LMFDB - Embedded newform 738.2.ba.a.521.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,-4,0,4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$3$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			521.1
Character	$\chi$	$=$	738.521
Dual form			738.2.ba.a.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.987688 + 0.156434i) q^{2} +(0.951057 + 0.309017i) q^{4} +(-1.48149 - 2.90758i) q^{5} +(2.16613 - 1.32741i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-1.00840 - 3.10354i) q^{10} +(-3.34354 - 0.263142i) q^{11} +(-0.135310 - 0.563607i) q^{13} +(2.34711 - 0.972206i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-1.23831 - 1.44987i) q^{17} +(1.37431 - 5.72443i) q^{19} +(-0.510485 - 3.22308i) q^{20} +(-3.26121 - 0.782948i) q^{22} +(-1.86113 + 1.35219i) q^{23} +(-3.32029 + 4.56999i) q^{25} +(-0.0454767 - 0.577836i) q^{26} +(2.47030 - 0.593067i) q^{28} +(4.84731 - 5.67547i) q^{29} +(0.557461 - 0.181130i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.996252 - 1.62574i) q^{34} +(-7.06863 - 4.33166i) q^{35} +(-0.294720 + 0.907054i) q^{37} +(2.25289 - 5.43896i) q^{38} -3.26325i q^{40} +(0.432093 + 6.38853i) q^{41} +(-0.642114 + 4.05415i) q^{43} +(-3.09858 - 1.28347i) q^{44} +(-2.04975 + 1.04440i) q^{46} +(4.74787 - 7.74782i) q^{47} +(-0.247820 + 0.486374i) q^{49} +(-3.99431 + 3.99431i) q^{50} +(0.0454767 - 0.577836i) q^{52} +(1.55539 + 1.32843i) q^{53} +(4.18830 + 10.1115i) q^{55} +(2.53267 - 0.199325i) q^{56} +(5.67547 - 4.84731i) q^{58} +(-5.35369 - 7.36872i) q^{59} +(14.3601 - 2.27442i) q^{61} +(0.578933 - 0.0916939i) q^{62} +(0.587785 + 0.809017i) q^{64} +(-1.43827 + 1.22840i) q^{65} +(4.21374 - 0.331628i) q^{67} +(-0.729665 - 1.76157i) q^{68} +(-6.30398 - 5.38411i) q^{70} +(-0.665395 + 8.45464i) q^{71} +(3.72370 - 3.72370i) q^{73} +(-0.432986 + 0.849782i) q^{74} +(3.07600 - 5.01957i) q^{76} +(-7.59184 + 3.86824i) q^{77} +(2.04711 + 0.847940i) q^{79} +(0.510485 - 3.22308i) q^{80} +(-0.572613 + 6.37747i) q^{82} +6.19990i q^{83} +(-2.38108 + 5.74844i) q^{85} +(-1.26842 + 3.90379i) q^{86} +(-2.85965 - 1.75240i) q^{88} +(4.49202 + 7.33031i) q^{89} +(-1.04124 - 1.04124i) q^{91} +(-2.18789 + 0.710889i) q^{92} +(5.90144 - 6.90970i) q^{94} +(-18.6803 + 4.48473i) q^{95} +(0.784784 + 9.97163i) q^{97} +(-0.320855 + 0.441619i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{40}\right)$

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 $

$2$	0.987688	+	0.156434i	0.698401	+	0.110616i
$2$	0.987688	+	0.156434i	0.698401	+	0.110616i
$3$		0			0
$3$		0			0
$4$	0.951057	+	0.309017i	0.475528	+	0.154508i
$5$	−1.48149	−	2.90758i	−0.662540	−	1.30031i	−0.940525	−	0.339723i	$-0.889667\pi$
$5$	−1.48149	−	2.90758i	−0.662540	−	1.30031i	0.277985	−	0.960585i	$-0.410333\pi$
$6$		0			0
$7$	2.16613	−	1.32741i	0.818720	−	0.501712i	−0.0489802	−	0.998800i	$-0.515597\pi$
$7$	2.16613	−	1.32741i	0.818720	−	0.501712i	0.867701	+	0.497087i	$0.165597\pi$
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$		0			0
$10$	−1.00840	−	3.10354i	−0.318884	−	0.981425i
$11$	−3.34354	−	0.263142i	−1.00812	−	0.0793404i	−0.436367	−	0.899769i	$-0.643735\pi$
$11$	−3.34354	−	0.263142i	−1.00812	−	0.0793404i	−0.571749	+	0.820429i	$0.693735\pi$
$12$		0			0
$13$	−0.135310	−	0.563607i	−0.0375283	−	0.156317i	0.950460	−	0.310848i	$-0.100613\pi$
$13$	−0.135310	−	0.563607i	−0.0375283	−	0.156317i	−0.987988	+	0.154532i	$0.950613\pi$
$14$	2.34711	−	0.972206i	0.627293	−	0.259833i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−1.23831	−	1.44987i	−0.300334	−	0.351645i	0.589633	−	0.807671i	$-0.299272\pi$
$17$	−1.23831	−	1.44987i	−0.300334	−	0.351645i	−0.889967	+	0.456026i	$0.849272\pi$
$18$		0			0
$19$	1.37431	−	5.72443i	0.315289	−	1.31327i	−0.559524	−	0.828814i	$-0.689016\pi$
$19$	1.37431	−	5.72443i	0.315289	−	1.31327i	0.874813	−	0.484460i	$-0.160984\pi$
$20$	−0.510485	−	3.22308i	−0.114148	−	0.720702i
$21$		0			0
$22$	−3.26121	−	0.782948i	−0.695293	−	0.166925i
$23$	−1.86113	+	1.35219i	−0.388073	+	0.281951i	−0.764665	−	0.644428i	$-0.777096\pi$
$23$	−1.86113	+	1.35219i	−0.388073	+	0.281951i	0.376593	+	0.926379i	$0.377096\pi$
$24$		0			0
$25$	−3.32029	+	4.56999i	−0.664058	+	0.913997i
$26$	−0.0454767	−	0.577836i	−0.00891871	−	0.113323i
$27$		0			0
$28$	2.47030	−	0.593067i	0.466844	−	0.112079i
$29$	4.84731	−	5.67547i	0.900123	−	1.05391i	−0.0981502	−	0.995172i	$-0.531293\pi$
$29$	4.84731	−	5.67547i	0.900123	−	1.05391i	0.998273	−	0.0587373i	$-0.0187074\pi$
$30$		0			0
$31$	0.557461	−	0.181130i	0.100123	−	0.0325319i	−0.258527	−	0.966004i	$-0.583237\pi$
$31$	0.557461	−	0.181130i	0.100123	−	0.0325319i	0.358650	+	0.933472i	$0.383237\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−0.996252	−	1.62574i	−0.170856	−	0.278811i
$35$	−7.06863	−	4.33166i	−1.19482	−	0.732184i
$36$		0			0
$37$	−0.294720	+	0.907054i	−0.0484516	+	0.149119i	−0.972355	−	0.233507i	$-0.924980\pi$
$37$	−0.294720	+	0.907054i	−0.0484516	+	0.149119i	0.923904	+	0.382625i	$0.124980\pi$
$38$	2.25289	−	5.43896i	0.365467	−	0.882317i
$39$		0			0
$40$		−	3.26325i		−	0.515965i
$41$	0.432093	+	6.38853i	0.0674816	+	0.997721i
$41$	0.432093	+	6.38853i	0.0674816	+	0.997721i
$42$		0			0
$43$	−0.642114	+	4.05415i	−0.0979215	+	0.618252i	0.889106	+	0.457701i	$0.151327\pi$
$43$	−0.642114	+	4.05415i	−0.0979215	+	0.618252i	−0.987028	+	0.160551i	$0.948673\pi$
$44$	−3.09858	−	1.28347i	−0.467129	−	0.193491i
$45$		0			0
$46$	−2.04975	+	1.04440i	−0.302219	+	0.153988i
$47$	4.74787	−	7.74782i	0.692548	−	1.13014i	−0.292235	−	0.956347i	$-0.594399\pi$
$47$	4.74787	−	7.74782i	0.692548	−	1.13014i	0.984783	−	0.173789i	$-0.0556011\pi$
$48$		0			0
$49$	−0.247820	+	0.486374i	−0.0354029	+	0.0694820i
$50$	−3.99431	+	3.99431i	−0.564881	+	0.564881i
$51$		0			0
$52$	0.0454767	−	0.577836i	0.00630648	−	0.0801314i
$53$	1.55539	+	1.32843i	0.213649	+	0.182474i	0.749832	−	0.661628i	$-0.230134\pi$
$53$	1.55539	+	1.32843i	0.213649	+	0.182474i	−0.536183	+	0.844102i	$0.680134\pi$
$54$		0			0
$55$	4.18830	+	10.1115i	0.564750	+	1.36343i
$56$	2.53267	−	0.199325i	0.338442	−	0.0266359i
$57$		0			0
$58$	5.67547	−	4.84731i	0.745226	−	0.636483i
$59$	−5.35369	−	7.36872i	−0.696991	−	0.959326i	−0.999980	−	0.00633188i	$-0.997984\pi$
$59$	−5.35369	−	7.36872i	−0.696991	−	0.959326i	0.302989	−	0.952994i	$-0.402016\pi$
$60$		0			0
$61$	14.3601	−	2.27442i	1.83862	−	0.291210i	0.862120	−	0.506704i	$-0.169136\pi$
$61$	14.3601	−	2.27442i	1.83862	−	0.291210i	0.976505	+	0.215495i	$0.0691365\pi$
$62$	0.578933	−	0.0916939i	0.0735245	−	0.0116451i
$63$		0			0
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−1.43827	+	1.22840i	−0.178396	+	0.152364i
$66$		0			0
$67$	4.21374	−	0.331628i	0.514790	−	0.0405149i	0.181596	−	0.983373i	$-0.441874\pi$
$67$	4.21374	−	0.331628i	0.514790	−	0.0405149i	0.333194	+	0.942858i	$0.391874\pi$
$68$	−0.729665	−	1.76157i	−0.0884849	−	0.213621i
$69$		0			0
$70$	−6.30398	−	5.38411i	−0.753470	−	0.643524i
$71$	−0.665395	+	8.45464i	−0.0789678	+	1.00338i	0.821998	+	0.569491i	$0.192860\pi$
$71$	−0.665395	+	8.45464i	−0.0789678	+	1.00338i	−0.900966	+	0.433891i	$0.857140\pi$
$72$		0			0
$73$	3.72370	−	3.72370i	0.435826	−	0.435826i	−0.454779	−	0.890604i	$-0.650282\pi$
$73$	3.72370	−	3.72370i	0.435826	−	0.435826i	0.890604	+	0.454779i	$0.150282\pi$
$74$	−0.432986	+	0.849782i	−0.0503336	+	0.0987852i
$75$		0			0
$76$	3.07600	−	5.01957i	0.352841	−	0.575784i
$77$	−7.59184	+	3.86824i	−0.865171	+	0.440827i
$78$		0			0
$79$	2.04711	+	0.847940i	0.230318	+	0.0954007i	0.494858	−	0.868974i	$-0.335220\pi$
$79$	2.04711	+	0.847940i	0.230318	+	0.0954007i	−0.264540	+	0.964375i	$0.585220\pi$
$80$	0.510485	−	3.22308i	0.0570740	−	0.360351i
$81$		0			0
$82$	−0.572613	+	6.37747i	−0.0632345	+	0.704274i
$83$			6.19990i			0.680527i	0.940330	+	0.340264i	$0.110516\pi$
$83$			6.19990i			0.680527i	−0.940330	+	0.340264i	$0.889484\pi$
$84$		0			0
$85$	−2.38108	+	5.74844i	−0.258265	+	0.623506i
$86$	−1.26842	+	3.90379i	−0.136777	+	0.420956i
$87$		0			0
$88$	−2.85965	−	1.75240i	−0.304840	−	0.186806i
$89$	4.49202	+	7.33031i	0.476153	+	0.777012i	0.997062	−	0.0766008i	$-0.0244067\pi$
$89$	4.49202	+	7.33031i	0.476153	+	0.777012i	−0.520908	+	0.853613i	$0.674407\pi$
$90$		0			0
$91$	−1.04124	−	1.04124i	−0.109151	−	0.109151i
$92$	−2.18789	+	0.710889i	−0.228103	+	0.0741153i
$93$		0			0
$94$	5.90144	−	6.90970i	0.608687	−	0.712681i
$95$	−18.6803	+	4.48473i	−1.91655	+	0.460124i
$96$		0			0
$97$	0.784784	+	9.97163i	0.0796828	+	1.01247i	0.898662	+	0.438642i	$0.144540\pi$
$97$	0.784784	+	9.97163i	0.0796828	+	1.01247i	−0.818979	+	0.573823i	$0.805460\pi$
$98$	−0.320855	+	0.441619i	−0.0324112	+	0.0446102i
$99$		0			0
$100$	−4.56999	+	3.32029i	−0.456999	+	0.332029i
$101$	12.4242	+	2.98278i	1.23625	+	0.296798i	0.798333	−	0.602216i	$-0.205716\pi$
$101$	12.4242	+	2.98278i	1.23625	+	0.296798i	0.437919	+	0.899014i	$0.355716\pi$
$102$		0			0
$103$	3.00842	+	18.9944i	0.296429	+	1.87158i	0.464169	+	0.885747i	$0.346353\pi$
$103$	3.00842	+	18.9944i	0.296429	+	1.87158i	−0.167740	+	0.985831i	$0.553647\pi$
$104$	0.135310	−	0.563607i	0.0132683	−	0.0552663i
$105$		0			0
$106$	1.32843	+	1.55539i	0.129029	+	0.151073i
$107$	8.44283	+	6.13408i	0.816199	+	0.593004i	0.915621	−	0.402042i	$-0.131699\pi$
$107$	8.44283	+	6.13408i	0.816199	+	0.593004i	−0.0994219	+	0.995045i	$0.531699\pi$
$108$		0			0
$109$	−12.2565	+	5.07681i	−1.17396	+	0.486271i	−0.882500	−	0.470312i	$-0.844141\pi$
$109$	−12.2565	+	5.07681i	−1.17396	+	0.486271i	−0.291461	+	0.956583i	$0.594141\pi$
$110$	2.55496	+	10.6422i	0.243605	+	1.01469i
$111$		0			0
$112$	2.53267	+	0.199325i	0.239314	+	0.0188345i
$113$	−3.39247	−	10.4410i	−0.319137	−	0.982203i	−0.974018	−	0.226471i	$-0.927281\pi$
$113$	−3.39247	−	10.4410i	−0.319137	−	0.982203i	0.654881	−	0.755732i	$-0.272719\pi$
$114$		0			0
$115$	6.68884	+	3.40813i	0.623738	+	0.317810i
$116$	6.36389	−	3.89979i	0.590872	−	0.362087i
$117$		0			0
$118$	−4.13506	−	8.11550i	−0.380663	−	0.747093i
$119$	−4.60690	−	1.49687i	−0.422314	−	0.137218i
$120$		0			0
$121$	0.245454	+	0.0388761i	0.0223140	+	0.00353419i
$122$	14.5391			1.31631
$123$		0			0
$124$	0.586149			0.0526378
$125$	2.09118	+	0.331210i	0.187040	+	0.0296243i
$126$		0			0
$127$	−16.1708	−	5.25423i	−1.43493	−	0.466237i	−0.514617	−	0.857420i	$-0.672066\pi$
$127$	−16.1708	−	5.25423i	−1.43493	−	0.466237i	−0.920313	+	0.391183i	$0.872066\pi$
$128$	0.453990	+	0.891007i	0.0401275	+	0.0787546i
$129$		0			0
$130$	−1.61273	+	0.988282i	−0.141446	+	0.0866781i
$131$	−14.3020	−	7.28721i	−1.24957	−	0.636687i	−0.301110	−	0.953589i	$-0.597357\pi$
$131$	−14.3020	−	7.28721i	−1.24957	−	0.636687i	−0.948458	+	0.316903i	$0.897357\pi$
$132$		0			0
$133$	−4.62170	−	14.2241i	−0.400753	−	1.23339i
$134$	4.21374	+	0.331628i	0.364012	+	0.0286483i
$135$		0			0
$136$	−0.445112	−	1.85402i	−0.0381680	−	0.158981i
$137$	9.29980	−	3.85210i	0.794536	−	0.329108i	0.0517702	−	0.998659i	$-0.483514\pi$
$137$	9.29980	−	3.85210i	0.794536	−	0.329108i	0.742766	+	0.669551i	$0.233514\pi$
$138$		0			0
$139$	0.211469	+	0.153641i	0.0179366	+	0.0130317i	0.596717	−	0.802451i	$-0.296471\pi$
$139$	0.211469	+	0.153641i	0.0179366	+	0.0130317i	−0.578781	+	0.815483i	$0.696471\pi$
$140$	−5.38411	−	6.30398i	−0.455040	−	0.532784i
$141$		0			0
$142$	−1.97980	+	8.24646i	−0.166141	+	0.692028i
$143$	0.304106	+	1.92005i	0.0254306	+	0.160563i
$144$		0			0
$145$	−23.6831	−	5.68581i	−1.96678	−	0.472181i
$146$	4.26037	−	3.09534i	0.352590	−	0.256172i
$147$		0			0
$148$	−0.560590	+	0.771586i	−0.0460802	+	0.0634240i
$149$	1.65160	+	20.9856i	0.135305	+	1.71921i	0.572553	+	0.819868i	$0.305953\pi$
$149$	1.65160	+	20.9856i	0.135305	+	1.71921i	−0.437248	+	0.899341i	$0.644047\pi$
$150$		0			0
$151$	−12.8173	+	3.07715i	−1.04305	+	0.250415i	−0.718555	−	0.695470i	$-0.755196\pi$
$151$	−12.8173	+	3.07715i	−1.04305	+	0.250415i	−0.324500	+	0.945886i	$0.605196\pi$
$152$	3.82336	−	4.47658i	0.310116	−	0.363099i
$153$		0			0
$154$	−8.10350	+	2.63299i	−0.652999	+	0.212172i
$155$	−1.35252	−	1.35252i	−0.108637	−	0.108637i
$156$		0			0
$157$	−6.48585	−	10.5839i	−0.517627	−	0.844690i	0.481875	−	0.876240i	$-0.339956\pi$
$157$	−6.48585	−	10.5839i	−0.517627	−	0.844690i	−0.999502	+	0.0315494i	$0.989956\pi$
$158$	1.88926	+	1.15774i	0.150301	+	0.0921047i
$159$		0			0
$160$	1.00840	−	3.10354i	0.0797210	−	0.245356i
$161$	−2.23655	+	5.39950i	−0.176265	+	0.425540i
$162$		0			0
$163$		−	7.01368i		−	0.549354i	−0.961537	−	0.274677i	$-0.911429\pi$
$163$		−	7.01368i		−	0.549354i	0.961537	−	0.274677i	$-0.0885709\pi$
$164$	−1.56322	+	6.20938i	−0.122067	+	0.484871i
$165$		0			0
$166$	−0.969878	+	6.12357i	−0.0752771	+	0.475281i
$167$	6.30278	+	2.61070i	0.487724	+	0.202022i	0.612974	−	0.790103i	$-0.289973\pi$
$167$	6.30278	+	2.61070i	0.487724	+	0.202022i	−0.125250	+	0.992125i	$0.539973\pi$
$168$		0			0
$169$	11.2837	−	5.74935i	0.867980	−	0.442258i
$170$	−3.25102	+	5.30518i	−0.249342	+	0.406889i
$171$		0			0
$172$	−1.86349	+	3.65730i	−0.142090	+	0.278867i
$173$	12.2109	−	12.2109i	0.928376	−	0.928376i	−0.0692247	−	0.997601i	$-0.522053\pi$
$173$	12.2109	−	12.2109i	0.928376	−	0.928376i	0.997601	+	0.0692247i	$0.0220525\pi$
$174$		0			0
$175$	−1.12595	+	14.3066i	−0.0851139	+	1.08147i
$176$	−2.55031	−	2.17817i	−0.192237	−	0.164186i
$177$		0			0
$178$	3.29000	+	7.94277i	0.246596	+	0.595336i
$179$	12.1702	−	0.957816i	0.909644	−	0.0715906i	0.385004	−	0.922915i	$-0.374200\pi$
$179$	12.1702	−	0.957816i	0.909644	−	0.0715906i	0.524640	+	0.851324i	$0.324200\pi$
$180$		0			0
$181$	11.7991	−	10.0774i	0.877022	−	0.749047i	−0.0920690	−	0.995753i	$-0.529348\pi$
$181$	11.7991	−	10.0774i	0.877022	−	0.749047i	0.969090	+	0.246706i	$0.0793480\pi$
$182$	−0.865531	−	1.19130i	−0.0641574	−	0.0883051i
$183$		0			0
$184$	−2.27216	+	0.359875i	−0.167506	+	0.0265303i
$185$	3.07395	−	0.486866i	0.226002	−	0.0357951i
$186$		0			0
$187$	3.75881	+	5.17356i	0.274871	+	0.378328i
$188$	6.90970	−	5.90144i	0.503942	−	0.430407i
$189$		0			0
$190$	−19.1518	+	1.50728i	−1.38942	+	0.109350i
$191$	7.85329	+	18.9595i	0.568244	+	1.37186i	0.903033	+	0.429570i	$0.141335\pi$
$191$	7.85329	+	18.9595i	0.568244	+	1.37186i	−0.334789	+	0.942293i	$0.608665\pi$
$192$		0			0
$193$	−12.5846	−	10.7482i	−0.905856	−	0.773674i	0.0687420	−	0.997634i	$-0.478101\pi$
$193$	−12.5846	−	10.7482i	−0.905856	−	0.773674i	−0.974598	+	0.223960i	$0.928101\pi$
$194$	−0.784784	+	9.97163i	−0.0563442	+	0.715921i
$195$		0			0
$196$	−0.385989	+	0.385989i	−0.0275706	+	0.0275706i
$197$	−0.448195	+	0.879632i	−0.0319326	+	0.0626712i	−0.906422	−	0.422374i	$-0.861197\pi$
$197$	−0.448195	+	0.879632i	−0.0319326	+	0.0626712i	0.874489	+	0.485045i	$0.161197\pi$
$198$		0			0
$199$	−2.51572	+	4.10529i	−0.178335	+	0.291016i	−0.929300	−	0.369326i	$-0.879589\pi$
$199$	−2.51572	+	4.10529i	−0.178335	+	0.291016i	0.750965	+	0.660342i	$0.229589\pi$
$200$	−5.03313	+	2.56451i	−0.355896	+	0.181338i
$201$		0			0
$202$	11.8046	+	4.88963i	0.830569	+	0.344033i
$203$	2.96625	−	18.7282i	0.208190	−	1.31446i
$204$		0			0
$205$	17.9350	−	10.7209i	1.25264	−	0.748777i
$206$			19.2312i			1.33990i
$207$		0			0
$208$	0.221812	−	0.535501i	0.0153799	−	0.0371303i
$209$	−6.10142	+	18.7782i	−0.422044	+	1.29892i
$210$		0			0
$211$	24.0178	+	14.7181i	1.65345	+	1.01324i	0.954565	+	0.298004i	$0.0963209\pi$
$211$	24.0178	+	14.7181i	1.65345	+	1.01324i	0.698887	+	0.715232i	$0.253679\pi$
$212$	1.06876	+	1.74405i	0.0734026	+	0.119782i
$213$		0			0
$214$	7.37931	+	7.37931i	0.504439	+	0.504439i
$215$	12.7390	−	4.13917i	0.868795	−	0.282289i
$216$		0			0
$217$	0.967100	−	1.13233i	0.0656510	−	0.0768675i
$218$	−12.8998	+	3.09697i	−0.873685	+	0.209753i
$219$		0			0
$220$	0.858700	+	10.9108i	0.0578935	+	0.735607i
$221$	−0.649603	+	0.894102i	−0.0436970	+	0.0601438i
$222$		0			0
$223$	−16.2426	+	11.8009i	−1.08769	+	0.790250i	−0.979007	−	0.203827i	$-0.934662\pi$
$223$	−16.2426	+	11.8009i	−1.08769	+	0.790250i	−0.108679	+	0.994077i	$0.534662\pi$
$224$	2.47030	+	0.593067i	0.165054	+	0.0396260i
$225$		0			0
$226$	−1.71738	−	10.8431i	−0.114238	−	0.721273i
$227$	−6.89751	+	28.7302i	−0.457804	+	1.90689i	−0.0379957	+	0.999278i	$0.512097\pi$
$227$	−6.89751	+	28.7302i	−0.457804	+	1.90689i	−0.419808	+	0.907613i	$0.637903\pi$
$228$		0			0
$229$	−5.34031	−	6.25270i	−0.352898	−	0.413190i	0.555354	−	0.831614i	$-0.312583\pi$
$229$	−5.34031	−	6.25270i	−0.352898	−	0.413190i	−0.908252	+	0.418424i	$0.862583\pi$
$230$	6.07334	+	4.41254i	0.400464	+	0.290954i
$231$		0			0
$232$	6.89560	−	2.85625i	0.452718	−	0.187522i
$233$	−1.62315	−	6.76091i	−0.106336	−	0.442922i	0.893647	−	0.448771i	$-0.148138\pi$
$233$	−1.62315	−	6.76091i	−0.106336	−	0.442922i	−0.999983	+	0.00584928i	$0.998138\pi$
$234$		0			0
$235$	−29.5613	−	2.32652i	−1.92837	−	0.151766i
$236$	−2.81460	−	8.66245i	−0.183215	−	0.563878i
$237$		0			0
$238$	−4.31602	−	2.19912i	−0.279766	−	0.142548i
$239$	−6.61003	+	4.05063i	−0.427568	+	0.262014i	−0.719592	−	0.694397i	$-0.755671\pi$
$239$	−6.61003	+	4.05063i	−0.427568	+	0.262014i	0.292024	+	0.956411i	$0.405671\pi$
$240$		0			0
$241$	−8.89620	−	17.4598i	−0.573055	−	1.12468i	−0.977660	−	0.210192i	$-0.932591\pi$
$241$	−8.89620	−	17.4598i	−0.573055	−	1.12468i	0.404605	−	0.914491i	$-0.367409\pi$
$242$	0.236350	+	0.0767949i	0.0151932	+	0.00493656i
$243$		0			0
$244$	14.3601	+	2.27442i	0.919312	+	0.145605i
$245$	1.78131			0.113804
$246$		0			0
$247$	−3.41229			−0.217119
$248$	0.578933	+	0.0916939i	0.0367623	+	0.00582257i
$249$		0			0
$250$	2.01362	+	0.654264i	0.127352	+	0.0413793i
$251$	−2.76793	−	5.43236i	−0.174710	−	0.342888i	0.787002	−	0.616951i	$-0.211632\pi$
$251$	−2.76793	−	5.43236i	−0.174710	−	0.342888i	−0.961712	+	0.274063i	$0.911632\pi$
$252$		0			0
$253$	6.57859	−	4.03136i	0.413592	−	0.253450i
$254$	−15.1498	−	7.71922i	−0.950584	−	0.484347i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	27.6547	+	2.17647i	1.72505	+	0.135764i	0.901868	−	0.432011i	$-0.142196\pi$
$257$	27.6547	+	2.17647i	1.72505	+	0.135764i	0.823183	+	0.567776i	$0.192196\pi$
$258$		0			0
$259$	0.565628	+	2.35601i	0.0351464	+	0.146395i
$260$	−1.74748	+	0.723828i	−0.108374	+	0.0448899i
$261$		0			0
$262$	−12.9859	−	9.43481i	−0.802272	−	0.582885i
$263$	−4.56727	−	5.34759i	−0.281630	−	0.329747i	0.601502	−	0.798872i	$-0.294569\pi$
$263$	−4.56727	−	5.34759i	−0.281630	−	0.329747i	−0.883132	+	0.469125i	$0.844569\pi$
$264$		0			0
$265$	1.55822	−	6.49047i	0.0957210	−	0.398707i
$266$	−2.33966	−	14.7720i	−0.143454	−	0.905730i
$267$		0			0
$268$	4.10998	+	0.986719i	0.251057	+	0.0602735i
$269$	19.3774	−	14.0785i	1.18146	−	0.858380i	0.189123	−	0.981953i	$-0.439435\pi$
$269$	19.3774	−	14.0785i	1.18146	−	0.858380i	0.992335	+	0.123573i	$0.0394354\pi$
$270$		0			0
$271$	0.403294	−	0.555087i	0.0244984	−	0.0337191i	−0.796592	−	0.604517i	$-0.793366\pi$
$271$	0.403294	−	0.555087i	0.0244984	−	0.0337191i	0.821090	+	0.570798i	$0.193366\pi$
$272$	−0.149599	−	1.90083i	−0.00907074	−	0.115255i
$273$		0			0
$274$	9.78791	−	2.34987i	0.591309	−	0.141961i
$275$	12.3041	−	14.4062i	0.741964	−	0.868728i
$276$		0			0
$277$	30.4552	−	9.89551i	1.82988	−	0.594564i	0.830588	−	0.556887i	$-0.188004\pi$
$277$	30.4552	−	9.89551i	1.82988	−	0.594564i	0.999290	−	0.0376768i	$-0.0119957\pi$
$278$	0.184831	+	0.184831i	0.0110854	+	0.0110854i
$279$		0			0
$280$	−4.33166	−	7.06863i	−0.258866	−	0.422431i
$281$	−14.9986	−	9.19114i	−0.894740	−	0.548297i	−0.00256978	−	0.999997i	$-0.500818\pi$
$281$	−14.9986	−	9.19114i	−0.894740	−	0.548297i	−0.892170	+	0.451699i	$0.850818\pi$
$282$		0			0
$283$	5.60368	−	17.2464i	0.333104	−	1.02519i	−0.634544	−	0.772887i	$-0.718812\pi$
$283$	5.60368	−	17.2464i	0.333104	−	1.02519i	0.967648	−	0.252303i	$-0.0811880\pi$
$284$	−3.24546	+	7.83523i	−0.192582	+	0.464935i
$285$		0			0
$286$			1.94398i			0.114950i
$287$	9.41614	+	13.2648i	0.555817	+	0.782998i
$288$		0			0
$289$	2.09066	−	13.1999i	0.122980	−	0.776466i
$290$	−22.5021	−	9.32066i	−1.32137	−	0.547328i
$291$		0			0
$292$	4.69213	−	2.39076i	0.274586	−	0.139909i
$293$	−2.58743	+	4.22229i	−0.151159	+	0.246669i	−0.919252	−	0.393669i	$-0.871206\pi$
$293$	−2.58743	+	4.22229i	−0.151159	+	0.246669i	0.768093	+	0.640338i	$0.221206\pi$
$294$		0			0
$295$	−13.4937	+	26.4829i	−0.785635	+	1.54190i
$296$	−0.674391	+	0.674391i	−0.0391982	+	0.0391982i
$297$		0			0
$298$	−1.65160	+	20.9856i	−0.0956748	+	1.21566i
$299$	1.01393	+	0.865982i	0.0586374	+	0.0500810i
$300$		0			0
$301$	3.99060	+	9.63416i	0.230014	+	0.555304i
$302$	−13.1408	+	1.03421i	−0.756171	+	0.0595119i
$303$		0			0
$304$	4.47658	−	3.82336i	0.256749	−	0.219285i
$305$	−27.8874	−	38.3837i	−1.59683	−	2.19784i
$306$		0			0
$307$	−5.96729	+	0.945126i	−0.340571	+	0.0539412i	−0.324378	−	0.945928i	$-0.605155\pi$
$307$	−5.96729	+	0.945126i	−0.340571	+	0.0539412i	−0.0161937	+	0.999869i	$0.505155\pi$
$308$	−8.41562	+	1.33290i	−0.479525	+	0.0759492i
$309$		0			0
$310$	−1.12429	−	1.54745i	−0.0638553	−	0.0878892i
$311$	−4.26840	+	3.64556i	−0.242039	+	0.206721i	−0.762190	−	0.647354i	$-0.775876\pi$
$311$	−4.26840	+	3.64556i	−0.242039	+	0.206721i	0.520151	+	0.854074i	$0.325876\pi$
$312$		0			0
$313$	2.85116	−	0.224391i	0.161157	−	0.0126834i	0.00237627	−	0.999997i	$-0.499244\pi$
$313$	2.85116	−	0.224391i	0.161157	−	0.0126834i	0.158781	+	0.987314i	$0.449244\pi$
$314$	−4.75030	−	11.4682i	−0.268075	−	0.647191i
$315$		0			0
$316$	1.68489	+	1.43903i	0.0947823	+	0.0809517i
$317$	0.719997	−	9.14843i	0.0404391	−	0.513827i	−0.943025	−	0.332723i	$-0.892033\pi$
$317$	0.719997	−	9.14843i	0.0404391	−	0.513827i	0.983464	−	0.181105i	$-0.0579673\pi$
$318$		0			0
$319$	−17.7006	+	17.7006i	−0.991046	+	0.991046i
$320$	1.48149	−	2.90758i	0.0828176	−	0.162539i
$321$		0			0
$322$	−3.05368	+	4.98315i	−0.170175	+	0.277700i
$323$	−10.0015	+	5.09603i	−0.556499	+	0.283550i
$324$		0			0
$325$	3.02495	+	1.25297i	0.167794	+	0.0695025i
$326$	1.09718	−	6.92733i	0.0607672	−	0.383669i
$327$		0			0
$328$	−2.51533	+	5.88839i	−0.138886	+	0.325132i
$329$		−	23.0851i		−	1.27273i
$330$		0			0
$331$	6.62283	−	15.9889i	0.364024	−	0.878831i	−0.630680	−	0.776043i	$-0.717224\pi$
$331$	6.62283	−	15.9889i	0.364024	−	0.878831i	0.994703	−	0.102788i	$-0.0327763\pi$
$332$	−1.91587	+	5.89645i	−0.105147	+	0.323610i
$333$		0			0
$334$	5.81678	+	3.56453i	0.318280	+	0.195042i
$335$	−7.20683	−	11.7605i	−0.393751	−	0.642543i
$336$		0			0
$337$	7.07791	+	7.07791i	0.385558	+	0.385558i	0.873100	−	0.487541i	$-0.162106\pi$
$337$	7.07791	+	7.07791i	0.385558	+	0.385558i	−0.487541	+	0.873100i	$0.662106\pi$
$338$	12.0442	−	3.91340i	0.655119	−	0.212861i
$339$		0			0
$340$	−4.04091	+	4.73130i	−0.219149	+	0.256591i
$341$	−1.91156	+	0.458924i	−0.103517	+	0.0248521i
$342$		0			0
$343$	1.50408	+	19.1112i	0.0812128	+	1.03191i
$344$	−2.41267	+	3.32076i	−0.130083	+	0.179043i
$345$		0			0
$346$	13.9708	−	10.1503i	0.751072	−	0.545686i
$347$	−18.6463	−	4.47658i	−1.00099	−	0.240315i	−0.300346	−	0.953830i	$-0.597102\pi$
$347$	−18.6463	−	4.47658i	−1.00099	−	0.240315i	−0.700640	+	0.713515i	$0.747102\pi$
$348$		0			0
$349$	−0.0307410	−	0.194091i	−0.00164553	−	0.0103895i	0.986852	−	0.161627i	$-0.0516742\pi$
$349$	−0.0307410	−	0.194091i	−0.00164553	−	0.0103895i	−0.988497	+	0.151238i	$0.951674\pi$
$350$	−3.35013	+	13.9543i	−0.179072	+	0.745888i
$351$		0			0
$352$	−2.17817	−	2.55031i	−0.116097	−	0.135932i
$353$	26.7133	+	19.4083i	1.42180	+	1.03300i	0.991471	+	0.130331i	$0.0416039\pi$
$353$	26.7133	+	19.4083i	1.42180	+	1.03300i	0.430333	+	0.902670i	$0.358396\pi$
$354$		0			0
$355$	25.5683	−	10.5907i	1.35703	−	0.562098i
$356$	2.00698	+	8.35965i	0.106369	+	0.443061i
$357$		0			0
$358$	12.1702	+	0.957816i	0.643216	+	0.0506222i
$359$	−2.35548	−	7.24943i	−0.124318	−	0.382610i	0.869459	−	0.494006i	$-0.164468\pi$
$359$	−2.35548	−	7.24943i	−0.124318	−	0.382610i	−0.993776	+	0.111396i	$0.964468\pi$
$360$		0			0
$361$	−13.9513	−	7.10852i	−0.734277	−	0.374133i
$362$	13.2303	−	8.10754i	0.695369	−	0.426123i
$363$		0			0
$364$	−0.668514	−	1.31203i	−0.0350397	−	0.0687692i
$365$	−16.3435	−	5.31034i	−0.855460	−	0.277956i
$366$		0			0
$367$	25.6990	+	4.07033i	1.34148	+	0.212469i	0.785569	−	0.618774i	$-0.212370\pi$
$367$	25.6990	+	4.07033i	1.34148	+	0.212469i	0.555909	+	0.831243i	$0.312370\pi$
$368$	−2.30048			−0.119921
$369$		0			0
$370$	3.11227			0.161799
$371$	5.13255	+	0.812916i	0.266469	+	0.0422045i
$372$		0			0
$373$	−25.2148	−	8.19278i	−1.30557	−	0.424206i	−0.428055	−	0.903753i	$-0.640801\pi$
$373$	−25.2148	−	8.19278i	−1.30557	−	0.424206i	−0.877516	+	0.479547i	$0.840801\pi$
$374$	2.90321	+	5.69787i	0.150121	+	0.294630i
$375$		0			0
$376$	7.74782	−	4.74787i	0.399563	−	0.244853i
$377$	−3.85463	−	1.96403i	−0.198524	−	0.101153i
$378$		0			0
$379$	−5.44659	−	16.7629i	−0.279772	−	0.861051i	−0.987917	−	0.154983i	$-0.950468\pi$
$379$	−5.44659	−	16.7629i	−0.279772	−	0.861051i	0.708145	−	0.706067i	$-0.249532\pi$
$380$	−19.1518	−	1.50728i	−0.982469	−	0.0773220i
$381$		0			0
$382$	4.79068	+	19.9546i	0.245113	+	1.02097i
$383$	26.5180	−	10.9841i	1.35501	−	0.561262i	0.417324	−	0.908758i	$-0.362968\pi$
$383$	26.5180	−	10.9841i	1.35501	−	0.561262i	0.937682	+	0.347496i	$0.112968\pi$
$384$		0			0
$385$	22.4944	+	16.3431i	1.14642	+	0.832924i
$386$	−10.7482	−	12.5846i	−0.547070	−	0.640537i
$387$		0			0
$388$	−2.33503	+	9.72609i	−0.118543	+	0.493768i
$389$	4.57097	+	28.8600i	0.231758	+	1.46326i	0.779389	+	0.626540i	$0.215529\pi$
$389$	4.57097	+	28.8600i	0.231758	+	1.46326i	−0.547632	+	0.836719i	$0.684471\pi$
$390$		0			0
$391$	4.26516	+	1.02397i	0.215698	+	0.0517846i
$392$	−0.441619	+	0.320855i	−0.0223051	+	0.0162056i
$393$		0			0
$394$	−0.580282	+	0.798689i	−0.0292342	+	0.0402374i
$395$	−0.567308	−	7.20834i	−0.0285444	−	0.362691i
$396$		0			0
$397$	−20.3696	+	4.89032i	−1.02232	+	0.245438i	−0.709748	−	0.704455i	$-0.751191\pi$
$397$	−20.3696	+	4.89032i	−1.02232	+	0.245438i	−0.312574	+	0.949893i	$0.601191\pi$
$398$	−3.12696	+	3.66120i	−0.156740	+	0.183519i
$399$		0			0
$400$	−5.37234	+	1.74558i	−0.268617	+	0.0872790i
$401$	−9.84930	−	9.84930i	−0.491850	−	0.491850i	0.417038	−	0.908889i	$-0.363068\pi$
$401$	−9.84930	−	9.84930i	−0.491850	−	0.491850i	−0.908889	+	0.417038i	$0.863068\pi$
$402$		0			0
$403$	−0.177516	−	0.289680i	−0.00884272	−	0.0144300i
$404$	10.8944	+	6.67608i	0.542015	+	0.332147i
$405$		0			0
$406$	5.85946	−	18.0336i	0.290800	−	0.894991i
$407$	1.22409	−	2.95522i	0.0606760	−	0.146485i
$408$		0			0
$409$		−	5.67865i		−	0.280791i	−0.990095	−	0.140396i	$-0.955163\pi$
$409$		−	5.67865i		−	0.280791i	0.990095	−	0.140396i	$-0.0448375\pi$
$410$	19.3913	−	7.78321i	0.957669	−	0.384385i
$411$		0			0
$412$	−3.00842	+	18.9944i	−0.148214	+	0.935789i
$413$	−21.3781	−	8.85509i	−1.05195	−	0.435731i
$414$		0			0
$415$	18.0267	−	9.18506i	0.884895	−	0.450877i
$416$	0.302852	−	0.494209i	0.0148485	−	0.0242306i
$417$		0			0
$418$	−8.96386	+	17.5926i	−0.438437	+	0.860481i
$419$	6.83414	−	6.83414i	0.333870	−	0.333870i	−0.520184	−	0.854054i	$-0.674137\pi$
$419$	6.83414	−	6.83414i	0.333870	−	0.333870i	0.854054	+	0.520184i	$0.174137\pi$
$420$		0			0
$421$	1.46647	−	18.6332i	0.0714713	−	0.908129i	−0.851772	−	0.523913i	$-0.824472\pi$
$421$	1.46647	−	18.6332i	0.0714713	−	0.908129i	0.923243	−	0.384216i	$-0.125528\pi$
$422$	21.4197	+	18.2941i	1.04269	+	0.890543i
$423$		0			0
$424$	0.782770	+	1.88977i	0.0380146	+	0.0917755i
$425$	10.7374	−	0.845054i	0.520842	−	0.0409911i
$426$		0			0
$427$	28.0868	−	23.9884i	1.35922	−	1.16088i
$428$	6.13408	+	8.44283i	0.296502	+	0.408100i
$429$		0			0
$430$	13.2297	−	2.09538i	0.637993	−	0.101048i
$431$	−36.7830	+	5.82585i	−1.77177	+	0.280621i	−0.955058	−	0.296420i	$-0.904207\pi$
$431$	−36.7830	+	5.82585i	−1.77177	+	0.280621i	−0.816715	+	0.577041i	$0.804207\pi$
$432$		0			0
$433$	−9.31339	−	12.8188i	−0.447573	−	0.616031i	0.524301	−	0.851533i	$-0.324327\pi$
$433$	−9.31339	−	12.8188i	−0.447573	−	0.616031i	−0.971874	+	0.235502i	$0.924327\pi$
$434$	1.13233	−	0.967100i	0.0543535	−	0.0464223i
$435$		0			0
$436$	−13.2255	+	1.04087i	−0.633385	+	0.0498485i
$437$	5.18275	+	12.5123i	0.247924	+	0.598542i
$438$		0			0
$439$	−12.1791	−	10.4019i	−0.581276	−	0.496456i	0.309500	−	0.950899i	$-0.399838\pi$
$439$	−12.1791	−	10.4019i	−0.581276	−	0.496456i	−0.890776	+	0.454443i	$0.849838\pi$
$440$	−0.858700	+	10.9108i	−0.0409369	+	0.520153i
$441$		0			0
$442$	−0.781473	+	0.781473i	−0.0371709	+	0.0371709i
$443$	−2.56115	+	5.02655i	−0.121684	+	0.238818i	−0.943811	−	0.330486i	$-0.892787\pi$
$443$	−2.56115	+	5.02655i	−0.121684	+	0.238818i	0.822127	+	0.569304i	$0.192787\pi$
$444$		0			0
$445$	14.6586	−	23.9207i	0.694884	−	1.13395i
$446$	−17.8887	+	9.11475i	−0.847055	+	0.431596i
$447$		0			0
$448$	2.34711	+	0.972206i	0.110891	+	0.0459324i
$449$	1.19456	−	7.54218i	0.0563750	−	0.355938i	−0.943335	−	0.331843i	$-0.892330\pi$
$449$	1.19456	−	7.54218i	0.0563750	−	0.355938i	0.999710	−	0.0240948i	$-0.00767035\pi$
$450$		0			0
$451$	0.236371	−	21.4740i	0.0111303	−	1.01117i
$452$		−	10.9783i		−	0.516375i
$453$		0			0
$454$	−11.3070	+	27.2975i	−0.530663	+	1.28113i
$455$	−1.48490	+	4.57005i	−0.0696132	+	0.214247i
$456$		0			0
$457$	18.4417	+	11.3011i	0.862665	+	0.528642i	0.882042	−	0.471171i	$-0.156168\pi$
$457$	18.4417	+	11.3011i	0.862665	+	0.528642i	−0.0193773	+	0.999812i	$0.506168\pi$
$458$	−4.29643	−	7.01113i	−0.200759	−	0.327609i
$459$		0			0
$460$	5.30829	+	5.30829i	0.247500	+	0.247500i
$461$	−15.6678	+	5.09078i	−0.729722	+	0.237101i	−0.650233	−	0.759735i	$-0.725329\pi$
$461$	−15.6678	+	5.09078i	−0.729722	+	0.237101i	−0.0794889	+	0.996836i	$0.525329\pi$
$462$		0			0
$463$	−4.66070	+	5.45697i	−0.216601	+	0.253607i	−0.858059	−	0.513551i	$-0.828330\pi$
$463$	−4.66070	+	5.45697i	−0.216601	+	0.253607i	0.641458	+	0.767158i	$0.278330\pi$
$464$	7.25752	−	1.74238i	0.336922	−	0.0808878i
$465$		0			0
$466$	−0.545528	−	6.93158i	−0.0252711	−	0.321099i
$467$	−7.30995	+	10.0613i	−0.338264	+	0.465581i	−0.943933	−	0.330136i	$-0.892905\pi$
$467$	−7.30995	+	10.0613i	−0.338264	+	0.465581i	0.605669	+	0.795717i	$0.292905\pi$
$468$		0			0
$469$	8.68730	−	6.31169i	0.401142	−	0.291447i
$470$	−28.8334	−	6.92229i	−1.32999	−	0.319301i
$471$		0			0
$472$	−1.42484	−	8.99610i	−0.0655837	−	0.414079i
$473$	3.21375	−	13.3862i	0.147769	−	0.615500i
$474$		0			0
$475$	21.5975	+	25.2874i	0.990959	+	1.16026i
$476$	−3.91887	−	2.84722i	−0.179621	−	0.130502i
$477$		0			0
$478$	−7.16231	+	2.96673i	−0.327597	+	0.135695i
$479$	3.41575	+	14.2276i	0.156070	+	0.650077i	0.994470	+	0.105022i	$0.0334912\pi$
$479$	3.41575	+	14.2276i	0.156070	+	0.650077i	−0.838400	+	0.545055i	$0.816509\pi$
$480$		0			0
$481$	0.551101	+	0.0433726i	0.0251280	+	0.00197762i
$482$	−6.05536	−	18.6365i	−0.275814	−	0.848869i
$483$		0			0
$484$	0.221427	+	0.112823i	0.0100649	+	0.00512831i
$485$	27.8307	−	17.0546i	1.26372	−	0.774412i
$486$		0			0
$487$	13.3145	+	26.1312i	0.603338	+	1.18412i	0.967521	+	0.252790i	$0.0813482\pi$
$487$	13.3145	+	26.1312i	0.603338	+	1.18412i	−0.364183	+	0.931327i	$0.618652\pi$
$488$	13.8275	+	4.49284i	0.625943	+	0.203381i
$489$		0			0
$490$	1.75938	+	0.278659i	0.0794808	+	0.0125885i
$491$	−27.2140			−1.22815			−0.614076	−	0.789247i	$-0.710471\pi$
$491$	−27.2140			−1.22815			−0.614076	+	0.789247i	$0.710471\pi$
$492$		0			0
$493$	−14.2312			−0.640940
$494$	−3.37028	−	0.533800i	−0.151636	−	0.0240168i
$495$		0			0
$496$	0.557461	+	0.181130i	0.0250307	+	0.00813298i
$497$	9.78142	+	19.1971i	0.438756	+	0.861108i
$498$		0			0
$499$	11.8188	−	7.24256i	0.529081	−	0.324221i	−0.232174	−	0.972674i	$-0.574584\pi$
$499$	11.8188	−	7.24256i	0.529081	−	0.324221i	0.761255	+	0.648453i	$0.224584\pi$
$500$	1.88648	+	0.961208i	0.0843658	+	0.0429865i
$501$		0			0
$502$	−1.88404	−	5.79848i	−0.0840888	−	0.258799i
$503$	−6.36304	−	0.500782i	−0.283714	−	0.0223288i	−0.0641962	−	0.997937i	$-0.520448\pi$
$503$	−6.36304	−	0.500782i	−0.283714	−	0.0223288i	−0.219518	+	0.975609i	$0.570448\pi$
$504$		0			0
$505$	−9.73357	−	40.5432i	−0.433138	−	1.80415i
$506$	7.12824	−	2.95261i	0.316889	−	0.131260i
$507$		0			0
$508$	−13.7557	−	9.99413i	−0.610312	−	0.443418i
$509$	−16.3116	−	19.0985i	−0.723000	−	0.846524i	0.270217	−	0.962799i	$-0.412904\pi$
$509$	−16.3116	−	19.0985i	−0.723000	−	0.846524i	−0.993217	+	0.116275i	$0.962904\pi$
$510$		0			0
$511$	3.12315	−	13.0089i	0.138160	−	0.575479i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$		0			0
$514$	26.9737	+	6.47582i	1.18976	+	0.285636i
$515$	50.7709	−	36.8872i	2.23723	−	1.62545i
$516$		0			0
$517$	−17.9135	+	24.6558i	−0.787834	+	1.08436i
$518$	0.190103	+	2.41549i	0.00835264	+	0.106130i
$519$		0			0
$520$	−1.83919	+	0.441551i	−0.0806540	+	0.0193633i
$521$	−4.35390	+	5.09777i	−0.190748	+	0.223337i	−0.847536	−	0.530738i	$-0.821915\pi$
$521$	−4.35390	+	5.09777i	−0.190748	+	0.223337i	0.656788	+	0.754075i	$0.271915\pi$
$522$		0			0
$523$	−38.6066	+	12.5440i	−1.68815	+	0.548512i	−0.986464	−	0.163977i	$-0.947568\pi$
$523$	−38.6066	+	12.5440i	−1.68815	+	0.548512i	−0.701683	+	0.712489i	$0.747568\pi$
$524$	−11.3501	−	11.3501i	−0.495831	−	0.495831i
$525$		0			0
$526$	−3.67450	−	5.99623i	−0.160216	−	0.261448i
$527$	−0.952923	−	0.583952i	−0.0415100	−	0.0254374i
$528$		0			0
$529$	−5.47200	+	16.8411i	−0.237913	+	0.732221i
$530$	2.55437	−	6.16680i	0.110955	−	0.267869i
$531$		0			0
$532$		−	14.9561i		−	0.648431i
$533$	3.54216	−	1.10796i	0.153428	−	0.0479912i
$534$		0			0
$535$	5.32738	−	33.6357i	0.230323	−	1.45420i
$536$	3.90502	+	1.61751i	0.168671	+	0.0698660i
$537$		0			0
$538$	21.3412	−	10.8739i	0.920083	−	0.468806i
$539$	0.956582	−	1.56100i	0.0412029	−	0.0672371i
$540$		0			0
$541$	−12.2986	+	24.1374i	−0.528759	+	1.03775i	0.459956	+	0.887942i	$0.347865\pi$
$541$	−12.2986	+	24.1374i	−0.528759	+	1.03775i	−0.988715	+	0.149807i	$0.952135\pi$
$542$	0.485164	−	0.485164i	0.0208396	−	0.0208396i
$543$		0			0
$544$	0.149599	−	1.90083i	0.00641398	−	0.0814974i
$545$	32.9191	+	28.1156i	1.41010	+	1.20434i
$546$		0			0
$547$	−3.60012	−	8.69147i	−0.153930	−	0.371620i	0.828037	−	0.560674i	$-0.189458\pi$
$547$	−3.60012	−	8.69147i	−0.153930	−	0.371620i	−0.981967	+	0.189054i	$0.939458\pi$
$548$	10.0350	−	0.789772i	0.428674	−	0.0337374i
$549$		0			0
$550$	14.4062	−	12.3041i	0.614284	−	0.524648i
$551$	−25.8271	−	35.5480i	−1.10027	−	1.51440i
$552$		0			0
$553$	5.55986	−	0.880596i	0.236429	−	0.0374467i
$554$	31.6283	−	5.00943i	1.34376	−	0.212830i
$555$		0			0
$556$	0.153641	+	0.211469i	0.00651584	+	0.00896828i
$557$	−9.07096	+	7.74733i	−0.384349	+	0.328265i	−0.820540	−	0.571589i	$-0.806327\pi$
$557$	−9.07096	+	7.74733i	−0.384349	+	0.328265i	0.436191	+	0.899854i	$0.356327\pi$
$558$		0			0
$559$	2.37183	−	0.186667i	0.100318	−	0.00789519i
$560$	−3.17255	−	7.65922i	−0.134065	−	0.323661i
$561$		0			0
$562$	−13.3761	−	11.4243i	−0.564237	−	0.481904i
$563$	−0.365726	+	4.64698i	−0.0154135	+	0.195847i	0.984390	+	0.176003i	$0.0563169\pi$
$563$	−0.365726	+	4.64698i	−0.0154135	+	0.195847i	−0.999803	+	0.0198438i	$0.993683\pi$
$564$		0			0
$565$	−25.3320	+	25.3320i	−1.06573	+	1.06573i
$566$	8.23262	−	16.1574i	0.346043	−	0.679147i
$567$		0			0
$568$	−4.43120	+	7.23106i	−0.185929	+	0.303409i
$569$	11.7505	−	5.98716i	0.492605	−	0.250995i	−0.189997	−	0.981785i	$-0.560848\pi$
$569$	11.7505	−	5.98716i	0.492605	−	0.250995i	0.682603	+	0.730790i	$0.260848\pi$
$570$		0			0
$571$	−20.3063	−	8.41113i	−0.849791	−	0.351995i	−0.0850844	−	0.996374i	$-0.527116\pi$
$571$	−20.3063	−	8.41113i	−0.849791	−	0.351995i	−0.764706	+	0.644379i	$0.777116\pi$
$572$	−0.304106	+	1.92005i	−0.0127153	+	0.0802814i
$573$		0			0
$574$	7.22514	+	14.5745i	0.301572	+	0.608329i
$575$		−	12.9950i		−	0.541929i
$576$		0			0
$577$	−13.9974	+	33.7927i	−0.582718	+	1.40681i	0.307621	+	0.951509i	$0.400467\pi$
$577$	−13.9974	+	33.7927i	−0.582718	+	1.40681i	−0.890339	+	0.455298i	$0.849533\pi$
$578$	4.12985	−	12.7104i	0.171779	−	0.528681i
$579$		0			0
$580$	−20.7670	−	12.7260i	−0.862301	−	0.528419i
$581$	8.22978	+	13.4298i	0.341429	+	0.557161i
$582$		0			0
$583$	−4.85095	−	4.85095i	−0.200906	−	0.200906i
$584$	5.00836	−	1.62732i	0.207247	−	0.0673388i
$585$		0			0
$586$	−3.21608	+	3.76555i	−0.132855	+	0.155553i
$587$	2.39227	−	0.574334i	0.0987397	−	0.0237053i	−0.183774	−	0.982968i	$-0.558832\pi$
$587$	2.39227	−	0.574334i	0.0987397	−	0.0237053i	0.282514	+	0.959263i	$0.408832\pi$
$588$		0			0
$589$	−0.270740	−	3.44008i	−0.0111556	−	0.141746i
$590$	−17.4704	+	24.0460i	−0.719247	+	0.989958i
$591$		0			0
$592$	−0.771586	+	0.560590i	−0.0317120	+	0.0230401i
$593$	32.2034	+	7.73136i	1.32244	+	0.317489i	0.832381	−	0.554203i	$-0.186977\pi$
$593$	32.2034	+	7.73136i	1.32244	+	0.317489i	0.490054	+	0.871692i	$0.336977\pi$
$594$		0			0
$595$	2.47278	+	15.6125i	0.101374	+	0.640051i
$596$	−4.91414	+	20.4689i	−0.201291	+	0.838438i
$597$		0			0
$598$	0.865982	+	1.01393i	0.0354126	+	0.0414629i
$599$	−32.2376	−	23.4220i	−1.31719	−	0.956997i	−0.999963	−	0.00864803i	$-0.997247\pi$
$599$	−32.2376	−	23.4220i	−1.31719	−	0.956997i	−0.317230	−	0.948349i	$-0.602753\pi$
$600$		0			0
$601$	29.9657	−	12.4122i	1.22233	−	0.506304i	0.324177	−	0.945996i	$-0.394913\pi$
$601$	29.9657	−	12.4122i	1.22233	−	0.506304i	0.898148	+	0.439693i	$0.144913\pi$
$602$	2.43435	+	10.1398i	0.0992169	+	0.413268i
$603$		0			0
$604$	−13.1408	−	1.03421i	−0.534693	−	0.0420813i
$605$	−0.250601	−	0.771271i	−0.0101884	−	0.0313566i
$606$		0			0
$607$	−4.11486	−	2.09662i	−0.167017	−	0.0850994i	0.368484	−	0.929634i	$-0.379877\pi$
$607$	−4.11486	−	2.09662i	−0.167017	−	0.0850994i	−0.535501	+	0.844535i	$0.679877\pi$
$608$	5.01957	−	3.07600i	0.203571	−	0.124748i
$609$		0			0
$610$	−21.5395	−	42.2736i	−0.872109	−	1.71161i
$611$	−5.00916	−	1.62758i	−0.202649	−	0.0658447i
$612$		0			0
$613$	−42.3104	−	6.70132i	−1.70890	−	0.270664i	−0.775984	−	0.630752i	$-0.782747\pi$
$613$	−42.3104	−	6.70132i	−1.70890	−	0.270664i	−0.932918	+	0.360088i	$0.882747\pi$
$614$	−6.04167			−0.243822
$615$		0			0
$616$	−8.52053			−0.343302
$617$	8.90585	+	1.41055i	0.358536	+	0.0567865i	0.333104	−	0.942890i	$-0.391904\pi$
$617$	8.90585	+	1.41055i	0.358536	+	0.0567865i	0.0254318	+	0.999677i	$0.491904\pi$
$618$		0			0
$619$	−39.8959	−	12.9630i	−1.60355	−	0.521026i	−0.635571	−	0.772043i	$-0.719235\pi$
$619$	−39.8959	−	12.9630i	−1.60355	−	0.521026i	−0.967983	+	0.251017i	$0.919235\pi$
$620$	−0.868372	−	1.70428i	−0.0348746	−	0.0684453i
$621$		0			0
$622$	−4.78614	+	2.93295i	−0.191907	+	0.117601i
$623$	19.4606	+	9.91568i	0.779673	+	0.397263i
$624$		0			0
$625$	6.59287	+	20.2908i	0.263715	+	0.811631i
$626$	2.85116	+	0.224391i	0.113955	+	0.00896849i
$627$		0			0
$628$	−2.89779	−	12.0702i	−0.115634	−	0.481652i
$629$	1.68006	−	0.695906i	0.0669886	−	0.0277476i
$630$		0			0
$631$	−4.18762	−	3.04248i	−0.166707	−	0.121119i	0.501304	−	0.865271i	$-0.332854\pi$
$631$	−4.18762	−	3.04248i	−0.166707	−	0.121119i	−0.668010	+	0.744152i	$0.732854\pi$
$632$	1.43903	+	1.68489i	0.0572415	+	0.0670212i
$633$		0			0
$634$	2.14226	−	8.92317i	0.0850801	−	0.354384i
$635$	8.67980	+	54.8021i	0.344447	+	2.17475i
$636$		0			0
$637$	0.307657	+	0.0738618i	0.0121898	+	0.00292651i
$638$	−20.2517	+	14.7137i	−0.801773	+	0.582522i
$639$		0			0
$640$	1.91809	−	2.64003i	0.0758192	−	0.104356i
$641$	0.460021	+	5.84512i	0.0181697	+	0.230868i	0.999297	+	0.0375028i	$0.0119403\pi$
$641$	0.460021	+	5.84512i	0.0181697	+	0.230868i	−0.981127	+	0.193365i	$0.938060\pi$
$642$		0			0
$643$	10.1002	−	2.42485i	0.398314	−	0.0956266i	−0.0293396	−	0.999570i	$-0.509340\pi$
$643$	10.1002	−	2.42485i	0.398314	−	0.0956266i	0.427653	+	0.903943i	$0.359340\pi$
$644$	−3.79562	+	4.44410i	−0.149568	+	0.175122i
$645$		0			0
$646$	−10.6756	+	3.46870i	−0.420025	+	0.136474i
$647$	5.26266	+	5.26266i	0.206897	+	0.206897i	0.802947	−	0.596050i	$-0.203264\pi$
$647$	5.26266	+	5.26266i	0.206897	+	0.206897i	−0.596050	+	0.802947i	$0.703264\pi$
$648$		0			0
$649$	15.9613	+	26.0464i	0.626534	+	1.02241i
$650$	2.79170	+	1.71075i	0.109499	+	0.0671013i
$651$		0			0
$652$	2.16735	−	6.67040i	0.0848798	−	0.261233i
$653$	−9.10338	+	21.9775i	−0.356243	+	0.860046i	0.639579	+	0.768725i	$0.279109\pi$
$653$	−9.10338	+	21.9775i	−0.356243	+	0.860046i	−0.995822	+	0.0913204i	$0.970891\pi$
$654$		0			0
$655$			52.3800i			2.04665i
$656$	−3.40551	+	5.42241i	−0.132963	+	0.211709i
$657$		0			0
$658$	3.61131	−	22.8009i	0.140784	−	0.888873i
$659$	−14.4923	−	6.00291i	−0.564541	−	0.233840i	0.0821145	−	0.996623i	$-0.473833\pi$
$659$	−14.4923	−	6.00291i	−0.564541	−	0.233840i	−0.646655	+	0.762783i	$0.723833\pi$
$660$		0			0
$661$	0.0943254	−	0.0480612i	0.00366883	−	0.00186936i	−0.452155	−	0.891939i	$-0.649345\pi$
$661$	0.0943254	−	0.0480612i	0.00366883	−	0.00186936i	0.455824	+	0.890070i	$0.349345\pi$
$662$	9.04251	−	14.7560i	0.351447	−	0.573510i
$663$		0			0
$664$	−2.81469	+	5.52415i	−0.109231	+	0.214379i
$665$	−34.5108	+	34.5108i	−1.33827	+	1.33827i
$666$		0			0
$667$	−1.34716	+	17.1173i	−0.0521622	+	0.662784i
$668$	5.18755	+	4.43059i	0.200712	+	0.171425i
$669$		0			0
$670$	−5.27836	−	12.7431i	−0.203921	−	0.492308i
$671$	−48.6121	+	3.82586i	−1.87665	+	0.147696i
$672$		0			0
$673$	4.50587	−	3.84838i	0.173689	−	0.148344i	−0.558354	−	0.829603i	$-0.688567\pi$
$673$	4.50587	−	3.84838i	0.173689	−	0.148344i	0.732043	+	0.681259i	$0.238567\pi$
$674$	5.88354	+	8.09800i	0.226626	+	0.311923i
$675$		0			0
$676$	12.5081	−	1.98109i	0.481082	−	0.0761958i
$677$	45.3855	−	7.18836i	1.74431	−	0.276271i	0.798734	−	0.601684i	$-0.205503\pi$
$677$	45.3855	−	7.18836i	1.74431	−	0.276271i	0.945572	+	0.325413i	$0.105503\pi$
$678$		0			0
$679$	14.9364	+	20.5581i	0.573205	+	0.788948i
$680$	−4.73130	+	4.04091i	−0.181437	+	0.154962i
$681$		0			0
$682$	−1.95981	+	0.154241i	−0.0750452	+	0.00590618i
$683$	13.9754	+	33.7395i	0.534753	+	1.29101i	0.928344	+	0.371722i	$0.121233\pi$
$683$	13.9754	+	33.7395i	0.534753	+	1.29101i	−0.393591	+	0.919286i	$0.628767\pi$
$684$		0			0
$685$	−24.9778	−	21.3331i	−0.954354	−	0.815095i
$686$	−1.50408	+	19.1112i	−0.0574261	+	0.729668i
$687$		0			0
$688$	−2.90245	+	2.90245i	−0.110655	+	0.110655i
$689$	0.538253	−	1.05638i	0.0205058	−	0.0402449i
$690$		0			0
$691$	9.29818	−	15.1733i	0.353720	−	0.577218i	−0.625449	−	0.780265i	$-0.715084\pi$
$691$	9.29818	−	15.1733i	0.353720	−	0.577218i	0.979169	+	0.203047i	$0.0650844\pi$
$692$	15.3866	−	7.83987i	0.584911	−	0.298027i
$693$		0			0
$694$	−17.7164	−	7.33839i	−0.672507	−	0.278562i
$695$	0.133436	−	0.842480i	0.00506150	−	0.0319571i
$696$		0			0
$697$	8.72748	−	8.53744i	0.330577	−	0.323379i
$698$		−	0.196511i		−	0.00743804i
$699$		0			0
$700$	−5.49181	+	13.2584i	−0.207571	+	0.501121i
$701$	−1.10963	+	3.41508i	−0.0419101	+	0.128986i	−0.969822	−	0.243813i	$-0.921602\pi$
$701$	−1.10963	+	3.41508i	−0.0419101	+	0.128986i	0.927912	+	0.372799i	$0.121602\pi$
$702$		0			0
$703$	4.78733	+	2.93368i	0.180558	+	0.110646i
$704$	−1.75240	−	2.85965i	−0.0660460	−	0.107777i
$705$		0			0
$706$	23.3482	+	23.3482i	0.878723	+	0.878723i
$707$	30.8718	−	10.0308i	1.16105	−	0.377249i
$708$		0			0
$709$	−23.7936	+	27.8587i	−0.893588	+	1.04626i	0.105070	+	0.994465i	$0.466493\pi$
$709$	−23.7936	+	27.8587i	−0.893588	+	1.04626i	−0.998658	+	0.0517921i	$0.983507\pi$
$710$	26.9103	−	6.46059i	1.00992	−	0.242462i
$711$		0			0
$712$	0.674528	+	8.57069i	0.0252790	+	0.321200i
$713$	−0.792586	+	1.09090i	−0.0296826	+	0.0408546i
$714$		0			0
$715$	5.13217	−	3.72874i	0.191932	−	0.139447i
$716$	11.8705	+	2.84986i	0.443623	+	0.106504i
$717$		0			0
$718$	−1.19242	−	7.52865i	−0.0445008	−	0.280967i
$719$	−7.66278	+	31.9178i	−0.285773	+	1.19033i	0.626061	+	0.779774i	$0.284666\pi$
$719$	−7.66278	+	31.9178i	−0.285773	+	1.19033i	−0.911834	+	0.410558i	$0.865334\pi$
$720$		0			0
$721$	31.7300	+	37.1510i	1.18169	+	1.38358i
$722$	−12.6675	−	9.20346i	−0.471435	−	0.342517i
$723$		0			0
$724$	14.3357	−	5.93805i	0.532783	−	0.220686i
$725$	9.84236	+	40.9964i	0.365536	+	1.52257i
$726$		0			0
$727$	−18.6181	−	1.46527i	−0.690506	−	0.0543440i	−0.271649	−	0.962396i	$-0.587569\pi$
$727$	−18.6181	−	1.46527i	−0.690506	−	0.0543440i	−0.418857	+	0.908052i	$0.637569\pi$
$728$	−0.455037	−	1.40046i	−0.0168648	−	0.0519045i
$729$		0			0
$730$	−15.3116	−	7.80165i	−0.566708	−	0.288752i
$731$	6.67313	−	4.08930i	0.246815	−	0.151248i
$732$		0			0
$733$	23.2139	+	45.5598i	0.857424	+	1.68279i	0.721880	+	0.692019i	$0.243278\pi$
$733$	23.2139	+	45.5598i	0.857424	+	1.68279i	0.135545	+	0.990771i	$0.456722\pi$
$734$	24.7459	+	8.04043i	0.913387	+	0.296778i
$735$		0			0
$736$	−2.27216	−	0.359875i	−0.0837530	−	0.0132652i
$737$	−14.1761			−0.522182
$738$		0			0
$739$	13.0022			0.478293			0.239146	−	0.970984i	$-0.423132\pi$
$739$	13.0022			0.478293			0.239146	+	0.970984i	$0.423132\pi$
$740$	3.07395	+	0.486866i	0.113001	+	0.0178976i
$741$		0			0
$742$	4.94219	+	1.60581i	0.181433	+	0.0589513i
$743$	−11.1280	−	21.8399i	−0.408245	−	0.801227i	0.591743	−	0.806127i	$-0.298440\pi$
$743$	−11.1280	−	21.8399i	−0.408245	−	0.801227i	−0.999988	+	0.00490029i	$0.998440\pi$
$744$		0			0
$745$	58.5705	−	35.8921i	2.14586	−	1.31498i
$746$	−23.6227	−	12.0364i	−0.864889	−	0.440683i
$747$		0			0
$748$	1.97612	+	6.08188i	0.0722542	+	0.222376i
$749$	26.4307	+	2.08014i	0.965756	+	0.0760067i
$750$		0			0
$751$	2.65200	+	11.0464i	0.0967729	+	0.403088i	0.999640	−	0.0268316i	$-0.00854179\pi$
$751$	2.65200	+	11.0464i	0.0967729	+	0.403088i	−0.902867	+	0.429920i	$0.858542\pi$
$752$	8.39516	−	3.47739i	0.306140	−	0.126807i
$753$		0			0
$754$	−3.49993	−	2.54285i	−0.127460	−	0.0926051i
$755$	27.9357	+	32.7085i	1.01668	+	1.19038i
$756$		0			0
$757$	−5.78512	+	24.0968i	−0.210264	+	0.875812i	0.763051	+	0.646338i	$0.223701\pi$
$757$	−5.78512	+	24.0968i	−0.210264	+	0.875812i	−0.973315	+	0.229474i	$0.926299\pi$
$758$	−2.75724	−	17.4085i	−0.100147	−	0.632306i
$759$		0			0
$760$	−18.6803	−	4.48473i	−0.677604	−	0.162678i
$761$	−15.9802	+	11.6103i	−0.579283	+	0.420874i	−0.838465	−	0.544955i	$-0.816547\pi$
$761$	−15.9802	+	11.6103i	−0.579283	+	0.420874i	0.259183	+	0.965828i	$0.416547\pi$
$762$		0			0
$763$	−19.8102	+	27.2664i	−0.717178	+	0.987111i
$764$	1.61011	+	20.4584i	0.0582517	+	0.740158i
$765$		0			0
$766$	27.9098	−	6.70055i	1.00842	−	0.242101i
$767$	−3.42866	+	4.01444i	−0.123802	+	0.144953i
$768$		0			0
$769$	−33.9657	+	11.0361i	−1.22483	+	0.397973i	−0.848840	−	0.528650i	$-0.822699\pi$
$769$	−33.9657	+	11.0361i	−1.22483	+	0.397973i	−0.375994	+	0.926622i	$0.622699\pi$
$770$	19.6608	+	19.6608i	0.708527	+	0.708527i
$771$		0			0
$772$	−8.64724	−	14.1110i	−0.311221	−	0.507867i
$773$	−34.6331	−	21.2232i	−1.24567	−	0.763345i	−0.265998	−	0.963974i	$-0.585702\pi$
$773$	−34.6331	−	21.2232i	−1.24567	−	0.763345i	−0.979667	+	0.200629i	$0.935702\pi$
$774$		0			0
$775$	−1.02317	+	3.14899i	−0.0367534	+	0.113115i
$776$	−3.82778	+	9.24107i	−0.137409	+	0.331735i
$777$		0			0
$778$			29.2197i			1.04758i
$779$	37.1645	+	6.30636i	1.33156	+	0.225949i
$780$		0			0
$781$	4.44955	−	28.0934i	0.159217	−	1.00526i
$782$	4.05246	+	1.67858i	0.144916	+	0.0600260i
$783$		0			0
$784$	−0.486374	+	0.247820i	−0.0173705	+	0.00885072i
$785$	−21.1650	+	34.5381i	−0.755410	+	1.23272i
$786$		0			0
$787$	−3.01531	+	5.91788i	−0.107484	+	0.210950i	−0.938484	−	0.345323i	$-0.887769\pi$
$787$	−3.01531	+	5.91788i	−0.107484	+	0.210950i	0.830999	+	0.556273i	$0.187769\pi$
$788$	−0.698080	+	0.698080i	−0.0248681	+	0.0248681i
$789$		0			0
$790$	0.567308	−	7.20834i	0.0201839	−	0.256461i
$791$	−21.2079	−	18.1133i	−0.754068	−	0.644035i
$792$		0			0
$793$	−3.22495	−	7.78572i	−0.114521	−	0.276479i
$794$	−20.8839	+	1.64360i	−0.741141	+	0.0583290i
$795$		0			0
$796$	−3.66120	+	3.12696i	−0.129768	+	0.110832i
$797$	21.2633	+	29.2665i	0.753186	+	1.03667i	0.997750	+	0.0670389i	$0.0213552\pi$
$797$	21.2633	+	29.2665i	0.753186	+	1.03667i	−0.244564	+	0.969633i	$0.578645\pi$
$798$		0			0
$799$	−17.1127	+	2.71038i	−0.605403	+	0.0958863i
$800$	−5.57927	+	0.883669i	−0.197257	+	0.0312424i
$801$		0			0
$802$	−8.18727	−	11.2688i	−0.289102	−	0.397915i
$803$	−13.4302	+	11.4705i	−0.473941	+	0.404784i
$804$		0			0
$805$	19.0129	−	1.49635i	0.670116	−	0.0527393i
$806$	−0.130015	−	0.313884i	−0.00457958	−	0.0110561i
$807$		0			0
$808$	9.71587	+	8.29814i	0.341803	+	0.291928i
$809$	3.32982	−	42.3094i	0.117070	−	1.48752i	−0.605292	−	0.796004i	$-0.706944\pi$
$809$	3.32982	−	42.3094i	0.117070	−	1.48752i	0.722362	−	0.691515i	$-0.243056\pi$
$810$		0			0
$811$	14.7676	−	14.7676i	0.518562	−	0.518562i	−0.398574	−	0.917136i	$-0.630495\pi$
$811$	14.7676	−	14.7676i	0.518562	−	0.518562i	0.917136	+	0.398574i	$0.130495\pi$
$812$	8.60839	−	16.8949i	0.302095	−	0.592896i
$813$		0			0
$814$	1.67132	−	2.72734i	0.0585797	−	0.0955934i
$815$	−20.3928	+	10.3907i	−0.714329	+	0.363969i
$816$		0			0
$817$	22.3252	+	9.24742i	0.781061	+	0.323526i
$818$	0.888337	−	5.60874i	0.0310600	−	0.196105i
$819$		0			0
$820$	20.3701	−	4.65392i	0.711356	−	0.162522i
$821$		−	35.0147i		−	1.22202i	−0.791622	−	0.611011i	$-0.790763\pi$
$821$		−	35.0147i		−	1.22202i	0.791622	−	0.611011i	$-0.209237\pi$
$822$		0			0
$823$	−9.86453	+	23.8151i	−0.343856	+	0.830141i	0.653463	+	0.756959i	$0.273316\pi$
$823$	−9.86453	+	23.8151i	−0.343856	+	0.830141i	−0.997319	+	0.0731827i	$0.976684\pi$
$824$	−5.94277	+	18.2900i	−0.207026	+	0.637161i
$825$		0			0
$826$	−19.7296	−	12.0903i	−0.686482	−	0.420677i
$827$	13.5483	+	22.1088i	0.471119	+	0.768797i	0.996633	−	0.0819882i	$-0.0261270\pi$
$827$	13.5483	+	22.1088i	0.471119	+	0.768797i	−0.525514	+	0.850785i	$0.676127\pi$
$828$		0			0
$829$	29.0170	+	29.0170i	1.00780	+	1.00780i	0.999969	+	0.00783276i	$0.00249327\pi$
$829$	29.0170	+	29.0170i	1.00780	+	1.00780i	0.00783276	+	0.999969i	$0.497507\pi$
$830$	19.2416	−	6.25198i	0.667886	−	0.217009i
$831$		0			0
$832$	0.376435	−	0.440748i	0.0130505	−	0.0152802i
$833$	1.01206	−	0.242974i	0.0350657	−	0.00841853i
$834$		0			0
$835$	−1.74667	−	22.1935i	−0.0604460	−	0.768039i
$836$	−11.6056	+	15.9737i	−0.401388	+	0.552463i
$837$		0			0
$838$	7.81910	−	5.68091i	0.270106	−	0.196244i
$839$	10.4628	+	2.51189i	0.361215	+	0.0867201i	0.409991	−	0.912090i	$-0.365532\pi$
$839$	10.4628	+	2.51189i	0.361215	+	0.0867201i	−0.0487756	+	0.998810i	$0.515532\pi$
$840$		0			0
$841$	−4.17796	−	26.3786i	−0.144068	−	0.909607i
$842$	4.36329	−	18.1744i	0.150369	−	0.626332i
$843$		0			0
$844$	18.2941	+	21.4197i	0.629709	+	0.737295i
$845$	−33.4334	−	24.2908i	−1.15014	−	0.835628i
$846$		0			0
$847$	0.583289	−	0.241606i	0.0200421	−	0.00830169i
$848$	0.477507	+	1.98896i	0.0163976	+	0.0683011i
$849$		0			0
$850$	10.7374	+	0.845054i	0.368291	+	0.0289851i
$851$	−0.677998	−	2.08666i	−0.0232415	−	0.0715299i
$852$		0			0
$853$	−0.743627	−	0.378897i	−0.0254613	−	0.0129732i	0.441213	−	0.897402i	$-0.354548\pi$
$853$	−0.743627	−	0.378897i	−0.0254613	−	0.0129732i	−0.466675	+	0.884429i	$0.654548\pi$
$854$	31.4936	−	19.2993i	1.07769	−	0.660409i
$855$		0			0
$856$	4.73781	+	9.29847i	0.161935	+	0.317815i
$857$	13.9120	+	4.52029i	0.475226	+	0.154410i	0.536830	−	0.843690i	$-0.319622\pi$
$857$	13.9120	+	4.52029i	0.475226	+	0.154410i	−0.0616042	+	0.998101i	$0.519622\pi$
$858$		0			0
$859$	−5.49436	−	0.870221i	−0.187465	−	0.0296916i	0.0619958	−	0.998076i	$-0.480253\pi$
$859$	−5.49436	−	0.870221i	−0.187465	−	0.0296916i	−0.249461	+	0.968385i	$0.580253\pi$
$860$	13.3946			0.456753
$861$		0			0
$862$	−37.2415			−1.26845
$863$	−33.9906	−	5.38358i	−1.15705	−	0.183259i	−0.451736	−	0.892152i	$-0.649195\pi$
$863$	−33.9906	−	5.38358i	−1.15705	−	0.183259i	−0.705317	+	0.708892i	$0.749195\pi$
$864$		0			0
$865$	−53.5944	−	17.4139i	−1.82226	−	0.592089i
$866$	−7.19343	−	14.1179i	−0.244443	−	0.479746i
$867$		0			0
$868$	1.26968	−	0.778058i	0.0430956	−	0.0264090i
$869$	−6.62146	−	3.37380i	−0.224618	−	0.114448i
$870$		0			0
$871$	−0.757070	−	2.33002i	−0.0256523	−	0.0789498i
$872$	−13.2255	−	1.04087i	−0.447871	−	0.0352482i
$873$		0			0
$874$	3.16159	+	13.1690i	0.106942	+	0.445447i
$875$	4.96941	−	2.05840i	0.167997	−	0.0695865i
$876$		0			0
$877$	38.8208	+	28.2049i	1.31088	+	0.952413i	0.999998	+	0.00196578i	$0.000625727\pi$
$877$	38.8208	+	28.2049i	1.31088	+	0.952413i	0.310886	+	0.950447i	$0.399374\pi$
$878$	−10.4019	−	12.1791i	−0.351048	−	0.411024i
$879$		0			0
$880$	−2.55496	+	10.6422i	−0.0861276	+	0.358747i
$881$	2.78081	+	17.5573i	0.0936878	+	0.591522i	0.989210	+	0.146505i	$0.0468023\pi$
$881$	2.78081	+	17.5573i	0.0936878	+	0.591522i	−0.895522	+	0.445017i	$0.853198\pi$
$882$		0			0
$883$	16.4042	+	3.93830i	0.552045	+	0.132534i	0.499865	−	0.866103i	$-0.333383\pi$
$883$	16.4042	+	3.93830i	0.552045	+	0.132534i	0.0521801	+	0.998638i	$0.483383\pi$
$884$	−0.894102	+	0.649603i	−0.0300719	+	0.0218485i
$885$		0			0
$886$	−3.31595	+	4.56401i	−0.111401	+	0.153331i
$887$	−0.423446	−	5.38039i	−0.0142179	−	0.180656i	−0.999926	−	0.0121915i	$-0.996119\pi$
$887$	−0.423446	−	5.38039i	−0.0142179	−	0.180656i	0.985708	−	0.168464i	$-0.0538808\pi$
$888$		0			0
$889$	−42.0027	+	10.0839i	−1.40872	+	0.338205i
$890$	18.2201	−	21.3330i	0.610741	−	0.715085i
$891$		0			0
$892$	−19.0943	+	6.20412i	−0.639326	+	0.207729i
$893$	−37.8268	−	37.8268i	−1.26583	−	1.26583i
$894$		0			0
$895$	−20.8149	−	33.9669i	−0.695766	−	1.13539i
$896$	2.16613	+	1.32741i	0.0723653	+	0.0443455i
$897$		0			0
$898$	2.35971	−	7.26245i	0.0787447	−	0.242351i
$899$	1.67419	−	4.04185i	0.0558373	−	0.134803i
$900$		0			0
$901$		−	3.90012i		−	0.129932i
$902$	3.59274	−	21.1727i	0.119625	−	0.704972i
$903$		0			0
$904$	1.71738	−	10.8431i	0.0571192	−	0.360637i
$905$	−46.7811	−	19.3773i	−1.55505	−	0.644125i
$906$		0			0
$907$	6.07646	−	3.09611i	0.201766	−	0.102805i	−0.350188	−	0.936679i	$-0.613882\pi$
$907$	6.07646	−	3.09611i	0.201766	−	0.102805i	0.551954	+	0.833875i	$0.313882\pi$
$908$	−15.4380	+	25.1926i	−0.512330	+	0.836046i
$909$		0			0
$910$	−2.18153	+	4.28150i	−0.0723171	+	0.141930i
$911$	−25.4117	+	25.4117i	−0.841927	+	0.841927i	−0.989109	−	0.147183i	$-0.952980\pi$
$911$	−25.4117	+	25.4117i	−0.841927	+	0.841927i	0.147183	+	0.989109i	$0.452980\pi$
$912$		0			0
$913$	1.63146	−	20.7296i	0.0539933	−	0.686050i
$914$	16.4467	+	14.0468i	0.544010	+	0.464628i
$915$		0			0
$916$	−3.14675	−	7.59692i	−0.103971	−	0.251009i
$917$	−40.6530	+	3.19946i	−1.34248	+	0.105655i
$918$		0			0
$919$	−17.7416	+	15.1527i	−0.585240	+	0.499842i	−0.892055	−	0.451927i	$-0.850737\pi$
$919$	−17.7416	+	15.1527i	−0.585240	+	0.499842i	0.306815	+	0.951769i	$0.400737\pi$
$920$	4.41254	+	6.07334i	0.145477	+	0.200232i
$921$		0			0
$922$	−16.2713	+	2.57712i	−0.535866	+	0.0848728i
$923$	4.85513	−	0.768978i	0.159809	−	0.0253112i
$924$		0			0
$925$	−3.16667	−	4.35855i	−0.104119	−	0.143308i
$926$	−5.45697	+	4.66070i	−0.179327	+	0.153160i
$927$		0			0
$928$	7.44073	−	0.585598i	0.244254	−	0.0192232i
$929$	3.40980	+	8.23198i	0.111872	+	0.270082i	0.969893	−	0.243532i	$-0.0783061\pi$
$929$	3.40980	+	8.23198i	0.111872	+	0.270082i	−0.858021	+	0.513615i	$0.828306\pi$
$930$		0			0
$931$	2.44363	+	2.08706i	0.0800869	+	0.0684006i
$932$	0.545528	−	6.93158i	0.0178693	−	0.227052i
$933$		0			0
$934$	−8.79389	+	8.79389i	−0.287745	+	0.287745i
$935$	9.47390	−	18.5936i	0.309830	−	0.608075i
$936$		0			0
$937$	−3.49615	+	5.70520i	−0.114214	+	0.186381i	−0.904639	−	0.426178i	$-0.859860\pi$
$937$	−3.49615	+	5.70520i	−0.114214	+	0.186381i	0.790425	+	0.612559i	$0.209860\pi$
$938$	9.56771	−	4.87499i	0.312397	−	0.159174i
$939$		0			0
$940$	−27.3955	−	11.3476i	−0.893544	−	0.370118i
$941$	3.73569	−	23.5862i	0.121780	−	0.768888i	−0.848907	−	0.528542i	$-0.822739\pi$
$941$	3.73569	−	23.5862i	0.121780	−	0.768888i	0.970687	−	0.240346i	$-0.0772609\pi$
$942$		0			0
$943$	−9.44269	−	11.3056i	−0.307496	−	0.368162i
$944$		−	9.10824i		−	0.296448i
$945$		0			0
$946$	5.26826	−	12.7187i	0.171286	−	0.413521i
$947$	2.85821	−	8.79667i	0.0928794	−	0.285853i	−0.893816	−	0.448434i	$-0.851982\pi$
$947$	2.85821	−	8.79667i	0.0928794	−	0.285853i	0.986695	+	0.162581i	$0.0519818\pi$
$948$		0			0
$949$	−2.60256	−	1.59485i	−0.0844826	−	0.0517710i
$950$	17.3757	+	28.3546i	0.563743	+	0.919946i
$951$		0			0
$952$	−3.42522	−	3.42522i	−0.111012	−	0.111012i
$953$	14.6929	−	4.77402i	0.475950	−	0.154646i	−0.0612115	−	0.998125i	$-0.519496\pi$
$953$	14.6929	−	4.77402i	0.475950	−	0.154646i	0.537162	+	0.843479i	$0.319496\pi$
$954$		0			0
$955$	43.4918	−	50.9223i	1.40736	−	1.64781i
$956$	−7.53823	+	1.80977i	−0.243804	+	0.0585321i
$957$		0			0
$958$	1.14801	+	14.5868i	0.0370904	+	0.471278i
$959$	15.0313	−	20.6888i	0.485385	−	0.668076i
$960$		0			0
$961$	−24.8016	+	18.0194i	−0.800051	+	0.581271i
$962$	0.537531	+	0.129050i	0.0173307	+	0.00416073i
$963$		0			0
$964$	−3.06542	−	19.3543i	−0.0987306	−	0.623361i
$965$	−12.6075	+	52.5139i	−0.405849	+	1.69048i
$966$		0			0
$967$	29.7598	+	34.8442i	0.957010	+	1.12051i	0.992634	+	0.121149i	$0.0386579\pi$
$967$	29.7598	+	34.8442i	0.957010	+	1.12051i	−0.0356247	+	0.999365i	$0.511342\pi$
$968$	0.201052	+	0.146073i	0.00646204	+	0.00469495i
$969$		0			0
$970$	30.1559	−	12.4910i	0.968249	−	0.401062i
$971$	−3.45780	−	14.4028i	−0.110966	−	0.462207i	−0.999991	−	0.00434705i	$-0.998616\pi$
$971$	−3.45780	−	14.4028i	−0.110966	−	0.462207i	0.889025	−	0.457859i	$-0.151384\pi$
$972$		0			0
$973$	0.662014	+	0.0521016i	0.0212232	+	0.00167030i
$974$	9.06277	+	27.8923i	0.290390	+	0.893728i
$975$		0			0
$976$	12.9545	+	6.60062i	0.414662	+	0.211281i
$977$	2.75675	−	1.68934i	0.0881964	−	0.0540468i	−0.477701	−	0.878522i	$-0.658530\pi$
$977$	2.75675	−	1.68934i	0.0881964	−	0.0540468i	0.565897	+	0.824476i	$0.308530\pi$
$978$		0			0
$979$	−13.0903	−	25.6912i	−0.418369	−	0.821096i
$980$	1.69413	+	0.550456i	0.0541170	+	0.0175837i
$981$		0			0
$982$	−26.8790	−	4.25721i	−0.857743	−	0.135853i
$983$	−52.5031			−1.67459			−0.837295	−	0.546751i	$-0.815864\pi$
$983$	−52.5031			−1.67459			−0.837295	+	0.546751i	$0.815864\pi$
$984$		0			0
$985$	3.22159			0.102648
$986$	−14.0560	−	2.22625i	−0.447633	−	0.0708981i
$987$		0			0
$988$	−3.24528	−	1.05446i	−0.103246	−	0.0335467i
$989$	−4.28693	−	8.41356i	−0.136316	−	0.267536i
$990$		0			0
$991$	40.4883	−	24.8113i	1.28615	−	0.788155i	0.299991	−	0.953942i	$-0.403016\pi$
$991$	40.4883	−	24.8113i	1.28615	−	0.788155i	0.986162	+	0.165786i	$0.0530163\pi$
$992$	0.522263	+	0.266106i	0.0165819	+	0.00844888i
$993$		0			0
$994$	6.65790	+	20.4909i	0.211176	+	0.649932i
$995$	15.6635	+	1.23274i	0.496565	+	0.0390805i
$996$		0			0
$997$	6.23221	+	25.9590i	0.197376	+	0.822131i	0.979897	+	0.199506i	$0.0639338\pi$
$997$	6.23221	+	25.9590i	0.197376	+	0.822131i	−0.782520	+	0.622625i	$0.786066\pi$
$998$	12.8063	−	5.30452i	0.405375	−	0.167912i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.a.521.1	yes	48
3.2	odd	2		738.2.ba.b.521.3	yes	48
41.17	odd	40		738.2.ba.b.17.3	yes	48
123.17	even	40	inner	738.2.ba.a.17.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.a.17.1	✓	48	123.17	even	40	inner
738.2.ba.a.521.1	yes	48	1.1	even	1	trivial
738.2.ba.b.17.3	yes	48	41.17	odd	40
738.2.ba.b.521.3	yes	48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 + 0.156434i) q^{2} +(0.951057 + 0.309017i) q^{4} +(-1.48149 - 2.90758i) q^{5} +(2.16613 - 1.32741i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-1.00840 - 3.10354i) q^{10} +(-3.34354 - 0.263142i) q^{11} +(-0.135310 - 0.563607i) q^{13} +(2.34711 - 0.972206i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-1.23831 - 1.44987i) q^{17} +(1.37431 - 5.72443i) q^{19} +(-0.510485 - 3.22308i) q^{20} +(-3.26121 - 0.782948i) q^{22} +(-1.86113 + 1.35219i) q^{23} +(-3.32029 + 4.56999i) q^{25} +(-0.0454767 - 0.577836i) q^{26} +(2.47030 - 0.593067i) q^{28} +(4.84731 - 5.67547i) q^{29} +(0.557461 - 0.181130i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.996252 - 1.62574i) q^{34} +(-7.06863 - 4.33166i) q^{35} +(-0.294720 + 0.907054i) q^{37} +(2.25289 - 5.43896i) q^{38} -3.26325i q^{40} +(0.432093 + 6.38853i) q^{41} +(-0.642114 + 4.05415i) q^{43} +(-3.09858 - 1.28347i) q^{44} +(-2.04975 + 1.04440i) q^{46} +(4.74787 - 7.74782i) q^{47} +(-0.247820 + 0.486374i) q^{49} +(-3.99431 + 3.99431i) q^{50} +(0.0454767 - 0.577836i) q^{52} +(1.55539 + 1.32843i) q^{53} +(4.18830 + 10.1115i) q^{55} +(2.53267 - 0.199325i) q^{56} +(5.67547 - 4.84731i) q^{58} +(-5.35369 - 7.36872i) q^{59} +(14.3601 - 2.27442i) q^{61} +(0.578933 - 0.0916939i) q^{62} +(0.587785 + 0.809017i) q^{64} +(-1.43827 + 1.22840i) q^{65} +(4.21374 - 0.331628i) q^{67} +(-0.729665 - 1.76157i) q^{68} +(-6.30398 - 5.38411i) q^{70} +(-0.665395 + 8.45464i) q^{71} +(3.72370 - 3.72370i) q^{73} +(-0.432986 + 0.849782i) q^{74} +(3.07600 - 5.01957i) q^{76} +(-7.59184 + 3.86824i) q^{77} +(2.04711 + 0.847940i) q^{79} +(0.510485 - 3.22308i) q^{80} +(-0.572613 + 6.37747i) q^{82} +6.19990i q^{83} +(-2.38108 + 5.74844i) q^{85} +(-1.26842 + 3.90379i) q^{86} +(-2.85965 - 1.75240i) q^{88} +(4.49202 + 7.33031i) q^{89} +(-1.04124 - 1.04124i) q^{91} +(-2.18789 + 0.710889i) q^{92} +(5.90144 - 6.90970i) q^{94} +(-18.6803 + 4.48473i) q^{95} +(0.784784 + 9.97163i) q^{97} +(-0.320855 + 0.441619i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Introduction

L-functions

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Database

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