LMFDB - Embedded newform 324.2.p.a.23.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			23.41
Character	$\chi$	$=$	324.23
Dual form			324.2.p.a.155.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09818 + 0.891069i) q^{2} +(0.890440 + 1.48564i) q^{3} +(0.411991 + 1.95711i) q^{4} +(-1.03261 + 1.57001i) q^{5} +(-0.345944 + 2.42494i) q^{6} +(3.59628 - 3.39292i) q^{7} +(-1.29148 + 2.51636i) q^{8} +(-1.41423 + 2.64574i) q^{9} +O(q^{10})$	\(q+(1.09818 + 0.891069i) q^{2} +(0.890440 + 1.48564i) q^{3} +(0.411991 + 1.95711i) q^{4} +(-1.03261 + 1.57001i) q^{5} +(-0.345944 + 2.42494i) q^{6} +(3.59628 - 3.39292i) q^{7} +(-1.29148 + 2.51636i) q^{8} +(-1.41423 + 2.64574i) q^{9} +(-2.53297 + 0.804020i) q^{10} +(-1.99888 - 1.00388i) q^{11} +(-2.54070 + 2.35475i) q^{12} +(1.56942 - 3.63833i) q^{13} +(6.97269 - 0.521491i) q^{14} +(-3.25194 - 0.136086i) q^{15} +(-3.66053 + 1.61262i) q^{16} +(-0.421668 + 0.502524i) q^{17} +(-3.91062 + 1.64532i) q^{18} +(-1.94981 - 2.32370i) q^{19} +(-3.49809 - 1.37410i) q^{20} +(8.24292 + 2.32158i) q^{21} +(-1.30060 - 2.88358i) q^{22} +(-0.969289 + 1.02739i) q^{23} +(-4.88839 + 0.322003i) q^{24} +(0.581761 + 1.34867i) q^{25} +(4.96551 - 2.59707i) q^{26} +(-5.18990 + 0.254837i) q^{27} +(8.12194 + 5.64046i) q^{28} +(0.764623 - 6.54177i) q^{29} +(-3.44994 - 3.04715i) q^{30} +(0.256353 - 1.08164i) q^{31} +(-5.45687 - 1.49084i) q^{32} +(-0.288489 - 3.86350i) q^{33} +(-0.910851 + 0.176126i) q^{34} +(1.61335 + 9.14975i) q^{35} +(-5.76065 - 1.67778i) q^{36} +(-1.45904 + 8.27461i) q^{37} +(-0.0706671 - 4.28925i) q^{38} +(6.80271 - 0.908123i) q^{39} +(-2.61711 - 4.62605i) q^{40} +(5.93169 - 4.41598i) q^{41} +(6.98350 + 9.89452i) q^{42} +(6.22042 - 0.362298i) q^{43} +(1.14117 - 4.32561i) q^{44} +(-2.69348 - 4.95237i) q^{45} +(-1.97992 + 0.264549i) q^{46} +(4.74488 - 1.12456i) q^{47} +(-5.65525 - 4.00227i) q^{48} +(1.01435 - 17.4156i) q^{49} +(-0.562884 + 1.99947i) q^{50} +(-1.12204 - 0.178978i) q^{51} +(7.76719 + 1.57257i) q^{52} +(5.22077 + 3.01422i) q^{53} +(-5.92651 - 4.34470i) q^{54} +(3.64016 - 2.10165i) q^{55} +(3.89329 + 13.4314i) q^{56} +(1.71598 - 4.96583i) q^{57} +(6.66887 - 6.50270i) q^{58} +(-13.0037 + 6.53070i) q^{59} +(-1.07343 - 6.42045i) q^{60} +(-3.33728 + 11.1473i) q^{61} +(1.24534 - 0.959405i) q^{62} +(3.89080 + 14.3132i) q^{63} +(-4.66417 - 6.49966i) q^{64} +(4.09160 + 6.22098i) q^{65} +(3.12584 - 4.49988i) q^{66} +(-0.556562 - 4.76169i) q^{67} +(-1.15722 - 0.618214i) q^{68} +(-2.38942 - 0.525185i) q^{69} +(-6.38132 + 11.4857i) q^{70} +(1.72416 - 0.627544i) q^{71} +(-4.83119 - 6.97564i) q^{72} +(0.516395 + 0.187953i) q^{73} +(-8.97553 + 7.78689i) q^{74} +(-1.48561 + 2.06520i) q^{75} +(3.74442 - 4.77333i) q^{76} +(-10.5946 + 3.17182i) q^{77} +(8.27979 + 5.06441i) q^{78} +(-12.2113 - 9.09094i) q^{79} +(1.24807 - 7.41226i) q^{80} +(-4.99989 - 7.48339i) q^{81} +(10.4490 + 0.436016i) q^{82} +(-5.49796 + 7.38504i) q^{83} +(-1.14757 + 17.0887i) q^{84} +(-0.353548 - 1.18093i) q^{85} +(7.15396 + 5.14496i) q^{86} +(10.3995 - 4.68910i) q^{87} +(5.10763 - 3.73343i) q^{88} +(1.92005 - 5.27530i) q^{89} +(1.45499 - 7.83867i) q^{90} +(-6.70047 - 18.4094i) q^{91} +(-2.41004 - 1.47373i) q^{92} +(1.83519 - 0.582288i) q^{93} +(6.21278 + 2.99305i) q^{94} +(5.66162 - 0.661748i) q^{95} +(-2.64416 - 9.43443i) q^{96} +(7.54904 - 4.96508i) q^{97} +(16.6325 - 18.2216i) q^{98} +(5.48288 - 3.86881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{54}\right)$

Coefficient data

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

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

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

$2$	1.09818	+	0.891069i	0.776529	+	0.630081i
$2$	1.09818	+	0.891069i	0.776529	+	0.630081i
$3$	0.890440	+	1.48564i	0.514096	+	0.857733i
$3$	0.890440	+	1.48564i	0.514096	+	0.857733i
$4$	0.411991	+	1.95711i	0.205995	+	0.978553i
$5$	−1.03261	+	1.57001i	−0.461797	+	0.702128i	−0.989050	−	0.147580i	$-0.952852\pi$
$5$	−1.03261	+	1.57001i	−0.461797	+	0.702128i	0.527253	+	0.849708i	$0.323222\pi$
$6$	−0.345944	+	2.42494i	−0.141231	+	0.989977i
$7$	3.59628	−	3.39292i	1.35927	−	1.28240i	0.435117	−	0.900374i	$-0.356707\pi$
$7$	3.59628	−	3.39292i	1.35927	−	1.28240i	0.924150	−	0.382029i	$-0.124774\pi$
$8$	−1.29148	+	2.51636i	−0.456607	+	0.889669i
$9$	−1.41423	+	2.64574i	−0.471411	+	0.881914i
$10$	−2.53297	+	0.804020i	−0.800997	+	0.254253i
$11$	−1.99888	−	1.00388i	−0.602685	−	0.302680i	0.121170	−	0.992632i	$-0.461335\pi$
$11$	−1.99888	−	1.00388i	−0.602685	−	0.302680i	−0.723855	+	0.689952i	$0.757632\pi$
$12$	−2.54070	+	2.35475i	−0.733436	+	0.679759i
$13$	1.56942	−	3.63833i	0.435279	−	1.00909i	−0.549533	−	0.835472i	$-0.685194\pi$
$13$	1.56942	−	3.63833i	0.435279	−	1.00909i	0.984813	−	0.173619i	$-0.0555463\pi$
$14$	6.97269	−	0.521491i	1.86353	−	0.139374i
$15$	−3.25194	−	0.136086i	−0.839646	−	0.0351373i
$16$	−3.66053	+	1.61262i	−0.915132	+	0.403155i
$17$	−0.421668	+	0.502524i	−0.102270	+	0.121880i	−0.814751	−	0.579810i	$-0.803127\pi$
$17$	−0.421668	+	0.502524i	−0.102270	+	0.121880i	0.712482	+	0.701691i	$0.247571\pi$
$18$	−3.91062	+	1.64532i	−0.921742	+	0.387804i
$19$	−1.94981	−	2.32370i	−0.447318	−	0.533093i	0.494517	−	0.869168i	$-0.335345\pi$
$19$	−1.94981	−	2.32370i	−0.447318	−	0.533093i	−0.941835	+	0.336075i	$0.890900\pi$
$20$	−3.49809	−	1.37410i	−0.782198	−	0.307258i
$21$	8.24292	+	2.32158i	1.79875	+	0.506610i
$22$	−1.30060	−	2.88358i	−0.277290	−	0.614781i
$23$	−0.969289	+	1.02739i	−0.202111	+	0.214225i	−0.820499	−	0.571648i	$-0.806304\pi$
$23$	−0.969289	+	1.02739i	−0.202111	+	0.214225i	0.618388	+	0.785873i	$0.287786\pi$
$24$	−4.88839	+	0.322003i	−0.997838	+	0.0657286i
$25$	0.581761	+	1.34867i	0.116352	+	0.269735i
$26$	4.96551	−	2.59707i	0.973817	−	0.509327i
$27$	−5.18990	+	0.254837i	−0.998797	+	0.0490434i
$28$	8.12194	+	5.64046i	1.53490	+	1.06595i
$29$	0.764623	−	6.54177i	0.141987	−	1.21478i	−0.714883	−	0.699244i	$-0.753520\pi$
$29$	0.764623	−	6.54177i	0.141987	−	1.21478i	0.856870	−	0.515532i	$-0.172406\pi$
$30$	−3.44994	−	3.04715i	−0.629871	−	0.556331i
$31$	0.256353	−	1.08164i	0.0460424	−	0.194268i	−0.945163	−	0.326598i	$-0.894098\pi$
$31$	0.256353	−	1.08164i	0.0460424	−	0.194268i	0.991206	+	0.132330i	$0.0422458\pi$
$32$	−5.45687	−	1.49084i	−0.964647	−	0.263546i
$33$	−0.288489	−	3.86350i	−0.0502195	−	0.672550i
$34$	−0.910851	+	0.176126i	−0.156210	+	0.0302053i
$35$	1.61335	+	9.14975i	0.272706	+	1.54659i
$36$	−5.76065	−	1.67778i	−0.960108	−	0.279631i
$37$	−1.45904	+	8.27461i	−0.239864	+	1.36034i	0.592260	+	0.805747i	$0.298236\pi$
$37$	−1.45904	+	8.27461i	−0.239864	+	1.36034i	−0.832124	+	0.554590i	$0.812875\pi$
$38$	−0.0706671	−	4.28925i	−0.0114637	−	0.695809i
$39$	6.80271	−	0.908123i	1.08931	−	0.145416i
$40$	−2.61711	−	4.62605i	−0.413802	−	0.731443i
$41$	5.93169	−	4.41598i	0.926375	−	0.689661i	−0.0243476	−	0.999704i	$-0.507751\pi$
$41$	5.93169	−	4.41598i	0.926375	−	0.689661i	0.950723	+	0.310043i	$0.100343\pi$
$42$	6.98350	+	9.89452i	1.07758	+	1.52676i
$43$	6.22042	−	0.362298i	0.948605	−	0.0552499i	0.423139	−	0.906065i	$-0.360928\pi$
$43$	6.22042	−	0.362298i	0.948605	−	0.0552499i	0.525466	+	0.850815i	$0.323891\pi$
$44$	1.14117	−	4.32561i	0.172038	−	0.652110i
$45$	−2.69348	−	4.95237i	−0.401520	−	0.738256i
$46$	−1.97992	+	0.264549i	−0.291924	+	0.0390057i
$47$	4.74488	−	1.12456i	0.692111	−	0.164033i	0.130517	−	0.991446i	$-0.458336\pi$
$47$	4.74488	−	1.12456i	0.692111	−	0.164033i	0.561594	+	0.827413i	$0.310188\pi$
$48$	−5.65525	−	4.00227i	−0.816264	−	0.577679i
$49$	1.01435	−	17.4156i	0.144906	−	2.48795i
$50$	−0.562884	+	1.99947i	−0.0796039	+	0.282768i
$51$	−1.12204	−	0.178978i	−0.157117	−	0.0250619i
$52$	7.76719	+	1.57257i	1.07711	+	0.218076i
$53$	5.22077	+	3.01422i	0.717129	+	0.414034i	0.813695	−	0.581292i	$-0.197453\pi$
$53$	5.22077	+	3.01422i	0.717129	+	0.414034i	−0.0965663	+	0.995327i	$0.530786\pi$
$54$	−5.92651	−	4.34470i	−0.806496	−	0.591239i
$55$	3.64016	−	2.10165i	0.490839	−	0.283386i
$56$	3.89329	+	13.4314i	0.520263	+	1.79485i
$57$	1.71598	−	4.96583i	0.227287	−	0.657740i
$58$	6.66887	−	6.50270i	0.875665	−	0.853846i
$59$	−13.0037	+	6.53070i	−1.69294	+	0.850224i	−0.702592	+	0.711593i	$0.747974\pi$
$59$	−13.0037	+	6.53070i	−1.69294	+	0.850224i	−0.990344	+	0.138632i	$0.955730\pi$
$60$	−1.07343	−	6.42045i	−0.138580	−	0.828877i
$61$	−3.33728	+	11.1473i	−0.427296	+	1.42727i	0.425470	+	0.904973i	$0.360109\pi$
$61$	−3.33728	+	11.1473i	−0.427296	+	1.42727i	−0.852766	+	0.522294i	$0.825076\pi$
$62$	1.24534	−	0.959405i	0.158158	−	0.121845i
$63$	3.89080	+	14.3132i	0.490195	+	1.80330i
$64$	−4.66417	−	6.49966i	−0.583021	−	0.812457i
$65$	4.09160	+	6.22098i	0.507501	+	0.771617i
$66$	3.12584	−	4.49988i	0.384764	−	0.553897i
$67$	−0.556562	−	4.76169i	−0.0679948	−	0.581733i	−0.983692	−	0.179863i	$-0.942435\pi$
$67$	−0.556562	−	4.76169i	−0.0679948	−	0.581733i	0.915697	−	0.401870i	$-0.131640\pi$
$68$	−1.15722	−	0.618214i	−0.140333	−	0.0749694i
$69$	−2.38942	−	0.525185i	−0.287652	−	0.0632249i
$70$	−6.38132	+	11.4857i	−0.762713	+	1.37280i
$71$	1.72416	−	0.627544i	0.204620	−	0.0744757i	−0.237677	−	0.971344i	$-0.576386\pi$
$71$	1.72416	−	0.627544i	0.204620	−	0.0744757i	0.442297	+	0.896869i	$0.354164\pi$
$72$	−4.83119	−	6.97564i	−0.569362	−	0.822087i
$73$	0.516395	+	0.187953i	0.0604395	+	0.0219982i	0.372063	−	0.928207i	$-0.378651\pi$
$73$	0.516395	+	0.187953i	0.0604395	+	0.0219982i	−0.311623	+	0.950206i	$0.600873\pi$
$74$	−8.97553	+	7.78689i	−1.04338	+	0.905207i
$75$	−1.48561	+	2.06520i	−0.171544	+	0.238468i
$76$	3.74442	−	4.77333i	0.429514	−	0.547539i
$77$	−10.5946	+	3.17182i	−1.20737	+	0.361462i
$78$	8.27979	+	5.06441i	0.937502	+	0.573431i
$79$	−12.2113	−	9.09094i	−1.37387	−	1.02281i	−0.995259	−	0.0972558i	$-0.968994\pi$
$79$	−12.2113	−	9.09094i	−1.37387	−	1.02281i	−0.378614	−	0.925555i	$-0.623599\pi$
$80$	1.24807	−	7.41226i	0.139539	−	0.828716i
$81$	−4.99989	−	7.48339i	−0.555543	−	0.831488i
$82$	10.4490	+	0.436016i	1.15390	+	0.0481499i
$83$	−5.49796	+	7.38504i	−0.603480	+	0.810614i	−0.993930	−	0.110010i	$-0.964912\pi$
$83$	−5.49796	+	7.38504i	−0.603480	+	0.810614i	0.390451	+	0.920624i	$0.372319\pi$
$84$	−1.14757	+	17.0887i	−0.125211	+	1.86453i
$85$	−0.353548	−	1.18093i	−0.0383477	−	0.128090i
$86$	7.15396	+	5.14496i	0.771431	+	0.554795i
$87$	10.3995	−	4.68910i	1.11495	−	0.502725i
$88$	5.10763	−	3.73343i	0.544475	−	0.397985i
$89$	1.92005	−	5.27530i	0.203525	−	0.559181i	−0.795373	−	0.606121i	$-0.792725\pi$
$89$	1.92005	−	5.27530i	0.203525	−	0.559181i	0.998898	+	0.0469402i	$0.0149470\pi$
$90$	1.45499	−	7.83867i	0.153369	−	0.826268i
$91$	−6.70047	−	18.4094i	−0.702400	−	1.92983i
$92$	−2.41004	−	1.47373i	−0.251264	−	0.153647i
$93$	1.83519	−	0.582288i	0.190301	−	0.0603804i
$94$	6.21278	+	2.99305i	0.640799	+	0.308710i
$95$	5.66162	−	0.661748i	0.580870	−	0.0678939i
$96$	−2.64416	−	9.43443i	−0.269869	−	0.962897i
$97$	7.54904	−	4.96508i	0.766488	−	0.504127i	−0.105043	−	0.994468i	$-0.533498\pi$
$97$	7.54904	−	4.96508i	0.766488	−	0.504127i	0.871531	+	0.490340i	$0.163128\pi$
$98$	16.6325	−	18.2216i	1.68013	−	1.84066i
$99$	5.48288	−	3.86881i	0.551050	−	0.388830i
$100$	−2.39982	+	1.69421i	−0.239982	+	0.169421i
$101$	12.8471	+	3.84617i	1.27833	+	0.382708i	0.852802	−	0.522235i	$-0.174902\pi$
$101$	12.8471	+	3.84617i	1.27833	+	0.382708i	0.425532	+	0.904943i	$0.360087\pi$
$102$	−1.07272	−	1.19636i	−0.106215	−	0.118458i
$103$	0.382373	+	0.761367i	0.0376763	+	0.0750197i	0.911683	−	0.410894i	$-0.134783\pi$
$103$	0.382373	+	0.761367i	0.0376763	+	0.0750197i	−0.874007	+	0.485913i	$0.838487\pi$
$104$	7.12849	+	8.64806i	0.699006	+	0.848012i
$105$	−12.1566	+	10.5442i	−1.18636	+	1.02900i
$106$	3.04747	+	7.96222i	0.295996	+	0.773359i
$107$	−5.12841	−	8.88267i	−0.495782	−	0.858720i	0.504206	−	0.863583i	$-0.331785\pi$
$107$	−5.12841	−	8.88267i	−0.495782	−	0.858720i	−0.999988	+	0.00486345i	$0.998452\pi$
$108$	−2.63693	−	10.0522i	−0.253739	−	0.967273i
$109$	−6.40576	+	11.0951i	−0.613560	+	1.06272i	0.377075	+	0.926183i	$0.376930\pi$
$109$	−6.40576	+	11.0951i	−0.613560	+	1.06272i	−0.990635	+	0.136535i	$0.956403\pi$
$110$	5.87025	+	0.935651i	0.559707	+	0.0892108i
$111$	−13.5922	+	5.20044i	−1.29012	+	0.493604i
$112$	−7.69281	+	18.2193i	−0.726902	+	1.72156i
$113$	−8.68116	−	0.505620i	−0.816655	−	0.0475648i	−0.355269	−	0.934764i	$-0.615611\pi$
$113$	−8.68116	−	0.505620i	−0.816655	−	0.0475648i	−0.461386	+	0.887199i	$0.652648\pi$
$114$	6.30935	−	3.92431i	0.590925	−	0.367545i
$115$	−0.612106	−	2.58268i	−0.0570792	−	0.240836i
$116$	13.1180	−	1.19870i	1.21797	−	0.111296i
$117$	7.40655	+	9.29773i	0.684736	+	0.859576i
$118$	−20.0997	−	4.41532i	−1.85032	−	0.406463i
$119$	0.188587	+	3.23791i	0.0172877	+	0.296818i
$120$	4.54225	−	8.00730i	0.414649	−	0.730963i
$121$	−3.58098	−	4.81010i	−0.325544	−	0.437282i
$122$	−13.5980	+	9.26798i	−1.23110	+	0.839083i
$123$	11.8424	+	4.88017i	1.06779	+	0.440031i
$124$	2.22250	+	0.0560853i	0.199586	+	0.00503661i
$125$	−11.9712	−	2.11084i	−1.07073	−	0.188799i
$126$	−8.48127	+	19.1854i	−0.755572	+	1.70917i
$127$	0.0115054	−	0.00202871i	0.00102094	−	0.000180019i	−0.173138	−	0.984898i	$-0.555391\pi$
$127$	0.0115054	−	0.00202871i	0.00102094	−	0.000180019i	0.174159	+	0.984718i	$0.444279\pi$
$128$	0.669558	−	11.2939i	0.0591811	−	0.998247i
$129$	6.07715	+	8.91868i	0.535063	+	0.785246i
$130$	−1.05002	+	10.4776i	−0.0920925	+	0.918950i
$131$	6.23391	+	1.47746i	0.544659	+	0.129087i	0.493729	−	0.869616i	$-0.335633\pi$
$131$	6.23391	+	1.47746i	0.544659	+	0.129087i	0.0509300	+	0.998702i	$0.483781\pi$
$132$	7.44243	−	2.15633i	0.647780	−	0.187684i
$133$	−14.8962	−	1.74112i	−1.29166	−	0.150974i
$134$	3.63179	−	5.72512i	0.313739	−	0.494575i
$135$	4.95904	−	8.41132i	0.426807	−	0.723931i
$136$	−0.719959	−	1.71007i	−0.0617360	−	0.146637i
$137$	−4.51931	+	1.94944i	−0.386110	+	0.166552i	−0.580282	−	0.814416i	$-0.697058\pi$
$137$	−4.51931	+	1.94944i	−0.386110	+	0.166552i	0.194171	+	0.980968i	$0.437798\pi$
$138$	−2.15603	−	2.70588i	−0.183533	−	0.230340i
$139$	−9.21314	−	8.69215i	−0.781448	−	0.737259i	0.188102	−	0.982149i	$-0.439766\pi$
$139$	−9.21314	−	8.69215i	−0.781448	−	0.737259i	−0.969551	+	0.244891i	$0.921248\pi$
$140$	−17.2423	+	6.92710i	−1.45724	+	0.585447i
$141$	5.89571	+	6.04781i	0.496508	+	0.509318i
$142$	2.45262	+	0.847194i	0.205820	+	0.0710949i
$143$	−6.78952	+	5.69709i	−0.567768	+	0.476414i
$144$	0.910269	−	11.9654i	0.0758557	−	0.997119i
$145$	9.48107	+	7.95556i	0.787360	+	0.660673i
$146$	0.399615	+	0.666549i	0.0330724	+	0.0551640i
$147$	26.7765	−	14.0006i	2.20849	−	1.15475i
$148$	−16.7954	+	0.553571i	−1.38057	+	0.0455033i
$149$	−14.5940	−	6.29524i	−1.19559	−	0.515726i	−0.297151	−	0.954831i	$-0.596036\pi$
$149$	−14.5940	−	6.29524i	−1.19559	−	0.515726i	−0.898436	+	0.439105i	$0.855296\pi$
$150$	−3.47170	+	0.944169i	−0.283463	+	0.0770910i
$151$	−6.07362	+	12.0936i	−0.494265	+	0.984162i	0.498814	+	0.866709i	$0.333769\pi$
$151$	−6.07362	+	12.0936i	−0.494265	+	0.984162i	−0.993078	+	0.117453i	$0.962527\pi$
$152$	8.36541	−	1.90544i	0.678524	−	0.154551i
$153$	−0.733213	−	1.82631i	−0.0592767	−	0.147649i
$154$	−14.4611	−	5.95731i	−1.16531	−	0.480054i
$155$	1.43347	+	1.51939i	0.115139	+	0.122040i
$156$	4.57995	+	12.9395i	0.366689	+	1.03599i
$157$	2.21879	+	1.45932i	0.177079	+	0.116467i	0.634954	−	0.772550i	$-0.281019\pi$
$157$	2.21879	+	1.45932i	0.177079	+	0.116467i	−0.457875	+	0.889017i	$0.651389\pi$
$158$	−5.30947	−	20.8645i	−0.422399	−	1.65989i
$159$	0.170757	+	10.4402i	0.0135419	+	0.827958i
$160$	7.97544	−	7.02786i	0.630514	−	0.555601i
$161$			6.98349i			0.550376i
$162$	1.17745	−	12.6733i	0.0925091	−	0.995712i
$163$			23.2941i			1.82453i	0.409598	+	0.912266i	$0.365669\pi$
$163$			23.2941i			1.82453i	−0.409598	+	0.912266i	$0.634331\pi$
$164$	11.0863	+	9.78961i	0.865698	+	0.764440i
$165$	6.36362	+	3.53656i	0.495407	+	0.275321i
$166$	−12.6183	+	3.21103i	−0.979372	+	0.249224i
$167$	15.5210	+	10.2083i	1.20105	+	0.789942i	0.982569	−	0.185900i	$-0.0595199\pi$
$167$	15.5210	+	10.2083i	1.20105	+	0.789942i	0.218480	+	0.975842i	$0.429890\pi$
$168$	−16.4875	+	17.7439i	−1.27204	+	1.36897i
$169$	−1.85322	−	1.96430i	−0.142555	−	0.151100i
$170$	0.664035	−	1.61191i	0.0509291	−	0.123628i
$171$	8.90540	−	1.87245i	0.681013	−	0.143190i
$172$	3.27181	+	12.0248i	0.249473	+	0.916879i
$173$	−4.57402	+	9.10763i	−0.347757	+	0.692440i	−0.997717	−	0.0675274i	$-0.978489\pi$
$173$	−4.57402	+	9.10763i	−0.347757	+	0.692440i	0.649961	+	0.759968i	$0.274785\pi$
$174$	15.5989	+	4.11725i	1.18255	+	0.312128i
$175$	6.66811	+	2.87634i	0.504062	+	0.217431i
$176$	8.93583	+	0.451283i	0.673564	+	0.0340167i
$177$	−21.2813	−	13.5036i	−1.59960	−	1.01499i
$178$	6.80922	−	4.08232i	0.510372	−	0.305983i
$179$	−15.1718	−	12.7306i	−1.13399	−	0.951533i	−0.134767	−	0.990877i	$-0.543029\pi$
$179$	−15.1718	−	12.7306i	−1.13399	−	0.951533i	−0.999226	+	0.0393444i	$0.987473\pi$
$180$	8.58263	−	7.31176i	0.639711	−	0.544986i
$181$	4.33766	−	3.63973i	0.322415	−	0.270539i	−0.467186	−	0.884159i	$-0.654732\pi$
$181$	4.33766	−	3.63973i	0.322415	−	0.270539i	0.789601	+	0.613621i	$0.210288\pi$
$182$	9.04573	−	26.1874i	0.670514	−	1.94114i
$183$	−19.5325	+	4.96802i	−1.44388	+	0.367246i
$184$	−1.33346	−	3.76593i	−0.0983040	−	0.277628i
$185$	−11.4846	−	10.8351i	−0.844362	−	0.796615i
$186$	2.53423	+	0.995828i	0.185818	+	0.0730176i
$187$	1.34734	−	0.581184i	0.0985270	−	0.0425004i
$188$	4.15572	+	8.82292i	0.303087	+	0.643477i
$189$	−17.7997	+	18.5254i	−1.29474	+	1.34752i
$190$	6.80713	+	4.31818i	0.493841	+	0.313274i
$191$	−14.9949	−	1.75265i	−1.08499	−	0.126817i	−0.445249	−	0.895407i	$-0.646885\pi$
$191$	−14.9949	−	1.75265i	−1.08499	−	0.126817i	−0.639742	+	0.768590i	$0.720959\pi$
$192$	5.50297	−	12.7168i	0.397142	−	0.917757i
$193$	−12.5857	−	2.98287i	−0.905939	−	0.214712i	−0.248866	−	0.968538i	$-0.580058\pi$
$193$	−12.5857	−	2.98287i	−0.905939	−	0.214712i	−0.657074	+	0.753826i	$0.728206\pi$
$194$	12.7144	+	1.27417i	0.912842	+	0.0914803i
$195$	−5.59879	+	11.6180i	−0.400938	+	0.831985i
$196$	34.5021	−	5.18990i	2.46444	−	0.370707i
$197$	9.25889	−	1.63259i	0.659669	−	0.116317i	0.166215	−	0.986089i	$-0.446845\pi$
$197$	9.25889	−	1.63259i	0.659669	−	0.116317i	0.493454	+	0.869772i	$0.335734\pi$
$198$	9.46856	+	0.636987i	0.672901	+	0.0452687i
$199$	26.2872	+	4.63514i	1.86345	+	0.328576i	0.987966	−	0.154674i	$-0.0494326\pi$
$199$	26.2872	+	4.63514i	1.86345	+	0.328576i	0.875483	+	0.483250i	$0.160544\pi$
$200$	−4.14508	−	0.277860i	−0.293102	−	0.0196477i
$201$	6.57855	−	5.06685i	0.464015	−	0.357388i
$202$	10.6812	+	15.6714i	0.751526	+	1.10264i
$203$	−19.4459	−	26.1204i	−1.36483	−	1.83329i
$204$	−0.111991	−	2.26969i	−0.00784095	−	0.158910i
$205$	0.807998	+	13.8728i	0.0564330	+	0.968917i
$206$	−0.258517	+	1.17684i	−0.0180117	+	0.0819941i
$207$	−1.34740	−	4.01745i	−0.0936506	−	0.279232i
$208$	0.122324	+	15.8491i	0.00848165	+	1.09894i
$209$	1.56474	+	6.60217i	0.108236	+	0.456682i
$210$	−22.7457	+	0.746970i	−1.56960	+	0.0515458i
$211$	3.96928	+	0.231184i	0.273257	+	0.0159154i	0.194226	−	0.980957i	$-0.437780\pi$
$211$	3.96928	+	0.231184i	0.273257	+	0.0159154i	0.0790307	+	0.996872i	$0.474817\pi$
$212$	−3.74823	+	11.4594i	−0.257429	+	0.787037i
$213$	2.46757	+	2.00269i	0.169075	+	0.137222i
$214$	2.28317	−	14.3245i	0.156074	−	0.979204i
$215$	−5.85445	+	10.1402i	−0.399270	+	0.691557i
$216$	6.06138	−	13.3888i	0.412425	−	0.910992i
$217$	−2.74800	−	4.75967i	−0.186546	−	0.323107i
$218$	−16.9212	+	6.47642i	−1.14605	+	0.438639i
$219$	0.180590	+	0.934536i	0.0122031	+	0.0631501i
$220$	5.61285	+	6.25831i	0.378418	+	0.421935i
$221$	1.16657	+	2.32284i	0.0784723	+	0.156251i
$222$	−19.5607	−	6.40062i	−1.31283	−	0.429581i
$223$	−8.60046	−	2.57481i	−0.575930	−	0.172422i	−0.0144255	−	0.999896i	$-0.504592\pi$
$223$	−8.60046	−	2.57481i	−0.575930	−	0.172422i	−0.561504	+	0.827474i	$0.689777\pi$
$224$	−24.6827	+	13.1532i	−1.64919	+	0.878836i
$225$	−4.39098	−	0.368150i	−0.292732	−	0.0245433i
$226$	−9.08292	−	8.29078i	−0.604187	−	0.551495i
$227$	−9.08197	+	5.97331i	−0.602792	+	0.396462i	−0.813904	−	0.581000i	$-0.802662\pi$
$227$	−9.08197	+	5.97331i	−0.602792	+	0.396462i	0.211112	+	0.977462i	$0.432291\pi$
$228$	10.4256	+	1.31248i	0.690454	+	0.0869209i
$229$	19.8919	−	2.32502i	1.31449	−	0.153642i	0.570205	−	0.821503i	$-0.306864\pi$
$229$	19.8919	−	2.32502i	1.31449	−	0.153642i	0.744286	+	0.667861i	$0.232790\pi$
$230$	1.62914	−	3.38167i	0.107423	−	0.222981i
$231$	−14.1460	−	12.9154i	−0.930741	−	0.849773i
$232$	15.4740	+	10.3726i	1.01592	+	0.680996i
$233$	5.68162	+	15.6101i	0.372215	+	1.02265i	0.974503	+	0.224374i	$0.0720336\pi$
$233$	5.68162	+	15.6101i	0.372215	+	1.02265i	−0.602288	+	0.798279i	$0.705744\pi$
$234$	−0.151213	+	16.8103i	−0.00988513	+	1.09892i
$235$	−3.13404	+	8.61071i	−0.204442	+	0.561701i
$236$	−18.1387	−	22.7590i	−1.18073	−	1.48149i
$237$	2.63245	−	26.2364i	0.170996	−	1.70424i
$238$	−2.67810	+	3.72384i	−0.173595	+	0.241381i
$239$	1.81805	+	6.07270i	0.117600	+	0.392810i	0.996440	−	0.0843059i	$-0.0268673\pi$
$239$	1.81805	+	6.07270i	0.117600	+	0.392810i	−0.878840	+	0.477116i	$0.841682\pi$
$240$	12.1233	−	4.74599i	0.782553	−	0.306352i
$241$	−1.57007	+	2.10897i	−0.101137	+	0.135851i	−0.849810	−	0.527088i	$-0.823284\pi$
$241$	−1.57007	+	2.10897i	−0.101137	+	0.135851i	0.748674	+	0.662939i	$0.230691\pi$
$242$	0.353571	−	8.47325i	0.0227284	−	0.544681i
$243$	6.66549	−	14.0915i	0.427592	−	0.903972i
$244$	−23.1914	−	1.93883i	−1.48468	−	0.124121i
$245$	26.2952	+	19.5761i	1.67994	+	1.25067i
$246$	8.65645	+	15.9117i	0.551915	+	1.01449i
$247$	−11.5145	+	3.44720i	−0.732648	+	0.219340i
$248$	2.39072	+	2.04199i	0.151811	+	0.129667i
$249$	−15.8671	−	1.59203i	−1.00554	−	0.100891i
$250$	−11.2656	−	12.9852i	−0.712497	−	0.821257i
$251$	13.2115	+	4.80859i	0.833902	+	0.303516i	0.723459	−	0.690367i	$-0.242551\pi$
$251$	13.2115	+	4.80859i	0.833902	+	0.303516i	0.110443	+	0.993882i	$0.464773\pi$
$252$	−26.4095	+	13.5116i	−1.66364	+	0.851152i
$253$	2.96886	−	1.08058i	0.186651	−	0.0679353i
$254$	0.0144427	+	0.00802422i	0.000906215	+	0.000503484i
$255$	1.43962	−	1.57679i	0.0901528	−	0.0987427i
$256$	10.7989	−	11.8061i	0.674933	−	0.737879i
$257$	−0.794794	−	6.79990i	−0.0495779	−	0.424166i	−0.995120	−	0.0986676i	$-0.968542\pi$
$257$	−0.794794	−	6.79990i	−0.0495779	−	0.424166i	0.945543	−	0.325499i	$-0.105532\pi$
$258$	−1.27336	+	15.2095i	−0.0792762	+	0.946900i
$259$	22.8280	+	34.7082i	1.41846	+	2.15666i
$260$	−10.4894	+	10.5707i	−0.650526	+	0.655566i
$261$	16.2265	+	11.2746i	1.00439	+	0.697879i
$262$	5.52942	+	7.17737i	0.341609	+	0.443419i
$263$	7.82585	−	26.1402i	0.482562	−	1.61187i	−0.276611	−	0.960982i	$-0.589211\pi$
$263$	7.82585	−	26.1402i	0.482562	−	1.61187i	0.759173	−	0.650889i	$-0.225604\pi$
$264$	10.0946	+	4.26369i	0.621277	+	0.262412i
$265$	−10.1234	+	5.08414i	−0.621873	+	0.312316i
$266$	−14.8072	−	15.1856i	−0.907889	−	0.931089i
$267$	9.54687	−	1.84484i	0.584259	−	0.112902i
$268$	9.08983	−	3.05102i	0.555250	−	0.186371i
$269$	−2.73455	+	1.57879i	−0.166729	+	0.0962608i	−0.581042	−	0.813873i	$-0.697355\pi$
$269$	−2.73455	+	1.57879i	−0.166729	+	0.0962608i	0.414314	+	0.910134i	$0.364022\pi$
$270$	12.9410	−	4.81828i	0.787563	−	0.293231i
$271$	11.3057	+	6.52734i	0.686771	+	0.396508i	0.802401	−	0.596785i	$-0.203555\pi$
$271$	11.3057	+	6.52734i	0.686771	+	0.396508i	−0.115630	+	0.993292i	$0.536889\pi$
$272$	0.733148	−	2.51949i	0.0444536	−	0.152767i
$273$	21.3833	−	26.3469i	1.29418	−	1.59459i
$274$	−6.70009	−	1.88619i	−0.404767	−	0.113949i
$275$	0.191030	−	3.27985i	0.0115195	−	0.197783i
$276$	0.0434264	−	4.89271i	0.00261396	−	0.294507i
$277$	−6.11196	+	1.44856i	−0.367232	+	0.0870356i	−0.410089	−	0.912046i	$-0.634502\pi$
$277$	−6.11196	+	1.44856i	−0.367232	+	0.0870356i	0.0428566	+	0.999081i	$0.486354\pi$
$278$	−2.37236	−	17.7551i	−0.142285	−	1.06488i
$279$	2.49920	+	2.20794i	0.149623	+	0.132186i
$280$	−25.1077	−	7.75693i	−1.50047	−	0.463565i
$281$	20.3261	−	1.18386i	1.21255	−	0.0706232i	0.560083	−	0.828437i	$-0.310769\pi$
$281$	20.3261	−	1.18386i	1.21255	−	0.0706232i	0.652471	+	0.757813i	$0.273732\pi$
$282$	1.08552	+	11.8951i	0.0646417	+	0.708341i
$283$	11.5568	−	8.60371i	0.686979	−	0.511437i	−0.196146	−	0.980575i	$-0.562843\pi$
$283$	11.5568	−	8.60371i	0.686979	−	0.511437i	0.883125	+	0.469138i	$0.155435\pi$
$284$	1.93851	+	3.11583i	0.115029	+	0.184890i
$285$	6.02445	+	7.82186i	0.356858	+	0.463327i
$286$	−12.5326	+	0.206479i	−0.741068	+	0.0122094i
$287$	6.34898	−	36.0069i	0.374769	−	2.12542i
$288$	11.6617	−	12.3291i	0.687170	−	0.726497i
$289$	2.87729	+	16.3179i	0.169252	+	0.959879i
$290$	3.32294	+	17.1849i	0.195130	+	1.00913i
$291$	14.0983	+	6.79402i	0.826455	+	0.398272i
$292$	−0.155093	+	1.08808i	−0.00907613	+	0.0636748i
$293$	7.48337	−	31.5748i	0.437183	−	1.84462i	−0.0915046	−	0.995805i	$-0.529168\pi$
$293$	7.48337	−	31.5748i	0.437183	−	1.84462i	0.528688	−	0.848816i	$-0.322684\pi$
$294$	41.8809	+	8.48455i	2.44255	+	0.494829i
$295$	3.17449	−	27.1595i	0.184826	−	1.58129i
$296$	−18.9376	−	14.3579i	−1.10073	−	0.834538i
$297$	10.6298	+	4.70063i	0.616805	+	0.272758i
$298$	−10.4173	−	19.9176i	−0.603459	−	1.15379i
$299$	2.21675	+	5.13899i	0.128198	+	0.297196i
$300$	−4.65387	−	2.05666i	−0.268691	−	0.118742i
$301$	21.1411	−	22.4083i	1.21855	−	1.29159i
$302$	−17.4461	+	7.86889i	−1.00391	+	0.452803i
$303$	5.72556	+	22.5109i	0.328925	+	1.29322i
$304$	10.8846	+	5.36165i	0.624274	+	0.307512i
$305$	−14.0552	−	16.7504i	−0.804800	−	0.959124i
$306$	0.822172	−	2.65896i	0.0470005	−	0.152003i
$307$	−16.8620	+	20.0954i	−0.962367	+	1.14690i	0.0267302	+	0.999643i	$0.491491\pi$
$307$	−16.8620	+	20.0954i	−0.962367	+	1.14690i	−0.989098	+	0.147262i	$0.952954\pi$
$308$	−10.5725	−	19.4280i	−0.602422	−	1.10701i
$309$	−0.790634	+	1.24602i	−0.0449776	+	0.0708835i
$310$	0.220324	+	2.94588i	0.0125136	+	0.167315i
$311$	3.55428	−	8.23974i	0.201544	−	0.467233i	−0.787228	−	0.616662i	$-0.788484\pi$
$311$	3.55428	−	8.23974i	0.201544	−	0.467233i	0.988772	+	0.149430i	$0.0477437\pi$
$312$	−6.50039	+	18.2909i	−0.368012	+	1.03552i
$313$	−15.0485	−	7.55765i	−0.850593	−	0.427184i	−0.0305824	−	0.999532i	$-0.509736\pi$
$313$	−15.0485	−	7.55765i	−0.850593	−	0.427184i	−0.820011	+	0.572348i	$0.806033\pi$
$314$	1.13627	+	3.57970i	0.0641236	+	0.202014i
$315$	−26.4895	−	8.67138i	−1.49252	−	0.488577i
$316$	12.7610	−	27.6441i	0.717863	−	1.55510i
$317$	7.53896	−	7.11264i	0.423430	−	0.399486i	−0.444814	−	0.895623i	$-0.646730\pi$
$317$	7.53896	−	7.11264i	0.423430	−	0.399486i	0.868244	+	0.496137i	$0.165249\pi$
$318$	−9.11538	+	11.6173i	−0.511165	+	0.651466i
$319$	−8.09552	+	12.3086i	−0.453262	+	0.689152i
$320$	15.0208	−	0.611167i	0.839686	−	0.0341652i
$321$	8.62988	−	15.5284i	0.481673	−	0.866713i
$322$	−6.22277	+	7.66911i	−0.346782	+	0.427383i
$323$	1.98989			0.110720
$324$	12.5859	−	12.8684i	0.699215	−	0.714911i
$325$	5.81995			0.322832
$326$	−20.7566	+	25.5810i	−1.14960	+	1.41680i
$327$	−22.1872	+	0.362890i	−1.22696	+	0.0200679i
$328$	3.45156	+	20.6294i	0.190581	+	1.13907i
$329$	13.2484	−	20.1432i	0.730407	−	1.11053i
$330$	3.83707	+	9.55420i	0.211224	+	0.525942i
$331$	−13.5269	+	12.7620i	−0.743506	+	0.701461i	−0.961597	−	0.274467i	$-0.911499\pi$
$331$	−13.5269	+	12.7620i	−0.743506	+	0.701461i	0.218091	+	0.975928i	$0.430017\pi$
$332$	−16.7184	−	7.71752i	−0.917542	−	0.423554i
$333$	−19.8290	−	15.5625i	−1.08662	−	0.852817i
$334$	7.94848	+	25.0408i	0.434922	+	1.37017i
$335$	8.05059	+	4.04316i	0.439851	+	0.220901i
$336$	−33.9173	+	4.79447i	−1.85034	+	0.261560i
$337$	4.82129	−	11.1770i	0.262632	−	0.608851i	−0.734967	−	0.678103i	$-0.762802\pi$
$337$	4.82129	−	11.1770i	0.262632	−	0.608851i	0.997599	+	0.0692527i	$0.0220615\pi$
$338$	−0.284839	−	3.80850i	−0.0154932	−	0.207155i
$339$	−6.97889	−	13.3473i	−0.379041	−	0.724925i
$340$	2.16555	−	1.17846i	0.117444	−	0.0639112i
$341$	−1.59825	+	1.90472i	−0.0865502	+	0.103147i
$342$	11.4482	+	5.87904i	0.619048	+	0.317902i
$343$	−33.1954	−	39.5608i	−1.79239	−	2.13608i
$344$	−7.12186	+	16.1207i	−0.383985	+	0.869172i
$345$	3.29188	−	3.20909i	0.177229	−	0.172771i
$346$	−13.1386	+	5.92603i	−0.706337	+	0.318585i
$347$	−1.35958	+	1.44107i	−0.0729863	+	0.0773609i	−0.762838	−	0.646590i	$-0.776194\pi$
$347$	−1.35958	+	1.44107i	−0.0729863	+	0.0773609i	0.689851	+	0.723951i	$0.257676\pi$
$348$	13.4616	+	18.4212i	0.721617	+	0.987477i
$349$	1.37157	+	3.17965i	0.0734182	+	0.170203i	0.950973	−	0.309274i	$-0.100086\pi$
$349$	1.37157	+	3.17965i	0.0734182	+	0.170203i	−0.877555	+	0.479476i	$0.840827\pi$
$350$	4.75975	+	9.10049i	0.254420	+	0.486442i
$351$	−7.21796	+	19.2825i	−0.385266	+	1.02922i
$352$	9.41101	+	8.45803i	0.501608	+	0.450815i
$353$	−0.509746	+	4.36115i	−0.0271310	+	0.232121i	0.972869	+	0.231358i	$0.0743169\pi$
$353$	−0.509746	+	4.36115i	−0.0271310	+	0.232121i	−1.00000		0.000762794i	$0.999757\pi$
$354$	−11.3380	−	33.7924i	−0.602608	−	1.79605i
$355$	−0.795139	+	3.35495i	−0.0422016	+	0.178062i
$356$	11.1154	+	1.58437i	0.589113	+	0.0839715i
$357$	−4.64243	+	3.16333i	−0.245703	+	0.167421i
$358$	−5.31744	−	27.4996i	−0.281035	−	1.45340i
$359$	3.66720	+	20.7977i	0.193547	+	1.09766i	0.914472	+	0.404649i	$0.132606\pi$
$359$	3.66720	+	20.7977i	0.193547	+	1.09766i	−0.720925	+	0.693013i	$0.756283\pi$
$360$	15.9405	−	0.381893i	0.840140	−	0.0201275i
$361$	1.70152	−	9.64979i	0.0895536	−	0.507884i
$362$	8.00677	−	0.131915i	0.420826	−	0.00693327i
$363$	3.95740	−	9.60314i	0.207710	−	0.504034i
$364$	33.2686	−	20.6980i	1.74375	−	1.08487i
$365$	−0.828322	+	0.616663i	−0.0433563	+	0.0322776i
$366$	−25.8770	−	11.9490i	−1.35261	−	0.624587i
$367$	5.45800	−	0.317892i	0.284905	−	0.0165938i	0.0849028	−	0.996389i	$-0.472942\pi$
$367$	5.45800	−	0.317892i	0.284905	−	0.0165938i	0.200002	+	0.979795i	$0.435905\pi$
$368$	1.89133	−	5.32387i	0.0985922	−	0.277526i
$369$	3.29475	+	21.9390i	0.171518	+	1.14210i
$370$	−2.95725	−	22.1325i	−0.153740	−	1.15061i
$371$	29.0024	−	6.87369i	1.50573	−	0.356864i
$372$	1.89568	+	3.35177i	0.0982864	+	0.173781i
$373$	0.232345	−	3.98922i	0.0120304	−	0.206554i	−0.986936	−	0.161110i	$-0.948493\pi$
$373$	0.232345	−	3.98922i	0.0120304	−	0.206554i	0.998967	−	0.0454441i	$-0.0144703\pi$
$374$	1.99749	+	0.562327i	0.103288	+	0.0290772i
$375$	−7.52366	−	19.6644i	−0.388520	−	1.01546i
$376$	−3.29811	+	13.3922i	−0.170087	+	0.690649i
$377$	−22.6011	−	13.0488i	−1.16402	−	0.672045i
$378$	−36.0546	+	4.48338i	−1.85445	+	0.230600i
$379$	9.35061	−	5.39858i	0.480309	−	0.277306i	−0.240236	−	0.970714i	$-0.577225\pi$
$379$	9.35061	−	5.39858i	0.480309	−	0.277306i	0.720545	+	0.693408i	$0.243892\pi$
$380$	3.62764	+	10.8078i	0.186094	+	0.554426i
$381$	0.0132588	+	0.0152864i	0.000679268	+	0.000783145i
$382$	−14.9053	−	15.2862i	−0.762622	−	0.782110i
$383$	5.26374	−	2.64355i	0.268965	−	0.135079i	−0.309206	−	0.950995i	$-0.600063\pi$
$383$	5.26374	−	2.64355i	0.268965	−	0.135079i	0.578170	+	0.815916i	$0.303767\pi$
$384$	17.3748	−	9.06180i	0.886654	−	0.462433i
$385$	5.96032	−	19.9089i	0.303766	−	1.01465i
$386$	−11.1634	−	14.4905i	−0.568203	−	0.737545i
$387$	−7.83857	+	16.9700i	−0.398457	+	0.862633i
$388$	12.8273	+	12.7287i	0.651208	+	0.646202i
$389$	−10.6132	−	16.1366i	−0.538111	−	0.818157i	0.459433	−	0.888213i	$-0.348053\pi$
$389$	−10.6132	−	16.1366i	−0.538111	−	0.818157i	−0.997543	+	0.0700554i	$0.977682\pi$
$390$	−16.5009	+	7.76977i	−0.835558	+	0.393438i
$391$	−0.107568	−	0.920307i	−0.00543997	−	0.0465419i
$392$	42.5141	+	25.0444i	2.14728	+	1.26493i
$393$	3.35595	+	10.5769i	0.169285	+	0.533535i
$394$	11.6227	+	6.45744i	0.585542	+	0.325321i
$395$	26.8823	−	9.78435i	1.35259	−	0.492304i
$396$	9.83056	+	9.13667i	0.494004	+	0.459135i
$397$	8.61212	+	3.13456i	0.432230	+	0.157319i	0.548967	−	0.835844i	$-0.315021\pi$
$397$	8.61212	+	3.13456i	0.432230	+	0.157319i	−0.116737	+	0.993163i	$0.537243\pi$
$398$	24.7378	+	28.5139i	1.23999	+	1.42927i
$399$	−10.6775	−	23.6807i	−0.534544	−	1.18552i
$400$	−4.30445	−	3.99870i	−0.215222	−	0.199935i
$401$	9.34389	−	2.79738i	0.466611	−	0.139694i	−0.0448624	−	0.998993i	$-0.514285\pi$
$401$	9.34389	−	2.79738i	0.466611	−	0.139694i	0.511474	+	0.859299i	$0.329100\pi$
$402$	11.7393	+	0.297649i	0.585505	+	0.0148454i
$403$	−3.53304	−	2.63025i	−0.175993	−	0.131022i
$404$	−2.23448	+	26.7277i	−0.111169	+	1.32975i
$405$	16.9119	−	0.122441i	0.840359	−	0.00608415i
$406$	1.92001	−	46.0125i	0.0952883	−	2.28356i
$407$	11.2231	−	15.0753i	0.556309	−	0.747253i
$408$	1.89946	−	2.59231i	0.0940374	−	0.128339i
$409$	5.09887	+	17.0314i	0.252123	+	0.842149i	0.986550	+	0.163461i	$0.0522659\pi$
$409$	5.09887	+	17.0314i	0.252123	+	0.842149i	−0.734427	+	0.678688i	$0.762549\pi$
$410$	−11.4743	+	15.9548i	−0.566675	+	0.787950i
$411$	−6.92033	−	4.97819i	−0.341355	−	0.245556i
$412$	−1.33254	+	1.06202i	−0.0656496	+	0.0523220i
$413$	−24.6068	+	67.6067i	−1.21082	+	3.32671i
$414$	2.10014	−	5.61250i	0.103216	−	0.275839i
$415$	−5.91732	−	16.2577i	−0.290470	−	0.798059i
$416$	−13.9883	+	17.5141i	−0.685833	+	0.858700i
$417$	4.70963	−	21.4272i	0.230631	−	1.04930i
$418$	−4.16462	+	8.64465i	−0.203698	+	0.422824i
$419$	−35.3442	+	4.13115i	−1.72668	+	0.201820i	−0.920739	−	0.390180i	$-0.872413\pi$
$419$	−35.3442	+	4.13115i	−1.72668	+	0.201820i	−0.805939	+	0.591999i	$0.798339\pi$
$420$	−25.6444	−	19.4477i	−1.25132	−	0.948950i
$421$	−3.44004	+	2.26255i	−0.167657	+	0.110270i	−0.630565	−	0.776137i	$-0.717177\pi$
$421$	−3.44004	+	2.26255i	−0.167657	+	0.110270i	0.462907	+	0.886407i	$0.346806\pi$
$422$	4.15298	+	3.79079i	0.202164	+	0.184533i
$423$	−3.73508	+	14.1441i	−0.181606	+	0.687710i
$424$	−14.3274	+	9.24457i	−0.695799	+	0.448956i
$425$	−0.923051	−	0.276343i	−0.0447746	−	0.0134046i
$426$	0.925292	+	4.39808i	0.0448305	+	0.213088i
$427$	25.8201	+	51.4120i	1.24952	+	2.48800i
$428$	15.2715	−	13.6964i	0.738174	−	0.662041i
$429$	−14.5095	−	5.01385i	−0.700523	−	0.242071i
$430$	−15.4649	+	5.91903i	−0.745782	+	0.285441i
$431$	17.0278	+	29.4930i	0.820201	+	1.42063i	0.905532	+	0.424277i	$0.139472\pi$
$431$	17.0278	+	29.4930i	0.820201	+	1.42063i	−0.0853314	+	0.996353i	$0.527195\pi$
$432$	18.5868	−	9.30217i	0.894259	−	0.447551i
$433$	10.0869	−	17.4711i	0.484747	−	0.839607i	−0.515099	−	0.857131i	$-0.672245\pi$
$433$	10.0869	−	17.4711i	0.484747	−	0.839607i	0.999846	+	0.0175237i	$0.00557825\pi$
$434$	1.22341	−	7.67562i	0.0587254	−	0.368442i
$435$	−3.37675	+	21.1694i	−0.161903	+	1.01499i
$436$	−24.3534	−	7.96567i	−1.16632	−	0.381487i
$437$	4.27727	+	0.249122i	0.204609	+	0.0119171i
$438$	−0.634417	+	1.18721i	−0.0303136	+	0.0567269i
$439$	0.0545755	+	0.230272i	0.00260474	+	0.0109903i	0.974332	−	0.225117i	$-0.0722765\pi$
$439$	0.0545755	+	0.230272i	0.00260474	+	0.0109903i	−0.971727	+	0.236107i	$0.924128\pi$
$440$	0.587320	+	11.8742i	0.0279994	+	0.566080i
$441$	44.6427	+	27.3135i	2.12584	+	1.30064i
$442$	−0.788706	+	3.59039i	−0.0375149	+	0.170778i
$443$	0.00762099	+	0.130847i	0.000362084	+	0.00621675i	0.998484	−	0.0550362i	$-0.0175274\pi$
$443$	0.00762099	+	0.130847i	0.000362084	+	0.00621675i	−0.998122	+	0.0612529i	$0.980490\pi$
$444$	−15.7777	−	24.4589i	−0.748776	−	1.16077i
$445$	6.29959	+	8.46182i	0.298629	+	0.401129i
$446$	−7.15051	−	10.4912i	−0.338586	−	0.496773i
$447$	−3.64265	−	27.2869i	−0.172291	−	1.29063i
$448$	−38.8265	−	7.54947i	−1.83438	−	0.356679i
$449$	−5.46082	−	0.962890i	−0.257712	−	0.0454416i	0.0432994	−	0.999062i	$-0.486213\pi$
$449$	−5.46082	−	0.962890i	−0.257712	−	0.0454416i	−0.301011	+	0.953621i	$0.597324\pi$
$450$	−4.49404	−	4.31697i	−0.211851	−	0.203504i
$451$	−16.2899	+	2.87234i	−0.767059	+	0.135253i
$452$	−2.58701	−	17.1983i	−0.121683	−	0.808939i
$453$	−23.3749	+	1.74541i	−1.09825	+	0.0820065i
$454$	−15.2963	−	1.53291i	−0.717889	−	0.0719431i
$455$	35.8218	+	8.48993i	1.67935	+	0.398014i
$456$	10.2797	+	10.7313i	0.481390	+	0.502539i
$457$	−2.31503	−	0.270588i	−0.108292	−	0.0126576i	0.0617740	−	0.998090i	$-0.480324\pi$
$457$	−2.31503	−	0.270588i	−0.108292	−	0.0126576i	−0.170067	+	0.985433i	$0.554398\pi$
$458$	23.9166	+	15.1717i	1.11755	+	0.708929i
$459$	2.06035	−	2.71551i	0.0961691	−	0.126749i
$460$	4.80239	−	2.26200i	0.223913	−	0.105466i
$461$	3.63570	−	1.56829i	0.169332	−	0.0730425i	−0.309727	−	0.950826i	$-0.600238\pi$
$461$	3.63570	−	1.56829i	0.169332	−	0.0730425i	0.479058	+	0.877783i	$0.340978\pi$
$462$	−4.02632	−	26.7885i	−0.187322	−	1.24632i
$463$	−7.05129	−	6.65255i	−0.327701	−	0.309170i	0.504753	−	0.863264i	$-0.331583\pi$
$463$	−7.05129	−	6.65255i	−0.327701	−	0.309170i	−0.832454	+	0.554094i	$0.813065\pi$
$464$	7.75046	+	25.1794i	0.359806	+	1.16892i
$465$	−0.980841	+	3.48254i	−0.0454854	+	0.161499i
$466$	−7.67027	+	22.2054i	−0.355318	+	1.02865i
$467$	9.91840	−	8.32253i	0.458969	−	0.385121i	−0.383783	−	0.923424i	$-0.625379\pi$
$467$	9.91840	−	8.32253i	0.458969	−	0.385121i	0.842751	+	0.538303i	$0.180934\pi$
$468$	−15.1452	+	18.3260i	−0.700088	+	0.847119i
$469$	−18.1576	−	15.2360i	−0.838439	−	0.703534i
$470$	−11.1145	+	6.66345i	−0.512673	+	0.307362i
$471$	−0.192322	+	4.59576i	−0.00886173	+	0.211762i
$472$	0.360373	−	41.1563i	0.0165875	−	1.89437i
$473$	−12.7976	−	5.52034i	−0.588433	−	0.253825i
$474$	26.2694	−	26.4666i	1.20659	−	1.21565i
$475$	1.99958	−	3.98150i	0.0917472	−	0.182684i
$476$	−6.25923	+	1.70307i	−0.286891	+	0.0780601i
$477$	−15.3582	+	9.55001i	−0.703205	+	0.437265i
$478$	−3.41466	+	8.28891i	−0.156183	+	0.379126i
$479$	11.7926	+	12.4995i	0.538819	+	0.571115i	0.938386	−	0.345589i	$-0.112321\pi$
$479$	11.7926	+	12.4995i	0.538819	+	0.571115i	−0.399567	+	0.916704i	$0.630839\pi$
$480$	17.5425	+	5.59073i	0.800702	+	0.255181i
$481$	27.8159	+	18.2948i	1.26830	+	0.834171i
$482$	−3.60345	+	0.916982i	−0.164133	+	0.0417674i
$483$	−10.3749	+	6.21838i	−0.472075	+	0.282946i
$484$	7.93854	−	8.99008i	0.360843	−	0.408640i
$485$			16.9790i			0.770978i
$486$	19.8764	−	9.53559i	0.901613	−	0.432543i
$487$			35.4143i			1.60477i	0.596804	+	0.802387i	$0.296437\pi$
$487$			35.4143i			1.60477i	−0.596804	+	0.802387i	$0.703563\pi$
$488$	−23.7406	−	22.7943i	−1.07469	−	1.03185i
$489$	−34.6065	+	20.7420i	−1.56496	+	0.937985i
$490$	11.4332	+	44.9289i	0.516500	+	2.02968i
$491$	−2.05751	−	1.35324i	−0.0928541	−	0.0610711i	0.502233	−	0.864732i	$-0.332512\pi$
$491$	−2.05751	−	1.35324i	−0.0928541	−	0.0610711i	−0.595087	+	0.803661i	$0.702882\pi$
$492$	−4.67208	+	25.1873i	−0.210634	+	1.13553i
$493$	2.96498	+	3.14270i	0.133536	+	0.141540i
$494$	−15.7166	−	6.47454i	−0.707125	−	0.291303i
$495$	0.412379	+	12.6031i	0.0185351	+	0.566468i
$496$	0.805884	+	4.37277i	0.0361853	+	0.196343i
$497$	4.07137	−	8.10677i	0.182626	−	0.363638i
$498$	−16.0063	−	15.8870i	−0.717259	−	0.711914i
$499$	−27.9614	−	12.0614i	−1.25172	−	0.539940i	−0.336042	−	0.941847i	$-0.609088\pi$
$499$	−27.9614	−	12.0614i	−1.25172	−	0.539940i	−0.915681	+	0.401907i	$0.868348\pi$
$500$	−0.800871	−	24.2985i	−0.0358160	−	1.08666i
$501$	−1.34534	+	32.1484i	−0.0601052	+	1.43628i
$502$	10.2238	+	17.0531i	0.456310	+	0.761115i
$503$	4.75280	+	3.98807i	0.211917	+	0.177819i	0.742567	−	0.669771i	$-0.233608\pi$
$503$	4.75280	+	3.98807i	0.211917	+	0.177819i	−0.530651	+	0.847591i	$0.678052\pi$
$504$	−41.0421	−	8.69453i	−1.82816	−	0.387285i
$505$	−19.3045	+	16.1984i	−0.859041	+	0.720821i
$506$	4.22321	+	1.45880i	0.187744	+	0.0648514i
$507$	1.26805	−	4.50230i	0.0563162	−	0.199954i
$508$	0.00871052	+	0.0216815i	0.000386467	+	0.000961959i
$509$	30.0369	+	28.3384i	1.33136	+	1.25608i	0.942260	+	0.334882i	$0.108697\pi$
$509$	30.0369	+	28.3384i	1.33136	+	1.25608i	0.389103	+	0.921194i	$0.372785\pi$
$510$	2.98600	−	0.448796i	0.132222	−	0.0198730i
$511$	2.49481	−	1.07616i	0.110364	−	0.0476064i
$512$	22.3792	−	3.34258i	0.989029	−	0.147722i
$513$	10.7115	+	11.5629i	0.472924	+	0.510513i
$514$	5.18636	−	8.17572i	0.228760	−	0.360615i
$515$	−1.59019	−	0.185867i	−0.0700723	−	0.00819027i
$516$	−14.9511	+	15.5680i	−0.658184	+	0.685345i
$517$	−10.6134	−	2.51541i	−0.466775	−	0.110628i
$518$	−5.85827	+	58.4571i	−0.257398	+	2.56846i
$519$	−17.6035	+	1.31446i	−0.772709	+	0.0576984i
$520$	−20.9385	+	2.26170i	−0.918212	+	0.0991820i
$521$	18.6529	−	3.28901i	0.817198	−	0.144094i	0.250602	−	0.968090i	$-0.419371\pi$
$521$	18.6529	−	3.28901i	0.817198	−	0.144094i	0.566596	+	0.823996i	$0.308260\pi$
$522$	7.77313	+	26.8404i	0.340220	+	1.17477i
$523$	31.7974	+	5.60673i	1.39040	+	0.245165i	0.818194	−	0.574943i	$-0.194976\pi$
$523$	31.7974	+	5.60673i	1.39040	+	0.245165i	0.572208	+	0.820108i	$0.306087\pi$
$524$	−0.323241	+	12.8091i	−0.0141209	+	0.559569i
$525$	1.66435	+	12.4676i	0.0726383	+	0.544131i
$526$	31.8869	−	21.7332i	1.39033	−	0.947611i
$527$	0.435455	+	0.584917i	0.0189687	+	0.0254794i
$528$	7.28638	+	13.6772i	0.317099	+	0.595225i
$529$	1.22133	+	20.9694i	0.0531013	+	0.911714i
$530$	−15.6476	−	3.43732i	−0.679687	−	0.149308i
$531$	1.11171	−	43.6403i	0.0482442	−	1.89383i
$532$	−2.72955	−	29.8708i	−0.118341	−	1.29506i
$533$	−6.75747	−	28.5120i	−0.292698	−	1.23499i
$534$	12.1280	+	6.48096i	0.524832	+	0.280459i
$535$	19.2415	+	1.12069i	0.831882	+	0.0484516i
$536$	12.7009	+	4.74911i	0.548596	+	0.205130i
$537$	5.40354	−	33.8756i	0.233180	−	1.46184i
$538$	−4.40984	−	0.702878i	−0.190122	−	0.0303032i
$539$	−19.5107	+	33.7935i	−0.840385	+	1.45559i
$540$	18.5049	+	6.23999i	0.796325	+	0.268526i
$541$	19.5908	+	33.9323i	0.842276	+	1.45886i	0.887966	+	0.459909i	$0.152118\pi$
$541$	19.5908	+	33.9323i	0.842276	+	1.45886i	−0.0456902	+	0.998956i	$0.514549\pi$
$542$	6.59934	+	17.2423i	0.283466	+	0.740621i
$543$	9.26973	+	3.20322i	0.397802	+	0.137463i
$544$	3.05017	−	2.11357i	0.130775	−	0.0906185i
$545$	−10.8047	−	21.5140i	−0.462824	−	0.921558i
$546$	46.9596	−	9.87961i	2.00969	−	0.422808i
$547$	27.0906	+	8.11040i	1.15831	+	0.346776i	0.807613	−	0.589713i	$-0.200759\pi$
$547$	27.0906	+	8.11040i	1.15831	+	0.346776i	0.350698	+	0.936488i	$0.385944\pi$
$548$	−5.67717	−	8.04161i	−0.242517	−	0.343521i
$549$	−24.7732	−	24.5945i	−1.05729	−	1.04967i
$550$	3.13236	−	3.43164i	0.133564	−	0.146326i
$551$	−16.6920	+	10.9785i	−0.711102	+	0.467699i
$552$	4.40743	−	5.33437i	0.187593	−	0.227046i
$553$	−74.7599	+	8.73818i	−3.17912	+	0.371585i
$554$	−8.00279	−	3.85540i	−0.340006	−	0.163800i
$555$	5.87075	−	26.7099i	0.249199	−	1.13377i
$556$	13.2157	−	21.6122i	0.560472	−	0.916561i
$557$	−2.91197	−	8.00057i	−0.123384	−	0.338995i	0.862588	−	0.505908i	$-0.168842\pi$
$557$	−2.91197	−	8.00057i	−0.123384	−	0.338995i	−0.985972	+	0.166913i	$0.946620\pi$
$558$	0.777138	+	4.65166i	0.0328989	+	0.196921i
$559$	8.44430	−	23.2005i	0.357156	−	0.981278i
$560$	−20.6608	−	30.8912i	−0.873076	−	1.30539i
$561$	2.06315	+	1.48414i	0.0871063	+	0.0626606i
$562$	23.3766	+	16.8119i	0.986082	+	0.709167i
$563$	5.64182	+	18.8450i	0.237774	+	0.794221i	0.990694	+	0.136109i	$0.0434597\pi$
$563$	5.64182	+	18.8450i	0.237774	+	0.794221i	−0.752920	+	0.658112i	$0.771355\pi$
$564$	−9.40723	+	14.0302i	−0.396116	+	0.590777i
$565$	9.75808	−	13.1074i	0.410526	−	0.551432i
$566$	20.3579	+	0.849494i	0.855707	+	0.0357069i
$567$	−43.3715	−	9.94817i	−1.82143	−	0.417784i
$568$	−0.647590	+	5.14908i	−0.0271723	+	0.216051i
$569$	−12.8099	−	9.53663i	−0.537019	−	0.399796i	0.294197	−	0.955745i	$-0.404948\pi$
$569$	−12.8099	−	9.53663i	−0.537019	−	0.399796i	−0.831217	+	0.555949i	$0.812355\pi$
$570$	−0.353903	+	13.9580i	−0.0148233	+	0.584636i
$571$	13.1248	−	3.92930i	0.549255	−	0.164436i	−0.000138408	−	1.00000i	$-0.500044\pi$
$571$	13.1248	−	3.92930i	0.549255	−	0.164436i	0.549393	+	0.835564i	$0.314859\pi$
$572$	−13.9470	−	10.9407i	−0.583154	−	0.457452i
$573$	−10.7482	−	23.8376i	−0.449014	−	0.995829i
$574$	39.0569	−	33.8846i	1.63021	−	1.41432i
$575$	−1.94950	−	0.709560i	−0.0812998	−	0.0295907i
$576$	23.7926	−	3.14815i	0.991360	−	0.131173i
$577$	−2.85350	+	1.03859i	−0.118793	+	0.0432370i	−0.400733	−	0.916195i	$-0.631244\pi$
$577$	−2.85350	+	1.03859i	−0.118793	+	0.0432370i	0.281940	+	0.959432i	$0.409022\pi$
$578$	−11.3806	+	20.4839i	−0.473372	+	0.852017i
$579$	−6.77536	−	21.3539i	−0.281574	−	0.887436i
$580$	−11.6638	+	21.8331i	−0.484311	+	0.906569i
$581$	5.28462	+	45.2128i	0.219243	+	1.87574i
$582$	9.42847	+	20.0236i	0.390822	+	0.830004i
$583$	−7.40981	−	11.2661i	−0.306883	−	0.466593i
$584$	−1.13987	+	1.05670i	−0.0471682	+	0.0437266i
$585$	−22.2456	+	2.02741i	−0.919741	+	0.0838229i
$586$	36.3534	−	28.0066i	1.50175	−	1.15694i
$587$	−0.579435	+	1.93545i	−0.0239158	+	0.0798844i	−0.969114	−	0.246612i	$-0.920683\pi$
$587$	−0.579435	+	1.93545i	−0.0239158	+	0.0798844i	0.945199	+	0.326496i	$0.105868\pi$
$588$	38.4324	+	46.6364i	1.58493	+	1.92325i
$589$	−3.01325	+	1.51331i	−0.124159	+	0.0623548i
$590$	27.6872	−	26.9973i	1.13986	−	1.11146i
$591$	10.6699	+	12.3016i	0.438902	+	0.506021i
$592$	−8.00294	−	32.6423i	−0.328919	−	1.34159i
$593$	4.15567	−	2.39928i	0.170653	−	0.0985265i	−0.412241	−	0.911075i	$-0.635254\pi$
$593$	4.15567	−	2.39928i	0.170653	−	0.0985265i	0.582894	+	0.812548i	$0.301920\pi$
$594$	7.48485	+	14.6340i	0.307107	+	0.600442i
$595$	−5.27827	−	3.04741i	−0.216388	−	0.124932i
$596$	6.30785	−	31.1556i	0.258380	−	1.27618i
$597$	16.5210	+	43.1805i	0.676160	+	1.76726i
$598$	−2.14482	+	7.61881i	−0.0877082	+	0.311556i
$599$	−0.722412	+	12.4033i	−0.0295170	+	0.506786i	0.950856	+	0.309634i	$0.100206\pi$
$599$	−0.722412	+	12.4033i	−0.0295170	+	0.506786i	−0.980373	+	0.197153i	$0.936831\pi$
$600$	−3.27815	−	6.40550i	−0.133830	−	0.261504i
$601$	−16.4685	+	3.90310i	−0.671762	+	0.159211i	−0.552322	−	0.833631i	$-0.686258\pi$
$601$	−16.4685	+	3.90310i	−0.671762	+	0.159211i	−0.119440	+	0.992841i	$0.538110\pi$
$602$	43.1841	−	5.77008i	1.76005	−	0.235171i
$603$	13.3853	+	5.26162i	0.545092	+	0.214270i
$604$	−26.1707	−	6.90429i	−1.06487	−	0.280931i
$605$	11.2496	−	0.655217i	0.457363	−	0.0266384i
$606$	−13.7711	+	29.8229i	−0.559412	+	1.21147i
$607$	−12.8233	+	9.54658i	−0.520481	+	0.387484i	−0.825097	−	0.564992i	$-0.808879\pi$
$607$	−12.8233	+	9.54658i	−0.520481	+	0.387484i	0.304616	+	0.952475i	$0.401472\pi$
$608$	7.17561	+	15.5870i	0.291009	+	0.632135i
$609$	21.4900	−	52.1482i	0.870818	−	2.11315i
$610$	−0.509404	−	30.9191i	−0.0206251	−	1.25188i
$611$	3.35521	−	19.0283i	0.135737	−	0.769804i
$612$	3.27221	−	2.18740i	0.132271	−	0.0884203i
$613$	−1.55833	−	8.83770i	−0.0629402	−	0.356951i	−0.999970	−	0.00770301i	$-0.997548\pi$
$613$	−1.55833	−	8.83770i	−0.0629402	−	0.356951i	0.937030	−	0.349248i	$-0.113563\pi$
$614$	−36.4239	+	7.04308i	−1.46995	+	0.284235i
$615$	−19.8904	+	13.5533i	−0.802060	+	0.546521i
$616$	5.70126	−	30.7562i	0.229710	−	1.23920i
$617$	−8.81096	+	37.1764i	−0.354716	+	1.49666i	0.444587	+	0.895736i	$0.353351\pi$
$617$	−8.81096	+	37.1764i	−0.354716	+	1.49666i	−0.799303	+	0.600929i	$0.794798\pi$
$618$	−1.97855	+	0.663840i	−0.0795888	+	0.0267036i
$619$	2.44377	−	20.9078i	0.0982234	−	0.840355i	−0.850873	−	0.525371i	$-0.823927\pi$
$619$	2.44377	−	20.9078i	0.0982234	−	0.840355i	0.949097	−	0.314984i	$-0.101999\pi$
$620$	−2.38303	+	3.43142i	−0.0957047	+	0.137809i
$621$	4.76869	−	5.57904i	0.191361	−	0.223879i
$622$	11.2454	−	5.88159i	0.450900	−	0.235830i
$623$	−10.9936	−	25.4860i	−0.440450	−	1.02108i
$624$	−23.4371	+	14.2944i	−0.938234	+	0.572234i
$625$	10.6358	−	11.2733i	0.425433	−	0.450932i
$626$	−9.79157	−	21.7089i	−0.391350	−	0.867663i
$627$	−8.41512	+	8.20348i	−0.336067	+	0.327615i
$628$	−1.94193	+	4.94364i	−0.0774914	+	0.197273i
$629$	−3.54296	−	4.22234i	−0.141267	−	0.168356i
$630$	−21.3634	−	33.1267i	−0.851138	−	1.31980i
$631$	−6.90687	+	8.23128i	−0.274958	+	0.327682i	−0.885797	−	0.464072i	$-0.846388\pi$
$631$	−6.90687	+	8.23128i	−0.274958	+	0.327682i	0.610839	+	0.791755i	$0.290832\pi$
$632$	38.6467	−	18.9872i	1.53728	−	0.755270i
$633$	3.19095	+	6.10277i	0.126829	+	0.242563i
$634$	14.6170	−	1.09321i	0.580514	−	0.0434170i
$635$	−0.00869549	+	0.0201584i	−0.000345070	+	0.000799962i
$636$	−20.3621	+	4.63543i	−0.807411	+	0.183807i
$637$	−61.7719	−	31.0230i	−2.44749	−	1.22918i
$638$	−19.8582	+	6.30341i	−0.786193	+	0.249554i
$639$	−0.778049	+	5.44918i	−0.0307792	+	0.215566i
$640$	17.0401	+	12.7134i	0.673568	+	0.502540i
$641$	−22.7928	+	21.5039i	−0.900261	+	0.849352i	−0.989183	−	0.146686i	$-0.953139\pi$
$641$	−22.7928	+	21.5039i	−0.900261	+	0.849352i	0.0889224	+	0.996039i	$0.471658\pi$
$642$	23.3141	−	9.36317i	0.920133	−	0.369535i
$643$	−6.46813	+	9.83431i	−0.255078	+	0.387827i	−0.940212	−	0.340590i	$-0.889373\pi$
$643$	−6.46813	+	9.83431i	−0.255078	+	0.387827i	0.685134	+	0.728417i	$0.259744\pi$
$644$	−13.6674	+	2.87713i	−0.538572	+	0.113375i
$645$	−20.2777	+	0.331659i	−0.798434	+	0.0130590i
$646$	2.18525	+	1.77313i	0.0859776	+	0.0697629i
$647$	−22.7096			−0.892808			−0.446404	−	0.894831i	$-0.647296\pi$
$647$	−22.7096			−0.892808			−0.446404	+	0.894831i	$0.647296\pi$
$648$	25.2882	−	2.91691i	0.993413	−	0.114587i
$649$	32.5488			1.27765
$650$	6.39134	+	5.18598i	0.250689	+	0.203411i
$651$	4.62421	−	8.32073i	0.181237	−	0.326115i
$652$	−45.5890	+	9.59694i	−1.78540	+	0.375845i
$653$	−3.87948	+	5.89847i	−0.151816	+	0.230825i	−0.903386	−	0.428828i	$-0.858926\pi$
$653$	−3.87948	+	5.89847i	−0.151816	+	0.230825i	0.751570	+	0.659653i	$0.229297\pi$
$654$	−24.6889	−	19.3718i	−0.965412	−	0.757499i
$655$	−8.75683	+	8.26164i	−0.342157	+	0.322809i
$656$	−14.5918	+	25.7304i	−0.569715	+	1.00460i
$657$	−1.22758	+	1.10044i	−0.0478923	+	0.0429322i
$658$	32.4981	−	10.3156i	1.26691	−	0.402143i
$659$	−31.7478	−	15.9444i	−1.23672	−	0.621104i	−0.294356	−	0.955696i	$-0.595105\pi$
$659$	−31.7478	−	15.9444i	−1.23672	−	0.621104i	−0.942363	+	0.334592i	$0.891401\pi$
$660$	−4.29967	+	13.9113i	−0.167365	+	0.541497i
$661$	0.613844	−	1.42305i	0.0238758	−	0.0553503i	−0.905861	−	0.423575i	$-0.860775\pi$
$661$	0.613844	−	1.42305i	0.0238758	−	0.0553503i	0.929737	+	0.368225i	$0.120034\pi$
$662$	−26.2268	+	1.96151i	−1.01933	+	0.0762363i
$663$	−2.41213	+	3.80146i	−0.0936795	+	0.147636i
$664$	−11.4830	−	23.3725i	−0.445625	−	0.907028i
$665$	18.1155	−	21.5892i	0.702490	−	0.837195i
$666$	−7.90860	−	34.7594i	−0.306452	−	1.34690i
$667$	5.97978	+	7.12643i	0.231538	+	0.275936i
$668$	−13.5842	+	34.5819i	−0.525590	+	1.33801i
$669$	−3.83297	−	15.0699i	−0.148191	−	0.582635i
$670$	5.23825	+	11.6137i	0.202371	+	0.448678i
$671$	17.8614	−	18.9319i	0.689530	−	0.730859i
$672$	−41.5194	−	24.9574i	−1.60165	−	0.962754i
$673$	11.4995	+	26.6589i	0.443274	+	1.02762i	0.982635	+	0.185549i	$0.0594065\pi$
$673$	11.4995	+	26.6589i	0.443274	+	1.02762i	−0.539361	+	0.842075i	$0.681334\pi$
$674$	15.2541	−	7.97824i	0.587567	−	0.307310i
$675$	−3.36297	−	6.85122i	−0.129441	−	0.263704i
$676$	3.08083	−	4.43622i	0.118493	−	0.170624i
$677$	3.52226	−	30.1349i	0.135372	−	1.15818i	−0.739271	−	0.673408i	$-0.764830\pi$
$677$	3.52226	−	30.1349i	0.135372	−	1.15818i	0.874642	−	0.484769i	$-0.161096\pi$
$678$	4.22929	−	20.8764i	0.162425	−	0.801752i
$679$	10.3024	−	43.4691i	0.395368	−	1.66819i
$680$	3.42826	+	0.635494i	0.131468	+	0.0243701i
$681$	−16.9611	−	8.17364i	−0.649951	−	0.313215i
$682$	−3.45241	+	0.667572i	−0.132199	+	0.0255626i
$683$	−2.79816	−	15.8691i	−0.107068	−	0.607215i	−0.990374	−	0.138418i	$-0.955798\pi$
$683$	−2.79816	−	15.8691i	−0.107068	−	0.607215i	0.883305	−	0.468798i	$-0.155313\pi$
$684$	7.33353	+	16.6574i	0.280404	+	0.636910i
$685$	1.60605	−	9.10835i	0.0613639	−	0.348012i
$686$	−1.20310	−	73.0243i	−0.0459346	−	2.78808i
$687$	21.1666	+	27.4818i	0.807558	+	1.04850i
$688$	−22.1858	+	11.3574i	−0.845824	+	0.432995i
$689$	19.1603	−	14.2643i	0.729950	−	0.543428i
$690$	6.47459	−	0.590858i	0.246483	−	0.0224936i
$691$	1.85710	−	0.108163i	0.0706472	−	0.00411473i	−0.0227848	−	0.999740i	$-0.507253\pi$
$691$	1.85710	−	0.108163i	0.0706472	−	0.00411473i	0.0934320	+	0.995626i	$0.470216\pi$
$692$	−19.7091	−	5.19959i	−0.749226	−	0.197659i
$693$	6.59144	−	32.5163i	0.250388	−	1.23519i
$694$	−2.77716	+	0.371073i	−0.105420	+	0.0140857i
$695$	23.1603	−	5.48909i	0.878521	−	0.208213i
$696$	−1.63130	+	32.2249i	−0.0618344	+	1.22148i
$697$	−0.282067	+	4.84290i	−0.0106840	+	0.183438i
$698$	−1.32706	+	4.71398i	−0.0502300	+	0.178427i
$699$	−18.1318	+	22.3407i	−0.685808	+	0.845002i
$700$	−2.88211	+	14.2352i	−0.108933	+	0.538041i
$701$	−7.71155	−	4.45227i	−0.291261	−	0.168160i	0.347249	−	0.937773i	$-0.387116\pi$
$701$	−7.71155	−	4.45227i	−0.291261	−	0.168160i	−0.638511	+	0.769613i	$0.720449\pi$
$702$	−25.1087	+	14.7439i	−0.947666	+	0.556474i
$703$	22.0725	−	12.7436i	0.832481	−	0.480633i
$704$	2.79827	+	17.6743i	0.105464	+	0.666125i
$705$	−15.5831	+	3.01127i	−0.586892	+	0.113411i
$706$	−4.44588	+	4.33511i	−0.167323	+	0.163154i
$707$	59.2515	−	29.7572i	2.22838	−	1.11914i
$708$	17.6602	−	47.2130i	0.663712	−	1.77437i
$709$	1.29501	−	4.32562i	0.0486350	−	0.162452i	−0.930222	−	0.366997i	$-0.880386\pi$
$709$	1.29501	−	4.32562i	0.0486350	−	0.162452i	0.978857	+	0.204544i	$0.0655713\pi$
$710$	−3.86270	+	2.97581i	−0.144965	+	0.111680i
$711$	41.3218	−	19.4511i	1.54969	−	0.729473i
$712$	10.7949	+	11.6445i	0.404555	+	0.436395i
$713$	0.862781	+	1.31180i	0.0323114	+	0.0491271i
$714$	−7.91696	−	0.662822i	−0.296285	−	0.0248055i
$715$	−1.93354	−	16.5425i	−0.0723102	−	0.618653i
$716$	18.6646	−	34.9377i	0.697528	−	1.30568i
$717$	−7.40296	+	8.10833i	−0.276469	+	0.302811i
$718$	−14.5050	+	26.1073i	−0.541321	+	0.974318i
$719$	24.1971	−	8.80702i	0.902399	−	0.328446i	0.151185	−	0.988505i	$-0.451691\pi$
$719$	24.1971	−	8.80702i	0.902399	−	0.328446i	0.751214	+	0.660059i	$0.229469\pi$
$720$	17.8458	+	13.7847i	0.665075	+	0.513727i
$721$	3.95838	+	1.44073i	0.147418	+	0.0536556i
$722$	10.4672	−	9.08102i	0.389549	−	0.337960i
$723$	−4.53121	−	0.454642i	−0.168518	−	0.0169083i
$724$	8.91040	+	6.98972i	0.331152	+	0.259771i
$725$	9.26754	−	2.77452i	0.344188	−	0.103043i
$726$	12.9030	−	7.01964i	0.478875	−	0.260523i
$727$	−15.4273	−	11.4852i	−0.572166	−	0.425962i	0.271803	−	0.962353i	$-0.412380\pi$
$727$	−15.4273	−	11.4852i	−0.572166	−	0.425962i	−0.843970	+	0.536391i	$0.819787\pi$
$728$	54.9782	+	6.91451i	2.03763	+	0.256269i
$729$	26.8701	−	2.64516i	0.995189	−	0.0979688i
$730$	−1.45913	−	0.0608867i	−0.0540050	−	0.00225352i
$731$	−2.44089	+	3.27868i	−0.0902795	+	0.121266i
$732$	−17.7701	−	36.1804i	−0.656803	−	1.33727i
$733$	5.08437	+	16.9830i	0.187796	+	0.627281i	0.999090	+	0.0426437i	$0.0135780\pi$
$733$	5.08437	+	16.9830i	0.187796	+	0.627281i	−0.811295	+	0.584637i	$0.801237\pi$
$734$	6.27712	+	4.51436i	0.231693	+	0.166628i
$735$	−5.66861	+	56.4965i	−0.209090	+	2.08390i
$736$	6.82095	−	4.16125i	0.251423	−	0.153386i
$737$	−3.66764	+	10.0768i	−0.135099	+	0.371183i
$738$	−15.9309	+	27.0287i	−0.586425	+	0.994941i
$739$	8.93259	+	24.5421i	0.328590	+	0.902795i	0.988469	+	0.151423i	$0.0483855\pi$
$739$	8.93259	+	24.5421i	0.328590	+	0.902795i	−0.659879	+	0.751372i	$0.729392\pi$
$740$	16.4740	−	26.9405i	0.605595	−	0.990352i
$741$	−15.3742	−	14.0368i	−0.564787	−	0.515654i
$742$	37.9747	+	18.2946i	1.39410	+	0.671616i
$743$	−21.5234	+	2.51572i	−0.789616	+	0.0922929i	−0.501335	−	0.865253i	$-0.667158\pi$
$743$	−21.5234	+	2.51572i	−0.789616	+	0.0922929i	−0.288281	+	0.957546i	$0.593084\pi$
$744$	−0.904863	+	5.37002i	−0.0331739	+	0.196875i
$745$	24.9535	−	16.4121i	0.914224	−	0.601295i
$746$	3.80983	−	4.17384i	0.139488	−	0.152815i
$747$	−11.7635	−	24.9904i	−0.430404	−	0.914349i
$748$	1.69253	+	2.39744i	0.0618850	+	0.0876590i
$749$	−48.5814	−	14.5443i	−1.77513	−	0.531438i
$750$	9.26000	−	28.2991i	0.338127	−	1.03334i
$751$	−0.459970	−	0.915875i	−0.0167845	−	0.0334208i	0.885084	−	0.465431i	$-0.154101\pi$
$751$	−0.459970	−	0.915875i	−0.0167845	−	0.0334208i	−0.901869	+	0.432010i	$0.857804\pi$
$752$	−15.5553	+	11.7681i	−0.567242	+	0.429140i
$753$	4.62023	+	23.9092i	0.168370	+	0.871301i
$754$	−13.1927	−	34.4690i	−0.480450	−	1.25529i
$755$	−12.7153	−	22.0236i	−0.462758	−	0.801520i
$756$	−43.5894	−	27.2036i	−1.58533	−	0.989387i
$757$	11.0146	−	19.0779i	0.400333	−	0.693397i	−0.593433	−	0.804883i	$-0.702228\pi$
$757$	11.0146	−	19.0779i	0.400333	−	0.693397i	0.993766	+	0.111487i	$0.0355612\pi$
$758$	15.0791	+	2.40344i	0.547699	+	0.0872970i
$759$	4.24894	+	3.44846i	0.154227	+	0.125171i
$760$	−5.64666	+	15.1013i	−0.204826	+	0.547783i
$761$	−6.54089	−	0.380963i	−0.237107	−	0.0138099i	−0.0608201	−	0.998149i	$-0.519372\pi$
$761$	−6.54089	−	0.380963i	−0.237107	−	0.0138099i	−0.176287	+	0.984339i	$0.556409\pi$
$762$	0.000939281		0.0286017i	3.40265e−5		0.00103613i
$763$	14.6078	+	61.6353i	0.528839	+	2.23135i
$764$	−2.74763	−	30.0686i	−0.0994056	−	1.08785i
$765$	3.62444	+	0.734718i	0.131042	+	0.0265638i
$766$	8.13611	+	1.78727i	0.293970	+	0.0645767i
$767$	3.35255	+	57.5611i	0.121054	+	2.07841i
$768$	27.1553	+	5.53068i	0.979883	+	0.199571i
$769$	−4.22827	−	5.67956i	−0.152475	−	0.204810i	0.719322	−	0.694677i	$-0.244453\pi$
$769$	−4.22827	−	5.67956i	−0.152475	−	0.204810i	−0.871797	+	0.489867i	$0.837045\pi$
$770$	24.2857	−	16.5524i	0.875195	−	0.596508i
$771$	9.39446	−	7.23568i	0.338333	−	0.260587i
$772$	0.652595	−	25.8605i	0.0234874	−	0.930739i
$773$	−10.1632	−	1.79204i	−0.365543	−	0.0644552i	−0.0121403	−	0.999926i	$-0.503864\pi$
$773$	−10.1632	−	1.79204i	−0.365543	−	0.0644552i	−0.353403	+	0.935471i	$0.614976\pi$
$774$	−23.7296	+	11.6514i	−0.852942	+	0.418799i
$775$	1.60791	−	0.283519i	0.0577580	−	0.0101843i
$776$	2.74453	+	25.4084i	0.0985228	+	0.912109i
$777$	−31.2369	+	64.8196i	−1.12062	+	2.32539i
$778$	2.72363	−	27.1779i	0.0976470	−	0.974376i
$779$	−21.8271	−	5.17312i	−0.782037	−	0.185346i
$780$	−25.0444	−	6.17090i	−0.896733	−	0.220954i
$781$	−4.07637	−	0.476460i	−0.145864	−	0.0170491i
$782$	0.701928	−	1.10651i	0.0251009	−	0.0395688i
$783$	−2.30123	+	34.1460i	−0.0822394	+	1.22028i
$784$	24.3717	+	65.3862i	0.870419	+	2.33522i
$785$	−4.58230	+	1.97661i	−0.163549	+	0.0705482i
$786$	−5.73934	+	14.6057i	−0.204715	+	0.520969i
$787$	−2.27711	−	2.14835i	−0.0811704	−	0.0765803i	0.644587	−	0.764531i	$-0.277029\pi$
$787$	−2.27711	−	2.14835i	−0.0811704	−	0.0765803i	−0.725758	+	0.687950i	$0.758511\pi$
$788$	7.00973	+	17.4480i	0.249711	+	0.621560i
$789$	45.8032	−	11.6499i	1.63064	−	0.414746i
$790$	38.2401	+	13.2090i	1.36052	+	0.469956i
$791$	−32.9355	+	27.6361i	−1.17105	+	0.982628i
$792$	2.65431	+	18.7934i	0.0943166	+	0.667794i
$793$	35.3200	+	29.6370i	1.25425	+	1.05244i
$794$	6.66454	+	11.1163i	0.236516	+	0.394503i
$795$	−16.5674	−	10.5125i	−0.587586	−	0.372840i
$796$	1.75861	+	53.3564i	0.0623323	+	1.89117i
$797$	−5.63584	−	2.43106i	−0.199632	−	0.0861127i	0.293917	−	0.955831i	$-0.405041\pi$
$797$	−5.63584	−	2.43106i	−0.199632	−	0.0861127i	−0.493548	+	0.869718i	$0.664300\pi$
$798$	9.37535	−	35.5200i	0.331884	−	1.25740i
$799$	−1.43565	+	2.85861i	−0.0507895	+	0.101130i
$800$	−1.16393	−	8.22684i	−0.0411512	−	0.290863i
$801$	11.2417	+	12.5405i	0.397205	+	0.443095i
$802$	12.7539	+	5.25403i	0.450356	+	0.185526i
$803$	−0.843532	−	0.894092i	−0.0297676	−	0.0315518i
$804$	12.6267	+	10.7874i	0.445308	+	0.380443i
$805$	−10.9641	−	7.21122i	−0.386435	−	0.254162i
$806$	−1.53617	−	6.03666i	−0.0541093	−	0.212632i
$807$	−4.78047	−	2.65673i	−0.168281	−	0.0935213i
$808$	−26.2701	+	27.3607i	−0.924179	+	0.962547i
$809$		−	2.39934i		−	0.0843563i	−0.999110	−	0.0421782i	$-0.986570\pi$
$809$		−	2.39934i		−	0.0843563i	0.999110	−	0.0421782i	$-0.0134297\pi$
$810$	18.6814	+	14.9352i	0.656397	+	0.524770i
$811$			4.44860i			0.156211i	0.996945	+	0.0781057i	$0.0248872\pi$
$811$			4.44860i			0.156211i	−0.996945	+	0.0781057i	$0.975113\pi$
$812$	43.1088	−	48.8190i	1.51282	−	1.71321i
$813$	0.369778	+	22.6083i	0.0129687	+	0.792909i
$814$	25.7581	−	6.55475i	0.902821	−	0.229744i
$815$	−36.5718	−	24.0537i	−1.28106	−	0.842564i
$816$	4.39588	−	1.15427i	0.153886	−	0.0404075i
$817$	−12.9705	−	13.7480i	−0.453781	−	0.480980i
$818$	−9.57671	+	23.2470i	−0.334842	+	0.812812i
$819$	58.1825	+	8.30746i	2.03306	+	0.290286i
$820$	−26.8176	+	7.29679i	−0.936512	+	0.254815i
$821$	12.5903	−	25.0693i	0.439404	−	0.874924i	−0.559533	−	0.828808i	$-0.689019\pi$
$821$	12.5903	−	25.0693i	0.439404	−	0.874924i	0.998936	−	0.0461160i	$-0.0146844\pi$
$822$	−3.16384	−	11.6334i	−0.110352	−	0.405763i
$823$	−39.9556	−	17.2352i	−1.39276	−	0.600780i	−0.438225	−	0.898865i	$-0.644393\pi$
$823$	−39.9556	−	17.2352i	−1.39276	−	0.600780i	−0.954539	+	0.298085i	$0.903652\pi$
$824$	−2.40970	−	0.0210998i	−0.0839459	−	0.000735048i
$825$	5.04277	−	2.63671i	0.175567	−	0.0917985i
$826$	−87.2649	+	52.3178i	−3.03634	+	1.82037i
$827$	−22.9248	−	19.2362i	−0.797175	−	0.668909i	0.150335	−	0.988635i	$-0.451965\pi$
$827$	−22.9248	−	19.2362i	−0.797175	−	0.668909i	−0.947510	+	0.319726i	$0.896409\pi$
$828$	7.30746	−	4.29215i	0.253952	−	0.149163i
$829$	20.2155	−	16.9628i	0.702115	−	0.589144i	−0.220260	−	0.975441i	$-0.570691\pi$
$829$	20.2155	−	16.9628i	0.702115	−	0.589144i	0.922374	+	0.386297i	$0.126246\pi$
$830$	7.98847	−	23.1266i	0.277284	−	0.802736i
$831$	−7.59437	−	7.79030i	−0.263446	−	0.270242i
$832$	−30.9679	+	6.76908i	−1.07362	+	0.234675i
$833$	8.32407	+	7.85335i	0.288412	+	0.272103i
$834$	24.2652	−	19.3343i	0.840234	−	0.669492i
$835$	−32.0542	+	13.8268i	−1.10928	+	0.478497i
$836$	−12.2765	+	5.78240i	−0.424591	+	0.199988i
$837$	−1.05481	+	5.67893i	−0.0364594	+	0.196293i
$838$	−42.4954	−	26.9574i	−1.46798	−	0.931228i
$839$	30.4065	+	3.55401i	1.04975	+	0.122698i	0.623434	−	0.781876i	$-0.285737\pi$
$839$	30.4065	+	3.55401i	1.04975	+	0.122698i	0.426316	+	0.904574i	$0.359811\pi$
$840$	−10.8329	−	44.2080i	−0.373771	−	1.52532i
$841$	−13.9918	−	3.31612i	−0.482477	−	0.114349i
$842$	−5.79386	−	0.580631i	−0.199670	−	0.0200099i
$843$	19.8580	+	29.1431i	0.683945	+	1.00374i
$844$	1.18286	+	7.86356i	0.0407155	+	0.270675i
$845$	4.99761	−	0.881214i	0.171923	−	0.0303147i
$846$	−16.7052	+	12.2045i	−0.574335	+	0.419600i
$847$	−29.1985	−	5.14848i	−1.00327	−	0.176904i
$848$	−23.9716	−	2.61450i	−0.823187	−	0.0897824i
$849$	23.0726	+	9.50810i	0.791850	+	0.326317i
$850$	−0.767433	−	1.12598i	−0.0263227	−	0.0386207i
$851$	−7.08699	−	9.51947i	−0.242939	−	0.326323i
$852$	−2.90286	+	5.65438i	−0.0994504	+	0.193716i
$853$	1.09214	+	18.7513i	0.0373941	+	0.642031i	0.963984	+	0.265959i	$0.0856886\pi$
$853$	1.09214	+	18.7513i	0.0373941	+	0.642031i	−0.926590	+	0.376072i	$0.877274\pi$
$854$	−17.4566	+	79.4670i	−0.597353	+	2.71931i
$855$	−6.25603	+	15.9150i	−0.213952	+	0.544283i
$856$	28.9753	−	1.43317i	0.990354	−	0.0489848i
$857$	3.70236	+	15.6215i	0.126470	+	0.533620i	0.998985	+	0.0450331i	$0.0143393\pi$
$857$	3.70236	+	15.6215i	0.126470	+	0.533620i	−0.872515	+	0.488587i	$0.837513\pi$
$858$	−11.4663	−	18.4350i	−0.391453	−	0.629362i
$859$	34.2151	+	1.99280i	1.16740	+	0.0679935i	0.630872	−	0.775887i	$-0.282697\pi$
$859$	34.2151	+	1.99280i	1.16740	+	0.0679935i	0.536532	+	0.843880i	$0.319734\pi$
$860$	−22.2574	−	7.28011i	−0.758973	−	0.248250i
$861$	59.1465	−	22.6297i	2.01571	−	0.771218i
$862$	−7.58077	+	47.5616i	−0.258202	+	1.61995i
$863$	20.0705	−	34.7631i	0.683207	−	1.18335i	−0.290789	−	0.956787i	$-0.593918\pi$
$863$	20.0705	−	34.7631i	0.683207	−	1.18335i	0.973997	−	0.226562i	$-0.0727488\pi$
$864$	28.7005	+	6.34671i	0.976411	+	0.215919i
$865$	−9.57586	−	16.5859i	−0.325589	−	0.563937i
$866$	26.6452	−	10.1982i	0.905441	−	0.346549i
$867$	−21.6805	+	18.8048i	−0.736307	+	0.638643i
$868$	8.18303	−	7.33906i	0.277750	−	0.249104i
$869$	15.2827	+	30.4303i	0.518429	+	1.03228i
$870$	−22.5717	+	20.2388i	−0.765251	+	0.686160i
$871$	−18.1981	−	5.44815i	−0.616618	−	0.184603i
$872$	−19.6464	−	30.4483i	−0.665311	−	1.03111i
$873$	2.46022	+	26.9946i	0.0832657	+	0.913628i
$874$	4.47522	+	4.08492i	0.151376	+	0.138175i
$875$	−50.2136	+	33.0260i	−1.69753	+	1.11648i
$876$	−1.75459	+	0.738454i	−0.0592819	+	0.0249500i
$877$	41.2763	−	4.82451i	1.39380	−	0.162912i	0.614182	−	0.789164i	$-0.289486\pi$
$877$	41.2763	−	4.82451i	1.39380	−	0.162912i	0.779621	+	0.626252i	$0.215412\pi$
$878$	−0.145255	+	0.301510i	−0.00490211	+	0.0101755i
$879$	53.5722	−	16.9979i	1.80695	−	0.573326i
$880$	−9.93574	+	13.5633i	−0.334934	+	0.457219i
$881$	11.8579	+	32.5794i	0.399504	+	1.09763i	0.962527	+	0.271187i	$0.0874161\pi$
$881$	11.8579	+	32.5794i	0.399504	+	1.09763i	−0.563023	+	0.826441i	$0.690362\pi$
$882$	24.6875	+	69.7748i	0.831271	+	2.34944i
$883$	7.39856	−	20.3274i	0.248981	−	0.684071i	−0.750743	−	0.660595i	$-0.770304\pi$
$883$	7.39856	−	20.3274i	0.248981	−	0.684071i	0.999724	−	0.0234765i	$-0.00747350\pi$
$884$	−4.06543	+	3.24010i	−0.136735	+	0.108976i
$885$	43.1759	−	19.4678i	1.45134	−	0.654403i
$886$	−0.108225	+	0.150485i	−0.00363589	+	0.00505563i
$887$	10.0492	+	33.5667i	0.337420	+	1.12706i	0.943421	+	0.331597i	$0.107588\pi$
$887$	10.0492	+	33.5667i	0.337420	+	1.12706i	−0.606001	+	0.795464i	$0.707227\pi$
$888$	4.46788	−	40.9193i	0.149932	−	1.37316i
$889$	0.0344934	−	0.0463327i	0.00115687	−	0.00155395i
$890$	−0.621995	+	14.9060i	−0.0208493	+	0.499649i
$891$	2.48179	+	19.9777i	0.0831432	+	0.669277i
$892$	1.49587	−	17.8928i	0.0500853	−	0.599096i
$893$	−11.8648	−	8.83298i	−0.397039	−	0.295585i
$894$	20.3143	−	33.2117i	0.679410	−	1.11077i
$895$	35.6537	−	10.6740i	1.19177	−	0.356793i
$896$	−35.9113	−	42.8877i	−1.19971	−	1.43278i
$897$	−5.66080	+	7.86925i	−0.189009	+	0.262746i
$898$	−5.13895	−	5.92339i	−0.171489	−	0.197666i
$899$	−6.87983	−	2.50405i	−0.229455	−	0.0835148i
$900$	−1.08854	−	8.74529i	−0.0362845	−	0.291510i
$901$	−3.71615	+	1.35257i	−0.123803	+	0.0450606i
$902$	−20.4486	−	11.3610i	−0.680864	−	0.378282i
$903$	52.1155	+	11.4548i	1.73430	+	0.381192i
$904$	12.4839	−	21.1920i	0.415207	−	0.704834i
$905$	1.23529	+	10.5686i	0.0410624	+	0.351311i
$906$	−27.2250	−	18.9119i	−0.904492	−	0.628304i
$907$	−19.2925	−	29.3328i	−0.640596	−	0.973979i	−0.999180	−	0.0404818i	$-0.987111\pi$
$907$	−19.2925	−	29.3328i	−0.640596	−	0.973979i	0.358584	−	0.933497i	$-0.383260\pi$
$908$	−15.4321	−	15.3134i	−0.512132	−	0.508194i
$909$	−28.3448	+	28.5507i	−0.940136	+	0.946967i
$910$	31.7736	+	41.2432i	1.05329	+	1.36720i
$911$	−3.38749	+	11.3150i	−0.112233	+	0.374883i	−0.995589	−	0.0938182i	$-0.970093\pi$
$911$	−3.38749	+	11.3150i	−0.112233	+	0.374883i	0.883357	+	0.468701i	$0.155278\pi$
$912$	1.72660	+	20.9448i	0.0571735	+	0.693551i
$913$	18.4034	−	9.24255i	0.609065	−	0.305884i
$914$	−2.30120	−	2.36000i	−0.0761170	−	0.0780620i
$915$	12.3696	−	35.7962i	0.408927	−	1.18339i
$916$	12.7456	+	37.9726i	0.421126	+	1.25465i
$917$	27.4318	−	15.8378i	0.905879	−	0.523009i
$918$	4.68234	−	1.14619i	0.154540	−	0.0378300i
$919$	14.5934	+	8.42548i	0.481391	+	0.277931i	0.720996	−	0.692939i	$-0.243685\pi$
$919$	14.5934	+	8.42548i	0.481391	+	0.277931i	−0.239605	+	0.970870i	$0.577018\pi$
$920$	7.28948	+	1.79519i	0.240327	+	0.0591857i
$921$	−44.8691	−	7.15712i	−1.47849	−	0.235835i
$922$	5.39011	+	1.51740i	0.177514	+	0.0499730i
$923$	0.422728	−	7.25795i	0.0139143	−	0.238898i
$924$	19.4488	−	33.0063i	0.639820	−	1.08583i
$925$	−12.0085	+	2.84608i	−0.394839	+	0.0935784i
$926$	−1.81569	−	13.5889i	−0.0596672	−	0.446558i
$927$	−2.55514	−	0.0650908i	−0.0839219	−	0.00213786i
$928$	−13.9252	+	34.5576i	−0.457117	+	1.13441i
$929$	−23.7381	+	1.38259i	−0.778822	+	0.0453612i	−0.442950	−	0.896546i	$-0.646068\pi$
$929$	−23.7381	+	1.38259i	−0.778822	+	0.0453612i	−0.335872	+	0.941908i	$0.609031\pi$
$930$	−4.18032	+	2.95045i	−0.137078	+	0.0967491i
$931$	−42.4465	+	31.6002i	−1.39113	+	1.03566i
$932$	−28.2099	+	17.5507i	−0.924045	+	0.574894i
$933$	15.4061	−	2.05663i	0.504374	−	0.0673310i
$934$	18.3081	−	0.301633i	0.599060	−	0.00986974i
$935$	−0.478810	+	2.71546i	−0.0156587	+	0.0888052i
$936$	−32.9619	+	6.62975i	−1.07739	+	0.216700i
$937$	−2.43125	−	13.7883i	−0.0794255	−	0.450444i	−0.998421	−	0.0561761i	$-0.982109\pi$
$937$	−2.43125	−	13.7883i	−0.0794255	−	0.450444i	0.918995	−	0.394268i	$-0.129002\pi$
$938$	−6.36390	−	32.9115i	−0.207789	−	1.07460i
$939$	−2.17188	−	29.0863i	−0.0708767	−	0.949195i
$940$	−18.1433	−	2.58612i	−0.591768	−	0.0843500i
$941$	7.12830	−	30.0767i	0.232376	−	0.980471i	−0.724339	−	0.689444i	$-0.757855\pi$
$941$	7.12830	−	30.0767i	0.232376	−	0.980471i	0.956715	−	0.291027i	$-0.0939970\pi$
$942$	−4.30635	+	4.87559i	−0.140308	+	0.158855i
$943$	−1.21261	+	10.3745i	−0.0394879	+	0.337840i
$944$	37.0688	−	44.8758i	1.20649	−	1.46058i
$945$	−10.7048	−	47.0751i	−0.348227	−	1.53135i
$946$	−9.13502	−	17.4658i	−0.297005	−	0.567864i
$947$	−1.85058	−	4.29013i	−0.0601359	−	0.139411i	0.885499	−	0.464642i	$-0.153817\pi$
$947$	−1.85058	−	4.29013i	−0.0601359	−	0.139411i	−0.945634	+	0.325232i	$0.894558\pi$
$948$	52.4320	−	5.65718i	1.70291	−	0.183737i
$949$	1.49428	−	1.58384i	0.0485062	−	0.0514136i
$950$	5.74369	−	2.59063i	0.186350	−	0.0840510i
$951$	17.2798	+	4.86677i	0.560336	+	0.157816i
$952$	−8.39130	−	3.70713i	−0.271964	−	0.120149i
$953$	−22.0596	−	26.2896i	−0.714581	−	0.851605i	0.279511	−	0.960142i	$-0.409828\pi$
$953$	−22.0596	−	26.2896i	−0.714581	−	0.851605i	−0.994092	+	0.108538i	$0.965383\pi$
$954$	−25.3758	−	3.19763i	−0.821572	−	0.103527i
$955$	18.2355	−	21.7323i	0.590088	−	0.703239i
$956$	−11.1359	+	6.06001i	−0.360161	+	0.195995i
$957$	−25.4947	−	1.06690i	−0.824128	−	0.0344878i
$958$	1.81253	+	24.2347i	0.0585600	+	0.782988i
$959$	−9.63842	+	22.3444i	−0.311241	+	0.721537i
$960$	14.2831	+	21.7712i	0.460984	+	0.702662i
$961$	26.5984	+	13.3582i	0.858012	+	0.430910i
$962$	14.2449	+	44.8769i	0.459273	+	1.44689i
$963$	30.7540	−	1.00628i	0.991034	−	0.0324270i
$964$	−4.77433	−	2.20392i	−0.153771	−	0.0709833i
$965$	17.6792	−	16.6795i	0.569115	−	0.536932i
$966$	−16.9345	−	2.41589i	−0.544859	−	0.0777301i
$967$	19.7776	−	30.0704i	0.636005	−	0.966998i	−0.363370	−	0.931645i	$-0.618374\pi$
$967$	19.7776	−	30.0704i	0.636005	−	0.966998i	0.999375	−	0.0353531i	$-0.0112556\pi$
$968$	16.7287	−	2.79892i	0.537681	−	0.0899608i
$969$	1.77188	+	2.95625i	0.0569209	+	0.0949685i
$970$	−15.1295	+	18.6460i	−0.485779	+	0.598687i
$971$	13.0028			0.417279			0.208639	−	0.977993i	$-0.433096\pi$
$971$	13.0028			0.417279			0.208639	+	0.977993i	$0.433096\pi$
$972$	30.3247	+	7.23950i	0.972666	+	0.232207i
$973$	−62.6248			−2.00766
$974$	−31.5566	+	38.8912i	−1.01114	+	1.24615i
$975$	5.18231	+	8.64632i	0.165967	+	0.276904i
$976$	−5.76013	−	46.1868i	−0.184377	−	1.47840i
$977$	−4.72223	+	7.17980i	−0.151078	+	0.229702i	−0.903095	−	0.429441i	$-0.858711\pi$
$977$	−4.72223	+	7.17980i	−0.151078	+	0.229702i	0.752017	+	0.659143i	$0.229081\pi$
$978$	−56.4867	−	8.05844i	−1.80624	−	0.257680i
$979$	−9.13370	+	8.61720i	−0.291914	+	0.275407i
$980$	−27.4791	+	59.5277i	−0.877787	+	1.90154i
$981$	−20.2955	−	32.6390i	−0.647986	−	1.04208i
$982$	−1.05368	−	3.31949i	−0.0336242	−	0.105929i
$983$	−27.7334	−	13.9282i	−0.884559	−	0.444242i	−0.0523012	−	0.998631i	$-0.516656\pi$
$983$	−27.7334	−	13.9282i	−0.884559	−	0.444242i	−0.832257	+	0.554389i	$0.812952\pi$
$984$	−27.5744	+	23.4970i	−0.879041	+	0.749059i
$985$	−6.99764	+	16.2224i	−0.222963	+	0.516887i
$986$	0.455717	+	6.09325i	0.0145130	+	0.194049i
$987$	41.7224	+	1.74598i	1.32804	+	0.0555753i
$988$	−11.4904	−	21.1148i	−0.365558	−	0.671752i
$989$	−5.65716	+	6.74194i	−0.179887	+	0.214381i
$990$	−10.7774	+	14.2079i	−0.342528	+	0.451558i
$991$	−30.1636	−	35.9476i	−0.958179	−	1.14191i	−0.989807	−	0.142414i	$-0.954514\pi$
$991$	−30.1636	−	35.9476i	−0.958179	−	1.14191i	0.0316279	−	0.999500i	$-0.489931\pi$
$992$	−3.01144	+	5.52018i	−0.0956133	+	0.175266i
$993$	−31.0046	−	8.73229i	−0.983900	−	0.277111i
$994$	11.6948	−	5.27480i	0.370936	−	0.167307i
$995$	−34.4216	+	36.4847i	−1.09124	+	1.15664i
$996$	−3.42131	−	31.7095i	−0.108408	−	1.00475i
$997$	−5.60864	−	13.0023i	−0.177628	−	0.411787i	0.806021	−	0.591887i	$-0.201617\pi$
$997$	−5.60864	−	13.0023i	−0.177628	−	0.411787i	−0.983648	+	0.180100i	$0.942358\pi$
$998$	−19.9591	−	38.1610i	−0.631793	−	1.20797i
$999$	5.46358	−	43.3162i	0.172860	−	1.37046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.23.41	✓	936
3.2	odd	2		972.2.p.a.503.12		936
4.3	odd	2	inner	324.2.p.a.23.43	yes	936
12.11	even	2		972.2.p.a.503.10		936
81.7	even	27		972.2.p.a.143.10		936
81.74	odd	54	inner	324.2.p.a.155.43	yes	936
324.7	odd	54		972.2.p.a.143.12		936
324.155	even	54	inner	324.2.p.a.155.41	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.23.41	✓	936	1.1	even	1	trivial
324.2.p.a.23.43	yes	936	4.3	odd	2	inner
324.2.p.a.155.41	yes	936	324.155	even	54	inner
324.2.p.a.155.43	yes	936	81.74	odd	54	inner
972.2.p.a.143.10		936	81.7	even	27
972.2.p.a.143.12		936	324.7	odd	54
972.2.p.a.503.10		936	12.11	even	2
972.2.p.a.503.12		936	3.2	odd	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09818 + 0.891069i) q^{2} +(0.890440 + 1.48564i) q^{3} +(0.411991 + 1.95711i) q^{4} +(-1.03261 + 1.57001i) q^{5} +(-0.345944 + 2.42494i) q^{6} +(3.59628 - 3.39292i) q^{7} +(-1.29148 + 2.51636i) q^{8} +(-1.41423 + 2.64574i) q^{9} +O(q^{10})\)	\(q+(1.09818 + 0.891069i) q^{2} +(0.890440 + 1.48564i) q^{3} +(0.411991 + 1.95711i) q^{4} +(-1.03261 + 1.57001i) q^{5} +(-0.345944 + 2.42494i) q^{6} +(3.59628 - 3.39292i) q^{7} +(-1.29148 + 2.51636i) q^{8} +(-1.41423 + 2.64574i) q^{9} +(-2.53297 + 0.804020i) q^{10} +(-1.99888 - 1.00388i) q^{11} +(-2.54070 + 2.35475i) q^{12} +(1.56942 - 3.63833i) q^{13} +(6.97269 - 0.521491i) q^{14} +(-3.25194 - 0.136086i) q^{15} +(-3.66053 + 1.61262i) q^{16} +(-0.421668 + 0.502524i) q^{17} +(-3.91062 + 1.64532i) q^{18} +(-1.94981 - 2.32370i) q^{19} +(-3.49809 - 1.37410i) q^{20} +(8.24292 + 2.32158i) q^{21} +(-1.30060 - 2.88358i) q^{22} +(-0.969289 + 1.02739i) q^{23} +(-4.88839 + 0.322003i) q^{24} +(0.581761 + 1.34867i) q^{25} +(4.96551 - 2.59707i) q^{26} +(-5.18990 + 0.254837i) q^{27} +(8.12194 + 5.64046i) q^{28} +(0.764623 - 6.54177i) q^{29} +(-3.44994 - 3.04715i) q^{30} +(0.256353 - 1.08164i) q^{31} +(-5.45687 - 1.49084i) q^{32} +(-0.288489 - 3.86350i) q^{33} +(-0.910851 + 0.176126i) q^{34} +(1.61335 + 9.14975i) q^{35} +(-5.76065 - 1.67778i) q^{36} +(-1.45904 + 8.27461i) q^{37} +(-0.0706671 - 4.28925i) q^{38} +(6.80271 - 0.908123i) q^{39} +(-2.61711 - 4.62605i) q^{40} +(5.93169 - 4.41598i) q^{41} +(6.98350 + 9.89452i) q^{42} +(6.22042 - 0.362298i) q^{43} +(1.14117 - 4.32561i) q^{44} +(-2.69348 - 4.95237i) q^{45} +(-1.97992 + 0.264549i) q^{46} +(4.74488 - 1.12456i) q^{47} +(-5.65525 - 4.00227i) q^{48} +(1.01435 - 17.4156i) q^{49} +(-0.562884 + 1.99947i) q^{50} +(-1.12204 - 0.178978i) q^{51} +(7.76719 + 1.57257i) q^{52} +(5.22077 + 3.01422i) q^{53} +(-5.92651 - 4.34470i) q^{54} +(3.64016 - 2.10165i) q^{55} +(3.89329 + 13.4314i) q^{56} +(1.71598 - 4.96583i) q^{57} +(6.66887 - 6.50270i) q^{58} +(-13.0037 + 6.53070i) q^{59} +(-1.07343 - 6.42045i) q^{60} +(-3.33728 + 11.1473i) q^{61} +(1.24534 - 0.959405i) q^{62} +(3.89080 + 14.3132i) q^{63} +(-4.66417 - 6.49966i) q^{64} +(4.09160 + 6.22098i) q^{65} +(3.12584 - 4.49988i) q^{66} +(-0.556562 - 4.76169i) q^{67} +(-1.15722 - 0.618214i) q^{68} +(-2.38942 - 0.525185i) q^{69} +(-6.38132 + 11.4857i) q^{70} +(1.72416 - 0.627544i) q^{71} +(-4.83119 - 6.97564i) q^{72} +(0.516395 + 0.187953i) q^{73} +(-8.97553 + 7.78689i) q^{74} +(-1.48561 + 2.06520i) q^{75} +(3.74442 - 4.77333i) q^{76} +(-10.5946 + 3.17182i) q^{77} +(8.27979 + 5.06441i) q^{78} +(-12.2113 - 9.09094i) q^{79} +(1.24807 - 7.41226i) q^{80} +(-4.99989 - 7.48339i) q^{81} +(10.4490 + 0.436016i) q^{82} +(-5.49796 + 7.38504i) q^{83} +(-1.14757 + 17.0887i) q^{84} +(-0.353548 - 1.18093i) q^{85} +(7.15396 + 5.14496i) q^{86} +(10.3995 - 4.68910i) q^{87} +(5.10763 - 3.73343i) q^{88} +(1.92005 - 5.27530i) q^{89} +(1.45499 - 7.83867i) q^{90} +(-6.70047 - 18.4094i) q^{91} +(-2.41004 - 1.47373i) q^{92} +(1.83519 - 0.582288i) q^{93} +(6.21278 + 2.99305i) q^{94} +(5.66162 - 0.661748i) q^{95} +(-2.64416 - 9.43443i) q^{96} +(7.54904 - 4.96508i) q^{97} +(16.6325 - 18.2216i) q^{98} +(5.48288 - 3.86881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

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