182i
$276$		0			0
$277$	−11.6375	+	4.23571i	−0.699231	+	0.254499i	−0.667083	−	0.744984i	$-0.732457\pi$
$277$	−11.6375	+	4.23571i	−0.699231	+	0.254499i	−0.0321485	+	0.999483i	$0.510235\pi$
$278$	31.1191			1.86640
$279$		0			0
$280$	−8.55811	−	66.4039i	−0.511445	−	3.96839i
$281$	15.3782	+	2.71159i	0.917385	+	0.161760i	0.612355	−	0.790583i	$-0.290222\pi$
$281$	15.3782	+	2.71159i	0.917385	+	0.161760i	0.305030	+	0.952343i	$0.401333\pi$
$282$		0			0
$283$	−14.6993	−	17.5180i	−0.873785	−	1.04134i	−0.998790	−	0.0491805i	$-0.984339\pi$
$283$	−14.6993	−	17.5180i	−0.873785	−	1.04134i	0.125005	−	0.992156i	$-0.460105\pi$
$284$	24.2622	+	28.9146i	1.43970	+	1.71577i
$285$		0			0
$286$	0.773831	+	0.136447i	0.0457576	+	0.00806830i
$287$	0.329113	−	0.788461i	0.0194269	−	0.0465414i
$288$		0			0
$289$	−0.987154			−0.0580679
$290$	−43.2986	+	15.7594i	−2.54258	+	0.925424i
$291$		0			0
$292$	−14.7650	−	17.5962i	−0.864056	−	1.02974i
$293$	−25.2580	+	21.1939i	−1.47559	+	1.23816i	−0.564837	+	0.825203i	$0.691061\pi$
$293$	−25.2580	+	21.1939i	−1.47559	+	1.23816i	−0.910749	+	0.412960i	$0.864495\pi$
$294$		0			0
$295$	−16.4941	+	6.00336i	−0.960323	+	0.349529i
$296$	75.5775	−	43.6347i	4.39285	−	2.53622i
$297$		0			0
$298$	31.5848	−	54.7065i	1.82966	−	3.16906i
$299$	2.04733	+	1.71791i	0.118400	+	0.0993493i
$300$		0			0
$301$	9.56936	+	2.14887i	0.551569	+	0.123859i
$302$	−0.617608	+	0.108901i	−0.0355393	+	0.00626654i
$303$		0			0
$304$	−15.0952	−	41.4738i	−0.865770	−	2.37868i
$305$	26.6954	−	15.4126i	1.52858	−	0.882523i
$306$		0			0
$307$	13.5558	−	7.82647i	0.773672	−	0.446680i	−0.0605107	−	0.998168i	$-0.519273\pi$
$307$	13.5558	−	7.82647i	0.773672	−	0.446680i	0.834183	+	0.551488i	$0.185940\pi$
$308$	−1.09664	+	1.71107i	−0.0624870	+	0.0974973i
$309$		0			0
$310$	5.47232	+	31.0351i	0.310807	+	1.76267i
$311$	20.3810	−	17.1017i	1.15570	−	0.969749i	0.155864	−	0.987778i	$-0.450184\pi$
$311$	20.3810	−	17.1017i	1.15570	−	0.969749i	0.999837	+	0.0180296i	$0.00573930\pi$
$312$		0			0
$313$	10.6716	+	29.3199i	0.603193	+	1.65726i	0.744762	+	0.667330i	$0.232563\pi$
$313$	10.6716	+	29.3199i	0.603193	+	1.65726i	−0.141569	+	0.989928i	$0.545215\pi$
$314$	−13.3978	−	23.2057i	−0.756084	−	1.30958i
$315$		0			0
$316$	−40.5623	+	70.2560i	−2.28181	+	3.95221i
$317$	−12.1904	−	2.14949i	−0.684679	−	0.120727i	−0.179521	−	0.983754i	$-0.557455\pi$
$317$	−12.1904	−	2.14949i	−0.684679	−	0.120727i	−0.505158	+	0.863027i	$0.668566\pi$
$318$		0			0
$319$	0.828984	+	0.301725i	0.0464142	+	0.0168934i
$320$	−71.2608	−	25.9368i	−3.98360	−	1.44991i
$321$		0			0
$322$	−8.40745	+	4.34754i	−0.468529	+	0.242279i
$323$		−	12.1780i		−	0.677602i
$324$		0			0
$325$	4.22711	+	2.44053i	0.234478	+	0.135376i
$326$	1.46231	+	0.257845i	0.0809898	+	0.0142807i
$327$		0			0
$328$	−1.93111	−	2.30140i	−0.106627	−	0.127074i
$329$	17.2311	+	3.86937i	0.949982	+	0.213325i
$330$		0			0
$331$	−3.30152	+	18.7238i	−0.181468	+	1.02916i	0.748942	+	0.662635i	$0.230562\pi$
$331$	−3.30152	+	18.7238i	−0.181468	+	1.02916i	−0.930410	+	0.366520i	$0.880549\pi$
$332$	−2.78573	−	4.82503i	−0.152887	−	0.264808i
$333$		0			0
$334$	−30.1849	−	17.4273i	−1.65164	−	0.953577i
$335$	0.847127	−	4.80430i	0.0462835	−	0.262487i
$336$		0			0
$337$	22.8085	+	8.30162i	1.24246	+	0.452218i	0.877847	−	0.478941i	$-0.158979\pi$
$337$	22.8085	+	8.30162i	1.24246	+	0.452218i	0.364612	+	0.931159i	$0.381201\pi$
$338$	−23.7641	+	4.19025i	−1.29260	+	0.227919i
$339$		0			0
$340$	−45.1619	−	37.8954i	−2.44925	−	2.05517i
$341$	0.301678	−	0.522521i	0.0163368	−	0.0282961i
$342$		0			0
$343$	2.56749	−	18.3414i	0.138632	−	0.990344i
$344$	22.1674	−	26.4180i	1.19518	−	1.42437i
$345$		0			0
$346$	3.13239	−	8.60617i	0.168398	−	0.462671i
$347$	−30.0193	+	5.29321i	−1.61152	+	0.284154i	−0.905598	−	0.424137i	$-0.860578\pi$
$347$	−30.0193	+	5.29321i	−1.61152	+	0.284154i	−0.705921	+	0.708291i	$0.749466\pi$
$348$		0			0
$349$	−3.07591	−	8.45099i	−0.164650	−	0.452371i	0.829740	−	0.558150i	$-0.188489\pi$
$349$	−3.07591	−	8.45099i	−0.164650	−	0.452371i	−0.994390	+	0.105779i	$0.966266\pi$
$350$	−13.7428	+	10.4858i	−0.734581	+	0.560488i
$351$		0			0
$352$	1.48123	+	2.56557i	0.0789500	+	0.136745i
$353$	−3.11622	+	17.6729i	−0.165860	+	0.940636i	0.782314	+	0.622884i	$0.214039\pi$
$353$	−3.11622	+	17.6729i	−0.165860	+	0.940636i	−0.948174	+	0.317752i	$0.897072\pi$
$354$		0			0
$355$	6.48357	−	17.8135i	0.344112	−	0.945440i
$356$	−4.86447	−	27.5878i	−0.257816	−	1.46215i
$357$		0			0
$358$	2.78259	+	2.33487i	0.147064	+	0.123402i
$359$		−	27.0082i		−	1.42544i	−0.701450	−	0.712719i	$-0.747464\pi$
$359$		−	27.0082i		−	1.42544i	0.701450	−	0.712719i	$-0.252536\pi$
$360$		0			0
$361$	9.73847			0.512551
$362$	−7.82100	+	2.84661i	−0.411063	+	0.149615i
$363$		0			0
$364$	−6.38759	+	28.4453i	−0.334801	+	1.49094i
$365$	−3.94563	+	10.8405i	−0.206524	+	0.567419i
$366$		0			0
$367$	10.3302	−	12.3111i	0.539232	−	0.642632i	−0.425783	−	0.904825i	$-0.640001\pi$
$367$	10.3302	−	12.3111i	0.539232	−	0.642632i	0.965015	+	0.262193i	$0.0844458\pi$
$368$			19.0514i			0.993125i
$369$		0			0
$370$	−60.1789	−	34.7443i	−3.12855	−	1.80627i
$371$	−10.8789	+	16.9741i	−0.564802	+	0.881250i
$372$		0			0
$373$	−15.0090	+	12.5940i	−0.777136	+	0.652095i	−0.942526	−	0.334134i	$-0.891556\pi$
$373$	−15.0090	+	12.5940i	−0.777136	+	0.652095i	0.165390	+	0.986228i	$0.447112\pi$
$374$	0.268379	+	1.52205i	0.0138775	+	0.0787034i
$375$		0			0
$376$	39.9158	−	47.5698i	2.05850	−	2.45322i
$377$	12.6549			0.651759
$378$		0			0
$379$	4.00603			0.205776			0.102888	−	0.994693i	$-0.467192\pi$
$379$	4.00603			0.205776			0.102888	+	0.994693i	$0.467192\pi$
$380$	−28.8200	+	34.3463i	−1.47843	+	1.76193i
$381$		0			0
$382$	7.15577	+	40.5824i	0.366121	+	2.07638i
$383$	16.2280	−	13.6169i	0.829211	−	0.695791i	−0.125899	−	0.992043i	$-0.540181\pi$
$383$	16.2280	−	13.6169i	0.829211	−	0.695791i	0.955110	+	0.296253i	$0.0957370\pi$
$384$		0			0
$385$	1.01959	+	0.0473021i	0.0519633	+	0.00241074i
$386$	−11.2651	−	6.50390i	−0.573377	−	0.331040i
$387$		0			0
$388$			39.9203i			2.02665i
$389$	−11.4973	+	13.7019i	−0.582936	+	0.694716i	−0.974232	−	0.225549i	$-0.927582\pi$
$389$	−11.4973	+	13.7019i	−0.582936	+	0.694716i	0.391296	+	0.920265i	$0.372027\pi$
$390$		0			0
$391$	−1.79791	+	4.93971i	−0.0909242	+	0.249812i
$392$	−53.1404	−	37.6428i	−2.68400	−	1.90125i
$393$		0			0
$394$	20.7608	−	7.55631i	1.04591	−	0.380681i
$395$	40.7429			2.05000
$396$		0			0
$397$			16.1300i			0.809544i	0.914418	+	0.404772i	$0.132649\pi$
$397$			16.1300i			0.809544i	−0.914418	+	0.404772i	$0.867351\pi$
$398$	−10.5173	−	8.82505i	−0.527184	−	0.442360i
$399$		0			0
$400$	6.04197	+	34.2657i	0.302098	+	1.71328i
$401$	1.01818	−	2.79743i	0.0508456	−	0.139697i	−0.911670	−	0.410923i	$-0.865207\pi$
$401$	1.01818	−	2.79743i	0.0508456	−	0.139697i	0.962516	+	0.271225i	$0.0874289\pi$
$402$		0			0
$403$	1.50294	−	8.52358i	0.0748667	−	0.424590i
$404$	18.2588	+	31.6251i	0.908407	+	1.57341i
$405$		0			0
$406$	−17.2637	+	41.3589i	−0.856781	+	2.05261i
$407$	0.455027	+	1.25018i	0.0225548	+	0.0619689i
$408$		0			0
$409$	−22.7127	+	4.00487i	−1.12307	+	0.198028i	−0.704189	−	0.710012i	$-0.748689\pi$
$409$	−22.7127	+	4.00487i	−1.12307	+	0.198028i	−0.418883	+	0.908040i	$0.637578\pi$
$410$	−0.818166	+	2.24789i	−0.0404064	+	0.111016i
$411$		0			0
$412$	39.9570	−	47.6189i	1.96854	−	2.34601i
$413$	−6.57639	+	15.7552i	−0.323603	+	0.775261i
$414$		0			0
$415$	−1.39906	+	2.42325i	−0.0686774	+	0.118953i
$416$	32.5541	+	27.3161i	1.59609	+	1.33928i
$417$		0			0
$418$	1.15754	−	0.204106i	0.0566172	−	0.00998314i
$419$	7.21684	+	2.62672i	0.352566	+	0.128323i	0.512231	−	0.858848i	$-0.328819\pi$
$419$	7.21684	+	2.62672i	0.352566	+	0.128323i	−0.159665	+	0.987171i	$0.551041\pi$
$420$		0			0
$421$	6.15920	−	34.9305i	0.300181	−	1.70241i	−0.345183	−	0.938535i	$-0.612183\pi$
$421$	6.15920	−	34.9305i	0.300181	−	1.70241i	0.645364	−	0.763875i	$-0.276706\pi$
$422$	7.25209	+	4.18700i	0.353026	+	0.203820i
$423$		0			0
$424$	35.4458	+	61.3939i	1.72140	+	2.98155i
$425$	−1.66712	+	9.45470i	−0.0808671	+	0.458620i
$426$		0			0
$427$	6.56912	−	29.2537i	0.317902	−	1.41569i
$428$	62.2114	+	74.1407i	3.00710	+	3.58373i
$429$		0			0
$430$	−27.0427	−	4.76835i	−1.30411	−	0.229950i
$431$	12.6881	+	7.32548i	0.611164	+	0.352856i	0.773421	−	0.633893i	$-0.218544\pi$
$431$	12.6881	+	7.32548i	0.611164	+	0.352856i	−0.162257	+	0.986749i	$0.551877\pi$
$432$		0			0
$433$		−	20.7962i		−	0.999403i	−0.866198	−	0.499701i	$-0.833443\pi$
$433$		−	20.7962i		−	0.999403i	0.866198	−	0.499701i	$-0.166557\pi$
$434$	25.8066	+	16.5397i	1.23876	+	0.793932i
$435$		0			0
$436$	48.2734	+	17.5701i	2.31187	+	0.841454i
$437$	3.75672	+	1.36733i	0.179708	+	0.0654085i
$438$		0			0
$439$	−25.8246	−	4.55358i	−1.23254	−	0.217331i	−0.480826	−	0.876816i	$-0.659663\pi$
$439$	−25.8246	−	4.55358i	−1.23254	−	0.217331i	−0.751717	+	0.659486i	$0.770774\pi$
$440$	1.79451	−	3.10818i	0.0855498	−	0.148177i
$441$		0			0
$442$	11.0852	+	19.2002i	0.527272	+	0.913261i
$443$	0.0493954	+	0.135713i	0.00234684	+	0.00644790i	0.940861	−	0.338794i	$-0.110019\pi$
$443$	0.0493954	+	0.135713i	0.00234684	+	0.00644790i	−0.938514	+	0.345242i	$0.887797\pi$
$444$		0			0
$445$	−10.7775	+	9.04340i	−0.510903	+	0.428698i
$446$	−8.41073	−	47.6996i	−0.398260	−	2.25864i
$447$		0			0
$448$	−65.5188	+	33.8802i	−3.09547	+	1.60069i
$449$	−15.6193	+	9.01783i	−0.737122	+	0.425578i	−0.821022	−	0.570897i	$-0.806596\pi$
$449$	−15.6193	+	9.01783i	−0.737122	+	0.425578i	0.0838999	+	0.996474i	$0.473262\pi$
$450$		0			0
$451$	0.0396636	−	0.0228998i	0.00186769	−	0.00107831i
$452$	−2.91261	−	8.00233i	−0.136998	−	0.376398i
$453$		0			0
$454$	−19.4001	+	3.42076i	−0.910492	+	0.160544i
$455$	13.9760	−	4.36476i	0.655205	−	0.204623i
$456$		0			0
$457$	−14.9995	−	12.5861i	−0.701647	−	0.588752i	0.220595	−	0.975366i	$-0.429200\pi$
$457$	−14.9995	−	12.5861i	−0.701647	−	0.588752i	−0.922242	+	0.386614i	$0.873645\pi$
$458$	−20.6860	+	35.8291i	−0.966591	+	1.67418i
$459$		0			0
$460$	16.7609	−	9.67690i	0.781480	−	0.451188i
$461$	−12.6847	+	4.61684i	−0.590784	+	0.215028i	−0.620074	−	0.784543i	$-0.712898\pi$
$461$	−12.6847	+	4.61684i	−0.590784	+	0.215028i	0.0292902	+	0.999571i	$0.490675\pi$
$462$		0			0
$463$	−6.46334	+	5.42339i	−0.300377	+	0.252046i	−0.780501	−	0.625154i	$-0.785036\pi$
$463$	−6.46334	+	5.42339i	−0.300377	+	0.252046i	0.480124	+	0.877200i	$0.340592\pi$
$464$	57.9856	+	69.1045i	2.69191	+	3.20810i
$465$		0			0
$466$	−31.7096	+	11.5413i	−1.46892	+	0.534642i
$467$	−13.9457			−0.645328			−0.322664	−	0.946514i	$-0.604578\pi$
$467$	−13.9457			−0.645328			−0.322664	+	0.946514i	$0.604578\pi$
$468$		0			0
$469$	−2.87829	−	3.77232i	−0.132907	−	0.174189i
$470$	−48.6945	−	8.58616i	−2.24611	−	0.396050i
$471$		0			0
$472$	38.5877	+	45.9870i	1.77614	+	2.11672i
$473$	0.337938	+	0.402739i	0.0155384	+	0.0185180i
$474$		0			0
$475$	7.19043	+	1.26787i	0.329920	+	0.0581737i
$476$	−56.8720	+	7.32965i	−2.60673	+	0.335954i
$477$		0			0
$478$	21.6905			0.992102
$479$	20.5798	−	7.49045i	0.940317	−	0.342247i	0.174026	−	0.984741i	$-0.444322\pi$
$479$	20.5798	−	7.49045i	0.940317	−	0.342247i	0.766291	+	0.642494i	$0.222100\pi$
$480$		0			0
$481$	12.2673	+	14.6196i	0.559343	+	0.666599i
$482$	−1.14392	+	0.959862i	−0.0521041	+	0.0437205i
$483$		0			0
$484$	55.8826	−	20.3396i	2.54012	−	0.924527i
$485$	17.3630	−	10.0245i	0.788411	−	0.455189i
$486$		0			0
$487$	4.85645	−	8.41162i	0.220067	−	0.381167i	−0.734761	−	0.678326i	$-0.762706\pi$
$487$	4.85645	−	8.41162i	0.220067	−	0.381167i	0.954828	+	0.297159i	$0.0960392\pi$
$488$	−80.7604	−	67.7660i	−3.65585	−	3.06762i
$489$		0			0
$490$	−4.80097	+	51.6310i	−0.216886	+	2.33245i
$491$	−26.7581	+	4.71818i	−1.20758	+	0.212928i	−0.740971	−	0.671537i	$-0.765634\pi$
$491$	−26.7581	+	4.71818i	−1.20758	+	0.212928i	−0.466606	+	0.884465i	$0.654523\pi$
$492$		0			0
$493$	8.51319	+	23.3898i	0.383415	+	1.05342i
$494$	14.6020	−	8.43049i	0.656976	−	0.379306i
$495$		0			0
$496$	53.4314	−	30.8486i	2.39914	−	1.38514i
$497$	−8.46921	−	16.3781i	−0.379896	−	0.734658i
$498$		0			0
$499$	−5.63790	−	31.9741i	−0.252387	−	1.43136i	−0.802692	−	0.596394i	$-0.796600\pi$
$499$	−5.63790	−	31.9741i	−0.252387	−	1.43136i	0.550305	−	0.834964i	$-0.314512\pi$
$500$	−29.3528	+	24.6299i	−1.31270	+	1.10148i
$501$		0			0
$502$	−16.5163	−	45.3781i	−0.737158	−	2.02532i
$503$	−12.9131	−	22.3661i	−0.575764	−	0.997253i	−0.995958	−	0.0898189i	$-0.971371\pi$
$503$	−12.9131	−	22.3661i	−0.575764	−	0.997253i	0.420194	−	0.907434i	$-0.361962\pi$
$504$		0			0
$505$	9.17002	−	15.8829i	0.408060	−	0.706781i
$506$	−0.499663	−	0.0881040i	−0.0222127	−	0.00391670i
$507$		0			0
$508$	−91.9923	−	33.4824i	−4.08150	−	1.48554i
$509$	−27.4413	−	9.98782i	−1.21631	−	0.442702i	−0.347425	−	0.937708i	$-0.612944\pi$
$509$	−27.4413	−	9.98782i	−1.21631	−	0.442702i	−0.868890	+	0.495006i	$0.835166\pi$
$510$		0			0
$511$	5.15401	+	9.96702i	0.228000	+	0.440915i
$512$			33.0926i			1.46250i
$513$		0			0
$514$	−65.9842	−	38.0960i	−2.91044	−	1.68034i
$515$	−30.7451	−	5.42119i	−1.35479	−	0.238886i
$516$		0			0
$517$	0.608510	+	0.725194i	0.0267623	+	0.0318940i
$518$	−64.5152	+	20.1483i	−2.83463	+	0.885267i
$519$		0			0
$520$	8.94012	−	50.7019i	0.392050	−	2.22343i
$521$	1.43518	+	2.48580i	0.0628763	+	0.108905i	0.895750	−	0.444558i	$-0.146639\pi$
$521$	1.43518	+	2.48580i	0.0628763	+	0.108905i	−0.832874	+	0.553463i	$0.813306\pi$
$522$		0			0
$523$	6.72356	+	3.88185i	0.294001	+	0.169742i	0.639745	−	0.768587i	$-0.279040\pi$
$523$	6.72356	+	3.88185i	0.294001	+	0.169742i	−0.345744	+	0.938329i	$0.612373\pi$
$524$	−5.15765	+	29.2505i	−0.225313	+	1.27781i
$525$		0			0
$526$	28.5509	+	10.3917i	1.24488	+	0.453098i
$527$	16.7651	−	2.95613i	0.730298	−	0.128771i
$528$		0			0
$529$	16.2971	+	13.6749i	0.708568	+	0.594559i
$530$	28.2238	−	48.8851i	1.22596	−	2.12343i
$531$		0			0
$532$	5.57430	+	43.2520i	0.241677	+	1.87521i
$533$	0.422306	−	0.503284i	0.0182921	−	0.0217997i
$534$		0			0
$535$	16.6247	−	45.6759i	0.718748	−	1.97474i
$536$	−16.4312	+	2.89726i	−0.709718	+	0.125142i
$537$		0			0
$538$	−4.45020	−	12.2268i	−0.191862	−	0.527136i
$539$	0.705817	−	0.698161i	0.0304017	−	0.0300719i
$540$		0			0
$541$	0.0411054	+	0.0711966i	0.00176726	+	0.00306098i	0.866908	−	0.498469i	$-0.166104\pi$
$541$	0.0411054	+	0.0711966i	0.00176726	+	0.00306098i	−0.865140	+	0.501530i	$0.832771\pi$
$542$	10.1165	−	57.3738i	0.434543	−	2.46441i
$543$		0			0
$544$	−28.5881	+	78.5453i	−1.22571	+	3.36760i
$545$	−4.48013	−	25.4081i	−0.191908	−	1.08836i
$546$		0			0
$547$	0.989409	+	0.830213i	0.0423041	+	0.0354973i	0.663695	−	0.748004i	$-0.268987\pi$
$547$	0.989409	+	0.830213i	0.0423041	+	0.0354973i	−0.621390	+	0.783501i	$0.713432\pi$
$548$		−	22.6751i		−	0.968631i
$549$		0			0
$550$	−0.926629			−0.0395116
$551$	17.7883	−	6.47440i	0.757806	−	0.275819i
$552$		0			0
$553$	26.8523	−	29.1442i	1.14187	−	1.23934i
$554$	11.5350	−	31.6921i	0.490074	−	1.34647i
$555$		0			0
$556$	−39.7829	+	47.4114i	−1.68717	+	2.01069i
$557$			40.7044i			1.72470i	0.506313	+	0.862350i	$0.331008\pi$
$557$			40.7044i			1.72470i	−0.506313	+	0.862350i	$0.668992\pi$
$558$		0			0
$559$	6.53128	+	3.77084i	0.276244	+	0.159489i
$560$	87.8738	+	56.3192i	3.71335	+	2.37992i
$561$		0			0
$562$	−32.5760	+	27.3345i	−1.37413	+	1.15304i
$563$	−6.08532	−	34.5115i	−0.256465	−	1.45449i	−0.792283	−	0.610154i	$-0.791108\pi$
$563$	−6.08532	−	34.5115i	−0.256465	−	1.45449i	0.535817	−	0.844334i	$-0.320004\pi$
$564$		0			0
$565$	−2.74914	+	3.27630i	−0.115657	+	0.137835i
$566$	62.2760			2.61765
$567$		0			0
$568$	−64.8337			−2.72036
$569$	−3.89713	+	4.64442i	−0.163376	+	0.194704i	−0.841521	−	0.540224i	$-0.818340\pi$
$569$	−3.89713	+	4.64442i	−0.163376	+	0.194704i	0.678145	+	0.734928i	$0.262784\pi$
$570$		0			0
$571$	−1.34728	−	7.64081i	−0.0563819	−	0.319758i	0.943552	−	0.331223i	$-0.107461\pi$
$571$	−1.34728	−	7.64081i	−0.0563819	−	0.319758i	−0.999934	+	0.0114657i	$0.996350\pi$
$572$	−1.19716	+	1.00454i	−0.0500557	+	0.0420017i
$573$		0			0
$574$	1.06874	+	2.06676i	0.0446082	+	0.0862650i
$575$	−2.72945	−	1.57585i	−0.113826	−	0.0657173i
$576$		0			0
$577$			28.1574i			1.17221i	0.810236	+	0.586104i	$0.199339\pi$
$577$			28.1574i			1.17221i	−0.810236	+	0.586104i	$0.800661\pi$
$578$	1.72800	−	2.05934i	0.0718751	−	0.0856575i
$579$		0			0
$580$	31.3431	−	86.1146i	1.30145	−	3.57571i
$581$	0.811322	+	2.59786i	0.0336593	+	0.107778i
$582$		0			0
$583$	−1.01556	+	0.369632i	−0.0420600	+	0.0153086i
$584$	39.4551			1.63266
$585$		0			0
$586$		−	89.7913i		−	3.70924i
$587$	14.0329	+	11.7750i	0.579200	+	0.486006i	0.884684	−	0.466191i	$-0.154374\pi$
$587$	14.0329	+	11.7750i	0.579200	+	0.486006i	−0.305484	+	0.952197i	$0.598818\pi$
$588$		0			0
$589$	−2.24818	−	12.7501i	−0.0926347	−	0.525357i
$590$	16.3487	−	44.9178i	0.673067	−	1.84924i
$591$		0			0
$592$	−23.6237	+	133.977i	−0.970928	+	5.50641i
$593$	−10.2123	−	17.6882i	−0.419367	−	0.726366i	0.576509	−	0.817091i	$-0.304415\pi$
$593$	−10.2123	−	17.6882i	−0.419367	−	0.726366i	−0.995876	+	0.0907255i	$0.971081\pi$
$594$		0			0
$595$	17.4693	+	22.8954i	0.716170	+	0.938619i
$596$	42.9697	+	118.058i	1.76011	+	4.83586i
$597$		0			0
$598$	−7.16761	+	1.26384i	−0.293105	+	0.0516824i
$599$	10.4791	−	28.7910i	0.428163	−	1.17637i	−0.518763	−	0.854918i	$-0.673607\pi$
$599$	10.4791	−	28.7910i	0.428163	−	1.17637i	0.946926	−	0.321451i	$-0.104170\pi$
$600$		0			0
$601$	−2.11771	+	2.52379i	−0.0863832	+	0.102947i	−0.807505	−	0.589861i	$-0.799182\pi$
$601$	−2.11771	+	2.52379i	−0.0863832	+	0.102947i	0.721122	+	0.692809i	$0.243627\pi$
$602$	−21.2338	+	16.2015i	−0.865426	+	0.660324i
$603$		0			0
$604$	0.623640	−	1.08018i	0.0253756	−	0.0439518i
$605$	−22.8793	−	19.1980i	−0.930177	−	0.780511i
$606$		0			0
$607$	−43.0659	+	7.59367i	−1.74799	+	0.308218i	−0.954021	−	0.299741i	$-0.903100\pi$
$607$	−43.0659	+	7.59367i	−1.74799	+	0.308218i	−0.793969	+	0.607959i	$0.791989\pi$
$608$	59.7348	+	21.7417i	2.42256	+	0.881741i
$609$		0			0
$610$	−14.5769	+	82.6699i	−0.590203	+	3.34721i
$611$	11.7606	+	6.78997i	0.475782	+	0.274693i
$612$		0			0
$613$	10.4406	+	18.0837i	0.421694	+	0.730395i	0.996105	−	0.0881718i	$-0.0281025\pi$
$613$	10.4406	+	18.0837i	0.421694	+	0.730395i	−0.574412	+	0.818567i	$0.694769\pi$
$614$	−7.40212	+	41.9795i	−0.298725	+	1.69415i
$615$		0			0
$616$	−1.04064	−	3.33215i	−0.0419286	−	0.134256i
$617$	−13.6109	−	16.2208i	−0.547954	−	0.653026i	0.418997	−	0.907988i	$-0.362382\pi$
$617$	−13.6109	−	16.2208i	−0.547954	−	0.653026i	−0.966951	+	0.254961i	$0.917937\pi$
$618$		0			0
$619$	3.76408	+	0.663709i	0.151291	+	0.0266767i	0.248781	−	0.968560i	$-0.419970\pi$
$619$	3.76408	+	0.663709i	0.151291	+	0.0266767i	−0.0974896	+	0.995237i	$0.531081\pi$
$620$	−54.2794	−	31.3382i	−2.17991	−	1.25857i
$621$		0			0
$622$			72.4539i			2.90514i
$623$	−0.634173	+	13.6696i	−0.0254076	+	0.547660i
$624$		0			0
$625$	29.3558	+	10.6847i	1.17423	+	0.427386i
$626$	−79.8459	−	29.0615i	−3.19128	−	1.16153i
$627$		0			0
$628$	52.4830	+	9.25417i	2.09430	+	0.369282i
$629$	−18.7688	+	32.5085i	−0.748360	+	1.29620i
$630$		0			0
$631$	−20.3234	−	35.2011i	−0.809061	−	1.40133i	−0.913515	−	0.406805i	$-0.866643\pi$
$631$	−20.3234	−	35.2011i	−0.809061	−	1.40133i	0.104454	−	0.994530i	$-0.466690\pi$
$632$	−47.6586	−	130.941i	−1.89576	−	5.20856i
$633$		0			0
$634$	25.8232	−	21.6682i	1.02557	−	0.860554i
$635$	8.53758	+	48.4190i	0.338803	+	1.92145i
$636$		0			0
$637$	6.08892	−	12.8740i	0.241252	−	0.510086i
$638$	−2.08056	+	1.20121i	−0.0823703	+	0.0475565i
$639$		0			0
$640$	80.4357	−	46.4396i	3.17950	−	1.83569i
$641$	3.63686	+	9.99218i	0.143647	+	0.394667i	0.990563	−	0.137060i	$-0.0437653\pi$
$641$	3.63686	+	9.99218i	0.143647	+	0.394667i	−0.846916	+	0.531727i	$0.821543\pi$
$642$		0			0
$643$	41.6989	−	7.35263i	1.64444	−	0.289960i	0.726646	−	0.687012i	$-0.241078\pi$
$643$	41.6989	−	7.35263i	1.64444	−	0.289960i	0.917796	+	0.397052i	$0.129967\pi$
$644$	4.12446	−	18.3671i	0.162527	−	0.723766i
$645$		0			0
$646$	25.4050	+	21.3173i	0.999547	+	0.838720i
$647$	−20.0622	+	34.7487i	−0.788726	+	1.36611i	0.138021	+	0.990429i	$0.455926\pi$
$647$	−20.0622	+	34.7487i	−0.788726	+	1.36611i	−0.926748	+	0.375685i	$0.877408\pi$
$648$		0			0
$649$	−0.792565	+	0.457588i	−0.0311109	+	0.0179619i
$650$	−12.4908	+	4.54627i	−0.489928	+	0.178319i
$651$		0			0
$652$	−2.26227	+	1.89827i	−0.0885974	+	0.0743420i
$653$	−14.3339	−	17.0825i	−0.560929	−	0.668489i	0.408814	−	0.912618i	$-0.365943\pi$
$653$	−14.3339	−	17.0825i	−0.560929	−	0.668489i	−0.969743	+	0.244129i	$0.921498\pi$
$654$		0			0
$655$	14.0174	−	5.10191i	0.547704	−	0.199348i
$656$	4.68333			0.182853
$657$		0			0
$658$	−38.2348	+	29.1733i	−1.49055	+	1.13729i
$659$	14.8769	+	2.62320i	0.579522	+	0.102185i	0.455723	−	0.890122i	$-0.349381\pi$
$659$	14.8769	+	2.62320i	0.579522	+	0.102185i	0.123800	+	0.992307i	$0.460492\pi$
$660$		0			0
$661$	−12.8484	−	15.3122i	−0.499746	−	0.595575i	0.455922	−	0.890020i	$-0.349310\pi$
$661$	−12.8484	−	15.3122i	−0.499746	−	0.595575i	−0.955668	+	0.294445i	$0.904865\pi$
$662$	−33.2813	−	39.6632i	−1.29352	−	1.54155i
$663$		0			0
$664$	9.42449	+	1.66179i	0.365741	+	0.0644900i
$665$	17.4122	−	13.2856i	0.675218	−	0.515194i
$666$		0			0
$667$	−8.17125			−0.316392
$668$	65.1400	−	23.7090i	2.52034	−	0.917329i
$669$		0			0
$670$	8.53956	+	10.1771i	0.329912	+	0.393174i
$671$	1.23118	−	1.03308i	0.0475292	−	0.0398818i
$672$		0			0
$673$	38.6509	−	14.0678i	1.48988	−	0.542273i	0.536463	−	0.843924i	$-0.319760\pi$
$673$	38.6509	−	14.0678i	1.48988	−	0.542273i	0.953418	+	0.301651i	$0.0975377\pi$
$674$	−57.2443	+	33.0500i	−2.20497	+	1.27304i
$675$		0			0
$676$	23.9962	−	41.5626i	0.922930	−	1.59856i
$677$	15.9513	+	13.3847i	0.613059	+	0.514418i	0.895613	−	0.444834i	$-0.146737\pi$
$677$	15.9513	+	13.3847i	0.613059	+	0.514418i	−0.282554	+	0.959251i	$0.591182\pi$
$678$		0			0
$679$	4.27262	−	19.0269i	0.163968	−	0.730185i
$680$	99.7258	−	17.5844i	3.82431	−	0.674329i
$681$		0			0
$682$	0.561972	+	1.54401i	0.0215190	+	0.0591231i
$683$	22.6357	−	13.0687i	0.866129	−	0.500060i	6.93731e−5	−	1.00000i	$-0.499978\pi$
$683$	22.6357	−	13.0687i	0.866129	−	0.500060i	0.866060	+	0.499940i	$0.166645\pi$
$684$		0			0
$685$	−9.86230	+	5.69400i	−0.376819	+	0.217557i
$686$	33.7685	+	37.4625i	1.28929	+	1.43032i
$687$		0			0
$688$	9.33540	+	52.9437i	0.355909	+	2.01846i
$689$	−11.8760	+	9.96513i	−0.452439	+	0.379641i
$690$		0			0
$691$	−10.6128	−	29.1584i	−0.403730	−	1.10924i	−0.960429	−	0.278525i	$-0.910155\pi$
$691$	−10.6128	−	29.1584i	−0.403730	−	1.10924i	0.556699	−	0.830714i	$-0.312068\pi$
$692$	9.10745	+	15.7746i	0.346213	+	0.599659i
$693$		0			0
$694$	41.5058	−	71.8901i	1.57554	−	2.72891i
$695$	30.6111	+	5.39757i	1.16115	+	0.204741i
$696$		0			0
$697$	1.21431	+	0.441972i	0.0459951	+	0.0167409i
$698$	23.0143	+	8.37652i	0.871104	+	0.317056i
$699$		0			0
$700$	1.59327	−	34.3429i	0.0602200	−	1.29804i
$701$		−	35.8873i		−	1.35545i	−0.735317	−	0.677723i	$-0.762967\pi$
$701$		−	35.8873i		−	1.35545i	0.735317	−	0.677723i	$-0.237033\pi$
$702$		0			0
$703$	24.7232	+	14.2739i	0.932451	+	0.538351i
$704$	−3.89384	−	0.686590i	−0.146755	−	0.0258768i
$705$		0			0
$706$	−31.4134	−	37.4370i	−1.18226	−	1.40896i
$707$	−5.31772	−	17.0274i	−0.199994	−	0.640381i
$708$		0			0
$709$	−8.77896	+	49.7879i	−0.329701	+	1.86983i	0.144640	+	0.989484i	$0.453798\pi$
$709$	−8.77896	+	49.7879i	−0.329701	+	1.86983i	−0.474341	+	0.880341i	$0.657314\pi$
$710$	25.8120	+	44.7078i	0.968709	+	1.67785i
$711$		0			0
$712$	41.6709	+	24.0587i	1.56168	+	0.901639i
$713$	−0.970447	+	5.50368i	−0.0363435	+	0.206114i
$714$		0			0
$715$	0.737535	+	0.268441i	0.0275822	+	0.0100391i
$716$	−7.11458	+	1.25449i	−0.265884	+	0.0468826i
$717$		0			0
$718$	56.3429	+	47.2773i	2.10270	+	1.76437i
$719$	−20.9466	+	36.2805i	−0.781175	+	1.35303i	0.150083	+	0.988673i	$0.452046\pi$
$719$	−20.9466	+	36.2805i	−0.781175	+	1.35303i	−0.931258	+	0.364361i	$0.881287\pi$
$720$		0			0
$721$	−24.1409	+	18.4196i	−0.899055	+	0.685983i
$722$	−17.0470	+	20.3158i	−0.634424	+	0.756077i
$723$		0			0
$724$	5.66149	−	15.5548i	0.210408	−	0.578091i
$725$	−14.6967	+	2.59143i	−0.545822	+	0.0962431i
$726$		0			0
$727$	−4.61680	−	12.6846i	−0.171228	−	0.470444i	0.824162	−	0.566354i	$-0.191646\pi$
$727$	−4.61680	−	12.6846i	−0.171228	−	0.470444i	−0.995390	+	0.0959094i	$0.969424\pi$
$728$	−30.3760	−	39.8110i	−1.12581	−	1.47549i
$729$		0			0
$730$	−15.7081	−	27.2073i	−0.581384	−	1.00699i
$731$	−2.57585	+	14.6084i	−0.0952713	+	0.540311i
$732$		0			0
$733$	−9.35508	+	25.7029i	−0.345538	+	0.949357i	0.638220	+	0.769854i	$0.279671\pi$
$733$	−9.35508	+	25.7029i	−0.345538	+	0.949357i	−0.983757	+	0.179503i	$0.942551\pi$
$734$	7.59979	+	43.1006i	0.280513	+	1.59087i
$735$		0			0
$736$	−21.0201	−	17.6380i	−0.774813	−	0.650145i
$737$		−	0.254355i		−	0.00936929i
$738$		0			0
$739$	17.0676			0.627840			0.313920	−	0.949449i	$-0.398358\pi$
$739$	17.0676			0.627840			0.313920	+	0.949449i	$0.398358\pi$
$740$	129.868	−	47.2681i	4.77404	−	1.73761i
$741$		0			0
$742$	−16.3671	−	52.4076i	−0.600855	−	1.92394i
$743$	−2.70067	+	7.42004i	−0.0990781	+	0.272215i	−0.979322	−	0.202306i	$-0.935156\pi$
$743$	−2.70067	+	7.42004i	−0.0990781	+	0.272215i	0.880244	+	0.474521i	$0.157379\pi$
$744$		0			0
$745$	40.5581	−	48.3352i	1.48593	−	1.77087i
$746$		−	53.3565i		−	1.95352i
$747$		0			0
$748$	−2.66202	−	1.53692i	−0.0973331	−	0.0561953i
$749$	−21.7161	−	41.9955i	−0.793490	−	1.53448i
$750$		0			0
$751$	−4.90779	+	4.11813i	−0.179088	+	0.150273i	−0.727925	−	0.685657i	$-0.759515\pi$
$751$	−4.90779	+	4.11813i	−0.179088	+	0.150273i	0.548837	+	0.835929i	$0.315071\pi$
$752$	16.8098	+	95.3333i	0.612991	+	3.47645i
$753$		0			0
$754$	−22.1521	+	26.3999i	−0.806732	+	0.961426i
$755$	−0.626416			−0.0227976
$756$		0			0
$757$	−31.0889			−1.12994			−0.564972	−	0.825110i	$-0.691113\pi$
$757$	−31.0889			−1.12994			−0.564972	+	0.825110i	$0.691113\pi$
$758$	−7.01248	+	8.35715i	−0.254705	+	0.303545i
$759$		0			0
$760$	−13.3731	−	75.8429i	−0.485095	−	2.75111i
$761$	−7.52660	+	6.31557i	−0.272839	+	0.228939i	−0.768932	−	0.639330i	$-0.779212\pi$
$761$	−7.52660	+	6.31557i	−0.272839	+	0.228939i	0.496093	+	0.868269i	$0.334767\pi$
$762$		0			0
$763$	−21.1276	−	13.5409i	−0.764871	−	0.490214i
$764$	−70.9773	−	40.9788i	−2.56787	−	1.48256i
$765$		0			0
$766$			57.6900i			2.08442i
$767$	−8.43858	+	10.0567i	−0.304700	+	0.363127i
$768$		0			0
$769$	−7.53988	+	20.7157i	−0.271895	+	0.747026i	0.726323	+	0.687354i	$0.241228\pi$
$769$	−7.53988	+	20.7157i	−0.271895	+	0.747026i	−0.998218	+	0.0596720i	$0.980995\pi$
$770$	−1.88346	+	2.04422i	−0.0678752	+	0.0736685i
$771$		0			0
$772$	24.3104	−	8.84826i	0.874951	−	0.318456i
$773$	9.25180			0.332764			0.166382	−	0.986061i	$-0.446792\pi$
$773$	9.25180			0.332764			0.166382	+	0.986061i	$0.446792\pi$
$774$		0			0
$775$			10.2066i			0.366632i
$776$	−52.5274	−	44.0757i	−1.88562	−	1.58222i
$777$		0			0
$778$	−8.45840	−	47.9700i	−0.303248	−	1.71981i
$779$	0.336125	−	0.923497i	0.0120429	−	0.0330877i
$780$		0			0
$781$	0.171631	−	0.973365i	0.00614143	−	0.0348298i
$782$	−7.15774	−	12.3976i	−0.255960	−	0.443336i
$783$		0			0
$784$	98.2009	−	25.7397i	3.50718	−	0.919276i
$785$	−9.15415	−	25.1508i	−0.326726	−	0.897671i
$786$		0			0
$787$	1.35789	−	0.239433i	0.0484036	−	0.00853486i	−0.149394	−	0.988778i	$-0.547732\pi$
$787$	1.35789	−	0.239433i	0.0484036	−	0.00853486i	0.197798	+	0.980243i	$0.436621\pi$
$788$	−15.0284	+	41.2902i	−0.535364	+	1.47090i
$789$		0			0
$790$	−71.3196	+	84.9954i	−2.53744	+	3.02400i
$791$	0.531734	+	4.12582i	0.0189063	+	0.146697i
$792$		0			0
$793$	11.5275	−	19.9662i	0.409354	−	0.709022i
$794$	−33.6496	−	28.2353i	−1.19418	−	1.00203i
$795$		0			0
$796$	26.8908	−	4.74158i	0.953119	−	0.168061i
$797$	13.4666	+	4.90146i	0.477013	+	0.173619i	0.569327	−	0.822111i	$-0.307204\pi$
$797$	13.4666	+	4.90146i	0.477013	+	0.173619i	−0.0923136	+	0.995730i	$0.529426\pi$
$798$		0			0
$799$	−4.63822	+	26.3047i	−0.164088	+	0.930592i
$800$	−43.4003	−	25.0572i	−1.53443	−	0.885905i
$801$		0			0
$802$	4.05353	+	7.02093i	0.143135	+	0.247918i
$803$	−0.104447	+	0.592350i	−0.00368586	+	0.0209036i
$804$		0			0
$805$	−9.02430	+	2.81832i	−0.318065	+	0.0993328i
$806$	15.1505	+	18.0557i	0.533655	+	0.635986i
$807$		0			0
$808$	−61.7718	−	10.8920i	−2.17312	−	0.383180i
$809$	25.1012	+	14.4922i	0.882512	+	0.509519i	0.871486	−	0.490420i	$-0.163157\pi$
$809$	25.1012	+	14.4922i	0.882512	+	0.509519i	0.0110264	+	0.999939i	$0.496490\pi$
$810$		0			0
$811$		−	16.8829i		−	0.592840i	−0.955058	−	0.296420i	$-0.904207\pi$
$811$		−	16.8829i		−	0.592840i	0.955058	−	0.296420i	$-0.0957928\pi$
$812$	−40.9422	−	79.1756i	−1.43679	−	2.77852i
$813$		0			0
$814$	−3.40456	−	1.23916i	−0.119330	−	0.0434325i
$815$	1.39372	+	0.507272i	0.0488199	+	0.0177690i
$816$		0			0
$817$	11.1099	+	1.95897i	0.388685	+	0.0685357i
$818$	31.4035	−	54.3924i	1.09800	−	1.90179i
$819$		0			0
$820$	−2.37883	−	4.12025i	−0.0830722	−	0.143885i
$821$	−1.38544	−	3.80647i	−0.0483522	−	0.132847i	0.913166	−	0.407588i	$-0.133630\pi$
$821$	−1.38544	−	3.80647i	−0.0483522	−	0.132847i	−0.961518	+	0.274741i	$0.911408\pi$
$822$		0			0
$823$	−9.48811	+	7.96147i	−0.330735	+	0.277519i	−0.792999	−	0.609223i	$-0.791482\pi$
$823$	−9.48811	+	7.96147i	−0.330735	+	0.277519i	0.462264	+	0.886742i	$0.347037\pi$
$824$	18.5410	+	105.151i	0.645906	+	3.66311i
$825$		0			0
$826$	−21.3557	−	41.2984i	−0.743059	−	1.43695i
$827$	5.99133	−	3.45910i	0.208339	−	0.120285i	−0.392200	−	0.919880i	$-0.628286\pi$
$827$	5.99133	−	3.45910i	0.208339	−	0.120285i	0.600539	+	0.799595i	$0.294953\pi$
$828$		0			0
$829$	−46.1745	+	26.6589i	−1.60371	+	0.925901i	−0.612972	+	0.790105i	$0.710026\pi$
$829$	−46.1745	+	26.6589i	−1.60371	+	0.925901i	−0.990737	+	0.135796i	$0.956641\pi$
$830$	−2.60621	−	7.16051i	−0.0904629	−	0.248545i
$831$		0			0
$832$	−55.8568	+	9.84906i	−1.93649	+	0.341455i
$833$	27.8909	+	2.59347i	0.966363	+	0.0898585i
$834$		0			0
$835$	−26.6695	−	22.3784i	−0.922936	−	0.774435i
$836$	−1.16885	+	2.02450i	−0.0404254	+	0.0700189i
$837$		0			0
$838$	−18.1127	+	10.4573i	−0.625691	+	0.361243i
$839$	−40.8924	+	14.8836i	−1.41176	+	0.513840i	−0.931647	−	0.363365i	$-0.881628\pi$
$839$	−40.8924	+	14.8836i	−1.41176	+	0.513840i	−0.480116	+	0.877205i	$0.659406\pi$
$840$		0			0
$841$	−7.42395	+	6.22943i	−0.255998	+	0.214808i
$842$	62.0885	+	73.9942i	2.13971	+	2.55001i
$843$		0			0
$844$	−15.6502	+	5.69622i	−0.538703	+	0.196072i
$845$	−24.1030			−0.829168
$846$		0			0
$847$	−28.8118	+	3.71325i	−0.989983	+	0.127589i
$848$	−108.833	−	19.1902i	−3.73735	−	0.658996i
$849$		0			0
$850$	−16.8056	−	20.0281i	−0.576427	−	0.686959i
$851$	−7.92102	−	9.43990i	−0.271529	−	0.323596i
$852$		0			0
$853$	52.2783	+	9.21807i	1.78997	+	0.315621i	0.967441	−	0.253097i	$-0.0814492\pi$
$853$	52.2783	+	9.21807i	1.78997	+	0.315621i	0.822533	+	0.568718i	$0.192560\pi$
$854$	49.5283	+	64.9122i	1.69482	+	2.22125i
$855$		0			0
$856$	−166.242			−5.68203
$857$	−37.6318	+	13.6969i	−1.28548	+	0.467876i	−0.892241	−	0.451560i	$-0.850868\pi$
$857$	−37.6318	+	13.6969i	−1.28548	+	0.467876i	−0.393239	+	0.919436i	$0.628645\pi$
$858$		0			0
$859$	−6.50751	−	7.75535i	−0.222033	−	0.264609i	0.643516	−	0.765433i	$-0.277475\pi$
$859$	−6.50751	−	7.75535i	−0.222033	−	0.264609i	−0.865549	+	0.500824i	$0.833031\pi$
$860$	41.8364	−	35.1049i	1.42661	−	1.19707i
$861$		0			0
$862$	−37.4923	+	13.6461i	−1.27699	+	0.464787i
$863$	26.6005	−	15.3578i	0.905490	−	0.522785i	0.0265129	−	0.999648i	$-0.491560\pi$
$863$	26.6005	−	15.3578i	0.905490	−	0.522785i	0.878977	+	0.476863i	$0.158226\pi$
$864$		0			0
$865$	4.57400	−	7.92240i	0.155521	−	0.269370i
$866$	43.3839	+	36.4034i	1.47424	+	1.23704i
$867$		0			0
$868$	−58.1906	+	18.1731i	−1.97512	+	0.616836i
$869$	2.09202	−	0.368879i	0.0709668	−	0.0125134i
$870$		0			0
$871$	−1.24793	−	3.42865i	−0.0422844	−	0.116175i
$872$	−76.4170	+	44.1194i	−2.58781	+	1.49407i
$873$		0			0
$874$	−9.42853	+	5.44356i	−0.318925	+	0.184131i
$875$	16.6263	−	8.59756i	0.562071	−	0.290650i
$876$		0			0
$877$	−4.14819	−	23.5256i	−0.140075	−	0.794402i	−0.971191	−	0.238303i	$-0.923409\pi$
$877$	−4.14819	−	23.5256i	−0.140075	−	0.794402i	0.831116	−	0.556099i	$-0.187702\pi$
$878$	54.7050	−	45.9029i	1.84620	−	1.54915i
$879$		0			0
$880$	1.91356	+	5.25748i	0.0645062	+	0.177229i
$881$	1.24040	+	2.14844i	0.0417902	+	0.0723828i	0.886164	−	0.463372i	$-0.153361\pi$
$881$	1.24040	+	2.14844i	0.0417902	+	0.0723828i	−0.844374	+	0.535755i	$0.820027\pi$
$882$		0			0
$883$	−17.2245	+	29.8337i	−0.579650	+	1.00398i	0.415870	+	0.909424i	$0.363477\pi$
$883$	−17.2245	+	29.8337i	−0.579650	+	1.00398i	−0.995519	+	0.0945585i	$0.969856\pi$
$884$	−43.4240	−	7.65682i	−1.46051	−	0.257527i
$885$		0			0
$886$	−0.369582	−	0.134517i	−0.0124163	−	0.00451918i
$887$	15.3931	+	5.60263i	0.516850	+	0.188118i	0.587257	−	0.809400i	$-0.300208\pi$
$887$	15.3931	+	5.60263i	0.516850	+	0.188118i	−0.0704076	+	0.997518i	$0.522430\pi$
$888$		0			0
$889$	40.2619	+	25.8043i	1.35034	+	0.865447i
$890$		−	38.3137i		−	1.28428i
$891$		0			0
$892$	83.4251	+	48.1655i	2.79328	+	1.61270i
$893$	20.0051	+	3.52743i	0.669444	+	0.118041i
$894$		0			0
$895$	2.33219	+	2.77940i	0.0779566	+	0.0929050i
$896$	19.7934	−	88.1440i	0.661250	−	2.94469i
$897$		0			0
$898$	8.52888	−	48.3697i	0.284613	−	1.61412i
$899$	13.2311	+	22.9169i	0.441282	+	0.764323i
$900$		0			0
$901$	−26.4076	−	15.2464i	−0.879765	−	0.507933i
$902$	−0.0216582	+	0.122830i	−0.000721139	+	0.00408978i
$903$		0			0
$904$	13.7453	+	5.00288i	0.457162	+	0.166393i
$905$	−8.18709	+	1.44361i	−0.272148	+	0.0479871i
$906$		0			0
$907$	−25.9558	−	21.7795i	−0.861847	−	0.723176i	0.100518	−	0.994935i	$-0.467950\pi$
$907$	−25.9558	−	21.7795i	−0.861847	−	0.723176i	−0.962365	+	0.271760i	$0.912394\pi$
$908$	19.5896	−	33.9302i	0.650103	−	1.12601i
$909$		0			0
$910$	−15.3592	+	36.7964i	−0.509153	+	1.21979i
$911$	4.91968	−	5.86305i	0.162996	−	0.194251i	−0.678364	−	0.734726i	$-0.737311\pi$
$911$	4.91968	−	5.86305i	0.162996	−	0.194251i	0.841360	+	0.540474i	$0.181755\pi$
$912$		0			0
$913$	−0.0498978	+	0.137093i	−0.00165138	+	0.00453712i
$914$	52.5127	−	9.25940i	1.73697	−	0.306274i
$915$		0			0
$916$	−28.1423	−	77.3204i	−0.929848	−	2.55474i
$917$	5.58889	−	13.3894i	0.184561	−	0.442157i
$918$		0			0
$919$	9.69700	+	16.7957i	0.319874	+	0.554039i	0.980462	−	0.196711i	$-0.0630260\pi$
$919$	9.69700	+	16.7957i	0.319874	+	0.554039i	−0.660587	+	0.750749i	$0.729693\pi$
$920$	−5.77263	+	32.7382i	−0.190318	+	1.07935i
$921$		0			0
$922$	12.5729	−	34.5437i	0.414066	−	1.13764i
$923$	−2.46202	−	13.9628i	−0.0810385	−	0.459592i
$924$		0			0
$925$	−17.2404	−	14.4664i	−0.566861	−	0.475653i
$926$		−	22.9770i		−	0.755071i
$927$		0			0
$928$	−129.929			−4.26513
$929$	9.88550	−	3.59803i	0.324333	−	0.118047i	−0.174722	−	0.984618i	$-0.555903\pi$
$929$	9.88550	−	3.59803i	0.324333	−	0.118047i	0.499055	+	0.866570i	$0.333681\pi$
$930$		0			0
$931$	1.97237	−	21.2114i	0.0646419	−	0.695177i
$932$	22.9540	−	63.0656i	0.751884	−	2.06578i
$933$		0			0
$934$	24.4116	−	29.0926i	0.798772	−	0.951940i
$935$			1.54376i			0.0504863i
$936$		0			0
$937$	−42.2539	−	24.3953i	−1.38038	−	0.796960i	−0.388172	−	0.921587i	$-0.626893\pi$
$937$	−42.2539	−	24.3953i	−1.38038	−	0.796960i	−0.992204	+	0.124627i	$0.960227\pi$
$938$	12.9080	+	0.598841i	0.421461	+	0.0195529i
$939$		0			0
$940$	75.3330	−	63.2119i	2.45709	−	2.06174i
$941$	−0.325805	−	1.84773i	−0.0106209	−	0.0602343i	0.979037	−	0.203684i	$-0.0652916\pi$
$941$	−0.325805	−	1.84773i	−0.0106209	−	0.0602343i	−0.989658	+	0.143450i	$0.954180\pi$
$942$		0			0
$943$	−0.272683	+	0.324971i	−0.00887977	+	0.0105825i
$944$	−93.5830			−3.04587
$945$		0			0
$946$	−1.43173			−0.0465494
$947$	−32.6945	+	38.9638i	−1.06243	+	1.26615i	−0.0998937	+	0.994998i	$0.531850\pi$
$947$	−32.6945	+	38.9638i	−1.06243	+	1.26615i	−0.962535	+	0.271156i	$0.912594\pi$
$948$		0			0
$949$	1.49829	+	8.49720i	0.0486364	+	0.275831i
$950$	−15.2317	+	12.7809i	−0.494181	+	0.414667i
$951$		0			0
$952$	53.1475	−	82.9251i	1.72252	−	2.68762i
$953$	42.4743	+	24.5225i	1.37588	+	0.794363i	0.991660	−	0.128880i	$-0.0411383\pi$
$953$	42.4743	+	24.5225i	1.37588	+	0.794363i	0.384216	+	0.923243i	$0.374472\pi$
$954$		0			0
$955$			41.1612i			1.33195i
$956$	−27.7294	+	33.0466i	−0.896833	+	1.06880i
$957$		0			0
$958$	−20.3985	+	56.0444i	−0.659045	+	1.81071i
$959$	−2.42688	+	10.8074i	−0.0783681	+	0.348990i
$960$		0			0
$961$	−12.1236	+	4.41262i	−0.391083	+	0.142343i
$962$	−51.9724			−1.67566
$963$		0			0
$964$		−	2.96992i		−	0.0956545i
$965$	−9.95312	−	8.35166i	−0.320402	−	0.268849i
$966$		0			0
$967$	9.57744	+	54.3164i	0.307990	+	1.74670i	0.609088	+	0.793103i	$0.291536\pi$
$967$	9.57744	+	54.3164i	0.307990	+	1.74670i	−0.301098	+	0.953593i	$0.597353\pi$
$968$	−34.9365	+	95.9873i	−1.12290	+	3.08515i
$969$		0			0
$970$	−9.48098	+	53.7693i	−0.304416	+	1.72643i
$971$	−10.1506	−	17.5814i	−0.325749	−	0.564214i	0.655915	−	0.754835i	$-0.272283\pi$
$971$	−10.1506	−	17.5814i	−0.325749	−	0.564214i	−0.981664	+	0.190621i	$0.938950\pi$
$972$		0			0
$973$	24.0358	−	18.3394i	0.770552	−	0.587934i
$974$	9.04671	+	24.8556i	0.289875	+	0.796426i
$975$		0			0
$976$	161.850	−	28.5385i	5.18068	−	0.913494i
$977$	−7.73545	+	21.2530i	−0.247479	+	0.679943i	0.752298	+	0.658823i	$0.228945\pi$
$977$	−7.73545	+	21.2530i	−0.247479	+	0.679943i	−0.999777	+	0.0211199i	$0.993277\pi$
$978$		0			0
$979$	−0.471513	+	0.561927i	−0.0150696	+	0.0179593i
$980$	−72.5247	−	73.3201i	−2.31672	−	2.34212i
$981$		0			0
$982$	36.9968	−	64.0803i	1.18061	−	2.04488i
$983$	−8.03958	−	6.74601i	−0.256423	−	0.215164i	0.505509	−	0.862821i	$-0.331305\pi$
$983$	−8.03958	−	6.74601i	−0.256423	−	0.215164i	−0.761932	+	0.647657i	$0.775749\pi$
$984$		0			0
$985$	21.7326	−	3.83204i	0.692457	−	0.122099i
$986$	−63.6966	−	23.1837i	−2.02851	−	0.738319i
$987$		0			0
$988$	−5.82312	+	33.0245i	−0.185258	+	1.05065i
$989$	−4.21725	−	2.43483i	−0.134101	−	0.0774230i
$990$		0			0
$991$	0.780011	+	1.35102i	0.0247779	+	0.0429165i	0.878148	−	0.478388i	$-0.158779\pi$
$991$	0.780011	+	1.35102i	0.0247779	+	0.0429165i	−0.853371	+	0.521305i	$0.825445\pi$
$992$	−15.4308	+	87.5127i	−0.489930	+	2.77853i
$993$		0			0
$994$	48.9922	+	11.0015i	1.55394	+	0.348948i
$995$	−8.81493	−	10.5052i	−0.279452	−	0.333038i
$996$		0			0
$997$	30.6280	+	5.40054i	0.969997	+	0.171037i	0.636129	−	0.771583i	$-0.280535\pi$
$997$	30.6280	+	5.40054i	0.969997	+	0.171037i	0.333869	+	0.942620i	$0.391646\pi$
$998$	76.5716	+	44.2086i	2.42383	+	1.39940i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.1		132
3.2	odd	2		189.2.ba.a.101.22	✓	132
7.5	odd	6		567.2.bd.a.467.22		132
21.5	even	6		189.2.bd.a.47.1	yes	132
27.4	even	9		189.2.bd.a.185.1	yes	132
27.23	odd	18		567.2.bd.a.17.22		132
189.131	even	18	inner	567.2.ba.a.341.1		132
189.166	odd	18		189.2.ba.a.131.22	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.22	✓	132	3.2	odd	2
189.2.ba.a.131.22	yes	132	189.166	odd	18
189.2.bd.a.47.1	yes	132	21.5	even	6
189.2.bd.a.185.1	yes	132	27.4	even	9
567.2.ba.a.143.1		132	1.1	even	1	trivial
567.2.ba.a.341.1		132	189.131	even	18	inner
567.2.bd.a.17.22		132	27.23	odd	18
567.2.bd.a.467.22		132	7.5	odd	6

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.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.75048 + 2.08614i) q^{2} +(-0.940509 - 5.33389i) q^{4} +(-2.08375 + 1.74847i) q^{5} +(-0.122613 + 2.64291i) q^{7} +(8.05677 + 4.65158i) q^{8} +O(q^{10})\)	\(q+(-1.75048 + 2.08614i) q^{2} +(-0.940509 - 5.33389i) q^{4} +(-2.08375 + 1.74847i) q^{5} +(-0.122613 + 2.64291i) q^{7} +(8.05677 + 4.65158i) q^{8} -7.40767i q^{10} +(-0.0911635 + 0.108644i) q^{11} +(-0.695830 + 1.91178i) q^{13} +(-5.29885 - 4.88215i) q^{14} +(-13.6280 + 4.96018i) q^{16} -4.00161 q^{17} +3.04328i q^{19} +(11.2860 + 9.47004i) q^{20} +(-0.0670678 - 0.380360i) q^{22} +(0.449297 - 1.23443i) q^{23} +(0.416612 - 2.36273i) q^{25} +(-2.77020 - 4.79813i) q^{26} +(14.2123 - 1.83168i) q^{28} +(-2.12744 - 5.84511i) q^{29} +(-4.18959 + 0.738737i) q^{31} +(7.14417 - 19.6284i) q^{32} +(7.00474 - 8.34792i) q^{34} +(-4.36556 - 5.72155i) q^{35} +(4.69031 - 8.12386i) q^{37} +(-6.34871 - 5.32720i) q^{38} +(-24.9215 + 4.39432i) q^{40} +(-0.303455 - 0.110449i) q^{41} +(0.643705 - 3.65063i) q^{43} +(0.665238 + 0.384075i) q^{44} +(1.78872 + 3.09815i) q^{46} +(1.15909 - 6.57353i) q^{47} +(-6.96993 - 0.648108i) q^{49} +(4.19971 + 5.00502i) q^{50} +(10.8516 + 1.91344i) q^{52} +(6.59926 + 3.81008i) q^{53} -0.385785i q^{55} +(-13.2816 + 20.7230i) q^{56} +(15.9178 + 5.79360i) q^{58} +(6.06369 + 2.20700i) q^{59} +(-11.1600 - 1.96782i) q^{61} +(5.79268 - 10.0332i) q^{62} +(13.9394 + 24.1437i) q^{64} +(-1.89276 - 5.20030i) q^{65} +(-1.37385 + 1.15280i) q^{67} +(3.76355 + 21.3441i) q^{68} +(19.5778 + 0.908274i) q^{70} +(-6.03534 + 3.48450i) q^{71} +(3.67285 - 2.12052i) q^{73} +(8.73722 + 24.0053i) q^{74} +(16.2325 - 2.86223i) q^{76} +(-0.275960 - 0.254258i) q^{77} +(-11.4740 - 9.62781i) q^{79} +(19.7246 - 34.1640i) q^{80} +(0.761604 - 0.439712i) q^{82} +(0.966634 - 0.351826i) q^{83} +(8.33835 - 6.99670i) q^{85} +(6.48894 + 7.73322i) q^{86} +(-1.23985 + 0.451269i) q^{88} +5.17217 q^{89} +(-4.96733 - 2.07342i) q^{91} +(-7.00690 - 1.23551i) q^{92} +(11.6843 + 13.9249i) q^{94} +(-5.32109 - 6.34143i) q^{95} +(-7.25860 - 1.27989i) q^{97} +(13.5528 - 13.4058i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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