LMFDB - Embedded newform 567.2.bd.a.17.2

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			17.2
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45739 + 0.433304i) q^{2} +(3.97163 - 1.44555i) q^{4} +(0.335948 - 0.122275i) q^{5} +(0.0666399 - 2.64491i) q^{7} +(-4.81149 + 2.77792i) q^{8} +O(q^{10})$	\(q+(-2.45739 + 0.433304i) q^{2} +(3.97163 - 1.44555i) q^{4} +(0.335948 - 0.122275i) q^{5} +(0.0666399 - 2.64491i) q^{7} +(-4.81149 + 2.77792i) q^{8} +(-0.772573 + 0.446045i) q^{10} +(1.17753 - 3.23525i) q^{11} +(0.362359 + 0.995572i) q^{13} +(0.982291 + 6.52846i) q^{14} +(4.14463 - 3.47775i) q^{16} +(-2.91185 - 5.04347i) q^{17} +(-3.53896 - 2.04322i) q^{19} +(1.15751 - 0.971262i) q^{20} +(-1.49181 + 8.46049i) q^{22} +(2.12375 + 0.374475i) q^{23} +(-3.73231 + 3.13178i) q^{25} +(-1.32184 - 2.28950i) q^{26} +(-3.55870 - 10.6009i) q^{28} +(-2.91124 + 7.99857i) q^{29} +(1.29102 + 3.54704i) q^{31} +(-1.53560 + 1.83005i) q^{32} +(9.34090 + 11.1321i) q^{34} +(-0.301019 - 0.896701i) q^{35} -1.87406 q^{37} +(9.58194 + 3.48754i) q^{38} +(-1.27674 + 1.52156i) q^{40} +(4.24450 - 1.54487i) q^{41} +(-1.24925 - 7.08485i) q^{43} -14.5514i q^{44} -5.38115 q^{46} +(-11.5236 - 4.19426i) q^{47} +(-6.99112 - 0.352513i) q^{49} +(7.81473 - 9.31324i) q^{50} +(2.87831 + 3.43023i) q^{52} +(-7.91413 - 4.56923i) q^{53} -1.23086i q^{55} +(7.02671 + 12.9111i) q^{56} +(3.68824 - 20.9171i) q^{58} +(3.15921 + 2.65089i) q^{59} +(4.54625 - 12.4907i) q^{61} +(-4.70948 - 8.15705i) q^{62} +(-2.42983 + 4.20859i) q^{64} +(0.243467 + 0.290153i) q^{65} +(0.801200 - 4.54383i) q^{67} +(-18.8554 - 15.8215i) q^{68} +(1.12827 + 2.07311i) q^{70} +(7.24109 + 4.18065i) q^{71} -7.45113i q^{73} +(4.60530 - 0.812039i) q^{74} +(-17.0090 - 2.99915i) q^{76} +(-8.47847 - 3.33007i) q^{77} +(-2.32947 - 13.2111i) q^{79} +(0.967136 - 1.67513i) q^{80} +(-9.76098 + 5.63551i) q^{82} +(3.80912 + 1.38640i) q^{83} +(-1.59492 - 1.33830i) q^{85} +(6.13979 + 16.8689i) q^{86} +(3.32155 + 18.8375i) q^{88} +(5.79564 - 10.0383i) q^{89} +(2.65735 - 0.892062i) q^{91} +(8.97607 - 1.58272i) q^{92} +(30.1354 + 5.31369i) q^{94} +(-1.43874 - 0.253689i) q^{95} +(-4.45675 + 0.785845i) q^{97} +(17.3327 - 2.16302i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.45739	+	0.433304i	−1.73764	+	0.306392i	−0.950578	−	0.310485i	$-0.899508\pi$
$2$	−2.45739	+	0.433304i	−1.73764	+	0.306392i	−0.787059	+	0.616878i	$0.788397\pi$
$3$		0			0
$3$		0			0
$4$	3.97163	−	1.44555i	1.98581	−	0.722777i
$5$	0.335948	−	0.122275i	0.150240	−	0.0546831i	−0.265805	−	0.964027i	$-0.585638\pi$
$5$	0.335948	−	0.122275i	0.150240	−	0.0546831i	0.416046	+	0.909344i	$0.363416\pi$
$6$		0			0
$7$	0.0666399	−	2.64491i	0.0251875	−	0.999683i
$7$	0.0666399	−	2.64491i	0.0251875	−	0.999683i
$8$	−4.81149	+	2.77792i	−1.70112	+	0.982141i
$9$		0			0
$10$	−0.772573	+	0.446045i	−0.244309	+	0.141052i
$11$	1.17753	−	3.23525i	0.355040	−	0.975464i	−0.625686	−	0.780075i	$-0.715181\pi$
$11$	1.17753	−	3.23525i	0.355040	−	0.975464i	0.980726	−	0.195389i	$-0.0625969\pi$
$12$		0			0
$13$	0.362359	+	0.995572i	0.100500	+	0.276122i	0.979745	−	0.200248i	$-0.0641746\pi$
$13$	0.362359	+	0.995572i	0.100500	+	0.276122i	−0.879245	+	0.476370i	$0.841952\pi$
$14$	0.982291	+	6.52846i	0.262528	+	1.74480i
$15$		0			0
$16$	4.14463	−	3.47775i	1.03616	−	0.869438i
$17$	−2.91185	−	5.04347i	−0.706227	−	1.22322i	−0.966247	−	0.257618i	$-0.917063\pi$
$17$	−2.91185	−	5.04347i	−0.706227	−	1.22322i	0.260020	−	0.965603i	$-0.416271\pi$
$18$		0			0
$19$	−3.53896	−	2.04322i	−0.811893	−	0.468746i	0.0357200	−	0.999362i	$-0.488628\pi$
$19$	−3.53896	−	2.04322i	−0.811893	−	0.468746i	−0.847613	+	0.530615i	$0.821961\pi$
$20$	1.15751	−	0.971262i	0.258826	−	0.217181i
$21$		0			0
$22$	−1.49181	+	8.46049i	−0.318056	+	1.80378i
$23$	2.12375	+	0.374475i	0.442833	+	0.0780834i	0.390619	−	0.920553i	$-0.372261\pi$
$23$	2.12375	+	0.374475i	0.442833	+	0.0780834i	0.0522140	+	0.998636i	$0.483372\pi$
$24$		0			0
$25$	−3.73231	+	3.13178i	−0.746462	+	0.626356i
$26$	−1.32184	−	2.28950i	−0.259235	−	0.449008i
$27$		0			0
$28$	−3.55870	−	10.6009i	−0.672530	−	2.00339i
$29$	−2.91124	+	7.99857i	−0.540604	+	1.48530i	0.305455	+	0.952207i	$0.401192\pi$
$29$	−2.91124	+	7.99857i	−0.540604	+	1.48530i	−0.846058	+	0.533090i	$0.821031\pi$
$30$		0			0
$31$	1.29102	+	3.54704i	0.231873	+	0.637067i	0.999995	−	0.00323735i	$-0.00103048\pi$
$31$	1.29102	+	3.54704i	0.231873	+	0.637067i	−0.768121	+	0.640304i	$0.778808\pi$
$32$	−1.53560	+	1.83005i	−0.271458	+	0.323511i
$33$		0			0
$34$	9.34090	+	11.1321i	1.60195	+	1.90913i
$35$	−0.301019	−	0.896701i	−0.0508815	−	0.151570i
$36$		0			0
$37$	−1.87406			−0.308094			−0.154047	−	0.988064i	$-0.549231\pi$
$37$	−1.87406			−0.308094			−0.154047	+	0.988064i	$0.549231\pi$
$38$	9.58194	+	3.48754i	1.55440	+	0.565754i
$39$		0			0
$40$	−1.27674	+	1.52156i	−0.201870	+	0.240580i
$41$	4.24450	−	1.54487i	0.662879	−	0.241268i	0.0114001	−	0.999935i	$-0.496371\pi$
$41$	4.24450	−	1.54487i	0.662879	−	0.241268i	0.651479	+	0.758667i	$0.274149\pi$
$42$		0			0
$43$	−1.24925	−	7.08485i	−0.190509	−	1.08043i	−0.918671	−	0.395024i	$-0.870736\pi$
$43$	−1.24925	−	7.08485i	−0.190509	−	1.08043i	0.728162	−	0.685405i	$-0.240375\pi$
$44$		−	14.5514i		−	2.19370i
$45$		0			0
$46$	−5.38115			−0.793407
$47$	−11.5236	−	4.19426i	−1.68089	−	0.611795i	−0.687462	−	0.726220i	$-0.741275\pi$
$47$	−11.5236	−	4.19426i	−1.68089	−	0.611795i	−0.993432	+	0.114425i	$0.963498\pi$
$48$		0			0
$49$	−6.99112	−	0.352513i	−0.998731	−	0.0503590i
$50$	7.81473	−	9.31324i	1.10517	−	1.31709i
$51$		0			0
$52$	2.87831	+	3.43023i	0.399150	+	0.475688i
$53$	−7.91413	−	4.56923i	−1.08709	−	0.627631i	−0.154289	−	0.988026i	$-0.549309\pi$
$53$	−7.91413	−	4.56923i	−1.08709	−	0.627631i	−0.932800	+	0.360394i	$0.882642\pi$
$54$		0			0
$55$		−	1.23086i		−	0.165969i
$56$	7.02671	+	12.9111i	0.938983	+	1.72532i
$57$		0			0
$58$	3.68824	−	20.9171i	0.484290	−	2.74654i
$59$	3.15921	+	2.65089i	0.411294	+	0.345117i	0.824840	−	0.565367i	$-0.191265\pi$
$59$	3.15921	+	2.65089i	0.411294	+	0.345117i	−0.413546	+	0.910483i	$0.635710\pi$
$60$		0			0
$61$	4.54625	−	12.4907i	0.582088	−	1.59927i	−0.202517	−	0.979279i	$-0.564912\pi$
$61$	4.54625	−	12.4907i	0.582088	−	1.59927i	0.784605	−	0.619995i	$-0.212866\pi$
$62$	−4.70948	−	8.15705i	−0.598104	−	1.03595i
$63$		0			0
$64$	−2.42983	+	4.20859i	−0.303729	+	0.526074i
$65$	0.243467	+	0.290153i	0.0301984	+	0.0359891i
$66$		0			0
$67$	0.801200	−	4.54383i	0.0978821	−	0.555117i	−0.895944	−	0.444167i	$-0.853500\pi$
$67$	0.801200	−	4.54383i	0.0978821	−	0.555117i	0.993826	−	0.110950i	$-0.0353893\pi$
$68$	−18.8554	−	15.8215i	−2.28655	−	1.91864i
$69$		0			0
$70$	1.12827	+	2.07311i	0.134854	+	0.247784i
$71$	7.24109	+	4.18065i	0.859359	+	0.496151i	0.863798	−	0.503839i	$-0.168079\pi$
$71$	7.24109	+	4.18065i	0.859359	+	0.496151i	−0.00443842	+	0.999990i	$0.501413\pi$
$72$		0			0
$73$		−	7.45113i		−	0.872089i	−0.899925	−	0.436045i	$-0.856379\pi$
$73$		−	7.45113i		−	0.872089i	0.899925	−	0.436045i	$-0.143621\pi$
$74$	4.60530	−	0.812039i	0.535355	−	0.0943976i
$75$		0			0
$76$	−17.0090	−	2.99915i	−1.95107	−	0.344026i
$77$	−8.47847	−	3.33007i	−0.966212	−	0.379497i
$78$		0			0
$79$	−2.32947	−	13.2111i	−0.262086	−	1.48636i	−0.777206	−	0.629246i	$-0.783364\pi$
$79$	−2.32947	−	13.2111i	−0.262086	−	1.48636i	0.515120	−	0.857118i	$-0.327747\pi$
$80$	0.967136	−	1.67513i	0.108129	−	0.187285i
$81$		0			0
$82$	−9.76098	+	5.63551i	−1.07792	+	0.622338i
$83$	3.80912	+	1.38640i	0.418105	+	0.152178i	0.542501	−	0.840055i	$-0.317477\pi$
$83$	3.80912	+	1.38640i	0.418105	+	0.152178i	−0.124397	+	0.992233i	$0.539700\pi$
$84$		0			0
$85$	−1.59492	−	1.33830i	−0.172993	−	0.145159i
$86$	6.13979	+	16.8689i	0.662070	+	1.81902i
$87$		0			0
$88$	3.32155	+	18.8375i	0.354078	+	2.00808i
$89$	5.79564	−	10.0383i	0.614337	−	1.06406i	−0.376164	−	0.926553i	$-0.622757\pi$
$89$	5.79564	−	10.0383i	0.614337	−	1.06406i	0.990501	−	0.137509i	$-0.0439096\pi$
$90$		0			0
$91$	2.65735	−	0.892062i	0.278566	−	0.0935135i
$92$	8.97607	−	1.58272i	0.935820	−	0.165010i
$93$		0			0
$94$	30.1354	+	5.31369i	3.10823	+	0.548065i
$95$	−1.43874	−	0.253689i	−0.147612	−	0.0260279i
$96$		0			0
$97$	−4.45675	+	0.785845i	−0.452515	+	0.0797905i	−0.395260	−	0.918569i	$-0.629346\pi$
$97$	−4.45675	+	0.785845i	−0.452515	+	0.0797905i	−0.0572541	+	0.998360i	$0.518235\pi$
$98$	17.3327	−	2.16302i	1.75086	−	0.218498i
$99$		0			0
$100$	−10.2962	+	17.8335i	−1.02962	+	1.78335i
$101$	0.374432	+	2.12351i	0.0372573	+	0.211297i	0.997753	−	0.0669976i	$-0.0213420\pi$
$101$	0.374432	+	2.12351i	0.0372573	+	0.211297i	−0.960496	+	0.278295i	$0.910231\pi$
$102$		0			0
$103$	1.52768	+	4.19726i	0.150527	+	0.413569i	0.991922	−	0.126852i	$-0.0404874\pi$
$103$	1.52768	+	4.19726i	0.150527	+	0.413569i	−0.841395	+	0.540421i	$0.818265\pi$
$104$	−4.50910	−	3.78359i	−0.442154	−	0.371011i
$105$		0			0
$106$	21.4280	+	7.79914i	2.08127	+	0.757520i
$107$	4.17439	−	2.41009i	0.403554	−	0.232992i	−0.284463	−	0.958687i	$-0.591815\pi$
$107$	4.17439	−	2.41009i	0.403554	−	0.232992i	0.688016	+	0.725695i	$0.258482\pi$
$108$		0			0
$109$	−10.0905	+	17.4773i	−0.966494	+	1.67402i	−0.260949	+	0.965353i	$0.584036\pi$
$109$	−10.0905	+	17.4773i	−0.966494	+	1.67402i	−0.705545	+	0.708665i	$0.749298\pi$
$110$	0.533336	+	3.02470i	0.0508516	+	0.288394i
$111$		0			0
$112$	−8.92216	−	11.1939i	−0.843064	−	1.05773i
$113$	−12.4855	−	2.20154i	−1.17454	−	0.207103i	−0.447876	−	0.894096i	$-0.647819\pi$
$113$	−12.4855	−	2.20154i	−1.17454	−	0.207103i	−0.726664	+	0.686993i	$0.758930\pi$
$114$		0			0
$115$	0.759259	−	0.133878i	0.0708012	−	0.0124842i
$116$			35.9757i			3.34026i
$117$		0			0
$118$	−8.91205	−	5.14538i	−0.820421	−	0.473670i
$119$	−13.5336	+	7.36548i	−1.24062	+	0.675193i
$120$		0			0
$121$	−0.653748	−	0.548560i	−0.0594317	−	0.0498691i
$122$	−5.75963	+	32.6645i	−0.521453	+	2.95731i
$123$		0			0
$124$	10.2549	+	12.2213i	0.920915	+	1.09750i
$125$	−1.76469	+	3.05654i	−0.157839	+	0.273385i
$126$		0			0
$127$	3.72128	+	6.44544i	0.330210	+	0.571940i	0.982553	−	0.185984i	$-0.0595471\pi$
$127$	3.72128	+	6.44544i	0.330210	+	0.571940i	−0.652343	+	0.757924i	$0.726214\pi$
$128$	5.78159	−	15.8848i	0.511025	−	1.40403i
$129$		0			0
$130$	−0.724019	−	0.607524i	−0.0635006	−	0.0532834i
$131$	−1.24502	+	7.06084i	−0.108778	+	0.616909i	0.880866	+	0.473365i	$0.156961\pi$
$131$	−1.24502	+	7.06084i	−0.108778	+	0.616909i	−0.989644	+	0.143544i	$0.954150\pi$
$132$		0			0
$133$	−5.63997	+	9.22407i	−0.489047	+	0.799829i
$134$			11.5131i			0.994582i
$135$		0			0
$136$	28.0207	+	16.1777i	2.40275	+	1.38723i
$137$	−2.39389	−	2.85292i	−0.204523	−	0.243742i	0.654026	−	0.756472i	$-0.273079\pi$
$137$	−2.39389	−	2.85292i	−0.204523	−	0.243742i	−0.858550	+	0.512730i	$0.828634\pi$
$138$		0			0
$139$	8.88294	−	10.5863i	0.753441	−	0.897916i	−0.243973	−	0.969782i	$-0.578451\pi$
$139$	8.88294	−	10.5863i	0.753441	−	0.897916i	0.997414	+	0.0718657i	$0.0228953\pi$
$140$	−2.49177	−	3.12622i	−0.210593	−	0.264214i
$141$		0			0
$142$	−19.6057	−	7.13588i	−1.64527	−	0.598830i
$143$	3.64761			0.305029
$144$		0			0
$145$			3.04307i			0.252714i
$146$	3.22861	+	18.3103i	0.267201	+	1.51537i
$147$		0			0
$148$	−7.44308	+	2.70906i	−0.611817	+	0.222683i
$149$	6.06042	−	7.22253i	0.496489	−	0.591693i	−0.458366	−	0.888763i	$-0.651565\pi$
$149$	6.06042	−	7.22253i	0.496489	−	0.591693i	0.954856	+	0.297071i	$0.0960097\pi$
$150$		0			0
$151$	4.34280	+	1.58065i	0.353412	+	0.128631i	0.512624	−	0.858613i	$-0.328673\pi$
$151$	4.34280	+	1.58065i	0.353412	+	0.128631i	−0.159213	+	0.987244i	$0.550896\pi$
$152$	22.7036			1.84150
$153$		0			0
$154$	22.2778	+	4.50952i	1.79520	+	0.363388i
$155$	0.867429	+	1.03376i	0.0696735	+	0.0830337i
$156$		0			0
$157$	−0.750398	+	0.894289i	−0.0598883	+	0.0713721i	−0.795157	−	0.606404i	$-0.792612\pi$
$157$	−0.750398	+	0.894289i	−0.0598883	+	0.0713721i	0.735269	+	0.677776i	$0.237056\pi$
$158$	11.4488	+	31.4554i	0.910821	+	2.50246i
$159$		0			0
$160$	−0.292111	+	0.802568i	−0.0230934	+	0.0634486i
$161$	1.13198	−	5.59218i	0.0892124	−	0.440726i
$162$		0			0
$163$	3.53124	+	6.11629i	0.276588	+	0.479065i	0.970535	−	0.240962i	$-0.0774629\pi$
$163$	3.53124	+	6.11629i	0.276588	+	0.479065i	−0.693947	+	0.720027i	$0.744130\pi$
$164$	14.6244	−	12.2713i	1.14197	−	0.958228i
$165$		0			0
$166$	−9.96122	−	1.75643i	−0.773140	−	0.136326i
$167$	2.87826	−	16.3234i	0.222726	−	1.26314i	−0.644259	−	0.764808i	$-0.722834\pi$
$167$	2.87826	−	16.3234i	0.222726	−	1.26314i	0.866985	−	0.498335i	$-0.166055\pi$
$168$		0			0
$169$	9.09872	−	7.63473i	0.699901	−	0.587287i
$170$	4.49923	+	2.59763i	0.345075	+	0.199229i
$171$		0			0
$172$	−15.2031	−	26.3325i	−1.15922	−	2.00784i
$173$	−2.48189	+	2.08255i	−0.188695	+	0.158334i	−0.732241	−	0.681045i	$-0.761526\pi$
$173$	−2.48189	+	2.08255i	−0.188695	+	0.158334i	0.543547	+	0.839379i	$0.317081\pi$
$174$		0			0
$175$	8.03457	+	10.0803i	0.607356	+	0.762002i
$176$	−6.37096	−	17.5041i	−0.480229	−	1.31942i
$177$		0			0
$178$	−9.89249	+	27.1794i	−0.741474	+	2.03718i
$179$	−4.43437	+	2.56018i	−0.331440	+	0.191357i	−0.656480	−	0.754343i	$-0.727956\pi$
$179$	−4.43437	+	2.56018i	−0.331440	+	0.191357i	0.325040	+	0.945700i	$0.394622\pi$
$180$		0			0
$181$	3.60530	−	2.08152i	0.267980	−	0.154718i	−0.359990	−	0.932956i	$-0.617220\pi$
$181$	3.60530	−	2.08152i	0.267980	−	0.154718i	0.627969	+	0.778238i	$0.283886\pi$
$182$	−6.14361	+	3.34358i	−0.455395	+	0.247843i
$183$		0			0
$184$	−11.2587	+	4.09782i	−0.830000	+	0.302095i
$185$	−0.629587	+	0.229151i	−0.0462882	+	0.0168475i
$186$		0			0
$187$	−19.7457	+	3.48169i	−1.44395	+	0.254607i
$188$	−51.8306			−3.78014
$189$		0			0
$190$	3.64547			0.264470
$191$	2.95620	−	0.521258i	0.213903	−	0.0377169i	−0.0656695	−	0.997841i	$-0.520918\pi$
$191$	2.95620	−	0.521258i	0.213903	−	0.0377169i	0.279573	+	0.960125i	$0.409807\pi$
$192$		0			0
$193$	15.5318	−	5.65312i	1.11801	−	0.406921i	0.284081	−	0.958800i	$-0.408311\pi$
$193$	15.5318	−	5.65312i	1.11801	−	0.406921i	0.833924	+	0.551880i	$0.186089\pi$
$194$	10.6115	−	3.86226i	0.761859	−	0.277294i
$195$		0			0
$196$	−28.2757	+	8.70599i	−2.01969	+	0.621857i
$197$	2.93897	−	1.69681i	0.209393	−	0.120893i	−0.391636	−	0.920120i	$-0.628091\pi$
$197$	2.93897	−	1.69681i	0.209393	−	0.120893i	0.601029	+	0.799227i	$0.294758\pi$
$198$		0			0
$199$	−3.64344	+	2.10354i	−0.258277	+	0.149116i	−0.623548	−	0.781785i	$-0.714310\pi$
$199$	−3.64344	+	2.10354i	−0.258277	+	0.149116i	0.365271	+	0.930901i	$0.380976\pi$
$200$	9.25816	−	25.4366i	0.654651	−	1.79864i
$201$		0			0
$202$	−1.84025	−	5.05604i	−0.129479	−	0.355742i
$203$	20.9615	+	8.23300i	1.47121	+	0.577843i
$204$		0			0
$205$	1.23703	−	1.03799i	0.0863980	−	0.0724965i
$206$	−5.57279	−	9.65236i	−0.388275	−	0.672512i
$207$		0			0
$208$	4.96420	+	2.86608i	0.344205	+	0.198727i
$209$	−10.7776	+	9.04345i	−0.745499	+	0.625548i
$210$		0			0
$211$	−3.10714	+	17.6215i	−0.213905	+	1.21311i	0.668893	+	0.743359i	$0.266768\pi$
$211$	−3.10714	+	17.6215i	−0.213905	+	1.21311i	−0.882797	+	0.469754i	$0.844343\pi$
$212$	−38.0371	−	6.70696i	−2.61240	−	0.460636i
$213$		0			0
$214$	−9.21381	+	7.73130i	−0.629843	+	0.528501i
$215$	−1.28598	−	2.22739i	−0.0877033	−	0.151907i
$216$		0			0
$217$	9.46764	−	3.17825i	0.642705	−	0.215754i
$218$	17.2233	−	47.3207i	1.16651	−	3.20496i
$219$		0			0
$220$	−1.77927	−	4.88851i	−0.119958	−	0.329583i
$221$	3.96600	−	4.72650i	0.266782	−	0.317939i
$222$		0			0
$223$	8.41245	+	10.0256i	0.563339	+	0.671361i	0.970250	−	0.242107i	$-0.0778384\pi$
$223$	8.41245	+	10.0256i	0.563339	+	0.671361i	−0.406911	+	0.913468i	$0.633394\pi$
$224$	4.73800	+	4.18348i	0.316571	+	0.279520i
$225$		0			0
$226$	31.6358			2.10438
$227$	−1.05435	−	0.383753i	−0.0699799	−	0.0254706i	0.306793	−	0.951776i	$-0.400744\pi$
$227$	−1.05435	−	0.383753i	−0.0699799	−	0.0254706i	−0.376773	+	0.926306i	$0.622966\pi$
$228$		0			0
$229$	0.819956	−	0.977186i	0.0541842	−	0.0645743i	−0.738272	−	0.674504i	$-0.764358\pi$
$229$	0.819956	−	0.977186i	0.0541842	−	0.0645743i	0.792456	+	0.609929i	$0.208802\pi$
$230$	−1.80778	+	0.657980i	−0.119202	+	0.0433859i
$231$		0			0
$232$	−8.21194	−	46.5722i	−0.539140	−	3.05762i
$233$			18.7681i			1.22954i	0.788707	+	0.614769i	$0.210751\pi$
$233$			18.7681i			1.22954i	−0.788707	+	0.614769i	$0.789249\pi$
$234$		0			0
$235$	−4.38419			−0.285993
$236$	16.3792	+	5.96155i	1.06620	+	0.388064i
$237$		0			0
$238$	30.0658	−	23.9640i	1.94887	−	1.55336i
$239$	−8.01259	+	9.54904i	−0.518292	+	0.617676i	−0.960176	−	0.279396i	$-0.909866\pi$
$239$	−8.01259	+	9.54904i	−0.518292	+	0.617676i	0.441884	+	0.897072i	$0.354310\pi$
$240$		0			0
$241$	−13.2440	−	15.7835i	−0.853118	−	1.01671i	−0.999622	−	0.0274964i	$-0.991247\pi$
$241$	−13.2440	−	15.7835i	−0.853118	−	1.01671i	0.146504	−	0.989210i	$-0.453198\pi$
$242$	1.84421	+	1.06475i	0.118550	+	0.0684450i
$243$		0			0
$244$		−	56.1804i		−	3.59658i
$245$	−2.39176	+	0.736413i	−0.152804	+	0.0470477i
$246$		0			0
$247$	0.751799	−	4.26367i	0.0478359	−	0.271291i
$248$	−16.0651	−	13.4802i	−1.02013	−	0.855994i
$249$		0			0
$250$	3.01213	−	8.27576i	0.190504	−	0.523405i
$251$	4.73924	+	8.20860i	0.299138	+	0.518122i	0.975939	−	0.218044i	$-0.0699676\pi$
$251$	4.73924	+	8.20860i	0.299138	+	0.518122i	−0.676801	+	0.736166i	$0.736634\pi$
$252$		0			0
$253$	3.71231	−	6.42990i	0.233391	−	0.404245i
$254$	−11.9375	−	14.2265i	−0.749023	−	0.892651i
$255$		0			0
$256$	−5.63694	+	31.9687i	−0.352309	+	1.99804i
$257$	−12.2968	−	10.3182i	−0.767053	−	0.643634i	0.172900	−	0.984939i	$-0.444686\pi$
$257$	−12.2968	−	10.3182i	−0.767053	−	0.643634i	−0.939952	+	0.341306i	$0.889131\pi$
$258$		0			0
$259$	−0.124887	+	4.95673i	−0.00776011	+	0.307996i
$260$	1.38639	+	0.800435i	0.0859805	+	0.0496409i
$261$		0			0
$262$		−	17.8907i		−	1.10529i
$263$	13.1434	−	2.31754i	0.810459	−	0.142906i	0.246963	−	0.969025i	$-0.420567\pi$
$263$	13.1434	−	2.31754i	0.810459	−	0.142906i	0.563496	+	0.826119i	$0.309456\pi$
$264$		0			0
$265$	−3.21744	−	0.567321i	−0.197646	−	0.0348503i
$266$	9.86277	−	25.1110i	0.604725	−	1.53965i
$267$		0			0
$268$	−3.38629	−	19.2046i	−0.206850	−	1.17311i
$269$	12.4472	−	21.5591i	0.758916	−	1.31448i	−0.184487	−	0.982835i	$-0.559062\pi$
$269$	12.4472	−	21.5591i	0.758916	−	1.31448i	0.943404	−	0.331647i	$-0.107604\pi$
$270$		0			0
$271$	7.54919	−	4.35853i	0.458581	−	0.264762i	−0.252867	−	0.967501i	$-0.581373\pi$
$271$	7.54919	−	4.35853i	0.458581	−	0.264762i	0.711447	+	0.702739i	$0.248040\pi$
$272$	−29.6085	−	10.7766i	−1.79528	−	0.653427i
$273$		0			0
$274$	7.11889	+	5.97346i	0.430068	+	0.360870i
$275$	5.73716	+	15.7627i	0.345964	+	0.950528i
$276$		0			0
$277$	−3.91568	−	22.2069i	−0.235271	−	1.33429i	−0.842043	−	0.539410i	$-0.818647\pi$
$277$	−3.91568	−	22.2069i	−0.235271	−	1.33429i	0.606772	−	0.794876i	$-0.292464\pi$
$278$	−17.2418	+	29.8636i	−1.03409	+	1.79110i
$279$		0			0
$280$	3.93931	+	3.47826i	0.235419	+	0.207866i
$281$	−11.7861	+	2.07821i	−0.703099	+	0.123975i	−0.513757	−	0.857936i	$-0.671747\pi$
$281$	−11.7861	+	2.07821i	−0.703099	+	0.123975i	−0.189342	+	0.981911i	$0.560636\pi$
$282$		0			0
$283$	−20.9003	−	3.68529i	−1.24239	−	0.219068i	−0.486453	−	0.873707i	$-0.661709\pi$
$283$	−20.9003	−	3.68529i	−1.24239	−	0.219068i	−0.755941	+	0.654639i	$0.772820\pi$
$284$	34.8023	+	6.13658i	2.06513	+	0.364139i
$285$		0			0
$286$	−8.96361	+	1.58053i	−0.530029	+	0.0934584i
$287$	−3.80319	−	11.3293i	−0.224495	−	0.668746i
$288$		0			0
$289$	−8.45772	+	14.6492i	−0.497513	+	0.861717i
$290$	−1.31858	−	7.47802i	−0.0774295	−	0.439125i
$291$		0			0
$292$	−10.7710	−	29.5931i	−0.630326	−	1.73181i
$293$	17.6180	+	14.7833i	1.02926	+	0.863649i	0.990762	−	0.135610i	$-0.0432994\pi$
$293$	17.6180	+	14.7833i	1.02926	+	0.863649i	0.0384944	+	0.999259i	$0.487744\pi$
$294$		0			0
$295$	1.38547	+	0.504269i	0.0806650	+	0.0293597i
$296$	9.01703	−	5.20598i	0.524104	−	0.302592i
$297$		0			0
$298$	−11.7633	+	20.3746i	−0.681428	+	1.18027i
$299$	0.396743	+	2.25004i	0.0229442	+	0.130123i
$300$		0			0
$301$	−18.8220	+	2.83202i	−1.08488	+	0.163235i
$302$	−11.3569	−	2.00252i	−0.653513	−	0.115232i
$303$		0			0
$304$	−21.7735	+	3.83925i	−1.24879	+	0.220196i
$305$		−	4.75213i		−	0.272106i
$306$		0			0
$307$	28.4532	+	16.4275i	1.62391	+	0.937565i	0.985860	+	0.167571i	$0.0535924\pi$
$307$	28.4532	+	16.4275i	1.62391	+	0.937565i	0.638051	+	0.769994i	$0.279741\pi$
$308$	−38.4871	−	0.969702i	−2.19301	−	0.0552539i
$309$		0			0
$310$	−2.57954	−	2.16449i	−0.146508	−	0.122935i
$311$	1.67256	−	9.48554i	0.0948420	−	0.537876i	−0.899954	−	0.435985i	$-0.856400\pi$
$311$	1.67256	−	9.48554i	0.0948420	−	0.537876i	0.994796	−	0.101890i	$-0.0324890\pi$
$312$		0			0
$313$	6.92621	+	8.25434i	0.391493	+	0.466563i	0.925406	−	0.378976i	$-0.123724\pi$
$313$	6.92621	+	8.25434i	0.391493	+	0.466563i	−0.533914	+	0.845539i	$0.679279\pi$
$314$	1.45652	−	2.52277i	0.0821962	−	0.142368i
$315$		0			0
$316$	−28.3492	−	49.1022i	−1.59477	−	2.76221i
$317$	−1.50889	+	4.14565i	−0.0847479	+	0.232843i	−0.974827	−	0.222964i	$-0.928427\pi$
$317$	−1.50889	+	4.14565i	−0.0847479	+	0.232843i	0.890079	+	0.455807i	$0.150649\pi$
$318$		0			0
$319$	22.4493	+	18.8372i	1.25692	+	1.05468i
$320$	−0.301691	+	1.71098i	−0.0168650	+	0.0956464i
$321$		0			0
$322$	−0.358599	+	14.2327i	−0.0199839	+	0.793155i
$323$			23.7982i			1.32417i
$324$		0			0
$325$	−4.47035	−	2.58096i	−0.247970	−	0.143166i
$326$	−11.3278	−	13.5000i	−0.627391	−	0.747696i
$327$		0			0
$328$	−16.1308	+	19.2240i	−0.890676	+	1.06147i
$329$	−11.8614	+	30.1995i	−0.653939	+	1.66495i
$330$		0			0
$331$	12.9721	+	4.72144i	0.713008	+	0.259514i	0.672955	−	0.739684i	$-0.265025\pi$
$331$	12.9721	+	4.72144i	0.713008	+	0.259514i	0.0400537	+	0.999198i	$0.487247\pi$
$332$	17.1325			0.940269
$333$		0			0
$334$			41.3601i			2.26312i
$335$	−0.286436	−	1.62446i	−0.0156496	−	0.0887535i
$336$		0			0
$337$	6.81432	−	2.48021i	0.371200	−	0.135106i	−0.149683	−	0.988734i	$-0.547825\pi$
$337$	6.81432	−	2.48021i	0.371200	−	0.135106i	0.520882	+	0.853628i	$0.325603\pi$
$338$	−19.0509	+	22.7040i	−1.03623	+	1.23494i
$339$		0			0
$340$	−8.26901	−	3.00967i	−0.448450	−	0.163222i
$341$	12.9958			0.703760
$342$		0			0
$343$	−1.39825	+	18.4674i	−0.0754986	+	0.997146i
$344$	25.6919	+	30.6184i	1.38521	+	1.65083i
$345$		0			0
$346$	5.19659	−	6.19306i	0.279371	−	0.332941i
$347$	−6.11295	−	16.7952i	−0.328161	−	0.901614i	−0.988577	−	0.150715i	$-0.951843\pi$
$347$	−6.11295	−	16.7952i	−0.328161	−	0.901614i	0.660417	−	0.750899i	$-0.270380\pi$
$348$		0			0
$349$	11.7174	−	32.1932i	0.627217	−	1.72326i	−0.0613741	−	0.998115i	$-0.519548\pi$
$349$	11.7174	−	32.1932i	0.627217	−	1.72326i	0.688591	−	0.725150i	$-0.258230\pi$
$350$	−24.1119	−	21.2899i	−1.28884	−	1.13799i
$351$		0			0
$352$	4.11246	+	7.12299i	0.219195	+	0.379657i
$353$	−12.4457	+	10.4432i	−0.662419	+	0.555835i	−0.910811	−	0.412824i	$-0.864542\pi$
$353$	−12.4457	+	10.4432i	−0.662419	+	0.555835i	0.248392	+	0.968660i	$0.420098\pi$
$354$		0			0
$355$	2.94382	+	0.519074i	0.156242	+	0.0275496i
$356$	8.50716	−	48.2465i	0.450878	−	2.55706i
$357$		0			0
$358$	9.78764	−	8.21280i	0.517293	−	0.434060i
$359$	15.1773	+	8.76262i	0.801027	+	0.462473i	0.843830	−	0.536610i	$-0.180295\pi$
$359$	15.1773	+	8.76262i	0.801027	+	0.462473i	−0.0428030	+	0.999084i	$0.513629\pi$
$360$		0			0
$361$	−1.15052	−	1.99275i	−0.0605535	−	0.104882i
$362$	−7.95769	+	6.67729i	−0.418247	+	0.350951i
$363$		0			0
$364$	9.26448	−	7.38428i	0.485591	−	0.387042i
$365$	−0.911088	−	2.50319i	−0.0476885	−	0.131023i
$366$		0			0
$367$	2.95846	−	8.12830i	0.154430	−	0.424294i	−0.838217	−	0.545337i	$-0.816402\pi$
$367$	2.95846	−	8.12830i	0.154430	−	0.424294i	0.992647	+	0.121043i	$0.0386239\pi$
$368$	10.1045	−	5.83383i	0.526733	−	0.304109i
$369$		0			0
$370$	1.44785	−	0.835916i	0.0752701	−	0.0434572i
$371$	−12.6126	+	20.6277i	−0.654813	+	1.07094i
$372$		0			0
$373$	−0.591203	+	0.215180i	−0.0306113	+	0.0111416i	−0.357280	−	0.933997i	$-0.616296\pi$
$373$	−0.591203	+	0.215180i	−0.0306113	+	0.0111416i	0.326669	+	0.945139i	$0.394074\pi$
$374$	47.0142	−	17.1118i	2.43104	−	0.884828i
$375$		0			0
$376$	67.0971	−	11.8310i	3.46027	−	0.610139i
$377$	−9.01807			−0.464454
$378$		0			0
$379$	−5.41656			−0.278230			−0.139115	−	0.990276i	$-0.544426\pi$
$379$	−5.41656			−0.278230			−0.139115	+	0.990276i	$0.544426\pi$
$380$	−6.08086	+	1.07222i	−0.311942	+	0.0550037i
$381$		0			0
$382$	−7.03868	+	2.56187i	−0.360130	+	0.131077i
$383$	15.3981	−	5.60444i	0.786804	−	0.286373i	0.0827973	−	0.996566i	$-0.473615\pi$
$383$	15.3981	−	5.60444i	0.786804	−	0.286373i	0.704007	+	0.710193i	$0.251392\pi$
$384$		0			0
$385$	−3.25551	−	0.0820242i	−0.165916	−	0.00418034i
$386$	−35.7182	+	20.6219i	−1.81801	+	1.04963i
$387$		0			0
$388$	−16.5646	+	9.56356i	−0.840939	+	0.485516i
$389$	−5.33745	+	14.6645i	−0.270619	+	0.743521i	0.727718	+	0.685877i	$0.240581\pi$
$389$	−5.33745	+	14.6645i	−0.270619	+	0.743521i	−0.998337	+	0.0576441i	$0.981641\pi$
$390$		0			0
$391$	−4.29539	−	11.8015i	−0.217227	−	0.596827i
$392$	34.6170	−	17.7246i	1.74842	−	0.895229i
$393$		0			0
$394$	−6.48695	+	5.44320i	−0.326808	+	0.274224i
$395$	−2.39797	−	4.15340i	−0.120655	−	0.208980i
$396$		0			0
$397$	5.68678	+	3.28326i	0.285411	+	0.164782i	0.635871	−	0.771796i	$-0.280641\pi$
$397$	5.68678	+	3.28326i	0.285411	+	0.164782i	−0.350459	+	0.936578i	$0.613975\pi$
$398$	8.04189	−	6.74795i	0.403104	−	0.338244i
$399$		0			0
$400$	−4.57747	+	25.9601i	−0.228874	+	1.29801i
$401$	−34.7683	−	6.13060i	−1.73625	−	0.306147i	−0.786136	−	0.618054i	$-0.787921\pi$
$401$	−34.7683	−	6.13060i	−1.73625	−	0.306147i	−0.950113	+	0.311907i	$0.899032\pi$
$402$		0			0
$403$	−3.06352	+	2.57060i	−0.152605	+	0.128051i
$404$	4.55675	+	7.89252i	0.226707	+	0.392668i
$405$		0			0
$406$	−55.0780	−	11.1490i	−2.73347	−	0.553315i
$407$	−2.20677	+	6.06305i	−0.109386	+	0.300534i
$408$		0			0
$409$	5.95427	+	16.3592i	0.294420	+	0.808912i	0.995407	+	0.0957376i	$0.0305210\pi$
$409$	5.95427	+	16.3592i	0.294420	+	0.808912i	−0.700987	+	0.713174i	$0.747257\pi$
$410$	−2.59010	+	3.08676i	−0.127916	+	0.152444i
$411$		0			0
$412$	12.1347	+	14.4616i	0.597836	+	0.712473i
$413$	7.22190	−	8.17917i	0.355367	−	0.402471i
$414$		0			0
$415$	1.44919			0.0711378
$416$	−2.37839	−	0.865663i	−0.116610	−	0.0424426i
$417$		0			0
$418$	22.5661	−	26.8932i	1.10374	−	1.31539i
$419$	16.1147	−	5.86527i	0.787254	−	0.286537i	0.0830600	−	0.996545i	$-0.473531\pi$
$419$	16.1147	−	5.86527i	0.787254	−	0.286537i	0.704194	+	0.710007i	$0.251308\pi$
$420$		0			0
$421$	4.49987	+	25.5201i	0.219310	+	1.24377i	0.873268	+	0.487240i	$0.161996\pi$
$421$	4.49987	+	25.5201i	0.219310	+	1.24377i	−0.653958	+	0.756531i	$0.726893\pi$
$422$		−	44.6492i		−	2.17349i
$423$		0			0
$424$	50.7717			2.46569
$425$	26.6630	+	9.70453i	1.29334	+	0.470739i
$426$		0			0
$427$	−32.7339	−	12.8568i	−1.58411	−	0.622185i
$428$	13.0952	−	15.6063i	0.632981	−	0.754358i
$429$		0			0
$430$	4.12530	+	4.91634i	0.198940	+	0.237087i
$431$	10.4907	+	6.05678i	0.505317	+	0.291745i	0.730907	−	0.682478i	$-0.239098\pi$
$431$	10.4907	+	6.05678i	0.505317	+	0.291745i	−0.225590	+	0.974222i	$0.572431\pi$
$432$		0			0
$433$		−	31.6375i		−	1.52040i	−0.649689	−	0.760200i	$-0.725101\pi$
$433$		−	31.6375i		−	1.52040i	0.649689	−	0.760200i	$-0.274899\pi$
$434$	−21.8885	+	11.9126i	−1.05068	+	0.571822i
$435$		0			0
$436$	−14.8114	+	83.9995i	−0.709337	+	4.02285i
$437$	−6.75073	−	5.66454i	−0.322931	−	0.270972i
$438$		0			0
$439$	1.33152	−	3.65831i	0.0635498	−	0.174602i	−0.903854	−	0.427842i	$-0.859274\pi$
$439$	1.33152	−	3.65831i	0.0635498	−	0.174602i	0.967403	+	0.253240i	$0.0814963\pi$
$440$	3.41922	+	5.92226i	0.163005	+	0.282333i
$441$		0			0
$442$	−7.69801	+	13.3333i	−0.366157	+	0.634202i
$443$	0.133902	+	0.159578i	0.00636188	+	0.00758180i	0.769216	−	0.638989i	$-0.220647\pi$
$443$	0.133902	+	0.159578i	0.00636188	+	0.00758180i	−0.762854	+	0.646571i	$0.776203\pi$
$444$		0			0
$445$	0.719594	−	4.08102i	0.0341120	−	0.193459i
$446$	−25.0168	−	20.9916i	−1.18458	−	0.993980i
$447$		0			0
$448$	10.9694	+	6.70715i	0.518257	+	0.316883i
$449$	11.7985	+	6.81187i	0.556806	+	0.321472i	0.751862	−	0.659320i	$-0.229156\pi$
$449$	11.7985	+	6.81187i	0.556806	+	0.321472i	−0.195057	+	0.980792i	$0.562489\pi$
$450$		0			0
$451$		−	15.5511i		−	0.732274i
$452$	−52.7703	+	9.30483i	−2.48211	+	0.437663i
$453$		0			0
$454$	2.75724	+	0.486176i	0.129404	+	0.0228174i
$455$	0.783654	−	0.624614i	0.0367383	−	0.0292823i
$456$		0			0
$457$	3.44960	+	19.5636i	0.161365	+	0.915148i	0.952733	+	0.303808i	$0.0982581\pi$
$457$	3.44960	+	19.5636i	0.161365	+	0.915148i	−0.791368	+	0.611340i	$0.790631\pi$
$458$	−1.59153	+	2.75662i	−0.0743675	+	0.128808i
$459$		0			0
$460$	2.82197	−	1.62926i	0.131575	−	0.0759648i
$461$	5.61005	+	2.04189i	0.261286	+	0.0951003i	0.469342	−	0.883017i	$-0.344491\pi$
$461$	5.61005	+	2.04189i	0.261286	+	0.0951003i	−0.208056	+	0.978117i	$0.566714\pi$
$462$		0			0
$463$	21.0832	+	17.6909i	0.979822	+	0.822168i	0.984062	−	0.177823i	$-0.0569055\pi$
$463$	21.0832	+	17.6909i	0.979822	+	0.822168i	−0.00424088	+	0.999991i	$0.501350\pi$
$464$	15.7510	+	43.2757i	0.731224	+	2.00902i
$465$		0			0
$466$	−8.13229	−	46.1205i	−0.376721	−	2.13649i
$467$	7.94133	−	13.7548i	0.367481	−	0.636495i	−0.621690	−	0.783263i	$-0.713554\pi$
$467$	7.94133	−	13.7548i	0.367481	−	0.636495i	0.989171	+	0.146768i	$0.0468870\pi$
$468$		0			0
$469$	−11.9646	−	2.42190i	−0.552476	−	0.111833i
$470$	10.7737	−	1.89969i	0.496952	−	0.0876261i
$471$		0			0
$472$	−22.5645	−	3.97872i	−1.03861	−	0.183136i
$473$	−24.3923	−	4.30101i	−1.12156	−	0.197761i
$474$		0			0
$475$	19.6074	−	3.45732i	0.899650	−	0.158633i
$476$	−43.1031	+	48.8165i	−1.97563	+	2.23750i
$477$		0			0
$478$	15.5524	−	26.9376i	0.711352	−	1.23210i
$479$	−1.86323	−	10.5669i	−0.0851332	−	0.482814i	−0.997328	−	0.0730570i	$-0.976724\pi$
$479$	−1.86323	−	10.5669i	−0.0851332	−	0.482814i	0.912195	−	0.409757i	$-0.134387\pi$
$480$		0			0
$481$	−0.679082	−	1.86576i	−0.0309635	−	0.0850715i
$482$	39.3846	+	33.0476i	1.79392	+	1.50528i
$483$		0			0
$484$	−3.38942	−	1.23365i	−0.154064	−	0.0560749i
$485$	−1.40115	+	0.808953i	−0.0636228	+	0.0367326i
$486$		0			0
$487$	−4.54921	+	7.87946i	−0.206144	+	0.357052i	−0.950497	−	0.310735i	$-0.899425\pi$
$487$	−4.54921	+	7.87946i	−0.206144	+	0.357052i	0.744352	+	0.667787i	$0.232758\pi$
$488$	12.8239	+	72.7281i	0.580512	+	3.29225i
$489$		0			0
$490$	5.55838	−	2.84601i	0.251102	−	0.128570i
$491$	−2.90320	−	0.511913i	−0.131020	−	0.0231023i	0.107754	−	0.994178i	$-0.465634\pi$
$491$	−2.90320	−	0.511913i	−0.131020	−	0.0231023i	−0.238773	+	0.971075i	$0.576745\pi$
$492$		0			0
$493$	48.8176	−	8.60786i	2.19863	−	0.387679i
$494$			10.8033i			0.486061i
$495$		0			0
$496$	17.6865	+	10.2113i	0.794148	+	0.458501i
$497$	11.5400	−	18.8734i	0.517639	−	0.846590i
$498$		0			0
$499$	8.16120	+	6.84806i	0.365345	+	0.306561i	0.806917	−	0.590665i	$-0.201134\pi$
$499$	8.16120	+	6.84806i	0.365345	+	0.306561i	−0.441572	+	0.897226i	$0.645579\pi$
$500$	−2.59032	+	14.6904i	−0.115842	+	0.656975i
$501$		0			0
$502$	−15.2030	−	18.1182i	−0.678542	−	0.808655i
$503$	8.22192	−	14.2408i	0.366597	−	0.634965i	−0.622434	−	0.782672i	$-0.713856\pi$
$503$	8.22192	−	14.2408i	0.366597	−	0.634965i	0.989031	+	0.147707i	$0.0471893\pi$
$504$		0			0
$505$	0.385441	+	0.667604i	0.0171519	+	0.0297080i
$506$	−6.33648	+	17.4093i	−0.281691	+	0.773939i
$507$		0			0
$508$	24.0968	+	20.2196i	1.06912	+	0.897099i
$509$	2.53332	−	14.3672i	0.112287	−	0.636813i	−0.875770	−	0.482728i	$-0.839646\pi$
$509$	2.53332	−	14.3672i	0.112287	−	0.636813i	0.988058	−	0.154085i	$-0.0492429\pi$
$510$		0			0
$511$	−19.7076	−	0.496542i	−0.871813	−	0.0219657i
$512$		−	47.1935i		−	2.08568i
$513$		0			0
$514$	34.6889	+	20.0277i	1.53006	+	0.883383i
$515$	1.02644	+	1.22326i	0.0452304	+	0.0539035i
$516$		0			0
$517$	−27.1389	+	32.3429i	−1.19357	+	1.42244i
$518$	−1.84087	−	12.2347i	−0.0808834	−	0.537563i
$519$		0			0
$520$	−1.97746	−	0.719737i	−0.0867174	−	0.0315626i
$521$	−16.9489			−0.742544			−0.371272	−	0.928524i	$-0.621078\pi$
$521$	−16.9489			−0.742544			−0.371272	+	0.928524i	$0.621078\pi$
$522$		0			0
$523$		−	31.2357i		−	1.36584i	−0.730493	−	0.682920i	$-0.760710\pi$
$523$		−	31.2357i		−	1.36584i	0.730493	−	0.682920i	$-0.239290\pi$
$524$	5.26209	+	29.8428i	0.229875	+	1.30369i
$525$		0			0
$526$	−31.2944	+	11.3902i	−1.36450	+	0.496637i
$527$	14.1301	−	16.8396i	0.615518	−	0.733546i
$528$		0			0
$529$	−17.2428	−	6.27588i	−0.749689	−	0.272864i
$530$	8.15232			0.354114
$531$		0			0
$532$	−9.06596	+	44.7875i	−0.393059	+	1.94178i
$533$	3.07606	+	3.66591i	0.133239	+	0.158788i
$534$		0			0
$535$	1.10768	−	1.32009i	0.0478894	−	0.0570723i
$536$	8.76741	+	24.0883i	0.378694	+	1.04045i
$537$		0			0
$538$	−21.2459	+	58.3725i	−0.915974	+	2.51662i
$539$	−9.37274	+	22.2029i	−0.403713	+	0.956346i
$540$		0			0
$541$	19.0672	+	33.0253i	0.819762	+	1.41987i	0.905858	+	0.423582i	$0.139228\pi$
$541$	19.0672	+	33.0253i	0.819762	+	1.41987i	−0.0860957	+	0.996287i	$0.527439\pi$
$542$	−16.6627	+	13.9817i	−0.715726	+	0.600566i
$543$		0			0
$544$	13.7012	+	2.41590i	0.587436	+	0.103581i
$545$	−1.25285	+	7.10526i	−0.0536662	+	0.304356i
$546$		0			0
$547$	−26.5978	+	22.3182i	−1.13724	+	0.954257i	−0.999345	−	0.0361899i	$-0.988478\pi$
$547$	−26.5978	+	22.3182i	−1.13724	+	0.954257i	−0.137894	+	0.990447i	$0.544033\pi$
$548$	−13.6317	−	7.87025i	−0.582316	−	0.336201i
$549$		0			0
$550$	−20.9285	−	36.2492i	−0.892395	−	1.54567i
$551$	26.6456	−	22.3583i	1.13514	−	0.952496i
$552$		0			0
$553$	−35.0974	+	5.28086i	−1.49249	+	0.224565i
$554$	19.2447	+	52.8744i	0.817630	+	2.24642i
$555$		0			0
$556$	19.9767	−	54.8855i	0.847201	−	2.32767i
$557$	−16.4754	+	9.51210i	−0.698087	+	0.403041i	−0.806634	−	0.591051i	$-0.798713\pi$
$557$	−16.4754	+	9.51210i	−0.698087	+	0.403041i	0.108548	+	0.994091i	$0.465380\pi$
$558$		0			0
$559$	6.60080	−	3.81097i	0.279184	−	0.161187i
$560$	−4.36612	−	2.66962i	−0.184502	−	0.112812i
$561$		0			0
$562$	28.0625	−	10.2139i	1.18375	−	0.430848i
$563$	29.3667	−	10.6886i	1.23766	−	0.450470i	0.361444	−	0.932394i	$-0.382284\pi$
$563$	29.3667	−	10.6886i	1.23766	−	0.450470i	0.876213	+	0.481923i	$0.160062\pi$
$564$		0			0
$565$	−4.46368	+	0.787067i	−0.187788	+	0.0331122i
$566$	52.9570			2.22595
$567$		0			0
$568$	−46.4539			−1.94916
$569$	8.44284	−	1.48870i	0.353942	−	0.0624095i	0.00614965	−	0.999981i	$-0.498042\pi$
$569$	8.44284	−	1.48870i	0.353942	−	0.0624095i	0.347792	+	0.937572i	$0.386931\pi$
$570$		0			0
$571$	−11.9162	+	4.33714i	−0.498677	+	0.181504i	−0.579099	−	0.815257i	$-0.696595\pi$
$571$	−11.9162	+	4.33714i	−0.498677	+	0.181504i	0.0804219	+	0.996761i	$0.474373\pi$
$572$	14.4870	−	5.27282i	0.605730	−	0.220468i
$573$		0			0
$574$	14.2549	+	26.1925i	0.594990	+	1.09325i
$575$	−9.09928	+	5.25347i	−0.379466	+	0.219085i
$576$		0			0
$577$	−30.9382	+	17.8622i	−1.28798	+	0.743613i	−0.978293	−	0.207227i	$-0.933556\pi$
$577$	−30.9382	+	17.8622i	−1.28798	+	0.743613i	−0.309683	+	0.950840i	$0.600223\pi$
$578$	14.4363	−	39.6635i	0.600473	−	1.64979i
$579$		0			0
$580$	4.39893	+	12.0860i	0.182656	+	0.501842i
$581$	3.92076	−	9.98239i	0.162660	−	0.414139i
$582$		0			0
$583$	−24.1017	+	20.2238i	−0.998192	+	0.837582i
$584$	20.6986	+	35.8511i	0.856515	+	1.48353i
$585$		0			0
$586$	−49.7000	−	28.6943i	−2.05309	−	1.18535i
$587$	23.8827	−	20.0400i	0.985744	−	0.827138i	0.000798351	−	1.00000i	$-0.499746\pi$
$587$	23.8827	−	20.0400i	0.985744	−	0.827138i	0.984946	+	0.172862i	$0.0553014\pi$
$588$		0			0
$589$	2.67852	−	15.1906i	0.110367	−	0.625920i
$590$	−3.62314	−	0.638857i	−0.149162	−	0.0263013i
$591$		0			0
$592$	−7.76728	+	6.51752i	−0.319233	+	0.267869i
$593$	−7.36449	−	12.7557i	−0.302423	−	0.523812i	0.674261	−	0.738493i	$-0.264462\pi$
$593$	−7.36449	−	12.7557i	−0.302423	−	0.523812i	−0.976684	+	0.214681i	$0.931129\pi$
$594$		0			0
$595$	−3.64596	+	4.12924i	−0.149470	+	0.169282i
$596$	13.6292	−	37.4459i	0.558273	−	1.53384i
$597$		0			0
$598$	−1.94991	−	5.35732i	−0.0797376	−	0.219077i
$599$	9.25646	−	11.0314i	0.378209	−	0.450732i	−0.543039	−	0.839707i	$-0.682727\pi$
$599$	9.25646	−	11.0314i	0.378209	−	0.450732i	0.921248	+	0.388976i	$0.127171\pi$
$600$		0			0
$601$	−23.1504	−	27.5895i	−0.944324	−	1.12540i	−0.991962	−	0.126537i	$-0.959614\pi$
$601$	−23.1504	−	27.5895i	−0.944324	−	1.12540i	0.0476382	−	0.998865i	$-0.484831\pi$
$602$	45.0260	−	15.1151i	1.83512	−	0.616044i
$603$		0			0
$604$	19.5329			0.794782
$605$	−0.286701	−	0.104350i	−0.0116560	−	0.00424245i
$606$		0			0
$607$	−1.50957	+	1.79904i	−0.0612717	+	0.0730208i	−0.795810	−	0.605547i	$-0.792954\pi$
$607$	−1.50957	+	1.79904i	−0.0612717	+	0.0730208i	0.734538	+	0.678568i	$0.237399\pi$
$608$	9.17362	−	3.33892i	0.372039	−	0.135411i
$609$		0			0
$610$	2.05912	+	11.6778i	0.0833712	+	0.472822i
$611$		−	12.9924i		−	0.525618i
$612$		0			0
$613$	27.3781			1.10579			0.552895	−	0.833251i	$-0.313523\pi$
$613$	27.3781			1.10579			0.552895	+	0.833251i	$0.313523\pi$
$614$	−77.0387	−	28.0398i	−3.10903	−	1.13159i
$615$		0			0
$616$	50.0447	−	7.52988i	2.01636	−	0.303388i
$617$	−20.2153	+	24.0916i	−0.813837	+	0.969893i	−0.999920	−	0.0126410i	$-0.995976\pi$
$617$	−20.2153	+	24.0916i	−0.813837	+	0.969893i	0.186083	+	0.982534i	$0.440421\pi$
$618$		0			0
$619$	−8.85224	−	10.5497i	−0.355802	−	0.424028i	0.558220	−	0.829693i	$-0.311484\pi$
$619$	−8.85224	−	10.5497i	−0.355802	−	0.424028i	−0.914022	+	0.405665i	$0.867040\pi$
$620$	4.93946	+	2.85180i	0.198374	+	0.114531i
$621$		0			0
$622$			24.0344i			0.963691i
$623$	−26.1643	−	15.9979i	−1.04825	−	0.640943i
$624$		0			0
$625$	4.01113	−	22.7482i	0.160445	−	0.909929i
$626$	−20.5970	−	17.2830i	−0.823223	−	0.690766i
$627$		0			0
$628$	−1.68756	+	4.63653i	−0.0673409	+	0.185018i
$629$	5.45698	+	9.45177i	0.217584	+	0.376867i
$630$		0			0
$631$	11.5471	−	20.0002i	0.459684	−	0.796197i	−0.539260	−	0.842140i	$-0.681296\pi$
$631$	11.5471	−	20.0002i	0.459684	−	0.796197i	0.998944	+	0.0459427i	$0.0146292\pi$
$632$	47.9076	+	57.0940i	1.90566	+	2.27108i
$633$		0			0
$634$	1.91161	−	10.8413i	0.0759198	−	0.430563i
$635$	2.03827	+	1.71031i	0.0808864	+	0.0678717i
$636$		0			0
$637$	−2.18234	−	7.08790i	−0.0864675	−	0.280833i
$638$	−63.3288	−	36.5629i	−2.50721	−	1.44754i
$639$		0			0
$640$		−	6.04341i		−	0.238887i
$641$	24.1857	−	4.26458i	0.955276	−	0.168441i	0.325781	−	0.945445i	$-0.394373\pi$
$641$	24.1857	−	4.26458i	0.955276	−	0.168441i	0.629495	+	0.777004i	$0.283262\pi$
$642$		0			0
$643$	37.4315	+	6.60018i	1.47615	+	0.260286i	0.853040	−	0.521846i	$-0.174756\pi$
$643$	37.4315	+	6.60018i	1.47615	+	0.260286i	0.623114	+	0.782131i	$0.285867\pi$
$644$	−3.58800	−	23.8464i	−0.141387	−	0.939680i
$645$		0			0
$646$	−10.3118	−	58.4814i	−0.405714	−	2.30092i
$647$	−1.12029	+	1.94040i	−0.0440432	+	0.0762851i	−0.887207	−	0.461372i	$-0.847357\pi$
$647$	−1.12029	+	1.94040i	−0.0440432	+	0.0762851i	0.843163	+	0.537657i	$0.180691\pi$
$648$		0			0
$649$	12.2964	−	7.09931i	0.482674	−	0.278672i
$650$	12.1037	+	4.40540i	0.474748	+	0.172794i
$651$		0			0
$652$	22.8662	+	19.1870i	0.895509	+	0.751422i
$653$	15.4956	+	42.5738i	0.606389	+	1.66604i	0.738051	+	0.674745i	$0.235746\pi$
$653$	15.4956	+	42.5738i	0.606389	+	1.66604i	−0.131662	+	0.991295i	$0.542031\pi$
$654$		0			0
$655$	0.445104	+	2.52431i	0.0173917	+	0.0986330i
$656$	12.2192	−	21.1642i	0.477078	−	0.826324i
$657$		0			0
$658$	16.0625	−	79.3515i	0.626180	−	3.09344i
$659$	43.6553	−	7.69760i	1.70057	−	0.299856i	0.762675	−	0.646782i	$-0.223886\pi$
$659$	43.6553	−	7.69760i	1.70057	−	0.299856i	0.937893	+	0.346926i	$0.112774\pi$
$660$		0			0
$661$	−25.8622	−	4.56021i	−1.00592	−	0.177372i	−0.353669	−	0.935371i	$-0.615066\pi$
$661$	−25.8622	−	4.56021i	−1.00592	−	0.177372i	−0.652256	+	0.757999i	$0.726177\pi$
$662$	−33.9232	−	5.98158i	−1.31846	−	0.232481i
$663$		0			0
$664$	−22.1788	+	3.91073i	−0.860706	+	0.151766i
$665$	−0.766862	+	3.78844i	−0.0297376	+	0.146909i
$666$		0			0
$667$	−9.17801	+	15.8968i	−0.355374	+	0.615526i
$668$	−12.1650	−	68.9911i	−0.470678	−	2.66935i
$669$		0			0
$670$	1.40777	+	3.86781i	0.0543868	+	0.149427i
$671$	−35.0572	−	29.4165i	−1.35337	−	1.13561i
$672$		0			0
$673$	−40.4246	−	14.7134i	−1.55825	−	0.567158i	−0.587918	−	0.808920i	$-0.700052\pi$
$673$	−40.4246	−	14.7134i	−1.55825	−	0.567158i	−0.970336	+	0.241762i	$0.922275\pi$
$674$	−15.6708	+	9.04751i	−0.603615	+	0.348497i
$675$		0			0
$676$	25.1003	−	43.4750i	0.965396	−	1.67212i
$677$	−7.21471	−	40.9166i	−0.277284	−	1.57255i	−0.731613	−	0.681720i	$-0.761232\pi$
$677$	−7.21471	−	40.9166i	−0.277284	−	1.57255i	0.454330	−	0.890834i	$-0.349879\pi$
$678$		0			0
$679$	1.78149	+	11.8401i	0.0683675	+	0.454381i
$680$	11.3916	+	2.00865i	0.436848	+	0.0770282i
$681$		0			0
$682$	−31.9357	+	5.63112i	−1.22288	+	0.215627i
$683$			8.71752i			0.333567i	0.985994	+	0.166783i	$0.0533380\pi$
$683$			8.71752i			0.333567i	−0.985994	+	0.166783i	$0.946662\pi$
$684$		0			0
$685$	−1.15306	−	0.665721i	−0.0440562	−	0.0254359i
$686$	−4.56595	−	45.9875i	−0.174329	−	1.75581i
$687$		0			0
$688$	−29.8170	−	25.0195i	−1.13676	−	0.953858i
$689$	1.68124	−	9.53479i	0.0640502	−	0.363247i
$690$		0			0
$691$	28.5754	+	34.0548i	1.08706	+	1.29551i	0.952479	+	0.304604i	$0.0985240\pi$
$691$	28.5754	+	34.0548i	1.08706	+	1.29551i	0.134580	+	0.990903i	$0.457032\pi$
$692$	−6.84670	+	11.8588i	−0.260273	+	0.450805i
$693$		0			0
$694$	22.2993	+	38.6236i	0.846472	+	1.46613i
$695$	1.68977	−	4.64260i	0.0640966	−	0.176104i
$696$		0			0
$697$	−20.1508	−	16.9086i	−0.763267	−	0.640457i
$698$	−14.8447	+	84.1885i	−0.561881	+	3.18658i
$699$		0			0
$700$	46.4820	+	28.4210i	1.75685	+	1.07421i
$701$		−	4.87126i		−	0.183985i	−0.995760	−	0.0919925i	$-0.970676\pi$
$701$		−	4.87126i		−	0.183985i	0.995760	−	0.0919925i	$-0.0293236\pi$
$702$		0			0
$703$	6.63222	+	3.82912i	0.250139	+	0.144418i
$704$	10.7546	+	12.8169i	0.405330	+	0.483054i
$705$		0			0
$706$	26.0589	−	31.0558i	0.980740	−	1.16880i
$707$	5.64144	−	0.848829i	0.212168	−	0.0319235i
$708$		0			0
$709$	−15.8865	−	5.78222i	−0.596631	−	0.217156i	0.0260126	−	0.999662i	$-0.491719\pi$
$709$	−15.8865	−	5.78222i	−0.596631	−	0.217156i	−0.622643	+	0.782506i	$0.713941\pi$
$710$	−7.45903			−0.279932
$711$		0			0
$712$			64.3992i			2.41346i
$713$	1.41352	+	8.01648i	0.0529368	+	0.300220i
$714$		0			0
$715$	1.22541	−	0.446012i	0.0458276	−	0.0166799i
$716$	−13.9108	+	16.5782i	−0.519870	+	0.619557i
$717$		0			0
$718$	−41.0934	−	14.9568i	−1.53359	−	0.558182i
$719$	5.55081			0.207010			0.103505	−	0.994629i	$-0.466994\pi$
$719$	5.55081			0.207010			0.103505	+	0.994629i	$0.466994\pi$
$720$		0			0
$721$	11.2032	−	3.76087i	0.417229	−	0.140062i
$722$	3.69074	+	4.39845i	0.137355	+	0.163693i
$723$		0			0
$724$	11.3099	−	13.4787i	0.420331	−	0.500931i
$725$	−14.1841	−	38.9705i	−0.526785	−	1.44733i
$726$		0			0
$727$	−11.3466	+	31.1745i	−0.420822	+	1.15620i	0.530415	+	0.847738i	$0.322036\pi$
$727$	−11.3466	+	31.1745i	−0.420822	+	1.15620i	−0.951237	+	0.308461i	$0.900186\pi$
$728$	−10.3077	+	11.6740i	−0.382030	+	0.432669i
$729$		0			0
$730$	3.32354	+	5.75654i	0.123010	+	0.213059i
$731$	−32.0946	+	26.9305i	−1.18706	+	0.996062i
$732$		0			0
$733$	−23.7652	−	4.19044i	−0.877787	−	0.154778i	−0.283444	−	0.958989i	$-0.591477\pi$
$733$	−23.7652	−	4.19044i	−0.877787	−	0.154778i	−0.594343	+	0.804211i	$0.702588\pi$
$734$	−3.74806	+	21.2563i	−0.138344	+	0.784585i
$735$		0			0
$736$	−3.94654	+	3.31154i	−0.145471	+	0.122065i
$737$	−13.7570	−	7.94259i	−0.506744	−	0.292569i
$738$		0			0
$739$	−13.0329	−	22.5736i	−0.479422	−	0.830383i	0.520300	−	0.853984i	$-0.325820\pi$
$739$	−13.0329	−	22.5736i	−0.479422	−	0.830383i	−0.999721	+	0.0236010i	$0.992487\pi$
$740$	−2.16924	+	1.82020i	−0.0797427	+	0.0669121i
$741$		0			0
$742$	22.0560	−	56.1554i	0.809701	−	2.06153i
$743$	−6.91069	−	18.9870i	−0.253528	−	0.696564i	−0.999531	−	0.0306207i	$-0.990252\pi$
$743$	−6.91069	−	18.9870i	−0.253528	−	0.696564i	0.746003	−	0.665943i	$-0.231971\pi$
$744$		0			0
$745$	1.15285	−	3.16743i	0.0422372	−	0.116046i
$746$	1.35958	−	0.784953i	0.0497777	−	0.0287392i
$747$		0			0
$748$	−73.3895	+	42.3714i	−2.68338	+	1.54925i
$749$	−6.09628	−	11.2015i	−0.222753	−	0.409294i
$750$		0			0
$751$	−10.4511	+	3.80390i	−0.381367	+	0.138806i	−0.525588	−	0.850739i	$-0.676155\pi$
$751$	−10.4511	+	3.80390i	−0.381367	+	0.138806i	0.144221	+	0.989546i	$0.453932\pi$
$752$	−62.3477	+	22.6927i	−2.27359	+	0.827518i
$753$		0			0
$754$	22.1609	−	3.90757i	0.807053	−	0.142305i
$755$	1.65223			0.0601307
$756$		0			0
$757$	52.3885			1.90409			0.952047	−	0.305952i	$-0.0989747\pi$
$757$	52.3885			1.90409			0.952047	+	0.305952i	$0.0989747\pi$
$758$	13.3106	−	2.34702i	0.483463	−	0.0852476i
$759$		0			0
$760$	7.62721	−	2.77608i	0.276668	−	0.100699i
$761$	11.7998	−	4.29476i	0.427741	−	0.155685i	−0.119173	−	0.992873i	$-0.538024\pi$
$761$	11.7998	−	4.29476i	0.427741	−	0.155685i	0.546915	+	0.837188i	$0.315802\pi$
$762$		0			0
$763$	45.5534	+	27.8532i	1.64914	+	1.00835i
$764$	10.9874	−	6.34360i	0.397511	−	0.229503i
$765$		0			0
$766$	−35.4106	+	20.4443i	−1.27944	+	0.738684i
$767$	−1.49439	+	4.10579i	−0.0539592	+	0.148252i
$768$		0			0
$769$	−5.13723	−	14.1144i	−0.185253	−	0.508979i	0.811949	−	0.583728i	$-0.198407\pi$
$769$	−5.13723	−	14.1144i	−0.185253	−	0.508979i	−0.997202	+	0.0747491i	$0.976184\pi$
$770$	8.03560	−	1.20906i	0.289583	−	0.0435715i
$771$		0			0
$772$	53.5147	−	44.9042i	1.92604	−	1.61614i
$773$	9.44708	+	16.3628i	0.339788	+	0.588530i	0.984393	−	0.175986i	$-0.0563114\pi$
$773$	9.44708	+	16.3628i	0.339788	+	0.588530i	−0.644605	+	0.764516i	$0.722978\pi$
$774$		0			0
$775$	−15.9270	−	9.19547i	−0.572116	−	0.330311i
$776$	19.2606	−	16.1616i	0.691415	−	0.580166i
$777$		0			0
$778$	6.76200	−	38.3492i	0.242429	−	1.37489i
$779$	−18.1776	−	3.20520i	−0.651280	−	0.114838i
$780$		0			0
$781$	22.0520	−	18.5039i	0.789084	−	0.662120i
$782$	15.6691	+	27.1396i	0.560325	+	0.970512i
$783$		0			0
$784$	−30.2015	+	22.8524i	−1.07863	+	0.816155i
$785$	−0.142745	+	0.392190i	−0.00509480	+	0.0139978i
$786$		0			0
$787$	−0.475365	−	1.30606i	−0.0169449	−	0.0465558i	0.930932	−	0.365193i	$-0.118997\pi$
$787$	−0.475365	−	1.30606i	−0.0169449	−	0.0465558i	−0.947877	+	0.318637i	$0.896775\pi$
$788$	9.21965	−	10.9875i	0.328436	−	0.391415i
$789$		0			0
$790$	7.69243	+	9.16748i	0.273684	+	0.326164i
$791$	−6.65490	+	32.8764i	−0.236621	+	1.16895i
$792$		0			0
$793$	14.0828			0.500095
$794$	−15.3973	−	5.60415i	−0.546429	−	0.198884i
$795$		0			0
$796$	−11.4296	+	13.6213i	−0.405112	+	0.482794i
$797$	−1.89028	+	0.688005i	−0.0669571	+	0.0243704i	−0.375282	−	0.926911i	$-0.622454\pi$
$797$	−1.89028	+	0.688005i	−0.0669571	+	0.0243704i	0.308324	+	0.951281i	$0.400232\pi$
$798$		0			0
$799$	12.4014	+	70.3321i	0.438732	+	2.48817i
$800$		−	11.6395i		−	0.411518i
$801$		0			0
$802$	88.0958			3.11077
$803$	−24.1063	−	8.77396i	−0.850691	−	0.309626i
$804$		0			0
$805$	−0.303498	−	2.01709i	−0.0106969	−	0.0710932i
$806$	6.41442	−	7.64441i	0.225938	−	0.269263i
$807$		0			0
$808$	−7.70050	−	9.17710i	−0.270903	−	0.322849i
$809$	4.13482	+	2.38724i	0.145373	+	0.0839309i	0.570922	−	0.821004i	$-0.306586\pi$
$809$	4.13482	+	2.38724i	0.145373	+	0.0839309i	−0.425550	+	0.904935i	$0.639919\pi$
$810$		0			0
$811$		−	17.2143i		−	0.604475i	−0.953233	−	0.302237i	$-0.902266\pi$
$811$		−	17.2143i		−	0.604475i	0.953233	−	0.302237i	$-0.0977336\pi$
$812$	95.1526	+	2.39742i	3.33920	+	0.0841328i
$813$		0			0
$814$	2.79575	−	15.8555i	0.0979910	−	0.555734i
$815$	1.93418	+	1.62297i	0.0677514	+	0.0568502i
$816$		0			0
$817$	−10.0548	+	27.6255i	−0.351775	+	0.966493i
$818$	−21.7205	−	37.6210i	−0.759439	−	1.31539i
$819$		0			0
$820$	3.41255	−	5.91071i	0.119171	−	0.206411i
$821$	5.60503	+	6.67982i	0.195617	+	0.233127i	0.854933	−	0.518739i	$-0.173598\pi$
$821$	5.60503	+	6.67982i	0.195617	+	0.233127i	−0.659316	+	0.751866i	$0.729154\pi$
$822$		0			0
$823$	−2.10852	+	11.9580i	−0.0734985	+	0.416831i	0.925752	+	0.378130i	$0.123433\pi$
$823$	−2.10852	+	11.9580i	−0.0734985	+	0.416831i	−0.999251	+	0.0387003i	$0.987678\pi$
$824$	−19.0101	−	15.9513i	−0.662247	−	0.555691i
$825$		0			0
$826$	−14.2030	+	23.2287i	−0.494184	+	0.808230i
$827$	17.3220	+	10.0009i	0.602346	+	0.347765i	0.769964	−	0.638087i	$-0.220274\pi$
$827$	17.3220	+	10.0009i	0.602346	+	0.347765i	−0.167618	+	0.985852i	$0.553607\pi$
$828$		0			0
$829$		−	14.7886i		−	0.513628i	−0.966461	−	0.256814i	$-0.917327\pi$
$829$		−	14.7886i		−	0.513628i	0.966461	−	0.256814i	$-0.0826728\pi$
$830$	−3.56122	+	0.627939i	−0.123612	+	0.0217961i
$831$		0			0
$832$	−5.07043	−	0.894053i	−0.175785	−	0.0309957i
$833$	18.5792	+	36.2859i	0.643731	+	1.25723i
$834$		0			0
$835$	−1.02900	−	5.83575i	−0.0356100	−	0.201954i
$836$	−29.7317	+	51.4968i	−1.02829	+	1.78105i
$837$		0			0
$838$	−37.0586	+	21.3958i	−1.28017	+	0.739106i
$839$	−9.90483	−	3.60506i	−0.341953	−	0.124461i	0.165335	−	0.986238i	$-0.447130\pi$
$839$	−9.90483	−	3.60506i	−0.341953	−	0.124461i	−0.507287	+	0.861777i	$0.669352\pi$
$840$		0			0
$841$	−33.2865	−	27.9307i	−1.14781	−	0.963127i
$842$	−22.1159	−	60.7629i	−0.762164	−	2.09403i
$843$		0			0
$844$	13.1324	+	74.4775i	0.452036	+	2.56362i
$845$	2.12316	−	3.67742i	0.0730389	−	0.126507i
$846$		0			0
$847$	−1.49446	+	1.69255i	−0.0513502	+	0.0581567i
$848$	−48.6918	+	8.58567i	−1.67208	+	0.294833i
$849$		0			0
$850$	−69.7263	−	12.2946i	−2.39159	−	0.421702i
$851$	−3.98004	−	0.701788i	−0.136434	−	0.0240570i
$852$		0			0
$853$	10.2716	−	1.81115i	0.351691	−	0.0620126i	0.00498807	−	0.999988i	$-0.498412\pi$
$853$	10.2716	−	1.81115i	0.351691	−	0.0620126i	0.346703	+	0.937975i	$0.387301\pi$
$854$	86.0109	+	17.4105i	2.94323	+	0.595774i
$855$		0			0
$856$	−13.3900	+	23.1922i	−0.457662	+	0.792694i
$857$	8.17214	+	46.3465i	0.279155	+	1.58317i	0.725446	+	0.688279i	$0.241633\pi$
$857$	8.17214	+	46.3465i	0.279155	+	1.58317i	−0.446291	+	0.894888i	$0.647255\pi$
$858$		0			0
$859$	−1.41263	−	3.88116i	−0.0481981	−	0.132423i	0.913258	−	0.407382i	$-0.133558\pi$
$859$	−1.41263	−	3.88116i	−0.0481981	−	0.132423i	−0.961456	+	0.274958i	$0.911336\pi$
$860$	−8.32726	−	6.98740i	−0.283957	−	0.238268i
$861$		0			0
$862$	−28.4040	−	10.3382i	−0.967446	−	0.352121i
$863$	24.3038	−	14.0318i	0.827311	−	0.477648i	−0.0256201	−	0.999672i	$-0.508156\pi$
$863$	24.3038	−	14.0318i	0.827311	−	0.477648i	0.852931	+	0.522024i	$0.174823\pi$
$864$		0			0
$865$	−0.579142	+	1.00310i	−0.0196914	+	0.0341065i
$866$	13.7087	+	77.7456i	0.465839	+	2.64190i
$867$		0			0
$868$	33.0076	−	26.3088i	1.12035	−	0.892980i
$869$	−45.4842	−	8.02009i	−1.54295	−	0.272063i
$870$		0			0
$871$	4.81403	−	0.848844i	0.163117	−	0.0287620i
$872$		−	112.122i		−	3.79694i
$873$		0			0
$874$	19.0437	+	10.9949i	0.644161	+	0.371907i
$875$	7.96668	+	4.87115i	0.269323	+	0.164675i
$876$		0			0
$877$	12.2587	+	10.2863i	0.413948	+	0.347344i	0.825855	−	0.563882i	$-0.190693\pi$
$877$	12.2587	+	10.2863i	0.413948	+	0.347344i	−0.411907	+	0.911226i	$0.635137\pi$
$878$	−1.68689	+	9.56684i	−0.0569299	+	0.322865i
$879$		0			0
$880$	−4.28062	−	5.10144i	−0.144300	−	0.171970i
$881$	−12.7246	+	22.0396i	−0.428702	+	0.742533i	−0.996758	−	0.0804564i	$-0.974362\pi$
$881$	−12.7246	+	22.0396i	−0.428702	+	0.742533i	0.568056	+	0.822990i	$0.307696\pi$
$882$		0			0
$883$	−5.39480	−	9.34406i	−0.181549	−	0.314453i	0.760859	−	0.648917i	$-0.224778\pi$
$883$	−5.39480	−	9.34406i	−0.181549	−	0.314453i	−0.942408	+	0.334465i	$0.891445\pi$
$884$	8.91908	−	24.5050i	0.299981	−	0.824192i
$885$		0			0
$886$	−0.398196	−	0.334126i	−0.0133776	−	0.0112252i
$887$	−3.90779	+	22.1622i	−0.131211	+	0.744133i	0.846213	+	0.532845i	$0.178877\pi$
$887$	−3.90779	+	22.1622i	−0.131211	+	0.744133i	−0.977424	+	0.211288i	$0.932234\pi$
$888$		0			0
$889$	17.2956	−	9.41293i	0.580076	−	0.315699i
$890$			10.3405i			0.346613i
$891$		0			0
$892$	47.9036	+	27.6572i	1.60393	+	0.926030i
$893$	32.2119	+	38.3886i	1.07793	+	1.28463i
$894$		0			0
$895$	−1.17667	+	1.40230i	−0.0393318	+	0.0468738i
$896$	−41.6286	−	16.3504i	−1.39071	−	0.546227i
$897$		0			0
$898$	−31.9451	−	11.6271i	−1.06602	−	0.388001i
$899$	−32.1297			−1.07159
$900$		0			0
$901$			53.2196i			1.77300i
$902$	6.73837	+	38.2152i	0.224363	+	1.27243i
$903$		0			0
$904$	66.1897	−	24.0911i	2.20144	−	0.801257i
$905$	0.956674	−	1.14012i	0.0318009	−	0.0378989i
$906$		0			0
$907$	16.2730	+	5.92288i	0.540336	+	0.196666i	0.597747	−	0.801684i	$-0.296063\pi$
$907$	16.2730	+	5.92288i	0.540336	+	0.196666i	−0.0574117	+	0.998351i	$0.518285\pi$
$908$	−4.74224			−0.157377
$909$		0			0
$910$	−1.65510	+	1.87448i	−0.0548659	+	0.0621384i
$911$	−20.4723	−	24.3979i	−0.678277	−	0.808339i	0.311608	−	0.950211i	$-0.399132\pi$
$911$	−20.4723	−	24.3979i	−0.678277	−	0.808339i	−0.989885	+	0.141872i	$0.954688\pi$
$912$		0			0
$913$	8.97072	−	10.6909i	0.296888	−	0.353817i
$914$	−16.9540	−	46.5807i	−0.560789	−	1.54075i
$915$		0			0
$916$	1.84399	−	5.06631i	0.0609270	−	0.167396i
$917$	18.5923	+	3.76349i	0.613973	+	0.124282i
$918$		0			0
$919$	−9.28327	−	16.0791i	−0.306227	−	0.530401i	0.671307	−	0.741180i	$-0.265733\pi$
$919$	−9.28327	−	16.0791i	−0.306227	−	0.530401i	−0.977534	+	0.210779i	$0.932400\pi$
$920$	−3.28126	+	2.75331i	−0.108180	+	0.0907739i
$921$		0			0
$922$	−14.6708	−	2.58686i	−0.483158	−	0.0851938i
$923$	−1.53826	+	8.72392i	−0.0506325	+	0.287151i
$924$		0			0
$925$	6.99458	−	5.86915i	0.229980	−	0.192977i
$926$	−59.4753	−	34.3381i	−1.95448	−	1.12842i
$927$		0			0
$928$	−10.1673	−	17.6103i	−0.333759	−	0.578087i
$929$	8.32914	−	6.98898i	0.273270	−	0.229301i	−0.495845	−	0.868411i	$-0.665142\pi$
$929$	8.32914	−	6.98898i	0.273270	−	0.229301i	0.769115	+	0.639110i	$0.220697\pi$
$930$		0			0
$931$	24.0210	+	15.5319i	0.787257	+	0.509038i
$932$	27.1303	+	74.5399i	0.888682	+	2.44163i
$933$		0			0
$934$	−13.5549	+	37.2419i	−0.443531	+	1.21859i
$935$	−6.20779	+	3.58407i	−0.203016	+	0.117212i
$936$		0			0
$937$	−18.3316	+	10.5838i	−0.598869	+	0.345757i	−0.768596	−	0.639734i	$-0.779045\pi$
$937$	−18.3316	+	10.5838i	−0.598869	+	0.345757i	0.169728	+	0.985491i	$0.445711\pi$
$938$	30.4512	+	0.767233i	0.994267	+	0.0250510i
$939$		0			0
$940$	−17.4124	+	6.33759i	−0.567929	+	0.206709i
$941$	4.87040	−	1.77268i	0.158770	−	0.0577877i	−0.261412	−	0.965227i	$-0.584188\pi$
$941$	4.87040	−	1.77268i	0.158770	−	0.0577877i	0.420183	+	0.907440i	$0.361966\pi$
$942$		0			0
$943$	9.59277	−	1.69146i	0.312384	−	0.0550816i
$944$	22.3129			0.726223
$945$		0			0
$946$	61.8050			2.00945
$947$	29.4381	−	5.19074i	0.956611	−	0.168676i	0.326514	−	0.945193i	$-0.394126\pi$
$947$	29.4381	−	5.19074i	0.956611	−	0.168676i	0.630097	+	0.776516i	$0.283015\pi$
$948$		0			0
$949$	7.41814	−	2.69998i	0.240803	−	0.0876452i
$950$	−46.6850	+	16.9919i	−1.51466	+	0.551292i
$951$		0			0
$952$	44.6560	−	73.0341i	1.44731	−	2.36705i
$953$	29.6132	−	17.0972i	0.959267	−	0.553833i	0.0633195	−	0.997993i	$-0.479831\pi$
$953$	29.6132	−	17.0972i	0.959267	−	0.553833i	0.895947	+	0.444160i	$0.146498\pi$
$954$		0			0
$955$	0.929393	−	0.536585i	0.0300745	−	0.0173635i
$956$	−18.0194	+	49.5079i	−0.582789	+	1.60120i
$957$		0			0
$958$	9.15737	+	25.1597i	0.295861	+	0.812872i
$959$	−7.70525	+	6.14150i	−0.248816	+	0.198319i
$960$		0			0
$961$	12.8326	−	10.7678i	0.413955	−	0.347350i
$962$	2.47721	+	4.29066i	0.0798686	+	0.138336i
$963$		0			0
$964$	−75.4160	−	43.5415i	−2.42899	−	1.40238i
$965$	4.52665	−	3.79831i	0.145718	−	0.122272i
$966$		0			0
$967$	7.82430	−	44.3738i	0.251612	−	1.42697i	−0.553008	−	0.833176i	$-0.686520\pi$
$967$	7.82430	−	44.3738i	0.251612	−	1.42697i	0.804621	−	0.593789i	$-0.202369\pi$
$968$	4.66936	+	0.823334i	0.150079	+	0.0264629i
$969$		0			0
$970$	3.09264	−	2.59503i	0.0992988	−	0.0833216i
$971$	16.1729	+	28.0122i	0.519012	+	0.898955i	0.999756	+	0.0220939i	$0.00703328\pi$
$971$	16.1729	+	28.0122i	0.519012	+	0.898955i	−0.480744	+	0.876861i	$0.659633\pi$
$972$		0			0
$973$	−27.4078	−	24.2001i	−0.878654	−	0.775818i
$974$	7.76498	−	21.3341i	0.248806	−	0.683589i
$975$		0			0
$976$	−24.5972	−	67.5802i	−0.787336	−	2.16319i
$977$	−19.8346	+	23.6380i	−0.634565	+	0.756245i	−0.983501	−	0.180901i	$-0.942099\pi$
$977$	−19.8346	+	23.6380i	−0.634565	+	0.756245i	0.348936	+	0.937146i	$0.386543\pi$
$978$		0			0
$979$	−25.6520	−	30.5708i	−0.819840	−	0.977047i
$980$	−8.43464	+	6.38217i	−0.269435	+	0.203871i
$981$		0			0
$982$	7.35611			0.234743
$983$	−10.8511	−	3.94948i	−0.346097	−	0.125969i	0.163122	−	0.986606i	$-0.447843\pi$
$983$	−10.8511	−	3.94948i	−0.346097	−	0.125969i	−0.509219	+	0.860637i	$0.670066\pi$
$984$		0			0
$985$	0.779862	−	0.929403i	0.0248485	−	0.0296132i
$986$	−116.234	+	42.3058i	−3.70165	+	1.34729i
$987$		0			0
$988$	−3.17749	−	18.0205i	−0.101090	−	0.573307i
$989$		−	15.5143i		−	0.493325i
$990$		0			0
$991$	−14.5997			−0.463776			−0.231888	−	0.972742i	$-0.574490\pi$
$991$	−14.5997			−0.463776			−0.231888	+	0.972742i	$0.574490\pi$
$992$	−8.47376	−	3.08419i	−0.269042	−	0.0979233i
$993$		0			0
$994$	−20.1803	+	51.3797i	−0.640080	+	1.62967i
$995$	−0.966797	+	1.15218i	−0.0306495	+	0.0365267i
$996$		0			0
$997$	25.7659	+	30.7067i	0.816016	+	0.972490i	0.999945	−	0.0104498i	$-0.00332634\pi$
$997$	25.7659	+	30.7067i	0.816016	+	0.972490i	−0.183930	+	0.982939i	$0.558882\pi$
$998$	−23.0225	−	13.2921i	−0.728766	−	0.420753i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.2		132
3.2	odd	2		189.2.bd.a.185.21	yes	132
7.5	odd	6		567.2.ba.a.341.21		132
21.5	even	6		189.2.ba.a.131.2	yes	132
27.7	even	9		189.2.ba.a.101.2	✓	132
27.20	odd	18		567.2.ba.a.143.21		132
189.47	even	18	inner	567.2.bd.a.467.2		132
189.61	odd	18		189.2.bd.a.47.21	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.2	✓	132	27.7	even	9
189.2.ba.a.131.2	yes	132	21.5	even	6
189.2.bd.a.47.21	yes	132	189.61	odd	18
189.2.bd.a.185.21	yes	132	3.2	odd	2
567.2.ba.a.143.21		132	27.20	odd	18
567.2.ba.a.341.21		132	7.5	odd	6
567.2.bd.a.17.2		132	1.1	even	1	trivial
567.2.bd.a.467.2		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)

\(f(q)\)	\(=\)	\(q+(-2.45739 + 0.433304i) q^{2} +(3.97163 - 1.44555i) q^{4} +(0.335948 - 0.122275i) q^{5} +(0.0666399 - 2.64491i) q^{7} +(-4.81149 + 2.77792i) q^{8} +O(q^{10})\)	\(q+(-2.45739 + 0.433304i) q^{2} +(3.97163 - 1.44555i) q^{4} +(0.335948 - 0.122275i) q^{5} +(0.0666399 - 2.64491i) q^{7} +(-4.81149 + 2.77792i) q^{8} +(-0.772573 + 0.446045i) q^{10} +(1.17753 - 3.23525i) q^{11} +(0.362359 + 0.995572i) q^{13} +(0.982291 + 6.52846i) q^{14} +(4.14463 - 3.47775i) q^{16} +(-2.91185 - 5.04347i) q^{17} +(-3.53896 - 2.04322i) q^{19} +(1.15751 - 0.971262i) q^{20} +(-1.49181 + 8.46049i) q^{22} +(2.12375 + 0.374475i) q^{23} +(-3.73231 + 3.13178i) q^{25} +(-1.32184 - 2.28950i) q^{26} +(-3.55870 - 10.6009i) q^{28} +(-2.91124 + 7.99857i) q^{29} +(1.29102 + 3.54704i) q^{31} +(-1.53560 + 1.83005i) q^{32} +(9.34090 + 11.1321i) q^{34} +(-0.301019 - 0.896701i) q^{35} -1.87406 q^{37} +(9.58194 + 3.48754i) q^{38} +(-1.27674 + 1.52156i) q^{40} +(4.24450 - 1.54487i) q^{41} +(-1.24925 - 7.08485i) q^{43} -14.5514i q^{44} -5.38115 q^{46} +(-11.5236 - 4.19426i) q^{47} +(-6.99112 - 0.352513i) q^{49} +(7.81473 - 9.31324i) q^{50} +(2.87831 + 3.43023i) q^{52} +(-7.91413 - 4.56923i) q^{53} -1.23086i q^{55} +(7.02671 + 12.9111i) q^{56} +(3.68824 - 20.9171i) q^{58} +(3.15921 + 2.65089i) q^{59} +(4.54625 - 12.4907i) q^{61} +(-4.70948 - 8.15705i) q^{62} +(-2.42983 + 4.20859i) q^{64} +(0.243467 + 0.290153i) q^{65} +(0.801200 - 4.54383i) q^{67} +(-18.8554 - 15.8215i) q^{68} +(1.12827 + 2.07311i) q^{70} +(7.24109 + 4.18065i) q^{71} -7.45113i q^{73} +(4.60530 - 0.812039i) q^{74} +(-17.0090 - 2.99915i) q^{76} +(-8.47847 - 3.33007i) q^{77} +(-2.32947 - 13.2111i) q^{79} +(0.967136 - 1.67513i) q^{80} +(-9.76098 + 5.63551i) q^{82} +(3.80912 + 1.38640i) q^{83} +(-1.59492 - 1.33830i) q^{85} +(6.13979 + 16.8689i) q^{86} +(3.32155 + 18.8375i) q^{88} +(5.79564 - 10.0383i) q^{89} +(2.65735 - 0.892062i) q^{91} +(8.97607 - 1.58272i) q^{92} +(30.1354 + 5.31369i) q^{94} +(-1.43874 - 0.253689i) q^{95} +(-4.45675 + 0.785845i) q^{97} +(17.3327 - 2.16302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 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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