LMFDB - Embedded newform 972.2.p.a.503.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(35,972)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 31]))

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

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

chi := DirichletCharacter("972.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.p (of order $54$, degree $18$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	no (minimal twist has level 324)
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			503.12
Character	$\chi$	$=$	972.503
Dual form			972.2.p.a.143.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09818 - 0.891069i) q^{2} +(0.411991 + 1.95711i) q^{4} +(1.03261 - 1.57001i) q^{5} +(3.59628 - 3.39292i) q^{7} +(1.29148 - 2.51636i) q^{8} +O(q^{10})$	\(q+(-1.09818 - 0.891069i) q^{2} +(0.411991 + 1.95711i) q^{4} +(1.03261 - 1.57001i) q^{5} +(3.59628 - 3.39292i) q^{7} +(1.29148 - 2.51636i) q^{8} +(-2.53297 + 0.804020i) q^{10} +(1.99888 + 1.00388i) q^{11} +(1.56942 - 3.63833i) q^{13} +(-6.97269 + 0.521491i) q^{14} +(-3.66053 + 1.61262i) q^{16} +(0.421668 - 0.502524i) q^{17} +(-1.94981 - 2.32370i) q^{19} +(3.49809 + 1.37410i) q^{20} +(-1.30060 - 2.88358i) q^{22} +(0.969289 - 1.02739i) q^{23} +(0.581761 + 1.34867i) q^{25} +(-4.96551 + 2.59707i) q^{26} +(8.12194 + 5.64046i) q^{28} +(-0.764623 + 6.54177i) q^{29} +(0.256353 - 1.08164i) q^{31} +(5.45687 + 1.49084i) q^{32} +(-0.910851 + 0.176126i) q^{34} +(-1.61335 - 9.14975i) q^{35} +(-1.45904 + 8.27461i) q^{37} +(0.0706671 + 4.28925i) q^{38} +(-2.61711 - 4.62605i) q^{40} +(-5.93169 + 4.41598i) q^{41} +(6.22042 - 0.362298i) q^{43} +(-1.14117 + 4.32561i) q^{44} +(-1.97992 + 0.264549i) q^{46} +(-4.74488 + 1.12456i) q^{47} +(1.01435 - 17.4156i) q^{49} +(0.562884 - 1.99947i) q^{50} +(7.76719 + 1.57257i) q^{52} +(-5.22077 - 3.01422i) q^{53} +(3.64016 - 2.10165i) q^{55} +(-3.89329 - 13.4314i) q^{56} +(6.66887 - 6.50270i) q^{58} +(13.0037 - 6.53070i) q^{59} +(-3.33728 + 11.1473i) q^{61} +(-1.24534 + 0.959405i) q^{62} +(-4.66417 - 6.49966i) q^{64} +(-4.09160 - 6.22098i) q^{65} +(-0.556562 - 4.76169i) q^{67} +(1.15722 + 0.618214i) q^{68} +(-6.38132 + 11.4857i) q^{70} +(-1.72416 + 0.627544i) q^{71} +(0.516395 + 0.187953i) q^{73} +(8.97553 - 7.78689i) q^{74} +(3.74442 - 4.77333i) q^{76} +(10.5946 - 3.17182i) q^{77} +(-12.2113 - 9.09094i) q^{79} +(-1.24807 + 7.41226i) q^{80} +(10.4490 + 0.436016i) q^{82} +(5.49796 - 7.38504i) q^{83} +(-0.353548 - 1.18093i) q^{85} +(-7.15396 - 5.14496i) q^{86} +(5.10763 - 3.73343i) q^{88} +(-1.92005 + 5.27530i) q^{89} +(-6.70047 - 18.4094i) q^{91} +(2.41004 + 1.47373i) q^{92} +(6.21278 + 2.99305i) q^{94} +(-5.66162 + 0.661748i) q^{95} +(7.54904 - 4.96508i) q^{97} +(-16.6325 + 18.2216i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8}+O(q^{10}) $ 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8	$ 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8} - 18 q^{10} - 36 q^{13} + 18 q^{14} - 18 q^{16} + 36 q^{17} + 18 q^{20} - 18 q^{22} - 36 q^{25} + 27 q^{26} - 9 q^{28} + 36 q^{29} + 18 q^{32} - 18 q^{34} - 36 q^{37} + 18 q^{38} - 18 q^{40} + 36 q^{41} + 90 q^{44} - 18 q^{46} - 36 q^{49} + 135 q^{50} - 18 q^{52} + 54 q^{53} + 144 q^{56} - 18 q^{58} - 36 q^{61} + 117 q^{62} - 18 q^{64} + 36 q^{65} + 63 q^{68} - 18 q^{70} - 36 q^{73} + 18 q^{74} - 18 q^{76} + 36 q^{77} - 36 q^{82} - 36 q^{85} + 18 q^{86} - 18 q^{88} + 54 q^{89} - 72 q^{92} - 18 q^{94} - 36 q^{97} - 153 q^{98}+O(q^{100}) $ 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8 - 18 * q^10 - 36 * q^13 + 18 * q^14 - 18 * q^16 + 36 * q^17 + 18 * q^20 - 18 * q^22 - 36 * q^25 + 27 * q^26 - 9 * q^28 + 36 * q^29 + 18 * q^32 - 18 * q^34 - 36 * q^37 + 18 * q^38 - 18 * q^40 + 36 * q^41 + 90 * q^44 - 18 * q^46 - 36 * q^49 + 135 * q^50 - 18 * q^52 + 54 * q^53 + 144 * q^56 - 18 * q^58 - 36 * q^61 + 117 * q^62 - 18 * q^64 + 36 * q^65 + 63 * q^68 - 18 * q^70 - 36 * q^73 + 18 * q^74 - 18 * q^76 + 36 * q^77 - 36 * q^82 - 36 * q^85 + 18 * q^86 - 18 * q^88 + 54 * q^89 - 72 * q^92 - 18 * q^94 - 36 * q^97 - 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{11}{54}\right)$	$-1$

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			0
$3$		0			0
$4$	0.411991	+	1.95711i	0.205995	+	0.978553i
$5$	1.03261	−	1.57001i	0.461797	−	0.702128i	−0.527253	−	0.849708i	$-0.676778\pi$
$5$	1.03261	−	1.57001i	0.461797	−	0.702128i	0.989050	+	0.147580i	$0.0471484\pi$
$6$		0			0
$7$	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
$9$		0			0
$10$	−2.53297	+	0.804020i	−0.800997	+	0.254253i
$11$	1.99888	+	1.00388i	0.602685	+	0.302680i	0.723855	−	0.689952i	$-0.242368\pi$
$11$	1.99888	+	1.00388i	0.602685	+	0.302680i	−0.121170	+	0.992632i	$0.538665\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−3.66053	+	1.61262i	−0.915132	+	0.403155i
$17$	0.421668	−	0.502524i	0.102270	−	0.121880i	−0.712482	−	0.701691i	$-0.752429\pi$
$17$	0.421668	−	0.502524i	0.102270	−	0.121880i	0.814751	+	0.579810i	$0.196873\pi$
$18$		0			0
$19$	−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
$21$		0			0
$22$	−1.30060	−	2.88358i	−0.277290	−	0.614781i
$23$	0.969289	−	1.02739i	0.202111	−	0.214225i	−0.618388	−	0.785873i	$-0.712214\pi$
$23$	0.969289	−	1.02739i	0.202111	−	0.214225i	0.820499	+	0.571648i	$0.193696\pi$
$24$		0			0
$25$	0.581761	+	1.34867i	0.116352	+	0.269735i
$26$	−4.96551	+	2.59707i	−0.973817	+	0.509327i
$27$		0			0
$28$	8.12194	+	5.64046i	1.53490	+	1.06595i
$29$	−0.764623	+	6.54177i	−0.141987	+	1.21478i	0.714883	+	0.699244i	$0.246480\pi$
$29$	−0.764623	+	6.54177i	−0.141987	+	1.21478i	−0.856870	+	0.515532i	$0.827594\pi$
$30$		0			0
$31$	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			0
$34$	−0.910851	+	0.176126i	−0.156210	+	0.0302053i
$35$	−1.61335	−	9.14975i	−0.272706	−	1.54659i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−2.61711	−	4.62605i	−0.413802	−	0.731443i
$41$	−5.93169	+	4.41598i	−0.926375	+	0.689661i	−0.950723	−	0.310043i	$-0.899657\pi$
$41$	−5.93169	+	4.41598i	−0.926375	+	0.689661i	0.0243476	+	0.999704i	$0.492249\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	−1.97992	+	0.264549i	−0.291924	+	0.0390057i
$47$	−4.74488	+	1.12456i	−0.692111	+	0.164033i	−0.561594	−	0.827413i	$-0.689812\pi$
$47$	−4.74488	+	1.12456i	−0.692111	+	0.164033i	−0.130517	+	0.991446i	$0.541664\pi$
$48$		0			0
$49$	1.01435	−	17.4156i	0.144906	−	2.48795i
$50$	0.562884	−	1.99947i	0.0796039	−	0.282768i
$51$		0			0
$52$	7.76719	+	1.57257i	1.07711	+	0.218076i
$53$	−5.22077	−	3.01422i	−0.717129	−	0.414034i	0.0965663	−	0.995327i	$-0.469214\pi$
$53$	−5.22077	−	3.01422i	−0.717129	−	0.414034i	−0.813695	+	0.581292i	$0.802547\pi$
$54$		0			0
$55$	3.64016	−	2.10165i	0.490839	−	0.283386i
$56$	−3.89329	−	13.4314i	−0.520263	−	1.79485i
$57$		0			0
$58$	6.66887	−	6.50270i	0.875665	−	0.853846i
$59$	13.0037	−	6.53070i	1.69294	−	0.850224i	0.702592	−	0.711593i	$-0.252026\pi$
$59$	13.0037	−	6.53070i	1.69294	−	0.850224i	0.990344	−	0.138632i	$-0.0442704\pi$
$60$		0			0
$61$	−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
$63$		0			0
$64$	−4.66417	−	6.49966i	−0.583021	−	0.812457i
$65$	−4.09160	−	6.22098i	−0.507501	−	0.771617i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−6.38132	+	11.4857i	−0.762713	+	1.37280i
$71$	−1.72416	+	0.627544i	−0.204620	+	0.0744757i	−0.442297	−	0.896869i	$-0.645836\pi$
$71$	−1.72416	+	0.627544i	−0.204620	+	0.0744757i	0.237677	+	0.971344i	$0.423614\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	3.74442	−	4.77333i	0.429514	−	0.547539i
$77$	10.5946	−	3.17182i	1.20737	−	0.361462i
$78$		0			0
$79$	−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
$81$		0			0
$82$	10.4490	+	0.436016i	1.15390	+	0.0481499i
$83$	5.49796	−	7.38504i	0.603480	−	0.810614i	−0.390451	−	0.920624i	$-0.627681\pi$
$83$	5.49796	−	7.38504i	0.603480	−	0.810614i	0.993930	+	0.110010i	$0.0350883\pi$
$84$		0			0
$85$	−0.353548	−	1.18093i	−0.0383477	−	0.128090i
$86$	−7.15396	−	5.14496i	−0.771431	−	0.554795i
$87$		0			0
$88$	5.10763	−	3.73343i	0.544475	−	0.397985i
$89$	−1.92005	+	5.27530i	−0.203525	+	0.559181i	−0.998898	−	0.0469402i	$-0.985053\pi$
$89$	−1.92005	+	5.27530i	−0.203525	+	0.559181i	0.795373	+	0.606121i	$0.207275\pi$
$90$		0			0
$91$	−6.70047	−	18.4094i	−0.702400	−	1.92983i
$92$	2.41004	+	1.47373i	0.251264	+	0.153647i
$93$		0			0
$94$	6.21278	+	2.99305i	0.640799	+	0.308710i
$95$	−5.66162	+	0.661748i	−0.580870	+	0.0678939i
$96$		0			0
$97$	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
$99$		0			0
$100$	−2.39982	+	1.69421i	−0.239982	+	0.169421i
$101$	−12.8471	−	3.84617i	−1.27833	−	0.382708i	−0.425532	−	0.904943i	$-0.639913\pi$
$101$	−12.8471	−	3.84617i	−1.27833	−	0.382708i	−0.852802	+	0.522235i	$0.825098\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	3.04747	+	7.96222i	0.295996	+	0.773359i
$107$	5.12841	+	8.88267i	0.495782	+	0.858720i	0.999988	−	0.00486345i	$-0.00154809\pi$
$107$	5.12841	+	8.88267i	0.495782	+	0.858720i	−0.504206	+	0.863583i	$0.668215\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	−7.69281	+	18.2193i	−0.726902	+	1.72156i
$113$	8.68116	+	0.505620i	0.816655	+	0.0475648i	0.461386	−	0.887199i	$-0.347352\pi$
$113$	8.68116	+	0.505620i	0.816655	+	0.0475648i	0.355269	+	0.934764i	$0.384389\pi$
$114$		0			0
$115$	−0.612106	−	2.58268i	−0.0570792	−	0.240836i
$116$	−13.1180	+	1.19870i	−1.21797	+	0.111296i
$117$		0			0
$118$	−20.0997	−	4.41532i	−1.85032	−	0.406463i
$119$	−0.188587	−	3.23791i	−0.0172877	−	0.296818i
$120$		0			0
$121$	−3.58098	−	4.81010i	−0.325544	−	0.437282i
$122$	13.5980	−	9.26798i	1.23110	−	0.839083i
$123$		0			0
$124$	2.22250	+	0.0560853i	0.199586	+	0.00503661i
$125$	11.9712	+	2.11084i	1.07073	+	0.188799i
$126$		0			0
$127$	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
$129$		0			0
$130$	−1.05002	+	10.4776i	−0.0920925	+	0.918950i
$131$	−6.23391	−	1.47746i	−0.544659	−	0.129087i	−0.0509300	−	0.998702i	$-0.516219\pi$
$131$	−6.23391	−	1.47746i	−0.544659	−	0.129087i	−0.493729	+	0.869616i	$0.664367\pi$
$132$		0			0
$133$	−14.8962	−	1.74112i	−1.29166	−	0.150974i
$134$	−3.63179	+	5.72512i	−0.313739	+	0.494575i
$135$		0			0
$136$	−0.719959	−	1.71007i	−0.0617360	−	0.146637i
$137$	4.51931	−	1.94944i	0.386110	−	0.166552i	−0.194171	−	0.980968i	$-0.562202\pi$
$137$	4.51931	−	1.94944i	0.386110	−	0.166552i	0.580282	+	0.814416i	$0.302942\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	2.45262	+	0.847194i	0.205820	+	0.0710949i
$143$	6.78952	−	5.69709i	0.567768	−	0.476414i
$144$		0			0
$145$	9.48107	+	7.95556i	0.787360	+	0.660673i
$146$	−0.399615	−	0.666549i	−0.0330724	−	0.0551640i
$147$		0			0
$148$	−16.7954	+	0.553571i	−1.38057	+	0.0455033i
$149$	14.5940	+	6.29524i	1.19559	+	0.515726i	0.898436	−	0.439105i	$-0.144704\pi$
$149$	14.5940	+	6.29524i	1.19559	+	0.515726i	0.297151	+	0.954831i	$0.403964\pi$
$150$		0			0
$151$	−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			0
$154$	−14.4611	−	5.95731i	−1.16531	−	0.480054i
$155$	−1.43347	−	1.51939i	−0.115139	−	0.122040i
$156$		0			0
$157$	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			0
$160$	7.97544	−	7.02786i	0.630514	−	0.555601i
$161$		−	6.98349i		−	0.550376i
$162$		0			0
$163$			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
$165$		0			0
$166$	−12.6183	+	3.21103i	−0.979372	+	0.249224i
$167$	−15.5210	−	10.2083i	−1.20105	−	0.789942i	−0.218480	−	0.975842i	$-0.570110\pi$
$167$	−15.5210	−	10.2083i	−1.20105	−	0.789942i	−0.982569	+	0.185900i	$0.940480\pi$
$168$		0			0
$169$	−1.85322	−	1.96430i	−0.142555	−	0.151100i
$170$	−0.664035	+	1.61191i	−0.0509291	+	0.123628i
$171$		0			0
$172$	3.27181	+	12.0248i	0.249473	+	0.916879i
$173$	4.57402	−	9.10763i	0.347757	−	0.692440i	−0.649961	−	0.759968i	$-0.725215\pi$
$173$	4.57402	−	9.10763i	0.347757	−	0.692440i	0.997717	+	0.0675274i	$0.0215110\pi$
$174$		0			0
$175$	6.66811	+	2.87634i	0.504062	+	0.217431i
$176$	−8.93583	−	0.451283i	−0.673564	−	0.0340167i
$177$		0			0
$178$	6.80922	−	4.08232i	0.510372	−	0.305983i
$179$	15.1718	+	12.7306i	1.13399	+	0.951533i	0.999226	−	0.0393444i	$-0.0125270\pi$
$179$	15.1718	+	12.7306i	1.13399	+	0.951533i	0.134767	+	0.990877i	$0.456971\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−1.33346	−	3.76593i	−0.0983040	−	0.277628i
$185$	11.4846	+	10.8351i	0.844362	+	0.796615i
$186$		0			0
$187$	1.34734	−	0.581184i	0.0985270	−	0.0425004i
$188$	−4.15572	−	8.82292i	−0.303087	−	0.643477i
$189$		0			0
$190$	6.80713	+	4.31818i	0.493841	+	0.313274i
$191$	14.9949	+	1.75265i	1.08499	+	0.126817i	0.639742	−	0.768590i	$-0.279041\pi$
$191$	14.9949	+	1.75265i	1.08499	+	0.126817i	0.445249	+	0.895407i	$0.353115\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	34.5021	−	5.18990i	2.46444	−	0.370707i
$197$	−9.25889	+	1.63259i	−0.659669	+	0.116317i	−0.493454	−	0.869772i	$-0.664266\pi$
$197$	−9.25889	+	1.63259i	−0.659669	+	0.116317i	−0.166215	+	0.986089i	$0.553155\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	10.6812	+	15.6714i	0.751526	+	1.10264i
$203$	19.4459	+	26.1204i	1.36483	+	1.83329i
$204$		0			0
$205$	0.807998	+	13.8728i	0.0564330	+	0.968917i
$206$	0.258517	−	1.17684i	0.0180117	−	0.0819941i
$207$		0			0
$208$	0.122324	+	15.8491i	0.00848165	+	1.09894i
$209$	−1.56474	−	6.60217i	−0.108236	−	0.456682i
$210$		0			0
$211$	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
$213$		0			0
$214$	2.28317	−	14.3245i	0.156074	−	0.979204i
$215$	5.85445	−	10.1402i	0.399270	−	0.691557i
$216$		0			0
$217$	−2.74800	−	4.75967i	−0.186546	−	0.323107i
$218$	16.9212	−	6.47642i	1.14605	−	0.438639i
$219$		0			0
$220$	5.61285	+	6.25831i	0.378418	+	0.421935i
$221$	−1.16657	−	2.32284i	−0.0784723	−	0.156251i
$222$		0			0
$223$	−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
$225$		0			0
$226$	−9.08292	−	8.29078i	−0.604187	−	0.551495i
$227$	9.08197	−	5.97331i	0.602792	−	0.396462i	−0.211112	−	0.977462i	$-0.567709\pi$
$227$	9.08197	−	5.97331i	0.602792	−	0.396462i	0.813904	+	0.581000i	$0.197338\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	15.4740	+	10.3726i	1.01592	+	0.680996i
$233$	−5.68162	−	15.6101i	−0.372215	−	1.02265i	−0.974503	−	0.224374i	$-0.927966\pi$
$233$	−5.68162	−	15.6101i	−0.372215	−	1.02265i	0.602288	−	0.798279i	$-0.294256\pi$
$234$		0			0
$235$	−3.13404	+	8.61071i	−0.204442	+	0.561701i
$236$	18.1387	+	22.7590i	1.18073	+	1.48149i
$237$		0			0
$238$	−2.67810	+	3.72384i	−0.173595	+	0.241381i
$239$	−1.81805	−	6.07270i	−0.117600	−	0.392810i	0.878840	−	0.477116i	$-0.158318\pi$
$239$	−1.81805	−	6.07270i	−0.117600	−	0.392810i	−0.996440	+	0.0843059i	$0.973133\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−23.1914	−	1.93883i	−1.48468	−	0.124121i
$245$	−26.2952	−	19.5761i	−1.67994	−	1.25067i
$246$		0			0
$247$	−11.5145	+	3.44720i	−0.732648	+	0.219340i
$248$	−2.39072	−	2.04199i	−0.151811	−	0.129667i
$249$		0			0
$250$	−11.2656	−	12.9852i	−0.712497	−	0.821257i
$251$	−13.2115	−	4.80859i	−0.833902	−	0.303516i	−0.110443	−	0.993882i	$-0.535227\pi$
$251$	−13.2115	−	4.80859i	−0.833902	−	0.303516i	−0.723459	+	0.690367i	$0.757449\pi$
$252$		0			0
$253$	2.96886	−	1.08058i	0.186651	−	0.0679353i
$254$	−0.0144427	−	0.00802422i	−0.000906215	−	0.000503484i
$255$		0			0
$256$	10.7989	−	11.8061i	0.674933	−	0.737879i
$257$	0.794794	+	6.79990i	0.0495779	+	0.424166i	0.995120	+	0.0986676i	$0.0314580\pi$
$257$	0.794794	+	6.79990i	0.0495779	+	0.424166i	−0.945543	+	0.325499i	$0.894468\pi$
$258$		0			0
$259$	22.8280	+	34.7082i	1.41846	+	2.15666i
$260$	10.4894	−	10.5707i	0.650526	−	0.655566i
$261$		0			0
$262$	5.52942	+	7.17737i	0.341609	+	0.443419i
$263$	−7.82585	+	26.1402i	−0.482562	+	1.61187i	0.276611	+	0.960982i	$0.410789\pi$
$263$	−7.82585	+	26.1402i	−0.482562	+	1.61187i	−0.759173	+	0.650889i	$0.774396\pi$
$264$		0			0
$265$	−10.1234	+	5.08414i	−0.621873	+	0.312316i
$266$	14.8072	+	15.1856i	0.907889	+	0.931089i
$267$		0			0
$268$	9.08983	−	3.05102i	0.555250	−	0.186371i
$269$	2.73455	−	1.57879i	0.166729	−	0.0962608i	−0.414314	−	0.910134i	$-0.635978\pi$
$269$	2.73455	−	1.57879i	0.166729	−	0.0962608i	0.581042	+	0.813873i	$0.302645\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	−6.70009	−	1.88619i	−0.404767	−	0.113949i
$275$	−0.191030	+	3.27985i	−0.0115195	+	0.197783i
$276$		0			0
$277$	−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
$279$		0			0
$280$	−25.1077	−	7.75693i	−1.50047	−	0.463565i
$281$	−20.3261	+	1.18386i	−1.21255	+	0.0706232i	−0.652471	−	0.757813i	$-0.726268\pi$
$281$	−20.3261	+	1.18386i	−1.21255	+	0.0706232i	−0.560083	+	0.828437i	$0.689231\pi$
$282$		0			0
$283$	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
$285$		0			0
$286$	−12.5326	+	0.206479i	−0.741068	+	0.0122094i
$287$	−6.34898	+	36.0069i	−0.374769	+	2.12542i
$288$		0			0
$289$	2.87729	+	16.3179i	0.169252	+	0.959879i
$290$	−3.32294	−	17.1849i	−0.195130	−	1.00913i
$291$		0			0
$292$	−0.155093	+	1.08808i	−0.00907613	+	0.0636748i
$293$	−7.48337	+	31.5748i	−0.437183	+	1.84462i	0.0915046	+	0.995805i	$0.470832\pi$
$293$	−7.48337	+	31.5748i	−0.437183	+	1.84462i	−0.528688	+	0.848816i	$0.677316\pi$
$294$		0			0
$295$	3.17449	−	27.1595i	0.184826	−	1.58129i
$296$	18.9376	+	14.3579i	1.10073	+	0.834538i
$297$		0			0
$298$	−10.4173	−	19.9176i	−0.603459	−	1.15379i
$299$	−2.21675	−	5.13899i	−0.128198	−	0.297196i
$300$		0			0
$301$	21.1411	−	22.4083i	1.21855	−	1.29159i
$302$	17.4461	−	7.86889i	1.00391	−	0.452803i
$303$		0			0
$304$	10.8846	+	5.36165i	0.624274	+	0.307512i
$305$	14.0552	+	16.7504i	0.804800	+	0.959124i
$306$		0			0
$307$	−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			0
$310$	0.220324	+	2.94588i	0.0125136	+	0.167315i
$311$	−3.55428	+	8.23974i	−0.201544	+	0.467233i	−0.988772	−	0.149430i	$-0.952256\pi$
$311$	−3.55428	+	8.23974i	−0.201544	+	0.467233i	0.787228	+	0.616662i	$0.211516\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	12.7610	−	27.6441i	0.717863	−	1.55510i
$317$	−7.53896	+	7.11264i	−0.423430	+	0.399486i	−0.868244	−	0.496137i	$-0.834751\pi$
$317$	−7.53896	+	7.11264i	−0.423430	+	0.399486i	0.444814	+	0.895623i	$0.353270\pi$
$318$		0			0
$319$	−8.09552	+	12.3086i	−0.453262	+	0.689152i
$320$	−15.0208	+	0.611167i	−0.839686	+	0.0341652i
$321$		0			0
$322$	−6.22277	+	7.66911i	−0.346782	+	0.427383i
$323$	−1.98989			−0.110720
$324$		0			0
$325$	5.81995			0.322832
$326$	20.7566	−	25.5810i	1.14960	−	1.41680i
$327$		0			0
$328$	3.45156	+	20.6294i	0.190581	+	1.13907i
$329$	−13.2484	+	20.1432i	−0.730407	+	1.11053i
$330$		0			0
$331$	−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
$333$		0			0
$334$	7.94848	+	25.0408i	0.434922	+	1.37017i
$335$	−8.05059	−	4.04316i	−0.439851	−	0.220901i
$336$		0			0
$337$	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
$339$		0			0
$340$	2.16555	−	1.17846i	0.117444	−	0.0639112i
$341$	1.59825	−	1.90472i	0.0865502	−	0.103147i
$342$		0			0
$343$	−33.1954	−	39.5608i	−1.79239	−	2.13608i
$344$	7.12186	−	16.1207i	0.383985	−	0.869172i
$345$		0			0
$346$	−13.1386	+	5.92603i	−0.706337	+	0.318585i
$347$	1.35958	−	1.44107i	0.0729863	−	0.0773609i	−0.689851	−	0.723951i	$-0.742324\pi$
$347$	1.35958	−	1.44107i	0.0729863	−	0.0773609i	0.762838	+	0.646590i	$0.223806\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	9.41101	+	8.45803i	0.501608	+	0.450815i
$353$	0.509746	−	4.36115i	0.0271310	−	0.232121i	−0.972869	−	0.231358i	$-0.925683\pi$
$353$	0.509746	−	4.36115i	0.0271310	−	0.232121i	1.00000		0.000762794i	$-0.000242805\pi$
$354$		0			0
$355$	−0.795139	+	3.35495i	−0.0422016	+	0.178062i
$356$	−11.1154	−	1.58437i	−0.589113	−	0.0839715i
$357$		0			0
$358$	−5.31744	−	27.4996i	−0.281035	−	1.45340i
$359$	−3.66720	−	20.7977i	−0.193547	−	1.09766i	−0.914472	−	0.404649i	$-0.867394\pi$
$359$	−3.66720	−	20.7977i	−0.193547	−	1.09766i	0.720925	−	0.693013i	$-0.243717\pi$
$360$		0			0
$361$	1.70152	−	9.64979i	0.0895536	−	0.507884i
$362$	−8.00677	+	0.131915i	−0.420826	+	0.00693327i
$363$		0			0
$364$	33.2686	−	20.6980i	1.74375	−	1.08487i
$365$	0.828322	−	0.616663i	0.0433563	−	0.0322776i
$366$		0			0
$367$	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
$369$		0			0
$370$	−2.95725	−	22.1325i	−0.153740	−	1.15061i
$371$	−29.0024	+	6.87369i	−1.50573	+	0.356864i
$372$		0			0
$373$	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
$375$		0			0
$376$	−3.29811	+	13.3922i	−0.170087	+	0.690649i
$377$	22.6011	+	13.0488i	1.16402	+	0.672045i
$378$		0			0
$379$	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			0
$382$	−14.9053	−	15.2862i	−0.762622	−	0.782110i
$383$	−5.26374	+	2.64355i	−0.268965	+	0.135079i	−0.578170	−	0.815916i	$-0.696233\pi$
$383$	−5.26374	+	2.64355i	−0.268965	+	0.135079i	0.309206	+	0.950995i	$0.399937\pi$
$384$		0			0
$385$	5.96032	−	19.9089i	0.303766	−	1.01465i
$386$	11.1634	+	14.4905i	0.568203	+	0.737545i
$387$		0			0
$388$	12.8273	+	12.7287i	0.651208	+	0.646202i
$389$	10.6132	+	16.1366i	0.538111	+	0.818157i	0.997543	−	0.0700554i	$-0.0223176\pi$
$389$	10.6132	+	16.1366i	0.538111	+	0.818157i	−0.459433	+	0.888213i	$0.651947\pi$
$390$		0			0
$391$	−0.107568	−	0.920307i	−0.00543997	−	0.0465419i
$392$	−42.5141	−	25.0444i	−2.14728	−	1.26493i
$393$		0			0
$394$	11.6227	+	6.45744i	0.585542	+	0.325321i
$395$	−26.8823	+	9.78435i	−1.35259	+	0.492304i
$396$		0			0
$397$	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
$399$		0			0
$400$	−4.30445	−	3.99870i	−0.215222	−	0.199935i
$401$	−9.34389	+	2.79738i	−0.466611	+	0.139694i	−0.511474	−	0.859299i	$-0.670900\pi$
$401$	−9.34389	+	2.79738i	−0.466611	+	0.139694i	0.0448624	+	0.998993i	$0.485715\pi$
$402$		0			0
$403$	−3.53304	−	2.63025i	−0.175993	−	0.131022i
$404$	2.23448	−	26.7277i	0.111169	−	1.32975i
$405$		0			0
$406$	1.92001	−	46.0125i	0.0952883	−	2.28356i
$407$	−11.2231	+	15.0753i	−0.556309	+	0.747253i
$408$		0			0
$409$	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
$411$		0			0
$412$	−1.33254	+	1.06202i	−0.0656496	+	0.0523220i
$413$	24.6068	−	67.6067i	1.21082	−	3.32671i
$414$		0			0
$415$	−5.91732	−	16.2577i	−0.290470	−	0.798059i
$416$	13.9883	−	17.5141i	0.685833	−	0.858700i
$417$		0			0
$418$	−4.16462	+	8.64465i	−0.203698	+	0.422824i
$419$	35.3442	−	4.13115i	1.72668	−	0.201820i	0.805939	−	0.591999i	$-0.201661\pi$
$419$	35.3442	−	4.13115i	1.72668	−	0.201820i	0.920739	+	0.390180i	$0.127587\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−14.3274	+	9.24457i	−0.695799	+	0.448956i
$425$	0.923051	+	0.276343i	0.0447746	+	0.0134046i
$426$		0			0
$427$	25.8201	+	51.4120i	1.24952	+	2.48800i
$428$	−15.2715	+	13.6964i	−0.738174	+	0.662041i
$429$		0			0
$430$	−15.4649	+	5.91903i	−0.745782	+	0.285441i
$431$	−17.0278	−	29.4930i	−0.820201	−	1.42063i	−0.905532	−	0.424277i	$-0.860528\pi$
$431$	−17.0278	−	29.4930i	−0.820201	−	1.42063i	0.0853314	−	0.996353i	$-0.472805\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−24.3534	−	7.96567i	−1.16632	−	0.381487i
$437$	−4.27727	−	0.249122i	−0.204609	−	0.0119171i
$438$		0			0
$439$	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
$441$		0			0
$442$	−0.788706	+	3.59039i	−0.0375149	+	0.170778i
$443$	−0.00762099	−	0.130847i	−0.000362084	−	0.00621675i	0.998122	−	0.0612529i	$-0.0195096\pi$
$443$	−0.00762099	−	0.130847i	−0.000362084	−	0.00621675i	−0.998484	+	0.0550362i	$0.982473\pi$
$444$		0			0
$445$	6.29959	+	8.46182i	0.298629	+	0.401129i
$446$	7.15051	+	10.4912i	0.338586	+	0.496773i
$447$		0			0
$448$	−38.8265	−	7.54947i	−1.83438	−	0.356679i
$449$	5.46082	+	0.962890i	0.257712	+	0.0454416i	0.301011	−	0.953621i	$-0.402676\pi$
$449$	5.46082	+	0.962890i	0.257712	+	0.0454416i	−0.0432994	+	0.999062i	$0.513787\pi$
$450$		0			0
$451$	−16.2899	+	2.87234i	−0.767059	+	0.135253i
$452$	2.58701	+	17.1983i	0.121683	+	0.808939i
$453$		0			0
$454$	−15.2963	−	1.53291i	−0.717889	−	0.0719431i
$455$	−35.8218	−	8.48993i	−1.67935	−	0.398014i
$456$		0			0
$457$	−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
$459$		0			0
$460$	4.80239	−	2.26200i	0.223913	−	0.105466i
$461$	−3.63570	+	1.56829i	−0.169332	+	0.0730425i	−0.479058	−	0.877783i	$-0.659022\pi$
$461$	−3.63570	+	1.56829i	−0.169332	+	0.0730425i	0.309727	+	0.950826i	$0.399762\pi$
$462$		0			0
$463$	−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			0
$466$	−7.67027	+	22.2054i	−0.355318	+	1.02865i
$467$	−9.91840	+	8.32253i	−0.458969	+	0.385121i	−0.842751	−	0.538303i	$-0.819066\pi$
$467$	−9.91840	+	8.32253i	−0.458969	+	0.385121i	0.383783	+	0.923424i	$0.374621\pi$
$468$		0			0
$469$	−18.1576	−	15.2360i	−0.838439	−	0.703534i
$470$	11.1145	−	6.66345i	0.512673	−	0.307362i
$471$		0			0
$472$	0.360373	−	41.1563i	0.0165875	−	1.89437i
$473$	12.7976	+	5.52034i	0.588433	+	0.253825i
$474$		0			0
$475$	1.99958	−	3.98150i	0.0917472	−	0.182684i
$476$	6.25923	−	1.70307i	0.286891	−	0.0780601i
$477$		0			0
$478$	−3.41466	+	8.28891i	−0.156183	+	0.379126i
$479$	−11.7926	−	12.4995i	−0.538819	−	0.571115i	0.399567	−	0.916704i	$-0.369161\pi$
$479$	−11.7926	−	12.4995i	−0.538819	−	0.571115i	−0.938386	+	0.345589i	$0.887679\pi$
$480$		0			0
$481$	27.8159	+	18.2948i	1.26830	+	0.834171i
$482$	3.60345	−	0.916982i	0.164133	−	0.0417674i
$483$		0			0
$484$	7.93854	−	8.99008i	0.360843	−	0.408640i
$485$		−	16.9790i		−	0.770978i
$486$		0			0
$487$			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
$489$		0			0
$490$	11.4332	+	44.9289i	0.516500	+	2.02968i
$491$	2.05751	+	1.35324i	0.0928541	+	0.0610711i	0.595087	−	0.803661i	$-0.297118\pi$
$491$	2.05751	+	1.35324i	0.0928541	+	0.0610711i	−0.502233	+	0.864732i	$0.667488\pi$
$492$		0			0
$493$	2.96498	+	3.14270i	0.133536	+	0.141540i
$494$	15.7166	+	6.47454i	0.707125	+	0.291303i
$495$		0			0
$496$	0.805884	+	4.37277i	0.0361853	+	0.196343i
$497$	−4.07137	+	8.10677i	−0.182626	+	0.363638i
$498$		0			0
$499$	−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
$501$		0			0
$502$	10.2238	+	17.0531i	0.456310	+	0.761115i
$503$	−4.75280	−	3.98807i	−0.211917	−	0.177819i	0.530651	−	0.847591i	$-0.321948\pi$
$503$	−4.75280	−	3.98807i	−0.211917	−	0.177819i	−0.742567	+	0.669771i	$0.766392\pi$
$504$		0			0
$505$	−19.3045	+	16.1984i	−0.859041	+	0.720821i
$506$	−4.22321	−	1.45880i	−0.187744	−	0.0648514i
$507$		0			0
$508$	0.00871052	+	0.0216815i	0.000386467	+	0.000961959i
$509$	−30.0369	−	28.3384i	−1.33136	−	1.25608i	−0.942260	−	0.334882i	$-0.891303\pi$
$509$	−30.0369	−	28.3384i	−1.33136	−	1.25608i	−0.389103	−	0.921194i	$-0.627215\pi$
$510$		0			0
$511$	2.49481	−	1.07616i	0.110364	−	0.0476064i
$512$	−22.3792	+	3.34258i	−0.989029	+	0.147722i
$513$		0			0
$514$	5.18636	−	8.17572i	0.228760	−	0.360615i
$515$	1.59019	+	0.185867i	0.0700723	+	0.00819027i
$516$		0			0
$517$	−10.6134	−	2.51541i	−0.466775	−	0.110628i
$518$	5.85827	−	58.4571i	0.257398	−	2.56846i
$519$		0			0
$520$	−20.9385	+	2.26170i	−0.918212	+	0.0991820i
$521$	−18.6529	+	3.28901i	−0.817198	+	0.144094i	−0.566596	−	0.823996i	$-0.691740\pi$
$521$	−18.6529	+	3.28901i	−0.817198	+	0.144094i	−0.250602	+	0.968090i	$0.580629\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	31.8869	−	21.7332i	1.39033	−	0.947611i
$527$	−0.435455	−	0.584917i	−0.0189687	−	0.0254794i
$528$		0			0
$529$	1.22133	+	20.9694i	0.0531013	+	0.911714i
$530$	15.6476	+	3.43732i	0.679687	+	0.149308i
$531$		0			0
$532$	−2.72955	−	29.8708i	−0.118341	−	1.29506i
$533$	6.75747	+	28.5120i	0.292698	+	1.23499i
$534$		0			0
$535$	19.2415	+	1.12069i	0.831882	+	0.0484516i
$536$	−12.7009	−	4.74911i	−0.548596	−	0.205130i
$537$		0			0
$538$	−4.40984	−	0.702878i	−0.190122	−	0.0303032i
$539$	19.5107	−	33.7935i	0.840385	−	1.45559i
$540$		0			0
$541$	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
$543$		0			0
$544$	3.05017	−	2.11357i	0.130775	−	0.0906185i
$545$	10.8047	+	21.5140i	0.462824	+	0.921558i
$546$		0			0
$547$	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
$549$		0			0
$550$	3.13236	−	3.43164i	0.133564	−	0.146326i
$551$	16.6920	−	10.9785i	0.711102	−	0.467699i
$552$		0			0
$553$	−74.7599	+	8.73818i	−3.17912	+	0.371585i
$554$	8.00279	+	3.85540i	0.340006	+	0.163800i
$555$		0			0
$556$	13.2157	−	21.6122i	0.560472	−	0.916561i
$557$	2.91197	+	8.00057i	0.123384	+	0.338995i	0.985972	−	0.166913i	$-0.0533798\pi$
$557$	2.91197	+	8.00057i	0.123384	+	0.338995i	−0.862588	+	0.505908i	$0.831158\pi$
$558$		0			0
$559$	8.44430	−	23.2005i	0.357156	−	0.981278i
$560$	20.6608	+	30.8912i	0.873076	+	1.30539i
$561$		0			0
$562$	23.3766	+	16.8119i	0.986082	+	0.709167i
$563$	−5.64182	−	18.8450i	−0.237774	−	0.794221i	−0.990694	−	0.136109i	$-0.956540\pi$
$563$	−5.64182	−	18.8450i	−0.237774	−	0.794221i	0.752920	−	0.658112i	$-0.228645\pi$
$564$		0			0
$565$	9.75808	−	13.1074i	0.410526	−	0.551432i
$566$	−20.3579	−	0.849494i	−0.855707	−	0.0357069i
$567$		0			0
$568$	−0.647590	+	5.14908i	−0.0271723	+	0.216051i
$569$	12.8099	+	9.53663i	0.537019	+	0.399796i	0.831217	−	0.555949i	$-0.187645\pi$
$569$	12.8099	+	9.53663i	0.537019	+	0.399796i	−0.294197	+	0.955745i	$0.595052\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	39.0569	−	33.8846i	1.63021	−	1.41432i
$575$	1.94950	+	0.709560i	0.0812998	+	0.0295907i
$576$		0			0
$577$	−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
$579$		0			0
$580$	−11.6638	+	21.8331i	−0.484311	+	0.906569i
$581$	−5.28462	−	45.2128i	−0.219243	−	1.87574i
$582$		0			0
$583$	−7.40981	−	11.2661i	−0.306883	−	0.466593i
$584$	1.13987	−	1.05670i	0.0471682	−	0.0437266i
$585$		0			0
$586$	36.3534	−	28.0066i	1.50175	−	1.15694i
$587$	0.579435	−	1.93545i	0.0239158	−	0.0798844i	−0.945199	−	0.326496i	$-0.894132\pi$
$587$	0.579435	−	1.93545i	0.0239158	−	0.0798844i	0.969114	+	0.246612i	$0.0793172\pi$
$588$		0			0
$589$	−3.01325	+	1.51331i	−0.124159	+	0.0623548i
$590$	−27.6872	+	26.9973i	−1.13986	+	1.11146i
$591$		0			0
$592$	−8.00294	−	32.6423i	−0.328919	−	1.34159i
$593$	−4.15567	+	2.39928i	−0.170653	+	0.0985265i	−0.582894	−	0.812548i	$-0.698080\pi$
$593$	−4.15567	+	2.39928i	−0.170653	+	0.0985265i	0.412241	+	0.911075i	$0.364746\pi$
$594$		0			0
$595$	−5.27827	−	3.04741i	−0.216388	−	0.124932i
$596$	−6.30785	+	31.1556i	−0.258380	+	1.27618i
$597$		0			0
$598$	−2.14482	+	7.61881i	−0.0877082	+	0.311556i
$599$	0.722412	−	12.4033i	0.0295170	−	0.506786i	−0.950856	−	0.309634i	$-0.899794\pi$
$599$	0.722412	−	12.4033i	0.0295170	−	0.506786i	0.980373	−	0.197153i	$-0.0631694\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−26.1707	−	6.90429i	−1.06487	−	0.280931i
$605$	−11.2496	+	0.655217i	−0.457363	+	0.0266384i
$606$		0			0
$607$	−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
$609$		0			0
$610$	−0.509404	−	30.9191i	−0.0206251	−	1.25188i
$611$	−3.35521	+	19.0283i	−0.135737	+	0.769804i
$612$		0			0
$613$	−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
$615$		0			0
$616$	5.70126	−	30.7562i	0.229710	−	1.23920i
$617$	8.81096	−	37.1764i	0.354716	−	1.49666i	−0.444587	−	0.895736i	$-0.646649\pi$
$617$	8.81096	−	37.1764i	0.354716	−	1.49666i	0.799303	−	0.600929i	$-0.205202\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	11.2454	−	5.88159i	0.450900	−	0.235830i
$623$	10.9936	+	25.4860i	0.440450	+	1.02108i
$624$		0			0
$625$	10.6358	−	11.2733i	0.425433	−	0.450932i
$626$	9.79157	+	21.7089i	0.391350	+	0.867663i
$627$		0			0
$628$	−1.94193	+	4.94364i	−0.0774914	+	0.197273i
$629$	3.54296	+	4.22234i	0.141267	+	0.168356i
$630$		0			0
$631$	−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
$633$		0			0
$634$	14.6170	−	1.09321i	0.580514	−	0.0434170i
$635$	0.00869549	−	0.0201584i	0.000345070	−	0.000799962i
$636$		0			0
$637$	−61.7719	−	31.0230i	−2.44749	−	1.22918i
$638$	19.8582	−	6.30341i	0.786193	−	0.249554i
$639$		0			0
$640$	17.0401	+	12.7134i	0.673568	+	0.502540i
$641$	22.7928	−	21.5039i	0.900261	−	0.849352i	−0.0889224	−	0.996039i	$-0.528342\pi$
$641$	22.7928	−	21.5039i	0.900261	−	0.849352i	0.989183	+	0.146686i	$0.0468608\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	2.18525	+	1.77313i	0.0859776	+	0.0697629i
$647$	22.7096			0.892808			0.446404	−	0.894831i	$-0.352704\pi$
$647$	22.7096			0.892808			0.446404	+	0.894831i	$0.352704\pi$
$648$		0			0
$649$	32.5488			1.27765
$650$	−6.39134	−	5.18598i	−0.250689	−	0.203411i
$651$		0			0
$652$	−45.5890	+	9.59694i	−1.78540	+	0.375845i
$653$	3.87948	−	5.89847i	0.151816	−	0.230825i	−0.751570	−	0.659653i	$-0.770703\pi$
$653$	3.87948	−	5.89847i	0.151816	−	0.230825i	0.903386	+	0.428828i	$0.141074\pi$
$654$		0			0
$655$	−8.75683	+	8.26164i	−0.342157	+	0.322809i
$656$	14.5918	−	25.7304i	0.569715	−	1.00460i
$657$		0			0
$658$	32.4981	−	10.3156i	1.26691	−	0.402143i
$659$	31.7478	+	15.9444i	1.23672	+	0.621104i	0.942363	−	0.334592i	$-0.108599\pi$
$659$	31.7478	+	15.9444i	1.23672	+	0.621104i	0.294356	+	0.955696i	$0.404895\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	−11.4830	−	23.3725i	−0.445625	−	0.907028i
$665$	−18.1155	+	21.5892i	−0.702490	+	0.837195i
$666$		0			0
$667$	5.97978	+	7.12643i	0.231538	+	0.275936i
$668$	13.5842	−	34.5819i	0.525590	−	1.33801i
$669$		0			0
$670$	5.23825	+	11.6137i	0.202371	+	0.448678i
$671$	−17.8614	+	18.9319i	−0.689530	+	0.730859i
$672$		0			0
$673$	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
$675$		0			0
$676$	3.08083	−	4.43622i	0.118493	−	0.170624i
$677$	−3.52226	+	30.1349i	−0.135372	+	1.15818i	0.739271	+	0.673408i	$0.235170\pi$
$677$	−3.52226	+	30.1349i	−0.135372	+	1.15818i	−0.874642	+	0.484769i	$0.838904\pi$
$678$		0			0
$679$	10.3024	−	43.4691i	0.395368	−	1.66819i
$680$	−3.42826	−	0.635494i	−0.131468	−	0.0243701i
$681$		0			0
$682$	−3.45241	+	0.667572i	−0.132199	+	0.0255626i
$683$	2.79816	+	15.8691i	0.107068	+	0.607215i	0.990374	+	0.138418i	$0.0442016\pi$
$683$	2.79816	+	15.8691i	0.107068	+	0.607215i	−0.883305	+	0.468798i	$0.844687\pi$
$684$		0			0
$685$	1.60605	−	9.10835i	0.0613639	−	0.348012i
$686$	1.20310	+	73.0243i	0.0459346	+	2.78808i
$687$		0			0
$688$	−22.1858	+	11.3574i	−0.845824	+	0.432995i
$689$	−19.1603	+	14.2643i	−0.729950	+	0.543428i
$690$		0			0
$691$	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
$693$		0			0
$694$	−2.77716	+	0.371073i	−0.105420	+	0.0140857i
$695$	−23.1603	+	5.48909i	−0.878521	+	0.208213i
$696$		0			0
$697$	−0.282067	+	4.84290i	−0.0106840	+	0.183438i
$698$	1.32706	−	4.71398i	0.0502300	−	0.178427i
$699$		0			0
$700$	−2.88211	+	14.2352i	−0.108933	+	0.538041i
$701$	7.71155	+	4.45227i	0.291261	+	0.168160i	0.638511	−	0.769613i	$-0.279551\pi$
$701$	7.71155	+	4.45227i	0.291261	+	0.168160i	−0.347249	+	0.937773i	$0.612884\pi$
$702$		0			0
$703$	22.0725	−	12.7436i	0.832481	−	0.480633i
$704$	−2.79827	−	17.6743i	−0.105464	−	0.666125i
$705$		0			0
$706$	−4.44588	+	4.33511i	−0.167323	+	0.163154i
$707$	−59.2515	+	29.7572i	−2.22838	+	1.11914i
$708$		0			0
$709$	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
$711$		0			0
$712$	10.7949	+	11.6445i	0.404555	+	0.436395i
$713$	−0.862781	−	1.31180i	−0.0323114	−	0.0491271i
$714$		0			0
$715$	−1.93354	−	16.5425i	−0.0723102	−	0.618653i
$716$	−18.6646	+	34.9377i	−0.697528	+	1.30568i
$717$		0			0
$718$	−14.5050	+	26.1073i	−0.541321	+	0.974318i
$719$	−24.1971	+	8.80702i	−0.902399	+	0.328446i	−0.751214	−	0.660059i	$-0.770531\pi$
$719$	−24.1971	+	8.80702i	−0.902399	+	0.328446i	−0.151185	+	0.988505i	$0.548309\pi$
$720$		0			0
$721$	3.95838	+	1.44073i	0.147418	+	0.0536556i
$722$	−10.4672	+	9.08102i	−0.389549	+	0.337960i
$723$		0			0
$724$	8.91040	+	6.98972i	0.331152	+	0.259771i
$725$	−9.26754	+	2.77452i	−0.344188	+	0.103043i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−1.45913	−	0.0608867i	−0.0540050	−	0.00225352i
$731$	2.44089	−	3.27868i	0.0902795	−	0.121266i
$732$		0			0
$733$	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
$735$		0			0
$736$	6.82095	−	4.16125i	0.251423	−	0.153386i
$737$	3.66764	−	10.0768i	0.135099	−	0.371183i
$738$		0			0
$739$	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
$741$		0			0
$742$	37.9747	+	18.2946i	1.39410	+	0.671616i
$743$	21.5234	−	2.51572i	0.789616	−	0.0922929i	0.288281	−	0.957546i	$-0.406916\pi$
$743$	21.5234	−	2.51572i	0.789616	−	0.0922929i	0.501335	+	0.865253i	$0.332842\pi$
$744$		0			0
$745$	24.9535	−	16.4121i	0.914224	−	0.601295i
$746$	−3.80983	+	4.17384i	−0.139488	+	0.152815i
$747$		0			0
$748$	1.69253	+	2.39744i	0.0618850	+	0.0876590i
$749$	48.5814	+	14.5443i	1.77513	+	0.531438i
$750$		0			0
$751$	−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
$753$		0			0
$754$	−13.1927	−	34.4690i	−0.480450	−	1.25529i
$755$	12.7153	+	22.0236i	0.462758	+	0.801520i
$756$		0			0
$757$	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
$759$		0			0
$760$	−5.64666	+	15.1013i	−0.204826	+	0.547783i
$761$	6.54089	+	0.380963i	0.237107	+	0.0138099i	0.176287	−	0.984339i	$-0.443591\pi$
$761$	6.54089	+	0.380963i	0.237107	+	0.0138099i	0.0608201	+	0.998149i	$0.480628\pi$
$762$		0			0
$763$	14.6078	+	61.6353i	0.528839	+	2.23135i
$764$	2.74763	+	30.0686i	0.0994056	+	1.08785i
$765$		0			0
$766$	8.13611	+	1.78727i	0.293970	+	0.0645767i
$767$	−3.35255	−	57.5611i	−0.121054	−	2.07841i
$768$		0			0
$769$	−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
$771$		0			0
$772$	0.652595	−	25.8605i	0.0234874	−	0.930739i
$773$	10.1632	+	1.79204i	0.365543	+	0.0644552i	0.353403	−	0.935471i	$-0.385024\pi$
$773$	10.1632	+	1.79204i	0.365543	+	0.0644552i	0.0121403	+	0.999926i	$0.496136\pi$
$774$		0			0
$775$	1.60791	−	0.283519i	0.0577580	−	0.0101843i
$776$	−2.74453	−	25.4084i	−0.0985228	−	0.912109i
$777$		0			0
$778$	2.72363	−	27.1779i	0.0976470	−	0.974376i
$779$	21.8271	+	5.17312i	0.782037	+	0.185346i
$780$		0			0
$781$	−4.07637	−	0.476460i	−0.145864	−	0.0170491i
$782$	−0.701928	+	1.10651i	−0.0251009	+	0.0395688i
$783$		0			0
$784$	24.3717	+	65.3862i	0.870419	+	2.33522i
$785$	4.58230	−	1.97661i	0.163549	−	0.0705482i
$786$		0			0
$787$	−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
$789$		0			0
$790$	38.2401	+	13.2090i	1.36052	+	0.469956i
$791$	32.9355	−	27.6361i	1.17105	−	0.982628i
$792$		0			0
$793$	35.3200	+	29.6370i	1.25425	+	1.05244i
$794$	−6.66454	−	11.1163i	−0.236516	−	0.394503i
$795$		0			0
$796$	1.75861	+	53.3564i	0.0623323	+	1.89117i
$797$	5.63584	+	2.43106i	0.199632	+	0.0861127i	0.493548	−	0.869718i	$-0.335700\pi$
$797$	5.63584	+	2.43106i	0.199632	+	0.0861127i	−0.293917	+	0.955831i	$0.594959\pi$
$798$		0			0
$799$	−1.43565	+	2.85861i	−0.0507895	+	0.101130i
$800$	1.16393	+	8.22684i	0.0411512	+	0.290863i
$801$		0			0
$802$	12.7539	+	5.25403i	0.450356	+	0.185526i
$803$	0.843532	+	0.894092i	0.0297676	+	0.0315518i
$804$		0			0
$805$	−10.9641	−	7.21122i	−0.386435	−	0.254162i
$806$	1.53617	+	6.03666i	0.0541093	+	0.212632i
$807$		0			0
$808$	−26.2701	+	27.3607i	−0.924179	+	0.962547i
$809$			2.39934i			0.0843563i	0.999110	+	0.0421782i	$0.0134297\pi$
$809$			2.39934i			0.0843563i	−0.999110	+	0.0421782i	$0.986570\pi$
$810$		0			0
$811$			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			0
$814$	25.7581	−	6.55475i	0.902821	−	0.229744i
$815$	36.5718	+	24.0537i	1.28106	+	0.842564i
$816$		0			0
$817$	−12.9705	−	13.7480i	−0.453781	−	0.480980i
$818$	9.57671	−	23.2470i	0.334842	−	0.812812i
$819$		0			0
$820$	−26.8176	+	7.29679i	−0.936512	+	0.254815i
$821$	−12.5903	+	25.0693i	−0.439404	+	0.874924i	0.559533	+	0.828808i	$0.310981\pi$
$821$	−12.5903	+	25.0693i	−0.439404	+	0.874924i	−0.998936	+	0.0461160i	$0.985316\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	−87.2649	+	52.3178i	−3.03634	+	1.82037i
$827$	22.9248	+	19.2362i	0.797175	+	0.668909i	0.947510	−	0.319726i	$-0.103591\pi$
$827$	22.9248	+	19.2362i	0.797175	+	0.668909i	−0.150335	+	0.988635i	$0.548035\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	−30.9679	+	6.76908i	−1.07362	+	0.234675i
$833$	−8.32407	−	7.85335i	−0.288412	−	0.272103i
$834$		0			0
$835$	−32.0542	+	13.8268i	−1.10928	+	0.478497i
$836$	12.2765	−	5.78240i	0.424591	−	0.199988i
$837$		0			0
$838$	−42.4954	−	26.9574i	−1.46798	−	0.931228i
$839$	−30.4065	−	3.55401i	−1.04975	−	0.122698i	−0.426316	−	0.904574i	$-0.640189\pi$
$839$	−30.4065	−	3.55401i	−1.04975	−	0.122698i	−0.623434	+	0.781876i	$0.714263\pi$
$840$		0			0
$841$	−13.9918	−	3.31612i	−0.482477	−	0.114349i
$842$	5.79386	+	0.580631i	0.199670	+	0.0200099i
$843$		0			0
$844$	1.18286	+	7.86356i	0.0407155	+	0.270675i
$845$	−4.99761	+	0.881214i	−0.171923	+	0.0303147i
$846$		0			0
$847$	−29.1985	−	5.14848i	−1.00327	−	0.176904i
$848$	23.9716	+	2.61450i	0.823187	+	0.0897824i
$849$		0			0
$850$	−0.767433	−	1.12598i	−0.0263227	−	0.0386207i
$851$	7.08699	+	9.51947i	0.242939	+	0.326323i
$852$		0			0
$853$	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
$855$		0			0
$856$	28.9753	−	1.43317i	0.990354	−	0.0489848i
$857$	−3.70236	−	15.6215i	−0.126470	−	0.533620i	−0.998985	−	0.0450331i	$-0.985661\pi$
$857$	−3.70236	−	15.6215i	−0.126470	−	0.533620i	0.872515	−	0.488587i	$-0.162487\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	−7.58077	+	47.5616i	−0.258202	+	1.61995i
$863$	−20.0705	+	34.7631i	−0.683207	+	1.18335i	0.290789	+	0.956787i	$0.406082\pi$
$863$	−20.0705	+	34.7631i	−0.683207	+	1.18335i	−0.973997	+	0.226562i	$0.927251\pi$
$864$		0			0
$865$	−9.57586	−	16.5859i	−0.325589	−	0.563937i
$866$	−26.6452	+	10.1982i	−0.905441	+	0.346549i
$867$		0			0
$868$	8.18303	−	7.33906i	0.277750	−	0.249104i
$869$	−15.2827	−	30.4303i	−0.518429	−	1.03228i
$870$		0			0
$871$	−18.1981	−	5.44815i	−0.616618	−	0.184603i
$872$	19.6464	+	30.4483i	0.665311	+	1.03111i
$873$		0			0
$874$	4.47522	+	4.08492i	0.151376	+	0.138175i
$875$	50.2136	−	33.0260i	1.69753	−	1.11648i
$876$		0			0
$877$	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
$879$		0			0
$880$	−9.93574	+	13.5633i	−0.334934	+	0.457219i
$881$	−11.8579	−	32.5794i	−0.399504	−	1.09763i	−0.962527	−	0.271187i	$-0.912584\pi$
$881$	−11.8579	−	32.5794i	−0.399504	−	1.09763i	0.563023	−	0.826441i	$-0.309638\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−0.108225	+	0.150485i	−0.00363589	+	0.00505563i
$887$	−10.0492	−	33.5667i	−0.337420	−	1.12706i	−0.943421	−	0.331597i	$-0.892412\pi$
$887$	−10.0492	−	33.5667i	−0.337420	−	1.12706i	0.606001	−	0.795464i	$-0.292773\pi$
$888$		0			0
$889$	0.0344934	−	0.0463327i	0.00115687	−	0.00155395i
$890$	0.621995	−	14.9060i	0.0208493	−	0.499649i
$891$		0			0
$892$	1.49587	−	17.8928i	0.0500853	−	0.599096i
$893$	11.8648	+	8.83298i	0.397039	+	0.295585i
$894$		0			0
$895$	35.6537	−	10.6740i	1.19177	−	0.356793i
$896$	35.9113	+	42.8877i	1.19971	+	1.43278i
$897$		0			0
$898$	−5.13895	−	5.92339i	−0.171489	−	0.197666i
$899$	6.87983	+	2.50405i	0.229455	+	0.0835148i
$900$		0			0
$901$	−3.71615	+	1.35257i	−0.123803	+	0.0450606i
$902$	20.4486	+	11.3610i	0.680864	+	0.378282i
$903$		0			0
$904$	12.4839	−	21.1920i	0.415207	−	0.704834i
$905$	−1.23529	−	10.5686i	−0.0410624	−	0.351311i
$906$		0			0
$907$	−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
$909$		0			0
$910$	31.7736	+	41.2432i	1.05329	+	1.36720i
$911$	3.38749	−	11.3150i	0.112233	−	0.374883i	−0.883357	−	0.468701i	$-0.844722\pi$
$911$	3.38749	−	11.3150i	0.112233	−	0.374883i	0.995589	+	0.0938182i	$0.0299073\pi$
$912$		0			0
$913$	18.4034	−	9.24255i	0.609065	−	0.305884i
$914$	2.30120	+	2.36000i	0.0761170	+	0.0780620i
$915$		0			0
$916$	12.7456	+	37.9726i	0.421126	+	1.25465i
$917$	−27.4318	+	15.8378i	−0.905879	+	0.523009i
$918$		0			0
$919$	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
$921$		0			0
$922$	5.39011	+	1.51740i	0.177514	+	0.0499730i
$923$	−0.422728	+	7.25795i	−0.0139143	+	0.238898i
$924$		0			0
$925$	−12.0085	+	2.84608i	−0.394839	+	0.0935784i
$926$	1.81569	+	13.5889i	0.0596672	+	0.446558i
$927$		0			0
$928$	−13.9252	+	34.5576i	−0.457117	+	1.13441i
$929$	23.7381	−	1.38259i	0.778822	−	0.0453612i	0.335872	−	0.941908i	$-0.390969\pi$
$929$	23.7381	−	1.38259i	0.778822	−	0.0453612i	0.442950	+	0.896546i	$0.353932\pi$
$930$		0			0
$931$	−42.4465	+	31.6002i	−1.39113	+	1.03566i
$932$	28.2099	−	17.5507i	0.924045	−	0.574894i
$933$		0			0
$934$	18.3081	−	0.301633i	0.599060	−	0.00986974i
$935$	0.478810	−	2.71546i	0.0156587	−	0.0888052i
$936$		0			0
$937$	−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
$939$		0			0
$940$	−18.1433	−	2.58612i	−0.591768	−	0.0843500i
$941$	−7.12830	+	30.0767i	−0.232376	+	0.980471i	0.724339	+	0.689444i	$0.242145\pi$
$941$	−7.12830	+	30.0767i	−0.232376	+	0.980471i	−0.956715	+	0.291027i	$0.906003\pi$
$942$		0			0
$943$	−1.21261	+	10.3745i	−0.0394879	+	0.337840i
$944$	−37.0688	+	44.8758i	−1.20649	+	1.46058i
$945$		0			0
$946$	−9.13502	−	17.4658i	−0.297005	−	0.567864i
$947$	1.85058	+	4.29013i	0.0601359	+	0.139411i	0.945634	−	0.325232i	$-0.105442\pi$
$947$	1.85058	+	4.29013i	0.0601359	+	0.139411i	−0.885499	+	0.464642i	$0.846183\pi$
$948$		0			0
$949$	1.49428	−	1.58384i	0.0485062	−	0.0514136i
$950$	−5.74369	+	2.59063i	−0.186350	+	0.0840510i
$951$		0			0
$952$	−8.39130	−	3.70713i	−0.271964	−	0.120149i
$953$	22.0596	+	26.2896i	0.714581	+	0.851605i	0.994092	−	0.108538i	$-0.0346169\pi$
$953$	22.0596	+	26.2896i	0.714581	+	0.851605i	−0.279511	+	0.960142i	$0.590172\pi$
$954$		0			0
$955$	18.2355	−	21.7323i	0.590088	−	0.703239i
$956$	11.1359	−	6.06001i	0.360161	−	0.195995i
$957$		0			0
$958$	1.81253	+	24.2347i	0.0585600	+	0.782988i
$959$	9.63842	−	22.3444i	0.311241	−	0.721537i
$960$		0			0
$961$	26.5984	+	13.3582i	0.858012	+	0.430910i
$962$	−14.2449	−	44.8769i	−0.459273	−	1.44689i
$963$		0			0
$964$	−4.77433	−	2.20392i	−0.153771	−	0.0709833i
$965$	−17.6792	+	16.6795i	−0.569115	+	0.536932i
$966$		0			0
$967$	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
$969$		0			0
$970$	−15.1295	+	18.6460i	−0.485779	+	0.598687i
$971$	−13.0028			−0.417279			−0.208639	−	0.977993i	$-0.566904\pi$
$971$	−13.0028			−0.417279			−0.208639	+	0.977993i	$0.566904\pi$
$972$		0			0
$973$	−62.6248			−2.00766
$974$	31.5566	−	38.8912i	1.01114	−	1.24615i
$975$		0			0
$976$	−5.76013	−	46.1868i	−0.184377	−	1.47840i
$977$	4.72223	−	7.17980i	0.151078	−	0.229702i	−0.752017	−	0.659143i	$-0.770919\pi$
$977$	4.72223	−	7.17980i	0.151078	−	0.229702i	0.903095	+	0.429441i	$0.141289\pi$
$978$		0			0
$979$	−9.13370	+	8.61720i	−0.291914	+	0.275407i
$980$	27.4791	−	59.5277i	0.877787	−	1.90154i
$981$		0			0
$982$	−1.05368	−	3.31949i	−0.0336242	−	0.105929i
$983$	27.7334	+	13.9282i	0.884559	+	0.444242i	0.832257	−	0.554389i	$-0.187048\pi$
$983$	27.7334	+	13.9282i	0.884559	+	0.444242i	0.0523012	+	0.998631i	$0.483344\pi$
$984$		0			0
$985$	−6.99764	+	16.2224i	−0.222963	+	0.516887i
$986$	−0.455717	−	6.09325i	−0.0145130	−	0.194049i
$987$		0			0
$988$	−11.4904	−	21.1148i	−0.365558	−	0.671752i
$989$	5.65716	−	6.74194i	0.179887	−	0.214381i
$990$		0			0
$991$	−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
$993$		0			0
$994$	11.6948	−	5.27480i	0.370936	−	0.167307i
$995$	34.4216	−	36.4847i	1.09124	−	1.15664i
$996$		0			0
$997$	−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
$999$		0			0

Twists

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

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

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.p (of order \(54\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09818 - 0.891069i) q^{2} +(0.411991 + 1.95711i) q^{4} +(1.03261 - 1.57001i) q^{5} +(3.59628 - 3.39292i) q^{7} +(1.29148 - 2.51636i) q^{8} +O(q^{10})\)	\(q+(-1.09818 - 0.891069i) q^{2} +(0.411991 + 1.95711i) q^{4} +(1.03261 - 1.57001i) q^{5} +(3.59628 - 3.39292i) q^{7} +(1.29148 - 2.51636i) q^{8} +(-2.53297 + 0.804020i) q^{10} +(1.99888 + 1.00388i) q^{11} +(1.56942 - 3.63833i) q^{13} +(-6.97269 + 0.521491i) q^{14} +(-3.66053 + 1.61262i) q^{16} +(0.421668 - 0.502524i) q^{17} +(-1.94981 - 2.32370i) q^{19} +(3.49809 + 1.37410i) q^{20} +(-1.30060 - 2.88358i) q^{22} +(0.969289 - 1.02739i) q^{23} +(0.581761 + 1.34867i) q^{25} +(-4.96551 + 2.59707i) q^{26} +(8.12194 + 5.64046i) q^{28} +(-0.764623 + 6.54177i) q^{29} +(0.256353 - 1.08164i) q^{31} +(5.45687 + 1.49084i) q^{32} +(-0.910851 + 0.176126i) q^{34} +(-1.61335 - 9.14975i) q^{35} +(-1.45904 + 8.27461i) q^{37} +(0.0706671 + 4.28925i) q^{38} +(-2.61711 - 4.62605i) q^{40} +(-5.93169 + 4.41598i) q^{41} +(6.22042 - 0.362298i) q^{43} +(-1.14117 + 4.32561i) q^{44} +(-1.97992 + 0.264549i) q^{46} +(-4.74488 + 1.12456i) q^{47} +(1.01435 - 17.4156i) q^{49} +(0.562884 - 1.99947i) q^{50} +(7.76719 + 1.57257i) q^{52} +(-5.22077 - 3.01422i) q^{53} +(3.64016 - 2.10165i) q^{55} +(-3.89329 - 13.4314i) q^{56} +(6.66887 - 6.50270i) q^{58} +(13.0037 - 6.53070i) q^{59} +(-3.33728 + 11.1473i) q^{61} +(-1.24534 + 0.959405i) q^{62} +(-4.66417 - 6.49966i) q^{64} +(-4.09160 - 6.22098i) q^{65} +(-0.556562 - 4.76169i) q^{67} +(1.15722 + 0.618214i) q^{68} +(-6.38132 + 11.4857i) q^{70} +(-1.72416 + 0.627544i) q^{71} +(0.516395 + 0.187953i) q^{73} +(8.97553 - 7.78689i) q^{74} +(3.74442 - 4.77333i) q^{76} +(10.5946 - 3.17182i) q^{77} +(-12.2113 - 9.09094i) q^{79} +(-1.24807 + 7.41226i) q^{80} +(10.4490 + 0.436016i) q^{82} +(5.49796 - 7.38504i) q^{83} +(-0.353548 - 1.18093i) q^{85} +(-7.15396 - 5.14496i) q^{86} +(5.10763 - 3.73343i) q^{88} +(-1.92005 + 5.27530i) q^{89} +(-6.70047 - 18.4094i) q^{91} +(2.41004 + 1.47373i) q^{92} +(6.21278 + 2.99305i) q^{94} +(-5.66162 + 0.661748i) q^{95} +(7.54904 - 4.96508i) q^{97} +(-16.6325 + 18.2216i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8}+O(q^{10}) \) 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8	\( 936 q + 18 q^{2} - 18 q^{4} + 36 q^{5} + 18 q^{8} - 18 q^{10} - 36 q^{13} + 18 q^{14} - 18 q^{16} + 36 q^{17} + 18 q^{20} - 18 q^{22} - 36 q^{25} + 27 q^{26} - 9 q^{28} + 36 q^{29} + 18 q^{32} - 18 q^{34} - 36 q^{37} + 18 q^{38} - 18 q^{40} + 36 q^{41} + 90 q^{44} - 18 q^{46} - 36 q^{49} + 135 q^{50} - 18 q^{52} + 54 q^{53} + 144 q^{56} - 18 q^{58} - 36 q^{61} + 117 q^{62} - 18 q^{64} + 36 q^{65} + 63 q^{68} - 18 q^{70} - 36 q^{73} + 18 q^{74} - 18 q^{76} + 36 q^{77} - 36 q^{82} - 36 q^{85} + 18 q^{86} - 18 q^{88} + 54 q^{89} - 72 q^{92} - 18 q^{94} - 36 q^{97} - 153 q^{98}+O(q^{100}) \) 936 * q + 18 * q^2 - 18 * q^4 + 36 * q^5 + 18 * q^8 - 18 * q^10 - 36 * q^13 + 18 * q^14 - 18 * q^16 + 36 * q^17 + 18 * q^20 - 18 * q^22 - 36 * q^25 + 27 * q^26 - 9 * q^28 + 36 * q^29 + 18 * q^32 - 18 * q^34 - 36 * q^37 + 18 * q^38 - 18 * q^40 + 36 * q^41 + 90 * q^44 - 18 * q^46 - 36 * q^49 + 135 * q^50 - 18 * q^52 + 54 * q^53 + 144 * q^56 - 18 * q^58 - 36 * q^61 + 117 * q^62 - 18 * q^64 + 36 * q^65 + 63 * q^68 - 18 * q^70 - 36 * q^73 + 18 * q^74 - 18 * q^76 + 36 * q^77 - 36 * q^82 - 36 * q^85 + 18 * q^86 - 18 * q^88 + 54 * q^89 - 72 * q^92 - 18 * q^94 - 36 * q^97 - 153 * q^98

Introduction

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