LMFDB - Embedded newform 189.2.bd.a.185.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.21
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.45739 - 0.433304i) q^{2} +(-1.54842 - 0.776137i) q^{3} +(3.97163 - 1.44555i) q^{4} +(-0.335948 + 0.122275i) q^{5} +(-4.14138 - 1.23633i) q^{6} +(0.0666399 - 2.64491i) q^{7} +(4.81149 - 2.77792i) q^{8} +(1.79522 + 2.40358i) q^{9} +O(q^{10})$	\(q+(2.45739 - 0.433304i) q^{2} +(-1.54842 - 0.776137i) q^{3} +(3.97163 - 1.44555i) q^{4} +(-0.335948 + 0.122275i) q^{5} +(-4.14138 - 1.23633i) q^{6} +(0.0666399 - 2.64491i) q^{7} +(4.81149 - 2.77792i) q^{8} +(1.79522 + 2.40358i) q^{9} +(-0.772573 + 0.446045i) q^{10} +(-1.17753 + 3.23525i) q^{11} +(-7.27171 - 0.844201i) q^{12} +(0.362359 + 0.995572i) q^{13} +(-0.982291 - 6.52846i) q^{14} +(0.615091 + 0.0714084i) q^{15} +(4.14463 - 3.47775i) q^{16} +(2.91185 + 5.04347i) q^{17} +(5.45304 + 5.12865i) q^{18} +(-3.53896 - 2.04322i) q^{19} +(-1.15751 + 0.971262i) q^{20} +(-2.15600 + 4.04372i) q^{21} +(-1.49181 + 8.46049i) q^{22} +(-2.12375 - 0.374475i) q^{23} +(-9.60626 + 0.567008i) q^{24} +(-3.73231 + 3.13178i) q^{25} +(1.32184 + 2.28950i) q^{26} +(-0.914255 - 5.11509i) q^{27} +(-3.55870 - 10.6009i) q^{28} +(2.91124 - 7.99857i) q^{29} +(1.54246 - 0.0910435i) q^{30} +(1.29102 + 3.54704i) q^{31} +(1.53560 - 1.83005i) q^{32} +(4.33431 - 4.09560i) q^{33} +(9.34090 + 11.1321i) q^{34} +(0.301019 + 0.896701i) q^{35} +(10.6045 + 6.95102i) q^{36} -1.87406 q^{37} +(-9.58194 - 3.48754i) q^{38} +(0.211617 - 1.82281i) q^{39} +(-1.27674 + 1.52156i) q^{40} +(-4.24450 + 1.54487i) q^{41} +(-3.54598 + 10.8712i) q^{42} +(-1.24925 - 7.08485i) q^{43} +14.5514i q^{44} +(-0.896998 - 0.587966i) q^{45} -5.38115 q^{46} +(11.5236 + 4.19426i) q^{47} +(-9.11684 + 2.16823i) q^{48} +(-6.99112 - 0.352513i) q^{49} +(-7.81473 + 9.31324i) q^{50} +(-0.594345 - 10.0694i) q^{51} +(2.87831 + 3.43023i) q^{52} +(7.91413 + 4.56923i) q^{53} +(-4.46307 - 12.1736i) q^{54} -1.23086i q^{55} +(-7.02671 - 12.9111i) q^{56} +(3.89398 + 5.91048i) q^{57} +(3.68824 - 20.9171i) q^{58} +(-3.15921 - 2.65089i) q^{59} +(2.54614 - 0.605541i) q^{60} +(4.54625 - 12.4907i) q^{61} +(4.70948 + 8.15705i) q^{62} +(6.47688 - 4.58803i) q^{63} +(-2.42983 + 4.20859i) q^{64} +(-0.243467 - 0.290153i) q^{65} +(8.87646 - 11.9426i) q^{66} +(0.801200 - 4.54383i) q^{67} +(18.8554 + 15.8215i) q^{68} +(2.99782 + 2.22817i) q^{69} +(1.12827 + 2.07311i) q^{70} +(-7.24109 - 4.18065i) q^{71} +(15.3146 + 6.57781i) q^{72} -7.45113i q^{73} +(-4.60530 + 0.812039i) q^{74} +(8.20989 - 1.95253i) q^{75} +(-17.0090 - 2.99915i) q^{76} +(8.47847 + 3.33007i) q^{77} +(-0.269805 - 4.57104i) q^{78} +(-2.32947 - 13.2111i) q^{79} +(-0.967136 + 1.67513i) q^{80} +(-2.55436 + 8.62990i) q^{81} +(-9.76098 + 5.63551i) q^{82} +(-3.80912 - 1.38640i) q^{83} +(-2.71742 + 19.1768i) q^{84} +(-1.59492 - 1.33830i) q^{85} +(-6.13979 - 16.8689i) q^{86} +(-10.7158 + 10.1256i) q^{87} +(3.32155 + 18.8375i) q^{88} +(-5.79564 + 10.0383i) q^{89} +(-2.45904 - 1.05619i) q^{90} +(2.65735 - 0.892062i) q^{91} +(-8.97607 + 1.58272i) q^{92} +(0.753951 - 6.49432i) q^{93} +(30.1354 + 5.31369i) q^{94} +(1.43874 + 0.253689i) q^{95} +(-3.79813 + 1.64186i) q^{96} +(-4.45675 + 0.785845i) q^{97} +(-17.3327 + 2.16302i) q^{98} +(-9.89010 + 2.97769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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	0.787059	−	0.616878i	$-0.211603\pi$
$2$	2.45739	−	0.433304i	1.73764	−	0.306392i	0.950578	+	0.310485i	$0.100492\pi$
$3$	−1.54842	−	0.776137i	−0.893982	−	0.448103i
$3$	−1.54842	−	0.776137i	−0.893982	−	0.448103i
$4$	3.97163	−	1.44555i	1.98581	−	0.722777i
$5$	−0.335948	+	0.122275i	−0.150240	+	0.0546831i	−0.416046	−	0.909344i	$-0.636584\pi$
$5$	−0.335948	+	0.122275i	−0.150240	+	0.0546831i	0.265805	+	0.964027i	$0.414362\pi$
$6$	−4.14138	−	1.23633i	−1.69071	−	0.504731i
$7$	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
$9$	1.79522	+	2.40358i	0.598407	+	0.801192i
$10$	−0.772573	+	0.446045i	−0.244309	+	0.141052i
$11$	−1.17753	+	3.23525i	−0.355040	+	0.975464i	0.625686	+	0.780075i	$0.284819\pi$
$11$	−1.17753	+	3.23525i	−0.355040	+	0.975464i	−0.980726	+	0.195389i	$0.937403\pi$
$12$	−7.27171	−	0.844201i	−2.09916	−	0.243700i
$13$	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
$15$	0.615091	+	0.0714084i	0.158816	+	0.0184376i
$16$	4.14463	−	3.47775i	1.03616	−	0.869438i
$17$	2.91185	+	5.04347i	0.706227	+	1.22322i	0.966247	+	0.257618i	$0.0829375\pi$
$17$	2.91185	+	5.04347i	0.706227	+	1.22322i	−0.260020	+	0.965603i	$0.583729\pi$
$18$	5.45304	+	5.12865i	1.28529	+	1.20883i
$19$	−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
$21$	−2.15600	+	4.04372i	−0.470478	+	0.882412i
$22$	−1.49181	+	8.46049i	−0.318056	+	1.80378i
$23$	−2.12375	−	0.374475i	−0.442833	−	0.0780834i	−0.0522140	−	0.998636i	$-0.516628\pi$
$23$	−2.12375	−	0.374475i	−0.442833	−	0.0780834i	−0.390619	+	0.920553i	$0.627739\pi$
$24$	−9.60626	+	0.567008i	−1.96087	+	0.115740i
$25$	−3.73231	+	3.13178i	−0.746462	+	0.626356i
$26$	1.32184	+	2.28950i	0.259235	+	0.449008i
$27$	−0.914255	−	5.11509i	−0.175948	−	0.984399i
$28$	−3.55870	−	10.6009i	−0.672530	−	2.00339i
$29$	2.91124	−	7.99857i	0.540604	−	1.48530i	−0.305455	−	0.952207i	$-0.598808\pi$
$29$	2.91124	−	7.99857i	0.540604	−	1.48530i	0.846058	−	0.533090i	$-0.178969\pi$
$30$	1.54246	−	0.0910435i	0.281614	−	0.0166222i
$31$	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
$33$	4.33431	−	4.09560i	0.754507	−	0.712952i
$34$	9.34090	+	11.1321i	1.60195	+	1.90913i
$35$	0.301019	+	0.896701i	0.0508815	+	0.151570i
$36$	10.6045	+	6.95102i	1.76741	+	1.15850i
$37$	−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
$39$	0.211617	−	1.82281i	0.0338858	−	0.291883i
$40$	−1.27674	+	1.52156i	−0.201870	+	0.240580i
$41$	−4.24450	+	1.54487i	−0.662879	+	0.241268i	−0.651479	−	0.758667i	$-0.725851\pi$
$41$	−4.24450	+	1.54487i	−0.662879	+	0.241268i	−0.0114001	+	0.999935i	$0.503629\pi$
$42$	−3.54598	+	10.8712i	−0.547156	+	1.67746i
$43$	−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
$45$	−0.896998	−	0.587966i	−0.133717	−	0.0876487i
$46$	−5.38115			−0.793407
$47$	11.5236	+	4.19426i	1.68089	+	0.611795i	0.993432	−	0.114425i	$-0.0365024\pi$
$47$	11.5236	+	4.19426i	1.68089	+	0.611795i	0.687462	+	0.726220i	$0.258725\pi$
$48$	−9.11684	+	2.16823i	−1.31590	+	0.312957i
$49$	−6.99112	−	0.352513i	−0.998731	−	0.0503590i
$50$	−7.81473	+	9.31324i	−1.10517	+	1.31709i
$51$	−0.594345	−	10.0694i	−0.0832250	−	1.41000i
$52$	2.87831	+	3.43023i	0.399150	+	0.475688i
$53$	7.91413	+	4.56923i	1.08709	+	0.627631i	0.932800	−	0.360394i	$-0.117358\pi$
$53$	7.91413	+	4.56923i	1.08709	+	0.627631i	0.154289	+	0.988026i	$0.450691\pi$
$54$	−4.46307	−	12.1736i	−0.607347	−	1.65662i
$55$		−	1.23086i		−	0.165969i
$56$	−7.02671	−	12.9111i	−0.938983	−	1.72532i
$57$	3.89398	+	5.91048i	0.515771	+	0.782862i
$58$	3.68824	−	20.9171i	0.484290	−	2.74654i
$59$	−3.15921	−	2.65089i	−0.411294	−	0.345117i	0.413546	−	0.910483i	$-0.364290\pi$
$59$	−3.15921	−	2.65089i	−0.411294	−	0.345117i	−0.824840	+	0.565367i	$0.808735\pi$
$60$	2.54614	−	0.605541i	0.328705	−	0.0781750i
$61$	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
$63$	6.47688	−	4.58803i	0.816010	−	0.578037i
$64$	−2.42983	+	4.20859i	−0.303729	+	0.526074i
$65$	−0.243467	−	0.290153i	−0.0301984	−	0.0359891i
$66$	8.87646	−	11.9426i	1.09262	−	1.47003i
$67$	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
$69$	2.99782	+	2.22817i	0.360895	+	0.268240i
$70$	1.12827	+	2.07311i	0.134854	+	0.247784i
$71$	−7.24109	−	4.18065i	−0.859359	−	0.496151i	0.00443842	−	0.999990i	$-0.498587\pi$
$71$	−7.24109	−	4.18065i	−0.859359	−	0.496151i	−0.863798	+	0.503839i	$0.831921\pi$
$72$	15.3146	+	6.57781i	1.80485	+	0.775203i
$73$		−	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
$75$	8.20989	−	1.95253i	0.947996	−	0.225459i
$76$	−17.0090	−	2.99915i	−1.95107	−	0.344026i
$77$	8.47847	+	3.33007i	0.966212	+	0.379497i
$78$	−0.269805	−	4.57104i	−0.0305494	−	0.517568i
$79$	−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
$81$	−2.55436	+	8.62990i	−0.283818	+	0.958878i
$82$	−9.76098	+	5.63551i	−1.07792	+	0.622338i
$83$	−3.80912	−	1.38640i	−0.418105	−	0.152178i	0.124397	−	0.992233i	$-0.460300\pi$
$83$	−3.80912	−	1.38640i	−0.418105	−	0.152178i	−0.542501	+	0.840055i	$0.682523\pi$
$84$	−2.71742	+	19.1768i	−0.296495	+	2.09236i
$85$	−1.59492	−	1.33830i	−0.172993	−	0.145159i
$86$	−6.13979	−	16.8689i	−0.662070	−	1.81902i
$87$	−10.7158	+	10.1256i	−1.14886	+	1.08558i
$88$	3.32155	+	18.8375i	0.354078	+	2.00808i
$89$	−5.79564	+	10.0383i	−0.614337	+	1.06406i	0.376164	+	0.926553i	$0.377243\pi$
$89$	−5.79564	+	10.0383i	−0.614337	+	1.06406i	−0.990501	+	0.137509i	$0.956090\pi$
$90$	−2.45904	−	1.05619i	−0.259206	−	0.111332i
$91$	2.65735	−	0.892062i	0.278566	−	0.0935135i
$92$	−8.97607	+	1.58272i	−0.935820	+	0.165010i
$93$	0.753951	−	6.49432i	0.0781811	−	0.673429i
$94$	30.1354	+	5.31369i	3.10823	+	0.548065i
$95$	1.43874	+	0.253689i	0.147612	+	0.0260279i
$96$	−3.79813	+	1.64186i	−0.387645	+	0.167572i
$97$	−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
$99$	−9.89010	+	2.97769i	−0.993992	+	0.299269i
$100$	−10.2962	+	17.8335i	−1.02962	+	1.78335i
$101$	−0.374432	−	2.12351i	−0.0372573	−	0.211297i	0.960496	−	0.278295i	$-0.0897691\pi$
$101$	−0.374432	−	2.12351i	−0.0372573	−	0.211297i	−0.997753	+	0.0669976i	$0.978658\pi$
$102$	−5.82366	−	24.4869i	−0.576628	−	2.42457i
$103$	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
$105$	0.229858	−	1.62210i	0.0224319	−	0.158301i
$106$	21.4280	+	7.79914i	2.08127	+	0.757520i
$107$	−4.17439	+	2.41009i	−0.403554	+	0.232992i	−0.688016	−	0.725695i	$-0.741518\pi$
$107$	−4.17439	+	2.41009i	−0.403554	+	0.232992i	0.284463	+	0.958687i	$0.408185\pi$
$108$	−11.0252	−	18.9936i	−1.06090	−	1.82766i
$109$	−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
$111$	2.90184	+	1.45453i	0.275430	+	0.138058i
$112$	−8.92216	−	11.1939i	−0.843064	−	1.05773i
$113$	12.4855	+	2.20154i	1.17454	+	0.207103i	0.726664	−	0.686993i	$-0.241070\pi$
$113$	12.4855	+	2.20154i	1.17454	+	0.207103i	0.447876	+	0.894096i	$0.352181\pi$
$114$	12.1301	+	12.8371i	1.13609	+	1.20230i
$115$	0.759259	−	0.133878i	0.0708012	−	0.0124842i
$116$		−	35.9757i		−	3.34026i
$117$	−1.74242	+	2.65823i	−0.161087	+	0.245753i
$118$	−8.91205	−	5.14538i	−0.820421	−	0.473670i
$119$	13.5336	−	7.36548i	1.24062	−	0.675193i
$120$	3.15787	−	1.36509i	0.288273	−	0.124615i
$121$	−0.653748	−	0.548560i	−0.0594317	−	0.0498691i
$122$	5.75963	−	32.6645i	0.521453	−	2.95731i
$123$	7.77130	+	0.902201i	0.700715	+	0.0813487i
$124$	10.2549	+	12.2213i	0.920915	+	1.09750i
$125$	1.76469	−	3.05654i	0.157839	−	0.273385i
$126$	13.9282	−	14.0810i	1.24082	−	1.25444i
$127$	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
$129$	−3.56445	+	11.9399i	−0.313832	+	1.05125i
$130$	−0.724019	−	0.607524i	−0.0635006	−	0.0532834i
$131$	1.24502	−	7.06084i	0.108778	−	0.616909i	−0.880866	−	0.473365i	$-0.843039\pi$
$131$	1.24502	−	7.06084i	0.108778	−	0.616909i	0.989644	−	0.143544i	$-0.0458498\pi$
$132$	11.2939	−	22.5317i	0.983006	−	1.96113i
$133$	−5.63997	+	9.22407i	−0.489047	+	0.799829i
$134$		−	11.5131i		−	0.994582i
$135$	0.932590	+	1.60661i	0.0802646	+	0.138275i
$136$	28.0207	+	16.1777i	2.40275	+	1.38723i
$137$	2.39389	+	2.85292i	0.204523	+	0.243742i	0.858550	−	0.512730i	$-0.171366\pi$
$137$	2.39389	+	2.85292i	0.204523	+	0.243742i	−0.654026	+	0.756472i	$0.726921\pi$
$138$	8.33229	+	4.17651i	0.709291	+	0.355528i
$139$	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
$141$	−14.5881	−	15.4384i	−1.22854	−	1.30015i
$142$	−19.6057	−	7.13588i	−1.64527	−	0.598830i
$143$	−3.64761			−0.305029
$144$	15.7996	+	3.71859i	1.31663	+	0.309882i
$145$			3.04307i			0.252714i
$146$	−3.22861	−	18.3103i	−0.267201	−	1.51537i
$147$	10.5516	+	5.97191i	0.870282	+	0.492555i
$148$	−7.44308	+	2.70906i	−0.611817	+	0.222683i
$149$	−6.06042	+	7.22253i	−0.496489	+	0.591693i	−0.954856	−	0.297071i	$-0.903990\pi$
$149$	−6.06042	+	7.22253i	−0.496489	+	0.591693i	0.458366	+	0.888763i	$0.348435\pi$
$150$	19.3289	−	8.35551i	1.57819	−	0.682225i
$151$	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
$153$	−6.89495	+	16.0530i	−0.557424	+	1.29781i
$154$	22.2778	+	4.50952i	1.79520	+	0.363388i
$155$	−0.867429	−	1.03376i	−0.0696735	−	0.0830337i
$156$	−1.79450	−	7.54541i	−0.143675	−	0.604117i
$157$	−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
$159$	−8.70807	−	13.2175i	−0.690595	−	1.04822i
$160$	−0.292111	+	0.802568i	−0.0230934	+	0.0634486i
$161$	−1.13198	+	5.59218i	−0.0892124	+	0.440726i
$162$	−2.53768	+	22.3139i	−0.199379	+	1.75314i
$163$	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
$165$	−0.955314	+	1.90589i	−0.0743711	+	0.148373i
$166$	−9.96122	−	1.75643i	−0.773140	−	0.136326i
$167$	−2.87826	+	16.3234i	−0.222726	+	1.26314i	0.644259	+	0.764808i	$0.277166\pi$
$167$	−2.87826	+	16.3234i	−0.222726	+	1.26314i	−0.866985	+	0.498335i	$0.833945\pi$
$168$	0.859526	+	25.4455i	0.0663139	+	1.96316i
$169$	9.09872	−	7.63473i	0.699901	−	0.587287i
$170$	−4.49923	−	2.59763i	−0.345075	−	0.199229i
$171$	−1.44218	−	12.1742i	−0.110286	−	0.930983i
$172$	−15.2031	−	26.3325i	−1.15922	−	2.00784i
$173$	2.48189	−	2.08255i	0.188695	−	0.158334i	−0.543547	−	0.839379i	$-0.682919\pi$
$173$	2.48189	−	2.08255i	0.188695	−	0.158334i	0.732241	+	0.681045i	$0.238474\pi$
$174$	−21.9455	+	29.5258i	−1.66368	+	2.23835i
$175$	8.03457	+	10.0803i	0.607356	+	0.762002i
$176$	6.37096	+	17.5041i	0.480229	+	1.31942i
$177$	2.83433	+	6.55668i	0.213042	+	0.492830i
$178$	−9.89249	+	27.1794i	−0.741474	+	2.03718i
$179$	4.43437	−	2.56018i	0.331440	−	0.191357i	−0.325040	−	0.945700i	$-0.605378\pi$
$179$	4.43437	−	2.56018i	0.331440	−	0.191357i	0.656480	+	0.754343i	$0.272044\pi$
$180$	−4.41248	−	1.03852i	−0.328887	−	0.0774068i
$181$	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
$183$	−16.7340	+	15.8124i	−1.23702	+	1.16889i
$184$	−11.2587	+	4.09782i	−0.830000	+	0.302095i
$185$	0.629587	−	0.229151i	0.0462882	−	0.0168475i
$186$	−0.961264	−	16.2858i	−0.0704833	−	1.19413i
$187$	−19.7457	+	3.48169i	−1.44395	+	0.254607i
$188$	51.8306			3.78014
$189$	−13.5899	+	2.07726i	−0.988519	+	0.151098i
$190$	3.64547			0.264470
$191$	−2.95620	+	0.521258i	−0.213903	+	0.0377169i	−0.279573	−	0.960125i	$-0.590193\pi$
$191$	−2.95620	+	0.521258i	−0.213903	+	0.0377169i	0.0656695	+	0.997841i	$0.479082\pi$
$192$	7.02885	−	4.63079i	0.507264	−	0.334199i
$193$	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
$195$	0.151792	+	0.638243i	0.0108700	+	0.0457056i
$196$	−28.2757	+	8.70599i	−2.01969	+	0.621857i
$197$	−2.93897	+	1.69681i	−0.209393	+	0.120893i	−0.601029	−	0.799227i	$-0.705242\pi$
$197$	−2.93897	+	1.69681i	−0.209393	+	0.120893i	0.391636	+	0.920120i	$0.371909\pi$
$198$	−23.0136	+	11.6028i	−1.63550	+	0.824573i
$199$	−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
$201$	−4.76723	+	6.41392i	−0.336255	+	0.452403i
$202$	−1.84025	−	5.05604i	−0.129479	−	0.355742i
$203$	−20.9615	−	8.23300i	−1.47121	−	0.577843i
$204$	−16.9164	−	39.1328i	−1.18439	−	2.73984i
$205$	1.23703	−	1.03799i	0.0863980	−	0.0724965i
$206$	5.57279	+	9.65236i	0.388275	+	0.672512i
$207$	−2.91253	−	5.77686i	−0.202435	−	0.401520i
$208$	4.96420	+	2.86608i	0.344205	+	0.198727i
$209$	10.7776	−	9.04345i	0.745499	−	0.625548i
$210$	−0.138013	−	4.08574i	−0.00952377	−	0.281943i
$211$	−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
$213$	7.96751	+	12.0935i	0.545925	+	0.828632i
$214$	−9.21381	+	7.73130i	−0.629843	+	0.528501i
$215$	1.28598	+	2.22739i	0.0877033	+	0.151907i
$216$	−18.6082	−	22.0715i	−1.26613	−	1.50177i
$217$	9.46764	−	3.17825i	0.642705	−	0.215754i
$218$	−17.2233	+	47.3207i	−1.16651	+	3.20496i
$219$	−5.78310	+	11.5375i	−0.390786	+	0.779632i
$220$	−1.77927	−	4.88851i	−0.119958	−	0.329583i
$221$	−3.96600	+	4.72650i	−0.266782	+	0.317939i
$222$	7.76120	+	2.31697i	0.520898	+	0.155505i
$223$	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
$225$	−14.2278	−	3.34866i	−0.948520	−	0.223244i
$226$	31.6358			2.10438
$227$	1.05435	+	0.383753i	0.0699799	+	0.0254706i	0.376773	−	0.926306i	$-0.377034\pi$
$227$	1.05435	+	0.383753i	0.0699799	+	0.0254706i	−0.306793	+	0.951776i	$0.599256\pi$
$228$	24.0094	+	17.8453i	1.59006	+	1.18183i
$229$	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
$231$	−10.5437	−	11.7368i	−0.693722	−	0.772225i
$232$	−8.21194	−	46.5722i	−0.539140	−	3.05762i
$233$		−	18.7681i		−	1.22954i	−0.788707	−	0.614769i	$-0.789249\pi$
$233$		−	18.7681i		−	1.22954i	0.788707	−	0.614769i	$-0.210751\pi$
$234$	−3.12998	+	7.28731i	−0.204613	+	0.476386i
$235$	−4.38419			−0.285993
$236$	−16.3792	−	5.96155i	−1.06620	−	0.388064i
$237$	−6.64662	+	22.2643i	−0.431744	+	1.44622i
$238$	30.0658	−	23.9640i	1.94887	−	1.55336i
$239$	8.01259	−	9.54904i	0.518292	−	0.617676i	−0.441884	−	0.897072i	$-0.645690\pi$
$239$	8.01259	−	9.54904i	0.518292	−	0.617676i	0.960176	+	0.279396i	$0.0901343\pi$
$240$	2.79766	−	1.84318i	0.180588	−	0.118976i
$241$	−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
$243$	10.6532	−	11.3802i	0.683404	−	0.730040i
$244$		−	56.1804i		−	3.59658i
$245$	2.39176	−	0.736413i	0.152804	−	0.0470477i
$246$	19.4881	−	1.15028i	1.24251	−	0.0733391i
$247$	0.751799	−	4.26367i	0.0478359	−	0.271291i
$248$	16.0651	+	13.4802i	1.02013	+	0.855994i
$249$	4.82208	+	5.10314i	0.305587	+	0.323398i
$250$	3.01213	−	8.27576i	0.190504	−	0.523405i
$251$	−4.73924	−	8.20860i	−0.299138	−	0.518122i	0.676801	−	0.736166i	$-0.263366\pi$
$251$	−4.73924	−	8.20860i	−0.299138	−	0.518122i	−0.975939	+	0.218044i	$0.930032\pi$
$252$	19.0915	−	27.5846i	1.20265	−	1.73767i
$253$	3.71231	−	6.42990i	0.233391	−	0.404245i
$254$	11.9375	+	14.2265i	0.749023	+	0.892651i
$255$	1.43091	+	3.31012i	0.0896068	+	0.207288i
$256$	−5.63694	+	31.9687i	−0.352309	+	1.99804i
$257$	12.2968	+	10.3182i	0.767053	+	0.643634i	0.939952	−	0.341306i	$-0.110869\pi$
$257$	12.2968	+	10.3182i	0.767053	+	0.643634i	−0.172900	+	0.984939i	$0.555314\pi$
$258$	−3.58562	+	30.8855i	−0.223231	+	1.92285i
$259$	−0.124887	+	4.95673i	−0.00776011	+	0.307996i
$260$	−1.38639	−	0.800435i	−0.0859805	−	0.0496409i
$261$	24.4515	−	7.36181i	1.51351	−	0.455685i
$262$		−	17.8907i		−	1.10529i
$263$	−13.1434	+	2.31754i	−0.810459	+	0.142906i	−0.563496	−	0.826119i	$-0.690544\pi$
$263$	−13.1434	+	2.31754i	−0.810459	+	0.142906i	−0.246963	+	0.969025i	$0.579433\pi$
$264$	9.47729	−	31.7463i	0.583287	−	1.95385i
$265$	−3.21744	−	0.567321i	−0.197646	−	0.0348503i
$266$	−9.86277	+	25.1110i	−0.604725	+	1.53965i
$267$	16.7652	−	11.0454i	1.02602	−	0.675966i
$268$	−3.38629	−	19.2046i	−0.206850	−	1.17311i
$269$	−12.4472	+	21.5591i	−0.758916	+	1.31448i	0.184487	+	0.982835i	$0.440938\pi$
$269$	−12.4472	+	21.5591i	−0.758916	+	1.31448i	−0.943404	+	0.331647i	$0.892396\pi$
$270$	2.98789	+	3.54398i	0.181837	+	0.215680i
$271$	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
$273$	−4.80706	−	0.681179i	−0.290936	−	0.0412268i
$274$	7.11889	+	5.97346i	0.430068	+	0.360870i
$275$	−5.73716	−	15.7627i	−0.345964	−	0.950528i
$276$	15.1272	+	4.51594i	0.910548	+	0.271828i
$277$	−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
$279$	−6.20792	+	9.47078i	−0.371658	+	0.567001i
$280$	3.93931	+	3.47826i	0.235419	+	0.207866i
$281$	11.7861	−	2.07821i	0.703099	−	0.123975i	0.189342	−	0.981911i	$-0.439364\pi$
$281$	11.7861	−	2.07821i	0.703099	−	0.123975i	0.513757	+	0.857936i	$0.328253\pi$
$282$	−42.5382	−	31.6171i	−2.53311	−	1.88277i
$283$	−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
$285$	−2.03088	−	1.50948i	−0.120299	−	0.0894137i
$286$	−8.96361	+	1.58053i	−0.530029	+	0.0934584i
$287$	3.80319	+	11.3293i	0.224495	+	0.668746i
$288$	7.15541	+	0.405574i	0.421637	+	0.0238987i
$289$	−8.45772	+	14.6492i	−0.497513	+	0.861717i
$290$	1.31858	+	7.47802i	0.0774295	+	0.439125i
$291$	7.51086	+	2.24223i	0.440294	+	0.131442i
$292$	−10.7710	−	29.5931i	−0.630326	−	1.73181i
$293$	−17.6180	−	14.7833i	−1.02926	−	0.863649i	−0.0384944	−	0.999259i	$-0.512256\pi$
$293$	−17.6180	−	14.7833i	−1.02926	−	0.863649i	−0.990762	+	0.135610i	$0.956701\pi$
$294$	28.5171	+	10.1033i	1.66315	+	0.589234i
$295$	1.38547	+	0.504269i	0.0806650	+	0.0293597i
$296$	−9.01703	+	5.20598i	−0.524104	+	0.302592i
$297$	17.6251	+	3.06535i	1.02271	+	0.177870i
$298$	−11.7633	+	20.3746i	−0.681428	+	1.18027i
$299$	−0.396743	−	2.25004i	−0.0229442	−	0.130123i
$300$	29.7841	−	19.6226i	1.71959	−	1.13291i
$301$	−18.8220	+	2.83202i	−1.08488	+	0.163235i
$302$	11.3569	+	2.00252i	0.653513	+	0.115232i
$303$	−1.06836	+	3.57870i	−0.0613754	+	0.205591i
$304$	−21.7735	+	3.83925i	−1.24879	+	0.220196i
$305$			4.75213i			0.272106i
$306$	−9.98775	+	42.4361i	−0.570962	+	2.42591i
$307$	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
$309$	0.892161	−	7.68482i	0.0507533	−	0.437174i
$310$	−2.57954	−	2.16449i	−0.146508	−	0.122935i
$311$	−1.67256	+	9.48554i	−0.0948420	+	0.537876i	0.899954	+	0.435985i	$0.143600\pi$
$311$	−1.67256	+	9.48554i	−0.0948420	+	0.537876i	−0.994796	+	0.101890i	$0.967511\pi$
$312$	−4.04541	−	9.35827i	−0.229026	−	0.529808i
$313$	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
$315$	−1.61489	+	2.33330i	−0.0909889	+	0.131467i
$316$	−28.3492	−	49.1022i	−1.59477	−	2.76221i
$317$	1.50889	−	4.14565i	0.0847479	−	0.232843i	−0.890079	−	0.455807i	$-0.849351\pi$
$317$	1.50889	−	4.14565i	0.0847479	−	0.232843i	0.974827	+	0.222964i	$0.0715731\pi$
$318$	−27.1263	−	28.7074i	−1.52117	−	1.60983i
$319$	22.4493	+	18.8372i	1.25692	+	1.05468i
$320$	0.301691	−	1.71098i	0.0168650	−	0.0956464i
$321$	8.33428	−	0.491929i	0.465174	−	0.0274568i
$322$	−0.358599	+	14.2327i	−0.0199839	+	0.793155i
$323$		−	23.7982i		−	1.32417i
$324$	2.33003	+	37.9672i	0.129446	+	2.10929i
$325$	−4.47035	−	2.58096i	−0.247970	−	0.143166i
$326$	11.3278	+	13.5000i	0.627391	+	0.747696i
$327$	29.1891	−	19.2306i	1.61416	−	1.06345i
$328$	−16.1308	+	19.2240i	−0.890676	+	1.06147i
$329$	11.8614	−	30.1995i	0.653939	−	1.66495i
$330$	−1.52175	+	5.09745i	−0.0837697	+	0.280605i
$331$	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
$333$	−3.36436	−	4.50445i	−0.184366	−	0.246842i
$334$			41.3601i			2.26312i
$335$	0.286436	+	1.62446i	0.0156496	+	0.0887535i
$336$	5.12724	+	24.2577i	0.279714	+	1.32337i
$337$	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
$339$	−17.6242	−	13.0994i	−0.957214	−	0.711461i
$340$	−8.26901	−	3.00967i	−0.448450	−	0.163222i
$341$	−12.9958			−0.703760
$342$	−8.81913	−	29.2918i	−0.476884	−	1.58392i
$343$	−1.39825	+	18.4674i	−0.0754986	+	0.997146i
$344$	−25.6919	−	30.6184i	−1.38521	−	1.65083i
$345$	−1.27956	−	0.381990i	−0.0688892	−	0.0205656i
$346$	5.19659	−	6.19306i	0.279371	−	0.332941i
$347$	6.11295	+	16.7952i	0.328161	+	0.901614i	0.988577	+	0.150715i	$0.0481574\pi$
$347$	6.11295	+	16.7952i	0.328161	+	0.901614i	−0.660417	+	0.750899i	$0.729620\pi$
$348$	−27.9221	+	55.7056i	−1.49678	+	2.98613i
$349$	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
$351$	4.76115	−	2.76370i	0.254132	−	0.147516i
$352$	4.11246	+	7.12299i	0.219195	+	0.379657i
$353$	12.4457	−	10.4432i	0.662419	−	0.555835i	−0.248392	−	0.968660i	$-0.579902\pi$
$353$	12.4457	−	10.4432i	0.662419	−	0.555835i	0.910811	+	0.412824i	$0.135458\pi$
$354$	9.80610	+	14.8842i	0.521188	+	0.791086i
$355$	2.94382	+	0.519074i	0.156242	+	0.0275496i
$356$	−8.50716	+	48.2465i	−0.450878	+	2.55706i
$357$	−26.6723	+	0.900966i	−1.41165	+	0.0476842i
$358$	9.78764	−	8.21280i	0.517293	−	0.434060i
$359$	−15.1773	−	8.76262i	−0.801027	−	0.462473i	0.0428030	−	0.999084i	$-0.486371\pi$
$359$	−15.1773	−	8.76262i	−0.801027	−	0.462473i	−0.843830	+	0.536610i	$0.819705\pi$
$360$	−5.94922	−	0.337206i	−0.313551	−	0.0177723i
$361$	−1.15052	−	1.99275i	−0.0605535	−	0.104882i
$362$	7.95769	−	6.67729i	0.418247	−	0.350951i
$363$	0.586520	+	1.35680i	0.0307843	+	0.0712136i
$364$	9.26448	−	7.38428i	0.485591	−	0.387042i
$365$	0.911088	+	2.50319i	0.0476885	+	0.131023i
$366$	−34.2705	+	46.1082i	−1.79135	+	2.41011i
$367$	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
$369$	−11.3330	−	7.42859i	−0.589974	−	0.386717i
$370$	1.44785	−	0.835916i	0.0752701	−	0.0434572i
$371$	12.6126	−	20.6277i	0.654813	−	1.07094i
$372$	−6.39348	−	26.8829i	−0.331486	−	1.39381i
$373$	−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
$375$	−5.10479	+	3.36317i	−0.263610	+	0.173673i
$376$	67.0971	−	11.8310i	3.46027	−	0.610139i
$377$	9.01807			0.464454
$378$	−32.4956	+	10.9932i	−1.67139	+	0.565428i
$379$	−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
$381$	−0.759560	−	12.8685i	−0.0389134	−	0.659272i
$382$	−7.03868	+	2.56187i	−0.360130	+	0.131077i
$383$	−15.3981	+	5.60444i	−0.786804	+	0.286373i	−0.704007	−	0.710193i	$-0.748608\pi$
$383$	−15.3981	+	5.60444i	−0.786804	+	0.286373i	−0.0827973	+	0.996566i	$0.526385\pi$
$384$	21.2811	−	20.1091i	1.08600	−	1.02619i
$385$	−3.25551	−	0.0820242i	−0.165916	−	0.00418034i
$386$	35.7182	−	20.6219i	1.81801	−	1.04963i
$387$	14.7863	−	15.7215i	0.751629	−	0.799171i
$388$	−16.5646	+	9.56356i	−0.840939	+	0.485516i
$389$	5.33745	−	14.6645i	0.270619	−	0.743521i	−0.727718	−	0.685877i	$-0.759419\pi$
$389$	5.33745	−	14.6645i	0.270619	−	0.743521i	0.998337	−	0.0576441i	$-0.0183589\pi$
$390$	0.649564	+	1.50264i	0.0328920	+	0.0760892i
$391$	−4.29539	−	11.8015i	−0.217227	−	0.596827i
$392$	−34.6170	+	17.7246i	−1.74842	+	0.895229i
$393$	−7.40800	+	9.96686i	−0.373684	+	0.502762i
$394$	−6.48695	+	5.44320i	−0.326808	+	0.274224i
$395$	2.39797	+	4.15340i	0.120655	+	0.208980i
$396$	−34.9754	+	26.1230i	−1.75758	+	1.31273i
$397$	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
$399$	15.8922	−	9.90537i	0.795605	−	0.495889i
$400$	−4.57747	+	25.9601i	−0.228874	+	1.29801i
$401$	34.7683	+	6.13060i	1.73625	+	0.306147i	0.950113	−	0.311907i	$-0.100968\pi$
$401$	34.7683	+	6.13060i	1.73625	+	0.306147i	0.786136	+	0.618054i	$0.212079\pi$
$402$	−8.93577	+	17.8272i	−0.445675	+	0.889139i
$403$	−3.06352	+	2.57060i	−0.152605	+	0.128051i
$404$	−4.55675	−	7.89252i	−0.226707	−	0.392668i
$405$	−0.197090	−	3.21153i	−0.00979350	−	0.159582i
$406$	−55.0780	−	11.1490i	−2.73347	−	0.553315i
$407$	2.20677	−	6.06305i	0.109386	−	0.300534i
$408$	−30.8317	−	46.7978i	−1.52639	−	2.31684i
$409$	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
$411$	−1.49249	−	6.27551i	−0.0736189	−	0.309548i
$412$	12.1347	+	14.4616i	0.597836	+	0.712473i
$413$	−7.22190	+	8.17917i	−0.355367	+	0.402471i
$414$	−9.66035	−	12.9340i	−0.474780	−	0.635671i
$415$	1.44919			0.0711378
$416$	2.37839	+	0.865663i	0.116610	+	0.0424426i
$417$	−21.9709	+	9.49764i	−1.07592	+	0.465102i
$418$	22.5661	−	26.8932i	1.10374	−	1.31539i
$419$	−16.1147	+	5.86527i	−0.787254	+	0.286537i	−0.704194	−	0.710007i	$-0.748692\pi$
$419$	−16.1147	+	5.86527i	−0.787254	+	0.286537i	−0.0830600	+	0.996545i	$0.526469\pi$
$420$	−1.43193	−	6.77467i	−0.0698709	−	0.330570i
$421$	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
$423$	10.6062	+	35.2275i	0.515693	+	1.71282i
$424$	50.7717			2.46569
$425$	−26.6630	−	9.70453i	−1.29334	−	0.470739i
$426$	24.8194	+	26.2661i	1.20251	+	1.27259i
$427$	−32.7339	−	12.8568i	−1.58411	−	0.622185i
$428$	−13.0952	+	15.6063i	−0.632981	+	0.754358i
$429$	5.64804	+	2.83105i	0.272690	+	0.136684i
$430$	4.12530	+	4.91634i	0.198940	+	0.237087i
$431$	−10.4907	−	6.05678i	−0.505317	−	0.291745i	0.225590	−	0.974222i	$-0.427569\pi$
$431$	−10.4907	−	6.05678i	−0.505317	−	0.291745i	−0.730907	+	0.682478i	$0.760902\pi$
$432$	−21.5783	−	18.0206i	−1.03818	−	0.867015i
$433$		−	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
$435$	2.36184	−	4.71196i	0.113242	−	0.225921i
$436$	−14.8114	+	83.9995i	−0.709337	+	4.02285i
$437$	6.75073	+	5.66454i	0.322931	+	0.270972i
$438$	−9.21209	+	30.8580i	−0.440171	+	1.47445i
$439$	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
$441$	−11.7033	−	17.4365i	−0.557301	−	0.830311i
$442$	−7.69801	+	13.3333i	−0.366157	+	0.634202i
$443$	−0.133902	−	0.159578i	−0.00636188	−	0.00758180i	0.762854	−	0.646571i	$-0.223797\pi$
$443$	−0.133902	−	0.159578i	−0.00636188	−	0.00758180i	−0.769216	+	0.638989i	$0.779353\pi$
$444$	13.6276	+	1.58208i	0.646738	+	0.0750824i
$445$	0.719594	−	4.08102i	0.0341120	−	0.193459i
$446$	25.0168	+	20.9916i	1.18458	+	0.993980i
$447$	14.9898	−	6.47981i	0.708992	−	0.306484i
$448$	10.9694	+	6.70715i	0.518257	+	0.316883i
$449$	−11.7985	−	6.81187i	−0.556806	−	0.321472i	0.195057	−	0.980792i	$-0.437511\pi$
$449$	−11.7985	−	6.81187i	−0.556806	−	0.321472i	−0.751862	+	0.659320i	$0.770844\pi$
$450$	−36.4143	−	2.06399i	−1.71658	−	0.0972972i
$451$		−	15.5511i		−	0.732274i
$452$	52.7703	−	9.30483i	2.48211	−	0.437663i
$453$	−5.49768	−	5.81812i	−0.258304	−	0.273359i
$454$	2.75724	+	0.486176i	0.129404	+	0.0228174i
$455$	−0.783654	+	0.624614i	−0.0367383	+	0.0292823i
$456$	35.1547	+	17.6211i	1.64627	+	0.825183i
$457$	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
$459$	23.1356	−	19.5054i	1.07988	−	0.910433i
$460$	2.82197	−	1.62926i	0.131575	−	0.0759648i
$461$	−5.61005	−	2.04189i	−0.261286	−	0.0951003i	0.208056	−	0.978117i	$-0.433286\pi$
$461$	−5.61005	−	2.04189i	−0.261286	−	0.0951003i	−0.469342	+	0.883017i	$0.655509\pi$
$462$	−30.9955	−	24.2733i	−1.44204	−	1.12930i
$463$	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
$465$	0.540805	+	2.27394i	0.0250792	+	0.105452i
$466$	−8.13229	−	46.1205i	−0.376721	−	2.13649i
$467$	−7.94133	+	13.7548i	−0.367481	+	0.636495i	−0.989171	−	0.146768i	$-0.953113\pi$
$467$	−7.94133	+	13.7548i	−0.367481	+	0.636495i	0.621690	+	0.783263i	$0.286446\pi$
$468$	−3.07763	+	13.0763i	−0.142263	+	0.604451i
$469$	−11.9646	−	2.42190i	−0.552476	−	0.111833i
$470$	−10.7737	+	1.89969i	−0.496952	+	0.0876261i
$471$	1.85602	−	0.802326i	0.0855211	−	0.0369692i
$472$	−22.5645	−	3.97872i	−1.03861	−	0.183136i
$473$	24.3923	+	4.30101i	1.12156	+	0.197761i
$474$	−6.68610	+	57.5922i	−0.307103	+	2.64530i
$475$	19.6074	−	3.45732i	0.899650	−	0.158633i
$476$	43.1031	−	48.8165i	1.97563	−	2.23750i
$477$	3.22514	+	27.2250i	0.147669	+	1.24655i
$478$	15.5524	−	26.9376i	0.711352	−	1.23210i
$479$	1.86323	+	10.5669i	0.0851332	+	0.482814i	0.997328	+	0.0730570i	$0.0232755\pi$
$479$	1.86323	+	10.5669i	0.0851332	+	0.482814i	−0.912195	+	0.409757i	$0.865613\pi$
$480$	1.07521	−	1.01600i	0.0490766	−	0.0463737i
$481$	−0.679082	−	1.86576i	−0.0309635	−	0.0850715i
$482$	−39.3846	−	33.0476i	−1.79392	−	1.50528i
$483$	6.09308	−	7.78048i	0.277245	−	0.354024i
$484$	−3.38942	−	1.23365i	−0.154064	−	0.0560749i
$485$	1.40115	−	0.808953i	0.0636228	−	0.0367326i
$486$	21.2480	−	32.5817i	0.963830	−	1.47793i
$487$	−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
$489$	−0.720771	−	12.2113i	−0.0325944	−	0.552215i
$490$	5.55838	−	2.84601i	0.251102	−	0.128570i
$491$	2.90320	+	0.511913i	0.131020	+	0.0231023i	0.238773	−	0.971075i	$-0.423255\pi$
$491$	2.90320	+	0.511913i	0.131020	+	0.0231023i	−0.107754	+	0.994178i	$0.534366\pi$
$492$	32.1689	−	7.65064i	1.45029	−	0.344917i
$493$	48.8176	−	8.60786i	2.19863	−	0.387679i
$494$		−	10.8033i		−	0.486061i
$495$	2.95846	−	2.20966i	0.132973	−	0.0993169i
$496$	17.6865	+	10.2113i	0.794148	+	0.458501i
$497$	−11.5400	+	18.8734i	−0.517639	+	0.846590i
$498$	14.0609	+	10.4510i	0.630086	+	0.468319i
$499$	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
$501$	17.1260	−	23.0416i	0.765131	−	1.02942i
$502$	−15.2030	−	18.1182i	−0.678542	−	0.808655i
$503$	−8.22192	+	14.2408i	−0.366597	+	0.634965i	−0.989031	−	0.147707i	$-0.952811\pi$
$503$	−8.22192	+	14.2408i	−0.366597	+	0.634965i	0.622434	+	0.782672i	$0.286144\pi$
$504$	18.4183	−	40.0675i	0.820416	−	1.78475i
$505$	0.385441	+	0.667604i	0.0171519	+	0.0297080i
$506$	6.33648	−	17.4093i	0.281691	−	0.773939i
$507$	−20.0143	+	4.75993i	−0.888864	+	0.211396i
$508$	24.0968	+	20.2196i	1.06912	+	0.897099i
$509$	−2.53332	+	14.3672i	−0.112287	+	0.636813i	0.875770	+	0.482728i	$0.160354\pi$
$509$	−2.53332	+	14.3672i	−0.112287	+	0.636813i	−0.988058	+	0.154085i	$0.950757\pi$
$510$	4.95059	+	7.51425i	0.219216	+	0.332737i
$511$	−19.7076	−	0.496542i	−0.871813	−	0.0219657i
$512$			47.1935i			2.08568i
$513$	−7.21573	+	19.9701i	−0.318582	+	0.881702i
$514$	34.6889	+	20.0277i	1.53006	+	0.883383i
$515$	−1.02644	−	1.22326i	−0.0452304	−	0.0539035i
$516$	3.10314	+	52.5735i	0.136608	+	2.31442i
$517$	−27.1389	+	32.3429i	−1.19357	+	1.42244i
$518$	1.84087	+	12.2347i	0.0808834	+	0.537563i
$519$	−5.45936	+	1.29838i	−0.239639	+	0.0569927i
$520$	−1.97746	−	0.719737i	−0.0867174	−	0.0315626i
$521$	16.9489			0.742544			0.371272	−	0.928524i	$-0.378922\pi$
$521$	16.9489			0.742544			0.371272	+	0.928524i	$0.378922\pi$
$522$	56.8970	−	28.6858i	2.49031	−	1.25554i
$523$		−	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
$525$	−4.61717	−	21.8445i	−0.201510	−	0.953374i
$526$	−31.2944	+	11.3902i	−1.36450	+	0.496637i
$527$	−14.1301	+	16.8396i	−0.615518	+	0.733546i
$528$	3.72062	−	32.0484i	0.161919	−	1.39473i
$529$	−17.2428	−	6.27588i	−0.749689	−	0.272864i
$530$	−8.15232			−0.354114
$531$	0.700139	−	12.3523i	0.0303835	−	0.536046i
$532$	−9.06596	+	44.7875i	−0.393059	+	1.94178i
$533$	−3.07606	−	3.66591i	−0.133239	−	0.158788i
$534$	36.4127	−	34.4072i	1.57573	−	1.48895i
$535$	1.10768	−	1.32009i	0.0478894	−	0.0570723i
$536$	−8.76741	−	24.0883i	−0.378694	−	1.04045i
$537$	−8.85333	+	0.522566i	−0.382049	+	0.0225504i
$538$	−21.2459	+	58.3725i	−0.915974	+	2.51662i
$539$	9.37274	−	22.2029i	0.403713	−	0.956346i
$540$	6.02635	+	5.03276i	0.259333	+	0.216576i
$541$	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
$543$	−7.19806	+	0.424864i	−0.308899	+	0.0182327i
$544$	13.7012	+	2.41590i	0.587436	+	0.103581i
$545$	1.25285	−	7.10526i	0.0536662	−	0.304356i
$546$	−12.1080	+	0.408996i	−0.518174	+	0.0175034i
$547$	−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
$549$	38.1840	−	11.4964i	1.62965	−	0.490653i
$550$	−20.9285	−	36.2492i	−0.892395	−	1.54567i
$551$	−26.6456	+	22.3583i	−1.13514	+	0.952496i
$552$	20.6136	+	2.39312i	0.877375	+	0.101858i
$553$	−35.0974	+	5.28086i	−1.49249	+	0.224565i
$554$	−19.2447	−	52.8744i	−0.817630	−	2.24642i
$555$	−1.15272	−	0.133824i	−0.0489302	−	0.00568050i
$556$	19.9767	−	54.8855i	0.847201	−	2.32767i
$557$	16.4754	−	9.51210i	0.698087	−	0.403041i	−0.108548	−	0.994091i	$-0.534620\pi$
$557$	16.4754	−	9.51210i	0.698087	−	0.403041i	0.806634	+	0.591051i	$0.201287\pi$
$558$	−11.1515	+	25.9633i	−0.472083	+	1.09911i
$559$	6.60080	−	3.81097i	0.279184	−	0.161187i
$560$	4.36612	+	2.66962i	0.184502	+	0.112812i
$561$	33.2769	+	9.93422i	1.40495	+	0.419423i
$562$	28.0625	−	10.2139i	1.18375	−	0.430848i
$563$	−29.3667	+	10.6886i	−1.23766	+	0.450470i	−0.876213	−	0.481923i	$-0.839938\pi$
$563$	−29.3667	+	10.6886i	−1.23766	+	0.450470i	−0.361444	+	0.932394i	$0.617716\pi$
$564$	−80.2557	−	40.2277i	−3.37937	−	1.69389i
$565$	−4.46368	+	0.787067i	−0.187788	+	0.0331122i
$566$	−52.9570			−2.22595
$567$	22.6551	+	7.33115i	0.951425	+	0.307879i
$568$	−46.4539			−1.94916
$569$	−8.44284	+	1.48870i	−0.353942	+	0.0624095i	−0.347792	−	0.937572i	$-0.613069\pi$
$569$	−8.44284	+	1.48870i	−0.353942	+	0.0624095i	−0.00614965	+	0.999981i	$0.501958\pi$
$570$	−5.64473	−	2.82939i	−0.236432	−	0.118510i
$571$	−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
$573$	4.98202	+	1.48729i	0.208127	+	0.0621325i
$574$	14.2549	+	26.1925i	0.594990	+	1.09325i
$575$	9.09928	−	5.25347i	0.379466	−	0.219085i
$576$	−14.4778	+	1.71507i	−0.603240	+	0.0714612i
$577$	−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
$579$	−28.4374	−	3.30141i	−1.18182	−	0.137202i
$580$	4.39893	+	12.0860i	0.182656	+	0.501842i
$581$	−3.92076	+	9.98239i	−0.162660	+	0.414139i
$582$	19.4287	+	2.25555i	0.805344	+	0.0934956i
$583$	−24.1017	+	20.2238i	−0.998192	+	0.837582i
$584$	−20.6986	−	35.8511i	−0.856515	−	1.48353i
$585$	0.260327	−	1.10608i	0.0107632	−	0.0457308i
$586$	−49.7000	−	28.6943i	−2.05309	−	1.18535i
$587$	−23.8827	+	20.0400i	−0.985744	+	0.827138i	−0.984946	−	0.172862i	$-0.944699\pi$
$587$	−23.8827	+	20.0400i	−0.985744	+	0.827138i	−0.000798351		1.00000i	$0.500254\pi$
$588$	50.5398	+	8.46528i	2.08422	+	0.349102i
$589$	2.67852	−	15.1906i	0.110367	−	0.625920i
$590$	3.62314	+	0.638857i	0.149162	+	0.0263013i
$591$	5.86772	−	0.346341i	0.241366	−	0.0142466i
$592$	−7.76728	+	6.51752i	−0.319233	+	0.267869i
$593$	7.36449	+	12.7557i	0.302423	+	0.523812i	0.976684	−	0.214681i	$-0.0688711\pi$
$593$	7.36449	+	12.7557i	0.302423	+	0.523812i	−0.674261	+	0.738493i	$0.735538\pi$
$594$	44.6401	−	0.104292i	1.83160	−	0.00427916i
$595$	−3.64596	+	4.12924i	−0.149470	+	0.169282i
$596$	−13.6292	+	37.4459i	−0.558273	+	1.53384i
$597$	7.27423	−	0.429360i	0.297714	−	0.0175725i
$598$	−1.94991	−	5.35732i	−0.0797376	−	0.219077i
$599$	−9.25646	+	11.0314i	−0.378209	+	0.450732i	−0.921248	−	0.388976i	$-0.872829\pi$
$599$	−9.25646	+	11.0314i	−0.378209	+	0.450732i	0.543039	+	0.839707i	$0.317273\pi$
$600$	34.0778	−	32.2010i	1.39122	−	1.31460i
$601$	−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
$603$	12.3598	−	6.23144i	0.503329	−	0.253764i
$604$	19.5329			0.794782
$605$	0.286701	+	0.104350i	0.0116560	+	0.00424245i
$606$	−1.07470	+	9.25718i	−0.0436568	+	0.376047i
$607$	−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
$609$	26.0673	+	29.0172i	1.05630	+	1.17583i
$610$	2.05912	+	11.6778i	0.0833712	+	0.472822i
$611$			12.9924i			0.525618i
$612$	−4.17870	+	73.7235i	−0.168914	+	2.98010i
$613$	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
$615$	−2.72107	+	0.647144i	−0.109724	+	0.0260954i
$616$	50.0447	−	7.52988i	2.01636	−	0.303388i
$617$	20.2153	−	24.0916i	0.813837	−	0.969893i	−0.186083	−	0.982534i	$-0.559579\pi$
$617$	20.2153	−	24.0916i	0.813837	−	0.969893i	0.999920	+	0.0126410i	$0.00402388\pi$
$618$	−1.13748	−	19.2712i	−0.0457561	−	0.775201i
$619$	−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
$621$	0.0261794	+	11.2055i	0.00105054	+	0.449663i
$622$			24.0344i			0.963691i
$623$	26.1643	+	15.9979i	1.04825	+	0.640943i
$624$	−5.46220	−	8.29080i	−0.218663	−	0.331898i
$625$	4.01113	−	22.7482i	0.160445	−	0.909929i
$626$	20.5970	+	17.2830i	0.823223	+	0.690766i
$627$	−23.7072	+	5.63820i	−0.946773	+	0.225168i
$628$	−1.68756	+	4.63653i	−0.0673409	+	0.185018i
$629$	−5.45698	−	9.45177i	−0.217584	−	0.376867i
$630$	−2.95739	+	6.43357i	−0.117825	+	0.256319i
$631$	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
$633$	18.4879	−	24.8739i	0.734826	−	0.988650i
$634$	1.91161	−	10.8413i	0.0759198	−	0.430563i
$635$	−2.03827	−	1.71031i	−0.0808864	−	0.0678717i
$636$	−53.6919	−	39.9072i	−2.12902	−	1.58242i
$637$	−2.18234	−	7.08790i	−0.0864675	−	0.280833i
$638$	63.3288	+	36.5629i	2.50721	+	1.44754i
$639$	−2.95086	−	24.9097i	−0.116734	−	0.985412i
$640$		−	6.04341i		−	0.238887i
$641$	−24.1857	+	4.26458i	−0.955276	+	0.168441i	−0.629495	−	0.777004i	$-0.716738\pi$
$641$	−24.1857	+	4.26458i	−0.955276	+	0.168441i	−0.325781	+	0.945445i	$0.605627\pi$
$642$	20.2674	−	4.82014i	0.799891	−	0.190236i
$643$	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
$645$	−0.262485	−	4.44704i	−0.0103354	−	0.175102i
$646$	−10.3118	−	58.4814i	−0.405714	−	2.30092i
$647$	1.12029	−	1.94040i	0.0440432	−	0.0762851i	−0.843163	−	0.537657i	$-0.819309\pi$
$647$	1.12029	−	1.94040i	0.0440432	−	0.0762851i	0.887207	+	0.461372i	$0.152643\pi$
$648$	11.6829	+	48.6185i	0.458947	+	1.90992i
$649$	12.2964	−	7.09931i	0.482674	−	0.278672i
$650$	−12.1037	−	4.40540i	−0.474748	−	0.172794i
$651$	−17.1267	−	2.42691i	−0.671247	−	0.0951183i
$652$	22.8662	+	19.1870i	0.895509	+	0.751422i
$653$	−15.4956	−	42.5738i	−0.606389	−	1.66604i	−0.738051	−	0.674745i	$-0.764254\pi$
$653$	−15.4956	−	42.5738i	−0.606389	−	1.66604i	0.131662	−	0.991295i	$-0.457969\pi$
$654$	63.3963	−	59.9047i	2.47899	−	2.34246i
$655$	0.445104	+	2.52431i	0.0173917	+	0.0986330i
$656$	−12.2192	+	21.1642i	−0.477078	+	0.826324i
$657$	17.9094	−	13.3764i	0.698711	−	0.521864i
$658$	16.0625	−	79.3515i	0.626180	−	3.09344i
$659$	−43.6553	+	7.69760i	−1.70057	+	0.299856i	−0.937893	−	0.346926i	$-0.887226\pi$
$659$	−43.6553	+	7.69760i	−1.70057	+	0.299856i	−0.762675	+	0.646782i	$0.776114\pi$
$660$	−1.03909	+	8.95043i	−0.0404466	+	0.348395i
$661$	−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
$663$	9.80946	−	4.24045i	0.380968	−	0.164686i
$664$	−22.1788	+	3.91073i	−0.860706	+	0.151766i
$665$	0.766862	−	3.78844i	0.0297376	−	0.146909i
$666$	−10.2193	−	9.61140i	−0.395991	−	0.372434i
$667$	−9.17801	+	15.8968i	−0.355374	+	0.615526i
$668$	12.1650	+	68.9911i	0.470678	+	2.66935i
$669$	−5.24480	−	22.0530i	−0.202776	−	0.852619i
$670$	1.40777	+	3.86781i	0.0543868	+	0.149427i
$671$	35.0572	+	29.4165i	1.35337	+	1.13561i
$672$	4.08947	+	10.1551i	0.157755	+	0.391742i
$673$	−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
$675$	19.4316	+	16.2279i	0.747924	+	0.624611i
$676$	25.1003	−	43.4750i	0.965396	−	1.67212i
$677$	7.21471	+	40.9166i	0.277284	+	1.57255i	0.731613	+	0.681720i	$0.238768\pi$
$677$	7.21471	+	40.9166i	0.277284	+	1.57255i	−0.454330	+	0.890834i	$0.650121\pi$
$678$	−48.9855	−	24.5537i	−1.88128	−	0.942979i
$679$	1.78149	+	11.8401i	0.0683675	+	0.454381i
$680$	−11.3916	−	2.00865i	−0.436848	−	0.0770282i
$681$	−1.33474	−	1.41253i	−0.0511473	−	0.0541284i
$682$	−31.9357	+	5.63112i	−1.22288	+	0.215627i
$683$		−	8.71752i		−	0.333567i	−0.985994	−	0.166783i	$-0.946662\pi$
$683$		−	8.71752i		−	0.333567i	0.985994	−	0.166783i	$-0.0533380\pi$
$684$	−23.3263	−	46.2666i	−0.891902	−	1.76905i
$685$	−1.15306	−	0.665721i	−0.0440562	−	0.0254359i
$686$	4.56595	+	45.9875i	0.174329	+	1.75581i
$687$	−2.02807	+	0.876697i	−0.0773756	+	0.0334481i
$688$	−29.8170	−	25.0195i	−1.13676	−	0.953858i
$689$	−1.68124	+	9.53479i	−0.0640502	+	0.363247i
$690$	−3.30990	−	0.384259i	−0.126006	−	0.0146285i
$691$	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
$693$	7.21666	+	26.3569i	0.274138	+	1.00121i
$694$	22.2993	+	38.6236i	0.846472	+	1.46613i
$695$	−1.68977	+	4.64260i	−0.0640966	+	0.176104i
$696$	−23.4309	+	78.4870i	−0.888146	+	2.97504i
$697$	−20.1508	−	16.9086i	−0.763267	−	0.640457i
$698$	14.8447	−	84.1885i	0.561881	−	3.18658i
$699$	−14.5666	+	29.0609i	−0.550960	+	1.09918i
$700$	46.4820	+	28.4210i	1.75685	+	1.07421i
$701$			4.87126i			0.183985i	0.995760	+	0.0919925i	$0.0293236\pi$
$701$			4.87126i			0.183985i	−0.995760	+	0.0919925i	$0.970676\pi$
$702$	10.5025	−	8.85453i	0.396391	−	0.334193i
$703$	6.63222	+	3.82912i	0.250139	+	0.144418i
$704$	−10.7546	−	12.8169i	−0.405330	−	0.483054i
$705$	6.78858	+	3.40274i	0.255673	+	0.128154i
$706$	26.0589	−	31.0558i	0.980740	−	1.16880i
$707$	−5.64144	+	0.848829i	−0.212168	+	0.0319235i
$708$	20.7350	+	21.9435i	0.779267	+	0.824688i
$709$	−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
$711$	27.5720	−	29.3159i	1.03403	−	1.09943i
$712$			64.3992i			2.41346i
$713$	−1.41352	−	8.01648i	−0.0529368	−	0.300220i
$714$	−65.1539	+	13.7713i	−2.43832	+	0.515376i
$715$	1.22541	−	0.446012i	0.0458276	−	0.0166799i
$716$	13.9108	−	16.5782i	0.519870	−	0.619557i
$717$	−19.8182	+	8.56707i	−0.740126	+	0.319943i
$718$	−41.0934	−	14.9568i	−1.53359	−	0.558182i
$719$	−5.55081			−0.207010			−0.103505	−	0.994629i	$-0.533006\pi$
$719$	−5.55081			−0.207010			−0.103505	+	0.994629i	$0.533006\pi$
$720$	−5.76252	+	0.682642i	−0.214757	+	0.0254406i
$721$	11.2032	−	3.76087i	0.417229	−	0.140062i
$722$	−3.69074	−	4.39845i	−0.137355	−	0.163693i
$723$	8.25704	+	34.7187i	0.307083	+	1.29120i
$724$	11.3099	−	13.4787i	0.420331	−	0.500931i
$725$	14.1841	+	38.9705i	0.526785	+	1.44733i
$726$	2.02922	+	3.08005i	0.0753113	+	0.114311i
$727$	−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
$729$	−25.3283	+	9.35299i	−0.938084	+	0.346407i
$730$	3.32354	+	5.75654i	0.123010	+	0.213059i
$731$	32.0946	−	26.9305i	1.18706	−	0.996062i
$732$	−43.6037	+	86.9910i	−1.61164	+	3.21528i
$733$	−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
$735$	−4.27500	−	0.716052i	−0.157686	−	0.0264120i
$736$	−3.94654	+	3.31154i	−0.145471	+	0.122065i
$737$	13.7570	+	7.94259i	0.506744	+	0.292569i
$738$	−31.0685	−	13.3443i	−1.14365	−	0.491210i
$739$	−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
$741$	−4.47329	+	6.01846i	−0.164331	+	0.221093i
$742$	22.0560	−	56.1554i	0.809701	−	2.06153i
$743$	6.91069	+	18.9870i	0.253528	+	0.696564i	0.999531	+	0.0306207i	$0.00974840\pi$
$743$	6.91069	+	18.9870i	0.253528	+	0.696564i	−0.746003	+	0.665943i	$0.768029\pi$
$744$	−14.4130	−	33.3418i	−0.528408	−	1.22237i
$745$	1.15285	−	3.16743i	0.0422372	−	0.116046i
$746$	−1.35958	+	0.784953i	−0.0497777	+	0.0287392i
$747$	−3.50588	−	11.6444i	−0.128273	−	0.426046i
$748$	−73.3895	+	42.3714i	−2.68338	+	1.54925i
$749$	6.09628	+	11.2015i	0.222753	+	0.409294i
$750$	−11.0872	+	10.4765i	−0.404847	+	0.382549i
$751$	−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
$753$	0.967338	+	16.3887i	0.0352518	+	0.597236i
$754$	22.1609	−	3.90757i	0.807053	−	0.142305i
$755$	−1.65223			−0.0601307
$756$	−50.9712	+	27.8950i	−1.85380	+	1.01453i
$757$	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
$759$	−10.7387	+	7.07494i	−0.389790	+	0.256804i
$760$	7.62721	−	2.77608i	0.276668	−	0.100699i
$761$	−11.7998	+	4.29476i	−0.427741	+	0.155685i	−0.546915	−	0.837188i	$-0.684198\pi$
$761$	−11.7998	+	4.29476i	−0.427741	+	0.155685i	0.119173	+	0.992873i	$0.461976\pi$
$762$	−7.44250	−	31.2938i	−0.269613	−	1.13365i
$763$	45.5534	+	27.8532i	1.64914	+	1.00835i
$764$	−10.9874	+	6.34360i	−0.397511	+	0.229503i
$765$	0.353464	−	6.23605i	0.0127795	−	0.225465i
$766$	−35.4106	+	20.4443i	−1.27944	+	0.738684i
$767$	1.49439	−	4.10579i	0.0539592	−	0.148252i
$768$	33.5404	−	45.1259i	1.21029	−	1.62834i
$769$	−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
$771$	−11.0323	−	25.5210i	−0.397317	−	0.919115i
$772$	53.5147	−	44.9042i	1.92604	−	1.61614i
$773$	−9.44708	−	16.3628i	−0.339788	−	0.588530i	0.644605	−	0.764516i	$-0.277022\pi$
$773$	−9.44708	−	16.3628i	−0.339788	−	0.588530i	−0.984393	+	0.175986i	$0.943689\pi$
$774$	29.5235	−	45.0409i	1.06120	−	1.61896i
$775$	−15.9270	−	9.19547i	−0.572116	−	0.330311i
$776$	−19.2606	+	16.1616i	−0.691415	+	0.580166i
$777$	4.04048	−	7.57818i	0.144951	−	0.271866i
$778$	6.76200	−	38.3492i	0.242429	−	1.37489i
$779$	18.1776	+	3.20520i	0.651280	+	0.114838i
$780$	1.52548	+	2.31544i	0.0546208	+	0.0829061i
$781$	22.0520	−	18.5039i	0.789084	−	0.662120i
$782$	−15.6691	−	27.1396i	−0.560325	−	0.970512i
$783$	−43.5750	−	7.57852i	−1.55724	−	0.270834i
$784$	−30.2015	+	22.8524i	−1.07863	+	0.816155i
$785$	0.142745	−	0.392190i	0.00509480	−	0.0139978i
$786$	−13.8857	+	27.7024i	−0.495285	+	0.988111i
$787$	−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
$789$	22.1503	+	6.61258i	0.788572	+	0.235414i
$790$	7.69243	+	9.16748i	0.273684	+	0.326164i
$791$	6.65490	−	32.8764i	0.236621	−	1.16895i
$792$	−39.3143	+	41.8010i	−1.39697	+	1.48533i
$793$	14.0828			0.500095
$794$	15.3973	+	5.60415i	0.546429	+	0.198884i
$795$	4.54163	+	3.37563i	0.161075	+	0.119721i
$796$	−11.4296	+	13.6213i	−0.405112	+	0.482794i
$797$	1.89028	−	0.688005i	0.0669571	−	0.0243704i	−0.308324	−	0.951281i	$-0.599768\pi$
$797$	1.89028	−	0.688005i	0.0669571	−	0.0243704i	0.375282	+	0.926911i	$0.377546\pi$
$798$	34.7613	−	31.2275i	1.23054	−	1.10544i
$799$	12.4014	+	70.3321i	0.438732	+	2.48817i
$800$			11.6395i			0.411518i
$801$	−34.5324	+	4.09079i	−1.22014	+	0.144541i
$802$	88.0958			3.11077
$803$	24.1063	+	8.77396i	0.850691	+	0.309626i
$804$	−9.66199	+	32.3650i	−0.340752	+	1.14143i
$805$	−0.303498	−	2.01709i	−0.0106969	−	0.0710932i
$806$	−6.41442	+	7.64441i	−0.225938	+	0.269263i
$807$	36.0063	−	23.7219i	1.26748	−	0.835050i
$808$	−7.70050	−	9.17710i	−0.270903	−	0.322849i
$809$	−4.13482	−	2.38724i	−0.145373	−	0.0839309i	0.425550	−	0.904935i	$-0.360081\pi$
$809$	−4.13482	−	2.38724i	−0.145373	−	0.0839309i	−0.570922	+	0.821004i	$0.693414\pi$
$810$	−1.87590	−	7.80659i	−0.0659124	−	0.274296i
$811$		−	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
$813$	−15.0722	+	0.889631i	−0.528604	+	0.0312007i
$814$	2.79575	−	15.8555i	0.0979910	−	0.555734i
$815$	−1.93418	−	1.62297i	−0.0677514	−	0.0568502i
$816$	−37.4823	−	39.6670i	−1.31214	−	1.38862i
$817$	−10.0548	+	27.6255i	−0.351775	+	0.966493i
$818$	21.7205	+	37.6210i	0.759439	+	1.31539i
$819$	6.91467	+	4.78569i	0.241618	+	0.167226i
$820$	3.41255	−	5.91071i	0.119171	−	0.206411i
$821$	−5.60503	−	6.67982i	−0.195617	−	0.233127i	0.659316	−	0.751866i	$-0.270846\pi$
$821$	−5.60503	−	6.67982i	−0.195617	−	0.233127i	−0.854933	+	0.518739i	$0.826402\pi$
$822$	−6.38682	−	14.7747i	−0.222766	−	0.515326i
$823$	−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
$825$	−3.35049	+	28.8602i	−0.116649	+	1.00478i
$826$	−14.2030	+	23.2287i	−0.494184	+	0.808230i
$827$	−17.3220	−	10.0009i	−0.602346	−	0.347765i	0.167618	−	0.985852i	$-0.446393\pi$
$827$	−17.3220	−	10.0009i	−0.602346	−	0.347765i	−0.769964	+	0.638087i	$0.779726\pi$
$828$	−19.9182	−	18.7333i	−0.692207	−	0.651029i
$829$		−	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
$831$	−11.1725	+	37.4248i	−0.387570	+	1.29825i
$832$	−5.07043	−	0.894053i	−0.175785	−	0.0309957i
$833$	−18.5792	−	36.2859i	−0.643731	−	1.25723i
$834$	−49.8758	+	32.8595i	−1.72706	+	1.13783i
$835$	−1.02900	−	5.83575i	−0.0356100	−	0.201954i
$836$	29.7317	−	51.4968i	1.02829	−	1.78105i
$837$	16.9631	−	9.84656i	0.586331	−	0.340347i
$838$	−37.0586	+	21.3958i	−1.28017	+	0.739106i
$839$	9.90483	+	3.60506i	0.341953	+	0.124461i	0.507287	−	0.861777i	$-0.330648\pi$
$839$	9.90483	+	3.60506i	0.341953	+	0.124461i	−0.165335	+	0.986238i	$0.552870\pi$
$840$	−3.40011	−	8.44327i	−0.117315	−	0.291320i
$841$	−33.2865	−	27.9307i	−1.14781	−	0.963127i
$842$	22.1159	+	60.7629i	0.762164	+	2.09403i
$843$	−19.8628	−	5.92968i	−0.684111	−	0.204229i
$844$	13.1324	+	74.4775i	0.452036	+	2.56362i
$845$	−2.12316	+	3.67742i	−0.0730389	+	0.126507i
$846$	41.3279	+	81.9721i	1.42088	+	2.81826i
$847$	−1.49446	+	1.69255i	−0.0513502	+	0.0581567i
$848$	48.6918	−	8.58567i	1.67208	−	0.294833i
$849$	29.5022	+	21.9279i	1.01251	+	0.752563i
$850$	−69.7263	−	12.2946i	−2.39159	−	0.421702i
$851$	3.98004	+	0.701788i	0.136434	+	0.0240570i
$852$	49.1258	+	36.5134i	1.68302	+	1.25093i
$853$	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
$855$	1.97310	+	3.91355i	0.0674785	+	0.133841i
$856$	−13.3900	+	23.1922i	−0.457662	+	0.792694i
$857$	−8.17214	−	46.3465i	−0.279155	−	1.58317i	−0.725446	−	0.688279i	$-0.758367\pi$
$857$	−8.17214	−	46.3465i	−0.279155	−	1.58317i	0.446291	−	0.894888i	$-0.352745\pi$
$858$	15.1061	+	4.50967i	0.515715	+	0.153958i
$859$	−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
$861$	2.90412	−	20.4943i	0.0989722	−	0.698443i
$862$	−28.4040	−	10.3382i	−0.967446	−	0.352121i
$863$	−24.3038	+	14.0318i	−0.827311	+	0.477648i	−0.852931	−	0.522024i	$-0.825177\pi$
$863$	−24.3038	+	14.0318i	−0.827311	+	0.477648i	0.0256201	+	0.999672i	$0.491844\pi$
$864$	−10.7648	−	6.18158i	−0.366227	−	0.210302i
$865$	−0.579142	+	1.00310i	−0.0196914	+	0.0341065i
$866$	−13.7087	−	77.7456i	−0.465839	−	2.64190i
$867$	24.4659	−	16.1188i	0.830905	−	0.547423i
$868$	33.0076	−	26.3088i	1.12035	−	0.892980i
$869$	45.4842	+	8.02009i	1.54295	+	0.272063i
$870$	3.76226	−	12.6025i	0.127552	−	0.427266i
$871$	4.81403	−	0.848844i	0.163117	−	0.0287620i
$872$			112.122i			3.79694i
$873$	−9.88970	−	9.30138i	−0.334715	−	0.314804i
$874$	19.0437	+	10.9949i	0.644161	+	0.371907i
$875$	−7.96668	−	4.87115i	−0.269323	−	0.164675i
$876$	−6.29025	+	54.1825i	−0.212528	+	1.83066i
$877$	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
$879$	15.8063	+	36.5648i	0.533133	+	1.23330i
$880$	−4.28062	−	5.10144i	−0.144300	−	0.171970i
$881$	12.7246	−	22.0396i	0.428702	−	0.742533i	−0.568056	−	0.822990i	$-0.692304\pi$
$881$	12.7246	−	22.0396i	0.428702	−	0.742533i	0.996758	+	0.0804564i	$0.0256378\pi$
$882$	−36.3149	−	37.7773i	−1.22279	−	1.27203i
$883$	−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
$885$	−1.75391	−	1.85613i	−0.0589569	−	0.0623933i
$886$	−0.398196	−	0.334126i	−0.0133776	−	0.0112252i
$887$	3.90779	−	22.1622i	0.131211	−	0.744133i	−0.846213	−	0.532845i	$-0.821123\pi$
$887$	3.90779	−	22.1622i	0.131211	−	0.744133i	0.977424	−	0.211288i	$-0.0677659\pi$
$888$	18.0027	−	1.06261i	0.604132	−	0.0356588i
$889$	17.2956	−	9.41293i	0.580076	−	0.315699i
$890$		−	10.3405i		−	0.346613i
$891$	−24.9120	−	18.4260i	−0.834584	−	0.617294i
$892$	47.9036	+	27.6572i	1.60393	+	0.926030i
$893$	−32.2119	−	38.3886i	−1.07793	−	1.28463i
$894$	34.0280	−	22.4185i	1.13807	−	0.749788i
$895$	−1.17667	+	1.40230i	−0.0393318	+	0.0468738i
$896$	41.6286	+	16.3504i	1.39071	+	0.546227i
$897$	−1.13202	+	3.79194i	−0.0377969	+	0.126609i
$898$	−31.9451	−	11.6271i	−1.06602	−	0.388001i
$899$	32.1297			1.07159
$900$	−61.3482	+	7.26745i	−2.04494	+	0.242248i
$901$			53.2196i			1.77300i
$902$	−6.73837	−	38.2152i	−0.224363	−	1.27243i
$903$	31.3425	+	10.2233i	1.04301	+	0.340211i
$904$	66.1897	−	24.0911i	2.20144	−	0.801257i
$905$	−0.956674	+	1.14012i	−0.0318009	+	0.0378989i
$906$	−16.0310	−	11.9152i	−0.532593	−	0.395857i
$907$	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
$909$	4.43182	−	4.71214i	0.146994	−	0.156292i
$910$	−1.65510	+	1.87448i	−0.0548659	+	0.0621384i
$911$	20.4723	+	24.3979i	0.678277	+	0.808339i	0.989885	−	0.141872i	$-0.0453121\pi$
$911$	20.4723	+	24.3979i	0.678277	+	0.808339i	−0.311608	+	0.950211i	$0.600868\pi$
$912$	36.6943	+	10.9544i	1.21507	+	0.362737i
$913$	8.97072	−	10.6909i	0.296888	−	0.353817i
$914$	16.9540	+	46.5807i	0.560789	+	1.54075i
$915$	3.68830	−	7.35830i	0.121932	−	0.243258i
$916$	1.84399	−	5.06631i	0.0609270	−	0.167396i
$917$	−18.5923	−	3.76349i	−0.613973	−	0.124282i
$918$	48.4015	−	57.9571i	1.59749	−	1.91287i
$919$	−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
$921$	−31.3076	−	47.5203i	−1.03162	−	1.56585i
$922$	−14.6708	−	2.58686i	−0.483158	−	0.0851938i
$923$	1.53826	−	8.72392i	0.0506325	−	0.287151i
$924$	−58.8417	−	31.3728i	−1.93575	−	1.03209i
$925$	6.99458	−	5.86915i	0.229980	−	0.192977i
$926$	59.4753	+	34.3381i	1.95448	+	1.12842i
$927$	−7.34592	+	11.2069i	−0.241272	+	0.368083i
$928$	−10.1673	−	17.6103i	−0.333759	−	0.578087i
$929$	−8.32914	+	6.98898i	−0.273270	+	0.229301i	−0.769115	−	0.639110i	$-0.779303\pi$
$929$	−8.32914	+	6.98898i	−0.273270	+	0.229301i	0.495845	+	0.868411i	$0.334858\pi$
$930$	2.31428	+	5.35363i	0.0758881	+	0.175552i
$931$	24.0210	+	15.5319i	0.787257	+	0.509038i
$932$	−27.1303	−	74.5399i	−0.888682	−	2.44163i
$933$	9.95190	−	13.3895i	0.325811	−	0.438352i
$934$	−13.5549	+	37.2419i	−0.443531	+	1.21859i
$935$	6.20779	−	3.58407i	0.203016	−	0.117212i
$936$	−0.999300	+	17.6303i	−0.0326632	+	0.576266i
$937$	−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
$939$	−4.31820	−	18.1569i	−0.140919	−	0.592528i
$940$	−17.4124	+	6.33759i	−0.567929	+	0.206709i
$941$	−4.87040	+	1.77268i	−0.158770	+	0.0577877i	−0.420183	−	0.907440i	$-0.638034\pi$
$941$	−4.87040	+	1.77268i	−0.158770	+	0.0577877i	0.261412	+	0.965227i	$0.415812\pi$
$942$	4.21332	−	2.77585i	0.137278	−	0.0904421i
$943$	9.59277	−	1.69146i	0.312384	−	0.0550816i
$944$	−22.3129			−0.726223
$945$	4.31150	−	2.35955i	0.140253	−	0.0767563i
$946$	61.8050			2.00945
$947$	−29.4381	+	5.19074i	−0.956611	+	0.168676i	−0.630097	−	0.776516i	$-0.716985\pi$
$947$	−29.4381	+	5.19074i	−0.956611	+	0.168676i	−0.326514	+	0.945193i	$0.605874\pi$
$948$	5.78642	+	98.0338i	0.187934	+	3.18399i
$949$	7.41814	−	2.69998i	0.240803	−	0.0876452i
$950$	46.6850	−	16.9919i	1.51466	−	0.551292i
$951$	−5.55400	+	5.24811i	−0.180101	+	0.170182i
$952$	44.6560	−	73.0341i	1.44731	−	2.36705i
$953$	−29.6132	+	17.0972i	−0.959267	+	0.553833i	−0.895947	−	0.444160i	$-0.853502\pi$
$953$	−29.6132	+	17.0972i	−0.959267	+	0.553833i	−0.0633195	+	0.997993i	$0.520169\pi$
$954$	19.7221	+	65.5050i	0.638527	+	2.12080i
$955$	0.929393	−	0.536585i	0.0300745	−	0.0173635i
$956$	18.0194	−	49.5079i	0.582789	−	1.60120i
$957$	−20.1407	−	46.5916i	−0.651056	−	1.50609i
$958$	9.15737	+	25.1597i	0.295861	+	0.812872i
$959$	7.70525	−	6.14150i	0.248816	−	0.198319i
$960$	−1.79510	+	2.41516i	−0.0579365	+	0.0779489i
$961$	12.8326	−	10.7678i	0.413955	−	0.347350i
$962$	−2.47721	−	4.29066i	−0.0798686	−	0.138336i
$963$	−13.2868	−	5.70683i	−0.428161	−	0.183900i
$964$	−75.4160	−	43.5415i	−2.42899	−	1.40238i
$965$	−4.52665	+	3.79831i	−0.145718	+	0.122272i
$966$	11.6018	−	21.7598i	0.373281	−	0.700111i
$967$	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
$969$	−18.4706	+	36.8496i	−0.593363	+	1.18378i
$970$	3.09264	−	2.59503i	0.0992988	−	0.0833216i
$971$	−16.1729	−	28.0122i	−0.519012	−	0.898955i	−0.999756	−	0.0220939i	$-0.992967\pi$
$971$	−16.1729	−	28.0122i	−0.519012	−	0.898955i	0.480744	−	0.876861i	$-0.340367\pi$
$972$	25.8599	−	60.5977i	0.829457	−	1.94367i
$973$	−27.4078	−	24.2001i	−0.878654	−	0.775818i
$974$	−7.76498	+	21.3341i	−0.248806	+	0.683589i
$975$	4.91881	+	7.46602i	0.157528	+	0.239104i
$976$	−24.5972	−	67.5802i	−0.787336	−	2.16319i
$977$	19.8346	−	23.6380i	0.634565	−	0.756245i	−0.348936	−	0.937146i	$-0.613457\pi$
$977$	19.8346	−	23.6380i	0.634565	−	0.756245i	0.983501	+	0.180901i	$0.0579015\pi$
$978$	−7.06243	−	29.6957i	−0.225832	−	0.949563i
$979$	−25.6520	−	30.5708i	−0.819840	−	0.977047i
$980$	8.43464	−	6.38217i	0.269435	−	0.203871i
$981$	−60.1226	+	7.12226i	−1.91957	+	0.227396i
$982$	7.35611			0.234743
$983$	10.8511	+	3.94948i	0.346097	+	0.125969i	0.509219	−	0.860637i	$-0.329934\pi$
$983$	10.8511	+	3.94948i	0.346097	+	0.125969i	−0.163122	+	0.986606i	$0.552157\pi$
$984$	39.8978	−	17.2471i	1.27190	−	0.549817i
$985$	0.779862	−	0.929403i	0.0248485	−	0.0296132i
$986$	116.234	−	42.3058i	3.70165	−	1.34729i
$987$	−41.8054	+	37.5555i	−1.33068	+	1.19540i
$988$	−3.17749	−	18.0205i	−0.101090	−	0.573307i
$989$			15.5143i			0.493325i
$990$	6.31263	−	6.71191i	0.200629	−	0.213319i
$991$	−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
$993$	−16.4217	−	17.3789i	−0.521128	−	0.551502i
$994$	−20.1803	+	51.3797i	−0.640080	+	1.62967i
$995$	0.966797	−	1.15218i	0.0306495	−	0.0365267i
$996$	26.5284	+	13.2972i	0.840583	+	0.421337i
$997$	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
$999$	1.71337	+	9.58599i	0.0542086	+	0.303287i

Twists

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

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

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.45739 - 0.433304i) q^{2} +(-1.54842 - 0.776137i) q^{3} +(3.97163 - 1.44555i) q^{4} +(-0.335948 + 0.122275i) q^{5} +(-4.14138 - 1.23633i) q^{6} +(0.0666399 - 2.64491i) q^{7} +(4.81149 - 2.77792i) q^{8} +(1.79522 + 2.40358i) q^{9} +O(q^{10})\)	\(q+(2.45739 - 0.433304i) q^{2} +(-1.54842 - 0.776137i) q^{3} +(3.97163 - 1.44555i) q^{4} +(-0.335948 + 0.122275i) q^{5} +(-4.14138 - 1.23633i) q^{6} +(0.0666399 - 2.64491i) q^{7} +(4.81149 - 2.77792i) q^{8} +(1.79522 + 2.40358i) q^{9} +(-0.772573 + 0.446045i) q^{10} +(-1.17753 + 3.23525i) q^{11} +(-7.27171 - 0.844201i) q^{12} +(0.362359 + 0.995572i) q^{13} +(-0.982291 - 6.52846i) q^{14} +(0.615091 + 0.0714084i) q^{15} +(4.14463 - 3.47775i) q^{16} +(2.91185 + 5.04347i) q^{17} +(5.45304 + 5.12865i) q^{18} +(-3.53896 - 2.04322i) q^{19} +(-1.15751 + 0.971262i) q^{20} +(-2.15600 + 4.04372i) q^{21} +(-1.49181 + 8.46049i) q^{22} +(-2.12375 - 0.374475i) q^{23} +(-9.60626 + 0.567008i) q^{24} +(-3.73231 + 3.13178i) q^{25} +(1.32184 + 2.28950i) q^{26} +(-0.914255 - 5.11509i) q^{27} +(-3.55870 - 10.6009i) q^{28} +(2.91124 - 7.99857i) q^{29} +(1.54246 - 0.0910435i) q^{30} +(1.29102 + 3.54704i) q^{31} +(1.53560 - 1.83005i) q^{32} +(4.33431 - 4.09560i) q^{33} +(9.34090 + 11.1321i) q^{34} +(0.301019 + 0.896701i) q^{35} +(10.6045 + 6.95102i) q^{36} -1.87406 q^{37} +(-9.58194 - 3.48754i) q^{38} +(0.211617 - 1.82281i) q^{39} +(-1.27674 + 1.52156i) q^{40} +(-4.24450 + 1.54487i) q^{41} +(-3.54598 + 10.8712i) q^{42} +(-1.24925 - 7.08485i) q^{43} +14.5514i q^{44} +(-0.896998 - 0.587966i) q^{45} -5.38115 q^{46} +(11.5236 + 4.19426i) q^{47} +(-9.11684 + 2.16823i) q^{48} +(-6.99112 - 0.352513i) q^{49} +(-7.81473 + 9.31324i) q^{50} +(-0.594345 - 10.0694i) q^{51} +(2.87831 + 3.43023i) q^{52} +(7.91413 + 4.56923i) q^{53} +(-4.46307 - 12.1736i) q^{54} -1.23086i q^{55} +(-7.02671 - 12.9111i) q^{56} +(3.89398 + 5.91048i) q^{57} +(3.68824 - 20.9171i) q^{58} +(-3.15921 - 2.65089i) q^{59} +(2.54614 - 0.605541i) q^{60} +(4.54625 - 12.4907i) q^{61} +(4.70948 + 8.15705i) q^{62} +(6.47688 - 4.58803i) q^{63} +(-2.42983 + 4.20859i) q^{64} +(-0.243467 - 0.290153i) q^{65} +(8.87646 - 11.9426i) q^{66} +(0.801200 - 4.54383i) q^{67} +(18.8554 + 15.8215i) q^{68} +(2.99782 + 2.22817i) q^{69} +(1.12827 + 2.07311i) q^{70} +(-7.24109 - 4.18065i) q^{71} +(15.3146 + 6.57781i) q^{72} -7.45113i q^{73} +(-4.60530 + 0.812039i) q^{74} +(8.20989 - 1.95253i) q^{75} +(-17.0090 - 2.99915i) q^{76} +(8.47847 + 3.33007i) q^{77} +(-0.269805 - 4.57104i) q^{78} +(-2.32947 - 13.2111i) q^{79} +(-0.967136 + 1.67513i) q^{80} +(-2.55436 + 8.62990i) q^{81} +(-9.76098 + 5.63551i) q^{82} +(-3.80912 - 1.38640i) q^{83} +(-2.71742 + 19.1768i) q^{84} +(-1.59492 - 1.33830i) q^{85} +(-6.13979 - 16.8689i) q^{86} +(-10.7158 + 10.1256i) q^{87} +(3.32155 + 18.8375i) q^{88} +(-5.79564 + 10.0383i) q^{89} +(-2.45904 - 1.05619i) q^{90} +(2.65735 - 0.892062i) q^{91} +(-8.97607 + 1.58272i) q^{92} +(0.753951 - 6.49432i) q^{93} +(30.1354 + 5.31369i) q^{94} +(1.43874 + 0.253689i) q^{95} +(-3.79813 + 1.64186i) q^{96} +(-4.45675 + 0.785845i) q^{97} +(-17.3327 + 2.16302i) q^{98} +(-9.89010 + 2.97769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

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